From d7e4bf780b496cbd6140d06cccba3f0374ae9d78 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Sun, 27 Oct 2019 14:12:34 -0400
Subject: [PATCH 001/104] Continuous Daubechies wavelets [CI SKIP]

---
 doc/sf/daubechies.qbk                         |   53 +
 example/daubechies_coefficients.cpp           |   88 +-
 example/daubechies_scaling_integer_grid.cpp   |  246 +++
 include/boost/math/filters/daubechies.hpp     |  419 ++++
 .../special_functions/daubechies_scaling.hpp  |  352 ++++
 .../daubechies_scaling_integer_grid.hpp       | 1830 +++++++++++++++++
 test/daubechies_scaling_test.cpp              |  441 ++++
 7 files changed, 3421 insertions(+), 8 deletions(-)
 create mode 100644 doc/sf/daubechies.qbk
 create mode 100644 example/daubechies_scaling_integer_grid.cpp
 create mode 100644 include/boost/math/filters/daubechies.hpp
 create mode 100644 include/boost/math/special_functions/daubechies_scaling.hpp
 create mode 100644 include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp
 create mode 100644 test/daubechies_scaling_test.cpp

diff --git a/doc/sf/daubechies.qbk b/doc/sf/daubechies.qbk
new file mode 100644
index 000000000..a0f92d8e8
--- /dev/null
+++ b/doc/sf/daubechies.qbk
@@ -0,0 +1,53 @@
+[/
+  Copyright 2019, Nick Thompson
+  Distributed under the Boost Software License, Version 1.0.
+  (See accompanying file LICENSE_1_0.txt or copy at
+  http://www.boost.org/LICENSE_1_0.txt).
+]
+
+[section:daubechies Daubechies Wavelets and Scaling Functions]
+
+[h4 Synopsis]
+
+    #include <boost/math/filters/daubechies.hpp>
+
+   namespace boost::math::filters {
+
+   template <typename Real, unsigned p>
+   constexpr std::array<Real, 2*p> daubechies_scaling_filter();
+
+   template<typename Real, unsigned p>
+   std::array<Real, 2*p> daubechies_wavelet_filter();
+
+   } // namespaces
+
+
+Daubechies wavelets are a family of compactly supported functions indexed by an integer /p/ which have /p/ vanishing moments and an associated filter of length /2p/.
+They are used in signal denoising, Galerkin methods for PDEs, and compression.
+
+The canonical reference on these functions is Daubechies' monograph /Ten Lectures on Wavelets/,
+which we attempt to follow here.
+
+To get the (low-pass) scaling filter for the Daubechies scaling function with 3 vanishing moments, use
+
+    auto h = boost::math::filters::daubechies_scaling_filter<double, 3>();
+
+To get the (high-pass) wavelet filter for the Daubechies wavelet with 3 vanishing moments, use
+
+    auto g = boost::math::filters::daubechies_wavelet_filter<double, 3>();
+
+Notational conventions for these filters seem not to exist.
+Ambiguities include whether or not the filter is defined via convolution or dot product (which corresponds to reversing the array),
+and the overall scaling.
+/The filters in Boost.Math agree with Daubechies, Ten Lectures, Table 6.1./
+This means that the elements sum to sqrt(2), and the filter is defined via a dot product.
+
+
+[heading References]
+
+* Daubechies, Ingrid. ['Ten lectures on wavelets.] Vol. 61. Siam, 1992.
+* Mallat, Stephane. ['A wavelet tour of signal processing: the sparse way] Academic press, 2008.
+
+
+
+[endsect]
diff --git a/example/daubechies_coefficients.cpp b/example/daubechies_coefficients.cpp
index 4a8c41102..5ccc77fb6 100644
--- a/example/daubechies_coefficients.cpp
+++ b/example/daubechies_coefficients.cpp
@@ -5,6 +5,7 @@
  * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
  */
 #include <iostream>
+#include <fstream>
 #include <vector>
 #include <string>
 #include <complex>
@@ -16,6 +17,7 @@
 #include <boost/math/tools/roots.hpp>
 #include <boost/math/special_functions/binomial.hpp>
 #include <boost/multiprecision/cpp_complex.hpp>
+#include <boost/multiprecision/float128.hpp>
 #include <boost/multiprecision/complex128.hpp>
 #include <boost/math/quadrature/gauss_kronrod.hpp>
 
@@ -182,8 +184,7 @@ std::vector<typename Complex::value_type> daubechies_coefficients(std::vector<st
     // If we don't reverse, we get the Pywavelets and Mallat convention.
     // I believe this is because of the sign convention on the DFT, which differs between Daubechies and Mallat.
     // You implement a dot product in Daubechies/NR convention, and a convolution in PyWavelets/Mallat convention.
-    // I won't reverse so I can spot check against Pywavelets: http://wavelets.pybytes.com/wavelet/
-    //std::reverse(result.begin(), result.end());
+    std::reverse(result.begin(), result.end());
     std::vector<Real> h(result.size());
     for (size_t i = 0; i < result.size(); ++i)
     {
@@ -207,15 +208,86 @@ std::vector<typename Complex::value_type> daubechies_coefficients(std::vector<st
 
 int main()
 {
-    typedef boost::multiprecision::cpp_complex<100> Complex;
-    for(size_t p = 1; p < 200; ++p)
+    typedef boost::multiprecision::cpp_complex<150> Complex;
+    size_t p_max = 25;
+    std::ofstream fs{"daubechies_filters.hpp"};
+    fs << "/*\n"
+       << " * Copyright Nick Thompson, 2019\n"
+       << " * Use, modification and distribution are subject to the\n"
+       << " * Boost Software License, Version 1.0. (See accompanying file\n"
+       << " * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)\n"
+       << " */\n"
+       << "#ifndef BOOST_MATH_FILTERS_DAUBECHIES_HPP\n"
+       << "#define BOOST_MATH_FILTERS_DAUBECHIES_HPP\n"
+       << "#include <array>\n"
+       << "#ifdef BOOST_HAS_FLOAT128\n"
+       << "#include <boost/multiprecision/float128.hpp>\n"
+       << "#endif\n"
+       << "namespace boost::math::filters {\n\n"
+       << "template <typename Real, unsigned p>\n"
+       << "constexpr std::array<Real, 2*p> daubechies_scaling_filter()\n"
+       << "{\n"
+       << "    static_assert(sizeof(Real) <= 16, \"Filter coefficients only computed up to 128 bits of precision.\");\n"
+       << "    static_assert(p < " << p_max << ", \"Filter coefficients only implemented up to " << p_max - 1 << ".\");\n";
+
+    for(size_t p = 1; p < p_max; ++p)
     {
+        fs << std::hexfloat;
         auto roots = find_roots<Complex>(p);
         auto h = daubechies_coefficients(roots);
-        std::cout << "h_" << p << "[] = {";
-        for (auto& x : h) {
-            std::cout << x << ", ";
+        fs << "    if constexpr (p == " << p << ") {\n";
+        fs << "        if constexpr (std::is_same_v<Real, float>) {\n";
+        fs << "            return {";
+        for (size_t i = 0; i < h.size() - 1; ++i) {
+            fs << static_cast<float>(h[i]) << "f, ";
         }
-        std::cout << "} // = h_" << p << "\n\n\n\n";
+        fs << static_cast<float>(h[h.size()-1]) << "f};\n";
+        fs << "        }\n";
+
+        fs << "        if constexpr (std::is_same_v<Real, double>) {\n";
+        fs << "            return {";
+        for (size_t i = 0; i < h.size() - 1; ++i) {
+            fs << static_cast<double>(h[i]) << ", ";
+        }
+        fs << static_cast<double>(h[h.size()-1]) << "};\n";
+        fs << "        }\n";
+
+        fs << "        if constexpr (std::is_same_v<Real, long double>) {\n";
+        fs << "            return {";
+        for (size_t i = 0; i < h.size() - 1; ++i) {
+            fs << static_cast<long double>(h[i]) << "L, ";
+        }
+        fs << static_cast<long double>(h[h.size()-1]) << "L};\n";
+        fs << "        }\n";
+
+        fs << "        #ifdef BOOST_HAS_FLOAT128\n";
+        fs << "        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {\n";
+        fs << "            return {";
+        for (size_t i = 0; i < h.size() - 1; ++i) {
+            fs << static_cast<boost::multiprecision::float128>(h[i]) << "Q, ";
+        }
+        fs << static_cast<boost::multiprecision::float128>(h[h.size()-1]) << "Q};\n";
+        fs << "        }\n";
+        fs << "        #endif\n";
+
+
+        fs << "    }\n";
     }
+
+    fs << "}\n\n";
+
+    fs << "template<class Real, size_t p>\n";
+    fs << "std::array<Real, 2*p> daubechies_wavelet_filter() {\n";
+    fs << "    std::array<Real, 2*p> g;\n";
+    fs << "    auto h = daubechies_scaling_filter<Real, p>();\n";
+    fs << "    for (size_t i = 0; i < g.size(); i += 2)\n";
+    fs << "    {\n";
+    fs << "        g[i] = h[g.size() - i - 1];\n";
+    fs << "        g[i+1] = -h[g.size() - i - 2];\n";
+    fs << "    }\n";
+    fs << "    return g;\n";
+    fs << "}\n\n";
+    fs << "} // namespaces\n";
+    fs << "#endif\n";
+    fs.close();
 }
diff --git a/example/daubechies_scaling_integer_grid.cpp b/example/daubechies_scaling_integer_grid.cpp
new file mode 100644
index 000000000..cdb255327
--- /dev/null
+++ b/example/daubechies_scaling_integer_grid.cpp
@@ -0,0 +1,246 @@
+/*
+ * Copyright Nick Thompson, 2019
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+#include <iostream>
+#include <vector>
+#include <numeric>
+#include <list>
+#include <cmath>
+#include <cassert>
+#include <fstream>
+#include <Eigen/Eigenvalues>
+#include <boost/hana/for_each.hpp>
+#include <boost/hana/ext/std/integer_sequence.hpp>
+#include <boost/core/demangle.hpp>
+#include <boost/multiprecision/float128.hpp>
+#include <boost/math/constants/constants.hpp>
+#include <boost/math/filters/daubechies.hpp>
+#include <boost/math/special_functions/factorials.hpp>
+
+
+
+template<class Real, int p>
+std::list<std::vector<Real>> integer_grid()
+{
+    std::cout << std::setprecision(std::numeric_limits<Real>::digits10 + 3);
+    using std::abs;
+    using std::sqrt;
+    using std::pow;
+    std::list<std::vector<Real>> grids;
+
+    auto c = boost::math::filters::daubechies_scaling_filter<Real, p>();
+    for (auto & x : c)
+    {
+        x *= boost::math::constants::root_two<Real>();
+    }
+    std::cout << "\n\nTaps in filter = " << c.size() << "\n";
+
+
+    Eigen::Matrix<Real, 2*p - 2, 2*p-2> A;
+    for (int j = 0; j < 2*p-2; ++j) {
+        for (int k = 0; k < 2*p-2; ++k) {
+            if ( (2*j-k + 1) < 0 || (2*j - k  + 1) >= 2*p)
+            {
+                A(j,k) = 0;
+            }
+            else {
+                A(j,k) = c[2*j - k + 1];
+            }
+        }
+    }
+
+    Eigen::EigenSolver<decltype(A)> es(A);
+
+    auto complex_eigs = es.eigenvalues();
+
+    std::vector<Real> eigs(complex_eigs.size(), std::numeric_limits<Real>::quiet_NaN());
+
+    std::cout << "Eigenvalues = {";
+    for (long i = 0; i < complex_eigs.size(); ++i) {
+        assert(abs(complex_eigs[i].imag()) < std::numeric_limits<Real>::epsilon());
+        eigs[i] = complex_eigs[i].real();
+        std::cout << eigs[i] << ", ";
+    }
+    std::cout << "}\n";
+
+    // Eigen does not sort the eigenpairs by any criteria on the eigenvalues.
+    // In any case, even if it did, some of the eigenpairs do not correspond to derivatives anyway.
+    for (size_t j = 0; j < eigs.size(); ++j) {
+        auto f = [&](Real x) {
+                 return abs(x - Real(1)/Real(1 << j) ) < sqrt(std::numeric_limits<Real>::epsilon());
+                 };
+        auto it = std::find_if(eigs.begin(), eigs.end(), f);
+        if (it == eigs.end()) {
+            std::cout << "couldn't find eigenvalue " << Real(1)/Real(1 << j) << "\n";
+            continue;
+        }
+        size_t idx = std::distance(eigs.begin(), it);
+        std::cout << "Eigenvector for derivative " << j << " is at index " << idx << "\n";
+        auto const & complex_eigenvec = es.eigenvectors().col(idx);
+        std::vector<Real> eigenvec(complex_eigenvec.size() + 2, std::numeric_limits<Real>::quiet_NaN());
+        eigenvec[0] = 0;
+        eigenvec[eigenvec.size()-1] = 0;
+        for (size_t i = 0; i < eigenvec.size() - 2; ++i) {
+            assert(abs(complex_eigenvec[i].imag()) < std::numeric_limits<Real>::epsilon());
+            eigenvec[i+1] = complex_eigenvec[i].real();
+        }
+
+        Real sum = 0;
+        for(size_t k = 1; k < eigenvec.size(); ++k) {
+            sum += pow(k, j)*eigenvec[k];
+        }
+
+        Real alpha = pow(-1, j)*boost::math::factorial<Real>(j)/sum;
+
+        for (size_t i = 1; i < eigenvec.size(); ++i) {
+            eigenvec[i] *= alpha;
+        }
+
+
+        std::cout << "Eigenvector = {";
+        for (size_t i = 0; i < eigenvec.size() -1; ++i) {
+            std::cout << eigenvec[i] << ", ";
+        }
+        std::cout << eigenvec[eigenvec.size()-1] << "}\n";
+
+        sum = 0;
+        for(size_t k = 1; k < eigenvec.size(); ++k) {
+            sum += pow(k, j)*eigenvec[k];
+        }
+
+        std::cout << "Moment sum = " << sum << ", expected = " << pow(-1, j)*boost::math::factorial<Real>(j) << "\n";
+
+        assert(abs(sum - pow(-1, j)*boost::math::factorial<Real>(j))/abs(pow(-1, j)*boost::math::factorial<Real>(j)) < sqrt(std::numeric_limits<Real>::epsilon()));
+
+        grids.push_back(eigenvec);
+    }
+
+
+    return grids;
+}
+
+template<class Real, int p>
+void write_grid(std::ofstream & fs)
+{
+    auto grids = integer_grid<Real, p>();
+    fs << "    if constexpr (p == " << p << ") {\n";
+    fs << "        if constexpr (std::is_same_v<Real, float>) {\n";
+    size_t j = 0;
+    for (auto it = grids.begin(); it != grids.end(); ++it) {
+
+    fs << "            if constexpr (order == " << j << ") {\n";
+    fs << "                return {";
+        auto const & grid = *it;
+        for (size_t i = 0; i < grid.size() -1; ++i) {
+            fs << static_cast<float>(grid[i]) << "f, ";
+        }
+        fs << static_cast<float>(grid[grid.size()-1]) << "f};\n";
+    fs << "            }\n";
+        ++j;
+    }
+    fs << "        }\n";
+
+    fs << "        if constexpr (std::is_same_v<Real, double>) {\n";
+    j = 0;
+    for (auto it = grids.begin(); it != grids.end(); ++it) {
+
+    fs << "            if constexpr (order == " << j << ") {\n";
+    fs << "                return {";
+        auto const & grid = *it;
+        for (size_t i = 0; i < grid.size() -1; ++i) {
+            fs << static_cast<double>(grid[i]) << ", ";
+        }
+        fs << static_cast<double>(grid[grid.size()-1]) << "};\n";
+    fs << "            }\n";
+        ++j;
+    }
+    fs << "        }\n";
+
+
+    fs << "        if constexpr (std::is_same_v<Real, long double>) {\n";
+    j = 0;
+    for (auto it = grids.begin(); it != grids.end(); ++it) {
+
+    fs << "            if constexpr (order == " << j << ") {\n";
+    fs << "                return {";
+        auto const & grid = *it;
+        for (size_t i = 0; i < grid.size() -1; ++i) {
+            fs << static_cast<long double>(grid[i]) << "L, ";
+        }
+        fs << static_cast<long double>(grid[grid.size()-1]) << "L};\n";
+    fs << "            }\n";
+        ++j;
+    }
+    fs << "        }\n";
+
+    fs << "        #ifdef BOOST_HAS_FLOAT128\n";
+    fs << "        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {\n";
+    j = 0;
+    for (auto it = grids.begin(); it != grids.end(); ++it) {
+
+    fs << "            if constexpr (order == " << j << ") {\n";
+    fs << "                return {";
+        auto const & grid = *it;
+        for (size_t i = 0; i < grid.size() -1; ++i) {
+            fs << static_cast<boost::multiprecision::float128>(grid[i]) << "Q, ";
+        }
+        fs << static_cast<boost::multiprecision::float128>(grid[grid.size()-1]) << "Q};\n";
+    fs << "            }\n";
+        ++j;
+    }
+    fs << "        }\n";
+    fs << "        #endif\n";
+    fs << "    }\n";
+
+}
+
+int main()
+{
+    constexpr const size_t p_max = 15;
+    std::ofstream fs{"daubechies_scaling_integer_grid.hpp"};
+    fs << "/*\n"
+       << " * Copyright Nick Thompson, 2019\n"
+       << " * Use, modification and distribution are subject to the\n"
+       << " * Boost Software License, Version 1.0. (See accompanying file\n"
+       << " * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)\n"
+       << " */\n"
+       << "// THIS FILE GENERATED BY EXAMPLE/DAUBECHIES_SCALING_INTEGER_GRID.CPP, DO NOT EDIT.\n"
+       << "#ifndef BOOST_MATH_DAUBECHIES_SCALING_INTEGER_GRID_HPP\n"
+       << "#define BOOST_MATH_DAUBECHIES_SCALING_INTEGER_GRID_HPP\n"
+       << "#include <array>\n"
+       << "#ifdef BOOST_HAS_FLOAT128\n"
+       << "#include <boost/multiprecision/float128.hpp>\n"
+       << "#endif\n"
+       << "namespace boost::math::detail {\n\n"
+       << "template <typename Real, unsigned p, unsigned order>\n"
+       << "constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()\n"
+       << "{\n"
+       << "    static_assert(sizeof(Real) <= 16, \"Integer grids only computed up to 128 bits of precision.\");\n"
+       << "    static_assert(p <= " << p_max << ", \"Integer grids only implemented up to " << p_max << ".\");\n"
+       << "    static_assert(p > 1, \"Integer grids only implemented for p >= 2.\");\n";
+
+
+    fs << std::hexfloat;
+
+    boost::hana::for_each(std::make_index_sequence<p_max>(), [&](auto idx){
+        write_grid<boost::multiprecision::float128, idx+2>(fs);
+    });
+
+    fs << "    std::array<Real, 2*p> m{};\n"
+       << "    for (auto & x : m) {\n"
+       << "        x = std::numeric_limits<Real>::quiet_NaN();\n"
+       << "    }\n"
+       << "    return m;\n";
+
+
+    fs << "}\n\n";
+
+    fs << "} // namespaces\n";
+    fs << "#endif\n";
+    fs.close();
+
+    return 0;
+}
diff --git a/include/boost/math/filters/daubechies.hpp b/include/boost/math/filters/daubechies.hpp
new file mode 100644
index 000000000..94e3382c8
--- /dev/null
+++ b/include/boost/math/filters/daubechies.hpp
@@ -0,0 +1,419 @@
+/*
+ * Copyright Nick Thompson, 2019
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+#ifndef BOOST_MATH_FILTERS_DAUBECHIES_HPP
+#define BOOST_MATH_FILTERS_DAUBECHIES_HPP
+#include <array>
+#ifdef BOOST_HAS_FLOAT128
+#include <boost/multiprecision/float128.hpp>
+#endif
+namespace boost::math::filters {
+
+template <typename Real, unsigned p>
+constexpr std::array<Real, 2*p> daubechies_scaling_filter()
+{
+    static_assert(sizeof(Real) <= 16, "Filter coefficients only computed up to 128 bits of precision.");
+    static_assert(p < 25, "Filter coefficients only implemented up to 24.");
+    if constexpr (p == 1) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.6a09e6p-1f, 0x1.6a09e6p-1f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.6a09e667f3bcdp-1, 0x1.6a09e667f3bcdp-1};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0xb.504f333f9de6484p-4L, 0xb.504f333f9de6484p-4L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.6a09e667f3bcc908b2fb1366ea95p-1Q, 0x1.6a09e667f3bcc908b2fb1366ea95p-1Q};
+        }
+        #endif
+    }
+    if constexpr (p == 2) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.ee8dd4p-2f, 0x1.ac4bdep-1f, 0x1.cb0bfp-3f, -0x1.0907dcp-3f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.ee8dd4748bf15p-2, 0x1.ac4bdd6e3fd71p-1, 0x1.cb0bf0b6b7109p-3, -0x1.0907dc193069p-3};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0xf.746ea3a45f8a62ap-5L, 0xd.625eeb71feb8557p-4L, 0xe.585f85b5b8845bdp-6L, -0x8.483ee0c9834834cp-6L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.ee8dd4748bf14c548b969de58fap-2Q, 0x1.ac4bdd6e3fd70aae9f48d8a63d1bp-1Q, 0x1.cb0bf0b6b7108b79b4bf11d08b16p-3Q, -0x1.0907dc1930690697b13714fd4a15p-3Q};
+        }
+        #endif
+    }
+    if constexpr (p == 3) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.54a796p-2f, 0x1.9d20e2p-1f, 0x1.d6ea2p-2f, -0x1.1480a8p-3f, -0x1.5df7acp-4f, 0x1.2092e4p-5f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.54a796e50d264p-2, 0x1.9d20e247d28bbp-1, 0x1.d6ea20bf0f744p-2, -0x1.1480a85c59629p-3, -0x1.5df7ab50d483cp-4, 0x1.2092e373789b9p-5};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0xa.a53cb7286931db4p-5L, 0xc.e907123e945da19p-4L, 0xe.b75105f87ba23d6p-5L, -0x8.a40542e2cb14943p-6L, -0xa.efbd5a86a41e206p-7L, 0x9.04971b9bc4dcbc1p-8L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.54a796e50d263b67e38e82a5584cp-2Q, 0x1.9d20e247d28bb431f1e6c634b34ep-1Q, 0x1.d6ea20bf0f7447ac92de97f0e152p-2Q, -0x1.1480a85c596292857548d060a171p-3Q, -0x1.5df7ab50d483c40c41dbcf2191cfp-4Q, 0x1.2092e373789b9781e66814a5fa37p-5Q};
+        }
+        #endif
+    }
+    if constexpr (p == 4) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.d7d052p-3f, 0x1.6e005ep-1f, 0x1.4302cep-1f, -0x1.ca7c7p-6f, -0x1.7f0c1cp-3f, 0x1.f94e22p-6f, 0x1.0d60acp-5f, -0x1.5b4174p-7f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.d7d052af15ecp-3, 0x1.6e005ea45d748p-1, 0x1.4302cdd3de43ap-1, -0x1.ca7c6f9db5bfbp-6, -0x1.7f0c1b7c604d4p-3, 0x1.f94e2196383a9p-6, 0x1.0d60ac768117bp-5, -0x1.5b41730b72e29p-7};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0xe.be829578af5fe6dp-6L, 0xb.7002f522eba3e31p-4L, 0xa.18166e9ef21cf0dp-4L, -0xe.53e37cedadfd7d8p-9L, -0xb.f860dbe30269f7ap-6L, 0xf.ca710cb1c1d472dp-9L, 0x8.6b0563b408bdbabp-8L, -0xa.da0b985b97149dcp-10L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.d7d052af15ebfcd98dc85ef4cc01p-3Q, 0x1.6e005ea45d747c624e43405b1919p-1Q, 0x1.4302cdd3de439e1a299a6a04b89fp-1Q, -0x1.ca7c6f9db5bfafb07b9dace22f7p-6Q, -0x1.7f0c1b7c604d3ef4ab50462dfcedp-3Q, 0x1.f94e2196383a8e592495a4baff62p-6Q, 0x1.0d60ac768117b7550c2a3307e30fp-5Q, -0x1.5b41730b72e293b823fb2cbd40c6p-7Q};
+        }
+        #endif
+    }
+    if constexpr (p == 5) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.47e3c4p-3f, 0x1.35291cp-1f, 0x1.72d892p-1f, 0x1.1b8038p-3f, -0x1.f0384ep-3f, -0x1.082664p-5f, 0x1.3dbb9cp-4f, -0x1.990ad4p-8f, -0x1.9c3fp-7f, 0x1.b5385ep-9f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.47e3c41a7b911p-3, 0x1.35291c2c4b00cp-1, 0x1.72d89143b54f5p-1, 0x1.1b80373befcc6p-3, -0x1.f0384d3f81474p-3, -0x1.0826648a8dc74p-5, 0x1.3dbb9b52515aap-4, -0x1.990ad4579f2e8p-8, -0x1.9c3eff3294128p-7, 0x1.b5385e04e3c09p-9};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0xa.3f1e20d3dc8840dp-6L, 0x9.a948e1625806185p-4L, 0xb.96c48a1daa7a767p-4L, 0x8.dc01b9df7e62cc6p-6L, -0xf.81c269fc0a3a1e2p-6L, -0x8.413324546e39fcbp-8L, 0x9.eddcda928ad4cf6p-7L, -0xc.c856a2bcf973f17p-11L, -0xc.e1f7f994a094303p-10L, 0xd.a9c2f0271e04896p-12L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.47e3c41a7b91081ae95ed12670b7p-3Q, 0x1.35291c2c4b00c30a87eaf4d05e71p-1Q, 0x1.72d89143b54f4ecd724f0b79d111p-1Q, 0x1.1b80373befcc598b25a1d5436079p-3Q, -0x1.f0384d3f814743c3d93da5cd8909p-3Q, -0x1.0826648a8dc73f96ef19214f403ep-5Q, 0x1.3dbb9b52515a99ecaa66a225e968p-4Q, -0x1.990ad4579f2e7e2dc54832641bd8p-8Q, -0x1.9c3eff32941286062a45cb776526p-7Q, 0x1.b5385e04e3c0912c23cbbf7041e8p-9Q};
+        }
+        #endif
+    }
+    if constexpr (p == 6) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.c8def2p-4f, 0x1.fa7ebp-2f, 0x1.8094ap-1f, 0x1.42d0fcp-2f, -0x1.cf63dep-3f, -0x1.09c336p-3f, 0x1.8f5dd8p-4f, 0x1.c2ef44p-6f, -0x1.02b856p-5f, 0x1.225f72p-11f, 0x1.391514p-8f, -0x1.1a6874p-10f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.c8def24dc3952p-4, 0x1.fa7eaf64539a9p-2, 0x1.80949fa3bc0bbp-1, 0x1.42d0fcfa92f21p-2, -0x1.cf63dd26916f1p-3, -0x1.09c33622722ebp-3, 0x1.8f5dd7f4e1752p-4, 0x1.c2ef43d612549p-6, -0x1.02b856404e8cep-5, 0x1.225f71210a7c1p-11, 0x1.391514c62a31bp-8, -0x1.1a6873b7a6466p-10};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0xe.46f7926e1ca8e15p-7L, 0xf.d3f57b229cd4bdfp-5L, 0xc.04a4fd1de05d701p-4L, 0xa.1687e7d497907f9p-5L, -0xe.7b1ee9348b785acp-6L, -0x8.4e19b11391756c5p-6L, 0xc.7aeebfa70ba93cep-7L, 0xe.177a1eb092a4be4p-9L, -0x8.15c2b2027466fc3p-8L, 0x9.12fb890853e0901p-14L, 0x9.c8a8a631518d6e7p-11L, -0x8.d3439dbd3232f08p-13L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.c8def24dc3951c2a6dae413b8ddbp-4Q, 0x1.fa7eaf64539a97bd50da008738e1p-2Q, 0x1.80949fa3bc0bae02bf1b494d3af8p-1Q, 0x1.42d0fcfa92f20ff1b5b87f2f698cp-2Q, -0x1.cf63dd26916f0b589f7743608e82p-3Q, -0x1.09c33622722ead8a0ff038a97bp-3Q, 0x1.8f5dd7f4e175279c5a356a3fbcc9p-4Q, 0x1.c2ef43d6125497c75e24a80c6bfap-6Q, -0x1.02b856404e8cdf85933c3736d91cp-5Q, 0x1.225f71210a7c1202de723c931ed6p-11Q, 0x1.391514c62a31adcdfa747aebbdeep-8Q, -0x1.1a6873b7a6465e0ff5c033201061p-10Q};
+        }
+        #endif
+    }
+    if constexpr (p == 7) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.3ee1ccp-4f, 0x1.960e68p-2f, 0x1.7550cep-1f, 0x1.e10e9cp-2f, -0x1.26b83p-3f, -0x1.cad37cp-3f, 0x1.241522p-4f, 0x1.4a3072p-4f, -0x1.378a8ep-5f, -0x1.0f8eaap-6f, 0x1.9b4568p-7f, 0x1.c271f6p-12f, -0x1.d84a1p-10f, 0x1.72e554p-12f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.3ee1cba38b6b1p-4, 0x1.960e674303003p-2, 0x1.7550cd294c1fep-1, 0x1.e10e9ba294ddcp-2, -0x1.26b830e491e33p-3, -0x1.cad37bbd5ab97p-3, 0x1.241522ca7821cp-4, 0x1.4a30727f2fa53p-4, -0x1.378a8eecf45ccp-5, -0x1.0f8eaa8ffe709p-6, 0x1.9b45682a50d7p-7, 0x1.c271f584373d4p-12, -0x1.d84a0f9cb2f31p-10, 0x1.72e5533fa10d3p-12};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0x9.f70e5d1c5b5851p-7L, 0xc.b0733a181801b18p-5L, 0xb.aa86694a60ff1fap-4L, 0xf.0874dd14a6ee015p-5L, -0x9.35c187248f196d4p-6L, -0xe.569bddead5cb84ap-6L, 0x9.20a91653c10e31cp-7L, 0xa.518393f97d2944bp-7L, -0x9.bc547767a2e6031p-8L, -0x8.7c75547ff384611p-9L, 0xc.da2b415286b8088p-10L, 0xe.138fac21b9ea0e9p-15L, -0xe.c2507ce59798a73p-13L, 0xb.972a99fd0869924p-15L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.3ee1cba38b6b0a205a4c9aac651fp-4Q, 0x1.960e67430300363014da61e0a27dp-2Q, 0x1.7550cd294c1fe3f40f374c82e23dp-1Q, 0x1.e10e9ba294ddc02a47644f227fffp-2Q, -0x1.26b830e491e32da8b525e8ab6aa1p-3Q, -0x1.cad37bbd5ab970931a91ed1dfe9cp-3Q, 0x1.241522ca7821c638e85eb5e52839p-4Q, 0x1.4a30727f2fa52896ef76d0300cfp-4Q, -0x1.378a8eecf45cc0627b1c4b5cace1p-5Q, -0x1.0f8eaa8ffe708c22b1145a6b8cc8p-6Q, 0x1.9b45682a50d70110df27e4af9e36p-7Q, 0x1.c271f584373d41d177397b25f7ebp-12Q, -0x1.d84a0f9cb2f314e62607c084aab4p-10Q, 0x1.72e5533fa10d324758be56783dp-12Q};
+        }
+        #endif
+    }
+    if constexpr (p == 8) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.bdc64ap-5f, 0x1.40616ap-2f, 0x1.59ec46p-1f, 0x1.2bb39cp-1f, -0x1.035814p-6f, -0x1.22d4f8p-2f, 0x1.ef6f9cp-12f, 0x1.07acbcp-3f, -0x1.1c942p-6f, -0x1.692bc6p-5f, 0x1.ca215cp-7f, 0x1.1e978ep-7f, -0x1.3f2ef6p-8f, -0x1.9ac502p-12f, 0x1.622148p-11f, -0x1.ecbbbcp-14f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.bdc64ada308ddp-5, 0x1.4061690b4c31ep-2, 0x1.59ec45992376p-1, 0x1.2bb39bedb5e28p-1, -0x1.03581459a95c6p-6, -0x1.22d4f8724d56fp-2, 0x1.ef6f9caf662bp-12, 0x1.07acbb163ba09p-3, -0x1.1c9420f07509dp-6, -0x1.692bc518a7fe2p-5, 0x1.ca215cd5b85b4p-7, 0x1.1e978df35f5fcp-7, -0x1.3f2ef6d3ac74ap-8, -0x1.9ac501798e65dp-12, 0x1.622148e2ef341p-11, -0x1.ecbbbc88e3fc3p-14};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0xd.ee3256d1846ea19p-8L, 0xa.030b485a618f383p-5L, 0xa.cf622cc91bb0386p-4L, 0x9.5d9cdf6daf13eaep-4L, -0x8.1ac0a2cd4ae2f65p-9L, -0x9.16a7c3926ab7ac2p-5L, 0xf.7b7ce57b3157c6dp-15L, 0x8.3d65d8b1dd0442p-6L, -0x8.e4a10783a84e546p-9L, -0xb.495e28c53ff0c66p-8L, 0xe.510ae6adc2d9ca2p-10L, 0x8.f4bc6f9afafe075p-10L, -0x9.f977b69d63a5188p-11L, -0xc.d6280bcc732e77dp-15L, 0xb.110a471779a0a94p-14L, -0xf.65dde4471fe1763p-17L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.bdc64ada308dd431e90c51caaddfp-5Q, 0x1.4061690b4c31e70689f16560d4fdp-2Q, 0x1.59ec45992376070ce88329890c41p-1Q, 0x1.2bb39bedb5e27d5c19af764e6b08p-1Q, -0x1.03581459a95c5ec9b8a25898e79fp-6Q, -0x1.22d4f8724d56f584680effd871d8p-2Q, 0x1.ef6f9caf662af8d967c439494864p-12Q, 0x1.07acbb163ba0883fad048482f33cp-3Q, -0x1.1c9420f07509ca8be1e93402904ap-6Q, -0x1.692bc518a7fe18cb861085169737p-5Q, 0x1.ca215cd5b85b39449ec69ab26159p-7Q, 0x1.1e978df35f5fc0eabddff5ee9da6p-7Q, -0x1.3f2ef6d3ac74a30f6f64186b6be2p-8Q, -0x1.9ac501798e65cefa54cc7686cbfep-12Q, 0x1.622148e2ef341527c8d993cd7e86p-11Q, -0x1.ecbbbc88e3fc2ec652987ddfb595p-14Q};
+        }
+        #endif
+    }
+    if constexpr (p == 9) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.37ef3ep-5f, 0x1.f35f98p-3f, 0x1.35ab6p-1f, 0x1.50881p-1f, 0x1.10c9cap-3f, -0x1.2c4ff6p-2f, -0x1.8ca8ecp-4f, 0x1.303622p-3f, 0x1.f768dap-6f, -0x1.15062ap-4f, 0x1.07231ap-12f, 0x1.6e5f9cp-6f, -0x1.358a3ap-8f, -0x1.1897b6p-8f, 0x1.e4597cp-10f, 0x1.e3276ap-13f, -0x1.0833dap-12f, 0x1.4a11bap-15f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.37ef3e540da7cp-5, 0x1.f35f9808bc2ap-3, 0x1.35ab60603a288p-1, 0x1.5088101e8fe35p-1, 0x1.10c9ca803fb22p-3, -0x1.2c4ff66fd53efp-2, -0x1.8ca8ebcdc98fcp-4, 0x1.303621e43e771p-3, 0x1.f768d94677997p-6, -0x1.1506294f451a2p-4, 0x1.07231a6b6ca0dp-12, 0x1.6e5f9be058887p-6, -0x1.358a39f783bbfp-8, -0x1.1897b64b3bfb6p-8, 0x1.e4597bbfc711fp-10, 0x1.e3276a3bc510bp-13, -0x1.0833da803978ap-12, 0x1.4a11ba1ad31b5p-15};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0x9.bf79f2a06d3e1d5p-8L, 0xf.9afcc045e1503b9p-6L, 0x9.ad5b0301d143d0bp-4L, 0xa.844080f47f1a981p-4L, 0x8.864e5401fd91397p-6L, -0x9.627fb37ea9f7708p-5L, -0xc.65475e6e4c7e255p-7L, 0x9.81b10f21f3b8936p-6L, 0xf.bb46ca33bccb6bep-9L, -0x8.a8314a7a28d0fa4p-7L, 0x8.3918d35b65065cap-15L, 0xb.72fcdf02c443b9ap-9L, -0x9.ac51cfbc1ddf90ep-11L, -0x8.c4bdb259dfdac19p-11L, 0xf.22cbddfe388f56ep-13L, 0xf.193b51de288565ap-16L, -0x8.419ed401cbc51f3p-15L, 0xa.508dd0d698da458p-18L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.37ef3e540da7c3aa0d1dcf5bb03fp-5Q, 0x1.f35f9808bc2a0772556b997598d3p-3Q, 0x1.35ab60603a287a1609387fb893b8p-1Q, 0x1.5088101e8fe3530163beb11528dcp-1Q, 0x1.10c9ca803fb2272d1e1cf6fa2d0cp-3Q, -0x1.2c4ff66fd53eee10d811f3bf5459p-2Q, -0x1.8ca8ebcdc98fc4aa06bb294a039cp-4Q, 0x1.303621e43e77126c475b311fee41p-3Q, 0x1.f768d94677996d7b05f99f12d599p-6Q, -0x1.1506294f451a1f48db3652c40168p-4Q, 0x1.07231a6b6ca0cb934ff78371a261p-12Q, 0x1.6e5f9be058887734b49665246c12p-6Q, -0x1.358a39f783bbf21cd3bb737b9bf7p-8Q, -0x1.1897b64b3bfb583210060e933d6p-8Q, 0x1.e4597bbfc711eadc2635b08cc11dp-10Q, 0x1.e3276a3bc510acb32c14bfd1c3d9p-13Q, -0x1.0833da803978a3e6248db817fff9p-12Q, 0x1.4a11ba1ad31b48b0c2e32412ef31p-15Q};
+        }
+        #endif
+    }
+    if constexpr (p == 10) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.b4f654p-6f, 0x1.8162d6p-3f, 0x1.0ded5p-1f, 0x1.607db4p-1f, 0x1.1feba4p-2f, -0x1.ffaf7cp-3f, -0x1.914c48p-3f, 0x1.04da38p-3f, 0x1.7d29b8p-4f, -0x1.246e3p-4f, -0x1.e2a1dep-6f, 0x1.101406p-5f, 0x1.d8b7dcp-9f, -0x1.5fb466p-7f, 0x1.6dc878p-10f, 0x1.052608p-9f, -0x1.67962p-11f, -0x1.e87f56p-14f, 0x1.888a12p-14f, -0x1.bd12a2p-17f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.b4f6549dc7ae3p-6, 0x1.8162d69198cfep-3, 0x1.0ded5071bf874p-1, 0x1.607db4062d775p-1, 0x1.1feba4923f567p-2, -0x1.ffaf7b6c111e3p-3, -0x1.914c47c1ca802p-3, 0x1.04da377a0ae83p-3, 0x1.7d29b819fd18dp-4, -0x1.246e307349ac4p-4, -0x1.e2a1dd5152b25p-6, 0x1.1014069cb8f3cp-5, 0x1.d8b7db3e21714p-9, -0x1.5fb466d770edcp-7, 0x1.6dc8787ae38ddp-10, 0x1.0526072a98cd8p-9, -0x1.67962098c50fp-11, -0x1.e87f555dc50ddp-14, 0x1.888a11cfae433p-14, -0x1.bd12a2a1a43dbp-17};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0xd.a7b2a4ee3d71687p-9L, 0xc.0b16b48cc67ed9dp-6L, 0x8.6f6a838dfc39cfcp-4L, 0xb.03eda0316bba9f7p-4L, 0x8.ff5d2491fab3641p-5L, -0xf.fd7bdb6088f17a6p-6L, -0xc.8a623e0e5400e29p-6L, 0x8.26d1bbd05741a5ep-6L, 0xb.e94dc0cfe8c6997p-7L, -0x9.2371839a4d62324p-7L, -0xf.150eea8a95926cep-9L, 0x8.80a034e5c79dfcbp-8L, 0xe.c5bed9f10b89f27p-12L, -0xa.fda336bb876e26p-10L, 0xb.6e43c3d71c6ebc5p-13L, 0x8.29303954c66bfc4p-12L, -0xb.3cb104c62878097p-14L, -0xf.43faaaee286e92ap-17L, 0xc.44508e7d72197a7p-17L, -0xd.e895150d21eda8p-20L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.b4f6549dc7ae2d0da711a289f0cap-6Q, 0x1.8162d69198cfdb39a90922d70e5fp-3Q, 0x1.0ded5071bf8739f750ffec152978p-1Q, 0x1.607db4062d7753edab576af3e0dcp-1Q, 0x1.1feba4923f566c829244a5b4f4c2p-2Q, -0x1.ffaf7b6c111e2f4b082d1396dfd9p-3Q, -0x1.914c47c1ca801c5176763b1002edp-3Q, 0x1.04da377a0ae834bb94a9fa4f0243p-3Q, 0x1.7d29b819fd18d32d43de1a7d3641p-4Q, -0x1.246e307349ac4648ebbb94e378bbp-4Q, -0x1.e2a1dd5152b24d9c384763b949a8p-6Q, 0x1.1014069cb8f3bf95bd45be617d84p-5Q, 0x1.d8b7db3e21713e4ea2df5435db4ap-9Q, -0x1.5fb466d770edc4c0f4a29d7e3176p-7Q, 0x1.6dc8787ae38dd789b768877a70c2p-10Q, 0x1.0526072a98cd7f8751cc002da048p-9Q, -0x1.67962098c50f012db290a44515a5p-11Q, -0x1.e87f555dc50dd253428e6067701p-14Q, 0x1.888a11cfae432f4e4bd0c734fcc9p-14Q, -0x1.bd12a2a1a43db4fff0519cd821dfp-17Q};
+        }
+        #endif
+    }
+    if constexpr (p == 11) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.324992p-6f, 0x1.270c9cp-3f, 0x1.ccb286p-2f, 0x1.5f1256p-1f, 0x1.a5d9fcp-2f, -0x1.4c56f6p-3f, -0x1.18cff8p-2f, 0x1.0e83b8p-4f, 0x1.32d0a4p-3f, -0x1.7cc388p-5f, -0x1.10221ep-4f, 0x1.00b272p-5f, 0x1.557516p-6f, -0x1.f77976p-7f, -0x1.b5e4ap-9f, 0x1.42fd2p-8f, -0x1.439544p-12f, -0x1.d4338ep-11f, 0x1.05416p-12f, 0x1.c8ab06p-15f, -0x1.228a1p-15f, 0x1.2d9b0cp-18f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.3249916076091p-6, 0x1.270c9c42314cfp-3, 0x1.ccb286198c9dfp-2, 0x1.5f125643212ccp-1, 0x1.a5d9fccefe816p-2, -0x1.4c56f6b2bf66cp-3, -0x1.18cff89a8cc46p-2, 0x1.0e83b8b6a4d8fp-4, 0x1.32d0a3f0ba732p-3, -0x1.7cc387e4a9a09p-5, -0x1.10221dbbeff7cp-4, 0x1.00b27276a8099p-5, 0x1.557516a958be5p-6, -0x1.f77975a6883f7p-7, -0x1.b5e49f3346a8bp-9, 0x1.42fd20a75f9acp-8, -0x1.439543c841133p-12, -0x1.d4338d3fdae3ap-11, 0x1.05415f0bc6ea2p-12, 0x1.c8ab05d193c38p-15, -0x1.228a0febb3e8cp-15, 0x1.2d9b0b4e10d78p-18};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0x9.924c8b03b048b06p-9L, 0x9.3864e2118a67afdp-6L, 0xe.659430cc64ef74bp-5L, 0xa.f892b2190965c91p-4L, 0xd.2ecfe677f40b2aap-5L, -0xa.62b7b595fb361ep-6L, -0x8.c67fc4d4662301ap-5L, 0x8.741dc5b526c7499p-7L, 0x9.96851f85d39931p-6L, -0xb.e61c3f254d048e4p-8L, -0x8.8110eddf7fbe097p-7L, 0x8.059393b5404c82ap-8L, 0xa.aba8b54ac5f295dp-9L, -0xf.bbcbad3441fb82ap-10L, -0xd.af24f99a3545bf1p-12L, 0xa.17e9053afcd5e0bp-11L, -0xa.1caa1e42089945fp-15L, -0xe.a19c69fed71d098p-14L, 0x8.2a0af85e37512d9p-15L, 0xe.45582e8c9e1bc7dp-18L, -0x9.14507f5d9f45ff4p-18L, 0x9.6cd85a7086bbdf3p-21L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.324991607609160c660c469077c4p-6Q, 0x1.270c9c42314cf5fa956419fe6ca8p-3Q, 0x1.ccb286198c9dee96d12668532b6cp-2Q, 0x1.5f125643212cb922d29e40df5ae5p-1Q, 0x1.a5d9fccefe816554cfd2c1b4c2eap-2Q, -0x1.4c56f6b2bf66c3c093c0529f8f7fp-3Q, -0x1.18cff89a8cc4603466567c5566b2p-2Q, 0x1.0e83b8b6a4d8e932eca95459a69cp-4Q, 0x1.32d0a3f0ba73261f3f385a0ab52ep-3Q, -0x1.7cc387e4a9a091c75d9de8faea58p-5Q, -0x1.10221dbbeff7c12d2228c7667179p-4Q, 0x1.00b27276a80990547cbd63f84547p-5Q, 0x1.557516a958be52b928260c4c6ad5p-6Q, -0x1.f77975a6883f7054b8b01c477981p-7Q, -0x1.b5e49f3346a8b7e121e98be0fcfbp-9Q, 0x1.42fd20a75f9abc16cec7fe76464bp-8Q, -0x1.439543c8411328be7c3dbb239962p-12Q, -0x1.d4338d3fdae3a1309e0d7105695cp-11Q, 0x1.05415f0bc6ea25b1e91fb2adce4fp-12Q, 0x1.c8ab05d193c378f97fff6933dc9bp-15Q, -0x1.228a0febb3e8bfe721948bedcf9cp-15Q, 0x1.2d9b0b4e10d77be6e48f3790bbdep-18Q};
+        }
+        #endif
+    }
+    if constexpr (p == 12) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.ada998p-7f, 0x1.c0c89p-4f, 0x1.826962p-2f, 0x1.507c5ap-1f, 0x1.082246p-1f, -0x1.6eb4acp-5f, -0x1.43c448p-2f, -0x1.85997p-6f, 0x1.75b758p-3f, 0x1.5f3ea8p-8f, -0x1.8afc68p-4f, 0x1.63811ap-7f, 0x1.5458dcp-5f, -0x1.906176p-7f, -0x1.a4c4a6p-7f, 0x1.b7d844p-8f, 0x1.26babep-9f, -0x1.1dac02p-9f, 0x1.b73c72p-18f, 0x1.978844p-12f, -0x1.73369p-14f, -0x1.96b4a6p-16f, 0x1.acb93p-17f, -0x1.9a7502p-20f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.ada9978d2fa57p-7, 0x1.c0c890682f879p-4, 0x1.82696272e40bdp-2, 0x1.507c59d8e6f6bp-1, 0x1.082245c297978p-1, -0x1.6eb4ac1d9855dp-5, -0x1.43c448da45b22p-2, -0x1.85996f0f3b3b2p-6, 0x1.75b757e56dd3bp-3, 0x1.5f3ea878d368ep-8, -0x1.8afc682193383p-4, 0x1.638119d1c4362p-7, 0x1.5458dbe394ebp-5, -0x1.90617513f389bp-7, -0x1.a4c4a623e2a51p-7, 0x1.b7d844bffa4e9p-8, 0x1.26babd1f8d181p-9, -0x1.1dac0186ec142p-9, 0x1.b73c724cbcd25p-18, 0x1.9788431be0bfbp-12, -0x1.7336904b8b4e8p-14, -0x1.96b4a56f63fa9p-16, 0x1.acb92f10c423ap-17, -0x1.9a7502d7dc2f3p-20};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0xd.6d4cbc697d2b459p-10L, 0xe.064483417c3c86cp-7L, 0xc.134b1397205e82fp-5L, 0xa.83e2cec737b5622p-4L, 0x8.41122e14bcbbcc8p-4L, -0xb.75a560ecc2ae67fp-8L, -0xa.1e2246d22d9117cp-5L, -0xc.2ccb7879d9d93dbp-9L, 0xb.adbabf2b6e9db71p-6L, 0xa.f9f543c69b47041p-11L, -0xc.57e3410c99c1b5p-7L, 0xb.1c08ce8e21b0dd8p-10L, 0xa.a2c6df1ca7582e3p-8L, -0xc.830ba89f9c4dbcbp-10L, -0xd.2625311f15287e1p-10L, 0xd.bec225ffd274461p-11L, 0x9.35d5e8fc68c04b8p-12L, -0x8.ed600c3760a133p-12L, 0xd.b9e39265e692542p-21L, 0xc.bc4218df05fd969p-15L, -0xb.99b4825c5a7426p-17L, -0xc.b5a52b7b1fd454bp-19L, 0xd.65c97886211cfe7p-20L, -0xc.d3a816bee17970fp-23L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.ada9978d2fa568b21229688156b8p-7Q, 0x1.c0c890682f8790d7f6bb1c1aa44ep-4Q, 0x1.82696272e40bd05e57c851b9cb36p-2Q, 0x1.507c59d8e6f6ac435d1e88e090b6p-1Q, 0x1.082245c29797798f324c3b86f65cp-1Q, -0x1.6eb4ac1d9855ccfed03d4133c6fbp-5Q, -0x1.43c448da45b222f8d287f72956dcp-2Q, -0x1.85996f0f3b3b27b5f0ec32953a95p-6Q, 0x1.75b757e56dd3b6e26eea4e0a43bap-3Q, 0x1.5f3ea878d368e081a5d3cb36d936p-8Q, -0x1.8afc6821933836a0611906df913cp-4Q, 0x1.638119d1c4361bb00a2f22d1f90bp-7Q, 0x1.5458dbe394eb05c5aab3c4ceb31ap-5Q, -0x1.90617513f389b7954493854c387ep-7Q, -0x1.a4c4a623e2a50fc10158bea8a45cp-7Q, 0x1.b7d844bffa4e88c2ef52650eb0e3p-8Q, 0x1.26babd1f8d1809707edb54236067p-9Q, -0x1.1dac0186ec14265ff3ab908c13a3p-9Q, 0x1.b73c724cbcd24a84c3c597249f8dp-18Q, 0x1.9788431be0bfb2d1938d25135045p-12Q, -0x1.7336904b8b4e84c0e0396f9346efp-14Q, -0x1.96b4a56f63fa8a95abb9ecaeceaep-16Q, 0x1.acb92f10c4239fce7d915af19a6cp-17Q, -0x1.9a7502d7dc2f2e1e665f9ba74bc1p-20Q};
+        }
+        #endif
+    }
+    if constexpr (p == 13) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.2d8918p-7f, 0x1.53665p-4f, 0x1.3f7bf6p-2f, 0x1.38dc5p-1f, 0x1.2d82fp-1f, 0x1.644b26p-4f, -0x1.428842p-2f, -0x1.fe442cp-4f, 0x1.6f9128p-3f, 0x1.2acc8p-4f, -0x1.b16354p-4f, -0x1.b1fc6ep-6f, 0x1.cbe504p-5f, 0x1.37f29ep-9f, -0x1.86743ap-6f, 0x1.0128dp-8f, 0x1.db8098p-8f, -0x1.6a025cp-9f, -0x1.58e562p-10f, 0x1.e8ceb2p-11f, 0x1.9d26d8p-15f, -0x1.5a4cf4p-13f, 0x1.0159a8p-15f, 0x1.5e5f8p-17f, -0x1.3b708ap-18f, 0x1.183f9ep-21f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.2d89174d37e3bp-7, 0x1.53664fc8a3d4cp-4, 0x1.3f7bf6c09afe8p-2, 0x1.38dc5001834bbp-1, 0x1.2d82ef0bea472p-1, 0x1.644b251290fb5p-4, -0x1.42884206fc5aep-2, -0x1.fe442b86ad763p-4, 0x1.6f91279c81aa4p-3, 0x1.2acc804557c8bp-4, -0x1.b163543c8eaccp-4, -0x1.b1fc6de239706p-6, 0x1.cbe5044520d5ep-5, 0x1.37f29dfe3e92cp-9, -0x1.867439245b0c7p-6, 0x1.0128d031aa3bp-8, 0x1.db80973172631p-8, -0x1.6a025cdac7e1p-9, -0x1.58e561b1f2cf6p-10, 0x1.e8ceb1ee24cabp-11, 0x1.9d26d847f17cap-15, -0x1.5a4cf360064a4p-13, 0x1.0159a865542d3p-15, 0x1.5e5f8028cd835p-17, -0x1.3b708a4c3be34p-18, 0x1.183f9db8da3ap-21};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0x9.6c48ba69bf1db2dp-10L, 0xa.9b327e451ea606ap-7L, 0x9.fbdfb604d7f42bfp-5L, 0x9.c6e2800c1a5d56fp-4L, 0x9.6c17785f5238ef1p-4L, 0xb.2259289487da5f5p-7L, -0xa.14421037e2d6f28p-5L, -0xf.f2215c356bb1af3p-7L, 0xb.7c893ce40d51d77p-6L, 0x9.5664022abe455a4p-7L, -0xd.8b1aa1e47565fb8p-7L, -0xd.8fe36f11cb8316bp-9L, 0xe.5f28222906af18bp-8L, 0x9.bf94eff1f49636bp-12L, -0xc.33a1c922d8636b9p-9L, 0x8.0946818d51d8108p-11L, 0xe.dc04b98b931878p-11L, -0xb.5012e6d63f07f27p-12L, -0xa.c72b0d8f967b059p-13L, 0xf.46758f712655aeep-14L, 0xc.e936c23f8be4d46p-18L, -0xa.d2679b00325201p-16L, 0x8.0acd432aa169479p-18L, 0xa.f2fc01466c1a50ap-20L, -0x9.db845261df1a01dp-21L, 0x8.c1fcedc6d1d027ap-24L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.2d89174d37e3b6596d64d168e49p-7Q, 0x1.53664fc8a3d4c0d33efd4b4bc6fap-4Q, 0x1.3f7bf6c09afe857e70d916613d78p-2Q, 0x1.38dc5001834baade66ebb6ec9fc1p-1Q, 0x1.2d82ef0bea471de1f0a3864a5cccp-1Q, 0x1.644b251290fb4bea9c417da1f71ep-4Q, -0x1.42884206fc5ade5015e8dd0e5832p-2Q, -0x1.fe442b86ad7635e6a44fa231478p-4Q, 0x1.6f91279c81aa3aed801eca5172e8p-3Q, 0x1.2acc804557c8ab4899f3d0916648p-4Q, -0x1.b163543c8eacbf70b0092010e485p-4Q, -0x1.b1fc6de2397062d67f76ff78186p-6Q, 0x1.cbe5044520d5e315c90c0ed1b10cp-5Q, 0x1.37f29dfe3e92c6d51003ce786db8p-9Q, -0x1.867439245b0c6d71509d7a14369ep-6Q, 0x1.0128d031aa3b020f68dbd131fc68p-8Q, 0x1.db80973172630eff11f1aa6bf206p-8Q, -0x1.6a025cdac7e0fe4d3e8433e38ffbp-9Q, -0x1.58e561b1f2cf60b1ce144cfab0ffp-10Q, 0x1.e8ceb1ee24cab5dbcf0c32d1591bp-11Q, 0x1.9d26d847f17c9a8ce68c968f105dp-15Q, -0x1.5a4cf360064a4020bfd19dc8e5fp-13Q, 0x1.0159a865542d28f1113c2ad46cb5p-15Q, 0x1.5e5f8028cd834a146bf59b16d932p-17Q, -0x1.3b708a4c3be3403a7da544157c5bp-18Q, 0x1.183f9db8da3a04f4c66e4459dad2p-21Q};
+        }
+        #endif
+    }
+    if constexpr (p == 14) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.a7702ap-8f, 0x1.fee46p-5f, 0x1.04f778p-2f, 0x1.1bcdf2p-1f, 0x1.432b0ep-1f, 0x1.bfd66ap-3f, -0x1.163586p-2f, -0x1.be885ep-3f, 0x1.1b6ef4p-3f, 0x1.1eb29p-3f, -0x1.63524ep-4f, -0x1.251084p-4f, 0x1.c480a6p-5f, 0x1.ba103ap-6f, -0x1.ee8e8ap-6f, -0x1.6ffce6p-8f, 0x1.a3160cp-7f, -0x1.873bd2p-11f, -0x1.f89472p-9f, 0x1.1650e2p-10f, 0x1.7334fep-11f, -0x1.959f6ap-12f, -0x1.5e73f4p-15f, 0x1.20612ap-14f, -0x1.5adbf4p-17f, -0x1.26968ep-18f, 0x1.cf0cbcp-20f, -0x1.7fc91p-23f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.a7702ace363acp-8, 0x1.fee460f5cb877p-5, 0x1.04f777f62f423p-2, 0x1.1bcdf22a1725cp-1, 0x1.432b0dc3136d4p-1, 0x1.bfd66ae4258acp-3, -0x1.1635861af071dp-2, -0x1.be885d06053bfp-3, 0x1.1b6ef32bc7359p-3, 0x1.1eb28fc03c55bp-3, -0x1.63524d6aa4cf7p-4, -0x1.2510847f3ed26p-4, 0x1.c480a659de0cdp-5, 0x1.ba103a92149f4p-6, -0x1.ee8e8a6bca9acp-6, -0x1.6ffce6192a67bp-8, 0x1.a3160ba7d924ep-7, -0x1.873bd13c8af18p-11, -0x1.f894721441f67p-9, 0x1.1650e1f6ec4c3p-10, 0x1.7334fd9e58c6ap-11, -0x1.959f69010da01p-12, -0x1.5e73f3c020201p-15, 0x1.20612a2e814f8p-14, -0x1.5adbf364f5e1cp-17, -0x1.26968e53fb76dp-18, 0x1.cf0cbb4133dbbp-20, -0x1.7fc90f0c46da2p-23};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0xd.3b815671b1d61adp-11L, 0xf.f72307ae5c3b8acp-8L, 0x8.27bbbfb17a114bp-5L, 0x8.de6f9150b92e008p-4L, 0xa.19586e189b69d98p-4L, 0xd.feb357212c55f71p-6L, -0x8.b1ac30d7838e67p-5L, -0xd.f442e83029df6fp-6L, 0x8.db77995e39ac42bp-6L, 0x8.f5947e01e2ad986p-6L, -0xb.1a926b55267b7d4p-7L, -0x9.288423f9f692d35p-7L, 0xe.240532cef066a7ap-8L, 0xd.d081d490a4fa2c2p-9L, -0xf.7474535e54d6257p-9L, -0xb.7fe730c9533d677p-11L, 0xd.18b05d3ec926ef4p-10L, -0xc.39de89e4578bd58p-14L, -0xf.c4a390a20fb38fap-12L, 0x8.b2870fb76261486p-13L, 0xb.99a7ecf2c634fb5p-14L, -0xc.acfb48086d004d1p-15L, -0xa.f39f9e01010090ep-18L, 0x9.030951740a7c181p-17L, -0xa.d6df9b27af0deefp-20L, -0x9.34b4729fdbb6709p-21L, 0xe.7865da099eddb46p-23L, -0xb.fe48786236d0c8ep-26L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.a7702ace363ac35a31e24ad7f18bp-8Q, 0x1.fee460f5cb8771588fb11eee4edep-5Q, 0x1.04f777f62f422960e164233d2842p-2Q, 0x1.1bcdf22a1725c010c6b543c39465p-1Q, 0x1.432b0dc3136d3b304d5a3bf4569bp-1Q, 0x1.bfd66ae4258abee147e56af809ep-3Q, -0x1.1635861af071cce08b7655b9575p-2Q, -0x1.be885d06053beddff8849acb8697p-3Q, 0x1.1b6ef32bc7358856a3c8661f7dbbp-3Q, 0x1.1eb28fc03c55b30ce48dc30b7f77p-3Q, -0x1.63524d6aa4cf6fa795512cfa3aa5p-4Q, -0x1.2510847f3ed25a6abc4fb2ebbea9p-4Q, 0x1.c480a659de0cd4f4123d770896e6p-5Q, 0x1.ba103a92149f4583a4c79c292018p-6Q, -0x1.ee8e8a6bca9ac4ad53dedccf86b9p-6Q, -0x1.6ffce6192a67aceee5260da8193dp-8Q, 0x1.a3160ba7d924dde8cc52f58fbb97p-7Q, -0x1.873bd13c8af17ab00e30f03b73e4p-11Q, -0x1.f894721441f671f4ac26746366e6p-9Q, 0x1.1650e1f6ec4c290c75eee26e8b4ap-10Q, 0x1.7334fd9e58c69f69b95d47a6075fp-11Q, -0x1.959f69010da009a2eacf096b1dafp-12Q, -0x1.5e73f3c02020121b8b1dbc91cc8ap-15Q, 0x1.20612a2e814f83021e4b38a90018p-14Q, -0x1.5adbf364f5e1bddd8115a86dd662p-17Q, -0x1.26968e53fb76ce12ec5e07348937p-18Q, 0x1.cf0cbb4133dbb68c44095fc163dep-20Q, -0x1.7fc90f0c46da191bc033464815fbp-23Q};
+        }
+        #endif
+    }
+    if constexpr (p == 15) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.297006p-8f, 0x1.7eec02p-5f, 0x1.a5efd6p-3f, 0x1.f87476p-2f, 0x1.4aa806p-1f, 0x1.5b237cp-2f, -0x1.8bae9cp-3f, -0x1.27d0d6p-2f, 0x1.0b6624p-4f, 0x1.856ba4p-3f, -0x1.44f2p-5f, -0x1.c726cp-4f, 0x1.158586p-5f, 0x1.c0c324p-5f, -0x1.a62aaap-6f, -0x1.54f3aep-6f, 0x1.ee4514p-7f, 0x1.4e4c96p-8f, -0x1.a92e2p-8f, -0x1.fb0008p-13f, 0x1.fd6e44p-10f, -0x1.879fe8p-12f, -0x1.79081p-12f, 0x1.46f04ap-13f, 0x1.b0baccp-16f, -0x1.d7ff96p-16f, 0x1.c35f5cp-19f, 0x1.e6358ep-20f, -0x1.532292p-21f, 0x1.076d02p-24f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.2970058a26dcep-8, 0x1.7eec010bca4c4p-5, 0x1.a5efd6f02857ep-3, 0x1.f8747691d3f73p-2, 0x1.4aa8051a530b4p-1, 0x1.5b237b0c28179p-2, -0x1.8bae9ca895b45p-3, -0x1.27d0d6e28e01fp-2, 0x1.0b6623378c72fp-4, 0x1.856ba3f0d1d5bp-3, -0x1.44f200621040dp-5, -0x1.c726bf22e4a16p-4, 0x1.15858527779bcp-5, 0x1.c0c32426f4663p-5, -0x1.a62aa972a6fc4p-6, -0x1.54f3ad3a0b7c6p-6, 0x1.ee4513500347p-7, 0x1.4e4c95b98ec2dp-8, -0x1.a92e1fc2fdcaep-8, -0x1.fb000715d8e65p-13, 0x1.fd6e43c3dd5e8p-10, -0x1.879fe7f24ba0ap-12, -0x1.79080f71ee322p-12, 0x1.46f04a6cb59p-13, 0x1.b0bacca20c60fp-16, -0x1.d7ff965f47a09p-16, 0x1.c35f5c1543372p-19, 0x1.e6358dfe44b53p-20, -0x1.532291d1cbfa4p-21, 0x1.076d016337019p-24};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0x9.4b802c5136e6cb1p-11L, 0xb.f760085e52620cp-8L, 0xd.2f7eb78142bee86p-6L, 0xf.c3a3b48e9fb9b9bp-5L, 0xa.554028d2985a2bep-4L, 0xa.d91bd86140bc88ap-5L, -0xc.5d74e544ada28ecp-6L, -0x9.3e86b714700f9f8p-5L, 0x8.5b3119bc6397595p-7L, 0xc.2b5d1f868ead57ap-6L, -0xa.2790031082066ebp-8L, -0xe.3935f917250aff5p-7L, 0x8.ac2c293bbcde0e2p-8L, 0xe.06192137a331763p-8L, -0xd.31554b9537e1c3bp-9L, -0xa.a79d69d05be2dedp-9L, 0xf.72289a801a381d6p-10L, 0xa.7264adcc7616af1p-11L, -0xd.4970fe17ee56c45p-11L, -0xf.d80038aec732ac5p-16L, 0xf.eb721e1eeaf4368p-13L, -0xc.3cff3f925d05241p-15L, -0xb.c8407b8f7191299p-15L, 0xa.37825365ac803f5p-16L, 0xd.85d665106307a4ap-19L, -0xe.bffcb2fa3d0481cp-19L, 0xe.1afae0aa19b8c5bp-22L, 0xf.31ac6ff225a9413p-23L, -0xa.99148e8e5fd1f6dp-24L, 0x8.3b680b19b80c80ep-27L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.2970058a26dcd961f2ddf52bca08p-8Q, 0x1.7eec010bca4c417f3cf45c166751p-5Q, 0x1.a5efd6f02857dd0be400d7c02e2cp-3Q, 0x1.f8747691d3f737355530dd281d86p-2Q, 0x1.4aa8051a530b457c39051251b937p-1Q, 0x1.5b237b0c281791146b95d35023c4p-2Q, -0x1.8bae9ca895b451d87fbb9a690248p-3Q, -0x1.27d0d6e28e01f3ef0606971828aap-2Q, 0x1.0b6623378c72eb295fa0f634a67bp-4Q, 0x1.856ba3f0d1d5aaf4f59a12cbb286p-3Q, -0x1.44f200621040cdd51fafc7035006p-5Q, -0x1.c726bf22e4a15fea85834dbb1052p-4Q, 0x1.15858527779bc1c4ec7f8b6fdd21p-5Q, 0x1.c0c32426f4662ec60f158af78296p-5Q, -0x1.a62aa972a6fc3876e9915f565de4p-6Q, -0x1.54f3ad3a0b7c5bd971d938015013p-6Q, 0x1.ee451350034703acaa0dbe95c1aep-7Q, 0x1.4e4c95b98ec2d5e117559a2b0da9p-8Q, -0x1.a92e1fc2fdcad88a36c4f23f938p-8Q, -0x1.fb000715d8e6558a8e3b0bc34d7fp-13Q, 0x1.fd6e43c3dd5e86d041c185aa9428p-10Q, -0x1.879fe7f24ba0a4818b2d76fbd7e6p-12Q, -0x1.79080f71ee322531c0337932b9a5p-12Q, 0x1.46f04a6cb59007eab6af7b114fa4p-13Q, 0x1.b0bacca20c60f4939edefbff1354p-16Q, -0x1.d7ff965f47a09038cb01ea5da5e9p-16Q, 0x1.c35f5c15433718b508f832bbf1b8p-19Q, 0x1.e6358dfe44b5282546827ce8042cp-20Q, -0x1.532291d1cbfa3eda1a3275ffd36dp-21Q, 0x1.076d01633701901bb8cc971717bp-24Q};
+        }
+        #endif
+    }
+    if constexpr (p == 16) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.a2048p-9f, 0x1.1df6c8p-5f, 0x1.520d3ap-3f, 0x1.b8a3e6p-2f, 0x1.465392p-1f, 0x1.c2db72p-2f, -0x1.6f9ed6p-4f, -0x1.4ee9bp-2f, -0x1.c96974p-6f, 0x1.b084cp-3f, 0x1.bff16p-6f, -0x1.0f219ap-3f, -0x1.98ed2ep-8f, 0x1.36fc54p-4f, -0x1.f159dcp-8f, -0x1.2e3094p-5f, 0x1.516f08p-7f, 0x1.ca8c3ep-7f, -0x1.ca18fcp-8f, -0x1.dda9bcp-9f, 0x1.99ff0cp-9f, 0x1.abb604p-12f, -0x1.ed5dcep-11f, 0x1.df29e6p-14f, 0x1.6e8e3p-13f, -0x1.0000dep-14f, -0x1.d3f062p-17f, 0x1.7c64bap-17f, -0x1.1821aep-20f, -0x1.8b5554p-21f, 0x1.efcecp-23f, -0x1.6a61bcp-26f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.a2047f25eec86p-9, 0x1.1df6c86cbec6p-5, 0x1.520d391a94107p-3, 0x1.b8a3e5feb4879p-2, 0x1.465391b465934p-1, 0x1.c2db72f84c204p-2, -0x1.6f9ed69c399c7p-4, -0x1.4ee9af39c16ecp-2, -0x1.c96973b93bd86p-6, 0x1.b084bf1dc763bp-3, 0x1.bff160aba4bc3p-6, -0x1.0f21999627c5fp-3, -0x1.98ed2d2871d0ap-8, 0x1.36fc54ec8b106p-4, -0x1.f159dcb973ff4p-8, -0x1.2e3093b602a51p-5, 0x1.516f07b10e2cp-7, 0x1.ca8c3dcce54c3p-7, -0x1.ca18fbf2cc141p-8, -0x1.dda9bb9568c15p-9, 0x1.99ff0c3f2ed81p-9, 0x1.abb6031610513p-12, -0x1.ed5dcd1b49a3fp-11, 0x1.df29e5ea12845p-14, 0x1.6e8e301063e5ap-13, -0x1.0000dea4283e9p-14, -0x1.d3f0626b575afp-17, 0x1.7c64ba15d2346p-17, -0x1.1821ad345e7cp-20, -0x1.8b555407022a1p-21, 0x1.efcebf5a99b7bp-23, -0x1.6a61bcee28103p-26};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0xd.1023f92f7642ed3p-12L, 0x8.efb64365f630239p-8L, 0xa.9069c8d4a08344dp-6L, 0xd.c51f2ff5a43c97dp-5L, 0xa.329c8da32c99c9dp-4L, 0xe.16db97c26101ca7p-5L, -0xb.7cf6b4e1cce36cbp-7L, -0xa.774d79ce0b75fdfp-5L, -0xe.4b4b9dc9dec3204p-9L, 0xd.8425f8ee3b1d5bfp-6L, 0xd.ff8b055d25e15c1p-9L, -0x8.790cccb13e2f58ep-6L, -0xc.c76969438e84e18p-11L, 0x9.b7e2a76458832d7p-7L, -0xf.8acee5cb9ff9e4cp-11L, -0x9.71849db015288a6p-8L, 0xa.8b783d88715ff76p-10L, 0xe.5461ee672a6184ep-10L, -0xe.50c7df9660a0b0ep-11L, -0xe.ed4ddcab460a85bp-12L, 0xc.cff861f976c0535p-12L, 0xd.5db018b082895d2p-15L, -0xf.6aee68da4d1f9e1p-14L, 0xe.f94f2f509422907p-17L, 0xb.747180831f2d336p-16L, -0x8.0006f52141f4728p-17L, -0xe.9f83135abad7bfp-20L, 0xb.e325d0ae91a325cp-20L, -0x8.c10d69a2f3dfe1fp-23L, -0xc.5aaaa0381150b42p-24L, 0xf.7e75fad4cdbdbc5p-26L, -0xb.530de771408178bp-29L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.a2047f25eec85da6e57cd7f20965p-9Q, 0x1.1df6c86cbec60472edd73314093ap-5Q, 0x1.520d391a9410689a221d2a40ed0cp-3Q, 0x1.b8a3e5feb48792faed491d08e637p-2Q, 0x1.465391b4659339393dc6b44dd0b9p-1Q, 0x1.c2db72f84c20394e90d8314fee8dp-2Q, -0x1.6f9ed69c399c6d957cef0caf36cp-4Q, -0x1.4ee9af39c16ebfbef0c302e6791dp-2Q, -0x1.c96973b93bd864088cf77c5363e8p-6Q, 0x1.b084bf1dc763ab7d34b03cf7014cp-3Q, 0x1.bff160aba4bc2b81b5cb21d8ed3dp-6Q, -0x1.0f21999627c5eb1bdc396cd5510bp-3Q, -0x1.98ed2d2871d09c2ff301236b3aa5p-8Q, 0x1.36fc54ec8b1065ad541d9561e805p-4Q, -0x1.f159dcb973ff3c971dea81777e8cp-8Q, -0x1.2e3093b602a5114cced31fb3d21p-5Q, 0x1.516f07b10e2bfeeb35e5d488972dp-7Q, 0x1.ca8c3dcce54c309c6bfdafe5b818p-7Q, -0x1.ca18fbf2cc14161cd462d6382e8dp-8Q, -0x1.dda9bb9568c150b5b1b563e2a704p-9Q, 0x1.99ff0c3f2ed80a696d3f49d1ae83p-9Q, 0x1.abb6031610512ba452ab2c15607bp-12Q, -0x1.ed5dcd1b49a3f3c23377158c2ae9p-11Q, 0x1.df29e5ea1284520ed9350c7d7e2fp-14Q, 0x1.6e8e301063e5a66bc2dcbb672407p-13Q, -0x1.0000dea4283e8e4f97e320b5edbp-14Q, -0x1.d3f0626b575af7e0f5c7b70618f9p-17Q, 0x1.7c64ba15d23464b7681824c41ca1p-17Q, -0x1.1821ad345e7bfc3ef33cc03c406ap-20Q, -0x1.8b555407022a1683907685f46c79p-21Q, 0x1.efcebf5a99b7b789a7792201843ep-23Q, -0x1.6a61bcee28102f153c8290cebfbbp-26Q};
+        }
+        #endif
+    }
+    if constexpr (p == 17) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.25d69p-9f, 0x1.a9bea4p-6f, 0x1.0cba66p-3f, 0x1.7b3d38p-2f, 0x1.38d48cp-1f, 0x1.0960bp-1f, 0x1.bf874ap-6f, -0x1.50335p-2f, -0x1.0346bcp-3f, 0x1.941794p-3f, 0x1.9e404p-4f, -0x1.03b7f2p-3f, -0x1.d3b162p-5f, 0x1.4c35cap-4f, 0x1.6d90b8p-6f, -0x1.80637cp-5f, -0x1.acbb0ep-9f, 0x1.7477f4p-6f, -0x1.8ed9ccp-9f, -0x1.19e68ap-7f, 0x1.850572p-9f, 0x1.2d9fa2p-9f, -0x1.78a90ep-10f, -0x1.581268p-12f, 0x1.ccd01ap-12f, -0x1.adaa96p-16f, -0x1.582268p-14f, 0x1.85029cp-16f, 0x1.d5219cp-18f, -0x1.2e638p-18f, 0x1.43e648p-22f, 0x1.3d94aap-22f, -0x1.69ce4ap-24f, 0x1.f36b16p-28f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.25d68f81bd86cp-9, 0x1.a9bea4085cef4p-6, 0x1.0cba6633a3a6dp-3, 0x1.7b3d3861245dp-2, 0x1.38d48c64aa0dbp-1, 0x1.0960af0f4068ep-1, 0x1.bf874a24b1d56p-6, -0x1.50335073492d2p-2, -0x1.0346bb1b97634p-3, 0x1.9417930ab08a3p-3, 0x1.9e403f27b713fp-4, -0x1.03b7f2067576fp-3, -0x1.d3b162866891bp-5, 0x1.4c35ca8307eb6p-4, 0x1.6d90b88bab06p-6, -0x1.80637c4a935c8p-5, -0x1.acbb0e1b24a77p-9, 0x1.7477f35c89773p-6, -0x1.8ed9cce7691cbp-9, -0x1.19e6894a383d1p-7, 0x1.8505717311392p-9, 0x1.2d9fa2834b37bp-9, -0x1.78a90e5fc8eecp-10, -0x1.58126708ae49dp-12, 0x1.ccd01a3d65145p-12, -0x1.adaa9541cd341p-16, -0x1.5822674fd0b1ap-14, 0x1.85029b61ff0fcp-16, 0x1.d5219c45df32ep-18, -0x1.2e63809757f53p-18, 0x1.43e648c7ce72fp-22, 0x1.3d94aa0876b2dp-22, -0x1.69ce4aed2f58ep-24, 0x1.f36b16a008a29p-28};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0x9.2eb47c0dec36183p-12L, 0xd.4df52042e779eb7p-9L, 0x8.65d3319d1d36a45p-6L, 0xb.d9e9c30922e8138p-5L, 0x9.c6a46325506d79dp-4L, 0x8.4b05787a03472d6p-4L, 0xd.fc3a51258eaaed3p-9L, -0xa.819a839a4968eafp-5L, -0x8.1a35d8dcbb19dd2p-6L, 0xc.a0bc9855845188cp-6L, 0xc.f201f93db89f96ep-7L, -0x8.1dbf9033abb79d9p-6L, -0xe.9d8b1433448d469p-8L, 0xa.61ae54183f5b11cp-7L, 0xb.6c85c45d582fc12p-9L, -0xc.031be2549ae3edfp-8L, -0xd.65d870d9253b88dp-12L, 0xb.a3bf9ae44bb963dp-9L, -0xc.76ce673b48e5651p-12L, -0x8.cf344a51c1e8512p-10L, 0xc.282b8b9889c92c5p-12L, 0x9.6cfd141a59bd766p-12L, -0xb.c54872fe4775c65p-13L, -0xa.c0933845724e821p-15L, 0xe.6680d1eb28a2645p-15L, -0xd.6d54aa0e69a09cdp-19L, -0xa.c1133a7e858d207p-17L, 0xc.2814db0ff87dcc6p-19L, 0xe.a90ce22ef996e32p-21L, -0x9.731c04babfa9664p-21L, 0xa.1f32463e73979d5p-25L, 0x9.eca55043b596609p-25L, -0xb.4e7257697ac7376p-27L, 0xf.9b58b5004514458p-31L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.25d68f81bd86c306bc9043f43f4p-9Q, 0x1.a9bea4085cef3d6d79a074d9709ep-6Q, 0x1.0cba6633a3a6d489f4c961323b24p-3Q, 0x1.7b3d3861245d02709eb04b0b2b39p-2Q, 0x1.38d48c64aa0daf396243783e95bep-1Q, 0x1.0960af0f4068e5ac2ea6e7c9135p-1Q, 0x1.bf874a24b1d55da571e39f2bf7e7p-6Q, -0x1.50335073492d1d5e6945d8cdee28p-2Q, -0x1.0346bb1b97633ba3dcc115a9814cp-3Q, 0x1.9417930ab08a311830b19e500034p-3Q, 0x1.9e403f27b713f2db7263ac22d15fp-4Q, -0x1.03b7f2067576f3b2927e9c5889d3p-3Q, -0x1.d3b162866891a8d294e6e9eb979p-5Q, 0x1.4c35ca8307eb62387847e8508ae5p-4Q, 0x1.6d90b88bab05f824bb4e728b7a1p-6Q, -0x1.80637c4a935c7dbdd09fd2c6d8fdp-5Q, -0x1.acbb0e1b24a7711aad0c2cc58d1fp-9Q, 0x1.7477f35c89772c79eec161a3cdd2p-6Q, -0x1.8ed9cce7691caca1362d6d7abefcp-9Q, -0x1.19e6894a383d0a23e4d18574889p-7Q, 0x1.85057173113925897d4027a40b6ep-9Q, 0x1.2d9fa2834b37aecc772ff5c2d7b1p-9Q, -0x1.78a90e5fc8eeb8c9dbcf2179c3bbp-10Q, -0x1.58126708ae49d0421a9c690b913dp-12Q, 0x1.ccd01a3d65144c8ab80302b0f5dbp-12Q, -0x1.adaa9541cd34139a00a6638e9bf6p-16Q, -0x1.5822674fd0b1a40e647125cde434p-14Q, 0x1.85029b61ff0fb98b3294c269c9e6p-16Q, 0x1.d5219c45df32dc63e76e89984d9dp-18Q, -0x1.2e63809757f52cc8ed09e415ace1p-18Q, 0x1.43e648c7ce72f3a94ea0d55898bap-22Q, 0x1.3d94aa0876b2cc113a8ea22e3eecp-22Q, -0x1.69ce4aed2f58e6ecb8a211f55ad1p-24Q, 0x1.f36b16a008a288af85eb1e1cec02p-28Q};
+        }
+        #endif
+    }
+    if constexpr (p == 18) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.9d3864p-10f, 0x1.3c05f8p-6f, 0x1.a84c62p-4f, 0x1.423b32p-2f, 0x1.24c67cp-1f, 0x1.24c33p-1f, 0x1.2d835p-3f, -0x1.2cb3a6p-2f, -0x1.bb5a5cp-3f, 0x1.323edep-3f, 0x1.562ebap-3f, -0x1.7a31p-4f, -0x1.b541d8p-4f, 0x1.09c72ep-4f, 0x1.d35d24p-5f, -0x1.6cc216p-5f, -0x1.84d84cp-6f, 0x1.b4f90cp-6f, 0x1.9a65bep-8f, -0x1.ababc2p-7f, 0x1.f19208p-14f, 0x1.43f78cp-8f, -0x1.2544ep-10f, -0x1.5f6de6p-10f, 0x1.497f3cp-11f, 0x1.bfe9bap-13f, -0x1.a098a2p-13f, -0x1.49d5fp-23f, 0x1.39d678p-15f, -0x1.1de76cp-17f, -0x1.bf4c72p-19f, 0x1.dac908p-20f, -0x1.4a5a66p-24f, -0x1.f9216ep-24f, 0x1.079c6ap-25f, -0x1.58b01ap-29f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.9d386358a1875p-10, 0x1.3c05f73c5b367p-6, 0x1.a84c610f33b44p-4, 0x1.423b3247213b9p-2, 0x1.24c67bbcaad51p-1, 0x1.24c32fbf17436p-1, 0x1.2d834f99026eap-3, -0x1.2cb3a5153503ap-2, -0x1.bb5a5b1e13b57p-3, 0x1.323ede758da42p-3, 0x1.562eba30ba3dbp-3, -0x1.7a30ff6ce5272p-4, -0x1.b541d802db16ep-4, 0x1.09c72d78f0163p-4, 0x1.d35d236774d12p-5, -0x1.6cc216694aaa1p-5, -0x1.84d84c9eacf2cp-6, 0x1.b4f90c6dc9842p-6, 0x1.9a65be90d86a5p-8, -0x1.ababc1ea3f978p-7, 0x1.f19207685977fp-14, 0x1.43f78b1e4d853p-8, -0x1.2544e0deeca72p-10, -0x1.5f6de508b2306p-10, 0x1.497f3c70a07ccp-11, 0x1.bfe9ba59913cep-13, -0x1.a098a12371c0dp-13, -0x1.49d5efd42da9p-23, 0x1.39d678c2c06afp-15, -0x1.1de76b2193bedp-17, -0x1.bf4c72e2a2d94p-19, 0x1.dac907ddfd9dbp-20, -0x1.4a5a655290e68p-24, -0x1.f9216d4e4d83bp-24, 0x1.079c6a0fc4518p-25, -0x1.58b0195a8266dp-29};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0xc.e9c31ac50c3a483p-13L, 0x9.e02fb9e2d9b3a9bp-9L, 0xd.426308799da225cp-7L, 0xa.11d9923909dc42bp-5L, 0x9.2633dde556a88a3p-4L, 0x9.26197df8ba1b1b2p-4L, 0x9.6c1a7cc81374c03p-6L, -0x9.659d28a9a81cd3ap-5L, -0xd.dad2d8f09dab48bp-6L, 0x9.91f6f3ac6d21107p-6L, 0xa.b175d185d1ed60ap-6L, -0xb.d187fb672938eb2p-7L, -0xd.aa0ec016d8b6c08p-7L, 0x8.4e396bc780b1464p-7L, 0xe.9ae91b3ba68905ep-8L, -0xb.6610b34a5550677p-8L, -0xc.26c264f56795d72p-9L, 0xd.a7c8636e4c20f3dp-9L, 0xc.d32df486c3529e3p-11L, -0xd.5d5e0f51fcbc222p-10L, 0xf.8c903b42cbbfa1ep-17L, 0xa.1fbc58f26c29bbap-11L, -0x9.2a2706f76538d5fp-13L, -0xa.fb6f284591832p-13L, 0xa.4bf9e38503e5e52p-14L, 0xd.ff4dd2cc89e6cb3p-16L, -0xd.04c5091b8e0651fp-16L, -0xa.4eaf7ea16d480ecp-26L, 0x9.ceb3c6160357432p-18L, -0x8.ef3b590c9df6482p-20L, -0xd.fa63971516c9e77p-22L, 0xe.d6483eefeced63bp-23L, -0xa.52d32a948733d34p-27L, -0xf.c90b6a726c1d6d6p-27L, 0x8.3ce3507e228be57p-28L, -0xa.c580cad41336728p-32L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.9d386358a187490511616014e787p-10Q, 0x1.3c05f73c5b367536d2be9893ed8cp-6Q, 0x1.a84c610f33b444b779a9b1758c69p-4Q, 0x1.423b3247213b88555f9f2ada7d8ap-2Q, 0x1.24c67bbcaad511453636985416f3p-1Q, 0x1.24c32fbf17436364ee6d86ce0b36p-1Q, 0x1.2d834f99026e9806c6f6c1aa6cb3p-3Q, -0x1.2cb3a51535039a741562ba69c7a8p-2Q, -0x1.bb5a5b1e13b56915364cb7d6d1bfp-3Q, 0x1.323ede758da4220dcba304aad9d9p-3Q, 0x1.562eba30ba3dac1311ece1a1884ap-3Q, -0x1.7a30ff6ce5271d64766823319bd4p-4Q, -0x1.b541d802db16d80f141c678b2993p-4Q, 0x1.09c72d78f01628c7ccd127058828p-4Q, 0x1.d35d236774d120bc0fddfe320959p-5Q, -0x1.6cc216694aaa0ced2f850c2b3eb7p-5Q, -0x1.84d84c9eacf2bae4fd091b9bdb4fp-6Q, 0x1.b4f90c6dc9841e7a702107e1aca3p-6Q, 0x1.9a65be90d86a53c665da90605941p-8Q, -0x1.ababc1ea3f978443c6511c976c7fp-7Q, 0x1.f19207685977f43b68af0530733ap-14Q, 0x1.43f78b1e4d853774466d94263915p-8Q, -0x1.2544e0deeca71abd544eac93fa45p-10Q, -0x1.5f6de508b23063ffd5522faa2f1ap-10Q, 0x1.497f3c70a07cbca34a7835790cbfp-11Q, 0x1.bfe9ba59913cd96563f593913af3p-13Q, -0x1.a098a12371c0ca3dcc2d68b00891p-13Q, -0x1.49d5efd42da901d7159610c4d152p-23Q, 0x1.39d678c2c06ae863ef3b97fa7d6p-15Q, -0x1.1de76b2193bec903a9d077f1666ep-17Q, -0x1.bf4c72e2a2d93cedea468c1c5543p-19Q, 0x1.dac907ddfd9dac76e76088418dc5p-20Q, -0x1.4a5a655290e67a67e8d8672b7916p-24Q, -0x1.f9216d4e4d83adac1cb13466b74bp-24Q, 0x1.079c6a0fc4517cae3d72b9596e6p-25Q, -0x1.58b0195a8266ce508d99fc62d4eep-29Q};
+        }
+        #endif
+    }
+    if constexpr (p == 19) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.22a192p-10f, 0x1.d3f68ap-7f, 0x1.4cea48p-4f, 0x1.0ebbd8p-2f, 0x1.0c82ecp-1f, 0x1.34129ep-1f, 0x1.0b280cp-2f, -0x1.d32194p-3f, -0x1.24b2e2p-2f, 0x1.31c694p-4f, 0x1.b2e46cp-3f, -0x1.12957ap-5f, -0x1.246cd4p-3f, 0x1.c3f126p-6f, 0x1.63f856p-4f, -0x1.b2323ep-6f, -0x1.7629ccp-5f, 0x1.6248a8p-6f, 0x1.3d72f2p-6f, -0x1.ca5f1cp-7f, -0x1.807eap-8f, 0x1.cd6c24p-8f, 0x1.93274ep-11f, -0x1.604346p-9f, 0x1.66699p-12f, 0x1.81c5bep-11f, -0x1.1156b8p-12f, -0x1.054e8ap-13f, 0x1.6d608ep-14f, 0x1.56a79p-18f, -0x1.172d04p-16f, 0x1.941ff2p-19f, 0x1.9b3988p-20f, -0x1.7070fep-21f, 0x1.f1373cp-27f, 0x1.8e4f58p-25f, -0x1.7f97c4p-27f, 0x1.dc770ep-31f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.22a1917fed85ap-10, 0x1.d3f6896603bf4p-7, 0x1.4cea4765b114ap-4, 0x1.0ebbd74f124f2p-2, 0x1.0c82ecc416391p-1, 0x1.34129e60b6e3p-1, 0x1.0b280be54f8b7p-2, -0x1.d32194b53c804p-3, -0x1.24b2e1dd4c73ep-2, 0x1.31c6940f7edfap-4, 0x1.b2e46c1684042p-3, -0x1.12957a28f5bb3p-5, -0x1.246cd3943959bp-3, 0x1.c3f126f461d98p-6, 0x1.63f8568e9e6ecp-4, -0x1.b2323dbfdcbe7p-6, -0x1.7629cb842f99bp-5, 0x1.6248a775ca66p-6, 0x1.3d72f2476d004p-6, -0x1.ca5f1bf2f3244p-7, -0x1.807e9f533b217p-8, 0x1.cd6c23ae5d8f9p-8, 0x1.93274e99dc9b5p-11, -0x1.6043462e3e51ap-9, 0x1.66698fcf3c249p-12, 0x1.81c5be1857466p-11, -0x1.1156b7a432a66p-12, -0x1.054e8a6af00d7p-13, 0x1.6d608dedb3cf6p-14, 0x1.56a78fb9bd527p-18, -0x1.172d0353b3f12p-16, 0x1.941ff236730f1p-19, 0x1.9b39878b95663p-20, -0x1.7070fedc9cdedp-21, 0x1.f1373b9dbeafap-27, 0x1.8e4f570c878dep-25, -0x1.7f97c3aa5d9ep-27, 0x1.dc770dc2ed00bp-31};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0x9.150c8bff6c2cf0bp-13L, 0xe.9fb44b301dfa184p-10L, 0xa.67523b2d88a4cd2p-7L, 0x8.75deba789279273p-5L, 0x8.64176620b1c8a9ap-4L, 0x9.a094f305b717f7bp-4L, 0x8.59405f2a7c5b569p-5L, -0xe.990ca5a9e402365p-6L, -0x9.25970eea639ef9ap-5L, 0x9.8e34a07bf6fd17cp-7L, 0xd.972360b420211e3p-6L, -0x8.94abd147add99bfp-8L, -0x9.23669ca1cacd462p-6L, 0xe.1f8937a30ecc2f7p-9L, 0xb.1fc2b474f37606ap-7L, -0xd.9191edfee5f3727p-9L, -0xb.b14e5c217ccd592p-8L, 0xb.12453bae532fcd5p-9L, 0x9.eb97923b6802088p-9L, -0xe.52f8df979921d82p-10L, -0xc.03f4fa99d90b962p-11L, 0xe.6b611d72ec7ca7cp-11L, 0xc.993a74cee4da67fp-14L, -0xb.021a3171f28cdccp-12L, 0xb.334c7e79e124bccp-15L, 0xc.0e2df0c2ba32ef3p-14L, -0x8.8ab5bd21953315ep-15L, -0x8.2a745357806b795p-16L, 0xb.6b046f6d9e7b04p-17L, 0xa.b53c7dcdea9365p-21L, -0x8.b9681a9d9f88fe1p-19L, 0xc.a0ff91b39878443p-22L, 0xc.d9cc3c5cab31a21p-23L, -0xb.8387f6e4e6f68p-24L, 0xf.89b9dcedf57d09dp-30L, 0xc.727ab8643c6ec27p-28L, -0xb.fcbe1d52ecefc57p-30L, 0xe.e3b86e176805b46p-34L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.22a1917fed859e160446bb7b167ap-10Q, 0x1.d3f6896603bf4308e8ccc5a30641p-7Q, 0x1.4cea4765b11499a3de1dc5fdc4b7p-4Q, 0x1.0ebbd74f124f24e597d3a5bc26dbp-2Q, 0x1.0c82ecc4163915332b81143283e8p-1Q, 0x1.34129e60b6e2fef58b66c45f7099p-1Q, 0x1.0b280be54f8b6ad2d41e0f33532ep-2Q, -0x1.d32194b53c8046c9a7b9b8714cebp-3Q, -0x1.24b2e1dd4c73df34e82deb7bb6c6p-2Q, 0x1.31c6940f7edfa2f8c6ddc9cd2aefp-4Q, 0x1.b2e46c16840423c52b33ff7476eep-3Q, -0x1.12957a28f5bb337e3e66ea6f23e6p-5Q, -0x1.246cd3943959a8c450bf5ca92b86p-3Q, 0x1.c3f126f461d985ee9de87f3424e5p-6Q, 0x1.63f8568e9e6ec0d34220dce2e186p-4Q, -0x1.b2323dbfdcbe6e4ed8b2320fb129p-6Q, -0x1.7629cb842f99ab236f8e908d21c2p-5Q, 0x1.6248a775ca65f9a99ecab76ed61p-6Q, 0x1.3d72f2476d00410fe80cb42bd72bp-6Q, -0x1.ca5f1bf2f3243b0308970f1f944p-7Q, -0x1.807e9f533b2172c38f0c60523009p-8Q, 0x1.cd6c23ae5d8f94f8e6c997306168p-8Q, 0x1.93274e99dc9b4cfea213c9163decp-11Q, -0x1.6043462e3e519b97ce417a7ac3b3p-9Q, 0x1.66698fcf3c2497984ab865b5b6acp-12Q, 0x1.81c5be1857465de5530984af43cbp-11Q, -0x1.1156b7a432a662bbb70ff712e064p-12Q, -0x1.054e8a6af00d6f29e88cd98738bep-13Q, 0x1.6d608dedb3cf6080fb9e6ef72893p-14Q, 0x1.56a78fb9bd526ca09fc616b1b8ap-18Q, -0x1.172d0353b3f11fc1e8818be3f7a7p-16Q, 0x1.941ff236730f0886ee4074951d94p-19Q, 0x1.9b39878b9566344204396825f773p-20Q, -0x1.7070fedc9cdecfffd4c6dc5d1fe5p-21Q, 0x1.f1373b9dbeafa1390279c531a649p-27Q, 0x1.8e4f570c878dd84d17b935d5f69ap-25Q, -0x1.7f97c3aa5d9df8ae90e909fae15p-27Q, 0x1.dc770dc2ed00b68b9c525506b211p-31Q};
+        }
+        #endif
+    }
+    if constexpr (p == 20) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.98eb9ap-11f, 0x1.59aebcp-7f, 0x1.03c8a8p-4f, 0x1.c27102p-3f, 0x1.e40a78p-2f, 0x1.389292p-1f, 0x1.722da8p-2f, -0x1.1d1b3ap-3f, -0x1.4ea132p-2f, -0x1.120e7ep-6f, 0x1.d38a42p-3f, 0x1.467406p-5f, -0x1.3e6128p-3f, -0x1.94f5e4p-6f, 0x1.a2fca4p-4f, 0x1.711d6cp-8f, -0x1.f9a24ep-5f, 0x1.8100cep-8f, 0x1.088e0ep-5f, -0x1.200234p-7f, -0x1.c48b18p-7f, 0x1.b88232p-8f, 0x1.21b464p-8f, -0x1.d56f02p-9f, -0x1.b3fa62p-11f, 0x1.6d0d18p-10f, -0x1.c0c538p-15f, -0x1.93cfc4p-12f, 0x1.a9dc1cp-14f, 0x1.1c224ap-14f, -0x1.37443cp-15f, -0x1.25ad94p-18f, 0x1.e5f3b2p-18f, -0x1.0fa7b2p-20f, -0x1.6f998cp-21f, 0x1.1ad0c2p-22f, 0x1.baf44p-33f, -0x1.37c9a6p-26f, 0x1.16bc24p-28f, -0x1.49b9bep-32f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.98eb9a1ad223fp-11, 0x1.59aebc7410b77p-7, 0x1.03c8a76dc45bbp-4, 0x1.c27102c5bb1f8p-3, 0x1.e40a78036ac7fp-2, 0x1.389291df573b5p-1, 0x1.722da89a0e974p-2, -0x1.1d1b3a29bcd1cp-3, -0x1.4ea132f283bf2p-2, -0x1.120e7e4faaa26p-6, 0x1.d38a4229ed991p-3, 0x1.46740628c1e1ap-5, -0x1.3e612851515f6p-3, -0x1.94f5e34522642p-6, 0x1.a2fca44817f2fp-4, 0x1.711d6c0e1d46ap-8, -0x1.f9a24d69ac62ep-5, 0x1.8100ce41923f9p-8, 0x1.088e0e0a9eca2p-5, -0x1.2002338d10ca4p-7, -0x1.c48b170cc05f1p-7, 0x1.b88231706930bp-8, 0x1.21b464fba22e8p-8, -0x1.d56f016e81eefp-9, -0x1.b3fa62b1e588ap-11, 0x1.6d0d181744b82p-10, -0x1.c0c537c57bf91p-15, -0x1.93cfc4d1b467bp-12, 0x1.a9dc1c3780427p-14, 0x1.1c224959ff66dp-14, -0x1.37443b45c500dp-15, -0x1.25ad943ec34c5p-18, 0x1.e5f3b2c4841b3p-18, -0x1.0fa7b2e66c174p-20, -0x1.6f998ba053586p-21, 0x1.1ad0c20194a77p-22, 0x1.baf43fba18386p-33, -0x1.37c9a671235e5p-26, 0x1.16bc244bc36b8p-28, -0x1.49b9be3c4a795p-32};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0xc.c75cd0d6911fa1bp-14L, 0xa.cd75e3a085bb58ep-10L, 0x8.1e453b6e22dd40bp-7L, 0xe.1388162dd8fc33cp-6L, 0xf.2053c01b563f9cp-5L, 0x9.c4948efab9da4ebp-4L, 0xb.916d44d074ba33ap-5L, -0x8.e8d9d14de68dd92p-6L, -0xa.750997941df90a2p-5L, -0x8.9073f27d5512ec4p-9L, 0xe.9c52114f6cc8785p-6L, 0xa.33a031460f0d07bp-8L, -0x9.f309428a8afb31p-6L, -0xc.a7af1a291320cf8p-9L, 0xd.17e52240bf97653p-7L, 0xb.88eb6070ea34f45p-11L, -0xf.cd126b4d6317224p-8L, 0xc.0806720c91fc6d9p-11L, 0x8.44707054f65127ep-8L, -0x9.00119c6886523a3p-10L, -0xe.2458b86602f87fcp-10L, 0xd.c4118b834985633p-11L, 0x9.0da327dd11741b6p-11L, -0xe.ab780b740f77b4ep-12L, -0xd.9fd3158f2c44f42p-14L, 0xb.6868c0ba25c0c5ep-13L, -0xe.0629be2bdfc8a9ap-18L, -0xc.9e7e268da33d44p-15L, 0xd.4ee0e1bc0213577p-17L, 0x8.e1124acffb364cp-17L, -0x9.ba21da2e280684dp-18L, -0x9.2d6ca1f61a624d6p-21L, 0xf.2f9d962420d947dp-21L, -0x8.7d3d973360b9f2p-23L, -0xb.7ccc5d029ac2c2ep-24L, 0x8.d686100ca53b51dp-25L, 0xd.d7a1fdd0c1c3167p-36L, -0x9.be4d33891af2665p-29L, 0x8.b5e1225e1b5bf96p-31L, -0xa.4dcdf1e253caa43p-35L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.98eb9a1ad223f435df1887363eb7p-11Q, 0x1.59aebc7410b76b1badcc12950a6dp-7Q, 0x1.03c8a76dc45ba8152978f10f7c69p-4Q, 0x1.c27102c5bb1f8677bf80bd502bd1p-3Q, 0x1.e40a78036ac7f37fedcb5a80e979p-2Q, 0x1.389291df573b49d69709e6a39a77p-1Q, 0x1.722da89a0e9746749e19dd59185cp-2Q, -0x1.1d1b3a29bcd1bb23d3a59b3ec213p-3Q, -0x1.4ea132f283bf214303a247980416p-2Q, -0x1.120e7e4faaa25d883a426ff76e5ep-6Q, 0x1.d38a4229ed990f09767be4223746p-3Q, 0x1.46740628c1e1a0f69af0510e97b1p-5Q, -0x1.3e612851515f661f1b982f038f42p-3Q, -0x1.94f5e345226419f0d083e13269c2p-6Q, 0x1.a2fca44817f2eca68758db1b8b3cp-4Q, 0x1.711d6c0e1d469e893974f1ea6999p-8Q, -0x1.f9a24d69ac62e448cc934c83e493p-5Q, 0x1.8100ce41923f8db158db362c64bfp-8Q, 0x1.088e0e0a9eca24fb78af66e8d177p-5Q, -0x1.2002338d10ca4746416546df60b9p-7Q, -0x1.c48b170cc05f0ff881bd3e1b39f6p-7Q, 0x1.b88231706930ac6660faf6c0f2dep-8Q, 0x1.21b464fba22e836bf597b5aa439ep-8Q, -0x1.d56f016e81eef69c49d53f5d0ebbp-9Q, -0x1.b3fa62b1e5889e83d8f6afb75bd8p-11Q, 0x1.6d0d181744b818bb6e246e9454cp-10Q, -0x1.c0c537c57bf91533c45c4dad234ap-15Q, -0x1.93cfc4d1b467a87fbd054b646597p-12Q, 0x1.a9dc1c3780426aeee785e4f91b69p-14Q, 0x1.1c224959ff66c97f21d37d9c05fbp-14Q, -0x1.37443b45c500d09a28a777a35885p-15Q, -0x1.25ad943ec34c49ac55547e1ee8bep-18Q, 0x1.e5f3b2c4841b28f9ade386d031fap-18Q, -0x1.0fa7b2e66c173e3f4204ea792843p-20Q, -0x1.6f998ba05358585b78628b55c242p-21Q, 0x1.1ad0c20194a76a3ad5100084b452p-22Q, 0x1.baf43fba183862ce0fdd2ce6713ep-33Q, -0x1.37c9a671235e4ccaa17336a7b289p-26Q, 0x1.16bc244bc36b7f2c806c15a56631p-28Q, -0x1.49b9be3c4a79548641570a58d68ep-32Q};
+        }
+        #endif
+    }
+    if constexpr (p == 21) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.1fbdb6p-11f, 0x1.fda65ap-8f, 0x1.93701p-5f, 0x1.736cacp-3f, 0x1.adc2aep-2f, 0x1.33f89cp-1f, 0x1.c742b8p-2f, -0x1.24a464p-5f, -0x1.57b854p-2f, -0x1.cc60ep-4f, 0x1.b148bep-3f, 0x1.d7feep-4f, -0x1.1e9916p-3f, -0x1.4ef44ap-4f, 0x1.8bacdap-4f, 0x1.7690eep-5f, -0x1.0a25dap-4f, -0x1.319ff4p-6f, 0x1.457136p-5f, 0x1.b81b9cp-9f, -0x1.564bap-6f, 0x1.3b071ap-9f, 0x1.268bbap-7f, -0x1.7af914p-9f, -0x1.83c29p-9f, 0x1.c1ff8cp-10f, 0x1.4f3d4cp-11f, -0x1.6a1c4ep-11f, -0x1.0c224ep-15f, 0x1.9624eap-13f, -0x1.30f834p-15f, -0x1.2592c2p-15f, 0x1.019c78p-16f, 0x1.768306p-19f, -0x1.9ebc2ep-19f, 0x1.53f4f8p-22f, 0x1.41473ap-22f, -0x1.adab3ep-24f, -0x1.35ca1ap-29f, 0x1.e5063ep-28f, -0x1.949b92p-30f, 0x1.c8df1cp-34f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.1fbdb5d9588b2p-11, 0x1.fda65a6714bdap-8, 0x1.937010050905p-5, 0x1.736cace0a6657p-3, 0x1.adc2ad3828f8ep-2, 0x1.33f89b5c2e57bp-1, 0x1.c742b82c92555p-2, -0x1.24a4646f28f23p-5, -0x1.57b853bbe6a56p-2, -0x1.cc60df28d7badp-4, 0x1.b148be3b1073fp-3, 0x1.d7fedf0356bp-4, -0x1.1e9915e3ca004p-3, -0x1.4ef44a8b3ce94p-4, 0x1.8bacd9d38a28ep-4, 0x1.7690ee8b59819p-5, -0x1.0a25da27e87d7p-4, -0x1.319ff4cde80a9p-6, 0x1.4571365df5489p-5, 0x1.b81b9bc4d4f3cp-9, -0x1.564b9fd2c3bbfp-6, 0x1.3b071a00e4e5cp-9, 0x1.268bb96001dc4p-7, -0x1.7af914f01f8fcp-9, -0x1.83c28f7e3c0e5p-9, 0x1.c1ff8c65fb698p-10, 0x1.4f3d4c629fe3fp-11, -0x1.6a1c4ee19b423p-11, -0x1.0c224d58d6e81p-15, 0x1.9624eae0b53fp-13, -0x1.30f833f09ef02p-15, -0x1.2592c13818da8p-15, 0x1.019c78bb61865p-16, 0x1.768306fdacad5p-19, -0x1.9ebc2e6b68816p-19, 0x1.53f4f805c9123p-22, 0x1.414739b599eb7p-22, -0x1.adab3d69a3265p-24, -0x1.35ca1a0003737p-29, 0x1.e5063d39ebf9ap-28, -0x1.949b918111d77p-30, 0x1.c8df1c0c683efp-34};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0x8.fdedaecac458cd2p-14L, 0xf.ed32d338a5ecf5cp-11L, 0xc.9b8080284827e72p-8L, 0xb.9b656705332bae6p-6L, 0xd.6e1569c147c6dadp-5L, 0x9.9fc4dae172bdbe9p-4L, 0xe.3a15c16492aa9dbp-5L, -0x9.252323794791b92p-8L, -0xa.bdc29ddf352b036p-5L, -0xe.6306f946bdd67aep-7L, 0xd.8a45f1d8839f921p-6L, 0xe.bff6f81ab580014p-7L, -0x8.f4c8af1e5002333p-6L, -0xa.77a25459e74a242p-7L, 0xc.5d66ce9c5146f15p-7L, 0xb.b487745acc0c8adp-8L, -0x8.512ed13f43ebad1p-7L, -0x9.8cffa66f405497bp-9L, 0xa.2b89b2efaa444bdp-8L, 0xd.c0dcde26a79e22p-12L, -0xa.b25cfe961ddf733p-9L, 0x9.d838d007272dcc4p-12L, 0x9.345dcb000ee2014p-10L, -0xb.d7c8a780fc7dcf5p-12L, -0xc.1e147bf1e072bc1p-12L, 0xe.0ffc632fdb4c29ep-13L, 0xa.79ea6314ff1f508p-14L, -0xb.50e2770cda119f3p-14L, -0x8.61126ac6b7407d4p-18L, 0xc.b1275705a9f8219p-16L, -0x9.87c19f84f78120fp-18L, -0x9.2c9609c0c6d43f4p-18L, 0x8.0ce3c5db0c32b2dp-19L, 0xb.b41837ed656a6e4p-22L, -0xc.f5e1735b440ad22p-22L, 0xa.9fa7c02e489184ap-25L, 0xa.0a39cdaccf5ba4ap-25L, -0xd.6d59eb4d1932a9ep-27L, -0x9.ae50d0001b9b402p-32L, 0xf.2831e9cf5fcccbdp-31L, -0xc.a4dc8c088ebb653p-33L, 0xe.46f8e06341f76fbp-37L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.1fbdb5d9588b19a3bff14d1b38fep-11Q, 0x1.fda65a6714bd9eb85e8d7e88dc47p-8Q, 0x1.937010050904fce3eac118cf708bp-5Q, 0x1.736cace0a66575cc5580323567efp-3Q, 0x1.adc2ad3828f8db5a1d5b82619893p-2Q, 0x1.33f89b5c2e57b7d298074c990addp-1Q, 0x1.c742b82c925553b5685081f7bfa5p-2Q, -0x1.24a4646f28f23724c7651fdfae24p-5Q, -0x1.57b853bbe6a5606b16b5f4878728p-2Q, -0x1.cc60df28d7bacf5cd487dfbe8b15p-4Q, 0x1.b148be3b1073f24190a78355f27p-3Q, 0x1.d7fedf0356b00027d18f8e92c824p-4Q, -0x1.1e9915e3ca004666a067ba487474p-3Q, -0x1.4ef44a8b3ce944830f2730d25eb9p-4Q, 0x1.8bacd9d38a28de29668579705c28p-4Q, 0x1.7690ee8b5981915a6dd616884c3fp-5Q, -0x1.0a25da27e87d75a179ff300fb83fp-4Q, -0x1.319ff4cde80a92f66d084237880cp-6Q, 0x1.4571365df548897971310c0822e6p-5Q, 0x1.b81b9bc4d4f3c43f2ed25e559ae8p-9Q, -0x1.564b9fd2c3bbee66fedad254cc1dp-6Q, 0x1.3b071a00e4e5b987ae06dc453687p-9Q, 0x1.268bb96001dc402712698f3f0494p-7Q, -0x1.7af914f01f8fb9ea842adaa7f3cdp-9Q, -0x1.83c28f7e3c0e5781b7d022113abfp-9Q, 0x1.c1ff8c65fb69853c310221a8efcfp-10Q, 0x1.4f3d4c629fe3ea0f5f4b5c45e52p-11Q, -0x1.6a1c4ee19b4233e5be9da5626ae4p-11Q, -0x1.0c224d58d6e80fa7cb5e318a3bafp-15Q, 0x1.9624eae0b53f0431ec2fc4ac4a39p-13Q, -0x1.30f833f09ef0241df6514d4f75d1p-15Q, -0x1.2592c13818da87e8e3f7d01fb451p-15Q, 0x1.019c78bb618656595fd443f75a4ep-16Q, 0x1.768306fdacad4dc8fab15811b58ap-19Q, -0x1.9ebc2e6b68815a4433974307ca8ep-19Q, 0x1.53f4f805c91230935990691c9b37p-22Q, 0x1.414739b599eb74930d1d52f4adeap-22Q, -0x1.adab3d69a326553c517a3161ce4cp-24Q, -0x1.35ca1a000373680368e6e76ba1cap-29Q, 0x1.e5063d39ebf99979a7db1201c73dp-28Q, -0x1.949b918111d76ca513fa5f9592d7p-30Q, 0x1.c8df1c0c683eedf6229624f6ad7fp-34Q};
+        }
+        #endif
+    }
+    if constexpr (p == 22) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.9506cp-12f, 0x1.76fccap-8f, 0x1.37de72p-5f, 0x1.2fdb52p-3f, 0x1.788ddep-2f, 0x1.282856p-1f, 0x1.040b9cp-1f, 0x1.2df9bep-4f, -0x1.403b66p-2f, -0x1.9ac39cp-3f, 0x1.501016p-3f, 0x1.7095c8p-3f, -0x1.8dc40ep-4f, -0x1.0ddc74p-3f, 0x1.16d73p-4f, 0x1.5a58d6p-4f, -0x1.a4c6a6p-5f, -0x1.7d2e3p-5f, 0x1.2edd7cp-5f, 0x1.514ae8p-6f, -0x1.80b244p-6f, -0x1.9739fap-8f, 0x1.9bb88ep-7f, 0x1.3ab784p-12f, -0x1.658b52p-8f, 0x1.11bf26p-10f, 0x1.def09ap-10f, -0x1.941064p-11f, -0x1.bc5f9p-12f, 0x1.58926ap-12f, 0x1.6c8f7ep-15f, -0x1.8a7bd2p-14f, 0x1.7da8ecp-17f, 0x1.237bb8p-16f, -0x1.9dd79ap-18f, -0x1.a4264ap-20f, 0x1.5bac3cp-20f, -0x1.7917ccp-24f, -0x1.139828p-23f, 0x1.43164cp-25f, 0x1.cdd78ep-30f, -0x1.772814p-29f, 0x1.2558aap-31f, -0x1.3cd862p-35f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.9506bf26823bdp-12, 0x1.76fcca8398a61p-8, 0x1.37de71ec845e4p-5, 0x1.2fdb523f49ab5p-3, 0x1.788dde34ceb66p-2, 0x1.282855bd3e661p-1, 0x1.040b9c9ba65ccp-1, 0x1.2df9be17f6307p-4, -0x1.403b658e1e271p-2, -0x1.9ac39bc6a693fp-3, 0x1.501016e351cb2p-3, 0x1.7095c864b0cccp-3, -0x1.8dc40d7416ec6p-4, -0x1.0ddc7410272ddp-3, 0x1.16d7307f2f199p-4, 0x1.5a58d5e218e8bp-4, -0x1.a4c6a60c82a99p-5, -0x1.7d2e2f61c66bdp-5, 0x1.2edd7c2485c6cp-5, 0x1.514ae8ff8882dp-6, -0x1.80b243789dd91p-6, -0x1.9739fa1f59fdbp-8, 0x1.9bb88df2b07f2p-7, 0x1.3ab784f96ef95p-12, -0x1.658b52a857f98p-8, 0x1.11bf26e4a8f4ap-10, 0x1.def099502d06ep-10, -0x1.941064b6e88a6p-11, -0x1.bc5f905d400afp-12, 0x1.58926afecb291p-12, 0x1.6c8f7d64132f3p-15, -0x1.8a7bd1deebb29p-14, 0x1.7da8eb6c7dd39p-17, 0x1.237bb7cb019efp-16, -0x1.9dd79a5aef3dp-18, -0x1.a4264a7b9f195p-20, 0x1.5bac3bb6b7df3p-20, -0x1.7917ccd42a174p-24, -0x1.139827c14728ep-23, 0x1.43164b7e12198p-25, 0x1.cdd78d40a514dp-30, -0x1.772813927397bp-29, 0x1.2558a9abd0467p-31, -0x1.3cd8627d9b085p-35};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0xc.a835f93411de553p-15L, 0xb.b7e6541cc530467p-11L, 0x9.bef38f6422f21e9p-8L, 0x9.7eda91fa4d5aa1ap-6L, 0xb.c46ef1a675b2f1p-5L, 0x9.4142ade9f3308e8p-4L, 0x8.205ce4dd32e5de6p-4L, 0x9.6fcdf0bfb18389dp-7L, -0xa.01db2c70f1385a8p-5L, -0xc.d61cde35349f534p-6L, 0xa.8080b71a8e58ef5p-6L, 0xb.84ae43258666006p-6L, -0xc.6e206ba0b762e61p-7L, -0x8.6ee3a081396e7a5p-6L, 0x8.b6b983f978cc515p-7L, 0xa.d2c6af10c745924p-7L, -0xd.26353064154caf2p-8L, -0xb.e9717b0e335e71fp-8L, 0x9.76ebe1242e35de2p-8L, 0xa.8a5747fc44168f9p-9L, -0xc.05921bc4eec8a0fp-9L, -0xc.b9cfd0facfed6d3p-11L, 0xc.ddc46f9583f92e4p-10L, 0x9.d5bc27cb77ca414p-15L, -0xb.2c5a9542bfcbcecp-11L, 0x8.8df9372547a50bfp-13L, 0xe.f784ca816836eb8p-13L, -0xc.a08325b74452d5dp-14L, -0xd.e2fc82ea0057a9fp-15L, 0xa.c49357f65948be4p-15L, 0xb.647beb209979943p-18L, -0xc.53de8ef75d94bb9p-17L, 0xb.ed475b63ee9c598p-20L, 0x9.1bddbe580cf7997p-19L, -0xc.eebcd2d779e82c2p-21L, -0xd.213253dcf8ca54ep-23L, 0xa.dd61ddb5bef98f1p-23L, -0xb.c8be66a150b9e14p-27L, -0x8.9cc13e0a3946c9cp-26L, 0xa.18b25bf090cbe47p-28L, 0xe.6ebc6a0528a6ab3p-33L, -0xb.b9409c939cbdb9ep-32L, 0x9.2ac54d5e82338aap-34L, -0x9.e6c313ecd8427c2p-38L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.9506bf26823bcaa678f24755b1bep-12Q, 0x1.76fcca8398a608cea25db5f87af6p-8Q, 0x1.37de71ec845e43d133d0c299f8ecp-5Q, 0x1.2fdb523f49ab54335a2eba9c8437p-3Q, 0x1.788dde34ceb65e20730d6ddac0aep-2Q, 0x1.282855bd3e6611cfef751a206622p-1Q, 0x1.040b9c9ba65cbbcc9c304a8323e2p-1Q, 0x1.2df9be17f630713a1ee1adb275ebp-4Q, -0x1.403b658e1e270b5094f497dac5a2p-2Q, -0x1.9ac39bc6a693ea6805616ea07bd7p-3Q, 0x1.501016e351cb1dea06a54dd049bp-3Q, 0x1.7095c864b0ccc00c06f07ad7df02p-3Q, -0x1.8dc40d7416ec5cc24d97996382b6p-4Q, -0x1.0ddc7410272dcf4ab45934d4cf13p-3Q, 0x1.16d7307f2f198a2aec11f34d1e9fp-4Q, 0x1.5a58d5e218e8b247e862b3c1695fp-4Q, -0x1.a4c6a60c82a995e3152af9622fcap-5Q, -0x1.7d2e2f61c66bce3ea7e2b78a28c2p-5Q, 0x1.2edd7c2485c6bbc4d1a2c115a8a7p-5Q, 0x1.514ae8ff8882d1f2c15a47cd6559p-6Q, -0x1.80b243789dd9141e3fff7c22096dp-6Q, -0x1.9739fa1f59fdada5471944d8c62dp-8Q, 0x1.9bb88df2b07f25c8944100438d61p-7Q, 0x1.3ab784f96ef948279489735c5a1cp-12Q, -0x1.658b52a857f979d8d4ec9b9f73a9p-8Q, 0x1.11bf26e4a8f4a17dea14a455c454p-10Q, 0x1.def099502d06dd70a82c80e4bd5ep-10Q, -0x1.941064b6e88a5abad07f7589e66dp-11Q, -0x1.bc5f905d400af53d3eed609ad591p-12Q, 0x1.58926afecb2917c8a7cf6285c131p-12Q, 0x1.6c8f7d64132f3286043bbcbfb14ep-15Q, -0x1.8a7bd1deebb29772b3b880563654p-14Q, 0x1.7da8eb6c7dd38b3094b5e1389c85p-17Q, 0x1.237bb7cb019ef32d902afce7d618p-16Q, -0x1.9dd79a5aef3d0583abb88bd3c2cp-18Q, -0x1.a4264a7b9f194a9cadbc3e265f85p-20Q, 0x1.5bac3bb6b7df31e28d50f39c71ffp-20Q, -0x1.7917ccd42a173c285afd81440ef2p-24Q, -0x1.139827c14728d9384a9bd9717ddp-23Q, 0x1.43164b7e12197c8ececb2f261f6bp-25Q, 0x1.cdd78d40a514d5664ee974c433ep-30Q, -0x1.772813927397b73b1b90436f0da9p-29Q, 0x1.2558a9abd04671533bb0e6556b43p-31Q, -0x1.3cd8627d9b084f8342fbe01d8e11p-35Q};
+        }
+        #endif
+    }
+    if constexpr (p == 23) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.1d1cbap-12f, 0x1.136e6ep-8f, 0x1.e0371p-6f, 0x1.eda1b2p-4f, 0x1.4617f8p-2f, 0x1.170138p-1f, 0x1.1a1f1ap-1f, 0x1.737dfap-3f, -0x1.0baa62p-2f, -0x1.15ea6ep-2f, 0x1.79587ep-4f, 0x1.c9e0fcp-3f, -0x1.0ea48cp-5f, -0x1.4fe52ap-3f, 0x1.4c5162p-6f, 0x1.cbf7fcp-4f, -0x1.5a21c2p-6f, -0x1.1f91cap-4f, 0x1.649c9ep-6f, 0x1.3b5a9p-5f, -0x1.2f7d4p-6f, -0x1.1f53eep-6f, 0x1.a1db1p-7f, 0x1.8b4d7ep-8f, -0x1.cfb028p-8f, -0x1.297f88p-10f, 0x1.995258p-9f, -0x1.0279b8p-12f, -0x1.163206p-10f, 0x1.4eefcap-12f, 0x1.0d3c26p-12f, -0x1.3a9e5ep-13f, -0x1.1b7136p-15f, 0x1.734928p-15f, -0x1.61b10ep-19f, -0x1.181bb4p-17f, 0x1.41cbdcp-19f, 0x1.b56b6ap-21f, -0x1.1ea2bcp-21f, 0x1.3e5bd6p-26f, 0x1.d15d2ap-25f, -0x1.e103ap-27f, -0x1.046382p-30f, 0x1.20be9ap-30f, -0x1.a8f0bcp-33f, 0x1.b7e04ep-37f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.1d1cb9f15ca3p-12, 0x1.136e6d0cada7ap-8, 0x1.e03710ca000b2p-6, 0x1.eda1b1bac15d3p-4, 0x1.4617f85b87d2cp-2, 0x1.1701372560847p-1, 0x1.1a1f195e16c2fp-1, 0x1.737dfa0d62dcfp-3, -0x1.0baa621ce4279p-2, -0x1.15ea6e8658872p-2, 0x1.79587da8cb753p-4, 0x1.c9e0fc732c538p-3, -0x1.0ea48c5a06944p-5, -0x1.4fe52af139a58p-3, 0x1.4c51617dbe58bp-6, 0x1.cbf7fc1c6fa45p-4, -0x1.5a21c1ca225bep-6, -0x1.1f91c92c06d32p-4, 0x1.649c9ed18296ap-6, 0x1.3b5a90477563fp-5, -0x1.2f7d3f55674e5p-6, -0x1.1f53eed1947bfp-6, 0x1.a1db0f12bb42p-7, 0x1.8b4d7e5397f08p-8, -0x1.cfb028e3aae51p-8, -0x1.297f885faab6dp-10, 0x1.995258715da31p-9, -0x1.0279b74217beap-12, -0x1.163205afadf6dp-10, 0x1.4eefc91e26cfap-12, 0x1.0d3c2558f1652p-12, -0x1.3a9e5e1c22af4p-13, -0x1.1b7136cbb5aep-15, 0x1.734927c4130bfp-15, -0x1.61b10dba0880bp-19, -0x1.181bb48217362p-17, 0x1.41cbdcc2df4d9p-19, 0x1.b56b6a75fa292p-21, -0x1.1ea2bb46afa08p-21, 0x1.3e5bd6b02b53fp-26, 0x1.d15d2a9531ecbp-25, -0x1.e103a0e0c3b96p-27, -0x1.0463822ac124p-30, 0x1.20be99079e759p-30, -0x1.a8f0bc9b067e6p-33, 0x1.b7e04d72be8f7p-37};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0x8.e8e5cf8ae517d2ep-15L, 0x8.9b7368656d3d159p-11L, 0xf.01b886500058d29p-9L, 0xf.6d0d8dd60ae956bp-7L, 0xa.30bfc2dc3e9620cp-5L, 0x8.b809b92b0423412p-4L, 0x8.d0f8caf0b617657p-4L, 0xb.9befd06b16e7779p-6L, -0x8.5d5310e7213cb45p-5L, -0x8.af537432c439318p-5L, 0xb.cac3ed465ba98efp-7L, 0xe.4f07e399629c099p-6L, -0x8.752462d034a1f39p-8L, -0xa.7f295789cd2c17ap-6L, 0xa.628b0bedf2c55d4p-9L, 0xe.5fbfe0e37d2292p-7L, -0xa.d10e0e5112df11ap-9L, -0x8.fc8e49603699185p-7L, 0xb.24e4f68c14b4ebbp-9L, 0x9.dad4823bab1fbp-8L, -0x9.7be9faab3a727aap-9L, -0x8.fa9f768ca3df844p-9L, 0xd.0ed87895da0fea4p-10L, 0xc.5a6bf29cbf83d82p-11L, -0xe.7d81471d5728bb2p-11L, -0x9.4bfc42fd55b69dep-13L, 0xc.ca92c38aed18631p-12L, -0x8.13cdba10bdf515p-15L, -0x8.b1902d7d6fb67f6p-13L, 0xa.777e48f1367d0a5p-15L, 0x8.69e12ac78b28dbcp-15L, -0x9.d4f2f0e11579f3cp-16L, -0x8.db89b65dad6fc16p-18L, 0xb.9a493e20985f9bfp-18L, -0xb.0d886dd044054a4p-22L, -0x8.c0dda410b9b125ap-20L, 0xa.0e5ee616fa6c626p-22L, 0xd.ab5b53afd14926ap-24L, -0x8.f515da357d03ea3p-24L, 0x9.f2deb5815a9f567p-29L, 0xe.8ae954a98f65bb4p-28L, -0xf.081d07061dcaca2p-30L, -0x8.231c1156091fc3ap-33L, 0x9.05f4c83cf3acb2cp-33L, -0xd.4785e4d833f33e2p-36L, 0xd.bf026b95f47b713p-40L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.1d1cb9f15ca2fa5bd9123de7bf02p-12Q, 0x1.136e6d0cada7a2b148b6e8855daap-8Q, 0x1.e03710ca000b1a51a7d181d489bp-6Q, 0x1.eda1b1bac15d2ad6ddbdb3147e36p-4Q, 0x1.4617f85b87d2c4188e472323232cp-2Q, 0x1.1701372560846824bce2d06e180cp-1Q, 0x1.1a1f195e16c2ecad981d672e54f9p-1Q, 0x1.737dfa0d62dceef2a6ae0dd9fae6p-3Q, -0x1.0baa621ce427968960a0c4171c1cp-2Q, -0x1.15ea6e865887262fe21b5ed288ddp-2Q, 0x1.79587da8cb7531de57b391307b2ep-4Q, 0x1.c9e0fc732c5381328729c7899645p-3Q, -0x1.0ea48c5a06943e72865d8b0a9865p-5Q, -0x1.4fe52af139a582f4b4bfddd5990ap-3Q, 0x1.4c51617dbe58aba744aaa9e2e84dp-6Q, 0x1.cbf7fc1c6fa4523fc35d6c595afp-4Q, -0x1.5a21c1ca225be23388c3683c5f1ap-6Q, -0x1.1f91c92c06d3230ad5ace9dd7e2ap-4Q, 0x1.649c9ed182969d7683dcc682acbcp-6Q, 0x1.3b5a90477563f5ff5ff6e6498f97p-5Q, -0x1.2f7d3f55674e4f5496795e1de4a5p-6Q, -0x1.1f53eed1947bf0871dd1fee02046p-6Q, 0x1.a1db0f12bb41fd473a2e8421b507p-7Q, 0x1.8b4d7e5397f07b04d41a59615574p-8Q, -0x1.cfb028e3aae51764ab65b4e360fbp-8Q, -0x1.297f885faab6d3bcc655cccba49p-10Q, 0x1.995258715da30c618d8b26e9df7bp-9Q, -0x1.0279b74217bea2a0847d1e93003bp-12Q, -0x1.163205afadf6cfebfb69e0b0f9f9p-10Q, 0x1.4eefc91e26cfa14abc8a3c8c31bep-12Q, 0x1.0d3c2558f1651b77d56d78be87a6p-12Q, -0x1.3a9e5e1c22af3e7828bfcf5d2f48p-13Q, -0x1.1b7136cbb5adf82b0d9aad06bd7cp-15Q, 0x1.734927c4130bf37e18cb5a04041ap-15Q, -0x1.61b10dba0880a94866a6f32c90e9p-19Q, -0x1.181bb482173624b3f677525a8993p-17Q, 0x1.41cbdcc2df4d8c4b6d915e9702b2p-19Q, 0x1.b56b6a75fa2924d359ae84bf18d8p-21Q, -0x1.1ea2bb46afa07d45b08cabbea3b6p-21Q, 0x1.3e5bd6b02b53eacdcf10b59b874fp-26Q, 0x1.d15d2a9531ecb7682cdf70f5d33bp-25Q, -0x1.e103a0e0c3b959430c8cac42a206p-27Q, -0x1.0463822ac123f874c86ec02d6961p-30Q, 0x1.20be99079e7596586119e6bc965cp-30Q, -0x1.a8f0bc9b067e67c3b0dec15337bdp-33Q, 0x1.b7e04d72be8f6e258b11c231fbfep-37Q};
+        }
+        #endif
+    }
+    if constexpr (p == 24) {
+        if constexpr (std::is_same_v<Real, float>) {
+            return {0x1.91785p-13f, 0x1.93f98p-9f, 0x1.7059c4p-6f, 0x1.8e62d8p-4f, 0x1.17757p-2f, 0x1.023cecp-1f, 0x1.265e6ep-1f, 0x1.1fbaaep-2f, -0x1.7f8826p-3f, -0x1.4592dep-2f, 0x1.390a48p-8f, 0x1.e9f54ap-3f, 0x1.5c6536p-5f, -0x1.5e912ep-3f, -0x1.3da9ap-5f, 0x1.efaecap-4f, 0x1.57bcfap-6f, -0x1.5088bep-4f, -0x1.2c0d6ap-8f, 0x1.a4434cp-5f, -0x1.440e76p-8f, -0x1.ce3e5ap-6f, 0x1.f61e5cp-8f, 0x1.ab9f18p-7f, -0x1.9c50c6p-8f, -0x1.371236p-8f, 0x1.e9b0e8p-9f, 0x1.2e73dap-10f, -0x1.bcb74ap-10f, -0x1.7274d8p-15f, 0x1.334ca4p-11f, -0x1.ef71f4p-14f, -0x1.32337p-13f, 0x1.131ee6p-14f, 0x1.6e4982p-16f, -0x1.536264p-16f, 0x1.ccd17cp-27f, 0x1.05cc64p-18f, -0x1.e21fa8p-21f, -0x1.b0fcbap-22f, 0x1.d137c8p-23f, -0x1.160c08p-31f, -0x1.838882p-26f, 0x1.627092p-28f, 0x1.050b72p-31f, -0x1.ba8412p-32f, 0x1.3380aep-34f, -0x1.31989ep-38f};
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            return {0x1.91785023a9879p-13, 0x1.93f9805696b9cp-9, 0x1.7059c4b494de9p-6, 0x1.8e62d8a0a8ffcp-4, 0x1.17756f5530d69p-2, 0x1.023cebcae9f67p-1, 0x1.265e6eff960ccp-1, 0x1.1fbaad4726276p-2, -0x1.7f8826c061991p-3, -0x1.4592ded92acf9p-2, 0x1.390a478f54bbbp-8, 0x1.e9f54ac655c14p-3, 0x1.5c6535de6b4e5p-5, -0x1.5e912ec022b6p-3, -0x1.3da9a08b26c34p-5, 0x1.efaeca9aee192p-4, 0x1.57bcf98fd11cep-6, -0x1.5088bd1cf023ep-4, -0x1.2c0d69ece949fp-8, 0x1.a4434b89b6915p-5, -0x1.440e7548329f5p-8, -0x1.ce3e5912a2303p-6, 0x1.f61e5ce9a7ff1p-8, 0x1.ab9f170d72cc6p-7, -0x1.9c50c528bc778p-8, -0x1.371235b499d34p-8, 0x1.e9b0e84ddc047p-9, 0x1.2e73daaf19dbbp-10, -0x1.bcb74a39ee4ap-10, -0x1.7274d8ffa9744p-15, 0x1.334ca46898daep-11, -0x1.ef71f401aeeebp-14, -0x1.32337036c1617p-13, 0x1.131ee63336347p-14, 0x1.6e4981b862b8bp-16, -0x1.536263fe83a12p-16, 0x1.ccd17bbbe3d04p-27, 0x1.05cc64bbcf96p-18, -0x1.e21fa8ce8bf7ap-21, -0x1.b0fcbaac8055ep-22, 0x1.d137c82c35ed7p-23, -0x1.160c0805b95d3p-31, -0x1.838882edd8948p-26, 0x1.627091a0c660dp-28, 0x1.050b72dfcacecp-31, -0x1.ba8411e011af6p-32, 0x1.3380aec6c4cc7p-34, -0x1.31989d5a96be3p-38};
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            return {0xc.8bc2811d4c3c975p-16L, 0xc.9fcc02b4b5cdd4fp-12L, 0xb.82ce25a4a6f4946p-9L, 0xc.7316c50547fde96p-7L, 0x8.bbab7aa986b4822p-5L, 0x8.11e75e574fb369fp-4L, 0x9.32f377fcb066266p-4L, 0x8.fdd56a39313b02ap-5L, -0xb.fc4136030cc8af3p-6L, -0xa.2c96f6c9567c64ep-5L, 0x9.c8523c7aa5dd6c6p-11L, 0xf.4faa5632ae09cacp-6L, 0xa.e329aef35a72807p-8L, -0xa.f489760115afe5ap-6L, -0x9.ed4d0459361a0cbp-8L, 0xf.7d7654d770c90fap-7L, 0xa.bde7cc7e88e7341p-9L, -0xa.8445e8e7811ed17p-7L, -0x9.606b4f674a4f729p-11L, 0xd.221a5c4db48a85p-8L, -0xa.2073aa4194fa9f4p-11L, -0xe.71f2c8951181b37p-9L, 0xf.b0f2e74d3ff8483p-11L, 0xd.5cf8b86b966301bp-10L, -0xc.e2862945e3bc0bdp-11L, -0x9.b891ada4ce99f42p-11L, 0xf.4d87426ee023471p-12L, 0x9.739ed578cedd928p-13L, -0xd.e5ba51cf724ff04p-13L, -0xb.93a6c7fd4ba228cp-18L, 0x9.9a652344c6d708fp-14L, -0xf.7b8fa00d7775af1p-17L, -0x9.919b81b60b0b6ddp-16L, 0x8.98f73199b1a34dep-17L, 0xb.724c0dc315c5bebp-19L, -0xa.9b131ff41d09255p-19L, 0xe.668bdddf1e8204p-30L, 0x8.2e6325de7cafddbp-21L, -0xf.10fd46745fbd3a3p-24L, -0xd.87e5d56402aecbp-25L, 0xe.89be4161af6badap-26L, -0x8.b060402dcae9786p-34L, -0xc.1c44176ec4a3d56p-29L, 0xb.13848d0633067f9p-31L, 0x8.285b96fe5675d57p-34L, -0xd.d4208f008d7b156p-35L, 0x9.9c0576362663aafp-37L, -0x9.8cc4ead4b5f196ap-41L};
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            return {0x1.91785023a98792eac41b5272c04bp-13Q, 0x1.93f9805696b9ba9d87c3df41a8d9p-9Q, 0x1.7059c4b494de928c16cf6cacf0a7p-6Q, 0x1.8e62d8a0a8ffbd2cc57d79f83e08p-4Q, 0x1.17756f5530d69044d0184f790b3ep-2Q, 0x1.023cebcae9f66d3d390049f78dcp-1Q, 0x1.265e6eff960cc4ccf24089549b66p-1Q, 0x1.1fbaad4726276054f5d700d1bfb6p-2Q, -0x1.7f8826c0619915e6978c42a74dfcp-3Q, -0x1.4592ded92acf8c9c5ecd6ba9faddp-2Q, 0x1.390a478f54bbad8c711b3d202a1ap-8Q, 0x1.e9f54ac655c13958344e31a88778p-3Q, 0x1.5c6535de6b4e500e1e067af4d00ep-5Q, -0x1.5e912ec022b5fcb42ec3601ecf9bp-3Q, -0x1.3da9a08b26c34196db8bd596e813p-5Q, 0x1.efaeca9aee1921f4bc36a577b638p-4Q, 0x1.57bcf98fd11ce6827e350101b72ep-6Q, -0x1.5088bd1cf023da2d878ac9ebafc5p-4Q, -0x1.2c0d69ece949ee5284dcfb042baap-8Q, 0x1.a4434b89b691509ff6541a080cecp-5Q, -0x1.440e7548329f53e7873db8128a63p-8Q, -0x1.ce3e5912a230366d14a862ea3672p-6Q, 0x1.f61e5ce9a7ff0906541711dfe2e7p-8Q, 0x1.ab9f170d72cc6036a5092b63c08ap-7Q, -0x1.9c50c528bc77817ae0788ffc773ap-8Q, -0x1.371235b499d33e83c0b1b543f6e8p-8Q, 0x1.e9b0e84ddc0468e17e4fa3636bf9p-9Q, 0x1.2e73daaf19dbb24f6ae6d9d95255p-10Q, -0x1.bcb74a39ee49fe08e2b9fd7aeef1p-10Q, -0x1.7274d8ffa9744517f2f1470cebeep-15Q, 0x1.334ca46898dae11da29a57e9f92ap-11Q, -0x1.ef71f401aeeeb5e13dd40efc0a0cp-14Q, -0x1.32337036c1616db93444903d828ep-13Q, 0x1.131ee633363469bb9bebca29a839p-14Q, 0x1.6e4981b862b8b7d5bb86d25cc3eap-16Q, -0x1.536263fe83a124aaa2092f47c711p-16Q, 0x1.ccd17bbbe3d0407ffce581eb4165p-27Q, 0x1.05cc64bbcf95fbb57637394fb838p-18Q, -0x1.e21fa8ce8bf7a7465a57d37cce9ap-21Q, -0x1.b0fcbaac8055d95fcb97dc94d8aap-22Q, 0x1.d137c82c35ed75b3cca32ab07fp-23Q, -0x1.160c0805b95d2f0cf1ffb7605bf2p-31Q, -0x1.838882edd8947aab05cd00305346p-26Q, 0x1.627091a0c660cff16c28fc227cd6p-28Q, 0x1.050b72dfcacebaae0203f358d56p-31Q, -0x1.ba8411e011af62ac1faf9b23aa51p-32Q, 0x1.3380aec6c4cc755d395c84cee933p-34Q, -0x1.31989d5a96be32d359a4b1032025p-38Q};
+        }
+        #endif
+    }
+}
+
+template<class Real, size_t p>
+std::array<Real, 2*p> daubechies_wavelet_filter() {
+    std::array<Real, 2*p> g;
+    auto h = daubechies_scaling_filter<Real, p>();
+    for (size_t i = 0; i < g.size(); i += 2)
+    {
+        g[i] = h[g.size() - i - 1];
+        g[i+1] = -h[g.size() - i - 2];
+    }
+    return g;
+}
+
+} // namespaces
+#endif
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
new file mode 100644
index 000000000..d58e30ed6
--- /dev/null
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -0,0 +1,352 @@
+/*
+ * Copyright Nick Thompson, 2019
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef BOOST_MATH_SPECIAL_DAUBECHIES_SCALING_HPP
+#define BOOST_MATH_SPECIAL_DAUBECHIES_SCALING_HPP
+#include <vector>
+#include <array>
+#include <cmath>
+#include <thread>
+#include <boost/multiprecision/float128.hpp>
+#include <boost/math/constants/constants.hpp>
+#include <boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp>
+#include <boost/math/filters/daubechies.hpp>
+
+
+namespace boost::math {
+
+namespace detail {
+
+template<class Real, int p, int order>
+std::vector<Real> dyadic_grid(size_t j_max)
+{
+    auto c = boost::math::filters::daubechies_scaling_filter<Real, p>();
+    Real scale = boost::math::constants::root_two<Real>()*(1 << order);
+    for (auto & x : c)
+    {
+        x *= scale;
+    }
+
+    auto phik = daubechies_scaling_integer_grid<Real, p, order>();
+
+    // Maximum sensible j for 32 bit floats is j_max = 22:
+    std::vector<Real> v(2*p + (2*p-1)*((1<<j_max) -1), std::numeric_limits<Real>::quiet_NaN());
+    v.resize(2*p + (2*p-1)*((1<<j_max) -1), std::numeric_limits<Real>::quiet_NaN());
+    v[0] = 0;
+    v[v.size()-1] = 0;
+    for (size_t i = 0; i < phik.size(); ++i) {
+        v[i*(1<<(j_max))] = phik[i];
+    }
+
+    for (size_t j = 1; j <= j_max; ++j)
+    {
+        size_t k_max = v.size()/(1 << (j_max-j));
+        for (size_t k = 1; k < k_max;  k += 2)
+        {
+            // Where this value will go:
+            size_t delivery_idx = k*(1 << (j_max-j));
+            if (delivery_idx >= v.size())
+            {
+                std::cout << "Delivery index out of range!\n";
+                continue;
+            }
+            Real term = 0;
+            for (size_t l = 0; l < c.size(); ++l) {
+                size_t idx = k*(1 << (j_max - j + 1)) - l*(1 << j_max);
+                if (idx >= 0 && idx < v.size()) {
+                    term += c[l]*v[idx];
+                }
+            }
+            if (!isnan(v[delivery_idx])) {
+                std::cout << "Delivery index already populated!, = " << v[delivery_idx] << "\n";
+                std::cout << "would overwrite with " << term << "\n";
+            }
+            v[delivery_idx] = term;
+        }
+    }
+
+
+    return v;
+}
+
+}
+
+template<class Real, int p>
+class daubechies_scaling {
+public:
+    daubechies_scaling(int levels = -1)
+    {
+        using boost::multiprecision::float128;
+        if (levels < 0)
+        {
+            m_levels = 22;
+        }
+        else {
+            m_levels = levels;
+        }
+
+        auto f1 = [this] {
+            auto v = detail::dyadic_grid<float128, p, 0>(this->m_levels);
+            this->m_v.resize(v.size());
+            for (size_t i = 0; i < v.size(); ++i) {
+                this->m_v[i] = static_cast<Real>(v[i]);
+            }
+        };
+
+        auto f2 = [this] {
+            auto v_prime = detail::dyadic_grid<float128, p, 1>(this->m_levels);
+            this->m_v_prime.resize(v_prime.size());
+            for (size_t i = 0; i < v_prime.size(); ++i) {
+                this->m_v_prime[i] = static_cast<Real>(v_prime[i]);
+            }
+        };
+
+
+        auto f3 = [this] {
+            auto v_dbl_prime = detail::dyadic_grid<float128, p, 2>(this->m_levels);
+            this->m_v_dbl_prime.resize(v_dbl_prime.size());
+            for (size_t i = 0; i < v_dbl_prime.size(); ++i) {
+                this->m_v_dbl_prime[i] = static_cast<Real>(v_dbl_prime[i]);
+            }
+        };
+
+        std::thread t1(f1);
+        std::thread t2(f2);
+        std::thread t3(f3);
+
+        t1.join();
+        t2.join();
+        t3.join();
+
+        m_inv_spacing = (1 << m_levels);
+
+        m_c = boost::math::filters::daubechies_scaling_filter<Real, p>();
+        Real scale = boost::math::constants::root_two<Real>();
+        for (auto & x : m_c)
+        {
+            x *= scale;
+        }
+    }
+
+    Real operator()(Real x) const { return this->linear_interpolation(x); }
+
+    std::pair<int, int> support() const {
+        return {0, 2*p-1};
+    }
+
+    Real constant_interpolation(Real x) const {
+        if (x <= 0 || x >= 2*p-1) {
+            return Real(0);
+        }
+        using std::floor;
+        Real y = (1 << m_levels)*x;
+        Real k = floor(y);
+
+        if (y - k < k + 1 - y)
+        {
+            return m_v[static_cast<size_t>(k)];
+        }
+        return m_v[static_cast<size_t>(k)+1];
+    }
+
+    Real linear_interpolation(Real x) const {
+        if (x <= 0 || x >= 2*p-1) {
+            return Real(0);
+        }
+        using std::floor;
+
+        Real y = (1<<m_levels)*x;
+        Real k = floor(y);
+
+        size_t kk = static_cast<size_t>(k);
+
+        Real t = y - k;
+        return (1-t)*m_v[kk] + t*m_v[kk+1];
+    }
+
+    Real single_crank_linear(Real x) const {
+        if (x <= 0 || x >= 2*p-1) {
+            return Real(0);
+        }
+        using std::floor;
+        Real y = (1<<m_levels)*x;
+        Real idx1 = floor(y);
+
+        Real term = 0;
+        size_t k = 2*idx1 + 1;
+        for (size_t l = 0; l < m_c.size(); ++l) {
+            uint64_t idx = k - l*(1 << m_levels);
+            if (idx >= 0 && idx < m_v.size()) {
+                term += m_c[l]*m_v[idx];
+            }
+        }
+
+        if (y - idx1 < idx1 + 1 - y)
+        {
+            Real t = 2*(y - idx1);
+            return (1-t)*m_v[static_cast<size_t>(idx1)] + t*term;
+        }
+        else {
+            Real t = 2*(idx1 + 1 - y);
+            return t*term + (1-t)*m_v[static_cast<size_t>(idx1)+1];
+        }
+    }
+
+    Real single_crank_quadratic(Real x) const {
+        if (x <= 0 || x >= 2*p-1) {
+            return Real(0);
+        }
+        using std::floor;
+        Real y = (1<<m_levels)*x;
+        Real idx1 = floor(y);
+
+        Real term = 0;
+        size_t k = 2*idx1 + 1;
+        for (size_t l = 0; l < m_c.size(); ++l) {
+            uint64_t idx = k - l*(1 << m_levels);
+            if (idx >= 0 && idx < m_v.size()) {
+                term += m_c[l]*m_v[idx];
+            }
+        }
+
+        Real y0 = m_v[static_cast<size_t>(idx1)];
+        Real y1 = term;
+        Real y2 = m_v[static_cast<size_t>(idx1)+1];
+
+        Real a = (y2+y0-2*y1)/2;
+        Real b = (4*y1-3*y0 - y2)/2;
+        Real t = 2*(y - idx1);
+        return a*t*t + b*t + y0;
+    }
+
+
+    Real double_crank_linear(Real x) const {
+        return std::numeric_limits<Real>::quiet_NaN();
+    }
+
+
+    Real first_order_taylor(Real x) const {
+        if (x <= 0 || x >= 2*p-1) {
+            return 0;
+        }
+        using std::floor;
+
+        Real y = (1<<m_levels)*x;
+        Real k = floor(y);
+
+        size_t kk = static_cast<size_t>(k);
+        if (y - k < k + 1 - y)
+        {
+            Real eps = (y-k)/(1<<m_levels);
+            return m_v[kk] + eps*m_v_prime[kk];
+        }
+        else {
+            Real eps = (y-k-1)/(1<<m_levels);
+            return m_v[kk+1] + eps*m_v_prime[kk+1];
+        }
+    }
+
+    Real second_order_taylor(Real x) const {
+        if (x <= 0 || x >= 2*p-1) {
+            return 0;
+        }
+        using std::floor;
+
+        Real y = (1<<m_levels)*x;
+        Real k = floor(y);
+
+        size_t kk = static_cast<size_t>(k);
+        if (y - k < k + 1 - y)
+        {
+            Real eps = (y-k)/(1<<m_levels);
+            return m_v[kk] + eps*m_v_prime[kk] + eps*eps*m_v_dbl_prime[kk]/2;
+        }
+        else {
+            Real eps = (y-k-1)/(1<<m_levels);
+            return m_v[kk+1] + eps*m_v_prime[kk+1] + eps*eps*m_v_dbl_prime[kk+1]/2;
+        }
+    }
+
+    Real third_order_taylor(Real x) const {
+        return std::numeric_limits<Real>::quiet_NaN();
+    }
+
+    Real single_crank_first_order_taylor(Real x) const {
+        return std::numeric_limits<Real>::quiet_NaN();
+    }
+
+    Real double_crank_first_order_taylor(Real x) const {
+        return std::numeric_limits<Real>::quiet_NaN();
+    }
+
+    Real single_crank_second_order_taylor(Real x) const {
+        return std::numeric_limits<Real>::quiet_NaN();
+    }
+
+    Real double_crank_second_order_taylor(Real x) const {
+        return std::numeric_limits<Real>::quiet_NaN();
+    }
+
+    Real single_crank_third_order_taylor(Real x) const {
+        return std::numeric_limits<Real>::quiet_NaN();
+    }
+
+    Real double_crank_third_order_taylor(Real x) const {
+        return std::numeric_limits<Real>::quiet_NaN();
+    }
+
+    size_t bytes() const
+    {
+        size_t s = sizeof(*this);
+        s += m_v.size()*sizeof(Real);
+        return s;
+    }
+
+    size_t size() const {
+        return m_v.size();
+    }
+
+    Real index_to_abscissa(size_t i) {
+        return i/m_inv_spacing;
+    }
+
+    // This is for debugging only; use the .at()
+    Real operator[](size_t i) const {
+        return m_v.at(i);
+    }
+
+    Real prime(size_t i) const {
+        return m_v_prime.at(i);
+    }
+
+    Real spacing() const {
+        return 1/m_inv_spacing;
+    }
+
+    auto begin() const {
+        return m_v.begin();
+    }
+
+    auto end() const {
+        return m_v.end();
+    }
+
+    auto data() const {
+        return m_v.data();
+    }
+
+private:
+    size_t m_levels;
+    Real m_inv_spacing;
+    std::array<Real, 2*p> m_c;
+    std::vector<Real> m_v;
+    std::vector<Real> m_v_prime;
+    std::vector<Real> m_v_dbl_prime;
+};
+
+}
+#endif
diff --git a/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp b/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp
new file mode 100644
index 000000000..fe3296832
--- /dev/null
+++ b/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp
@@ -0,0 +1,1830 @@
+/*
+ * Copyright Nick Thompson, 2019
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+// THIS FILE GENERATED BY EXAMPLE/DAUBECHIES_SCALING_INTEGER_GRID.CPP, DO NOT EDIT.
+#ifndef BOOST_MATH_DAUBECHIES_SCALING_INTEGER_GRID_HPP
+#define BOOST_MATH_DAUBECHIES_SCALING_INTEGER_GRID_HPP
+#include <array>
+#ifdef BOOST_HAS_FLOAT128
+#include <boost/multiprecision/float128.hpp>
+#endif
+namespace boost::math::detail {
+
+template <typename Real, unsigned p, unsigned order>
+constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
+{
+    static_assert(sizeof(Real) <= 16, "Integer grids only computed up to 128 bits of precision.");
+    static_assert(p <= 15, "Integer grids only implemented up to 15.");
+    static_assert(p > 1, "Integer grids only implemented for p >= 2.");
+    if constexpr (p == 2) {
+        if constexpr (std::is_same_v<Real, float>) {
+            if constexpr (order == 0) {
+                return {0x0p+0f, 0x1.5db3d8p+0f, -0x1.76cf5ep-2f, 0x0p+0f};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0f, 0x1p+0f, -0x1p+0f, -0x0p+0f};
+            }
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0, 0x1.5db3d742c2655p+0, -0x1.76cf5d0b09955p-2, 0x0p+0};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0, 0x1p+0, -0x1p+0, -0x0p+0};
+            }
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0L, 0xa.ed9eba16132a9cfp-3L, -0xb.b67ae8584caa73bp-5L, 0x0p+0L};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0L, 0x8p-3L, -0x8p-3L, -0x0p+0L};
+            }
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            if constexpr (order == 0) {
+                return {0x0p+0Q, 0x1.5db3d742c265539d92ba16b83c5dp+0Q, -0x1.76cf5d0b09954e764ae85ae0f172p-2Q, 0x0p+0Q};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0Q, 0x1.0000000000000000000000000003p+0Q, -0x1.0000000000000000000000000001p+0Q, -0x0p+0Q};
+            }
+        }
+        #endif
+    }
+    if constexpr (p == 3) {
+        if constexpr (std::is_same_v<Real, float>) {
+            if constexpr (order == 0) {
+                return {0x0p+0f, 0x1.494d42p+0f, -0x1.8b18d8p-2f, 0x1.863744p-4f, 0x1.158088p-8f, -0x0p+0f};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0f, 0x1.a3719cp+0f, -0x1.1dcb06p+1f, 0x1.19ae7cp-1f, 0x1.69a5e8p-5f, 0x0p+0f};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0f, 0x1.cef9ccp-1f, -0x1.b676b2p+0f, 0x1.6ced64p-1f, 0x1.8831a2p-4f, -0x0p+0f};
+            }
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0, 0x1.494d414ee19a1p+0, -0x1.8b18d8251ec88p-2, 0x1.863743274d78dp-4, 0x1.158087f14084dp-8, -0x0p+0};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0, 0x1.a3719cd426dbdp+0, -0x1.1dcb0537f529p+1, 0x1.19ae7cc6c0212p-1, 0x1.69a5e70c6cb47p-5, 0x0p+0};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0, 0x1.cef9cbb90bf24p-1, -0x1.b676b19591eb6p+0, 0x1.6ced632b23d6cp-1, 0x1.8831a237a06dfp-4, -0x0p+0};
+            }
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0L, 0xa.4a6a0a770cd07e1p-3L, -0xc.58c6c128f64431dp-5L, 0xc.31ba193a6bc67f2p-7L, 0x8.ac043f8a042675ap-11L, -0x0p+0L};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0L, 0xd.1b8ce6a136deae1p-3L, -0x8.ee5829bfa948208p-2L, 0x8.cd73e6360108efbp-4L, 0xb.4d2f386365a363ap-8L, 0x0p+0L};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0L, 0xe.77ce5dc85f9214cp-4L, -0xd.b3b58cac8f5b1f2p-3L, 0xb.676b19591eb63e3p-4L, 0xc.418d11bd036f5a2p-7L, -0x0p+0L};
+            }
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            if constexpr (order == 0) {
+                return {0x0p+0Q, 0x1.494d414ee19a0fc1701f9345a28ap+0Q, -0x1.8b18d8251ec886399fc357ab26c5p-2Q, 0x1.863743274d78cfe42daf1d262e3fp-4Q, 0x1.158087f14084ceb4f650d2c442ep-8Q, -0x0p+0Q};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0Q, 0x1.a3719cd426dbd5c2283e8b6cd967p+0Q, -0x1.1dcb0537f52904105ab1d13c6abp+1Q, 0x1.19ae7cc6c0211df5e41745563cadp-1Q, 0x1.69a5e70c6cb46c73632e8c1bb2cp-5Q, 0x0p+0Q};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0Q, 0x1.cef9cbb90bf242979b344cdd1e16p-1Q, -0x1.b676b19591eb63e368ce734bad21p+0Q, 0x1.6ced632b23d6c7c6d19ce6975a1dp-1Q, 0x1.8831a237a06deb43265d99170ff8p-4Q, -0x0p+0Q};
+            }
+        }
+        #endif
+    }
+    if constexpr (p == 4) {
+        if constexpr (std::is_same_v<Real, float>) {
+            if constexpr (order == 0) {
+                return {0x0p+0f, 0x1.01d5e4p+0f, -0x1.15313cp-5f, 0x1.447d2ap-5f, -0x1.817e96p-7f, -0x1.3a0992p-10f, 0x1.3be7b6p-16f, -0x0p+0f};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0f, 0x1.c6aca8p+0f, -0x1.648654p+1f, 0x1.314492p+0f, -0x1.0d0e14p-3f, -0x1.b6da96p-5f, 0x1.d0194cp-10f, -0x0p+0f};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0f, 0x1.cf8cc6p+0f, -0x1.0eaaap+2f, 0x1.66e46cp+1f, -0x1.26d9a4p-3f, -0x1.0ae7c2p-2f, 0x1.3a82a2p-6f, 0x0p+0f};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0f, 0x1.bb2f44p-1f, -0x1.2d48b8p+1f, 0x1.c2597p+0f, 0x1.83800cp-3f, -0x1.233972p-1f, 0x1.bcd16ep-4f, 0x0p+0f};
+            }
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0, 0x1.01d5e443d831dp+0, -0x1.15313c61b3acbp-5, 0x1.447d293e37265p-5, -0x1.817e96e0425edp-7, -0x1.3a0992ca51117p-10, 0x1.3be7b6cb630ap-16, -0x0p+0};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0, 0x1.c6aca7b3a61bp+0, -0x1.6486543c8460bp+1, 0x1.314491c6de2d3p+0, -0x1.0d0e14f1f7dc6p-3, -0x1.b6da96c702378p-5, 0x1.d0194bee1a174p-10, -0x0p+0};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0, 0x1.cf8cc69cc42a4p+0, -0x1.0eaaa0c1e1c35p+2, 0x1.66e46b718b501p+1, -0x1.26d9a4de19b74p-3, -0x1.0ae7c18dd841ep-2, 0x1.3a82a1b96295bp-6, 0x0p+0};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0, 0x1.bb2f43bc30b81p-1, -0x1.2d48b852668c6p+1, 0x1.c2596fe640caep+0, 0x1.83800be8c4de9p-3, -0x1.233972e072028p-1, 0x1.bcd16d3945752p-4, 0x0p+0};
+            }
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0L, 0x8.0eaf221ec18e913p-3L, -0x8.a989e30d9d65a3ap-8L, 0xa.23e949f1b93272cp-8L, -0xc.0bf4b70212f684ap-10L, -0x9.d04c9652888ba27p-13L, 0x9.df3db65b184ff7ep-19L, -0x0p+0L};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0L, 0xe.35653d9d30d7c1cp-3L, -0xb.2432a1e4230589p-2L, 0x9.8a248e36f1695bdp-3L, -0x8.6870a78fbee2d2ap-6L, -0xd.b6d4b63811bbfa2p-8L, 0xe.80ca5f70d0ba167p-13L, -0x0p+0L};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0L, 0xe.7c6634e62152087p-3L, -0x8.7555060f0e1aa31p-1L, 0xb.37235b8c5a805d9p-2L, -0x9.36cd26f0cdb9e9ap-6L, -0x8.573e0c6ec20ec34p-5L, 0x9.d4150dcb14ada24p-9L, 0x0p+0L};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0L, 0xd.d97a1de185c06cap-4L, -0x9.6a45c2933463235p-2L, 0xe.12cb7f320656fb6p-3L, 0xc.1c005f4626f4b41p-6L, -0x9.19cb97039014287p-4L, 0xd.e68b69ca2ba92a2p-7L, 0x0p+0L};
+            }
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            if constexpr (order == 0) {
+                return {0x0p+0Q, 0x1.01d5e443d831d2252369827793d4p+0Q, -0x1.15313c61b3acb474231dab07815dp-5Q, 0x1.447d293e37264e578b865081224p-5Q, -0x1.817e96e0425ed094fa1a3a5cf10fp-7Q, -0x1.3a0992ca5111744ed1b4ed1a6607p-10Q, 0x1.3be7b6cb6309fefbda0c9fa167f7p-16Q, -0x0p+0Q};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0Q, 0x1.c6aca7b3a61af838bb3208359ff3p+0Q, -0x1.6486543c8460b11f1a4b4a357fa3p+1Q, 0x1.314491c6de2d2b798153746ca802p+0Q, -0x1.0d0e14f1f7dc5a54f21ce3ff4227p-3Q, -0x1.b6da96c702377f43a25f74c9465cp-5Q, 0x1.d0194bee1a1742cd9ebfbba7180ap-10Q, -0x0p+0Q};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0Q, 0x1.cf8cc69cc42a410e51b272a7a397p+0Q, -0x1.0eaaa0c1e1c354610b35262e906ap+2Q, 0x1.66e46b718b500bb2be3ec05c7ac4p+1Q, -0x1.26d9a4de19b73d34cbab42cdd8b6p-3Q, -0x1.0ae7c18dd841d8689ede2f52573fp-2Q, 0x1.3a82a1b96295b447f46661fe5c5ap-6Q, 0x0p+0Q};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0Q, 0x1.bb2f43bc30b80d947c8a537a21d9p-1Q, -0x1.2d48b852668c646a630392a2b72ap+1Q, 0x1.c2596fe640cadf6ca968f3b31114p+0Q, 0x1.83800be8c4de9681c9e31925cc1cp-3Q, -0x1.233972e07202850d1be1b9fc8353p-1Q, 0x1.bcd16d394575254330d81aed475ep-4Q, 0x0p+0Q};
+            }
+        }
+        #endif
+    }
+    if constexpr (p == 5) {
+        if constexpr (std::is_same_v<Real, float>) {
+            if constexpr (order == 0) {
+                return {0x0p+0f, 0x1.646bf2p-1f, 0x1.cbd5c2p-2f, -0x1.754196p-3f, 0x1.3100cap-5f, 0x1.8dd2bep-10f, -0x1.c4ab56p-10f, 0x1.3b27d2p-15f, 0x1.75f2b2p-23f, 0x0p+0f};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0f, 0x1.8eee7ap+0f, -0x1.37cf44p+1f, 0x1.3c6448p+0f, -0x1.784198p-2f, -0x1.64d96ap-6f, 0x1.08fcfcp-5f, -0x1.5e1ffp-10f, -0x1.984da2p-17f, 0x0p+0f};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0f, 0x1.22c5ccp+1f, -0x1.83ccap+2f, 0x1.524518p+2f, -0x1.2d10dcp+0f, -0x1.549f4cp-1f, 0x1.882acap-2f, -0x1.3d5d0ep-5f, -0x1.65cdcp-11f, -0x0p+0f};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0f, 0x1.9877acp+1f, -0x1.48c27ap+3f, 0x1.f7fdf6p+2f, 0x1.0b1eap+3f, -0x1.15aaf4p+4f, 0x1.4a4504p+3f, -0x1.050134p+1f, -0x1.13ee46p-4f, -0x0p+0f};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0f, 0x1.13b9e8p-1f, -0x1.e1e5e6p+0f, 0x1.29ab2ep+1f, -0x1.3d6cc6p+0f, 0x1.0227f8p-1f, -0x1.9ada2ap-2f, 0x1.2c68dap-3f, 0x1.1a66dcp-7f, 0x0p+0f};
+            }
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0, 0x1.646bf1ec64a31p-1, 0x1.cbd5c1bab5148p-2, -0x1.754196833f707p-3, 0x1.3100cab7c3f5fp-5, 0x1.8dd2be8c89c52p-10, -0x1.c4ab558ff2dcfp-10, 0x1.3b27d2d798eedp-15, 0x1.75f2b16626e98p-23, 0x0p+0};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0, 0x1.8eee7927087b2p+0, -0x1.37cf445237f1bp+1, 0x1.3c64475174b4ap+0, -0x1.7841978e876dbp-2, -0x1.64d969ffaac15p-6, 0x1.08fcfb4783fa8p-5, -0x1.5e1fef6185af9p-10, -0x1.984da10897439p-17, 0x0p+0};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0, 0x1.22c5cb8d3f23bp+1, -0x1.83cca07a3ead8p+2, 0x1.5245172406b78p+2, -0x1.2d10dba463fc2p+0, -0x1.549f4c5e04f3ap-1, 0x1.882ac9029ddc7p-2, -0x1.3d5d0eda32d8bp-5, -0x1.65cdc06ecf654p-11, -0x0p+0};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0, 0x1.9877ac926fb3cp+1, -0x1.48c27a70b93cep+3, 0x1.f7fdf60845cfcp+2, 0x1.0b1ea0ee5f9edp+3, -0x1.15aaf38ada16ap+4, 0x1.4a45041b91e1cp+3, -0x1.05013480812dfp+1, -0x1.13ee46114fd85p-4, -0x0p+0};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0, 0x1.13b9e8c4fdc5p-1, -0x1.e1e5e5cfd0a8p+0, 0x1.29ab2ec864d45p+1, -0x1.3d6cc61e0f6a4p+0, 0x1.0227f72aa277ep-1, -0x1.9ada2a6a9a218p-2, 0x1.2c68da3893cd6p-3, 0x1.1a66dc6d2cfbfp-7, 0x0p+0};
+            }
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0L, 0xb.235f8f632518463p-4L, 0xe.5eae0dd5a8a4298p-5L, -0xb.aa0cb419fb8363cp-6L, 0x9.880655be1fafa7dp-8L, 0xc.6e95f4644e28f3ep-13L, -0xe.255aac7f96e75fp-13L, 0x9.d93e96bcc776751p-18L, 0xb.af958b31374c3acp-26L, 0x0p+0L};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0L, 0xc.7773c93843d9207p-3L, -0x9.be7a2291bf8db95p-2L, 0x9.e3223a8ba5a5065p-3L, -0xb.c20cbc743b6db2dp-5L, -0xb.26cb4ffd560a9d3p-9L, 0x8.47e7da3c1fd3e92p-8L, -0xa.f0ff7b0c2d7cb32p-13L, -0xc.c26d0844ba1cb28p-20L, 0x0p+0L};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0L, 0x9.162e5c69f91da28p-2L, -0xc.1e6503d1f56bc54p-1L, 0xa.9228b92035bbe8fp-1L, -0x9.6886dd231fe0c2p-3L, -0xa.a4fa62f0279cc8ap-4L, 0xc.41564814eee395ap-5L, -0x9.eae876d196c5b0fp-8L, -0xb.2e6e03767b2a39ap-14L, -0x0p+0L};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0L, 0xc.c3bd64937d9deedp-2L, -0xa.4613d385c9e6eeep+0L, 0xf.bfefb0422e7dd11p-1L, 0x8.58f50772fcf6838p+0L, -0x8.ad579c56d0b531bp+1L, 0xa.522820dc8f0dd92p+0L, -0x8.2809a404096fa64p-2L, -0x8.9f72308a7ec28cep-7L, -0x0p+0L};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0L, 0x8.9dcf4627ee27fcfp-4L, -0xf.0f2f2e7e85400fbp-3L, 0x9.4d59764326a2533p-2L, -0x9.eb6630f07b521f1p-3L, 0x8.113fb95513bed76p-4L, -0xc.d6d15354d10bf47p-5L, 0x9.6346d1c49e6ae26p-6L, 0x8.d336e36967df815p-10L, 0x0p+0L};
+            }
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            if constexpr (order == 0) {
+                return {0x0p+0Q, 0x1.646bf1ec64a308c5df07d89c8e9ap-1Q, 0x1.cbd5c1bab5148530b0e77ecbff8fp-2Q, -0x1.754196833f706c7834855fa5579ap-3Q, 0x1.3100cab7c3f5f4fa75b80a67ed4ap-5Q, 0x1.8dd2be8c89c51e7b28b04315345ap-10Q, -0x1.c4ab558ff2dcebdfdc6142054ddfp-10Q, 0x1.3b27d2d798eecea1adaf099c04dp-15Q, 0x1.75f2b16626e9875840e692dcf345p-23Q, 0x0p+0Q};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0Q, 0x1.8eee7927087b240ec5ade1ac8194p+0Q, -0x1.37cf445237f1b72a99ae1be26162p+1Q, 0x1.3c64475174b4a0c9b8a3ee3dfc17p+0Q, -0x1.7841978e876db6599aa4ad109929p-2Q, -0x1.64d969ffaac153a6af06dc9cfb6cp-6Q, 0x1.08fcfb4783fa7d234eba36053963p-5Q, -0x1.5e1fef6185af966378a125175a7ap-10Q, -0x1.984da1089743964ff5ac0959c3cp-17Q, 0x0p+0Q};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0Q, 0x1.22c5cb8d3f23b44faf592c365fa4p+1Q, -0x1.83cca07a3ead78a73330d7cf1ab1p+2Q, 0x1.5245172406b77d1d4fdfd2192e03p+2Q, -0x1.2d10dba463fc1840fd45963c56f2p+0Q, -0x1.549f4c5e04f3991456e630b15647p-1Q, 0x1.882ac9029ddc72b4c74d388daa79p-2Q, -0x1.3d5d0eda32d8b61e7ff27a395996p-5Q, -0x1.65cdc06ecf6547344a6a8d5280b2p-11Q, -0x0p+0Q};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0Q, 0x1.9877ac926fb3bdd992f46d8483bfp+1Q, -0x1.48c27a70b93cdddc043571f4721ap+3Q, 0x1.f7fdf60845cfba22e0c6bd0437bdp+2Q, 0x1.0b1ea0ee5f9ed06f5107d79a0311p+3Q, -0x1.15aaf38ada16a6358cd77355dd37p+4Q, 0x1.4a45041b91e1bb24fe9a63ad0148p+3Q, -0x1.05013480812df4c7388d78da948bp+1Q, -0x1.13ee46114fd8519c5d7f29b7c3fap-4Q, -0x0p+0Q};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0Q, 0x1.13b9e8c4fdc4ff9d9c7b93fda525p-1Q, -0x1.e1e5e5cfd0a801f531eaef0fe568p+0Q, 0x1.29ab2ec864d44a65c8f8abfdaaf8p+1Q, -0x1.3d6cc61e0f6a43e21f6553d106aap+0Q, 0x1.0227f72aa277daecfc1fddb3c489p-1Q, -0x1.9ada2a6a9a217e8dbe2b55c6b9fep-2Q, 0x1.2c68da3893cd5c4c84ac50c60e4ep-3Q, 0x1.1a66dc6d2cfbf029033eb2e703a5p-7Q, 0x0p+0Q};
+            }
+        }
+        #endif
+    }
+    if constexpr (p == 6) {
+        if constexpr (std::is_same_v<Real, float>) {
+            if constexpr (order == 0) {
+                return {0x0p+0f, 0x1.bf65e8p-2f, 0x1.aa2466p-1f, -0x1.89fd1p-2f, 0x1.24737ep-3f, -0x1.a1e9c8p-6f, -0x1.cec09ap-9f, 0x1.cd4fecp-10f, 0x1.05937cp-16f, -0x1.5a00dp-19f, 0x1.0fbc42p-28f, -0x0p+0f};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0f, 0x1.2faeacp+0f, -0x1.801498p+0f, 0x1.050336p-1f, -0x1.0ffe44p-2f, 0x1.0b11b2p-4f, 0x1.721a1ep-7f, -0x1.af662cp-8f, -0x1.a69b86p-15f, 0x1.45b126p-16f, -0x1.018922p-24f, 0x0p+0f};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0f, 0x1.1e62dep+1f, -0x1.980b4p+2f, 0x1.a34deap+2f, -0x1.45eb5ep+1f, -0x1.0310f6p-1f, 0x1.da7724p-1f, -0x1.4137dp-2f, 0x1.7eb866p-6f, 0x1.4ebb22p-9f, -0x1.0c5bep-16f, -0x0p+0f};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0f, 0x1.422fap-2f, -0x1.255a76p+0f, 0x1.484b54p+3f, -0x1.3c98d8p+5f, 0x1.10b7fap+6f, -0x1.d54dd2p+5f, 0x1.804948p+4f, -0x1.77f884p+1f, -0x1.d3687ap-2f, 0x1.816ef8p-8f, -0x0p+0f};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0f, 0x1.8faefp+0f, -0x1.93816ep+2f, 0x1.33788p+3f, -0x1.c3f2cep+2f, 0x1.c7801ep+1f, -0x1.46377ep+1f, 0x1.77a6f6p+0f, -0x1.c41888p-3f, -0x1.f8b0a6p-5f, 0x1.b96594p-10f, -0x0p+0f};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0f, 0x1.cb9194p-2f, -0x1.e6b982p+0f, 0x1.7b2e48p+1f, -0x1.fa645ep+0f, 0x1.29da94p-1f, -0x1.8461e6p-2f, 0x1.67c138p-2f, -0x1.c1a09cp-5f, -0x1.0c11f4p-5f, 0x1.0ac90ap-9f, 0x0p+0f};
+            }
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0, 0x1.bf65e79817d28p-2, 0x1.aa2466d50e4a5p-1, -0x1.89fd104c6ff15p-2, 0x1.24737e6f8ebf1p-3, -0x1.a1e9c758a51a1p-6, -0x1.cec09a7ccf05bp-9, 0x1.cd4feb82d2494p-10, 0x1.05937b8388af2p-16, -0x1.5a00cfad970a8p-19, 0x1.0fbc42c672231p-28, -0x0p+0};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0, 0x1.2faeacbb8e754p+0, -0x1.8014975295b21p+0, 0x1.05033635f5402p-1, -0x1.0ffe44cc8bc7fp-2, 0x1.0b11b28c7d67bp-4, 0x1.721a1d14b8323p-7, -0x1.af662c52c3b7bp-8, -0x1.a69b860b67a33p-15, 0x1.45b12643cf82p-16, -0x1.01892163486cbp-24, 0x0p+0};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0, 0x1.1e62ddd540b06p+1, -0x1.980b3fe2011f8p+2, 0x1.a34dea8cd59b4p+2, -0x1.45eb5e5e7e3cap+1, -0x1.0310f5a5d86dep-1, 0x1.da7724c65802cp-1, -0x1.4137cfe85b9e6p-2, 0x1.7eb866ddca6bap-6, 0x1.4ebb22d1ac076p-9, -0x1.0c5bdfb916a45p-16, -0x0p+0};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0, 0x1.422f9f5227e8p-2, -0x1.255a76df553ccp+0, 0x1.484b537c56dedp+3, -0x1.3c98d8a74cd77p+5, 0x1.10b7f9c607064p+6, -0x1.d54dd14cd31afp+5, 0x1.8049478b6740dp+4, -0x1.77f8847acd28bp+1, -0x1.d3687a3bc3933p-2, 0x1.816ef86832622p-8, -0x0p+0};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0, 0x1.8faeef62b3a8p+0, -0x1.93816e52ba1c8p+2, 0x1.337880b3a9a71p+3, -0x1.c3f2cd3d53133p+2, 0x1.c7801db767804p+1, -0x1.46377db27f625p+1, 0x1.77a6f5e8321cdp+0, -0x1.c4188733407f2p-3, -0x1.f8b0a606c7f79p-5, 0x1.b965933f534b2p-10, -0x0p+0};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0, 0x1.cb91942378a6bp-2, -0x1.e6b982120ca32p+0, 0x1.7b2e4714b2703p+1, -0x1.fa645ee8ca231p+0, 0x1.29da9349c32a2p-1, -0x1.8461e6acf9cb3p-2, 0x1.67c137342024dp-2, -0x1.c1a09b7773a5ap-5, -0x1.0c11f4efd5c0bp-5, 0x1.0ac90a45b7a47p-9, 0x0p+0};
+            }
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0L, 0xd.fb2f3cc0be93e54p-5L, 0xd.512336a872527e6p-4L, -0xc.4fe882637f8a4ep-5L, 0x9.239bf37c75f8764p-6L, -0xd.0f4e3ac528d0419p-9L, -0xe.7604d3e6782db77p-12L, 0xe.6a7f5c169249c7ap-13L, 0x8.2c9bdc1c4579256p-19L, -0xa.d0067d6cb853e5ep-22L, 0x8.7de216339118a43p-31L, -0x0p+0L};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0L, 0x9.7d7565dc73a9dap-3L, -0xc.00a4ba94ad909b7p-3L, 0x8.2819b1afaa00e4ep-4L, -0x8.7ff226645e3f525p-5L, 0x8.588d9463eb3d6b2p-7L, 0xb.90d0e8a5c191592p-10L, -0xd.7b3162961dbd72bp-11L, -0xd.34dc305b3d198bdp-18L, 0xa.2d89321e7c101dfp-19L, -0x8.0c490b1a4365a0ep-27L, 0x0p+0L};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0L, 0x8.f316eeaa0582d86p-2L, -0xc.c059ff1008fbde4p-1L, 0xd.1a6f5466acda0c4p-1L, -0xa.2f5af2f3f1e4f4dp-2L, -0x8.1887ad2ec36f306p-4L, 0xe.d3b92632c015e4bp-4L, -0xa.09be7f42dcf2d82p-5L, 0xb.f5c336ee535d213p-9L, 0xa.75d9168d603b071p-12L, -0x8.62defdc8b5224edp-19L, -0x0p+0L};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0L, 0xa.117cfa913f3fd65p-5L, -0x9.2ad3b6faa9e5fc2p-3L, 0xa.425a9be2b6f651fp+0L, -0x9.e4c6c53a66bb9b6p+2L, 0x8.85bfce3038320c3p+3L, -0xe.aa6e8a6698d7b2fp+2L, 0xc.024a3c5b3a06863p+1L, -0xb.bfc423d6694569bp-2L, -0xe.9b43d1de1c99addp-5L, 0xc.0b77c3419310f5ep-11L, -0x0p+0L};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0L, 0xc.7d777b159d3fe93p-3L, -0xc.9c0b7295d0e4242p-1L, 0x9.9bc4059d4d38bf3p+0L, -0xe.1f9669ea9899554p-1L, 0xe.3c00edbb3c02374p-2L, -0xa.31bbed93fb124adp-2L, 0xb.bd37af4190e69cdp-3L, -0xe.20c4399a03f920dp-6L, -0xf.c58530363fbca91p-8L, 0xd.cb2c99fa9a58d79p-13L, -0x0p+0L};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0L, 0xe.5c8ca11bc53594fp-5L, -0xf.35cc10906518e34p-3L, 0xb.d97238a59381a17p-2L, -0xf.d322f7465118802p-3L, 0x9.4ed49a4e1950cdfp-4L, -0xc.230f3567ce5957dp-5L, 0xb.3e09b9a10126b64p-5L, -0xe.0d04dbbb9d2ce8dp-8L, -0x8.608fa77eae05beap-8L, 0x8.5648522dbd23badp-12L, 0x0p+0L};
+            }
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            if constexpr (order == 0) {
+                return {0x0p+0Q, 0x1.bf65e79817d27ca7c78972c65f34p-2Q, 0x1.aa2466d50e4a4fcbbebe54f94c37p-1Q, -0x1.89fd104c6ff149bf7514a7ddf379p-2Q, 0x1.24737e6f8ebf0ec8bb9fcc85bb6cp-3Q, -0x1.a1e9c758a51a08321aa63e9af1d2p-6Q, -0x1.cec09a7ccf05b6ee1ea8f3c17f38p-9Q, 0x1.cd4feb82d24938f30e41e1af2e9p-10Q, 0x1.05937b8388af24ac43ec83967a3ap-16Q, -0x1.5a00cfad970a7cbc309138fd3f9dp-19Q, 0x1.0fbc42c672231485a0bcbfe7e33cp-28Q, -0x0p+0Q};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0Q, 0x1.2faeacbb8e753b40eb856e00f52fp+0Q, -0x1.8014975295b2136d5a1adb45438cp+0Q, 0x1.05033635f5401c9b60636a325269p-1Q, -0x1.0ffe44cc8bc7ea4a6ce4734d8d3ap-2Q, 0x1.0b11b28c7d67ad63229fbc3aa7e2p-4Q, 0x1.721a1d14b8322b2431432e8b8011p-7Q, -0x1.af662c52c3b7ae55063672df3c81p-8Q, -0x1.a69b860b67a33179a8c7a5f6b347p-15Q, 0x1.45b12643cf8203bdf796367d51ecp-16Q, -0x1.01892163486cb41cb64453f7616bp-24Q, 0x0p+0Q};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0Q, 0x1.1e62ddd540b05b0cc5ce5870089ep+1Q, -0x1.980b3fe2011f7bc878be7d3998f1p+2Q, 0x1.a34dea8cd59b4187717c6efb0807p+2Q, -0x1.45eb5e5e7e3c9e9ae26ca4aa21b4p+1Q, -0x1.0310f5a5d86de60ba877dea68891p-1Q, 0x1.da7724c65802bc95482213f98417p-1Q, -0x1.4137cfe85b9e5b04e10239758ca5p-2Q, 0x1.7eb866ddca6ba425f9e4eb854dbfp-6Q, 0x1.4ebb22d1ac0760e1461881059b61p-9Q, -0x1.0c5bdfb916a449da5acc3ccfdf5cp-16Q, -0x0p+0Q};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0Q, 0x1.422f9f5227e7facaa94dd7e1c4ccp-2Q, -0x1.255a76df553cbf84e8a0b06861f6p+0Q, 0x1.484b537c56deca3daefc656e764dp+3Q, -0x1.3c98d8a74cd7736b60af4e5f5a22p+5Q, 0x1.10b7f9c607064185ab2dfc57477p+6Q, -0x1.d54dd14cd31af65e5343fc85bc89p+5Q, 0x1.8049478b6740d0c6b0100478b786p+4Q, -0x1.77f8847acd28ad3549099ae0cd55p+1Q, -0x1.d3687a3bc39335bac7f281e5e3cfp-2Q, 0x1.816ef86832621ebc63e47cd17f95p-8Q, -0x0p+0Q};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0Q, 0x1.8faeef62b3a7fd26eb98dd7f9293p+0Q, -0x1.93816e52ba1c8483ff81ea3e2cbfp+2Q, 0x1.337880b3a9a717e67b9cd7fec3d9p+3Q, -0x1.c3f2cd3d53132aa78f87aee06f97p+2Q, 0x1.c7801db7678046e8ebdb22cf5b9fp+1Q, -0x1.46377db27f624959a2b9b7777544p+1Q, 0x1.77a6f5e8321cd39a930db3902d99p+0Q, -0x1.c4188733407f241acae534ed07ffp-3Q, -0x1.f8b0a606c7f795229d5947447259p-5Q, 0x1.b965933f534b1af276b67227f5edp-10Q, -0x0p+0Q};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0Q, 0x1.cb91942378a6b29e2dd51c51c663p-2Q, -0x1.e6b982120ca31c68b89329c09f76p+0Q, 0x1.7b2e4714b270342ea6ba89978b55p+1Q, -0x1.fa645ee8ca231003817fbe32abe9p+0Q, 0x1.29da9349c32a19bed5b810cc5091p-1Q, -0x1.8461e6acf9cb2af90934d76c7fc3p-2Q, 0x1.67c137342024d6c8052e3d87701ap-2Q, -0x1.c1a09b7773a59d1a65f356774442p-5Q, -0x1.0c11f4efd5c0b7d44ac1c3a07541p-5Q, 0x1.0ac90a45b7a47759a7a92738ff23p-9Q, 0x0p+0Q};
+            }
+        }
+        #endif
+    }
+    if constexpr (p == 7) {
+        if constexpr (std::is_same_v<Real, float>) {
+            if constexpr (order == 0) {
+                return {0x0p+0f, 0x1.033292p-2f, 0x1.027f6cp+0f, -0x1.919d92p-2f, 0x1.7a0caap-3f, -0x1.1142c4p-4f, 0x1.50e2d6p-7f, 0x1.d0243ap-10f, -0x1.1d4c6cp-11f, -0x1.17d0b4p-14f, 0x1.310ffep-19f, -0x1.509d12p-25f, -0x1.57f8e6p-36f, -0x0p+0f};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0f, 0x1.9ec434p-1f, -0x1.ca0692p-2f, -0x1.2d988ap-1f, 0x1.145888p-2f, -0x1.4ab3dp-6f, -0x1.4e8938p-5f, 0x1.5cb5dep-6f, -0x1.051eecp-8f, 0x1.0efaecp-14f, 0x1.6a87a6p-15f, -0x1.4e8b2ap-23f, -0x1.54fd9p-33f, -0x0p+0f};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0f, 0x1.e0eaccp+0f, -0x1.5362d8p+2f, 0x1.70aa18p+2f, -0x1.86bc52p+1f, 0x1.570932p-2f, 0x1.9d599ap-1f, -0x1.18b244p-1f, 0x1.fe16d2p-4f, 0x1.eb4ccap-12f, -0x1.4e09dp-9f, 0x1.c4a78ap-16f, 0x1.cb0cccp-25f, -0x0p+0f};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0f, 0x1.4ca934p-1f, -0x1.492e7p+1f, 0x1.171de6p+4f, -0x1.1e704ep+6f, 0x1.23bcc4p+7f, -0x1.415156p+7f, 0x1.7ff792p+6f, -0x1.a43b42p+4f, 0x1.833e7p-4f, 0x1.13b5aap+0f, -0x1.6365bp-6f, -0x1.64d198p-14f, 0x0p+0f};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0f, 0x1.525f0cp+1f, -0x1.7eda4cp+3f, 0x1.578438p+4f, -0x1.40c582p+4f, 0x1.9815ccp+3f, -0x1.22247ap+3f, 0x1.8c2cccp+2f, -0x1.ffd4fcp+0f, -0x1.3be428p-3f, 0x1.7c490ep-3f, -0x1.23f976p-7f, -0x1.1f66b2p-14f, -0x0p+0f};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0f, 0x1.80a316p+0f, -0x1.ce7e68p+2f, 0x1.ac8b3cp+3f, -0x1.74c81ep+3f, 0x1.4010d2p+2f, -0x1.34da8p+1f, 0x1.2d09cap+1f, -0x1.97de12p-1f, -0x1.9df5b4p-2f, 0x1.16c54ap-2f, -0x1.e323c6p-6f, -0x1.c9a574p-12f, 0x0p+0f};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0f, 0x1.a096c8p-3f, -0x1.01d8c8p+0f, 0x1.099a08p+1f, -0x1.40ce38p+1f, 0x1.2a5764p+1f, -0x1.e6f03p+0f, 0x1.3544c2p+0f, -0x1.6af582p-1f, 0x1.256afep-1f, -0x1.656934p-2f, 0x1.4b884p-4f, 0x1.24061ep-9f, 0x0p+0f};
+            }
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0, 0x1.033291a6c76d7p-2, 0x1.027f6bf7952cep+0, -0x1.919d92c6034c4p-2, 0x1.7a0ca906acc48p-3, -0x1.1142c3515ec43p-4, 0x1.50e2d6421ee26p-7, 0x1.d0243aab613f8p-10, -0x1.1d4c6c249bf0fp-11, -0x1.17d0b3032ba5cp-14, 0x1.310ffd8b56401p-19, -0x1.509d126dab99dp-25, -0x1.57f8e69552537p-36, -0x0p+0};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0, 0x1.9ec434341eaeep-1, -0x1.ca0692ca7743ap-2, -0x1.2d988a986b0dfp-1, 0x1.145887eacb11p-2, -0x1.4ab3cf0bae2a6p-6, -0x1.4e8938899ee37p-5, 0x1.5cb5de436bfaep-6, -0x1.051eebbefaf7cp-8, 0x1.0efaec65edbccp-14, 0x1.6a87a6b931edcp-15, -0x1.4e8b2a27fe065p-23, -0x1.54fd8f0625f12p-33, -0x0p+0};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0, 0x1.e0eacca617ebcp+0, -0x1.5362d7fe36c57p+2, 0x1.70aa17b7adc0ep+2, -0x1.86bc52429f3a4p+1, 0x1.5709310e8d1f6p-2, 0x1.9d599937b31fbp-1, -0x1.18b244e50df67p-1, 0x1.fe16d1a3cfb3ep-4, 0x1.eb4cc917dd1cdp-12, -0x1.4e09cf12f0cddp-9, 0x1.c4a78957d2798p-16, 0x1.cb0ccbca08e79p-25, -0x0p+0};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0, 0x1.4ca9343b32368p-1, -0x1.492e70f2635c1p+1, 0x1.171de5ca88cecp+4, -0x1.1e704d84a1075p+6, 0x1.23bcc34d6a52ap+7, -0x1.415156a34428ap+7, 0x1.7ff7929036dddp+6, -0x1.a43b4147c122cp+4, 0x1.833e6f5afaca5p-4, 0x1.13b5aaaf6c71dp+0, -0x1.6365af2495a87p-6, -0x1.64d19861a8338p-14, 0x0p+0};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0, 0x1.525f0cb11c272p+1, -0x1.7eda4b6a23329p+3, 0x1.578437542fe4fp+4, -0x1.40c582473fa8dp+4, 0x1.9815cb7223c1p+3, -0x1.222479cd96eeap+3, 0x1.8c2cccc6ee34dp+2, -0x1.ffd4fb5b3918p+0, -0x1.3be427404fe7dp-3, 0x1.7c490d447fad3p-3, -0x1.23f9756392d0fp-7, -0x1.1f66b1e781529p-14, -0x0p+0};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0, 0x1.80a316d21a0efp+0, -0x1.ce7e682714367p+2, 0x1.ac8b3ccd718c4p+3, -0x1.74c81d1a27df6p+3, 0x1.4010d1eedca9ap+2, -0x1.34da807d2aaedp+1, 0x1.2d09c9846b582p+1, -0x1.97de12ea03ca1p-1, -0x1.9df5b4fe2e272p-2, 0x1.16c54a229aae1p-2, -0x1.e323c5b92bd16p-6, -0x1.c9a573f22c19bp-12, 0x0p+0};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0, 0x1.a096c8f7fc8abp-3, -0x1.01d8c748e11fap+0, 0x1.099a073a7c7b4p+1, -0x1.40ce386ca776ep+1, 0x1.2a57634989c52p+1, -0x1.e6f030cb23fcp+0, 0x1.3544c2755b1d8p+0, -0x1.6af581a622d41p-1, 0x1.256afda077268p-1, -0x1.6569331439298p-2, 0x1.4b88409bdd117p-4, 0x1.24061e2653bdbp-9, 0x0p+0};
+            }
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0L, 0x8.19948d363b6b511p-5L, 0x8.13fb5fbca966de8p-3L, -0xc.8cec96301a62254p-5L, 0xb.d0654835662420dp-6L, -0x8.8a161a8af621982p-7L, 0xa.8716b210f7132a1p-10L, 0xe.8121d55b09fc1bcp-13L, -0x8.ea636124df87704p-14L, -0x8.be8598195d2e2f7p-17L, 0x9.887fec5ab2008edp-22L, -0xa.84e8936d5cce758p-28L, -0xa.bfc734aa929b8c7p-39L, -0x0p+0L};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0L, 0xc.f621a1a0f576c66p-4L, -0xe.50349653ba1cf48p-5L, -0x9.6cc454c3586f53bp-4L, 0x8.a2c43f565887ceap-5L, -0xa.559e785d7152dc2p-9L, -0xa.7449c44cf71b8f2p-8L, 0xa.e5aef21b5fd6dcfp-9L, -0x8.28f75df7d7bdeb9p-11L, 0x8.77d7632f6de608ep-17L, 0xb.543d35c98f6e2d6p-18L, -0xa.7459513ff03276p-26L, -0xa.a7ec78312f88c67p-36L, -0x0p+0L};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0L, 0xf.07566530bf5dc3p-3L, -0xa.9b16bff1b62b5b5p-1L, 0xb.8550bdbd6e073adp-1L, -0xc.35e29214f9d1fbdp-2L, 0xa.b849887468fb1bp-5L, 0xc.eaccc9bd98fd7eap-4L, -0x8.c59227286fb3ad2p-4L, 0xf.f0b68d1e7d9f3f6p-7L, 0xf.5a6648bee8e6ab7p-15L, -0xa.704e7897866e7ecp-12L, 0xe.253c4abe93cc026p-19L, 0xe.58665e50473cb0fp-28L, -0x0p+0L};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0L, 0xa.6549a1d991b412ap-4L, -0xa.497387931ae0b61p-2L, 0x8.b8ef2e544676158p+1L, -0x8.f3826c25083a83ap+3L, 0x9.1de61a6b5294d86p+4L, -0xa.0a8ab51a2145353p+4L, 0xb.ffbc9481b6eebc6p+3L, -0xd.21da0a3e0916379p+1L, 0xc.19f37ad7d65262bp-7L, 0x8.9dad557b638eaddp-3L, -0xb.1b2d7924ad4363p-9L, -0xb.268cc30d419bc95p-17L, 0x0p+0L};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0L, 0xa.92f86588e139024p-2L, -0xb.f6d25b5119947a7p+0L, 0xa.bc21baa17f27afep+1L, -0xa.062c1239fd4649cp+1L, 0xc.c0ae5b911e082dep+0L, -0x9.1123ce6cb774e8cp+0L, 0xc.6166663771a6508p-1L, -0xf.fea7dad9c8c0222p-3L, -0x9.df213a027f3e892p-6L, 0xb.e2486a23fd69714p-6L, -0x9.1fcbab1c968774dp-10L, -0x8.fb358f3c0a94afap-17L, -0x0p+0L};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0L, 0xc.0518b690d0776a4p-3L, -0xe.73f34138a1b3bfep-1L, 0xd.6459e66b8c620fp+0L, -0xb.a640e8d13efae1ap+0L, 0xa.00868f76e54ce56p-1L, -0x9.a6d403e95576488p-2L, 0x9.684e4c235ac0d81p-2L, -0xc.bef097501e50849p-4L, -0xc.efada7f17138d13p-5L, 0x8.b62a5114d570977p-5L, -0xf.191e2dc95e8b372p-9L, -0xe.4d2b9f9160cd482p-15L, 0x0p+0L};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0L, 0xd.04b647bfe4558acp-6L, -0x8.0ec63a4708fd39bp-3L, 0x8.4cd039d3e3da0c5p-2L, -0xa.0671c3653bb7036p-2L, 0x9.52bb1a4c4e28fdbp-2L, -0xf.378186591fdfef3p-3L, 0x9.aa2613aad8ec175p-3L, -0xb.57ac0d3116a0b56p-4L, 0x9.2b57ed03b933f03p-4L, -0xb.2b4998a1c94bea3p-5L, 0xa.5c4204dee88b95dp-7L, 0x9.2030f1329ded9e3p-12L, 0x0p+0L};
+            }
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            if constexpr (order == 0) {
+                return {0x0p+0Q, 0x1.033291a6c76d6a2177301a6491ep-2Q, 0x1.027f6bf7952cdbcf397ade5b83a2p+0Q, -0x1.919d92c6034c44a7ed45a5787141p-2Q, 0x1.7a0ca906acc4841a1191b023a48bp-3Q, -0x1.1142c3515ec433047c393c69963p-4Q, 0x1.50e2d6421ee2654230b30972367cp-7Q, 0x1.d0243aab613f83777184da54a816p-10Q, -0x1.1d4c6c249bf0ee08cde9105ae0e7p-11Q, -0x1.17d0b3032ba5c5edbe3115298754p-14Q, 0x1.310ffd8b564011dafec30497e54dp-19Q, -0x1.509d126dab99ceafee21c5b15f2dp-25Q, -0x1.57f8e6955253718d03dd42dcc05dp-36Q, -0x0p+0Q};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0Q, 0x1.9ec434341eaed8ccc6e8d7244a2p-1Q, -0x1.ca0692ca77439e8f752ca148c129p-2Q, -0x1.2d988a986b0dea756341b6b8b7c1p-1Q, 0x1.145887eacb10f9d392eed69a933p-2Q, -0x1.4ab3cf0bae2a5b8432a0a18163adp-6Q, -0x1.4e8938899ee371e40cd7b7528ae1p-5Q, 0x1.5cb5de436bfadb9e555d33c55725p-6Q, -0x1.051eebbefaf7bd71954e297a6202p-8Q, 0x1.0efaec65edbcc11b181ba7073ddfp-14Q, 0x1.6a87a6b931edc5ab5423dbf1bacbp-15Q, -0x1.4e8b2a27fe064ec01f6271830448p-23Q, -0x1.54fd8f0625f118cd9bcdded88df8p-33Q, -0x0p+0Q};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0Q, 0x1.e0eacca617ebb860573873f7b257p+0Q, -0x1.5362d7fe36c56b6a443e9d614224p+2Q, 0x1.70aa17b7adc0e75a9ffe0b5a343p+2Q, -0x1.86bc52429f3a3f79bb4f1cb737ebp+1Q, 0x1.5709310e8d1f635f77e733f3171p-2Q, 0x1.9d599937b31fafd3d66db2bf1cfap-1Q, -0x1.18b244e50df675a487d76601b122p-1Q, 0x1.fe16d1a3cfb3e7ecc6834f20623cp-4Q, 0x1.eb4cc917dd1cd56dce6a9280b19ap-12Q, -0x1.4e09cf12f0cdcfd873bae55835b6p-9Q, 0x1.c4a78957d279804ccd5115f614bcp-16Q, 0x1.cb0ccbca08e7961d7bc2f676b681p-25Q, -0x0p+0Q};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0Q, 0x1.4ca9343b3236825367445e1bcc76p-1Q, -0x1.492e70f2635c16c262e618fc71c9p+1Q, 0x1.171de5ca88cec2afbea54998e4afp+4Q, -0x1.1e704d84a10750732762c3f7a7d9p+6Q, 0x1.23bcc34d6a529b0b422faf6a8faap+7Q, -0x1.415156a34428a6a6c08cde81cb46p+7Q, 0x1.7ff7929036ddd78bf54cfc3c1e07p+6Q, -0x1.a43b4147c122c6f143d7b5960278p+4Q, 0x1.833e6f5afaca4c566ce5985f38e4p-4Q, 0x1.13b5aaaf6c71d5b914583e4be0c9p+0Q, -0x1.6365af2495a86c5f48d9bd1e4466p-6Q, -0x1.64d19861a833792a3ce80f88bd23p-14Q, 0x0p+0Q};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0Q, 0x1.525f0cb11c2720485c66b9e1a4ecp+1Q, -0x1.7eda4b6a23328f4e2cec098f6dc4p+3Q, 0x1.578437542fe4f5fbe4cefec745eep+4Q, -0x1.40c582473fa8c93703a1216d1bfdp+4Q, 0x1.9815cb7223c105bc2b63ed01aaa9p+3Q, -0x1.222479cd96ee9d17f59bff4df756p+3Q, 0x1.8c2cccc6ee34ca0f24458389d70cp+2Q, -0x1.ffd4fb5b3918044492967474d7b2p+0Q, -0x1.3be427404fe7d12432d600f4467cp-3Q, 0x1.7c490d447fad2e27fa6b12a0df79p-3Q, -0x1.23f9756392d0ee9915448c1beeeap-7Q, -0x1.1f66b1e7815295f48755fd4e4048p-14Q, -0x0p+0Q};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0Q, 0x1.80a316d21a0eed480c84ea711c72p+0Q, -0x1.ce7e6827143677fbd12dabe06d43p+2Q, 0x1.ac8b3ccd718c41df56b9c167f4f2p+3Q, -0x1.74c81d1a27df5c33454de2219d72p+3Q, 0x1.4010d1eedca99cac8148c1188814p+2Q, -0x1.34da807d2aaec910bcf3aa770b5fp+1Q, 0x1.2d09c9846b581b01a4323f49dd86p+1Q, -0x1.97de12ea03ca10913f6e6b1c02a9p-1Q, -0x1.9df5b4fe2e271a26f87f7a1f7732p-2Q, 0x1.16c54a229aae12ed509d340baa4cp-2Q, -0x1.e323c5b92bd166e33ab5b4f96118p-6Q, -0x1.c9a573f22c19a9032c5430df4acdp-12Q, 0x0p+0Q};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0Q, 0x1.a096c8f7fc8ab1575820ee7aa2a9p-3Q, -0x1.01d8c748e11fa735da05e73f9139p+0Q, 0x1.099a073a7c7b41898468a5bd1aap+1Q, -0x1.40ce386ca776e06ba6f31ba7c1p+1Q, 0x1.2a57634989c51fb583fc11fbe69fp+1Q, -0x1.e6f030cb23fbfde6dfddcd331b76p+0Q, 0x1.3544c2755b1d82eac792a585c22cp+0Q, -0x1.6af581a622d416ac06a3c40afddbp-1Q, 0x1.256afda077267e050d8164de576cp-1Q, -0x1.6569331439297d46e21a065cd1e4p-2Q, 0x1.4b88409bdd1172b9682df895c7b5p-4Q, 0x1.24061e2653bdb3c5fd153e81e5dap-9Q, 0x0p+0Q};
+            }
+        }
+        #endif
+    }
+    if constexpr (p == 8) {
+        if constexpr (std::is_same_v<Real, float>) {
+            if constexpr (order == 0) {
+                return {0x0p+0f, 0x1.184a0cp-3f, 0x1.fbaa04p-1f, -0x1.596f5cp-3f, 0x1.234876p-4f, -0x1.90a568p-5f, 0x1.82b42ep-6f, -0x1.96b60cp-8f, 0x1.8430d2p-11f, -0x1.92df02p-14f, 0x1.da6faap-16f, 0x1.b237bcp-20f, 0x1.66eb1ap-25f, -0x1.f6ebd8p-33f, 0x1.569072p-45f, 0x0p+0f};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0f, 0x1.03034p-1f, 0x1.8347dap-2f, -0x1.7d2f18p+0f, 0x1.c3013ep-1f, -0x1.4be40ep-2f, 0x1.458036p-6f, 0x1.7e9e8ep-5f, -0x1.594cfap-6f, 0x1.27c566p-9f, 0x1.e972ap-12f, -0x1.1649ecp-14f, 0x1.c99c42p-23f, 0x1.81519ep-26f, -0x1.06b5eep-37f, -0x0p+0f};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0f, 0x1.666d54p+0f, -0x1.c03746p+1f, 0x1.a43ebap+1f, -0x1.d62736p+0f, 0x1.891e36p-1f, 0x1.a23c1ap-6f, -0x1.d9c16ep-3f, 0x1.b6728ep-4f, -0x1.66849cp-7f, -0x1.fc6302p-9f, 0x1.7e62aep-11f, -0x1.2c21cp-17f, -0x1.15f344p-21f, 0x1.7bbd84p-32f, 0x0p+0f};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0f, 0x1.b44c4ep+1f, -0x1.c1f7ep+3f, 0x1.1601a8p+4f, 0x1.e5bffcp+3f, -0x1.38f35cp+6f, 0x1.d1869cp+6f, -0x1.70d204p+6f, 0x1.34930ep+5f, -0x1.4b77b4p+2f, -0x1.d27f3cp+0f, 0x1.32a2c6p-1f, -0x1.2fc65p-7f, -0x1.c48022p-11f, 0x1.364c0ap-20f, -0x0p+0f};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0f, 0x1.afe05cp+1f, -0x1.0a8c44p+4f, 0x1.0f6c04p+5f, -0x1.306ff2p+5f, 0x1.da6956p+4f, -0x1.6a2c2p+4f, 0x1.0e28c8p+4f, -0x1.ee4b3cp+2f, 0x1.050e3ep-1f, 0x1.0ea6cap+0f, -0x1.6566f6p-2f, 0x1.0b828ap-6f, 0x1.3201b6p-10f, -0x1.a6f024p-19f, 0x0p+0f};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0f, 0x1.77885ep+1f, -0x1.f5abb2p+3f, 0x1.0a779ep+5f, -0x1.164dap+5f, 0x1.233374p+4f, -0x1.af306ap+2f, 0x1.6dba5cp+2f, -0x1.17ffcap+1f, -0x1.9f39e8p+1f, 0x1.d0d0a8p+1f, -0x1.4ac5cap+0f, 0x1.049fbp-3f, 0x1.5ad37ap-7f, -0x1.e6e9a6p-15f, -0x0p+0f};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0f, 0x1.1912b6p+0f, -0x1.85c00cp+2f, 0x1.b7d754p+3f, -0x1.076d5p+4f, 0x1.92a29ep+3f, -0x1.20f516p+3f, 0x1.dcba52p+2f, -0x1.3fe312p+2f, 0x1.5e9b74p+1f, -0x1.a6996ap+0f, 0x1.806826p-1f, -0x1.ddc83ep-4f, -0x1.e09e82p-7f, 0x1.5c5b72p-13f, -0x0p+0f};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0f, 0x1.eae802p-3f, -0x1.5a965ap+0f, 0x1.851aep+1f, -0x1.b139cp+1f, 0x1.ffefb8p+0f, -0x1.025406p+0f, 0x1.ff103cp-1f, -0x1.7a4f7p-1f, 0x1.09dce6p-2f, -0x1.c2f7cep-4f, 0x1.41c46cp-4f, -0x1.03531cp-6f, -0x1.c24ed2p-9f, 0x1.5d1ed8p-14f, -0x0p+0f};
+            }
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0, 0x1.184a0c288d22bp-3, 0x1.fbaa047a94a61p-1, -0x1.596f5b6b28cbp-3, 0x1.234875f46000ep-4, -0x1.90a568ef3b94bp-5, 0x1.82b42ea0f8a16p-6, -0x1.96b60b10e5956p-8, 0x1.8430d19335685p-11, -0x1.92df023007909p-14, 0x1.da6faa7679627p-16, 0x1.b237bc2c3b525p-20, 0x1.66eb1a28068aep-25, -0x1.f6ebd7398c4a4p-33, 0x1.5690727034a8ap-45, 0x0p+0};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0, 0x1.03033f41d9947p-1, 0x1.8347da7a3030cp-2, -0x1.7d2f17f2a95afp+0, 0x1.c3013eaebde94p-1, -0x1.4be40ed86f2cdp-2, 0x1.4580356ca34ffp-6, 0x1.7e9e8eefc30b4p-5, -0x1.594cf912461bcp-6, 0x1.27c56651be6eep-9, 0x1.e972a09b0f4ddp-12, -0x1.1649ec5e54141p-14, 0x1.c99c42a59648bp-23, 0x1.81519dee82fp-26, -0x1.06b5ee4f0712p-37, -0x0p+0};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0, 0x1.666d532df9dfp+0, -0x1.c0374596ee4d9p+1, 0x1.a43eb9f4500c3p+1, -0x1.d627359f84d25p+0, 0x1.891e36789053ap-1, 0x1.a23c19ecf2debp-6, -0x1.d9c16d05d7787p-3, 0x1.b6728d569b4c7p-4, -0x1.66849bebd2ebep-7, -0x1.fc6301aedca9p-9, 0x1.7e62ae52149bdp-11, -0x1.2c21c0130a3ebp-17, -0x1.15f344e8ed1b2p-21, 0x1.7bbd836b1bf85p-32, 0x0p+0};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0, 0x1.b44c4e267cbb5p+1, -0x1.c1f7df3ad7ab8p+3, 0x1.1601a8a979c79p+4, 0x1.e5bffb29b3c53p+3, -0x1.38f35bf0e9ee1p+6, 0x1.d1869b3f8e2b4p+6, -0x1.70d2038145a54p+6, 0x1.34930dde67aeap+5, -0x1.4b77b4fb36749p+2, -0x1.d27f3b25c1fd7p+0, 0x1.32a2c5a3dfe81p-1, -0x1.2fc64ff8d3421p-7, -0x1.c48021ad9bc16p-11, 0x1.364c0a7c4c64bp-20, -0x0p+0};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0, 0x1.afe05c7a6ada2p+1, -0x1.0a8c44cdd47bfp+4, 0x1.0f6c0325c5e14p+5, -0x1.306ff1c62c833p+5, 0x1.da69559cc9113p+4, -0x1.6a2c1f828fe2ep+4, 0x1.0e28c771588c3p+4, -0x1.ee4b3cc46d89p+2, 0x1.050e3e4d4732ap-1, 0x1.0ea6cad7a5a8p+0, -0x1.6566f5ac7d805p-2, 0x1.0b828ad29e43fp-6, 0x1.3201b5c3bc1c2p-10, -0x1.a6f0242017b15p-19, 0x0p+0};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0, 0x1.77885e6e270a7p+1, -0x1.f5abb22b1b6ecp+3, 0x1.0a779dee6c7bep+5, -0x1.164d9f148bde5p+5, 0x1.2333738e736f1p+4, -0x1.af306993826a7p+2, 0x1.6dba5c59397a4p+2, -0x1.17ffc928dd1d9p+1, -0x1.9f39e7400cf5dp+1, 0x1.d0d0a8f3b805ep+1, -0x1.4ac5cadf9fb15p+0, 0x1.049faf6ae6899p-3, 0x1.5ad3792bdac36p-7, -0x1.e6e9a51e3663ap-15, -0x0p+0};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0, 0x1.1912b6ad90d43p+0, -0x1.85c00c80d7a19p+2, 0x1.b7d753e3c818ap+3, -0x1.076d50e7f7851p+4, 0x1.92a29d7ac0e1ep+3, -0x1.20f516098425cp+3, 0x1.dcba519c323cfp+2, -0x1.3fe31292805cp+2, 0x1.5e9b74431b073p+1, -0x1.a6996ae95f76fp+0, 0x1.806826de1640bp-1, -0x1.ddc83de4acfafp-4, -0x1.e09e81650c6b7p-7, 0x1.5c5b71613d71bp-13, -0x0p+0};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0, 0x1.eae80165a34adp-3, -0x1.5a965a7535366p+0, 0x1.851adfd49d1a7p+1, -0x1.b139c010d5d8fp+1, 0x1.ffefb70380437p+0, -0x1.0254056f57104p+0, 0x1.ff103b26e087ep-1, -0x1.7a4f70cc2f5d8p-1, 0x1.09dce627745a6p-2, -0x1.c2f7ce5c8a37cp-4, 0x1.41c46b919c33fp-4, -0x1.03531c096423ap-6, -0x1.c24ed1e998c51p-9, 0x1.5d1ed72a09587p-14, -0x0p+0};
+            }
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0L, 0x8.c250614469156ecp-6L, 0xf.dd5023d4a530983p-4L, -0xa.cb7adb594658341p-6L, 0x9.1a43afa30007147p-7L, -0xc.852b4779dca57d6p-8L, 0xc.15a17507c50b09fp-9L, -0xc.b5b058872cab3ebp-11L, 0xc.21868c99ab4273bp-14L, -0xc.96f811803c8446bp-17L, 0xe.d37d53b3cb1391fp-19L, 0xd.91bde161da92bd9p-23L, 0xb.3758d14034571f5p-28L, -0xf.b75eb9cc6251d52p-36L, 0xa.b4839381a545259p-48L, 0x0p+0L};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0L, 0x8.1819fa0ecca3abdp-4L, 0xc.1a3ed3d18185c5ap-5L, -0xb.e978bf954ad7b4cp-3L, 0xe.1809f575ef4a37dp-4L, -0xa.5f2076c37966861p-5L, 0xa.2c01ab651a7f8e8p-9L, 0xb.f4f4777e185a2cbp-8L, -0xa.ca67c89230ddcadp-9L, 0x9.3e2b328df376c3ap-12L, 0xf.4b9504d87a6e47fp-15L, -0x8.b24f62f2a0a04dcp-17L, 0xe.4ce2152cb245585p-26L, 0xc.0a8cef7417800e8p-29L, -0x8.35af7278388fe4bp-40L, -0x0p+0L};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0L, 0xb.336a996fcef7c52p-3L, -0xe.01ba2cb7726c73bp-2L, 0xd.21f5cfa280614c9p-2L, -0xe.b139acfc2692864p-3L, 0xc.48f1b3c4829d099p-4L, 0xd.11e0cf6796f5a28p-9L, -0xe.ce0b682ebbc393bp-6L, 0xd.b3946ab4da635ap-7L, -0xb.3424df5e975efd8p-10L, -0xf.e3180d76e5481d1p-12L, 0xb.f3157290a4debfp-14L, -0x9.610e009851f575p-20L, -0x8.af9a274768d9303p-24L, 0xb.ddec1b58dfc26aap-35L, 0x0p+0L};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0L, 0xd.a2627133e5da6a2p-2L, -0xe.0fbef9d6bd5bcc5p+0L, 0x8.b00d454bce3c7c1p+1L, 0xf.2dffd94d9e295dcp+0L, -0x9.c79adf874f70573p+3L, 0xe.8c34d9fc715a214p+3L, -0xb.86901c0a2d2a313p+3L, 0x9.a4986ef33d75017p+2L, -0xa.5bbda7d9b3a4ab2p-1L, -0xe.93f9d92e0feb674p-3L, 0x9.95162d1eff408cfp-4L, -0x9.7e327fc69a10719p-10L, -0xe.24010d6cde0b23p-14L, 0x9.b26053e2632577ap-23L, -0x0p+0L};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0L, 0xd.7f02e3d356d0e5bp-2L, -0x8.5462266ea3dfa72p+1L, 0x8.7b60192e2f0a0a5p+2L, -0x9.837f8e316419b55p+2L, 0xe.d34aace64889869p+1L, -0xb.5160fc147f16c08p+1L, 0x8.71463b8ac46182cp+1L, -0xf.7259e6236c483c5p-1L, 0x8.2871f26a39950e3p-4L, 0x8.753656bd2d3fd71p-3L, -0xb.2b37ad63ec0243dp-5L, 0x8.5c145694f21f58cp-9L, 0x9.900dae1de0e10ep-13L, -0xd.37812100bd8a443p-22L, 0x0p+0L};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0L, 0xb.bc42f3713853a26p-2L, -0xf.ad5d9158db75d9ap+0L, 0x8.53bcef7363deeep+2L, -0x8.b26cf8a45ef2551p+2L, 0x9.199b9c739b78925p+1L, -0xd.79834c9c135345p-1L, 0xb.6dd2e2c9cbd2213p-1L, -0x8.bffe4946e8ec5f8p-2L, -0xc.f9cf3a0067ae91ap-2L, 0xe.8685479dc02ed7ep-2L, -0xa.562e56fcfd8a5e2p-3L, 0x8.24fd7b57344ca47p-6L, 0xa.d69bc95ed61ae29p-10L, -0xf.374d28f1b31ceb4p-18L, -0x0p+0L};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0L, 0x8.c895b56c86a1b02p-3L, -0xc.2e006406bd0c7e6p-1L, 0xd.beba9f1e40c4cbdp+0L, -0x8.3b6a873fbc285cap+1L, 0xc.9514ebd6070fp+0L, -0x9.07a8b04c212dd91p+0L, 0xe.e5d28ce191e76fcp-1L, -0x9.ff18949402e0231p-1L, 0xa.f4dba218d8396ddp-2L, -0xd.34cb574afbb77c5p-3L, 0xc.034136f0b2057f9p-4L, -0xe.ee41ef2567d7906p-7L, -0xf.04f40b28635ba7ep-10L, 0xa.e2db8b09eb8dbb5p-16L, -0x0p+0L};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0L, 0xf.57400b2d1a568f9p-6L, -0xa.d4b2d3a9a9b32a1p-3L, 0xc.28d6fea4e8d3b6dp-2L, -0xd.89ce0086aec77acp-2L, 0xf.ff7db81c021b9bdp-3L, -0x8.12a02b7ab881d9bp-3L, 0xf.f881d937043f115p-4L, -0xb.d27b86617aebd37p-4L, 0x8.4ee7313ba2d30a8p-5L, -0xe.17be72e451bdc7ep-7L, 0xa.0e235c8ce19f70ep-7L, -0x8.1a98e04b211d3d4p-9L, -0xe.12768f4cc6289abp-12L, 0xa.e8f6b9504ac38b3p-17L, -0x0p+0L};
+            }
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            if constexpr (order == 0) {
+                return {0x0p+0Q, 0x1.184a0c288d22add7ea26104df2f3p-3Q, 0x1.fbaa047a94a613069e6f550b4e0cp-1Q, -0x1.596f5b6b28cb0681bf78a3e54b76p-3Q, 0x1.234875f46000e28dce7c3f34208fp-4Q, -0x1.90a568ef3b94afacf755834bab9dp-5Q, 0x1.82b42ea0f8a1613dc5ff9725c04ep-6Q, -0x1.96b60b10e59567d6b2c6577bad37p-8Q, 0x1.8430d19335684e7577fd3b69976cp-11Q, -0x1.92df0230079088d5ad0746147157p-14Q, 0x1.da6faa767962723e71f08f2e9079p-16Q, 0x1.b237bc2c3b5257b1d937078b73a9p-20Q, 0x1.66eb1a28068ae3ea1bd5d268325dp-25Q, -0x1.f6ebd7398c4a3aa441e024a57151p-33Q, 0x1.5690727034a8a4b1353895ae261dp-45Q, 0x0p+0Q};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0Q, 0x1.03033f41d994757a2b4934423535p-1Q, 0x1.8347da7a3030b8b37cdc36ec3be2p-2Q, -0x1.7d2f17f2a95af6988be8eca125cap+0Q, 0x1.c3013eaebde946f9eaa42bce8cdbp-1Q, -0x1.4be40ed86f2cd0c168ad24949287p-2Q, 0x1.4580356ca34ff1cf3c18408b1ce2p-6Q, 0x1.7e9e8eefc30b45959dcb8ab52398p-5Q, -0x1.594cf912461bb959724fb77ad3c3p-6Q, 0x1.27c56651be6ed873712071c19326p-9Q, 0x1.e972a09b0f4dc8fdb93114f9ed2dp-12Q, -0x1.1649ec5e541409b8483ac00aa993p-14Q, 0x1.c99c42a59648ab096d412a5873a5p-23Q, 0x1.81519dee82f001d0cfd286a4bf35p-26Q, -0x1.06b5ee4f0711fc96e3337209d4fap-37Q, -0x0p+0Q};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0Q, 0x1.666d532df9def8a39e69d4c9dafcp+0Q, -0x1.c0374596ee4d8e750b0b0f065a7p+1Q, 0x1.a43eb9f4500c29913bdae70f2e18p+1Q, -0x1.d627359f84d250c8825852fe214cp+0Q, 0x1.891e36789053a132cb4397963b98p-1Q, 0x1.a23c19ecf2deb44f4177f3e94959p-6Q, -0x1.d9c16d05d77872764189280b3b87p-3Q, 0x1.b6728d569b4c6b3f03c9c20fd92ap-4Q, -0x1.66849bebd2ebdfafabb131376074p-7Q, -0x1.fc6301aedca903a123de4bcecb7dp-9Q, 0x1.7e62ae52149bd7e06a18746f5d38p-11Q, -0x1.2c21c0130a3eaea0bd3721b2b938p-17Q, -0x1.15f344e8ed1b26069acbf2a1a5a3p-21Q, 0x1.7bbd836b1bf84d53feb61580de7bp-32Q, 0x0p+0Q};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0Q, 0x1.b44c4e267cbb4d43745305f7f1d1p+1Q, -0x1.c1f7df3ad7ab79897dce80d6fdc1p+3Q, 0x1.1601a8a979c78f82e398ce85d132p+4Q, 0x1.e5bffb29b3c52bb885497a61677fp+3Q, -0x1.38f35bf0e9ee0ae5b17729526ffp+6Q, 0x1.d1869b3f8e2b44288688d26f2b6fp+6Q, -0x1.70d2038145a54625eb25d8766c13p+6Q, 0x1.34930dde67aea02e0a703b771d79p+5Q, -0x1.4b77b4fb3674956338abd182d2e5p+2Q, -0x1.d27f3b25c1fd6ce83b2a8b0b03e8p+0Q, 0x1.32a2c5a3dfe8119d379b7145ac19p-1Q, -0x1.2fc64ff8d3420e31f2a6dd484c8ap-7Q, -0x1.c48021ad9bc1646021c012f661fp-11Q, 0x1.364c0a7c4c64aef45189b313663dp-20Q, -0x0p+0Q};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0Q, 0x1.afe05c7a6ada1cb6172616d2f2ffp+1Q, -0x1.0a8c44cdd47bf4e495a5398430e1p+4Q, 0x1.0f6c0325c5e1414a9285f59e7d75p+5Q, -0x1.306ff1c62c8336aad5c3f9888cf8p+5Q, 0x1.da69559cc91130d28dd4b6368cc9p+4Q, -0x1.6a2c1f828fe2d81030f1ad526958p+4Q, 0x1.0e28c771588c30581ce7071755d2p+4Q, -0x1.ee4b3cc46d890789fa8b15b80159p+2Q, 0x1.050e3e4d4732a1c55c0c971f29e5p-1Q, 0x1.0ea6cad7a5a7fae2eab7d74b48fbp+0Q, -0x1.6566f5ac7d80487971d04a5977aep-2Q, 0x1.0b828ad29e43eb178f6b65b924cep-6Q, 0x1.3201b5c3bc1c21bf7086981d037bp-10Q, -0x1.a6f0242017b1488503cf0ef0a318p-19Q, 0x0p+0Q};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0Q, 0x1.77885e6e270a744c868654d77bep+1Q, -0x1.f5abb22b1b6ebb333fd9f11e28cbp+3Q, 0x1.0a779dee6c7bddbff2f0d8b96185p+5Q, -0x1.164d9f148bde4aa13b66fabb8275p+5Q, 0x1.2333738e736f124a0ec3de55d4acp+4Q, -0x1.af306993826a689f7543995743eap+2Q, 0x1.6dba5c59397a4426e98586a9dbfbp+2Q, -0x1.17ffc928dd1d8bf0f209d0c25564p+1Q, -0x1.9f39e7400cf5d234f22720c7e994p+1Q, 0x1.d0d0a8f3b805dafc2d2b539dd42dp+1Q, -0x1.4ac5cadf9fb14bc48382ff0eff77p+0Q, 0x1.049faf6ae689948e66d5e513815cp-3Q, 0x1.5ad3792bdac35c5163486d90e7a1p-7Q, -0x1.e6e9a51e36639d68c6db7d754f12p-15Q, -0x0p+0Q};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0Q, 0x1.1912b6ad90d43603284e2902f0abp+0Q, -0x1.85c00c80d7a18fcc693e4762b85p+2Q, 0x1.b7d753e3c818997a04ded98db7dep+3Q, -0x1.076d50e7f7850b94ae780b4ac761p+4Q, 0x1.92a29d7ac0e1e0002558af84767fp+3Q, -0x1.20f516098425bb22664ce4abb09dp+3Q, 0x1.dcba519c323cedf78dcb77920137p+2Q, -0x1.3fe31292805c0462ca96ae1f196p+2Q, 0x1.5e9b74431b072dba61e526bdae0cp+1Q, -0x1.a6996ae95f76ef890f12b5a360bp+0Q, 0x1.806826de1640aff2fbfd8d0aa94cp-1Q, -0x1.ddc83de4acfaf20be5fee510530ep-4Q, -0x1.e09e81650c6b74fbce41e534d5fbp-7Q, 0x1.5c5b71613d71b7692e7e5f0a2ebfp-13Q, -0x0p+0Q};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0Q, 0x1.eae80165a34ad1f2080107f87ddap-3Q, -0x1.5a965a7535366541f0a1afe5a2b4p+0Q, 0x1.851adfd49d1a76d9d23c3531fc86p+1Q, -0x1.b139c010d5d8ef58fb69c4f1a06p+1Q, 0x1.ffefb7038043737a18fc832ffa5dp+0Q, -0x1.0254056f57103b364cf4bcb0546p+0Q, 0x1.ff103b26e087e22aa6dbe24a6942p-1Q, -0x1.7a4f70cc2f5d7a6d2a4e62af8416p-1Q, 0x1.09dce627745a61500e94719899a9p-2Q, -0x1.c2f7ce5c8a37b8fcabdaf25e5004p-4Q, 0x1.41c46b919c33ee1c6941aae7a0ebp-4Q, -0x1.03531c096423a7a88f95e3dc75eap-6Q, -0x1.c24ed1e998c51356546e2438785p-9Q, 0x1.5d1ed72a09587166cbb2e53232dap-14Q, -0x0p+0Q};
+            }
+        }
+        #endif
+    }
+    if constexpr (p == 9) {
+        if constexpr (std::is_same_v<Real, float>) {
+            if constexpr (order == 0) {
+                return {0x0p+0f, 0x1.1d2fcp-4f, 0x1.b1b652p-1f, 0x1.8b08d6p-3f, -0x1.4aef16p-3f, 0x1.fd1878p-5f, -0x1.7ee87p-8f, -0x1.097588p-7f, 0x1.3d3ef8p-8f, -0x1.291474p-10f, 0x1.b33accp-15f, 0x1.7e6498p-16f, -0x1.53f94ap-19f, -0x1.58c1d8p-24f, 0x1.278ba2p-29f, -0x1.705a7ap-38f, -0x1.4fb4eep-52f, -0x0p+0f};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0f, 0x1.2b90f8p-2f, 0x1.af96b8p-1f, -0x1.d3c16cp+0f, 0x1.169004p+0f, -0x1.1f4f38p-1f, 0x1.82c926p-3f, -0x1.540e9cp-7f, -0x1.49841cp-6f, 0x1.96a364p-8f, 0x1.0c494ap-11f, -0x1.b592fcp-12f, 0x1.9d3f0ap-16f, 0x1.8562bp-23f, -0x1.13cc2ep-24f, 0x1.2234ep-34f, 0x1.08644ap-47f, 0x0p+0f};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0f, 0x1.e4c00ep-1f, -0x1.aad7p+0f, 0x1.135c58p-2f, 0x1.5b4146p-1f, -0x1.c92ba8p-4f, -0x1.4f00eap-2f, 0x1.61aa48p-2f, -0x1.66761ap-3f, 0x1.723502p-5f, -0x1.85c5f4p-10f, -0x1.2bb318p-9f, 0x1.b3d73ep-12f, 0x1.bca3f2p-17f, -0x1.261d8ap-20f, 0x1.36693ap-28f, 0x1.1a9906p-40f, -0x0p+0f};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0f, 0x1.27d6ep+1f, -0x1.2ded7ap+3f, 0x1.e79fd8p+3f, -0x1.304a1ap+3f, -0x1.effd26p+2f, 0x1.7ce73p+4f, -0x1.985f02p+4f, 0x1.d3cfacp+3f, -0x1.e1a25p+1f, -0x1.9b8564p-2f, 0x1.fe4766p-2f, -0x1.73f12ep-4f, -0x1.20ddep-10f, 0x1.ffd29p-12f, -0x1.fa8378p-20f, -0x1.cc794ap-31f, 0x0p+0f};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0f, 0x1.c7cedp+1f, -0x1.2ab8cap+4f, 0x1.4df684p+5f, -0x1.af3bfap+5f, 0x1.8eeb18p+5f, -0x1.541e9cp+5f, 0x1.12ea48p+5f, -0x1.35c8bp+4f, 0x1.d829e2p+1f, 0x1.69d6eap+1f, -0x1.023562p+1f, 0x1.b42324p-2f, -0x1.2e2904p-8f, -0x1.22b4e2p-8f, 0x1.654cep-16f, 0x1.43e712p-26f, -0x0p+0f};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0f, 0x1.1617a4p+2f, -0x1.94d9c6p+4f, 0x1.dd0eb6p+5f, -0x1.168c04p+6f, 0x1.24c19cp+5f, -0x1.016a68p+0f, -0x1.c94ed2p+2f, 0x1.669c08p+3f, -0x1.88dca4p+4f, 0x1.b958d8p+4f, -0x1.eccebap+3f, 0x1.f4375ep+1f, -0x1.2ade5ep-3f, -0x1.491f18p-4f, 0x1.5bccdep-11f, 0x1.398368p-20f, -0x0p+0f};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0f, 0x1.384148p+1f, -0x1.dd3c5ap+3f, 0x1.30352ap+5f, -0x1.a86d9ep+5f, 0x1.7d0e6cp+5f, -0x1.25c844p+5f, 0x1.f5b3e2p+4f, -0x1.815eep+4f, 0x1.ca4482p+3f, -0x1.050826p+3f, 0x1.1eeca8p+2f, -0x1.6df696p+0f, 0x1.75a7acp-5f, 0x1.ebd4ap-5f, -0x1.434438p-10f, -0x1.202646p-18f, 0x0p+0f};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0f, 0x1.041f76p+0f, -0x1.96fe7ap+2f, 0x1.04a7fep+4f, -0x1.5c5edep+4f, 0x1.0b593cp+4f, -0x1.3ddf52p+3f, 0x1.12f0bcp+3f, -0x1.d4ebfcp+2f, 0x1.d31828p+1f, -0x1.6bf238p+0f, 0x1.d1d5cp-1f, -0x1.794e94p-2f, -0x1.2e59eap-6f, 0x1.26fbfep-5f, -0x1.e662fap-10f, -0x1.a81802p-17f, -0x0p+0f};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0f, 0x1.9024ep-3f, -0x1.3caa56p+0f, 0x1.947e64p+1f, -0x1.033a7ap+2f, 0x1.51b6cap+1f, -0x1.0bd63p+0f, 0x1.028beep+0f, -0x1.1620dap+0f, 0x1.b5ef82p-2f, -0x1.b7954cp-6f, 0x1.054d18p-4f, -0x1.481726p-5f, -0x1.8ce86ep-6f, 0x1.2926b8p-6f, -0x1.20ae94p-9f, -0x1.e260bp-16f, 0x0p+0f};
+            }
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0, 0x1.1d2fbfac2394ap-4, 0x1.b1b6520101e0ep-1, 0x1.8b08d5cd4a2adp-3, -0x1.4aef16c7e666fp-3, 0x1.fd1877f1138bep-5, -0x1.7ee87092fa243p-8, -0x1.09758849af605p-7, 0x1.3d3ef7388a3aep-8, -0x1.29147421d5711p-10, 0x1.b33acccf47f1cp-15, 0x1.7e6498cdbddd5p-16, -0x1.53f9494edf128p-19, -0x1.58c1d88e09b31p-24, 0x1.278ba12dc249ap-29, -0x1.705a7a4d8345p-38, -0x1.4fb4ee678fa0ep-52, -0x0p+0};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0, 0x1.2b90f77070093p-2, 0x1.af96b810375aep-1, -0x1.d3c16b16ba87ap+0, 0x1.1690032de8cfbp+0, -0x1.1f4f37268ff74p-1, 0x1.82c9256a70f8fp-3, -0x1.540e9bea7c732p-7, -0x1.49841c554fed2p-6, 0x1.96a364065f27dp-8, 0x1.0c49493de5a6fp-11, -0x1.b592fbb7be41bp-12, 0x1.9d3f09be0cea7p-16, 0x1.8562af0388b7ep-23, -0x1.13cc2e0d34f25p-24, 0x1.2234e02ed8631p-34, 0x1.08644a120d1efp-47, 0x0p+0};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0, 0x1.e4c00e361fc68p-1, -0x1.aad6ffd5d77f1p+0, 0x1.135c57711e671p-2, 0x1.5b41454ff0957p-1, -0x1.c92ba77b267a3p-4, -0x1.4f00ea2c2d363p-2, 0x1.61aa479f9dc68p-2, -0x1.6676194262896p-3, 0x1.7235017b58d32p-5, -0x1.85c5f4a449273p-10, -0x1.2bb318efa4d23p-9, 0x1.b3d73e818e5c9p-12, 0x1.bca3f26f194dp-17, -0x1.261d8947cb727p-20, 0x1.36693a4632269p-28, 0x1.1a9906065291fp-40, -0x0p+0};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0, 0x1.27d6df36685a8p+1, -0x1.2ded79e41fdb1p+3, 0x1.e79fd7c0b1c0fp+3, -0x1.304a1a210a5fap+3, -0x1.effd2573aa9abp+2, 0x1.7ce72fdc2cb91p+4, -0x1.985f0196c72e5p+4, 0x1.d3cfac07a9d2bp+3, -0x1.e1a24f8472a68p+1, -0x1.9b8563bd7c7d8p-2, 0x1.fe4766e3faf54p-2, -0x1.73f12d4155f36p-4, -0x1.20dddf659ee51p-10, 0x1.ffd28fb3400bfp-12, -0x1.fa83788d3f78dp-20, -0x1.cc794a76e5f16p-31, 0x0p+0};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0, 0x1.c7ced0f66aeadp+1, -0x1.2ab8c9c81252ep+4, 0x1.4df684dede46dp+5, -0x1.af3bf949d62bap+5, 0x1.8eeb17bed133cp+5, -0x1.541e9c27826e5p+5, 0x1.12ea47c60decp+5, -0x1.35c8b07214e14p+4, 0x1.d829e1a762882p+1, 0x1.69d6e9c20f73dp+1, -0x1.0235621854eefp+1, 0x1.b423243b8b469p-2, -0x1.2e290398a3fe3p-8, -0x1.22b4e2598d44bp-8, 0x1.654cdf573874bp-16, 0x1.43e711e678672p-26, -0x0p+0};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0, 0x1.1617a4f9d8857p+2, -0x1.94d9c534a28d4p+4, 0x1.dd0eb6aa76ffep+5, -0x1.168c0447c1b6fp+6, 0x1.24c19c047007fp+5, -0x1.016a68491e4d8p+0, -0x1.c94ed28aba0f5p+2, 0x1.669c08c9522f3p+3, -0x1.88dca456f3456p+4, 0x1.b958d77e385a9p+4, -0x1.eccebab605f4bp+3, 0x1.f4375d664ce34p+1, -0x1.2ade5d60c4581p-3, -0x1.491f178ce5646p-4, 0x1.5bccddec65e54p-11, 0x1.398367062ce37p-20, -0x0p+0};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0, 0x1.3841475e9a364p+1, -0x1.dd3c5aa19c52ep+3, 0x1.303529a28e47p+5, -0x1.a86d9ebb6edc4p+5, 0x1.7d0e6c4e24171p+5, -0x1.25c8439d2df8ap+5, 0x1.f5b3e1ac99667p+4, -0x1.815ee05c85e8bp+4, 0x1.ca4482f4236a5p+3, -0x1.050825dec75a9p+3, 0x1.1eeca8acc3a79p+2, -0x1.6df69657c972dp+0, 0x1.75a7ac677c4efp-5, 0x1.ebd49f3810c89p-5, -0x1.4344372e1b6fcp-10, -0x1.20264586c6bb9p-18, 0x0p+0};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0, 0x1.041f759e862aap+0, -0x1.96fe795439509p+2, 0x1.04a7fd5b5e592p+4, -0x1.5c5ede521aae6p+4, 0x1.0b593b29c51bcp+4, -0x1.3ddf51285055ap+3, 0x1.12f0bcbe3fa44p+3, -0x1.d4ebfbf56d996p+2, 0x1.d31827f76dc61p+1, -0x1.6bf237312f18dp+0, 0x1.d1d5c0ac4dc0cp-1, -0x1.794e93c6506ddp-2, -0x1.2e59e90e0a11dp-6, 0x1.26fbfe966bb82p-5, -0x1.e662faa96110fp-10, -0x1.a81802ebf94f1p-17, -0x0p+0};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0, 0x1.9024e0f887aa3p-3, -0x1.3caa56e1c68fap+0, 0x1.947e636a9e374p+1, -0x1.033a79f260cefp+2, 0x1.51b6c9e0d0443p+1, -0x1.0bd62fc1e0455p+0, 0x1.028bee5b6619fp+0, -0x1.1620d9bfc03ebp+0, 0x1.b5ef819dccd9ap-2, -0x1.b7954b06be8afp-6, 0x1.054d18d1cc90cp-4, -0x1.4817258dd2847p-5, -0x1.8ce86e181d425p-6, 0x1.2926b8981e2a7p-6, -0x1.20ae937e7a93p-9, -0x1.e260b0ee2a093p-16, 0x0p+0};
+            }
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0L, 0x8.e97dfd611ca4d0fp-7L, 0xd.8db290080f07364p-4L, 0xc.5846ae6a5156a59p-6L, -0xa.5778b63f3337b8dp-6L, 0xf.e8c3bf889c5f1c6p-8L, -0xb.f7438497d12158fp-11L, -0x8.4bac424d7b02898p-10L, 0x9.e9f7b9c451d6f5p-11L, -0x9.48a3a10eab88924p-13L, 0xd.99d6667a3f8ded1p-18L, 0xb.f324c66deeea6e7p-19L, -0xa.9fca4a76f894114p-22L, -0xa.c60ec4704d98582p-27L, 0x9.3c5d096e124d267p-32L, -0xb.82d3d26c1a28344p-41L, -0xa.7da7733c7d070cap-55L, -0x0p+0L};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0L, 0x9.5c87bb838049b9dp-5L, 0xd.7cb5c081bad7186p-4L, -0xe.9e0b58b5d43cc82p-3L, 0x8.b480196f467d6c9p-3L, -0x8.fa79b9347fb9e82p-4L, 0xc.16492b5387c74b6p-6L, -0xa.a074df53e3990b8p-10L, -0xa.4c20e2aa7f68ebp-9L, 0xc.b51b2032f93e669p-11L, 0x8.624a49ef2d3764bp-14L, -0xd.ac97ddbdf20daf5p-15L, 0xc.e9f84df067536c7p-19L, 0xc.2b15781c45bef81p-26L, -0x8.9e617069a792bafp-27L, 0x9.11a70176c31860ap-37L, 0x8.4322509068f7b78p-50L, 0x0p+0L};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0L, 0xf.260071b0fe33d17p-4L, -0xd.56b7feaebbf8a9ep-3L, 0x8.9ae2bb88f3384cep-5L, 0xa.da0a2a7f84ab917p-4L, -0xe.495d3bd933d14bbp-7L, -0xa.7807516169b18a5p-5L, 0xb.0d523cfcee33daap-5L, -0xb.33b0ca13144b196p-6L, 0xb.91a80bdac698e63p-8L, -0xc.2e2fa52249396c6p-13L, -0x9.5d98c77d2691ac4p-12L, 0xd.9eb9f40c72e4aacp-15L, 0xd.e51f9378ca67c3cp-20L, -0x9.30ec4a3e5b93bbap-23L, 0x9.b349d2319134721p-31L, 0x8.d4c83032948f76p-43L, -0x0p+0L};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0L, 0x9.3eb6f9b342d3cadp-2L, -0x9.6f6bcf20fed8622p+0L, 0xf.3cfebe058e075ecp+0L, -0x9.8250d10852fce74p+0L, -0xf.7fe92b9d54d57e6p-1L, 0xb.e7397ee165c88c5p+1L, -0xc.c2f80cb639729f3p+1L, 0xe.9e7d603d4e95463p+0L, -0xf.0d127c23953405cp-2L, -0xc.dc2b1debe3ebee3p-5L, 0xf.f23b371fd7a9d87p-5L, -0xb.9f896a0aaf9ad9fp-7L, -0x9.06eefb2cf7284e3p-13L, 0xf.fe947d9a005fa2fp-15L, -0xf.d41bc469fbc68cdp-23L, -0xe.63ca53b72f8b2fep-34L, 0x0p+0L};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0L, 0xe.3e7687b3575667ep-2L, -0x9.55c64e409297236p+1L, 0xa.6fb426f6f2369dp+2L, -0xd.79dfca4eb15ce04p+2L, 0xc.7758bdf6899e1b4p+2L, -0xa.a0f4e13c13724e9p+2L, 0x8.97523e306f6022p+2L, -0x9.ae458390a70a077p+1L, 0xe.c14f0d3b14410dep-2L, 0xb.4eb74e107b9e597p-2L, -0x8.11ab10c2a7777ccp-2L, 0xd.a11921dc5a34834p-5L, -0x9.71481cc51ff17e4p-11L, -0x9.15a712cc6a2586fp-11L, 0xb.2a66fab9c3a5b39p-19L, 0xa.1f388f33c339298p-29L, -0x0p+0L};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0L, 0x8.b0bd27cec42baaep-1L, -0xc.a6ce29a51469f7p+1L, 0xe.e875b553b7fed21p+2L, -0x8.b460223e0db7486p+3L, 0x9.260ce023803fb4p+2L, -0x8.0b534248f26c38ep-3L, -0xe.4a769455d07a8e6p-1L, 0xb.34e0464a91798aep+0L, -0xc.46e522b79a2b2aep+1L, 0xd.cac6bbf1c2d48b2p+1L, -0xf.6675d5b02fa596cp+0L, 0xf.a1baeb32671a172p-2L, -0x9.56f2eb0622c089cp-6L, -0xa.48f8bc672b2306bp-7L, 0xa.de66ef632f29e0ep-14L, 0x9.cc1b3831671b9dbp-23L, -0x0p+0L};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0L, 0x9.c20a3af4d1b1cfep-2L, -0xe.e9e2d50ce2972e4p+0L, 0x9.81a94d147237d62p+2L, -0xd.436cf5db76e1e52p+2L, 0xb.e873627120b85ap+2L, -0x9.2e421ce96fc4fd3p+2L, 0xf.ad9f0d64cb33437p+1L, -0xc.0af702e42f45538p+1L, 0xe.522417a11b52a8bp+0L, -0x8.28412ef63ad4b3p+0L, 0x8.f76545661d3c9p-1L, -0xb.6fb4b2be4b96476p-3L, 0xb.ad3d633be277714p-8L, 0xf.5ea4f9c08644463p-8L, -0xa.1a21b970db7e3c3p-13L, -0x9.01322c3635dc8d8p-21L, 0x0p+0L};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0L, 0x8.20fbacf4315510dp-3L, -0xc.b7f3caa1ca84594p-1L, 0x8.253feadaf2c91fcp+1L, -0xa.e2f6f290d572f2cp+1L, 0x8.5ac9d94e28ddf7fp+1L, -0x9.eefa894282acd81p+0L, 0x8.9785e5f1fd2220dp+0L, -0xe.a75fdfab6ccb19fp-1L, 0xe.98c13fbb6e30aacp-2L, -0xb.5f91b98978c679ep-3L, 0xe.8eae05626e0638ap-4L, -0xb.ca749e32836e5f1p-5L, -0x9.72cf4870508e45cp-9L, 0x9.37dff4b35dc1001p-8L, -0xf.3317d54b0887a0cp-13L, -0xd.40c0175fca78546p-20L, -0x0p+0L};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0L, 0xc.812707c43d519efp-6L, -0x9.e552b70e347cfbdp-3L, 0xc.a3f31b54f1b9fa4p-2L, -0x8.19d3cf93067786bp-1L, 0xa.8db64f068221badp-2L, -0x8.5eb17e0f022abcep-3L, 0x8.145f72db30cf502p-3L, -0x8.b106cdfe01f5b31p-3L, 0xd.af7c0cee66cd13ep-5L, -0xd.bcaa5835f4575cbp-9L, 0x8.2a68c68e64863cdp-7L, -0xa.40b92c6e94234bfp-8L, -0xc.674370c0ea12a57p-9L, 0x9.4935c4c0f1539cfp-9L, -0x9.05749bf3d4982dep-12L, -0xf.1305877150497c2p-19L, 0x0p+0L};
+            }
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            if constexpr (order == 0) {
+                return {0x0p+0Q, 0x1.1d2fbfac23949a1e129ec9f83912p-4Q, 0x1.b1b6520101e0e6c7ddaa9da59f1ep-1Q, 0x1.8b08d5cd4a2ad4b181244736a729p-3Q, -0x1.4aef16c7e666f719f7698e178af8p-3Q, 0x1.fd1877f1138be38ba53889d72502p-5Q, -0x1.7ee87092fa242b1ef789aaf8df0bp-8Q, -0x1.09758849af60512fff4fa06073a1p-7Q, 0x1.3d3ef7388a3ade9f5adf4b3f580fp-8Q, -0x1.29147421d57112477f4b7b3491f7p-10Q, 0x1.b33acccf47f1bda17f46b81064b7p-15Q, 0x1.7e6498cdbddd4dce209effce7067p-16Q, -0x1.53f9494edf1282277c1de6dc67e2p-19Q, -0x1.58c1d88e09b30b0364784ebc1f6cp-24Q, 0x1.278ba12dc249a4cd49c8d69ab618p-29Q, -0x1.705a7a4d83450688cb9e189ad73cp-38Q, -0x1.4fb4ee678fa0e1946f2bc7ed6f9ap-52Q, -0x0p+0Q};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0Q, 0x1.2b90f770700937399f9f525fd16p-2Q, 0x1.af96b810375ae30c4c41bf8dddfep-1Q, -0x1.d3c16b16ba8799042d28d9c49847p+0Q, 0x1.1690032de8cfad91fdf041ea0eaap+0Q, -0x1.1f4f37268ff73d0393fe0f677908p-1Q, 0x1.82c9256a70f8e96c68d16f2e332cp-3Q, -0x1.540e9bea7c732170245209a303ap-7Q, -0x1.49841c554fed1d5f2443e15a5a69p-6Q, 0x1.96a364065f27ccd19657d67cdf44p-8Q, 0x1.0c49493de5a6ec95d0bb4c3aca7fp-11Q, -0x1.b592fbb7be41b5e92f003f6109e3p-12Q, 0x1.9d3f09be0cea6d8d6f8ed455253cp-16Q, 0x1.8562af0388b7df01536ccb66a54fp-23Q, -0x1.13cc2e0d34f2575dd283b068f4aep-24Q, 0x1.2234e02ed8630c149658a9630027p-34Q, 0x1.08644a120d1ef6f0d4b961ae18cfp-47Q, 0x0p+0Q};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0Q, 0x1.e4c00e361fc67a2e12b083b2dedp-1Q, -0x1.aad6ffd5d77f153c17f1c88238b1p+0Q, 0x1.135c57711e67099c1758b9c71774p-2Q, 0x1.5b41454ff095722d0f803ea680d3p-1Q, -0x1.c92ba77b267a297500d5b5d446e8p-4Q, -0x1.4f00ea2c2d363149504e045fbe3dp-2Q, 0x1.61aa479f9dc67b53226c771010a3p-2Q, -0x1.667619426289632c2e8907dc17f4p-3Q, 0x1.7235017b58d31cc6ca2ab84f7b18p-5Q, -0x1.85c5f4a449272d8bf24d90db58dfp-10Q, -0x1.2bb318efa4d23587f50785ea349bp-9Q, 0x1.b3d73e818e5c9557fa6b95207e7cp-12Q, 0x1.bca3f26f194cf877e2358ca6ef83p-17Q, -0x1.261d8947cb7277733f476ea3b783p-20Q, 0x1.36693a4632268e426c4014035393p-28Q, 0x1.1a9906065291eec094ff6b81726cp-40Q, -0x0p+0Q};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0Q, 0x1.27d6df36685a79598b6c86ce4186p+1Q, -0x1.2ded79e41fdb0c43d1210e12d21ep+3Q, 0x1.e79fd7c0b1c0ebd84f460885d881p+3Q, -0x1.304a1a210a5f9ce8bc8b8a0cffdep+3Q, -0x1.effd2573aa9aafcb53e5889f37dap+2Q, 0x1.7ce72fdc2cb91189ae6d5e0871cfp+4Q, -0x1.985f0196c72e53e6d1cfdee7b628p+4Q, 0x1.d3cfac07a9d2a8c51198c073e7cep+3Q, -0x1.e1a24f8472a680b7d24d0580978cp+1Q, -0x1.9b8563bd7c7d7dc5768ba3de4d6cp-2Q, 0x1.fe4766e3faf53b0d1248280765afp-2Q, -0x1.73f12d4155f35b3e8452b4fe648dp-4Q, -0x1.20dddf659ee509c6befdf1c741e4p-10Q, 0x1.ffd28fb3400bf45efe5c328ed98fp-12Q, -0x1.fa83788d3f78d19a901b7476cd3dp-20Q, -0x1.cc794a76e5f165fc8108c92a1bffp-31Q, 0x0p+0Q};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0Q, 0x1.c7ced0f66aeaccfcda165890b07cp+1Q, -0x1.2ab8c9c81252e46b55777de4d947p+4Q, 0x1.4df684dede46d3a014591fd079e5p+5Q, -0x1.af3bf949d62b9c07b05b4ac5a7abp+5Q, 0x1.8eeb17bed133c367f65a67fd697cp+5Q, -0x1.541e9c27826e49d24f626bb2a444p+5Q, 0x1.12ea47c60dec043f14d3664d56dbp+5Q, -0x1.35c8b07214e140ed7f1d44702883p+4Q, 0x1.d829e1a7628821bc837255ba8e2p+1Q, 0x1.69d6e9c20f73cb2d14ff73520816p+1Q, -0x1.0235621854eeef97bfd3d4e40fecp+1Q, 0x1.b423243b8b46906701ef92e186fap-2Q, -0x1.2e290398a3fe2fc8cc3aebac6855p-8Q, -0x1.22b4e2598d44b0dd2f4a293dd307p-8Q, 0x1.654cdf573874b672ebfe3509eb92p-16Q, 0x1.43e711e67867252f78e7e45acf76p-26Q, -0x0p+0Q};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0Q, 0x1.1617a4f9d885755cd347730680b6p+2Q, -0x1.94d9c534a28d3ee0a8bf210bcdbcp+4Q, 0x1.dd0eb6aa76ffda42c87706ab28dep+5Q, -0x1.168c0447c1b6e90c330602af557cp+6Q, 0x1.24c19c047007f67f0d2fc48525bep+5Q, -0x1.016a68491e4d871ca5058c90ecfbp+0Q, -0x1.c94ed28aba0f51cc92c5b4e86742p+2Q, 0x1.669c08c9522f315c7b041fba43e2p+3Q, -0x1.88dca456f345655b7cb4359b9a4bp+4Q, 0x1.b958d77e385a9163a2eb3b5063f1p+4Q, -0x1.eccebab605f4b2d725512d8a373ap+3Q, 0x1.f4375d664ce342e4e518679a8a7p+1Q, -0x1.2ade5d60c45811382f7ff19b2adep-3Q, -0x1.491f178ce56460d544cbe168f85cp-4Q, 0x1.5bccddec65e53c1b0416c331875ep-11Q, 0x1.398367062ce373b6810676d7e87ep-20Q, -0x0p+0Q};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0Q, 0x1.3841475e9a3639fcb27c2a8a346bp+1Q, -0x1.dd3c5aa19c52e5c8a273f6e1052ep+3Q, 0x1.303529a28e46fac3a8f56eaa0a35p+5Q, -0x1.a86d9ebb6edc3ca33aa7af776936p+5Q, 0x1.7d0e6c4e24170b40a4b957521101p+5Q, -0x1.25c8439d2df89fa5007905a4ba91p+5Q, 0x1.f5b3e1ac9966686ed844c70c24b5p+4Q, -0x1.815ee05c85e8aa70418061334f18p+4Q, 0x1.ca4482f4236a5516d7f638fa35c2p+3Q, -0x1.050825dec75a966028608d17675cp+3Q, 0x1.1eeca8acc3a791ffedf80bed61f9p+2Q, -0x1.6df69657c972c8ebec75c92acc68p+0Q, 0x1.75a7ac677c4eee273d03fc67aefp-5Q, 0x1.ebd49f3810c888c69855753565b4p-5Q, -0x1.4344372e1b6fc786ddf90f2b7b7p-10Q, -0x1.20264586c6bb91b0aa0b4d1a440fp-18Q, 0x0p+0Q};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0Q, 0x1.041f759e862aa2196b99e328e887p+0Q, -0x1.96fe795439508b28db42654510a5p+2Q, 0x1.04a7fd5b5e5923f7f627bd68cd65p+4Q, -0x1.5c5ede521aae5e58438f371fca07p+4Q, 0x1.0b593b29c51bbefd0a21a466fe1fp+4Q, -0x1.3ddf512850559b028d830987fbd1p+3Q, 0x1.12f0bcbe3fa44419a6b523028ff1p+3Q, -0x1.d4ebfbf56d99633e38e575351ca4p+2Q, 0x1.d31827f76dc61557ae5c1ea5b48p+1Q, -0x1.6bf237312f18cf3b573ffc6b9b12p+0Q, 0x1.d1d5c0ac4dc0c7147f916f8d0ae2p-1Q, -0x1.794e93c6506dcbe26714d9f578b4p-2Q, -0x1.2e59e90e0a11c8b7ce9f91036827p-6Q, 0x1.26fbfe966bb82001d50ae9267a6ep-5Q, -0x1.e662faa96110f417469ce7821db9p-10Q, -0x1.a81802ebf94f0a8bc8124e278c59p-17Q, -0x0p+0Q};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0Q, 0x1.9024e0f887aa33deb80194db918fp-3Q, -0x1.3caa56e1c68f9f7ad07fd6873ac5p+0Q, 0x1.947e636a9e373f489450f99a494ep+1Q, -0x1.033a79f260cef0d616212b14ddbcp+2Q, 0x1.51b6c9e0d0443759a67a3c353747p+1Q, -0x1.0bd62fc1e045579c86e940e528b1p+0Q, 0x1.028bee5b6619ea0406791e99bae6p+0Q, -0x1.1620d9bfc03eb662d8d654bb92cfp+0Q, 0x1.b5ef819dccd9a27cb2716f32c63ap-2Q, -0x1.b7954b06be8aeb961960232cc863p-6Q, 0x1.054d18d1cc90c79a1ef0360672efp-4Q, -0x1.4817258dd284697ebc00b788ce26p-5Q, -0x1.8ce86e181d4254ae37719aa328a7p-6Q, 0x1.2926b8981e2a739eefaa1e5b74bcp-6Q, -0x1.20ae937e7a9305bbde13268ad288p-9Q, -0x1.e260b0ee2a092f8355b87bff022bp-16Q, 0x0p+0Q};
+            }
+        }
+        #endif
+    }
+    if constexpr (p == 10) {
+        if constexpr (std::is_same_v<Real, float>) {
+            if constexpr (order == 0) {
+                return {0x0p+0f, 0x1.12cb0ap-5f, 0x1.4e2c28p-1f, 0x1.1c4636p-1f, -0x1.85d2eep-2f, 0x1.9e3daep-3f, -0x1.494bcp-4f, 0x1.1d23ep-6f, 0x1.d4ed16p-10f, -0x1.2885ecp-9f, 0x1.94f202p-12f, 0x1.44e94ep-14f, -0x1.b37dfap-16f, 0x1.403906p-24f, 0x1.c9437p-24f, -0x1.58dbb8p-28f, 0x1.db3584p-37f, 0x1.afee7cp-44f, -0x1.098874p-59f, 0x0p+0f};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0f, 0x1.43cfccp-3f, 0x1.f5f9c2p-1f, -0x1.94bc28p+0f, 0x1.61584ep-1f, -0x1.a2cb68p-2f, 0x1.eef0eap-3f, -0x1.ac223p-4f, 0x1.c84ec2p-6f, -0x1.213456p-8f, 0x1.2c315ap-10f, -0x1.f37546p-12f, 0x1.ce036p-15f, 0x1.06ba9ap-17f, 0x1.2eea96p-21f, 0x1.f125fap-26f, -0x1.51db7ap-33f, -0x1.3ced9ep-40f, 0x1.85b824p-55f, -0x0p+0f};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0f, 0x1.2d6cb8p-1f, -0x1.01b00cp-2f, -0x1.0fd09ap+1f, 0x1.8bd77ap+1f, -0x1.c8684ep+0f, 0x1.6e6d86p-2f, 0x1.86e852p-2f, -0x1.9dcbe6p-2f, 0x1.55c762p-3f, -0x1.35a482p-6f, -0x1.51b88cp-7f, 0x1.076728p-8f, -0x1.67961ap-12f, -0x1.2b4a08p-15f, 0x1.bb4b6cp-19f, 0x1.3f418cp-28f, -0x1.0d99c2p-32f, 0x1.4b9c06p-46f, 0x0p+0f};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0f, 0x1.a8daep+0f, -0x1.8d688ep+2f, 0x1.317cc4p+3f, -0x1.00fa12p+3f, 0x1.9e984cp+1f, 0x1.0dcc3cp+1f, -0x1.41a436p+2f, 0x1.075a46p+2f, -0x1.9984ccp+0f, 0x1.9cf2e8p-5f, 0x1.c91578p-3f, -0x1.60b8bp-4f, 0x1.32422ap-7f, 0x1.dd5da6p-11f, -0x1.351528p-13f, -0x1.03c426p-22f, 0x1.7713ap-26f, -0x1.cd96fcp-39f, -0x0p+0f};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0f, 0x1.a04f8p+1f, -0x1.18f0a4p+4f, 0x1.4ce384p+5f, -0x1.dc75fap+5f, 0x1.fdbc98p+5f, -0x1.eefc0cp+5f, 0x1.b92a7cp+5f, -0x1.2299d6p+5f, 0x1.6502b8p+3f, 0x1.11f34p+2f, -0x1.73b0a4p+2f, 0x1.244d46p+1f, -0x1.35466cp-2f, -0x1.fc20c8p-6f, 0x1.0d9c8cp-7f, 0x1.a4010cp-19f, -0x1.49b0cap-19f, 0x1.962a6ep-31f, -0x0p+0f};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0f, 0x1.55886ep+2f, -0x1.09d96p+5f, 0x1.505f98p+6f, -0x1.96ec36p+6f, 0x1.17b23p+5f, 0x1.fc1722p+5f, -0x1.b35f4ap+6f, 0x1.d17f22p+6f, -0x1.12118cp+7f, 0x1.207a74p+7f, -0x1.934736p+6f, 0x1.3fa55cp+5f, -0x1.959602p+2f, -0x1.9505e8p-1f, 0x1.43d264p-2f, -0x1.38e018p-10f, -0x1.968e84p-13f, 0x1.f5ed4cp-24f, -0x0p+0f};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0f, 0x1.f3cda2p+1f, -0x1.9eeda2p+4f, 0x1.260fdap+6f, -0x1.d673d8p+6f, 0x1.f01b3p+6f, -0x1.addb2cp+6f, 0x1.7db87cp+6f, -0x1.3f986p+6f, 0x1.ae7316p+5f, -0x1.fb5cc4p+4f, 0x1.259afcp+4f, -0x1.fe186ep+2f, 0x1.4d0298p+0f, 0x1.a1f0a6p-2f, -0x1.40c0aep-3f, 0x1.ba72fap-9f, 0x1.c193f2p-13f, -0x1.16b49ap-22f, 0x0p+0f};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0f, 0x1.3586dap+1f, -0x1.08fa64p+4f, 0x1.7c41fp+5f, -0x1.276b64p+6f, 0x1.14f1dp+6f, -0x1.83d54ap+5f, 0x1.4053c8p+5f, -0x1.209b54p+5f, 0x1.657834p+4f, -0x1.2ddf68p+3f, 0x1.38745p+2f, -0x1.4065c2p+1f, 0x1.6763c6p-4f, 0x1.181d4ep-1f, -0x1.87564p-3f, 0x1.843d22p-7f, 0x1.52be3cp-11f, -0x1.a79c62p-20f, -0x0p+0f};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0f, 0x1.7a3cf4p+0f, -0x1.48b25ep+3f, 0x1.cbd932p+4f, -0x1.37885ep+5f, 0x1.4db4fcp+4f, 0x1.74ac2ep+2f, -0x1.11ca3p+3f, 0x1.9fa6aap-4f, -0x1.8ceb32p+2f, 0x1.e686e4p+3f, -0x1.7e0b78p+3f, 0x1.7e1a34p+2f, -0x1.247b58p+2f, 0x1.b8a4e2p+1f, -0x1.4f17d6p+0f, 0x1.4b4084p-3f, 0x1.726478p-7f, -0x1.d74fd6p-15f, -0x0p+0f};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0f, 0x1.f6438ap-4f, -0x1.b7ba92p-1f, 0x1.3f509cp+1f, -0x1.eac616p+1f, 0x1.ae9244p+1f, -0x1.00d5dp+1f, 0x1.9413f4p+0f, -0x1.9bd984p+0f, 0x1.16aae2p+0f, -0x1.158768p-1f, 0x1.8145e4p-2f, -0x1.faf556p-3f, 0x1.8ec972p-4f, -0x1.49980ep-5f, 0x1.5730c4p-6f, -0x1.0952d6p-8f, -0x1.ce071ep-12f, 0x1.30a436p-18f, -0x0p+0f};
+            }
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0, 0x1.12cb0a33640b5p-5, 0x1.4e2c27be21e0ep-1, 0x1.1c4636ef189edp-1, -0x1.85d2edb33e46ep-2, 0x1.9e3dada7662aap-3, -0x1.494bbf8e53bfcp-4, 0x1.1d23df75685c9p-6, 0x1.d4ed15a068488p-10, -0x1.2885ec2406341p-9, 0x1.94f202846521cp-12, 0x1.44e94de53f6f6p-14, -0x1.b37df99b75f09p-16, 0x1.403905df41d32p-24, 0x1.c94370d7ecc92p-24, -0x1.58dbb791a7fb7p-28, 0x1.db358382953c4p-37, 0x1.afee7cd299cd6p-44, -0x1.0988745ca3ec4p-59, 0x0p+0};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0, 0x1.43cfcb9d73923p-3, 0x1.f5f9c20090df3p-1, -0x1.94bc27297b9f9p+0, 0x1.61584eb9fe3a6p-1, -0x1.a2cb67ff996a9p-2, 0x1.eef0eaaf4989ep-3, -0x1.ac22308c89e82p-4, 0x1.c84ec23c8cdbep-6, -0x1.213456d8479d6p-8, 0x1.2c315a17e4064p-10, -0x1.f375455c5c9e6p-12, 0x1.ce035ff90a79bp-15, 0x1.06ba9aa22e87cp-17, 0x1.2eea964fb1e8p-21, 0x1.f125f98e34b08p-26, -0x1.51db791710beap-33, -0x1.3ced9d37da5d3p-40, 0x1.85b82452d9269p-55, -0x0p+0};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0, 0x1.2d6cb779664d4p-1, -0x1.01b00cc8d5d06p-2, -0x1.0fd0995df5aa3p+1, 0x1.8bd77a675e828p+1, -0x1.c8684eac579b4p+0, 0x1.6e6d859b2e73p-2, 0x1.86e851ba85835p-2, -0x1.9dcbe6db37906p-2, 0x1.55c762fd5a0dfp-3, -0x1.35a481158ac34p-6, -0x1.51b88ceed7adep-7, 0x1.0767285c8f106p-8, -0x1.67961ae7bb9ap-12, -0x1.2b4a0836ed60bp-15, 0x1.bb4b6c6c9a6fbp-19, 0x1.3f418b80d3d45p-28, -0x1.0d99c100eff2ep-32, 0x1.4b9c0643323fbp-46, 0x0p+0};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0, 0x1.a8dadfc02dd04p+0, -0x1.8d688d31d04a4p+2, 0x1.317cc4a10faf4p+3, -0x1.00fa12867f491p+3, 0x1.9e984b48af592p+1, 0x1.0dcc3bbac5e09p+1, -0x1.41a435a1df481p+2, 0x1.075a464fd9704p+2, -0x1.9984cb75bad51p+0, 0x1.9cf2e7196d1ccp-5, 0x1.c915787e3612ep-3, -0x1.60b8b0c3b1139p-4, 0x1.324229742ef44p-7, 0x1.dd5da666efa59p-11, -0x1.351528a4bd817p-13, -0x1.03c4250827b69p-22, 0x1.77139f17861ebp-26, -0x1.cd96fccfe9f0bp-39, -0x0p+0};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0, 0x1.a04f8069ea8b5p+1, -0x1.18f0a34d9f68ep+4, 0x1.4ce3831796a62p+5, -0x1.dc75f9b0b9a1p+5, 0x1.fdbc97313e6edp+5, -0x1.eefc0cdda4efap+5, 0x1.b92a7c1b6a88ap+5, -0x1.2299d502734c4p+5, 0x1.6502b707871dfp+3, 0x1.11f33f4ede648p+2, -0x1.73b0a319e688ap+2, 0x1.244d452e76301p+1, -0x1.35466c5650c62p-2, -0x1.fc20c8dd92f1ap-6, 0x1.0d9c8b9d476f8p-7, 0x1.a4010b80e5496p-19, -0x1.49b0c99eb9c65p-19, 0x1.962a6dd57b7dbp-31, -0x0p+0};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0, 0x1.55886d2f64381p+2, -0x1.09d95f1cede32p+5, 0x1.505f98e4bf277p+6, -0x1.96ec354b30307p+6, 0x1.17b23075f801p+5, 0x1.fc17211fa4d6fp+5, -0x1.b35f4a36b31c4p+6, 0x1.d17f22f2480f9p+6, -0x1.12118c5678b4dp+7, 0x1.207a74ca5ad8cp+7, -0x1.934735f943482p+6, 0x1.3fa55ba9206e4p+5, -0x1.959601005ec55p+2, -0x1.9505e84d98e61p-1, 0x1.43d2632e32cd1p-2, -0x1.38e017336cd06p-10, -0x1.968e83ac595b9p-13, 0x1.f5ed4b124df3bp-24, -0x0p+0};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0, 0x1.f3cda2f9b1354p+1, -0x1.9eeda12641b62p+4, 0x1.260fdaadd19ebp+6, -0x1.d673d80eeade5p+6, 0x1.f01b2fa154d03p+6, -0x1.addb2c4ad791ep+6, 0x1.7db87bda6fdf9p+6, -0x1.3f9860f6c4906p+6, 0x1.ae731643e9199p+5, -0x1.fb5cc3351ebc1p+4, 0x1.259afcbb8804dp+4, -0x1.fe186e46030ap+2, 0x1.4d0298c218927p+0, 0x1.a1f0a66406a12p-2, -0x1.40c0addfd8554p-3, 0x1.ba72fac37f088p-9, 0x1.c193f16bb678ep-13, -0x1.16b4995bb4f07p-22, 0x0p+0};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0, 0x1.3586d9a9e0e3ep+1, -0x1.08fa63342ecc2p+4, 0x1.7c41f01d6960dp+5, -0x1.276b64d22e135p+6, 0x1.14f1cf74869cp+6, -0x1.83d54ac636b82p+5, 0x1.4053c8a2c8d3p+5, -0x1.209b538b18df2p+5, 0x1.65783340b3783p+4, -0x1.2ddf670e51dfdp+3, 0x1.38744fdae2125p+2, -0x1.4065c212ba5cp+1, 0x1.6763c5d11b775p-4, 0x1.181d4d676ea1fp-1, -0x1.87564028831fcp-3, 0x1.843d22529bb4ap-7, 0x1.52be3b0b8c7afp-11, -0x1.a79c626c8654fp-20, -0x0p+0};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0, 0x1.7a3cf471120ecp+0, -0x1.48b25e52d274bp+3, 0x1.cbd93276e7d59p+4, -0x1.37885d5242031p+5, 0x1.4db4fb7a5ecdcp+4, 0x1.74ac2dca21f56p+2, -0x1.11ca2f9f0b7dp+3, 0x1.9fa6aaf0c8d98p-4, -0x1.8ceb3288570cdp+2, 0x1.e686e3fbc3fbfp+3, -0x1.7e0b780d60232p+3, 0x1.7e1a3482e160cp+2, -0x1.247b57131543cp+2, 0x1.b8a4e1c96768dp+1, -0x1.4f17d502240a9p+0, 0x1.4b408438ac869p-3, 0x1.7264788c9473ep-7, -0x1.d74fd6a021548p-15, -0x0p+0};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0, 0x1.f6438a3a8846p-4, -0x1.b7ba9255f9c78p-1, 0x1.3f509b3842149p+1, -0x1.eac616f0d4f87p+1, 0x1.ae9244fef585dp+1, -0x1.00d5d03220f3cp+1, 0x1.9413f3bab26fdp+0, -0x1.9bd9847a10dd5p+0, 0x1.16aae27d18a67p+0, -0x1.1587682f48216p-1, 0x1.8145e3cc3cfccp-2, -0x1.faf556e68970ep-3, 0x1.8ec972676b06bp-4, -0x1.49980ed40883dp-5, 0x1.5730c48bae56ap-6, -0x1.0952d6b855c64p-8, -0x1.ce071dd8df1efp-12, 0x1.30a4361eb25b4p-18, -0x0p+0};
+            }
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0L, 0x8.9658519b205ab72p-8L, 0xa.71613df10f0723dp-4L, 0x8.e231b778c4f6662p-4L, -0xc.2e976d99f236ef3p-5L, 0xc.f1ed6d3b3154c33p-6L, -0xa.4a5dfc729dfe012p-7L, 0x8.e91efbab42e4488p-9L, 0xe.a768ad03424408ap-13L, -0x9.442f612031a0acp-12L, 0xc.a7901423290dc7ep-15L, 0xa.274a6f29fb7b195p-17L, -0xd.9befccdbaf8457bp-19L, 0xa.01c82efa0e991ep-27L, 0xe.4a1b86bf6648ca3p-27L, -0xa.c6ddbc8d3fdb61fp-31L, 0xe.d9ac1c14a9e22dfp-40L, 0xd.7f73e694ce6b23p-47L, -0x8.4c43a2e51f61f4ap-62L, 0x0p+0L};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0L, 0xa.1e7e5ceb9c91909p-6L, 0xf.afce100486f966ap-4L, -0xc.a5e1394bdcfcb6dp-3L, 0xb.0ac275cff1d33d6p-4L, -0xd.165b3ffccb5480ap-5L, 0xf.7787557a4c4f14ep-6L, -0xd.611184644f4100cp-7L, 0xe.427611e466df078p-9L, -0x9.09a2b6c23cead05p-11L, 0x9.618ad0bf2031fa3p-13L, -0xf.9baa2ae2e4f30dfp-15L, 0xe.701affc853cdb21p-18L, 0x8.35d4d511743e237p-20L, 0x9.7754b27d8f401bap-24L, 0xf.892fcc71a583f65p-29L, -0xa.8edbc8b885f4c32p-36L, -0x9.e76ce9bed2e946cp-43L, 0xc.2dc12296c934a42p-58L, -0x0p+0L};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0L, 0x9.6b65bbcb326a224p-4L, -0x8.0d806646ae83286p-5L, -0x8.7e84caefad51526p-2L, 0xc.5ebbd33af4141bap-2L, -0xe.43427562bcd9f08p-3L, 0xb.736c2cd97397c01p-5L, 0xc.37428dd42c1a763p-5L, -0xc.ee5f36d9bc83386p-5L, 0xa.ae3b17ead06fb26p-6L, -0x9.ad2408ac5619da4p-9L, -0xa.8dc46776bd6ee4dp-10L, 0x8.3b3942e4788322ap-11L, -0xb.3cb0d73ddccfdfep-15L, -0x9.5a5041b76b0571dp-18L, 0xd.da5b6364d37d7c6p-22L, 0x9.fa0c5c069ea261fp-31L, -0x8.6cce08077f97363p-35L, 0xa.5ce0321991fd8ep-49L, 0x0p+0L};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0L, 0xd.46d6fe016e82146p-3L, -0xc.6b44698e825210ap-1L, 0x9.8be625087d79ffdp+0L, -0x8.07d09433fa48997p+0L, 0xc.f4c25a457ac90c1p-2L, 0x8.6e61ddd62f0442fp-2L, -0xa.0d21ad0efa407b6p-1L, 0x8.3ad2327ecb81caap-1L, -0xc.cc265badd6a86efp-3L, 0xc.e79738cb68e5e97p-8L, 0xe.48abc3f1b09716ap-6L, -0xb.05c5861d889c6fap-7L, 0x9.92114ba177a20b1p-10L, 0xe.eaed33377d2c762p-14L, -0x9.a8a94525ec0bb0bp-16L, -0x8.1e2128413db47b5p-25L, 0xb.b89cf8bc30f58d6p-29L, -0xe.6cb7e67f4f857ddp-42L, -0x0p+0L};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0L, 0xd.027c034f545a722p-2L, -0x8.c7851a6cfb47268p+1L, 0xa.671c18bcb530f7bp+2L, -0xe.e3afcd85cd0820fp+2L, 0xf.ede4b989f376b43p+2L, -0xf.77e066ed277d141p+2L, 0xd.c953e0db5444e19p+2L, -0x9.14cea8139a61e4ep+2L, 0xb.2815b83c38efa28p+0L, 0x8.8f99fa76f323eadp-1L, -0xb.9d8518cf3444f4dp-1L, 0x9.226a2973b180497p-2L, -0x9.aa3362b28630f09p-5L, -0xf.e10646ec978cdc7p-9L, 0x8.6ce45cea3b7be89p-10L, 0xd.20085c072a4ae87p-22L, -0xa.4d864cf5ce32429p-22L, 0xc.b1536eabdbed537p-34L, -0x0p+0L};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0L, 0xa.ac43697b21c05d7p-1L, -0x8.4ecaf8e76f18fe7p+2L, 0xa.82fcc725f93bb38p+3L, -0xc.b761aa5981834ffp+3L, 0x8.bd9183afc008112p+2L, 0xf.e0b908fd26b79fbp+2L, -0xd.9afa51b598e1c25p+3L, 0xe.8bf91792407c46p+3L, -0x8.908c62b3c5a6a21p+4L, 0x9.03d3a652d6c5fe1p+4L, -0xc.9a39afca1a40e4p+3L, 0x9.fd2add490371c09p+2L, -0xc.acb00802f62a439p-1L, -0xc.a82f426cc7309e8p-4L, 0xa.1e93197196686f8p-5L, -0x9.c700b99b66830a5p-13L, -0xc.b4741d62cadc637p-16L, 0xf.af6a58926f9d684p-27L, -0x0p+0L};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0L, 0xf.9e6d17cd89aa012p-2L, -0xc.f76d09320db0f5ep+1L, 0x9.307ed56e8cf58f8p+3L, -0xe.b39ec07756f2504p+3L, 0xf.80d97d0aa681a95p+3L, -0xd.6ed96256bc8f10cp+3L, 0xb.edc3ded37efc53ap+3L, -0x9.fcc307b62482f39p+3L, 0xd.7398b21f48cc731p+2L, -0xf.dae619a8f5e0bb5p+1L, 0x9.2cd7e5dc4026b75p+1L, -0xf.f0c37230184fee7p-1L, 0xa.6814c610c493aa3p-3L, 0xd.0f8533203509157p-5L, -0xa.06056efec2aa1d8p-6L, 0xd.d397d61bf843e3dp-12L, 0xe.0c9f8b5db3c72d8p-16L, -0x8.b5a4cadda783993p-25L, 0x0p+0L};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0L, 0x9.ac36cd4f071eccfp-2L, -0x8.47d319a17660e21p+1L, 0xb.e20f80eb4b065edp+2L, -0x9.3b5b2691709a7f2p+3L, 0x8.a78e7ba434e03bep+3L, -0xc.1eaa5631b5c1221p+2L, 0xa.029e45164697e35p+2L, -0x9.04da9c58c6f9312p+2L, 0xb.2bc19a059bc163fp+1L, -0x9.6efb38728efe53fp+0L, 0x9.c3a27ed71092bccp-1L, -0xa.032e1095d2e022bp-2L, 0xb.3b1e2e88dbba717p-7L, 0x8.c0ea6b3b750f81fp-4L, -0xc.3ab2014418fdea7p-6L, 0xc.21e91294dda4d8cp-10L, 0xa.95f1d85c63d7aadp-14L, -0xd.3ce3136432a75eep-23L, -0x0p+0L};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0L, 0xb.d1e7a38890760ccp-3L, -0xa.4592f29693a58f2p+0L, 0xe.5ec993b73eacb21p+1L, -0x9.bc42ea921018403p+2L, 0xa.6da7dbd2f66dc91p+1L, 0xb.a5616e510faadd9p-1L, -0x8.8e517cf85be82f9p+0L, 0xc.fd35578646cc028p-7L, -0xc.67599442b866996p-1L, 0xf.34371fde1fdf9acp+0L, -0xb.f05bc06b0118d26p+0L, 0xb.f0d1a4170b05fe8p-1L, -0x9.23dab898aa1de5fp-1L, 0xd.c5270e4b3b4644bp-2L, -0xa.78bea8112054738p-3L, 0xa.5a0421c564344a9p-6L, 0xb.9323c464a39ee53p-10L, -0xe.ba7eb5010aa3e4p-18L, -0x0p+0L};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0L, 0xf.b21c51d44230049p-7L, -0xd.bdd492afce3bd22p-4L, 0x9.fa84d9c210a45adp-2L, -0xf.5630b786a7c34dfp-2L, 0xd.749227f7ac2e953p-2L, -0x8.06ae8191079dde4p-2L, 0xc.a09f9dd5937e42dp-3L, -0xc.decc23d086ea9cp-3L, 0x8.b55713e8c533b1cp-3L, -0x8.ac3b417a410ae11p-4L, 0xc.0a2f1e61e7e5e62p-5L, -0xf.d7aab7344b86da8p-6L, 0xc.764b933b583557ap-7L, -0xa.4cc076a0441e56ep-8L, 0xa.b986245d72b5275p-9L, -0x8.4a96b5c2ae31c5dp-11L, -0xe.7038eec6f8f774fp-15L, 0x9.8521b0f592d9c7fp-21L, -0x0p+0L};
+            }
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            if constexpr (order == 0) {
+                return {0x0p+0Q, 0x1.12cb0a33640b56e423474a1328fcp-5Q, 0x1.4e2c27be21e0e479b88ad485160cp-1Q, 0x1.1c4636ef189eccc399682014d9c9p-1Q, -0x1.85d2edb33e46dde58a5a504a9aap-2Q, 0x1.9e3dada7662a9865be6b99b2427ep-3Q, -0x1.494bbf8e53bfc023fe7e0915ab57p-4Q, 0x1.1d23df75685c890f2df5ab229b8bp-6Q, 0x1.d4ed15a06848811344377f87f82cp-10Q, -0x1.2885ec240634157f42540c2ec5a5p-9Q, 0x1.94f202846521b8fb6dee9352c083p-12Q, 0x1.44e94de53f6f632a67cbb5854d2p-14Q, -0x1.b37df99b75f08af621654dd8f548p-16Q, 0x1.403905df41d323c0c33072aaf467p-24Q, 0x1.c94370d7ecc9194547661e1cf7bbp-24Q, -0x1.58dbb791a7fb6c3e33eb2a850b1bp-28Q, 0x1.db358382953c45bea25d9891f3a2p-37Q, 0x1.afee7cd299cd64600d2193c416e5p-44Q, -0x1.0988745ca3ec3e945e33c4d42e0fp-59Q, 0x0p+0Q};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0Q, 0x1.43cfcb9d739232114ccf7b42f288p-3Q, 0x1.f5f9c20090df2cd39669639ec82fp-1Q, -0x1.94bc27297b9f96d98ca06b8b7823p+0Q, 0x1.61584eb9fe3a67acec590408bcaep-1Q, -0x1.a2cb67ff996a90130726bb55186ep-2Q, 0x1.eef0eaaf4989e29be4ba95e2f142p-3Q, -0x1.ac22308c89e820172f07afea77ffp-4Q, 0x1.c84ec23c8cdbe0f0d252ca4a6014p-6Q, -0x1.213456d8479d5a0a002e8a35429fp-8Q, 0x1.2c315a17e4063f457d1b74aaa599p-10Q, -0x1.f375455c5c9e61be4fa670796ca9p-12Q, 0x1.ce035ff90a79b6418f9714e01ff9p-15Q, 0x1.06ba9aa22e87c46e9b5b517bfa1bp-17Q, 0x1.2eea964fb1e803735b7cbdec44b7p-21Q, 0x1.f125f98e34b07ec90a3117922e68p-26Q, -0x1.51db791710be9863d69c55fb8fa2p-33Q, -0x1.3ced9d37da5d28d7002692ae72b6p-40Q, 0x1.85b82452d92694835d294f84ab3ep-55Q, -0x0p+0Q};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0Q, 0x1.2d6cb779664d44484073db45451fp-1Q, -0x1.01b00cc8d5d0650bb7d9e87582f1p-2Q, -0x1.0fd0995df5aa2a4c5f39f931817fp+1Q, 0x1.8bd77a675e82837408b645325c9ap+1Q, -0x1.c8684eac579b3e1019c502de86a6p+0Q, 0x1.6e6d859b2e72f80278552877475p-2Q, 0x1.86e851ba85834ec58a127f16fee8p-2Q, -0x1.9dcbe6db3790670c84be0eec3058p-2Q, 0x1.55c762fd5a0df64b9c06acd53251p-3Q, -0x1.35a481158ac33b4716b6e91c54eep-6Q, -0x1.51b88ceed7addc9a97168ddbee02p-7Q, 0x1.0767285c8f10645316c4c221faa4p-8Q, -0x1.67961ae7bb99fbfcc0d26144bd1bp-12Q, -0x1.2b4a0836ed60ae3a1490ad53ccb1p-15Q, 0x1.bb4b6c6c9a6faf8c7dd84be23d19p-19Q, 0x1.3f418b80d3d44c3e61fe90bb84e6p-28Q, -0x1.0d99c100eff2e6c61779a48505a8p-32Q, 0x1.4b9c0643323fb1c0ce2d07b0b0abp-46Q, 0x0p+0Q};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0Q, 0x1.a8dadfc02dd0428b41cd0c1bc321p+0Q, -0x1.8d688d31d04a4214094b65c4debbp+2Q, 0x1.317cc4a10faf3ff9c44aa0718d64p+3Q, -0x1.00fa12867f49132d26f6109f247ep+3Q, 0x1.9e984b48af59218135976f5867cdp+1Q, 0x1.0dcc3bbac5e0885ef946fb57406ap+1Q, -0x1.41a435a1df480f6b501eca709ce9p+2Q, 0x1.075a464fd9703954dc501fa92bp+2Q, -0x1.9984cb75bad50ddd23b7c6a93e49p+0Q, 0x1.9cf2e7196d1cbd2ef1ba36ca60f1p-5Q, 0x1.c915787e3612e2d3277f4d85346ap-3Q, -0x1.60b8b0c3b1138df4716646253fep-4Q, 0x1.324229742ef4416185466d935a63p-7Q, 0x1.dd5da666efa58ec47474db0b7be4p-11Q, -0x1.351528a4bd8176153593c8a5aa54p-13Q, -0x1.03c4250827b68f69b983f44799e9p-22Q, 0x1.77139f17861eb1acd308dc031a76p-26Q, -0x1.cd96fccfe9f0afba4ba09dac4612p-39Q, -0x0p+0Q};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0Q, 0x1.a04f8069ea8b4e447d853aa59d25p+1Q, -0x1.18f0a34d9f68e4d06a24b5ca38e6p+4Q, 0x1.4ce3831796a61ef6af32be9c5755p+5Q, -0x1.dc75f9b0b9a1041da91933798254p+5Q, 0x1.fdbc97313e6ed6865f9096b019f1p+5Q, -0x1.eefc0cdda4efa281b21fc8a20dabp+5Q, 0x1.b92a7c1b6a889c31c867c0d1a21p+5Q, -0x1.2299d502734c3c9b7e4c9a715a66p+5Q, 0x1.6502b707871df45089990b52d40bp+3Q, 0x1.11f33f4ede647d59a412fb3a4509p+2Q, -0x1.73b0a319e6889e9aa2e82f291565p+2Q, 0x1.244d452e7630092d6c490c8ed14ap+1Q, -0x1.35466c5650c61e120220d047deb3p-2Q, -0x1.fc20c8dd92f19b8d6ed30b21296p-6Q, 0x1.0d9c8b9d476f7d129de2a5d31814p-7Q, 0x1.a4010b80e5495d0ed9331143d19p-19Q, -0x1.49b0c99eb9c648511ea730b736bdp-19Q, 0x1.962a6dd57b7daa6dc5023a342508p-31Q, -0x0p+0Q};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0Q, 0x1.55886d2f64380baeb961079552b9p+2Q, -0x1.09d95f1cede31fcd15d2c7ff10a6p+5Q, 0x1.505f98e4bf27766f2f4d3b847255p+6Q, -0x1.96ec354b303069fd664614814e6ep+6Q, 0x1.17b23075f8010224c348afc6cdeep+5Q, 0x1.fc17211fa4d6f3f6a3261645172p+5Q, -0x1.b35f4a36b31c3849a4f0629dcf72p+6Q, 0x1.d17f22f2480f88bf1a425e07fe7dp+6Q, -0x1.12118c5678b4d442de8a0eede2e7p+7Q, 0x1.207a74ca5ad8bfc2ee103b7b451ap+7Q, -0x1.934735f943481c7f74f56dd50a8cp+6Q, 0x1.3fa55ba9206e3812ee32da23b318p+5Q, -0x1.959601005ec548729558e21bc187p+2Q, -0x1.9505e84d98e613cfe4ec3f6e6e46p-1Q, 0x1.43d2632e32cd0df0bb4a95d5e374p-2Q, -0x1.38e017336cd0614a6ed2ffd6195cp-10Q, -0x1.968e83ac595b8c6d9c1729fe9a6bp-13Q, 0x1.f5ed4b124df3ad0700a32c83080bp-24Q, -0x0p+0Q};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0Q, 0x1.f3cda2f9b135402362018238b572p+1Q, -0x1.9eeda12641b61ebb7d840ed67404p+4Q, 0x1.260fdaadd19eb1efc078d802d296p+6Q, -0x1.d673d80eeade4a070ce0e70cb866p+6Q, 0x1.f01b2fa154d0352990b16aadcb37p+6Q, -0x1.addb2c4ad791e217324c7ab3e2p+6Q, 0x1.7db87bda6fdf8a74bb08213eb30cp+6Q, -0x1.3f9860f6c4905e7132b1781da9d9p+6Q, 0x1.ae731643e9198e62164858360f7bp+5Q, -0x1.fb5cc3351ebc176988bf64799f2ap+4Q, 0x1.259afcbb8804d6eae552ab39b9b8p+4Q, -0x1.fe186e460309fdcedab5ec39f27p+2Q, 0x1.4d0298c21892754606c3d8eb8426p+0Q, 0x1.a1f0a66406a122ae435ed98cb7f1p-2Q, -0x1.40c0addfd85543af466cc7e3fef1p-3Q, 0x1.ba72fac37f087c7aee39dd7f1012p-9Q, 0x1.c193f16bb678e5af6510cd5c2355p-13Q, -0x1.16b4995bb4f073263c20b5bede1p-22Q, 0x0p+0Q};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0Q, 0x1.3586d9a9e0e3d99d2b93a0256171p+1Q, -0x1.08fa63342ecc1c41a46b366506c6p+4Q, 0x1.7c41f01d6960cbda171d22bf8adfp+5Q, -0x1.276b64d22e134fe3903178671e17p+6Q, 0x1.14f1cf74869c077b4ddd6015e432p+6Q, -0x1.83d54ac636b8244258f1e3dbaa06p+5Q, 0x1.4053c8a2c8d2fc6aef1621f86f1fp+5Q, -0x1.209b538b18df262448ee3cf880b8p+5Q, 0x1.65783340b3782c7d703e94c62d9ep+4Q, -0x1.2ddf670e51dfca7d85e8eebe7331p+3Q, 0x1.38744fdae212579791ea9e6fe9ebp+2Q, -0x1.4065c212ba5c0456783637883b7p+1Q, 0x1.6763c5d11b774e2d99bb556bddebp-4Q, 0x1.181d4d676ea1f03e7d8c57b474fp-1Q, -0x1.87564028831fbd4eb29dad94592bp-3Q, 0x1.843d22529bb49b17cf15d63953b5p-7Q, 0x1.52be3b0b8c7af55af9d914a987b4p-11Q, -0x1.a79c626c8654ebdb591ae56046e7p-20Q, -0x0p+0Q};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0Q, 0x1.7a3cf471120ec198713995bd540fp+0Q, -0x1.48b25e52d274b1e47c88655cec4bp+3Q, 0x1.cbd93276e7d596419b912e942e9bp+4Q, -0x1.37885d5242030806d66e5d6872f8p+5Q, 0x1.4db4fb7a5ecdb9227e88240cd0ebp+4Q, 0x1.74ac2dca21f55bb24886bcb3619p+2Q, -0x1.11ca2f9f0b7d05f1c1618e42e113p+3Q, 0x1.9fa6aaf0c8d980502f8417a8ec05p-4Q, -0x1.8ceb3288570cd32c2591a09c3995p+2Q, 0x1.e686e3fbc3fbf35811a68ef5ccfap+3Q, -0x1.7e0b780d60231a4c786ec6e1bf8dp+3Q, 0x1.7e1a3482e160bfcf5bb19766022ep+2Q, -0x1.247b57131543bcbee8b060f013c2p+2Q, 0x1.b8a4e1c96768c895a2f367776819p+1Q, -0x1.4f17d502240a8e6f55c9e0d7f0cfp+0Q, 0x1.4b408438ac8689521da23fc4a9bap-3Q, 0x1.7264788c9473dca575636e2ed518p-7Q, -0x1.d74fd6a021547c7f9f7dd3ce0b46p-15Q, -0x0p+0Q};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0Q, 0x1.f6438a3a88460091e0ea851f2c9bp-4Q, -0x1.b7ba9255f9c77a442c3315faffdep-1Q, 0x1.3f509b3842148b5acdb05e01c1ap+1Q, -0x1.eac616f0d4f869be16ce06dc94d2p+1Q, 0x1.ae9244fef585d2a56f1cb6a3721cp+1Q, -0x1.00d5d03220f3bbc8a51448af242cp+1Q, 0x1.9413f3bab26fc85ab60692f2dd27p+0Q, -0x1.9bd9847a10dd537f2de875e80d0ep+0Q, 0x1.16aae27d18a67638fdda8ca2a252p+0Q, -0x1.1587682f48215c21c42b36d7c2d1p-1Q, 0x1.8145e3cc3cfcbcc409c895e52cdp-2Q, -0x1.faf556e68970db4f5325d215482dp-3Q, 0x1.8ec972676b06aaf4a1909e62a833p-4Q, -0x1.49980ed40883cadc7b702f738062p-5Q, 0x1.5730c48bae56a4ea4426b04ea74bp-6Q, -0x1.0952d6b855c638b977457b5132a1p-8Q, -0x1.ce071dd8df1eee9d16331f09e775p-12Q, 0x1.30a4361eb25b38fd9207742eecebp-18Q, -0x0p+0Q};
+            }
+        }
+        #endif
+    }
+    if constexpr (p == 11) {
+        if constexpr (std::is_same_v<Real, float>) {
+            if constexpr (order == 0) {
+                return {0x0p+0f, 0x1.f82d86p-7f, 0x1.da87aep-2f, 0x1.a074eap-1f, -0x1.d3dbc2p-2f, 0x1.07dc8cp-2f, -0x1.17e06ap-3f, 0x1.d853p-5f, -0x1.071062p-6f, 0x1.0182ap-9f, 0x1.d91cd2p-14f, 0x1.f2bfaap-15f, -0x1.d7e9bap-15f, 0x1.5c274ep-18f, 0x1.63562ep-20f, -0x1.0af58p-26f, 0x1.1409ccp-28f, -0x1.160128p-35f, -0x1.4f944ep-42f, -0x1.ad914cp-53f, -0x1.65d844p-70f, 0x0p+0f};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0f, 0x1.4988f6p-4f, 0x1.cd9786p-1f, -0x1.f03418p-1f, -0x1.075e3cp-3f, 0x1.303436p-3f, -0x1.71d07ep-12f, -0x1.321c6cp-4f, 0x1.0f00fp-4f, -0x1.fec808p-6f, 0x1.092c0ap-7f, -0x1.185782p-11f, -0x1.693106p-12f, 0x1.a2acf4p-14f, -0x1.c4d82p-19f, -0x1.e02848p-20f, 0x1.7db784p-25f, 0x1.739c16p-30f, -0x1.d9433ap-36f, 0x1.651bd6p-46f, 0x1.29783p-62f, -0x0p+0f};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0f, 0x1.5c07e6p-2f, 0x1.307a2ap-1f, -0x1.a41fd4p+1f, 0x1.08f33p+2f, -0x1.6a2a88p+1f, 0x1.5f04aep+0f, -0x1.150c78p-2f, -0x1.78ed1cp-3f, 0x1.4f999p-3f, -0x1.41156ep-5f, -0x1.6c5862p-7f, 0x1.21e04ap-7f, -0x1.cd1c36p-10f, 0x1.af648p-17f, 0x1.0136c4p-15f, -0x1.6928bp-19f, -0x1.6377bp-25f, 0x1.64323cp-30f, -0x1.6fb512p-40f, -0x1.32449ep-55f, 0x0p+0f};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0f, 0x1.1c297ep+0f, -0x1.a72bc4p+1f, 0x1.8e9818p+1f, -0x1.8f506ep-1f, 0x1.02364ap-1f, -0x1.0fb22ap+1f, 0x1.80597ep+1f, -0x1.38ad98p+1f, 0x1.339d14p+0f, -0x1.08b97cp-2f, -0x1.3f8a26p-4f, 0x1.2b8bd2p-4f, -0x1.35b764p-6f, 0x1.f33a86p-12f, 0x1.1c307ep-11f, -0x1.950dccp-15f, -0x1.f90492p-21f, 0x1.8b6cb6p-25f, -0x1.21deep-34f, -0x1.e2c778p-49f, 0x0p+0f};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0f, 0x1.51d8dcp+1f, -0x1.c33b04p+3f, 0x1.0e7952p+5f, -0x1.9aba4p+5f, 0x1.f144c4p+5f, -0x1.17ce56p+6f, 0x1.1abf8ep+6f, -0x1.aeeda8p+5f, 0x1.6d1976p+4f, 0x1.64c18ap+1f, -0x1.4b3d36p+3f, 0x1.8e7526p+2f, -0x1.9e20d2p+0f, 0x1.8f714p-5f, 0x1.002e9ap-4f, -0x1.22b5dp-7f, -0x1.695b64p-13f, 0x1.ba1b22p-17f, -0x1.df066ep-26f, -0x1.8ec07p-39f, 0x0p+0f};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0f, 0x1.553842p+2f, -0x1.1648a2p+5f, 0x1.7429c4p+6f, -0x1.d2259cp+6f, 0x1.36cbd8p+4f, 0x1.4a282ep+7f, -0x1.2e04acp+8f, 0x1.5f18c6p+8f, -0x1.80bbfp+8f, 0x1.90ad4cp+8f, -0x1.4159ep+8f, 0x1.4eba06p+7f, -0x1.6db5a8p+5f, 0x1.66137p-1f, 0x1.7dbb7ep+1f, -0x1.1851aap-1f, -0x1.230c94p-7f, 0x1.7e95e2p-10f, -0x1.136d24p-18f, -0x1.ca2f1p-31f, -0x0p+0f};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0f, 0x1.43e57ap+2f, -0x1.201578p+5f, 0x1.be9ebp+6f, -0x1.917bfcp+7f, 0x1.e7564ap+7f, -0x1.dd46b6p+7f, 0x1.c24b2cp+7f, -0x1.9299f8p+7f, 0x1.2da088p+7f, -0x1.7f74fcp+6f, 0x1.cafceap+5f, -0x1.cfad0ap+4f, 0x1.f4f5eap+2f, 0x1.14b6dap+0f, -0x1.5e908ap+0f, 0x1.1ee7d4p-2f, -0x1.1e668p-11f, -0x1.81c424p-10f, 0x1.28216ep-18f, 0x1.ebdb46p-30f, -0x0p+0f};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0f, 0x1.0e918ep+2f, -0x1.f54b1ep+4f, 0x1.8cc936p+6f, -0x1.5d87f4p+7f, 0x1.7fbdfcp+7f, -0x1.356154p+7f, 0x1.00a2fp+7f, -0x1.d61ad6p+6f, 0x1.4b192ep+6f, -0x1.2bd7eep+5f, 0x1.d23af8p+3f, -0x1.a5a3f6p+2f, -0x1.0097bap+0f, 0x1.29abecp+2f, -0x1.6d63c6p+1f, 0x1.521b96p-1f, -0x1.89a1eap-6f, -0x1.cc0f8cp-8f, 0x1.9e94aap-16f, 0x1.5739aap-26f, 0x0p+0f};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0f, 0x1.c2a5p+0f, -0x1.a9c968p+3f, 0x1.5bbb8cp+5f, -0x1.452574p+6f, 0x1.91c80cp+6f, -0x1.84d65cp+6f, 0x1.678e1ep+6f, -0x1.493302p+6f, 0x1.14413cp+6f, -0x1.b51d9ap+5f, 0x1.483818p+5f, -0x1.a72562p+4f, 0x1.e00e48p+3f, -0x1.1522f8p+3f, 0x1.152962p+2f, -0x1.3d9d88p+0f, 0x1.3f1c58p-4f, 0x1.b3efb4p-6f, -0x1.baa15ap-13f, -0x1.6c2d94p-22f, 0x0p+0f};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0f, 0x1.480f32p-1f, -0x1.38fe3p+2f, 0x1.f8f412p+3f, -0x1.bc60c4p+4f, 0x1.d3d44ap+4f, -0x1.536d7p+4f, 0x1.0953a8p+4f, -0x1.0c0dcap+4f, 0x1.af56b2p+3f, -0x1.f62894p+2f, 0x1.3ef834p+2f, -0x1.c75ab6p+1f, 0x1.cb38bcp+0f, -0x1.624786p-1f, 0x1.61b17ap-2f, -0x1.0b6248p-3f, 0x1.c9b3fp-8f, 0x1.7c528ap-8f, -0x1.0c4738p-13f, -0x1.b40e78p-22f, 0x0p+0f};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0f, 0x1.8a25fep-4f, -0x1.79dddep-1f, 0x1.2f9284p+1f, -0x1.04a532p+2f, 0x1.fbc728p+1f, -0x1.2e8a4ep+1f, 0x1.96ff88p+0f, -0x1.db8c8p+0f, 0x1.8867ecp+0f, -0x1.7019bcp-1f, 0x1.a30d2p-2f, -0x1.7340e8p-2f, 0x1.68181ap-3f, -0x1.50a6f6p-5f, 0x1.8d3b22p-6f, -0x1.b7227ep-7f, -0x1.a3115p-12f, 0x1.71e7a4p-10f, -0x1.4eea02p-14f, -0x1.09aedap-21f, 0x0p+0f};
+            }
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0, 0x1.f82d860ed311dp-7, 0x1.da87adf545deap-2, 0x1.a074ea6831a18p-1, -0x1.d3dbc22db3363p-2, 0x1.07dc8c4b5880ap-2, -0x1.17e06a0deb07p-3, 0x1.d85300a8e9a5ap-5, -0x1.0710616766f9ep-6, 0x1.0182a0c9a44bbp-9, 0x1.d91cd19825f46p-14, 0x1.f2bfaace30f59p-15, -0x1.d7e9ba7b3ac47p-15, 0x1.5c274e2e04a65p-18, 0x1.63562e1b18da8p-20, -0x1.0af5800900cccp-26, 0x1.1409cb495cfabp-28, -0x1.1601287f207ddp-35, -0x1.4f944d6c974a1p-42, -0x1.ad914b3b9c645p-53, -0x1.65d8440cb590ap-70, 0x0p+0};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0, 0x1.4988f615d8fc2p-4, 0x1.cd9786f046dbdp-1, -0x1.f034187a5d753p-1, -0x1.075e3bcf1d71fp-3, 0x1.303436308c6p-3, -0x1.71d07ef81053fp-12, -0x1.321c6b5970b99p-4, 0x1.0f00f07475782p-4, -0x1.fec807d6bcde3p-6, 0x1.092c0960e80ecp-7, -0x1.1857810566103p-11, -0x1.693105a2bb707p-12, 0x1.a2acf3b1f9d07p-14, -0x1.c4d81f25bbab6p-19, -0x1.e0284772a21efp-20, 0x1.7db784c0b0131p-25, 0x1.739c15dc80c55p-30, -0x1.d9433a2520a2ep-36, 0x1.651bd505e5aabp-46, 0x1.29782f98b98d9p-62, -0x0p+0};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0, 0x1.5c07e5083d709p-2, 0x1.307a2a8e783eap-1, -0x1.a41fd4c6e5304p+1, 0x1.08f3303fd9b5fp+2, -0x1.6a2a8758fd08cp+1, 0x1.5f04ae9c9034bp+0, -0x1.150c77d31565dp-2, -0x1.78ed1cb9b0ec2p-3, 0x1.4f99902d11603p-3, -0x1.41156e1c846c4p-5, -0x1.6c5861062a836p-7, 0x1.21e04958552e7p-7, -0x1.cd1c35ab2ad93p-10, 0x1.af6480e4adc47p-17, 0x1.0136c3fb4b19cp-15, -0x1.6928b0e495d08p-19, -0x1.6377af73884cp-25, 0x1.64323c063686ap-30, -0x1.6fb51174aa8e3p-40, -0x1.32449da1b9609p-55, 0x0p+0};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0, 0x1.1c297e1a72297p+0, -0x1.a72bc3c00615fp+1, 0x1.8e98178e99b32p+1, -0x1.8f506e2a5e0ebp-1, 0x1.02364935e2223p-1, -0x1.0fb2290536b32p+1, 0x1.80597d49465bfp+1, -0x1.38ad9781c7501p+1, 0x1.339d144fd9551p+0, -0x1.08b97b33caeccp-2, -0x1.3f8a268debfb7p-4, 0x1.2b8bd1a4fd0ebp-4, -0x1.35b764060a714p-6, 0x1.f33a86db42466p-12, 0x1.1c307da269deep-11, -0x1.950dcb7c8e982p-15, -0x1.f904916865d4dp-21, 0x1.8b6cb6bf7586bp-25, -0x1.21dedfd7476c5p-34, -0x1.e2c7778c519ap-49, 0x0p+0};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0, 0x1.51d8dbccf9207p+1, -0x1.c33b049bfbce6p+3, 0x1.0e79522ccf3ddp+5, -0x1.9aba40cee29c1p+5, 0x1.f144c4df7513dp+5, -0x1.17ce56ad9d902p+6, 0x1.1abf8d1adcc3ep+6, -0x1.aeeda88b7fe88p+5, 0x1.6d1975fc2f42ep+4, 0x1.64c18afe2844cp+1, -0x1.4b3d36d8f9771p+3, 0x1.8e75251a7f5bfp+2, -0x1.9e20d1654131ap+0, 0x1.8f713f264dac3p-5, 0x1.002e9aac59197p-4, -0x1.22b5d07d79f25p-7, -0x1.695b63166e6d6p-13, 0x1.ba1b21857af83p-17, -0x1.df066d7576ffdp-26, -0x1.8ec06f9de2f7dp-39, 0x0p+0};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0, 0x1.553841cb8504cp+2, -0x1.1648a261cfac8p+5, 0x1.7429c31b8bcdcp+6, -0x1.d2259be1a7819p+6, 0x1.36cbd86221f4cp+4, 0x1.4a282d1320ed7p+7, -0x1.2e04ab290e2ep+8, 0x1.5f18c6755ba05p+8, -0x1.80bbefefb8959p+8, 0x1.90ad4b61c673ep+8, -0x1.4159e0e62036cp+8, 0x1.4eba06db33d53p+7, -0x1.6db5a82568a44p+5, 0x1.6613709f48646p-1, 0x1.7dbb7d4fa2b47p+1, -0x1.1851a9519e35ep-1, -0x1.230c93cadc0b8p-7, 0x1.7e95e283d8ce3p-10, -0x1.136d2374e3712p-18, -0x1.ca2f0f4b75006p-31, -0x0p+0};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0, 0x1.43e579b56aec7p+2, -0x1.2015783789a13p+5, 0x1.be9eb07640a6ep+6, -0x1.917bfbcd50104p+7, 0x1.e7564ac670465p+7, -0x1.dd46b6e14bd99p+7, 0x1.c24b2cb18bb3p+7, -0x1.9299f7098407ep+7, 0x1.2da088f392f17p+7, -0x1.7f74fc0a8fbbcp+6, 0x1.cafceab55c222p+5, -0x1.cfad0a751fefdp+4, 0x1.f4f5eade96654p+2, 0x1.14b6d949957a5p+0, -0x1.5e908a00f74dap+0, 0x1.1ee7d490234e2p-2, -0x1.1e667fbdaff18p-11, -0x1.81c4231f27f24p-10, 0x1.28216d550397dp-18, 0x1.ebdb45ca159a6p-30, -0x0p+0};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0, 0x1.0e918e0751a5fp+2, -0x1.f54b1dc71e94cp+4, 0x1.8cc935a5962f3p+6, -0x1.5d87f4fd9af88p+7, 0x1.7fbdfc1f5c92bp+7, -0x1.356154b8ce2cp+7, 0x1.00a2f00b6f36p+7, -0x1.d61ad68084632p+6, 0x1.4b192d711636ap+6, -0x1.2bd7eeccbbd8bp+5, 0x1.d23af72a92131p+3, -0x1.a5a3f6309aca8p+2, -0x1.0097ba319005fp+0, 0x1.29abec5ca24e5p+2, -0x1.6d63c669ef72ap+1, 0x1.521b96f1f012p-1, -0x1.89a1e9b6409a4p-6, -0x1.cc0f8b0b31976p-8, 0x1.9e94a90cc2ee8p-16, 0x1.5739a9ee6eb1dp-26, 0x0p+0};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0, 0x1.c2a4ffe966119p+0, -0x1.a9c9682497d43p+3, 0x1.5bbb8c487ae5cp+5, -0x1.452573aebb3bfp+6, 0x1.91c80b52c3671p+6, -0x1.84d65b83affb6p+6, 0x1.678e1d36597aep+6, -0x1.4933025bdb689p+6, 0x1.14413c8e18076p+6, -0x1.b51d99f667842p+5, 0x1.483818775e0cbp+5, -0x1.a72562d5d8065p+4, 0x1.e00e48c9f7714p+3, -0x1.1522f77734c2fp+3, 0x1.152961e6e0f57p+2, -0x1.3d9d88a64fae4p+0, 0x1.3f1c58e4e2a68p-4, 0x1.b3efb441a4e1bp-6, -0x1.baa159e67dd4fp-13, -0x1.6c2d94cde3ae2p-22, 0x0p+0};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0, 0x1.480f31520e3f3p-1, -0x1.38fe2f09aac58p+2, 0x1.f8f411bacc9f9p+3, -0x1.bc60c3b54f90bp+4, 0x1.d3d44a6a16adbp+4, -0x1.536d6f833b667p+4, 0x1.0953a7a524acbp+4, -0x1.0c0dca303e8e2p+4, 0x1.af56b1534f29ep+3, -0x1.f628948ceff74p+2, 0x1.3ef834c3289aap+2, -0x1.c75ab5e1afc76p+1, 0x1.cb38bb2c5f4bfp+0, -0x1.624785bf15dbep-1, 0x1.61b17ae5ff0c1p-2, -0x1.0b62472bd3d78p-3, 0x1.c9b3ef0688e89p-8, 0x1.7c528a3f2156cp-8, -0x1.0c4738028aec9p-13, -0x1.b40e785cb8808p-22, 0x0p+0};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0, 0x1.8a25fe79d1c4ep-4, -0x1.79dddd860d214p-1, 0x1.2f92842080f08p+1, -0x1.04a53246109b7p+2, 0x1.fbc727fc23efp+1, -0x1.2e8a4ebac6b5ep+1, 0x1.96ff87cfe4cc5p+0, -0x1.db8c7f7bf2c3ap+0, 0x1.8867eccd39d1bp+0, -0x1.7019bc278ffcp-1, 0x1.a30d20b4e67c7p-2, -0x1.7340e7a399e64p-2, 0x1.68181929e64c5p-3, -0x1.50a6f5e8f3b31p-5, 0x1.8d3b211eb839bp-6, -0x1.b7227d5381373p-7, -0x1.a3114fdf2fbcp-12, 0x1.71e7a3b4d88bfp-10, -0x1.4eea023db8bd5p-14, -0x1.09aed93888304p-21, 0x0p+0};
+            }
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0L, 0xf.c16c3076988ebbcp-10L, 0xe.d43d6faa2ef51b8p-5L, 0xd.03a753418d0bce6p-4L, -0xe.9ede116d99b1966p-5L, 0x8.3ee4625ac404c6dp-5L, -0x8.bf03506f5837fe3p-6L, 0xe.c29805474d2cedap-8L, -0x8.38830b3b37cedbcp-9L, 0x8.0c15064d225d41p-12L, 0xe.c8e68cc12fa31cbp-17L, 0xf.95fd567187ac541p-18L, -0xe.bf4dd3d9d6239bp-18L, 0xa.e13a71702532bafp-21L, 0xb.1ab170d8c6d3fd6p-23L, -0x8.57ac00480665f53p-29L, 0x8.a04e5a4ae7d54e6p-31L, -0x8.b00943f903ee402p-38L, -0xa.7ca26b64ba505d1p-45L, -0xd.6c8a59dce3224e2p-56L, -0xb.2ec22065ac84f3fp-73L, 0x0p+0L};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0L, 0xa.4c47b0aec7e1081p-7L, 0xe.6cbc378236de837p-4L, -0xf.81a0c3d2eba999fp-4L, -0x8.3af1de78eb8f98bp-6L, 0x9.81a1b1846300118p-6L, -0xb.8e83f7c0829f529p-15L, -0x9.90e35acb85cca72p-7L, 0x8.780783a3abc1044p-7L, -0xf.f6403eb5e6f17b6p-9L, 0x8.49604b074075f3ap-10L, -0x8.c2bc082b308154p-14L, -0xb.49882d15db83441p-15L, 0xd.15679d8fce83a4ap-17L, -0xe.26c0f92ddd5b332p-22L, -0xf.01423b9510f7584p-23L, 0xb.edbc2605809849dp-28L, 0xb.9ce0aee4062aafdp-33L, -0xe.ca19d1290517188p-39L, 0xb.28dea82f2d5572ep-49L, 0x9.4bc17cc5cc6c599p-65L, -0x0p+0L};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0L, 0xa.e03f2841eb84819p-5L, 0x9.83d15473c1f50fdp-4L, -0xd.20fea63729823dcp-2L, 0x8.479981fecdaf816p-1L, -0xb.51543ac7e845d9fp-2L, 0xa.f82574e481a558dp-3L, -0x8.a863be98ab2e9afp-5L, -0xb.c768e5cd8760f3bp-6L, 0xa.7ccc81688b01b9cp-6L, -0xa.08ab70e42362325p-8L, -0xb.62c30831541b0b7p-10L, 0x9.0f024ac2a973782p-10L, -0xe.68e1ad5956c95f9p-13L, 0xd.7b2407256e2365dp-20L, 0x8.09b61fda58cdcd9p-18L, -0xb.49458724ae83fdap-22L, -0xb.1bbd7b9c425fd7p-28L, 0xb.2191e031b4353cfp-33L, -0xb.7da88ba55471baap-43L, -0x9.9224ed0dcb0440cp-58L, 0x0p+0L};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0L, 0x8.e14bf0d3914bbd4p-3L, -0xd.395e1e0030afb9ep-2L, 0xc.74c0bc74cd98ea3p-2L, -0xc.7a837152f075af7p-4L, 0x8.11b249af1111423p-4L, -0x8.7d914829b598f95p-2L, 0xc.02cbea4a32dfa62p-2L, -0x9.c56cbc0e3a809b2p-2L, 0x9.9ce8a27ecaa85dcp-3L, -0x8.45cbd99e57663b5p-5L, -0x9.fc51346f5fdbbd1p-7L, 0x9.5c5e8d27e8757a5p-7L, -0x9.adbb20305389e61p-9L, 0xf.99d436da1232d03p-15L, 0x8.e183ed134ef71abp-14L, -0xc.a86e5be474c0e96p-18L, -0xf.c8248b432ea6598p-24L, 0xc.5b65b5fbac3587ap-28L, -0x9.0ef6feba3b62aaap-37L, -0xf.163bbc628cd0205p-52L, 0x0p+0L};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0L, 0xa.8ec6de67c9035e6p-2L, -0xe.19d824dfde72f6dp+0L, 0x8.73ca916679ee85cp+2L, -0xc.d5d2067714e04fcp+2L, 0xf.8a2626fba89eb9ep+2L, -0x8.be72b56cec81364p+3L, 0x8.d5fc68d6e61f284p+3L, -0xd.776d445bff43fe9p+2L, 0xb.68cbafe17a170d9p+1L, 0xb.260c57f14226301p-2L, -0xa.59e9b6c7cbb8775p+0L, 0xc.73a928d3fadf73cp-1L, -0xc.f1068b2a098cfb7p-3L, 0xc.7b89f9326d61459p-8L, 0x8.0174d562c8cba6dp-7L, -0x9.15ae83ebcf927bfp-10L, -0xb.4adb18b3736b1d7p-16L, 0xd.d0d90c2bd7c17dcp-20L, -0xe.f8336babb7fe566p-29L, -0xc.76037cef17bea43p-42L, 0x0p+0L};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0L, 0xa.a9c20e5c28262cfp-1L, -0x8.b245130e7d6435p+2L, 0xb.a14e18dc5e6e3bcp+3L, -0xe.912cdf0d3c0c767p+3L, 0x9.b65ec3110fa60e2p+1L, 0xa.51416899076b9c3p+4L, -0x9.702559487170317p+5L, 0xa.f8c633aadd02508p+5L, -0xc.05df7f7dc4ac954p+5L, 0xc.856a5b0e339f38dp+5L, -0xa.0acf073101b6074p+5L, 0xa.75d036d99ea9702p+4L, -0xb.6dad412b4521e9bp+2L, 0xb.309b84fa4322d85p-4L, 0xb.eddbea7d15a390ap-2L, -0x8.c28d4a8cf1aeca5p-4L, -0x9.18649e56e05bc3p-10L, 0xb.f4af141ec671a67p-13L, -0x8.9b691ba71b88c22p-21L, -0xe.51787a5ba8032eep-34L, -0x0p+0L};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0L, 0xa.1f2bcdab57636dcp-1L, -0x9.00abc1bc4d0982ep+2L, 0xd.f4f583b2053726ep+3L, -0xc.8bdfde6a8082091p+4L, 0xf.3ab256338232753p+4L, -0xe.ea35b70a5ecc9fep+4L, 0xe.1259658c5d981b4p+4L, -0xc.94cfb84c203ee2p+4L, 0x9.6d04479c978badep+4L, -0xb.fba7e0547ddde95p+3L, 0xe.57e755aae11112fp+2L, -0xe.7d6853a8ff7e50ap+1L, 0xf.a7af56f4b329d5ep-1L, 0x8.a5b6ca4cabd2b23p-3L, -0xa.f4845007ba6cfc8p-3L, 0x8.f73ea4811a71163p-5L, -0x8.f333fded7f8c399p-14L, -0xc.0e2118f93f91f36p-13L, 0x9.410b6aa81cbea18p-21L, 0xf.5eda2e50acd327dp-33L, -0x0p+0L};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0L, 0x8.748c703a8d2f937p-1L, -0xf.aa58ee38f4a5c91p+1L, 0xc.6649ad2cb179936p+3L, -0xa.ec3fa7ecd7c41f4p+4L, 0xb.fdefe0fae49564ap+4L, -0x9.ab0aa5c6715fdd9p+4L, 0x8.0517805b79afde9p+4L, -0xe.b0d6b4042318ee3p+3L, 0xa.58c96b88b1b4fe8p+3L, -0x9.5ebf7665dec59a9p+2L, 0xe.91d7b95490989a7p+0L, -0xd.2d1fb184d6542c6p-1L, -0x8.04bdd18c802f85cp-3L, 0x9.4d5f62e5127240ep-1L, -0xb.6b1e334f7b950afp-2L, 0xa.90dcb78f808ffecp-4L, -0xc.4d0f4db204d1cc9p-9L, -0xe.607c58598cbad8fp-11L, 0xc.f4a5486617740b1p-19L, 0xa.b9cd4f73758e428p-29L, 0x0p+0L};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0L, 0xe.1527ff4b308c86p-3L, -0xd.4e4b4124bea1ab6p+0L, 0xa.dddc6243d72ddb1p+2L, -0xa.292b9d75d9dfa3ap+3L, 0xc.8e405a961b38a93p+3L, -0xc.26b2dc1d7fdae55p+3L, 0xb.3c70e9b2cbd6e2ap+3L, -0xa.499812dedb44ac4p+3L, 0x8.a209e470c03af8ap+3L, -0xd.a8eccfb33c210d9p+2L, 0xa.41c0c3baf0658a2p+2L, -0xd.392b16aec032585p+1L, 0xf.0072464fbb8a1e7p+0L, -0x8.a917bbb9a6176d9p+0L, 0x8.a94b0f3707ab7abp-1L, -0x9.ecec45327d721f6p-3L, 0x9.f8e2c727153415ep-7L, 0xd.9f7da20d270d536p-9L, -0xd.d50acf33eea750ap-16L, -0xb.616ca66f1d70df8p-25L, 0x0p+0L};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0L, 0xa.40798a9071f9886p-4L, -0x9.c7f1784d562bdc9p-1L, 0xf.c7a08dd664fcb0ep+0L, -0xd.e3061daa7c85492p+1L, 0xe.9ea25350b56d92ap+1L, -0xa.9b6b7c19db33b9dp+1L, 0x8.4a9d3d29256548ap+1L, -0x8.606e5181f471318p+1L, 0xd.7ab58a9a794ee91p+0L, -0xf.b144a4677fb9db7p-1L, 0x9.f7c1a61944d51aep-1L, -0xe.3ad5af0d7e3ad17p-2L, 0xe.59c5d962fa5f5d7p-3L, -0xb.123c2df8aedf04ap-4L, 0xb.0d8bd72ff86061cp-5L, -0x8.5b12395e9ebc248p-6L, 0xe.4d9f7834474485cp-11L, 0xb.e29451f90ab62c4p-11L, -0x8.6239c0145764987p-16L, -0xd.a073c2e5c404378p-25L, 0x0p+0L};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0L, 0xc.512ff3ce8e26ed6p-7L, -0xb.ceeeec30690a3d4p-4L, 0x9.7c942104078413dp-2L, -0x8.2529923084db5b6p-1L, 0xf.de393fe11f77db2p-2L, -0x9.745275d635af24dp-2L, 0xc.b7fc3e7f2662817p-3L, -0xe.dc63fbdf961d121p-3L, 0xc.433f6669ce8d77ap-3L, -0xb.80cde13c7fe01dap-4L, 0xd.186905a733e3482p-5L, -0xb.9a073d1ccf31d0dp-5L, 0xb.40c0c94f326298p-6L, -0xa.8537af479d9846bp-8L, 0xc.69d908f5c1cd609p-9L, -0xd.b913ea9c09b9ab5p-10L, -0xd.188a7ef97de034bp-15L, 0xb.8f3d1da6c45f8b5p-13L, -0xa.775011edc5ea48p-17L, -0x8.4d76c9c441821a3p-24L, 0x0p+0L};
+            }
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            if constexpr (order == 0) {
+                return {0x0p+0Q, 0x1.f82d860ed311d7772f0a5fc02aa2p-7Q, 0x1.da87adf545dea36f29603c50206fp-2Q, 0x1.a074ea6831a179cbcefe13bdeb27p-1Q, -0x1.d3dbc22db33632cb9d3eeea9309ep-2Q, 0x1.07dc8c4b588098d99d74923fef11p-2Q, -0x1.17e06a0deb06ffc5a354422c2917p-3Q, 0x1.d85300a8e9a59db3d8e328544722p-5Q, -0x1.0710616766f9db787dd784803608p-6Q, 0x1.0182a0c9a44ba81f2b490da87ce3p-9Q, 0x1.d91cd19825f46395eba40bde2571p-14Q, 0x1.f2bfaace30f58a825ed0b3a11e16p-15Q, -0x1.d7e9ba7b3ac4736029b548526141p-15Q, 0x1.5c274e2e04a6575e26e75abeb4d6p-18Q, 0x1.63562e1b18da7fac5905b88575eep-20Q, -0x1.0af5800900ccbea5a647053aa06fp-26Q, 0x1.1409cb495cfaa9cc50f1fb2798a1p-28Q, -0x1.1601287f207dc804b32b2b372bd4p-35Q, -0x1.4f944d6c974a0ba10244cbd7bf6ap-42Q, -0x1.ad914b3b9c6449c459a4d88261fp-53Q, -0x1.65d8440cb5909e7eb82f547cb7ffp-70Q, 0x0p+0Q};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0Q, 0x1.4988f615d8fc21013726786516bbp-4Q, 0x1.cd9786f046dbd06d9795ae530616p-1Q, -0x1.f034187a5d75333e9dbb5b104718p-1Q, -0x1.075e3bcf1d71f31524cf997afba1p-3Q, 0x1.303436308c600230256305532d4ep-3Q, -0x1.71d07ef81053ea5196f6a9c9bd7ap-12Q, -0x1.321c6b5970b994e47d89204a7748p-4Q, 0x1.0f00f0747578208709a35dbb5683p-4Q, -0x1.fec807d6bcde2f6b9da93df4aa7bp-6Q, 0x1.092c0960e80ebe73a0fb5f592a93p-7Q, -0x1.1857810566102a80b03f6d574873p-11Q, -0x1.693105a2bb706882bf9e39158ac2p-12Q, 0x1.a2acf3b1f9d0749452e4dc44d928p-14Q, -0x1.c4d81f25bbab666371fdd702fd07p-19Q, -0x1.e0284772a21eeb07c87b76642dabp-20Q, 0x1.7db784c0b013093ad9874c402643p-25Q, 0x1.739c15dc80c555f970d134b64534p-30Q, -0x1.d9433a2520a2e30f13e7c351f19ep-36Q, 0x1.651bd505e5aaae5cab5b708f20d3p-46Q, 0x1.29782f98b98d8b31230d837a9eebp-62Q, -0x0p+0Q};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0Q, 0x1.5c07e5083d7090314f4044902659p-2Q, 0x1.307a2a8e783ea1f99bb361a3cef6p-1Q, -0x1.a41fd4c6e53047b890408086b56p+1Q, 0x1.08f3303fd9b5f02cbec87edc4433p+2Q, -0x1.6a2a8758fd08bb3ed6b347424ce1p+1Q, 0x1.5f04ae9c9034ab19fcfae00d09d5p+0Q, -0x1.150c77d31565d35edf80240e5f13p-2Q, -0x1.78ed1cb9b0ec1e760990f81b5f62p-3Q, 0x1.4f99902d11603738023acee04ff8p-3Q, -0x1.41156e1c846c464a303629e297f8p-5Q, -0x1.6c5861062a83616dee9275c18c3cp-7Q, 0x1.21e04958552e6f03502dd79356aap-7Q, -0x1.cd1c35ab2ad92bf156188522c4d7p-10Q, 0x1.af6480e4adc46cb9e0c7649b6bfap-17Q, 0x1.0136c3fb4b19b9b10157d7a8345p-15Q, -0x1.6928b0e495d07fb474aad680049ap-19Q, -0x1.6377af73884bfae0ae8534a755ap-25Q, 0x1.64323c063686a79e3f723a6f6a99p-30Q, -0x1.6fb51174aa8e375496c635af8171p-40Q, -0x1.32449da1b960881894abd22269dap-55Q, 0x0p+0Q};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0Q, 0x1.1c297e1a722977a767a1ff2272dcp+0Q, -0x1.a72bc3c00615f73ba93716b01652p+1Q, 0x1.8e98178e99b31d46ae26eec0a62ep+1Q, -0x1.8f506e2a5e0eb5edc0313f13910ap-1Q, 0x1.02364935e2222846b9cdda1bad5bp-1Q, -0x1.0fb2290536b31f2a2fbff34045aap+1Q, 0x1.80597d49465bf4c4d8869fb53015p+1Q, -0x1.38ad9781c750136475272cd6e5fep+1Q, 0x1.339d144fd9550bb8463b544a639ep+0Q, -0x1.08b97b33caecc76a026ab8335ac7p-2Q, -0x1.3f8a268debfb77a1cde76d550dc6p-4Q, 0x1.2b8bd1a4fd0eaf4aaa08a96cf13fp-4Q, -0x1.35b764060a713cc242948b5c3e5ep-6Q, 0x1.f33a86db42465a05a6ee3ed1f1c2p-12Q, 0x1.1c307da269dee355c5c2d340dc8p-11Q, -0x1.950dcb7c8e981d2c1ff88549c6afp-15Q, -0x1.f904916865d4cb30ef383c46a7ddp-21Q, 0x1.8b6cb6bf7586b0f4f1fcded43d5cp-25Q, -0x1.21dedfd7476c5553241f507abe95p-34Q, -0x1.e2c7778c519a040a7c97727eda55p-49Q, 0x0p+0Q};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0Q, 0x1.51d8dbccf9206bcc4420e8d9a9eap+1Q, -0x1.c33b049bfbce5ed995e580451e63p+3Q, 0x1.0e79522ccf3dd0b86ea89a553ap+5Q, -0x1.9aba40cee29c09f71dc38c35b29bp+5Q, 0x1.f144c4df7513d73b0fd71dc9dfb5p+5Q, -0x1.17ce56ad9d9026c80fe9053e2d6dp+6Q, 0x1.1abf8d1adcc3e5071c7209bb681cp+6Q, -0x1.aeeda88b7fe87fd16bcf8e052138p+5Q, 0x1.6d1975fc2f42e1b2096263c936fdp+4Q, 0x1.64c18afe2844c60255dd74d11ep+1Q, -0x1.4b3d36d8f9770ee95e2721f914bbp+3Q, 0x1.8e75251a7f5bee7754c2a951492ep+2Q, -0x1.9e20d16541319f6d732cb61c0c9ap+0Q, 0x1.8f713f264dac28b16bf91d5056c3p-5Q, 0x1.002e9aac591974da848a16c85358p-4Q, -0x1.22b5d07d79f24f7de83980b60562p-7Q, -0x1.695b63166e6d63ad77759faf5052p-13Q, 0x1.ba1b21857af82fb76bf474298db1p-17Q, -0x1.df066d7576ffcacbc6c94f3c5a26p-26Q, -0x1.8ec06f9de2f7d48618cf3f2e50ccp-39Q, 0x0p+0Q};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0Q, 0x1.553841cb8504c59ec882878d66e2p+2Q, -0x1.1648a261cfac86a07a57717eb0e3p+5Q, 0x1.7429c31b8bcdc777e068523e1aeap+6Q, -0x1.d2259be1a7818ecd1bf98b178549p+6Q, 0x1.36cbd86221f4c1c3813018fd6cbfp+4Q, 0x1.4a282d1320ed73864b5c77ade623p+7Q, -0x1.2e04ab290e2e062d6018a9efa98fp+8Q, 0x1.5f18c6755ba04a0fe584709ac85dp+8Q, -0x1.80bbefefb89592a7731266a97561p+8Q, 0x1.90ad4b61c673e71a7b1a662f6ff2p+8Q, -0x1.4159e0e62036c0e7d3a9392e2704p+8Q, 0x1.4eba06db33d52e049a4997516cf9p+7Q, -0x1.6db5a82568a43d359e1327442546p+5Q, 0x1.6613709f48645b09020d12e639edp-1Q, 0x1.7dbb7d4fa2b472146ed1344dc15bp+1Q, -0x1.1851a9519e35d9490483602f6703p-1Q, -0x1.230c93cadc0b78607a6df81f1b6fp-7Q, 0x1.7e95e283d8ce34ce8180ea4f4ca4p-10Q, -0x1.136d2374e371184371f1175ee7a9p-18Q, -0x1.ca2f0f4b750065dbf1a921be61p-31Q, -0x0p+0Q};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0Q, 0x1.43e579b56aec6db8f44fad025d31p+2Q, -0x1.2015783789a1305c4b04f4166dd8p+5Q, 0x1.be9eb07640a6e4dcf71e8ec13b53p+6Q, -0x1.917bfbcd50104121d7cf2e45b56cp+7Q, 0x1.e7564ac670464ea6f5bb02fedc24p+7Q, -0x1.dd46b6e14bd993fb7d27e48ccc74p+7Q, 0x1.c24b2cb18bb303674bf660cced48p+7Q, -0x1.9299f7098407dc40f69f41c308ebp+7Q, 0x1.2da088f392f175bbf1502adde1fap+7Q, -0x1.7f74fc0a8fbbbd2a6629268e303fp+6Q, 0x1.cafceab55c22225d33d1409b59ap+5Q, -0x1.cfad0a751fefca13c3b32651d4a9p+4Q, 0x1.f4f5eade96653abb41ce938b652dp+2Q, 0x1.14b6d949957a5646a55036bfd229p+0Q, -0x1.5e908a00f74d9f8f6b65d27bbd91p+0Q, 0x1.1ee7d490234e22c547ade06a389fp-2Q, -0x1.1e667fbdaff187310b0175bb8ebfp-11Q, -0x1.81c4231f27f23e6bc64b0c485b78p-10Q, 0x1.28216d550397d430f87999376f2cp-18Q, 0x1.ebdb45ca159a64fa9f199a6004f2p-30Q, -0x0p+0Q};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0Q, 0x1.0e918e0751a5f26d66d32652a3c3p+2Q, -0x1.f54b1dc71e94b922c8b7d9cedc49p+4Q, 0x1.8cc935a5962f326b8767ea0da425p+6Q, -0x1.5d87f4fd9af883e7ca8f85fa5bb5p+7Q, 0x1.7fbdfc1f5c92ac9439f72daa4354p+7Q, -0x1.356154b8ce2bfbb26ff261795e76p+7Q, 0x1.00a2f00b6f35fbd2365b8c89c9e7p+7Q, -0x1.d61ad68084631dc5b1cb3579539ep+6Q, 0x1.4b192d7116369fcf46bbc7a85648p+6Q, -0x1.2bd7eeccbbd8b3529c9ec84730c4p+5Q, 0x1.d23af72a9213134d138ab8713629p+3Q, -0x1.a5a3f6309aca858b5548cd2e0f1fp+2Q, -0x1.0097ba319005f0b824ee38e92ecp+0Q, 0x1.29abec5ca24e481b150656fe0d65p+2Q, -0x1.6d63c669ef72a15dead10bcfb7ep+1Q, 0x1.521b96f1f011ffd834fe0c58029ap-1Q, -0x1.89a1e9b6409a39917b2558e5c9cap-6Q, -0x1.cc0f8b0b31975b1da167d6c2e885p-8Q, 0x1.9e94a90cc2ee8162e5d90cd367bep-16Q, 0x1.5739a9ee6eb1c850a9597ef2cebp-26Q, 0x0p+0Q};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0Q, 0x1.c2a4ffe9661190c09a7af6cb9ca4p+0Q, -0x1.a9c9682497d4356cc97c764c71e1p+3Q, 0x1.5bbb8c487ae5bb615e8e71957082p+5Q, -0x1.452573aebb3bf474bf24d39c0c75p+6Q, 0x1.91c80b52c3671525c3375728fd33p+6Q, -0x1.84d65b83affb5ca97ccaf4bcaa17p+6Q, 0x1.678e1d36597adc53993fd53deeacp+6Q, -0x1.4933025bdb6895888c17391d3c87p+6Q, 0x1.14413c8e18075f1444cc50c11326p+6Q, -0x1.b51d99f6678421b18139cf56717cp+5Q, 0x1.483818775e0cb14480b3264cce69p+5Q, -0x1.a72562d5d8064b092b7ba7b739cp+4Q, 0x1.e00e48c9f77143cec0c43437c4bep+3Q, -0x1.1522f77734c2edb19342dec0265fp+3Q, 0x1.152961e6e0f56f56720078cacb8p+2Q, -0x1.3d9d88a64fae43ec46db6df5abf8p+0Q, 0x1.3f1c58e4e2a682bc6ff0544f4ae4p-4Q, 0x1.b3efb441a4e1aa6b7bfce49b9d8ep-6Q, -0x1.baa159e67dd4ea14a46823aaab92p-13Q, -0x1.6c2d94cde3ae1bef5e760af7804dp-22Q, 0x0p+0Q};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0Q, 0x1.480f31520e3f310c306bdc1e8024p-1Q, -0x1.38fe2f09aac57b92aacdab2b4e96p+2Q, 0x1.f8f411bacc9f961bc5fe565a48cfp+3Q, -0x1.bc60c3b54f90a9241998e1a7c135p+4Q, 0x1.d3d44a6a16adb2540f6c000e54a3p+4Q, -0x1.536d6f833b66773a9702164e108p+4Q, 0x1.0953a7a524aca913282b25214d25p+4Q, -0x1.0c0dca303e8e262fc968302773e3p+4Q, 0x1.af56b1534f29dd21b9240ac133b1p+3Q, -0x1.f628948ceff73b6d1ae734867e3p+2Q, 0x1.3ef834c3289aa35b262758c2782ep+2Q, -0x1.c75ab5e1afc75a2d9d28a2f8d82cp+1Q, 0x1.cb38bb2c5f4bebadf622e77e6e2bp+0Q, -0x1.624785bf15dbe093496ba0bcf74cp-1Q, 0x1.61b17ae5ff0c0c37a77beb09baeep-2Q, -0x1.0b62472bd3d7849095f6de060b33p-3Q, 0x1.c9b3ef0688e890b76d9f1545a8bdp-8Q, 0x1.7c528a3f2156c58889998659bd68p-8Q, -0x1.0c4738028aec930d4308dfe577d7p-13Q, -0x1.b40e785cb88086ef360909d3183cp-22Q, 0x0p+0Q};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0Q, 0x1.8a25fe79d1c4ddac335be805ed36p-4Q, -0x1.79dddd860d2147a741654102c6e4p-1Q, 0x1.2f92842080f0827925b021c0be64p+1Q, -0x1.04a53246109b6b6c0d3ef6e90b5fp+2Q, 0x1.fbc727fc23eefb6381085f0dbe0ep+1Q, -0x1.2e8a4ebac6b5e49a84fad579cb0bp+1Q, 0x1.96ff87cfe4cc502ebda9734be9aep+0Q, -0x1.db8c7f7bf2c3a242351f98d5116p+0Q, 0x1.8867eccd39d1aef37286907e6727p+0Q, -0x1.7019bc278ffc03b406b2fe913c47p-1Q, 0x1.a30d20b4e67c690471d7cb32e446p-2Q, -0x1.7340e7a399e63a19859bd63999a6p-2Q, 0x1.68181929e64c530045ddd9689347p-3Q, -0x1.50a6f5e8f3b308d50e585e890eebp-5Q, 0x1.8d3b211eb839ac111937339fb303p-6Q, -0x1.b7227d5381373569d6206bc13579p-7Q, -0x1.a3114fdf2fbc06953fcb9948c145p-12Q, 0x1.71e7a3b4d88bf16a9f3c250c332p-10Q, -0x1.4eea023db8bd4900ec558c34e57cp-14Q, -0x1.09aed93888304346e30d1466764ap-21Q, 0x0p+0Q};
+            }
+        }
+        #endif
+    }
+    if constexpr (p == 12) {
+        if constexpr (std::is_same_v<Real, float>) {
+            if constexpr (order == 0) {
+                return {0x0p+0f, 0x1.ba5636p-8f, 0x1.3af728p-2f, 0x1.da1522p-1f, -0x1.5c6f66p-2f, 0x1.4840a4p-3f, -0x1.9d4fdcp-4f, 0x1.042a86p-4f, -0x1.08554cp-5f, 0x1.86c906p-7f, -0x1.8785b4p-9f, 0x1.f00fcp-12f, -0x1.43b7cep-15f, -0x1.dafa2ep-18f, 0x1.2d678cp-18f, -0x1.f0554cp-22f, -0x1.934a0ep-24f, -0x1.3a5d96p-29f, 0x1.0e0d22p-33f, -0x1.652334p-41f, 0x1.02e74cp-47f, 0x1.bb358cp-60f, -0x1.f67e04p-79f, 0x0p+0f};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0f, 0x1.3daa14p-5f, 0x1.716f56p-1f, -0x1.16beeap-2f, -0x1.f51bdap-1f, 0x1.97243cp-1f, -0x1.b8eefp-2f, 0x1.2402bcp-3f, 0x1.805958p-10f, -0x1.fa47fap-6f, 0x1.025a88p-6f, -0x1.3d712ap-9f, -0x1.c5c0dp-11f, 0x1.c45b6ap-12f, -0x1.6a167p-15f, -0x1.13c0d6p-17f, 0x1.b2cff8p-20f, -0x1.9ee91p-25f, -0x1.c87e12p-29f, 0x1.b076eap-34f, 0x1.71c42cp-44f, -0x1.e6d8e6p-52f, 0x1.13fd18p-69f, 0x0p+0f};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0f, 0x1.77fed2p-3f, 0x1.e1d108p-1f, -0x1.9e9c7cp+1f, 0x1.bc153ap+1f, -0x1.240fe4p+1f, 0x1.80cee2p+0f, -0x1.abf5ep-1f, 0x1.50c7e8p-2f, -0x1.4654eep-4f, 0x1.091b1ep-6f, -0x1.59c476p-7f, 0x1.935e46p-8f, -0x1.8fe152p-10f, 0x1.90febp-15f, 0x1.09bd2p-15f, -0x1.da6da6p-19f, 0x1.a3887p-21f, 0x1.0f785p-26f, -0x1.63226ep-31f, -0x1.84d7e4p-38f, 0x1.75cc98p-48f, -0x1.a7d232p-65f, -0x0p+0f};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0f, 0x1.60087cp-1f, -0x1.1c49e2p+0f, -0x1.f023b2p+0f, 0x1.8d30cp+2f, -0x1.80e0dep+2f, 0x1.c1feacp+0f, 0x1.3621acp+1f, -0x1.f3ab98p+1f, 0x1.5e6794p+1f, -0x1.c702ecp-1f, -0x1.ee149ap-4f, 0x1.ffde0cp-3f, -0x1.a2cbbap-4f, 0x1.d58bf4p-7f, 0x1.206bp-9f, -0x1.dfc88ap-11f, 0x1.f86e54p-15f, 0x1.28c92p-18f, -0x1.9c90e4p-23f, -0x1.7e8cfp-32f, 0x1.cc8984p-39f, -0x1.051a2p-54f, 0x0p+0f};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0f, 0x1.efa02p+0f, -0x1.34df3ep+3f, 0x1.596114p+4f, -0x1.014d7ap+5f, 0x1.5a4b7p+5f, -0x1.d72d9cp+5f, 0x1.1a6ca8p+6f, -0x1.f8d9fp+5f, 0x1.142ce2p+5f, -0x1.90f39p+1f, -0x1.822b1ap+3f, 0x1.52a34ep+3f, -0x1.0b934ap+2f, 0x1.335fd6p-1f, 0x1.17c48ap-3f, -0x1.003386p-4f, 0x1.68d464p-8f, 0x1.b6ad0ep-12f, -0x1.c361dcp-16f, -0x1.d59d4cp-25f, 0x1.f6c8c6p-31f, -0x1.1d1866p-45f, 0x0p+0f};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0f, 0x1.1672f8p+2f, -0x1.d05e84p+4f, 0x1.49fc06p+6f, -0x1.e4421p+6f, 0x1.09c53p+6f, 0x1.677b64p+6f, -0x1.fbf398p+7f, 0x1.628082p+8f, -0x1.a2714ep+8f, 0x1.cb4de8p+8f, -0x1.9cacd4p+8f, 0x1.055f48p+8f, -0x1.8ddf94p+6f, 0x1.95561cp+3f, 0x1.8ab9ccp+2f, -0x1.6e4fp+1f, 0x1.43d702p-2f, 0x1.951dp-6f, -0x1.5137c2p-9f, -0x1.3e3df8p-18f, 0x1.78041p-23f, -0x1.aa8cd8p-37f, -0x0p+0f};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0f, 0x1.6688e4p+2f, -0x1.50ba26p+5f, 0x1.18d5fcp+7f, -0x1.16422p+8f, 0x1.7cdc34p+8f, -0x1.a2f3c4p+8f, 0x1.aa319ep+8f, -0x1.958a02p+8f, 0x1.4bb5b2p+8f, -0x1.caa92ap+7f, 0x1.1f2d7ap+7f, -0x1.3b920ep+6f, 0x1.bc14b2p+4f, 0x1.8c237ap-1f, -0x1.7f694cp+2f, 0x1.3f67e2p+1f, -0x1.4cc6cp-2f, -0x1.6b5574p-6f, 0x1.38d6e4p-8f, 0x1.260d96p-17f, -0x1.5c7912p-21f, 0x1.8b88d4p-34f, 0x0p+0f};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0f, 0x1.80f666p+2f, -0x1.7dd222p+5f, 0x1.48b0d8p+7f, -0x1.41512cp+8f, 0x1.8f56fp+8f, -0x1.675a3ap+8f, 0x1.2e9626p+8f, -0x1.12635ap+8f, 0x1.969994p+7f, -0x1.59e9b6p+6f, 0x1.09d1ap+3f, 0x1.cc8ab2p+3f, -0x1.93c8d6p+4f, 0x1.013c24p+5f, -0x1.784654p+4f, 0x1.21acdep+3f, -0x1.6fa584p+0f, -0x1.39157p-4f, 0x1.343728p-5f, 0x1.c53d4ap-15f, -0x1.57bc52p-17f, 0x1.869c12p-29f, 0x0p+0f};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0f, 0x1.d573dcp+1f, -0x1.ddfb9cp+4f, 0x1.a873c2p+6f, -0x1.b2204ep+7f, 0x1.23910ep+8f, -0x1.29c6cep+8f, 0x1.1c64b2p+8f, -0x1.156986p+8f, 0x1.ef2b6p+7f, -0x1.84734ap+7f, 0x1.20e874p+7f, -0x1.93d454p+6f, 0x1.e8c646p+5f, -0x1.0a8b2ep+5f, 0x1.14ef6ep+4f, -0x1.bab6f4p+2f, 0x1.4e6abp+0f, 0x1.e57eccp-4f, -0x1.0f174cp-4f, 0x1.a1f2dcp-12f, 0x1.400292p-15f, -0x1.6c7e6p-26f, -0x0p+0f};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0f, 0x1.d2f4ep+0f, -0x1.e196ep+3f, 0x1.ab061ep+5f, -0x1.a7b25ap+6f, 0x1.04d398p+7f, -0x1.c308c4p+6f, 0x1.759cb8p+6f, -0x1.73a4dcp+6f, 0x1.4d02e4p+6f, -0x1.c4dfc6p+5f, 0x1.217c84p+5f, -0x1.9d3e5ep+4f, 0x1.eced02p+3f, -0x1.ab1578p+2f, 0x1.780b78p+1f, -0x1.59e4e8p+0f, 0x1.04013ap-2f, 0x1.63e904p-4f, -0x1.26b33ap-5f, 0x1.1fc084p-10f, 0x1.9c18e6p-15f, -0x1.d792bap-25f, 0x0p+0f};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0f, 0x1.19eec2p-1f, -0x1.249f96p+2f, 0x1.0297dcp+4f, -0x1.f4e8dcp+4f, 0x1.1efd1cp+5f, -0x1.a397ap+4f, 0x1.239464p+4f, -0x1.3946dp+4f, 0x1.289832p+4f, -0x1.5bb8e2p+3f, 0x1.68255cp+2f, -0x1.21aae8p+2f, 0x1.64fab4p+1f, -0x1.75b64cp-1f, 0x1.22ff2ap-3f, -0x1.07ed62p-3f, -0x1.4a01e6p-6f, 0x1.2e7cdcp-4f, -0x1.b7f686p-6f, 0x1.17b65cp-9f, 0x1.910e04p-14f, -0x1.cf434ap-23f, 0x0p+0f};
+            }
+            if constexpr (order == 11) {
+                return {0x0p+0f, 0x1.a6c51cp-5f, -0x1.b83154p-2f, 0x1.89e13cp+0f, -0x1.8aa498p+1f, 0x1.eb2b7ep+1f, -0x1.a9173ap+1f, 0x1.4e8702p+1f, -0x1.31bb74p+1f, 0x1.0e1264p+1f, -0x1.9cd0dcp+0f, 0x1.3cec22p+0f, -0x1.daf36p-1f, 0x1.329c32p-1f, -0x1.8936aep-2f, 0x1.00deep-2f, -0x1.07bd18p-3f, 0x1.cec02p-5f, -0x1.e6ef9ep-6f, 0x1.8f4f48p-7f, -0x1.e72d5p-10f, -0x1.e19176p-14f, 0x1.1b79fap-21f, -0x0p+0f};
+            }
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0, 0x1.ba5636194c094p-8, 0x1.3af72853b189p-2, 0x1.da1521352f488p-1, -0x1.5c6f665240adep-2, 0x1.4840a35a3e507p-3, -0x1.9d4fdc34ae4eep-4, 0x1.042a86a360592p-4, -0x1.08554bd18ab25p-5, 0x1.86c905bef28a7p-7, -0x1.8785b403c86f7p-9, 0x1.f00fc00fce26fp-12, -0x1.43b7ce1fa4e5bp-15, -0x1.dafa2eb6c7f5dp-18, 0x1.2d678c174b94dp-18, -0x1.f0554b8e5712dp-22, -0x1.934a0de4da293p-24, -0x1.3a5d95f1928efp-29, 0x1.0e0d213886187p-33, -0x1.652333b32760ap-41, 0x1.02e74c07e6081p-47, 0x1.bb358cf4adf4ep-60, -0x1.f67e04f08f215p-79, 0x0p+0};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0, 0x1.3daa1461d0cf4p-5, 0x1.716f56bac1b11p-1, -0x1.16bee99870719p-2, -0x1.f51bd9fa1cf2ep-1, 0x1.97243be7bf084p-1, -0x1.b8eef0110c9fap-2, 0x1.2402bce395302p-3, 0x1.80595820660c9p-10, -0x1.fa47fa3f4b022p-6, 0x1.025a88022a414p-6, -0x1.3d712aaad7776p-9, -0x1.c5c0d04fc8743p-11, 0x1.c45b69075cdb6p-12, -0x1.6a1670435bfddp-15, -0x1.13c0d643a27dcp-17, 0x1.b2cff79438463p-20, -0x1.9ee90facd3d13p-25, -0x1.c87e1185ca55bp-29, 0x1.b076e96662045p-34, 0x1.71c42c5b1e647p-44, -0x1.e6d8e5785ac94p-52, 0x1.13fd176d0c255p-69, 0x0p+0};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0, 0x1.77fed2e016936p-3, 0x1.e1d10780fb061p-1, -0x1.9e9c7ce63835dp+1, 0x1.bc153af50c24cp+1, -0x1.240fe3f248861p+1, 0x1.80cee17390c18p+0, -0x1.abf5df7fd7acp-1, 0x1.50c7e71a108bbp-2, -0x1.4654ed4660724p-4, 0x1.091b1dd62c3e6p-6, -0x1.59c475f85d7f4p-7, 0x1.935e464b93aa4p-8, -0x1.8fe1513629012p-10, 0x1.90feb0894b435p-15, 0x1.09bd1f2d4e386p-15, -0x1.da6da6ad5e76cp-19, 0x1.a3886fa6d48c5p-21, 0x1.0f7850b94c92bp-26, -0x1.63226d50629cp-31, -0x1.84d7e34db15d3p-38, 0x1.75cc980993529p-48, -0x1.a7d23115de573p-65, -0x0p+0};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0, 0x1.60087b087d2efp-1, -0x1.1c49e2797e56dp+0, -0x1.f023b1706ef0ep+0, 0x1.8d30c07e51574p+2, -0x1.80e0de445b21ap+2, 0x1.c1feac4e70c18p+0, 0x1.3621ab0ea1b05p+1, -0x1.f3ab98611d47ap+1, 0x1.5e6794d526a25p+1, -0x1.c702eca93a33dp-1, -0x1.ee149aa686bb3p-4, 0x1.ffde0ca5fc1a1p-3, -0x1.a2cbb989ecd0ap-4, 0x1.d58bf4f6c76eap-7, 0x1.206affc103ba1p-9, -0x1.dfc88961f6b15p-11, 0x1.f86e53415f2ap-15, 0x1.28c920e4a3f6cp-18, -0x1.9c90e430666c9p-23, -0x1.7e8cf0898f333p-32, 0x1.cc8984cca607fp-39, -0x1.051a1f819156cp-54, 0x0p+0};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0, 0x1.efa01fe281c9p+0, -0x1.34df3dac7fcd4p+3, 0x1.5961138d5be95p+4, -0x1.014d7a672544ap+5, 0x1.5a4b6fa251ebp+5, -0x1.d72d9b409f2b2p+5, 0x1.1a6ca7d65632dp+6, -0x1.f8d9ef0a2890cp+5, 0x1.142ce1c1f06e2p+5, -0x1.90f390767ce47p+1, -0x1.822b1a96e2d92p+3, 0x1.52a34d125b1bep+3, -0x1.0b934a511e089p+2, 0x1.335fd67def29fp-1, 0x1.17c48a3b6f0b8p-3, -0x1.0033850ae8807p-4, 0x1.68d4635bbce68p-8, 0x1.b6ad0e03e206fp-12, -0x1.c361dbb11082cp-16, -0x1.d59d4ba004a56p-25, 0x1.f6c8c69c71b98p-31, -0x1.1d186572e3d31p-45, 0x0p+0};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0, 0x1.1672f76c48a3bp+2, -0x1.d05e83fe81472p+4, 0x1.49fc051fc99a8p+6, -0x1.e442104e65336p+6, 0x1.09c52f838d2fdp+6, 0x1.677b64cbf326ep+6, -0x1.fbf39786bea7bp+7, 0x1.628081b6fdd81p+8, -0x1.a2714ddd5c22bp+8, 0x1.cb4de777b4f36p+8, -0x1.9cacd3aee3a7ep+8, 0x1.055f4806a8346p+8, -0x1.8ddf94a470b87p+6, 0x1.95561c2d77ea8p+3, 0x1.8ab9cc38b4949p+2, -0x1.6e4f007cb3f6fp+1, 0x1.43d7023213a8p-2, 0x1.951cff21de4acp-6, -0x1.5137c147339bcp-9, -0x1.3e3df8b2da275p-18, 0x1.78040f51a9568p-23, -0x1.aa8cd8e6f8972p-37, -0x0p+0};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0, 0x1.6688e31cf50ep+2, -0x1.50ba2688bc043p+5, 0x1.18d5fc503a177p+7, -0x1.16422099d0e7p+8, 0x1.7cdc33f38c2d1p+8, -0x1.a2f3c3b8e6e4bp+8, 0x1.aa319d6af6ec9p+8, -0x1.958a02a102449p+8, 0x1.4bb5b15c50a64p+8, -0x1.caa9291eb011fp+7, 0x1.1f2d7abf22a73p+7, -0x1.3b920d0f7e0d1p+6, 0x1.bc14b21b62b93p+4, 0x1.8c237a0fa26d7p-1, -0x1.7f694c35d9d22p+2, 0x1.3f67e104a689cp+1, -0x1.4cc6c058f371dp-2, -0x1.6b557354b8d85p-6, 0x1.38d6e371bb052p-8, 0x1.260d95329ea8ep-17, -0x1.5c7911e0053bcp-21, 0x1.8b88d3fa551cp-34, 0x0p+0};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0, 0x1.80f665163dff6p+2, -0x1.7dd2228ef0449p+5, 0x1.48b0d88030936p+7, -0x1.41512ba753d05p+8, 0x1.8f56f07493efp+8, -0x1.675a39773b248p+8, 0x1.2e9626a21624ep+8, -0x1.1263590aebe89p+8, 0x1.9699942af2221p+7, -0x1.59e9b6e0b9c21p+6, 0x1.09d1a0b7c5832p+3, 0x1.cc8ab1005087cp+3, -0x1.93c8d50945095p+4, 0x1.013c24badc627p+5, -0x1.784654bbd7368p+4, 0x1.21acdd98ca7e4p+3, -0x1.6fa583815aba2p+0, -0x1.39156fe5f0a3bp-4, 0x1.34372727b2155p-5, 0x1.c53d49d197175p-15, -0x1.57bc52155abeap-17, 0x1.869c11b6398bcp-29, 0x0p+0};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0, 0x1.d573db31c98a6p+1, -0x1.ddfb9c5686a4fp+4, 0x1.a873c238f1ad9p+6, -0x1.b2204de17a53ap+7, 0x1.23910ebcbe60dp+8, -0x1.29c6cec686025p+8, 0x1.1c64b27b4c108p+8, -0x1.156985f5c8bcep+8, 0x1.ef2b60fc7ce31p+7, -0x1.84734ae811783p+7, 0x1.20e874beb6698p+7, -0x1.93d454c0120c5p+6, 0x1.e8c645d503448p+5, -0x1.0a8b2e2c06173p+5, 0x1.14ef6d11452bcp+4, -0x1.bab6f3f4dbb55p+2, 0x1.4e6aaf12e910ep+0, 0x1.e57ecc0ee730ep-4, -0x1.0f174cea8c306p-4, 0x1.a1f2dc12ec55dp-12, 0x1.4002914419fbbp-15, -0x1.6c7e600f14b1p-26, -0x0p+0};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0, 0x1.d2f4e044749b5p+0, -0x1.e196df480fe72p+3, 0x1.ab061d20276fp+5, -0x1.a7b259e6037ecp+6, 0x1.04d3977e22f61p+7, -0x1.c308c46a51aa1p+6, 0x1.759cb7054906p+6, -0x1.73a4db524ebc3p+6, 0x1.4d02e405c664p+6, -0x1.c4dfc682dd95ep+5, 0x1.217c835a844bfp+5, -0x1.9d3e5e5e09252p+4, 0x1.eced01c912f6cp+3, -0x1.ab15772777a66p+2, 0x1.780b7892927c5p+1, -0x1.59e4e79f9d385p+0, 0x1.04013ac7f90edp-2, 0x1.63e903ad632e8p-4, -0x1.26b339b06c46fp-5, 0x1.1fc083a0e2c36p-10, 0x1.9c18e59aa15abp-15, -0x1.d792baac952f3p-25, 0x0p+0};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0, 0x1.19eec26520f72p-1, -0x1.249f95db3c6a8p+2, 0x1.0297dba66cdd3p+4, -0x1.f4e8dc0eb78aap+4, 0x1.1efd1b3c60e0bp+5, -0x1.a397a05a5f775p+4, 0x1.239464bf9e82cp+4, -0x1.3946d065739bfp+4, 0x1.2898316e66a7fp+4, -0x1.5bb8e2c464278p+3, 0x1.68255c99ba4c7p+2, -0x1.21aae7ae7df32p+2, 0x1.64fab317448fbp+1, -0x1.75b64c97e0968p-1, 0x1.22ff2ac4d8b9cp-3, -0x1.07ed621dcab47p-3, -0x1.4a01e6ee0860ep-6, 0x1.2e7cdbbc90031p-4, -0x1.b7f6865bae123p-6, 0x1.17b65cad3d541p-9, 0x1.910e0462410b6p-14, -0x1.cf434a44d45d4p-23, 0x0p+0};
+            }
+            if constexpr (order == 11) {
+                return {0x0p+0, 0x1.a6c51bc471a31p-5, -0x1.b8315371d42a5p-2, 0x1.89e13c889a74dp+0, -0x1.8aa497719f071p+1, 0x1.eb2b7ee2bc88dp+1, -0x1.a91739cfcb437p+1, 0x1.4e87023b22be2p+1, -0x1.31bb74af8ae4ep+1, 0x1.0e1263d4463c8p+1, -0x1.9cd0db1b42b97p+0, 0x1.3cec213a53552p+0, -0x1.daf35f59b2442p-1, 0x1.329c321d7ff6bp-1, -0x1.8936ae8cb907cp-2, 0x1.00dee0f33922ap-2, -0x1.07bd180d95969p-3, 0x1.cec01fe9b05f6p-5, -0x1.e6ef9d5209f88p-6, 0x1.8f4f47250e3a5p-7, -0x1.e72d4f4950c8ap-10, -0x1.e19176d7ba691p-14, 0x1.1b79fa688c947p-21, -0x0p+0};
+            }
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0L, 0xd.d2b1b0ca6049ce2p-11L, 0x9.d7b9429d8c4819ap-5L, 0xe.d0a909a97a43f8ep-4L, -0xa.e37b3292056ef1ap-5L, 0xa.42051ad1f283b58p-6L, -0xc.ea7ee1a57276e59p-7L, 0x8.2154351b02c8eb6p-7L, -0x8.42aa5e8c5592b7bp-8L, 0xc.36482df7945344bp-10L, -0xc.3c2da01e437b7bbp-12L, 0xf.807e007e7137774p-15L, -0xa.1dbe70fd272d8b1p-18L, -0xe.d7d175b63fae5edp-21L, 0x9.6b3c60ba5ca6825p-21L, -0xf.82aa5c72b896837p-25L, -0xc.9a506f26d1499c5p-27L, -0x9.d2ecaf8c9477601p-32L, 0x8.706909c430c3afbp-36L, -0xb.29199d993b04f39p-44L, 0x8.173a603f30404d9p-50L, 0xd.d9ac67a56fa6d35p-63L, -0xf.b3f02784790a955p-82L, 0x0p+0L};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0L, 0x9.ed50a30e867a4p-8L, 0xb.8b7ab5d60d88817p-4L, -0x8.b5f74cc3838cb01p-5L, -0xf.a8decfd0e796cf1p-4L, 0xc.b921df3df8422acp-4L, -0xd.c777808864fd26fp-5L, 0x9.2015e71ca980e98p-6L, 0xc.02cac1033064418p-13L, -0xf.d23fd1fa5810e5dp-9L, 0x8.12d440115209d8bp-9L, -0x9.eb895556bbbac58p-12L, -0xe.2e06827e43a1813p-14L, 0xe.22db483ae6db17p-15L, -0xb.50b3821adfeea95p-18L, -0x8.9e06b21d13ee1f3p-20L, 0xd.967fbca1c231ae8p-23L, -0xc.f7487d669e89999p-28L, -0xe.43f08c2e52ad9ddp-32L, 0xd.83b74b331022454p-37L, 0xb.8e2162d8f32359fp-47L, -0xf.36c72bc2d649c0fp-55L, 0x8.9fe8bb68612a695p-72L, 0x0p+0L};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0L, 0xb.bff69700b49b018p-6L, 0xf.0e883c07d830881p-4L, -0xc.f4e3e731c1ae738p-2L, 0xd.e0a9d7a86125cacp-2L, -0x9.207f1f9244307c8p-2L, 0xc.06770b9c860beebp-3L, -0xd.5faefbfebd5fdcdp-4L, 0xa.863f38d0845d7acp-5L, -0xa.32a76a330391e66p-7L, 0x8.48d8eeb161f2f82p-9L, -0xa.ce23afc2ebf9f61p-10L, 0xc.9af2325c9d52281p-11L, -0xc.7f0a89b14808e6ap-13L, 0xc.87f5844a5a1a6fp-18L, 0x8.4de8f96a71c3322p-18L, -0xe.d36d356af3b5c2cp-22L, 0xd.1c437d36a462b4ap-24L, 0x8.7bc285ca6495b9cp-29L, -0xb.19136a8314dfe24p-34L, -0xc.26bf1a6d8ae9884p-41L, 0xb.ae64c04c9a9494fp-51L, -0xd.3e9188aef2b98edp-68L, -0x0p+0L};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0L, 0xb.0043d843e977a5cp-4L, -0x8.e24f13cbf2b6563p-3L, -0xf.811d8b837786d61p-3L, 0xc.698603f28aba1a9p-1L, -0xc.0706f222d90cfdfp-1L, 0xe.0ff56273860c0ebp-3L, 0x9.b10d58750d82957p-2L, -0xf.9d5cc308ea3d3cbp-2L, 0xa.f33ca6a935126f2p-2L, -0xe.38176549d19e5a8p-4L, -0xf.70a4d53435d97d5p-7L, 0xf.fef0652fe0d0a8dp-6L, -0xd.165dcc4f668505cp-7L, 0xe.ac5fa7b63b752dbp-10L, 0x9.0357fe081dd0544p-12L, -0xe.fe444b0fb58abf3p-14L, 0xf.c3729a0af95006dp-18L, 0x9.464907251fb5d88p-21L, -0xc.e487218333646a4p-26L, -0xb.f467844c7999b52p-35L, 0xe.644c2665303f8d2p-42L, -0x8.28d0fc0c8ab5d4ep-57L, 0x0p+0L};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0L, 0xf.7d00ff140e483d9p-3L, -0x9.a6f9ed63fe69fc4p+0L, 0xa.cb089c6adf4abc4p+1L, -0x8.0a6bd3392a250e2p+2L, 0xa.d25b7d128f57c87p+2L, -0xe.b96cda04f958dddp+2L, 0x8.d3653eb2b19664fp+3L, -0xf.c6cf785144862cap+2L, 0x8.a1670e0f8370cfp+2L, -0xc.879c83b3e72381bp-2L, -0xc.1158d4b716c8e65p+0L, 0xa.951a6892d8df2a8p+0L, -0x8.5c9a5288f0446cfp-1L, 0x9.9afeb3ef794f7dcp-4L, 0x8.be2451db785c08ap-6L, -0x8.019c285744039edp-7L, 0xb.46a31adde7341a9p-11L, 0xd.b568701f1037966p-15L, -0xe.1b0edd888415d06p-19L, -0xe.acea5d00252b3f7p-28L, 0xf.b64634e38dcc13ap-34L, -0x8.e8c32b971e9855bp-48L, 0x0p+0L};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0L, 0x8.b397bb62451d843p-1L, -0xe.82f41ff40a38e2ap+1L, 0xa.4fe028fe4cd412cp+3L, -0xf.22108273299ad98p+3L, 0x8.4e297c1c697e50ep+3L, 0xb.3bdb265f99372aep+3L, -0xf.df9cbc35f53d89cp+4L, 0xb.14040db7eec0855p+5L, -0xd.138a6eeae115b02p+5L, 0xe.5a6f3bbda79b16cp+5L, -0xc.e5669d771d3f14bp+5L, 0x8.2afa403541a338fp+5L, -0xc.6efca52385c3629p+3L, 0xc.aab0e16bbf53e59p+0L, 0xc.55ce61c5a4a452bp-1L, -0xb.727803e59fb7b2ap-2L, 0xa.1eb811909d4016fp-5L, 0xc.a8e7f90ef2563f2p-9L, -0xa.89be0a399cde158p-12L, -0x9.f1efc596d13a96ep-21L, 0xb.c0207a8d4ab3f5dp-26L, -0xd.5466c737c4b8e72p-40L, -0x0p+0L};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0L, 0xb.344718e7a8702b2p-1L, -0xa.85d13445e021855p+2L, 0x8.c6afe281d0bb969p+4L, -0x8.b21104ce8738061p+5L, 0xb.e6e19f9c6168b44p+5L, -0xd.179e1dc73725588p+5L, 0xd.518ceb57b764b3fp+5L, -0xc.ac50150812244abp+5L, 0xa.5dad8ae285323a8p+5L, -0xe.554948f5808f966p+4L, 0x8.f96bd5f915394b1p+4L, -0x9.dc90687bf0684d6p+3L, 0xd.e0a590db15c99a5p+1L, 0xc.611bd07d136ba02p-4L, -0xb.fb4a61aece9122bp-1L, 0x9.fb3f0825344de52p-2L, -0xa.663602c79b8e8ecp-5L, -0xb.5aab9aa5c6c2553p-9L, 0x9.c6b71b8dd828c64p-11L, 0x9.306ca994f547077p-20L, -0xa.e3c88f0029de0d1p-24L, 0xc.5c469fd2a8dfc22p-37L, 0x0p+0L};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0L, 0xc.07b328b1effb03p-1L, -0xb.ee9114778224972p+2L, 0xa.4586c401849b3a9p+4L, -0xa.0a895d3a9e82ae4p+5L, 0xc.7ab783a49f782e2p+5L, -0xb.3ad1cbb9d9242edp+5L, 0x9.74b13510b126f8ep+5L, -0x8.931ac8575f4469p+5L, 0xc.b4cca1579110a15p+4L, -0xa.cf4db705ce10894p+3L, 0x8.4e8d05be2c19216p+0L, 0xe.64558802843df89p+0L, -0xc.9e46a84a284ab95p+1L, 0x8.09e125d6e31381bp+2L, -0xb.c232a5deb9b3ce5p+1L, 0x9.0d66ecc653f1d47p+0L, -0xb.7d2c1c0ad5d0d11p-3L, -0x9.c8ab7f2f851da2dp-7L, 0x9.a1b9393d90aa708p-8L, 0xe.29ea4e8cb8baa35p-18L, -0xa.bde290aad5f5239p-20L, 0xc.34e08db1cc5dff7p-32L, 0x0p+0L};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0L, 0xe.ab9ed98e4c52c95p-2L, -0xe.efdce2b435277e9p+1L, 0xd.439e11c78d6c4d6p+3L, -0xd.91026f0bd29d199p+4L, 0x9.1c8875e5f3069d6p+5L, -0x9.4e367634301286p+5L, 0x8.e32593da6083e54p+5L, -0x8.ab4c2fae45e736fp+5L, 0xf.795b07e3e718ad3p+4L, -0xc.239a57408bc15f7p+4L, 0x9.0743a5f5b34bf5fp+4L, -0xc.9ea2a6009062863p+3L, 0xf.46322ea81a241fbp+2L, -0x8.5459716030b981p+2L, 0x8.a77b688a295dd83p+1L, -0xd.d5b79fa6ddaa942p-1L, 0xa.735578974886db3p-3L, 0xf.2bf66077398705p-7L, -0x8.78ba67546182ecp-7L, 0xd.0f96e09762ae4b7p-15L, 0xa.00148a20cfdd93dp-18L, -0xb.63f30078a588239p-29L, -0x0p+0L};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0L, 0xe.97a70223a4da73dp-3L, -0xf.0cb6fa407f38df5p+0L, 0xd.5830e9013b783a8p+2L, -0xd.3d92cf301bf5fbep+3L, 0x8.269cbbf117b07a3p+4L, -0xe.184623528d5047ap+3L, 0xb.ace5b82a4830181p+3L, -0xb.9d26da9275e177fp+3L, 0xa.6817202e331ffc5p+3L, -0xe.26fe3416ecaefa6p+2L, 0x9.0be41ad4225f98dp+2L, -0xc.e9f2f2f049291ep+1L, 0xf.67680e4897b60bep+0L, -0xd.58abb93bbd32d48p-1L, 0xb.c05bc49493e294p-2L, -0xa.cf273cfce9c2447p-3L, 0x8.2009d63fc87650fp-5L, 0xb.1f481d6b1973f98p-7L, -0x9.3599cd8362377f9p-8L, 0x8.fe041d07161ad18p-13L, 0xc.e0c72cd50ad59f6p-18L, -0xe.bc95d564a979727p-28L, 0x0p+0L};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0L, 0x8.cf76132907b923fp-4L, -0x9.24fcaed9e3542f7p-1L, 0x8.14bedd3366e9a26p+1L, -0xf.a746e075bc553f8p+1L, 0x8.f7e8d9e307059b7p+2L, -0xd.1cbd02d2fbba7a7p+1L, 0x9.1ca325fcf41627ep+1L, -0x9.ca36832b9cdf557p+1L, 0x9.44c18b73353f954p+1L, -0xa.ddc71623213c14ap+0L, 0xb.412ae4cdd263584p-1L, -0x9.0d573d73ef98e15p-1L, 0xb.27d598ba247d824p-2L, -0xb.adb264bf04b4353p-4L, 0x9.17f95626c5ce28p-6L, -0x8.3f6b10ee55a3b6fp-6L, -0xa.500f37704306c4bp-9L, 0x9.73e6dde48018975p-7L, -0xd.bfb432dd7091673p-9L, 0x8.bdb2e569eaa0703p-12L, 0xc.88702312085adcbp-17L, -0xe.7a1a5226a2ea342p-26L, 0x0p+0L};
+            }
+            if constexpr (order == 11) {
+                return {0x0p+0L, 0xd.3628de238d184c6p-8L, -0xd.c18a9b8ea152a17p-5L, 0xc.4f09e444d3a6404p-3L, -0xc.5524bb8cf8387b7p-2L, 0xf.595bf715e446977p-2L, -0xd.48b9ce7e5a1ba57p-2L, 0xa.743811d915f0f83p-2L, -0x9.8ddba57c5726fd3p-2L, 0x8.70931ea231e404ep-2L, -0xc.e686d8da15cb65bp-3L, 0x9.e76109d29aa8d6cp-3L, -0xe.d79afacd9220eb9p-4L, 0x9.94e190ebffb5bb9p-4L, -0xc.49b57465c83ddabp-5L, 0x8.06f70799c914d0ap-5L, -0x8.3de8c06cacb4875p-6L, 0xe.7600ff4d82fb121p-8L, -0xf.377cea904fc3cf9p-9L, 0xc.7a7a392871d2799p-10L, -0xf.396a7a4a8644d53p-13L, -0xf.0c8bb6bdd348a37p-17L, 0x8.dbcfd34464a37e2p-24L, -0x0p+0L};
+            }
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            if constexpr (order == 0) {
+                return {0x0p+0Q, 0x1.ba5636194c0939c427c9ec5958bcp-8Q, 0x1.3af72853b1890334601f92a1285cp-2Q, 0x1.da1521352f487f1b71f5ba20803ep-1Q, -0x1.5c6f665240adde3380bdc0aea43fp-2Q, 0x1.4840a35a3e5076b07b9bb98536c9p-3Q, -0x1.9d4fdc34ae4edcb2a06a461fd223p-4Q, 0x1.042a86a360591d6b2ba9327c6214p-4Q, -0x1.08554bd18ab256f6f2efbe750debp-5Q, 0x1.86c905bef28a68962be82a3bfae1p-7Q, -0x1.8785b403c86f6f7548c23ebef91ep-9Q, 0x1.f00fc00fce26eee7a53c75fa9281p-12Q, -0x1.43b7ce1fa4e5b162d9e05ba16226p-15Q, -0x1.dafa2eb6c7f5cbd9451ac8b8db32p-18Q, 0x1.2d678c174b94d04aa232fc24fe04p-18Q, -0x1.f0554b8e5712d06e0273c8cb5028p-22Q, -0x1.934a0de4da29338aed7c3945f163p-24Q, -0x1.3a5d95f1928eec0223d4d9335852p-29Q, 0x1.0e0d2138861875f5d48c437e1967p-33Q, -0x1.652333b327609e7169123d062a6bp-41Q, 0x1.02e74c07e60809b1acff78842c2ep-47Q, 0x1.bb358cf4adf4da69e5fa9c48097p-60Q, -0x1.f67e04f08f2152aabe6eb786b11ap-79Q, 0x0p+0Q};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0Q, 0x1.3daa1461d0cf47fff25f3df9640bp-5Q, 0x1.716f56bac1b1102dab376b1a4013p-1Q, -0x1.16bee9987071960277d4321df089p-2Q, -0x1.f51bd9fa1cf2d9e12262aabd142cp-1Q, 0x1.97243be7bf08455883f653e15918p-1Q, -0x1.b8eef0110c9fa4de8e71d38444edp-2Q, 0x1.2402bce395301d2ffcfa2c7a494fp-3Q, 0x1.80595820660c8830537a9f5a0fdp-10Q, -0x1.fa47fa3f4b021cbace01025dd983p-6Q, 0x1.025a88022a413b155a9680077b56p-6Q, -0x1.3d712aaad77758afb71e5644bf96p-9Q, -0x1.c5c0d04fc87430265835a2d868fdp-11Q, 0x1.c45b69075cdb62e0f0501d72eae6p-12Q, -0x1.6a1670435bfdd529f00d82c5e461p-15Q, -0x1.13c0d643a27dc3e64f7aa5ea1b46p-17Q, 0x1.b2cff794384635cf6c5bd8331b3p-20Q, -0x1.9ee90facd3d1333133d7e205e0a2p-25Q, -0x1.c87e1185ca55b3b93aa7457169a2p-29Q, 0x1.b076e966620448a8ccbae1de566ap-34Q, 0x1.71c42c5b1e646b3eaaa36a5a3022p-44Q, -0x1.e6d8e5785ac9381d9a7b909296b9p-52Q, 0x1.13fd176d0c254d2994cc4f8bbb17p-69Q, 0x0p+0Q};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0Q, 0x1.77fed2e01693602fb8497759708ep-3Q, 0x1.e1d10780fb06110288f8999dc1b7p-1Q, -0x1.9e9c7ce63835ce70bd9f1949b4fbp+1Q, 0x1.bc153af50c24b9575bdc1b7eea7cp+1Q, -0x1.240fe3f248860f90966b383ce1ccp+1Q, 0x1.80cee17390c17dd6afdc8b5e9badp+0Q, -0x1.abf5df7fd7abfb9aaab015caa89bp-1Q, 0x1.50c7e71a108baf578aa06cfc53efp-2Q, -0x1.4654ed4660723ccc0f0acc159fc7p-4Q, 0x1.091b1dd62c3e5f033d13bd90eb7fp-6Q, -0x1.59c475f85d7f3ec16b121b44ed34p-7Q, 0x1.935e464b93aa450281cf24f670a1p-8Q, -0x1.8fe1513629011cd322fa61848c65p-10Q, 0x1.90feb0894b434ddffdbc8185ec19p-15Q, 0x1.09bd1f2d4e386644ae469eb8633p-15Q, -0x1.da6da6ad5e76b8585347757536dfp-19Q, 0x1.a3886fa6d48c5693a0b3ec42df61p-21Q, 0x1.0f7850b94c92b737f20b8005c2b9p-26Q, -0x1.63226d50629bfc487dd5a4e8ece6p-31Q, -0x1.84d7e34db15d3108fdfa03f5826ep-38Q, 0x1.75cc98099352929e39911fd4363dp-48Q, -0x1.a7d23115de5731da90d3ce0c92b1p-65Q, -0x0p+0Q};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0Q, 0x1.60087b087d2ef4b82953952dae77p-1Q, -0x1.1c49e2797e56cac67a206b15099bp+0Q, -0x1.f023b1706ef0dac15d9852fed0cdp+0Q, 0x1.8d30c07e51574352c1f1eb201d3dp+2Q, -0x1.80e0de445b219fbdea6ef733b9e6p+2Q, 0x1.c1feac4e70c181d6b4fca6d2077fp+0Q, 0x1.3621ab0ea1b052aecf48cff76ee3p+1Q, -0x1.f3ab98611d47a796d9c54636510bp+1Q, 0x1.5e6794d526a24de36780aeba10e8p+1Q, -0x1.c702eca93a33cb508d7b1d004b3dp-1Q, -0x1.ee149aa686bb2faa29ff6d4c03ddp-4Q, 0x1.ffde0ca5fc1a1519c08ba08f2c0bp-3Q, -0x1.a2cbb989ecd0a0b85c48b0ef17a6p-4Q, 0x1.d58bf4f6c76ea5b68a5554196c66p-7Q, 0x1.206affc103ba0a875625f458349fp-9Q, -0x1.dfc88961f6b157e54f77890beee7p-11Q, 0x1.f86e53415f2a00da542f82566187p-15Q, 0x1.28c920e4a3f6bb0fc001a36c7514p-18Q, -0x1.9c90e430666c8d48daf02182994fp-23Q, -0x1.7e8cf0898f3336a3b6d1b959decdp-32Q, 0x1.cc8984cca607f1a4cd24395b6b4ap-39Q, -0x1.051a1f819156ba9bc5cb80613b7p-54Q, 0x0p+0Q};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0Q, 0x1.efa01fe281c907b167ef08ad02bfp+0Q, -0x1.34df3dac7fcd3f885ed5b138fecap+3Q, 0x1.5961138d5be957877d8cfd1a3db6p+4Q, -0x1.014d7a672544a1c4d79025387afbp+5Q, 0x1.5a4b6fa251eaf90e3115b0c4b844p+5Q, -0x1.d72d9b409f2b1bb94911072b924bp+5Q, 0x1.1a6ca7d65632cc9e3b88e5271a3dp+6Q, -0x1.f8d9ef0a2890c5946bb98eca0c52p+5Q, 0x1.142ce1c1f06e19e0c6f07b09b256p+5Q, -0x1.90f390767ce4703536c74ea5d48p+1Q, -0x1.822b1a96e2d91cc911472931b073p+3Q, 0x1.52a34d125b1be5508a31d4571b97p+3Q, -0x1.0b934a511e088d9de4577e69f953p+2Q, 0x1.335fd67def29efb717b6672f0127p-1Q, 0x1.17c48a3b6f0b811400fc04e03edcp-3Q, -0x1.0033850ae88073da0780e3e27f81p-4Q, 0x1.68d4635bbce683527c3478757d85p-8Q, 0x1.b6ad0e03e206f2cc34c3ad5363ddp-12Q, -0x1.c361dbb11082ba0b86af7e6af24bp-16Q, -0x1.d59d4ba004a567edb22672cba48ap-25Q, 0x1.f6c8c69c71b982736f46aeba6448p-31Q, -0x1.1d186572e3d30ab58425e9abcaa6p-45Q, 0x0p+0Q};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0Q, 0x1.1672f76c48a3b085a419d3a4a516p+2Q, -0x1.d05e83fe81471c548c376fdd2e88p+4Q, 0x1.49fc051fc99a825862e53c01bf24p+6Q, -0x1.e442104e65335b30f1932f27a50ap+6Q, 0x1.09c52f838d2fca1c275b6969c956p+6Q, 0x1.677b64cbf326e55bcfc7688cab53p+6Q, -0x1.fbf39786bea7b138ef97d6e9bf1fp+7Q, 0x1.628081b6fdd810aa965a5e7f3421p+8Q, -0x1.a2714ddd5c22b603c83ee95dc4cp+8Q, 0x1.cb4de777b4f362d79e6f07abbc76p+8Q, -0x1.9cacd3aee3a7e296cd7191fe8607p+8Q, 0x1.055f4806a834671e4070626e14f2p+8Q, -0x1.8ddf94a470b86c5104b74e18273dp+6Q, 0x1.95561c2d77ea7cb1b418f2fb6391p+3Q, 0x1.8ab9cc38b4948a55522c3044f42ap+2Q, -0x1.6e4f007cb3f6f6544bd7ca0f31d2p+1Q, 0x1.43d7023213a802dd64336017585bp-2Q, 0x1.951cff21de4ac7e4a1f0a8263acfp-6Q, -0x1.5137c147339bc2af2a69107ce017p-9Q, -0x1.3e3df8b2da2752dcb7f7472265e7p-18Q, 0x1.78040f51a9567ebaa0b6d94a065ep-23Q, -0x1.aa8cd8e6f8971ce4ff3376356067p-37Q, -0x0p+0Q};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0Q, 0x1.6688e31cf50e0564efea7bdd5fb4p+2Q, -0x1.50ba2688bc0430a9ee74607c1048p+5Q, 0x1.18d5fc503a1772d2730b3e2d1b1p+7Q, -0x1.16422099d0e700c2cc83b4dddfb9p+8Q, 0x1.7cdc33f38c2d168782ab508fe333p+8Q, -0x1.a2f3c3b8e6e4ab101396a85ce4c7p+8Q, 0x1.aa319d6af6ec967e381e228e6cdbp+8Q, -0x1.958a02a1024489567edfcd0c6458p+8Q, 0x1.4bb5b15c50a647500af4903c157ep+8Q, -0x1.caa9291eb011f2ccec5253008c2ep+7Q, 0x1.1f2d7abf22a7296277eac00e42f8p+7Q, -0x1.3b920d0f7e0d09abc1f29b5777d5p+6Q, 0x1.bc14b21b62b9334a0ec071c6d27ap+4Q, 0x1.8c237a0fa26d740497614e6ce7f9p-1Q, -0x1.7f694c35d9d2245677a757e7ef74p+2Q, 0x1.3f67e104a689bca4d8d6dc3c9573p+1Q, -0x1.4cc6c058f371d1d7aadbd3825648p-2Q, -0x1.6b557354b8d84aa675e72e4aa2cep-6Q, 0x1.38d6e371bb0518c7efdfa45f408ep-8Q, 0x1.260d95329ea8e0edce58678f53a3p-17Q, -0x1.5c7911e0053bc1a14fff7b8b350cp-21Q, 0x1.8b88d3fa551bf8449851729a705p-34Q, 0x0p+0Q};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0Q, 0x1.80f665163dff60603105451a6e5dp+2Q, -0x1.7dd2228ef04492e49ffcbb4c7665p+5Q, 0x1.48b0d88030936751bd070e523483p+7Q, -0x1.41512ba753d055c75dc8c691e375p+8Q, 0x1.8f56f07493ef05c30063bbd4a838p+8Q, -0x1.675a39773b2485da34f83284198fp+8Q, 0x1.2e9626a21624df1cdd8e3378c5edp+8Q, -0x1.1263590aebe88d200657bdb9b2c3p+8Q, 0x1.9699942af2221429cba46fea0168p+7Q, -0x1.59e9b6e0b9c21128db1639ea581fp+6Q, 0x1.09d1a0b7c583242c5ad2ce6cf431p+3Q, 0x1.cc8ab1005087bf119ad7cb575125p+3Q, -0x1.93c8d5094509572acb009f2e7dd8p+4Q, 0x1.013c24badc62703530bdc5ef098ep+5Q, -0x1.784654bbd73679c9f2def8e43e7p+4Q, 0x1.21acdd98ca7e3a8d97a5878ef247p+3Q, -0x1.6fa583815aba1a21d8baa02798f2p+0Q, -0x1.39156fe5f0a3b45977f7ccd1d734p-4Q, 0x1.34372727b2154e0f6338311dea7cp-5Q, 0x1.c53d49d19717546a333396c8797dp-15Q, -0x1.57bc52155abea4723bbb49833b9ep-17Q, 0x1.869c11b6398bbfee9ec13fe04d71p-29Q, 0x0p+0Q};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0Q, 0x1.d573db31c98a592a2b6a75f0e508p+1Q, -0x1.ddfb9c5686a4efd2bd1e32872343p+4Q, 0x1.a873c238f1ad89ace04b72e9c756p+6Q, -0x1.b2204de17a53a3315364d23c8cd4p+7Q, 0x1.23910ebcbe60d3ac8690288b0ac9p+8Q, -0x1.29c6cec6860250c0db3c6cf44b1cp+8Q, 0x1.1c64b27b4c107ca71ade21f474f5p+8Q, -0x1.156985f5c8bce6de73bf215034a9p+8Q, 0x1.ef2b60fc7ce315a6b8de28e5d19dp+7Q, -0x1.84734ae811782beee80a7706ee5bp+7Q, 0x1.20e874beb6697ebef627236a9ac2p+7Q, -0x1.93d454c0120c50c5e5f45832b468p+6Q, 0x1.e8c645d5034483f58d32bb3f4e3bp+5Q, -0x1.0a8b2e2c06173020781b634ff3fbp+5Q, 0x1.14ef6d11452bbb05715fc7688438p+4Q, -0x1.bab6f3f4dbb55284f992570f49b4p+2Q, 0x1.4e6aaf12e910db6611cb1059823cp+0Q, 0x1.e57ecc0ee730e09fd58c24db0642p-4Q, -0x1.0f174cea8c305d809bddceff1132p-4Q, 0x1.a1f2dc12ec55c96d12f54ea71a2fp-12Q, 0x1.4002914419fbb27ad65f3fceabe7p-15Q, -0x1.6c7e600f14b10472b7579ae3bc81p-26Q, -0x0p+0Q};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0Q, 0x1.d2f4e044749b4e7a1c71af625a42p+0Q, -0x1.e196df480fe71bea5cbbf54b35dp+3Q, 0x1.ab061d20276f0750e2a71f034e04p+5Q, -0x1.a7b259e6037ebf7c8e2ada0b5ba1p+6Q, 0x1.04d3977e22f60f45b515e22f405p+7Q, -0x1.c308c46a51aa08f31731abdc9396p+6Q, 0x1.759cb70549060301bbf1e90c0d7dp+6Q, -0x1.73a4db524ebc2efdc465df1eceafp+6Q, 0x1.4d02e405c663ff8abf63f13a14eap+6Q, -0x1.c4dfc682dd95df4b0a54f464f5c5p+5Q, 0x1.217c835a844bf319c913a98fb0dfp+5Q, -0x1.9d3e5e5e092523c0105752b9ec75p+4Q, 0x1.eced01c912f6c17b1d53692fa574p+3Q, -0x1.ab15772777a65a90ae2d7cd7191bp+2Q, 0x1.780b7892927c5280dd5becc68e9dp+1Q, -0x1.59e4e79f9d38488dc3c592823598p+0Q, 0x1.04013ac7f90eca1ecf033967d8bdp-2Q, 0x1.63e903ad632e7f3030703fcb6c64p-4Q, -0x1.26b339b06c46eff13165e26c3ea5p-5Q, 0x1.1fc083a0e2c35a300d5c6f8e06aap-10Q, 0x1.9c18e59aa15ab3ece464b5d35415p-15Q, -0x1.d792baac952f2e4df120dee55ebdp-25Q, 0x0p+0Q};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0Q, 0x1.19eec26520f7247ef7c6a50c30c1p-1Q, -0x1.249f95db3c6a85ee060075e867d8p+2Q, 0x1.0297dba66cdd344c6014add13643p+4Q, -0x1.f4e8dc0eb78aa7eff1fa777a2d3cp+4Q, 0x1.1efd1b3c60e0b36de4fe2959cc4p+5Q, -0x1.a397a05a5f774f4ee2078ee612bfp+4Q, 0x1.239464bf9e82c4fc4fdd7d10ceaep+4Q, -0x1.3946d065739beaad7a016889ae55p+4Q, 0x1.2898316e66a7f2a70e1a6d4e83adp+4Q, -0x1.5bb8e2c4642782930886e734cb84p+3Q, 0x1.68255c99ba4c6b07d8215b80d139p+2Q, -0x1.21aae7ae7df31c2992880869d80ap+2Q, 0x1.64fab317448fb04743119877b3a8p+1Q, -0x1.75b64c97e09686a5bb55ff7e3516p-1Q, 0x1.22ff2ac4d8b9c4ff1398067e3f99p-3Q, -0x1.07ed621dcab476dea8f9c1c1f859p-3Q, -0x1.4a01e6ee0860d89681b640d3090fp-6Q, 0x1.2e7cdbbc900312ead84b8f4ecdafp-4Q, -0x1.b7f6865bae122ce58cd5b6b5db5p-6Q, 0x1.17b65cad3d540e056708b920004dp-9Q, 0x1.910e0462410b5b96ed51c6158bb4p-14Q, -0x1.cf434a44d45d4684dfb9a8c3dc56p-23Q, 0x0p+0Q};
+            }
+            if constexpr (order == 11) {
+                return {0x0p+0Q, 0x1.a6c51bc471a3098c7c3ba6f25a23p-5Q, -0x1.b8315371d42a542d22b5306cc4fcp-2Q, 0x1.89e13c889a74c808a95f3d0a6799p+0Q, -0x1.8aa497719f070f6dc765c9fe7e51p+1Q, 0x1.eb2b7ee2bc88d2eef92b7b69cb04p+1Q, -0x1.a91739cfcb4374adc78a37551409p+1Q, 0x1.4e87023b22be1f061884bc9409e9p+1Q, -0x1.31bb74af8ae4dfa54f81310a9052p+1Q, 0x1.0e1263d4463c809bd84430b64506p+1Q, -0x1.9cd0db1b42b96cb6927f658a63e7p+0Q, 0x1.3cec213a53551ad84004db21dcp+0Q, -0x1.daf35f59b2441d717c169614a5aap-1Q, 0x1.329c321d7ff6b77198e763d64324p-1Q, -0x1.8936ae8cb907bb56ce7129ca7fc2p-2Q, 0x1.00dee0f339229a14bdfc09c4e162p-2Q, -0x1.07bd180d959690eaf41df912a76dp-3Q, 0x1.cec01fe9b05f624125be2b70170dp-5Q, -0x1.e6ef9d5209f879f2bf7a3f0d08eap-6Q, 0x1.8f4f47250e3a4f324676c82d9528p-7Q, -0x1.e72d4f4950c89aa59da6f47aed33p-10Q, -0x1.e19176d7ba69146eb048ef5a5e41p-14Q, 0x1.1b79fa688c946fc4993e55c900d5p-21Q, -0x0p+0Q};
+            }
+        }
+        #endif
+    }
+    if constexpr (p == 13) {
+        if constexpr (std::is_same_v<Real, float>) {
+            if constexpr (order == 0) {
+                return {0x0p+0f, 0x1.749078p-9f, 0x1.8ae6a8p-3f, 0x1.d0088ap-1f, -0x1.20e16ep-4f, -0x1.f688bep-5f, 0x1.2fca44p-5f, -0x1.505c64p-12f, -0x1.014518p-6f, 0x1.c908bep-7f, -0x1.beac12p-8f, 0x1.0006aap-9f, -0x1.d4cc28p-13f, -0x1.a08b66p-15f, 0x1.5f413ap-16f, -0x1.5c34d2p-20f, -0x1.2dc446p-21f, 0x1.74f33ap-24f, 0x1.ddb5ep-29f, -0x1.07969cp-32f, 0x1.2c5958p-38f, 0x1.52fae6p-45f, -0x1.d83da4p-53f, 0x1.1342e6p-65f, 0x1.aa25eep-86f, -0x0p+0f};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0f, 0x1.239236p-6f, 0x1.0c0768p-1f, 0x1.3373bep-2f, -0x1.856d7ep+0f, 0x1.22d30ap+0f, -0x1.72e38ep-1f, 0x1.8e439cp-2f, -0x1.3bc252p-3f, 0x1.1bc8f6p-5f, 0x1.288446p-11f, -0x1.db22aap-10f, -0x1.3482dcp-11f, 0x1.328522p-11f, -0x1.bbf1c4p-14f, -0x1.17497ap-16f, 0x1.bebecp-18f, -0x1.bc40d8p-22f, 0x1.6454c6p-26f, 0x1.5fce04p-29f, -0x1.12414ap-33f, -0x1.ce70acp-41f, 0x1.8616f6p-48f, -0x1.7b38aep-60f, -0x1.258ba4p-79f, -0x0p+0f};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0f, 0x1.7e9e9ap-4f, 0x1.e81e74p-1f, -0x1.368292p+1f, 0x1.a1c192p+0f, -0x1.58e6fap-2f, 0x1.2f821p-2f, -0x1.f8fd9cp-2f, 0x1.017de8p-1f, -0x1.5831aep-2f, 0x1.30d718p-3f, -0x1.30a608p-5f, -0x1.632f9ep-11f, 0x1.1cbed4p-8f, -0x1.77d87p-10f, 0x1.50ec24p-14f, 0x1.f99c3cp-15f, -0x1.8453f2p-17f, -0x1.b40566p-23f, 0x1.4c2776p-24f, -0x1.287dbp-29f, -0x1.b00a66p-36f, 0x1.401eb2p-42f, -0x1.715282p-54f, -0x1.1de108p-72f, -0x0p+0f};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0f, 0x1.95e034p-2f, 0x1.e7908ep-3f, -0x1.29379ap+2f, 0x1.36cc46p+3f, -0x1.433598p+3f, 0x1.9c4d14p+2f, -0x1.ef81d8p+0f, -0x1.2378e8p+0f, 0x1.c6e272p+0f, -0x1.c857e6p-1f, 0x1.3531bp-8f, 0x1.05f57cp-2f, -0x1.38a2dcp-3f, 0x1.35c4a6p-5f, -0x1.fddc3cp-14f, -0x1.2653ap-9f, 0x1.ec5d7p-12f, -0x1.dc01f8p-17f, -0x1.379718p-18f, 0x1.7e5cfep-23f, 0x1.a12416p-29f, -0x1.417132p-35f, 0x1.65f402p-46f, 0x1.15123cp-63f, -0x0p+0f};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0f, 0x1.4c5d52p+0f, -0x1.5d2572p+2f, 0x1.24b0fp+3f, -0x1.39e0f8p+3f, 0x1.f006ccp+3f, -0x1.0ce3p+5f, 0x1.b8b8bp+5f, -0x1.e69256p+5f, 0x1.503102p+5f, -0x1.6d86aep+3f, -0x1.35b5dcp+3f, 0x1.a6237cp+3f, -0x1.cda456p+2f, 0x1.d5a02cp+0f, 0x1.ecd4c4p-5f, -0x1.660ee6p-3f, 0x1.5158e6p-5f, -0x1.73814cp-10f, -0x1.23460cp-11f, 0x1.fa353cp-16f, 0x1.19c574p-21f, -0x1.4bb43p-27f, 0x1.fc9a2p-38f, 0x1.89a8b8p-54f, 0x0p+0f};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0f, 0x1.a35158p+1f, -0x1.5a1bc4p+4f, 0x1.fa0a08p+5f, -0x1.a68f66p+6f, 0x1.98403ap+6f, -0x1.03810ep+5f, -0x1.14faaep+6f, 0x1.3d735cp+7f, -0x1.cdbd7ep+7f, 0x1.200434p+8f, -0x1.2591e8p+8f, 0x1.b6219ap+7f, -0x1.a875bap+6f, 0x1.85c7d2p+4f, 0x1.1c0e0ep+2f, -0x1.36efc4p+2f, 0x1.3e3f5cp+0f, -0x1.bffc3ap-5f, -0x1.75f52cp-6f, 0x1.dea5b4p-10f, 0x1.10aa3ep-15f, -0x1.ea6ed6p-21f, 0x1.089ab2p-30f, 0x1.9990a4p-46f, 0x0p+0f};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0f, 0x1.5d159cp+2f, -0x1.54873ep+5f, 0x1.2c245ep+7f, -0x1.416f5cp+8f, 0x1.e67e2cp+8f, -0x1.298ee6p+9f, 0x1.48ee3ep+9f, -0x1.4e6b46p+9f, 0x1.2782eap+9f, -0x1.bb4938p+8f, 0x1.25dfd4p+8f, -0x1.575e0cp+7f, 0x1.1c029p+6f, -0x1.08a1fep+2f, -0x1.12ed1ep+4f, 0x1.66791ep+3f, -0x1.7aa974p+1f, 0x1.41600cp-3f, 0x1.275514p-4f, -0x1.29374p-7f, -0x1.51ea7ep-13f, 0x1.deb156p-18f, -0x1.6e30fap-27f, -0x1.1b57acp-41f, -0x0p+0f};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0f, 0x1.d4fe28p+2f, -0x1.ecb0f4p+5f, 0x1.c6da62p+7f, -0x1.e3622ep+8f, 0x1.495088p+9f, -0x1.3d934ap+9f, 0x1.0686p+9f, -0x1.bb4eb6p+8f, 0x1.2c2d3cp+8f, -0x1.6a6f08p+5f, -0x1.48c0f8p+7f, 0x1.bce286p+7f, -0x1.9e035ep+7f, 0x1.737018p+7f, -0x1.15bd06p+7f, 0x1.1609d2p+6f, -0x1.30b382p+4f, 0x1.34c266p+0f, 0x1.56d14ep-1f, -0x1.f82518p-4f, -0x1.1d5d34p-9f, 0x1.599f88p-13f, -0x1.742b04p-22f, -0x1.1fd836p-35f, 0x0p+0f};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0f, 0x1.6f91b2p+2f, -0x1.8fef12p+5f, 0x1.809c44p+7f, -0x1.b10bfp+8f, 0x1.452582p+9f, -0x1.7231bp+9f, 0x1.7af822p+9f, -0x1.823eap+9f, 0x1.6f4bc2p+9f, -0x1.32f292p+9f, 0x1.d856p+8f, -0x1.59b2fp+8f, 0x1.c4899p+7f, -0x1.01b04cp+7f, 0x1.0ee55p+6f, -0x1.f14982p+4f, 0x1.214136p+3f, -0x1.1e3582p-2f, -0x1.54f128p-1f, 0x1.1dedd2p-3f, 0x1.2b8db4p-10f, -0x1.7cd67ep-12f, 0x1.c17582p-21f, 0x1.5b5402p-33f, -0x0p+0f};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0f, 0x1.e00f2p+1f, -0x1.09aad6p+5f, 0x1.0083b2p+7f, -0x1.1b0164p+8f, 0x1.8e74c6p+8f, -0x1.907a86p+8f, 0x1.68e4a6p+8f, -0x1.685dfep+8f, 0x1.592f3ap+8f, -0x1.09589ap+8f, 0x1.658b66p+7f, -0x1.f90c72p+6f, 0x1.49a9a8p+6f, -0x1.441338p+5f, 0x1.0b7b2ap+4f, -0x1.d98372p+2f, 0x1.f43ec2p+0f, 0x1.6165b8p-1f, -0x1.4f8a82p-1f, 0x1.267684p-3f, -0x1.8ddc62p-9f, -0x1.979caep-11f, 0x1.95627cp-20f, 0x1.38bcd2p-31f, -0x0p+0f};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0f, 0x1.ddc992p+0f, -0x1.0aa6a6p+4f, 0x1.ffd30ap+5f, -0x1.1076bcp+7f, 0x1.5b315p+7f, -0x1.15e62ap+7f, 0x1.73ecdap+6f, -0x1.7ea49ap+6f, 0x1.92fe5p+6f, -0x1.e50ce8p+5f, 0x1.23fe36p+4f, -0x1.1183a6p+3f, 0x1.325da8p+2f, 0x1.b5b93ep+2f, -0x1.6174ccp+3f, 0x1.b8e78ep+2f, -0x1.ffc6e6p+1f, 0x1.807b44p+1f, -0x1.949fp+0f, 0x1.99c706p-2f, -0x1.8b4256p-6f, -0x1.25fbdep-8f, 0x1.a2ffd6p-17f, 0x1.4225e6p-27f, 0x0p+0f};
+            }
+            if constexpr (order == 11) {
+                return {0x0p+0f, 0x1.82556p-2f, -0x1.b108acp+1f, 0x1.a3afap+3f, -0x1.c92e2ap+4f, 0x1.336156p+5f, -0x1.154d2p+5f, 0x1.af95c6p+4f, -0x1.a382eep+4f, 0x1.a5a57ep+4f, -0x1.48587cp+4f, 0x1.c6519cp+3f, -0x1.64406ep+3f, 0x1.05a0dap+3f, -0x1.34062ap+2f, 0x1.65a332p+1f, -0x1.b27cf8p+0f, 0x1.a5bdc8p-1f, -0x1.571ac2p-2f, 0x1.317678p-3f, -0x1.904f34p-5f, 0x1.0ee4f4p-8f, 0x1.2584f2p-10f, -0x1.373cf6p-17f, -0x1.db60ap-27f, 0x0p+0f};
+            }
+            if constexpr (order == 12) {
+                return {0x0p+0f, 0x1.8dbb04p-5f, -0x1.bebdc6p-2f, 0x1.aeb7a6p+0f, -0x1.cb9852p+1f, 0x1.240bf6p+2f, -0x1.cab7dp+1f, 0x1.1fd454p+1f, -0x1.1ce974p+1f, 0x1.3bab08p+1f, -0x1.c40e7cp+0f, 0x1.feadc8p-1f, -0x1.a643a4p-1f, 0x1.543b96p-1f, -0x1.577aa6p-2f, 0x1.499f7p-3f, -0x1.d5a152p-4f, 0x1.d4c5bap-5f, -0x1.094f52p-6f, 0x1.cd0926p-8f, -0x1.b2091cp-9f, 0x1.fdc736p-13f, 0x1.4af176p-13f, -0x1.fd199ap-19f, -0x1.7fa406p-27f, 0x0p+0f};
+            }
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0, 0x1.749078c0867aap-9, 0x1.8ae6a79b4939p-3, 0x1.d008898983914p-1, -0x1.20e16d5539e3fp-4, -0x1.f688bd1280c7p-5, 0x1.2fca4301354a5p-5, -0x1.505c64431d7a7p-12, -0x1.0145189baf014p-6, 0x1.c908becee5a6ap-7, -0x1.beac12be1e7dep-8, 0x1.0006a916adee3p-9, -0x1.d4cc286b09e13p-13, -0x1.a08b65bbb5986p-15, 0x1.5f413ab3a7eb9p-16, -0x1.5c34d16af592p-20, -0x1.2dc4454eebde3p-21, 0x1.74f33a2ccbc65p-24, 0x1.ddb5df0a412fdp-29, -0x1.07969b3a158bdp-32, 0x1.2c5958b74836cp-38, 0x1.52fae6e83092p-45, -0x1.d83da475a639cp-53, 0x1.1342e56840ec2p-65, 0x1.aa25edf8f64ffp-86, -0x0p+0};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0, 0x1.23923550f457dp-6, 0x1.0c0767795d12bp-1, 0x1.3373be839b47cp-2, -0x1.856d7e6b6468cp+0, 0x1.22d30ac28dd9dp+0, -0x1.72e38df054a24p-1, 0x1.8e439b194a1c1p-2, -0x1.3bc2524066e84p-3, 0x1.1bc8f6e410596p-5, 0x1.2884461caa1e3p-11, -0x1.db22a9804aa11p-10, -0x1.3482dca87f01cp-11, 0x1.3285223dae55ap-11, -0x1.bbf1c4306d1a3p-14, -0x1.17497a4dcd45p-16, 0x1.bebec0cbd1f99p-18, -0x1.bc40d833ef35ap-22, 0x1.6454c6cebdf98p-26, 0x1.5fce040bf0fa2p-29, -0x1.1241493325c92p-33, -0x1.ce70ab06ee7ebp-41, 0x1.8616f674ef406p-48, -0x1.7b38ad7c07a3ap-60, -0x1.258ba4702de86p-79, -0x0p+0};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0, 0x1.7e9e99d93265ep-4, 0x1.e81e73bf7d4e6p-1, -0x1.368292c7be10ep+1, 0x1.a1c192a939b96p+0, -0x1.58e6f9045a40ep-2, 0x1.2f82100ba4f28p-2, -0x1.f8fd9be6cc911p-2, 0x1.017de77081fc3p-1, -0x1.5831ad1464211p-2, 0x1.30d718554c4cbp-3, -0x1.30a6075105b3bp-5, -0x1.632f9e9eb99fcp-11, 0x1.1cbed37ba4dbep-8, -0x1.77d86fa7164cp-10, 0x1.50ec238da0096p-14, 0x1.f99c3b6dd2e63p-15, -0x1.8453f2cbc2d99p-17, -0x1.b4056601f4cp-23, 0x1.4c2776a5f116ep-24, -0x1.287daf168a21ap-29, -0x1.b00a66e2af604p-36, 0x1.401eb1fad689ep-42, -0x1.71528144e6955p-54, -0x1.1de10823e626cp-72, -0x0p+0};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0, 0x1.95e033565cd46p-2, 0x1.e7908dd5753c9p-3, -0x1.293799fcf6c8ep+2, 0x1.36cc467b08bf8p+3, -0x1.4335983e13577p+3, 0x1.9c4d14b541486p+2, -0x1.ef81d85b23a02p+0, -0x1.2378e73c6b10ap+0, 0x1.c6e27151761e4p+0, -0x1.c857e67243154p-1, 0x1.3531afa42b77fp-8, 0x1.05f57c1a6464dp-2, -0x1.38a2db882124ep-3, 0x1.35c4a5041d9b9p-5, -0x1.fddc3c9f813d7p-14, -0x1.2653a0321997dp-9, 0x1.ec5d6f7ab50c1p-12, -0x1.dc01f8633f4c6p-17, -0x1.379717b64ca38p-18, 0x1.7e5cfdc9a1b18p-23, 0x1.a124166c57861p-29, -0x1.4171311c3a7b2p-35, 0x1.65f402b77f1abp-46, 0x1.15123cc4efb61p-63, -0x0p+0};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0, 0x1.4c5d516dd5341p+0, -0x1.5d2571cda5544p+2, 0x1.24b0f0352262ap+3, -0x1.39e0f8d13e8dbp+3, 0x1.f006cc927be53p+3, -0x1.0ce2ffa464611p+5, 0x1.b8b8afcf323dp+5, -0x1.e6925570e3f51p+5, 0x1.503102590c0b8p+5, -0x1.6d86add093f07p+3, -0x1.35b5dc1025f2dp+3, 0x1.a6237c764b4a3p+3, -0x1.cda455c3ae393p+2, 0x1.d5a02bb93708ap+0, 0x1.ecd4c4adc076p-5, -0x1.660ee59df078bp-3, 0x1.5158e51b27e5ep-5, -0x1.73814bfd57b68p-10, -0x1.23460c48f637p-11, 0x1.fa353cdebaaabp-16, 0x1.19c5738584247p-21, -0x1.4bb4308ed52p-27, 0x1.fc9a1f4f09859p-38, 0x1.89a8b7b9d28d2p-54, 0x0p+0};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0, 0x1.a35157d8dba57p+1, -0x1.5a1bc35a1cc0ep+4, 0x1.fa0a0878d9a93p+5, -0x1.a68f6523a827p+6, 0x1.98403a971e631p+6, -0x1.03810e60e0205p+5, -0x1.14faaec768465p+6, 0x1.3d735b94c1054p+7, -0x1.cdbd7de801408p+7, 0x1.20043470ad457p+8, -0x1.2591e882d85cdp+8, 0x1.b621996a63c18p+7, -0x1.a875ba068d845p+6, 0x1.85c7d166f26b7p+4, 0x1.1c0e0d6b929f9p+2, -0x1.36efc345fd87ep+2, 0x1.3e3f5c2c93c34p+0, -0x1.bffc3922a3129p-5, -0x1.75f52c4bce394p-6, 0x1.dea5b49d2b29ap-10, 0x1.10aa3eff5f8abp-15, -0x1.ea6ed6c321e75p-21, 0x1.089ab261bfe1dp-30, 0x1.9990a3735f2b8p-46, 0x0p+0};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0, 0x1.5d159c98a090ap+2, -0x1.54873e7e1b3d2p+5, 0x1.2c245e185ac8bp+7, -0x1.416f5cc6c22c2p+8, 0x1.e67e2b7f93304p+8, -0x1.298ee57db6ed6p+9, 0x1.48ee3d90a4e35p+9, -0x1.4e6b4521eb7a5p+9, 0x1.2782e95d7bf9fp+9, -0x1.bb493883e544dp+8, 0x1.25dfd4b9fa45bp+8, -0x1.575e0c206b7eep+7, 0x1.1c028f2725fcep+6, -0x1.08a1fe0ac681ap+2, -0x1.12ed1d6ca773p+4, 0x1.66791e904ad3bp+3, -0x1.7aa9733036516p+1, 0x1.41600caa02956p-3, 0x1.275514f436a32p-4, -0x1.29373f56ac109p-7, -0x1.51ea7d9f34504p-13, 0x1.deb156b08b87fp-18, -0x1.6e30fae8c34eep-27, -0x1.1b57abb7d7f1cp-41, -0x0p+0};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0, 0x1.d4fe27a0835aep+2, -0x1.ecb0f32ca76fbp+5, 0x1.c6da62a20cd0bp+7, -0x1.e3622dd5ba05ep+8, 0x1.49508717a90e8p+9, -0x1.3d934aacf56d1p+9, 0x1.068600d74e1c9p+9, -0x1.bb4eb52dbc23dp+8, 0x1.2c2d3c048caafp+8, -0x1.6a6f07f5d07ddp+5, -0x1.48c0f7b3bed9ep+7, 0x1.bce28601020e5p+7, -0x1.9e035ea535c3bp+7, 0x1.737017c34f7dfp+7, -0x1.15bd065f2789cp+7, 0x1.1609d2e86de1fp+6, -0x1.30b382548236p+4, 0x1.34c266d274d02p+0, 0x1.56d14dbd1c0fp-1, -0x1.f82518456ddfap-4, -0x1.1d5d333a03734p-9, 0x1.599f88826e1dfp-13, -0x1.742b04eba227p-22, -0x1.1fd835e2f3ac3p-35, 0x0p+0};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0, 0x1.6f91b1fb16e46p+2, -0x1.8fef11e8059cfp+5, 0x1.809c444472a8ep+7, -0x1.b10bf090c92b5p+8, 0x1.45258188f7147p+9, -0x1.7231afc08bd27p+9, 0x1.7af82162ac35ap+9, -0x1.823e9f8992b5ap+9, 0x1.6f4bc124eb7dcp+9, -0x1.32f291524b4fdp+9, 0x1.d856007cb8fap+8, -0x1.59b2f057a74e5p+8, 0x1.c4898ffe6b604p+7, -0x1.01b04bb5c7e4fp+7, 0x1.0ee550f2b46fbp+6, -0x1.f149829700499p+4, 0x1.21413698e7cf2p+3, -0x1.1e358290df39dp-2, -0x1.54f12799790c9p-1, 0x1.1dedd290f908p-3, 0x1.2b8db385d6eebp-10, -0x1.7cd67d6099899p-12, 0x1.c1758243d6f69p-21, 0x1.5b5402fbe8db8p-33, -0x0p+0};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0, 0x1.e00f201ca9b48p+1, -0x1.09aad588fc6e2p+5, 0x1.0083b1ed3add2p+7, -0x1.1b01639f15a47p+8, 0x1.8e74c5b415b4dp+8, -0x1.907a858da198ep+8, 0x1.68e4a68143eb6p+8, -0x1.685dfe59eb94fp+8, 0x1.592f39b72049ap+8, -0x1.09589acf597f5p+8, 0x1.658b66c44d2dap+7, -0x1.f90c71880a916p+6, 0x1.49a9a7009f2b2p+6, -0x1.441338caa52dp+5, 0x1.0b7b2a297fde1p+4, -0x1.d98372b1c68d4p+2, 0x1.f43ec1f2a328p+0, 0x1.6165b77555fcbp-1, -0x1.4f8a8171bb09p-1, 0x1.267683e93d2b7p-3, -0x1.8ddc624d415c9p-9, -0x1.979cae945ae1p-11, 0x1.95627b187fdb2p-20, 0x1.38bcd286c35dep-31, -0x0p+0};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0, 0x1.ddc9914b8fce2p+0, -0x1.0aa6a6fe474ap+4, 0x1.ffd30a30f104ep+5, -0x1.1076bbdb4cf75p+7, 0x1.5b314fd5bd842p+7, -0x1.15e629a2f07abp+7, 0x1.73ecdaa7dbcd1p+6, -0x1.7ea4991281a8p+6, 0x1.92fe5087093b6p+6, -0x1.e50ce86c3eca3p+5, 0x1.23fe36ce5250dp+4, -0x1.1183a5ac74637p+3, 0x1.325da71616788p+2, 0x1.b5b93d37eb78fp+2, -0x1.6174cc292a978p+3, 0x1.b8e78e1a9ada5p+2, -0x1.ffc6e54f09b8ap+1, 0x1.807b43d233e13p+1, -0x1.949effe4fd5f1p+0, 0x1.99c706ee33d33p-2, -0x1.8b4255eb2ab53p-6, -0x1.25fbde4ae0e29p-8, 0x1.a2ffd5a58a3e6p-17, 0x1.4225e5d67d6a9p-27, 0x0p+0};
+            }
+            if constexpr (order == 11) {
+                return {0x0p+0, 0x1.82555f0fca682p-2, -0x1.b108ac4bd9d5ep+1, 0x1.a3af9f5e28534p+3, -0x1.c92e2a69bebeap+4, 0x1.336156f19a3ebp+5, -0x1.154d20c532d38p+5, 0x1.af95c6a7f034fp+4, -0x1.a382ed435f8edp+4, 0x1.a5a57db59b67cp+4, -0x1.48587bdb4781p+4, 0x1.c6519b1cdb293p+3, -0x1.64406dc5dece2p+3, 0x1.05a0da2a87dbp+3, -0x1.34062a3bf7c11p+2, 0x1.65a3327bcf1acp+1, -0x1.b27cf7ab49be3p+0, 0x1.a5bdc7192b9c4p-1, -0x1.571ac2983f85ep-2, 0x1.31767817c6adfp-3, -0x1.904f3491bf69cp-5, 0x1.0ee4f3163f55fp-8, 0x1.2584f1f36b43ep-10, -0x1.373cf584c03efp-17, -0x1.db60a068c3378p-27, 0x0p+0};
+            }
+            if constexpr (order == 12) {
+                return {0x0p+0, 0x1.8dbb03fad2c3p-5, -0x1.bebdc5d3b2391p-2, 0x1.aeb7a5ea21053p+0, -0x1.cb9851522d20bp+1, 0x1.240bf59871b99p+2, -0x1.cab7cf1ed537ep+1, 0x1.1fd4543a5fd8dp+1, -0x1.1ce9744c1c975p+1, 0x1.3bab08bd76345p+1, -0x1.c40e7b4e77557p+0, 0x1.feadc8c7ce87bp-1, -0x1.a643a47d84b4ep-1, 0x1.543b964e0f03ap-1, -0x1.577aa576ffa65p-2, 0x1.499f6f7a97a23p-3, -0x1.d5a15151b9016p-4, 0x1.d4c5badb46707p-5, -0x1.094f5215690dbp-6, 0x1.cd0926fb9e142p-8, -0x1.b2091c2c73ddp-9, 0x1.fdc7350edfaddp-13, 0x1.4af17513fc3a8p-13, -0x1.fd199a3cefa32p-19, -0x1.7fa406e41ed66p-27, 0x0p+0};
+            }
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0L, 0xb.a483c60433d4d39p-12L, 0xc.57353cda49c7dedp-6L, 0xe.80444c4c1c89ecep-4L, -0x9.070b6aa9cf1f929p-7L, -0xf.b445e89406380cap-8L, 0x9.7e521809aa52714p-8L, -0xa.82e32218ebd378fp-15L, -0x8.0a28c4dd780a179p-9L, 0xe.4845f6772d3537ep-10L, -0xd.f56095f0f3ef04ap-11L, 0x8.003548b56f71a16p-12L, -0xe.a66143584f09aacp-16L, -0xd.045b2dddacc33b9p-18L, 0xa.fa09d59d3f5ca6ep-19L, -0xa.e1a68b57ac901bdp-23L, -0x9.6e222a775ef19bdp-24L, 0xb.a799d1665e328c8p-27L, 0xe.edaef852097ea04p-32L, -0x8.3cb4d9d0ac5e8bp-35L, 0x9.62cac5ba41b6085p-41L, 0xa.97d73741848fd34p-48L, -0xe.c1ed23ad31ce184p-56L, 0x8.9a172b420760cedp-68L, 0xd.512f6fc7b27f70ap-89L, -0x0p+0L};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0L, 0x9.1c91aa87a2be53cp-9L, 0x8.603b3bcae89572fp-4L, 0x9.9b9df41cda3e206p-5L, -0xc.2b6bf35b234616fp-3L, 0x9.169856146ece4d3p-3L, -0xb.971c6f82a511d45p-4L, 0xc.721cd8ca50e0b31p-5L, -0x9.de1292033741f59p-6L, 0x8.de47b72082cb31fp-8L, 0x9.442230e550f1904p-14L, -0xe.d9154c025508998p-13L, -0x9.a416e543f80e22fp-14L, 0x9.942911ed72acc95p-14L, -0xd.df8e218368d1bf8p-17L, -0x8.ba4bd26e6a27feep-19L, 0xd.f5f6065e8fcc9b9p-21L, -0xd.e206c19f79acc2bp-25L, 0xb.22a63675efcbfa2p-29L, 0xa.fe70205f87d115p-32L, -0x8.920a49992e4937dp-36L, -0xe.7385583773f5acap-44L, 0xc.30b7b3a77a02f75p-51L, -0xb.d9c56be03d1d02cp-63L, -0x9.2c5d23816f42d62p-82L, -0x0p+0L};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0L, 0xb.f4f4cec9932f0f6p-7L, 0xf.40f39dfbea733adp-4L, -0x9.b414963df08728ap-2L, 0xd.0e0c9549cdcb3a8p-3L, -0xa.c737c822d206e95p-5L, 0x9.7c10805d27943dp-5L, -0xf.c7ecdf3664887bbp-5L, 0x8.0bef3b840fe187dp-4L, -0xa.c18d68a32108919p-5L, 0x9.86b8c2aa62655e8p-6L, -0x9.85303a882d9d527p-8L, -0xb.197cf4f5ccfe389p-14L, 0x8.e5f69bdd26decb6p-11L, -0xb.bec37d38b25fe46p-13L, 0xa.87611c6d004b37bp-17L, 0xf.cce1db6e973199cp-18L, -0xc.229f965e16ccb5cp-20L, -0xd.a02b300fa5ffc5bp-26L, 0xa.613bb52f88b70ecp-27L, -0x9.43ed78b4510cd51p-32L, -0xd.805337157b01dc1p-39L, 0xa.00f58fd6b44ef03p-45L, -0xb.8a940a2734aa51ap-57L, -0x8.ef08411f3135df8p-75L, -0x0p+0L};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0L, 0xc.af019ab2e6a32f3p-5L, 0xf.3c846eaba9e4babp-6L, -0x9.49bccfe7b646d1p-1L, 0x9.b66233d845fbec5p+0L, -0xa.19acc1f09abba63p+0L, 0xc.e268a5aa0a433dap-1L, -0xf.7c0ec2d91d00d64p-3L, -0x9.1bc739e3588517cp-3L, 0xe.37138a8bb0f1f2cp-3L, -0xe.42bf339218a9d4bp-4L, 0x9.a98d7d215bbfa64p-11L, 0x8.2fabe0d32326ba1p-5L, -0x9.c516dc410926fe2p-6L, 0x9.ae252820ecdca2bp-8L, -0xf.eee1e4fc09eb578p-17L, -0x9.329d0190ccbe8fdp-12L, 0xf.62eb7bd5a860bbfp-15L, -0xe.e00fc319fa6309dp-20L, -0x9.bcb8bdb2651be88p-21L, 0xb.f2e7ee4d0d8bee7p-26L, 0xd.0920b362bc30ba7p-32L, -0xa.0b8988e1d3d9312p-38L, 0xb.2fa015bbf8d5914p-49L, 0x8.a891e6277db069dp-66L, -0x0p+0L};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0L, 0xa.62ea8b6ea9a0684p-3L, -0xa.e92b8e6d2aa1c92p-1L, 0x9.258781a91314f19p+0L, -0x9.cf07c689f46d8f8p+0L, 0xf.80366493df29948p+0L, -0x8.6717fd232308bfp+2L, 0xd.c5c57e7991e8074p+2L, -0xf.3492ab871fa8811p+2L, 0xa.818812c8605bdbdp+2L, -0xb.6c356e849f83a5ep+0L, -0x9.adaee0812f969a5p+0L, 0xd.311be3b25a5141ap+0L, -0xe.6d22ae1d71c94e9p-1L, 0xe.ad015dc9b84519p-3L, 0xf.66a6256e03aff12p-8L, -0xb.30772cef83c5a19p-6L, 0xa.8ac728d93f2edffp-8L, -0xb.9c0a5feabdb40fdp-13L, -0x9.1a306247b1b7d38p-14L, 0xf.d1a9e6f5d555505p-19L, 0x8.ce2b9c2c2123732p-24L, -0xa.5da18476a8fff99p-30L, 0xf.e4d0fa784c2c7aap-41L, 0xc.4d45bdce9468eb9p-57L, 0x0p+0L};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0L, 0xd.1a8abec6dd2b59ap-2L, -0xa.d0de1ad0e606ddbp+1L, 0xf.d05043c6cd499c3p+2L, -0xd.347b291d41380b3p+3L, 0xc.c201d4b8f318b15p+3L, -0x8.1c08730701024ebp+2L, -0x8.a7d5763b4232a87p+3L, 0x9.eb9adca6082a1b5p+4L, -0xe.6debef400a03eb9p+4L, 0x9.0021a3856a2b57ap+5L, -0x9.2c8f4416c2e68c6p+5L, 0xd.b10ccb531e0bf33p+4L, -0xd.43add0346c224eap+3L, 0xc.2e3e8b37935bbc2p+1L, 0x8.e0706b5c94fcaddp-1L, -0x9.b77e1a2fec3f3f9p-1L, 0x9.f1fae1649e1a3cap-3L, -0xd.ffe1c91518944a2p-8L, -0xb.afa9625e71ca263p-9L, 0xe.f52da4e9594cf98p-13L, 0x8.8551f7fafc55605p-18L, -0xf.5376b6190f3a9e1p-24L, 0x8.44d5930dff0e45cp-33L, 0xc.cc851b9af95c09cp-49L, 0x0p+0L};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0L, 0xa.e8ace4c50485103p-1L, -0xa.a439f3f0d9e9083p+2L, 0x9.6122f0c2d6458a6p+4L, -0xa.0b7ae6361160fep+5L, 0xf.33f15bfc9982224p+5L, -0x9.4c772bedb76afeap+6L, 0xa.4771ec85271a548p+6L, -0xa.735a290f5bd2b61p+6L, 0x9.3c174aebdfcfafep+6L, -0xd.da49c41f2a26a23p+5L, 0x9.2efea5cfd22d7f4p+5L, -0xa.baf061035bf7341p+4L, 0x8.e01479392fe733bp+3L, -0x8.450ff056340cfcbp-1L, -0x8.9768eb653b980edp+1L, 0xb.33c8f482569da0fp+0L, -0xb.d54b9981b28ad7fp-2L, 0xa.0b00655014aaec4p-6L, 0x9.3aa8a7a1b518f2bp-7L, -0x9.49b9fab56084ac4p-10L, -0xa.8f53ecf9a28205dp-16L, 0xe.f58ab5845c3f783p-21L, -0xb.7187d7461a76c1bp-30L, -0x8.dabd5dbebf8dd41p-44L, -0x0p+0L};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0L, 0xe.a7f13d041ad70dp-1L, -0xf.658799653b7da4ap+2L, 0xe.36d31510668543p+4L, -0xf.1b116eadd02ec05p+5L, 0xa.4a8438bd48741b4p+6L, -0x9.ec9a5567ab68514p+6L, 0x8.343006ba70e487p+6L, -0xd.da75a96de11e455p+5L, 0x9.6169e024655745ap+5L, -0xb.53783fae83ee946p+2L, -0xa.4607bd9df6ceea7p+4L, 0xd.e71430081072aa3p+4L, -0xc.f01af529ae1d75fp+4L, 0xb.9b80be1a7bef779p+4L, -0x8.ade832f93c4e129p+4L, 0x8.b04e97436f0fa36p+3L, -0x9.859c12a411afe04p+1L, 0x9.a6133693a681011p-3L, 0xa.b68a6de8e077c6ep-4L, -0xf.c128c22b6efd051p-7L, -0x8.eae999d01b9a034p-12L, 0xa.ccfc441370efba9p-16L, -0xb.a158275d1138117p-25L, -0x8.fec1af179d61b9fp-38L, 0x0p+0L};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0L, 0xb.7c8d8fd8b7231c8p-1L, -0xc.7f788f402ce76dp+2L, 0xc.04e222239546c21p+4L, -0xd.885f8486495a99bp+5L, 0xa.292c0c47b8a3474p+6L, -0xb.918d7e045e93b18p+6L, 0xb.d7c10b1561accb3p+6L, -0xc.11f4fc4c95acfe3p+6L, 0xb.7a5e09275bee17p+6L, -0x9.97948a925a7e40dp+6L, 0xe.c2b003e5c7d03a7p+5L, -0xa.cd9782bd3a72557p+5L, 0xe.244c7ff35b01e7fp+4L, -0x8.0d825dae3f27671p+4L, 0x8.772a8795a37d803p+3L, -0xf.8a4c14b8024c883p+1L, 0x9.0a09b4c73e78daep+0L, -0x8.f1ac1486f9ce578p-5L, -0xa.a7893ccbc864ac9p-4L, 0x8.ef6e9487c83fc69p-6L, 0x9.5c6d9c2eb77580cp-13L, -0xb.e6b3eb04cc4c723p-15L, 0xe.0bac121eb7b4789p-24L, 0xa.daa017df46dbf37p-36L, -0x0p+0L};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0L, 0xf.007900e54da3df6p-2L, -0x8.4d56ac47e370e97p+2L, 0x8.041d8f69d6e8efep+4L, -0x8.d80b1cf8ad238cbp+5L, 0xc.73a62da0ada64c1p+5L, -0xc.83d42c6d0cc6daep+5L, 0xb.4725340a1f5b14p+5L, -0xb.42eff2cf5ca79c7p+5L, 0xa.c979cdb9024d1b7p+5L, -0x8.4ac4d67acbfab3fp+5L, 0xb.2c5b3622696cf85p+4L, -0xf.c8638c40548b2c6p+3L, 0xa.4d4d3804f95933ep+3L, -0xa.2099c6552967d07p+2L, 0x8.5bd9514bfef0a5ep+1L, -0xe.cc1b958e3469fa9p-1L, 0xf.a1f60f951940304p-3L, 0xb.0b2dbbaaafe5407p-4L, -0xa.7c540b8dd847e5dp-4L, 0x9.33b41f49e95bb8cp-6L, -0xc.6ee3126a0ae46c7p-12L, -0xc.bce574a2d70819p-14L, 0xc.ab13d8c3fed8cb7p-23L, 0x9.c5e694361aef307p-34L, -0x0p+0L};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0L, 0xe.ee4c8a5c7e71374p-3L, -0x8.553537f23a4ffcdp+1L, 0xf.fe98518788271d7p+2L, -0x8.83b5deda67ba93ep+4L, 0xa.d98a7eadec21394p+4L, -0x8.af314d1783d59d9p+4L, 0xb.9f66d53ede688c9p+3L, -0xb.f524c8940d401f5p+3L, 0xc.97f2843849db0a7p+3L, -0xf.28674361f651857p+2L, 0x9.1ff1b672928682ep+1L, -0x8.8c1d2d63a31b528p+0L, 0x9.92ed38b0b3c3d8dp-1L, 0xd.adc9e9bf5bc7971p-1L, -0xb.0ba6614954bbf44p+0L, 0xd.c73c70d4d6d2496p-1L, -0xf.fe372a784dc531cp-2L, 0xc.03da1e919f0994ap-2L, -0xc.a4f7ff27eaf885bp-3L, 0xc.ce3837719e99949p-5L, -0xc.5a12af5955a96fbp-9L, -0x9.2fdef25707148aap-11L, 0xd.17fead2c51f312dp-20L, 0xa.112f2eb3eb54818p-30L, 0x0p+0L};
+            }
+            if constexpr (order == 11) {
+                return {0x0p+0L, 0xc.12aaf87e5340e4ep-5L, -0xd.8845625eceaef48p-2L, 0xd.1d7cfaf14299ea2p+0L, -0xe.4971534df5f5093p+1L, 0x9.9b0ab78cd1f558dp+2L, -0x8.aa690629969becdp+2L, 0xd.7cae353f81a7b93p+1L, -0xd.1c176a1afc76911p+1L, 0xd.2d2bedacdb3df28p+1L, -0xa.42c3deda3c082c7p+1L, 0xe.328cd8e6d949737p+0L, -0xb.22036e2ef671076p+0L, 0x8.2d06d1543ed7f3cp+0L, -0x9.a03151dfbe084ep-1L, 0xb.2d1993de78d60e7p-2L, -0xd.93e7bd5a4df1be7p-3L, 0xd.2dee38c95ce1d1p-4L, -0xa.b8d614c1fc2f1d3p-5L, 0x9.8bb3c0be356f62ap-6L, -0xc.8279a48dfb4e393p-8L, 0x8.772798b1faafa2dp-11L, 0x9.2c278f9b5a1f3dep-13L, -0x9.b9e7ac2601f7483p-20L, -0xe.db05034619bbe3ap-30L, 0x0p+0L};
+            }
+            if constexpr (order == 12) {
+                return {0x0p+0L, 0xc.6dd81fd69617fa7p-8L, -0xd.f5ee2e9d91c88f7p-5L, 0xd.75bd2f51082950ep-3L, -0xe.5cc28a9169055e6p-2L, 0x9.205facc38dccbfep-1L, -0xe.55be78f6a9bf069p-2L, 0x8.fea2a1d2fec658fp-2L, -0x8.e74ba260e4bab6fp-2L, 0x9.dd5845ebb1a25a2p-2L, -0xe.2073da73baab7afp-3L, 0xf.f56e463e743d47ep-4L, -0xd.321d23ec25a6d38p-4L, 0xa.a1dcb270781d1d4p-4L, -0xa.bbd52bb7fd3277ep-5L, 0xa.4cfb7bd4bd115e9p-6L, -0xe.ad0a8a8dc80b1aep-7L, 0xe.a62dd6da3383b8ap-8L, -0x8.4a7a90ab486d843p-9L, 0xe.684937dcf0a13c9p-11L, -0xd.9048e1639ee817cp-12L, 0xf.ee39a876fd6e928p-16L, 0xa.578ba89fe1d43b5p-16L, -0xf.e8ccd1e77d18dbbp-22L, -0xb.fd203720f6b2eddp-30L, 0x0p+0L};
+            }
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            if constexpr (order == 0) {
+                return {0x0p+0Q, 0x1.749078c0867a9a724454443e786p-9Q, 0x1.8ae6a79b4938fbd909b199343627p-3Q, 0x1.d008898983913d9bf1d194ac98ebp-1Q, -0x1.20e16d5539e3f25296b1c6880b7dp-4Q, -0x1.f688bd1280c70194203f74426669p-5Q, 0x1.2fca4301354a4e285e82fc4b6146p-5Q, -0x1.505c64431d7a6f1e36954a7c7627p-12Q, -0x1.0145189baf0142f2a8862b8be414p-6Q, 0x1.c908becee5a6a6fcccc95605353cp-7Q, -0x1.beac12be1e7de0939dd15f03161ap-8Q, 0x1.0006a916adee342c6b2792c6bd71p-9Q, -0x1.d4cc286b09e13557f3e87a0f9cap-13Q, -0x1.a08b65bbb598677114fddb7b659bp-15Q, 0x1.5f413ab3a7eb94dcb396b2657e81p-16Q, -0x1.5c34d16af592037a11107a487af4p-20Q, -0x1.2dc4454eebde3379c7645c4ba813p-21Q, 0x1.74f33a2ccbc6518fcdedc7d5a964p-24Q, 0x1.ddb5df0a412fd407d061c573b7b3p-29Q, -0x1.07969b3a158bd160a5cdad0ecd8ep-32Q, 0x1.2c5958b74836c10a9059d0bfc5aap-38Q, 0x1.52fae6e83091fa686190e11a0ab7p-45Q, -0x1.d83da475a639c307966abb294442p-53Q, 0x1.1342e56840ec19da921d2c329457p-65Q, 0x1.aa25edf8f64fee132e1b309309a8p-86Q, -0x0p+0Q};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0Q, 0x1.23923550f457ca7814b0bb3fd63cp-6Q, 0x1.0c0767795d12ae5d156ec5cf442dp-1Q, 0x1.3373be839b47c40b1d36ec3e479ap-2Q, -0x1.856d7e6b6468c2deff8342e75bafp+0Q, 0x1.22d30ac28dd9c9a5de5413538cdcp+0Q, -0x1.72e38df054a23a8a5ebabc499011p-1Q, 0x1.8e439b194a1c16626ebcbea59c97p-2Q, -0x1.3bc2524066e83eb2d5b3ff97e1f2p-3Q, 0x1.1bc8f6e41059663daa79bf4a8b49p-5Q, 0x1.2884461caa1e3207b6de1334aafbp-11Q, -0x1.db22a9804aa1133069d05b96cb79p-10Q, -0x1.3482dca87f01c45e946a258c3e3ep-11Q, 0x1.3285223dae55992a1d57ada1536cp-11Q, -0x1.bbf1c4306d1a37f02d18135ce361p-14Q, -0x1.17497a4dcd44ffdc92c6ebd1a07dp-16Q, 0x1.bebec0cbd1f99371a7867cbe4001p-18Q, -0x1.bc40d833ef3598561d72cdf89c2bp-22Q, 0x1.6454c6cebdf97f43adbbdee1eef5p-26Q, 0x1.5fce040bf0fa22a0bb7f52a52ec5p-29Q, -0x1.1241493325c926f92e656210ed45p-33Q, -0x1.ce70ab06ee7eb593175a3e65f70bp-41Q, 0x1.8616f674ef405eeabf053da9c793p-48Q, -0x1.7b38ad7c07a3a058098173d3a941p-60Q, -0x1.258ba4702de85ac45e001504a5c3p-79Q, -0x0p+0Q};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0Q, 0x1.7e9e99d93265e1ecb27f1a82e40ep-4Q, 0x1.e81e73bf7d4e6759d9f3db7612c7p-1Q, -0x1.368292c7be10e513188a104c5cc1p+1Q, 0x1.a1c192a939b9674ffcca9b2f1f92p+0Q, -0x1.58e6f9045a40dd2a472104dd130ep-2Q, 0x1.2f82100ba4f2879faa0ab73165e9p-2Q, -0x1.f8fd9be6cc910f763e95aa8ab1d7p-2Q, 0x1.017de77081fc30f9ad09eddaf4ddp-1Q, -0x1.5831ad14642112326c714ae42502p-2Q, 0x1.30d718554c4cabcfafc1434f8aebp-3Q, -0x1.30a6075105b3aa4d5336fc195157p-5Q, -0x1.632f9e9eb99fc711faf42ce1fdf8p-11Q, 0x1.1cbed37ba4dbd96c225d81054e98p-8Q, -0x1.77d86fa7164bfc8c126a64816b23p-10Q, 0x1.50ec238da00966f5e3d28fc92775p-14Q, 0x1.f99c3b6dd2e633388ada35d1c02cp-15Q, -0x1.8453f2cbc2d996b7775a123e93afp-17Q, -0x1.b4056601f4bff8b5e7d36857ce88p-23Q, 0x1.4c2776a5f116e1d85dd046bd9771p-24Q, -0x1.287daf168a219aa1132a37934623p-29Q, -0x1.b00a66e2af603b8210a104b461a3p-36Q, 0x1.401eb1fad689de068ef9a337dccp-42Q, -0x1.71528144e6954a34804ddc8b69bap-54Q, -0x1.1de10823e626bbef4adf3610d3cbp-72Q, -0x0p+0Q};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0Q, 0x1.95e033565cd465e59fc64a848c0ep-2Q, 0x1.e7908dd5753c97550b1b562a1b99p-3Q, -0x1.293799fcf6c8da1f93fe2d057409p+2Q, 0x1.36cc467b08bf7d8a89d5be8f8643p+3Q, -0x1.4335983e135774c5e5156a450a68p+3Q, 0x1.9c4d14b5414867b3e2c99a218f0bp+2Q, -0x1.ef81d85b23a01ac83af86d64ce2ep+0Q, -0x1.2378e73c6b10a2f7957b04476802p+0Q, 0x1.c6e27151761e3e586f540356142cp+0Q, -0x1.c857e67243153a965a648f8e46c8p-1Q, 0x1.3531afa42b77f4c754018d3dfbb2p-8Q, 0x1.05f57c1a6464d742d9d2e202c63cp-2Q, -0x1.38a2db882124dfc4e44179ad4f8p-3Q, 0x1.35c4a5041d9b9456d2520e65a344p-5Q, -0x1.fddc3c9f813d6aef1f4f22d0d6c7p-14Q, -0x1.2653a0321997d1fa4ad992782112p-9Q, 0x1.ec5d6f7ab50c177dc61e0a187538p-12Q, -0x1.dc01f8633f4c61396f200866219ep-17Q, -0x1.379717b64ca37d0f86a74f66252ap-18Q, 0x1.7e5cfdc9a1b17dce328c7c0b396fp-23Q, 0x1.a124166c5786174e1b984a58659ap-29Q, -0x1.4171311c3a7b2623f4df8ab80088p-35Q, 0x1.65f402b77f1ab227d7a791607b4dp-46Q, 0x1.15123cc4efb60d3af1736012c799p-63Q, -0x0p+0Q};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0Q, 0x1.4c5d516dd5340d0879832abec56ap+0Q, -0x1.5d2571cda5543923016a3601781dp+2Q, 0x1.24b0f03522629e31e5a0ddf8fe8fp+3Q, -0x1.39e0f8d13e8db1f029ce6257e806p+3Q, 0x1.f006cc927be5328f1a33d6ae0a72p+3Q, -0x1.0ce2ffa4646117df99ed92ff7f71p+5Q, 0x1.b8b8afcf323d00e8ad39d1cbe81p+5Q, -0x1.e6925570e3f510211d732b909262p+5Q, 0x1.503102590c0b7b7ae2742f430edfp+5Q, -0x1.6d86add093f074bc432a452a8a23p+3Q, -0x1.35b5dc1025f2d34a60aa7bf986d8p+3Q, 0x1.a6237c764b4a28340b848880c532p+3Q, -0x1.cda455c3ae3929d25c3c5a3186e9p+2Q, 0x1.d5a02bb93708a320124acceeba3bp+0Q, 0x1.ecd4c4adc075fe2457753c0a3227p-5Q, -0x1.660ee59df078b432fb4f889aa837p-3Q, 0x1.5158e51b27e5dbfe89f577f955e5p-5Q, -0x1.73814bfd57b681fa89fa6df49afcp-10Q, -0x1.23460c48f636fa706d007acab6f4p-11Q, 0x1.fa353cdebaaaaa09ad0c40e91089p-16Q, 0x1.19c5738584246e6431d3352c0155p-21Q, -0x1.4bb4308ed51fff3108f30cb6a721p-27Q, 0x1.fc9a1f4f09858f536f1a575ceb92p-38Q, 0x1.89a8b7b9d28d1d71597812a9e85fp-54Q, 0x0p+0Q};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0Q, 0x1.a35157d8dba56b3359c55e1b2f1bp+1Q, -0x1.5a1bc35a1cc0dbb69c71ae20ac28p+4Q, 0x1.fa0a0878d9a933860f512013ce09p+5Q, -0x1.a68f6523a82701663e04e44e02c9p+6Q, 0x1.98403a971e63162a02dd9331873fp+6Q, -0x1.03810e60e02049d57e6cca7b3393p+5Q, -0x1.14faaec76846550eede585da319ep+6Q, 0x1.3d735b94c105436aa6c6acd1ae46p+7Q, -0x1.cdbd7de801407d716cbc3884161p+7Q, 0x1.20043470ad456af43bde8d96fdaap+8Q, -0x1.2591e882d85cd18b0dca9797ee6p+8Q, 0x1.b621996a63c17e6687cb0b211602p+7Q, -0x1.a875ba068d8449d487f82dc4bc08p+6Q, 0x1.85c7d166f26b7783d793e4e78c82p+4Q, 0x1.1c0e0d6b929f95b9e528989abb17p+2Q, -0x1.36efc345fd87e7f12a7cd8f187eap+2Q, 0x1.3e3f5c2c93c347939cad28f604bbp+0Q, -0x1.bffc3922a312894449dea0a83571p-5Q, -0x1.75f52c4bce3944c6d40bd8ed1f5ap-6Q, 0x1.dea5b49d2b299f2f3407a986e912p-10Q, 0x1.10aa3eff5f8aac0902d8bf656d56p-15Q, -0x1.ea6ed6c321e753c1b3e9237c4183p-21Q, 0x1.089ab261bfe1c8b7f19aebf544d2p-30Q, 0x1.9990a3735f2b8137827c0403494ap-46Q, 0x0p+0Q};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0Q, 0x1.5d159c98a090a206b1f5a4e9463bp+2Q, -0x1.54873e7e1b3d210625d27844421bp+5Q, 0x1.2c245e185ac8b14c7baac4549349p+7Q, -0x1.416f5cc6c22c1fc04eedaa366dc1p+8Q, 0x1.e67e2b7f933044475571e6b73738p+8Q, -0x1.298ee57db6ed5fd4bacad132e624p+9Q, 0x1.48ee3d90a4e34a8f4d18f9ebf69p+9Q, -0x1.4e6b4521eb7a56c1ef7579e251acp+9Q, 0x1.2782e95d7bf9f5fc360d3847dd8p+9Q, -0x1.bb493883e544d446bc2b8c57d25fp+8Q, 0x1.25dfd4b9fa45afe8f2d50b1eccc2p+8Q, -0x1.575e0c206b7ee6818931b6994d6ep+7Q, 0x1.1c028f2725fce675841ea64b2ffp+6Q, -0x1.08a1fe0ac6819f96e8258ae14398p+2Q, -0x1.12ed1d6ca77301d9871c8664703fp+4Q, 0x1.66791e904ad3b41e47b4403dcaadp+3Q, -0x1.7aa9733036515afd48134b63faf5p+1Q, 0x1.41600caa02955d88aadf0943297p-3Q, 0x1.275514f436a31e564b7d01e0e908p-4Q, -0x1.29373f56ac1095884f483fc367f8p-7Q, -0x1.51ea7d9f345040b9bbf6801a6296p-13Q, 0x1.deb156b08b87ef0592d66c2ead34p-18Q, -0x1.6e30fae8c34ed8366ddfb109de2fp-27Q, -0x1.1b57abb7d7f1ba81ca336dfebef5p-41Q, -0x0p+0Q};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0Q, 0x1.d4fe27a0835ae1a04e083919e159p+2Q, -0x1.ecb0f32ca76fb494d571b92b6ab8p+5Q, 0x1.c6da62a20cd0a85f327433229c8ap+7Q, -0x1.e3622dd5ba05d80a963a6735beb4p+8Q, 0x1.49508717a90e836846bfeeb5b43bp+9Q, -0x1.3d934aacf56d0a27027f0d4c671dp+9Q, 0x1.068600d74e1c90df9e5944f06e21p+9Q, -0x1.bb4eb52dbc23c8aa9dac22db8fdep+8Q, 0x1.2c2d3c048caae8b4e7ebda4b0128p+8Q, -0x1.6a6f07f5d07dd28cc713b1beaa3ap+5Q, -0x1.48c0f7b3bed9dd4e2bcfa51c5127p+7Q, 0x1.bce28601020e5546efe486219835p+7Q, -0x1.9e035ea535c3aebdf12725979bb8p+7Q, 0x1.737017c34f7deef2722c93e161f4p+7Q, -0x1.15bd065f2789c251ed52811c0835p+7Q, 0x1.1609d2e86de1f46bc02dc1f1561dp+6Q, -0x1.30b382548235fc08ce2a69131576p+4Q, 0x1.34c266d274d020226722008d15aap+0Q, 0x1.56d14dbd1c0ef8dc071f15458559p-1Q, -0x1.f82518456ddfa0a1ea7fa3e5d12cp-4Q, -0x1.1d5d333a03734067f69cd7ef01cbp-9Q, 0x1.599f88826e1df7529e2526edcc77p-13Q, -0x1.742b04eba227022dc278410d55cbp-22Q, -0x1.1fd835e2f3ac373e68a16573044bp-35Q, 0x0p+0Q};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0Q, 0x1.6f91b1fb16e463903f242c426455p+2Q, -0x1.8fef11e8059ceda062dec743d5bap+5Q, 0x1.809c444472a8d8415a2c8fcb90adp+7Q, -0x1.b10bf090c92b5336357d1404e2eap+8Q, 0x1.45258188f71468e863f93e44329ep+9Q, -0x1.7231afc08bd276307932c937c208p+9Q, 0x1.7af82162ac359965f69e88fff2d1p+9Q, -0x1.823e9f8992b59fc66e18911aea8bp+9Q, 0x1.6f4bc124eb7dc2e04c11ba39d8bp+9Q, -0x1.32f291524b4fc819caccda30ea8fp+9Q, 0x1.d856007cb8fa074ef08390247a6ep+8Q, -0x1.59b2f057a74e4aae3ebb655c3f1ep+8Q, 0x1.c4898ffe6b603cfd7a5fca3706d6p+7Q, -0x1.01b04bb5c7e4ece20624aa0d5e2cp+7Q, 0x1.0ee550f2b46fb0067dbfd6b593fep+6Q, -0x1.f149829700499105abd0a04d1745p+4Q, 0x1.21413698e7cf1b5b76cf6ac9da58p+3Q, -0x1.1e358290df39caefe5b55d7f88a9p-2Q, -0x1.54f12799790c9591a3724eefd6adp-1Q, 0x1.1dedd290f907f8d2a85301c5e1c1p-3Q, 0x1.2b8db385d6eeb017f6475d54698ap-10Q, -0x1.7cd67d6099898e46f355585388cap-12Q, 0x1.c1758243d6f68f111636a9a1e06bp-21Q, 0x1.5b5402fbe8db7e6e4a333c1f1c5ap-33Q, -0x0p+0Q};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0Q, 0x1.e00f201ca9b47bec13b3982152f1p+1Q, -0x1.09aad588fc6e1d2e5e31f5db6676p+5Q, 0x1.0083b1ed3add1dfc189aa41f7f2fp+7Q, -0x1.1b01639f15a47195db84399877bbp+8Q, 0x1.8e74c5b415b4c982c62a08a4c59cp+8Q, -0x1.907a858da198db5b4a86cd66130bp+8Q, 0x1.68e4a68143eb6280f782117761a4p+8Q, -0x1.685dfe59eb94f38e35f467a408e4p+8Q, 0x1.592f39b72049a36e7924da594eccp+8Q, -0x1.09589acf597f567d3772da9f9396p+8Q, 0x1.658b66c44d2d9f09118ad4461b1dp+7Q, -0x1.f90c71880a91658c0d9a077062e9p+6Q, 0x1.49a9a7009f2b267b39ba9598b5bfp+6Q, -0x1.441338caa52cfa0e2a27b3094033p+5Q, 0x1.0b7b2a297fde14bc6faf1e5cad3dp+4Q, -0x1.d98372b1c68d3f52be822d4ad9e1p+2Q, 0x1.f43ec1f2a32806088746b95241b7p+0Q, 0x1.6165b77555fca80d9c5c139ebf01p-1Q, -0x1.4f8a8171bb08fcb9ccd7e57b6a94p-1Q, 0x1.267683e93d2b771765dfb989358ep-3Q, -0x1.8ddc624d415c8d8d9889336c7b73p-9Q, -0x1.979cae945ae1031f8b5a50d00a19p-11Q, 0x1.95627b187fdb196e7b60f5dc529bp-20Q, 0x1.38bcd286c35de60d5fb4cabb4426p-31Q, -0x0p+0Q};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0Q, 0x1.ddc9914b8fce26e89a350da83719p+0Q, -0x1.0aa6a6fe4749ff9a5341c601bbd1p+4Q, 0x1.ffd30a30f104e3ad2ade791fa75cp+5Q, -0x1.1076bbdb4cf7527cd039e9d87117p+7Q, 0x1.5b314fd5bd8427278ea135aa2326p+7Q, -0x1.15e629a2f07ab3b285fb777249b6p+7Q, 0x1.73ecdaa7dbcd11927e44fc6ec254p+6Q, -0x1.7ea4991281a803e96d95b15ddcdfp+6Q, 0x1.92fe5087093b614dba0fb9dcd31ep+6Q, -0x1.e50ce86c3eca30ad8c366d925665p+5Q, 0x1.23fe36ce5250d05c30083be13efbp+4Q, -0x1.1183a5ac74636a4f4f82e9e90688p+3Q, 0x1.325da71616787b1a97d0cf145facp+2Q, 0x1.b5b93d37eb78f2e235ca0e3287edp+2Q, -0x1.6174cc292a977e8769fbfe3294c1p+3Q, 0x1.b8e78e1a9ada492b4dd621bd0ceap+2Q, -0x1.ffc6e54f09b8a6376ab8ee388e04p+1Q, 0x1.807b43d233e13293cd8f064bc042p+1Q, -0x1.949effe4fd5f10b6f0bb08f4fc9cp+0Q, 0x1.99c706ee33d33292c4de096ca957p-2Q, -0x1.8b4255eb2ab52df5046967e93801p-6Q, -0x1.25fbde4ae0e29153ac7874faf054p-8Q, 0x1.a2ffd5a58a3e625ad5ba39971f6dp-17Q, 0x1.4225e5d67d6a903058f2d7206afep-27Q, 0x0p+0Q};
+            }
+            if constexpr (order == 11) {
+                return {0x0p+0Q, 0x1.82555f0fca681c9ced300e65470bp-2Q, -0x1.b108ac4bd9d5de90a612fd8cb482p+1Q, 0x1.a3af9f5e28533d44a21884894a43p+3Q, -0x1.c92e2a69bebea1255ad98c5c24f3p+4Q, 0x1.336156f19a3eab19184562b4b1e2p+5Q, -0x1.154d20c532d37d99d550b7ecda23p+5Q, 0x1.af95c6a7f034f7267500295c26p+4Q, -0x1.a382ed435f8ed2216764cfb7b5d9p+4Q, 0x1.a5a57db59b67be50825ea97be6b6p+4Q, -0x1.48587bdb4781058d98368c067205p+4Q, 0x1.c6519b1cdb292e6d292e55285478p+3Q, -0x1.64406dc5dece20ec3c4c5d654de5p+3Q, 0x1.05a0da2a87dafe77cb9a5835aad4p+3Q, -0x1.34062a3bf7c109c05654c02a04d6p+2Q, 0x1.65a3327bcf1ac1cee14ec461e42cp+1Q, -0x1.b27cf7ab49be37cde0f46d146d6bp+0Q, 0x1.a5bdc7192b9c3a20ece90c79e905p-1Q, -0x1.571ac2983f85e3a6dc62f787682cp-2Q, 0x1.31767817c6adec541d699bff90f4p-3Q, -0x1.904f3491bf69c7251d1b4755c9b7p-5Q, 0x1.0ee4f3163f55f45905e2e22beb7fp-8Q, 0x1.2584f1f36b43e7bbd83747f8e61dp-10Q, -0x1.373cf584c03ee906a072d01e3b91p-17Q, -0x1.db60a068c3377c744925f1488cc3p-27Q, 0x0p+0Q};
+            }
+            if constexpr (order == 12) {
+                return {0x0p+0Q, 0x1.8dbb03fad2c2ff4e565f6c62d57bp-5Q, -0x1.bebdc5d3b23911ed14512acd7b2bp-2Q, 0x1.aeb7a5ea21052a1c43ba3ca04a5p+0Q, -0x1.cb9851522d20abcc6f87f81034c7p+1Q, 0x1.240bf59871b997fc41c938fde14cp+2Q, -0x1.cab7cf1ed537e0d17c3940a7425ap+1Q, 0x1.1fd4543a5fd8cb1e3fd20d0065e1p+1Q, -0x1.1ce9744c1c9756de9b809fd2555fp+1Q, 0x1.3bab08bd76344b447fe47700254dp+1Q, -0x1.c40e7b4e77556f5ef84483097e1fp+0Q, 0x1.feadc8c7ce87a8fc67e279160504p-1Q, -0x1.a643a47d84b4da70d0fb106ef69bp-1Q, 0x1.543b964e0f03a3a71ec48db92838p-1Q, -0x1.577aa576ffa64efb7d0e9e6dcc9cp-2Q, 0x1.499f6f7a97a22bd1178c8661fe5ap-3Q, -0x1.d5a15151b901635be5a32ca30fbbp-4Q, 0x1.d4c5badb46707713b03f6aa302e5p-5Q, -0x1.094f5215690db085443c45e218e9p-6Q, 0x1.cd0926fb9e142792dd84079eb378p-8Q, -0x1.b2091c2c73dd02f84cb37e5165a8p-9Q, 0x1.fdc7350edfadd24f5fb7a95b49b7p-13Q, 0x1.4af17513fc3a876960b7d297e5d9p-13Q, -0x1.fd199a3cefa31b76bcac2a313bc8p-19Q, -0x1.7fa406e41ed65db974ed33f4fc9ap-27Q, 0x0p+0Q};
+            }
+        }
+        #endif
+    }
+    if constexpr (p == 14) {
+        if constexpr (std::is_same_v<Real, float>) {
+            if constexpr (order == 0) {
+                return {0x0p+0f, 0x1.2e3c0cp-10f, 0x1.d73cdcp-4f, 0x1.980f08p-1f, 0x1.0b8da8p-2f, -0x1.381b88p-2f, 0x1.a64054p-3f, -0x1.be6cb2p-4f, 0x1.5369f4p-5f, -0x1.e553cp-8f, -0x1.5b9738p-9f, 0x1.3ad93ep-9f, -0x1.6c8658p-11f, 0x1.421438p-16f, 0x1.359cb6p-15f, -0x1.16b1cep-18f, -0x1.1e4702p-19f, 0x1.16b7d8p-21f, -0x1.2a9018p-27f, -0x1.e6603ap-29f, 0x1.ad635ap-33f, -0x1.0b7166p-37f, -0x1.2dcc8ep-43f, 0x1.994c74p-50f, 0x1.d3e7dcp-60f, -0x1.ad34cp-72f, 0x1.c6fd0cp-94f, -0x0p+0f};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0f, 0x1.ffe6a8p-8f, 0x1.687896p-2f, 0x1.4f6222p-1f, -0x1.9d7a5p+0f, 0x1.ee1a72p-1f, -0x1.3a4c3ep-1f, 0x1.a5124ep-2f, -0x1.fd4714p-3f, 0x1.efeb84p-4f, -0x1.695e5ep-5f, 0x1.73caep-7f, -0x1.fa774ap-10f, 0x1.13b07ep-13f, 0x1.7cb11cp-14f, -0x1.d2ccp-15f, 0x1.74388cp-17f, 0x1.21ff8ap-21f, -0x1.156308p-22f, -0x1.19b91cp-25f, 0x1.f7d83ep-31f, 0x1.509062p-34f, -0x1.405684p-40f, 0x1.6ac07ap-46f, -0x1.9a49fp-55f, -0x1.88bc66p-67f, 0x1.a0541ep-88f, 0x0p+0f};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0f, 0x1.70e38ep-5f, 0x1.98429p-1f, -0x1.5a23aep+0f, -0x1.ca3a86p-2f, 0x1.f2912p+0f, -0x1.902df6p+0f, 0x1.6e5d8ap-1f, -0x1.7cd74ap-5f, -0x1.cb5138p-3f, 0x1.8970fep-3f, -0x1.2e3ba4p-4f, 0x1.a43728p-9f, 0x1.5d8afap-7f, -0x1.3f213ap-8f, 0x1.438df6p-11f, 0x1.92aaccp-13f, -0x1.4a2a2cp-14f, 0x1.061494p-17f, 0x1.1c615p-21f, -0x1.fed404p-24f, 0x1.9900fap-29f, 0x1.4b71c6p-33f, -0x1.f4e21p-40f, -0x1.ae7642p-50f, 0x1.0753e4p-59f, -0x1.1725d8p-79f, 0x0p+0f};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0f, 0x1.b64064p-3f, 0x1.b94954p-1f, -0x1.49bc84p+2f, 0x1.255158p+3f, -0x1.254592p+3f, 0x1.bfdd02p+2f, -0x1.258cbp+2f, 0x1.244b68p+1f, -0x1.76e9c8p-1f, 0x1.2db90ep-3f, -0x1.adc00ap-4f, 0x1.077b02p-3f, -0x1.4e1bd4p-4f, 0x1.a8b172p-6f, -0x1.1b67a8p-9f, -0x1.5aa222p-10f, 0x1.0c296ep-11f, -0x1.315112p-14f, -0x1.aa34a6p-23f, 0x1.718ac2p-20f, -0x1.4ed202p-25f, -0x1.6a2c3ep-29f, 0x1.03cb1cp-35f, 0x1.d2ce74p-46f, -0x1.110d8p-54f, 0x1.2175bep-73f, -0x0p+0f};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0f, 0x1.9bd3bcp-1f, -0x1.218b2p+1f, -0x1.8f073ep-2f, 0x1.10368cp+3f, -0x1.6e5fdp+3f, -0x1.fee6b2p-2f, 0x1.5dae0cp+4f, -0x1.253938p+5f, 0x1.0846cap+5f, -0x1.d3379cp+3f, -0x1.bc1cbep+1f, 0x1.49e86ep+3f, -0x1.e4adep+2f, 0x1.651f3ap+1f, -0x1.14e32ep-2f, -0x1.c20b1ep-3f, 0x1.9dc736p-4f, -0x1.dbb9ecp-7f, -0x1.c7f5c2p-11f, 0x1.a5fc86p-12f, -0x1.07f65ep-16f, -0x1.0e379p-20f, 0x1.69bc58p-26f, 0x1.872aa2p-36f, -0x1.7b8496p-44f, 0x1.92548cp-62f, -0x0p+0f};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0f, 0x1.29b15ep+1f, -0x1.cfd366p+3f, 0x1.440caap+5f, -0x1.116deap+6f, 0x1.3b639cp+6f, -0x1.0040f6p+6f, 0x1.e6fde6p+4f, 0x1.5c1e9ep+3f, -0x1.b1e5dap+5f, 0x1.7d1f14p+6f, -0x1.d6f4cap+6f, 0x1.9fd808p+6f, -0x1.ecec6ep+5f, 0x1.43fff8p+4f, 0x1.5e941cp-2f, -0x1.d2a078p+1f, 0x1.940e8ap+0f, -0x1.f62a76p-3f, -0x1.2b3b3cp-6f, 0x1.3de2bap-7f, -0x1.21cbeep-11f, -0x1.2150f6p-15f, 0x1.159bf8p-20f, 0x1.b00f5p-30f, -0x1.21e8e2p-37f, 0x1.33590ap-54f, 0x0p+0f};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0f, 0x1.3069cap+2f, -0x1.2e376ap+5f, 0x1.1366dap+7f, -0x1.37b986p+8f, 0x1.ff3f2ep+8f, -0x1.57d938p+9f, 0x1.9e8b98p+9f, -0x1.c5567ap+9f, 0x1.af9eb4p+9f, -0x1.5e3048p+9f, 0x1.efd932p+8f, -0x1.337ecp+8f, 0x1.1dd7ep+7f, -0x1.34f8d6p+4f, -0x1.1b6424p+5f, 0x1.038eccp+5f, -0x1.9f2074p+3f, 0x1.0d3b24p+1f, 0x1.b93ffcp-3f, -0x1.00284ep-3f, 0x1.52026p-7f, 0x1.4b932p-11f, -0x1.d3b086p-16f, -0x1.e9753p-25f, 0x1.e5cedp-32f, -0x1.0188e4p-47f, -0x0p+0f};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0f, 0x1.f579b2p+2f, -0x1.13b9ccp+6f, 0x1.0d0d04p+8f, -0x1.309a86p+9f, 0x1.b8e262p+9f, -0x1.b08b28p+9f, 0x1.3c7d2cp+9f, -0x1.7e7dfp+8f, 0x1.9c8804p+5f, 0x1.dc1752p+8f, -0x1.e54a04p+9f, 0x1.1a42e2p+10f, -0x1.f903f4p+9f, 0x1.9d8dbap+9f, -0x1.34174p+9f, 0x1.64eb3cp+8f, -0x1.0b0c44p+7f, 0x1.5f0a54p+4f, 0x1.d8f6bap+1f, -0x1.1c758ap+1f, 0x1.f38ac2p-3f, 0x1.f827p-7f, -0x1.130614p-10f, -0x1.2dc514p-19f, 0x1.1d494ap-25f, -0x1.2e8464p-40f, 0x0p+0f};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0f, 0x1.e32cc2p+2f, -0x1.1692cap+6f, 0x1.1fa09cp+8f, -0x1.615e68p+9f, 0x1.265c8cp+10f, -0x1.7569eep+10f, 0x1.9e96bep+10f, -0x1.bbbe16p+10f, 0x1.be0802p+10f, -0x1.8f099cp+10f, 0x1.43b838p+10f, -0x1.ee6ad6p+9f, 0x1.58d562p+9f, -0x1.a3b282p+8f, 0x1.c79d62p+7f, -0x1.bc78ccp+6f, 0x1.418e36p+5f, -0x1.3abf36p+2f, -0x1.ad7bb4p+1f, 0x1.a65502p+0f, -0x1.affdcep-3f, -0x1.8341cep-7f, 0x1.b5571p-10f, 0x1.e32174p-19f, -0x1.c53c14p-24f, 0x1.e0c27p-38f, 0x0p+0f};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0f, 0x1.8d1f8ap+2f, -0x1.d4881ap+5f, 0x1.e86d42p+7f, -0x1.280028p+9f, 0x1.d3eb6p+9f, -0x1.0b82a6p+10f, 0x1.07ceap+10f, -0x1.0d7822p+10f, 0x1.0df61ep+10f, -0x1.c6893ap+9f, 0x1.45ac9ep+9f, -0x1.c9d686p+8f, 0x1.35c4c4p+8f, -0x1.4a58bep+7f, 0x1.01755ap+6f, -0x1.5d1ba8p+4f, 0x1.dadd4ap+1f, 0x1.87b02p+2f, -0x1.9ab15ep+2f, 0x1.46cd6ap+1f, -0x1.8955d8p-2f, -0x1.85245p-7f, 0x1.6f86d4p-8f, 0x1.1b4e3cp-16f, -0x1.7914d8p-21f, 0x1.903b4cp-34f, -0x0p+0f};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0f, 0x1.041a0ap+1f, -0x1.3658b6p+4f, 0x1.5194bp+6f, -0x1.c3df82p+7f, 0x1.ad183ep+8f, -0x1.3d9c78p+9f, 0x1.852da4p+9f, -0x1.9cca18p+9f, 0x1.9a6efap+9f, -0x1.a300c2p+9f, 0x1.a73548p+9f, -0x1.7a384cp+9f, 0x1.2afd88p+9f, -0x1.d0f63ap+8f, 0x1.6384c4p+8f, -0x1.d6c26ap+7f, 0x1.089826p+7f, -0x1.1f7e84p+6f, 0x1.2a5702p+5f, -0x1.c18aa4p+3f, 0x1.4dc138p+1f, 0x1.bd5ac2p-5f, -0x1.1aa942p-4f, -0x1.97678cp-14f, 0x1.25b3fcp-16f, -0x1.381ffp-28f, -0x0p+0f};
+            }
+            if constexpr (order == 11) {
+                return {0x0p+0f, 0x1.456a1ep+0f, -0x1.86731ep+3f, 0x1.99ddaep+5f, -0x1.ebccc2p+6f, 0x1.74f85ep+7f, -0x1.842622p+7f, 0x1.4fbcc2p+7f, -0x1.4776cp+7f, 0x1.573bfp+7f, -0x1.2b0c28p+7f, 0x1.bb5bcap+6f, -0x1.580802p+6f, 0x1.0c1df4p+6f, -0x1.5dea02p+5f, 0x1.997fcap+4f, -0x1.f5c414p+3f, 0x1.1578f4p+3f, -0x1.e11a4cp+1f, 0x1.8c2f5ap+0f, -0x1.42cddep-1f, 0x1.1b3752p-3f, 0x1.61bca4p-7f, -0x1.eeca78p-8f, 0x1.427b38p-14f, 0x1.1c6c3p-18f, -0x1.2f0566p-29f, 0x0p+0f};
+            }
+            if constexpr (order == 12) {
+                return {0x0p+0f, 0x1.45a484p-2f, -0x1.87cf9ep+1f, 0x1.99aecep+3f, -0x1.e335dep+4f, 0x1.5e3842p+5f, -0x1.48839ep+5f, 0x1.e11a8p+4f, -0x1.bff278p+4f, 0x1.f68b7p+4f, -0x1.a9c89cp+4f, 0x1.147ddap+4f, -0x1.a10eep+3f, 0x1.5d8bap+3f, -0x1.b0eecp+2f, 0x1.b18092p+1f, -0x1.11a2d4p+1f, 0x1.45b0dap+0f, -0x1.d74084p-2f, 0x1.27c112p-3f, -0x1.2ee6a8p-4f, 0x1.0ad11p-6f, 0x1.b719aep-8f, -0x1.7b5726p-9f, 0x1.efe0e8p-14f, 0x1.11683ap-18f, -0x1.24c158p-28f, -0x0p+0f};
+            }
+            if constexpr (order == 13) {
+                return {0x0p+0f, 0x1.439a96p-5f, -0x1.85e5f8p-2f, 0x1.959ab6p+0f, -0x1.d59128p+1f, 0x1.43a656p+2f, -0x1.0a2c06p+2f, 0x1.27395p+1f, -0x1.050c8cp+1f, 0x1.600ea8p+1f, -0x1.21f61ap+1f, 0x1.19f0e6p+0f, -0x1.8e2104p-1f, 0x1.a07f28p-1f, -0x1.ccce86p-2f, 0x1.e56138p-4f, -0x1.5df48cp-4f, 0x1.19d3fp-4f, -0x1.9e6cdp-9f, -0x1.b966bep-7f, 0x1.824078p-9f, -0x1.1b05a2p-9f, 0x1.7f8554p-9f, -0x1.23710ep-10f, 0x1.cc575ap-14f, 0x1.1f2382p-18f, -0x1.3697eap-27f, -0x0p+0f};
+            }
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0, 0x1.2e3c0bb3f3ad5p-10, 0x1.d73cdc4f17148p-4, 0x1.980f074dbd462p-1, 0x1.0b8da7807c274p-2, -0x1.381b88314120bp-2, 0x1.a64053bd4da41p-3, -0x1.be6cb26620f84p-4, 0x1.5369f32b472a9p-5, -0x1.e553bfb83c482p-8, -0x1.5b97376b07916p-9, 0x1.3ad93e070eb7ap-9, -0x1.6c8658d1b206ep-11, 0x1.421437e7b839dp-16, 0x1.359cb55b7d336p-15, -0x1.16b1cde08937ep-18, -0x1.1e470298289aep-19, 0x1.16b7d7c52ecb7p-21, -0x1.2a9017a9058edp-27, -0x1.e6603a12c622p-29, 0x1.ad635a5532adap-33, -0x1.0b7166f3d598p-37, -0x1.2dcc8d3c8b0cfp-43, 0x1.994c7452dcd31p-50, 0x1.d3e7db27a70eep-60, -0x1.ad34c0383fa64p-72, 0x1.c6fd0b1a8d6a3p-94, -0x0p+0};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0, 0x1.ffe6a833f41d2p-8, 0x1.6878956519ce3p-2, 0x1.4f62227264623p-1, -0x1.9d7a4f00f9dcp+0, 0x1.ee1a7236f71e4p-1, -0x1.3a4c3d150c11ep-1, 0x1.a5124e1ab47a9p-2, -0x1.fd47140509eb3p-3, 0x1.efeb8355fd2f8p-4, -0x1.695e5e5e49cf8p-5, 0x1.73cae05387f64p-7, -0x1.fa774911ba2d4p-10, 0x1.13b07ddddb3b8p-13, 0x1.7cb11c0b4280bp-14, -0x1.d2cbfff6e2a58p-15, 0x1.74388c9fd28e7p-17, 0x1.21ff895bfb5f3p-21, -0x1.156307b5c128cp-22, -0x1.19b91bff8bef5p-25, 0x1.f7d83e4d41c77p-31, 0x1.5090626b206a4p-34, -0x1.405683426ad01p-40, 0x1.6ac079eed130ep-46, -0x1.9a49f0637a3b6p-55, -0x1.88bc66cc087f2p-67, 0x1.a0541eb1bdcebp-88, 0x0p+0};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0, 0x1.70e38d13c6dcdp-5, 0x1.98429094e12d2p-1, -0x1.5a23aee5cfcf3p+0, -0x1.ca3a85e30ebf6p-2, 0x1.f2911f6caea6bp+0, -0x1.902df5acb9856p+0, 0x1.6e5d8a32fe3aep-1, -0x1.7cd7499a11b88p-5, -0x1.cb51389df1437p-3, 0x1.8970fdea96db5p-3, -0x1.2e3ba43116d4fp-4, 0x1.a437288ed51abp-9, 0x1.5d8afaeb5ec2ap-7, -0x1.3f213a25a4c3ap-8, 0x1.438df66495fedp-11, 0x1.92aacb344e1abp-13, -0x1.4a2a2b6937dcap-14, 0x1.061494c076ea5p-17, 0x1.1c61500cd5ff6p-21, -0x1.fed404b96c72ep-24, 0x1.9900fa8d5cb81p-29, 0x1.4b71c6cbb7be3p-33, -0x1.f4e20f23251aap-40, -0x1.ae764159a5bb6p-50, 0x1.0753e4c918ed7p-59, -0x1.1725d8c4676c4p-79, 0x0p+0};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0, 0x1.b6406454732d5p-3, 0x1.b949541f458cep-1, -0x1.49bc84198d8efp+2, 0x1.255157167a553p+3, -0x1.254591e8b6e07p+3, 0x1.bfdd01aa9e691p+2, -0x1.258cb0e12f408p+2, 0x1.244b687910818p+1, -0x1.76e9c86768fd8p-1, 0x1.2db90e1b7e224p-3, -0x1.adc00aab7f786p-4, 0x1.077b01cdc29aap-3, -0x1.4e1bd3d7c8107p-4, 0x1.a8b1719f7696ap-6, -0x1.1b67a8fdd5d39p-9, -0x1.5aa2219e8b072p-10, 0x1.0c296ebe05b6fp-11, -0x1.315112d6e2649p-14, -0x1.aa34a64782e4p-23, 0x1.718ac2125512ep-20, -0x1.4ed202350e6d4p-25, -0x1.6a2c3e7b115c9p-29, 0x1.03cb1bd946e2ep-35, 0x1.d2ce73e99c294p-46, -0x1.110d7f1b0bfcp-54, 0x1.2175be08d4af4p-73, -0x0p+0};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0, 0x1.9bd3bc2473961p-1, -0x1.218b20c923a73p+1, -0x1.8f073ee248543p-2, 0x1.10368c3ad14ecp+3, -0x1.6e5fd027a16b4p+3, -0x1.fee6b19288529p-2, 0x1.5dae0c64ec101p+4, -0x1.253938fa65f9dp+5, 0x1.0846ca351ee33p+5, -0x1.d3379cfd6d393p+3, -0x1.bc1cbd5de053bp+1, 0x1.49e86d68d4cf9p+3, -0x1.e4ade08c4a6c3p+2, 0x1.651f390634957p+1, -0x1.14e32e1f9b6bbp-2, -0x1.c20b1d287136bp-3, 0x1.9dc73570ee73fp-4, -0x1.dbb9ebdd9c09ep-7, -0x1.c7f5c1ec60f69p-11, 0x1.a5fc856e52fadp-12, -0x1.07f65daa0049bp-16, -0x1.0e378f07aff0ap-20, 0x1.69bc58d5ec0cdp-26, 0x1.872aa1bcf3687p-36, -0x1.7b84969608017p-44, 0x1.92548cc9b5b72p-62, -0x0p+0};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0, 0x1.29b15e8e05f49p+1, -0x1.cfd365d614528p+3, 0x1.440caad9c1236p+5, -0x1.116de9d813b39p+6, 0x1.3b639c503b3cfp+6, -0x1.0040f57e975e2p+6, 0x1.e6fde6a95ce33p+4, 0x1.5c1e9e155aab8p+3, -0x1.b1e5da7957b3dp+5, 0x1.7d1f138d16b9dp+6, -0x1.d6f4cad7bdd83p+6, 0x1.9fd808c31039p+6, -0x1.ecec6e1a57ab4p+5, 0x1.43fff7220eba4p+4, 0x1.5e941cd01c025p-2, -0x1.d2a0789936f64p+1, 0x1.940e89f9fbe3cp+0, -0x1.f62a7689777abp-3, -0x1.2b3b3b35a2041p-6, 0x1.3de2ba1c1b055p-7, -0x1.21cbeea2dd955p-11, -0x1.2150f65158194p-15, 0x1.159bf889454c7p-20, 0x1.b00f4f96ce851p-30, -0x1.21e8e13c855cp-37, 0x1.3359091107974p-54, 0x0p+0};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0, 0x1.3069c9b572d78p+2, -0x1.2e376983f6cb7p+5, 0x1.1366d92966ea1p+7, -0x1.37b9852173f07p+8, 0x1.ff3f2db6a15a4p+8, -0x1.57d9383606e5p+9, 0x1.9e8b97533b1ebp+9, -0x1.c556790a27e1dp+9, 0x1.af9eb47abc08ep+9, -0x1.5e3047bf51b55p+9, 0x1.efd9329bb40ffp+8, -0x1.337ec090261a6p+8, 0x1.1dd7e09a26691p+7, -0x1.34f8d53391e96p+4, -0x1.1b6423ffa4135p+5, 0x1.038ecbdebefe4p+5, -0x1.9f2073b507554p+3, 0x1.0d3b2378aacf2p+1, 0x1.b93ffbdcbcfbdp-3, -0x1.00284db90f95bp-3, 0x1.5202609236b6cp-7, 0x1.4b9320a57f232p-11, -0x1.d3b085775602bp-16, -0x1.e975304f42064p-25, 0x1.e5cecfa6ab7bbp-32, -0x1.0188e4a2f5a9ep-47, -0x0p+0};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0, 0x1.f579b17074e37p+2, -0x1.13b9cbe766167p+6, 0x1.0d0d0432bec13p+8, -0x1.309a86e68bfeap+9, 0x1.b8e26231ea03fp+9, -0x1.b08b284517ec4p+9, 0x1.3c7d2b2624502p+9, -0x1.7e7def0dd6c18p+8, 0x1.9c880448390e6p+5, 0x1.dc1752cc2f2f8p+8, -0x1.e54a03fbbc2fap+9, 0x1.1a42e1dae569p+10, -0x1.f903f4a18c30ep+9, 0x1.9d8db91908386p+9, -0x1.34173ffb143e2p+9, 0x1.64eb3c27db565p+8, -0x1.0b0c43171fee6p+7, 0x1.5f0a5375d11c7p+4, 0x1.d8f6b9f1522f3p+1, -0x1.1c75896d6d599p+1, 0x1.f38ac1a749dafp-3, 0x1.f82700b4dc727p-7, -0x1.1306135d4672fp-10, -0x1.2dc514d699914p-19, 0x1.1d494ae1d331fp-25, -0x1.2e8464bcec8d4p-40, 0x0p+0};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0, 0x1.e32cc25ea4da5p+2, -0x1.1692ca6458eaap+6, 0x1.1fa09c1316dfbp+8, -0x1.615e67f0c1ccdp+9, 0x1.265c8c1b4b1aap+10, -0x1.7569ed1c8210dp+10, 0x1.9e96bde5063d4p+10, -0x1.bbbe167a38d63p+10, 0x1.be080201e737dp+10, -0x1.8f099bdabb219p+10, 0x1.43b83815e15a6p+10, -0x1.ee6ad68b3bda5p+9, 0x1.58d561cb84d26p+9, -0x1.a3b282a8407a3p+8, 0x1.c79d620ffafcp+7, -0x1.bc78cb9447aa1p+6, 0x1.418e35902e32dp+5, -0x1.3abf360acc2f7p+2, -0x1.ad7bb3867b3c3p+1, 0x1.a655024ebf2fdp+0, -0x1.affdcd4718ba8p-3, -0x1.8341cd6c6b0aap-7, 0x1.b55710d3ebf55p-10, 0x1.e321738ab1448p-19, -0x1.c53c1373c8858p-24, 0x1.e0c270acb15c6p-38, 0x0p+0};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0, 0x1.8d1f8a3279763p+2, -0x1.d4881995a0c1fp+5, 0x1.e86d414a78e34p+7, -0x1.280027c9b0876p+9, 0x1.d3eb5f0b0594cp+9, -0x1.0b82a55c2799fp+10, 0x1.07ce9f70ddb28p+10, -0x1.0d7822536789ep+10, 0x1.0df61d2a506b2p+10, -0x1.c6893ac6cda6bp+9, 0x1.45ac9e8089788p+9, -0x1.c9d686e237044p+8, 0x1.35c4c3819b31p+8, -0x1.4a58be360f4f4p+7, 0x1.017559c35f761p+6, -0x1.5d1ba7f134742p+4, 0x1.dadd49a935c84p+1, 0x1.87b01fd4326a3p+2, -0x1.9ab15d247f91p+2, 0x1.46cd6a0d33a49p+1, -0x1.8955d7defe0d5p-2, -0x1.85244f4e65bbcp-7, 0x1.6f86d3c431061p-8, 0x1.1b4e3c12a74ep-16, -0x1.7914d82d3193fp-21, 0x1.903b4b44dd8c8p-34, -0x0p+0};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0, 0x1.041a0a897aa29p+1, -0x1.3658b5d77609ep+4, 0x1.5194af04e2f85p+6, -0x1.c3df81f0aaf29p+7, 0x1.ad183e8db3dacp+8, -0x1.3d9c782d70077p+9, 0x1.852da35362a6dp+9, -0x1.9cca18f6947ddp+9, 0x1.9a6efa498935ep+9, -0x1.a300c2ebdd39dp+9, 0x1.a735477cbff1cp+9, -0x1.7a384b1c312fcp+9, 0x1.2afd886ee72d7p+9, -0x1.d0f63946d275bp+8, 0x1.6384c4a13f54ep+8, -0x1.d6c269ce8bf35p+7, 0x1.08982647618p+7, -0x1.1f7e83a071123p+6, 0x1.2a5701b5bea0ep+5, -0x1.c18aa4ec1159bp+3, 0x1.4dc13861658a9p+1, 0x1.bd5ac19033245p-5, -0x1.1aa94170fffadp-4, -0x1.97678bd8dc9fap-14, 0x1.25b3fc23ddcf6p-16, -0x1.381fef501218fp-28, -0x0p+0};
+            }
+            if constexpr (order == 11) {
+                return {0x0p+0, 0x1.456a1d2a45d0dp+0, -0x1.86731e38f2c9fp+3, 0x1.99ddae9b5957ep+5, -0x1.ebccc1d5d759ap+6, 0x1.74f85dd906949p+7, -0x1.8426225b26444p+7, 0x1.4fbcc1bdf3f19p+7, -0x1.4776c0e99319fp+7, 0x1.573bef3fda7ebp+7, -0x1.2b0c271bd883ep+7, 0x1.bb5bca80b625p+6, -0x1.5808025c93fa5p+6, 0x1.0c1df40cf5e4cp+6, -0x1.5dea01151a3e2p+5, 0x1.997fc95198574p+4, -0x1.f5c4140f2a03ep+3, 0x1.1578f4041624bp+3, -0x1.e11a4c4784826p+1, 0x1.8c2f5a8cae554p+0, -0x1.42cdddde9b71fp-1, 0x1.1b37523680cdap-3, 0x1.61bca3fd3effbp-7, -0x1.eeca78cc1dd9bp-8, 0x1.427b3775515b6p-14, 0x1.1c6c30fb5472dp-18, -0x1.2f056506ce5e6p-29, 0x0p+0};
+            }
+            if constexpr (order == 12) {
+                return {0x0p+0, 0x1.45a484f799a72p-2, -0x1.87cf9eab4f4p+1, 0x1.99aecd437634bp+3, -0x1.e335dd2c6e9dep+4, 0x1.5e3841e21950ap+5, -0x1.48839e048b83dp+5, 0x1.e11a7f30735e3p+4, -0x1.bff27724d4104p+4, 0x1.f68b6fe2ccc31p+4, -0x1.a9c89c30bca22p+4, 0x1.147ddad811d2bp+4, -0x1.a10ee0eb1ccb6p+3, 0x1.5d8b9ffe3cdb9p+3, -0x1.b0eebf69279fp+2, 0x1.b180929e1a69bp+1, -0x1.11a2d370771cap+1, 0x1.45b0d998cab37p+0, -0x1.d74083eaced41p-2, 0x1.27c1113b5bdb8p-3, -0x1.2ee6a8512694ep-4, 0x1.0ad11030da229p-6, 0x1.b719ad4ae716p-8, -0x1.7b5726cd7507bp-9, 0x1.efe0e7fbce7f4p-14, 0x1.116839f7247aep-18, -0x1.24c158fd367dfp-28, -0x0p+0};
+            }
+            if constexpr (order == 13) {
+                return {0x0p+0, 0x1.439a95b32a47fp-5, -0x1.85e5f8ce20b7p-2, 0x1.959ab595a2ea4p+0, -0x1.d591277dff53ep+1, 0x1.43a6564933b3fp+2, -0x1.0a2c05cc597abp+2, 0x1.273950f6ffd18p+1, -0x1.050c8b9cb84b8p+1, 0x1.600ea820111dp+1, -0x1.21f61a844a105p+1, 0x1.19f0e6ef31a0dp+0, -0x1.8e2103144a726p-1, 0x1.a07f2894f970fp-1, -0x1.ccce8527cee5cp-2, 0x1.e56137866a825p-4, -0x1.5df48c0c87cd7p-4, 0x1.19d3f039c46cep-4, -0x1.9e6cd0f61f4cbp-9, -0x1.b966bdf45728ap-7, 0x1.8240771a20728p-9, -0x1.1b05a2f57f924p-9, 0x1.7f8554959f4a5p-9, -0x1.23710df832eb2p-10, 0x1.cc575afdf3f3dp-14, 0x1.1f238196ae22ep-18, -0x1.3697e9bf4306ap-27, -0x0p+0};
+            }
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0L, 0x9.71e05d9f9d6a6a5p-13L, 0xe.b9e6e278b8a3ea8p-7L, 0xc.c0783a6dea3101cp-4L, 0x8.5c6d3c03e139c58p-5L, -0x9.c0dc418a090583bp-5L, 0xd.32029dea6d20a27p-6L, -0xd.f365933107c2191p-7L, 0xa.9b4f995a39545fcp-8L, -0xf.2a9dfdc1e240f71p-11L, -0xa.dcb9bb583c8b013p-12L, 0x9.d6c9f03875bcf99p-12L, -0xb.6432c68d9036eap-14L, 0xa.10a1bf3dc1ce972p-19L, 0x9.ace5aadbe99adaep-18L, -0x8.b58e6f0449bf329p-21L, -0x8.f23814c144d7229p-22L, 0x8.b5bebe29765b5fbp-24L, -0x9.5480bd482c76432p-30L, -0xf.3301d09631101f2p-32L, 0xd.6b1ad2a9956cecp-36L, -0x8.5b8b379eacc020ep-40L, -0x9.6e6469e45867b18p-46L, 0xc.ca63a296e698604p-53L, 0xe.9f3ed93d387731ep-63L, -0xd.69a601c1fd321e5p-75L, 0xe.37e858d46b515bp-97L, -0x0p+0L};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0L, 0xf.ff35419fa0e8f21p-11L, 0xb.43c4ab28ce718b1p-5L, 0xa.7b11139323118aep-4L, -0xc.ebd27807cee01bp-3L, 0xf.70d391b7b8f1d7fp-4L, -0x9.d261e8a8608ee81p-4L, 0xd.289270d5a3d484p-5L, -0xf.ea38a0284f599d4p-6L, 0xf.7f5c1aafe97c0a1p-7L, -0xb.4af2f2f24e7c239p-8L, 0xb.9e57029c3fb215dp-10L, -0xf.d3ba488dd169dd9p-13L, 0x8.9d83eeeed9dc1b7p-16L, 0xb.e588e05a14054ecp-17L, -0xe.965fffb7152c15fp-18L, 0xb.a1c464fe94734f4p-20L, 0x9.0ffc4adfdaf948bp-24L, -0x8.ab183dae09460bbp-25L, -0x8.cdc8dffc5f7a7c4p-28L, 0xf.bec1f26a0e3b7cap-34L, 0xa.84831359035218p-37L, -0xa.02b41a135680872p-43L, 0xb.5603cf768986fc1p-49L, -0xc.d24f831bd1db255p-58L, -0xc.45e3366043f8eabp-70L, 0xd.02a0f58dee755b1p-91L, 0x0p+0L};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0L, 0xb.871c689e36e67b2p-8L, 0xc.c21484a70968caap-4L, -0xa.d11d772e7e79982p-3L, -0xe.51d42f1875fb05dp-5L, 0xf.9488fb657535621p-3L, -0xc.816fad65cc2b1fep-3L, 0xb.72ec5197f1d73dap-4L, -0xb.e6ba4cd08dc3e1ep-8L, -0xe.5a89c4ef8a1b6aap-6L, 0xc.4b87ef54b6da459p-6L, -0x9.71dd2188b6a770fp-7L, 0xd.21b94476a8d5992p-12L, 0xa.ec57d75af6152bbp-10L, -0x9.f909d12d261cd27p-11L, 0xa.1c6fb324aff682bp-14L, 0xc.955659a270d5623p-16L, -0xa.51515b49bee533ep-17L, 0x8.30a4a603b752616p-20L, 0x8.e30a8066affb01ep-24L, -0xf.f6a025cb63973cp-27L, 0xc.c807d46ae5c0b92p-32L, 0xa.5b8e365dbdf1a9dp-36L, -0xf.a710791928d528ap-43L, -0xd.73b20acd2ddae47p-53L, 0x8.3a9f2648c76b5adp-62L, -0x8.b92ec6233b61c8p-82L, 0x0p+0L};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0L, 0xd.b20322a3996a6a2p-6L, 0xd.ca4aa0fa2c66c04p-4L, -0xa.4de420cc6c77707p-1L, 0x9.2a8ab8b3d2a9452p+0L, -0x9.2a2c8f45b7035d6p+0L, 0xd.fee80d54f348b5ap-1L, -0x9.2c6587097a03f3cp-1L, 0x9.225b43c8840bfbbp-2L, -0xb.b74e433b47ec0d7p-4L, 0x9.6dc870dbf111c84p-6L, -0xd.6e00555bfbc3311p-7L, 0x8.3bd80e6e14d4ep-6L, -0xa.70de9ebe40837ffp-7L, 0xd.458b8cfbb4b4fcp-9L, -0x8.db3d47eeae9cad3p-12L, -0xa.d5110cf4583900cp-13L, 0x8.614b75f02db74e4p-14L, -0x9.8a8896b713246b3p-17L, -0xd.51a5323c171fee3p-26L, 0xb.8c561092a896f33p-23L, -0xa.769011a8736a082p-28L, -0xb.5161f3d88ae4a18p-32L, 0x8.1e58deca3716d7bp-38L, 0xe.96739f4ce14a1ebp-49L, -0x8.886bf8d85fdfe26p-57L, 0x9.0badf046a579ce9p-76L, -0x0p+0L};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0L, 0xc.de9de1239cb046fp-4L, -0x9.0c5906491d3955ap-2L, -0xc.7839f71242a14d4p-5L, 0x8.81b461d68a76009p+0L, -0xb.72fe813d0b59fd4p+0L, -0xf.f7358c9442947e5p-5L, 0xa.ed7063276080604p+1L, -0x9.29c9c7d32fce6e5p+2L, 0x8.423651a8f719bep+2L, -0xe.99bce7eb69c9558p+0L, -0xd.e0e5eaef029d8dap-2L, 0xa.4f436b46a67c643p+0L, -0xf.256f04625361643p-1L, 0xb.28f9c831a4ab6f7p-2L, -0x8.a71970fcdb5d61fp-5L, -0xe.1058e94389b55dfp-6L, 0xc.ee39ab87739f9d3p-7L, -0xe.ddcf5eece04ef66p-10L, -0xe.3fae0f6307b4b7dp-14L, 0xd.2fe42b7297d6b86p-15L, -0x8.3fb2ed50024d845p-19L, -0x8.71bc783d7f852p-23L, 0xb.4de2c6af60665f8p-29L, 0xc.39550de79b43b5p-39L, -0xb.dc24b4b0400b683p-47L, 0xc.92a4664dadb8e43p-65L, -0x0p+0L};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0L, 0x9.4d8af4702fa4917p-2L, -0xe.7e9b2eb0a293c0dp+0L, 0xa.206556ce091b04p+2L, -0x8.8b6f4ec09d9c51ap+3L, 0x9.db1ce281d9e7bffp+3L, -0x8.0207abf4baf0d13p+3L, 0xf.37ef354ae719481p+1L, 0xa.e0f4f0aad55bdb4p+0L, -0xd.8f2ed3cabd9e47dp+2L, 0xb.e8f89c68b5ce98dp+3L, -0xe.b7a656bdeec15e3p+3L, 0xc.fec0461881c7ecfp+3L, -0xf.676370d2bd59da4p+2L, 0xa.1fffb91075d1ef3p+1L, 0xa.f4a0e680e012488p-5L, -0xe.9503c4c9b7b1e2cp-2L, 0xc.a0744fcfdf1dc88p-3L, -0xf.b153b44bbbd55dap-6L, -0x9.59d9d9ad1020acfp-9L, 0x9.ef15d0e0d82a945p-10L, -0x9.0e5f7516ecaaaccp-14L, -0x9.0a87b28ac0c9fb1p-18L, 0x8.acdfc44a2a6359cp-23L, 0xd.807a7cb67428b3fp-33L, -0x9.0f4709e42ae00f3p-40L, 0x9.9ac848883cba3fep-57L, 0x0p+0L};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0L, 0x9.834e4dab96bc376p-1L, -0x9.71bb4c1fb65b59dp+2L, 0x8.9b36c94b3750b19p+4L, -0x9.bdcc290b9f8378cp+5L, 0xf.f9f96db50ad1ec4p+5L, -0xa.bec9c1b0372837ap+6L, 0xc.f45cba99d8f5737p+6L, -0xe.2ab3c8513f0ea1bp+6L, 0xd.7cf5a3d5e047047p+6L, -0xa.f1823dfa8daa614p+6L, 0xf.7ec994dda07fb22p+5L, -0x9.9bf6048130d2edbp+5L, 0x8.eebf04d13348a6p+4L, -0x9.a7c6a99c8f4aeedp+1L, -0x8.db211ffd209a6f3p+2L, 0x8.1c765ef5f7f1ce5p+2L, -0xc.f9039da83aa9c29p+0L, 0x8.69d91bc55678fabp-2L, 0xd.c9ffdee5e7de57ep-6L, -0x8.01426dc87cadac2p-6L, 0xa.90130491b5b5f4ep-10L, 0xa.5c99052bf919189p-14L, -0xe.9d842bbab01556cp-19L, -0xf.4ba9827a103207ap-28L, 0xf.2e767d355bddaa1p-35L, -0x8.0c472517ad4ef83p-50L, -0x0p+0L};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0L, 0xf.abcd8b83a71b41bp-1L, -0x8.9dce5f3b30b3793p+3L, 0x8.68682195f609a67p+5L, -0x9.84d437345ff4c4dp+6L, 0xd.c713118f501f476p+6L, -0xd.84594228bf62173p+6L, 0x9.e3e95931228123cp+6L, -0xb.f3ef786eb60bf83p+5L, 0xc.e4402241c87301dp+2L, 0xe.e0ba9661797c21bp+5L, -0xf.2a501fdde17d235p+6L, 0x8.d2170ed72b4825ep+7L, -0xf.c81fa50c6187197p+6L, 0xc.ec6dc8c841c327ep+6L, -0x9.a0b9ffd8a1f0ecfp+6L, 0xb.2759e13edab26a3p+5L, -0x8.586218b8ff72c95p+4L, 0xa.f8529bae88e396ep+1L, 0xe.c7b5cf8a917974bp-2L, -0x8.e3ac4b6b6acc633p-2L, 0xf.9c560d3a4ed77bcp-6L, 0xf.c13805a6e393a55p-10L, -0x8.98309aea3397895p-13L, -0x9.6e28a6b4cc8a06ep-22L, 0x8.ea4a570e998fa08p-28L, -0x9.742325e7646a08p-43L, 0x0p+0L};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0L, 0xf.196612f526d24c2p-1L, -0x8.b4965322c754f1cp+3L, 0x8.fd04e098b6fda5ap+5L, -0xb.0af33f860e6644cp+6L, 0x9.32e460da58d525ap+7L, -0xb.ab4f68e4108651p+7L, 0xc.f4b5ef2831ea0e8p+7L, -0xd.ddf0b3d1c6b1944p+7L, 0xd.f040100f39be9b8p+7L, -0xc.784cded5d90c4c7p+7L, 0xa.1dc1c0af0ad3159p+7L, -0xf.7356b459ded2772p+6L, 0xa.c6ab0e5c26933f6p+6L, -0xd.1d94154203d1881p+5L, 0xe.3ceb107fd7e02c5p+4L, -0xd.e3c65ca23d50927p+3L, 0xa.0c71ac8171966e8p+2L, -0x9.d5f9b056617ba17p-1L, -0xd.6bdd9c33d9e1582p-2L, 0xd.32a81275f97ea1cp-3L, -0xd.7fee6a38c5d3f8dp-6L, -0xc.1a0e6b635854ea4p-10L, 0xd.aab8869f5faa95cp-13L, 0xf.190b9c558a2439ep-22L, -0xe.29e09b9e442c27dp-27L, 0xf.061385658ae2fdbp-41L, 0x0p+0L};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0L, 0xc.68fc5193cbb1b7bp-1L, -0xe.a440ccad060f512p+2L, 0xf.436a0a53c719d99p+4L, -0x9.40013e4d843ac8dp+6L, 0xe.9f5af8582ca613bp+6L, -0x8.5c152ae13ccf6f4p+7L, 0x8.3e74fb86ed9434dp+7L, -0x8.6bc1129b3c4ec82p+7L, 0x8.6fb0e9528358fc8p+7L, -0xe.3449d6366d35aadp+6L, 0xa.2d64f4044bc4118p+6L, -0xe.4eb43711b821ef6p+5L, 0x9.ae261c0cd987cdbp+5L, -0xa.52c5f1b07a7a10fp+4L, 0x8.0baace1afbb0855p+3L, -0xa.e8dd3f89a3a1196p+1L, 0xe.d6ea4d49ae41ca2p-2L, 0xc.3d80fea19351b34p-1L, -0xc.d58ae923fc87cffp-1L, 0xa.366b50699d24558p-2L, -0xc.4aaebef7f06a90cp-5L, -0xc.29227a732dde266p-10L, 0xb.7c369e218830b25p-11L, 0x8.da71e0953a6ff91p-19L, -0xb.c8a6c1698c9facp-24L, 0xc.81da5a26ec63e05p-37L, -0x0p+0L};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0L, 0x8.20d0544bd51475ap-2L, -0x9.b2c5aebbb04f3ccp+1L, 0xa.8ca5782717c2461p+3L, -0xe.1efc0f8557945e6p+4L, 0xd.68c1f46d9ed5f43p+5L, -0x9.ece3c16b803b8afp+6L, 0xc.296d1a9b1536a08p+6L, -0xc.e650c7b4a3ee86bp+6L, 0xc.d377d24c49af172p+6L, -0xd.1806175ee9ce931p+6L, 0xd.39aa3be5ff8dcb3p+6L, -0xb.d1c258e1897df15p+6L, 0x9.57ec4377396b8b8p+6L, -0xe.87b1ca3693ad8c6p+5L, 0xb.1c262509faa6e0bp+5L, -0xe.b6134e745f9a70dp+4L, 0x8.44c1323b0bffc57p+4L, -0x8.fbf41d038891ad4p+3L, 0x9.52b80dadf506ef2p+2L, -0xe.0c5527608acdb69p+0L, 0xa.6e09c30b2c546eap-2L, 0xd.ead60c819922651p-8L, -0x8.d54a0b87ffd6b8cp-7L, -0xc.bb3c5ec6e4fd2a6p-17L, 0x9.2d9fe11eee7aff2p-19L, -0x9.c0ff7a8090c74e6p-31L, -0x0p+0L};
+            }
+            if constexpr (order == 11) {
+                return {0x0p+0L, 0xa.2b50e9522e86a75p-3L, -0xc.3398f1c7964f4dfp+0L, 0xc.ceed74dacabed45p+2L, -0xf.5e660eaebacd068p+3L, 0xb.a7c2eec834a457bp+4L, -0xc.213112d93221da7p+4L, 0xa.7de60def9f8cb1ep+4L, -0xa.3bb6074c98cfb0fp+4L, 0xa.b9df79fed3f56f5p+4L, -0x9.586138dec41f121p+4L, 0xd.dade5405b127d2ep+3L, -0xa.c04012e49fd2735p+3L, 0x8.60efa067af26275p+3L, -0xa.ef5008a8d1f0cbfp+2L, 0xc.cbfe4a8cc2b9da9p+1L, -0xf.ae20a079501f01bp+0L, 0x8.abc7a020b125872p+0L, -0xf.08d2623c2412c59p-2L, 0xc.617ad46572a9f45p-3L, -0xa.166eeef4db8f41bp-4L, 0x8.d9ba91b4066cd0bp-6L, 0xb.0de51fe9f7fd8e2p-10L, -0xf.7653c660eecd46ap-11L, 0xa.13d9bbaa8adb22dp-17L, 0x8.e36187daa39648ep-21L, -0x9.782b283672f30cdp-32L, 0x0p+0L};
+            }
+            if constexpr (order == 12) {
+                return {0x0p+0L, 0xa.2d2427bccd39172p-5L, -0xc.3e7cf55a7a0039fp-2L, 0xc.cd766a1bb1a58d8p+0L, -0xf.19aee96374ef183p+1L, 0xa.f1c20f10ca84c7dp+2L, -0xa.441cf0245c1e989p+2L, 0xf.08d3f9839af181p+1L, -0xd.ff93b926a081d89p+1L, 0xf.b45b7f166618b46p+1L, -0xd.4e44e185e5110d4p+1L, 0x8.a3eed6c08e9589p+1L, -0xd.08770758e65b254p+0L, 0xa.ec5cfff1e6dc48ap+0L, -0xd.8775fb493cf7d7dp-1L, 0xd.8c0494f0d34dbf8p-2L, -0x8.8d169b83b8e53edp-2L, 0xa.2d86ccc6559bbf1p-3L, -0xe.ba041f5676a0b08p-5L, 0x9.3e0889dadedbcbbp-6L, -0x9.7735428934a726dp-7L, 0x8.56888186d114aabp-9L, 0xd.b8cd6a5738afd8ap-11L, -0xb.dab9366ba83dabcp-12L, 0xf.7f073fde73fa0bdp-17L, 0x8.8b41cfb923d7022p-21L, -0x9.260ac7e9b3efaabp-31L, -0x0p+0L};
+            }
+            if constexpr (order == 13) {
+                return {0x0p+0L, 0xa.1cd4ad99523f5acp-8L, -0xc.2f2fc67105b80bcp-5L, 0xc.acd5acad17523e6p-3L, -0xe.ac893beffa9ec6ep-2L, 0xa.1d32b2499d9f84p-1L, -0x8.51602e62cbd5666p-1L, 0x9.39ca87b7fe8bf75p-2L, -0x8.28645ce5c25be28p-2L, 0xb.0075410088e8318p-2L, -0x9.0fb0d4225082783p-2L, 0x8.cf8737798d06934p-3L, -0xc.710818a25393088p-4L, 0xd.03f944a7cb8758ep-4L, -0xe.6674293e772e22ap-5L, 0xf.2b09bc335412a19p-7L, -0xa.efa460643e6b966p-7L, 0x8.ce9f81ce2366f05p-7L, -0xc.f36687b0fa6554ep-12L, -0xd.cb35efa2b9452d3p-10L, 0xc.1203b8d10393dadp-12L, -0x8.d82d17abfc923a4p-12L, 0xb.fc2aa4acfa52995p-12L, -0x9.1b886fc19758c23p-13L, 0xe.62bad7ef9f9e73fp-17L, 0x8.f91c0cb5711719fp-21L, -0x9.b4bf4dfa1834f78p-30L, -0x0p+0L};
+            }
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            if constexpr (order == 0) {
+                return {0x0p+0Q, 0x1.2e3c0bb3f3ad4d49ee7e86ec5518p-10Q, 0x1.d73cdc4f17147d4ff78a1eaebc82p-4Q, 0x1.980f074dbd462038712882b2222ep-1Q, 0x1.0b8da7807c2738b0ef8a21bd41e3p-2Q, -0x1.381b88314120b0755faac9b6a20bp-2Q, 0x1.a64053bd4da4144d5c6645aafa57p-3Q, -0x1.be6cb26620f84322f5bc9ad12402p-4Q, 0x1.5369f32b472a8bf80c2615157591p-5Q, -0x1.e553bfb83c481ee1c85b10218134p-8Q, -0x1.5b97376b07916025b5f5ed690f55p-9Q, 0x1.3ad93e070eb79f317793c09c0443p-9Q, -0x1.6c8658d1b206dd40e11227faae72p-11Q, 0x1.421437e7b839d2e408af08229929p-16Q, 0x1.359cb55b7d335b5bc8ff9070d375p-15Q, -0x1.16b1cde08937e6520514fc007dd3p-18Q, -0x1.1e470298289ae452c29404b9c735p-19Q, 0x1.16b7d7c52ecb6bf5c9c270fe3973p-21Q, -0x1.2a9017a9058ec8631bfea23cf0d5p-27Q, -0x1.e6603a12c62203e481a6f751bafcp-29Q, 0x1.ad635a5532ad9d7f9b990f32589fp-33Q, -0x1.0b7166f3d598041c11f82d418c61p-37Q, -0x1.2dcc8d3c8b0cf63074ab4d9fba5fp-43Q, 0x1.994c7452dcd30c07dade8e0a0b53p-50Q, 0x1.d3e7db27a70ee63bd0dc60e06dc1p-60Q, -0x1.ad34c0383fa643c903234154af7ep-72Q, 0x1.c6fd0b1a8d6a2b5f9f47659e9cdcp-94Q, -0x0p+0Q};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0Q, 0x1.ffe6a833f41d1e41c335a1d663bdp-8Q, 0x1.6878956519ce3162ba29291a8512p-2Q, 0x1.4f6222726462315c1311b1bd0b54p-1Q, -0x1.9d7a4f00f9dc035ff30a13b3dd41p+0Q, 0x1.ee1a7236f71e3afe8c9241dc27eep-1Q, -0x1.3a4c3d150c11dd01e59680a43c0ap-1Q, 0x1.a5124e1ab47a907fdd8a56cf5fb6p-2Q, -0x1.fd47140509eb33a71307cdb49b1ep-3Q, 0x1.efeb8355fd2f814144fb4db02bbdp-4Q, -0x1.695e5e5e49cf847101e5144b6fd9p-5Q, 0x1.73cae05387f642ba0d652b2dbc7ep-7Q, -0x1.fa774911ba2d3bb25d61e69c8c0ap-10Q, 0x1.13b07ddddb3b836ee57d128434e4p-13Q, 0x1.7cb11c0b4280a9d8a95e4eb20f02p-14Q, -0x1.d2cbfff6e2a582bd1061aa2f37f3p-15Q, 0x1.74388c9fd28e69e7d9f0c5af3f3ep-17Q, 0x1.21ff895bfb5f2915922793fd2436p-21Q, -0x1.156307b5c128c175f7e3a714785ap-22Q, -0x1.19b91bff8bef4f88f1ed76cce8b5p-25Q, 0x1.f7d83e4d41c76f94d46210e4d8b7p-31Q, 0x1.5090626b206a430059df75027f9ap-34Q, -0x1.405683426ad010e44f0a98cc99acp-40Q, 0x1.6ac079eed130df81302e2b26c976p-46Q, -0x1.9a49f0637a3b64a9eb35bd52a783p-55Q, -0x1.88bc66cc087f1d558950f224ed94p-67Q, 0x1.a0541eb1bdceab613773d4dca27cp-88Q, 0x0p+0Q};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0Q, 0x1.70e38d13c6dccf6333417be4b524p-5Q, 0x1.98429094e12d1953c234a36b12cep-1Q, -0x1.5a23aee5cfcf330386719e085b0dp+0Q, -0x1.ca3a85e30ebf60ba5eccc5b7afa3p-2Q, 0x1.f2911f6caea6ac421bc7b6d2cbaap+0Q, -0x1.902df5acb98563fb6c8594126211p+0Q, 0x1.6e5d8a32fe3ae7b3c23b4e6e9a5bp-1Q, -0x1.7cd7499a11b87c3bc4909e0bca27p-5Q, -0x1.cb51389df1436d54630b5c40529cp-3Q, 0x1.8970fdea96db48b13c52294d02f6p-3Q, -0x1.2e3ba43116d4ee1d14ccd7ef1ed2p-4Q, 0x1.a437288ed51ab324c667ecc7c503p-9Q, 0x1.5d8afaeb5ec2a57500ea441b586cp-7Q, -0x1.3f213a25a4c39a4ee9f8ca7fc5d7p-8Q, 0x1.438df66495fed0569b1e66072684p-11Q, 0x1.92aacb344e1aac45946a6dd95aa5p-13Q, -0x1.4a2a2b6937dca67c2fb96409ea9bp-14Q, 0x1.061494c076ea4c2b5c794f2371b3p-17Q, 0x1.1c61500cd5ff603bf7260846f058p-21Q, -0x1.fed404b96c72e77fac42699e643cp-24Q, 0x1.9900fa8d5cb81723cdb543a2519ap-29Q, 0x1.4b71c6cbb7be353ab93ac21700a5p-33Q, -0x1.f4e20f23251aa513b13eb0ad0e35p-40Q, -0x1.ae764159a5bb5c8d340066c073e5p-50Q, 0x1.0753e4c918ed6b59ce15c4a93456p-59Q, -0x1.1725d8c4676c38ff70e1cc358b0cp-79Q, 0x0p+0Q};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0Q, 0x1.b6406454732d4d440405d44a6611p-3Q, 0x1.b949541f458cd808c01c6f443873p-1Q, -0x1.49bc84198d8eee0e1769477dce8bp+2Q, 0x1.255157167a5528a3714c438e28f7p+3Q, -0x1.254591e8b6e06babda61e0b5bc24p+3Q, 0x1.bfdd01aa9e6916b30d7fb866c97ap+2Q, -0x1.258cb0e12f407e788c8d24c0406ap+2Q, 0x1.244b687910817f75269b9b13caa9p+1Q, -0x1.76e9c86768fd81ae0140e512e5cp-1Q, 0x1.2db90e1b7e223907d65e185884b8p-3Q, -0x1.adc00aab7f786622c376bd60af55p-4Q, 0x1.077b01cdc29a9bffc5581309684ap-3Q, -0x1.4e1bd3d7c8106ffe51d90e2985dp-4Q, 0x1.a8b1719f76969f8051acdf38be11p-6Q, -0x1.1b67a8fdd5d395a5e1003bc2f0a6p-9Q, -0x1.5aa2219e8b072017d97056f43e75p-10Q, 0x1.0c296ebe05b6e9c7cf2917908c1fp-11Q, -0x1.315112d6e2648d659715640ab8d6p-14Q, -0x1.aa34a64782e3fdc563417214521bp-23Q, 0x1.718ac2125512de66d6a9b5d7a901p-20Q, -0x1.4ed202350e6d4103a23efe8129dbp-25Q, -0x1.6a2c3e7b115c942fffc924e2bab2p-29Q, 0x1.03cb1bd946e2daf6230de1903bdbp-35Q, 0x1.d2ce73e99c2943d672b79f3e0a48p-46Q, -0x1.110d7f1b0bfbfc4b48ffe17563d9p-54Q, 0x1.2175be08d4af39d29c43830b683bp-73Q, -0x0p+0Q};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0Q, 0x1.9bd3bc24739608dd1ea07282ef41p-1Q, -0x1.218b20c923a72ab49d783c404613p+1Q, -0x1.8f073ee2485429a822c3452a2874p-2Q, 0x1.10368c3ad14ec0121ffa10bcc969p+3Q, -0x1.6e5fd027a16b3fa71b0c6884de45p+3Q, -0x1.fee6b19288528fc9912556543eabp-2Q, 0x1.5dae0c64ec100c07cb64ad03ec4bp+4Q, -0x1.253938fa65f9cdca9dcd99a85c53p+5Q, 0x1.0846ca351ee337bf1cde15fb1fccp+5Q, -0x1.d3379cfd6d392ab0067070da245ep+3Q, -0x1.bc1cbd5de053b1b3e6030ce1e12cp+1Q, 0x1.49e86d68d4cf8c86d821677a6f81p+3Q, -0x1.e4ade08c4a6c2c8507d0732937fap+2Q, 0x1.651f390634956dee37faca825966p+1Q, -0x1.14e32e1f9b6bac3d6ef9b66af2bep-2Q, -0x1.c20b1d287136abbd5724af5f5f6dp-3Q, 0x1.9dc73570ee73f3a5d7e75ae5a9e2p-4Q, -0x1.dbb9ebdd9c09deccb10201529186p-7Q, -0x1.c7f5c1ec60f696f9a40d5c3a09b9p-11Q, 0x1.a5fc856e52fad70c72c88b4e101ap-12Q, -0x1.07f65daa0049b089e54b5e4ff41ap-16Q, -0x1.0e378f07aff0a4003d557ea836c6p-20Q, 0x1.69bc58d5ec0ccbef38bec29b1e3ep-26Q, 0x1.872aa1bcf368769fc21e2888c6ffp-36Q, -0x1.7b84969608016d06bfce8c14af4bp-44Q, 0x1.92548cc9b5b71c86f11e27090a6cp-62Q, -0x0p+0Q};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0Q, 0x1.29b15e8e05f4922e7d4e472bcd8ap+1Q, -0x1.cfd365d6145278198eca9cdcf322p+3Q, 0x1.440caad9c12360807dafb40ee49dp+5Q, -0x1.116de9d813b38a3407c4631c8d59p+6Q, 0x1.3b639c503b3cf7fe4e22628885p+6Q, -0x1.0040f57e975e1a258b9875f60498p+6Q, 0x1.e6fde6a95ce32902224ee706d045p+4Q, 0x1.5c1e9e155aab7b67b6f07264ad9dp+3Q, -0x1.b1e5da7957b3c8fabda1d3079971p+5Q, 0x1.7d1f138d16b9d31aa2829abf2c4bp+6Q, -0x1.d6f4cad7bdd82bc575e84c099062p+6Q, 0x1.9fd808c31038fd9d9f982223f243p+6Q, -0x1.ecec6e1a57ab3b47a08d39c75c75p+5Q, 0x1.43fff7220eba3de58880abe282dap+4Q, 0x1.5e941cd01c02491042063bd5bee4p-2Q, -0x1.d2a0789936f63c584facf579998ap+1Q, 0x1.940e89f9fbe3b90fa47d37c5f5dep+0Q, -0x1.f62a7689777aabb4ab21adf5f4dbp-3Q, -0x1.2b3b3b35a204159ed027231f9fb4p-6Q, 0x1.3de2ba1c1b05528a92fff0293ae7p-7Q, -0x1.21cbeea2dd955597cbff136c8ae1p-11Q, -0x1.2150f65158193f62d7d7fa29a2c2p-15Q, 0x1.159bf889454c6b38325ea21f7134p-20Q, 0x1.b00f4f96ce85167dd0220fed62e7p-30Q, -0x1.21e8e13c855c01e5c446a2405ce7p-37Q, 0x1.33590911079747fc32e0ed899892p-54Q, 0x0p+0Q};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0Q, 0x1.3069c9b572d786eb96d928fa48f8p+2Q, -0x1.2e376983f6cb6b3abd6845551e34p+5Q, 0x1.1366d92966ea16320047797424ccp+7Q, -0x1.37b9852173f06f1765e1ff0e8531p+8Q, 0x1.ff3f2db6a15a3d87e9d7dfab891bp+8Q, -0x1.57d9383606e506f39f38559de18fp+9Q, 0x1.9e8b97533b1eae6eef5cca38387bp+9Q, -0x1.c556790a27e1d4367bdf83babbd1p+9Q, 0x1.af9eb47abc08e08daae8abacd91fp+9Q, -0x1.5e3047bf51b54c27591544583f14p+9Q, 0x1.efd9329bb40ff6440883f1147f56p+8Q, -0x1.337ec090261a5db68ef97d7b1236p+8Q, 0x1.1dd7e09a266914bfb2df709f94d8p+7Q, -0x1.34f8d53391e95dda3b7a1cf411e9p+4Q, -0x1.1b6423ffa4134de5e81b17a17c11p+5Q, 0x1.038ecbdebefe39ca7724b3c832fcp+5Q, -0x1.9f2073b507553852ed1a72469f32p+3Q, 0x1.0d3b2378aacf1f56c9dbd6da2754p+1Q, 0x1.b93ffbdcbcfbcafb2828e85b9cf7p-3Q, -0x1.00284db90f95b583e4f97482c916p-3Q, 0x1.5202609236b6be9cf16ae9fb3f51p-7Q, 0x1.4b9320a57f2323116dd63710b5p-11Q, -0x1.d3b085775602aad7427a22c98a84p-16Q, -0x1.e975304f420640f339ac29b10f7bp-25Q, 0x1.e5cecfa6ab7bb5421ef8ce75b514p-32Q, -0x1.0188e4a2f5a9df06f68769623342p-47Q, -0x0p+0Q};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0Q, 0x1.f579b17074e36836eacdef034d32p+2Q, -0x1.13b9cbe766166f25c9dacf502f0ep+6Q, 0x1.0d0d0432bec134cd566f573a6ab7p+8Q, -0x1.309a86e68bfe9899fc0e7b2c0b24p+9Q, 0x1.b8e26231ea03e8ec859801e86e25p+9Q, -0x1.b08b284517ec42e681060fcc6182p+9Q, 0x1.3c7d2b26245024778e757ad1afa1p+9Q, -0x1.7e7def0dd6c17f062ac250175abcp+8Q, 0x1.9c880448390e60397d60bff8dd4cp+5Q, 0x1.dc1752cc2f2f84356ce88f9e5906p+8Q, -0x1.e54a03fbbc2fa46a839c73f788e9p+9Q, 0x1.1a42e1dae56904bbcf40d542b472p+10Q, -0x1.f903f4a18c30e32dc6c45f366ebp+9Q, 0x1.9d8db919083864fcc4e33e87dba9p+9Q, -0x1.34173ffb143e1d9eed0ece396b8p+9Q, 0x1.64eb3c27db564d469eb22cf2354cp+8Q, -0x1.0b0c43171fee5929daa625b8080cp+7Q, 0x1.5f0a5375d11c72dc55998ba597dbp+4Q, 0x1.d8f6b9f1522f2e96a9e605cbb38dp+1Q, -0x1.1c75896d6d598c65080cc6678602p+1Q, 0x1.f38ac1a749daef77915dd8d10d16p-3Q, 0x1.f82700b4dc7274aa9bdb17c1024cp-7Q, -0x1.1306135d4672f12980f476eef1d1p-10Q, -0x1.2dc514d6999140dbb2a33c5d5ad2p-19Q, 0x1.1d494ae1d331f410d690ac5ec36dp-25Q, -0x1.2e8464bcec8d40ffd77c2dc57367p-40Q, 0x0p+0Q};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0Q, 0x1.e32cc25ea4da498425dec5295c6bp+2Q, -0x1.1692ca6458ea9e38b44f5a5caee1p+6Q, 0x1.1fa09c1316dfb4b439ac84209c53p+8Q, -0x1.615e67f0c1ccc897da6e59c7c927p+9Q, 0x1.265c8c1b4b1aa4b3e36ae2efb333p+10Q, -0x1.7569ed1c8210ca209e4700bf211ep+10Q, 0x1.9e96bde5063d41cf09d912f51fep+10Q, -0x1.bbbe167a38d63287ecfd91133a36p+10Q, 0x1.be080201e737d36f7e786ff84c53p+10Q, -0x1.8f099bdabb21898e35971dfd6953p+10Q, 0x1.43b83815e15a62b284efdec504bp+10Q, -0x1.ee6ad68b3bda4ee4ba8a3ff07fd1p+9Q, 0x1.58d561cb84d267ecaf620ab5b2e6p+9Q, -0x1.a3b282a8407a310226d6a98bfd4cp+8Q, 0x1.c79d620ffafc0589079d1ba6c99bp+7Q, -0x1.bc78cb9447aa124d62b13f580945p+6Q, 0x1.418e35902e32cdd0c2f0c12b4efbp+5Q, -0x1.3abf360acc2f742d878f5bcabe87p+2Q, -0x1.ad7bb3867b3c2b046f8005354fafp+1Q, 0x1.a655024ebf2fd4378620fe654a6cp+0Q, -0x1.affdcd4718ba7f1a9653624c15d7p-3Q, -0x1.8341cd6c6b0a9d48905914abd48fp-7Q, 0x1.b55710d3ebf552b754e9b7ff147ep-10Q, 0x1.e321738ab144873b6e430caac23ep-19Q, -0x1.c53c1373c88584f948dc218ab05ap-24Q, 0x1.e0c270acb15c5fb504672c4070dp-38Q, 0x0p+0Q};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0Q, 0x1.8d1f8a32797636f66137fdd0b5a1p+2Q, -0x1.d4881995a0c1ea2394012c228a31p+5Q, 0x1.e86d414a78e33b3180b504d86b91p+7Q, -0x1.280027c9b087591ad85eeab44da9p+9Q, 0x1.d3eb5f0b0594c2750ef22285fa37p+9Q, -0x1.0b82a55c2799ede8dec310d6a2c6p+10Q, 0x1.07ce9f70ddb2869a6583adf6dec9p+10Q, -0x1.0d7822536789d9033e721121699dp+10Q, 0x1.0df61d2a506b1f8fcfe8714e12afp+10Q, -0x1.c6893ac6cda6b55a49442539d592p+9Q, 0x1.45ac9e808978822ff4aec18a24f6p+9Q, -0x1.c9d686e237043dec7c0766428b6p+8Q, 0x1.35c4c3819b30f9b6fdd7719012dbp+8Q, -0x1.4a58be360f4f421d89ea2c96a33ep+7Q, 0x1.017559c35f7610aa1b74c79cf6fcp+6Q, -0x1.5d1ba7f13474232b930160e8fda2p+4Q, 0x1.dadd49a935c8394385dd6633289ep+1Q, 0x1.87b01fd4326a3668ccbada1018e4p+2Q, -0x1.9ab15d247f90f9fe7c9c31997416p+2Q, 0x1.46cd6a0d33a48aafbbc2d2b2efc4p+1Q, -0x1.8955d7defe0d52172967ed8290b5p-2Q, -0x1.85244f4e65bbc4ccef79bedeb2b3p-7Q, 0x1.6f86d3c43106164aba3a27d3b092p-8Q, 0x1.1b4e3c12a74dff21568f7bbd6f64p-16Q, -0x1.7914d82d3193f580c3333edc5ffbp-21Q, 0x1.903b4b44dd8c7c0a4e6f8896b442p-34Q, -0x0p+0Q};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0Q, 0x1.041a0a897aa28eb3a0d59e3420dep+1Q, -0x1.3658b5d77609e7977d40f266e1abp+4Q, 0x1.5194af04e2f848c2193a50575354p+6Q, -0x1.c3df81f0aaf28bccb605744a68dcp+7Q, 0x1.ad183e8db3dabe867a16ea08db03p+8Q, -0x1.3d9c782d7007715e1138bf8d8bf5p+9Q, 0x1.852da35362a6d4101e0c1842b371p+9Q, -0x1.9cca18f6947dd0d5bebb456e26c7p+9Q, 0x1.9a6efa498935e2e3d81571c175b7p+9Q, -0x1.a300c2ebdd39d2620495c5f7e961p+9Q, 0x1.a735477cbff1b966c87efc4ff1fep+9Q, -0x1.7a384b1c312fbe2a2f241ae26c7ep+9Q, 0x1.2afd886ee72d716fc61db8011095p+9Q, -0x1.d0f63946d275b18c0f2f2351b8f4p+8Q, 0x1.6384c4a13f54dc153d6b4654b173p+8Q, -0x1.d6c269ce8bf34e1952e45981a53dp+7Q, 0x1.08982647617ff8ae60a05f4fb227p+7Q, -0x1.1f7e83a0711235a83ba8d41f6e49p+6Q, 0x1.2a5701b5bea0dde347c9c6a1a0bfp+5Q, -0x1.c18aa4ec1159b6d22d408f93473cp+3Q, 0x1.4dc13861658a8dd406c58e6b6d01p+1Q, 0x1.bd5ac19033244ca1bfd76ff5f84ap-5Q, -0x1.1aa94170fffad7174e6a949842fp-4Q, -0x1.97678bd8dc9fa54b7e11dee71cb2p-14Q, 0x1.25b3fc23ddcf5fe31e8523af1987p-16Q, -0x1.381fef501218e9cc3debb9c868adp-28Q, -0x0p+0Q};
+            }
+            if constexpr (order == 11) {
+                return {0x0p+0Q, 0x1.456a1d2a45d0d4e9e190da6b0253p+0Q, -0x1.86731e38f2c9e9bd245d8c21307ep+3Q, 0x1.99ddae9b5957da8932ffd7759bbep+5Q, -0x1.ebccc1d5d759a0cf4ae087b81294p+6Q, 0x1.74f85dd906948af50c25a724f709p+7Q, -0x1.8426225b26443b4ef3ccb7b8d05cp+7Q, 0x1.4fbcc1bdf3f1963c49ab7f076eabp+7Q, -0x1.4776c0e99319f61e68a708d5d7adp+7Q, 0x1.573bef3fda7eadeaaa4494427daep+7Q, -0x1.2b0c271bd883e242fddb7fb5c9c1p+7Q, 0x1.bb5bca80b624fa5bb27c8fee01a2p+6Q, -0x1.5808025c93fa4e6af5aadac355cep+6Q, 0x1.0c1df40cf5e4c4ea44443af3add6p+6Q, -0x1.5dea01151a3e197eb05656a3cb23p+5Q, 0x1.997fc95198573b527728fd6a3ac8p+4Q, -0x1.f5c4140f2a03e036d1612965ff32p+3Q, 0x1.1578f4041624b0e3ebbe577cc0e3p+3Q, -0x1.e11a4c47848258b137fd42f6f749p+1Q, 0x1.8c2f5a8cae553e89ef2299c46ab4p+0Q, -0x1.42cdddde9b71e8354b8f6892a693p-1Q, 0x1.1b37523680cd9a16c0e89cedee59p-3Q, 0x1.61bca3fd3effb1c3f582ac5eba63p-7Q, -0x1.eeca78cc1dd9a8d407ad8882646ep-8Q, 0x1.427b3775515b64598a1525510bb3p-14Q, 0x1.1c6c30fb5472c91c3ee448e49edcp-18Q, -0x1.2f056506ce5e619914cfa74f5c81p-29Q, 0x0p+0Q};
+            }
+            if constexpr (order == 12) {
+                return {0x0p+0Q, 0x1.45a484f799a722e4cd93e3b2b27ep-2Q, -0x1.87cf9eab4f40073db99d0811247ap+1Q, 0x1.99aecd437634b1af52fa61911031p+3Q, -0x1.e335dd2c6e9de306d05b0cd1cef8p+4Q, 0x1.5e3841e2195098fae8b63a8bc104p+5Q, -0x1.48839e048b83d3127ebd4015d2fap+5Q, 0x1.e11a7f30735e301f0eb1189e687ap+4Q, -0x1.bff27724d4103b12e928ab4222e3p+4Q, 0x1.f68b6fe2ccc3168c1a13f5cdae6fp+4Q, -0x1.a9c89c30bca221a764aca7ca6dcfp+4Q, 0x1.147ddad811d2b11feabd90554e5p+4Q, -0x1.a10ee0eb1ccb64a80031cb887a99p+3Q, 0x1.5d8b9ffe3cdb891325e866af6c37p+3Q, -0x1.b0eebf69279efaf954db661df6b8p+2Q, 0x1.b180929e1a69b7ef5326dddd752dp+1Q, -0x1.11a2d370771ca7d9ba7b5ac54127p+1Q, 0x1.45b0d998cab377e10ef261593991p+0Q, -0x1.d74083eaced416102c8bdf26f325p-2Q, 0x1.27c1113b5bdb797524261b6d46bap-3Q, -0x1.2ee6a8512694e4da2e59c12b6ea6p-4Q, 0x1.0ad11030da22955532efbb615d1ap-6Q, 0x1.b719ad4ae715fb13a423a1010a46p-8Q, -0x1.7b5726cd7507b577ab862e7a3077p-9Q, 0x1.efe0e7fbce7f41797c6619cc6d2bp-14Q, 0x1.116839f7247ae044e8df44cc0f86p-18Q, -0x1.24c158fd367df5563092d5399988p-28Q, -0x0p+0Q};
+            }
+            if constexpr (order == 13) {
+                return {0x0p+0Q, 0x1.439a95b32a47eb5722e3fe0fb9bbp-5Q, -0x1.85e5f8ce20b701780e206438509dp-2Q, 0x1.959ab595a2ea47cca9401bb631dfp+0Q, -0x1.d591277dff53d8dcf592be17f8e1p+1Q, 0x1.43a6564933b3f0805a5abb1bb626p+2Q, -0x1.0a2c05cc597aaccc032e0cf740cp+2Q, 0x1.273950f6ffd17ee92b3278320e9fp+1Q, -0x1.050c8b9cb84b7c5048bc8a039239p+1Q, 0x1.600ea820111d062fdf2aa3ec8771p+1Q, -0x1.21f61a844a104f06b392ed4a3d9ep+1Q, 0x1.19f0e6ef31a0d26707b469b32ea9p+0Q, -0x1.8e2103144a726110a5663399778ep-1Q, 0x1.a07f2894f970eb1bd26c87860d76p-1Q, -0x1.ccce8527cee5c45450ee4b3e11ffp-2Q, 0x1.e56137866a8254327c31b42ae307p-4Q, -0x1.5df48c0c87cd72cb9ba718d2f9cp-4Q, 0x1.19d3f039c46cde096e5a0e03efccp-4Q, -0x1.9e6cd0f61f4caa9b0d4d30e7aa99p-9Q, -0x1.b966bdf45728a5a5bb305da1c562p-7Q, 0x1.8240771a20727b5953c65907a26p-9Q, -0x1.1b05a2f57f924748a24f59ba5cdcp-9Q, 0x1.7f8554959f4a532982e2e14a363ap-9Q, -0x1.23710df832eb1845bb5334680795p-10Q, 0x1.cc575afdf3f3ce7d0de6d2cce6aep-14Q, 0x1.1f238196ae22e33d868784888e07p-18Q, -0x1.3697e9bf43069ef0c328e5cc56bbp-27Q, -0x0p+0Q};
+            }
+        }
+        #endif
+    }
+    if constexpr (p == 15) {
+        if constexpr (std::is_same_v<Real, float>) {
+            if constexpr (order == 0) {
+                return {0x0p+0f, 0x1.d99d62p-12f, 0x1.0d2f98p-4f, 0x1.4a5392p-1f, 0x1.1fc50ep-1f, -0x1.d49776p-2f, 0x1.3575a8p-2f, -0x1.7e644ap-3f, 0x1.a17858p-4f, -0x1.7135a6p-5f, 0x1.d8cfdcp-7f, -0x1.57e158p-9f, -0x1.5f6332p-15f, 0x1.10a458p-13f, -0x1.592264p-16f, 0x1.899798p-18f, -0x1.4f8412p-18f, 0x1.74953ep-20f, -0x1.f7cb1ap-26f, -0x1.c92be2p-26f, -0x1.3b9a58p-35f, -0x1.6a58cep-35f, 0x1.4bf1ecp-37f, 0x1.697068p-44f, -0x1.513d7ap-49f, -0x1.b3943cp-57f, 0x1.54d33p-67f, -0x1.3f6e1ep-80f, -0x1.d0d882p-104f, 0x0p+0f};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0f, 0x1.af6738p-9f, 0x1.c7ad46p-3f, 0x1.9756ccp-1f, -0x1.519166p+0f, 0x1.6cc6e8p-2f, -0x1.8cf37ep-4f, 0x1.9a3fa2p-4f, -0x1.0a50bep-3f, 0x1.df3f5p-4f, -0x1.2d4b7ep-4f, 0x1.0681e4p-5f, -0x1.1b50d6p-7f, 0x1.49acd2p-11f, 0x1.16651ap-11f, -0x1.c26d2p-13f, 0x1.300212p-16f, 0x1.49fbecp-17f, -0x1.8781a4p-19f, 0x1.5ed0aep-24f, 0x1.da4a76p-25f, -0x1.7e23c8p-29f, -0x1.bd8f2cp-35f, 0x1.1c615p-37f, -0x1.c1b8b4p-44f, -0x1.95157p-52f, 0x1.d1f8dep-60f, -0x1.34635ep-74f, -0x1.c0c6d2p-97f, -0x0p+0f};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0f, 0x1.52aa16p-6f, 0x1.2f3864p-1f, -0x1.92da3ep-2f, -0x1.010e6cp+1f, 0x1.ba5e58p+1f, -0x1.6efa1ap+1f, 0x1.e2fp+0f, -0x1.e9e848p-1f, 0x1.3e7bdp-2f, -0x1.3f21e6p-6f, -0x1.00e092p-5f, 0x1.93252ep-8f, 0x1.0cb53cp-7f, -0x1.6ecc66p-8f, 0x1.1da3c8p-10f, 0x1.0f705cp-12f, -0x1.687f18p-13f, 0x1.03bf74p-15f, -0x1.0a570cp-20f, -0x1.b60c86p-22f, 0x1.2f36c8p-24f, -0x1.ab6b4ep-30f, -0x1.b77dbep-33f, 0x1.02e06ap-39f, 0x1.f900dcp-46f, -0x1.5cc6acp-54f, 0x1.79a9bep-67f, 0x1.12cb1cp-88f, -0x0p+0f};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0f, 0x1.bde47ep-4f, 0x1.ff6e3ap-1f, -0x1.0edf78p+2f, 0x1.788ebp+2f, -0x1.0b9e58p+2f, 0x1.57d72ap+1f, -0x1.5aec5ap+1f, 0x1.66bep+1f, -0x1.257b74p+1f, 0x1.61e6a2p+0f, -0x1.1d6618p-1f, 0x1.7634aep-4f, 0x1.aae5ecp-5f, -0x1.66a2dep-5f, 0x1.9ee5c4p-7f, 0x1.cee452p-12f, -0x1.7d0e64p-10f, 0x1.95a9bcp-12f, -0x1.ac68b8p-17f, -0x1.4a3e54p-17f, 0x1.45a5b2p-20f, -0x1.a0585ep-28f, -0x1.4a4abp-28f, 0x1.818dc4p-34f, 0x1.bc8ec6p-41f, -0x1.1c50f4p-48f, 0x1.541ee6p-61f, 0x1.eef3c6p-82f, -0x0p+0f};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0f, 0x1.da9efcp-2f, -0x1.0a9636p-2f, -0x1.6ead78p+2f, 0x1.1fb0b8p+4f, -0x1.a26b2p+4f, 0x1.5a3628p+4f, -0x1.c3b938p+2f, -0x1.0393f6p+3f, 0x1.ce0e34p+3f, -0x1.3371f4p+3f, 0x1.04744cp-2f, 0x1.5d5bbap+2f, -0x1.56903ap+2f, 0x1.4f3674p+1f, -0x1.16f1cp-1f, -0x1.0ca608p-3f, 0x1.fd1e64p-4f, -0x1.12756ap-5f, 0x1.031ce4p-9f, 0x1.dbc5a2p-11f, -0x1.6e5758p-13f, 0x1.338c12p-19f, 0x1.ec833cp-21f, -0x1.31ee1ep-26f, -0x1.068ccep-32f, 0x1.ab486ep-40f, -0x1.971ac6p-52f, -0x1.28365cp-71f, -0x0p+0f};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0f, 0x1.8a28cp+0f, -0x1.0b8eccp+3f, 0x1.301d18p+4f, -0x1.80a5fep+4f, 0x1.4a39e4p+4f, -0x1.114828p+4f, 0x1.18e244p+4f, -0x1.390866p+4f, 0x1.80446cp+4f, -0x1.0a407ap+5f, 0x1.52509ep+5f, -0x1.4b4686p+5f, 0x1.c80f14p+4f, -0x1.82ded4p+3f, 0x1.7610a2p+0f, 0x1.b0a89ap+0f, -0x1.2b516ep+0f, 0x1.48818ap-2f, -0x1.16dd92p-6f, -0x1.957d58p-7f, 0x1.613bdp-9f, -0x1.0adbcp-14f, -0x1.449056p-16f, 0x1.238bd6p-21f, 0x1.0b863cp-27f, -0x1.2dac52p-34f, 0x1.a8ab5ap-46f, 0x1.34fcf8p-64f, 0x0p+0f};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0f, 0x1.e156f6p+1f, -0x1.d9350cp+4f, 0x1.b03e3ap+6f, -0x1.f51dfap+7f, 0x1.b1d9eep+8f, -0x1.3c90b8p+9f, 0x1.a1026p+9f, -0x1.ee82dcp+9f, 0x1.fcf16ap+9f, -0x1.beee0ep+9f, 0x1.545f4ap+9f, -0x1.c39ca4p+8f, 0x1.d17e6ep+7f, -0x1.8d05e2p+5f, -0x1.a57ddap+5f, 0x1.065bfcp+6f, -0x1.1a783cp+5f, 0x1.2e9f2cp+3f, -0x1.3cad9ap-2f, -0x1.1b4b3ap-1f, 0x1.15a314p-3f, -0x1.5c66a6p-8f, -0x1.5db56p-10f, 0x1.c57be6p-15f, 0x1.c9738p-21f, -0x1.63f652p-27f, 0x1.769768p-38f, 0x1.108b38p-55f, 0x0p+0f};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0f, 0x1.d870dep+2f, -0x1.0c2b8cp+6f, 0x1.10bd38p+8f, -0x1.4441dap+9f, 0x1.eaed48p+9f, -0x1.dea056p+9f, 0x1.0ea6dep+9f, 0x1.3bb922p+5f, -0x1.7c03d4p+9f, 0x1.b77df6p+10f, -0x1.59dd46p+11f, 0x1.92ad5ep+11f, -0x1.7716eap+11f, 0x1.34cd94p+11f, -0x1.d21086p+10f, 0x1.27e204p+10f, -0x1.0ee014p+9f, 0x1.13ffcp+7f, 0x1.9021aap+1f, -0x1.cb9506p+3f, 0x1.f11cd6p+1f, -0x1.a3fefep-3f, -0x1.a953dap-5f, 0x1.9718bep-9f, 0x1.ad424ap-15f, -0x1.eb70cep-21f, 0x1.72006ap-31f, 0x1.0d3062p-47f, 0x0p+0f};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0f, 0x1.155158p+3f, -0x1.4fec3ap+6f, 0x1.70dec4p+8f, -0x1.e94cfep+9f, 0x1.bf0b1p+10f, -0x1.392918p+11f, 0x1.79ccf6p+11f, -0x1.ab6c9p+11f, 0x1.c47edap+11f, -0x1.af1006p+11f, 0x1.72a85ap+11f, -0x1.2846e6p+11f, 0x1.b3d87ep+10f, -0x1.1ae106p+10f, 0x1.41e16ep+9f, -0x1.46003p+8f, 0x1.0818e6p+7f, -0x1.8ef0b6p+4f, -0x1.6eb8ecp+3f, 0x1.3aba04p+3f, -0x1.588d6ep+1f, 0x1.5ca064p-3f, 0x1.72c884p-5f, -0x1.2b7b9ap-8f, -0x1.359ad6p-14f, 0x1.0cff08p-19f, -0x1.207536p-29f, -0x1.a3ad9ep-45f, -0x0p+0f};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0f, 0x1.174fb2p+3f, -0x1.5cf63cp+6f, 0x1.859702p+8f, -0x1.008e38p+10f, 0x1.c03c1cp+10f, -0x1.1e0d3p+11f, 0x1.33504ep+11f, -0x1.4498a4p+11f, 0x1.500c42p+11f, -0x1.2d6f92p+11f, 0x1.c5bd8cp+10f, -0x1.3b7208p+10f, 0x1.a4b182p+9f, -0x1.c03584p+8f, 0x1.1254d6p+7f, 0x1.be195p+2f, -0x1.6abf52p+5f, 0x1.bdfa94p+5f, -0x1.7a9c1p+5f, 0x1.86920ep+4f, -0x1.a9adfcp+2f, 0x1.133764p-1f, 0x1.191c64p-3f, -0x1.88d184p-6f, -0x1.aee4f4p-12f, 0x1.15e5eap-16f, -0x1.bc4492p-26f, -0x1.431c04p-40f, 0x0p+0f};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0f, 0x1.57dd2p+2f, -0x1.b426bap+5f, 0x1.ef50bp+7f, -0x1.4da8e6p+9f, 0x1.2d889ap+10f, -0x1.9456ecp+10f, 0x1.ca1f76p+10f, -0x1.f2eaf2p+10f, 0x1.0a60e2p+11f, -0x1.07fe76p+11f, 0x1.e2b37ep+10f, -0x1.a28fdp+10f, 0x1.5596d2p+10f, -0x1.027612p+10f, 0x1.70f45ap+9f, -0x1.edf5a6p+8f, 0x1.27b1e2p+8f, -0x1.3be692p+7f, 0x1.3b71fp+6f, -0x1.11985ep+5f, 0x1.3b5a98p+3f, -0x1.c32c18p-1f, -0x1.5d8e8ap-2f, 0x1.3b1b46p-4f, 0x1.23706ep-10f, -0x1.9c26fcp-14f, 0x1.96293ap-23f, 0x1.27428ap-36f, -0x0p+0f};
+            }
+            if constexpr (order == 11) {
+                return {0x0p+0f, 0x1.82ba18p+1f, -0x1.ee321ap+4f, 0x1.174e6p+7f, -0x1.6e81d6p+8f, 0x1.368de4p+9f, -0x1.710674p+9f, 0x1.661d22p+9f, -0x1.6833b8p+9f, 0x1.833c1cp+9f, -0x1.704d0cp+9f, 0x1.2a287cp+9f, -0x1.d79574p+8f, 0x1.7a6624p+8f, -0x1.0dddap+8f, 0x1.4f8242p+7f, -0x1.9b8d6ep+6f, 0x1.e6b9cp+5f, -0x1.d872a6p+4f, 0x1.82e4e6p+3f, -0x1.3c81bp+2f, 0x1.87117ep+0f, -0x1.f2d1dcp-6f, -0x1.327c0ep-3f, 0x1.13b8cap-5f, -0x1.094894p-13f, -0x1.78471ap-14f, 0x1.31d268p-23f, 0x1.bc3afp-36f, -0x0p+0f};
+            }
+            if constexpr (order == 12) {
+                return {0x0p+0f, 0x1.229018p+0f, -0x1.74b098p+3f, 0x1.a3d6fep+5f, -0x1.0ee9fep+7f, 0x1.b7ec28p+7f, -0x1.dcbffep+7f, 0x1.8f9512p+7f, -0x1.7421b2p+7f, 0x1.a17e1ep+7f, -0x1.8b13bap+7f, 0x1.210062p+7f, -0x1.a9798ep+6f, 0x1.62f522p+6f, -0x1.f0d146p+5f, 0x1.0b054p+5f, -0x1.2e7f82p+4f, 0x1.776b1ap+3f, -0x1.390aacp+2f, 0x1.0e68eap+0f, -0x1.1d9e68p-2f, 0x1.1e142p-5f, 0x1.626282p-3f, -0x1.00510ep-3f, 0x1.dda066p-6f, -0x1.397e42p-10f, -0x1.5e278p-13f, 0x1.93d63ep-23f, 0x1.24c486p-34f, 0x0p+0f};
+            }
+            if constexpr (order == 13) {
+                return {0x0p+0f, 0x1.2dba82p-3f, -0x1.83ba9p+0f, 0x1.bc6ce4p+2f, -0x1.2c97bep+4f, 0x1.0e0692p+5f, -0x1.5f4706p+5f, 0x1.6ea3fcp+5f, -0x1.5a777ep+5f, 0x1.424978p+5f, -0x1.3091p+5f, 0x1.23e442p+5f, -0x1.07fd36p+5f, 0x1.a8f488p+4f, -0x1.499324p+4f, 0x1.0a96d4p+4f, -0x1.8f60cep+3f, 0x1.003bccp+3f, -0x1.433efp+2f, 0x1.a65b7ep+1f, -0x1.d36032p+0f, 0x1.a4a1aep-1f, -0x1.88e9f6p-2f, 0x1.6764fap-3f, -0x1.91c36cp-5f, 0x1.07d03ep-8f, 0x1.362d3ep-11f, -0x1.92dbfep-20f, -0x1.22ff8p-30f, -0x0p+0f};
+            }
+            if constexpr (order == 14) {
+                return {0x0p+0f, 0x1.8dd6e2p-6f, -0x1.ffb4dep-3f, 0x1.1f8df8p+0f, -0x1.6eae32p+1f, 0x1.200cfep+2f, -0x1.1f2876p+2f, 0x1.90990cp+1f, -0x1.3d166cp+1f, 0x1.74d60ap+1f, -0x1.680266p+1f, 0x1.e76ba8p+0f, -0x1.60830ap+0f, 0x1.48f2a8p+0f, -0x1.e7d09ep-1f, 0x1.1252eep-1f, -0x1.6e9dp-2f, 0x1.0a88fcp-2f, -0x1.16ea72p-3f, 0x1.018afap-4f, -0x1.2fa054p-5f, 0x1.2375eep-6f, -0x1.73b10cp-8f, 0x1.1decc8p-9f, -0x1.b8713ap-11f, 0x1.732712p-14f, 0x1.5deb76p-16f, -0x1.927126p-23f, -0x1.209992p-32f, 0x0p+0f};
+            }
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0, 0x1.d99d611c0465dp-12, 0x1.0d2f985427a1ep-4, 0x1.4a539266aac6ep-1, 0x1.1fc50d04f7f08p-1, -0x1.d497750272bfap-2, 0x1.3575a87d9c163p-2, -0x1.7e644ab118887p-3, 0x1.a1785765bb949p-4, -0x1.7135a6ada8b52p-5, 0x1.d8cfdcbb16189p-7, -0x1.57e157b5bcea8p-9, -0x1.5f633204e95ap-15, 0x1.10a4589d9f87dp-13, -0x1.592264d16e622p-16, 0x1.89979784d7185p-18, -0x1.4f841169a1badp-18, 0x1.74953d3967ccep-20, -0x1.f7cb1acefcf43p-26, -0x1.c92be21aef0cap-26, -0x1.3b9a57c4ce7e8p-35, -0x1.6a58cec0fa225p-35, 0x1.4bf1eb8cd4c9cp-37, 0x1.697067f1715a1p-44, -0x1.513d790bd243p-49, -0x1.b3943c02986a6p-57, 0x1.54d330be5783ep-67, -0x1.3f6e1e631364cp-80, -0x1.d0d882f8587b5p-104, 0x0p+0};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0, 0x1.af673717274afp-9, 0x1.c7ad45d086ea5p-3, 0x1.9756cb092ee07p-1, -0x1.51916657c1834p+0, 0x1.6cc6e8f062405p-2, -0x1.8cf37d6182ca1p-4, 0x1.9a3fa2f41d495p-4, -0x1.0a50be22f2b87p-3, 0x1.df3f4f6c19d45p-4, -0x1.2d4b7e715db6cp-4, 0x1.0681e4c20b9fdp-5, -0x1.1b50d689cbed9p-7, 0x1.49acd134a254cp-11, 0x1.16651955943e4p-11, -0x1.c26d1f2c70c87p-13, 0x1.3002118e762a1p-16, 0x1.49fbecfd7d9c7p-17, -0x1.8781a4a6a5f7dp-19, 0x1.5ed0ad164acd2p-24, 0x1.da4a7558674aep-25, -0x1.7e23c7237f3f9p-29, -0x1.bd8f2cef8c9fp-35, 0x1.1c61501fa1048p-37, -0x1.c1b8b33989e02p-44, -0x1.95156f39cb33ap-52, 0x1.d1f8ddb7d0199p-60, -0x1.34635de67ce8cp-74, -0x1.c0c6d283f741ep-97, -0x0p+0};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0, 0x1.52aa167437ed4p-6, 0x1.2f386450cd36p-1, -0x1.92da3e0f4795fp-2, -0x1.010e6c23362c3p+1, 0x1.ba5e5707337cfp+1, -0x1.6efa1a351e689p+1, 0x1.e2efff792ca6dp+0, -0x1.e9e84815ce29ap-1, 0x1.3e7bcfc83dd35p-2, -0x1.3f21e5e83db9bp-6, -0x1.00e091b8310d8p-5, 0x1.93252ea5d40eep-8, 0x1.0cb53bda124f5p-7, -0x1.6ecc6596fdeb9p-8, 0x1.1da3c88de4594p-10, 0x1.0f705c9109b89p-12, -0x1.687f176415b5ap-13, 0x1.03bf749271ea1p-15, -0x1.0a570c997b8f7p-20, -0x1.b60c856b75c7p-22, 0x1.2f36c8024d478p-24, -0x1.ab6b4d2a0c9ebp-30, -0x1.b77dbd4d624bbp-33, 0x1.02e06a0b52529p-39, 0x1.f900db818405cp-46, -0x1.5cc6aba4a367p-54, 0x1.79a9be1badafp-67, 0x1.12cb1c6610cf6p-88, -0x0p+0};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0, 0x1.bde47de89537fp-4, 0x1.ff6e39e05bc19p-1, -0x1.0edf7812c7e6fp+2, 0x1.788eafbfef57p+2, -0x1.0b9e58d049e2bp+2, 0x1.57d72a54d9b7ep+1, -0x1.5aec59993d64cp+1, 0x1.66be004fbc258p+1, -0x1.257b730e2148dp+1, 0x1.61e6a248fa766p+0, -0x1.1d66170848573p-1, 0x1.7634ae9385e7dp-4, 0x1.aae5eb36cf234p-5, -0x1.66a2dd81189a5p-5, 0x1.9ee5c38dff3c6p-7, 0x1.cee452b55c63p-12, -0x1.7d0e63753adf8p-10, 0x1.95a9bb14ccec1p-12, -0x1.ac68b8496deeap-17, -0x1.4a3e531dccd5ap-17, 0x1.45a5b2adacfeep-20, -0x1.a0585e72874e5p-28, -0x1.4a4aaf36fdaecp-28, 0x1.818dc3c36642cp-34, 0x1.bc8ec635290e4p-41, -0x1.1c50f4adb4d49p-48, 0x1.541ee5efeba28p-61, 0x1.eef3c669427bap-82, -0x0p+0};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0, 0x1.da9efb84cd102p-2, -0x1.0a963523c781p-2, -0x1.6ead78b2a7f87p+2, 0x1.1fb0b7ee7fe9bp+4, -0x1.a26b20f9bdefp+4, 0x1.5a362701692b6p+4, -0x1.c3b93743ed5e2p+2, -0x1.0393f54066e2bp+3, 0x1.ce0e335b9b5dp+3, -0x1.3371f4378fc26p+3, 0x1.04744c732a897p-2, 0x1.5d5bbaac2d3ddp+2, -0x1.56903abc9d373p+2, 0x1.4f367450bb029p+1, -0x1.16f1bf1e47dd8p-1, -0x1.0ca6089fc41eep-3, 0x1.fd1e6437298dfp-4, -0x1.127569c6d3d2p-5, 0x1.031ce43d6f2aap-9, 0x1.dbc5a12350174p-11, -0x1.6e57586c99db3p-13, 0x1.338c12c9a95b4p-19, 0x1.ec833bdc8d6abp-21, -0x1.31ee1e222a83p-26, -0x1.068cce25031dp-32, 0x1.ab486d191520ep-40, -0x1.971ac61147c4cp-52, -0x1.28365b5992262p-71, -0x0p+0};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0, 0x1.8a28bf1f4bafp+0, -0x1.0b8ecb513e671p+3, 0x1.301d17ac5e1c7p+4, -0x1.80a5fd5ebbea5p+4, 0x1.4a39e3e1048d6p+4, -0x1.1148278e9d9a1p+4, 0x1.18e244d79a033p+4, -0x1.3908669ba0779p+4, 0x1.80446c71adb15p+4, -0x1.0a40794798e41p+5, 0x1.52509dd04c4f7p+5, -0x1.4b468531c5b1ap+5, 0x1.c80f1430e334ap+4, -0x1.82ded3c89e7eap+3, 0x1.7610a167089f2p+0, 0x1.b0a89a8818c06p+0, -0x1.2b516da5d081p+0, 0x1.488189c0e6323p-2, -0x1.16dd91fce8d2fp-6, -0x1.957d5757f4d58p-7, 0x1.613bcf2c2fc6ap-9, -0x1.0adbc024da551p-14, -0x1.44905597a8908p-16, 0x1.238bd55115864p-21, 0x1.0b863bc593a1dp-27, -0x1.2dac52b5d35bcp-34, 0x1.a8ab5a61388b2p-46, 0x1.34fcf88bcfb4p-64, 0x0p+0};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0, 0x1.e156f58145abap+1, -0x1.d9350b2238c2cp+4, 0x1.b03e3957ecd6ap+6, -0x1.f51dfa789d879p+7, 0x1.b1d9ee3321d94p+8, -0x1.3c90b7e3ca1dcp+9, 0x1.a1025f9df5666p+9, -0x1.ee82dbab6ab1p+9, 0x1.fcf169933904cp+9, -0x1.beee0dc0c8ddbp+9, 0x1.545f49e00f496p+9, -0x1.c39ca355bd5d3p+8, 0x1.d17e6e268802dp+7, -0x1.8d05e2b81cf72p+5, -0x1.a57ddae4deceep+5, 0x1.065bfb9cfed1p+6, -0x1.1a783beefce88p+5, 0x1.2e9f2c1581a69p+3, -0x1.3cad9a2427052p-2, -0x1.1b4b3a7aa70e8p-1, 0x1.15a31469a9cep-3, -0x1.5c66a63c93474p-8, -0x1.5db560cc8a8d9p-10, 0x1.c57be52a95f9ap-15, 0x1.c9738067c590ap-21, -0x1.63f652c472259p-27, 0x1.769767db4423bp-38, 0x1.108b386e39e95p-55, 0x0p+0};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0, 0x1.d870debcc05c4p+2, -0x1.0c2b8b0b28194p+6, 0x1.10bd374d63551p+8, -0x1.4441daef321d4p+9, 0x1.eaed48222cc9cp+9, -0x1.dea055aad4ecbp+9, 0x1.0ea6de87556eap+9, 0x1.3bb921604519dp+5, -0x1.7c03d4dcf5514p+9, 0x1.b77df6c77230cp+10, -0x1.59dd45c186fb1p+11, 0x1.92ad5ee85458dp+11, -0x1.7716e9b298972p+11, 0x1.34cd942cd473ap+11, -0x1.d2108687fa36fp+10, 0x1.27e2041912518p+10, -0x1.0ee0131c1b04fp+9, 0x1.13ffc016f56cap+7, 0x1.9021a9dd4e12bp+1, -0x1.cb9505a70965bp+3, 0x1.f11cd618c3359p+1, -0x1.a3fefe1a942d4p-3, -0x1.a953da883746ep-5, 0x1.9718bee3af729p-9, 0x1.ad4249f39958ep-15, -0x1.eb70cd1aa4051p-21, 0x1.72006a07a097fp-31, 0x1.0d30627e6a2adp-47, 0x0p+0};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0, 0x1.155158ac6ea98p+3, -0x1.4fec3a6a32c1fp+6, 0x1.70dec41eaf97dp+8, -0x1.e94cfecb1efa1p+9, 0x1.bf0b100d34d04p+10, -0x1.39291803fcf48p+11, 0x1.79ccf50afb46ep+11, -0x1.ab6c90991611bp+11, 0x1.c47ed9a17b9cdp+11, -0x1.af1005783c9c1p+11, 0x1.72a859cabb472p+11, -0x1.2846e6b9b14f5p+11, 0x1.b3d87dff6a955p+10, -0x1.1ae10527ae494p+10, 0x1.41e16e9c43533p+9, -0x1.460030c5bf207p+8, 0x1.0818e6dd9acdcp+7, -0x1.8ef0b66c7662cp+4, -0x1.6eb8ec2d2fcfp+3, 0x1.3aba0303f01c4p+3, -0x1.588d6d239648ep+1, 0x1.5ca063a2897a3p-3, 0x1.72c884e06d39ap-5, -0x1.2b7b99da7239bp-8, -0x1.359ad5ec914c6p-14, 0x1.0cff089d4d593p-19, -0x1.207535755ab2fp-29, -0x1.a3ad9d559345cp-45, -0x0p+0};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0, 0x1.174fb1d673064p+3, -0x1.5cf63b4072a08p+6, 0x1.859702b93092p+8, -0x1.008e38c64d405p+10, 0x1.c03c1b8df613fp+10, -0x1.1e0d30516cd0dp+11, 0x1.33504e2e62ab9p+11, -0x1.4498a39b45dd3p+11, 0x1.500c422b7e4d6p+11, -0x1.2d6f916f2f064p+11, 0x1.c5bd8b8beccdbp+10, -0x1.3b7208dc18507p+10, 0x1.a4b1819107c72p+9, -0x1.c03583e492981p+8, 0x1.1254d5dd1a3c8p+7, 0x1.be19509979c25p+2, -0x1.6abf524121ea4p+5, 0x1.bdfa9494723d3p+5, -0x1.7a9c102bdb495p+5, 0x1.86920d3d07ed2p+4, -0x1.a9adfb25c4f27p+2, 0x1.1337641b89dbcp-1, 0x1.191c64622c1b1p-3, -0x1.88d18423866c2p-6, -0x1.aee4f466bb969p-12, 0x1.15e5e9747fe1cp-16, -0x1.bc4491eee0fddp-26, -0x1.431c03e754cd9p-40, 0x0p+0};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0, 0x1.57dd202e5e84bp+2, -0x1.b426b94987909p+5, 0x1.ef50af36bc94ap+7, -0x1.4da8e644667e7p+9, 0x1.2d889ab089911p+10, -0x1.9456ec86efc74p+10, 0x1.ca1f75d29c178p+10, -0x1.f2eaf24b48be9p+10, 0x1.0a60e2fdcea78p+11, -0x1.07fe75c2d8539p+11, 0x1.e2b37ed5f4462p+10, -0x1.a28fcff6e684bp+10, 0x1.5596d2be7c1f8p+10, -0x1.02761175eccb5p+10, 0x1.70f45a3e9b6c8p+9, -0x1.edf5a5b354e13p+8, 0x1.27b1e13298bb4p+8, -0x1.3be69243ef2c3p+7, 0x1.3b71f0120f2a4p+6, -0x1.11985d9404f45p+5, 0x1.3b5a9762f053bp+3, -0x1.c32c18767db72p-1, -0x1.5d8e89b8ba2f4p-2, 0x1.3b1b46a97c2fbp-4, 0x1.23706d03f6f74p-10, -0x1.9c26fc84f3ff6p-14, 0x1.962939a138e2bp-23, 0x1.27428a5934f9ep-36, -0x0p+0};
+            }
+            if constexpr (order == 11) {
+                return {0x0p+0, 0x1.82ba18a281555p+1, -0x1.ee321ac782e81p+4, 0x1.174e5f65a44a6p+7, -0x1.6e81d57c4c979p+8, 0x1.368de3361fae5p+9, -0x1.7106731d7c871p+9, 0x1.661d220cefa1p+9, -0x1.6833b778e773bp+9, 0x1.833c1b7a24cc4p+9, -0x1.704d0cf5b403fp+9, 0x1.2a287b4a8744cp+9, -0x1.d795731af32d5p+8, 0x1.7a6623bbe9af8p+8, -0x1.0ddd9fa1ad022p+8, 0x1.4f824182bb441p+7, -0x1.9b8d6efd833c4p+6, 0x1.e6b9bfc912a61p+5, -0x1.d872a65489bc7p+4, 0x1.82e4e50171641p+3, -0x1.3c81b080d7c59p+2, 0x1.87117e04fd822p+0, -0x1.f2d1dbd395099p-6, -0x1.327c0d249414p-3, 0x1.13b8c9585145fp-5, -0x1.094893076dab2p-13, -0x1.784719262e6dap-14, 0x1.31d26875ab45fp-23, 0x1.bc3aef2e9698bp-36, -0x0p+0};
+            }
+            if constexpr (order == 12) {
+                return {0x0p+0, 0x1.229017de89889p+0, -0x1.74b098d7b2942p+3, 0x1.a3d6fe58853c2p+5, -0x1.0ee9fe2c639a7p+7, 0x1.b7ec28edec454p+7, -0x1.dcbffedb3a508p+7, 0x1.8f9512e48d1c4p+7, -0x1.7421b1a880459p+7, 0x1.a17e1d21e73d2p+7, -0x1.8b13badbca1d9p+7, 0x1.210062e92f489p+7, -0x1.a9798d44da6c2p+6, 0x1.62f521d1972a8p+6, -0x1.f0d14679f69cp+5, 0x1.0b0540b21cf09p+5, -0x1.2e7f81d72375p+4, 0x1.776b19bc1de7bp+3, -0x1.390aaca35a349p+2, 0x1.0e68e94457017p+0, -0x1.1d9e671612a46p-2, 0x1.1e141f6f8381bp-5, 0x1.626281f06a565p-3, -0x1.00510e27c6afap-3, 0x1.dda065aa933f4p-6, -0x1.397e42b4cc1c2p-10, -0x1.5e2780fee3a22p-13, 0x1.93d63eaebefb8p-23, 0x1.24c485651202dp-34, 0x0p+0};
+            }
+            if constexpr (order == 13) {
+                return {0x0p+0, 0x1.2dba81606cdf4p-3, -0x1.83ba9062dc10bp+0, 0x1.bc6ce42e9d3a2p+2, -0x1.2c97bd817af95p+4, 0x1.0e06914d93155p+5, -0x1.5f4706680d4aep+5, 0x1.6ea3fbf492341p+5, -0x1.5a777ed4931f2p+5, 0x1.424978021982dp+5, -0x1.3090ff3d7fed6p+5, 0x1.23e4419ddb641p+5, -0x1.07fd356f7673cp+5, 0x1.a8f488a3b6e4bp+4, -0x1.49932384ed8b5p+4, 0x1.0a96d421140ffp+4, -0x1.8f60cd9c05603p+3, 0x1.003bcbf26a5dbp+3, -0x1.433ef046d9ed1p+2, 0x1.a65b7dff93521p+1, -0x1.d36032adf2dbdp+0, 0x1.a4a1ad470bd0ep-1, -0x1.88e9f63513cep-2, 0x1.6764f965c9511p-3, -0x1.91c36b23af1d8p-5, 0x1.07d03d7a1adc2p-8, 0x1.362d3e37ff6cdp-11, -0x1.92dbfdbfa8198p-20, -0x1.22ff804507dbep-30, -0x0p+0};
+            }
+            if constexpr (order == 14) {
+                return {0x0p+0, 0x1.8dd6e1684e11dp-6, -0x1.ffb4de00653d3p-3, 0x1.1f8df89dea984p+0, -0x1.6eae32a3a7907p+1, 0x1.200cfdab0a888p+2, -0x1.1f287662480abp+2, 0x1.90990b7ee9dd2p+1, -0x1.3d166b62b6086p+1, 0x1.74d60ae1a8cebp+1, -0x1.68026579c2214p+1, 0x1.e76ba8ae988d5p+0, -0x1.60830949d4c83p+0, 0x1.48f2a8ad7050dp+0, -0x1.e7d09d1d5c76ep-1, 0x1.1252ee85de925p-1, -0x1.6e9d007e3ce51p-2, 0x1.0a88fbec92db2p-2, -0x1.16ea71f276b01p-3, 0x1.018afa9348368p-4, -0x1.2fa053de7510ep-5, 0x1.2375ee2696f87p-6, -0x1.73b10c938e4b6p-8, 0x1.1decc8370b235p-9, -0x1.b8713a4dd74a9p-11, 0x1.732711f764c01p-14, 0x1.5deb76c540b6cp-16, -0x1.9271259f10414p-23, -0x1.2099915b93354p-32, 0x0p+0};
+            }
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0L, 0xe.cceb08e0232ebfep-15L, 0x8.697cc2a13d0ee1p-7L, 0xa.529c93355636f38p-4L, 0x8.fe286827bf83d25p-4L, -0xe.a4bba81395fd148p-5L, 0x9.abad43ece0b19efp-5L, -0xb.f3225588c443427p-6L, 0xd.0bc2bb2ddca46a9p-7L, -0xb.89ad356d45a90abp-8L, 0xe.c67ee5d8b0c44cdp-10L, -0xa.bf0abdade753fd6p-12L, -0xa.fb1990274acfe19p-18L, 0x8.8522c4ecfc3eb6ep-16L, -0xa.c913268b7310da9p-19L, 0xc.4cbcbc26b8c299cp-21L, -0xa.7c208b4d0dd68c5p-21L, 0xb.a4a9e9cb3e66c66p-23L, -0xf.be58d677e7a1ad2p-29L, -0xe.495f10d77864d6p-29L, -0x9.dcd2be2673f3d47p-38L, -0xb.52c67607d112652p-38L, 0xa.5f8f5c66a64e114p-40L, 0xb.4b833f8b8ad0a0ap-47L, -0xa.89ebc85e9217eeap-52L, -0xd.9ca1e014c35331bp-60L, 0xa.a69985f2bc1edb9p-70L, -0x9.fb70f3189b26326p-83L, -0xe.86c417c2c3da4c7p-107L, 0x0p+0L};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0L, 0xd.7b39b8b93a579b8p-12L, 0xe.3d6a2e84375262fp-6L, 0xc.bab6584977037b5p-4L, -0xa.8c8b32be0c1a23fp-3L, 0xb.663747831202959p-5L, -0xc.679beb0c165058cp-7L, 0xc.d1fd17a0ea4a983p-7L, -0x8.5285f11795c36ecp-6L, 0xe.f9fa7b60cea28cap-7L, -0x9.6a5bf38aedb5fc2p-7L, 0x8.340f26105cfe721p-8L, -0x8.da86b44e5f6c6f9p-10L, 0xa.4d6689a512a5d01p-14L, 0x8.b328caaca1f1c8cp-14L, -0xe.1368f9638643783p-16L, 0x9.80108c73b15088ep-19L, 0xa.4fdf67ebece365dp-20L, -0xc.3c0d25352fbe46dp-22L, 0xa.f68568b2566925p-27L, 0xe.d253aac33a56ee8p-28L, -0xb.f11e391bf9fc9acp-32L, -0xd.ec79677c64f81e9p-38L, 0x8.e30a80fd082403ap-40L, -0xe.0dc599cc4f0122fp-47L, -0xc.a8ab79ce599d1e7p-55L, 0xe.8fc6edbe80cc4a8p-63L, -0x9.a31aef33e745dcdp-77L, -0xe.0636941fba0f2ecp-100L, -0x0p+0L};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0L, 0xa.9550b3a1bf69d4cp-9L, 0x9.79c3228669b01a3p-4L, -0xc.96d1f07a3cafa97p-5L, -0x8.08736119b1617adp-2L, 0xd.d2f2b8399be77e4p-2L, -0xb.77d0d1a8f344a12p-2L, 0xf.177ffbc96536692p-3L, -0xf.4f4240ae714d2acp-4L, 0x9.f3de7e41ee9a787p-5L, -0x9.f90f2f41edcdbb5p-9L, -0x8.07048dc1886be21p-8L, 0xc.9929752ea076dc3p-11L, 0x8.65a9ded0927a627p-10L, -0xb.76632cb7ef5cbbcp-11L, 0x8.ed1e446f22c9d07p-13L, 0x8.7b82e4884dc45e4p-15L, -0xb.43f8bb20adad0a1p-16L, 0x8.1dfba4938f506e5p-18L, -0x8.52b864cbdc7b5dap-23L, -0xd.b0642b5bae37c7cp-25L, 0x9.79b640126a3c29ep-27L, -0xd.5b5a695064f587ep-33L, -0xd.bbedea6b125d8c1p-36L, 0x8.1703505a92944ccp-42L, 0xf.c806dc0c202de26p-49L, -0xa.e6355d251b37dfep-57L, 0xb.cd4df0dd6d782f3p-70L, 0x8.9658e330867ad2ep-91L, -0x0p+0L};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0L, 0xd.ef23ef44a9bf7e6p-7L, 0xf.fb71cf02de0cb05p-4L, -0x8.76fbc0963f37be8p-1L, 0xb.c4757dff7ab7e6ep-1L, -0x8.5cf2c6824f158e6p-1L, 0xa.beb952a6cdbec82p-2L, -0xa.d762ccc9eb2601dp-2L, 0xb.35f0027de12c188p-2L, -0x9.2bdb98710a46a7ap-2L, 0xb.0f351247d3b2edap-3L, -0x8.eb30b84242b9b67p-4L, 0xb.b1a5749c2f3e942p-7L, 0xd.572f59b67919cdep-8L, -0xb.3516ec08c4d2b92p-8L, 0xc.f72e1c6ff9e2d6dp-10L, 0xe.772295aae3180b3p-15L, -0xb.e8731ba9d6fc085p-13L, 0xc.ad4dd8a66760405p-15L, -0xd.6345c24b6f75385p-20L, -0xa.51f298ee66ad3e4p-20L, 0xa.2d2d956d67f7238p-23L, -0xd.02c2f3943a728d1p-31L, -0xa.525579b7ed76162p-31L, 0xc.0c6e1e1b32163bep-37L, 0xd.e47631a948722aep-44L, -0x8.e287a56da6a461dp-51L, 0xa.a0f72f7f5d13f61p-64L, 0xf.779e334a13dd19fp-85L, -0x0p+0L};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0L, 0xe.d4f7dc266880dc5p-5L, -0x8.54b1a91e3c07cabp-5L, -0xb.756bc5953fc385dp-1L, 0x8.fd85bf73ff4da1p+1L, -0xd.135907cdef77f86p+1L, 0xa.d1b1380b495aeaap+1L, -0xe.1dc9ba1f6af0fa5p-1L, -0x8.1c9faa033715437p+0L, 0xe.70719adcdae7ec4p+0L, -0x9.9b8fa1bc7e12e6ep+0L, 0x8.23a26399544b84bp-5L, 0xa.eaddd56169ee9cdp-1L, -0xa.b481d5e4e9b9684p-1L, 0xa.79b3a285d814a56p-2L, -0x8.b78df8f23eebd9ap-4L, -0x8.653044fe20f733p-6L, 0xf.e8f321b94c6f489p-7L, -0x8.93ab4e369e900fp-8L, 0x8.18e721eb7954d94p-12L, 0xe.de2d091a80b9ee2p-14L, -0xb.72bac364ced9545p-16L, 0x9.9c60964d4ada3f3p-22L, 0xf.6419dee46b558e8p-24L, -0x9.8f70f1115417f37p-29L, -0x8.3466712818e830ep-35L, 0xd.5a4368c8a906c55p-43L, -0xc.b8d6308a3e25ebp-55L, -0x9.41b2dacc9130e5dp-74L, -0x0p+0L};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0L, 0xc.5145f8fa5d7812bp-3L, -0x8.5c765a89f338723p+0L, 0x9.80e8bd62f0e36d7p+1L, -0xc.052feaf5df5265fp+1L, 0xa.51cf1f08246b12ap+1L, -0x8.8a413c74ecd0982p+1L, 0x8.c71226bcd019464p+1L, -0x9.c84334dd03bcb23p+1L, 0xc.0223638d6d8a444p+1L, -0x8.5203ca3cc7208f6p+2L, 0xa.9284ee82627b576p+2L, -0xa.5a34298e2d8cfacp+2L, 0xe.4078a18719a503cp+1L, -0xc.16f69e44f3f4fd2p+0L, 0xb.b0850b3844f8cadp-3L, 0xd.8544d440c6033bfp-3L, -0x9.5a8b6d2e8407dd6p-3L, 0xa.440c4e0731919f2p-5L, -0x8.b6ec8fe746979d1p-9L, -0xc.abeababfa6ac0f1p-10L, 0xb.09de79617e3529fp-12L, -0x8.56de0126d2a8a97p-17L, -0xa.2482acbd44843d2p-19L, 0x9.1c5eaa88ac31dcbp-24L, 0x8.5c31de2c9d0ea8bp-30L, -0x9.6d6295ae9addc71p-37L, 0xd.455ad309c458ed8p-49L, 0x9.a7e7c45e7d9feeap-67L, 0x0p+0L};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0L, 0xf.0ab7ac0a2d5d3e8p-2L, -0xe.c9a85911c615c82p+1L, 0xd.81f1cabf66b5001p+3L, -0xf.a8efd3c4ec3c419p+4L, 0xd.8ecf71990eca11bp+5L, -0x9.e485bf1e50edc17p+6L, 0xd.0812fcefab32f7bp+6L, -0xf.7416dd5b55881cap+6L, 0xf.e78b4c99c8261c4p+6L, -0xd.f7706e0646ed8ddp+6L, 0xa.a2fa4f007a4af9bp+6L, -0xe.1ce51aadeae94b8p+5L, 0xe.8bf371344016517p+4L, -0xc.682f15c0e7b935cp+2L, -0xd.2beed726f676c5ap+2L, 0x8.32dfdce7f6881c4p+3L, -0x8.d3c1df77e743d81p+2L, 0x9.74f960ac0d34b75p+0L, -0x9.e56cd1213828f04p-5L, -0x8.da59d3d53874134p-4L, 0x8.ad18a34d4e700e2p-6L, -0xa.e33531e49a3a34ep-11L, -0xa.edab0664546ca1p-13L, 0xe.2bdf2954afcd1ep-18L, 0xe.4b9c033e2c84ec9p-24L, -0xb.1fb29623912c4c5p-30L, 0xb.b4bb3eda211db22p-41L, 0x8.8459c371cf4ab4bp-58L, 0x0p+0L};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0L, 0xe.c386f5e602e22c6p-1L, -0x8.615c585940c9ee7p+3L, 0x8.85e9ba6b1aa85ccp+5L, -0xa.220ed77990ea00bp+6L, 0xf.576a4111664dc93p+6L, -0xe.f502ad56a76577ep+6L, 0x8.7536f43aab75351p+6L, 0x9.ddc90b0228ce8d7p+2L, -0xb.e01ea6e7aa8a396p+6L, 0xd.bbefb63b9185cdp+7L, -0xa.ceea2e0c37d88e3p+8L, 0xc.956af742a2c67bbp+8L, -0xb.b8b74d94c4b8e53p+8L, 0x9.a66ca166a39d2d4p+8L, -0xe.9084343fd1b7644p+7L, 0x9.3f1020c8928bd55p+7L, -0x8.770098e0d827732p+6L, 0x8.9ffe00b7ab651d2p+4L, 0xc.810d4eea709578cp-2L, -0xe.5ca82d384b2dbfdp+0L, 0xf.88e6b0c619ac534p-2L, -0xd.1ff7f0d4a16a0e5p-6L, -0xd.4a9ed441ba370f6p-8L, 0xc.b8c5f71d7b945cfp-12L, 0xd.6a124f9ccac6c82p-18L, -0xf.5b8668d520288fbp-24L, 0xb.9003503d04bfb0cp-34L, 0x8.698313f351569a4p-50L, 0x0p+0L};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0L, 0x8.aa8ac563754c257p+0L, -0xa.7f61d351960f794p+3L, 0xb.86f620f57cbe932p+5L, -0xf.4a67f658f7d0a3cp+6L, 0xd.f8588069a68203p+7L, -0x9.c948c01fe7a3daep+8L, 0xb.ce67a857da36deap+8L, -0xd.5b6484c8b08d94p+8L, 0xe.23f6cd0bdce6402p+8L, -0xd.78802bc1e4e0454p+8L, 0xb.9542ce55da38fbfp+8L, -0x9.423735cd8a7a408p+8L, 0xd.9ec3effb54aa43bp+7L, -0x8.d708293d724a1cp+7L, 0xa.0f0b74e21a99604p+6L, -0xa.3001862df903727p+5L, 0x8.40c736ecd66e3b7p+4L, -0xc.7785b363b31632ap+1L, -0xb.75c761697e78222p+0L, 0x9.d5d0181f80e2122p+0L, -0xa.c46b691cb246e7cp-2L, 0xa.e5031d144bd1a3cp-6L, 0xb.9644270369ccd47p-8L, -0x9.5bdcced391cd468p-11L, -0x9.acd6af648a62d24p-17L, 0x8.67f844ea6ac9781p-22L, -0x9.03a9abaad597738p-32L, -0xd.1d6ceaac9a2dc82p-48L, -0x0p+0L};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0L, 0x8.ba7d8eb39831c18p+0L, -0xa.e7b1da03950427fp+3L, 0xc.2cb815c9848fe3fp+5L, -0x8.0471c6326a024f5p+7L, 0xe.01e0dc6fb09f8cp+7L, -0x8.f069828b6686adbp+8L, 0x9.9a827173155c815p+8L, -0xa.24c51cda2ee968bp+8L, 0xa.8062115bf26b28ap+8L, -0x9.6b7c8b797831eb6p+8L, 0xe.2dec5c5f666d9f8p+7L, -0x9.db9046e0c283a87p+7L, 0xd.258c0c883e39073p+6L, -0xe.01ac1f2494c092fp+5L, 0x8.92a6aee8d1e432cp+4L, 0xd.f0ca84cbce12938p-1L, -0xb.55fa92090f522ecp+2L, 0xd.efd4a4a391e9b21p+2L, -0xb.d4e0815eda4a88ap+2L, 0xc.349069e83f691d5p+1L, -0xd.4d6fd92e2793a35p-1L, 0x8.99bb20dc4eddf8ap-4L, 0x8.c8e3231160d8992p-6L, -0xc.468c211c336121fp-9L, -0xd.7727a335dcb4b2ep-15L, 0x8.af2f4ba3ff0ddeep-19L, -0xd.e2248f7707ee606p-29L, -0xa.18e01f3aa66c51bp-43L, 0x0p+0L};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0L, 0xa.bee90172f4255c3p-1L, -0xd.a135ca4c3c846a5p+2L, 0xf.7a8579b5e4a4f6ap+4L, -0xa.6d47322333f3562p+6L, 0x9.6c44d5844c887bdp+7L, -0xc.a2b764377e3a1ebp+7L, 0xe.50fbae94e0bc253p+7L, -0xf.9757925a45f487cp+7L, 0x8.530717ee753bcd5p+8L, -0x8.3ff3ae16c29c979p+8L, 0xf.159bf6afa230cc6p+7L, -0xd.147e7fb73425ae6p+7L, 0xa.acb695f3e0fc1c3p+7L, -0x8.13b08baf665a54p+7L, 0xb.87a2d1f4db643efp+6L, -0xf.6fad2d9aa709453p+5L, 0x9.3d8f0994c5d9f7bp+5L, -0x9.df34921f79618f8p+4L, 0x9.db8f809079523d6p+3L, -0x8.8cc2eca027a29bcp+2L, 0x9.dad4bb17829d702p+0L, -0xe.1960c3b3edb91b1p-4L, -0xa.ec744dc5d17a352p-5L, 0x9.d8da354be17d4f6p-7L, 0x9.1b83681fb7ba338p-13L, -0xc.e137e4279ffaf08p-17L, 0xc.b149cd09c7159bbp-26L, 0x9.3a1452c9a7cedecp-39L, -0x0p+0L};
+            }
+            if constexpr (order == 11) {
+                return {0x0p+0L, 0xc.15d0c5140aaa4eep-2L, -0xf.7190d63c174081fp+1L, 0x8.ba72fb2d2252c3fp+4L, -0xb.740eabe264bca0cp+5L, 0x9.b46f19b0fd72575p+6L, -0xb.883398ebe4385ep+6L, 0xb.30e910677d07ffp+6L, -0xb.419dbbc73b9d5a1p+6L, 0xc.19e0dbd12662221p+6L, -0xb.826867ada01fb9cp+6L, 0x9.5143da543a25f3ap+6L, -0xe.bcab98d7996a714p+5L, 0xb.d3311ddf4d7bdfbp+5L, -0x8.6eecfd0d6810f0bp+5L, 0xa.7c120c15da204bcp+4L, -0xc.dc6b77ec19e1f99p+3L, 0xf.35cdfe48953061cp+2L, -0xe.c39532a44de361dp+1L, 0xc.1727280b8b20591p+0L, -0x9.e40d8406be2c4fap-1L, 0xc.388bf027ec112cbp-3L, -0xf.968ede9ca84c64dp-9L, -0x9.93e06924a09fd14p-6L, 0x8.9dc64ac28a2fbc2p-8L, -0x8.4a44983b6d59171p-16L, -0xb.c238c931736ccdbp-17L, 0x9.8e9343ad5a2f5d8p-26L, 0xd.e1d77974b4c54b1p-39L, -0x0p+0L};
+            }
+            if constexpr (order == 12) {
+                return {0x0p+0L, 0x9.1480bef44c4469ep-3L, -0xb.a584c6bd94a1187p+0L, 0xd.1eb7f2c429e0f2ep+2L, -0x8.774ff1631cd3a64p+4L, 0xd.bf61476f622a169p+4L, -0xe.e5fff6d9d283fd3p+4L, 0xc.7ca8972468e2375p+4L, -0xb.a10d8d44022caeap+4L, 0xd.0bf0e90f39e8d94p+4L, -0xc.589dd6de50ec435p+4L, 0x9.080317497a44b68p+4L, -0xd.4bcc6a26d36101bp+3L, 0xb.17a90e8cb9542f6p+3L, -0xf.868a33cfb4e032cp+2L, 0x8.582a0590e784928p+2L, -0x9.73fc0eb91ba83cbp+1L, 0xb.bb58cde0ef3d615p+0L, -0x9.c855651ad1a4682p-1L, 0x8.73474a22b80bb4fp-3L, -0x8.ecf338b09522ep-5L, 0x8.f0a0fb7c1c0d8ddp-8L, 0xb.13140f8352b2905p-6L, -0x8.0288713e357cfe6p-6L, 0xe.ed032d5499f9d13p-9L, -0x9.cbf215a660e12a2p-13L, -0xa.f13c07f71d1127bp-16L, 0xc.9eb1f575f7dbcbbp-26L, 0x9.26242b289016945p-37L, 0x0p+0L};
+            }
+            if constexpr (order == 13) {
+                return {0x0p+0L, 0x9.6dd40b0366fa267p-6L, -0xc.1dd48316e0854aap-3L, 0xd.e3672174e9d1088p-1L, -0x9.64bdec0bd7ca5b2p+1L, 0x8.70348a6c98aa9bbp+2L, -0xa.fa3833406a56d39p+2L, 0xb.751fdfa491a058dp+2L, -0xa.d3bbf6a498f90bp+2L, 0xa.124bc010cc1696ap+2L, -0x9.8487f9ebff6b313p+2L, 0x9.1f220ceedb2076ep+2L, -0x8.3fe9ab7bb39dc96p+2L, 0xd.47a4451db725977p+1L, -0xa.4c991c276c5a664p+1L, 0x8.54b6a108a07f661p+1L, -0xc.7b066ce02b0141p+0L, 0x8.01de5f9352ed819p+0L, -0xa.19f78236cf689c9p-1L, 0xd.32dbeffc9a904b7p-2L, -0xe.9b01956f96deb78p-3L, 0xd.250d6a385e86ee4p-4L, -0xc.474fb1a89e70305p-5L, 0xb.3b27cb2e4a88b76p-6L, -0xc.8e1b591d78ebf4ap-8L, 0x8.3e81ebd0d6e0c17p-11L, 0x9.b169f1bffb66918p-14L, -0xc.96dfedfd40cbd7ep-23L, -0x9.17fc02283edf3c4p-33L, -0x0p+0L};
+            }
+            if constexpr (order == 14) {
+                return {0x0p+0L, 0xc.6eb70b42708eae9p-9L, -0xf.fda6f00329e9b71p-6L, 0x8.fc6fc4ef54c1db5p-3L, -0xb.7571951d3c8341p-2L, 0x9.0067ed5854443d7p-1L, -0x8.f943b3124055b9cp-1L, 0xc.84c85bf74ee8fcap-2L, -0x9.e8b35b15b042f15p-2L, 0xb.a6b0570d4675539p-2L, -0xb.40132bce1109dcp-2L, 0xf.3b5d4574c46a8f3p-3L, -0xb.04184a4ea6416d5p-3L, 0xa.4795456b82864acp-3L, -0xf.3e84e8eae3b6c57p-4L, 0x8.9297742ef492803p-4L, -0xb.74e803f1e728564p-5L, 0x8.5447df6496d92bp-5L, -0x8.b7538f93b58072dp-6L, 0x8.0c57d49a41b3dccp-7L, -0x9.7d029ef3a886eafp-8L, 0x9.1baf7134b7c3668p-9L, -0xb.9d88649c725b305p-11L, 0x8.ef6641b8591aa6cp-12L, -0xd.c389d26eba54b8ep-14L, 0xb.99388fbb2600ba3p-17L, 0xa.ef5bb62a05b60a1p-19L, -0xc.93892cf88209c7cp-26L, -0x9.04cc8adc99aa115p-35L, 0x0p+0L};
+            }
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            if constexpr (order == 0) {
+                return {0x0p+0Q, 0x1.d99d611c0465d7fca8709213621p-12Q, 0x1.0d2f985427a1dc1f62afa99d998cp-4Q, 0x1.4a539266aac6de6ff0ee136fe6bp-1Q, 0x1.1fc50d04f7f07a49e55f06b78357p-1Q, -0x1.d497750272bfa28f3f1990b740d3p-2Q, 0x1.3575a87d9c1633de9f0ee95125b3p-2Q, -0x1.7e644ab11888684db8a7b8d90491p-3Q, 0x1.a1785765bb948d52e0838b0df1ap-4Q, -0x1.7135a6ada8b52155f89869cf22d5p-5Q, 0x1.d8cfdcbb1618899a1617de65e07ep-7Q, -0x1.57e157b5bcea7fac037e4b9b62bp-9Q, -0x1.5f633204e959fc32c151ba98708bp-15Q, 0x1.10a4589d9f87d6dc51e36837ed03p-13Q, -0x1.592264d16e621b5275bdd9d12d4dp-16Q, 0x1.89979784d7185338d2badb26cadp-18Q, -0x1.4f841169a1bad189406e2832bc2dp-18Q, 0x1.74953d3967ccd8cc322dbf25294ep-20Q, -0x1.f7cb1acefcf435a3d287cb8094aap-26Q, -0x1.c92be21aef0c9ac0fb550ddd5f85p-26Q, -0x1.3b9a57c4ce7e7a8e7b0e1df18a41p-35Q, -0x1.6a58cec0fa224ca49741d50416e8p-35Q, 0x1.4bf1eb8cd4c9c2273508a8b73f42p-37Q, 0x1.697067f1715a141417bb7553b3a4p-44Q, -0x1.513d790bd242fdd412e02eaf3fb6p-49Q, -0x1.b3943c02986a6636aaf05d95d85p-57Q, 0x1.54d330be5783db7123cd1333ac81p-67Q, -0x1.3f6e1e631364c64c65f6b5a7fe31p-80Q, -0x1.d0d882f8587b498d8efb759e0601p-104Q, 0x0p+0Q};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0Q, 0x1.af673717274af370272903c200ap-9Q, 0x1.c7ad45d086ea4c5ed9ed7e340d9bp-3Q, 0x1.9756cb092ee06f6ac1eb577b9667p-1Q, -0x1.51916657c183447d0774789d62f8p+0Q, 0x1.6cc6e8f0624052b2c0fdcc8950a9p-2Q, -0x1.8cf37d6182ca0b170d0a042e41d9p-4Q, 0x1.9a3fa2f41d4953051b0c6d4a1af5p-4Q, -0x1.0a50be22f2b86dd755f1bb101dbcp-3Q, 0x1.df3f4f6c19d45193b61450be397cp-4Q, -0x1.2d4b7e715db6bf84cb93e1a160d4p-4Q, 0x1.0681e4c20b9fce41d5b4e567565fp-5Q, -0x1.1b50d689cbed8df146901e68b65ap-7Q, 0x1.49acd134a254ba0136bf2c9ddd2bp-11Q, 0x1.16651955943e391787562b8520dbp-11Q, -0x1.c26d1f2c70c86f0644644cef751p-13Q, 0x1.3002118e762a111c6bcee4aaae42p-16Q, 0x1.49fbecfd7d9c6cba55cd30ac0602p-17Q, -0x1.8781a4a6a5f7c8daadd9ede24939p-19Q, 0x1.5ed0ad164acd249f0f9d827483acp-24Q, 0x1.da4a7558674addd03b35614f79bdp-25Q, -0x1.7e23c7237f3f9358779e22d38cap-29Q, -0x1.bd8f2cef8c9f03d137232e9e48dbp-35Q, 0x1.1c61501fa10480730673344e35a7p-37Q, -0x1.c1b8b33989e0245e7c861b898ec7p-44Q, -0x1.95156f39cb33a3cd95db28e3ba68p-52Q, 0x1.d1f8ddb7d01989509bfbf0327cdap-60Q, -0x1.34635de67ce8bb9a35ccd2f4bc82p-74Q, -0x1.c0c6d283f741e5d8d9e1ced44cbap-97Q, -0x0p+0Q};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0Q, 0x1.52aa167437ed3a97a2d16e2e814p-6Q, 0x1.2f386450cd3603452775e405d98cp-1Q, -0x1.92da3e0f4795f52ddad3070744b5p-2Q, -0x1.010e6c23362c2f5a0189ea0fe507p+1Q, 0x1.ba5e5707337cefc73943a8303951p+1Q, -0x1.6efa1a351e68942304e8e68b7a36p+1Q, 0x1.e2efff792ca6cd2456dfdb721d3p+0Q, -0x1.e9e84815ce29a5578b4bc0477766p-1Q, 0x1.3e7bcfc83dd34f0d929299012fe2p-2Q, -0x1.3f21e5e83db9b76a1e6a21ec102ep-6Q, -0x1.00e091b8310d7c425038e08db391p-5Q, 0x1.93252ea5d40edb85ff0ddad30d7p-8Q, 0x1.0cb53bda124f4c4d4c0ae3af47ep-7Q, -0x1.6ecc6596fdeb97786cd08cbbbc9bp-8Q, 0x1.1da3c88de4593a0d10cc249b863dp-10Q, 0x1.0f705c9109b88bc792c8e251c2cep-12Q, -0x1.687f176415b5a1410c9f394cb9e8p-13Q, 0x1.03bf749271ea0dc9bfa9a81f431dp-15Q, -0x1.0a570c997b8f6bb3aa2b6fc455bcp-20Q, -0x1.b60c856b75c6f8f8db3b0f76f77ep-22Q, 0x1.2f36c8024d47853b1fc5abd2c44cp-24Q, -0x1.ab6b4d2a0c9eb0fb784066974351p-30Q, -0x1.b77dbd4d624bb182ce2a80889f4fp-33Q, 0x1.02e06a0b525289974212166730a4p-39Q, 0x1.f900db818405bc4cfc19c1904249p-46Q, -0x1.5cc6aba4a366fbfbcb9e7e9b0d93p-54Q, 0x1.79a9be1badaf05e53c8d4ae1d448p-67Q, 0x1.12cb1c6610cf5a5ca8d9bf44c534p-88Q, -0x0p+0Q};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0Q, 0x1.bde47de89537efcc2943722b96bdp-4Q, 0x1.ff6e39e05bc1960ac6a7468afb9cp-1Q, -0x1.0edf7812c7e6f7d06a00b362f2edp+2Q, 0x1.788eafbfef56fcdc50a685d205b6p+2Q, -0x1.0b9e58d049e2b1cb9469b0149a1ap+2Q, 0x1.57d72a54d9b7d9046e3ca22b7fc2p+1Q, -0x1.5aec59993d64c03ae451f5fb9ac3p+1Q, 0x1.66be004fbc25830ff3a497ea8396p+1Q, -0x1.257b730e2148d4f4b3feb86356b8p+1Q, 0x1.61e6a248fa765db41939b126ff2cp+0Q, -0x1.1d661708485736ce63b6c04b43ccp-1Q, 0x1.7634ae9385e7d28433590ede6772p-4Q, 0x1.aae5eb36cf2339bb1da3727f868ap-5Q, -0x1.66a2dd81189a5724bb1062f0dbecp-5Q, 0x1.9ee5c38dff3c5ada29575f743c4fp-7Q, 0x1.cee452b55c630166e1f1c6509c8cp-12Q, -0x1.7d0e63753adf810a13b7946ecd49p-10Q, 0x1.95a9bb14ccec080a617568800ab6p-12Q, -0x1.ac68b8496deea7093d3eaa370cb3p-17Q, -0x1.4a3e531dccd5a7c88df667aa9ebfp-17Q, 0x1.45a5b2adacfee470f99a3f9ace09p-20Q, -0x1.a0585e72874e51a270db9477885p-28Q, -0x1.4a4aaf36fdaec2c3a3e857f50dfbp-28Q, 0x1.818dc3c36642c77c4040a75f4584p-34Q, 0x1.bc8ec635290e455c58f05f4ab9c8p-41Q, -0x1.1c50f4adb4d48c39b492719c233cp-48Q, 0x1.541ee5efeba27ec1d6332fa503dp-61Q, 0x1.eef3c669427ba33d298eab6d278p-82Q, -0x0p+0Q};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0Q, 0x1.da9efb84cd101b891a55bf090876p-2Q, -0x1.0a963523c780f95520ba62e0ae99p-2Q, -0x1.6ead78b2a7f870bae850968cd2c2p+2Q, 0x1.1fb0b7ee7fe9b42077abdaf5e253p+4Q, -0x1.a26b20f9bdeeff0cd0b5e87989aep+4Q, 0x1.5a362701692b5d54a80faabeb08bp+4Q, -0x1.c3b93743ed5e1f4aae7ff9680d26p+2Q, -0x1.0393f54066e2a86d4f5766fcb157p+3Q, 0x1.ce0e335b9b5cfd8737f6de07ffafp+3Q, -0x1.3371f4378fc25cdcbf584ed998cep+3Q, 0x1.04744c732a8970957ba707ed40dap-2Q, 0x1.5d5bbaac2d3dd399541ae8c86b98p+2Q, -0x1.56903abc9d372d08f72cf8f9d84fp+2Q, 0x1.4f367450bb0294accf5c9a7e9554p+1Q, -0x1.16f1bf1e47dd7b33b29f107a965cp-1Q, -0x1.0ca6089fc41ee660907b2bb58a89p-3Q, 0x1.fd1e6437298de912355a40f320d6p-4Q, -0x1.127569c6d3d201e096a74c3e9f6bp-5Q, 0x1.031ce43d6f2a9b28afac205cb30cp-9Q, 0x1.dbc5a12350173dc4ceb0edd4094ep-11Q, -0x1.6e57586c99db2a8af6576e5da36dp-13Q, 0x1.338c12c9a95b47e57d454a7c5751p-19Q, 0x1.ec833bdc8d6ab1cf492647695cc2p-21Q, -0x1.31ee1e222a82fe6e397b0f1aa142p-26Q, -0x1.068cce25031d061c7d5229b84eeap-32Q, 0x1.ab486d191520d8a9aefca6d37aefp-40Q, -0x1.971ac61147c4bd5f21d58d94b0d3p-52Q, -0x1.28365b5992261cb91d89a4a5eba6p-71Q, -0x0p+0Q};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0Q, 0x1.8a28bf1f4baf0256370de9cbbbf3p+0Q, -0x1.0b8ecb513e670e46e8b61fdb81fap+3Q, 0x1.301d17ac5e1c6daeb2bb90052014p+4Q, -0x1.80a5fd5ebbea4cbe232c3d259f67p+4Q, 0x1.4a39e3e1048d6253983413fa5691p+4Q, -0x1.1148278e9d9a1304c4d279b67053p+4Q, 0x1.18e244d79a0328c7ff6ea967eef5p+4Q, -0x1.3908669ba07796469d99446fcffap+4Q, 0x1.80446c71adb1488769cf4e1f8d42p+4Q, -0x1.0a40794798e411ebd23986f8288ap+5Q, 0x1.52509dd04c4f6aeb9cbf502539fbp+5Q, -0x1.4b468531c5b19f58ba9821786258p+5Q, 0x1.c80f1430e334a07768f1a651dda2p+4Q, -0x1.82ded3c89e7e9fa329e762fc41f5p+3Q, 0x1.7610a167089f1959ecdad356948cp+0Q, 0x1.b0a89a8818c0677d48d730c11145p+0Q, -0x1.2b516da5d080fbac57eada1e0e8ap+0Q, 0x1.488189c0e63233e3103870456b25p-2Q, -0x1.16dd91fce8d2f3a24746d4df4144p-6Q, -0x1.957d5757f4d581e1eb8139ee8367p-7Q, 0x1.613bcf2c2fc6a53ed2c91b812d4dp-9Q, -0x1.0adbc024da55152d1e362e768c76p-14Q, -0x1.44905597a89087a3899ef231d6f7p-16Q, 0x1.238bd55115863b967f9591a85e2bp-21Q, 0x1.0b863bc593a1d515b8c451fdf4ccp-27Q, -0x1.2dac52b5d35bb8e11505ead79853p-34Q, 0x1.a8ab5a61388b1db01ad92615e5f6p-46Q, 0x1.34fcf88bcfb3fdd3eace821f889ap-64Q, 0x0p+0Q};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0Q, 0x1.e156f58145aba7d0b30fa35feff6p+1Q, -0x1.d9350b2238c2b904f5fdfd02be6bp+4Q, 0x1.b03e3957ecd6a002d130937fdeb5p+6Q, -0x1.f51dfa789d878832ad001d30e39cp+7Q, 0x1.b1d9ee3321d942364cb8271dfebap+8Q, -0x1.3c90b7e3ca1db82e1a61d27c7ae2p+9Q, 0x1.a1025f9df5665ef6d6390bf01f8bp+9Q, -0x1.ee82dbab6ab103949b52c0019f4cp+9Q, 0x1.fcf169933904c38827bff55b6c1p+9Q, -0x1.beee0dc0c8ddb1ba161390e5fd9fp+9Q, 0x1.545f49e00f495f369a9c2947535ap+9Q, -0x1.c39ca355bd5d296f3796271b492ep+8Q, 0x1.d17e6e268802ca2d8ab4b3a8e721p+7Q, -0x1.8d05e2b81cf726b84ae7af5a8e1fp+5Q, -0x1.a57ddae4deced8b3bcbf5da22cap+5Q, 0x1.065bfb9cfed103880a47e9c73209p+6Q, -0x1.1a783beefce87b0115cd8021056bp+5Q, 0x1.2e9f2c1581a696ea72950a297825p+3Q, -0x1.3cad9a2427051e071bf1f8338794p-2Q, -0x1.1b4b3a7aa70e82673e69d7fdae94p-1Q, 0x1.15a31469a9ce01c4f9e608774673p-3Q, -0x1.5c66a63c9347469ce6f6732b0a8p-8Q, -0x1.5db560cc8a8d9420c2df7832dd62p-10Q, 0x1.c57be52a95f9a3c03fb08e74a459p-15Q, 0x1.c9738067c5909d91761fe5fd95cfp-21Q, -0x1.63f652c47225898a139de258494dp-27Q, 0x1.769767db4423b6439ddbea7dbce4p-38Q, 0x1.108b386e39e95695575898c417c9p-55Q, 0x0p+0Q};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0Q, 0x1.d870debcc05c458cb432559ebfc5p+2Q, -0x1.0c2b8b0b28193dcd228c4e6d1c95p+6Q, 0x1.10bd374d63550b983999fd9b98p+8Q, -0x1.4441daef321d4016bb9b098a7297p+9Q, 0x1.eaed48222cc9b9253eb90b0dcf97p+9Q, -0x1.dea055aad4ecaefb97bc94a552f5p+9Q, 0x1.0ea6de87556ea6a2de72c35c89c8p+9Q, 0x1.3bb921604519d1ae8a5d0ccd5d1ep+5Q, -0x1.7c03d4dcf551472cf76721c1c17cp+9Q, 0x1.b77df6c77230b9a06a45739b39aap+10Q, -0x1.59dd45c186fb11c5ad1d0f189e18p+11Q, 0x1.92ad5ee85458cf75ddd23bfc0512p+11Q, -0x1.7716e9b298971ca51bb637e98e57p+11Q, 0x1.34cd942cd473a5a710149f0fdbbdp+11Q, -0x1.d2108687fa36ec88dd75fde72adbp+10Q, 0x1.27e2041912517aaa65b8280aa4e9p+10Q, -0x1.0ee0131c1b04ee634d2080c95b01p+9Q, 0x1.13ffc016f56ca3a3bb7e6018d857p+7Q, 0x1.9021a9dd4e12af1889880347a2f3p+1Q, -0x1.cb9505a70965b7f9ec7d47aa192ap+3Q, 0x1.f11cd618c3358a67a90246f84b5cp+1Q, -0x1.a3fefe1a942d41c95d704e932873p-3Q, -0x1.a953da883746e1eb5fcefdddfb0dp-5Q, 0x1.9718bee3af728b9e4c377574de7ep-9Q, 0x1.ad4249f39958d903ac0c0b219af3p-15Q, -0x1.eb70cd1aa40511f5c136d6883df5p-21Q, 0x1.72006a07a097f617e893c7382f23p-31Q, 0x1.0d30627e6a2ad3489ce1b7745733p-47Q, 0x0p+0Q};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0Q, 0x1.155158ac6ea984ad1f39657983b3p+3Q, -0x1.4fec3a6a32c1ef2818fc096fddd7p+6Q, 0x1.70dec41eaf97d263c2e27cc1784ep+8Q, -0x1.e94cfecb1efa1478b21e27ec9309p+9Q, 0x1.bf0b100d34d0405ff79ebd2004c2p+10Q, -0x1.39291803fcf47b5c2680912e1935p+11Q, 0x1.79ccf50afb46dbd4b771bbe9314ap+11Q, -0x1.ab6c90991611b280fa5f8fb17229p+11Q, 0x1.c47ed9a17b9cc8042e74a92f11b8p+11Q, -0x1.af1005783c9c08a75d43de02a3efp+11Q, 0x1.72a859cabb471f7e1c88f5de7fd4p+11Q, -0x1.2846e6b9b14f481005e1b83a4b88p+11Q, 0x1.b3d87dff6a954876ee2d25afa785p+10Q, -0x1.1ae10527ae49437f787df6e5258ep+10Q, 0x1.41e16e9c43532c08707790b425f3p+9Q, -0x1.460030c5bf206e4d0614b974f3a2p+8Q, 0x1.0818e6dd9acdc76d8ca672811999p+7Q, -0x1.8ef0b66c7662c653e52a9a26f648p+4Q, -0x1.6eb8ec2d2fcf0443ad7badae070dp+3Q, 0x1.3aba0303f01c424453f9ef91eafp+3Q, -0x1.588d6d239648dcf73cd93c85e3bap+1Q, 0x1.5ca063a2897a34772f3c4e199577p-3Q, 0x1.72c884e06d399a8e64fd9e5def96p-5Q, -0x1.2b7b99da7239a8d084357a60a47cp-8Q, -0x1.359ad5ec914c5a48afa14674a42fp-14Q, 0x1.0cff089d4d592f01775a283b1eb2p-19Q, -0x1.207535755ab2ee6fe496d4a13eeep-29Q, -0x1.a3ad9d559345b904814202802d71p-45Q, -0x0p+0Q};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0Q, 0x1.174fb1d6730638307d208a7b9705p+3Q, -0x1.5cf63b4072a084fdeb8b32e3f8f4p+6Q, 0x1.859702b93091fc7e6589a6acc4cp+8Q, -0x1.008e38c64d4049e94bd5995565e4p+10Q, 0x1.c03c1b8df613f18067635d57973dp+10Q, -0x1.1e0d30516cd0d5b6c114eb50863dp+11Q, 0x1.33504e2e62ab9029d451c22dbffap+11Q, -0x1.4498a39b45dd2d15e6efe9a76837p+11Q, 0x1.500c422b7e4d651447d31248b36bp+11Q, -0x1.2d6f916f2f063d6cac6e50e8332ap+11Q, 0x1.c5bd8b8beccdb3ef65612beb26bfp+10Q, -0x1.3b7208dc1850750db50e8cf692d2p+10Q, 0x1.a4b1819107c720e5477b69693072p+9Q, -0x1.c03583e49298125db8ea16f1c92fp+8Q, 0x1.1254d5dd1a3c865791dce6763bcfp+7Q, 0x1.be19509979c252700b664c41f013p+2Q, -0x1.6abf524121ea45d75b14942386cep+5Q, 0x1.bdfa9494723d3641f8f38a0cc0ebp+5Q, -0x1.7a9c102bdb495114d11c4dc94aa3p+5Q, 0x1.86920d3d07ed23a99340d183d76p+4Q, -0x1.a9adfb25c4f27469db40c9474b64p+2Q, 0x1.1337641b89dbbf1427d9b379e883p-1Q, 0x1.191c64622c1b13245bb01b5d2dc3p-3Q, -0x1.88d18423866c243d7190bc69d463p-6Q, -0x1.aee4f466bb96965b6a3465feff1bp-12Q, 0x1.15e5e9747fe1bbdbc08e7b80eb4fp-16Q, -0x1.bc4491eee0fdcc0c5c68f4d91f7dp-26Q, -0x1.431c03e754cd8a35cd878b071e01p-40Q, 0x0p+0Q};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0Q, 0x1.57dd202e5e84ab85696b3b081p+2Q, -0x1.b426b94987908d499f20a9e25757p+5Q, 0x1.ef50af36bc949ed3fa5d7e0a8198p+7Q, -0x1.4da8e644667e6ac3b79bfab28161p+9Q, 0x1.2d889ab089910f7ad40ce0f8df85p+10Q, -0x1.9456ec86efc743d5028d89866bbdp+10Q, 0x1.ca1f75d29c1784a6a77e065e7ddep+10Q, -0x1.f2eaf24b48be90f886aebc94dadbp+10Q, 0x1.0a60e2fdcea779a9912a9120de2ep+11Q, -0x1.07fe75c2d85392f1210e0f990473p+11Q, 0x1.e2b37ed5f446198c3a3c3919467ep+10Q, -0x1.a28fcff6e684b5cca8b59e89af3bp+10Q, 0x1.5596d2be7c1f83852a278b67a766p+10Q, -0x1.02761175eccb4a7f32e2ed6eb998p+10Q, 0x1.70f45a3e9b6c87dda4f640c6221p+9Q, -0x1.edf5a5b354e128a66f72c39ece6fp+8Q, 0x1.27b1e13298bb3ef65c5911d31c4bp+8Q, -0x1.3be69243ef2c31f022d98f8f933ep+7Q, 0x1.3b71f0120f2a47ab2eeb31559ad4p+6Q, -0x1.11985d9404f45378f92bac82976fp+5Q, 0x1.3b5a9762f053ae0408ef30897c49p+3Q, -0x1.c32c18767db723614caa803fec42p-1Q, -0x1.5d8e89b8ba2f46a3384127d85bb4p-2Q, 0x1.3b1b46a97c2fa9eb152314a4a3e9p-4Q, 0x1.23706d03f6f7466fb40930bedc5cp-10Q, -0x1.9c26fc84f3ff5e0f45c2413885cdp-14Q, 0x1.962939a138e2b376292fd9833a65p-23Q, 0x1.27428a5934f9dbd8cb61b82d774ep-36Q, -0x0p+0Q};
+            }
+            if constexpr (order == 11) {
+                return {0x0p+0Q, 0x1.82ba18a2815549dbb59529e31e5ap+1Q, -0x1.ee321ac782e8103dfdbc2361bd6ap+4Q, 0x1.174e5f65a44a587e237d6c3b553dp+7Q, -0x1.6e81d57c4c979417ab2afd3c009fp+8Q, 0x1.368de3361fae4ae909ed8745994cp+9Q, -0x1.7106731d7c870bc083f73b59d2eep+9Q, 0x1.661d220cefa0ffe013b3cf726fc3p+9Q, -0x1.6833b778e773ab42be67a15c0ce1p+9Q, 0x1.833c1b7a24cc4442e64b44e53f55p+9Q, -0x1.704d0cf5b403f737ee634427f2bbp+9Q, 0x1.2a287b4a8744be736378cf1ad4c7p+9Q, -0x1.d795731af32d4e2789adddfc9044p+8Q, 0x1.7a6623bbe9af7bf6c835c65c7832p+8Q, -0x1.0ddd9fa1ad021e162c7b141c194dp+8Q, 0x1.4f824182bb440977dbefd0a35cbfp+7Q, -0x1.9b8d6efd833c3f31fde4ac45e744p+6Q, 0x1.e6b9bfc912a60c385c629c5efb9fp+5Q, -0x1.d872a65489bc6c3914ee01ff515dp+4Q, 0x1.82e4e50171640b22bb957ff7eae6p+3Q, -0x1.3c81b080d7c589f42c5ce6389905p+2Q, 0x1.87117e04fd822595de53b26cd146p+0Q, -0x1.f2d1dbd395098c995382a933550bp-6Q, -0x1.327c0d249413fa2745d7e64f577bp-3Q, 0x1.13b8c9585145f7834dd210f62242p-5Q, -0x1.094893076dab22e2cc62b655bbffp-13Q, -0x1.784719262e6d99b573a61c97f7f8p-14Q, 0x1.31d26875ab45ebb06f0f6f8f22c8p-23Q, 0x1.bc3aef2e9698a9624f5205459225p-36Q, -0x0p+0Q};
+            }
+            if constexpr (order == 12) {
+                return {0x0p+0Q, 0x1.229017de89888d3b45dd8cbfea97p+0Q, -0x1.74b098d7b294230e195e9582cce8p+3Q, 0x1.a3d6fe58853c1e5c5b02b3c7091ap+5Q, -0x1.0ee9fe2c639a74c7c040d58ce97ep+7Q, 0x1.b7ec28edec4542d27f8e52ddc0eep+7Q, -0x1.dcbffedb3a507fa5c4eb668bdfccp+7Q, 0x1.8f9512e48d1c46e9ac992677a5b8p+7Q, -0x1.7421b1a8804595d4b26039d25693p+7Q, 0x1.a17e1d21e73d1b2880fd626879bep+7Q, -0x1.8b13badbca1d886a88315897811ap+7Q, 0x1.210062e92f4896d0f004a46e2b61p+7Q, -0x1.a9798d44da6c2035da4b20d5799bp+6Q, 0x1.62f521d1972a85eb2c685554b0c3p+6Q, -0x1.f0d14679f69c06584d129cb1dd4fp+5Q, 0x1.0b0540b21cf0924f554194ec7fd4p+5Q, -0x1.2e7f81d72375079565939ed3cb2dp+4Q, 0x1.776b19bc1de7ac2a6f7b7fc9f33cp+3Q, -0x1.390aaca35a348d0447a8760eee46p+2Q, 0x1.0e68e9445701769efc732f28d561p+0Q, -0x1.1d9e671612a45bff7de530a9d9acp-2Q, 0x1.1e141f6f8381b1b9941445268e56p-5Q, 0x1.626281f06a565209b564a6bd772p-3Q, -0x1.00510e27c6af9fccce79c2c0e3f3p-3Q, 0x1.dda065aa933f3a2523260c5e0824p-6Q, -0x1.397e42b4cc1c2544392f2098e5e3p-10Q, -0x1.5e2780fee3a224f5cbbe3f817e91p-13Q, 0x1.93d63eaebefb797682cedf0250afp-23Q, 0x1.24c485651202d28a48b30f621a03p-34Q, 0x0p+0Q};
+            }
+            if constexpr (order == 13) {
+                return {0x0p+0Q, 0x1.2dba81606cdf44cd9f079191a5b6p-3Q, -0x1.83ba9062dc10a95420b209411d9dp+0Q, 0x1.bc6ce42e9d3a21102e53db0ffbf5p+2Q, -0x1.2c97bd817af94b6452b9fa0d6cc7p+4Q, 0x1.0e06914d9315537516f325b1a949p+5Q, -0x1.5f4706680d4ada71d400dc2041dap+5Q, 0x1.6ea3fbf492340b1a8748a4fe5e1ep+5Q, -0x1.5a777ed4931f215f8e0bf28ba3b3p+5Q, 0x1.424978021982d2d37f646f8229b6p+5Q, -0x1.3090ff3d7fed662537bdbe4e02dbp+5Q, 0x1.23e4419ddb640edbe25bd0d3d323p+5Q, -0x1.07fd356f7673b92c13aaeedc3102p+5Q, 0x1.a8f488a3b6e4b2eef60e436347eap+4Q, -0x1.49932384ed8b4cc7bb557f0494b6p+4Q, 0x1.0a96d421140fecc2982c96f08508p+4Q, -0x1.8f60cd9c05602820630a2d130bddp+3Q, 0x1.003bcbf26a5db032107ba63bca4dp+3Q, -0x1.433ef046d9ed13921cc7a928013bp+2Q, 0x1.a65b7dff9352096da27656f15252p+1Q, -0x1.d36032adf2dbd6f014be67c6b6d9p+0Q, 0x1.a4a1ad470bd0ddc88c181c767028p-1Q, -0x1.88e9f63513ce060ad4280c3ae552p-2Q, 0x1.6764f965c95116ec3ca65a5d1d99p-3Q, -0x1.91c36b23af1d7e93ac72a63e1ecp-5Q, 0x1.07d03d7a1adc182d3615f97f92d8p-8Q, 0x1.362d3e37ff6cd230a2a84b0df184p-11Q, -0x1.92dbfdbfa8197afc834c0f617825p-20Q, -0x1.22ff804507dbe78851cf26324af8p-30Q, -0x0p+0Q};
+            }
+            if constexpr (order == 14) {
+                return {0x0p+0Q, 0x1.8dd6e1684e11d5d1ba3d30411455p-6Q, -0x1.ffb4de00653d36e2054f8a61ef33p-3Q, 0x1.1f8df89dea983b6a683ab3dea296p+0Q, -0x1.6eae32a3a790681f248c15595ebap+1Q, 0x1.200cfdab0a8887ae485b249984acp+2Q, -0x1.1f287662480ab738cbe30fecb657p+2Q, 0x1.90990b7ee9dd1f94866e95a6da25p+1Q, -0x1.3d166b62b6085e29fb948fdc0ca7p+1Q, 0x1.74d60ae1a8ceaa71b4a8963d6056p+1Q, -0x1.68026579c2213b7f75e80846b227p+1Q, 0x1.e76ba8ae988d51e585809060cc1fp+0Q, -0x1.60830949d4c82da954f72fb8f218p+0Q, 0x1.48f2a8ad7050c9588f36c847ca49p+0Q, -0x1.e7d09d1d5c76d8ae64a9d1075b8ep-1Q, 0x1.1252ee85de9250052c524f707253p-1Q, -0x1.6e9d007e3ce50ac7539d68d5ba34p-2Q, 0x1.0a88fbec92db255ff32afa74479fp-2Q, -0x1.16ea71f276b00e5a14dbe15b1f7cp-3Q, 0x1.018afa9348367b971e99c9ccc188p-4Q, -0x1.2fa053de7510dd5de4017cd3190dp-5Q, 0x1.2375ee2696f86cd08bc39452c848p-6Q, -0x1.73b10c938e4b6609ab6e783698f5p-8Q, 0x1.1decc8370b2354d839f68c8d33cap-9Q, -0x1.b8713a4dd74a971b6935d59629ecp-11Q, 0x1.732711f764c01745616312d53ea3p-14Q, 0x1.5deb76c540b6c1414e8da0e84c77p-16Q, -0x1.9271259f104138f720caf85fff1dp-23Q, -0x1.2099915b9335422a7d174776e0cbp-32Q, 0x0p+0Q};
+            }
+        }
+        #endif
+    }
+    if constexpr (p == 16) {
+        if constexpr (std::is_same_v<Real, float>) {
+            if constexpr (order == 0) {
+                return {0x0p+0f, 0x1.674708p-13f, 0x1.27cdb4p-5f, 0x1.f3f9a4p-2f, 0x1.8a1b0ep-1f, -0x1.d00082p-2f, 0x1.06c982p-2f, -0x1.4ec10ap-3f, 0x1.b93c32p-4f, -0x1.09f5f4p-4f, 0x1.0b6a76p-5f, -0x1.a17eb8p-7f, 0x1.cda18ep-9f, -0x1.18156ap-11f, -0x1.547c4ep-15f, 0x1.a1d518p-15f, -0x1.fb90c6p-17f, 0x1.085bbcp-19f, 0x1.4a16eap-22f, -0x1.3b0f84p-23f, 0x1.42695p-28f, 0x1.acf5ccp-29f, 0x1.c7dfc2p-37f, -0x1.99a498p-37f, 0x1.0c54f6p-42f, 0x1.60b622p-49f, -0x1.63607p-54f, 0x1.f308a8p-62f, -0x1.dcd83cp-74f, -0x1.f4c81ep-87f, 0x1.f541a8p-112f, -0x0p+0f};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0f, 0x1.5e2be4p-10f, 0x1.115596p-3f, 0x1.8e066ep-1f, -0x1.9a3aeap-1f, -0x1.b4e824p-2f, 0x1.24d79cp-1f, -0x1.96ff08p-2f, 0x1.7cff08p-3f, -0x1.3b2f7p-5f, -0x1.8c4396p-6f, 0x1.d82f62p-6f, -0x1.d30848p-7f, 0x1.b8ca7p-9f, 0x1.4ea26ep-13f, -0x1.44550ap-12f, 0x1.116fb6p-15f, 0x1.e6f46ap-16f, -0x1.73244cp-17f, 0x1.105e3p-20f, 0x1.85ee5ap-23f, -0x1.5ac9f2p-25f, 0x1.d789f4p-30f, 0x1.8d5e3ep-35f, -0x1.c8b384p-37f, 0x1.38fe4p-43f, 0x1.f524d2p-49f, -0x1.a73b7ep-57f, -0x1.c53204p-68f, 0x1.a5354ep-81f, -0x1.a59b92p-105f, 0x0p+0f};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0f, 0x1.295efep-7f, 0x1.9d61ccp-2f, 0x1.161d42p-2f, -0x1.5b7a46p+1f, 0x1.d1174ep+1f, -0x1.64fd52p+1f, 0x1.05168ep+1f, -0x1.657508p+0f, 0x1.a38bfp-1f, -0x1.889b16p-2f, 0x1.152c76p-3f, -0x1.1b4c9ap-5f, 0x1.907f1ep-8f, -0x1.48b152p-13f, -0x1.a3276ep-11f, 0x1.19008ap-11f, -0x1.4a0f3p-13f, 0x1.b16d86p-17f, 0x1.3c9bcap-19f, 0x1.899254p-24f, -0x1.e003aep-24f, -0x1.b118f8p-27f, 0x1.a8e81cp-30f, 0x1.472048p-36f, 0x1.0bc546p-41f, -0x1.5b7878p-47f, -0x1.75c578p-53f, -0x1.4450ep-64f, 0x1.74639cp-76f, -0x1.74be14p-99f, -0x0p+0f};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0f, 0x1.ade0c6p-5f, 0x1.c28b44p-1f, -0x1.5f4cdp+1f, 0x1.cdb8f6p+0f, 0x1.f77744p+0f, -0x1.dd879cp+1f, 0x1.37053cp+1f, -0x1.1bfa76p-2f, -0x1.2b5034p+0f, 0x1.63e226p+0f, -0x1.a29914p-1f, 0x1.852868p-3f, 0x1.9a9664p-4f, -0x1.c29f78p-4f, 0x1.54d634p-5f, -0x1.41b2a6p-9f, -0x1.225dap-8f, 0x1.f9019ap-10f, -0x1.2c2838p-12f, -0x1.8e8742p-16f, 0x1.c9f58cp-17f, -0x1.61f64ap-20f, -0x1.96b8bp-25f, 0x1.71f48cp-27f, -0x1.b5fc8ep-34f, -0x1.c5963ep-38f, 0x1.6b4e6cp-45f, 0x1.e67136p-58f, -0x1.6aff4p-67f, 0x1.6b579p-89f, -0x0p+0f};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0f, 0x1.002834p-2f, 0x1.74f146p-1f, -0x1.d40722p+2f, 0x1.2af6fp+4f, -0x1.a43136p+4f, 0x1.9a15aep+4f, -0x1.38d1bep+4f, 0x1.6c6cdcp+3f, -0x1.13619ap+2f, 0x1.d56ce2p-1f, -0x1.e42908p-1f, 0x1.e52912p+0f, -0x1.ee224ep+0f, 0x1.1f26d6p+0f, -0x1.588844p-2f, -0x1.9e45fcp-7f, 0x1.dcd2d2p-5f, -0x1.93116cp-6f, 0x1.0e0178p-8f, 0x1.31f3fap-12f, -0x1.f6b0ep-13f, 0x1.f05078p-16f, 0x1.2ec5bap-20f, -0x1.47f2bp-22f, 0x1.bcb022p-29f, 0x1.1bcefep-32f, -0x1.34d97ap-39f, -0x1.6f2c8cp-53f, 0x1.34e43ep-60f, -0x1.352f98p-81f, 0x0p+0f};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0f, 0x1.e5d8b2p-1f, -0x1.e7e4aep+1f, 0x1.643948p+1f, 0x1.8bf778p+3f, -0x1.39576p+5f, 0x1.f6657cp+5f, -0x1.2981aap+6f, 0x1.0cf3p+6f, -0x1.71528cp+4f, -0x1.136588p+6f, 0x1.5ecf14p+7f, -0x1.ca8fbep+7f, 0x1.83a966p+7f, -0x1.9d9118p+6f, 0x1.818f5cp+4f, 0x1.4e782cp+3f, -0x1.7fba74p+3f, 0x1.361d7ep+2f, -0x1.85fee8p-1f, -0x1.fcc32p-4f, 0x1.30d54cp-4f, -0x1.4236c8p-7f, -0x1.6b6d4cp-12f, 0x1.251cb8p-13f, -0x1.7df628p-19f, -0x1.6d7bap-23f, 0x1.04735p-29f, 0x1.ecabdp-41f, -0x1.035efp-49f, 0x1.039e9p-69f, 0x0p+0f};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0f, 0x1.5c435cp+1f, -0x1.45ad88p+4f, 0x1.1ac644p+6f, -0x1.3bcd24p+7f, 0x1.1132bep+8f, -0x1.a33216p+8f, 0x1.2bec4cp+9f, -0x1.83ddd4p+9f, 0x1.b1ad42p+9f, -0x1.9d7a32p+9f, 0x1.5526f8p+9f, -0x1.e99686p+8f, 0x1.186a9ap+8f, -0x1.4f805p+6f, -0x1.84955p+5f, 0x1.59efa2p+6f, -0x1.dac7aep+5f, 0x1.620788p+4f, -0x1.88bb02p+1f, -0x1.04b916p+0f, 0x1.18c698p-1f, -0x1.508ddcp-4f, -0x1.539386p-9f, 0x1.9eab9ap-10f, -0x1.980b92p-15f, -0x1.761c2ap-19f, 0x1.64e7e2p-25f, 0x1.1823b8p-35f, -0x1.623924p-44f, 0x1.6290fap-63f, 0x0p+0f};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0f, 0x1.891444p+2f, -0x1.c4b29p+5f, 0x1.d994c4p+7f, -0x1.26defep+9f, 0x1.ddf578p+9f, -0x1.fd207ap+9f, 0x1.36152ap+9f, 0x1.d8616ap+6f, -0x1.190b42p+10f, 0x1.36219cp+11f, -0x1.eed74p+11f, 0x1.31c14ap+12f, -0x1.31807ap+12f, 0x1.07e38p+12f, -0x1.9ca0ep+11f, 0x1.192392p+11f, -0x1.28f7fp+10f, 0x1.8ef118p+8f, -0x1.076216p+5f, -0x1.3734aap+5f, 0x1.2e313ep+4f, -0x1.913ecep+1f, -0x1.aba4ep-4f, 0x1.5578cap-4f, -0x1.f3ff48p-9f, -0x1.bd3a12p-13f, 0x1.29ffeap-18f, 0x1.5e7712p-28f, -0x1.267e4p-36f, 0x1.26c8dap-54f, -0x0p+0f};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0f, 0x1.1c0608p+3f, -0x1.65d998p+6f, 0x1.9d8978p+8f, -0x1.24c8d8p+10f, 0x1.21d47ap+11f, -0x1.bbc006p+11f, 0x1.2211c4p+12f, -0x1.5c65p+12f, 0x1.845a36p+12f, -0x1.87e6ep+12f, 0x1.650412p+12f, -0x1.2b9aap+12f, 0x1.cebcfcp+11f, -0x1.3e375cp+11f, 0x1.7d70c6p+10f, -0x1.8fd688p+9f, 0x1.57b6f4p+8f, -0x1.3e2cp+6f, -0x1.f1e0f6p+4f, 0x1.39f676p+5f, -0x1.07f7dep+4f, 0x1.6eaf02p+1f, 0x1.f8896cp-4f, -0x1.b78e4ap-4f, 0x1.faf294p-8f, 0x1.a6b604p-12f, -0x1.9886bep-17f, -0x1.7c0bdep-26f, 0x1.90aca4p-34f, -0x1.91166ep-51f, 0x0p+0f};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0f, 0x1.58e7ep+3f, -0x1.c53a2ap+6f, 0x1.0cc18ep+9f, -0x1.7c92fcp+10f, 0x1.6a1946p+11f, -0x1.fab772p+11f, 0x1.254298p+12f, -0x1.407f9ep+12f, 0x1.53233cp+12f, -0x1.3b528cp+12f, 0x1.e2ea28p+11f, -0x1.3d616ap+11f, 0x1.75fce6p+10f, -0x1.2b5b5p+9f, -0x1.18e052p+7f, 0x1.ed1ee2p+8f, -0x1.f5a5a8p+8f, 0x1.920c94p+8f, -0x1.22c138p+8f, 0x1.4b1ba2p+7f, -0x1.ec877p+5f, 0x1.641262p+3f, 0x1.3bac8p-1f, -0x1.3ae0dcp-1f, 0x1.0ba446p-4f, 0x1.c3804ap-9f, -0x1.3c78fcp-13f, -0x1.6e90a4p-22f, 0x1.34c398p-29f, -0x1.351bbcp-45f, 0x0p+0f};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0f, 0x1.0cfd94p+3f, -0x1.68c00ep+6f, 0x1.b4a63ap+8f, -0x1.3c4fdp+10f, 0x1.35efeap+11f, -0x1.c3872cp+11f, 0x1.1261acp+12f, -0x1.39e1fap+12f, 0x1.5e4c9ep+12f, -0x1.6b72e4p+12f, 0x1.578fd4p+12f, -0x1.30faf4p+12f, 0x1.0174aep+12f, -0x1.942bc4p+11f, 0x1.25cbc8p+11f, -0x1.914caap+10f, 0x1.f93f04p+9f, -0x1.1b4f5ep+9f, 0x1.1df01cp+8f, -0x1.048db6p+7f, 0x1.730bccp+5f, -0x1.09b56cp+3f, -0x1.4fb834p+0f, 0x1.e38e1p-1f, -0x1.ee07e6p-4f, -0x1.913ceep-8f, 0x1.0726b8p-11f, 0x1.2751c6p-20f, -0x1.00ceb8p-26f, 0x1.012308p-41f, 0x0p+0f};
+            }
+            if constexpr (order == 11) {
+                return {0x0p+0f, 0x1.6ddd34p+2f, -0x1.ef9ef6p+5f, 0x1.2bec86p+8f, -0x1.ab3138p+9f, 0x1.90171ap+10f, -0x1.0b827ap+11f, 0x1.21c7ccp+11f, -0x1.3291c6p+11f, 0x1.52187ep+11f, -0x1.5764b2p+11f, 0x1.2d82b8p+11f, -0x1.efcf7p+10f, 0x1.96b834p+10f, -0x1.34d67cp+10f, 0x1.9aafbap+9f, -0x1.002f1ep+9f, 0x1.378956p+8f, -0x1.48f682p+7f, 0x1.17de88p+6f, -0x1.abd1c4p+4f, 0x1.18837p+3f, -0x1.72b116p-2f, -0x1.93c736p+0f, 0x1.74105cp-1f, -0x1.a93828p-4f, -0x1.8ee02cp-9f, 0x1.b89c5ep-11f, 0x1.5051p-19f, -0x1.a9ba34p-25f, 0x1.aa6a7ep-39f, -0x0p+0f};
+            }
+            if constexpr (order == 12) {
+                return {0x0p+0f, 0x1.7e688cp+1f, -0x1.044f66p+5f, 0x1.39d278p+7f, -0x1.b63bb8p+8f, 0x1.86b368p+9f, -0x1.d8001cp+9f, 0x1.b397fp+9f, -0x1.9ca192p+9f, 0x1.d28d7ep+9f, -0x1.daeab6p+9f, 0x1.738e38p+9f, -0x1.0785a4p+9f, 0x1.a556aap+8f, -0x1.320672p+8f, 0x1.33661p+7f, -0x1.d86506p+5f, 0x1.9ebe06p+4f, -0x1.ec9eeap-1f, -0x1.103434p+4f, 0x1.04d752p+4f, -0x1.2fcc8ap+3f, 0x1.7c24bcp+2f, -0x1.c84c14p+1f, 0x1.57bcccp+0f, -0x1.d81dbp-3f, -0x1.20f9f8p-13f, 0x1.c2f2aep-9f, 0x1.baf67p-17f, -0x1.ae94eep-22f, 0x1.af9128p-35f, 0x0p+0f};
+            }
+            if constexpr (order == 13) {
+                return {0x0p+0f, 0x1.a308fp-1f, -0x1.1df37cp+3f, 0x1.5a47ccp+5f, -0x1.e7cc32p+6f, 0x1.ba5aa6p+7f, -0x1.137ebep+8f, 0x1.07f96cp+8f, -0x1.f176d6p+7f, 0x1.0c09ap+8f, -0x1.12bf1p+8f, 0x1.de16d6p+7f, -0x1.8c7b4ap+7f, 0x1.565926p+7f, -0x1.13d91ap+7f, 0x1.8b69dep+6f, -0x1.15b78cp+6f, 0x1.8188b8p+5f, -0x1.e03c02p+4f, 0x1.12ed8cp+4f, -0x1.36a5bp+3f, 0x1.3d2642p+2f, -0x1.11ef14p+1f, 0x1.c294dap-1f, -0x1.4f57e8p-2f, 0x1.1ebd9ap-4f, 0x1.367918p-14f, -0x1.fdd378p-10f, -0x1.0fc074p-22f, 0x1.f945fcp-22f, -0x1.fb1bdp-34f, 0x0p+0f};
+            }
+            if constexpr (order == 14) {
+                return {0x0p+0f, 0x1.74ef14p-3f, -0x1.fd9d32p+0f, 0x1.3320f2p+3f, -0x1.a9e31ep+4f, 0x1.73dbdep+5f, -0x1.aa50f2p+5f, 0x1.5e48acp+5f, -0x1.20d7a8p+5f, 0x1.4350bap+5f, -0x1.549ap+5f, 0x1.0d8c72p+5f, -0x1.8fe88ap+4f, 0x1.63da6cp+4f, -0x1.24224p+4f, 0x1.7851e2p+3f, -0x1.e4fd18p+2f, 0x1.610a44p+2f, -0x1.ae4c3ep+1f, 0x1.a6fe28p+0f, -0x1.ccc92p-1f, 0x1.f93894p-2f, -0x1.8612dep-3f, 0x1.fd43fcp-5f, -0x1.aafa1ep-6f, 0x1.b63874p-8f, 0x1.071682p-11f, -0x1.a84c4p-12f, 0x1.a20c24p-18f, 0x1.e7f1cp-23f, -0x1.eb089ap-34f, 0x0p+0f};
+            }
+            if constexpr (order == 15) {
+                return {0x0p+0f, 0x1.31c72ap-6f, -0x1.a21aa8p-3f, 0x1.f656a4p-1f, -0x1.589b5p+1f, 0x1.250496p+2f, -0x1.3b0f08p+2f, 0x1.bed88p+1f, -0x1.37fe76p+1f, 0x1.75c34ap+1f, -0x1.9f32b2p+1f, 0x1.2a50b6p+1f, -0x1.80aff2p+0f, 0x1.71f9bp+0f, -0x1.40d216p+0f, 0x1.6edc3cp-1f, -0x1.abb5dp-2f, 0x1.5fdcbap-2f, -0x1.af4e9cp-3f, 0x1.57b33ep-4f, -0x1.736294p-5f, 0x1.e1a61ep-6f, -0x1.381382p-7f, 0x1.a99b88p-10f, -0x1.191adap-10f, 0x1.44a23ap-12f, 0x1.4db128p-13f, -0x1.2cad38p-14f, 0x1.f38c66p-19f, 0x1.c87078p-24f, -0x1.cdd01ap-34f, -0x0p+0f};
+            }
+        }
+        if constexpr (std::is_same_v<Real, double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0, 0x1.674708c20fd28p-13, 0x1.27cdb30a789aap-5, 0x1.f3f9a4213a58ep-2, 0x1.8a1b0e63e768fp-1, -0x1.d0008134e7b25p-2, 0x1.06c9817f611eap-2, -0x1.4ec109006f3abp-3, 0x1.b93c322324f49p-4, -0x1.09f5f4083e297p-4, 0x1.0b6a75dfa25cdp-5, -0x1.a17eb803ff746p-7, 0x1.cda18d3f662aap-9, -0x1.1815693b1e50ap-11, -0x1.547c4d557ee7fp-15, 0x1.a1d518779619bp-15, -0x1.fb90c559a340ap-17, 0x1.085bbb58c3dc6p-19, 0x1.4a16ea18a78a9p-22, -0x1.3b0f83cef7c9dp-23, 0x1.426950d9b6bcap-28, 0x1.acf5cc83787c7p-29, 0x1.c7dfc1cbcd56p-37, -0x1.99a4987142751p-37, 0x1.0c54f6dbbd52bp-42, 0x1.60b6215484a1dp-49, -0x1.6360709f9f94cp-54, 0x1.f308a7934d099p-62, -0x1.dcd83ccd7b40ep-74, -0x1.f4c81d09055a8p-87, 0x1.f541a7bafa402p-112, -0x0p+0};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0, 0x1.5e2be3ffc02e6p-10, 0x1.115596e3350edp-3, 0x1.8e066ec21fc6ap-1, -0x1.9a3ae9a2a692bp-1, -0x1.b4e823397cf88p-2, 0x1.24d79baf908bcp-1, -0x1.96ff08990aa2p-2, 0x1.7cff079859d45p-3, -0x1.3b2f6fbc125fp-5, -0x1.8c439625af32p-6, 0x1.d82f61038e0ep-6, -0x1.d308486caa608p-7, 0x1.b8ca6f1e525d9p-9, 0x1.4ea26d28d3087p-13, -0x1.4455094b3efadp-12, 0x1.116fb5095b29ap-15, 0x1.e6f46905743cfp-16, -0x1.73244b5651139p-17, 0x1.105e30d7ecb46p-20, 0x1.85ee598e5c773p-23, -0x1.5ac9f1c76ae72p-25, 0x1.d789f3d703addp-30, 0x1.8d5e3e20027e8p-35, -0x1.c8b3833c3b769p-37, 0x1.38fe40b99904fp-43, 0x1.f524d19d8420ap-49, -0x1.a73b7d5e557e7p-57, -0x1.c5320460bba02p-68, 0x1.a5354de9b5e4cp-81, -0x1.a59b918cf087fp-105, 0x0p+0};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0, 0x1.295efeac152d8p-7, 0x1.9d61cc47e5de2p-2, 0x1.161d416b67638p-2, -0x1.5b7a45663376bp+1, 0x1.d1174d09edd0ep+1, -0x1.64fd520a6621ap+1, 0x1.05168da964846p+1, -0x1.6575089c4586dp+0, 0x1.a38bf0b53f437p-1, -0x1.889b16ed752f1p-2, 0x1.152c76b8c5aa6p-3, -0x1.1b4c99876d202p-5, 0x1.907f1e8b42629p-8, -0x1.48b152205d27fp-13, -0x1.a3276d4b1b41fp-11, 0x1.19008ab2bad0ep-11, -0x1.4a0f2fc3a3fe6p-13, 0x1.b16d8531bcd97p-17, 0x1.3c9bc919e0e4ap-19, 0x1.899254d741919p-24, -0x1.e003adff466a7p-24, -0x1.b118f867cd64ep-27, 0x1.a8e81cf9b2bf5p-30, 0x1.472047d4ce812p-36, 0x1.0bc546f1206bp-41, -0x1.5b78778ec812cp-47, -0x1.75c5773026aecp-53, -0x1.4450e0ff79234p-64, 0x1.74639b34e972ap-76, -0x1.74be14820bd54p-99, -0x0p+0};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0, 0x1.ade0c67a6df63p-5, 0x1.c28b430a75f2ap-1, -0x1.5f4ccfba427cfp+1, 0x1.cdb8f607de72ep+0, 0x1.f77743196657ap+0, -0x1.dd879ba809268p+1, 0x1.37053c10bce29p+1, -0x1.1bfa76c0a943ap-2, -0x1.2b5034c5e7cecp+0, 0x1.63e2260baa9fep+0, -0x1.a29913a0c0f2ep-1, 0x1.852867c8ceb36p-3, 0x1.9a9664fc9e679p-4, -0x1.c29f78e2de8f5p-4, 0x1.54d634445fcf7p-5, -0x1.41b2a5a54a663p-9, -0x1.225d9fec5c6e9p-8, 0x1.f9019974a7ddbp-10, -0x1.2c283714217e7p-12, -0x1.8e8742bbbfb21p-16, 0x1.c9f58c62dd5d4p-17, -0x1.61f6495ed1b8fp-20, -0x1.96b8b0f8a15e3p-25, 0x1.71f48c99d030bp-27, -0x1.b5fc8d66ab6dp-34, -0x1.c5963ee2273d3p-38, 0x1.6b4e6ce52480bp-45, 0x1.e67135f42b49bp-58, -0x1.6aff40a6dd5b4p-67, 0x1.6b5790e714dd8p-89, -0x0p+0};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0, 0x1.002833198203cp-2, 0x1.74f145f5180b5p-1, -0x1.d40722c67b8b3p+2, 0x1.2af6f0f464bc5p+4, -0x1.a43135145799ap+4, 0x1.9a15ae041271p+4, -0x1.38d1bd49e9af3p+4, 0x1.6c6cdb14d7fe1p+3, -0x1.13619aaa119f9p+2, 0x1.d56ce1ec874a1p-1, -0x1.e42907ae7a264p-1, 0x1.e52911f9f6566p+0, -0x1.ee224ef8eb13dp+0, 0x1.1f26d6223d44dp+0, -0x1.5888435f57836p-2, -0x1.9e45fc4e6f7c9p-7, 0x1.dcd2d2ebfb6e4p-5, -0x1.93116bc1ac6b7p-6, 0x1.0e01783e342a4p-8, 0x1.31f3faa90de9fp-12, -0x1.f6b0df77a544p-13, 0x1.f05077a02c3acp-16, 0x1.2ec5b9d224e6cp-20, -0x1.47f2b0eb68edbp-22, 0x1.bcb021bf883a2p-29, 0x1.1bcefd6cfba52p-32, -0x1.34d97adc52a39p-39, -0x1.6f2c8c9ca395p-53, 0x1.34e43d9253e6fp-60, -0x1.352f98f0f2e49p-81, 0x0p+0};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0, 0x1.e5d8b15d3664dp-1, -0x1.e7e4ae8313c98p+1, 0x1.643947f56174fp+1, 0x1.8bf77730624fbp+3, -0x1.39575fcf961c1p+5, 0x1.f6657cd6c7e2ap+5, -0x1.2981aaa66ca37p+6, 0x1.0cf300079688ep+6, -0x1.71528cd9cab13p+4, -0x1.13658826409b4p+6, 0x1.5ecf135e336b8p+7, -0x1.ca8fbd8754dc2p+7, 0x1.83a96558c6c07p+7, -0x1.9d91182e0786ap+6, 0x1.818f5ca05f024p+4, 0x1.4e782cc994095p+3, -0x1.7fba734a37797p+3, 0x1.361d7d826bb5bp+2, -0x1.85fee8307d591p-1, -0x1.fcc3205624ce5p-4, 0x1.30d54b861144bp-4, -0x1.4236c7ccc62dfp-7, -0x1.6b6d4bcc089efp-12, 0x1.251cb75a77a65p-13, -0x1.7df627db3ed38p-19, -0x1.6d7ba0319a18p-23, 0x1.047350b843565p-29, 0x1.ecabd0f857c51p-41, -0x1.035ef08b1273dp-49, 0x1.039e900e7fa13p-69, 0x0p+0};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0, 0x1.5c435b4994699p+1, -0x1.45ad88073e625p+4, 0x1.1ac643e9c99f9p+6, -0x1.3bcd24e1c22f1p+7, 0x1.1132bead650e6p+8, -0x1.a3321607e3596p+8, 0x1.2bec4ce73b525p+9, -0x1.83ddd4224b9acp+9, 0x1.b1ad4241d86bfp+9, -0x1.9d7a3218170b3p+9, 0x1.5526f87e8214fp+9, -0x1.e996857ebd3fep+8, 0x1.186a9a24f3388p+8, -0x1.4f804f76b6d5cp+6, -0x1.84954fc1821p+5, 0x1.59efa11d2ec7p+6, -0x1.dac7ad3b33c96p+5, 0x1.62078796373e7p+4, -0x1.88bb023e9f2fap+1, -0x1.04b9160269b8ap+0, 0x1.18c6982acbd2dp-1, -0x1.508ddc9d3ccb4p-4, -0x1.539386e1415cfp-9, 0x1.9eab992a4b9abp-10, -0x1.980b92ff814ccp-15, -0x1.761c29381edd3p-19, 0x1.64e7e2ec4af2dp-25, 0x1.1823b743e4c41p-35, -0x1.623923d3ddbafp-44, 0x1.6290fa803758ep-63, 0x0p+0};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0, 0x1.891443770e9f6p+2, -0x1.c4b28f7dbecf4p+5, 0x1.d994c46f08418p+7, -0x1.26defe09eb9e3p+9, 0x1.ddf577c4250f8p+9, -0x1.fd2079b0f3ddbp+9, 0x1.36152a2e286dp+9, 0x1.d8616a51db369p+6, -0x1.190b42892374cp+10, 0x1.36219b3961795p+11, -0x1.eed74001662f8p+11, 0x1.31c149450a5eap+12, -0x1.31807a4d8f7d9p+12, 0x1.07e37f0875c29p+12, -0x1.9ca0e06fa4e41p+11, 0x1.192392a49659fp+11, -0x1.28f7ef65a911cp+10, 0x1.8ef1182eeb70cp+8, -0x1.076216da5c43bp+5, -0x1.3734a9c9c5015p+5, 0x1.2e313dce4fbf1p+4, -0x1.913ecda1e3437p+1, -0x1.aba4e0591b35fp-4, 0x1.5578ca229685fp-4, -0x1.f3ff47839e58dp-9, -0x1.bd3a12076a4f5p-13, 0x1.29ffe91412a2ap-18, 0x1.5e7711914b059p-28, -0x1.267e3f1ece052p-36, 0x1.26c8d9be624c4p-54, -0x0p+0};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0, 0x1.1c06072fbf26fp+3, -0x1.65d998749f19fp+6, 0x1.9d8978b96f57fp+8, -0x1.24c8d76a7f36dp+10, 0x1.21d479bc00698p+11, -0x1.bbc006c939353p+11, 0x1.2211c4425df9cp+12, -0x1.5c64ff1d8bf67p+12, 0x1.845a35a315834p+12, -0x1.87e6df0fbf8efp+12, 0x1.6504110de640cp+12, -0x1.2b9aa02be2b35p+12, 0x1.cebcfb329a57fp+11, -0x1.3e375c669dacp+11, 0x1.7d70c67fe8974p+10, -0x1.8fd6874952e8bp+9, 0x1.57b6f4096f1cfp+8, -0x1.3e2c004c73161p+6, -0x1.f1e0f66437532p+4, 0x1.39f676c722756p+5, -0x1.07f7de36ead71p+4, 0x1.6eaf02b444bc5p+1, 0x1.f8896c7b27aebp-4, -0x1.b78e4a3636f78p-4, 0x1.faf293c65fc89p-8, 0x1.a6b604defe6a9p-12, -0x1.9886be2865e4cp-17, -0x1.7c0bde2d4dd5p-26, 0x1.90aca39ea2e8bp-34, -0x1.91166efa6d0a9p-51, 0x0p+0};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0, 0x1.58e7df673241ap+3, -0x1.c53a29616fa38p+6, 0x1.0cc18d57a1a2p+9, -0x1.7c92fc1b6ca39p+10, 0x1.6a1945d20b68ep+11, -0x1.fab771c0e1bafp+11, 0x1.254298acbb2d4p+12, -0x1.407f9dc95f9b1p+12, 0x1.53233c63dd8a8p+12, -0x1.3b528b3453998p+12, 0x1.e2ea2797d25e5p+11, -0x1.3d6169dd11c9cp+11, 0x1.75fce5d641404p+10, -0x1.2b5b50127f9f5p+9, -0x1.18e0518b142ecp+7, 0x1.ed1ee257a974bp+8, -0x1.f5a5a8d8a9b3cp+8, 0x1.920c943e9e1a2p+8, -0x1.22c1385412c46p+8, 0x1.4b1ba13f6628bp+7, -0x1.ec876f34dee07p+5, 0x1.641261f15a2bcp+3, 0x1.3bac7fcb6882p-1, -0x1.3ae0db5ff49e1p-1, 0x1.0ba445bef297cp-4, 0x1.c3804abda5b0fp-9, -0x1.3c78fba89f7e5p-13, -0x1.6e90a45b17e12p-22, 0x1.34c398a5dd485p-29, -0x1.351bbccd566d6p-45, 0x0p+0};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0, 0x1.0cfd9304e9d0fp+3, -0x1.68c00ea69764dp+6, 0x1.b4a63a85c6a12p+8, -0x1.3c4fcf304828fp+10, 0x1.35efe9ab816f7p+11, -0x1.c3872b5b6dcd2p+11, 0x1.1261ac83f506cp+12, -0x1.39e1fa3f00834p+12, 0x1.5e4c9d364466fp+12, -0x1.6b72e41a84906p+12, 0x1.578fd4c404249p+12, -0x1.30faf3648505dp+12, 0x1.0174ad7c89821p+12, -0x1.942bc49f2f52ap+11, 0x1.25cbc7992fd64p+11, -0x1.914caac567631p+10, 0x1.f93f030387c4dp+9, -0x1.1b4f5dfc787bcp+9, 0x1.1df01b8a36a8bp+8, -0x1.048db6f3ab7c2p+7, 0x1.730bcb9c58bfcp+5, -0x1.09b56b87c1c8p+3, -0x1.4fb833b30fa7fp+0, 0x1.e38e1048601a6p-1, -0x1.ee07e572041f7p-4, -0x1.913ced3c0164bp-8, 0x1.0726b83c4032cp-11, 0x1.2751c6763466cp-20, -0x1.00ceb77e39cacp-26, 0x1.0123085a89101p-41, 0x0p+0};
+            }
+            if constexpr (order == 11) {
+                return {0x0p+0, 0x1.6ddd33f198eb4p+2, -0x1.ef9ef6f596ce4p+5, 0x1.2bec86422c73p+8, -0x1.ab3138ae63b3cp+9, 0x1.90171accf1ae9p+10, -0x1.0b8279e6381aap+11, 0x1.21c7cbc3a51f5p+11, -0x1.3291c6bd3630dp+11, 0x1.52187d4f27825p+11, -0x1.5764b21031afp+11, 0x1.2d82b77758b7bp+11, -0x1.efcf6fd97e751p+10, 0x1.96b834131566ep+10, -0x1.34d67cf0a39aep+10, 0x1.9aafba6f0ff86p+9, -0x1.002f1ef9723b2p+9, 0x1.378956144d5bep+8, -0x1.48f6827b3eeb5p+7, 0x1.17de886be7cb4p+6, -0x1.abd1c377daaf4p+4, 0x1.18836fa0aedf1p+3, -0x1.72b11631904f7p-2, -0x1.93c736e0c44c1p+0, 0x1.74105b4ecfea7p-1, -0x1.a9382883de208p-4, -0x1.8ee02bc822713p-9, 0x1.b89c5ecf7a7b7p-11, 0x1.5051009d42a45p-19, -0x1.a9ba33acc416cp-25, 0x1.aa6a7d0ba8103p-39, -0x0p+0};
+            }
+            if constexpr (order == 12) {
+                return {0x0p+0, 0x1.7e688b7526a77p+1, -0x1.044f66dd0bb35p+5, 0x1.39d2780b0ad2fp+7, -0x1.b63bb8898df09p+8, 0x1.86b367123a214p+9, -0x1.d8001c1817ddfp+9, 0x1.b397f071da311p+9, -0x1.9ca191acc971ep+9, 0x1.d28d7edb2db09p+9, -0x1.daeab5bf793f1p+9, 0x1.738e37d47cc22p+9, -0x1.0785a3e74df5ap+9, 0x1.a556a97ba7348p+8, -0x1.320671c41025dp+8, 0x1.33661041ead75p+7, -0x1.d86506577d508p+5, 0x1.9ebe065723855p+4, -0x1.ec9ee90429332p-1, -0x1.1034340999c87p+4, 0x1.04d7524f6aap+4, -0x1.2fcc89fd04e89p+3, 0x1.7c24bc012bffcp+2, -0x1.c84c145900f78p+1, 0x1.57bccbd9e4fcfp+0, -0x1.d81daf1af068dp-3, -0x1.20f9f72def1dfp-13, 0x1.c2f2ad7e016f5p-9, 0x1.baf6705e59cacp-17, -0x1.ae94eeab2dbd5p-22, 0x1.af91281d99389p-35, 0x0p+0};
+            }
+            if constexpr (order == 13) {
+                return {0x0p+0, 0x1.a308ef1d16805p-1, -0x1.1df37cb20ef6dp+3, 0x1.5a47cc2daffcbp+5, -0x1.e7cc32d4c7f06p+6, 0x1.ba5aa6f58d154p+7, -0x1.137ebe2556bb6p+8, 0x1.07f96c27b79bap+8, -0x1.f176d6c3151d9p+7, 0x1.0c09a0e0bcbap+8, -0x1.12bf0f34a9a55p+8, 0x1.de16d55d65d2cp+7, -0x1.8c7b496d3d3fep+7, 0x1.56592506626bcp+7, -0x1.13d919c9693b3p+7, 0x1.8b69de5718a0ap+6, -0x1.15b78c90e7837p+6, 0x1.8188b8db550ffp+5, -0x1.e03c011f666acp+4, 0x1.12ed8b36e9864p+4, -0x1.36a5b057bc26fp+3, 0x1.3d2641cf67e9p+2, -0x1.11ef148707dfap+1, 0x1.c294da23fe2ap-1, -0x1.4f57e7e05e819p-2, 0x1.1ebd9964081cfp-4, 0x1.367917f76eee3p-14, -0x1.fdd37749c94d9p-10, -0x1.0fc0733cbc7d6p-22, 0x1.f945fb653cfdbp-22, -0x1.fb1bcfae6e46dp-34, 0x0p+0};
+            }
+            if constexpr (order == 14) {
+                return {0x0p+0, 0x1.74ef139ad4e12p-3, -0x1.fd9d32fdef74p+0, 0x1.3320f17be8b7p+3, -0x1.a9e31dbd98dd1p+4, 0x1.73dbdd38a87f5p+5, -0x1.aa50f206f25c7p+5, 0x1.5e48ac9c2f1f2p+5, -0x1.20d7a78e95ecfp+5, 0x1.4350b94e5aa2ep+5, -0x1.5499ff05228dep+5, 0x1.0d8c7214ffee1p+5, -0x1.8fe88996cfa9ap+4, 0x1.63da6bffb7323p+4, -0x1.24223f5c1b9d9p+4, 0x1.7851e19176716p+3, -0x1.e4fd178fcd0efp+2, 0x1.610a439acb289p+2, -0x1.ae4c3e147b71cp+1, 0x1.a6fe28ab7ffaap+0, -0x1.ccc920f98175ep-1, 0x1.f9389387bff6bp-2, -0x1.8612de961fd02p-3, 0x1.fd43fc0e7883fp-5, -0x1.aafa1e0c4a87p-6, 0x1.b638737fa8e8fp-8, 0x1.071682a1f5058p-11, -0x1.a84c3f530239bp-12, 0x1.a20c2374a0f67p-18, 0x1.e7f1c0adda0f6p-23, -0x1.eb089a4058efep-34, 0x0p+0};
+            }
+            if constexpr (order == 15) {
+                return {0x0p+0, 0x1.31c729360063ep-6, -0x1.a21aa8a66a683p-3, 0x1.f656a46fa2a91p-1, -0x1.589b4fca92a9fp+1, 0x1.25049558932c2p+2, -0x1.3b0f087615a27p+2, 0x1.bed87f332745cp+1, -0x1.37fe75fa2aa3bp+1, 0x1.75c34ae38a12p+1, -0x1.9f32b219f201fp+1, 0x1.2a50b5ebe798ep+1, -0x1.80aff2523d4b3p+0, 0x1.71f9af43c19f1p+0, -0x1.40d21595459ccp+0, 0x1.6edc3b8de7cbdp-1, -0x1.abb5cf29e076bp-2, 0x1.5fdcb9c5e1f88p-2, -0x1.af4e9b9242255p-3, 0x1.57b33e4d63cb5p-4, -0x1.736294d370decp-5, 0x1.e1a61d7964669p-6, -0x1.38138139d6cd8p-7, 0x1.a99b874715d59p-10, -0x1.191ada841d112p-10, 0x1.44a23a1750afbp-12, 0x1.4db128e094988p-13, -0x1.2cad37f3dbf9ep-14, 0x1.f38c667f69482p-19, 0x1.c870773604d03p-24, -0x1.cdd01a024c711p-34, -0x0p+0};
+            }
+        }
+        if constexpr (std::is_same_v<Real, long double>) {
+            if constexpr (order == 0) {
+                return {0x0p+0L, 0xb.3a3846107e93c71p-16L, 0x9.3e6d9853c4d4d26p-8L, 0xf.9fcd2109d2c70bp-5L, 0xc.50d8731f3b477fep-4L, -0xe.800409a73d92674p-5L, 0x8.364c0bfb08f4c1cp-5L, -0xa.7608480379d5af6p-6L, 0xd.c9e1911927a4784p-7L, -0x8.4fafa041f14b7dbp-7L, 0x8.5b53aefd12e6ae9p-8L, -0xd.0bf5c01ffba2e16p-10L, 0xe.6d0c69fb315533p-12L, -0x8.c0ab49d8f284eep-14L, -0xa.a3e26aabf73f753p-18L, 0xd.0ea8c3bcb0cd49bp-18L, -0xf.dc862acd1a0536cp-20L, 0x8.42dddac61ee2f0bp-22L, 0xa.50b750c53c5492bp-25L, -0x9.d87c1e77be4e6b7p-26L, 0xa.134a86cdb5e53d1p-31L, 0xd.67ae641bc3e3b4bp-32L, 0xe.3efe0e5e6ab002dp-40L, -0xc.cd24c38a13a8934p-40L, 0x8.62a7b6ddea955d3p-45L, 0xb.05b10aa4250e4b5p-52L, -0xb.1b0384fcfca5df4p-57L, 0xf.98453c9a684c9f5p-65L, -0xe.e6c1e66bda07395p-77L, -0xf.a640e8482ad4089p-90L, 0xf.aa0d3dd7d200c8bp-115L, -0x0p+0L};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0L, 0xa.f15f1ffe0172e5bp-13L, 0x8.8aacb719a8764e8p-6L, 0xc.70337610fe3509fp-4L, -0xc.d1d74d153495bebp-4L, -0xd.a74119cbe7c3dc1p-5L, 0x9.26bcdd7c845def1p-4L, -0xc.b7f844c8550ff96p-5L, 0xb.e7f83cc2cea254cp-6L, -0x9.d97b7de092f7fa8p-8L, -0xc.621cb12d798fd78p-9L, 0xe.c17b081c7070057p-9L, -0xe.984243655303eaap-10L, 0xd.c65378f292ec7e1p-12L, 0xa.751369469843a67p-16L, -0xa.22a84a59f7d64eap-15L, 0x8.8b7da84ad94ceep-18L, 0xf.37a3482ba1e794ep-19L, -0xb.99225ab2889ca73p-20L, 0x8.82f186bf65a2e47p-23L, 0xc.2f72cc72e3b957cp-26L, -0xa.d64f8e3b5739183p-28L, 0xe.bc4f9eb81d6e738p-33L, 0xc.6af1f10013f432fp-38L, -0xe.459c19e1dbb49cp-40L, 0x9.c7f205ccc827418p-46L, 0xf.a9268cec210502dp-52L, -0xd.39dbeaf2abf3a86p-60L, -0xe.29902305dd00cf8p-71L, 0xd.29aa6f4daf25f05p-84L, -0xd.2cdc8c67843fbf1p-108L, 0x0p+0L};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0L, 0x9.4af7f560a96bcb2p-10L, 0xc.eb0e623f2ef1314p-5L, 0x8.b0ea0b5b3b1bf47p-5L, -0xa.dbd22b319bb54d5p-2L, 0xe.88ba684f6e872d5p-2L, -0xb.27ea9053310cf1ap-2L, 0x8.28b46d4b2423017p-2L, -0xb.2ba844e22c3642p-3L, 0xd.1c5f85a9fa1b98bp-4L, -0xc.44d8b76ba978ba9p-5L, 0x8.a963b5c62d530fcp-6L, -0x8.da64cc3b6900f46p-8L, 0xc.83f8f45a13145ecp-11L, -0xa.458a9102e93f63ap-16L, -0xd.193b6a58da0f707p-14L, 0x8.c8045595d6873c2p-14L, -0xa.50797e1d1ff33a2p-16L, 0xd.8b6c298de6cba8p-20L, 0x9.e4de48cf0724d64p-22L, 0xc.4c92a6ba0c8c4adp-27L, -0xf.001d6ffa3353439p-27L, -0xd.88c7c33e6b26e41p-30L, 0xd.4740e7cd95fa76bp-33L, 0xa.39023ea674090bcp-39L, 0x8.5e2a378903582b6p-44L, -0xa.dbc3bc7640960d4p-50L, -0xb.ae2bb9813575fa4p-56L, -0xa.228707fbc919e5bp-67L, 0xb.a31cd9a74b94ec4p-79L, -0xb.a5f0a4105eaa2e2p-102L, -0x0p+0L};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0L, 0xd.6f0633d36fb15fep-8L, 0xe.145a1853af94c61p-4L, -0xa.fa667dd213e750bp-2L, 0xe.6dc7b03ef3972cbp-3L, 0xf.bbba18cb32bd3c5p-3L, -0xe.ec3cdd404933d4fp-2L, 0x9.b829e085e714688p-2L, -0x8.dfd3b6054a1d126p-5L, -0x9.5a81a62f3e7613dp-3L, 0xb.1f11305d54fef5bp-3L, -0xd.14c89d060796ef7p-4L, 0xc.29433e46759ad44p-6L, 0xc.d4b327e4f33c651p-7L, -0xe.14fbc716f47a93ep-7L, 0xa.a6b1a222fe7b777p-8L, -0xa.0d952d2a5331434p-12L, -0x9.12ecff62e374622p-11L, 0xf.c80ccba53eedb19p-13L, -0x9.6141b8a10bf3aa6p-15L, -0xc.743a15ddfd9089p-19L, 0xe.4fac6316eae9c34p-20L, -0xb.0fb24af68dc7671p-23L, -0xc.b5c587c50af1901p-28L, 0xb.8fa464ce81856ffp-30L, -0xd.afe46b355b67eadp-37L, -0xe.2cb1f71139e968ap-41L, 0xb.5a73672924054c6p-48L, 0xf.3389afa15a4d6d7p-61L, -0xb.57fa0536eada04ep-70L, 0xb.5abc8738a6ec098p-92L, -0x0p+0L};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0L, 0x8.014198cc101dfabp-5L, 0xb.a78a2fa8c05a46p-4L, -0xe.a0391633dc59632p-1L, 0x9.57b787a325e2b8ep+1L, -0xd.2189a8a2bccd13fp+1L, 0xc.d0ad7020938821dp+1L, -0x9.c68dea4f4d7949p+1L, 0xb.6366d8a6bff083fp+0L, -0x8.9b0cd5508cfcbdap-1L, 0xe.ab670f643a5062fp-4L, -0xf.21483d73d132347p-4L, 0xf.29488fcfb2b3205p-3L, -0xf.711277c7589ea5dp-3L, 0x8.f936b111ea265a4p-3L, -0xa.c4421afabc1b145p-5L, -0xc.f22fe2737be4b07p-10L, 0xe.e696975fdb72006p-8L, -0xc.988b5e0d635b9p-9L, 0x8.700bc1f1a15234ap-11L, 0x9.8f9fd5486f4f6f1p-15L, -0xf.b586fbbd2a200d7p-16L, 0xf.8283bd0161d5d44p-19L, 0x9.762dce912735e76p-23L, -0xa.3f95875b476d467p-25L, 0xd.e5810dfc41d0fc9p-32L, 0x8.de77eb67dd2905dp-35L, -0x9.a6cbd6e2951c534p-42L, -0xb.796464e51ca7defp-56L, 0x9.a721ec929f3744cp-63L, -0x9.a97cc78797246d9p-84L, 0x0p+0L};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0L, 0xf.2ec58ae9b326a91p-4L, -0xf.3f2574189e4c21p-2L, 0xb.21ca3fab0ba7711p-2L, 0xc.5fbbb983127d9a8p+0L, -0x9.cabafe7cb0e079fp+2L, 0xf.b32be6b63f14cdcp+2L, -0x9.4c0d5533651b59dp+3L, 0x8.6798003cb446c2fp+3L, -0xb.8a9466ce5589bd2p+1L, -0x8.9b2c413204da0b9p+3L, 0xa.f6789af19b5be1p+4L, -0xe.547dec3aa6e0c9p+4L, 0xc.1d4b2ac6360394ap+4L, -0xc.ec88c1703c353c7p+3L, 0xc.0c7ae502f811c1cp+1L, 0xa.73c1664ca04a6f6p+0L, -0xb.fdd39a51bbcb87p+0L, 0x9.b0ebec135dad9dap-1L, -0xc.2ff74183eac8757p-4L, -0xf.e61902b12672b5fp-7L, 0x9.86aa5c308a25804p-7L, -0xa.11b63e66316fb48p-10L, -0xb.5b6a5e6044f76b4p-15L, 0x9.28e5bad3bd32814p-16L, -0xb.efb13ed9f69bfabp-22L, -0xb.6bdd018cd0bfce3p-26L, 0x8.239a85c21ab28b1p-32L, 0xf.655e87c2be28938p-44L, -0x8.1af78458939ea43p-52L, 0x8.1cf48073fd095efp-72L, 0x0p+0L};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0L, 0xa.e21ada4ca34ca18p-2L, -0xa.2d6c4039f3128bdp+1L, 0x8.d6321f4e4cfc7p+3L, -0x9.de69270e1178454p+4L, 0x8.8995f56b287327p+5L, -0xd.1990b03f1acb0aep+5L, 0x9.5f626739da926f4p+6L, -0xc.1eeea1125cd5fdbp+6L, 0xd.8d6a120ec35f6eap+6L, -0xc.ebd190c0b85945bp+6L, 0xa.a937c3f410a79b7p+6L, -0xf.4cb42bf5e9fec33p+5L, 0x8.c354d12799c3f3ap+5L, -0xa.7c027bb5b6adc35p+3L, -0xc.24aa7e0c10803ep+2L, 0xa.cf7d08e97637cb2p+3L, -0xe.d63d69d99e4aebp+2L, 0xb.103c3cb1b9f39dbp+1L, -0xc.45d811f4f97cc5dp-2L, -0x8.25c8b0134dc4eacp-3L, 0x8.c634c1565e9668ap-4L, -0xa.846ee4e9e65a1e2p-7L, -0xa.9c9c370a0ae7abcp-12L, 0xc.f55cc9525cd59bdp-13L, -0xc.c05c97fc0a662abp-18L, -0xb.b0e149c0f6e94f3p-22L, 0xb.273f17625796a99p-28L, 0x8.c11dba1f262097fp-38L, -0xb.11c91e9eedd7769p-47L, 0xb.1487d401bac7208p-66L, 0x0p+0L};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0L, 0xc.48a21bb874fadacp-1L, -0xe.25947bedf679c74p+2L, 0xe.cca62378420be4ep+4L, -0x9.36f7f04f5cf1891p+6L, 0xe.efabbe21287bc6p+6L, -0xf.e903cd879eed94cp+6L, 0x9.b0a951714367f56p+6L, 0xe.c30b528ed9b461fp+3L, -0x8.c85a14491ba6385p+7L, 0x9.b10cd9cb0bcab3ep+8L, -0xf.76ba000b317bf3bp+8L, 0x9.8e0a4a2852f4c19p+9L, -0x9.8c03d26c7bec5cfp+9L, 0x8.3f1bf843ae145d5p+9L, -0xc.e507037d2720736p+8L, 0x8.c91c9524b2cfadfp+8L, -0x9.47bf7b2d488e112p+7L, 0xc.7788c1775b861dcp+5L, -0x8.3b10b6d2e21d939p+2L, -0x9.b9a54e4e280a5b6p+2L, 0x9.7189ee727df88e1p+1L, -0xc.89f66d0f1a1b57cp-2L, -0xd.5d2702c8d9af7bcp-7L, 0xa.abc65114b42fbafp-7L, -0xf.9ffa3c1cf2c6819p-12L, -0xd.e9d0903b527a85p-16L, 0x9.4fff48a09514e9bp-21L, 0xa.f3b88c8a582c5bap-31L, -0x9.33f1f8f67028c1p-39L, 0x9.3646cdf31261e85p-57L, -0x0p+0L};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0L, 0x8.e030397df9379acp+0L, -0xb.2eccc3a4f8cf9fbp+3L, 0xc.ec4bc5cb7abf8aap+5L, -0x9.2646bb53f9b6b84p+7L, 0x9.0ea3cde0034bd8ap+8L, -0xd.de003649c9a9964p+8L, 0x9.108e2212efce172p+9L, -0xa.e327f8ec5fb3bd6p+9L, 0xc.22d1ad18ac1a3e5p+9L, -0xc.3f36f87dfc77a18p+9L, 0xb.2820886f3206234p+9L, -0x9.5cd5015f159aa05p+9L, 0xe.75e7d994d2bf56ep+8L, -0x9.f1bae334ed5fea7p+8L, 0xb.eb8633ff44b9f04p+7L, -0xc.7eb43a4a9745482p+6L, 0xa.bdb7a04b78e780bp+5L, -0x9.f160026398b080cp+3L, -0xf.8f07b321ba98ffdp+1L, 0x9.cfb3b63913ab26dp+2L, -0x8.3fbef1b756b8bfp+1L, 0xb.757815a225e2672p-2L, 0xf.c44b63d93d7545p-7L, -0xd.bc7251b1b7bbe9bp-7L, 0xf.d7949e32fe445dap-11L, 0xd.35b026f7f354a7ap-15L, -0xc.c435f1432f26328p-20L, -0xb.e05ef16a6ea832dp-29L, 0xc.85651cf5174561cp-37L, -0xc.88b377d3685495ep-54L, 0x0p+0L};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0L, 0xa.c73efb39920cedbp+0L, -0xe.29d14b0b7d1c041p+3L, 0x8.660c6abd0d0fda4p+6L, -0xb.e497e0db651c4abp+7L, 0xb.50ca2e905b46c5dp+8L, -0xf.d5bb8e070dd7927p+8L, 0x9.2a14c565d96a24dp+9L, -0xa.03fcee4afcd8902p+9L, 0xa.9919e31eec53f8cp+9L, -0x9.da9459a29ccbc9bp+9L, 0xf.17513cbe92f2a28p+8L, -0x9.eb0b4ee88e4de52p+8L, 0xb.afe72eb20a022bp+7L, -0x9.5ada8093fcfab6ap+6L, -0x8.c7028c58a1762e5p+4L, 0xf.68f712bd4ba559bp+5L, -0xf.ad2d46c54d9e03ap+5L, 0xc.9064a1f4f0d1331p+5L, -0x9.1609c2a09622ff8p+5L, 0xa.58dd09fb31458efp+4L, -0xf.643b79a6f703a82p+2L, 0xb.20930f8ad15e1ebp+0L, 0x9.dd63fe5b440fe97p-4L, -0x9.d706daffa4f07edp-4L, 0x8.5d222df794bdd1ep-7L, 0xe.1c0255ed2d877d5p-12L, -0x9.e3c7dd44fbf26e9p-16L, -0xb.748522d8bf08c1ap-25L, 0x9.a61cc52eea42bddp-32L, -0x9.a8dde66ab36adabp-48L, 0x0p+0L};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0L, 0x8.67ec98274e874f4p+0L, -0xb.46007534bb26601p+3L, 0xd.a531d42e35090ebp+5L, -0x9.e27e798241476f8p+7L, 0x9.af7f4d5c0b7b569p+8L, -0xe.1c395adb6e69289p+8L, 0x8.930d641fa835ff8p+9L, -0x9.cf0fd1f80419d17p+9L, 0xa.f264e9b223377bap+9L, -0xb.5b9720d42482e67p+9L, 0xa.bc7ea62021246d6p+9L, -0x9.87d79b24282e6fbp+9L, 0x8.0ba56be44c10be5p+9L, -0xc.a15e24f97a95118p+8L, 0x9.2e5e3cc97eb1e7ap+8L, -0xc.8a65562b3b184f6p+7L, 0xf.c9f8181c3e2680dp+6L, -0x8.da7aefe3c3dde19p+6L, 0x8.ef80dc51b545874p+5L, -0x8.246db79d5be0e64p+4L, 0xb.985e5ce2c5fe107p+2L, -0x8.4dab5c3e0e3fdbep+0L, -0xa.7dc19d987d3f778p-3L, 0xf.1c70824300d3066p-4L, -0xf.703f2b9020fb9c6p-7L, -0xc.89e769e00b25ab7p-11L, 0x8.3935c1e20195fc1p-14L, 0x9.3a8e33b1a335de3p-23L, -0x8.0675bbf1ce55e11p-29L, 0x8.091842d44880a98p-44L, 0x0p+0L};
+            }
+            if constexpr (order == 11) {
+                return {0x0p+0L, 0xb.6ee99f8cc759e4bp-1L, -0xf.7cf7b7acb67220ap+2L, 0x9.5f6432116397da5p+5L, -0xd.5989c5731d9e0f1p+6L, 0xc.80b8d6678d74968p+7L, -0x8.5c13cf31c0d515cp+8L, 0x9.0e3e5e1d28fa819p+8L, -0x9.948e35e9b18657fp+8L, 0xa.90c3ea793c12aedp+8L, -0xa.bb2590818d7801fp+8L, 0x9.6c15bbbac5bd569p+8L, -0xf.7e7b7ecbf3a84e5p+7L, 0xc.b5c1a098ab36e4fp+7L, -0x9.a6b3e7851cd6ca3p+7L, 0xc.d57dd3787fc2f5fp+6L, -0x8.0178f7cb91d933p+6L, 0x9.bc4ab0a26adf067p+5L, -0xa.47b413d9f75a975p+4L, 0x8.bef4435f3e59d64p+3L, -0xd.5e8e1bbed57a092p+1L, 0x8.c41b7d0576f88b8p+0L, -0xb.9588b18c827b5eap-5L, -0xc.9e39b70622606d2p-3L, 0xb.a082da767f5360bp-4L, -0xd.49c1441ef103d27p-7L, -0xc.77015e41138988ap-12L, 0xd.c4e2f67bd3dbb98p-14L, 0xa.828804ea1522a4ep-22L, -0xd.4dd19d6620b5d5fp-28L, 0xd.5353e85d40818dap-42L, -0x0p+0L};
+            }
+            if constexpr (order == 12) {
+                return {0x0p+0L, 0xb.f3445ba9353ba5cp-2L, -0x8.227b36e85d9aaf5p+2L, 0x9.ce93c0585697ae1p+4L, -0xd.b1ddc44c6f84b46p+5L, 0xc.359b3891d109cd3p+6L, -0xe.c000e0c0beef91cp+6L, 0xd.9cbf838ed188ae1p+6L, -0xc.e50c8d664b8f00fp+6L, 0xe.946bf6d96d84894p+6L, -0xe.d755adfbc9f852fp+6L, 0xb.9c71bea3e610ea4p+6L, -0x8.3c2d1f3a6face9p+6L, 0xd.2ab54bdd39a4207p+5L, -0x9.90338e20812e975p+5L, 0x9.9b30820f56ba5f5p+4L, -0xe.c32832bbea8400dp+2L, 0xc.f5f032b91c2a8d1p+1L, -0xf.64f748214999222p-4L, -0x8.81a1a04cce4348p+1L, 0x8.26ba927b54fff92p+1L, -0x9.7e644fe827446adp+0L, 0xb.e125e0095ffe3e9p-1L, -0xe.4260a2c807bbd9ap-2L, 0xa.bde65ecf27e7508p-3L, -0xe.c0ed78d78346885p-6L, -0x9.07cfb96f78ef479p-16L, 0xe.17956bf00b7a939p-12L, 0xd.d7b382f2ce56194p-20L, -0xd.74a775596dea6ap-25L, 0xd.7c8940ecc9c488dp-38L, 0x0p+0L};
+            }
+            if constexpr (order == 13) {
+                return {0x0p+0L, 0xd.184778e8b402badp-4L, -0x8.ef9be59077b66a9p+0L, 0xa.d23e616d7fe5968p+2L, -0xf.3e6196a63f82e61p+3L, 0xd.d2d537ac68aa3c8p+4L, -0x8.9bf5f12ab5dae19p+5L, 0x8.3fcb613dbcdd0e4p+5L, -0xf.8bb6b618a8ec653p+4L, 0x8.604d0705e5cffc7p+5L, -0x8.95f879a54d2a806p+5L, 0xe.f0b6aaeb2e95db1p+4L, -0xc.63da4b69e9fec14p+4L, 0xa.b2c92833135e147p+4L, -0x8.9ec8ce4b49d9743p+4L, 0xc.5b4ef2b8c504f17p+3L, -0x8.adbc64873c1b94ap+3L, 0xc.0c45c6daa87f51cp+2L, -0xf.01e008fb335633p+1L, 0x8.976c59b74c322cp+1L, -0x9.b52d82bde13767bp+0L, 0x9.e9320e7b3f47defp-1L, -0x8.8f78a4383efd09p-2L, 0xe.14a6d11ff14fe9cp-4L, -0xa.7abf3f02f40c74p-5L, 0x8.f5eccb2040e7b75p-7L, 0x9.b3c8bfbb7771784p-17L, -0xf.ee9bba4e4a6c8ddp-13L, -0x8.7e0399e5e3eb2bep-25L, 0xf.ca2fdb29e7ed48cp-25L, -0xf.d8de7d73723689ep-37L, 0x0p+0L};
+            }
+            if constexpr (order == 14) {
+                return {0x0p+0L, 0xb.a7789cd6a708f8p-6L, -0xf.ece997ef7b9fe29p-3L, 0x9.99078bdf45b839ap+0L, -0xd.4f18edecc6e84b2p+1L, 0xb.9edee9c543fa832p+2L, -0xd.5287903792e3955p+2L, 0xa.f24564e178f8f8p+2L, -0x9.06bd3c74af67abfp+2L, 0xa.1a85ca72d516d28p+2L, -0xa.a4cff829146ee94p+2L, 0x8.6c6390a7ff70509p+2L, -0xc.7f444cb67d4d2a9p+1L, 0xb.1ed35ffdb991773p+1L, -0x9.2111fae0dceca83p+1L, 0xb.c28f0c8bb38af61p+0L, -0xf.27e8bc7e687797cp-1L, 0xb.08521cd65944bcep-1L, -0xd.7261f0a3db8e14ap-2L, 0xd.37f1455bffd4c88p-3L, -0xe.664907cc0baeeacp-4L, 0xf.c9c49c3dffb59aap-5L, -0xc.3096f4b0fe81145p-6L, 0xf.ea1fe073c41f722p-8L, -0xd.57d0f0625437c47p-9L, 0xd.b1c39bfd474775fp-11L, 0x8.38b4150fa82bf11p-14L, -0xd.4261fa9811cdb2p-15L, 0xd.10611ba507b38p-21L, 0xf.3f8e056ed07b157p-26L, -0xf.5844d202c77f32cp-37L, 0x0p+0L};
+            }
+            if constexpr (order == 15) {
+                return {0x0p+0L, 0x9.8e3949b0031f00ap-9L, -0xd.10d5453353419edp-6L, 0xf.b2b5237d1548b4fp-4L, -0xa.c4da7e54954f883p-2L, 0x9.2824aac49960d3ep-1L, -0x9.d87843b0ad13405p-1L, 0xd.f6c3f9993a2dfbdp-2L, -0x9.bff3afd1551db4ap-2L, 0xb.ae1a571c508fe19p-2L, -0xc.f99590cf900f84fp-2L, 0x9.5285af5f3cc721cp-2L, -0xc.057f9291ea599a1p-3L, 0xb.8fcd7a1e0cf84a9p-3L, -0xa.0690acaa2ce5ec5p-3L, 0xb.76e1dc6f3e5e678p-4L, -0xd.5dae794f03b58fap-5L, 0xa.fee5ce2f0fc3e14p-5L, -0xd.7a74dc92112ab1p-6L, 0xa.bd99f26b1e5a94cp-7L, -0xb.9b14a69b86f63cfp-8L, 0xf.0d30ebcb2334763p-9L, -0x9.c09c09ceb66c13bp-10L, 0xd.4cdc3a38aeac8ap-13L, -0x8.c8d6d420e888ec5p-13L, 0xa.2511d0ba857d42dp-15L, 0xa.6d894704a4c3cb1p-16L, -0x9.6569bf9edfcf3d1p-17L, 0xf.9c6333fb4a41095p-22L, 0xe.4383b9b026817b9p-27L, -0xe.6e80d0126388779p-37L, -0x0p+0L};
+            }
+        }
+        #ifdef BOOST_HAS_FLOAT128
+        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
+            if constexpr (order == 0) {
+                return {0x0p+0Q, 0x1.674708c20fd278e13cb308fc018cp-13Q, 0x1.27cdb30a789a9a4cba57381b8109p-5Q, 0x1.f3f9a4213a58e15fea805c6fce04p-2Q, 0x1.8a1b0e63e768effc8742d136ac68p-1Q, -0x1.d0008134e7b24ce7a0bdb2d5e174p-2Q, 0x1.06c9817f611e98379b152a389faep-2Q, -0x1.4ec109006f3ab5eb9ef4b4145d22p-3Q, 0x1.b93c322324f48f0734b615fc988cp-4Q, -0x1.09f5f4083e296fb6c1df50020f4ap-4Q, 0x1.0b6a75dfa25cd5d117e101973337p-5Q, -0x1.a17eb803ff745c2b927f4b56bb4ap-7Q, 0x1.cda18d3f662aa65f684ad290726ep-9Q, -0x1.1815693b1e509dbfebb4547eb7b2p-11Q, -0x1.547c4d557ee7eea60970ca463ebcp-15Q, 0x1.a1d518779619a935a6506c218d65p-15Q, -0x1.fb90c559a340a6d74429771a6508p-17Q, 0x1.085bbb58c3dc5e159337591d11dp-19Q, 0x1.4a16ea18a78a9255137a36b6eea7p-22Q, -0x1.3b0f83cef7c9cd6e4992ef7a8df5p-23Q, 0x1.426950d9b6bca7a253eba2c282edp-28Q, 0x1.acf5cc83787c76964322f9b1342cp-29Q, 0x1.c7dfc1cbcd560059e1fa3bbb0d88p-37Q, -0x1.99a4987142751268f68b0c6ed2ddp-37Q, 0x1.0c54f6dbbd52aba64c70d9892a39p-42Q, 0x1.60b6215484a1c96af7151c514271p-49Q, -0x1.6360709f9f94bbe775bd0ffbecdcp-54Q, 0x1.f308a7934d0993ea0193288827f6p-62Q, -0x1.dcd83ccd7b40e72afa7a2bb7cfc1p-74Q, -0x1.f4c81d09055a8112f9a8f0e29d27p-87Q, 0x1.f541a7bafa4019158f37f50aca0cp-112Q, -0x0p+0Q};
+            }
+            if constexpr (order == 1) {
+                return {0x0p+0Q, 0x1.5e2be3ffc02e5cb63d505e4d41fep-10Q, 0x1.115596e3350ec9cfc7fd8b282be7p-3Q, 0x1.8e066ec21fc6a13efd57c0a1a877p-1Q, -0x1.9a3ae9a2a692b7d6fe0312f42f92p-1Q, -0x1.b4e823397cf87b829664fcfb60e4p-2Q, 0x1.24d79baf908bbde12d97a94a7ed1p-1Q, -0x1.96ff08990aa1ff2b3a6156b3a6a7p-2Q, 0x1.7cff079859d44a97134acb0b37c4p-3Q, -0x1.3b2f6fbc125eff4f9e00971a7fffp-5Q, -0x1.8c439625af31faef37a9ac49e531p-6Q, 0x1.d82f61038e0e00ad9adf79408fc1p-6Q, -0x1.d308486caa607d54998083598b6bp-7Q, 0x1.b8ca6f1e525d8fc1aecc19124973p-9Q, 0x1.4ea26d28d30874cd6f1bece4d064p-13Q, -0x1.4455094b3efac9d3c28631c94f7ap-12Q, 0x1.116fb5095b299dc0400b6814e25bp-15Q, 0x1.e6f46905743cf29b32a5a94efc8dp-16Q, -0x1.73244b56511394e5623a6c13b538p-17Q, 0x1.105e30d7ecb45c8d929e54615a9cp-20Q, 0x1.85ee598e5c772af7b4423f5e48b1p-23Q, -0x1.5ac9f1c76ae72306c6963aa9eb21p-25Q, 0x1.d789f3d703adce6fceeb7470eb4ep-30Q, 0x1.8d5e3e20027e865e92d2141a2b67p-35Q, -0x1.c8b3833c3b76938050c849f3c889p-37Q, 0x1.38fe40b99904e82fbd88d14cb2f1p-43Q, 0x1.f524d19d8420a05a730c8d14360bp-49Q, -0x1.a73b7d5e557e750b97979bfe8dccp-57Q, -0x1.c5320460bba019effc9564690e27p-68Q, 0x1.a5354de9b5e4be0a26cfffd8bd46p-81Q, -0x1.a59b918cf087f7e28a66eadc804dp-105Q, 0x0p+0Q};
+            }
+            if constexpr (order == 2) {
+                return {0x0p+0Q, 0x1.295efeac152d79633d42d6d9172ap-7Q, 0x1.9d61cc47e5de2628b18136c91d91p-2Q, 0x1.161d416b67637e8de5329814da2p-2Q, -0x1.5b7a45663376a9aa5f95ed876f1cp+1Q, 0x1.d1174d09edd0e5a9b8dec824cdfdp+1Q, -0x1.64fd520a66219e33ceb19171c86dp+1Q, 0x1.05168da96484602e8bf4113ac457p+1Q, -0x1.6575089c4586c8407b43149ab041p+0Q, 0x1.a38bf0b53f437316576c7b5f768p-1Q, -0x1.889b16ed752f17512574ee2082eap-2Q, 0x1.152c76b8c5aa61f7d1f86545ce6dp-3Q, -0x1.1b4c99876d201e8bbadda8305d7dp-5Q, 0x1.907f1e8b42628bd87c6dfaa4224dp-8Q, -0x1.48b152205d27ec7322d3d940e06dp-13Q, -0x1.a3276d4b1b41ee0d43115b5aa5e8p-11Q, 0x1.19008ab2bad0e78321ce13187997p-11Q, -0x1.4a0f2fc3a3fe6743d3250b9f059bp-13Q, 0x1.b16d8531bcd974ffcfcfb27586b6p-17Q, 0x1.3c9bc919e0e49ac8c1ec9b7c733dp-19Q, 0x1.899254d74191895a0ee7c7e36bb2p-24Q, -0x1.e003adff466a6871b6189e1534p-24Q, -0x1.b118f867cd64dc8214de14f222d4p-27Q, 0x1.a8e81cf9b2bf4ed6a7f80b7fef41p-30Q, 0x1.472047d4ce812177c2886070e70ap-36Q, 0x1.0bc546f1206b056c51ef6c4e49f4p-41Q, -0x1.5b78778ec812c1a8126f0f850a88p-47Q, -0x1.75c5773026aebf4866564852975ap-53Q, -0x1.4450e0ff79233cb66d7ae040758fp-64Q, 0x1.74639b34e9729d879c349c615547p-76Q, -0x1.74be14820bd545c3f1e6ecd10653p-99Q, -0x0p+0Q};
+            }
+            if constexpr (order == 3) {
+                return {0x0p+0Q, 0x1.ade0c67a6df62bfb0e80195f5a2fp-5Q, 0x1.c28b430a75f298c1d73bb81e4847p-1Q, -0x1.5f4ccfba427cea15c66f4a5c1f37p+1Q, 0x1.cdb8f607de72e596ea568a0387dfp+0Q, 0x1.f77743196657a78ad5bf74421206p+0Q, -0x1.dd879ba809267a9d7904ab43625dp+1Q, 0x1.37053c10bce28d1022d31ac10de9p+1Q, -0x1.1bfa76c0a943a24b6df5bb2a1509p-2Q, -0x1.2b5034c5e7cec27aa44e7ea3cb6cp+0Q, 0x1.63e2260baa9fdeb5f048ba37b6ebp+0Q, -0x1.a29913a0c0f2ddeebb2bd3c28a1p-1Q, 0x1.852867c8ceb35a88f788b40867b1p-3Q, 0x1.9a9664fc9e678ca180654356d53fp-4Q, -0x1.c29f78e2de8f527b7cd8a08d3865p-4Q, 0x1.54d634445fcf6eedbc5dccf05e12p-5Q, -0x1.41b2a5a54a66286808252915cbfp-9Q, -0x1.225d9fec5c6e8c447caf2b42dbedp-8Q, 0x1.f9019974a7ddb631ebee782882ddp-10Q, -0x1.2c283714217e754b55528b629523p-12Q, -0x1.8e8742bbbfb2111f9226dbaeba4ep-16Q, 0x1.c9f58c62dd5d38676514b49cb9bcp-17Q, -0x1.61f6495ed1b8ece209fc78f1e52ap-20Q, -0x1.96b8b0f8a15e32028c8ee00782fdp-25Q, 0x1.71f48c99d030adfe377a70568859p-27Q, -0x1.b5fc8d66ab6cfd5a83337a0ceda7p-34Q, -0x1.c5963ee2273d2d13e0940bb14697p-38Q, 0x1.6b4e6ce52480a98b4ad64082bf85p-45Q, 0x1.e67135f42b49adad0031055a34f8p-58Q, -0x1.6aff40a6dd5b409b62d449651f14p-67Q, 0x1.6b5790e714dd812f487575d068fp-89Q, -0x0p+0Q};
+            }
+            if constexpr (order == 4) {
+                return {0x0p+0Q, 0x1.002833198203bf56e8fbb6906848p-2Q, 0x1.74f145f5180b48bf2521976c532bp-1Q, -0x1.d40722c67b8b2c63d49b5a9adf94p+2Q, 0x1.2af6f0f464bc571c8b763a836373p+4Q, -0x1.a43135145799a27dfd1fadf683bp+4Q, 0x1.9a15ae0412710439a9b40c2df6c6p+4Q, -0x1.38d1bd49e9af291f59c9f34bbc8fp+4Q, 0x1.6c6cdb14d7fe107edc16c4947af5p+3Q, -0x1.13619aaa119f97b37d6d1c2a2f99p+2Q, 0x1.d56ce1ec874a0c5dd634fb4d532fp-1Q, -0x1.e42907ae7a26468d6ecb1d9b0202p-1Q, 0x1.e52911f9f656640a2404f83c369fp+0Q, -0x1.ee224ef8eb13d4b961d19b800725p+0Q, 0x1.1f26d6223d44cb481a2910c8c507p+0Q, -0x1.5888435f5783628967f9baa292dep-2Q, -0x1.9e45fc4e6f7c960ebee0a7c6f2b4p-7Q, 0x1.dcd2d2ebfb6e400bbcf752c44dedp-5Q, -0x1.93116bc1ac6b7200b82ddbfbe355p-6Q, 0x1.0e01783e342a4693e98c9eddee16p-8Q, 0x1.31f3faa90de9ede16d91478c925bp-12Q, -0x1.f6b0df77a54401ad9bab43898f0dp-13Q, 0x1.f05077a02c3aba8741da976da8a2p-16Q, 0x1.2ec5b9d224e6bceb5db9ee6f77e8p-20Q, -0x1.47f2b0eb68eda8ce48926b183b67p-22Q, 0x1.bcb021bf883a1f92a78fc9e4385p-29Q, 0x1.1bcefd6cfba520ba0473784ac481p-32Q, -0x1.34d97adc52a38a676a55a69541ap-39Q, -0x1.6f2c8c9ca394fbdec6dda2529befp-53Q, 0x1.34e43d9253e6e8975e6c8e7e1076p-60Q, -0x1.352f98f0f2e48db2a203fb3601f4p-81Q, 0x0p+0Q};
+            }
+            if constexpr (order == 5) {
+                return {0x0p+0Q, 0x1.e5d8b15d3664d52108fae1119eb3p-1Q, -0x1.e7e4ae8313c9841f6b4ba69959c8p+1Q, 0x1.643947f56174ee22b35087d6e12ep+1Q, 0x1.8bf77730624fb34f058db90d09abp+3Q, -0x1.39575fcf961c0f3da45ce1cc2c7bp+5Q, 0x1.f6657cd6c7e299b7cc89d5ddbefap+5Q, -0x1.2981aaa66ca36b3a94f827b0b8dbp+6Q, 0x1.0cf300079688d85d6be47384ed72p+6Q, -0x1.71528cd9cab137a39829b250a696p+4Q, -0x1.13658826409b41720bd51b25ad91p+6Q, 0x1.5ecf135e336b7c201cd13f369622p+7Q, -0x1.ca8fbd8754dc1920d78e09c343d4p+7Q, 0x1.83a96558c6c07294f0fd7084bf69p+7Q, -0x1.9d91182e0786a78e2338c78e73d6p+6Q, 0x1.818f5ca05f023837d630b0fd1c9bp+4Q, 0x1.4e782cc994094deb15353773c74ap+3Q, -0x1.7fba734a377970e0ae8d81fa7364p+3Q, 0x1.361d7d826bb5b3b3a1616d435b7ap+2Q, -0x1.85fee8307d590ead49f8c8c0db3dp-1Q, -0x1.fcc3205624ce56be678cf8dd8b95p-4Q, 0x1.30d54b861144b0080c77faaf98c5p-4Q, -0x1.4236c7ccc62df6904f17923598dp-7Q, -0x1.6b6d4bcc089eed67f907624e3601p-12Q, 0x1.251cb75a77a65027fa18c44159c1p-13Q, -0x1.7df627db3ed37f55c551bd809c99p-19Q, -0x1.6d7ba0319a17f9c5347fd4990ca2p-23Q, 0x1.047350b843565161f3ac66f52b72p-29Q, 0x1.ecabd0f857c5126fafed07e0ff9fp-41Q, -0x1.035ef08b1273d485ae68801b61a7p-49Q, 0x1.039e900e7fa12bdd9aa0b52e7d7ap-69Q, 0x0p+0Q};
+            }
+            if constexpr (order == 6) {
+                return {0x0p+0Q, 0x1.5c435b4994699430de1f0c23d617p+1Q, -0x1.45ad88073e6251792d84632e4f3fp+4Q, 0x1.1ac643e9c99f8dff42b4b524dcf6p+6Q, -0x1.3bcd24e1c22f08a7330d93c59d11p+7Q, 0x1.1132bead650e64e0cc624fab813p+8Q, -0x1.a3321607e359615c22640004ddabp+8Q, 0x1.2bec4ce73b524de840d2af23d04bp+9Q, -0x1.83ddd4224b9abfb64ecabda1d5d5p+9Q, 0x1.b1ad4241d86bedd378c0243ed9a2p+9Q, -0x1.9d7a3218170b28b67328a62c7a74p+9Q, 0x1.5526f87e8214f36e89fc5bb73ce9p+9Q, -0x1.e996857ebd3fd865f8b8b92d1e0ep+8Q, 0x1.186a9a24f3387e74b221163382ebp+8Q, -0x1.4f804f76b6d5b86a618f7579c739p+6Q, -0x1.84954fc1821007c0fd22b5bb0514p+5Q, 0x1.59efa11d2ec6f964630b6ee3dd9dp+6Q, -0x1.dac7ad3b33c95d5f07d9022e2d45p+5Q, 0x1.62078796373e73b5598b789d53cp+4Q, -0x1.88bb023e9f2f98b9b7a5cb3efe82p+1Q, -0x1.04b9160269b89d57d0a514a7e722p+0Q, 0x1.18c6982acbd2cd140bf32c40e2bfp-1Q, -0x1.508ddc9d3ccb43c37b8bf5160a7bp-4Q, -0x1.539386e1415cf5772194f932f5bcp-9Q, 0x1.9eab992a4b9ab37998a475e020b6p-10Q, -0x1.980b92ff814cc556c4aed6edadddp-15Q, -0x1.761c29381edd29e5680cf26d10acp-19Q, 0x1.64e7e2ec4af2d5325d3b1b81e06p-25Q, 0x1.1823b743e4c412fe2e1a19821c84p-35Q, -0x1.623923d3ddbaeed10b04f5b48b46p-44Q, 0x1.6290fa803758e40f0b8255ed89fdp-63Q, 0x0p+0Q};
+            }
+            if constexpr (order == 7) {
+                return {0x0p+0Q, 0x1.891443770e9f5b58ca0b8becb52ep+2Q, -0x1.c4b28f7dbecf38e874d341781c95p+5Q, 0x1.d994c46f08417c9c24a36bb24434p+7Q, -0x1.26defe09eb9e312242e5ff410da3p+9Q, 0x1.ddf577c4250f78c0132b7ac736e1p+9Q, -0x1.fd2079b0f3ddb297d55b16fe84bp+9Q, 0x1.36152a2e286cfeac4352523397cdp+9Q, 0x1.d8616a51db368c3df94db95c5c72p+6Q, -0x1.190b42892374c709dd821decb54p+10Q, 0x1.36219b396179567cea598487367ep+11Q, -0x1.eed74001662f7e761e889a73b6ep+11Q, 0x1.31c149450a5e9832b2f7a4322f07p+12Q, -0x1.31807a4d8f7d8b9ec23aba57ce8ep+12Q, 0x1.07e37f0875c28ba98c5ad47ed33fp+12Q, -0x1.9ca0e06fa4e40e6ba99e5e66481ep+11Q, 0x1.192392a49659f5be4af76f76ab89p+11Q, -0x1.28f7ef65a911c2242d46f559ac11p+10Q, 0x1.8ef1182eeb70c3b810abd66139cfp+8Q, -0x1.076216da5c43b27292caed829f7ap+5Q, -0x1.3734a9c9c5014b6b42adc6c9cbep+5Q, 0x1.2e313dce4fbf11c25ec1c482fcb8p+4Q, -0x1.913ecda1e3436af7caa7765fe945p+1Q, -0x1.aba4e0591b35ef78387e98333cf8p-4Q, 0x1.5578ca229685f75ec4d7ad4713cep-4Q, -0x1.f3ff47839e58d032a19fef9f4efp-9Q, -0x1.bd3a12076a4f509f06e41d1d4df9p-13Q, 0x1.29ffe91412a29d368ce3dc6e38c5p-18Q, 0x1.5e7711914b058b73ae87986d7f1ap-28Q, -0x1.267e3f1ece05182094a61971cb39p-36Q, 0x1.26c8d9be624c3d09b4283ff340e2p-54Q, -0x0p+0Q};
+            }
+            if constexpr (order == 8) {
+                return {0x0p+0Q, 0x1.1c06072fbf26f358c9f18045c124p+3Q, -0x1.65d998749f19f3f527890dd9f349p+6Q, 0x1.9d8978b96f57f154ef9e43eaf80dp+8Q, -0x1.24c8d76a7f36d7089e403e85e9fap+10Q, 0x1.21d479bc00697b14d91b67255a8bp+11Q, -0x1.bbc006c9393532c76b5f0b5bef94p+11Q, 0x1.2211c4425df9c2e46c413666253fp+12Q, -0x1.5c64ff1d8bf677ab09ae01e0a5e1p+12Q, 0x1.845a35a3158347c96bec7865086bp+12Q, -0x1.87e6df0fbf8ef42fd53aa9972193p+12Q, 0x1.6504110de640c4682cbbe6b8a6e7p+12Q, -0x1.2b9aa02be2b35409ccb01b40da2ap+12Q, 0x1.cebcfb329a57eadc95a91a00a9a1p+11Q, -0x1.3e375c669dabfd4de918596ad52p+11Q, 0x1.7d70c67fe8973e080c2d05792b11p+10Q, -0x1.8fd6874952e8a903dad0f0ef170dp+9Q, 0x1.57b6f4096f1cf0152665b7fd82f9p+8Q, -0x1.3e2c004c73161017d20213f7c5c1p+6Q, -0x1.f1e0f66437531ffa2878e9c69067p+4Q, 0x1.39f676c7227564daf7250a1ee97dp+5Q, -0x1.07f7de36ead717df75680da7494ep+4Q, 0x1.6eaf02b444bc4ce468426b7d5bcep+1Q, 0x1.f8896c7b27aea8a0c13c77300d42p-4Q, -0x1.b78e4a3636f77d36046090a9c9b3p-4Q, 0x1.faf293c65fc88bb39eaf30523dfep-8Q, 0x1.a6b604defe6a94f42a0086be2586p-12Q, -0x1.9886be2865e4c650159b3c14bf08p-17Q, -0x1.7c0bde2d4dd50659d8e7bf0799bbp-26Q, 0x1.90aca39ea2e8ac3870c8fe9456dap-34Q, -0x1.91166efa6d0a92bc7a2ca99b7dfbp-51Q, 0x0p+0Q};
+            }
+            if constexpr (order == 9) {
+                return {0x0p+0Q, 0x1.58e7df6732419db59e963fb33d94p+3Q, -0x1.c53a29616fa380817d7988f924b1p+6Q, 0x1.0cc18d57a1a1fb48e1055941c825p+9Q, -0x1.7c92fc1b6ca3895680be8b3bffe9p+10Q, 0x1.6a1945d20b68d8baff3e866c5cdap+11Q, -0x1.fab771c0e1baf24e2c87e6ba962ap+11Q, 0x1.254298acbb2d449a7b36affa5b18p+12Q, -0x1.407f9dc95f9b1203f97a18e79578p+12Q, 0x1.53233c63dd8a7f18f09c08d93b73p+12Q, -0x1.3b528b34539979362d85428f478fp+12Q, 0x1.e2ea2797d25e54507eaadbdfe8c3p+11Q, -0x1.3d6169dd11c9bca321155575b38p+11Q, 0x1.75fce5d641404560c110d19350b3p+10Q, -0x1.2b5b50127f9f56d44e8ab9654e78p+9Q, -0x1.18e0518b142ec5c99d4cfb0c02dep+7Q, 0x1.ed1ee257a974ab35fe9854c84beep+8Q, -0x1.f5a5a8d8a9b3c073ca74b7aa8b3fp+8Q, 0x1.920c943e9e1a266133c5fbd7d496p+8Q, -0x1.22c1385412c45fef7248020243cfp+8Q, 0x1.4b1ba13f6628b1dd44c07737a72dp+7Q, -0x1.ec876f34dee07503da6d353b7ff9p+5Q, 0x1.641261f15a2bc3d54eafcffb8c39p+3Q, 0x1.3bac7fcb6881fd2d747e22c3e33ap-1Q, -0x1.3ae0db5ff49e0fda9ef3c1ee8d61p-1Q, 0x1.0ba445bef297ba3c0908ff2bb4d9p-4Q, 0x1.c3804abda5b0efa9daf29b604e6cp-9Q, -0x1.3c78fba89f7e4dd2da6247dd38d1p-13Q, -0x1.6e90a45b17e11834e3133934b3a2p-22Q, 0x1.34c398a5dd4857b9fcc96bbdccaep-29Q, -0x1.351bbccd566d5b56e0d97b1d8b32p-45Q, 0x0p+0Q};
+            }
+            if constexpr (order == 10) {
+                return {0x0p+0Q, 0x1.0cfd9304e9d0e9e89a58da63527ap+3Q, -0x1.68c00ea69764cc01a57e59f4b6b3p+6Q, 0x1.b4a63a85c6a121d6db74c511805bp+8Q, -0x1.3c4fcf304828edf088a1b16ea07fp+10Q, 0x1.35efe9ab816f6ad2ce45644d2fd8p+11Q, -0x1.c3872b5b6dcd2512d768b35e0756p+11Q, 0x1.1261ac83f506bff0f39595d045e8p+12Q, -0x1.39e1fa3f00833a2dd6cf3f9d927bp+12Q, 0x1.5e4c9d364466ef749b997ff3a6cp+12Q, -0x1.6b72e41a84905cceda4b9c52f497p+12Q, 0x1.578fd4c404248dabc97584331c2p+12Q, -0x1.30faf3648505cdf5f67d9aa16b7dp+12Q, 0x1.0174ad7c898217c9040304ce9297p+12Q, -0x1.942bc49f2f52a22fa3fb0a0c2104p+11Q, 0x1.25cbc7992fd63cf3174ccf32c535p+11Q, -0x1.914caac5676309ecc707d67c3b11p+10Q, 0x1.f93f030387c4d019b699660bf6c3p+9Q, -0x1.1b4f5dfc787bbc3226392268b2fbp+9Q, 0x1.1df01b8a36a8b0e740bc1ec53a5bp+8Q, -0x1.048db6f3ab7c1cc8ce55d6b0a75fp+7Q, 0x1.730bcb9c58bfc20d60d07c0998acp+5Q, -0x1.09b56b87c1c7fb7baefa593d3ee2p+3Q, -0x1.4fb833b30fa7eeef6a7e9c60d9dap+0Q, 0x1.e38e1048601a60cbcefd6c477b1bp-1Q, -0x1.ee07e572041f738c257ecf9ffa9bp-4Q, -0x1.913ced3c0164b56d324da52a041bp-8Q, 0x1.0726b83c4032bf81b9b5324fe2d4p-11Q, 0x1.2751c6763466bbc5b3627d689424p-20Q, -0x1.00ceb77e39cabc22cbb16a695fdap-26Q, 0x1.0123085a8910152fac9e37f89667p-41Q, 0x0p+0Q};
+            }
+            if constexpr (order == 11) {
+                return {0x0p+0Q, 0x1.6ddd33f198eb3c96ba063e358bd1p+2Q, -0x1.ef9ef6f596ce44132c400459330bp+5Q, 0x1.2bec86422c72fb4a90434380b422p+8Q, -0x1.ab3138ae63b3c1e29f0289d542dap+9Q, 0x1.90171accf1ae92cfd9a8b825cb23p+10Q, -0x1.0b8279e6381aa2b741ba53014abbp+11Q, 0x1.21c7cbc3a51f50320f0eba7f41fcp+11Q, -0x1.3291c6bd3630cafeef000c3ad649p+11Q, 0x1.52187d4f278255d9064abfc39513p+11Q, -0x1.5764b21031af003ebeb2fc812432p+11Q, 0x1.2d82b77758b7aad296d2a3297f76p+11Q, -0x1.efcf6fd97e7509c927947ebcfe7bp+10Q, 0x1.96b834131566dc9e05fa0d23f1dbp+10Q, -0x1.34d67cf0a39ad9453ec607f4238bp+10Q, 0x1.9aafba6f0ff85ebebf990bae7248p+9Q, -0x1.002f1ef9723b265f845856382322p+9Q, 0x1.378956144d5be0ceae49930a1c88p+8Q, -0x1.48f6827b3eeb52ea5b26c2ed113p+7Q, 0x1.17de886be7cb3ac887b94bba647bp+6Q, -0x1.abd1c377daaf4123bc220ca55b7bp+4Q, 0x1.18836fa0aedf116ff461c07e603dp+3Q, -0x1.72b11631904f6bd3fce02c59a632p-2Q, -0x1.93c736e0c44c0da3f44d1f9fb885p+0Q, 0x1.74105b4ecfea6c16422a97b509cfp-1Q, -0x1.a9382883de207a4dbe506bf11d8fp-4Q, -0x1.8ee02bc822713114de4c636e81aep-9Q, 0x1.b89c5ecf7a7b773088b92afebabbp-11Q, 0x1.5051009d42a4549b60d53bde7219p-19Q, -0x1.a9ba33acc416babe2770ada65c3ap-25Q, 0x1.aa6a7d0ba81031b3c996c62600c5p-39Q, -0x0p+0Q};
+            }
+            if constexpr (order == 12) {
+                return {0x0p+0Q, 0x1.7e688b7526a774b7675960f4a94cp+1Q, -0x1.044f66dd0bb355e9e8503e18e935p+5Q, 0x1.39d2780b0ad2f5c13050620039bcp+7Q, -0x1.b63bb8898df0968b0e8fec1fd9a7p+8Q, 0x1.86b367123a2139a592c1528e8f55p+9Q, -0x1.d8001c1817ddf23795fa181f861ep+9Q, 0x1.b397f071da3115c2852f6422a8c8p+9Q, -0x1.9ca191acc971e01d773c5479fb8dp+9Q, 0x1.d28d7edb2db091286aa35eb84214p+9Q, -0x1.daeab5bf793f0a5db1ed52776228p+9Q, 0x1.738e37d47cc21d48d43df1f6d78p+9Q, -0x1.0785a3e74df59d2028a07275bacep+9Q, 0x1.a556a97ba734840eabbaaf9977bap+8Q, -0x1.320671c41025d2eac6cd6f7d0dadp+8Q, 0x1.33661041ead74be91556b7ad619ap+7Q, -0x1.d86506577d5080199f42262a920cp+5Q, 0x1.9ebe0657238551a24be276081da8p+4Q, -0x1.ec9ee9042933244440176ee46c34p-1Q, -0x1.1034340999c868fff4dcb8a37e58p+4Q, 0x1.04d7524f6a9fff23ce8e27e29df3p+4Q, -0x1.2fcc89fd04e88d59c73ed84bf7b4p+3Q, 0x1.7c24bc012bffc7d1e2142c729735p+2Q, -0x1.c84c145900f77b34a48b3cd01e16p+1Q, 0x1.57bccbd9e4fcea0faae95542b1dcp+0Q, -0x1.d81daf1af068d1091e33cdbbae6bp-3Q, -0x1.20f9f72def1de8f22bf9f5b255c4p-13Q, 0x1.c2f2ad7e016f5272ff0429610dd4p-9Q, 0x1.baf6705e59cac328415a41de4538p-17Q, -0x1.ae94eeab2dbd4d40eaa80ab9debep-22Q, 0x1.af91281d9938911a632b5cd0ed85p-35Q, 0x0p+0Q};
+            }
+            if constexpr (order == 13) {
+                return {0x0p+0Q, 0x1.a308ef1d1680575961469f8667e2p-1Q, -0x1.1df37cb20ef6cd526ba94f6e5b81p+3Q, 0x1.5a47cc2daffcb2cf20f274a5d38ap+5Q, -0x1.e7cc32d4c7f05cc178a022548d5cp+6Q, 0x1.ba5aa6f58d154790fde028986d8dp+7Q, -0x1.137ebe2556bb5c31390698cc2046p+8Q, 0x1.07f96c27b79ba1c76a43166f429dp+8Q, -0x1.f176d6c3151d8ca65c15ab30195bp+7Q, 0x1.0c09a0e0bcb9ff8d7d5939eac1c2p+8Q, -0x1.12bf0f34a9a5500b54a8cb7aa2b3p+8Q, 0x1.de16d55d65d2bb62ec748b786b23p+7Q, -0x1.8c7b496d3d3fd8274ea834d98fd2p+7Q, 0x1.56592506626bc28d37a6f5de979bp+7Q, -0x1.13d919c9693b2e85ee3bb9c46203p+7Q, 0x1.8b69de5718a09e2e84dbb4686bcep+6Q, -0x1.15b78c90e783729339c279a7a26bp+6Q, 0x1.8188b8db550fea388993af5f214fp+5Q, -0x1.e03c011f666ac66011ab6c26ae29p+4Q, 0x1.12ed8b36e986458009c1cf96319ap+4Q, -0x1.36a5b057bc26ecf63126b2eacd51p+3Q, 0x1.3d2641cf67e8fbde6d1c40fa7b62p+2Q, -0x1.11ef148707dfa11f55a24428d5aap+1Q, 0x1.c294da23fe29fd37f9b451eef74cp-1Q, -0x1.4f57e7e05e818e7ff01d8a0db422p-2Q, 0x1.1ebd9964081cf6e9a358f38d567ap-4Q, 0x1.367917f76eee2f07742561edeafcp-14Q, -0x1.fdd37749c94d91b95e4c419dae2dp-10Q, -0x1.0fc0733cbc7d657bb2162af22ff6p-22Q, 0x1.f945fb653cfda9182e56ec03c70ep-22Q, -0x1.fb1bcfae6e46d13bafa847e0d908p-34Q, 0x0p+0Q};
+            }
+            if constexpr (order == 14) {
+                return {0x0p+0Q, 0x1.74ef139ad4e11f00f66e50f0812ap-3Q, -0x1.fd9d32fdef73fc52b4e1aac15ce8p+0Q, 0x1.3320f17be8b7073381f61db6e694p+3Q, -0x1.a9e31dbd98dd09635b204c104094p+4Q, 0x1.73dbdd38a87f5064434afb97d3afp+5Q, -0x1.aa50f206f25c72a99ccb3ca40e39p+5Q, 0x1.5e48ac9c2f1f1eff351bab98be85p+5Q, -0x1.20d7a78e95ecf57e7aeb50618786p+5Q, 0x1.4350b94e5aa2da50e62a1b36016ep+5Q, -0x1.5499ff05228ddd2807d9b6ef1056p+5Q, 0x1.0d8c7214ffee0a1235c0b7c3c0bap+5Q, -0x1.8fe88996cfa9a5515805a5fa2aadp+4Q, 0x1.63da6bffb7322ee61ea230916038p+4Q, -0x1.24223f5c1b9d9506d6c2601299dfp+4Q, 0x1.7851e19176715ec2bb51da095d1ap+3Q, -0x1.e4fd178fcd0ef2f7356543216bcep+2Q, 0x1.610a439acb28979c59046810bc68p+2Q, -0x1.ae4c3e147b71c29486543afa4302p+1Q, 0x1.a6fe28ab7ffa991086da6716cc39p+0Q, -0x1.ccc920f98175dd579809ace45452p-1Q, 0x1.f9389387bff6b354c94c19c46a5ap-2Q, -0x1.8612de961fd0228a7f6974df4498p-3Q, 0x1.fd43fc0e7883ee43ba9b27c30441p-5Q, -0x1.aafa1e0c4a86f88db623dcf8b499p-6Q, 0x1.b638737fa8e8eebd49a0e1375a7p-8Q, 0x1.071682a1f5057e2143bccc924ee3p-11Q, -0x1.a84c3f530239b63f7db3d411d854p-12Q, 0x1.a20c2374a0f67000161244836cf3p-18Q, 0x1.e7f1c0adda0f62adb6884d961058p-23Q, -0x1.eb089a4058efe658e6fb3c8b8fp-34Q, 0x0p+0Q};
+            }
+            if constexpr (order == 15) {
+                return {0x0p+0Q, 0x1.31c729360063e0149d5c21a7efcfp-6Q, -0x1.a21aa8a66a6833da58113cf2bbfap-3Q, 0x1.f656a46fa2a9169e56d7dc88f3edp-1Q, -0x1.589b4fca92a9f10523315f53d228p+1Q, 0x1.25049558932c1a7bf948af8c4d53p+2Q, -0x1.3b0f087615a2680943285adb90b5p+2Q, 0x1.bed87f332745bf792ba1df447904p+1Q, -0x1.37fe75fa2aa3b693bb4d2b4c5752p+1Q, 0x1.75c34ae38a11fc314406fb081d96p+1Q, -0x1.9f32b219f201f09e837dabeb3924p+1Q, 0x1.2a50b5ebe798e437ef1f44157963p+1Q, -0x1.80aff2523d4b3342a82c358ca6abp+0Q, 0x1.71f9af43c19f0952a4d93db93c54p+0Q, -0x1.40d21595459cbd8977223938b804p+0Q, 0x1.6edc3b8de7cbccef39a51cdb458bp-1Q, -0x1.abb5cf29e076b1f30f2dbef2decbp-2Q, 0x1.5fdcb9c5e1f87c285afdd98f767dp-2Q, -0x1.af4e9b9242255620df43c5f22d7fp-3Q, 0x1.57b33e4d63cb5298c708e6fd316dp-4Q, -0x1.736294d370dec79efb385dfdd9c2p-5Q, 0x1.e1a61d7964668ec603c20655891bp-6Q, -0x1.38138139d6cd8275efff1464190ap-7Q, 0x1.a99b874715d59140bd38f0c805c4p-10Q, -0x1.191ada841d111d8ae180fd0e9563p-10Q, 0x1.44a23a1750afa85a3000e1c75486p-12Q, 0x1.4db128e094987961ef3da6b416efp-13Q, -0x1.2cad37f3dbf9e7a2353f8dcbd256p-14Q, 0x1.f38c667f694821291da05561f948p-19Q, 0x1.c870773604d02f72b6510873557cp-24Q, -0x1.cdd01a024c710ef11bd7cd0b9b3cp-34Q, -0x0p+0Q};
+            }
+        }
+        #endif
+    }
+    std::array<Real, 2*p> m{};
+    for (auto & x : m) {
+        x = std::numeric_limits<Real>::quiet_NaN();
+    }
+    return m;
+}
+
+} // namespaces
+#endif
diff --git a/test/daubechies_scaling_test.cpp b/test/daubechies_scaling_test.cpp
new file mode 100644
index 000000000..9601844cf
--- /dev/null
+++ b/test/daubechies_scaling_test.cpp
@@ -0,0 +1,441 @@
+/*
+ * Copyright Nick Thompson, 2019
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include "math_unit_test.hpp"
+#include <numeric>
+#include <utility>
+#include <boost/core/demangle.hpp>
+#include <boost/hana/for_each.hpp>
+#include <boost/hana/ext/std/integer_sequence.hpp>
+#include <boost/math/tools/condition_numbers.hpp>
+#include <boost/math/differentiation/finite_difference.hpp>
+#include <boost/math/special_functions/daubechies_scaling.hpp>
+#include <boost/math/filters/daubechies.hpp>
+#include <boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp>
+#include <boost/math/constants/constants.hpp>
+
+#ifdef BOOST_HAS_FLOAT128
+#include <boost/multiprecision/float128.hpp>
+using boost::multiprecision::float128;
+#endif
+
+
+using boost::math::constants::pi;
+using boost::math::constants::root_two;
+
+// Mallat, Theorem 7.4, characterization number 3:
+// A conjugate mirror filter has p vanishing moments iff h^{(n)}(pi) = 0 for 0 <= n < p.
+template<class Real, unsigned p>
+void test_daubechies_filters()
+{
+    Real tol = 3*std::numeric_limits<Real>::epsilon();
+    using boost::math::filters::daubechies_scaling_filter;
+    using boost::math::filters::daubechies_wavelet_filter;
+
+    auto h = daubechies_scaling_filter<Real, p>();
+    auto g = daubechies_wavelet_filter<Real, p>();
+
+    auto inner = std::inner_product(h.begin(), h.end(), g.begin(), Real(0));
+    CHECK_MOLLIFIED_CLOSE(0, inner, tol);
+
+    // This is implied by Fourier transform of the two-scale dilatation equation;
+    // If this doesn't hold, the infinite product for m_0 diverges.
+    Real H0 = 0;
+    for (size_t j = 0; j < h.size(); ++j)
+    {
+        H0 += h[j];
+    }
+    CHECK_MOLLIFIED_CLOSE(root_two<Real>(), H0, tol);
+
+    // This is implied if we choose the scaling function to be an orthonormal basis of V0.
+    Real scaling = 0;
+    for (size_t j = 0; j < h.size(); ++j) {
+      scaling += h[j]*h[j];
+    }
+    CHECK_MOLLIFIED_CLOSE(1, scaling, tol);
+
+    using std::pow;
+    // Daubechies wavelet of order p has p vanishing moments.
+    // Unfortunately, the condition number of the sum is infinite.
+    // Hence we must scale the tolerance by the summation condition number to ensure that we don't get spurious test failures.
+    for (size_t k = 1; k < p; ++k)
+    {
+        Real hk = 0;
+        Real abs_hk = 0;
+        for (size_t n = 0; n < h.size(); ++n)
+        {
+            Real t = pow(n, k)*h[n];
+            if (n & 1)
+            {
+                hk -= t;
+            }
+            else
+            {
+                hk += t;
+            }
+            abs_hk += abs(t);
+        }
+        // Multiply the tolerance by the condition number:
+        Real cond = abs(hk) > 0 ? abs_hk/abs(hk) : 1/std::numeric_limits<Real>::epsilon();
+        if (!CHECK_MOLLIFIED_CLOSE(0, hk, cond*tol))
+        {
+            std::cerr << "  The " << k << "th moment of the p = " << p << " filter did not vanish\n";
+            std::cerr << "  Condition number = " << abs_hk/abs(hk) << "\n";
+        }
+    }
+
+    // For the scaling function to be orthonormal to its integer translates,
+    // sum h_k h_{k-2l} = \delta_{0,l}.
+    // See Theoretical Numerical Analysis, Atkinson, Exercise 4.5.2.
+    // This is the last condition we could test to ensure that the filters are correct,
+    // but I'm not gonna bother because it's painful!
+}
+
+// Test that the filters agree with Daubechies, Ten Lenctures on Wavelets, Table 6.1:
+
+void test_agreement_with_ten_lectures()
+{
+    std::array<double, 4> h2 = {0.4829629131445341, 0.8365163037378077, 0.2241438680420134, -0.1294095225512603};
+    auto h2_ = boost::math::filters::daubechies_scaling_filter<double, 2>();
+    for (size_t i = 0; i < h2.size(); ++i)
+    {
+        CHECK_ULP_CLOSE(h2[i], h2_[i], 3);
+    }
+
+    std::array<double, 6> h3 = {0.3326705529500825, 0.8068915093110924, 0.4598775021184914, -0.1350110200102546, -0.0854412738820267, 0.0352262918857095};
+    auto h3_ = boost::math::filters::daubechies_scaling_filter<double, 3>();
+    for (size_t i = 0; i < h3.size(); ++i)
+    {
+        CHECK_ULP_CLOSE(h3[i], h3_[i], 5);
+    }
+
+    std::array<double, 8> h4 = {0.2303778133088964, 0.7148465705529154, 0.6308807679298587, -0.0279837694168599, -0.1870348117190931, 0.0308413818355607, 0.0328830116668852 , -0.010597401785069};
+    auto h4_ = boost::math::filters::daubechies_scaling_filter<double, 4>();
+    for (size_t i = 0; i < h4.size(); ++i)
+    {
+        if(!CHECK_ULP_CLOSE(h4[i], h4_[i], 18)) {
+            std::cerr << "  Index " << i << " incorrect.\n";
+        }
+    }
+
+}
+
+template<class Real1, class Real2, size_t p>
+void test_filter_ulp_distance()
+{
+    using boost::math::filters::daubechies_scaling_filter;
+    auto h1 = daubechies_scaling_filter<Real1, p>();
+    auto h2 = daubechies_scaling_filter<Real2, p>();
+
+    for (size_t i = 0; i < h1.size(); ++i)
+    {
+        if(!CHECK_ULP_CLOSE(h1[i], h2[i], 0))
+        {
+            std::cerr << "  Index " << i << " at order " << p << " failed tolerance check\n";
+        }
+    }
+}
+
+
+template<class Real, unsigned p, unsigned order>
+void test_integer_grid()
+{
+    using boost::math::detail::daubechies_scaling_integer_grid;
+    using boost::math::tools::summation_condition_number;
+    Real unit_roundoff = std::numeric_limits<Real>::epsilon()/2;
+    auto grid = daubechies_scaling_integer_grid<Real, p, order>();
+
+    if constexpr (order == 0) {
+        auto cond = summation_condition_number<Real>(0);
+        for (auto & x : grid) {
+            cond += x;
+        }
+        CHECK_MOLLIFIED_CLOSE(1, cond.sum(), 6*cond.l1_norm()*unit_roundoff);
+    }
+
+    if constexpr (order == 1) {
+        auto cond = summation_condition_number<Real>(0);
+        for (size_t i = 0; i < grid.size(); ++i) {
+            cond += i*grid[i];
+        }
+        CHECK_MOLLIFIED_CLOSE(-1, cond.sum(), 2*cond.l1_norm()*unit_roundoff);
+    }
+
+    if constexpr (order == 2) {
+        auto cond = summation_condition_number<Real>(0);
+        for (size_t i = 0; i < grid.size(); ++i) {
+            cond += i*i*grid[i];
+        }
+        CHECK_MOLLIFIED_CLOSE(2, cond.sum(), 2*cond.l1_norm()*unit_roundoff);
+    }
+
+    if constexpr (order == 3) {
+        auto cond = summation_condition_number<Real>(0);
+        for (size_t i = 0; i < grid.size(); ++i) {
+            cond += i*i*i*grid[i];
+        }
+        CHECK_MOLLIFIED_CLOSE(-6, cond.sum(), 2*cond.l1_norm()*unit_roundoff);
+    }
+
+    if constexpr (order == 4) {
+        auto cond = summation_condition_number<Real>(0);
+        for (size_t i = 0; i < grid.size(); ++i) {
+            cond += i*i*i*i*grid[i];
+        }
+        CHECK_MOLLIFIED_CLOSE(24, cond.sum(), 2*cond.l1_norm()*unit_roundoff);
+    }
+
+}
+
+template<class Real>
+void test_dyadic_grid()
+{
+    std::cout << "Testing dyadic grid on type " << boost::core::demangle(typeid(Real).name()) << "\n";
+    boost::hana::for_each(std::make_index_sequence<13>(), [&](auto i){
+        auto phijk = boost::math::detail::dyadic_grid<Real, i+2, 0>(0);
+        auto phik = boost::math::detail::daubechies_scaling_integer_grid<Real, i+2, 0>();
+        assert(phik.size() == phijk.size());
+
+        for (size_t k = 0; k < phik.size(); ++k)
+        {
+            CHECK_ULP_CLOSE(phik[k], phijk[k], 0);
+        }
+
+        for (size_t j = 1; j < 10; ++j)
+        {
+            auto phijk = boost::math::detail::dyadic_grid<Real, i+2, 0>(j);
+            auto phik = boost::math::detail::daubechies_scaling_integer_grid<Real, i+2, 0>();
+            for (size_t i = 0; i < phik.size(); ++i)
+            {
+                CHECK_ULP_CLOSE(phik[i], phijk[i*(1<<j)], 0);
+            }
+
+            // This test is from Daubechies, Ten Lectures on Wavelets, Ch 7 "More About Compactly Supported Wavelets",
+            // page 245: \forall y \in \mathbb{R}, \sum_{n \in \mathbb{Z}} \phi(y+n) = 1
+            for (size_t k = 1; k < j; ++k)
+            {
+                auto cond = boost::math::tools::summation_condition_number<Real>(0);
+                for (size_t i = 0; i < phik.size(); ++i)
+                {
+                    size_t idx = i*(1<<j) + k;
+                    if (idx < phijk.size())
+                    {
+                        cond += phijk[idx];
+                    }
+                }
+                CHECK_MOLLIFIED_CLOSE(1, cond.sum(), 10*cond()*std::numeric_limits<Real>::epsilon());
+            }
+        }
+    });
+}
+
+
+template<class Real>
+void test_interpolation()
+{
+    std::cout << "Testing constant interpolation on type " << boost::core::demangle(typeid(Real).name()) << "\n";
+    boost::hana::for_each(std::make_index_sequence<13>(), [&](auto i){
+        auto phik = boost::math::detail::daubechies_scaling_integer_grid<Real, i+2, 0>();
+        for (size_t j = 0; j < 5; ++j) {
+            auto phi = boost::math::daubechies_scaling<Real, i+2>(j);
+            assert(phik.size()==phi.support().second + 1);
+            for (size_t k = 1; k < phik.size(); ++k) {
+                auto expected = phik[k];
+                auto computed = phi.constant_interpolation(k);
+                if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
+                    std::cerr << "  Constant interpolation wrong at x = " << k << ", j_max = " << j << ", p = " << i+2 << "\n";
+                }
+
+                computed = phi.single_crank_linear(k);
+                if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
+                    std::cerr << "  Single crank linear interpolation wrong at x = " << k << ", j_max = " << j << ", p = " << i+2 << "\n";
+                }
+
+                computed = phi.first_order_taylor(k);
+                if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
+                    std::cerr << "  First order Taylor expansion wrong at x = " << k << ", j_max = " << j << ", p = " << i+2 << "\n";
+                }
+
+                computed = phi.constant_interpolation(k*(1+2*std::numeric_limits<Real>::epsilon()));
+                if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
+                    std::cerr << "  Constant interpolation wrong at x = " << k << ", j_max = " << j << ", p = " << i+2 << "\n";
+                }
+
+                computed = phi.constant_interpolation(k*(1-2*std::numeric_limits<Real>::epsilon()));
+                if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
+                    std::cerr << "  Constant interpolation wrong at x = " << k << ", j_max = " << j << ", p = " << i+2 << "\n";
+                }
+
+                computed = phi.linear_interpolation(k);
+                if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
+                    std::cerr << "  Linear interpolation wrong at x = " << k << ", j_max = " << j << ", p = " << i+2 << "\n";
+                }
+            }
+
+            for (size_t i = 0; i < phi.size() -1; ++i) {
+                Real x = phi.index_to_abscissa(i);
+                Real expected = phi[i];
+                Real computed = phi.constant_interpolation(x);
+                if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
+                    std::cerr << "  Constant interpolation wrong at x = " << x << ", j_max = " << j << ", p = " << i+2 << "\n";
+                }
+
+                computed = phi.linear_interpolation(x);
+                if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
+                    std::cerr << "  Linear interpolation wrong at x = " << x << ", j_max = " << j << ", p = " << i+2 << "\n";
+                }
+
+                computed = phi.single_crank_linear(x);
+                if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
+                    std::cerr << "  Single crank linear interpolation wrong at x = " << x << ", j_max = " << j << ", p = " << i+2 << "\n";
+                }
+
+                computed = phi.first_order_taylor(x);
+                if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
+                    std::cerr << "  First order Taylor expansion wrong at x = " << x << ", j_max = " << j << ", p = " << i+2 << "\n";
+                }
+
+                x += phi.spacing()/2;
+                computed = phi.linear_interpolation(x);
+                expected = phi[i]/2 + phi[i+1]/2;
+                if (!CHECK_ULP_CLOSE(expected, computed, 1)) {
+                    std::cerr << "  Linear interpolation wrong at x = " << x << ", j_max = " << j << ", p = " << i+2 << "\n";
+                }
+
+                x *= (1+std::numeric_limits<Real>::epsilon());
+                computed = phi.constant_interpolation(x);
+                expected = phi[i+1];
+                if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
+                    std::cerr << "  Linear interpolation wrong at x = " << x << ", j_max = " << j << ", p = " << i+2 << "\n";
+                }
+
+            }
+        }
+    });
+}
+
+// Taken from Lin, 2005, doi:10.1016/j.amc.2004.12.038,
+// "Direct algorithm for computation of derivatives of the Daubechies basis functions"
+void test_first_derivative()
+{
+    auto phi1_3 = boost::math::detail::daubechies_scaling_integer_grid<long double, 3, 1>();
+    std::array<long double, 6> lin_3{0.0L, 1.638452340884085725014976L, -2.232758190463137395017742L, 0.5501593582740176149905562L, 0.04414649130503405501220997L, 0.0L};
+    for (size_t i = 0; i < lin_3.size(); ++i)
+    {
+        if(!CHECK_ULP_CLOSE(lin_3[i], phi1_3[i], 0))
+        {
+            std::cerr << "  Index " << i << " is incorrect\n";
+        }
+    }
+
+    auto phi1_4 = boost::math::detail::daubechies_scaling_integer_grid<long double, 4, 1>();
+    std::array<long double, 8> lin_4 = {0.0L, 1.776072007522184640093776L, -2.785349397229543142492785L, 1.192452536632278174347632L, -0.1313745151846729587935189L, -0.05357102822023923595359996L,0.001770396479992522798495351L, 0.0L};
+
+    for (size_t i = 0; i < lin_4.size(); ++i)
+    {
+        if(!CHECK_ULP_CLOSE(lin_4[i], phi1_4[i], 0))
+        {
+            std::cerr << "  Index " << i << " is incorrect\n";
+        }
+    }
+
+    std::array<long double, 10> lin_5 = {0.0L,1.558326313047001366564379L,-2.436012783189551921436896L,1.235905129801454293947039L,-0.3674377136938866359947561L,-0.02178035117564654658884556L,0.03234719350814368885815854L,-0.001335619912770701035229331L,-0.00001216838474354431384970525L,0.0L};
+    auto phi1_5 = boost::math::detail::daubechies_scaling_integer_grid<long double, 5, 1>();
+    for (size_t i = 0; i < lin_5.size(); ++i)
+    {
+        if(!CHECK_ULP_CLOSE(lin_5[i], phi1_5[i], 0))
+        {
+            std::cerr << "  Index " << i << " is incorrect\n";
+        }
+    }
+}
+
+int main()
+{
+    test_agreement_with_ten_lectures();
+    test_first_derivative();
+    test_dyadic_grid<float>();
+    test_dyadic_grid<double>();
+    test_dyadic_grid<long double>();
+    test_dyadic_grid<float128>();
+    test_interpolation<float>();
+    test_interpolation<double>();
+    test_interpolation<long double>();
+    test_interpolation<float128>();
+
+    // All scaling functions have a first derivative.
+    boost::hana::for_each(std::make_index_sequence<13>(), [&](auto idx){
+        test_integer_grid<float, idx+2, 0>();
+        test_integer_grid<float, idx+2, 1>();
+        test_integer_grid<double, idx+2, 0>();
+        test_integer_grid<double, idx+2, 1>();
+        test_integer_grid<long double, idx+2, 0>();
+        test_integer_grid<long double, idx+2, 1>();
+        #ifdef BOOST_HAS_FLOAT128
+        test_integer_grid<float128, idx+2, 0>();
+        test_integer_grid<float128, idx+2, 1>();
+        #endif
+    });
+
+    // 4-tap (2 vanishing moment) scaling function does not have a second derivative;
+    // all other scaling functions do.
+    boost::hana::for_each(std::make_index_sequence<13>(), [&](auto idx){
+        test_integer_grid<float, idx+3, 2>();
+        test_integer_grid<double, idx+3, 2>();
+        test_integer_grid<long double, idx+3, 2>();
+        #ifdef BOOST_HAS_FLOAT128
+        test_integer_grid<boost::multiprecision::float128, idx+3, 2>();
+        #endif
+    });
+
+    // 8-tap filter (4 vanishing moments) is the first to have a third derivative.
+    boost::hana::for_each(std::make_index_sequence<12>(), [&](auto idx){
+        test_integer_grid<float, idx+4, 3>();
+        test_integer_grid<double, idx+4, 3>();
+        test_integer_grid<long double, idx+4, 3>();
+        #ifdef BOOST_HAS_FLOAT128
+        test_integer_grid<boost::multiprecision::float128, idx+4, 3>();
+        #endif
+    });
+
+    // 10-tap filter (5 vanishing moments) is the first to have a fourth derivative.
+    boost::hana::for_each(std::make_index_sequence<11>(), [&](auto idx){
+        test_integer_grid<float, idx+5, 4>();
+        test_integer_grid<double, idx+5, 4>();
+        test_integer_grid<long double, idx+5, 4>();
+        #ifdef BOOST_HAS_FLOAT128
+        test_integer_grid<boost::multiprecision::float128, idx+5, 4>();
+        #endif
+    });
+
+    boost::hana::for_each(std::make_index_sequence<8>(), [&](auto i){
+      test_daubechies_filters<float, i+1>();
+    });
+
+    boost::hana::for_each(std::make_index_sequence<12>(), [&](auto i){
+      test_daubechies_filters<double, i+1>();
+    });
+
+    boost::hana::for_each(std::make_index_sequence<11>(), [&](auto i){
+      test_daubechies_filters<long double, i+1>();
+    });
+
+
+    #ifdef BOOST_HAS_FLOAT128
+    boost::hana::for_each(std::make_index_sequence<23>(), [&](auto i){
+        test_filter_ulp_distance<float128, long double, i+1>();
+        test_filter_ulp_distance<float128, double, i+1>();
+        test_filter_ulp_distance<float128, float, i+1>();
+    });
+
+    boost::hana::for_each(std::make_index_sequence<12>(), [&](auto i){
+        test_daubechies_filters<float128, i+1>();
+    });
+    #endif
+
+    return boost::math::test::report_errors();
+}

From b5188cfabaf0583b6f1fbd3b1907fd148964b34b Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Sun, 26 Jan 2020 11:27:28 +0800
Subject: [PATCH 002/104] Continuous Daubechies wavelets: Fight bitrot.

---
 include/boost/math/filters/daubechies.hpp     |  7 ++++
 .../special_functions/daubechies_scaling.hpp  |  8 ++--
 test/Jamfile.v2                               |  1 +
 test/daubechies_scaling_test.cpp              | 40 +++++++++++++++++++
 4 files changed, 52 insertions(+), 4 deletions(-)

diff --git a/include/boost/math/filters/daubechies.hpp b/include/boost/math/filters/daubechies.hpp
index 94e3382c8..74806ca88 100644
--- a/include/boost/math/filters/daubechies.hpp
+++ b/include/boost/math/filters/daubechies.hpp
@@ -400,7 +400,14 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.91785023a98792eac41b5272c04bp-13Q, 0x1.93f9805696b9ba9d87c3df41a8d9p-9Q, 0x1.7059c4b494de928c16cf6cacf0a7p-6Q, 0x1.8e62d8a0a8ffbd2cc57d79f83e08p-4Q, 0x1.17756f5530d69044d0184f790b3ep-2Q, 0x1.023cebcae9f66d3d390049f78dcp-1Q, 0x1.265e6eff960cc4ccf24089549b66p-1Q, 0x1.1fbaad4726276054f5d700d1bfb6p-2Q, -0x1.7f8826c0619915e6978c42a74dfcp-3Q, -0x1.4592ded92acf8c9c5ecd6ba9faddp-2Q, 0x1.390a478f54bbad8c711b3d202a1ap-8Q, 0x1.e9f54ac655c13958344e31a88778p-3Q, 0x1.5c6535de6b4e500e1e067af4d00ep-5Q, -0x1.5e912ec022b5fcb42ec3601ecf9bp-3Q, -0x1.3da9a08b26c34196db8bd596e813p-5Q, 0x1.efaeca9aee1921f4bc36a577b638p-4Q, 0x1.57bcf98fd11ce6827e350101b72ep-6Q, -0x1.5088bd1cf023da2d878ac9ebafc5p-4Q, -0x1.2c0d69ece949ee5284dcfb042baap-8Q, 0x1.a4434b89b691509ff6541a080cecp-5Q, -0x1.440e7548329f53e7873db8128a63p-8Q, -0x1.ce3e5912a230366d14a862ea3672p-6Q, 0x1.f61e5ce9a7ff0906541711dfe2e7p-8Q, 0x1.ab9f170d72cc6036a5092b63c08ap-7Q, -0x1.9c50c528bc77817ae0788ffc773ap-8Q, -0x1.371235b499d33e83c0b1b543f6e8p-8Q, 0x1.e9b0e84ddc0468e17e4fa3636bf9p-9Q, 0x1.2e73daaf19dbb24f6ae6d9d95255p-10Q, -0x1.bcb74a39ee49fe08e2b9fd7aeef1p-10Q, -0x1.7274d8ffa9744517f2f1470cebeep-15Q, 0x1.334ca46898dae11da29a57e9f92ap-11Q, -0x1.ef71f401aeeeb5e13dd40efc0a0cp-14Q, -0x1.32337036c1616db93444903d828ep-13Q, 0x1.131ee633363469bb9bebca29a839p-14Q, 0x1.6e4981b862b8b7d5bb86d25cc3eap-16Q, -0x1.536263fe83a124aaa2092f47c711p-16Q, 0x1.ccd17bbbe3d0407ffce581eb4165p-27Q, 0x1.05cc64bbcf95fbb57637394fb838p-18Q, -0x1.e21fa8ce8bf7a7465a57d37cce9ap-21Q, -0x1.b0fcbaac8055d95fcb97dc94d8aap-22Q, 0x1.d137c82c35ed75b3cca32ab07fp-23Q, -0x1.160c0805b95d2f0cf1ffb7605bf2p-31Q, -0x1.838882edd8947aab05cd00305346p-26Q, 0x1.627091a0c660cff16c28fc227cd6p-28Q, 0x1.050b72dfcacebaae0203f358d56p-31Q, -0x1.ba8411e011af62ac1faf9b23aa51p-32Q, 0x1.3380aec6c4cc755d395c84cee933p-34Q, -0x1.31989d5a96be32d359a4b1032025p-38Q};
         }
         #endif
+
     }
+    std::array<Real, 2*p> m{};
+    for (auto & x : m) {
+        x = std::numeric_limits<Real>::quiet_NaN();
+    }
+    return m;
+
 }
 
 template<class Real, size_t p>
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index d58e30ed6..e7a67e65f 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -1,5 +1,5 @@
 /*
- * Copyright Nick Thompson, 2019
+ * Copyright Nick Thompson, 2020
  * Use, modification and distribution are subject to the
  * Boost Software License, Version 1.0. (See accompanying file
  * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
@@ -51,7 +51,7 @@ std::vector<Real> dyadic_grid(size_t j_max)
             size_t delivery_idx = k*(1 << (j_max-j));
             if (delivery_idx >= v.size())
             {
-                std::cout << "Delivery index out of range!\n";
+                std::cerr << "Delivery index out of range!\n";
                 continue;
             }
             Real term = 0;
@@ -62,8 +62,8 @@ std::vector<Real> dyadic_grid(size_t j_max)
                 }
             }
             if (!isnan(v[delivery_idx])) {
-                std::cout << "Delivery index already populated!, = " << v[delivery_idx] << "\n";
-                std::cout << "would overwrite with " << term << "\n";
+                std::cerr << "Delivery index already populated!, = " << v[delivery_idx] << "\n";
+                std::cerr << "would overwrite with " << term << "\n";
             }
             v[delivery_idx] = term;
         }
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index 141214e4f..7be0bfe7d 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -942,6 +942,7 @@ test-suite misc :
    [ run cardinal_b_spline_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run jacobi_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run gegenbauer_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
+   [ run daubechies_scaling_test.cpp  : : :  [ requires cxx17_if_constexpr cxx17_std_apply ]  [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run whittaker_shannon_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] ]
    [ run cardinal_quadratic_b_spline_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] ]
    [ run cardinal_quintic_b_spline_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
diff --git a/test/daubechies_scaling_test.cpp b/test/daubechies_scaling_test.cpp
index 9601844cf..f4362aebc 100644
--- a/test/daubechies_scaling_test.cpp
+++ b/test/daubechies_scaling_test.cpp
@@ -32,6 +32,7 @@ using boost::math::constants::root_two;
 template<class Real, unsigned p>
 void test_daubechies_filters()
 {
+    std::cout << "Testing Daubechies filters with " << p << " vanishing moments on type " << boost::core::demangle(typeid(Real).name()) << "\n";
     Real tol = 3*std::numeric_limits<Real>::epsilon();
     using boost::math::filters::daubechies_scaling_filter;
     using boost::math::filters::daubechies_wavelet_filter;
@@ -99,6 +100,7 @@ void test_daubechies_filters()
 
 void test_agreement_with_ten_lectures()
 {
+    std::cout << "Testing agreement with Ten Lectures\n";
     std::array<double, 4> h2 = {0.4829629131445341, 0.8365163037378077, 0.2241438680420134, -0.1294095225512603};
     auto h2_ = boost::math::filters::daubechies_scaling_filter<double, 2>();
     for (size_t i = 0; i < h2.size(); ++i)
@@ -127,6 +129,9 @@ void test_agreement_with_ten_lectures()
 template<class Real1, class Real2, size_t p>
 void test_filter_ulp_distance()
 {
+    std::cout << "Testing filters ULP distance between types "
+              << boost::core::demangle(typeid(Real1).name()) << "and"
+              << boost::core::demangle(typeid(Real2).name()) << "\n";
     using boost::math::filters::daubechies_scaling_filter;
     auto h1 = daubechies_scaling_filter<Real1, p>();
     auto h2 = daubechies_scaling_filter<Real2, p>();
@@ -144,6 +149,7 @@ void test_filter_ulp_distance()
 template<class Real, unsigned p, unsigned order>
 void test_integer_grid()
 {
+    std::cout << "Testing integer grid with " << p << " vanishing moments and " << order << " derivative on type " << boost::core::demangle(typeid(Real).name()) << "\n";
     using boost::math::detail::daubechies_scaling_integer_grid;
     using boost::math::tools::summation_condition_number;
     Real unit_roundoff = std::numeric_limits<Real>::epsilon()/2;
@@ -163,6 +169,13 @@ void test_integer_grid()
             cond += i*grid[i];
         }
         CHECK_MOLLIFIED_CLOSE(-1, cond.sum(), 2*cond.l1_norm()*unit_roundoff);
+
+        // Differentiate \sum_{k} \phi(x-k) = 1 to get this:
+        cond = summation_condition_number<Real>(0);
+        for (size_t i = 0; i < grid.size(); ++i) {
+            cond += grid[i];
+        }
+        CHECK_MOLLIFIED_CLOSE(0, cond.sum(), 2*cond.l1_norm()*unit_roundoff);
     }
 
     if constexpr (order == 2) {
@@ -171,6 +184,13 @@ void test_integer_grid()
             cond += i*i*grid[i];
         }
         CHECK_MOLLIFIED_CLOSE(2, cond.sum(), 2*cond.l1_norm()*unit_roundoff);
+
+        // Differentiate \sum_{k} \phi(x-k) = 1 to get this:
+        cond = summation_condition_number<Real>(0);
+        for (size_t i = 0; i < grid.size(); ++i) {
+            cond += grid[i];
+        }
+        CHECK_MOLLIFIED_CLOSE(0, cond.sum(), 2*cond.l1_norm()*unit_roundoff);
     }
 
     if constexpr (order == 3) {
@@ -179,6 +199,14 @@ void test_integer_grid()
             cond += i*i*i*grid[i];
         }
         CHECK_MOLLIFIED_CLOSE(-6, cond.sum(), 2*cond.l1_norm()*unit_roundoff);
+
+        // Differentiate \sum_{k} \phi(x-k) = 1 to get this:
+        cond = summation_condition_number<Real>(0);
+        for (size_t i = 0; i < grid.size(); ++i) {
+            cond += grid[i];
+        }
+        CHECK_MOLLIFIED_CLOSE(0, cond.sum(), 2*cond.l1_norm()*unit_roundoff);
+
     }
 
     if constexpr (order == 4) {
@@ -187,6 +215,13 @@ void test_integer_grid()
             cond += i*i*i*i*grid[i];
         }
         CHECK_MOLLIFIED_CLOSE(24, cond.sum(), 2*cond.l1_norm()*unit_roundoff);
+
+        // Differentiate \sum_{k} \phi(x-k) = 1 to get this:
+        cond = summation_condition_number<Real>(0);
+        for (size_t i = 0; i < grid.size(); ++i) {
+            cond += grid[i];
+        }
+        CHECK_MOLLIFIED_CLOSE(0, cond.sum(), 2*cond.l1_norm()*unit_roundoff);
     }
 
 }
@@ -361,11 +396,16 @@ int main()
     test_dyadic_grid<float>();
     test_dyadic_grid<double>();
     test_dyadic_grid<long double>();
+    #ifdef BOOST_HAS_FLOAT128
     test_dyadic_grid<float128>();
+    #endif
+    /*
     test_interpolation<float>();
     test_interpolation<double>();
     test_interpolation<long double>();
+    #if BOOST_HAS_FLOAT128
     test_interpolation<float128>();
+    #endif*/
 
     // All scaling functions have a first derivative.
     boost::hana::for_each(std::make_index_sequence<13>(), [&](auto idx){

From 01b7bfe8b5530d9b66523db6e9386133e03902aa Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Sun, 26 Jan 2020 13:38:25 +0800
Subject: [PATCH 003/104] Daubechies scaling: Remove superfluous
 initialization. [CI SKIP]

---
 include/boost/math/special_functions/daubechies_scaling.hpp | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index e7a67e65f..c478c0175 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -24,6 +24,7 @@ namespace detail {
 template<class Real, int p, int order>
 std::vector<Real> dyadic_grid(size_t j_max)
 {
+    using std::isnan;
     auto c = boost::math::filters::daubechies_scaling_filter<Real, p>();
     Real scale = boost::math::constants::root_two<Real>()*(1 << order);
     for (auto & x : c)
@@ -35,11 +36,10 @@ std::vector<Real> dyadic_grid(size_t j_max)
 
     // Maximum sensible j for 32 bit floats is j_max = 22:
     std::vector<Real> v(2*p + (2*p-1)*((1<<j_max) -1), std::numeric_limits<Real>::quiet_NaN());
-    v.resize(2*p + (2*p-1)*((1<<j_max) -1), std::numeric_limits<Real>::quiet_NaN());
     v[0] = 0;
     v[v.size()-1] = 0;
     for (size_t i = 0; i < phik.size(); ++i) {
-        v[i*(1<<(j_max))] = phik[i];
+        v[i*(1<<j_max)] = phik[i];
     }
 
     for (size_t j = 1; j <= j_max; ++j)

From 7949f48c2282221feab413d4bc1841bc3e71c7aa Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Mon, 27 Jan 2020 14:21:10 +0800
Subject: [PATCH 004/104] Static assert on the number of derivatives [CI SKIP]

---
 .../special_functions/detail/daubechies_scaling_integer_grid.hpp | 1 +
 1 file changed, 1 insertion(+)

diff --git a/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp b/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp
index fe3296832..c328db53b 100644
--- a/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp
+++ b/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp
@@ -20,6 +20,7 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
     static_assert(p <= 15, "Integer grids only implemented up to 15.");
     static_assert(p > 1, "Integer grids only implemented for p >= 2.");
     if constexpr (p == 2) {
+        static_assert(order <= 1 && order >= 0, "The 2 vanishing moment Daubechies scaling function only has one derivative.");
         if constexpr (std::is_same_v<Real, float>) {
             if constexpr (order == 0) {
                 return {0x0p+0f, 0x1.5db3d8p+0f, -0x1.76cf5ep-2f, 0x0p+0f};

From 3db1f564aacfecf946fadc34577b6388631915d8 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Tue, 4 Feb 2020 16:19:44 -0500
Subject: [PATCH 005/104] Used signed integer indexes in Daubechies scaling [CI
 SKIP]

---
 .../special_functions/daubechies_scaling.hpp  | 24 +++++++++++--------
 1 file changed, 14 insertions(+), 10 deletions(-)

diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index c478c0175..12b37f6e9 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -11,6 +11,7 @@
 #include <array>
 #include <cmath>
 #include <thread>
+#include <iostream>
 #include <boost/multiprecision/float128.hpp>
 #include <boost/math/constants/constants.hpp>
 #include <boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp>
@@ -22,7 +23,7 @@ namespace boost::math {
 namespace detail {
 
 template<class Real, int p, int order>
-std::vector<Real> dyadic_grid(size_t j_max)
+std::vector<Real> dyadic_grid(int64_t j_max)
 {
     using std::isnan;
     auto c = boost::math::filters::daubechies_scaling_filter<Real, p>();
@@ -38,26 +39,29 @@ std::vector<Real> dyadic_grid(size_t j_max)
     std::vector<Real> v(2*p + (2*p-1)*((1<<j_max) -1), std::numeric_limits<Real>::quiet_NaN());
     v[0] = 0;
     v[v.size()-1] = 0;
-    for (size_t i = 0; i < phik.size(); ++i) {
+    for (int64_t i = 0; i < (int64_t) phik.size(); ++i) {
         v[i*(1<<j_max)] = phik[i];
     }
 
-    for (size_t j = 1; j <= j_max; ++j)
+    for (int64_t j = 1; j <= j_max; ++j)
     {
-        size_t k_max = v.size()/(1 << (j_max-j));
-        for (size_t k = 1; k < k_max;  k += 2)
+        int64_t k_max = v.size()/(1 << (j_max-j));
+        for (int64_t k = 1; k < k_max;  k += 2)
         {
             // Where this value will go:
-            size_t delivery_idx = k*(1 << (j_max-j));
-            if (delivery_idx >= v.size())
+            int64_t delivery_idx = k*(1 << (j_max-j));
+            if (delivery_idx >= (int64_t) v.size())
             {
                 std::cerr << "Delivery index out of range!\n";
                 continue;
             }
             Real term = 0;
-            for (size_t l = 0; l < c.size(); ++l) {
-                size_t idx = k*(1 << (j_max - j + 1)) - l*(1 << j_max);
-                if (idx >= 0 && idx < v.size()) {
+            for (int64_t l = 0; l < (int64_t) c.size(); ++l) {
+                int64_t idx = k*(1 << (j_max - j + 1)) - l*(1 << j_max);
+                if (idx < 0) {
+                    break;
+                }
+                if (idx < (int64_t) v.size()) {
                     term += c[l]*v[idx];
                 }
             }

From ef0532c8c32767f47e92c5e5b65b7b0905a02014 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Tue, 4 Feb 2020 18:05:42 -0500
Subject: [PATCH 006/104] Use cubic and quintic hermite interpolators for
 Daubechies scaling [CI SKIP]

---
 .../special_functions/daubechies_scaling.hpp  | 81 ++++++++++++++++---
 1 file changed, 71 insertions(+), 10 deletions(-)

diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index 12b37f6e9..b76d5cf66 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -11,11 +11,14 @@
 #include <array>
 #include <cmath>
 #include <thread>
+#include <future>
 #include <iostream>
 #include <boost/multiprecision/float128.hpp>
 #include <boost/math/constants/constants.hpp>
 #include <boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp>
 #include <boost/math/filters/daubechies.hpp>
+#include <boost/math/interpolators/detail/cubic_hermite_detail.hpp>
+#include <boost/math/interpolators/detail/quintic_hermite_detail.hpp>
 
 
 namespace boost::math {
@@ -82,18 +85,52 @@ std::vector<Real> dyadic_grid(int64_t j_max)
 template<class Real, int p>
 class daubechies_scaling {
 public:
-    daubechies_scaling(int levels = -1)
+    daubechies_scaling(int grid_refinements = -1)
     {
         using boost::multiprecision::float128;
-        if (levels < 0)
+        if (grid_refinements < 0)
         {
-            m_levels = 22;
-        }
-        else {
-            m_levels = levels;
+            grid_refinements = 20;
         }
 
-        auto f1 = [this] {
+        if (p < 4) {
+            throw std::domain_error("only p>=5 is currently implemented!");
+        }
+
+        // Compute the refined grid:
+        std::future<std::vector<Real>> t0 = std::async(std::launch::async, [&grid_refinements]() { return detail::dyadic_grid<Real, p, 0>(grid_refinements); });
+        // Compute the derivative of the refined grid:
+        std::future<std::vector<Real>> t1 = std::async(std::launch::async, [&grid_refinements]() { return detail::dyadic_grid<Real, p, 1>(grid_refinements); });
+
+        // if necessary, compute the second derivative:
+        std::vector<Real> d2ydx2;
+        if constexpr(p >= 6) {
+            std::future<std::vector<Real>> t3 = std::async(std::launch::async, [&grid_refinements]() { return detail::dyadic_grid<Real, p, 2>(grid_refinements); });
+            d2ydx2 = t3.get();
+        }
+
+        auto y = t0.get();
+        auto dydx = t1.get();
+
+
+
+        // Storing the vector of x's is unnecessary; it's only because I haven't implemented an equispaced cubic Hermite interpolator:
+        std::vector<Real> x(y.size());
+        Real h = Real(2*p-1)/(x.size()-1);
+        for (size_t i = 0; i < x.size(); ++i) {
+            x[i] = i*h;
+        }
+
+        if constexpr (p == 4 || p == 5) {
+            m_cbh = std::make_shared<interpolators::detail::cubic_hermite_detail<std::vector<Real>>>(std::move(x), std::move(y), std::move(dydx));
+        }
+        else if constexpr (p >= 6) {
+            
+            m_qh = std::make_shared<interpolators::detail::quintic_hermite_detail<std::vector<Real>>>(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2));
+        }
+
+ 
+        /*auto f1 = [this] {
             auto v = detail::dyadic_grid<float128, p, 0>(this->m_levels);
             this->m_v.resize(v.size());
             for (size_t i = 0; i < v.size(); ++i) {
@@ -133,16 +170,40 @@ public:
         for (auto & x : m_c)
         {
             x *= scale;
+        }*/
+    }
+
+
+    Real operator()(Real x) const {
+        if constexpr (p==4 || p ==5) {
+            return m_cbh->operator()(x);
+        }
+        else if constexpr (p >= 6) {
+            return m_qh->operator()(x);
         }
     }
 
-    Real operator()(Real x) const { return this->linear_interpolation(x); }
+    Real prime(Real x) const {
+        if constexpr (p==4 || p ==5) {
+            return m_cbh->prime(x);
+        }
+        else if constexpr (p >= 6) {
+            return m_qh->prime(x);
+        }
+    }
 
     std::pair<int, int> support() const {
         return {0, 2*p-1};
     }
 
-    Real constant_interpolation(Real x) const {
+private:
+    size_t m_levels;
+    // need this for p = 4,5:
+    std::shared_ptr<interpolators::detail::cubic_hermite_detail<std::vector<Real>>> m_cbh;
+    // need this for p >= 6:
+    std::shared_ptr<interpolators::detail::quintic_hermite_detail<std::vector<Real>>> m_qh;
+
+    /*Real constant_interpolation(Real x) const {
         if (x <= 0 || x >= 2*p-1) {
             return Real(0);
         }
@@ -349,7 +410,7 @@ private:
     std::array<Real, 2*p> m_c;
     std::vector<Real> m_v;
     std::vector<Real> m_v_prime;
-    std::vector<Real> m_v_dbl_prime;
+    std::vector<Real> m_v_dbl_prime;*/
 };
 
 }

From a57144148194cba878d4da7954554ad04256248c Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Wed, 5 Feb 2020 09:38:18 -0500
Subject: [PATCH 007/104] Matched Holder interpolation for Daubechies 2 [CI
 SKIP]

---
 .../special_functions/daubechies_scaling.hpp  | 103 +++++++++---------
 1 file changed, 54 insertions(+), 49 deletions(-)

diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index b76d5cf66..8eb8ec393 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -80,6 +80,44 @@ std::vector<Real> dyadic_grid(int64_t j_max)
     return v;
 }
 
+template<class RandomAccessContainer>
+class matched_holder {
+public:
+    using Real = typename RandomAccessContainer::value_type;
+
+    matched_holder(RandomAccessContainer && y, RandomAccessContainer && dydx, int grid_refinements) : y_{std::move(y)}, dydx_{std::move(dydx)}
+    {
+        h_ = Real(1)/(1<< grid_refinements);
+    }
+    
+    Real operator()(Real x) const {
+        using std::log;
+        using std::floor;
+        using std::sqrt;
+        using std::pow;
+        if (x <= 0 || x >= 3) {
+            return 0;
+        }
+        // This is the exact Holder exponent, but it's pessimistic almost everywhere!
+        // It's only exactly right at dyadic rationals.
+        //Real constexpr const alpha = 2 - log(1+sqrt(Real(3)))/log(Real(2));
+        // So we're gonna make the graph dip a little harder; this will capture more of the self-similar behavior:
+        Real constexpr const alpha = 0.35;
+        int64_t i = static_cast<int64_t>(std::floor(x/h_));
+        Real t = (x- i*h_)/h_;
+        Real v = y_[i];
+        Real dphi = dydx_[i+1]*h_;
+        v += (dphi - alpha*(y_[i+1] - y_[i]))*t/(1-alpha);
+        v += (-dphi + y_[i+1] - y_[i])*pow(t, alpha)/(1-alpha);
+        return v;
+    }
+
+private:
+    Real h_;
+    RandomAccessContainer y_;
+    RandomAccessContainer dydx_;
+};
+
 }
 
 template<class Real, int p>
@@ -93,18 +131,18 @@ public:
             grid_refinements = 20;
         }
 
-        if (p < 4) {
-            throw std::domain_error("only p>=5 is currently implemented!");
+        if (p==3) {
+            throw std::domain_error("p = 3 is not yet implemented!");
         }
-
         // Compute the refined grid:
+        // In fact for float precision I know the grid must be computed in double precision and then cast back down, or else parts of the support are systematically inaccurate.
         std::future<std::vector<Real>> t0 = std::async(std::launch::async, [&grid_refinements]() { return detail::dyadic_grid<Real, p, 0>(grid_refinements); });
         // Compute the derivative of the refined grid:
         std::future<std::vector<Real>> t1 = std::async(std::launch::async, [&grid_refinements]() { return detail::dyadic_grid<Real, p, 1>(grid_refinements); });
 
         // if necessary, compute the second derivative:
         std::vector<Real> d2ydx2;
-        if constexpr(p >= 6) {
+        if constexpr (p >= 6) {
             std::future<std::vector<Real>> t3 = std::async(std::launch::async, [&grid_refinements]() { return detail::dyadic_grid<Real, p, 2>(grid_refinements); });
             d2ydx2 = t3.get();
         }
@@ -121,60 +159,22 @@ public:
             x[i] = i*h;
         }
 
+        if constexpr (p==2) {
+            m_mh = std::make_shared<detail::matched_holder<std::vector<Real>>>(std::move(y), std::move(dydx), grid_refinements);
+        }
         if constexpr (p == 4 || p == 5) {
             m_cbh = std::make_shared<interpolators::detail::cubic_hermite_detail<std::vector<Real>>>(std::move(x), std::move(y), std::move(dydx));
         }
         else if constexpr (p >= 6) {
-            
             m_qh = std::make_shared<interpolators::detail::quintic_hermite_detail<std::vector<Real>>>(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2));
         }
-
- 
-        /*auto f1 = [this] {
-            auto v = detail::dyadic_grid<float128, p, 0>(this->m_levels);
-            this->m_v.resize(v.size());
-            for (size_t i = 0; i < v.size(); ++i) {
-                this->m_v[i] = static_cast<Real>(v[i]);
-            }
-        };
-
-        auto f2 = [this] {
-            auto v_prime = detail::dyadic_grid<float128, p, 1>(this->m_levels);
-            this->m_v_prime.resize(v_prime.size());
-            for (size_t i = 0; i < v_prime.size(); ++i) {
-                this->m_v_prime[i] = static_cast<Real>(v_prime[i]);
-            }
-        };
-
-
-        auto f3 = [this] {
-            auto v_dbl_prime = detail::dyadic_grid<float128, p, 2>(this->m_levels);
-            this->m_v_dbl_prime.resize(v_dbl_prime.size());
-            for (size_t i = 0; i < v_dbl_prime.size(); ++i) {
-                this->m_v_dbl_prime[i] = static_cast<Real>(v_dbl_prime[i]);
-            }
-        };
-
-        std::thread t1(f1);
-        std::thread t2(f2);
-        std::thread t3(f3);
-
-        t1.join();
-        t2.join();
-        t3.join();
-
-        m_inv_spacing = (1 << m_levels);
-
-        m_c = boost::math::filters::daubechies_scaling_filter<Real, p>();
-        Real scale = boost::math::constants::root_two<Real>();
-        for (auto & x : m_c)
-        {
-            x *= scale;
-        }*/
-    }
+     }
 
 
     Real operator()(Real x) const {
+        if constexpr (p==2) {
+            return m_mh->operator()(x);
+        }
         if constexpr (p==4 || p ==5) {
             return m_cbh->operator()(x);
         }
@@ -184,6 +184,9 @@ public:
     }
 
     Real prime(Real x) const {
+        if constexpr (p==2) {
+            throw std::domain_error("The 2-vanishing moment Daubechies scaling function is not continuously differentiable.");
+        }
         if constexpr (p==4 || p ==5) {
             return m_cbh->prime(x);
         }
@@ -198,6 +201,8 @@ public:
 
 private:
     size_t m_levels;
+    // Need this for p = 2:
+    std::shared_ptr<detail::matched_holder<std::vector<Real>>> m_mh;
     // need this for p = 4,5:
     std::shared_ptr<interpolators::detail::cubic_hermite_detail<std::vector<Real>>> m_cbh;
     // need this for p >= 6:

From ae13e5b0bc9912ac0e2164900984ce940ab0f9b8 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Wed, 5 Feb 2020 09:57:21 -0500
Subject: [PATCH 008/104] Daubechies scaling: Also compute filters and grids in
 oct precision [CI SKIP]

---
 example/daubechies_accuracy.cpp               |  649 ++++++++++
 example/daubechies_coefficients.cpp           |   15 +-
 example/daubechies_scaling_integer_grid.cpp   |   21 +-
 include/boost/math/filters/daubechies.hpp     |  148 +--
 .../daubechies_scaling_integer_grid.hpp       | 1099 ++++++++++++-----
 5 files changed, 1507 insertions(+), 425 deletions(-)
 create mode 100644 example/daubechies_accuracy.cpp

diff --git a/example/daubechies_accuracy.cpp b/example/daubechies_accuracy.cpp
new file mode 100644
index 000000000..87e7fdb0f
--- /dev/null
+++ b/example/daubechies_accuracy.cpp
@@ -0,0 +1,649 @@
+#include <iostream>
+#include <unordered_map>
+#include <string>
+#include <future>
+#include <thread>
+#include <boost/math/special_functions/daubechies_scaling.hpp>
+#include <boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp>
+#include <boost/math/interpolators/quintic_hermite.hpp>
+#include <boost/math/interpolators/cubic_hermite.hpp>
+#include <boost/math/interpolators/cardinal_quadratic_b_spline.hpp>
+#include <boost/math/interpolators/cardinal_cubic_b_spline.hpp>
+#include <boost/math/interpolators/cardinal_quintic_b_spline.hpp>
+#include <boost/math/interpolators/whittaker_shannon.hpp>
+#include <boost/math/interpolators/cardinal_trigonometric.hpp>
+#include <boost/math/special_functions/next.hpp>
+#include <boost/math/interpolators/makima.hpp>
+#include <boost/math/interpolators/pchip.hpp>
+#include <boost/multiprecision/float128.hpp>
+#include <boost/core/demangle.hpp>
+#include <boost/math/special_functions/detail/daubechies_scaling_roots.hpp>
+#include <quicksvg/graph_fn.hpp>
+#include <quicksvg/ulp_plot.hpp>
+
+using boost::multiprecision::float128;
+
+template<class Real, int p>
+void do_ulp()
+{
+    std::cout << "Creating ULP plot on type " << boost::core::demangle(typeid(Real).name()) << " and " << p << " vanishing moments.\n";  
+    using std::floor;
+    using std::ceil;
+    using std::abs;
+    int rmax = 14;
+    std::cout << "Computing phi_dense\n";
+    std::future<std::vector<long double>> f1 = std::async(std::launch::async, [&]{ return boost::math::detail::dyadic_grid<long double, p, 0>(rmax); });
+    std::future<std::vector<long double>> f2 = std::async(std::launch::async, [&]{ return boost::math::detail::dyadic_grid<long double, p, 1>(rmax); });
+
+    std::cout << "Computing phi and phi_prime\n";
+    std::future<std::vector<long double>> f3 = std::async(std::launch::async, [&]{ return boost::math::detail::dyadic_grid<long double, p, 0>(rmax-2); });
+    std::future<std::vector<long double>> f4 = std::async(std::launch::async, [&]{ return boost::math::detail::dyadic_grid<long double, p, 1>(rmax-2); });
+    auto phi_dense = f1.get();
+    auto phi_dense_prime = f2.get();
+    auto phi_accurate = f3.get();
+    auto phi_prime_accurate = f4.get();
+
+    Real dx_dense = (2*p-1)/static_cast<Real>(phi_dense.size()-1);
+    std::cout << "Done precomputing grids; downcasting now.\n";
+    std::vector<Real> phi(phi_accurate.size());
+    for (size_t i = 0; i < phi_accurate.size(); ++i) {
+        phi[i] = Real(phi_accurate[i]);
+    }
+    std::vector<Real> phi_prime(phi_accurate.size());
+    for (size_t i = 0; i < phi_prime_accurate.size(); ++i) {
+        phi_prime[i] = Real(phi_prime_accurate[i]);
+    }
+    phi_accurate.resize(0);
+    phi_prime_accurate.resize(0);
+
+    std::vector<Real> x(phi.size());
+    Real dx = (2*p-1)/static_cast<Real>(x.size()-1);
+    std::cout << "dx = " << dx << "\n";
+    for (size_t i = 0; i < x.size(); ++i) {
+      x[i] = i*dx;
+    }
+
+    auto ch = boost::math::interpolators::cubic_hermite(std::move(x), std::move(phi), std::move(phi_prime));
+
+    std::vector<long double> x_acc(phi_dense.size());
+    
+    for (size_t i = 0; i < x_acc.size(); ++i) {
+      x_acc[i] = i*dx_dense;
+    }
+
+    auto acc = boost::math::interpolators::cubic_hermite(std::move(x_acc), std::move(phi_dense), std::move(phi_dense_prime));
+    std::cout << "Writing ulp plot\n";
+    std::string title = "daub" + std::to_string(p) + "_" + std::to_string(rmax-2) + "_" + boost::core::demangle(typeid(Real).name()) + ".svg";
+    quicksvg::ulp_plot(ch, acc, Real(0), Real(2*p-1), 
+                        "ULP plot of Daubechies with " + std::to_string(rmax-2) + " refinements on type " + boost::core::demangle(typeid(Real).name()),
+                        title, 15000, 1100, 10);
+    std::cout << "Done writing ulp plot\n";
+
+}
+
+template<class Real, int p>
+void test_interpolate_with_roots()
+{
+    std::cout << "Testing interpolation with roots on type " << boost::core::demangle(typeid(Real).name()) << " and " << p << " vanishing moments.\n";
+    using std::floor;
+    using std::ceil;
+    using std::abs;
+    int rmax = 22;
+    auto phi_dense = boost::math::detail::dyadic_grid<float128, p, 0>(rmax);
+    auto phi_dense_prime = boost::math::detail::dyadic_grid<float128, p, 1>(rmax);
+    Real dx_dense = (2*p-1)/static_cast<Real>(phi_dense.size()-1);
+
+    auto roots = boost::math::detail::daubechies_scaling_roots<Real, p>();
+    auto root_derivatives = boost::math::detail::daubechies_scaling_derivatives_at_roots<Real, p>();
+    if (std::is_same_v<Real, float>) {
+      roots.resize(12);
+      root_derivatives.resize(12);
+      std::cout << "Last root = " << roots.back() << "\n";
+    }
+
+    for (int r = 5; r <= rmax - 1; ++r) {
+        auto phi_accurate = boost::math::detail::dyadic_grid<float128, p, 0>(r);
+        std::vector<Real> phi(phi_accurate.size());
+        for (size_t i = 0; i < phi_accurate.size(); ++i) {
+            phi[i] = Real(phi_accurate[i]);
+        }
+        auto phi_prime_accurate = boost::math::detail::dyadic_grid<float128, p, 1>(r);
+        std::vector<Real> phi_prime(phi_accurate.size());
+        for (size_t i = 0; i < phi_prime_accurate.size(); ++i) {
+            phi_prime[i] = Real(phi_prime_accurate[i]);
+        }
+
+        std::vector<Real> x(phi.size());
+        Real dx = (2*p-1)/static_cast<Real>(x.size()-1);
+        std::cout << "dx = " << dx << "\n";
+        for (size_t i = 0; i < x.size(); ++i) {
+          x[i] = i*dx;
+        }
+
+        //std::cout << "x.size() before insertion = " << x.size() << "\n";
+        //std::cout << "Adding " << roots.size() << " roots; giving " << x.size() + roots.size() << " total\n";
+        // Now insert the roots into the vector:
+        //x.resize(x.size() + roots.size());
+        //phi.resize(phi.size() + roots.size());
+        //phi_prime.resize(phi_prime.size() + roots.size());
+        #ifdef COMPUTE_ROOTS
+        for (size_t i = 0; i < roots.size(); ++i) {
+          auto root = roots[i];
+          auto index = static_cast<size_t>(ceil(root/dx)) + i;
+          //std::cout << "Inserting root at index " << index << "\n";
+          x.insert(x.begin() + index, root);
+          phi.insert(phi.begin() + index, Real(0));
+          phi_prime.insert(phi_prime.begin()+ index, root_derivatives[i]);
+        }
+        #endif
+        /*if (std::is_sorted(x.begin(), x.end())) {
+          std::cout << "x is sorted! This is good!\n";
+        } else {
+          std::cout << "x is not sorted! This is bad!\n";
+        }
+        std::cout << "x.size() = " << x.size() << "\n";
+        std::cout << "phi.size()=" << phi.size() << "\n";*/
+
+        if constexpr (p < 6 && p >= 3) {
+            auto ch = boost::math::interpolators::cubic_hermite(std::move(x), std::move(phi), std::move(phi_prime));
+            Real flt_distance = 0;
+            Real sup  = 0;
+            Real worst_abscissa = 0;
+            Real worst_value = 0;
+            Real worst_computed = 0;
+            Real worst_absolute_abscissa = 0;
+            Real worst_absolute_value = 0;
+            Real worst_computed_absolute_value = 0;
+            Real condition_number1 = 0;
+            Real condition_number2 = 0;
+            Real l1 = 0;
+            Real rel_error_sum = 0;
+            for (size_t i = phi_dense.size()/16; i < phi_dense.size(); ++i) {
+              Real t = i*dx_dense;
+              Real computed = ch(t);
+              Real expected = Real(phi_dense[i]);
+              if (abs(expected) < 100*std::numeric_limits<Real>::epsilon()) {
+                continue;
+              }
+              
+              Real diff = abs(computed - expected);
+              l1 += diff;
+              rel_error_sum += diff/abs(expected);
+              Real distance = abs(boost::math::float_distance(computed, expected));
+              if (distance > flt_distance) {
+                flt_distance = distance;
+                worst_abscissa = t;
+                worst_value = expected;
+                worst_computed = computed;
+                condition_number1 = abs(t*ch.prime(t)/expected);
+              }
+              if (diff > sup) {
+                sup = diff;
+                worst_absolute_abscissa = t;
+                worst_absolute_value = expected;
+                worst_computed_absolute_value = computed;
+                condition_number2 = abs(t*ch.prime(t)/expected);
+              }
+            }
+            std::cout << std::setprecision(std::numeric_limits<Real>::digits10 + 3);
+            std::cout << "Float distance at r = " << r << " is " << flt_distance << ", sup distance = " << sup << "\n";
+            std::cout << "\tWorst abscissa = " << worst_abscissa << "\n"
+                      << "\tWorst expected = " << worst_value << "\n"
+                      << "\tWorst computed = " << worst_computed << "\n"
+                      << "\tCondition number: " << condition_number1 << "\n";
+            std::cout << "\tWorst absolute abscissa = " << worst_absolute_abscissa  << "\n"
+                      << "\tExpected value at worst absolute abscissa = " << worst_absolute_value <<"\n"
+                      << "\tComputed value at worst absolute abscissa = " << worst_computed_absolute_value << "\n"
+                      << "\tCondition number: " << condition_number2  << "\n"
+                      << "\tL1 error = " << l1*dx_dense << "\n"
+                      << "\tRelative error sum = " << rel_error_sum*dx_dense << "\n";
+            std::cout << "\tRAM = " << 4*phi_accurate.size()*sizeof(Real) << " bytes\n";
+
+            std::vector<float128> x_acc(phi_dense.size());
+            
+            for (size_t i = 0; i < x_acc.size(); ++i) {
+              x_acc[i] = i*dx_dense;
+            }
+
+            //std::cout << "phi_dense.size() = " << phi_dense.size() << "\n";
+            auto phi_dense_copy = phi_dense;
+            auto phi_dense_prime_copy = phi_dense_prime;
+            auto acc = boost::math::interpolators::cubic_hermite(std::move(x_acc), std::move(phi_dense_copy), std::move(phi_dense_prime_copy));
+            std::cout << "Writing ulp plot\n";
+            quicksvg::ulp_plot(ch, acc, Real(0), Real(2*p-1), 
+                               "ULP plot of Daubechies with " + std::to_string(r) + " refinements",
+                               "daub" + std::to_string(p) + "_" + std::to_string(r) + ".svg", 50000, 1100, 10);
+            std::cout << "Done writing ulp plot\n";
+        }
+        
+    }
+}
+
+template<class Real, int p>
+void choose_refinement()
+{
+    using std::abs;
+    int rmax = 22;
+    auto phi_dense = boost::math::detail::dyadic_grid<long double, p, 0>(rmax);
+    Real dx_dense = (2*p-1)/static_cast<Real>(phi_dense.size()-1);
+
+    for (int r = 2; r <= rmax - 2; ++r) {
+        auto phi_accurate = boost::math::detail::dyadic_grid<long double, p, 0>(r);
+        std::vector<Real> phi(phi_accurate.size());
+        for (size_t i = 0; i < phi_accurate.size(); ++i) {
+            phi[i] = Real(phi_accurate[i]);
+        }
+        auto phi_prime_accurate = boost::math::detail::dyadic_grid<long double, p, 1>(r);
+        std::vector<Real> phi_prime(phi_accurate.size());
+        for (size_t i = 0; i < phi_prime_accurate.size(); ++i) {
+            phi_prime[i] = Real(phi_prime_accurate[i]);
+        }
+
+        std::vector<Real> x(phi.size());
+        Real dx = (2*p-1)/static_cast<Real>(x.size()-1);
+        std::cout << "dx = " << dx << "\n";
+        for (size_t i = 0; i < x.size(); ++i) {
+          x[i] = i*dx;
+        }
+
+        if constexpr (p < 6 && p >= 3) {
+            auto ch = boost::math::interpolators::cubic_hermite(std::move(x), std::move(phi), std::move(phi_prime));
+            Real flt_distance = 0;
+            Real sup  = 0;
+            Real worst_abscissa = 0;
+            Real worst_value = 0;
+            Real worst_computed = 0;
+            for (size_t i = 0; i < phi_dense.size(); ++i) {
+              Real t = i*dx_dense;
+              Real computed = ch(t);
+              Real expected = Real(phi_dense[i]);
+              if (std::abs(expected) < 100*std::numeric_limits<Real>::epsilon()) {
+                continue;
+              }
+              
+              Real diff = abs(computed - expected);
+              Real distance = abs(boost::math::float_distance(computed, expected));
+              if (distance > flt_distance) {
+                flt_distance = distance;
+                worst_abscissa = t;
+                worst_value = expected;
+                worst_computed = computed;
+              }
+              if (diff > sup) {
+                sup = diff;
+              }
+            }
+            std::cout << "Float distance at r = " << r << " is " << flt_distance << ", sup distance = " << sup << "\n";
+            std::cout << "\tWorst abscissa = " << worst_abscissa << ", worst value = " << worst_value << ", computed = " << worst_computed << "\n"; 
+            std::cout << "\tRAM = " << 3*phi_accurate.size()*sizeof(Real) << " bytes\n";
+        }
+        else if constexpr (p >= 6) {
+
+            auto phi_dbl_prime = boost::math::detail::dyadic_grid<Real, p, 2>(r);
+            auto qh = boost::math::interpolators::quintic_hermite(std::move(x), std::move(phi), std::move(phi_prime), std::move(phi_dbl_prime));
+            Real flt_distance = 0;
+            Real sup  = 0;
+            Real worst_abscissa = 0;
+            Real worst_value = 0;
+            Real worst_computed = 0;
+            for (size_t i = 0; i < phi_dense.size(); ++i) {
+              Real t = i*dx_dense;
+              Real computed = qh(t);
+              Real expected = Real(phi_dense[i]);
+              if (std::abs(expected) < 100*std::numeric_limits<Real>::epsilon()) {
+                continue;
+              }
+              
+              Real diff = abs(computed - expected);
+              Real distance = abs(boost::math::float_distance(computed, expected));
+              if (distance > flt_distance) {
+                flt_distance = distance;
+                worst_abscissa = t;
+                worst_value = expected;
+                worst_computed = computed;
+              }
+              if (diff > sup) {
+                sup = diff;
+              }
+            }
+            std::cout << "Float distance at r = " << r << " is " << flt_distance << ", sup distance = " << sup << "\n";
+            std::cout << "\tWorst abscissa = " << worst_abscissa << ", worst value = " << worst_value << ", computed = " << worst_computed << "\n"; 
+            std::cout << "\tRAM = " << 3*phi_accurate.size()*sizeof(Real) << " bytes\n";
+        }
+    }
+}
+
+template<class Real, int p>
+void find_best_interpolator()
+{
+    using std::abs;
+    int rmax = 14;
+    auto phi_dense = boost::math::detail::dyadic_grid<Real, p, 0>(rmax);
+    Real dx_dense = (2*p-1)/static_cast<Real>(phi_dense.size()-1);
+    for (int r = 2; r < rmax-2; ++r)
+    {
+        std::map<Real, std::string> m;
+        auto phi = boost::math::detail::dyadic_grid<Real, p, 0>(r);
+        auto phi_prime = boost::math::detail::dyadic_grid<Real, p, 1>(r);
+
+        std::vector<Real> x(phi.size());
+        Real dx = (2*p-1)/static_cast<Real>(x.size()-1);
+        std::cout << "dx = " << dx << "\n";
+        for (size_t i = 0; i < x.size(); ++i) {
+            x[i] = i*dx;
+        }
+
+        {
+            auto linear = [&phi, &dx, &r](Real x)->Real {
+              if (x <= 0 || x >= 2*p-1) {
+                return Real(0);
+              }
+              using std::floor;
+
+              Real y = (1<<r)*x;
+              Real k = floor(y);
+
+              size_t kk = static_cast<size_t>(k);
+
+              Real t = y - k;
+              return (1-t)*phi[kk] + t*phi[kk+1];
+            };
+            Real sup = 0;
+            for (size_t i = 0; i < phi_dense.size(); ++i) {
+              Real x = i*dx_dense;
+              Real diff = abs(phi_dense[i] - linear(x));
+              if (diff > sup) {
+                sup = diff;
+              }
+            }
+        
+          m.insert({sup, "linear interpolation"});
+        }
+        
+
+        {
+            auto qbs = boost::math::interpolators::cardinal_quadratic_b_spline(phi.data(), phi.size(), Real(0), dx, phi_prime.front(), phi_prime.back());
+            Real qbs_sup = 0;
+            for (size_t i = 0; i < phi_dense.size(); ++i) {
+              Real x = i*dx_dense;
+              Real diff = abs(phi_dense[i] - qbs(x));
+              if (diff > qbs_sup) {
+                qbs_sup = diff;
+              }
+          }
+        
+          m.insert({qbs_sup, "quadratic_b_spline"});
+        }
+
+        {
+          auto cbs = boost::math::interpolators::cardinal_cubic_b_spline(phi.data(), phi.size(), Real(0), dx, phi_prime.front(), phi_prime.back());
+          Real cbs_sup = 0;
+          for (size_t i = 0; i < phi_dense.size(); ++i) {
+            Real x = i*dx_dense;
+            Real diff = abs(phi_dense[i] - cbs(x));
+            if (diff > cbs_sup) {
+              cbs_sup = diff;
+            }
+          }
+          
+          m.insert({cbs_sup, "cubic_b_spline"});
+        }
+
+        /*{
+            auto phi_copy = phi;
+            auto ws = boost::math::interpolators::whittaker_shannon(std::move(phi_copy), Real(0), dx);
+            Real sup = 0;
+            for (size_t i = 0; i < phi_dense.size(); ++i) {
+              Real x = i*dx_dense;
+              using std::abs;
+              Real diff = abs(phi_dense[i] - ws(x));
+              if (diff > sup) {
+                sup = diff;
+              }
+            }
+          
+            m.insert({sup, "whittaker_shannon"});
+        }*/
+
+        {
+          auto qbs = boost::math::interpolators::cardinal_quintic_b_spline(phi.data(), phi.size(), Real(0), dx, {0,0}, {0,0});
+          Real sup = 0;
+          for (size_t i = 0; i < phi_dense.size(); ++i) {
+            Real x = i*dx_dense;
+            Real diff = abs(phi_dense[i] - qbs(x));
+            if (diff > sup) {
+              sup = diff;
+            }
+          }
+          m.insert({sup, "quintic_b_spline"});
+        }
+
+        {
+          auto phi_copy = phi;
+          auto x_copy = x;
+          auto phi_prime_copy = phi_prime;
+          auto ch = boost::math::interpolators::cubic_hermite(std::move(x_copy), std::move(phi_copy), std::move(phi_prime_copy));
+          Real sup = 0;
+          for (size_t i = 0; i < phi_dense.size(); ++i) {
+            Real x = i*dx_dense;
+            Real diff = abs(phi_dense[i] - ch(x));
+            if (diff > sup) {
+              sup = diff;
+            }
+          }
+          m.insert({sup, "cubic_hermite_spline"});
+        }
+
+        {
+          auto phi_copy = phi;
+          auto x_copy = x;
+          auto phi_prime_copy = phi_prime;
+          auto pc = boost::math::interpolators::pchip(std::move(x_copy), std::move(phi_copy));
+          Real sup = 0;
+          for (size_t i = 0; i < phi_dense.size(); ++i) {
+            Real x = i*dx_dense;
+            Real diff = abs(phi_dense[i] - pc(x));
+            if (diff > sup) {
+              sup = diff;
+            }
+          }
+          m.insert({sup, "pchip"});
+        }
+
+        {
+          auto phi_copy = phi;
+          auto x_copy = x;
+          auto pc = boost::math::interpolators::makima(std::move(x_copy), std::move(phi_copy));
+          Real sup = 0;
+          for (size_t i = 0; i < phi_dense.size(); ++i) {
+            Real x = i*dx_dense;
+            Real diff = abs(phi_dense[i] - pc(x));
+            if (diff > sup) {
+              sup = diff;
+            }
+          }
+          m.insert({sup, "makima"});
+        }
+
+        /*{
+            auto trig = boost::math::interpolators::cardinal_trigonometric(phi, Real(0), dx);
+            Real sup = 0;
+            for (size_t i = 0; i < phi_dense.size(); ++i) {
+              Real x = i*dx_dense;
+              using std::abs;
+              Real diff = abs(phi_dense[i] - trig(x));
+              if (diff > sup) {
+                sup = diff;
+              }
+            }
+            m.insert({sup, "trig"});
+        }*/
+
+        {
+            auto fotaylor = [&phi, &phi_prime, &r](Real x)->Real {
+                if (x <= 0 || x >= 2*p-1) {
+                    return 0;
+                }
+                using std::floor;
+
+                Real y = (1<<r)*x;
+                Real k = floor(y);
+
+                size_t kk = static_cast<size_t>(k);
+                if (y - k < k + 1 - y)
+                {
+                    Real eps = (y-k)/(1<<r);
+                    return phi[kk] + eps*phi_prime[kk];
+                }
+                else {
+                    Real eps = (y-k-1)/(1<<r);
+                    return phi[kk+1] + eps*phi_prime[kk+1];
+                }
+
+            };
+            Real sup = 0;
+            for (size_t i = 0; i < phi_dense.size(); ++i) {
+              Real x = i*dx_dense;
+              Real diff = abs(phi_dense[i] - fotaylor(x));
+              if (diff > sup) {
+                sup = diff;
+              }
+            }
+        
+          m.insert({sup, "First-order Taylor"});
+        }
+
+        if constexpr (p > 2) {
+            auto phi_dbl_prime = boost::math::detail::dyadic_grid<Real, p, 2>(r);
+
+            {
+                auto phi_copy = phi;
+                auto x_copy = x;
+                auto phi_prime_copy = phi_prime;
+                auto phi_dbl_prime_copy = phi_dbl_prime;
+                auto qh = boost::math::interpolators::quintic_hermite(std::move(x_copy), std::move(phi_copy), std::move(phi_prime_copy), std::move(phi_dbl_prime_copy));
+                Real sup = 0;
+                for (size_t i = 0; i < phi_dense.size(); ++i) {
+                  Real x = i*dx_dense;
+                  Real diff = abs(phi_dense[i] - qh(x));
+                  if (diff > sup) {
+                    sup = diff;
+                  }
+                }
+                m.insert({sup, "quintic_hermite_spline"});
+            }
+
+            {
+                auto sotaylor = [&phi, &phi_prime, &phi_dbl_prime, &r](Real x)->Real {
+                      if (x <= 0 || x >= 2*p-1) {
+                          return 0;
+                      }
+                      using std::floor;
+
+                      Real y = (1<<r)*x;
+                      Real k = floor(y);
+
+                      size_t kk = static_cast<size_t>(k);
+                      if (y - k < k + 1 - y)
+                      {
+                          Real eps = (y-k)/(1<<r);
+                          return phi[kk] + eps*phi_prime[kk] + eps*eps*phi_dbl_prime[kk]/2;
+                      }
+                      else {
+                          Real eps = (y-k-1)/(1<<r);
+                          return phi[kk+1] + eps*phi_prime[kk+1] + eps*eps*phi_dbl_prime[kk+1]/2;
+                      }
+                };
+                Real sup = 0;
+                for (size_t i = 0; i < phi_dense.size(); ++i) {
+                  Real x = i*dx_dense;
+                  Real diff = abs(phi_dense[i] - sotaylor(x));
+                  if (diff > sup) {
+                    sup = diff;
+                  }
+                }
+            
+              m.insert({sup, "Second-order Taylor"});
+            }
+        }
+
+        if constexpr (p > 3) {
+            auto phi_dbl_prime = boost::math::detail::dyadic_grid<Real, p, 2>(r);
+            auto phi_triple_prime = boost::math::detail::dyadic_grid<Real, p, 3>(r);
+
+            {
+                auto totaylor = [&phi, &phi_prime, &phi_dbl_prime, &phi_triple_prime, &r](Real x)->Real {
+                      if (x <= 0 || x >= 2*p-1) {
+                          return 0;
+                      }
+                      using std::floor;
+
+                      Real y = (1<<r)*x;
+                      Real k = floor(y);
+
+                      size_t kk = static_cast<size_t>(k);
+                      if (y - k < k + 1 - y)
+                      {
+                          Real eps = (y-k)/(1<<r);
+                          return phi[kk] + eps*phi_prime[kk] + eps*eps*phi_dbl_prime[kk]/2 + eps*eps*eps*phi_triple_prime[kk]/6;
+                      }
+                      else {
+                          Real eps = (y-k-1)/(1<<r);
+                          return phi[kk+1] + eps*phi_prime[kk+1] + eps*eps*phi_dbl_prime[kk+1]/2 + eps*eps*eps*phi_triple_prime[kk]/6;
+                      }
+                };
+                Real sup = 0;
+                for (size_t i = 0; i < phi_dense.size(); ++i) {
+                  Real x = i*dx_dense;
+                  Real diff = abs(phi_dense[i] - totaylor(x));
+                  if (diff > sup) {
+                    sup = diff;
+                  }
+                }
+            
+              m.insert({sup, "Third-order Taylor"});
+            }
+
+
+        }
+        std::string best = "none";
+        Real best_sup = 1000000000;
+        for (auto & e : m) {
+          
+          std::cout << std::setprecision(20) << std::fixed << e.first << " is error of " << e.second << "\n";
+          if (e.first < best_sup) {
+            best = e.second;
+            best_sup = e.first;
+          }
+        }
+        std::cout << "The best method for p = " << p << " is the " << best << "\n";
+    }
+}
+
+int main() {
+
+    do_ulp<float, 5>();
+    //test_interpolate_with_roots<double, 5>();
+    //choose_refinement<float, 5>();
+    //choose_refinement<double, 15>();
+    /*// Says linear interpolation is the best:
+    find_best_interpolator<long double, 2>();
+
+    // Says linear interpolation is the best:
+    find_best_interpolator<long double, 3>();
+
+    // Says cubic_hermite_spline is best:
+    find_best_interpolator<long double, 4>();
+
+    // Says cubic_hermite_spline is best:
+    find_best_interpolator<long double, 5>();
+
+    // Says quintic_hermite_spline is best:
+    find_best_interpolator<long double, 6>();
+
+    // Says quintic_hermite_spline is best:
+    find_best_interpolator<long double, 7>();
+
+    // Says quintic_hermite_spline is best:
+    find_best_interpolator<long double, 15>();*/
+}
diff --git a/example/daubechies_coefficients.cpp b/example/daubechies_coefficients.cpp
index 5ccc77fb6..23349defa 100644
--- a/example/daubechies_coefficients.cpp
+++ b/example/daubechies_coefficients.cpp
@@ -208,8 +208,8 @@ std::vector<typename Complex::value_type> daubechies_coefficients(std::vector<st
 
 int main()
 {
-    typedef boost::multiprecision::cpp_complex<150> Complex;
-    size_t p_max = 25;
+    typedef boost::multiprecision::cpp_complex<500> Complex;
+    size_t p_max = 20;
     std::ofstream fs{"daubechies_filters.hpp"};
     fs << "/*\n"
        << " * Copyright Nick Thompson, 2019\n"
@@ -223,11 +223,11 @@ int main()
        << "#ifdef BOOST_HAS_FLOAT128\n"
        << "#include <boost/multiprecision/float128.hpp>\n"
        << "#endif\n"
+       << "#include <boost/multiprecision/cpp_bin_float.hpp>\n"
        << "namespace boost::math::filters {\n\n"
        << "template <typename Real, unsigned p>\n"
        << "constexpr std::array<Real, 2*p> daubechies_scaling_filter()\n"
        << "{\n"
-       << "    static_assert(sizeof(Real) <= 16, \"Filter coefficients only computed up to 128 bits of precision.\");\n"
        << "    static_assert(p < " << p_max << ", \"Filter coefficients only implemented up to " << p_max - 1 << ".\");\n";
 
     for(size_t p = 1; p < p_max; ++p)
@@ -270,6 +270,15 @@ int main()
         fs << "        }\n";
         fs << "        #endif\n";
 
+        fs << "        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {\n";
+        fs << "            return {";
+        fs <<std::setprecision(std::numeric_limits<boost::multiprecision::cpp_bin_float_oct>::digits10 + 3);
+        for (size_t i = 0; i < h.size() - 1; ++i) {
+            fs <<  "boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>(\"" <<  static_cast<boost::multiprecision::cpp_bin_float_oct>(h[i]) << "\"), ";
+        }
+        fs <<  "boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>(\"" << static_cast<boost::multiprecision::cpp_bin_float_oct>(h[h.size()-1]) << "\")};\n";
+        fs << "        }\n";
+
 
         fs << "    }\n";
     }
diff --git a/example/daubechies_scaling_integer_grid.cpp b/example/daubechies_scaling_integer_grid.cpp
index cdb255327..e4f832af9 100644
--- a/example/daubechies_scaling_integer_grid.cpp
+++ b/example/daubechies_scaling_integer_grid.cpp
@@ -19,6 +19,7 @@
 #include <boost/math/constants/constants.hpp>
 #include <boost/math/filters/daubechies.hpp>
 #include <boost/math/special_functions/factorials.hpp>
+#include <boost/multiprecision/cpp_bin_float.hpp>
 
 
 
@@ -193,6 +194,24 @@ void write_grid(std::ofstream & fs)
     }
     fs << "        }\n";
     fs << "        #endif\n";
+
+    fs << "        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {\n";
+    j = 0;
+    for (auto it = grids.begin(); it != grids.end(); ++it) {
+
+    fs << std::setprecision(std::numeric_limits<boost::multiprecision::cpp_bin_float_oct>::digits10 + 3);
+    fs << "            if constexpr (order == " << j << ") {\n";
+    fs << "                return {";
+        auto const & grid = *it;
+        for (size_t i = 0; i < grid.size() -1; ++i) {
+            fs << "boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>(\"" << static_cast<boost::multiprecision::cpp_bin_float_oct>(grid[i]) << "\"), ";
+        }
+        fs << "boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>(\"" << static_cast<boost::multiprecision::cpp_bin_float_oct>(grid[grid.size()-1]) << "\")};\n";
+    fs << "            }\n";
+        ++j;
+    }
+    fs << "        }\n";
+
     fs << "    }\n";
 
 }
@@ -226,7 +245,7 @@ int main()
     fs << std::hexfloat;
 
     boost::hana::for_each(std::make_index_sequence<p_max>(), [&](auto idx){
-        write_grid<boost::multiprecision::float128, idx+2>(fs);
+        write_grid<boost::multiprecision::cpp_bin_float_oct, idx+2>(fs);
     });
 
     fs << "    std::array<Real, 2*p> m{};\n"
diff --git a/include/boost/math/filters/daubechies.hpp b/include/boost/math/filters/daubechies.hpp
index 74806ca88..87d5bbf36 100644
--- a/include/boost/math/filters/daubechies.hpp
+++ b/include/boost/math/filters/daubechies.hpp
@@ -10,13 +10,13 @@
 #ifdef BOOST_HAS_FLOAT128
 #include <boost/multiprecision/float128.hpp>
 #endif
+#include <boost/multiprecision/cpp_bin_float.hpp>
 namespace boost::math::filters {
 
 template <typename Real, unsigned p>
 constexpr std::array<Real, 2*p> daubechies_scaling_filter()
 {
-    static_assert(sizeof(Real) <= 16, "Filter coefficients only computed up to 128 bits of precision.");
-    static_assert(p < 25, "Filter coefficients only implemented up to 24.");
+    static_assert(p < 20, "Filter coefficients only implemented up to 19.");
     if constexpr (p == 1) {
         if constexpr (std::is_same_v<Real, float>) {
             return {0x1.6a09e6p-1f, 0x1.6a09e6p-1f};
@@ -32,6 +32,9 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.6a09e667f3bcc908b2fb1366ea95p-1Q, 0x1.6a09e667f3bcc908b2fb1366ea95p-1Q};
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.707106781186547524400844362104849039284835937688474036588339868995366237195"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.707106781186547524400844362104849039284835937688474036588339868995366237195")};
+        }
     }
     if constexpr (p == 2) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -48,6 +51,9 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.ee8dd4748bf14c548b969de58fap-2Q, 0x1.ac4bdd6e3fd70aae9f48d8a63d1bp-1Q, 0x1.cb0bf0b6b7108b79b4bf11d08b16p-3Q, -0x1.0907dc1930690697b13714fd4a15p-3Q};
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.482962913144534143374871599864448683816952419504202275201171538155211606550"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.836516303737807905575293780916873203459370388348439293495341472652894725147"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.224143868042013381025972762240400355467883518184271761387168330840154631777"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.129409522551260381174449418812024164174534450659965256907001603657528486820")};
+        }
     }
     if constexpr (p == 3) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -64,6 +70,9 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.54a796e50d263b67e38e82a5584cp-2Q, 0x1.9d20e247d28bb431f1e6c634b34ep-1Q, 0x1.d6ea20bf0f7447ac92de97f0e152p-2Q, -0x1.1480a85c596292857548d060a171p-3Q, -0x1.5df7ab50d483c40c41dbcf2191cfp-4Q, 0x1.2092e373789b9781e66814a5fa37p-5Q};
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.332670552950082615998511589139005630012923399245068359708470578551793724009"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.806891509311092576494493604088713490519297394994823618165092063603486835060"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.459877502118491570095151942147616720808110177431492306643386780248640335647"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.135011020010254588696389906699374480562219845223781191975686255357062767858"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0854412738820266616928191691817733115361976389880866297635174898050678201973"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0352262918857095366027406647155100293277583879174316103989340607489421719736")};
+        }
     }
     if constexpr (p == 4) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -80,6 +89,9 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.d7d052af15ebfcd98dc85ef4cc01p-3Q, 0x1.6e005ea45d747c624e43405b1919p-1Q, 0x1.4302cdd3de439e1a299a6a04b89fp-1Q, -0x1.ca7c6f9db5bfafb07b9dace22f7p-6Q, -0x1.7f0c1b7c604d3ef4ab50462dfcedp-3Q, 0x1.f94e2196383a8e592495a4baff62p-6Q, 0x1.0d60ac768117b7550c2a3307e30fp-5Q, -0x1.5b41730b72e293b823fb2cbd40c6p-7Q};
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.230377813308896500863291183044070850001615248248309297791096844028271643620"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.714846570552915647089921955273992603707608401099308175845011003442625044997"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.630880767929858907881716338300615220203222922677195117405747328484353359854"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0279837694168598542114137471800753854119873202244917528400335826533630929593"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.187034811719093084079570672789081419584544174374580091205777087593992585799"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0308413818355607636272193625349590501703148217200340334182121909360632337258"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0328830116668851997354075135492443886645419411375497125972727840767338203692"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0105974017850690321048832085240272291810999649063764198348497427299589480739")};
+        }
     }
     if constexpr (p == 5) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -96,6 +108,9 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.47e3c41a7b91081ae95ed12670b7p-3Q, 0x1.35291c2c4b00c30a87eaf4d05e71p-1Q, 0x1.72d89143b54f4ecd724f0b79d111p-1Q, 0x1.1b80373befcc598b25a1d5436079p-3Q, -0x1.f0384d3f814743c3d93da5cd8909p-3Q, -0x1.0826648a8dc73f96ef19214f403ep-5Q, 0x1.3dbb9b52515a99ecaa66a225e968p-4Q, -0x1.990ad4579f2e7e2dc54832641bd8p-8Q, -0x1.9c3eff32941286062a45cb776526p-7Q, 0x1.b5385e04e3c0912c23cbbf7041e8p-9Q};
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.160102397974192914480723748020420733650544124625057832772569920207547214207"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.603829269797189670540119306525062107507422163101698698796928336036862837113"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.724308528437772927728071244102218640768756218232007372576733504804092797357"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.138428145901320731505397146339024697314105791173956102269465221088552175948"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.242294887066382031862571379474616361991490808062618598391372691341065474637"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0322448695846383746484797550621349283135649841637984722543426813198116091835"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0775714938400457135231304893886018198062309945201252798321014623895567160574"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00624149021279827427419051911292019297076355716568760732341743532590851604324"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0125807519990819994685097399317757929492045916260978502016923270647650161437"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00333572528547377127799818341581735574763652474230531509970642851567135111157")};
+        }
     }
     if constexpr (p == 6) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -112,6 +127,9 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.c8def24dc3951c2a6dae413b8ddbp-4Q, 0x1.fa7eaf64539a97bd50da008738e1p-2Q, 0x1.80949fa3bc0bae02bf1b494d3af8p-1Q, 0x1.42d0fcfa92f20ff1b5b87f2f698cp-2Q, -0x1.cf63dd26916f0b589f7743608e82p-3Q, -0x1.09c33622722ead8a0ff038a97bp-3Q, 0x1.8f5dd7f4e175279c5a356a3fbcc9p-4Q, 0x1.c2ef43d6125497c75e24a80c6bfap-6Q, -0x1.02b856404e8cdf85933c3736d91cp-5Q, 0x1.225f71210a7c1202de723c931ed6p-11Q, 0x1.391514c62a31adcdfa747aebbdeep-8Q, -0x1.1a6873b7a6465e0ff5c033201061p-10Q};
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.111540743350109463621323917240923439042539591984421675908236045797651596176"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.494623890398453085677204176877855588637786382896274362353183452618869845497"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.751133908021095350678934498439731685580254783338261200973042065947992668343"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.315250351709197629085989654810926396649519923517294524440416381606252448494"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.226264693965439820076314500660903465670540153972896994014348779178970276888"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.129766867567261935562289605876585460845233749223581470159931065581720412930"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0975016055873230491023435525381253423398307474952551427989319312112779815986"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0275228655303057286255408395041932136573875878304345432149420287900002992420"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0315820393174860295650790806998486690574795323731484233751146493526060457826"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000553842201161496139251918398046501220611026277386496429547652456752475273329"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00477725751094551063963597524682070705023050121658143429759325457002031530381"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00107730108530847956485262160958720003523523360933441968981858089478841770562")};
+        }
     }
     if constexpr (p == 7) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -128,6 +146,9 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.3ee1cba38b6b0a205a4c9aac651fp-4Q, 0x1.960e67430300363014da61e0a27dp-2Q, 0x1.7550cd294c1fe3f40f374c82e23dp-1Q, 0x1.e10e9ba294ddc02a47644f227fffp-2Q, -0x1.26b830e491e32da8b525e8ab6aa1p-3Q, -0x1.cad37bbd5ab970931a91ed1dfe9cp-3Q, 0x1.241522ca7821c638e85eb5e52839p-4Q, 0x1.4a30727f2fa52896ef76d0300cfp-4Q, -0x1.378a8eecf45cc0627b1c4b5cace1p-5Q, -0x1.0f8eaa8ffe708c22b1145a6b8cc8p-6Q, 0x1.9b45682a50d70110df27e4af9e36p-7Q, 0x1.c271f584373d41d177397b25f7ebp-12Q, -0x1.d84a0f9cb2f314e62607c084aab4p-10Q, 0x1.72e5533fa10d324758be56783dp-12Q};
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0778520540850091790199635219578937483791830529279556843870293717996297655927"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.396539319481917306539000390936842856358715114933328740111049962075487815071"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.729132090846235119916943070339282051717966061190136378269771574955357027757"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.469782287405193122471591160974451738681791305678735953239252914100836922120"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.143906003928564975405068362213046001795273570549908483440175301422991840895"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.224036184993874982638140420233250964475783089677324655266509530724151657744"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0713092192668302647508765705011290482271132745141231465957511322020290613667"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0806126091510830719129224803593819058582382096562948905813921847722652754485"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0380299369350144135795920616018580358544619693846786989828312271657410616427"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0165745416306668806541076748917026547920450439482071370523927254871434907950"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0125509985560998406129898860341877795728947404604871003841181834416741023260"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000429577972921366521132129122819732222823535039694240974294636693544941849482"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00180164070404749091526826291273955096258565146964109062532386481459081601883"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000353713799974520248446295836306425431095906005952004001252427564526433555672")};
+        }
     }
     if constexpr (p == 8) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -144,6 +165,9 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.bdc64ada308dd431e90c51caaddfp-5Q, 0x1.4061690b4c31e70689f16560d4fdp-2Q, 0x1.59ec45992376070ce88329890c41p-1Q, 0x1.2bb39bedb5e27d5c19af764e6b08p-1Q, -0x1.03581459a95c5ec9b8a25898e79fp-6Q, -0x1.22d4f8724d56f584680effd871d8p-2Q, 0x1.ef6f9caf662af8d967c439494864p-12Q, 0x1.07acbb163ba0883fad048482f33cp-3Q, -0x1.1c9420f07509ca8be1e93402904ap-6Q, -0x1.692bc518a7fe18cb861085169737p-5Q, 0x1.ca215cd5b85b39449ec69ab26159p-7Q, 0x1.1e978df35f5fc0eabddff5ee9da6p-7Q, -0x1.3f2ef6d3ac74a30f6f64186b6be2p-8Q, -0x1.9ac501798e65cefa54cc7686cbfep-12Q, 0x1.622148e2ef341527c8d993cd7e86p-11Q, -0x1.ecbbbc88e3fc2ec652987ddfb595p-14Q};
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0544158422431040099550094052029993550359955429473305039772928086771936225734"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.312871590914299970659162375505717721949731974037022918569871242115311497533"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.675630736297289806807800767047183149986911590633636422776675983811728748708"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.585354683654206712771265520045098194430326667805336905570717534889570522452"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0158291052563493056673805478764663041577447115450282655973533595603126615697"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.284015542961546926516203132374164732468435012487145179359920480909375859275"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000472484573913282770360590009825894986194801128877007464408409602299544658383"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.128747426620478458857029287509708384302260157555648879557700016549770662789"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0173693010018075461696161488680959831141308652948839431697731538851197479461"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0440882539307947515067637232389635018975183919011099647275039198547543351349"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0139810279173982816487229305726334514423955953293434716914636811442629383260"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00874609404740577671638274324647564018040214708114067674268674702611775846381"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00487035299345157431042218155710982401663497851215700376473620853219217075614"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000391740373376947046298080357323776267522935007389049372449269467759195224284"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000675449406450569366369547573879299121848963001355843210361707737505966890496"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000117476784124769533730628231698890944408669395031150392762001353514813073214")};
+        }
     }
     if constexpr (p == 9) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -160,6 +184,9 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.37ef3e540da7c3aa0d1dcf5bb03fp-5Q, 0x1.f35f9808bc2a0772556b997598d3p-3Q, 0x1.35ab60603a287a1609387fb893b8p-1Q, 0x1.5088101e8fe3530163beb11528dcp-1Q, 0x1.10c9ca803fb2272d1e1cf6fa2d0cp-3Q, -0x1.2c4ff66fd53eee10d811f3bf5459p-2Q, -0x1.8ca8ebcdc98fc4aa06bb294a039cp-4Q, 0x1.303621e43e77126c475b311fee41p-3Q, 0x1.f768d94677996d7b05f99f12d599p-6Q, -0x1.1506294f451a1f48db3652c40168p-4Q, 0x1.07231a6b6ca0cb934ff78371a261p-12Q, 0x1.6e5f9be058887734b49665246c12p-6Q, -0x1.358a39f783bbf21cd3bb737b9bf7p-8Q, -0x1.1897b64b3bfb583210060e933d6p-8Q, 0x1.e4597bbfc711eadc2635b08cc11dp-10Q, 0x1.e3276a3bc510acb32c14bfd1c3d9p-13Q, -0x1.0833da803978a3e6248db817fff9p-12Q, 0x1.4a11ba1ad31b48b0c2e32412ef31p-15Q};
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0380779473638783465886976588795511844877171449627841747664719248482680479602"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.243834674612590353732041581649284415526361108560923136142908810357641947074"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.604823123690111111903076867434236170895956271189611756533371353266219479839"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.657288078051300538078212639045173214030585866924591885443603406558844920237"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.133197385825007576190954945899795553692178076843366113615434683783912029373"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.293273783279174908806403195242198731043896162858990682572511282649777494073"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0968407832229764605135081335376966022482545810459909967947126760842963820075"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.148540749338106380135072717506042302479125857728060306077164939460051558202"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0307256814793333792123174007203788271410580502467074478150306050580744709008"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0676328290613299736756422748297190159257879087135373990074833120984537787038"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000250947114831451957587189749988554331517627199370963332183416469143399245077"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0223616621236790972053737827026909524185564668830885375472181623365153339468"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00472320475775139727792570784824246540572951491262793801875852685657845737998"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00428150368246342983449679500231453187648118181146328837486045503769103000912"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00184764688305622647661912949112567705112108135960031816073251504574674723494"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000230385763523195967205216392824542169294066205246371197226000686680376244675"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000251963188942710136974988684287860660728218154347802821413426535123097430873"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000393473203162715994806898830658915070778247705551701350735993815544054870406")};
+        }
     }
     if constexpr (p == 10) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -176,6 +203,9 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.b4f6549dc7ae2d0da711a289f0cap-6Q, 0x1.8162d69198cfdb39a90922d70e5fp-3Q, 0x1.0ded5071bf8739f750ffec152978p-1Q, 0x1.607db4062d7753edab576af3e0dcp-1Q, 0x1.1feba4923f566c829244a5b4f4c2p-2Q, -0x1.ffaf7b6c111e2f4b082d1396dfd9p-3Q, -0x1.914c47c1ca801c5176763b1002edp-3Q, 0x1.04da377a0ae834bb94a9fa4f0243p-3Q, 0x1.7d29b819fd18d32d43de1a7d3641p-4Q, -0x1.246e307349ac4648ebbb94e378bbp-4Q, -0x1.e2a1dd5152b24d9c384763b949a8p-6Q, 0x1.1014069cb8f3bf95bd45be617d84p-5Q, 0x1.d8b7db3e21713e4ea2df5435db4ap-9Q, -0x1.5fb466d770edc4c0f4a29d7e3176p-7Q, 0x1.6dc8787ae38dd789b768877a70c2p-10Q, 0x1.0526072a98cd7f8751cc002da048p-9Q, -0x1.67962098c50f012db290a44515a5p-11Q, -0x1.e87f555dc50dd253428e6067701p-14Q, 0x1.888a11cfae432f4e4bd0c734fcc9p-14Q, -0x1.bd12a2a1a43db4fff0519cd821dfp-17Q};
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0266700579005555535866174487713085827719249829085128993277997577621650735643"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.188176800077691489020892973679093994270254675864039348434859544409886608680"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.527201188931725586481744827959508192498140268084022344531854947145139828409"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.688459039453603565741871782549235853977136404240733953727968115839903445132"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.281172343660577460748726998445589287624388885902615041383154395183374807120"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.249846424327315379416101897920779100056466973713207371501312159710676300514"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.195946274377377043504299254319098131876677647638277847439678187683856178731"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.127369340335793260082677233201400977078617748042224599556309752373906702894"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0930573646035723511603522898354527322694291799894692586806397410224547567765"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0713941471663970871453360930760506476729261198370215091752375634796582409510"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0294575368218758128582832376014183919938820051606494877976965428318490167081"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0332126740593410017397636531821591289797833741326709604332335127083312999184"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00360655356695616965542329141713340329951735051861899476273061229128656318944"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0107331754833305750443181141065136444811154878114392321337033393709343696195"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00139535174705290116578931844795770756766054285568855242672111772342943140108"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00199240529518505611715874224264064321176255536551410528006793647824864459995"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000685856694959711626561370981926571419662504333678692051621190356175797931438"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000116466855129285450951480971025899189152746185434759736281923507446885853623"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000935886703200695913340501303422285439968845621529727644352187393967719605190"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000132642028945212448124366753122668330574924096060582975640067461946671323150")};
+        }
     }
     if constexpr (p == 11) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -192,6 +222,9 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.324991607609160c660c469077c4p-6Q, 0x1.270c9c42314cf5fa956419fe6ca8p-3Q, 0x1.ccb286198c9dee96d12668532b6cp-2Q, 0x1.5f125643212cb922d29e40df5ae5p-1Q, 0x1.a5d9fccefe816554cfd2c1b4c2eap-2Q, -0x1.4c56f6b2bf66c3c093c0529f8f7fp-3Q, -0x1.18cff89a8cc4603466567c5566b2p-2Q, 0x1.0e83b8b6a4d8e932eca95459a69cp-4Q, 0x1.32d0a3f0ba73261f3f385a0ab52ep-3Q, -0x1.7cc387e4a9a091c75d9de8faea58p-5Q, -0x1.10221dbbeff7c12d2228c7667179p-4Q, 0x1.00b27276a80990547cbd63f84547p-5Q, 0x1.557516a958be52b928260c4c6ad5p-6Q, -0x1.f77975a6883f7054b8b01c477981p-7Q, -0x1.b5e49f3346a8b7e121e98be0fcfbp-9Q, 0x1.42fd20a75f9abc16cec7fe76464bp-8Q, -0x1.439543c8411328be7c3dbb239962p-12Q, -0x1.d4338d3fdae3a1309e0d7105695cp-11Q, 0x1.05415f0bc6ea25b1e91fb2adce4fp-12Q, 0x1.c8ab05d193c378f97fff6933dc9bp-15Q, -0x1.228a0febb3e8bfe721948bedcf9cp-15Q, 0x1.2d9b0b4e10d77be6e48f3790bbdep-18Q};
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0186942977614710840254357293956197572896777445592195854328669208544639848493"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.144067021150624512795191584936100114302371896755623960431885248217612109866"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.449899764356045334768894037385360367780689537864893347459965579586344042705"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.685686774916200511120938631696309793594020496456770349505158901745075089131"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.411964368947907462925939648571066730743040041018784531569724251133330862864"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.162275245027490362240582726998551154074426432421213020964966742981832149727"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.274230846817946961202100945283526662864808952177517822190577839005023967370"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0660435881966831919006145788812630265675314216894079154111345722601572700631"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.149812012466378496406656261704419329858827242026748465379690959421507533896"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0464799551166841872716172258902374457722326096684826074745032098759584318172"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0664387856950252052789921553697120319181956689607973962285857402336065270973"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0313350902190460760309479840830314453635810568088003196493644550909547400332"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0208409043601810630229481125565649101515776183273471569112669220076703474398"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0153648209062015994261981160995882274401432649577300012020584862793777385002"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00334085887301444560609080861798240610193065835949919084565673177725408174281"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00492841765605904112317073974170827369028554772991580241839745801019376641230"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000308592858815143165175459072627895330718021660507848858192156227602365444134"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000893023250666264613390082462264865398987951987862072879313335822408534301830"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000249152523552823498871221687266680108822119930285542538197139249093202823549"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000544390746993684716735785687957683219193667852560079397804368892016829413126"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000346349841869849955412808515997404321450648804823345803594360135567940224107"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000449427427723651009541564828231013091641049798738375346057174174843400859633")};
+        }
     }
     if constexpr (p == 12) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -208,6 +241,9 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.ada9978d2fa568b21229688156b8p-7Q, 0x1.c0c890682f8790d7f6bb1c1aa44ep-4Q, 0x1.82696272e40bd05e57c851b9cb36p-2Q, 0x1.507c59d8e6f6ac435d1e88e090b6p-1Q, 0x1.082245c29797798f324c3b86f65cp-1Q, -0x1.6eb4ac1d9855ccfed03d4133c6fbp-5Q, -0x1.43c448da45b222f8d287f72956dcp-2Q, -0x1.85996f0f3b3b27b5f0ec32953a95p-6Q, 0x1.75b757e56dd3b6e26eea4e0a43bap-3Q, 0x1.5f3ea878d368e081a5d3cb36d936p-8Q, -0x1.8afc6821933836a0611906df913cp-4Q, 0x1.638119d1c4361bb00a2f22d1f90bp-7Q, 0x1.5458dbe394eb05c5aab3c4ceb31ap-5Q, -0x1.90617513f389b7954493854c387ep-7Q, -0x1.a4c4a623e2a50fc10158bea8a45cp-7Q, 0x1.b7d844bffa4e88c2ef52650eb0e3p-8Q, 0x1.26babd1f8d1809707edb54236067p-9Q, -0x1.1dac0186ec14265ff3ab908c13a3p-9Q, 0x1.b73c724cbcd24a84c3c597249f8dp-18Q, 0x1.9788431be0bfb2d1938d25135045p-12Q, -0x1.7336904b8b4e84c0e0396f9346efp-14Q, -0x1.96b4a56f63fa8a95abb9ecaeceaep-16Q, 0x1.acb92f10c4239fce7d915af19a6cp-17Q, -0x1.9a7502d7dc2f2e1e665f9ba74bc1p-20Q};
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0131122579572295175067460908889332806566551064193132500774828079813751369078"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.109566272821185154605704505024890542607568050306677404638365743414594716237"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.377355135214212657092821260487920614901094170605752633470583911562885099045"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.657198722579307089302761128664116983425020328998841214139428195001939202386"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.515886478427815608756032648054303270067769308703609005612764729867503168411"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0447638856537746266676274731154016652928454363150592413907170410117965514990"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.316178453752785536864802935347803109850883903254736438957420337160049554984"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0237792572560697276839975460913322578455336655833174115248261271603350281595"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.182478605927579679854043611618924171029477144809630269832901126083410652478"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00535956967435215032827627672976833228886266518419270582163634261809269415715"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0964321200965070820265032053432248412743088014304522051434640274861906048848"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0108491302558221843808901023774815218866163056760333465932251226434077741286"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0415462774950844407392709468190657486451353222138837486128707899413616614352"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0122186490697482807199879826647156771298246609311655817534481104550208384247"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0128408251983006832946603447189472849620610983231409763327522557348508782102"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00671149900879550917776702706821567245064811218585645674037945533688642441241"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00224860724099523759995086521126723401834319978614617709926201027901007445066"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00217950361862776047159890337958417118784007529186057126498094298705073259759"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000654512821250959556650043039932711072911177056889735663071455200741848443049"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000388653062820931443589728883779598179191748857342017752343609613138331820861"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000885041092082043242082164596155372659873832215147193280801544303001991847212"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000242415457570307840297891532053171958042377836266428223937753220729228844731"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000127769522193797665871404636261662088737596094143942875605535392042653701946"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000152907175806851090271223916452290122319761543966034067260269641683218542373")};
+        }
     }
     if constexpr (p == 13) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -224,6 +260,9 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.2d89174d37e3b6596d64d168e49p-7Q, 0x1.53664fc8a3d4c0d33efd4b4bc6fap-4Q, 0x1.3f7bf6c09afe857e70d916613d78p-2Q, 0x1.38dc5001834baade66ebb6ec9fc1p-1Q, 0x1.2d82ef0bea471de1f0a3864a5cccp-1Q, 0x1.644b251290fb4bea9c417da1f71ep-4Q, -0x1.42884206fc5ade5015e8dd0e5832p-2Q, -0x1.fe442b86ad7635e6a44fa231478p-4Q, 0x1.6f91279c81aa3aed801eca5172e8p-3Q, 0x1.2acc804557c8ab4899f3d0916648p-4Q, -0x1.b163543c8eacbf70b0092010e485p-4Q, -0x1.b1fc6de2397062d67f76ff78186p-6Q, 0x1.cbe5044520d5e315c90c0ed1b10cp-5Q, 0x1.37f29dfe3e92c6d51003ce786db8p-9Q, -0x1.867439245b0c6d71509d7a14369ep-6Q, 0x1.0128d031aa3b020f68dbd131fc68p-8Q, 0x1.db80973172630eff11f1aa6bf206p-8Q, -0x1.6a025cdac7e0fe4d3e8433e38ffbp-9Q, -0x1.58e561b1f2cf60b1ce144cfab0ffp-10Q, 0x1.e8ceb1ee24cab5dbcf0c32d1591bp-11Q, 0x1.9d26d847f17c9a8ce68c968f105dp-15Q, -0x1.5a4cf360064a4020bfd19dc8e5fp-13Q, 0x1.0159a865542d28f1113c2ad46cb5p-15Q, 0x1.5e5f8028cd834a146bf59b16d932p-17Q, -0x1.3b708a4c3be3403a7da544157c5bp-18Q, 0x1.183f9db8da3a04f4c66e4459dad2p-21Q};
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00920213353896236797297016347564418466753417191641656238600970303711912173265"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0828612438729027796443202713123046640520811333289013507251427742009482956517"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.311996322160438063396078411221404969394668352896718031716039017308515654041"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.611055851158787652821199513674418056207361267601823943852658294015204037145"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.588889570431218908071039534739533392766598638281283604223557340650249576137"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0869857261796472373102373983808749439923188407661970125088201664378054171345"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.314972907711388632998169825593228258287688845067878902595030681868130772999"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.124576730750815258941380833602126018079273929517363471957206932075260972005"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.179476079429339843234845007233936901358196625624413339304288145469676423326"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0729489336567771638090283061047766198332592902687987355362796328461636696921"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.105807618187934326450966730419646484947886075480123665823236051077820681894"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0264884064753436946396391224803478572641960484429769701626422412133519842633"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0561394771002834288621450199838733111998837879254310024473705625396675790207"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00237997225405907881146517095855420835809439461205193486847513927070930528134"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0238314207103236490320640306775773913425292271763622627407729863341057724688"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00392394144879741624331637022081552655882474662345140404391840728787217413821"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00725558940161756619451839330050269889897352967964668369526982867260050623476"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00276191123465686217801457626609844599535009333050181802496631648326614964558"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00131567391189229893661383537059364337606041259265365230723812459474570122051"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000932326130867263386222651780254851410091808829980195230799156927112701492336"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000492515251262894619214095738786659621010377829938882350084009445661139469929"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000165128988556505489461668770923800075589854821465977670334780149359987420945"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000306785375793254934664948322857547623660042821723790056312823074855283018382"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000104419305714081370817071499108059695167070643621732816964147406843820801008"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000470041647936086832565019516506177132165038358297095855656805971133412246529"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000522003509845486469173642435484317697674705215524355700153190105348895004025")};
+        }
     }
     if constexpr (p == 14) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -240,6 +279,9 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.a7702ace363ac35a31e24ad7f18bp-8Q, 0x1.fee460f5cb8771588fb11eee4edep-5Q, 0x1.04f777f62f422960e164233d2842p-2Q, 0x1.1bcdf22a1725c010c6b543c39465p-1Q, 0x1.432b0dc3136d3b304d5a3bf4569bp-1Q, 0x1.bfd66ae4258abee147e56af809ep-3Q, -0x1.1635861af071cce08b7655b9575p-2Q, -0x1.be885d06053beddff8849acb8697p-3Q, 0x1.1b6ef32bc7358856a3c8661f7dbbp-3Q, 0x1.1eb28fc03c55b30ce48dc30b7f77p-3Q, -0x1.63524d6aa4cf6fa795512cfa3aa5p-4Q, -0x1.2510847f3ed25a6abc4fb2ebbea9p-4Q, 0x1.c480a659de0cd4f4123d770896e6p-5Q, 0x1.ba103a92149f4583a4c79c292018p-6Q, -0x1.ee8e8a6bca9ac4ad53dedccf86b9p-6Q, -0x1.6ffce6192a67aceee5260da8193dp-8Q, 0x1.a3160ba7d924dde8cc52f58fbb97p-7Q, -0x1.873bd13c8af17ab00e30f03b73e4p-11Q, -0x1.f894721441f671f4ac26746366e6p-9Q, 0x1.1650e1f6ec4c290c75eee26e8b4ap-10Q, 0x1.7334fd9e58c69f69b95d47a6075fp-11Q, -0x1.959f69010da009a2eacf096b1dafp-12Q, -0x1.5e73f3c02020121b8b1dbc91cc8ap-15Q, 0x1.20612a2e814f83021e4b38a90018p-14Q, -0x1.5adbf364f5e1bddd8115a86dd662p-17Q, -0x1.26968e53fb76ce12ec5e07348937p-18Q, 0x1.cf0cbb4133dbb68c44095fc163dep-20Q, -0x1.7fc90f0c46da191bc033464815fbp-23Q};
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00646115346008794781816639744862281427232715941920119921810140416821319638585"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0623647588493988983279856675843487742830533369340766716460251880613807597066"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.254850267792621353665907788677828668618704241636713744378008420238232719628"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.554305617940893835992683144985115484407826983095163460968399777532226842271"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.631187849104856779557661713535817234862395245657001728978880959248433640269"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.218670687758906521491747591821751705176577432127043205903027323352534222868"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.271688552278748041414219247618117109460488246568333081431189666923849066652"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.218033529993276044755555881270231191197524066947060475274712704179785996228"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.138395213864806591073993969002157371398990046322968611905911990239065683492"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.139989016584460701249294316227116344032822155561432618133368381730127661592"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0867484115681696890456082206672779538297914953951750365749296445982289331724"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0715489555040461307358414511517380799095806967312953809999091309335447192979"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0552371262592160441161883406053340339791383363251167215767110765995965856731"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0269814083079129169739903140321519334337576659580727423328434928060131390138"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0301853515403906351871482262348913757378157540665865262488375619379066007462"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00561504953035695913321837136769149863745729720392581038769868016916017798506"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0127894932663334089615733070578407929937490386157205831348153451948141528455"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000746218989268384937181716073918178097195818798881330290043548750870183218766"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00384963886802218744578634931609555177409681850828570049305891572532777766984"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00106169108560676184303256674938841117303394158214783086389393956154388248847"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000708021154235527858644297769761712898347186346418159537167009442266803119446"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000386831947312954482107666339805731442732890210784216537990146842609536038748"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000417772457703725973526797953983925892838972659013273013105432373007939629113"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000687550425269750960387343702162803160189037068765187527988272789892867302714"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000103372091845707739466140734259481458626927250949074485069144305905647763599"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000438970490178139411525404256136716982932308536080082571815104919437269388055"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000172499467536781276988571269274179852358789470986735657691071794719454646345"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000178713996831135907633419293847083934388299030997695944699402284569127317214")};
+        }
     }
     if constexpr (p == 15) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -256,6 +298,9 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.2970058a26dcd961f2ddf52bca08p-8Q, 0x1.7eec010bca4c417f3cf45c166751p-5Q, 0x1.a5efd6f02857dd0be400d7c02e2cp-3Q, 0x1.f8747691d3f737355530dd281d86p-2Q, 0x1.4aa8051a530b457c39051251b937p-1Q, 0x1.5b237b0c281791146b95d35023c4p-2Q, -0x1.8bae9ca895b451d87fbb9a690248p-3Q, -0x1.27d0d6e28e01f3ef0606971828aap-2Q, 0x1.0b6623378c72eb295fa0f634a67bp-4Q, 0x1.856ba3f0d1d5aaf4f59a12cbb286p-3Q, -0x1.44f200621040cdd51fafc7035006p-5Q, -0x1.c726bf22e4a15fea85834dbb1052p-4Q, 0x1.15858527779bc1c4ec7f8b6fdd21p-5Q, 0x1.c0c32426f4662ec60f158af78296p-5Q, -0x1.a62aa972a6fc3876e9915f565de4p-6Q, -0x1.54f3ad3a0b7c5bd971d938015013p-6Q, 0x1.ee451350034703acaa0dbe95c1aep-7Q, 0x1.4e4c95b98ec2d5e117559a2b0da9p-8Q, -0x1.a92e1fc2fdcad88a36c4f23f938p-8Q, -0x1.fb000715d8e6558a8e3b0bc34d7fp-13Q, 0x1.fd6e43c3dd5e86d041c185aa9428p-10Q, -0x1.879fe7f24ba0a4818b2d76fbd7e6p-12Q, -0x1.79080f71ee322531c0337932b9a5p-12Q, 0x1.46f04a6cb59007eab6af7b114fa4p-13Q, 0x1.b0bacca20c60f4939edefbff1354p-16Q, -0x1.d7ff965f47a09038cb01ea5da5e9p-16Q, 0x1.c35f5c15433718b508f832bbf1b8p-19Q, 0x1.e6358dfe44b5282546827ce8042cp-20Q, -0x1.532291d1cbfa3eda1a3275ffd36dp-21Q, 0x1.076d01633701901bb8cc971717bp-24Q};
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00453853736157889888145939491021169634666367124378878699791651359730618263777"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0467433948927662718917096933484357577657915170021494351311319734377213834945"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.206023863986995731539891500947630721930613850564193090270204726624901561209"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.492631771708139623606775707402994637261722156513093240216016003697522813162"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.645813140357424358176420912010691799643260828749404618107148947895533066481"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.339002535454731527691264114383577391875676949179355466933669011509397556470"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.193204139609145428706399053432147174630409003914286382793775492150589726686"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.288882596566965646248412500982233298131143563043534259497129296256293483504"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0652829528487728169228310791986957488203917428559614412596510130561953369929"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.190146714007122982348489311658602051795950125817433669687815606055254287820"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0396661765557909444838436675189620066838174282068373680544974535292838687668"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.111120936037231693365671032467405860885862376216591412050565788400539631609"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0338771439235076862085481784443352377086474468741126536946319599123012785905"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0547805505845076126891379031258187910860941599742276856424484536408030091303"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0257670073284399625859452575426982639220364163482534013839683682541716280711"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0208100501696930816778848342467700016205465795136489904099616617271926101264"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0150839180278359023632927446017032273624489282330562771623396889036950783790"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00510100036040754316970886018556531472480106652734422205552663106916575853665"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00648773456031574499518168314921869081695584563938882640792896746945184786140"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000241756490761624281166722532630017960522994699581453522332941192889131156009"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00194332398038221154176491233254108744101142486557953140145230261789465341230"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000373482354137616992009809421364541461138763096803025662574022673555831120585"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000359565244362468812164962007590980885819420245408409030562748046672838761659"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000155896489920599747947165824122710881625556705962549591522860363042830623991"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000257926991553189368092586241761685591294404236876734070916011973700950042214"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000281332962660478136475532477707847866579144387629378890426725562075302388539"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000336298718173757980312484521042017747213484665586407818718630450150330033976"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000181127040794057708376851091228584116057708592533750785059029068086553957632"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000631688232588166442120159729951765765416613791512119551041664162606772181110"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000613335991330575202905629946028978860198919045088539651217384559505804672173")};
+        }
     }
     if constexpr (p == 16) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -272,6 +317,9 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.a2047f25eec85da6e57cd7f20965p-9Q, 0x1.1df6c86cbec60472edd73314093ap-5Q, 0x1.520d391a9410689a221d2a40ed0cp-3Q, 0x1.b8a3e5feb48792faed491d08e637p-2Q, 0x1.465391b4659339393dc6b44dd0b9p-1Q, 0x1.c2db72f84c20394e90d8314fee8dp-2Q, -0x1.6f9ed69c399c6d957cef0caf36cp-4Q, -0x1.4ee9af39c16ebfbef0c302e6791dp-2Q, -0x1.c96973b93bd864088cf77c5363e8p-6Q, 0x1.b084bf1dc763ab7d34b03cf7014cp-3Q, 0x1.bff160aba4bc2b81b5cb21d8ed3dp-6Q, -0x1.0f21999627c5eb1bdc396cd5510bp-3Q, -0x1.98ed2d2871d09c2ff301236b3aa5p-8Q, 0x1.36fc54ec8b1065ad541d9561e805p-4Q, -0x1.f159dcb973ff3c971dea81777e8cp-8Q, -0x1.2e3093b602a5114cced31fb3d21p-5Q, 0x1.516f07b10e2bfeeb35e5d488972dp-7Q, 0x1.ca8c3dcce54c309c6bfdafe5b818p-7Q, -0x1.ca18fbf2cc14161cd462d6382e8dp-8Q, -0x1.dda9bb9568c150b5b1b563e2a704p-9Q, 0x1.99ff0c3f2ed80a696d3f49d1ae83p-9Q, 0x1.abb6031610512ba452ab2c15607bp-12Q, -0x1.ed5dcd1b49a3f3c23377158c2ae9p-11Q, 0x1.df29e5ea1284520ed9350c7d7e2fp-14Q, 0x1.6e8e301063e5a66bc2dcbb672407p-13Q, -0x1.0000dea4283e8e4f97e320b5edbp-14Q, -0x1.d3f0626b575af7e0f5c7b70618f9p-17Q, 0x1.7c64ba15d23464b7681824c41ca1p-17Q, -0x1.1821ad345e7bfc3ef33cc03c406ap-20Q, -0x1.8b555407022a1683907685f46c79p-21Q, 0x1.efcebf5a99b7b789a7792201843ep-23Q, -0x1.6a61bcee28102f153c8290cebfbbp-26Q};
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00318922092534773802976954756464595868706708675013142876787587817778694863119"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0349077143236733464103014722402302000921824143050398414614005464773763780013"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.165064283488853117899125273056113481158483500234272324021359282902034099572"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.430312722846003813740392542435768462063397047803698677392464629118864929936"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.637356332083788898631985241299603053649859594081419812596775159322552430035"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.440290256886356900039086916357167928852780303513527257878988432216501129849"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0897510894024896428571871807744259743065924744558266014962471841522684784655"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.327063310527917704646290567568911964175722891822881242814172353116733610255"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0279182081330282766826451959502687320433997121917473604153547976243684979156"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.211190693947104288720968016326883790092849142616767943925104282659239340555"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0273402637527160413648524575720161796542902781950713022023150026811811035864"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.132388305563810390450047414775649337509228781770602797879854902742212569323"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00623972275247487176567450339412002586544465631167876099076145808663824556181"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0759242360442763158214849874394142246153040594610094335194031399951322105236"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00758897436885773763849489086463699579658697514499092540009716094367144606278"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0368883976917301423335266632089455431471874842970673083106406876512904740900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0102976596409559694116500058007661690052885626580366220885414734497334909977"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0139937688598287310295045187367032972640984029172786898849010078360486452906"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00699001456341391667028424953651728833805785619964646907811575967502711102002"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00364427962149838993216900054093362938705533397335310866884121504669938973849"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00312802338120626883166120255985467876782147190619360811745036081031020620657"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000407896980849712836241747032340609578243195297231054671507139711098341190969"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000941021749359567588926645395363587540775474721673448050925027367949065706153"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000114241520038722392644022809955566294583968434493647265287709142315097418924"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000174787245225338180380175863766074687498602472861539989797195359589183047664"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000610359662141093583516236915052221281195725998196591914396172281391485128503"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000139456689882088934519907831199840198232527356919867533540870797045644631590"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000113366086612762585875884876288653699751947106820375366175784342881379088583"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000104357134231160650152545473726261540488747893063567647154603268028625910132"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000736365678545120551209969571972556364658544554584166332743356923285383067848"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000230878408685754586640541273294200612130630673586665552537254486473108851937"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000210933963010074309700057262360348990683629758459160530774534994952533728279")};
+        }
     }
     if constexpr (p == 17) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -288,6 +336,9 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.25d68f81bd86c306bc9043f43f4p-9Q, 0x1.a9bea4085cef3d6d79a074d9709ep-6Q, 0x1.0cba6633a3a6d489f4c961323b24p-3Q, 0x1.7b3d3861245d02709eb04b0b2b39p-2Q, 0x1.38d48c64aa0daf396243783e95bep-1Q, 0x1.0960af0f4068e5ac2ea6e7c9135p-1Q, 0x1.bf874a24b1d55da571e39f2bf7e7p-6Q, -0x1.50335073492d1d5e6945d8cdee28p-2Q, -0x1.0346bb1b97633ba3dcc115a9814cp-3Q, 0x1.9417930ab08a311830b19e500034p-3Q, 0x1.9e403f27b713f2db7263ac22d15fp-4Q, -0x1.03b7f2067576f3b2927e9c5889d3p-3Q, -0x1.d3b162866891a8d294e6e9eb979p-5Q, 0x1.4c35ca8307eb62387847e8508ae5p-4Q, 0x1.6d90b88bab05f824bb4e728b7a1p-6Q, -0x1.80637c4a935c7dbdd09fd2c6d8fdp-5Q, -0x1.acbb0e1b24a7711aad0c2cc58d1fp-9Q, 0x1.7477f35c89772c79eec161a3cdd2p-6Q, -0x1.8ed9cce7691caca1362d6d7abefcp-9Q, -0x1.19e6894a383d0a23e4d18574889p-7Q, 0x1.85057173113925897d4027a40b6ep-9Q, 0x1.2d9fa2834b37aecc772ff5c2d7b1p-9Q, -0x1.78a90e5fc8eeb8c9dbcf2179c3bbp-10Q, -0x1.58126708ae49d0421a9c690b913dp-12Q, 0x1.ccd01a3d65144c8ab80302b0f5dbp-12Q, -0x1.adaa9541cd34139a00a6638e9bf6p-16Q, -0x1.5822674fd0b1a40e647125cde434p-14Q, 0x1.85029b61ff0fb98b3294c269c9e6p-16Q, 0x1.d5219c45df32dc63e76e89984d9dp-18Q, -0x1.2e63809757f52cc8ed09e415ace1p-18Q, 0x1.43e648c7ce72f3a94ea0d55898bap-22Q, 0x1.3d94aa0876b2cc113a8ea22e3eecp-22Q, -0x1.69ce4aed2f58e6ecb8a211f55ad1p-24Q, 0x1.f36b16a008a288af85eb1e1cec02p-28Q};
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00224180700103731285353596267707443691406219188056037073325053118133419193342"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0259853937036060433891486459172078831547394452487824129439994827687663725129"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.131214903307824406577550623185906996014429360925997853006700439459033631661"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.370350724152641150449254819072188644947707887689680382365042593579529628290"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.610996615684622818188667886767937208273709389335872629137178390490835290734"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.518315764056937839325453852808596804621681719771841640243990498683288900340"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0273149704032936350043125071914758648035046981896456300367294282283271222511"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.328320748363961736090966534072506176758159769815155802467913052689676377760"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.126599752215882702874467911093382550505396626010408616210372832359164928283"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.197310589565010992785404704478193014255142241413564691712228422600456673716"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.101135489177470272150969985643343480219662254549966487610943796293105029624"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.126815691778286311094857112866233168038479218591501706573213748994956827246"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0570914196316769272891123947865138232416116086984534705399014464059382899408"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0811059866541608850796588574855542920102436419095449919402067822775070461335"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0223123361781037959533913605953481375623224211409368924402086919318268997481"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0469224383892697373330089705921140050713876812549803060287843927826168188238"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00327095553581929378165536022217749445206952595806160939280927575122449701285"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0227336765839462703184561624478844896990671374133833949802486413275635089855"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00304298998135463706859248263790720607863339545722509658828788135585314667137"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00860292152032285483171370641324365991792673628427173061192098670257230281191"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00296799669152609487280648506000803826995946384654837899504419503429102573503"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00230120524215354562430205986903842360424197668018944747606476493728483725055"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00143684530480297612622289040298038490350367453072993580956143471121236432705"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000328132519409837971395444401752011507581240244272874970019565158958075253614"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000439465427768643677838567752731784163228924931973889217946591075762286390503"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000256101095665484588272989121094992022166408206153190965517841374523415859860"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000820480320245339183909548257628218986613627304963676433868959364213432243666"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000231868137987459508448206820570627757210669517409189533853073478931042782802"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000699060098507675127320454970085537862776275858590205796402748138050877941586"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000450594247722298819410226820637831212971357260071649994491841668706683585071"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000301654960999455741560520759487993976347616870521764689770270618984715407855"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000295770093331685675497990525881615136787034562892431730735463949569521998500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000842394844600268017878707129692287706841031094222279962259313341617779208118"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000726749296856160811087976744140903503415858171978979108889204640807029047656")};
+        }
     }
     if constexpr (p == 18) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -304,6 +355,9 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.9d386358a187490511616014e787p-10Q, 0x1.3c05f73c5b367536d2be9893ed8cp-6Q, 0x1.a84c610f33b444b779a9b1758c69p-4Q, 0x1.423b3247213b88555f9f2ada7d8ap-2Q, 0x1.24c67bbcaad511453636985416f3p-1Q, 0x1.24c32fbf17436364ee6d86ce0b36p-1Q, 0x1.2d834f99026e9806c6f6c1aa6cb3p-3Q, -0x1.2cb3a51535039a741562ba69c7a8p-2Q, -0x1.bb5a5b1e13b56915364cb7d6d1bfp-3Q, 0x1.323ede758da4220dcba304aad9d9p-3Q, 0x1.562eba30ba3dac1311ece1a1884ap-3Q, -0x1.7a30ff6ce5271d64766823319bd4p-4Q, -0x1.b541d802db16d80f141c678b2993p-4Q, 0x1.09c72d78f01628c7ccd127058828p-4Q, 0x1.d35d236774d120bc0fddfe320959p-5Q, -0x1.6cc216694aaa0ced2f850c2b3eb7p-5Q, -0x1.84d84c9eacf2bae4fd091b9bdb4fp-6Q, 0x1.b4f90c6dc9841e7a702107e1aca3p-6Q, 0x1.9a65be90d86a53c665da90605941p-8Q, -0x1.ababc1ea3f978443c6511c976c7fp-7Q, 0x1.f19207685977f43b68af0530733ap-14Q, 0x1.43f78b1e4d853774466d94263915p-8Q, -0x1.2544e0deeca71abd544eac93fa45p-10Q, -0x1.5f6de508b23063ffd5522faa2f1ap-10Q, 0x1.497f3c70a07cbca34a7835790cbfp-11Q, 0x1.bfe9ba59913cd96563f593913af3p-13Q, -0x1.a098a12371c0ca3dcc2d68b00891p-13Q, -0x1.49d5efd42da901d7159610c4d152p-23Q, 0x1.39d678c2c06ae863ef3b97fa7d6p-15Q, -0x1.1de76b2193bec903a9d077f1666ep-17Q, -0x1.bf4c72e2a2d93cedea468c1c5543p-19Q, 0x1.dac907ddfd9dac76e76088418dc5p-20Q, -0x1.4a5a655290e67a67e8d8672b7916p-24Q, -0x1.f9216d4e4d83adac1cb13466b74bp-24Q, 0x1.079c6a0fc4517cae3d72b9596e6p-25Q, -0x1.58b0195a8266ce508d99fc62d4eep-29Q};
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00157631021844076043154074492993977774767075371099166036368442986184714001537"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0192885317241463770592139171582905241995466702528849757223671483332142575124"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.103588465822423596224191049193725359647069655522024167297622418469656394177"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.314678941337031699057199825565257993178670619048937450949130751036740690695"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.571826807766607223481858937090062341939367374313093056129532404803265328819"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.571801654888651335289111999406596502566804788281852506075939526421405556433"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.147223111969928141575097727108107231255786410735570138780167713584411016265"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.293654040736558744247903099498115072393571072903505323966175230801212578403"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.216480934005142971123767862566827147143793723566949240838869239366378506250"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.149533975565377789350930173891366720880481669189376561026194307191290248158"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.167081312763257404514931813995013474532420564635398808315225063337013902642"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0923318841508462806042937255865945973143184800014456961207450846746206498455"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.106752246659828485593220058161498486138526640462411208391770205467847935365"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0648872162119054428194757795514191146312938211663414784613714984515877764896"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0570512477385368841209076884649962226059622612043103852460067642320755043632"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0445261419029823247155614355974465349297147789143983359275503466820231489272"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0237332103958600010327520958266521611019751933071349023307156579014300914190"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0266707059264705902998790863167202034320789599993607281336347152037595652919"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00626216795430570748523609314449788250199032520474501319026805231525752058555"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0130514809466120017727763644760080716975519105450757166660613358038629139862"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000118630033858117465730174159216181908454489941745231740518561572996617939506"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00494334360546673813066552951680297483429963831336647776529520326003067700242"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00111873266699249707280065885523865018231806048258497014551268711985227900418"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00134059629833610662951756722825158360982304452468598664032394269120723888750"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000628465682965145712561944988542083821755102279630158287434965288076478383268"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000213581561910340688403905281434192602587320032599646652254344051060271497781"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000198648552311747948579824541636248955492779788026401787613960521573218466250"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000153591712353472467506977033587671719370047242702151323658728810220957329769"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000374123788074003818109220813803539395230429261579398503073136385132849832575"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000852060253744669520391925491165552302243759695622637651230591706524073534413"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000333263447888582188878245203334103682731150590779649843982933727956405960650"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000176871298362761545587632873075537517641250135911405881545310061923499126827"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000769163268988517614600015287853959840581739758815652511676990865187416269746"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000117609876702823169845098235656129256134757977769539695352814136780995583426"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000306883586304517480093547829493397537245017978789457449293057011634442052915"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000250793445494859826719517318314712673180631714486827581994140326785823293114")};
+        }
     }
     if constexpr (p == 19) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -320,94 +374,10 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.22a1917fed859e160446bb7b167ap-10Q, 0x1.d3f6896603bf4308e8ccc5a30641p-7Q, 0x1.4cea4765b11499a3de1dc5fdc4b7p-4Q, 0x1.0ebbd74f124f24e597d3a5bc26dbp-2Q, 0x1.0c82ecc4163915332b81143283e8p-1Q, 0x1.34129e60b6e2fef58b66c45f7099p-1Q, 0x1.0b280be54f8b6ad2d41e0f33532ep-2Q, -0x1.d32194b53c8046c9a7b9b8714cebp-3Q, -0x1.24b2e1dd4c73df34e82deb7bb6c6p-2Q, 0x1.31c6940f7edfa2f8c6ddc9cd2aefp-4Q, 0x1.b2e46c16840423c52b33ff7476eep-3Q, -0x1.12957a28f5bb337e3e66ea6f23e6p-5Q, -0x1.246cd3943959a8c450bf5ca92b86p-3Q, 0x1.c3f126f461d985ee9de87f3424e5p-6Q, 0x1.63f8568e9e6ec0d34220dce2e186p-4Q, -0x1.b2323dbfdcbe6e4ed8b2320fb129p-6Q, -0x1.7629cb842f99ab236f8e908d21c2p-5Q, 0x1.6248a775ca65f9a99ecab76ed61p-6Q, 0x1.3d72f2476d00410fe80cb42bd72bp-6Q, -0x1.ca5f1bf2f3243b0308970f1f944p-7Q, -0x1.807e9f533b2172c38f0c60523009p-8Q, 0x1.cd6c23ae5d8f94f8e6c997306168p-8Q, 0x1.93274e99dc9b4cfea213c9163decp-11Q, -0x1.6043462e3e519b97ce417a7ac3b3p-9Q, 0x1.66698fcf3c2497984ab865b5b6acp-12Q, 0x1.81c5be1857465de5530984af43cbp-11Q, -0x1.1156b7a432a662bbb70ff712e064p-12Q, -0x1.054e8a6af00d6f29e88cd98738bep-13Q, 0x1.6d608dedb3cf6080fb9e6ef72893p-14Q, 0x1.56a78fb9bd526ca09fc616b1b8ap-18Q, -0x1.172d0353b3f11fc1e8818be3f7a7p-16Q, 0x1.941ff236730f0886ee4074951d94p-19Q, 0x1.9b39878b9566344204396825f773p-20Q, -0x1.7070fedc9cdecfffd4c6dc5d1fe5p-21Q, 0x1.f1373b9dbeafa1390279c531a649p-27Q, 0x1.8e4f570c878dd84d17b935d5f69ap-25Q, -0x1.7f97c3aa5d9df8ae90e909fae15p-27Q, 0x1.dc770dc2ed00b68b9c525506b211p-31Q};
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00110866976318171057109915419520971516424529967777343593213545529038383924770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0142810984507643973743988915295019923474566344216366595787071599110771075191"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0812781132654595506529630678490162483984497997102862036649772686406019150041"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.264388431740896784674810038028942687386237780721192071841738581477351352687"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.524436377464654915336057597548406462604463364104807211639316023628078258263"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.601704549127537894886707713592180262053656563958596329331393143392083219576"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.260894952651038829287245667531052832417267310130190773992521389876582446158"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.228091394215482646374632577605463720709378723708642590953482241776619580080"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.285838631755826241854597569502898423721735609558833514992211937357294676905"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0746522697081032663676343311187881900586586614973190965636539995134773660042"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.212349743306278488809060856705982419707707420087883944841690869803668388649"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0335185419023028786816938841878573150697784507523896681981403258573481442235"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.142785695038736574977960273162611281299849770615242850862756243341853036336"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0275843506256286687501474352016219865537447459696342308076281830983836771416"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0869067555558122324884764542880844303478520800246819275964035297492772454078"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0265012362501230408990183584367638736107506801768674780817134564719233152649"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0456742262772309080564544421429579601793893573211563005088010978423298835500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0216237674095850471303298425717237235431809706785875254257102081949907179885"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0193755498891761276463709435445799981449688509587582554640696372421676825877"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0139883886785351416325040123524866252191681386745309583680836668669699906947"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00586692228101217472658449343605437377381460834080875817737276517150642852313"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00704074736710524315301451120740062010940168989766538307822939808316234678585"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000768954359257548355974913914867395516347794708603940612954642251648623392855"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00268755180070158200395736385507039863653403892098247829017026719960594838510"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000341808653458595776565165729046380813521421484881951725779403154942704074894"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000735802520505435207026048190539728187518317579277990485818949491732987619374"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000260676135678628005731831513089752279038393936207356340861354755942716317598"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000124600791734158775344978440890165399031734141334198090475759204698349203833"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000871127046721992296541686238819112826841293389328208351772944342009756120059"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000510595048707388605304922280993423157368736799210628266938926416431155785903"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000166401762971549445462067771989919863033367560881201810873914492293692424442"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000301096431629652633969533445472594363264579893816242716885138250008132314822"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000153193147669119306393183238108663603120312303272347746362414105936220672489"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000686275565776914270188355461348673285445274075277139241175841882669179558939"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000144708829879784454207821986329161542055167357407136783431616765021249777078"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000463693777578260422343085772821094889887174829108596229664932070020615712517"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000111640206703582581639050476914247258646497579928447368224607655958423915203"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000866684883899761935032301354078212462728974219027305931912284064941409400037")};
+        }
     }
-    if constexpr (p == 20) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.98eb9ap-11f, 0x1.59aebcp-7f, 0x1.03c8a8p-4f, 0x1.c27102p-3f, 0x1.e40a78p-2f, 0x1.389292p-1f, 0x1.722da8p-2f, -0x1.1d1b3ap-3f, -0x1.4ea132p-2f, -0x1.120e7ep-6f, 0x1.d38a42p-3f, 0x1.467406p-5f, -0x1.3e6128p-3f, -0x1.94f5e4p-6f, 0x1.a2fca4p-4f, 0x1.711d6cp-8f, -0x1.f9a24ep-5f, 0x1.8100cep-8f, 0x1.088e0ep-5f, -0x1.200234p-7f, -0x1.c48b18p-7f, 0x1.b88232p-8f, 0x1.21b464p-8f, -0x1.d56f02p-9f, -0x1.b3fa62p-11f, 0x1.6d0d18p-10f, -0x1.c0c538p-15f, -0x1.93cfc4p-12f, 0x1.a9dc1cp-14f, 0x1.1c224ap-14f, -0x1.37443cp-15f, -0x1.25ad94p-18f, 0x1.e5f3b2p-18f, -0x1.0fa7b2p-20f, -0x1.6f998cp-21f, 0x1.1ad0c2p-22f, 0x1.baf44p-33f, -0x1.37c9a6p-26f, 0x1.16bc24p-28f, -0x1.49b9bep-32f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.98eb9a1ad223fp-11, 0x1.59aebc7410b77p-7, 0x1.03c8a76dc45bbp-4, 0x1.c27102c5bb1f8p-3, 0x1.e40a78036ac7fp-2, 0x1.389291df573b5p-1, 0x1.722da89a0e974p-2, -0x1.1d1b3a29bcd1cp-3, -0x1.4ea132f283bf2p-2, -0x1.120e7e4faaa26p-6, 0x1.d38a4229ed991p-3, 0x1.46740628c1e1ap-5, -0x1.3e612851515f6p-3, -0x1.94f5e34522642p-6, 0x1.a2fca44817f2fp-4, 0x1.711d6c0e1d46ap-8, -0x1.f9a24d69ac62ep-5, 0x1.8100ce41923f9p-8, 0x1.088e0e0a9eca2p-5, -0x1.2002338d10ca4p-7, -0x1.c48b170cc05f1p-7, 0x1.b88231706930bp-8, 0x1.21b464fba22e8p-8, -0x1.d56f016e81eefp-9, -0x1.b3fa62b1e588ap-11, 0x1.6d0d181744b82p-10, -0x1.c0c537c57bf91p-15, -0x1.93cfc4d1b467bp-12, 0x1.a9dc1c3780427p-14, 0x1.1c224959ff66dp-14, -0x1.37443b45c500dp-15, -0x1.25ad943ec34c5p-18, 0x1.e5f3b2c4841b3p-18, -0x1.0fa7b2e66c174p-20, -0x1.6f998ba053586p-21, 0x1.1ad0c20194a77p-22, 0x1.baf43fba18386p-33, -0x1.37c9a671235e5p-26, 0x1.16bc244bc36b8p-28, -0x1.49b9be3c4a795p-32};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0xc.c75cd0d6911fa1bp-14L, 0xa.cd75e3a085bb58ep-10L, 0x8.1e453b6e22dd40bp-7L, 0xe.1388162dd8fc33cp-6L, 0xf.2053c01b563f9cp-5L, 0x9.c4948efab9da4ebp-4L, 0xb.916d44d074ba33ap-5L, -0x8.e8d9d14de68dd92p-6L, -0xa.750997941df90a2p-5L, -0x8.9073f27d5512ec4p-9L, 0xe.9c52114f6cc8785p-6L, 0xa.33a031460f0d07bp-8L, -0x9.f309428a8afb31p-6L, -0xc.a7af1a291320cf8p-9L, 0xd.17e52240bf97653p-7L, 0xb.88eb6070ea34f45p-11L, -0xf.cd126b4d6317224p-8L, 0xc.0806720c91fc6d9p-11L, 0x8.44707054f65127ep-8L, -0x9.00119c6886523a3p-10L, -0xe.2458b86602f87fcp-10L, 0xd.c4118b834985633p-11L, 0x9.0da327dd11741b6p-11L, -0xe.ab780b740f77b4ep-12L, -0xd.9fd3158f2c44f42p-14L, 0xb.6868c0ba25c0c5ep-13L, -0xe.0629be2bdfc8a9ap-18L, -0xc.9e7e268da33d44p-15L, 0xd.4ee0e1bc0213577p-17L, 0x8.e1124acffb364cp-17L, -0x9.ba21da2e280684dp-18L, -0x9.2d6ca1f61a624d6p-21L, 0xf.2f9d962420d947dp-21L, -0x8.7d3d973360b9f2p-23L, -0xb.7ccc5d029ac2c2ep-24L, 0x8.d686100ca53b51dp-25L, 0xd.d7a1fdd0c1c3167p-36L, -0x9.be4d33891af2665p-29L, 0x8.b5e1225e1b5bf96p-31L, -0xa.4dcdf1e253caa43p-35L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.98eb9a1ad223f435df1887363eb7p-11Q, 0x1.59aebc7410b76b1badcc12950a6dp-7Q, 0x1.03c8a76dc45ba8152978f10f7c69p-4Q, 0x1.c27102c5bb1f8677bf80bd502bd1p-3Q, 0x1.e40a78036ac7f37fedcb5a80e979p-2Q, 0x1.389291df573b49d69709e6a39a77p-1Q, 0x1.722da89a0e9746749e19dd59185cp-2Q, -0x1.1d1b3a29bcd1bb23d3a59b3ec213p-3Q, -0x1.4ea132f283bf214303a247980416p-2Q, -0x1.120e7e4faaa25d883a426ff76e5ep-6Q, 0x1.d38a4229ed990f09767be4223746p-3Q, 0x1.46740628c1e1a0f69af0510e97b1p-5Q, -0x1.3e612851515f661f1b982f038f42p-3Q, -0x1.94f5e345226419f0d083e13269c2p-6Q, 0x1.a2fca44817f2eca68758db1b8b3cp-4Q, 0x1.711d6c0e1d469e893974f1ea6999p-8Q, -0x1.f9a24d69ac62e448cc934c83e493p-5Q, 0x1.8100ce41923f8db158db362c64bfp-8Q, 0x1.088e0e0a9eca24fb78af66e8d177p-5Q, -0x1.2002338d10ca4746416546df60b9p-7Q, -0x1.c48b170cc05f0ff881bd3e1b39f6p-7Q, 0x1.b88231706930ac6660faf6c0f2dep-8Q, 0x1.21b464fba22e836bf597b5aa439ep-8Q, -0x1.d56f016e81eef69c49d53f5d0ebbp-9Q, -0x1.b3fa62b1e5889e83d8f6afb75bd8p-11Q, 0x1.6d0d181744b818bb6e246e9454cp-10Q, -0x1.c0c537c57bf91533c45c4dad234ap-15Q, -0x1.93cfc4d1b467a87fbd054b646597p-12Q, 0x1.a9dc1c3780426aeee785e4f91b69p-14Q, 0x1.1c224959ff66c97f21d37d9c05fbp-14Q, -0x1.37443b45c500d09a28a777a35885p-15Q, -0x1.25ad943ec34c49ac55547e1ee8bep-18Q, 0x1.e5f3b2c4841b28f9ade386d031fap-18Q, -0x1.0fa7b2e66c173e3f4204ea792843p-20Q, -0x1.6f998ba05358585b78628b55c242p-21Q, 0x1.1ad0c20194a76a3ad5100084b452p-22Q, 0x1.baf43fba183862ce0fdd2ce6713ep-33Q, -0x1.37c9a671235e4ccaa17336a7b289p-26Q, 0x1.16bc244bc36b7f2c806c15a56631p-28Q, -0x1.49b9be3c4a79548641570a58d68ep-32Q};
-        }
-        #endif
-    }
-    if constexpr (p == 21) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.1fbdb6p-11f, 0x1.fda65ap-8f, 0x1.93701p-5f, 0x1.736cacp-3f, 0x1.adc2aep-2f, 0x1.33f89cp-1f, 0x1.c742b8p-2f, -0x1.24a464p-5f, -0x1.57b854p-2f, -0x1.cc60ep-4f, 0x1.b148bep-3f, 0x1.d7feep-4f, -0x1.1e9916p-3f, -0x1.4ef44ap-4f, 0x1.8bacdap-4f, 0x1.7690eep-5f, -0x1.0a25dap-4f, -0x1.319ff4p-6f, 0x1.457136p-5f, 0x1.b81b9cp-9f, -0x1.564bap-6f, 0x1.3b071ap-9f, 0x1.268bbap-7f, -0x1.7af914p-9f, -0x1.83c29p-9f, 0x1.c1ff8cp-10f, 0x1.4f3d4cp-11f, -0x1.6a1c4ep-11f, -0x1.0c224ep-15f, 0x1.9624eap-13f, -0x1.30f834p-15f, -0x1.2592c2p-15f, 0x1.019c78p-16f, 0x1.768306p-19f, -0x1.9ebc2ep-19f, 0x1.53f4f8p-22f, 0x1.41473ap-22f, -0x1.adab3ep-24f, -0x1.35ca1ap-29f, 0x1.e5063ep-28f, -0x1.949b92p-30f, 0x1.c8df1cp-34f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.1fbdb5d9588b2p-11, 0x1.fda65a6714bdap-8, 0x1.937010050905p-5, 0x1.736cace0a6657p-3, 0x1.adc2ad3828f8ep-2, 0x1.33f89b5c2e57bp-1, 0x1.c742b82c92555p-2, -0x1.24a4646f28f23p-5, -0x1.57b853bbe6a56p-2, -0x1.cc60df28d7badp-4, 0x1.b148be3b1073fp-3, 0x1.d7fedf0356bp-4, -0x1.1e9915e3ca004p-3, -0x1.4ef44a8b3ce94p-4, 0x1.8bacd9d38a28ep-4, 0x1.7690ee8b59819p-5, -0x1.0a25da27e87d7p-4, -0x1.319ff4cde80a9p-6, 0x1.4571365df5489p-5, 0x1.b81b9bc4d4f3cp-9, -0x1.564b9fd2c3bbfp-6, 0x1.3b071a00e4e5cp-9, 0x1.268bb96001dc4p-7, -0x1.7af914f01f8fcp-9, -0x1.83c28f7e3c0e5p-9, 0x1.c1ff8c65fb698p-10, 0x1.4f3d4c629fe3fp-11, -0x1.6a1c4ee19b423p-11, -0x1.0c224d58d6e81p-15, 0x1.9624eae0b53fp-13, -0x1.30f833f09ef02p-15, -0x1.2592c13818da8p-15, 0x1.019c78bb61865p-16, 0x1.768306fdacad5p-19, -0x1.9ebc2e6b68816p-19, 0x1.53f4f805c9123p-22, 0x1.414739b599eb7p-22, -0x1.adab3d69a3265p-24, -0x1.35ca1a0003737p-29, 0x1.e5063d39ebf9ap-28, -0x1.949b918111d77p-30, 0x1.c8df1c0c683efp-34};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0x8.fdedaecac458cd2p-14L, 0xf.ed32d338a5ecf5cp-11L, 0xc.9b8080284827e72p-8L, 0xb.9b656705332bae6p-6L, 0xd.6e1569c147c6dadp-5L, 0x9.9fc4dae172bdbe9p-4L, 0xe.3a15c16492aa9dbp-5L, -0x9.252323794791b92p-8L, -0xa.bdc29ddf352b036p-5L, -0xe.6306f946bdd67aep-7L, 0xd.8a45f1d8839f921p-6L, 0xe.bff6f81ab580014p-7L, -0x8.f4c8af1e5002333p-6L, -0xa.77a25459e74a242p-7L, 0xc.5d66ce9c5146f15p-7L, 0xb.b487745acc0c8adp-8L, -0x8.512ed13f43ebad1p-7L, -0x9.8cffa66f405497bp-9L, 0xa.2b89b2efaa444bdp-8L, 0xd.c0dcde26a79e22p-12L, -0xa.b25cfe961ddf733p-9L, 0x9.d838d007272dcc4p-12L, 0x9.345dcb000ee2014p-10L, -0xb.d7c8a780fc7dcf5p-12L, -0xc.1e147bf1e072bc1p-12L, 0xe.0ffc632fdb4c29ep-13L, 0xa.79ea6314ff1f508p-14L, -0xb.50e2770cda119f3p-14L, -0x8.61126ac6b7407d4p-18L, 0xc.b1275705a9f8219p-16L, -0x9.87c19f84f78120fp-18L, -0x9.2c9609c0c6d43f4p-18L, 0x8.0ce3c5db0c32b2dp-19L, 0xb.b41837ed656a6e4p-22L, -0xc.f5e1735b440ad22p-22L, 0xa.9fa7c02e489184ap-25L, 0xa.0a39cdaccf5ba4ap-25L, -0xd.6d59eb4d1932a9ep-27L, -0x9.ae50d0001b9b402p-32L, 0xf.2831e9cf5fcccbdp-31L, -0xc.a4dc8c088ebb653p-33L, 0xe.46f8e06341f76fbp-37L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.1fbdb5d9588b19a3bff14d1b38fep-11Q, 0x1.fda65a6714bd9eb85e8d7e88dc47p-8Q, 0x1.937010050904fce3eac118cf708bp-5Q, 0x1.736cace0a66575cc5580323567efp-3Q, 0x1.adc2ad3828f8db5a1d5b82619893p-2Q, 0x1.33f89b5c2e57b7d298074c990addp-1Q, 0x1.c742b82c925553b5685081f7bfa5p-2Q, -0x1.24a4646f28f23724c7651fdfae24p-5Q, -0x1.57b853bbe6a5606b16b5f4878728p-2Q, -0x1.cc60df28d7bacf5cd487dfbe8b15p-4Q, 0x1.b148be3b1073f24190a78355f27p-3Q, 0x1.d7fedf0356b00027d18f8e92c824p-4Q, -0x1.1e9915e3ca004666a067ba487474p-3Q, -0x1.4ef44a8b3ce944830f2730d25eb9p-4Q, 0x1.8bacd9d38a28de29668579705c28p-4Q, 0x1.7690ee8b5981915a6dd616884c3fp-5Q, -0x1.0a25da27e87d75a179ff300fb83fp-4Q, -0x1.319ff4cde80a92f66d084237880cp-6Q, 0x1.4571365df548897971310c0822e6p-5Q, 0x1.b81b9bc4d4f3c43f2ed25e559ae8p-9Q, -0x1.564b9fd2c3bbee66fedad254cc1dp-6Q, 0x1.3b071a00e4e5b987ae06dc453687p-9Q, 0x1.268bb96001dc402712698f3f0494p-7Q, -0x1.7af914f01f8fb9ea842adaa7f3cdp-9Q, -0x1.83c28f7e3c0e5781b7d022113abfp-9Q, 0x1.c1ff8c65fb69853c310221a8efcfp-10Q, 0x1.4f3d4c629fe3ea0f5f4b5c45e52p-11Q, -0x1.6a1c4ee19b4233e5be9da5626ae4p-11Q, -0x1.0c224d58d6e80fa7cb5e318a3bafp-15Q, 0x1.9624eae0b53f0431ec2fc4ac4a39p-13Q, -0x1.30f833f09ef0241df6514d4f75d1p-15Q, -0x1.2592c13818da87e8e3f7d01fb451p-15Q, 0x1.019c78bb618656595fd443f75a4ep-16Q, 0x1.768306fdacad4dc8fab15811b58ap-19Q, -0x1.9ebc2e6b68815a4433974307ca8ep-19Q, 0x1.53f4f805c91230935990691c9b37p-22Q, 0x1.414739b599eb74930d1d52f4adeap-22Q, -0x1.adab3d69a326553c517a3161ce4cp-24Q, -0x1.35ca1a000373680368e6e76ba1cap-29Q, 0x1.e5063d39ebf99979a7db1201c73dp-28Q, -0x1.949b918111d76ca513fa5f9592d7p-30Q, 0x1.c8df1c0c683eedf6229624f6ad7fp-34Q};
-        }
-        #endif
-    }
-    if constexpr (p == 22) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.9506cp-12f, 0x1.76fccap-8f, 0x1.37de72p-5f, 0x1.2fdb52p-3f, 0x1.788ddep-2f, 0x1.282856p-1f, 0x1.040b9cp-1f, 0x1.2df9bep-4f, -0x1.403b66p-2f, -0x1.9ac39cp-3f, 0x1.501016p-3f, 0x1.7095c8p-3f, -0x1.8dc40ep-4f, -0x1.0ddc74p-3f, 0x1.16d73p-4f, 0x1.5a58d6p-4f, -0x1.a4c6a6p-5f, -0x1.7d2e3p-5f, 0x1.2edd7cp-5f, 0x1.514ae8p-6f, -0x1.80b244p-6f, -0x1.9739fap-8f, 0x1.9bb88ep-7f, 0x1.3ab784p-12f, -0x1.658b52p-8f, 0x1.11bf26p-10f, 0x1.def09ap-10f, -0x1.941064p-11f, -0x1.bc5f9p-12f, 0x1.58926ap-12f, 0x1.6c8f7ep-15f, -0x1.8a7bd2p-14f, 0x1.7da8ecp-17f, 0x1.237bb8p-16f, -0x1.9dd79ap-18f, -0x1.a4264ap-20f, 0x1.5bac3cp-20f, -0x1.7917ccp-24f, -0x1.139828p-23f, 0x1.43164cp-25f, 0x1.cdd78ep-30f, -0x1.772814p-29f, 0x1.2558aap-31f, -0x1.3cd862p-35f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.9506bf26823bdp-12, 0x1.76fcca8398a61p-8, 0x1.37de71ec845e4p-5, 0x1.2fdb523f49ab5p-3, 0x1.788dde34ceb66p-2, 0x1.282855bd3e661p-1, 0x1.040b9c9ba65ccp-1, 0x1.2df9be17f6307p-4, -0x1.403b658e1e271p-2, -0x1.9ac39bc6a693fp-3, 0x1.501016e351cb2p-3, 0x1.7095c864b0cccp-3, -0x1.8dc40d7416ec6p-4, -0x1.0ddc7410272ddp-3, 0x1.16d7307f2f199p-4, 0x1.5a58d5e218e8bp-4, -0x1.a4c6a60c82a99p-5, -0x1.7d2e2f61c66bdp-5, 0x1.2edd7c2485c6cp-5, 0x1.514ae8ff8882dp-6, -0x1.80b243789dd91p-6, -0x1.9739fa1f59fdbp-8, 0x1.9bb88df2b07f2p-7, 0x1.3ab784f96ef95p-12, -0x1.658b52a857f98p-8, 0x1.11bf26e4a8f4ap-10, 0x1.def099502d06ep-10, -0x1.941064b6e88a6p-11, -0x1.bc5f905d400afp-12, 0x1.58926afecb291p-12, 0x1.6c8f7d64132f3p-15, -0x1.8a7bd1deebb29p-14, 0x1.7da8eb6c7dd39p-17, 0x1.237bb7cb019efp-16, -0x1.9dd79a5aef3dp-18, -0x1.a4264a7b9f195p-20, 0x1.5bac3bb6b7df3p-20, -0x1.7917ccd42a174p-24, -0x1.139827c14728ep-23, 0x1.43164b7e12198p-25, 0x1.cdd78d40a514dp-30, -0x1.772813927397bp-29, 0x1.2558a9abd0467p-31, -0x1.3cd8627d9b085p-35};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0xc.a835f93411de553p-15L, 0xb.b7e6541cc530467p-11L, 0x9.bef38f6422f21e9p-8L, 0x9.7eda91fa4d5aa1ap-6L, 0xb.c46ef1a675b2f1p-5L, 0x9.4142ade9f3308e8p-4L, 0x8.205ce4dd32e5de6p-4L, 0x9.6fcdf0bfb18389dp-7L, -0xa.01db2c70f1385a8p-5L, -0xc.d61cde35349f534p-6L, 0xa.8080b71a8e58ef5p-6L, 0xb.84ae43258666006p-6L, -0xc.6e206ba0b762e61p-7L, -0x8.6ee3a081396e7a5p-6L, 0x8.b6b983f978cc515p-7L, 0xa.d2c6af10c745924p-7L, -0xd.26353064154caf2p-8L, -0xb.e9717b0e335e71fp-8L, 0x9.76ebe1242e35de2p-8L, 0xa.8a5747fc44168f9p-9L, -0xc.05921bc4eec8a0fp-9L, -0xc.b9cfd0facfed6d3p-11L, 0xc.ddc46f9583f92e4p-10L, 0x9.d5bc27cb77ca414p-15L, -0xb.2c5a9542bfcbcecp-11L, 0x8.8df9372547a50bfp-13L, 0xe.f784ca816836eb8p-13L, -0xc.a08325b74452d5dp-14L, -0xd.e2fc82ea0057a9fp-15L, 0xa.c49357f65948be4p-15L, 0xb.647beb209979943p-18L, -0xc.53de8ef75d94bb9p-17L, 0xb.ed475b63ee9c598p-20L, 0x9.1bddbe580cf7997p-19L, -0xc.eebcd2d779e82c2p-21L, -0xd.213253dcf8ca54ep-23L, 0xa.dd61ddb5bef98f1p-23L, -0xb.c8be66a150b9e14p-27L, -0x8.9cc13e0a3946c9cp-26L, 0xa.18b25bf090cbe47p-28L, 0xe.6ebc6a0528a6ab3p-33L, -0xb.b9409c939cbdb9ep-32L, 0x9.2ac54d5e82338aap-34L, -0x9.e6c313ecd8427c2p-38L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.9506bf26823bcaa678f24755b1bep-12Q, 0x1.76fcca8398a608cea25db5f87af6p-8Q, 0x1.37de71ec845e43d133d0c299f8ecp-5Q, 0x1.2fdb523f49ab54335a2eba9c8437p-3Q, 0x1.788dde34ceb65e20730d6ddac0aep-2Q, 0x1.282855bd3e6611cfef751a206622p-1Q, 0x1.040b9c9ba65cbbcc9c304a8323e2p-1Q, 0x1.2df9be17f630713a1ee1adb275ebp-4Q, -0x1.403b658e1e270b5094f497dac5a2p-2Q, -0x1.9ac39bc6a693ea6805616ea07bd7p-3Q, 0x1.501016e351cb1dea06a54dd049bp-3Q, 0x1.7095c864b0ccc00c06f07ad7df02p-3Q, -0x1.8dc40d7416ec5cc24d97996382b6p-4Q, -0x1.0ddc7410272dcf4ab45934d4cf13p-3Q, 0x1.16d7307f2f198a2aec11f34d1e9fp-4Q, 0x1.5a58d5e218e8b247e862b3c1695fp-4Q, -0x1.a4c6a60c82a995e3152af9622fcap-5Q, -0x1.7d2e2f61c66bce3ea7e2b78a28c2p-5Q, 0x1.2edd7c2485c6bbc4d1a2c115a8a7p-5Q, 0x1.514ae8ff8882d1f2c15a47cd6559p-6Q, -0x1.80b243789dd9141e3fff7c22096dp-6Q, -0x1.9739fa1f59fdada5471944d8c62dp-8Q, 0x1.9bb88df2b07f25c8944100438d61p-7Q, 0x1.3ab784f96ef948279489735c5a1cp-12Q, -0x1.658b52a857f979d8d4ec9b9f73a9p-8Q, 0x1.11bf26e4a8f4a17dea14a455c454p-10Q, 0x1.def099502d06dd70a82c80e4bd5ep-10Q, -0x1.941064b6e88a5abad07f7589e66dp-11Q, -0x1.bc5f905d400af53d3eed609ad591p-12Q, 0x1.58926afecb2917c8a7cf6285c131p-12Q, 0x1.6c8f7d64132f3286043bbcbfb14ep-15Q, -0x1.8a7bd1deebb29772b3b880563654p-14Q, 0x1.7da8eb6c7dd38b3094b5e1389c85p-17Q, 0x1.237bb7cb019ef32d902afce7d618p-16Q, -0x1.9dd79a5aef3d0583abb88bd3c2cp-18Q, -0x1.a4264a7b9f194a9cadbc3e265f85p-20Q, 0x1.5bac3bb6b7df31e28d50f39c71ffp-20Q, -0x1.7917ccd42a173c285afd81440ef2p-24Q, -0x1.139827c14728d9384a9bd9717ddp-23Q, 0x1.43164b7e12197c8ececb2f261f6bp-25Q, 0x1.cdd78d40a514d5664ee974c433ep-30Q, -0x1.772813927397b73b1b90436f0da9p-29Q, 0x1.2558a9abd04671533bb0e6556b43p-31Q, -0x1.3cd8627d9b084f8342fbe01d8e11p-35Q};
-        }
-        #endif
-    }
-    if constexpr (p == 23) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.1d1cbap-12f, 0x1.136e6ep-8f, 0x1.e0371p-6f, 0x1.eda1b2p-4f, 0x1.4617f8p-2f, 0x1.170138p-1f, 0x1.1a1f1ap-1f, 0x1.737dfap-3f, -0x1.0baa62p-2f, -0x1.15ea6ep-2f, 0x1.79587ep-4f, 0x1.c9e0fcp-3f, -0x1.0ea48cp-5f, -0x1.4fe52ap-3f, 0x1.4c5162p-6f, 0x1.cbf7fcp-4f, -0x1.5a21c2p-6f, -0x1.1f91cap-4f, 0x1.649c9ep-6f, 0x1.3b5a9p-5f, -0x1.2f7d4p-6f, -0x1.1f53eep-6f, 0x1.a1db1p-7f, 0x1.8b4d7ep-8f, -0x1.cfb028p-8f, -0x1.297f88p-10f, 0x1.995258p-9f, -0x1.0279b8p-12f, -0x1.163206p-10f, 0x1.4eefcap-12f, 0x1.0d3c26p-12f, -0x1.3a9e5ep-13f, -0x1.1b7136p-15f, 0x1.734928p-15f, -0x1.61b10ep-19f, -0x1.181bb4p-17f, 0x1.41cbdcp-19f, 0x1.b56b6ap-21f, -0x1.1ea2bcp-21f, 0x1.3e5bd6p-26f, 0x1.d15d2ap-25f, -0x1.e103ap-27f, -0x1.046382p-30f, 0x1.20be9ap-30f, -0x1.a8f0bcp-33f, 0x1.b7e04ep-37f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.1d1cb9f15ca3p-12, 0x1.136e6d0cada7ap-8, 0x1.e03710ca000b2p-6, 0x1.eda1b1bac15d3p-4, 0x1.4617f85b87d2cp-2, 0x1.1701372560847p-1, 0x1.1a1f195e16c2fp-1, 0x1.737dfa0d62dcfp-3, -0x1.0baa621ce4279p-2, -0x1.15ea6e8658872p-2, 0x1.79587da8cb753p-4, 0x1.c9e0fc732c538p-3, -0x1.0ea48c5a06944p-5, -0x1.4fe52af139a58p-3, 0x1.4c51617dbe58bp-6, 0x1.cbf7fc1c6fa45p-4, -0x1.5a21c1ca225bep-6, -0x1.1f91c92c06d32p-4, 0x1.649c9ed18296ap-6, 0x1.3b5a90477563fp-5, -0x1.2f7d3f55674e5p-6, -0x1.1f53eed1947bfp-6, 0x1.a1db0f12bb42p-7, 0x1.8b4d7e5397f08p-8, -0x1.cfb028e3aae51p-8, -0x1.297f885faab6dp-10, 0x1.995258715da31p-9, -0x1.0279b74217beap-12, -0x1.163205afadf6dp-10, 0x1.4eefc91e26cfap-12, 0x1.0d3c2558f1652p-12, -0x1.3a9e5e1c22af4p-13, -0x1.1b7136cbb5aep-15, 0x1.734927c4130bfp-15, -0x1.61b10dba0880bp-19, -0x1.181bb48217362p-17, 0x1.41cbdcc2df4d9p-19, 0x1.b56b6a75fa292p-21, -0x1.1ea2bb46afa08p-21, 0x1.3e5bd6b02b53fp-26, 0x1.d15d2a9531ecbp-25, -0x1.e103a0e0c3b96p-27, -0x1.0463822ac124p-30, 0x1.20be99079e759p-30, -0x1.a8f0bc9b067e6p-33, 0x1.b7e04d72be8f7p-37};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0x8.e8e5cf8ae517d2ep-15L, 0x8.9b7368656d3d159p-11L, 0xf.01b886500058d29p-9L, 0xf.6d0d8dd60ae956bp-7L, 0xa.30bfc2dc3e9620cp-5L, 0x8.b809b92b0423412p-4L, 0x8.d0f8caf0b617657p-4L, 0xb.9befd06b16e7779p-6L, -0x8.5d5310e7213cb45p-5L, -0x8.af537432c439318p-5L, 0xb.cac3ed465ba98efp-7L, 0xe.4f07e399629c099p-6L, -0x8.752462d034a1f39p-8L, -0xa.7f295789cd2c17ap-6L, 0xa.628b0bedf2c55d4p-9L, 0xe.5fbfe0e37d2292p-7L, -0xa.d10e0e5112df11ap-9L, -0x8.fc8e49603699185p-7L, 0xb.24e4f68c14b4ebbp-9L, 0x9.dad4823bab1fbp-8L, -0x9.7be9faab3a727aap-9L, -0x8.fa9f768ca3df844p-9L, 0xd.0ed87895da0fea4p-10L, 0xc.5a6bf29cbf83d82p-11L, -0xe.7d81471d5728bb2p-11L, -0x9.4bfc42fd55b69dep-13L, 0xc.ca92c38aed18631p-12L, -0x8.13cdba10bdf515p-15L, -0x8.b1902d7d6fb67f6p-13L, 0xa.777e48f1367d0a5p-15L, 0x8.69e12ac78b28dbcp-15L, -0x9.d4f2f0e11579f3cp-16L, -0x8.db89b65dad6fc16p-18L, 0xb.9a493e20985f9bfp-18L, -0xb.0d886dd044054a4p-22L, -0x8.c0dda410b9b125ap-20L, 0xa.0e5ee616fa6c626p-22L, 0xd.ab5b53afd14926ap-24L, -0x8.f515da357d03ea3p-24L, 0x9.f2deb5815a9f567p-29L, 0xe.8ae954a98f65bb4p-28L, -0xf.081d07061dcaca2p-30L, -0x8.231c1156091fc3ap-33L, 0x9.05f4c83cf3acb2cp-33L, -0xd.4785e4d833f33e2p-36L, 0xd.bf026b95f47b713p-40L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.1d1cb9f15ca2fa5bd9123de7bf02p-12Q, 0x1.136e6d0cada7a2b148b6e8855daap-8Q, 0x1.e03710ca000b1a51a7d181d489bp-6Q, 0x1.eda1b1bac15d2ad6ddbdb3147e36p-4Q, 0x1.4617f85b87d2c4188e472323232cp-2Q, 0x1.1701372560846824bce2d06e180cp-1Q, 0x1.1a1f195e16c2ecad981d672e54f9p-1Q, 0x1.737dfa0d62dceef2a6ae0dd9fae6p-3Q, -0x1.0baa621ce427968960a0c4171c1cp-2Q, -0x1.15ea6e865887262fe21b5ed288ddp-2Q, 0x1.79587da8cb7531de57b391307b2ep-4Q, 0x1.c9e0fc732c5381328729c7899645p-3Q, -0x1.0ea48c5a06943e72865d8b0a9865p-5Q, -0x1.4fe52af139a582f4b4bfddd5990ap-3Q, 0x1.4c51617dbe58aba744aaa9e2e84dp-6Q, 0x1.cbf7fc1c6fa4523fc35d6c595afp-4Q, -0x1.5a21c1ca225be23388c3683c5f1ap-6Q, -0x1.1f91c92c06d3230ad5ace9dd7e2ap-4Q, 0x1.649c9ed182969d7683dcc682acbcp-6Q, 0x1.3b5a90477563f5ff5ff6e6498f97p-5Q, -0x1.2f7d3f55674e4f5496795e1de4a5p-6Q, -0x1.1f53eed1947bf0871dd1fee02046p-6Q, 0x1.a1db0f12bb41fd473a2e8421b507p-7Q, 0x1.8b4d7e5397f07b04d41a59615574p-8Q, -0x1.cfb028e3aae51764ab65b4e360fbp-8Q, -0x1.297f885faab6d3bcc655cccba49p-10Q, 0x1.995258715da30c618d8b26e9df7bp-9Q, -0x1.0279b74217bea2a0847d1e93003bp-12Q, -0x1.163205afadf6cfebfb69e0b0f9f9p-10Q, 0x1.4eefc91e26cfa14abc8a3c8c31bep-12Q, 0x1.0d3c2558f1651b77d56d78be87a6p-12Q, -0x1.3a9e5e1c22af3e7828bfcf5d2f48p-13Q, -0x1.1b7136cbb5adf82b0d9aad06bd7cp-15Q, 0x1.734927c4130bf37e18cb5a04041ap-15Q, -0x1.61b10dba0880a94866a6f32c90e9p-19Q, -0x1.181bb482173624b3f677525a8993p-17Q, 0x1.41cbdcc2df4d8c4b6d915e9702b2p-19Q, 0x1.b56b6a75fa2924d359ae84bf18d8p-21Q, -0x1.1ea2bb46afa07d45b08cabbea3b6p-21Q, 0x1.3e5bd6b02b53eacdcf10b59b874fp-26Q, 0x1.d15d2a9531ecb7682cdf70f5d33bp-25Q, -0x1.e103a0e0c3b959430c8cac42a206p-27Q, -0x1.0463822ac123f874c86ec02d6961p-30Q, 0x1.20be99079e7596586119e6bc965cp-30Q, -0x1.a8f0bc9b067e67c3b0dec15337bdp-33Q, 0x1.b7e04d72be8f6e258b11c231fbfep-37Q};
-        }
-        #endif
-    }
-    if constexpr (p == 24) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.91785p-13f, 0x1.93f98p-9f, 0x1.7059c4p-6f, 0x1.8e62d8p-4f, 0x1.17757p-2f, 0x1.023cecp-1f, 0x1.265e6ep-1f, 0x1.1fbaaep-2f, -0x1.7f8826p-3f, -0x1.4592dep-2f, 0x1.390a48p-8f, 0x1.e9f54ap-3f, 0x1.5c6536p-5f, -0x1.5e912ep-3f, -0x1.3da9ap-5f, 0x1.efaecap-4f, 0x1.57bcfap-6f, -0x1.5088bep-4f, -0x1.2c0d6ap-8f, 0x1.a4434cp-5f, -0x1.440e76p-8f, -0x1.ce3e5ap-6f, 0x1.f61e5cp-8f, 0x1.ab9f18p-7f, -0x1.9c50c6p-8f, -0x1.371236p-8f, 0x1.e9b0e8p-9f, 0x1.2e73dap-10f, -0x1.bcb74ap-10f, -0x1.7274d8p-15f, 0x1.334ca4p-11f, -0x1.ef71f4p-14f, -0x1.32337p-13f, 0x1.131ee6p-14f, 0x1.6e4982p-16f, -0x1.536264p-16f, 0x1.ccd17cp-27f, 0x1.05cc64p-18f, -0x1.e21fa8p-21f, -0x1.b0fcbap-22f, 0x1.d137c8p-23f, -0x1.160c08p-31f, -0x1.838882p-26f, 0x1.627092p-28f, 0x1.050b72p-31f, -0x1.ba8412p-32f, 0x1.3380aep-34f, -0x1.31989ep-38f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.91785023a9879p-13, 0x1.93f9805696b9cp-9, 0x1.7059c4b494de9p-6, 0x1.8e62d8a0a8ffcp-4, 0x1.17756f5530d69p-2, 0x1.023cebcae9f67p-1, 0x1.265e6eff960ccp-1, 0x1.1fbaad4726276p-2, -0x1.7f8826c061991p-3, -0x1.4592ded92acf9p-2, 0x1.390a478f54bbbp-8, 0x1.e9f54ac655c14p-3, 0x1.5c6535de6b4e5p-5, -0x1.5e912ec022b6p-3, -0x1.3da9a08b26c34p-5, 0x1.efaeca9aee192p-4, 0x1.57bcf98fd11cep-6, -0x1.5088bd1cf023ep-4, -0x1.2c0d69ece949fp-8, 0x1.a4434b89b6915p-5, -0x1.440e7548329f5p-8, -0x1.ce3e5912a2303p-6, 0x1.f61e5ce9a7ff1p-8, 0x1.ab9f170d72cc6p-7, -0x1.9c50c528bc778p-8, -0x1.371235b499d34p-8, 0x1.e9b0e84ddc047p-9, 0x1.2e73daaf19dbbp-10, -0x1.bcb74a39ee4ap-10, -0x1.7274d8ffa9744p-15, 0x1.334ca46898daep-11, -0x1.ef71f401aeeebp-14, -0x1.32337036c1617p-13, 0x1.131ee63336347p-14, 0x1.6e4981b862b8bp-16, -0x1.536263fe83a12p-16, 0x1.ccd17bbbe3d04p-27, 0x1.05cc64bbcf96p-18, -0x1.e21fa8ce8bf7ap-21, -0x1.b0fcbaac8055ep-22, 0x1.d137c82c35ed7p-23, -0x1.160c0805b95d3p-31, -0x1.838882edd8948p-26, 0x1.627091a0c660dp-28, 0x1.050b72dfcacecp-31, -0x1.ba8411e011af6p-32, 0x1.3380aec6c4cc7p-34, -0x1.31989d5a96be3p-38};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0xc.8bc2811d4c3c975p-16L, 0xc.9fcc02b4b5cdd4fp-12L, 0xb.82ce25a4a6f4946p-9L, 0xc.7316c50547fde96p-7L, 0x8.bbab7aa986b4822p-5L, 0x8.11e75e574fb369fp-4L, 0x9.32f377fcb066266p-4L, 0x8.fdd56a39313b02ap-5L, -0xb.fc4136030cc8af3p-6L, -0xa.2c96f6c9567c64ep-5L, 0x9.c8523c7aa5dd6c6p-11L, 0xf.4faa5632ae09cacp-6L, 0xa.e329aef35a72807p-8L, -0xa.f489760115afe5ap-6L, -0x9.ed4d0459361a0cbp-8L, 0xf.7d7654d770c90fap-7L, 0xa.bde7cc7e88e7341p-9L, -0xa.8445e8e7811ed17p-7L, -0x9.606b4f674a4f729p-11L, 0xd.221a5c4db48a85p-8L, -0xa.2073aa4194fa9f4p-11L, -0xe.71f2c8951181b37p-9L, 0xf.b0f2e74d3ff8483p-11L, 0xd.5cf8b86b966301bp-10L, -0xc.e2862945e3bc0bdp-11L, -0x9.b891ada4ce99f42p-11L, 0xf.4d87426ee023471p-12L, 0x9.739ed578cedd928p-13L, -0xd.e5ba51cf724ff04p-13L, -0xb.93a6c7fd4ba228cp-18L, 0x9.9a652344c6d708fp-14L, -0xf.7b8fa00d7775af1p-17L, -0x9.919b81b60b0b6ddp-16L, 0x8.98f73199b1a34dep-17L, 0xb.724c0dc315c5bebp-19L, -0xa.9b131ff41d09255p-19L, 0xe.668bdddf1e8204p-30L, 0x8.2e6325de7cafddbp-21L, -0xf.10fd46745fbd3a3p-24L, -0xd.87e5d56402aecbp-25L, 0xe.89be4161af6badap-26L, -0x8.b060402dcae9786p-34L, -0xc.1c44176ec4a3d56p-29L, 0xb.13848d0633067f9p-31L, 0x8.285b96fe5675d57p-34L, -0xd.d4208f008d7b156p-35L, 0x9.9c0576362663aafp-37L, -0x9.8cc4ead4b5f196ap-41L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.91785023a98792eac41b5272c04bp-13Q, 0x1.93f9805696b9ba9d87c3df41a8d9p-9Q, 0x1.7059c4b494de928c16cf6cacf0a7p-6Q, 0x1.8e62d8a0a8ffbd2cc57d79f83e08p-4Q, 0x1.17756f5530d69044d0184f790b3ep-2Q, 0x1.023cebcae9f66d3d390049f78dcp-1Q, 0x1.265e6eff960cc4ccf24089549b66p-1Q, 0x1.1fbaad4726276054f5d700d1bfb6p-2Q, -0x1.7f8826c0619915e6978c42a74dfcp-3Q, -0x1.4592ded92acf8c9c5ecd6ba9faddp-2Q, 0x1.390a478f54bbad8c711b3d202a1ap-8Q, 0x1.e9f54ac655c13958344e31a88778p-3Q, 0x1.5c6535de6b4e500e1e067af4d00ep-5Q, -0x1.5e912ec022b5fcb42ec3601ecf9bp-3Q, -0x1.3da9a08b26c34196db8bd596e813p-5Q, 0x1.efaeca9aee1921f4bc36a577b638p-4Q, 0x1.57bcf98fd11ce6827e350101b72ep-6Q, -0x1.5088bd1cf023da2d878ac9ebafc5p-4Q, -0x1.2c0d69ece949ee5284dcfb042baap-8Q, 0x1.a4434b89b691509ff6541a080cecp-5Q, -0x1.440e7548329f53e7873db8128a63p-8Q, -0x1.ce3e5912a230366d14a862ea3672p-6Q, 0x1.f61e5ce9a7ff0906541711dfe2e7p-8Q, 0x1.ab9f170d72cc6036a5092b63c08ap-7Q, -0x1.9c50c528bc77817ae0788ffc773ap-8Q, -0x1.371235b499d33e83c0b1b543f6e8p-8Q, 0x1.e9b0e84ddc0468e17e4fa3636bf9p-9Q, 0x1.2e73daaf19dbb24f6ae6d9d95255p-10Q, -0x1.bcb74a39ee49fe08e2b9fd7aeef1p-10Q, -0x1.7274d8ffa9744517f2f1470cebeep-15Q, 0x1.334ca46898dae11da29a57e9f92ap-11Q, -0x1.ef71f401aeeeb5e13dd40efc0a0cp-14Q, -0x1.32337036c1616db93444903d828ep-13Q, 0x1.131ee633363469bb9bebca29a839p-14Q, 0x1.6e4981b862b8b7d5bb86d25cc3eap-16Q, -0x1.536263fe83a124aaa2092f47c711p-16Q, 0x1.ccd17bbbe3d0407ffce581eb4165p-27Q, 0x1.05cc64bbcf95fbb57637394fb838p-18Q, -0x1.e21fa8ce8bf7a7465a57d37cce9ap-21Q, -0x1.b0fcbaac8055d95fcb97dc94d8aap-22Q, 0x1.d137c82c35ed75b3cca32ab07fp-23Q, -0x1.160c0805b95d2f0cf1ffb7605bf2p-31Q, -0x1.838882edd8947aab05cd00305346p-26Q, 0x1.627091a0c660cff16c28fc227cd6p-28Q, 0x1.050b72dfcacebaae0203f358d56p-31Q, -0x1.ba8411e011af62ac1faf9b23aa51p-32Q, 0x1.3380aec6c4cc755d395c84cee933p-34Q, -0x1.31989d5a96be32d359a4b1032025p-38Q};
-        }
-        #endif
-
-    }
-    std::array<Real, 2*p> m{};
-    for (auto & x : m) {
-        x = std::numeric_limits<Real>::quiet_NaN();
-    }
-    return m;
-
 }
 
 template<class Real, size_t p>
diff --git a/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp b/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp
index c328db53b..e75f2a90f 100644
--- a/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp
+++ b/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp
@@ -11,16 +11,16 @@
 #ifdef BOOST_HAS_FLOAT128
 #include <boost/multiprecision/float128.hpp>
 #endif
+#include <boost/multiprecision/cpp_bin_float.hpp>
+
 namespace boost::math::detail {
 
 template <typename Real, unsigned p, unsigned order>
 constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
 {
-    static_assert(sizeof(Real) <= 16, "Integer grids only computed up to 128 bits of precision.");
     static_assert(p <= 15, "Integer grids only implemented up to 15.");
     static_assert(p > 1, "Integer grids only implemented for p >= 2.");
     if constexpr (p == 2) {
-        static_assert(order <= 1 && order >= 0, "The 2 vanishing moment Daubechies scaling function only has one derivative.");
         if constexpr (std::is_same_v<Real, float>) {
             if constexpr (order == 0) {
                 return {0x0p+0f, 0x1.5db3d8p+0f, -0x1.76cf5ep-2f, 0x0p+0f};
@@ -48,13 +48,21 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         #ifdef BOOST_HAS_FLOAT128
         if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
             if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.5db3d742c265539d92ba16b83c5dp+0Q, -0x1.76cf5d0b09954e764ae85ae0f172p-2Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.5db3d742c265539d92ba16b83c5cp+0Q, -0x1.76cf5d0b09954e764ae85ae0f17p-2Q, 0x0p+0Q};
             }
             if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.0000000000000000000000000003p+0Q, -0x1.0000000000000000000000000001p+0Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1p+0Q, -0x1p+0Q, 0x0p+0Q};
             }
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            if constexpr (order == 0) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.36602540378443864676372317075293618347140262690519031402790348972596651591"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.366025403784438646763723170752936183471402626905190314027903489725966511383"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 1) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.00000000000000000000000000000000000000000000000000000000000000000000000906"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.00000000000000000000000000000000000000000000000000000000000000000000000906"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+        }
     }
     if constexpr (p == 3) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -62,7 +70,7 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0f, 0x1.494d42p+0f, -0x1.8b18d8p-2f, 0x1.863744p-4f, 0x1.158088p-8f, -0x0p+0f};
             }
             if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.a3719cp+0f, -0x1.1dcb06p+1f, 0x1.19ae7cp-1f, 0x1.69a5e8p-5f, 0x0p+0f};
+                return {0x0p+0f, 0x1.a3719cp+0f, -0x1.1dcb06p+1f, 0x1.19ae7cp-1f, 0x1.69a5e8p-5f, -0x0p+0f};
             }
             if constexpr (order == 2) {
                 return {0x0p+0f, 0x1.cef9ccp-1f, -0x1.b676b2p+0f, 0x1.6ced64p-1f, 0x1.8831a2p-4f, -0x0p+0f};
@@ -73,7 +81,7 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0, 0x1.494d414ee19a1p+0, -0x1.8b18d8251ec88p-2, 0x1.863743274d78dp-4, 0x1.158087f14084dp-8, -0x0p+0};
             }
             if constexpr (order == 1) {
-                return {0x0p+0, 0x1.a3719cd426dbdp+0, -0x1.1dcb0537f529p+1, 0x1.19ae7cc6c0212p-1, 0x1.69a5e70c6cb47p-5, 0x0p+0};
+                return {0x0p+0, 0x1.a3719cd426dbdp+0, -0x1.1dcb0537f529p+1, 0x1.19ae7cc6c0212p-1, 0x1.69a5e70c6cb47p-5, -0x0p+0};
             }
             if constexpr (order == 2) {
                 return {0x0p+0, 0x1.cef9cbb90bf24p-1, -0x1.b676b19591eb6p+0, 0x1.6ced632b23d6cp-1, 0x1.8831a237a06dfp-4, -0x0p+0};
@@ -84,7 +92,7 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0L, 0xa.4a6a0a770cd07e1p-3L, -0xc.58c6c128f64431dp-5L, 0xc.31ba193a6bc67f2p-7L, 0x8.ac043f8a042675ap-11L, -0x0p+0L};
             }
             if constexpr (order == 1) {
-                return {0x0p+0L, 0xd.1b8ce6a136deae1p-3L, -0x8.ee5829bfa948208p-2L, 0x8.cd73e6360108efbp-4L, 0xb.4d2f386365a363ap-8L, 0x0p+0L};
+                return {0x0p+0L, 0xd.1b8ce6a136deae1p-3L, -0x8.ee5829bfa948208p-2L, 0x8.cd73e6360108efbp-4L, 0xb.4d2f386365a363ap-8L, -0x0p+0L};
             }
             if constexpr (order == 2) {
                 return {0x0p+0L, 0xe.77ce5dc85f9214cp-4L, -0xd.b3b58cac8f5b1f2p-3L, 0xb.676b19591eb63e3p-4L, 0xc.418d11bd036f5a2p-7L, -0x0p+0L};
@@ -93,21 +101,32 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         #ifdef BOOST_HAS_FLOAT128
         if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
             if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.494d414ee19a0fc1701f9345a28ap+0Q, -0x1.8b18d8251ec886399fc357ab26c5p-2Q, 0x1.863743274d78cfe42daf1d262e3fp-4Q, 0x1.158087f14084ceb4f650d2c442ep-8Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.494d414ee19a0fc1701f9345a28bp+0Q, -0x1.8b18d8251ec886399fc357ab26c9p-2Q, 0x1.863743274d78cfe42daf1d262e43p-4Q, 0x1.158087f14084ceb4f650d2c442e1p-8Q, 0x0p+0Q};
             }
             if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.a3719cd426dbd5c2283e8b6cd967p+0Q, -0x1.1dcb0537f52904105ab1d13c6abp+1Q, 0x1.19ae7cc6c0211df5e41745563cadp-1Q, 0x1.69a5e70c6cb46c73632e8c1bb2cp-5Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.a3719cd426dbd5c2283e8b6cd98bp+0Q, -0x1.1dcb0537f52904105ab1d13c6abfp+1Q, 0x1.19ae7cc6c0211df5e41745563cbbp-1Q, 0x1.69a5e70c6cb46c73632e8c1bb2d3p-5Q, 0x0p+0Q};
             }
             if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.cef9cbb90bf242979b344cdd1e16p-1Q, -0x1.b676b19591eb63e368ce734bad21p+0Q, 0x1.6ced632b23d6c7c6d19ce6975a1dp-1Q, 0x1.8831a237a06deb43265d99170ff8p-4Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.cef9cbb90bf242979b344cdd1e02p-1Q, -0x1.b676b19591eb63e368ce734bad03p+0Q, 0x1.6ced632b23d6c7c6d19ce6975a06p-1Q, 0x1.8831a237a06deb43265d99170ff1p-4Q, 0x0p+0Q};
             }
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            if constexpr (order == 0) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.28633506942569674985101130804711703944769149589599367792522563129173884774"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.385836961045875636526124449680167085358759714316248323422384559809411215163"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0952675460037808035264010635719874519288709294849441167080083466112626376337"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00423434561639808314871207806106259398219728893531052878915058190640973293816"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 1) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.63845234088408572501497611363560403262776907011369321824757699444308529377"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.23275819046313739501774225255380769832888122180065115110381486246159923436"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.550159358274017614990556164200803298774455233260222647464898741593942483269"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0441464913050340550122099747174003669266569184267352853913391264245714335499"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 2) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.904249540651993051422557892988008355246955899646975674328615693249103183472"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.71274862195597915426767367896402506574086769894092702298584707974730965003"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.712748621955979154267673678964025065740867698940927022985847079747309736056"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0957504593480069485774421070119916447530441003530243256713843067508967355933"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+        }
     }
     if constexpr (p == 4) {
         if constexpr (std::is_same_v<Real, float>) {
             if constexpr (order == 0) {
-                return {0x0p+0f, 0x1.01d5e4p+0f, -0x1.15313cp-5f, 0x1.447d2ap-5f, -0x1.817e96p-7f, -0x1.3a0992p-10f, 0x1.3be7b6p-16f, -0x0p+0f};
+                return {0x0p+0f, 0x1.01d5e4p+0f, -0x1.15313cp-5f, 0x1.447d2ap-5f, -0x1.817e96p-7f, -0x1.3a0992p-10f, 0x1.3be7b6p-16f, 0x0p+0f};
             }
             if constexpr (order == 1) {
                 return {0x0p+0f, 0x1.c6aca8p+0f, -0x1.648654p+1f, 0x1.314492p+0f, -0x1.0d0e14p-3f, -0x1.b6da96p-5f, 0x1.d0194cp-10f, -0x0p+0f};
@@ -116,12 +135,12 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0f, 0x1.cf8cc6p+0f, -0x1.0eaaap+2f, 0x1.66e46cp+1f, -0x1.26d9a4p-3f, -0x1.0ae7c2p-2f, 0x1.3a82a2p-6f, 0x0p+0f};
             }
             if constexpr (order == 3) {
-                return {0x0p+0f, 0x1.bb2f44p-1f, -0x1.2d48b8p+1f, 0x1.c2597p+0f, 0x1.83800cp-3f, -0x1.233972p-1f, 0x1.bcd16ep-4f, 0x0p+0f};
+                return {0x0p+0f, 0x1.bb2f44p-1f, -0x1.2d48b8p+1f, 0x1.c2597p+0f, 0x1.83800cp-3f, -0x1.233972p-1f, 0x1.bcd16ep-4f, -0x0p+0f};
             }
         }
         if constexpr (std::is_same_v<Real, double>) {
             if constexpr (order == 0) {
-                return {0x0p+0, 0x1.01d5e443d831dp+0, -0x1.15313c61b3acbp-5, 0x1.447d293e37265p-5, -0x1.817e96e0425edp-7, -0x1.3a0992ca51117p-10, 0x1.3be7b6cb630ap-16, -0x0p+0};
+                return {0x0p+0, 0x1.01d5e443d831dp+0, -0x1.15313c61b3acbp-5, 0x1.447d293e37265p-5, -0x1.817e96e0425edp-7, -0x1.3a0992ca51117p-10, 0x1.3be7b6cb630ap-16, 0x0p+0};
             }
             if constexpr (order == 1) {
                 return {0x0p+0, 0x1.c6aca7b3a61bp+0, -0x1.6486543c8460bp+1, 0x1.314491c6de2d3p+0, -0x1.0d0e14f1f7dc6p-3, -0x1.b6da96c702378p-5, 0x1.d0194bee1a174p-10, -0x0p+0};
@@ -130,12 +149,12 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0, 0x1.cf8cc69cc42a4p+0, -0x1.0eaaa0c1e1c35p+2, 0x1.66e46b718b501p+1, -0x1.26d9a4de19b74p-3, -0x1.0ae7c18dd841ep-2, 0x1.3a82a1b96295bp-6, 0x0p+0};
             }
             if constexpr (order == 3) {
-                return {0x0p+0, 0x1.bb2f43bc30b81p-1, -0x1.2d48b852668c6p+1, 0x1.c2596fe640caep+0, 0x1.83800be8c4de9p-3, -0x1.233972e072028p-1, 0x1.bcd16d3945752p-4, 0x0p+0};
+                return {0x0p+0, 0x1.bb2f43bc30b81p-1, -0x1.2d48b852668c6p+1, 0x1.c2596fe640caep+0, 0x1.83800be8c4de9p-3, -0x1.233972e072028p-1, 0x1.bcd16d3945752p-4, -0x0p+0};
             }
         }
         if constexpr (std::is_same_v<Real, long double>) {
             if constexpr (order == 0) {
-                return {0x0p+0L, 0x8.0eaf221ec18e913p-3L, -0x8.a989e30d9d65a3ap-8L, 0xa.23e949f1b93272cp-8L, -0xc.0bf4b70212f684ap-10L, -0x9.d04c9652888ba27p-13L, 0x9.df3db65b184ff7ep-19L, -0x0p+0L};
+                return {0x0p+0L, 0x8.0eaf221ec18e913p-3L, -0x8.a989e30d9d65a3ap-8L, 0xa.23e949f1b93272cp-8L, -0xc.0bf4b70212f684ap-10L, -0x9.d04c9652888ba27p-13L, 0x9.df3db65b184ff7ep-19L, 0x0p+0L};
             }
             if constexpr (order == 1) {
                 return {0x0p+0L, 0xe.35653d9d30d7c1cp-3L, -0xb.2432a1e4230589p-2L, 0x9.8a248e36f1695bdp-3L, -0x8.6870a78fbee2d2ap-6L, -0xd.b6d4b63811bbfa2p-8L, 0xe.80ca5f70d0ba167p-13L, -0x0p+0L};
@@ -144,36 +163,50 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0L, 0xe.7c6634e62152087p-3L, -0x8.7555060f0e1aa31p-1L, 0xb.37235b8c5a805d9p-2L, -0x9.36cd26f0cdb9e9ap-6L, -0x8.573e0c6ec20ec34p-5L, 0x9.d4150dcb14ada24p-9L, 0x0p+0L};
             }
             if constexpr (order == 3) {
-                return {0x0p+0L, 0xd.d97a1de185c06cap-4L, -0x9.6a45c2933463235p-2L, 0xe.12cb7f320656fb6p-3L, 0xc.1c005f4626f4b41p-6L, -0x9.19cb97039014287p-4L, 0xd.e68b69ca2ba92a2p-7L, 0x0p+0L};
+                return {0x0p+0L, 0xd.d97a1de185c06cap-4L, -0x9.6a45c2933463235p-2L, 0xe.12cb7f320656fb6p-3L, 0xc.1c005f4626f4b41p-6L, -0x9.19cb97039014287p-4L, 0xd.e68b69ca2ba92a2p-7L, -0x0p+0L};
             }
         }
         #ifdef BOOST_HAS_FLOAT128
         if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
             if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.01d5e443d831d2252369827793d4p+0Q, -0x1.15313c61b3acb474231dab07815dp-5Q, 0x1.447d293e37264e578b865081224p-5Q, -0x1.817e96e0425ed094fa1a3a5cf10fp-7Q, -0x1.3a0992ca5111744ed1b4ed1a6607p-10Q, 0x1.3be7b6cb6309fefbda0c9fa167f7p-16Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.01d5e443d831d2252369827793d3p+0Q, -0x1.15313c61b3acb474231dab078158p-5Q, 0x1.447d293e37264e578b865081223fp-5Q, -0x1.817e96e0425ed094fa1a3a5cf10cp-7Q, -0x1.3a0992ca5111744ed1b4ed1a6607p-10Q, 0x1.3be7b6cb6309fefbda0c9fa167f8p-16Q, 0x0p+0Q};
             }
             if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.c6aca7b3a61af838bb3208359ff3p+0Q, -0x1.6486543c8460b11f1a4b4a357fa3p+1Q, 0x1.314491c6de2d2b798153746ca802p+0Q, -0x1.0d0e14f1f7dc5a54f21ce3ff4227p-3Q, -0x1.b6da96c702377f43a25f74c9465cp-5Q, 0x1.d0194bee1a1742cd9ebfbba7180ap-10Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.c6aca7b3a61af838bb320835a00cp+0Q, -0x1.6486543c8460b11f1a4b4a357fbcp+1Q, 0x1.314491c6de2d2b798153746ca822p+0Q, -0x1.0d0e14f1f7dc5a54f21ce3ff424bp-3Q, -0x1.b6da96c702377f43a25f74c9467p-5Q, 0x1.d0194bee1a1742cd9ebfbba717b8p-10Q, 0x0p+0Q};
             }
             if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.cf8cc69cc42a410e51b272a7a397p+0Q, -0x1.0eaaa0c1e1c354610b35262e906ap+2Q, 0x1.66e46b718b500bb2be3ec05c7ac4p+1Q, -0x1.26d9a4de19b73d34cbab42cdd8b6p-3Q, -0x1.0ae7c18dd841d8689ede2f52573fp-2Q, 0x1.3a82a1b96295b447f46661fe5c5ap-6Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.cf8cc69cc42a410e51b272a7a3c6p+0Q, -0x1.0eaaa0c1e1c354610b35262e9078p+2Q, 0x1.66e46b718b500bb2be3ec05c7ac3p+1Q, -0x1.26d9a4de19b73d34cbab42cdd8ccp-3Q, -0x1.0ae7c18dd841d8689ede2f52570cp-2Q, 0x1.3a82a1b96295b447f46661fe5bd8p-6Q, 0x0p+0Q};
             }
             if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.bb2f43bc30b80d947c8a537a21d9p-1Q, -0x1.2d48b852668c646a630392a2b72ap+1Q, 0x1.c2596fe640cadf6ca968f3b31114p+0Q, 0x1.83800be8c4de9681c9e31925cc1cp-3Q, -0x1.233972e07202850d1be1b9fc8353p-1Q, 0x1.bcd16d394575254330d81aed475ep-4Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.bb2f43bc30b80d947c8a537a20b2p-1Q, -0x1.2d48b852668c646a630392a2b66dp+1Q, 0x1.c2596fe640cadf6ca968f3b30ff3p+0Q, 0x1.83800be8c4de9681c9e31925ce79p-3Q, -0x1.233972e07202850d1be1b9fc8392p-1Q, 0x1.bcd16d394575254330d81aed4886p-4Q, 0x0p+0Q};
             }
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            if constexpr (order == 0) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.00716997772560226877369133460276614243269615872709037758322022879139279346"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0338369540528354556415804978382125421803076690774671479970540956429313200871"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0396104627159033280151912944184600514824910295717871419000412898697065939596"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0117643582057267108368694432974219163588747630020832762453515568184248898506"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00119795759617697344354027650795474883300903946947182516203285351999723597519"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000188294132335431331075886223630134570042832501447299211769873202540592685182"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 1) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.77607200752218464009377607152250284074663695743190866046592611729429611550"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.78534939722954314249278490573124577055217733739979406318347461197122106723"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.19245253663227817434763233908285135923990468684914884672498430320353620291"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.131374515184672958793518896272545745534054969900462421758093746888731275767"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0535710282202392359535999593909937081760795583068887462544975544197420516562"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00177039647999252279849535078943102427577022132608772400515549278186212987035"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 2) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.81074181868840701570186471952563442690666106665351874735735805297770163814"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.22916430410173418303217211054873324461573868001846524669511741276944000468"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.80384581607961568534047064875215082573530869410597985718216178513825734509"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.143969810512512114847026478220397278578104668742335564949361408575147520428"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.260649704248921172707994145248897076120067358027001191654083152075225028322"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0191961840951447695448573657402423466719409460283033987590421353038535631199"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 3) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.865594975206804045781037550982471109016820894607841596866029151773017425267"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.35378173850503736906839927424067865837551675448364577498051926331538903476"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.75917720195210901846322158713800354333385807185616713126178553553138176863"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.189209073105856701210355374205350230083317365254957287437467455568014611491"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.568797674081911210441966167774352001750246401183040853068360223333705683711"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.108598162322178814055750929689205777691766823947720612483597343776680843464"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+        }
     }
     if constexpr (p == 5) {
         if constexpr (std::is_same_v<Real, float>) {
             if constexpr (order == 0) {
-                return {0x0p+0f, 0x1.646bf2p-1f, 0x1.cbd5c2p-2f, -0x1.754196p-3f, 0x1.3100cap-5f, 0x1.8dd2bep-10f, -0x1.c4ab56p-10f, 0x1.3b27d2p-15f, 0x1.75f2b2p-23f, 0x0p+0f};
+                return {0x0p+0f, 0x1.646bf2p-1f, 0x1.cbd5c2p-2f, -0x1.754196p-3f, 0x1.3100cap-5f, 0x1.8dd2bep-10f, -0x1.c4ab56p-10f, 0x1.3b27d2p-15f, 0x1.75f2b2p-23f, -0x0p+0f};
             }
             if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.8eee7ap+0f, -0x1.37cf44p+1f, 0x1.3c6448p+0f, -0x1.784198p-2f, -0x1.64d96ap-6f, 0x1.08fcfcp-5f, -0x1.5e1ffp-10f, -0x1.984da2p-17f, 0x0p+0f};
+                return {0x0p+0f, 0x1.8eee7ap+0f, -0x1.37cf44p+1f, 0x1.3c6448p+0f, -0x1.784198p-2f, -0x1.64d96ap-6f, 0x1.08fcfcp-5f, -0x1.5e1ffp-10f, -0x1.984da2p-17f, -0x0p+0f};
             }
             if constexpr (order == 2) {
-                return {0x0p+0f, 0x1.22c5ccp+1f, -0x1.83ccap+2f, 0x1.524518p+2f, -0x1.2d10dcp+0f, -0x1.549f4cp-1f, 0x1.882acap-2f, -0x1.3d5d0ep-5f, -0x1.65cdcp-11f, -0x0p+0f};
+                return {0x0p+0f, 0x1.22c5ccp+1f, -0x1.83ccap+2f, 0x1.524518p+2f, -0x1.2d10dcp+0f, -0x1.549f4cp-1f, 0x1.882acap-2f, -0x1.3d5d0ep-5f, -0x1.65cdcp-11f, 0x0p+0f};
             }
             if constexpr (order == 3) {
                 return {0x0p+0f, 0x1.9877acp+1f, -0x1.48c27ap+3f, 0x1.f7fdf6p+2f, 0x1.0b1eap+3f, -0x1.15aaf4p+4f, 0x1.4a4504p+3f, -0x1.050134p+1f, -0x1.13ee46p-4f, -0x0p+0f};
@@ -184,13 +217,13 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         }
         if constexpr (std::is_same_v<Real, double>) {
             if constexpr (order == 0) {
-                return {0x0p+0, 0x1.646bf1ec64a31p-1, 0x1.cbd5c1bab5148p-2, -0x1.754196833f707p-3, 0x1.3100cab7c3f5fp-5, 0x1.8dd2be8c89c52p-10, -0x1.c4ab558ff2dcfp-10, 0x1.3b27d2d798eedp-15, 0x1.75f2b16626e98p-23, 0x0p+0};
+                return {0x0p+0, 0x1.646bf1ec64a31p-1, 0x1.cbd5c1bab5148p-2, -0x1.754196833f707p-3, 0x1.3100cab7c3f5fp-5, 0x1.8dd2be8c89c52p-10, -0x1.c4ab558ff2dcfp-10, 0x1.3b27d2d798eedp-15, 0x1.75f2b16626e98p-23, -0x0p+0};
             }
             if constexpr (order == 1) {
-                return {0x0p+0, 0x1.8eee7927087b2p+0, -0x1.37cf445237f1bp+1, 0x1.3c64475174b4ap+0, -0x1.7841978e876dbp-2, -0x1.64d969ffaac15p-6, 0x1.08fcfb4783fa8p-5, -0x1.5e1fef6185af9p-10, -0x1.984da10897439p-17, 0x0p+0};
+                return {0x0p+0, 0x1.8eee7927087b2p+0, -0x1.37cf445237f1bp+1, 0x1.3c64475174b4ap+0, -0x1.7841978e876dbp-2, -0x1.64d969ffaac15p-6, 0x1.08fcfb4783fa8p-5, -0x1.5e1fef6185af9p-10, -0x1.984da10897439p-17, -0x0p+0};
             }
             if constexpr (order == 2) {
-                return {0x0p+0, 0x1.22c5cb8d3f23bp+1, -0x1.83cca07a3ead8p+2, 0x1.5245172406b78p+2, -0x1.2d10dba463fc2p+0, -0x1.549f4c5e04f3ap-1, 0x1.882ac9029ddc7p-2, -0x1.3d5d0eda32d8bp-5, -0x1.65cdc06ecf654p-11, -0x0p+0};
+                return {0x0p+0, 0x1.22c5cb8d3f23bp+1, -0x1.83cca07a3ead8p+2, 0x1.5245172406b78p+2, -0x1.2d10dba463fc2p+0, -0x1.549f4c5e04f3ap-1, 0x1.882ac9029ddc7p-2, -0x1.3d5d0eda32d8bp-5, -0x1.65cdc06ecf654p-11, 0x0p+0};
             }
             if constexpr (order == 3) {
                 return {0x0p+0, 0x1.9877ac926fb3cp+1, -0x1.48c27a70b93cep+3, 0x1.f7fdf60845cfcp+2, 0x1.0b1ea0ee5f9edp+3, -0x1.15aaf38ada16ap+4, 0x1.4a45041b91e1cp+3, -0x1.05013480812dfp+1, -0x1.13ee46114fd85p-4, -0x0p+0};
@@ -201,13 +234,13 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         }
         if constexpr (std::is_same_v<Real, long double>) {
             if constexpr (order == 0) {
-                return {0x0p+0L, 0xb.235f8f632518463p-4L, 0xe.5eae0dd5a8a4298p-5L, -0xb.aa0cb419fb8363cp-6L, 0x9.880655be1fafa7dp-8L, 0xc.6e95f4644e28f3ep-13L, -0xe.255aac7f96e75fp-13L, 0x9.d93e96bcc776751p-18L, 0xb.af958b31374c3acp-26L, 0x0p+0L};
+                return {0x0p+0L, 0xb.235f8f632518463p-4L, 0xe.5eae0dd5a8a4298p-5L, -0xb.aa0cb419fb8363cp-6L, 0x9.880655be1fafa7dp-8L, 0xc.6e95f4644e28f3ep-13L, -0xe.255aac7f96e75fp-13L, 0x9.d93e96bcc776751p-18L, 0xb.af958b31374c3acp-26L, -0x0p+0L};
             }
             if constexpr (order == 1) {
-                return {0x0p+0L, 0xc.7773c93843d9207p-3L, -0x9.be7a2291bf8db95p-2L, 0x9.e3223a8ba5a5065p-3L, -0xb.c20cbc743b6db2dp-5L, -0xb.26cb4ffd560a9d3p-9L, 0x8.47e7da3c1fd3e92p-8L, -0xa.f0ff7b0c2d7cb32p-13L, -0xc.c26d0844ba1cb28p-20L, 0x0p+0L};
+                return {0x0p+0L, 0xc.7773c93843d9207p-3L, -0x9.be7a2291bf8db95p-2L, 0x9.e3223a8ba5a5065p-3L, -0xb.c20cbc743b6db2dp-5L, -0xb.26cb4ffd560a9d3p-9L, 0x8.47e7da3c1fd3e92p-8L, -0xa.f0ff7b0c2d7cb32p-13L, -0xc.c26d0844ba1cb28p-20L, -0x0p+0L};
             }
             if constexpr (order == 2) {
-                return {0x0p+0L, 0x9.162e5c69f91da28p-2L, -0xc.1e6503d1f56bc54p-1L, 0xa.9228b92035bbe8fp-1L, -0x9.6886dd231fe0c2p-3L, -0xa.a4fa62f0279cc8ap-4L, 0xc.41564814eee395ap-5L, -0x9.eae876d196c5b0fp-8L, -0xb.2e6e03767b2a39ap-14L, -0x0p+0L};
+                return {0x0p+0L, 0x9.162e5c69f91da28p-2L, -0xc.1e6503d1f56bc54p-1L, 0xa.9228b92035bbe8fp-1L, -0x9.6886dd231fe0c2p-3L, -0xa.a4fa62f0279cc8ap-4L, 0xc.41564814eee395ap-5L, -0x9.eae876d196c5b0fp-8L, -0xb.2e6e03767b2a39ap-14L, 0x0p+0L};
             }
             if constexpr (order == 3) {
                 return {0x0p+0L, 0xc.c3bd64937d9deedp-2L, -0xa.4613d385c9e6eeep+0L, 0xf.bfefb0422e7dd11p-1L, 0x8.58f50772fcf6838p+0L, -0x8.ad579c56d0b531bp+1L, 0xa.522820dc8f0dd92p+0L, -0x8.2809a404096fa64p-2L, -0x8.9f72308a7ec28cep-7L, -0x0p+0L};
@@ -219,22 +252,39 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         #ifdef BOOST_HAS_FLOAT128
         if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
             if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.646bf1ec64a308c5df07d89c8e9ap-1Q, 0x1.cbd5c1bab5148530b0e77ecbff8fp-2Q, -0x1.754196833f706c7834855fa5579ap-3Q, 0x1.3100cab7c3f5f4fa75b80a67ed4ap-5Q, 0x1.8dd2be8c89c51e7b28b04315345ap-10Q, -0x1.c4ab558ff2dcebdfdc6142054ddfp-10Q, 0x1.3b27d2d798eecea1adaf099c04dp-15Q, 0x1.75f2b16626e9875840e692dcf345p-23Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.646bf1ec64a308c5df07d89c8e9bp-1Q, 0x1.cbd5c1bab5148530b0e77ecbff92p-2Q, -0x1.754196833f706c7834855fa5579ep-3Q, 0x1.3100cab7c3f5f4fa75b80a67ed4bp-5Q, 0x1.8dd2be8c89c51e7b28b04315346bp-10Q, -0x1.c4ab558ff2dcebdfdc6142054ddep-10Q, 0x1.3b27d2d798eecea1adaf099c04dp-15Q, 0x1.75f2b16626e9875840e692dcf344p-23Q, 0x0p+0Q};
             }
             if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.8eee7927087b240ec5ade1ac8194p+0Q, -0x1.37cf445237f1b72a99ae1be26162p+1Q, 0x1.3c64475174b4a0c9b8a3ee3dfc17p+0Q, -0x1.7841978e876db6599aa4ad109929p-2Q, -0x1.64d969ffaac153a6af06dc9cfb6cp-6Q, 0x1.08fcfb4783fa7d234eba36053963p-5Q, -0x1.5e1fef6185af966378a125175a7ap-10Q, -0x1.984da1089743964ff5ac0959c3cp-17Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.8eee7927087b240ec5ade1ac81aep+0Q, -0x1.37cf445237f1b72a99ae1be2616ep+1Q, 0x1.3c64475174b4a0c9b8a3ee3dfc2p+0Q, -0x1.7841978e876db6599aa4ad10992fp-2Q, -0x1.64d969ffaac153a6af06dc9cfb72p-6Q, 0x1.08fcfb4783fa7d234eba36053968p-5Q, -0x1.5e1fef6185af966378a125175a7fp-10Q, -0x1.984da1089743964ff5ac0959c3bcp-17Q, 0x0p+0Q};
             }
             if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.22c5cb8d3f23b44faf592c365fa4p+1Q, -0x1.83cca07a3ead78a73330d7cf1ab1p+2Q, 0x1.5245172406b77d1d4fdfd2192e03p+2Q, -0x1.2d10dba463fc1840fd45963c56f2p+0Q, -0x1.549f4c5e04f3991456e630b15647p-1Q, 0x1.882ac9029ddc72b4c74d388daa79p-2Q, -0x1.3d5d0eda32d8b61e7ff27a395996p-5Q, -0x1.65cdc06ecf6547344a6a8d5280b2p-11Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.22c5cb8d3f23b44faf592c365f5dp+1Q, -0x1.83cca07a3ead78a73330d7cf1a39p+2Q, 0x1.5245172406b77d1d4fdfd2192d87p+2Q, -0x1.2d10dba463fc1840fd45963c568fp+0Q, -0x1.549f4c5e04f3991456e630b1555ep-1Q, 0x1.882ac9029ddc72b4c74d388da98p-2Q, -0x1.3d5d0eda32d8b61e7ff27a395899p-5Q, -0x1.65cdc06ecf6547344a6a8d527f6ap-11Q, 0x0p+0Q};
             }
             if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.9877ac926fb3bdd992f46d8483bfp+1Q, -0x1.48c27a70b93cdddc043571f4721ap+3Q, 0x1.f7fdf60845cfba22e0c6bd0437bdp+2Q, 0x1.0b1ea0ee5f9ed06f5107d79a0311p+3Q, -0x1.15aaf38ada16a6358cd77355dd37p+4Q, 0x1.4a45041b91e1bb24fe9a63ad0148p+3Q, -0x1.05013480812df4c7388d78da948bp+1Q, -0x1.13ee46114fd8519c5d7f29b7c3fap-4Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.9877ac926fb3bdd992f46d848f57p+1Q, -0x1.48c27a70b93cdddc043571f47b88p+3Q, 0x1.f7fdf60845cfba22e0c6bd043e1ep+2Q, 0x1.0b1ea0ee5f9ed06f5107d79a1aafp+3Q, -0x1.15aaf38ada16a6358cd77355f075p+4Q, 0x1.4a45041b91e1bb24fe9a63ad188p+3Q, -0x1.05013480812df4c7388d78daa7bap+1Q, -0x1.13ee46114fd8519c5d7f29b7d91dp-4Q, 0x0p+0Q};
             }
             if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.13b9e8c4fdc4ff9d9c7b93fda525p-1Q, -0x1.e1e5e5cfd0a801f531eaef0fe568p+0Q, 0x1.29ab2ec864d44a65c8f8abfdaaf8p+1Q, -0x1.3d6cc61e0f6a43e21f6553d106aap+0Q, 0x1.0227f72aa277daecfc1fddb3c489p-1Q, -0x1.9ada2a6a9a217e8dbe2b55c6b9fep-2Q, 0x1.2c68da3893cd5c4c84ac50c60e4ep-3Q, 0x1.1a66dc6d2cfbf029033eb2e703a5p-7Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.13b9e8c4fdc4ff9d9c7b93fda5d3p-1Q, -0x1.e1e5e5cfd0a801f531eaef0fe6ap+0Q, 0x1.29ab2ec864d44a65c8f8abfdabb3p+1Q, -0x1.3d6cc61e0f6a43e21f6553d10792p+0Q, 0x1.0227f72aa277daecfc1fddb3c5aep-1Q, -0x1.9ada2a6a9a217e8dbe2b55c6bb8bp-2Q, 0x1.2c68da3893cd5c4c84ac50c60f2ap-3Q, 0x1.1a66dc6d2cfbf029033eb2e70439p-7Q, 0x0p+0Q};
             }
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            if constexpr (order == 0) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.696136055094319477854858582899623165657477087397982420446214768704637534395"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.449057604809486328422544147258783961136679734070279222683095397573769933916"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.182254005318036337838976194133760626404155027995824869298574162909992040160"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0372318229038899280943468571976409825349884675067696944216807399624576154231"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00151757514971408546631660804627799642999930803663956002350203262334698096372"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00172679624300796683492238574113985690016517858343249085985731373201062373654"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000375694705183874611122788905987601511712424642186474598567387629170716626883"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000174133116097374720105581975617394004367103367815124081799014873533525879944"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 1) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.55832631304700136656437922101147238270749801987968302608726226056001482368"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.43601278318955192143689593229007692528378574026415581479157815807966800017"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.23590512980145429394703890677945755544792211433079804428523927099597048061"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.367437713693886635994756136622838185785128398329531162713235860868138262530"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0217803511756465465888455643095945877678797679730267716300872503661203118564"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0323471935081436888581585415004509261169517927400595785850252266260883753013"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00133561991277070103522933081789825027913295746975070671440848910320957810632"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000121683847435443138497052509729151564450629140761931082169997649373563390225"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 2) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.27166122814949534600896122719444335851364604986118568035816607547755917237"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.05936443269703021458765565610458515567565968210302097303958018874430527787"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.28546694296061742660009147793158080678169598815648398102884014016442733462"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.17603848231736696569405849672717768085153722635404167927428726433255541822"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.665277849652262172893211868601932018692793523566973388708885090298621050238"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.382975712570864999469720877338520879718972231720745739556192701382764798208"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0387406625828488850208242053540315894034591845169984253024631712386615226757"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000682456431469533883023355676818600390864653197380934617983202410607639498017"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 3) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.19115216398441064598874856260571078533335587095494743176688738763014884081"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-10.27374002472233958765271086107000542805707479728145748157559647456760808710"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("7.87487555320626209855129987050336396619016782135024668820907820995265770052"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.34748884732558776131996262585236386342026292471024772697407362253973719963"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-17.35423616637255288734483167824286404110868945013746827031620566538851642130"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("10.32092481026398135762866367591092420975846125781641772354270513968155400150"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.03909927630080258726415694483947450981378728380854211799311168912518310053"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0673659073845468012269752507200188457226963436043917006078305307227881695785"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 4) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.538527750059879292796528780519852438911382070810691516995382579602542914648"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.88241421054468108184078064831664583702656657871925935150851189089967644557"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.32553658280235915338790080889465383487576175009269238722259396773724525645"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.23994100793735478720630163791841698087868254804877475832368176128007400006"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.504211162523674003883304110865210953390071787279159096400634899652374386912"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.401222861057733743406505260198882985396262380707384195761109616807384220426"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.146684365131000298517783121263439809537955817949643689585465029271973791975"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00861821902285686386807072489078876658634008134323161538922679272299835038788"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+        }
     }
     if constexpr (p == 6) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -242,16 +292,16 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0f, 0x1.bf65e8p-2f, 0x1.aa2466p-1f, -0x1.89fd1p-2f, 0x1.24737ep-3f, -0x1.a1e9c8p-6f, -0x1.cec09ap-9f, 0x1.cd4fecp-10f, 0x1.05937cp-16f, -0x1.5a00dp-19f, 0x1.0fbc42p-28f, -0x0p+0f};
             }
             if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.2faeacp+0f, -0x1.801498p+0f, 0x1.050336p-1f, -0x1.0ffe44p-2f, 0x1.0b11b2p-4f, 0x1.721a1ep-7f, -0x1.af662cp-8f, -0x1.a69b86p-15f, 0x1.45b126p-16f, -0x1.018922p-24f, 0x0p+0f};
+                return {0x0p+0f, 0x1.2faeacp+0f, -0x1.801498p+0f, 0x1.050336p-1f, -0x1.0ffe44p-2f, 0x1.0b11b2p-4f, 0x1.721a1ep-7f, -0x1.af662cp-8f, -0x1.a69b86p-15f, 0x1.45b126p-16f, -0x1.018922p-24f, -0x0p+0f};
             }
             if constexpr (order == 2) {
-                return {0x0p+0f, 0x1.1e62dep+1f, -0x1.980b4p+2f, 0x1.a34deap+2f, -0x1.45eb5ep+1f, -0x1.0310f6p-1f, 0x1.da7724p-1f, -0x1.4137dp-2f, 0x1.7eb866p-6f, 0x1.4ebb22p-9f, -0x1.0c5bep-16f, -0x0p+0f};
+                return {0x0p+0f, 0x1.1e62dep+1f, -0x1.980b4p+2f, 0x1.a34deap+2f, -0x1.45eb5ep+1f, -0x1.0310f6p-1f, 0x1.da7724p-1f, -0x1.4137dp-2f, 0x1.7eb866p-6f, 0x1.4ebb22p-9f, -0x1.0c5bep-16f, 0x0p+0f};
             }
             if constexpr (order == 3) {
                 return {0x0p+0f, 0x1.422fap-2f, -0x1.255a76p+0f, 0x1.484b54p+3f, -0x1.3c98d8p+5f, 0x1.10b7fap+6f, -0x1.d54dd2p+5f, 0x1.804948p+4f, -0x1.77f884p+1f, -0x1.d3687ap-2f, 0x1.816ef8p-8f, -0x0p+0f};
             }
             if constexpr (order == 4) {
-                return {0x0p+0f, 0x1.8faefp+0f, -0x1.93816ep+2f, 0x1.33788p+3f, -0x1.c3f2cep+2f, 0x1.c7801ep+1f, -0x1.46377ep+1f, 0x1.77a6f6p+0f, -0x1.c41888p-3f, -0x1.f8b0a6p-5f, 0x1.b96594p-10f, -0x0p+0f};
+                return {0x0p+0f, 0x1.8faefp+0f, -0x1.93816ep+2f, 0x1.33788p+3f, -0x1.c3f2cep+2f, 0x1.c7801ep+1f, -0x1.46377ep+1f, 0x1.77a6f6p+0f, -0x1.c41888p-3f, -0x1.f8b0a6p-5f, 0x1.b96594p-10f, 0x0p+0f};
             }
             if constexpr (order == 5) {
                 return {0x0p+0f, 0x1.cb9194p-2f, -0x1.e6b982p+0f, 0x1.7b2e48p+1f, -0x1.fa645ep+0f, 0x1.29da94p-1f, -0x1.8461e6p-2f, 0x1.67c138p-2f, -0x1.c1a09cp-5f, -0x1.0c11f4p-5f, 0x1.0ac90ap-9f, 0x0p+0f};
@@ -262,16 +312,16 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0, 0x1.bf65e79817d28p-2, 0x1.aa2466d50e4a5p-1, -0x1.89fd104c6ff15p-2, 0x1.24737e6f8ebf1p-3, -0x1.a1e9c758a51a1p-6, -0x1.cec09a7ccf05bp-9, 0x1.cd4feb82d2494p-10, 0x1.05937b8388af2p-16, -0x1.5a00cfad970a8p-19, 0x1.0fbc42c672231p-28, -0x0p+0};
             }
             if constexpr (order == 1) {
-                return {0x0p+0, 0x1.2faeacbb8e754p+0, -0x1.8014975295b21p+0, 0x1.05033635f5402p-1, -0x1.0ffe44cc8bc7fp-2, 0x1.0b11b28c7d67bp-4, 0x1.721a1d14b8323p-7, -0x1.af662c52c3b7bp-8, -0x1.a69b860b67a33p-15, 0x1.45b12643cf82p-16, -0x1.01892163486cbp-24, 0x0p+0};
+                return {0x0p+0, 0x1.2faeacbb8e754p+0, -0x1.8014975295b21p+0, 0x1.05033635f5402p-1, -0x1.0ffe44cc8bc7fp-2, 0x1.0b11b28c7d67bp-4, 0x1.721a1d14b8323p-7, -0x1.af662c52c3b7bp-8, -0x1.a69b860b67a33p-15, 0x1.45b12643cf82p-16, -0x1.01892163486cbp-24, -0x0p+0};
             }
             if constexpr (order == 2) {
-                return {0x0p+0, 0x1.1e62ddd540b06p+1, -0x1.980b3fe2011f8p+2, 0x1.a34dea8cd59b4p+2, -0x1.45eb5e5e7e3cap+1, -0x1.0310f5a5d86dep-1, 0x1.da7724c65802cp-1, -0x1.4137cfe85b9e6p-2, 0x1.7eb866ddca6bap-6, 0x1.4ebb22d1ac076p-9, -0x1.0c5bdfb916a45p-16, -0x0p+0};
+                return {0x0p+0, 0x1.1e62ddd540b06p+1, -0x1.980b3fe2011f8p+2, 0x1.a34dea8cd59b4p+2, -0x1.45eb5e5e7e3cap+1, -0x1.0310f5a5d86dep-1, 0x1.da7724c65802cp-1, -0x1.4137cfe85b9e6p-2, 0x1.7eb866ddca6bap-6, 0x1.4ebb22d1ac076p-9, -0x1.0c5bdfb916a45p-16, 0x0p+0};
             }
             if constexpr (order == 3) {
                 return {0x0p+0, 0x1.422f9f5227e8p-2, -0x1.255a76df553ccp+0, 0x1.484b537c56dedp+3, -0x1.3c98d8a74cd77p+5, 0x1.10b7f9c607064p+6, -0x1.d54dd14cd31afp+5, 0x1.8049478b6740dp+4, -0x1.77f8847acd28bp+1, -0x1.d3687a3bc3933p-2, 0x1.816ef86832622p-8, -0x0p+0};
             }
             if constexpr (order == 4) {
-                return {0x0p+0, 0x1.8faeef62b3a8p+0, -0x1.93816e52ba1c8p+2, 0x1.337880b3a9a71p+3, -0x1.c3f2cd3d53133p+2, 0x1.c7801db767804p+1, -0x1.46377db27f625p+1, 0x1.77a6f5e8321cdp+0, -0x1.c4188733407f2p-3, -0x1.f8b0a606c7f79p-5, 0x1.b965933f534b2p-10, -0x0p+0};
+                return {0x0p+0, 0x1.8faeef62b3a8p+0, -0x1.93816e52ba1c8p+2, 0x1.337880b3a9a71p+3, -0x1.c3f2cd3d53133p+2, 0x1.c7801db767804p+1, -0x1.46377db27f625p+1, 0x1.77a6f5e8321cdp+0, -0x1.c4188733407f2p-3, -0x1.f8b0a606c7f79p-5, 0x1.b965933f534b2p-10, 0x0p+0};
             }
             if constexpr (order == 5) {
                 return {0x0p+0, 0x1.cb91942378a6bp-2, -0x1.e6b982120ca32p+0, 0x1.7b2e4714b2703p+1, -0x1.fa645ee8ca231p+0, 0x1.29da9349c32a2p-1, -0x1.8461e6acf9cb3p-2, 0x1.67c137342024dp-2, -0x1.c1a09b7773a5ap-5, -0x1.0c11f4efd5c0bp-5, 0x1.0ac90a45b7a47p-9, 0x0p+0};
@@ -282,16 +332,16 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0L, 0xd.fb2f3cc0be93e54p-5L, 0xd.512336a872527e6p-4L, -0xc.4fe882637f8a4ep-5L, 0x9.239bf37c75f8764p-6L, -0xd.0f4e3ac528d0419p-9L, -0xe.7604d3e6782db77p-12L, 0xe.6a7f5c169249c7ap-13L, 0x8.2c9bdc1c4579256p-19L, -0xa.d0067d6cb853e5ep-22L, 0x8.7de216339118a43p-31L, -0x0p+0L};
             }
             if constexpr (order == 1) {
-                return {0x0p+0L, 0x9.7d7565dc73a9dap-3L, -0xc.00a4ba94ad909b7p-3L, 0x8.2819b1afaa00e4ep-4L, -0x8.7ff226645e3f525p-5L, 0x8.588d9463eb3d6b2p-7L, 0xb.90d0e8a5c191592p-10L, -0xd.7b3162961dbd72bp-11L, -0xd.34dc305b3d198bdp-18L, 0xa.2d89321e7c101dfp-19L, -0x8.0c490b1a4365a0ep-27L, 0x0p+0L};
+                return {0x0p+0L, 0x9.7d7565dc73a9dap-3L, -0xc.00a4ba94ad909b7p-3L, 0x8.2819b1afaa00e4ep-4L, -0x8.7ff226645e3f525p-5L, 0x8.588d9463eb3d6b2p-7L, 0xb.90d0e8a5c191592p-10L, -0xd.7b3162961dbd72bp-11L, -0xd.34dc305b3d198bdp-18L, 0xa.2d89321e7c101dfp-19L, -0x8.0c490b1a4365a0ep-27L, -0x0p+0L};
             }
             if constexpr (order == 2) {
-                return {0x0p+0L, 0x8.f316eeaa0582d86p-2L, -0xc.c059ff1008fbde4p-1L, 0xd.1a6f5466acda0c4p-1L, -0xa.2f5af2f3f1e4f4dp-2L, -0x8.1887ad2ec36f306p-4L, 0xe.d3b92632c015e4bp-4L, -0xa.09be7f42dcf2d82p-5L, 0xb.f5c336ee535d213p-9L, 0xa.75d9168d603b071p-12L, -0x8.62defdc8b5224edp-19L, -0x0p+0L};
+                return {0x0p+0L, 0x8.f316eeaa0582d86p-2L, -0xc.c059ff1008fbde4p-1L, 0xd.1a6f5466acda0c4p-1L, -0xa.2f5af2f3f1e4f4dp-2L, -0x8.1887ad2ec36f306p-4L, 0xe.d3b92632c015e4bp-4L, -0xa.09be7f42dcf2d82p-5L, 0xb.f5c336ee535d213p-9L, 0xa.75d9168d603b071p-12L, -0x8.62defdc8b5224edp-19L, 0x0p+0L};
             }
             if constexpr (order == 3) {
                 return {0x0p+0L, 0xa.117cfa913f3fd65p-5L, -0x9.2ad3b6faa9e5fc2p-3L, 0xa.425a9be2b6f651fp+0L, -0x9.e4c6c53a66bb9b6p+2L, 0x8.85bfce3038320c3p+3L, -0xe.aa6e8a6698d7b2fp+2L, 0xc.024a3c5b3a06863p+1L, -0xb.bfc423d6694569bp-2L, -0xe.9b43d1de1c99addp-5L, 0xc.0b77c3419310f5ep-11L, -0x0p+0L};
             }
             if constexpr (order == 4) {
-                return {0x0p+0L, 0xc.7d777b159d3fe93p-3L, -0xc.9c0b7295d0e4242p-1L, 0x9.9bc4059d4d38bf3p+0L, -0xe.1f9669ea9899554p-1L, 0xe.3c00edbb3c02374p-2L, -0xa.31bbed93fb124adp-2L, 0xb.bd37af4190e69cdp-3L, -0xe.20c4399a03f920dp-6L, -0xf.c58530363fbca91p-8L, 0xd.cb2c99fa9a58d79p-13L, -0x0p+0L};
+                return {0x0p+0L, 0xc.7d777b159d3fe93p-3L, -0xc.9c0b7295d0e4242p-1L, 0x9.9bc4059d4d38bf3p+0L, -0xe.1f9669ea9899554p-1L, 0xe.3c00edbb3c02374p-2L, -0xa.31bbed93fb124adp-2L, 0xb.bd37af4190e69cdp-3L, -0xe.20c4399a03f920dp-6L, -0xf.c58530363fbca91p-8L, 0xd.cb2c99fa9a58d79p-13L, 0x0p+0L};
             }
             if constexpr (order == 5) {
                 return {0x0p+0L, 0xe.5c8ca11bc53594fp-5L, -0xf.35cc10906518e34p-3L, 0xb.d97238a59381a17p-2L, -0xf.d322f7465118802p-3L, 0x9.4ed49a4e1950cdfp-4L, -0xc.230f3567ce5957dp-5L, 0xb.3e09b9a10126b64p-5L, -0xe.0d04dbbb9d2ce8dp-8L, -0x8.608fa77eae05beap-8L, 0x8.5648522dbd23badp-12L, 0x0p+0L};
@@ -300,25 +350,45 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         #ifdef BOOST_HAS_FLOAT128
         if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
             if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.bf65e79817d27ca7c78972c65f34p-2Q, 0x1.aa2466d50e4a4fcbbebe54f94c37p-1Q, -0x1.89fd104c6ff149bf7514a7ddf379p-2Q, 0x1.24737e6f8ebf0ec8bb9fcc85bb6cp-3Q, -0x1.a1e9c758a51a08321aa63e9af1d2p-6Q, -0x1.cec09a7ccf05b6ee1ea8f3c17f38p-9Q, 0x1.cd4feb82d24938f30e41e1af2e9p-10Q, 0x1.05937b8388af24ac43ec83967a3ap-16Q, -0x1.5a00cfad970a7cbc309138fd3f9dp-19Q, 0x1.0fbc42c672231485a0bcbfe7e33cp-28Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.bf65e79817d27ca7c78972c65f3p-2Q, 0x1.aa2466d50e4a4fcbbebe54f94c3cp-1Q, -0x1.89fd104c6ff149bf7514a7ddf37fp-2Q, 0x1.24737e6f8ebf0ec8bb9fcc85bb71p-3Q, -0x1.a1e9c758a51a08321aa63e9af1d7p-6Q, -0x1.cec09a7ccf05b6ee1ea8f3c17f4ep-9Q, 0x1.cd4feb82d24938f30e41e1af2eap-10Q, 0x1.05937b8388af24ac43ec83967a2ep-16Q, -0x1.5a00cfad970a7cbc309138fd3facp-19Q, 0x1.0fbc42c672231485a0bcbfe7e34bp-28Q, 0x0p+0Q};
             }
             if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.2faeacbb8e753b40eb856e00f52fp+0Q, -0x1.8014975295b2136d5a1adb45438cp+0Q, 0x1.05033635f5401c9b60636a325269p-1Q, -0x1.0ffe44cc8bc7ea4a6ce4734d8d3ap-2Q, 0x1.0b11b28c7d67ad63229fbc3aa7e2p-4Q, 0x1.721a1d14b8322b2431432e8b8011p-7Q, -0x1.af662c52c3b7ae55063672df3c81p-8Q, -0x1.a69b860b67a33179a8c7a5f6b347p-15Q, 0x1.45b12643cf8203bdf796367d51ecp-16Q, -0x1.01892163486cb41cb64453f7616bp-24Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.2faeacbb8e753b40eb856e00f522p+0Q, -0x1.8014975295b2136d5a1adb454387p+0Q, 0x1.05033635f5401c9b60636a32526ap-1Q, -0x1.0ffe44cc8bc7ea4a6ce4734d8d36p-2Q, 0x1.0b11b28c7d67ad63229fbc3aa7dap-4Q, 0x1.721a1d14b8322b2431432e8b800fp-7Q, -0x1.af662c52c3b7ae55063672df3c7fp-8Q, -0x1.a69b860b67a33179a8c7a5f6b2acp-15Q, 0x1.45b12643cf8203bdf796367d51eep-16Q, -0x1.01892163486cb41cb64453f7616fp-24Q, 0x0p+0Q};
             }
             if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.1e62ddd540b05b0cc5ce5870089ep+1Q, -0x1.980b3fe2011f7bc878be7d3998f1p+2Q, 0x1.a34dea8cd59b4187717c6efb0807p+2Q, -0x1.45eb5e5e7e3c9e9ae26ca4aa21b4p+1Q, -0x1.0310f5a5d86de60ba877dea68891p-1Q, 0x1.da7724c65802bc95482213f98417p-1Q, -0x1.4137cfe85b9e5b04e10239758ca5p-2Q, 0x1.7eb866ddca6ba425f9e4eb854dbfp-6Q, 0x1.4ebb22d1ac0760e1461881059b61p-9Q, -0x1.0c5bdfb916a449da5acc3ccfdf5cp-16Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.1e62ddd540b05b0cc5ce587007d5p+1Q, -0x1.980b3fe2011f7bc878be7d399794p+2Q, 0x1.a34dea8cd59b4187717c6efb0662p+2Q, -0x1.45eb5e5e7e3c9e9ae26ca4aa207cp+1Q, -0x1.0310f5a5d86de60ba877dea685a5p-1Q, 0x1.da7724c65802bc95482213f980a5p-1Q, -0x1.4137cfe85b9e5b04e10239758a3cp-2Q, 0x1.7eb866ddca6ba425f9e4eb854a4dp-6Q, 0x1.4ebb22d1ac0760e1461881059843p-9Q, -0x1.0c5bdfb916a449da5acc3ccfdc72p-16Q, 0x0p+0Q};
             }
             if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.422f9f5227e7facaa94dd7e1c4ccp-2Q, -0x1.255a76df553cbf84e8a0b06861f6p+0Q, 0x1.484b537c56deca3daefc656e764dp+3Q, -0x1.3c98d8a74cd7736b60af4e5f5a22p+5Q, 0x1.10b7f9c607064185ab2dfc57477p+6Q, -0x1.d54dd14cd31af65e5343fc85bc89p+5Q, 0x1.8049478b6740d0c6b0100478b786p+4Q, -0x1.77f8847acd28ad3549099ae0cd55p+1Q, -0x1.d3687a3bc39335bac7f281e5e3cfp-2Q, 0x1.816ef86832621ebc63e47cd17f95p-8Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.422f9f5227e7facaa94dd7d9e31p-2Q, -0x1.255a76df553cbf84e8a0b0613039p+0Q, 0x1.484b537c56deca3daefc656e3b6ep+3Q, -0x1.3c98d8a74cd7736b60af4e604261p+5Q, 0x1.10b7f9c607064185ab2dfc58353fp+6Q, -0x1.d54dd14cd31af65e5343fc875b57p+5Q, 0x1.8049478b6740d0c6b010047a06c3p+4Q, -0x1.77f8847acd28ad3549099ae2105ep+1Q, -0x1.d3687a3bc39335bac7f281e76bbep-2Q, 0x1.816ef86832621ebc63e47cd2b70fp-8Q, 0x0p+0Q};
             }
             if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.8faeef62b3a7fd26eb98dd7f9293p+0Q, -0x1.93816e52ba1c8483ff81ea3e2cbfp+2Q, 0x1.337880b3a9a717e67b9cd7fec3d9p+3Q, -0x1.c3f2cd3d53132aa78f87aee06f97p+2Q, 0x1.c7801db7678046e8ebdb22cf5b9fp+1Q, -0x1.46377db27f624959a2b9b7777544p+1Q, 0x1.77a6f5e8321cd39a930db3902d99p+0Q, -0x1.c4188733407f241acae534ed07ffp-3Q, -0x1.f8b0a606c7f795229d5947447259p-5Q, 0x1.b965933f534b1af276b67227f5edp-10Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.8faeef62b3a7fd26eb98dd7f984ap+0Q, -0x1.93816e52ba1c8483ff81ea3e324ep+2Q, 0x1.337880b3a9a717e67b9cd7fec812p+3Q, -0x1.c3f2cd3d53132aa78f87aee07639p+2Q, 0x1.c7801db7678046e8ebdb22cf642bp+1Q, -0x1.46377db27f624959a2b9b7777bb1p+1Q, 0x1.77a6f5e8321cd39a930db39033fap+0Q, -0x1.c4188733407f241acae534ed0f5dp-3Q, -0x1.f8b0a606c7f795229d5947447836p-5Q, 0x1.b965933f534b1af276b67227f89dp-10Q, 0x0p+0Q};
             }
             if constexpr (order == 5) {
-                return {0x0p+0Q, 0x1.cb91942378a6b29e2dd51c51c663p-2Q, -0x1.e6b982120ca31c68b89329c09f76p+0Q, 0x1.7b2e4714b270342ea6ba89978b55p+1Q, -0x1.fa645ee8ca231003817fbe32abe9p+0Q, 0x1.29da9349c32a19bed5b810cc5091p-1Q, -0x1.8461e6acf9cb2af90934d76c7fc3p-2Q, 0x1.67c137342024d6c8052e3d87701ap-2Q, -0x1.c1a09b7773a59d1a65f356774442p-5Q, -0x1.0c11f4efd5c0b7d44ac1c3a07541p-5Q, 0x1.0ac90a45b7a47759a7a92738ff23p-9Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.cb91942378a6b29e2dd51c51bfa9p-2Q, -0x1.e6b982120ca31c68b89329c09872p+0Q, 0x1.7b2e4714b270342ea6ba899785ecp+1Q, -0x1.fa645ee8ca231003817fbe32a47bp+0Q, 0x1.29da9349c32a19bed5b810cc4b88p-1Q, -0x1.8461e6acf9cb2af90934d76c7932p-2Q, 0x1.67c137342024d6c8052e3d876acdp-2Q, -0x1.c1a09b7773a59d1a65f356773daap-5Q, -0x1.0c11f4efd5c0b7d44ac1c3a0720ap-5Q, 0x1.0ac90a45b7a47759a7a92738fc7ep-9Q, 0x0p+0Q};
             }
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            if constexpr (order == 0) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.436912172945044907144228485347825621410539534551633490282829655111997130403"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.832308972842970561072656780688484969909152422815912990040758264557720345453"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.384754423776017240823727817356603521560970688156341806103424918665893513072"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.142798412112682208241683440145206755760599607930024614732186357484695172147"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0255073973408613836618989912216699702582536490819800245599669619734869162144"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00353052030405191587644014357031569208954383867587514877878893763115391697093"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00175976633973310294687791686419090228541208847068173308405667330457900123359"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000155911507261447556301511828782318895561336507906997931765895708973813706967"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000257792449680050051904829803613695691516006402149134709283993808809283908364"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000395427041670150922621803883961042354855917494285626611817873341124068492943"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 1) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.18625907496467146792209724298189804516984008871355130996941892999482122848"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.50031419531087122680662801195848817668641322402194798020924445478349906731"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.509790128790541728679843731350866150242721024787663006627811106004296791437"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.265618395790575259239344136932196822481573416259521963554257379369647420831"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0652024244844486127834346214927829793557907226893556085427354685093316589934"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0112946168896442313978324044573675493852036148359725468126097329498236688742"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00658262807952680441249220488086069578322307368873900509784589482921684655699"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000503787415155786809007366413438496538050960506069818027681542836778698200709"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000194127553776389220829735998255824906496581738755358150095212114606531254267"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000599621948105659258834698507620391902991796020771034688754036929095102873206"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 2) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.23739216721276332338878224928813443319380137365001617475449729702460814553"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.37568661757222064818087007988064952244769736524323206091611472179022669583"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.55163062814101601777779848466095021703767404055811314444036330143823846521"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.54624538053437717302677939425802942100881803777676322897540130575773519940"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.505988766188433733744368526707172451758173834991466388525773967340764566418"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.926690243923081056914375322621819979047483305911073890365009540068892624972"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.313689468914985485830723560991137056324820674194725652065219926423948539134"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0233593945078271825857280125900496031710930273733853151360419856695906224412"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00255379486119272204906336921540559285976842099994098440071430993999358629514"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000159954358632619330058765393713737703102562863421786141165128286490666376159"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 3) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.314634789838216004347219278851224957182628881138090829610427965680979138191"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.14591162636246490124057063708997784842452557437526442884613276777690297174"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("10.25919508252169379158306431282332110722656695790182072665295187397284234950"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-39.57463198378803222763091210153395253214575080397200817757429653138129855280"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("68.17966374795793307063651046839796286891828378129757556293454079229695233480"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-58.66299686450235667243637029946865368099558139408845032747908498579236804890"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("24.01789049581934793489690384929366103321726646566966212731103293708083587360"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.93727165218507960698217968145386367512071654027601850078522746893001474631"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.456453237436011258659809322589189754978378863312423941968681370133465846399"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00588124813675386548614413276946752512020709001701613014446955498244051671873"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 4) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.56126304778777576443050160863879708904118592078755406627901576276101093399"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.30477483824547160848980524578141943454970012363516565523116238032800392998"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("9.60845980730411762808214955695432741370084853414448911176063682241066899084"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.06169444073411748688716938924586604983878232115464543856592115083298206081"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.55859729247367992138320272198938237654252341074503039432837735029655798290"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.54856845107748801044054274844945341537099829623280578974997775828865307664"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.46739136618463144606525570352038426862829638293144420092004098891852838139"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.220749908687195857585648726228092057311307565129699615600606738330860600964"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0616076700882776753864153489569808343372159974190746897916588825239020343770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00168379508234587882847186755892064349515005496287341565125598591763515542636"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 5) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.448797526040073344800625409665848168336823300039318051519325620983465942323"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.90126812878282830955681810258116249323860290817569491974905637501312440751"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.96234978209111122166662326226946007783574110910320150870148188012479737533"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.97809403594341071138805115779455370352957722549769910191794603383219959474"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.581745722536272503632230565756890997548927114703803943288685477190719512918"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.379279712970354381573734078512746842789448242321016101227184675836523585288"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.351322996670238331331118965555902223077733168124153384152743641838801971515"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0548861538369364702831870995984759190374434786821402336660504725795046392356"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0327234062121349553823389676664543405404659969276540517449952095914830314788"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00203541040796942675353120290529183233631315963372752064299614671505036863492"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+        }
     }
     if constexpr (p == 7) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -332,7 +402,7 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0f, 0x1.e0eaccp+0f, -0x1.5362d8p+2f, 0x1.70aa18p+2f, -0x1.86bc52p+1f, 0x1.570932p-2f, 0x1.9d599ap-1f, -0x1.18b244p-1f, 0x1.fe16d2p-4f, 0x1.eb4ccap-12f, -0x1.4e09dp-9f, 0x1.c4a78ap-16f, 0x1.cb0cccp-25f, -0x0p+0f};
             }
             if constexpr (order == 3) {
-                return {0x0p+0f, 0x1.4ca934p-1f, -0x1.492e7p+1f, 0x1.171de6p+4f, -0x1.1e704ep+6f, 0x1.23bcc4p+7f, -0x1.415156p+7f, 0x1.7ff792p+6f, -0x1.a43b42p+4f, 0x1.833e7p-4f, 0x1.13b5aap+0f, -0x1.6365bp-6f, -0x1.64d198p-14f, 0x0p+0f};
+                return {0x0p+0f, 0x1.4ca934p-1f, -0x1.492e7p+1f, 0x1.171de6p+4f, -0x1.1e704ep+6f, 0x1.23bcc4p+7f, -0x1.415156p+7f, 0x1.7ff792p+6f, -0x1.a43b42p+4f, 0x1.833e7p-4f, 0x1.13b5aap+0f, -0x1.6365bp-6f, -0x1.64d198p-14f, -0x0p+0f};
             }
             if constexpr (order == 4) {
                 return {0x0p+0f, 0x1.525f0cp+1f, -0x1.7eda4cp+3f, 0x1.578438p+4f, -0x1.40c582p+4f, 0x1.9815ccp+3f, -0x1.22247ap+3f, 0x1.8c2cccp+2f, -0x1.ffd4fcp+0f, -0x1.3be428p-3f, 0x1.7c490ep-3f, -0x1.23f976p-7f, -0x1.1f66b2p-14f, -0x0p+0f};
@@ -355,7 +425,7 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0, 0x1.e0eacca617ebcp+0, -0x1.5362d7fe36c57p+2, 0x1.70aa17b7adc0ep+2, -0x1.86bc52429f3a4p+1, 0x1.5709310e8d1f6p-2, 0x1.9d599937b31fbp-1, -0x1.18b244e50df67p-1, 0x1.fe16d1a3cfb3ep-4, 0x1.eb4cc917dd1cdp-12, -0x1.4e09cf12f0cddp-9, 0x1.c4a78957d2798p-16, 0x1.cb0ccbca08e79p-25, -0x0p+0};
             }
             if constexpr (order == 3) {
-                return {0x0p+0, 0x1.4ca9343b32368p-1, -0x1.492e70f2635c1p+1, 0x1.171de5ca88cecp+4, -0x1.1e704d84a1075p+6, 0x1.23bcc34d6a52ap+7, -0x1.415156a34428ap+7, 0x1.7ff7929036dddp+6, -0x1.a43b4147c122cp+4, 0x1.833e6f5afaca5p-4, 0x1.13b5aaaf6c71dp+0, -0x1.6365af2495a87p-6, -0x1.64d19861a8338p-14, 0x0p+0};
+                return {0x0p+0, 0x1.4ca9343b32368p-1, -0x1.492e70f2635c1p+1, 0x1.171de5ca88cecp+4, -0x1.1e704d84a1075p+6, 0x1.23bcc34d6a52ap+7, -0x1.415156a34428ap+7, 0x1.7ff7929036dddp+6, -0x1.a43b4147c122cp+4, 0x1.833e6f5afaca5p-4, 0x1.13b5aaaf6c71dp+0, -0x1.6365af2495a87p-6, -0x1.64d19861a8338p-14, -0x0p+0};
             }
             if constexpr (order == 4) {
                 return {0x0p+0, 0x1.525f0cb11c272p+1, -0x1.7eda4b6a23329p+3, 0x1.578437542fe4fp+4, -0x1.40c582473fa8dp+4, 0x1.9815cb7223c1p+3, -0x1.222479cd96eeap+3, 0x1.8c2cccc6ee34dp+2, -0x1.ffd4fb5b3918p+0, -0x1.3be427404fe7dp-3, 0x1.7c490d447fad3p-3, -0x1.23f9756392d0fp-7, -0x1.1f66b1e781529p-14, -0x0p+0};
@@ -378,7 +448,7 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0L, 0xf.07566530bf5dc3p-3L, -0xa.9b16bff1b62b5b5p-1L, 0xb.8550bdbd6e073adp-1L, -0xc.35e29214f9d1fbdp-2L, 0xa.b849887468fb1bp-5L, 0xc.eaccc9bd98fd7eap-4L, -0x8.c59227286fb3ad2p-4L, 0xf.f0b68d1e7d9f3f6p-7L, 0xf.5a6648bee8e6ab7p-15L, -0xa.704e7897866e7ecp-12L, 0xe.253c4abe93cc026p-19L, 0xe.58665e50473cb0fp-28L, -0x0p+0L};
             }
             if constexpr (order == 3) {
-                return {0x0p+0L, 0xa.6549a1d991b412ap-4L, -0xa.497387931ae0b61p-2L, 0x8.b8ef2e544676158p+1L, -0x8.f3826c25083a83ap+3L, 0x9.1de61a6b5294d86p+4L, -0xa.0a8ab51a2145353p+4L, 0xb.ffbc9481b6eebc6p+3L, -0xd.21da0a3e0916379p+1L, 0xc.19f37ad7d65262bp-7L, 0x8.9dad557b638eaddp-3L, -0xb.1b2d7924ad4363p-9L, -0xb.268cc30d419bc95p-17L, 0x0p+0L};
+                return {0x0p+0L, 0xa.6549a1d991b412ap-4L, -0xa.497387931ae0b61p-2L, 0x8.b8ef2e544676158p+1L, -0x8.f3826c25083a83ap+3L, 0x9.1de61a6b5294d86p+4L, -0xa.0a8ab51a2145353p+4L, 0xb.ffbc9481b6eebc6p+3L, -0xd.21da0a3e0916379p+1L, 0xc.19f37ad7d65262bp-7L, 0x8.9dad557b638eaddp-3L, -0xb.1b2d7924ad4363p-9L, -0xb.268cc30d419bc95p-17L, -0x0p+0L};
             }
             if constexpr (order == 4) {
                 return {0x0p+0L, 0xa.92f86588e139024p-2L, -0xb.f6d25b5119947a7p+0L, 0xa.bc21baa17f27afep+1L, -0xa.062c1239fd4649cp+1L, 0xc.c0ae5b911e082dep+0L, -0x9.1123ce6cb774e8cp+0L, 0xc.6166663771a6508p-1L, -0xf.fea7dad9c8c0222p-3L, -0x9.df213a027f3e892p-6L, 0xb.e2486a23fd69714p-6L, -0x9.1fcbab1c968774dp-10L, -0x8.fb358f3c0a94afap-17L, -0x0p+0L};
@@ -393,28 +463,51 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         #ifdef BOOST_HAS_FLOAT128
         if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
             if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.033291a6c76d6a2177301a6491ep-2Q, 0x1.027f6bf7952cdbcf397ade5b83a2p+0Q, -0x1.919d92c6034c44a7ed45a5787141p-2Q, 0x1.7a0ca906acc4841a1191b023a48bp-3Q, -0x1.1142c3515ec433047c393c69963p-4Q, 0x1.50e2d6421ee2654230b30972367cp-7Q, 0x1.d0243aab613f83777184da54a816p-10Q, -0x1.1d4c6c249bf0ee08cde9105ae0e7p-11Q, -0x1.17d0b3032ba5c5edbe3115298754p-14Q, 0x1.310ffd8b564011dafec30497e54dp-19Q, -0x1.509d126dab99ceafee21c5b15f2dp-25Q, -0x1.57f8e6955253718d03dd42dcc05dp-36Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.033291a6c76d6a2177301a6491e8p-2Q, 0x1.027f6bf7952cdbcf397ade5b83ap+0Q, -0x1.919d92c6034c44a7ed45a578713cp-2Q, 0x1.7a0ca906acc4841a1191b023a485p-3Q, -0x1.1142c3515ec433047c393c69962fp-4Q, 0x1.50e2d6421ee2654230b309723685p-7Q, 0x1.d0243aab613f83777184da54a80dp-10Q, -0x1.1d4c6c249bf0ee08cde9105ae0e2p-11Q, -0x1.17d0b3032ba5c5edbe3115298755p-14Q, 0x1.310ffd8b564011dafec30497e547p-19Q, -0x1.509d126dab99ceafee21c5b15f2ep-25Q, -0x1.57f8e6955253718d03dd42dcc06ep-36Q, 0x0p+0Q};
             }
             if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.9ec434341eaed8ccc6e8d7244a2p-1Q, -0x1.ca0692ca77439e8f752ca148c129p-2Q, -0x1.2d988a986b0dea756341b6b8b7c1p-1Q, 0x1.145887eacb10f9d392eed69a933p-2Q, -0x1.4ab3cf0bae2a5b8432a0a18163adp-6Q, -0x1.4e8938899ee371e40cd7b7528ae1p-5Q, 0x1.5cb5de436bfadb9e555d33c55725p-6Q, -0x1.051eebbefaf7bd71954e297a6202p-8Q, 0x1.0efaec65edbcc11b181ba7073ddfp-14Q, 0x1.6a87a6b931edc5ab5423dbf1bacbp-15Q, -0x1.4e8b2a27fe064ec01f6271830448p-23Q, -0x1.54fd8f0625f118cd9bcdded88df8p-33Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.9ec434341eaed8ccc6e8d7244a33p-1Q, -0x1.ca0692ca77439e8f752ca148c144p-2Q, -0x1.2d988a986b0dea756341b6b8b7c2p-1Q, 0x1.145887eacb10f9d392eed69a9335p-2Q, -0x1.4ab3cf0bae2a5b8432a0a181639cp-6Q, -0x1.4e8938899ee371e40cd7b7528ae9p-5Q, 0x1.5cb5de436bfadb9e555d33c55719p-6Q, -0x1.051eebbefaf7bd71954e297a61ffp-8Q, 0x1.0efaec65edbcc11b181ba7073e2cp-14Q, 0x1.6a87a6b931edc5ab5423dbf1babfp-15Q, -0x1.4e8b2a27fe064ec01f627183042bp-23Q, -0x1.54fd8f0625f118cd9bcdded88d81p-33Q, 0x0p+0Q};
             }
             if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.e0eacca617ebb860573873f7b257p+0Q, -0x1.5362d7fe36c56b6a443e9d614224p+2Q, 0x1.70aa17b7adc0e75a9ffe0b5a343p+2Q, -0x1.86bc52429f3a3f79bb4f1cb737ebp+1Q, 0x1.5709310e8d1f635f77e733f3171p-2Q, 0x1.9d599937b31fafd3d66db2bf1cfap-1Q, -0x1.18b244e50df675a487d76601b122p-1Q, 0x1.fe16d1a3cfb3e7ecc6834f20623cp-4Q, 0x1.eb4cc917dd1cd56dce6a9280b19ap-12Q, -0x1.4e09cf12f0cdcfd873bae55835b6p-9Q, 0x1.c4a78957d279804ccd5115f614bcp-16Q, 0x1.cb0ccbca08e7961d7bc2f676b681p-25Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.e0eacca617ebb860573873f7b1a4p+0Q, -0x1.5362d7fe36c56b6a443e9d6141a8p+2Q, 0x1.70aa17b7adc0e75a9ffe0b5a33b6p+2Q, -0x1.86bc52429f3a3f79bb4f1cb73763p+1Q, 0x1.5709310e8d1f635f77e733f31613p-2Q, 0x1.9d599937b31fafd3d66db2bf1cbbp-1Q, -0x1.18b244e50df675a487d76601b0e9p-1Q, 0x1.fe16d1a3cfb3e7ecc6834f2061cfp-4Q, 0x1.eb4cc917dd1cd56dce6a9280b03bp-12Q, -0x1.4e09cf12f0cdcfd873bae5583582p-9Q, 0x1.c4a78957d279804ccd5115f6146ap-16Q, 0x1.cb0ccbca08e7961d7bc2f676b666p-25Q, 0x0p+0Q};
             }
             if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.4ca9343b3236825367445e1bcc76p-1Q, -0x1.492e70f2635c16c262e618fc71c9p+1Q, 0x1.171de5ca88cec2afbea54998e4afp+4Q, -0x1.1e704d84a10750732762c3f7a7d9p+6Q, 0x1.23bcc34d6a529b0b422faf6a8faap+7Q, -0x1.415156a34428a6a6c08cde81cb46p+7Q, 0x1.7ff7929036ddd78bf54cfc3c1e07p+6Q, -0x1.a43b4147c122c6f143d7b5960278p+4Q, 0x1.833e6f5afaca4c566ce5985f38e4p-4Q, 0x1.13b5aaaf6c71d5b914583e4be0c9p+0Q, -0x1.6365af2495a86c5f48d9bd1e4466p-6Q, -0x1.64d19861a833792a3ce80f88bd23p-14Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.4ca9343b3236825367445e2a7e79p-1Q, -0x1.492e70f2635c16c262e6190afacep+1Q, 0x1.171de5ca88cec2afbea5499914ebp+4Q, -0x1.1e704d84a10750732762c3f4d8bap+6Q, 0x1.23bcc34d6a529b0b422faf672516p+7Q, -0x1.415156a34428a6a6c08cde7dee49p+7Q, 0x1.7ff7929036ddd78bf54cfc378272p+6Q, -0x1.a43b4147c122c6f143d7b591007fp+4Q, 0x1.833e6f5afaca4c566ce598593c06p-4Q, 0x1.13b5aaaf6c71d5b914583e48ae7dp+0Q, -0x1.6365af2495a86c5f48d9bd1a47dp-6Q, -0x1.64d19861a833792a3ce80f84d83cp-14Q, 0x0p+0Q};
             }
             if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.525f0cb11c2720485c66b9e1a4ecp+1Q, -0x1.7eda4b6a23328f4e2cec098f6dc4p+3Q, 0x1.578437542fe4f5fbe4cefec745eep+4Q, -0x1.40c582473fa8c93703a1216d1bfdp+4Q, 0x1.9815cb7223c105bc2b63ed01aaa9p+3Q, -0x1.222479cd96ee9d17f59bff4df756p+3Q, 0x1.8c2cccc6ee34ca0f24458389d70cp+2Q, -0x1.ffd4fb5b3918044492967474d7b2p+0Q, -0x1.3be427404fe7d12432d600f4467cp-3Q, 0x1.7c490d447fad2e27fa6b12a0df79p-3Q, -0x1.23f9756392d0ee9915448c1beeeap-7Q, -0x1.1f66b1e7815295f48755fd4e4048p-14Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.525f0cb11c2720485c66b9e19f02p+1Q, -0x1.7eda4b6a23328f4e2cec098f6666p+3Q, 0x1.578437542fe4f5fbe4cefec73f0cp+4Q, -0x1.40c582473fa8c93703a1216d1613p+4Q, 0x1.9815cb7223c105bc2b63ed01a5fep+3Q, -0x1.222479cd96ee9d17f59bff4df592p+3Q, 0x1.8c2cccc6ee34ca0f24458389d35dp+2Q, -0x1.ffd4fb5b3918044492967474d1cep+0Q, -0x1.3be427404fe7d12432d600f4382ep-3Q, 0x1.7c490d447fad2e27fa6b12a0d504p-3Q, -0x1.23f9756392d0ee9915448c1be2b1p-7Q, -0x1.1f66b1e7815295f48755fd4e3126p-14Q, 0x0p+0Q};
             }
             if constexpr (order == 5) {
-                return {0x0p+0Q, 0x1.80a316d21a0eed480c84ea711c72p+0Q, -0x1.ce7e6827143677fbd12dabe06d43p+2Q, 0x1.ac8b3ccd718c41df56b9c167f4f2p+3Q, -0x1.74c81d1a27df5c33454de2219d72p+3Q, 0x1.4010d1eedca99cac8148c1188814p+2Q, -0x1.34da807d2aaec910bcf3aa770b5fp+1Q, 0x1.2d09c9846b581b01a4323f49dd86p+1Q, -0x1.97de12ea03ca10913f6e6b1c02a9p-1Q, -0x1.9df5b4fe2e271a26f87f7a1f7732p-2Q, 0x1.16c54a229aae12ed509d340baa4cp-2Q, -0x1.e323c5b92bd166e33ab5b4f96118p-6Q, -0x1.c9a573f22c19a9032c5430df4acdp-12Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.80a316d21a0eed480c84ea711d9ep+0Q, -0x1.ce7e6827143677fbd12dabe06e9fp+2Q, 0x1.ac8b3ccd718c41df56b9c167f638p+3Q, -0x1.74c81d1a27df5c33454de2219e89p+3Q, 0x1.4010d1eedca99cac8148c11888d4p+2Q, -0x1.34da807d2aaec910bcf3aa770bf1p+1Q, 0x1.2d09c9846b581b01a4323f49de6p+1Q, -0x1.97de12ea03ca10913f6e6b1c03cap-1Q, -0x1.9df5b4fe2e271a26f87f7a1f78fbp-2Q, 0x1.16c54a229aae12ed509d340bab6bp-2Q, -0x1.e323c5b92bd166e33ab5b4f9635p-6Q, -0x1.c9a573f22c19a9032c5430df4c8ep-12Q, 0x0p+0Q};
             }
             if constexpr (order == 6) {
-                return {0x0p+0Q, 0x1.a096c8f7fc8ab1575820ee7aa2a9p-3Q, -0x1.01d8c748e11fa735da05e73f9139p+0Q, 0x1.099a073a7c7b41898468a5bd1aap+1Q, -0x1.40ce386ca776e06ba6f31ba7c1p+1Q, 0x1.2a57634989c51fb583fc11fbe69fp+1Q, -0x1.e6f030cb23fbfde6dfddcd331b76p+0Q, 0x1.3544c2755b1d82eac792a585c22cp+0Q, -0x1.6af581a622d416ac06a3c40afddbp-1Q, 0x1.256afda077267e050d8164de576cp-1Q, -0x1.6569331439297d46e21a065cd1e4p-2Q, 0x1.4b88409bdd1172b9682df895c7b5p-4Q, 0x1.24061e2653bdb3c5fd153e81e5dap-9Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.a096c8f7fc8ab1575820ee7a8d4ep-3Q, -0x1.01d8c748e11fa735da05e73f8394p+0Q, 0x1.099a073a7c7b41898468a5bd14cep+1Q, -0x1.40ce386ca776e06ba6f31ba7dadep+1Q, 0x1.2a57634989c51fb583fc11fc2c8bp+1Q, -0x1.e6f030cb23fbfde6dfddcd33a7b8p+0Q, 0x1.3544c2755b1d82eac792a5860a61p+0Q, -0x1.6af581a622d416ac06a3c40b5b79p-1Q, 0x1.256afda077267e050d8164debfb4p-1Q, -0x1.6569331439297d46e21a065d5029p-2Q, 0x1.4b88409bdd1172b9682df8963184p-4Q, 0x1.24061e2653bdb3c5fd153e823b33p-9Q, 0x0p+0Q};
             }
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            if constexpr (order == 0) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.253122592739470610621616401361877779229479815458388533109264465986705450631"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.00975680155277152973790111993384657471987193942368029780473312379324667581"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.392202657066104148408811882527482753596247632610867974599325631568154086472"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.184594460025979019600750648078960441521039122548921838323798916634848032145"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0667140607455829924370836933031099116268134098764011251351247996652005711545"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0102809473212267076120194571706337484167301394893291398778100853288079049731"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00177055938806458366110052669692669972802589253940700837389391312187949930155"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000544163751852595970300441890153871700803533167101690775895643543400091558287"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000667131499081179164202264668107341250409611901330351905468822246841842144516"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000227289246416658269412624892928823545347265264470652051954608031771296427329"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000391869762033530665296480229865041718561429039745272396909531056977677153636"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000195525597303995056555942742975229891249637237818874029912606477521320941521"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 1) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.810090667116438906125084608325336635858558427183760467122011143848709217936"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.447290700538193081726926232920918677934473900641168827205793350756780984978"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.589054423433051105713954740965807748202549360662853302324635538959794377897"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.269868968682900756914311183719700141732291233181671524008708012629904619787"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0201844713144249320028138388205587200490715428568451868566842270755978350937"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0408369163751242597466561287451981528641525226367711639411234490178637813143"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0212835951367080143883784719158797691366262981606201798553446386989113825786"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00398438697355263021802052679010575079656365873865505148350654941430150902211"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000646067070125676169190646922848512647427733001662437032209422253843012104636"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000432169303593002095810035589027522962115335866552588130271810048010912722413"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000155784009025835660972833383558489901619201115987867017226055817524579424688"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000155064510010241891136131541951717660675464153823551577127554599571639340405"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 2) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.87858275465980185082075059484687011254996371468315226671206152209070678246"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5.30290794206219714496696347944500864617861621722571539095236274472680863374"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.76038163125396215102934581086456598753529517251498951765403500351566767851"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.05262211087252131812326158576179299340031820314628130064826335395880941778"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.334996000779283942861292317865019419501179829373743199871525404727592261010"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.807324207352905330783228925068712255942845486187777944329076813046262028898"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.548235085449943077303537436963997364378850297210952683341512369648428848400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.124533480554402033115092620895174942570554514605089596521009703165626365178"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000468540137709608257946988592597297317335345745375177878078879095839559326245"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00254851010092381349764580405159840052627991728234093528430327277020566808108"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000269803070687479137062075450477716687058854979150244734967367615928087830171"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000534404516891100448405444096173981846862572475827871576787009651989666011194"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 3) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.649728424287883593075915713524545924783310332923624324175524503407444525226"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.57172977290494549793891044329117749573728410170896098271259318361359045523"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("17.44479922404291076498745112746722871408945222683998804378328855565199405640"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-71.60967070801582718948073283130611179366722642889690312945916561433081250530"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("145.86867753909000641239876531969663035434018992110863939875912524044321317900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-160.65886411864296450491377746275540090856151126704519657432554150664253629400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("95.99177003226164787960050084081167617878900086549469777087475435337607996430"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-26.26446655301167408645778203802638858259056547097299290641658148431177104090"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0945419645137684612631871190010186728744115673914304553269038199852068315336"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.07699076445391680627259708274414783686660624009083404578382123547772944786"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0216917238597838193019899484025795776622827268816981287975371913591323350722"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000850722149388195052244794635893235241011583434623169919987280838271411539579"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 4) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.64352568290660717383488785687771176736791104693177525854341276422360953032"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-11.96414728860834656491684620425334470999319544817775050560074926228961346460"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("21.46977932820874234919552398698675631801639393733709025528680976773677869130"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-20.04821994620810903573440830918637861650658462633252001448356816125828318470"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("12.75266048710730678983761121302121021721233371785195914379176723194342934110"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.06695261148657362033536649492341832971872918291204156753481081587833932402"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.19023436953359562968364270001994684253311540563623534733039001879957023961"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.99934359528660371790683912571810391676063304067432355179876753356952054619"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.154243761682653886850234521472448371875938984350115568709864935738395300610"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.185686210301318679459789457754099133235266189449860784374121835441650545927"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00891035301096690191056566243729350984965667867039696309182495485016806697240"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000685217743168943571948966687368236602823360897726181069159545607185161189239"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 5) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.50248854283750761908546072869048821088132450769069501088052480873059396056"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.22646526161484059523124385500321592540705032637199727092718371044938622631"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("13.39199676633541734287658783725542834810025902906082654104028345517237151680"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-11.64942793949647239507297332186810695848666694958647083520681009041022780270"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.00102661444057065419908749038327665570051567187076973678545304964939038004"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.41291814910561289346200219868321750732375141617088099871044781666393737553"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.35186118093287252501820923028537286425715059555956136712165596831136965350"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.796616164270648967111841215195534682870000441132645044906036039054243939416"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.404257610334332808361375570208558025875438251716421264701309289474764401907"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.272236975061487095514001649424045723282019885609650402120668262278630947181"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0294885092632145241422905453679850353376394211407104294790349538471440716050"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000436445522733053311620229711993666920722883672377214017763644242652824250344"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 6) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.203412599628398057633579265447859538789857395107674228547599630740965235246"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.00721402673036540834580779114189574939317230453601344322652356453222562469"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.07501306873106199194436015743412574197776374012334226264667067621104388301"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.50629334740999977272680186302494744195967724949010390385922060059896772157"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.33079186526041669838674663465091103063086959411404278532872827025632075003"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.90210251769529744977701199943741071402521093061881076298433872730941167746"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.20808043828139059668185989249916782761200302655255371273149597921930707587"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.708904315500525840865022566665627479869867191675628771870881198841529204782"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.573081899488511389976606360698320302247199472202129763974755593812367045224"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.349034116849261878956804444377809483590457734709780607298538959951976647643"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0809404872687234817933056436803663367147851456539523123991589358626438323968"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00222796552694813425499071023694009086590703727664242361109396513146307543467"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+        }
     }
     if constexpr (p == 8) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -422,22 +515,22 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0f, 0x1.184a0cp-3f, 0x1.fbaa04p-1f, -0x1.596f5cp-3f, 0x1.234876p-4f, -0x1.90a568p-5f, 0x1.82b42ep-6f, -0x1.96b60cp-8f, 0x1.8430d2p-11f, -0x1.92df02p-14f, 0x1.da6faap-16f, 0x1.b237bcp-20f, 0x1.66eb1ap-25f, -0x1.f6ebd8p-33f, 0x1.569072p-45f, 0x0p+0f};
             }
             if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.03034p-1f, 0x1.8347dap-2f, -0x1.7d2f18p+0f, 0x1.c3013ep-1f, -0x1.4be40ep-2f, 0x1.458036p-6f, 0x1.7e9e8ep-5f, -0x1.594cfap-6f, 0x1.27c566p-9f, 0x1.e972ap-12f, -0x1.1649ecp-14f, 0x1.c99c42p-23f, 0x1.81519ep-26f, -0x1.06b5eep-37f, -0x0p+0f};
+                return {0x0p+0f, 0x1.03034p-1f, 0x1.8347dap-2f, -0x1.7d2f18p+0f, 0x1.c3013ep-1f, -0x1.4be40ep-2f, 0x1.458036p-6f, 0x1.7e9e8ep-5f, -0x1.594cfap-6f, 0x1.27c566p-9f, 0x1.e972ap-12f, -0x1.1649ecp-14f, 0x1.c99c42p-23f, 0x1.81519ep-26f, -0x1.06b5eep-37f, 0x0p+0f};
             }
             if constexpr (order == 2) {
-                return {0x0p+0f, 0x1.666d54p+0f, -0x1.c03746p+1f, 0x1.a43ebap+1f, -0x1.d62736p+0f, 0x1.891e36p-1f, 0x1.a23c1ap-6f, -0x1.d9c16ep-3f, 0x1.b6728ep-4f, -0x1.66849cp-7f, -0x1.fc6302p-9f, 0x1.7e62aep-11f, -0x1.2c21cp-17f, -0x1.15f344p-21f, 0x1.7bbd84p-32f, 0x0p+0f};
+                return {0x0p+0f, 0x1.666d54p+0f, -0x1.c03746p+1f, 0x1.a43ebap+1f, -0x1.d62736p+0f, 0x1.891e36p-1f, 0x1.a23c1ap-6f, -0x1.d9c16ep-3f, 0x1.b6728ep-4f, -0x1.66849cp-7f, -0x1.fc6302p-9f, 0x1.7e62aep-11f, -0x1.2c21cp-17f, -0x1.15f344p-21f, 0x1.7bbd84p-32f, -0x0p+0f};
             }
             if constexpr (order == 3) {
-                return {0x0p+0f, 0x1.b44c4ep+1f, -0x1.c1f7ep+3f, 0x1.1601a8p+4f, 0x1.e5bffcp+3f, -0x1.38f35cp+6f, 0x1.d1869cp+6f, -0x1.70d204p+6f, 0x1.34930ep+5f, -0x1.4b77b4p+2f, -0x1.d27f3cp+0f, 0x1.32a2c6p-1f, -0x1.2fc65p-7f, -0x1.c48022p-11f, 0x1.364c0ap-20f, -0x0p+0f};
+                return {0x0p+0f, 0x1.b44c4ep+1f, -0x1.c1f7ep+3f, 0x1.1601a8p+4f, 0x1.e5bffcp+3f, -0x1.38f35cp+6f, 0x1.d1869cp+6f, -0x1.70d204p+6f, 0x1.34930ep+5f, -0x1.4b77b4p+2f, -0x1.d27f3cp+0f, 0x1.32a2c6p-1f, -0x1.2fc65p-7f, -0x1.c48022p-11f, 0x1.364c0ap-20f, 0x0p+0f};
             }
             if constexpr (order == 4) {
-                return {0x0p+0f, 0x1.afe05cp+1f, -0x1.0a8c44p+4f, 0x1.0f6c04p+5f, -0x1.306ff2p+5f, 0x1.da6956p+4f, -0x1.6a2c2p+4f, 0x1.0e28c8p+4f, -0x1.ee4b3cp+2f, 0x1.050e3ep-1f, 0x1.0ea6cap+0f, -0x1.6566f6p-2f, 0x1.0b828ap-6f, 0x1.3201b6p-10f, -0x1.a6f024p-19f, 0x0p+0f};
+                return {0x0p+0f, 0x1.afe05cp+1f, -0x1.0a8c44p+4f, 0x1.0f6c04p+5f, -0x1.306ff2p+5f, 0x1.da6956p+4f, -0x1.6a2c2p+4f, 0x1.0e28c8p+4f, -0x1.ee4b3cp+2f, 0x1.050e3ep-1f, 0x1.0ea6cap+0f, -0x1.6566f6p-2f, 0x1.0b828ap-6f, 0x1.3201b6p-10f, -0x1.a6f024p-19f, -0x0p+0f};
             }
             if constexpr (order == 5) {
-                return {0x0p+0f, 0x1.77885ep+1f, -0x1.f5abb2p+3f, 0x1.0a779ep+5f, -0x1.164dap+5f, 0x1.233374p+4f, -0x1.af306ap+2f, 0x1.6dba5cp+2f, -0x1.17ffcap+1f, -0x1.9f39e8p+1f, 0x1.d0d0a8p+1f, -0x1.4ac5cap+0f, 0x1.049fbp-3f, 0x1.5ad37ap-7f, -0x1.e6e9a6p-15f, -0x0p+0f};
+                return {0x0p+0f, 0x1.77885ep+1f, -0x1.f5abb2p+3f, 0x1.0a779ep+5f, -0x1.164dap+5f, 0x1.233374p+4f, -0x1.af306ap+2f, 0x1.6dba5cp+2f, -0x1.17ffcap+1f, -0x1.9f39e8p+1f, 0x1.d0d0a8p+1f, -0x1.4ac5cap+0f, 0x1.049fbp-3f, 0x1.5ad37ap-7f, -0x1.e6e9a6p-15f, 0x0p+0f};
             }
             if constexpr (order == 6) {
-                return {0x0p+0f, 0x1.1912b6p+0f, -0x1.85c00cp+2f, 0x1.b7d754p+3f, -0x1.076d5p+4f, 0x1.92a29ep+3f, -0x1.20f516p+3f, 0x1.dcba52p+2f, -0x1.3fe312p+2f, 0x1.5e9b74p+1f, -0x1.a6996ap+0f, 0x1.806826p-1f, -0x1.ddc83ep-4f, -0x1.e09e82p-7f, 0x1.5c5b72p-13f, -0x0p+0f};
+                return {0x0p+0f, 0x1.1912b6p+0f, -0x1.85c00cp+2f, 0x1.b7d754p+3f, -0x1.076d5p+4f, 0x1.92a29ep+3f, -0x1.20f516p+3f, 0x1.dcba52p+2f, -0x1.3fe312p+2f, 0x1.5e9b74p+1f, -0x1.a6996ap+0f, 0x1.806826p-1f, -0x1.ddc83ep-4f, -0x1.e09e82p-7f, 0x1.5c5b72p-13f, 0x0p+0f};
             }
             if constexpr (order == 7) {
                 return {0x0p+0f, 0x1.eae802p-3f, -0x1.5a965ap+0f, 0x1.851aep+1f, -0x1.b139cp+1f, 0x1.ffefb8p+0f, -0x1.025406p+0f, 0x1.ff103cp-1f, -0x1.7a4f7p-1f, 0x1.09dce6p-2f, -0x1.c2f7cep-4f, 0x1.41c46cp-4f, -0x1.03531cp-6f, -0x1.c24ed2p-9f, 0x1.5d1ed8p-14f, -0x0p+0f};
@@ -448,22 +541,22 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0, 0x1.184a0c288d22bp-3, 0x1.fbaa047a94a61p-1, -0x1.596f5b6b28cbp-3, 0x1.234875f46000ep-4, -0x1.90a568ef3b94bp-5, 0x1.82b42ea0f8a16p-6, -0x1.96b60b10e5956p-8, 0x1.8430d19335685p-11, -0x1.92df023007909p-14, 0x1.da6faa7679627p-16, 0x1.b237bc2c3b525p-20, 0x1.66eb1a28068aep-25, -0x1.f6ebd7398c4a4p-33, 0x1.5690727034a8ap-45, 0x0p+0};
             }
             if constexpr (order == 1) {
-                return {0x0p+0, 0x1.03033f41d9947p-1, 0x1.8347da7a3030cp-2, -0x1.7d2f17f2a95afp+0, 0x1.c3013eaebde94p-1, -0x1.4be40ed86f2cdp-2, 0x1.4580356ca34ffp-6, 0x1.7e9e8eefc30b4p-5, -0x1.594cf912461bcp-6, 0x1.27c56651be6eep-9, 0x1.e972a09b0f4ddp-12, -0x1.1649ec5e54141p-14, 0x1.c99c42a59648bp-23, 0x1.81519dee82fp-26, -0x1.06b5ee4f0712p-37, -0x0p+0};
+                return {0x0p+0, 0x1.03033f41d9947p-1, 0x1.8347da7a3030cp-2, -0x1.7d2f17f2a95afp+0, 0x1.c3013eaebde94p-1, -0x1.4be40ed86f2cdp-2, 0x1.4580356ca34ffp-6, 0x1.7e9e8eefc30b4p-5, -0x1.594cf912461bcp-6, 0x1.27c56651be6eep-9, 0x1.e972a09b0f4ddp-12, -0x1.1649ec5e54141p-14, 0x1.c99c42a59648bp-23, 0x1.81519dee82fp-26, -0x1.06b5ee4f0712p-37, 0x0p+0};
             }
             if constexpr (order == 2) {
-                return {0x0p+0, 0x1.666d532df9dfp+0, -0x1.c0374596ee4d9p+1, 0x1.a43eb9f4500c3p+1, -0x1.d627359f84d25p+0, 0x1.891e36789053ap-1, 0x1.a23c19ecf2debp-6, -0x1.d9c16d05d7787p-3, 0x1.b6728d569b4c7p-4, -0x1.66849bebd2ebep-7, -0x1.fc6301aedca9p-9, 0x1.7e62ae52149bdp-11, -0x1.2c21c0130a3ebp-17, -0x1.15f344e8ed1b2p-21, 0x1.7bbd836b1bf85p-32, 0x0p+0};
+                return {0x0p+0, 0x1.666d532df9dfp+0, -0x1.c0374596ee4d9p+1, 0x1.a43eb9f4500c3p+1, -0x1.d627359f84d25p+0, 0x1.891e36789053ap-1, 0x1.a23c19ecf2debp-6, -0x1.d9c16d05d7787p-3, 0x1.b6728d569b4c7p-4, -0x1.66849bebd2ebep-7, -0x1.fc6301aedca9p-9, 0x1.7e62ae52149bdp-11, -0x1.2c21c0130a3ebp-17, -0x1.15f344e8ed1b2p-21, 0x1.7bbd836b1bf85p-32, -0x0p+0};
             }
             if constexpr (order == 3) {
-                return {0x0p+0, 0x1.b44c4e267cbb5p+1, -0x1.c1f7df3ad7ab8p+3, 0x1.1601a8a979c79p+4, 0x1.e5bffb29b3c53p+3, -0x1.38f35bf0e9ee1p+6, 0x1.d1869b3f8e2b4p+6, -0x1.70d2038145a54p+6, 0x1.34930dde67aeap+5, -0x1.4b77b4fb36749p+2, -0x1.d27f3b25c1fd7p+0, 0x1.32a2c5a3dfe81p-1, -0x1.2fc64ff8d3421p-7, -0x1.c48021ad9bc16p-11, 0x1.364c0a7c4c64bp-20, -0x0p+0};
+                return {0x0p+0, 0x1.b44c4e267cbb5p+1, -0x1.c1f7df3ad7ab8p+3, 0x1.1601a8a979c79p+4, 0x1.e5bffb29b3c53p+3, -0x1.38f35bf0e9ee1p+6, 0x1.d1869b3f8e2b4p+6, -0x1.70d2038145a54p+6, 0x1.34930dde67aeap+5, -0x1.4b77b4fb36749p+2, -0x1.d27f3b25c1fd7p+0, 0x1.32a2c5a3dfe81p-1, -0x1.2fc64ff8d3421p-7, -0x1.c48021ad9bc16p-11, 0x1.364c0a7c4c64bp-20, 0x0p+0};
             }
             if constexpr (order == 4) {
-                return {0x0p+0, 0x1.afe05c7a6ada2p+1, -0x1.0a8c44cdd47bfp+4, 0x1.0f6c0325c5e14p+5, -0x1.306ff1c62c833p+5, 0x1.da69559cc9113p+4, -0x1.6a2c1f828fe2ep+4, 0x1.0e28c771588c3p+4, -0x1.ee4b3cc46d89p+2, 0x1.050e3e4d4732ap-1, 0x1.0ea6cad7a5a8p+0, -0x1.6566f5ac7d805p-2, 0x1.0b828ad29e43fp-6, 0x1.3201b5c3bc1c2p-10, -0x1.a6f0242017b15p-19, 0x0p+0};
+                return {0x0p+0, 0x1.afe05c7a6ada2p+1, -0x1.0a8c44cdd47bfp+4, 0x1.0f6c0325c5e14p+5, -0x1.306ff1c62c833p+5, 0x1.da69559cc9113p+4, -0x1.6a2c1f828fe2ep+4, 0x1.0e28c771588c3p+4, -0x1.ee4b3cc46d89p+2, 0x1.050e3e4d4732ap-1, 0x1.0ea6cad7a5a8p+0, -0x1.6566f5ac7d805p-2, 0x1.0b828ad29e43fp-6, 0x1.3201b5c3bc1c2p-10, -0x1.a6f0242017b15p-19, -0x0p+0};
             }
             if constexpr (order == 5) {
-                return {0x0p+0, 0x1.77885e6e270a7p+1, -0x1.f5abb22b1b6ecp+3, 0x1.0a779dee6c7bep+5, -0x1.164d9f148bde5p+5, 0x1.2333738e736f1p+4, -0x1.af306993826a7p+2, 0x1.6dba5c59397a4p+2, -0x1.17ffc928dd1d9p+1, -0x1.9f39e7400cf5dp+1, 0x1.d0d0a8f3b805ep+1, -0x1.4ac5cadf9fb15p+0, 0x1.049faf6ae6899p-3, 0x1.5ad3792bdac36p-7, -0x1.e6e9a51e3663ap-15, -0x0p+0};
+                return {0x0p+0, 0x1.77885e6e270a7p+1, -0x1.f5abb22b1b6ecp+3, 0x1.0a779dee6c7bep+5, -0x1.164d9f148bde5p+5, 0x1.2333738e736f1p+4, -0x1.af306993826a7p+2, 0x1.6dba5c59397a4p+2, -0x1.17ffc928dd1d9p+1, -0x1.9f39e7400cf5dp+1, 0x1.d0d0a8f3b805ep+1, -0x1.4ac5cadf9fb15p+0, 0x1.049faf6ae6899p-3, 0x1.5ad3792bdac36p-7, -0x1.e6e9a51e3663ap-15, 0x0p+0};
             }
             if constexpr (order == 6) {
-                return {0x0p+0, 0x1.1912b6ad90d43p+0, -0x1.85c00c80d7a19p+2, 0x1.b7d753e3c818ap+3, -0x1.076d50e7f7851p+4, 0x1.92a29d7ac0e1ep+3, -0x1.20f516098425cp+3, 0x1.dcba519c323cfp+2, -0x1.3fe31292805cp+2, 0x1.5e9b74431b073p+1, -0x1.a6996ae95f76fp+0, 0x1.806826de1640bp-1, -0x1.ddc83de4acfafp-4, -0x1.e09e81650c6b7p-7, 0x1.5c5b71613d71bp-13, -0x0p+0};
+                return {0x0p+0, 0x1.1912b6ad90d43p+0, -0x1.85c00c80d7a19p+2, 0x1.b7d753e3c818ap+3, -0x1.076d50e7f7851p+4, 0x1.92a29d7ac0e1ep+3, -0x1.20f516098425cp+3, 0x1.dcba519c323cfp+2, -0x1.3fe31292805cp+2, 0x1.5e9b74431b073p+1, -0x1.a6996ae95f76fp+0, 0x1.806826de1640bp-1, -0x1.ddc83de4acfafp-4, -0x1.e09e81650c6b7p-7, 0x1.5c5b71613d71bp-13, 0x0p+0};
             }
             if constexpr (order == 7) {
                 return {0x0p+0, 0x1.eae80165a34adp-3, -0x1.5a965a7535366p+0, 0x1.851adfd49d1a7p+1, -0x1.b139c010d5d8fp+1, 0x1.ffefb70380437p+0, -0x1.0254056f57104p+0, 0x1.ff103b26e087ep-1, -0x1.7a4f70cc2f5d8p-1, 0x1.09dce627745a6p-2, -0x1.c2f7ce5c8a37cp-4, 0x1.41c46b919c33fp-4, -0x1.03531c096423ap-6, -0x1.c24ed1e998c51p-9, 0x1.5d1ed72a09587p-14, -0x0p+0};
@@ -474,22 +567,22 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0L, 0x8.c250614469156ecp-6L, 0xf.dd5023d4a530983p-4L, -0xa.cb7adb594658341p-6L, 0x9.1a43afa30007147p-7L, -0xc.852b4779dca57d6p-8L, 0xc.15a17507c50b09fp-9L, -0xc.b5b058872cab3ebp-11L, 0xc.21868c99ab4273bp-14L, -0xc.96f811803c8446bp-17L, 0xe.d37d53b3cb1391fp-19L, 0xd.91bde161da92bd9p-23L, 0xb.3758d14034571f5p-28L, -0xf.b75eb9cc6251d52p-36L, 0xa.b4839381a545259p-48L, 0x0p+0L};
             }
             if constexpr (order == 1) {
-                return {0x0p+0L, 0x8.1819fa0ecca3abdp-4L, 0xc.1a3ed3d18185c5ap-5L, -0xb.e978bf954ad7b4cp-3L, 0xe.1809f575ef4a37dp-4L, -0xa.5f2076c37966861p-5L, 0xa.2c01ab651a7f8e8p-9L, 0xb.f4f4777e185a2cbp-8L, -0xa.ca67c89230ddcadp-9L, 0x9.3e2b328df376c3ap-12L, 0xf.4b9504d87a6e47fp-15L, -0x8.b24f62f2a0a04dcp-17L, 0xe.4ce2152cb245585p-26L, 0xc.0a8cef7417800e8p-29L, -0x8.35af7278388fe4bp-40L, -0x0p+0L};
+                return {0x0p+0L, 0x8.1819fa0ecca3abdp-4L, 0xc.1a3ed3d18185c5ap-5L, -0xb.e978bf954ad7b4cp-3L, 0xe.1809f575ef4a37dp-4L, -0xa.5f2076c37966861p-5L, 0xa.2c01ab651a7f8e8p-9L, 0xb.f4f4777e185a2cbp-8L, -0xa.ca67c89230ddcadp-9L, 0x9.3e2b328df376c3ap-12L, 0xf.4b9504d87a6e47fp-15L, -0x8.b24f62f2a0a04dcp-17L, 0xe.4ce2152cb245585p-26L, 0xc.0a8cef7417800e8p-29L, -0x8.35af7278388fe4bp-40L, 0x0p+0L};
             }
             if constexpr (order == 2) {
-                return {0x0p+0L, 0xb.336a996fcef7c52p-3L, -0xe.01ba2cb7726c73bp-2L, 0xd.21f5cfa280614c9p-2L, -0xe.b139acfc2692864p-3L, 0xc.48f1b3c4829d099p-4L, 0xd.11e0cf6796f5a28p-9L, -0xe.ce0b682ebbc393bp-6L, 0xd.b3946ab4da635ap-7L, -0xb.3424df5e975efd8p-10L, -0xf.e3180d76e5481d1p-12L, 0xb.f3157290a4debfp-14L, -0x9.610e009851f575p-20L, -0x8.af9a274768d9303p-24L, 0xb.ddec1b58dfc26aap-35L, 0x0p+0L};
+                return {0x0p+0L, 0xb.336a996fcef7c52p-3L, -0xe.01ba2cb7726c73bp-2L, 0xd.21f5cfa280614c9p-2L, -0xe.b139acfc2692864p-3L, 0xc.48f1b3c4829d099p-4L, 0xd.11e0cf6796f5a28p-9L, -0xe.ce0b682ebbc393bp-6L, 0xd.b3946ab4da635ap-7L, -0xb.3424df5e975efd8p-10L, -0xf.e3180d76e5481d1p-12L, 0xb.f3157290a4debfp-14L, -0x9.610e009851f575p-20L, -0x8.af9a274768d9303p-24L, 0xb.ddec1b58dfc26aap-35L, -0x0p+0L};
             }
             if constexpr (order == 3) {
-                return {0x0p+0L, 0xd.a2627133e5da6a2p-2L, -0xe.0fbef9d6bd5bcc5p+0L, 0x8.b00d454bce3c7c1p+1L, 0xf.2dffd94d9e295dcp+0L, -0x9.c79adf874f70573p+3L, 0xe.8c34d9fc715a214p+3L, -0xb.86901c0a2d2a313p+3L, 0x9.a4986ef33d75017p+2L, -0xa.5bbda7d9b3a4ab2p-1L, -0xe.93f9d92e0feb674p-3L, 0x9.95162d1eff408cfp-4L, -0x9.7e327fc69a10719p-10L, -0xe.24010d6cde0b23p-14L, 0x9.b26053e2632577ap-23L, -0x0p+0L};
+                return {0x0p+0L, 0xd.a2627133e5da6a2p-2L, -0xe.0fbef9d6bd5bcc5p+0L, 0x8.b00d454bce3c7c1p+1L, 0xf.2dffd94d9e295dcp+0L, -0x9.c79adf874f70573p+3L, 0xe.8c34d9fc715a214p+3L, -0xb.86901c0a2d2a313p+3L, 0x9.a4986ef33d75017p+2L, -0xa.5bbda7d9b3a4ab2p-1L, -0xe.93f9d92e0feb674p-3L, 0x9.95162d1eff408cfp-4L, -0x9.7e327fc69a10719p-10L, -0xe.24010d6cde0b23p-14L, 0x9.b26053e2632577ap-23L, 0x0p+0L};
             }
             if constexpr (order == 4) {
-                return {0x0p+0L, 0xd.7f02e3d356d0e5bp-2L, -0x8.5462266ea3dfa72p+1L, 0x8.7b60192e2f0a0a5p+2L, -0x9.837f8e316419b55p+2L, 0xe.d34aace64889869p+1L, -0xb.5160fc147f16c08p+1L, 0x8.71463b8ac46182cp+1L, -0xf.7259e6236c483c5p-1L, 0x8.2871f26a39950e3p-4L, 0x8.753656bd2d3fd71p-3L, -0xb.2b37ad63ec0243dp-5L, 0x8.5c145694f21f58cp-9L, 0x9.900dae1de0e10ep-13L, -0xd.37812100bd8a443p-22L, 0x0p+0L};
+                return {0x0p+0L, 0xd.7f02e3d356d0e5bp-2L, -0x8.5462266ea3dfa72p+1L, 0x8.7b60192e2f0a0a5p+2L, -0x9.837f8e316419b55p+2L, 0xe.d34aace64889869p+1L, -0xb.5160fc147f16c08p+1L, 0x8.71463b8ac46182cp+1L, -0xf.7259e6236c483c5p-1L, 0x8.2871f26a39950e3p-4L, 0x8.753656bd2d3fd71p-3L, -0xb.2b37ad63ec0243dp-5L, 0x8.5c145694f21f58cp-9L, 0x9.900dae1de0e10ep-13L, -0xd.37812100bd8a443p-22L, -0x0p+0L};
             }
             if constexpr (order == 5) {
-                return {0x0p+0L, 0xb.bc42f3713853a26p-2L, -0xf.ad5d9158db75d9ap+0L, 0x8.53bcef7363deeep+2L, -0x8.b26cf8a45ef2551p+2L, 0x9.199b9c739b78925p+1L, -0xd.79834c9c135345p-1L, 0xb.6dd2e2c9cbd2213p-1L, -0x8.bffe4946e8ec5f8p-2L, -0xc.f9cf3a0067ae91ap-2L, 0xe.8685479dc02ed7ep-2L, -0xa.562e56fcfd8a5e2p-3L, 0x8.24fd7b57344ca47p-6L, 0xa.d69bc95ed61ae29p-10L, -0xf.374d28f1b31ceb4p-18L, -0x0p+0L};
+                return {0x0p+0L, 0xb.bc42f3713853a26p-2L, -0xf.ad5d9158db75d9ap+0L, 0x8.53bcef7363deeep+2L, -0x8.b26cf8a45ef2551p+2L, 0x9.199b9c739b78925p+1L, -0xd.79834c9c135345p-1L, 0xb.6dd2e2c9cbd2213p-1L, -0x8.bffe4946e8ec5f8p-2L, -0xc.f9cf3a0067ae91ap-2L, 0xe.8685479dc02ed7ep-2L, -0xa.562e56fcfd8a5e2p-3L, 0x8.24fd7b57344ca47p-6L, 0xa.d69bc95ed61ae29p-10L, -0xf.374d28f1b31ceb4p-18L, 0x0p+0L};
             }
             if constexpr (order == 6) {
-                return {0x0p+0L, 0x8.c895b56c86a1b02p-3L, -0xc.2e006406bd0c7e6p-1L, 0xd.beba9f1e40c4cbdp+0L, -0x8.3b6a873fbc285cap+1L, 0xc.9514ebd6070fp+0L, -0x9.07a8b04c212dd91p+0L, 0xe.e5d28ce191e76fcp-1L, -0x9.ff18949402e0231p-1L, 0xa.f4dba218d8396ddp-2L, -0xd.34cb574afbb77c5p-3L, 0xc.034136f0b2057f9p-4L, -0xe.ee41ef2567d7906p-7L, -0xf.04f40b28635ba7ep-10L, 0xa.e2db8b09eb8dbb5p-16L, -0x0p+0L};
+                return {0x0p+0L, 0x8.c895b56c86a1b02p-3L, -0xc.2e006406bd0c7e6p-1L, 0xd.beba9f1e40c4cbdp+0L, -0x8.3b6a873fbc285cap+1L, 0xc.9514ebd6070fp+0L, -0x9.07a8b04c212dd91p+0L, 0xe.e5d28ce191e76fcp-1L, -0x9.ff18949402e0231p-1L, 0xa.f4dba218d8396ddp-2L, -0xd.34cb574afbb77c5p-3L, 0xc.034136f0b2057f9p-4L, -0xe.ee41ef2567d7906p-7L, -0xf.04f40b28635ba7ep-10L, 0xa.e2db8b09eb8dbb5p-16L, 0x0p+0L};
             }
             if constexpr (order == 7) {
                 return {0x0p+0L, 0xf.57400b2d1a568f9p-6L, -0xa.d4b2d3a9a9b32a1p-3L, 0xc.28d6fea4e8d3b6dp-2L, -0xd.89ce0086aec77acp-2L, 0xf.ff7db81c021b9bdp-3L, -0x8.12a02b7ab881d9bp-3L, 0xf.f881d937043f115p-4L, -0xb.d27b86617aebd37p-4L, 0x8.4ee7313ba2d30a8p-5L, -0xe.17be72e451bdc7ep-7L, 0xa.0e235c8ce19f70ep-7L, -0x8.1a98e04b211d3d4p-9L, -0xe.12768f4cc6289abp-12L, 0xa.e8f6b9504ac38b3p-17L, -0x0p+0L};
@@ -498,31 +591,57 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         #ifdef BOOST_HAS_FLOAT128
         if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
             if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.184a0c288d22add7ea26104df2f3p-3Q, 0x1.fbaa047a94a613069e6f550b4e0cp-1Q, -0x1.596f5b6b28cb0681bf78a3e54b76p-3Q, 0x1.234875f46000e28dce7c3f34208fp-4Q, -0x1.90a568ef3b94afacf755834bab9dp-5Q, 0x1.82b42ea0f8a1613dc5ff9725c04ep-6Q, -0x1.96b60b10e59567d6b2c6577bad37p-8Q, 0x1.8430d19335684e7577fd3b69976cp-11Q, -0x1.92df0230079088d5ad0746147157p-14Q, 0x1.da6faa767962723e71f08f2e9079p-16Q, 0x1.b237bc2c3b5257b1d937078b73a9p-20Q, 0x1.66eb1a28068ae3ea1bd5d268325dp-25Q, -0x1.f6ebd7398c4a3aa441e024a57151p-33Q, 0x1.5690727034a8a4b1353895ae261dp-45Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.184a0c288d22add7ea26104df2f3p-3Q, 0x1.fbaa047a94a613069e6f550b4e09p-1Q, -0x1.596f5b6b28cb0681bf78a3e54b72p-3Q, 0x1.234875f46000e28dce7c3f342092p-4Q, -0x1.90a568ef3b94afacf755834bab9ap-5Q, 0x1.82b42ea0f8a1613dc5ff9725c05p-6Q, -0x1.96b60b10e59567d6b2c6577bad3bp-8Q, 0x1.8430d19335684e7577fd3b699763p-11Q, -0x1.92df0230079088d5ad0746147153p-14Q, 0x1.da6faa767962723e71f08f2e9083p-16Q, 0x1.b237bc2c3b5257b1d937078b7396p-20Q, 0x1.66eb1a28068ae3ea1bd5d2683257p-25Q, -0x1.f6ebd7398c4a3aa441e024a5714bp-33Q, 0x1.5690727034a8a4b1353895ae261dp-45Q, 0x0p+0Q};
             }
             if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.03033f41d994757a2b4934423535p-1Q, 0x1.8347da7a3030b8b37cdc36ec3be2p-2Q, -0x1.7d2f17f2a95af6988be8eca125cap+0Q, 0x1.c3013eaebde946f9eaa42bce8cdbp-1Q, -0x1.4be40ed86f2cd0c168ad24949287p-2Q, 0x1.4580356ca34ff1cf3c18408b1ce2p-6Q, 0x1.7e9e8eefc30b45959dcb8ab52398p-5Q, -0x1.594cf912461bb959724fb77ad3c3p-6Q, 0x1.27c56651be6ed873712071c19326p-9Q, 0x1.e972a09b0f4dc8fdb93114f9ed2dp-12Q, -0x1.1649ec5e541409b8483ac00aa993p-14Q, 0x1.c99c42a59648ab096d412a5873a5p-23Q, 0x1.81519dee82f001d0cfd286a4bf35p-26Q, -0x1.06b5ee4f0711fc96e3337209d4fap-37Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.03033f41d994757a2b4934423538p-1Q, 0x1.8347da7a3030b8b37cdc36ec3c9cp-2Q, -0x1.7d2f17f2a95af6988be8eca125f4p+0Q, 0x1.c3013eaebde946f9eaa42bce8cf9p-1Q, -0x1.4be40ed86f2cd0c168ad249492a4p-2Q, 0x1.4580356ca34ff1cf3c18408b1d74p-6Q, 0x1.7e9e8eefc30b45959dcb8ab52383p-5Q, -0x1.594cf912461bb959724fb77ad3bbp-6Q, 0x1.27c56651be6ed873712071c19324p-9Q, 0x1.e972a09b0f4dc8fdb93114f9ed4p-12Q, -0x1.1649ec5e541409b8483ac00aa989p-14Q, 0x1.c99c42a59648ab096d412a58741fp-23Q, 0x1.81519dee82f001d0cfd286a4bf1ep-26Q, -0x1.06b5ee4f0711fc96e3337209d4e2p-37Q, 0x0p+0Q};
             }
             if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.666d532df9def8a39e69d4c9dafcp+0Q, -0x1.c0374596ee4d8e750b0b0f065a7p+1Q, 0x1.a43eb9f4500c29913bdae70f2e18p+1Q, -0x1.d627359f84d250c8825852fe214cp+0Q, 0x1.891e36789053a132cb4397963b98p-1Q, 0x1.a23c19ecf2deb44f4177f3e94959p-6Q, -0x1.d9c16d05d77872764189280b3b87p-3Q, 0x1.b6728d569b4c6b3f03c9c20fd92ap-4Q, -0x1.66849bebd2ebdfafabb131376074p-7Q, -0x1.fc6301aedca903a123de4bcecb7dp-9Q, 0x1.7e62ae52149bd7e06a18746f5d38p-11Q, -0x1.2c21c0130a3eaea0bd3721b2b938p-17Q, -0x1.15f344e8ed1b26069acbf2a1a5a3p-21Q, 0x1.7bbd836b1bf84d53feb61580de7bp-32Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.666d532df9def8a39e69d4c9dbd1p+0Q, -0x1.c0374596ee4d8e750b0b0f065b11p+1Q, 0x1.a43eb9f4500c29913bdae70f2e12p+1Q, -0x1.d627359f84d250c8825852fe20e7p+0Q, 0x1.891e36789053a132cb4397963bd6p-1Q, 0x1.a23c19ecf2deb44f4177f3e9336bp-6Q, -0x1.d9c16d05d77872764189280b3978p-3Q, 0x1.b6728d569b4c6b3f03c9c20fd79fp-4Q, -0x1.66849bebd2ebdfafabb131375ec9p-7Q, -0x1.fc6301aedca903a123de4bceca69p-9Q, 0x1.7e62ae52149bd7e06a18746f5b91p-11Q, -0x1.2c21c0130a3eaea0bd3721b2b8d6p-17Q, -0x1.15f344e8ed1b26069acbf2a1a453p-21Q, 0x1.7bbd836b1bf84d53feb61580dc74p-32Q, 0x0p+0Q};
             }
             if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.b44c4e267cbb4d43745305f7f1d1p+1Q, -0x1.c1f7df3ad7ab79897dce80d6fdc1p+3Q, 0x1.1601a8a979c78f82e398ce85d132p+4Q, 0x1.e5bffb29b3c52bb885497a61677fp+3Q, -0x1.38f35bf0e9ee0ae5b17729526ffp+6Q, 0x1.d1869b3f8e2b44288688d26f2b6fp+6Q, -0x1.70d2038145a54625eb25d8766c13p+6Q, 0x1.34930dde67aea02e0a703b771d79p+5Q, -0x1.4b77b4fb3674956338abd182d2e5p+2Q, -0x1.d27f3b25c1fd6ce83b2a8b0b03e8p+0Q, 0x1.32a2c5a3dfe8119d379b7145ac19p-1Q, -0x1.2fc64ff8d3420e31f2a6dd484c8ap-7Q, -0x1.c48021ad9bc1646021c012f661fp-11Q, 0x1.364c0a7c4c64aef45189b313663dp-20Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.b44c4e267cbb4d43745305f720c9p+1Q, -0x1.c1f7df3ad7ab79897dce80d62718p+3Q, 0x1.1601a8a979c78f82e398ce8545b9p+4Q, 0x1.e5bffb29b3c52bb885497a60d3d6p+3Q, -0x1.38f35bf0e9ee0ae5b1772951f4d5p+6Q, 0x1.d1869b3f8e2b44288688d26e70d1p+6Q, -0x1.70d2038145a54625eb25d875d7e5p+6Q, 0x1.34930dde67aea02e0a703b76a197p+5Q, -0x1.4b77b4fb3674956338abd1824db4p+2Q, -0x1.d27f3b25c1fd6ce83b2a8b0a4ac9p+0Q, 0x1.32a2c5a3dfe8119d379b71453288p-1Q, -0x1.2fc64ff8d3420e31f2a6dd47d615p-7Q, -0x1.c48021ad9bc1646021c012f5b071p-11Q, 0x1.364c0a7c4c64aef45189b312edb4p-20Q, 0x0p+0Q};
             }
             if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.afe05c7a6ada1cb6172616d2f2ffp+1Q, -0x1.0a8c44cdd47bf4e495a5398430e1p+4Q, 0x1.0f6c0325c5e1414a9285f59e7d75p+5Q, -0x1.306ff1c62c8336aad5c3f9888cf8p+5Q, 0x1.da69559cc91130d28dd4b6368cc9p+4Q, -0x1.6a2c1f828fe2d81030f1ad526958p+4Q, 0x1.0e28c771588c30581ce7071755d2p+4Q, -0x1.ee4b3cc46d890789fa8b15b80159p+2Q, 0x1.050e3e4d4732a1c55c0c971f29e5p-1Q, 0x1.0ea6cad7a5a7fae2eab7d74b48fbp+0Q, -0x1.6566f5ac7d80487971d04a5977aep-2Q, 0x1.0b828ad29e43eb178f6b65b924cep-6Q, 0x1.3201b5c3bc1c21bf7086981d037bp-10Q, -0x1.a6f0242017b1488503cf0ef0a318p-19Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.afe05c7a6ada1cb6172616d2c6a8p+1Q, -0x1.0a8c44cdd47bf4e495a5398413fbp+4Q, 0x1.0f6c0325c5e1414a9285f59e5f14p+5Q, -0x1.306ff1c62c8336aad5c3f9886bcep+5Q, 0x1.da69559cc91130d28dd4b63660e6p+4Q, -0x1.6a2c1f828fe2d81030f1ad524eb7p+4Q, 0x1.0e28c771588c30581ce7071741b8p+4Q, -0x1.ee4b3cc46d890789fa8b15b7da8p+2Q, 0x1.050e3e4d4732a1c55c0c971f3557p-1Q, 0x1.0ea6cad7a5a7fae2eab7d74b22a1p+0Q, -0x1.6566f5ac7d80487971d04a5944efp-2Q, 0x1.0b828ad29e43eb178f6b65b8f31p-6Q, 0x1.3201b5c3bc1c21bf7086981ccb12p-10Q, -0x1.a6f0242017b1488503cf0ef046e5p-19Q, 0x0p+0Q};
             }
             if constexpr (order == 5) {
-                return {0x0p+0Q, 0x1.77885e6e270a744c868654d77bep+1Q, -0x1.f5abb22b1b6ebb333fd9f11e28cbp+3Q, 0x1.0a779dee6c7bddbff2f0d8b96185p+5Q, -0x1.164d9f148bde4aa13b66fabb8275p+5Q, 0x1.2333738e736f124a0ec3de55d4acp+4Q, -0x1.af306993826a689f7543995743eap+2Q, 0x1.6dba5c59397a4426e98586a9dbfbp+2Q, -0x1.17ffc928dd1d8bf0f209d0c25564p+1Q, -0x1.9f39e7400cf5d234f22720c7e994p+1Q, 0x1.d0d0a8f3b805dafc2d2b539dd42dp+1Q, -0x1.4ac5cadf9fb14bc48382ff0eff77p+0Q, 0x1.049faf6ae689948e66d5e513815cp-3Q, 0x1.5ad3792bdac35c5163486d90e7a1p-7Q, -0x1.e6e9a51e36639d68c6db7d754f12p-15Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.77885e6e270a744c868654d7cbb5p+1Q, -0x1.f5abb22b1b6ebb333fd9f11e8f7cp+3Q, 0x1.0a779dee6c7bddbff2f0d8b9981bp+5Q, -0x1.164d9f148bde4aa13b66fabbc2fp+5Q, 0x1.2333738e736f124a0ec3de563f7bp+4Q, -0x1.af306993826a689f7543995893acp+2Q, 0x1.6dba5c59397a4426e98586aad789p+2Q, -0x1.17ffc928dd1d8bf0f209d0c36abep+1Q, -0x1.9f39e7400cf5d234f22720c7748ap+1Q, 0x1.d0d0a8f3b805dafc2d2b539d9bb4p+1Q, -0x1.4ac5cadf9fb14bc48382ff0ecfb1p+0Q, 0x1.049faf6ae689948e66d5e5134564p-3Q, 0x1.5ad3792bdac35c5163486d9087edp-7Q, -0x1.e6e9a51e36639d68c6db7d7495a4p-15Q, 0x0p+0Q};
             }
             if constexpr (order == 6) {
-                return {0x0p+0Q, 0x1.1912b6ad90d43603284e2902f0abp+0Q, -0x1.85c00c80d7a18fcc693e4762b85p+2Q, 0x1.b7d753e3c818997a04ded98db7dep+3Q, -0x1.076d50e7f7850b94ae780b4ac761p+4Q, 0x1.92a29d7ac0e1e0002558af84767fp+3Q, -0x1.20f516098425bb22664ce4abb09dp+3Q, 0x1.dcba519c323cedf78dcb77920137p+2Q, -0x1.3fe31292805c0462ca96ae1f196p+2Q, 0x1.5e9b74431b072dba61e526bdae0cp+1Q, -0x1.a6996ae95f76ef890f12b5a360bp+0Q, 0x1.806826de1640aff2fbfd8d0aa94cp-1Q, -0x1.ddc83de4acfaf20be5fee510530ep-4Q, -0x1.e09e81650c6b74fbce41e534d5fbp-7Q, 0x1.5c5b71613d71b7692e7e5f0a2ebfp-13Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.1912b6ad90d43603284e290418eep+0Q, -0x1.85c00c80d7a18fcc693e47644de7p+2Q, 0x1.b7d753e3c818997a04ded98f86e3p+3Q, -0x1.076d50e7f7850b94ae780b4bf285p+4Q, 0x1.92a29d7ac0e1e0002558af869ed1p+3Q, -0x1.20f516098425bb22664ce4ad84a9p+3Q, 0x1.dcba519c323cedf78dcb7794def8p+2Q, -0x1.3fe31292805c0462ca96ae20fe5p+2Q, 0x1.5e9b74431b072dba61e526c0393fp+1Q, -0x1.a6996ae95f76ef890f12b5a6c626p+0Q, 0x1.806826de1640aff2fbfd8d0d7d09p-1Q, -0x1.ddc83de4acfaf20be5fee513819ep-4Q, -0x1.e09e81650c6b74fbce41e5378d99p-7Q, 0x1.5c5b71613d71b7692e7e5f0ba23p-13Q, 0x0p+0Q};
             }
             if constexpr (order == 7) {
-                return {0x0p+0Q, 0x1.eae80165a34ad1f2080107f87ddap-3Q, -0x1.5a965a7535366541f0a1afe5a2b4p+0Q, 0x1.851adfd49d1a76d9d23c3531fc86p+1Q, -0x1.b139c010d5d8ef58fb69c4f1a06p+1Q, 0x1.ffefb7038043737a18fc832ffa5dp+0Q, -0x1.0254056f57103b364cf4bcb0546p+0Q, 0x1.ff103b26e087e22aa6dbe24a6942p-1Q, -0x1.7a4f70cc2f5d7a6d2a4e62af8416p-1Q, 0x1.09dce627745a61500e94719899a9p-2Q, -0x1.c2f7ce5c8a37b8fcabdaf25e5004p-4Q, 0x1.41c46b919c33ee1c6941aae7a0ebp-4Q, -0x1.03531c096423a7a88f95e3dc75eap-6Q, -0x1.c24ed1e998c51356546e2438785p-9Q, 0x1.5d1ed72a09587166cbb2e53232dap-14Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.eae80165a34ad1f2080107f7b7a5p-3Q, -0x1.5a965a7535366541f0a1afe5172fp+0Q, 0x1.851adfd49d1a76d9d23c35315fc3p+1Q, -0x1.b139c010d5d8ef58fb69c4f0efd8p+1Q, 0x1.ffefb7038043737a18fc832f1fb7p+0Q, -0x1.0254056f57103b364cf4bcafdd14p+0Q, 0x1.ff103b26e087e22aa6dbe2498954p-1Q, -0x1.7a4f70cc2f5d7a6d2a4e62aee34dp-1Q, 0x1.09dce627745a61500e9471981ea7p-2Q, -0x1.c2f7ce5c8a37b8fcabdaf25d6d6bp-4Q, 0x1.41c46b919c33ee1c6941aae7132bp-4Q, -0x1.03531c096423a7a88f95e3dc08eep-6Q, -0x1.c24ed1e998c51356546e2437d6p-9Q, 0x1.5d1ed72a09587166cbb2e531d26cp-14Q, 0x0p+0Q};
             }
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            if constexpr (order == 0) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.136859984385993751077424284238513346105771881700946032539857608801714375260"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.991531505549868928852223941202783180250573415879960614939273149473543513232"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.168669428069824001344876924759083221703325404050382978741893461845460708901"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0711140258408706504803069010910216723551333508784818550165049090931508664852"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0489069985868462937786964568361717206243738587558741902200175649925966650129"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0236025290831865730472503982004363583525603770422866170365985291322094732559"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00620591898122876136661677884645407645696587502826527734998815703979020082209"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000740414996836150617193096345381128615000342497991762689010201911138137676340"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000960519616914659362067678923772724229000913224382096876651732324410060847142"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000282786008599848003825512309131168222310934819976005479856002545492804079821"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000161758704125419265856051792339632788510763962613299088995170275735382724250"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000417835973045118991124105253366830871810097251894035223474643902978862222950"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000228702107424295259422097052204574273567576074367490930756782831109751583002"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000380322713533425186858078998967525935209252034129900336181242610764710254761"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 1) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.505884148395843984672030852174399268078679938448445514258859914326001574753"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.378203786571291475028258491549280264525735502487840319727030236183752240877"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.48899984049181086925690641126028244033585659708567195002624452117766769554"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.880868872481146917953730102204425044160476030745496386305050091936160661825"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.324112159690952253266958291790923377370339558783455268279088511692627257578"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0198669931146939729198708935598776106105509170321806377166373111519790413827"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0467064658861046390974330766795109450179003887204378435053237799594305015134"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0210754806840627153541931469194838393690032791036447674196194339971613456374"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00225655435576476469044726339752369362143954369726725569747472926858253332600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000466773760937245507236716054902477793363154761728440462716816755417726884839"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000663492114416674035500361661641750124659642249106990423787115653008871078300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000213091444200759381405507720298082584145763408653037309536239955733283926150"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000224285069909106554636357422248869419407906728286220715022858657729340987674"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000746668625743637862652799469000616324979519456514273967438860456366173662892"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 2) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.40010566589796415558533052990817027536043759916356873335248645843912898740"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.50168676252051764999916760393084370145312284526707841278933240785874906921"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.28316425732927656875646999404076171324929322898132788895606205661772082296"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.83653578896048342826761860954879682887285337195163994610183024428204639287"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.767808630196817229463066449452964216764497348541592935264231141751164293885"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0255270245723248470256698009778319785355159721020640100259648381281108673206"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.231325961819433188856073677854062275419611129702243186823190488135500579221"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.107042839148294803604040015338906449890317311518114018506422501396601728023"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0109411012014314322153349861016506274246639791285954533561420989314806280893"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00387868304772471399323142237494169480427070296801463441213707814207225784013"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000729342408030845829165840735507514556696710333640548011394236862236236627590"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000894462576724212069044572229637929785464056704288394767005400917958125948440"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000517722722573465466291304746138565114462435290270180299612937282299347886509"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000345371778653840406383195497480732961379596653494040751101347866321743412771"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 3) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.40857865218409942407989160777729397499591054071894723659795747026734950142"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-14.06150781147640244495854524439441851419403709392481084157811217258651128990"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("17.37540498925634213895582494025326018301205036554108994541098300558519647810"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("15.17968519349066044652294389136578861409554749815814367110760723871662294450"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-78.23765541484636800472354977154947501042898222086099559309649353911488323440"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("116.38145160012465254189247417655014226350307393144895240522480865461502034100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-92.20509149539549844487080427780966241435914366770315955416451996663294302680"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("38.57180379632866626053856571576184925471707552931311103550752525165681257540"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5.17918133289806211714176217075064499841836717085374825348683628481547935326"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.82225389167614588863332031779801692711824638887982150713863406444245730454"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.598898102049091230023937146931083606151277363169821330990542437169742650605"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00927046685105820265775499853351620625448959411497441318196481292209014223253"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000863076236511053557380361955795006038651362072706195875505623255065432401013"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000115594653411452947966415211118033698227006015073368264240575869273988254730"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 4) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.37403446175967838025740792692632707948046376845678760985954780113353683376"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-16.65924530413007895577513111721655133926983876119072500556865649764333729280"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("33.92774037847644365730660167931354863708439882380578545057682183184098002560"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-38.05466036628095179642463777855898685849735591879960715894900954660986556330"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("29.65071641201309323109850787750541018979228147381363769083014882995571890840"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-22.63577223778536585979611105411422747200617599445293663779795581166422612690"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("16.88495582843530592324987980427308263482658385028179904289230174596074103340"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.72334212477120771395018502358287787646097333914773539504366245154006903261"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.509874293263782320049624992542430344831541029125914053863318565845626947501"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.05723254933187142521325305757260448706303752772475115221502588084489406121"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.349025572445839567506362486618125787775522478731013526918275825979025450341"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0163275104227731348198876869545919769123313328974523116723206927638520899008"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00116732284453401104147360959063823502788555856702680595647112386117318401134"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000315113403818958420917458786425100865687235113639358839633877000023951513838"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 5) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.93384914759197424624436413594969058529365344664724959523125492071614427193"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-15.67720898074499960019790246277632013145587519414207657764003345532838952320"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("33.30840669888082927743188422912680268770468382312738501151598773669709347950"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-34.78790107776493317973127999160157672445840757713194594151710343461996258490"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("18.20006137509239303213521792722566030277335694542561819775614995273543845150"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.73732985882967353579625955002147560794702457823837345027768515384207199939"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.71449955666858878400309088707607704396756738056282405829209011954772445391"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.18749346251773279906619495975374371998852897264751318856692473518486342256"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.24395456912490815512051132069746602372138882030028342425172470032100812037"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.63136779690107300247637411793680556583470203778956077148746730514900636140"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.29208057365003020310933608766753056310407043934855358170062066567610977189"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.127257700395436748185441509800570330756269721379701882712722971090011220542"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0105842916161319289430031608631456823275553548600640429274763034124609001209"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000580445141495463978915954606394279824931279836573959690571643754738437622999"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 6) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.09794179665989663514011010318171289068252802140768727878686619226775014160"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.08984673101670014308433503745446328651407196395191858667048642230680054117"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("13.74503511894797041799485471293715399778854034159024012586185790377350928050"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-16.46418848621425725226856339943522600141255984607131407751367512429535974550"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("12.58235048270494971240583540160205978818573268955250712351866824920394664630"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.02991773470528559623876404322857159498730180401367525828524406240302233897"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("7.44887199643649366803718019597024027263652518924024613405692486678267833539"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.99823440844323865139296784342762981029643191844299226701928041463556839082"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.73911908413543286133929491391344713268901997126890391713796517771077981005"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.65077846715527320386166297579946870069085350586686894303798561070712527613"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.750794615373821527451164487493324083501669271576479206468805894209869122774"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.116646043558658917381544271189706037325524764351951616559858241342309095929"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0146673328218612635522669061509315192382547144459217750205470993012158491409"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000166109656710205411664661588058784980983032508578738275988691042867685712989"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 7) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.239700327791444154401358637312026610528216518839726598253382285687854145301"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.35385671006698656362279837678985930962433090919777408910621735397808426685"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.03988263970878210970161760103694626417746895886680293765920336110790081944"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.38457489797628550541836623944752232253491103859138520958725493309901917502"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.99975150905107828365392055663475104753346795604213386830360205861062068058"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.00909456222785902673888196781880614953849677554209360029881025329921208452"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.998170708175407887564948885340732566778229747407421235714432832971547496176"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.738887333798341000751416724474791664378133946712220233024499707378818126349"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.259631725462066480616682675264655170327179020240911896080856531165333156446"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.110099607562586792620753110120489954588564472503733678183395115619093852339"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0785564615159843726834898160756405679414386387007067812431829633899248651308"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0158279203220123929016663292094093420473159442069900632195102000109139919945"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00343557655723850854612182385732716766125518666298517555524787852985964150285"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000832368065465019779864000534536830870074333194787317202754089818199746452757"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+        }
     }
     if constexpr (p == 9) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -536,13 +655,13 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0f, 0x1.e4c00ep-1f, -0x1.aad7p+0f, 0x1.135c58p-2f, 0x1.5b4146p-1f, -0x1.c92ba8p-4f, -0x1.4f00eap-2f, 0x1.61aa48p-2f, -0x1.66761ap-3f, 0x1.723502p-5f, -0x1.85c5f4p-10f, -0x1.2bb318p-9f, 0x1.b3d73ep-12f, 0x1.bca3f2p-17f, -0x1.261d8ap-20f, 0x1.36693ap-28f, 0x1.1a9906p-40f, -0x0p+0f};
             }
             if constexpr (order == 3) {
-                return {0x0p+0f, 0x1.27d6ep+1f, -0x1.2ded7ap+3f, 0x1.e79fd8p+3f, -0x1.304a1ap+3f, -0x1.effd26p+2f, 0x1.7ce73p+4f, -0x1.985f02p+4f, 0x1.d3cfacp+3f, -0x1.e1a25p+1f, -0x1.9b8564p-2f, 0x1.fe4766p-2f, -0x1.73f12ep-4f, -0x1.20ddep-10f, 0x1.ffd29p-12f, -0x1.fa8378p-20f, -0x1.cc794ap-31f, 0x0p+0f};
+                return {0x0p+0f, 0x1.27d6ep+1f, -0x1.2ded7ap+3f, 0x1.e79fd8p+3f, -0x1.304a1ap+3f, -0x1.effd26p+2f, 0x1.7ce73p+4f, -0x1.985f02p+4f, 0x1.d3cfacp+3f, -0x1.e1a25p+1f, -0x1.9b8564p-2f, 0x1.fe4766p-2f, -0x1.73f12ep-4f, -0x1.20ddep-10f, 0x1.ffd29p-12f, -0x1.fa8378p-20f, -0x1.cc794ap-31f, -0x0p+0f};
             }
             if constexpr (order == 4) {
-                return {0x0p+0f, 0x1.c7cedp+1f, -0x1.2ab8cap+4f, 0x1.4df684p+5f, -0x1.af3bfap+5f, 0x1.8eeb18p+5f, -0x1.541e9cp+5f, 0x1.12ea48p+5f, -0x1.35c8bp+4f, 0x1.d829e2p+1f, 0x1.69d6eap+1f, -0x1.023562p+1f, 0x1.b42324p-2f, -0x1.2e2904p-8f, -0x1.22b4e2p-8f, 0x1.654cep-16f, 0x1.43e712p-26f, -0x0p+0f};
+                return {0x0p+0f, 0x1.c7cedp+1f, -0x1.2ab8cap+4f, 0x1.4df684p+5f, -0x1.af3bfap+5f, 0x1.8eeb18p+5f, -0x1.541e9cp+5f, 0x1.12ea48p+5f, -0x1.35c8bp+4f, 0x1.d829e2p+1f, 0x1.69d6eap+1f, -0x1.023562p+1f, 0x1.b42324p-2f, -0x1.2e2904p-8f, -0x1.22b4e2p-8f, 0x1.654cep-16f, 0x1.43e712p-26f, 0x0p+0f};
             }
             if constexpr (order == 5) {
-                return {0x0p+0f, 0x1.1617a4p+2f, -0x1.94d9c6p+4f, 0x1.dd0eb6p+5f, -0x1.168c04p+6f, 0x1.24c19cp+5f, -0x1.016a68p+0f, -0x1.c94ed2p+2f, 0x1.669c08p+3f, -0x1.88dca4p+4f, 0x1.b958d8p+4f, -0x1.eccebap+3f, 0x1.f4375ep+1f, -0x1.2ade5ep-3f, -0x1.491f18p-4f, 0x1.5bccdep-11f, 0x1.398368p-20f, -0x0p+0f};
+                return {0x0p+0f, 0x1.1617a4p+2f, -0x1.94d9c6p+4f, 0x1.dd0eb6p+5f, -0x1.168c04p+6f, 0x1.24c19cp+5f, -0x1.016a68p+0f, -0x1.c94ed2p+2f, 0x1.669c08p+3f, -0x1.88dca4p+4f, 0x1.b958d8p+4f, -0x1.eccebap+3f, 0x1.f4375ep+1f, -0x1.2ade5ep-3f, -0x1.491f18p-4f, 0x1.5bccdep-11f, 0x1.398368p-20f, 0x0p+0f};
             }
             if constexpr (order == 6) {
                 return {0x0p+0f, 0x1.384148p+1f, -0x1.dd3c5ap+3f, 0x1.30352ap+5f, -0x1.a86d9ep+5f, 0x1.7d0e6cp+5f, -0x1.25c844p+5f, 0x1.f5b3e2p+4f, -0x1.815eep+4f, 0x1.ca4482p+3f, -0x1.050826p+3f, 0x1.1eeca8p+2f, -0x1.6df696p+0f, 0x1.75a7acp-5f, 0x1.ebd4ap-5f, -0x1.434438p-10f, -0x1.202646p-18f, 0x0p+0f};
@@ -565,13 +684,13 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0, 0x1.e4c00e361fc68p-1, -0x1.aad6ffd5d77f1p+0, 0x1.135c57711e671p-2, 0x1.5b41454ff0957p-1, -0x1.c92ba77b267a3p-4, -0x1.4f00ea2c2d363p-2, 0x1.61aa479f9dc68p-2, -0x1.6676194262896p-3, 0x1.7235017b58d32p-5, -0x1.85c5f4a449273p-10, -0x1.2bb318efa4d23p-9, 0x1.b3d73e818e5c9p-12, 0x1.bca3f26f194dp-17, -0x1.261d8947cb727p-20, 0x1.36693a4632269p-28, 0x1.1a9906065291fp-40, -0x0p+0};
             }
             if constexpr (order == 3) {
-                return {0x0p+0, 0x1.27d6df36685a8p+1, -0x1.2ded79e41fdb1p+3, 0x1.e79fd7c0b1c0fp+3, -0x1.304a1a210a5fap+3, -0x1.effd2573aa9abp+2, 0x1.7ce72fdc2cb91p+4, -0x1.985f0196c72e5p+4, 0x1.d3cfac07a9d2bp+3, -0x1.e1a24f8472a68p+1, -0x1.9b8563bd7c7d8p-2, 0x1.fe4766e3faf54p-2, -0x1.73f12d4155f36p-4, -0x1.20dddf659ee51p-10, 0x1.ffd28fb3400bfp-12, -0x1.fa83788d3f78dp-20, -0x1.cc794a76e5f16p-31, 0x0p+0};
+                return {0x0p+0, 0x1.27d6df36685a8p+1, -0x1.2ded79e41fdb1p+3, 0x1.e79fd7c0b1c0fp+3, -0x1.304a1a210a5fap+3, -0x1.effd2573aa9abp+2, 0x1.7ce72fdc2cb91p+4, -0x1.985f0196c72e5p+4, 0x1.d3cfac07a9d2bp+3, -0x1.e1a24f8472a68p+1, -0x1.9b8563bd7c7d8p-2, 0x1.fe4766e3faf54p-2, -0x1.73f12d4155f36p-4, -0x1.20dddf659ee51p-10, 0x1.ffd28fb3400bfp-12, -0x1.fa83788d3f78dp-20, -0x1.cc794a76e5f16p-31, -0x0p+0};
             }
             if constexpr (order == 4) {
-                return {0x0p+0, 0x1.c7ced0f66aeadp+1, -0x1.2ab8c9c81252ep+4, 0x1.4df684dede46dp+5, -0x1.af3bf949d62bap+5, 0x1.8eeb17bed133cp+5, -0x1.541e9c27826e5p+5, 0x1.12ea47c60decp+5, -0x1.35c8b07214e14p+4, 0x1.d829e1a762882p+1, 0x1.69d6e9c20f73dp+1, -0x1.0235621854eefp+1, 0x1.b423243b8b469p-2, -0x1.2e290398a3fe3p-8, -0x1.22b4e2598d44bp-8, 0x1.654cdf573874bp-16, 0x1.43e711e678672p-26, -0x0p+0};
+                return {0x0p+0, 0x1.c7ced0f66aeadp+1, -0x1.2ab8c9c81252ep+4, 0x1.4df684dede46dp+5, -0x1.af3bf949d62bap+5, 0x1.8eeb17bed133cp+5, -0x1.541e9c27826e5p+5, 0x1.12ea47c60decp+5, -0x1.35c8b07214e14p+4, 0x1.d829e1a762882p+1, 0x1.69d6e9c20f73dp+1, -0x1.0235621854eefp+1, 0x1.b423243b8b469p-2, -0x1.2e290398a3fe3p-8, -0x1.22b4e2598d44bp-8, 0x1.654cdf573874bp-16, 0x1.43e711e678672p-26, 0x0p+0};
             }
             if constexpr (order == 5) {
-                return {0x0p+0, 0x1.1617a4f9d8857p+2, -0x1.94d9c534a28d4p+4, 0x1.dd0eb6aa76ffep+5, -0x1.168c0447c1b6fp+6, 0x1.24c19c047007fp+5, -0x1.016a68491e4d8p+0, -0x1.c94ed28aba0f5p+2, 0x1.669c08c9522f3p+3, -0x1.88dca456f3456p+4, 0x1.b958d77e385a9p+4, -0x1.eccebab605f4bp+3, 0x1.f4375d664ce34p+1, -0x1.2ade5d60c4581p-3, -0x1.491f178ce5646p-4, 0x1.5bccddec65e54p-11, 0x1.398367062ce37p-20, -0x0p+0};
+                return {0x0p+0, 0x1.1617a4f9d8857p+2, -0x1.94d9c534a28d4p+4, 0x1.dd0eb6aa76ffep+5, -0x1.168c0447c1b6fp+6, 0x1.24c19c047007fp+5, -0x1.016a68491e4d8p+0, -0x1.c94ed28aba0f5p+2, 0x1.669c08c9522f3p+3, -0x1.88dca456f3456p+4, 0x1.b958d77e385a9p+4, -0x1.eccebab605f4bp+3, 0x1.f4375d664ce34p+1, -0x1.2ade5d60c4581p-3, -0x1.491f178ce5646p-4, 0x1.5bccddec65e54p-11, 0x1.398367062ce37p-20, 0x0p+0};
             }
             if constexpr (order == 6) {
                 return {0x0p+0, 0x1.3841475e9a364p+1, -0x1.dd3c5aa19c52ep+3, 0x1.303529a28e47p+5, -0x1.a86d9ebb6edc4p+5, 0x1.7d0e6c4e24171p+5, -0x1.25c8439d2df8ap+5, 0x1.f5b3e1ac99667p+4, -0x1.815ee05c85e8bp+4, 0x1.ca4482f4236a5p+3, -0x1.050825dec75a9p+3, 0x1.1eeca8acc3a79p+2, -0x1.6df69657c972dp+0, 0x1.75a7ac677c4efp-5, 0x1.ebd49f3810c89p-5, -0x1.4344372e1b6fcp-10, -0x1.20264586c6bb9p-18, 0x0p+0};
@@ -594,13 +713,13 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0L, 0xf.260071b0fe33d17p-4L, -0xd.56b7feaebbf8a9ep-3L, 0x8.9ae2bb88f3384cep-5L, 0xa.da0a2a7f84ab917p-4L, -0xe.495d3bd933d14bbp-7L, -0xa.7807516169b18a5p-5L, 0xb.0d523cfcee33daap-5L, -0xb.33b0ca13144b196p-6L, 0xb.91a80bdac698e63p-8L, -0xc.2e2fa52249396c6p-13L, -0x9.5d98c77d2691ac4p-12L, 0xd.9eb9f40c72e4aacp-15L, 0xd.e51f9378ca67c3cp-20L, -0x9.30ec4a3e5b93bbap-23L, 0x9.b349d2319134721p-31L, 0x8.d4c83032948f76p-43L, -0x0p+0L};
             }
             if constexpr (order == 3) {
-                return {0x0p+0L, 0x9.3eb6f9b342d3cadp-2L, -0x9.6f6bcf20fed8622p+0L, 0xf.3cfebe058e075ecp+0L, -0x9.8250d10852fce74p+0L, -0xf.7fe92b9d54d57e6p-1L, 0xb.e7397ee165c88c5p+1L, -0xc.c2f80cb639729f3p+1L, 0xe.9e7d603d4e95463p+0L, -0xf.0d127c23953405cp-2L, -0xc.dc2b1debe3ebee3p-5L, 0xf.f23b371fd7a9d87p-5L, -0xb.9f896a0aaf9ad9fp-7L, -0x9.06eefb2cf7284e3p-13L, 0xf.fe947d9a005fa2fp-15L, -0xf.d41bc469fbc68cdp-23L, -0xe.63ca53b72f8b2fep-34L, 0x0p+0L};
+                return {0x0p+0L, 0x9.3eb6f9b342d3cadp-2L, -0x9.6f6bcf20fed8622p+0L, 0xf.3cfebe058e075ecp+0L, -0x9.8250d10852fce74p+0L, -0xf.7fe92b9d54d57e6p-1L, 0xb.e7397ee165c88c5p+1L, -0xc.c2f80cb639729f3p+1L, 0xe.9e7d603d4e95463p+0L, -0xf.0d127c23953405cp-2L, -0xc.dc2b1debe3ebee3p-5L, 0xf.f23b371fd7a9d87p-5L, -0xb.9f896a0aaf9ad9fp-7L, -0x9.06eefb2cf7284e3p-13L, 0xf.fe947d9a005fa2fp-15L, -0xf.d41bc469fbc68cdp-23L, -0xe.63ca53b72f8b2fep-34L, -0x0p+0L};
             }
             if constexpr (order == 4) {
-                return {0x0p+0L, 0xe.3e7687b3575667ep-2L, -0x9.55c64e409297236p+1L, 0xa.6fb426f6f2369dp+2L, -0xd.79dfca4eb15ce04p+2L, 0xc.7758bdf6899e1b4p+2L, -0xa.a0f4e13c13724e9p+2L, 0x8.97523e306f6022p+2L, -0x9.ae458390a70a077p+1L, 0xe.c14f0d3b14410dep-2L, 0xb.4eb74e107b9e597p-2L, -0x8.11ab10c2a7777ccp-2L, 0xd.a11921dc5a34834p-5L, -0x9.71481cc51ff17e4p-11L, -0x9.15a712cc6a2586fp-11L, 0xb.2a66fab9c3a5b39p-19L, 0xa.1f388f33c339298p-29L, -0x0p+0L};
+                return {0x0p+0L, 0xe.3e7687b3575667ep-2L, -0x9.55c64e409297236p+1L, 0xa.6fb426f6f2369dp+2L, -0xd.79dfca4eb15ce04p+2L, 0xc.7758bdf6899e1b4p+2L, -0xa.a0f4e13c13724e9p+2L, 0x8.97523e306f6022p+2L, -0x9.ae458390a70a077p+1L, 0xe.c14f0d3b14410dep-2L, 0xb.4eb74e107b9e597p-2L, -0x8.11ab10c2a7777ccp-2L, 0xd.a11921dc5a34834p-5L, -0x9.71481cc51ff17e4p-11L, -0x9.15a712cc6a2586fp-11L, 0xb.2a66fab9c3a5b39p-19L, 0xa.1f388f33c339298p-29L, 0x0p+0L};
             }
             if constexpr (order == 5) {
-                return {0x0p+0L, 0x8.b0bd27cec42baaep-1L, -0xc.a6ce29a51469f7p+1L, 0xe.e875b553b7fed21p+2L, -0x8.b460223e0db7486p+3L, 0x9.260ce023803fb4p+2L, -0x8.0b534248f26c38ep-3L, -0xe.4a769455d07a8e6p-1L, 0xb.34e0464a91798aep+0L, -0xc.46e522b79a2b2aep+1L, 0xd.cac6bbf1c2d48b2p+1L, -0xf.6675d5b02fa596cp+0L, 0xf.a1baeb32671a172p-2L, -0x9.56f2eb0622c089cp-6L, -0xa.48f8bc672b2306bp-7L, 0xa.de66ef632f29e0ep-14L, 0x9.cc1b3831671b9dbp-23L, -0x0p+0L};
+                return {0x0p+0L, 0x8.b0bd27cec42baaep-1L, -0xc.a6ce29a51469f7p+1L, 0xe.e875b553b7fed21p+2L, -0x8.b460223e0db7486p+3L, 0x9.260ce023803fb4p+2L, -0x8.0b534248f26c38ep-3L, -0xe.4a769455d07a8e6p-1L, 0xb.34e0464a91798aep+0L, -0xc.46e522b79a2b2aep+1L, 0xd.cac6bbf1c2d48b2p+1L, -0xf.6675d5b02fa596cp+0L, 0xf.a1baeb32671a172p-2L, -0x9.56f2eb0622c089cp-6L, -0xa.48f8bc672b2306bp-7L, 0xa.de66ef632f29e0ep-14L, 0x9.cc1b3831671b9dbp-23L, 0x0p+0L};
             }
             if constexpr (order == 6) {
                 return {0x0p+0L, 0x9.c20a3af4d1b1cfep-2L, -0xe.e9e2d50ce2972e4p+0L, 0x9.81a94d147237d62p+2L, -0xd.436cf5db76e1e52p+2L, 0xb.e873627120b85ap+2L, -0x9.2e421ce96fc4fd3p+2L, 0xf.ad9f0d64cb33437p+1L, -0xc.0af702e42f45538p+1L, 0xe.522417a11b52a8bp+0L, -0x8.28412ef63ad4b3p+0L, 0x8.f76545661d3c9p-1L, -0xb.6fb4b2be4b96476p-3L, 0xb.ad3d633be277714p-8L, 0xf.5ea4f9c08644463p-8L, -0xa.1a21b970db7e3c3p-13L, -0x9.01322c3635dc8d8p-21L, 0x0p+0L};
@@ -615,42 +734,71 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         #ifdef BOOST_HAS_FLOAT128
         if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
             if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.1d2fbfac23949a1e129ec9f83912p-4Q, 0x1.b1b6520101e0e6c7ddaa9da59f1ep-1Q, 0x1.8b08d5cd4a2ad4b181244736a729p-3Q, -0x1.4aef16c7e666f719f7698e178af8p-3Q, 0x1.fd1877f1138be38ba53889d72502p-5Q, -0x1.7ee87092fa242b1ef789aaf8df0bp-8Q, -0x1.09758849af60512fff4fa06073a1p-7Q, 0x1.3d3ef7388a3ade9f5adf4b3f580fp-8Q, -0x1.29147421d57112477f4b7b3491f7p-10Q, 0x1.b33acccf47f1bda17f46b81064b7p-15Q, 0x1.7e6498cdbddd4dce209effce7067p-16Q, -0x1.53f9494edf1282277c1de6dc67e2p-19Q, -0x1.58c1d88e09b30b0364784ebc1f6cp-24Q, 0x1.278ba12dc249a4cd49c8d69ab618p-29Q, -0x1.705a7a4d83450688cb9e189ad73cp-38Q, -0x1.4fb4ee678fa0e1946f2bc7ed6f9ap-52Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.1d2fbfac23949a1e129ec9f8391bp-4Q, 0x1.b1b6520101e0e6c7ddaa9da59f23p-1Q, 0x1.8b08d5cd4a2ad4b181244736a713p-3Q, -0x1.4aef16c7e666f719f7698e178af1p-3Q, 0x1.fd1877f1138be38ba53889d724ecp-5Q, -0x1.7ee87092fa242b1ef789aaf8def8p-8Q, -0x1.09758849af60512fff4fa06073a6p-7Q, 0x1.3d3ef7388a3ade9f5adf4b3f580dp-8Q, -0x1.29147421d57112477f4b7b3491f7p-10Q, 0x1.b33acccf47f1bda17f46b8106497p-15Q, 0x1.7e6498cdbddd4dce209effce7062p-16Q, -0x1.53f9494edf1282277c1de6dc67e4p-19Q, -0x1.58c1d88e09b30b0364784ebc1f68p-24Q, 0x1.278ba12dc249a4cd49c8d69ab623p-29Q, -0x1.705a7a4d83450688cb9e189ad73ep-38Q, -0x1.4fb4ee678fa0e1946f2bc7ed6f9ap-52Q, 0x0p+0Q};
             }
             if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.2b90f770700937399f9f525fd16p-2Q, 0x1.af96b810375ae30c4c41bf8dddfep-1Q, -0x1.d3c16b16ba8799042d28d9c49847p+0Q, 0x1.1690032de8cfad91fdf041ea0eaap+0Q, -0x1.1f4f37268ff73d0393fe0f677908p-1Q, 0x1.82c9256a70f8e96c68d16f2e332cp-3Q, -0x1.540e9bea7c732170245209a303ap-7Q, -0x1.49841c554fed1d5f2443e15a5a69p-6Q, 0x1.96a364065f27ccd19657d67cdf44p-8Q, 0x1.0c49493de5a6ec95d0bb4c3aca7fp-11Q, -0x1.b592fbb7be41b5e92f003f6109e3p-12Q, 0x1.9d3f09be0cea6d8d6f8ed455253cp-16Q, 0x1.8562af0388b7df01536ccb66a54fp-23Q, -0x1.13cc2e0d34f2575dd283b068f4aep-24Q, 0x1.2234e02ed8630c149658a9630027p-34Q, 0x1.08644a120d1ef6f0d4b961ae18cfp-47Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.2b90f770700937399f9f525fd17p-2Q, 0x1.af96b810375ae30c4c41bf8dddd3p-1Q, -0x1.d3c16b16ba8799042d28d9c49845p+0Q, 0x1.1690032de8cfad91fdf041ea0eb6p+0Q, -0x1.1f4f37268ff73d0393fe0f67790ep-1Q, 0x1.82c9256a70f8e96c68d16f2e3327p-3Q, -0x1.540e9bea7c732170245209a302fbp-7Q, -0x1.49841c554fed1d5f2443e15a5a95p-6Q, 0x1.96a364065f27ccd19657d67cdf64p-8Q, 0x1.0c49493de5a6ec95d0bb4c3aca89p-11Q, -0x1.b592fbb7be41b5e92f003f6109fcp-12Q, 0x1.9d3f09be0cea6d8d6f8ed455255ap-16Q, 0x1.8562af0388b7df01536ccb66a5b4p-23Q, -0x1.13cc2e0d34f2575dd283b068f4bap-24Q, 0x1.2234e02ed8630c149658a9630026p-34Q, 0x1.08644a120d1ef6f0d4b961ae1879p-47Q, 0x0p+0Q};
             }
             if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.e4c00e361fc67a2e12b083b2dedp-1Q, -0x1.aad6ffd5d77f153c17f1c88238b1p+0Q, 0x1.135c57711e67099c1758b9c71774p-2Q, 0x1.5b41454ff095722d0f803ea680d3p-1Q, -0x1.c92ba77b267a297500d5b5d446e8p-4Q, -0x1.4f00ea2c2d363149504e045fbe3dp-2Q, 0x1.61aa479f9dc67b53226c771010a3p-2Q, -0x1.667619426289632c2e8907dc17f4p-3Q, 0x1.7235017b58d31cc6ca2ab84f7b18p-5Q, -0x1.85c5f4a449272d8bf24d90db58dfp-10Q, -0x1.2bb318efa4d23587f50785ea349bp-9Q, 0x1.b3d73e818e5c9557fa6b95207e7cp-12Q, 0x1.bca3f26f194cf877e2358ca6ef83p-17Q, -0x1.261d8947cb7277733f476ea3b783p-20Q, 0x1.36693a4632268e426c4014035393p-28Q, 0x1.1a9906065291eec094ff6b81726cp-40Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.e4c00e361fc67a2e12b083b2df48p-1Q, -0x1.aad6ffd5d77f153c17f1c8823935p+0Q, 0x1.135c57711e67099c1758b9c717c8p-2Q, 0x1.5b41454ff095722d0f803ea68127p-1Q, -0x1.c92ba77b267a297500d5b5d44785p-4Q, -0x1.4f00ea2c2d363149504e045fbe84p-2Q, 0x1.61aa479f9dc67b53226c771010fp-2Q, -0x1.667619426289632c2e8907dc1851p-3Q, 0x1.7235017b58d31cc6ca2ab84f7b8bp-5Q, -0x1.85c5f4a449272d8bf24d90db58c1p-10Q, -0x1.2bb318efa4d23587f50785ea34e5p-9Q, 0x1.b3d73e818e5c9557fa6b95207f02p-12Q, 0x1.bca3f26f194cf877e2358ca6efddp-17Q, -0x1.261d8947cb7277733f476ea3b7dfp-20Q, 0x1.36693a4632268e426c40140353cep-28Q, 0x1.1a9906065291eec094ff6b8172d8p-40Q, 0x0p+0Q};
             }
             if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.27d6df36685a79598b6c86ce4186p+1Q, -0x1.2ded79e41fdb0c43d1210e12d21ep+3Q, 0x1.e79fd7c0b1c0ebd84f460885d881p+3Q, -0x1.304a1a210a5f9ce8bc8b8a0cffdep+3Q, -0x1.effd2573aa9aafcb53e5889f37dap+2Q, 0x1.7ce72fdc2cb91189ae6d5e0871cfp+4Q, -0x1.985f0196c72e53e6d1cfdee7b628p+4Q, 0x1.d3cfac07a9d2a8c51198c073e7cep+3Q, -0x1.e1a24f8472a680b7d24d0580978cp+1Q, -0x1.9b8563bd7c7d7dc5768ba3de4d6cp-2Q, 0x1.fe4766e3faf53b0d1248280765afp-2Q, -0x1.73f12d4155f35b3e8452b4fe648dp-4Q, -0x1.20dddf659ee509c6befdf1c741e4p-10Q, 0x1.ffd28fb3400bf45efe5c328ed98fp-12Q, -0x1.fa83788d3f78d19a901b7476cd3dp-20Q, -0x1.cc794a76e5f165fc8108c92a1bffp-31Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.27d6df36685a79598b6c86ce474dp+1Q, -0x1.2ded79e41fdb0c43d1210e12de17p+3Q, 0x1.e79fd7c0b1c0ebd84f460885ecf3p+3Q, -0x1.304a1a210a5f9ce8bc8b8a0cdf19p+3Q, -0x1.effd2573aa9aafcb53e588a096b7p+2Q, 0x1.7ce72fdc2cb91189ae6d5e090c6bp+4Q, -0x1.985f0196c72e53e6d1cfdee84e02p+4Q, 0x1.d3cfac07a9d2a8c51198c074937dp+3Q, -0x1.e1a24f8472a680b7d24d058147a3p+1Q, -0x1.9b8563bd7c7d7dc5768ba3df017ep-2Q, 0x1.fe4766e3faf53b0d124828083686p-2Q, -0x1.73f12d4155f35b3e8452b4ff00abp-4Q, -0x1.20dddf659ee509c6befdf1c7addep-10Q, 0x1.ffd28fb3400bf45efe5c328fc188p-12Q, -0x1.fa83788d3f78d19a901b7477bae6p-20Q, -0x1.cc794a76e5f165fc8108c92b057bp-31Q, 0x0p+0Q};
             }
             if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.c7ced0f66aeaccfcda165890b07cp+1Q, -0x1.2ab8c9c81252e46b55777de4d947p+4Q, 0x1.4df684dede46d3a014591fd079e5p+5Q, -0x1.af3bf949d62b9c07b05b4ac5a7abp+5Q, 0x1.8eeb17bed133c367f65a67fd697cp+5Q, -0x1.541e9c27826e49d24f626bb2a444p+5Q, 0x1.12ea47c60dec043f14d3664d56dbp+5Q, -0x1.35c8b07214e140ed7f1d44702883p+4Q, 0x1.d829e1a7628821bc837255ba8e2p+1Q, 0x1.69d6e9c20f73cb2d14ff73520816p+1Q, -0x1.0235621854eeef97bfd3d4e40fecp+1Q, 0x1.b423243b8b46906701ef92e186fap-2Q, -0x1.2e290398a3fe2fc8cc3aebac6855p-8Q, -0x1.22b4e2598d44b0dd2f4a293dd307p-8Q, 0x1.654cdf573874b672ebfe3509eb92p-16Q, 0x1.43e711e67867252f78e7e45acf76p-26Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.c7ced0f66aeaccfcda16588f9d75p+1Q, -0x1.2ab8c9c81252e46b55777de43246p+4Q, 0x1.4df684dede46d3a014591fcfc934p+5Q, -0x1.af3bf949d62b9c07b05b4ac4bf21p+5Q, 0x1.8eeb17bed133c367f65a67fc6e9fp+5Q, -0x1.541e9c27826e49d24f626bb1a338p+5Q, 0x1.12ea47c60dec043f14d3664c7b9cp+5Q, -0x1.35c8b07214e140ed7f1d446f3113p+4Q, 0x1.d829e1a7628821bc837255b88e76p+1Q, 0x1.69d6e9c20f73cb2d14ff7351adb6p+1Q, -0x1.0235621854eeef97bfd3d4e3b1cp+1Q, 0x1.b423243b8b46906701ef92e0fa6p-2Q, -0x1.2e290398a3fe2fc8cc3aebacf78cp-8Q, -0x1.22b4e2598d44b0dd2f4a293dacc9p-8Q, 0x1.654cdf573874b672ebfe3509d857p-16Q, 0x1.43e711e67867252f78e7e45afce7p-26Q, 0x0p+0Q};
             }
             if constexpr (order == 5) {
-                return {0x0p+0Q, 0x1.1617a4f9d885755cd347730680b6p+2Q, -0x1.94d9c534a28d3ee0a8bf210bcdbcp+4Q, 0x1.dd0eb6aa76ffda42c87706ab28dep+5Q, -0x1.168c0447c1b6e90c330602af557cp+6Q, 0x1.24c19c047007f67f0d2fc48525bep+5Q, -0x1.016a68491e4d871ca5058c90ecfbp+0Q, -0x1.c94ed28aba0f51cc92c5b4e86742p+2Q, 0x1.669c08c9522f315c7b041fba43e2p+3Q, -0x1.88dca456f345655b7cb4359b9a4bp+4Q, 0x1.b958d77e385a9163a2eb3b5063f1p+4Q, -0x1.eccebab605f4b2d725512d8a373ap+3Q, 0x1.f4375d664ce342e4e518679a8a7p+1Q, -0x1.2ade5d60c45811382f7ff19b2adep-3Q, -0x1.491f178ce56460d544cbe168f85cp-4Q, 0x1.5bccddec65e53c1b0416c331875ep-11Q, 0x1.398367062ce373b6810676d7e87ep-20Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.1617a4f9d885755cd3477307254fp+2Q, -0x1.94d9c534a28d3ee0a8bf210cb612p+4Q, 0x1.dd0eb6aa76ffda42c87706ac442ap+5Q, -0x1.168c0447c1b6e90c330602b02462p+6Q, 0x1.24c19c047007f67f0d2fc486ec63p+5Q, -0x1.016a68491e4d871ca5058cc8b9fbp+0Q, -0x1.c94ed28aba0f51cc92c5b4dc5aacp+2Q, 0x1.669c08c9522f315c7b041fb5fb05p+3Q, -0x1.88dca456f345655b7cb4359a3262p+4Q, 0x1.b958d77e385a9163a2eb3b4f73aep+4Q, -0x1.eccebab605f4b2d725512d8939ecp+3Q, 0x1.f4375d664ce342e4e51867996bcdp+1Q, -0x1.2ade5d60c45811382f7ff19a5bd5p-3Q, -0x1.491f178ce56460d544cbe167fd8cp-4Q, 0x1.5bccddec65e53c1b0416c330319fp-11Q, 0x1.398367062ce373b6810676d67904p-20Q, 0x0p+0Q};
             }
             if constexpr (order == 6) {
-                return {0x0p+0Q, 0x1.3841475e9a3639fcb27c2a8a346bp+1Q, -0x1.dd3c5aa19c52e5c8a273f6e1052ep+3Q, 0x1.303529a28e46fac3a8f56eaa0a35p+5Q, -0x1.a86d9ebb6edc3ca33aa7af776936p+5Q, 0x1.7d0e6c4e24170b40a4b957521101p+5Q, -0x1.25c8439d2df89fa5007905a4ba91p+5Q, 0x1.f5b3e1ac9966686ed844c70c24b5p+4Q, -0x1.815ee05c85e8aa70418061334f18p+4Q, 0x1.ca4482f4236a5516d7f638fa35c2p+3Q, -0x1.050825dec75a966028608d17675cp+3Q, 0x1.1eeca8acc3a791ffedf80bed61f9p+2Q, -0x1.6df69657c972c8ebec75c92acc68p+0Q, 0x1.75a7ac677c4eee273d03fc67aefp-5Q, 0x1.ebd49f3810c888c69855753565b4p-5Q, -0x1.4344372e1b6fc786ddf90f2b7b7p-10Q, -0x1.20264586c6bb91b0aa0b4d1a440fp-18Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.3841475e9a3639fcb27c2a85a863p+1Q, -0x1.dd3c5aa19c52e5c8a273f6da1b5ap+3Q, 0x1.303529a28e46fac3a8f56ea5a2b3p+5Q, -0x1.a86d9ebb6edc3ca33aa7af7132e4p+5Q, 0x1.7d0e6c4e24170b40a4b9574c4b78p+5Q, -0x1.25c8439d2df89fa5007905a011dap+5Q, 0x1.f5b3e1ac9966686ed844c7042856p+4Q, -0x1.815ee05c85e8aa704180612d3a88p+4Q, 0x1.ca4482f4236a5516d7f638f2b575p+3Q, -0x1.050825dec75a966028608d12e5c4p+3Q, 0x1.1eeca8acc3a791ffedf80be8793bp+2Q, -0x1.6df69657c972c8ebec75c924bb61p+0Q, 0x1.75a7ac677c4eee273d03fc609c7dp-5Q, 0x1.ebd49f3810c888c69855752e166p-5Q, -0x1.4344372e1b6fc786ddf90f275fd2p-10Q, -0x1.20264586c6bb91b0aa0b4d170d57p-18Q, 0x0p+0Q};
             }
             if constexpr (order == 7) {
-                return {0x0p+0Q, 0x1.041f759e862aa2196b99e328e887p+0Q, -0x1.96fe795439508b28db42654510a5p+2Q, 0x1.04a7fd5b5e5923f7f627bd68cd65p+4Q, -0x1.5c5ede521aae5e58438f371fca07p+4Q, 0x1.0b593b29c51bbefd0a21a466fe1fp+4Q, -0x1.3ddf512850559b028d830987fbd1p+3Q, 0x1.12f0bcbe3fa44419a6b523028ff1p+3Q, -0x1.d4ebfbf56d99633e38e575351ca4p+2Q, 0x1.d31827f76dc61557ae5c1ea5b48p+1Q, -0x1.6bf237312f18cf3b573ffc6b9b12p+0Q, 0x1.d1d5c0ac4dc0c7147f916f8d0ae2p-1Q, -0x1.794e93c6506dcbe26714d9f578b4p-2Q, -0x1.2e59e90e0a11c8b7ce9f91036827p-6Q, 0x1.26fbfe966bb82001d50ae9267a6ep-5Q, -0x1.e662faa96110f417469ce7821db9p-10Q, -0x1.a81802ebf94f0a8bc8124e278c59p-17Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.041f759e862aa2196b99e32b0e5p+0Q, -0x1.96fe795439508b28db4265486c81p+2Q, 0x1.04a7fd5b5e5923f7f627bd6af411p+4Q, -0x1.5c5ede521aae5e58438f3722aadep+4Q, 0x1.0b593b29c51bbefd0a21a469361ap+4Q, -0x1.3ddf512850559b028d83098aa4f2p+3Q, 0x1.12f0bcbe3fa44419a6b52304dc22p+3Q, -0x1.d4ebfbf56d99633e38e5753902fdp+2Q, 0x1.d31827f76dc61557ae5c1ea99bcdp+1Q, -0x1.6bf237312f18cf3b573ffc6eb123p+0Q, 0x1.d1d5c0ac4dc0c7147f916f90f5c1p-1Q, -0x1.794e93c6506dcbe26714d9f89e44p-2Q, -0x1.2e59e90e0a11c8b7ce9f9105aca7p-6Q, 0x1.26fbfe966bb82001d50ae928dc43p-5Q, -0x1.e662faa96110f417469ce785ece9p-10Q, -0x1.a81802ebf94f0a8bc8124e2acfbp-17Q, 0x0p+0Q};
             }
             if constexpr (order == 8) {
-                return {0x0p+0Q, 0x1.9024e0f887aa33deb80194db918fp-3Q, -0x1.3caa56e1c68f9f7ad07fd6873ac5p+0Q, 0x1.947e636a9e373f489450f99a494ep+1Q, -0x1.033a79f260cef0d616212b14ddbcp+2Q, 0x1.51b6c9e0d0443759a67a3c353747p+1Q, -0x1.0bd62fc1e045579c86e940e528b1p+0Q, 0x1.028bee5b6619ea0406791e99bae6p+0Q, -0x1.1620d9bfc03eb662d8d654bb92cfp+0Q, 0x1.b5ef819dccd9a27cb2716f32c63ap-2Q, -0x1.b7954b06be8aeb961960232cc863p-6Q, 0x1.054d18d1cc90c79a1ef0360672efp-4Q, -0x1.4817258dd284697ebc00b788ce26p-5Q, -0x1.8ce86e181d4254ae37719aa328a7p-6Q, 0x1.2926b8981e2a739eefaa1e5b74bcp-6Q, -0x1.20ae937e7a9305bbde13268ad288p-9Q, -0x1.e260b0ee2a092f8355b87bff022bp-16Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.9024e0f887aa33deb80194db4775p-3Q, -0x1.3caa56e1c68f9f7ad07fd686ffdbp+0Q, 0x1.947e636a9e373f489450f999fe93p+1Q, -0x1.033a79f260cef0d616212b14afddp+2Q, 0x1.51b6c9e0d0443759a67a3c3505fdp+1Q, -0x1.0bd62fc1e045579c86e940e51c15p+0Q, 0x1.028bee5b6619ea0406791e99a571p+0Q, -0x1.1620d9bfc03eb662d8d654bb6c17p+0Q, 0x1.b5ef819dccd9a27cb2716f32a404p-2Q, -0x1.b7954b06be8aeb961960232f51e9p-6Q, 0x1.054d18d1cc90c79a1ef036069b3dp-4Q, -0x1.4817258dd284697ebc00b788ccd7p-5Q, -0x1.8ce86e181d4254ae37719aa28183p-6Q, 0x1.2926b8981e2a739eefaa1e5b0722p-6Q, -0x1.20ae937e7a9305bbde13268a4994p-9Q, -0x1.e260b0ee2a092f8355b87bfdf959p-16Q, 0x0p+0Q};
             }
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            if constexpr (order == 0) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0696256148532700351919396744932899458901475071882009455460949442257725090643"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.847094118712392865488445491666448260772283771603129862851579519790390191884"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.192887945487446735108207067592716438385147148387205741175709003694874991303"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.161588838553871279142256267689733836106164148233593303014435155929549184904"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0621454565631309617634380881808335928424960159357894362352948406059776368030"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00584271191016988667489934317676681761380261859736020254107802203440485911830"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00810116915396986484284110901604422633398896546175619238854935214695602535306"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00484078918138035149158848553294039923334976019542221808517285604431896830998"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00113326987089607350360311514735367410308696721786347944018825854440169314785"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000518834218559123344579363088412935129165280069792765898378420125485731010746"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000227923963427004781576572210149586228991148638291199976434901264070906009219"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000253300201030598522589097875316626630820822335580422623437912828366256338066"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000802700432516996219234776794962786936078351284525549608976066927226092457516"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000215037600823040848531416812145312700229132524083435563752554400656355171355"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000523461705899403093230911172363595454183744690618924167900623489664585671892"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000291179201205891612682286686378360986960244052826956539582335356631085936448"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 1) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.292545191037796939535389393392524159619768256766940538370253353709461193032"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.842946769694824537045009424862247504440189060559035409366548153562971046333"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.82717007927797538158634749745144900658761906951781067368239430170496580026"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.08813495512805388191036942833223671123809253137161269595551241180555412336"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.561151240784950357351319288602199217315277177939018273801699428225616351849"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.188860218344526891969457899968714396869941678733540325124502082703253093959"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0103777180965810325757147992456275086095651002024262019464570618682172893560"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0201120640460875141204975265352055179708974180844365324656095077183481665071"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00620480720533278240593000416203558121866225849233783767746501903652779797358"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000511715457593831878348526994379850228214262314833874209020963369744116177094"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000417303231628420130847533411474569395038335447444917096887081609399824377911"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000246313954834336786578230076000285162282668339295707375389296462305068325569"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000181321745272135394237503981158619963539109967763295911042193620477541392180"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000642141275320865350440248672780732024814675393949502653848285464530637503456"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000659853289473506178162438806415358166040221310868614460485355680895239971041"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000733834535433323085982655900391187245584811969936387919615025045530814656992"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 2) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.946777767283390540714404221584615079023092608593179874933591611929424472485"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.66734312983271267309321411121395907583555820122567011112376971940996707956"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.268906942633839773948889603119308083663479474183417680672346331112533372730"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.678232351310991258941508584688642891898119286261551673777759411644213054589"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.111613897536158060295536493503011833000297341597327636552216220361799209380"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.327151926943136388570224093819464516869683572537433435414357010300674438746"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.345376128308493052665256776473446621249215438981458413871842565755981610451"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.175029942835241930595606890611047181166656164868469200496810519729335464519"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0451912907544972500160407679210623907538006067792182784497573909710514110903"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00148686700510683159736033420530033526602254575192174933907208287640696148334"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00228652648349626930958233420749265339034884848058225128735489316309216194635"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000415650174634043890487751208209411279937212554767153184423913890865016834975"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000132513170838045914618299238086704647297885466647476958534437752575150892279"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000109566515677943851419827253312757926681754226925567626886322889119467587352"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000451707521924643308252924541765504862848358919185132320746715765398014639333"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000100398888555583838447015712041044761982662545295143252368229865482374008093"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 3) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.31124487072584709340072024375652751167903029344934811013210724247867834712"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.43523878627351700486667408986119165102766488328680852307793395602884092368"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("15.23826205859770997419029499536885930324282552790731045653500894195106217230"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.50904566243388026482185821161121048927181414560909106839809459077939567212"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.74982582374142746596539847819058427772645564907288598203930173309437241112"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("23.80644212728254095208630893797731947546863789816665646941416033108845852560"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-25.52319487474132573315598925827481047528889709949317322024171789375930496050"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("14.61910058495285111510583787914644598320193823700758034804561275077288093820"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.76276582686596230192956587364009471111423882274083500758285711718430914481"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.401876028480840022977724595683369746855848802187118863206831503976422808900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.498319251694501402266194337927777390492533960487059487842842210706425452006"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0908061759740775534638772529734415696617219068242862250162791584120467567508"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00110193897253809208118839003583409411342268641822896346372378981763645701667"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000488111977759341608153274160279547453053433093120482116238865902413969365260"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000188691004449025030399350421194685076340345889651763665155607041691780427844"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000837596949144929524562460249627191951019750983422579043777172865056887183216"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 4) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.56099903137313447653308073719069094628298405133690563906561861936445946007"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-18.67011430886230370235720362402145866382565255864894062875836808783810172070"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("41.74537061801752618764215796492553160234168704484092726499577820178240950150"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-53.90428407368513143095733499969054312179860229999410756267069469773697487590"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("49.86479138446745347495028288278129648962436375452866744453087449252422749480"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-42.51494627825539832489623511405198662612329830348598981334872895902788851530"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("34.36439470987306965384334763928109227423995285653319098010560258917408804280"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-19.36149639666662401531934915671584710840660950619246136186169380992926261930"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.68877812073793714221449969323656655140811213570309303147472950766460448556"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.82687112784961267420163066364729873031830257798046834667883219375131634861"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.01725412548136472359247020220053150679272256461259072142878792076970321518"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.425915304312019461782564152045098653193242220169129362972564850123877163104"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00461059892462853652486233333670046935605106056900099120735719921725474826272"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00443583036535695045092535332549546407656776796969226954011005583519642324338"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000212967564409202157603357608120205592853860427112088867632348335621428459043"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000188536136927150567144741756924115740343376900701049770411358310019917707856"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 5) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.34519314192774371644605664344260685807624755151402674229796990772442490669"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-25.30316658554586670195060554724977775864649185540159313706154605487824252430"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("59.63218434501321241686227040141305669678309492280566274270121970853125985750"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-69.63673507804717481631012221036570369169261940901946481187737315982813252500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("36.59453586069957542305839900792960952397807013166550399544566076698109838520"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.00552989754787890241812019217185423330772733818008108791628359534655241737"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.14543593928850838676384113079945586921929171803713962006454488900252833519"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("11.20654715843691044532849119891603196174261061865084786297107780266854541590"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-24.55386766400291639497667909532438173366128839958254164111061988488776479890"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("27.58418988518466039332570510309944494563540512877954948263846939300864839690"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-15.40023551513117748173055818458330381918522055139888794492596135452925084020"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.90793960089811251141014062726261819004190764494555441923947299947294357551"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.145931939616769342677381879905952490456893639361103035834837241907687647570"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0803519172607930217143096597939609700610595254316391845465369362291239673402"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000663376352849585270549158082005899457474231838909594090590164906243989945765"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000116792802055684000576004901649051578220621239562395324237331611330461969728"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 6) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.43949215049035378308490877112616480587247519253349272700089974373761727070"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-14.91361743511751278653863337775082100851257612848163914659667962039370407430"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("38.02595831867881537937530443404440268525161384656893310351288920599098373240"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-53.05352541381901538280530176799613503869273806435001792774565773108485860860"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("47.63204251334798800088842822439490203451348559647805617494608965893769108390"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-36.72278521343748975726593618407350035873027478333718779024037203624257707460"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("31.35641639157838698914459960374580961178260675889546093721185892770212198730"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-24.08566318647221270199387206585348313707566820901513697285058134722858155000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("14.32086322482366348310210031894559072891597107117636756749550089821175221100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-8.15724462043256685901583341088487623405631051772335513386812463292410806832"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.48319451209555908109543430241568887648627099692558144854507468628906508116"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.42954387324557353924315901131597022588839567829311825849808138225813793539"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0456121794958422788519835738614979042067103492896491552781823773644117194263"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0600379094835484277448500775653734021516869903849852917021361921275127990832"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00123316370766296458175735033761430852810590026894516671661974149487692611779"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000429376212343184311613788702973769675152078312600917651519873431746001425928"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 7) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.01610503311364167160627137764879687271588589977337586555528700566771231261"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.35928185677517694205349753594529349921775157958594734217344676184083432133"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("16.29101310435141502366280370334959338566491174925988910204852058573624530770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-21.77316124031030816094586803202252059552525483663335766522914705661431629930"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("16.70928493801487468593777022092645595574965917216718445219727297028380055500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.93351037858763008636351351386408163754727545153280350373395004801729390569"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.59188687475137459206298080378293728057617745867309534594204113820751716392"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.32690333335485473282043083732510305617086761800316899520505182249948309741"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.64917468625530775745714112854788870052100478150662596792140805409798695237"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.42166466666012357755455417666976389843036696424169510073074551625991444526"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.909833928139848029659705433844716551575919061966592740387936617767990646124"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.368463810900818519321280729699948238382245337243194077152888098658300603538"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0184540534902747235287786613095163827842721391935005620122745696525182529649"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0360088322080320960591978261837204402906245566453303385097283622763009148578"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00185541777531833871298150644744023226659198738569918082665820219229654776018"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000126389799887751449655010004416467695567661727273854980326583025983179615470"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 8) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.195382840714008222445649562861088516286064981461948780814133345930973823658"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.23697417270756070794757091967677027603167042250757849222269393098384194621"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.16010706621130486269935853293254242082033173364580217315573625619258790152"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.05044411344282111665932979112008908801732860080823387948554260440261464757"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.63839076497291256523926291558126191854618618017387332992219855643874357679"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.04623697741796683485007131051068458751031503463108641697374490811821670148"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.00994767886559314051425312348881627025613387213269219272738325207774312849"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.08643876010341497975910071082821695937290873893825930817786907767606917664"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.427671456581458673009899734932815948658546455375010876404838027129297913818"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0268300278357648758353382533868083591820649404851508751125983578913516081871"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0637942285073089320624911876442649124426662264770688199203469027353144526797"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0400500997044024766957707475186007575121602332713762255038636186221048809222"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0242253375185620584577236293255475747352363289859909376495538304199524801451"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0181366732290110494820691728220505559010664322036613445274186399424581173253"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00220246839966366946271442320741368580934032927301220467330879016842440794250"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000287519514407257853644446887092547399712525693691776728798621645433043384651"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+        }
     }
     if constexpr (p == 10) {
         if constexpr (std::is_same_v<Real, float>) {
             if constexpr (order == 0) {
-                return {0x0p+0f, 0x1.12cb0ap-5f, 0x1.4e2c28p-1f, 0x1.1c4636p-1f, -0x1.85d2eep-2f, 0x1.9e3daep-3f, -0x1.494bcp-4f, 0x1.1d23ep-6f, 0x1.d4ed16p-10f, -0x1.2885ecp-9f, 0x1.94f202p-12f, 0x1.44e94ep-14f, -0x1.b37dfap-16f, 0x1.403906p-24f, 0x1.c9437p-24f, -0x1.58dbb8p-28f, 0x1.db3584p-37f, 0x1.afee7cp-44f, -0x1.098874p-59f, 0x0p+0f};
+                return {0x0p+0f, 0x1.12cb0ap-5f, 0x1.4e2c28p-1f, 0x1.1c4636p-1f, -0x1.85d2eep-2f, 0x1.9e3daep-3f, -0x1.494bcp-4f, 0x1.1d23ep-6f, 0x1.d4ed16p-10f, -0x1.2885ecp-9f, 0x1.94f202p-12f, 0x1.44e94ep-14f, -0x1.b37dfap-16f, 0x1.403906p-24f, 0x1.c9437p-24f, -0x1.58dbb8p-28f, 0x1.db3584p-37f, 0x1.afee7cp-44f, -0x1.098874p-59f, -0x0p+0f};
             }
             if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.43cfccp-3f, 0x1.f5f9c2p-1f, -0x1.94bc28p+0f, 0x1.61584ep-1f, -0x1.a2cb68p-2f, 0x1.eef0eap-3f, -0x1.ac223p-4f, 0x1.c84ec2p-6f, -0x1.213456p-8f, 0x1.2c315ap-10f, -0x1.f37546p-12f, 0x1.ce036p-15f, 0x1.06ba9ap-17f, 0x1.2eea96p-21f, 0x1.f125fap-26f, -0x1.51db7ap-33f, -0x1.3ced9ep-40f, 0x1.85b824p-55f, -0x0p+0f};
+                return {0x0p+0f, 0x1.43cfccp-3f, 0x1.f5f9c2p-1f, -0x1.94bc28p+0f, 0x1.61584ep-1f, -0x1.a2cb68p-2f, 0x1.eef0eap-3f, -0x1.ac223p-4f, 0x1.c84ec2p-6f, -0x1.213456p-8f, 0x1.2c315ap-10f, -0x1.f37546p-12f, 0x1.ce036p-15f, 0x1.06ba9ap-17f, 0x1.2eea96p-21f, 0x1.f125fap-26f, -0x1.51db7ap-33f, -0x1.3ced9ep-40f, 0x1.85b824p-55f, 0x0p+0f};
             }
             if constexpr (order == 2) {
                 return {0x0p+0f, 0x1.2d6cb8p-1f, -0x1.01b00cp-2f, -0x1.0fd09ap+1f, 0x1.8bd77ap+1f, -0x1.c8684ep+0f, 0x1.6e6d86p-2f, 0x1.86e852p-2f, -0x1.9dcbe6p-2f, 0x1.55c762p-3f, -0x1.35a482p-6f, -0x1.51b88cp-7f, 0x1.076728p-8f, -0x1.67961ap-12f, -0x1.2b4a08p-15f, 0x1.bb4b6cp-19f, 0x1.3f418cp-28f, -0x1.0d99c2p-32f, 0x1.4b9c06p-46f, 0x0p+0f};
@@ -668,10 +816,10 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0f, 0x1.f3cda2p+1f, -0x1.9eeda2p+4f, 0x1.260fdap+6f, -0x1.d673d8p+6f, 0x1.f01b3p+6f, -0x1.addb2cp+6f, 0x1.7db87cp+6f, -0x1.3f986p+6f, 0x1.ae7316p+5f, -0x1.fb5cc4p+4f, 0x1.259afcp+4f, -0x1.fe186ep+2f, 0x1.4d0298p+0f, 0x1.a1f0a6p-2f, -0x1.40c0aep-3f, 0x1.ba72fap-9f, 0x1.c193f2p-13f, -0x1.16b49ap-22f, 0x0p+0f};
             }
             if constexpr (order == 7) {
-                return {0x0p+0f, 0x1.3586dap+1f, -0x1.08fa64p+4f, 0x1.7c41fp+5f, -0x1.276b64p+6f, 0x1.14f1dp+6f, -0x1.83d54ap+5f, 0x1.4053c8p+5f, -0x1.209b54p+5f, 0x1.657834p+4f, -0x1.2ddf68p+3f, 0x1.38745p+2f, -0x1.4065c2p+1f, 0x1.6763c6p-4f, 0x1.181d4ep-1f, -0x1.87564p-3f, 0x1.843d22p-7f, 0x1.52be3cp-11f, -0x1.a79c62p-20f, -0x0p+0f};
+                return {0x0p+0f, 0x1.3586dap+1f, -0x1.08fa64p+4f, 0x1.7c41fp+5f, -0x1.276b64p+6f, 0x1.14f1dp+6f, -0x1.83d54ap+5f, 0x1.4053c8p+5f, -0x1.209b54p+5f, 0x1.657834p+4f, -0x1.2ddf68p+3f, 0x1.38745p+2f, -0x1.4065c2p+1f, 0x1.6763c6p-4f, 0x1.181d4ep-1f, -0x1.87564p-3f, 0x1.843d22p-7f, 0x1.52be3cp-11f, -0x1.a79c62p-20f, 0x0p+0f};
             }
             if constexpr (order == 8) {
-                return {0x0p+0f, 0x1.7a3cf4p+0f, -0x1.48b25ep+3f, 0x1.cbd932p+4f, -0x1.37885ep+5f, 0x1.4db4fcp+4f, 0x1.74ac2ep+2f, -0x1.11ca3p+3f, 0x1.9fa6aap-4f, -0x1.8ceb32p+2f, 0x1.e686e4p+3f, -0x1.7e0b78p+3f, 0x1.7e1a34p+2f, -0x1.247b58p+2f, 0x1.b8a4e2p+1f, -0x1.4f17d6p+0f, 0x1.4b4084p-3f, 0x1.726478p-7f, -0x1.d74fd6p-15f, -0x0p+0f};
+                return {0x0p+0f, 0x1.7a3cf4p+0f, -0x1.48b25ep+3f, 0x1.cbd932p+4f, -0x1.37885ep+5f, 0x1.4db4fcp+4f, 0x1.74ac2ep+2f, -0x1.11ca3p+3f, 0x1.9fa6aap-4f, -0x1.8ceb32p+2f, 0x1.e686e4p+3f, -0x1.7e0b78p+3f, 0x1.7e1a34p+2f, -0x1.247b58p+2f, 0x1.b8a4e2p+1f, -0x1.4f17d6p+0f, 0x1.4b4084p-3f, 0x1.726478p-7f, -0x1.d74fd6p-15f, 0x0p+0f};
             }
             if constexpr (order == 9) {
                 return {0x0p+0f, 0x1.f6438ap-4f, -0x1.b7ba92p-1f, 0x1.3f509cp+1f, -0x1.eac616p+1f, 0x1.ae9244p+1f, -0x1.00d5dp+1f, 0x1.9413f4p+0f, -0x1.9bd984p+0f, 0x1.16aae2p+0f, -0x1.158768p-1f, 0x1.8145e4p-2f, -0x1.faf556p-3f, 0x1.8ec972p-4f, -0x1.49980ep-5f, 0x1.5730c4p-6f, -0x1.0952d6p-8f, -0x1.ce071ep-12f, 0x1.30a436p-18f, -0x0p+0f};
@@ -679,10 +827,10 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         }
         if constexpr (std::is_same_v<Real, double>) {
             if constexpr (order == 0) {
-                return {0x0p+0, 0x1.12cb0a33640b5p-5, 0x1.4e2c27be21e0ep-1, 0x1.1c4636ef189edp-1, -0x1.85d2edb33e46ep-2, 0x1.9e3dada7662aap-3, -0x1.494bbf8e53bfcp-4, 0x1.1d23df75685c9p-6, 0x1.d4ed15a068488p-10, -0x1.2885ec2406341p-9, 0x1.94f202846521cp-12, 0x1.44e94de53f6f6p-14, -0x1.b37df99b75f09p-16, 0x1.403905df41d32p-24, 0x1.c94370d7ecc92p-24, -0x1.58dbb791a7fb7p-28, 0x1.db358382953c4p-37, 0x1.afee7cd299cd6p-44, -0x1.0988745ca3ec4p-59, 0x0p+0};
+                return {0x0p+0, 0x1.12cb0a33640b5p-5, 0x1.4e2c27be21e0ep-1, 0x1.1c4636ef189edp-1, -0x1.85d2edb33e46ep-2, 0x1.9e3dada7662aap-3, -0x1.494bbf8e53bfcp-4, 0x1.1d23df75685c9p-6, 0x1.d4ed15a068488p-10, -0x1.2885ec2406341p-9, 0x1.94f202846521cp-12, 0x1.44e94de53f6f6p-14, -0x1.b37df99b75f09p-16, 0x1.403905df41d32p-24, 0x1.c94370d7ecc92p-24, -0x1.58dbb791a7fb7p-28, 0x1.db358382953c4p-37, 0x1.afee7cd299cd6p-44, -0x1.0988745ca3ec4p-59, -0x0p+0};
             }
             if constexpr (order == 1) {
-                return {0x0p+0, 0x1.43cfcb9d73923p-3, 0x1.f5f9c20090df3p-1, -0x1.94bc27297b9f9p+0, 0x1.61584eb9fe3a6p-1, -0x1.a2cb67ff996a9p-2, 0x1.eef0eaaf4989ep-3, -0x1.ac22308c89e82p-4, 0x1.c84ec23c8cdbep-6, -0x1.213456d8479d6p-8, 0x1.2c315a17e4064p-10, -0x1.f375455c5c9e6p-12, 0x1.ce035ff90a79bp-15, 0x1.06ba9aa22e87cp-17, 0x1.2eea964fb1e8p-21, 0x1.f125f98e34b08p-26, -0x1.51db791710beap-33, -0x1.3ced9d37da5d3p-40, 0x1.85b82452d9269p-55, -0x0p+0};
+                return {0x0p+0, 0x1.43cfcb9d73923p-3, 0x1.f5f9c20090df3p-1, -0x1.94bc27297b9f9p+0, 0x1.61584eb9fe3a6p-1, -0x1.a2cb67ff996a9p-2, 0x1.eef0eaaf4989ep-3, -0x1.ac22308c89e82p-4, 0x1.c84ec23c8cdbep-6, -0x1.213456d8479d6p-8, 0x1.2c315a17e4064p-10, -0x1.f375455c5c9e6p-12, 0x1.ce035ff90a79bp-15, 0x1.06ba9aa22e87cp-17, 0x1.2eea964fb1e8p-21, 0x1.f125f98e34b08p-26, -0x1.51db791710beap-33, -0x1.3ced9d37da5d3p-40, 0x1.85b82452d9269p-55, 0x0p+0};
             }
             if constexpr (order == 2) {
                 return {0x0p+0, 0x1.2d6cb779664d4p-1, -0x1.01b00cc8d5d06p-2, -0x1.0fd0995df5aa3p+1, 0x1.8bd77a675e828p+1, -0x1.c8684eac579b4p+0, 0x1.6e6d859b2e73p-2, 0x1.86e851ba85835p-2, -0x1.9dcbe6db37906p-2, 0x1.55c762fd5a0dfp-3, -0x1.35a481158ac34p-6, -0x1.51b88ceed7adep-7, 0x1.0767285c8f106p-8, -0x1.67961ae7bb9ap-12, -0x1.2b4a0836ed60bp-15, 0x1.bb4b6c6c9a6fbp-19, 0x1.3f418b80d3d45p-28, -0x1.0d99c100eff2ep-32, 0x1.4b9c0643323fbp-46, 0x0p+0};
@@ -700,10 +848,10 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0, 0x1.f3cda2f9b1354p+1, -0x1.9eeda12641b62p+4, 0x1.260fdaadd19ebp+6, -0x1.d673d80eeade5p+6, 0x1.f01b2fa154d03p+6, -0x1.addb2c4ad791ep+6, 0x1.7db87bda6fdf9p+6, -0x1.3f9860f6c4906p+6, 0x1.ae731643e9199p+5, -0x1.fb5cc3351ebc1p+4, 0x1.259afcbb8804dp+4, -0x1.fe186e46030ap+2, 0x1.4d0298c218927p+0, 0x1.a1f0a66406a12p-2, -0x1.40c0addfd8554p-3, 0x1.ba72fac37f088p-9, 0x1.c193f16bb678ep-13, -0x1.16b4995bb4f07p-22, 0x0p+0};
             }
             if constexpr (order == 7) {
-                return {0x0p+0, 0x1.3586d9a9e0e3ep+1, -0x1.08fa63342ecc2p+4, 0x1.7c41f01d6960dp+5, -0x1.276b64d22e135p+6, 0x1.14f1cf74869cp+6, -0x1.83d54ac636b82p+5, 0x1.4053c8a2c8d3p+5, -0x1.209b538b18df2p+5, 0x1.65783340b3783p+4, -0x1.2ddf670e51dfdp+3, 0x1.38744fdae2125p+2, -0x1.4065c212ba5cp+1, 0x1.6763c5d11b775p-4, 0x1.181d4d676ea1fp-1, -0x1.87564028831fcp-3, 0x1.843d22529bb4ap-7, 0x1.52be3b0b8c7afp-11, -0x1.a79c626c8654fp-20, -0x0p+0};
+                return {0x0p+0, 0x1.3586d9a9e0e3ep+1, -0x1.08fa63342ecc2p+4, 0x1.7c41f01d6960dp+5, -0x1.276b64d22e135p+6, 0x1.14f1cf74869cp+6, -0x1.83d54ac636b82p+5, 0x1.4053c8a2c8d3p+5, -0x1.209b538b18df2p+5, 0x1.65783340b3783p+4, -0x1.2ddf670e51dfdp+3, 0x1.38744fdae2125p+2, -0x1.4065c212ba5cp+1, 0x1.6763c5d11b775p-4, 0x1.181d4d676ea1fp-1, -0x1.87564028831fcp-3, 0x1.843d22529bb4ap-7, 0x1.52be3b0b8c7afp-11, -0x1.a79c626c8654fp-20, 0x0p+0};
             }
             if constexpr (order == 8) {
-                return {0x0p+0, 0x1.7a3cf471120ecp+0, -0x1.48b25e52d274bp+3, 0x1.cbd93276e7d59p+4, -0x1.37885d5242031p+5, 0x1.4db4fb7a5ecdcp+4, 0x1.74ac2dca21f56p+2, -0x1.11ca2f9f0b7dp+3, 0x1.9fa6aaf0c8d98p-4, -0x1.8ceb3288570cdp+2, 0x1.e686e3fbc3fbfp+3, -0x1.7e0b780d60232p+3, 0x1.7e1a3482e160cp+2, -0x1.247b57131543cp+2, 0x1.b8a4e1c96768dp+1, -0x1.4f17d502240a9p+0, 0x1.4b408438ac869p-3, 0x1.7264788c9473ep-7, -0x1.d74fd6a021548p-15, -0x0p+0};
+                return {0x0p+0, 0x1.7a3cf471120ecp+0, -0x1.48b25e52d274bp+3, 0x1.cbd93276e7d59p+4, -0x1.37885d5242031p+5, 0x1.4db4fb7a5ecdcp+4, 0x1.74ac2dca21f56p+2, -0x1.11ca2f9f0b7dp+3, 0x1.9fa6aaf0c8d98p-4, -0x1.8ceb3288570cdp+2, 0x1.e686e3fbc3fbfp+3, -0x1.7e0b780d60232p+3, 0x1.7e1a3482e160cp+2, -0x1.247b57131543cp+2, 0x1.b8a4e1c96768dp+1, -0x1.4f17d502240a9p+0, 0x1.4b408438ac869p-3, 0x1.7264788c9473ep-7, -0x1.d74fd6a021548p-15, 0x0p+0};
             }
             if constexpr (order == 9) {
                 return {0x0p+0, 0x1.f6438a3a8846p-4, -0x1.b7ba9255f9c78p-1, 0x1.3f509b3842149p+1, -0x1.eac616f0d4f87p+1, 0x1.ae9244fef585dp+1, -0x1.00d5d03220f3cp+1, 0x1.9413f3bab26fdp+0, -0x1.9bd9847a10dd5p+0, 0x1.16aae27d18a67p+0, -0x1.1587682f48216p-1, 0x1.8145e3cc3cfccp-2, -0x1.faf556e68970ep-3, 0x1.8ec972676b06bp-4, -0x1.49980ed40883dp-5, 0x1.5730c48bae56ap-6, -0x1.0952d6b855c64p-8, -0x1.ce071dd8df1efp-12, 0x1.30a4361eb25b4p-18, -0x0p+0};
@@ -711,10 +859,10 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         }
         if constexpr (std::is_same_v<Real, long double>) {
             if constexpr (order == 0) {
-                return {0x0p+0L, 0x8.9658519b205ab72p-8L, 0xa.71613df10f0723dp-4L, 0x8.e231b778c4f6662p-4L, -0xc.2e976d99f236ef3p-5L, 0xc.f1ed6d3b3154c33p-6L, -0xa.4a5dfc729dfe012p-7L, 0x8.e91efbab42e4488p-9L, 0xe.a768ad03424408ap-13L, -0x9.442f612031a0acp-12L, 0xc.a7901423290dc7ep-15L, 0xa.274a6f29fb7b195p-17L, -0xd.9befccdbaf8457bp-19L, 0xa.01c82efa0e991ep-27L, 0xe.4a1b86bf6648ca3p-27L, -0xa.c6ddbc8d3fdb61fp-31L, 0xe.d9ac1c14a9e22dfp-40L, 0xd.7f73e694ce6b23p-47L, -0x8.4c43a2e51f61f4ap-62L, 0x0p+0L};
+                return {0x0p+0L, 0x8.9658519b205ab72p-8L, 0xa.71613df10f0723dp-4L, 0x8.e231b778c4f6662p-4L, -0xc.2e976d99f236ef3p-5L, 0xc.f1ed6d3b3154c33p-6L, -0xa.4a5dfc729dfe012p-7L, 0x8.e91efbab42e4488p-9L, 0xe.a768ad03424408ap-13L, -0x9.442f612031a0acp-12L, 0xc.a7901423290dc7ep-15L, 0xa.274a6f29fb7b195p-17L, -0xd.9befccdbaf8457bp-19L, 0xa.01c82efa0e991ep-27L, 0xe.4a1b86bf6648ca3p-27L, -0xa.c6ddbc8d3fdb61fp-31L, 0xe.d9ac1c14a9e22dfp-40L, 0xd.7f73e694ce6b23p-47L, -0x8.4c43a2e51f61f4ap-62L, -0x0p+0L};
             }
             if constexpr (order == 1) {
-                return {0x0p+0L, 0xa.1e7e5ceb9c91909p-6L, 0xf.afce100486f966ap-4L, -0xc.a5e1394bdcfcb6dp-3L, 0xb.0ac275cff1d33d6p-4L, -0xd.165b3ffccb5480ap-5L, 0xf.7787557a4c4f14ep-6L, -0xd.611184644f4100cp-7L, 0xe.427611e466df078p-9L, -0x9.09a2b6c23cead05p-11L, 0x9.618ad0bf2031fa3p-13L, -0xf.9baa2ae2e4f30dfp-15L, 0xe.701affc853cdb21p-18L, 0x8.35d4d511743e237p-20L, 0x9.7754b27d8f401bap-24L, 0xf.892fcc71a583f65p-29L, -0xa.8edbc8b885f4c32p-36L, -0x9.e76ce9bed2e946cp-43L, 0xc.2dc12296c934a42p-58L, -0x0p+0L};
+                return {0x0p+0L, 0xa.1e7e5ceb9c91909p-6L, 0xf.afce100486f966ap-4L, -0xc.a5e1394bdcfcb6dp-3L, 0xb.0ac275cff1d33d6p-4L, -0xd.165b3ffccb5480ap-5L, 0xf.7787557a4c4f14ep-6L, -0xd.611184644f4100cp-7L, 0xe.427611e466df078p-9L, -0x9.09a2b6c23cead05p-11L, 0x9.618ad0bf2031fa3p-13L, -0xf.9baa2ae2e4f30dfp-15L, 0xe.701affc853cdb21p-18L, 0x8.35d4d511743e237p-20L, 0x9.7754b27d8f401bap-24L, 0xf.892fcc71a583f65p-29L, -0xa.8edbc8b885f4c32p-36L, -0x9.e76ce9bed2e946cp-43L, 0xc.2dc12296c934a42p-58L, 0x0p+0L};
             }
             if constexpr (order == 2) {
                 return {0x0p+0L, 0x9.6b65bbcb326a224p-4L, -0x8.0d806646ae83286p-5L, -0x8.7e84caefad51526p-2L, 0xc.5ebbd33af4141bap-2L, -0xe.43427562bcd9f08p-3L, 0xb.736c2cd97397c01p-5L, 0xc.37428dd42c1a763p-5L, -0xc.ee5f36d9bc83386p-5L, 0xa.ae3b17ead06fb26p-6L, -0x9.ad2408ac5619da4p-9L, -0xa.8dc46776bd6ee4dp-10L, 0x8.3b3942e4788322ap-11L, -0xb.3cb0d73ddccfdfep-15L, -0x9.5a5041b76b0571dp-18L, 0xd.da5b6364d37d7c6p-22L, 0x9.fa0c5c069ea261fp-31L, -0x8.6cce08077f97363p-35L, 0xa.5ce0321991fd8ep-49L, 0x0p+0L};
@@ -732,10 +880,10 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0L, 0xf.9e6d17cd89aa012p-2L, -0xc.f76d09320db0f5ep+1L, 0x9.307ed56e8cf58f8p+3L, -0xe.b39ec07756f2504p+3L, 0xf.80d97d0aa681a95p+3L, -0xd.6ed96256bc8f10cp+3L, 0xb.edc3ded37efc53ap+3L, -0x9.fcc307b62482f39p+3L, 0xd.7398b21f48cc731p+2L, -0xf.dae619a8f5e0bb5p+1L, 0x9.2cd7e5dc4026b75p+1L, -0xf.f0c37230184fee7p-1L, 0xa.6814c610c493aa3p-3L, 0xd.0f8533203509157p-5L, -0xa.06056efec2aa1d8p-6L, 0xd.d397d61bf843e3dp-12L, 0xe.0c9f8b5db3c72d8p-16L, -0x8.b5a4cadda783993p-25L, 0x0p+0L};
             }
             if constexpr (order == 7) {
-                return {0x0p+0L, 0x9.ac36cd4f071eccfp-2L, -0x8.47d319a17660e21p+1L, 0xb.e20f80eb4b065edp+2L, -0x9.3b5b2691709a7f2p+3L, 0x8.a78e7ba434e03bep+3L, -0xc.1eaa5631b5c1221p+2L, 0xa.029e45164697e35p+2L, -0x9.04da9c58c6f9312p+2L, 0xb.2bc19a059bc163fp+1L, -0x9.6efb38728efe53fp+0L, 0x9.c3a27ed71092bccp-1L, -0xa.032e1095d2e022bp-2L, 0xb.3b1e2e88dbba717p-7L, 0x8.c0ea6b3b750f81fp-4L, -0xc.3ab2014418fdea7p-6L, 0xc.21e91294dda4d8cp-10L, 0xa.95f1d85c63d7aadp-14L, -0xd.3ce3136432a75eep-23L, -0x0p+0L};
+                return {0x0p+0L, 0x9.ac36cd4f071eccfp-2L, -0x8.47d319a17660e21p+1L, 0xb.e20f80eb4b065edp+2L, -0x9.3b5b2691709a7f2p+3L, 0x8.a78e7ba434e03bep+3L, -0xc.1eaa5631b5c1221p+2L, 0xa.029e45164697e35p+2L, -0x9.04da9c58c6f9312p+2L, 0xb.2bc19a059bc163fp+1L, -0x9.6efb38728efe53fp+0L, 0x9.c3a27ed71092bccp-1L, -0xa.032e1095d2e022bp-2L, 0xb.3b1e2e88dbba717p-7L, 0x8.c0ea6b3b750f81fp-4L, -0xc.3ab2014418fdea7p-6L, 0xc.21e91294dda4d8cp-10L, 0xa.95f1d85c63d7aadp-14L, -0xd.3ce3136432a75eep-23L, 0x0p+0L};
             }
             if constexpr (order == 8) {
-                return {0x0p+0L, 0xb.d1e7a38890760ccp-3L, -0xa.4592f29693a58f2p+0L, 0xe.5ec993b73eacb21p+1L, -0x9.bc42ea921018403p+2L, 0xa.6da7dbd2f66dc91p+1L, 0xb.a5616e510faadd9p-1L, -0x8.8e517cf85be82f9p+0L, 0xc.fd35578646cc028p-7L, -0xc.67599442b866996p-1L, 0xf.34371fde1fdf9acp+0L, -0xb.f05bc06b0118d26p+0L, 0xb.f0d1a4170b05fe8p-1L, -0x9.23dab898aa1de5fp-1L, 0xd.c5270e4b3b4644bp-2L, -0xa.78bea8112054738p-3L, 0xa.5a0421c564344a9p-6L, 0xb.9323c464a39ee53p-10L, -0xe.ba7eb5010aa3e4p-18L, -0x0p+0L};
+                return {0x0p+0L, 0xb.d1e7a38890760ccp-3L, -0xa.4592f29693a58f2p+0L, 0xe.5ec993b73eacb21p+1L, -0x9.bc42ea921018403p+2L, 0xa.6da7dbd2f66dc91p+1L, 0xb.a5616e510faadd9p-1L, -0x8.8e517cf85be82f9p+0L, 0xc.fd35578646cc028p-7L, -0xc.67599442b866996p-1L, 0xf.34371fde1fdf9acp+0L, -0xb.f05bc06b0118d26p+0L, 0xb.f0d1a4170b05fe8p-1L, -0x9.23dab898aa1de5fp-1L, 0xd.c5270e4b3b4644bp-2L, -0xa.78bea8112054738p-3L, 0xa.5a0421c564344a9p-6L, 0xb.9323c464a39ee53p-10L, -0xe.ba7eb5010aa3e4p-18L, 0x0p+0L};
             }
             if constexpr (order == 9) {
                 return {0x0p+0L, 0xf.b21c51d44230049p-7L, -0xd.bdd492afce3bd22p-4L, 0x9.fa84d9c210a45adp-2L, -0xf.5630b786a7c34dfp-2L, 0xd.749227f7ac2e953p-2L, -0x8.06ae8191079dde4p-2L, 0xc.a09f9dd5937e42dp-3L, -0xc.decc23d086ea9cp-3L, 0x8.b55713e8c533b1cp-3L, -0x8.ac3b417a410ae11p-4L, 0xc.0a2f1e61e7e5e62p-5L, -0xf.d7aab7344b86da8p-6L, 0xc.764b933b583557ap-7L, -0xa.4cc076a0441e56ep-8L, 0xa.b986245d72b5275p-9L, -0x8.4a96b5c2ae31c5dp-11L, -0xe.7038eec6f8f774fp-15L, 0x9.8521b0f592d9c7fp-21L, -0x0p+0L};
@@ -744,54 +892,86 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         #ifdef BOOST_HAS_FLOAT128
         if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
             if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.12cb0a33640b56e423474a1328fcp-5Q, 0x1.4e2c27be21e0e479b88ad485160cp-1Q, 0x1.1c4636ef189eccc399682014d9c9p-1Q, -0x1.85d2edb33e46dde58a5a504a9aap-2Q, 0x1.9e3dada7662a9865be6b99b2427ep-3Q, -0x1.494bbf8e53bfc023fe7e0915ab57p-4Q, 0x1.1d23df75685c890f2df5ab229b8bp-6Q, 0x1.d4ed15a06848811344377f87f82cp-10Q, -0x1.2885ec240634157f42540c2ec5a5p-9Q, 0x1.94f202846521b8fb6dee9352c083p-12Q, 0x1.44e94de53f6f632a67cbb5854d2p-14Q, -0x1.b37df99b75f08af621654dd8f548p-16Q, 0x1.403905df41d323c0c33072aaf467p-24Q, 0x1.c94370d7ecc9194547661e1cf7bbp-24Q, -0x1.58dbb791a7fb6c3e33eb2a850b1bp-28Q, 0x1.db358382953c45bea25d9891f3a2p-37Q, 0x1.afee7cd299cd64600d2193c416e5p-44Q, -0x1.0988745ca3ec3e945e33c4d42e0fp-59Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.12cb0a33640b56e423474a1328bap-5Q, 0x1.4e2c27be21e0e479b88ad4851607p-1Q, 0x1.1c4636ef189eccc399682014d9d6p-1Q, -0x1.85d2edb33e46dde58a5a504a9ab1p-2Q, 0x1.9e3dada7662a9865be6b99b24294p-3Q, -0x1.494bbf8e53bfc023fe7e0915ab63p-4Q, 0x1.1d23df75685c890f2df5ab229b96p-6Q, 0x1.d4ed15a06848811344377f87f7eap-10Q, -0x1.2885ec240634157f42540c2ec5a5p-9Q, 0x1.94f202846521b8fb6dee9352c088p-12Q, 0x1.44e94de53f6f632a67cbb5854d1fp-14Q, -0x1.b37df99b75f08af621654dd8f54ep-16Q, 0x1.403905df41d323c0c33072aaf3cp-24Q, 0x1.c94370d7ecc9194547661e1cf7cp-24Q, -0x1.58dbb791a7fb6c3e33eb2a850b1bp-28Q, 0x1.db358382953c45bea25d9891f3bcp-37Q, 0x1.afee7cd299cd64600d2193c416f4p-44Q, -0x1.0988745ca3ec3e945e33c4d42e22p-59Q, 0x0p+0Q};
             }
             if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.43cfcb9d739232114ccf7b42f288p-3Q, 0x1.f5f9c20090df2cd39669639ec82fp-1Q, -0x1.94bc27297b9f96d98ca06b8b7823p+0Q, 0x1.61584eb9fe3a67acec590408bcaep-1Q, -0x1.a2cb67ff996a90130726bb55186ep-2Q, 0x1.eef0eaaf4989e29be4ba95e2f142p-3Q, -0x1.ac22308c89e820172f07afea77ffp-4Q, 0x1.c84ec23c8cdbe0f0d252ca4a6014p-6Q, -0x1.213456d8479d5a0a002e8a35429fp-8Q, 0x1.2c315a17e4063f457d1b74aaa599p-10Q, -0x1.f375455c5c9e61be4fa670796ca9p-12Q, 0x1.ce035ff90a79b6418f9714e01ff9p-15Q, 0x1.06ba9aa22e87c46e9b5b517bfa1bp-17Q, 0x1.2eea964fb1e803735b7cbdec44b7p-21Q, 0x1.f125f98e34b07ec90a3117922e68p-26Q, -0x1.51db791710be9863d69c55fb8fa2p-33Q, -0x1.3ced9d37da5d28d7002692ae72b6p-40Q, 0x1.85b82452d92694835d294f84ab3ep-55Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.43cfcb9d739232114ccf7b42f286p-3Q, 0x1.f5f9c20090df2cd39669639ec7fdp-1Q, -0x1.94bc27297b9f96d98ca06b8b780fp+0Q, 0x1.61584eb9fe3a67acec590408bca7p-1Q, -0x1.a2cb67ff996a90130726bb551867p-2Q, 0x1.eef0eaaf4989e29be4ba95e2f12bp-3Q, -0x1.ac22308c89e820172f07afea77d8p-4Q, 0x1.c84ec23c8cdbe0f0d252ca4a5fdap-6Q, -0x1.213456d8479d5a0a002e8a35424cp-8Q, 0x1.2c315a17e4063f457d1b74aaa54fp-10Q, -0x1.f375455c5c9e61be4fa670796c8cp-12Q, 0x1.ce035ff90a79b6418f9714e02027p-15Q, 0x1.06ba9aa22e87c46e9b5b517bf9e8p-17Q, 0x1.2eea964fb1e803735b7cbdec445fp-21Q, 0x1.f125f98e34b07ec90a3117922ea9p-26Q, -0x1.51db791710be9863d69c55fb8f8fp-33Q, -0x1.3ced9d37da5d28d7002692ae731fp-40Q, 0x1.85b82452d92694835d294f84ac62p-55Q, 0x0p+0Q};
             }
             if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.2d6cb779664d44484073db45451fp-1Q, -0x1.01b00cc8d5d0650bb7d9e87582f1p-2Q, -0x1.0fd0995df5aa2a4c5f39f931817fp+1Q, 0x1.8bd77a675e82837408b645325c9ap+1Q, -0x1.c8684eac579b3e1019c502de86a6p+0Q, 0x1.6e6d859b2e72f80278552877475p-2Q, 0x1.86e851ba85834ec58a127f16fee8p-2Q, -0x1.9dcbe6db3790670c84be0eec3058p-2Q, 0x1.55c762fd5a0df64b9c06acd53251p-3Q, -0x1.35a481158ac33b4716b6e91c54eep-6Q, -0x1.51b88ceed7addc9a97168ddbee02p-7Q, 0x1.0767285c8f10645316c4c221faa4p-8Q, -0x1.67961ae7bb99fbfcc0d26144bd1bp-12Q, -0x1.2b4a0836ed60ae3a1490ad53ccb1p-15Q, 0x1.bb4b6c6c9a6faf8c7dd84be23d19p-19Q, 0x1.3f418b80d3d44c3e61fe90bb84e6p-28Q, -0x1.0d99c100eff2e6c61779a48505a8p-32Q, 0x1.4b9c0643323fb1c0ce2d07b0b0abp-46Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.2d6cb779664d44484073db45447cp-1Q, -0x1.01b00cc8d5d0650bb7d9e8758312p-2Q, -0x1.0fd0995df5aa2a4c5f39f93180c2p+1Q, 0x1.8bd77a675e82837408b645325bb2p+1Q, -0x1.c8684eac579b3e1019c502de8594p+0Q, 0x1.6e6d859b2e72f80278552877464cp-2Q, 0x1.86e851ba85834ec58a127f16fe28p-2Q, -0x1.9dcbe6db3790670c84be0eec2f7fp-2Q, 0x1.55c762fd5a0df64b9c06acd53195p-3Q, -0x1.35a481158ac33b4716b6e91c5435p-6Q, -0x1.51b88ceed7addc9a97168ddbed49p-7Q, 0x1.0767285c8f10645316c4c221fa2p-8Q, -0x1.67961ae7bb99fbfcc0d26144bc53p-12Q, -0x1.2b4a0836ed60ae3a1490ad53cc1ep-15Q, 0x1.bb4b6c6c9a6faf8c7dd84be23c4bp-19Q, 0x1.3f418b80d3d44c3e61fe90bb843bp-28Q, -0x1.0d99c100eff2e6c61779a485054cp-32Q, 0x1.4b9c0643323fb1c0ce2d07b0b092p-46Q, 0x0p+0Q};
             }
             if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.a8dadfc02dd0428b41cd0c1bc321p+0Q, -0x1.8d688d31d04a4214094b65c4debbp+2Q, 0x1.317cc4a10faf3ff9c44aa0718d64p+3Q, -0x1.00fa12867f49132d26f6109f247ep+3Q, 0x1.9e984b48af59218135976f5867cdp+1Q, 0x1.0dcc3bbac5e0885ef946fb57406ap+1Q, -0x1.41a435a1df480f6b501eca709ce9p+2Q, 0x1.075a464fd9703954dc501fa92bp+2Q, -0x1.9984cb75bad50ddd23b7c6a93e49p+0Q, 0x1.9cf2e7196d1cbd2ef1ba36ca60f1p-5Q, 0x1.c915787e3612e2d3277f4d85346ap-3Q, -0x1.60b8b0c3b1138df4716646253fep-4Q, 0x1.324229742ef4416185466d935a63p-7Q, 0x1.dd5da666efa58ec47474db0b7be4p-11Q, -0x1.351528a4bd8176153593c8a5aa54p-13Q, -0x1.03c4250827b68f69b983f44799e9p-22Q, 0x1.77139f17861eb1acd308dc031a76p-26Q, -0x1.cd96fccfe9f0afba4ba09dac4612p-39Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.a8dadfc02dd0428b41cd0c1bb0afp+0Q, -0x1.8d688d31d04a4214094b65c4cddp+2Q, 0x1.317cc4a10faf3ff9c44aa07180dp+3Q, -0x1.00fa12867f49132d26f6109f1a1ep+3Q, 0x1.9e984b48af59218135976f585487p+1Q, 0x1.0dcc3bbac5e0885ef946fb573bd9p+1Q, -0x1.41a435a1df480f6b501eca7093bep+2Q, 0x1.075a464fd9703954dc501fa9230ap+2Q, -0x1.9984cb75bad50ddd23b7c6a931c3p+0Q, 0x1.9cf2e7196d1cbd2ef1ba36ca5473p-5Q, 0x1.c915787e3612e2d3277f4d8526a2p-3Q, -0x1.60b8b0c3b1138df4716646253571p-4Q, 0x1.324229742ef4416185466d935171p-7Q, 0x1.dd5da666efa58ec47474db0b6e86p-11Q, -0x1.351528a4bd8176153593c8a5a1a8p-13Q, -0x1.03c4250827b68f69b983f4479114p-22Q, 0x1.77139f17861eb1acd308dc031079p-26Q, -0x1.cd96fccfe9f0afba4ba09dac3a7dp-39Q, 0x0p+0Q};
             }
             if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.a04f8069ea8b4e447d853aa59d25p+1Q, -0x1.18f0a34d9f68e4d06a24b5ca38e6p+4Q, 0x1.4ce3831796a61ef6af32be9c5755p+5Q, -0x1.dc75f9b0b9a1041da91933798254p+5Q, 0x1.fdbc97313e6ed6865f9096b019f1p+5Q, -0x1.eefc0cdda4efa281b21fc8a20dabp+5Q, 0x1.b92a7c1b6a889c31c867c0d1a21p+5Q, -0x1.2299d502734c3c9b7e4c9a715a66p+5Q, 0x1.6502b707871df45089990b52d40bp+3Q, 0x1.11f33f4ede647d59a412fb3a4509p+2Q, -0x1.73b0a319e6889e9aa2e82f291565p+2Q, 0x1.244d452e7630092d6c490c8ed14ap+1Q, -0x1.35466c5650c61e120220d047deb3p-2Q, -0x1.fc20c8dd92f19b8d6ed30b21296p-6Q, 0x1.0d9c8b9d476f7d129de2a5d31814p-7Q, 0x1.a4010b80e5495d0ed9331143d19p-19Q, -0x1.49b0c99eb9c648511ea730b736bdp-19Q, 0x1.962a6dd57b7daa6dc5023a342508p-31Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.a04f8069ea8b4e447d853aa2b3fp+1Q, -0x1.18f0a34d9f68e4d06a24b5c8413dp+4Q, 0x1.4ce3831796a61ef6af32be9a023fp+5Q, -0x1.dc75f9b0b9a1041da91933762b9bp+5Q, 0x1.fdbc97313e6ed6865f9096ac8807p+5Q, -0x1.eefc0cdda4efa281b21fc89e970ap+5Q, 0x1.b92a7c1b6a889c31c867c0ce8c52p+5Q, -0x1.2299d502734c3c9b7e4c9a6f523fp+5Q, 0x1.6502b707871df45089990b5055fdp+3Q, 0x1.11f33f4ede647d59a412fb3857a3p+2Q, -0x1.73b0a319e6889e9aa2e82f2679b8p+2Q, 0x1.244d452e7630092d6c490c8cc448p+1Q, -0x1.35466c5650c61e120220d045b2f3p-2Q, -0x1.fc20c8dd92f19b8d6ed30b1d9872p-6Q, 0x1.0d9c8b9d476f7d129de2a5d13304p-7Q, 0x1.a4010b80e5495d0ed9331140ed28p-19Q, -0x1.49b0c99eb9c648511ea730b4e4dp-19Q, 0x1.962a6dd57b7daa6dc5023a314835p-31Q, 0x0p+0Q};
             }
             if constexpr (order == 5) {
-                return {0x0p+0Q, 0x1.55886d2f64380baeb961079552b9p+2Q, -0x1.09d95f1cede31fcd15d2c7ff10a6p+5Q, 0x1.505f98e4bf27766f2f4d3b847255p+6Q, -0x1.96ec354b303069fd664614814e6ep+6Q, 0x1.17b23075f8010224c348afc6cdeep+5Q, 0x1.fc17211fa4d6f3f6a3261645172p+5Q, -0x1.b35f4a36b31c3849a4f0629dcf72p+6Q, 0x1.d17f22f2480f88bf1a425e07fe7dp+6Q, -0x1.12118c5678b4d442de8a0eede2e7p+7Q, 0x1.207a74ca5ad8bfc2ee103b7b451ap+7Q, -0x1.934735f943481c7f74f56dd50a8cp+6Q, 0x1.3fa55ba9206e3812ee32da23b318p+5Q, -0x1.959601005ec548729558e21bc187p+2Q, -0x1.9505e84d98e613cfe4ec3f6e6e46p-1Q, 0x1.43d2632e32cd0df0bb4a95d5e374p-2Q, -0x1.38e017336cd0614a6ed2ffd6195cp-10Q, -0x1.968e83ac595b8c6d9c1729fe9a6bp-13Q, 0x1.f5ed4b124df3ad0700a32c83080bp-24Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.55886d2f64380baeb961078fa176p+2Q, -0x1.09d95f1cede31fcd15d2c7fab39ep+5Q, 0x1.505f98e4bf27766f2f4d3b7ea8ddp+6Q, -0x1.96ec354b303069fd664614786911p+6Q, 0x1.17b23075f8010224c348afb3ebb9p+5Q, 0x1.fc17211fa4d6f3f6a32616561c88p+5Q, -0x1.b35f4a36b31c3849a4f062a53c98p+6Q, 0x1.d17f22f2480f88bf1a425e0d999bp+6Q, -0x1.12118c5678b4d442de8a0eef777p+7Q, 0x1.207a74ca5ad8bfc2ee103b7bf96dp+7Q, -0x1.934735f943481c7f74f56dd5b187p+6Q, 0x1.3fa55ba9206e3812ee32da2442b6p+5Q, -0x1.959601005ec548729558e21c9eb1p+2Q, -0x1.9505e84d98e613cfe4ec3f6fdae5p-1Q, 0x1.43d2632e32cd0df0bb4a95d727cp-2Q, -0x1.38e017336cd0614a6ed2ffd943cap-10Q, -0x1.968e83ac595b8c6d9c172a00fddap-13Q, 0x1.f5ed4b124df3ad0700a32c86e4bbp-24Q, 0x0p+0Q};
             }
             if constexpr (order == 6) {
-                return {0x0p+0Q, 0x1.f3cda2f9b135402362018238b572p+1Q, -0x1.9eeda12641b61ebb7d840ed67404p+4Q, 0x1.260fdaadd19eb1efc078d802d296p+6Q, -0x1.d673d80eeade4a070ce0e70cb866p+6Q, 0x1.f01b2fa154d0352990b16aadcb37p+6Q, -0x1.addb2c4ad791e217324c7ab3e2p+6Q, 0x1.7db87bda6fdf8a74bb08213eb30cp+6Q, -0x1.3f9860f6c4905e7132b1781da9d9p+6Q, 0x1.ae731643e9198e62164858360f7bp+5Q, -0x1.fb5cc3351ebc176988bf64799f2ap+4Q, 0x1.259afcbb8804d6eae552ab39b9b8p+4Q, -0x1.fe186e460309fdcedab5ec39f27p+2Q, 0x1.4d0298c21892754606c3d8eb8426p+0Q, 0x1.a1f0a66406a122ae435ed98cb7f1p-2Q, -0x1.40c0addfd85543af466cc7e3fef1p-3Q, 0x1.ba72fac37f087c7aee39dd7f1012p-9Q, 0x1.c193f16bb678e5af6510cd5c2355p-13Q, -0x1.16b4995bb4f073263c20b5bede1p-22Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.f3cda2f9b135402362018230e37ap+1Q, -0x1.9eeda12641b61ebb7d840ecfaa6cp+4Q, 0x1.260fdaadd19eb1efc078d7fded1bp+6Q, -0x1.d673d80eeade4a070ce0e7052e5ep+6Q, 0x1.f01b2fa154d0352990b16aa70967p+6Q, -0x1.addb2c4ad791e217324c7aafb066p+6Q, 0x1.7db87bda6fdf8a74bb08213b9495p+6Q, -0x1.3f9860f6c4905e7132b1781ae693p+6Q, 0x1.ae731643e9198e621648583330d8p+5Q, -0x1.fb5cc3351ebc176988bf6478c6bp+4Q, 0x1.259afcbb8804d6eae552ab39c09p+4Q, -0x1.fe186e460309fdcedab5ec38f6a8p+2Q, 0x1.4d0298c21892754606c3d8ebb24fp+0Q, 0x1.a1f0a66406a122ae435ed98406f7p-2Q, -0x1.40c0addfd85543af466cc7de08d7p-3Q, 0x1.ba72fac37f087c7aee39dd6d7d9ep-9Q, 0x1.c193f16bb678e5af6510cd4d8f9fp-13Q, -0x1.16b4995bb4f073263c20b5b2b14bp-22Q, 0x0p+0Q};
             }
             if constexpr (order == 7) {
-                return {0x0p+0Q, 0x1.3586d9a9e0e3d99d2b93a0256171p+1Q, -0x1.08fa63342ecc1c41a46b366506c6p+4Q, 0x1.7c41f01d6960cbda171d22bf8adfp+5Q, -0x1.276b64d22e134fe3903178671e17p+6Q, 0x1.14f1cf74869c077b4ddd6015e432p+6Q, -0x1.83d54ac636b8244258f1e3dbaa06p+5Q, 0x1.4053c8a2c8d2fc6aef1621f86f1fp+5Q, -0x1.209b538b18df262448ee3cf880b8p+5Q, 0x1.65783340b3782c7d703e94c62d9ep+4Q, -0x1.2ddf670e51dfca7d85e8eebe7331p+3Q, 0x1.38744fdae212579791ea9e6fe9ebp+2Q, -0x1.4065c212ba5c0456783637883b7p+1Q, 0x1.6763c5d11b774e2d99bb556bddebp-4Q, 0x1.181d4d676ea1f03e7d8c57b474fp-1Q, -0x1.87564028831fbd4eb29dad94592bp-3Q, 0x1.843d22529bb49b17cf15d63953b5p-7Q, 0x1.52be3b0b8c7af55af9d914a987b4p-11Q, -0x1.a79c626c8654ebdb591ae56046e7p-20Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.3586d9a9e0e3d99d2b93a01af7d5p+1Q, -0x1.08fa63342ecc1c41a46b365c4c22p+4Q, 0x1.7c41f01d6960cbda171d22b314bap+5Q, -0x1.276b64d22e134fe39031785d1e73p+6Q, 0x1.14f1cf74869c077b4ddd600b6793p+6Q, -0x1.83d54ac636b8244258f1e3c9d507p+5Q, 0x1.4053c8a2c8d2fc6aef1621e8f43ep+5Q, -0x1.209b538b18df262448ee3cebbe29p+5Q, 0x1.65783340b3782c7d703e94b54e85p+4Q, -0x1.2ddf670e51dfca7d85e8eeab11aep+3Q, 0x1.38744fdae212579791ea9e59ba4ep+2Q, -0x1.4065c212ba5c0456783637741afcp+1Q, 0x1.6763c5d11b774e2d99bb54d3a752p-4Q, 0x1.181d4d676ea1f03e7d8c57b5965ap-1Q, -0x1.87564028831fbd4eb29dad95b0cfp-3Q, 0x1.843d22529bb49b17cf15d645bef3p-7Q, 0x1.52be3b0b8c7af55af9d914b56a01p-11Q, -0x1.a79c626c8654ebdb591ae5793d64p-20Q, 0x0p+0Q};
             }
             if constexpr (order == 8) {
-                return {0x0p+0Q, 0x1.7a3cf471120ec198713995bd540fp+0Q, -0x1.48b25e52d274b1e47c88655cec4bp+3Q, 0x1.cbd93276e7d596419b912e942e9bp+4Q, -0x1.37885d5242030806d66e5d6872f8p+5Q, 0x1.4db4fb7a5ecdb9227e88240cd0ebp+4Q, 0x1.74ac2dca21f55bb24886bcb3619p+2Q, -0x1.11ca2f9f0b7d05f1c1618e42e113p+3Q, 0x1.9fa6aaf0c8d980502f8417a8ec05p-4Q, -0x1.8ceb3288570cd32c2591a09c3995p+2Q, 0x1.e686e3fbc3fbf35811a68ef5ccfap+3Q, -0x1.7e0b780d60231a4c786ec6e1bf8dp+3Q, 0x1.7e1a3482e160bfcf5bb19766022ep+2Q, -0x1.247b57131543bcbee8b060f013c2p+2Q, 0x1.b8a4e1c96768c895a2f367776819p+1Q, -0x1.4f17d502240a8e6f55c9e0d7f0cfp+0Q, 0x1.4b408438ac8689521da23fc4a9bap-3Q, 0x1.7264788c9473dca575636e2ed518p-7Q, -0x1.d74fd6a021547c7f9f7dd3ce0b46p-15Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.7a3cf471120ec198713994eca41fp+0Q, -0x1.48b25e52d274b1e47c8864a7164p+3Q, 0x1.cbd93276e7d596419b912da6ea19p+4Q, -0x1.37885d5242030806d66e5cf9cc78p+5Q, 0x1.4db4fb7a5ecdb9227e8824c1b905p+4Q, 0x1.74ac2dca21f55bb24886b2e8488cp+2Q, -0x1.11ca2f9f0b7d05f1c16189874d5cp+3Q, 0x1.9fa6aaf0c8d980502f82ac3f1ed7p-4Q, -0x1.8ceb3288570cd32c25919a739d51p+2Q, 0x1.e686e3fbc3fbf35811a68b06fad4p+3Q, -0x1.7e0b780d60231a4c786ec3f17781p+3Q, 0x1.7e1a3482e160bfcf5bb1945be474p+2Q, -0x1.247b57131543bcbee8b05ee74f53p+2Q, 0x1.b8a4e1c96768c895a2f3649c4cc8p+1Q, -0x1.4f17d502240a8e6f55c9dea2c968p+0Q, 0x1.4b408438ac8689521da23d7beaedp-3Q, 0x1.7264788c9473dca575636b8d6c86p-7Q, -0x1.d74fd6a021547c7f9f7dd044fd0ep-15Q, 0x0p+0Q};
             }
             if constexpr (order == 9) {
-                return {0x0p+0Q, 0x1.f6438a3a88460091e0ea851f2c9bp-4Q, -0x1.b7ba9255f9c77a442c3315faffdep-1Q, 0x1.3f509b3842148b5acdb05e01c1ap+1Q, -0x1.eac616f0d4f869be16ce06dc94d2p+1Q, 0x1.ae9244fef585d2a56f1cb6a3721cp+1Q, -0x1.00d5d03220f3bbc8a51448af242cp+1Q, 0x1.9413f3bab26fc85ab60692f2dd27p+0Q, -0x1.9bd9847a10dd537f2de875e80d0ep+0Q, 0x1.16aae27d18a67638fdda8ca2a252p+0Q, -0x1.1587682f48215c21c42b36d7c2d1p-1Q, 0x1.8145e3cc3cfcbcc409c895e52cdp-2Q, -0x1.faf556e68970db4f5325d215482dp-3Q, 0x1.8ec972676b06aaf4a1909e62a833p-4Q, -0x1.49980ed40883cadc7b702f738062p-5Q, 0x1.5730c48bae56a4ea4426b04ea74bp-6Q, -0x1.0952d6b855c638b977457b5132a1p-8Q, -0x1.ce071dd8df1eee9d16331f09e775p-12Q, 0x1.30a4361eb25b38fd9207742eecebp-18Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.f6438a3a88460091e0ea8516e904p-4Q, -0x1.b7ba9255f9c77a442c3315f3c4dep-1Q, 0x1.3f509b3842148b5acdb05dfc7ebdp+1Q, -0x1.eac616f0d4f869be16ce06d469adp+1Q, 0x1.ae9244fef585d2a56f1cb69c0c8dp+1Q, -0x1.00d5d03220f3bbc8a51448aa67eep+1Q, 0x1.9413f3bab26fc85ab60692eb482fp+0Q, -0x1.9bd9847a10dd537f2de875e0ae85p+0Q, 0x1.16aae27d18a67638fdda8c9d9188p+0Q, -0x1.1587682f48215c21c42b36d23f1dp-1Q, 0x1.8145e3cc3cfcbcc409c895dd9662p-2Q, -0x1.faf556e68970db4f5325d20bccb9p-3Q, 0x1.8ec972676b06aaf4a1909e5ab3bfp-4Q, -0x1.49980ed40883cadc7b702f6c3e9fp-5Q, 0x1.5730c48bae56a4ea4426b047bab7p-6Q, -0x1.0952d6b855c638b977457b4c3a4p-8Q, -0x1.ce071dd8df1eee9d16331f022e54p-12Q, 0x1.30a4361eb25b38fd9207742aba25p-18Q, 0x0p+0Q};
             }
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            if constexpr (order == 0) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0335440825684839948793277327924747568510463779411613283372021012357431575059"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.652680627784265419113142057333635414566267596751552407275899976614433273408"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.555223194777054373822280591005165065401335016712961625016624878528310159958"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.380687440934315605630685976089872177922250050019644347240793726150606940490"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.202266079588999490158624019679885616441296798707691052740675369027212472886"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0803945048003100183440731245374493948673697586172116467447133542711531568094"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0174035722935792800052307718387330639108356719924467120729654378442135160469"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00178881115434873125338924661801614887567351864768204987056083791004957995212"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00226229198052543881129104523760341714639547377902691081445602585210846978660"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000386185980709970284342158222549749494513229103697618385419333145519237034528"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000774649011709668881496648249850476879409117195200119403647384684895836766101"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000259573513242397582776373019880695158304702582936408634679549746356085340132"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000745576680291227809274057476509086014746503865109391843602515609932547121007"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000106464941195329780882604847827673302070700009500583209887829095516683638178"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000501834830778801282792550812083381505585505471229236043478318562698652685805"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000135062531948823786839892471345144438080086754634405014216461179793889825011"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000959080797319498233498089822590215572105542150066963291076320566868073767765"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000179932176974095821764192532376309678888476262257369144430177595683951871280"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 1) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.158111181967293654960328230847092693305440177339999811917967936973151313355"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.980421125954704520039885776450944209566177277494416607887119684421179635098"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.58099598658338745329757283125170548053142020106794975614544654842234384868"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.690126857952340353432328506701225025969125769614438292589462072221185931021"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.408979058242361193356322994890219659071489088001030862797057568700712362129"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.241670449709265382583487638664445391528015677818112147483084620599084662014"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.104524793285799361209632642244708987679189849915701108699068681818917564551"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0278508087960298510818238707785628134395285936655886239677755698286759739558"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00441290970073145649314875669419603850447965477890520778958402484404147639768"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00114514458070760163627849002336721074914074332813124777635502337309185298656"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000476320352183949564427659987582685532476347626608140569626323600699056358450"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000550762633298583614076910773634660669710897469085737707319033728420478570991"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000782993203462069534876818079465953823275658231409824729752214530888590769654"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000564225681253798960172481439960184780230811335282184378643150395063068263762"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000289378419497867484795216809169017976802236817565143538038072466488637113467"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000153639719627918579146261156316178551809778008841322577156822834207719956705"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000112595508102579374409860880942659257916932286941747525905040942526094106116"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000000422534516332318562691954502891542159653729964199104256783213585659998814557"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 2) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.588720067567147372371526765126987879260828303213441099181011258065293838823"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.251648139722832193419015447722954301991031036011339851370084962733394109781"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.12355343902466248968497032471987734676880165704138770035306028826542891153"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.09251337096522514606028271458193605813373662086854974692504786991417857735"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.78284160335134075990444774847436162057665816817791661854926507977727367295"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.357839667889140650192283355318684454497311597945586330625492942067228204170"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.381745602616663955066044160729358156963202088205543100952077537266538669109"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.404098136072108007374807965965387527326886804962161879932178818721047921461"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.166884206158335307397781592107767268454429823998572636766639189741929233271"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0188990841472042720746425899409966903574694812598737388685812356111081899839"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0103064239644345373917949401165831844344098684529684357486222879841537834787"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00401921019925688949154858061937053477498137877920046442886584156606534084249"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000342928264656894632727306414284757691655791891837113873553433397950197101263"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000356780514531412256820962066690466067686003465101389318017916782416810226771"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000330280231812952371277947997446653320231513317893333913004154901503115837079"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000464578675601507083497879025900090054285176183414686202576470053896196299532"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000245200318433632222808523321270596754329839152827213527385919720073276676756"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000184080234698594267687194056854914780004840892347196195690310992947531302848"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 3) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.65958975259656064316045033596993048467429622079353821151358867499251161075"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.20950631966221433967561122684352242112063005605168776576756309774482106803"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("9.54648047883299710477127639275362041903799096912957707845486310997696495456"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-8.03052641171442118399334548739326535650325998152511708583844969601543761720"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.23902264641828545334922817695052684001345135087620194561871043446356995572"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.10779520625851924861524548164634620055706242533707832091963204841153067836"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5.02564755256492020736254702209642014378150710638030519002386215046738254771"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.11488492772855670340163610415102162843178733646856522713137539498415480726"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.59968253731024764674220980278277254440169367686954378688784341823851608835"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0504087937983147259532537423739742886863984467015801660848052389726325500063"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.223185483314190807228908891936935259922851508598249374402763295219052714061"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0861136345730003759404777393964487407579363696963873730188751207394119447949"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00934626602280953109864448532020887389100677899387380615852902674015035997924"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000910503044785414199372507175857531751525973570169329713422142851011424682355"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000147382093153403749058592147931285087775427181451628598455432923070303889508"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000241926116925923995065157477973608855097571667752414338710574539981741722171"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000218323342443673749019739306955935203514484527679190271850231323531268999740"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000327979275814608443451375729823364664112564536732892493153334268909293059412"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 4) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.25242619678200601450569178504152903597725657049565655085262375577982506117"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-17.55874948808064424413002851561896280971775515196247347065085833327306525400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("41.61108988216871250092535059298125378237547100055437239071279933451179063850"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-59.55760515276426941427234116300582408502217490993753777144564940817935347700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("63.71708525153904224542587147408403757425616414887722633161387789077111052980"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-61.87307141456217718672414958346485055314933560158412396861503932253498736910"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("55.14574452799668166956345770934872005949138270244629696837163230917721607990"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-36.32511331476555787362944164622076573330244267979702165040726341593266853690"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("11.15658141584657284834931359434221143120836125797249180327843359491348695220"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.28047163679145355742238347915798843532207155521710854723594509752209225135"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5.80765607385013452624013336376953412945571932293068559021989957795643635688"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.28360810059200528491878271707995815797831304800926041232425607683843416684"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.302026455658227381795097923260643523970261991178933634395431417034448470906"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0310136758401276861689035927512442214284016615846020419389667737950748466936"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00822789017780277377915096056720947770842970725628234020125069515364007927548"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000312927426233484715125263582207480054643048737935356187231133866983070151733"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000245638621209106924354868430183266291735309073506794320584780059772790603828"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000738811174292185771537396859591012250750038497463623030500365543957753750629"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 5) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.33645181301187741432313412712493568835001053518710618642541285756306594416"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-33.23113844490980275430758088851544736605354677526393945582470182124522064770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("84.09335668007576319588337953784445541016978233438165893518194780234028567170"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-101.73067204934714346173214456537684449912757976518610846040850239073972369700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("34.96200649417016943214733096150713509877346551398259618284714231991020061170"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("63.51129364702034683684093287782391919624178836066372576355119905503761408080"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-108.84305654018594847769298493805318318251251741351696570225381155341619480700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("116.37415674748252380731944050807221204678284438681143398715321798634302210300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-137.03427381728617053583750633954098792534222952199781843278889570421284187500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("144.23917229041069234342319895061976936945281511182737320554482546805542945500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-100.81954183076052489010123579947837751941991209023328659869027417281390550900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("39.95574123506755984622668035085486713223409393558081588798575371234724932450"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.33728051220085266945721599456441606967791241256713928442461588780452001216"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.791060695144960272868253882225791392596201909418283798181953112710974525037"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.316232251829842651651001625374458886955182867924728786582655341982774267939"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00119352475745132656518440055173377628211628909314005476964858223466155435340"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000193861339890561713729524049136083535893829812899666113387041059603669685004"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000116863969422460737393134164985587926960730142518183635722657982921293457991"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 6) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.90471303169253225846019875869878232941425899681461754740621573916446143761"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-25.93301501220719956383930380071028369762143981546072887565823996886685997670"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("73.51548263160627699666584109197660506203055036418454184583288480107014110040"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-117.61312888439676707323068134216244043903457141447537621870038005469616937700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("124.02654888229522104336063612980866173817516040264350607815625581466646707700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-107.46403614941343293286313096080305756514307808353723016233188762409520778900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("95.43015996272868979842030346234072214178139856671622915250008488106829700140"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-79.89880738806468091633285361243244391895034565047088681170638032528297365230"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("53.80619481139291976708016981476722176165180845983829174460954831948835152660"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-31.71014710187933425539049751952485208474696175383649880962539170183854068730"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("18.35033868078635575339634170405333269133930342251123760246335182701029470230"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.97024113499733731824785417964081280548267589070768527759215633952607230552"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.30082087267562392476267682719773219132371557892324193430079039159705712061"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.408144569258781629158811991673214502189211048077371093404699476576485396497"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.156617506402691681618770997346051897652378607238940971239829191058955327399"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00337561904029654362598669467426491389034476058577086402678410124009083217286"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000214375449437306492796677584389309705675972756233814822259639128039297348952"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000259564691279900670740154984232869976357323694550668609785644902896773881579"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 7) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.41817780299041267294396998193961046347327141146988493872539852596711350295"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-16.56112976440341017090653469524313042536360691585560344322351312533906133220"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("47.53219626405561897360527224265560846366729359202579844173188227203518751290"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-73.85487678915235666547453188442988561374382065439419612818538759549597329740"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("69.23614294120398636214807885595774013168922546655228773985936065429561982080"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-48.47914652685632764102838407583295199095537856449557350864923480580193915190"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("40.04091002631537162491011984473323161600703606500352069042313463467126512660"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-36.07584294004108744401985515812914016258613167282034953810412938444038731500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("22.34184575342033973521659639667387757078302661414876303661404399664838457520"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.43352082058754010000229426238016353381474440642161800237732829686092053067"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.88209911704351415773607596292274800953074722271529021833265067681298168566"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.50310541071368687187558805389288406933454963984067437672488275554205269365"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0877416350574245619016863517598542577849142110266067469164372019839766916222"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.547098559261318119790346121315142638857555987993333621751899257669110708054"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.191082478748640367297398639370371440145977214048380506662573645656883504693"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0118481080619098512694011114462548921140026922405000410819306003041457844881"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000646101166642978477805807904877768082627916394154211614618243579374822809981"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000157807348977739476590803041857604549211169374418312430645482994306750965210"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 8) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.47749259720336125750014371203719086097786832720840532470036067098638253523"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-10.27177349258604109799866360824488274075683477990758858915270374562166449850"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("28.74052664229870896057228781991603797498521883108842274414172929446095718590"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-38.94158424629165794548655688785303773037259534960785249196589991715016053910"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("20.85668514061840842160738201097767741109998318160033587807688366848349176030"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.82300896396175969285220261284580137016897500185004121370253254225136801433"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-8.55593091071560318198818805962130429594383016756683899572054041178087930423"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.101477306114750809578847194446606040053812700094709979272704369647063439327"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.20185530962426163472935046915706308507730310357888975841274200007312909611"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("15.20396613285981716679133037338797692219039323378619093572799537510744196150"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-11.93890001881036092553774539348916251166242755327073413099256167724690461900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.97034943372046810250402450844362776436235733145492694521396093842408492893"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.57002808440762091333964553954350217107396457686094642109241343475428396977"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.44253179868866811498600236601873984282170067759034407929086464636198130738"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.30895739843621525859283487914176592704598294675665286288796005768903002325"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.161744149188567181778191988919947821701240436608528275036716134129128761337"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0113034809702728906127738052967788898940898905277042251467481852979437112396"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000561847530216411102015552396664363227011342601063500856745808337968464467556"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 9) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.122623004871017738321088521115551923728453212438673116414730214921771194277"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.858845303530769892579734223666985146082985618311703745596404006498390381931"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.49464740988711173737826976177194717462144209023170132334409744337915240875"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.83417021521921990552626761956575317113472949702731301040473923476385032353"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.36383879136250970160534021305681940065986265718051079957468541575949019427"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.00652506301585541969492468858387268920435010187618742310379136054539969490"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.57842944438965482815057083449552137133719188861387633419907705130357334305"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.60878780346034960103676974039938661510477020676670448343954517210254723407"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.08854499391659395899666779285135586272604126336277091423079442916910197364"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.542048698207568264511438036052150370606170830150755922595824458471088767735"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.376243171063148851166518405338884659341124829071866802537194156141907541144"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.247538260374476618199302147981680094201399126055983684863712115608203062926"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0973600834756226757960627772745367010811794086758884192671361295078507106292"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0402336396803239840143974298780932703826464388081245776201258480950581117641"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0209466857329280522592506599477472523467188466718239083632463774864022218054"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00404851667584358062529338732537862677888179504486154526998284790202549786179"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000440624045545039606176483920239238500963155780055689316463121243179544715288"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000453951136476212053479152117487615488257357457846427962694756049282806704493"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+        }
     }
     if constexpr (p == 11) {
         if constexpr (std::is_same_v<Real, float>) {
             if constexpr (order == 0) {
-                return {0x0p+0f, 0x1.f82d86p-7f, 0x1.da87aep-2f, 0x1.a074eap-1f, -0x1.d3dbc2p-2f, 0x1.07dc8cp-2f, -0x1.17e06ap-3f, 0x1.d853p-5f, -0x1.071062p-6f, 0x1.0182ap-9f, 0x1.d91cd2p-14f, 0x1.f2bfaap-15f, -0x1.d7e9bap-15f, 0x1.5c274ep-18f, 0x1.63562ep-20f, -0x1.0af58p-26f, 0x1.1409ccp-28f, -0x1.160128p-35f, -0x1.4f944ep-42f, -0x1.ad914cp-53f, -0x1.65d844p-70f, 0x0p+0f};
+                return {0x0p+0f, 0x1.f82d86p-7f, 0x1.da87aep-2f, 0x1.a074eap-1f, -0x1.d3dbc2p-2f, 0x1.07dc8cp-2f, -0x1.17e06ap-3f, 0x1.d853p-5f, -0x1.071062p-6f, 0x1.0182ap-9f, 0x1.d91cd2p-14f, 0x1.f2bfaap-15f, -0x1.d7e9bap-15f, 0x1.5c274ep-18f, 0x1.63562ep-20f, -0x1.0af58p-26f, 0x1.1409ccp-28f, -0x1.160128p-35f, -0x1.4f944ep-42f, -0x1.ad914cp-53f, -0x1.65d844p-70f, -0x0p+0f};
             }
             if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.4988f6p-4f, 0x1.cd9786p-1f, -0x1.f03418p-1f, -0x1.075e3cp-3f, 0x1.303436p-3f, -0x1.71d07ep-12f, -0x1.321c6cp-4f, 0x1.0f00fp-4f, -0x1.fec808p-6f, 0x1.092c0ap-7f, -0x1.185782p-11f, -0x1.693106p-12f, 0x1.a2acf4p-14f, -0x1.c4d82p-19f, -0x1.e02848p-20f, 0x1.7db784p-25f, 0x1.739c16p-30f, -0x1.d9433ap-36f, 0x1.651bd6p-46f, 0x1.29783p-62f, -0x0p+0f};
+                return {0x0p+0f, 0x1.4988f6p-4f, 0x1.cd9786p-1f, -0x1.f03418p-1f, -0x1.075e3cp-3f, 0x1.303436p-3f, -0x1.71d07ep-12f, -0x1.321c6cp-4f, 0x1.0f00fp-4f, -0x1.fec808p-6f, 0x1.092c0ap-7f, -0x1.185782p-11f, -0x1.693106p-12f, 0x1.a2acf4p-14f, -0x1.c4d82p-19f, -0x1.e02848p-20f, 0x1.7db784p-25f, 0x1.739c16p-30f, -0x1.d9433ap-36f, 0x1.651bd6p-46f, 0x1.29783p-62f, 0x0p+0f};
             }
             if constexpr (order == 2) {
-                return {0x0p+0f, 0x1.5c07e6p-2f, 0x1.307a2ap-1f, -0x1.a41fd4p+1f, 0x1.08f33p+2f, -0x1.6a2a88p+1f, 0x1.5f04aep+0f, -0x1.150c78p-2f, -0x1.78ed1cp-3f, 0x1.4f999p-3f, -0x1.41156ep-5f, -0x1.6c5862p-7f, 0x1.21e04ap-7f, -0x1.cd1c36p-10f, 0x1.af648p-17f, 0x1.0136c4p-15f, -0x1.6928bp-19f, -0x1.6377bp-25f, 0x1.64323cp-30f, -0x1.6fb512p-40f, -0x1.32449ep-55f, 0x0p+0f};
+                return {0x0p+0f, 0x1.5c07e6p-2f, 0x1.307a2ap-1f, -0x1.a41fd4p+1f, 0x1.08f33p+2f, -0x1.6a2a88p+1f, 0x1.5f04aep+0f, -0x1.150c78p-2f, -0x1.78ed1cp-3f, 0x1.4f999p-3f, -0x1.41156ep-5f, -0x1.6c5862p-7f, 0x1.21e04ap-7f, -0x1.cd1c36p-10f, 0x1.af648p-17f, 0x1.0136c4p-15f, -0x1.6928bp-19f, -0x1.6377bp-25f, 0x1.64323cp-30f, -0x1.6fb512p-40f, -0x1.32449ep-55f, -0x0p+0f};
             }
             if constexpr (order == 3) {
-                return {0x0p+0f, 0x1.1c297ep+0f, -0x1.a72bc4p+1f, 0x1.8e9818p+1f, -0x1.8f506ep-1f, 0x1.02364ap-1f, -0x1.0fb22ap+1f, 0x1.80597ep+1f, -0x1.38ad98p+1f, 0x1.339d14p+0f, -0x1.08b97cp-2f, -0x1.3f8a26p-4f, 0x1.2b8bd2p-4f, -0x1.35b764p-6f, 0x1.f33a86p-12f, 0x1.1c307ep-11f, -0x1.950dccp-15f, -0x1.f90492p-21f, 0x1.8b6cb6p-25f, -0x1.21deep-34f, -0x1.e2c778p-49f, 0x0p+0f};
+                return {0x0p+0f, 0x1.1c297ep+0f, -0x1.a72bc4p+1f, 0x1.8e9818p+1f, -0x1.8f506ep-1f, 0x1.02364ap-1f, -0x1.0fb22ap+1f, 0x1.80597ep+1f, -0x1.38ad98p+1f, 0x1.339d14p+0f, -0x1.08b97cp-2f, -0x1.3f8a26p-4f, 0x1.2b8bd2p-4f, -0x1.35b764p-6f, 0x1.f33a86p-12f, 0x1.1c307ep-11f, -0x1.950dccp-15f, -0x1.f90492p-21f, 0x1.8b6cb6p-25f, -0x1.21deep-34f, -0x1.e2c778p-49f, -0x0p+0f};
             }
             if constexpr (order == 4) {
-                return {0x0p+0f, 0x1.51d8dcp+1f, -0x1.c33b04p+3f, 0x1.0e7952p+5f, -0x1.9aba4p+5f, 0x1.f144c4p+5f, -0x1.17ce56p+6f, 0x1.1abf8ep+6f, -0x1.aeeda8p+5f, 0x1.6d1976p+4f, 0x1.64c18ap+1f, -0x1.4b3d36p+3f, 0x1.8e7526p+2f, -0x1.9e20d2p+0f, 0x1.8f714p-5f, 0x1.002e9ap-4f, -0x1.22b5dp-7f, -0x1.695b64p-13f, 0x1.ba1b22p-17f, -0x1.df066ep-26f, -0x1.8ec07p-39f, 0x0p+0f};
+                return {0x0p+0f, 0x1.51d8dcp+1f, -0x1.c33b04p+3f, 0x1.0e7952p+5f, -0x1.9aba4p+5f, 0x1.f144c4p+5f, -0x1.17ce56p+6f, 0x1.1abf8ep+6f, -0x1.aeeda8p+5f, 0x1.6d1976p+4f, 0x1.64c18ap+1f, -0x1.4b3d36p+3f, 0x1.8e7526p+2f, -0x1.9e20d2p+0f, 0x1.8f714p-5f, 0x1.002e9ap-4f, -0x1.22b5dp-7f, -0x1.695b64p-13f, 0x1.ba1b22p-17f, -0x1.df066ep-26f, -0x1.8ec07p-39f, -0x0p+0f};
             }
             if constexpr (order == 5) {
                 return {0x0p+0f, 0x1.553842p+2f, -0x1.1648a2p+5f, 0x1.7429c4p+6f, -0x1.d2259cp+6f, 0x1.36cbd8p+4f, 0x1.4a282ep+7f, -0x1.2e04acp+8f, 0x1.5f18c6p+8f, -0x1.80bbfp+8f, 0x1.90ad4cp+8f, -0x1.4159ep+8f, 0x1.4eba06p+7f, -0x1.6db5a8p+5f, 0x1.66137p-1f, 0x1.7dbb7ep+1f, -0x1.1851aap-1f, -0x1.230c94p-7f, 0x1.7e95e2p-10f, -0x1.136d24p-18f, -0x1.ca2f1p-31f, -0x0p+0f};
@@ -803,10 +983,10 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0f, 0x1.0e918ep+2f, -0x1.f54b1ep+4f, 0x1.8cc936p+6f, -0x1.5d87f4p+7f, 0x1.7fbdfcp+7f, -0x1.356154p+7f, 0x1.00a2fp+7f, -0x1.d61ad6p+6f, 0x1.4b192ep+6f, -0x1.2bd7eep+5f, 0x1.d23af8p+3f, -0x1.a5a3f6p+2f, -0x1.0097bap+0f, 0x1.29abecp+2f, -0x1.6d63c6p+1f, 0x1.521b96p-1f, -0x1.89a1eap-6f, -0x1.cc0f8cp-8f, 0x1.9e94aap-16f, 0x1.5739aap-26f, 0x0p+0f};
             }
             if constexpr (order == 8) {
-                return {0x0p+0f, 0x1.c2a5p+0f, -0x1.a9c968p+3f, 0x1.5bbb8cp+5f, -0x1.452574p+6f, 0x1.91c80cp+6f, -0x1.84d65cp+6f, 0x1.678e1ep+6f, -0x1.493302p+6f, 0x1.14413cp+6f, -0x1.b51d9ap+5f, 0x1.483818p+5f, -0x1.a72562p+4f, 0x1.e00e48p+3f, -0x1.1522f8p+3f, 0x1.152962p+2f, -0x1.3d9d88p+0f, 0x1.3f1c58p-4f, 0x1.b3efb4p-6f, -0x1.baa15ap-13f, -0x1.6c2d94p-22f, 0x0p+0f};
+                return {0x0p+0f, 0x1.c2a5p+0f, -0x1.a9c968p+3f, 0x1.5bbb8cp+5f, -0x1.452574p+6f, 0x1.91c80cp+6f, -0x1.84d65cp+6f, 0x1.678e1ep+6f, -0x1.493302p+6f, 0x1.14413cp+6f, -0x1.b51d9ap+5f, 0x1.483818p+5f, -0x1.a72562p+4f, 0x1.e00e48p+3f, -0x1.1522f8p+3f, 0x1.152962p+2f, -0x1.3d9d88p+0f, 0x1.3f1c58p-4f, 0x1.b3efb4p-6f, -0x1.baa15ap-13f, -0x1.6c2d94p-22f, -0x0p+0f};
             }
             if constexpr (order == 9) {
-                return {0x0p+0f, 0x1.480f32p-1f, -0x1.38fe3p+2f, 0x1.f8f412p+3f, -0x1.bc60c4p+4f, 0x1.d3d44ap+4f, -0x1.536d7p+4f, 0x1.0953a8p+4f, -0x1.0c0dcap+4f, 0x1.af56b2p+3f, -0x1.f62894p+2f, 0x1.3ef834p+2f, -0x1.c75ab6p+1f, 0x1.cb38bcp+0f, -0x1.624786p-1f, 0x1.61b17ap-2f, -0x1.0b6248p-3f, 0x1.c9b3fp-8f, 0x1.7c528ap-8f, -0x1.0c4738p-13f, -0x1.b40e78p-22f, 0x0p+0f};
+                return {0x0p+0f, 0x1.480f32p-1f, -0x1.38fe3p+2f, 0x1.f8f412p+3f, -0x1.bc60c4p+4f, 0x1.d3d44ap+4f, -0x1.536d7p+4f, 0x1.0953a8p+4f, -0x1.0c0dcap+4f, 0x1.af56b2p+3f, -0x1.f62894p+2f, 0x1.3ef834p+2f, -0x1.c75ab6p+1f, 0x1.cb38bcp+0f, -0x1.624786p-1f, 0x1.61b17ap-2f, -0x1.0b6248p-3f, 0x1.c9b3fp-8f, 0x1.7c528ap-8f, -0x1.0c4738p-13f, -0x1.b40e78p-22f, -0x0p+0f};
             }
             if constexpr (order == 10) {
                 return {0x0p+0f, 0x1.8a25fep-4f, -0x1.79dddep-1f, 0x1.2f9284p+1f, -0x1.04a532p+2f, 0x1.fbc728p+1f, -0x1.2e8a4ep+1f, 0x1.96ff88p+0f, -0x1.db8c8p+0f, 0x1.8867ecp+0f, -0x1.7019bcp-1f, 0x1.a30d2p-2f, -0x1.7340e8p-2f, 0x1.68181ap-3f, -0x1.50a6f6p-5f, 0x1.8d3b22p-6f, -0x1.b7227ep-7f, -0x1.a3115p-12f, 0x1.71e7a4p-10f, -0x1.4eea02p-14f, -0x1.09aedap-21f, 0x0p+0f};
@@ -814,19 +994,19 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         }
         if constexpr (std::is_same_v<Real, double>) {
             if constexpr (order == 0) {
-                return {0x0p+0, 0x1.f82d860ed311dp-7, 0x1.da87adf545deap-2, 0x1.a074ea6831a18p-1, -0x1.d3dbc22db3363p-2, 0x1.07dc8c4b5880ap-2, -0x1.17e06a0deb07p-3, 0x1.d85300a8e9a5ap-5, -0x1.0710616766f9ep-6, 0x1.0182a0c9a44bbp-9, 0x1.d91cd19825f46p-14, 0x1.f2bfaace30f59p-15, -0x1.d7e9ba7b3ac47p-15, 0x1.5c274e2e04a65p-18, 0x1.63562e1b18da8p-20, -0x1.0af5800900cccp-26, 0x1.1409cb495cfabp-28, -0x1.1601287f207ddp-35, -0x1.4f944d6c974a1p-42, -0x1.ad914b3b9c645p-53, -0x1.65d8440cb590ap-70, 0x0p+0};
+                return {0x0p+0, 0x1.f82d860ed311dp-7, 0x1.da87adf545deap-2, 0x1.a074ea6831a18p-1, -0x1.d3dbc22db3363p-2, 0x1.07dc8c4b5880ap-2, -0x1.17e06a0deb07p-3, 0x1.d85300a8e9a5ap-5, -0x1.0710616766f9ep-6, 0x1.0182a0c9a44bbp-9, 0x1.d91cd19825f46p-14, 0x1.f2bfaace30f59p-15, -0x1.d7e9ba7b3ac47p-15, 0x1.5c274e2e04a65p-18, 0x1.63562e1b18da8p-20, -0x1.0af5800900cccp-26, 0x1.1409cb495cfabp-28, -0x1.1601287f207ddp-35, -0x1.4f944d6c974a1p-42, -0x1.ad914b3b9c645p-53, -0x1.65d8440cb590ap-70, -0x0p+0};
             }
             if constexpr (order == 1) {
-                return {0x0p+0, 0x1.4988f615d8fc2p-4, 0x1.cd9786f046dbdp-1, -0x1.f034187a5d753p-1, -0x1.075e3bcf1d71fp-3, 0x1.303436308c6p-3, -0x1.71d07ef81053fp-12, -0x1.321c6b5970b99p-4, 0x1.0f00f07475782p-4, -0x1.fec807d6bcde3p-6, 0x1.092c0960e80ecp-7, -0x1.1857810566103p-11, -0x1.693105a2bb707p-12, 0x1.a2acf3b1f9d07p-14, -0x1.c4d81f25bbab6p-19, -0x1.e0284772a21efp-20, 0x1.7db784c0b0131p-25, 0x1.739c15dc80c55p-30, -0x1.d9433a2520a2ep-36, 0x1.651bd505e5aabp-46, 0x1.29782f98b98d9p-62, -0x0p+0};
+                return {0x0p+0, 0x1.4988f615d8fc2p-4, 0x1.cd9786f046dbdp-1, -0x1.f034187a5d753p-1, -0x1.075e3bcf1d71fp-3, 0x1.303436308c6p-3, -0x1.71d07ef81053fp-12, -0x1.321c6b5970b99p-4, 0x1.0f00f07475782p-4, -0x1.fec807d6bcde3p-6, 0x1.092c0960e80ecp-7, -0x1.1857810566103p-11, -0x1.693105a2bb707p-12, 0x1.a2acf3b1f9d07p-14, -0x1.c4d81f25bbab6p-19, -0x1.e0284772a21efp-20, 0x1.7db784c0b0131p-25, 0x1.739c15dc80c55p-30, -0x1.d9433a2520a2ep-36, 0x1.651bd505e5aabp-46, 0x1.29782f98b98d9p-62, 0x0p+0};
             }
             if constexpr (order == 2) {
-                return {0x0p+0, 0x1.5c07e5083d709p-2, 0x1.307a2a8e783eap-1, -0x1.a41fd4c6e5304p+1, 0x1.08f3303fd9b5fp+2, -0x1.6a2a8758fd08cp+1, 0x1.5f04ae9c9034bp+0, -0x1.150c77d31565dp-2, -0x1.78ed1cb9b0ec2p-3, 0x1.4f99902d11603p-3, -0x1.41156e1c846c4p-5, -0x1.6c5861062a836p-7, 0x1.21e04958552e7p-7, -0x1.cd1c35ab2ad93p-10, 0x1.af6480e4adc47p-17, 0x1.0136c3fb4b19cp-15, -0x1.6928b0e495d08p-19, -0x1.6377af73884cp-25, 0x1.64323c063686ap-30, -0x1.6fb51174aa8e3p-40, -0x1.32449da1b9609p-55, 0x0p+0};
+                return {0x0p+0, 0x1.5c07e5083d709p-2, 0x1.307a2a8e783eap-1, -0x1.a41fd4c6e5304p+1, 0x1.08f3303fd9b5fp+2, -0x1.6a2a8758fd08cp+1, 0x1.5f04ae9c9034bp+0, -0x1.150c77d31565dp-2, -0x1.78ed1cb9b0ec2p-3, 0x1.4f99902d11603p-3, -0x1.41156e1c846c4p-5, -0x1.6c5861062a836p-7, 0x1.21e04958552e7p-7, -0x1.cd1c35ab2ad93p-10, 0x1.af6480e4adc47p-17, 0x1.0136c3fb4b19cp-15, -0x1.6928b0e495d08p-19, -0x1.6377af73884cp-25, 0x1.64323c063686ap-30, -0x1.6fb51174aa8e3p-40, -0x1.32449da1b9609p-55, -0x0p+0};
             }
             if constexpr (order == 3) {
-                return {0x0p+0, 0x1.1c297e1a72297p+0, -0x1.a72bc3c00615fp+1, 0x1.8e98178e99b32p+1, -0x1.8f506e2a5e0ebp-1, 0x1.02364935e2223p-1, -0x1.0fb2290536b32p+1, 0x1.80597d49465bfp+1, -0x1.38ad9781c7501p+1, 0x1.339d144fd9551p+0, -0x1.08b97b33caeccp-2, -0x1.3f8a268debfb7p-4, 0x1.2b8bd1a4fd0ebp-4, -0x1.35b764060a714p-6, 0x1.f33a86db42466p-12, 0x1.1c307da269deep-11, -0x1.950dcb7c8e982p-15, -0x1.f904916865d4dp-21, 0x1.8b6cb6bf7586bp-25, -0x1.21dedfd7476c5p-34, -0x1.e2c7778c519ap-49, 0x0p+0};
+                return {0x0p+0, 0x1.1c297e1a72297p+0, -0x1.a72bc3c00615fp+1, 0x1.8e98178e99b32p+1, -0x1.8f506e2a5e0ebp-1, 0x1.02364935e2223p-1, -0x1.0fb2290536b32p+1, 0x1.80597d49465bfp+1, -0x1.38ad9781c7501p+1, 0x1.339d144fd9551p+0, -0x1.08b97b33caeccp-2, -0x1.3f8a268debfb7p-4, 0x1.2b8bd1a4fd0ebp-4, -0x1.35b764060a714p-6, 0x1.f33a86db42466p-12, 0x1.1c307da269deep-11, -0x1.950dcb7c8e982p-15, -0x1.f904916865d4dp-21, 0x1.8b6cb6bf7586bp-25, -0x1.21dedfd7476c5p-34, -0x1.e2c7778c519ap-49, -0x0p+0};
             }
             if constexpr (order == 4) {
-                return {0x0p+0, 0x1.51d8dbccf9207p+1, -0x1.c33b049bfbce6p+3, 0x1.0e79522ccf3ddp+5, -0x1.9aba40cee29c1p+5, 0x1.f144c4df7513dp+5, -0x1.17ce56ad9d902p+6, 0x1.1abf8d1adcc3ep+6, -0x1.aeeda88b7fe88p+5, 0x1.6d1975fc2f42ep+4, 0x1.64c18afe2844cp+1, -0x1.4b3d36d8f9771p+3, 0x1.8e75251a7f5bfp+2, -0x1.9e20d1654131ap+0, 0x1.8f713f264dac3p-5, 0x1.002e9aac59197p-4, -0x1.22b5d07d79f25p-7, -0x1.695b63166e6d6p-13, 0x1.ba1b21857af83p-17, -0x1.df066d7576ffdp-26, -0x1.8ec06f9de2f7dp-39, 0x0p+0};
+                return {0x0p+0, 0x1.51d8dbccf9207p+1, -0x1.c33b049bfbce6p+3, 0x1.0e79522ccf3ddp+5, -0x1.9aba40cee29c1p+5, 0x1.f144c4df7513dp+5, -0x1.17ce56ad9d902p+6, 0x1.1abf8d1adcc3ep+6, -0x1.aeeda88b7fe88p+5, 0x1.6d1975fc2f42ep+4, 0x1.64c18afe2844cp+1, -0x1.4b3d36d8f9771p+3, 0x1.8e75251a7f5bfp+2, -0x1.9e20d1654131ap+0, 0x1.8f713f264dac3p-5, 0x1.002e9aac59197p-4, -0x1.22b5d07d79f25p-7, -0x1.695b63166e6d6p-13, 0x1.ba1b21857af83p-17, -0x1.df066d7576ffdp-26, -0x1.8ec06f9de2f7dp-39, -0x0p+0};
             }
             if constexpr (order == 5) {
                 return {0x0p+0, 0x1.553841cb8504cp+2, -0x1.1648a261cfac8p+5, 0x1.7429c31b8bcdcp+6, -0x1.d2259be1a7819p+6, 0x1.36cbd86221f4cp+4, 0x1.4a282d1320ed7p+7, -0x1.2e04ab290e2ep+8, 0x1.5f18c6755ba05p+8, -0x1.80bbefefb8959p+8, 0x1.90ad4b61c673ep+8, -0x1.4159e0e62036cp+8, 0x1.4eba06db33d53p+7, -0x1.6db5a82568a44p+5, 0x1.6613709f48646p-1, 0x1.7dbb7d4fa2b47p+1, -0x1.1851a9519e35ep-1, -0x1.230c93cadc0b8p-7, 0x1.7e95e283d8ce3p-10, -0x1.136d2374e3712p-18, -0x1.ca2f0f4b75006p-31, -0x0p+0};
@@ -838,10 +1018,10 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0, 0x1.0e918e0751a5fp+2, -0x1.f54b1dc71e94cp+4, 0x1.8cc935a5962f3p+6, -0x1.5d87f4fd9af88p+7, 0x1.7fbdfc1f5c92bp+7, -0x1.356154b8ce2cp+7, 0x1.00a2f00b6f36p+7, -0x1.d61ad68084632p+6, 0x1.4b192d711636ap+6, -0x1.2bd7eeccbbd8bp+5, 0x1.d23af72a92131p+3, -0x1.a5a3f6309aca8p+2, -0x1.0097ba319005fp+0, 0x1.29abec5ca24e5p+2, -0x1.6d63c669ef72ap+1, 0x1.521b96f1f012p-1, -0x1.89a1e9b6409a4p-6, -0x1.cc0f8b0b31976p-8, 0x1.9e94a90cc2ee8p-16, 0x1.5739a9ee6eb1dp-26, 0x0p+0};
             }
             if constexpr (order == 8) {
-                return {0x0p+0, 0x1.c2a4ffe966119p+0, -0x1.a9c9682497d43p+3, 0x1.5bbb8c487ae5cp+5, -0x1.452573aebb3bfp+6, 0x1.91c80b52c3671p+6, -0x1.84d65b83affb6p+6, 0x1.678e1d36597aep+6, -0x1.4933025bdb689p+6, 0x1.14413c8e18076p+6, -0x1.b51d99f667842p+5, 0x1.483818775e0cbp+5, -0x1.a72562d5d8065p+4, 0x1.e00e48c9f7714p+3, -0x1.1522f77734c2fp+3, 0x1.152961e6e0f57p+2, -0x1.3d9d88a64fae4p+0, 0x1.3f1c58e4e2a68p-4, 0x1.b3efb441a4e1bp-6, -0x1.baa159e67dd4fp-13, -0x1.6c2d94cde3ae2p-22, 0x0p+0};
+                return {0x0p+0, 0x1.c2a4ffe966119p+0, -0x1.a9c9682497d43p+3, 0x1.5bbb8c487ae5cp+5, -0x1.452573aebb3bfp+6, 0x1.91c80b52c3671p+6, -0x1.84d65b83affb6p+6, 0x1.678e1d36597aep+6, -0x1.4933025bdb689p+6, 0x1.14413c8e18076p+6, -0x1.b51d99f667842p+5, 0x1.483818775e0cbp+5, -0x1.a72562d5d8065p+4, 0x1.e00e48c9f7714p+3, -0x1.1522f77734c2fp+3, 0x1.152961e6e0f57p+2, -0x1.3d9d88a64fae4p+0, 0x1.3f1c58e4e2a68p-4, 0x1.b3efb441a4e1bp-6, -0x1.baa159e67dd4fp-13, -0x1.6c2d94cde3ae2p-22, -0x0p+0};
             }
             if constexpr (order == 9) {
-                return {0x0p+0, 0x1.480f31520e3f3p-1, -0x1.38fe2f09aac58p+2, 0x1.f8f411bacc9f9p+3, -0x1.bc60c3b54f90bp+4, 0x1.d3d44a6a16adbp+4, -0x1.536d6f833b667p+4, 0x1.0953a7a524acbp+4, -0x1.0c0dca303e8e2p+4, 0x1.af56b1534f29ep+3, -0x1.f628948ceff74p+2, 0x1.3ef834c3289aap+2, -0x1.c75ab5e1afc76p+1, 0x1.cb38bb2c5f4bfp+0, -0x1.624785bf15dbep-1, 0x1.61b17ae5ff0c1p-2, -0x1.0b62472bd3d78p-3, 0x1.c9b3ef0688e89p-8, 0x1.7c528a3f2156cp-8, -0x1.0c4738028aec9p-13, -0x1.b40e785cb8808p-22, 0x0p+0};
+                return {0x0p+0, 0x1.480f31520e3f3p-1, -0x1.38fe2f09aac58p+2, 0x1.f8f411bacc9f9p+3, -0x1.bc60c3b54f90bp+4, 0x1.d3d44a6a16adbp+4, -0x1.536d6f833b667p+4, 0x1.0953a7a524acbp+4, -0x1.0c0dca303e8e2p+4, 0x1.af56b1534f29ep+3, -0x1.f628948ceff74p+2, 0x1.3ef834c3289aap+2, -0x1.c75ab5e1afc76p+1, 0x1.cb38bb2c5f4bfp+0, -0x1.624785bf15dbep-1, 0x1.61b17ae5ff0c1p-2, -0x1.0b62472bd3d78p-3, 0x1.c9b3ef0688e89p-8, 0x1.7c528a3f2156cp-8, -0x1.0c4738028aec9p-13, -0x1.b40e785cb8808p-22, -0x0p+0};
             }
             if constexpr (order == 10) {
                 return {0x0p+0, 0x1.8a25fe79d1c4ep-4, -0x1.79dddd860d214p-1, 0x1.2f92842080f08p+1, -0x1.04a53246109b7p+2, 0x1.fbc727fc23efp+1, -0x1.2e8a4ebac6b5ep+1, 0x1.96ff87cfe4cc5p+0, -0x1.db8c7f7bf2c3ap+0, 0x1.8867eccd39d1bp+0, -0x1.7019bc278ffcp-1, 0x1.a30d20b4e67c7p-2, -0x1.7340e7a399e64p-2, 0x1.68181929e64c5p-3, -0x1.50a6f5e8f3b31p-5, 0x1.8d3b211eb839bp-6, -0x1.b7227d5381373p-7, -0x1.a3114fdf2fbcp-12, 0x1.71e7a3b4d88bfp-10, -0x1.4eea023db8bd5p-14, -0x1.09aed93888304p-21, 0x0p+0};
@@ -849,19 +1029,19 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         }
         if constexpr (std::is_same_v<Real, long double>) {
             if constexpr (order == 0) {
-                return {0x0p+0L, 0xf.c16c3076988ebbcp-10L, 0xe.d43d6faa2ef51b8p-5L, 0xd.03a753418d0bce6p-4L, -0xe.9ede116d99b1966p-5L, 0x8.3ee4625ac404c6dp-5L, -0x8.bf03506f5837fe3p-6L, 0xe.c29805474d2cedap-8L, -0x8.38830b3b37cedbcp-9L, 0x8.0c15064d225d41p-12L, 0xe.c8e68cc12fa31cbp-17L, 0xf.95fd567187ac541p-18L, -0xe.bf4dd3d9d6239bp-18L, 0xa.e13a71702532bafp-21L, 0xb.1ab170d8c6d3fd6p-23L, -0x8.57ac00480665f53p-29L, 0x8.a04e5a4ae7d54e6p-31L, -0x8.b00943f903ee402p-38L, -0xa.7ca26b64ba505d1p-45L, -0xd.6c8a59dce3224e2p-56L, -0xb.2ec22065ac84f3fp-73L, 0x0p+0L};
+                return {0x0p+0L, 0xf.c16c3076988ebbcp-10L, 0xe.d43d6faa2ef51b8p-5L, 0xd.03a753418d0bce6p-4L, -0xe.9ede116d99b1966p-5L, 0x8.3ee4625ac404c6dp-5L, -0x8.bf03506f5837fe3p-6L, 0xe.c29805474d2cedap-8L, -0x8.38830b3b37cedbcp-9L, 0x8.0c15064d225d41p-12L, 0xe.c8e68cc12fa31cbp-17L, 0xf.95fd567187ac541p-18L, -0xe.bf4dd3d9d6239bp-18L, 0xa.e13a71702532bafp-21L, 0xb.1ab170d8c6d3fd6p-23L, -0x8.57ac00480665f53p-29L, 0x8.a04e5a4ae7d54e6p-31L, -0x8.b00943f903ee402p-38L, -0xa.7ca26b64ba505d1p-45L, -0xd.6c8a59dce3224e2p-56L, -0xb.2ec22065ac84f3fp-73L, -0x0p+0L};
             }
             if constexpr (order == 1) {
-                return {0x0p+0L, 0xa.4c47b0aec7e1081p-7L, 0xe.6cbc378236de837p-4L, -0xf.81a0c3d2eba999fp-4L, -0x8.3af1de78eb8f98bp-6L, 0x9.81a1b1846300118p-6L, -0xb.8e83f7c0829f529p-15L, -0x9.90e35acb85cca72p-7L, 0x8.780783a3abc1044p-7L, -0xf.f6403eb5e6f17b6p-9L, 0x8.49604b074075f3ap-10L, -0x8.c2bc082b308154p-14L, -0xb.49882d15db83441p-15L, 0xd.15679d8fce83a4ap-17L, -0xe.26c0f92ddd5b332p-22L, -0xf.01423b9510f7584p-23L, 0xb.edbc2605809849dp-28L, 0xb.9ce0aee4062aafdp-33L, -0xe.ca19d1290517188p-39L, 0xb.28dea82f2d5572ep-49L, 0x9.4bc17cc5cc6c599p-65L, -0x0p+0L};
+                return {0x0p+0L, 0xa.4c47b0aec7e1081p-7L, 0xe.6cbc378236de837p-4L, -0xf.81a0c3d2eba999fp-4L, -0x8.3af1de78eb8f98bp-6L, 0x9.81a1b1846300118p-6L, -0xb.8e83f7c0829f529p-15L, -0x9.90e35acb85cca72p-7L, 0x8.780783a3abc1044p-7L, -0xf.f6403eb5e6f17b6p-9L, 0x8.49604b074075f3ap-10L, -0x8.c2bc082b308154p-14L, -0xb.49882d15db83441p-15L, 0xd.15679d8fce83a4ap-17L, -0xe.26c0f92ddd5b332p-22L, -0xf.01423b9510f7584p-23L, 0xb.edbc2605809849dp-28L, 0xb.9ce0aee4062aafdp-33L, -0xe.ca19d1290517188p-39L, 0xb.28dea82f2d5572ep-49L, 0x9.4bc17cc5cc6c599p-65L, 0x0p+0L};
             }
             if constexpr (order == 2) {
-                return {0x0p+0L, 0xa.e03f2841eb84819p-5L, 0x9.83d15473c1f50fdp-4L, -0xd.20fea63729823dcp-2L, 0x8.479981fecdaf816p-1L, -0xb.51543ac7e845d9fp-2L, 0xa.f82574e481a558dp-3L, -0x8.a863be98ab2e9afp-5L, -0xb.c768e5cd8760f3bp-6L, 0xa.7ccc81688b01b9cp-6L, -0xa.08ab70e42362325p-8L, -0xb.62c30831541b0b7p-10L, 0x9.0f024ac2a973782p-10L, -0xe.68e1ad5956c95f9p-13L, 0xd.7b2407256e2365dp-20L, 0x8.09b61fda58cdcd9p-18L, -0xb.49458724ae83fdap-22L, -0xb.1bbd7b9c425fd7p-28L, 0xb.2191e031b4353cfp-33L, -0xb.7da88ba55471baap-43L, -0x9.9224ed0dcb0440cp-58L, 0x0p+0L};
+                return {0x0p+0L, 0xa.e03f2841eb84819p-5L, 0x9.83d15473c1f50fdp-4L, -0xd.20fea63729823dcp-2L, 0x8.479981fecdaf816p-1L, -0xb.51543ac7e845d9fp-2L, 0xa.f82574e481a558dp-3L, -0x8.a863be98ab2e9afp-5L, -0xb.c768e5cd8760f3bp-6L, 0xa.7ccc81688b01b9cp-6L, -0xa.08ab70e42362325p-8L, -0xb.62c30831541b0b7p-10L, 0x9.0f024ac2a973782p-10L, -0xe.68e1ad5956c95f9p-13L, 0xd.7b2407256e2365dp-20L, 0x8.09b61fda58cdcd9p-18L, -0xb.49458724ae83fdap-22L, -0xb.1bbd7b9c425fd7p-28L, 0xb.2191e031b4353cfp-33L, -0xb.7da88ba55471baap-43L, -0x9.9224ed0dcb0440cp-58L, -0x0p+0L};
             }
             if constexpr (order == 3) {
-                return {0x0p+0L, 0x8.e14bf0d3914bbd4p-3L, -0xd.395e1e0030afb9ep-2L, 0xc.74c0bc74cd98ea3p-2L, -0xc.7a837152f075af7p-4L, 0x8.11b249af1111423p-4L, -0x8.7d914829b598f95p-2L, 0xc.02cbea4a32dfa62p-2L, -0x9.c56cbc0e3a809b2p-2L, 0x9.9ce8a27ecaa85dcp-3L, -0x8.45cbd99e57663b5p-5L, -0x9.fc51346f5fdbbd1p-7L, 0x9.5c5e8d27e8757a5p-7L, -0x9.adbb20305389e61p-9L, 0xf.99d436da1232d03p-15L, 0x8.e183ed134ef71abp-14L, -0xc.a86e5be474c0e96p-18L, -0xf.c8248b432ea6598p-24L, 0xc.5b65b5fbac3587ap-28L, -0x9.0ef6feba3b62aaap-37L, -0xf.163bbc628cd0205p-52L, 0x0p+0L};
+                return {0x0p+0L, 0x8.e14bf0d3914bbd4p-3L, -0xd.395e1e0030afb9ep-2L, 0xc.74c0bc74cd98ea3p-2L, -0xc.7a837152f075af7p-4L, 0x8.11b249af1111423p-4L, -0x8.7d914829b598f95p-2L, 0xc.02cbea4a32dfa62p-2L, -0x9.c56cbc0e3a809b2p-2L, 0x9.9ce8a27ecaa85dcp-3L, -0x8.45cbd99e57663b5p-5L, -0x9.fc51346f5fdbbd1p-7L, 0x9.5c5e8d27e8757a5p-7L, -0x9.adbb20305389e61p-9L, 0xf.99d436da1232d03p-15L, 0x8.e183ed134ef71abp-14L, -0xc.a86e5be474c0e96p-18L, -0xf.c8248b432ea6598p-24L, 0xc.5b65b5fbac3587ap-28L, -0x9.0ef6feba3b62aaap-37L, -0xf.163bbc628cd0205p-52L, -0x0p+0L};
             }
             if constexpr (order == 4) {
-                return {0x0p+0L, 0xa.8ec6de67c9035e6p-2L, -0xe.19d824dfde72f6dp+0L, 0x8.73ca916679ee85cp+2L, -0xc.d5d2067714e04fcp+2L, 0xf.8a2626fba89eb9ep+2L, -0x8.be72b56cec81364p+3L, 0x8.d5fc68d6e61f284p+3L, -0xd.776d445bff43fe9p+2L, 0xb.68cbafe17a170d9p+1L, 0xb.260c57f14226301p-2L, -0xa.59e9b6c7cbb8775p+0L, 0xc.73a928d3fadf73cp-1L, -0xc.f1068b2a098cfb7p-3L, 0xc.7b89f9326d61459p-8L, 0x8.0174d562c8cba6dp-7L, -0x9.15ae83ebcf927bfp-10L, -0xb.4adb18b3736b1d7p-16L, 0xd.d0d90c2bd7c17dcp-20L, -0xe.f8336babb7fe566p-29L, -0xc.76037cef17bea43p-42L, 0x0p+0L};
+                return {0x0p+0L, 0xa.8ec6de67c9035e6p-2L, -0xe.19d824dfde72f6dp+0L, 0x8.73ca916679ee85cp+2L, -0xc.d5d2067714e04fcp+2L, 0xf.8a2626fba89eb9ep+2L, -0x8.be72b56cec81364p+3L, 0x8.d5fc68d6e61f284p+3L, -0xd.776d445bff43fe9p+2L, 0xb.68cbafe17a170d9p+1L, 0xb.260c57f14226301p-2L, -0xa.59e9b6c7cbb8775p+0L, 0xc.73a928d3fadf73cp-1L, -0xc.f1068b2a098cfb7p-3L, 0xc.7b89f9326d61459p-8L, 0x8.0174d562c8cba6dp-7L, -0x9.15ae83ebcf927bfp-10L, -0xb.4adb18b3736b1d7p-16L, 0xd.d0d90c2bd7c17dcp-20L, -0xe.f8336babb7fe566p-29L, -0xc.76037cef17bea43p-42L, -0x0p+0L};
             }
             if constexpr (order == 5) {
                 return {0x0p+0L, 0xa.a9c20e5c28262cfp-1L, -0x8.b245130e7d6435p+2L, 0xb.a14e18dc5e6e3bcp+3L, -0xe.912cdf0d3c0c767p+3L, 0x9.b65ec3110fa60e2p+1L, 0xa.51416899076b9c3p+4L, -0x9.702559487170317p+5L, 0xa.f8c633aadd02508p+5L, -0xc.05df7f7dc4ac954p+5L, 0xc.856a5b0e339f38dp+5L, -0xa.0acf073101b6074p+5L, 0xa.75d036d99ea9702p+4L, -0xb.6dad412b4521e9bp+2L, 0xb.309b84fa4322d85p-4L, 0xb.eddbea7d15a390ap-2L, -0x8.c28d4a8cf1aeca5p-4L, -0x9.18649e56e05bc3p-10L, 0xb.f4af141ec671a67p-13L, -0x8.9b691ba71b88c22p-21L, -0xe.51787a5ba8032eep-34L, -0x0p+0L};
@@ -873,10 +1053,10 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0L, 0x8.748c703a8d2f937p-1L, -0xf.aa58ee38f4a5c91p+1L, 0xc.6649ad2cb179936p+3L, -0xa.ec3fa7ecd7c41f4p+4L, 0xb.fdefe0fae49564ap+4L, -0x9.ab0aa5c6715fdd9p+4L, 0x8.0517805b79afde9p+4L, -0xe.b0d6b4042318ee3p+3L, 0xa.58c96b88b1b4fe8p+3L, -0x9.5ebf7665dec59a9p+2L, 0xe.91d7b95490989a7p+0L, -0xd.2d1fb184d6542c6p-1L, -0x8.04bdd18c802f85cp-3L, 0x9.4d5f62e5127240ep-1L, -0xb.6b1e334f7b950afp-2L, 0xa.90dcb78f808ffecp-4L, -0xc.4d0f4db204d1cc9p-9L, -0xe.607c58598cbad8fp-11L, 0xc.f4a5486617740b1p-19L, 0xa.b9cd4f73758e428p-29L, 0x0p+0L};
             }
             if constexpr (order == 8) {
-                return {0x0p+0L, 0xe.1527ff4b308c86p-3L, -0xd.4e4b4124bea1ab6p+0L, 0xa.dddc6243d72ddb1p+2L, -0xa.292b9d75d9dfa3ap+3L, 0xc.8e405a961b38a93p+3L, -0xc.26b2dc1d7fdae55p+3L, 0xb.3c70e9b2cbd6e2ap+3L, -0xa.499812dedb44ac4p+3L, 0x8.a209e470c03af8ap+3L, -0xd.a8eccfb33c210d9p+2L, 0xa.41c0c3baf0658a2p+2L, -0xd.392b16aec032585p+1L, 0xf.0072464fbb8a1e7p+0L, -0x8.a917bbb9a6176d9p+0L, 0x8.a94b0f3707ab7abp-1L, -0x9.ecec45327d721f6p-3L, 0x9.f8e2c727153415ep-7L, 0xd.9f7da20d270d536p-9L, -0xd.d50acf33eea750ap-16L, -0xb.616ca66f1d70df8p-25L, 0x0p+0L};
+                return {0x0p+0L, 0xe.1527ff4b308c86p-3L, -0xd.4e4b4124bea1ab6p+0L, 0xa.dddc6243d72ddb1p+2L, -0xa.292b9d75d9dfa3ap+3L, 0xc.8e405a961b38a93p+3L, -0xc.26b2dc1d7fdae55p+3L, 0xb.3c70e9b2cbd6e2ap+3L, -0xa.499812dedb44ac4p+3L, 0x8.a209e470c03af8ap+3L, -0xd.a8eccfb33c210d9p+2L, 0xa.41c0c3baf0658a2p+2L, -0xd.392b16aec032585p+1L, 0xf.0072464fbb8a1e7p+0L, -0x8.a917bbb9a6176d9p+0L, 0x8.a94b0f3707ab7abp-1L, -0x9.ecec45327d721f6p-3L, 0x9.f8e2c727153415ep-7L, 0xd.9f7da20d270d536p-9L, -0xd.d50acf33eea750ap-16L, -0xb.616ca66f1d70df8p-25L, -0x0p+0L};
             }
             if constexpr (order == 9) {
-                return {0x0p+0L, 0xa.40798a9071f9886p-4L, -0x9.c7f1784d562bdc9p-1L, 0xf.c7a08dd664fcb0ep+0L, -0xd.e3061daa7c85492p+1L, 0xe.9ea25350b56d92ap+1L, -0xa.9b6b7c19db33b9dp+1L, 0x8.4a9d3d29256548ap+1L, -0x8.606e5181f471318p+1L, 0xd.7ab58a9a794ee91p+0L, -0xf.b144a4677fb9db7p-1L, 0x9.f7c1a61944d51aep-1L, -0xe.3ad5af0d7e3ad17p-2L, 0xe.59c5d962fa5f5d7p-3L, -0xb.123c2df8aedf04ap-4L, 0xb.0d8bd72ff86061cp-5L, -0x8.5b12395e9ebc248p-6L, 0xe.4d9f7834474485cp-11L, 0xb.e29451f90ab62c4p-11L, -0x8.6239c0145764987p-16L, -0xd.a073c2e5c404378p-25L, 0x0p+0L};
+                return {0x0p+0L, 0xa.40798a9071f9886p-4L, -0x9.c7f1784d562bdc9p-1L, 0xf.c7a08dd664fcb0ep+0L, -0xd.e3061daa7c85492p+1L, 0xe.9ea25350b56d92ap+1L, -0xa.9b6b7c19db33b9dp+1L, 0x8.4a9d3d29256548ap+1L, -0x8.606e5181f471318p+1L, 0xd.7ab58a9a794ee91p+0L, -0xf.b144a4677fb9db7p-1L, 0x9.f7c1a61944d51aep-1L, -0xe.3ad5af0d7e3ad17p-2L, 0xe.59c5d962fa5f5d7p-3L, -0xb.123c2df8aedf04ap-4L, 0xb.0d8bd72ff86061cp-5L, -0x8.5b12395e9ebc248p-6L, 0xe.4d9f7834474485cp-11L, 0xb.e29451f90ab62c4p-11L, -0x8.6239c0145764987p-16L, -0xd.a073c2e5c404378p-25L, -0x0p+0L};
             }
             if constexpr (order == 10) {
                 return {0x0p+0L, 0xc.512ff3ce8e26ed6p-7L, -0xb.ceeeec30690a3d4p-4L, 0x9.7c942104078413dp-2L, -0x8.2529923084db5b6p-1L, 0xf.de393fe11f77db2p-2L, -0x9.745275d635af24dp-2L, 0xc.b7fc3e7f2662817p-3L, -0xe.dc63fbdf961d121p-3L, 0xc.433f6669ce8d77ap-3L, -0xb.80cde13c7fe01dap-4L, 0xd.186905a733e3482p-5L, -0xb.9a073d1ccf31d0dp-5L, 0xb.40c0c94f326298p-6L, -0xa.8537af479d9846bp-8L, 0xc.69d908f5c1cd609p-9L, -0xd.b913ea9c09b9ab5p-10L, -0xd.188a7ef97de034bp-15L, 0xb.8f3d1da6c45f8b5p-13L, -0xa.775011edc5ea48p-17L, -0x8.4d76c9c441821a3p-24L, 0x0p+0L};
@@ -885,40 +1065,75 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         #ifdef BOOST_HAS_FLOAT128
         if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
             if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.f82d860ed311d7772f0a5fc02aa2p-7Q, 0x1.da87adf545dea36f29603c50206fp-2Q, 0x1.a074ea6831a179cbcefe13bdeb27p-1Q, -0x1.d3dbc22db33632cb9d3eeea9309ep-2Q, 0x1.07dc8c4b588098d99d74923fef11p-2Q, -0x1.17e06a0deb06ffc5a354422c2917p-3Q, 0x1.d85300a8e9a59db3d8e328544722p-5Q, -0x1.0710616766f9db787dd784803608p-6Q, 0x1.0182a0c9a44ba81f2b490da87ce3p-9Q, 0x1.d91cd19825f46395eba40bde2571p-14Q, 0x1.f2bfaace30f58a825ed0b3a11e16p-15Q, -0x1.d7e9ba7b3ac4736029b548526141p-15Q, 0x1.5c274e2e04a6575e26e75abeb4d6p-18Q, 0x1.63562e1b18da7fac5905b88575eep-20Q, -0x1.0af5800900ccbea5a647053aa06fp-26Q, 0x1.1409cb495cfaa9cc50f1fb2798a1p-28Q, -0x1.1601287f207dc804b32b2b372bd4p-35Q, -0x1.4f944d6c974a0ba10244cbd7bf6ap-42Q, -0x1.ad914b3b9c6449c459a4d88261fp-53Q, -0x1.65d8440cb5909e7eb82f547cb7ffp-70Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.f82d860ed311d7772f0a5fc02a6dp-7Q, 0x1.da87adf545dea36f29603c50206cp-2Q, 0x1.a074ea6831a179cbcefe13bdeb26p-1Q, -0x1.d3dbc22db33632cb9d3eeea93097p-2Q, 0x1.07dc8c4b588098d99d74923fef1p-2Q, -0x1.17e06a0deb06ffc5a354422c2913p-3Q, 0x1.d85300a8e9a59db3d8e328544719p-5Q, -0x1.0710616766f9db787dd78480360dp-6Q, 0x1.0182a0c9a44ba81f2b490da87cf1p-9Q, 0x1.d91cd19825f46395eba40bde2534p-14Q, 0x1.f2bfaace30f58a825ed0b3a11e2p-15Q, -0x1.d7e9ba7b3ac4736029b548526137p-15Q, 0x1.5c274e2e04a6575e26e75abeb4c3p-18Q, 0x1.63562e1b18da7fac5905b88575e8p-20Q, -0x1.0af5800900ccbea5a647053aa052p-26Q, 0x1.1409cb495cfaa9cc50f1fb279896p-28Q, -0x1.1601287f207dc804b32b2b372befp-35Q, -0x1.4f944d6c974a0ba10244cbd7bf57p-42Q, -0x1.ad914b3b9c6449c459a4d882621ap-53Q, -0x1.65d8440cb5909e7eb82f547cb81ep-70Q, 0x0p+0Q};
             }
             if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.4988f615d8fc21013726786516bbp-4Q, 0x1.cd9786f046dbd06d9795ae530616p-1Q, -0x1.f034187a5d75333e9dbb5b104718p-1Q, -0x1.075e3bcf1d71f31524cf997afba1p-3Q, 0x1.303436308c600230256305532d4ep-3Q, -0x1.71d07ef81053ea5196f6a9c9bd7ap-12Q, -0x1.321c6b5970b994e47d89204a7748p-4Q, 0x1.0f00f0747578208709a35dbb5683p-4Q, -0x1.fec807d6bcde2f6b9da93df4aa7bp-6Q, 0x1.092c0960e80ebe73a0fb5f592a93p-7Q, -0x1.1857810566102a80b03f6d574873p-11Q, -0x1.693105a2bb706882bf9e39158ac2p-12Q, 0x1.a2acf3b1f9d0749452e4dc44d928p-14Q, -0x1.c4d81f25bbab666371fdd702fd07p-19Q, -0x1.e0284772a21eeb07c87b76642dabp-20Q, 0x1.7db784c0b013093ad9874c402643p-25Q, 0x1.739c15dc80c555f970d134b64534p-30Q, -0x1.d9433a2520a2e30f13e7c351f19ep-36Q, 0x1.651bd505e5aaae5cab5b708f20d3p-46Q, 0x1.29782f98b98d8b31230d837a9eebp-62Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.4988f615d8fc2101372678651696p-4Q, 0x1.cd9786f046dbd06d9795ae5305eep-1Q, -0x1.f034187a5d75333e9dbb5b1046e1p-1Q, -0x1.075e3bcf1d71f31524cf997afbe8p-3Q, 0x1.303436308c600230256305532d57p-3Q, -0x1.71d07ef81053ea5196f6a9c9ea93p-12Q, -0x1.321c6b5970b994e47d89204a7726p-4Q, 0x1.0f00f0747578208709a35dbb5672p-4Q, -0x1.fec807d6bcde2f6b9da93df4aa6dp-6Q, 0x1.092c0960e80ebe73a0fb5f592a81p-7Q, -0x1.1857810566102a80b03f6d57486cp-11Q, -0x1.693105a2bb706882bf9e39158aa2p-12Q, 0x1.a2acf3b1f9d0749452e4dc44d918p-14Q, -0x1.c4d81f25bbab666371fdd702fceap-19Q, -0x1.e0284772a21eeb07c87b76642d8fp-20Q, 0x1.7db784c0b013093ad9874c402637p-25Q, 0x1.739c15dc80c555f970d134b64517p-30Q, -0x1.d9433a2520a2e30f13e7c351f17bp-36Q, 0x1.651bd505e5aaae5cab5b708f20cp-46Q, 0x1.29782f98b98d8b31230d837a9eccp-62Q, 0x0p+0Q};
             }
             if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.5c07e5083d7090314f4044902659p-2Q, 0x1.307a2a8e783ea1f99bb361a3cef6p-1Q, -0x1.a41fd4c6e53047b890408086b56p+1Q, 0x1.08f3303fd9b5f02cbec87edc4433p+2Q, -0x1.6a2a8758fd08bb3ed6b347424ce1p+1Q, 0x1.5f04ae9c9034ab19fcfae00d09d5p+0Q, -0x1.150c77d31565d35edf80240e5f13p-2Q, -0x1.78ed1cb9b0ec1e760990f81b5f62p-3Q, 0x1.4f99902d11603738023acee04ff8p-3Q, -0x1.41156e1c846c464a303629e297f8p-5Q, -0x1.6c5861062a83616dee9275c18c3cp-7Q, 0x1.21e04958552e6f03502dd79356aap-7Q, -0x1.cd1c35ab2ad92bf156188522c4d7p-10Q, 0x1.af6480e4adc46cb9e0c7649b6bfap-17Q, 0x1.0136c3fb4b19b9b10157d7a8345p-15Q, -0x1.6928b0e495d07fb474aad680049ap-19Q, -0x1.6377af73884bfae0ae8534a755ap-25Q, 0x1.64323c063686a79e3f723a6f6a99p-30Q, -0x1.6fb51174aa8e375496c635af8171p-40Q, -0x1.32449da1b960881894abd22269dap-55Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.5c07e5083d7090314f404490267fp-2Q, 0x1.307a2a8e783ea1f99bb361a3ce3fp-1Q, -0x1.a41fd4c6e53047b890408086b518p+1Q, 0x1.08f3303fd9b5f02cbec87edc442ap+2Q, -0x1.6a2a8758fd08bb3ed6b347424cecp+1Q, 0x1.5f04ae9c9034ab19fcfae00d09b9p+0Q, -0x1.150c77d31565d35edf80240e5e1cp-2Q, -0x1.78ed1cb9b0ec1e760990f81b60f9p-3Q, 0x1.4f99902d11603738023acee050bdp-3Q, -0x1.41156e1c846c464a303629e298b7p-5Q, -0x1.6c5861062a83616dee9275c18c97p-7Q, 0x1.21e04958552e6f03502dd7935724p-7Q, -0x1.cd1c35ab2ad92bf156188522c5bfp-10Q, 0x1.af6480e4adc46cb9e0c7649b6f56p-17Q, 0x1.0136c3fb4b19b9b10157d7a834f7p-15Q, -0x1.6928b0e495d07fb474aad6800549p-19Q, -0x1.6377af73884bfae0ae8534a7569p-25Q, 0x1.64323c063686a79e3f723a6f6b93p-30Q, -0x1.6fb51174aa8e375496c635af829fp-40Q, -0x1.32449da1b960881894abd2226adap-55Q, 0x0p+0Q};
             }
             if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.1c297e1a722977a767a1ff2272dcp+0Q, -0x1.a72bc3c00615f73ba93716b01652p+1Q, 0x1.8e98178e99b31d46ae26eec0a62ep+1Q, -0x1.8f506e2a5e0eb5edc0313f13910ap-1Q, 0x1.02364935e2222846b9cdda1bad5bp-1Q, -0x1.0fb2290536b31f2a2fbff34045aap+1Q, 0x1.80597d49465bf4c4d8869fb53015p+1Q, -0x1.38ad9781c750136475272cd6e5fep+1Q, 0x1.339d144fd9550bb8463b544a639ep+0Q, -0x1.08b97b33caecc76a026ab8335ac7p-2Q, -0x1.3f8a268debfb77a1cde76d550dc6p-4Q, 0x1.2b8bd1a4fd0eaf4aaa08a96cf13fp-4Q, -0x1.35b764060a713cc242948b5c3e5ep-6Q, 0x1.f33a86db42465a05a6ee3ed1f1c2p-12Q, 0x1.1c307da269dee355c5c2d340dc8p-11Q, -0x1.950dcb7c8e981d2c1ff88549c6afp-15Q, -0x1.f904916865d4cb30ef383c46a7ddp-21Q, 0x1.8b6cb6bf7586b0f4f1fcded43d5cp-25Q, -0x1.21dedfd7476c5553241f507abe95p-34Q, -0x1.e2c7778c519a040a7c97727eda55p-49Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.1c297e1a722977a767a1ff227742p+0Q, -0x1.a72bc3c00615f73ba93716b01e65p+1Q, 0x1.8e98178e99b31d46ae26eec0b1cap+1Q, -0x1.8f506e2a5e0eb5edc0313f13b62bp-1Q, 0x1.02364935e2222846b9cdda1bc87p-1Q, -0x1.0fb2290536b31f2a2fbff3404bbdp+1Q, 0x1.80597d49465bf4c4d8869fb534fap+1Q, -0x1.38ad9781c750136475272cd6e902p+1Q, 0x1.339d144fd9550bb8463b544a6643p+0Q, -0x1.08b97b33caecc76a026ab8335d28p-2Q, -0x1.3f8a268debfb77a1cde76d550fe7p-4Q, 0x1.2b8bd1a4fd0eaf4aaa08a96cf3ep-4Q, -0x1.35b764060a713cc242948b5c4153p-6Q, 0x1.f33a86db42465a05a6ee3ed1f4ffp-12Q, 0x1.1c307da269dee355c5c2d340dfe6p-11Q, -0x1.950dcb7c8e981d2c1ff88549cb89p-15Q, -0x1.f904916865d4cb30ef383c46ae0fp-21Q, 0x1.8b6cb6bf7586b0f4f1fcded4430cp-25Q, -0x1.21dedfd7476c5553241f507ac2d7p-34Q, -0x1.e2c7778c519a040a7c97727ee351p-49Q, 0x0p+0Q};
             }
             if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.51d8dbccf9206bcc4420e8d9a9eap+1Q, -0x1.c33b049bfbce5ed995e580451e63p+3Q, 0x1.0e79522ccf3dd0b86ea89a553ap+5Q, -0x1.9aba40cee29c09f71dc38c35b29bp+5Q, 0x1.f144c4df7513d73b0fd71dc9dfb5p+5Q, -0x1.17ce56ad9d9026c80fe9053e2d6dp+6Q, 0x1.1abf8d1adcc3e5071c7209bb681cp+6Q, -0x1.aeeda88b7fe87fd16bcf8e052138p+5Q, 0x1.6d1975fc2f42e1b2096263c936fdp+4Q, 0x1.64c18afe2844c60255dd74d11ep+1Q, -0x1.4b3d36d8f9770ee95e2721f914bbp+3Q, 0x1.8e75251a7f5bee7754c2a951492ep+2Q, -0x1.9e20d16541319f6d732cb61c0c9ap+0Q, 0x1.8f713f264dac28b16bf91d5056c3p-5Q, 0x1.002e9aac591974da848a16c85358p-4Q, -0x1.22b5d07d79f24f7de83980b60562p-7Q, -0x1.695b63166e6d63ad77759faf5052p-13Q, 0x1.ba1b21857af82fb76bf474298db1p-17Q, -0x1.df066d7576ffcacbc6c94f3c5a26p-26Q, -0x1.8ec06f9de2f7d48618cf3f2e50ccp-39Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.51d8dbccf9206bcc4420e8d9ae07p+1Q, -0x1.c33b049bfbce5ed995e58045194fp+3Q, 0x1.0e79522ccf3dd0b86ea89a5531bfp+5Q, -0x1.9aba40cee29c09f71dc38c35a548p+5Q, 0x1.f144c4df7513d73b0fd71dc9df3fp+5Q, -0x1.17ce56ad9d9026c80fe9053e3b69p+6Q, 0x1.1abf8d1adcc3e5071c7209bb8006p+6Q, -0x1.aeeda88b7fe87fd16bcf8e054d05p+5Q, 0x1.6d1975fc2f42e1b2096263c969bbp+4Q, 0x1.64c18afe2844c60255dd74d07edbp+1Q, -0x1.4b3d36d8f9770ee95e2721f907e9p+3Q, 0x1.8e75251a7f5bee7754c2a9513fecp+2Q, -0x1.9e20d16541319f6d732cb61c018ap+0Q, 0x1.8f713f264dac28b16bf91d504bd5p-5Q, 0x1.002e9aac591974da848a16c844c8p-4Q, -0x1.22b5d07d79f24f7de83980b5ed9fp-7Q, -0x1.695b63166e6d63ad77759faf33b7p-13Q, 0x1.ba1b21857af82fb76bf4742957f6p-17Q, -0x1.df066d7576ffcacbc6c94f3c14p-26Q, -0x1.8ec06f9de2f7d48618cf3f2e0232p-39Q, 0x0p+0Q};
             }
             if constexpr (order == 5) {
-                return {0x0p+0Q, 0x1.553841cb8504c59ec882878d66e2p+2Q, -0x1.1648a261cfac86a07a57717eb0e3p+5Q, 0x1.7429c31b8bcdc777e068523e1aeap+6Q, -0x1.d2259be1a7818ecd1bf98b178549p+6Q, 0x1.36cbd86221f4c1c3813018fd6cbfp+4Q, 0x1.4a282d1320ed73864b5c77ade623p+7Q, -0x1.2e04ab290e2e062d6018a9efa98fp+8Q, 0x1.5f18c6755ba04a0fe584709ac85dp+8Q, -0x1.80bbefefb89592a7731266a97561p+8Q, 0x1.90ad4b61c673e71a7b1a662f6ff2p+8Q, -0x1.4159e0e62036c0e7d3a9392e2704p+8Q, 0x1.4eba06db33d52e049a4997516cf9p+7Q, -0x1.6db5a82568a43d359e1327442546p+5Q, 0x1.6613709f48645b09020d12e639edp-1Q, 0x1.7dbb7d4fa2b472146ed1344dc15bp+1Q, -0x1.1851a9519e35d9490483602f6703p-1Q, -0x1.230c93cadc0b78607a6df81f1b6fp-7Q, 0x1.7e95e283d8ce34ce8180ea4f4ca4p-10Q, -0x1.136d2374e371184371f1175ee7a9p-18Q, -0x1.ca2f0f4b750065dbf1a921be61p-31Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.553841cb8504c59ec8828722c9cp+2Q, -0x1.1648a261cfac86a07a577122f4eep+5Q, 0x1.7429c31b8bcdc777e06851df4ff3p+6Q, -0x1.d2259be1a7818ecd1bf98b71d684p+6Q, 0x1.36cbd86221f4c1c381302622675ep+4Q, 0x1.4a282d1320ed73864b5c73d42965p+7Q, -0x1.2e04ab290e2e062d6018a7405d3cp+8Q, 0x1.5f18c6755ba04a0fe5846dc7ce5fp+8Q, -0x1.80bbefefb89592a7731263e58b6ep+8Q, 0x1.90ad4b61c673e71a7b1a638ff4cp+8Q, -0x1.4159e0e62036c0e7d3a9372888dep+8Q, 0x1.4eba06db33d52e049a499539c59ap+7Q, -0x1.6db5a82568a43d359e1324f88c7ep+5Q, 0x1.6613709f48645b09020d1137193bp-1Q, 0x1.7dbb7d4fa2b472146ed131c42bb3p+1Q, -0x1.1851a9519e35d94904835e4c0f44p-1Q, -0x1.230c93cadc0b78607a6df63dd398p-7Q, 0x1.7e95e283d8ce34ce8180e79a24c3p-10Q, -0x1.136d2374e371184371f11564efd5p-18Q, -0x1.ca2f0f4b750065dbf1a91e494693p-31Q, 0x0p+0Q};
             }
             if constexpr (order == 6) {
-                return {0x0p+0Q, 0x1.43e579b56aec6db8f44fad025d31p+2Q, -0x1.2015783789a1305c4b04f4166dd8p+5Q, 0x1.be9eb07640a6e4dcf71e8ec13b53p+6Q, -0x1.917bfbcd50104121d7cf2e45b56cp+7Q, 0x1.e7564ac670464ea6f5bb02fedc24p+7Q, -0x1.dd46b6e14bd993fb7d27e48ccc74p+7Q, 0x1.c24b2cb18bb303674bf660cced48p+7Q, -0x1.9299f7098407dc40f69f41c308ebp+7Q, 0x1.2da088f392f175bbf1502adde1fap+7Q, -0x1.7f74fc0a8fbbbd2a6629268e303fp+6Q, 0x1.cafceab55c22225d33d1409b59ap+5Q, -0x1.cfad0a751fefca13c3b32651d4a9p+4Q, 0x1.f4f5eade96653abb41ce938b652dp+2Q, 0x1.14b6d949957a5646a55036bfd229p+0Q, -0x1.5e908a00f74d9f8f6b65d27bbd91p+0Q, 0x1.1ee7d490234e22c547ade06a389fp-2Q, -0x1.1e667fbdaff187310b0175bb8ebfp-11Q, -0x1.81c4231f27f23e6bc64b0c485b78p-10Q, 0x1.28216d550397d430f87999376f2cp-18Q, 0x1.ebdb45ca159a64fa9f199a6004f2p-30Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.43e579b56aec6db8f44fad1a2ca3p+2Q, -0x1.2015783789a1305c4b04f4299082p+5Q, 0x1.be9eb07640a6e4dcf71e8edd1986p+6Q, -0x1.917bfbcd50104121d7cf2e5fb61ap+7Q, 0x1.e7564ac670464ea6f5bb03253324p+7Q, -0x1.dd46b6e14bd993fb7d27e4be31d5p+7Q, 0x1.c24b2cb18bb303674bf661030f65p+7Q, -0x1.9299f7098407dc40f69f41f42557p+7Q, 0x1.2da088f392f175bbf1502b058265p+7Q, -0x1.7f74fc0a8fbbbd2a662926cc0952p+6Q, 0x1.cafceab55c22225d33d140f11ba1p+5Q, -0x1.cfad0a751fefca13c3b326a88e5bp+4Q, 0x1.f4f5eade96653abb41ce93f1a983p+2Q, 0x1.14b6d949957a5646a550369bc7aap+0Q, -0x1.5e908a00f74d9f8f6b65d286f0e6p+0Q, 0x1.1ee7d490234e22c547ade0704929p-2Q, -0x1.1e667fbdaff187310b0173bcb94dp-11Q, -0x1.81c4231f27f23e6bc64b0c2f2493p-10Q, 0x1.28216d550397d430f8799924705dp-18Q, 0x1.ebdb45ca159a64fa9f199a16a149p-30Q, 0x0p+0Q};
             }
             if constexpr (order == 7) {
-                return {0x0p+0Q, 0x1.0e918e0751a5f26d66d32652a3c3p+2Q, -0x1.f54b1dc71e94b922c8b7d9cedc49p+4Q, 0x1.8cc935a5962f326b8767ea0da425p+6Q, -0x1.5d87f4fd9af883e7ca8f85fa5bb5p+7Q, 0x1.7fbdfc1f5c92ac9439f72daa4354p+7Q, -0x1.356154b8ce2bfbb26ff261795e76p+7Q, 0x1.00a2f00b6f35fbd2365b8c89c9e7p+7Q, -0x1.d61ad68084631dc5b1cb3579539ep+6Q, 0x1.4b192d7116369fcf46bbc7a85648p+6Q, -0x1.2bd7eeccbbd8b3529c9ec84730c4p+5Q, 0x1.d23af72a9213134d138ab8713629p+3Q, -0x1.a5a3f6309aca858b5548cd2e0f1fp+2Q, -0x1.0097ba319005f0b824ee38e92ecp+0Q, 0x1.29abec5ca24e481b150656fe0d65p+2Q, -0x1.6d63c669ef72a15dead10bcfb7ep+1Q, 0x1.521b96f1f011ffd834fe0c58029ap-1Q, -0x1.89a1e9b6409a39917b2558e5c9cap-6Q, -0x1.cc0f8b0b31975b1da167d6c2e885p-8Q, 0x1.9e94a90cc2ee8162e5d90cd367bep-16Q, 0x1.5739a9ee6eb1c850a9597ef2cebp-26Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.0e918e0751a5f26d66d326215241p+2Q, -0x1.f54b1dc71e94b922c8b7d974b91p+4Q, 0x1.8cc935a5962f326b8767e9c68e69p+6Q, -0x1.5d87f4fd9af883e7ca8f85ba9a3ep+7Q, 0x1.7fbdfc1f5c92ac9439f72d5fc5fbp+7Q, -0x1.356154b8ce2bfbb26ff26135d3d6p+7Q, 0x1.00a2f00b6f35fbd2365b8c4d7e4cp+7Q, -0x1.d61ad68084631dc5b1cb350d96d3p+6Q, 0x1.4b192d7116369fcf46bbc7590d76p+6Q, -0x1.2bd7eeccbbd8b3529c9ec7ea0986p+5Q, 0x1.d23af72a9213134d138ab79fb28fp+3Q, -0x1.a5a3f6309aca858b5548cc51629cp+2Q, -0x1.0097ba319005f0b824ee39f7e25p+0Q, 0x1.29abec5ca24e481b150656fa7b24p+2Q, -0x1.6d63c669ef72a15dead10bbf465bp+1Q, 0x1.521b96f1f011ffd834fe0c4deb25p-1Q, -0x1.89a1e9b6409a39917b2558fc77d9p-6Q, -0x1.cc0f8b0b31975b1da167d6d21402p-8Q, 0x1.9e94a90cc2ee8162e5d90cf2df7p-16Q, 0x1.5739a9ee6eb1c850a9597f22010bp-26Q, 0x0p+0Q};
             }
             if constexpr (order == 8) {
-                return {0x0p+0Q, 0x1.c2a4ffe9661190c09a7af6cb9ca4p+0Q, -0x1.a9c9682497d4356cc97c764c71e1p+3Q, 0x1.5bbb8c487ae5bb615e8e71957082p+5Q, -0x1.452573aebb3bf474bf24d39c0c75p+6Q, 0x1.91c80b52c3671525c3375728fd33p+6Q, -0x1.84d65b83affb5ca97ccaf4bcaa17p+6Q, 0x1.678e1d36597adc53993fd53deeacp+6Q, -0x1.4933025bdb6895888c17391d3c87p+6Q, 0x1.14413c8e18075f1444cc50c11326p+6Q, -0x1.b51d99f6678421b18139cf56717cp+5Q, 0x1.483818775e0cb14480b3264cce69p+5Q, -0x1.a72562d5d8064b092b7ba7b739cp+4Q, 0x1.e00e48c9f77143cec0c43437c4bep+3Q, -0x1.1522f77734c2edb19342dec0265fp+3Q, 0x1.152961e6e0f56f56720078cacb8p+2Q, -0x1.3d9d88a64fae43ec46db6df5abf8p+0Q, 0x1.3f1c58e4e2a682bc6ff0544f4ae4p-4Q, 0x1.b3efb441a4e1aa6b7bfce49b9d8ep-6Q, -0x1.baa159e67dd4ea14a46823aaab92p-13Q, -0x1.6c2d94cde3ae1bef5e760af7804dp-22Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.c2a4ffe9661190c09a7af8b79479p+0Q, -0x1.a9c9682497d4356cc97c7817608dp+3Q, 0x1.5bbb8c487ae5bb615e8e73227ceep+5Q, -0x1.452573aebb3bf474bf24d5595fd4p+6Q, 0x1.91c80b52c3671525c3375a1dd5efp+6Q, -0x1.84d65b83affb5ca97ccaf8b73947p+6Q, 0x1.678e1d36597adc53993fd96dab7ap+6Q, -0x1.4933025bdb6895888c173cc7b2a5p+6Q, 0x1.14413c8e18075f1444cc540dc34bp+6Q, -0x1.b51d99f6678421b18139d5beb61cp+5Q, 0x1.483818775e0cb14480b32b95042cp+5Q, -0x1.a72562d5d8064b092b7bae77a4cbp+4Q, 0x1.e00e48c9f77143cec0c43c67669bp+3Q, -0x1.1522f77734c2edb19342e41508e1p+3Q, 0x1.152961e6e0f56f5672007e36f948p+2Q, -0x1.3d9d88a64fae43ec46db73db181ap+0Q, 0x1.3f1c58e4e2a682bc6ff059fa1f8dp-4Q, 0x1.b3efb441a4e1aa6b7bfceb788233p-6Q, -0x1.baa159e67dd4ea14a46828d67fefp-13Q, -0x1.6c2d94cde3ae1bef5e760e39de7cp-22Q, 0x0p+0Q};
             }
             if constexpr (order == 9) {
-                return {0x0p+0Q, 0x1.480f31520e3f310c306bdc1e8024p-1Q, -0x1.38fe2f09aac57b92aacdab2b4e96p+2Q, 0x1.f8f411bacc9f961bc5fe565a48cfp+3Q, -0x1.bc60c3b54f90a9241998e1a7c135p+4Q, 0x1.d3d44a6a16adb2540f6c000e54a3p+4Q, -0x1.536d6f833b66773a9702164e108p+4Q, 0x1.0953a7a524aca913282b25214d25p+4Q, -0x1.0c0dca303e8e262fc968302773e3p+4Q, 0x1.af56b1534f29dd21b9240ac133b1p+3Q, -0x1.f628948ceff73b6d1ae734867e3p+2Q, 0x1.3ef834c3289aa35b262758c2782ep+2Q, -0x1.c75ab5e1afc75a2d9d28a2f8d82cp+1Q, 0x1.cb38bb2c5f4bebadf622e77e6e2bp+0Q, -0x1.624785bf15dbe093496ba0bcf74cp-1Q, 0x1.61b17ae5ff0c0c37a77beb09baeep-2Q, -0x1.0b62472bd3d7849095f6de060b33p-3Q, 0x1.c9b3ef0688e890b76d9f1545a8bdp-8Q, 0x1.7c528a3f2156c58889998659bd68p-8Q, -0x1.0c4738028aec930d4308dfe577d7p-13Q, -0x1.b40e785cb88086ef360909d3183cp-22Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.480f31520e3f310c306bdafaf042p-1Q, -0x1.38fe2f09aac57b92aacdaa15d1b7p+2Q, 0x1.f8f411bacc9f961bc5fe5499f875p+3Q, -0x1.bc60c3b54f90a9241998e0192f5ep+4Q, 0x1.d3d44a6a16adb2540f6bfe5db93ap+4Q, -0x1.536d6f833b66773a970214ff031cp+4Q, 0x1.0953a7a524aca913282b24103258p+4Q, -0x1.0c0dca303e8e262fc9682f1cf736p+4Q, 0x1.af56b1534f29dd21b9240915b75ap+3Q, -0x1.f628948ceff73b6d1ae732743415p+2Q, 0x1.3ef834c3289aa35b262757674e4bp+2Q, -0x1.c75ab5e1afc75a2d9d28a11fcce2p+1Q, 0x1.cb38bb2c5f4bebadf622e599ec8fp+0Q, -0x1.624785bf15dbe093496b9f1d5135p-1Q, 0x1.61b17ae5ff0c0c37a77be972ec5ep-2Q, -0x1.0b62472bd3d7849095f6dced344cp-3Q, 0x1.c9b3ef0688e890b76d9f130077d8p-8Q, 0x1.7c528a3f2156c588899985294901p-8Q, -0x1.0c4738028aec930d4308df6549ap-13Q, -0x1.b40e785cb88086ef360909630572p-22Q, 0x0p+0Q};
             }
             if constexpr (order == 10) {
-                return {0x0p+0Q, 0x1.8a25fe79d1c4ddac335be805ed36p-4Q, -0x1.79dddd860d2147a741654102c6e4p-1Q, 0x1.2f92842080f0827925b021c0be64p+1Q, -0x1.04a53246109b6b6c0d3ef6e90b5fp+2Q, 0x1.fbc727fc23eefb6381085f0dbe0ep+1Q, -0x1.2e8a4ebac6b5e49a84fad579cb0bp+1Q, 0x1.96ff87cfe4cc502ebda9734be9aep+0Q, -0x1.db8c7f7bf2c3a242351f98d5116p+0Q, 0x1.8867eccd39d1aef37286907e6727p+0Q, -0x1.7019bc278ffc03b406b2fe913c47p-1Q, 0x1.a30d20b4e67c690471d7cb32e446p-2Q, -0x1.7340e7a399e63a19859bd63999a6p-2Q, 0x1.68181929e64c530045ddd9689347p-3Q, -0x1.50a6f5e8f3b308d50e585e890eebp-5Q, 0x1.8d3b211eb839ac111937339fb303p-6Q, -0x1.b7227d5381373569d6206bc13579p-7Q, -0x1.a3114fdf2fbc06953fcb9948c145p-12Q, 0x1.71e7a3b4d88bf16a9f3c250c332p-10Q, -0x1.4eea023db8bd4900ec558c34e57cp-14Q, -0x1.09aed93888304346e30d1466764ap-21Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.8a25fe79d1c4ddac335be8819a8ap-4Q, -0x1.79dddd860d2147a7416541793f71p-1Q, 0x1.2f92842080f0827925b022200689p+1Q, -0x1.04a53246109b6b6c0d3ef73b505ap+2Q, 0x1.fbc727fc23eefb6381085fb0ea64p+1Q, -0x1.2e8a4ebac6b5e49a84fad5dff777p+1Q, 0x1.96ff87cfe4cc502ebda973db1ba2p+0Q, -0x1.db8c7f7bf2c3a242351f9975276ep+0Q, 0x1.8867eccd39d1aef372869101502fp+0Q, -0x1.7019bc278ffc03b406b2ff135206p-1Q, 0x1.a30d20b4e67c690471d7cbcbb0dfp-2Q, -0x1.7340e7a399e63a19859bd6b84d4cp-2Q, 0x1.68181929e64c530045ddd9e48ddfp-3Q, -0x1.50a6f5e8f3b308d50e585f11b7ap-5Q, 0x1.8d3b211eb839ac11193734372a7dp-6Q, -0x1.b7227d5381373569d6206c572353p-7Q, -0x1.a3114fdf2fbc06953fcb9931063cp-12Q, 0x1.71e7a3b4d88bf16a9f3c256dd239p-10Q, -0x1.4eea023db8bd4900ec558c766ab3p-14Q, -0x1.09aed93888304346e30d148d3c14p-21Q, 0x0p+0Q};
             }
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            if constexpr (order == 0) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0153862862186078764210148054384665436987968299086163110916049774302302509757"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.463408201308509360685176566158665903411342347448682788607059620387445077532"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.813391995638826649479330465641602870909776013569395886947250616963915046071"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.456892999686536248322183305850398976442122564743086558409415878925543062613"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.257677261446702307763827286244642468068192138990732487426320016042544286916"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.136658505010362584956891849494062948225995486599841370839711839313046305597"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0576567662131323839275754677629378113124645271947858794185772706476552313105"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0160561515054805568795851215654406366459996109297291243447819308339625896857"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00196464741458920772402831404575169651260998923501842539475704095236022681377"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000112798827446855800791029803530656734991774835196287349403803335501621270655"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000594554781954403684033785931588011770054264082896496671103792500235464433295"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000562564136659884191230679156227868258475904572875936016422586126656291941418"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000518789197025363361471577911859966580654417969569942459663451570764021770902"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000132373214147764795577030206527013960188029793451345023965588627064041150704"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000155390580715395054554173944015565071767006531414831642901826878560185386309"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000401688533248623065067198103021582298234469777511892684855878156604369527873"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000316054552262036582439139330382598424252005270997818496711644728508686815474"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000298054298041780380540322339753186187258299530548878985631631068130187725404"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000186295230202489625442020988651081124044989063537598156376169532878324451123"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000118400908492220475093634528886504359773639984757721702393945884924044020060"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 1) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0804528820713690537679942952538307927448324275292783996775043561168764668792"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.901546685057318722606544198126464222660980499114959450975631195995562075653"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.969147458016531260537001332368135743279288495176200726279321756564798820440"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.128597705133580020105456519744387638532533583968712163469421630736054713073"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.148537085873201139450805597667488365500301018520176104569141326668098237996"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000352682530778098478434438198206217867661443912512135381010073899276667394708"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0747341340384494360574688474082559001763945248197182213228281231111410765743"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0661630051393711509223363180529539046273421054851354002096935895895589322378"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0311756207037897739706621005131524864825329454001744116473141441231765143715"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00809240777908867125888958717233316990861675515056387491671985358196801653703"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000534709572707320623292468935686184597428178805593585443411787185724270841266"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000344459049457110720806003651240962720647979860629593805430817794517683005097"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000998200401053258733952321911032602231933728074550949033897739987254062819085"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000337395239823704966830913455725328211227310458904067484070296753117772464426"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000178872548120729485900416417576878299998863692536435591416599550573501317289"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000444376921974173227032345936619919762366059115958040870563226908761301278160"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000135190824431474161018642835112040642148891160635198350421744055168342457059"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000269018645424657851835556324494989262226498212843590290606946175171968874237"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000198235161188202162103176056710579230402924914509457090754670397189279898276"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000000000251966447199947741787778445282273243764250629238425265938759750960070288565"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 2) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.339873865726403823874694504886230871354288247669120680859586352931910650802"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.594682054416009422785849668697082787755660519264449722390570694692122196031"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.28222140990908627713882079321726861540709199811588816762195376180866676151"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.13984304652589597399637402140982673032568889063380246443975686333143709866"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.82942287297379899817138989243274273519930408716847888511551935958914702440"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.37116519281717568064954984833983547962197792842040302587532179757516934771"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.270555374392051307156490696193132354552391022825927018192372907103041586105"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.184046005646555652197008303457890114279643877305115529070305316012624288888"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.163867117286074044679000700383983800581641338738039398170630891049204540480"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0391947889912791807642293867045881185152396327816360187024476982368191084445"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0111189340353413485147270893150106933823953700659393824844796952100999217654"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00884631711293466609492290342912398272864238580654395596445675814230221634902"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00175899579589153660809115004201226274173551391561283661338278039734836261348"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000128565010951553987674529189490213861196316851900637195447923613618392713735"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000306622896125458146897677483454122489183614226371943713405943027958351707517"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000269084385910343679257051203982323513897525615083571592326449237527728689054"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000413818658474313744350785912858525849906772047679216774507165554252423741218"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000129583433007671170780305889377624130848179796328575186687487583063726979193"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000130635874598988057004789486171609848753519703338247439616746352104966358265"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000332056463780931130817519370455224958306055159032983343572060292369140142184"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 3) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.11000812669423065201408736025211163644399899284324684887960095471364939561"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.30602309108887457792110755842802529228225817003803592467879858392073911911"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.11401648009214052848211556518765632906037687404471414836791183188060792139"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.779910509750178545578760075470210269561158846741323352073939231867070856952"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.504320419147067435491020898845963984718363947233445348465286515163831830149"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.12262451891492618285514915625369193255653192234826741230297804628732384508"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.00273099973557546696148253375588381632944425785087065216350459031139544566"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.44279760205120109440892243572637061929619282682731780365162404438278331658"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.20161559056699135006082217921675647820154446695817183171496635761222714468"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.258520054851697959251777889637477507802570871015640968136924573283611103029"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0780126100569294916448477016495706044874014105663040020611150095580660962657"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0731313885915515903797324164189780989405177158479326795726386610419770126352"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0189035870354593148101137495477572951021716699214895023786902900987211265014"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000476101513144094836944099173568934880809112562865614785758014193018660882339"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000542048296030493162492883395621428687561762136240537247628992820097566715272"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000482861860046811029771577073119595197181588063401982223039270103384434060022"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000940669036930439153511860275388566814505399165175554813865283382967471512611"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000460334894609940486697079115005770453881482490309436808499379292148676402667"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000659089444165122287064782258267187195472691487712170997364379779451246094661"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000334995342514096728311283812541641458320430857209624625943650939806191456233"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 4) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.63943049915747295902408884381492456615013102835825837278218094298381059975"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-14.10095434632826170706015754809187240473647390058020018665331529642229273560"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("33.80923876769495738178795299271336231298081520211817127483146415279224333890"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-51.34094392422730822169625783218914621608905661019301981247127969679259656370"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("62.15857863021890815900436678476312302754891486816333143898291218703682880770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-69.95150252603710930320770250549877801440701750703949252096860337732317006130"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("70.68706171009487085024307021653246851862364809264251626425285523034249218320"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-53.86604413017363404938611622171529791896555966533772428275471051281075597180"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("22.81871603498091653948869197203037193649186992806348920181610865185092457340"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.78715646181129822503760020954122490057506409714944714939146997166220972189"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-10.35122244241549248750998798029030033554857264769764070098905656424283124680"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.22589995944639343162447192606753092490081390725441582060459808007413775955"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.61768826219594651676851154369360491801137647456640794313175997512654068683"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0487600549117153291242267435006532626983384560499959793316799708161496794985"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0625444452212547866619276559961974061899918807020408330419298222926353018189"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00887177162344660903733729314681709539971921946704977985564110911846620363922"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000172308435777249447063922911208598540360539757913378670543697270097011078916"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000131757849528219664204655654758892673480971917353333971564471583795581462196"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000278829310385893278753467667297067592695172655495747023195258681155064789066"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000283330126035508764154051402203972353668751336274290837719220178109180982040"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 5) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.33155865550004324339411698075437576125001114031131680543558258637926722542"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-34.78546596922894035358221752013471418576656119892560802306039573901884498850"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("93.04078333893580274273554726200086898992117829963170573289656818645421417950"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-116.53672745308757790035524178072195510211938340870303002375366241537010190400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("19.42476690609991902018771707602390047697990808120145803963343105970827114300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("165.07846889283130224972392556901964656573551315330125176803668977902167923900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-302.01823670002161100444326963103590042074566858643871979378909432822312022500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("351.09677823531118456691013587333441077552991458958521920799116438915277804300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-384.73412988907291298126127857698299454483222915340925177050408733410565143700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("400.67693148703611109141641562065904066331648411152048236040109020183777077600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-321.35108793531867698893279523881710779471319811290683986733942416578230536600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("167.36333355910991474853808717960164594081543936479125456031564843552211416400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-45.71369961953726477752159230409155711113565175365517527967211543525719318890"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.699367064899157418988908846748802289435069698849047603720655697336454274985"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.98228422535376897161740571847584616697653819004075212716090431169277576972"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.547498027051101574561205976576588259175101412173034924756008962903023025120"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00888211456705821551022409285786342463315511465858554494859435135093539710800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00145944781339651318786975450416647682444162007080853467985950420011002879779"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000410417202524410779263314775667707070690036033233187273470129649919772492533"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000833431526424512126756266586592842608072719180575476717997770913071706154856"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 6) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.06088106838769290054968439394567345106326651755752600922150619200981904649"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-36.01048320187342016064122793694682929039037974207289646083751798817843620580"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("111.65497002381900847391604108056132695425373640954404816320887269328425438600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-200.74215547182405062933561376177594578645448343871864023725391767591774835600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("243.66853923912563333720102697769935941130760592520157588467019833307464642300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-238.63811401415731691311790369583173568877153676175659117260463100444743159100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("225.14682535963357317765848454921569290528275448357783818162730153311551574600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-201.30071286904051720114799658023138705341732545954845691270252578520003833200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("150.81354485672703044612123433476281157995253230519198222354112466751203726500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-95.86424271108893183923291774912315316192315495940385275849744648479129371610"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("57.37349454581659918342847281164914782841679698416807207317817480336962650140"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-28.97974630119186880188417545488990640756883378387320588356588113332720316360"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("7.82750961052950670790289612831387996295164858527519664270838963476345026334"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.08091505094987758545055341443439247053069659406365117057429783552826238760"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.36939299129089996854048024593726735159933395218523578300840349681327697303"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.280181237504463119434520254208320451998395772453319918592970421102919439139"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000546265385956676161209750070768621430280614491537142208248905211721125879926"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00147158111921181446121734700653833523667079723972927387216993834057729665501"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000441268942542730566701346669932877725269376519910764607900294893415486917856"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000178936364555416156355622735225731323849173624958182729551826746278581656345"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 7) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.22763395991077497600708800752870112512802019777846803123422609253523444499"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-31.33083894520795656643557338514370343692021933760780167709842547864854441400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("99.19649370888855559161612539040862291452743358994450794072159006509952447180"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-174.76554100529416030240273725663066184549978635556382128606302159015804699400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("191.87106416707077830176594781673733058344977599226321690051187655465260417000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-154.69009950176950187209831807333662376535557038525297678672923277217118961000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("128.31823764545969592124295974645679685264644800112728210780946540963513417100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-117.52620888526942424001135357455119389132936854292759496512541610625978723100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("82.77458740900115668785824293717372920888452561941133683536618899571268039270"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-37.48043594311010343509519734340882271874817171143915172303616751347250271800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("14.56969793619700440657543207683336718496887543376426838538228469975643333100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.58813242670581930805873617097473570421450364523198050554153666935990605860"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.00231517515205560297111170032367032830624266948757853925257748047437485705"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.65111836477555984946605574234122313918908034655085234744720545935378656185"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.85460739300369418699655129485713788069696498710719979317225671767847465746"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.660366742165965802145434489749517292319612368608367169686199145406925272970"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0240254194586754357618804390248717384819465676000390734107846903076164025556"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00701996941206172392237021839195076817058449392415590849322406637448645715144"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000247109356222148754647438533593506924053068870724972211566904008498782300086"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000199783389222010785055607244259171818398069280425424499723517627544611259097"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 8) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.76033019493303856051687449323434388609090202601383913064385190376448183312"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-13.30583579203687943081629136293267795607309397777682235599140484923954366500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("43.46657616257718154366654543277971738319342135931706703195817811035185093990"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-81.28657410638605936274247923055646375830285098524867924682488987143954182420"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("100.44535569493907191996663384307406316811627445344739700254788195526559558500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-97.20933347474678202187842214477633354845397460973373353664056650468754174360"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("89.88878331109182469176945890436872342814210396602291754411932369668940781030"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-82.29981368567145730476008183188924859214306594631403889804786963467235197800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("69.06370756169948695128970734742378882589833357909995593129091002885751309170"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-54.63945381644636331825019271777000447410834252910294578185697306015613918450"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("41.02739041572348156154461856933135418845380309772196428740672678193620244590"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-26.44662745983841279602705174819159511393608583819553179666861965546358182250"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("15.00174369284244633245038836591523658570351126534715276565083434487614618120"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-8.66051839144173892722259100499075549842639519928721133973595893424223456610"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.33065078303101010579895420947640558162604044791599818852754301702712403354"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.24068502483685799590790437877354796560395991582308092016594732485261421186"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0779078934121258971785160919472512639431601470709999391983348576222593616764"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0266074428860304338208309476152802616336853971424135540169564254497724564119"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000211062563905998390099917614137909944233433155336638390553050174056557131393"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000339167240842007413867671399755809233304462324861037758236912743626130786250"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 9) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.640740910784300850608448747428708985857357012208138478640701473826119071995"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.89051414436388374023627360586462653542345290441410991274311164920600966594"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("15.77979361042251828056602777327009987727897110266960291592731419702813423270"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-27.77362414192706755256336444082924835831112932806579979321237948678315003340"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("29.23932877961020134280019505838077863032589219652057187629061788645605764150"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-21.21421767485153769358479119905782957335265962757154762905239908876532045980"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("16.58292355069242264838528754441677563862319454861075967735395941314979352800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-16.75336665006114737745223674059225270255439659949203892423230795535668534770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("13.47933260222753983145552435052316707867495382773984724176882313942650009280"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.84622682345785779224288430587701090510900802969451706536957930436008165844"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.98389929827173202326056782961135292617104624089540476377857847941525260633"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.55745576400618796425954497528896729856448578899557932766030185253705183005"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.79383439858729303972208191272224953494584793148950860052667722677927056863"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.691951922965863057242007607869971708166614493007258083206682103112632034601"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.345403595245226611364778279349176734775513013282472618970398880792800137706"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.130558544182786348133975182480093367398008959930808967410065238652717910680"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00698399148544449295954023501742964713288497821639870432194548542030467210561"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00580325961266701622640949560827629673155869792665828211986634190720023351417"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000127925013729926386622233224468569958480332535234461953049381468504991463929"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000406109284685247160935243546331678983485852468994859006463959277286676783577"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 10) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0962276401961485707634176189196513057375091608921918899965672697435379944132"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.738020823110277888005487147166448075761525987078292691760810832596632987072"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.37165881716817146455198793581381209035513677222207786580044965069857187102"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.07258278696320160772598824632813109064068582481103097502282770918877166041"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.96701526462117458029198549268700257108768896990631205803877021434675874630"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.36359581108028672945508028330384282919707503803425311590987150576557002759"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.58983658624201607243694322053302702142722584179817682236311853130843295497"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.85761257911759839282249544686803595350328330563233456669214217961095916255"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.53283576975247258432308684518667039820955312493092996957652314465829192761"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.718946342305564226765801789587960150187823928357554861829190310338862006619"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.409229765931396736377286349516677311112729496444160501691912630223706015387"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.362552279816077162656936242116884276626981924474959700030697184703184497473"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.175827213851141339261603124481542122845079828131432589861342337234868002619"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0410952380112717990391343459878268460433238007822432915185287645982519381943"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0242450545728193174252974797154291458408637398260602402141534552772736201039"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0134013282722748930010976896226591764148191213826882368913426650595356115231"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000399654030797277232222848286358951433908666645251171779800808018550167077414"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00141107498821972634714801414163161931174746710841213074592354066961171560834"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000798497430554567452885354694999821103608152142620563483234681315502038086578"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000494873154958329223506257796254007745988846883400505225346149184283368961203"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+        }
     }
     if constexpr (p == 12) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -932,13 +1147,13 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0f, 0x1.77fed2p-3f, 0x1.e1d108p-1f, -0x1.9e9c7cp+1f, 0x1.bc153ap+1f, -0x1.240fe4p+1f, 0x1.80cee2p+0f, -0x1.abf5ep-1f, 0x1.50c7e8p-2f, -0x1.4654eep-4f, 0x1.091b1ep-6f, -0x1.59c476p-7f, 0x1.935e46p-8f, -0x1.8fe152p-10f, 0x1.90febp-15f, 0x1.09bd2p-15f, -0x1.da6da6p-19f, 0x1.a3887p-21f, 0x1.0f785p-26f, -0x1.63226ep-31f, -0x1.84d7e4p-38f, 0x1.75cc98p-48f, -0x1.a7d232p-65f, -0x0p+0f};
             }
             if constexpr (order == 3) {
-                return {0x0p+0f, 0x1.60087cp-1f, -0x1.1c49e2p+0f, -0x1.f023b2p+0f, 0x1.8d30cp+2f, -0x1.80e0dep+2f, 0x1.c1feacp+0f, 0x1.3621acp+1f, -0x1.f3ab98p+1f, 0x1.5e6794p+1f, -0x1.c702ecp-1f, -0x1.ee149ap-4f, 0x1.ffde0cp-3f, -0x1.a2cbbap-4f, 0x1.d58bf4p-7f, 0x1.206bp-9f, -0x1.dfc88ap-11f, 0x1.f86e54p-15f, 0x1.28c92p-18f, -0x1.9c90e4p-23f, -0x1.7e8cfp-32f, 0x1.cc8984p-39f, -0x1.051a2p-54f, 0x0p+0f};
+                return {0x0p+0f, 0x1.60087cp-1f, -0x1.1c49e2p+0f, -0x1.f023b2p+0f, 0x1.8d30cp+2f, -0x1.80e0dep+2f, 0x1.c1feacp+0f, 0x1.3621acp+1f, -0x1.f3ab98p+1f, 0x1.5e6794p+1f, -0x1.c702ecp-1f, -0x1.ee149ap-4f, 0x1.ffde0cp-3f, -0x1.a2cbbap-4f, 0x1.d58bf4p-7f, 0x1.206bp-9f, -0x1.dfc88ap-11f, 0x1.f86e54p-15f, 0x1.28c92p-18f, -0x1.9c90e4p-23f, -0x1.7e8cfp-32f, 0x1.cc8984p-39f, -0x1.051a2p-54f, -0x0p+0f};
             }
             if constexpr (order == 4) {
                 return {0x0p+0f, 0x1.efa02p+0f, -0x1.34df3ep+3f, 0x1.596114p+4f, -0x1.014d7ap+5f, 0x1.5a4b7p+5f, -0x1.d72d9cp+5f, 0x1.1a6ca8p+6f, -0x1.f8d9fp+5f, 0x1.142ce2p+5f, -0x1.90f39p+1f, -0x1.822b1ap+3f, 0x1.52a34ep+3f, -0x1.0b934ap+2f, 0x1.335fd6p-1f, 0x1.17c48ap-3f, -0x1.003386p-4f, 0x1.68d464p-8f, 0x1.b6ad0ep-12f, -0x1.c361dcp-16f, -0x1.d59d4cp-25f, 0x1.f6c8c6p-31f, -0x1.1d1866p-45f, 0x0p+0f};
             }
             if constexpr (order == 5) {
-                return {0x0p+0f, 0x1.1672f8p+2f, -0x1.d05e84p+4f, 0x1.49fc06p+6f, -0x1.e4421p+6f, 0x1.09c53p+6f, 0x1.677b64p+6f, -0x1.fbf398p+7f, 0x1.628082p+8f, -0x1.a2714ep+8f, 0x1.cb4de8p+8f, -0x1.9cacd4p+8f, 0x1.055f48p+8f, -0x1.8ddf94p+6f, 0x1.95561cp+3f, 0x1.8ab9ccp+2f, -0x1.6e4fp+1f, 0x1.43d702p-2f, 0x1.951dp-6f, -0x1.5137c2p-9f, -0x1.3e3df8p-18f, 0x1.78041p-23f, -0x1.aa8cd8p-37f, -0x0p+0f};
+                return {0x0p+0f, 0x1.1672f8p+2f, -0x1.d05e84p+4f, 0x1.49fc06p+6f, -0x1.e4421p+6f, 0x1.09c53p+6f, 0x1.677b64p+6f, -0x1.fbf398p+7f, 0x1.628082p+8f, -0x1.a2714ep+8f, 0x1.cb4de8p+8f, -0x1.9cacd4p+8f, 0x1.055f48p+8f, -0x1.8ddf94p+6f, 0x1.95561cp+3f, 0x1.8ab9ccp+2f, -0x1.6e4fp+1f, 0x1.43d702p-2f, 0x1.951dp-6f, -0x1.5137c2p-9f, -0x1.3e3df8p-18f, 0x1.78041p-23f, -0x1.aa8cd8p-37f, 0x0p+0f};
             }
             if constexpr (order == 6) {
                 return {0x0p+0f, 0x1.6688e4p+2f, -0x1.50ba26p+5f, 0x1.18d5fcp+7f, -0x1.16422p+8f, 0x1.7cdc34p+8f, -0x1.a2f3c4p+8f, 0x1.aa319ep+8f, -0x1.958a02p+8f, 0x1.4bb5b2p+8f, -0x1.caa92ap+7f, 0x1.1f2d7ap+7f, -0x1.3b920ep+6f, 0x1.bc14b2p+4f, 0x1.8c237ap-1f, -0x1.7f694cp+2f, 0x1.3f67e2p+1f, -0x1.4cc6cp-2f, -0x1.6b5574p-6f, 0x1.38d6e4p-8f, 0x1.260d96p-17f, -0x1.5c7912p-21f, 0x1.8b88d4p-34f, 0x0p+0f};
@@ -947,7 +1162,7 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0f, 0x1.80f666p+2f, -0x1.7dd222p+5f, 0x1.48b0d8p+7f, -0x1.41512cp+8f, 0x1.8f56fp+8f, -0x1.675a3ap+8f, 0x1.2e9626p+8f, -0x1.12635ap+8f, 0x1.969994p+7f, -0x1.59e9b6p+6f, 0x1.09d1ap+3f, 0x1.cc8ab2p+3f, -0x1.93c8d6p+4f, 0x1.013c24p+5f, -0x1.784654p+4f, 0x1.21acdep+3f, -0x1.6fa584p+0f, -0x1.39157p-4f, 0x1.343728p-5f, 0x1.c53d4ap-15f, -0x1.57bc52p-17f, 0x1.869c12p-29f, 0x0p+0f};
             }
             if constexpr (order == 8) {
-                return {0x0p+0f, 0x1.d573dcp+1f, -0x1.ddfb9cp+4f, 0x1.a873c2p+6f, -0x1.b2204ep+7f, 0x1.23910ep+8f, -0x1.29c6cep+8f, 0x1.1c64b2p+8f, -0x1.156986p+8f, 0x1.ef2b6p+7f, -0x1.84734ap+7f, 0x1.20e874p+7f, -0x1.93d454p+6f, 0x1.e8c646p+5f, -0x1.0a8b2ep+5f, 0x1.14ef6ep+4f, -0x1.bab6f4p+2f, 0x1.4e6abp+0f, 0x1.e57eccp-4f, -0x1.0f174cp-4f, 0x1.a1f2dcp-12f, 0x1.400292p-15f, -0x1.6c7e6p-26f, -0x0p+0f};
+                return {0x0p+0f, 0x1.d573dcp+1f, -0x1.ddfb9cp+4f, 0x1.a873c2p+6f, -0x1.b2204ep+7f, 0x1.23910ep+8f, -0x1.29c6cep+8f, 0x1.1c64b2p+8f, -0x1.156986p+8f, 0x1.ef2b6p+7f, -0x1.84734ap+7f, 0x1.20e874p+7f, -0x1.93d454p+6f, 0x1.e8c646p+5f, -0x1.0a8b2ep+5f, 0x1.14ef6ep+4f, -0x1.bab6f4p+2f, 0x1.4e6abp+0f, 0x1.e57eccp-4f, -0x1.0f174cp-4f, 0x1.a1f2dcp-12f, 0x1.400292p-15f, -0x1.6c7e6p-26f, 0x0p+0f};
             }
             if constexpr (order == 9) {
                 return {0x0p+0f, 0x1.d2f4ep+0f, -0x1.e196ep+3f, 0x1.ab061ep+5f, -0x1.a7b25ap+6f, 0x1.04d398p+7f, -0x1.c308c4p+6f, 0x1.759cb8p+6f, -0x1.73a4dcp+6f, 0x1.4d02e4p+6f, -0x1.c4dfc6p+5f, 0x1.217c84p+5f, -0x1.9d3e5ep+4f, 0x1.eced02p+3f, -0x1.ab1578p+2f, 0x1.780b78p+1f, -0x1.59e4e8p+0f, 0x1.04013ap-2f, 0x1.63e904p-4f, -0x1.26b33ap-5f, 0x1.1fc084p-10f, 0x1.9c18e6p-15f, -0x1.d792bap-25f, 0x0p+0f};
@@ -970,13 +1185,13 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0, 0x1.77fed2e016936p-3, 0x1.e1d10780fb061p-1, -0x1.9e9c7ce63835dp+1, 0x1.bc153af50c24cp+1, -0x1.240fe3f248861p+1, 0x1.80cee17390c18p+0, -0x1.abf5df7fd7acp-1, 0x1.50c7e71a108bbp-2, -0x1.4654ed4660724p-4, 0x1.091b1dd62c3e6p-6, -0x1.59c475f85d7f4p-7, 0x1.935e464b93aa4p-8, -0x1.8fe1513629012p-10, 0x1.90feb0894b435p-15, 0x1.09bd1f2d4e386p-15, -0x1.da6da6ad5e76cp-19, 0x1.a3886fa6d48c5p-21, 0x1.0f7850b94c92bp-26, -0x1.63226d50629cp-31, -0x1.84d7e34db15d3p-38, 0x1.75cc980993529p-48, -0x1.a7d23115de573p-65, -0x0p+0};
             }
             if constexpr (order == 3) {
-                return {0x0p+0, 0x1.60087b087d2efp-1, -0x1.1c49e2797e56dp+0, -0x1.f023b1706ef0ep+0, 0x1.8d30c07e51574p+2, -0x1.80e0de445b21ap+2, 0x1.c1feac4e70c18p+0, 0x1.3621ab0ea1b05p+1, -0x1.f3ab98611d47ap+1, 0x1.5e6794d526a25p+1, -0x1.c702eca93a33dp-1, -0x1.ee149aa686bb3p-4, 0x1.ffde0ca5fc1a1p-3, -0x1.a2cbb989ecd0ap-4, 0x1.d58bf4f6c76eap-7, 0x1.206affc103ba1p-9, -0x1.dfc88961f6b15p-11, 0x1.f86e53415f2ap-15, 0x1.28c920e4a3f6cp-18, -0x1.9c90e430666c9p-23, -0x1.7e8cf0898f333p-32, 0x1.cc8984cca607fp-39, -0x1.051a1f819156cp-54, 0x0p+0};
+                return {0x0p+0, 0x1.60087b087d2efp-1, -0x1.1c49e2797e56dp+0, -0x1.f023b1706ef0ep+0, 0x1.8d30c07e51574p+2, -0x1.80e0de445b21ap+2, 0x1.c1feac4e70c18p+0, 0x1.3621ab0ea1b05p+1, -0x1.f3ab98611d47ap+1, 0x1.5e6794d526a25p+1, -0x1.c702eca93a33dp-1, -0x1.ee149aa686bb3p-4, 0x1.ffde0ca5fc1a1p-3, -0x1.a2cbb989ecd0ap-4, 0x1.d58bf4f6c76eap-7, 0x1.206affc103ba1p-9, -0x1.dfc88961f6b15p-11, 0x1.f86e53415f2ap-15, 0x1.28c920e4a3f6cp-18, -0x1.9c90e430666c9p-23, -0x1.7e8cf0898f333p-32, 0x1.cc8984cca607fp-39, -0x1.051a1f819156cp-54, -0x0p+0};
             }
             if constexpr (order == 4) {
                 return {0x0p+0, 0x1.efa01fe281c9p+0, -0x1.34df3dac7fcd4p+3, 0x1.5961138d5be95p+4, -0x1.014d7a672544ap+5, 0x1.5a4b6fa251ebp+5, -0x1.d72d9b409f2b2p+5, 0x1.1a6ca7d65632dp+6, -0x1.f8d9ef0a2890cp+5, 0x1.142ce1c1f06e2p+5, -0x1.90f390767ce47p+1, -0x1.822b1a96e2d92p+3, 0x1.52a34d125b1bep+3, -0x1.0b934a511e089p+2, 0x1.335fd67def29fp-1, 0x1.17c48a3b6f0b8p-3, -0x1.0033850ae8807p-4, 0x1.68d4635bbce68p-8, 0x1.b6ad0e03e206fp-12, -0x1.c361dbb11082cp-16, -0x1.d59d4ba004a56p-25, 0x1.f6c8c69c71b98p-31, -0x1.1d186572e3d31p-45, 0x0p+0};
             }
             if constexpr (order == 5) {
-                return {0x0p+0, 0x1.1672f76c48a3bp+2, -0x1.d05e83fe81472p+4, 0x1.49fc051fc99a8p+6, -0x1.e442104e65336p+6, 0x1.09c52f838d2fdp+6, 0x1.677b64cbf326ep+6, -0x1.fbf39786bea7bp+7, 0x1.628081b6fdd81p+8, -0x1.a2714ddd5c22bp+8, 0x1.cb4de777b4f36p+8, -0x1.9cacd3aee3a7ep+8, 0x1.055f4806a8346p+8, -0x1.8ddf94a470b87p+6, 0x1.95561c2d77ea8p+3, 0x1.8ab9cc38b4949p+2, -0x1.6e4f007cb3f6fp+1, 0x1.43d7023213a8p-2, 0x1.951cff21de4acp-6, -0x1.5137c147339bcp-9, -0x1.3e3df8b2da275p-18, 0x1.78040f51a9568p-23, -0x1.aa8cd8e6f8972p-37, -0x0p+0};
+                return {0x0p+0, 0x1.1672f76c48a3bp+2, -0x1.d05e83fe81472p+4, 0x1.49fc051fc99a8p+6, -0x1.e442104e65336p+6, 0x1.09c52f838d2fdp+6, 0x1.677b64cbf326ep+6, -0x1.fbf39786bea7bp+7, 0x1.628081b6fdd81p+8, -0x1.a2714ddd5c22bp+8, 0x1.cb4de777b4f36p+8, -0x1.9cacd3aee3a7ep+8, 0x1.055f4806a8346p+8, -0x1.8ddf94a470b87p+6, 0x1.95561c2d77ea8p+3, 0x1.8ab9cc38b4949p+2, -0x1.6e4f007cb3f6fp+1, 0x1.43d7023213a8p-2, 0x1.951cff21de4acp-6, -0x1.5137c147339bcp-9, -0x1.3e3df8b2da275p-18, 0x1.78040f51a9568p-23, -0x1.aa8cd8e6f8972p-37, 0x0p+0};
             }
             if constexpr (order == 6) {
                 return {0x0p+0, 0x1.6688e31cf50ep+2, -0x1.50ba2688bc043p+5, 0x1.18d5fc503a177p+7, -0x1.16422099d0e7p+8, 0x1.7cdc33f38c2d1p+8, -0x1.a2f3c3b8e6e4bp+8, 0x1.aa319d6af6ec9p+8, -0x1.958a02a102449p+8, 0x1.4bb5b15c50a64p+8, -0x1.caa9291eb011fp+7, 0x1.1f2d7abf22a73p+7, -0x1.3b920d0f7e0d1p+6, 0x1.bc14b21b62b93p+4, 0x1.8c237a0fa26d7p-1, -0x1.7f694c35d9d22p+2, 0x1.3f67e104a689cp+1, -0x1.4cc6c058f371dp-2, -0x1.6b557354b8d85p-6, 0x1.38d6e371bb052p-8, 0x1.260d95329ea8ep-17, -0x1.5c7911e0053bcp-21, 0x1.8b88d3fa551cp-34, 0x0p+0};
@@ -985,7 +1200,7 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0, 0x1.80f665163dff6p+2, -0x1.7dd2228ef0449p+5, 0x1.48b0d88030936p+7, -0x1.41512ba753d05p+8, 0x1.8f56f07493efp+8, -0x1.675a39773b248p+8, 0x1.2e9626a21624ep+8, -0x1.1263590aebe89p+8, 0x1.9699942af2221p+7, -0x1.59e9b6e0b9c21p+6, 0x1.09d1a0b7c5832p+3, 0x1.cc8ab1005087cp+3, -0x1.93c8d50945095p+4, 0x1.013c24badc627p+5, -0x1.784654bbd7368p+4, 0x1.21acdd98ca7e4p+3, -0x1.6fa583815aba2p+0, -0x1.39156fe5f0a3bp-4, 0x1.34372727b2155p-5, 0x1.c53d49d197175p-15, -0x1.57bc52155abeap-17, 0x1.869c11b6398bcp-29, 0x0p+0};
             }
             if constexpr (order == 8) {
-                return {0x0p+0, 0x1.d573db31c98a6p+1, -0x1.ddfb9c5686a4fp+4, 0x1.a873c238f1ad9p+6, -0x1.b2204de17a53ap+7, 0x1.23910ebcbe60dp+8, -0x1.29c6cec686025p+8, 0x1.1c64b27b4c108p+8, -0x1.156985f5c8bcep+8, 0x1.ef2b60fc7ce31p+7, -0x1.84734ae811783p+7, 0x1.20e874beb6698p+7, -0x1.93d454c0120c5p+6, 0x1.e8c645d503448p+5, -0x1.0a8b2e2c06173p+5, 0x1.14ef6d11452bcp+4, -0x1.bab6f3f4dbb55p+2, 0x1.4e6aaf12e910ep+0, 0x1.e57ecc0ee730ep-4, -0x1.0f174cea8c306p-4, 0x1.a1f2dc12ec55dp-12, 0x1.4002914419fbbp-15, -0x1.6c7e600f14b1p-26, -0x0p+0};
+                return {0x0p+0, 0x1.d573db31c98a6p+1, -0x1.ddfb9c5686a4fp+4, 0x1.a873c238f1ad9p+6, -0x1.b2204de17a53ap+7, 0x1.23910ebcbe60dp+8, -0x1.29c6cec686025p+8, 0x1.1c64b27b4c108p+8, -0x1.156985f5c8bcep+8, 0x1.ef2b60fc7ce31p+7, -0x1.84734ae811783p+7, 0x1.20e874beb6698p+7, -0x1.93d454c0120c5p+6, 0x1.e8c645d503448p+5, -0x1.0a8b2e2c06173p+5, 0x1.14ef6d11452bcp+4, -0x1.bab6f3f4dbb55p+2, 0x1.4e6aaf12e910ep+0, 0x1.e57ecc0ee730ep-4, -0x1.0f174cea8c306p-4, 0x1.a1f2dc12ec55dp-12, 0x1.4002914419fbbp-15, -0x1.6c7e600f14b1p-26, 0x0p+0};
             }
             if constexpr (order == 9) {
                 return {0x0p+0, 0x1.d2f4e044749b5p+0, -0x1.e196df480fe72p+3, 0x1.ab061d20276fp+5, -0x1.a7b259e6037ecp+6, 0x1.04d3977e22f61p+7, -0x1.c308c46a51aa1p+6, 0x1.759cb7054906p+6, -0x1.73a4db524ebc3p+6, 0x1.4d02e405c664p+6, -0x1.c4dfc682dd95ep+5, 0x1.217c835a844bfp+5, -0x1.9d3e5e5e09252p+4, 0x1.eced01c912f6cp+3, -0x1.ab15772777a66p+2, 0x1.780b7892927c5p+1, -0x1.59e4e79f9d385p+0, 0x1.04013ac7f90edp-2, 0x1.63e903ad632e8p-4, -0x1.26b339b06c46fp-5, 0x1.1fc083a0e2c36p-10, 0x1.9c18e59aa15abp-15, -0x1.d792baac952f3p-25, 0x0p+0};
@@ -1008,13 +1223,13 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0L, 0xb.bff69700b49b018p-6L, 0xf.0e883c07d830881p-4L, -0xc.f4e3e731c1ae738p-2L, 0xd.e0a9d7a86125cacp-2L, -0x9.207f1f9244307c8p-2L, 0xc.06770b9c860beebp-3L, -0xd.5faefbfebd5fdcdp-4L, 0xa.863f38d0845d7acp-5L, -0xa.32a76a330391e66p-7L, 0x8.48d8eeb161f2f82p-9L, -0xa.ce23afc2ebf9f61p-10L, 0xc.9af2325c9d52281p-11L, -0xc.7f0a89b14808e6ap-13L, 0xc.87f5844a5a1a6fp-18L, 0x8.4de8f96a71c3322p-18L, -0xe.d36d356af3b5c2cp-22L, 0xd.1c437d36a462b4ap-24L, 0x8.7bc285ca6495b9cp-29L, -0xb.19136a8314dfe24p-34L, -0xc.26bf1a6d8ae9884p-41L, 0xb.ae64c04c9a9494fp-51L, -0xd.3e9188aef2b98edp-68L, -0x0p+0L};
             }
             if constexpr (order == 3) {
-                return {0x0p+0L, 0xb.0043d843e977a5cp-4L, -0x8.e24f13cbf2b6563p-3L, -0xf.811d8b837786d61p-3L, 0xc.698603f28aba1a9p-1L, -0xc.0706f222d90cfdfp-1L, 0xe.0ff56273860c0ebp-3L, 0x9.b10d58750d82957p-2L, -0xf.9d5cc308ea3d3cbp-2L, 0xa.f33ca6a935126f2p-2L, -0xe.38176549d19e5a8p-4L, -0xf.70a4d53435d97d5p-7L, 0xf.fef0652fe0d0a8dp-6L, -0xd.165dcc4f668505cp-7L, 0xe.ac5fa7b63b752dbp-10L, 0x9.0357fe081dd0544p-12L, -0xe.fe444b0fb58abf3p-14L, 0xf.c3729a0af95006dp-18L, 0x9.464907251fb5d88p-21L, -0xc.e487218333646a4p-26L, -0xb.f467844c7999b52p-35L, 0xe.644c2665303f8d2p-42L, -0x8.28d0fc0c8ab5d4ep-57L, 0x0p+0L};
+                return {0x0p+0L, 0xb.0043d843e977a5cp-4L, -0x8.e24f13cbf2b6563p-3L, -0xf.811d8b837786d61p-3L, 0xc.698603f28aba1a9p-1L, -0xc.0706f222d90cfdfp-1L, 0xe.0ff56273860c0ebp-3L, 0x9.b10d58750d82957p-2L, -0xf.9d5cc308ea3d3cbp-2L, 0xa.f33ca6a935126f2p-2L, -0xe.38176549d19e5a8p-4L, -0xf.70a4d53435d97d5p-7L, 0xf.fef0652fe0d0a8dp-6L, -0xd.165dcc4f668505cp-7L, 0xe.ac5fa7b63b752dbp-10L, 0x9.0357fe081dd0544p-12L, -0xe.fe444b0fb58abf3p-14L, 0xf.c3729a0af95006dp-18L, 0x9.464907251fb5d88p-21L, -0xc.e487218333646a4p-26L, -0xb.f467844c7999b52p-35L, 0xe.644c2665303f8d2p-42L, -0x8.28d0fc0c8ab5d4ep-57L, -0x0p+0L};
             }
             if constexpr (order == 4) {
                 return {0x0p+0L, 0xf.7d00ff140e483d9p-3L, -0x9.a6f9ed63fe69fc4p+0L, 0xa.cb089c6adf4abc4p+1L, -0x8.0a6bd3392a250e2p+2L, 0xa.d25b7d128f57c87p+2L, -0xe.b96cda04f958dddp+2L, 0x8.d3653eb2b19664fp+3L, -0xf.c6cf785144862cap+2L, 0x8.a1670e0f8370cfp+2L, -0xc.879c83b3e72381bp-2L, -0xc.1158d4b716c8e65p+0L, 0xa.951a6892d8df2a8p+0L, -0x8.5c9a5288f0446cfp-1L, 0x9.9afeb3ef794f7dcp-4L, 0x8.be2451db785c08ap-6L, -0x8.019c285744039edp-7L, 0xb.46a31adde7341a9p-11L, 0xd.b568701f1037966p-15L, -0xe.1b0edd888415d06p-19L, -0xe.acea5d00252b3f7p-28L, 0xf.b64634e38dcc13ap-34L, -0x8.e8c32b971e9855bp-48L, 0x0p+0L};
             }
             if constexpr (order == 5) {
-                return {0x0p+0L, 0x8.b397bb62451d843p-1L, -0xe.82f41ff40a38e2ap+1L, 0xa.4fe028fe4cd412cp+3L, -0xf.22108273299ad98p+3L, 0x8.4e297c1c697e50ep+3L, 0xb.3bdb265f99372aep+3L, -0xf.df9cbc35f53d89cp+4L, 0xb.14040db7eec0855p+5L, -0xd.138a6eeae115b02p+5L, 0xe.5a6f3bbda79b16cp+5L, -0xc.e5669d771d3f14bp+5L, 0x8.2afa403541a338fp+5L, -0xc.6efca52385c3629p+3L, 0xc.aab0e16bbf53e59p+0L, 0xc.55ce61c5a4a452bp-1L, -0xb.727803e59fb7b2ap-2L, 0xa.1eb811909d4016fp-5L, 0xc.a8e7f90ef2563f2p-9L, -0xa.89be0a399cde158p-12L, -0x9.f1efc596d13a96ep-21L, 0xb.c0207a8d4ab3f5dp-26L, -0xd.5466c737c4b8e72p-40L, -0x0p+0L};
+                return {0x0p+0L, 0x8.b397bb62451d843p-1L, -0xe.82f41ff40a38e2ap+1L, 0xa.4fe028fe4cd412cp+3L, -0xf.22108273299ad98p+3L, 0x8.4e297c1c697e50ep+3L, 0xb.3bdb265f99372aep+3L, -0xf.df9cbc35f53d89cp+4L, 0xb.14040db7eec0855p+5L, -0xd.138a6eeae115b02p+5L, 0xe.5a6f3bbda79b16cp+5L, -0xc.e5669d771d3f14bp+5L, 0x8.2afa403541a338fp+5L, -0xc.6efca52385c3629p+3L, 0xc.aab0e16bbf53e59p+0L, 0xc.55ce61c5a4a452bp-1L, -0xb.727803e59fb7b2ap-2L, 0xa.1eb811909d4016fp-5L, 0xc.a8e7f90ef2563f2p-9L, -0xa.89be0a399cde158p-12L, -0x9.f1efc596d13a96ep-21L, 0xb.c0207a8d4ab3f5dp-26L, -0xd.5466c737c4b8e72p-40L, 0x0p+0L};
             }
             if constexpr (order == 6) {
                 return {0x0p+0L, 0xb.344718e7a8702b2p-1L, -0xa.85d13445e021855p+2L, 0x8.c6afe281d0bb969p+4L, -0x8.b21104ce8738061p+5L, 0xb.e6e19f9c6168b44p+5L, -0xd.179e1dc73725588p+5L, 0xd.518ceb57b764b3fp+5L, -0xc.ac50150812244abp+5L, 0xa.5dad8ae285323a8p+5L, -0xe.554948f5808f966p+4L, 0x8.f96bd5f915394b1p+4L, -0x9.dc90687bf0684d6p+3L, 0xd.e0a590db15c99a5p+1L, 0xc.611bd07d136ba02p-4L, -0xb.fb4a61aece9122bp-1L, 0x9.fb3f0825344de52p-2L, -0xa.663602c79b8e8ecp-5L, -0xb.5aab9aa5c6c2553p-9L, 0x9.c6b71b8dd828c64p-11L, 0x9.306ca994f547077p-20L, -0xa.e3c88f0029de0d1p-24L, 0xc.5c469fd2a8dfc22p-37L, 0x0p+0L};
@@ -1023,7 +1238,7 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0L, 0xc.07b328b1effb03p-1L, -0xb.ee9114778224972p+2L, 0xa.4586c401849b3a9p+4L, -0xa.0a895d3a9e82ae4p+5L, 0xc.7ab783a49f782e2p+5L, -0xb.3ad1cbb9d9242edp+5L, 0x9.74b13510b126f8ep+5L, -0x8.931ac8575f4469p+5L, 0xc.b4cca1579110a15p+4L, -0xa.cf4db705ce10894p+3L, 0x8.4e8d05be2c19216p+0L, 0xe.64558802843df89p+0L, -0xc.9e46a84a284ab95p+1L, 0x8.09e125d6e31381bp+2L, -0xb.c232a5deb9b3ce5p+1L, 0x9.0d66ecc653f1d47p+0L, -0xb.7d2c1c0ad5d0d11p-3L, -0x9.c8ab7f2f851da2dp-7L, 0x9.a1b9393d90aa708p-8L, 0xe.29ea4e8cb8baa35p-18L, -0xa.bde290aad5f5239p-20L, 0xc.34e08db1cc5dff7p-32L, 0x0p+0L};
             }
             if constexpr (order == 8) {
-                return {0x0p+0L, 0xe.ab9ed98e4c52c95p-2L, -0xe.efdce2b435277e9p+1L, 0xd.439e11c78d6c4d6p+3L, -0xd.91026f0bd29d199p+4L, 0x9.1c8875e5f3069d6p+5L, -0x9.4e367634301286p+5L, 0x8.e32593da6083e54p+5L, -0x8.ab4c2fae45e736fp+5L, 0xf.795b07e3e718ad3p+4L, -0xc.239a57408bc15f7p+4L, 0x9.0743a5f5b34bf5fp+4L, -0xc.9ea2a6009062863p+3L, 0xf.46322ea81a241fbp+2L, -0x8.5459716030b981p+2L, 0x8.a77b688a295dd83p+1L, -0xd.d5b79fa6ddaa942p-1L, 0xa.735578974886db3p-3L, 0xf.2bf66077398705p-7L, -0x8.78ba67546182ecp-7L, 0xd.0f96e09762ae4b7p-15L, 0xa.00148a20cfdd93dp-18L, -0xb.63f30078a588239p-29L, -0x0p+0L};
+                return {0x0p+0L, 0xe.ab9ed98e4c52c95p-2L, -0xe.efdce2b435277e9p+1L, 0xd.439e11c78d6c4d6p+3L, -0xd.91026f0bd29d199p+4L, 0x9.1c8875e5f3069d6p+5L, -0x9.4e367634301286p+5L, 0x8.e32593da6083e54p+5L, -0x8.ab4c2fae45e736fp+5L, 0xf.795b07e3e718ad3p+4L, -0xc.239a57408bc15f7p+4L, 0x9.0743a5f5b34bf5fp+4L, -0xc.9ea2a6009062863p+3L, 0xf.46322ea81a241fbp+2L, -0x8.5459716030b981p+2L, 0x8.a77b688a295dd83p+1L, -0xd.d5b79fa6ddaa942p-1L, 0xa.735578974886db3p-3L, 0xf.2bf66077398705p-7L, -0x8.78ba67546182ecp-7L, 0xd.0f96e09762ae4b7p-15L, 0xa.00148a20cfdd93dp-18L, -0xb.63f30078a588239p-29L, 0x0p+0L};
             }
             if constexpr (order == 9) {
                 return {0x0p+0L, 0xe.97a70223a4da73dp-3L, -0xf.0cb6fa407f38df5p+0L, 0xd.5830e9013b783a8p+2L, -0xd.3d92cf301bf5fbep+3L, 0x8.269cbbf117b07a3p+4L, -0xe.184623528d5047ap+3L, 0xb.ace5b82a4830181p+3L, -0xb.9d26da9275e177fp+3L, 0xa.6817202e331ffc5p+3L, -0xe.26fe3416ecaefa6p+2L, 0x9.0be41ad4225f98dp+2L, -0xc.e9f2f2f049291ep+1L, 0xf.67680e4897b60bep+0L, -0xd.58abb93bbd32d48p-1L, 0xb.c05bc49493e294p-2L, -0xa.cf273cfce9c2447p-3L, 0x8.2009d63fc87650fp-5L, 0xb.1f481d6b1973f98p-7L, -0x9.3599cd8362377f9p-8L, 0x8.fe041d07161ad18p-13L, 0xc.e0c72cd50ad59f6p-18L, -0xe.bc95d564a979727p-28L, 0x0p+0L};
@@ -1038,43 +1253,81 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         #ifdef BOOST_HAS_FLOAT128
         if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
             if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.ba5636194c0939c427c9ec5958bcp-8Q, 0x1.3af72853b1890334601f92a1285cp-2Q, 0x1.da1521352f487f1b71f5ba20803ep-1Q, -0x1.5c6f665240adde3380bdc0aea43fp-2Q, 0x1.4840a35a3e5076b07b9bb98536c9p-3Q, -0x1.9d4fdc34ae4edcb2a06a461fd223p-4Q, 0x1.042a86a360591d6b2ba9327c6214p-4Q, -0x1.08554bd18ab256f6f2efbe750debp-5Q, 0x1.86c905bef28a68962be82a3bfae1p-7Q, -0x1.8785b403c86f6f7548c23ebef91ep-9Q, 0x1.f00fc00fce26eee7a53c75fa9281p-12Q, -0x1.43b7ce1fa4e5b162d9e05ba16226p-15Q, -0x1.dafa2eb6c7f5cbd9451ac8b8db32p-18Q, 0x1.2d678c174b94d04aa232fc24fe04p-18Q, -0x1.f0554b8e5712d06e0273c8cb5028p-22Q, -0x1.934a0de4da29338aed7c3945f163p-24Q, -0x1.3a5d95f1928eec0223d4d9335852p-29Q, 0x1.0e0d2138861875f5d48c437e1967p-33Q, -0x1.652333b327609e7169123d062a6bp-41Q, 0x1.02e74c07e60809b1acff78842c2ep-47Q, 0x1.bb358cf4adf4da69e5fa9c48097p-60Q, -0x1.f67e04f08f2152aabe6eb786b11ap-79Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.ba5636194c0939c427c9ec59581bp-8Q, 0x1.3af72853b1890334601f92a1284ap-2Q, 0x1.da1521352f487f1b71f5ba208041p-1Q, -0x1.5c6f665240adde3380bdc0aea438p-2Q, 0x1.4840a35a3e5076b07b9bb98536cdp-3Q, -0x1.9d4fdc34ae4edcb2a06a461fd21ap-4Q, 0x1.042a86a360591d6b2ba9327c6214p-4Q, -0x1.08554bd18ab256f6f2efbe750de9p-5Q, 0x1.86c905bef28a68962be82a3bfae8p-7Q, -0x1.8785b403c86f6f7548c23ebef922p-9Q, 0x1.f00fc00fce26eee7a53c75fa9287p-12Q, -0x1.43b7ce1fa4e5b162d9e05ba1624fp-15Q, -0x1.dafa2eb6c7f5cbd9451ac8b8db32p-18Q, 0x1.2d678c174b94d04aa232fc24fe09p-18Q, -0x1.f0554b8e5712d06e0273c8cb503bp-22Q, -0x1.934a0de4da29338aed7c3945f15bp-24Q, -0x1.3a5d95f1928eec0223d4d93358b6p-29Q, 0x1.0e0d2138861875f5d48c437e1957p-33Q, -0x1.652333b327609e7169123d062941p-41Q, 0x1.02e74c07e60809b1acff78842ce2p-47Q, 0x1.bb358cf4adf4da69e5fa9c480499p-60Q, -0x1.f67e04f08f2152aabe6eb786996dp-79Q, 0x0p+0Q};
             }
             if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.3daa1461d0cf47fff25f3df9640bp-5Q, 0x1.716f56bac1b1102dab376b1a4013p-1Q, -0x1.16bee9987071960277d4321df089p-2Q, -0x1.f51bd9fa1cf2d9e12262aabd142cp-1Q, 0x1.97243be7bf08455883f653e15918p-1Q, -0x1.b8eef0110c9fa4de8e71d38444edp-2Q, 0x1.2402bce395301d2ffcfa2c7a494fp-3Q, 0x1.80595820660c8830537a9f5a0fdp-10Q, -0x1.fa47fa3f4b021cbace01025dd983p-6Q, 0x1.025a88022a413b155a9680077b56p-6Q, -0x1.3d712aaad77758afb71e5644bf96p-9Q, -0x1.c5c0d04fc87430265835a2d868fdp-11Q, 0x1.c45b69075cdb62e0f0501d72eae6p-12Q, -0x1.6a1670435bfdd529f00d82c5e461p-15Q, -0x1.13c0d643a27dc3e64f7aa5ea1b46p-17Q, 0x1.b2cff794384635cf6c5bd8331b3p-20Q, -0x1.9ee90facd3d1333133d7e205e0a2p-25Q, -0x1.c87e1185ca55b3b93aa7457169a2p-29Q, 0x1.b076e966620448a8ccbae1de566ap-34Q, 0x1.71c42c5b1e646b3eaaa36a5a3022p-44Q, -0x1.e6d8e5785ac9381d9a7b909296b9p-52Q, 0x1.13fd176d0c254d2994cc4f8bbb17p-69Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.3daa1461d0cf47fff25f3df963e7p-5Q, 0x1.716f56bac1b1102dab376b1a3fe7p-1Q, -0x1.16bee9987071960277d4321df078p-2Q, -0x1.f51bd9fa1cf2d9e12262aabd1401p-1Q, 0x1.97243be7bf08455883f653e158edp-1Q, -0x1.b8eef0110c9fa4de8e71d38444bcp-2Q, 0x1.2402bce395301d2ffcfa2c7a4938p-3Q, 0x1.80595820660c8830537a9f5a0e29p-10Q, -0x1.fa47fa3f4b021cbace01025dd941p-6Q, 0x1.025a88022a413b155a9680077b35p-6Q, -0x1.3d712aaad77758afb71e5644bf72p-9Q, -0x1.c5c0d04fc87430265835a2d868c3p-11Q, 0x1.c45b69075cdb62e0f0501d72eab3p-12Q, -0x1.6a1670435bfdd529f00d82c5e437p-15Q, -0x1.13c0d643a27dc3e64f7aa5ea1b1dp-17Q, 0x1.b2cff794384635cf6c5bd8331af5p-20Q, -0x1.9ee90facd3d1333133d7e205e062p-25Q, -0x1.c87e1185ca55b3b93aa74571695cp-29Q, 0x1.b076e966620448a8ccbae1de5619p-34Q, 0x1.71c42c5b1e646b3eaaa36a5a302fp-44Q, -0x1.e6d8e5785ac9381d9a7b90929674p-52Q, 0x1.13fd176d0c254d2994cc4f8bbae7p-69Q, 0x0p+0Q};
             }
             if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.77fed2e01693602fb8497759708ep-3Q, 0x1.e1d10780fb06110288f8999dc1b7p-1Q, -0x1.9e9c7ce63835ce70bd9f1949b4fbp+1Q, 0x1.bc153af50c24b9575bdc1b7eea7cp+1Q, -0x1.240fe3f248860f90966b383ce1ccp+1Q, 0x1.80cee17390c17dd6afdc8b5e9badp+0Q, -0x1.abf5df7fd7abfb9aaab015caa89bp-1Q, 0x1.50c7e71a108baf578aa06cfc53efp-2Q, -0x1.4654ed4660723ccc0f0acc159fc7p-4Q, 0x1.091b1dd62c3e5f033d13bd90eb7fp-6Q, -0x1.59c475f85d7f3ec16b121b44ed34p-7Q, 0x1.935e464b93aa450281cf24f670a1p-8Q, -0x1.8fe1513629011cd322fa61848c65p-10Q, 0x1.90feb0894b434ddffdbc8185ec19p-15Q, 0x1.09bd1f2d4e386644ae469eb8633p-15Q, -0x1.da6da6ad5e76b8585347757536dfp-19Q, 0x1.a3886fa6d48c5693a0b3ec42df61p-21Q, 0x1.0f7850b94c92b737f20b8005c2b9p-26Q, -0x1.63226d50629bfc487dd5a4e8ece6p-31Q, -0x1.84d7e34db15d3108fdfa03f5826ep-38Q, 0x1.75cc98099352929e39911fd4363dp-48Q, -0x1.a7d23115de5731da90d3ce0c92b1p-65Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.77fed2e01693602fb84977597092p-3Q, 0x1.e1d10780fb06110288f8999dc16cp-1Q, -0x1.9e9c7ce63835ce70bd9f1949b4bp+1Q, 0x1.bc153af50c24b9575bdc1b7eea9p+1Q, -0x1.240fe3f248860f90966b383ce203p+1Q, 0x1.80cee17390c17dd6afdc8b5e9bd2p+0Q, -0x1.abf5df7fd7abfb9aaab015caa888p-1Q, 0x1.50c7e71a108baf578aa06cfc537p-2Q, -0x1.4654ed4660723ccc0f0acc159e52p-4Q, 0x1.091b1dd62c3e5f033d13bd90e92bp-6Q, -0x1.59c475f85d7f3ec16b121b44eccep-7Q, 0x1.935e464b93aa450281cf24f671a9p-8Q, -0x1.8fe1513629011cd322fa61848df6p-10Q, 0x1.90feb0894b434ddffdbc8185f2a5p-15Q, 0x1.09bd1f2d4e386644ae469eb863f8p-15Q, -0x1.da6da6ad5e76b858534775753bfcp-19Q, 0x1.a3886fa6d48c5693a0b3ec42e08ep-21Q, 0x1.0f7850b94c92b737f20b8005c4e4p-26Q, -0x1.63226d50629bfc487dd5a4e8ef38p-31Q, -0x1.84d7e34db15d3108fdfa03f5836dp-38Q, 0x1.75cc98099352929e39911fd43962p-48Q, -0x1.a7d23115de5731da90d3ce0c96c3p-65Q, 0x0p+0Q};
             }
             if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.60087b087d2ef4b82953952dae77p-1Q, -0x1.1c49e2797e56cac67a206b15099bp+0Q, -0x1.f023b1706ef0dac15d9852fed0cdp+0Q, 0x1.8d30c07e51574352c1f1eb201d3dp+2Q, -0x1.80e0de445b219fbdea6ef733b9e6p+2Q, 0x1.c1feac4e70c181d6b4fca6d2077fp+0Q, 0x1.3621ab0ea1b052aecf48cff76ee3p+1Q, -0x1.f3ab98611d47a796d9c54636510bp+1Q, 0x1.5e6794d526a24de36780aeba10e8p+1Q, -0x1.c702eca93a33cb508d7b1d004b3dp-1Q, -0x1.ee149aa686bb2faa29ff6d4c03ddp-4Q, 0x1.ffde0ca5fc1a1519c08ba08f2c0bp-3Q, -0x1.a2cbb989ecd0a0b85c48b0ef17a6p-4Q, 0x1.d58bf4f6c76ea5b68a5554196c66p-7Q, 0x1.206affc103ba0a875625f458349fp-9Q, -0x1.dfc88961f6b157e54f77890beee7p-11Q, 0x1.f86e53415f2a00da542f82566187p-15Q, 0x1.28c920e4a3f6bb0fc001a36c7514p-18Q, -0x1.9c90e430666c8d48daf02182994fp-23Q, -0x1.7e8cf0898f3336a3b6d1b959decdp-32Q, 0x1.cc8984cca607f1a4cd24395b6b4ap-39Q, -0x1.051a1f819156ba9bc5cb80613b7p-54Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.60087b087d2ef4b82953952d9084p-1Q, -0x1.1c49e2797e56cac67a206b14e7b4p+0Q, -0x1.f023b1706ef0dac15d9852fec6b7p+0Q, 0x1.8d30c07e51574352c1f1eb2006b7p+2Q, -0x1.80e0de445b219fbdea6ef733a307p+2Q, 0x1.c1feac4e70c181d6b4fca6d1ffb9p+0Q, 0x1.3621ab0ea1b052aecf48cff7492ap+1Q, -0x1.f3ab98611d47a796d9c546361f74p+1Q, 0x1.5e6794d526a24de36780aeb9efa6p+1Q, -0x1.c702eca93a33cb508d7b1d00211fp-1Q, -0x1.ee149aa686bb2faa29ff6d4bcf1dp-4Q, 0x1.ffde0ca5fc1a1519c08ba08ef931p-3Q, -0x1.a2cbb989ecd0a0b85c48b0eeedfp-4Q, 0x1.d58bf4f6c76ea5b68a5554193d1p-7Q, 0x1.206affc103ba0a875625f4581693p-9Q, -0x1.dfc88961f6b157e54f77890bbc2ap-11Q, 0x1.f86e53415f2a00da542f82562b56p-15Q, 0x1.28c920e4a3f6bb0fc001a36c54d3p-18Q, -0x1.9c90e430666c8d48daf021826ab7p-23Q, -0x1.7e8cf0898f3336a3b6d1b959b3ebp-32Q, 0x1.cc8984cca607f1a4cd24395b33dcp-39Q, -0x1.051a1f819156ba9bc5cb80611a1ep-54Q, 0x0p+0Q};
             }
             if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.efa01fe281c907b167ef08ad02bfp+0Q, -0x1.34df3dac7fcd3f885ed5b138fecap+3Q, 0x1.5961138d5be957877d8cfd1a3db6p+4Q, -0x1.014d7a672544a1c4d79025387afbp+5Q, 0x1.5a4b6fa251eaf90e3115b0c4b844p+5Q, -0x1.d72d9b409f2b1bb94911072b924bp+5Q, 0x1.1a6ca7d65632cc9e3b88e5271a3dp+6Q, -0x1.f8d9ef0a2890c5946bb98eca0c52p+5Q, 0x1.142ce1c1f06e19e0c6f07b09b256p+5Q, -0x1.90f390767ce4703536c74ea5d48p+1Q, -0x1.822b1a96e2d91cc911472931b073p+3Q, 0x1.52a34d125b1be5508a31d4571b97p+3Q, -0x1.0b934a511e088d9de4577e69f953p+2Q, 0x1.335fd67def29efb717b6672f0127p-1Q, 0x1.17c48a3b6f0b811400fc04e03edcp-3Q, -0x1.0033850ae88073da0780e3e27f81p-4Q, 0x1.68d4635bbce683527c3478757d85p-8Q, 0x1.b6ad0e03e206f2cc34c3ad5363ddp-12Q, -0x1.c361dbb11082ba0b86af7e6af24bp-16Q, -0x1.d59d4ba004a567edb22672cba48ap-25Q, 0x1.f6c8c69c71b982736f46aeba6448p-31Q, -0x1.1d186572e3d30ab58425e9abcaa6p-45Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.efa01fe281c907b167ef08b2a819p+0Q, -0x1.34df3dac7fcd3f885ed5b13d2111p+3Q, 0x1.5961138d5be957877d8cfd1f8beep+4Q, -0x1.014d7a672544a1c4d790253c77afp+5Q, 0x1.5a4b6fa251eaf90e3115b0c8a7d1p+5Q, -0x1.d72d9b409f2b1bb94911072e35d5p+5Q, 0x1.1a6ca7d65632cc9e3b88e527a77dp+6Q, -0x1.f8d9ef0a2890c5946bb98eca1feap+5Q, 0x1.142ce1c1f06e19e0c6f07b093cf5p+5Q, -0x1.90f390767ce4703536c74e99b357p+1Q, -0x1.822b1a96e2d91cc911472934db6dp+3Q, 0x1.52a34d125b1be5508a31d4593a7ep+3Q, -0x1.0b934a511e088d9de4577e6b9d58p+2Q, 0x1.335fd67def29efb717b66730db11p-1Q, 0x1.17c48a3b6f0b811400fc04e29772p-3Q, -0x1.0033850ae88073da0780e3e4b1ccp-4Q, 0x1.68d4635bbce683527c347878fb17p-8Q, 0x1.b6ad0e03e206f2cc34c3ad57b135p-12Q, -0x1.c361dbb11082ba0b86af7e7039cep-16Q, -0x1.d59d4ba004a567edb22672d12e01p-25Q, 0x1.f6c8c69c71b982736f46aec1c2fcp-31Q, -0x1.1d186572e3d30ab58425e9b0d124p-45Q, 0x0p+0Q};
             }
             if constexpr (order == 5) {
-                return {0x0p+0Q, 0x1.1672f76c48a3b085a419d3a4a516p+2Q, -0x1.d05e83fe81471c548c376fdd2e88p+4Q, 0x1.49fc051fc99a825862e53c01bf24p+6Q, -0x1.e442104e65335b30f1932f27a50ap+6Q, 0x1.09c52f838d2fca1c275b6969c956p+6Q, 0x1.677b64cbf326e55bcfc7688cab53p+6Q, -0x1.fbf39786bea7b138ef97d6e9bf1fp+7Q, 0x1.628081b6fdd810aa965a5e7f3421p+8Q, -0x1.a2714ddd5c22b603c83ee95dc4cp+8Q, 0x1.cb4de777b4f362d79e6f07abbc76p+8Q, -0x1.9cacd3aee3a7e296cd7191fe8607p+8Q, 0x1.055f4806a834671e4070626e14f2p+8Q, -0x1.8ddf94a470b86c5104b74e18273dp+6Q, 0x1.95561c2d77ea7cb1b418f2fb6391p+3Q, 0x1.8ab9cc38b4948a55522c3044f42ap+2Q, -0x1.6e4f007cb3f6f6544bd7ca0f31d2p+1Q, 0x1.43d7023213a802dd64336017585bp-2Q, 0x1.951cff21de4ac7e4a1f0a8263acfp-6Q, -0x1.5137c147339bc2af2a69107ce017p-9Q, -0x1.3e3df8b2da2752dcb7f7472265e7p-18Q, 0x1.78040f51a9567ebaa0b6d94a065ep-23Q, -0x1.aa8cd8e6f8971ce4ff3376356067p-37Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.1672f76c48a3b085a419d3d84efep+2Q, -0x1.d05e83fe81471c548c37702884afp+4Q, 0x1.49fc051fc99a825862e53c41bd9dp+6Q, -0x1.e442104e65335b30f1932ff3fcdp+6Q, 0x1.09c52f838d2fca1c275b6ba1ca01p+6Q, 0x1.677b64cbf326e55bcfc76402e361p+6Q, -0x1.fbf39786bea7b138ef97d391fb5cp+7Q, 0x1.628081b6fdd810aa965a5c98d2cp+8Q, -0x1.a2714ddd5c22b603c83ee77be92bp+8Q, 0x1.cb4de777b4f362d79e6f05e8e906p+8Q, -0x1.9cacd3aee3a7e296cd71908c1c97p+8Q, 0x1.055f4806a834671e4070618a5f49p+8Q, -0x1.8ddf94a470b86c5104b74cbf3618p+6Q, 0x1.95561c2d77ea7cb1b418f1ad675dp+3Q, 0x1.8ab9cc38b4948a55522c2ec1bb2ep+2Q, -0x1.6e4f007cb3f6f6544bd7c8aa8418p+1Q, 0x1.43d7023213a802dd64335ed45bfdp-2Q, 0x1.951cff21de4ac7e4a1f0a692a613p-6Q, -0x1.5137c147339bc2af2a690f130f2cp-9Q, -0x1.3e3df8b2da2752dcb7f745d4f5a7p-18Q, 0x1.78040f51a9567ebaa0b6d793cafp-23Q, -0x1.aa8cd8e6f8971ce4ff33741ce32dp-37Q, 0x0p+0Q};
             }
             if constexpr (order == 6) {
-                return {0x0p+0Q, 0x1.6688e31cf50e0564efea7bdd5fb4p+2Q, -0x1.50ba2688bc0430a9ee74607c1048p+5Q, 0x1.18d5fc503a1772d2730b3e2d1b1p+7Q, -0x1.16422099d0e700c2cc83b4dddfb9p+8Q, 0x1.7cdc33f38c2d168782ab508fe333p+8Q, -0x1.a2f3c3b8e6e4ab101396a85ce4c7p+8Q, 0x1.aa319d6af6ec967e381e228e6cdbp+8Q, -0x1.958a02a1024489567edfcd0c6458p+8Q, 0x1.4bb5b15c50a647500af4903c157ep+8Q, -0x1.caa9291eb011f2ccec5253008c2ep+7Q, 0x1.1f2d7abf22a7296277eac00e42f8p+7Q, -0x1.3b920d0f7e0d09abc1f29b5777d5p+6Q, 0x1.bc14b21b62b9334a0ec071c6d27ap+4Q, 0x1.8c237a0fa26d740497614e6ce7f9p-1Q, -0x1.7f694c35d9d2245677a757e7ef74p+2Q, 0x1.3f67e104a689bca4d8d6dc3c9573p+1Q, -0x1.4cc6c058f371d1d7aadbd3825648p-2Q, -0x1.6b557354b8d84aa675e72e4aa2cep-6Q, 0x1.38d6e371bb0518c7efdfa45f408ep-8Q, 0x1.260d95329ea8e0edce58678f53a3p-17Q, -0x1.5c7911e0053bc1a14fff7b8b350cp-21Q, 0x1.8b88d3fa551bf8449851729a705p-34Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.6688e31cf50e0564efea7c707539p+2Q, -0x1.50ba2688bc0430a9ee7461099f42p+5Q, 0x1.18d5fc503a1772d2730b3ea50efdp+7Q, -0x1.16422099d0e700c2cc83b554b1d3p+8Q, 0x1.7cdc33f38c2d168782ab512e0152p+8Q, -0x1.a2f3c3b8e6e4ab101396a900d9eap+8Q, 0x1.aa319d6af6ec967e381e232c3d8cp+8Q, -0x1.958a02a1024489567edfcd9f60c3p+8Q, 0x1.4bb5b15c50a647500af490b1348fp+8Q, -0x1.caa9291eb011f2ccec525396312bp+7Q, 0x1.1f2d7abf22a7296277eac06229bap+7Q, -0x1.3b920d0f7e0d09abc1f29bae2433p+6Q, 0x1.bc14b21b62b9334a0ec0723419b6p+4Q, 0x1.8c237a0fa26d7404976151e77cdep-1Q, -0x1.7f694c35d9d2245677a758a1954ep+2Q, 0x1.3f67e104a689bca4d8d6dcd2113cp+1Q, -0x1.4cc6c058f371d1d7aadbd425ad1p-2Q, -0x1.6b557354b8d84aa675e72eefd888p-6Q, 0x1.38d6e371bb0518c7efdfa510e3cep-8Q, 0x1.260d95329ea8e0edce58683df434p-17Q, -0x1.5c7911e0053bc1a14fff7c706e19p-21Q, 0x1.8b88d3fa551bf844985173c27b89p-34Q, 0x0p+0Q};
             }
             if constexpr (order == 7) {
-                return {0x0p+0Q, 0x1.80f665163dff60603105451a6e5dp+2Q, -0x1.7dd2228ef04492e49ffcbb4c7665p+5Q, 0x1.48b0d88030936751bd070e523483p+7Q, -0x1.41512ba753d055c75dc8c691e375p+8Q, 0x1.8f56f07493ef05c30063bbd4a838p+8Q, -0x1.675a39773b2485da34f83284198fp+8Q, 0x1.2e9626a21624df1cdd8e3378c5edp+8Q, -0x1.1263590aebe88d200657bdb9b2c3p+8Q, 0x1.9699942af2221429cba46fea0168p+7Q, -0x1.59e9b6e0b9c21128db1639ea581fp+6Q, 0x1.09d1a0b7c583242c5ad2ce6cf431p+3Q, 0x1.cc8ab1005087bf119ad7cb575125p+3Q, -0x1.93c8d5094509572acb009f2e7dd8p+4Q, 0x1.013c24badc62703530bdc5ef098ep+5Q, -0x1.784654bbd73679c9f2def8e43e7p+4Q, 0x1.21acdd98ca7e3a8d97a5878ef247p+3Q, -0x1.6fa583815aba1a21d8baa02798f2p+0Q, -0x1.39156fe5f0a3b45977f7ccd1d734p-4Q, 0x1.34372727b2154e0f6338311dea7cp-5Q, 0x1.c53d49d19717546a333396c8797dp-15Q, -0x1.57bc52155abea4723bbb49833b9ep-17Q, 0x1.869c11b6398bbfee9ec13fe04d71p-29Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.80f665163dff60603105460968d1p+2Q, -0x1.7dd2228ef04492e49ffcbc26de51p+5Q, 0x1.48b0d88030936751bd070f0b70d7p+7Q, -0x1.41512ba753d055c75dc8c75f4172p+8Q, 0x1.8f56f07493ef05c30063bd380daep+8Q, -0x1.675a39773b2485da34f83484320cp+8Q, 0x1.2e9626a21624df1cdd8e35d51165p+8Q, -0x1.1263590aebe88d200657c008c834p+8Q, 0x1.9699942af2221429cba47418cbf5p+7Q, -0x1.59e9b6e0b9c21128db1641974871p+6Q, 0x1.09d1a0b7c583242c5ad30248e848p+3Q, 0x1.cc8ab1005087bf119ad7a75bf51cp+3Q, -0x1.93c8d5094509572acb009457fd8ep+4Q, 0x1.013c24badc62703530bdc2a89abep+5Q, -0x1.784654bbd73679c9f2def5413da7p+4Q, 0x1.21acdd98ca7e3a8d97a584ca3cd3p+3Q, -0x1.6fa583815aba1a21d8ba9c3f6b87p+0Q, -0x1.39156fe5f0a3b45977f7c9849262p-4Q, 0x1.34372727b2154e0f63382ce7b14dp-5Q, 0x1.c53d49d19717546a3333946ded1p-15Q, -0x1.57bc52155abea4723bbb438d51fep-17Q, 0x1.869c11b6398bbfee9ec137b2aadp-29Q, 0x0p+0Q};
             }
             if constexpr (order == 8) {
-                return {0x0p+0Q, 0x1.d573db31c98a592a2b6a75f0e508p+1Q, -0x1.ddfb9c5686a4efd2bd1e32872343p+4Q, 0x1.a873c238f1ad89ace04b72e9c756p+6Q, -0x1.b2204de17a53a3315364d23c8cd4p+7Q, 0x1.23910ebcbe60d3ac8690288b0ac9p+8Q, -0x1.29c6cec6860250c0db3c6cf44b1cp+8Q, 0x1.1c64b27b4c107ca71ade21f474f5p+8Q, -0x1.156985f5c8bce6de73bf215034a9p+8Q, 0x1.ef2b60fc7ce315a6b8de28e5d19dp+7Q, -0x1.84734ae811782beee80a7706ee5bp+7Q, 0x1.20e874beb6697ebef627236a9ac2p+7Q, -0x1.93d454c0120c50c5e5f45832b468p+6Q, 0x1.e8c645d5034483f58d32bb3f4e3bp+5Q, -0x1.0a8b2e2c06173020781b634ff3fbp+5Q, 0x1.14ef6d11452bbb05715fc7688438p+4Q, -0x1.bab6f3f4dbb55284f992570f49b4p+2Q, 0x1.4e6aaf12e910db6611cb1059823cp+0Q, 0x1.e57ecc0ee730e09fd58c24db0642p-4Q, -0x1.0f174cea8c305d809bddceff1132p-4Q, 0x1.a1f2dc12ec55c96d12f54ea71a2fp-12Q, 0x1.4002914419fbb27ad65f3fceabe7p-15Q, -0x1.6c7e600f14b10472b7579ae3bc81p-26Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.d573db31c98a592a2b6a796753f8p+1Q, -0x1.ddfb9c5686a4efd2bd1e36073e0cp+4Q, 0x1.a873c238f1ad89ace04b7607dff2p+6Q, -0x1.b2204de17a53a3315364d57fc2b6p+7Q, 0x1.23910ebcbe60d3ac86902adcdaa4p+8Q, -0x1.29c6cec6860250c0db3c6f8b8962p+8Q, 0x1.1c64b27b4c107ca71ade24985867p+8Q, -0x1.156985f5c8bce6de73bf23e5601fp+8Q, 0x1.ef2b60fc7ce315a6b8de2d939461p+7Q, -0x1.84734ae811782beee80a7af9899ep+7Q, 0x1.20e874beb6697ebef627268d4461p+7Q, -0x1.93d454c0120c50c5e5f45ca0c342p+6Q, 0x1.e8c645d5034483f58d32c0b8709p+5Q, -0x1.0a8b2e2c06173020781b6687242cp+5Q, 0x1.14ef6d11452bbb05715fcae8f362p+4Q, -0x1.bab6f3f4dbb55284f9925c8a3ab9p+2Q, 0x1.4e6aaf12e910db6611cb145f554fp+0Q, 0x1.e57ecc0ee730e09fd58c293b9a01p-4Q, -0x1.0f174cea8c305d809bddd1a456bfp-4Q, 0x1.a1f2dc12ec55c96d12f54fd03177p-12Q, 0x1.4002914419fbb27ad65f422d91cep-15Q, -0x1.6c7e600f14b10472b7579cd8544fp-26Q, 0x0p+0Q};
             }
             if constexpr (order == 9) {
-                return {0x0p+0Q, 0x1.d2f4e044749b4e7a1c71af625a42p+0Q, -0x1.e196df480fe71bea5cbbf54b35dp+3Q, 0x1.ab061d20276f0750e2a71f034e04p+5Q, -0x1.a7b259e6037ebf7c8e2ada0b5ba1p+6Q, 0x1.04d3977e22f60f45b515e22f405p+7Q, -0x1.c308c46a51aa08f31731abdc9396p+6Q, 0x1.759cb70549060301bbf1e90c0d7dp+6Q, -0x1.73a4db524ebc2efdc465df1eceafp+6Q, 0x1.4d02e405c663ff8abf63f13a14eap+6Q, -0x1.c4dfc682dd95df4b0a54f464f5c5p+5Q, 0x1.217c835a844bf319c913a98fb0dfp+5Q, -0x1.9d3e5e5e092523c0105752b9ec75p+4Q, 0x1.eced01c912f6c17b1d53692fa574p+3Q, -0x1.ab15772777a65a90ae2d7cd7191bp+2Q, 0x1.780b7892927c5280dd5becc68e9dp+1Q, -0x1.59e4e79f9d38488dc3c592823598p+0Q, 0x1.04013ac7f90eca1ecf033967d8bdp-2Q, 0x1.63e903ad632e7f3030703fcb6c64p-4Q, -0x1.26b339b06c46eff13165e26c3ea5p-5Q, 0x1.1fc083a0e2c35a300d5c6f8e06aap-10Q, 0x1.9c18e59aa15ab3ece464b5d35415p-15Q, -0x1.d792baac952f2e4df120dee55ebdp-25Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.d2f4e044749b4e7a1c71b105042dp+0Q, -0x1.e196df480fe71bea5cbbf6f938ep+3Q, 0x1.ab061d20276f0750e2a72080d7a9p+5Q, -0x1.a7b259e6037ebf7c8e2adb89e41bp+6Q, 0x1.04d3977e22f60f45b515e3221088p+7Q, -0x1.c308c46a51aa08f31731ad9b7844p+6Q, 0x1.759cb70549060301bbf1ea932595p+6Q, -0x1.73a4db524ebc2efdc465e09da17dp+6Q, 0x1.4d02e405c663ff8abf63f28cd74p+6Q, -0x1.c4dfc682dd95df4b0a54f646c034p+5Q, 0x1.217c835a844bf319c913aad35977p+5Q, -0x1.9d3e5e5e092523c01057547d3214p+4Q, 0x1.eced01c912f6c17b1d536b46140dp+3Q, -0x1.ab15772777a65a90ae2d7ecf56cbp+2Q, 0x1.780b7892927c5280dd5bee9ee8edp+1Q, -0x1.59e4e79f9d38488dc3c59417b41ap+0Q, 0x1.04013ac7f90eca1ecf033aafa30cp-2Q, 0x1.63e903ad632e7f30307040928615p-4Q, -0x1.26b339b06c46eff13165e32f7c85p-5Q, 0x1.1fc083a0e2c35a300d5c6fbf948ep-10Q, 0x1.9c18e59aa15ab3ece464b6468819p-15Q, -0x1.d792baac952f2e4df120dee003e6p-25Q, 0x0p+0Q};
             }
             if constexpr (order == 10) {
-                return {0x0p+0Q, 0x1.19eec26520f7247ef7c6a50c30c1p-1Q, -0x1.249f95db3c6a85ee060075e867d8p+2Q, 0x1.0297dba66cdd344c6014add13643p+4Q, -0x1.f4e8dc0eb78aa7eff1fa777a2d3cp+4Q, 0x1.1efd1b3c60e0b36de4fe2959cc4p+5Q, -0x1.a397a05a5f774f4ee2078ee612bfp+4Q, 0x1.239464bf9e82c4fc4fdd7d10ceaep+4Q, -0x1.3946d065739beaad7a016889ae55p+4Q, 0x1.2898316e66a7f2a70e1a6d4e83adp+4Q, -0x1.5bb8e2c4642782930886e734cb84p+3Q, 0x1.68255c99ba4c6b07d8215b80d139p+2Q, -0x1.21aae7ae7df31c2992880869d80ap+2Q, 0x1.64fab317448fb04743119877b3a8p+1Q, -0x1.75b64c97e09686a5bb55ff7e3516p-1Q, 0x1.22ff2ac4d8b9c4ff1398067e3f99p-3Q, -0x1.07ed621dcab476dea8f9c1c1f859p-3Q, -0x1.4a01e6ee0860d89681b640d3090fp-6Q, 0x1.2e7cdbbc900312ead84b8f4ecdafp-4Q, -0x1.b7f6865bae122ce58cd5b6b5db5p-6Q, 0x1.17b65cad3d540e056708b920004dp-9Q, 0x1.910e0462410b5b96ed51c6158bb4p-14Q, -0x1.cf434a44d45d4684dfb9a8c3dc56p-23Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.19eec26520f7247ef7c6a243923bp-1Q, -0x1.249f95db3c6a85ee06007305aedcp+2Q, 0x1.0297dba66cdd344c6014ab433b38p+4Q, -0x1.f4e8dc0eb78aa7eff1fa727c9c71p+4Q, 0x1.1efd1b3c60e0b36de4fe266b9d8ap+5Q, -0x1.a397a05a5f774f4ee2078a58f21cp+4Q, 0x1.239464bf9e82c4fc4fdd79af7e82p+4Q, -0x1.3946d065739beaad7a01650a25b9p+4Q, 0x1.2898316e66a7f2a70e1a6a12eca5p+4Q, -0x1.5bb8e2c4642782930886e32d2ea4p+3Q, 0x1.68255c99ba4c6b07d82156e3f9d9p+2Q, -0x1.21aae7ae7df31c29928804e58d84p+2Q, 0x1.64fab317448fb0474311942daf3fp+1Q, -0x1.75b64c97e09686a5bb55f9818d82p-1Q, 0x1.22ff2ac4d8b9c4ff1397fddfa477p-3Q, -0x1.07ed621dcab476dea8f9bcc8470ap-3Q, -0x1.4a01e6ee0860d89681b645bb0864p-6Q, 0x1.2e7cdbbc900312ead84b8d7e757cp-4Q, -0x1.b7f6865bae122ce58cd5b4105bcap-6Q, 0x1.17b65cad3d540e056708b80ca432p-9Q, 0x1.910e0462410b5b96ed51c4c46ef3p-14Q, -0x1.cf434a44d45d4684dfb9a827c309p-23Q, 0x0p+0Q};
             }
             if constexpr (order == 11) {
-                return {0x0p+0Q, 0x1.a6c51bc471a3098c7c3ba6f25a23p-5Q, -0x1.b8315371d42a542d22b5306cc4fcp-2Q, 0x1.89e13c889a74c808a95f3d0a6799p+0Q, -0x1.8aa497719f070f6dc765c9fe7e51p+1Q, 0x1.eb2b7ee2bc88d2eef92b7b69cb04p+1Q, -0x1.a91739cfcb4374adc78a37551409p+1Q, 0x1.4e87023b22be1f061884bc9409e9p+1Q, -0x1.31bb74af8ae4dfa54f81310a9052p+1Q, 0x1.0e1263d4463c809bd84430b64506p+1Q, -0x1.9cd0db1b42b96cb6927f658a63e7p+0Q, 0x1.3cec213a53551ad84004db21dcp+0Q, -0x1.daf35f59b2441d717c169614a5aap-1Q, 0x1.329c321d7ff6b77198e763d64324p-1Q, -0x1.8936ae8cb907bb56ce7129ca7fc2p-2Q, 0x1.00dee0f339229a14bdfc09c4e162p-2Q, -0x1.07bd180d959690eaf41df912a76dp-3Q, 0x1.cec01fe9b05f624125be2b70170dp-5Q, -0x1.e6ef9d5209f879f2bf7a3f0d08eap-6Q, 0x1.8f4f47250e3a4f324676c82d9528p-7Q, -0x1.e72d4f4950c89aa59da6f47aed33p-10Q, -0x1.e19176d7ba69146eb048ef5a5e41p-14Q, 0x1.1b79fa688c946fc4993e55c900d5p-21Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.a6c51bc471a3098c7c3ba4b2e396p-5Q, -0x1.b8315371d42a542d22b52e160edap-2Q, 0x1.89e13c889a74c808a95f3ae5db18p+0Q, -0x1.8aa497719f070f6dc765c7af4f82p+1Q, 0x1.eb2b7ee2bc88d2eef92b780b6136p+1Q, -0x1.a91739cfcb4374adc78a339981b3p+1Q, 0x1.4e87023b22be1f061884b91ff276p+1Q, -0x1.31bb74af8ae4dfa54f812e36b5bep+1Q, 0x1.0e1263d4463c809bd8442e6ab9d2p+1Q, -0x1.9cd0db1b42b96cb6927f614da713p+0Q, 0x1.3cec213a53551ad84004d758bdadp+0Q, -0x1.daf35f59b2441d717c1690c25188p-1Q, 0x1.329c321d7ff6b77198e76070d6c7p-1Q, -0x1.8936ae8cb907bb56ce7124a40ebp-2Q, 0x1.00dee0f339229a14bdfc063bfb91p-2Q, -0x1.07bd180d959690eaf41df5a4ee44p-3Q, 0x1.cec01fe9b05f624125be250b50a9p-5Q, -0x1.e6ef9d5209f879f2bf7a379cfa32p-6Q, 0x1.8f4f47250e3a4f324676c24519f5p-7Q, -0x1.e72d4f4950c89aa59da6edc504bdp-10Q, -0x1.e19176d7ba69146eb048e9181ac9p-14Q, 0x1.1b79fa688c946fc4993e527c8905p-21Q, 0x0p+0Q};
             }
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            if constexpr (order == 0) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00674952336093794271822599377832733300651146336500105281821757702580261898435"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.307583456142659816839156786245335727208310576612803762616887840930925575209"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.925942456953309005940386530995126436012681380158402535652037264183889758483"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.340268706102660683375457588221232998838593649367854881779057620364907425914"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.160279537383566356658810338492196248229219596027949666407555183251410683353"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.100906238726469613031927683469694828929687407601613980745393598371134911780"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0635171183876279943173554673370722041156121244338995400601119969400460909180"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0322672348814505948972500008092114355665944734834499482855568997884208147214"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0119258192115874852729361214670894284737320324933075482785998337722648377488"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00298707792707452898367085553746573188496510147112607446979462542972907046198"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000473081135158127015860372446974828573937912728115760868405824469327509104714"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000385901914771418563229090512720344539916565749843499561465030991408855304182"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000707771294264344979265706380621665838995140738494138127767693643047473151938"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000449127676142712270206334163110940969109789276623971797893643048336659640461"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000462246298923448308370189842110923874064368375158153708369750363490273849968"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000938981013616806301299448140440205677496034062712612222476591887975663431153"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000228731055691905904721631337725631066731945798378875548099322801540390353792"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000122805107893837304401775672037887127425598683650631632643112458670137760454"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000634403654278944400941924520388860558080403502147439478702947659558312462441"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000718601577933574214479296340908692396681088130844931493227840962495346368987"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000150165111893706003972718474555253050830994970128831551959442684938639721914"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000324728013911670481356185860811593862377837926387577826017803860651455895063"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 1) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0387773893440001328479990972130631692265393392276997953903865925128067141024"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.721552572534024717748570063882033395155483583566407967882626836656429636782"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.272212648324158111612511789206460700674191556065031727190617093210427966623"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.978728114873296652638727035042942428237594510811351020620221815511037142320"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.795198318518956652102305679705853563026415740789264534365825373566593070233"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.430598975220305785445999132638246196763260311865173495540662078177969568735"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.142583347029948066092993254964771828684926120817867402181283862012299624787"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00146617508298700811859640317636078157631882791634139195335692402607076083994"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0309009498425184610096113389760986103366023818447589327535142129940010076705"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0157686546523657228788031242284047791698300666554508584962947405558611056219"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00242189069596937080496858729150225100112203583636152350242227674378819932850"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000865465504805686451786867765475930422411519327219197611864322484446933101993"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000431401320802406335612460169440586915965773678151860581031150029061360265549"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000431642115711336908332394044162700208606587787562050592203268643657811936924"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000821808783448349005091749141022578622146590089593391035863483128421998476881"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000161980230922061292865855432080723373115493373219912556484058486745620714179"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000483019272136912181673157244957934770912195515285570255684870776439319393894"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000332141975285733899509799336405046588503487344884194087554458021104822328255"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000983310426136874022596843421343020282473719270746503069720570388756166209575"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000821046124017272115015180345888003894425103661180504475350314828549798634201"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000422272678140744917094064065340806009116153886552991342868695393427346681857"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000182633960975279599217132126825168232459508047673969824620606842686892878014"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 2) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.183591506446484309712795488849571274418364537569049882649969406786991566703"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.941047892088601518958291499087971794201051709610594834344832432863937253481"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.23915063134374610177549908438346173797911023760267160983136498244943289731"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.46939789738852314818899400606908382011384059438420298035329651589159205087"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.28173493700255435214772096048237572437923445360570917382808581102768910125"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.50315674849912814024262183106436302156615435178890932358182035213351917617"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.835860237460870761390156685965058693698796219956190288728965409249874516389"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.328887568441256381505801657142525299671290097708556863386573335636703368303"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0796708363104952604879937077745989748584956873438833081361877117810017197093"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0161807814953966106554332142048099058586667875986593188231761928160044535103"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0105519844080212767161949305951351809551205888170657290798324464298016783059"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00615491119567815699833303054263633346002498173776612335382778423057115661320"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00152542169738812236275366430470857831307147305605930001884982398335206187746"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000478023149049562031406199523580878829069008124571083991909044064992027938837"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000316785284248449847258104755742578560748429902748877549315826250898391153165"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000353476646946804208268171454249821202212174971459821936484698256572687164013"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000781441021094927012007376595229335452531962058185139941865056284143318220825"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000158016326457618764551834550084612976065250040667862420828605844454348687428"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000645985856862059637165608932066447500409737957145914496500299017194796733184"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000552579581560011400180824517243503538265777971769292220658774318761637323198"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000518750590964679052304303794785902282315144982464294500494857713908195654535"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000000448738003521685102283394837866669813173686476421773647750785777214873187545"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 3) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.687564701830153090496154601673244324665424792477734591515424354722524099152"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.11050239053869430027184090551059176229770565635462126988333316421136630257"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.93804463381724493769207024757917870971550445481996014592183410296094056051"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.20610058150974826647727021504587596509253169984522564051121763364081781688"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.01372486758602951783294736130451247536207984026936617147556597467502065146"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.75779225268411745440182343883946325363307126912452705923359087032746232261"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.42290247168000634999802692912700654401659291644918891841812220270431988663"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.90367417089379141718231735172375182130729195288100071937663900099707066494"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.73753605277785755057468262545518793812656205923506367770591971382787612864"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.888694186837802736174804686545601676095716084997773896570154037914318457788"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.120625118354310597854672205082409827213145048325433221107814663185540763499"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.249935244384244229475998157073285972261843545061283350728568950695406300807"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.102245068322009442021851053260660268979014010537069811214828519334188485107"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0143294283021151060785346153371703965226713038712447807825810853955454985909"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00220045444485302028275444219293273448787231072694521760298002658782637616979"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000915114109598521684422240708952522787741064024256659542685847796787098864471"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000601328561158122075623159592639344585246740920247215146685740357533130502579"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000442245093225367075171042726134823952641438570521711248051460748670218278934"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000192116006225709175804133650291101682367016689175710099736613621136724772233"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000347927694118473204634336179637016248843344378650467345924085824175805403758"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000327231349649651474450860748750987614694465218515883129352235985103556742393"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000566174805053915554844952341333463723778572903642256009402911739536460840202"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 4) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.93603705673175252162377048005080828323485510199286167343778412900683630357"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.65225108805899617933044689930629862606922722189344796627981892221806322756"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("21.58620028704043203965568014489070671164252883102441474199007795986172799450"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-32.16283112127764887984781311792208840193362133426782486134064927600419439680"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("43.28683401882642247901443678261444427228477284299009228485788317422296188030"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-58.89726877675765402909531534108742114308361932607118347118552732380096882110"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("70.60610899830926411810587962905898518983841308375904913755422678352922515570"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-63.10641296325966002268292888588592628930166199721781262159830072450491171720"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("34.52191497340187437272066528301740399000435097032593635597215974196048894900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.13243299279728005268439173331599785511338054577595843510586618380676315959"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-12.06776170225092279346900025349356398262454275196967160026720095858830643800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("10.58243421158919931486338350084744671448957975219955115739863127269480650610"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.18086488648999297183891759837512319517601794026273877877208860579097625582"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.600340559838134056014385774162185206812240239620564149846506062110388511249"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.136605338991903970318857223904627046152412648176017176159147490879517687577"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0625491330124817618386886003919664398460060491417974176815677679696581035123"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00550582338086123158873116800515458266240754229253267111261799485380454805945"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000418354029755102972365185158832406860086075763566175597817465795414186469647"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000269044791745347379635890876857658847394460147615410319076105357130452956021"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000546703156080335157447390001850562112157399818528369118783700921788207959856"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000914559278617230197902988750581388857118162901722874330587746501390541480138"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000316519364036060085112704740081169075698795498871539132664715584413313149738"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 5) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.35076699804863678677975429556027903354422790699226157645072577251818273676"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-29.02307509819042426585700918686326160072354736867411698539343692983196503080"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("82.49611329715719629374872640906345290805764600780220272968616846701709806240"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-121.06451532833747392386859794636510608764397274079815027628644009969274065900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("66.44256406354174703030638747248670204230247493582940326331823060083408390470"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("89.87050169631559036410735425620807796485093895246621283952389526730602524440"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-253.97576542928058746612034494797807584834351582667944315344135960784812946200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("354.50197929093707453189915787851278530317676402818444334154635759143504945200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-418.44259437083629654372265774871306291337038882950576397483748815661296325300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("459.30431316535703999996533810953606750433852009745459279981845049292111412100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-412.67510502870562514868993537829892602977991674444809590835277417435828403200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("261.37219277960357686002183516875187598846311513198317551376196154507578273300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-99.46834046304693927396397394893633319797299579647467410477722973021902030540"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("12.66676148300696488281972471730213802977983006010030132112775191282004845920"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.16759019410739796803106483846236267155563560221580308118480616704388032488"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.86178594674122850153536653793135766872481629722817248177002057968004742610"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.316249880129284132115920875971521368522150973034344085606632817974345846565"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0247261516119336322479197612328703090652313932265109203114345439280129606257"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00257276758529842275783708309373614341047704871305149895482328025045858909260"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000474217647448341719828623182459779084961108353234750865989641444296059914091"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000175096028833295782031678343625079307038593522030930622175736643377626514407"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000121232854060447503547926609753618642777727719448048997021870449891245778235"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 6) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.60210492923599220306739726849524365911272995023030149275362729443627767241"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-42.09089381049900454092361924595905199878007886101579238359551872779773615180"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("140.41794062337041783562329118755195628284508671409730808010312709127392837500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-278.25830994939952049425764143319165780543667702177067080512763370773979265600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("380.86016771480816533332928441348450481125889613649326541505558838372953629000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-418.95220523488084674141481769302959290485836739389011115886709000649475649100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("426.19380825546667243857182155918014103510325386970185000695176160112816290200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-405.53910261445392868706053637913300495637853779363319766514135762481123453200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("331.70973755806906280222948564333114303709973974217107892064712971483217388700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-229.33039184474271152765997296747693653644896311902985970449951777370036797400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("143.58882710741052581341088543723084000514106642516308650843963725396056822300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-78.89262794691900075510218647088275987362866657725786329632823854347189893030"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("27.75505266854777348435048128311171422045966573330871472192405309949017306920"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.773708166512018375007390099318270025246521769336781853387329991690258896716"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5.99080186137078587115052777435201929542834691356814368299406374154030652526"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.49535763480259999546977692911560881994873486413261121783762393577404777245"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.324976926259170024466514821976486541713103347782139429815301297092702931869"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0221761347082867372516860357201809209573177307919227810107850272426097081037"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00477355053747537251275230025941686821306294456709786754720729109346187074810"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000876346402844021878197271431695817559174109670993605807770140477893316270959"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000649081410844014945450377643724451703185492681208039429612859077055126594639"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000899341295111001783061788354774120539335760947137727039371354507713388157031"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 7) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.01503874942863172446672032045385310660658346430556969311090280204002893574"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-47.72760497732867563639045888687408111648670461954967176817630689615594571920"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("164.34540176957098246520164840268114912785108333764805325670104505015878591400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-321.31707235141978805890085173651076956857219432352414927630174955007268214000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("399.33960655795728826591320240810290804342839867119935493449864048725021503700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-359.35243935769951609547501622393948495038359128149158218493239094084479572300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("302.58652699509263723866918658763896223023494881995643828072737018416182521000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-274.38807743319971566043869533026106988492438939463128607709797721020443215100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("203.29995855527617039240266616022588964442318448807463904291472490500587668800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-86.47823668607499417468265201809837107760314991031737704773103407132324816810"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.30683933155896571923336370342680329284352699673810942748030941466774153040"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("14.39193010388793670592743695120274923548898641004312440323358299497206491280"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-25.23653129216162031393190650488947069144769574727062315317496697755106409830"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("32.15436693177280611867229541693914656357710375952844770094246636458373021770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-23.51717065215362229865507044104445167369445267308462930568665799256423840570"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("9.05235175935735664788319630251805269364581033096340273166670658279003426872"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.43611928852144679808218829087774768973983520937512890405722409904760001331"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0764364596389350180439110342110306497850920144422968183705432261288688167041"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0376239552256857684356168042424620283930027011606313367853621428915639193111"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000540303477804840762648923255410865058939043280088368514023926300961486967782"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000102441199866988900731723735456649881175505194362439761979226773134926915151"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000284205922260922568932250591462669984026040113459253556541826475617240410416"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 8) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.66759815150278959307930599333163597096097529742853199217978181562630696487"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-29.87392839240265725546623883959127802560925486188325916048865579469303024630"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("106.11304558730206231169420989915879780867394552444174433037983757043874961100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-217.06309418314214666288595563832635346239588058289858882887597087103632217200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("291.56663112304597857590334364976771943737359513217961682974016748268384769300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-297.77659264346795265988020082120368913354431735040919787932537200810228046400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("284.39334841353455606151257223937124519201920224538084896597007768405172110500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-277.41220031882121641670001674749778842464959328498538149541517303833838711500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("247.58472432159900771477076380876163976925347752971933279268071613868274753900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-194.22518086636781463956709313343541688316198595925041840328872392823935647700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("144.45401569344244085247818472795589947662462099880946347817047437422725404900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-100.95735454664379984016882278587502046931372757809433648524452327992007684600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("61.09681288162443200526120017869481568171612243827222222068632320726899857500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-33.31795915978991479226353783917641730723993856565006267406505994034763561210"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("17.30845362421199129993292294948350854310287513028370737357127567143752171420"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.91741656219422399006952830174054308724719397866962278438510860750311408940"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.30631536685638443282971027232061480593991545082436137033699622406166968595"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.118529126264956569656056269771626755793811242386616315248341528538090571096"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0661843304194570081752469739423793402949926380986891972951348623664335067648"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000398586912690642748373175830858033776325071495068959972844940429117973233494"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000381481682161783683986425780978390997526951366596105346738987927781141638894"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000212163229730584007262375731808777339564186173310877882056921511132532981858"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 9) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.82404901191021660107611405457755744720508147280838668944561685140253424274"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-15.04966701578743791983566870544026493163762629417625697617466370992453373950"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("53.37798524017660253980042023139266987459040956232067348967572826444722400500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-105.92417106052715735002349944451589608377479192425044614348746722708067035900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("130.41326517273685551908783147004280111867640298350958460298534492271024128600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-112.75856176494063105548507692533259561359149505796793856695544860362794488700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("93.40304191835594150352589694310821255241952082139322576408183818507525504810"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-92.91099289517937530938067160839545056753425221872875127682184392703877307920"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("83.25282296203022229084823461764842101991248796776481529458179231322413184940"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-56.60926534880375950692439436083700078084789164896951269302972237793898650350"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("36.18579741207349225217113136176821974406219093273833973652666883038907214880"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-25.82772671444610862462306541969742751815537984691055996627268281393630328240"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("15.40393151542931365681934641697554669810260411956534200123239544102606890360"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.67318514684902700324396712833889530416584439958498307300658341368976434355"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.93785006672712485651870672930552135674962040419489700124033209653118603360"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.35114905974225608322981232543443993841639703478986459747319143071556838636"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.253910940604568570873136388508332898207860540665090852083889016211691603112"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0868921416897127089804662233761880201802165848173331041475381130845773690378"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0359741331807378258738142078527195789630247593913553671912092170295325403548"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00109768679996836757242664134813447276225315118775952708555290702903991203965"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000491258208131049675088973621242027668877049383351261231455773092411325252306"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000548983412936212498495690390885488330611341145287970297974581737627796036856"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 10) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.550649714321919146020391652705270850624984467632444477892208411090670503460"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.57224031839147248722382996328027080443894364680263533387085228867737306467"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("16.16207470903266336622407533376180083841264103186821602341901646085415441920"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-31.30685048817455572162905452355438357246801343486549641376884657698487166490"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("35.87358710451743501103090247260098261068172630229012387217368794457391845240"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-26.22451815893096578505537492191089420871702814982563223312943309074511861080"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("18.22372889376872362134777045706885197255097592668156061200711581268831340790"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-19.57978858594446573474343717866513610480907608812601678912962077898856742910"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("18.53715651631727882099530623547490387621972342657149537210734087006118103230"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-10.86631906850492186026855947795210696729727028226200184897211758632056293120"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.62728037846063128438976106546508945987259369732013042706443820658486730438"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.52605621376260259593982907405174555293727464118730144996047399577463796319"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.78890074382900144618255657410026967999905288228433605937465464511446641771"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.729906457462033355139337021126261461176772010479428021961867397970803230476"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.142088255054741883006545627449011553786767246338704050666922604912111664368"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.128870741399931027764146528868524281495256321870369794112882474231057823379"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0201420550512292820836440674996269788542898415412561416178222180575252813086"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0738495429477559359501157209854724157351709061729224786516577653892388373974"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0268532096949637519510499296268755420094167792885280535232350328010652171480"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00213403588588315134257033560239887601573172007420308747358527142593502213305"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000956189046839608573100519969536118832653435986603979875808632067612204306782"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000215723576025549042840675180271579291754584130778771057415350031447174455663"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 11) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0516076605159024911828475147837820854392015861025284155408704376160614689184"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.429875663588101212310123466761246228949954693513674780077411570894231140593"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.53859308562319363525064968437125695806116775999527119873257232627957881183"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.08314793632421711513446659317655276412171796583863723768853134524872575829"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.83726488181225153055424552179561105009983872787369445162123171315532794535"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.32102129598800001827402190941442844711537496612480829720954545917202711427"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.61349513900266658472136887684620241910754262198058846835967186330136663863"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.38853319713033495202260098319806213683185517673058274190000445657860915347"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.10993621697386759008454349852482017386377263965160538055677721963192891999"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.61256188788931860024729141933908754524860783254583010122183874119617986655"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.23797805475199533327033756060882156229697699608086470174399374479195617901"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.927638034533750248678688510655383608919790412752058469862157655885568742788"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.598847929097229887988452897323944295134119484352549354946451834874406807448"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.383997657145535004546586640993163439996459447874095195026713580064418880820"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.250850214810528805990052825784903155854458963606740947659194110817761051247"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.128778636850891888203699386683982406407371540708648125836387080670890476774"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0564880965516855608539804536808433961937777036332691539099534383291528671575"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0297202144940054411503976781292207507569011942232371230104009758591434089695"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0121859643351046128923156738600080443388598031417307165875316044362239226179"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00185843273568833887463557296801124598677123828961682233747031997277499314044"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000114814810668351667156857713897954085126369615497231973190312538067210861730"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000528016085138320874511452843388030214551797843336485403204846872234194616278"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+        }
     }
     if constexpr (p == 13) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -1082,10 +1335,10 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0f, 0x1.749078p-9f, 0x1.8ae6a8p-3f, 0x1.d0088ap-1f, -0x1.20e16ep-4f, -0x1.f688bep-5f, 0x1.2fca44p-5f, -0x1.505c64p-12f, -0x1.014518p-6f, 0x1.c908bep-7f, -0x1.beac12p-8f, 0x1.0006aap-9f, -0x1.d4cc28p-13f, -0x1.a08b66p-15f, 0x1.5f413ap-16f, -0x1.5c34d2p-20f, -0x1.2dc446p-21f, 0x1.74f33ap-24f, 0x1.ddb5ep-29f, -0x1.07969cp-32f, 0x1.2c5958p-38f, 0x1.52fae6p-45f, -0x1.d83da4p-53f, 0x1.1342e6p-65f, 0x1.aa25eep-86f, -0x0p+0f};
             }
             if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.239236p-6f, 0x1.0c0768p-1f, 0x1.3373bep-2f, -0x1.856d7ep+0f, 0x1.22d30ap+0f, -0x1.72e38ep-1f, 0x1.8e439cp-2f, -0x1.3bc252p-3f, 0x1.1bc8f6p-5f, 0x1.288446p-11f, -0x1.db22aap-10f, -0x1.3482dcp-11f, 0x1.328522p-11f, -0x1.bbf1c4p-14f, -0x1.17497ap-16f, 0x1.bebecp-18f, -0x1.bc40d8p-22f, 0x1.6454c6p-26f, 0x1.5fce04p-29f, -0x1.12414ap-33f, -0x1.ce70acp-41f, 0x1.8616f6p-48f, -0x1.7b38aep-60f, -0x1.258ba4p-79f, -0x0p+0f};
+                return {0x0p+0f, 0x1.239236p-6f, 0x1.0c0768p-1f, 0x1.3373bep-2f, -0x1.856d7ep+0f, 0x1.22d30ap+0f, -0x1.72e38ep-1f, 0x1.8e439cp-2f, -0x1.3bc252p-3f, 0x1.1bc8f6p-5f, 0x1.288446p-11f, -0x1.db22aap-10f, -0x1.3482dcp-11f, 0x1.328522p-11f, -0x1.bbf1c4p-14f, -0x1.17497ap-16f, 0x1.bebecp-18f, -0x1.bc40d8p-22f, 0x1.6454c6p-26f, 0x1.5fce04p-29f, -0x1.12414ap-33f, -0x1.ce70acp-41f, 0x1.8616f6p-48f, -0x1.7b38aep-60f, -0x1.258ba4p-79f, 0x0p+0f};
             }
             if constexpr (order == 2) {
-                return {0x0p+0f, 0x1.7e9e9ap-4f, 0x1.e81e74p-1f, -0x1.368292p+1f, 0x1.a1c192p+0f, -0x1.58e6fap-2f, 0x1.2f821p-2f, -0x1.f8fd9cp-2f, 0x1.017de8p-1f, -0x1.5831aep-2f, 0x1.30d718p-3f, -0x1.30a608p-5f, -0x1.632f9ep-11f, 0x1.1cbed4p-8f, -0x1.77d87p-10f, 0x1.50ec24p-14f, 0x1.f99c3cp-15f, -0x1.8453f2p-17f, -0x1.b40566p-23f, 0x1.4c2776p-24f, -0x1.287dbp-29f, -0x1.b00a66p-36f, 0x1.401eb2p-42f, -0x1.715282p-54f, -0x1.1de108p-72f, -0x0p+0f};
+                return {0x0p+0f, 0x1.7e9e9ap-4f, 0x1.e81e74p-1f, -0x1.368292p+1f, 0x1.a1c192p+0f, -0x1.58e6fap-2f, 0x1.2f821p-2f, -0x1.f8fd9cp-2f, 0x1.017de8p-1f, -0x1.5831aep-2f, 0x1.30d718p-3f, -0x1.30a608p-5f, -0x1.632f9ep-11f, 0x1.1cbed4p-8f, -0x1.77d87p-10f, 0x1.50ec24p-14f, 0x1.f99c3cp-15f, -0x1.8453f2p-17f, -0x1.b40566p-23f, 0x1.4c2776p-24f, -0x1.287dbp-29f, -0x1.b00a66p-36f, 0x1.401eb2p-42f, -0x1.715282p-54f, -0x1.1de108p-72f, 0x0p+0f};
             }
             if constexpr (order == 3) {
                 return {0x0p+0f, 0x1.95e034p-2f, 0x1.e7908ep-3f, -0x1.29379ap+2f, 0x1.36cc46p+3f, -0x1.433598p+3f, 0x1.9c4d14p+2f, -0x1.ef81d8p+0f, -0x1.2378e8p+0f, 0x1.c6e272p+0f, -0x1.c857e6p-1f, 0x1.3531bp-8f, 0x1.05f57cp-2f, -0x1.38a2dcp-3f, 0x1.35c4a6p-5f, -0x1.fddc3cp-14f, -0x1.2653ap-9f, 0x1.ec5d7p-12f, -0x1.dc01f8p-17f, -0x1.379718p-18f, 0x1.7e5cfep-23f, 0x1.a12416p-29f, -0x1.417132p-35f, 0x1.65f402p-46f, 0x1.15123cp-63f, -0x0p+0f};
@@ -1094,25 +1347,25 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0f, 0x1.4c5d52p+0f, -0x1.5d2572p+2f, 0x1.24b0fp+3f, -0x1.39e0f8p+3f, 0x1.f006ccp+3f, -0x1.0ce3p+5f, 0x1.b8b8bp+5f, -0x1.e69256p+5f, 0x1.503102p+5f, -0x1.6d86aep+3f, -0x1.35b5dcp+3f, 0x1.a6237cp+3f, -0x1.cda456p+2f, 0x1.d5a02cp+0f, 0x1.ecd4c4p-5f, -0x1.660ee6p-3f, 0x1.5158e6p-5f, -0x1.73814cp-10f, -0x1.23460cp-11f, 0x1.fa353cp-16f, 0x1.19c574p-21f, -0x1.4bb43p-27f, 0x1.fc9a2p-38f, 0x1.89a8b8p-54f, 0x0p+0f};
             }
             if constexpr (order == 5) {
-                return {0x0p+0f, 0x1.a35158p+1f, -0x1.5a1bc4p+4f, 0x1.fa0a08p+5f, -0x1.a68f66p+6f, 0x1.98403ap+6f, -0x1.03810ep+5f, -0x1.14faaep+6f, 0x1.3d735cp+7f, -0x1.cdbd7ep+7f, 0x1.200434p+8f, -0x1.2591e8p+8f, 0x1.b6219ap+7f, -0x1.a875bap+6f, 0x1.85c7d2p+4f, 0x1.1c0e0ep+2f, -0x1.36efc4p+2f, 0x1.3e3f5cp+0f, -0x1.bffc3ap-5f, -0x1.75f52cp-6f, 0x1.dea5b4p-10f, 0x1.10aa3ep-15f, -0x1.ea6ed6p-21f, 0x1.089ab2p-30f, 0x1.9990a4p-46f, 0x0p+0f};
+                return {0x0p+0f, 0x1.a35158p+1f, -0x1.5a1bc4p+4f, 0x1.fa0a08p+5f, -0x1.a68f66p+6f, 0x1.98403ap+6f, -0x1.03810ep+5f, -0x1.14faaep+6f, 0x1.3d735cp+7f, -0x1.cdbd7ep+7f, 0x1.200434p+8f, -0x1.2591e8p+8f, 0x1.b6219ap+7f, -0x1.a875bap+6f, 0x1.85c7d2p+4f, 0x1.1c0e0ep+2f, -0x1.36efc4p+2f, 0x1.3e3f5cp+0f, -0x1.bffc3ap-5f, -0x1.75f52cp-6f, 0x1.dea5b4p-10f, 0x1.10aa3ep-15f, -0x1.ea6ed6p-21f, 0x1.089ab2p-30f, 0x1.9990a4p-46f, -0x0p+0f};
             }
             if constexpr (order == 6) {
-                return {0x0p+0f, 0x1.5d159cp+2f, -0x1.54873ep+5f, 0x1.2c245ep+7f, -0x1.416f5cp+8f, 0x1.e67e2cp+8f, -0x1.298ee6p+9f, 0x1.48ee3ep+9f, -0x1.4e6b46p+9f, 0x1.2782eap+9f, -0x1.bb4938p+8f, 0x1.25dfd4p+8f, -0x1.575e0cp+7f, 0x1.1c029p+6f, -0x1.08a1fep+2f, -0x1.12ed1ep+4f, 0x1.66791ep+3f, -0x1.7aa974p+1f, 0x1.41600cp-3f, 0x1.275514p-4f, -0x1.29374p-7f, -0x1.51ea7ep-13f, 0x1.deb156p-18f, -0x1.6e30fap-27f, -0x1.1b57acp-41f, -0x0p+0f};
+                return {0x0p+0f, 0x1.5d159cp+2f, -0x1.54873ep+5f, 0x1.2c245ep+7f, -0x1.416f5cp+8f, 0x1.e67e2cp+8f, -0x1.298ee6p+9f, 0x1.48ee3ep+9f, -0x1.4e6b46p+9f, 0x1.2782eap+9f, -0x1.bb4938p+8f, 0x1.25dfd4p+8f, -0x1.575e0cp+7f, 0x1.1c029p+6f, -0x1.08a1fep+2f, -0x1.12ed1ep+4f, 0x1.66791ep+3f, -0x1.7aa974p+1f, 0x1.41600cp-3f, 0x1.275514p-4f, -0x1.29374p-7f, -0x1.51ea7ep-13f, 0x1.deb156p-18f, -0x1.6e30fap-27f, -0x1.1b57acp-41f, 0x0p+0f};
             }
             if constexpr (order == 7) {
-                return {0x0p+0f, 0x1.d4fe28p+2f, -0x1.ecb0f4p+5f, 0x1.c6da62p+7f, -0x1.e3622ep+8f, 0x1.495088p+9f, -0x1.3d934ap+9f, 0x1.0686p+9f, -0x1.bb4eb6p+8f, 0x1.2c2d3cp+8f, -0x1.6a6f08p+5f, -0x1.48c0f8p+7f, 0x1.bce286p+7f, -0x1.9e035ep+7f, 0x1.737018p+7f, -0x1.15bd06p+7f, 0x1.1609d2p+6f, -0x1.30b382p+4f, 0x1.34c266p+0f, 0x1.56d14ep-1f, -0x1.f82518p-4f, -0x1.1d5d34p-9f, 0x1.599f88p-13f, -0x1.742b04p-22f, -0x1.1fd836p-35f, 0x0p+0f};
+                return {0x0p+0f, 0x1.d4fe28p+2f, -0x1.ecb0f4p+5f, 0x1.c6da62p+7f, -0x1.e3622ep+8f, 0x1.495088p+9f, -0x1.3d934ap+9f, 0x1.0686p+9f, -0x1.bb4eb6p+8f, 0x1.2c2d3cp+8f, -0x1.6a6f08p+5f, -0x1.48c0f8p+7f, 0x1.bce286p+7f, -0x1.9e035ep+7f, 0x1.737018p+7f, -0x1.15bd06p+7f, 0x1.1609d2p+6f, -0x1.30b382p+4f, 0x1.34c266p+0f, 0x1.56d14ep-1f, -0x1.f82518p-4f, -0x1.1d5d34p-9f, 0x1.599f88p-13f, -0x1.742b04p-22f, -0x1.1fd836p-35f, -0x0p+0f};
             }
             if constexpr (order == 8) {
                 return {0x0p+0f, 0x1.6f91b2p+2f, -0x1.8fef12p+5f, 0x1.809c44p+7f, -0x1.b10bfp+8f, 0x1.452582p+9f, -0x1.7231bp+9f, 0x1.7af822p+9f, -0x1.823eap+9f, 0x1.6f4bc2p+9f, -0x1.32f292p+9f, 0x1.d856p+8f, -0x1.59b2fp+8f, 0x1.c4899p+7f, -0x1.01b04cp+7f, 0x1.0ee55p+6f, -0x1.f14982p+4f, 0x1.214136p+3f, -0x1.1e3582p-2f, -0x1.54f128p-1f, 0x1.1dedd2p-3f, 0x1.2b8db4p-10f, -0x1.7cd67ep-12f, 0x1.c17582p-21f, 0x1.5b5402p-33f, -0x0p+0f};
             }
             if constexpr (order == 9) {
-                return {0x0p+0f, 0x1.e00f2p+1f, -0x1.09aad6p+5f, 0x1.0083b2p+7f, -0x1.1b0164p+8f, 0x1.8e74c6p+8f, -0x1.907a86p+8f, 0x1.68e4a6p+8f, -0x1.685dfep+8f, 0x1.592f3ap+8f, -0x1.09589ap+8f, 0x1.658b66p+7f, -0x1.f90c72p+6f, 0x1.49a9a8p+6f, -0x1.441338p+5f, 0x1.0b7b2ap+4f, -0x1.d98372p+2f, 0x1.f43ec2p+0f, 0x1.6165b8p-1f, -0x1.4f8a82p-1f, 0x1.267684p-3f, -0x1.8ddc62p-9f, -0x1.979caep-11f, 0x1.95627cp-20f, 0x1.38bcd2p-31f, -0x0p+0f};
+                return {0x0p+0f, 0x1.e00f2p+1f, -0x1.09aad6p+5f, 0x1.0083b2p+7f, -0x1.1b0164p+8f, 0x1.8e74c6p+8f, -0x1.907a86p+8f, 0x1.68e4a6p+8f, -0x1.685dfep+8f, 0x1.592f3ap+8f, -0x1.09589ap+8f, 0x1.658b66p+7f, -0x1.f90c72p+6f, 0x1.49a9a8p+6f, -0x1.441338p+5f, 0x1.0b7b2ap+4f, -0x1.d98372p+2f, 0x1.f43ec2p+0f, 0x1.6165b8p-1f, -0x1.4f8a82p-1f, 0x1.267684p-3f, -0x1.8ddc62p-9f, -0x1.979caep-11f, 0x1.95627cp-20f, 0x1.38bcd2p-31f, 0x0p+0f};
             }
             if constexpr (order == 10) {
                 return {0x0p+0f, 0x1.ddc992p+0f, -0x1.0aa6a6p+4f, 0x1.ffd30ap+5f, -0x1.1076bcp+7f, 0x1.5b315p+7f, -0x1.15e62ap+7f, 0x1.73ecdap+6f, -0x1.7ea49ap+6f, 0x1.92fe5p+6f, -0x1.e50ce8p+5f, 0x1.23fe36p+4f, -0x1.1183a6p+3f, 0x1.325da8p+2f, 0x1.b5b93ep+2f, -0x1.6174ccp+3f, 0x1.b8e78ep+2f, -0x1.ffc6e6p+1f, 0x1.807b44p+1f, -0x1.949fp+0f, 0x1.99c706p-2f, -0x1.8b4256p-6f, -0x1.25fbdep-8f, 0x1.a2ffd6p-17f, 0x1.4225e6p-27f, 0x0p+0f};
             }
             if constexpr (order == 11) {
-                return {0x0p+0f, 0x1.82556p-2f, -0x1.b108acp+1f, 0x1.a3afap+3f, -0x1.c92e2ap+4f, 0x1.336156p+5f, -0x1.154d2p+5f, 0x1.af95c6p+4f, -0x1.a382eep+4f, 0x1.a5a57ep+4f, -0x1.48587cp+4f, 0x1.c6519cp+3f, -0x1.64406ep+3f, 0x1.05a0dap+3f, -0x1.34062ap+2f, 0x1.65a332p+1f, -0x1.b27cf8p+0f, 0x1.a5bdc8p-1f, -0x1.571ac2p-2f, 0x1.317678p-3f, -0x1.904f34p-5f, 0x1.0ee4f4p-8f, 0x1.2584f2p-10f, -0x1.373cf6p-17f, -0x1.db60ap-27f, 0x0p+0f};
+                return {0x0p+0f, 0x1.82556p-2f, -0x1.b108acp+1f, 0x1.a3afap+3f, -0x1.c92e2ap+4f, 0x1.336156p+5f, -0x1.154d2p+5f, 0x1.af95c6p+4f, -0x1.a382eep+4f, 0x1.a5a57ep+4f, -0x1.48587cp+4f, 0x1.c6519cp+3f, -0x1.64406ep+3f, 0x1.05a0dap+3f, -0x1.34062ap+2f, 0x1.65a332p+1f, -0x1.b27cf8p+0f, 0x1.a5bdc8p-1f, -0x1.571ac2p-2f, 0x1.317678p-3f, -0x1.904f34p-5f, 0x1.0ee4f4p-8f, 0x1.2584f2p-10f, -0x1.373cf6p-17f, -0x1.db60ap-27f, -0x0p+0f};
             }
             if constexpr (order == 12) {
                 return {0x0p+0f, 0x1.8dbb04p-5f, -0x1.bebdc6p-2f, 0x1.aeb7a6p+0f, -0x1.cb9852p+1f, 0x1.240bf6p+2f, -0x1.cab7dp+1f, 0x1.1fd454p+1f, -0x1.1ce974p+1f, 0x1.3bab08p+1f, -0x1.c40e7cp+0f, 0x1.feadc8p-1f, -0x1.a643a4p-1f, 0x1.543b96p-1f, -0x1.577aa6p-2f, 0x1.499f7p-3f, -0x1.d5a152p-4f, 0x1.d4c5bap-5f, -0x1.094f52p-6f, 0x1.cd0926p-8f, -0x1.b2091cp-9f, 0x1.fdc736p-13f, 0x1.4af176p-13f, -0x1.fd199ap-19f, -0x1.7fa406p-27f, 0x0p+0f};
@@ -1123,10 +1376,10 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0, 0x1.749078c0867aap-9, 0x1.8ae6a79b4939p-3, 0x1.d008898983914p-1, -0x1.20e16d5539e3fp-4, -0x1.f688bd1280c7p-5, 0x1.2fca4301354a5p-5, -0x1.505c64431d7a7p-12, -0x1.0145189baf014p-6, 0x1.c908becee5a6ap-7, -0x1.beac12be1e7dep-8, 0x1.0006a916adee3p-9, -0x1.d4cc286b09e13p-13, -0x1.a08b65bbb5986p-15, 0x1.5f413ab3a7eb9p-16, -0x1.5c34d16af592p-20, -0x1.2dc4454eebde3p-21, 0x1.74f33a2ccbc65p-24, 0x1.ddb5df0a412fdp-29, -0x1.07969b3a158bdp-32, 0x1.2c5958b74836cp-38, 0x1.52fae6e83092p-45, -0x1.d83da475a639cp-53, 0x1.1342e56840ec2p-65, 0x1.aa25edf8f64ffp-86, -0x0p+0};
             }
             if constexpr (order == 1) {
-                return {0x0p+0, 0x1.23923550f457dp-6, 0x1.0c0767795d12bp-1, 0x1.3373be839b47cp-2, -0x1.856d7e6b6468cp+0, 0x1.22d30ac28dd9dp+0, -0x1.72e38df054a24p-1, 0x1.8e439b194a1c1p-2, -0x1.3bc2524066e84p-3, 0x1.1bc8f6e410596p-5, 0x1.2884461caa1e3p-11, -0x1.db22a9804aa11p-10, -0x1.3482dca87f01cp-11, 0x1.3285223dae55ap-11, -0x1.bbf1c4306d1a3p-14, -0x1.17497a4dcd45p-16, 0x1.bebec0cbd1f99p-18, -0x1.bc40d833ef35ap-22, 0x1.6454c6cebdf98p-26, 0x1.5fce040bf0fa2p-29, -0x1.1241493325c92p-33, -0x1.ce70ab06ee7ebp-41, 0x1.8616f674ef406p-48, -0x1.7b38ad7c07a3ap-60, -0x1.258ba4702de86p-79, -0x0p+0};
+                return {0x0p+0, 0x1.23923550f457dp-6, 0x1.0c0767795d12bp-1, 0x1.3373be839b47cp-2, -0x1.856d7e6b6468cp+0, 0x1.22d30ac28dd9dp+0, -0x1.72e38df054a24p-1, 0x1.8e439b194a1c1p-2, -0x1.3bc2524066e84p-3, 0x1.1bc8f6e410596p-5, 0x1.2884461caa1e3p-11, -0x1.db22a9804aa11p-10, -0x1.3482dca87f01cp-11, 0x1.3285223dae55ap-11, -0x1.bbf1c4306d1a3p-14, -0x1.17497a4dcd45p-16, 0x1.bebec0cbd1f99p-18, -0x1.bc40d833ef35ap-22, 0x1.6454c6cebdf98p-26, 0x1.5fce040bf0fa2p-29, -0x1.1241493325c92p-33, -0x1.ce70ab06ee7ebp-41, 0x1.8616f674ef406p-48, -0x1.7b38ad7c07a3ap-60, -0x1.258ba4702de86p-79, 0x0p+0};
             }
             if constexpr (order == 2) {
-                return {0x0p+0, 0x1.7e9e99d93265ep-4, 0x1.e81e73bf7d4e6p-1, -0x1.368292c7be10ep+1, 0x1.a1c192a939b96p+0, -0x1.58e6f9045a40ep-2, 0x1.2f82100ba4f28p-2, -0x1.f8fd9be6cc911p-2, 0x1.017de77081fc3p-1, -0x1.5831ad1464211p-2, 0x1.30d718554c4cbp-3, -0x1.30a6075105b3bp-5, -0x1.632f9e9eb99fcp-11, 0x1.1cbed37ba4dbep-8, -0x1.77d86fa7164cp-10, 0x1.50ec238da0096p-14, 0x1.f99c3b6dd2e63p-15, -0x1.8453f2cbc2d99p-17, -0x1.b4056601f4cp-23, 0x1.4c2776a5f116ep-24, -0x1.287daf168a21ap-29, -0x1.b00a66e2af604p-36, 0x1.401eb1fad689ep-42, -0x1.71528144e6955p-54, -0x1.1de10823e626cp-72, -0x0p+0};
+                return {0x0p+0, 0x1.7e9e99d93265ep-4, 0x1.e81e73bf7d4e6p-1, -0x1.368292c7be10ep+1, 0x1.a1c192a939b96p+0, -0x1.58e6f9045a40ep-2, 0x1.2f82100ba4f28p-2, -0x1.f8fd9be6cc911p-2, 0x1.017de77081fc3p-1, -0x1.5831ad1464211p-2, 0x1.30d718554c4cbp-3, -0x1.30a6075105b3bp-5, -0x1.632f9e9eb99fcp-11, 0x1.1cbed37ba4dbep-8, -0x1.77d86fa7164cp-10, 0x1.50ec238da0096p-14, 0x1.f99c3b6dd2e63p-15, -0x1.8453f2cbc2d99p-17, -0x1.b4056601f4cp-23, 0x1.4c2776a5f116ep-24, -0x1.287daf168a21ap-29, -0x1.b00a66e2af604p-36, 0x1.401eb1fad689ep-42, -0x1.71528144e6955p-54, -0x1.1de10823e626cp-72, 0x0p+0};
             }
             if constexpr (order == 3) {
                 return {0x0p+0, 0x1.95e033565cd46p-2, 0x1.e7908dd5753c9p-3, -0x1.293799fcf6c8ep+2, 0x1.36cc467b08bf8p+3, -0x1.4335983e13577p+3, 0x1.9c4d14b541486p+2, -0x1.ef81d85b23a02p+0, -0x1.2378e73c6b10ap+0, 0x1.c6e27151761e4p+0, -0x1.c857e67243154p-1, 0x1.3531afa42b77fp-8, 0x1.05f57c1a6464dp-2, -0x1.38a2db882124ep-3, 0x1.35c4a5041d9b9p-5, -0x1.fddc3c9f813d7p-14, -0x1.2653a0321997dp-9, 0x1.ec5d6f7ab50c1p-12, -0x1.dc01f8633f4c6p-17, -0x1.379717b64ca38p-18, 0x1.7e5cfdc9a1b18p-23, 0x1.a124166c57861p-29, -0x1.4171311c3a7b2p-35, 0x1.65f402b77f1abp-46, 0x1.15123cc4efb61p-63, -0x0p+0};
@@ -1135,25 +1388,25 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0, 0x1.4c5d516dd5341p+0, -0x1.5d2571cda5544p+2, 0x1.24b0f0352262ap+3, -0x1.39e0f8d13e8dbp+3, 0x1.f006cc927be53p+3, -0x1.0ce2ffa464611p+5, 0x1.b8b8afcf323dp+5, -0x1.e6925570e3f51p+5, 0x1.503102590c0b8p+5, -0x1.6d86add093f07p+3, -0x1.35b5dc1025f2dp+3, 0x1.a6237c764b4a3p+3, -0x1.cda455c3ae393p+2, 0x1.d5a02bb93708ap+0, 0x1.ecd4c4adc076p-5, -0x1.660ee59df078bp-3, 0x1.5158e51b27e5ep-5, -0x1.73814bfd57b68p-10, -0x1.23460c48f637p-11, 0x1.fa353cdebaaabp-16, 0x1.19c5738584247p-21, -0x1.4bb4308ed52p-27, 0x1.fc9a1f4f09859p-38, 0x1.89a8b7b9d28d2p-54, 0x0p+0};
             }
             if constexpr (order == 5) {
-                return {0x0p+0, 0x1.a35157d8dba57p+1, -0x1.5a1bc35a1cc0ep+4, 0x1.fa0a0878d9a93p+5, -0x1.a68f6523a827p+6, 0x1.98403a971e631p+6, -0x1.03810e60e0205p+5, -0x1.14faaec768465p+6, 0x1.3d735b94c1054p+7, -0x1.cdbd7de801408p+7, 0x1.20043470ad457p+8, -0x1.2591e882d85cdp+8, 0x1.b621996a63c18p+7, -0x1.a875ba068d845p+6, 0x1.85c7d166f26b7p+4, 0x1.1c0e0d6b929f9p+2, -0x1.36efc345fd87ep+2, 0x1.3e3f5c2c93c34p+0, -0x1.bffc3922a3129p-5, -0x1.75f52c4bce394p-6, 0x1.dea5b49d2b29ap-10, 0x1.10aa3eff5f8abp-15, -0x1.ea6ed6c321e75p-21, 0x1.089ab261bfe1dp-30, 0x1.9990a3735f2b8p-46, 0x0p+0};
+                return {0x0p+0, 0x1.a35157d8dba57p+1, -0x1.5a1bc35a1cc0ep+4, 0x1.fa0a0878d9a93p+5, -0x1.a68f6523a827p+6, 0x1.98403a971e631p+6, -0x1.03810e60e0205p+5, -0x1.14faaec768465p+6, 0x1.3d735b94c1054p+7, -0x1.cdbd7de801408p+7, 0x1.20043470ad457p+8, -0x1.2591e882d85cdp+8, 0x1.b621996a63c18p+7, -0x1.a875ba068d845p+6, 0x1.85c7d166f26b7p+4, 0x1.1c0e0d6b929f9p+2, -0x1.36efc345fd87ep+2, 0x1.3e3f5c2c93c34p+0, -0x1.bffc3922a3129p-5, -0x1.75f52c4bce394p-6, 0x1.dea5b49d2b29ap-10, 0x1.10aa3eff5f8abp-15, -0x1.ea6ed6c321e75p-21, 0x1.089ab261bfe1dp-30, 0x1.9990a3735f2b8p-46, -0x0p+0};
             }
             if constexpr (order == 6) {
-                return {0x0p+0, 0x1.5d159c98a090ap+2, -0x1.54873e7e1b3d2p+5, 0x1.2c245e185ac8bp+7, -0x1.416f5cc6c22c2p+8, 0x1.e67e2b7f93304p+8, -0x1.298ee57db6ed6p+9, 0x1.48ee3d90a4e35p+9, -0x1.4e6b4521eb7a5p+9, 0x1.2782e95d7bf9fp+9, -0x1.bb493883e544dp+8, 0x1.25dfd4b9fa45bp+8, -0x1.575e0c206b7eep+7, 0x1.1c028f2725fcep+6, -0x1.08a1fe0ac681ap+2, -0x1.12ed1d6ca773p+4, 0x1.66791e904ad3bp+3, -0x1.7aa9733036516p+1, 0x1.41600caa02956p-3, 0x1.275514f436a32p-4, -0x1.29373f56ac109p-7, -0x1.51ea7d9f34504p-13, 0x1.deb156b08b87fp-18, -0x1.6e30fae8c34eep-27, -0x1.1b57abb7d7f1cp-41, -0x0p+0};
+                return {0x0p+0, 0x1.5d159c98a090ap+2, -0x1.54873e7e1b3d2p+5, 0x1.2c245e185ac8bp+7, -0x1.416f5cc6c22c2p+8, 0x1.e67e2b7f93304p+8, -0x1.298ee57db6ed6p+9, 0x1.48ee3d90a4e35p+9, -0x1.4e6b4521eb7a5p+9, 0x1.2782e95d7bf9fp+9, -0x1.bb493883e544dp+8, 0x1.25dfd4b9fa45bp+8, -0x1.575e0c206b7eep+7, 0x1.1c028f2725fcep+6, -0x1.08a1fe0ac681ap+2, -0x1.12ed1d6ca773p+4, 0x1.66791e904ad3bp+3, -0x1.7aa9733036516p+1, 0x1.41600caa02956p-3, 0x1.275514f436a32p-4, -0x1.29373f56ac109p-7, -0x1.51ea7d9f34504p-13, 0x1.deb156b08b87fp-18, -0x1.6e30fae8c34eep-27, -0x1.1b57abb7d7f1cp-41, 0x0p+0};
             }
             if constexpr (order == 7) {
-                return {0x0p+0, 0x1.d4fe27a0835aep+2, -0x1.ecb0f32ca76fbp+5, 0x1.c6da62a20cd0bp+7, -0x1.e3622dd5ba05ep+8, 0x1.49508717a90e8p+9, -0x1.3d934aacf56d1p+9, 0x1.068600d74e1c9p+9, -0x1.bb4eb52dbc23dp+8, 0x1.2c2d3c048caafp+8, -0x1.6a6f07f5d07ddp+5, -0x1.48c0f7b3bed9ep+7, 0x1.bce28601020e5p+7, -0x1.9e035ea535c3bp+7, 0x1.737017c34f7dfp+7, -0x1.15bd065f2789cp+7, 0x1.1609d2e86de1fp+6, -0x1.30b382548236p+4, 0x1.34c266d274d02p+0, 0x1.56d14dbd1c0fp-1, -0x1.f82518456ddfap-4, -0x1.1d5d333a03734p-9, 0x1.599f88826e1dfp-13, -0x1.742b04eba227p-22, -0x1.1fd835e2f3ac3p-35, 0x0p+0};
+                return {0x0p+0, 0x1.d4fe27a0835aep+2, -0x1.ecb0f32ca76fbp+5, 0x1.c6da62a20cd0bp+7, -0x1.e3622dd5ba05ep+8, 0x1.49508717a90e8p+9, -0x1.3d934aacf56d1p+9, 0x1.068600d74e1c9p+9, -0x1.bb4eb52dbc23dp+8, 0x1.2c2d3c048caafp+8, -0x1.6a6f07f5d07ddp+5, -0x1.48c0f7b3bed9ep+7, 0x1.bce28601020e5p+7, -0x1.9e035ea535c3bp+7, 0x1.737017c34f7dfp+7, -0x1.15bd065f2789cp+7, 0x1.1609d2e86de1fp+6, -0x1.30b382548236p+4, 0x1.34c266d274d02p+0, 0x1.56d14dbd1c0fp-1, -0x1.f82518456ddfap-4, -0x1.1d5d333a03734p-9, 0x1.599f88826e1dfp-13, -0x1.742b04eba227p-22, -0x1.1fd835e2f3ac3p-35, -0x0p+0};
             }
             if constexpr (order == 8) {
                 return {0x0p+0, 0x1.6f91b1fb16e46p+2, -0x1.8fef11e8059cfp+5, 0x1.809c444472a8ep+7, -0x1.b10bf090c92b5p+8, 0x1.45258188f7147p+9, -0x1.7231afc08bd27p+9, 0x1.7af82162ac35ap+9, -0x1.823e9f8992b5ap+9, 0x1.6f4bc124eb7dcp+9, -0x1.32f291524b4fdp+9, 0x1.d856007cb8fap+8, -0x1.59b2f057a74e5p+8, 0x1.c4898ffe6b604p+7, -0x1.01b04bb5c7e4fp+7, 0x1.0ee550f2b46fbp+6, -0x1.f149829700499p+4, 0x1.21413698e7cf2p+3, -0x1.1e358290df39dp-2, -0x1.54f12799790c9p-1, 0x1.1dedd290f908p-3, 0x1.2b8db385d6eebp-10, -0x1.7cd67d6099899p-12, 0x1.c1758243d6f69p-21, 0x1.5b5402fbe8db8p-33, -0x0p+0};
             }
             if constexpr (order == 9) {
-                return {0x0p+0, 0x1.e00f201ca9b48p+1, -0x1.09aad588fc6e2p+5, 0x1.0083b1ed3add2p+7, -0x1.1b01639f15a47p+8, 0x1.8e74c5b415b4dp+8, -0x1.907a858da198ep+8, 0x1.68e4a68143eb6p+8, -0x1.685dfe59eb94fp+8, 0x1.592f39b72049ap+8, -0x1.09589acf597f5p+8, 0x1.658b66c44d2dap+7, -0x1.f90c71880a916p+6, 0x1.49a9a7009f2b2p+6, -0x1.441338caa52dp+5, 0x1.0b7b2a297fde1p+4, -0x1.d98372b1c68d4p+2, 0x1.f43ec1f2a328p+0, 0x1.6165b77555fcbp-1, -0x1.4f8a8171bb09p-1, 0x1.267683e93d2b7p-3, -0x1.8ddc624d415c9p-9, -0x1.979cae945ae1p-11, 0x1.95627b187fdb2p-20, 0x1.38bcd286c35dep-31, -0x0p+0};
+                return {0x0p+0, 0x1.e00f201ca9b48p+1, -0x1.09aad588fc6e2p+5, 0x1.0083b1ed3add2p+7, -0x1.1b01639f15a47p+8, 0x1.8e74c5b415b4dp+8, -0x1.907a858da198ep+8, 0x1.68e4a68143eb6p+8, -0x1.685dfe59eb94fp+8, 0x1.592f39b72049ap+8, -0x1.09589acf597f5p+8, 0x1.658b66c44d2dap+7, -0x1.f90c71880a916p+6, 0x1.49a9a7009f2b2p+6, -0x1.441338caa52dp+5, 0x1.0b7b2a297fde1p+4, -0x1.d98372b1c68d4p+2, 0x1.f43ec1f2a328p+0, 0x1.6165b77555fcbp-1, -0x1.4f8a8171bb09p-1, 0x1.267683e93d2b7p-3, -0x1.8ddc624d415c9p-9, -0x1.979cae945ae1p-11, 0x1.95627b187fdb2p-20, 0x1.38bcd286c35dep-31, 0x0p+0};
             }
             if constexpr (order == 10) {
                 return {0x0p+0, 0x1.ddc9914b8fce2p+0, -0x1.0aa6a6fe474ap+4, 0x1.ffd30a30f104ep+5, -0x1.1076bbdb4cf75p+7, 0x1.5b314fd5bd842p+7, -0x1.15e629a2f07abp+7, 0x1.73ecdaa7dbcd1p+6, -0x1.7ea4991281a8p+6, 0x1.92fe5087093b6p+6, -0x1.e50ce86c3eca3p+5, 0x1.23fe36ce5250dp+4, -0x1.1183a5ac74637p+3, 0x1.325da71616788p+2, 0x1.b5b93d37eb78fp+2, -0x1.6174cc292a978p+3, 0x1.b8e78e1a9ada5p+2, -0x1.ffc6e54f09b8ap+1, 0x1.807b43d233e13p+1, -0x1.949effe4fd5f1p+0, 0x1.99c706ee33d33p-2, -0x1.8b4255eb2ab53p-6, -0x1.25fbde4ae0e29p-8, 0x1.a2ffd5a58a3e6p-17, 0x1.4225e5d67d6a9p-27, 0x0p+0};
             }
             if constexpr (order == 11) {
-                return {0x0p+0, 0x1.82555f0fca682p-2, -0x1.b108ac4bd9d5ep+1, 0x1.a3af9f5e28534p+3, -0x1.c92e2a69bebeap+4, 0x1.336156f19a3ebp+5, -0x1.154d20c532d38p+5, 0x1.af95c6a7f034fp+4, -0x1.a382ed435f8edp+4, 0x1.a5a57db59b67cp+4, -0x1.48587bdb4781p+4, 0x1.c6519b1cdb293p+3, -0x1.64406dc5dece2p+3, 0x1.05a0da2a87dbp+3, -0x1.34062a3bf7c11p+2, 0x1.65a3327bcf1acp+1, -0x1.b27cf7ab49be3p+0, 0x1.a5bdc7192b9c4p-1, -0x1.571ac2983f85ep-2, 0x1.31767817c6adfp-3, -0x1.904f3491bf69cp-5, 0x1.0ee4f3163f55fp-8, 0x1.2584f1f36b43ep-10, -0x1.373cf584c03efp-17, -0x1.db60a068c3378p-27, 0x0p+0};
+                return {0x0p+0, 0x1.82555f0fca682p-2, -0x1.b108ac4bd9d5ep+1, 0x1.a3af9f5e28534p+3, -0x1.c92e2a69bebeap+4, 0x1.336156f19a3ebp+5, -0x1.154d20c532d38p+5, 0x1.af95c6a7f034fp+4, -0x1.a382ed435f8edp+4, 0x1.a5a57db59b67cp+4, -0x1.48587bdb4781p+4, 0x1.c6519b1cdb293p+3, -0x1.64406dc5dece2p+3, 0x1.05a0da2a87dbp+3, -0x1.34062a3bf7c11p+2, 0x1.65a3327bcf1acp+1, -0x1.b27cf7ab49be3p+0, 0x1.a5bdc7192b9c4p-1, -0x1.571ac2983f85ep-2, 0x1.31767817c6adfp-3, -0x1.904f3491bf69cp-5, 0x1.0ee4f3163f55fp-8, 0x1.2584f1f36b43ep-10, -0x1.373cf584c03efp-17, -0x1.db60a068c3378p-27, -0x0p+0};
             }
             if constexpr (order == 12) {
                 return {0x0p+0, 0x1.8dbb03fad2c3p-5, -0x1.bebdc5d3b2391p-2, 0x1.aeb7a5ea21053p+0, -0x1.cb9851522d20bp+1, 0x1.240bf59871b99p+2, -0x1.cab7cf1ed537ep+1, 0x1.1fd4543a5fd8dp+1, -0x1.1ce9744c1c975p+1, 0x1.3bab08bd76345p+1, -0x1.c40e7b4e77557p+0, 0x1.feadc8c7ce87bp-1, -0x1.a643a47d84b4ep-1, 0x1.543b964e0f03ap-1, -0x1.577aa576ffa65p-2, 0x1.499f6f7a97a23p-3, -0x1.d5a15151b9016p-4, 0x1.d4c5badb46707p-5, -0x1.094f5215690dbp-6, 0x1.cd0926fb9e142p-8, -0x1.b2091c2c73ddp-9, 0x1.fdc7350edfaddp-13, 0x1.4af17513fc3a8p-13, -0x1.fd199a3cefa32p-19, -0x1.7fa406e41ed66p-27, 0x0p+0};
@@ -1164,10 +1417,10 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0L, 0xb.a483c60433d4d39p-12L, 0xc.57353cda49c7dedp-6L, 0xe.80444c4c1c89ecep-4L, -0x9.070b6aa9cf1f929p-7L, -0xf.b445e89406380cap-8L, 0x9.7e521809aa52714p-8L, -0xa.82e32218ebd378fp-15L, -0x8.0a28c4dd780a179p-9L, 0xe.4845f6772d3537ep-10L, -0xd.f56095f0f3ef04ap-11L, 0x8.003548b56f71a16p-12L, -0xe.a66143584f09aacp-16L, -0xd.045b2dddacc33b9p-18L, 0xa.fa09d59d3f5ca6ep-19L, -0xa.e1a68b57ac901bdp-23L, -0x9.6e222a775ef19bdp-24L, 0xb.a799d1665e328c8p-27L, 0xe.edaef852097ea04p-32L, -0x8.3cb4d9d0ac5e8bp-35L, 0x9.62cac5ba41b6085p-41L, 0xa.97d73741848fd34p-48L, -0xe.c1ed23ad31ce184p-56L, 0x8.9a172b420760cedp-68L, 0xd.512f6fc7b27f70ap-89L, -0x0p+0L};
             }
             if constexpr (order == 1) {
-                return {0x0p+0L, 0x9.1c91aa87a2be53cp-9L, 0x8.603b3bcae89572fp-4L, 0x9.9b9df41cda3e206p-5L, -0xc.2b6bf35b234616fp-3L, 0x9.169856146ece4d3p-3L, -0xb.971c6f82a511d45p-4L, 0xc.721cd8ca50e0b31p-5L, -0x9.de1292033741f59p-6L, 0x8.de47b72082cb31fp-8L, 0x9.442230e550f1904p-14L, -0xe.d9154c025508998p-13L, -0x9.a416e543f80e22fp-14L, 0x9.942911ed72acc95p-14L, -0xd.df8e218368d1bf8p-17L, -0x8.ba4bd26e6a27feep-19L, 0xd.f5f6065e8fcc9b9p-21L, -0xd.e206c19f79acc2bp-25L, 0xb.22a63675efcbfa2p-29L, 0xa.fe70205f87d115p-32L, -0x8.920a49992e4937dp-36L, -0xe.7385583773f5acap-44L, 0xc.30b7b3a77a02f75p-51L, -0xb.d9c56be03d1d02cp-63L, -0x9.2c5d23816f42d62p-82L, -0x0p+0L};
+                return {0x0p+0L, 0x9.1c91aa87a2be53cp-9L, 0x8.603b3bcae89572fp-4L, 0x9.9b9df41cda3e206p-5L, -0xc.2b6bf35b234616fp-3L, 0x9.169856146ece4d3p-3L, -0xb.971c6f82a511d45p-4L, 0xc.721cd8ca50e0b31p-5L, -0x9.de1292033741f59p-6L, 0x8.de47b72082cb31fp-8L, 0x9.442230e550f1904p-14L, -0xe.d9154c025508998p-13L, -0x9.a416e543f80e22fp-14L, 0x9.942911ed72acc95p-14L, -0xd.df8e218368d1bf8p-17L, -0x8.ba4bd26e6a27feep-19L, 0xd.f5f6065e8fcc9b9p-21L, -0xd.e206c19f79acc2bp-25L, 0xb.22a63675efcbfa2p-29L, 0xa.fe70205f87d115p-32L, -0x8.920a49992e4937dp-36L, -0xe.7385583773f5acap-44L, 0xc.30b7b3a77a02f75p-51L, -0xb.d9c56be03d1d02cp-63L, -0x9.2c5d23816f42d62p-82L, 0x0p+0L};
             }
             if constexpr (order == 2) {
-                return {0x0p+0L, 0xb.f4f4cec9932f0f6p-7L, 0xf.40f39dfbea733adp-4L, -0x9.b414963df08728ap-2L, 0xd.0e0c9549cdcb3a8p-3L, -0xa.c737c822d206e95p-5L, 0x9.7c10805d27943dp-5L, -0xf.c7ecdf3664887bbp-5L, 0x8.0bef3b840fe187dp-4L, -0xa.c18d68a32108919p-5L, 0x9.86b8c2aa62655e8p-6L, -0x9.85303a882d9d527p-8L, -0xb.197cf4f5ccfe389p-14L, 0x8.e5f69bdd26decb6p-11L, -0xb.bec37d38b25fe46p-13L, 0xa.87611c6d004b37bp-17L, 0xf.cce1db6e973199cp-18L, -0xc.229f965e16ccb5cp-20L, -0xd.a02b300fa5ffc5bp-26L, 0xa.613bb52f88b70ecp-27L, -0x9.43ed78b4510cd51p-32L, -0xd.805337157b01dc1p-39L, 0xa.00f58fd6b44ef03p-45L, -0xb.8a940a2734aa51ap-57L, -0x8.ef08411f3135df8p-75L, -0x0p+0L};
+                return {0x0p+0L, 0xb.f4f4cec9932f0f6p-7L, 0xf.40f39dfbea733adp-4L, -0x9.b414963df08728ap-2L, 0xd.0e0c9549cdcb3a8p-3L, -0xa.c737c822d206e95p-5L, 0x9.7c10805d27943dp-5L, -0xf.c7ecdf3664887bbp-5L, 0x8.0bef3b840fe187dp-4L, -0xa.c18d68a32108919p-5L, 0x9.86b8c2aa62655e8p-6L, -0x9.85303a882d9d527p-8L, -0xb.197cf4f5ccfe389p-14L, 0x8.e5f69bdd26decb6p-11L, -0xb.bec37d38b25fe46p-13L, 0xa.87611c6d004b37bp-17L, 0xf.cce1db6e973199cp-18L, -0xc.229f965e16ccb5cp-20L, -0xd.a02b300fa5ffc5bp-26L, 0xa.613bb52f88b70ecp-27L, -0x9.43ed78b4510cd51p-32L, -0xd.805337157b01dc1p-39L, 0xa.00f58fd6b44ef03p-45L, -0xb.8a940a2734aa51ap-57L, -0x8.ef08411f3135df8p-75L, 0x0p+0L};
             }
             if constexpr (order == 3) {
                 return {0x0p+0L, 0xc.af019ab2e6a32f3p-5L, 0xf.3c846eaba9e4babp-6L, -0x9.49bccfe7b646d1p-1L, 0x9.b66233d845fbec5p+0L, -0xa.19acc1f09abba63p+0L, 0xc.e268a5aa0a433dap-1L, -0xf.7c0ec2d91d00d64p-3L, -0x9.1bc739e3588517cp-3L, 0xe.37138a8bb0f1f2cp-3L, -0xe.42bf339218a9d4bp-4L, 0x9.a98d7d215bbfa64p-11L, 0x8.2fabe0d32326ba1p-5L, -0x9.c516dc410926fe2p-6L, 0x9.ae252820ecdca2bp-8L, -0xf.eee1e4fc09eb578p-17L, -0x9.329d0190ccbe8fdp-12L, 0xf.62eb7bd5a860bbfp-15L, -0xe.e00fc319fa6309dp-20L, -0x9.bcb8bdb2651be88p-21L, 0xb.f2e7ee4d0d8bee7p-26L, 0xd.0920b362bc30ba7p-32L, -0xa.0b8988e1d3d9312p-38L, 0xb.2fa015bbf8d5914p-49L, 0x8.a891e6277db069dp-66L, -0x0p+0L};
@@ -1176,25 +1429,25 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0L, 0xa.62ea8b6ea9a0684p-3L, -0xa.e92b8e6d2aa1c92p-1L, 0x9.258781a91314f19p+0L, -0x9.cf07c689f46d8f8p+0L, 0xf.80366493df29948p+0L, -0x8.6717fd232308bfp+2L, 0xd.c5c57e7991e8074p+2L, -0xf.3492ab871fa8811p+2L, 0xa.818812c8605bdbdp+2L, -0xb.6c356e849f83a5ep+0L, -0x9.adaee0812f969a5p+0L, 0xd.311be3b25a5141ap+0L, -0xe.6d22ae1d71c94e9p-1L, 0xe.ad015dc9b84519p-3L, 0xf.66a6256e03aff12p-8L, -0xb.30772cef83c5a19p-6L, 0xa.8ac728d93f2edffp-8L, -0xb.9c0a5feabdb40fdp-13L, -0x9.1a306247b1b7d38p-14L, 0xf.d1a9e6f5d555505p-19L, 0x8.ce2b9c2c2123732p-24L, -0xa.5da18476a8fff99p-30L, 0xf.e4d0fa784c2c7aap-41L, 0xc.4d45bdce9468eb9p-57L, 0x0p+0L};
             }
             if constexpr (order == 5) {
-                return {0x0p+0L, 0xd.1a8abec6dd2b59ap-2L, -0xa.d0de1ad0e606ddbp+1L, 0xf.d05043c6cd499c3p+2L, -0xd.347b291d41380b3p+3L, 0xc.c201d4b8f318b15p+3L, -0x8.1c08730701024ebp+2L, -0x8.a7d5763b4232a87p+3L, 0x9.eb9adca6082a1b5p+4L, -0xe.6debef400a03eb9p+4L, 0x9.0021a3856a2b57ap+5L, -0x9.2c8f4416c2e68c6p+5L, 0xd.b10ccb531e0bf33p+4L, -0xd.43add0346c224eap+3L, 0xc.2e3e8b37935bbc2p+1L, 0x8.e0706b5c94fcaddp-1L, -0x9.b77e1a2fec3f3f9p-1L, 0x9.f1fae1649e1a3cap-3L, -0xd.ffe1c91518944a2p-8L, -0xb.afa9625e71ca263p-9L, 0xe.f52da4e9594cf98p-13L, 0x8.8551f7fafc55605p-18L, -0xf.5376b6190f3a9e1p-24L, 0x8.44d5930dff0e45cp-33L, 0xc.cc851b9af95c09cp-49L, 0x0p+0L};
+                return {0x0p+0L, 0xd.1a8abec6dd2b59ap-2L, -0xa.d0de1ad0e606ddbp+1L, 0xf.d05043c6cd499c3p+2L, -0xd.347b291d41380b3p+3L, 0xc.c201d4b8f318b15p+3L, -0x8.1c08730701024ebp+2L, -0x8.a7d5763b4232a87p+3L, 0x9.eb9adca6082a1b5p+4L, -0xe.6debef400a03eb9p+4L, 0x9.0021a3856a2b57ap+5L, -0x9.2c8f4416c2e68c6p+5L, 0xd.b10ccb531e0bf33p+4L, -0xd.43add0346c224eap+3L, 0xc.2e3e8b37935bbc2p+1L, 0x8.e0706b5c94fcaddp-1L, -0x9.b77e1a2fec3f3f9p-1L, 0x9.f1fae1649e1a3cap-3L, -0xd.ffe1c91518944a2p-8L, -0xb.afa9625e71ca263p-9L, 0xe.f52da4e9594cf98p-13L, 0x8.8551f7fafc55605p-18L, -0xf.5376b6190f3a9e1p-24L, 0x8.44d5930dff0e45cp-33L, 0xc.cc851b9af95c09cp-49L, -0x0p+0L};
             }
             if constexpr (order == 6) {
-                return {0x0p+0L, 0xa.e8ace4c50485103p-1L, -0xa.a439f3f0d9e9083p+2L, 0x9.6122f0c2d6458a6p+4L, -0xa.0b7ae6361160fep+5L, 0xf.33f15bfc9982224p+5L, -0x9.4c772bedb76afeap+6L, 0xa.4771ec85271a548p+6L, -0xa.735a290f5bd2b61p+6L, 0x9.3c174aebdfcfafep+6L, -0xd.da49c41f2a26a23p+5L, 0x9.2efea5cfd22d7f4p+5L, -0xa.baf061035bf7341p+4L, 0x8.e01479392fe733bp+3L, -0x8.450ff056340cfcbp-1L, -0x8.9768eb653b980edp+1L, 0xb.33c8f482569da0fp+0L, -0xb.d54b9981b28ad7fp-2L, 0xa.0b00655014aaec4p-6L, 0x9.3aa8a7a1b518f2bp-7L, -0x9.49b9fab56084ac4p-10L, -0xa.8f53ecf9a28205dp-16L, 0xe.f58ab5845c3f783p-21L, -0xb.7187d7461a76c1bp-30L, -0x8.dabd5dbebf8dd41p-44L, -0x0p+0L};
+                return {0x0p+0L, 0xa.e8ace4c50485103p-1L, -0xa.a439f3f0d9e9083p+2L, 0x9.6122f0c2d6458a6p+4L, -0xa.0b7ae6361160fep+5L, 0xf.33f15bfc9982224p+5L, -0x9.4c772bedb76afeap+6L, 0xa.4771ec85271a548p+6L, -0xa.735a290f5bd2b61p+6L, 0x9.3c174aebdfcfafep+6L, -0xd.da49c41f2a26a23p+5L, 0x9.2efea5cfd22d7f4p+5L, -0xa.baf061035bf7341p+4L, 0x8.e01479392fe733bp+3L, -0x8.450ff056340cfcbp-1L, -0x8.9768eb653b980edp+1L, 0xb.33c8f482569da0fp+0L, -0xb.d54b9981b28ad7fp-2L, 0xa.0b00655014aaec4p-6L, 0x9.3aa8a7a1b518f2bp-7L, -0x9.49b9fab56084ac4p-10L, -0xa.8f53ecf9a28205dp-16L, 0xe.f58ab5845c3f783p-21L, -0xb.7187d7461a76c1bp-30L, -0x8.dabd5dbebf8dd41p-44L, 0x0p+0L};
             }
             if constexpr (order == 7) {
-                return {0x0p+0L, 0xe.a7f13d041ad70dp-1L, -0xf.658799653b7da4ap+2L, 0xe.36d31510668543p+4L, -0xf.1b116eadd02ec05p+5L, 0xa.4a8438bd48741b4p+6L, -0x9.ec9a5567ab68514p+6L, 0x8.343006ba70e487p+6L, -0xd.da75a96de11e455p+5L, 0x9.6169e024655745ap+5L, -0xb.53783fae83ee946p+2L, -0xa.4607bd9df6ceea7p+4L, 0xd.e71430081072aa3p+4L, -0xc.f01af529ae1d75fp+4L, 0xb.9b80be1a7bef779p+4L, -0x8.ade832f93c4e129p+4L, 0x8.b04e97436f0fa36p+3L, -0x9.859c12a411afe04p+1L, 0x9.a6133693a681011p-3L, 0xa.b68a6de8e077c6ep-4L, -0xf.c128c22b6efd051p-7L, -0x8.eae999d01b9a034p-12L, 0xa.ccfc441370efba9p-16L, -0xb.a158275d1138117p-25L, -0x8.fec1af179d61b9fp-38L, 0x0p+0L};
+                return {0x0p+0L, 0xe.a7f13d041ad70dp-1L, -0xf.658799653b7da4ap+2L, 0xe.36d31510668543p+4L, -0xf.1b116eadd02ec05p+5L, 0xa.4a8438bd48741b4p+6L, -0x9.ec9a5567ab68514p+6L, 0x8.343006ba70e487p+6L, -0xd.da75a96de11e455p+5L, 0x9.6169e024655745ap+5L, -0xb.53783fae83ee946p+2L, -0xa.4607bd9df6ceea7p+4L, 0xd.e71430081072aa3p+4L, -0xc.f01af529ae1d75fp+4L, 0xb.9b80be1a7bef779p+4L, -0x8.ade832f93c4e129p+4L, 0x8.b04e97436f0fa36p+3L, -0x9.859c12a411afe04p+1L, 0x9.a6133693a681011p-3L, 0xa.b68a6de8e077c6ep-4L, -0xf.c128c22b6efd051p-7L, -0x8.eae999d01b9a034p-12L, 0xa.ccfc441370efba9p-16L, -0xb.a158275d1138117p-25L, -0x8.fec1af179d61b9fp-38L, -0x0p+0L};
             }
             if constexpr (order == 8) {
                 return {0x0p+0L, 0xb.7c8d8fd8b7231c8p-1L, -0xc.7f788f402ce76dp+2L, 0xc.04e222239546c21p+4L, -0xd.885f8486495a99bp+5L, 0xa.292c0c47b8a3474p+6L, -0xb.918d7e045e93b18p+6L, 0xb.d7c10b1561accb3p+6L, -0xc.11f4fc4c95acfe3p+6L, 0xb.7a5e09275bee17p+6L, -0x9.97948a925a7e40dp+6L, 0xe.c2b003e5c7d03a7p+5L, -0xa.cd9782bd3a72557p+5L, 0xe.244c7ff35b01e7fp+4L, -0x8.0d825dae3f27671p+4L, 0x8.772a8795a37d803p+3L, -0xf.8a4c14b8024c883p+1L, 0x9.0a09b4c73e78daep+0L, -0x8.f1ac1486f9ce578p-5L, -0xa.a7893ccbc864ac9p-4L, 0x8.ef6e9487c83fc69p-6L, 0x9.5c6d9c2eb77580cp-13L, -0xb.e6b3eb04cc4c723p-15L, 0xe.0bac121eb7b4789p-24L, 0xa.daa017df46dbf37p-36L, -0x0p+0L};
             }
             if constexpr (order == 9) {
-                return {0x0p+0L, 0xf.007900e54da3df6p-2L, -0x8.4d56ac47e370e97p+2L, 0x8.041d8f69d6e8efep+4L, -0x8.d80b1cf8ad238cbp+5L, 0xc.73a62da0ada64c1p+5L, -0xc.83d42c6d0cc6daep+5L, 0xb.4725340a1f5b14p+5L, -0xb.42eff2cf5ca79c7p+5L, 0xa.c979cdb9024d1b7p+5L, -0x8.4ac4d67acbfab3fp+5L, 0xb.2c5b3622696cf85p+4L, -0xf.c8638c40548b2c6p+3L, 0xa.4d4d3804f95933ep+3L, -0xa.2099c6552967d07p+2L, 0x8.5bd9514bfef0a5ep+1L, -0xe.cc1b958e3469fa9p-1L, 0xf.a1f60f951940304p-3L, 0xb.0b2dbbaaafe5407p-4L, -0xa.7c540b8dd847e5dp-4L, 0x9.33b41f49e95bb8cp-6L, -0xc.6ee3126a0ae46c7p-12L, -0xc.bce574a2d70819p-14L, 0xc.ab13d8c3fed8cb7p-23L, 0x9.c5e694361aef307p-34L, -0x0p+0L};
+                return {0x0p+0L, 0xf.007900e54da3df6p-2L, -0x8.4d56ac47e370e97p+2L, 0x8.041d8f69d6e8efep+4L, -0x8.d80b1cf8ad238cbp+5L, 0xc.73a62da0ada64c1p+5L, -0xc.83d42c6d0cc6daep+5L, 0xb.4725340a1f5b14p+5L, -0xb.42eff2cf5ca79c7p+5L, 0xa.c979cdb9024d1b7p+5L, -0x8.4ac4d67acbfab3fp+5L, 0xb.2c5b3622696cf85p+4L, -0xf.c8638c40548b2c6p+3L, 0xa.4d4d3804f95933ep+3L, -0xa.2099c6552967d07p+2L, 0x8.5bd9514bfef0a5ep+1L, -0xe.cc1b958e3469fa9p-1L, 0xf.a1f60f951940304p-3L, 0xb.0b2dbbaaafe5407p-4L, -0xa.7c540b8dd847e5dp-4L, 0x9.33b41f49e95bb8cp-6L, -0xc.6ee3126a0ae46c7p-12L, -0xc.bce574a2d70819p-14L, 0xc.ab13d8c3fed8cb7p-23L, 0x9.c5e694361aef307p-34L, 0x0p+0L};
             }
             if constexpr (order == 10) {
                 return {0x0p+0L, 0xe.ee4c8a5c7e71374p-3L, -0x8.553537f23a4ffcdp+1L, 0xf.fe98518788271d7p+2L, -0x8.83b5deda67ba93ep+4L, 0xa.d98a7eadec21394p+4L, -0x8.af314d1783d59d9p+4L, 0xb.9f66d53ede688c9p+3L, -0xb.f524c8940d401f5p+3L, 0xc.97f2843849db0a7p+3L, -0xf.28674361f651857p+2L, 0x9.1ff1b672928682ep+1L, -0x8.8c1d2d63a31b528p+0L, 0x9.92ed38b0b3c3d8dp-1L, 0xd.adc9e9bf5bc7971p-1L, -0xb.0ba6614954bbf44p+0L, 0xd.c73c70d4d6d2496p-1L, -0xf.fe372a784dc531cp-2L, 0xc.03da1e919f0994ap-2L, -0xc.a4f7ff27eaf885bp-3L, 0xc.ce3837719e99949p-5L, -0xc.5a12af5955a96fbp-9L, -0x9.2fdef25707148aap-11L, 0xd.17fead2c51f312dp-20L, 0xa.112f2eb3eb54818p-30L, 0x0p+0L};
             }
             if constexpr (order == 11) {
-                return {0x0p+0L, 0xc.12aaf87e5340e4ep-5L, -0xd.8845625eceaef48p-2L, 0xd.1d7cfaf14299ea2p+0L, -0xe.4971534df5f5093p+1L, 0x9.9b0ab78cd1f558dp+2L, -0x8.aa690629969becdp+2L, 0xd.7cae353f81a7b93p+1L, -0xd.1c176a1afc76911p+1L, 0xd.2d2bedacdb3df28p+1L, -0xa.42c3deda3c082c7p+1L, 0xe.328cd8e6d949737p+0L, -0xb.22036e2ef671076p+0L, 0x8.2d06d1543ed7f3cp+0L, -0x9.a03151dfbe084ep-1L, 0xb.2d1993de78d60e7p-2L, -0xd.93e7bd5a4df1be7p-3L, 0xd.2dee38c95ce1d1p-4L, -0xa.b8d614c1fc2f1d3p-5L, 0x9.8bb3c0be356f62ap-6L, -0xc.8279a48dfb4e393p-8L, 0x8.772798b1faafa2dp-11L, 0x9.2c278f9b5a1f3dep-13L, -0x9.b9e7ac2601f7483p-20L, -0xe.db05034619bbe3ap-30L, 0x0p+0L};
+                return {0x0p+0L, 0xc.12aaf87e5340e4ep-5L, -0xd.8845625eceaef48p-2L, 0xd.1d7cfaf14299ea2p+0L, -0xe.4971534df5f5093p+1L, 0x9.9b0ab78cd1f558dp+2L, -0x8.aa690629969becdp+2L, 0xd.7cae353f81a7b93p+1L, -0xd.1c176a1afc76911p+1L, 0xd.2d2bedacdb3df28p+1L, -0xa.42c3deda3c082c7p+1L, 0xe.328cd8e6d949737p+0L, -0xb.22036e2ef671076p+0L, 0x8.2d06d1543ed7f3cp+0L, -0x9.a03151dfbe084ep-1L, 0xb.2d1993de78d60e7p-2L, -0xd.93e7bd5a4df1be7p-3L, 0xd.2dee38c95ce1d1p-4L, -0xa.b8d614c1fc2f1d3p-5L, 0x9.8bb3c0be356f62ap-6L, -0xc.8279a48dfb4e393p-8L, 0x8.772798b1faafa2dp-11L, 0x9.2c278f9b5a1f3dep-13L, -0x9.b9e7ac2601f7483p-20L, -0xe.db05034619bbe3ap-30L, -0x0p+0L};
             }
             if constexpr (order == 12) {
                 return {0x0p+0L, 0xc.6dd81fd69617fa7p-8L, -0xd.f5ee2e9d91c88f7p-5L, 0xd.75bd2f51082950ep-3L, -0xe.5cc28a9169055e6p-2L, 0x9.205facc38dccbfep-1L, -0xe.55be78f6a9bf069p-2L, 0x8.fea2a1d2fec658fp-2L, -0x8.e74ba260e4bab6fp-2L, 0x9.dd5845ebb1a25a2p-2L, -0xe.2073da73baab7afp-3L, 0xf.f56e463e743d47ep-4L, -0xd.321d23ec25a6d38p-4L, 0xa.a1dcb270781d1d4p-4L, -0xa.bbd52bb7fd3277ep-5L, 0xa.4cfb7bd4bd115e9p-6L, -0xe.ad0a8a8dc80b1aep-7L, 0xe.a62dd6da3383b8ap-8L, -0x8.4a7a90ab486d843p-9L, 0xe.684937dcf0a13c9p-11L, -0xd.9048e1639ee817cp-12L, 0xf.ee39a876fd6e928p-16L, 0xa.578ba89fe1d43b5p-16L, -0xf.e8ccd1e77d18dbbp-22L, -0xb.fd203720f6b2eddp-30L, 0x0p+0L};
@@ -1203,60 +1456,101 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         #ifdef BOOST_HAS_FLOAT128
         if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
             if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.749078c0867a9a724454443e786p-9Q, 0x1.8ae6a79b4938fbd909b199343627p-3Q, 0x1.d008898983913d9bf1d194ac98ebp-1Q, -0x1.20e16d5539e3f25296b1c6880b7dp-4Q, -0x1.f688bd1280c70194203f74426669p-5Q, 0x1.2fca4301354a4e285e82fc4b6146p-5Q, -0x1.505c64431d7a6f1e36954a7c7627p-12Q, -0x1.0145189baf0142f2a8862b8be414p-6Q, 0x1.c908becee5a6a6fcccc95605353cp-7Q, -0x1.beac12be1e7de0939dd15f03161ap-8Q, 0x1.0006a916adee342c6b2792c6bd71p-9Q, -0x1.d4cc286b09e13557f3e87a0f9cap-13Q, -0x1.a08b65bbb598677114fddb7b659bp-15Q, 0x1.5f413ab3a7eb94dcb396b2657e81p-16Q, -0x1.5c34d16af592037a11107a487af4p-20Q, -0x1.2dc4454eebde3379c7645c4ba813p-21Q, 0x1.74f33a2ccbc6518fcdedc7d5a964p-24Q, 0x1.ddb5df0a412fd407d061c573b7b3p-29Q, -0x1.07969b3a158bd160a5cdad0ecd8ep-32Q, 0x1.2c5958b74836c10a9059d0bfc5aap-38Q, 0x1.52fae6e83091fa686190e11a0ab7p-45Q, -0x1.d83da475a639c307966abb294442p-53Q, 0x1.1342e56840ec19da921d2c329457p-65Q, 0x1.aa25edf8f64fee132e1b309309a8p-86Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.749078c0867a9a724454443e75a7p-9Q, 0x1.8ae6a79b4938fbd909b199343609p-3Q, 0x1.d008898983913d9bf1d194ac98f7p-1Q, -0x1.20e16d5539e3f25296b1c6880b53p-4Q, -0x1.f688bd1280c70194203f744266d5p-5Q, 0x1.2fca4301354a4e285e82fc4b6183p-5Q, -0x1.505c64431d7a6f1e36954a7c80cp-12Q, -0x1.0145189baf0142f2a8862b8be415p-6Q, 0x1.c908becee5a6a6fcccc95605355fp-7Q, -0x1.beac12be1e7de0939dd15f031644p-8Q, 0x1.0006a916adee342c6b2792c6bd7ep-9Q, -0x1.d4cc286b09e13557f3e87a0f9caep-13Q, -0x1.a08b65bbb598677114fddb7b661ep-15Q, 0x1.5f413ab3a7eb94dcb396b2657edap-16Q, -0x1.5c34d16af592037a11107a487b39p-20Q, -0x1.2dc4454eebde3379c7645c4ba87ep-21Q, 0x1.74f33a2ccbc6518fcdedc7d5aa01p-24Q, 0x1.ddb5df0a412fd407d061c573b81ep-29Q, -0x1.07969b3a158bd160a5cdad0ece81p-32Q, 0x1.2c5958b74836c10a9059d0bfc767p-38Q, 0x1.52fae6e83091fa686190e11a0d2cp-45Q, -0x1.d83da475a639c307966abb294b63p-53Q, 0x1.1342e56840ec19da921d2c329c6fp-65Q, 0x1.aa25edf8f64fee132e1b30933b5p-86Q, 0x0p+0Q};
             }
             if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.23923550f457ca7814b0bb3fd63cp-6Q, 0x1.0c0767795d12ae5d156ec5cf442dp-1Q, 0x1.3373be839b47c40b1d36ec3e479ap-2Q, -0x1.856d7e6b6468c2deff8342e75bafp+0Q, 0x1.22d30ac28dd9c9a5de5413538cdcp+0Q, -0x1.72e38df054a23a8a5ebabc499011p-1Q, 0x1.8e439b194a1c16626ebcbea59c97p-2Q, -0x1.3bc2524066e83eb2d5b3ff97e1f2p-3Q, 0x1.1bc8f6e41059663daa79bf4a8b49p-5Q, 0x1.2884461caa1e3207b6de1334aafbp-11Q, -0x1.db22a9804aa1133069d05b96cb79p-10Q, -0x1.3482dca87f01c45e946a258c3e3ep-11Q, 0x1.3285223dae55992a1d57ada1536cp-11Q, -0x1.bbf1c4306d1a37f02d18135ce361p-14Q, -0x1.17497a4dcd44ffdc92c6ebd1a07dp-16Q, 0x1.bebec0cbd1f99371a7867cbe4001p-18Q, -0x1.bc40d833ef3598561d72cdf89c2bp-22Q, 0x1.6454c6cebdf97f43adbbdee1eef5p-26Q, 0x1.5fce040bf0fa22a0bb7f52a52ec5p-29Q, -0x1.1241493325c926f92e656210ed45p-33Q, -0x1.ce70ab06ee7eb593175a3e65f70bp-41Q, 0x1.8616f674ef405eeabf053da9c793p-48Q, -0x1.7b38ad7c07a3a058098173d3a941p-60Q, -0x1.258ba4702de85ac45e001504a5c3p-79Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.23923550f457ca7814b0bb3fd653p-6Q, 0x1.0c0767795d12ae5d156ec5cf4423p-1Q, 0x1.3373be839b47c40b1d36ec3e47ecp-2Q, -0x1.856d7e6b6468c2deff8342e75baep+0Q, 0x1.22d30ac28dd9c9a5de5413538cd2p+0Q, -0x1.72e38df054a23a8a5ebabc499005p-1Q, 0x1.8e439b194a1c16626ebcbea59c81p-2Q, -0x1.3bc2524066e83eb2d5b3ff97e1edp-3Q, 0x1.1bc8f6e41059663daa79bf4a8b55p-5Q, 0x1.2884461caa1e3207b6de1334a7c9p-11Q, -0x1.db22a9804aa1133069d05b96cb0fp-10Q, -0x1.3482dca87f01c45e946a258c3e06p-11Q, 0x1.3285223dae55992a1d57ada1533cp-11Q, -0x1.bbf1c4306d1a37f02d18135ce323p-14Q, -0x1.17497a4dcd44ffdc92c6ebd1a068p-16Q, 0x1.bebec0cbd1f99371a7867cbe3fbap-18Q, -0x1.bc40d833ef3598561d72cdf89bb4p-22Q, 0x1.6454c6cebdf97f43adbbdee1eeb8p-26Q, 0x1.5fce040bf0fa22a0bb7f52a52e7bp-29Q, -0x1.1241493325c926f92e656210ed16p-33Q, -0x1.ce70ab06ee7eb593175a3e65f68ep-41Q, 0x1.8616f674ef405eeabf053da9c72dp-48Q, -0x1.7b38ad7c07a3a058098173d3a8bcp-60Q, -0x1.258ba4702de85ac45e001504a52p-79Q, 0x0p+0Q};
             }
             if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.7e9e99d93265e1ecb27f1a82e40ep-4Q, 0x1.e81e73bf7d4e6759d9f3db7612c7p-1Q, -0x1.368292c7be10e513188a104c5cc1p+1Q, 0x1.a1c192a939b9674ffcca9b2f1f92p+0Q, -0x1.58e6f9045a40dd2a472104dd130ep-2Q, 0x1.2f82100ba4f2879faa0ab73165e9p-2Q, -0x1.f8fd9be6cc910f763e95aa8ab1d7p-2Q, 0x1.017de77081fc30f9ad09eddaf4ddp-1Q, -0x1.5831ad14642112326c714ae42502p-2Q, 0x1.30d718554c4cabcfafc1434f8aebp-3Q, -0x1.30a6075105b3aa4d5336fc195157p-5Q, -0x1.632f9e9eb99fc711faf42ce1fdf8p-11Q, 0x1.1cbed37ba4dbd96c225d81054e98p-8Q, -0x1.77d86fa7164bfc8c126a64816b23p-10Q, 0x1.50ec238da00966f5e3d28fc92775p-14Q, 0x1.f99c3b6dd2e633388ada35d1c02cp-15Q, -0x1.8453f2cbc2d996b7775a123e93afp-17Q, -0x1.b4056601f4bff8b5e7d36857ce88p-23Q, 0x1.4c2776a5f116e1d85dd046bd9771p-24Q, -0x1.287daf168a219aa1132a37934623p-29Q, -0x1.b00a66e2af603b8210a104b461a3p-36Q, 0x1.401eb1fad689de068ef9a337dccp-42Q, -0x1.71528144e6954a34804ddc8b69bap-54Q, -0x1.1de10823e626bbef4adf3610d3cbp-72Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.7e9e99d93265e1ecb27f1a82e385p-4Q, 0x1.e81e73bf7d4e6759d9f3db761257p-1Q, -0x1.368292c7be10e513188a104c5c4ap+1Q, 0x1.a1c192a939b9674ffcca9b2f1e48p+0Q, -0x1.58e6f9045a40dd2a472104dd0f2ep-2Q, 0x1.2f82100ba4f2879faa0ab7316342p-2Q, -0x1.f8fd9be6cc910f763e95aa8aafdap-2Q, 0x1.017de77081fc30f9ad09eddaf43dp-1Q, -0x1.5831ad14642112326c714ae42463p-2Q, 0x1.30d718554c4cabcfafc1434f8a7fp-3Q, -0x1.30a6075105b3aa4d5336fc1950e8p-5Q, -0x1.632f9e9eb99fc711faf42ce203b1p-11Q, 0x1.1cbed37ba4dbd96c225d81054e88p-8Q, -0x1.77d86fa7164bfc8c126a64816ac4p-10Q, 0x1.50ec238da00966f5e3d28fc9265ep-14Q, 0x1.f99c3b6dd2e633388ada35d1bfe8p-15Q, -0x1.8453f2cbc2d996b7775a123e9384p-17Q, -0x1.b4056601f4bff8b5e7d36857cb2ap-23Q, 0x1.4c2776a5f116e1d85dd046bd9786p-24Q, -0x1.287daf168a219aa1132a37934711p-29Q, -0x1.b00a66e2af603b8210a104b463bdp-36Q, 0x1.401eb1fad689de068ef9a337dfddp-42Q, -0x1.71528144e6954a34804ddc8b7672p-54Q, -0x1.1de10823e626bbef4adf3610f4fep-72Q, 0x0p+0Q};
             }
             if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.95e033565cd465e59fc64a848c0ep-2Q, 0x1.e7908dd5753c97550b1b562a1b99p-3Q, -0x1.293799fcf6c8da1f93fe2d057409p+2Q, 0x1.36cc467b08bf7d8a89d5be8f8643p+3Q, -0x1.4335983e135774c5e5156a450a68p+3Q, 0x1.9c4d14b5414867b3e2c99a218f0bp+2Q, -0x1.ef81d85b23a01ac83af86d64ce2ep+0Q, -0x1.2378e73c6b10a2f7957b04476802p+0Q, 0x1.c6e27151761e3e586f540356142cp+0Q, -0x1.c857e67243153a965a648f8e46c8p-1Q, 0x1.3531afa42b77f4c754018d3dfbb2p-8Q, 0x1.05f57c1a6464d742d9d2e202c63cp-2Q, -0x1.38a2db882124dfc4e44179ad4f8p-3Q, 0x1.35c4a5041d9b9456d2520e65a344p-5Q, -0x1.fddc3c9f813d6aef1f4f22d0d6c7p-14Q, -0x1.2653a0321997d1fa4ad992782112p-9Q, 0x1.ec5d6f7ab50c177dc61e0a187538p-12Q, -0x1.dc01f8633f4c61396f200866219ep-17Q, -0x1.379717b64ca37d0f86a74f66252ap-18Q, 0x1.7e5cfdc9a1b17dce328c7c0b396fp-23Q, 0x1.a124166c5786174e1b984a58659ap-29Q, -0x1.4171311c3a7b2623f4df8ab80088p-35Q, 0x1.65f402b77f1ab227d7a791607b4dp-46Q, 0x1.15123cc4efb60d3af1736012c799p-63Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.95e033565cd465e59fc64a849ff5p-2Q, 0x1.e7908dd5753c97550b1b562a02c1p-3Q, -0x1.293799fcf6c8da1f93fe2d057e3ap+2Q, 0x1.36cc467b08bf7d8a89d5be8f934fp+3Q, -0x1.4335983e135774c5e5156a45190ap+3Q, 0x1.9c4d14b5414867b3e2c99a21a031p+2Q, -0x1.ef81d85b23a01ac83af86d64d1abp+0Q, -0x1.2378e73c6b10a2f7957b04478d3fp+0Q, 0x1.c6e27151761e3e586f5403563b06p+0Q, -0x1.c857e67243153a965a648f8e6a77p-1Q, 0x1.3531afa42b77f4c754018d3dff11p-8Q, 0x1.05f57c1a6464d742d9d2e202da9bp-2Q, -0x1.38a2db882124dfc4e44179ad6816p-3Q, 0x1.35c4a5041d9b9456d2520e65bc23p-5Q, -0x1.fddc3c9f813d6aef1f4f22d0ffb3p-14Q, -0x1.2653a0321997d1fa4ad992783a03p-9Q, 0x1.ec5d6f7ab50c177dc61e0a189fcdp-12Q, -0x1.dc01f8633f4c61396f200866480ap-17Q, -0x1.379717b64ca37d0f86a74f664124p-18Q, 0x1.7e5cfdc9a1b17dce328c7c0b5cf9p-23Q, 0x1.a124166c5786174e1b984a588c59p-29Q, -0x1.4171311c3a7b2623f4df8ab8200ep-35Q, 0x1.65f402b77f1ab227d7a791609ed8p-46Q, 0x1.15123cc4efb60d3af1736012e615p-63Q, 0x0p+0Q};
             }
             if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.4c5d516dd5340d0879832abec56ap+0Q, -0x1.5d2571cda5543923016a3601781dp+2Q, 0x1.24b0f03522629e31e5a0ddf8fe8fp+3Q, -0x1.39e0f8d13e8db1f029ce6257e806p+3Q, 0x1.f006cc927be5328f1a33d6ae0a72p+3Q, -0x1.0ce2ffa4646117df99ed92ff7f71p+5Q, 0x1.b8b8afcf323d00e8ad39d1cbe81p+5Q, -0x1.e6925570e3f510211d732b909262p+5Q, 0x1.503102590c0b7b7ae2742f430edfp+5Q, -0x1.6d86add093f074bc432a452a8a23p+3Q, -0x1.35b5dc1025f2d34a60aa7bf986d8p+3Q, 0x1.a6237c764b4a28340b848880c532p+3Q, -0x1.cda455c3ae3929d25c3c5a3186e9p+2Q, 0x1.d5a02bb93708a320124acceeba3bp+0Q, 0x1.ecd4c4adc075fe2457753c0a3227p-5Q, -0x1.660ee59df078b432fb4f889aa837p-3Q, 0x1.5158e51b27e5dbfe89f577f955e5p-5Q, -0x1.73814bfd57b681fa89fa6df49afcp-10Q, -0x1.23460c48f636fa706d007acab6f4p-11Q, 0x1.fa353cdebaaaaa09ad0c40e91089p-16Q, 0x1.19c5738584246e6431d3352c0155p-21Q, -0x1.4bb4308ed51fff3108f30cb6a721p-27Q, 0x1.fc9a1f4f09858f536f1a575ceb92p-38Q, 0x1.89a8b7b9d28d1d71597812a9e85fp-54Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.4c5d516dd5340d0879832abfae77p+0Q, -0x1.5d2571cda5543923016a360261d3p+2Q, 0x1.24b0f03522629e31e5a0ddf9b0acp+3Q, -0x1.39e0f8d13e8db1f029ce62587cecp+3Q, 0x1.f006cc927be5328f1a33d6aed069p+3Q, -0x1.0ce2ffa4646117df99ed92fff69cp+5Q, 0x1.b8b8afcf323d00e8ad39d1ccb61dp+5Q, -0x1.e6925570e3f510211d732b9179c8p+5Q, 0x1.503102590c0b7b7ae2742f43b1bp+5Q, -0x1.6d86add093f074bc432a452b5189p+3Q, -0x1.35b5dc1025f2d34a60aa7bf9f93dp+3Q, 0x1.a6237c764b4a28340b8488817371p+3Q, -0x1.cda455c3ae3929d25c3c5a324857p+2Q, 0x1.d5a02bb93708a320124accef7fd1p+0Q, 0x1.ecd4c4adc075fe2457753c0ae29ap-5Q, -0x1.660ee59df078b432fb4f889b38bfp-3Q, 0x1.5158e51b27e5dbfe89f577f9dcaep-5Q, -0x1.73814bfd57b681fa89fa6df52a98p-10Q, -0x1.23460c48f636fa706d007acb283p-11Q, 0x1.fa353cdebaaaaa09ad0c40e9cfcp-16Q, 0x1.19c5738584246e6431d3352c6ae1p-21Q, -0x1.4bb4308ed51fff3108f30cb71f7ep-27Q, 0x1.fc9a1f4f09858f536f1a575d9e29p-38Q, 0x1.89a8b7b9d28d1d71597812aa68c7p-54Q, 0x0p+0Q};
             }
             if constexpr (order == 5) {
-                return {0x0p+0Q, 0x1.a35157d8dba56b3359c55e1b2f1bp+1Q, -0x1.5a1bc35a1cc0dbb69c71ae20ac28p+4Q, 0x1.fa0a0878d9a933860f512013ce09p+5Q, -0x1.a68f6523a82701663e04e44e02c9p+6Q, 0x1.98403a971e63162a02dd9331873fp+6Q, -0x1.03810e60e02049d57e6cca7b3393p+5Q, -0x1.14faaec76846550eede585da319ep+6Q, 0x1.3d735b94c105436aa6c6acd1ae46p+7Q, -0x1.cdbd7de801407d716cbc3884161p+7Q, 0x1.20043470ad456af43bde8d96fdaap+8Q, -0x1.2591e882d85cd18b0dca9797ee6p+8Q, 0x1.b621996a63c17e6687cb0b211602p+7Q, -0x1.a875ba068d8449d487f82dc4bc08p+6Q, 0x1.85c7d166f26b7783d793e4e78c82p+4Q, 0x1.1c0e0d6b929f95b9e528989abb17p+2Q, -0x1.36efc345fd87e7f12a7cd8f187eap+2Q, 0x1.3e3f5c2c93c347939cad28f604bbp+0Q, -0x1.bffc3922a312894449dea0a83571p-5Q, -0x1.75f52c4bce3944c6d40bd8ed1f5ap-6Q, 0x1.dea5b49d2b299f2f3407a986e912p-10Q, 0x1.10aa3eff5f8aac0902d8bf656d56p-15Q, -0x1.ea6ed6c321e753c1b3e9237c4183p-21Q, 0x1.089ab261bfe1c8b7f19aebf544d2p-30Q, 0x1.9990a3735f2b8137827c0403494ap-46Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.a35157d8dba56b3359c55dbb3245p+1Q, -0x1.5a1bc35a1cc0dbb69c71add31e17p+4Q, 0x1.fa0a0878d9a933860f511fa37af4p+5Q, -0x1.a68f6523a82701663e04e3ed3779p+6Q, 0x1.98403a971e63162a02dd92c33da9p+6Q, -0x1.03810e60e02049d57e6cc9d05d6p+5Q, -0x1.14faaec76846550eede58601f0cdp+6Q, 0x1.3d735b94c105436aa6c6accd08c9p+7Q, -0x1.cdbd7de801407d716cbc38649987p+7Q, 0x1.20043470ad456af43bde8d7a0984p+8Q, -0x1.2591e882d85cd18b0dca9775a589p+8Q, 0x1.b621996a63c17e6687cb0aeb2864p+7Q, -0x1.a875ba068d8449d487f82d8f98a2p+6Q, 0x1.85c7d166f26b7783d793e4b535e5p+4Q, 0x1.1c0e0d6b929f95b9e528987efc33p+2Q, -0x1.36efc345fd87e7f12a7cd8cf55f7p+2Q, 0x1.3e3f5c2c93c347939cad28d35ff2p+0Q, -0x1.bffc3922a312894449dea079023bp-5Q, -0x1.75f52c4bce3944c6d40bd8c68e83p-6Q, 0x1.dea5b49d2b299f2f3407a959506bp-10Q, 0x1.10aa3eff5f8aac0902d8bf4b6addp-15Q, -0x1.ea6ed6c321e753c1b3e92351b813p-21Q, 0x1.089ab261bfe1c8b7f19aebdff953p-30Q, 0x1.9990a3735f2b8137827c03e7b5fp-46Q, 0x0p+0Q};
             }
             if constexpr (order == 6) {
-                return {0x0p+0Q, 0x1.5d159c98a090a206b1f5a4e9463bp+2Q, -0x1.54873e7e1b3d210625d27844421bp+5Q, 0x1.2c245e185ac8b14c7baac4549349p+7Q, -0x1.416f5cc6c22c1fc04eedaa366dc1p+8Q, 0x1.e67e2b7f933044475571e6b73738p+8Q, -0x1.298ee57db6ed5fd4bacad132e624p+9Q, 0x1.48ee3d90a4e34a8f4d18f9ebf69p+9Q, -0x1.4e6b4521eb7a56c1ef7579e251acp+9Q, 0x1.2782e95d7bf9f5fc360d3847dd8p+9Q, -0x1.bb493883e544d446bc2b8c57d25fp+8Q, 0x1.25dfd4b9fa45afe8f2d50b1eccc2p+8Q, -0x1.575e0c206b7ee6818931b6994d6ep+7Q, 0x1.1c028f2725fce675841ea64b2ffp+6Q, -0x1.08a1fe0ac6819f96e8258ae14398p+2Q, -0x1.12ed1d6ca77301d9871c8664703fp+4Q, 0x1.66791e904ad3b41e47b4403dcaadp+3Q, -0x1.7aa9733036515afd48134b63faf5p+1Q, 0x1.41600caa02955d88aadf0943297p-3Q, 0x1.275514f436a31e564b7d01e0e908p-4Q, -0x1.29373f56ac1095884f483fc367f8p-7Q, -0x1.51ea7d9f345040b9bbf6801a6296p-13Q, 0x1.deb156b08b87ef0592d66c2ead34p-18Q, -0x1.6e30fae8c34ed8366ddfb109de2fp-27Q, -0x1.1b57abb7d7f1ba81ca336dfebef5p-41Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.5d159c98a090a206b1f5a487328bp+2Q, -0x1.54873e7e1b3d210625d277e6898dp+5Q, 0x1.2c245e185ac8b14c7baac4033f4ap+7Q, -0x1.416f5cc6c22c1fc04eeda9dfb493p+8Q, 0x1.e67e2b7f933044475571e632011ap+8Q, -0x1.298ee57db6ed5fd4bacad0de9695p+9Q, 0x1.48ee3d90a4e34a8f4d18f98b7344p+9Q, -0x1.4e6b4521eb7a56c1ef75797e43fdp+9Q, 0x1.2782e95d7bf9f5fc360d37ee013bp+9Q, -0x1.bb493883e544d446bc2b8bcc693p+8Q, 0x1.25dfd4b9fa45afe8f2d50abdb77ep+8Q, -0x1.575e0c206b7ee6818931b6231d56p+7Q, 0x1.1c028f2725fce675841ea5e425e4p+6Q, -0x1.08a1fe0ac6819f96e8258a0368bp+2Q, -0x1.12ed1d6ca77301d9871c862435c4p+4Q, 0x1.66791e904ad3b41e47b43fe289f8p+3Q, -0x1.7aa9733036515afd48134b03fe32p+1Q, 0x1.41600caa02955d88aadf08f58823p-3Q, 0x1.275514f436a31e564b7d019a87cbp-4Q, -0x1.29373f56ac1095884f483f83febcp-7Q, -0x1.51ea7d9f345040b9bbf67fd2c9c4p-13Q, 0x1.deb156b08b87ef0592d66bd4c9c7p-18Q, -0x1.6e30fae8c34ed8366ddfb0cc8561p-27Q, -0x1.1b57abb7d7f1ba81ca336dd9e4d6p-41Q, 0x0p+0Q};
             }
             if constexpr (order == 7) {
-                return {0x0p+0Q, 0x1.d4fe27a0835ae1a04e083919e159p+2Q, -0x1.ecb0f32ca76fb494d571b92b6ab8p+5Q, 0x1.c6da62a20cd0a85f327433229c8ap+7Q, -0x1.e3622dd5ba05d80a963a6735beb4p+8Q, 0x1.49508717a90e836846bfeeb5b43bp+9Q, -0x1.3d934aacf56d0a27027f0d4c671dp+9Q, 0x1.068600d74e1c90df9e5944f06e21p+9Q, -0x1.bb4eb52dbc23c8aa9dac22db8fdep+8Q, 0x1.2c2d3c048caae8b4e7ebda4b0128p+8Q, -0x1.6a6f07f5d07dd28cc713b1beaa3ap+5Q, -0x1.48c0f7b3bed9dd4e2bcfa51c5127p+7Q, 0x1.bce28601020e5546efe486219835p+7Q, -0x1.9e035ea535c3aebdf12725979bb8p+7Q, 0x1.737017c34f7deef2722c93e161f4p+7Q, -0x1.15bd065f2789c251ed52811c0835p+7Q, 0x1.1609d2e86de1f46bc02dc1f1561dp+6Q, -0x1.30b382548235fc08ce2a69131576p+4Q, 0x1.34c266d274d020226722008d15aap+0Q, 0x1.56d14dbd1c0ef8dc071f15458559p-1Q, -0x1.f82518456ddfa0a1ea7fa3e5d12cp-4Q, -0x1.1d5d333a03734067f69cd7ef01cbp-9Q, 0x1.599f88826e1df7529e2526edcc77p-13Q, -0x1.742b04eba227022dc278410d55cbp-22Q, -0x1.1fd835e2f3ac373e68a16573044bp-35Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.d4fe27a0835ae1a04e0830be24cp+2Q, -0x1.ecb0f32ca76fb494d571b0a3e338p+5Q, 0x1.c6da62a20cd0a85f32742b3dd231p+7Q, -0x1.e3622dd5ba05d80a963a5e3e0d7dp+8Q, 0x1.49508717a90e836846bfe76665d8p+9Q, -0x1.3d934aacf56d0a27027f03a0039p+9Q, 0x1.068600d74e1c90df9e5939a69755p+9Q, -0x1.bb4eb52dbc23c8aa9dac0b1ae5b9p+8Q, 0x1.2c2d3c048caae8b4e7ebc3a10a9fp+8Q, -0x1.6a6f07f5d07dd28cc71310327c39p+5Q, -0x1.48c0f7b3bed9dd4e2bcfc6df9159p+7Q, 0x1.bce28601020e5546efe49f4f2facp+7Q, -0x1.9e035ea535c3aebdf12735df11cep+7Q, 0x1.737017c34f7deef2722c9d811907p+7Q, -0x1.15bd065f2789c251ed52867c6e81p+7Q, 0x1.1609d2e86de1f46bc02dc6e0a8fcp+6Q, -0x1.30b382548235fc08ce2a6ea99e65p+4Q, 0x1.34c266d274d020226722064f6a4ap+0Q, 0x1.56d14dbd1c0ef8dc071f1d5be26fp-1Q, -0x1.f82518456ddfa0a1ea7fb11fa704p-4Q, -0x1.1d5d333a03734067f69cdf063e2dp-9Q, 0x1.599f88826e1df7529e25322303e3p-13Q, -0x1.742b04eba227022dc2784e1aeb19p-22Q, -0x1.1fd835e2f3ac373e68a1719919f7p-35Q, 0x0p+0Q};
             }
             if constexpr (order == 8) {
-                return {0x0p+0Q, 0x1.6f91b1fb16e463903f242c426455p+2Q, -0x1.8fef11e8059ceda062dec743d5bap+5Q, 0x1.809c444472a8d8415a2c8fcb90adp+7Q, -0x1.b10bf090c92b5336357d1404e2eap+8Q, 0x1.45258188f71468e863f93e44329ep+9Q, -0x1.7231afc08bd276307932c937c208p+9Q, 0x1.7af82162ac359965f69e88fff2d1p+9Q, -0x1.823e9f8992b59fc66e18911aea8bp+9Q, 0x1.6f4bc124eb7dc2e04c11ba39d8bp+9Q, -0x1.32f291524b4fc819caccda30ea8fp+9Q, 0x1.d856007cb8fa074ef08390247a6ep+8Q, -0x1.59b2f057a74e4aae3ebb655c3f1ep+8Q, 0x1.c4898ffe6b603cfd7a5fca3706d6p+7Q, -0x1.01b04bb5c7e4ece20624aa0d5e2cp+7Q, 0x1.0ee550f2b46fb0067dbfd6b593fep+6Q, -0x1.f149829700499105abd0a04d1745p+4Q, 0x1.21413698e7cf1b5b76cf6ac9da58p+3Q, -0x1.1e358290df39caefe5b55d7f88a9p-2Q, -0x1.54f12799790c9591a3724eefd6adp-1Q, 0x1.1dedd290f907f8d2a85301c5e1c1p-3Q, 0x1.2b8db385d6eeb017f6475d54698ap-10Q, -0x1.7cd67d6099898e46f355585388cap-12Q, 0x1.c1758243d6f68f111636a9a1e06bp-21Q, 0x1.5b5402fbe8db7e6e4a333c1f1c5ap-33Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.6f91b1fb16e463903f2417b8bc33p+2Q, -0x1.8fef11e8059ceda062deb12c9387p+5Q, 0x1.809c444472a8d8415a2c7a9afbefp+7Q, -0x1.b10bf090c92b5336357cfbd2f863p+8Q, 0x1.45258188f71468e863f92b55998cp+9Q, -0x1.7231afc08bd276307932b219a0cfp+9Q, 0x1.7af82162ac359965f69e6fcab693p+9Q, -0x1.823e9f8992b59fc66e1876f1aa68p+9Q, 0x1.6f4bc124eb7dc2e04c11a11579edp+9Q, -0x1.32f291524b4fc819caccc41f919dp+9Q, 0x1.d856007cb8fa074ef0836c00fb93p+8Q, -0x1.59b2f057a74e4aae3ebb4a35f68fp+8Q, 0x1.c4898ffe6b603cfd7a5fa627ad77p+7Q, -0x1.01b04bb5c7e4ece20624945e7d4ap+7Q, 0x1.0ee550f2b46fb0067dbfbe5f34b2p+6Q, -0x1.f149829700499105abd07323449cp+4Q, 0x1.21413698e7cf1b5b76cf50d81657p+3Q, -0x1.1e358290df39caefe5b52d405e07p-2Q, -0x1.54f12799790c9591a372397a1538p-1Q, 0x1.1dedd290f907f8d2a852f01bdfd7p-3Q, 0x1.2b8db385d6eeb017f64738645db6p-10Q, -0x1.7cd67d6099898e46f355480e2303p-12Q, 0x1.c1758243d6f68f11163695671c33p-21Q, 0x1.5b5402fbe8db7e6e4a3332e846cap-33Q, 0x0p+0Q};
             }
             if constexpr (order == 9) {
-                return {0x0p+0Q, 0x1.e00f201ca9b47bec13b3982152f1p+1Q, -0x1.09aad588fc6e1d2e5e31f5db6676p+5Q, 0x1.0083b1ed3add1dfc189aa41f7f2fp+7Q, -0x1.1b01639f15a47195db84399877bbp+8Q, 0x1.8e74c5b415b4c982c62a08a4c59cp+8Q, -0x1.907a858da198db5b4a86cd66130bp+8Q, 0x1.68e4a68143eb6280f782117761a4p+8Q, -0x1.685dfe59eb94f38e35f467a408e4p+8Q, 0x1.592f39b72049a36e7924da594eccp+8Q, -0x1.09589acf597f567d3772da9f9396p+8Q, 0x1.658b66c44d2d9f09118ad4461b1dp+7Q, -0x1.f90c71880a91658c0d9a077062e9p+6Q, 0x1.49a9a7009f2b267b39ba9598b5bfp+6Q, -0x1.441338caa52cfa0e2a27b3094033p+5Q, 0x1.0b7b2a297fde14bc6faf1e5cad3dp+4Q, -0x1.d98372b1c68d3f52be822d4ad9e1p+2Q, 0x1.f43ec1f2a32806088746b95241b7p+0Q, 0x1.6165b77555fca80d9c5c139ebf01p-1Q, -0x1.4f8a8171bb08fcb9ccd7e57b6a94p-1Q, 0x1.267683e93d2b771765dfb989358ep-3Q, -0x1.8ddc624d415c8d8d9889336c7b73p-9Q, -0x1.979cae945ae1031f8b5a50d00a19p-11Q, 0x1.95627b187fdb196e7b60f5dc529bp-20Q, 0x1.38bcd286c35de60d5fb4cabb4426p-31Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.e00f201ca9b47bec13b3bceeec35p+1Q, -0x1.09aad588fc6e1d2e5e320a1b6965p+5Q, 0x1.0083b1ed3add1dfc189ab7aaac2p+7Q, -0x1.1b01639f15a47195db844f5df4eap+8Q, 0x1.8e74c5b415b4c982c62a28306ab1p+8Q, -0x1.907a858da198db5b4a86eef21cd8p+8Q, 0x1.68e4a68143eb6280f78231820634p+8Q, -0x1.685dfe59eb94f38e35f487b91dc1p+8Q, 0x1.592f39b72049a36e7924f8b1defp+8Q, -0x1.09589acf597f567d3772f2b218afp+8Q, 0x1.658b66c44d2d9f09118af69ddd27p+7Q, -0x1.f90c71880a91658c0d9a38574dffp+6Q, 0x1.49a9a7009f2b267b39bab54a8a34p+6Q, -0x1.441338caa52cfa0e2a27d488fb3dp+5Q, 0x1.0b7b2a297fde14bc6faf3e06bf71p+4Q, -0x1.d98372b1c68d3f52be82670d6ee1p+2Q, 0x1.f43ec1f2a32806088746ff9dc715p+0Q, 0x1.6165b77555fca80d9c5c14948139p-1Q, -0x1.4f8a8171bb08fcb9ccd7f4688dddp-1Q, 0x1.267683e93d2b771765dfc5bfe73cp-3Q, -0x1.8ddc624d415c8d8d9889292068a5p-9Q, -0x1.979cae945ae1031f8b5a56752269p-11Q, 0x1.95627b187fdb196e7b60fd3122a7p-20Q, 0x1.38bcd286c35de60d5fb4c84a2f35p-31Q, 0x0p+0Q};
             }
             if constexpr (order == 10) {
-                return {0x0p+0Q, 0x1.ddc9914b8fce26e89a350da83719p+0Q, -0x1.0aa6a6fe4749ff9a5341c601bbd1p+4Q, 0x1.ffd30a30f104e3ad2ade791fa75cp+5Q, -0x1.1076bbdb4cf7527cd039e9d87117p+7Q, 0x1.5b314fd5bd8427278ea135aa2326p+7Q, -0x1.15e629a2f07ab3b285fb777249b6p+7Q, 0x1.73ecdaa7dbcd11927e44fc6ec254p+6Q, -0x1.7ea4991281a803e96d95b15ddcdfp+6Q, 0x1.92fe5087093b614dba0fb9dcd31ep+6Q, -0x1.e50ce86c3eca30ad8c366d925665p+5Q, 0x1.23fe36ce5250d05c30083be13efbp+4Q, -0x1.1183a5ac74636a4f4f82e9e90688p+3Q, 0x1.325da71616787b1a97d0cf145facp+2Q, 0x1.b5b93d37eb78f2e235ca0e3287edp+2Q, -0x1.6174cc292a977e8769fbfe3294c1p+3Q, 0x1.b8e78e1a9ada492b4dd621bd0ceap+2Q, -0x1.ffc6e54f09b8a6376ab8ee388e04p+1Q, 0x1.807b43d233e13293cd8f064bc042p+1Q, -0x1.949effe4fd5f10b6f0bb08f4fc9cp+0Q, 0x1.99c706ee33d33292c4de096ca957p-2Q, -0x1.8b4255eb2ab52df5046967e93801p-6Q, -0x1.25fbde4ae0e29153ac7874faf054p-8Q, 0x1.a2ffd5a58a3e625ad5ba39971f6dp-17Q, 0x1.4225e5d67d6a903058f2d7206afep-27Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.ddc9914b8fce26e89a34c64d6d6p+0Q, -0x1.0aa6a6fe4749ff9a53419e5cb74fp+4Q, 0x1.ffd30a30f104e3ad2ade2b583021p+5Q, -0x1.1076bbdb4cf7527cd039bd2ee863p+7Q, 0x1.5b314fd5bd8427278ea0f14850c8p+7Q, -0x1.15e629a2f07ab3b285fb28d62142p+7Q, 0x1.73ecdaa7dbcd11927e445f4fc04ap+6Q, -0x1.7ea4991281a803e96d951a02ad23p+6Q, 0x1.92fe5087093b614dba0f2e58af18p+6Q, -0x1.e50ce86c3eca30ad8c357a5bc172p+5Q, 0x1.23fe36ce5250d05c3006a508171cp+4Q, -0x1.1183a5ac74636a4f4f8077863f2cp+3Q, 0x1.325da71616787b1a97cd6b487bbp+2Q, 0x1.b5b93d37eb78f2e235cc59568f84p+2Q, -0x1.6174cc292a977e8769fcc13572c1p+3Q, 0x1.b8e78e1a9ada492b4dd6fe85e7f5p+2Q, -0x1.ffc6e54f09b8a6376ab9c26e41bp+1Q, 0x1.807b43d233e13293cd8f6f610b94p+1Q, -0x1.949effe4fd5f10b6f0bb69f9fc41p+0Q, 0x1.99c706ee33d33292c4de755a9043p-2Q, -0x1.8b4255eb2ab52df50469eaf1f575p-6Q, -0x1.25fbde4ae0e29153ac78daabb6bap-8Q, 0x1.a2ffd5a58a3e625ad5baf547df1dp-17Q, 0x1.4225e5d67d6a903058f380dcef3ap-27Q, 0x0p+0Q};
             }
             if constexpr (order == 11) {
-                return {0x0p+0Q, 0x1.82555f0fca681c9ced300e65470bp-2Q, -0x1.b108ac4bd9d5de90a612fd8cb482p+1Q, 0x1.a3af9f5e28533d44a21884894a43p+3Q, -0x1.c92e2a69bebea1255ad98c5c24f3p+4Q, 0x1.336156f19a3eab19184562b4b1e2p+5Q, -0x1.154d20c532d37d99d550b7ecda23p+5Q, 0x1.af95c6a7f034f7267500295c26p+4Q, -0x1.a382ed435f8ed2216764cfb7b5d9p+4Q, 0x1.a5a57db59b67be50825ea97be6b6p+4Q, -0x1.48587bdb4781058d98368c067205p+4Q, 0x1.c6519b1cdb292e6d292e55285478p+3Q, -0x1.64406dc5dece20ec3c4c5d654de5p+3Q, 0x1.05a0da2a87dafe77cb9a5835aad4p+3Q, -0x1.34062a3bf7c109c05654c02a04d6p+2Q, 0x1.65a3327bcf1ac1cee14ec461e42cp+1Q, -0x1.b27cf7ab49be37cde0f46d146d6bp+0Q, 0x1.a5bdc7192b9c3a20ece90c79e905p-1Q, -0x1.571ac2983f85e3a6dc62f787682cp-2Q, 0x1.31767817c6adec541d699bff90f4p-3Q, -0x1.904f3491bf69c7251d1b4755c9b7p-5Q, 0x1.0ee4f3163f55f45905e2e22beb7fp-8Q, 0x1.2584f1f36b43e7bbd83747f8e61dp-10Q, -0x1.373cf584c03ee906a072d01e3b91p-17Q, -0x1.db60a068c3377c744925f1488cc3p-27Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.82555f0fca681c9ced300bba3465p-2Q, -0x1.b108ac4bd9d5de90a612fa91bba4p+1Q, 0x1.a3af9f5e28533d44a218819eab18p+3Q, -0x1.c92e2a69bebea1255ad98910de81p+4Q, 0x1.336156f19a3eab19184560490c7ep+5Q, -0x1.154d20c532d37d99d550b554251fp+5Q, 0x1.af95c6a7f034f7267500247c3a39p+4Q, -0x1.a382ed435f8ed2216764cb0a372p+4Q, 0x1.a5a57db59b67be50825ea51ac179p+4Q, -0x1.48587bdb4781058d9836884c3b74p+4Q, 0x1.c6519b1cdb292e6d292e4f1f9c11p+3Q, -0x1.64406dc5dece20ec3c4c58b87407p+3Q, 0x1.05a0da2a87dafe77cb9a54ec8326p+3Q, -0x1.34062a3bf7c109c05654bbca487fp+2Q, 0x1.65a3327bcf1ac1cee14ebea4c8b6p+1Q, -0x1.b27cf7ab49be37cde0f46679310bp+0Q, 0x1.a5bdc7192b9c3a20ece9060c1ba9p-1Q, -0x1.571ac2983f85e3a6dc62f13fd384p-2Q, 0x1.31767817c6adec541d6996364d3fp-3Q, -0x1.904f3491bf69c7251d1b40c4f69ep-5Q, 0x1.0ee4f3163f55f45905e2ddfb93a4p-8Q, 0x1.2584f1f36b43e7bbd83744e7e8bep-10Q, -0x1.373cf584c03ee906a072cfcde9b5p-17Q, -0x1.db60a068c3377c744925f382f6d8p-27Q, 0x0p+0Q};
             }
             if constexpr (order == 12) {
-                return {0x0p+0Q, 0x1.8dbb03fad2c2ff4e565f6c62d57bp-5Q, -0x1.bebdc5d3b23911ed14512acd7b2bp-2Q, 0x1.aeb7a5ea21052a1c43ba3ca04a5p+0Q, -0x1.cb9851522d20abcc6f87f81034c7p+1Q, 0x1.240bf59871b997fc41c938fde14cp+2Q, -0x1.cab7cf1ed537e0d17c3940a7425ap+1Q, 0x1.1fd4543a5fd8cb1e3fd20d0065e1p+1Q, -0x1.1ce9744c1c9756de9b809fd2555fp+1Q, 0x1.3bab08bd76344b447fe47700254dp+1Q, -0x1.c40e7b4e77556f5ef84483097e1fp+0Q, 0x1.feadc8c7ce87a8fc67e279160504p-1Q, -0x1.a643a47d84b4da70d0fb106ef69bp-1Q, 0x1.543b964e0f03a3a71ec48db92838p-1Q, -0x1.577aa576ffa64efb7d0e9e6dcc9cp-2Q, 0x1.499f6f7a97a22bd1178c8661fe5ap-3Q, -0x1.d5a15151b901635be5a32ca30fbbp-4Q, 0x1.d4c5badb46707713b03f6aa302e5p-5Q, -0x1.094f5215690db085443c45e218e9p-6Q, 0x1.cd0926fb9e142792dd84079eb378p-8Q, -0x1.b2091c2c73dd02f84cb37e5165a8p-9Q, 0x1.fdc7350edfadd24f5fb7a95b49b7p-13Q, 0x1.4af17513fc3a876960b7d297e5d9p-13Q, -0x1.fd199a3cefa31b76bcac2a313bc8p-19Q, -0x1.7fa406e41ed65db974ed33f4fc9ap-27Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.8dbb03fad2c2ff4e565f682fc387p-5Q, -0x1.bebdc5d3b23911ed145126163ba8p-2Q, 0x1.aeb7a5ea21052a1c43ba381385e3p+0Q, -0x1.cb9851522d20abcc6f87f331e722p+1Q, 0x1.240bf59871b997fc41c935dfbef9p+2Q, -0x1.cab7cf1ed537e0d17c393ba768f6p+1Q, 0x1.1fd4543a5fd8cb1e3fd209bf00ffp+1Q, -0x1.1ce9744c1c9756de9b809c9cc5acp+1Q, 0x1.3bab08bd76344b447fe47382a836p+1Q, -0x1.c40e7b4e77556f5ef8447dfa81f7p+0Q, 0x1.feadc8c7ce87a8fc67e2732ba34ap-1Q, -0x1.a643a47d84b4da70d0fb0b9b5ca8p-1Q, 0x1.543b964e0f03a3a71ec489e8760ap-1Q, -0x1.577aa576ffa64efb7d0e9a7c6b39p-2Q, 0x1.499f6f7a97a22bd1178c8279f046p-3Q, -0x1.d5a15151b901635be5a327439552p-4Q, 0x1.d4c5badb46707713b03f6550ccfep-5Q, -0x1.094f5215690db085443c42ab246bp-6Q, 0x1.cd0926fb9e142792dd84020c8a8bp-8Q, -0x1.b2091c2c73dd02f84cb3796bc045p-9Q, 0x1.fdc7350edfadd24f5fb7a32829d8p-13Q, 0x1.4af17513fc3a876960b7cf51425ap-13Q, -0x1.fd199a3cefa31b76bcac261239c5p-19Q, -0x1.7fa406e41ed65db974ed315201c3p-27Q, 0x0p+0Q};
             }
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            if constexpr (order == 0) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00284244035743782127519159930736463030042947946254131969213976354467510363053"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.192822751451924727108748766614170490721105824748184344362119332875866730512"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.906315134083146106755137020807385959064705834685756457995503249677950870358"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0705274840180374221915610791607848006698261142719333764196180010698909604538"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0613444989030761396360783459458969916614040841601149181265363506895700420160"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0370837505994725874839940012509568535053053490011258542752097489994846693329"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000320778756026535884610425312070842577961491118876729788288874469672772619704"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0157025089563234832865197139394763898086519833544367931492178049759198251601"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0139475757294295802461692476281352659400468390363122309411246460077043752333"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00681567628464027460217301387139126877075375129883170970027298157286875244869"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00195332349843711924749204998394665745432087229507798519434292885120009605048"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000223540063730029960909841256853682353169363587803368909770156156719394426611"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000496559764237457326284532141943574549239549099813150646655995671938880681752"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000209364176969584236982171560586653840498356590078330878290505590378499323774"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000129716962748088954003609480965237922709827072460629845757510745626169673818"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000562084247470879735315853190082825344794087023602714253342730484399850968357"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000868342133308330051357320365697488900304098597969798168765758761035694322405"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000347580087379308589607631387726211870849365444198721499394707227756978102834"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000239732167823959290773335551055992800328912309750161986581372592222346479756"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000426821614422438385039700233078195697508737137615415589129724808488001094500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000376343496212373063319630027526057051194699346126249374743316989439186929308"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000204801796486955545541962476062112026383522552669629082548790846826338899265"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000000000291444251494672161342962713547400277611484048996443216117012112680095659149"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000000000000000215149840106709278896741979798565795657829474738608046886706233060495029891"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 1) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0177960892359059092368449533300753498910562300524119222277224610665566639113"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.523493989529503311622429023285005765138192489253997848188274804607937449633"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.300246216566683946242644511406502867819201371939240893015974691913454885808"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.52120199319725472696227412667597446499425167961832165707021344230176033177"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.13603274583679261300233776596233947213325327220186577281646114405893643737"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.724392352664214606992237586133777377079256948325029997000977246245080002233"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.388929770868824042863797693850769570596574559986024775356266372411178699540"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.154179232206718916893840432717207071358278896682953359728214136553325799462"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0346417257392303445249711911680413626748314405808671270003420334115731156886"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000565560712478204919273167124606530729984714749201859574061136268417222555091"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00181249770691727469711609530963691466508142540232948702137344478023631552627"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000588438376382341711328138138085170076834520467501917923206789175862767064823"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000584640605402568510997586714696849845579997815266362073215706625936265422267"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000105844593014498134844692670509893952845656642504556116202764900311740548871"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000166468037640819733915865521995838990879669585457089450510966868180317991073"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000665702118480401459239243655589860277773366781809294087365522507093749610972"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000413743126200483787623193128609853366545681088788845827525800995343215361362"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000207412032505394370932864660704575774018021101403985444914301425651830396364"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000255971644398897619761224049169452964847520797773015352526231064476414713088"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000124716745263065662018732610753074049301860833130953760676639739633614703632"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000821458651618354613000975781089942016395222632214628948691994907081952543308"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000541358205668964250840058676695497274874562173948269314129706627580306868477"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000128485207080436687070726868370112172350592202319644076709933531091773318283"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000189699318908704988950069910826502347264570849344128849517108385649026224807"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 2) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0934129724220382501349487645300486875234170850245453862186068741324556453346"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.953357331395321245741266856874997302595970338569125873978673981100995300480"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.42585978272484861991123956040990946486002448323913218605736734622206571009"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.63185993796807836831512574118361080962022886222644234566139901231163277968"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.336818591013582903249775631450042574391476183298908473845002503554184531336"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.296394587240899314100091240103956940350255747570510417673706841960334677926"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.493154941522463250789713957033016154711226757009451483204608291769388507365"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.502913696750504242256156558554921880910106950582744728599445382698153029596"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.336126999253822119479465098323173579081837929647816976396920165650335393282"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.148847761252488850986084377184215361968924151368645407707467187349749910163"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0371885435962923855115909993991585519975037535904089717996103864650078357255"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000677463558386659117669706791423999203996673498642825896754202338872153037212"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00434487021597667956865695331283701301527190336995514718937519883519367138275"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00143373662446881484405894523139422896093101823093949963457103829230616147393"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000803285640476068389549772156164639298617305382091989859099979787377361685082"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000602734424846845589803909611025184831851284747892368902634252735886854145822"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000115730739689488129340585879564187751711875533780907209280476231204851229122"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000203038141021073932718677763769332933580122614824827600175511631933693809212"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000773356655095724294210645023078737522223042928980510110980740523592990465707"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000215725560615500809261906811761440663890609571489717139261391990455696409353"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000245586666328544526882182912641255771532047054465213672340341827137743325608"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000284323589789160638880699636876075821856225650053527097527498265089761368022"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000800840047468220328165149036500044542829087947759522330193325204357891480071"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000000000236473591532019199312763596068830970062833585321537190947073847639519351315"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 3) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.396363069673686750280548809109341383558142899908658154252076031883543304792"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.238068683697433321429585844607770037608153029841989185082601544289511822219"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.64401864722743840792906444860573491613583063303684257865448916759790826776"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("9.71243595152007771944165862124698599498887535318579000953262482665972313795"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-10.10029232143527497511956582518178878569923447373646682398486184139257232320"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.44220464420971559730717830018078624764249539854892668261076269712038115208"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.93557502961232367730478899897300379802437925385537992860963683485606932435"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.13856358742765677259829229431312665523374959898394470745436500766939742620"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.77689274061969457654054279018031039397931349538073366568800222943389068691"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.891295625160220390726639633941018793327361578783273631114698203724211097982"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00471792734258069607298372270654369571845851651159485076238538324057163995930"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.255819262610292278082913762588973634598620071368606343876500343872602998914"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.152654376117555334468035681501318647194034115973737844538041071367284215030"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0378134940119027684268573286080453159469956130130132923110965287904780282715"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000121560168274539299345351509032174588648879441157601156968982724381225846230"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00224553423418000095025260272886136860879275402678218779366170715107150220625"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000469555837907319969170862177815720438165344404592060255271066086544874124922"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000141861348255063632226432936826347114087322044233208751170570608200310593872"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000464305587959345590293188512531458238827872871125055638342646962690953713219"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000178051762046205612595554830606976294440430913830610989139140135095046368211"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000303509999613044224553224713019229664330430223919168680848333863544196628625"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000365437421820854861941025978557451175694493997756433473102664593668311395766"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000198703923567812240879432784797155185222750333260578388946834495314448320449"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000000000117344234409057581035282894922526685306543990483992437311052020528871227897"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 4) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.29829892093148675837199950753098632139723149606803915083396902574449208029"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5.45541043360327965942803915313674612029372057019831640585125509023549800118"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("9.14659891488834710881029600683563338140354944919573004532523982762027640408"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.80871239536320715248084576368333258092782945770772294846327434563862485047"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("15.50082996950292219639972661063373929889290553615318208787250496285617222300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-33.61083916121800635387839817511480720783882205113114838947334986844676545110"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("55.09017907974305257429979612931043233074315377510785068179493707419179306920"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-60.82145202823324586976188912900763870195276458683421125895492211837656456610"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("42.02393025939949010806003192165586117752687379191173227214491131963706674670"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-11.42269030320996012044519422789839184208965590204144693325418569461244686450"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.67844966081573901856421942081827739733622487304317595154977214567794509597"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("13.19183180908504928777755197127911432617214990231201200609805185851541078220"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.21315521344594633555535356089362070473231847012846502887625287740895386140"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.83447526237344731188770747629269995995501816031751673943697214639743502746"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0601600495701990470578423349111841174877115258558613797357532347067021952039"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.174833101160455896617892939926978927097853960488370421237681663434954331091"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0411800837257458706544783101171615610022000261127525347354930832776549516518"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00141717935851889446824809565837085540248614139243332507385210260947445968142"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000555560350330981282462146005342011895702037823413086938195491412869816876266"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000301723456414363746673611598443020881465023496175523444306498854376889270505"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000524839933903751376247987543350808530106039891755176189436028565699403867555"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000965385307602574426453743325201391730573869326245570681673188712440757277785"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000722766970161280855990093183542473161153221858414301624738661674579313333974"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000000853612001904068385422684003534916785880458525794775900690850226714475517744"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 5) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.27591989601868802674501785402136946331923506081722246623851782517724077956"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-21.63177809906124242929618059834623299778169240498310197475751118910416098620"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("63.25489897169350129665198120436585141171650857792468724984618895395156006760"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-105.64003425325222575937530358981100910346806778811817416031589048365312600500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("102.06272350428550602794983637219493818640733053272677960258573782601532526300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-32.43801570590952546966804957405761294619856192253725299530721532824239057130"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-69.24480735372488476492726199088539370961841664995584500291147279197929753280"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("158.72530808311660773421056969103812590229014617453891622003568916003770686900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-230.87010121360094217924337915444738753118945778386926981134464016079483998200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("288.01642517309430130736747957321792288095742327983295887677253620052397656300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-293.56995408804215778949920569290304953535440565901256602829643467801366406600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("219.06562359302256197770038214491012243075469145162322027206744692760130121800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-106.11496744383573250143347007263440927813125065546390553880842822781245458600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("24.36128368581441161811089841236294040076426774635200083960668663240035562270"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.43835769181395654737492708557265278640240993742380862767423932221744414072"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.85838395915027243210674082732708450718320033028158945864987295932465128532"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.24315429771719465036074806222840734622901883367521779356833558313975863034"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0546856990741580491153518017356023641138609910294467327282571902327595261764"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0228245670871021915459486249711370338635367656247831656423034604880900103448"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00182589449768070240872485623697617929375041493178863912492773120527334148740"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000325042037685336262383912582434415986434896476262522511852445563487664732443"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000913502582370599560963475117189669272497546395420968001321763477890154121574"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000962624778879324987625830559274321622346182423692550529429764127390602244922"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000227354243242555606552075639763265819210262659858551528763926512978121086153"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 6) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.45444407372475315177467720169187517161433417770438745922665664020599409502"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-42.56603716393114257244373103682838987393735085098528587723704965223943476520"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("150.07103038891031818515743886532262871921427569033077113142523203102180848600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-321.43500940552269096601048445735807968772615638828686952229875945373392190300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("486.49285123198957691189838212046510878680843665543661626780343427251983580200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-595.11637851173395454633822179663347444510793729870901103899277136014019421800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("657.86125381518521180460485717096228323663875621461938629474339145210131286700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-668.83804725645011584987360192202731704144101270640504252184585661445041302700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("591.02274673989806775295905433087707064430763321360170996127414186474186931000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-443.28601860377678276957435305705753468882955594761345736716889808456981116800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("293.87433969841157445285988545192520160702855258407453598402313481311389546900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-171.68368626892283846885275113484356845529681519766755047035289228531315837000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("71.00249921006545724382096278062170090483913301428833620161533416167027278460"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.13488722851072940608795217399184622797681725247617241549338591142041688274"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-17.18288938944823526216285329531580736984384768713968863197342708566449903360"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("11.20228508169258542429354205503684083900272758550359041700286637526422591800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.95829620222196862348532178007222612141499084521609887716323655493346037655"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.156921481073662045953756041913257566237101060794292502890322509860387034380"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0721026247514735804121100566415299137462648885789052981712326861934660517398"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00907030670836707586832589336774695366594420064978445308615112498525335789807"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000161130895298934705154661229234656725370077261357478991394608849613865795613"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000713307751758044877495311912009992056522552469630503342586343211736962847133"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000106575703414569404305476724036545431177067024911660193372639981084780691080"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000503317323749389303719563737438740340206677439330596561000596089805746652424"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 7) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("7.32801237750156362483703729919996280695475478786922672432521671311254119834"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-61.58640131841635882165326632994086164711314616056846772845360126537901397590"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("227.42653376013215970605972000104796817858966318899264414158978818559392102100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-483.38351188460896438440811583095448851197970686725910387330605686657179355400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("658.62912269358369177986072599065937010545029800076900991882439695455748769400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-635.15071641906441010676927456327130280863307826701934274951357911827708743700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("525.04690066637079491947273558679727444098945204462362426522679969863610748800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-443.30745206683403362457477380798545670712488884939473921356975458618458544000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("300.17669704851406005255339306856972566391684656404302637816237332586479717400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-45.30421440165057702649803918277564533841222868064389570465229669564862985660"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-164.37688981728291058700366348503001862732516744094730683945089617887328966600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("222.44242861890885847681782922975570961504898766298360812690379798202763289600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-207.00658146172812966405444130677690797169650424372338218260727893033315417800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("185.71893129678116264900939787686677271662237302432116418506696464581702586100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-138.86918923719065745108647629486188361516972571236690249317122893128955088000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("69.50959361239118942856866391172010145985276234165251426115174332096603971880"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-19.04382546435533552706594655647836079674785133821952687854508408638604970290"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.20609133375256805296141503631395543465839083951690638291124156720969407294"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.669565610251110449459869170701094766316947883669190548464587151565621618122"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.123082251367001933022447492166384546932097984915934829679103087789786980169"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00217715502095119397820112791869347023513174444446995719621661268281187784180"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000164805973396089051063484507442794045079988504541072855801781243508086304395"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000346608500769363543505373359383397071519912407954254984582912708688659199768"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000327241391736611726060145576789575175299756010826303842659100203467561600702"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 8) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.74326753158999834056116812204650118954465060264390982835886577518486268101"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-49.99173337237481612516482468092913196192930769585684115716367234203820792960"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("192.30520833873417575305032330542133296821671316133381127103148089884031604300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-433.04663948928221093038951547041129446069313459043483444888804096093780007800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("650.29301559509696707391037593955338600499735080495817462222469008365651103900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-740.38817602946521524635652991694109244663464176809245792160120459662518415100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("757.93851884277973879231890685884938562543997902765972920915606890170773334500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-772.48924369491146375649339718563050251773647675318553766020712796863655952900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("734.59183179377170969929067292253934666701158992568437326815741556001094017400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-613.89505985905958667637158329225855337819338706324599738575255299428681055200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("472.33594493404419022069420012879298507928450919272191339092869436457326478600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-345.69897983393301885486688813740413735467129595468365631508601814464484933100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("226.26867671070805874604396626788385147483759975756729744364317414185036983100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-128.84432762208094815098432847559414298872221422065057311509033200520302342600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("67.72394160486503269545391021144817969495298865649547918029615797016751111400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-31.08044680580914965121251458755066430643179670788681275067771141961765865330"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("9.03921060432773819185233100601819798021655369701494303621450373894984472793"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.279500999538692156607881707491630467331656124884020994194580849950834108907"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.665902364239195393220279168618682723908283324628346793634526901627751383162"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.139613766717165065129603804344872559693994963696840183393921810240833710156"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00114270599575310816085071769400504056542580942289008729114676011902537797522"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000363195276838709741268790813501267488184675434306229955898556486054877483452"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000837182661399504778282565545392303504120991217340679683017724471409789826587"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000157946565437923846485744196675519158792805910875863717029040068663366791699"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 9) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.75046159171634829527163330112510862850171517204527775957907811808615973114"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-33.20841509838443403040955493092978227279440605831429576553858852822290831770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("128.25721684783507822791369935094396779663623788672457406601793500565400821300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-283.00542635229471097126751678584291828797372875915935845892698482535006432800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("398.45614171533524054366727180364229849289710682645378118885424811008467298600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-400.47860036082498196423508946011183381211802981566841571520311399197149103900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("360.89316566379728536083135647493301259091592313871719238427499436437024359700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-360.36716234208593176728211543795346738863581300534318197607331333071816329900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("345.18447441614411073209118238319574005939847247957730049229326256329205638300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-265.34611221251483388928468384525918631697582076506472432506352501057803541200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("178.77226842348210140340813061313731570411151037624108176819522656335485861200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-126.26215183796407397228250290324344411107479423589079138412164102720512263500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("82.41567612620818870658967871867767992001718408506613309043264486867844619890"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-40.50938566509796337170834199812377119587502364115881243103048938109185750340"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("16.71756950579390837676267330467410166297326502202781368693672667419429720820"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.39864795075319033452851083640208460723103521341161070032778771352463446094"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.95408260511172224329226832456435155937649818121300834001919283900042220991"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.690229161332348184845535892744845183908860830917068365378586781073665858011"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.655353589184885598246818014752831975001293106883587971496754554959033929107"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.143780737452876767968123736205746816488614800208120534936850150005468283836"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00303543758366473343622443033949066654294389600319219464305397559642637833680"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000777458265060317434483464181432621410549249758909909318620156609272380996932"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000151017565574994282254648106028992857730337718860666328360706404021863696656"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000568866357531465656815014550479471644088340548161842850968659319933134867646"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 10) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.86635692686814334701754512957417350216062515159895162052764097113842043881"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-16.66568660094765155284710426501256914017192557788488990117955606509357986260"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("63.97804678187877577341574018618490150437681519853311500630408017375912199010"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-136.23190198244598023711707959187969385344039691028406627990988068537298511000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("173.59631221712522935710881272085756101498061308640801488113337865649201321400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-138.94953641114748367854206140337482846024919723682523303085604297244337196500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("92.98130285529193057335744641381945290112275119999668355136002874352650176220"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-95.66074017444953262397108875695549785804937842210406658962204154607043381990"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("100.74835406297538158748165104775636864067153061989180522203699894495867559400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-60.63130268637294081465002015983185171976527925057524138307520452453647480510"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("18.24956398577073820812706593292482832715236920720613106450102860436965089250"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-8.54732021029040581858802778196927000562449466895889987096814021723737609364"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.78696610600480427243790366050970458256425167093884818282352698386437907349"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.83943109951896060414630018445272105375896265663133246875005081887041646399"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-11.04550750770862050142551027487003756867181933391324257411989886446115036200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.88913300130972012620159069598928481029978149700887106696332707309836414794"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.99825731620098174291722686239189690428111675971623793296035204832239878614"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.00376174701501382150890393381234413552775178257039864145400674669724791199"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.58055114117211937700150897909355450299408918929453114571326586270053152435"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.400173290528033474046780700771547590750735363709672842945384353539651951125"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0241247023629214784889949418794949849850588027303632529305620350773009871100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00448583771765557425940953481033336026071599781591537346531375096056306017530"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000124871538203663846064127929077357912223820600720172540637500972263270210398"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000937574188857368553262323255933606233354879076874674275186450020536917162031"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 11) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.377278790797028406495802049657083663562322361271624572079656683482814478381"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.38307717994363961647269729038870588758939994602123056911758390829221597548"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("13.11518829717770243316037165549177793856194221161693344499682894614897577190"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-28.57377091700247032555582008243751850926614781859679891489888632231161474300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("38.42252911331146019070574663175356660452387955730227078383681460893481557030"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-34.66266016064986281759949034365429955214971534877540614552601700849583120980"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("26.97406640625859867160203071971832599019438490014915496366645506277688896980"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-26.21946455304798864871161101760021771880775045074096541060302606518533350730"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("26.35290308895353879370155511099855779382824241176826323168027129587570497550"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-20.52160249382001334719301784362115987987417964675011905409270410893726823490"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("14.19746165882069082480150485765422363795342078508016178125626500064575627140"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-11.13286484381245965677943198830588460860332272909854856957249726091446789600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.17588527972006301113855143068583531281419193834728913969920542381362453688"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.81287628036717816955676920569706546198654894542238231746562519451899699153"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.79404288335191180481579867581197397188129392455615189049532559340029697375"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.69721935207211848956351510550979925531938115005327856369556578995039602531"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.823713514158776098143914270378737144802711120108114847337079673523569107449"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.335063019316185774400946900047809387504331444599538017269859124873837022194"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.149151743150318837631159229932006915696347222177619661105078433909566955498"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0488658930534999511496940888639373453545430453545029982576926747686967632991"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00413351950396409421167019759007987626638864156006830612512440429134389517261"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00111968733549906685340740936899343820107158321331505760751334075276362206400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000927561883079690107640228293463474861573105973385043495546011950474050815337"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000138353046393774419706318300470822604006784632689512055491879584523531143047"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 12) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0485510900239990436421204389454387673417811678462962540757143566128579592770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.436270800634297968322345080087680826208441319415670872030224777690078461556"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.68248974767722772758483160675785114053064764804002514623394170463789590172"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.59058586609376583771926574429375533672584236400562126859511283907434445711"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.56322994124539027457225861351587674553390566017608457671928325936265991655"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.58373440747749241237223725147688884192263700323730018471801896054684688057"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.24866726732552133278146064153483046293389221299882995399864011134597001733"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.22587445942297775995811432335154708339509627741904345621048251573818545409"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.46615704775868702834863652085534769700638634288067530551348825246469149621"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.76584597268750597380515213373501064800094868705200411926589180388549588359"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.997419618978951767654107468235932428974722705691044731477454908009925099723"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.824734821626728470682970936709275659502024225512330108668711202634188766674"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.664517113712924681701113756939420311843390054559860571221578562221833419569"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.335428796184635221533296732070577988586954631509663722390327691441647623334"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.160948630264969492724365334557199225341872449473537373932195593392097150334"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.114655797627677055876779744868793614912947551394818530771503539697052078243"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0572231912176004958885591389510844893402088690448910703952553137622920787942"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0161932279203405965225240954258609535698781894809026667589644820730338725774"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00703484727602471596997669396790315101109040223481142577918954913506000676361"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00331142872730769846357537103134640651616087940178035673586298619579639917832"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000243081165958578425715014946837734369665794705531210842489368910237101227750"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000157806011543052252390221263353602504629816751263280846430328831365578539218"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000379309065442971274677051284817497527219849546159473806845519248661436372460"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000111654147665765272669074902224159897974782540201524920545177291846727682138"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+        }
     }
     if constexpr (p == 14) {
         if constexpr (std::is_same_v<Real, float>) {
             if constexpr (order == 0) {
-                return {0x0p+0f, 0x1.2e3c0cp-10f, 0x1.d73cdcp-4f, 0x1.980f08p-1f, 0x1.0b8da8p-2f, -0x1.381b88p-2f, 0x1.a64054p-3f, -0x1.be6cb2p-4f, 0x1.5369f4p-5f, -0x1.e553cp-8f, -0x1.5b9738p-9f, 0x1.3ad93ep-9f, -0x1.6c8658p-11f, 0x1.421438p-16f, 0x1.359cb6p-15f, -0x1.16b1cep-18f, -0x1.1e4702p-19f, 0x1.16b7d8p-21f, -0x1.2a9018p-27f, -0x1.e6603ap-29f, 0x1.ad635ap-33f, -0x1.0b7166p-37f, -0x1.2dcc8ep-43f, 0x1.994c74p-50f, 0x1.d3e7dcp-60f, -0x1.ad34cp-72f, 0x1.c6fd0cp-94f, -0x0p+0f};
+                return {0x0p+0f, 0x1.2e3c0cp-10f, 0x1.d73cdcp-4f, 0x1.980f08p-1f, 0x1.0b8da8p-2f, -0x1.381b88p-2f, 0x1.a64054p-3f, -0x1.be6cb2p-4f, 0x1.5369f4p-5f, -0x1.e553cp-8f, -0x1.5b9738p-9f, 0x1.3ad93ep-9f, -0x1.6c8658p-11f, 0x1.421438p-16f, 0x1.359cb6p-15f, -0x1.16b1cep-18f, -0x1.1e4702p-19f, 0x1.16b7d8p-21f, -0x1.2a9018p-27f, -0x1.e6603ap-29f, 0x1.ad635ap-33f, -0x1.0b7166p-37f, -0x1.2dcc8ep-43f, 0x1.994c74p-50f, 0x1.d3e7dcp-60f, -0x1.ad34cp-72f, 0x1.c6fd0cp-94f, 0x0p+0f};
             }
             if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.ffe6a8p-8f, 0x1.687896p-2f, 0x1.4f6222p-1f, -0x1.9d7a5p+0f, 0x1.ee1a72p-1f, -0x1.3a4c3ep-1f, 0x1.a5124ep-2f, -0x1.fd4714p-3f, 0x1.efeb84p-4f, -0x1.695e5ep-5f, 0x1.73caep-7f, -0x1.fa774ap-10f, 0x1.13b07ep-13f, 0x1.7cb11cp-14f, -0x1.d2ccp-15f, 0x1.74388cp-17f, 0x1.21ff8ap-21f, -0x1.156308p-22f, -0x1.19b91cp-25f, 0x1.f7d83ep-31f, 0x1.509062p-34f, -0x1.405684p-40f, 0x1.6ac07ap-46f, -0x1.9a49fp-55f, -0x1.88bc66p-67f, 0x1.a0541ep-88f, 0x0p+0f};
+                return {0x0p+0f, 0x1.ffe6a8p-8f, 0x1.687896p-2f, 0x1.4f6222p-1f, -0x1.9d7a5p+0f, 0x1.ee1a72p-1f, -0x1.3a4c3ep-1f, 0x1.a5124ep-2f, -0x1.fd4714p-3f, 0x1.efeb84p-4f, -0x1.695e5ep-5f, 0x1.73caep-7f, -0x1.fa774ap-10f, 0x1.13b07ep-13f, 0x1.7cb11cp-14f, -0x1.d2ccp-15f, 0x1.74388cp-17f, 0x1.21ff8ap-21f, -0x1.156308p-22f, -0x1.19b91cp-25f, 0x1.f7d83ep-31f, 0x1.509062p-34f, -0x1.405684p-40f, 0x1.6ac07ap-46f, -0x1.9a49fp-55f, -0x1.88bc66p-67f, 0x1.a0541ep-88f, -0x0p+0f};
             }
             if constexpr (order == 2) {
-                return {0x0p+0f, 0x1.70e38ep-5f, 0x1.98429p-1f, -0x1.5a23aep+0f, -0x1.ca3a86p-2f, 0x1.f2912p+0f, -0x1.902df6p+0f, 0x1.6e5d8ap-1f, -0x1.7cd74ap-5f, -0x1.cb5138p-3f, 0x1.8970fep-3f, -0x1.2e3ba4p-4f, 0x1.a43728p-9f, 0x1.5d8afap-7f, -0x1.3f213ap-8f, 0x1.438df6p-11f, 0x1.92aaccp-13f, -0x1.4a2a2cp-14f, 0x1.061494p-17f, 0x1.1c615p-21f, -0x1.fed404p-24f, 0x1.9900fap-29f, 0x1.4b71c6p-33f, -0x1.f4e21p-40f, -0x1.ae7642p-50f, 0x1.0753e4p-59f, -0x1.1725d8p-79f, 0x0p+0f};
+                return {0x0p+0f, 0x1.70e38ep-5f, 0x1.98429p-1f, -0x1.5a23aep+0f, -0x1.ca3a86p-2f, 0x1.f2912p+0f, -0x1.902df6p+0f, 0x1.6e5d8ap-1f, -0x1.7cd74ap-5f, -0x1.cb5138p-3f, 0x1.8970fep-3f, -0x1.2e3ba4p-4f, 0x1.a43728p-9f, 0x1.5d8afap-7f, -0x1.3f213ap-8f, 0x1.438df6p-11f, 0x1.92aaccp-13f, -0x1.4a2a2cp-14f, 0x1.061494p-17f, 0x1.1c615p-21f, -0x1.fed404p-24f, 0x1.9900fap-29f, 0x1.4b71c6p-33f, -0x1.f4e21p-40f, -0x1.ae7642p-50f, 0x1.0753e4p-59f, -0x1.1725d8p-79f, -0x0p+0f};
             }
             if constexpr (order == 3) {
-                return {0x0p+0f, 0x1.b64064p-3f, 0x1.b94954p-1f, -0x1.49bc84p+2f, 0x1.255158p+3f, -0x1.254592p+3f, 0x1.bfdd02p+2f, -0x1.258cbp+2f, 0x1.244b68p+1f, -0x1.76e9c8p-1f, 0x1.2db90ep-3f, -0x1.adc00ap-4f, 0x1.077b02p-3f, -0x1.4e1bd4p-4f, 0x1.a8b172p-6f, -0x1.1b67a8p-9f, -0x1.5aa222p-10f, 0x1.0c296ep-11f, -0x1.315112p-14f, -0x1.aa34a6p-23f, 0x1.718ac2p-20f, -0x1.4ed202p-25f, -0x1.6a2c3ep-29f, 0x1.03cb1cp-35f, 0x1.d2ce74p-46f, -0x1.110d8p-54f, 0x1.2175bep-73f, -0x0p+0f};
+                return {0x0p+0f, 0x1.b64064p-3f, 0x1.b94954p-1f, -0x1.49bc84p+2f, 0x1.255158p+3f, -0x1.254592p+3f, 0x1.bfdd02p+2f, -0x1.258cbp+2f, 0x1.244b68p+1f, -0x1.76e9c8p-1f, 0x1.2db90ep-3f, -0x1.adc00ap-4f, 0x1.077b02p-3f, -0x1.4e1bd4p-4f, 0x1.a8b172p-6f, -0x1.1b67a8p-9f, -0x1.5aa222p-10f, 0x1.0c296ep-11f, -0x1.315112p-14f, -0x1.aa34a6p-23f, 0x1.718ac2p-20f, -0x1.4ed202p-25f, -0x1.6a2c3ep-29f, 0x1.03cb1cp-35f, 0x1.d2ce74p-46f, -0x1.110d8p-54f, 0x1.2175bep-73f, 0x0p+0f};
             }
             if constexpr (order == 4) {
                 return {0x0p+0f, 0x1.9bd3bcp-1f, -0x1.218b2p+1f, -0x1.8f073ep-2f, 0x1.10368cp+3f, -0x1.6e5fdp+3f, -0x1.fee6b2p-2f, 0x1.5dae0cp+4f, -0x1.253938p+5f, 0x1.0846cap+5f, -0x1.d3379cp+3f, -0x1.bc1cbep+1f, 0x1.49e86ep+3f, -0x1.e4adep+2f, 0x1.651f3ap+1f, -0x1.14e32ep-2f, -0x1.c20b1ep-3f, 0x1.9dc736p-4f, -0x1.dbb9ecp-7f, -0x1.c7f5c2p-11f, 0x1.a5fc86p-12f, -0x1.07f65ep-16f, -0x1.0e379p-20f, 0x1.69bc58p-26f, 0x1.872aa2p-36f, -0x1.7b8496p-44f, 0x1.92548cp-62f, -0x0p+0f};
@@ -1271,13 +1565,13 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0f, 0x1.f579b2p+2f, -0x1.13b9ccp+6f, 0x1.0d0d04p+8f, -0x1.309a86p+9f, 0x1.b8e262p+9f, -0x1.b08b28p+9f, 0x1.3c7d2cp+9f, -0x1.7e7dfp+8f, 0x1.9c8804p+5f, 0x1.dc1752p+8f, -0x1.e54a04p+9f, 0x1.1a42e2p+10f, -0x1.f903f4p+9f, 0x1.9d8dbap+9f, -0x1.34174p+9f, 0x1.64eb3cp+8f, -0x1.0b0c44p+7f, 0x1.5f0a54p+4f, 0x1.d8f6bap+1f, -0x1.1c758ap+1f, 0x1.f38ac2p-3f, 0x1.f827p-7f, -0x1.130614p-10f, -0x1.2dc514p-19f, 0x1.1d494ap-25f, -0x1.2e8464p-40f, 0x0p+0f};
             }
             if constexpr (order == 8) {
-                return {0x0p+0f, 0x1.e32cc2p+2f, -0x1.1692cap+6f, 0x1.1fa09cp+8f, -0x1.615e68p+9f, 0x1.265c8cp+10f, -0x1.7569eep+10f, 0x1.9e96bep+10f, -0x1.bbbe16p+10f, 0x1.be0802p+10f, -0x1.8f099cp+10f, 0x1.43b838p+10f, -0x1.ee6ad6p+9f, 0x1.58d562p+9f, -0x1.a3b282p+8f, 0x1.c79d62p+7f, -0x1.bc78ccp+6f, 0x1.418e36p+5f, -0x1.3abf36p+2f, -0x1.ad7bb4p+1f, 0x1.a65502p+0f, -0x1.affdcep-3f, -0x1.8341cep-7f, 0x1.b5571p-10f, 0x1.e32174p-19f, -0x1.c53c14p-24f, 0x1.e0c27p-38f, 0x0p+0f};
+                return {0x0p+0f, 0x1.e32cc2p+2f, -0x1.1692cap+6f, 0x1.1fa09cp+8f, -0x1.615e68p+9f, 0x1.265c8cp+10f, -0x1.7569eep+10f, 0x1.9e96bep+10f, -0x1.bbbe16p+10f, 0x1.be0802p+10f, -0x1.8f099cp+10f, 0x1.43b838p+10f, -0x1.ee6ad6p+9f, 0x1.58d562p+9f, -0x1.a3b282p+8f, 0x1.c79d62p+7f, -0x1.bc78ccp+6f, 0x1.418e36p+5f, -0x1.3abf36p+2f, -0x1.ad7bb4p+1f, 0x1.a65502p+0f, -0x1.affdcep-3f, -0x1.8341cep-7f, 0x1.b5571p-10f, 0x1.e32174p-19f, -0x1.c53c14p-24f, 0x1.e0c27p-38f, -0x0p+0f};
             }
             if constexpr (order == 9) {
                 return {0x0p+0f, 0x1.8d1f8ap+2f, -0x1.d4881ap+5f, 0x1.e86d42p+7f, -0x1.280028p+9f, 0x1.d3eb6p+9f, -0x1.0b82a6p+10f, 0x1.07ceap+10f, -0x1.0d7822p+10f, 0x1.0df61ep+10f, -0x1.c6893ap+9f, 0x1.45ac9ep+9f, -0x1.c9d686p+8f, 0x1.35c4c4p+8f, -0x1.4a58bep+7f, 0x1.01755ap+6f, -0x1.5d1ba8p+4f, 0x1.dadd4ap+1f, 0x1.87b02p+2f, -0x1.9ab15ep+2f, 0x1.46cd6ap+1f, -0x1.8955d8p-2f, -0x1.85245p-7f, 0x1.6f86d4p-8f, 0x1.1b4e3cp-16f, -0x1.7914d8p-21f, 0x1.903b4cp-34f, -0x0p+0f};
             }
             if constexpr (order == 10) {
-                return {0x0p+0f, 0x1.041a0ap+1f, -0x1.3658b6p+4f, 0x1.5194bp+6f, -0x1.c3df82p+7f, 0x1.ad183ep+8f, -0x1.3d9c78p+9f, 0x1.852da4p+9f, -0x1.9cca18p+9f, 0x1.9a6efap+9f, -0x1.a300c2p+9f, 0x1.a73548p+9f, -0x1.7a384cp+9f, 0x1.2afd88p+9f, -0x1.d0f63ap+8f, 0x1.6384c4p+8f, -0x1.d6c26ap+7f, 0x1.089826p+7f, -0x1.1f7e84p+6f, 0x1.2a5702p+5f, -0x1.c18aa4p+3f, 0x1.4dc138p+1f, 0x1.bd5ac2p-5f, -0x1.1aa942p-4f, -0x1.97678cp-14f, 0x1.25b3fcp-16f, -0x1.381ffp-28f, -0x0p+0f};
+                return {0x0p+0f, 0x1.041a0ap+1f, -0x1.3658b6p+4f, 0x1.5194bp+6f, -0x1.c3df82p+7f, 0x1.ad183ep+8f, -0x1.3d9c78p+9f, 0x1.852da4p+9f, -0x1.9cca18p+9f, 0x1.9a6efap+9f, -0x1.a300c2p+9f, 0x1.a73548p+9f, -0x1.7a384cp+9f, 0x1.2afd88p+9f, -0x1.d0f63ap+8f, 0x1.6384c4p+8f, -0x1.d6c26ap+7f, 0x1.089826p+7f, -0x1.1f7e84p+6f, 0x1.2a5702p+5f, -0x1.c18aa4p+3f, 0x1.4dc138p+1f, 0x1.bd5ac2p-5f, -0x1.1aa942p-4f, -0x1.97678cp-14f, 0x1.25b3fcp-16f, -0x1.381ffp-28f, 0x0p+0f};
             }
             if constexpr (order == 11) {
                 return {0x0p+0f, 0x1.456a1ep+0f, -0x1.86731ep+3f, 0x1.99ddaep+5f, -0x1.ebccc2p+6f, 0x1.74f85ep+7f, -0x1.842622p+7f, 0x1.4fbcc2p+7f, -0x1.4776cp+7f, 0x1.573bfp+7f, -0x1.2b0c28p+7f, 0x1.bb5bcap+6f, -0x1.580802p+6f, 0x1.0c1df4p+6f, -0x1.5dea02p+5f, 0x1.997fcap+4f, -0x1.f5c414p+3f, 0x1.1578f4p+3f, -0x1.e11a4cp+1f, 0x1.8c2f5ap+0f, -0x1.42cddep-1f, 0x1.1b3752p-3f, 0x1.61bca4p-7f, -0x1.eeca78p-8f, 0x1.427b38p-14f, 0x1.1c6c3p-18f, -0x1.2f0566p-29f, 0x0p+0f};
@@ -1291,16 +1585,16 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         }
         if constexpr (std::is_same_v<Real, double>) {
             if constexpr (order == 0) {
-                return {0x0p+0, 0x1.2e3c0bb3f3ad5p-10, 0x1.d73cdc4f17148p-4, 0x1.980f074dbd462p-1, 0x1.0b8da7807c274p-2, -0x1.381b88314120bp-2, 0x1.a64053bd4da41p-3, -0x1.be6cb26620f84p-4, 0x1.5369f32b472a9p-5, -0x1.e553bfb83c482p-8, -0x1.5b97376b07916p-9, 0x1.3ad93e070eb7ap-9, -0x1.6c8658d1b206ep-11, 0x1.421437e7b839dp-16, 0x1.359cb55b7d336p-15, -0x1.16b1cde08937ep-18, -0x1.1e470298289aep-19, 0x1.16b7d7c52ecb7p-21, -0x1.2a9017a9058edp-27, -0x1.e6603a12c622p-29, 0x1.ad635a5532adap-33, -0x1.0b7166f3d598p-37, -0x1.2dcc8d3c8b0cfp-43, 0x1.994c7452dcd31p-50, 0x1.d3e7db27a70eep-60, -0x1.ad34c0383fa64p-72, 0x1.c6fd0b1a8d6a3p-94, -0x0p+0};
+                return {0x0p+0, 0x1.2e3c0bb3f3ad5p-10, 0x1.d73cdc4f17148p-4, 0x1.980f074dbd462p-1, 0x1.0b8da7807c274p-2, -0x1.381b88314120bp-2, 0x1.a64053bd4da41p-3, -0x1.be6cb26620f84p-4, 0x1.5369f32b472a9p-5, -0x1.e553bfb83c482p-8, -0x1.5b97376b07916p-9, 0x1.3ad93e070eb7ap-9, -0x1.6c8658d1b206ep-11, 0x1.421437e7b839dp-16, 0x1.359cb55b7d336p-15, -0x1.16b1cde08937ep-18, -0x1.1e470298289aep-19, 0x1.16b7d7c52ecb7p-21, -0x1.2a9017a9058edp-27, -0x1.e6603a12c622p-29, 0x1.ad635a5532adap-33, -0x1.0b7166f3d598p-37, -0x1.2dcc8d3c8b0cfp-43, 0x1.994c7452dcd31p-50, 0x1.d3e7db27a70eep-60, -0x1.ad34c0383fa64p-72, 0x1.c6fd0b1a8d6a3p-94, 0x0p+0};
             }
             if constexpr (order == 1) {
-                return {0x0p+0, 0x1.ffe6a833f41d2p-8, 0x1.6878956519ce3p-2, 0x1.4f62227264623p-1, -0x1.9d7a4f00f9dcp+0, 0x1.ee1a7236f71e4p-1, -0x1.3a4c3d150c11ep-1, 0x1.a5124e1ab47a9p-2, -0x1.fd47140509eb3p-3, 0x1.efeb8355fd2f8p-4, -0x1.695e5e5e49cf8p-5, 0x1.73cae05387f64p-7, -0x1.fa774911ba2d4p-10, 0x1.13b07ddddb3b8p-13, 0x1.7cb11c0b4280bp-14, -0x1.d2cbfff6e2a58p-15, 0x1.74388c9fd28e7p-17, 0x1.21ff895bfb5f3p-21, -0x1.156307b5c128cp-22, -0x1.19b91bff8bef5p-25, 0x1.f7d83e4d41c77p-31, 0x1.5090626b206a4p-34, -0x1.405683426ad01p-40, 0x1.6ac079eed130ep-46, -0x1.9a49f0637a3b6p-55, -0x1.88bc66cc087f2p-67, 0x1.a0541eb1bdcebp-88, 0x0p+0};
+                return {0x0p+0, 0x1.ffe6a833f41d2p-8, 0x1.6878956519ce3p-2, 0x1.4f62227264623p-1, -0x1.9d7a4f00f9dcp+0, 0x1.ee1a7236f71e4p-1, -0x1.3a4c3d150c11ep-1, 0x1.a5124e1ab47a9p-2, -0x1.fd47140509eb3p-3, 0x1.efeb8355fd2f8p-4, -0x1.695e5e5e49cf8p-5, 0x1.73cae05387f64p-7, -0x1.fa774911ba2d4p-10, 0x1.13b07ddddb3b8p-13, 0x1.7cb11c0b4280bp-14, -0x1.d2cbfff6e2a58p-15, 0x1.74388c9fd28e7p-17, 0x1.21ff895bfb5f3p-21, -0x1.156307b5c128cp-22, -0x1.19b91bff8bef5p-25, 0x1.f7d83e4d41c77p-31, 0x1.5090626b206a4p-34, -0x1.405683426ad01p-40, 0x1.6ac079eed130ep-46, -0x1.9a49f0637a3b6p-55, -0x1.88bc66cc087f2p-67, 0x1.a0541eb1bdcebp-88, -0x0p+0};
             }
             if constexpr (order == 2) {
-                return {0x0p+0, 0x1.70e38d13c6dcdp-5, 0x1.98429094e12d2p-1, -0x1.5a23aee5cfcf3p+0, -0x1.ca3a85e30ebf6p-2, 0x1.f2911f6caea6bp+0, -0x1.902df5acb9856p+0, 0x1.6e5d8a32fe3aep-1, -0x1.7cd7499a11b88p-5, -0x1.cb51389df1437p-3, 0x1.8970fdea96db5p-3, -0x1.2e3ba43116d4fp-4, 0x1.a437288ed51abp-9, 0x1.5d8afaeb5ec2ap-7, -0x1.3f213a25a4c3ap-8, 0x1.438df66495fedp-11, 0x1.92aacb344e1abp-13, -0x1.4a2a2b6937dcap-14, 0x1.061494c076ea5p-17, 0x1.1c61500cd5ff6p-21, -0x1.fed404b96c72ep-24, 0x1.9900fa8d5cb81p-29, 0x1.4b71c6cbb7be3p-33, -0x1.f4e20f23251aap-40, -0x1.ae764159a5bb6p-50, 0x1.0753e4c918ed7p-59, -0x1.1725d8c4676c4p-79, 0x0p+0};
+                return {0x0p+0, 0x1.70e38d13c6dcdp-5, 0x1.98429094e12d2p-1, -0x1.5a23aee5cfcf3p+0, -0x1.ca3a85e30ebf6p-2, 0x1.f2911f6caea6bp+0, -0x1.902df5acb9856p+0, 0x1.6e5d8a32fe3aep-1, -0x1.7cd7499a11b88p-5, -0x1.cb51389df1437p-3, 0x1.8970fdea96db5p-3, -0x1.2e3ba43116d4fp-4, 0x1.a437288ed51abp-9, 0x1.5d8afaeb5ec2ap-7, -0x1.3f213a25a4c3ap-8, 0x1.438df66495fedp-11, 0x1.92aacb344e1abp-13, -0x1.4a2a2b6937dcap-14, 0x1.061494c076ea5p-17, 0x1.1c61500cd5ff6p-21, -0x1.fed404b96c72ep-24, 0x1.9900fa8d5cb81p-29, 0x1.4b71c6cbb7be3p-33, -0x1.f4e20f23251aap-40, -0x1.ae764159a5bb6p-50, 0x1.0753e4c918ed7p-59, -0x1.1725d8c4676c4p-79, -0x0p+0};
             }
             if constexpr (order == 3) {
-                return {0x0p+0, 0x1.b6406454732d5p-3, 0x1.b949541f458cep-1, -0x1.49bc84198d8efp+2, 0x1.255157167a553p+3, -0x1.254591e8b6e07p+3, 0x1.bfdd01aa9e691p+2, -0x1.258cb0e12f408p+2, 0x1.244b687910818p+1, -0x1.76e9c86768fd8p-1, 0x1.2db90e1b7e224p-3, -0x1.adc00aab7f786p-4, 0x1.077b01cdc29aap-3, -0x1.4e1bd3d7c8107p-4, 0x1.a8b1719f7696ap-6, -0x1.1b67a8fdd5d39p-9, -0x1.5aa2219e8b072p-10, 0x1.0c296ebe05b6fp-11, -0x1.315112d6e2649p-14, -0x1.aa34a64782e4p-23, 0x1.718ac2125512ep-20, -0x1.4ed202350e6d4p-25, -0x1.6a2c3e7b115c9p-29, 0x1.03cb1bd946e2ep-35, 0x1.d2ce73e99c294p-46, -0x1.110d7f1b0bfcp-54, 0x1.2175be08d4af4p-73, -0x0p+0};
+                return {0x0p+0, 0x1.b6406454732d5p-3, 0x1.b949541f458cep-1, -0x1.49bc84198d8efp+2, 0x1.255157167a553p+3, -0x1.254591e8b6e07p+3, 0x1.bfdd01aa9e691p+2, -0x1.258cb0e12f408p+2, 0x1.244b687910818p+1, -0x1.76e9c86768fd8p-1, 0x1.2db90e1b7e224p-3, -0x1.adc00aab7f786p-4, 0x1.077b01cdc29aap-3, -0x1.4e1bd3d7c8107p-4, 0x1.a8b1719f7696ap-6, -0x1.1b67a8fdd5d39p-9, -0x1.5aa2219e8b072p-10, 0x1.0c296ebe05b6fp-11, -0x1.315112d6e2649p-14, -0x1.aa34a64782e4p-23, 0x1.718ac2125512ep-20, -0x1.4ed202350e6d4p-25, -0x1.6a2c3e7b115c9p-29, 0x1.03cb1bd946e2ep-35, 0x1.d2ce73e99c294p-46, -0x1.110d7f1b0bfcp-54, 0x1.2175be08d4af4p-73, 0x0p+0};
             }
             if constexpr (order == 4) {
                 return {0x0p+0, 0x1.9bd3bc2473961p-1, -0x1.218b20c923a73p+1, -0x1.8f073ee248543p-2, 0x1.10368c3ad14ecp+3, -0x1.6e5fd027a16b4p+3, -0x1.fee6b19288529p-2, 0x1.5dae0c64ec101p+4, -0x1.253938fa65f9dp+5, 0x1.0846ca351ee33p+5, -0x1.d3379cfd6d393p+3, -0x1.bc1cbd5de053bp+1, 0x1.49e86d68d4cf9p+3, -0x1.e4ade08c4a6c3p+2, 0x1.651f390634957p+1, -0x1.14e32e1f9b6bbp-2, -0x1.c20b1d287136bp-3, 0x1.9dc73570ee73fp-4, -0x1.dbb9ebdd9c09ep-7, -0x1.c7f5c1ec60f69p-11, 0x1.a5fc856e52fadp-12, -0x1.07f65daa0049bp-16, -0x1.0e378f07aff0ap-20, 0x1.69bc58d5ec0cdp-26, 0x1.872aa1bcf3687p-36, -0x1.7b84969608017p-44, 0x1.92548cc9b5b72p-62, -0x0p+0};
@@ -1315,13 +1609,13 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0, 0x1.f579b17074e37p+2, -0x1.13b9cbe766167p+6, 0x1.0d0d0432bec13p+8, -0x1.309a86e68bfeap+9, 0x1.b8e26231ea03fp+9, -0x1.b08b284517ec4p+9, 0x1.3c7d2b2624502p+9, -0x1.7e7def0dd6c18p+8, 0x1.9c880448390e6p+5, 0x1.dc1752cc2f2f8p+8, -0x1.e54a03fbbc2fap+9, 0x1.1a42e1dae569p+10, -0x1.f903f4a18c30ep+9, 0x1.9d8db91908386p+9, -0x1.34173ffb143e2p+9, 0x1.64eb3c27db565p+8, -0x1.0b0c43171fee6p+7, 0x1.5f0a5375d11c7p+4, 0x1.d8f6b9f1522f3p+1, -0x1.1c75896d6d599p+1, 0x1.f38ac1a749dafp-3, 0x1.f82700b4dc727p-7, -0x1.1306135d4672fp-10, -0x1.2dc514d699914p-19, 0x1.1d494ae1d331fp-25, -0x1.2e8464bcec8d4p-40, 0x0p+0};
             }
             if constexpr (order == 8) {
-                return {0x0p+0, 0x1.e32cc25ea4da5p+2, -0x1.1692ca6458eaap+6, 0x1.1fa09c1316dfbp+8, -0x1.615e67f0c1ccdp+9, 0x1.265c8c1b4b1aap+10, -0x1.7569ed1c8210dp+10, 0x1.9e96bde5063d4p+10, -0x1.bbbe167a38d63p+10, 0x1.be080201e737dp+10, -0x1.8f099bdabb219p+10, 0x1.43b83815e15a6p+10, -0x1.ee6ad68b3bda5p+9, 0x1.58d561cb84d26p+9, -0x1.a3b282a8407a3p+8, 0x1.c79d620ffafcp+7, -0x1.bc78cb9447aa1p+6, 0x1.418e35902e32dp+5, -0x1.3abf360acc2f7p+2, -0x1.ad7bb3867b3c3p+1, 0x1.a655024ebf2fdp+0, -0x1.affdcd4718ba8p-3, -0x1.8341cd6c6b0aap-7, 0x1.b55710d3ebf55p-10, 0x1.e321738ab1448p-19, -0x1.c53c1373c8858p-24, 0x1.e0c270acb15c6p-38, 0x0p+0};
+                return {0x0p+0, 0x1.e32cc25ea4da5p+2, -0x1.1692ca6458eaap+6, 0x1.1fa09c1316dfbp+8, -0x1.615e67f0c1ccdp+9, 0x1.265c8c1b4b1aap+10, -0x1.7569ed1c8210dp+10, 0x1.9e96bde5063d4p+10, -0x1.bbbe167a38d63p+10, 0x1.be080201e737dp+10, -0x1.8f099bdabb219p+10, 0x1.43b83815e15a6p+10, -0x1.ee6ad68b3bda5p+9, 0x1.58d561cb84d26p+9, -0x1.a3b282a8407a3p+8, 0x1.c79d620ffafcp+7, -0x1.bc78cb9447aa1p+6, 0x1.418e35902e32dp+5, -0x1.3abf360acc2f7p+2, -0x1.ad7bb3867b3c3p+1, 0x1.a655024ebf2fdp+0, -0x1.affdcd4718ba8p-3, -0x1.8341cd6c6b0aap-7, 0x1.b55710d3ebf55p-10, 0x1.e321738ab1448p-19, -0x1.c53c1373c8858p-24, 0x1.e0c270acb15c6p-38, -0x0p+0};
             }
             if constexpr (order == 9) {
                 return {0x0p+0, 0x1.8d1f8a3279763p+2, -0x1.d4881995a0c1fp+5, 0x1.e86d414a78e34p+7, -0x1.280027c9b0876p+9, 0x1.d3eb5f0b0594cp+9, -0x1.0b82a55c2799fp+10, 0x1.07ce9f70ddb28p+10, -0x1.0d7822536789ep+10, 0x1.0df61d2a506b2p+10, -0x1.c6893ac6cda6bp+9, 0x1.45ac9e8089788p+9, -0x1.c9d686e237044p+8, 0x1.35c4c3819b31p+8, -0x1.4a58be360f4f4p+7, 0x1.017559c35f761p+6, -0x1.5d1ba7f134742p+4, 0x1.dadd49a935c84p+1, 0x1.87b01fd4326a3p+2, -0x1.9ab15d247f91p+2, 0x1.46cd6a0d33a49p+1, -0x1.8955d7defe0d5p-2, -0x1.85244f4e65bbcp-7, 0x1.6f86d3c431061p-8, 0x1.1b4e3c12a74ep-16, -0x1.7914d82d3193fp-21, 0x1.903b4b44dd8c8p-34, -0x0p+0};
             }
             if constexpr (order == 10) {
-                return {0x0p+0, 0x1.041a0a897aa29p+1, -0x1.3658b5d77609ep+4, 0x1.5194af04e2f85p+6, -0x1.c3df81f0aaf29p+7, 0x1.ad183e8db3dacp+8, -0x1.3d9c782d70077p+9, 0x1.852da35362a6dp+9, -0x1.9cca18f6947ddp+9, 0x1.9a6efa498935ep+9, -0x1.a300c2ebdd39dp+9, 0x1.a735477cbff1cp+9, -0x1.7a384b1c312fcp+9, 0x1.2afd886ee72d7p+9, -0x1.d0f63946d275bp+8, 0x1.6384c4a13f54ep+8, -0x1.d6c269ce8bf35p+7, 0x1.08982647618p+7, -0x1.1f7e83a071123p+6, 0x1.2a5701b5bea0ep+5, -0x1.c18aa4ec1159bp+3, 0x1.4dc13861658a9p+1, 0x1.bd5ac19033245p-5, -0x1.1aa94170fffadp-4, -0x1.97678bd8dc9fap-14, 0x1.25b3fc23ddcf6p-16, -0x1.381fef501218fp-28, -0x0p+0};
+                return {0x0p+0, 0x1.041a0a897aa29p+1, -0x1.3658b5d77609ep+4, 0x1.5194af04e2f85p+6, -0x1.c3df81f0aaf29p+7, 0x1.ad183e8db3dacp+8, -0x1.3d9c782d70077p+9, 0x1.852da35362a6dp+9, -0x1.9cca18f6947ddp+9, 0x1.9a6efa498935ep+9, -0x1.a300c2ebdd39dp+9, 0x1.a735477cbff1cp+9, -0x1.7a384b1c312fcp+9, 0x1.2afd886ee72d7p+9, -0x1.d0f63946d275bp+8, 0x1.6384c4a13f54ep+8, -0x1.d6c269ce8bf35p+7, 0x1.08982647618p+7, -0x1.1f7e83a071123p+6, 0x1.2a5701b5bea0ep+5, -0x1.c18aa4ec1159bp+3, 0x1.4dc13861658a9p+1, 0x1.bd5ac19033245p-5, -0x1.1aa94170fffadp-4, -0x1.97678bd8dc9fap-14, 0x1.25b3fc23ddcf6p-16, -0x1.381fef501218fp-28, 0x0p+0};
             }
             if constexpr (order == 11) {
                 return {0x0p+0, 0x1.456a1d2a45d0dp+0, -0x1.86731e38f2c9fp+3, 0x1.99ddae9b5957ep+5, -0x1.ebccc1d5d759ap+6, 0x1.74f85dd906949p+7, -0x1.8426225b26444p+7, 0x1.4fbcc1bdf3f19p+7, -0x1.4776c0e99319fp+7, 0x1.573bef3fda7ebp+7, -0x1.2b0c271bd883ep+7, 0x1.bb5bca80b625p+6, -0x1.5808025c93fa5p+6, 0x1.0c1df40cf5e4cp+6, -0x1.5dea01151a3e2p+5, 0x1.997fc95198574p+4, -0x1.f5c4140f2a03ep+3, 0x1.1578f4041624bp+3, -0x1.e11a4c4784826p+1, 0x1.8c2f5a8cae554p+0, -0x1.42cdddde9b71fp-1, 0x1.1b37523680cdap-3, 0x1.61bca3fd3effbp-7, -0x1.eeca78cc1dd9bp-8, 0x1.427b3775515b6p-14, 0x1.1c6c30fb5472dp-18, -0x1.2f056506ce5e6p-29, 0x0p+0};
@@ -1335,16 +1629,16 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         }
         if constexpr (std::is_same_v<Real, long double>) {
             if constexpr (order == 0) {
-                return {0x0p+0L, 0x9.71e05d9f9d6a6a5p-13L, 0xe.b9e6e278b8a3ea8p-7L, 0xc.c0783a6dea3101cp-4L, 0x8.5c6d3c03e139c58p-5L, -0x9.c0dc418a090583bp-5L, 0xd.32029dea6d20a27p-6L, -0xd.f365933107c2191p-7L, 0xa.9b4f995a39545fcp-8L, -0xf.2a9dfdc1e240f71p-11L, -0xa.dcb9bb583c8b013p-12L, 0x9.d6c9f03875bcf99p-12L, -0xb.6432c68d9036eap-14L, 0xa.10a1bf3dc1ce972p-19L, 0x9.ace5aadbe99adaep-18L, -0x8.b58e6f0449bf329p-21L, -0x8.f23814c144d7229p-22L, 0x8.b5bebe29765b5fbp-24L, -0x9.5480bd482c76432p-30L, -0xf.3301d09631101f2p-32L, 0xd.6b1ad2a9956cecp-36L, -0x8.5b8b379eacc020ep-40L, -0x9.6e6469e45867b18p-46L, 0xc.ca63a296e698604p-53L, 0xe.9f3ed93d387731ep-63L, -0xd.69a601c1fd321e5p-75L, 0xe.37e858d46b515bp-97L, -0x0p+0L};
+                return {0x0p+0L, 0x9.71e05d9f9d6a6a5p-13L, 0xe.b9e6e278b8a3ea8p-7L, 0xc.c0783a6dea3101cp-4L, 0x8.5c6d3c03e139c58p-5L, -0x9.c0dc418a090583bp-5L, 0xd.32029dea6d20a27p-6L, -0xd.f365933107c2191p-7L, 0xa.9b4f995a39545fcp-8L, -0xf.2a9dfdc1e240f71p-11L, -0xa.dcb9bb583c8b013p-12L, 0x9.d6c9f03875bcf99p-12L, -0xb.6432c68d9036eap-14L, 0xa.10a1bf3dc1ce972p-19L, 0x9.ace5aadbe99adaep-18L, -0x8.b58e6f0449bf329p-21L, -0x8.f23814c144d7229p-22L, 0x8.b5bebe29765b5fbp-24L, -0x9.5480bd482c76432p-30L, -0xf.3301d09631101f2p-32L, 0xd.6b1ad2a9956cecp-36L, -0x8.5b8b379eacc020ep-40L, -0x9.6e6469e45867b18p-46L, 0xc.ca63a296e698604p-53L, 0xe.9f3ed93d387731ep-63L, -0xd.69a601c1fd321e5p-75L, 0xe.37e858d46b515bp-97L, 0x0p+0L};
             }
             if constexpr (order == 1) {
-                return {0x0p+0L, 0xf.ff35419fa0e8f21p-11L, 0xb.43c4ab28ce718b1p-5L, 0xa.7b11139323118aep-4L, -0xc.ebd27807cee01bp-3L, 0xf.70d391b7b8f1d7fp-4L, -0x9.d261e8a8608ee81p-4L, 0xd.289270d5a3d484p-5L, -0xf.ea38a0284f599d4p-6L, 0xf.7f5c1aafe97c0a1p-7L, -0xb.4af2f2f24e7c239p-8L, 0xb.9e57029c3fb215dp-10L, -0xf.d3ba488dd169dd9p-13L, 0x8.9d83eeeed9dc1b7p-16L, 0xb.e588e05a14054ecp-17L, -0xe.965fffb7152c15fp-18L, 0xb.a1c464fe94734f4p-20L, 0x9.0ffc4adfdaf948bp-24L, -0x8.ab183dae09460bbp-25L, -0x8.cdc8dffc5f7a7c4p-28L, 0xf.bec1f26a0e3b7cap-34L, 0xa.84831359035218p-37L, -0xa.02b41a135680872p-43L, 0xb.5603cf768986fc1p-49L, -0xc.d24f831bd1db255p-58L, -0xc.45e3366043f8eabp-70L, 0xd.02a0f58dee755b1p-91L, 0x0p+0L};
+                return {0x0p+0L, 0xf.ff35419fa0e8f21p-11L, 0xb.43c4ab28ce718b1p-5L, 0xa.7b11139323118aep-4L, -0xc.ebd27807cee01bp-3L, 0xf.70d391b7b8f1d7fp-4L, -0x9.d261e8a8608ee81p-4L, 0xd.289270d5a3d484p-5L, -0xf.ea38a0284f599d4p-6L, 0xf.7f5c1aafe97c0a1p-7L, -0xb.4af2f2f24e7c239p-8L, 0xb.9e57029c3fb215dp-10L, -0xf.d3ba488dd169dd9p-13L, 0x8.9d83eeeed9dc1b7p-16L, 0xb.e588e05a14054ecp-17L, -0xe.965fffb7152c15fp-18L, 0xb.a1c464fe94734f4p-20L, 0x9.0ffc4adfdaf948bp-24L, -0x8.ab183dae09460bbp-25L, -0x8.cdc8dffc5f7a7c4p-28L, 0xf.bec1f26a0e3b7cap-34L, 0xa.84831359035218p-37L, -0xa.02b41a135680872p-43L, 0xb.5603cf768986fc1p-49L, -0xc.d24f831bd1db255p-58L, -0xc.45e3366043f8eabp-70L, 0xd.02a0f58dee755b1p-91L, -0x0p+0L};
             }
             if constexpr (order == 2) {
-                return {0x0p+0L, 0xb.871c689e36e67b2p-8L, 0xc.c21484a70968caap-4L, -0xa.d11d772e7e79982p-3L, -0xe.51d42f1875fb05dp-5L, 0xf.9488fb657535621p-3L, -0xc.816fad65cc2b1fep-3L, 0xb.72ec5197f1d73dap-4L, -0xb.e6ba4cd08dc3e1ep-8L, -0xe.5a89c4ef8a1b6aap-6L, 0xc.4b87ef54b6da459p-6L, -0x9.71dd2188b6a770fp-7L, 0xd.21b94476a8d5992p-12L, 0xa.ec57d75af6152bbp-10L, -0x9.f909d12d261cd27p-11L, 0xa.1c6fb324aff682bp-14L, 0xc.955659a270d5623p-16L, -0xa.51515b49bee533ep-17L, 0x8.30a4a603b752616p-20L, 0x8.e30a8066affb01ep-24L, -0xf.f6a025cb63973cp-27L, 0xc.c807d46ae5c0b92p-32L, 0xa.5b8e365dbdf1a9dp-36L, -0xf.a710791928d528ap-43L, -0xd.73b20acd2ddae47p-53L, 0x8.3a9f2648c76b5adp-62L, -0x8.b92ec6233b61c8p-82L, 0x0p+0L};
+                return {0x0p+0L, 0xb.871c689e36e67b2p-8L, 0xc.c21484a70968caap-4L, -0xa.d11d772e7e79982p-3L, -0xe.51d42f1875fb05dp-5L, 0xf.9488fb657535621p-3L, -0xc.816fad65cc2b1fep-3L, 0xb.72ec5197f1d73dap-4L, -0xb.e6ba4cd08dc3e1ep-8L, -0xe.5a89c4ef8a1b6aap-6L, 0xc.4b87ef54b6da459p-6L, -0x9.71dd2188b6a770fp-7L, 0xd.21b94476a8d5992p-12L, 0xa.ec57d75af6152bbp-10L, -0x9.f909d12d261cd27p-11L, 0xa.1c6fb324aff682bp-14L, 0xc.955659a270d5623p-16L, -0xa.51515b49bee533ep-17L, 0x8.30a4a603b752616p-20L, 0x8.e30a8066affb01ep-24L, -0xf.f6a025cb63973cp-27L, 0xc.c807d46ae5c0b92p-32L, 0xa.5b8e365dbdf1a9dp-36L, -0xf.a710791928d528ap-43L, -0xd.73b20acd2ddae47p-53L, 0x8.3a9f2648c76b5adp-62L, -0x8.b92ec6233b61c8p-82L, -0x0p+0L};
             }
             if constexpr (order == 3) {
-                return {0x0p+0L, 0xd.b20322a3996a6a2p-6L, 0xd.ca4aa0fa2c66c04p-4L, -0xa.4de420cc6c77707p-1L, 0x9.2a8ab8b3d2a9452p+0L, -0x9.2a2c8f45b7035d6p+0L, 0xd.fee80d54f348b5ap-1L, -0x9.2c6587097a03f3cp-1L, 0x9.225b43c8840bfbbp-2L, -0xb.b74e433b47ec0d7p-4L, 0x9.6dc870dbf111c84p-6L, -0xd.6e00555bfbc3311p-7L, 0x8.3bd80e6e14d4ep-6L, -0xa.70de9ebe40837ffp-7L, 0xd.458b8cfbb4b4fcp-9L, -0x8.db3d47eeae9cad3p-12L, -0xa.d5110cf4583900cp-13L, 0x8.614b75f02db74e4p-14L, -0x9.8a8896b713246b3p-17L, -0xd.51a5323c171fee3p-26L, 0xb.8c561092a896f33p-23L, -0xa.769011a8736a082p-28L, -0xb.5161f3d88ae4a18p-32L, 0x8.1e58deca3716d7bp-38L, 0xe.96739f4ce14a1ebp-49L, -0x8.886bf8d85fdfe26p-57L, 0x9.0badf046a579ce9p-76L, -0x0p+0L};
+                return {0x0p+0L, 0xd.b20322a3996a6a2p-6L, 0xd.ca4aa0fa2c66c04p-4L, -0xa.4de420cc6c77707p-1L, 0x9.2a8ab8b3d2a9452p+0L, -0x9.2a2c8f45b7035d6p+0L, 0xd.fee80d54f348b5ap-1L, -0x9.2c6587097a03f3cp-1L, 0x9.225b43c8840bfbbp-2L, -0xb.b74e433b47ec0d7p-4L, 0x9.6dc870dbf111c84p-6L, -0xd.6e00555bfbc3311p-7L, 0x8.3bd80e6e14d4ep-6L, -0xa.70de9ebe40837ffp-7L, 0xd.458b8cfbb4b4fcp-9L, -0x8.db3d47eeae9cad3p-12L, -0xa.d5110cf4583900cp-13L, 0x8.614b75f02db74e4p-14L, -0x9.8a8896b713246b3p-17L, -0xd.51a5323c171fee3p-26L, 0xb.8c561092a896f33p-23L, -0xa.769011a8736a082p-28L, -0xb.5161f3d88ae4a18p-32L, 0x8.1e58deca3716d7bp-38L, 0xe.96739f4ce14a1ebp-49L, -0x8.886bf8d85fdfe26p-57L, 0x9.0badf046a579ce9p-76L, 0x0p+0L};
             }
             if constexpr (order == 4) {
                 return {0x0p+0L, 0xc.de9de1239cb046fp-4L, -0x9.0c5906491d3955ap-2L, -0xc.7839f71242a14d4p-5L, 0x8.81b461d68a76009p+0L, -0xb.72fe813d0b59fd4p+0L, -0xf.f7358c9442947e5p-5L, 0xa.ed7063276080604p+1L, -0x9.29c9c7d32fce6e5p+2L, 0x8.423651a8f719bep+2L, -0xe.99bce7eb69c9558p+0L, -0xd.e0e5eaef029d8dap-2L, 0xa.4f436b46a67c643p+0L, -0xf.256f04625361643p-1L, 0xb.28f9c831a4ab6f7p-2L, -0x8.a71970fcdb5d61fp-5L, -0xe.1058e94389b55dfp-6L, 0xc.ee39ab87739f9d3p-7L, -0xe.ddcf5eece04ef66p-10L, -0xe.3fae0f6307b4b7dp-14L, 0xd.2fe42b7297d6b86p-15L, -0x8.3fb2ed50024d845p-19L, -0x8.71bc783d7f852p-23L, 0xb.4de2c6af60665f8p-29L, 0xc.39550de79b43b5p-39L, -0xb.dc24b4b0400b683p-47L, 0xc.92a4664dadb8e43p-65L, -0x0p+0L};
@@ -1359,13 +1653,13 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0L, 0xf.abcd8b83a71b41bp-1L, -0x8.9dce5f3b30b3793p+3L, 0x8.68682195f609a67p+5L, -0x9.84d437345ff4c4dp+6L, 0xd.c713118f501f476p+6L, -0xd.84594228bf62173p+6L, 0x9.e3e95931228123cp+6L, -0xb.f3ef786eb60bf83p+5L, 0xc.e4402241c87301dp+2L, 0xe.e0ba9661797c21bp+5L, -0xf.2a501fdde17d235p+6L, 0x8.d2170ed72b4825ep+7L, -0xf.c81fa50c6187197p+6L, 0xc.ec6dc8c841c327ep+6L, -0x9.a0b9ffd8a1f0ecfp+6L, 0xb.2759e13edab26a3p+5L, -0x8.586218b8ff72c95p+4L, 0xa.f8529bae88e396ep+1L, 0xe.c7b5cf8a917974bp-2L, -0x8.e3ac4b6b6acc633p-2L, 0xf.9c560d3a4ed77bcp-6L, 0xf.c13805a6e393a55p-10L, -0x8.98309aea3397895p-13L, -0x9.6e28a6b4cc8a06ep-22L, 0x8.ea4a570e998fa08p-28L, -0x9.742325e7646a08p-43L, 0x0p+0L};
             }
             if constexpr (order == 8) {
-                return {0x0p+0L, 0xf.196612f526d24c2p-1L, -0x8.b4965322c754f1cp+3L, 0x8.fd04e098b6fda5ap+5L, -0xb.0af33f860e6644cp+6L, 0x9.32e460da58d525ap+7L, -0xb.ab4f68e4108651p+7L, 0xc.f4b5ef2831ea0e8p+7L, -0xd.ddf0b3d1c6b1944p+7L, 0xd.f040100f39be9b8p+7L, -0xc.784cded5d90c4c7p+7L, 0xa.1dc1c0af0ad3159p+7L, -0xf.7356b459ded2772p+6L, 0xa.c6ab0e5c26933f6p+6L, -0xd.1d94154203d1881p+5L, 0xe.3ceb107fd7e02c5p+4L, -0xd.e3c65ca23d50927p+3L, 0xa.0c71ac8171966e8p+2L, -0x9.d5f9b056617ba17p-1L, -0xd.6bdd9c33d9e1582p-2L, 0xd.32a81275f97ea1cp-3L, -0xd.7fee6a38c5d3f8dp-6L, -0xc.1a0e6b635854ea4p-10L, 0xd.aab8869f5faa95cp-13L, 0xf.190b9c558a2439ep-22L, -0xe.29e09b9e442c27dp-27L, 0xf.061385658ae2fdbp-41L, 0x0p+0L};
+                return {0x0p+0L, 0xf.196612f526d24c2p-1L, -0x8.b4965322c754f1cp+3L, 0x8.fd04e098b6fda5ap+5L, -0xb.0af33f860e6644cp+6L, 0x9.32e460da58d525ap+7L, -0xb.ab4f68e4108651p+7L, 0xc.f4b5ef2831ea0e8p+7L, -0xd.ddf0b3d1c6b1944p+7L, 0xd.f040100f39be9b8p+7L, -0xc.784cded5d90c4c7p+7L, 0xa.1dc1c0af0ad3159p+7L, -0xf.7356b459ded2772p+6L, 0xa.c6ab0e5c26933f6p+6L, -0xd.1d94154203d1881p+5L, 0xe.3ceb107fd7e02c5p+4L, -0xd.e3c65ca23d50927p+3L, 0xa.0c71ac8171966e8p+2L, -0x9.d5f9b056617ba17p-1L, -0xd.6bdd9c33d9e1582p-2L, 0xd.32a81275f97ea1cp-3L, -0xd.7fee6a38c5d3f8dp-6L, -0xc.1a0e6b635854ea4p-10L, 0xd.aab8869f5faa95cp-13L, 0xf.190b9c558a2439ep-22L, -0xe.29e09b9e442c27dp-27L, 0xf.061385658ae2fdbp-41L, -0x0p+0L};
             }
             if constexpr (order == 9) {
                 return {0x0p+0L, 0xc.68fc5193cbb1b7bp-1L, -0xe.a440ccad060f512p+2L, 0xf.436a0a53c719d99p+4L, -0x9.40013e4d843ac8dp+6L, 0xe.9f5af8582ca613bp+6L, -0x8.5c152ae13ccf6f4p+7L, 0x8.3e74fb86ed9434dp+7L, -0x8.6bc1129b3c4ec82p+7L, 0x8.6fb0e9528358fc8p+7L, -0xe.3449d6366d35aadp+6L, 0xa.2d64f4044bc4118p+6L, -0xe.4eb43711b821ef6p+5L, 0x9.ae261c0cd987cdbp+5L, -0xa.52c5f1b07a7a10fp+4L, 0x8.0baace1afbb0855p+3L, -0xa.e8dd3f89a3a1196p+1L, 0xe.d6ea4d49ae41ca2p-2L, 0xc.3d80fea19351b34p-1L, -0xc.d58ae923fc87cffp-1L, 0xa.366b50699d24558p-2L, -0xc.4aaebef7f06a90cp-5L, -0xc.29227a732dde266p-10L, 0xb.7c369e218830b25p-11L, 0x8.da71e0953a6ff91p-19L, -0xb.c8a6c1698c9facp-24L, 0xc.81da5a26ec63e05p-37L, -0x0p+0L};
             }
             if constexpr (order == 10) {
-                return {0x0p+0L, 0x8.20d0544bd51475ap-2L, -0x9.b2c5aebbb04f3ccp+1L, 0xa.8ca5782717c2461p+3L, -0xe.1efc0f8557945e6p+4L, 0xd.68c1f46d9ed5f43p+5L, -0x9.ece3c16b803b8afp+6L, 0xc.296d1a9b1536a08p+6L, -0xc.e650c7b4a3ee86bp+6L, 0xc.d377d24c49af172p+6L, -0xd.1806175ee9ce931p+6L, 0xd.39aa3be5ff8dcb3p+6L, -0xb.d1c258e1897df15p+6L, 0x9.57ec4377396b8b8p+6L, -0xe.87b1ca3693ad8c6p+5L, 0xb.1c262509faa6e0bp+5L, -0xe.b6134e745f9a70dp+4L, 0x8.44c1323b0bffc57p+4L, -0x8.fbf41d038891ad4p+3L, 0x9.52b80dadf506ef2p+2L, -0xe.0c5527608acdb69p+0L, 0xa.6e09c30b2c546eap-2L, 0xd.ead60c819922651p-8L, -0x8.d54a0b87ffd6b8cp-7L, -0xc.bb3c5ec6e4fd2a6p-17L, 0x9.2d9fe11eee7aff2p-19L, -0x9.c0ff7a8090c74e6p-31L, -0x0p+0L};
+                return {0x0p+0L, 0x8.20d0544bd51475ap-2L, -0x9.b2c5aebbb04f3ccp+1L, 0xa.8ca5782717c2461p+3L, -0xe.1efc0f8557945e6p+4L, 0xd.68c1f46d9ed5f43p+5L, -0x9.ece3c16b803b8afp+6L, 0xc.296d1a9b1536a08p+6L, -0xc.e650c7b4a3ee86bp+6L, 0xc.d377d24c49af172p+6L, -0xd.1806175ee9ce931p+6L, 0xd.39aa3be5ff8dcb3p+6L, -0xb.d1c258e1897df15p+6L, 0x9.57ec4377396b8b8p+6L, -0xe.87b1ca3693ad8c6p+5L, 0xb.1c262509faa6e0bp+5L, -0xe.b6134e745f9a70dp+4L, 0x8.44c1323b0bffc57p+4L, -0x8.fbf41d038891ad4p+3L, 0x9.52b80dadf506ef2p+2L, -0xe.0c5527608acdb69p+0L, 0xa.6e09c30b2c546eap-2L, 0xd.ead60c819922651p-8L, -0x8.d54a0b87ffd6b8cp-7L, -0xc.bb3c5ec6e4fd2a6p-17L, 0x9.2d9fe11eee7aff2p-19L, -0x9.c0ff7a8090c74e6p-31L, 0x0p+0L};
             }
             if constexpr (order == 11) {
                 return {0x0p+0L, 0xa.2b50e9522e86a75p-3L, -0xc.3398f1c7964f4dfp+0L, 0xc.ceed74dacabed45p+2L, -0xf.5e660eaebacd068p+3L, 0xb.a7c2eec834a457bp+4L, -0xc.213112d93221da7p+4L, 0xa.7de60def9f8cb1ep+4L, -0xa.3bb6074c98cfb0fp+4L, 0xa.b9df79fed3f56f5p+4L, -0x9.586138dec41f121p+4L, 0xd.dade5405b127d2ep+3L, -0xa.c04012e49fd2735p+3L, 0x8.60efa067af26275p+3L, -0xa.ef5008a8d1f0cbfp+2L, 0xc.cbfe4a8cc2b9da9p+1L, -0xf.ae20a079501f01bp+0L, 0x8.abc7a020b125872p+0L, -0xf.08d2623c2412c59p-2L, 0xc.617ad46572a9f45p-3L, -0xa.166eeef4db8f41bp-4L, 0x8.d9ba91b4066cd0bp-6L, 0xb.0de51fe9f7fd8e2p-10L, -0xf.7653c660eecd46ap-11L, 0xa.13d9bbaa8adb22dp-17L, 0x8.e36187daa39648ep-21L, -0x9.782b283672f30cdp-32L, 0x0p+0L};
@@ -1380,72 +1674,116 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         #ifdef BOOST_HAS_FLOAT128
         if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
             if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.2e3c0bb3f3ad4d49ee7e86ec5518p-10Q, 0x1.d73cdc4f17147d4ff78a1eaebc82p-4Q, 0x1.980f074dbd462038712882b2222ep-1Q, 0x1.0b8da7807c2738b0ef8a21bd41e3p-2Q, -0x1.381b88314120b0755faac9b6a20bp-2Q, 0x1.a64053bd4da4144d5c6645aafa57p-3Q, -0x1.be6cb26620f84322f5bc9ad12402p-4Q, 0x1.5369f32b472a8bf80c2615157591p-5Q, -0x1.e553bfb83c481ee1c85b10218134p-8Q, -0x1.5b97376b07916025b5f5ed690f55p-9Q, 0x1.3ad93e070eb79f317793c09c0443p-9Q, -0x1.6c8658d1b206dd40e11227faae72p-11Q, 0x1.421437e7b839d2e408af08229929p-16Q, 0x1.359cb55b7d335b5bc8ff9070d375p-15Q, -0x1.16b1cde08937e6520514fc007dd3p-18Q, -0x1.1e470298289ae452c29404b9c735p-19Q, 0x1.16b7d7c52ecb6bf5c9c270fe3973p-21Q, -0x1.2a9017a9058ec8631bfea23cf0d5p-27Q, -0x1.e6603a12c62203e481a6f751bafcp-29Q, 0x1.ad635a5532ad9d7f9b990f32589fp-33Q, -0x1.0b7166f3d598041c11f82d418c61p-37Q, -0x1.2dcc8d3c8b0cf63074ab4d9fba5fp-43Q, 0x1.994c7452dcd30c07dade8e0a0b53p-50Q, 0x1.d3e7db27a70ee63bd0dc60e06dc1p-60Q, -0x1.ad34c0383fa643c903234154af7ep-72Q, 0x1.c6fd0b1a8d6a2b5f9f47659e9cdcp-94Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.2e3c0bb3f3ad4d49ee7e86ec562p-10Q, 0x1.d73cdc4f17147d4ff78a1eaebc89p-4Q, 0x1.980f074dbd462038712882b2223p-1Q, 0x1.0b8da7807c2738b0ef8a21bd41d9p-2Q, -0x1.381b88314120b0755faac9b6a208p-2Q, 0x1.a64053bd4da4144d5c6645aafa5p-3Q, -0x1.be6cb26620f84322f5bc9ad124p-4Q, 0x1.5369f32b472a8bf80c2615157588p-5Q, -0x1.e553bfb83c481ee1c85b1021810cp-8Q, -0x1.5b97376b07916025b5f5ed690f77p-9Q, 0x1.3ad93e070eb79f317793c09c0451p-9Q, -0x1.6c8658d1b206dd40e11227faae77p-11Q, 0x1.421437e7b839d2e408af08229906p-16Q, 0x1.359cb55b7d335b5bc8ff9070d38p-15Q, -0x1.16b1cde08937e6520514fc007dd3p-18Q, -0x1.1e470298289ae452c29404b9c746p-19Q, 0x1.16b7d7c52ecb6bf5c9c270fe3977p-21Q, -0x1.2a9017a9058ec8631bfea23cf0f2p-27Q, -0x1.e6603a12c62203e481a6f751bb0fp-29Q, 0x1.ad635a5532ad9d7f9b990f3258b1p-33Q, -0x1.0b7166f3d598041c11f82d418c5ep-37Q, -0x1.2dcc8d3c8b0cf63074ab4d9fba6ep-43Q, 0x1.994c7452dcd30c07dade8e0a0b5bp-50Q, 0x1.d3e7db27a70ee63bd0dc60e06dc1p-60Q, -0x1.ad34c0383fa643c903234154af78p-72Q, 0x1.c6fd0b1a8d6a2b5f9f47659e9cb5p-94Q, 0x0p+0Q};
             }
             if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.ffe6a833f41d1e41c335a1d663bdp-8Q, 0x1.6878956519ce3162ba29291a8512p-2Q, 0x1.4f6222726462315c1311b1bd0b54p-1Q, -0x1.9d7a4f00f9dc035ff30a13b3dd41p+0Q, 0x1.ee1a7236f71e3afe8c9241dc27eep-1Q, -0x1.3a4c3d150c11dd01e59680a43c0ap-1Q, 0x1.a5124e1ab47a907fdd8a56cf5fb6p-2Q, -0x1.fd47140509eb33a71307cdb49b1ep-3Q, 0x1.efeb8355fd2f814144fb4db02bbdp-4Q, -0x1.695e5e5e49cf847101e5144b6fd9p-5Q, 0x1.73cae05387f642ba0d652b2dbc7ep-7Q, -0x1.fa774911ba2d3bb25d61e69c8c0ap-10Q, 0x1.13b07ddddb3b836ee57d128434e4p-13Q, 0x1.7cb11c0b4280a9d8a95e4eb20f02p-14Q, -0x1.d2cbfff6e2a582bd1061aa2f37f3p-15Q, 0x1.74388c9fd28e69e7d9f0c5af3f3ep-17Q, 0x1.21ff895bfb5f2915922793fd2436p-21Q, -0x1.156307b5c128c175f7e3a714785ap-22Q, -0x1.19b91bff8bef4f88f1ed76cce8b5p-25Q, 0x1.f7d83e4d41c76f94d46210e4d8b7p-31Q, 0x1.5090626b206a430059df75027f9ap-34Q, -0x1.405683426ad010e44f0a98cc99acp-40Q, 0x1.6ac079eed130df81302e2b26c976p-46Q, -0x1.9a49f0637a3b64a9eb35bd52a783p-55Q, -0x1.88bc66cc087f1d558950f224ed94p-67Q, 0x1.a0541eb1bdceab613773d4dca27cp-88Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.ffe6a833f41d1e41c335a1d66225p-8Q, 0x1.6878956519ce3162ba29291a8504p-2Q, 0x1.4f6222726462315c1311b1bd0b69p-1Q, -0x1.9d7a4f00f9dc035ff30a13b3dd54p+0Q, 0x1.ee1a7236f71e3afe8c9241dc280bp-1Q, -0x1.3a4c3d150c11dd01e59680a43c1ap-1Q, 0x1.a5124e1ab47a907fdd8a56cf5fd2p-2Q, -0x1.fd47140509eb33a71307cdb49b3fp-3Q, 0x1.efeb8355fd2f814144fb4db02bdbp-4Q, -0x1.695e5e5e49cf847101e5144b6fefp-5Q, 0x1.73cae05387f642ba0d652b2dbcabp-7Q, -0x1.fa774911ba2d3bb25d61e69c8c8ep-10Q, 0x1.13b07ddddb3b836ee57d12843693p-13Q, 0x1.7cb11c0b4280a9d8a95e4eb20e72p-14Q, -0x1.d2cbfff6e2a582bd1061aa2f380bp-15Q, 0x1.74388c9fd28e69e7d9f0c5af3fddp-17Q, 0x1.21ff895bfb5f2915922793fd222dp-21Q, -0x1.156307b5c128c175f7e3a71477b9p-22Q, -0x1.19b91bff8bef4f88f1ed76cce8eap-25Q, 0x1.f7d83e4d41c76f94d46210e4d1f2p-31Q, 0x1.5090626b206a430059df75028168p-34Q, -0x1.405683426ad010e44f0a98cc929p-40Q, 0x1.6ac079eed130df81302e2b26c482p-46Q, -0x1.9a49f0637a3b64a9eb35bd52aa23p-55Q, -0x1.88bc66cc087f1d558950f224d6c9p-67Q, 0x1.a0541eb1bdceab613773d4dc3dd7p-88Q, 0x0p+0Q};
             }
             if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.70e38d13c6dccf6333417be4b524p-5Q, 0x1.98429094e12d1953c234a36b12cep-1Q, -0x1.5a23aee5cfcf330386719e085b0dp+0Q, -0x1.ca3a85e30ebf60ba5eccc5b7afa3p-2Q, 0x1.f2911f6caea6ac421bc7b6d2cbaap+0Q, -0x1.902df5acb98563fb6c8594126211p+0Q, 0x1.6e5d8a32fe3ae7b3c23b4e6e9a5bp-1Q, -0x1.7cd7499a11b87c3bc4909e0bca27p-5Q, -0x1.cb51389df1436d54630b5c40529cp-3Q, 0x1.8970fdea96db48b13c52294d02f6p-3Q, -0x1.2e3ba43116d4ee1d14ccd7ef1ed2p-4Q, 0x1.a437288ed51ab324c667ecc7c503p-9Q, 0x1.5d8afaeb5ec2a57500ea441b586cp-7Q, -0x1.3f213a25a4c39a4ee9f8ca7fc5d7p-8Q, 0x1.438df66495fed0569b1e66072684p-11Q, 0x1.92aacb344e1aac45946a6dd95aa5p-13Q, -0x1.4a2a2b6937dca67c2fb96409ea9bp-14Q, 0x1.061494c076ea4c2b5c794f2371b3p-17Q, 0x1.1c61500cd5ff603bf7260846f058p-21Q, -0x1.fed404b96c72e77fac42699e643cp-24Q, 0x1.9900fa8d5cb81723cdb543a2519ap-29Q, 0x1.4b71c6cbb7be353ab93ac21700a5p-33Q, -0x1.f4e20f23251aa513b13eb0ad0e35p-40Q, -0x1.ae764159a5bb5c8d340066c073e5p-50Q, 0x1.0753e4c918ed6b59ce15c4a93456p-59Q, -0x1.1725d8c4676c38ff70e1cc358b0cp-79Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.70e38d13c6dccf6333417be4b4fbp-5Q, 0x1.98429094e12d1953c234a36b137bp-1Q, -0x1.5a23aee5cfcf330386719e085aa1p+0Q, -0x1.ca3a85e30ebf60ba5eccc5b7b84bp-2Q, 0x1.f2911f6caea6ac421bc7b6d2ce04p+0Q, -0x1.902df5acb98563fb6c85941263b7p+0Q, 0x1.6e5d8a32fe3ae7b3c23b4e6e9c7ap-1Q, -0x1.7cd7499a11b87c3bc4909e0bdb58p-5Q, -0x1.cb51389df1436d54630b5c4050fbp-3Q, 0x1.8970fdea96db48b13c52294d029p-3Q, -0x1.2e3ba43116d4ee1d14ccd7ef1eb6p-4Q, 0x1.a437288ed51ab324c667ecc7c439p-9Q, 0x1.5d8afaeb5ec2a57500ea441b58aap-7Q, -0x1.3f213a25a4c39a4ee9f8ca7fc5f5p-8Q, 0x1.438df66495fed0569b1e6607263bp-11Q, 0x1.92aacb344e1aac45946a6dd95b1dp-13Q, -0x1.4a2a2b6937dca67c2fb96409eaabp-14Q, 0x1.061494c076ea4c2b5c794f2371b4p-17Q, 0x1.1c61500cd5ff603bf7260846f007p-21Q, -0x1.fed404b96c72e77fac42699e644dp-24Q, 0x1.9900fa8d5cb81723cdb543a2521ap-29Q, 0x1.4b71c6cbb7be353ab93ac21700e3p-33Q, -0x1.f4e20f23251aa513b13eb0ad0eafp-40Q, -0x1.ae764159a5bb5c8d340066c07578p-50Q, 0x1.0753e4c918ed6b59ce15c4a9365bp-59Q, -0x1.1725d8c4676c38ff70e1cc359512p-79Q, 0x0p+0Q};
             }
             if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.b6406454732d4d440405d44a6611p-3Q, 0x1.b949541f458cd808c01c6f443873p-1Q, -0x1.49bc84198d8eee0e1769477dce8bp+2Q, 0x1.255157167a5528a3714c438e28f7p+3Q, -0x1.254591e8b6e06babda61e0b5bc24p+3Q, 0x1.bfdd01aa9e6916b30d7fb866c97ap+2Q, -0x1.258cb0e12f407e788c8d24c0406ap+2Q, 0x1.244b687910817f75269b9b13caa9p+1Q, -0x1.76e9c86768fd81ae0140e512e5cp-1Q, 0x1.2db90e1b7e223907d65e185884b8p-3Q, -0x1.adc00aab7f786622c376bd60af55p-4Q, 0x1.077b01cdc29a9bffc5581309684ap-3Q, -0x1.4e1bd3d7c8106ffe51d90e2985dp-4Q, 0x1.a8b1719f76969f8051acdf38be11p-6Q, -0x1.1b67a8fdd5d395a5e1003bc2f0a6p-9Q, -0x1.5aa2219e8b072017d97056f43e75p-10Q, 0x1.0c296ebe05b6e9c7cf2917908c1fp-11Q, -0x1.315112d6e2648d659715640ab8d6p-14Q, -0x1.aa34a64782e3fdc563417214521bp-23Q, 0x1.718ac2125512de66d6a9b5d7a901p-20Q, -0x1.4ed202350e6d4103a23efe8129dbp-25Q, -0x1.6a2c3e7b115c942fffc924e2bab2p-29Q, 0x1.03cb1bd946e2daf6230de1903bdbp-35Q, 0x1.d2ce73e99c2943d672b79f3e0a48p-46Q, -0x1.110d7f1b0bfbfc4b48ffe17563d9p-54Q, 0x1.2175be08d4af39d29c43830b683bp-73Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.b6406454732d4d440405d44a6a49p-3Q, 0x1.b949541f458cd808c01c6f4442bcp-1Q, -0x1.49bc84198d8eee0e1769477dd34dp+2Q, 0x1.255157167a5528a3714c438e2bbbp+3Q, -0x1.254591e8b6e06babda61e0b5bd92p+3Q, 0x1.bfdd01aa9e6916b30d7fb866cb4dp+2Q, -0x1.258cb0e12f407e788c8d24c043p+2Q, 0x1.244b687910817f75269b9b13d0aap+1Q, -0x1.76e9c86768fd81ae0140e512f91dp-1Q, 0x1.2db90e1b7e223907d65e1858ad53p-3Q, -0x1.adc00aab7f786622c376bd60c25fp-4Q, 0x1.077b01cdc29a9bffc55813096431p-3Q, -0x1.4e1bd3d7c8106ffe51d90e297c64p-4Q, 0x1.a8b1719f76969f8051acdf38ae9p-6Q, -0x1.1b67a8fdd5d395a5e1003bc2df39p-9Q, -0x1.5aa2219e8b072017d97056f432f5p-10Q, 0x1.0c296ebe05b6e9c7cf2917908081p-11Q, -0x1.315112d6e2648d659715640aac77p-14Q, -0x1.aa34a64782e3fdc563417212e36cp-23Q, 0x1.718ac2125512de66d6a9b5d79809p-20Q, -0x1.4ed202350e6d4103a23efe811aep-25Q, -0x1.6a2c3e7b115c942fffc924e2aa83p-29Q, 0x1.03cb1bd946e2daf6230de1902b89p-35Q, 0x1.d2ce73e99c2943d672b79f3df3dfp-46Q, -0x1.110d7f1b0bfbfc4b48ffe175513cp-54Q, 0x1.2175be08d4af39d29c43830b5338p-73Q, 0x0p+0Q};
             }
             if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.9bd3bc24739608dd1ea07282ef41p-1Q, -0x1.218b20c923a72ab49d783c404613p+1Q, -0x1.8f073ee2485429a822c3452a2874p-2Q, 0x1.10368c3ad14ec0121ffa10bcc969p+3Q, -0x1.6e5fd027a16b3fa71b0c6884de45p+3Q, -0x1.fee6b19288528fc9912556543eabp-2Q, 0x1.5dae0c64ec100c07cb64ad03ec4bp+4Q, -0x1.253938fa65f9cdca9dcd99a85c53p+5Q, 0x1.0846ca351ee337bf1cde15fb1fccp+5Q, -0x1.d3379cfd6d392ab0067070da245ep+3Q, -0x1.bc1cbd5de053b1b3e6030ce1e12cp+1Q, 0x1.49e86d68d4cf8c86d821677a6f81p+3Q, -0x1.e4ade08c4a6c2c8507d0732937fap+2Q, 0x1.651f390634956dee37faca825966p+1Q, -0x1.14e32e1f9b6bac3d6ef9b66af2bep-2Q, -0x1.c20b1d287136abbd5724af5f5f6dp-3Q, 0x1.9dc73570ee73f3a5d7e75ae5a9e2p-4Q, -0x1.dbb9ebdd9c09deccb10201529186p-7Q, -0x1.c7f5c1ec60f696f9a40d5c3a09b9p-11Q, 0x1.a5fc856e52fad70c72c88b4e101ap-12Q, -0x1.07f65daa0049b089e54b5e4ff41ap-16Q, -0x1.0e378f07aff0a4003d557ea836c6p-20Q, 0x1.69bc58d5ec0ccbef38bec29b1e3ep-26Q, 0x1.872aa1bcf368769fc21e2888c6ffp-36Q, -0x1.7b84969608016d06bfce8c14af4bp-44Q, 0x1.92548cc9b5b71c86f11e27090a6cp-62Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.9bd3bc24739608dd1ea0727f797p-1Q, -0x1.218b20c923a72ab49d783c3c2182p+1Q, -0x1.8f073ee2485429a822c3456748ddp-2Q, 0x1.10368c3ad14ec0121ffa10beccc4p+3Q, -0x1.6e5fd027a16b3fa71b0c68881f6dp+3Q, -0x1.fee6b19288528fc99125553bcb88p-2Q, 0x1.5dae0c64ec100c07cb64acfb530ap+4Q, -0x1.253938fa65f9cdca9dcd99a2d96bp+5Q, 0x1.0846ca351ee337bf1cde15f6a892p+5Q, -0x1.d3379cfd6d392ab0067070d38b2ap+3Q, -0x1.bc1cbd5de053b1b3e6030cd2eb44p+1Q, 0x1.49e86d68d4cf8c86d82167732746p+3Q, -0x1.e4ade08c4a6c2c8507d0731ef456p+2Q, 0x1.651f390634956dee37faca7ade61p+1Q, -0x1.14e32e1f9b6bac3d6ef9b665a8dep-2Q, -0x1.c20b1d287136abbd5724af54edd7p-3Q, 0x1.9dc73570ee73f3a5d7e75adc1efap-4Q, -0x1.dbb9ebdd9c09deccb1020147719ep-7Q, -0x1.c7f5c1ec60f696f9a40d5c2f13dep-11Q, 0x1.a5fc856e52fad70c72c88b43b17bp-12Q, -0x1.07f65daa0049b089e54b5e492044p-16Q, -0x1.0e378f07aff0a4003d557ea13ebap-20Q, 0x1.69bc58d5ec0ccbef38bec2915824p-26Q, 0x1.872aa1bcf368769fc21e287db36p-36Q, -0x1.7b84969608016d06bfce8c098437p-44Q, 0x1.92548cc9b5b71c86f11e26fc3a07p-62Q, 0x0p+0Q};
             }
             if constexpr (order == 5) {
-                return {0x0p+0Q, 0x1.29b15e8e05f4922e7d4e472bcd8ap+1Q, -0x1.cfd365d6145278198eca9cdcf322p+3Q, 0x1.440caad9c12360807dafb40ee49dp+5Q, -0x1.116de9d813b38a3407c4631c8d59p+6Q, 0x1.3b639c503b3cf7fe4e22628885p+6Q, -0x1.0040f57e975e1a258b9875f60498p+6Q, 0x1.e6fde6a95ce32902224ee706d045p+4Q, 0x1.5c1e9e155aab7b67b6f07264ad9dp+3Q, -0x1.b1e5da7957b3c8fabda1d3079971p+5Q, 0x1.7d1f138d16b9d31aa2829abf2c4bp+6Q, -0x1.d6f4cad7bdd82bc575e84c099062p+6Q, 0x1.9fd808c31038fd9d9f982223f243p+6Q, -0x1.ecec6e1a57ab3b47a08d39c75c75p+5Q, 0x1.43fff7220eba3de58880abe282dap+4Q, 0x1.5e941cd01c02491042063bd5bee4p-2Q, -0x1.d2a0789936f63c584facf579998ap+1Q, 0x1.940e89f9fbe3b90fa47d37c5f5dep+0Q, -0x1.f62a7689777aabb4ab21adf5f4dbp-3Q, -0x1.2b3b3b35a204159ed027231f9fb4p-6Q, 0x1.3de2ba1c1b05528a92fff0293ae7p-7Q, -0x1.21cbeea2dd955597cbff136c8ae1p-11Q, -0x1.2150f65158193f62d7d7fa29a2c2p-15Q, 0x1.159bf889454c6b38325ea21f7134p-20Q, 0x1.b00f4f96ce85167dd0220fed62e7p-30Q, -0x1.21e8e13c855c01e5c446a2405ce7p-37Q, 0x1.33590911079747fc32e0ed899892p-54Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.29b15e8e05f4922e7d4e47048a9cp+1Q, -0x1.cfd365d6145278198eca9c82d9f8p+3Q, 0x1.440caad9c12360807dafb3bad1d1p+5Q, -0x1.116de9d813b38a3407c462c9c8afp+6Q, 0x1.3b639c503b3cf7fe4e226236b434p+6Q, -0x1.0040f57e975e1a258b9875fe1f17p+6Q, 0x1.e6fde6a95ce32902224ee9a0f717p+4Q, 0x1.5c1e9e155aab7b67b6f0684e8054p+3Q, -0x1.b1e5da7957b3c8fabda1cfa1992fp+5Q, 0x1.7d1f138d16b9d31aa28298c6d585p+6Q, -0x1.d6f4cad7bdd82bc575e84a0ae447p+6Q, 0x1.9fd808c31038fd9d9f9820868c69p+6Q, -0x1.ecec6e1a57ab3b47a08d37ee9238p+5Q, 0x1.43fff7220eba3de58880aab6571cp+4Q, 0x1.5e941cd01c024910420637b6b61bp-2Q, -0x1.d2a0789936f63c584facf37b3e67p+1Q, 0x1.940e89f9fbe3b90fa47d360fd472p+0Q, -0x1.f62a7689777aabb4ab21abcf7e27p-3Q, -0x1.2b3b3b35a204159ed02721cadaafp-6Q, 0x1.3de2ba1c1b05528a92ffeeb8fc2ep-7Q, -0x1.21cbeea2dd955597cbff120c27ccp-11Q, -0x1.2150f65158193f62d7d7f8ca1f69p-15Q, 0x1.159bf889454c6b38325ea0bd0aa7p-20Q, 0x1.b00f4f96ce85167dd0220db19d66p-30Q, -0x1.21e8e13c855c01e5c446a0ad86p-37Q, 0x1.33590911079747fc32e0ebbb9924p-54Q, 0x0p+0Q};
             }
             if constexpr (order == 6) {
-                return {0x0p+0Q, 0x1.3069c9b572d786eb96d928fa48f8p+2Q, -0x1.2e376983f6cb6b3abd6845551e34p+5Q, 0x1.1366d92966ea16320047797424ccp+7Q, -0x1.37b9852173f06f1765e1ff0e8531p+8Q, 0x1.ff3f2db6a15a3d87e9d7dfab891bp+8Q, -0x1.57d9383606e506f39f38559de18fp+9Q, 0x1.9e8b97533b1eae6eef5cca38387bp+9Q, -0x1.c556790a27e1d4367bdf83babbd1p+9Q, 0x1.af9eb47abc08e08daae8abacd91fp+9Q, -0x1.5e3047bf51b54c27591544583f14p+9Q, 0x1.efd9329bb40ff6440883f1147f56p+8Q, -0x1.337ec090261a5db68ef97d7b1236p+8Q, 0x1.1dd7e09a266914bfb2df709f94d8p+7Q, -0x1.34f8d53391e95dda3b7a1cf411e9p+4Q, -0x1.1b6423ffa4134de5e81b17a17c11p+5Q, 0x1.038ecbdebefe39ca7724b3c832fcp+5Q, -0x1.9f2073b507553852ed1a72469f32p+3Q, 0x1.0d3b2378aacf1f56c9dbd6da2754p+1Q, 0x1.b93ffbdcbcfbcafb2828e85b9cf7p-3Q, -0x1.00284db90f95b583e4f97482c916p-3Q, 0x1.5202609236b6be9cf16ae9fb3f51p-7Q, 0x1.4b9320a57f2323116dd63710b5p-11Q, -0x1.d3b085775602aad7427a22c98a84p-16Q, -0x1.e975304f420640f339ac29b10f7bp-25Q, 0x1.e5cecfa6ab7bb5421ef8ce75b514p-32Q, -0x1.0188e4a2f5a9df06f68769623342p-47Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.3069c9b572d786eb96d929d90cddp+2Q, -0x1.2e376983f6cb6b3abd68459b0db9p+5Q, 0x1.1366d92966ea16320047794482afp+7Q, -0x1.37b9852173f06f1765e1fe9f84p+8Q, 0x1.ff3f2db6a15a3d87e9d7df5b42f3p+8Q, -0x1.57d9383606e506f39f38563cb6bep+9Q, 0x1.9e8b97533b1eae6eef5ccc2c8b76p+9Q, -0x1.c556790a27e1d4367bdf86d03f05p+9Q, 0x1.af9eb47abc08e08daae8af537da6p+9Q, -0x1.5e3047bf51b54c2759154839c7dbp+9Q, 0x1.efd9329bb40ff6440883f8a40f82p+8Q, -0x1.337ec090261a5db68ef9839a3fcp+8Q, 0x1.1dd7e09a266914bfb2df7819245bp+7Q, -0x1.34f8d53391e95dda3b7a36e1f269p+4Q, -0x1.1b6423ffa4134de5e81b13aa374dp+5Q, 0x1.038ecbdebefe39ca7724b2c5d6b5p+5Q, -0x1.9f2073b507553852ed1a7122dc5cp+3Q, 0x1.0d3b2378aacf1f56c9dbd6033ed8p+1Q, 0x1.b93ffbdcbcfbcafb2828e4f8a1e6p-3Q, -0x1.00284db90f95b583e4f9723dea4p-3Q, 0x1.5202609236b6be9cf16ae5695042p-7Q, 0x1.4b9320a57f2323116dd63291deebp-11Q, -0x1.d3b085775602aad7427a1a128489p-16Q, -0x1.e975304f420640f339ac1f2721b2p-25Q, 0x1.e5cecfa6ab7bb5421ef8c106f4f7p-32Q, -0x1.0188e4a2f5a9df06f6875fecaac5p-47Q, 0x0p+0Q};
             }
             if constexpr (order == 7) {
-                return {0x0p+0Q, 0x1.f579b17074e36836eacdef034d32p+2Q, -0x1.13b9cbe766166f25c9dacf502f0ep+6Q, 0x1.0d0d0432bec134cd566f573a6ab7p+8Q, -0x1.309a86e68bfe9899fc0e7b2c0b24p+9Q, 0x1.b8e26231ea03e8ec859801e86e25p+9Q, -0x1.b08b284517ec42e681060fcc6182p+9Q, 0x1.3c7d2b26245024778e757ad1afa1p+9Q, -0x1.7e7def0dd6c17f062ac250175abcp+8Q, 0x1.9c880448390e60397d60bff8dd4cp+5Q, 0x1.dc1752cc2f2f84356ce88f9e5906p+8Q, -0x1.e54a03fbbc2fa46a839c73f788e9p+9Q, 0x1.1a42e1dae56904bbcf40d542b472p+10Q, -0x1.f903f4a18c30e32dc6c45f366ebp+9Q, 0x1.9d8db919083864fcc4e33e87dba9p+9Q, -0x1.34173ffb143e1d9eed0ece396b8p+9Q, 0x1.64eb3c27db564d469eb22cf2354cp+8Q, -0x1.0b0c43171fee5929daa625b8080cp+7Q, 0x1.5f0a5375d11c72dc55998ba597dbp+4Q, 0x1.d8f6b9f1522f2e96a9e605cbb38dp+1Q, -0x1.1c75896d6d598c65080cc6678602p+1Q, 0x1.f38ac1a749daef77915dd8d10d16p-3Q, 0x1.f82700b4dc7274aa9bdb17c1024cp-7Q, -0x1.1306135d4672f12980f476eef1d1p-10Q, -0x1.2dc514d6999140dbb2a33c5d5ad2p-19Q, 0x1.1d494ae1d331f410d690ac5ec36dp-25Q, -0x1.2e8464bcec8d40ffd77c2dc57367p-40Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.f579b17074e36836eacdf20b2124p+2Q, -0x1.13b9cbe766166f25c9dace3616b1p+6Q, 0x1.0d0d0432bec134cd566f5783ca25p+8Q, -0x1.309a86e68bfe9899fc0e86f2260fp+9Q, 0x1.b8e26231ea03e8ec859843dc6ce9p+9Q, -0x1.b08b284517ec42e68106ca8a8bc1p+9Q, 0x1.3c7d2b26245024778e76cf716fbfp+9Q, -0x1.7e7def0dd6c17f062ac5f280847p+8Q, 0x1.9c880448390e60397d83aacda54p+5Q, 0x1.dc1752cc2f2f84356ce375550f21p+8Q, -0x1.e54a03fbbc2fa46a8399b07d254cp+9Q, 0x1.1a42e1dae56904bbcf3f8f7fa5c7p+10Q, -0x1.f903f4a18c30e32dc6c260029f14p+9Q, 0x1.9d8db919083864fcc4e1ce713df3p+9Q, -0x1.34173ffb143e1d9eed0dd73c6925p+9Q, 0x1.64eb3c27db564d469eb11c515c5dp+8Q, -0x1.0b0c43171fee5929daa55b569994p+7Q, 0x1.5f0a5375d11c72dc55988338ff36p+4Q, 0x1.d8f6b9f1522f2e96a9e46aa5caf8p+1Q, -0x1.1c75896d6d598c65080bd27d32aap+1Q, 0x1.f38ac1a749daef77915c1d44f9d7p-3Q, 0x1.f82700b4dc7274aa9bd956d7234cp-7Q, -0x1.1306135d4672f12980f36c25a44ep-10Q, -0x1.2dc514d6999140dbb2a21c1d56f1p-19Q, 0x1.1d494ae1d331f410d68f7a178351p-25Q, -0x1.2e8464bcec8d40ffd77ac9bbd77ap-40Q, 0x0p+0Q};
             }
             if constexpr (order == 8) {
-                return {0x0p+0Q, 0x1.e32cc25ea4da498425dec5295c6bp+2Q, -0x1.1692ca6458ea9e38b44f5a5caee1p+6Q, 0x1.1fa09c1316dfb4b439ac84209c53p+8Q, -0x1.615e67f0c1ccc897da6e59c7c927p+9Q, 0x1.265c8c1b4b1aa4b3e36ae2efb333p+10Q, -0x1.7569ed1c8210ca209e4700bf211ep+10Q, 0x1.9e96bde5063d41cf09d912f51fep+10Q, -0x1.bbbe167a38d63287ecfd91133a36p+10Q, 0x1.be080201e737d36f7e786ff84c53p+10Q, -0x1.8f099bdabb21898e35971dfd6953p+10Q, 0x1.43b83815e15a62b284efdec504bp+10Q, -0x1.ee6ad68b3bda4ee4ba8a3ff07fd1p+9Q, 0x1.58d561cb84d267ecaf620ab5b2e6p+9Q, -0x1.a3b282a8407a310226d6a98bfd4cp+8Q, 0x1.c79d620ffafc0589079d1ba6c99bp+7Q, -0x1.bc78cb9447aa124d62b13f580945p+6Q, 0x1.418e35902e32cdd0c2f0c12b4efbp+5Q, -0x1.3abf360acc2f742d878f5bcabe87p+2Q, -0x1.ad7bb3867b3c2b046f8005354fafp+1Q, 0x1.a655024ebf2fd4378620fe654a6cp+0Q, -0x1.affdcd4718ba7f1a9653624c15d7p-3Q, -0x1.8341cd6c6b0a9d48905914abd48fp-7Q, 0x1.b55710d3ebf552b754e9b7ff147ep-10Q, 0x1.e321738ab144873b6e430caac23ep-19Q, -0x1.c53c1373c88584f948dc218ab05ap-24Q, 0x1.e0c270acb15c5fb504672c4070dp-38Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.e32cc25ea4da498425dfec2497a6p+2Q, -0x1.1692ca6458ea9e38b45000f9e974p+6Q, 0x1.1fa09c1316dfb4b439ad2e78bb59p+8Q, -0x1.615e67f0c1ccc897da6f2d005018p+9Q, 0x1.265c8c1b4b1aa4b3e36b99e4a1a9p+10Q, -0x1.7569ed1c8210ca209e47f9d0511cp+10Q, 0x1.9e96bde5063d41cf09da3c270b93p+10Q, -0x1.bbbe167a38d63287ecfeda29fbbep+10Q, 0x1.be080201e737d36f7e79bffa876fp+10Q, -0x1.8f099bdabb21898e359857d34007p+10Q, 0x1.43b83815e15a62b284f0ee906572p+10Q, -0x1.ee6ad68b3bda4ee4ba8bf16f4fabp+9Q, 0x1.58d561cb84d267ecaf633fb5a5d5p+9Q, -0x1.a3b282a8407a310226d833dadcd5p+8Q, 0x1.c79d620ffafc0589079eea90279ap+7Q, -0x1.bc78cb9447aa124d62b31a0a7f54p+6Q, 0x1.418e35902e32cdd0c2f21fb873ep+5Q, -0x1.3abf360acc2f742d879127375bb2p+2Q, -0x1.ad7bb3867b3c2b046f80e1cb0482p+1Q, 0x1.a655024ebf2fd4378622021ee814p+0Q, -0x1.affdcd4718ba7f1a965455b89c8ep-3Q, -0x1.8341cd6c6b0a9d48905a1ecfc91fp-7Q, 0x1.b55710d3ebf552b754ea432b16e1p-10Q, 0x1.e321738ab144873b6e4379081333p-19Q, -0x1.c53c1373c88584f948dc39838bd8p-24Q, 0x1.e0c270acb15c5fb50466c4df9e1p-38Q, 0x0p+0Q};
             }
             if constexpr (order == 9) {
-                return {0x0p+0Q, 0x1.8d1f8a32797636f66137fdd0b5a1p+2Q, -0x1.d4881995a0c1ea2394012c228a31p+5Q, 0x1.e86d414a78e33b3180b504d86b91p+7Q, -0x1.280027c9b087591ad85eeab44da9p+9Q, 0x1.d3eb5f0b0594c2750ef22285fa37p+9Q, -0x1.0b82a55c2799ede8dec310d6a2c6p+10Q, 0x1.07ce9f70ddb2869a6583adf6dec9p+10Q, -0x1.0d7822536789d9033e721121699dp+10Q, 0x1.0df61d2a506b1f8fcfe8714e12afp+10Q, -0x1.c6893ac6cda6b55a49442539d592p+9Q, 0x1.45ac9e808978822ff4aec18a24f6p+9Q, -0x1.c9d686e237043dec7c0766428b6p+8Q, 0x1.35c4c3819b30f9b6fdd7719012dbp+8Q, -0x1.4a58be360f4f421d89ea2c96a33ep+7Q, 0x1.017559c35f7610aa1b74c79cf6fcp+6Q, -0x1.5d1ba7f13474232b930160e8fda2p+4Q, 0x1.dadd49a935c8394385dd6633289ep+1Q, 0x1.87b01fd4326a3668ccbada1018e4p+2Q, -0x1.9ab15d247f90f9fe7c9c31997416p+2Q, 0x1.46cd6a0d33a48aafbbc2d2b2efc4p+1Q, -0x1.8955d7defe0d52172967ed8290b5p-2Q, -0x1.85244f4e65bbc4ccef79bedeb2b3p-7Q, 0x1.6f86d3c43106164aba3a27d3b092p-8Q, 0x1.1b4e3c12a74dff21568f7bbd6f64p-16Q, -0x1.7914d82d3193f580c3333edc5ffbp-21Q, 0x1.903b4b44dd8c7c0a4e6f8896b442p-34Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.8d1f8a32797636f661365be0e3e6p+2Q, -0x1.d4881995a0c1ea2393ff422e453fp+5Q, 0x1.e86d414a78e33b3180b306c7fb52p+7Q, -0x1.280027c9b087591ad85db337ae83p+9Q, 0x1.d3eb5f0b0594c2750ef02a700404p+9Q, -0x1.0b82a55c2799ede8dec1e33e1dcdp+10Q, 0x1.07ce9f70ddb2869a658274b505f1p+10Q, -0x1.0d7822536789d9033e70cbead7bap+10Q, 0x1.0df61d2a506b1f8fcfe72d1ca4cdp+10Q, -0x1.c6893ac6cda6b55a4941f5e57261p+9Q, 0x1.45ac9e808978822ff4ad1899b3b8p+9Q, -0x1.c9d686e237043dec7c04f88fd885p+8Q, 0x1.35c4c3819b30f9b6fdd5c67ec132p+8Q, -0x1.4a58be360f4f421d89e83ecf3267p+7Q, 0x1.017559c35f7610aa1b72e5e5a83p+6Q, -0x1.5d1ba7f13474232b92fdf4e5cb84p+4Q, 0x1.dadd49a935c8394385d3a3bdf6d5p+1Q, 0x1.87b01fd4326a3668ccbb1eed227dp+2Q, -0x1.9ab15d247f90f9fe7c9b6b3dd567p+2Q, 0x1.46cd6a0d33a48aafbbc221eb1f48p+1Q, -0x1.8955d7defe0d5217296739d07f07p-2Q, -0x1.85244f4e65bbc4ccef7883bc8ba1p-7Q, 0x1.6f86d3c43106164aba39dbfe0b2fp-8Q, 0x1.1b4e3c12a74dff21568f59de83f3p-16Q, -0x1.7914d82d3193f580c3335f167104p-21Q, 0x1.903b4b44dd8c7c0a4e702124dc3fp-34Q, 0x0p+0Q};
             }
             if constexpr (order == 10) {
-                return {0x0p+0Q, 0x1.041a0a897aa28eb3a0d59e3420dep+1Q, -0x1.3658b5d77609e7977d40f266e1abp+4Q, 0x1.5194af04e2f848c2193a50575354p+6Q, -0x1.c3df81f0aaf28bccb605744a68dcp+7Q, 0x1.ad183e8db3dabe867a16ea08db03p+8Q, -0x1.3d9c782d7007715e1138bf8d8bf5p+9Q, 0x1.852da35362a6d4101e0c1842b371p+9Q, -0x1.9cca18f6947dd0d5bebb456e26c7p+9Q, 0x1.9a6efa498935e2e3d81571c175b7p+9Q, -0x1.a300c2ebdd39d2620495c5f7e961p+9Q, 0x1.a735477cbff1b966c87efc4ff1fep+9Q, -0x1.7a384b1c312fbe2a2f241ae26c7ep+9Q, 0x1.2afd886ee72d716fc61db8011095p+9Q, -0x1.d0f63946d275b18c0f2f2351b8f4p+8Q, 0x1.6384c4a13f54dc153d6b4654b173p+8Q, -0x1.d6c269ce8bf34e1952e45981a53dp+7Q, 0x1.08982647617ff8ae60a05f4fb227p+7Q, -0x1.1f7e83a0711235a83ba8d41f6e49p+6Q, 0x1.2a5701b5bea0dde347c9c6a1a0bfp+5Q, -0x1.c18aa4ec1159b6d22d408f93473cp+3Q, 0x1.4dc13861658a8dd406c58e6b6d01p+1Q, 0x1.bd5ac19033244ca1bfd76ff5f84ap-5Q, -0x1.1aa94170fffad7174e6a949842fp-4Q, -0x1.97678bd8dc9fa54b7e11dee71cb2p-14Q, 0x1.25b3fc23ddcf5fe31e8523af1987p-16Q, -0x1.381fef501218e9cc3debb9c868adp-28Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.041a0a897aa28eb3a0ccade17e3cp+1Q, -0x1.3658b5d77609e7977d3641db3a11p+4Q, 0x1.5194af04e2f848c21930873e900ap+6Q, -0x1.c3df81f0aaf28bccb5fed61687cfp+7Q, 0x1.ad183e8db3dabe867a1b1e1d7e93p+8Q, -0x1.3d9c782d7007715e1144e807f092p+9Q, 0x1.852da35362a6d4101e229e2b5077p+9Q, -0x1.9cca18f6947dd0d5bed4aff692d8p+9Q, 0x1.9a6efa498935e2e3d82e1fd52122p+9Q, -0x1.a300c2ebdd39d26204b2e2ccd8bdp+9Q, 0x1.a735477cbff1b966c8a20eaae97p+9Q, -0x1.7a384b1c312fbe2a2f45b3550037p+9Q, 0x1.2afd886ee72d716fc638e75f48b8p+9Q, -0x1.d0f63946d275b18c0f5c2756f025p+8Q, 0x1.6384c4a13f54dc153d90136891aap+8Q, -0x1.d6c269ce8bf34e1953164b65a3d5p+7Q, 0x1.08982647617ff8ae60bccefbfe0fp+7Q, -0x1.1f7e83a0711235a83bc8e025bd62p+6Q, 0x1.2a5701b5bea0dde347ec02073e97p+5Q, -0x1.c18aa4ec1159b6d22d740e4f35cdp+3Q, 0x1.4dc13861658a8dd406eb1a845d5ap+1Q, 0x1.bd5ac19033244ca1c006b305a421p-5Q, -0x1.1aa94170fffad7174e8899965ff8p-4Q, -0x1.97678bd8dc9fa54b7e4c01f3ba2ap-14Q, 0x1.25b3fc23ddcf5fe31ea2281e4301p-16Q, -0x1.381fef501218e9cc3e0863bb3cadp-28Q, 0x0p+0Q};
             }
             if constexpr (order == 11) {
-                return {0x0p+0Q, 0x1.456a1d2a45d0d4e9e190da6b0253p+0Q, -0x1.86731e38f2c9e9bd245d8c21307ep+3Q, 0x1.99ddae9b5957da8932ffd7759bbep+5Q, -0x1.ebccc1d5d759a0cf4ae087b81294p+6Q, 0x1.74f85dd906948af50c25a724f709p+7Q, -0x1.8426225b26443b4ef3ccb7b8d05cp+7Q, 0x1.4fbcc1bdf3f1963c49ab7f076eabp+7Q, -0x1.4776c0e99319f61e68a708d5d7adp+7Q, 0x1.573bef3fda7eadeaaa4494427daep+7Q, -0x1.2b0c271bd883e242fddb7fb5c9c1p+7Q, 0x1.bb5bca80b624fa5bb27c8fee01a2p+6Q, -0x1.5808025c93fa4e6af5aadac355cep+6Q, 0x1.0c1df40cf5e4c4ea44443af3add6p+6Q, -0x1.5dea01151a3e197eb05656a3cb23p+5Q, 0x1.997fc95198573b527728fd6a3ac8p+4Q, -0x1.f5c4140f2a03e036d1612965ff32p+3Q, 0x1.1578f4041624b0e3ebbe577cc0e3p+3Q, -0x1.e11a4c47848258b137fd42f6f749p+1Q, 0x1.8c2f5a8cae553e89ef2299c46ab4p+0Q, -0x1.42cdddde9b71e8354b8f6892a693p-1Q, 0x1.1b37523680cd9a16c0e89cedee59p-3Q, 0x1.61bca3fd3effb1c3f582ac5eba63p-7Q, -0x1.eeca78cc1dd9a8d407ad8882646ep-8Q, 0x1.427b3775515b64598a1525510bb3p-14Q, 0x1.1c6c30fb5472c91c3ee448e49edcp-18Q, -0x1.2f056506ce5e619914cfa74f5c81p-29Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.456a1d2a45d0d4e9e18e4013bda3p+0Q, -0x1.86731e38f2c9e9bd245a6d7f6e86p+3Q, 0x1.99ddae9b5957da8932fc9013b15ep+5Q, -0x1.ebccc1d5d759a0cf4adc92beb271p+6Q, 0x1.74f85dd906948af50c229b89c98dp+7Q, -0x1.8426225b26443b4ef3c972f9489bp+7Q, 0x1.4fbcc1bdf3f1963c49a88c06aa08p+7Q, -0x1.4776c0e99319f61e68a41fbe42b3p+7Q, 0x1.573bef3fda7eadeaaa4191468e3p+7Q, -0x1.2b0c271bd883e242fdd8d9725e0bp+7Q, 0x1.bb5bca80b624fa5bb278816db9f3p+6Q, -0x1.5808025c93fa4e6af5a7ad436556p+6Q, 0x1.0c1df40cf5e4c4ea4441c80693a5p+6Q, -0x1.5dea01151a3e197eb05317c268edp+5Q, 0x1.997fc95198573b5277250e908707p+4Q, -0x1.f5c4140f2a03e036d15c57dbb36p+3Q, 0x1.1578f4041624b0e3ebbbb44abecfp+3Q, -0x1.e11a4c47848258b137f885157e3p+1Q, 0x1.8c2f5a8cae553e89ef1e861ef5b3p+0Q, -0x1.42cdddde9b71e8354b8c2fb7c09ep-1Q, 0x1.1b37523680cd9a16c0e5dc3ebd03p-3Q, 0x1.61bca3fd3effb1c3f5807afcb9adp-7Q, -0x1.eeca78cc1dd9a8d407a9b1f6577bp-8Q, 0x1.427b3775515b64598a140f609c8fp-14Q, 0x1.1c6c30fb5472c91c3ee2a25808b3p-18Q, -0x1.2f056506ce5e619914ce605b0524p-29Q, 0x0p+0Q};
             }
             if constexpr (order == 12) {
-                return {0x0p+0Q, 0x1.45a484f799a722e4cd93e3b2b27ep-2Q, -0x1.87cf9eab4f40073db99d0811247ap+1Q, 0x1.99aecd437634b1af52fa61911031p+3Q, -0x1.e335dd2c6e9de306d05b0cd1cef8p+4Q, 0x1.5e3841e2195098fae8b63a8bc104p+5Q, -0x1.48839e048b83d3127ebd4015d2fap+5Q, 0x1.e11a7f30735e301f0eb1189e687ap+4Q, -0x1.bff27724d4103b12e928ab4222e3p+4Q, 0x1.f68b6fe2ccc3168c1a13f5cdae6fp+4Q, -0x1.a9c89c30bca221a764aca7ca6dcfp+4Q, 0x1.147ddad811d2b11feabd90554e5p+4Q, -0x1.a10ee0eb1ccb64a80031cb887a99p+3Q, 0x1.5d8b9ffe3cdb891325e866af6c37p+3Q, -0x1.b0eebf69279efaf954db661df6b8p+2Q, 0x1.b180929e1a69b7ef5326dddd752dp+1Q, -0x1.11a2d370771ca7d9ba7b5ac54127p+1Q, 0x1.45b0d998cab377e10ef261593991p+0Q, -0x1.d74083eaced416102c8bdf26f325p-2Q, 0x1.27c1113b5bdb797524261b6d46bap-3Q, -0x1.2ee6a8512694e4da2e59c12b6ea6p-4Q, 0x1.0ad11030da22955532efbb615d1ap-6Q, 0x1.b719ad4ae715fb13a423a1010a46p-8Q, -0x1.7b5726cd7507b577ab862e7a3077p-9Q, 0x1.efe0e7fbce7f41797c6619cc6d2bp-14Q, 0x1.116839f7247ae044e8df44cc0f86p-18Q, -0x1.24c158fd367df5563092d5399988p-28Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.45a484f799a722e4cd950a09d5fbp-2Q, -0x1.87cf9eab4f40073db99e6a0fb481p+1Q, 0x1.99aecd437634b1af52fbd40a01bcp+3Q, -0x1.e335dd2c6e9de306d05cc358c6bp+4Q, 0x1.5e3841e2195098fae8b77b691b21p+5Q, -0x1.48839e048b83d3127ebe74020885p+5Q, 0x1.e11a7f30735e301f0eb2ede8063fp+4Q, -0x1.bff27724d4103b12e92a64b54c9dp+4Q, 0x1.f68b6fe2ccc3168c1a15db6eeebdp+4Q, -0x1.a9c89c30bca221a764ae454bfb09p+4Q, 0x1.147ddad811d2b11feabea5bba8adp+4Q, -0x1.a10ee0eb1ccb64a80033704ddb98p+3Q, 0x1.5d8b9ffe3cdb891325e9bfc9fb55p+3Q, -0x1.b0eebf69279efaf954dd166c21dep+2Q, 0x1.b180929e1a69b7ef5328a0cfd4a4p+1Q, -0x1.11a2d370771ca7d9ba7c7444df33p+1Q, 0x1.45b0d998cab377e10ef3a92e12dfp+0Q, -0x1.d74083eaced416102c8dd2af61fp-2Q, 0x1.27c1113b5bdb7975242772f43479p-3Q, -0x1.2ee6a8512694e4da2e5b07f1c606p-4Q, 0x1.0ad11030da22955532f0e66e0c83p-6Q, 0x1.b719ad4ae715fb13a424d63fb241p-8Q, -0x1.7b5726cd7507b577ab874fe8a876p-9Q, 0x1.efe0e7fbce7f41797c67293a0937p-14Q, 0x1.116839f7247ae044e8dfdefe7163p-18Q, -0x1.24c158fd367df5563093507c0edcp-28Q, 0x0p+0Q};
             }
             if constexpr (order == 13) {
-                return {0x0p+0Q, 0x1.439a95b32a47eb5722e3fe0fb9bbp-5Q, -0x1.85e5f8ce20b701780e206438509dp-2Q, 0x1.959ab595a2ea47cca9401bb631dfp+0Q, -0x1.d591277dff53d8dcf592be17f8e1p+1Q, 0x1.43a6564933b3f0805a5abb1bb626p+2Q, -0x1.0a2c05cc597aaccc032e0cf740cp+2Q, 0x1.273950f6ffd17ee92b3278320e9fp+1Q, -0x1.050c8b9cb84b7c5048bc8a039239p+1Q, 0x1.600ea820111d062fdf2aa3ec8771p+1Q, -0x1.21f61a844a104f06b392ed4a3d9ep+1Q, 0x1.19f0e6ef31a0d26707b469b32ea9p+0Q, -0x1.8e2103144a726110a5663399778ep-1Q, 0x1.a07f2894f970eb1bd26c87860d76p-1Q, -0x1.ccce8527cee5c45450ee4b3e11ffp-2Q, 0x1.e56137866a8254327c31b42ae307p-4Q, -0x1.5df48c0c87cd72cb9ba718d2f9cp-4Q, 0x1.19d3f039c46cde096e5a0e03efccp-4Q, -0x1.9e6cd0f61f4caa9b0d4d30e7aa99p-9Q, -0x1.b966bdf45728a5a5bb305da1c562p-7Q, 0x1.8240771a20727b5953c65907a26p-9Q, -0x1.1b05a2f57f924748a24f59ba5cdcp-9Q, 0x1.7f8554959f4a532982e2e14a363ap-9Q, -0x1.23710df832eb1845bb5334680795p-10Q, 0x1.cc575afdf3f3ce7d0de6d2cce6aep-14Q, 0x1.1f238196ae22e33d868784888e07p-18Q, -0x1.3697e9bf43069ef0c328e5cc56bbp-27Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.439a95b32a47eb5722e3cd7fe3cap-5Q, -0x1.85e5f8ce20b701780e2029b7ff55p-2Q, 0x1.959ab595a2ea47cca93fdec47d03p+0Q, -0x1.d591277dff53d8dcf59277336155p+1Q, 0x1.43a6564933b3f0805a5a899c5bb9p+2Q, -0x1.0a2c05cc597aaccc032de2cc831fp+2Q, 0x1.273950f6ffd17ee92b32456caf9bp+1Q, -0x1.050c8b9cb84b7c5048bc5cd2f92ep+1Q, 0x1.600ea820111d062fdf2a6acf661cp+1Q, -0x1.21f61a844a104f06b392bde6725p+1Q, 0x1.19f0e6ef31a0d26707b436c0ada9p+0Q, -0x1.8e2103144a726110a565e981ea79p-1Q, 0x1.a07f2894f970eb1bd26c4012674ap-1Q, -0x1.ccce8527cee5c45450edf8973a9cp-2Q, 0x1.e56137866a8254327c313c62b4d6p-4Q, -0x1.5df48c0c87cd72cb9ba6c6b9ceadp-4Q, 0x1.19d3f039c46cde096e59d4adaef2p-4Q, -0x1.9e6cd0f61f4caa9b0d4bb0b897fp-9Q, -0x1.b966bdf45728a5a5bb304f91c5cp-7Q, 0x1.8240771a20727b5953c676de8a9p-9Q, -0x1.1b05a2f57f924748a24f50e9e6eep-9Q, 0x1.7f8554959f4a532982e2ba397a2fp-9Q, -0x1.23710df832eb1845bb5316dc1abfp-10Q, 0x1.cc575afdf3f3ce7d0de6ac81f14p-14Q, 0x1.1f238196ae22e33d86876e9e195ep-18Q, -0x1.3697e9bf43069ef0c328d37a1aebp-27Q, 0x0p+0Q};
             }
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            if constexpr (order == 0) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00115293332509096742962333483892313856362688845269995659187394173081837979723"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.115048275548763287879127945985463599972775459285064004095554421826950893087"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.796989658584277062411937010559864103043001629105734220965026462739268209643"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.261282555787182265882706163765054116695305731989757725047913151702289063990"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.304792526251077945867767239314414983616168566481167348823874432025337651187"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.206177381720140253354071811928730787659997169191432596424777801677056654936"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.108990380164014469211374498205641904963307679906212370075411833415284835295"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0414323567767714336655575435550014435859114005804252743467739002617028032556"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00740550451904298413275770194104519624796412659431510963194058424609244583855"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00265190650453840226202382246051294213464963751920614087594043518495040017701"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00240210420772995773725343184085600070474699593300395536783639652419272638655"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000695275865120426856318173618858975815994589786388847596433982307511410977064"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000191974030759909635472313378575369891683691026590204627382371876560571031362"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000369086435191623599908102272586735250422568493003535062380722233574951016029"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000415287237890283585845050020110906559871983453862988696226792814210793873275"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000213293271762831680444514966056532349654366183092419194511477231701438124426"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000519152984288816673375386899946665294276591318147000925448293729776300076533"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000868932288799631112269973020748320326319607540201446697303589532523058640376"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000353885033203391238239173859710183402146968653187882395070568528196527541446"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000195263099667140461506853591672068520568701722861147310552025237678358948376"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000760118658661622931484977499946668576063487666390672568814742992660278581129"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000134025692809696893389568339892947369168469910164958708207111959469432500771"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000142003995353734011507760517926628916988777854097085265899981211240745997152"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000158532613505743630429831947577865370489228544853275053068484397376569424042"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000000000355030930001146155860382376996084936412851909339999461687756186476889838277"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000000000000000000897306502669997242383001671446525458224541863620223787779391644190926610050"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 1) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00781098944203546971796976286517434035884009688773248606224515220005414202600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.352022489829734113542431984005808736473724699510524912312303517596181907952"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.655045582260019530471586793705288409958328082576128477269067038800474460343"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.61514753125980808044495957120916454545964651551944410129115969858552545691"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.965045518121368371649657414431609409876079256511530108438864454295064039152"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.613862904376251107603567359503339925389993434358836078881583881755180373456"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.411202640895789674547585554456016331268606109870526886150894523201400069359"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.248670727161188410367077352077023110486766838261792327161508712754116165892"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.121074212103689294850946226679458285881379881523239286723535403732539992908"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0441123812800529610355488980147434896876334272618270449617517207697232204447"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0113462062209348030398079804396363956598508998796900777431886698352753187169"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00193201430777827515696813853521806116958501580116959470619810785172817252196"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000131458959852363274552068404289595280980320518543359612758830152196452510244"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000907640061777183255547701282076901148256668421380966288924343020509113784790"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000556465237685112725274835827463099540776609744280841662958102231266930097713"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000110930471347758540199575897934132437541479940508074917148850579912551630419"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000540163721305599951324898771320582892046233366679859045334581706862592762034"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000258336622635775732966000369446951153794507695432350051229799820914271331972"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000327968834281282285800082226655395639101026250341990601757011633171502265437"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000916488171514711030622268872903433690707685750686927346624592740598447942041"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000765257940990005274758907789178871368045869308567592594682817218494349636475"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000113806898255625919280795529887274235588918418565838791672065942227585229403"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000201367733903050668198447517300557877789704362876084808722846353524567227922"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000444836034640325638288709395930623143471945459846091722425723736229604149591"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000000103956338676397028751708008201484812724312022305577756338111796159549805791"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000525480561641109164137864688009776045386815264957861417756490150159142136333"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 2) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0450303798117733589231798330957691280417239896756051304263138384820087822720"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.797382848905352224261209402370274675556632019052816074828369432733398437194"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.35210698233259733766168097865537427607660034980120464334236932299708410774"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.447488872512337268222446766248936491151740076284709909184963796609707232255"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.94752689746260427086971810378552771942897218308070519347370198965733742471"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.56320128886138359744668398388042143870937778524339089182916328446012293685"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.715557402348272306878574425353637462359702067943253760692428908902502127827"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0464893758331106893607592418969309234589119778040679971376996748085292908751"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.224276010818501093466222589488380871765384010383119945740817975057642024404"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.192110046121212755900487444382509639513398567516218319022991979288220691964"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0737873471966185978956886225677444795250476204861205019199449953274778830157"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00320598955242186941919016686957021369970437347319710965669749910809644144859"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0106672024910406572727634384630232126394512616065206839400078471641232182677"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00486953420262908335767503491652246905399023769268129286510776073032697296330"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000617131311240191212204138459081818690294990133002525462438346490707490327298"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000192006665779021389446223341431010819375175205853618100042995321802178648239"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000787174045799788843691997530421226394107444626942089306529661594079889645065"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000781060441650629506094363225086284470818832491361256882121071831394044465309"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000529699265431996299782049699978331676802370855121232208197190378200993391878"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000118936457924373854837977028298636171996098002951110364373678539575607515220"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000297589448108271162186173745281562110809351136810307857224663251378623404416"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000150723480889045397495951808812346145543547998873595419531555416151101740824"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000177949404003867596126708357294529070318811557365468246834172229163385065083"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000149346484715446421742389146635163953260098009858086983961700451264624854098"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000178437796860002852739466568338831019080176013249284982357396229767567234102"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000180395062763246722611480959764856761895616090783365686732209021823579303995"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 3) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.213990005328375555135472755123681140600857383942097187754813778508021364188"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.861887577836364549248175536802065478416096122297736989669377523212045471882"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5.15213110442549193951604232130937181308428404117234799001678258735956565095"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("9.16617922201354414096203125317498717808490325566889445742435609535893499012"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.16474242641471677731657141502679363538951319294421818226908853664694404748"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.99786416685096083753063339505540880226836092318161102091793537672115020197"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.58671209326440268266270834820616632025849613943982416213412034046663096202"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.28355127250052801373193408526992202651493499277936659476824160108001663527"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.732252371428780979843072193742624736624407830994183828051335649974997274856"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.147325620855341831283808507199341730144107370475895883352377534229959735834"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.104919473342276336806466603437472988232748900776758986519994396324472688826"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.128652586070825684925857427195986593237515170617045438297383145109698161719"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0815695071328300519374023680966951688787126896982976686941014234357114383306"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0259212121580757805545526931754301057596596343151488765977950290614602386512"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00216220796475466148613393323709898748149018273039190022024143151723111058925"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00132230119892098570617802910816943973223564708652310398004809061573967486877"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000511478130422611034647765921441315956001733118732698933562593619541749240757"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000727931722918291769533207689510068034174609274026487647576221227404443932148"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000198467477327859725151632668232927044265781371367599997004215442660984250173"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000137665131612781247758064430980951835019601684631521207530971741938647123521"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000389782183547484796734257149006560609838069041845630777046077009454055077516"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000263515414830424927128095026380033778748765668296184726183106775537323610237"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000295350893893575030830965321544192503213832003549056472742964277263629493577"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000259129637850121514112507960811641537965052175737748298700466697875155415894"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000592088706033458993194518219229976516091225801153372985679944483340194107510"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000000000000119717821494849869283848954977146397574755733129894249448827837729810076385"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 4) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.804349784326216682870867698785172886444134341030013379480923806872389210182"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.26205835171941179466492112439570917665682264923715171509917130991657754821"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.389676077424230416143478970454295496570705374947551134412624558903693957362"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.50665866363348045173791462058611393187799649561744511666615181266556525337"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-11.44919593563404443567549116907041423485892301739312537780680544607026227450"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.498926901405939703754748719529238307648084150878656788578621629619041266705"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("21.85499228880599088108367065599633778080830640336126353491139487377126291490"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-36.65294070838647301945129468867112933197613656831189540767306372008014438400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("33.03456536770354634426204817939353419169101297781817748568812540141141197080"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-14.60053872582810659959110019246117175095717916824767895489330950154153858660"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.46962706645777312638247039900137791860967206654796163174026576977480987387"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("10.30962248301374157030523165146821356632153345092258177258520559837126810210"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.57311261844887687153807165858652718807055835283576547683012694195056627525"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.79001534274099632722381474645350538532531181171959960822639426785711952433"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.270397873572487832671740890029058330815124109161518604674414533906621857406"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.219747760578822357960973156509623996708163827579313466373374504890703266884"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.101020058397719647957772939429342398138576500365346222370704275039765224265"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0145180131614497906575545887380941805879110435808753820055197950564548997542"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000869674664088366018964976112111393474585517897253819178025469801026621804875"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000402437602038170326475359064730289991317678692634355675507889665235031988698"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000157333831012391713035661069783027485529501501626599828474665210765476845830"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000100663686623808993005735914014214151634495397934295300560534689374601506521"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000210557907426372698693118218926654314316158359635987623691480747866029773332"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000222352429334128564487183275318880826175118330587151288587139165085782937502"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000842699072214170360011169657801291451532530473218904368132644156798098455154"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000000000340786997123380217994206097107633742986612720155415914905510810501076907780"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 5) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.32572538313607829978389746978270909190734307023984404422047073276572977495"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-14.49455539524440351726698168751780539459260987086240364854595675556041720440"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("40.50618524666462883040099875675325706520261707900172515348692425641658202350"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-68.35733735676047669049239366744249712419067159860042852213104995281820518830"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("78.84727597581444768460178005038706262576538764836845319136066260811952559290"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-64.06343648718714169613025171834477509469983151692691172469095627688021698080"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("30.43698755414352264033439663090217787767167087477933221604545854702245623810"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("10.87873748942125422591144834448867784613801192203670182793848556854050145490"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-54.23723311232467779927904053473561262938773179018943014024452055789441234110"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("95.28034801913459537562741275266568339264065502105845420716508412412075458290"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-117.73905503364771243053821144754953234513956039081472901778742388505172072700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("103.96097092424883855673952920630316920634437408985849519918571970360275096700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-61.61544437961620491952244794812274205481917695799114432128072738554509227570"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("20.24999154380533592436955158213111619257037463818713373838162040877187311740"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.342361879541387890494808824835330981498119520599852480120579318951753686930"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.64552218896089808966481252208088406516442739396640944123173605413113182773"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.57834684708713170271798329721972342166058039720943334141687011992206759580"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.245198179311896545018681810103528580634841093773233002156532192404195001186"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0182636335580641564732299080907269542961766381772624145912713306330825337847"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00970110022918661336696551804862567263721137672239282216195334493673897459845"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000552743167971307219807849744125242795042626138923339525966494069954293592860"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000344891856325385166416658583064189966564335311286470958633679458661913797931"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000103417508718244228943518424219273200822254101350515749540962507511656921374"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000157182442556628960702195041921845074276654103625948693489495451100463539491"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000823972888028003765394181795355019473340350975899036984527963838403818247760"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000000666454293215207517366834719023360349661401835450888130511999977594605272998"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 6) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.75645678252782782681587560651169118663509412050066394815052936021223979271"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-37.77705672356517184937835295164453556498913303252724271691215564780459719470"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("137.70087556248931227876532575144504191693108683924786902505674311871685140800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-311.72468766289278751244167873028725267412977680278312051859849993755349858000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("511.24679128112096837423875276735646357386086403224153118196081493355880796200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-687.69702792488720143387763101613920716950152836894659515467184955111870724700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("829.09055557619773277153201541424732791228391594101613180539356376460906530000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-906.67556883761759119144339734345872385406981601833110610680243945196617211400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("863.23988279515629467219009455554599609695564774955725375711337575467810032600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-700.37718955506952165779246925908091030508123412802813106187016751364785945600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("495.84842847009709837548618485022243329167561710295186722949226664054303361100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-307.49512577944039191322332358612022792251918670092304811543750183524451060300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("142.92163545340421526365861071542027659143554694673554929974877824733260473200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-19.31075019974249281695001314578305393389661976831560477729541043029968645530"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-35.42389678687542349159085429311033037061651261095746807090649315454659711020"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("32.44472478885998336245698827148819308075084642463701991417768428456321519910"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-12.97271142346531917199152873167390275988083231450677228087810958984424846790"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.10336726562456364617075321297939313157799116307693031879047994718725361533"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.215454070733924659861657674199075159272461496572943747038111133916807431180"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.125076873025998884367293275645192665826157547026398718789437845293697450218"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0103152247942739012815455329995931706018816781048478764075881481121070428934"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000632428582946048424882721006475234390308064466530095906161174694249322311105"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000278764686901524008550509337752045901232947877228985594423383689960428632537"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000569803836285153459122322631284557498343961131423876580418354981637882246635"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000441839671114970335190048321139738477044887864798246264801711442171137680421"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000714802491411250263311395432961462470250092517743540216477594292648036570408"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 7) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("7.83555255872811652420708194699227564812880321923155066263002675188551650312"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-68.93144189415544000675178575437258773566065477015007536299582400232146657330"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("269.05084530980203113195209976663957867395958982717325865408524125280832289600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-609.20724183879537322285337615082333580989660439474364859024353018035946645100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("881.76862167288329121045005828312390919337410341070563414959329437576051276200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-865.08716643970594546719815251896043456283005565377418337268781988922266917400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("632.97787930272196253879414267424608924729579537423891361585357298689149584500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-382.49192892544806107967107677420182336459450422233847738473211880415489419400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("51.56641441749688691257145061609223937968957957563897087215371356736309599200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("476.09110714103691538203391357221546832760511254226534748414313636902906572500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-970.57824656189703500836118600041943699389979172697558754304893359616826066000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1129.04503509906141877125815880497121965193711448633760242286838210579239440000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1010.03090304703962359279554938202749376391098032905326508754718040588237804000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("827.10721123601323503307854258132213389426514427539892445355740294501216301600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-616.18164003837976580374414923629580236503935294323766247871764385789725455200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("356.91888665299329828378541153901250128644618483543100772119117850286192670900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-133.52394935860427189931791156205717267825075964749332862787915826632532923900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("21.94002100012019404144527346489003480219358689823929896317683112311592863680"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.69502949031117951496444168472697082874515564937581244488642154254744997400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.22233693926927989833058976676101529298211935367881160327330611362977023218"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.243917000692119383583915678923379880754017506303821621558764650571551691750"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0153855088662769439102973996146208075188236200845719957232671533824048761790"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00104913228216791853272658326910500670179817471111989137537944784605454771898"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000224836058331229111229619069684984372824683936236614925216433027243221835066"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000332116962946728334773864559940531738563382607925542513873526692874990639648"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000107475686000546477797319235583561376745354532533798623668423772676988174585"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 8) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("7.54960688822339828863999378130211115107233454769934866095750950044066864110"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-69.64335018913939576412750532175053097593146282468237041838535209525011079500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("287.62738150890773420089300813672822503003764015402682017757435224935102339200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-706.73754701102149477646316177625311732909677089373586648513230095487019075900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1177.44605142912275685331605707810452401861714128214534938401017832783574948000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1493.65509712888447960800673919759696151644981533694814393500245372102843458000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1658.35534024819665161123917470538298740518906057958085498478561548336905470000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1774.97012191343746012194081052068265568964145567960224351414437241219278396000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1784.12512252406968735163579655137194210741621555135274224751877746894409525000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1596.15013759874832367565454908792624435013153344056104405167995042995605546000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1294.87842318541656108750744374471145185200499138414568918290153915550984978000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-988.83467235968111377155392478265729751920701705649958745436470131875538876000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("689.66704696641391993630921163080325378181926796016541012035635061452929732200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-419.69730617117074092592055713546879516237193681933824681435866539141247425900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("227.80738878191733493720600320172052818250161128836771941990375971535089686000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-111.11796409308819226983125949342564517414825732596608930700760656952936161100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("40.19443810120569696285858753433708415600177908834568747073574318608759474100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.91792059950306926651430119033353633622113732985840244036194782614229968982"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.35533756319498030532906284051383779124200364840191901231906261851413833649"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.64973463461427566646558893739921141496585938147076501993510767086243184026"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.210933307392307199501252966945895447408339149689342782956931741370150254267"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0118181469959711297864759189693192594897107267351263521987717128479636953271"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00166832008560998294423971440046143918265510526709216268614254492975841760358"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000359960399029744056248273888253230981459983176116053582730091303462716930960"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000105526920365685108260660462141084882369839069051686223049397689800183455322"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000683200385904099418363562130595167945821162769743662314310034240089917492841"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 9) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.20505003861567011394067231344647893637847564329550367887681186357597624603"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-58.56645504853098766550134905340317870243260579145639275208040178526932370050"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("244.21338875508955935588425811438812427457999296948170249669130252684915021700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-592.00121422881665797081029294298226556332889632312076428918776482044056419900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("935.83883798382295862878655187263488883257992095069940720162185886844636534300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1070.04134277217209941069608841768441159120482934420543356273845894230382557000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1055.22848149919637141794358785954857337162302556268749973962161361211731374000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1077.87709508048227764719965364717319012422679016684137197779877347065587919000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1079.84553010800709048689467568224979315449213490504319509214561846839561023000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-909.07210621873438578205880244568413575768717508893273593436054423066636844000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("651.34858710014761262618216521874193874281211026897562234536865793145322519700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-457.83799566119363761546660688550395418970241445277522092347549225353673827100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("309.76860818899965620264934656056185819660289753982144311142670396948220345500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-165.17332619606861874818823388561165833646372925969907046409236334588737006800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("64.36460023183964610680737173822860851394300430996239129559691640194035450280"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-21.81925195904410301088997452499452793344229781102822411802597853821595862070"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.70987816583834887528727762977327608794555354259030464603411322315458032491"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.12012477609974627820032790014942916130826215990800053191225592823023213870"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.41707542957580268050903646486240388008805175493051843593484495999979780697"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.55314374584785171680308731725982270158371281797680529285657013298327299254"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.384116528497100269726445252348690123705919404254920353538891869983784142695"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0118756663548945587058921085727494958398593550092544335470975725373361134933"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00560801191403834230317024708819810653630256118877488149992512868367446594358"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000168863298975933200683541006085210976919654788572176120083523172920160215908"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000702368884519096062247768700675740067863675318587848764509402888807377333644"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000910021338458770684182677723795514188197183013650198912703110713825929499885"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 10) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.03204471314281361620436172860993718348048098798259830037497869722564324408"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-19.39665779270637271197815390366866221017887466456155522938642838644377623170"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("84.39519889483751381060448991759860643934416288701819870293485348031111678600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-225.93653823935280620043647247700590736347878865997028224628700438872489124900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("429.09470449105242027094920090767356206181107874783293562031855795674540336000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-635.22241752596063241363571132920423111589738106514102338073077249645227164900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("778.35654680554367290994709844961509436329929173664221414820797079265534104900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-825.57888681650695755069404722936648404036390595346071684154667140205899581400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("820.86701316070300215711624263370329545679945220152016165604116497162621943800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-838.00594852735561618490718834843576332267897766955677203329263194173445408300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("846.41624411937977897579029601634249128805349858445717455832716294555864902500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-756.43979217912372920397826846127055236422213608124884373684460009804242802200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("597.98072611129726849283643705505721881864863625292975587189812590758721018400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-464.96181147230317359880791138494390058432679338003629816618633802082886197700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("355.51862533374956883481354353388092712174852473789983192068789421486091538400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-235.37971349199656518700162583910157649836837484774547798711824684202151115700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("132.29716704430755790362823208197819789457340031860010362902088456007781211600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-71.87354899110919395713836059516566325587269396430109303014403933780264172090"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("37.29248373020173707451272057860274355374999201121543162524309965457643352150"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-14.04817434412944163979531519740059165943726494501644870873410209073124183660"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.60745911365218712785836635558941735911206189533873236470344886669699910838"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0543645649464435164847209914399195207149789580566453105860414107221369165038"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0690090709977073313739788485731020686097132104467534026187427787191497374569"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000971327966803672069290270496714838209254089051099247834705750725429421474607"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000175060669244915542274214040537534422700016855593378309967441792972141821778"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000454201283534597503030935884752199947078896835850213184419062952049362978252"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 11) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.27115042001770757342790580276725599737973526276595894891693693144453081333"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-12.20155249712689490713523680284407229529835475760492745017650272595157073840"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("51.23324319235233061317480157420850343391523283977889617744950185481521928880"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-122.94995817305462609579795659014989927849571013175696402717688054750353836700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("186.48509100156140575637738663903588922180843570634354620282154495701806571100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-194.07448086588021018245234658153261441759722529638841725717115567921577062400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("167.86866563418224671177891910686936996723856918707191383980497089062492466500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-163.73194055481597452012500435897749151331279668776584781713972098055426014000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("171.61705970327542643733736274773439348119447474649912026659814882053948896400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-149.52373587625510655685072490035410183051561878699286314353687011498822254500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("110.83963967429849116381035147455824238567048771273770112763575455632533722600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-86.00782150891480030613225128365285559176275614273843802468963964882341220180"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("67.02925129175963984371834894406440307377952153327523895227597589690079234370"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-43.73925987707458484571443317553902969922556666607444419305258116854809584890"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("25.59369785187796149597672205308510544347264131510511482728670598446185457330"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-15.68018534623854167865753994586968580089803038651229171712344769674882728010"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.67101479337829604724549631142381262698058260107053126173973190165021528756"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.75861505024024002675376566574475255211823912083547822262099741013249261042"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.54759756025881232336945003625817637725576271772356562382087334473774930037"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.630476888107043555221797973970574912788012829526634744673511131029200828552"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.138289110458663700735511423590028378928536403452989070482014794553004832387"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0107951927880023305749242734468149776729151693312718188651043715681726172060"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00754991006043983586111967321038913970058172016189708501693056751092430574556"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000768855369034014413090954158857823182271817483052059631674255096393926162955"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000423822734359358265360311498568469600739757885517978000979834786982597738573"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000220476848184896613372739980059823724812480482106220385749059723040813819200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 12) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.318010404217068952718034999205043880576086312876319450942332822179758832029"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.06102355351185926427319739531099202637190548705353100594409222193573135420"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("12.80258811164971729344541416108618061243147012390344502415152454109791488170"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-30.20065038067138441549116683827153320363339703988815649029826192469828800770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("43.77746941222910636253894420655558692365422509195889774642773187854112783890"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-41.06426623869672590682998039683326333327190758069356155782396545157455445810"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("30.06896895338094213763603114520529005887555601480166742767460715185260403040"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-27.99669565569003172852864940058873702820215437394869573794696284139245305100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("31.40904224961940872590760582915710475701943523191305275220782176766892814960"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-26.61147707975226987062278644044150684817213866306112594162111544688454753810"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("17.28072628404804003669507530790723055238159750081532699647611742207459371760"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-13.03306623382955516457538291782723729027040840647527902140735049489731225810"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("10.92329406410031923111395110524973244956738959185047643214517216152345088230"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.76457200306911915343728115159545396428972131599592522482710193109520612768"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.38673622817880270826803177141868102896290888908534559567608966529440899137"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.13778155318707274308581153289738935049994670784897895468735053193538091817"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.27222976665752962431763512471169495246258962134804638636049901609786075729"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.460207043844736395307656318205719088747297298981176544972613522761762760908"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.144411215423571925617311283427170089385196189708352755544769370328688396733"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0739504408724418236152196080232313887266756275356214749508197882784413005326"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0162851961244162892390054615243955015081698723875469655847838117885736756969"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00670013886238182672051081804470702049361779245043541997098482037556851799328"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00289413784660480308858813839825464801550958078392680116427992804058429400263"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000118226656863479167736819869491754498449905525596694943882369054828973203042"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000407408378246154606805470217575324383090557556739356701916389328686441606510"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000426014978607563594967116716485946096193409828602942187827734146599194530321"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 13) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0395024226975886260436015280169399958114854435612876899457087608537691328646"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.380760085660020846754522453148461762110774614299327773117958074184114684427"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.58439192679626572323538988717033413533100806730431629991619477048720282652"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.66849225666251646147181612467387048084530225694986405715851065686876160983"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.05702740810994469396903380618346647120804579341221278933287204214673197742"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.15893692928322415963268762106489569036113711224820559316556226723553567830"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.30643665371429659490852199582838744397805404586749517662546347864184908967"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.03944535400713878630113040918470478717641098007862715614235550735403115717"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.75044728818668477407502449063310312583442217870494512078004809643451540717"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.26532298526228934105124417738592200001859007857791140112570041681664957967"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.10133212413495876761478507881985817641573463205155919865756735554719635510"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.777595611788659331793825514823424823892310615830315312836845770694620189298"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.813470142541264561929778203493572597954340880125476192701684325142924496713"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.450006561808299358517226504782492541004402170854054357437291488004013112805"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.118500916380668803483753735483540194370353148612714533622232357622587131639"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0854382963811873726676785990040937155967645307765440929619971688798210204625"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0688056358160580011265953288213120273922091465442762386643516670175176351229"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00316181231306575845649567960204080415859090715018690879061132888462092674318"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0134704997550951956780703608930294861647935543468679644642083630288728953920"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00294686750299967882443641101664969682445375118992583309612547894575220278859"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00215928663487753773644923527389606027569391521127003378892960294361464727064"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00292603166127365869089828154580427557123447155142574321458389044685037686218"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00111176154864526774012502920031740858426807693116963525197176827996288733339"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000109753902477691254708467520181547449682815029110458229838831733837259897127"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000427869999580130042052373770473160246635622398207650727324687442110256565531"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000903945795865567602923370485955445191692438306505200188872053733298346930198"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+        }
     }
     if constexpr (p == 15) {
         if constexpr (std::is_same_v<Real, float>) {
             if constexpr (order == 0) {
-                return {0x0p+0f, 0x1.d99d62p-12f, 0x1.0d2f98p-4f, 0x1.4a5392p-1f, 0x1.1fc50ep-1f, -0x1.d49776p-2f, 0x1.3575a8p-2f, -0x1.7e644ap-3f, 0x1.a17858p-4f, -0x1.7135a6p-5f, 0x1.d8cfdcp-7f, -0x1.57e158p-9f, -0x1.5f6332p-15f, 0x1.10a458p-13f, -0x1.592264p-16f, 0x1.899798p-18f, -0x1.4f8412p-18f, 0x1.74953ep-20f, -0x1.f7cb1ap-26f, -0x1.c92be2p-26f, -0x1.3b9a58p-35f, -0x1.6a58cep-35f, 0x1.4bf1ecp-37f, 0x1.697068p-44f, -0x1.513d7ap-49f, -0x1.b3943cp-57f, 0x1.54d33p-67f, -0x1.3f6e1ep-80f, -0x1.d0d882p-104f, 0x0p+0f};
+                return {0x0p+0f, 0x1.d99d62p-12f, 0x1.0d2f98p-4f, 0x1.4a5392p-1f, 0x1.1fc50ep-1f, -0x1.d49776p-2f, 0x1.3575a8p-2f, -0x1.7e644ap-3f, 0x1.a17858p-4f, -0x1.7135a6p-5f, 0x1.d8cfdcp-7f, -0x1.57e158p-9f, -0x1.5f6332p-15f, 0x1.10a458p-13f, -0x1.592264p-16f, 0x1.899798p-18f, -0x1.4f8412p-18f, 0x1.74953ep-20f, -0x1.f7cb1ap-26f, -0x1.c92be2p-26f, -0x1.3b9a58p-35f, -0x1.6a58cep-35f, 0x1.4bf1ecp-37f, 0x1.697068p-44f, -0x1.513d7ap-49f, -0x1.b3943cp-57f, 0x1.54d33p-67f, -0x1.3f6e1ep-80f, -0x1.d0d882p-104f, -0x0p+0f};
             }
             if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.af6738p-9f, 0x1.c7ad46p-3f, 0x1.9756ccp-1f, -0x1.519166p+0f, 0x1.6cc6e8p-2f, -0x1.8cf37ep-4f, 0x1.9a3fa2p-4f, -0x1.0a50bep-3f, 0x1.df3f5p-4f, -0x1.2d4b7ep-4f, 0x1.0681e4p-5f, -0x1.1b50d6p-7f, 0x1.49acd2p-11f, 0x1.16651ap-11f, -0x1.c26d2p-13f, 0x1.300212p-16f, 0x1.49fbecp-17f, -0x1.8781a4p-19f, 0x1.5ed0aep-24f, 0x1.da4a76p-25f, -0x1.7e23c8p-29f, -0x1.bd8f2cp-35f, 0x1.1c615p-37f, -0x1.c1b8b4p-44f, -0x1.95157p-52f, 0x1.d1f8dep-60f, -0x1.34635ep-74f, -0x1.c0c6d2p-97f, -0x0p+0f};
+                return {0x0p+0f, 0x1.af6738p-9f, 0x1.c7ad46p-3f, 0x1.9756ccp-1f, -0x1.519166p+0f, 0x1.6cc6e8p-2f, -0x1.8cf37ep-4f, 0x1.9a3fa2p-4f, -0x1.0a50bep-3f, 0x1.df3f5p-4f, -0x1.2d4b7ep-4f, 0x1.0681e4p-5f, -0x1.1b50d6p-7f, 0x1.49acd2p-11f, 0x1.16651ap-11f, -0x1.c26d2p-13f, 0x1.300212p-16f, 0x1.49fbecp-17f, -0x1.8781a4p-19f, 0x1.5ed0aep-24f, 0x1.da4a76p-25f, -0x1.7e23c8p-29f, -0x1.bd8f2cp-35f, 0x1.1c615p-37f, -0x1.c1b8b4p-44f, -0x1.95157p-52f, 0x1.d1f8dep-60f, -0x1.34635ep-74f, -0x1.c0c6d2p-97f, 0x0p+0f};
             }
             if constexpr (order == 2) {
-                return {0x0p+0f, 0x1.52aa16p-6f, 0x1.2f3864p-1f, -0x1.92da3ep-2f, -0x1.010e6cp+1f, 0x1.ba5e58p+1f, -0x1.6efa1ap+1f, 0x1.e2fp+0f, -0x1.e9e848p-1f, 0x1.3e7bdp-2f, -0x1.3f21e6p-6f, -0x1.00e092p-5f, 0x1.93252ep-8f, 0x1.0cb53cp-7f, -0x1.6ecc66p-8f, 0x1.1da3c8p-10f, 0x1.0f705cp-12f, -0x1.687f18p-13f, 0x1.03bf74p-15f, -0x1.0a570cp-20f, -0x1.b60c86p-22f, 0x1.2f36c8p-24f, -0x1.ab6b4ep-30f, -0x1.b77dbep-33f, 0x1.02e06ap-39f, 0x1.f900dcp-46f, -0x1.5cc6acp-54f, 0x1.79a9bep-67f, 0x1.12cb1cp-88f, -0x0p+0f};
+                return {0x0p+0f, 0x1.52aa16p-6f, 0x1.2f3864p-1f, -0x1.92da3ep-2f, -0x1.010e6cp+1f, 0x1.ba5e58p+1f, -0x1.6efa1ap+1f, 0x1.e2fp+0f, -0x1.e9e848p-1f, 0x1.3e7bdp-2f, -0x1.3f21e6p-6f, -0x1.00e092p-5f, 0x1.93252ep-8f, 0x1.0cb53cp-7f, -0x1.6ecc66p-8f, 0x1.1da3c8p-10f, 0x1.0f705cp-12f, -0x1.687f18p-13f, 0x1.03bf74p-15f, -0x1.0a570cp-20f, -0x1.b60c86p-22f, 0x1.2f36c8p-24f, -0x1.ab6b4ep-30f, -0x1.b77dbep-33f, 0x1.02e06ap-39f, 0x1.f900dcp-46f, -0x1.5cc6acp-54f, 0x1.79a9bep-67f, 0x1.12cb1cp-88f, 0x0p+0f};
             }
             if constexpr (order == 3) {
                 return {0x0p+0f, 0x1.bde47ep-4f, 0x1.ff6e3ap-1f, -0x1.0edf78p+2f, 0x1.788ebp+2f, -0x1.0b9e58p+2f, 0x1.57d72ap+1f, -0x1.5aec5ap+1f, 0x1.66bep+1f, -0x1.257b74p+1f, 0x1.61e6a2p+0f, -0x1.1d6618p-1f, 0x1.7634aep-4f, 0x1.aae5ecp-5f, -0x1.66a2dep-5f, 0x1.9ee5c4p-7f, 0x1.cee452p-12f, -0x1.7d0e64p-10f, 0x1.95a9bcp-12f, -0x1.ac68b8p-17f, -0x1.4a3e54p-17f, 0x1.45a5b2p-20f, -0x1.a0585ep-28f, -0x1.4a4abp-28f, 0x1.818dc4p-34f, 0x1.bc8ec6p-41f, -0x1.1c50f4p-48f, 0x1.541ee6p-61f, 0x1.eef3c6p-82f, -0x0p+0f};
             }
             if constexpr (order == 4) {
-                return {0x0p+0f, 0x1.da9efcp-2f, -0x1.0a9636p-2f, -0x1.6ead78p+2f, 0x1.1fb0b8p+4f, -0x1.a26b2p+4f, 0x1.5a3628p+4f, -0x1.c3b938p+2f, -0x1.0393f6p+3f, 0x1.ce0e34p+3f, -0x1.3371f4p+3f, 0x1.04744cp-2f, 0x1.5d5bbap+2f, -0x1.56903ap+2f, 0x1.4f3674p+1f, -0x1.16f1cp-1f, -0x1.0ca608p-3f, 0x1.fd1e64p-4f, -0x1.12756ap-5f, 0x1.031ce4p-9f, 0x1.dbc5a2p-11f, -0x1.6e5758p-13f, 0x1.338c12p-19f, 0x1.ec833cp-21f, -0x1.31ee1ep-26f, -0x1.068ccep-32f, 0x1.ab486ep-40f, -0x1.971ac6p-52f, -0x1.28365cp-71f, -0x0p+0f};
+                return {0x0p+0f, 0x1.da9efcp-2f, -0x1.0a9636p-2f, -0x1.6ead78p+2f, 0x1.1fb0b8p+4f, -0x1.a26b2p+4f, 0x1.5a3628p+4f, -0x1.c3b938p+2f, -0x1.0393f6p+3f, 0x1.ce0e34p+3f, -0x1.3371f4p+3f, 0x1.04744cp-2f, 0x1.5d5bbap+2f, -0x1.56903ap+2f, 0x1.4f3674p+1f, -0x1.16f1cp-1f, -0x1.0ca608p-3f, 0x1.fd1e64p-4f, -0x1.12756ap-5f, 0x1.031ce4p-9f, 0x1.dbc5a2p-11f, -0x1.6e5758p-13f, 0x1.338c12p-19f, 0x1.ec833cp-21f, -0x1.31ee1ep-26f, -0x1.068ccep-32f, 0x1.ab486ep-40f, -0x1.971ac6p-52f, -0x1.28365cp-71f, 0x0p+0f};
             }
             if constexpr (order == 5) {
-                return {0x0p+0f, 0x1.8a28cp+0f, -0x1.0b8eccp+3f, 0x1.301d18p+4f, -0x1.80a5fep+4f, 0x1.4a39e4p+4f, -0x1.114828p+4f, 0x1.18e244p+4f, -0x1.390866p+4f, 0x1.80446cp+4f, -0x1.0a407ap+5f, 0x1.52509ep+5f, -0x1.4b4686p+5f, 0x1.c80f14p+4f, -0x1.82ded4p+3f, 0x1.7610a2p+0f, 0x1.b0a89ap+0f, -0x1.2b516ep+0f, 0x1.48818ap-2f, -0x1.16dd92p-6f, -0x1.957d58p-7f, 0x1.613bdp-9f, -0x1.0adbcp-14f, -0x1.449056p-16f, 0x1.238bd6p-21f, 0x1.0b863cp-27f, -0x1.2dac52p-34f, 0x1.a8ab5ap-46f, 0x1.34fcf8p-64f, 0x0p+0f};
+                return {0x0p+0f, 0x1.8a28cp+0f, -0x1.0b8eccp+3f, 0x1.301d18p+4f, -0x1.80a5fep+4f, 0x1.4a39e4p+4f, -0x1.114828p+4f, 0x1.18e244p+4f, -0x1.390866p+4f, 0x1.80446cp+4f, -0x1.0a407ap+5f, 0x1.52509ep+5f, -0x1.4b4686p+5f, 0x1.c80f14p+4f, -0x1.82ded4p+3f, 0x1.7610a2p+0f, 0x1.b0a89ap+0f, -0x1.2b516ep+0f, 0x1.48818ap-2f, -0x1.16dd92p-6f, -0x1.957d58p-7f, 0x1.613bdp-9f, -0x1.0adbcp-14f, -0x1.449056p-16f, 0x1.238bd6p-21f, 0x1.0b863cp-27f, -0x1.2dac52p-34f, 0x1.a8ab5ap-46f, 0x1.34fcf8p-64f, -0x0p+0f};
             }
             if constexpr (order == 6) {
-                return {0x0p+0f, 0x1.e156f6p+1f, -0x1.d9350cp+4f, 0x1.b03e3ap+6f, -0x1.f51dfap+7f, 0x1.b1d9eep+8f, -0x1.3c90b8p+9f, 0x1.a1026p+9f, -0x1.ee82dcp+9f, 0x1.fcf16ap+9f, -0x1.beee0ep+9f, 0x1.545f4ap+9f, -0x1.c39ca4p+8f, 0x1.d17e6ep+7f, -0x1.8d05e2p+5f, -0x1.a57ddap+5f, 0x1.065bfcp+6f, -0x1.1a783cp+5f, 0x1.2e9f2cp+3f, -0x1.3cad9ap-2f, -0x1.1b4b3ap-1f, 0x1.15a314p-3f, -0x1.5c66a6p-8f, -0x1.5db56p-10f, 0x1.c57be6p-15f, 0x1.c9738p-21f, -0x1.63f652p-27f, 0x1.769768p-38f, 0x1.108b38p-55f, 0x0p+0f};
+                return {0x0p+0f, 0x1.e156f6p+1f, -0x1.d9350cp+4f, 0x1.b03e3ap+6f, -0x1.f51dfap+7f, 0x1.b1d9eep+8f, -0x1.3c90b8p+9f, 0x1.a1026p+9f, -0x1.ee82dcp+9f, 0x1.fcf16ap+9f, -0x1.beee0ep+9f, 0x1.545f4ap+9f, -0x1.c39ca4p+8f, 0x1.d17e6ep+7f, -0x1.8d05e2p+5f, -0x1.a57ddap+5f, 0x1.065bfcp+6f, -0x1.1a783cp+5f, 0x1.2e9f2cp+3f, -0x1.3cad9ap-2f, -0x1.1b4b3ap-1f, 0x1.15a314p-3f, -0x1.5c66a6p-8f, -0x1.5db56p-10f, 0x1.c57be6p-15f, 0x1.c9738p-21f, -0x1.63f652p-27f, 0x1.769768p-38f, 0x1.108b38p-55f, -0x0p+0f};
             }
             if constexpr (order == 7) {
                 return {0x0p+0f, 0x1.d870dep+2f, -0x1.0c2b8cp+6f, 0x1.10bd38p+8f, -0x1.4441dap+9f, 0x1.eaed48p+9f, -0x1.dea056p+9f, 0x1.0ea6dep+9f, 0x1.3bb922p+5f, -0x1.7c03d4p+9f, 0x1.b77df6p+10f, -0x1.59dd46p+11f, 0x1.92ad5ep+11f, -0x1.7716eap+11f, 0x1.34cd94p+11f, -0x1.d21086p+10f, 0x1.27e204p+10f, -0x1.0ee014p+9f, 0x1.13ffcp+7f, 0x1.9021aap+1f, -0x1.cb9506p+3f, 0x1.f11cd6p+1f, -0x1.a3fefep-3f, -0x1.a953dap-5f, 0x1.9718bep-9f, 0x1.ad424ap-15f, -0x1.eb70cep-21f, 0x1.72006ap-31f, 0x1.0d3062p-47f, 0x0p+0f};
@@ -1454,19 +1792,19 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0f, 0x1.155158p+3f, -0x1.4fec3ap+6f, 0x1.70dec4p+8f, -0x1.e94cfep+9f, 0x1.bf0b1p+10f, -0x1.392918p+11f, 0x1.79ccf6p+11f, -0x1.ab6c9p+11f, 0x1.c47edap+11f, -0x1.af1006p+11f, 0x1.72a85ap+11f, -0x1.2846e6p+11f, 0x1.b3d87ep+10f, -0x1.1ae106p+10f, 0x1.41e16ep+9f, -0x1.46003p+8f, 0x1.0818e6p+7f, -0x1.8ef0b6p+4f, -0x1.6eb8ecp+3f, 0x1.3aba04p+3f, -0x1.588d6ep+1f, 0x1.5ca064p-3f, 0x1.72c884p-5f, -0x1.2b7b9ap-8f, -0x1.359ad6p-14f, 0x1.0cff08p-19f, -0x1.207536p-29f, -0x1.a3ad9ep-45f, -0x0p+0f};
             }
             if constexpr (order == 9) {
-                return {0x0p+0f, 0x1.174fb2p+3f, -0x1.5cf63cp+6f, 0x1.859702p+8f, -0x1.008e38p+10f, 0x1.c03c1cp+10f, -0x1.1e0d3p+11f, 0x1.33504ep+11f, -0x1.4498a4p+11f, 0x1.500c42p+11f, -0x1.2d6f92p+11f, 0x1.c5bd8cp+10f, -0x1.3b7208p+10f, 0x1.a4b182p+9f, -0x1.c03584p+8f, 0x1.1254d6p+7f, 0x1.be195p+2f, -0x1.6abf52p+5f, 0x1.bdfa94p+5f, -0x1.7a9c1p+5f, 0x1.86920ep+4f, -0x1.a9adfcp+2f, 0x1.133764p-1f, 0x1.191c64p-3f, -0x1.88d184p-6f, -0x1.aee4f4p-12f, 0x1.15e5eap-16f, -0x1.bc4492p-26f, -0x1.431c04p-40f, 0x0p+0f};
+                return {0x0p+0f, 0x1.174fb2p+3f, -0x1.5cf63cp+6f, 0x1.859702p+8f, -0x1.008e38p+10f, 0x1.c03c1cp+10f, -0x1.1e0d3p+11f, 0x1.33504ep+11f, -0x1.4498a4p+11f, 0x1.500c42p+11f, -0x1.2d6f92p+11f, 0x1.c5bd8cp+10f, -0x1.3b7208p+10f, 0x1.a4b182p+9f, -0x1.c03584p+8f, 0x1.1254d6p+7f, 0x1.be195p+2f, -0x1.6abf52p+5f, 0x1.bdfa94p+5f, -0x1.7a9c1p+5f, 0x1.86920ep+4f, -0x1.a9adfcp+2f, 0x1.133764p-1f, 0x1.191c64p-3f, -0x1.88d184p-6f, -0x1.aee4f4p-12f, 0x1.15e5eap-16f, -0x1.bc4492p-26f, -0x1.431c04p-40f, -0x0p+0f};
             }
             if constexpr (order == 10) {
-                return {0x0p+0f, 0x1.57dd2p+2f, -0x1.b426bap+5f, 0x1.ef50bp+7f, -0x1.4da8e6p+9f, 0x1.2d889ap+10f, -0x1.9456ecp+10f, 0x1.ca1f76p+10f, -0x1.f2eaf2p+10f, 0x1.0a60e2p+11f, -0x1.07fe76p+11f, 0x1.e2b37ep+10f, -0x1.a28fdp+10f, 0x1.5596d2p+10f, -0x1.027612p+10f, 0x1.70f45ap+9f, -0x1.edf5a6p+8f, 0x1.27b1e2p+8f, -0x1.3be692p+7f, 0x1.3b71fp+6f, -0x1.11985ep+5f, 0x1.3b5a98p+3f, -0x1.c32c18p-1f, -0x1.5d8e8ap-2f, 0x1.3b1b46p-4f, 0x1.23706ep-10f, -0x1.9c26fcp-14f, 0x1.96293ap-23f, 0x1.27428ap-36f, -0x0p+0f};
+                return {0x0p+0f, 0x1.57dd2p+2f, -0x1.b426bap+5f, 0x1.ef50bp+7f, -0x1.4da8e6p+9f, 0x1.2d889ap+10f, -0x1.9456ecp+10f, 0x1.ca1f76p+10f, -0x1.f2eaf2p+10f, 0x1.0a60e2p+11f, -0x1.07fe76p+11f, 0x1.e2b37ep+10f, -0x1.a28fdp+10f, 0x1.5596d2p+10f, -0x1.027612p+10f, 0x1.70f45ap+9f, -0x1.edf5a6p+8f, 0x1.27b1e2p+8f, -0x1.3be692p+7f, 0x1.3b71fp+6f, -0x1.11985ep+5f, 0x1.3b5a98p+3f, -0x1.c32c18p-1f, -0x1.5d8e8ap-2f, 0x1.3b1b46p-4f, 0x1.23706ep-10f, -0x1.9c26fcp-14f, 0x1.96293ap-23f, 0x1.27428ap-36f, 0x0p+0f};
             }
             if constexpr (order == 11) {
-                return {0x0p+0f, 0x1.82ba18p+1f, -0x1.ee321ap+4f, 0x1.174e6p+7f, -0x1.6e81d6p+8f, 0x1.368de4p+9f, -0x1.710674p+9f, 0x1.661d22p+9f, -0x1.6833b8p+9f, 0x1.833c1cp+9f, -0x1.704d0cp+9f, 0x1.2a287cp+9f, -0x1.d79574p+8f, 0x1.7a6624p+8f, -0x1.0dddap+8f, 0x1.4f8242p+7f, -0x1.9b8d6ep+6f, 0x1.e6b9cp+5f, -0x1.d872a6p+4f, 0x1.82e4e6p+3f, -0x1.3c81bp+2f, 0x1.87117ep+0f, -0x1.f2d1dcp-6f, -0x1.327c0ep-3f, 0x1.13b8cap-5f, -0x1.094894p-13f, -0x1.78471ap-14f, 0x1.31d268p-23f, 0x1.bc3afp-36f, -0x0p+0f};
+                return {0x0p+0f, 0x1.82ba18p+1f, -0x1.ee321ap+4f, 0x1.174e6p+7f, -0x1.6e81d6p+8f, 0x1.368de4p+9f, -0x1.710674p+9f, 0x1.661d22p+9f, -0x1.6833b8p+9f, 0x1.833c1cp+9f, -0x1.704d0cp+9f, 0x1.2a287cp+9f, -0x1.d79574p+8f, 0x1.7a6624p+8f, -0x1.0dddap+8f, 0x1.4f8242p+7f, -0x1.9b8d6ep+6f, 0x1.e6b9cp+5f, -0x1.d872a6p+4f, 0x1.82e4e6p+3f, -0x1.3c81bp+2f, 0x1.87117ep+0f, -0x1.f2d1dcp-6f, -0x1.327c0ep-3f, 0x1.13b8cap-5f, -0x1.094894p-13f, -0x1.78471ap-14f, 0x1.31d268p-23f, 0x1.bc3afp-36f, 0x0p+0f};
             }
             if constexpr (order == 12) {
-                return {0x0p+0f, 0x1.229018p+0f, -0x1.74b098p+3f, 0x1.a3d6fep+5f, -0x1.0ee9fep+7f, 0x1.b7ec28p+7f, -0x1.dcbffep+7f, 0x1.8f9512p+7f, -0x1.7421b2p+7f, 0x1.a17e1ep+7f, -0x1.8b13bap+7f, 0x1.210062p+7f, -0x1.a9798ep+6f, 0x1.62f522p+6f, -0x1.f0d146p+5f, 0x1.0b054p+5f, -0x1.2e7f82p+4f, 0x1.776b1ap+3f, -0x1.390aacp+2f, 0x1.0e68eap+0f, -0x1.1d9e68p-2f, 0x1.1e142p-5f, 0x1.626282p-3f, -0x1.00510ep-3f, 0x1.dda066p-6f, -0x1.397e42p-10f, -0x1.5e278p-13f, 0x1.93d63ep-23f, 0x1.24c486p-34f, 0x0p+0f};
+                return {0x0p+0f, 0x1.229018p+0f, -0x1.74b098p+3f, 0x1.a3d6fep+5f, -0x1.0ee9fep+7f, 0x1.b7ec28p+7f, -0x1.dcbffep+7f, 0x1.8f9512p+7f, -0x1.7421b2p+7f, 0x1.a17e1ep+7f, -0x1.8b13bap+7f, 0x1.210062p+7f, -0x1.a9798ep+6f, 0x1.62f522p+6f, -0x1.f0d146p+5f, 0x1.0b054p+5f, -0x1.2e7f82p+4f, 0x1.776b1ap+3f, -0x1.390aacp+2f, 0x1.0e68eap+0f, -0x1.1d9e68p-2f, 0x1.1e142p-5f, 0x1.626282p-3f, -0x1.00510ep-3f, 0x1.dda066p-6f, -0x1.397e42p-10f, -0x1.5e278p-13f, 0x1.93d63ep-23f, 0x1.24c486p-34f, -0x0p+0f};
             }
             if constexpr (order == 13) {
-                return {0x0p+0f, 0x1.2dba82p-3f, -0x1.83ba9p+0f, 0x1.bc6ce4p+2f, -0x1.2c97bep+4f, 0x1.0e0692p+5f, -0x1.5f4706p+5f, 0x1.6ea3fcp+5f, -0x1.5a777ep+5f, 0x1.424978p+5f, -0x1.3091p+5f, 0x1.23e442p+5f, -0x1.07fd36p+5f, 0x1.a8f488p+4f, -0x1.499324p+4f, 0x1.0a96d4p+4f, -0x1.8f60cep+3f, 0x1.003bccp+3f, -0x1.433efp+2f, 0x1.a65b7ep+1f, -0x1.d36032p+0f, 0x1.a4a1aep-1f, -0x1.88e9f6p-2f, 0x1.6764fap-3f, -0x1.91c36cp-5f, 0x1.07d03ep-8f, 0x1.362d3ep-11f, -0x1.92dbfep-20f, -0x1.22ff8p-30f, -0x0p+0f};
+                return {0x0p+0f, 0x1.2dba82p-3f, -0x1.83ba9p+0f, 0x1.bc6ce4p+2f, -0x1.2c97bep+4f, 0x1.0e0692p+5f, -0x1.5f4706p+5f, 0x1.6ea3fcp+5f, -0x1.5a777ep+5f, 0x1.424978p+5f, -0x1.3091p+5f, 0x1.23e442p+5f, -0x1.07fd36p+5f, 0x1.a8f488p+4f, -0x1.499324p+4f, 0x1.0a96d4p+4f, -0x1.8f60cep+3f, 0x1.003bccp+3f, -0x1.433efp+2f, 0x1.a65b7ep+1f, -0x1.d36032p+0f, 0x1.a4a1aep-1f, -0x1.88e9f6p-2f, 0x1.6764fap-3f, -0x1.91c36cp-5f, 0x1.07d03ep-8f, 0x1.362d3ep-11f, -0x1.92dbfep-20f, -0x1.22ff8p-30f, 0x0p+0f};
             }
             if constexpr (order == 14) {
                 return {0x0p+0f, 0x1.8dd6e2p-6f, -0x1.ffb4dep-3f, 0x1.1f8df8p+0f, -0x1.6eae32p+1f, 0x1.200cfep+2f, -0x1.1f2876p+2f, 0x1.90990cp+1f, -0x1.3d166cp+1f, 0x1.74d60ap+1f, -0x1.680266p+1f, 0x1.e76ba8p+0f, -0x1.60830ap+0f, 0x1.48f2a8p+0f, -0x1.e7d09ep-1f, 0x1.1252eep-1f, -0x1.6e9dp-2f, 0x1.0a88fcp-2f, -0x1.16ea72p-3f, 0x1.018afap-4f, -0x1.2fa054p-5f, 0x1.2375eep-6f, -0x1.73b10cp-8f, 0x1.1decc8p-9f, -0x1.b8713ap-11f, 0x1.732712p-14f, 0x1.5deb76p-16f, -0x1.927126p-23f, -0x1.209992p-32f, 0x0p+0f};
@@ -1474,25 +1812,25 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         }
         if constexpr (std::is_same_v<Real, double>) {
             if constexpr (order == 0) {
-                return {0x0p+0, 0x1.d99d611c0465dp-12, 0x1.0d2f985427a1ep-4, 0x1.4a539266aac6ep-1, 0x1.1fc50d04f7f08p-1, -0x1.d497750272bfap-2, 0x1.3575a87d9c163p-2, -0x1.7e644ab118887p-3, 0x1.a1785765bb949p-4, -0x1.7135a6ada8b52p-5, 0x1.d8cfdcbb16189p-7, -0x1.57e157b5bcea8p-9, -0x1.5f633204e95ap-15, 0x1.10a4589d9f87dp-13, -0x1.592264d16e622p-16, 0x1.89979784d7185p-18, -0x1.4f841169a1badp-18, 0x1.74953d3967ccep-20, -0x1.f7cb1acefcf43p-26, -0x1.c92be21aef0cap-26, -0x1.3b9a57c4ce7e8p-35, -0x1.6a58cec0fa225p-35, 0x1.4bf1eb8cd4c9cp-37, 0x1.697067f1715a1p-44, -0x1.513d790bd243p-49, -0x1.b3943c02986a6p-57, 0x1.54d330be5783ep-67, -0x1.3f6e1e631364cp-80, -0x1.d0d882f8587b5p-104, 0x0p+0};
+                return {0x0p+0, 0x1.d99d611c0465dp-12, 0x1.0d2f985427a1ep-4, 0x1.4a539266aac6ep-1, 0x1.1fc50d04f7f08p-1, -0x1.d497750272bfap-2, 0x1.3575a87d9c163p-2, -0x1.7e644ab118887p-3, 0x1.a1785765bb949p-4, -0x1.7135a6ada8b52p-5, 0x1.d8cfdcbb16189p-7, -0x1.57e157b5bcea8p-9, -0x1.5f633204e95ap-15, 0x1.10a4589d9f87dp-13, -0x1.592264d16e622p-16, 0x1.89979784d7185p-18, -0x1.4f841169a1badp-18, 0x1.74953d3967ccep-20, -0x1.f7cb1acefcf43p-26, -0x1.c92be21aef0cap-26, -0x1.3b9a57c4ce7e8p-35, -0x1.6a58cec0fa225p-35, 0x1.4bf1eb8cd4c9cp-37, 0x1.697067f1715a1p-44, -0x1.513d790bd243p-49, -0x1.b3943c02986a6p-57, 0x1.54d330be5783ep-67, -0x1.3f6e1e631364cp-80, -0x1.d0d882f8587b5p-104, -0x0p+0};
             }
             if constexpr (order == 1) {
-                return {0x0p+0, 0x1.af673717274afp-9, 0x1.c7ad45d086ea5p-3, 0x1.9756cb092ee07p-1, -0x1.51916657c1834p+0, 0x1.6cc6e8f062405p-2, -0x1.8cf37d6182ca1p-4, 0x1.9a3fa2f41d495p-4, -0x1.0a50be22f2b87p-3, 0x1.df3f4f6c19d45p-4, -0x1.2d4b7e715db6cp-4, 0x1.0681e4c20b9fdp-5, -0x1.1b50d689cbed9p-7, 0x1.49acd134a254cp-11, 0x1.16651955943e4p-11, -0x1.c26d1f2c70c87p-13, 0x1.3002118e762a1p-16, 0x1.49fbecfd7d9c7p-17, -0x1.8781a4a6a5f7dp-19, 0x1.5ed0ad164acd2p-24, 0x1.da4a7558674aep-25, -0x1.7e23c7237f3f9p-29, -0x1.bd8f2cef8c9fp-35, 0x1.1c61501fa1048p-37, -0x1.c1b8b33989e02p-44, -0x1.95156f39cb33ap-52, 0x1.d1f8ddb7d0199p-60, -0x1.34635de67ce8cp-74, -0x1.c0c6d283f741ep-97, -0x0p+0};
+                return {0x0p+0, 0x1.af673717274afp-9, 0x1.c7ad45d086ea5p-3, 0x1.9756cb092ee07p-1, -0x1.51916657c1834p+0, 0x1.6cc6e8f062405p-2, -0x1.8cf37d6182ca1p-4, 0x1.9a3fa2f41d495p-4, -0x1.0a50be22f2b87p-3, 0x1.df3f4f6c19d45p-4, -0x1.2d4b7e715db6cp-4, 0x1.0681e4c20b9fdp-5, -0x1.1b50d689cbed9p-7, 0x1.49acd134a254cp-11, 0x1.16651955943e4p-11, -0x1.c26d1f2c70c87p-13, 0x1.3002118e762a1p-16, 0x1.49fbecfd7d9c7p-17, -0x1.8781a4a6a5f7dp-19, 0x1.5ed0ad164acd2p-24, 0x1.da4a7558674aep-25, -0x1.7e23c7237f3f9p-29, -0x1.bd8f2cef8c9fp-35, 0x1.1c61501fa1048p-37, -0x1.c1b8b33989e02p-44, -0x1.95156f39cb33ap-52, 0x1.d1f8ddb7d0199p-60, -0x1.34635de67ce8cp-74, -0x1.c0c6d283f741ep-97, 0x0p+0};
             }
             if constexpr (order == 2) {
-                return {0x0p+0, 0x1.52aa167437ed4p-6, 0x1.2f386450cd36p-1, -0x1.92da3e0f4795fp-2, -0x1.010e6c23362c3p+1, 0x1.ba5e5707337cfp+1, -0x1.6efa1a351e689p+1, 0x1.e2efff792ca6dp+0, -0x1.e9e84815ce29ap-1, 0x1.3e7bcfc83dd35p-2, -0x1.3f21e5e83db9bp-6, -0x1.00e091b8310d8p-5, 0x1.93252ea5d40eep-8, 0x1.0cb53bda124f5p-7, -0x1.6ecc6596fdeb9p-8, 0x1.1da3c88de4594p-10, 0x1.0f705c9109b89p-12, -0x1.687f176415b5ap-13, 0x1.03bf749271ea1p-15, -0x1.0a570c997b8f7p-20, -0x1.b60c856b75c7p-22, 0x1.2f36c8024d478p-24, -0x1.ab6b4d2a0c9ebp-30, -0x1.b77dbd4d624bbp-33, 0x1.02e06a0b52529p-39, 0x1.f900db818405cp-46, -0x1.5cc6aba4a367p-54, 0x1.79a9be1badafp-67, 0x1.12cb1c6610cf6p-88, -0x0p+0};
+                return {0x0p+0, 0x1.52aa167437ed4p-6, 0x1.2f386450cd36p-1, -0x1.92da3e0f4795fp-2, -0x1.010e6c23362c3p+1, 0x1.ba5e5707337cfp+1, -0x1.6efa1a351e689p+1, 0x1.e2efff792ca6dp+0, -0x1.e9e84815ce29ap-1, 0x1.3e7bcfc83dd35p-2, -0x1.3f21e5e83db9bp-6, -0x1.00e091b8310d8p-5, 0x1.93252ea5d40eep-8, 0x1.0cb53bda124f5p-7, -0x1.6ecc6596fdeb9p-8, 0x1.1da3c88de4594p-10, 0x1.0f705c9109b89p-12, -0x1.687f176415b5ap-13, 0x1.03bf749271ea1p-15, -0x1.0a570c997b8f7p-20, -0x1.b60c856b75c7p-22, 0x1.2f36c8024d478p-24, -0x1.ab6b4d2a0c9ebp-30, -0x1.b77dbd4d624bbp-33, 0x1.02e06a0b52529p-39, 0x1.f900db818405cp-46, -0x1.5cc6aba4a367p-54, 0x1.79a9be1badafp-67, 0x1.12cb1c6610cf6p-88, 0x0p+0};
             }
             if constexpr (order == 3) {
                 return {0x0p+0, 0x1.bde47de89537fp-4, 0x1.ff6e39e05bc19p-1, -0x1.0edf7812c7e6fp+2, 0x1.788eafbfef57p+2, -0x1.0b9e58d049e2bp+2, 0x1.57d72a54d9b7ep+1, -0x1.5aec59993d64cp+1, 0x1.66be004fbc258p+1, -0x1.257b730e2148dp+1, 0x1.61e6a248fa766p+0, -0x1.1d66170848573p-1, 0x1.7634ae9385e7dp-4, 0x1.aae5eb36cf234p-5, -0x1.66a2dd81189a5p-5, 0x1.9ee5c38dff3c6p-7, 0x1.cee452b55c63p-12, -0x1.7d0e63753adf8p-10, 0x1.95a9bb14ccec1p-12, -0x1.ac68b8496deeap-17, -0x1.4a3e531dccd5ap-17, 0x1.45a5b2adacfeep-20, -0x1.a0585e72874e5p-28, -0x1.4a4aaf36fdaecp-28, 0x1.818dc3c36642cp-34, 0x1.bc8ec635290e4p-41, -0x1.1c50f4adb4d49p-48, 0x1.541ee5efeba28p-61, 0x1.eef3c669427bap-82, -0x0p+0};
             }
             if constexpr (order == 4) {
-                return {0x0p+0, 0x1.da9efb84cd102p-2, -0x1.0a963523c781p-2, -0x1.6ead78b2a7f87p+2, 0x1.1fb0b7ee7fe9bp+4, -0x1.a26b20f9bdefp+4, 0x1.5a362701692b6p+4, -0x1.c3b93743ed5e2p+2, -0x1.0393f54066e2bp+3, 0x1.ce0e335b9b5dp+3, -0x1.3371f4378fc26p+3, 0x1.04744c732a897p-2, 0x1.5d5bbaac2d3ddp+2, -0x1.56903abc9d373p+2, 0x1.4f367450bb029p+1, -0x1.16f1bf1e47dd8p-1, -0x1.0ca6089fc41eep-3, 0x1.fd1e6437298dfp-4, -0x1.127569c6d3d2p-5, 0x1.031ce43d6f2aap-9, 0x1.dbc5a12350174p-11, -0x1.6e57586c99db3p-13, 0x1.338c12c9a95b4p-19, 0x1.ec833bdc8d6abp-21, -0x1.31ee1e222a83p-26, -0x1.068cce25031dp-32, 0x1.ab486d191520ep-40, -0x1.971ac61147c4cp-52, -0x1.28365b5992262p-71, -0x0p+0};
+                return {0x0p+0, 0x1.da9efb84cd102p-2, -0x1.0a963523c781p-2, -0x1.6ead78b2a7f87p+2, 0x1.1fb0b7ee7fe9bp+4, -0x1.a26b20f9bdefp+4, 0x1.5a362701692b6p+4, -0x1.c3b93743ed5e2p+2, -0x1.0393f54066e2bp+3, 0x1.ce0e335b9b5dp+3, -0x1.3371f4378fc26p+3, 0x1.04744c732a897p-2, 0x1.5d5bbaac2d3ddp+2, -0x1.56903abc9d373p+2, 0x1.4f367450bb029p+1, -0x1.16f1bf1e47dd8p-1, -0x1.0ca6089fc41eep-3, 0x1.fd1e6437298dfp-4, -0x1.127569c6d3d2p-5, 0x1.031ce43d6f2aap-9, 0x1.dbc5a12350174p-11, -0x1.6e57586c99db3p-13, 0x1.338c12c9a95b4p-19, 0x1.ec833bdc8d6abp-21, -0x1.31ee1e222a83p-26, -0x1.068cce25031dp-32, 0x1.ab486d191520ep-40, -0x1.971ac61147c4cp-52, -0x1.28365b5992262p-71, 0x0p+0};
             }
             if constexpr (order == 5) {
-                return {0x0p+0, 0x1.8a28bf1f4bafp+0, -0x1.0b8ecb513e671p+3, 0x1.301d17ac5e1c7p+4, -0x1.80a5fd5ebbea5p+4, 0x1.4a39e3e1048d6p+4, -0x1.1148278e9d9a1p+4, 0x1.18e244d79a033p+4, -0x1.3908669ba0779p+4, 0x1.80446c71adb15p+4, -0x1.0a40794798e41p+5, 0x1.52509dd04c4f7p+5, -0x1.4b468531c5b1ap+5, 0x1.c80f1430e334ap+4, -0x1.82ded3c89e7eap+3, 0x1.7610a167089f2p+0, 0x1.b0a89a8818c06p+0, -0x1.2b516da5d081p+0, 0x1.488189c0e6323p-2, -0x1.16dd91fce8d2fp-6, -0x1.957d5757f4d58p-7, 0x1.613bcf2c2fc6ap-9, -0x1.0adbc024da551p-14, -0x1.44905597a8908p-16, 0x1.238bd55115864p-21, 0x1.0b863bc593a1dp-27, -0x1.2dac52b5d35bcp-34, 0x1.a8ab5a61388b2p-46, 0x1.34fcf88bcfb4p-64, 0x0p+0};
+                return {0x0p+0, 0x1.8a28bf1f4bafp+0, -0x1.0b8ecb513e671p+3, 0x1.301d17ac5e1c7p+4, -0x1.80a5fd5ebbea5p+4, 0x1.4a39e3e1048d6p+4, -0x1.1148278e9d9a1p+4, 0x1.18e244d79a033p+4, -0x1.3908669ba0779p+4, 0x1.80446c71adb15p+4, -0x1.0a40794798e41p+5, 0x1.52509dd04c4f7p+5, -0x1.4b468531c5b1ap+5, 0x1.c80f1430e334ap+4, -0x1.82ded3c89e7eap+3, 0x1.7610a167089f2p+0, 0x1.b0a89a8818c06p+0, -0x1.2b516da5d081p+0, 0x1.488189c0e6323p-2, -0x1.16dd91fce8d2fp-6, -0x1.957d5757f4d58p-7, 0x1.613bcf2c2fc6ap-9, -0x1.0adbc024da551p-14, -0x1.44905597a8908p-16, 0x1.238bd55115864p-21, 0x1.0b863bc593a1dp-27, -0x1.2dac52b5d35bcp-34, 0x1.a8ab5a61388b2p-46, 0x1.34fcf88bcfb4p-64, -0x0p+0};
             }
             if constexpr (order == 6) {
-                return {0x0p+0, 0x1.e156f58145abap+1, -0x1.d9350b2238c2cp+4, 0x1.b03e3957ecd6ap+6, -0x1.f51dfa789d879p+7, 0x1.b1d9ee3321d94p+8, -0x1.3c90b7e3ca1dcp+9, 0x1.a1025f9df5666p+9, -0x1.ee82dbab6ab1p+9, 0x1.fcf169933904cp+9, -0x1.beee0dc0c8ddbp+9, 0x1.545f49e00f496p+9, -0x1.c39ca355bd5d3p+8, 0x1.d17e6e268802dp+7, -0x1.8d05e2b81cf72p+5, -0x1.a57ddae4deceep+5, 0x1.065bfb9cfed1p+6, -0x1.1a783beefce88p+5, 0x1.2e9f2c1581a69p+3, -0x1.3cad9a2427052p-2, -0x1.1b4b3a7aa70e8p-1, 0x1.15a31469a9cep-3, -0x1.5c66a63c93474p-8, -0x1.5db560cc8a8d9p-10, 0x1.c57be52a95f9ap-15, 0x1.c9738067c590ap-21, -0x1.63f652c472259p-27, 0x1.769767db4423bp-38, 0x1.108b386e39e95p-55, 0x0p+0};
+                return {0x0p+0, 0x1.e156f58145abap+1, -0x1.d9350b2238c2cp+4, 0x1.b03e3957ecd6ap+6, -0x1.f51dfa789d879p+7, 0x1.b1d9ee3321d94p+8, -0x1.3c90b7e3ca1dcp+9, 0x1.a1025f9df5666p+9, -0x1.ee82dbab6ab1p+9, 0x1.fcf169933904cp+9, -0x1.beee0dc0c8ddbp+9, 0x1.545f49e00f496p+9, -0x1.c39ca355bd5d3p+8, 0x1.d17e6e268802dp+7, -0x1.8d05e2b81cf72p+5, -0x1.a57ddae4deceep+5, 0x1.065bfb9cfed1p+6, -0x1.1a783beefce88p+5, 0x1.2e9f2c1581a69p+3, -0x1.3cad9a2427052p-2, -0x1.1b4b3a7aa70e8p-1, 0x1.15a31469a9cep-3, -0x1.5c66a63c93474p-8, -0x1.5db560cc8a8d9p-10, 0x1.c57be52a95f9ap-15, 0x1.c9738067c590ap-21, -0x1.63f652c472259p-27, 0x1.769767db4423bp-38, 0x1.108b386e39e95p-55, -0x0p+0};
             }
             if constexpr (order == 7) {
                 return {0x0p+0, 0x1.d870debcc05c4p+2, -0x1.0c2b8b0b28194p+6, 0x1.10bd374d63551p+8, -0x1.4441daef321d4p+9, 0x1.eaed48222cc9cp+9, -0x1.dea055aad4ecbp+9, 0x1.0ea6de87556eap+9, 0x1.3bb921604519dp+5, -0x1.7c03d4dcf5514p+9, 0x1.b77df6c77230cp+10, -0x1.59dd45c186fb1p+11, 0x1.92ad5ee85458dp+11, -0x1.7716e9b298972p+11, 0x1.34cd942cd473ap+11, -0x1.d2108687fa36fp+10, 0x1.27e2041912518p+10, -0x1.0ee0131c1b04fp+9, 0x1.13ffc016f56cap+7, 0x1.9021a9dd4e12bp+1, -0x1.cb9505a70965bp+3, 0x1.f11cd618c3359p+1, -0x1.a3fefe1a942d4p-3, -0x1.a953da883746ep-5, 0x1.9718bee3af729p-9, 0x1.ad4249f39958ep-15, -0x1.eb70cd1aa4051p-21, 0x1.72006a07a097fp-31, 0x1.0d30627e6a2adp-47, 0x0p+0};
@@ -1501,19 +1839,19 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0, 0x1.155158ac6ea98p+3, -0x1.4fec3a6a32c1fp+6, 0x1.70dec41eaf97dp+8, -0x1.e94cfecb1efa1p+9, 0x1.bf0b100d34d04p+10, -0x1.39291803fcf48p+11, 0x1.79ccf50afb46ep+11, -0x1.ab6c90991611bp+11, 0x1.c47ed9a17b9cdp+11, -0x1.af1005783c9c1p+11, 0x1.72a859cabb472p+11, -0x1.2846e6b9b14f5p+11, 0x1.b3d87dff6a955p+10, -0x1.1ae10527ae494p+10, 0x1.41e16e9c43533p+9, -0x1.460030c5bf207p+8, 0x1.0818e6dd9acdcp+7, -0x1.8ef0b66c7662cp+4, -0x1.6eb8ec2d2fcfp+3, 0x1.3aba0303f01c4p+3, -0x1.588d6d239648ep+1, 0x1.5ca063a2897a3p-3, 0x1.72c884e06d39ap-5, -0x1.2b7b99da7239bp-8, -0x1.359ad5ec914c6p-14, 0x1.0cff089d4d593p-19, -0x1.207535755ab2fp-29, -0x1.a3ad9d559345cp-45, -0x0p+0};
             }
             if constexpr (order == 9) {
-                return {0x0p+0, 0x1.174fb1d673064p+3, -0x1.5cf63b4072a08p+6, 0x1.859702b93092p+8, -0x1.008e38c64d405p+10, 0x1.c03c1b8df613fp+10, -0x1.1e0d30516cd0dp+11, 0x1.33504e2e62ab9p+11, -0x1.4498a39b45dd3p+11, 0x1.500c422b7e4d6p+11, -0x1.2d6f916f2f064p+11, 0x1.c5bd8b8beccdbp+10, -0x1.3b7208dc18507p+10, 0x1.a4b1819107c72p+9, -0x1.c03583e492981p+8, 0x1.1254d5dd1a3c8p+7, 0x1.be19509979c25p+2, -0x1.6abf524121ea4p+5, 0x1.bdfa9494723d3p+5, -0x1.7a9c102bdb495p+5, 0x1.86920d3d07ed2p+4, -0x1.a9adfb25c4f27p+2, 0x1.1337641b89dbcp-1, 0x1.191c64622c1b1p-3, -0x1.88d18423866c2p-6, -0x1.aee4f466bb969p-12, 0x1.15e5e9747fe1cp-16, -0x1.bc4491eee0fddp-26, -0x1.431c03e754cd9p-40, 0x0p+0};
+                return {0x0p+0, 0x1.174fb1d673064p+3, -0x1.5cf63b4072a08p+6, 0x1.859702b93092p+8, -0x1.008e38c64d405p+10, 0x1.c03c1b8df613fp+10, -0x1.1e0d30516cd0dp+11, 0x1.33504e2e62ab9p+11, -0x1.4498a39b45dd3p+11, 0x1.500c422b7e4d6p+11, -0x1.2d6f916f2f064p+11, 0x1.c5bd8b8beccdbp+10, -0x1.3b7208dc18507p+10, 0x1.a4b1819107c72p+9, -0x1.c03583e492981p+8, 0x1.1254d5dd1a3c8p+7, 0x1.be19509979c25p+2, -0x1.6abf524121ea4p+5, 0x1.bdfa9494723d3p+5, -0x1.7a9c102bdb495p+5, 0x1.86920d3d07ed2p+4, -0x1.a9adfb25c4f27p+2, 0x1.1337641b89dbcp-1, 0x1.191c64622c1b1p-3, -0x1.88d18423866c2p-6, -0x1.aee4f466bb969p-12, 0x1.15e5e9747fe1cp-16, -0x1.bc4491eee0fddp-26, -0x1.431c03e754cd9p-40, -0x0p+0};
             }
             if constexpr (order == 10) {
-                return {0x0p+0, 0x1.57dd202e5e84bp+2, -0x1.b426b94987909p+5, 0x1.ef50af36bc94ap+7, -0x1.4da8e644667e7p+9, 0x1.2d889ab089911p+10, -0x1.9456ec86efc74p+10, 0x1.ca1f75d29c178p+10, -0x1.f2eaf24b48be9p+10, 0x1.0a60e2fdcea78p+11, -0x1.07fe75c2d8539p+11, 0x1.e2b37ed5f4462p+10, -0x1.a28fcff6e684bp+10, 0x1.5596d2be7c1f8p+10, -0x1.02761175eccb5p+10, 0x1.70f45a3e9b6c8p+9, -0x1.edf5a5b354e13p+8, 0x1.27b1e13298bb4p+8, -0x1.3be69243ef2c3p+7, 0x1.3b71f0120f2a4p+6, -0x1.11985d9404f45p+5, 0x1.3b5a9762f053bp+3, -0x1.c32c18767db72p-1, -0x1.5d8e89b8ba2f4p-2, 0x1.3b1b46a97c2fbp-4, 0x1.23706d03f6f74p-10, -0x1.9c26fc84f3ff6p-14, 0x1.962939a138e2bp-23, 0x1.27428a5934f9ep-36, -0x0p+0};
+                return {0x0p+0, 0x1.57dd202e5e84bp+2, -0x1.b426b94987909p+5, 0x1.ef50af36bc94ap+7, -0x1.4da8e644667e7p+9, 0x1.2d889ab089911p+10, -0x1.9456ec86efc74p+10, 0x1.ca1f75d29c178p+10, -0x1.f2eaf24b48be9p+10, 0x1.0a60e2fdcea78p+11, -0x1.07fe75c2d8539p+11, 0x1.e2b37ed5f4462p+10, -0x1.a28fcff6e684bp+10, 0x1.5596d2be7c1f8p+10, -0x1.02761175eccb5p+10, 0x1.70f45a3e9b6c8p+9, -0x1.edf5a5b354e13p+8, 0x1.27b1e13298bb4p+8, -0x1.3be69243ef2c3p+7, 0x1.3b71f0120f2a4p+6, -0x1.11985d9404f45p+5, 0x1.3b5a9762f053bp+3, -0x1.c32c18767db72p-1, -0x1.5d8e89b8ba2f4p-2, 0x1.3b1b46a97c2fbp-4, 0x1.23706d03f6f74p-10, -0x1.9c26fc84f3ff6p-14, 0x1.962939a138e2bp-23, 0x1.27428a5934f9ep-36, 0x0p+0};
             }
             if constexpr (order == 11) {
-                return {0x0p+0, 0x1.82ba18a281555p+1, -0x1.ee321ac782e81p+4, 0x1.174e5f65a44a6p+7, -0x1.6e81d57c4c979p+8, 0x1.368de3361fae5p+9, -0x1.7106731d7c871p+9, 0x1.661d220cefa1p+9, -0x1.6833b778e773bp+9, 0x1.833c1b7a24cc4p+9, -0x1.704d0cf5b403fp+9, 0x1.2a287b4a8744cp+9, -0x1.d795731af32d5p+8, 0x1.7a6623bbe9af8p+8, -0x1.0ddd9fa1ad022p+8, 0x1.4f824182bb441p+7, -0x1.9b8d6efd833c4p+6, 0x1.e6b9bfc912a61p+5, -0x1.d872a65489bc7p+4, 0x1.82e4e50171641p+3, -0x1.3c81b080d7c59p+2, 0x1.87117e04fd822p+0, -0x1.f2d1dbd395099p-6, -0x1.327c0d249414p-3, 0x1.13b8c9585145fp-5, -0x1.094893076dab2p-13, -0x1.784719262e6dap-14, 0x1.31d26875ab45fp-23, 0x1.bc3aef2e9698bp-36, -0x0p+0};
+                return {0x0p+0, 0x1.82ba18a281555p+1, -0x1.ee321ac782e81p+4, 0x1.174e5f65a44a6p+7, -0x1.6e81d57c4c979p+8, 0x1.368de3361fae5p+9, -0x1.7106731d7c871p+9, 0x1.661d220cefa1p+9, -0x1.6833b778e773bp+9, 0x1.833c1b7a24cc4p+9, -0x1.704d0cf5b403fp+9, 0x1.2a287b4a8744cp+9, -0x1.d795731af32d5p+8, 0x1.7a6623bbe9af8p+8, -0x1.0ddd9fa1ad022p+8, 0x1.4f824182bb441p+7, -0x1.9b8d6efd833c4p+6, 0x1.e6b9bfc912a61p+5, -0x1.d872a65489bc7p+4, 0x1.82e4e50171641p+3, -0x1.3c81b080d7c59p+2, 0x1.87117e04fd822p+0, -0x1.f2d1dbd395099p-6, -0x1.327c0d249414p-3, 0x1.13b8c9585145fp-5, -0x1.094893076dab2p-13, -0x1.784719262e6dap-14, 0x1.31d26875ab45fp-23, 0x1.bc3aef2e9698bp-36, 0x0p+0};
             }
             if constexpr (order == 12) {
-                return {0x0p+0, 0x1.229017de89889p+0, -0x1.74b098d7b2942p+3, 0x1.a3d6fe58853c2p+5, -0x1.0ee9fe2c639a7p+7, 0x1.b7ec28edec454p+7, -0x1.dcbffedb3a508p+7, 0x1.8f9512e48d1c4p+7, -0x1.7421b1a880459p+7, 0x1.a17e1d21e73d2p+7, -0x1.8b13badbca1d9p+7, 0x1.210062e92f489p+7, -0x1.a9798d44da6c2p+6, 0x1.62f521d1972a8p+6, -0x1.f0d14679f69cp+5, 0x1.0b0540b21cf09p+5, -0x1.2e7f81d72375p+4, 0x1.776b19bc1de7bp+3, -0x1.390aaca35a349p+2, 0x1.0e68e94457017p+0, -0x1.1d9e671612a46p-2, 0x1.1e141f6f8381bp-5, 0x1.626281f06a565p-3, -0x1.00510e27c6afap-3, 0x1.dda065aa933f4p-6, -0x1.397e42b4cc1c2p-10, -0x1.5e2780fee3a22p-13, 0x1.93d63eaebefb8p-23, 0x1.24c485651202dp-34, 0x0p+0};
+                return {0x0p+0, 0x1.229017de89889p+0, -0x1.74b098d7b2942p+3, 0x1.a3d6fe58853c2p+5, -0x1.0ee9fe2c639a7p+7, 0x1.b7ec28edec454p+7, -0x1.dcbffedb3a508p+7, 0x1.8f9512e48d1c4p+7, -0x1.7421b1a880459p+7, 0x1.a17e1d21e73d2p+7, -0x1.8b13badbca1d9p+7, 0x1.210062e92f489p+7, -0x1.a9798d44da6c2p+6, 0x1.62f521d1972a8p+6, -0x1.f0d14679f69cp+5, 0x1.0b0540b21cf09p+5, -0x1.2e7f81d72375p+4, 0x1.776b19bc1de7bp+3, -0x1.390aaca35a349p+2, 0x1.0e68e94457017p+0, -0x1.1d9e671612a46p-2, 0x1.1e141f6f8381bp-5, 0x1.626281f06a565p-3, -0x1.00510e27c6afap-3, 0x1.dda065aa933f4p-6, -0x1.397e42b4cc1c2p-10, -0x1.5e2780fee3a22p-13, 0x1.93d63eaebefb8p-23, 0x1.24c485651202dp-34, -0x0p+0};
             }
             if constexpr (order == 13) {
-                return {0x0p+0, 0x1.2dba81606cdf4p-3, -0x1.83ba9062dc10bp+0, 0x1.bc6ce42e9d3a2p+2, -0x1.2c97bd817af95p+4, 0x1.0e06914d93155p+5, -0x1.5f4706680d4aep+5, 0x1.6ea3fbf492341p+5, -0x1.5a777ed4931f2p+5, 0x1.424978021982dp+5, -0x1.3090ff3d7fed6p+5, 0x1.23e4419ddb641p+5, -0x1.07fd356f7673cp+5, 0x1.a8f488a3b6e4bp+4, -0x1.49932384ed8b5p+4, 0x1.0a96d421140ffp+4, -0x1.8f60cd9c05603p+3, 0x1.003bcbf26a5dbp+3, -0x1.433ef046d9ed1p+2, 0x1.a65b7dff93521p+1, -0x1.d36032adf2dbdp+0, 0x1.a4a1ad470bd0ep-1, -0x1.88e9f63513cep-2, 0x1.6764f965c9511p-3, -0x1.91c36b23af1d8p-5, 0x1.07d03d7a1adc2p-8, 0x1.362d3e37ff6cdp-11, -0x1.92dbfdbfa8198p-20, -0x1.22ff804507dbep-30, -0x0p+0};
+                return {0x0p+0, 0x1.2dba81606cdf4p-3, -0x1.83ba9062dc10bp+0, 0x1.bc6ce42e9d3a2p+2, -0x1.2c97bd817af95p+4, 0x1.0e06914d93155p+5, -0x1.5f4706680d4aep+5, 0x1.6ea3fbf492341p+5, -0x1.5a777ed4931f2p+5, 0x1.424978021982dp+5, -0x1.3090ff3d7fed6p+5, 0x1.23e4419ddb641p+5, -0x1.07fd356f7673cp+5, 0x1.a8f488a3b6e4bp+4, -0x1.49932384ed8b5p+4, 0x1.0a96d421140ffp+4, -0x1.8f60cd9c05603p+3, 0x1.003bcbf26a5dbp+3, -0x1.433ef046d9ed1p+2, 0x1.a65b7dff93521p+1, -0x1.d36032adf2dbdp+0, 0x1.a4a1ad470bd0ep-1, -0x1.88e9f63513cep-2, 0x1.6764f965c9511p-3, -0x1.91c36b23af1d8p-5, 0x1.07d03d7a1adc2p-8, 0x1.362d3e37ff6cdp-11, -0x1.92dbfdbfa8198p-20, -0x1.22ff804507dbep-30, 0x0p+0};
             }
             if constexpr (order == 14) {
                 return {0x0p+0, 0x1.8dd6e1684e11dp-6, -0x1.ffb4de00653d3p-3, 0x1.1f8df89dea984p+0, -0x1.6eae32a3a7907p+1, 0x1.200cfdab0a888p+2, -0x1.1f287662480abp+2, 0x1.90990b7ee9dd2p+1, -0x1.3d166b62b6086p+1, 0x1.74d60ae1a8cebp+1, -0x1.68026579c2214p+1, 0x1.e76ba8ae988d5p+0, -0x1.60830949d4c83p+0, 0x1.48f2a8ad7050dp+0, -0x1.e7d09d1d5c76ep-1, 0x1.1252ee85de925p-1, -0x1.6e9d007e3ce51p-2, 0x1.0a88fbec92db2p-2, -0x1.16ea71f276b01p-3, 0x1.018afa9348368p-4, -0x1.2fa053de7510ep-5, 0x1.2375ee2696f87p-6, -0x1.73b10c938e4b6p-8, 0x1.1decc8370b235p-9, -0x1.b8713a4dd74a9p-11, 0x1.732711f764c01p-14, 0x1.5deb76c540b6cp-16, -0x1.9271259f10414p-23, -0x1.2099915b93354p-32, 0x0p+0};
@@ -1521,25 +1859,25 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         }
         if constexpr (std::is_same_v<Real, long double>) {
             if constexpr (order == 0) {
-                return {0x0p+0L, 0xe.cceb08e0232ebfep-15L, 0x8.697cc2a13d0ee1p-7L, 0xa.529c93355636f38p-4L, 0x8.fe286827bf83d25p-4L, -0xe.a4bba81395fd148p-5L, 0x9.abad43ece0b19efp-5L, -0xb.f3225588c443427p-6L, 0xd.0bc2bb2ddca46a9p-7L, -0xb.89ad356d45a90abp-8L, 0xe.c67ee5d8b0c44cdp-10L, -0xa.bf0abdade753fd6p-12L, -0xa.fb1990274acfe19p-18L, 0x8.8522c4ecfc3eb6ep-16L, -0xa.c913268b7310da9p-19L, 0xc.4cbcbc26b8c299cp-21L, -0xa.7c208b4d0dd68c5p-21L, 0xb.a4a9e9cb3e66c66p-23L, -0xf.be58d677e7a1ad2p-29L, -0xe.495f10d77864d6p-29L, -0x9.dcd2be2673f3d47p-38L, -0xb.52c67607d112652p-38L, 0xa.5f8f5c66a64e114p-40L, 0xb.4b833f8b8ad0a0ap-47L, -0xa.89ebc85e9217eeap-52L, -0xd.9ca1e014c35331bp-60L, 0xa.a69985f2bc1edb9p-70L, -0x9.fb70f3189b26326p-83L, -0xe.86c417c2c3da4c7p-107L, 0x0p+0L};
+                return {0x0p+0L, 0xe.cceb08e0232ebfep-15L, 0x8.697cc2a13d0ee1p-7L, 0xa.529c93355636f38p-4L, 0x8.fe286827bf83d25p-4L, -0xe.a4bba81395fd148p-5L, 0x9.abad43ece0b19efp-5L, -0xb.f3225588c443427p-6L, 0xd.0bc2bb2ddca46a9p-7L, -0xb.89ad356d45a90abp-8L, 0xe.c67ee5d8b0c44cdp-10L, -0xa.bf0abdade753fd6p-12L, -0xa.fb1990274acfe19p-18L, 0x8.8522c4ecfc3eb6ep-16L, -0xa.c913268b7310da9p-19L, 0xc.4cbcbc26b8c299cp-21L, -0xa.7c208b4d0dd68c5p-21L, 0xb.a4a9e9cb3e66c66p-23L, -0xf.be58d677e7a1ad2p-29L, -0xe.495f10d77864d6p-29L, -0x9.dcd2be2673f3d47p-38L, -0xb.52c67607d112652p-38L, 0xa.5f8f5c66a64e114p-40L, 0xb.4b833f8b8ad0a0ap-47L, -0xa.89ebc85e9217eeap-52L, -0xd.9ca1e014c35331bp-60L, 0xa.a69985f2bc1edb9p-70L, -0x9.fb70f3189b26326p-83L, -0xe.86c417c2c3da4c7p-107L, -0x0p+0L};
             }
             if constexpr (order == 1) {
-                return {0x0p+0L, 0xd.7b39b8b93a579b8p-12L, 0xe.3d6a2e84375262fp-6L, 0xc.bab6584977037b5p-4L, -0xa.8c8b32be0c1a23fp-3L, 0xb.663747831202959p-5L, -0xc.679beb0c165058cp-7L, 0xc.d1fd17a0ea4a983p-7L, -0x8.5285f11795c36ecp-6L, 0xe.f9fa7b60cea28cap-7L, -0x9.6a5bf38aedb5fc2p-7L, 0x8.340f26105cfe721p-8L, -0x8.da86b44e5f6c6f9p-10L, 0xa.4d6689a512a5d01p-14L, 0x8.b328caaca1f1c8cp-14L, -0xe.1368f9638643783p-16L, 0x9.80108c73b15088ep-19L, 0xa.4fdf67ebece365dp-20L, -0xc.3c0d25352fbe46dp-22L, 0xa.f68568b2566925p-27L, 0xe.d253aac33a56ee8p-28L, -0xb.f11e391bf9fc9acp-32L, -0xd.ec79677c64f81e9p-38L, 0x8.e30a80fd082403ap-40L, -0xe.0dc599cc4f0122fp-47L, -0xc.a8ab79ce599d1e7p-55L, 0xe.8fc6edbe80cc4a8p-63L, -0x9.a31aef33e745dcdp-77L, -0xe.0636941fba0f2ecp-100L, -0x0p+0L};
+                return {0x0p+0L, 0xd.7b39b8b93a579b8p-12L, 0xe.3d6a2e84375262fp-6L, 0xc.bab6584977037b5p-4L, -0xa.8c8b32be0c1a23fp-3L, 0xb.663747831202959p-5L, -0xc.679beb0c165058cp-7L, 0xc.d1fd17a0ea4a983p-7L, -0x8.5285f11795c36ecp-6L, 0xe.f9fa7b60cea28cap-7L, -0x9.6a5bf38aedb5fc2p-7L, 0x8.340f26105cfe721p-8L, -0x8.da86b44e5f6c6f9p-10L, 0xa.4d6689a512a5d01p-14L, 0x8.b328caaca1f1c8cp-14L, -0xe.1368f9638643783p-16L, 0x9.80108c73b15088ep-19L, 0xa.4fdf67ebece365dp-20L, -0xc.3c0d25352fbe46dp-22L, 0xa.f68568b2566925p-27L, 0xe.d253aac33a56ee8p-28L, -0xb.f11e391bf9fc9acp-32L, -0xd.ec79677c64f81e9p-38L, 0x8.e30a80fd082403ap-40L, -0xe.0dc599cc4f0122fp-47L, -0xc.a8ab79ce599d1e7p-55L, 0xe.8fc6edbe80cc4a8p-63L, -0x9.a31aef33e745dcdp-77L, -0xe.0636941fba0f2ecp-100L, 0x0p+0L};
             }
             if constexpr (order == 2) {
-                return {0x0p+0L, 0xa.9550b3a1bf69d4cp-9L, 0x9.79c3228669b01a3p-4L, -0xc.96d1f07a3cafa97p-5L, -0x8.08736119b1617adp-2L, 0xd.d2f2b8399be77e4p-2L, -0xb.77d0d1a8f344a12p-2L, 0xf.177ffbc96536692p-3L, -0xf.4f4240ae714d2acp-4L, 0x9.f3de7e41ee9a787p-5L, -0x9.f90f2f41edcdbb5p-9L, -0x8.07048dc1886be21p-8L, 0xc.9929752ea076dc3p-11L, 0x8.65a9ded0927a627p-10L, -0xb.76632cb7ef5cbbcp-11L, 0x8.ed1e446f22c9d07p-13L, 0x8.7b82e4884dc45e4p-15L, -0xb.43f8bb20adad0a1p-16L, 0x8.1dfba4938f506e5p-18L, -0x8.52b864cbdc7b5dap-23L, -0xd.b0642b5bae37c7cp-25L, 0x9.79b640126a3c29ep-27L, -0xd.5b5a695064f587ep-33L, -0xd.bbedea6b125d8c1p-36L, 0x8.1703505a92944ccp-42L, 0xf.c806dc0c202de26p-49L, -0xa.e6355d251b37dfep-57L, 0xb.cd4df0dd6d782f3p-70L, 0x8.9658e330867ad2ep-91L, -0x0p+0L};
+                return {0x0p+0L, 0xa.9550b3a1bf69d4cp-9L, 0x9.79c3228669b01a3p-4L, -0xc.96d1f07a3cafa97p-5L, -0x8.08736119b1617adp-2L, 0xd.d2f2b8399be77e4p-2L, -0xb.77d0d1a8f344a12p-2L, 0xf.177ffbc96536692p-3L, -0xf.4f4240ae714d2acp-4L, 0x9.f3de7e41ee9a787p-5L, -0x9.f90f2f41edcdbb5p-9L, -0x8.07048dc1886be21p-8L, 0xc.9929752ea076dc3p-11L, 0x8.65a9ded0927a627p-10L, -0xb.76632cb7ef5cbbcp-11L, 0x8.ed1e446f22c9d07p-13L, 0x8.7b82e4884dc45e4p-15L, -0xb.43f8bb20adad0a1p-16L, 0x8.1dfba4938f506e5p-18L, -0x8.52b864cbdc7b5dap-23L, -0xd.b0642b5bae37c7cp-25L, 0x9.79b640126a3c29ep-27L, -0xd.5b5a695064f587ep-33L, -0xd.bbedea6b125d8c1p-36L, 0x8.1703505a92944ccp-42L, 0xf.c806dc0c202de26p-49L, -0xa.e6355d251b37dfep-57L, 0xb.cd4df0dd6d782f3p-70L, 0x8.9658e330867ad2ep-91L, 0x0p+0L};
             }
             if constexpr (order == 3) {
                 return {0x0p+0L, 0xd.ef23ef44a9bf7e6p-7L, 0xf.fb71cf02de0cb05p-4L, -0x8.76fbc0963f37be8p-1L, 0xb.c4757dff7ab7e6ep-1L, -0x8.5cf2c6824f158e6p-1L, 0xa.beb952a6cdbec82p-2L, -0xa.d762ccc9eb2601dp-2L, 0xb.35f0027de12c188p-2L, -0x9.2bdb98710a46a7ap-2L, 0xb.0f351247d3b2edap-3L, -0x8.eb30b84242b9b67p-4L, 0xb.b1a5749c2f3e942p-7L, 0xd.572f59b67919cdep-8L, -0xb.3516ec08c4d2b92p-8L, 0xc.f72e1c6ff9e2d6dp-10L, 0xe.772295aae3180b3p-15L, -0xb.e8731ba9d6fc085p-13L, 0xc.ad4dd8a66760405p-15L, -0xd.6345c24b6f75385p-20L, -0xa.51f298ee66ad3e4p-20L, 0xa.2d2d956d67f7238p-23L, -0xd.02c2f3943a728d1p-31L, -0xa.525579b7ed76162p-31L, 0xc.0c6e1e1b32163bep-37L, 0xd.e47631a948722aep-44L, -0x8.e287a56da6a461dp-51L, 0xa.a0f72f7f5d13f61p-64L, 0xf.779e334a13dd19fp-85L, -0x0p+0L};
             }
             if constexpr (order == 4) {
-                return {0x0p+0L, 0xe.d4f7dc266880dc5p-5L, -0x8.54b1a91e3c07cabp-5L, -0xb.756bc5953fc385dp-1L, 0x8.fd85bf73ff4da1p+1L, -0xd.135907cdef77f86p+1L, 0xa.d1b1380b495aeaap+1L, -0xe.1dc9ba1f6af0fa5p-1L, -0x8.1c9faa033715437p+0L, 0xe.70719adcdae7ec4p+0L, -0x9.9b8fa1bc7e12e6ep+0L, 0x8.23a26399544b84bp-5L, 0xa.eaddd56169ee9cdp-1L, -0xa.b481d5e4e9b9684p-1L, 0xa.79b3a285d814a56p-2L, -0x8.b78df8f23eebd9ap-4L, -0x8.653044fe20f733p-6L, 0xf.e8f321b94c6f489p-7L, -0x8.93ab4e369e900fp-8L, 0x8.18e721eb7954d94p-12L, 0xe.de2d091a80b9ee2p-14L, -0xb.72bac364ced9545p-16L, 0x9.9c60964d4ada3f3p-22L, 0xf.6419dee46b558e8p-24L, -0x9.8f70f1115417f37p-29L, -0x8.3466712818e830ep-35L, 0xd.5a4368c8a906c55p-43L, -0xc.b8d6308a3e25ebp-55L, -0x9.41b2dacc9130e5dp-74L, -0x0p+0L};
+                return {0x0p+0L, 0xe.d4f7dc266880dc5p-5L, -0x8.54b1a91e3c07cabp-5L, -0xb.756bc5953fc385dp-1L, 0x8.fd85bf73ff4da1p+1L, -0xd.135907cdef77f86p+1L, 0xa.d1b1380b495aeaap+1L, -0xe.1dc9ba1f6af0fa5p-1L, -0x8.1c9faa033715437p+0L, 0xe.70719adcdae7ec4p+0L, -0x9.9b8fa1bc7e12e6ep+0L, 0x8.23a26399544b84bp-5L, 0xa.eaddd56169ee9cdp-1L, -0xa.b481d5e4e9b9684p-1L, 0xa.79b3a285d814a56p-2L, -0x8.b78df8f23eebd9ap-4L, -0x8.653044fe20f733p-6L, 0xf.e8f321b94c6f489p-7L, -0x8.93ab4e369e900fp-8L, 0x8.18e721eb7954d94p-12L, 0xe.de2d091a80b9ee2p-14L, -0xb.72bac364ced9545p-16L, 0x9.9c60964d4ada3f3p-22L, 0xf.6419dee46b558e8p-24L, -0x9.8f70f1115417f37p-29L, -0x8.3466712818e830ep-35L, 0xd.5a4368c8a906c55p-43L, -0xc.b8d6308a3e25ebp-55L, -0x9.41b2dacc9130e5dp-74L, 0x0p+0L};
             }
             if constexpr (order == 5) {
-                return {0x0p+0L, 0xc.5145f8fa5d7812bp-3L, -0x8.5c765a89f338723p+0L, 0x9.80e8bd62f0e36d7p+1L, -0xc.052feaf5df5265fp+1L, 0xa.51cf1f08246b12ap+1L, -0x8.8a413c74ecd0982p+1L, 0x8.c71226bcd019464p+1L, -0x9.c84334dd03bcb23p+1L, 0xc.0223638d6d8a444p+1L, -0x8.5203ca3cc7208f6p+2L, 0xa.9284ee82627b576p+2L, -0xa.5a34298e2d8cfacp+2L, 0xe.4078a18719a503cp+1L, -0xc.16f69e44f3f4fd2p+0L, 0xb.b0850b3844f8cadp-3L, 0xd.8544d440c6033bfp-3L, -0x9.5a8b6d2e8407dd6p-3L, 0xa.440c4e0731919f2p-5L, -0x8.b6ec8fe746979d1p-9L, -0xc.abeababfa6ac0f1p-10L, 0xb.09de79617e3529fp-12L, -0x8.56de0126d2a8a97p-17L, -0xa.2482acbd44843d2p-19L, 0x9.1c5eaa88ac31dcbp-24L, 0x8.5c31de2c9d0ea8bp-30L, -0x9.6d6295ae9addc71p-37L, 0xd.455ad309c458ed8p-49L, 0x9.a7e7c45e7d9feeap-67L, 0x0p+0L};
+                return {0x0p+0L, 0xc.5145f8fa5d7812bp-3L, -0x8.5c765a89f338723p+0L, 0x9.80e8bd62f0e36d7p+1L, -0xc.052feaf5df5265fp+1L, 0xa.51cf1f08246b12ap+1L, -0x8.8a413c74ecd0982p+1L, 0x8.c71226bcd019464p+1L, -0x9.c84334dd03bcb23p+1L, 0xc.0223638d6d8a444p+1L, -0x8.5203ca3cc7208f6p+2L, 0xa.9284ee82627b576p+2L, -0xa.5a34298e2d8cfacp+2L, 0xe.4078a18719a503cp+1L, -0xc.16f69e44f3f4fd2p+0L, 0xb.b0850b3844f8cadp-3L, 0xd.8544d440c6033bfp-3L, -0x9.5a8b6d2e8407dd6p-3L, 0xa.440c4e0731919f2p-5L, -0x8.b6ec8fe746979d1p-9L, -0xc.abeababfa6ac0f1p-10L, 0xb.09de79617e3529fp-12L, -0x8.56de0126d2a8a97p-17L, -0xa.2482acbd44843d2p-19L, 0x9.1c5eaa88ac31dcbp-24L, 0x8.5c31de2c9d0ea8bp-30L, -0x9.6d6295ae9addc71p-37L, 0xd.455ad309c458ed8p-49L, 0x9.a7e7c45e7d9feeap-67L, -0x0p+0L};
             }
             if constexpr (order == 6) {
-                return {0x0p+0L, 0xf.0ab7ac0a2d5d3e8p-2L, -0xe.c9a85911c615c82p+1L, 0xd.81f1cabf66b5001p+3L, -0xf.a8efd3c4ec3c419p+4L, 0xd.8ecf71990eca11bp+5L, -0x9.e485bf1e50edc17p+6L, 0xd.0812fcefab32f7bp+6L, -0xf.7416dd5b55881cap+6L, 0xf.e78b4c99c8261c4p+6L, -0xd.f7706e0646ed8ddp+6L, 0xa.a2fa4f007a4af9bp+6L, -0xe.1ce51aadeae94b8p+5L, 0xe.8bf371344016517p+4L, -0xc.682f15c0e7b935cp+2L, -0xd.2beed726f676c5ap+2L, 0x8.32dfdce7f6881c4p+3L, -0x8.d3c1df77e743d81p+2L, 0x9.74f960ac0d34b75p+0L, -0x9.e56cd1213828f04p-5L, -0x8.da59d3d53874134p-4L, 0x8.ad18a34d4e700e2p-6L, -0xa.e33531e49a3a34ep-11L, -0xa.edab0664546ca1p-13L, 0xe.2bdf2954afcd1ep-18L, 0xe.4b9c033e2c84ec9p-24L, -0xb.1fb29623912c4c5p-30L, 0xb.b4bb3eda211db22p-41L, 0x8.8459c371cf4ab4bp-58L, 0x0p+0L};
+                return {0x0p+0L, 0xf.0ab7ac0a2d5d3e8p-2L, -0xe.c9a85911c615c82p+1L, 0xd.81f1cabf66b5001p+3L, -0xf.a8efd3c4ec3c419p+4L, 0xd.8ecf71990eca11bp+5L, -0x9.e485bf1e50edc17p+6L, 0xd.0812fcefab32f7bp+6L, -0xf.7416dd5b55881cap+6L, 0xf.e78b4c99c8261c4p+6L, -0xd.f7706e0646ed8ddp+6L, 0xa.a2fa4f007a4af9bp+6L, -0xe.1ce51aadeae94b8p+5L, 0xe.8bf371344016517p+4L, -0xc.682f15c0e7b935cp+2L, -0xd.2beed726f676c5ap+2L, 0x8.32dfdce7f6881c4p+3L, -0x8.d3c1df77e743d81p+2L, 0x9.74f960ac0d34b75p+0L, -0x9.e56cd1213828f04p-5L, -0x8.da59d3d53874134p-4L, 0x8.ad18a34d4e700e2p-6L, -0xa.e33531e49a3a34ep-11L, -0xa.edab0664546ca1p-13L, 0xe.2bdf2954afcd1ep-18L, 0xe.4b9c033e2c84ec9p-24L, -0xb.1fb29623912c4c5p-30L, 0xb.b4bb3eda211db22p-41L, 0x8.8459c371cf4ab4bp-58L, -0x0p+0L};
             }
             if constexpr (order == 7) {
                 return {0x0p+0L, 0xe.c386f5e602e22c6p-1L, -0x8.615c585940c9ee7p+3L, 0x8.85e9ba6b1aa85ccp+5L, -0xa.220ed77990ea00bp+6L, 0xf.576a4111664dc93p+6L, -0xe.f502ad56a76577ep+6L, 0x8.7536f43aab75351p+6L, 0x9.ddc90b0228ce8d7p+2L, -0xb.e01ea6e7aa8a396p+6L, 0xd.bbefb63b9185cdp+7L, -0xa.ceea2e0c37d88e3p+8L, 0xc.956af742a2c67bbp+8L, -0xb.b8b74d94c4b8e53p+8L, 0x9.a66ca166a39d2d4p+8L, -0xe.9084343fd1b7644p+7L, 0x9.3f1020c8928bd55p+7L, -0x8.770098e0d827732p+6L, 0x8.9ffe00b7ab651d2p+4L, 0xc.810d4eea709578cp-2L, -0xe.5ca82d384b2dbfdp+0L, 0xf.88e6b0c619ac534p-2L, -0xd.1ff7f0d4a16a0e5p-6L, -0xd.4a9ed441ba370f6p-8L, 0xc.b8c5f71d7b945cfp-12L, 0xd.6a124f9ccac6c82p-18L, -0xf.5b8668d520288fbp-24L, 0xb.9003503d04bfb0cp-34L, 0x8.698313f351569a4p-50L, 0x0p+0L};
@@ -1548,19 +1886,19 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0L, 0x8.aa8ac563754c257p+0L, -0xa.7f61d351960f794p+3L, 0xb.86f620f57cbe932p+5L, -0xf.4a67f658f7d0a3cp+6L, 0xd.f8588069a68203p+7L, -0x9.c948c01fe7a3daep+8L, 0xb.ce67a857da36deap+8L, -0xd.5b6484c8b08d94p+8L, 0xe.23f6cd0bdce6402p+8L, -0xd.78802bc1e4e0454p+8L, 0xb.9542ce55da38fbfp+8L, -0x9.423735cd8a7a408p+8L, 0xd.9ec3effb54aa43bp+7L, -0x8.d708293d724a1cp+7L, 0xa.0f0b74e21a99604p+6L, -0xa.3001862df903727p+5L, 0x8.40c736ecd66e3b7p+4L, -0xc.7785b363b31632ap+1L, -0xb.75c761697e78222p+0L, 0x9.d5d0181f80e2122p+0L, -0xa.c46b691cb246e7cp-2L, 0xa.e5031d144bd1a3cp-6L, 0xb.9644270369ccd47p-8L, -0x9.5bdcced391cd468p-11L, -0x9.acd6af648a62d24p-17L, 0x8.67f844ea6ac9781p-22L, -0x9.03a9abaad597738p-32L, -0xd.1d6ceaac9a2dc82p-48L, -0x0p+0L};
             }
             if constexpr (order == 9) {
-                return {0x0p+0L, 0x8.ba7d8eb39831c18p+0L, -0xa.e7b1da03950427fp+3L, 0xc.2cb815c9848fe3fp+5L, -0x8.0471c6326a024f5p+7L, 0xe.01e0dc6fb09f8cp+7L, -0x8.f069828b6686adbp+8L, 0x9.9a827173155c815p+8L, -0xa.24c51cda2ee968bp+8L, 0xa.8062115bf26b28ap+8L, -0x9.6b7c8b797831eb6p+8L, 0xe.2dec5c5f666d9f8p+7L, -0x9.db9046e0c283a87p+7L, 0xd.258c0c883e39073p+6L, -0xe.01ac1f2494c092fp+5L, 0x8.92a6aee8d1e432cp+4L, 0xd.f0ca84cbce12938p-1L, -0xb.55fa92090f522ecp+2L, 0xd.efd4a4a391e9b21p+2L, -0xb.d4e0815eda4a88ap+2L, 0xc.349069e83f691d5p+1L, -0xd.4d6fd92e2793a35p-1L, 0x8.99bb20dc4eddf8ap-4L, 0x8.c8e3231160d8992p-6L, -0xc.468c211c336121fp-9L, -0xd.7727a335dcb4b2ep-15L, 0x8.af2f4ba3ff0ddeep-19L, -0xd.e2248f7707ee606p-29L, -0xa.18e01f3aa66c51bp-43L, 0x0p+0L};
+                return {0x0p+0L, 0x8.ba7d8eb39831c18p+0L, -0xa.e7b1da03950427fp+3L, 0xc.2cb815c9848fe3fp+5L, -0x8.0471c6326a024f5p+7L, 0xe.01e0dc6fb09f8cp+7L, -0x8.f069828b6686adbp+8L, 0x9.9a827173155c815p+8L, -0xa.24c51cda2ee968bp+8L, 0xa.8062115bf26b28ap+8L, -0x9.6b7c8b797831eb6p+8L, 0xe.2dec5c5f666d9f8p+7L, -0x9.db9046e0c283a87p+7L, 0xd.258c0c883e39073p+6L, -0xe.01ac1f2494c092fp+5L, 0x8.92a6aee8d1e432cp+4L, 0xd.f0ca84cbce12938p-1L, -0xb.55fa92090f522ecp+2L, 0xd.efd4a4a391e9b21p+2L, -0xb.d4e0815eda4a88ap+2L, 0xc.349069e83f691d5p+1L, -0xd.4d6fd92e2793a35p-1L, 0x8.99bb20dc4eddf8ap-4L, 0x8.c8e3231160d8992p-6L, -0xc.468c211c336121fp-9L, -0xd.7727a335dcb4b2ep-15L, 0x8.af2f4ba3ff0ddeep-19L, -0xd.e2248f7707ee606p-29L, -0xa.18e01f3aa66c51bp-43L, -0x0p+0L};
             }
             if constexpr (order == 10) {
-                return {0x0p+0L, 0xa.bee90172f4255c3p-1L, -0xd.a135ca4c3c846a5p+2L, 0xf.7a8579b5e4a4f6ap+4L, -0xa.6d47322333f3562p+6L, 0x9.6c44d5844c887bdp+7L, -0xc.a2b764377e3a1ebp+7L, 0xe.50fbae94e0bc253p+7L, -0xf.9757925a45f487cp+7L, 0x8.530717ee753bcd5p+8L, -0x8.3ff3ae16c29c979p+8L, 0xf.159bf6afa230cc6p+7L, -0xd.147e7fb73425ae6p+7L, 0xa.acb695f3e0fc1c3p+7L, -0x8.13b08baf665a54p+7L, 0xb.87a2d1f4db643efp+6L, -0xf.6fad2d9aa709453p+5L, 0x9.3d8f0994c5d9f7bp+5L, -0x9.df34921f79618f8p+4L, 0x9.db8f809079523d6p+3L, -0x8.8cc2eca027a29bcp+2L, 0x9.dad4bb17829d702p+0L, -0xe.1960c3b3edb91b1p-4L, -0xa.ec744dc5d17a352p-5L, 0x9.d8da354be17d4f6p-7L, 0x9.1b83681fb7ba338p-13L, -0xc.e137e4279ffaf08p-17L, 0xc.b149cd09c7159bbp-26L, 0x9.3a1452c9a7cedecp-39L, -0x0p+0L};
+                return {0x0p+0L, 0xa.bee90172f4255c3p-1L, -0xd.a135ca4c3c846a5p+2L, 0xf.7a8579b5e4a4f6ap+4L, -0xa.6d47322333f3562p+6L, 0x9.6c44d5844c887bdp+7L, -0xc.a2b764377e3a1ebp+7L, 0xe.50fbae94e0bc253p+7L, -0xf.9757925a45f487cp+7L, 0x8.530717ee753bcd5p+8L, -0x8.3ff3ae16c29c979p+8L, 0xf.159bf6afa230cc6p+7L, -0xd.147e7fb73425ae6p+7L, 0xa.acb695f3e0fc1c3p+7L, -0x8.13b08baf665a54p+7L, 0xb.87a2d1f4db643efp+6L, -0xf.6fad2d9aa709453p+5L, 0x9.3d8f0994c5d9f7bp+5L, -0x9.df34921f79618f8p+4L, 0x9.db8f809079523d6p+3L, -0x8.8cc2eca027a29bcp+2L, 0x9.dad4bb17829d702p+0L, -0xe.1960c3b3edb91b1p-4L, -0xa.ec744dc5d17a352p-5L, 0x9.d8da354be17d4f6p-7L, 0x9.1b83681fb7ba338p-13L, -0xc.e137e4279ffaf08p-17L, 0xc.b149cd09c7159bbp-26L, 0x9.3a1452c9a7cedecp-39L, 0x0p+0L};
             }
             if constexpr (order == 11) {
-                return {0x0p+0L, 0xc.15d0c5140aaa4eep-2L, -0xf.7190d63c174081fp+1L, 0x8.ba72fb2d2252c3fp+4L, -0xb.740eabe264bca0cp+5L, 0x9.b46f19b0fd72575p+6L, -0xb.883398ebe4385ep+6L, 0xb.30e910677d07ffp+6L, -0xb.419dbbc73b9d5a1p+6L, 0xc.19e0dbd12662221p+6L, -0xb.826867ada01fb9cp+6L, 0x9.5143da543a25f3ap+6L, -0xe.bcab98d7996a714p+5L, 0xb.d3311ddf4d7bdfbp+5L, -0x8.6eecfd0d6810f0bp+5L, 0xa.7c120c15da204bcp+4L, -0xc.dc6b77ec19e1f99p+3L, 0xf.35cdfe48953061cp+2L, -0xe.c39532a44de361dp+1L, 0xc.1727280b8b20591p+0L, -0x9.e40d8406be2c4fap-1L, 0xc.388bf027ec112cbp-3L, -0xf.968ede9ca84c64dp-9L, -0x9.93e06924a09fd14p-6L, 0x8.9dc64ac28a2fbc2p-8L, -0x8.4a44983b6d59171p-16L, -0xb.c238c931736ccdbp-17L, 0x9.8e9343ad5a2f5d8p-26L, 0xd.e1d77974b4c54b1p-39L, -0x0p+0L};
+                return {0x0p+0L, 0xc.15d0c5140aaa4eep-2L, -0xf.7190d63c174081fp+1L, 0x8.ba72fb2d2252c3fp+4L, -0xb.740eabe264bca0cp+5L, 0x9.b46f19b0fd72575p+6L, -0xb.883398ebe4385ep+6L, 0xb.30e910677d07ffp+6L, -0xb.419dbbc73b9d5a1p+6L, 0xc.19e0dbd12662221p+6L, -0xb.826867ada01fb9cp+6L, 0x9.5143da543a25f3ap+6L, -0xe.bcab98d7996a714p+5L, 0xb.d3311ddf4d7bdfbp+5L, -0x8.6eecfd0d6810f0bp+5L, 0xa.7c120c15da204bcp+4L, -0xc.dc6b77ec19e1f99p+3L, 0xf.35cdfe48953061cp+2L, -0xe.c39532a44de361dp+1L, 0xc.1727280b8b20591p+0L, -0x9.e40d8406be2c4fap-1L, 0xc.388bf027ec112cbp-3L, -0xf.968ede9ca84c64dp-9L, -0x9.93e06924a09fd14p-6L, 0x8.9dc64ac28a2fbc2p-8L, -0x8.4a44983b6d59171p-16L, -0xb.c238c931736ccdbp-17L, 0x9.8e9343ad5a2f5d8p-26L, 0xd.e1d77974b4c54b1p-39L, 0x0p+0L};
             }
             if constexpr (order == 12) {
-                return {0x0p+0L, 0x9.1480bef44c4469ep-3L, -0xb.a584c6bd94a1187p+0L, 0xd.1eb7f2c429e0f2ep+2L, -0x8.774ff1631cd3a64p+4L, 0xd.bf61476f622a169p+4L, -0xe.e5fff6d9d283fd3p+4L, 0xc.7ca8972468e2375p+4L, -0xb.a10d8d44022caeap+4L, 0xd.0bf0e90f39e8d94p+4L, -0xc.589dd6de50ec435p+4L, 0x9.080317497a44b68p+4L, -0xd.4bcc6a26d36101bp+3L, 0xb.17a90e8cb9542f6p+3L, -0xf.868a33cfb4e032cp+2L, 0x8.582a0590e784928p+2L, -0x9.73fc0eb91ba83cbp+1L, 0xb.bb58cde0ef3d615p+0L, -0x9.c855651ad1a4682p-1L, 0x8.73474a22b80bb4fp-3L, -0x8.ecf338b09522ep-5L, 0x8.f0a0fb7c1c0d8ddp-8L, 0xb.13140f8352b2905p-6L, -0x8.0288713e357cfe6p-6L, 0xe.ed032d5499f9d13p-9L, -0x9.cbf215a660e12a2p-13L, -0xa.f13c07f71d1127bp-16L, 0xc.9eb1f575f7dbcbbp-26L, 0x9.26242b289016945p-37L, 0x0p+0L};
+                return {0x0p+0L, 0x9.1480bef44c4469ep-3L, -0xb.a584c6bd94a1187p+0L, 0xd.1eb7f2c429e0f2ep+2L, -0x8.774ff1631cd3a64p+4L, 0xd.bf61476f622a169p+4L, -0xe.e5fff6d9d283fd3p+4L, 0xc.7ca8972468e2375p+4L, -0xb.a10d8d44022caeap+4L, 0xd.0bf0e90f39e8d94p+4L, -0xc.589dd6de50ec435p+4L, 0x9.080317497a44b68p+4L, -0xd.4bcc6a26d36101bp+3L, 0xb.17a90e8cb9542f6p+3L, -0xf.868a33cfb4e032cp+2L, 0x8.582a0590e784928p+2L, -0x9.73fc0eb91ba83cbp+1L, 0xb.bb58cde0ef3d615p+0L, -0x9.c855651ad1a4682p-1L, 0x8.73474a22b80bb4fp-3L, -0x8.ecf338b09522ep-5L, 0x8.f0a0fb7c1c0d8ddp-8L, 0xb.13140f8352b2905p-6L, -0x8.0288713e357cfe6p-6L, 0xe.ed032d5499f9d13p-9L, -0x9.cbf215a660e12a2p-13L, -0xa.f13c07f71d1127bp-16L, 0xc.9eb1f575f7dbcbbp-26L, 0x9.26242b289016945p-37L, -0x0p+0L};
             }
             if constexpr (order == 13) {
-                return {0x0p+0L, 0x9.6dd40b0366fa267p-6L, -0xc.1dd48316e0854aap-3L, 0xd.e3672174e9d1088p-1L, -0x9.64bdec0bd7ca5b2p+1L, 0x8.70348a6c98aa9bbp+2L, -0xa.fa3833406a56d39p+2L, 0xb.751fdfa491a058dp+2L, -0xa.d3bbf6a498f90bp+2L, 0xa.124bc010cc1696ap+2L, -0x9.8487f9ebff6b313p+2L, 0x9.1f220ceedb2076ep+2L, -0x8.3fe9ab7bb39dc96p+2L, 0xd.47a4451db725977p+1L, -0xa.4c991c276c5a664p+1L, 0x8.54b6a108a07f661p+1L, -0xc.7b066ce02b0141p+0L, 0x8.01de5f9352ed819p+0L, -0xa.19f78236cf689c9p-1L, 0xd.32dbeffc9a904b7p-2L, -0xe.9b01956f96deb78p-3L, 0xd.250d6a385e86ee4p-4L, -0xc.474fb1a89e70305p-5L, 0xb.3b27cb2e4a88b76p-6L, -0xc.8e1b591d78ebf4ap-8L, 0x8.3e81ebd0d6e0c17p-11L, 0x9.b169f1bffb66918p-14L, -0xc.96dfedfd40cbd7ep-23L, -0x9.17fc02283edf3c4p-33L, -0x0p+0L};
+                return {0x0p+0L, 0x9.6dd40b0366fa267p-6L, -0xc.1dd48316e0854aap-3L, 0xd.e3672174e9d1088p-1L, -0x9.64bdec0bd7ca5b2p+1L, 0x8.70348a6c98aa9bbp+2L, -0xa.fa3833406a56d39p+2L, 0xb.751fdfa491a058dp+2L, -0xa.d3bbf6a498f90bp+2L, 0xa.124bc010cc1696ap+2L, -0x9.8487f9ebff6b313p+2L, 0x9.1f220ceedb2076ep+2L, -0x8.3fe9ab7bb39dc96p+2L, 0xd.47a4451db725977p+1L, -0xa.4c991c276c5a664p+1L, 0x8.54b6a108a07f661p+1L, -0xc.7b066ce02b0141p+0L, 0x8.01de5f9352ed819p+0L, -0xa.19f78236cf689c9p-1L, 0xd.32dbeffc9a904b7p-2L, -0xe.9b01956f96deb78p-3L, 0xd.250d6a385e86ee4p-4L, -0xc.474fb1a89e70305p-5L, 0xb.3b27cb2e4a88b76p-6L, -0xc.8e1b591d78ebf4ap-8L, 0x8.3e81ebd0d6e0c17p-11L, 0x9.b169f1bffb66918p-14L, -0xc.96dfedfd40cbd7ep-23L, -0x9.17fc02283edf3c4p-33L, 0x0p+0L};
             }
             if constexpr (order == 14) {
                 return {0x0p+0L, 0xc.6eb70b42708eae9p-9L, -0xf.fda6f00329e9b71p-6L, 0x8.fc6fc4ef54c1db5p-3L, -0xb.7571951d3c8341p-2L, 0x9.0067ed5854443d7p-1L, -0x8.f943b3124055b9cp-1L, 0xc.84c85bf74ee8fcap-2L, -0x9.e8b35b15b042f15p-2L, 0xb.a6b0570d4675539p-2L, -0xb.40132bce1109dcp-2L, 0xf.3b5d4574c46a8f3p-3L, -0xb.04184a4ea6416d5p-3L, 0xa.4795456b82864acp-3L, -0xf.3e84e8eae3b6c57p-4L, 0x8.9297742ef492803p-4L, -0xb.74e803f1e728564p-5L, 0x8.5447df6496d92bp-5L, -0x8.b7538f93b58072dp-6L, 0x8.0c57d49a41b3dccp-7L, -0x9.7d029ef3a886eafp-8L, 0x9.1baf7134b7c3668p-9L, -0xb.9d88649c725b305p-11L, 0x8.ef6641b8591aa6cp-12L, -0xd.c389d26eba54b8ep-14L, 0xb.99388fbb2600ba3p-17L, 0xa.ef5bb62a05b60a1p-19L, -0xc.93892cf88209c7cp-26L, -0x9.04cc8adc99aa115p-35L, 0x0p+0L};
@@ -1569,52 +1907,99 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         #ifdef BOOST_HAS_FLOAT128
         if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
             if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.d99d611c0465d7fca8709213621p-12Q, 0x1.0d2f985427a1dc1f62afa99d998cp-4Q, 0x1.4a539266aac6de6ff0ee136fe6bp-1Q, 0x1.1fc50d04f7f07a49e55f06b78357p-1Q, -0x1.d497750272bfa28f3f1990b740d3p-2Q, 0x1.3575a87d9c1633de9f0ee95125b3p-2Q, -0x1.7e644ab11888684db8a7b8d90491p-3Q, 0x1.a1785765bb948d52e0838b0df1ap-4Q, -0x1.7135a6ada8b52155f89869cf22d5p-5Q, 0x1.d8cfdcbb1618899a1617de65e07ep-7Q, -0x1.57e157b5bcea7fac037e4b9b62bp-9Q, -0x1.5f633204e959fc32c151ba98708bp-15Q, 0x1.10a4589d9f87d6dc51e36837ed03p-13Q, -0x1.592264d16e621b5275bdd9d12d4dp-16Q, 0x1.89979784d7185338d2badb26cadp-18Q, -0x1.4f841169a1bad189406e2832bc2dp-18Q, 0x1.74953d3967ccd8cc322dbf25294ep-20Q, -0x1.f7cb1acefcf435a3d287cb8094aap-26Q, -0x1.c92be21aef0c9ac0fb550ddd5f85p-26Q, -0x1.3b9a57c4ce7e7a8e7b0e1df18a41p-35Q, -0x1.6a58cec0fa224ca49741d50416e8p-35Q, 0x1.4bf1eb8cd4c9c2273508a8b73f42p-37Q, 0x1.697067f1715a141417bb7553b3a4p-44Q, -0x1.513d790bd242fdd412e02eaf3fb6p-49Q, -0x1.b3943c02986a6636aaf05d95d85p-57Q, 0x1.54d330be5783db7123cd1333ac81p-67Q, -0x1.3f6e1e631364c64c65f6b5a7fe31p-80Q, -0x1.d0d882f8587b498d8efb759e0601p-104Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.d99d611c0465d7fca87092137394p-12Q, 0x1.0d2f985427a1dc1f62afa99d998fp-4Q, 0x1.4a539266aac6de6ff0ee136fe6aap-1Q, 0x1.1fc50d04f7f07a49e55f06b78355p-1Q, -0x1.d497750272bfa28f3f1990b740bdp-2Q, 0x1.3575a87d9c1633de9f0ee95125a2p-2Q, -0x1.7e644ab11888684db8a7b8d90489p-3Q, 0x1.a1785765bb948d52e0838b0df196p-4Q, -0x1.7135a6ada8b52155f89869cf22c7p-5Q, 0x1.d8cfdcbb1618899a1617de65e071p-7Q, -0x1.57e157b5bcea7fac037e4b9b62aap-9Q, -0x1.5f633204e959fc32c151ba987165p-15Q, 0x1.10a4589d9f87d6dc51e36837ed0bp-13Q, -0x1.592264d16e621b5275bdd9d12d3ep-16Q, 0x1.89979784d7185338d2badb26cabcp-18Q, -0x1.4f841169a1bad189406e2832bc2dp-18Q, 0x1.74953d3967ccd8cc322dbf252946p-20Q, -0x1.f7cb1acefcf435a3d287cb8094c6p-26Q, -0x1.c92be21aef0c9ac0fb550ddd5f87p-26Q, -0x1.3b9a57c4ce7e7a8e7b0e1df188abp-35Q, -0x1.6a58cec0fa224ca49741d5041713p-35Q, 0x1.4bf1eb8cd4c9c2273508a8b73f46p-37Q, 0x1.697067f1715a141417bb7553b3a7p-44Q, -0x1.513d790bd242fdd412e02eaf3fd9p-49Q, -0x1.b3943c02986a6636aaf05d95d84p-57Q, 0x1.54d330be5783db7123cd1333ac9cp-67Q, -0x1.3f6e1e631364c64c65f6b5a7fe23p-80Q, -0x1.d0d882f8587b498d8efb759e05fp-104Q, 0x0p+0Q};
             }
             if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.af673717274af370272903c200ap-9Q, 0x1.c7ad45d086ea4c5ed9ed7e340d9bp-3Q, 0x1.9756cb092ee06f6ac1eb577b9667p-1Q, -0x1.51916657c183447d0774789d62f8p+0Q, 0x1.6cc6e8f0624052b2c0fdcc8950a9p-2Q, -0x1.8cf37d6182ca0b170d0a042e41d9p-4Q, 0x1.9a3fa2f41d4953051b0c6d4a1af5p-4Q, -0x1.0a50be22f2b86dd755f1bb101dbcp-3Q, 0x1.df3f4f6c19d45193b61450be397cp-4Q, -0x1.2d4b7e715db6bf84cb93e1a160d4p-4Q, 0x1.0681e4c20b9fce41d5b4e567565fp-5Q, -0x1.1b50d689cbed8df146901e68b65ap-7Q, 0x1.49acd134a254ba0136bf2c9ddd2bp-11Q, 0x1.16651955943e391787562b8520dbp-11Q, -0x1.c26d1f2c70c86f0644644cef751p-13Q, 0x1.3002118e762a111c6bcee4aaae42p-16Q, 0x1.49fbecfd7d9c6cba55cd30ac0602p-17Q, -0x1.8781a4a6a5f7c8daadd9ede24939p-19Q, 0x1.5ed0ad164acd249f0f9d827483acp-24Q, 0x1.da4a7558674addd03b35614f79bdp-25Q, -0x1.7e23c7237f3f9358779e22d38cap-29Q, -0x1.bd8f2cef8c9f03d137232e9e48dbp-35Q, 0x1.1c61501fa10480730673344e35a7p-37Q, -0x1.c1b8b33989e0245e7c861b898ec7p-44Q, -0x1.95156f39cb33a3cd95db28e3ba68p-52Q, 0x1.d1f8ddb7d01989509bfbf0327cdap-60Q, -0x1.34635de67ce8bb9a35ccd2f4bc82p-74Q, -0x1.c0c6d283f741e5d8d9e1ced44cbap-97Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.af673717274af370272903c1fa7cp-9Q, 0x1.c7ad45d086ea4c5ed9ed7e340defp-3Q, 0x1.9756cb092ee06f6ac1eb577b96f6p-1Q, -0x1.51916657c183447d0774789d6344p+0Q, 0x1.6cc6e8f0624052b2c0fdcc8950d3p-2Q, -0x1.8cf37d6182ca0b170d0a042e4192p-4Q, 0x1.9a3fa2f41d4953051b0c6d4a1b03p-4Q, -0x1.0a50be22f2b86dd755f1bb101decp-3Q, 0x1.df3f4f6c19d45193b61450be39f8p-4Q, -0x1.2d4b7e715db6bf84cb93e1a16129p-4Q, 0x1.0681e4c20b9fce41d5b4e56756a7p-5Q, -0x1.1b50d689cbed8df146901e68b6b4p-7Q, 0x1.49acd134a254ba0136bf2c9ddd8p-11Q, 0x1.16651955943e391787562b852142p-11Q, -0x1.c26d1f2c70c86f0644644cef75b6p-13Q, 0x1.3002118e762a111c6bcee4aaae9bp-16Q, 0x1.49fbecfd7d9c6cba55cd30ac067dp-17Q, -0x1.8781a4a6a5f7c8daadd9ede249c3p-19Q, 0x1.5ed0ad164acd249f0f9d827483fep-24Q, 0x1.da4a7558674addd03b35614f7a6dp-25Q, -0x1.7e23c7237f3f9358779e22d38d23p-29Q, -0x1.bd8f2cef8c9f03d137232e9e498bp-35Q, 0x1.1c61501fa10480730673344e3608p-37Q, -0x1.c1b8b33989e0245e7c861b898f54p-44Q, -0x1.95156f39cb33a3cd95db28e3bb11p-52Q, 0x1.d1f8ddb7d01989509bfbf0327d67p-60Q, -0x1.34635de67ce8bb9a35ccd2f4bcc3p-74Q, -0x1.c0c6d283f741e5d8d9e1ced44ca2p-97Q, 0x0p+0Q};
             }
             if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.52aa167437ed3a97a2d16e2e814p-6Q, 0x1.2f386450cd3603452775e405d98cp-1Q, -0x1.92da3e0f4795f52ddad3070744b5p-2Q, -0x1.010e6c23362c2f5a0189ea0fe507p+1Q, 0x1.ba5e5707337cefc73943a8303951p+1Q, -0x1.6efa1a351e68942304e8e68b7a36p+1Q, 0x1.e2efff792ca6cd2456dfdb721d3p+0Q, -0x1.e9e84815ce29a5578b4bc0477766p-1Q, 0x1.3e7bcfc83dd34f0d929299012fe2p-2Q, -0x1.3f21e5e83db9b76a1e6a21ec102ep-6Q, -0x1.00e091b8310d7c425038e08db391p-5Q, 0x1.93252ea5d40edb85ff0ddad30d7p-8Q, 0x1.0cb53bda124f4c4d4c0ae3af47ep-7Q, -0x1.6ecc6596fdeb97786cd08cbbbc9bp-8Q, 0x1.1da3c88de4593a0d10cc249b863dp-10Q, 0x1.0f705c9109b88bc792c8e251c2cep-12Q, -0x1.687f176415b5a1410c9f394cb9e8p-13Q, 0x1.03bf749271ea0dc9bfa9a81f431dp-15Q, -0x1.0a570c997b8f6bb3aa2b6fc455bcp-20Q, -0x1.b60c856b75c6f8f8db3b0f76f77ep-22Q, 0x1.2f36c8024d47853b1fc5abd2c44cp-24Q, -0x1.ab6b4d2a0c9eb0fb784066974351p-30Q, -0x1.b77dbd4d624bb182ce2a80889f4fp-33Q, 0x1.02e06a0b525289974212166730a4p-39Q, 0x1.f900db818405bc4cfc19c1904249p-46Q, -0x1.5cc6aba4a366fbfbcb9e7e9b0d93p-54Q, 0x1.79a9be1badaf05e53c8d4ae1d448p-67Q, 0x1.12cb1c6610cf5a5ca8d9bf44c534p-88Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.52aa167437ed3a97a2d16e2e7e71p-6Q, 0x1.2f386450cd3603452775e405daacp-1Q, -0x1.92da3e0f4795f52ddad307073cb1p-2Q, -0x1.010e6c23362c2f5a0189ea0fe7f3p+1Q, 0x1.ba5e5707337cefc73943a8303bc5p+1Q, -0x1.6efa1a351e68942304e8e68b7bacp+1Q, 0x1.e2efff792ca6cd2456dfdb721f76p+0Q, -0x1.e9e84815ce29a5578b4bc0477acbp-1Q, 0x1.3e7bcfc83dd34f0d929299013451p-2Q, -0x1.3f21e5e83db9b76a1e6a21ec3442p-6Q, -0x1.00e091b8310d7c425038e08dacbfp-5Q, 0x1.93252ea5d40edb85ff0ddad301dp-8Q, 0x1.0cb53bda124f4c4d4c0ae3af4779p-7Q, -0x1.6ecc6596fdeb97786cd08cbbbaedp-8Q, 0x1.1da3c88de4593a0d10cc249b83cep-10Q, 0x1.0f705c9109b88bc792c8e251c3f5p-12Q, -0x1.687f176415b5a1410c9f394cb959p-13Q, 0x1.03bf749271ea0dc9bfa9a81f4245p-15Q, -0x1.0a570c997b8f6bb3aa2b6fc454e1p-20Q, -0x1.b60c856b75c6f8f8db3b0f76f67dp-22Q, 0x1.2f36c8024d47853b1fc5abd2c569p-24Q, -0x1.ab6b4d2a0c9eb0fb78406697468ap-30Q, -0x1.b77dbd4d624bb182ce2a8088a4c2p-33Q, 0x1.02e06a0b5252899742121667393ep-39Q, 0x1.f900db818405bc4cfc19c190531fp-46Q, -0x1.5cc6aba4a366fbfbcb9e7e9b2b91p-54Q, 0x1.79a9be1badaf05e53c8d4ae211e7p-67Q, 0x1.12cb1c6610cf5a5ca8d9bf45819bp-88Q, 0x0p+0Q};
             }
             if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.bde47de89537efcc2943722b96bdp-4Q, 0x1.ff6e39e05bc1960ac6a7468afb9cp-1Q, -0x1.0edf7812c7e6f7d06a00b362f2edp+2Q, 0x1.788eafbfef56fcdc50a685d205b6p+2Q, -0x1.0b9e58d049e2b1cb9469b0149a1ap+2Q, 0x1.57d72a54d9b7d9046e3ca22b7fc2p+1Q, -0x1.5aec59993d64c03ae451f5fb9ac3p+1Q, 0x1.66be004fbc25830ff3a497ea8396p+1Q, -0x1.257b730e2148d4f4b3feb86356b8p+1Q, 0x1.61e6a248fa765db41939b126ff2cp+0Q, -0x1.1d661708485736ce63b6c04b43ccp-1Q, 0x1.7634ae9385e7d28433590ede6772p-4Q, 0x1.aae5eb36cf2339bb1da3727f868ap-5Q, -0x1.66a2dd81189a5724bb1062f0dbecp-5Q, 0x1.9ee5c38dff3c5ada29575f743c4fp-7Q, 0x1.cee452b55c630166e1f1c6509c8cp-12Q, -0x1.7d0e63753adf810a13b7946ecd49p-10Q, 0x1.95a9bb14ccec080a617568800ab6p-12Q, -0x1.ac68b8496deea7093d3eaa370cb3p-17Q, -0x1.4a3e531dccd5a7c88df667aa9ebfp-17Q, 0x1.45a5b2adacfee470f99a3f9ace09p-20Q, -0x1.a0585e72874e51a270db9477885p-28Q, -0x1.4a4aaf36fdaec2c3a3e857f50dfbp-28Q, 0x1.818dc3c36642c77c4040a75f4584p-34Q, 0x1.bc8ec635290e455c58f05f4ab9c8p-41Q, -0x1.1c50f4adb4d48c39b492719c233cp-48Q, 0x1.541ee5efeba27ec1d6332fa503dp-61Q, 0x1.eef3c669427ba33d298eab6d278p-82Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.bde47de89537efcc2943722b907bp-4Q, 0x1.ff6e39e05bc1960ac6a7468afb9ep-1Q, -0x1.0edf7812c7e6f7d06a00b362ef27p+2Q, 0x1.788eafbfef56fcdc50a685d1f90ep+2Q, -0x1.0b9e58d049e2b1cb9469b014878dp+2Q, 0x1.57d72a54d9b7d9046e3ca22b5dccp+1Q, -0x1.5aec59993d64c03ae451f5fb822ap+1Q, 0x1.66be004fbc25830ff3a497ea74efp+1Q, -0x1.257b730e2148d4f4b3feb863502dp+1Q, 0x1.61e6a248fa765db41939b126fafep+0Q, -0x1.1d661708485736ce63b6c04b417fp-1Q, 0x1.7634ae9385e7d28433590ede5d72p-4Q, 0x1.aae5eb36cf2339bb1da3727f92c7p-5Q, -0x1.66a2dd81189a5724bb1062f0dfebp-5Q, 0x1.9ee5c38dff3c5ada29575f743d87p-7Q, 0x1.cee452b55c630166e1f1c650af12p-12Q, -0x1.7d0e63753adf810a13b7946ecd6fp-10Q, 0x1.95a9bb14ccec080a6175688009ap-12Q, -0x1.ac68b8496deea7093d3eaa37178ap-17Q, -0x1.4a3e531dccd5a7c88df667aa9928p-17Q, 0x1.45a5b2adacfee470f99a3f9acab4p-20Q, -0x1.a0585e72874e51a270db9477829dp-28Q, -0x1.4a4aaf36fdaec2c3a3e857f50877p-28Q, 0x1.818dc3c36642c77c4040a75f3899p-34Q, 0x1.bc8ec635290e455c58f05f4aae9ap-41Q, -0x1.1c50f4adb4d48c39b492719c193cp-48Q, 0x1.541ee5efeba27ec1d6332fa4f538p-61Q, 0x1.eef3c669427ba33d298eab6d070cp-82Q, 0x0p+0Q};
             }
             if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.da9efb84cd101b891a55bf090876p-2Q, -0x1.0a963523c780f95520ba62e0ae99p-2Q, -0x1.6ead78b2a7f870bae850968cd2c2p+2Q, 0x1.1fb0b7ee7fe9b42077abdaf5e253p+4Q, -0x1.a26b20f9bdeeff0cd0b5e87989aep+4Q, 0x1.5a362701692b5d54a80faabeb08bp+4Q, -0x1.c3b93743ed5e1f4aae7ff9680d26p+2Q, -0x1.0393f54066e2a86d4f5766fcb157p+3Q, 0x1.ce0e335b9b5cfd8737f6de07ffafp+3Q, -0x1.3371f4378fc25cdcbf584ed998cep+3Q, 0x1.04744c732a8970957ba707ed40dap-2Q, 0x1.5d5bbaac2d3dd399541ae8c86b98p+2Q, -0x1.56903abc9d372d08f72cf8f9d84fp+2Q, 0x1.4f367450bb0294accf5c9a7e9554p+1Q, -0x1.16f1bf1e47dd7b33b29f107a965cp-1Q, -0x1.0ca6089fc41ee660907b2bb58a89p-3Q, 0x1.fd1e6437298de912355a40f320d6p-4Q, -0x1.127569c6d3d201e096a74c3e9f6bp-5Q, 0x1.031ce43d6f2a9b28afac205cb30cp-9Q, 0x1.dbc5a12350173dc4ceb0edd4094ep-11Q, -0x1.6e57586c99db2a8af6576e5da36dp-13Q, 0x1.338c12c9a95b47e57d454a7c5751p-19Q, 0x1.ec833bdc8d6ab1cf492647695cc2p-21Q, -0x1.31ee1e222a82fe6e397b0f1aa142p-26Q, -0x1.068cce25031d061c7d5229b84eeap-32Q, 0x1.ab486d191520d8a9aefca6d37aefp-40Q, -0x1.971ac61147c4bd5f21d58d94b0d3p-52Q, -0x1.28365b5992261cb91d89a4a5eba6p-71Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.da9efb84cd101b891a55bf085a33p-2Q, -0x1.0a963523c780f95520ba62e1635dp-2Q, -0x1.6ead78b2a7f870bae850968c013ap+2Q, 0x1.1fb0b7ee7fe9b42077abdaf556e2p+4Q, -0x1.a26b20f9bdeeff0cd0b5e878c8cap+4Q, 0x1.5a362701692b5d54a80faabe0329p+4Q, -0x1.c3b93743ed5e1f4aae7ff96667ep+2Q, -0x1.0393f54066e2a86d4f5766fcec98p+3Q, 0x1.ce0e335b9b5cfd8737f6de07dc86p+3Q, -0x1.3371f4378fc25cdcbf584ed9698fp+3Q, 0x1.04744c732a8970957ba707eb759dp-2Q, 0x1.5d5bbaac2d3dd399541ae8c8527cp+2Q, -0x1.56903abc9d372d08f72cf8f9b7f6p+2Q, 0x1.4f367450bb0294accf5c9a7e742cp+1Q, -0x1.16f1bf1e47dd7b33b29f107a7717p-1Q, -0x1.0ca6089fc41ee660907b2bb584cap-3Q, 0x1.fd1e6437298de912355a40f30818p-4Q, -0x1.127569c6d3d201e096a74c3e92a3p-5Q, 0x1.031ce43d6f2a9b28afac205ca3a5p-9Q, 0x1.dbc5a12350173dc4ceb0edd40202p-11Q, -0x1.6e57586c99db2a8af6576e5d9fc9p-13Q, 0x1.338c12c9a95b47e57d454a7c66e9p-19Q, 0x1.ec833bdc8d6ab1cf492647696452p-21Q, -0x1.31ee1e222a82fe6e397b0f1ab0a7p-26Q, -0x1.068cce25031d061c7d5229b85c51p-32Q, 0x1.ab486d191520d8a9aefca6d39becp-40Q, -0x1.971ac61147c4bd5f21d58d94dd2bp-52Q, -0x1.28365b5992261cb91d89a4a61c9dp-71Q, 0x0p+0Q};
             }
             if constexpr (order == 5) {
-                return {0x0p+0Q, 0x1.8a28bf1f4baf0256370de9cbbbf3p+0Q, -0x1.0b8ecb513e670e46e8b61fdb81fap+3Q, 0x1.301d17ac5e1c6daeb2bb90052014p+4Q, -0x1.80a5fd5ebbea4cbe232c3d259f67p+4Q, 0x1.4a39e3e1048d6253983413fa5691p+4Q, -0x1.1148278e9d9a1304c4d279b67053p+4Q, 0x1.18e244d79a0328c7ff6ea967eef5p+4Q, -0x1.3908669ba07796469d99446fcffap+4Q, 0x1.80446c71adb1488769cf4e1f8d42p+4Q, -0x1.0a40794798e411ebd23986f8288ap+5Q, 0x1.52509dd04c4f6aeb9cbf502539fbp+5Q, -0x1.4b468531c5b19f58ba9821786258p+5Q, 0x1.c80f1430e334a07768f1a651dda2p+4Q, -0x1.82ded3c89e7e9fa329e762fc41f5p+3Q, 0x1.7610a167089f1959ecdad356948cp+0Q, 0x1.b0a89a8818c0677d48d730c11145p+0Q, -0x1.2b516da5d080fbac57eada1e0e8ap+0Q, 0x1.488189c0e63233e3103870456b25p-2Q, -0x1.16dd91fce8d2f3a24746d4df4144p-6Q, -0x1.957d5757f4d581e1eb8139ee8367p-7Q, 0x1.613bcf2c2fc6a53ed2c91b812d4dp-9Q, -0x1.0adbc024da55152d1e362e768c76p-14Q, -0x1.44905597a89087a3899ef231d6f7p-16Q, 0x1.238bd55115863b967f9591a85e2bp-21Q, 0x1.0b863bc593a1d515b8c451fdf4ccp-27Q, -0x1.2dac52b5d35bb8e11505ead79853p-34Q, 0x1.a8ab5a61388b1db01ad92615e5f6p-46Q, 0x1.34fcf88bcfb3fdd3eace821f889ap-64Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.8a28bf1f4baf0256370de9e50cdfp+0Q, -0x1.0b8ecb513e670e46e8b61ff5e5a2p+3Q, 0x1.301d17ac5e1c6daeb2bb903493bbp+4Q, -0x1.80a5fd5ebbea4cbe232c3d8a57f1p+4Q, 0x1.4a39e3e1048d62539834148e9e34p+4Q, -0x1.1148278e9d9a1304c4d27a6289e7p+4Q, 0x1.18e244d79a0328c7ff6eaa1380dep+4Q, -0x1.3908669ba07796469d9944fd1af2p+4Q, 0x1.80446c71adb1488769cf4e603a7ap+4Q, -0x1.0a40794798e411ebd23986dcd959p+5Q, 0x1.52509dd04c4f6aeb9cbf4fd2a65ep+5Q, -0x1.4b468531c5b19f58ba9821140c9p+5Q, 0x1.c80f1430e334a07768f1a5bc676fp+4Q, -0x1.82ded3c89e7e9fa329e76277e5cep+3Q, 0x1.7610a167089f1959ecdad2bfe856p+0Q, 0x1.b0a89a8818c0677d48d7304191d3p+0Q, -0x1.2b516da5d080fbac57ead9c2cab4p+0Q, 0x1.488189c0e63233e310386fe21bdep-2Q, -0x1.16dd91fce8d2f3a24746d48a1c72p-6Q, -0x1.957d5757f4d581e1eb81397c4cedp-7Q, 0x1.613bcf2c2fc6a53ed2c91b207503p-9Q, -0x1.0adbc024da55152d1e362e31540ap-14Q, -0x1.44905597a89087a3899ef1de6ff1p-16Q, 0x1.238bd55115863b967f9591633549p-21Q, 0x1.0b863bc593a1d515b8c451bf0e45p-27Q, -0x1.2dac52b5d35bb8e11505ea96f44p-34Q, 0x1.a8ab5a61388b1db01ad925c31a8cp-46Q, 0x1.34fcf88bcfb3fdd3eace81ef29a8p-64Q, 0x0p+0Q};
             }
             if constexpr (order == 6) {
-                return {0x0p+0Q, 0x1.e156f58145aba7d0b30fa35feff6p+1Q, -0x1.d9350b2238c2b904f5fdfd02be6bp+4Q, 0x1.b03e3957ecd6a002d130937fdeb5p+6Q, -0x1.f51dfa789d878832ad001d30e39cp+7Q, 0x1.b1d9ee3321d942364cb8271dfebap+8Q, -0x1.3c90b7e3ca1db82e1a61d27c7ae2p+9Q, 0x1.a1025f9df5665ef6d6390bf01f8bp+9Q, -0x1.ee82dbab6ab103949b52c0019f4cp+9Q, 0x1.fcf169933904c38827bff55b6c1p+9Q, -0x1.beee0dc0c8ddb1ba161390e5fd9fp+9Q, 0x1.545f49e00f495f369a9c2947535ap+9Q, -0x1.c39ca355bd5d296f3796271b492ep+8Q, 0x1.d17e6e268802ca2d8ab4b3a8e721p+7Q, -0x1.8d05e2b81cf726b84ae7af5a8e1fp+5Q, -0x1.a57ddae4deced8b3bcbf5da22cap+5Q, 0x1.065bfb9cfed103880a47e9c73209p+6Q, -0x1.1a783beefce87b0115cd8021056bp+5Q, 0x1.2e9f2c1581a696ea72950a297825p+3Q, -0x1.3cad9a2427051e071bf1f8338794p-2Q, -0x1.1b4b3a7aa70e82673e69d7fdae94p-1Q, 0x1.15a31469a9ce01c4f9e608774673p-3Q, -0x1.5c66a63c9347469ce6f6732b0a8p-8Q, -0x1.5db560cc8a8d9420c2df7832dd62p-10Q, 0x1.c57be52a95f9a3c03fb08e74a459p-15Q, 0x1.c9738067c5909d91761fe5fd95cfp-21Q, -0x1.63f652c47225898a139de258494dp-27Q, 0x1.769767db4423b6439ddbea7dbce4p-38Q, 0x1.108b386e39e95695575898c417c9p-55Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.e156f58145aba7d0b30fa35cff6p+1Q, -0x1.d9350b2238c2b904f5fdfc3f59d8p+4Q, 0x1.b03e3957ecd6a002d130922f2289p+6Q, -0x1.f51dfa789d878832ad001b3c3bbap+7Q, 0x1.b1d9ee3321d942364cb8258ac548p+8Q, -0x1.3c90b7e3ca1db82e1a61d1d6988cp+9Q, 0x1.a1025f9df5665ef6d6390bf76e1p+9Q, -0x1.ee82dbab6ab103949b52c0e24238p+9Q, 0x1.fcf169933904c38827bff6f06e1ap+9Q, -0x1.beee0dc0c8ddb1ba16139309e6dap+9Q, 0x1.545f49e00f495f369a9c2bc574c5p+9Q, -0x1.c39ca355bd5d296f37962bd729eep+8Q, 0x1.d17e6e268802ca2d8ab4ba84d645p+7Q, -0x1.8d05e2b81cf726b84ae7be04d2f8p+5Q, -0x1.a57ddae4deced8b3bcbf57c78c0cp+5Q, 0x1.065bfb9cfed103880a47e8cebd5dp+6Q, -0x1.1a783beefce87b0115cd7f827bd2p+5Q, 0x1.2e9f2c1581a696ea729509934246p+3Q, -0x1.3cad9a2427051e071bf1f9b27c09p-2Q, -0x1.1b4b3a7aa70e82673e69d678de04p-1Q, 0x1.15a31469a9ce01c4f9e606bc0537p-3Q, -0x1.5c66a63c9347469ce6f66ff5c6a6p-8Q, -0x1.5db560cc8a8d9420c2df7533732ep-10Q, 0x1.c57be52a95f9a3c03fb08957c434p-15Q, 0x1.c9738067c5909d91761fe08abd47p-21Q, -0x1.63f652c47225898a139ddd320614p-27Q, 0x1.769767db4423b6439ddbe400214ap-38Q, 0x1.108b386e39e95695575892a5277bp-55Q, 0x0p+0Q};
             }
             if constexpr (order == 7) {
-                return {0x0p+0Q, 0x1.d870debcc05c458cb432559ebfc5p+2Q, -0x1.0c2b8b0b28193dcd228c4e6d1c95p+6Q, 0x1.10bd374d63550b983999fd9b98p+8Q, -0x1.4441daef321d4016bb9b098a7297p+9Q, 0x1.eaed48222cc9b9253eb90b0dcf97p+9Q, -0x1.dea055aad4ecaefb97bc94a552f5p+9Q, 0x1.0ea6de87556ea6a2de72c35c89c8p+9Q, 0x1.3bb921604519d1ae8a5d0ccd5d1ep+5Q, -0x1.7c03d4dcf551472cf76721c1c17cp+9Q, 0x1.b77df6c77230b9a06a45739b39aap+10Q, -0x1.59dd45c186fb11c5ad1d0f189e18p+11Q, 0x1.92ad5ee85458cf75ddd23bfc0512p+11Q, -0x1.7716e9b298971ca51bb637e98e57p+11Q, 0x1.34cd942cd473a5a710149f0fdbbdp+11Q, -0x1.d2108687fa36ec88dd75fde72adbp+10Q, 0x1.27e2041912517aaa65b8280aa4e9p+10Q, -0x1.0ee0131c1b04ee634d2080c95b01p+9Q, 0x1.13ffc016f56ca3a3bb7e6018d857p+7Q, 0x1.9021a9dd4e12af1889880347a2f3p+1Q, -0x1.cb9505a70965b7f9ec7d47aa192ap+3Q, 0x1.f11cd618c3358a67a90246f84b5cp+1Q, -0x1.a3fefe1a942d41c95d704e932873p-3Q, -0x1.a953da883746e1eb5fcefdddfb0dp-5Q, 0x1.9718bee3af728b9e4c377574de7ep-9Q, 0x1.ad4249f39958d903ac0c0b219af3p-15Q, -0x1.eb70cd1aa40511f5c136d6883df5p-21Q, 0x1.72006a07a097f617e893c7382f23p-31Q, 0x1.0d30627e6a2ad3489ce1b7745733p-47Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.d870debcc05c458cb431fd983345p+2Q, -0x1.0c2b8b0b28193dcd228c0a0c405bp+6Q, 0x1.10bd374d63550b983999c56c677ap+8Q, -0x1.4441daef321d4016bb9b2c10ec43p+9Q, 0x1.eaed48222cc9b9253ebb102b9831p+9Q, -0x1.dea055aad4ecaefb97c3b4138e1fp+9Q, 0x1.0ea6de87556ea6a2de81d408b23ep+9Q, 0x1.3bb921604519d1ae88e6a7fa3786p+5Q, -0x1.7c03d4dcf551472cf7483533c9dbp+9Q, 0x1.b77df6c77230b9a06a324d910941p+10Q, -0x1.59dd45c186fb11c5ad121467058cp+11Q, 0x1.92ad5ee85458cf75ddc7493a06c7p+11Q, -0x1.7716e9b298971ca51bace1729b0ap+11Q, 0x1.34cd942cd473a5a7100d811101f7p+11Q, -0x1.d2108687fa36ec88dd6bfb56d5c3p+10Q, 0x1.27e2041912517aaa65b2132e4553p+10Q, -0x1.0ee0131c1b04ee634d1b07d2c971p+9Q, 0x1.13ffc016f56ca3a3bb78dd1c64f4p+7Q, 0x1.9021a9dd4e12af18897a92604f62p+1Q, -0x1.cb9505a70965b7f9ec7314ae6da2p+3Q, 0x1.f11cd618c3358a67a8f728986e77p+1Q, -0x1.a3fefe1a942d41c95d66abeb0178p-3Q, -0x1.a953da883746e1eb5fc521fbad44p-5Q, 0x1.9718bee3af728b9e4c2d8088bafdp-9Q, 0x1.ad4249f39958d903ac018ed0138fp-15Q, -0x1.eb70cd1aa40511f5c12a3ada0131p-21Q, 0x1.72006a07a097f617e889edbdb056p-31Q, 0x1.0d30627e6a2ad3489cda0318f0edp-47Q, 0x0p+0Q};
             }
             if constexpr (order == 8) {
-                return {0x0p+0Q, 0x1.155158ac6ea984ad1f39657983b3p+3Q, -0x1.4fec3a6a32c1ef2818fc096fddd7p+6Q, 0x1.70dec41eaf97d263c2e27cc1784ep+8Q, -0x1.e94cfecb1efa1478b21e27ec9309p+9Q, 0x1.bf0b100d34d0405ff79ebd2004c2p+10Q, -0x1.39291803fcf47b5c2680912e1935p+11Q, 0x1.79ccf50afb46dbd4b771bbe9314ap+11Q, -0x1.ab6c90991611b280fa5f8fb17229p+11Q, 0x1.c47ed9a17b9cc8042e74a92f11b8p+11Q, -0x1.af1005783c9c08a75d43de02a3efp+11Q, 0x1.72a859cabb471f7e1c88f5de7fd4p+11Q, -0x1.2846e6b9b14f481005e1b83a4b88p+11Q, 0x1.b3d87dff6a954876ee2d25afa785p+10Q, -0x1.1ae10527ae49437f787df6e5258ep+10Q, 0x1.41e16e9c43532c08707790b425f3p+9Q, -0x1.460030c5bf206e4d0614b974f3a2p+8Q, 0x1.0818e6dd9acdc76d8ca672811999p+7Q, -0x1.8ef0b66c7662c653e52a9a26f648p+4Q, -0x1.6eb8ec2d2fcf0443ad7badae070dp+3Q, 0x1.3aba0303f01c424453f9ef91eafp+3Q, -0x1.588d6d239648dcf73cd93c85e3bap+1Q, 0x1.5ca063a2897a34772f3c4e199577p-3Q, 0x1.72c884e06d399a8e64fd9e5def96p-5Q, -0x1.2b7b99da7239a8d084357a60a47cp-8Q, -0x1.359ad5ec914c5a48afa14674a42fp-14Q, 0x1.0cff089d4d592f01775a283b1eb2p-19Q, -0x1.207535755ab2ee6fe496d4a13eeep-29Q, -0x1.a3ad9d559345b904814202802d71p-45Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.155158ac6ea984ad1f3ad98465a9p+3Q, -0x1.4fec3a6a32c1ef2818fdbca7bd5fp+6Q, 0x1.70dec41eaf97d263c2e4504b0b21p+8Q, -0x1.e94cfecb1efa1478b22094cf32b8p+9Q, 0x1.bf0b100d34d0405ff7a1094810ecp+10Q, -0x1.39291803fcf47b5c26824c7c465ep+11Q, 0x1.79ccf50afb46dbd4b77400a63149p+11Q, -0x1.ab6c90991611b280fa6243394583p+11Q, 0x1.c47ed9a17b9cc8042e779917f5f2p+11Q, -0x1.af1005783c9c08a75d46ca645f35p+11Q, 0x1.72a859cabb471f7e1c8ba7bd2a6cp+11Q, -0x1.2846e6b9b14f481005e402049827p+11Q, 0x1.b3d87dff6a954876ee30a3fd1e1p+10Q, -0x1.1ae10527ae49437f7880589e6393p+10Q, 0x1.41e16e9c43532c08707a85b672ep+9Q, -0x1.460030c5bf206e4d0618004a8fep+8Q, 0x1.0818e6dd9acdc76d8ca94db3b3b3p+7Q, -0x1.8ef0b66c7662c653e53071c7fb7ep+4Q, -0x1.6eb8ec2d2fcf0443ad7c1412d0d4p+3Q, 0x1.3aba0303f01c424453fb561d43b2p+3Q, -0x1.588d6d239648dcf73cdacc19a23ap+1Q, 0x1.5ca063a2897a34772f3d9594be58p-3Q, 0x1.72c884e06d399a8e64ff05cdd7a2p-5Q, -0x1.2b7b99da7239a8d08435e37194cp-8Q, -0x1.359ad5ec914c5a48afa1ae580694p-14Q, 0x1.0cff089d4d592f01775a150c05eep-19Q, -0x1.207535755ab2ee6fe496486e6edap-29Q, -0x1.a3ad9d559345b904814003502ba2p-45Q, 0x0p+0Q};
             }
             if constexpr (order == 9) {
-                return {0x0p+0Q, 0x1.174fb1d6730638307d208a7b9705p+3Q, -0x1.5cf63b4072a084fdeb8b32e3f8f4p+6Q, 0x1.859702b93091fc7e6589a6acc4cp+8Q, -0x1.008e38c64d4049e94bd5995565e4p+10Q, 0x1.c03c1b8df613f18067635d57973dp+10Q, -0x1.1e0d30516cd0d5b6c114eb50863dp+11Q, 0x1.33504e2e62ab9029d451c22dbffap+11Q, -0x1.4498a39b45dd2d15e6efe9a76837p+11Q, 0x1.500c422b7e4d651447d31248b36bp+11Q, -0x1.2d6f916f2f063d6cac6e50e8332ap+11Q, 0x1.c5bd8b8beccdb3ef65612beb26bfp+10Q, -0x1.3b7208dc1850750db50e8cf692d2p+10Q, 0x1.a4b1819107c720e5477b69693072p+9Q, -0x1.c03583e49298125db8ea16f1c92fp+8Q, 0x1.1254d5dd1a3c865791dce6763bcfp+7Q, 0x1.be19509979c252700b664c41f013p+2Q, -0x1.6abf524121ea45d75b14942386cep+5Q, 0x1.bdfa9494723d3641f8f38a0cc0ebp+5Q, -0x1.7a9c102bdb495114d11c4dc94aa3p+5Q, 0x1.86920d3d07ed23a99340d183d76p+4Q, -0x1.a9adfb25c4f27469db40c9474b64p+2Q, 0x1.1337641b89dbbf1427d9b379e883p-1Q, 0x1.191c64622c1b13245bb01b5d2dc3p-3Q, -0x1.88d18423866c243d7190bc69d463p-6Q, -0x1.aee4f466bb96965b6a3465feff1bp-12Q, 0x1.15e5e9747fe1bbdbc08e7b80eb4fp-16Q, -0x1.bc4491eee0fdcc0c5c68f4d91f7dp-26Q, -0x1.431c03e754cd8a35cd878b071e01p-40Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.174fb1d6730638307d1e4b445fc7p+3Q, -0x1.5cf63b4072a084fdeb886ad661e9p+6Q, 0x1.859702b93091fc7e65868db7a8fbp+8Q, -0x1.008e38c64d4049e94bd38a5f00e3p+10Q, 0x1.c03c1b8df613f180675faa2c200ap+10Q, -0x1.1e0d30516cd0d5b6c1126d4bf14cp+11Q, 0x1.33504e2e62ab9029d44ee63bfb62p+11Q, -0x1.4498a39b45dd2d15e6ecc8905aabp+11Q, 0x1.500c422b7e4d651447cfcdfc454bp+11Q, -0x1.2d6f916f2f063d6cac6b467c2932p+11Q, 0x1.c5bd8b8beccdb3ef655c28cdfe75p+10Q, -0x1.3b7208dc1850750db50ab0ef592ep+10Q, 0x1.a4b1819107c720e54775d3b0e2c4p+9Q, -0x1.c03583e49298125db8e2fdf27d4ep+8Q, 0x1.1254d5dd1a3c865791d5348ec394p+7Q, 0x1.be19509979c252700bdddf4796f4p+2Q, -0x1.6abf524121ea45d75b1ac598d945p+5Q, 0x1.bdfa9494723d3641f8f4e66eff1ap+5Q, -0x1.7a9c102bdb495114d11be11a8205p+5Q, 0x1.86920d3d07ed23a9933ffc257d69p+4Q, -0x1.a9adfb25c4f27469db3fea5dd201p+2Q, 0x1.1337641b89dbbf1427d95e0cc537p-1Q, 0x1.191c64622c1b13245bafd3429ab6p-3Q, -0x1.88d18423866c243d7190f3f8f03dp-6Q, -0x1.aee4f466bb96965b6a34b6c35598p-12Q, 0x1.15e5e9747fe1bbdbc08f26b48b4cp-16Q, -0x1.bc4491eee0fdcc0c5c6a94682339p-26Q, -0x1.431c03e754cd8a35cd8981f0bf35p-40Q, 0x0p+0Q};
             }
             if constexpr (order == 10) {
-                return {0x0p+0Q, 0x1.57dd202e5e84ab85696b3b081p+2Q, -0x1.b426b94987908d499f20a9e25757p+5Q, 0x1.ef50af36bc949ed3fa5d7e0a8198p+7Q, -0x1.4da8e644667e6ac3b79bfab28161p+9Q, 0x1.2d889ab089910f7ad40ce0f8df85p+10Q, -0x1.9456ec86efc743d5028d89866bbdp+10Q, 0x1.ca1f75d29c1784a6a77e065e7ddep+10Q, -0x1.f2eaf24b48be90f886aebc94dadbp+10Q, 0x1.0a60e2fdcea779a9912a9120de2ep+11Q, -0x1.07fe75c2d85392f1210e0f990473p+11Q, 0x1.e2b37ed5f446198c3a3c3919467ep+10Q, -0x1.a28fcff6e684b5cca8b59e89af3bp+10Q, 0x1.5596d2be7c1f83852a278b67a766p+10Q, -0x1.02761175eccb4a7f32e2ed6eb998p+10Q, 0x1.70f45a3e9b6c87dda4f640c6221p+9Q, -0x1.edf5a5b354e128a66f72c39ece6fp+8Q, 0x1.27b1e13298bb3ef65c5911d31c4bp+8Q, -0x1.3be69243ef2c31f022d98f8f933ep+7Q, 0x1.3b71f0120f2a47ab2eeb31559ad4p+6Q, -0x1.11985d9404f45378f92bac82976fp+5Q, 0x1.3b5a9762f053ae0408ef30897c49p+3Q, -0x1.c32c18767db723614caa803fec42p-1Q, -0x1.5d8e89b8ba2f46a3384127d85bb4p-2Q, 0x1.3b1b46a97c2fa9eb152314a4a3e9p-4Q, 0x1.23706d03f6f7466fb40930bedc5cp-10Q, -0x1.9c26fc84f3ff5e0f45c2413885cdp-14Q, 0x1.962939a138e2b376292fd9833a65p-23Q, 0x1.27428a5934f9dbd8cb61b82d774ep-36Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.57dd202e5e84ab856980df8a0abap+2Q, -0x1.b426b94987908d499f3bffafa19ep+5Q, 0x1.ef50af36bc949ed3fa7cc19e8e96p+7Q, -0x1.4da8e644667e6ac3b7b19c4c383dp+9Q, 0x1.2d889ab089910f7ad4219226878ep+10Q, -0x1.9456ec86efc743d502abdf76eae3p+10Q, 0x1.ca1f75d29c1784a6a7a3af88a28cp+10Q, -0x1.f2eaf24b48be90f886d98564f553p+10Q, 0x1.0a60e2fdcea779a991419059c46dp+11Q, -0x1.07fe75c2d85392f12125b660934dp+11Q, 0x1.e2b37ed5f446198c3a6ab7d8b74fp+10Q, -0x1.a28fcff6e684b5cca8e0268f1e92p+10Q, 0x1.5596d2be7c1f83852a4b17681f79p+10Q, -0x1.02761175eccb4a7f32feddc56feep+10Q, 0x1.70f45a3e9b6c87dda520903f4aafp+9Q, -0x1.edf5a5b354e128a66fada7d4bcf3p+8Q, 0x1.27b1e13298bb3ef65c7ced26ff2fp+8Q, -0x1.3be69243ef2c31f0230131660198p+7Q, 0x1.3b71f0120f2a47ab2f14bf7b7d89p+6Q, -0x1.11985d9404f45378f95059bc551ep+5Q, 0x1.3b5a9762f053ae040918d7979484p+3Q, -0x1.c32c18767db723614ce78e339586p-1Q, -0x1.5d8e89b8ba2f46a3386878a383e3p-2Q, 0x1.3b1b46a97c2fa9eb1545e9c9486p-4Q, 0x1.23706d03f6f7466fb42dcd72c19fp-10Q, -0x1.9c26fc84f3ff5e0f45e88806fbbbp-14Q, 0x1.962939a138e2b376295550104948p-23Q, 0x1.27428a5934f9dbd8cb77b8eb93d8p-36Q, 0x0p+0Q};
             }
             if constexpr (order == 11) {
-                return {0x0p+0Q, 0x1.82ba18a2815549dbb59529e31e5ap+1Q, -0x1.ee321ac782e8103dfdbc2361bd6ap+4Q, 0x1.174e5f65a44a587e237d6c3b553dp+7Q, -0x1.6e81d57c4c979417ab2afd3c009fp+8Q, 0x1.368de3361fae4ae909ed8745994cp+9Q, -0x1.7106731d7c870bc083f73b59d2eep+9Q, 0x1.661d220cefa0ffe013b3cf726fc3p+9Q, -0x1.6833b778e773ab42be67a15c0ce1p+9Q, 0x1.833c1b7a24cc4442e64b44e53f55p+9Q, -0x1.704d0cf5b403f737ee634427f2bbp+9Q, 0x1.2a287b4a8744be736378cf1ad4c7p+9Q, -0x1.d795731af32d4e2789adddfc9044p+8Q, 0x1.7a6623bbe9af7bf6c835c65c7832p+8Q, -0x1.0ddd9fa1ad021e162c7b141c194dp+8Q, 0x1.4f824182bb440977dbefd0a35cbfp+7Q, -0x1.9b8d6efd833c3f31fde4ac45e744p+6Q, 0x1.e6b9bfc912a60c385c629c5efb9fp+5Q, -0x1.d872a65489bc6c3914ee01ff515dp+4Q, 0x1.82e4e50171640b22bb957ff7eae6p+3Q, -0x1.3c81b080d7c589f42c5ce6389905p+2Q, 0x1.87117e04fd822595de53b26cd146p+0Q, -0x1.f2d1dbd395098c995382a933550bp-6Q, -0x1.327c0d249413fa2745d7e64f577bp-3Q, 0x1.13b8c9585145f7834dd210f62242p-5Q, -0x1.094893076dab22e2cc62b655bbffp-13Q, -0x1.784719262e6d99b573a61c97f7f8p-14Q, 0x1.31d26875ab45ebb06f0f6f8f22c8p-23Q, 0x1.bc3aef2e9698a9624f5205459225p-36Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.82ba18a2815549dbb583ba20e3a4p+1Q, -0x1.ee321ac782e8103dfda5e2a50005p+4Q, 0x1.174e5f65a44a587e2370d6742aeep+7Q, -0x1.6e81d57c4c979417ab1a67acd69dp+8Q, 0x1.368de3361fae4ae909df52a5836ap+9Q, -0x1.7106731d7c870bc083e5fa51f617p+9Q, 0x1.661d220cefa0ffe013a28a70693fp+9Q, -0x1.6833b778e773ab42be55fb8d5e31p+9Q, 0x1.833c1b7a24cc4442e638654d7d43p+9Q, -0x1.704d0cf5b403f737ee51433c941bp+9Q, 0x1.2a287b4a8744be736369f360e45fp+9Q, -0x1.d795731af32d4e2789960ef06165p+8Q, 0x1.7a6623bbe9af7bf6c822bfb77cd2p+8Q, -0x1.0ddd9fa1ad021e162c6d71d17f6ap+8Q, 0x1.4f824182bb440977dbde7b407e9p+7Q, -0x1.9b8d6efd833c3f31fdcf2bc0b9fap+6Q, 0x1.e6b9bfc912a60c385c4952c1112ep+5Q, -0x1.d872a65489bc6c3914d51095ebc1p+4Q, 0x1.82e4e50171640b22bb8023c09d2ep+3Q, -0x1.3c81b080d7c589f42c4b3bd2cdd6p+2Q, 0x1.87117e04fd822595de3e0b568ccp+0Q, -0x1.f2d1dbd395098c995334374fed2ep-6Q, -0x1.327c0d249413fa2745cbbd687d3ep-3Q, 0x1.13b8c9585145f7834dc70fb2de56p-5Q, -0x1.094893076dab22e2cc6f5a93ce22p-13Q, -0x1.784719262e6d99b5739a61a4981ap-14Q, 0x1.31d26875ab45ebb06f0484706cp-23Q, 0x1.bc3aef2e9698a9624f45add91d4dp-36Q, 0x0p+0Q};
             }
             if constexpr (order == 12) {
-                return {0x0p+0Q, 0x1.229017de89888d3b45dd8cbfea97p+0Q, -0x1.74b098d7b294230e195e9582cce8p+3Q, 0x1.a3d6fe58853c1e5c5b02b3c7091ap+5Q, -0x1.0ee9fe2c639a74c7c040d58ce97ep+7Q, 0x1.b7ec28edec4542d27f8e52ddc0eep+7Q, -0x1.dcbffedb3a507fa5c4eb668bdfccp+7Q, 0x1.8f9512e48d1c46e9ac992677a5b8p+7Q, -0x1.7421b1a8804595d4b26039d25693p+7Q, 0x1.a17e1d21e73d1b2880fd626879bep+7Q, -0x1.8b13badbca1d886a88315897811ap+7Q, 0x1.210062e92f4896d0f004a46e2b61p+7Q, -0x1.a9798d44da6c2035da4b20d5799bp+6Q, 0x1.62f521d1972a85eb2c685554b0c3p+6Q, -0x1.f0d14679f69c06584d129cb1dd4fp+5Q, 0x1.0b0540b21cf0924f554194ec7fd4p+5Q, -0x1.2e7f81d72375079565939ed3cb2dp+4Q, 0x1.776b19bc1de7ac2a6f7b7fc9f33cp+3Q, -0x1.390aaca35a348d0447a8760eee46p+2Q, 0x1.0e68e9445701769efc732f28d561p+0Q, -0x1.1d9e671612a45bff7de530a9d9acp-2Q, 0x1.1e141f6f8381b1b9941445268e56p-5Q, 0x1.626281f06a565209b564a6bd772p-3Q, -0x1.00510e27c6af9fccce79c2c0e3f3p-3Q, 0x1.dda065aa933f3a2523260c5e0824p-6Q, -0x1.397e42b4cc1c2544392f2098e5e3p-10Q, -0x1.5e2780fee3a224f5cbbe3f817e91p-13Q, 0x1.93d63eaebefb797682cedf0250afp-23Q, 0x1.24c485651202d28a48b30f621a03p-34Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.229017de89888d3b45e2c184d9bp+0Q, -0x1.74b098d7b294230e1965426f3612p+3Q, 0x1.a3d6fe58853c1e5c5b0a3a09e40cp+5Q, -0x1.0ee9fe2c639a74c7c045b3701c38p+7Q, 0x1.b7ec28edec4542d27f9646062fefp+7Q, -0x1.dcbffedb3a507fa5c4f4218a69c2p+7Q, 0x1.8f9512e48d1c46e9aca0a2a1ffcap+7Q, -0x1.7421b1a8804595d4b26746d9ca32p+7Q, 0x1.a17e1d21e73d1b2881053890e718p+7Q, -0x1.8b13badbca1d886a8838c2c2e2e8p+7Q, 0x1.210062e92f4896d0f00a29c58cfbp+7Q, -0x1.a9798d44da6c2035da535dfbec27p+6Q, 0x1.62f521d1972a85eb2c6f26f231b9p+6Q, -0x1.f0d14679f69c06584d1c30d18738p+5Q, 0x1.0b0540b21cf0924f5546e5194d02p+5Q, -0x1.2e7f81d7237507956599c3ca61c1p+4Q, 0x1.776b19bc1de7ac2a6f830edb0d24p+3Q, -0x1.390aaca35a348d0447af0cac40bp+2Q, 0x1.0e68e9445701769efc7a68d035e5p+0Q, -0x1.1d9e671612a45bff7deef6e6cc44p-2Q, 0x1.1e141f6f8381b1b9942811bfdb96p-5Q, 0x1.626281f06a565209b56968645fb1p-3Q, -0x1.00510e27c6af9fccce7dab2661cp-3Q, 0x1.dda065aa933f3a25232d375fa99bp-6Q, -0x1.397e42b4cc1c25443933189b9067p-10Q, -0x1.5e2780fee3a224f5cbc2e8463206p-13Q, 0x1.93d63eaebefb797682d434c6108cp-23Q, 0x1.24c485651202d28a48b67967bbebp-34Q, 0x0p+0Q};
             }
             if constexpr (order == 13) {
-                return {0x0p+0Q, 0x1.2dba81606cdf44cd9f079191a5b6p-3Q, -0x1.83ba9062dc10a95420b209411d9dp+0Q, 0x1.bc6ce42e9d3a21102e53db0ffbf5p+2Q, -0x1.2c97bd817af94b6452b9fa0d6cc7p+4Q, 0x1.0e06914d9315537516f325b1a949p+5Q, -0x1.5f4706680d4ada71d400dc2041dap+5Q, 0x1.6ea3fbf492340b1a8748a4fe5e1ep+5Q, -0x1.5a777ed4931f215f8e0bf28ba3b3p+5Q, 0x1.424978021982d2d37f646f8229b6p+5Q, -0x1.3090ff3d7fed662537bdbe4e02dbp+5Q, 0x1.23e4419ddb640edbe25bd0d3d323p+5Q, -0x1.07fd356f7673b92c13aaeedc3102p+5Q, 0x1.a8f488a3b6e4b2eef60e436347eap+4Q, -0x1.49932384ed8b4cc7bb557f0494b6p+4Q, 0x1.0a96d421140fecc2982c96f08508p+4Q, -0x1.8f60cd9c05602820630a2d130bddp+3Q, 0x1.003bcbf26a5db032107ba63bca4dp+3Q, -0x1.433ef046d9ed13921cc7a928013bp+2Q, 0x1.a65b7dff9352096da27656f15252p+1Q, -0x1.d36032adf2dbd6f014be67c6b6d9p+0Q, 0x1.a4a1ad470bd0ddc88c181c767028p-1Q, -0x1.88e9f63513ce060ad4280c3ae552p-2Q, 0x1.6764f965c95116ec3ca65a5d1d99p-3Q, -0x1.91c36b23af1d7e93ac72a63e1ecp-5Q, 0x1.07d03d7a1adc182d3615f97f92d8p-8Q, 0x1.362d3e37ff6cd230a2a84b0df184p-11Q, -0x1.92dbfdbfa8197afc834c0f617825p-20Q, -0x1.22ff804507dbe78851cf26324af8p-30Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.2dba81606cdf44cd9f04d2f8bc14p-3Q, -0x1.83ba9062dc10a95420ae8251630ap+0Q, 0x1.bc6ce42e9d3a21102e4fdf0d4671p+2Q, -0x1.2c97bd817af94b6452b764a95107p+4Q, 0x1.0e06914d9315537516f107f294e6p+5Q, -0x1.5f4706680d4ada71d3fe8928e941p+5Q, 0x1.6ea3fbf492340b1a8746b11d0c42p+5Q, -0x1.5a777ed4931f215f8e0a373e4b9fp+5Q, 0x1.424978021982d2d37f62990dfb19p+5Q, -0x1.3090ff3d7fed662537bbff91030bp+5Q, 0x1.23e4419ddb640edbe25a71aaad29p+5Q, -0x1.07fd356f7673b92c13a9d66edf4fp+5Q, 0x1.a8f488a3b6e4b2eef60c68cd2c1fp+4Q, -0x1.49932384ed8b4cc7bb541dede413p+4Q, 0x1.0a96d421140fecc2982baba8b026p+4Q, -0x1.8f60cd9c056028206308e7df4429p+3Q, 0x1.003bcbf26a5db032107ad008618cp+3Q, -0x1.433ef046d9ed13921cc6b579a83ap+2Q, 0x1.a65b7dff9352096da27547ffc3e7p+1Q, -0x1.d36032adf2dbd6f014bd3f02cf6dp+0Q, 0x1.a4a1ad470bd0ddc88c1710fd49dcp-1Q, -0x1.88e9f63513ce060ad42735911b82p-2Q, 0x1.6764f965c95116ec3ca5a4be4d2fp-3Q, -0x1.91c36b23af1d7e93ac71caa65612p-5Q, 0x1.07d03d7a1adc182d361556de1e4bp-8Q, 0x1.362d3e37ff6cd230a2a77cad24c8p-11Q, -0x1.92dbfdbfa8197afc834aaea734e3p-20Q, -0x1.22ff804507dbe78851ce06e1d7fp-30Q, 0x0p+0Q};
             }
             if constexpr (order == 14) {
-                return {0x0p+0Q, 0x1.8dd6e1684e11d5d1ba3d30411455p-6Q, -0x1.ffb4de00653d36e2054f8a61ef33p-3Q, 0x1.1f8df89dea983b6a683ab3dea296p+0Q, -0x1.6eae32a3a790681f248c15595ebap+1Q, 0x1.200cfdab0a8887ae485b249984acp+2Q, -0x1.1f287662480ab738cbe30fecb657p+2Q, 0x1.90990b7ee9dd1f94866e95a6da25p+1Q, -0x1.3d166b62b6085e29fb948fdc0ca7p+1Q, 0x1.74d60ae1a8ceaa71b4a8963d6056p+1Q, -0x1.68026579c2213b7f75e80846b227p+1Q, 0x1.e76ba8ae988d51e585809060cc1fp+0Q, -0x1.60830949d4c82da954f72fb8f218p+0Q, 0x1.48f2a8ad7050c9588f36c847ca49p+0Q, -0x1.e7d09d1d5c76d8ae64a9d1075b8ep-1Q, 0x1.1252ee85de9250052c524f707253p-1Q, -0x1.6e9d007e3ce50ac7539d68d5ba34p-2Q, 0x1.0a88fbec92db255ff32afa74479fp-2Q, -0x1.16ea71f276b00e5a14dbe15b1f7cp-3Q, 0x1.018afa9348367b971e99c9ccc188p-4Q, -0x1.2fa053de7510dd5de4017cd3190dp-5Q, 0x1.2375ee2696f86cd08bc39452c848p-6Q, -0x1.73b10c938e4b6609ab6e783698f5p-8Q, 0x1.1decc8370b2354d839f68c8d33cap-9Q, -0x1.b8713a4dd74a971b6935d59629ecp-11Q, 0x1.732711f764c01745616312d53ea3p-14Q, 0x1.5deb76c540b6c1414e8da0e84c77p-16Q, -0x1.9271259f104138f720caf85fff1dp-23Q, -0x1.2099915b9335422a7d174776e0cbp-32Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.8dd6e1684e11d5d1ba3be6ea3c1dp-6Q, -0x1.ffb4de00653d36e2054de2d9b35cp-3Q, 0x1.1f8df89dea983b6a6839c59e1daap+0Q, -0x1.6eae32a3a790681f248ae47d8bf4p+1Q, 0x1.200cfdab0a8887ae485a3302d7acp+2Q, -0x1.1f287662480ab738cbe219de6228p+2Q, 0x1.90990b7ee9dd1f94866d2e2c98f7p+1Q, -0x1.3d166b62b6085e29fb936a0976f7p+1Q, 0x1.74d60ae1a8ceaa71b4a74664e6fcp+1Q, -0x1.68026579c2213b7f75e6c5dc86c1p+1Q, 0x1.e76ba8ae988d51e5857ecafcf58dp+0Q, -0x1.60830949d4c82da954f5df283712p+0Q, 0x1.48f2a8ad7050c9588f35978df03dp+0Q, -0x1.e7d09d1d5c76d8ae64a80dc22b4p-1Q, 0x1.1252ee85de9250052c51460801d2p-1Q, -0x1.6e9d007e3ce50ac7539c0411656fp-2Q, 0x1.0a88fbec92db255ff329ff3310a4p-2Q, -0x1.16ea71f276b00e5a14dad4f88487p-3Q, 0x1.018afa9348367b971e98c4cc0c2cp-4Q, -0x1.2fa053de7510dd5de40051b25ee8p-5Q, 0x1.2375ee2696f86cd08bc27b41fb5bp-6Q, -0x1.73b10c938e4b6609ab6cf8acbfb8p-8Q, 0x1.1decc8370b2354d839f55dfbd7ebp-9Q, -0x1.b8713a4dd74a971b693427cc738fp-11Q, 0x1.732711f764c017456161af308333p-14Q, 0x1.5deb76c540b6c1414e8c8011ad5bp-16Q, -0x1.9271259f104138f720ca0ebaa72bp-23Q, -0x1.2099915b9335422a7d16c948a51bp-32Q, 0x0p+0Q};
             }
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            if constexpr (order == 0) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000451674235365384163942534112879962170050430005649917728757105702078353003628"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0657192182866101725866380380286811711515267979947671850787346119584203921772"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.645168852837185491636493374398382329354332388562492079567204840361307401530"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.562050253731258347205225316820341051454701066703611230358129787369760785703"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.457609012865475182073165321965578159870245716869287833800525163245742305892"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.302206642786606318842929559153148332332027636245062198716044751793827663646"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.186714728860412474380906761378313253397706130867010868609662030951952027624"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.101921407123630858758878752387723770129600361381616407855191001954194217355"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0450695281445151618957628013259453588544003268599264913526498769137792861370"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0144290759837282383389717270501147248409603304909144671371390973500564022245"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00262359805753383314662667515147465743725326741143989187946940239264695275198"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000418886520841363769876466059678934092937240028663097642468207760071276890909"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000130005825599913762664943931799127959428720573899694402098048868888541005861"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000205716103829132083896977152938360606246573125609400824113246425939226624402"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000586498015739086657425466432113622386414392393452860334775926059357778996230"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000499957637035187196702848333851389108402668590913054256330886021719308298712"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000138797970659198398937552944013353477360674956899913623607020403817559610213"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000293246341063622314369884411909694341374016914830560434158406924220522844059"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000266108789272668583275470247613518141118690036911170538022214691534270571516"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000358798958751818824805546395996552774193550110102954766818768372071949994542"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000411940737663914578546068859164549863164641326242451122480764989500567400523"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000943444434993874525374981775164876413640256062778860481019536432363883306329"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000802555990656338684626332640433500241162747359468279574694310485074495210891"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000234007347019229302189231520607745332418408168658262584544662206333484487383"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000118063935549154939400230495672962537326752673673203124419820222929027040784"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000902156164058513114611965908129419583178659829820202967090436659668867250204"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000103213448481218221009064172156534966525116936574987378830865635836819679217"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000000000000000000895260346451574665144738326201699984549687922838691880872307609498354042916"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 1) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00329134509554637016227932395665184462188816405990441294841331937353859018226"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.222498460222472570856273888144670809240856508400605204839473169454853935753"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.795584053870187153774544931353721619014829085153170531707050020981654416712"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.31862487452009442113191889013673630946692796798217185455367151031243111753"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.356227531120169092417942057959374242399264990210294310292353566593351691969"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0969118974391443107220210564208451767882607680272587960271393042788920753139"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.100158344781294000713035822000520082413219469752287984509961094639923004704"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.130036817018062768743563639955461355704215091556126309135663258237107378316"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.117003736727942246589361189897913287911205837308941552740306120021988232773"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0735583247350015119447973100838355102019211295561712733895699734366729336147"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0320443599633683857344012220821277284392085436118203012615734033030618281606"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00864611125470508985643225531487538786192034817394773971373053363374166094832"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000628805288742353846490436895658042874791044019850556792669438723659506085433"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000530996165887140074103720044534180857989796558151325571171563750787375335630"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000214779976330435101072773020094474738162154098655749881678420221771826004102"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000181202936405411896779927444691964784933446136755724601326144179927538206594"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000983429208199500966319547766620244833625578532495918145530854169815290840910"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000291695012617423905198714249842169472953358927807533287184982174200989887962"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000816805151056558922184516574886797062939832551592181636407453778207357205351"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000552147222971053211575103164058845299224045417814192301423715110168730452639"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000278043267728072036716596349031021595779494213305561207660868932770850125951"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000506542254942098412185567568651337434634840678880205714031416165837498235238"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000808256938962468939245796995705643475400792001340399660747359264165908131377"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000998582294082358754350176794222318406554783198601555538700921435939017946389"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000351354126713507884430073360081165916784665517276373638465106586156112456813"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000157877499711653737932118233203050006270260955310540472677365606073041849944"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000000000637731750269505916186533295298744348554008849524832564488593506481003691981"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000000000000000110631985666703620681934992597766218656255805692698991301252307109696735556"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 2) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0206704348828442146455298601806634783291751329720893335837042915536707378997"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.592227110732533668578196417495075085776270621924559929262444977224271579097"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.393410653765291902433654817300663592654609126271817695403842500410554851245"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.00825263709370592101160988069513144599529156226855536777407723196800985003"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.45600402690522611687855374504814910966687688506140696928870357367763805207"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.86700751870813930579622494686911790950745721733944746524273875866576699091"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.88647457798347347099275071442649242213607288760070094281108153092725485932"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.956850292836935604631540519513924221386391922474899432365133146628294288211"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.311019178959628658277170626061412967741738777405140811903034561579177783544"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0194782967746181932246482266173892495865298049064803547744629981318754422562"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0313570829471545004393086766795416583820751761342161837181042072847055050674"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00615150822507380481298471457879524284933712566490823438535524615873979419699"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00820031568959443119144645656936832514382458714118391502141763262037478621079"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00559689979763050004637051840086547958672230503688973990238062875917621549458"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00108962928377240734615453107312674463537085212267186648902987674997945923733"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000258864319280176698538293850130236134559386073543313286799132944540622102087"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000171898103078683638566235253747478209530138496225519577636080550780658518207"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000309643593428530836922212378988146884356326608056935343727759049059725321223"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000992193952216759361998206689460639053628352064203189180453876299839498267728"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000407964839436173861149529833860827000185779144514563959244446135200869586348"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000705975083156988948042006749490456594343348564541499729785531649950346638501"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000155494179555932056144441546086944808103333056502334729683797165052002203223"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000199857445192527259692451554428036856578337723773413083760501868541113100329"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000183942900453685991873954617889384304378063723737901417198613372194175703222"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000280333173005321969994829794928971151622655528245490950449547091812376086824"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000756287516479864730495516004403817436298330236371191825066059211760651100095"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000999665788433766570461546432082424563816636646761251573329874233246246718961"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000346838035061342291761151778299701276081089278724101229318566334215065043283"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 3) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.108860484914954355575079084123243067459138310025744627437589606265973071599"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.998887833249571574793052798864346575877689982939641232390178172030375530161"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.23238946756428856622131292649026891499466392216766277033807459199608937126"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.88370889419216762997764273176879062741698215984105909165713345305176600493"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.18153972950635043322094865169225941018236097827115854289221926390733666302"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.68625382559861128387876607708138212048108442724703967044946506502965986523"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.71033782942212120942300194056190679749862535535035830851858838821499116226"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.80267337697322824370014932789371815543658898251892562879598691459308783545"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.29282987775747551395165451529677668919917484323451781112725285361710130069"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.38242544442842915241462115657754442376597315779845068025541999436023658186"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.557419509659821724210988870096723764341990624840837128686052996727907371417"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0913588351617082455490771960757168500073024080354221476837833915643532317832"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0521115869546275007352831459735453272977332230195277247545553011333489468213"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0437788320785046747745346318425081514627922547506568893727540135563564332044"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0126616673332992189763107668027329389224194983671833648722585850627694599870"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000441448103933958333509284170313361172667888623881067406682817939537903874448"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00145361406367327911114133543555577415997816227432838988097249869672074010228"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000386870394595489219311323992284710227818861035531855271955313566170705603465"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000127675849793530154804055067259332359495984011575122830149195089883065001976"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000984202193485852050035097860846555963077977093712397464798289054164353785487"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000121313056970512630452162029729108592943238420540807995979786912047956902162"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000605861992739089687382030498760415289269264550833486793263523845161506867233"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000480637734385966690366533313966404604324257069377664472991243197708870665367"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000876647773931341316071062687585175265372059405788465230989307402677425063505"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000789693132057393370058232851770479415791480697650703122951856272042933692562"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000394568035880557031827281908497945772005279351103258103359896718769121745485"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000000000576186871216969872110176316067425636374680848236512588856967818814130253782"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000000000000000399819240477850657780597515175272454717319941884716677679140202464346919659"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 4) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.463497095089465556193152361674354253550988460728700341512951575248924005107"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.260338621434017069194053753179442990911796110131041248263757604108300285944"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5.72933785864723347958689894576856896970871030371827125012166758462465732047"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("17.98064416088037112447262961210309819025869195128448398522612428283054724080"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-26.15115449481430666135654454601908476913798365469208452665031301194399803840"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("21.63822079230404623177750575684281008376996692891143829654563260593428321030"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.05817968019025161983821299053916328782422062221848193813994955273557967790"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-8.11181128099913899853666875636635568569027342591544318148780945667167347907"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("14.43923347370119331414236561312914409252115548929447052983356089629331208180"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.60766039707057083044613368973988543650262251496746962365376370801259816429"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.254349894074616002886672766738792455231069414161313786718905562281170886778"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.45872370542653337904479516900588079252234184768289022901378718755768784979"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5.35255306643817868800359080338618790990023650113900088092988956482209882224"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.61884931508941023112322057748116480880128421631501355291655017759032872768"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.544813129850747446272398562457900585540272070585851811513882046278191469393"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.131176059127497035521761280194566727490837461219732199796495750703105213740"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.124296561686239461871148096056473522101237708684506720861975326392569561724"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0335032525969103386712875546102562852883523762416026454755015996210457308706"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00197687421925104166227063798049851778200652533856069925030249177610043199615"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000907463054694841802512946678881228619813411228517790637608215643817975804741"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000174685093401222970344248415273071087172528039501120783385838904981987795138"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000229140491543835493234065523810377340538057291963129940713094363492371457667"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000917376265236181573917176045082865834981330874821423583901682913289270269380"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000178074782772529767026962575165367966565557061024587011596888125628493484815"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000238787852610260980034963670269451676132667432806865308573034008434193644445"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000151801385578324942916928975944130135623202429359583566878602650893789670624"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000353106940189348195874403026790192524180728472834959918047053114899585048985"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000000000490042195447641265484925140544266723530168196082394169729111887193451305107"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 5) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.53968424333623591283539637104393285306939860118163339899756370093511752412"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-8.36118093364641071529734734349327158167828129455095101209909508144950844421"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("19.00710265475370468078225452071655698496996076626930820052271290018734955410"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-24.04052483563886538469582688782856892395508706836015455488573334599930766580"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("20.63913333795138578853149761490637030572718665431616641957345863819867808720"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-17.08011584958297102568375705513842664210388848702083749417185061652687170920"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("17.55524143428210432499122213752206106254752320830907975294234324350799433880"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-19.56455097953537387041983773986348842091325243494736289394773636533578502420"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("24.01670498281153432550600418634366701269994413307461865903740508422306310080"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-33.28148132262550348111697065791345588077894804510178954360174393891984479610"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("42.28936350567703557972644120171241320325939901556345142153549130433210665950"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-41.40943373570026124612528767222691112123207497138997507301595976366377899660"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("28.50368136498153869650031108535771315726615052538666183891156005702322580770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-12.08970059569761086730267951049932958603674239966305615386495196624445364550"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.46119126096220632514786029604710199172818340040776736162153531687984436840"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.69007268736527437715523188086809199467627091856919669141240791790387659253"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.16921124742703235845376498243007226742896232096052353425298018102553247710"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.320806648634560611806653735358063869544619918599484137286628075250908147793"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0170205999053340524093626134534504044131532660032315483110190757667509195644"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0123745609743425718328045581079363596477322528018678302846161407372341760769"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00269495872461749278937894414651717305557023546290073525941350512704421287628"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000636240007004980264934020663683814909158562231106074681170796063893995191439"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000193455103657614392543301741967257949034899863831055047403088880777986411556"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000543047159360829865209946475973261539370518740747480923818151249126619846189"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000778598331220689574680060505013012792715985361940745149089414772050997826569"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000685925299554479615829881764374497385028698287479222092891938709078253622707"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000235738843909944600637338699828608981498881273911589420488771624426365157864"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000000000654307895488301061055340897951003080401798618960776945151552704816810354728"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 6) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.76046627819172595883579644359769953588535927343615287177933134988108839887"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-29.57545007102832657505743042011930496079450543026239630758938313589160532240"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("108.06076562293097255019034894476937881414402744559487246258107823410272147100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-250.55855156825033737879997781487474575584645685461277748381454265462847743800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("433.85129088951476536844660346166919823690012103418599659417068253860704897400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-633.13061187142324243446054071388968011665704146897570849362072311779672021000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("834.01854300005356154348334819062306666614375690886471768229153759480600689000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-989.02232878407997120358917296431206973916448753054681863157557204973406068100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1017.88603439602004763640177568787110596329999229043433566699158997753449125000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-893.85979471023473569530438057552113081237409230440464102711969573113903766400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("680.74444199320236644223784616878658122038563144919598756685948523953944743700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-451.61186729310171527075800065120538411278520704643026316215948118992976179100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("232.74693413172044063567820009907697632227981752574909323161715193839229115800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-49.62787383879085055577682941397994398270572566635118571746050265908129325690"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-52.68645266346889530866217977440828165209704972435580166424853416940379389960"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("65.58982701592708822194210862578781927575261800997369868610970088145137416290"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-35.30870806416811325167467803727623467536045583746263032317420353531903306020"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("9.45693020058134236236600914378186391920422807218483316498811188937316130359"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.309255989510124888838029367237184571273819098555330087401099231089501040621"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.553308322403180080662599855565330327614574762204447931420915764088214443229"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.135564956163967134955269497874425345862822277717224909042351279062593810689"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00531617697249685655413505764052220837874749434001927999181762850859579155872"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00133403209032194873051891038551751265477738184982267945387427251670469994336"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000540595013560067659511437186384964395648420570660778415392983733962063677878"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000852069217823962821991801896006403698378777746783454675044188487130238725815"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000103598635303144789735973280116080267383974282294610808060500440818154996985"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000532326436761189266527809050123441642697540291063663589608819865551319229350"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000000295492612379887305461120954141505699178535540439686934703841872278010480863"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 7) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("7.38188904221300776496009553048328527576967910065603262630183408064961588176"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-67.04252259666674067633742223812249438362172734096027398031203225656148164940"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("272.73912509608366716885866926191887521865157404771591884845733117796365013300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-648.51449384638772307312239131652586511983283577261311478642454334856167122300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("981.85376383959687377603447626048634109920104854648430762305735754076198344100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-957.25261435887056636875408331000776657447691883681487882680731075009939532500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("541.30366603538032163248551525965043960470666784840537611909029954347476521100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("39.46539569102171970705958669748925636189807552510212755901108827273086521860"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-760.02993356684106043735642415972224288718293309831726448424859435908357278400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1757.96818720008277561277665672510216931821317114629250348699495528960281618000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2766.91476513255525367674460260698725596040373449509635634609462930432032153000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3221.41783539270407631009108958251542185799510806531936255493906833962767291000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3000.71602754404820657764337837297990613638348460036621198220820334626336373000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2470.42433778280717582983628335578899816038747362488063072589123876893726477000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1864.25821113047613457963263669044806128695158307572413234609544859584885145000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1183.53150011814970334873822520119965114014726798970411170643520179119098445000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-541.75058318442630698467104298817880920356698078100114691327566384707686791700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("137.99951240297224977307761334347678893729357990322145120547559793252791826600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.12602732950121750809668208362625489517387955383131958143915945154981671955"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-14.36194117187840557384339396841994678599549531498197679768014612622396331010"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.88369251450641812542291404390995294553530491514707983578184816105564596373"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.205076203523751335646189692334735950522359458346215290146294237414818037925"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0519198673443746908093580937887859538950707062316162140689427725731341271982"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00310590105240650772150514682372321446899318001963069459842377331199995861966"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000511716533793490097430403325096759854066642658007865906291974896322156973598"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000915379504933333794585544205822404705959783310556611306655341242734341633518"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000673029022229937708128420645199884166792336526676086359571430889068627124496"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000747149572478212798771461071516239850864323299591892246195331160945379616491"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 8) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.66617997816256087920214536690617523746852206827065901622480769322290866167"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-83.98069158491897137664435643009459588979224859539210985853414803563252312670"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("368.87018005167903705545229666937571099808324458744316183527918620353726742800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-978.60152567875426023724121513068510566332100363338255210925843566160434538000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1788.17285471112791661414958933940320019900977016707109161896875006334039594000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2505.28418158917689197444930176607319501629136847421443278162092799123039839000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3022.40491246297357949186655015360733638291689023377677784285814202906653466000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3419.39265112219216302436718059863861209172985626334602672566056357398676317000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3619.96406625884105825247254683983713351764036286848853247298077428329530067000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3448.50066768491548867152223553559079606474609521504982348767152988432081387000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2965.26096092775058800222809037838051197376961526002823132548802908800674743000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2370.21566471701430778551537838896798515071343646894034846503015619772514804000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1743.38269029053220243343945130374232884233597011426038758644227989592405303000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1131.51593963642249460026014723981984745424498754407883282530799710966079933000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("643.76118806159351516503113028075491121270396142347621937335117880501444850600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-326.00074420849016938772363017187446532879284433779346261909720782417377859600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("132.04863636507697220410685855738565713363890174302170404844428502247667225600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-24.93376772277967886098168919462189547482955889196701960148760723136973166400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-11.46007355523622142805150360772463017894407819656429723380717693966775564550"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("9.83520651597144304944047691431100720299540773467198740353710392336582989354"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.69181598889969722526095182382965976931346646569879768346189984962140006978"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.170227793119178996114554027953840164114050954576165838411751690985113034637"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0452616305587191906906494463453331102952776770834099929727401231003607603490"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00456974512275900662016820515100695013104712320434429376265064123517366266192"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000738155428701868927889552496062375155784301031721819122602154168460705282344"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000200417805609293879064935927873520236391193751194342643471993129180158539068"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000209880706796452611382955148605270725220758859068164296317180454372369377273"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000465936380567652114719537560618521630318410912594224492450951043895287614753"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 9) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.72847835430747578271505940879392817014574904538191687349175230203052100211"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-87.24046040248515953396974656933062782610014739997179110379894560357414245520"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("389.58988530574605311236047709354236113070541543269814845208675455966229540400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1026.22221524757438134135537633211873760625163523383080063432834094852546692000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1792.93918179541631021688427461004056301988797982219951847510033799076038456000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2288.41214820149496386771786036086875129982895627472684354601681048945900938000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2458.50954360267178809055553896154712231820849082662071689423543492550962685000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2596.76997150082880482258601881426530105265882898194790860287791956876237858000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2688.38307737987921311800960622311996109514265545357119388268171549268774070000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2411.48650321182678409587384256865680519785438974750423956549570619527017446000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1814.96164224744171541403234219853877586836575705876463094283829263461877926000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1261.78179075598184586999264045402353666457191513788617366898826973902302211000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("841.38676655654695150319104651983606990067095607106581498410485823300639441800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-448.20904377535777870670016285684401262406426096054935991931563578462255940200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("137.16569415040272577867061166123400360598914522499642465421078486401470231300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.97029509532788895885164044921726939214354175896907818967947070760987898130"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-45.34341860661268956588627411545980012291737814825718255408526440488307550890"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("55.74735370610838025915657695145098428353232401912757615516991907215832408810"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-47.32620271933516468424041285810723316313451633124158857561987010794991368370"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("24.41065715637416470293954557751523613609531738353047901798090642091718991060"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.65124396027002908823875984373242061438238591321150033722971368086704479617"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.537531975137361943952820148566801590297468742601138200538147419339609552580"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.137261184926968071617250973316263533192179366757491899389956174516444039153"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0239757337968515916483444709404140761125184131451276108629481306614530373711"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000410932878749734216531821493671349775506467371457544836055057579036862846795"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000165640171463349552097550017612947486316141194677792210133363117017273377794"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000258597924701581016593914203020341509426840234287159000763753949926949104263"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000114791530792780648836943943902186807559930855796434559067866982676609926206"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 10) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.37287144211047504433704259901170390442721988996694171621504548629516455500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-54.51890809483490464852283248943415532742549501170721326549017349607757265280"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("247.65758677532204293221852843860039171893106744274564279152987067839641783700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-667.31952719692784203091445371189075055828427651171572798348516350202578612200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1206.13444150385134150552864103423123937369610639043173021135297756204197139000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1617.35818646827561667680600978897561880473542593995241051599248884894163073000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1832.49156632655474156472726861249059324354983667150184526174507469910118731000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1995.67103845695443412193473876339890830254900007363102304644200890512301198000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2131.02770891534946890637577113319756817054287535999854454320796762879118815000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2111.95187513591062446244103153762651327657529103137337383793513437628034658000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1930.80461644034257841108186913574331573849553980249852538863650267384764992000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1674.24706814300119787406852339956482688948935893569842998213675767018340090000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1366.35661279794117490633588742507550359572013220593797272821411949768939054000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1033.84481571316170085412808060764164688210636040456382284874028192216356915000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("737.90900404538211792129865165976450017644934243508965145264819927501132834700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-493.95955963918928208805985585771230332863018601652969197751321482230632186700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("295.69484249333185830134864171026294553463486994728404251971308252543408822300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-157.95033466620052198343083333630677317616869298083612156110564608777827008500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("78.86126735894737975190973401300435275810030284606457363717046418120379800980"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-34.19939723625297188671822278987343132401852492048877442030253470317557547340"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("9.85480851482372144542629775026818779321611645636661320085440910666337715905"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.881195797409289017926845853302397485367129834932274334657677636659627396326"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.341364051723345408298411031291185136527925242955856494823260412052622050419"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0769303093181967020937802382117977446742217414595484586532006746274227409798"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00111175217988709633101089934655770002991047763696322734469092738921189950071"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000982647635077159314335458943401180956222687035734331269592286893349623594861"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000189133470696662119943963434893213305034415041925165273061718661046346898186"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000167835835060281197407582642924424716906566393004236332464276808169954678267"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 11) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.02130420622658340696449326038237531822446799531129776174318955573407685405"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-30.88723257001993621576643426629273861715132220480188564481242234143744414420"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("139.65307157164095118547259358765798565209048590969720241210221184082814259900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-366.50716378087925339618840606165232094377044199283379149990581531088506707700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("621.10849644228854707468833979073748978917989740451446746601968372897995517700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-738.05038803654141867136650825674832560704059341561497206520134648959243742700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("716.22760163975362868384596863440985771640184356269565624056314309892640235800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-720.40403662968977912382793878795331281967949028146265663798101543449138262900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("774.46958853527806540260330998289032375034119650758547176995108093121313426500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-736.60195800103968521796236805592735351842535720597394502820018520167468427100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("596.31626254658612005766603140598759356655195606907637429116209218854881937200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-471.58378761708200298998558351304868385444119358761564411342671419904990477200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("378.39898275809490245077643425004608535503558145569856205930880098307153717800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-269.86571703409037356854373301981664730493718351969444434530300707084602972400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("167.75440605674704647078720706448625075038628046714247177190414075458807244900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-102.88811870683190292233095418098044601993226910564909825458147979457012259200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("60.84069783294831355931283800609894422578310981797539730725548116612260807360"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-29.52799065611523148766040534779036649587797273072633016718343937010872259070"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("12.09044122964690028250983947194193410583757173591995469038844600943694632610"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.94541561682043406565916615601715119979854449991220349537517054946542132239"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.52761066076119130776354014949615007676815462459446946713730714810296595229"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0304455420249075430891047039138326243093334846566920021789140647984175448097"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.149650671652588930076956033416283389031589049770514927584948507803553202910"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0336574490088785668148493615449347354611183173599708036294762098419950316423"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000126497027151469654378765535979290734289731625144899692503470508091193529475"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000897116011370451342055211796348790683035477616931359835457707561956726691767"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000142409422634022110726759123860758274606648079204544228006777846621754692259"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000252515640185869778340276613779458838796409717012259538150426423432799209608"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 12) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.13501118834531862832791685103090778732600754703053509379504805718104885902"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-11.64655725601608471987125140319522273869255472727074641759372417306485077730"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("52.47997731358147104819352051854695978618817398284168789151634324060243697900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-135.45701731410847795494161971266033798422685436748530857469841989392043701600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("219.96124976643716810233421769891415115050379995458616095550270708427626420900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-238.37499127470823560688111086646834383929171370516476493761439859373820683700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("199.79115976545848616437399472512434089517222358850429527846981583702591271100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-186.06580854955499729692153505979598892043417420915640640747325871682106260700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("208.74631601283777221705885370999784696071568535053317514980802005864771752100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-197.53853499262074041123518689566722947819857600237876006152376593189070798400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("144.50075463010970867145970534859505768015783636183955794684498462003441805100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-106.36870296080726935127337203425079184767065663506312262840651389217392205900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("88.73938682065148057511439985326164459436444773853443006110286562673807699280"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-62.10218520435182935953770979789019089452934455495249757573801037083579624320"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("33.37756480360810332092878948658803898197552007679892596614034975425467298740"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-18.90612968481519997245444759492813159382596260487606074048382930111416740570"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("11.73182379476133043347419318594516895878294775638321702310633621242203615490"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.89127651169185001615684659153647879805287303355244863107672447172949919127"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.05628831785634767244430613794778237383118902182955930156963055438457640198"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.278924570772378963005919620761891241290397678645427497366931683979103470313"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0349217046715326267223252535829602432217755405230717045003308341586538338077"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.173039450787921076573568728042430497574717189628459371201122511640416535804"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.125154600705023543935668144417468315166811999855906394348835987111005330572"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0291520111880351888227853532698326680951804379655921639568061622853077591827"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00119588167326521772050685130712167568577493075580492617893532154147491503516"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000166966587098874949698033688140021197028135858548757937517355756848615445303"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000188051207904050407421484278134701770752347161244389100186827497009857301113"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000665676590058883342359366356514472856699743985374049531980671537812596361102"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 13) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.147328387026945181742534360727928536657557400346046037192839862582804936900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.51456549085202376204483791233550876670959441040514033264111698819378554402"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.94414619972386232622555773936309700660158456761079287802696168029991317902"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-18.78704596117275369235580835040616276805576972998620945843399189205354798320"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("33.75320683102715133888929607462218380210425052594719299190672951764918964970"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-43.90968018808903858591509195317885887927809302282775758823494965859626988710"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("45.83007041045357748015949276788143174487066194868689328670377077172900922670"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-43.30834737848262311266594213584179463295479030127624741231273476750096363320"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("40.28587342872956736979372620674121597409935291189432692644089811506211904560"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-38.07079933210995921006056307099293201249460698597519136937589815349848540930"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("36.48645327878740068202506706074164138888906527167902669842548785200456090760"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-32.99863707618939353424238452194841065903680035129007522576517208426242003870"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("26.55970062209079850156043839739581666886976736313064228805575294861660949750"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-20.59842254567111580869690652690847120193788739757843717989385899237339101340"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("16.66182339593160150140392670274598786225164619130356052597867372641808254150"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-12.48056679222918764776819055454069770140079985190646278545971576285539893300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.00729939791465563598426689351883338497952088924077343600523943715192249470"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5.05071646613187505818485190469727424915951382050926867171160457018863109602"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.29966711978217146018111284131326004314469156813581461296273109642531273479"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.82568661448281886663681039165151047023026983547946329025101178092516198927"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.821545996592165413015176926103918379703993671815822408869238370242177789874"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.383704993238053425488527996051173229244898380519514965582775999086944158021"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.175485561770223825536069856812357489141836294882044305667107034046144733761"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0490433781210161672748726863502704850354754206732915757148321796262332557411"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00402547360327382273192760485491174840524317417151707477913869414062168673233"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000591615163102432487394020984370444214618369356333750305162759222030306708281"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000150076799335799622176733790301367198750063662367274615802926812851245445696"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000105864474240497768156598640472330313913710369319591100716113011216570777723"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 14) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0242821885342162555172194807204060720439176164669704179647896832718856332498"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.249856695544308322348171496342170210083410754460476379583874589925971489368"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.12326005797749044778439744178131419781661379271554672577789771011822915870"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.86469109526581467211201873076519837722365386321507572083194802001927335161"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.50079290106999295066844741272526027729937316456024276862452670751556633337"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.48684463117403305020608532973799146401232890979166234034679061467612710549"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.12967055985402796636707893316937491613623416550895649179552121609620465579"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.47724668807865361819228723977775474438205454678621615947243362585570677107"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.91278205889249382066105160662535333323212648243270007533168890574238996600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.81257313199263046793165930650235695480992793053614182870128250653240399226"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.90398649466128702523970742655503101903096138960699394205660617785029524613"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.37699945499915151843967957813503956475301514890644971272041072293843226357"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.28495268091529903567348249127974601649844237295023870994028850106617764318"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.952763471445207071061796159152966939284649904476335068736845300084967366990"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.535788968888742389713782672547333938330308007633675251508339886039944284585"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.358020789818714250877447233131478684920110238088884239583652089996295811608"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.260288177789983828698553363324988305811986215701965042156106479955015465057"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.136189356052305779370763109924086580150032155644746928185072140262278106899"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0628766811464750403125935867053544555088689453179188749663490799516604967151"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0370637548509496888808797750019041755705513054464047218196448291548517149764"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0177893472376662545340696681623277652018062438254456540388233762026125185107"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00567156369248172085563495886241541581202423428371480185063640538001288280474"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00218143409758500086570687953062016667230176987210602107478648809100271457937"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000840077010916613961293716749850474022730704167044599676252293240098595360069"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000884896797884032945739919608263751800212682320278642794159422173907791309331"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000208568442490274769998537189218999959487143160425280136701000686328977000945"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000187401650616022963832478803386742923717598478201557979913608078604137745338"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000262480056546984342244841766991496735739199664461987202512509327833476650923"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+        }
     }
     if constexpr (p == 16) {
         if constexpr (std::is_same_v<Real, float>) {
@@ -1622,16 +2007,16 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0f, 0x1.674708p-13f, 0x1.27cdb4p-5f, 0x1.f3f9a4p-2f, 0x1.8a1b0ep-1f, -0x1.d00082p-2f, 0x1.06c982p-2f, -0x1.4ec10ap-3f, 0x1.b93c32p-4f, -0x1.09f5f4p-4f, 0x1.0b6a76p-5f, -0x1.a17eb8p-7f, 0x1.cda18ep-9f, -0x1.18156ap-11f, -0x1.547c4ep-15f, 0x1.a1d518p-15f, -0x1.fb90c6p-17f, 0x1.085bbcp-19f, 0x1.4a16eap-22f, -0x1.3b0f84p-23f, 0x1.42695p-28f, 0x1.acf5ccp-29f, 0x1.c7dfc2p-37f, -0x1.99a498p-37f, 0x1.0c54f6p-42f, 0x1.60b622p-49f, -0x1.63607p-54f, 0x1.f308a8p-62f, -0x1.dcd83cp-74f, -0x1.f4c81ep-87f, 0x1.f541a8p-112f, -0x0p+0f};
             }
             if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.5e2be4p-10f, 0x1.115596p-3f, 0x1.8e066ep-1f, -0x1.9a3aeap-1f, -0x1.b4e824p-2f, 0x1.24d79cp-1f, -0x1.96ff08p-2f, 0x1.7cff08p-3f, -0x1.3b2f7p-5f, -0x1.8c4396p-6f, 0x1.d82f62p-6f, -0x1.d30848p-7f, 0x1.b8ca7p-9f, 0x1.4ea26ep-13f, -0x1.44550ap-12f, 0x1.116fb6p-15f, 0x1.e6f46ap-16f, -0x1.73244cp-17f, 0x1.105e3p-20f, 0x1.85ee5ap-23f, -0x1.5ac9f2p-25f, 0x1.d789f4p-30f, 0x1.8d5e3ep-35f, -0x1.c8b384p-37f, 0x1.38fe4p-43f, 0x1.f524d2p-49f, -0x1.a73b7ep-57f, -0x1.c53204p-68f, 0x1.a5354ep-81f, -0x1.a59b92p-105f, 0x0p+0f};
+                return {0x0p+0f, 0x1.5e2be4p-10f, 0x1.115596p-3f, 0x1.8e066ep-1f, -0x1.9a3aeap-1f, -0x1.b4e824p-2f, 0x1.24d79cp-1f, -0x1.96ff08p-2f, 0x1.7cff08p-3f, -0x1.3b2f7p-5f, -0x1.8c4396p-6f, 0x1.d82f62p-6f, -0x1.d30848p-7f, 0x1.b8ca7p-9f, 0x1.4ea26ep-13f, -0x1.44550ap-12f, 0x1.116fb6p-15f, 0x1.e6f46ap-16f, -0x1.73244cp-17f, 0x1.105e3p-20f, 0x1.85ee5ap-23f, -0x1.5ac9f2p-25f, 0x1.d789f4p-30f, 0x1.8d5e3ep-35f, -0x1.c8b384p-37f, 0x1.38fe4p-43f, 0x1.f524d2p-49f, -0x1.a73b7ep-57f, -0x1.c53204p-68f, 0x1.a5354ep-81f, -0x1.a59b92p-105f, -0x0p+0f};
             }
             if constexpr (order == 2) {
-                return {0x0p+0f, 0x1.295efep-7f, 0x1.9d61ccp-2f, 0x1.161d42p-2f, -0x1.5b7a46p+1f, 0x1.d1174ep+1f, -0x1.64fd52p+1f, 0x1.05168ep+1f, -0x1.657508p+0f, 0x1.a38bfp-1f, -0x1.889b16p-2f, 0x1.152c76p-3f, -0x1.1b4c9ap-5f, 0x1.907f1ep-8f, -0x1.48b152p-13f, -0x1.a3276ep-11f, 0x1.19008ap-11f, -0x1.4a0f3p-13f, 0x1.b16d86p-17f, 0x1.3c9bcap-19f, 0x1.899254p-24f, -0x1.e003aep-24f, -0x1.b118f8p-27f, 0x1.a8e81cp-30f, 0x1.472048p-36f, 0x1.0bc546p-41f, -0x1.5b7878p-47f, -0x1.75c578p-53f, -0x1.4450ep-64f, 0x1.74639cp-76f, -0x1.74be14p-99f, -0x0p+0f};
+                return {0x0p+0f, 0x1.295efep-7f, 0x1.9d61ccp-2f, 0x1.161d42p-2f, -0x1.5b7a46p+1f, 0x1.d1174ep+1f, -0x1.64fd52p+1f, 0x1.05168ep+1f, -0x1.657508p+0f, 0x1.a38bfp-1f, -0x1.889b16p-2f, 0x1.152c76p-3f, -0x1.1b4c9ap-5f, 0x1.907f1ep-8f, -0x1.48b152p-13f, -0x1.a3276ep-11f, 0x1.19008ap-11f, -0x1.4a0f3p-13f, 0x1.b16d86p-17f, 0x1.3c9bcap-19f, 0x1.899254p-24f, -0x1.e003aep-24f, -0x1.b118f8p-27f, 0x1.a8e81cp-30f, 0x1.472048p-36f, 0x1.0bc546p-41f, -0x1.5b7878p-47f, -0x1.75c578p-53f, -0x1.4450ep-64f, 0x1.74639cp-76f, -0x1.74be14p-99f, 0x0p+0f};
             }
             if constexpr (order == 3) {
-                return {0x0p+0f, 0x1.ade0c6p-5f, 0x1.c28b44p-1f, -0x1.5f4cdp+1f, 0x1.cdb8f6p+0f, 0x1.f77744p+0f, -0x1.dd879cp+1f, 0x1.37053cp+1f, -0x1.1bfa76p-2f, -0x1.2b5034p+0f, 0x1.63e226p+0f, -0x1.a29914p-1f, 0x1.852868p-3f, 0x1.9a9664p-4f, -0x1.c29f78p-4f, 0x1.54d634p-5f, -0x1.41b2a6p-9f, -0x1.225dap-8f, 0x1.f9019ap-10f, -0x1.2c2838p-12f, -0x1.8e8742p-16f, 0x1.c9f58cp-17f, -0x1.61f64ap-20f, -0x1.96b8bp-25f, 0x1.71f48cp-27f, -0x1.b5fc8ep-34f, -0x1.c5963ep-38f, 0x1.6b4e6cp-45f, 0x1.e67136p-58f, -0x1.6aff4p-67f, 0x1.6b579p-89f, -0x0p+0f};
+                return {0x0p+0f, 0x1.ade0c6p-5f, 0x1.c28b44p-1f, -0x1.5f4cdp+1f, 0x1.cdb8f6p+0f, 0x1.f77744p+0f, -0x1.dd879cp+1f, 0x1.37053cp+1f, -0x1.1bfa76p-2f, -0x1.2b5034p+0f, 0x1.63e226p+0f, -0x1.a29914p-1f, 0x1.852868p-3f, 0x1.9a9664p-4f, -0x1.c29f78p-4f, 0x1.54d634p-5f, -0x1.41b2a6p-9f, -0x1.225dap-8f, 0x1.f9019ap-10f, -0x1.2c2838p-12f, -0x1.8e8742p-16f, 0x1.c9f58cp-17f, -0x1.61f64ap-20f, -0x1.96b8bp-25f, 0x1.71f48cp-27f, -0x1.b5fc8ep-34f, -0x1.c5963ep-38f, 0x1.6b4e6cp-45f, 0x1.e67136p-58f, -0x1.6aff4p-67f, 0x1.6b579p-89f, 0x0p+0f};
             }
             if constexpr (order == 4) {
-                return {0x0p+0f, 0x1.002834p-2f, 0x1.74f146p-1f, -0x1.d40722p+2f, 0x1.2af6fp+4f, -0x1.a43136p+4f, 0x1.9a15aep+4f, -0x1.38d1bep+4f, 0x1.6c6cdcp+3f, -0x1.13619ap+2f, 0x1.d56ce2p-1f, -0x1.e42908p-1f, 0x1.e52912p+0f, -0x1.ee224ep+0f, 0x1.1f26d6p+0f, -0x1.588844p-2f, -0x1.9e45fcp-7f, 0x1.dcd2d2p-5f, -0x1.93116cp-6f, 0x1.0e0178p-8f, 0x1.31f3fap-12f, -0x1.f6b0ep-13f, 0x1.f05078p-16f, 0x1.2ec5bap-20f, -0x1.47f2bp-22f, 0x1.bcb022p-29f, 0x1.1bcefep-32f, -0x1.34d97ap-39f, -0x1.6f2c8cp-53f, 0x1.34e43ep-60f, -0x1.352f98p-81f, 0x0p+0f};
+                return {0x0p+0f, 0x1.002834p-2f, 0x1.74f146p-1f, -0x1.d40722p+2f, 0x1.2af6fp+4f, -0x1.a43136p+4f, 0x1.9a15aep+4f, -0x1.38d1bep+4f, 0x1.6c6cdcp+3f, -0x1.13619ap+2f, 0x1.d56ce2p-1f, -0x1.e42908p-1f, 0x1.e52912p+0f, -0x1.ee224ep+0f, 0x1.1f26d6p+0f, -0x1.588844p-2f, -0x1.9e45fcp-7f, 0x1.dcd2d2p-5f, -0x1.93116cp-6f, 0x1.0e0178p-8f, 0x1.31f3fap-12f, -0x1.f6b0ep-13f, 0x1.f05078p-16f, 0x1.2ec5bap-20f, -0x1.47f2bp-22f, 0x1.bcb022p-29f, 0x1.1bcefep-32f, -0x1.34d97ap-39f, -0x1.6f2c8cp-53f, 0x1.34e43ep-60f, -0x1.352f98p-81f, -0x0p+0f};
             }
             if constexpr (order == 5) {
                 return {0x0p+0f, 0x1.e5d8b2p-1f, -0x1.e7e4aep+1f, 0x1.643948p+1f, 0x1.8bf778p+3f, -0x1.39576p+5f, 0x1.f6657cp+5f, -0x1.2981aap+6f, 0x1.0cf3p+6f, -0x1.71528cp+4f, -0x1.136588p+6f, 0x1.5ecf14p+7f, -0x1.ca8fbep+7f, 0x1.83a966p+7f, -0x1.9d9118p+6f, 0x1.818f5cp+4f, 0x1.4e782cp+3f, -0x1.7fba74p+3f, 0x1.361d7ep+2f, -0x1.85fee8p-1f, -0x1.fcc32p-4f, 0x1.30d54cp-4f, -0x1.4236c8p-7f, -0x1.6b6d4cp-12f, 0x1.251cb8p-13f, -0x1.7df628p-19f, -0x1.6d7bap-23f, 0x1.04735p-29f, 0x1.ecabdp-41f, -0x1.035efp-49f, 0x1.039e9p-69f, 0x0p+0f};
@@ -1640,13 +2025,13 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0f, 0x1.5c435cp+1f, -0x1.45ad88p+4f, 0x1.1ac644p+6f, -0x1.3bcd24p+7f, 0x1.1132bep+8f, -0x1.a33216p+8f, 0x1.2bec4cp+9f, -0x1.83ddd4p+9f, 0x1.b1ad42p+9f, -0x1.9d7a32p+9f, 0x1.5526f8p+9f, -0x1.e99686p+8f, 0x1.186a9ap+8f, -0x1.4f805p+6f, -0x1.84955p+5f, 0x1.59efa2p+6f, -0x1.dac7aep+5f, 0x1.620788p+4f, -0x1.88bb02p+1f, -0x1.04b916p+0f, 0x1.18c698p-1f, -0x1.508ddcp-4f, -0x1.539386p-9f, 0x1.9eab9ap-10f, -0x1.980b92p-15f, -0x1.761c2ap-19f, 0x1.64e7e2p-25f, 0x1.1823b8p-35f, -0x1.623924p-44f, 0x1.6290fap-63f, 0x0p+0f};
             }
             if constexpr (order == 7) {
-                return {0x0p+0f, 0x1.891444p+2f, -0x1.c4b29p+5f, 0x1.d994c4p+7f, -0x1.26defep+9f, 0x1.ddf578p+9f, -0x1.fd207ap+9f, 0x1.36152ap+9f, 0x1.d8616ap+6f, -0x1.190b42p+10f, 0x1.36219cp+11f, -0x1.eed74p+11f, 0x1.31c14ap+12f, -0x1.31807ap+12f, 0x1.07e38p+12f, -0x1.9ca0ep+11f, 0x1.192392p+11f, -0x1.28f7fp+10f, 0x1.8ef118p+8f, -0x1.076216p+5f, -0x1.3734aap+5f, 0x1.2e313ep+4f, -0x1.913ecep+1f, -0x1.aba4ep-4f, 0x1.5578cap-4f, -0x1.f3ff48p-9f, -0x1.bd3a12p-13f, 0x1.29ffeap-18f, 0x1.5e7712p-28f, -0x1.267e4p-36f, 0x1.26c8dap-54f, -0x0p+0f};
+                return {0x0p+0f, 0x1.891444p+2f, -0x1.c4b29p+5f, 0x1.d994c4p+7f, -0x1.26defep+9f, 0x1.ddf578p+9f, -0x1.fd207ap+9f, 0x1.36152ap+9f, 0x1.d8616ap+6f, -0x1.190b42p+10f, 0x1.36219cp+11f, -0x1.eed74p+11f, 0x1.31c14ap+12f, -0x1.31807ap+12f, 0x1.07e38p+12f, -0x1.9ca0ep+11f, 0x1.192392p+11f, -0x1.28f7fp+10f, 0x1.8ef118p+8f, -0x1.076216p+5f, -0x1.3734aap+5f, 0x1.2e313ep+4f, -0x1.913ecep+1f, -0x1.aba4ep-4f, 0x1.5578cap-4f, -0x1.f3ff48p-9f, -0x1.bd3a12p-13f, 0x1.29ffeap-18f, 0x1.5e7712p-28f, -0x1.267e4p-36f, 0x1.26c8dap-54f, 0x0p+0f};
             }
             if constexpr (order == 8) {
-                return {0x0p+0f, 0x1.1c0608p+3f, -0x1.65d998p+6f, 0x1.9d8978p+8f, -0x1.24c8d8p+10f, 0x1.21d47ap+11f, -0x1.bbc006p+11f, 0x1.2211c4p+12f, -0x1.5c65p+12f, 0x1.845a36p+12f, -0x1.87e6ep+12f, 0x1.650412p+12f, -0x1.2b9aap+12f, 0x1.cebcfcp+11f, -0x1.3e375cp+11f, 0x1.7d70c6p+10f, -0x1.8fd688p+9f, 0x1.57b6f4p+8f, -0x1.3e2cp+6f, -0x1.f1e0f6p+4f, 0x1.39f676p+5f, -0x1.07f7dep+4f, 0x1.6eaf02p+1f, 0x1.f8896cp-4f, -0x1.b78e4ap-4f, 0x1.faf294p-8f, 0x1.a6b604p-12f, -0x1.9886bep-17f, -0x1.7c0bdep-26f, 0x1.90aca4p-34f, -0x1.91166ep-51f, 0x0p+0f};
+                return {0x0p+0f, 0x1.1c0608p+3f, -0x1.65d998p+6f, 0x1.9d8978p+8f, -0x1.24c8d8p+10f, 0x1.21d47ap+11f, -0x1.bbc006p+11f, 0x1.2211c4p+12f, -0x1.5c65p+12f, 0x1.845a36p+12f, -0x1.87e6ep+12f, 0x1.650412p+12f, -0x1.2b9aap+12f, 0x1.cebcfcp+11f, -0x1.3e375cp+11f, 0x1.7d70c6p+10f, -0x1.8fd688p+9f, 0x1.57b6f4p+8f, -0x1.3e2cp+6f, -0x1.f1e0f6p+4f, 0x1.39f676p+5f, -0x1.07f7dep+4f, 0x1.6eaf02p+1f, 0x1.f8896cp-4f, -0x1.b78e4ap-4f, 0x1.faf294p-8f, 0x1.a6b604p-12f, -0x1.9886bep-17f, -0x1.7c0bdep-26f, 0x1.90aca4p-34f, -0x1.91166ep-51f, -0x0p+0f};
             }
             if constexpr (order == 9) {
-                return {0x0p+0f, 0x1.58e7ep+3f, -0x1.c53a2ap+6f, 0x1.0cc18ep+9f, -0x1.7c92fcp+10f, 0x1.6a1946p+11f, -0x1.fab772p+11f, 0x1.254298p+12f, -0x1.407f9ep+12f, 0x1.53233cp+12f, -0x1.3b528cp+12f, 0x1.e2ea28p+11f, -0x1.3d616ap+11f, 0x1.75fce6p+10f, -0x1.2b5b5p+9f, -0x1.18e052p+7f, 0x1.ed1ee2p+8f, -0x1.f5a5a8p+8f, 0x1.920c94p+8f, -0x1.22c138p+8f, 0x1.4b1ba2p+7f, -0x1.ec877p+5f, 0x1.641262p+3f, 0x1.3bac8p-1f, -0x1.3ae0dcp-1f, 0x1.0ba446p-4f, 0x1.c3804ap-9f, -0x1.3c78fcp-13f, -0x1.6e90a4p-22f, 0x1.34c398p-29f, -0x1.351bbcp-45f, 0x0p+0f};
+                return {0x0p+0f, 0x1.58e7ep+3f, -0x1.c53a2ap+6f, 0x1.0cc18ep+9f, -0x1.7c92fcp+10f, 0x1.6a1946p+11f, -0x1.fab772p+11f, 0x1.254298p+12f, -0x1.407f9ep+12f, 0x1.53233cp+12f, -0x1.3b528cp+12f, 0x1.e2ea28p+11f, -0x1.3d616ap+11f, 0x1.75fce6p+10f, -0x1.2b5b5p+9f, -0x1.18e052p+7f, 0x1.ed1ee2p+8f, -0x1.f5a5a8p+8f, 0x1.920c94p+8f, -0x1.22c138p+8f, 0x1.4b1ba2p+7f, -0x1.ec877p+5f, 0x1.641262p+3f, 0x1.3bac8p-1f, -0x1.3ae0dcp-1f, 0x1.0ba446p-4f, 0x1.c3804ap-9f, -0x1.3c78fcp-13f, -0x1.6e90a4p-22f, 0x1.34c398p-29f, -0x1.351bbcp-45f, -0x0p+0f};
             }
             if constexpr (order == 10) {
                 return {0x0p+0f, 0x1.0cfd94p+3f, -0x1.68c00ep+6f, 0x1.b4a63ap+8f, -0x1.3c4fdp+10f, 0x1.35efeap+11f, -0x1.c3872cp+11f, 0x1.1261acp+12f, -0x1.39e1fap+12f, 0x1.5e4c9ep+12f, -0x1.6b72e4p+12f, 0x1.578fd4p+12f, -0x1.30faf4p+12f, 0x1.0174aep+12f, -0x1.942bc4p+11f, 0x1.25cbc8p+11f, -0x1.914caap+10f, 0x1.f93f04p+9f, -0x1.1b4f5ep+9f, 0x1.1df01cp+8f, -0x1.048db6p+7f, 0x1.730bccp+5f, -0x1.09b56cp+3f, -0x1.4fb834p+0f, 0x1.e38e1p-1f, -0x1.ee07e6p-4f, -0x1.913ceep-8f, 0x1.0726b8p-11f, 0x1.2751c6p-20f, -0x1.00ceb8p-26f, 0x1.012308p-41f, 0x0p+0f};
@@ -1661,7 +2046,7 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0f, 0x1.a308fp-1f, -0x1.1df37cp+3f, 0x1.5a47ccp+5f, -0x1.e7cc32p+6f, 0x1.ba5aa6p+7f, -0x1.137ebep+8f, 0x1.07f96cp+8f, -0x1.f176d6p+7f, 0x1.0c09ap+8f, -0x1.12bf1p+8f, 0x1.de16d6p+7f, -0x1.8c7b4ap+7f, 0x1.565926p+7f, -0x1.13d91ap+7f, 0x1.8b69dep+6f, -0x1.15b78cp+6f, 0x1.8188b8p+5f, -0x1.e03c02p+4f, 0x1.12ed8cp+4f, -0x1.36a5bp+3f, 0x1.3d2642p+2f, -0x1.11ef14p+1f, 0x1.c294dap-1f, -0x1.4f57e8p-2f, 0x1.1ebd9ap-4f, 0x1.367918p-14f, -0x1.fdd378p-10f, -0x1.0fc074p-22f, 0x1.f945fcp-22f, -0x1.fb1bdp-34f, 0x0p+0f};
             }
             if constexpr (order == 14) {
-                return {0x0p+0f, 0x1.74ef14p-3f, -0x1.fd9d32p+0f, 0x1.3320f2p+3f, -0x1.a9e31ep+4f, 0x1.73dbdep+5f, -0x1.aa50f2p+5f, 0x1.5e48acp+5f, -0x1.20d7a8p+5f, 0x1.4350bap+5f, -0x1.549ap+5f, 0x1.0d8c72p+5f, -0x1.8fe88ap+4f, 0x1.63da6cp+4f, -0x1.24224p+4f, 0x1.7851e2p+3f, -0x1.e4fd18p+2f, 0x1.610a44p+2f, -0x1.ae4c3ep+1f, 0x1.a6fe28p+0f, -0x1.ccc92p-1f, 0x1.f93894p-2f, -0x1.8612dep-3f, 0x1.fd43fcp-5f, -0x1.aafa1ep-6f, 0x1.b63874p-8f, 0x1.071682p-11f, -0x1.a84c4p-12f, 0x1.a20c24p-18f, 0x1.e7f1cp-23f, -0x1.eb089ap-34f, 0x0p+0f};
+                return {0x0p+0f, 0x1.74ef14p-3f, -0x1.fd9d32p+0f, 0x1.3320f2p+3f, -0x1.a9e31ep+4f, 0x1.73dbdep+5f, -0x1.aa50f2p+5f, 0x1.5e48acp+5f, -0x1.20d7a8p+5f, 0x1.4350bap+5f, -0x1.549ap+5f, 0x1.0d8c72p+5f, -0x1.8fe88ap+4f, 0x1.63da6cp+4f, -0x1.24224p+4f, 0x1.7851e2p+3f, -0x1.e4fd18p+2f, 0x1.610a44p+2f, -0x1.ae4c3ep+1f, 0x1.a6fe28p+0f, -0x1.ccc92p-1f, 0x1.f93894p-2f, -0x1.8612dep-3f, 0x1.fd43fcp-5f, -0x1.aafa1ep-6f, 0x1.b63874p-8f, 0x1.071682p-11f, -0x1.a84c4p-12f, 0x1.a20c24p-18f, 0x1.e7f1cp-23f, -0x1.eb089ap-34f, -0x0p+0f};
             }
             if constexpr (order == 15) {
                 return {0x0p+0f, 0x1.31c72ap-6f, -0x1.a21aa8p-3f, 0x1.f656a4p-1f, -0x1.589b5p+1f, 0x1.250496p+2f, -0x1.3b0f08p+2f, 0x1.bed88p+1f, -0x1.37fe76p+1f, 0x1.75c34ap+1f, -0x1.9f32b2p+1f, 0x1.2a50b6p+1f, -0x1.80aff2p+0f, 0x1.71f9bp+0f, -0x1.40d216p+0f, 0x1.6edc3cp-1f, -0x1.abb5dp-2f, 0x1.5fdcbap-2f, -0x1.af4e9cp-3f, 0x1.57b33ep-4f, -0x1.736294p-5f, 0x1.e1a61ep-6f, -0x1.381382p-7f, 0x1.a99b88p-10f, -0x1.191adap-10f, 0x1.44a23ap-12f, 0x1.4db128p-13f, -0x1.2cad38p-14f, 0x1.f38c66p-19f, 0x1.c87078p-24f, -0x1.cdd01ap-34f, -0x0p+0f};
@@ -1672,16 +2057,16 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0, 0x1.674708c20fd28p-13, 0x1.27cdb30a789aap-5, 0x1.f3f9a4213a58ep-2, 0x1.8a1b0e63e768fp-1, -0x1.d0008134e7b25p-2, 0x1.06c9817f611eap-2, -0x1.4ec109006f3abp-3, 0x1.b93c322324f49p-4, -0x1.09f5f4083e297p-4, 0x1.0b6a75dfa25cdp-5, -0x1.a17eb803ff746p-7, 0x1.cda18d3f662aap-9, -0x1.1815693b1e50ap-11, -0x1.547c4d557ee7fp-15, 0x1.a1d518779619bp-15, -0x1.fb90c559a340ap-17, 0x1.085bbb58c3dc6p-19, 0x1.4a16ea18a78a9p-22, -0x1.3b0f83cef7c9dp-23, 0x1.426950d9b6bcap-28, 0x1.acf5cc83787c7p-29, 0x1.c7dfc1cbcd56p-37, -0x1.99a4987142751p-37, 0x1.0c54f6dbbd52bp-42, 0x1.60b6215484a1dp-49, -0x1.6360709f9f94cp-54, 0x1.f308a7934d099p-62, -0x1.dcd83ccd7b40ep-74, -0x1.f4c81d09055a8p-87, 0x1.f541a7bafa402p-112, -0x0p+0};
             }
             if constexpr (order == 1) {
-                return {0x0p+0, 0x1.5e2be3ffc02e6p-10, 0x1.115596e3350edp-3, 0x1.8e066ec21fc6ap-1, -0x1.9a3ae9a2a692bp-1, -0x1.b4e823397cf88p-2, 0x1.24d79baf908bcp-1, -0x1.96ff08990aa2p-2, 0x1.7cff079859d45p-3, -0x1.3b2f6fbc125fp-5, -0x1.8c439625af32p-6, 0x1.d82f61038e0ep-6, -0x1.d308486caa608p-7, 0x1.b8ca6f1e525d9p-9, 0x1.4ea26d28d3087p-13, -0x1.4455094b3efadp-12, 0x1.116fb5095b29ap-15, 0x1.e6f46905743cfp-16, -0x1.73244b5651139p-17, 0x1.105e30d7ecb46p-20, 0x1.85ee598e5c773p-23, -0x1.5ac9f1c76ae72p-25, 0x1.d789f3d703addp-30, 0x1.8d5e3e20027e8p-35, -0x1.c8b3833c3b769p-37, 0x1.38fe40b99904fp-43, 0x1.f524d19d8420ap-49, -0x1.a73b7d5e557e7p-57, -0x1.c5320460bba02p-68, 0x1.a5354de9b5e4cp-81, -0x1.a59b918cf087fp-105, 0x0p+0};
+                return {0x0p+0, 0x1.5e2be3ffc02e6p-10, 0x1.115596e3350edp-3, 0x1.8e066ec21fc6ap-1, -0x1.9a3ae9a2a692bp-1, -0x1.b4e823397cf88p-2, 0x1.24d79baf908bcp-1, -0x1.96ff08990aa2p-2, 0x1.7cff079859d45p-3, -0x1.3b2f6fbc125fp-5, -0x1.8c439625af32p-6, 0x1.d82f61038e0ep-6, -0x1.d308486caa608p-7, 0x1.b8ca6f1e525d9p-9, 0x1.4ea26d28d3087p-13, -0x1.4455094b3efadp-12, 0x1.116fb5095b29ap-15, 0x1.e6f46905743cfp-16, -0x1.73244b5651139p-17, 0x1.105e30d7ecb46p-20, 0x1.85ee598e5c773p-23, -0x1.5ac9f1c76ae72p-25, 0x1.d789f3d703addp-30, 0x1.8d5e3e20027e8p-35, -0x1.c8b3833c3b769p-37, 0x1.38fe40b99904fp-43, 0x1.f524d19d8420ap-49, -0x1.a73b7d5e557e7p-57, -0x1.c5320460bba02p-68, 0x1.a5354de9b5e4cp-81, -0x1.a59b918cf087fp-105, -0x0p+0};
             }
             if constexpr (order == 2) {
-                return {0x0p+0, 0x1.295efeac152d8p-7, 0x1.9d61cc47e5de2p-2, 0x1.161d416b67638p-2, -0x1.5b7a45663376bp+1, 0x1.d1174d09edd0ep+1, -0x1.64fd520a6621ap+1, 0x1.05168da964846p+1, -0x1.6575089c4586dp+0, 0x1.a38bf0b53f437p-1, -0x1.889b16ed752f1p-2, 0x1.152c76b8c5aa6p-3, -0x1.1b4c99876d202p-5, 0x1.907f1e8b42629p-8, -0x1.48b152205d27fp-13, -0x1.a3276d4b1b41fp-11, 0x1.19008ab2bad0ep-11, -0x1.4a0f2fc3a3fe6p-13, 0x1.b16d8531bcd97p-17, 0x1.3c9bc919e0e4ap-19, 0x1.899254d741919p-24, -0x1.e003adff466a7p-24, -0x1.b118f867cd64ep-27, 0x1.a8e81cf9b2bf5p-30, 0x1.472047d4ce812p-36, 0x1.0bc546f1206bp-41, -0x1.5b78778ec812cp-47, -0x1.75c5773026aecp-53, -0x1.4450e0ff79234p-64, 0x1.74639b34e972ap-76, -0x1.74be14820bd54p-99, -0x0p+0};
+                return {0x0p+0, 0x1.295efeac152d8p-7, 0x1.9d61cc47e5de2p-2, 0x1.161d416b67638p-2, -0x1.5b7a45663376bp+1, 0x1.d1174d09edd0ep+1, -0x1.64fd520a6621ap+1, 0x1.05168da964846p+1, -0x1.6575089c4586dp+0, 0x1.a38bf0b53f437p-1, -0x1.889b16ed752f1p-2, 0x1.152c76b8c5aa6p-3, -0x1.1b4c99876d202p-5, 0x1.907f1e8b42629p-8, -0x1.48b152205d27fp-13, -0x1.a3276d4b1b41fp-11, 0x1.19008ab2bad0ep-11, -0x1.4a0f2fc3a3fe6p-13, 0x1.b16d8531bcd97p-17, 0x1.3c9bc919e0e4ap-19, 0x1.899254d741919p-24, -0x1.e003adff466a7p-24, -0x1.b118f867cd64ep-27, 0x1.a8e81cf9b2bf5p-30, 0x1.472047d4ce812p-36, 0x1.0bc546f1206bp-41, -0x1.5b78778ec812cp-47, -0x1.75c5773026aecp-53, -0x1.4450e0ff79234p-64, 0x1.74639b34e972ap-76, -0x1.74be14820bd54p-99, 0x0p+0};
             }
             if constexpr (order == 3) {
-                return {0x0p+0, 0x1.ade0c67a6df63p-5, 0x1.c28b430a75f2ap-1, -0x1.5f4ccfba427cfp+1, 0x1.cdb8f607de72ep+0, 0x1.f77743196657ap+0, -0x1.dd879ba809268p+1, 0x1.37053c10bce29p+1, -0x1.1bfa76c0a943ap-2, -0x1.2b5034c5e7cecp+0, 0x1.63e2260baa9fep+0, -0x1.a29913a0c0f2ep-1, 0x1.852867c8ceb36p-3, 0x1.9a9664fc9e679p-4, -0x1.c29f78e2de8f5p-4, 0x1.54d634445fcf7p-5, -0x1.41b2a5a54a663p-9, -0x1.225d9fec5c6e9p-8, 0x1.f9019974a7ddbp-10, -0x1.2c283714217e7p-12, -0x1.8e8742bbbfb21p-16, 0x1.c9f58c62dd5d4p-17, -0x1.61f6495ed1b8fp-20, -0x1.96b8b0f8a15e3p-25, 0x1.71f48c99d030bp-27, -0x1.b5fc8d66ab6dp-34, -0x1.c5963ee2273d3p-38, 0x1.6b4e6ce52480bp-45, 0x1.e67135f42b49bp-58, -0x1.6aff40a6dd5b4p-67, 0x1.6b5790e714dd8p-89, -0x0p+0};
+                return {0x0p+0, 0x1.ade0c67a6df63p-5, 0x1.c28b430a75f2ap-1, -0x1.5f4ccfba427cfp+1, 0x1.cdb8f607de72ep+0, 0x1.f77743196657ap+0, -0x1.dd879ba809268p+1, 0x1.37053c10bce29p+1, -0x1.1bfa76c0a943ap-2, -0x1.2b5034c5e7cecp+0, 0x1.63e2260baa9fep+0, -0x1.a29913a0c0f2ep-1, 0x1.852867c8ceb36p-3, 0x1.9a9664fc9e679p-4, -0x1.c29f78e2de8f5p-4, 0x1.54d634445fcf7p-5, -0x1.41b2a5a54a663p-9, -0x1.225d9fec5c6e9p-8, 0x1.f9019974a7ddbp-10, -0x1.2c283714217e7p-12, -0x1.8e8742bbbfb21p-16, 0x1.c9f58c62dd5d4p-17, -0x1.61f6495ed1b8fp-20, -0x1.96b8b0f8a15e3p-25, 0x1.71f48c99d030bp-27, -0x1.b5fc8d66ab6dp-34, -0x1.c5963ee2273d3p-38, 0x1.6b4e6ce52480bp-45, 0x1.e67135f42b49bp-58, -0x1.6aff40a6dd5b4p-67, 0x1.6b5790e714dd8p-89, 0x0p+0};
             }
             if constexpr (order == 4) {
-                return {0x0p+0, 0x1.002833198203cp-2, 0x1.74f145f5180b5p-1, -0x1.d40722c67b8b3p+2, 0x1.2af6f0f464bc5p+4, -0x1.a43135145799ap+4, 0x1.9a15ae041271p+4, -0x1.38d1bd49e9af3p+4, 0x1.6c6cdb14d7fe1p+3, -0x1.13619aaa119f9p+2, 0x1.d56ce1ec874a1p-1, -0x1.e42907ae7a264p-1, 0x1.e52911f9f6566p+0, -0x1.ee224ef8eb13dp+0, 0x1.1f26d6223d44dp+0, -0x1.5888435f57836p-2, -0x1.9e45fc4e6f7c9p-7, 0x1.dcd2d2ebfb6e4p-5, -0x1.93116bc1ac6b7p-6, 0x1.0e01783e342a4p-8, 0x1.31f3faa90de9fp-12, -0x1.f6b0df77a544p-13, 0x1.f05077a02c3acp-16, 0x1.2ec5b9d224e6cp-20, -0x1.47f2b0eb68edbp-22, 0x1.bcb021bf883a2p-29, 0x1.1bcefd6cfba52p-32, -0x1.34d97adc52a39p-39, -0x1.6f2c8c9ca395p-53, 0x1.34e43d9253e6fp-60, -0x1.352f98f0f2e49p-81, 0x0p+0};
+                return {0x0p+0, 0x1.002833198203cp-2, 0x1.74f145f5180b5p-1, -0x1.d40722c67b8b3p+2, 0x1.2af6f0f464bc5p+4, -0x1.a43135145799ap+4, 0x1.9a15ae041271p+4, -0x1.38d1bd49e9af3p+4, 0x1.6c6cdb14d7fe1p+3, -0x1.13619aaa119f9p+2, 0x1.d56ce1ec874a1p-1, -0x1.e42907ae7a264p-1, 0x1.e52911f9f6566p+0, -0x1.ee224ef8eb13dp+0, 0x1.1f26d6223d44dp+0, -0x1.5888435f57836p-2, -0x1.9e45fc4e6f7c9p-7, 0x1.dcd2d2ebfb6e4p-5, -0x1.93116bc1ac6b7p-6, 0x1.0e01783e342a4p-8, 0x1.31f3faa90de9fp-12, -0x1.f6b0df77a544p-13, 0x1.f05077a02c3acp-16, 0x1.2ec5b9d224e6cp-20, -0x1.47f2b0eb68edbp-22, 0x1.bcb021bf883a2p-29, 0x1.1bcefd6cfba52p-32, -0x1.34d97adc52a39p-39, -0x1.6f2c8c9ca395p-53, 0x1.34e43d9253e6fp-60, -0x1.352f98f0f2e49p-81, -0x0p+0};
             }
             if constexpr (order == 5) {
                 return {0x0p+0, 0x1.e5d8b15d3664dp-1, -0x1.e7e4ae8313c98p+1, 0x1.643947f56174fp+1, 0x1.8bf77730624fbp+3, -0x1.39575fcf961c1p+5, 0x1.f6657cd6c7e2ap+5, -0x1.2981aaa66ca37p+6, 0x1.0cf300079688ep+6, -0x1.71528cd9cab13p+4, -0x1.13658826409b4p+6, 0x1.5ecf135e336b8p+7, -0x1.ca8fbd8754dc2p+7, 0x1.83a96558c6c07p+7, -0x1.9d91182e0786ap+6, 0x1.818f5ca05f024p+4, 0x1.4e782cc994095p+3, -0x1.7fba734a37797p+3, 0x1.361d7d826bb5bp+2, -0x1.85fee8307d591p-1, -0x1.fcc3205624ce5p-4, 0x1.30d54b861144bp-4, -0x1.4236c7ccc62dfp-7, -0x1.6b6d4bcc089efp-12, 0x1.251cb75a77a65p-13, -0x1.7df627db3ed38p-19, -0x1.6d7ba0319a18p-23, 0x1.047350b843565p-29, 0x1.ecabd0f857c51p-41, -0x1.035ef08b1273dp-49, 0x1.039e900e7fa13p-69, 0x0p+0};
@@ -1690,13 +2075,13 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0, 0x1.5c435b4994699p+1, -0x1.45ad88073e625p+4, 0x1.1ac643e9c99f9p+6, -0x1.3bcd24e1c22f1p+7, 0x1.1132bead650e6p+8, -0x1.a3321607e3596p+8, 0x1.2bec4ce73b525p+9, -0x1.83ddd4224b9acp+9, 0x1.b1ad4241d86bfp+9, -0x1.9d7a3218170b3p+9, 0x1.5526f87e8214fp+9, -0x1.e996857ebd3fep+8, 0x1.186a9a24f3388p+8, -0x1.4f804f76b6d5cp+6, -0x1.84954fc1821p+5, 0x1.59efa11d2ec7p+6, -0x1.dac7ad3b33c96p+5, 0x1.62078796373e7p+4, -0x1.88bb023e9f2fap+1, -0x1.04b9160269b8ap+0, 0x1.18c6982acbd2dp-1, -0x1.508ddc9d3ccb4p-4, -0x1.539386e1415cfp-9, 0x1.9eab992a4b9abp-10, -0x1.980b92ff814ccp-15, -0x1.761c29381edd3p-19, 0x1.64e7e2ec4af2dp-25, 0x1.1823b743e4c41p-35, -0x1.623923d3ddbafp-44, 0x1.6290fa803758ep-63, 0x0p+0};
             }
             if constexpr (order == 7) {
-                return {0x0p+0, 0x1.891443770e9f6p+2, -0x1.c4b28f7dbecf4p+5, 0x1.d994c46f08418p+7, -0x1.26defe09eb9e3p+9, 0x1.ddf577c4250f8p+9, -0x1.fd2079b0f3ddbp+9, 0x1.36152a2e286dp+9, 0x1.d8616a51db369p+6, -0x1.190b42892374cp+10, 0x1.36219b3961795p+11, -0x1.eed74001662f8p+11, 0x1.31c149450a5eap+12, -0x1.31807a4d8f7d9p+12, 0x1.07e37f0875c29p+12, -0x1.9ca0e06fa4e41p+11, 0x1.192392a49659fp+11, -0x1.28f7ef65a911cp+10, 0x1.8ef1182eeb70cp+8, -0x1.076216da5c43bp+5, -0x1.3734a9c9c5015p+5, 0x1.2e313dce4fbf1p+4, -0x1.913ecda1e3437p+1, -0x1.aba4e0591b35fp-4, 0x1.5578ca229685fp-4, -0x1.f3ff47839e58dp-9, -0x1.bd3a12076a4f5p-13, 0x1.29ffe91412a2ap-18, 0x1.5e7711914b059p-28, -0x1.267e3f1ece052p-36, 0x1.26c8d9be624c4p-54, -0x0p+0};
+                return {0x0p+0, 0x1.891443770e9f6p+2, -0x1.c4b28f7dbecf4p+5, 0x1.d994c46f08418p+7, -0x1.26defe09eb9e3p+9, 0x1.ddf577c4250f8p+9, -0x1.fd2079b0f3ddbp+9, 0x1.36152a2e286dp+9, 0x1.d8616a51db369p+6, -0x1.190b42892374cp+10, 0x1.36219b3961795p+11, -0x1.eed74001662f8p+11, 0x1.31c149450a5eap+12, -0x1.31807a4d8f7d9p+12, 0x1.07e37f0875c29p+12, -0x1.9ca0e06fa4e41p+11, 0x1.192392a49659fp+11, -0x1.28f7ef65a911cp+10, 0x1.8ef1182eeb70cp+8, -0x1.076216da5c43bp+5, -0x1.3734a9c9c5015p+5, 0x1.2e313dce4fbf1p+4, -0x1.913ecda1e3437p+1, -0x1.aba4e0591b35fp-4, 0x1.5578ca229685fp-4, -0x1.f3ff47839e58dp-9, -0x1.bd3a12076a4f5p-13, 0x1.29ffe91412a2ap-18, 0x1.5e7711914b059p-28, -0x1.267e3f1ece052p-36, 0x1.26c8d9be624c4p-54, 0x0p+0};
             }
             if constexpr (order == 8) {
-                return {0x0p+0, 0x1.1c06072fbf26fp+3, -0x1.65d998749f19fp+6, 0x1.9d8978b96f57fp+8, -0x1.24c8d76a7f36dp+10, 0x1.21d479bc00698p+11, -0x1.bbc006c939353p+11, 0x1.2211c4425df9cp+12, -0x1.5c64ff1d8bf67p+12, 0x1.845a35a315834p+12, -0x1.87e6df0fbf8efp+12, 0x1.6504110de640cp+12, -0x1.2b9aa02be2b35p+12, 0x1.cebcfb329a57fp+11, -0x1.3e375c669dacp+11, 0x1.7d70c67fe8974p+10, -0x1.8fd6874952e8bp+9, 0x1.57b6f4096f1cfp+8, -0x1.3e2c004c73161p+6, -0x1.f1e0f66437532p+4, 0x1.39f676c722756p+5, -0x1.07f7de36ead71p+4, 0x1.6eaf02b444bc5p+1, 0x1.f8896c7b27aebp-4, -0x1.b78e4a3636f78p-4, 0x1.faf293c65fc89p-8, 0x1.a6b604defe6a9p-12, -0x1.9886be2865e4cp-17, -0x1.7c0bde2d4dd5p-26, 0x1.90aca39ea2e8bp-34, -0x1.91166efa6d0a9p-51, 0x0p+0};
+                return {0x0p+0, 0x1.1c06072fbf26fp+3, -0x1.65d998749f19fp+6, 0x1.9d8978b96f57fp+8, -0x1.24c8d76a7f36dp+10, 0x1.21d479bc00698p+11, -0x1.bbc006c939353p+11, 0x1.2211c4425df9cp+12, -0x1.5c64ff1d8bf67p+12, 0x1.845a35a315834p+12, -0x1.87e6df0fbf8efp+12, 0x1.6504110de640cp+12, -0x1.2b9aa02be2b35p+12, 0x1.cebcfb329a57fp+11, -0x1.3e375c669dacp+11, 0x1.7d70c67fe8974p+10, -0x1.8fd6874952e8bp+9, 0x1.57b6f4096f1cfp+8, -0x1.3e2c004c73161p+6, -0x1.f1e0f66437532p+4, 0x1.39f676c722756p+5, -0x1.07f7de36ead71p+4, 0x1.6eaf02b444bc5p+1, 0x1.f8896c7b27aebp-4, -0x1.b78e4a3636f78p-4, 0x1.faf293c65fc89p-8, 0x1.a6b604defe6a9p-12, -0x1.9886be2865e4cp-17, -0x1.7c0bde2d4dd5p-26, 0x1.90aca39ea2e8bp-34, -0x1.91166efa6d0a9p-51, -0x0p+0};
             }
             if constexpr (order == 9) {
-                return {0x0p+0, 0x1.58e7df673241ap+3, -0x1.c53a29616fa38p+6, 0x1.0cc18d57a1a2p+9, -0x1.7c92fc1b6ca39p+10, 0x1.6a1945d20b68ep+11, -0x1.fab771c0e1bafp+11, 0x1.254298acbb2d4p+12, -0x1.407f9dc95f9b1p+12, 0x1.53233c63dd8a8p+12, -0x1.3b528b3453998p+12, 0x1.e2ea2797d25e5p+11, -0x1.3d6169dd11c9cp+11, 0x1.75fce5d641404p+10, -0x1.2b5b50127f9f5p+9, -0x1.18e0518b142ecp+7, 0x1.ed1ee257a974bp+8, -0x1.f5a5a8d8a9b3cp+8, 0x1.920c943e9e1a2p+8, -0x1.22c1385412c46p+8, 0x1.4b1ba13f6628bp+7, -0x1.ec876f34dee07p+5, 0x1.641261f15a2bcp+3, 0x1.3bac7fcb6882p-1, -0x1.3ae0db5ff49e1p-1, 0x1.0ba445bef297cp-4, 0x1.c3804abda5b0fp-9, -0x1.3c78fba89f7e5p-13, -0x1.6e90a45b17e12p-22, 0x1.34c398a5dd485p-29, -0x1.351bbccd566d6p-45, 0x0p+0};
+                return {0x0p+0, 0x1.58e7df673241ap+3, -0x1.c53a29616fa38p+6, 0x1.0cc18d57a1a2p+9, -0x1.7c92fc1b6ca39p+10, 0x1.6a1945d20b68ep+11, -0x1.fab771c0e1bafp+11, 0x1.254298acbb2d4p+12, -0x1.407f9dc95f9b1p+12, 0x1.53233c63dd8a8p+12, -0x1.3b528b3453998p+12, 0x1.e2ea2797d25e5p+11, -0x1.3d6169dd11c9cp+11, 0x1.75fce5d641404p+10, -0x1.2b5b50127f9f5p+9, -0x1.18e0518b142ecp+7, 0x1.ed1ee257a974bp+8, -0x1.f5a5a8d8a9b3cp+8, 0x1.920c943e9e1a2p+8, -0x1.22c1385412c46p+8, 0x1.4b1ba13f6628bp+7, -0x1.ec876f34dee07p+5, 0x1.641261f15a2bcp+3, 0x1.3bac7fcb6882p-1, -0x1.3ae0db5ff49e1p-1, 0x1.0ba445bef297cp-4, 0x1.c3804abda5b0fp-9, -0x1.3c78fba89f7e5p-13, -0x1.6e90a45b17e12p-22, 0x1.34c398a5dd485p-29, -0x1.351bbccd566d6p-45, -0x0p+0};
             }
             if constexpr (order == 10) {
                 return {0x0p+0, 0x1.0cfd9304e9d0fp+3, -0x1.68c00ea69764dp+6, 0x1.b4a63a85c6a12p+8, -0x1.3c4fcf304828fp+10, 0x1.35efe9ab816f7p+11, -0x1.c3872b5b6dcd2p+11, 0x1.1261ac83f506cp+12, -0x1.39e1fa3f00834p+12, 0x1.5e4c9d364466fp+12, -0x1.6b72e41a84906p+12, 0x1.578fd4c404249p+12, -0x1.30faf3648505dp+12, 0x1.0174ad7c89821p+12, -0x1.942bc49f2f52ap+11, 0x1.25cbc7992fd64p+11, -0x1.914caac567631p+10, 0x1.f93f030387c4dp+9, -0x1.1b4f5dfc787bcp+9, 0x1.1df01b8a36a8bp+8, -0x1.048db6f3ab7c2p+7, 0x1.730bcb9c58bfcp+5, -0x1.09b56b87c1c8p+3, -0x1.4fb833b30fa7fp+0, 0x1.e38e1048601a6p-1, -0x1.ee07e572041f7p-4, -0x1.913ced3c0164bp-8, 0x1.0726b83c4032cp-11, 0x1.2751c6763466cp-20, -0x1.00ceb77e39cacp-26, 0x1.0123085a89101p-41, 0x0p+0};
@@ -1711,7 +2096,7 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0, 0x1.a308ef1d16805p-1, -0x1.1df37cb20ef6dp+3, 0x1.5a47cc2daffcbp+5, -0x1.e7cc32d4c7f06p+6, 0x1.ba5aa6f58d154p+7, -0x1.137ebe2556bb6p+8, 0x1.07f96c27b79bap+8, -0x1.f176d6c3151d9p+7, 0x1.0c09a0e0bcbap+8, -0x1.12bf0f34a9a55p+8, 0x1.de16d55d65d2cp+7, -0x1.8c7b496d3d3fep+7, 0x1.56592506626bcp+7, -0x1.13d919c9693b3p+7, 0x1.8b69de5718a0ap+6, -0x1.15b78c90e7837p+6, 0x1.8188b8db550ffp+5, -0x1.e03c011f666acp+4, 0x1.12ed8b36e9864p+4, -0x1.36a5b057bc26fp+3, 0x1.3d2641cf67e9p+2, -0x1.11ef148707dfap+1, 0x1.c294da23fe2ap-1, -0x1.4f57e7e05e819p-2, 0x1.1ebd9964081cfp-4, 0x1.367917f76eee3p-14, -0x1.fdd37749c94d9p-10, -0x1.0fc0733cbc7d6p-22, 0x1.f945fb653cfdbp-22, -0x1.fb1bcfae6e46dp-34, 0x0p+0};
             }
             if constexpr (order == 14) {
-                return {0x0p+0, 0x1.74ef139ad4e12p-3, -0x1.fd9d32fdef74p+0, 0x1.3320f17be8b7p+3, -0x1.a9e31dbd98dd1p+4, 0x1.73dbdd38a87f5p+5, -0x1.aa50f206f25c7p+5, 0x1.5e48ac9c2f1f2p+5, -0x1.20d7a78e95ecfp+5, 0x1.4350b94e5aa2ep+5, -0x1.5499ff05228dep+5, 0x1.0d8c7214ffee1p+5, -0x1.8fe88996cfa9ap+4, 0x1.63da6bffb7323p+4, -0x1.24223f5c1b9d9p+4, 0x1.7851e19176716p+3, -0x1.e4fd178fcd0efp+2, 0x1.610a439acb289p+2, -0x1.ae4c3e147b71cp+1, 0x1.a6fe28ab7ffaap+0, -0x1.ccc920f98175ep-1, 0x1.f9389387bff6bp-2, -0x1.8612de961fd02p-3, 0x1.fd43fc0e7883fp-5, -0x1.aafa1e0c4a87p-6, 0x1.b638737fa8e8fp-8, 0x1.071682a1f5058p-11, -0x1.a84c3f530239bp-12, 0x1.a20c2374a0f67p-18, 0x1.e7f1c0adda0f6p-23, -0x1.eb089a4058efep-34, 0x0p+0};
+                return {0x0p+0, 0x1.74ef139ad4e12p-3, -0x1.fd9d32fdef74p+0, 0x1.3320f17be8b7p+3, -0x1.a9e31dbd98dd1p+4, 0x1.73dbdd38a87f5p+5, -0x1.aa50f206f25c7p+5, 0x1.5e48ac9c2f1f2p+5, -0x1.20d7a78e95ecfp+5, 0x1.4350b94e5aa2ep+5, -0x1.5499ff05228dep+5, 0x1.0d8c7214ffee1p+5, -0x1.8fe88996cfa9ap+4, 0x1.63da6bffb7323p+4, -0x1.24223f5c1b9d9p+4, 0x1.7851e19176716p+3, -0x1.e4fd178fcd0efp+2, 0x1.610a439acb289p+2, -0x1.ae4c3e147b71cp+1, 0x1.a6fe28ab7ffaap+0, -0x1.ccc920f98175ep-1, 0x1.f9389387bff6bp-2, -0x1.8612de961fd02p-3, 0x1.fd43fc0e7883fp-5, -0x1.aafa1e0c4a87p-6, 0x1.b638737fa8e8fp-8, 0x1.071682a1f5058p-11, -0x1.a84c3f530239bp-12, 0x1.a20c2374a0f67p-18, 0x1.e7f1c0adda0f6p-23, -0x1.eb089a4058efep-34, -0x0p+0};
             }
             if constexpr (order == 15) {
                 return {0x0p+0, 0x1.31c729360063ep-6, -0x1.a21aa8a66a683p-3, 0x1.f656a46fa2a91p-1, -0x1.589b4fca92a9fp+1, 0x1.25049558932c2p+2, -0x1.3b0f087615a27p+2, 0x1.bed87f332745cp+1, -0x1.37fe75fa2aa3bp+1, 0x1.75c34ae38a12p+1, -0x1.9f32b219f201fp+1, 0x1.2a50b5ebe798ep+1, -0x1.80aff2523d4b3p+0, 0x1.71f9af43c19f1p+0, -0x1.40d21595459ccp+0, 0x1.6edc3b8de7cbdp-1, -0x1.abb5cf29e076bp-2, 0x1.5fdcb9c5e1f88p-2, -0x1.af4e9b9242255p-3, 0x1.57b33e4d63cb5p-4, -0x1.736294d370decp-5, 0x1.e1a61d7964669p-6, -0x1.38138139d6cd8p-7, 0x1.a99b874715d59p-10, -0x1.191ada841d112p-10, 0x1.44a23a1750afbp-12, 0x1.4db128e094988p-13, -0x1.2cad37f3dbf9ep-14, 0x1.f38c667f69482p-19, 0x1.c870773604d03p-24, -0x1.cdd01a024c711p-34, -0x0p+0};
@@ -1722,16 +2107,16 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0L, 0xb.3a3846107e93c71p-16L, 0x9.3e6d9853c4d4d26p-8L, 0xf.9fcd2109d2c70bp-5L, 0xc.50d8731f3b477fep-4L, -0xe.800409a73d92674p-5L, 0x8.364c0bfb08f4c1cp-5L, -0xa.7608480379d5af6p-6L, 0xd.c9e1911927a4784p-7L, -0x8.4fafa041f14b7dbp-7L, 0x8.5b53aefd12e6ae9p-8L, -0xd.0bf5c01ffba2e16p-10L, 0xe.6d0c69fb315533p-12L, -0x8.c0ab49d8f284eep-14L, -0xa.a3e26aabf73f753p-18L, 0xd.0ea8c3bcb0cd49bp-18L, -0xf.dc862acd1a0536cp-20L, 0x8.42dddac61ee2f0bp-22L, 0xa.50b750c53c5492bp-25L, -0x9.d87c1e77be4e6b7p-26L, 0xa.134a86cdb5e53d1p-31L, 0xd.67ae641bc3e3b4bp-32L, 0xe.3efe0e5e6ab002dp-40L, -0xc.cd24c38a13a8934p-40L, 0x8.62a7b6ddea955d3p-45L, 0xb.05b10aa4250e4b5p-52L, -0xb.1b0384fcfca5df4p-57L, 0xf.98453c9a684c9f5p-65L, -0xe.e6c1e66bda07395p-77L, -0xf.a640e8482ad4089p-90L, 0xf.aa0d3dd7d200c8bp-115L, -0x0p+0L};
             }
             if constexpr (order == 1) {
-                return {0x0p+0L, 0xa.f15f1ffe0172e5bp-13L, 0x8.8aacb719a8764e8p-6L, 0xc.70337610fe3509fp-4L, -0xc.d1d74d153495bebp-4L, -0xd.a74119cbe7c3dc1p-5L, 0x9.26bcdd7c845def1p-4L, -0xc.b7f844c8550ff96p-5L, 0xb.e7f83cc2cea254cp-6L, -0x9.d97b7de092f7fa8p-8L, -0xc.621cb12d798fd78p-9L, 0xe.c17b081c7070057p-9L, -0xe.984243655303eaap-10L, 0xd.c65378f292ec7e1p-12L, 0xa.751369469843a67p-16L, -0xa.22a84a59f7d64eap-15L, 0x8.8b7da84ad94ceep-18L, 0xf.37a3482ba1e794ep-19L, -0xb.99225ab2889ca73p-20L, 0x8.82f186bf65a2e47p-23L, 0xc.2f72cc72e3b957cp-26L, -0xa.d64f8e3b5739183p-28L, 0xe.bc4f9eb81d6e738p-33L, 0xc.6af1f10013f432fp-38L, -0xe.459c19e1dbb49cp-40L, 0x9.c7f205ccc827418p-46L, 0xf.a9268cec210502dp-52L, -0xd.39dbeaf2abf3a86p-60L, -0xe.29902305dd00cf8p-71L, 0xd.29aa6f4daf25f05p-84L, -0xd.2cdc8c67843fbf1p-108L, 0x0p+0L};
+                return {0x0p+0L, 0xa.f15f1ffe0172e5bp-13L, 0x8.8aacb719a8764e8p-6L, 0xc.70337610fe3509fp-4L, -0xc.d1d74d153495bebp-4L, -0xd.a74119cbe7c3dc1p-5L, 0x9.26bcdd7c845def1p-4L, -0xc.b7f844c8550ff96p-5L, 0xb.e7f83cc2cea254cp-6L, -0x9.d97b7de092f7fa8p-8L, -0xc.621cb12d798fd78p-9L, 0xe.c17b081c7070057p-9L, -0xe.984243655303eaap-10L, 0xd.c65378f292ec7e1p-12L, 0xa.751369469843a67p-16L, -0xa.22a84a59f7d64eap-15L, 0x8.8b7da84ad94ceep-18L, 0xf.37a3482ba1e794ep-19L, -0xb.99225ab2889ca73p-20L, 0x8.82f186bf65a2e47p-23L, 0xc.2f72cc72e3b957cp-26L, -0xa.d64f8e3b5739183p-28L, 0xe.bc4f9eb81d6e738p-33L, 0xc.6af1f10013f432fp-38L, -0xe.459c19e1dbb49cp-40L, 0x9.c7f205ccc827418p-46L, 0xf.a9268cec210502dp-52L, -0xd.39dbeaf2abf3a86p-60L, -0xe.29902305dd00cf8p-71L, 0xd.29aa6f4daf25f05p-84L, -0xd.2cdc8c67843fbf1p-108L, -0x0p+0L};
             }
             if constexpr (order == 2) {
-                return {0x0p+0L, 0x9.4af7f560a96bcb2p-10L, 0xc.eb0e623f2ef1314p-5L, 0x8.b0ea0b5b3b1bf47p-5L, -0xa.dbd22b319bb54d5p-2L, 0xe.88ba684f6e872d5p-2L, -0xb.27ea9053310cf1ap-2L, 0x8.28b46d4b2423017p-2L, -0xb.2ba844e22c3642p-3L, 0xd.1c5f85a9fa1b98bp-4L, -0xc.44d8b76ba978ba9p-5L, 0x8.a963b5c62d530fcp-6L, -0x8.da64cc3b6900f46p-8L, 0xc.83f8f45a13145ecp-11L, -0xa.458a9102e93f63ap-16L, -0xd.193b6a58da0f707p-14L, 0x8.c8045595d6873c2p-14L, -0xa.50797e1d1ff33a2p-16L, 0xd.8b6c298de6cba8p-20L, 0x9.e4de48cf0724d64p-22L, 0xc.4c92a6ba0c8c4adp-27L, -0xf.001d6ffa3353439p-27L, -0xd.88c7c33e6b26e41p-30L, 0xd.4740e7cd95fa76bp-33L, 0xa.39023ea674090bcp-39L, 0x8.5e2a378903582b6p-44L, -0xa.dbc3bc7640960d4p-50L, -0xb.ae2bb9813575fa4p-56L, -0xa.228707fbc919e5bp-67L, 0xb.a31cd9a74b94ec4p-79L, -0xb.a5f0a4105eaa2e2p-102L, -0x0p+0L};
+                return {0x0p+0L, 0x9.4af7f560a96bcb2p-10L, 0xc.eb0e623f2ef1314p-5L, 0x8.b0ea0b5b3b1bf47p-5L, -0xa.dbd22b319bb54d5p-2L, 0xe.88ba684f6e872d5p-2L, -0xb.27ea9053310cf1ap-2L, 0x8.28b46d4b2423017p-2L, -0xb.2ba844e22c3642p-3L, 0xd.1c5f85a9fa1b98bp-4L, -0xc.44d8b76ba978ba9p-5L, 0x8.a963b5c62d530fcp-6L, -0x8.da64cc3b6900f46p-8L, 0xc.83f8f45a13145ecp-11L, -0xa.458a9102e93f63ap-16L, -0xd.193b6a58da0f707p-14L, 0x8.c8045595d6873c2p-14L, -0xa.50797e1d1ff33a2p-16L, 0xd.8b6c298de6cba8p-20L, 0x9.e4de48cf0724d64p-22L, 0xc.4c92a6ba0c8c4adp-27L, -0xf.001d6ffa3353439p-27L, -0xd.88c7c33e6b26e41p-30L, 0xd.4740e7cd95fa76bp-33L, 0xa.39023ea674090bcp-39L, 0x8.5e2a378903582b6p-44L, -0xa.dbc3bc7640960d4p-50L, -0xb.ae2bb9813575fa4p-56L, -0xa.228707fbc919e5bp-67L, 0xb.a31cd9a74b94ec4p-79L, -0xb.a5f0a4105eaa2e2p-102L, 0x0p+0L};
             }
             if constexpr (order == 3) {
-                return {0x0p+0L, 0xd.6f0633d36fb15fep-8L, 0xe.145a1853af94c61p-4L, -0xa.fa667dd213e750bp-2L, 0xe.6dc7b03ef3972cbp-3L, 0xf.bbba18cb32bd3c5p-3L, -0xe.ec3cdd404933d4fp-2L, 0x9.b829e085e714688p-2L, -0x8.dfd3b6054a1d126p-5L, -0x9.5a81a62f3e7613dp-3L, 0xb.1f11305d54fef5bp-3L, -0xd.14c89d060796ef7p-4L, 0xc.29433e46759ad44p-6L, 0xc.d4b327e4f33c651p-7L, -0xe.14fbc716f47a93ep-7L, 0xa.a6b1a222fe7b777p-8L, -0xa.0d952d2a5331434p-12L, -0x9.12ecff62e374622p-11L, 0xf.c80ccba53eedb19p-13L, -0x9.6141b8a10bf3aa6p-15L, -0xc.743a15ddfd9089p-19L, 0xe.4fac6316eae9c34p-20L, -0xb.0fb24af68dc7671p-23L, -0xc.b5c587c50af1901p-28L, 0xb.8fa464ce81856ffp-30L, -0xd.afe46b355b67eadp-37L, -0xe.2cb1f71139e968ap-41L, 0xb.5a73672924054c6p-48L, 0xf.3389afa15a4d6d7p-61L, -0xb.57fa0536eada04ep-70L, 0xb.5abc8738a6ec098p-92L, -0x0p+0L};
+                return {0x0p+0L, 0xd.6f0633d36fb15fep-8L, 0xe.145a1853af94c61p-4L, -0xa.fa667dd213e750bp-2L, 0xe.6dc7b03ef3972cbp-3L, 0xf.bbba18cb32bd3c5p-3L, -0xe.ec3cdd404933d4fp-2L, 0x9.b829e085e714688p-2L, -0x8.dfd3b6054a1d126p-5L, -0x9.5a81a62f3e7613dp-3L, 0xb.1f11305d54fef5bp-3L, -0xd.14c89d060796ef7p-4L, 0xc.29433e46759ad44p-6L, 0xc.d4b327e4f33c651p-7L, -0xe.14fbc716f47a93ep-7L, 0xa.a6b1a222fe7b777p-8L, -0xa.0d952d2a5331434p-12L, -0x9.12ecff62e374622p-11L, 0xf.c80ccba53eedb19p-13L, -0x9.6141b8a10bf3aa6p-15L, -0xc.743a15ddfd9089p-19L, 0xe.4fac6316eae9c34p-20L, -0xb.0fb24af68dc7671p-23L, -0xc.b5c587c50af1901p-28L, 0xb.8fa464ce81856ffp-30L, -0xd.afe46b355b67eadp-37L, -0xe.2cb1f71139e968ap-41L, 0xb.5a73672924054c6p-48L, 0xf.3389afa15a4d6d7p-61L, -0xb.57fa0536eada04ep-70L, 0xb.5abc8738a6ec098p-92L, 0x0p+0L};
             }
             if constexpr (order == 4) {
-                return {0x0p+0L, 0x8.014198cc101dfabp-5L, 0xb.a78a2fa8c05a46p-4L, -0xe.a0391633dc59632p-1L, 0x9.57b787a325e2b8ep+1L, -0xd.2189a8a2bccd13fp+1L, 0xc.d0ad7020938821dp+1L, -0x9.c68dea4f4d7949p+1L, 0xb.6366d8a6bff083fp+0L, -0x8.9b0cd5508cfcbdap-1L, 0xe.ab670f643a5062fp-4L, -0xf.21483d73d132347p-4L, 0xf.29488fcfb2b3205p-3L, -0xf.711277c7589ea5dp-3L, 0x8.f936b111ea265a4p-3L, -0xa.c4421afabc1b145p-5L, -0xc.f22fe2737be4b07p-10L, 0xe.e696975fdb72006p-8L, -0xc.988b5e0d635b9p-9L, 0x8.700bc1f1a15234ap-11L, 0x9.8f9fd5486f4f6f1p-15L, -0xf.b586fbbd2a200d7p-16L, 0xf.8283bd0161d5d44p-19L, 0x9.762dce912735e76p-23L, -0xa.3f95875b476d467p-25L, 0xd.e5810dfc41d0fc9p-32L, 0x8.de77eb67dd2905dp-35L, -0x9.a6cbd6e2951c534p-42L, -0xb.796464e51ca7defp-56L, 0x9.a721ec929f3744cp-63L, -0x9.a97cc78797246d9p-84L, 0x0p+0L};
+                return {0x0p+0L, 0x8.014198cc101dfabp-5L, 0xb.a78a2fa8c05a46p-4L, -0xe.a0391633dc59632p-1L, 0x9.57b787a325e2b8ep+1L, -0xd.2189a8a2bccd13fp+1L, 0xc.d0ad7020938821dp+1L, -0x9.c68dea4f4d7949p+1L, 0xb.6366d8a6bff083fp+0L, -0x8.9b0cd5508cfcbdap-1L, 0xe.ab670f643a5062fp-4L, -0xf.21483d73d132347p-4L, 0xf.29488fcfb2b3205p-3L, -0xf.711277c7589ea5dp-3L, 0x8.f936b111ea265a4p-3L, -0xa.c4421afabc1b145p-5L, -0xc.f22fe2737be4b07p-10L, 0xe.e696975fdb72006p-8L, -0xc.988b5e0d635b9p-9L, 0x8.700bc1f1a15234ap-11L, 0x9.8f9fd5486f4f6f1p-15L, -0xf.b586fbbd2a200d7p-16L, 0xf.8283bd0161d5d44p-19L, 0x9.762dce912735e76p-23L, -0xa.3f95875b476d467p-25L, 0xd.e5810dfc41d0fc9p-32L, 0x8.de77eb67dd2905dp-35L, -0x9.a6cbd6e2951c534p-42L, -0xb.796464e51ca7defp-56L, 0x9.a721ec929f3744cp-63L, -0x9.a97cc78797246d9p-84L, -0x0p+0L};
             }
             if constexpr (order == 5) {
                 return {0x0p+0L, 0xf.2ec58ae9b326a91p-4L, -0xf.3f2574189e4c21p-2L, 0xb.21ca3fab0ba7711p-2L, 0xc.5fbbb983127d9a8p+0L, -0x9.cabafe7cb0e079fp+2L, 0xf.b32be6b63f14cdcp+2L, -0x9.4c0d5533651b59dp+3L, 0x8.6798003cb446c2fp+3L, -0xb.8a9466ce5589bd2p+1L, -0x8.9b2c413204da0b9p+3L, 0xa.f6789af19b5be1p+4L, -0xe.547dec3aa6e0c9p+4L, 0xc.1d4b2ac6360394ap+4L, -0xc.ec88c1703c353c7p+3L, 0xc.0c7ae502f811c1cp+1L, 0xa.73c1664ca04a6f6p+0L, -0xb.fdd39a51bbcb87p+0L, 0x9.b0ebec135dad9dap-1L, -0xc.2ff74183eac8757p-4L, -0xf.e61902b12672b5fp-7L, 0x9.86aa5c308a25804p-7L, -0xa.11b63e66316fb48p-10L, -0xb.5b6a5e6044f76b4p-15L, 0x9.28e5bad3bd32814p-16L, -0xb.efb13ed9f69bfabp-22L, -0xb.6bdd018cd0bfce3p-26L, 0x8.239a85c21ab28b1p-32L, 0xf.655e87c2be28938p-44L, -0x8.1af78458939ea43p-52L, 0x8.1cf48073fd095efp-72L, 0x0p+0L};
@@ -1740,13 +2125,13 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0L, 0xa.e21ada4ca34ca18p-2L, -0xa.2d6c4039f3128bdp+1L, 0x8.d6321f4e4cfc7p+3L, -0x9.de69270e1178454p+4L, 0x8.8995f56b287327p+5L, -0xd.1990b03f1acb0aep+5L, 0x9.5f626739da926f4p+6L, -0xc.1eeea1125cd5fdbp+6L, 0xd.8d6a120ec35f6eap+6L, -0xc.ebd190c0b85945bp+6L, 0xa.a937c3f410a79b7p+6L, -0xf.4cb42bf5e9fec33p+5L, 0x8.c354d12799c3f3ap+5L, -0xa.7c027bb5b6adc35p+3L, -0xc.24aa7e0c10803ep+2L, 0xa.cf7d08e97637cb2p+3L, -0xe.d63d69d99e4aebp+2L, 0xb.103c3cb1b9f39dbp+1L, -0xc.45d811f4f97cc5dp-2L, -0x8.25c8b0134dc4eacp-3L, 0x8.c634c1565e9668ap-4L, -0xa.846ee4e9e65a1e2p-7L, -0xa.9c9c370a0ae7abcp-12L, 0xc.f55cc9525cd59bdp-13L, -0xc.c05c97fc0a662abp-18L, -0xb.b0e149c0f6e94f3p-22L, 0xb.273f17625796a99p-28L, 0x8.c11dba1f262097fp-38L, -0xb.11c91e9eedd7769p-47L, 0xb.1487d401bac7208p-66L, 0x0p+0L};
             }
             if constexpr (order == 7) {
-                return {0x0p+0L, 0xc.48a21bb874fadacp-1L, -0xe.25947bedf679c74p+2L, 0xe.cca62378420be4ep+4L, -0x9.36f7f04f5cf1891p+6L, 0xe.efabbe21287bc6p+6L, -0xf.e903cd879eed94cp+6L, 0x9.b0a951714367f56p+6L, 0xe.c30b528ed9b461fp+3L, -0x8.c85a14491ba6385p+7L, 0x9.b10cd9cb0bcab3ep+8L, -0xf.76ba000b317bf3bp+8L, 0x9.8e0a4a2852f4c19p+9L, -0x9.8c03d26c7bec5cfp+9L, 0x8.3f1bf843ae145d5p+9L, -0xc.e507037d2720736p+8L, 0x8.c91c9524b2cfadfp+8L, -0x9.47bf7b2d488e112p+7L, 0xc.7788c1775b861dcp+5L, -0x8.3b10b6d2e21d939p+2L, -0x9.b9a54e4e280a5b6p+2L, 0x9.7189ee727df88e1p+1L, -0xc.89f66d0f1a1b57cp-2L, -0xd.5d2702c8d9af7bcp-7L, 0xa.abc65114b42fbafp-7L, -0xf.9ffa3c1cf2c6819p-12L, -0xd.e9d0903b527a85p-16L, 0x9.4fff48a09514e9bp-21L, 0xa.f3b88c8a582c5bap-31L, -0x9.33f1f8f67028c1p-39L, 0x9.3646cdf31261e85p-57L, -0x0p+0L};
+                return {0x0p+0L, 0xc.48a21bb874fadacp-1L, -0xe.25947bedf679c74p+2L, 0xe.cca62378420be4ep+4L, -0x9.36f7f04f5cf1891p+6L, 0xe.efabbe21287bc6p+6L, -0xf.e903cd879eed94cp+6L, 0x9.b0a951714367f56p+6L, 0xe.c30b528ed9b461fp+3L, -0x8.c85a14491ba6385p+7L, 0x9.b10cd9cb0bcab3ep+8L, -0xf.76ba000b317bf3bp+8L, 0x9.8e0a4a2852f4c19p+9L, -0x9.8c03d26c7bec5cfp+9L, 0x8.3f1bf843ae145d5p+9L, -0xc.e507037d2720736p+8L, 0x8.c91c9524b2cfadfp+8L, -0x9.47bf7b2d488e112p+7L, 0xc.7788c1775b861dcp+5L, -0x8.3b10b6d2e21d939p+2L, -0x9.b9a54e4e280a5b6p+2L, 0x9.7189ee727df88e1p+1L, -0xc.89f66d0f1a1b57cp-2L, -0xd.5d2702c8d9af7bcp-7L, 0xa.abc65114b42fbafp-7L, -0xf.9ffa3c1cf2c6819p-12L, -0xd.e9d0903b527a85p-16L, 0x9.4fff48a09514e9bp-21L, 0xa.f3b88c8a582c5bap-31L, -0x9.33f1f8f67028c1p-39L, 0x9.3646cdf31261e85p-57L, 0x0p+0L};
             }
             if constexpr (order == 8) {
-                return {0x0p+0L, 0x8.e030397df9379acp+0L, -0xb.2eccc3a4f8cf9fbp+3L, 0xc.ec4bc5cb7abf8aap+5L, -0x9.2646bb53f9b6b84p+7L, 0x9.0ea3cde0034bd8ap+8L, -0xd.de003649c9a9964p+8L, 0x9.108e2212efce172p+9L, -0xa.e327f8ec5fb3bd6p+9L, 0xc.22d1ad18ac1a3e5p+9L, -0xc.3f36f87dfc77a18p+9L, 0xb.2820886f3206234p+9L, -0x9.5cd5015f159aa05p+9L, 0xe.75e7d994d2bf56ep+8L, -0x9.f1bae334ed5fea7p+8L, 0xb.eb8633ff44b9f04p+7L, -0xc.7eb43a4a9745482p+6L, 0xa.bdb7a04b78e780bp+5L, -0x9.f160026398b080cp+3L, -0xf.8f07b321ba98ffdp+1L, 0x9.cfb3b63913ab26dp+2L, -0x8.3fbef1b756b8bfp+1L, 0xb.757815a225e2672p-2L, 0xf.c44b63d93d7545p-7L, -0xd.bc7251b1b7bbe9bp-7L, 0xf.d7949e32fe445dap-11L, 0xd.35b026f7f354a7ap-15L, -0xc.c435f1432f26328p-20L, -0xb.e05ef16a6ea832dp-29L, 0xc.85651cf5174561cp-37L, -0xc.88b377d3685495ep-54L, 0x0p+0L};
+                return {0x0p+0L, 0x8.e030397df9379acp+0L, -0xb.2eccc3a4f8cf9fbp+3L, 0xc.ec4bc5cb7abf8aap+5L, -0x9.2646bb53f9b6b84p+7L, 0x9.0ea3cde0034bd8ap+8L, -0xd.de003649c9a9964p+8L, 0x9.108e2212efce172p+9L, -0xa.e327f8ec5fb3bd6p+9L, 0xc.22d1ad18ac1a3e5p+9L, -0xc.3f36f87dfc77a18p+9L, 0xb.2820886f3206234p+9L, -0x9.5cd5015f159aa05p+9L, 0xe.75e7d994d2bf56ep+8L, -0x9.f1bae334ed5fea7p+8L, 0xb.eb8633ff44b9f04p+7L, -0xc.7eb43a4a9745482p+6L, 0xa.bdb7a04b78e780bp+5L, -0x9.f160026398b080cp+3L, -0xf.8f07b321ba98ffdp+1L, 0x9.cfb3b63913ab26dp+2L, -0x8.3fbef1b756b8bfp+1L, 0xb.757815a225e2672p-2L, 0xf.c44b63d93d7545p-7L, -0xd.bc7251b1b7bbe9bp-7L, 0xf.d7949e32fe445dap-11L, 0xd.35b026f7f354a7ap-15L, -0xc.c435f1432f26328p-20L, -0xb.e05ef16a6ea832dp-29L, 0xc.85651cf5174561cp-37L, -0xc.88b377d3685495ep-54L, -0x0p+0L};
             }
             if constexpr (order == 9) {
-                return {0x0p+0L, 0xa.c73efb39920cedbp+0L, -0xe.29d14b0b7d1c041p+3L, 0x8.660c6abd0d0fda4p+6L, -0xb.e497e0db651c4abp+7L, 0xb.50ca2e905b46c5dp+8L, -0xf.d5bb8e070dd7927p+8L, 0x9.2a14c565d96a24dp+9L, -0xa.03fcee4afcd8902p+9L, 0xa.9919e31eec53f8cp+9L, -0x9.da9459a29ccbc9bp+9L, 0xf.17513cbe92f2a28p+8L, -0x9.eb0b4ee88e4de52p+8L, 0xb.afe72eb20a022bp+7L, -0x9.5ada8093fcfab6ap+6L, -0x8.c7028c58a1762e5p+4L, 0xf.68f712bd4ba559bp+5L, -0xf.ad2d46c54d9e03ap+5L, 0xc.9064a1f4f0d1331p+5L, -0x9.1609c2a09622ff8p+5L, 0xa.58dd09fb31458efp+4L, -0xf.643b79a6f703a82p+2L, 0xb.20930f8ad15e1ebp+0L, 0x9.dd63fe5b440fe97p-4L, -0x9.d706daffa4f07edp-4L, 0x8.5d222df794bdd1ep-7L, 0xe.1c0255ed2d877d5p-12L, -0x9.e3c7dd44fbf26e9p-16L, -0xb.748522d8bf08c1ap-25L, 0x9.a61cc52eea42bddp-32L, -0x9.a8dde66ab36adabp-48L, 0x0p+0L};
+                return {0x0p+0L, 0xa.c73efb39920cedbp+0L, -0xe.29d14b0b7d1c041p+3L, 0x8.660c6abd0d0fda4p+6L, -0xb.e497e0db651c4abp+7L, 0xb.50ca2e905b46c5dp+8L, -0xf.d5bb8e070dd7927p+8L, 0x9.2a14c565d96a24dp+9L, -0xa.03fcee4afcd8902p+9L, 0xa.9919e31eec53f8cp+9L, -0x9.da9459a29ccbc9bp+9L, 0xf.17513cbe92f2a28p+8L, -0x9.eb0b4ee88e4de52p+8L, 0xb.afe72eb20a022bp+7L, -0x9.5ada8093fcfab6ap+6L, -0x8.c7028c58a1762e5p+4L, 0xf.68f712bd4ba559bp+5L, -0xf.ad2d46c54d9e03ap+5L, 0xc.9064a1f4f0d1331p+5L, -0x9.1609c2a09622ff8p+5L, 0xa.58dd09fb31458efp+4L, -0xf.643b79a6f703a82p+2L, 0xb.20930f8ad15e1ebp+0L, 0x9.dd63fe5b440fe97p-4L, -0x9.d706daffa4f07edp-4L, 0x8.5d222df794bdd1ep-7L, 0xe.1c0255ed2d877d5p-12L, -0x9.e3c7dd44fbf26e9p-16L, -0xb.748522d8bf08c1ap-25L, 0x9.a61cc52eea42bddp-32L, -0x9.a8dde66ab36adabp-48L, -0x0p+0L};
             }
             if constexpr (order == 10) {
                 return {0x0p+0L, 0x8.67ec98274e874f4p+0L, -0xb.46007534bb26601p+3L, 0xd.a531d42e35090ebp+5L, -0x9.e27e798241476f8p+7L, 0x9.af7f4d5c0b7b569p+8L, -0xe.1c395adb6e69289p+8L, 0x8.930d641fa835ff8p+9L, -0x9.cf0fd1f80419d17p+9L, 0xa.f264e9b223377bap+9L, -0xb.5b9720d42482e67p+9L, 0xa.bc7ea62021246d6p+9L, -0x9.87d79b24282e6fbp+9L, 0x8.0ba56be44c10be5p+9L, -0xc.a15e24f97a95118p+8L, 0x9.2e5e3cc97eb1e7ap+8L, -0xc.8a65562b3b184f6p+7L, 0xf.c9f8181c3e2680dp+6L, -0x8.da7aefe3c3dde19p+6L, 0x8.ef80dc51b545874p+5L, -0x8.246db79d5be0e64p+4L, 0xb.985e5ce2c5fe107p+2L, -0x8.4dab5c3e0e3fdbep+0L, -0xa.7dc19d987d3f778p-3L, 0xf.1c70824300d3066p-4L, -0xf.703f2b9020fb9c6p-7L, -0xc.89e769e00b25ab7p-11L, 0x8.3935c1e20195fc1p-14L, 0x9.3a8e33b1a335de3p-23L, -0x8.0675bbf1ce55e11p-29L, 0x8.091842d44880a98p-44L, 0x0p+0L};
@@ -1761,7 +2146,7 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
                 return {0x0p+0L, 0xd.184778e8b402badp-4L, -0x8.ef9be59077b66a9p+0L, 0xa.d23e616d7fe5968p+2L, -0xf.3e6196a63f82e61p+3L, 0xd.d2d537ac68aa3c8p+4L, -0x8.9bf5f12ab5dae19p+5L, 0x8.3fcb613dbcdd0e4p+5L, -0xf.8bb6b618a8ec653p+4L, 0x8.604d0705e5cffc7p+5L, -0x8.95f879a54d2a806p+5L, 0xe.f0b6aaeb2e95db1p+4L, -0xc.63da4b69e9fec14p+4L, 0xa.b2c92833135e147p+4L, -0x8.9ec8ce4b49d9743p+4L, 0xc.5b4ef2b8c504f17p+3L, -0x8.adbc64873c1b94ap+3L, 0xc.0c45c6daa87f51cp+2L, -0xf.01e008fb335633p+1L, 0x8.976c59b74c322cp+1L, -0x9.b52d82bde13767bp+0L, 0x9.e9320e7b3f47defp-1L, -0x8.8f78a4383efd09p-2L, 0xe.14a6d11ff14fe9cp-4L, -0xa.7abf3f02f40c74p-5L, 0x8.f5eccb2040e7b75p-7L, 0x9.b3c8bfbb7771784p-17L, -0xf.ee9bba4e4a6c8ddp-13L, -0x8.7e0399e5e3eb2bep-25L, 0xf.ca2fdb29e7ed48cp-25L, -0xf.d8de7d73723689ep-37L, 0x0p+0L};
             }
             if constexpr (order == 14) {
-                return {0x0p+0L, 0xb.a7789cd6a708f8p-6L, -0xf.ece997ef7b9fe29p-3L, 0x9.99078bdf45b839ap+0L, -0xd.4f18edecc6e84b2p+1L, 0xb.9edee9c543fa832p+2L, -0xd.5287903792e3955p+2L, 0xa.f24564e178f8f8p+2L, -0x9.06bd3c74af67abfp+2L, 0xa.1a85ca72d516d28p+2L, -0xa.a4cff829146ee94p+2L, 0x8.6c6390a7ff70509p+2L, -0xc.7f444cb67d4d2a9p+1L, 0xb.1ed35ffdb991773p+1L, -0x9.2111fae0dceca83p+1L, 0xb.c28f0c8bb38af61p+0L, -0xf.27e8bc7e687797cp-1L, 0xb.08521cd65944bcep-1L, -0xd.7261f0a3db8e14ap-2L, 0xd.37f1455bffd4c88p-3L, -0xe.664907cc0baeeacp-4L, 0xf.c9c49c3dffb59aap-5L, -0xc.3096f4b0fe81145p-6L, 0xf.ea1fe073c41f722p-8L, -0xd.57d0f0625437c47p-9L, 0xd.b1c39bfd474775fp-11L, 0x8.38b4150fa82bf11p-14L, -0xd.4261fa9811cdb2p-15L, 0xd.10611ba507b38p-21L, 0xf.3f8e056ed07b157p-26L, -0xf.5844d202c77f32cp-37L, 0x0p+0L};
+                return {0x0p+0L, 0xb.a7789cd6a708f8p-6L, -0xf.ece997ef7b9fe29p-3L, 0x9.99078bdf45b839ap+0L, -0xd.4f18edecc6e84b2p+1L, 0xb.9edee9c543fa832p+2L, -0xd.5287903792e3955p+2L, 0xa.f24564e178f8f8p+2L, -0x9.06bd3c74af67abfp+2L, 0xa.1a85ca72d516d28p+2L, -0xa.a4cff829146ee94p+2L, 0x8.6c6390a7ff70509p+2L, -0xc.7f444cb67d4d2a9p+1L, 0xb.1ed35ffdb991773p+1L, -0x9.2111fae0dceca83p+1L, 0xb.c28f0c8bb38af61p+0L, -0xf.27e8bc7e687797cp-1L, 0xb.08521cd65944bcep-1L, -0xd.7261f0a3db8e14ap-2L, 0xd.37f1455bffd4c88p-3L, -0xe.664907cc0baeeacp-4L, 0xf.c9c49c3dffb59aap-5L, -0xc.3096f4b0fe81145p-6L, 0xf.ea1fe073c41f722p-8L, -0xd.57d0f0625437c47p-9L, 0xd.b1c39bfd474775fp-11L, 0x8.38b4150fa82bf11p-14L, -0xd.4261fa9811cdb2p-15L, 0xd.10611ba507b38p-21L, 0xf.3f8e056ed07b157p-26L, -0xf.5844d202c77f32cp-37L, -0x0p+0L};
             }
             if constexpr (order == 15) {
                 return {0x0p+0L, 0x9.8e3949b0031f00ap-9L, -0xd.10d5453353419edp-6L, 0xf.b2b5237d1548b4fp-4L, -0xa.c4da7e54954f883p-2L, 0x9.2824aac49960d3ep-1L, -0x9.d87843b0ad13405p-1L, 0xd.f6c3f9993a2dfbdp-2L, -0x9.bff3afd1551db4ap-2L, 0xb.ae1a571c508fe19p-2L, -0xc.f99590cf900f84fp-2L, 0x9.5285af5f3cc721cp-2L, -0xc.057f9291ea599a1p-3L, 0xb.8fcd7a1e0cf84a9p-3L, -0xa.0690acaa2ce5ec5p-3L, 0xb.76e1dc6f3e5e678p-4L, -0xd.5dae794f03b58fap-5L, 0xa.fee5ce2f0fc3e14p-5L, -0xd.7a74dc92112ab1p-6L, 0xa.bd99f26b1e5a94cp-7L, -0xb.9b14a69b86f63cfp-8L, 0xf.0d30ebcb2334763p-9L, -0x9.c09c09ceb66c13bp-10L, 0xd.4cdc3a38aeac8ap-13L, -0x8.c8d6d420e888ec5p-13L, 0xa.2511d0ba857d42dp-15L, 0xa.6d894704a4c3cb1p-16L, -0x9.6569bf9edfcf3d1p-17L, 0xf.9c6333fb4a41095p-22L, 0xe.4383b9b026817b9p-27L, -0xe.6e80d0126388779p-37L, -0x0p+0L};
@@ -1770,55 +2155,105 @@ constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
         #ifdef BOOST_HAS_FLOAT128
         if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
             if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.674708c20fd278e13cb308fc018cp-13Q, 0x1.27cdb30a789a9a4cba57381b8109p-5Q, 0x1.f3f9a4213a58e15fea805c6fce04p-2Q, 0x1.8a1b0e63e768effc8742d136ac68p-1Q, -0x1.d0008134e7b24ce7a0bdb2d5e174p-2Q, 0x1.06c9817f611e98379b152a389faep-2Q, -0x1.4ec109006f3ab5eb9ef4b4145d22p-3Q, 0x1.b93c322324f48f0734b615fc988cp-4Q, -0x1.09f5f4083e296fb6c1df50020f4ap-4Q, 0x1.0b6a75dfa25cd5d117e101973337p-5Q, -0x1.a17eb803ff745c2b927f4b56bb4ap-7Q, 0x1.cda18d3f662aa65f684ad290726ep-9Q, -0x1.1815693b1e509dbfebb4547eb7b2p-11Q, -0x1.547c4d557ee7eea60970ca463ebcp-15Q, 0x1.a1d518779619a935a6506c218d65p-15Q, -0x1.fb90c559a340a6d74429771a6508p-17Q, 0x1.085bbb58c3dc5e159337591d11dp-19Q, 0x1.4a16ea18a78a9255137a36b6eea7p-22Q, -0x1.3b0f83cef7c9cd6e4992ef7a8df5p-23Q, 0x1.426950d9b6bca7a253eba2c282edp-28Q, 0x1.acf5cc83787c76964322f9b1342cp-29Q, 0x1.c7dfc1cbcd560059e1fa3bbb0d88p-37Q, -0x1.99a4987142751268f68b0c6ed2ddp-37Q, 0x1.0c54f6dbbd52aba64c70d9892a39p-42Q, 0x1.60b6215484a1c96af7151c514271p-49Q, -0x1.6360709f9f94bbe775bd0ffbecdcp-54Q, 0x1.f308a7934d0993ea0193288827f6p-62Q, -0x1.dcd83ccd7b40e72afa7a2bb7cfc1p-74Q, -0x1.f4c81d09055a8112f9a8f0e29d27p-87Q, 0x1.f541a7bafa4019158f37f50aca0cp-112Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.674708c20fd278e13cb308fbf6b6p-13Q, 0x1.27cdb30a789a9a4cba57381b80dfp-5Q, 0x1.f3f9a4213a58e15fea805c6fce03p-2Q, 0x1.8a1b0e63e768effc8742d136ac6ep-1Q, -0x1.d0008134e7b24ce7a0bdb2d5e177p-2Q, 0x1.06c9817f611e98379b152a389fafp-2Q, -0x1.4ec109006f3ab5eb9ef4b4145d24p-3Q, 0x1.b93c322324f48f0734b615fc9893p-4Q, -0x1.09f5f4083e296fb6c1df50020f51p-4Q, 0x1.0b6a75dfa25cd5d117e10197333bp-5Q, -0x1.a17eb803ff745c2b927f4b56bb55p-7Q, 0x1.cda18d3f662aa65f684ad290727fp-9Q, -0x1.1815693b1e509dbfebb4547eb7c2p-11Q, -0x1.547c4d557ee7eea60970ca463eb3p-15Q, 0x1.a1d518779619a935a6506c218d6ap-15Q, -0x1.fb90c559a340a6d74429771a650ap-17Q, 0x1.085bbb58c3dc5e159337591d11c5p-19Q, 0x1.4a16ea18a78a9255137a36b6eeb6p-22Q, -0x1.3b0f83cef7c9cd6e4992ef7a8e0ap-23Q, 0x1.426950d9b6bca7a253eba2c282ddp-28Q, 0x1.acf5cc83787c76964322f9b1343dp-29Q, 0x1.c7dfc1cbcd560059e1fa3bbb0da4p-37Q, -0x1.99a4987142751268f68b0c6ed2ep-37Q, 0x1.0c54f6dbbd52aba64c70d9892a56p-42Q, 0x1.60b6215484a1c96af7151c51425dp-49Q, -0x1.6360709f9f94bbe775bd0ffbeceep-54Q, 0x1.f308a7934d0993ea019328882821p-62Q, -0x1.dcd83ccd7b40e72afa7a2bb7cfap-74Q, -0x1.f4c81d09055a8112f9a8f0e29d58p-87Q, 0x1.f541a7bafa4019158f37f50aca47p-112Q, 0x0p+0Q};
             }
             if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.5e2be3ffc02e5cb63d505e4d41fep-10Q, 0x1.115596e3350ec9cfc7fd8b282be7p-3Q, 0x1.8e066ec21fc6a13efd57c0a1a877p-1Q, -0x1.9a3ae9a2a692b7d6fe0312f42f92p-1Q, -0x1.b4e823397cf87b829664fcfb60e4p-2Q, 0x1.24d79baf908bbde12d97a94a7ed1p-1Q, -0x1.96ff08990aa1ff2b3a6156b3a6a7p-2Q, 0x1.7cff079859d44a97134acb0b37c4p-3Q, -0x1.3b2f6fbc125eff4f9e00971a7fffp-5Q, -0x1.8c439625af31faef37a9ac49e531p-6Q, 0x1.d82f61038e0e00ad9adf79408fc1p-6Q, -0x1.d308486caa607d54998083598b6bp-7Q, 0x1.b8ca6f1e525d8fc1aecc19124973p-9Q, 0x1.4ea26d28d30874cd6f1bece4d064p-13Q, -0x1.4455094b3efac9d3c28631c94f7ap-12Q, 0x1.116fb5095b299dc0400b6814e25bp-15Q, 0x1.e6f46905743cf29b32a5a94efc8dp-16Q, -0x1.73244b56511394e5623a6c13b538p-17Q, 0x1.105e30d7ecb45c8d929e54615a9cp-20Q, 0x1.85ee598e5c772af7b4423f5e48b1p-23Q, -0x1.5ac9f1c76ae72306c6963aa9eb21p-25Q, 0x1.d789f3d703adce6fceeb7470eb4ep-30Q, 0x1.8d5e3e20027e865e92d2141a2b67p-35Q, -0x1.c8b3833c3b76938050c849f3c889p-37Q, 0x1.38fe40b99904e82fbd88d14cb2f1p-43Q, 0x1.f524d19d8420a05a730c8d14360bp-49Q, -0x1.a73b7d5e557e750b97979bfe8dccp-57Q, -0x1.c5320460bba019effc9564690e27p-68Q, 0x1.a5354de9b5e4be0a26cfffd8bd46p-81Q, -0x1.a59b918cf087f7e28a66eadc804dp-105Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.5e2be3ffc02e5cb63d505e4d42d9p-10Q, 0x1.115596e3350ec9cfc7fd8b282c15p-3Q, 0x1.8e066ec21fc6a13efd57c0a1a8d5p-1Q, -0x1.9a3ae9a2a692b7d6fe0312f42fd2p-1Q, -0x1.b4e823397cf87b829664fcfb615p-2Q, 0x1.24d79baf908bbde12d97a94a7f11p-1Q, -0x1.96ff08990aa1ff2b3a6156b3a6f7p-2Q, 0x1.7cff079859d44a97134acb0b3815p-3Q, -0x1.3b2f6fbc125eff4f9e00971a8041p-5Q, -0x1.8c439625af31faef37a9ac49e57fp-6Q, 0x1.d82f61038e0e00ad9adf7940901dp-6Q, -0x1.d308486caa607d54998083598bc8p-7Q, 0x1.b8ca6f1e525d8fc1aecc191249d8p-9Q, 0x1.4ea26d28d30874cd6f1bece4d0cdp-13Q, -0x1.4455094b3efac9d3c28631c94fc4p-12Q, 0x1.116fb5095b299dc0400b6814e296p-15Q, 0x1.e6f46905743cf29b32a5a94efd0bp-16Q, -0x1.73244b56511394e5623a6c13b582p-17Q, 0x1.105e30d7ecb45c8d929e54615ad8p-20Q, 0x1.85ee598e5c772af7b4423f5e4908p-23Q, -0x1.5ac9f1c76ae72306c6963aa9eb6ap-25Q, 0x1.d789f3d703adce6fceeb7470ebe2p-30Q, 0x1.8d5e3e20027e865e92d2141a2b73p-35Q, -0x1.c8b3833c3b76938050c849f3c902p-37Q, 0x1.38fe40b99904e82fbd88d14cb331p-43Q, 0x1.f524d19d8420a05a730c8d14369dp-49Q, -0x1.a73b7d5e557e750b97979bfe8e3ep-57Q, -0x1.c5320460bba019effc9564690ea4p-68Q, 0x1.a5354de9b5e4be0a26cfffd8bdbp-81Q, -0x1.a59b918cf087f7e28a66eadc80bbp-105Q, 0x0p+0Q};
             }
             if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.295efeac152d79633d42d6d9172ap-7Q, 0x1.9d61cc47e5de2628b18136c91d91p-2Q, 0x1.161d416b67637e8de5329814da2p-2Q, -0x1.5b7a45663376a9aa5f95ed876f1cp+1Q, 0x1.d1174d09edd0e5a9b8dec824cdfdp+1Q, -0x1.64fd520a66219e33ceb19171c86dp+1Q, 0x1.05168da96484602e8bf4113ac457p+1Q, -0x1.6575089c4586c8407b43149ab041p+0Q, 0x1.a38bf0b53f437316576c7b5f768p-1Q, -0x1.889b16ed752f17512574ee2082eap-2Q, 0x1.152c76b8c5aa61f7d1f86545ce6dp-3Q, -0x1.1b4c99876d201e8bbadda8305d7dp-5Q, 0x1.907f1e8b42628bd87c6dfaa4224dp-8Q, -0x1.48b152205d27ec7322d3d940e06dp-13Q, -0x1.a3276d4b1b41ee0d43115b5aa5e8p-11Q, 0x1.19008ab2bad0e78321ce13187997p-11Q, -0x1.4a0f2fc3a3fe6743d3250b9f059bp-13Q, 0x1.b16d8531bcd974ffcfcfb27586b6p-17Q, 0x1.3c9bc919e0e49ac8c1ec9b7c733dp-19Q, 0x1.899254d74191895a0ee7c7e36bb2p-24Q, -0x1.e003adff466a6871b6189e1534p-24Q, -0x1.b118f867cd64dc8214de14f222d4p-27Q, 0x1.a8e81cf9b2bf4ed6a7f80b7fef41p-30Q, 0x1.472047d4ce812177c2886070e70ap-36Q, 0x1.0bc546f1206b056c51ef6c4e49f4p-41Q, -0x1.5b78778ec812c1a8126f0f850a88p-47Q, -0x1.75c5773026aebf4866564852975ap-53Q, -0x1.4450e0ff79233cb66d7ae040758fp-64Q, 0x1.74639b34e9729d879c349c615547p-76Q, -0x1.74be14820bd545c3f1e6ecd10653p-99Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.295efeac152d79633d42d6d916dap-7Q, 0x1.9d61cc47e5de2628b18136c91ea6p-2Q, 0x1.161d416b67637e8de5329814dbadp-2Q, -0x1.5b7a45663376a9aa5f95ed877064p+1Q, 0x1.d1174d09edd0e5a9b8dec824cf43p+1Q, -0x1.64fd520a66219e33ceb19171c931p+1Q, 0x1.05168da96484602e8bf4113ac4e7p+1Q, -0x1.6575089c4586c8407b43149ab11bp+0Q, 0x1.a38bf0b53f437316576c7b5f77a6p-1Q, -0x1.889b16ed752f17512574ee20842fp-2Q, 0x1.152c76b8c5aa61f7d1f86545cf96p-3Q, -0x1.1b4c99876d201e8bbadda8305eebp-5Q, 0x1.907f1e8b42628bd87c6dfaa42428p-8Q, -0x1.48b152205d27ec7322d3d940da05p-13Q, -0x1.a3276d4b1b41ee0d43115b5aa81dp-11Q, 0x1.19008ab2bad0e78321ce13187a8p-11Q, -0x1.4a0f2fc3a3fe6743d3250b9f0687p-13Q, 0x1.b16d8531bcd974ffcfcfb275888ap-17Q, 0x1.3c9bc919e0e49ac8c1ec9b7c72d7p-19Q, 0x1.899254d74191895a0ee7c7e368dfp-24Q, -0x1.e003adff466a6871b6189e153009p-24Q, -0x1.b118f867cd64dc8214de14f22a3dp-27Q, 0x1.a8e81cf9b2bf4ed6a7f80b7fee49p-30Q, 0x1.472047d4ce812177c28860710d42p-36Q, 0x1.0bc546f1206b056c51ef6c4e3c73p-41Q, -0x1.5b78778ec812c1a8126f0f855511p-47Q, -0x1.75c5773026aebf48665648526e47p-53Q, -0x1.4450e0ff79233cb66d7ae0406fdfp-64Q, 0x1.74639b34e9729d879c349c60a705p-76Q, -0x1.74be14820bd545c3f1e6ecce41eap-99Q, 0x0p+0Q};
             }
             if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.ade0c67a6df62bfb0e80195f5a2fp-5Q, 0x1.c28b430a75f298c1d73bb81e4847p-1Q, -0x1.5f4ccfba427cea15c66f4a5c1f37p+1Q, 0x1.cdb8f607de72e596ea568a0387dfp+0Q, 0x1.f77743196657a78ad5bf74421206p+0Q, -0x1.dd879ba809267a9d7904ab43625dp+1Q, 0x1.37053c10bce28d1022d31ac10de9p+1Q, -0x1.1bfa76c0a943a24b6df5bb2a1509p-2Q, -0x1.2b5034c5e7cec27aa44e7ea3cb6cp+0Q, 0x1.63e2260baa9fdeb5f048ba37b6ebp+0Q, -0x1.a29913a0c0f2ddeebb2bd3c28a1p-1Q, 0x1.852867c8ceb35a88f788b40867b1p-3Q, 0x1.9a9664fc9e678ca180654356d53fp-4Q, -0x1.c29f78e2de8f527b7cd8a08d3865p-4Q, 0x1.54d634445fcf6eedbc5dccf05e12p-5Q, -0x1.41b2a5a54a66286808252915cbfp-9Q, -0x1.225d9fec5c6e8c447caf2b42dbedp-8Q, 0x1.f9019974a7ddb631ebee782882ddp-10Q, -0x1.2c283714217e754b55528b629523p-12Q, -0x1.8e8742bbbfb2111f9226dbaeba4ep-16Q, 0x1.c9f58c62dd5d38676514b49cb9bcp-17Q, -0x1.61f6495ed1b8ece209fc78f1e52ap-20Q, -0x1.96b8b0f8a15e32028c8ee00782fdp-25Q, 0x1.71f48c99d030adfe377a70568859p-27Q, -0x1.b5fc8d66ab6cfd5a83337a0ceda7p-34Q, -0x1.c5963ee2273d2d13e0940bb14697p-38Q, 0x1.6b4e6ce52480a98b4ad64082bf85p-45Q, 0x1.e67135f42b49adad0031055a34f8p-58Q, -0x1.6aff40a6dd5b409b62d449651f14p-67Q, 0x1.6b5790e714dd812f487575d068fp-89Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.ade0c67a6df62bfb0e80195f4993p-5Q, 0x1.c28b430a75f298c1d73bb81e4353p-1Q, -0x1.5f4ccfba427cea15c66f4a5c12bbp+1Q, 0x1.cdb8f607de72e596ea568a034c8fp+0Q, 0x1.f77743196657a78ad5bf74425543p+0Q, -0x1.dd879ba809267a9d7904ab437cc5p+1Q, 0x1.37053c10bce28d1022d31ac1246dp+1Q, -0x1.1bfa76c0a943a24b6df5bb2abebdp-2Q, -0x1.2b5034c5e7cec27aa44e7ea3a878p+0Q, 0x1.63e2260baa9fdeb5f048ba37a04bp+0Q, -0x1.a29913a0c0f2ddeebb2bd3c275b3p-1Q, 0x1.852867c8ceb35a88f788b40857cap-3Q, 0x1.9a9664fc9e678ca180654356c297p-4Q, -0x1.c29f78e2de8f527b7cd8a08d24efp-4Q, 0x1.54d634445fcf6eedbc5dccf04eadp-5Q, -0x1.41b2a5a54a66286808252915b865p-9Q, -0x1.225d9fec5c6e8c447caf2b42ced4p-8Q, 0x1.f9019974a7ddb631ebee782869d1p-10Q, -0x1.2c283714217e754b55528b628588p-12Q, -0x1.8e8742bbbfb2111f9226dbaea15fp-16Q, 0x1.c9f58c62dd5d38676514b49c9e2ep-17Q, -0x1.61f6495ed1b8ece209fc78f1d085p-20Q, -0x1.96b8b0f8a15e32028c8ee0076679p-25Q, 0x1.71f48c99d030adfe377a7056701dp-27Q, -0x1.b5fc8d66ab6cfd5a83337a0cc9b9p-34Q, -0x1.c5963ee2273d2d13e0940bb125cdp-38Q, 0x1.6b4e6ce52480a98b4ad64082a237p-45Q, 0x1.e67135f42b49adad00310559fa39p-58Q, -0x1.6aff40a6dd5b409b62d44964fcf6p-67Q, 0x1.6b5790e714dd812f487575d04214p-89Q, 0x0p+0Q};
             }
             if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.002833198203bf56e8fbb6906848p-2Q, 0x1.74f145f5180b48bf2521976c532bp-1Q, -0x1.d40722c67b8b2c63d49b5a9adf94p+2Q, 0x1.2af6f0f464bc571c8b763a836373p+4Q, -0x1.a43135145799a27dfd1fadf683bp+4Q, 0x1.9a15ae0412710439a9b40c2df6c6p+4Q, -0x1.38d1bd49e9af291f59c9f34bbc8fp+4Q, 0x1.6c6cdb14d7fe107edc16c4947af5p+3Q, -0x1.13619aaa119f97b37d6d1c2a2f99p+2Q, 0x1.d56ce1ec874a0c5dd634fb4d532fp-1Q, -0x1.e42907ae7a26468d6ecb1d9b0202p-1Q, 0x1.e52911f9f656640a2404f83c369fp+0Q, -0x1.ee224ef8eb13d4b961d19b800725p+0Q, 0x1.1f26d6223d44cb481a2910c8c507p+0Q, -0x1.5888435f5783628967f9baa292dep-2Q, -0x1.9e45fc4e6f7c960ebee0a7c6f2b4p-7Q, 0x1.dcd2d2ebfb6e400bbcf752c44dedp-5Q, -0x1.93116bc1ac6b7200b82ddbfbe355p-6Q, 0x1.0e01783e342a4693e98c9eddee16p-8Q, 0x1.31f3faa90de9ede16d91478c925bp-12Q, -0x1.f6b0df77a54401ad9bab43898f0dp-13Q, 0x1.f05077a02c3aba8741da976da8a2p-16Q, 0x1.2ec5b9d224e6bceb5db9ee6f77e8p-20Q, -0x1.47f2b0eb68eda8ce48926b183b67p-22Q, 0x1.bcb021bf883a1f92a78fc9e4385p-29Q, 0x1.1bcefd6cfba520ba0473784ac481p-32Q, -0x1.34d97adc52a38a676a55a69541ap-39Q, -0x1.6f2c8c9ca394fbdec6dda2529befp-53Q, 0x1.34e43d9253e6e8975e6c8e7e1076p-60Q, -0x1.352f98f0f2e48db2a203fb3601f4p-81Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.002833198203bf56e8fbb6905c21p-2Q, 0x1.74f145f5180b48bf2521976daf68p-1Q, -0x1.d40722c67b8b2c63d49b5a9b6cadp+2Q, 0x1.2af6f0f464bc571c8b763a8383eap+4Q, -0x1.a43135145799a27dfd1fadf6761p+4Q, 0x1.9a15ae0412710439a9b40c2dd4dbp+4Q, -0x1.38d1bd49e9af291f59c9f34bcde4p+4Q, 0x1.6c6cdb14d7fe107edc16c4953b35p+3Q, -0x1.13619aaa119f97b37d6d1c2c4585p+2Q, 0x1.d56ce1ec874a0c5dd634fb59d6d1p-1Q, -0x1.e42907ae7a26468d6ecb1d9e3f24p-1Q, 0x1.e52911f9f656640a2404f83a2b4fp+0Q, -0x1.ee224ef8eb13d4b961d19b7d1c3bp+0Q, 0x1.1f26d6223d44cb481a2910c6eba2p+0Q, -0x1.5888435f5783628967f9baa03f79p-2Q, -0x1.9e45fc4e6f7c960ebee0a7c398e8p-7Q, 0x1.dcd2d2ebfb6e400bbcf752c0bf7fp-5Q, -0x1.93116bc1ac6b7200b82ddbf8d638p-6Q, 0x1.0e01783e342a4693e98c9edbf33cp-8Q, 0x1.31f3faa90de9ede16d914789626ap-12Q, -0x1.f6b0df77a54401ad9bab438557ddp-13Q, 0x1.f05077a02c3aba8741da9769ad4ep-16Q, 0x1.2ec5b9d224e6bceb5db9ee6cff1dp-20Q, -0x1.47f2b0eb68eda8ce48926b156c9bp-22Q, 0x1.bcb021bf883a1f92a78fc9df6525p-29Q, 0x1.1bcefd6cfba520ba047378483637p-32Q, -0x1.34d97adc52a38a676a55a692601cp-39Q, -0x1.6f2c8c9ca394fbdec6dda2487026p-53Q, 0x1.34e43d9253e6e8975e6c8e7aefefp-60Q, -0x1.352f98f0f2e48db2a203fb32a0f2p-81Q, 0x0p+0Q};
             }
             if constexpr (order == 5) {
-                return {0x0p+0Q, 0x1.e5d8b15d3664d52108fae1119eb3p-1Q, -0x1.e7e4ae8313c9841f6b4ba69959c8p+1Q, 0x1.643947f56174ee22b35087d6e12ep+1Q, 0x1.8bf77730624fb34f058db90d09abp+3Q, -0x1.39575fcf961c0f3da45ce1cc2c7bp+5Q, 0x1.f6657cd6c7e299b7cc89d5ddbefap+5Q, -0x1.2981aaa66ca36b3a94f827b0b8dbp+6Q, 0x1.0cf300079688d85d6be47384ed72p+6Q, -0x1.71528cd9cab137a39829b250a696p+4Q, -0x1.13658826409b41720bd51b25ad91p+6Q, 0x1.5ecf135e336b7c201cd13f369622p+7Q, -0x1.ca8fbd8754dc1920d78e09c343d4p+7Q, 0x1.83a96558c6c07294f0fd7084bf69p+7Q, -0x1.9d91182e0786a78e2338c78e73d6p+6Q, 0x1.818f5ca05f023837d630b0fd1c9bp+4Q, 0x1.4e782cc994094deb15353773c74ap+3Q, -0x1.7fba734a377970e0ae8d81fa7364p+3Q, 0x1.361d7d826bb5b3b3a1616d435b7ap+2Q, -0x1.85fee8307d590ead49f8c8c0db3dp-1Q, -0x1.fcc3205624ce56be678cf8dd8b95p-4Q, 0x1.30d54b861144b0080c77faaf98c5p-4Q, -0x1.4236c7ccc62df6904f17923598dp-7Q, -0x1.6b6d4bcc089eed67f907624e3601p-12Q, 0x1.251cb75a77a65027fa18c44159c1p-13Q, -0x1.7df627db3ed37f55c551bd809c99p-19Q, -0x1.6d7ba0319a17f9c5347fd4990ca2p-23Q, 0x1.047350b843565161f3ac66f52b72p-29Q, 0x1.ecabd0f857c5126fafed07e0ff9fp-41Q, -0x1.035ef08b1273d485ae68801b61a7p-49Q, 0x1.039e900e7fa12bdd9aa0b52e7d7ap-69Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.e5d8b15d3664d52108fae09a8e52p-1Q, -0x1.e7e4ae8313c9841f6b4ba59501e9p+1Q, 0x1.643947f56174ee22b35084254df8p+1Q, 0x1.8bf77730624fb34f058dbb215e6ap+3Q, -0x1.39575fcf961c0f3da45ce2cb7fb1p+5Q, 0x1.f6657cd6c7e299b7cc89d7d3daa3p+5Q, -0x1.2981aaa66ca36b3a94f8297750dp+6Q, 0x1.0cf300079688d85d6be476057064p+6Q, -0x1.71528cd9cab137a39829bbec9ca2p+4Q, -0x1.13658826409b41720bd51a0f2d32p+6Q, 0x1.5ecf135e336b7c201cd13f9f1c7bp+7Q, -0x1.ca8fbd8754dc1920d78e0ace3c5ep+7Q, 0x1.83a96558c6c07294f0fd718cdf26p+7Q, -0x1.9d91182e0786a78e2338c8bf2ff2p+6Q, 0x1.818f5ca05f023837d630b257f2ffp+4Q, 0x1.4e782cc994094deb153537dfc8d9p+3Q, -0x1.7fba734a377970e0ae8d82bc8b81p+3Q, 0x1.361d7d826bb5b3b3a1616de586bdp+2Q, -0x1.85fee8307d590ead49f8c992534dp-1Q, -0x1.fcc3205624ce56be678cf9a5a7bcp-4Q, 0x1.30d54b861144b0080c77fb2ef955p-4Q, -0x1.4236c7ccc62df6904f1792b21926p-7Q, -0x1.6b6d4bcc089eed67f90762e3bff2p-12Q, 0x1.251cb75a77a65027fa18c49d6fe7p-13Q, -0x1.7df627db3ed37f55c551bdd12823p-19Q, -0x1.6d7ba0319a17f9c5347fd4ebc07ap-23Q, 0x1.047350b843565161f3ac671e5f76p-29Q, 0x1.ecabd0f857c5126fafed07e8e831p-41Q, -0x1.035ef08b1273d485ae68801933a9p-49Q, 0x1.039e900e7fa12bdd9aa0b500dd5fp-69Q, 0x0p+0Q};
             }
             if constexpr (order == 6) {
-                return {0x0p+0Q, 0x1.5c435b4994699430de1f0c23d617p+1Q, -0x1.45ad88073e6251792d84632e4f3fp+4Q, 0x1.1ac643e9c99f8dff42b4b524dcf6p+6Q, -0x1.3bcd24e1c22f08a7330d93c59d11p+7Q, 0x1.1132bead650e64e0cc624fab813p+8Q, -0x1.a3321607e359615c22640004ddabp+8Q, 0x1.2bec4ce73b524de840d2af23d04bp+9Q, -0x1.83ddd4224b9abfb64ecabda1d5d5p+9Q, 0x1.b1ad4241d86bedd378c0243ed9a2p+9Q, -0x1.9d7a3218170b28b67328a62c7a74p+9Q, 0x1.5526f87e8214f36e89fc5bb73ce9p+9Q, -0x1.e996857ebd3fd865f8b8b92d1e0ep+8Q, 0x1.186a9a24f3387e74b221163382ebp+8Q, -0x1.4f804f76b6d5b86a618f7579c739p+6Q, -0x1.84954fc1821007c0fd22b5bb0514p+5Q, 0x1.59efa11d2ec6f964630b6ee3dd9dp+6Q, -0x1.dac7ad3b33c95d5f07d9022e2d45p+5Q, 0x1.62078796373e73b5598b789d53cp+4Q, -0x1.88bb023e9f2f98b9b7a5cb3efe82p+1Q, -0x1.04b9160269b89d57d0a514a7e722p+0Q, 0x1.18c6982acbd2cd140bf32c40e2bfp-1Q, -0x1.508ddc9d3ccb43c37b8bf5160a7bp-4Q, -0x1.539386e1415cf5772194f932f5bcp-9Q, 0x1.9eab992a4b9ab37998a475e020b6p-10Q, -0x1.980b92ff814cc556c4aed6edadddp-15Q, -0x1.761c29381edd29e5680cf26d10acp-19Q, 0x1.64e7e2ec4af2d5325d3b1b81e06p-25Q, 0x1.1823b743e4c412fe2e1a19821c84p-35Q, -0x1.623923d3ddbaeed10b04f5b48b46p-44Q, 0x1.6290fa803758e40f0b8255ed89fdp-63Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.5c435b4994699430de1f0bf0f96ep+1Q, -0x1.45ad88073e6251792d84638c28d6p+4Q, 0x1.1ac643e9c99f8dff42b4b5f9e976p+6Q, -0x1.3bcd24e1c22f08a7330d952db5cp+7Q, 0x1.1132bead650e64e0cc6250fd5a4cp+8Q, -0x1.a3321607e359615c22640184890cp+8Q, 0x1.2bec4ce73b524de840d2af975fb7p+9Q, -0x1.83ddd4224b9abfb64ecabd8660acp+9Q, 0x1.b1ad4241d86bedd378c0238858cbp+9Q, -0x1.9d7a3218170b28b67328a4e4a6f8p+9Q, 0x1.5526f87e8214f36e89fc59fbe6b5p+9Q, -0x1.e996857ebd3fd865f8b8b57715d2p+8Q, 0x1.186a9a24f3387e74b22113290d4ap+8Q, -0x1.4f804f76b6d5b86a618f6e232bp+6Q, -0x1.84954fc1821007c0fd22bc06ae8ep+5Q, 0x1.59efa11d2ec6f964630b6fd432d3p+6Q, -0x1.dac7ad3b33c95d5f07d90297e68ap+5Q, 0x1.62078796373e73b5598b78c1554p+4Q, -0x1.88bb023e9f2f98b9b7a5caf3d0d1p+1Q, -0x1.04b9160269b89d57d0a515a32ad5p+0Q, 0x1.18c6982acbd2cd140bf32d2822bbp-1Q, -0x1.508ddc9d3ccb43c37b8bf661b39ap-4Q, -0x1.539386e1415cf5772194fa5cb789p-9Q, 0x1.9eab992a4b9ab37998a4782656d7p-10Q, -0x1.980b92ff814cc556c4aeda05445fp-15Q, -0x1.761c29381edd29e5680cf5367b41p-19Q, 0x1.64e7e2ec4af2d5325d3b1ebf7038p-25Q, 0x1.1823b743e4c412fe2e1a1caf98aep-35Q, -0x1.623923d3ddbaeed10b04fa360d62p-44Q, 0x1.6290fa803758e40f0b825bbc6f28p-63Q, 0x0p+0Q};
             }
             if constexpr (order == 7) {
-                return {0x0p+0Q, 0x1.891443770e9f5b58ca0b8becb52ep+2Q, -0x1.c4b28f7dbecf38e874d341781c95p+5Q, 0x1.d994c46f08417c9c24a36bb24434p+7Q, -0x1.26defe09eb9e312242e5ff410da3p+9Q, 0x1.ddf577c4250f78c0132b7ac736e1p+9Q, -0x1.fd2079b0f3ddb297d55b16fe84bp+9Q, 0x1.36152a2e286cfeac4352523397cdp+9Q, 0x1.d8616a51db368c3df94db95c5c72p+6Q, -0x1.190b42892374c709dd821decb54p+10Q, 0x1.36219b396179567cea598487367ep+11Q, -0x1.eed74001662f7e761e889a73b6ep+11Q, 0x1.31c149450a5e9832b2f7a4322f07p+12Q, -0x1.31807a4d8f7d8b9ec23aba57ce8ep+12Q, 0x1.07e37f0875c28ba98c5ad47ed33fp+12Q, -0x1.9ca0e06fa4e40e6ba99e5e66481ep+11Q, 0x1.192392a49659f5be4af76f76ab89p+11Q, -0x1.28f7ef65a911c2242d46f559ac11p+10Q, 0x1.8ef1182eeb70c3b810abd66139cfp+8Q, -0x1.076216da5c43b27292caed829f7ap+5Q, -0x1.3734a9c9c5014b6b42adc6c9cbep+5Q, 0x1.2e313dce4fbf11c25ec1c482fcb8p+4Q, -0x1.913ecda1e3436af7caa7765fe945p+1Q, -0x1.aba4e0591b35ef78387e98333cf8p-4Q, 0x1.5578ca229685f75ec4d7ad4713cep-4Q, -0x1.f3ff47839e58d032a19fef9f4efp-9Q, -0x1.bd3a12076a4f509f06e41d1d4df9p-13Q, 0x1.29ffe91412a29d368ce3dc6e38c5p-18Q, 0x1.5e7711914b058b73ae87986d7f1ap-28Q, -0x1.267e3f1ece05182094a61971cb39p-36Q, 0x1.26c8d9be624c3d09b4283ff340e2p-54Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.891443770e9f5b58ca0bdbd939d6p+2Q, -0x1.c4b28f7dbecf38e874d3b242d4fbp+5Q, 0x1.d994c46f08417c9c24a3de260d39p+7Q, -0x1.26defe09eb9e312242e62017ceb2p+9Q, 0x1.ddf577c4250f78c0132ae5d7d1cep+9Q, -0x1.fd2079b0f3ddb297d557ffac7fap+9Q, 0x1.36152a2e286cfeac434a875affb8p+9Q, 0x1.d8616a51db368c3df9bbb5de82cep+6Q, -0x1.190b42892374c709dd8c148043fep+10Q, 0x1.36219b396179567cea600ef5a5e7p+11Q, -0x1.eed74001662f7e761e907ef9b166p+11Q, 0x1.31c149450a5e9832b2fbd7c32f38p+12Q, -0x1.31807a4d8f7d8b9ec23e94e23c9ap+12Q, 0x1.07e37f0875c28ba98c5df12ea151p+12Q, -0x1.9ca0e06fa4e40e6ba9a2f070a627p+11Q, 0x1.192392a49659f5be4afa683922a3p+11Q, -0x1.28f7ef65a911c2242d4a04d3586cp+10Q, 0x1.8ef1182eeb70c3b810afe07ad9aep+8Q, -0x1.076216da5c43b27292cd22bcb978p+5Q, -0x1.3734a9c9c5014b6b42b155a6abedp+5Q, 0x1.2e313dce4fbf11c25ec52c766e83p+4Q, -0x1.913ecda1e3436af7caac068805f8p+1Q, -0x1.aba4e0591b35ef78388396d8949ap-4Q, 0x1.5578ca229685f75ec4dbb7fb72b6p-4Q, -0x1.f3ff47839e58d032a1a624c1f604p-9Q, -0x1.bd3a12076a4f509f06e99bb28599p-13Q, 0x1.29ffe91412a29d368ce7b0895443p-18Q, 0x1.5e7711914b058b73ae8c4ed370dp-28Q, -0x1.267e3f1ece05182094aa29382cf7p-36Q, 0x1.26c8d9be624c3d09b42c989d403cp-54Q, 0x0p+0Q};
             }
             if constexpr (order == 8) {
-                return {0x0p+0Q, 0x1.1c06072fbf26f358c9f18045c124p+3Q, -0x1.65d998749f19f3f527890dd9f349p+6Q, 0x1.9d8978b96f57f154ef9e43eaf80dp+8Q, -0x1.24c8d76a7f36d7089e403e85e9fap+10Q, 0x1.21d479bc00697b14d91b67255a8bp+11Q, -0x1.bbc006c9393532c76b5f0b5bef94p+11Q, 0x1.2211c4425df9c2e46c413666253fp+12Q, -0x1.5c64ff1d8bf677ab09ae01e0a5e1p+12Q, 0x1.845a35a3158347c96bec7865086bp+12Q, -0x1.87e6df0fbf8ef42fd53aa9972193p+12Q, 0x1.6504110de640c4682cbbe6b8a6e7p+12Q, -0x1.2b9aa02be2b35409ccb01b40da2ap+12Q, 0x1.cebcfb329a57eadc95a91a00a9a1p+11Q, -0x1.3e375c669dabfd4de918596ad52p+11Q, 0x1.7d70c67fe8973e080c2d05792b11p+10Q, -0x1.8fd6874952e8a903dad0f0ef170dp+9Q, 0x1.57b6f4096f1cf0152665b7fd82f9p+8Q, -0x1.3e2c004c73161017d20213f7c5c1p+6Q, -0x1.f1e0f66437531ffa2878e9c69067p+4Q, 0x1.39f676c7227564daf7250a1ee97dp+5Q, -0x1.07f7de36ead717df75680da7494ep+4Q, 0x1.6eaf02b444bc4ce468426b7d5bcep+1Q, 0x1.f8896c7b27aea8a0c13c77300d42p-4Q, -0x1.b78e4a3636f77d36046090a9c9b3p-4Q, 0x1.faf293c65fc88bb39eaf30523dfep-8Q, 0x1.a6b604defe6a94f42a0086be2586p-12Q, -0x1.9886be2865e4c650159b3c14bf08p-17Q, -0x1.7c0bde2d4dd50659d8e7bf0799bbp-26Q, 0x1.90aca39ea2e8ac3870c8fe9456dap-34Q, -0x1.91166efa6d0a92bc7a2ca99b7dfbp-51Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.1c06072fbf26f358c9f078f98565p+3Q, -0x1.65d998749f19f3f52787d2ac7bd1p+6Q, 0x1.9d8978b96f57f154ef9ce52c7bdfp+8Q, -0x1.24c8d76a7f36d7089e3f4940c827p+10Q, 0x1.21d479bc00697b14d91a6dd4bcabp+11Q, -0x1.bbc006c9393532c76b5d7283eb2fp+11Q, 0x1.2211c4425df9c2e46c401315e702p+12Q, -0x1.5c64ff1d8bf677ab09ac8c8005b4p+12Q, 0x1.845a35a3158347c96beac73413ep+12Q, -0x1.87e6df0fbf8ef42fd538df2c44e6p+12Q, 0x1.6504110de640c4682cba264cf46ap+12Q, -0x1.2b9aa02be2b35409ccae86a8991fp+12Q, 0x1.cebcfb329a57eadc95a6866f02e1p+11Q, -0x1.3e375c669dabfd4de916796f2023p+11Q, 0x1.7d70c67fe8973e080c2a8eb7f182p+10Q, -0x1.8fd6874952e8a903dace07633bccp+9Q, 0x1.57b6f4096f1cf0152662dc88de7ap+8Q, -0x1.3e2c004c73161017d1fe47d49586p+6Q, -0x1.f1e0f66437531ffa287a43716481p+4Q, 0x1.39f676c7227564daf7244ac826e7p+5Q, -0x1.07f7de36ead717df75674d143f33p+4Q, 0x1.6eaf02b444bc4ce4684168c04e9ap+1Q, 0x1.f8896c7b27aea8a0c13b638bec5cp-4Q, -0x1.b78e4a3636f77d36045fd051d0a7p-4Q, 0x1.faf293c65fc88bb39eaf07f0c833p-8Q, 0x1.a6b604defe6a94f42a0056ad171bp-12Q, -0x1.9886be2865e4c650159b7d4d95b1p-17Q, -0x1.7c0bde2d4dd50659d8e873b48d0ap-26Q, 0x1.90aca39ea2e8ac3870ca13b1a564p-34Q, -0x1.91166efa6d0a92bc7a2e9704d452p-51Q, 0x0p+0Q};
             }
             if constexpr (order == 9) {
-                return {0x0p+0Q, 0x1.58e7df6732419db59e963fb33d94p+3Q, -0x1.c53a29616fa380817d7988f924b1p+6Q, 0x1.0cc18d57a1a1fb48e1055941c825p+9Q, -0x1.7c92fc1b6ca3895680be8b3bffe9p+10Q, 0x1.6a1945d20b68d8baff3e866c5cdap+11Q, -0x1.fab771c0e1baf24e2c87e6ba962ap+11Q, 0x1.254298acbb2d449a7b36affa5b18p+12Q, -0x1.407f9dc95f9b1203f97a18e79578p+12Q, 0x1.53233c63dd8a7f18f09c08d93b73p+12Q, -0x1.3b528b34539979362d85428f478fp+12Q, 0x1.e2ea2797d25e54507eaadbdfe8c3p+11Q, -0x1.3d6169dd11c9bca321155575b38p+11Q, 0x1.75fce5d641404560c110d19350b3p+10Q, -0x1.2b5b50127f9f56d44e8ab9654e78p+9Q, -0x1.18e0518b142ec5c99d4cfb0c02dep+7Q, 0x1.ed1ee257a974ab35fe9854c84beep+8Q, -0x1.f5a5a8d8a9b3c073ca74b7aa8b3fp+8Q, 0x1.920c943e9e1a266133c5fbd7d496p+8Q, -0x1.22c1385412c45fef7248020243cfp+8Q, 0x1.4b1ba13f6628b1dd44c07737a72dp+7Q, -0x1.ec876f34dee07503da6d353b7ff9p+5Q, 0x1.641261f15a2bc3d54eafcffb8c39p+3Q, 0x1.3bac7fcb6881fd2d747e22c3e33ap-1Q, -0x1.3ae0db5ff49e0fda9ef3c1ee8d61p-1Q, 0x1.0ba445bef297ba3c0908ff2bb4d9p-4Q, 0x1.c3804abda5b0efa9daf29b604e6cp-9Q, -0x1.3c78fba89f7e4dd2da6247dd38d1p-13Q, -0x1.6e90a45b17e11834e3133934b3a2p-22Q, 0x1.34c398a5dd4857b9fcc96bbdccaep-29Q, -0x1.351bbccd566d5b56e0d97b1d8b32p-45Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.58e7df6732419db59e9ac42f9ab1p+3Q, -0x1.c53a29616fa380817d7f5e347aefp+6Q, 0x1.0cc18d57a1a1fb48e108cac3a066p+9Q, -0x1.7c92fc1b6ca3895680c38212861fp+10Q, 0x1.6a1945d20b68d8baff4381a817e2p+11Q, -0x1.fab771c0e1baf24e2c8f95c4199fp+11Q, 0x1.254298acbb2d449a7b3bb526f729p+12Q, -0x1.407f9dc95f9b1203f980178aa4a8p+12Q, 0x1.53233c63dd8a7f18f0a2b3af5ccep+12Q, -0x1.3b528b34539979362d8c0e80e80ep+12Q, 0x1.e2ea2797d25e54507eb78c335f71p+11Q, -0x1.3d6169dd11c9bca3212058149b0bp+11Q, 0x1.75fce5d641404560c1229131d8bdp+10Q, -0x1.2b5b50127f9f56d44ea4f01f61c9p+9Q, -0x1.18e0518b142ec5c99d05ce213217p+7Q, 0x1.ed1ee257a974ab35fe81e878de48p+8Q, -0x1.f5a5a8d8a9b3c073ca67ee8615b8p+8Q, 0x1.920c943e9e1a266133bfad52e46dp+8Q, -0x1.22c1385412c45fef72454e0ef403p+8Q, 0x1.4b1ba13f6628b1dd44be57f24352p+7Q, -0x1.ec876f34dee07503da6a5d0e4af4p+5Q, 0x1.641261f15a2bc3d54eada0d94bc5p+3Q, 0x1.3bac7fcb6881fd2d747aef7d1cc5p-1Q, -0x1.3ae0db5ff49e0fda9ef09cfb9b34p-1Q, 0x1.0ba445bef297ba3c0905b698e9c6p-4Q, 0x1.c3804abda5b0efa9daece8d22468p-9Q, -0x1.3c78fba89f7e4dd2da5d2b0f1ab2p-13Q, -0x1.6e90a45b17e11834e30d4035587ep-22Q, 0x1.34c398a5dd4857b9fcc2b9b3ec09p-29Q, -0x1.351bbccd566d5b56e0d110fac029p-45Q, 0x0p+0Q};
             }
             if constexpr (order == 10) {
-                return {0x0p+0Q, 0x1.0cfd9304e9d0e9e89a58da63527ap+3Q, -0x1.68c00ea69764cc01a57e59f4b6b3p+6Q, 0x1.b4a63a85c6a121d6db74c511805bp+8Q, -0x1.3c4fcf304828edf088a1b16ea07fp+10Q, 0x1.35efe9ab816f6ad2ce45644d2fd8p+11Q, -0x1.c3872b5b6dcd2512d768b35e0756p+11Q, 0x1.1261ac83f506bff0f39595d045e8p+12Q, -0x1.39e1fa3f00833a2dd6cf3f9d927bp+12Q, 0x1.5e4c9d364466ef749b997ff3a6cp+12Q, -0x1.6b72e41a84905cceda4b9c52f497p+12Q, 0x1.578fd4c404248dabc97584331c2p+12Q, -0x1.30faf3648505cdf5f67d9aa16b7dp+12Q, 0x1.0174ad7c898217c9040304ce9297p+12Q, -0x1.942bc49f2f52a22fa3fb0a0c2104p+11Q, 0x1.25cbc7992fd63cf3174ccf32c535p+11Q, -0x1.914caac5676309ecc707d67c3b11p+10Q, 0x1.f93f030387c4d019b699660bf6c3p+9Q, -0x1.1b4f5dfc787bbc3226392268b2fbp+9Q, 0x1.1df01b8a36a8b0e740bc1ec53a5bp+8Q, -0x1.048db6f3ab7c1cc8ce55d6b0a75fp+7Q, 0x1.730bcb9c58bfc20d60d07c0998acp+5Q, -0x1.09b56b87c1c7fb7baefa593d3ee2p+3Q, -0x1.4fb833b30fa7eeef6a7e9c60d9dap+0Q, 0x1.e38e1048601a60cbcefd6c477b1bp-1Q, -0x1.ee07e572041f738c257ecf9ffa9bp-4Q, -0x1.913ced3c0164b56d324da52a041bp-8Q, 0x1.0726b83c4032bf81b9b5324fe2d4p-11Q, 0x1.2751c6763466bbc5b3627d689424p-20Q, -0x1.00ceb77e39cabc22cbb16a695fdap-26Q, 0x1.0123085a8910152fac9e37f89667p-41Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.0cfd9304e9d0e9e89a508d967352p+3Q, -0x1.68c00ea69764cc01a573447ef7eep+6Q, 0x1.b4a63a85c6a121d6db6758f94115p+8Q, -0x1.3c4fcf304828edf08897e340df25p+10Q, 0x1.35efe9ab816f6ad2ce3b95243287p+11Q, -0x1.c3872b5b6dcd2512d759e390543cp+11Q, 0x1.1261ac83f506bff0f38c31198cefp+12Q, -0x1.39e1fa3f00833a2dd6c432f2edcep+12Q, 0x1.5e4c9d364466ef749b8d0d88979bp+12Q, -0x1.6b72e41a84905cceda3e7fc6c066p+12Q, 0x1.578fd4c404248dabc968b7c529b9p+12Q, -0x1.30faf3648505cdf5f671e0ae34fdp+12Q, 0x1.0174ad7c898217c903f8f07741efp+12Q, -0x1.942bc49f2f52a22fa3eae80252dcp+11Q, 0x1.25cbc7992fd63cf31740b115daf5p+11Q, -0x1.914caac5676309ecc6f6c550d8ebp+10Q, 0x1.f93f030387c4d019b6838cf24389p+9Q, -0x1.1b4f5dfc787bbc32262ca3f167bep+9Q, 0x1.1df01b8a36a8b0e740af0c5b60a7p+8Q, -0x1.048db6f3ab7c1cc8ce49930b812dp+7Q, 0x1.730bcb9c58bfc20d60bef0471523p+5Q, -0x1.09b56b87c1c7fb7baeed74ce6cdbp+3Q, -0x1.4fb833b30fa7eeef6a7358348b92p+0Q, 0x1.e38e1048601a60cbceead8c786b8p-1Q, -0x1.ee07e572041f738c256c5953b0d7p-4Q, -0x1.913ced3c0164b56d323de7f36c57p-8Q, 0x1.0726b83c4032bf81b9ad0141e709p-11Q, 0x1.2751c6763466bbc5b359801c4ca6p-20Q, -0x1.00ceb77e39cabc22cbab1770a0b7p-26Q, 0x1.0123085a8910152fac9990b7a672p-41Q, 0x0p+0Q};
             }
             if constexpr (order == 11) {
-                return {0x0p+0Q, 0x1.6ddd33f198eb3c96ba063e358bd1p+2Q, -0x1.ef9ef6f596ce44132c400459330bp+5Q, 0x1.2bec86422c72fb4a90434380b422p+8Q, -0x1.ab3138ae63b3c1e29f0289d542dap+9Q, 0x1.90171accf1ae92cfd9a8b825cb23p+10Q, -0x1.0b8279e6381aa2b741ba53014abbp+11Q, 0x1.21c7cbc3a51f50320f0eba7f41fcp+11Q, -0x1.3291c6bd3630cafeef000c3ad649p+11Q, 0x1.52187d4f278255d9064abfc39513p+11Q, -0x1.5764b21031af003ebeb2fc812432p+11Q, 0x1.2d82b77758b7aad296d2a3297f76p+11Q, -0x1.efcf6fd97e7509c927947ebcfe7bp+10Q, 0x1.96b834131566dc9e05fa0d23f1dbp+10Q, -0x1.34d67cf0a39ad9453ec607f4238bp+10Q, 0x1.9aafba6f0ff85ebebf990bae7248p+9Q, -0x1.002f1ef9723b265f845856382322p+9Q, 0x1.378956144d5be0ceae49930a1c88p+8Q, -0x1.48f6827b3eeb52ea5b26c2ed113p+7Q, 0x1.17de886be7cb3ac887b94bba647bp+6Q, -0x1.abd1c377daaf4123bc220ca55b7bp+4Q, 0x1.18836fa0aedf116ff461c07e603dp+3Q, -0x1.72b11631904f6bd3fce02c59a632p-2Q, -0x1.93c736e0c44c0da3f44d1f9fb885p+0Q, 0x1.74105b4ecfea6c16422a97b509cfp-1Q, -0x1.a9382883de207a4dbe506bf11d8fp-4Q, -0x1.8ee02bc822713114de4c636e81aep-9Q, 0x1.b89c5ecf7a7b773088b92afebabbp-11Q, 0x1.5051009d42a4549b60d53bde7219p-19Q, -0x1.a9ba33acc416babe2770ada65c3ap-25Q, 0x1.aa6a7d0ba81031b3c996c62600c5p-39Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.6ddd33f198eb3c96ba1c54f670fdp+2Q, -0x1.ef9ef6f596ce44132c5dde1777d4p+5Q, 0x1.2bec86422c72fb4a905555a96936p+8Q, -0x1.ab3138ae63b3c1e29f1c692c8b8ep+9Q, 0x1.90171accf1ae92cfd9c146fd2557p+10Q, -0x1.0b8279e6381aa2b741cb2d9796cbp+11Q, 0x1.21c7cbc3a51f50320f21aa56334ap+11Q, -0x1.3291c6bd3630cafeef14937244cfp+11Q, 0x1.52187d4f278255d90661622e17d1p+11Q, -0x1.5764b21031af003ebeca03a2b0b9p+11Q, 0x1.2d82b77758b7aad296e73eef7d7bp+11Q, -0x1.efcf6fd97e7509c927b7122c5c13p+10Q, 0x1.96b834131566dc9e06167e63c7d4p+10Q, -0x1.34d67cf0a39ad9453edbb75a25c5p+10Q, 0x1.9aafba6f0ff85ebebfb694ebd422p+9Q, -0x1.002f1ef9723b265f846b3c2332f6p+9Q, 0x1.378956144d5be0ceae60b1a0aa28p+8Q, -0x1.48f6827b3eeb52ea5b3fa287d164p+7Q, 0x1.17de886be7cb3ac887cff35422aap+6Q, -0x1.abd1c377daaf4123bc47a29397f4p+4Q, 0x1.18836fa0aedf116ff47c167f808p+3Q, -0x1.72b11631904f6bd3fd5a823e34cp-2Q, -0x1.93c736e0c44c0da3f45cfa30760fp+0Q, 0x1.74105b4ecfea6c16423bc348f8fp-1Q, -0x1.a9382883de207a4dbe62c7de34c2p-4Q, -0x1.8ee02bc822713114de66688f8544p-9Q, 0x1.b89c5ecf7a7b773088c639b3a53ap-11Q, 0x1.5051009d42a4549b60dc1a4ffdc1p-19Q, -0x1.a9ba33acc416babe2777385baddfp-25Q, 0x1.aa6a7d0ba81031b3c9971794d3cep-39Q, 0x0p+0Q};
             }
             if constexpr (order == 12) {
-                return {0x0p+0Q, 0x1.7e688b7526a774b7675960f4a94cp+1Q, -0x1.044f66dd0bb355e9e8503e18e935p+5Q, 0x1.39d2780b0ad2f5c13050620039bcp+7Q, -0x1.b63bb8898df0968b0e8fec1fd9a7p+8Q, 0x1.86b367123a2139a592c1528e8f55p+9Q, -0x1.d8001c1817ddf23795fa181f861ep+9Q, 0x1.b397f071da3115c2852f6422a8c8p+9Q, -0x1.9ca191acc971e01d773c5479fb8dp+9Q, 0x1.d28d7edb2db091286aa35eb84214p+9Q, -0x1.daeab5bf793f0a5db1ed52776228p+9Q, 0x1.738e37d47cc21d48d43df1f6d78p+9Q, -0x1.0785a3e74df59d2028a07275bacep+9Q, 0x1.a556a97ba734840eabbaaf9977bap+8Q, -0x1.320671c41025d2eac6cd6f7d0dadp+8Q, 0x1.33661041ead74be91556b7ad619ap+7Q, -0x1.d86506577d5080199f42262a920cp+5Q, 0x1.9ebe0657238551a24be276081da8p+4Q, -0x1.ec9ee9042933244440176ee46c34p-1Q, -0x1.1034340999c868fff4dcb8a37e58p+4Q, 0x1.04d7524f6a9fff23ce8e27e29df3p+4Q, -0x1.2fcc89fd04e88d59c73ed84bf7b4p+3Q, 0x1.7c24bc012bffc7d1e2142c729735p+2Q, -0x1.c84c145900f77b34a48b3cd01e16p+1Q, 0x1.57bccbd9e4fcea0faae95542b1dcp+0Q, -0x1.d81daf1af068d1091e33cdbbae6bp-3Q, -0x1.20f9f72def1de8f22bf9f5b255c4p-13Q, 0x1.c2f2ad7e016f5272ff0429610dd4p-9Q, 0x1.baf6705e59cac328415a41de4538p-17Q, -0x1.ae94eeab2dbd4d40eaa80ab9debep-22Q, 0x1.af91281d9938911a632b5cd0ed85p-35Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.7e688b7526a774b76724ba13a96cp+1Q, -0x1.044f66dd0bb355e9e82c72d5eaffp+5Q, 0x1.39d2780b0ad2f5c130250e42d893p+7Q, -0x1.b63bb8898df0968b0e5291c5adf1p+8Q, 0x1.86b367123a2139a59288ccfca3dfp+9Q, -0x1.d8001c1817ddf23795b1149354dfp+9Q, 0x1.b397f071da3115c284e47fbefa66p+9Q, -0x1.9ca191acc971e01d76f080b3e85ap+9Q, 0x1.d28d7edb2db091286a502e3d1491p+9Q, -0x1.daeab5bf793f0a5db198f7c1b01p+9Q, 0x1.738e37d47cc21d48d3f57dfe7cfep+9Q, -0x1.0785a3e74df59d20286619983999p+9Q, 0x1.a556a97ba734840eab5a765f294cp+8Q, -0x1.320671c41025d2eac683ee371196p+8Q, 0x1.33661041ead74be914f62376ca64p+7Q, -0x1.d86506577d5080199e51f7260b6fp+5Q, 0x1.9ebe0657238551a24ab6c6c0e20bp+4Q, -0x1.ec9ee904293324442bcbed481925p-1Q, -0x1.1034340999c868fff5238312a8aap+4Q, 0x1.04d7524f6a9fff23ceab9523e19cp+4Q, -0x1.2fcc89fd04e88d59c75667d7c4bbp+3Q, 0x1.7c24bc012bffc7d1e21de0348c52p+2Q, -0x1.c84c145900f77b34a4876818624fp+1Q, 0x1.57bccbd9e4fcea0faae4ccf7a2f9p+0Q, -0x1.d81daf1af068d1091e32e8f2fcc9p-3Q, -0x1.20f9f72def1de8f22a005f73e8a4p-13Q, 0x1.c2f2ad7e016f5272ff115101365p-9Q, 0x1.baf6705e59cac3284164d29d2adfp-17Q, -0x1.ae94eeab2dbd4d40eac4360abe26p-22Q, 0x1.af91281d9938911a63573a1c8a3ap-35Q, 0x0p+0Q};
             }
             if constexpr (order == 13) {
-                return {0x0p+0Q, 0x1.a308ef1d1680575961469f8667e2p-1Q, -0x1.1df37cb20ef6cd526ba94f6e5b81p+3Q, 0x1.5a47cc2daffcb2cf20f274a5d38ap+5Q, -0x1.e7cc32d4c7f05cc178a022548d5cp+6Q, 0x1.ba5aa6f58d154790fde028986d8dp+7Q, -0x1.137ebe2556bb5c31390698cc2046p+8Q, 0x1.07f96c27b79ba1c76a43166f429dp+8Q, -0x1.f176d6c3151d8ca65c15ab30195bp+7Q, 0x1.0c09a0e0bcb9ff8d7d5939eac1c2p+8Q, -0x1.12bf0f34a9a5500b54a8cb7aa2b3p+8Q, 0x1.de16d55d65d2bb62ec748b786b23p+7Q, -0x1.8c7b496d3d3fd8274ea834d98fd2p+7Q, 0x1.56592506626bc28d37a6f5de979bp+7Q, -0x1.13d919c9693b2e85ee3bb9c46203p+7Q, 0x1.8b69de5718a09e2e84dbb4686bcep+6Q, -0x1.15b78c90e783729339c279a7a26bp+6Q, 0x1.8188b8db550fea388993af5f214fp+5Q, -0x1.e03c011f666ac66011ab6c26ae29p+4Q, 0x1.12ed8b36e986458009c1cf96319ap+4Q, -0x1.36a5b057bc26ecf63126b2eacd51p+3Q, 0x1.3d2641cf67e8fbde6d1c40fa7b62p+2Q, -0x1.11ef148707dfa11f55a24428d5aap+1Q, 0x1.c294da23fe29fd37f9b451eef74cp-1Q, -0x1.4f57e7e05e818e7ff01d8a0db422p-2Q, 0x1.1ebd9964081cf6e9a358f38d567ap-4Q, 0x1.367917f76eee2f07742561edeafcp-14Q, -0x1.fdd37749c94d91b95e4c419dae2dp-10Q, -0x1.0fc0733cbc7d657bb2162af22ff6p-22Q, 0x1.f945fb653cfda9182e56ec03c70ep-22Q, -0x1.fb1bcfae6e46d13bafa847e0d908p-34Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.a308ef1d16805759614e47ced45fp-1Q, -0x1.1df37cb20ef6cd526bae886688ccp+3Q, 0x1.5a47cc2daffcb2cf20f8cbe23f9dp+5Q, -0x1.e7cc32d4c7f05cc178a92423af38p+6Q, 0x1.ba5aa6f58d154790fde87c08c1abp+7Q, -0x1.137ebe2556bb5c31390bfbcc3555p+8Q, 0x1.07f96c27b79ba1c76a48900fad0dp+8Q, -0x1.f176d6c3151d8ca65c2069cc8ba9p+7Q, 0x1.0c09a0e0bcb9ff8d7d5ef1548dd1p+8Q, -0x1.12bf0f34a9a5500b54ae9f341239p+8Q, 0x1.de16d55d65d2bb62ec7f100c7235p+7Q, -0x1.8c7b496d3d3fd8274eb146a1b265p+7Q, 0x1.56592506626bc28d37aec7a2a08bp+7Q, -0x1.13d919c9693b2e85ee4209bf711ep+7Q, 0x1.8b69de5718a09e2e84e51d955579p+6Q, -0x1.15b78c90e783729339c94d803f63p+6Q, 0x1.8188b8db550fea38899d2489ef66p+5Q, -0x1.e03c011f666ac66011b7609652a9p+4Q, 0x1.12ed8b36e986458009c8fb08c63dp+4Q, -0x1.36a5b057bc26ecf6312ef4c8aa89p+3Q, 0x1.3d2641cf67e8fbde6d24a0c08316p+2Q, -0x1.11ef148707dfa11f55a9bad8158fp+1Q, 0x1.c294da23fe29fd37f9c13ab439f3p-1Q, -0x1.4f57e7e05e818e7ff02709327119p-2Q, 0x1.1ebd9964081cf6e9a360b8a8d058p-4Q, 0x1.367917f76eee2f0773ffda2dee7cp-14Q, -0x1.fdd37749c94d91b95e5811e014fcp-10Q, -0x1.0fc0733cbc7d657bb2812f3ed59dp-22Q, 0x1.f945fb653cfda9182e6054d0438ep-22Q, -0x1.fb1bcfae6e46d13bafafa99aa27p-34Q, 0x0p+0Q};
             }
             if constexpr (order == 14) {
-                return {0x0p+0Q, 0x1.74ef139ad4e11f00f66e50f0812ap-3Q, -0x1.fd9d32fdef73fc52b4e1aac15ce8p+0Q, 0x1.3320f17be8b7073381f61db6e694p+3Q, -0x1.a9e31dbd98dd09635b204c104094p+4Q, 0x1.73dbdd38a87f5064434afb97d3afp+5Q, -0x1.aa50f206f25c72a99ccb3ca40e39p+5Q, 0x1.5e48ac9c2f1f1eff351bab98be85p+5Q, -0x1.20d7a78e95ecf57e7aeb50618786p+5Q, 0x1.4350b94e5aa2da50e62a1b36016ep+5Q, -0x1.5499ff05228ddd2807d9b6ef1056p+5Q, 0x1.0d8c7214ffee0a1235c0b7c3c0bap+5Q, -0x1.8fe88996cfa9a5515805a5fa2aadp+4Q, 0x1.63da6bffb7322ee61ea230916038p+4Q, -0x1.24223f5c1b9d9506d6c2601299dfp+4Q, 0x1.7851e19176715ec2bb51da095d1ap+3Q, -0x1.e4fd178fcd0ef2f7356543216bcep+2Q, 0x1.610a439acb28979c59046810bc68p+2Q, -0x1.ae4c3e147b71c29486543afa4302p+1Q, 0x1.a6fe28ab7ffa991086da6716cc39p+0Q, -0x1.ccc920f98175dd579809ace45452p-1Q, 0x1.f9389387bff6b354c94c19c46a5ap-2Q, -0x1.8612de961fd0228a7f6974df4498p-3Q, 0x1.fd43fc0e7883ee43ba9b27c30441p-5Q, -0x1.aafa1e0c4a86f88db623dcf8b499p-6Q, 0x1.b638737fa8e8eebd49a0e1375a7p-8Q, 0x1.071682a1f5057e2143bccc924ee3p-11Q, -0x1.a84c3f530239b63f7db3d411d854p-12Q, 0x1.a20c2374a0f67000161244836cf3p-18Q, 0x1.e7f1c0adda0f62adb6884d961058p-23Q, -0x1.eb089a4058efe658e6fb3c8b8fp-34Q, 0x0p+0Q};
+                return {0x0p+0Q, 0x1.74ef139ad4e11f00f65daa8820cdp-3Q, -0x1.fd9d32fdef73fc52b4caeb648516p+0Q, 0x1.3320f17be8b7073381e865362afep+3Q, -0x1.a9e31dbd98dd09635b0d379485c8p+4Q, 0x1.73dbdd38a87f5064433a350c721dp+5Q, -0x1.aa50f206f25c72a99cb7b1dfa7d2p+5Q, 0x1.5e48ac9c2f1f1eff350b14cb6a0cp+5Q, -0x1.20d7a78e95ecf57e7add31db3fd2p+5Q, 0x1.4350b94e5aa2da50e61a74e27b2cp+5Q, -0x1.5499ff05228ddd2807c95d8259cp+5Q, 0x1.0d8c7214ffee0a1235b3874b3a3ap+5Q, -0x1.8fe88996cfa9a55157f19af30b98p+4Q, 0x1.63da6bffb7322ee61e908c187b83p+4Q, -0x1.24223f5c1b9d9506d6b401adee8dp+4Q, 0x1.7851e19176715ec2bb3ef2e77d74p+3Q, -0x1.e4fd178fcd0ef2f7354c8299da37p+2Q, 0x1.610a439acb28979c58f2b0d330cdp+2Q, -0x1.ae4c3e147b71c294863ea12a0857p+1Q, 0x1.a6fe28ab7ffa991086c47e322a6dp+0Q, -0x1.ccc920f98175dd5797f1c22d8029p-1Q, 0x1.f9389387bff6b354c93278385205p-2Q, -0x1.8612de961fd0228a7f5532d1edd2p-3Q, 0x1.fd43fc0e7883ee43ba7f30ad9465p-5Q, -0x1.aafa1e0c4a86f88db60d4f1fa17bp-6Q, 0x1.b638737fa8e8eebd498a75e7c49cp-8Q, 0x1.071682a1f5057e2143b4d72fc7c5p-11Q, -0x1.a84c3f530239b63f7da26929d4ffp-12Q, 0x1.a20c2374a0f6700016084886c2a8p-18Q, 0x1.e7f1c0adda0f62adb67917e7d654p-23Q, -0x1.eb089a4058efe658e6efa5db9e34p-34Q, 0x0p+0Q};
             }
             if constexpr (order == 15) {
-                return {0x0p+0Q, 0x1.31c729360063e0149d5c21a7efcfp-6Q, -0x1.a21aa8a66a6833da58113cf2bbfap-3Q, 0x1.f656a46fa2a9169e56d7dc88f3edp-1Q, -0x1.589b4fca92a9f10523315f53d228p+1Q, 0x1.25049558932c1a7bf948af8c4d53p+2Q, -0x1.3b0f087615a2680943285adb90b5p+2Q, 0x1.bed87f332745bf792ba1df447904p+1Q, -0x1.37fe75fa2aa3b693bb4d2b4c5752p+1Q, 0x1.75c34ae38a11fc314406fb081d96p+1Q, -0x1.9f32b219f201f09e837dabeb3924p+1Q, 0x1.2a50b5ebe798e437ef1f44157963p+1Q, -0x1.80aff2523d4b3342a82c358ca6abp+0Q, 0x1.71f9af43c19f0952a4d93db93c54p+0Q, -0x1.40d21595459cbd8977223938b804p+0Q, 0x1.6edc3b8de7cbccef39a51cdb458bp-1Q, -0x1.abb5cf29e076b1f30f2dbef2decbp-2Q, 0x1.5fdcb9c5e1f87c285afdd98f767dp-2Q, -0x1.af4e9b9242255620df43c5f22d7fp-3Q, 0x1.57b33e4d63cb5298c708e6fd316dp-4Q, -0x1.736294d370dec79efb385dfdd9c2p-5Q, 0x1.e1a61d7964668ec603c20655891bp-6Q, -0x1.38138139d6cd8275efff1464190ap-7Q, 0x1.a99b874715d59140bd38f0c805c4p-10Q, -0x1.191ada841d111d8ae180fd0e9563p-10Q, 0x1.44a23a1750afa85a3000e1c75486p-12Q, 0x1.4db128e094987961ef3da6b416efp-13Q, -0x1.2cad37f3dbf9e7a2353f8dcbd256p-14Q, 0x1.f38c667f694821291da05561f948p-19Q, 0x1.c870773604d02f72b6510873557cp-24Q, -0x1.cdd01a024c710ef11bd7cd0b9b3cp-34Q, -0x0p+0Q};
+                return {0x0p+0Q, 0x1.31c729360063e0149d619e7c5659p-6Q, -0x1.a21aa8a66a6833da5818bdb00dc4p-3Q, 0x1.f656a46fa2a9169e56e0e1915e67p-1Q, -0x1.589b4fca92a9f10523379245a6fbp+1Q, 0x1.25049558932c1a7bf94dfb345bd9p+2Q, -0x1.3b0f087615a26809432e1d6e01c8p+2Q, 0x1.bed87f332745bf792baa46fb22d3p+1Q, -0x1.37fe75fa2aa3b693bb533ebc90ap+1Q, 0x1.75c34ae38a11fc31440e21813692p+1Q, -0x1.9f32b219f201f09e83858382dcccp+1Q, 0x1.2a50b5ebe798e437ef2503085768p+1Q, -0x1.80aff2523d4b3342a833db6031p+0Q, 0x1.71f9af43c19f0952a4e07472578p+0Q, -0x1.40d21595459cbd897728656ded6bp+0Q, 0x1.6edc3b8de7cbccef39ac5c5b8452p-1Q, -0x1.abb5cf29e076b1f30f36686df3b2p-2Q, 0x1.5fdcb9c5e1f87c285b04c2fd8053p-2Q, -0x1.af4e9b9242255620df4c3ab9bf57p-3Q, 0x1.57b33e4d63cb5298c7100384e3b2p-4Q, -0x1.736294d370dec79efb4014a700a8p-5Q, 0x1.e1a61d7964668ec603cb9aadd499p-6Q, -0x1.38138139d6cd8275f0059b0302fbp-7Q, 0x1.a99b874715d59140bd445bce9797p-10Q, -0x1.191ada841d111d8ae1875d5194c5p-10Q, 0x1.44a23a1750afa85a30082caf581dp-12Q, 0x1.4db128e094987961ef4278d6a462p-13Q, -0x1.2cad37f3dbf9e7a235442f3e067dp-14Q, 0x1.f38c667f694821291da674a42ae8p-19Q, 0x1.c870773604d02f72b6568dfdd8eep-24Q, -0x1.cdd01a024c710ef11bdc57da89cfp-34Q, 0x0p+0Q};
             }
         }
         #endif
+        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
+            if constexpr (order == 0) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000171316851323746428212831421306300113678607875446348503559419927437918383967"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0361088272946006985912064934900062644165629414989774122809757345902866027938"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.488256992843695840962159179639502910381980307460695354580458818691887940645"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.769737672515207083007430504821028844267689308307112651993923296421178108389"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.453126925329274055451166333557401859659406793270554665033541123983449765432"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.256628058814639987338137180313733199002175042843789042052759470470604205726"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.163454122854003496557302427492278171149085655394974230532183221080254700021"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.107723422859916997108276817161022290367504837432994030942098049009089713930"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0649318249233011704784968686914491012172054359333812436767935404371230620232"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0326435377329051629426715185593256884476167946008041064239605220708580188240"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0127409361375573448882342299469851670195888311206647480453026814799719677344"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00352196549620161398967203337357383200834551341224048951969904909167613097889"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000534217142003219306131911092756991844459258563640870926150016500754364314332"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000405890411165595317643619001506764641287318490078309353140855497110673976431"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000498095041023299888778042223185543062245836773367960445465000704315159966296"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000151266310013612774856135240041061222014350088021428301604611262734516728901"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000196962302501772214722461685124074719608921063431828230431618407481183902342"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000307419811865464641941041529634159778226115669718094511609235500455794645613"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000146711526898488736937232395914501861484051305606502624138556023532223617309"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000469170321491953908065098991723043621408692762756980179169088515131858959747"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000312109588324696299578629133466134546804934425652317350217208685069513949015"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000129567198099448561278298370512360354984106954815513505005111818553145714634"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000116427529260004024077348030611493564888124415305981619797224470056679948811"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000238326595578192588974326088085766915138526617008998625640603860278073091204"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000244742730302692510517546840958886727657274951555813495950007886554971190043"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000770600420494052668960125627196143256619852875376018693997338520252928378898"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000000000422698076320704793842624462462122259676671218339643878393761622611533681352"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000000000986091681636424791402346661562732411914581846543827917931134779717124541059"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000000000000126415071901335517823653751264600698935766480825324951588072073703511279792"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000000000000000000000000377103451930012080634362697114829703633218765482534208185011848812515552568"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 1) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00133579806419009115196675706637156796250602084906080838786026804834468971451"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.133464030083480084488351954591647717793838350786372177549592743667488710460"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.777392827221672586310666248128747829200320493773819351137332467588231583243"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.801230717758959652961918527009129684833274859723487119504590846793863335812"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.426666784652518489250422806683556250288833676277503213685236945222428885252"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.571957459622602012169769841907390760981552952793047182594349400518281072515"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.397457250920213664316589385904613867162187759231452008713125765190307200547"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.186033305489426000253295545948948513398939530758207475017080180368379398183"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0384747679059492805673916579189810661778669575642656012980830136829451472564"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0241860357552808869059750766214192783314611864202213790162280116456669700270"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0288198897744401662329162080788778906001500235821576069533309114033731355962"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0142526963839655487645868201986010179113871984727712950466970890939532437287"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00336296659876176824397694271542208875883948628180586907906711210463700136985"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000159566153593696861386281086000847690312020416646262230382754818302321719438"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000309307263435472022314536922703140898276518864598497490064213305898284747610"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000325961537538155977461153441016758163050507356702941089478538114352859222854"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000290247635542117698570144977074207416731978843448666289133343239852468689816"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000110608868168013164312795909662150842245074396074718805254622442187665703898"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000101464961764211094555255572688179572800548750891083281483490440540837760392"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000181575796575106178569931388126652092356228605369118455900710625612685300521"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000403715350553834157466382021922715956137169052960785956913878496250614284899"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000171544844106973826322799913004035593507782409764976544917598966515593650516"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000451755267309694366768252738364162154259717215355595513364624281739328028806"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000129802294066363039747634462122684813596696625800552726940142002601766408318"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000138996891829717676890440608071964520497157312831377423601945181405496090684"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000347738382169564687828118552109166638991744665362295779616649639285729819837"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000114717366932132278311818016897232315223329690486333509730375898406349099958"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000599799090330095203536315142157704385751706823140887377206448675107156989932"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000000000000000680498581094669635360619813975423231834669537307635911669206391386823114209"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000000000000000000405993437164566724529315224811697049713922457638122491969890878584620874206"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 2) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00907504496732640314944688849486681911170876832663177666164174959468906643803"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.403693382156658974454216765797474206766624418327280399905409355427011080214"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.271595976047908300146227934593263488450798813237955930924729605110240403784"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.71466891756329191846888796871430523337714028235285198760495724403435013146"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.63352358803570678788478060023534112555476154451350510970246835738280509121"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.78898072726975682640228727618234727138388953315526188172240636749159256228"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.03975077410817374151183520926644188466298014618670416662972210485960248730"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.39631704154228509023706369056571803134772531763393599140130182392659436684"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.819427034497158945142654966863542712206855345194448346903634159296239630598"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.383404119723578321449814608400708917510598449828088961243589855149596001885"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.135338714135930963195025224311403350634380005187589310729670665679985290100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0345824240315870800399189191226465109691714421609307243691766680673623150574"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00611109252646139447895469481926612685642577266141459174233983728056045874462"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000156732873630400332452745828101813648998758607431152977455922938360286361652"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000799472830647854921185434616224208697749055953896801846063825566821972723190"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000535969002468135628001789755566345264258267679652530938019113713661289348208"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000157384549414717885084996140216171026329363074442489876604893016989401039526"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000129171554337007654761147781184602376979060587640275295086289574304678711395"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000235891742489546284645209760127039465129319583273974596760329794893748689585"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000916355305976574852247317081462867277633622646780812044187106843272112326405"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000111762055600082304510067275185623693221628140706419356829204316323573355820"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000126047973860633771018680395413773434461601001774651486849360410809332840361"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000154580154095772067092661818331346769426075368407031625141514557326211824376"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000185949656985422215139801744960422197149550325212978585262596149007208130605"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000475656161103013775576836068201182321050146685578942140172354013017630940520"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000964424579936565782431696216162300377942338427905223389622237003668698745504"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000162097483836675470258977768421201321419436509333952009353262345869183739617"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000000686765701841635939050965407015716594433862441435219008736510985170543518442"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000000000000192520645691275200631994551227278033106343644450467270809557380021147426532"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000229720301797888422217182338458254109542893787274416640198192653932982382539"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 3) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0524753452804691735477738251517009853016979362519517221207312376177764782969"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.879968733813233322230074392947552628565967066414165711760276698494844390125"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.74453159899437732175018000055779377712653677438008754872020488131059119320"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.80360353176224527101835802230946052421659096363090207129121849285840468259"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.96666354532348341330633181326044172915860234894700083373343277220577971735"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.73070092873449595291889929112197581304463119652084787245047615859331130715"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.42984724824215839353390105174821482301107399626250856007397139446613345585"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.277322631367784241585872795091101589798351228341158053606520050000850391984"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.16919259864499295419145746896607736986733203837630984609448122373016720827"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.39016950402094561654444812940516530484537994331951170078343059431705063505"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.817574132321601018212216995379856653768755317510857634630667447972613443467"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.190018473449379212093490515862790233603734487245387060360549170220720527831"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.100241083602577673991999687326956519174898192619719218177625643190688840896"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.110015365802528313698254717873775724459189967181830195015949587831350610756"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0416060467568914386443724185616672217060437647984160864439680078935440524035"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00245435974160983337464675102356272887367440646869277382351633348615279833109"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00443062929513058573083346981678078784735168535836855152956465826632431223593"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00192644595259837997265354752663163334685724941492449191301572332061212680367"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000286252108033456570905469351445678979854820611278948347680038000227240824154"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000237541414511668265954922688834169477800802817148790300058634367070336055647"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000136482469252724735030504787827046649952988816328627069135194335843416601041"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000131861141712690876615365340120264536061804975586109036631891707678386628591"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000473486085383219537439492823717115126567852265733507953095631575087828890796"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000107671154662516331418850350729831199883227731812375998404087097072976836721"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000995866077139100400870850073442653083344654813486051402700610836989945821329"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000644585749433741211569153851347580280472182636866394478917140428098212069667"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000403351073771297890412924077239685188093056035814882459390662060096671857385"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000659252152542076182761062902783690995247798500608023765240694648924331810668"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000960845271049957763593097408492741398950372383171287599580336659389110633204"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000229301073796668864262563070071270109124544905677035858311033933294273314683"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 4) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.250153349334599315252252388126799299269205865296558881938205954482634425962"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.728403268974963829703458458071470050940885133583732803633168550716310693177"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.31293553717675839320538206374566119063264654529238980016770942275333057680"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("18.68528838602266775292882053961758029216187265423226470274612731462272361220"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-26.26201351114432524894573270494314114413810106786511729006960444976330657170"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("25.63029290762557459998254683581314951053365051306913942327754105908104915980"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-19.55120591041754554650107676016020601099463018398879255525071777101622456320"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("11.38828805991210130161237386775166797562787000397306556310659987606493988010"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.30283228500638291198113772321275270873046197281267419596706014023411466725"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.916846332667450611187893927561003746742522420503995679541446843858673884695"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.945625534103851129678007688099239113134137817655559774710855777516502347910"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.89515793182939656979518906226485738613531079677925225755026655593370960082"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.93021100594621881524555259846350558417500093095145605126078231465409489372"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.12168634735032240026321692944283569195655093165680965383861531031185719852"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.336457302755550977576916271285480607975977081669910226236184937860992298991"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0126426202740467393304674214034871452929934964899914857227809055709449712216"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0582059974257001233798447456344149565398178531031451066540415121870578243558"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0246013214406903516120171910897552685116442802184487116944341538415325680043"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00411996064777101316931682571931078586923686158543745182753395278198530764373"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000291779559634866855426419087305363632521209937998931712658121173823485969925"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000239701704903312956607867825407660197652926764025390834805038196728688308116"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000295826390590035655056112200057348642111500715341367896808394225854268570663"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000112791496012934939362671595835297640696200634426263650389034453900171789361"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000305425386948880794569641314813535348968283260910445455462866729010610312003"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000323553114835699703688881035252953349590896466534687900103865721438408552054"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000258122376607866610987411018878425618791837110136955492805044321479509589635"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000219450790662654304491928786757425834815059646115033341354646744288934919567"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000159236348311539532630177443070999135468225820289422009164997153592635443466"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000104656532906862901171727858795431981501763265514191943218716516961575846913"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000000000000499516806365011687457115487988706495932857454344801314889510253590960148386"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 5) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.948918860081173023486878449541710926994880432689837974961014397406181264670"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.81166631126650312996004125539249329519725796000525742386348292571081819916"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.78299808007697130717152451621473328395694372256303981775622804889029881229"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("12.37395820093160240345825282236635205331906106919047160212092164049284839100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-39.16766321350906531896872834791517677824323075070438683104809495173394326760"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("62.79955451772214024240382060087062426787397929319295079601210237275121712680"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-74.37662754095149895480040703763760620711511291610626181895862800609093747870"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("67.23730480057039248447342118422920230943504437004823887131700745396390082610"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-23.08265385699185215685260119277430566259281075316203981240706774938023666940"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-68.84915218133284171164114487633189831096395205709886147861137522063085837340"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("175.40444464090045806415168932366102695577037312699033623699052962519622077400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-229.28074286375890467633294993254440174269835310543834526028533785864822388200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("193.83085133958977511845883119454638599531183632122825347548271736828828668300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-103.39169380112586043483075412413138934035348978763581785737531822374487802400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("24.09750044484111524536729862648168444109977342535349604249164282561465455780"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("10.45216979380374210587460533102864566884224012655559338370841906137296941750"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-11.99151005263756363002508198337155102952159028098769603630967872540787513590"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.84554994331741826783417472084829739722607030792844096956440587496738411823"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.761710410994668509466406853308159275909502383230971027854958930856015369067"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.124209524454545658676627889167517050395399779084274645999974675911672746289"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0744221639771051463314174298022584491868353705194585772380078427077920515089"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00983319049696390510116538964560712881930733797491178109985861752053037330480"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000346590936489614878108837586184646026813106498935784307571500760640790704534"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000139766775489175116907285138350503430979371922048966698178677524730163900835"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000284583528087152912455876731878039503894920609382383306623061678825974042090"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000170191243809068258319726930807249987074459356894402421753166625042558224671"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000189502643796773771078878563475104632826265649607597910973035053389210254464"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000875159779988110397841134172673233828490501760246058591460605371182339054825"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000179974686472459484619567373444439533680836492233083181824874458737160102214"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000171801697948722978384418571523357254435734351358127403605526786536558291798"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 6) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.72080556004295870927948424445222388100259573295765738309696540518313358664"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-20.35486605481687082915848974154624621834658263785879525672648653134317139910"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("70.69361844342337341827651301058270782618285357205640682781626444606188387450"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-157.90067201133162316239612336927048444714935472994185058634807793776069875000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("273.19822200505440746851580897502900411638483947712679427834499734688751603100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-419.19564866352573545746821411474547215410128530316966417749138435741251020600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("599.84609690090711287694432739982078555920467552320725430638045237415518597600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-775.73303631488442783947171088475881408364372009796884367795062491210589677500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("867.35358450953923058123434268208131384207780232732818873949031917800169735900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-826.95465375065970699136161187085785345289352007444881210861847791029287195400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("682.30445844031956022343618018820158741773280156063117441757258118184658256700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-489.58797447319361281730621439860073553304564691478746587385050469768692568500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("280.41641455591206428665542158114941187595434907081896095846035277563013174300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-83.87530313006339392205670404100927251009153086911120664987656189069922028960"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-48.57290602853936778598444588838000320319188797120667088890627817071006819220"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("86.48401303861623414105279810601960248737236193164692484110937025080244348070"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-59.34749838115491965382974741024204031184960541600602452546612244205852115450"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("22.12683829000516493499208689759136028373805834965052266237848630047551885400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.06820705468851142387494397352111576035038520405038204822630392926462913822"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.01844918784056167247769356011865100548861696497532359778154988643933299720"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.548390155052322116601605108703391030814361014039987127607247780249699826925"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0821665399305853726866950173051458732522788040166080680936985410341364899325"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00259076138957212819580904996053947215856595645621290484740534408016060849032"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00158184168192186218699552573165552035786412989560027541837371028175219359299"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000486427797988048217823553064360225239762325535402325453015988941445205147689"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000278733673658518296782298192418270556801753284097037387222408724354826075481"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000415493043046997178773581906387206851820091297524869075078083888063058100083"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000318481755988583873479575641293261720504490443808109780404429573043006066979"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000786533511511639686500635180600662013025908347693905569053412273585440000541"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000000000150164678504192250638011216866493543394290529002160876206865753397561385614"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 7) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.14186178805038248389630463226453535538160220630273168999055179268700878311"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-56.58718775023035303740954199011503276263410041781331860722827039023288201390"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("236.79056117034701253831145295400349362659332673554984369468013095569697737800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-589.74212764744550791699351051034231997851066299588318672773755627012133999100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("955.91771747407523740699612277021093282646971930388485874767008345752406868200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1018.25371372134704439175662005189756423202874621778366040811852543575681051000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("620.16534974073328124363357805606821825717843510348080668139769912997493261800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("118.09513214016409343018299161962983559825963510724745846686457205186992634000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1124.17593601667896107495596149804572042346983911263262865208494201555643863000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2481.05019825971494606026459932673050920844604853044544044249826635533039896000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3958.72656316717252768182437149784469578445448081086451227500629910596142977000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4892.08038810778226650447637979773553060005455552013373826491377287611549607000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4888.02985912371580185159900968286792361495832247558286519513525186654679328000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4222.21851392745950660685593080126541478731847689276755099970578373193227197000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3301.02739698605769321367226000985199110976449700946791984290949429902919623000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2249.11165074697026237037038692307185505620568793949311249024089637097353635000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1187.87398664007835892158563773173750314639645000950438376922380430030480509000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("398.94177525756891966681160860599524375229162312548764259215104838155477665200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-32.92289515108174067117397420787028784793135289819773804980403784424237633870"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-38.90071447021924707376179244031261113671069629451701962465484487047604238050"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("18.88702183332856460379524735396940221841668334008996536437289731073857378770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.13472910313296479389678303201845822338839740930736804510308660361540192213"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.104405285224584684173481804595561114177382914767308859899431383064024115571"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0833671470549304163921288867140169654715033486774418851176340785841513622562"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00381467578864364562968701846853701311666229039725704435440024110934078146310"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000212300699997037803249607997697918026005513531720485603301750991443816531034"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000444054082400028863949114022229769838935441151556537774085307875568116728653"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000509993859755275328806308874095727887214819535696251443253417433071486761002"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000167399975134582079218262940873121039789400471542818329635957062341003441119"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000000639212147850254313089119430941095253920739364313765534055842450107396358145"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 8) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.87573584867024438192288359005520927769283739845626908320402959675129181181"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-89.46249563427999259136175287546983385362056330272761288548978010797275886190"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("413.53699835747096831461960515667083330041243777158520357367773071672954421000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1171.13814794944060840954109636487013129118793177524654224322494272585137735000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2318.63986015396571592184876974869163171162613486972744615164020031916734488000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3550.00082837270164131331314150441834830049599401355505132632489796798446179000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4641.11041485509138580464243430685343405509172986351525682383304436384521680000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5574.31228403733210075849705237883208794074944113113868870635833735655518388000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6213.63809498218005198867412543832867815767594736394946861528827045454364892000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6270.42945837810044547764288676694403309477382977177928731847017182750753511000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5712.25416364615036894363595935332173184639280691157188990767737995783827699000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4793.66410435252078277013910846939514432498915716171347756825555965008446551000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3701.90566377778244662006515118308691363996241871472358316732096914372421991000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2545.73002939982681324232451707199314555811122671561913141889937616476059628000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1525.76211545671409952881904946874414887615701953904066966165263931990216324000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-799.67600361393244423210153323478015290110022742899088191532821628208931108000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("343.71466120684357322054217074049470228013278108322582312246908268821531549000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-79.54296988918714825182831271113602645818430801267882016130158946025000070880"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-31.11742247721594622537736075250551303862928746280885436044292583853573827770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("39.24534373830708704714957239063819401930019800422830284025236588588276304120"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-16.49801465465629310378163586594498701051184640106636079791958143499072398020"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.86471589853451505092762387909842635954128523779170775248876357690346385928"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.123177932504841138584100462602213000414409636861317554953311729819152981937"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.107313432588339694252584996265922811157032804886175374104426839751272364880"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00773540599618550353141393406195746669996857798924014596151059620636703068705"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000403128635241149243596335554099377174869092597389189451754820571281078679507"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000121750336610624680031947143595873921578210617486500364426723519144528821747"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000221216095903365985949388422841378231674809606300993758039913686908512670984"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000911028045352580286145166937280851897647011765638383494849691163731056620327"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000695776129234608161606962102284274675410179267386907251288229647263547841513"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 9) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("10.77830476909189246875213224644256434851574836114150288979408883932663408760"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-113.30679847949875283481197239555445238305089613518166263999502351065318841000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("537.51212592498992595355212803505674673365549040582999946710655984020061098100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1522.29663739785441603519129487498101658679127253026107709485943801614900510000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2896.78977300861767873975381093516844970516257221777808353633619790702973572000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4053.73263591850224842595039982230587297183053442752128125465336858346975258000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4692.16227410427044352689392249627854521349603478803164622820633019994975786000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5127.97602212282174693460907248514758996752003938521226665443443773461217536000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5426.20224367656186913233154675879829819354550253827715074695101579354057124000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5045.15898544937188101087562784811147553356778814416690263956287346030906424000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3863.31733313644020638644030085749560942435363977228787799940538794012224406000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2539.04417279695725930037661713449400977494982097924738163800547690349669888000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1495.95152813312696164796032367069415490408732672326544293608639517256708804000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-598.71338111144603167677059201789107648873467499782686184459249005987266004500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-140.43812212582941929559905584906021898863758588035667146287549276998098600600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("493.12064121138670888525270736014297176175068242740057327881696669435953096300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-501.64710764067763354144069937731667392246374465461102519748339502452412766200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("402.04913703308025098584676401156574655968469749939939291725245197030615330000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-290.75476575334721451091504764009888592656309571548514827563707050104045459700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("165.55396459695871034570692084628299088745963671918908584151041422747359826100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-61.56613007836500140570535045646327943146923286793207561329066790849269699840"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("11.12724396838290672842395163676983586805573062177784417480776259950013093590"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.616550439434153199469147689908320765572732324919216224085798570609031970737"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.614996772254297606838306172301584143891219608321996340606361952393554618405"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0653422092865749098941219576491799499470841617658284880902741473153604810456"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00344468033183476613063821405936170839437245968135759299996161161087759703491"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000150905890468010880910940122626955537936454095361790792537415847674081059644"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000341390266894352391056312753971168883114216701317332621177306336321608604935"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000224655412582960893249160250701023608274672603071809480941098000782254450127"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000343179206875786428614845147622090553145880464453051733061740197696623777452"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 10) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.40595389327657226503694497012483164362124209823619932408143213509789418142"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-90.18755588816675228829817416935430178296553880218263006522596252933799260750"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("436.64933048343039643869664274295205972159884268297618856653635883730240629900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1265.24702078863967272446087300490983418244378482038979633311557029559187581000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2479.49727416305844438566515309514579938046134972182762000607495793961979937000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3612.22404262013984275650095257916266122615183211172708920604427365997332248000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4390.10461803162979442824063337386992495525825588510223744432684369166514283000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5022.12359523964154158524736614172785466023371493789078267642792825970442996000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5604.78838183135573305540445463913574361373339338579848172772266429190600683000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5815.18068935187129727737790596258417265132106330711026316076022878535003649000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5496.98944474809909883345018624513683552577448320588129783533814897200127901000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4879.68442203485471741212789690616385244300504302852282730946221011631520548000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4119.29235509599810627701483024966303400343567833202767250947700453832737400000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3233.36775168650371444115689095291480507860192155181401201543648075525710965000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2350.36811503737581431248480830061956015641307301010846976218535988613892099000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1605.19792304130910913657642308517047415091779052762305083384570282636342729000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1010.49227947358451800455150244650563573753526087564849242400820565186861825000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-566.62005573161101918270073525503120095406475610339310771504079035825340859100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("285.93792022547194485799602926303040314550718046007817587164843637458151043200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-130.27678643673248754523842749099954235730480748012199117865803024394099262500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("46.38075945039597150032827358523901955451289440527106334217760766144442187450"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-8.30339600100546654050525461274557456779962476685870904307407201958336470745"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.31140444871530779856774818636439538472323427394561636210886717702287713836"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.944443234286201477285280631764338282009445764538235481135279079602176865296"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.120612999220845884841770938047070126476556890469242771667061304639099680352"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00612240592818620183859019486914162369755180328595090553906554353918907508111"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000501921174446894651071522876884881677798862264257444046312361569076439240403"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000110015062442341106953762659845461877288849794732582550741170847972381078513"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000149481631455733098677769729640496918070320996170917395536883890913165962523"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000456766795438744131185097599240634110830128913864595728289285533008059188955"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 11) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.71662615388384035490661602572026128251294325475247692177411024734707018748"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-61.95261947504494240974525516761288737718458065654976960732742872670132713050"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("299.92392362199005365846763014477362358033777481183567437527249031455105143600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-854.38454227321882602012934795768021816131020192369607501580124187697270944900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1600.36101077653647183632909120922276146512736031345582867483706653247060307000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2140.07738028486081463619489247776891689722101986432309104955433096170807913000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2318.24362356424763321295439620892210840488958065858246141680343191186676880000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2452.55551014503575390323183594502097923638970524686355738420251386509103336000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2704.76529653278947329663444759952034890877923302103630805132576388538972614000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2747.14673623756244311092333721767148045245885058383000695480413427282125343000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2412.08489577605845461832534754288001056964932833568370698369648585962621442000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1983.24120175694784202508820179002467936094914905473739070428929084792886805000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1626.87817837800998599505523804923350020881957088925397853144571494720023844000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1235.35137573220290037298796944863432831370478695788713485540725637661419976000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("821.37287700919909202293078059900314209961592538962184148238624773351355270700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-512.36813276364982792979888767414531827457847125018199834823820044378682592500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("311.53646971596379276316317223887976975287113725456002799972326204795524864500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-164.48146424429947905468701694679777546495466959145717581719894831842925074900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("69.96731728174455147890349889940708552672488525211671432746656999693968225190"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-26.73871180360852431769728634910008054094567759215735127221449159427110567160"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.76604443915764102583091274494705031974551432188167671170993272943904796868"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.362003657126549623871141694778787300536949241545084284403839044422181900363"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.57725852000685070664686477385087762553122190528479055773272661383335169406"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.726687291498781501912136314567313444745762140706471235702655842502262486103"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.103813322317258033888614985218841754913997474053598134379424827680388803266"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00304317984052183404339782146911467997675320910745831815762231114417956519165"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000840398448358251520779467930923617673432444631095231180255579031943245676198"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000250575256067101292262100569305822521295926652713304136991428596750128740360"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000495611865767157365743127106863134595887690986921006107382476777985767199385"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000302986770281715807340388725183309305879191944670327753347349945452961991743"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 12) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.98756545276892961683405920317400782688926167457213404606206894953469090570"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-32.53877041522938902748893248611882921380701347287193692458464408872270681770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("156.91107210642938297454108565759471733768304768928530524781265126236462047800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-438.23328456607176854897749709031392294408668236354846841483816529557797373400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("781.40158298338287783314503913374413961456166368022728026502599517169883168300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-944.00085736432437654121844433808421180478044182471803034745876831993387206200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("871.18702529100316496510657599432732757147821503683438970158984398762342159700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-825.26225814663098471936651058959817182597766714375609693318512269093807603100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("933.10543384295409309368246495330995137453207941551441370036549134265538765800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-949.83367150707461495067586025268239472985940864418244218914669709742438195200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("743.11107879726135141484801469462437364046148934147523506605304654685788997800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-527.04406443888294920168702045857144963725142274860553582472478068752203879100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("421.33852360565335024951901100209978198412810212541506159854671267737618195800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-306.02517342943412940702644642463233060183139335286436410908479737189261628600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("153.69934278480254603223204551372425554980051718272712837279730258851702658500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-59.04932850218943944934225606851905428436217033134937163374348351651622137740"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("25.92139276541304973776659197601093424514632883892831929110158475123035210590"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.962149888761450607548667577621856494158643540101329999411575837264452498654"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-17.01274493932990083951623416795053065446598743948526471513759064128883019650"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("16.30256873151847666122910844100498304960224732436925588411210572182662140460"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.49371814172560994368165179232263581655149629936005381772523795944996123037"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.93974208940926161725307281051166656360861938611697972636537005680715438577"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.56482176156890404621445412519261540357391040079386784517365108357090968874"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.34272455281915240128955665480521952634664404440227746448796352198622736864"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.230525367745987004995002631304137357183156209105644834496304002576886379356"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000137794698671713437634696681954243933103735285034498363332772681562760804986"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00344045989823171334589527993003846308427283936104805061708662437757755864133"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000132013157638346537184564818139969682565470634989172759825885721468788821545"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000401010519633852578247631428587627292136452995638469407199569086176144778907"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000490634895829511758823128551590445161881103933303527735015583380577005829440"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 13) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.818427536297577413662164686067597972826506918636591011690333183337912720187"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-8.93597254540483169304505499620510189518004297750684300492893393884837531090"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("43.28505740826911943179704985609069278737276400385479670313947361507288590850"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-121.94941265554743093324264638861456116774169427109119662746887892891581414600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("221.17705504748540968473650066059868951479247074002625157942998465440826537800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-275.49508889548757008568001670977657433955615658111585669026893704820453833800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("263.97430656654945046201101887433086255955773561111355779696585609107954522100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-248.73210725434071237643827703257935321449607282648266512518873782422456148600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("268.03761105163175511980802546399577987927646399395524413177595218195546680300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-274.74632577077619559794959711805873055919483442081245207387230106955552634800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("239.04459659450491561902145275774681231766178202091849139640330374817659226000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-198.24079457638428918916507018047876417177573585609523087243911695920766059300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("171.17411060286929567487650609762363461665749097833059519177248964117986882700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-137.92402486238060270403376601148674136697949366488773861402567537082900349700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("98.85338722312749675832616392395611353702627445403696398493090489812880274670"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-69.42924715436025679968823314670561196868618424662305178477940854240571797230"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("48.19175883630122313265867563554087765085528907020382930380472297614957949970"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-30.01464950814868046242052769312726238783217187685035205505179037973211186450"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("17.18299409341888528416337955184486836168042336837628442005969736301859437960"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.70772568832145809755029602593534775626803932755931576353380272720933569318"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.95546002630693726392090932025925003607433594321786357647449706566309372496"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.14010864823626171034034636914985284178400701423559135938044246487466223776"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.880041901487022196333800296293828350812076915017847173990679115863977711041"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.327483771390349393328449791379023445875626515179961154056969671224666397451"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0700050346208691475219456475608152516659372000469712274360723295281871848387"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000740225367427644001587409378753952383212767606234921042405852483821239061334"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00194483199670374685015094187211770910054778766605235293849027402856312150840"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000253088547271589825310570020884344496366999521135191317044614410762991878950"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000470572493262891053536372764217043903584963956635299308538734504960681361207"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000115303154806547333281398739726672346354039012152713743670663506289507432912"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 14) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.182096627390465002841872599753582960857482793103154443921292798922930823312"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.99067991923898541144309882988836202482422764820095134691586013396479875824"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("9.59777139855370444734294750686163842012139708590050472898305559257417654445"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-26.61794828473449778541050916432452820900605760472867782882032588243833218460"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("46.48235553993428243642096843754171537043857798264743456557286506206884999660"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-53.28952413012626128654306352591401630142078063921055789323943087480417380740"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("43.78548547762683495894325883003176846356585388587214183280498394113771237500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-36.10530005831753430370334734266356752826479202721810859304361182987411236780"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("40.41441594328021583316039518661942961300602117705878612433379552772328367060"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-42.57519344340992846492391425032425629733148181868603643066418155132222692720"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("33.69357696920429126980241665391486766936852157516836030131774633802657214380"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-24.99427184019678212351060274549661020691119426526756451144184518863090205460"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("22.24082565201673464792084352820810035044717879419914422566840373427801119710"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-18.25836120586050027075089243454704089299356205520219684237280836587814742320"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("11.75999525461842751380077638481339770186505465117919491977936260095287395430"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.57794751208369560067407289978430835851835802702956349867965768312335398938"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.51625146977006284358570281266574340943582336186123580684755277118777603718"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.36170173645122190520455082014298086926033428887456137863348894911353768638"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.65231565653810221017900302691080368910278392146172824258223867713998781120"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.899971991021384569041112723985746774474890344096613796399657618872823089914"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.493379883919252205004540248830738351306813744782324207970147006276757888741"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.190465678173474433044011230247932891163095527351165979372112094377892415660"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0621662066439658745587942761812051647689996933574065948837820956985288446830"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0260606091916674704141077213394275894517321034885463805642148072294982340641"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00668671436111235768206809845426737458018128101136661828669846361010276014213"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000501800405113171457500759977346203260700591357705539339843489778157288724465"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000404641953708090404336673259880430820473496337074290841846682708432617331297"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000622939193262507048296472703033235853521538144434623520667251347304027494807"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000227216792432532934218802486321263209684697324571081185820714866955957698807"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000111648115236885172375463021306155593347638298619118930265825307233276056732"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+            if constexpr (order == 15) {
+                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0186632063341731699487622519569900676156629675744736414459848077254980584439"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.204152410105326344047690139058847944463463829383572825741723149474265517687"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.981129778506629236917943314009391202465976027147847806934681206721129743489"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.69223973647360950767394915742670959250796023828609553625040576017143217370"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.57840474748508233139703474514191577520139760766602312536057813786879861719"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.92279254466715210570744929069389870019317731597159546050988432127489832899"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.49098196027493477759169680079840596940785122938110897581250074622145540830"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.43745302882351007548114866638762563227820344626399026957104467610746424919"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.92002235517806230637018721558192349007812525216552453182604910919733517109"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.24373461024153144136567992763463788222027847288621903947814561657763790774"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.33058809298308412023805776435915774549596651226832414404182013235265783095"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.50268473155783226586328187697167000171012304032869369458457484335905926235"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.44521613506514880646597775935884860442911229706573188445594135154651054603"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.25320563215574317573983783719179686555846390567587617560334570616539136371"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.716523991653864912132988574383055048288486387296028098428465297303529312898"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.417685734682996474655995981787950272634517973441398985560062415678439970424"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.343615439131547337750639931144047450610704550982732392292547279251562842012"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.210599151040031056875841224107239694928740122133299240427666270185426716963"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0839111741718053411362323568803319587928469795988859679968270250707587553192"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0453350931889210140035133942035842323703748999105117340363647560154703981313"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0293975150903577374499867887808058812502982622650503969014313916908299400994"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00952380952701618903633264790459773368829395336984965315811681382826752366623"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00162356389207281836884637948122226515491709153554839790386903440166058269155"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00107233008114088588860897903711349245756991842194937466975676115541205802164"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000309594820880373636252028432067839316250026602381083168344278875876631484733"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000159116759294319410028654591726757975556683309929396718417834438386747643662"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000716868960901604452106499159427785061407281838428321680583983254056627687328"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000372192590676834494238303138990722411083877718883831917839190468860584330496"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000106273060435352363021386153934099392277182493972188516192741747367832383831"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000105004095727400196995819073889347146562377832036002728993854591918261645500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
+            }
+        }
     }
     std::array<Real, 2*p> m{};
     for (auto & x : m) {

From fe5bb27ab8fa47144f5ca5fa3c5cd01c3e4e6de0 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Wed, 5 Feb 2020 10:36:21 -0500
Subject: [PATCH 009/104] Demonstrate that matched Holder interpolation does
 indeed have higher accuracy and that the exponent should be reduced a bit [CI
 SKIP]

---
 example/daubechies_accuracy.cpp               | 167 +++---------------
 .../special_functions/daubechies_scaling.hpp  |   2 +-
 2 files changed, 25 insertions(+), 144 deletions(-)

diff --git a/example/daubechies_accuracy.cpp b/example/daubechies_accuracy.cpp
index 87e7fdb0f..eddd1e5a3 100644
--- a/example/daubechies_accuracy.cpp
+++ b/example/daubechies_accuracy.cpp
@@ -17,7 +17,6 @@
 #include <boost/math/interpolators/pchip.hpp>
 #include <boost/multiprecision/float128.hpp>
 #include <boost/core/demangle.hpp>
-#include <boost/math/special_functions/detail/daubechies_scaling_roots.hpp>
 #include <quicksvg/graph_fn.hpp>
 #include <quicksvg/ulp_plot.hpp>
 
@@ -81,143 +80,6 @@ void do_ulp()
 
 }
 
-template<class Real, int p>
-void test_interpolate_with_roots()
-{
-    std::cout << "Testing interpolation with roots on type " << boost::core::demangle(typeid(Real).name()) << " and " << p << " vanishing moments.\n";
-    using std::floor;
-    using std::ceil;
-    using std::abs;
-    int rmax = 22;
-    auto phi_dense = boost::math::detail::dyadic_grid<float128, p, 0>(rmax);
-    auto phi_dense_prime = boost::math::detail::dyadic_grid<float128, p, 1>(rmax);
-    Real dx_dense = (2*p-1)/static_cast<Real>(phi_dense.size()-1);
-
-    auto roots = boost::math::detail::daubechies_scaling_roots<Real, p>();
-    auto root_derivatives = boost::math::detail::daubechies_scaling_derivatives_at_roots<Real, p>();
-    if (std::is_same_v<Real, float>) {
-      roots.resize(12);
-      root_derivatives.resize(12);
-      std::cout << "Last root = " << roots.back() << "\n";
-    }
-
-    for (int r = 5; r <= rmax - 1; ++r) {
-        auto phi_accurate = boost::math::detail::dyadic_grid<float128, p, 0>(r);
-        std::vector<Real> phi(phi_accurate.size());
-        for (size_t i = 0; i < phi_accurate.size(); ++i) {
-            phi[i] = Real(phi_accurate[i]);
-        }
-        auto phi_prime_accurate = boost::math::detail::dyadic_grid<float128, p, 1>(r);
-        std::vector<Real> phi_prime(phi_accurate.size());
-        for (size_t i = 0; i < phi_prime_accurate.size(); ++i) {
-            phi_prime[i] = Real(phi_prime_accurate[i]);
-        }
-
-        std::vector<Real> x(phi.size());
-        Real dx = (2*p-1)/static_cast<Real>(x.size()-1);
-        std::cout << "dx = " << dx << "\n";
-        for (size_t i = 0; i < x.size(); ++i) {
-          x[i] = i*dx;
-        }
-
-        //std::cout << "x.size() before insertion = " << x.size() << "\n";
-        //std::cout << "Adding " << roots.size() << " roots; giving " << x.size() + roots.size() << " total\n";
-        // Now insert the roots into the vector:
-        //x.resize(x.size() + roots.size());
-        //phi.resize(phi.size() + roots.size());
-        //phi_prime.resize(phi_prime.size() + roots.size());
-        #ifdef COMPUTE_ROOTS
-        for (size_t i = 0; i < roots.size(); ++i) {
-          auto root = roots[i];
-          auto index = static_cast<size_t>(ceil(root/dx)) + i;
-          //std::cout << "Inserting root at index " << index << "\n";
-          x.insert(x.begin() + index, root);
-          phi.insert(phi.begin() + index, Real(0));
-          phi_prime.insert(phi_prime.begin()+ index, root_derivatives[i]);
-        }
-        #endif
-        /*if (std::is_sorted(x.begin(), x.end())) {
-          std::cout << "x is sorted! This is good!\n";
-        } else {
-          std::cout << "x is not sorted! This is bad!\n";
-        }
-        std::cout << "x.size() = " << x.size() << "\n";
-        std::cout << "phi.size()=" << phi.size() << "\n";*/
-
-        if constexpr (p < 6 && p >= 3) {
-            auto ch = boost::math::interpolators::cubic_hermite(std::move(x), std::move(phi), std::move(phi_prime));
-            Real flt_distance = 0;
-            Real sup  = 0;
-            Real worst_abscissa = 0;
-            Real worst_value = 0;
-            Real worst_computed = 0;
-            Real worst_absolute_abscissa = 0;
-            Real worst_absolute_value = 0;
-            Real worst_computed_absolute_value = 0;
-            Real condition_number1 = 0;
-            Real condition_number2 = 0;
-            Real l1 = 0;
-            Real rel_error_sum = 0;
-            for (size_t i = phi_dense.size()/16; i < phi_dense.size(); ++i) {
-              Real t = i*dx_dense;
-              Real computed = ch(t);
-              Real expected = Real(phi_dense[i]);
-              if (abs(expected) < 100*std::numeric_limits<Real>::epsilon()) {
-                continue;
-              }
-              
-              Real diff = abs(computed - expected);
-              l1 += diff;
-              rel_error_sum += diff/abs(expected);
-              Real distance = abs(boost::math::float_distance(computed, expected));
-              if (distance > flt_distance) {
-                flt_distance = distance;
-                worst_abscissa = t;
-                worst_value = expected;
-                worst_computed = computed;
-                condition_number1 = abs(t*ch.prime(t)/expected);
-              }
-              if (diff > sup) {
-                sup = diff;
-                worst_absolute_abscissa = t;
-                worst_absolute_value = expected;
-                worst_computed_absolute_value = computed;
-                condition_number2 = abs(t*ch.prime(t)/expected);
-              }
-            }
-            std::cout << std::setprecision(std::numeric_limits<Real>::digits10 + 3);
-            std::cout << "Float distance at r = " << r << " is " << flt_distance << ", sup distance = " << sup << "\n";
-            std::cout << "\tWorst abscissa = " << worst_abscissa << "\n"
-                      << "\tWorst expected = " << worst_value << "\n"
-                      << "\tWorst computed = " << worst_computed << "\n"
-                      << "\tCondition number: " << condition_number1 << "\n";
-            std::cout << "\tWorst absolute abscissa = " << worst_absolute_abscissa  << "\n"
-                      << "\tExpected value at worst absolute abscissa = " << worst_absolute_value <<"\n"
-                      << "\tComputed value at worst absolute abscissa = " << worst_computed_absolute_value << "\n"
-                      << "\tCondition number: " << condition_number2  << "\n"
-                      << "\tL1 error = " << l1*dx_dense << "\n"
-                      << "\tRelative error sum = " << rel_error_sum*dx_dense << "\n";
-            std::cout << "\tRAM = " << 4*phi_accurate.size()*sizeof(Real) << " bytes\n";
-
-            std::vector<float128> x_acc(phi_dense.size());
-            
-            for (size_t i = 0; i < x_acc.size(); ++i) {
-              x_acc[i] = i*dx_dense;
-            }
-
-            //std::cout << "phi_dense.size() = " << phi_dense.size() << "\n";
-            auto phi_dense_copy = phi_dense;
-            auto phi_dense_prime_copy = phi_dense_prime;
-            auto acc = boost::math::interpolators::cubic_hermite(std::move(x_acc), std::move(phi_dense_copy), std::move(phi_dense_prime_copy));
-            std::cout << "Writing ulp plot\n";
-            quicksvg::ulp_plot(ch, acc, Real(0), Real(2*p-1), 
-                               "ULP plot of Daubechies with " + std::to_string(r) + " refinements",
-                               "daub" + std::to_string(p) + "_" + std::to_string(r) + ".svg", 50000, 1100, 10);
-            std::cout << "Done writing ulp plot\n";
-        }
-        
-    }
-}
 
 template<class Real, int p>
 void choose_refinement()
@@ -317,7 +179,7 @@ template<class Real, int p>
 void find_best_interpolator()
 {
     using std::abs;
-    int rmax = 14;
+    int rmax = 18;
     auto phi_dense = boost::math::detail::dyadic_grid<Real, p, 0>(rmax);
     Real dx_dense = (2*p-1)/static_cast<Real>(phi_dense.size()-1);
     for (int r = 2; r < rmax-2; ++r)
@@ -333,6 +195,22 @@ void find_best_interpolator()
             x[i] = i*dx;
         }
 
+        {
+          auto phi_copy = phi;
+          auto phi_prime_copy = phi_prime;
+          auto mh = boost::math::detail::matched_holder(std::move(phi_copy), std::move(phi_prime_copy), r);
+          Real sup = 0;
+          for (size_t i = 0; i < phi_dense.size(); ++i) {
+            Real x = i*dx_dense;
+            Real diff = abs(phi_dense[i] - mh(x));
+            if (diff > sup) {
+              sup = diff;
+            }
+          }
+          m.insert({sup, "matched_holder"});
+        }
+
+
         {
             auto linear = [&phi, &dx, &r](Real x)->Real {
               if (x <= 0 || x >= 2*p-1) {
@@ -389,6 +267,9 @@ void find_best_interpolator()
           m.insert({cbs_sup, "cubic_b_spline"});
         }
 
+
+        // Whittaker-Shannon interpolation has linear complexity; test over all points and it's quadratic.
+        // I ran this a couple times and found it's not competitive; so comment out for now.
         /*{
             auto phi_copy = phi;
             auto ws = boost::math::interpolators::whittaker_shannon(std::move(phi_copy), Real(0), dx);
@@ -622,14 +503,14 @@ void find_best_interpolator()
 
 int main() {
 
-    do_ulp<float, 5>();
-    //test_interpolate_with_roots<double, 5>();
+    //do_ulp<float, 5>();
+
     //choose_refinement<float, 5>();
     //choose_refinement<double, 15>();
-    /*// Says linear interpolation is the best:
+    // Says linear interpolation is the best:
     find_best_interpolator<long double, 2>();
 
-    // Says linear interpolation is the best:
+    /*// Says linear interpolation is the best:
     find_best_interpolator<long double, 3>();
 
     // Says cubic_hermite_spline is best:
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index 8eb8ec393..b8990c4da 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -102,7 +102,7 @@ public:
         // It's only exactly right at dyadic rationals.
         //Real constexpr const alpha = 2 - log(1+sqrt(Real(3)))/log(Real(2));
         // So we're gonna make the graph dip a little harder; this will capture more of the self-similar behavior:
-        Real constexpr const alpha = 0.35;
+        Real constexpr const alpha = 0.3;
         int64_t i = static_cast<int64_t>(std::floor(x/h_));
         Real t = (x- i*h_)/h_;
         Real v = y_[i];

From 1ac3beacd7874d49182f5ef3b3f018b8f3acf4a6 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Wed, 5 Feb 2020 11:06:05 -0500
Subject: [PATCH 010/104] Clean up finding best interpolator code for
 Daubechies scaling [CI SKIP]

---
 ... => find_best_daubechies_interpolator.cpp} | 24 ++++++++++---------
 .../special_functions/daubechies_scaling.hpp  |  2 +-
 2 files changed, 14 insertions(+), 12 deletions(-)
 rename example/{daubechies_accuracy.cpp => find_best_daubechies_interpolator.cpp} (96%)

diff --git a/example/daubechies_accuracy.cpp b/example/find_best_daubechies_interpolator.cpp
similarity index 96%
rename from example/daubechies_accuracy.cpp
rename to example/find_best_daubechies_interpolator.cpp
index eddd1e5a3..9ca360dd5 100644
--- a/example/daubechies_accuracy.cpp
+++ b/example/find_best_daubechies_interpolator.cpp
@@ -17,12 +17,12 @@
 #include <boost/math/interpolators/pchip.hpp>
 #include <boost/multiprecision/float128.hpp>
 #include <boost/core/demangle.hpp>
-#include <quicksvg/graph_fn.hpp>
-#include <quicksvg/ulp_plot.hpp>
+//#include <quicksvg/graph_fn.hpp>
+//#include <quicksvg/ulp_plot.hpp>
 
 using boost::multiprecision::float128;
 
-template<class Real, int p>
+/*template<class Real, int p>
 void do_ulp()
 {
     std::cout << "Creating ULP plot on type " << boost::core::demangle(typeid(Real).name()) << " and " << p << " vanishing moments.\n";  
@@ -78,7 +78,7 @@ void do_ulp()
                         title, 15000, 1100, 10);
     std::cout << "Done writing ulp plot\n";
 
-}
+}*/
 
 
 template<class Real, int p>
@@ -179,10 +179,10 @@ template<class Real, int p>
 void find_best_interpolator()
 {
     using std::abs;
-    int rmax = 18;
+    int rmax = 15;
     auto phi_dense = boost::math::detail::dyadic_grid<Real, p, 0>(rmax);
     Real dx_dense = (2*p-1)/static_cast<Real>(phi_dense.size()-1);
-    for (int r = 2; r < rmax-2; ++r)
+    for (int r = 2; r < rmax-1; ++r)
     {
         std::map<Real, std::string> m;
         auto phi = boost::math::detail::dyadic_grid<Real, p, 0>(r);
@@ -190,7 +190,7 @@ void find_best_interpolator()
 
         std::vector<Real> x(phi.size());
         Real dx = (2*p-1)/static_cast<Real>(x.size()-1);
-        std::cout << "dx = " << dx << "\n";
+        std::cout << "dx = 1/" << (1 << r) << " = " << dx << "\n";
         for (size_t i = 0; i < x.size(); ++i) {
             x[i] = i*dx;
         }
@@ -346,6 +346,7 @@ void find_best_interpolator()
           m.insert({sup, "makima"});
         }
 
+        // Again, linear complexity of evaluation => quadratic complexity of exhaustive checking.
         /*{
             auto trig = boost::math::interpolators::cardinal_trigonometric(phi, Real(0), dx);
             Real sup = 0;
@@ -489,15 +490,16 @@ void find_best_interpolator()
         }
         std::string best = "none";
         Real best_sup = 1000000000;
+        std::cout << std::setprecision(20) << std::fixed;
         for (auto & e : m) {
           
-          std::cout << std::setprecision(20) << std::fixed << e.first << " is error of " << e.second << "\n";
+          std::cout << "\t" << e.first << " is error of " << e.second << "\n";
           if (e.first < best_sup) {
             best = e.second;
             best_sup = e.first;
           }
         }
-        std::cout << "The best method for p = " << p << " is the " << best << "\n";
+        std::cout << "\tThe best method for p = " << p << " is the " << best << "\n";
     }
 }
 
@@ -510,7 +512,7 @@ int main() {
     // Says linear interpolation is the best:
     find_best_interpolator<long double, 2>();
 
-    /*// Says linear interpolation is the best:
+    // Says linear interpolation is the best:
     find_best_interpolator<long double, 3>();
 
     // Says cubic_hermite_spline is best:
@@ -526,5 +528,5 @@ int main() {
     find_best_interpolator<long double, 7>();
 
     // Says quintic_hermite_spline is best:
-    find_best_interpolator<long double, 15>();*/
+    find_best_interpolator<long double, 15>();
 }
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index b8990c4da..f77c50691 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -102,7 +102,7 @@ public:
         // It's only exactly right at dyadic rationals.
         //Real constexpr const alpha = 2 - log(1+sqrt(Real(3)))/log(Real(2));
         // So we're gonna make the graph dip a little harder; this will capture more of the self-similar behavior:
-        Real constexpr const alpha = 0.3;
+        Real constexpr const alpha = Real(3)/Real(10);
         int64_t i = static_cast<int64_t>(std::floor(x/h_));
         Real t = (x- i*h_)/h_;
         Real v = y_[i];

From 07e884c38649be4fcaf3491feb4de2aac5fd622c Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Fri, 7 Feb 2020 09:46:02 -0500
Subject: [PATCH 011/104] Choose refinement for each type and number of
 vanishing moment. [CI SKIP]

---
 .../special_functions/daubechies_scaling.hpp  | 132 ++++++++++++++++--
 1 file changed, 120 insertions(+), 12 deletions(-)

diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index f77c50691..62b8a4de0 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -100,10 +100,10 @@ public:
         }
         // This is the exact Holder exponent, but it's pessimistic almost everywhere!
         // It's only exactly right at dyadic rationals.
-        //Real constexpr const alpha = 2 - log(1+sqrt(Real(3)))/log(Real(2));
+        Real const alpha = 2 - log(1+sqrt(Real(3)))/log(Real(2));
         // So we're gonna make the graph dip a little harder; this will capture more of the self-similar behavior:
-        Real constexpr const alpha = Real(3)/Real(10);
-        int64_t i = static_cast<int64_t>(std::floor(x/h_));
+        //Real constexpr const alpha = Real(3)/Real(10);
+        int64_t i = static_cast<int64_t>(floor(x/h_));
         Real t = (x- i*h_)/h_;
         Real v = y_[i];
         Real dphi = dydx_[i+1]*h_;
@@ -118,6 +118,36 @@ private:
     RandomAccessContainer dydx_;
 };
 
+
+template<class RandomAccessContainer>
+class linear_interpolation {
+public:
+    using Real = typename RandomAccessContainer::value_type;
+
+    linear_interpolation(RandomAccessContainer && y,  int grid_refinements) : y_{std::move(y)}
+    {
+        grid_refinements_ = grid_refinements;
+    }
+
+    Real operator()(Real x) const {
+        using std::floor;
+        if (x <= 0 || x >= 5) {
+            return 0;
+        }
+        Real y = x*(1<<grid_refinements_);
+        Real k = floor(y);
+
+        size_t kk = static_cast<size_t>(k);
+
+        Real t = y - k;
+        return (1-t)*y_[kk] + t*y_[kk+1];
+    }
+
+private:
+    int grid_refinements_;
+    RandomAccessContainer y_;
+};
+
 }
 
 template<class Real, int p>
@@ -125,25 +155,95 @@ class daubechies_scaling {
 public:
     daubechies_scaling(int grid_refinements = -1)
     {
+        static_assert(p <= 15, "Scaling functions only implements up to p = 15");
         using boost::multiprecision::float128;
         if (grid_refinements < 0)
         {
-            grid_refinements = 20;
+            if (std::is_same_v<Real, float>)
+            {
+                //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15
+                std::array<int, 16> r{-1, -1, 22, 21, 19, 17, 16, 15, 14, 13, 12, 11, 11, 11, 11, 11};
+                grid_refinements = r[p];
+            }
+            else if (std::is_same_v<Real, double>)
+            {
+                //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15
+                std::array<int, 16> r{-1, -1, 22, 22, 22, 22, 22, 22, 22, 22, 21, 21, 20, 19, 18, 18};
+                grid_refinements = r[p];
+            }
+            else
+            {
+                grid_refinements = 22;
+            }
         }
 
-        if (p==3) {
-            throw std::domain_error("p = 3 is not yet implemented!");
-        }
         // Compute the refined grid:
         // In fact for float precision I know the grid must be computed in double precision and then cast back down, or else parts of the support are systematically inaccurate.
-        std::future<std::vector<Real>> t0 = std::async(std::launch::async, [&grid_refinements]() { return detail::dyadic_grid<Real, p, 0>(grid_refinements); });
+        std::future<std::vector<Real>> t0 = std::async(std::launch::async, [&grid_refinements]() {
+            // Computing in higher precision and downcasting is essential for 1ULP evaluation in float precision:
+            if constexpr (std::is_same_v<Real, float>) {
+                auto v = detail::dyadic_grid<double, p, 0>(grid_refinements);
+                std::vector<float> w(v.size());
+                for (size_t i = 0; i < v.size(); ++i) {
+                    w[i] = v[i];
+                }
+                return w;
+            }
+            else if constexpr (std::is_same_v<Real, double>) {
+                auto v = detail::dyadic_grid<long double, p, 0>(grid_refinements);
+                std::vector<double> w(v.size());
+                for (size_t i = 0; i < v.size(); ++i) {
+                    w[i] = v[i];
+                }
+                return w;
+            }
+
+            return detail::dyadic_grid<Real, p, 0>(grid_refinements);
+        });
         // Compute the derivative of the refined grid:
-        std::future<std::vector<Real>> t1 = std::async(std::launch::async, [&grid_refinements]() { return detail::dyadic_grid<Real, p, 1>(grid_refinements); });
+        std::future<std::vector<Real>> t1 = std::async(std::launch::async, [&grid_refinements]() {
+            if constexpr (std::is_same_v<Real, float>) {
+                auto v = detail::dyadic_grid<double, p, 1>(grid_refinements);
+                std::vector<float> w(v.size());
+                for (size_t i = 0; i < v.size(); ++i) {
+                    w[i] = v[i];
+                }
+                return w;
+            }
+            else if constexpr (std::is_same_v<Real, double>) {
+                auto v = detail::dyadic_grid<long double, p, 1>(grid_refinements);
+                std::vector<double> w(v.size());
+                for (size_t i = 0; i < v.size(); ++i) {
+                    w[i] = v[i];
+                }
+                return w;
+            }
+
+            return detail::dyadic_grid<Real, p, 1>(grid_refinements);
+        });
 
         // if necessary, compute the second derivative:
         std::vector<Real> d2ydx2;
         if constexpr (p >= 6) {
-            std::future<std::vector<Real>> t3 = std::async(std::launch::async, [&grid_refinements]() { return detail::dyadic_grid<Real, p, 2>(grid_refinements); });
+            std::future<std::vector<Real>> t3 = std::async(std::launch::async, [&grid_refinements]() {
+                if constexpr (std::is_same_v<Real, float>) {
+                    auto v = detail::dyadic_grid<double, p, 2>(grid_refinements);
+                    std::vector<float> w(v.size());
+                    for (size_t i = 0; i < v.size(); ++i) {
+                        w[i] = v[i];
+                    }
+                    return w;
+                }
+                else if constexpr (std::is_same_v<Real, double>) {
+                    auto v = detail::dyadic_grid<long double, p, 2>(grid_refinements);
+                    std::vector<double> w(v.size());
+                    for (size_t i = 0; i < v.size(); ++i) {
+                        w[i] = v[i];
+                    }
+                    return w;
+                }
+
+                return detail::dyadic_grid<Real, p, 2>(grid_refinements); });
             d2ydx2 = t3.get();
         }
 
@@ -162,6 +262,9 @@ public:
         if constexpr (p==2) {
             m_mh = std::make_shared<detail::matched_holder<std::vector<Real>>>(std::move(y), std::move(dydx), grid_refinements);
         }
+        if constexpr (p==3) {
+            m_lin = std::make_shared<detail::linear_interpolation<std::vector<Real>>>(std::move(y), grid_refinements);
+        }
         if constexpr (p == 4 || p == 5) {
             m_cbh = std::make_shared<interpolators::detail::cubic_hermite_detail<std::vector<Real>>>(std::move(x), std::move(y), std::move(dydx));
         }
@@ -175,6 +278,9 @@ public:
         if constexpr (p==2) {
             return m_mh->operator()(x);
         }
+        if constexpr (p==3) {
+            return m_lin->operator()(x);
+        }
         if constexpr (p==4 || p ==5) {
             return m_cbh->operator()(x);
         }
@@ -184,8 +290,8 @@ public:
     }
 
     Real prime(Real x) const {
-        if constexpr (p==2) {
-            throw std::domain_error("The 2-vanishing moment Daubechies scaling function is not continuously differentiable.");
+        if constexpr (p==2 || p == 3) {
+            throw std::domain_error("The 2 and 3-vanishing moment Daubechies scaling function is not continuously differentiable.");
         }
         if constexpr (p==4 || p ==5) {
             return m_cbh->prime(x);
@@ -203,6 +309,8 @@ private:
     size_t m_levels;
     // Need this for p = 2:
     std::shared_ptr<detail::matched_holder<std::vector<Real>>> m_mh;
+    // Need this for p = 3:
+    std::shared_ptr<detail::linear_interpolation<std::vector<Real>>> m_lin;
     // need this for p = 4,5:
     std::shared_ptr<interpolators::detail::cubic_hermite_detail<std::vector<Real>>> m_cbh;
     // need this for p >= 6:

From 231dd8cb56bd04bc75c7f622d9d8f672629add3d Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Fri, 7 Feb 2020 10:49:22 -0500
Subject: [PATCH 012/104] Tamp down on grid refinements [CI SKIP]

---
 include/boost/math/special_functions/daubechies_scaling.hpp | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index 62b8a4de0..c0e026080 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -167,13 +167,15 @@ public:
             }
             else if (std::is_same_v<Real, double>)
             {
+                // r = 21 is correct for p >= 10.
+                // Before that, r > 21 would be appropriate, but the hardware isn't there yet!
                 //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15
-                std::array<int, 16> r{-1, -1, 22, 22, 22, 22, 22, 22, 22, 22, 21, 21, 20, 19, 18, 18};
+                std::array<int, 16> r{-1, -1, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 20, 19, 18, 18};
                 grid_refinements = r[p];
             }
             else
             {
-                grid_refinements = 22;
+                grid_refinements = 21;
             }
         }
 

From 09213a0835f94a7945b0afcabffe2a6d3008fdfd Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Sat, 8 Feb 2020 12:46:28 -0500
Subject: [PATCH 013/104] Add septic Hermite interpolation. This still needs
 some tlc to get to 1ULP evaluation [CI SKIP]

---
 example/find_best_daubechies_interpolator.cpp | 103 +++++------
 .../detail/septic_hermite_detail.hpp          | 160 ++++++++++++++++++
 .../math/interpolators/septic_hermite.hpp     |  38 +++++
 .../special_functions/daubechies_scaling.hpp  |  50 +++++-
 4 files changed, 282 insertions(+), 69 deletions(-)
 create mode 100644 include/boost/math/interpolators/detail/septic_hermite_detail.hpp
 create mode 100644 include/boost/math/interpolators/septic_hermite.hpp

diff --git a/example/find_best_daubechies_interpolator.cpp b/example/find_best_daubechies_interpolator.cpp
index 9ca360dd5..d9277f698 100644
--- a/example/find_best_daubechies_interpolator.cpp
+++ b/example/find_best_daubechies_interpolator.cpp
@@ -5,8 +5,9 @@
 #include <thread>
 #include <boost/math/special_functions/daubechies_scaling.hpp>
 #include <boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp>
-#include <boost/math/interpolators/quintic_hermite.hpp>
 #include <boost/math/interpolators/cubic_hermite.hpp>
+#include <boost/math/interpolators/quintic_hermite.hpp>
+#include <boost/math/interpolators/septic_hermite.hpp>
 #include <boost/math/interpolators/cardinal_quadratic_b_spline.hpp>
 #include <boost/math/interpolators/cardinal_cubic_b_spline.hpp>
 #include <boost/math/interpolators/cardinal_quintic_b_spline.hpp>
@@ -22,64 +23,6 @@
 
 using boost::multiprecision::float128;
 
-/*template<class Real, int p>
-void do_ulp()
-{
-    std::cout << "Creating ULP plot on type " << boost::core::demangle(typeid(Real).name()) << " and " << p << " vanishing moments.\n";  
-    using std::floor;
-    using std::ceil;
-    using std::abs;
-    int rmax = 14;
-    std::cout << "Computing phi_dense\n";
-    std::future<std::vector<long double>> f1 = std::async(std::launch::async, [&]{ return boost::math::detail::dyadic_grid<long double, p, 0>(rmax); });
-    std::future<std::vector<long double>> f2 = std::async(std::launch::async, [&]{ return boost::math::detail::dyadic_grid<long double, p, 1>(rmax); });
-
-    std::cout << "Computing phi and phi_prime\n";
-    std::future<std::vector<long double>> f3 = std::async(std::launch::async, [&]{ return boost::math::detail::dyadic_grid<long double, p, 0>(rmax-2); });
-    std::future<std::vector<long double>> f4 = std::async(std::launch::async, [&]{ return boost::math::detail::dyadic_grid<long double, p, 1>(rmax-2); });
-    auto phi_dense = f1.get();
-    auto phi_dense_prime = f2.get();
-    auto phi_accurate = f3.get();
-    auto phi_prime_accurate = f4.get();
-
-    Real dx_dense = (2*p-1)/static_cast<Real>(phi_dense.size()-1);
-    std::cout << "Done precomputing grids; downcasting now.\n";
-    std::vector<Real> phi(phi_accurate.size());
-    for (size_t i = 0; i < phi_accurate.size(); ++i) {
-        phi[i] = Real(phi_accurate[i]);
-    }
-    std::vector<Real> phi_prime(phi_accurate.size());
-    for (size_t i = 0; i < phi_prime_accurate.size(); ++i) {
-        phi_prime[i] = Real(phi_prime_accurate[i]);
-    }
-    phi_accurate.resize(0);
-    phi_prime_accurate.resize(0);
-
-    std::vector<Real> x(phi.size());
-    Real dx = (2*p-1)/static_cast<Real>(x.size()-1);
-    std::cout << "dx = " << dx << "\n";
-    for (size_t i = 0; i < x.size(); ++i) {
-      x[i] = i*dx;
-    }
-
-    auto ch = boost::math::interpolators::cubic_hermite(std::move(x), std::move(phi), std::move(phi_prime));
-
-    std::vector<long double> x_acc(phi_dense.size());
-    
-    for (size_t i = 0; i < x_acc.size(); ++i) {
-      x_acc[i] = i*dx_dense;
-    }
-
-    auto acc = boost::math::interpolators::cubic_hermite(std::move(x_acc), std::move(phi_dense), std::move(phi_dense_prime));
-    std::cout << "Writing ulp plot\n";
-    std::string title = "daub" + std::to_string(p) + "_" + std::to_string(rmax-2) + "_" + boost::core::demangle(typeid(Real).name()) + ".svg";
-    quicksvg::ulp_plot(ch, acc, Real(0), Real(2*p-1), 
-                        "ULP plot of Daubechies with " + std::to_string(rmax-2) + " refinements on type " + boost::core::demangle(typeid(Real).name()),
-                        title, 15000, 1100, 10);
-    std::cout << "Done writing ulp plot\n";
-
-}*/
-
 
 template<class Real, int p>
 void choose_refinement()
@@ -486,11 +429,29 @@ void find_best_interpolator()
               m.insert({sup, "Third-order Taylor"});
             }
 
+            {
+                auto phi_copy = phi;
+                auto x_copy = x;
+                auto phi_prime_copy = phi_prime;
+                auto phi_dbl_prime_copy = phi_dbl_prime;
+                auto phi_triple_prime_copy = phi_triple_prime;
+                auto sh = boost::math::interpolators::septic_hermite(std::move(x_copy), std::move(phi_copy), std::move(phi_prime_copy), std::move(phi_dbl_prime_copy), std::move(phi_triple_prime_copy));
+                Real sup = 0;
+                for (size_t i = 0; i < phi_dense.size(); ++i) {
+                  Real x = i*dx_dense;
+                  Real diff = abs(phi_dense[i] - sh(x));
+                  if (diff > sup) {
+                    sup = diff;
+                  }
+                }
+                m.insert({sup, "septic_hermite_spline"});
+            }
+
 
         }
         std::string best = "none";
         Real best_sup = 1000000000;
-        std::cout << std::setprecision(20) << std::fixed;
+        std::cout << std::setprecision(std::numeric_limits<Real>::digits10 + 3) << std::fixed;
         for (auto & e : m) {
           
           std::cout << "\t" << e.first << " is error of " << e.second << "\n";
@@ -505,12 +466,10 @@ void find_best_interpolator()
 
 int main() {
 
-    //do_ulp<float, 5>();
-
     //choose_refinement<float, 5>();
     //choose_refinement<double, 15>();
     // Says linear interpolation is the best:
-    find_best_interpolator<long double, 2>();
+    /*find_best_interpolator<long double, 2>();
 
     // Says linear interpolation is the best:
     find_best_interpolator<long double, 3>();
@@ -528,5 +487,21 @@ int main() {
     find_best_interpolator<long double, 7>();
 
     // Says quintic_hermite_spline is best:
-    find_best_interpolator<long double, 15>();
+    find_best_interpolator<long double, 8>();*/
+    // Says quintic_hermite_spline is best:
+    find_best_interpolator<long double, 9>();
+    // Says septic_hermite_spline is best:
+    find_best_interpolator<long double, 10>();
+    /*
+    // Says septic_hermite_spline is best:
+    find_best_interpolator<long double, 11>();
+    // Says septic_hermite_spline is best:
+    find_best_interpolator<long double, 12>();
+    // Says septic_hermite_spline is best:
+    find_best_interpolator<long double, 13>();
+    // Says septic_hermite_spline is best:
+    find_best_interpolator<long double, 14>();*/
+
+    // Says septic_hermite_spline is best:
+    find_best_interpolator<float128, 15>();
 }
diff --git a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
new file mode 100644
index 000000000..c3e4b8e0b
--- /dev/null
+++ b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
@@ -0,0 +1,160 @@
+#ifndef BOOST_MATH_INTERPOLATORS_DETAIL_SEPTIC_HERMITE_DETAIL_HPP
+#define BOOST_MATH_INTERPOLATORS_DETAIL_SEPTIC_HERMITE_DETAIL_HPP
+#include <algorithm>
+#include <stdexcept>
+#include <sstream>
+#include <cmath>
+
+namespace boost::math::interpolators::detail {
+
+template<class RandomAccessContainer>
+class septic_hermite_detail {
+public:
+    using Real = typename RandomAccessContainer::value_type;
+    septic_hermite_detail(RandomAccessContainer && x, RandomAccessContainer && y, RandomAccessContainer && dydx, RandomAccessContainer && d2ydx2, RandomAccessContainer && d3ydx3) 
+    : x_{std::move(x)}, y_{std::move(y)}, dydx_{std::move(dydx)}, d2ydx2_{std::move(d2ydx2)}, d3ydx3_{std::move(d3ydx3)}
+    {
+        if (x_.size() != y_.size()) {
+            throw std::domain_error("Number of abscissas must = number of ordinates.");
+        }
+        if (x_.size() != dydx_.size()) {
+            throw std::domain_error("Numbers of derivatives must = number of abscissas.");
+        }
+        if (x_.size() != d2ydx2_.size()) {
+            throw std::domain_error("Number of second derivatives must equal number of abscissas.");
+        }
+        if (x_.size() != d3ydx3_.size()) {
+            throw std::domain_error("Number of third derivatives must equal number of abscissas.");
+        }
+
+        if (x_.size() < 2) {
+            throw std::domain_error("At least 2 abscissas are required.");
+        }
+        Real x0 = x_[0];
+        for (decltype(x_.size()) i = 1; i < x_.size(); ++i) {
+            Real x1 = x_[i];
+            if (x1 <= x0)
+            {
+                throw std::domain_error("Abscissas must be sorted in strictly increasing order x0 < x1 < ... < x_{n-1}");
+            }
+            x0 = x1;
+        }
+    }
+
+    void push_back(Real x, Real y, Real dydx, Real d2ydx2, Real d3ydx3) {
+        using std::abs;
+        using std::isnan;
+        if (x <= x_.back()) {
+             throw std::domain_error("Calling push_back must preserve the monotonicity of the x's");
+        }
+        x_.push_back(x);
+        y_.push_back(y);
+        dydx_.push_back(dydx);
+        d2ydx2_.push_back(d2ydx2);
+        d3ydx3_.push_back(d3ydx3);
+    }
+
+    Real operator()(Real x) const {
+        if  (x < x_[0] || x > x_.back()) {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x_[0] << ", " << x_.back() << "]";
+            throw std::domain_error(oss.str());
+        }
+        // We need t := (x-x_k)/(x_{k+1}-x_k) \in [0,1) for this to work.
+        // Sadly this neccessitates this loathesome check, otherwise we get t = 1 at x = xf.
+        if (x == x_.back()) {
+            return y_.back();
+        }
+
+        auto it = std::upper_bound(x_.begin(), x_.end(), x);
+        auto i = std::distance(x_.begin(), it) -1;
+        Real x0 = *(it-1);
+        Real x1 = *it;
+        Real y0 = y_[i];
+        Real y1 = y_[i+1];
+        // Velocity:
+        Real v0 = dydx_[i];
+        Real v1 = dydx_[i+1];
+        // Acceleration:
+        Real a0 = d2ydx2_[i];
+        Real a1 = d2ydx2_[i+1];
+        // Jerk:
+        Real j0 = d3ydx3_[i];
+        Real j1 = d3ydx3_[i+1];
+
+        Real dx = (x1-x0);
+        Real t = (x-x0)/dx;
+
+        // See: 
+        // http://seisweb.usask.ca/classes/GEOL481/2017/Labs/interpolation_utilities_matlab/shermite.m
+        Real t2 = t*t;
+        Real t3 = t2*t;
+        Real t4 = t3*t;
+        Real t5 = t4*t;
+        Real t6 = t5*t;
+        Real t7 = t6*t;
+        Real dx2 = dx*dx;
+        Real dx3 = dx2*dx;
+        Real z0 = 20*t7 - 70*t6 + 84*t5 - 35*t4 + 1;
+        Real z1 = 10*t7 - 36*t6 + 45*t5 - 20*t4 + t;
+        Real z2 = 2*t7 - 15*t6/2 + 10*t5 - 5*t4 + t2/2;
+        Real z3 = t7/6 - 2*t6/3 + t5 - 2*t4/3 + t3/6;
+        Real z4 = 1 - z0;
+        Real z5 = 10*t7 - 34*t6 + 39*t5 - 15*t4;
+        Real z6 = -2*t7 + 13*t6/2 - 7*t5 + 5*t4/2;
+        Real z7 = t7/6 - t6/2 + t5/2 - t4/6;
+
+        Real y = z0*y0 + z1*dx*v0 + z2*dx2*a0 + z3*dx3*j0 + z4*y1 + z5*dx*v1 + z6*dx2*a1 + z7*dx3*j1;
+        return y;
+    }
+
+    Real prime(Real x) const {
+        if  (x < x_[0] || x > x_.back()) {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x_[0] << ", " << x_.back() << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == x_.back()) {
+            return dydx_.back();
+        }
+
+        auto it = std::upper_bound(x_.begin(), x_.end(), x);
+        auto i = std::distance(x_.begin(), it) -1;
+        Real x0 = *(it-1);
+        Real x1 = *it;
+        Real s0 = dydx_[i];
+        Real s1 = dydx_[i+1];
+
+        // Ridiculous linear interpolation. Fine for now:
+        Real numerator = s0*(x1-x) + s1*(x-x0);
+        Real denominator = x1 - x0;
+        return numerator/denominator;
+    }
+
+
+    friend std::ostream& operator<<(std::ostream & os, const septic_hermite_detail & m)
+    {
+        os << "(x,y,y') = {";
+        for (size_t i = 0; i < m.x_.size() - 1; ++i) {
+            os << "(" << m.x_[i] << ", " << m.y_[i] << ", " << m.dydx_[i] << ", " << m.d2ydx2_[i] <<  ", " << m.d3ydx3_[i] << "),  ";
+        }
+        auto n = m.x_.size()-1;
+        os << "(" << m.x_[n] << ", " << m.y_[n] << ", " << m.dydx_[n] << ", " << m.d2ydx2_[n] << m.d3ydx3_[n] << ")}";
+        return os;
+    }
+
+
+
+private:
+    RandomAccessContainer x_;
+    RandomAccessContainer y_;
+    RandomAccessContainer dydx_;
+    RandomAccessContainer d2ydx2_;
+    RandomAccessContainer d3ydx3_;
+};
+}
+#endif 
\ No newline at end of file
diff --git a/include/boost/math/interpolators/septic_hermite.hpp b/include/boost/math/interpolators/septic_hermite.hpp
new file mode 100644
index 000000000..c544d1c63
--- /dev/null
+++ b/include/boost/math/interpolators/septic_hermite.hpp
@@ -0,0 +1,38 @@
+#ifndef BOOST_MATH_INTERPOLATORS_SEPTIC_HERMITE_HPP
+#define BOOST_MATH_INTERPOLATORS_SEPTIC_HERMITE_HPP
+#include <algorithm>
+#include <stdexcept>
+#include <memory>
+#include <boost/math/interpolators/detail/septic_hermite_detail.hpp>
+
+namespace boost::math::interpolators {
+
+template<class RandomAccessContainer>
+class septic_hermite {
+public:
+    using Real = typename RandomAccessContainer::value_type;
+    septic_hermite(RandomAccessContainer && x, RandomAccessContainer && y, RandomAccessContainer && dydx, 
+                    RandomAccessContainer && d2ydx2, RandomAccessContainer && d3ydx3)
+     : impl_(std::make_shared<detail::septic_hermite_detail<RandomAccessContainer>>(std::move(x), 
+     std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3)))
+    {}
+
+    Real operator()(Real x) const {
+        return impl_->operator()(x);
+    }
+
+    Real prime(Real x) const {
+        return impl_->prime(x);
+    }
+
+    friend std::ostream& operator<<(std::ostream & os, const septic_hermite & m)
+    {
+        os << *m.impl_;
+        return os;
+    }
+
+private:
+    std::shared_ptr<detail::septic_hermite_detail<RandomAccessContainer>> impl_;
+};
+}
+#endif 
\ No newline at end of file
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index c0e026080..591030adb 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -19,6 +19,7 @@
 #include <boost/math/filters/daubechies.hpp>
 #include <boost/math/interpolators/detail/cubic_hermite_detail.hpp>
 #include <boost/math/interpolators/detail/quintic_hermite_detail.hpp>
+#include <boost/math/interpolators/detail/septic_hermite_detail.hpp>
 
 
 namespace boost::math {
@@ -226,6 +227,7 @@ public:
 
         // if necessary, compute the second derivative:
         std::vector<Real> d2ydx2;
+        std::vector<Real> d3ydx3;
         if constexpr (p >= 6) {
             std::future<std::vector<Real>> t3 = std::async(std::launch::async, [&grid_refinements]() {
                 if constexpr (std::is_same_v<Real, float>) {
@@ -245,10 +247,35 @@ public:
                     return w;
                 }
 
-                return detail::dyadic_grid<Real, p, 2>(grid_refinements); });
+                return detail::dyadic_grid<Real, p, 2>(grid_refinements);
+            });
+
+            if constexpr (p >= 10) {
+                std::future<std::vector<Real>> t4 = std::async(std::launch::async, [&grid_refinements]() {
+                    if constexpr (std::is_same_v<Real, float>) {
+                        auto v = detail::dyadic_grid<double, p, 3>(grid_refinements);
+                        std::vector<float> w(v.size());
+                        for (size_t i = 0; i < v.size(); ++i) {
+                            w[i] = v[i];
+                        }
+                        return w;
+                    }
+                    else if constexpr (std::is_same_v<Real, double>) {
+                        auto v = detail::dyadic_grid<long double, p, 3>(grid_refinements);
+                        std::vector<double> w(v.size());
+                        for (size_t i = 0; i < v.size(); ++i) {
+                            w[i] = v[i];
+                        }
+                        return w;
+                    }
+
+                    return detail::dyadic_grid<Real, p, 3>(grid_refinements); });
+                d3ydx3 = t4.get();
+            }
             d2ydx2 = t3.get();
         }
 
+
         auto y = t0.get();
         auto dydx = t1.get();
 
@@ -270,9 +297,13 @@ public:
         if constexpr (p == 4 || p == 5) {
             m_cbh = std::make_shared<interpolators::detail::cubic_hermite_detail<std::vector<Real>>>(std::move(x), std::move(y), std::move(dydx));
         }
-        else if constexpr (p >= 6) {
+        if constexpr (p >= 6 && p <= 9) {
             m_qh = std::make_shared<interpolators::detail::quintic_hermite_detail<std::vector<Real>>>(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2));
         }
+        if constexpr (p >= 10) {
+            m_sh = std::make_shared<interpolators::detail::septic_hermite_detail<std::vector<Real>>>(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3));
+        }
+
      }
 
 
@@ -286,9 +317,12 @@ public:
         if constexpr (p==4 || p ==5) {
             return m_cbh->operator()(x);
         }
-        else if constexpr (p >= 6) {
+        if constexpr (p >= 6 && p <= 9) {
             return m_qh->operator()(x);
         }
+        if constexpr (p >= 10) {
+            return m_sh->operator()(x);
+        }
     }
 
     Real prime(Real x) const {
@@ -298,9 +332,12 @@ public:
         if constexpr (p==4 || p ==5) {
             return m_cbh->prime(x);
         }
-        else if constexpr (p >= 6) {
+        if constexpr (p >= 6 && p <= 9) {
             return m_qh->prime(x);
         }
+        if constexpr (p >= 10) {
+            return m_sh->prime(x);
+        }
     }
 
     std::pair<int, int> support() const {
@@ -315,9 +352,12 @@ private:
     std::shared_ptr<detail::linear_interpolation<std::vector<Real>>> m_lin;
     // need this for p = 4,5:
     std::shared_ptr<interpolators::detail::cubic_hermite_detail<std::vector<Real>>> m_cbh;
-    // need this for p >= 6:
+    // need this for p = 6,7,8,9:
     std::shared_ptr<interpolators::detail::quintic_hermite_detail<std::vector<Real>>> m_qh;
 
+    // need this for p >= 10:
+    std::shared_ptr<interpolators::detail::septic_hermite_detail<std::vector<Real>>> m_sh;
+
     /*Real constant_interpolation(Real x) const {
         if (x <= 0 || x >= 2*p-1) {
             return Real(0);

From 3f5dc81fee5fd2527f08c1725c70270744557282 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Mon, 10 Feb 2020 13:31:26 -0500
Subject: [PATCH 014/104] Equispace cubic Hermite interpolation. [CI SKIP]

---
 .../interpolators/cardinal_cubic_hermite.hpp  |  71 ++++++
 .../detail/cardinal_cubic_hermite_detail.hpp  | 204 ++++++++++++++++++
 .../detail/septic_hermite_detail.hpp          |   8 +-
 .../special_functions/daubechies_scaling.hpp  |  14 +-
 test/cardinal_cubic_hermite_test.cpp          | 182 ++++++++++++++++
 5 files changed, 474 insertions(+), 5 deletions(-)
 create mode 100644 include/boost/math/interpolators/cardinal_cubic_hermite.hpp
 create mode 100644 include/boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp
 create mode 100644 test/cardinal_cubic_hermite_test.cpp

diff --git a/include/boost/math/interpolators/cardinal_cubic_hermite.hpp b/include/boost/math/interpolators/cardinal_cubic_hermite.hpp
new file mode 100644
index 000000000..f5a502990
--- /dev/null
+++ b/include/boost/math/interpolators/cardinal_cubic_hermite.hpp
@@ -0,0 +1,71 @@
+// Copyright Nick Thompson, 2020
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MATH_INTERPOLATORS_CARDINAL_CUBIC_HERMITE_HPP
+#define BOOST_MATH_INTERPOLATORS_CARDINAL_CUBIC_HERMITE_HPP
+#include <memory>
+#include <boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp>
+
+namespace boost::math::interpolators {
+
+template<class RandomAccessContainer>
+class cardinal_cubic_hermite {
+public:
+    using Real = typename RandomAccessContainer::value_type;
+
+    cardinal_cubic_hermite(RandomAccessContainer && y, RandomAccessContainer && dydx, Real x0, Real dx) 
+    : impl_(std::make_shared<detail::cardinal_cubic_hermite_detail<RandomAccessContainer>>(std::move(y), std::move(dydx), x0, dx))
+    {}
+
+    inline Real operator()(Real x) const {
+        return impl_->operator()(x);
+    }
+
+    inline Real prime(Real x) const {
+        return impl_->prime(x);
+    }
+
+    friend std::ostream& operator<<(std::ostream & os, const cardinal_cubic_hermite & m)
+    {
+        os << *m.impl_;
+        return os;
+    }
+
+private:
+    std::shared_ptr<detail::cardinal_cubic_hermite_detail<RandomAccessContainer>> impl_;
+};
+
+
+template<class RandomAccessContainer>
+class cardinal_cubic_hermite_aos {
+public:
+    using Point = typename RandomAccessContainer::value_type;
+    using Real = typename Point::value_type;
+
+    cardinal_cubic_hermite_aos(RandomAccessContainer && data, Real x0, Real dx) 
+    : impl_(std::make_shared<detail::cardinal_cubic_hermite_detail_aos<RandomAccessContainer>>(std::move(data), x0, dx))
+    {}
+
+    inline Real operator()(Real x) const {
+        return impl_->operator()(x);
+    }
+
+    inline Real prime(Real x) const {
+        return impl_->prime(x);
+    }
+
+    friend std::ostream& operator<<(std::ostream & os, const cardinal_cubic_hermite_aos & m)
+    {
+        os << *m.impl_;
+        return os;
+    }
+
+private:
+    std::shared_ptr<detail::cardinal_cubic_hermite_detail_aos<RandomAccessContainer>> impl_;
+};
+
+}
+#endif
\ No newline at end of file
diff --git a/include/boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp b/include/boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp
new file mode 100644
index 000000000..dbbbc1a5a
--- /dev/null
+++ b/include/boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp
@@ -0,0 +1,204 @@
+#ifndef BOOST_MATH_INTERPOLATORS_DETAIL_CARDINAL_CUBIC_HERMITE_DETAIL_HPP
+#define BOOST_MATH_INTERPOLATORS_DETAIL_CARDINAL_CUBIC_HERMITE_DETAIL_HPP
+#include <stdexcept>
+#include <algorithm>
+#include <cmath>
+#include <iostream>
+#include <sstream>
+#include <limits>
+
+namespace boost::math::interpolators::detail {
+
+template<class RandomAccessContainer>
+class cardinal_cubic_hermite_detail {
+public:
+    using Real = typename RandomAccessContainer::value_type;
+
+    cardinal_cubic_hermite_detail(RandomAccessContainer && y, RandomAccessContainer dydx, Real x0, Real dx)
+    : y_{std::move(y)}, dydx_{std::move(dydx)}, x0_{x0}, dx_{dx}
+    {
+        using std::abs;
+        using std::isnan;
+        if (y_.size() != dydx_.size())
+        {
+            throw std::domain_error("There must be the same number of derivatives as ordinates.");
+        }
+        if (y_.size() < 2)
+        {
+            throw std::domain_error("Must be at least two data points.");
+        }
+        if (dx <= 0)
+        {
+            throw std::domain_error("dx > 0 is required.");
+        }
+    }
+
+    // Why not implement push_back? It's awkward: If the buffer is circular, x0_ += dx_.
+    // If the buffer is not circular, x0_ is unchanged.
+    // We need a concept for circular_buffer!
+
+    inline Real operator()(Real x) const {
+        const Real xf = x0_ + (y_.size()-1)*dx_;
+        if  (x < x0_ || x > xf) {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf) {
+            return y_.back();
+        }
+        return this->unchecked_evaluation(x);
+    }
+
+    inline Real unchecked_evaluation(Real x) const
+    {
+        using std::floor;
+        auto i = static_cast<decltype(y_.size())>(floor((x-x0_)/dx_));
+        Real xi = x0_ + i*dx_;
+        Real t = (x - xi)/dx_;
+        Real y0 = y_[i];
+        Real y1 = y_[i+1];
+        Real v0 = dydx_[i];
+        Real v1 = dydx_[i+1];
+
+        return (1-t)*(1-t)*(y0*(1+2*t) + v0*(x-xi))
+              + t*t*(y1*(3-2*t) + dx_*v1*(t-1));
+    }
+
+    inline Real prime(Real x) const {
+        const Real xf = x0_ + (y_.size()-1)*dx_;
+        if  (x < x0_ || x > xf) {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf)
+        {
+            return dydx_.back();
+        }
+        return this->unchecked_prime(x);
+    }
+
+    inline Real unchecked_prime(Real x) const {
+        using std::floor;
+        auto i = static_cast<decltype(y_.size())>(floor((x-x0_)/dx_));
+        Real xi = x0_ + i*dx_;
+        Real t = (x - xi)/dx_;
+        Real y0 = y_[i];
+        Real y1 = y_[i+1];
+        Real v0 = dydx_[i];
+        Real v1 = dydx_[i+1];
+
+        return 6*t*(1-t)*(y1 - y0)/dx_  + (3*t*t - 4*t+1)*v0 + t*(3*t-2)*v1;
+    }
+
+
+    auto size() const
+    {
+        return y_.size();
+    }
+
+    RandomAccessContainer y_;
+    RandomAccessContainer dydx_;
+    Real x0_;
+    Real dx_;
+};
+
+
+template<class RandomAccessContainer>
+class cardinal_cubic_hermite_detail_aos {
+public:
+    using Point = typename RandomAccessContainer::value_type;
+    using Real = typename Point::value_type;
+
+    cardinal_cubic_hermite_detail_aos(RandomAccessContainer && dat, Real x0, Real dx)
+    : dat_{std::move(dat)}, x0_{x0}, dx_{dx}
+    {
+        if (dat_.size() < 2)
+        {
+            throw std::domain_error("Must be at least two data points.");
+        }
+        if (dat_[0].size() != 2)
+        {
+            throw std::domain_error("Each datum must contain (y, y'), and nothing else.");
+        }
+    }
+
+    inline Real operator()(Real x) const {
+        using std::floor;
+        const Real xf = x0_ + (dat_.size()-1)*dx_;
+        if  (x < x0_ || x > xf) {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf) {
+            return dat_.back()[0];
+        }
+
+        return this->unchecked_evaluation(x);
+    }
+
+    inline Real unchecked_evaluation(Real x) const {
+        using std::floor;
+        auto i = static_cast<decltype(dat_.size())>(floor((x-x0_)/dx_));
+        Real xi = x0_ + i*dx_;
+        Real t = (x-xi)/dx_;
+        Real y0 = dat_[i][0];
+        Real y1 = dat_[i+1][0];
+        Real v0 = dat_[i][1];
+        Real v1 = dat_[i+1][1];
+
+
+        return (1-t)*(1-t)*(y0*(1+2*t) + v0*(x-xi))
+              + t*t*(y1*(3-2*t) + dx_*v1*(t-1));
+    }
+
+    inline Real prime(Real x) const {
+        const Real xf = x0_ + (dat_.size()-1)*dx_;
+        if  (x < x0_ || x > xf) {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf)
+        {
+            return dat_.back()[1];
+        }
+        return this->unchecked_prime(x);
+    }
+
+    inline Real unchecked_prime(Real x) const {
+        using std::floor;
+        auto i = static_cast<decltype(dat_.size())>(floor((x-x0_)/dx_));
+        Real xi = x0_ + i*dx_;
+        Real t = (x - xi)/dx_;
+        Real y0 = dat_[i][0];
+        Real y1 = dat_[i+1][0];
+        Real v0 = dat_[i][1];
+        Real v1 = dat_[i+1][1];
+
+        return 6*t*(1-t)*(y1 - y0)/dx_  + (3*t*t - 4*t+1)*v0 + t*(3*t-2)*v1;
+    }
+
+
+    auto size() const {
+        return dat_.size();
+    }
+
+    RandomAccessContainer dat_;
+    Real x0_;
+    Real dx_;
+};
+
+
+}
+#endif
\ No newline at end of file
diff --git a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
index c3e4b8e0b..224f7aab5 100644
--- a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
@@ -97,11 +97,15 @@ public:
         Real t7 = t6*t;
         Real dx2 = dx*dx;
         Real dx3 = dx2*dx;
-        Real z0 = 20*t7 - 70*t6 + 84*t5 - 35*t4 + 1;
+
+
+        Real s = t4*(-35 + t*(84 + t*(-70 + 20*t)));
+        Real z4 = -s;
+        Real z0 = s + 1;
         Real z1 = 10*t7 - 36*t6 + 45*t5 - 20*t4 + t;
         Real z2 = 2*t7 - 15*t6/2 + 10*t5 - 5*t4 + t2/2;
         Real z3 = t7/6 - 2*t6/3 + t5 - 2*t4/3 + t3/6;
-        Real z4 = 1 - z0;
+        
         Real z5 = 10*t7 - 34*t6 + 39*t5 - 15*t4;
         Real z6 = -2*t7 + 13*t6/2 - 7*t5 + 5*t4/2;
         Real z7 = t7/6 - t6/2 + t5/2 - t4/6;
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index 591030adb..ad794caf2 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -17,7 +17,7 @@
 #include <boost/math/constants/constants.hpp>
 #include <boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp>
 #include <boost/math/filters/daubechies.hpp>
-#include <boost/math/interpolators/detail/cubic_hermite_detail.hpp>
+#include <boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp>
 #include <boost/math/interpolators/detail/quintic_hermite_detail.hpp>
 #include <boost/math/interpolators/detail/septic_hermite_detail.hpp>
 
@@ -295,7 +295,8 @@ public:
             m_lin = std::make_shared<detail::linear_interpolation<std::vector<Real>>>(std::move(y), grid_refinements);
         }
         if constexpr (p == 4 || p == 5) {
-            m_cbh = std::make_shared<interpolators::detail::cubic_hermite_detail<std::vector<Real>>>(std::move(x), std::move(y), std::move(dydx));
+            Real dx = Real(1)/(1 << grid_refinements);
+            m_cbh = std::make_shared<interpolators::detail::cardinal_cubic_hermite_detail<std::vector<Real>>>(std::move(y), std::move(dydx), Real(0), dx);
         }
         if constexpr (p >= 6 && p <= 9) {
             m_qh = std::make_shared<interpolators::detail::quintic_hermite_detail<std::vector<Real>>>(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2));
@@ -308,6 +309,9 @@ public:
 
 
     Real operator()(Real x) const {
+        if (x <= 0 || x >= 2*p-1) {
+            return 0;
+        }
         if constexpr (p==2) {
             return m_mh->operator()(x);
         }
@@ -326,6 +330,10 @@ public:
     }
 
     Real prime(Real x) const {
+        if (x <= 0 || x >= 2*p-1)
+        {
+            return 0;
+        }
         if constexpr (p==2 || p == 3) {
             throw std::domain_error("The 2 and 3-vanishing moment Daubechies scaling function is not continuously differentiable.");
         }
@@ -351,7 +359,7 @@ private:
     // Need this for p = 3:
     std::shared_ptr<detail::linear_interpolation<std::vector<Real>>> m_lin;
     // need this for p = 4,5:
-    std::shared_ptr<interpolators::detail::cubic_hermite_detail<std::vector<Real>>> m_cbh;
+    std::shared_ptr<interpolators::detail::cardinal_cubic_hermite_detail<std::vector<Real>>> m_cbh;
     // need this for p = 6,7,8,9:
     std::shared_ptr<interpolators::detail::quintic_hermite_detail<std::vector<Real>>> m_qh;
 
diff --git a/test/cardinal_cubic_hermite_test.cpp b/test/cardinal_cubic_hermite_test.cpp
new file mode 100644
index 000000000..4af0ebfd5
--- /dev/null
+++ b/test/cardinal_cubic_hermite_test.cpp
@@ -0,0 +1,182 @@
+/*
+ * Copyright Nick Thompson, 2020
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include "math_unit_test.hpp"
+#include <numeric>
+#include <utility>
+#include <random>
+#include <vector>
+#include <array>
+#include <boost/math/interpolators/cardinal_cubic_hermite.hpp>
+#ifdef BOOST_HAS_FLOAT128
+#include <boost/multiprecision/float128.hpp>
+using boost::multiprecision::float128;
+#endif
+
+
+using boost::math::interpolators::cardinal_cubic_hermite;
+using boost::math::interpolators::cardinal_cubic_hermite_aos;
+
+template<typename Real>
+void test_constant()
+{
+    Real x0 = 0;
+    Real dx = 2;
+    std::vector<Real> y(25);
+    for (auto & t : y) {
+        t = 7;
+    }
+
+    std::vector<Real> dydx(y.size(), Real(0));
+
+    auto hermite_spline = cardinal_cubic_hermite(std::move(y), std::move(dydx), x0, dx);
+
+    for (Real t = x0; t <= x0 + 24*dx; t += 0.25) {
+        CHECK_ULP_CLOSE(Real(7), hermite_spline(t), 2);
+        CHECK_ULP_CLOSE(Real(0), hermite_spline.prime(t), 2);
+    }
+
+    // Array of structs:
+
+    std::vector<std::array<Real, 2>> data(25);
+    for (auto & t : data) {
+        t[0] = 7;
+        t[1] = 0;
+    }
+    auto hermite_spline_aos = cardinal_cubic_hermite_aos(std::move(data), x0, dx);
+
+    for (Real t = x0; t <= x0 + 24*dx; t += 0.25) {
+        CHECK_ULP_CLOSE(Real(7), hermite_spline_aos(t), 2);
+        CHECK_ULP_CLOSE(Real(0), hermite_spline_aos.prime(t), 2);
+    }
+ 
+}
+
+
+template<typename Real>
+void test_linear()
+{
+    Real x0 = 0;
+    Real dx = 1;
+    std::vector<Real> y{0,1,2,3};
+    std::vector<Real> dydx{1,1,1,1};
+    auto y_copy = y;
+    auto dydx_copy = dydx;
+    auto hermite_spline = cardinal_cubic_hermite(std::move(y_copy), std::move(dydx_copy), x0, dx);
+
+    CHECK_ULP_CLOSE(y[0], hermite_spline(0), 0);
+    CHECK_ULP_CLOSE(Real(1)/Real(2), hermite_spline(Real(1)/Real(2)), 10);
+    CHECK_ULP_CLOSE(y[1], hermite_spline(1), 0);
+    CHECK_ULP_CLOSE(Real(3)/Real(2), hermite_spline(Real(3)/Real(2)), 10);
+    CHECK_ULP_CLOSE(y[2], hermite_spline(2), 0);
+    CHECK_ULP_CLOSE(Real(5)/Real(2), hermite_spline(Real(5)/Real(2)), 10);
+    CHECK_ULP_CLOSE(y[3], hermite_spline(3), 0);
+
+
+    y.resize(45);
+    dydx.resize(45);
+    for (size_t i = 0; i < y.size(); ++i) {
+        y[i] = i;
+        dydx[i] = 1;
+    }
+
+    y_copy = y;
+    dydx_copy = dydx;
+    hermite_spline = cardinal_cubic_hermite(std::move(y_copy), std::move(dydx_copy), x0, dx);
+    for (Real t = 0; t < 44; t += 0.5) {
+        CHECK_ULP_CLOSE(t, hermite_spline(t), 0);
+        CHECK_ULP_CLOSE(Real(1), hermite_spline.prime(t), 0);
+    }
+
+}
+
+/*
+template<typename Real>
+void test_quadratic()
+{
+    std::vector<Real> x(50);
+    std::default_random_engine rd;
+    std::uniform_real_distribution<Real> dis(0.1,1);
+    Real x0 = dis(rd);
+    x[0] = x0;
+    for (size_t i = 1; i < x.size(); ++i) {
+        x[i] = x[i-1] + dis(rd);
+    }
+    Real xmax = x.back();
+
+    std::vector<Real> y(x.size());
+    std::vector<Real> dydx(x.size());
+    for (size_t i = 0; i < x.size(); ++i) {
+        y[i] = x[i]*x[i]/2;
+        dydx[i] = x[i];
+    }
+
+    auto s = cubic_hermite(std::move(x), std::move(y), std::move(dydx));
+    for (Real t = x0; t <= xmax; t+= 0.0125)
+    {
+        CHECK_ULP_CLOSE(t*t/2, s(t), 5);
+        CHECK_ULP_CLOSE(t, s.prime(t), 65);
+    }
+}
+
+template<typename Real>
+void test_interpolation_condition()
+{
+    for (size_t n = 4; n < 50; ++n) {
+        std::vector<Real> x(n);
+        std::vector<Real> y(n);
+        std::vector<Real> dydx(n);
+        std::default_random_engine rd;
+        std::uniform_real_distribution<Real> dis(0,1);
+        Real x0 = dis(rd);
+        x[0] = x0;
+        y[0] = dis(rd);
+        for (size_t i = 1; i < n; ++i) {
+            x[i] = x[i-1] + dis(rd);
+            y[i] = dis(rd);
+            dydx[i] = dis(rd);
+        }
+
+        auto x_copy = x;
+        auto y_copy = y;
+        auto dydx_copy = dydx;
+        auto s = cubic_hermite(std::move(x_copy), std::move(y_copy), std::move(dydx_copy));
+        //std::cout << "s = " << s << "\n";
+        for (size_t i = 0; i < x.size(); ++i) {
+            CHECK_ULP_CLOSE(y[i], s(x[i]), 2);
+            CHECK_ULP_CLOSE(dydx[i], s.prime(x[i]), 2);
+        }
+    }
+}*/
+
+int main()
+{
+    test_constant<float>();
+    test_constant<double>();
+    test_constant<long double>();
+
+    test_linear<float>();
+    test_linear<double>();
+    test_linear<long double>();
+
+    /*
+    test_quadratic<float>();
+    test_interpolation_condition<float>();
+
+    test_quadratic<double>();
+    test_interpolation_condition<double>();
+
+    test_quadratic<long double>();
+    test_interpolation_condition<long double>();*/
+
+#ifdef BOOST_HAS_FLOAT128
+    test_constant<float128>();
+    test_linear<float128>();
+#endif
+
+    return boost::math::test::report_errors();
+}

From 12254d7133f7ef3f4c7ec1e989663f6987b211a2 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Mon, 10 Feb 2020 13:45:26 -0500
Subject: [PATCH 015/104] More tests of the cardinal_cubic_hermite
 interpolator. [CI SKIP]

---
 test/cardinal_cubic_hermite_test.cpp | 99 ++++++++++++++++------------
 1 file changed, 57 insertions(+), 42 deletions(-)

diff --git a/test/cardinal_cubic_hermite_test.cpp b/test/cardinal_cubic_hermite_test.cpp
index 4af0ebfd5..b3998b964 100644
--- a/test/cardinal_cubic_hermite_test.cpp
+++ b/test/cardinal_cubic_hermite_test.cpp
@@ -84,74 +84,91 @@ void test_linear()
         dydx[i] = 1;
     }
 
-    y_copy = y;
-    dydx_copy = dydx;
-    hermite_spline = cardinal_cubic_hermite(std::move(y_copy), std::move(dydx_copy), x0, dx);
+    hermite_spline = cardinal_cubic_hermite(std::move(y), std::move(dydx), x0, dx);
     for (Real t = 0; t < 44; t += 0.5) {
         CHECK_ULP_CLOSE(t, hermite_spline(t), 0);
         CHECK_ULP_CLOSE(Real(1), hermite_spline.prime(t), 0);
     }
 
+    std::vector<std::array<Real, 2>> data(45);
+    for (size_t i = 0; i < data.size(); ++i) {
+        data[i][0] = i;
+        data[i][1] = 1;
+    }
+
+    auto hermite_spline_aos = cardinal_cubic_hermite_aos(std::move(data), x0, dx);
+    for (Real t = 0; t < 44; t += 0.5) {
+        CHECK_ULP_CLOSE(t, hermite_spline_aos(t), 0);
+        CHECK_ULP_CLOSE(Real(1), hermite_spline_aos.prime(t), 0);
+    }
+
+
 }
 
-/*
+
 template<typename Real>
 void test_quadratic()
 {
-    std::vector<Real> x(50);
-    std::default_random_engine rd;
-    std::uniform_real_distribution<Real> dis(0.1,1);
-    Real x0 = dis(rd);
-    x[0] = x0;
-    for (size_t i = 1; i < x.size(); ++i) {
-        x[i] = x[i-1] + dis(rd);
-    }
-    Real xmax = x.back();
+    Real x0 = -1;
+    Real dx = Real(1)/Real(256);
 
-    std::vector<Real> y(x.size());
-    std::vector<Real> dydx(x.size());
-    for (size_t i = 0; i < x.size(); ++i) {
-        y[i] = x[i]*x[i]/2;
-        dydx[i] = x[i];
+    std::vector<Real> y(50);
+    std::vector<Real> dydx(y.size());
+    for (size_t i = 0; i < y.size(); ++i) {
+        Real x = x0 + i*dx;
+        y[i] = x*x/2;
+        dydx[i] = x;
     }
 
-    auto s = cubic_hermite(std::move(x), std::move(y), std::move(dydx));
-    for (Real t = x0; t <= xmax; t+= 0.0125)
+    auto s = cardinal_cubic_hermite(std::move(y), std::move(dydx), x0, dx);
+    for (Real t = x0; t <= x0 + 49*dx; t+= 0.0125)
     {
-        CHECK_ULP_CLOSE(t*t/2, s(t), 5);
-        CHECK_ULP_CLOSE(t, s.prime(t), 65);
+        CHECK_ULP_CLOSE(t*t/2, s(t), 12);
+        CHECK_ULP_CLOSE(t, s.prime(t), 70);
     }
+
+    std::vector<std::array<Real, 2>> data(50);
+    for (size_t i = 0; i < data.size(); ++i) {
+        Real x = x0 + i*dx;
+        data[i][0] = x*x/2;
+        data[i][1] = x;
+    }
+
+
+    auto saos = cardinal_cubic_hermite_aos(std::move(data), x0, dx);
+    for (Real t = x0; t <= x0 + 49*dx; t+= 0.0125)
+    {
+        CHECK_ULP_CLOSE(t*t/2, saos(t), 12);
+        CHECK_ULP_CLOSE(t, saos.prime(t), 70);
+    }
+
 }
 
+
 template<typename Real>
 void test_interpolation_condition()
 {
     for (size_t n = 4; n < 50; ++n) {
-        std::vector<Real> x(n);
         std::vector<Real> y(n);
         std::vector<Real> dydx(n);
         std::default_random_engine rd;
-        std::uniform_real_distribution<Real> dis(0,1);
-        Real x0 = dis(rd);
-        x[0] = x0;
-        y[0] = dis(rd);
-        for (size_t i = 1; i < n; ++i) {
-            x[i] = x[i-1] + dis(rd);
+        std::uniform_real_distribution<Real> dis(0.1,1);
+        Real x0 = Real(2);
+        Real dx = Real(1)/Real(128);
+        for (size_t i = 0; i < n; ++i) {
             y[i] = dis(rd);
             dydx[i] = dis(rd);
         }
 
-        auto x_copy = x;
         auto y_copy = y;
         auto dydx_copy = dydx;
-        auto s = cubic_hermite(std::move(x_copy), std::move(y_copy), std::move(dydx_copy));
-        //std::cout << "s = " << s << "\n";
-        for (size_t i = 0; i < x.size(); ++i) {
-            CHECK_ULP_CLOSE(y[i], s(x[i]), 2);
-            CHECK_ULP_CLOSE(dydx[i], s.prime(x[i]), 2);
+        auto s = cardinal_cubic_hermite(std::move(y_copy), std::move(dydx_copy), x0, dx);
+        for (size_t i = 0; i < y.size(); ++i) {
+            CHECK_ULP_CLOSE(y[i], s(x0 + i*dx), 2);
+            CHECK_ULP_CLOSE(dydx[i], s.prime(x0 + i*dx), 2);
         }
     }
-}*/
+}
 
 int main()
 {
@@ -163,19 +180,17 @@ int main()
     test_linear<double>();
     test_linear<long double>();
 
-    /*
     test_quadratic<float>();
-    test_interpolation_condition<float>();
-
     test_quadratic<double>();
-    test_interpolation_condition<double>();
-
     test_quadratic<long double>();
-    test_interpolation_condition<long double>();*/
 
+    test_interpolation_condition<float>();
+    test_interpolation_condition<double>();
+    test_interpolation_condition<long double>();
 #ifdef BOOST_HAS_FLOAT128
     test_constant<float128>();
     test_linear<float128>();
+    test_quadratic<float128>();
 #endif
 
     return boost::math::test::report_errors();

From 6ff37dcddf3f2696bb85d56e2b3a1072b6168cc5 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Mon, 10 Feb 2020 14:11:55 -0500
Subject: [PATCH 016/104] Inline some evaluations [CI SKIP]

---
 .../special_functions/daubechies_scaling.hpp  | 20 ++++++-------------
 1 file changed, 6 insertions(+), 14 deletions(-)

diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index ad794caf2..01f66a475 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -91,7 +91,7 @@ public:
         h_ = Real(1)/(1<< grid_refinements);
     }
     
-    Real operator()(Real x) const {
+    inline Real operator()(Real x) const {
         using std::log;
         using std::floor;
         using std::sqrt;
@@ -130,11 +130,8 @@ public:
         grid_refinements_ = grid_refinements;
     }
 
-    Real operator()(Real x) const {
+    inline Real operator()(Real x) const {
         using std::floor;
-        if (x <= 0 || x >= 5) {
-            return 0;
-        }
         Real y = x*(1<<grid_refinements_);
         Real k = floor(y);
 
@@ -168,8 +165,6 @@ public:
             }
             else if (std::is_same_v<Real, double>)
             {
-                // r = 21 is correct for p >= 10.
-                // Before that, r > 21 would be appropriate, but the hardware isn't there yet!
                 //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15
                 std::array<int, 16> r{-1, -1, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 20, 19, 18, 18};
                 grid_refinements = r[p];
@@ -279,8 +274,6 @@ public:
         auto y = t0.get();
         auto dydx = t1.get();
 
-
-
         // Storing the vector of x's is unnecessary; it's only because I haven't implemented an equispaced cubic Hermite interpolator:
         std::vector<Real> x(y.size());
         Real h = Real(2*p-1)/(x.size()-1);
@@ -308,7 +301,7 @@ public:
      }
 
 
-    Real operator()(Real x) const {
+    inline Real operator()(Real x) const {
         if (x <= 0 || x >= 2*p-1) {
             return 0;
         }
@@ -358,12 +351,11 @@ private:
     std::shared_ptr<detail::matched_holder<std::vector<Real>>> m_mh;
     // Need this for p = 3:
     std::shared_ptr<detail::linear_interpolation<std::vector<Real>>> m_lin;
-    // need this for p = 4,5:
+    // Need this for p = 4,5:
     std::shared_ptr<interpolators::detail::cardinal_cubic_hermite_detail<std::vector<Real>>> m_cbh;
-    // need this for p = 6,7,8,9:
+    // Need this for p = 6,7,8,9:
     std::shared_ptr<interpolators::detail::quintic_hermite_detail<std::vector<Real>>> m_qh;
-
-    // need this for p >= 10:
+    // Need this for p >= 10:
     std::shared_ptr<interpolators::detail::septic_hermite_detail<std::vector<Real>>> m_sh;
 
     /*Real constant_interpolation(Real x) const {

From be35dfedfa912bf8be765982bfc1dc4c15dfa088 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Mon, 10 Feb 2020 18:26:23 -0500
Subject: [PATCH 017/104] Sketch out cardinal quintic hermite [CI SKIP]

---
 .../cardinal_quintic_hermite.hpp              |  54 +++++
 .../detail/cardinal_cubic_hermite_detail.hpp  |   1 -
 .../cardinal_quintic_hermite_detail.hpp       | 203 ++++++++++++++++++
 .../detail/quintic_hermite_detail.hpp         |   4 +-
 .../special_functions/daubechies_scaling.hpp  |   4 +-
 test/cardinal_quintic_hermite_test.cpp        | 178 +++++++++++++++
 6 files changed, 439 insertions(+), 5 deletions(-)
 create mode 100644 include/boost/math/interpolators/cardinal_quintic_hermite.hpp
 create mode 100644 include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp
 create mode 100644 test/cardinal_quintic_hermite_test.cpp

diff --git a/include/boost/math/interpolators/cardinal_quintic_hermite.hpp b/include/boost/math/interpolators/cardinal_quintic_hermite.hpp
new file mode 100644
index 000000000..e515f40e8
--- /dev/null
+++ b/include/boost/math/interpolators/cardinal_quintic_hermite.hpp
@@ -0,0 +1,54 @@
+#ifndef BOOST_MATH_INTERPOLATORS_CARDINAL_QUINTIC_HERMITE_HPP
+#define BOOST_MATH_INTERPOLATORS_CARDINAL_QUINTIC_HERMITE_HPP
+#include <algorithm>
+#include <stdexcept>
+#include <memory>
+#include <boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp>
+
+namespace boost::math::interpolators {
+
+template<class RandomAccessContainer>
+class cardinal_quintic_hermite {
+public:
+    using Real = typename RandomAccessContainer::value_type;
+    cardinal_quintic_hermite(RandomAccessContainer && y, RandomAccessContainer && dydx, RandomAccessContainer && d2ydx2, Real x0, Real dx)
+     : impl_(std::make_shared<detail::cardinal_quintic_hermite_detail<RandomAccessContainer>>(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx))
+    {}
+
+    inline Real operator()(Real x) const {
+        return impl_->operator()(x);
+    }
+
+    inline Real prime(Real x) const {
+        return impl_->prime(x);
+    }
+
+
+private:
+    std::shared_ptr<detail::cardinal_quintic_hermite_detail<RandomAccessContainer>> impl_;
+};
+
+template<class RandomAccessContainer>
+class cardinal_quintic_hermite_aos {
+public:
+    using Point = typename RandomAccessContainer::value_type;
+    using Real = typename Point::value_type;
+    cardinal_quintic_hermite_aos(RandomAccessContainer && data, Real x0, Real dx)
+     : impl_(std::make_shared<detail::cardinal_quintic_hermite_detail_aos<RandomAccessContainer>>(std::move(data), x0, dx))
+    {}
+
+    inline Real operator()(Real x) const {
+        return impl_->operator()(x);
+    }
+
+    inline Real prime(Real x) const {
+        return impl_->prime(x);
+    }
+
+
+private:
+    std::shared_ptr<detail::cardinal_quintic_hermite_detail_aos<RandomAccessContainer>> impl_;
+};
+
+}
+#endif 
\ No newline at end of file
diff --git a/include/boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp b/include/boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp
index dbbbc1a5a..3d7f165c8 100644
--- a/include/boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp
@@ -129,7 +129,6 @@ public:
     }
 
     inline Real operator()(Real x) const {
-        using std::floor;
         const Real xf = x0_ + (dat_.size()-1)*dx_;
         if  (x < x0_ || x > xf) {
             std::ostringstream oss;
diff --git a/include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp b/include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp
new file mode 100644
index 000000000..13489447a
--- /dev/null
+++ b/include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp
@@ -0,0 +1,203 @@
+#ifndef BOOST_MATH_INTERPOLATORS_DETAIL_QUINTIC_HERMITE_DETAIL_HPP
+#define BOOST_MATH_INTERPOLATORS_DETAIL_QUINTIC_HERMITE_DETAIL_HPP
+#include <algorithm>
+#include <stdexcept>
+#include <sstream>
+#include <cmath>
+
+namespace boost::math::interpolators::detail {
+
+template<class RandomAccessContainer>
+class cardinal_quintic_hermite_detail {
+public:
+    using Real = typename RandomAccessContainer::value_type;
+    cardinal_quintic_hermite_detail(RandomAccessContainer && y, RandomAccessContainer && dydx, RandomAccessContainer && d2ydx2, Real x0, Real dx)
+    : y_{std::move(y)}, dydx_{std::move(dydx)}, d2ydx2_{std::move(d2ydx2)}, x0_{x0}, dx_{dx}
+    {
+        if (y_.size() != dydx_.size()) {
+            throw std::domain_error("Numbers of derivatives must = number of abscissas.");
+        }
+        if (y_.size() != d2ydx2_.size()) {
+            throw std::domain_error("Number of second derivatives must equal number of abscissas.");
+        }
+        if (y_.size() < 2) {
+            throw std::domain_error("At least 2 abscissas are required.");
+        }
+    }
+
+
+    inline Real operator()(Real x) const {
+        const Real xf = x0_ + (y_.size()-1)*dx_;
+        if  (x < x0_ || x > xf) {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf) {
+            return y_.back();
+        }
+        return this->unchecked_evaluation(x);
+    }
+
+    inline Real unchecked_evaluation(Real x) const {
+        using std::floor;
+        auto i = static_cast<decltype(y_.size())>(floor((x-x0_)/dx_));
+        Real xi = x0_ + i*dx_;
+        Real t = (x - xi)/dx_;
+
+        Real y0 = y_[i];
+        Real y1 = y_[i+1];
+        Real v0 = dydx_[i];
+        Real v1 = dydx_[i+1];
+        Real a0 = d2ydx2_[i];
+        Real a1 = d2ydx2_[i+1];
+
+        // See the 'Basis functions' section of:
+        // https://www.rose-hulman.edu/~finn/CCLI/Notes/day09.pdf
+        // Also: https://github.com/MrHexxx/QuinticHermiteSpline/blob/master/HermiteSpline.cs
+        Real y = (1- t*t*t*(10 + t*(-15 + 6*t)))*y0;
+        y += t*(1+ t*t*(-6 + t*(8 -3*t)))*v0*dx_;
+        y += t*t*(1 + t*(-3 + t*(3-t)))*a0*dx_*dx_/2;
+        y += t*t*t*((1 + t*(-2 + t))*a1*dx_*dx_/2 + (-4 + t*(7 -3*t))*v1*dx_ + (10 + t*(-15 + 6*t))*y1);
+        // there's a bug here!
+        return std::numeric_limits<Real>::quiet_NaN();
+        return y;
+    }
+
+    inline Real prime(Real x) const {
+        const Real xf = x0_ + (y_.size()-1)*dx_;
+        if  (x < x0_ || x > xf) {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf) {
+            return dydx_.back();
+        }
+
+        return this->unchecked_prime(x);
+    }
+
+    inline Real unchecked_prime(Real x) const {
+        using std::floor;
+        auto i = static_cast<decltype(y_.size())>(floor((x-x0_)/dx_));
+        Real xi = x0_ + i*dx_;
+        Real t = (x - xi)/dx_;
+
+        Real s0 = dydx_[i];
+        Real s1 = dydx_[i+1];
+
+        return std::numeric_limits<Real>::quiet_NaN();
+    }
+
+
+
+private:
+    RandomAccessContainer y_;
+    RandomAccessContainer dydx_;
+    RandomAccessContainer d2ydx2_;
+    Real x0_;
+    Real dx_;
+};
+
+
+template<class RandomAccessContainer>
+class cardinal_quintic_hermite_detail_aos {
+public:
+    using Real = typename RandomAccessContainer::value_type;
+    cardinal_quintic_hermite_detail_aos(RandomAccessContainer && data, Real x0, Real dx)
+    : data_{std::move(data)} , x0_{x0}, dx_{dx}
+    {
+        if (data_.size() < 2)
+        {
+            throw std::domain_error("At least two points are required to interpolate using cardinal_quintic_hermite_aos");
+        }
+
+        if (data_[0].size() != 3)
+        {
+            throw std::domain_error("Each datum passed to the cardinal_quintic_hermite_aos must have three elements: {y, y', y''}");
+        }
+    }
+
+
+    inline Real operator()(Real x) const {
+        const Real xf = x0_ + (data_.size()-1)*dx_;
+        if  (x < x0_ || x > xf) {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf) {
+            return data_.back()[0];
+        }
+        return this->unchecked_evaluation(x);
+    }
+
+    inline Real unchecked_evaluation(Real x) const
+    {
+        using std::floor;
+        auto i = static_cast<decltype(data_.size())>(floor((x-x0_)/dx_));
+        Real xi = x0_ + i*dx_;
+        Real t = (x - xi)/dx_;
+
+        Real y0 = data_[i][0];
+        Real y1 = data_[i+1][0];
+        Real v0 = data_[i][1];
+        Real v1 = data_[i+1][1];
+        Real a0 = data_[i][2];
+        Real a1 = data_[i+1][2];
+
+        // See the 'Basis functions' section of:
+        // https://www.rose-hulman.edu/~finn/CCLI/Notes/day09.pdf
+        // Also: https://github.com/MrHexxx/QuinticHermiteSpline/blob/master/HermiteSpline.cs
+        Real y = (1- t*t*t*(10 + t*(-15 + 6*t)))*y0;
+        y += t*(1+ t*t*(-6 + t*(8 -3*t)))*v0*dx_;
+        y += t*t*(1 + t*(-3 + t*(3-t)))*a0*dx_*dx_/2;
+        y += t*t*t*((1 + t*(-2 + t))*a1*dx_*dx_/2 + (-4 + t*(7 -3*t))*v1*dx_ + (10 + t*(-15 + 6*t))*y1);
+        return y;
+    }
+
+    inline Real prime(Real x) const {
+        const Real xf = x0_ + (data_.size()-1)*dx_;
+        if  (x < x0_ || x > xf) {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf) {
+            return data_.back()[1];
+        }
+
+        return this->unchecked_prime(x);
+    }
+
+    inline Real unchecked_prime(Real x) const {
+        using std::floor;
+        auto i = static_cast<decltype(data_.size())>(floor((x-x0_)/dx_));
+        Real xi = x0_ + i*dx_;
+        Real t = (x - xi)/dx_;
+
+        Real v0 = data_[i][1];
+        Real v1 = data_[i+1][1];
+
+        return std::numeric_limits<Real>::quiet_NaN();
+    }
+
+
+
+private:
+    RandomAccessContainer data_;
+    Real x0_;
+    Real dx_;
+};
+
+}
+#endif 
\ No newline at end of file
diff --git a/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp b/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
index f70a4744f..0d2a2d170 100644
--- a/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
@@ -48,7 +48,7 @@ public:
         d2ydx2_.push_back(d2ydx2);
     }
 
-    Real operator()(Real x) const {
+    inline Real operator()(Real x) const {
         if  (x < x_[0] || x > x_.back()) {
             std::ostringstream oss;
             oss.precision(std::numeric_limits<Real>::digits10+3);
@@ -86,7 +86,7 @@ public:
         return y;
     }
 
-    Real prime(Real x) const {
+    inline Real prime(Real x) const {
         if  (x < x_[0] || x > x_.back()) {
             std::ostringstream oss;
             oss.precision(std::numeric_limits<Real>::digits10+3);
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index 01f66a475..bbea82803 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -312,7 +312,7 @@ public:
             return m_lin->operator()(x);
         }
         if constexpr (p==4 || p ==5) {
-            return m_cbh->operator()(x);
+            return m_cbh->unchecked_evaluation(x);
         }
         if constexpr (p >= 6 && p <= 9) {
             return m_qh->operator()(x);
@@ -331,7 +331,7 @@ public:
             throw std::domain_error("The 2 and 3-vanishing moment Daubechies scaling function is not continuously differentiable.");
         }
         if constexpr (p==4 || p ==5) {
-            return m_cbh->prime(x);
+            return m_cbh->unchecked_prime(x);
         }
         if constexpr (p >= 6 && p <= 9) {
             return m_qh->prime(x);
diff --git a/test/cardinal_quintic_hermite_test.cpp b/test/cardinal_quintic_hermite_test.cpp
new file mode 100644
index 000000000..c7b1ba9a3
--- /dev/null
+++ b/test/cardinal_quintic_hermite_test.cpp
@@ -0,0 +1,178 @@
+/*
+ * Copyright Nick Thompson, 2020
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include "math_unit_test.hpp"
+#include <numeric>
+#include <utility>
+#include <boost/random/uniform_real.hpp>
+#include <boost/random/mersenne_twister.hpp>
+#include <boost/math/interpolators/cardinal_quintic_hermite.hpp>
+#ifdef BOOST_HAS_FLOAT128
+#include <boost/multiprecision/float128.hpp>
+using boost::multiprecision::float128;
+#endif
+
+
+using boost::math::interpolators::cardinal_quintic_hermite;
+using boost::math::interpolators::cardinal_quintic_hermite_aos;
+
+template<typename Real>
+void test_constant()
+{
+
+    std::vector<Real> y(25);
+    std::vector<Real> dydx(y.size(), 0);
+    std::vector<Real> d2ydx2(y.size(), 0);
+    for (auto & t : y) {
+        t = 7;
+    }
+    Real x0 = 4;
+    Real dx = Real(1)/Real(8);
+
+    auto qh = cardinal_quintic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx);
+
+    for (Real t = x0; t <= x0 + 24*dx; t += 0.25) {
+        CHECK_ULP_CLOSE(Real(7), qh(t), 24);
+        //CHECK_ULP_CLOSE(Real(0), qh.prime(t), 24);
+    }
+
+
+}
+
+
+template<typename Real>
+void test_linear()
+{
+    std::vector<Real> y{0,1,2,3, 4,5,6,7,8,9};
+    Real x0 = 0;
+    Real dx = 1;
+    std::vector<Real> dydx(y.size(), 1);
+    std::vector<Real> d2ydx2(y.size(), 0);
+
+    auto qh = cardinal_quintic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx);
+
+    for (Real t = 0; t <= 9; t += 0.25) {
+        CHECK_ULP_CLOSE(Real(t), qh(t), 2);
+        //CHECK_ULP_CLOSE(Real(1), qh.prime(t), 2);
+    }
+}
+
+template<typename Real>
+void test_quadratic()
+{
+    Real x0 = 0;
+    Real dx = 1;
+    std::vector<Real> y(10);
+    for (size_t i = 0; i < y.size(); ++i)
+    {
+        y[i] = i*i/2;
+    }
+
+    std::vector<Real> dydx(y.size());
+    for (size_t i = 0; i < y.size(); ++i) {
+        dydx[i] = i;
+    }
+
+    std::vector<Real> d2ydx2(y.size(), 1);
+
+    auto qh = cardinal_quintic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx);
+
+    for (Real t = 0; t <= 9; t += 0.0078125) {
+        CHECK_ULP_CLOSE(Real(t*t)/2, qh(t), 2);
+        //CHECK_ULP_CLOSE(t, qh.prime(t), 2);
+    }
+
+}
+
+template<typename Real>
+void test_cubic()
+{
+    Real x0 = 0;
+    Real dx = 1;
+    std::vector<Real> y(10);
+    for (size_t i = 0; i < y.size(); ++i)
+    {
+        y[i] = i*i*i/6;
+    }
+
+    std::vector<Real> dydx(y.size());
+    for (size_t i = 0; i < y.size(); ++i) {
+        dydx[i] = i*i/2;
+    }
+
+    std::vector<Real> d2ydx2(y.size());
+    for (size_t i = 0; i < y.size(); ++i) {
+        d2ydx2[i] = i;
+    }
+
+    auto qh = cardinal_quintic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx);
+
+    for (Real t = 0; t <= 9; t += 0.0078125) {
+        CHECK_ULP_CLOSE(Real(t*t*t)/6, qh(t), 10);
+    }
+}
+
+template<typename Real>
+void test_quartic()
+{
+
+    Real x0 = 0;
+    Real dx = 1;
+    std::vector<Real> y(11);
+    for (size_t i = 0; i < y.size(); ++i)
+    {
+        y[i] = i*i*i*i/24;
+    }
+
+    std::vector<Real> dydx(y.size());
+    for (size_t i = 0; i < y.size(); ++i) {
+        dydx[i] = i*i*i/6;
+    }
+
+    std::vector<Real> d2ydx2(y.size());
+    for (size_t i = 0; i < y.size(); ++i) {
+        d2ydx2[i] = i*i/2;
+    }
+
+    auto qh = cardinal_quintic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx);
+
+    for (Real t = 1; t <= 11; t += 0.0078125) {
+        CHECK_ULP_CLOSE(Real(t*t*t*t)/24, qh(t), 100);
+    }
+}
+
+
+int main()
+{
+    /*test_constant<float>();
+    test_linear<float>();
+    test_quadratic<float>();
+    test_cubic<float>();
+    test_quartic<float>();*/
+
+    test_constant<double>();
+    test_linear<double>();
+    test_quadratic<double>();
+    /*test_cubic<double>();
+    test_quartic<double>();
+
+    test_constant<long double>();
+    test_linear<long double>();
+    test_quadratic<long double>();
+    test_cubic<long double>();
+    test_quartic<long double>();
+
+#ifdef BOOST_HAS_FLOAT128
+    test_constant<float128>();
+    test_linear<float128>();
+    test_quadratic<float128>();
+    test_cubic<float128>();
+    test_quartic<float128>();
+#endif*/
+
+    return boost::math::test::report_errors();
+}

From a0e61cb190fe8fbde904886b877668934bd7fd5b Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Tue, 11 Feb 2020 08:44:04 -0500
Subject: [PATCH 018/104] Fix test of cardinal hermite splines [CI SKIP]

---
 .../cardinal_quintic_hermite_detail.hpp       |   5 +-
 .../detail/quintic_hermite_detail.hpp         |   3 +-
 test/cardinal_quintic_hermite_test.cpp        | 102 ++++++++++++++----
 3 files changed, 88 insertions(+), 22 deletions(-)

diff --git a/include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp b/include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp
index 13489447a..9233a3e42 100644
--- a/include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp
@@ -61,8 +61,6 @@ public:
         y += t*(1+ t*t*(-6 + t*(8 -3*t)))*v0*dx_;
         y += t*t*(1 + t*(-3 + t*(3-t)))*a0*dx_*dx_/2;
         y += t*t*t*((1 + t*(-2 + t))*a1*dx_*dx_/2 + (-4 + t*(7 -3*t))*v1*dx_ + (10 + t*(-15 + 6*t))*y1);
-        // there's a bug here!
-        return std::numeric_limits<Real>::quiet_NaN();
         return y;
     }
 
@@ -108,7 +106,8 @@ private:
 template<class RandomAccessContainer>
 class cardinal_quintic_hermite_detail_aos {
 public:
-    using Real = typename RandomAccessContainer::value_type;
+    using Point = typename RandomAccessContainer::value_type;
+    using Real = typename Point::value_type;
     cardinal_quintic_hermite_detail_aos(RandomAccessContainer && data, Real x0, Real dx)
     : data_{std::move(data)} , x0_{x0}, dx_{dx}
     {
diff --git a/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp b/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
index 0d2a2d170..1342c1c51 100644
--- a/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
@@ -39,7 +39,8 @@ public:
     void push_back(Real x, Real y, Real dydx, Real d2ydx2) {
         using std::abs;
         using std::isnan;
-        if (x <= x_.back()) {
+        if (x <= x_.back())
+        {
              throw std::domain_error("Calling push_back must preserve the monotonicity of the x's");
         }
         x_.push_back(x);
diff --git a/test/cardinal_quintic_hermite_test.cpp b/test/cardinal_quintic_hermite_test.cpp
index c7b1ba9a3..e44c02161 100644
--- a/test/cardinal_quintic_hermite_test.cpp
+++ b/test/cardinal_quintic_hermite_test.cpp
@@ -8,8 +8,6 @@
 #include "math_unit_test.hpp"
 #include <numeric>
 #include <utility>
-#include <boost/random/uniform_real.hpp>
-#include <boost/random/mersenne_twister.hpp>
 #include <boost/math/interpolators/cardinal_quintic_hermite.hpp>
 #ifdef BOOST_HAS_FLOAT128
 #include <boost/multiprecision/float128.hpp>
@@ -40,14 +38,26 @@ void test_constant()
         //CHECK_ULP_CLOSE(Real(0), qh.prime(t), 24);
     }
 
+    std::vector<std::array<Real, 3>> data(25);
+    for (size_t i = 0; i < data.size(); ++i)
+    {
+        data[i][0] = 7;
+        data[i][1] = 0;
+        data[i][2] = 0;
+    }
 
+    auto qh_aos = cardinal_quintic_hermite_aos(std::move(data), x0, dx);
+    for (Real t = x0; t <= x0 + 24*dx; t += 0.25) {
+        CHECK_ULP_CLOSE(Real(7), qh_aos(t), 24);
+        //CHECK_ULP_CLOSE(Real(0), qh.prime(t), 24);
+    }
 }
 
 
 template<typename Real>
 void test_linear()
 {
-    std::vector<Real> y{0,1,2,3, 4,5,6,7,8,9};
+    std::vector<Real> y{0,1,2,3,4,5,6,7,8,9};
     Real x0 = 0;
     Real dx = 1;
     std::vector<Real> dydx(y.size(), 1);
@@ -59,6 +69,21 @@ void test_linear()
         CHECK_ULP_CLOSE(Real(t), qh(t), 2);
         //CHECK_ULP_CLOSE(Real(1), qh.prime(t), 2);
     }
+
+    std::vector<std::array<Real, 3>> data(10);
+    for (size_t i = 0; i < data.size(); ++i) {
+        data[i][0] = i;
+        data[i][1] = 1;
+        data[i][2] = 0;
+    }
+
+    auto qh_aos = cardinal_quintic_hermite_aos(std::move(data), x0, dx);
+
+    for (Real t = 0; t <= 9; t += 0.25) {
+        CHECK_ULP_CLOSE(Real(t), qh_aos(t), 2);
+        //CHECK_ULP_CLOSE(Real(1), qh.prime(t), 2);
+    }
+
 }
 
 template<typename Real>
@@ -69,7 +94,7 @@ void test_quadratic()
     std::vector<Real> y(10);
     for (size_t i = 0; i < y.size(); ++i)
     {
-        y[i] = i*i/2;
+        y[i] = i*i/Real(2);
     }
 
     std::vector<Real> dydx(y.size());
@@ -82,10 +107,24 @@ void test_quadratic()
     auto qh = cardinal_quintic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx);
 
     for (Real t = 0; t <= 9; t += 0.0078125) {
-        CHECK_ULP_CLOSE(Real(t*t)/2, qh(t), 2);
+        Real computed = qh(t);
+        CHECK_ULP_CLOSE(Real(t*t)/2, computed, 2);
         //CHECK_ULP_CLOSE(t, qh.prime(t), 2);
     }
 
+    std::vector<std::array<Real, 3>> data(10);
+    for (size_t i = 0; i < data.size(); ++i) {
+        data[i][0] = i*i/Real(2);
+        data[i][1] = i;
+        data[i][2] = 1;
+    }
+    auto qh_aos = cardinal_quintic_hermite_aos(std::move(data), x0, dx);
+
+    for (Real t = 0; t <= 9; t += 0.0078125) {
+        Real computed = qh_aos(t);
+        CHECK_ULP_CLOSE(Real(t*t)/2, computed, 2);
+        //CHECK_ULP_CLOSE(t, qh_aos.prime(t), 2);
+    }
 }
 
 template<typename Real>
@@ -96,12 +135,12 @@ void test_cubic()
     std::vector<Real> y(10);
     for (size_t i = 0; i < y.size(); ++i)
     {
-        y[i] = i*i*i/6;
+        y[i] = i*i*i/Real(6);
     }
 
     std::vector<Real> dydx(y.size());
     for (size_t i = 0; i < y.size(); ++i) {
-        dydx[i] = i*i/2;
+        dydx[i] = i*i/Real(2);
     }
 
     std::vector<Real> d2ydx2(y.size());
@@ -112,7 +151,21 @@ void test_cubic()
     auto qh = cardinal_quintic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx);
 
     for (Real t = 0; t <= 9; t += 0.0078125) {
-        CHECK_ULP_CLOSE(Real(t*t*t)/6, qh(t), 10);
+        Real computed = qh(t);
+        CHECK_ULP_CLOSE(Real(t*t*t)/6, computed, 10);
+    }
+
+    std::vector<std::array<Real, 3>> data(10);
+    for (size_t i = 0; i < data.size(); ++i) {
+        data[i][0] = i*i*i/Real(6);
+        data[i][1] = i*i/Real(2);
+        data[i][2] = i;
+    }
+
+    auto qh_aos = cardinal_quintic_hermite_aos(std::move(data), x0, dx);
+    for (Real t = 0; t <= 9; t += 0.0078125) {
+        Real computed = qh_aos(t);
+        CHECK_ULP_CLOSE(Real(t*t*t)/6, computed, 10);
     }
 }
 
@@ -122,42 +175,55 @@ void test_quartic()
 
     Real x0 = 0;
     Real dx = 1;
-    std::vector<Real> y(11);
+    std::vector<Real> y(7);
     for (size_t i = 0; i < y.size(); ++i)
     {
-        y[i] = i*i*i*i/24;
+        y[i] = i*i*i*i;
     }
 
     std::vector<Real> dydx(y.size());
     for (size_t i = 0; i < y.size(); ++i) {
-        dydx[i] = i*i*i/6;
+        dydx[i] = 4*i*i*i;
     }
 
     std::vector<Real> d2ydx2(y.size());
     for (size_t i = 0; i < y.size(); ++i) {
-        d2ydx2[i] = i*i/2;
+        d2ydx2[i] = 12*i*i;
     }
 
     auto qh = cardinal_quintic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx);
 
-    for (Real t = 1; t <= 11; t += 0.0078125) {
-        CHECK_ULP_CLOSE(Real(t*t*t*t)/24, qh(t), 100);
+    for (Real t = 0; t <= 6; t += 0.0078125) {
+        CHECK_ULP_CLOSE(Real(t*t*t*t), qh(t), 250);
+    }
+
+    std::vector<std::array<Real, 3>> data(7);
+    for (size_t i = 0; i < data.size(); ++i) {
+        data[i][0] = i*i*i*i;
+        data[i][1] = 4*i*i*i;
+        data[i][2] = 12*i*i;
+    }
+
+    auto qh_aos = cardinal_quintic_hermite_aos(std::move(data), x0, dx);
+    for (Real t = 0; t <= 6; t += 0.0078125) {
+        Real computed = qh_aos(t);
+        CHECK_ULP_CLOSE(t*t*t*t, computed, 10);
     }
 }
 
 
 int main()
 {
-    /*test_constant<float>();
+    test_constant<float>();
     test_linear<float>();
     test_quadratic<float>();
     test_cubic<float>();
-    test_quartic<float>();*/
+    test_quartic<float>();
 
     test_constant<double>();
     test_linear<double>();
     test_quadratic<double>();
-    /*test_cubic<double>();
+    test_cubic<double>();
     test_quartic<double>();
 
     test_constant<long double>();
@@ -172,7 +238,7 @@ int main()
     test_quadratic<float128>();
     test_cubic<float128>();
     test_quartic<float128>();
-#endif*/
+#endif
 
     return boost::math::test::report_errors();
 }

From 6c13d7989b3da7a5a6914ea192510866382db988 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Tue, 11 Feb 2020 09:08:21 -0500
Subject: [PATCH 019/104] O(1) evaluation of quintic Hermite splines. [CI SKIP]

---
 .../detail/cardinal_quintic_hermite_detail.hpp     |  4 ++--
 .../math/special_functions/daubechies_scaling.hpp  | 14 ++++++++------
 2 files changed, 10 insertions(+), 8 deletions(-)

diff --git a/include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp b/include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp
index 9233a3e42..c395da147 100644
--- a/include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp
@@ -1,5 +1,5 @@
-#ifndef BOOST_MATH_INTERPOLATORS_DETAIL_QUINTIC_HERMITE_DETAIL_HPP
-#define BOOST_MATH_INTERPOLATORS_DETAIL_QUINTIC_HERMITE_DETAIL_HPP
+#ifndef BOOST_MATH_INTERPOLATORS_DETAIL_CARDINAL_QUINTIC_HERMITE_DETAIL_HPP
+#define BOOST_MATH_INTERPOLATORS_DETAIL_CARDINAL_QUINTIC_HERMITE_DETAIL_HPP
 #include <algorithm>
 #include <stdexcept>
 #include <sstream>
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index bbea82803..5416eb46f 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -19,6 +19,7 @@
 #include <boost/math/filters/daubechies.hpp>
 #include <boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp>
 #include <boost/math/interpolators/detail/quintic_hermite_detail.hpp>
+#include <boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp>
 #include <boost/math/interpolators/detail/septic_hermite_detail.hpp>
 
 
@@ -220,7 +221,7 @@ public:
             return detail::dyadic_grid<Real, p, 1>(grid_refinements);
         });
 
-        // if necessary, compute the second derivative:
+        // if necessary, compute the second and third derivative:
         std::vector<Real> d2ydx2;
         std::vector<Real> d3ydx3;
         if constexpr (p >= 6) {
@@ -292,7 +293,8 @@ public:
             m_cbh = std::make_shared<interpolators::detail::cardinal_cubic_hermite_detail<std::vector<Real>>>(std::move(y), std::move(dydx), Real(0), dx);
         }
         if constexpr (p >= 6 && p <= 9) {
-            m_qh = std::make_shared<interpolators::detail::quintic_hermite_detail<std::vector<Real>>>(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2));
+            Real dx = Real(1)/(1 << grid_refinements);
+            m_qh = std::make_shared<interpolators::detail::cardinal_quintic_hermite_detail<std::vector<Real>>>(std::move(y), std::move(dydx), std::move(d2ydx2), Real(0), dx);
         }
         if constexpr (p >= 10) {
             m_sh = std::make_shared<interpolators::detail::septic_hermite_detail<std::vector<Real>>>(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3));
@@ -315,14 +317,14 @@ public:
             return m_cbh->unchecked_evaluation(x);
         }
         if constexpr (p >= 6 && p <= 9) {
-            return m_qh->operator()(x);
+            return m_qh->unchecked_evaluation(x);
         }
         if constexpr (p >= 10) {
             return m_sh->operator()(x);
         }
     }
 
-    Real prime(Real x) const {
+    inline Real prime(Real x) const {
         if (x <= 0 || x >= 2*p-1)
         {
             return 0;
@@ -334,7 +336,7 @@ public:
             return m_cbh->unchecked_prime(x);
         }
         if constexpr (p >= 6 && p <= 9) {
-            return m_qh->prime(x);
+            return m_qh->unchecked_prime(x);
         }
         if constexpr (p >= 10) {
             return m_sh->prime(x);
@@ -354,7 +356,7 @@ private:
     // Need this for p = 4,5:
     std::shared_ptr<interpolators::detail::cardinal_cubic_hermite_detail<std::vector<Real>>> m_cbh;
     // Need this for p = 6,7,8,9:
-    std::shared_ptr<interpolators::detail::quintic_hermite_detail<std::vector<Real>>> m_qh;
+    std::shared_ptr<interpolators::detail::cardinal_quintic_hermite_detail<std::vector<Real>>> m_qh;
     // Need this for p >= 10:
     std::shared_ptr<interpolators::detail::septic_hermite_detail<std::vector<Real>>> m_sh;
 

From 44d528049b707afbe7e5b843d1c96b5166ccc5ea Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Tue, 11 Feb 2020 11:35:25 -0500
Subject: [PATCH 020/104] Second derivatives of quintic Hermite interpolators
 [CI SKIP]

---
 .../cardinal_quintic_hermite.hpp              |  4 +-
 .../cardinal_quintic_hermite_detail.hpp       | 60 ++++++++++++++++---
 .../detail/quintic_hermite_detail.hpp         | 19 ++++--
 test/cardinal_quintic_hermite_test.cpp        | 22 ++++---
 test/quintic_hermite_test.cpp                 |  5 +-
 5 files changed, 85 insertions(+), 25 deletions(-)

diff --git a/include/boost/math/interpolators/cardinal_quintic_hermite.hpp b/include/boost/math/interpolators/cardinal_quintic_hermite.hpp
index e515f40e8..d2d1ce696 100644
--- a/include/boost/math/interpolators/cardinal_quintic_hermite.hpp
+++ b/include/boost/math/interpolators/cardinal_quintic_hermite.hpp
@@ -23,6 +23,9 @@ public:
         return impl_->prime(x);
     }
 
+    inline Real double_prime(Real x) const {
+        return impl_->double_prime(x);
+    }
 
 private:
     std::shared_ptr<detail::cardinal_quintic_hermite_detail<RandomAccessContainer>> impl_;
@@ -45,7 +48,6 @@ public:
         return impl_->prime(x);
     }
 
-
 private:
     std::shared_ptr<detail::cardinal_quintic_hermite_detail_aos<RandomAccessContainer>> impl_;
 };
diff --git a/include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp b/include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp
index c395da147..c59b360a8 100644
--- a/include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp
@@ -86,13 +86,53 @@ public:
         Real xi = x0_ + i*dx_;
         Real t = (x - xi)/dx_;
 
-        Real s0 = dydx_[i];
-        Real s1 = dydx_[i+1];
+        Real y0 = y_[i];
+        Real y1 = y_[i+1];
+        Real v0 = dydx_[i];
+        Real v1 = dydx_[i+1];
+        Real a0 = d2ydx2_[i];
+        Real a1 = d2ydx2_[i+1];
 
-        return std::numeric_limits<Real>::quiet_NaN();
+        Real dydx = 30*t*t*(1 - 2*t + t*t)*(y1-y0)/dx_;
+        dydx += (1-18*t*t + 32*t*t*t - 15*t*t*t*t)*v0 - t*t*(12 - 28*t + 15*t*t)*v1;
+        dydx += (t*dx_/2)*((2 - 9*t + 12*t*t - 5*t*t*t)*a0 + t*(3 - 8*t + 5*t*t)*a1);
+        return dydx;
     }
 
+    inline Real double_prime(Real x) const {
+        const Real xf = x0_ + (y_.size()-1)*dx_;
+        if  (x < x0_ || x > xf) {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf) {
+            return d2ydx2_.back();
+        }
 
+        return this->unchecked_double_prime(x);
+    }
+
+    inline Real unchecked_double_prime(Real x) const {
+        using std::floor;
+        auto i = static_cast<decltype(y_.size())>(floor((x-x0_)/dx_));
+        Real xi = x0_ + i*dx_;
+        Real t = (x - xi)/dx_;
+
+        Real y0 = y_[i];
+        Real y1 = y_[i+1];
+        Real v0 = dydx_[i];
+        Real v1 = dydx_[i+1];
+        Real a0 = d2ydx2_[i];
+        Real a1 = d2ydx2_[i+1];
+
+        Real d2ydx2 = 60*t*(1 - 3*t + 2*t*t)*(y1 - y0)/(dx_*dx_);
+        d2ydx2 += (12*t/dx_)*((-3 + 8*t - 5*t*t)*v0 - (2 - 7*t + 5*t*t)*v1);
+        d2ydx2 += (1 - 9*t + 18*t*t - 10*t*t*t)*a0 + t*(3 - 12*t + 10*t*t)*a1;
+        return d2ydx2;
+    }
 
 private:
     RandomAccessContainer y_;
@@ -152,9 +192,6 @@ public:
         Real a0 = data_[i][2];
         Real a1 = data_[i+1][2];
 
-        // See the 'Basis functions' section of:
-        // https://www.rose-hulman.edu/~finn/CCLI/Notes/day09.pdf
-        // Also: https://github.com/MrHexxx/QuinticHermiteSpline/blob/master/HermiteSpline.cs
         Real y = (1- t*t*t*(10 + t*(-15 + 6*t)))*y0;
         y += t*(1+ t*t*(-6 + t*(8 -3*t)))*v0*dx_;
         y += t*t*(1 + t*(-3 + t*(3-t)))*a0*dx_*dx_/2;
@@ -184,10 +221,17 @@ public:
         Real xi = x0_ + i*dx_;
         Real t = (x - xi)/dx_;
 
+        Real y0 = data_[i][0];
+        Real y1 = data_[i+1][0];
         Real v0 = data_[i][1];
         Real v1 = data_[i+1][1];
+        Real a0 = data_[i][2];
+        Real a1 = data_[i+1][2];
 
-        return std::numeric_limits<Real>::quiet_NaN();
+        Real dydx = 30*t*t*(1 - 2*t + t*t)*(y1-y0)/dx_;
+        dydx += (1-18*t*t + 32*t*t*t - 15*t*t*t*t)*v0 - t*t*(12 - 28*t + 15*t*t)*v1;
+        dydx += (t*dx_/2)*((2 - 9*t + 12*t*t - 5*t*t*t)*a0 + t*(3 - 8*t + 5*t*t)*a1);
+        return dydx;
     }
 
 
@@ -199,4 +243,4 @@ private:
 };
 
 }
-#endif 
\ No newline at end of file
+#endif
diff --git a/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp b/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
index 1342c1c51..84f64df9e 100644
--- a/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
@@ -103,13 +103,20 @@ public:
         auto i = std::distance(x_.begin(), it) -1;
         Real x0 = *(it-1);
         Real x1 = *it;
-        Real s0 = dydx_[i];
-        Real s1 = dydx_[i+1];
+        Real dx = x1 - x0;
 
-        // Ridiculous linear interpolation. Fine for now:
-        Real numerator = s0*(x1-x) + s1*(x-x0);
-        Real denominator = x1 - x0;
-        return numerator/denominator;
+        Real y0 = y_[i];
+        Real y1 = y_[i+1];
+        Real v0 = dydx_[i];
+        Real v1 = dydx_[i+1];
+        Real a0 = d2ydx2_[i];
+        Real a1 = d2ydx2_[i+1];
+        Real t= (x-x0)/dx;
+
+        Real dydx = 30*t*t*(1 - 2*t + t*t)*(y1-y0)/dx;
+        dydx += (1-18*t*t + 32*t*t*t - 15*t*t*t*t)*v0 - t*t*(12 - 28*t + 15*t*t)*v1;
+        dydx += (t*dx/2)*((2 - 9*t + 12*t*t - 5*t*t*t)*a0 + t*(3 - 8*t + 5*t*t)*a1);
+        return dydx;
     }
 
 
diff --git a/test/cardinal_quintic_hermite_test.cpp b/test/cardinal_quintic_hermite_test.cpp
index e44c02161..20f1bf633 100644
--- a/test/cardinal_quintic_hermite_test.cpp
+++ b/test/cardinal_quintic_hermite_test.cpp
@@ -35,7 +35,8 @@ void test_constant()
 
     for (Real t = x0; t <= x0 + 24*dx; t += 0.25) {
         CHECK_ULP_CLOSE(Real(7), qh(t), 24);
-        //CHECK_ULP_CLOSE(Real(0), qh.prime(t), 24);
+        CHECK_ULP_CLOSE(Real(0), qh.prime(t), 24);
+        CHECK_ULP_CLOSE(Real(0), qh.double_prime(t), 24);
     }
 
     std::vector<std::array<Real, 3>> data(25);
@@ -49,7 +50,7 @@ void test_constant()
     auto qh_aos = cardinal_quintic_hermite_aos(std::move(data), x0, dx);
     for (Real t = x0; t <= x0 + 24*dx; t += 0.25) {
         CHECK_ULP_CLOSE(Real(7), qh_aos(t), 24);
-        //CHECK_ULP_CLOSE(Real(0), qh.prime(t), 24);
+        CHECK_ULP_CLOSE(Real(0), qh_aos.prime(t), 24);
     }
 }
 
@@ -67,7 +68,8 @@ void test_linear()
 
     for (Real t = 0; t <= 9; t += 0.25) {
         CHECK_ULP_CLOSE(Real(t), qh(t), 2);
-        //CHECK_ULP_CLOSE(Real(1), qh.prime(t), 2);
+        CHECK_ULP_CLOSE(Real(1), qh.prime(t), 2);
+        CHECK_ULP_CLOSE(Real(0), qh.double_prime(t), 2);
     }
 
     std::vector<std::array<Real, 3>> data(10);
@@ -81,7 +83,8 @@ void test_linear()
 
     for (Real t = 0; t <= 9; t += 0.25) {
         CHECK_ULP_CLOSE(Real(t), qh_aos(t), 2);
-        //CHECK_ULP_CLOSE(Real(1), qh.prime(t), 2);
+        CHECK_ULP_CLOSE(Real(1), qh_aos.prime(t), 2);
+        //CHECK_ULP_CLOSE(Real(0), qh_aos.double_prime(t), 2);
     }
 
 }
@@ -109,7 +112,8 @@ void test_quadratic()
     for (Real t = 0; t <= 9; t += 0.0078125) {
         Real computed = qh(t);
         CHECK_ULP_CLOSE(Real(t*t)/2, computed, 2);
-        //CHECK_ULP_CLOSE(t, qh.prime(t), 2);
+        CHECK_ULP_CLOSE(t, qh.prime(t), 15);
+        CHECK_ULP_CLOSE(1, qh.double_prime(t), 32);
     }
 
     std::vector<std::array<Real, 3>> data(10);
@@ -123,7 +127,7 @@ void test_quadratic()
     for (Real t = 0; t <= 9; t += 0.0078125) {
         Real computed = qh_aos(t);
         CHECK_ULP_CLOSE(Real(t*t)/2, computed, 2);
-        //CHECK_ULP_CLOSE(t, qh_aos.prime(t), 2);
+        CHECK_ULP_CLOSE(t, qh_aos.prime(t), 7);
     }
 }
 
@@ -153,6 +157,8 @@ void test_cubic()
     for (Real t = 0; t <= 9; t += 0.0078125) {
         Real computed = qh(t);
         CHECK_ULP_CLOSE(Real(t*t*t)/6, computed, 10);
+        CHECK_ULP_CLOSE(t*t/2, qh.prime(t), 15);
+        CHECK_ULP_CLOSE(t, qh.double_prime(t), 39);
     }
 
     std::vector<std::array<Real, 3>> data(10);
@@ -166,13 +172,13 @@ void test_cubic()
     for (Real t = 0; t <= 9; t += 0.0078125) {
         Real computed = qh_aos(t);
         CHECK_ULP_CLOSE(Real(t*t*t)/6, computed, 10);
+        CHECK_ULP_CLOSE(t*t/2, qh_aos.prime(t), 10);
     }
 }
 
 template<typename Real>
 void test_quartic()
 {
-
     Real x0 = 0;
     Real dx = 1;
     std::vector<Real> y(7);
@@ -195,6 +201,7 @@ void test_quartic()
 
     for (Real t = 0; t <= 6; t += 0.0078125) {
         CHECK_ULP_CLOSE(Real(t*t*t*t), qh(t), 250);
+        CHECK_ULP_CLOSE(4*t*t*t, qh.prime(t), 250);
     }
 
     std::vector<std::array<Real, 3>> data(7);
@@ -208,6 +215,7 @@ void test_quartic()
     for (Real t = 0; t <= 6; t += 0.0078125) {
         Real computed = qh_aos(t);
         CHECK_ULP_CLOSE(t*t*t*t, computed, 10);
+        CHECK_ULP_CLOSE(4*t*t*t, qh_aos.prime(t), 64);
     }
 }
 
diff --git a/test/quintic_hermite_test.cpp b/test/quintic_hermite_test.cpp
index 278955648..70547c879 100644
--- a/test/quintic_hermite_test.cpp
+++ b/test/quintic_hermite_test.cpp
@@ -103,7 +103,7 @@ void test_quadratic()
 
     for (Real t = 0; t <= 9; t += 0.0078125) {
         CHECK_ULP_CLOSE(Real(t*t)/2, qh(t), 2);
-        CHECK_ULP_CLOSE(t, qh.prime(t), 2);
+        CHECK_ULP_CLOSE(t, qh.prime(t), 7);
     }
 
     boost::random::mt19937 rng;
@@ -133,9 +133,8 @@ void test_quadratic()
 
     for (Real t = xmin; t <= xmax; t += 0.125) {
         CHECK_ULP_CLOSE(Real(t*t)/2, qh(t), 4);
+        CHECK_ULP_CLOSE(t, qh.prime(t), 36);
     }
-
-
 }
 
 template<typename Real>

From 0da0bc855b312bbab49f859da4c8cea795748928 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Thu, 13 Feb 2020 14:52:44 -0500
Subject: [PATCH 021/104] Never use Eigen + auto [CI SKIP]

---
 example/daubechies_scaling_integer_grid.cpp | 9 +++++----
 1 file changed, 5 insertions(+), 4 deletions(-)

diff --git a/example/daubechies_scaling_integer_grid.cpp b/example/daubechies_scaling_integer_grid.cpp
index e4f832af9..3c7377a6a 100644
--- a/example/daubechies_scaling_integer_grid.cpp
+++ b/example/daubechies_scaling_integer_grid.cpp
@@ -1,5 +1,5 @@
 /*
- * Copyright Nick Thompson, 2019
+ * Copyright Nick Thompson, John Maddock 2020
  * Use, modification and distribution are subject to the
  * Boost Software License, Version 1.0. (See accompanying file
  * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
@@ -55,7 +55,7 @@ std::list<std::vector<Real>> integer_grid()
 
     Eigen::EigenSolver<decltype(A)> es(A);
 
-    auto complex_eigs = es.eigenvalues();
+    typename Eigen::EigenSolver<decltype(A)>::EigenvalueType complex_eigs = es.eigenvalues();
 
     std::vector<Real> eigs(complex_eigs.size(), std::numeric_limits<Real>::quiet_NaN());
 
@@ -80,7 +80,8 @@ std::list<std::vector<Real>> integer_grid()
         }
         size_t idx = std::distance(eigs.begin(), it);
         std::cout << "Eigenvector for derivative " << j << " is at index " << idx << "\n";
-        auto const & complex_eigenvec = es.eigenvectors().col(idx);
+        typename Eigen::EigenSolver<decltype(A)>::EigenvectorsType complex_eigenvectors = es.eigenvectors();
+        auto complex_eigenvec = complex_eigenvectors.col(idx);
         std::vector<Real> eigenvec(complex_eigenvec.size() + 2, std::numeric_limits<Real>::quiet_NaN());
         eigenvec[0] = 0;
         eigenvec[eigenvec.size()-1] = 0;
@@ -221,7 +222,7 @@ int main()
     constexpr const size_t p_max = 15;
     std::ofstream fs{"daubechies_scaling_integer_grid.hpp"};
     fs << "/*\n"
-       << " * Copyright Nick Thompson, 2019\n"
+       << " * Copyright Nick Thompson, John Maddock, 2020\n"
        << " * Use, modification and distribution are subject to the\n"
        << " * Boost Software License, Version 1.0. (See accompanying file\n"
        << " * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)\n"

From 9397b01a3f6525f377fa18efc9f8b8501a4c8554 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Thu, 13 Feb 2020 17:34:52 -0500
Subject: [PATCH 022/104] O(1) septic Hermite splines [CI SKIP]

---
 .../detail/septic_hermite_detail.hpp          | 222 +++++++++++++-
 .../math/interpolators/septic_hermite.hpp     |  23 ++
 .../special_functions/daubechies_scaling.hpp  |  43 ++-
 test/septic_hermite_test.cpp                  | 288 ++++++++++++++++++
 4 files changed, 553 insertions(+), 23 deletions(-)
 create mode 100644 test/septic_hermite_test.cpp

diff --git a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
index 224f7aab5..1df68f69e 100644
--- a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
@@ -160,5 +160,225 @@ private:
     RandomAccessContainer d2ydx2_;
     RandomAccessContainer d3ydx3_;
 };
+
+template<class RandomAccessContainer>
+class cardinal_septic_hermite_detail {
+public:
+    using Real = typename RandomAccessContainer::value_type;
+    cardinal_septic_hermite_detail(RandomAccessContainer && y, RandomAccessContainer && dydx, RandomAccessContainer && d2ydx2, RandomAccessContainer && d3ydx3, Real x0, Real dx)
+    : y_{std::move(y)}, dydx_{std::move(dydx)}, d2ydx2_{std::move(d2ydx2)}, d3ydx3_{std::move(d3ydx3)}, x0_{x0}, dx_{dx}
+    {
+        if (y_.size() != dydx_.size()) {
+            throw std::domain_error("Numbers of derivatives must = number of ordinates.");
+        }
+        if (y_.size() != d2ydx2_.size()) {
+            throw std::domain_error("Number of second derivatives must equal number of ordinates.");
+        }
+        if (y_.size() != d3ydx3_.size()) {
+            throw std::domain_error("Number of third derivatives must equal number of ordinates.");
+        }
+
+        if (y_.size() < 2) {
+            throw std::domain_error("At least 2 abscissas are required.");
+        }
+    }
+
+    inline Real operator()(Real x) const {
+        Real xf = x0_ + (y_.size()-1)*dx_;
+        if  (x < x0_ || x > xf) {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        // We need t := (x-x_k)/(x_{k+1}-x_k) \in [0,1) for this to work.
+        // Sadly this neccessitates this loathesome check, otherwise we get t = 1 at x = xf.
+        if (x == xf)
+        {
+            return y_.back();
+        }
+        return this->unchecked_evaluation(x);
+    }
+
+    inline Real unchecked_evaluation(Real x) const {
+        using std::floor;
+        auto i = static_cast<decltype(y_.size())>(floor((x-x0_)/dx_));
+        Real xi = x0_ + i*dx_;
+        Real t = (x - xi)/dx_;
+
+        Real y0 = y_[i];
+        Real y1 = y_[i+1];
+        // Velocity:
+        Real v0 = dydx_[i];
+        Real v1 = dydx_[i+1];
+        // Acceleration:
+        Real a0 = d2ydx2_[i];
+        Real a1 = d2ydx2_[i+1];
+        // Jerk:
+        Real j0 = d3ydx3_[i];
+        Real j1 = d3ydx3_[i+1];
+
+        // See:
+        // http://seisweb.usask.ca/classes/GEOL481/2017/Labs/interpolation_utilities_matlab/shermite.m
+        Real t2 = t*t;
+        Real t3 = t2*t;
+        Real t4 = t3*t;
+        Real t5 = t4*t;
+        Real t6 = t5*t;
+        Real t7 = t6*t;
+        Real dx2 = dx_*dx_;
+        Real dx3 = dx2*dx_;
+
+        Real s = t4*(-35 + t*(84 + t*(-70 + 20*t)));
+        Real z4 = -s;
+        Real z0 = s + 1;
+        Real z1 = 10*t7 - 36*t6 + 45*t5 - 20*t4 + t;
+        Real z2 = 2*t7 - 15*t6/2 + 10*t5 - 5*t4 + t2/2;
+        Real z3 = t7/6 - 2*t6/3 + t5 - 2*t4/3 + t3/6;
+
+        Real z5 = 10*t7 - 34*t6 + 39*t5 - 15*t4;
+        Real z6 = -2*t7 + 13*t6/2 - 7*t5 + 5*t4/2;
+        Real z7 = t7/6 - t6/2 + t5/2 - t4/6;
+
+        return z0*y0 + z1*dx_*v0 + z2*dx2*a0 + z3*dx3*j0 + z4*y1 + z5*dx_*v1 + z6*dx2*a1 + z7*dx3*j1;
+    }
+
+    inline Real prime(Real x) const {
+        Real xf = x0_ + (y_.size()-1)*dx_;
+        if  (x < x0_ || x > xf)
+        {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf)
+        {
+            return dydx_.back();
+        }
+
+        return this->unchecked_prime(x);
+    }
+
+    inline Real unchecked_prime(Real x) const {
+        return std::numeric_limits<Real>::quiet_NaN();
+    }
+
+private:
+    RandomAccessContainer y_;
+    RandomAccessContainer dydx_;
+    RandomAccessContainer d2ydx2_;
+    RandomAccessContainer d3ydx3_;
+    Real x0_;
+    Real dx_;
+};
+
+
+template<class RandomAccessContainer>
+class cardinal_septic_hermite_detail_aos {
+public:
+    using Point = typename RandomAccessContainer::value_type;
+    using Real = typename Point::value_type;
+    cardinal_septic_hermite_detail_aos(RandomAccessContainer && dat, Real x0, Real dx)
+    : data_{std::move(dat)}, x0_{x0}, dx_{dx}
+    {
+        if (data_.size() < 2) {
+            throw std::domain_error("At least 2 abscissas are required.");
+        }
+        if (data_[0].size() != 4) {
+            throw std::domain_error("There must be 4 data items per struct.");
+        }
+    }
+
+    inline Real operator()(Real x) const {
+        Real xf = x0_ + (data_.size()-1)*dx_;
+        if  (x < x0_ || x > xf) {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        // We need t := (x-x_k)/(x_{k+1}-x_k) \in [0,1) for this to work.
+        // Sadly this neccessitates this loathesome check, otherwise we get t = 1 at x = xf.
+        if (x == xf)
+        {
+            return data_.back()[0];
+        }
+        return this->unchecked_evaluation(x);
+    }
+
+    inline Real unchecked_evaluation(Real x) const {
+        using std::floor;
+        auto i = static_cast<decltype(data_.size())>(floor((x-x0_)/dx_));
+        Real xi = x0_ + i*dx_;
+        Real t = (x - xi)/dx_;
+
+        Real y0 = data_[i][0];
+        Real y1 = data_[i+1][0];
+        // Velocity:
+        Real v0 = data_[i][1];
+        Real v1 = data_[i+1][1];
+        // Acceleration:
+        Real a0 = data_[i][2];
+        Real a1 = data_[i+1][2];
+        // Jerk:
+        Real j0 = data_[i][3];
+        Real j1 = data_[i+1][3];
+
+        Real t2 = t*t;
+        Real t3 = t2*t;
+        Real t4 = t3*t;
+        Real t5 = t4*t;
+        Real t6 = t5*t;
+        Real t7 = t6*t;
+        Real dx2 = dx_*dx_;
+        Real dx3 = dx2*dx_;
+
+        Real s = t4*(-35 + t*(84 + t*(-70 + 20*t)));
+        Real z4 = -s;
+        Real z0 = s + 1;
+        Real z1 = 10*t7 - 36*t6 + 45*t5 - 20*t4 + t;
+        Real z2 = 2*t7 - 15*t6/2 + 10*t5 - 5*t4 + t2/2;
+        Real z3 = t7/6 - 2*t6/3 + t5 - 2*t4/3 + t3/6;
+
+        Real z5 = 10*t7 - 34*t6 + 39*t5 - 15*t4;
+        Real z6 = -2*t7 + 13*t6/2 - 7*t5 + 5*t4/2;
+        Real z7 = t7/6 - t6/2 + t5/2 - t4/6;
+
+        return z0*y0 + z1*dx_*v0 + z2*dx2*a0 + z3*dx3*j0 + z4*y1 + z5*dx_*v1 + z6*dx2*a1 + z7*dx3*j1;
+    }
+
+    inline Real prime(Real x) const {
+        Real xf = x0_ + (data_.size()-1)*dx_;
+        if  (x < x0_ || x > xf)
+        {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf)
+        {
+            return data_.back()[1];
+        }
+
+        return this->unchecked_prime(x);
+    }
+
+    inline Real unchecked_prime(Real x) const {
+        return std::numeric_limits<Real>::quiet_NaN();
+    }
+
+private:
+    RandomAccessContainer data_;
+    Real x0_;
+    Real dx_;
+};
+
+
 }
-#endif 
\ No newline at end of file
+#endif
diff --git a/include/boost/math/interpolators/septic_hermite.hpp b/include/boost/math/interpolators/septic_hermite.hpp
index c544d1c63..54da49a02 100644
--- a/include/boost/math/interpolators/septic_hermite.hpp
+++ b/include/boost/math/interpolators/septic_hermite.hpp
@@ -34,5 +34,28 @@ public:
 private:
     std::shared_ptr<detail::septic_hermite_detail<RandomAccessContainer>> impl_;
 };
+
+template<class RandomAccessContainer>
+class cardinal_septic_hermite {
+public:
+    using Real = typename RandomAccessContainer::value_type;
+    cardinal_septic_hermite(RandomAccessContainer && y, RandomAccessContainer && dydx,
+                    RandomAccessContainer && d2ydx2, RandomAccessContainer && d3ydx3, Real x0, Real dx)
+     : impl_(std::make_shared<detail::cardinal_septic_hermite_detail<RandomAccessContainer>>(
+     std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3), x0, dx))
+    {}
+
+    Real operator()(Real x) const {
+        return impl_->operator()(x);
+    }
+
+    Real prime(Real x) const {
+        return impl_->prime(x);
+    }
+
+private:
+    std::shared_ptr<detail::cardinal_septic_hermite_detail<RandomAccessContainer>> impl_;
+};
+
 }
 #endif 
\ No newline at end of file
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index 5416eb46f..43037e9f3 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -13,7 +13,9 @@
 #include <thread>
 #include <future>
 #include <iostream>
+#if BOOST_HAS_FLOAT128
 #include <boost/multiprecision/float128.hpp>
+#endif
 #include <boost/math/constants/constants.hpp>
 #include <boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp>
 #include <boost/math/filters/daubechies.hpp>
@@ -89,7 +91,7 @@ public:
 
     matched_holder(RandomAccessContainer && y, RandomAccessContainer && dydx, int grid_refinements) : y_{std::move(y)}, dydx_{std::move(dydx)}
     {
-        h_ = Real(1)/(1<< grid_refinements);
+        inv_h_ = 1<< grid_refinements;
     }
     
     inline Real operator()(Real x) const {
@@ -97,25 +99,27 @@ public:
         using std::floor;
         using std::sqrt;
         using std::pow;
-        if (x <= 0 || x >= 3) {
-            return 0;
-        }
         // This is the exact Holder exponent, but it's pessimistic almost everywhere!
         // It's only exactly right at dyadic rationals.
+        // Some compilers do not evaluate this at compile time:
         Real const alpha = 2 - log(1+sqrt(Real(3)))/log(Real(2));
+        Real const onemalpham1 = 1/(1-alpha);
+        //const Real alpha = 0.5500156865235042;
         // So we're gonna make the graph dip a little harder; this will capture more of the self-similar behavior:
         //Real constexpr const alpha = Real(3)/Real(10);
-        int64_t i = static_cast<int64_t>(floor(x/h_));
-        Real t = (x- i*h_)/h_;
+        Real s = x*inv_h_;
+        Real ii = floor(s);
+        int64_t i = static_cast<int64_t>(ii);
+        Real t = s - ii;
         Real v = y_[i];
-        Real dphi = dydx_[i+1]*h_;
-        v += (dphi - alpha*(y_[i+1] - y_[i]))*t/(1-alpha);
-        v += (-dphi + y_[i+1] - y_[i])*pow(t, alpha)/(1-alpha);
+        Real dphi = dydx_[i+1]/inv_h_;
+        Real diff = y_[i+1] - y_[i];
+        v += ((dphi - alpha*diff)*t + (-dphi + diff)*pow(t, alpha) )*onemalpham1;
         return v;
     }
 
 private:
-    Real h_;
+    Real inv_h_;
     RandomAccessContainer y_;
     RandomAccessContainer dydx_;
 };
@@ -155,7 +159,9 @@ public:
     daubechies_scaling(int grid_refinements = -1)
     {
         static_assert(p <= 15, "Scaling functions only implements up to p = 15");
+        #if BOOST_HAS_FLOAT128
         using boost::multiprecision::float128;
+        #endif
         if (grid_refinements < 0)
         {
             if (std::is_same_v<Real, float>)
@@ -275,13 +281,6 @@ public:
         auto y = t0.get();
         auto dydx = t1.get();
 
-        // Storing the vector of x's is unnecessary; it's only because I haven't implemented an equispaced cubic Hermite interpolator:
-        std::vector<Real> x(y.size());
-        Real h = Real(2*p-1)/(x.size()-1);
-        for (size_t i = 0; i < x.size(); ++i) {
-            x[i] = i*h;
-        }
-
         if constexpr (p==2) {
             m_mh = std::make_shared<detail::matched_holder<std::vector<Real>>>(std::move(y), std::move(dydx), grid_refinements);
         }
@@ -297,9 +296,9 @@ public:
             m_qh = std::make_shared<interpolators::detail::cardinal_quintic_hermite_detail<std::vector<Real>>>(std::move(y), std::move(dydx), std::move(d2ydx2), Real(0), dx);
         }
         if constexpr (p >= 10) {
-            m_sh = std::make_shared<interpolators::detail::septic_hermite_detail<std::vector<Real>>>(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3));
+            Real dx = Real(1)/(1 << grid_refinements);
+            m_sh = std::make_shared<interpolators::detail::cardinal_septic_hermite_detail<std::vector<Real>>>(std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3), Real(0), dx);
         }
-
      }
 
 
@@ -320,7 +319,7 @@ public:
             return m_qh->unchecked_evaluation(x);
         }
         if constexpr (p >= 10) {
-            return m_sh->operator()(x);
+            return m_sh->unchecked_evaluation(x);
         }
     }
 
@@ -339,7 +338,7 @@ public:
             return m_qh->unchecked_prime(x);
         }
         if constexpr (p >= 10) {
-            return m_sh->prime(x);
+            return m_sh->unchecked_prime(x);
         }
     }
 
@@ -358,7 +357,7 @@ private:
     // Need this for p = 6,7,8,9:
     std::shared_ptr<interpolators::detail::cardinal_quintic_hermite_detail<std::vector<Real>>> m_qh;
     // Need this for p >= 10:
-    std::shared_ptr<interpolators::detail::septic_hermite_detail<std::vector<Real>>> m_sh;
+    std::shared_ptr<interpolators::detail::cardinal_septic_hermite_detail<std::vector<Real>>> m_sh;
 
     /*Real constant_interpolation(Real x) const {
         if (x <= 0 || x >= 2*p-1) {
diff --git a/test/septic_hermite_test.cpp b/test/septic_hermite_test.cpp
new file mode 100644
index 000000000..ed9772328
--- /dev/null
+++ b/test/septic_hermite_test.cpp
@@ -0,0 +1,288 @@
+/*
+ * Copyright Nick Thompson, 2020
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include "math_unit_test.hpp"
+#include <numeric>
+#include <utility>
+#include <boost/random/uniform_real.hpp>
+#include <boost/random/mersenne_twister.hpp>
+#include <boost/math/interpolators/septic_hermite.hpp>
+#ifdef BOOST_HAS_FLOAT128
+#include <boost/multiprecision/float128.hpp>
+using boost::multiprecision::float128;
+#endif
+
+
+using boost::math::interpolators::septic_hermite;
+using boost::math::interpolators::cardinal_septic_hermite;
+
+template<typename Real>
+void test_constant()
+{
+
+    std::vector<Real> x{0,1,2,3, 9, 22, 81};
+    std::vector<Real> y(x.size());
+    std::vector<Real> dydx(x.size(), 0);
+    std::vector<Real> d2ydx2(x.size(), 0);
+    std::vector<Real> d3ydx3(x.size(), 0);
+    for (auto & t : y) {
+        t = 7;
+    }
+
+    auto sh = septic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3));
+
+    for (Real t = 0; t <= 81; t += 0.25) {
+        CHECK_ULP_CLOSE(Real(7), sh(t), 24);
+        CHECK_ULP_CLOSE(Real(0), sh.prime(t), 24);
+    }
+
+    Real x0 = 0;
+    Real dx = 1;
+    y.resize(128, 7);
+    dydx.resize(128, 0);
+    d2ydx2.resize(128, 0);
+    d3ydx3.resize(128, 0);
+    auto csh = cardinal_septic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3), x0, dx);
+    for (Real t = x0; t <= 127; t += 0.25) {
+        CHECK_ULP_CLOSE(Real(7), csh(t), 24);
+        //CHECK_ULP_CLOSE(Real(0), csh.prime(t), 24);
+    }
+
+}
+
+
+template<typename Real>
+void test_linear()
+{
+    std::vector<Real> x{0,1,2,3, 4,5,6,7,8,9};
+    std::vector<Real> y = x;
+    std::vector<Real> dydx(x.size(), 1);
+    std::vector<Real> d2ydx2(x.size(), 0);
+    std::vector<Real> d3ydx3(x.size(), 0);
+
+    auto sh = septic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3));
+
+    for (Real t = 0; t <= 9; t += 0.25) {
+        CHECK_ULP_CLOSE(Real(t), sh(t), 2);
+        //CHECK_ULP_CLOSE(Real(1), qh.prime(t), 2);
+    }
+
+    boost::random::mt19937 rng;
+    boost::random::uniform_real_distribution<Real> dis(0.5,1);
+    x.resize(512);
+    x[0] = dis(rng);
+    Real xmin = x[0];
+    for (size_t i = 1; i < x.size(); ++i) {
+        x[i] = x[i-1] + dis(rng);
+    }
+    Real xmax = x.back();
+
+    y = x;
+    dydx.resize(x.size(), 1);
+    d2ydx2.resize(x.size(), 0);
+    d3ydx3.resize(x.size(), 0);
+
+    sh = septic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3));
+
+    for (Real t = xmin; t <= xmax; t += 0.125) {
+        CHECK_ULP_CLOSE(t, sh(t), 15);
+    }
+}
+
+template<typename Real>
+void test_quadratic()
+{
+    std::vector<Real> x{0,1,2,3,4,5,6,7,8,9};
+    std::vector<Real> y(x.size());
+    for (size_t i = 0; i < y.size(); ++i)
+    {
+        y[i] = x[i]*x[i]/2;
+    }
+
+    std::vector<Real> dydx(x.size());
+    for (size_t i = 0; i < y.size(); ++i) {
+        dydx[i] = x[i];
+    }
+
+    std::vector<Real> d2ydx2(x.size(), 1);
+    std::vector<Real> d3ydx3(x.size(), 0);
+
+    auto sh = septic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3));
+
+    for (Real t = 0; t <= 9; t += 0.0078125) {
+        CHECK_ULP_CLOSE(t*t/2, sh(t), 100);
+        //CHECK_ULP_CLOSE(t, qh.prime(t), 7);
+    }
+
+    boost::random::mt19937 rng;
+    boost::random::uniform_real_distribution<Real> dis(0.5,1);
+    x.resize(8);
+    x[0] = dis(rng);
+    Real xmin = x[0];
+    for (size_t i = 1; i < x.size(); ++i) {
+        x[i] = x[i-1] + dis(rng);
+    }
+    Real xmax = x.back();
+
+    y.resize(x.size());
+    for (size_t i = 0; i < y.size(); ++i)
+    {
+        y[i] = x[i]*x[i]/2;
+    }
+
+    dydx.resize(x.size());
+    for (size_t i = 0; i < y.size(); ++i) {
+        dydx[i] = x[i];
+    }
+
+    d2ydx2.resize(x.size(), 1);
+    d3ydx3.resize(x.size(), 0); 
+
+    sh = septic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3));
+
+    for (Real t = xmin; t <= xmax; t += 0.125) {
+        CHECK_ULP_CLOSE(t*t/2, sh(t), 24);
+        //CHECK_ULP_CLOSE(t, qh.prime(t), 36);
+    }
+}
+
+template<typename Real>
+void test_cubic()
+{
+
+    std::vector<Real> x{0,1,2,3,4,5,6,7};
+    Real xmax = x.back();
+    std::vector<Real> y(x.size());
+    for (size_t i = 0; i < y.size(); ++i)
+    {
+        y[i] = x[i]*x[i]*x[i];
+    }
+
+    std::vector<Real> dydx(x.size());
+    for (size_t i = 0; i < y.size(); ++i) {
+        dydx[i] = 3*x[i]*x[i];
+    }
+
+    std::vector<Real> d2ydx2(x.size());
+    for (size_t i = 0; i < y.size(); ++i) {
+        d2ydx2[i] = 6*x[i];
+    }
+    std::vector<Real> d3ydx3(x.size(), 6);
+
+    auto sh = septic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3));
+
+    for (Real t = 0; t <= xmax; t += 0.0078125) {
+        CHECK_ULP_CLOSE(t*t*t, sh(t), 151);
+    }
+}
+
+template<typename Real>
+void test_quartic()
+{
+
+    std::vector<Real> x{0,1,2,3,4,5,6,7,8,9};
+    Real xmax = x.back();
+    std::vector<Real> y(x.size());
+    for (size_t i = 0; i < y.size(); ++i)
+    {
+        y[i] = x[i]*x[i]*x[i]*x[i];
+    }
+
+    std::vector<Real> dydx(x.size());
+    for (size_t i = 0; i < y.size(); ++i) {
+        dydx[i] = 4*x[i]*x[i]*x[i];
+    }
+
+    std::vector<Real> d2ydx2(x.size());
+    for (size_t i = 0; i < y.size(); ++i) {
+        d2ydx2[i] = 12*x[i]*x[i];
+    }
+
+    std::vector<Real> d3ydx3(x.size());
+    for (size_t i = 0; i < y.size(); ++i) {
+        d3ydx3[i] = 24*x[i];
+    }
+
+    auto sh = septic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3));
+
+    for (Real t = 1; t <= xmax; t += 0.0078125) {
+        CHECK_ULP_CLOSE(t*t*t*t, sh(t), 117);
+    }
+}
+
+
+template<typename Real>
+void test_interpolation_condition()
+{
+    for (size_t n = 4; n < 50; ++n) {
+        std::vector<Real> x(n);
+        std::vector<Real> y(n);
+        std::vector<Real> dydx(n);
+        std::vector<Real> d2ydx2(n);
+        std::vector<Real> d3ydx3(n);
+        boost::random::mt19937 rd; 
+        boost::random::uniform_real_distribution<Real> dis(0,1);
+        Real x0 = dis(rd);
+        x[0] = x0;
+        y[0] = dis(rd);
+        for (size_t i = 1; i < n; ++i) {
+            x[i] = x[i-1] + dis(rd);
+            y[i] = dis(rd);
+            dydx[i] = dis(rd);
+            d2ydx2[i] = dis(rd);
+            d3ydx3[i] = dis(rd);
+        }
+
+        auto x_copy = x;
+        auto y_copy = y;
+        auto dydx_copy = dydx;
+        auto d2ydx2_copy = d2ydx2;
+        auto d3ydx3_copy = d3ydx3;
+        auto s = septic_hermite(std::move(x_copy), std::move(y_copy), std::move(dydx_copy), std::move(d2ydx2_copy), std::move(d3ydx3_copy));
+
+        for (size_t i = 0; i < x.size(); ++i) {
+            CHECK_ULP_CLOSE(y[i], s(x[i]), 2);
+            //CHECK_ULP_CLOSE(dydx[i], s.prime(x[i]), 2);
+        }
+    }
+}
+
+
+int main()
+{
+    test_constant<float>();
+    test_linear<float>();
+    test_quadratic<float>();
+    test_cubic<float>();
+    test_quartic<float>();
+    test_interpolation_condition<float>();
+
+    test_constant<double>();
+    test_linear<double>();
+    test_quadratic<double>();
+    test_cubic<double>();
+    test_quartic<double>();
+    test_interpolation_condition<double>();
+
+    test_constant<long double>();
+    test_linear<long double>();
+    test_quadratic<long double>();
+    test_cubic<long double>();
+    test_quartic<long double>();
+    test_interpolation_condition<long double>();
+
+#ifdef BOOST_HAS_FLOAT128
+    test_constant<float128>();
+    test_linear<float128>();
+    test_quadratic<float128>();
+    test_cubic<float128>();
+    test_quartic<float128>();
+    test_interpolation_condition<float128>();
+#endif
+
+    return boost::math::test::report_errors();
+}

From 2134a9c914e620bb9120a3189771e1d0bd5081f2 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Sat, 15 Feb 2020 08:36:38 -0500
Subject: [PATCH 023/104] Move examples/daubechies_files.cpp to
 examples/daubechies_wavelets/some_file.cpp [CI SKIP]

---
 .../daubechies_coefficients.cpp               |   0
 .../daubechies_scaling_integer_grid.cpp       |   0
 .../find_best_daubechies_interpolator.cpp     | 584 ++++++++++++++++++
 example/find_best_daubechies_interpolator.cpp | 507 ---------------
 .../detail/septic_hermite_detail.hpp          |  11 +-
 .../special_functions/daubechies_scaling.hpp  |   4 +-
 6 files changed, 596 insertions(+), 510 deletions(-)
 rename example/{ => daubechies_wavelets}/daubechies_coefficients.cpp (100%)
 rename example/{ => daubechies_wavelets}/daubechies_scaling_integer_grid.cpp (100%)
 create mode 100644 example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
 delete mode 100644 example/find_best_daubechies_interpolator.cpp

diff --git a/example/daubechies_coefficients.cpp b/example/daubechies_wavelets/daubechies_coefficients.cpp
similarity index 100%
rename from example/daubechies_coefficients.cpp
rename to example/daubechies_wavelets/daubechies_coefficients.cpp
diff --git a/example/daubechies_scaling_integer_grid.cpp b/example/daubechies_wavelets/daubechies_scaling_integer_grid.cpp
similarity index 100%
rename from example/daubechies_scaling_integer_grid.cpp
rename to example/daubechies_wavelets/daubechies_scaling_integer_grid.cpp
diff --git a/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp b/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
new file mode 100644
index 000000000..09292ebca
--- /dev/null
+++ b/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
@@ -0,0 +1,584 @@
+#include <iostream>
+#include <unordered_map>
+#include <string>
+#include <future>
+#include <thread>
+#include <fstream>
+#include <boost/math/special_functions/daubechies_scaling.hpp>
+#include <boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp>
+#include <boost/math/interpolators/cubic_hermite.hpp>
+#include <boost/math/interpolators/cardinal_cubic_hermite.hpp>
+#include <boost/math/interpolators/quintic_hermite.hpp>
+#include <boost/math/interpolators/cardinal_quintic_hermite.hpp>
+#include <boost/math/interpolators/septic_hermite.hpp>
+#include <boost/math/interpolators/cardinal_quadratic_b_spline.hpp>
+#include <boost/math/interpolators/cardinal_cubic_b_spline.hpp>
+#include <boost/math/interpolators/cardinal_quintic_b_spline.hpp>
+#include <boost/math/interpolators/whittaker_shannon.hpp>
+#include <boost/math/interpolators/cardinal_trigonometric.hpp>
+#include <boost/math/special_functions/next.hpp>
+#include <boost/math/interpolators/makima.hpp>
+#include <boost/math/interpolators/pchip.hpp>
+#include <boost/multiprecision/float128.hpp>
+#include <boost/core/demangle.hpp>
+//#include <quicksvg/graph_fn.hpp>
+//#include <quicksvg/ulp_plot.hpp>
+
+using boost::multiprecision::float128;
+
+
+template<typename Real, typename PreciseReal, int p>
+void choose_refinement()
+{
+    std::cout << "Choosing refinement for " << boost::core::demangle(typeid(Real).name()) << " precision Daubechies scaling function with " << p << " vanishing moments.\n";
+    using std::abs;
+    int rmax = 21;
+    auto phi_dense = boost::math::detail::dyadic_grid<PreciseReal, p, 0>(rmax);
+    Real dx_dense = (2*p-1)/static_cast<Real>(phi_dense.size()-1);
+
+    for (int r = 2; r <= rmax - 2; ++r)
+    {
+        auto phi_accurate = boost::math::detail::dyadic_grid<PreciseReal, p, 0>(r);
+        std::vector<Real> phi(phi_accurate.size());
+        for (size_t i = 0; i < phi_accurate.size(); ++i)
+        {
+            phi[i] = Real(phi_accurate[i]);
+        }
+        auto phi_prime_accurate = boost::math::detail::dyadic_grid<PreciseReal, p, 1>(r);
+        std::vector<Real> phi_prime(phi_accurate.size());
+        for (size_t i = 0; i < phi_prime_accurate.size(); ++i)
+        {
+            phi_prime[i] = Real(phi_prime_accurate[i]);
+        }
+
+        Real dx = (2*p-1)/static_cast<Real>(phi.size()-1);
+        std::cout << "\tdx = 1/" << (1/dx) << " = " << dx << "\n";
+
+        if constexpr (p < 6 && p >= 3)
+        {
+            auto ch = boost::math::interpolators::cardinal_cubic_hermite(std::move(phi), std::move(phi_prime), Real(0), Real(dx));
+            Real flt_distance = 0;
+            Real sup  = 0;
+            Real worst_abscissa = 0;
+            Real worst_value = 0;
+            Real worst_computed = 0;
+            for (size_t i = 0; i < phi_dense.size(); ++i)
+            {
+                Real t = i*dx_dense;
+                Real computed = ch(t);
+                Real expected = Real(phi_dense[i]);
+                if (std::abs(expected) < 100*std::numeric_limits<Real>::epsilon())
+                {
+                    continue;
+                }
+                Real diff = abs(computed - expected);
+                Real distance = abs(boost::math::float_distance(computed, expected));
+                if (distance > flt_distance)
+                {
+                    flt_distance = distance;
+                    worst_abscissa = t;
+                    worst_value = expected;
+                    worst_computed = computed;
+                }
+                if (diff > sup)
+                {
+                    sup = diff;
+                }
+            }
+            std::cout << "\t\tFloat distance at r = " << r << " is " << flt_distance << ", sup distance = " << sup << "\n";
+            std::cout << "\t\tWorst abscissa = " << worst_abscissa << ", worst value = " << worst_value << ", computed = " << worst_computed << "\n";
+        }
+        else if constexpr (p >= 6)
+        {
+            auto phi_dbl_prime = boost::math::detail::dyadic_grid<Real, p, 2>(r);
+            auto qh = boost::math::interpolators::cardinal_quintic_hermite(std::move(phi), std::move(phi_prime), std::move(phi_dbl_prime), Real(0), dx);
+            Real flt_distance = 0;
+            Real sup  = 0;
+            Real worst_abscissa = 0;
+            Real worst_value = 0;
+            Real worst_computed = 0;
+            for (size_t i = 0; i < phi_dense.size(); ++i)
+            {
+                Real t = i*dx_dense;
+                Real computed = qh(t);
+                Real expected = Real(phi_dense[i]);
+                if (std::abs(expected) < 100*std::numeric_limits<Real>::epsilon())
+                {
+                    continue;
+                }
+
+                Real diff = abs(computed - expected);
+                Real distance = abs(boost::math::float_distance(computed, expected));
+                if (distance > flt_distance)
+                {
+                    flt_distance = distance;
+                    worst_abscissa = t;
+                    worst_value = expected;
+                    worst_computed = computed;
+                }
+                if (diff > sup)
+                {
+                    sup = diff;
+                }
+                std::cout << "Float distance at r = " << r << " is " << flt_distance << ", sup distance = " << sup << "\n";
+                std::cout << "\tWorst abscissa = " << worst_abscissa << ", worst value = " << worst_value << ", computed = " << worst_computed << "\n"; 
+            }
+        }
+    }
+}
+
+template<typename Real, typename PreciseReal, int p>
+void find_best_interpolator()
+{
+    std::string filename = "daubechies_" + std::to_string(p) + "_scaling_convergence.csv";
+    std::ofstream fs{filename};
+    static_assert(sizeof(PreciseReal) >= sizeof(Real), "sizeof(PreciseReal) >= sizeof(Real) is required.");
+    using std::abs;
+    int rmax = 21;
+    auto phi_dense_precise = boost::math::detail::dyadic_grid<PreciseReal, p, 0>(rmax);
+    std::vector<Real> phi_dense(phi_dense_precise.size());
+    for (size_t i = 0; i < phi_dense.size(); ++i)
+    {
+        phi_dense[i] = static_cast<Real>(phi_dense_precise[i]);
+    }
+    phi_dense_precise.resize(0);
+
+    Real dx_dense = (2*p-1)/static_cast<Real>(phi_dense.size()-1);
+    fs << std::setprecision(std::numeric_limits<Real>::digits10 + 3);
+    fs << std::fixed;
+    fs << "r, matched_holder, linear, quadratic B-spline, cubic B-spline, quintic B-spline, cubic Hermite, pchip, makima, fo_taylor";
+    if (p==2) {
+      fs << "\n";
+    }
+    else {
+      fs << ", quintic hermite, second-order taylor";
+      if (p > 3)
+      {
+        fs << ", third order taylor, septic_hermite\n";
+      }
+      else {
+        fs << "\n";
+      }
+    }
+    for (int r = 2; r < rmax-1; ++r)
+    {
+        fs << r << ", ";
+        std::map<Real, std::string> m;
+        auto phi = boost::math::detail::dyadic_grid<Real, p, 0>(r);
+        auto phi_prime = boost::math::detail::dyadic_grid<Real, p, 1>(r);
+
+        std::vector<Real> x(phi.size());
+        Real dx = (2*p-1)/static_cast<Real>(x.size()-1);
+        std::cout << "dx = 1/" << (1 << r) << " = " << dx << "\n";
+        for (size_t i = 0; i < x.size(); ++i)
+        {
+            x[i] = i*dx;
+        }
+
+        {
+            auto phi_copy = phi;
+            auto phi_prime_copy = phi_prime;
+            auto mh = boost::math::detail::matched_holder(std::move(phi_copy), std::move(phi_prime_copy), r);
+            Real sup = 0;
+            // call to matched_holder is unchecked:
+            for (size_t i = 0; i < phi_dense.size() - 1; ++i)
+            {
+                Real x = i*dx_dense;
+                Real diff = abs(phi_dense[i] - mh(x));
+                if (diff > sup)
+                {
+                    sup = diff;
+                }
+            }
+            m.insert({sup, "matched_holder"});
+            fs << sup << ", ";
+        }
+
+
+        {
+            auto linear = [&phi, &dx, &r](Real x)->Real {
+              if (x <= 0 || x >= 2*p-1)
+              {
+                return Real(0);
+              }
+              using std::floor;
+
+              Real y = (1<<r)*x;
+              Real k = floor(y);
+
+              size_t kk = static_cast<size_t>(k);
+
+              Real t = y - k;
+              return (1-t)*phi[kk] + t*phi[kk+1];
+            };
+
+            Real linear_sup = 0;
+            for (size_t i = 0; i < phi_dense.size(); ++i)
+            {
+                Real x = i*dx_dense;
+                Real diff = abs(phi_dense[i] - linear(x));
+                if (diff > linear_sup)
+                {
+                    linear_sup = diff;
+                }
+            }
+            m.insert({linear_sup, "linear interpolation"});
+            fs << linear_sup << ", ";
+        }
+        
+
+        {
+            auto qbs = boost::math::interpolators::cardinal_quadratic_b_spline(phi.data(), phi.size(), Real(0), dx, phi_prime.front(), phi_prime.back());
+            Real qbs_sup = 0;
+            for (size_t i = 0; i < phi_dense.size(); ++i)
+            {
+                Real x = i*dx_dense;
+                Real diff = abs(phi_dense[i] - qbs(x));
+                if (diff > qbs_sup) {
+                    qbs_sup = diff;
+                }
+            }
+            m.insert({qbs_sup, "quadratic_b_spline"});
+            fs << qbs_sup << ", ";
+        }
+
+        {
+            auto cbs = boost::math::interpolators::cardinal_cubic_b_spline(phi.data(), phi.size(), Real(0), dx, phi_prime.front(), phi_prime.back());
+            Real cbs_sup = 0;
+            for (size_t i = 0; i < phi_dense.size(); ++i)
+            {
+                Real x = i*dx_dense;
+                Real diff = abs(phi_dense[i] - cbs(x));
+                if (diff > cbs_sup)
+                {
+                    cbs_sup = diff;
+                }
+            }
+            m.insert({cbs_sup, "cubic_b_spline"});
+            fs << cbs_sup << ", ";
+        }
+
+        {
+            auto qbs = boost::math::interpolators::cardinal_quintic_b_spline(phi.data(), phi.size(), Real(0), dx, {0,0}, {0,0});
+            Real qbs_sup = 0;
+            for (size_t i = 0; i < phi_dense.size(); ++i)
+            {
+                Real x = i*dx_dense;
+                Real diff = abs(phi_dense[i] - qbs(x));
+                if (diff > qbs_sup)
+                {
+                    qbs_sup = diff;
+                }
+            }
+            m.insert({qbs_sup, "quintic_b_spline"});
+            fs << qbs_sup << ", ";
+        }
+
+        {
+            auto phi_copy = phi;
+            auto phi_prime_copy = phi_prime;
+            auto ch = boost::math::interpolators::cardinal_cubic_hermite(std::move(phi_copy), std::move(phi_prime_copy), Real(0), dx);
+            Real chs_sup = 0;
+            for (size_t i = 0; i < phi_dense.size(); ++i)
+            {
+                Real x = i*dx_dense;
+                Real diff = abs(phi_dense[i] - ch(x));
+                if (diff > chs_sup)
+                {
+                    chs_sup = diff;
+                }
+            }
+            m.insert({chs_sup, "cubic_hermite_spline"});
+            fs << chs_sup << ", ";
+        }
+
+        {
+            auto phi_copy = phi;
+            auto x_copy = x;
+            auto phi_prime_copy = phi_prime;
+            auto pc = boost::math::interpolators::pchip(std::move(x_copy), std::move(phi_copy));
+            Real pchip_sup = 0;
+            for (size_t i = 0; i < phi_dense.size(); ++i)
+            {
+                Real x = i*dx_dense;
+                Real diff = abs(phi_dense[i] - pc(x));
+                if (diff > pchip_sup)
+                {
+                  pchip_sup = diff;
+                }
+            }
+            m.insert({pchip_sup, "pchip"});
+            fs << pchip_sup << ", ";
+        }
+
+        {
+            auto phi_copy = phi;
+            auto x_copy = x;
+            auto pc = boost::math::interpolators::makima(std::move(x_copy), std::move(phi_copy));
+            Real makima_sup = 0;
+            for (size_t i = 0; i < phi_dense.size(); ++i) {
+              Real x = i*dx_dense;
+              Real diff = abs(phi_dense[i] - pc(x));
+              if (diff > makima_sup)
+              {
+                  makima_sup = diff;
+              }
+            }
+            m.insert({makima_sup, "makima"});
+            fs << makima_sup << ", ";
+        }
+
+        // Whittaker-Shannon interpolation has linear complexity; test over all points and it's quadratic.
+        // I ran this a couple times and found it's not competitive; so comment out for now.
+        /*{
+            auto phi_copy = phi;
+            auto ws = boost::math::interpolators::whittaker_shannon(std::move(phi_copy), Real(0), dx);
+            Real sup = 0;
+            for (size_t i = 0; i < phi_dense.size(); ++i) {
+              Real x = i*dx_dense;
+              using std::abs;
+              Real diff = abs(phi_dense[i] - ws(x));
+              if (diff > sup) {
+                sup = diff;
+              }
+            }
+          
+            m.insert({sup, "whittaker_shannon"});
+        }
+
+        // Again, linear complexity of evaluation => quadratic complexity of exhaustive checking.
+        {
+            auto trig = boost::math::interpolators::cardinal_trigonometric(phi, Real(0), dx);
+            Real sup = 0;
+            for (size_t i = 0; i < phi_dense.size(); ++i) {
+              Real x = i*dx_dense;
+              using std::abs;
+              Real diff = abs(phi_dense[i] - trig(x));
+              if (diff > sup) {
+                sup = diff;
+              }
+            }
+            m.insert({sup, "trig"});
+        }*/
+
+        {
+            auto fotaylor = [&phi, &phi_prime, &r](Real x)->Real
+            {
+                if (x <= 0 || x >= 2*p-1)
+                {
+                    return 0;
+                }
+                using std::floor;
+
+                Real y = (1<<r)*x;
+                Real k = floor(y);
+
+                size_t kk = static_cast<size_t>(k);
+                if (y - k < k + 1 - y)
+                {
+                    Real eps = (y-k)/(1<<r);
+                    return phi[kk] + eps*phi_prime[kk];
+                }
+                else {
+                    Real eps = (y-k-1)/(1<<r);
+                    return phi[kk+1] + eps*phi_prime[kk+1];
+                }
+            };
+            Real fo_sup = 0;
+            for (size_t i = 0; i < phi_dense.size(); ++i)
+            {
+                Real x = i*dx_dense;
+                Real diff = abs(phi_dense[i] - fotaylor(x));
+                if (diff > fo_sup)
+                {
+                  fo_sup = diff;
+                }
+            }
+            m.insert({fo_sup, "First-order Taylor"});
+            if (p==2) {
+            fs << fo_sup << "\n";
+            }
+            else {
+              fs << fo_sup << ", ";
+            }
+        }
+
+        if constexpr (p > 2) {
+            auto phi_dbl_prime = boost::math::detail::dyadic_grid<Real, p, 2>(r);
+
+            {
+                auto phi_copy = phi;
+                auto phi_prime_copy = phi_prime;
+                auto phi_dbl_prime_copy = phi_dbl_prime;
+                auto qh = boost::math::interpolators::cardinal_quintic_hermite(std::move(phi_copy), std::move(phi_prime_copy), std::move(phi_dbl_prime_copy), Real(0), dx);
+                Real qh_sup = 0;
+                for (size_t i = 0; i < phi_dense.size(); ++i)
+                {
+                    Real x = i*dx_dense;
+                    Real diff = abs(phi_dense[i] - qh(x));
+                    if (diff > qh_sup)
+                    {
+                        qh_sup = diff;
+                    }
+                }
+                m.insert({qh_sup, "quintic_hermite_spline"});
+                fs << qh_sup << ", ";
+            }
+
+            {
+                auto sotaylor = [&phi, &phi_prime, &phi_dbl_prime, &r](Real x)->Real {
+                      if (x <= 0 || x >= 2*p-1)
+                      {
+                          return 0;
+                      }
+                      using std::floor;
+
+                      Real y = (1<<r)*x;
+                      Real k = floor(y);
+
+                      size_t kk = static_cast<size_t>(k);
+                      if (y - k < k + 1 - y)
+                      {
+                          Real eps = (y-k)/(1<<r);
+                          return phi[kk] + eps*phi_prime[kk] + eps*eps*phi_dbl_prime[kk]/2;
+                      }
+                      else {
+                          Real eps = (y-k-1)/(1<<r);
+                          return phi[kk+1] + eps*phi_prime[kk+1] + eps*eps*phi_dbl_prime[kk+1]/2;
+                      }
+                };
+                Real so_sup = 0;
+                for (size_t i = 0; i < phi_dense.size(); ++i)
+                {
+                    Real x = i*dx_dense;
+                    Real diff = abs(phi_dense[i] - sotaylor(x));
+                    if (diff > so_sup)
+                    {
+                        so_sup = diff;
+                    }
+                }
+                m.insert({so_sup, "Second-order Taylor"});
+                if (p > 3)
+                {
+                    fs << so_sup << ", ";  
+                }
+                else
+                {
+                    fs << so_sup << "\n";
+                }
+                
+            }
+        }
+
+        if constexpr (p > 3)
+        {
+            auto phi_dbl_prime = boost::math::detail::dyadic_grid<Real, p, 2>(r);
+            auto phi_triple_prime = boost::math::detail::dyadic_grid<Real, p, 3>(r);
+
+            {
+                auto totaylor = [&phi, &phi_prime, &phi_dbl_prime, &phi_triple_prime, &r](Real x)->Real {
+                      if (x <= 0 || x >= 2*p-1) {
+                          return 0;
+                      }
+                      using std::floor;
+
+                      Real y = (1<<r)*x;
+                      Real k = floor(y);
+
+                      size_t kk = static_cast<size_t>(k);
+                      if (y - k < k + 1 - y)
+                      {
+                          Real eps = (y-k)/(1<<r);
+                          return phi[kk] + eps*phi_prime[kk] + eps*eps*phi_dbl_prime[kk]/2 + eps*eps*eps*phi_triple_prime[kk]/6;
+                      }
+                      else {
+                          Real eps = (y-k-1)/(1<<r);
+                          return phi[kk+1] + eps*phi_prime[kk+1] + eps*eps*phi_dbl_prime[kk+1]/2 + eps*eps*eps*phi_triple_prime[kk]/6;
+                      }
+                };
+                Real to_sup = 0;
+                for (size_t i = 0; i < phi_dense.size(); ++i)
+                {
+                    Real x = i*dx_dense;
+                    Real diff = abs(phi_dense[i] - totaylor(x));
+                    if (diff > to_sup)
+                    {
+                        to_sup = diff;
+                    }
+                }
+            
+                m.insert({to_sup, "Third-order Taylor"});
+                fs << to_sup << ", ";
+            }
+
+            {
+                auto phi_copy = phi;
+                auto phi_prime_copy = phi_prime;
+                auto phi_dbl_prime_copy = phi_dbl_prime;
+                auto phi_triple_prime_copy = phi_triple_prime;
+                auto sh = boost::math::interpolators::cardinal_septic_hermite(std::move(phi_copy), std::move(phi_prime_copy), std::move(phi_dbl_prime_copy), std::move(phi_triple_prime_copy), Real(0), dx);
+                Real septic_sup = 0;
+                for (size_t i = 0; i < phi_dense.size(); ++i)
+                {
+                    Real x = i*dx_dense;
+                    Real diff = abs(phi_dense[i] - sh(x));
+                    if (diff > septic_sup)
+                    {
+                        septic_sup = diff;
+                    }
+                }
+                m.insert({septic_sup, "septic_hermite_spline"});
+                fs << septic_sup << ", ";
+            }
+
+
+        }
+        std::string best = "none";
+        Real best_sup = 1000000000;
+        std::cout << std::setprecision(std::numeric_limits<Real>::digits10 + 3) << std::fixed;
+        for (auto & e : m)
+        {
+            std::cout << "\t" << e.first << " is error of " << e.second << "\n";
+            if (e.first < best_sup)
+            {
+                best = e.second;
+                best_sup = e.first;
+            }
+        }
+        std::cout << "\tThe best method for p = " << p << " is the " << best << "\n";
+    }
+}
+
+int main() {
+    //choose_refinement<float, double, 5>();
+    //choose_refinement<float, long double, 5>();
+    //choose_refinement<double, float128, 15>();
+    // Says linear interpolation is the best:
+    find_best_interpolator<double, float128, 2>();
+    // Says linear interpolation is the best:
+    find_best_interpolator<double, float128, 3>();
+    // Says cubic_hermite_spline is best:
+    find_best_interpolator<double, float128, 4>();
+    // Says cubic_hermite_spline is best:
+    find_best_interpolator<double, float128, 5>();
+    // Says quintic_hermite_spline is best:
+    find_best_interpolator<double, float128, 6>();
+    // Says quintic_hermite_spline is best:
+    find_best_interpolator<double, float128, 7>();
+    // Says quintic_hermite_spline is best:
+    find_best_interpolator<double, float128, 8>();
+    // Says quintic_hermite_spline is best:
+    find_best_interpolator<double, float128, 9>();
+    // Says septic_hermite_spline is best:
+    find_best_interpolator<double, float128, 10>();
+    // Says septic_hermite_spline is best:
+    find_best_interpolator<double, float128, 11>();
+    // Says septic_hermite_spline is best:
+    find_best_interpolator<double, float128, 12>();
+    // Says septic_hermite_spline is best:
+    find_best_interpolator<double, float128, 13>();
+    // Says septic_hermite_spline is best:
+    find_best_interpolator<double, float128, 14>();
+    // Says septic_hermite_spline is best:
+    find_best_interpolator<double, float128, 15>();
+}
diff --git a/example/find_best_daubechies_interpolator.cpp b/example/find_best_daubechies_interpolator.cpp
deleted file mode 100644
index d9277f698..000000000
--- a/example/find_best_daubechies_interpolator.cpp
+++ /dev/null
@@ -1,507 +0,0 @@
-#include <iostream>
-#include <unordered_map>
-#include <string>
-#include <future>
-#include <thread>
-#include <boost/math/special_functions/daubechies_scaling.hpp>
-#include <boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp>
-#include <boost/math/interpolators/cubic_hermite.hpp>
-#include <boost/math/interpolators/quintic_hermite.hpp>
-#include <boost/math/interpolators/septic_hermite.hpp>
-#include <boost/math/interpolators/cardinal_quadratic_b_spline.hpp>
-#include <boost/math/interpolators/cardinal_cubic_b_spline.hpp>
-#include <boost/math/interpolators/cardinal_quintic_b_spline.hpp>
-#include <boost/math/interpolators/whittaker_shannon.hpp>
-#include <boost/math/interpolators/cardinal_trigonometric.hpp>
-#include <boost/math/special_functions/next.hpp>
-#include <boost/math/interpolators/makima.hpp>
-#include <boost/math/interpolators/pchip.hpp>
-#include <boost/multiprecision/float128.hpp>
-#include <boost/core/demangle.hpp>
-//#include <quicksvg/graph_fn.hpp>
-//#include <quicksvg/ulp_plot.hpp>
-
-using boost::multiprecision::float128;
-
-
-template<class Real, int p>
-void choose_refinement()
-{
-    using std::abs;
-    int rmax = 22;
-    auto phi_dense = boost::math::detail::dyadic_grid<long double, p, 0>(rmax);
-    Real dx_dense = (2*p-1)/static_cast<Real>(phi_dense.size()-1);
-
-    for (int r = 2; r <= rmax - 2; ++r) {
-        auto phi_accurate = boost::math::detail::dyadic_grid<long double, p, 0>(r);
-        std::vector<Real> phi(phi_accurate.size());
-        for (size_t i = 0; i < phi_accurate.size(); ++i) {
-            phi[i] = Real(phi_accurate[i]);
-        }
-        auto phi_prime_accurate = boost::math::detail::dyadic_grid<long double, p, 1>(r);
-        std::vector<Real> phi_prime(phi_accurate.size());
-        for (size_t i = 0; i < phi_prime_accurate.size(); ++i) {
-            phi_prime[i] = Real(phi_prime_accurate[i]);
-        }
-
-        std::vector<Real> x(phi.size());
-        Real dx = (2*p-1)/static_cast<Real>(x.size()-1);
-        std::cout << "dx = " << dx << "\n";
-        for (size_t i = 0; i < x.size(); ++i) {
-          x[i] = i*dx;
-        }
-
-        if constexpr (p < 6 && p >= 3) {
-            auto ch = boost::math::interpolators::cubic_hermite(std::move(x), std::move(phi), std::move(phi_prime));
-            Real flt_distance = 0;
-            Real sup  = 0;
-            Real worst_abscissa = 0;
-            Real worst_value = 0;
-            Real worst_computed = 0;
-            for (size_t i = 0; i < phi_dense.size(); ++i) {
-              Real t = i*dx_dense;
-              Real computed = ch(t);
-              Real expected = Real(phi_dense[i]);
-              if (std::abs(expected) < 100*std::numeric_limits<Real>::epsilon()) {
-                continue;
-              }
-              
-              Real diff = abs(computed - expected);
-              Real distance = abs(boost::math::float_distance(computed, expected));
-              if (distance > flt_distance) {
-                flt_distance = distance;
-                worst_abscissa = t;
-                worst_value = expected;
-                worst_computed = computed;
-              }
-              if (diff > sup) {
-                sup = diff;
-              }
-            }
-            std::cout << "Float distance at r = " << r << " is " << flt_distance << ", sup distance = " << sup << "\n";
-            std::cout << "\tWorst abscissa = " << worst_abscissa << ", worst value = " << worst_value << ", computed = " << worst_computed << "\n"; 
-            std::cout << "\tRAM = " << 3*phi_accurate.size()*sizeof(Real) << " bytes\n";
-        }
-        else if constexpr (p >= 6) {
-
-            auto phi_dbl_prime = boost::math::detail::dyadic_grid<Real, p, 2>(r);
-            auto qh = boost::math::interpolators::quintic_hermite(std::move(x), std::move(phi), std::move(phi_prime), std::move(phi_dbl_prime));
-            Real flt_distance = 0;
-            Real sup  = 0;
-            Real worst_abscissa = 0;
-            Real worst_value = 0;
-            Real worst_computed = 0;
-            for (size_t i = 0; i < phi_dense.size(); ++i) {
-              Real t = i*dx_dense;
-              Real computed = qh(t);
-              Real expected = Real(phi_dense[i]);
-              if (std::abs(expected) < 100*std::numeric_limits<Real>::epsilon()) {
-                continue;
-              }
-              
-              Real diff = abs(computed - expected);
-              Real distance = abs(boost::math::float_distance(computed, expected));
-              if (distance > flt_distance) {
-                flt_distance = distance;
-                worst_abscissa = t;
-                worst_value = expected;
-                worst_computed = computed;
-              }
-              if (diff > sup) {
-                sup = diff;
-              }
-            }
-            std::cout << "Float distance at r = " << r << " is " << flt_distance << ", sup distance = " << sup << "\n";
-            std::cout << "\tWorst abscissa = " << worst_abscissa << ", worst value = " << worst_value << ", computed = " << worst_computed << "\n"; 
-            std::cout << "\tRAM = " << 3*phi_accurate.size()*sizeof(Real) << " bytes\n";
-        }
-    }
-}
-
-template<class Real, int p>
-void find_best_interpolator()
-{
-    using std::abs;
-    int rmax = 15;
-    auto phi_dense = boost::math::detail::dyadic_grid<Real, p, 0>(rmax);
-    Real dx_dense = (2*p-1)/static_cast<Real>(phi_dense.size()-1);
-    for (int r = 2; r < rmax-1; ++r)
-    {
-        std::map<Real, std::string> m;
-        auto phi = boost::math::detail::dyadic_grid<Real, p, 0>(r);
-        auto phi_prime = boost::math::detail::dyadic_grid<Real, p, 1>(r);
-
-        std::vector<Real> x(phi.size());
-        Real dx = (2*p-1)/static_cast<Real>(x.size()-1);
-        std::cout << "dx = 1/" << (1 << r) << " = " << dx << "\n";
-        for (size_t i = 0; i < x.size(); ++i) {
-            x[i] = i*dx;
-        }
-
-        {
-          auto phi_copy = phi;
-          auto phi_prime_copy = phi_prime;
-          auto mh = boost::math::detail::matched_holder(std::move(phi_copy), std::move(phi_prime_copy), r);
-          Real sup = 0;
-          for (size_t i = 0; i < phi_dense.size(); ++i) {
-            Real x = i*dx_dense;
-            Real diff = abs(phi_dense[i] - mh(x));
-            if (diff > sup) {
-              sup = diff;
-            }
-          }
-          m.insert({sup, "matched_holder"});
-        }
-
-
-        {
-            auto linear = [&phi, &dx, &r](Real x)->Real {
-              if (x <= 0 || x >= 2*p-1) {
-                return Real(0);
-              }
-              using std::floor;
-
-              Real y = (1<<r)*x;
-              Real k = floor(y);
-
-              size_t kk = static_cast<size_t>(k);
-
-              Real t = y - k;
-              return (1-t)*phi[kk] + t*phi[kk+1];
-            };
-            Real sup = 0;
-            for (size_t i = 0; i < phi_dense.size(); ++i) {
-              Real x = i*dx_dense;
-              Real diff = abs(phi_dense[i] - linear(x));
-              if (diff > sup) {
-                sup = diff;
-              }
-            }
-        
-          m.insert({sup, "linear interpolation"});
-        }
-        
-
-        {
-            auto qbs = boost::math::interpolators::cardinal_quadratic_b_spline(phi.data(), phi.size(), Real(0), dx, phi_prime.front(), phi_prime.back());
-            Real qbs_sup = 0;
-            for (size_t i = 0; i < phi_dense.size(); ++i) {
-              Real x = i*dx_dense;
-              Real diff = abs(phi_dense[i] - qbs(x));
-              if (diff > qbs_sup) {
-                qbs_sup = diff;
-              }
-          }
-        
-          m.insert({qbs_sup, "quadratic_b_spline"});
-        }
-
-        {
-          auto cbs = boost::math::interpolators::cardinal_cubic_b_spline(phi.data(), phi.size(), Real(0), dx, phi_prime.front(), phi_prime.back());
-          Real cbs_sup = 0;
-          for (size_t i = 0; i < phi_dense.size(); ++i) {
-            Real x = i*dx_dense;
-            Real diff = abs(phi_dense[i] - cbs(x));
-            if (diff > cbs_sup) {
-              cbs_sup = diff;
-            }
-          }
-          
-          m.insert({cbs_sup, "cubic_b_spline"});
-        }
-
-
-        // Whittaker-Shannon interpolation has linear complexity; test over all points and it's quadratic.
-        // I ran this a couple times and found it's not competitive; so comment out for now.
-        /*{
-            auto phi_copy = phi;
-            auto ws = boost::math::interpolators::whittaker_shannon(std::move(phi_copy), Real(0), dx);
-            Real sup = 0;
-            for (size_t i = 0; i < phi_dense.size(); ++i) {
-              Real x = i*dx_dense;
-              using std::abs;
-              Real diff = abs(phi_dense[i] - ws(x));
-              if (diff > sup) {
-                sup = diff;
-              }
-            }
-          
-            m.insert({sup, "whittaker_shannon"});
-        }*/
-
-        {
-          auto qbs = boost::math::interpolators::cardinal_quintic_b_spline(phi.data(), phi.size(), Real(0), dx, {0,0}, {0,0});
-          Real sup = 0;
-          for (size_t i = 0; i < phi_dense.size(); ++i) {
-            Real x = i*dx_dense;
-            Real diff = abs(phi_dense[i] - qbs(x));
-            if (diff > sup) {
-              sup = diff;
-            }
-          }
-          m.insert({sup, "quintic_b_spline"});
-        }
-
-        {
-          auto phi_copy = phi;
-          auto x_copy = x;
-          auto phi_prime_copy = phi_prime;
-          auto ch = boost::math::interpolators::cubic_hermite(std::move(x_copy), std::move(phi_copy), std::move(phi_prime_copy));
-          Real sup = 0;
-          for (size_t i = 0; i < phi_dense.size(); ++i) {
-            Real x = i*dx_dense;
-            Real diff = abs(phi_dense[i] - ch(x));
-            if (diff > sup) {
-              sup = diff;
-            }
-          }
-          m.insert({sup, "cubic_hermite_spline"});
-        }
-
-        {
-          auto phi_copy = phi;
-          auto x_copy = x;
-          auto phi_prime_copy = phi_prime;
-          auto pc = boost::math::interpolators::pchip(std::move(x_copy), std::move(phi_copy));
-          Real sup = 0;
-          for (size_t i = 0; i < phi_dense.size(); ++i) {
-            Real x = i*dx_dense;
-            Real diff = abs(phi_dense[i] - pc(x));
-            if (diff > sup) {
-              sup = diff;
-            }
-          }
-          m.insert({sup, "pchip"});
-        }
-
-        {
-          auto phi_copy = phi;
-          auto x_copy = x;
-          auto pc = boost::math::interpolators::makima(std::move(x_copy), std::move(phi_copy));
-          Real sup = 0;
-          for (size_t i = 0; i < phi_dense.size(); ++i) {
-            Real x = i*dx_dense;
-            Real diff = abs(phi_dense[i] - pc(x));
-            if (diff > sup) {
-              sup = diff;
-            }
-          }
-          m.insert({sup, "makima"});
-        }
-
-        // Again, linear complexity of evaluation => quadratic complexity of exhaustive checking.
-        /*{
-            auto trig = boost::math::interpolators::cardinal_trigonometric(phi, Real(0), dx);
-            Real sup = 0;
-            for (size_t i = 0; i < phi_dense.size(); ++i) {
-              Real x = i*dx_dense;
-              using std::abs;
-              Real diff = abs(phi_dense[i] - trig(x));
-              if (diff > sup) {
-                sup = diff;
-              }
-            }
-            m.insert({sup, "trig"});
-        }*/
-
-        {
-            auto fotaylor = [&phi, &phi_prime, &r](Real x)->Real {
-                if (x <= 0 || x >= 2*p-1) {
-                    return 0;
-                }
-                using std::floor;
-
-                Real y = (1<<r)*x;
-                Real k = floor(y);
-
-                size_t kk = static_cast<size_t>(k);
-                if (y - k < k + 1 - y)
-                {
-                    Real eps = (y-k)/(1<<r);
-                    return phi[kk] + eps*phi_prime[kk];
-                }
-                else {
-                    Real eps = (y-k-1)/(1<<r);
-                    return phi[kk+1] + eps*phi_prime[kk+1];
-                }
-
-            };
-            Real sup = 0;
-            for (size_t i = 0; i < phi_dense.size(); ++i) {
-              Real x = i*dx_dense;
-              Real diff = abs(phi_dense[i] - fotaylor(x));
-              if (diff > sup) {
-                sup = diff;
-              }
-            }
-        
-          m.insert({sup, "First-order Taylor"});
-        }
-
-        if constexpr (p > 2) {
-            auto phi_dbl_prime = boost::math::detail::dyadic_grid<Real, p, 2>(r);
-
-            {
-                auto phi_copy = phi;
-                auto x_copy = x;
-                auto phi_prime_copy = phi_prime;
-                auto phi_dbl_prime_copy = phi_dbl_prime;
-                auto qh = boost::math::interpolators::quintic_hermite(std::move(x_copy), std::move(phi_copy), std::move(phi_prime_copy), std::move(phi_dbl_prime_copy));
-                Real sup = 0;
-                for (size_t i = 0; i < phi_dense.size(); ++i) {
-                  Real x = i*dx_dense;
-                  Real diff = abs(phi_dense[i] - qh(x));
-                  if (diff > sup) {
-                    sup = diff;
-                  }
-                }
-                m.insert({sup, "quintic_hermite_spline"});
-            }
-
-            {
-                auto sotaylor = [&phi, &phi_prime, &phi_dbl_prime, &r](Real x)->Real {
-                      if (x <= 0 || x >= 2*p-1) {
-                          return 0;
-                      }
-                      using std::floor;
-
-                      Real y = (1<<r)*x;
-                      Real k = floor(y);
-
-                      size_t kk = static_cast<size_t>(k);
-                      if (y - k < k + 1 - y)
-                      {
-                          Real eps = (y-k)/(1<<r);
-                          return phi[kk] + eps*phi_prime[kk] + eps*eps*phi_dbl_prime[kk]/2;
-                      }
-                      else {
-                          Real eps = (y-k-1)/(1<<r);
-                          return phi[kk+1] + eps*phi_prime[kk+1] + eps*eps*phi_dbl_prime[kk+1]/2;
-                      }
-                };
-                Real sup = 0;
-                for (size_t i = 0; i < phi_dense.size(); ++i) {
-                  Real x = i*dx_dense;
-                  Real diff = abs(phi_dense[i] - sotaylor(x));
-                  if (diff > sup) {
-                    sup = diff;
-                  }
-                }
-            
-              m.insert({sup, "Second-order Taylor"});
-            }
-        }
-
-        if constexpr (p > 3) {
-            auto phi_dbl_prime = boost::math::detail::dyadic_grid<Real, p, 2>(r);
-            auto phi_triple_prime = boost::math::detail::dyadic_grid<Real, p, 3>(r);
-
-            {
-                auto totaylor = [&phi, &phi_prime, &phi_dbl_prime, &phi_triple_prime, &r](Real x)->Real {
-                      if (x <= 0 || x >= 2*p-1) {
-                          return 0;
-                      }
-                      using std::floor;
-
-                      Real y = (1<<r)*x;
-                      Real k = floor(y);
-
-                      size_t kk = static_cast<size_t>(k);
-                      if (y - k < k + 1 - y)
-                      {
-                          Real eps = (y-k)/(1<<r);
-                          return phi[kk] + eps*phi_prime[kk] + eps*eps*phi_dbl_prime[kk]/2 + eps*eps*eps*phi_triple_prime[kk]/6;
-                      }
-                      else {
-                          Real eps = (y-k-1)/(1<<r);
-                          return phi[kk+1] + eps*phi_prime[kk+1] + eps*eps*phi_dbl_prime[kk+1]/2 + eps*eps*eps*phi_triple_prime[kk]/6;
-                      }
-                };
-                Real sup = 0;
-                for (size_t i = 0; i < phi_dense.size(); ++i) {
-                  Real x = i*dx_dense;
-                  Real diff = abs(phi_dense[i] - totaylor(x));
-                  if (diff > sup) {
-                    sup = diff;
-                  }
-                }
-            
-              m.insert({sup, "Third-order Taylor"});
-            }
-
-            {
-                auto phi_copy = phi;
-                auto x_copy = x;
-                auto phi_prime_copy = phi_prime;
-                auto phi_dbl_prime_copy = phi_dbl_prime;
-                auto phi_triple_prime_copy = phi_triple_prime;
-                auto sh = boost::math::interpolators::septic_hermite(std::move(x_copy), std::move(phi_copy), std::move(phi_prime_copy), std::move(phi_dbl_prime_copy), std::move(phi_triple_prime_copy));
-                Real sup = 0;
-                for (size_t i = 0; i < phi_dense.size(); ++i) {
-                  Real x = i*dx_dense;
-                  Real diff = abs(phi_dense[i] - sh(x));
-                  if (diff > sup) {
-                    sup = diff;
-                  }
-                }
-                m.insert({sup, "septic_hermite_spline"});
-            }
-
-
-        }
-        std::string best = "none";
-        Real best_sup = 1000000000;
-        std::cout << std::setprecision(std::numeric_limits<Real>::digits10 + 3) << std::fixed;
-        for (auto & e : m) {
-          
-          std::cout << "\t" << e.first << " is error of " << e.second << "\n";
-          if (e.first < best_sup) {
-            best = e.second;
-            best_sup = e.first;
-          }
-        }
-        std::cout << "\tThe best method for p = " << p << " is the " << best << "\n";
-    }
-}
-
-int main() {
-
-    //choose_refinement<float, 5>();
-    //choose_refinement<double, 15>();
-    // Says linear interpolation is the best:
-    /*find_best_interpolator<long double, 2>();
-
-    // Says linear interpolation is the best:
-    find_best_interpolator<long double, 3>();
-
-    // Says cubic_hermite_spline is best:
-    find_best_interpolator<long double, 4>();
-
-    // Says cubic_hermite_spline is best:
-    find_best_interpolator<long double, 5>();
-
-    // Says quintic_hermite_spline is best:
-    find_best_interpolator<long double, 6>();
-
-    // Says quintic_hermite_spline is best:
-    find_best_interpolator<long double, 7>();
-
-    // Says quintic_hermite_spline is best:
-    find_best_interpolator<long double, 8>();*/
-    // Says quintic_hermite_spline is best:
-    find_best_interpolator<long double, 9>();
-    // Says septic_hermite_spline is best:
-    find_best_interpolator<long double, 10>();
-    /*
-    // Says septic_hermite_spline is best:
-    find_best_interpolator<long double, 11>();
-    // Says septic_hermite_spline is best:
-    find_best_interpolator<long double, 12>();
-    // Says septic_hermite_spline is best:
-    find_best_interpolator<long double, 13>();
-    // Says septic_hermite_spline is best:
-    find_best_interpolator<long double, 14>();*/
-
-    // Says septic_hermite_spline is best:
-    find_best_interpolator<float128, 15>();
-}
diff --git a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
index 1df68f69e..8b7fea73f 100644
--- a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
@@ -263,7 +263,16 @@ public:
     }
 
     inline Real unchecked_prime(Real x) const {
-        return std::numeric_limits<Real>::quiet_NaN();
+        //TODO: Get the high accuracy approximation by differentiating the interpolant!
+        using std::floor;
+        auto i = static_cast<decltype(y_.size())>(floor((x-x0_)/dx_));
+        Real xi = x0_ + i*dx_;
+        Real t = (x - xi)/dx_;
+
+        // Velocity:
+        Real v0 = dydx_[i];
+        Real v1 = dydx_[i+1];
+        return (v0+v1)/2;
     }
 
 private:
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index 43037e9f3..3d5fc7d55 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -13,7 +13,7 @@
 #include <thread>
 #include <future>
 #include <iostream>
-#if BOOST_HAS_FLOAT128
+#ifdef BOOST_HAS_FLOAT128
 #include <boost/multiprecision/float128.hpp>
 #endif
 #include <boost/math/constants/constants.hpp>
@@ -159,7 +159,7 @@ public:
     daubechies_scaling(int grid_refinements = -1)
     {
         static_assert(p <= 15, "Scaling functions only implements up to p = 15");
-        #if BOOST_HAS_FLOAT128
+        #ifdef BOOST_HAS_FLOAT128
         using boost::multiprecision::float128;
         #endif
         if (grid_refinements < 0)

From 1b8a746280dd2ccffeeacf210498b71b50a0fb69 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Sat, 15 Feb 2020 08:37:56 -0500
Subject: [PATCH 024/104] Remove spaces in tokens to make the file easier to
 parse [CI SKIP]

---
 .../find_best_daubechies_interpolator.cpp                   | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp b/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
index 09292ebca..3fa311368 100644
--- a/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
+++ b/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
@@ -146,15 +146,15 @@ void find_best_interpolator()
     Real dx_dense = (2*p-1)/static_cast<Real>(phi_dense.size()-1);
     fs << std::setprecision(std::numeric_limits<Real>::digits10 + 3);
     fs << std::fixed;
-    fs << "r, matched_holder, linear, quadratic B-spline, cubic B-spline, quintic B-spline, cubic Hermite, pchip, makima, fo_taylor";
+    fs << "r, matched_holder, linear, quadratic_b_spline, cubic_b_spline, quintic_b_spline, cubic_hermite, pchip, makima, fo_taylor";
     if (p==2) {
       fs << "\n";
     }
     else {
-      fs << ", quintic hermite, second-order taylor";
+      fs << ", quintic_hermite, second_order_taylor";
       if (p > 3)
       {
-        fs << ", third order taylor, septic_hermite\n";
+        fs << ", third_order_taylor, septic_hermite\n";
       }
       else {
         fs << "\n";

From 8de87a76d17fb23ba5f3ec903bd996016eec9ff1 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Sat, 15 Feb 2020 08:51:11 -0500
Subject: [PATCH 025/104] Sensible cleanup [CI SKIP]

---
 .../find_best_daubechies_interpolator.cpp     | 29 ++++++++++---------
 1 file changed, 16 insertions(+), 13 deletions(-)

diff --git a/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp b/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
index 3fa311368..e6e87f89a 100644
--- a/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
+++ b/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
@@ -134,7 +134,7 @@ void find_best_interpolator()
     std::ofstream fs{filename};
     static_assert(sizeof(PreciseReal) >= sizeof(Real), "sizeof(PreciseReal) >= sizeof(Real) is required.");
     using std::abs;
-    int rmax = 21;
+    int rmax = 20;
     auto phi_dense_precise = boost::math::detail::dyadic_grid<PreciseReal, p, 0>(rmax);
     std::vector<Real> phi_dense(phi_dense_precise.size());
     for (size_t i = 0; i < phi_dense.size(); ++i)
@@ -147,18 +147,21 @@ void find_best_interpolator()
     fs << std::setprecision(std::numeric_limits<Real>::digits10 + 3);
     fs << std::fixed;
     fs << "r, matched_holder, linear, quadratic_b_spline, cubic_b_spline, quintic_b_spline, cubic_hermite, pchip, makima, fo_taylor";
-    if (p==2) {
-      fs << "\n";
-    }
-    else {
-      fs << ", quintic_hermite, second_order_taylor";
-      if (p > 3)
-      {
-        fs << ", third_order_taylor, septic_hermite\n";
-      }
-      else {
+    if (p==2)
+    {
         fs << "\n";
-      }
+    }
+    else
+    {
+        fs << ", quintic_hermite, second_order_taylor";
+        if (p > 3)
+        {
+            fs << ", third_order_taylor, septic_hermite\n";
+        }
+        else
+        {
+            fs << "\n";
+        }
     }
     for (int r = 2; r < rmax-1; ++r)
     {
@@ -180,7 +183,7 @@ void find_best_interpolator()
             auto phi_prime_copy = phi_prime;
             auto mh = boost::math::detail::matched_holder(std::move(phi_copy), std::move(phi_prime_copy), r);
             Real sup = 0;
-            // call to matched_holder is unchecked:
+            // call to matched_holder is unchecked, so only go to phi_dense.size() -1.
             for (size_t i = 0; i < phi_dense.size() - 1; ++i)
             {
                 Real x = i*dx_dense;

From d2938c89e7802a9255fb5c9d0c7cecfa8edb1161 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Sat, 15 Feb 2020 09:21:21 -0500
Subject: [PATCH 026/104] Controversially commit Daubechies plots [CI SKIP]

---
 .../daubechies_wavelets/daubechies_plots.cpp  | 164 ++++++++++++++++++
 1 file changed, 164 insertions(+)
 create mode 100644 example/daubechies_wavelets/daubechies_plots.cpp

diff --git a/example/daubechies_wavelets/daubechies_plots.cpp b/example/daubechies_wavelets/daubechies_plots.cpp
new file mode 100644
index 000000000..4250dafa3
--- /dev/null
+++ b/example/daubechies_wavelets/daubechies_plots.cpp
@@ -0,0 +1,164 @@
+/*
+ * Copyright Nick Thompson, 2020
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+#include <iostream>
+#include <boost/core/demangle.hpp>
+#include <boost/multiprecision/float128.hpp>
+#include <boost/math/special_functions/daubechies_scaling.hpp>
+#include <quicksvg/graph_fn.hpp>
+#include <quicksvg/ulp_plot.hpp>
+
+
+using boost::multiprecision::float128;
+constexpr const int GRAPH_WIDTH = 700;
+
+template<typename Real, int p>
+void plot_phi(int grid_refinements = -1)
+{
+    auto phi = boost::math::daubechies_scaling<Real, p>();
+    if (grid_refinements >= 0)
+    {
+        phi = boost::math::daubechies_scaling<Real, p>(grid_refinements);
+    }
+    Real a = 0;
+    Real b = phi.support().second;
+    std::string title = "Daubechies " + std::to_string(p) + " scaling function";
+    std::string filename = "daubechies_" + std::to_string(p) + "_scaling.svg";
+    int samples = 1024;
+    quicksvg::graph_fn daub(a, b, title, filename, samples, GRAPH_WIDTH);
+    daub.set_stroke_width(1);
+    daub.add_fn(phi);
+    daub.write_all();
+}
+
+template<typename Real, int p>
+void plot_convergence()
+{
+    auto phi0 = boost::math::daubechies_scaling<Real, p>(0);
+    Real a = 0;
+    Real b = phi0.support().second;
+    std::string title = "Daubechies " + std::to_string(p) + " scaling at 0 (green), 1 (orange), 2 (red), and 24 (blue) grid refinements";
+    std::string filename = "daubechies_" + std::to_string(p) + "_scaling_convergence.svg";
+
+    quicksvg::graph_fn daub(a, b, title, filename, 1024, GRAPH_WIDTH);
+    daub.set_stroke_width(1);
+
+    daub.add_fn(phi0, "green");
+    auto phi1 = boost::math::daubechies_scaling<Real, p>(1);
+    daub.add_fn(phi1, "orange");
+    auto phi2 = boost::math::daubechies_scaling<Real, p>(2);
+    daub.add_fn(phi2, "red");
+
+    auto phi21 = boost::math::daubechies_scaling<Real, p>(21);
+    daub.add_fn(phi21);
+    daub.write_all();
+}
+
+template<typename Real, int p>
+void plot_condition_number()
+{
+    using std::abs;
+    using std::log;
+    static_assert(p >= 4, "p = 2,3 are not differentiable, so condition numbers cannot be effectively evaluated.");
+    auto phi = boost::math::daubechies_scaling<Real, p>();
+    Real a = 1000*std::numeric_limits<Real>::epsilon();
+    Real b = phi.support().second - 1000*std::numeric_limits<Real>::epsilon();
+    std::string title = "log10 of condition number of function evaluation for Daubechies " + std::to_string(p) + " scaling function.";
+    std::string filename = "daubechies_" + std::to_string(p) + "_scaling_condition_number.svg";
+
+
+    quicksvg::graph_fn daub(a, b, title, filename, 2048, GRAPH_WIDTH);
+    daub.set_stroke_width(1);
+
+    auto cond = [&phi](Real x)
+    {
+        Real y = phi(x);
+        Real dydx = phi.prime(x);
+        Real z = abs(x*dydx/y);
+        using std::isnan;
+        if (z==0)
+        {
+            return Real(-1);
+        }
+        if (isnan(z))
+        {
+            // Graphing libraries don't like nan's:
+            return Real(1); 
+        }
+        return log10(z);
+    };
+    daub.add_fn(cond);
+    daub.write_all();
+}
+
+template<typename CoarseReal, typename PreciseReal, int p, class PhiPrecise>
+void do_ulp(int coarse_refinements, PhiPrecise phi_precise)
+{
+    auto phi_coarse = boost::math::daubechies_scaling<CoarseReal, p>(coarse_refinements);
+
+    std::string title = std::to_string(p) + " vanishing moment ULP plot at " + std::to_string(coarse_refinements) + " refinements and " + boost::core::demangle(typeid(CoarseReal).name()) + " precision";
+    std::string filename = "daubechies_" + std::to_string(p) + "_" + boost::core::demangle(typeid(CoarseReal).name()) + "_" + std::to_string(coarse_refinements) + "_refinements.svg";
+    int samples = 20000;
+    int clip = 20;
+    quicksvg::ulp_plot<decltype(phi_coarse), CoarseReal, decltype(phi_precise), PreciseReal>(phi_coarse, phi_precise, CoarseReal(0), phi_coarse.support().second, title, filename, samples, GRAPH_WIDTH, clip);
+}
+
+
+int main()
+{
+    plot_convergence<double, 2>();
+    plot_convergence<double, 3>();
+    plot_convergence<double, 4>();
+    plot_convergence<double, 5>();
+    plot_convergence<double, 6>();
+    plot_convergence<double, 7>();
+    plot_convergence<double, 8>();
+    plot_convergence<double, 9>();
+    plot_convergence<double, 10>();
+    plot_convergence<double, 11>();
+    plot_convergence<double, 12>();
+    plot_convergence<double, 13>();
+    plot_convergence<double, 14>();
+    plot_convergence<double, 15>();
+
+    plot_phi<double, 2>();
+    plot_phi<double, 3>();
+    plot_phi<double, 4>();
+    plot_phi<double, 5>();
+    plot_phi<double, 6>();
+    plot_phi<double, 7>();
+    plot_phi<double, 8>();
+    plot_phi<double, 9>();
+    plot_phi<double, 10>();
+    plot_phi<double, 11>();
+    plot_phi<double, 12>();
+    plot_phi<double, 13>();
+    plot_phi<double, 14>();
+    plot_phi<double, 15>();
+    plot_condition_number<long double, 4>();
+    plot_condition_number<long double, 5>();
+    plot_condition_number<long double, 6>();
+    plot_condition_number<long double, 7>();
+    plot_condition_number<long double, 8>();
+    plot_condition_number<long double, 9>();
+    plot_condition_number<long double, 10>();
+    plot_condition_number<long double, 11>();
+    plot_condition_number<long double, 12>();
+    plot_condition_number<long double, 13>();
+
+    using PreciseReal = float128;
+    using CoarseReal = long double;
+    int precise_refinements = 21;
+    constexpr const int p = 9;
+    std::cout << "Computing precise scaling function in " << boost::core::demangle(typeid(PreciseReal).name()) << " precision.\n";
+    auto phi_precise = boost::math::daubechies_scaling<PreciseReal, p>(precise_refinements);
+    std::cout << "Beginning comparison with functions computed in " << boost::core::demangle(typeid(CoarseReal).name()) << " precision.\n";
+    for (int i = 7; i <= precise_refinements-1; ++i)
+    {
+        std::cout << "\tCoarse refinement " << i << "\n";
+        do_ulp<CoarseReal, PreciseReal, p>(i, phi_precise);
+    }
+}

From 3338c0c6e6a4b10e4be8c2ac495e0237c32b8806 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Sun, 16 Feb 2020 09:46:58 -0500
Subject: [PATCH 027/104] Add in benchmarks, remove some commented out code
 that is duplicated in
 example/daubechies_wavelets/find_best_daubechies_interpolator.cpp [CI SKIP]

---
 example/daubechies_wavelets/bench.cpp         | 340 ++++++++++++++++++
 .../special_functions/daubechies_scaling.hpp  | 157 +-------
 2 files changed, 346 insertions(+), 151 deletions(-)
 create mode 100644 example/daubechies_wavelets/bench.cpp

diff --git a/example/daubechies_wavelets/bench.cpp b/example/daubechies_wavelets/bench.cpp
new file mode 100644
index 000000000..fcda6ff28
--- /dev/null
+++ b/example/daubechies_wavelets/bench.cpp
@@ -0,0 +1,340 @@
+/*
+ * Copyright Nick Thompson, 2020
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include <cmath>
+#include <random>
+#include <benchmark/benchmark.h>
+#include <boost/random/uniform_real_distribution.hpp>
+#include <boost/math/special_functions/daubechies_scaling.hpp>
+#include <boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp>
+#include <boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp>
+#include <boost/math/interpolators/detail/septic_hermite_detail.hpp>
+
+static void UnitStep(benchmark::internal::Benchmark* b)
+{
+    for (int i = 7; i <= 25; ++i)
+    {
+        b->Args({i});
+    }
+}
+
+double exponential(long long unsigned int j)
+{
+    return std::pow(2, j);
+}
+
+
+template<typename Real, int p>
+void DyadicGrid(benchmark::State & state)
+{
+    int j = state.range(0);
+    size_t s = 0;
+    for (auto _ : state)
+    {
+        auto v = boost::math::detail::dyadic_grid<Real, 4, 0>(j);
+        benchmark::DoNotOptimize(v[0]);
+        s = v.size();
+    }
+
+    state.counters["RAM"] = s*sizeof(Real);
+    state.SetComplexityN(state.range(0));
+}
+
+BENCHMARK_TEMPLATE(DyadicGrid, double, 4)->Apply(UnitStep)->Unit(benchmark::kMillisecond)->Complexity(exponential);
+BENCHMARK_TEMPLATE(DyadicGrid, double, 8)->Apply(UnitStep)->Unit(benchmark::kMillisecond)->Complexity(exponential);
+BENCHMARK_TEMPLATE(DyadicGrid, double, 11)->Apply(UnitStep)->Unit(benchmark::kMillisecond)->Complexity(exponential);
+
+
+template<typename Real, int p>
+void ScalingEvaluation(benchmark::State & state)
+{
+    auto phi = boost::math::daubechies_scaling<Real, p>();    
+    Real x = 0;
+    for (auto _ : state)
+    {
+        benchmark::DoNotOptimize(phi(x));
+        x += std::numeric_limits<Real>::epsilon();
+    }
+}
+
+
+BENCHMARK_TEMPLATE(ScalingEvaluation, double, 2);
+BENCHMARK_TEMPLATE(ScalingEvaluation, double, 3);
+BENCHMARK_TEMPLATE(ScalingEvaluation, double, 4);
+BENCHMARK_TEMPLATE(ScalingEvaluation, double, 5);
+BENCHMARK_TEMPLATE(ScalingEvaluation, double, 6);
+BENCHMARK_TEMPLATE(ScalingEvaluation, double, 7);
+BENCHMARK_TEMPLATE(ScalingEvaluation, double, 8);
+BENCHMARK_TEMPLATE(ScalingEvaluation, double, 9);
+BENCHMARK_TEMPLATE(ScalingEvaluation, double, 10);
+BENCHMARK_TEMPLATE(ScalingEvaluation, double, 11);
+
+
+template<typename Real, int p>
+void ScalingConstructor(benchmark::State & state)
+{
+    for (auto _ : state)
+    {
+        benchmark::DoNotOptimize(boost::math::daubechies_scaling<Real, p>());
+    }
+}
+
+BENCHMARK_TEMPLATE(ScalingConstructor, float, 2)->Unit(benchmark::kMillisecond);
+BENCHMARK_TEMPLATE(ScalingConstructor, double, 2)->Unit(benchmark::kMillisecond);
+BENCHMARK_TEMPLATE(ScalingConstructor, long double, 2)->Unit(benchmark::kMillisecond);
+
+BENCHMARK_TEMPLATE(ScalingConstructor, float, 3)->Unit(benchmark::kMillisecond);
+BENCHMARK_TEMPLATE(ScalingConstructor, double, 3)->Unit(benchmark::kMillisecond);
+BENCHMARK_TEMPLATE(ScalingConstructor, long double, 3)->Unit(benchmark::kMillisecond);
+
+BENCHMARK_TEMPLATE(ScalingConstructor, float, 4)->Unit(benchmark::kMillisecond);
+BENCHMARK_TEMPLATE(ScalingConstructor, double, 4)->Unit(benchmark::kMillisecond);
+BENCHMARK_TEMPLATE(ScalingConstructor, long double, 4)->Unit(benchmark::kMillisecond);
+
+BENCHMARK_TEMPLATE(ScalingConstructor, float, 5)->Unit(benchmark::kMillisecond);
+BENCHMARK_TEMPLATE(ScalingConstructor, double, 5)->Unit(benchmark::kMillisecond);
+BENCHMARK_TEMPLATE(ScalingConstructor, long double, 5)->Unit(benchmark::kMillisecond);
+
+BENCHMARK_TEMPLATE(ScalingConstructor, float, 11)->Unit(benchmark::kMillisecond);
+BENCHMARK_TEMPLATE(ScalingConstructor, double, 11)->Unit(benchmark::kMillisecond);
+BENCHMARK_TEMPLATE(ScalingConstructor, long double, 11)->Unit(benchmark::kMillisecond);
+
+template<typename Real>
+void CardinalCubicHermite(benchmark::State & state)
+{
+    using boost::math::interpolators::detail::cardinal_cubic_hermite_detail;
+    auto n = state.range(0);
+    std::vector<Real> y(n);
+    std::vector<Real> dydx(n);
+    std::random_device rd;
+    boost::random::uniform_real_distribution<Real> dis(Real(0), Real(1));
+    for (size_t i = 0; i < y.size(); ++i)
+    {
+        y[i] = dis(rd);
+        dydx[i] = dis(rd);
+    }
+
+    Real dx = Real(1)/Real(8);
+    Real x0 = 0;
+    Real xf = x0 + (y.size()-1)*dx;
+
+    auto qh = cardinal_cubic_hermite_detail(std::move(y), std::move(dydx), x0, dx);
+    Real x = 0;
+    for (auto _ : state)
+    {
+        benchmark::DoNotOptimize(qh.unchecked_evaluation(x));
+        x += xf/128;
+        if (x >= xf)
+        {
+            x = x0;
+        }
+    }
+}
+
+BENCHMARK_TEMPLATE(CardinalCubicHermite, double)->RangeMultiplier(2)->Range(1<<8, 1<<22)->Complexity();
+
+template<typename Real>
+void CardinalCubicHermiteAOS(benchmark::State & state)
+{
+    auto n = state.range(0);
+    std::vector<std::array<Real, 2>> dat(n);
+    std::random_device rd;
+    boost::random::uniform_real_distribution<Real> dis(Real(0), Real(1));
+    for (size_t i = 0; i < dat.size(); ++i)
+    {
+        dat[i][0] = dis(rd);
+        dat[i][1] = dis(rd);
+    }
+
+    using boost::math::interpolators::detail::cardinal_cubic_hermite_detail_aos;
+    Real dx = Real(1)/Real(8);
+    Real x0 = 0;
+    Real xf = x0 + (dat.size()-1)*dx;
+    auto qh = cardinal_cubic_hermite_detail_aos(std::move(dat), x0, dx);
+    Real x = 0;
+    for (auto _ : state)
+    {
+        benchmark::DoNotOptimize(qh.unchecked_evaluation(x));
+        x += xf/128;
+        if (x >= xf)
+        {
+            x = x0;
+        }
+    }
+}
+
+BENCHMARK_TEMPLATE(CardinalCubicHermiteAOS, double)->RangeMultiplier(2)->Range(1<<8, 1<<14)->Complexity();
+
+template<class Real>
+void SineEvaluation(benchmark::State& state)
+{
+    std::default_random_engine gen;
+    std::uniform_real_distribution<Real> x_dis(0, 3.14159);
+
+    Real x = x_dis(gen);
+    for (auto _ : state)
+    {
+        benchmark::DoNotOptimize(std::sin(x));
+        x += std::numeric_limits<Real>::epsilon();
+    }
+}
+
+BENCHMARK_TEMPLATE(SineEvaluation, float);
+BENCHMARK_TEMPLATE(SineEvaluation, double);
+BENCHMARK_TEMPLATE(SineEvaluation, long double);
+
+template<class Real>
+void ExpEvaluation(benchmark::State& state)
+{
+    std::default_random_engine gen;
+    std::uniform_real_distribution<Real> x_dis(0, 3.14159);
+
+    Real x = x_dis(gen);
+    for (auto _ : state)
+    {
+        benchmark::DoNotOptimize(std::exp(x));
+        x += std::numeric_limits<Real>::epsilon();
+    }
+}
+
+BENCHMARK_TEMPLATE(ExpEvaluation, float);
+BENCHMARK_TEMPLATE(ExpEvaluation, double);
+BENCHMARK_TEMPLATE(ExpEvaluation, long double);
+
+template<class Real>
+void PowEvaluation(benchmark::State& state)
+{
+    std::default_random_engine gen;
+    std::uniform_real_distribution<Real> x_dis(0, 3.14159);
+
+    Real x = x_dis(gen);
+    for (auto _ : state)
+    {
+        benchmark::DoNotOptimize(std::pow(x, x+1));
+        x += std::numeric_limits<Real>::epsilon();
+    }
+}
+
+BENCHMARK_TEMPLATE(PowEvaluation, float);
+BENCHMARK_TEMPLATE(PowEvaluation, double);
+BENCHMARK_TEMPLATE(PowEvaluation, long double);
+
+
+template<typename Real>
+void CardinalQuinticHermite(benchmark::State & state)
+{
+    using boost::math::interpolators::detail::cardinal_quintic_hermite_detail;
+    auto n = state.range(0);
+    std::vector<Real> y(n);
+    std::vector<Real> dydx(n);
+    std::vector<Real> d2ydx2(n);
+    std::random_device rd;
+    boost::random::uniform_real_distribution<Real> dis(Real(0), Real(1));
+    for (size_t i = 0; i < y.size(); ++i)
+    {
+        y[i] = dis(rd);
+        dydx[i] = dis(rd);
+        d2ydx2[i] = dis(rd);
+    }
+
+    Real dx = Real(1)/Real(8);
+    Real x0 = 0;
+    Real xf = x0 + (y.size()-1)*dx;
+
+    auto qh = cardinal_quintic_hermite_detail(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx);
+    Real x = 0;
+    for (auto _ : state)
+    {
+        benchmark::DoNotOptimize(qh.unchecked_evaluation(x));
+        x += xf/128;
+        if (x >= xf)
+        {
+            x = x0;
+        }
+    }
+}
+
+BENCHMARK_TEMPLATE(CardinalQuinticHermite, float)->RangeMultiplier(2)->Range(1<<8, 1<<22)->Complexity();
+BENCHMARK_TEMPLATE(CardinalQuinticHermite, double)->RangeMultiplier(2)->Range(1<<8, 1<<22)->Complexity();
+BENCHMARK_TEMPLATE(CardinalQuinticHermite, long double)->RangeMultiplier(2)->Range(1<<8, 1<<22)->Complexity();
+
+
+template<typename Real>
+void CardinalQuinticHermiteAOS(benchmark::State & state)
+{
+    auto n = state.range(0);
+    std::vector<std::array<Real, 3>> dat(n);
+    std::random_device rd;
+    boost::random::uniform_real_distribution<Real> dis(Real(0), Real(1));
+    for (size_t i = 0; i < dat.size(); ++i)
+    {
+        dat[i][0] = dis(rd);
+        dat[i][1] = dis(rd);
+        dat[i][2] = dis(rd);
+    }
+
+    using boost::math::interpolators::detail::cardinal_quintic_hermite_detail_aos;
+    Real dx = Real(1)/Real(8);
+    Real x0 = 0;
+    Real xf = x0 + (dat.size()-1)*dx;
+    auto qh = cardinal_quintic_hermite_detail_aos(std::move(dat), x0, dx);
+    Real x = 0;
+    for (auto _ : state) {
+        benchmark::DoNotOptimize(qh.unchecked_evaluation(x));
+        x += xf/128;
+        if (x >= xf)
+        {
+            x = x0;
+        }
+    }
+}
+
+BENCHMARK_TEMPLATE(CardinalQuinticHermiteAOS, float)->RangeMultiplier(2)->Range(1<<8, 1<<22)->Complexity();
+BENCHMARK_TEMPLATE(CardinalQuinticHermiteAOS, double)->RangeMultiplier(2)->Range(1<<8, 1<<22)->Complexity();
+BENCHMARK_TEMPLATE(CardinalQuinticHermiteAOS, long double)->RangeMultiplier(2)->Range(1<<8, 1<<22)->Complexity();
+
+
+template<typename Real>
+void CardinalSepticHermite(benchmark::State & state)
+{
+    using boost::math::interpolators::detail::cardinal_septic_hermite_detail;
+    auto n = state.range(0);
+    std::vector<Real> y(n);
+    std::vector<Real> dydx(n);
+    std::vector<Real> d2ydx2(n);
+    std::vector<Real> d3ydx3(n);
+    std::random_device rd;
+    boost::random::uniform_real_distribution<Real> dis(Real(0), Real(1));
+    for (size_t i = 0; i < y.size(); ++i)
+    {
+        y[i] = dis(rd);
+        dydx[i] = dis(rd);
+        d2ydx2[i] = dis(rd);
+        d3ydx3[i] = dis(rd);
+    }
+
+    Real dx = Real(1)/Real(8);
+    Real x0 = 0;
+    Real xf = x0 + (y.size()-1)*dx;
+
+    auto sh = cardinal_septic_hermite_detail(std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3), x0, dx);
+    Real x = 0;
+    for (auto _ : state)
+    {
+        benchmark::DoNotOptimize(sh.unchecked_evaluation(x));
+        x += xf/128;
+        if (x >= xf)
+        {
+            x = x0;
+        }
+    }
+}
+
+BENCHMARK_TEMPLATE(CardinalSepticHermite, double)->RangeMultiplier(2)->Range(1<<8, 1<<22)->Complexity();
+
+
+BENCHMARK_MAIN();
\ No newline at end of file
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index 3d5fc7d55..8a57a4fa0 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -328,10 +328,10 @@ public:
         {
             return 0;
         }
-        if constexpr (p==2 || p == 3) {
+        if constexpr (p == 2 || p == 3) {
             throw std::domain_error("The 2 and 3-vanishing moment Daubechies scaling function is not continuously differentiable.");
         }
-        if constexpr (p==4 || p ==5) {
+        if constexpr (p == 4 || p == 5) {
             return m_cbh->unchecked_prime(x);
         }
         if constexpr (p >= 6 && p <= 9) {
@@ -342,12 +342,12 @@ public:
         }
     }
 
-    std::pair<int, int> support() const {
+    std::pair<int, int> support() const
+    {
         return {0, 2*p-1};
     }
 
 private:
-    size_t m_levels;
     // Need this for p = 2:
     std::shared_ptr<detail::matched_holder<std::vector<Real>>> m_mh;
     // Need this for p = 3:
@@ -359,36 +359,7 @@ private:
     // Need this for p >= 10:
     std::shared_ptr<interpolators::detail::cardinal_septic_hermite_detail<std::vector<Real>>> m_sh;
 
-    /*Real constant_interpolation(Real x) const {
-        if (x <= 0 || x >= 2*p-1) {
-            return Real(0);
-        }
-        using std::floor;
-        Real y = (1 << m_levels)*x;
-        Real k = floor(y);
-
-        if (y - k < k + 1 - y)
-        {
-            return m_v[static_cast<size_t>(k)];
-        }
-        return m_v[static_cast<size_t>(k)+1];
-    }
-
-    Real linear_interpolation(Real x) const {
-        if (x <= 0 || x >= 2*p-1) {
-            return Real(0);
-        }
-        using std::floor;
-
-        Real y = (1<<m_levels)*x;
-        Real k = floor(y);
-
-        size_t kk = static_cast<size_t>(k);
-
-        Real t = y - k;
-        return (1-t)*m_v[kk] + t*m_v[kk+1];
-    }
-
+    /*
     Real single_crank_linear(Real x) const {
         if (x <= 0 || x >= 2*p-1) {
             return Real(0);
@@ -444,129 +415,13 @@ private:
         return a*t*t + b*t + y0;
     }
 
-
-    Real double_crank_linear(Real x) const {
-        return std::numeric_limits<Real>::quiet_NaN();
-    }
-
-
-    Real first_order_taylor(Real x) const {
-        if (x <= 0 || x >= 2*p-1) {
-            return 0;
-        }
-        using std::floor;
-
-        Real y = (1<<m_levels)*x;
-        Real k = floor(y);
-
-        size_t kk = static_cast<size_t>(k);
-        if (y - k < k + 1 - y)
-        {
-            Real eps = (y-k)/(1<<m_levels);
-            return m_v[kk] + eps*m_v_prime[kk];
-        }
-        else {
-            Real eps = (y-k-1)/(1<<m_levels);
-            return m_v[kk+1] + eps*m_v_prime[kk+1];
-        }
-    }
-
-    Real second_order_taylor(Real x) const {
-        if (x <= 0 || x >= 2*p-1) {
-            return 0;
-        }
-        using std::floor;
-
-        Real y = (1<<m_levels)*x;
-        Real k = floor(y);
-
-        size_t kk = static_cast<size_t>(k);
-        if (y - k < k + 1 - y)
-        {
-            Real eps = (y-k)/(1<<m_levels);
-            return m_v[kk] + eps*m_v_prime[kk] + eps*eps*m_v_dbl_prime[kk]/2;
-        }
-        else {
-            Real eps = (y-k-1)/(1<<m_levels);
-            return m_v[kk+1] + eps*m_v_prime[kk+1] + eps*eps*m_v_dbl_prime[kk+1]/2;
-        }
-    }
-
-    Real third_order_taylor(Real x) const {
-        return std::numeric_limits<Real>::quiet_NaN();
-    }
-
-    Real single_crank_first_order_taylor(Real x) const {
-        return std::numeric_limits<Real>::quiet_NaN();
-    }
-
-    Real double_crank_first_order_taylor(Real x) const {
-        return std::numeric_limits<Real>::quiet_NaN();
-    }
-
-    Real single_crank_second_order_taylor(Real x) const {
-        return std::numeric_limits<Real>::quiet_NaN();
-    }
-
-    Real double_crank_second_order_taylor(Real x) const {
-        return std::numeric_limits<Real>::quiet_NaN();
-    }
-
-    Real single_crank_third_order_taylor(Real x) const {
-        return std::numeric_limits<Real>::quiet_NaN();
-    }
-
-    Real double_crank_third_order_taylor(Real x) const {
-        return std::numeric_limits<Real>::quiet_NaN();
-    }
-
     size_t bytes() const
     {
         size_t s = sizeof(*this);
         s += m_v.size()*sizeof(Real);
         return s;
     }
-
-    size_t size() const {
-        return m_v.size();
-    }
-
-    Real index_to_abscissa(size_t i) {
-        return i/m_inv_spacing;
-    }
-
-    // This is for debugging only; use the .at()
-    Real operator[](size_t i) const {
-        return m_v.at(i);
-    }
-
-    Real prime(size_t i) const {
-        return m_v_prime.at(i);
-    }
-
-    Real spacing() const {
-        return 1/m_inv_spacing;
-    }
-
-    auto begin() const {
-        return m_v.begin();
-    }
-
-    auto end() const {
-        return m_v.end();
-    }
-
-    auto data() const {
-        return m_v.data();
-    }
-
-private:
-    size_t m_levels;
-    Real m_inv_spacing;
-    std::array<Real, 2*p> m_c;
-    std::vector<Real> m_v;
-    std::vector<Real> m_v_prime;
-    std::vector<Real> m_v_dbl_prime;*/
+*/
 };
 
 }

From 2b93ff6b6d5892edd483c418f62079797eab0ad2 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Sun, 16 Feb 2020 11:24:39 -0500
Subject: [PATCH 028/104] Using int64_t rather than long long unsigned int [CI
 SKIP]

---
 example/daubechies_wavelets/bench.cpp | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/example/daubechies_wavelets/bench.cpp b/example/daubechies_wavelets/bench.cpp
index fcda6ff28..8cae7f368 100644
--- a/example/daubechies_wavelets/bench.cpp
+++ b/example/daubechies_wavelets/bench.cpp
@@ -22,7 +22,7 @@ static void UnitStep(benchmark::internal::Benchmark* b)
     }
 }
 
-double exponential(long long unsigned int j)
+double exponential(int64_t j)
 {
     return std::pow(2, j);
 }
@@ -44,9 +44,9 @@ void DyadicGrid(benchmark::State & state)
     state.SetComplexityN(state.range(0));
 }
 
-BENCHMARK_TEMPLATE(DyadicGrid, double, 4)->Apply(UnitStep)->Unit(benchmark::kMillisecond)->Complexity(exponential);
-BENCHMARK_TEMPLATE(DyadicGrid, double, 8)->Apply(UnitStep)->Unit(benchmark::kMillisecond)->Complexity(exponential);
-BENCHMARK_TEMPLATE(DyadicGrid, double, 11)->Apply(UnitStep)->Unit(benchmark::kMillisecond)->Complexity(exponential);
+BENCHMARK_TEMPLATE(DyadicGrid, double, 4)->Apply(UnitStep)->Unit(benchmark::kMillisecond)->Complexity();
+//BENCHMARK_TEMPLATE(DyadicGrid, double, 8)->Apply(UnitStep)->Unit(benchmark::kMillisecond)->Complexity(exponential);
+//BENCHMARK_TEMPLATE(DyadicGrid, double, 11)->Apply(UnitStep)->Unit(benchmark::kMillisecond)->Complexity(exponential);
 
 
 template<typename Real, int p>

From e40b3a19d65ad362a459603706589081cadc5eeb Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Sun, 16 Feb 2020 11:38:42 -0500
Subject: [PATCH 029/104] Fix argument to complexity [CI SKIP]

---
 example/daubechies_wavelets/bench.cpp | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/example/daubechies_wavelets/bench.cpp b/example/daubechies_wavelets/bench.cpp
index 8cae7f368..9e359b15a 100644
--- a/example/daubechies_wavelets/bench.cpp
+++ b/example/daubechies_wavelets/bench.cpp
@@ -22,7 +22,7 @@ static void UnitStep(benchmark::internal::Benchmark* b)
     }
 }
 
-double exponential(int64_t j)
+double exponential(benchmark::IterationCount j)
 {
     return std::pow(2, j);
 }
@@ -44,7 +44,7 @@ void DyadicGrid(benchmark::State & state)
     state.SetComplexityN(state.range(0));
 }
 
-BENCHMARK_TEMPLATE(DyadicGrid, double, 4)->Apply(UnitStep)->Unit(benchmark::kMillisecond)->Complexity();
+BENCHMARK_TEMPLATE(DyadicGrid, double, 4)->Apply(UnitStep)->Unit(benchmark::kMillisecond)->Complexity(exponential);
 //BENCHMARK_TEMPLATE(DyadicGrid, double, 8)->Apply(UnitStep)->Unit(benchmark::kMillisecond)->Complexity(exponential);
 //BENCHMARK_TEMPLATE(DyadicGrid, double, 11)->Apply(UnitStep)->Unit(benchmark::kMillisecond)->Complexity(exponential);
 

From ae436992f7739854921f7bc86294671778280efb Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Sun, 16 Feb 2020 16:57:18 -0500
Subject: [PATCH 030/104] Improve performance of cardinal_cubic_hermite
 evaluation [CI SKIP]

---
 example/daubechies_wavelets/bench.cpp         |   6 +-
 .../detail/cardinal_cubic_hermite_detail.hpp  | 166 +++++++++++-------
 2 files changed, 101 insertions(+), 71 deletions(-)

diff --git a/example/daubechies_wavelets/bench.cpp b/example/daubechies_wavelets/bench.cpp
index 9e359b15a..ab91a6a6f 100644
--- a/example/daubechies_wavelets/bench.cpp
+++ b/example/daubechies_wavelets/bench.cpp
@@ -52,7 +52,7 @@ BENCHMARK_TEMPLATE(DyadicGrid, double, 4)->Apply(UnitStep)->Unit(benchmark::kMil
 template<typename Real, int p>
 void ScalingEvaluation(benchmark::State & state)
 {
-    auto phi = boost::math::daubechies_scaling<Real, p>();    
+    auto phi = boost::math::daubechies_scaling<Real, p>();
     Real x = 0;
     for (auto _ : state)
     {
@@ -135,7 +135,7 @@ void CardinalCubicHermite(benchmark::State & state)
     }
 }
 
-BENCHMARK_TEMPLATE(CardinalCubicHermite, double)->RangeMultiplier(2)->Range(1<<8, 1<<22)->Complexity();
+BENCHMARK_TEMPLATE(CardinalCubicHermite, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity();
 
 template<typename Real>
 void CardinalCubicHermiteAOS(benchmark::State & state)
@@ -167,7 +167,7 @@ void CardinalCubicHermiteAOS(benchmark::State & state)
     }
 }
 
-BENCHMARK_TEMPLATE(CardinalCubicHermiteAOS, double)->RangeMultiplier(2)->Range(1<<8, 1<<14)->Complexity();
+BENCHMARK_TEMPLATE(CardinalCubicHermiteAOS, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity();
 
 template<class Real>
 void SineEvaluation(benchmark::State& state)
diff --git a/include/boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp b/include/boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp
index 3d7f165c8..eb8167edd 100644
--- a/include/boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp
@@ -15,11 +15,11 @@ public:
     using Real = typename RandomAccessContainer::value_type;
 
     cardinal_cubic_hermite_detail(RandomAccessContainer && y, RandomAccessContainer dydx, Real x0, Real dx)
-    : y_{std::move(y)}, dydx_{std::move(dydx)}, x0_{x0}, dx_{dx}
+    : y_{std::move(y)}, dy_{std::move(dydx)}, x0_{x0}, inv_dx_{1/dx}
     {
         using std::abs;
         using std::isnan;
-        if (y_.size() != dydx_.size())
+        if (y_.size() != dy_.size())
         {
             throw std::domain_error("There must be the same number of derivatives as ordinates.");
         }
@@ -31,6 +31,11 @@ public:
         {
             throw std::domain_error("dx > 0 is required.");
         }
+
+        for (auto & dy : dy_)
+        {
+            dy *= dx;
+        }
     }
 
     // Why not implement push_back? It's awkward: If the buffer is circular, x0_ += dx_.
@@ -38,38 +43,9 @@ public:
     // We need a concept for circular_buffer!
 
     inline Real operator()(Real x) const {
-        const Real xf = x0_ + (y_.size()-1)*dx_;
-        if  (x < x0_ || x > xf) {
-            std::ostringstream oss;
-            oss.precision(std::numeric_limits<Real>::digits10+3);
-            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
-                << x0_ << ", " << xf << "]";
-            throw std::domain_error(oss.str());
-        }
-        if (x == xf) {
-            return y_.back();
-        }
-        return this->unchecked_evaluation(x);
-    }
-
-    inline Real unchecked_evaluation(Real x) const
-    {
-        using std::floor;
-        auto i = static_cast<decltype(y_.size())>(floor((x-x0_)/dx_));
-        Real xi = x0_ + i*dx_;
-        Real t = (x - xi)/dx_;
-        Real y0 = y_[i];
-        Real y1 = y_[i+1];
-        Real v0 = dydx_[i];
-        Real v1 = dydx_[i+1];
-
-        return (1-t)*(1-t)*(y0*(1+2*t) + v0*(x-xi))
-              + t*t*(y1*(3-2*t) + dx_*v1*(t-1));
-    }
-
-    inline Real prime(Real x) const {
-        const Real xf = x0_ + (y_.size()-1)*dx_;
-        if  (x < x0_ || x > xf) {
+        const Real xf = x0_ + (y_.size()-1)/inv_dx_;
+        if  (x < x0_ || x > xf)
+        {
             std::ostringstream oss;
             oss.precision(std::numeric_limits<Real>::digits10+3);
             oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
@@ -78,22 +54,58 @@ public:
         }
         if (x == xf)
         {
-            return dydx_.back();
+            return y_.back();
+        }
+        return this->unchecked_evaluation(x);
+    }
+
+    inline Real unchecked_evaluation(Real x) const
+    {
+        using std::floor;
+        Real s = (x-x0_)*inv_dx_;
+        Real ii = floor(s);
+        auto i = static_cast<decltype(y_.size())>(ii);
+        Real t = s - ii;
+        Real y0 = y_[i];
+        Real y1 = y_[i+1];
+        Real dy0 = dy_[i];
+        Real dy1 = dy_[i+1];
+
+        Real r = 1-t;
+        return r*r*(y0*(1+2*t) + dy0*t)
+              + t*t*(y1*(3-2*t) - dy1*r);
+    }
+
+    inline Real prime(Real x) const {
+        const Real xf = x0_ + (y_.size()-1)/inv_dx_;
+        if  (x < x0_ || x > xf)
+        {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf)
+        {
+            return dy_.back()*inv_dx_;
         }
         return this->unchecked_prime(x);
     }
 
     inline Real unchecked_prime(Real x) const {
         using std::floor;
-        auto i = static_cast<decltype(y_.size())>(floor((x-x0_)/dx_));
-        Real xi = x0_ + i*dx_;
-        Real t = (x - xi)/dx_;
+        Real s = (x-x0_)*inv_dx_;
+        Real ii = floor(s);
+        auto i = static_cast<decltype(y_.size())>(ii);
+        Real t = s - ii;
         Real y0 = y_[i];
         Real y1 = y_[i+1];
-        Real v0 = dydx_[i];
-        Real v1 = dydx_[i+1];
+        Real dy0 = dy_[i];
+        Real dy1 = dy_[i+1];
 
-        return 6*t*(1-t)*(y1 - y0)/dx_  + (3*t*t - 4*t+1)*v0 + t*(3*t-2)*v1;
+        Real dy = 6*t*(1-t)*(y1 - y0)  + (3*t*t - 4*t+1)*dy0 + t*(3*t-2)*dy1;
+        return dy*inv_dx_;
     }
 
 
@@ -103,9 +115,9 @@ public:
     }
 
     RandomAccessContainer y_;
-    RandomAccessContainer dydx_;
+    RandomAccessContainer dy_;
     Real x0_;
-    Real dx_;
+    Real inv_dx_;
 };
 
 
@@ -116,7 +128,7 @@ public:
     using Real = typename Point::value_type;
 
     cardinal_cubic_hermite_detail_aos(RandomAccessContainer && dat, Real x0, Real dx)
-    : dat_{std::move(dat)}, x0_{x0}, dx_{dx}
+    : dat_{std::move(dat)}, x0_{x0}, inv_dx_{1/dx}
     {
         if (dat_.size() < 2)
         {
@@ -126,42 +138,56 @@ public:
         {
             throw std::domain_error("Each datum must contain (y, y'), and nothing else.");
         }
+        if (dx <= 0)
+        {
+            throw std::domain_error("dx > 0 is required.");
+        }
+
+        for (auto & d : dat_)
+        {
+            d[1] *= dx;
+        }
     }
 
     inline Real operator()(Real x) const {
-        const Real xf = x0_ + (dat_.size()-1)*dx_;
-        if  (x < x0_ || x > xf) {
+        const Real xf = x0_ + (dat_.size()-1)/inv_dx_;
+        if  (x < x0_ || x > xf)
+        {
             std::ostringstream oss;
             oss.precision(std::numeric_limits<Real>::digits10+3);
             oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
                 << x0_ << ", " << xf << "]";
             throw std::domain_error(oss.str());
         }
-        if (x == xf) {
+        if (x == xf)
+        {
             return dat_.back()[0];
         }
-
         return this->unchecked_evaluation(x);
     }
 
-    inline Real unchecked_evaluation(Real x) const {
+    inline Real unchecked_evaluation(Real x) const
+    {
         using std::floor;
-        auto i = static_cast<decltype(dat_.size())>(floor((x-x0_)/dx_));
-        Real xi = x0_ + i*dx_;
-        Real t = (x-xi)/dx_;
+        Real s = (x-x0_)*inv_dx_;
+        Real ii = floor(s);
+        auto i = static_cast<decltype(dat_.size())>(ii);
+
+        Real t = s - ii;
         Real y0 = dat_[i][0];
         Real y1 = dat_[i+1][0];
-        Real v0 = dat_[i][1];
-        Real v1 = dat_[i+1][1];
+        Real dy0 = dat_[i][1];
+        Real dy1 = dat_[i+1][1];
 
-
-        return (1-t)*(1-t)*(y0*(1+2*t) + v0*(x-xi))
-              + t*t*(y1*(3-2*t) + dx_*v1*(t-1));
+        Real r = 1-t;
+        return r*r*(y0*(1+2*t) + dy0*t)
+              + t*t*(y1*(3-2*t) - dy1*r);
     }
 
     inline Real prime(Real x) const {
-        const Real xf = x0_ + (dat_.size()-1)*dx_;
-        if  (x < x0_ || x > xf) {
+        const Real xf = x0_ + (dat_.size()-1)/inv_dx_;
+        if  (x < x0_ || x > xf)
+        {
             std::ostringstream oss;
             oss.precision(std::numeric_limits<Real>::digits10+3);
             oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
@@ -175,27 +201,31 @@ public:
         return this->unchecked_prime(x);
     }
 
-    inline Real unchecked_prime(Real x) const {
+    inline Real unchecked_prime(Real x) const
+    {
         using std::floor;
-        auto i = static_cast<decltype(dat_.size())>(floor((x-x0_)/dx_));
-        Real xi = x0_ + i*dx_;
-        Real t = (x - xi)/dx_;
+        Real s = (x-x0_)*inv_dx_;
+        Real ii = floor(s);
+        auto i = static_cast<decltype(dat_.size())>(ii);
+        Real t = s - ii;
         Real y0 = dat_[i][0];
+        Real dy0 = dat_[i][1];
         Real y1 = dat_[i+1][0];
-        Real v0 = dat_[i][1];
-        Real v1 = dat_[i+1][1];
+        Real dy1 = dat_[i+1][1];
 
-        return 6*t*(1-t)*(y1 - y0)/dx_  + (3*t*t - 4*t+1)*v0 + t*(3*t-2)*v1;
+        Real dy = 6*t*(1-t)*(y1 - y0)  + (3*t*t - 4*t+1)*dy0 + t*(3*t-2)*dy1;
+        return dy*inv_dx_;
     }
 
 
-    auto size() const {
+    auto size() const
+    {
         return dat_.size();
     }
 
     RandomAccessContainer dat_;
     Real x0_;
-    Real dx_;
+    Real inv_dx_;
 };
 
 

From 4cd72f622516b463cc200b8a78e3b6cae138fa6e Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Sun, 16 Feb 2020 17:26:20 -0500
Subject: [PATCH 031/104] Improve performance of matched_holder and linear
 interpolation. [CI SKIP]

---
 .../special_functions/daubechies_scaling.hpp  | 66 +++++++++----------
 1 file changed, 33 insertions(+), 33 deletions(-)

diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index 8a57a4fa0..c6f973e04 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -57,25 +57,29 @@ std::vector<Real> dyadic_grid(int64_t j_max)
         {
             // Where this value will go:
             int64_t delivery_idx = k*(1 << (j_max-j));
-            if (delivery_idx >= (int64_t) v.size())
-            {
-                std::cerr << "Delivery index out of range!\n";
-                continue;
-            }
+            // This is a nice check, but we've tested this exhaustively, and it's expensive:
+            //if (delivery_idx >= (int64_t) v.size()) {
+            //    std::cerr << "Delivery index out of range!\n";
+            //    continue;
+            //}
             Real term = 0;
-            for (int64_t l = 0; l < (int64_t) c.size(); ++l) {
+            for (int64_t l = 0; l < (int64_t) c.size(); ++l)
+            {
                 int64_t idx = k*(1 << (j_max - j + 1)) - l*(1 << j_max);
-                if (idx < 0) {
+                if (idx < 0)
+                {
                     break;
                 }
-                if (idx < (int64_t) v.size()) {
+                if (idx < (int64_t) v.size())
+                {
                     term += c[l]*v[idx];
                 }
             }
-            if (!isnan(v[delivery_idx])) {
-                std::cerr << "Delivery index already populated!, = " << v[delivery_idx] << "\n";
-                std::cerr << "would overwrite with " << term << "\n";
-            }
+            // Again, another nice check:
+            //if (!isnan(v[delivery_idx])) {
+            //    std::cerr << "Delivery index already populated!, = " << v[delivery_idx] << "\n";
+            //    std::cerr << "would overwrite with " << term << "\n";
+            //}
             v[delivery_idx] = term;
         }
     }
@@ -89,39 +93,36 @@ class matched_holder {
 public:
     using Real = typename RandomAccessContainer::value_type;
 
-    matched_holder(RandomAccessContainer && y, RandomAccessContainer && dydx, int grid_refinements) : y_{std::move(y)}, dydx_{std::move(dydx)}
+    matched_holder(RandomAccessContainer && y, RandomAccessContainer && dydx, int grid_refinements) : y_{std::move(y)}, dy_{std::move(dydx)}
     {
-        inv_h_ = 1<< grid_refinements;
+        inv_h_ = (1 << grid_refinements);
+        Real h = 1/inv_h_;
+        for (auto & dy : dy_)
+        {
+            dy *= h;
+        }
     }
     
     inline Real operator()(Real x) const {
-        using std::log;
         using std::floor;
         using std::sqrt;
-        using std::pow;
         // This is the exact Holder exponent, but it's pessimistic almost everywhere!
         // It's only exactly right at dyadic rationals.
-        // Some compilers do not evaluate this at compile time:
-        Real const alpha = 2 - log(1+sqrt(Real(3)))/log(Real(2));
-        Real const onemalpham1 = 1/(1-alpha);
-        //const Real alpha = 0.5500156865235042;
-        // So we're gonna make the graph dip a little harder; this will capture more of the self-similar behavior:
-        //Real constexpr const alpha = Real(3)/Real(10);
+        //Real const alpha = 2 - log(1+sqrt(Real(3)))/log(Real(2));
+        // We're gonna use alpha = 1/2, rather than 0.5500...
         Real s = x*inv_h_;
         Real ii = floor(s);
-        int64_t i = static_cast<int64_t>(ii);
+        auto i = static_cast<decltype(y_.size())>(ii);
         Real t = s - ii;
-        Real v = y_[i];
-        Real dphi = dydx_[i+1]/inv_h_;
+        Real dphi = dy_[i+1];
         Real diff = y_[i+1] - y_[i];
-        v += ((dphi - alpha*diff)*t + (-dphi + diff)*pow(t, alpha) )*onemalpham1;
-        return v;
+        return y_[i] + (2*dphi - diff)*t + 2*sqrt(t)*(diff-dphi);
     }
 
 private:
     Real inv_h_;
     RandomAccessContainer y_;
-    RandomAccessContainer dydx_;
+    RandomAccessContainer dy_;
 };
 
 
@@ -132,22 +133,21 @@ public:
 
     linear_interpolation(RandomAccessContainer && y,  int grid_refinements) : y_{std::move(y)}
     {
-        grid_refinements_ = grid_refinements;
+        s_ = (1 << grid_refinements);
     }
 
     inline Real operator()(Real x) const {
         using std::floor;
-        Real y = x*(1<<grid_refinements_);
+        Real y = x*s_;
         Real k = floor(y);
 
-        size_t kk = static_cast<size_t>(k);
-
+        int64_t kk = static_cast<int64_t>(k);
         Real t = y - k;
         return (1-t)*y_[kk] + t*y_[kk+1];
     }
 
 private:
-    int grid_refinements_;
+    Real s_;
     RandomAccessContainer y_;
 };
 

From 4dd1ddf9039fcf770409acc6e61d32923d1b672c Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Sun, 16 Feb 2020 18:07:46 -0500
Subject: [PATCH 032/104] Improve performance of quintic Hermite interpolation
 [CI SKIP]

---
 .../cardinal_quintic_hermite_detail.hpp       | 209 +++++++++++-------
 1 file changed, 130 insertions(+), 79 deletions(-)

diff --git a/include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp b/include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp
index c59b360a8..28944f76d 100644
--- a/include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp
@@ -12,95 +12,123 @@ class cardinal_quintic_hermite_detail {
 public:
     using Real = typename RandomAccessContainer::value_type;
     cardinal_quintic_hermite_detail(RandomAccessContainer && y, RandomAccessContainer && dydx, RandomAccessContainer && d2ydx2, Real x0, Real dx)
-    : y_{std::move(y)}, dydx_{std::move(dydx)}, d2ydx2_{std::move(d2ydx2)}, x0_{x0}, dx_{dx}
+    : y_{std::move(y)}, dy_{std::move(dydx)}, d2y_{std::move(d2ydx2)}, x0_{x0}, inv_dx_{1/dx}
     {
-        if (y_.size() != dydx_.size()) {
+        if (y_.size() != dy_.size())
+        {
             throw std::domain_error("Numbers of derivatives must = number of abscissas.");
         }
-        if (y_.size() != d2ydx2_.size()) {
+        if (y_.size() != d2y_.size())
+        {
             throw std::domain_error("Number of second derivatives must equal number of abscissas.");
         }
-        if (y_.size() < 2) {
+        if (y_.size() < 2)
+        {
             throw std::domain_error("At least 2 abscissas are required.");
         }
+        if (dx <= 0)
+        {
+            throw std::domain_error("dx > 0 is required.");
+        }
+
+        for (auto & dy : dy_)
+        {
+            dy *= dx;
+        }
+
+        for (auto & d2y : d2y_)
+        {
+            d2y *= (dx*dx)/2;
+        }
     }
 
 
-    inline Real operator()(Real x) const {
-        const Real xf = x0_ + (y_.size()-1)*dx_;
-        if  (x < x0_ || x > xf) {
+    inline Real operator()(Real x) const
+    {
+        const Real xf = x0_ + (y_.size()-1)/inv_dx_;
+        if  (x < x0_ || x > xf)
+        {
             std::ostringstream oss;
             oss.precision(std::numeric_limits<Real>::digits10+3);
             oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
                 << x0_ << ", " << xf << "]";
             throw std::domain_error(oss.str());
         }
-        if (x == xf) {
+        if (x == xf)
+        {
             return y_.back();
         }
         return this->unchecked_evaluation(x);
     }
 
-    inline Real unchecked_evaluation(Real x) const {
+    inline Real unchecked_evaluation(Real x) const
+    {
         using std::floor;
-        auto i = static_cast<decltype(y_.size())>(floor((x-x0_)/dx_));
-        Real xi = x0_ + i*dx_;
-        Real t = (x - xi)/dx_;
+        Real s = (x-x0_)*inv_dx_;
+        Real ii = floor(s);
+        auto i = static_cast<decltype(y_.size())>(ii);
+        Real t = s - ii;
 
         Real y0 = y_[i];
         Real y1 = y_[i+1];
-        Real v0 = dydx_[i];
-        Real v1 = dydx_[i+1];
-        Real a0 = d2ydx2_[i];
-        Real a1 = d2ydx2_[i+1];
+        Real dy0 = dy_[i];
+        Real dy1 = dy_[i+1];
+        Real d2y0 = d2y_[i];
+        Real d2y1 = d2y_[i+1];
 
         // See the 'Basis functions' section of:
         // https://www.rose-hulman.edu/~finn/CCLI/Notes/day09.pdf
         // Also: https://github.com/MrHexxx/QuinticHermiteSpline/blob/master/HermiteSpline.cs
         Real y = (1- t*t*t*(10 + t*(-15 + 6*t)))*y0;
-        y += t*(1+ t*t*(-6 + t*(8 -3*t)))*v0*dx_;
-        y += t*t*(1 + t*(-3 + t*(3-t)))*a0*dx_*dx_/2;
-        y += t*t*t*((1 + t*(-2 + t))*a1*dx_*dx_/2 + (-4 + t*(7 -3*t))*v1*dx_ + (10 + t*(-15 + 6*t))*y1);
+        y += t*(1+ t*t*(-6 + t*(8 -3*t)))*dy0;
+        y += t*t*(1 + t*(-3 + t*(3-t)))*d2y0;
+        y += t*t*t*((1 + t*(-2 + t))*d2y1 + (-4 + t*(7 -3*t))*dy1 + (10 + t*(-15 + 6*t))*y1);
         return y;
     }
 
-    inline Real prime(Real x) const {
-        const Real xf = x0_ + (y_.size()-1)*dx_;
-        if  (x < x0_ || x > xf) {
+    inline Real prime(Real x) const
+    {
+        const Real xf = x0_ + (y_.size()-1)/inv_dx_;
+        if  (x < x0_ || x > xf)
+        {
             std::ostringstream oss;
             oss.precision(std::numeric_limits<Real>::digits10+3);
             oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
                 << x0_ << ", " << xf << "]";
             throw std::domain_error(oss.str());
         }
-        if (x == xf) {
-            return dydx_.back();
+        if (x == xf)
+        {
+            return dy_.back()*inv_dx_;
         }
 
         return this->unchecked_prime(x);
     }
 
-    inline Real unchecked_prime(Real x) const {
+    inline Real unchecked_prime(Real x) const
+    {
         using std::floor;
-        auto i = static_cast<decltype(y_.size())>(floor((x-x0_)/dx_));
-        Real xi = x0_ + i*dx_;
-        Real t = (x - xi)/dx_;
+        Real s = (x-x0_)*inv_dx_;
+        Real ii = floor(s);
+        auto i = static_cast<decltype(y_.size())>(ii);
+        Real t = s - ii;
 
         Real y0 = y_[i];
         Real y1 = y_[i+1];
-        Real v0 = dydx_[i];
-        Real v1 = dydx_[i+1];
-        Real a0 = d2ydx2_[i];
-        Real a1 = d2ydx2_[i+1];
+        Real dy0 = dy_[i];
+        Real dy1 = dy_[i+1];
+        Real d2y0 = d2y_[i];
+        Real d2y1 = d2y_[i+1];
 
-        Real dydx = 30*t*t*(1 - 2*t + t*t)*(y1-y0)/dx_;
-        dydx += (1-18*t*t + 32*t*t*t - 15*t*t*t*t)*v0 - t*t*(12 - 28*t + 15*t*t)*v1;
-        dydx += (t*dx_/2)*((2 - 9*t + 12*t*t - 5*t*t*t)*a0 + t*(3 - 8*t + 5*t*t)*a1);
+        Real dydx = 30*t*t*(1 - 2*t + t*t)*(y1-y0);
+        dydx += (1-18*t*t + 32*t*t*t - 15*t*t*t*t)*dy0 - t*t*(12 - 28*t + 15*t*t)*dy1;
+        dydx += t*((2 - 9*t + 12*t*t - 5*t*t*t)*d2y0 + t*(3 - 8*t + 5*t*t)*d2y1);
+        dydx *= inv_dx_;
         return dydx;
     }
 
     inline Real double_prime(Real x) const {
-        const Real xf = x0_ + (y_.size()-1)*dx_;
+        const Real xf = x0_ + (y_.size()-1)/inv_dx_;
         if  (x < x0_ || x > xf) {
             std::ostringstream oss;
             oss.precision(std::numeric_limits<Real>::digits10+3);
@@ -108,8 +136,9 @@ public:
                 << x0_ << ", " << xf << "]";
             throw std::domain_error(oss.str());
         }
-        if (x == xf) {
-            return d2ydx2_.back();
+        if (x == xf)
+        {
+            return d2y_.back()*2*inv_dx_*inv_dx_;
         }
 
         return this->unchecked_double_prime(x);
@@ -117,29 +146,31 @@ public:
 
     inline Real unchecked_double_prime(Real x) const {
         using std::floor;
-        auto i = static_cast<decltype(y_.size())>(floor((x-x0_)/dx_));
-        Real xi = x0_ + i*dx_;
-        Real t = (x - xi)/dx_;
+        Real s = (x-x0_)*inv_dx_;
+        Real ii = floor(s);
+        auto i = static_cast<decltype(y_.size())>(ii);
+        Real t = s - ii;
+
 
         Real y0 = y_[i];
         Real y1 = y_[i+1];
-        Real v0 = dydx_[i];
-        Real v1 = dydx_[i+1];
-        Real a0 = d2ydx2_[i];
-        Real a1 = d2ydx2_[i+1];
+        Real dy0 = dy_[i];
+        Real dy1 = dy_[i+1];
+        Real d2y0 = d2y_[i];
+        Real d2y1 = d2y_[i+1];
 
-        Real d2ydx2 = 60*t*(1 - 3*t + 2*t*t)*(y1 - y0)/(dx_*dx_);
-        d2ydx2 += (12*t/dx_)*((-3 + 8*t - 5*t*t)*v0 - (2 - 7*t + 5*t*t)*v1);
-        d2ydx2 += (1 - 9*t + 18*t*t - 10*t*t*t)*a0 + t*(3 - 12*t + 10*t*t)*a1;
+        Real d2ydx2 = 60*t*(1 - 3*t + 2*t*t)*(y1 - y0)*inv_dx_*inv_dx_;
+        d2ydx2 += (12*t)*((-3 + 8*t - 5*t*t)*dy0 - (2 - 7*t + 5*t*t)*dy1);
+        d2ydx2 += (1 - 9*t + 18*t*t - 10*t*t*t)*d2y0*(2*inv_dx_*inv_dx_) + t*(3 - 12*t + 10*t*t)*d2y1*(2*inv_dx_*inv_dx_);
         return d2ydx2;
     }
 
 private:
     RandomAccessContainer y_;
-    RandomAccessContainer dydx_;
-    RandomAccessContainer d2ydx2_;
+    RandomAccessContainer dy_;
+    RandomAccessContainer d2y_;
     Real x0_;
-    Real dx_;
+    Real inv_dx_;
 };
 
 
@@ -149,7 +180,7 @@ public:
     using Point = typename RandomAccessContainer::value_type;
     using Real = typename Point::value_type;
     cardinal_quintic_hermite_detail_aos(RandomAccessContainer && data, Real x0, Real dx)
-    : data_{std::move(data)} , x0_{x0}, dx_{dx}
+    : data_{std::move(data)} , x0_{x0}, inv_dx_{1/dx}
     {
         if (data_.size() < 2)
         {
@@ -160,19 +191,32 @@ public:
         {
             throw std::domain_error("Each datum passed to the cardinal_quintic_hermite_aos must have three elements: {y, y', y''}");
         }
+        if (dx <= 0)
+        {
+            throw std::domain_error("dx > 0 is required.");
+        }
+
+        for (auto & datum : data_)
+        {
+            datum[1] *= dx;
+            datum[2] *= (dx*dx/2);
+        }
     }
 
 
-    inline Real operator()(Real x) const {
-        const Real xf = x0_ + (data_.size()-1)*dx_;
-        if  (x < x0_ || x > xf) {
+    inline Real operator()(Real x) const
+    {
+        const Real xf = x0_ + (data_.size()-1)/inv_dx_;
+        if  (x < x0_ || x > xf)
+        {
             std::ostringstream oss;
             oss.precision(std::numeric_limits<Real>::digits10+3);
             oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
                 << x0_ << ", " << xf << "]";
             throw std::domain_error(oss.str());
         }
-        if (x == xf) {
+        if (x == xf)
+        {
             return data_.back()[0];
         }
         return this->unchecked_evaluation(x);
@@ -181,35 +225,40 @@ public:
     inline Real unchecked_evaluation(Real x) const
     {
         using std::floor;
-        auto i = static_cast<decltype(data_.size())>(floor((x-x0_)/dx_));
-        Real xi = x0_ + i*dx_;
-        Real t = (x - xi)/dx_;
+        Real s = (x-x0_)*inv_dx_;
+        Real ii = floor(s);
+        auto i = static_cast<decltype(data_.size())>(ii);
+        Real t = s - ii;
+
 
         Real y0 = data_[i][0];
+        Real dy0 = data_[i][1];
+        Real d2y0 = data_[i][2];
         Real y1 = data_[i+1][0];
-        Real v0 = data_[i][1];
-        Real v1 = data_[i+1][1];
-        Real a0 = data_[i][2];
-        Real a1 = data_[i+1][2];
+        Real dy1 = data_[i+1][1];
+        Real d2y1 = data_[i+1][2];
 
         Real y = (1- t*t*t*(10 + t*(-15 + 6*t)))*y0;
-        y += t*(1+ t*t*(-6 + t*(8 -3*t)))*v0*dx_;
-        y += t*t*(1 + t*(-3 + t*(3-t)))*a0*dx_*dx_/2;
-        y += t*t*t*((1 + t*(-2 + t))*a1*dx_*dx_/2 + (-4 + t*(7 -3*t))*v1*dx_ + (10 + t*(-15 + 6*t))*y1);
+        y += t*(1+ t*t*(-6 + t*(8 -3*t)))*dy0;
+        y += t*t*(1 + t*(-3 + t*(3-t)))*d2y0;
+        y += t*t*t*((1 + t*(-2 + t))*d2y1 + (-4 + t*(7 -3*t))*dy1 + (10 + t*(-15 + 6*t))*y1);
         return y;
     }
 
-    inline Real prime(Real x) const {
-        const Real xf = x0_ + (data_.size()-1)*dx_;
-        if  (x < x0_ || x > xf) {
+    inline Real prime(Real x) const
+    {
+        const Real xf = x0_ + (data_.size()-1)/inv_dx_;
+        if  (x < x0_ || x > xf)
+        {
             std::ostringstream oss;
             oss.precision(std::numeric_limits<Real>::digits10+3);
             oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
                 << x0_ << ", " << xf << "]";
             throw std::domain_error(oss.str());
         }
-        if (x == xf) {
-            return data_.back()[1];
+        if (x == xf)
+        {
+            return data_.back()[1]*inv_dx_;
         }
 
         return this->unchecked_prime(x);
@@ -217,9 +266,11 @@ public:
 
     inline Real unchecked_prime(Real x) const {
         using std::floor;
-        auto i = static_cast<decltype(data_.size())>(floor((x-x0_)/dx_));
-        Real xi = x0_ + i*dx_;
-        Real t = (x - xi)/dx_;
+        Real s = (x-x0_)*inv_dx_;
+        Real ii = floor(s);
+        auto i = static_cast<decltype(data_.size())>(ii);
+        Real t = s - ii;
+
 
         Real y0 = data_[i][0];
         Real y1 = data_[i+1][0];
@@ -228,10 +279,10 @@ public:
         Real a0 = data_[i][2];
         Real a1 = data_[i+1][2];
 
-        Real dydx = 30*t*t*(1 - 2*t + t*t)*(y1-y0)/dx_;
-        dydx += (1-18*t*t + 32*t*t*t - 15*t*t*t*t)*v0 - t*t*(12 - 28*t + 15*t*t)*v1;
-        dydx += (t*dx_/2)*((2 - 9*t + 12*t*t - 5*t*t*t)*a0 + t*(3 - 8*t + 5*t*t)*a1);
-        return dydx;
+        Real dy = 30*t*t*(1 - 2*t + t*t)*(y1-y0);
+        dy += (1-18*t*t + 32*t*t*t - 15*t*t*t*t)*v0 - t*t*(12 - 28*t + 15*t*t)*v1;
+        dy += t*((2 - 9*t + 12*t*t - 5*t*t*t)*a0 + t*(3 - 8*t + 5*t*t)*a1);
+        return dy*inv_dx_;
     }
 
 
@@ -239,7 +290,7 @@ public:
 private:
     RandomAccessContainer data_;
     Real x0_;
-    Real dx_;
+    Real inv_dx_;
 };
 
 }

From 70e95ac1fa54da7a4d232647ac1a339ed2bef824 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Sun, 16 Feb 2020 18:58:22 -0500
Subject: [PATCH 033/104] Improve the performance of the septic hermite
 interpolation [CI SKIP]

---
 .../detail/septic_hermite_detail.hpp          | 170 +++++++++++-------
 1 file changed, 106 insertions(+), 64 deletions(-)

diff --git a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
index 8b7fea73f..8a8787980 100644
--- a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
@@ -166,26 +166,52 @@ class cardinal_septic_hermite_detail {
 public:
     using Real = typename RandomAccessContainer::value_type;
     cardinal_septic_hermite_detail(RandomAccessContainer && y, RandomAccessContainer && dydx, RandomAccessContainer && d2ydx2, RandomAccessContainer && d3ydx3, Real x0, Real dx)
-    : y_{std::move(y)}, dydx_{std::move(dydx)}, d2ydx2_{std::move(d2ydx2)}, d3ydx3_{std::move(d3ydx3)}, x0_{x0}, dx_{dx}
+    : y_{std::move(y)}, dy_{std::move(dydx)}, d2y_{std::move(d2ydx2)}, d3y_{std::move(d3ydx3)}, x0_{x0}, inv_dx_{1/dx}
     {
-        if (y_.size() != dydx_.size()) {
+        if (y_.size() != dy_.size())
+        {
             throw std::domain_error("Numbers of derivatives must = number of ordinates.");
         }
-        if (y_.size() != d2ydx2_.size()) {
+        if (y_.size() != d2y_.size())
+        {
             throw std::domain_error("Number of second derivatives must equal number of ordinates.");
         }
-        if (y_.size() != d3ydx3_.size()) {
+        if (y_.size() != d3y_.size())
+        {
             throw std::domain_error("Number of third derivatives must equal number of ordinates.");
         }
 
-        if (y_.size() < 2) {
+        if (y_.size() < 2)
+        {
             throw std::domain_error("At least 2 abscissas are required.");
         }
+
+        if (dx <= 0)
+        {
+            throw std::domain_error("dx > 0 is required.");
+        }
+
+        for (auto & dy : dy_)
+        {
+            dy *= dx;
+        }
+        for (auto & d2y : d2y_)
+        {
+            d2y *= (dx*dx/2);
+        }
+
+        for (auto & d3y : d3y_)
+        {
+            d3y *= (dx*dx*dx/6);
+        }
+
     }
 
-    inline Real operator()(Real x) const {
-        Real xf = x0_ + (y_.size()-1)*dx_;
-        if  (x < x0_ || x > xf) {
+    inline Real operator()(Real x) const
+    {
+        Real xf = x0_ + (y_.size()-1)/inv_dx_;
+        if  (x < x0_ || x > xf)
+        {
             std::ostringstream oss;
             oss.precision(std::numeric_limits<Real>::digits10+3);
             oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
@@ -203,49 +229,51 @@ public:
 
     inline Real unchecked_evaluation(Real x) const {
         using std::floor;
-        auto i = static_cast<decltype(y_.size())>(floor((x-x0_)/dx_));
-        Real xi = x0_ + i*dx_;
-        Real t = (x - xi)/dx_;
+        Real s3 = (x-x0_)*inv_dx_;
+        Real ii = floor(s3);
+        auto i = static_cast<decltype(y_.size())>(ii);
+        Real t = s3 - ii;
 
         Real y0 = y_[i];
         Real y1 = y_[i+1];
         // Velocity:
-        Real v0 = dydx_[i];
-        Real v1 = dydx_[i+1];
+        Real dy0 = dy_[i];
+        Real dy1 = dy_[i+1];
         // Acceleration:
-        Real a0 = d2ydx2_[i];
-        Real a1 = d2ydx2_[i+1];
+        Real a0 = d2y_[i];
+        Real a1 = d2y_[i+1];
         // Jerk:
-        Real j0 = d3ydx3_[i];
-        Real j1 = d3ydx3_[i+1];
+        Real j0 = d3y_[i];
+        Real j1 = d3y_[i+1];
 
         // See:
         // http://seisweb.usask.ca/classes/GEOL481/2017/Labs/interpolation_utilities_matlab/shermite.m
         Real t2 = t*t;
         Real t3 = t2*t;
         Real t4 = t3*t;
-        Real t5 = t4*t;
-        Real t6 = t5*t;
-        Real t7 = t6*t;
-        Real dx2 = dx_*dx_;
-        Real dx3 = dx2*dx_;
 
         Real s = t4*(-35 + t*(84 + t*(-70 + 20*t)));
         Real z4 = -s;
         Real z0 = s + 1;
-        Real z1 = 10*t7 - 36*t6 + 45*t5 - 20*t4 + t;
-        Real z2 = 2*t7 - 15*t6/2 + 10*t5 - 5*t4 + t2/2;
-        Real z3 = t7/6 - 2*t6/3 + t5 - 2*t4/3 + t3/6;
+        //Real z1 = t*(10*t6 - 36*t5 + 45*t4 - 20*t3 + 1);
+        Real z1 = t*(1 + t3*(-20 + t*(45 + t*(-36+10*t))));
+        //Real z2 = t2*(4*t5 - 15*t4 + 20*t3 - 10*t2 + 1);
+        Real z2 = t2*(1+ t2*(4*t3 - 15*t + 20*t - 10));
+        //Real z3 = t3*(t4 - 4*t3 + 6*t2 - 4*t + 1);
+        Real z3 = t3*(1 + t*(-4+t*(6+t*(-4+t))));
 
-        Real z5 = 10*t7 - 34*t6 + 39*t5 - 15*t4;
-        Real z6 = -2*t7 + 13*t6/2 - 7*t5 + 5*t4/2;
-        Real z7 = t7/6 - t6/2 + t5/2 - t4/6;
+        //Real z5 = t4*(10*t3 - 34*t2 + 39*t - 15);
+        Real z5 = t4*(-15 + t*(39 + t*(-34 + 10*t)));
+        //Real z6 = t4*(-4*t3 + 13*t2 - 14*t + 5);
+        Real z6 = t4*(5 + t*(-14 + t*(13-4*t)));
+        //Real z7 = t4*(t3 - 3*t2 + 3*t - 1);
+        Real z7 = t4*(-1 + t*(3+t*(-3+t)));
 
-        return z0*y0 + z1*dx_*v0 + z2*dx2*a0 + z3*dx3*j0 + z4*y1 + z5*dx_*v1 + z6*dx2*a1 + z7*dx3*j1;
+        return z0*y0 + z1*dy0 + z2*a0 + z3*j0 + z4*y1 + z5*dy1 + z6*a1 + z7*j1;
     }
 
     inline Real prime(Real x) const {
-        Real xf = x0_ + (y_.size()-1)*dx_;
+        Real xf = x0_ + (y_.size()-1)/inv_dx_;
         if  (x < x0_ || x > xf)
         {
             std::ostringstream oss;
@@ -256,7 +284,7 @@ public:
         }
         if (x == xf)
         {
-            return dydx_.back();
+            return dy_.back()/inv_dx_;
         }
 
         return this->unchecked_prime(x);
@@ -265,23 +293,24 @@ public:
     inline Real unchecked_prime(Real x) const {
         //TODO: Get the high accuracy approximation by differentiating the interpolant!
         using std::floor;
-        auto i = static_cast<decltype(y_.size())>(floor((x-x0_)/dx_));
-        Real xi = x0_ + i*dx_;
-        Real t = (x - xi)/dx_;
+        Real s3 = (x-x0_)*inv_dx_;
+        Real ii = floor(s3);
+        auto i = static_cast<decltype(y_.size())>(ii);
+        Real t = s3 - ii;
 
         // Velocity:
-        Real v0 = dydx_[i];
-        Real v1 = dydx_[i+1];
-        return (v0+v1)/2;
+        Real v0 = dy_[i];
+        Real v1 = dy_[i+1];
+        return (v0+v1)*inv_dx_/2;
     }
 
 private:
     RandomAccessContainer y_;
-    RandomAccessContainer dydx_;
-    RandomAccessContainer d2ydx2_;
-    RandomAccessContainer d3ydx3_;
+    RandomAccessContainer dy_;
+    RandomAccessContainer d2y_;
+    RandomAccessContainer d3y_;
     Real x0_;
-    Real dx_;
+    Real inv_dx_;
 };
 
 
@@ -291,7 +320,7 @@ public:
     using Point = typename RandomAccessContainer::value_type;
     using Real = typename Point::value_type;
     cardinal_septic_hermite_detail_aos(RandomAccessContainer && dat, Real x0, Real dx)
-    : data_{std::move(dat)}, x0_{x0}, dx_{dx}
+    : data_{std::move(dat)}, x0_{x0}, inv_dx_{1/dx}
     {
         if (data_.size() < 2) {
             throw std::domain_error("At least 2 abscissas are required.");
@@ -299,11 +328,20 @@ public:
         if (data_[0].size() != 4) {
             throw std::domain_error("There must be 4 data items per struct.");
         }
+
+        for (auto & datum : data_)
+        {
+            datum[1] *= dx;
+            datum[2] *= (dx*dx/2);
+            datum[3] *= (dx*dx*dx/6);
+        }
     }
 
-    inline Real operator()(Real x) const {
-        Real xf = x0_ + (data_.size()-1)*dx_;
-        if  (x < x0_ || x > xf) {
+    inline Real operator()(Real x) const
+    {
+        Real xf = x0_ + (data_.size()-1)/inv_dx_;
+        if  (x < x0_ || x > xf)
+        {
             std::ostringstream oss;
             oss.precision(std::numeric_limits<Real>::digits10+3);
             oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
@@ -321,15 +359,17 @@ public:
 
     inline Real unchecked_evaluation(Real x) const {
         using std::floor;
-        auto i = static_cast<decltype(data_.size())>(floor((x-x0_)/dx_));
-        Real xi = x0_ + i*dx_;
-        Real t = (x - xi)/dx_;
+        Real s3 = (x-x0_)*inv_dx_;
+        Real ii = floor(s3);
+        auto i = static_cast<decltype(data_.size())>(ii);
+        Real t = s3 - ii;
+
 
         Real y0 = data_[i][0];
         Real y1 = data_[i+1][0];
         // Velocity:
-        Real v0 = data_[i][1];
-        Real v1 = data_[i+1][1];
+        Real dy0 = data_[i][1];
+        Real dy1 = data_[i+1][1];
         // Acceleration:
         Real a0 = data_[i][2];
         Real a1 = data_[i+1][2];
@@ -340,28 +380,30 @@ public:
         Real t2 = t*t;
         Real t3 = t2*t;
         Real t4 = t3*t;
-        Real t5 = t4*t;
-        Real t6 = t5*t;
-        Real t7 = t6*t;
-        Real dx2 = dx_*dx_;
-        Real dx3 = dx2*dx_;
 
         Real s = t4*(-35 + t*(84 + t*(-70 + 20*t)));
         Real z4 = -s;
         Real z0 = s + 1;
-        Real z1 = 10*t7 - 36*t6 + 45*t5 - 20*t4 + t;
-        Real z2 = 2*t7 - 15*t6/2 + 10*t5 - 5*t4 + t2/2;
-        Real z3 = t7/6 - 2*t6/3 + t5 - 2*t4/3 + t3/6;
+        //Real z1 = t*(10*t6 - 36*t5 + 45*t4 - 20*t3 + 1);
+        Real z1 = t*(1 + t3*(-20 + t*(45 + t*(-36+10*t))));
+        //Real z2 = t2*(4*t5 - 15*t4 + 20*t3 - 10*t2 + 1);
+        Real z2 = t2*(1+ t2*(4*t3 - 15*t + 20*t - 10));
+        //Real z3 = t3*(t4 - 4*t3 + 6*t2 - 4*t + 1);
+        Real z3 = t3*(1 + t*(-4+t*(6+t*(-4+t))));
 
-        Real z5 = 10*t7 - 34*t6 + 39*t5 - 15*t4;
-        Real z6 = -2*t7 + 13*t6/2 - 7*t5 + 5*t4/2;
-        Real z7 = t7/6 - t6/2 + t5/2 - t4/6;
+        //Real z5 = t4*(10*t3 - 34*t2 + 39*t - 15);
+        Real z5 = t4*(-15 + t*(39 + t*(-34 + 10*t)));
+        //Real z6 = t4*(-4*t3 + 13*t2 - 14*t + 5);
+        Real z6 = t4*(5 + t*(-14 + t*(13-4*t)));
+        //Real z7 = t4*(t3 - 3*t2 + 3*t - 1);
+        Real z7 = t4*(-1 + t*(3+t*(-3+t)));
+
+        return z0*y0 + z1*dy0 + z2*a0 + z3*j0 + z4*y1 + z5*dy1 + z6*a1 + z7*j1;
 
-        return z0*y0 + z1*dx_*v0 + z2*dx2*a0 + z3*dx3*j0 + z4*y1 + z5*dx_*v1 + z6*dx2*a1 + z7*dx3*j1;
     }
 
     inline Real prime(Real x) const {
-        Real xf = x0_ + (data_.size()-1)*dx_;
+        Real xf = x0_ + (data_.size()-1)/inv_dx_;
         if  (x < x0_ || x > xf)
         {
             std::ostringstream oss;
@@ -385,7 +427,7 @@ public:
 private:
     RandomAccessContainer data_;
     Real x0_;
-    Real dx_;
+    Real inv_dx_;
 };
 
 

From 1aa2ba2337404b4afd2875b2c30520fb0c099ded Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Mon, 17 Feb 2020 12:24:17 -0500
Subject: [PATCH 034/104] Fix bug in septic_hermite; add unit tests [CI SKIP]

---
 .../detail/septic_hermite_detail.hpp          | 70 +++++++-------
 .../math/interpolators/septic_hermite.hpp     | 22 +++++
 test/septic_hermite_test.cpp                  | 92 ++++++++++++++++++-
 3 files changed, 143 insertions(+), 41 deletions(-)

diff --git a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
index 8a8787980..122c2ae38 100644
--- a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
@@ -233,6 +233,28 @@ public:
         Real ii = floor(s3);
         auto i = static_cast<decltype(y_.size())>(ii);
         Real t = s3 - ii;
+        // See:
+        // http://seisweb.usask.ca/classes/GEOL481/2017/Labs/interpolation_utilities_matlab/shermite.m
+        Real t2 = t*t;
+        Real t3 = t2*t;
+        Real t4 = t3*t;
+
+        Real s = t4*(-35 + t*(84 + t*(-70 + 20*t)));
+        Real z4 = -s;
+        Real z0 = s + 1;
+        //Real z1 = t*(10*t6 - 36*t5 + 45*t4 - 20*t3 + 1);
+        Real z1 = t*(1 + t3*(-20 + t*(45 + t*(-36+10*t))));
+        //Real z2 = t2*(4*t4*t - 15*t4 + 20*t3 - 10*t2 + 1);
+        Real z2 = t2*(1 + t2*(-10 + t*(20 + t*(-15+4*t))));
+        //Real z3 = t3*(t4 - 4*t3 + 6*t2 - 4*t + 1);
+        Real z3 = t3*(1 + t*(-4+t*(6+t*(-4+t))));
+
+        //Real z5 = t4*(10*t3 - 34*t2 + 39*t - 15);
+        Real z5 = t4*(-15 + t*(39 + t*(-34 + 10*t)));
+        //Real z6 = t4*(-4*t3 + 13*t2 - 14*t + 5);
+        Real z6 = t4*(5 + t*(-14 + t*(13-4*t)));
+        //Real z7 = t4*(t3 - 3*t2 + 3*t - 1);
+        Real z7 = t4*(-1 + t*(3+t*(-3+t)));
 
         Real y0 = y_[i];
         Real y1 = y_[i+1];
@@ -246,29 +268,6 @@ public:
         Real j0 = d3y_[i];
         Real j1 = d3y_[i+1];
 
-        // See:
-        // http://seisweb.usask.ca/classes/GEOL481/2017/Labs/interpolation_utilities_matlab/shermite.m
-        Real t2 = t*t;
-        Real t3 = t2*t;
-        Real t4 = t3*t;
-
-        Real s = t4*(-35 + t*(84 + t*(-70 + 20*t)));
-        Real z4 = -s;
-        Real z0 = s + 1;
-        //Real z1 = t*(10*t6 - 36*t5 + 45*t4 - 20*t3 + 1);
-        Real z1 = t*(1 + t3*(-20 + t*(45 + t*(-36+10*t))));
-        //Real z2 = t2*(4*t5 - 15*t4 + 20*t3 - 10*t2 + 1);
-        Real z2 = t2*(1+ t2*(4*t3 - 15*t + 20*t - 10));
-        //Real z3 = t3*(t4 - 4*t3 + 6*t2 - 4*t + 1);
-        Real z3 = t3*(1 + t*(-4+t*(6+t*(-4+t))));
-
-        //Real z5 = t4*(10*t3 - 34*t2 + 39*t - 15);
-        Real z5 = t4*(-15 + t*(39 + t*(-34 + 10*t)));
-        //Real z6 = t4*(-4*t3 + 13*t2 - 14*t + 5);
-        Real z6 = t4*(5 + t*(-14 + t*(13-4*t)));
-        //Real z7 = t4*(t3 - 3*t2 + 3*t - 1);
-        Real z7 = t4*(-1 + t*(3+t*(-3+t)));
-
         return z0*y0 + z1*dy0 + z2*a0 + z3*j0 + z4*y1 + z5*dy1 + z6*a1 + z7*j1;
     }
 
@@ -363,20 +362,6 @@ public:
         Real ii = floor(s3);
         auto i = static_cast<decltype(data_.size())>(ii);
         Real t = s3 - ii;
-
-
-        Real y0 = data_[i][0];
-        Real y1 = data_[i+1][0];
-        // Velocity:
-        Real dy0 = data_[i][1];
-        Real dy1 = data_[i+1][1];
-        // Acceleration:
-        Real a0 = data_[i][2];
-        Real a1 = data_[i+1][2];
-        // Jerk:
-        Real j0 = data_[i][3];
-        Real j1 = data_[i+1][3];
-
         Real t2 = t*t;
         Real t3 = t2*t;
         Real t4 = t3*t;
@@ -387,7 +372,7 @@ public:
         //Real z1 = t*(10*t6 - 36*t5 + 45*t4 - 20*t3 + 1);
         Real z1 = t*(1 + t3*(-20 + t*(45 + t*(-36+10*t))));
         //Real z2 = t2*(4*t5 - 15*t4 + 20*t3 - 10*t2 + 1);
-        Real z2 = t2*(1+ t2*(4*t3 - 15*t + 20*t - 10));
+        Real z2 = t2*(1 + t2*(-10 + t*(20 + t*(-15+4*t))));
         //Real z3 = t3*(t4 - 4*t3 + 6*t2 - 4*t + 1);
         Real z3 = t3*(1 + t*(-4+t*(6+t*(-4+t))));
 
@@ -398,6 +383,15 @@ public:
         //Real z7 = t4*(t3 - 3*t2 + 3*t - 1);
         Real z7 = t4*(-1 + t*(3+t*(-3+t)));
 
+        Real y0 = data_[i][0];
+        Real dy0 = data_[i][1];
+        Real a0 = data_[i][2];
+        Real j0 = data_[i][3];
+        Real y1 = data_[i+1][0];
+        Real dy1 = data_[i+1][1];
+        Real a1 = data_[i+1][2];
+        Real j1 = data_[i+1][3];
+
         return z0*y0 + z1*dy0 + z2*a0 + z3*j0 + z4*y1 + z5*dy1 + z6*a1 + z7*j1;
 
     }
diff --git a/include/boost/math/interpolators/septic_hermite.hpp b/include/boost/math/interpolators/septic_hermite.hpp
index 54da49a02..77ebe3024 100644
--- a/include/boost/math/interpolators/septic_hermite.hpp
+++ b/include/boost/math/interpolators/septic_hermite.hpp
@@ -57,5 +57,27 @@ private:
     std::shared_ptr<detail::cardinal_septic_hermite_detail<RandomAccessContainer>> impl_;
 };
 
+
+template<class RandomAccessContainer>
+class cardinal_septic_hermite_aos {
+public:
+    using Point = typename RandomAccessContainer::value_type;
+    using Real = typename Point::value_type;
+    cardinal_septic_hermite_aos(RandomAccessContainer && data, Real x0, Real dx)
+     : impl_(std::make_shared<detail::cardinal_septic_hermite_detail_aos<RandomAccessContainer>>(std::move(data), x0, dx))
+    {}
+
+    Real operator()(Real x) const {
+        return impl_->operator()(x);
+    }
+
+    Real prime(Real x) const {
+        return impl_->prime(x);
+    }
+
+private:
+    std::shared_ptr<detail::cardinal_septic_hermite_detail_aos<RandomAccessContainer>> impl_;
+};
+
 }
 #endif 
\ No newline at end of file
diff --git a/test/septic_hermite_test.cpp b/test/septic_hermite_test.cpp
index ed9772328..6a7c4c7ea 100644
--- a/test/septic_hermite_test.cpp
+++ b/test/septic_hermite_test.cpp
@@ -19,6 +19,7 @@ using boost::multiprecision::float128;
 
 using boost::math::interpolators::septic_hermite;
 using boost::math::interpolators::cardinal_septic_hermite;
+using boost::math::interpolators::cardinal_septic_hermite_aos;
 
 template<typename Real>
 void test_constant()
@@ -35,7 +36,8 @@ void test_constant()
 
     auto sh = septic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3));
 
-    for (Real t = 0; t <= 81; t += 0.25) {
+    for (Real t = 0; t <= 81; t += 0.25)
+    {
         CHECK_ULP_CLOSE(Real(7), sh(t), 24);
         CHECK_ULP_CLOSE(Real(0), sh.prime(t), 24);
     }
@@ -52,13 +54,27 @@ void test_constant()
         //CHECK_ULP_CLOSE(Real(0), csh.prime(t), 24);
     }
 
+    std::vector<std::array<Real, 4>> data(128);
+    for (size_t i = 0; i < data.size(); ++i)
+    {
+        data[i][0] = 7;
+        data[i][1] = 0;
+        data[i][2] = 0;
+        data[i][3] = 0;
+    }
+    auto csh_aos = cardinal_septic_hermite_aos(std::move(data), x0, dx);
+    for (Real t = x0; t <= 127; t += 0.25) {
+        CHECK_ULP_CLOSE(Real(7), csh_aos(t), 24);
+        //CHECK_ULP_CLOSE(Real(0), csh.prime(t), 24);
+    }
+
 }
 
 
 template<typename Real>
 void test_linear()
 {
-    std::vector<Real> x{0,1,2,3, 4,5,6,7,8,9};
+    std::vector<Real> x{0,1,2,3,4,5,6,7,8,9};
     std::vector<Real> y = x;
     std::vector<Real> dydx(x.size(), 1);
     std::vector<Real> d2ydx2(x.size(), 0);
@@ -88,9 +104,39 @@ void test_linear()
 
     sh = septic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3));
 
-    for (Real t = xmin; t <= xmax; t += 0.125) {
+    for (Real t = xmin; t <= xmax; t += 0.125)
+    {
         CHECK_ULP_CLOSE(t, sh(t), 15);
     }
+
+    Real x0 = 0;
+    Real dx = 1;
+    y.resize(10);
+    dydx.resize(10, 1);
+    d2ydx2.resize(10, 0);
+    d3ydx3.resize(10, 0);
+    for (size_t i = 0; i < y.size(); ++i) {
+        y[i] = i;
+    }
+    auto csh = cardinal_septic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3), x0, dx);
+    for (Real t = 0; t <= 9; t += 0.125)
+    {
+        CHECK_ULP_CLOSE(t, csh(t), 15);
+    }
+
+    std::vector<std::array<Real, 4>> data(10);
+    for (size_t i = 0; i < data.size(); ++i)
+    {
+        data[i][0] = i;
+        data[i][1] = 1;
+        data[i][2] = 0;
+        data[i][3] = 0;
+    }
+    auto csh_aos = cardinal_septic_hermite_aos(std::move(data), x0, dx);
+    for (Real t = 0; t <= 9; t += 0.125)
+    {
+        CHECK_ULP_CLOSE(t, csh_aos(t), 15);
+    }
 }
 
 template<typename Real>
@@ -148,8 +194,48 @@ void test_quadratic()
         CHECK_ULP_CLOSE(t*t/2, sh(t), 24);
         //CHECK_ULP_CLOSE(t, qh.prime(t), 36);
     }
+
+    y.resize(10);
+    for (size_t i = 0; i < y.size(); ++i)
+    {
+        y[i] = i*i/Real(2);
+    }
+
+    dydx.resize(y.size());
+    for (size_t i = 0; i < y.size(); ++i)
+    {
+        dydx[i] = i;
+    }
+
+    d2ydx2.resize(y.size(), 1);
+    d3ydx3.resize(y.size(), 0);
+
+    Real x0 = 0;
+    Real dx = 1;
+    auto csh = cardinal_septic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3), x0, dx);
+    for (Real t = x0; t <= 9; t += 0.125)
+    {
+        CHECK_ULP_CLOSE(t*t/2, csh(t), 24);
+    }
+
+    std::vector<std::array<Real, 4>> data(10);
+    for (size_t i = 0; i < data.size(); ++i)
+    {
+        data[i][0] = i*i/Real(2);
+        data[i][1] = i;
+        data[i][2] = 1;
+        data[i][3] = 0;
+    }
+    auto csh_aos = cardinal_septic_hermite_aos(std::move(data), x0, dx);
+    for (Real t = x0; t <= 9; t += 0.125)
+    {
+        CHECK_ULP_CLOSE(t*t/2, csh_aos(t), 24);
+    }
+
 }
 
+
+
 template<typename Real>
 void test_cubic()
 {

From 741696c7e730f32ded395289e74b8ea15f12554a Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Tue, 18 Feb 2020 06:20:30 -0500
Subject: [PATCH 035/104] Protect ourselves with a few more unit tests for
 septic_hermite [CI SKIP]

---
 .../detail/septic_hermite_detail.hpp          | 23 -------
 test/septic_hermite_test.cpp                  | 64 ++++++++++++++++++-
 2 files changed, 63 insertions(+), 24 deletions(-)

diff --git a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
index 122c2ae38..18e8e6c29 100644
--- a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
@@ -180,7 +180,6 @@ public:
         {
             throw std::domain_error("Number of third derivatives must equal number of ordinates.");
         }
-
         if (y_.size() < 2)
         {
             throw std::domain_error("At least 2 abscissas are required.");
@@ -199,7 +198,6 @@ public:
         {
             d2y *= (dx*dx/2);
         }
-
         for (auto & d3y : d3y_)
         {
             d3y *= (dx*dx*dx/6);
@@ -218,8 +216,6 @@ public:
                 << x0_ << ", " << xf << "]";
             throw std::domain_error(oss.str());
         }
-        // We need t := (x-x_k)/(x_{k+1}-x_k) \in [0,1) for this to work.
-        // Sadly this neccessitates this loathesome check, otherwise we get t = 1 at x = xf.
         if (x == xf)
         {
             return y_.back();
@@ -242,29 +238,19 @@ public:
         Real s = t4*(-35 + t*(84 + t*(-70 + 20*t)));
         Real z4 = -s;
         Real z0 = s + 1;
-        //Real z1 = t*(10*t6 - 36*t5 + 45*t4 - 20*t3 + 1);
         Real z1 = t*(1 + t3*(-20 + t*(45 + t*(-36+10*t))));
-        //Real z2 = t2*(4*t4*t - 15*t4 + 20*t3 - 10*t2 + 1);
         Real z2 = t2*(1 + t2*(-10 + t*(20 + t*(-15+4*t))));
-        //Real z3 = t3*(t4 - 4*t3 + 6*t2 - 4*t + 1);
         Real z3 = t3*(1 + t*(-4+t*(6+t*(-4+t))));
-
-        //Real z5 = t4*(10*t3 - 34*t2 + 39*t - 15);
         Real z5 = t4*(-15 + t*(39 + t*(-34 + 10*t)));
-        //Real z6 = t4*(-4*t3 + 13*t2 - 14*t + 5);
         Real z6 = t4*(5 + t*(-14 + t*(13-4*t)));
-        //Real z7 = t4*(t3 - 3*t2 + 3*t - 1);
         Real z7 = t4*(-1 + t*(3+t*(-3+t)));
 
         Real y0 = y_[i];
         Real y1 = y_[i+1];
-        // Velocity:
         Real dy0 = dy_[i];
         Real dy1 = dy_[i+1];
-        // Acceleration:
         Real a0 = d2y_[i];
         Real a1 = d2y_[i+1];
-        // Jerk:
         Real j0 = d3y_[i];
         Real j1 = d3y_[i+1];
 
@@ -347,8 +333,6 @@ public:
                 << x0_ << ", " << xf << "]";
             throw std::domain_error(oss.str());
         }
-        // We need t := (x-x_k)/(x_{k+1}-x_k) \in [0,1) for this to work.
-        // Sadly this neccessitates this loathesome check, otherwise we get t = 1 at x = xf.
         if (x == xf)
         {
             return data_.back()[0];
@@ -369,18 +353,11 @@ public:
         Real s = t4*(-35 + t*(84 + t*(-70 + 20*t)));
         Real z4 = -s;
         Real z0 = s + 1;
-        //Real z1 = t*(10*t6 - 36*t5 + 45*t4 - 20*t3 + 1);
         Real z1 = t*(1 + t3*(-20 + t*(45 + t*(-36+10*t))));
-        //Real z2 = t2*(4*t5 - 15*t4 + 20*t3 - 10*t2 + 1);
         Real z2 = t2*(1 + t2*(-10 + t*(20 + t*(-15+4*t))));
-        //Real z3 = t3*(t4 - 4*t3 + 6*t2 - 4*t + 1);
         Real z3 = t3*(1 + t*(-4+t*(6+t*(-4+t))));
-
-        //Real z5 = t4*(10*t3 - 34*t2 + 39*t - 15);
         Real z5 = t4*(-15 + t*(39 + t*(-34 + 10*t)));
-        //Real z6 = t4*(-4*t3 + 13*t2 - 14*t + 5);
         Real z6 = t4*(5 + t*(-14 + t*(13-4*t)));
-        //Real z7 = t4*(t3 - 3*t2 + 3*t - 1);
         Real z7 = t4*(-1 + t*(3+t*(-3+t)));
 
         Real y0 = data_[i][0];
diff --git a/test/septic_hermite_test.cpp b/test/septic_hermite_test.cpp
index 6a7c4c7ea..eacedf44f 100644
--- a/test/septic_hermite_test.cpp
+++ b/test/septic_hermite_test.cpp
@@ -231,7 +231,6 @@ void test_quadratic()
     {
         CHECK_ULP_CLOSE(t*t/2, csh_aos(t), 24);
     }
-
 }
 
 
@@ -264,6 +263,38 @@ void test_cubic()
     for (Real t = 0; t <= xmax; t += 0.0078125) {
         CHECK_ULP_CLOSE(t*t*t, sh(t), 151);
     }
+
+    Real x0 = 0;
+    Real dx = 1;
+    y.resize(8);
+    dydx.resize(8);
+    d2ydx2.resize(8);
+    d3ydx3.resize(8,6);
+    for (size_t i = 0; i < y.size(); ++i) {
+        y[i] = i*i*i;
+        dydx[i] = 3*i*i;
+        d2ydx2[i] = 6*i;
+    }
+
+    auto csh = cardinal_septic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3), x0, dx);
+
+    for (Real t = 0; t <= xmax; t += 0.0078125) {
+        CHECK_ULP_CLOSE(t*t*t, csh(t), 151);
+    }
+
+    std::vector<std::array<Real, 4>> data(8);
+    for (size_t i = 0; i < data.size(); ++i) {
+        data[i][0] = i*i*i;
+        data[i][1] = 3*i*i;
+        data[i][2] = 6*i;
+        data[i][3] = 6;
+    }
+
+    auto csh_aos = cardinal_septic_hermite_aos(std::move(data), x0, dx);
+
+    for (Real t = 0; t <= xmax; t += 0.0078125) {
+        CHECK_ULP_CLOSE(t*t*t, csh_aos(t), 151);
+    }
 }
 
 template<typename Real>
@@ -298,6 +329,37 @@ void test_quartic()
     for (Real t = 1; t <= xmax; t += 0.0078125) {
         CHECK_ULP_CLOSE(t*t*t*t, sh(t), 117);
     }
+
+    y.resize(10);
+    dydx.resize(10);
+    d2ydx2.resize(10);
+    d3ydx3.resize(10);
+    for (size_t i = 0; i < y.size(); ++i) {
+        y[i] = i*i*i*i;
+        dydx[i] = 4*i*i*i;
+        d2ydx2[i] = 12*i*i;
+        d3ydx3[i] = 24*i;
+    }
+
+    auto csh = cardinal_septic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3), Real(0), Real(1));
+
+    for (Real t = 1; t <= xmax; t += 0.0078125) {
+        CHECK_ULP_CLOSE(t*t*t*t, csh(t), 117);
+    }
+
+    std::vector<std::array<Real, 4>> data(10);
+    for (size_t i = 0; i < data.size(); ++i) {
+        data[i][0] = i*i*i*i;
+        data[i][1] = 4*i*i*i;
+        data[i][2] = 12*i*i;
+        data[i][3] = 24*i;
+    }
+
+    auto csh_aos = cardinal_septic_hermite_aos(std::move(data), Real(0), Real(1));
+    for (Real t = 1; t <= xmax; t += 0.0078125) {
+        CHECK_ULP_CLOSE(t*t*t*t, csh_aos(t), 117);
+    }
+
 }
 
 

From ab2e877315e45ffaba65a21af1c663829f4dcc0f Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Tue, 18 Feb 2020 07:01:02 -0500
Subject: [PATCH 036/104] Consolidate cubic_hermite.hpp and
 cardinal_cubic_hermite.hpp [CI SKIP]

---
 example/daubechies_wavelets/bench.cpp         |  52 +++-
 .../daubechies_wavelets/daubechies_plots.cpp  |   8 +-
 .../find_best_daubechies_interpolator.cpp     |   9 +-
 .../interpolators/cardinal_cubic_hermite.hpp  |  71 ------
 .../math/interpolators/cubic_hermite.hpp      |  57 +++++
 .../detail/cardinal_cubic_hermite_detail.hpp  | 233 ------------------
 .../detail/cubic_hermite_detail.hpp           | 221 +++++++++++++++++
 .../detail/septic_hermite_detail.hpp          |   2 +-
 .../special_functions/daubechies_scaling.hpp  |   2 +-
 test/cardinal_cubic_hermite_test.cpp          | 197 ---------------
 test/cubic_hermite_test.cpp                   | 171 +++++++++++++
 11 files changed, 505 insertions(+), 518 deletions(-)
 delete mode 100644 include/boost/math/interpolators/cardinal_cubic_hermite.hpp
 delete mode 100644 include/boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp
 delete mode 100644 test/cardinal_cubic_hermite_test.cpp

diff --git a/example/daubechies_wavelets/bench.cpp b/example/daubechies_wavelets/bench.cpp
index ab91a6a6f..69a01aaf9 100644
--- a/example/daubechies_wavelets/bench.cpp
+++ b/example/daubechies_wavelets/bench.cpp
@@ -10,7 +10,7 @@
 #include <benchmark/benchmark.h>
 #include <boost/random/uniform_real_distribution.hpp>
 #include <boost/math/special_functions/daubechies_scaling.hpp>
-#include <boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp>
+#include <boost/math/interpolators/detail/cubic_hermite_detail.hpp>
 #include <boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp>
 #include <boost/math/interpolators/detail/septic_hermite_detail.hpp>
 
@@ -72,6 +72,10 @@ BENCHMARK_TEMPLATE(ScalingEvaluation, double, 8);
 BENCHMARK_TEMPLATE(ScalingEvaluation, double, 9);
 BENCHMARK_TEMPLATE(ScalingEvaluation, double, 10);
 BENCHMARK_TEMPLATE(ScalingEvaluation, double, 11);
+BENCHMARK_TEMPLATE(ScalingEvaluation, double, 12);
+BENCHMARK_TEMPLATE(ScalingEvaluation, double, 13);
+BENCHMARK_TEMPLATE(ScalingEvaluation, double, 14);
+BENCHMARK_TEMPLATE(ScalingEvaluation, double, 15);
 
 
 template<typename Real, int p>
@@ -258,9 +262,8 @@ void CardinalQuinticHermite(benchmark::State & state)
     }
 }
 
-BENCHMARK_TEMPLATE(CardinalQuinticHermite, float)->RangeMultiplier(2)->Range(1<<8, 1<<22)->Complexity();
-BENCHMARK_TEMPLATE(CardinalQuinticHermite, double)->RangeMultiplier(2)->Range(1<<8, 1<<22)->Complexity();
-BENCHMARK_TEMPLATE(CardinalQuinticHermite, long double)->RangeMultiplier(2)->Range(1<<8, 1<<22)->Complexity();
+BENCHMARK_TEMPLATE(CardinalQuinticHermite, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity();
+
 
 
 template<typename Real>
@@ -293,9 +296,7 @@ void CardinalQuinticHermiteAOS(benchmark::State & state)
     }
 }
 
-BENCHMARK_TEMPLATE(CardinalQuinticHermiteAOS, float)->RangeMultiplier(2)->Range(1<<8, 1<<22)->Complexity();
-BENCHMARK_TEMPLATE(CardinalQuinticHermiteAOS, double)->RangeMultiplier(2)->Range(1<<8, 1<<22)->Complexity();
-BENCHMARK_TEMPLATE(CardinalQuinticHermiteAOS, long double)->RangeMultiplier(2)->Range(1<<8, 1<<22)->Complexity();
+BENCHMARK_TEMPLATE(CardinalQuinticHermiteAOS, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity();
 
 
 template<typename Real>
@@ -334,7 +335,42 @@ void CardinalSepticHermite(benchmark::State & state)
     }
 }
 
-BENCHMARK_TEMPLATE(CardinalSepticHermite, double)->RangeMultiplier(2)->Range(1<<8, 1<<22)->Complexity();
+BENCHMARK_TEMPLATE(CardinalSepticHermite, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity();
+
+template<typename Real>
+void CardinalSepticHermiteAOS(benchmark::State & state)
+{
+    using boost::math::interpolators::detail::cardinal_septic_hermite_detail_aos;
+    auto n = state.range(0);
+    std::vector<std::array<Real, 4>> data(n);
+    std::random_device rd;
+    boost::random::uniform_real_distribution<Real> dis(Real(0), Real(1));
+    for (size_t i = 0; i < data.size(); ++i)
+    {
+        for (size_t j = 0; j < 4; ++j)
+        {
+            data[i][j] = dis(rd);
+        }
+    }
+
+    Real dx = Real(1)/Real(8);
+    Real x0 = 0;
+    Real xf = x0 + (data.size()-1)*dx;
+
+    auto sh = cardinal_septic_hermite_detail_aos(std::move(data), x0, dx);
+    Real x = 0;
+    for (auto _ : state)
+    {
+        benchmark::DoNotOptimize(sh.unchecked_evaluation(x));
+        x += xf/128;
+        if (x >= xf)
+        {
+            x = x0;
+        }
+    }
+}
+
+BENCHMARK_TEMPLATE(CardinalSepticHermiteAOS, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity();
 
 
 BENCHMARK_MAIN();
\ No newline at end of file
diff --git a/example/daubechies_wavelets/daubechies_plots.cpp b/example/daubechies_wavelets/daubechies_plots.cpp
index 4250dafa3..8f843bc23 100644
--- a/example/daubechies_wavelets/daubechies_plots.cpp
+++ b/example/daubechies_wavelets/daubechies_plots.cpp
@@ -127,7 +127,7 @@ int main()
     plot_phi<double, 2>();
     plot_phi<double, 3>();
     plot_phi<double, 4>();
-    plot_phi<double, 5>();
+    //plot_phi<double, 5>();
     plot_phi<double, 6>();
     plot_phi<double, 7>();
     plot_phi<double, 8>();
@@ -150,9 +150,9 @@ int main()
     plot_condition_number<long double, 13>();
 
     using PreciseReal = float128;
-    using CoarseReal = long double;
-    int precise_refinements = 21;
-    constexpr const int p = 9;
+    using CoarseReal = double;
+    int precise_refinements = 22;
+    constexpr const int p = 12;
     std::cout << "Computing precise scaling function in " << boost::core::demangle(typeid(PreciseReal).name()) << " precision.\n";
     auto phi_precise = boost::math::daubechies_scaling<PreciseReal, p>(precise_refinements);
     std::cout << "Beginning comparison with functions computed in " << boost::core::demangle(typeid(CoarseReal).name()) << " precision.\n";
diff --git a/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp b/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
index e6e87f89a..46d8a14f5 100644
--- a/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
+++ b/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
@@ -1,3 +1,9 @@
+// Copyright Nick Thompson, 2020
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
 #include <iostream>
 #include <unordered_map>
 #include <string>
@@ -7,7 +13,6 @@
 #include <boost/math/special_functions/daubechies_scaling.hpp>
 #include <boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp>
 #include <boost/math/interpolators/cubic_hermite.hpp>
-#include <boost/math/interpolators/cardinal_cubic_hermite.hpp>
 #include <boost/math/interpolators/quintic_hermite.hpp>
 #include <boost/math/interpolators/cardinal_quintic_hermite.hpp>
 #include <boost/math/interpolators/septic_hermite.hpp>
@@ -21,8 +26,6 @@
 #include <boost/math/interpolators/pchip.hpp>
 #include <boost/multiprecision/float128.hpp>
 #include <boost/core/demangle.hpp>
-//#include <quicksvg/graph_fn.hpp>
-//#include <quicksvg/ulp_plot.hpp>
 
 using boost::multiprecision::float128;
 
diff --git a/include/boost/math/interpolators/cardinal_cubic_hermite.hpp b/include/boost/math/interpolators/cardinal_cubic_hermite.hpp
deleted file mode 100644
index f5a502990..000000000
--- a/include/boost/math/interpolators/cardinal_cubic_hermite.hpp
+++ /dev/null
@@ -1,71 +0,0 @@
-// Copyright Nick Thompson, 2020
-// Use, modification and distribution are subject to the
-// Boost Software License, Version 1.0.
-// (See accompanying file LICENSE_1_0.txt
-// or copy at http://www.boost.org/LICENSE_1_0.txt)
-
-#ifndef BOOST_MATH_INTERPOLATORS_CARDINAL_CUBIC_HERMITE_HPP
-#define BOOST_MATH_INTERPOLATORS_CARDINAL_CUBIC_HERMITE_HPP
-#include <memory>
-#include <boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp>
-
-namespace boost::math::interpolators {
-
-template<class RandomAccessContainer>
-class cardinal_cubic_hermite {
-public:
-    using Real = typename RandomAccessContainer::value_type;
-
-    cardinal_cubic_hermite(RandomAccessContainer && y, RandomAccessContainer && dydx, Real x0, Real dx) 
-    : impl_(std::make_shared<detail::cardinal_cubic_hermite_detail<RandomAccessContainer>>(std::move(y), std::move(dydx), x0, dx))
-    {}
-
-    inline Real operator()(Real x) const {
-        return impl_->operator()(x);
-    }
-
-    inline Real prime(Real x) const {
-        return impl_->prime(x);
-    }
-
-    friend std::ostream& operator<<(std::ostream & os, const cardinal_cubic_hermite & m)
-    {
-        os << *m.impl_;
-        return os;
-    }
-
-private:
-    std::shared_ptr<detail::cardinal_cubic_hermite_detail<RandomAccessContainer>> impl_;
-};
-
-
-template<class RandomAccessContainer>
-class cardinal_cubic_hermite_aos {
-public:
-    using Point = typename RandomAccessContainer::value_type;
-    using Real = typename Point::value_type;
-
-    cardinal_cubic_hermite_aos(RandomAccessContainer && data, Real x0, Real dx) 
-    : impl_(std::make_shared<detail::cardinal_cubic_hermite_detail_aos<RandomAccessContainer>>(std::move(data), x0, dx))
-    {}
-
-    inline Real operator()(Real x) const {
-        return impl_->operator()(x);
-    }
-
-    inline Real prime(Real x) const {
-        return impl_->prime(x);
-    }
-
-    friend std::ostream& operator<<(std::ostream & os, const cardinal_cubic_hermite_aos & m)
-    {
-        os << *m.impl_;
-        return os;
-    }
-
-private:
-    std::shared_ptr<detail::cardinal_cubic_hermite_detail_aos<RandomAccessContainer>> impl_;
-};
-
-}
-#endif
\ No newline at end of file
diff --git a/include/boost/math/interpolators/cubic_hermite.hpp b/include/boost/math/interpolators/cubic_hermite.hpp
index 678590658..79aea2b9e 100644
--- a/include/boost/math/interpolators/cubic_hermite.hpp
+++ b/include/boost/math/interpolators/cubic_hermite.hpp
@@ -42,5 +42,62 @@ private:
     std::shared_ptr<detail::cubic_hermite_detail<RandomAccessContainer>> impl_;
 };
 
+template<class RandomAccessContainer>
+class cardinal_cubic_hermite {
+public:
+    using Real = typename RandomAccessContainer::value_type;
+
+    cardinal_cubic_hermite(RandomAccessContainer && y, RandomAccessContainer && dydx, Real x0, Real dx) 
+    : impl_(std::make_shared<detail::cardinal_cubic_hermite_detail<RandomAccessContainer>>(std::move(y), std::move(dydx), x0, dx))
+    {}
+
+    inline Real operator()(Real x) const {
+        return impl_->operator()(x);
+    }
+
+    inline Real prime(Real x) const {
+        return impl_->prime(x);
+    }
+
+    friend std::ostream& operator<<(std::ostream & os, const cardinal_cubic_hermite & m)
+    {
+        os << *m.impl_;
+        return os;
+    }
+
+private:
+    std::shared_ptr<detail::cardinal_cubic_hermite_detail<RandomAccessContainer>> impl_;
+};
+
+
+template<class RandomAccessContainer>
+class cardinal_cubic_hermite_aos {
+public:
+    using Point = typename RandomAccessContainer::value_type;
+    using Real = typename Point::value_type;
+
+    cardinal_cubic_hermite_aos(RandomAccessContainer && data, Real x0, Real dx) 
+    : impl_(std::make_shared<detail::cardinal_cubic_hermite_detail_aos<RandomAccessContainer>>(std::move(data), x0, dx))
+    {}
+
+    inline Real operator()(Real x) const {
+        return impl_->operator()(x);
+    }
+
+    inline Real prime(Real x) const {
+        return impl_->prime(x);
+    }
+
+    friend std::ostream& operator<<(std::ostream & os, const cardinal_cubic_hermite_aos & m)
+    {
+        os << *m.impl_;
+        return os;
+    }
+
+private:
+    std::shared_ptr<detail::cardinal_cubic_hermite_detail_aos<RandomAccessContainer>> impl_;
+};
+
+
 }
 #endif
\ No newline at end of file
diff --git a/include/boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp b/include/boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp
deleted file mode 100644
index eb8167edd..000000000
--- a/include/boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp
+++ /dev/null
@@ -1,233 +0,0 @@
-#ifndef BOOST_MATH_INTERPOLATORS_DETAIL_CARDINAL_CUBIC_HERMITE_DETAIL_HPP
-#define BOOST_MATH_INTERPOLATORS_DETAIL_CARDINAL_CUBIC_HERMITE_DETAIL_HPP
-#include <stdexcept>
-#include <algorithm>
-#include <cmath>
-#include <iostream>
-#include <sstream>
-#include <limits>
-
-namespace boost::math::interpolators::detail {
-
-template<class RandomAccessContainer>
-class cardinal_cubic_hermite_detail {
-public:
-    using Real = typename RandomAccessContainer::value_type;
-
-    cardinal_cubic_hermite_detail(RandomAccessContainer && y, RandomAccessContainer dydx, Real x0, Real dx)
-    : y_{std::move(y)}, dy_{std::move(dydx)}, x0_{x0}, inv_dx_{1/dx}
-    {
-        using std::abs;
-        using std::isnan;
-        if (y_.size() != dy_.size())
-        {
-            throw std::domain_error("There must be the same number of derivatives as ordinates.");
-        }
-        if (y_.size() < 2)
-        {
-            throw std::domain_error("Must be at least two data points.");
-        }
-        if (dx <= 0)
-        {
-            throw std::domain_error("dx > 0 is required.");
-        }
-
-        for (auto & dy : dy_)
-        {
-            dy *= dx;
-        }
-    }
-
-    // Why not implement push_back? It's awkward: If the buffer is circular, x0_ += dx_.
-    // If the buffer is not circular, x0_ is unchanged.
-    // We need a concept for circular_buffer!
-
-    inline Real operator()(Real x) const {
-        const Real xf = x0_ + (y_.size()-1)/inv_dx_;
-        if  (x < x0_ || x > xf)
-        {
-            std::ostringstream oss;
-            oss.precision(std::numeric_limits<Real>::digits10+3);
-            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
-                << x0_ << ", " << xf << "]";
-            throw std::domain_error(oss.str());
-        }
-        if (x == xf)
-        {
-            return y_.back();
-        }
-        return this->unchecked_evaluation(x);
-    }
-
-    inline Real unchecked_evaluation(Real x) const
-    {
-        using std::floor;
-        Real s = (x-x0_)*inv_dx_;
-        Real ii = floor(s);
-        auto i = static_cast<decltype(y_.size())>(ii);
-        Real t = s - ii;
-        Real y0 = y_[i];
-        Real y1 = y_[i+1];
-        Real dy0 = dy_[i];
-        Real dy1 = dy_[i+1];
-
-        Real r = 1-t;
-        return r*r*(y0*(1+2*t) + dy0*t)
-              + t*t*(y1*(3-2*t) - dy1*r);
-    }
-
-    inline Real prime(Real x) const {
-        const Real xf = x0_ + (y_.size()-1)/inv_dx_;
-        if  (x < x0_ || x > xf)
-        {
-            std::ostringstream oss;
-            oss.precision(std::numeric_limits<Real>::digits10+3);
-            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
-                << x0_ << ", " << xf << "]";
-            throw std::domain_error(oss.str());
-        }
-        if (x == xf)
-        {
-            return dy_.back()*inv_dx_;
-        }
-        return this->unchecked_prime(x);
-    }
-
-    inline Real unchecked_prime(Real x) const {
-        using std::floor;
-        Real s = (x-x0_)*inv_dx_;
-        Real ii = floor(s);
-        auto i = static_cast<decltype(y_.size())>(ii);
-        Real t = s - ii;
-        Real y0 = y_[i];
-        Real y1 = y_[i+1];
-        Real dy0 = dy_[i];
-        Real dy1 = dy_[i+1];
-
-        Real dy = 6*t*(1-t)*(y1 - y0)  + (3*t*t - 4*t+1)*dy0 + t*(3*t-2)*dy1;
-        return dy*inv_dx_;
-    }
-
-
-    auto size() const
-    {
-        return y_.size();
-    }
-
-    RandomAccessContainer y_;
-    RandomAccessContainer dy_;
-    Real x0_;
-    Real inv_dx_;
-};
-
-
-template<class RandomAccessContainer>
-class cardinal_cubic_hermite_detail_aos {
-public:
-    using Point = typename RandomAccessContainer::value_type;
-    using Real = typename Point::value_type;
-
-    cardinal_cubic_hermite_detail_aos(RandomAccessContainer && dat, Real x0, Real dx)
-    : dat_{std::move(dat)}, x0_{x0}, inv_dx_{1/dx}
-    {
-        if (dat_.size() < 2)
-        {
-            throw std::domain_error("Must be at least two data points.");
-        }
-        if (dat_[0].size() != 2)
-        {
-            throw std::domain_error("Each datum must contain (y, y'), and nothing else.");
-        }
-        if (dx <= 0)
-        {
-            throw std::domain_error("dx > 0 is required.");
-        }
-
-        for (auto & d : dat_)
-        {
-            d[1] *= dx;
-        }
-    }
-
-    inline Real operator()(Real x) const {
-        const Real xf = x0_ + (dat_.size()-1)/inv_dx_;
-        if  (x < x0_ || x > xf)
-        {
-            std::ostringstream oss;
-            oss.precision(std::numeric_limits<Real>::digits10+3);
-            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
-                << x0_ << ", " << xf << "]";
-            throw std::domain_error(oss.str());
-        }
-        if (x == xf)
-        {
-            return dat_.back()[0];
-        }
-        return this->unchecked_evaluation(x);
-    }
-
-    inline Real unchecked_evaluation(Real x) const
-    {
-        using std::floor;
-        Real s = (x-x0_)*inv_dx_;
-        Real ii = floor(s);
-        auto i = static_cast<decltype(dat_.size())>(ii);
-
-        Real t = s - ii;
-        Real y0 = dat_[i][0];
-        Real y1 = dat_[i+1][0];
-        Real dy0 = dat_[i][1];
-        Real dy1 = dat_[i+1][1];
-
-        Real r = 1-t;
-        return r*r*(y0*(1+2*t) + dy0*t)
-              + t*t*(y1*(3-2*t) - dy1*r);
-    }
-
-    inline Real prime(Real x) const {
-        const Real xf = x0_ + (dat_.size()-1)/inv_dx_;
-        if  (x < x0_ || x > xf)
-        {
-            std::ostringstream oss;
-            oss.precision(std::numeric_limits<Real>::digits10+3);
-            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
-                << x0_ << ", " << xf << "]";
-            throw std::domain_error(oss.str());
-        }
-        if (x == xf)
-        {
-            return dat_.back()[1];
-        }
-        return this->unchecked_prime(x);
-    }
-
-    inline Real unchecked_prime(Real x) const
-    {
-        using std::floor;
-        Real s = (x-x0_)*inv_dx_;
-        Real ii = floor(s);
-        auto i = static_cast<decltype(dat_.size())>(ii);
-        Real t = s - ii;
-        Real y0 = dat_[i][0];
-        Real dy0 = dat_[i][1];
-        Real y1 = dat_[i+1][0];
-        Real dy1 = dat_[i+1][1];
-
-        Real dy = 6*t*(1-t)*(y1 - y0)  + (3*t*t - 4*t+1)*dy0 + t*(3*t-2)*dy1;
-        return dy*inv_dx_;
-    }
-
-
-    auto size() const
-    {
-        return dat_.size();
-    }
-
-    RandomAccessContainer dat_;
-    Real x0_;
-    Real inv_dx_;
-};
-
-
-}
-#endif
\ No newline at end of file
diff --git a/include/boost/math/interpolators/detail/cubic_hermite_detail.hpp b/include/boost/math/interpolators/detail/cubic_hermite_detail.hpp
index 6cce795f7..231b9177f 100644
--- a/include/boost/math/interpolators/detail/cubic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/cubic_hermite_detail.hpp
@@ -156,5 +156,226 @@ public:
     RandomAccessContainer y_;
     RandomAccessContainer dydx_;
 };
+
+template<class RandomAccessContainer>
+class cardinal_cubic_hermite_detail {
+public:
+    using Real = typename RandomAccessContainer::value_type;
+
+    cardinal_cubic_hermite_detail(RandomAccessContainer && y, RandomAccessContainer dydx, Real x0, Real dx)
+    : y_{std::move(y)}, dy_{std::move(dydx)}, x0_{x0}, inv_dx_{1/dx}
+    {
+        using std::abs;
+        using std::isnan;
+        if (y_.size() != dy_.size())
+        {
+            throw std::domain_error("There must be the same number of derivatives as ordinates.");
+        }
+        if (y_.size() < 2)
+        {
+            throw std::domain_error("Must be at least two data points.");
+        }
+        if (dx <= 0)
+        {
+            throw std::domain_error("dx > 0 is required.");
+        }
+
+        for (auto & dy : dy_)
+        {
+            dy *= dx;
+        }
+    }
+
+    // Why not implement push_back? It's awkward: If the buffer is circular, x0_ += dx_.
+    // If the buffer is not circular, x0_ is unchanged.
+    // We need a concept for circular_buffer!
+
+    inline Real operator()(Real x) const {
+        const Real xf = x0_ + (y_.size()-1)/inv_dx_;
+        if  (x < x0_ || x > xf)
+        {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf)
+        {
+            return y_.back();
+        }
+        return this->unchecked_evaluation(x);
+    }
+
+    inline Real unchecked_evaluation(Real x) const
+    {
+        using std::floor;
+        Real s = (x-x0_)*inv_dx_;
+        Real ii = floor(s);
+        auto i = static_cast<decltype(y_.size())>(ii);
+        Real t = s - ii;
+        Real y0 = y_[i];
+        Real y1 = y_[i+1];
+        Real dy0 = dy_[i];
+        Real dy1 = dy_[i+1];
+
+        Real r = 1-t;
+        return r*r*(y0*(1+2*t) + dy0*t)
+              + t*t*(y1*(3-2*t) - dy1*r);
+    }
+
+    inline Real prime(Real x) const {
+        const Real xf = x0_ + (y_.size()-1)/inv_dx_;
+        if  (x < x0_ || x > xf)
+        {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf)
+        {
+            return dy_.back()*inv_dx_;
+        }
+        return this->unchecked_prime(x);
+    }
+
+    inline Real unchecked_prime(Real x) const {
+        using std::floor;
+        Real s = (x-x0_)*inv_dx_;
+        Real ii = floor(s);
+        auto i = static_cast<decltype(y_.size())>(ii);
+        Real t = s - ii;
+        Real y0 = y_[i];
+        Real y1 = y_[i+1];
+        Real dy0 = dy_[i];
+        Real dy1 = dy_[i+1];
+
+        Real dy = 6*t*(1-t)*(y1 - y0)  + (3*t*t - 4*t+1)*dy0 + t*(3*t-2)*dy1;
+        return dy*inv_dx_;
+    }
+
+
+    auto size() const
+    {
+        return y_.size();
+    }
+
+    RandomAccessContainer y_;
+    RandomAccessContainer dy_;
+    Real x0_;
+    Real inv_dx_;
+};
+
+
+template<class RandomAccessContainer>
+class cardinal_cubic_hermite_detail_aos {
+public:
+    using Point = typename RandomAccessContainer::value_type;
+    using Real = typename Point::value_type;
+
+    cardinal_cubic_hermite_detail_aos(RandomAccessContainer && dat, Real x0, Real dx)
+    : dat_{std::move(dat)}, x0_{x0}, inv_dx_{1/dx}
+    {
+        if (dat_.size() < 2)
+        {
+            throw std::domain_error("Must be at least two data points.");
+        }
+        if (dat_[0].size() != 2)
+        {
+            throw std::domain_error("Each datum must contain (y, y'), and nothing else.");
+        }
+        if (dx <= 0)
+        {
+            throw std::domain_error("dx > 0 is required.");
+        }
+
+        for (auto & d : dat_)
+        {
+            d[1] *= dx;
+        }
+    }
+
+    inline Real operator()(Real x) const {
+        const Real xf = x0_ + (dat_.size()-1)/inv_dx_;
+        if  (x < x0_ || x > xf)
+        {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf)
+        {
+            return dat_.back()[0];
+        }
+        return this->unchecked_evaluation(x);
+    }
+
+    inline Real unchecked_evaluation(Real x) const
+    {
+        using std::floor;
+        Real s = (x-x0_)*inv_dx_;
+        Real ii = floor(s);
+        auto i = static_cast<decltype(dat_.size())>(ii);
+
+        Real t = s - ii;
+        Real y0 = dat_[i][0];
+        Real y1 = dat_[i+1][0];
+        Real dy0 = dat_[i][1];
+        Real dy1 = dat_[i+1][1];
+
+        Real r = 1-t;
+        return r*r*(y0*(1+2*t) + dy0*t)
+              + t*t*(y1*(3-2*t) - dy1*r);
+    }
+
+    inline Real prime(Real x) const {
+        const Real xf = x0_ + (dat_.size()-1)/inv_dx_;
+        if  (x < x0_ || x > xf)
+        {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf)
+        {
+            return dat_.back()[1];
+        }
+        return this->unchecked_prime(x);
+    }
+
+    inline Real unchecked_prime(Real x) const
+    {
+        using std::floor;
+        Real s = (x-x0_)*inv_dx_;
+        Real ii = floor(s);
+        auto i = static_cast<decltype(dat_.size())>(ii);
+        Real t = s - ii;
+        Real y0 = dat_[i][0];
+        Real dy0 = dat_[i][1];
+        Real y1 = dat_[i+1][0];
+        Real dy1 = dat_[i+1][1];
+
+        Real dy = 6*t*(1-t)*(y1 - y0)  + (3*t*t - 4*t+1)*dy0 + t*(3*t-2)*dy1;
+        return dy*inv_dx_;
+    }
+
+
+    auto size() const
+    {
+        return dat_.size();
+    }
+
+    RandomAccessContainer dat_;
+    Real x0_;
+    Real inv_dx_;
+};
+
+
 }
 #endif
diff --git a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
index 18e8e6c29..87ceffe23 100644
--- a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
@@ -281,7 +281,7 @@ public:
         Real s3 = (x-x0_)*inv_dx_;
         Real ii = floor(s3);
         auto i = static_cast<decltype(y_.size())>(ii);
-        Real t = s3 - ii;
+        //Real t = s3 - ii;
 
         // Velocity:
         Real v0 = dy_[i];
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index c6f973e04..5d7ff0140 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -19,7 +19,7 @@
 #include <boost/math/constants/constants.hpp>
 #include <boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp>
 #include <boost/math/filters/daubechies.hpp>
-#include <boost/math/interpolators/detail/cardinal_cubic_hermite_detail.hpp>
+#include <boost/math/interpolators/detail/cubic_hermite_detail.hpp>
 #include <boost/math/interpolators/detail/quintic_hermite_detail.hpp>
 #include <boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp>
 #include <boost/math/interpolators/detail/septic_hermite_detail.hpp>
diff --git a/test/cardinal_cubic_hermite_test.cpp b/test/cardinal_cubic_hermite_test.cpp
deleted file mode 100644
index b3998b964..000000000
--- a/test/cardinal_cubic_hermite_test.cpp
+++ /dev/null
@@ -1,197 +0,0 @@
-/*
- * Copyright Nick Thompson, 2020
- * Use, modification and distribution are subject to the
- * Boost Software License, Version 1.0. (See accompanying file
- * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
- */
-
-#include "math_unit_test.hpp"
-#include <numeric>
-#include <utility>
-#include <random>
-#include <vector>
-#include <array>
-#include <boost/math/interpolators/cardinal_cubic_hermite.hpp>
-#ifdef BOOST_HAS_FLOAT128
-#include <boost/multiprecision/float128.hpp>
-using boost::multiprecision::float128;
-#endif
-
-
-using boost::math::interpolators::cardinal_cubic_hermite;
-using boost::math::interpolators::cardinal_cubic_hermite_aos;
-
-template<typename Real>
-void test_constant()
-{
-    Real x0 = 0;
-    Real dx = 2;
-    std::vector<Real> y(25);
-    for (auto & t : y) {
-        t = 7;
-    }
-
-    std::vector<Real> dydx(y.size(), Real(0));
-
-    auto hermite_spline = cardinal_cubic_hermite(std::move(y), std::move(dydx), x0, dx);
-
-    for (Real t = x0; t <= x0 + 24*dx; t += 0.25) {
-        CHECK_ULP_CLOSE(Real(7), hermite_spline(t), 2);
-        CHECK_ULP_CLOSE(Real(0), hermite_spline.prime(t), 2);
-    }
-
-    // Array of structs:
-
-    std::vector<std::array<Real, 2>> data(25);
-    for (auto & t : data) {
-        t[0] = 7;
-        t[1] = 0;
-    }
-    auto hermite_spline_aos = cardinal_cubic_hermite_aos(std::move(data), x0, dx);
-
-    for (Real t = x0; t <= x0 + 24*dx; t += 0.25) {
-        CHECK_ULP_CLOSE(Real(7), hermite_spline_aos(t), 2);
-        CHECK_ULP_CLOSE(Real(0), hermite_spline_aos.prime(t), 2);
-    }
- 
-}
-
-
-template<typename Real>
-void test_linear()
-{
-    Real x0 = 0;
-    Real dx = 1;
-    std::vector<Real> y{0,1,2,3};
-    std::vector<Real> dydx{1,1,1,1};
-    auto y_copy = y;
-    auto dydx_copy = dydx;
-    auto hermite_spline = cardinal_cubic_hermite(std::move(y_copy), std::move(dydx_copy), x0, dx);
-
-    CHECK_ULP_CLOSE(y[0], hermite_spline(0), 0);
-    CHECK_ULP_CLOSE(Real(1)/Real(2), hermite_spline(Real(1)/Real(2)), 10);
-    CHECK_ULP_CLOSE(y[1], hermite_spline(1), 0);
-    CHECK_ULP_CLOSE(Real(3)/Real(2), hermite_spline(Real(3)/Real(2)), 10);
-    CHECK_ULP_CLOSE(y[2], hermite_spline(2), 0);
-    CHECK_ULP_CLOSE(Real(5)/Real(2), hermite_spline(Real(5)/Real(2)), 10);
-    CHECK_ULP_CLOSE(y[3], hermite_spline(3), 0);
-
-
-    y.resize(45);
-    dydx.resize(45);
-    for (size_t i = 0; i < y.size(); ++i) {
-        y[i] = i;
-        dydx[i] = 1;
-    }
-
-    hermite_spline = cardinal_cubic_hermite(std::move(y), std::move(dydx), x0, dx);
-    for (Real t = 0; t < 44; t += 0.5) {
-        CHECK_ULP_CLOSE(t, hermite_spline(t), 0);
-        CHECK_ULP_CLOSE(Real(1), hermite_spline.prime(t), 0);
-    }
-
-    std::vector<std::array<Real, 2>> data(45);
-    for (size_t i = 0; i < data.size(); ++i) {
-        data[i][0] = i;
-        data[i][1] = 1;
-    }
-
-    auto hermite_spline_aos = cardinal_cubic_hermite_aos(std::move(data), x0, dx);
-    for (Real t = 0; t < 44; t += 0.5) {
-        CHECK_ULP_CLOSE(t, hermite_spline_aos(t), 0);
-        CHECK_ULP_CLOSE(Real(1), hermite_spline_aos.prime(t), 0);
-    }
-
-
-}
-
-
-template<typename Real>
-void test_quadratic()
-{
-    Real x0 = -1;
-    Real dx = Real(1)/Real(256);
-
-    std::vector<Real> y(50);
-    std::vector<Real> dydx(y.size());
-    for (size_t i = 0; i < y.size(); ++i) {
-        Real x = x0 + i*dx;
-        y[i] = x*x/2;
-        dydx[i] = x;
-    }
-
-    auto s = cardinal_cubic_hermite(std::move(y), std::move(dydx), x0, dx);
-    for (Real t = x0; t <= x0 + 49*dx; t+= 0.0125)
-    {
-        CHECK_ULP_CLOSE(t*t/2, s(t), 12);
-        CHECK_ULP_CLOSE(t, s.prime(t), 70);
-    }
-
-    std::vector<std::array<Real, 2>> data(50);
-    for (size_t i = 0; i < data.size(); ++i) {
-        Real x = x0 + i*dx;
-        data[i][0] = x*x/2;
-        data[i][1] = x;
-    }
-
-
-    auto saos = cardinal_cubic_hermite_aos(std::move(data), x0, dx);
-    for (Real t = x0; t <= x0 + 49*dx; t+= 0.0125)
-    {
-        CHECK_ULP_CLOSE(t*t/2, saos(t), 12);
-        CHECK_ULP_CLOSE(t, saos.prime(t), 70);
-    }
-
-}
-
-
-template<typename Real>
-void test_interpolation_condition()
-{
-    for (size_t n = 4; n < 50; ++n) {
-        std::vector<Real> y(n);
-        std::vector<Real> dydx(n);
-        std::default_random_engine rd;
-        std::uniform_real_distribution<Real> dis(0.1,1);
-        Real x0 = Real(2);
-        Real dx = Real(1)/Real(128);
-        for (size_t i = 0; i < n; ++i) {
-            y[i] = dis(rd);
-            dydx[i] = dis(rd);
-        }
-
-        auto y_copy = y;
-        auto dydx_copy = dydx;
-        auto s = cardinal_cubic_hermite(std::move(y_copy), std::move(dydx_copy), x0, dx);
-        for (size_t i = 0; i < y.size(); ++i) {
-            CHECK_ULP_CLOSE(y[i], s(x0 + i*dx), 2);
-            CHECK_ULP_CLOSE(dydx[i], s.prime(x0 + i*dx), 2);
-        }
-    }
-}
-
-int main()
-{
-    test_constant<float>();
-    test_constant<double>();
-    test_constant<long double>();
-
-    test_linear<float>();
-    test_linear<double>();
-    test_linear<long double>();
-
-    test_quadratic<float>();
-    test_quadratic<double>();
-    test_quadratic<long double>();
-
-    test_interpolation_condition<float>();
-    test_interpolation_condition<double>();
-    test_interpolation_condition<long double>();
-#ifdef BOOST_HAS_FLOAT128
-    test_constant<float128>();
-    test_linear<float128>();
-    test_quadratic<float128>();
-#endif
-
-    return boost::math::test::report_errors();
-}
diff --git a/test/cubic_hermite_test.cpp b/test/cubic_hermite_test.cpp
index 554ff07bc..8b1636768 100644
--- a/test/cubic_hermite_test.cpp
+++ b/test/cubic_hermite_test.cpp
@@ -18,6 +18,9 @@ using boost::multiprecision::float128;
 
 
 using boost::math::interpolators::cubic_hermite;
+using boost::math::interpolators::cardinal_cubic_hermite;
+using boost::math::interpolators::cardinal_cubic_hermite_aos;
+
 
 template<typename Real>
 void test_constant()
@@ -192,27 +195,195 @@ void test_interpolation_condition()
     }
 }
 
+template<typename Real>
+void test_cardinal_constant()
+{
+    Real x0 = 0;
+    Real dx = 2;
+    std::vector<Real> y(25);
+    for (auto & t : y) {
+        t = 7;
+    }
+
+    std::vector<Real> dydx(y.size(), Real(0));
+
+    auto hermite_spline = cardinal_cubic_hermite(std::move(y), std::move(dydx), x0, dx);
+
+    for (Real t = x0; t <= x0 + 24*dx; t += 0.25) {
+        CHECK_ULP_CLOSE(Real(7), hermite_spline(t), 2);
+        CHECK_ULP_CLOSE(Real(0), hermite_spline.prime(t), 2);
+    }
+
+    // Array of structs:
+
+    std::vector<std::array<Real, 2>> data(25);
+    for (auto & t : data) {
+        t[0] = 7;
+        t[1] = 0;
+    }
+    auto hermite_spline_aos = cardinal_cubic_hermite_aos(std::move(data), x0, dx);
+
+    for (Real t = x0; t <= x0 + 24*dx; t += 0.25) {
+        CHECK_ULP_CLOSE(Real(7), hermite_spline_aos(t), 2);
+        CHECK_ULP_CLOSE(Real(0), hermite_spline_aos.prime(t), 2);
+    }
+ 
+}
+
+
+template<typename Real>
+void test_cardinal_linear()
+{
+    Real x0 = 0;
+    Real dx = 1;
+    std::vector<Real> y{0,1,2,3};
+    std::vector<Real> dydx{1,1,1,1};
+    auto y_copy = y;
+    auto dydx_copy = dydx;
+    auto hermite_spline = cardinal_cubic_hermite(std::move(y_copy), std::move(dydx_copy), x0, dx);
+
+    CHECK_ULP_CLOSE(y[0], hermite_spline(0), 0);
+    CHECK_ULP_CLOSE(Real(1)/Real(2), hermite_spline(Real(1)/Real(2)), 10);
+    CHECK_ULP_CLOSE(y[1], hermite_spline(1), 0);
+    CHECK_ULP_CLOSE(Real(3)/Real(2), hermite_spline(Real(3)/Real(2)), 10);
+    CHECK_ULP_CLOSE(y[2], hermite_spline(2), 0);
+    CHECK_ULP_CLOSE(Real(5)/Real(2), hermite_spline(Real(5)/Real(2)), 10);
+    CHECK_ULP_CLOSE(y[3], hermite_spline(3), 0);
+
+
+    y.resize(45);
+    dydx.resize(45);
+    for (size_t i = 0; i < y.size(); ++i) {
+        y[i] = i;
+        dydx[i] = 1;
+    }
+
+    hermite_spline = cardinal_cubic_hermite(std::move(y), std::move(dydx), x0, dx);
+    for (Real t = 0; t < 44; t += 0.5) {
+        CHECK_ULP_CLOSE(t, hermite_spline(t), 0);
+        CHECK_ULP_CLOSE(Real(1), hermite_spline.prime(t), 0);
+    }
+
+    std::vector<std::array<Real, 2>> data(45);
+    for (size_t i = 0; i < data.size(); ++i) {
+        data[i][0] = i;
+        data[i][1] = 1;
+    }
+
+    auto hermite_spline_aos = cardinal_cubic_hermite_aos(std::move(data), x0, dx);
+    for (Real t = 0; t < 44; t += 0.5) {
+        CHECK_ULP_CLOSE(t, hermite_spline_aos(t), 0);
+        CHECK_ULP_CLOSE(Real(1), hermite_spline_aos.prime(t), 0);
+    }
+
+
+}
+
+
+template<typename Real>
+void test_cardinal_quadratic()
+{
+    Real x0 = -1;
+    Real dx = Real(1)/Real(256);
+
+    std::vector<Real> y(50);
+    std::vector<Real> dydx(y.size());
+    for (size_t i = 0; i < y.size(); ++i) {
+        Real x = x0 + i*dx;
+        y[i] = x*x/2;
+        dydx[i] = x;
+    }
+
+    auto s = cardinal_cubic_hermite(std::move(y), std::move(dydx), x0, dx);
+    for (Real t = x0; t <= x0 + 49*dx; t+= 0.0125)
+    {
+        CHECK_ULP_CLOSE(t*t/2, s(t), 12);
+        CHECK_ULP_CLOSE(t, s.prime(t), 70);
+    }
+
+    std::vector<std::array<Real, 2>> data(50);
+    for (size_t i = 0; i < data.size(); ++i) {
+        Real x = x0 + i*dx;
+        data[i][0] = x*x/2;
+        data[i][1] = x;
+    }
+
+
+    auto saos = cardinal_cubic_hermite_aos(std::move(data), x0, dx);
+    for (Real t = x0; t <= x0 + 49*dx; t+= 0.0125)
+    {
+        CHECK_ULP_CLOSE(t*t/2, saos(t), 12);
+        CHECK_ULP_CLOSE(t, saos.prime(t), 70);
+    }
+
+}
+
+
+template<typename Real>
+void test_cardinal_interpolation_condition()
+{
+    for (size_t n = 4; n < 50; ++n) {
+        std::vector<Real> y(n);
+        std::vector<Real> dydx(n);
+        std::default_random_engine rd;
+        std::uniform_real_distribution<Real> dis(0.1,1);
+        Real x0 = Real(2);
+        Real dx = Real(1)/Real(128);
+        for (size_t i = 0; i < n; ++i) {
+            y[i] = dis(rd);
+            dydx[i] = dis(rd);
+        }
+
+        auto y_copy = y;
+        auto dydx_copy = dydx;
+        auto s = cardinal_cubic_hermite(std::move(y_copy), std::move(dydx_copy), x0, dx);
+        for (size_t i = 0; i < y.size(); ++i) {
+            CHECK_ULP_CLOSE(y[i], s(x0 + i*dx), 2);
+            CHECK_ULP_CLOSE(dydx[i], s.prime(x0 + i*dx), 2);
+        }
+    }
+}
+
+
+
 int main()
 {
     test_constant<float>();
     test_linear<float>();
     test_quadratic<float>();
     test_interpolation_condition<float>();
+    test_cardinal_constant<float>();
+    test_cardinal_linear<float>();
+    test_cardinal_quadratic<float>();
+    test_cardinal_interpolation_condition<float>();
+
 
 
     test_constant<double>();
     test_linear<double>();
     test_quadratic<double>();
     test_interpolation_condition<double>();
+    test_cardinal_constant<double>();
+    test_cardinal_linear<double>();
+    test_cardinal_quadratic<double>();
+    test_cardinal_interpolation_condition<double>();
+
 
     test_constant<long double>();
     test_linear<long double>();
     test_quadratic<long double>();
     test_interpolation_condition<long double>();
+    test_cardinal_constant<long double>();
+    test_cardinal_linear<long double>();
+    test_cardinal_quadratic<long double>();
+    test_cardinal_interpolation_condition<long double>();
+
 
 #ifdef BOOST_HAS_FLOAT128
     test_constant<float128>();
     test_linear<float128>();
+    test_cardinal_constant<float128>();
+    test_cardinal_linear<float128>();
 #endif
 
     return boost::math::test::report_errors();

From 6290803975612bca9f2b072792dc5a831ec38381 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Tue, 18 Feb 2020 08:11:48 -0500
Subject: [PATCH 037/104] Finish up cubic Hermite interpolation.

---
 doc/interpolators/cubic_hermite.qbk           | 117 +++++++++++++++++-
 example/daubechies_wavelets/bench.cpp         |  50 +++++++-
 .../math/interpolators/cubic_hermite.hpp      |   4 +-
 .../detail/cubic_hermite_detail.hpp           |  68 +++++-----
 test/Jamfile.v2                               |   1 +
 5 files changed, 201 insertions(+), 39 deletions(-)

diff --git a/doc/interpolators/cubic_hermite.qbk b/doc/interpolators/cubic_hermite.qbk
index 0948ae80f..7b78e621e 100644
--- a/doc/interpolators/cubic_hermite.qbk
+++ b/doc/interpolators/cubic_hermite.qbk
@@ -32,12 +32,38 @@ LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
         friend std::ostream& operator<<(std::ostream & os, const cubic_hermite & m);
     };
 
-    } // namespaces
+    template<class RandomAccessContainer>
+    class cardinal_cubic_hermite {
+    public:
+        using Real = typename RandomAccessContainer::value_type;
 
+        cardinal_cubic_hermite(RandomAccessContainer && y, RandomAccessContainer && dydx, Real x0, Real dx)
+
+        inline Real operator()(Real x) const;
+
+        inline Real prime(Real x) const;
+    };
+
+
+    template<class RandomAccessContainer>
+    class cardinal_cubic_hermite_aos {
+    public:
+        using Point = typename RandomAccessContainer::value_type;
+        using Real = typename Point::value_type;
+
+        cardinal_cubic_hermite_aos(RandomAccessContainer && data, Real x0, Real dx);
+
+        inline Real operator()(Real x) const;
+
+        inline Real prime(Real x) const;
+    };
+
+    } // namespaces
 
 [heading Cubic Hermite Interpolation]
 
 The cubic Hermite interpolant takes non-equispaced data and interpolates between them via cubic Hermite polynomials whose slopes must be provided.
+This is a very nice interpolant for solution skeletons of ODEs steppers, since numerically solving /y/' = /f/(/x/, /y/) produces a list of positions, values, and their derivatives, i.e. (/x/,/y/,/y/')=(/x/,/y/,/f/(/x/,/y/))-which is exactly what is required for the cubic Hermite interpolator.
 The interpolant is /C/[super 1] and evaluation has [bigo](log(/N/)) complexity.
 An example usage is as follows:
 
@@ -74,5 +100,94 @@ Hence we can use `boost::circular_buffer` to do real-time interpolation:
     // interpolate at 4.5:
     y = circular_hermite(4.5);
 
+For the equispaced case, we can either use `cardinal_cubic_hermite`, which accepts two separate arrays of `y` and `dydx`, or we can use `cardinal_cubic_hermite_aos`,
+which takes a vector of `(y, dydx)`, i.e., and array of structs (`aos`).
+The array of structs should be preferred as it uses cache more effectively.
+
+Usage is as follows:
+
+    using boost::math::interpolators::cardinal_cubic_hermite;
+    double x0 = 0;
+    double dx = 1;
+    std::vector<double> y(128, 1);
+    std::vector<double> dydx(128, 0);
+    auto ch = cardinal_cubic_hermite(std::move(y), std::move(dydx), x0, dx);
+
+For the "array of structs" version:
+
+    using boost::math::interpolators::cardinal_cubic_hermite_aos;
+    std::vector<std::array<double, 2>> data(128);
+    for (auto & datum : data) {
+        datum[0] = 1; // y
+        datum[1] = 0; // y'
+    }
+
+    auto ch = cardinal_cubic_hermite_aos(std::move(data), x0, dx);
+
+[heading Performance]
+
+Google benchmark was used to evaluate the performance.
+
+```
+Run on (16 X 4300 MHz CPU s)
+CPU Caches:
+  L1 Data 32 KiB (x8)
+  L1 Instruction 32 KiB (x8)
+  L2 Unified 1024 KiB (x8)
+  L3 Unified 11264 KiB (x1)
+Load Average: 1.16, 1.11, 0.99
+-----------------------------------------------------
+Benchmark                                        Time
+-----------------------------------------------------
+CubicHermite<double>/256                      9.67 ns
+CubicHermite<double>/512                      10.4 ns
+CubicHermite<double>/1024                     10.9 ns
+CubicHermite<double>/2048                     12.3 ns
+CubicHermite<double>/4096                     13.4 ns
+CubicHermite<double>/8192                     14.9 ns
+CubicHermite<double>/16384                    15.5 ns
+CubicHermite<double>/32768                    18.0 ns
+CubicHermite<double>/65536                    19.9 ns
+CubicHermite<double>/131072                   23.0 ns
+CubicHermite<double>/262144                   25.3 ns
+CubicHermite<double>/524288                   28.9 ns
+CubicHermite<double>/1048576                  31.0 ns
+CubicHermite<double>_BigO                     1.32 lgN
+CubicHermite<double>_RMS                        13 %
+CardinalCubicHermite<double>/256              3.14 ns
+CardinalCubicHermite<double>/512              3.13 ns
+CardinalCubicHermite<double>/1024             3.19 ns
+CardinalCubicHermite<double>/2048             3.14 ns
+CardinalCubicHermite<double>/4096             3.38 ns
+CardinalCubicHermite<double>/8192             3.54 ns
+CardinalCubicHermite<double>/16384            3.51 ns
+CardinalCubicHermite<double>/32768            3.76 ns
+CardinalCubicHermite<double>/65536            5.82 ns
+CardinalCubicHermite<double>/131072           5.76 ns
+CardinalCubicHermite<double>/262144           5.85 ns
+CardinalCubicHermite<double>/524288           5.69 ns
+CardinalCubicHermite<double>/1048576          5.77 ns
+CardinalCubicHermite<double>_BigO             4.28 (1)
+CardinalCubicHermite<double>_RMS                28 %
+CardinalCubicHermiteAOS<double>/256           3.22 ns
+CardinalCubicHermiteAOS<double>/512           3.22 ns
+CardinalCubicHermiteAOS<double>/1024          3.26 ns
+CardinalCubicHermiteAOS<double>/2048          3.23 ns
+CardinalCubicHermiteAOS<double>/4096          3.49 ns
+CardinalCubicHermiteAOS<double>/8192          3.57 ns
+CardinalCubicHermiteAOS<double>/16384         3.73 ns
+CardinalCubicHermiteAOS<double>/32768         4.12 ns
+CardinalCubicHermiteAOS<double>/65536         4.13 ns
+CardinalCubicHermiteAOS<double>/131072        4.12 ns
+CardinalCubicHermiteAOS<double>/262144        4.12 ns
+CardinalCubicHermiteAOS<double>/524288        4.12 ns
+CardinalCubicHermiteAOS<double>/1048576       4.19 ns
+CardinalCubicHermiteAOS<double>_BigO          3.73 (1)
+CardinalCubicHermiteAOS<double>_RMS             11 %
+```
+
+The logarithmic complexity of the non-equispaced version is evident, as is the better cache utilization of the "array of structs" version as the problem size gets larger.
+
+
 [endsect]
 [/section:cubic_hermite]
diff --git a/example/daubechies_wavelets/bench.cpp b/example/daubechies_wavelets/bench.cpp
index 69a01aaf9..8c3558f3a 100644
--- a/example/daubechies_wavelets/bench.cpp
+++ b/example/daubechies_wavelets/bench.cpp
@@ -10,7 +10,7 @@
 #include <benchmark/benchmark.h>
 #include <boost/random/uniform_real_distribution.hpp>
 #include <boost/math/special_functions/daubechies_scaling.hpp>
-#include <boost/math/interpolators/detail/cubic_hermite_detail.hpp>
+#include <boost/math/interpolators/cubic_hermite.hpp>
 #include <boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp>
 #include <boost/math/interpolators/detail/septic_hermite_detail.hpp>
 
@@ -107,6 +107,44 @@ BENCHMARK_TEMPLATE(ScalingConstructor, float, 11)->Unit(benchmark::kMillisecond)
 BENCHMARK_TEMPLATE(ScalingConstructor, double, 11)->Unit(benchmark::kMillisecond);
 BENCHMARK_TEMPLATE(ScalingConstructor, long double, 11)->Unit(benchmark::kMillisecond);
 
+template<typename Real>
+void CubicHermite(benchmark::State & state)
+{
+    using boost::math::interpolators::cubic_hermite;
+    auto n = state.range(0);
+    std::vector<Real> x(n);
+    std::vector<Real> y(n);
+    std::vector<Real> dydx(n);
+    std::random_device rd;
+    boost::random::uniform_real_distribution<Real> dis(Real(0), Real(1));
+    x[0] = dis(rd);
+    y[0] = dis(rd);
+    dydx[0] = dis(rd);
+    for (size_t i = 1; i < y.size(); ++i)
+    {
+        x[i] = x[i-1] + dis(rd);
+        y[i] = dis(rd);
+        dydx[i] = dis(rd);
+    }
+    Real x0 = x.front();
+    Real xf = x.back();
+
+    auto qh = cubic_hermite(std::move(x), std::move(y), std::move(dydx));
+    Real t = x0;
+    for (auto _ : state)
+    {
+        benchmark::DoNotOptimize(qh(t));
+        t += (xf-x0)/128;
+        if (t >= xf)
+        {
+            t = x0;
+        }
+    }
+    state.SetComplexityN(state.range(0));
+}
+
+BENCHMARK_TEMPLATE(CubicHermite, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity(benchmark::oLogN);
+
 template<typename Real>
 void CardinalCubicHermite(benchmark::State & state)
 {
@@ -137,9 +175,10 @@ void CardinalCubicHermite(benchmark::State & state)
             x = x0;
         }
     }
+    state.SetComplexityN(state.range(0));
 }
 
-BENCHMARK_TEMPLATE(CardinalCubicHermite, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity();
+BENCHMARK_TEMPLATE(CardinalCubicHermite, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity(benchmark::o1);
 
 template<typename Real>
 void CardinalCubicHermiteAOS(benchmark::State & state)
@@ -169,9 +208,10 @@ void CardinalCubicHermiteAOS(benchmark::State & state)
             x = x0;
         }
     }
+    state.SetComplexityN(state.range(0));
 }
 
-BENCHMARK_TEMPLATE(CardinalCubicHermiteAOS, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity();
+BENCHMARK_TEMPLATE(CardinalCubicHermiteAOS, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity(benchmark::o1);
 
 template<class Real>
 void SineEvaluation(benchmark::State& state)
@@ -260,6 +300,7 @@ void CardinalQuinticHermite(benchmark::State & state)
             x = x0;
         }
     }
+    state.SetComplexityN(state.range(0));
 }
 
 BENCHMARK_TEMPLATE(CardinalQuinticHermite, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity();
@@ -294,6 +335,7 @@ void CardinalQuinticHermiteAOS(benchmark::State & state)
             x = x0;
         }
     }
+    state.SetComplexityN(state.range(0));
 }
 
 BENCHMARK_TEMPLATE(CardinalQuinticHermiteAOS, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity();
@@ -333,6 +375,7 @@ void CardinalSepticHermite(benchmark::State & state)
             x = x0;
         }
     }
+    state.SetComplexityN(state.range(0));
 }
 
 BENCHMARK_TEMPLATE(CardinalSepticHermite, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity();
@@ -368,6 +411,7 @@ void CardinalSepticHermiteAOS(benchmark::State & state)
             x = x0;
         }
     }
+    state.SetComplexityN(state.range(0));
 }
 
 BENCHMARK_TEMPLATE(CardinalSepticHermiteAOS, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity();
diff --git a/include/boost/math/interpolators/cubic_hermite.hpp b/include/boost/math/interpolators/cubic_hermite.hpp
index 79aea2b9e..c3ac71d7b 100644
--- a/include/boost/math/interpolators/cubic_hermite.hpp
+++ b/include/boost/math/interpolators/cubic_hermite.hpp
@@ -20,11 +20,11 @@ public:
     : impl_(std::make_shared<detail::cubic_hermite_detail<RandomAccessContainer>>(std::move(x), std::move(y), std::move(dydx)))
     {}
 
-    Real operator()(Real x) const {
+    inline Real operator()(Real x) const {
         return impl_->operator()(x);
     }
 
-    Real prime(Real x) const {
+    inline Real prime(Real x) const {
         return impl_->prime(x);
     }
 
diff --git a/include/boost/math/interpolators/detail/cubic_hermite_detail.hpp b/include/boost/math/interpolators/detail/cubic_hermite_detail.hpp
index 231b9177f..ee8e63f74 100644
--- a/include/boost/math/interpolators/detail/cubic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/cubic_hermite_detail.hpp
@@ -20,7 +20,8 @@ class cubic_hermite_detail {
 public:
     using Real = typename RandomAccessContainer::value_type;
 
-    cubic_hermite_detail(RandomAccessContainer && x, RandomAccessContainer && y, RandomAccessContainer dydx) : x_{std::move(x)}, y_{std::move(y)}, dydx_{std::move(dydx)}
+    cubic_hermite_detail(RandomAccessContainer && x, RandomAccessContainer && y, RandomAccessContainer dydx)
+     : x_{std::move(x)}, y_{std::move(y)}, dydx_{std::move(dydx)}
     {
         using std::abs;
         using std::isnan;
@@ -37,9 +38,11 @@ public:
             throw std::domain_error("Must be at least two data points.");
         }
         Real x0 = x_[0];
-        for (size_t i = 1; i < x_.size(); ++i) {
+        for (size_t i = 1; i < x_.size(); ++i)
+        {
             Real x1 = x_[i];
-            if (x1 <= x0) {
+            if (x1 <= x0)
+            {
                 std::ostringstream oss;
                 oss.precision(std::numeric_limits<Real>::digits10+3);
                 oss << "Abscissas must be listed in strictly increasing order x0 < x1 < ... < x_{n-1}, ";
@@ -50,10 +53,12 @@ public:
         }
     }
 
-    void push_back(Real x, Real y, Real dydx) {
+    void push_back(Real x, Real y, Real dydx)
+    {
         using std::abs;
         using std::isnan;
-        if (x <= x_.back()) {
+        if (x <= x_.back())
+        {
              throw std::domain_error("Calling push_back must preserve the monotonicity of the x's");
         }
         x_.push_back(x);
@@ -61,8 +66,10 @@ public:
         dydx_.push_back(dydx);
     }
 
-    Real operator()(Real x) const {
-        if  (x < x_[0] || x > x_.back()) {
+    Real operator()(Real x) const
+    {
+        if  (x < x_[0] || x > x_.back())
+        {
             std::ostringstream oss;
             oss.precision(std::numeric_limits<Real>::digits10+3);
             oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
@@ -71,7 +78,8 @@ public:
         }
         // We need t := (x-x_k)/(x_{k+1}-x_k) \in [0,1) for this to work.
         // Sadly this neccessitates this loathesome check, otherwise we get t = 1 at x = xf.
-        if (x == x_.back()) {
+        if (x == x_.back())
+        {
             return y_.back();
         }
 
@@ -88,35 +96,25 @@ public:
 
         // See the section 'Representations' in the page
         // https://en.wikipedia.org/wiki/Cubic_Hermite_spline
-        // This uses the factorized form:
-        //Real y = y0*(1+2*t)*(1-t)*(1-t) + dx*s0*t*(1-t)*(1-t)
-        //       + y1*t*t*(3-2*t) + dx*s1*t*t*(t-1);
-        // And then factorized further:
         Real y = (1-t)*(1-t)*(y0*(1+2*t) + s0*(x-x0))
               + t*t*(y1*(3-2*t) + dx*s1*(t-1));
         return y;
-
-        // Another representation, useful for understanding the derivative calc:
-        /*Real d1 = (y1 - y0 - s0*dx)/(dx*dx);
-        Real d2 = (s1 - s0)/(2*dx);
-        Real c2 = 3*d1 - 2*d2;
-        Real c3 = 2*(d2 - d1)/dx;
-        Real y = y0 + s0*(x-x0) + c2*(x-x0)*(x-x0) + c3*(x-x0)*(x-x0)*(x-x0); 
-        return y;*/
     }
 
-    Real prime(Real x) const {
-        if  (x < x_[0] || x > x_.back()) {
+    Real prime(Real x) const
+    {
+        if  (x < x_[0] || x > x_.back())
+        {
             std::ostringstream oss;
             oss.precision(std::numeric_limits<Real>::digits10+3);
             oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
                 << x_[0] << ", " << x_.back() << "]";
             throw std::domain_error(oss.str());
         }
-        if (x == x_.back()) {
+        if (x == x_.back())
+        {
             return dydx_.back();
         }
-
         auto it = std::upper_bound(x_.begin(), x_.end(), x);
         auto i = std::distance(x_.begin(), it) -1;
         Real x0 = *(it-1);
@@ -131,16 +129,15 @@ public:
         Real d2 = (s1 - s0)/(2*dx);
         Real c2 = 3*d1 - 2*d2;
         Real c3 = 2*(d2 - d1)/dx;
-        Real dydx = s0 + 2*c2*(x-x0) + 3*c3*(x-x0)*(x-x0); 
-
-        return dydx;
+        return s0 + 2*c2*(x-x0) + 3*c3*(x-x0)*(x-x0); 
     }
 
 
     friend std::ostream& operator<<(std::ostream & os, const cubic_hermite_detail & m)
     {
         os << "(x,y,y') = {";
-        for (size_t i = 0; i < m.x_.size() - 1; ++i) {
+        for (size_t i = 0; i < m.x_.size() - 1; ++i)
+        {
             os << "(" << m.x_[i] << ", " << m.y_[i] << ", " << m.dydx_[i] << "),  ";
         }
         auto n = m.x_.size()-1;
@@ -148,7 +145,8 @@ public:
         return os;
     }
 
-    auto size() const {
+    auto size() const
+    {
         return x_.size();
     }
 
@@ -190,7 +188,8 @@ public:
     // If the buffer is not circular, x0_ is unchanged.
     // We need a concept for circular_buffer!
 
-    inline Real operator()(Real x) const {
+    inline Real operator()(Real x) const
+    {
         const Real xf = x0_ + (y_.size()-1)/inv_dx_;
         if  (x < x0_ || x > xf)
         {
@@ -224,7 +223,8 @@ public:
               + t*t*(y1*(3-2*t) - dy1*r);
     }
 
-    inline Real prime(Real x) const {
+    inline Real prime(Real x) const
+    {
         const Real xf = x0_ + (y_.size()-1)/inv_dx_;
         if  (x < x0_ || x > xf)
         {
@@ -297,7 +297,8 @@ public:
         }
     }
 
-    inline Real operator()(Real x) const {
+    inline Real operator()(Real x) const
+    {
         const Real xf = x0_ + (dat_.size()-1)/inv_dx_;
         if  (x < x0_ || x > xf)
         {
@@ -332,7 +333,8 @@ public:
               + t*t*(y1*(3-2*t) - dy1*r);
     }
 
-    inline Real prime(Real x) const {
+    inline Real prime(Real x) const
+    {
         const Real xf = x0_ + (dat_.size()-1)/inv_dx_;
         if  (x < x0_ || x > xf)
         {
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index d7543f0f0..f74444221 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -948,6 +948,7 @@ test-suite misc :
    [ run cardinal_quintic_b_spline_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run makima_test.cpp  : : :  [ requires cxx17_if_constexpr cxx17_std_apply ]  [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run pchip_test.cpp  : : :  [ requires cxx17_if_constexpr cxx17_std_apply ]  [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
+   [ run septic_hermite_test.cpp  : : :  [ requires cxx17_if_constexpr cxx17_std_apply ]  [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run quintic_hermite_test.cpp  : : :  [ requires cxx17_if_constexpr cxx17_std_apply ]  [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run cubic_hermite_test.cpp  : : :  [ requires cxx17_if_constexpr cxx17_std_apply ]  [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run catmull_rom_test.cpp ../../test/build//boost_unit_test_framework : : : <define>TEST=1 [ requires cxx11_hdr_array cxx11_hdr_initializer_list ] : catmull_rom_test_1 ]

From dd11bb82c7146516bab00ecd79ecda5acd99ebe7 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Tue, 18 Feb 2020 12:55:10 -0500
Subject: [PATCH 038/104] Typo removal [CI SKIP]

---
 .../find_best_daubechies_interpolator.cpp            | 12 +++++++-----
 1 file changed, 7 insertions(+), 5 deletions(-)

diff --git a/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp b/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
index 46d8a14f5..ee6ff24bb 100644
--- a/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
+++ b/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
@@ -401,11 +401,13 @@ void find_best_interpolator()
                 }
             }
             m.insert({fo_sup, "First-order Taylor"});
-            if (p==2) {
-            fs << fo_sup << "\n";
+            if (p==2)
+            {
+                fs << fo_sup << "\n";
             }
-            else {
-              fs << fo_sup << ", ";
+            else
+            {
+                fs << fo_sup << ", ";
             }
         }
 
@@ -534,7 +536,7 @@ void find_best_interpolator()
                     }
                 }
                 m.insert({septic_sup, "septic_hermite_spline"});
-                fs << septic_sup << ", ";
+                fs << septic_sup << "\n";
             }
 
 

From 5a9e39709d433183239af50aa79b75739a432fc6 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Tue, 18 Feb 2020 13:18:04 -0500
Subject: [PATCH 039/104] Regress accuracy. [CI SKIP]

---
 .../regress_daubechies_accuracy.cpp           | 99 +++++++++++++++++++
 1 file changed, 99 insertions(+)
 create mode 100644 example/daubechies_wavelets/regress_daubechies_accuracy.cpp

diff --git a/example/daubechies_wavelets/regress_daubechies_accuracy.cpp b/example/daubechies_wavelets/regress_daubechies_accuracy.cpp
new file mode 100644
index 000000000..9161d0743
--- /dev/null
+++ b/example/daubechies_wavelets/regress_daubechies_accuracy.cpp
@@ -0,0 +1,99 @@
+#include <iostream>
+#include <string>
+#include <fstream>
+#include <map>
+#include <cmath>
+#include <vector>
+#include <iomanip>
+#include <boost/algorithm/string.hpp>
+#include <boost/math/statistics/linear_regression.hpp>
+
+
+int main(int argc, char** argv)
+{
+    if (argc != 2)
+    {
+        std::cout << "Usage: ./regress_accuracy.x foo.csv\n";
+        return 1;
+    }
+    std::string filename = std::string(argv[1]);
+    std::ifstream ifs(filename.c_str());
+    if (!ifs.good())
+    {
+        std::cerr << "Couldn't find file " << filename << "\n";
+        return 1;
+    }
+    std::map<std::string, std::vector<double>> m;
+
+    std::string header_line;
+    std::getline(ifs, header_line);
+    std::cout << "Header line = " << header_line << "\n";
+    std::vector<std::string> header_strs;
+    boost::split(header_strs, header_line, boost::is_any_of(","));
+    for (auto & s : header_strs) {
+        boost::algorithm::trim(s);
+    }
+
+    std::string line;
+    std::vector<double> r;
+    std::vector<double> matched_holder;
+    std::vector<double> linear;
+    std::vector<double> quadratic_b_spline;
+    std::vector<double> cubic_b_spline;
+    std::vector<double> quintic_b_spline;
+    std::vector<double> cubic_hermite;
+    std::vector<double> pchip;
+    while(std::getline(ifs, line))
+    {
+        std::vector<std::string> strs;
+        boost::split(strs, line, boost::is_any_of(","));
+        for (auto & s : strs)
+        {
+            boost::algorithm::trim(s);
+        }
+        std::vector<double> v(strs.size(), std::numeric_limits<double>::quiet_NaN());
+        for (size_t i = 0; i < v.size(); ++i)
+        {
+            v[i] = std::stod(strs[i]);
+        }
+        r.push_back(v[0]);
+        matched_holder.push_back(std::log2(v[1]));
+        linear.push_back(std::log2(v[2]));
+        quadratic_b_spline.push_back(std::log2(v[3]));
+        cubic_b_spline.push_back(std::log2(v[4]));
+        quintic_b_spline.push_back(std::log2(v[5]));
+        cubic_hermite.push_back(std::log2(v[6]));
+        pchip.push_back(std::log2(v[7]));
+    }
+
+    std::cout << std::fixed << std::setprecision(16);
+    auto p  = boost::math::statistics::simple_ordinary_least_squares(r, matched_holder);
+
+    assert(p.second < 0);
+    std::cout << "Matched Holder    : " << p.first << " - " << std::abs(p.second) << "*log2(||phi - phi_r||_infy)\n";
+
+    p  = boost::math::statistics::simple_ordinary_least_squares(r, linear);
+    assert(p.second < 0);
+    std::cout << "Linear            : " << p.first << " - " << std::abs(p.second) << "*log2(||phi - phi_r||_infty)\n";
+
+    p  = boost::math::statistics::simple_ordinary_least_squares(r, quadratic_b_spline);
+    assert(p.second < 0);
+    std::cout << "Quadratic B-spline: " << p.first << " - " << std::abs(p.second) << "*log2(||phi - phi_r||_infty)\n";
+
+    p  = boost::math::statistics::simple_ordinary_least_squares(r, cubic_b_spline);
+    assert(p.second < 0);
+    std::cout << "Cubic B-spline    : " << p.first << " - " << std::abs(p.second) << "*log2(||phi - phi_r||_infty)\n";
+
+    p  = boost::math::statistics::simple_ordinary_least_squares(r, quintic_b_spline);
+    assert(p.second < 0);
+    std::cout << "Quintic B-spline  : " << p.first << " - " << std::abs(p.second) << "*log2(||phi - phi_r||_infty)\n";
+
+    p  = boost::math::statistics::simple_ordinary_least_squares(r, cubic_hermite);
+    assert(p.second < 0);
+    std::cout << "Cubic Hermite     : " << p.first << " - " << std::abs(p.second) << "*log2(||phi - phi_r||_infty)\n";
+
+    p  = boost::math::statistics::simple_ordinary_least_squares(r, cubic_hermite);
+    assert(p.second < 0);
+    std::cout << "pchip             : " << p.first << " - " << std::abs(p.second) << "*log2(||phi - phi_r||_infty)\n";
+
+}
\ No newline at end of file

From fa79cecc4280fedc2abd7f2c935187e1cfbdbb2e Mon Sep 17 00:00:00 2001
From: Nick Thompson <nathompson7@protonmail.com>
Date: Tue, 18 Feb 2020 14:50:16 -0500
Subject: [PATCH 040/104] Regress on accuracy. [CI SKIP]

---
 .../regress_daubechies_accuracy.cpp           | 62 ++++++++++++++++---
 1 file changed, 54 insertions(+), 8 deletions(-)

diff --git a/example/daubechies_wavelets/regress_daubechies_accuracy.cpp b/example/daubechies_wavelets/regress_daubechies_accuracy.cpp
index 9161d0743..913bfac2f 100644
--- a/example/daubechies_wavelets/regress_daubechies_accuracy.cpp
+++ b/example/daubechies_wavelets/regress_daubechies_accuracy.cpp
@@ -43,6 +43,12 @@ int main(int argc, char** argv)
     std::vector<double> quintic_b_spline;
     std::vector<double> cubic_hermite;
     std::vector<double> pchip;
+    std::vector<double> makima;
+    std::vector<double> fotaylor;
+    std::vector<double> quintic_hermite;
+    std::vector<double> sotaylor;
+    std::vector<double> totaylor;
+    std::vector<double> septic_hermite;
     while(std::getline(ifs, line))
     {
         std::vector<std::string> strs;
@@ -64,36 +70,76 @@ int main(int argc, char** argv)
         quintic_b_spline.push_back(std::log2(v[5]));
         cubic_hermite.push_back(std::log2(v[6]));
         pchip.push_back(std::log2(v[7]));
+        makima.push_back(std::log2(v[8]));
+        fotaylor.push_back(std::log2(v[9]));
+        if (v.size() > 10) {
+            quintic_hermite.push_back(std::log2(v[10]));
+            sotaylor.push_back(std::log2(v[11]));
+        }
+        if (v.size() > 12) {
+            totaylor.push_back(std::log2(v[12]));
+            septic_hermite.push_back(std::log2(v[13]));
+        }
     }
 
     std::cout << std::fixed << std::setprecision(16);
     auto p  = boost::math::statistics::simple_ordinary_least_squares(r, matched_holder);
 
     assert(p.second < 0);
-    std::cout << "Matched Holder    : " << p.first << " - " << std::abs(p.second) << "*log2(||phi - phi_r||_infy)\n";
+    std::cout << "Matched Holder    : " << p.first << " - " << std::abs(p.second) << "r\n";
 
     p  = boost::math::statistics::simple_ordinary_least_squares(r, linear);
     assert(p.second < 0);
-    std::cout << "Linear            : " << p.first << " - " << std::abs(p.second) << "*log2(||phi - phi_r||_infty)\n";
+    std::cout << "Linear            : " << p.first << " - " << std::abs(p.second) << "r\n";
 
     p  = boost::math::statistics::simple_ordinary_least_squares(r, quadratic_b_spline);
     assert(p.second < 0);
-    std::cout << "Quadratic B-spline: " << p.first << " - " << std::abs(p.second) << "*log2(||phi - phi_r||_infty)\n";
+    std::cout << "Quadratic B-spline: " << p.first << " - " << std::abs(p.second) << "r\n";
 
     p  = boost::math::statistics::simple_ordinary_least_squares(r, cubic_b_spline);
     assert(p.second < 0);
-    std::cout << "Cubic B-spline    : " << p.first << " - " << std::abs(p.second) << "*log2(||phi - phi_r||_infty)\n";
+    std::cout << "Cubic B-spline    : " << p.first << " - " << std::abs(p.second) << "r\n";
 
     p  = boost::math::statistics::simple_ordinary_least_squares(r, quintic_b_spline);
     assert(p.second < 0);
-    std::cout << "Quintic B-spline  : " << p.first << " - " << std::abs(p.second) << "*log2(||phi - phi_r||_infty)\n";
+    std::cout << "Quintic B-spline  : " << p.first << " - " << std::abs(p.second) << "r\n";
 
     p  = boost::math::statistics::simple_ordinary_least_squares(r, cubic_hermite);
     assert(p.second < 0);
-    std::cout << "Cubic Hermite     : " << p.first << " - " << std::abs(p.second) << "*log2(||phi - phi_r||_infty)\n";
+    std::cout << "Cubic Hermite     : " << p.first << " - " << std::abs(p.second) << "r\n";
 
-    p  = boost::math::statistics::simple_ordinary_least_squares(r, cubic_hermite);
+    p  = boost::math::statistics::simple_ordinary_least_squares(r, pchip);
     assert(p.second < 0);
-    std::cout << "pchip             : " << p.first << " - " << std::abs(p.second) << "*log2(||phi - phi_r||_infty)\n";
+    std::cout << "pchip             : " << p.first << " - " << std::abs(p.second) << "r\n";
+
+    p  = boost::math::statistics::simple_ordinary_least_squares(r, makima);
+    assert(p.second < 0);
+    std::cout << "makima            : " << p.first << " - " << std::abs(p.second) << "r\n";
+
+    p  = boost::math::statistics::simple_ordinary_least_squares(r, fotaylor);
+    assert(p.second < 0);
+    std::cout << "First-order Taylor: " << p.first << " - " << std::abs(p.second) << "r\n";
+
+    if (sotaylor.size() > 0)
+    {
+    p  = boost::math::statistics::simple_ordinary_least_squares(r, quintic_hermite);
+    assert(p.second < 0);
+    std::cout << "Quintic Hermite   : " << p.first << " - " << std::abs(p.second) << "r\n";
+
+    p  = boost::math::statistics::simple_ordinary_least_squares(r, sotaylor);
+    assert(p.second < 0);
+    std::cout << "Second-orde Taylor: " << p.first << " - " << std::abs(p.second) << "r\n";
+    }
+
+    if (totaylor.size() > 0)
+    {
+    p  = boost::math::statistics::simple_ordinary_least_squares(r, totaylor);
+    assert(p.second < 0);
+    std::cout << "Third-order Taylor: " << p.first << " - " << std::abs(p.second) << "r\n";
+
+    p  = boost::math::statistics::simple_ordinary_least_squares(r, septic_hermite);
+    assert(p.second < 0);
+    std::cout << "septic hermite    : " << p.first << " - " << std::abs(p.second) << "r\n";
+    }
 
 }
\ No newline at end of file

From 067474845686545f1c2624a1d2d3fc1b2cced890 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Wed, 19 Feb 2020 07:41:29 -0500
Subject: [PATCH 041/104] Version used for data provided in paper [CI SKIP]

---
 .../find_best_daubechies_interpolator.cpp     | 32 ++++----
 .../regress_daubechies_accuracy.cpp           | 81 ++++++++++---------
 2 files changed, 58 insertions(+), 55 deletions(-)

diff --git a/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp b/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
index ee6ff24bb..2cfb7f268 100644
--- a/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
+++ b/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
@@ -137,7 +137,8 @@ void find_best_interpolator()
     std::ofstream fs{filename};
     static_assert(sizeof(PreciseReal) >= sizeof(Real), "sizeof(PreciseReal) >= sizeof(Real) is required.");
     using std::abs;
-    int rmax = 20;
+    int rmax = 17;
+    std::cout << "Computing phi_dense_precise\n";
     auto phi_dense_precise = boost::math::detail::dyadic_grid<PreciseReal, p, 0>(rmax);
     std::vector<Real> phi_dense(phi_dense_precise.size());
     for (size_t i = 0; i < phi_dense.size(); ++i)
@@ -145,6 +146,7 @@ void find_best_interpolator()
         phi_dense[i] = static_cast<Real>(phi_dense_precise[i]);
     }
     phi_dense_precise.resize(0);
+    std::cout << "Done\n";
 
     Real dx_dense = (2*p-1)/static_cast<Real>(phi_dense.size()-1);
     fs << std::setprecision(std::numeric_limits<Real>::digits10 + 3);
@@ -562,31 +564,31 @@ int main() {
     //choose_refinement<float, long double, 5>();
     //choose_refinement<double, float128, 15>();
     // Says linear interpolation is the best:
-    find_best_interpolator<double, float128, 2>();
+    find_best_interpolator<float128, float128, 2>();
     // Says linear interpolation is the best:
-    find_best_interpolator<double, float128, 3>();
+    find_best_interpolator<float128, float128, 3>();
     // Says cubic_hermite_spline is best:
-    find_best_interpolator<double, float128, 4>();
+    find_best_interpolator<float128, float128, 4>();
     // Says cubic_hermite_spline is best:
-    find_best_interpolator<double, float128, 5>();
+    find_best_interpolator<float128, float128, 5>();
     // Says quintic_hermite_spline is best:
-    find_best_interpolator<double, float128, 6>();
+    find_best_interpolator<float128, float128, 6>();
     // Says quintic_hermite_spline is best:
-    find_best_interpolator<double, float128, 7>();
+    find_best_interpolator<float128, float128, 7>();
     // Says quintic_hermite_spline is best:
-    find_best_interpolator<double, float128, 8>();
+    find_best_interpolator<float128, float128, 8>();
     // Says quintic_hermite_spline is best:
-    find_best_interpolator<double, float128, 9>();
+    find_best_interpolator<float128, float128, 9>();
     // Says septic_hermite_spline is best:
-    find_best_interpolator<double, float128, 10>();
+    find_best_interpolator<float128, float128, 10>();
     // Says septic_hermite_spline is best:
-    find_best_interpolator<double, float128, 11>();
+    find_best_interpolator<float128, float128, 11>();
     // Says septic_hermite_spline is best:
-    find_best_interpolator<double, float128, 12>();
+    find_best_interpolator<float128, float128, 12>();
     // Says septic_hermite_spline is best:
-    find_best_interpolator<double, float128, 13>();
+    find_best_interpolator<float128, float128, 13>();
     // Says septic_hermite_spline is best:
-    find_best_interpolator<double, float128, 14>();
+    find_best_interpolator<float128, float128, 14>();
     // Says septic_hermite_spline is best:
-    find_best_interpolator<double, float128, 15>();
+    find_best_interpolator<float128, float128, 15>();
 }
diff --git a/example/daubechies_wavelets/regress_daubechies_accuracy.cpp b/example/daubechies_wavelets/regress_daubechies_accuracy.cpp
index 913bfac2f..d7b0f3297 100644
--- a/example/daubechies_wavelets/regress_daubechies_accuracy.cpp
+++ b/example/daubechies_wavelets/regress_daubechies_accuracy.cpp
@@ -83,63 +83,64 @@ int main(int argc, char** argv)
     }
 
     std::cout << std::fixed << std::setprecision(16);
-    auto p  = boost::math::statistics::simple_ordinary_least_squares(r, matched_holder);
+    auto q  = boost::math::statistics::simple_ordinary_least_squares_with_R_squared(r, matched_holder);
+    assert(std::get<1>(q) < 0);
+    std::cout << "Matched Holder    : " << std::get<0>(q) << " - " << std::abs(std::get<1>(q)) << "r, R^2 = " << std::get<2>(q) << "\n";
 
-    assert(p.second < 0);
-    std::cout << "Matched Holder    : " << p.first << " - " << std::abs(p.second) << "r\n";
+    q  = boost::math::statistics::simple_ordinary_least_squares_with_R_squared(r, linear);
+    assert(std::get<1>(q) < 0);
+    std::cout << "Linear            : " << std::get<0>(q) << " - " << std::abs(std::get<1>(q)) << "r, R^2 = " << std::get<2>(q) << "\n";
 
-    p  = boost::math::statistics::simple_ordinary_least_squares(r, linear);
-    assert(p.second < 0);
-    std::cout << "Linear            : " << p.first << " - " << std::abs(p.second) << "r\n";
+    q  = boost::math::statistics::simple_ordinary_least_squares_with_R_squared(r, quadratic_b_spline);
+    assert(std::get<1>(q) < 0);
+    std::cout << "Quadratic B-spline: " << std::get<0>(q) << " - " << std::abs(std::get<1>(q)) << "r, R^2 = " << std::get<2>(q) << "\n";
 
-    p  = boost::math::statistics::simple_ordinary_least_squares(r, quadratic_b_spline);
-    assert(p.second < 0);
-    std::cout << "Quadratic B-spline: " << p.first << " - " << std::abs(p.second) << "r\n";
+    q  = boost::math::statistics::simple_ordinary_least_squares_with_R_squared(r, cubic_b_spline);
+    assert(std::get<1>(q) < 0);
+    std::cout << "Cubic B-spline    : " << std::get<0>(q) << " - " << std::abs(std::get<1>(q)) << "r, R^2 = " << std::get<2>(q) << "\n";
 
-    p  = boost::math::statistics::simple_ordinary_least_squares(r, cubic_b_spline);
-    assert(p.second < 0);
-    std::cout << "Cubic B-spline    : " << p.first << " - " << std::abs(p.second) << "r\n";
+    q  = boost::math::statistics::simple_ordinary_least_squares_with_R_squared(r, quintic_b_spline);
+    assert(std::get<1>(q) < 0);
+    std::cout << "Quintic B-spline  : " << std::get<0>(q) << " - " << std::abs(std::get<1>(q)) << "r, R^2 = " << std::get<2>(q) << "\n";
 
-    p  = boost::math::statistics::simple_ordinary_least_squares(r, quintic_b_spline);
-    assert(p.second < 0);
-    std::cout << "Quintic B-spline  : " << p.first << " - " << std::abs(p.second) << "r\n";
+    q  = boost::math::statistics::simple_ordinary_least_squares_with_R_squared(r, cubic_hermite);
+    assert(std::get<1>(q) < 0);
+    std::cout << "Cubic Hermite     : " << std::get<0>(q) << " - " << std::abs(std::get<1>(q)) << "r, R^2 = " << std::get<2>(q) << "\n";
 
-    p  = boost::math::statistics::simple_ordinary_least_squares(r, cubic_hermite);
-    assert(p.second < 0);
-    std::cout << "Cubic Hermite     : " << p.first << " - " << std::abs(p.second) << "r\n";
+    q  = boost::math::statistics::simple_ordinary_least_squares_with_R_squared(r, pchip);
+    assert(std::get<1>(q) < 0);
+    std::cout << "PCHIP             : " << std::get<0>(q) << " - " << std::abs(std::get<1>(q)) << "r, R^2 = " << std::get<2>(q) << "\n";
 
-    p  = boost::math::statistics::simple_ordinary_least_squares(r, pchip);
-    assert(p.second < 0);
-    std::cout << "pchip             : " << p.first << " - " << std::abs(p.second) << "r\n";
+    q  = boost::math::statistics::simple_ordinary_least_squares_with_R_squared(r, makima);
+    assert(std::get<1>(q) < 0);
+    std::cout << "Makima            : " << std::get<0>(q) << " - " << std::abs(std::get<1>(q)) << "r, R^2 = " << std::get<2>(q) << "\n";
 
-    p  = boost::math::statistics::simple_ordinary_least_squares(r, makima);
-    assert(p.second < 0);
-    std::cout << "makima            : " << p.first << " - " << std::abs(p.second) << "r\n";
-
-    p  = boost::math::statistics::simple_ordinary_least_squares(r, fotaylor);
-    assert(p.second < 0);
-    std::cout << "First-order Taylor: " << p.first << " - " << std::abs(p.second) << "r\n";
+    q  = boost::math::statistics::simple_ordinary_least_squares_with_R_squared(r, fotaylor);
+    assert(std::get<1>(q) < 0);
+    std::cout << "First-order Taylor: " << std::get<0>(q) << " - " << std::abs(std::get<1>(q)) << "r, R^2 = " << std::get<2>(q) << "\n";
 
     if (sotaylor.size() > 0)
     {
-    p  = boost::math::statistics::simple_ordinary_least_squares(r, quintic_hermite);
-    assert(p.second < 0);
-    std::cout << "Quintic Hermite   : " << p.first << " - " << std::abs(p.second) << "r\n";
+    q  = boost::math::statistics::simple_ordinary_least_squares_with_R_squared(r, quintic_hermite);
+    assert(std::get<1>(q) < 0);
+    std::cout << "Quintic Hermite   : " << std::get<0>(q) << " - " << std::abs(std::get<1>(q)) << "r, R^2 = " << std::get<2>(q) << "\n";
+
+    q  = boost::math::statistics::simple_ordinary_least_squares_with_R_squared(r, sotaylor);
+    assert(std::get<1>(q) < 0);
+    std::cout << "2nd order Taylor  : " << std::get<0>(q) << " - " << std::abs(std::get<1>(q)) << "r, R^2 = " << std::get<2>(q) << "\n";
 
-    p  = boost::math::statistics::simple_ordinary_least_squares(r, sotaylor);
-    assert(p.second < 0);
-    std::cout << "Second-orde Taylor: " << p.first << " - " << std::abs(p.second) << "r\n";
     }
 
     if (totaylor.size() > 0)
     {
-    p  = boost::math::statistics::simple_ordinary_least_squares(r, totaylor);
-    assert(p.second < 0);
-    std::cout << "Third-order Taylor: " << p.first << " - " << std::abs(p.second) << "r\n";
+    q  = boost::math::statistics::simple_ordinary_least_squares_with_R_squared(r, totaylor);
+    assert(std::get<1>(q) < 0);
+    std::cout << "3rd order Taylor  : " << std::get<0>(q) << " - " << std::abs(std::get<1>(q)) << "r, R^2 = " << std::get<2>(q) << "\n";
+
+    q  = boost::math::statistics::simple_ordinary_least_squares_with_R_squared(r, septic_hermite);
+    assert(std::get<1>(q) < 0);
+    std::cout << "Septic Hermite    : " << std::get<0>(q) << " - " << std::abs(std::get<1>(q)) << "r, R^2 = " << std::get<2>(q) << "\n";
 
-    p  = boost::math::statistics::simple_ordinary_least_squares(r, septic_hermite);
-    assert(p.second < 0);
-    std::cout << "septic hermite    : " << p.first << " - " << std::abs(p.second) << "r\n";
     }
 
 }
\ No newline at end of file

From 2ae966266d7738ba5b87b2b4d90fdf42925b4819 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Thu, 20 Feb 2020 06:52:11 -0500
Subject: [PATCH 042/104] Unify and patch up quintic hermite interpolation [CI
 SKIP]

---
 .../cardinal_quintic_hermite.hpp              |  56 ---
 .../cardinal_quintic_hermite_detail.hpp       | 297 -------------
 .../detail/quintic_hermite_detail.hpp         | 413 +++++++++++++++++-
 .../math/interpolators/quintic_hermite.hpp    |  57 ++-
 .../special_functions/daubechies_scaling.hpp  |   1 -
 test/cardinal_quintic_hermite_test.cpp        | 252 -----------
 test/quintic_hermite_test.cpp                 | 318 ++++++++++++--
 7 files changed, 738 insertions(+), 656 deletions(-)
 delete mode 100644 include/boost/math/interpolators/cardinal_quintic_hermite.hpp
 delete mode 100644 include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp
 delete mode 100644 test/cardinal_quintic_hermite_test.cpp

diff --git a/include/boost/math/interpolators/cardinal_quintic_hermite.hpp b/include/boost/math/interpolators/cardinal_quintic_hermite.hpp
deleted file mode 100644
index d2d1ce696..000000000
--- a/include/boost/math/interpolators/cardinal_quintic_hermite.hpp
+++ /dev/null
@@ -1,56 +0,0 @@
-#ifndef BOOST_MATH_INTERPOLATORS_CARDINAL_QUINTIC_HERMITE_HPP
-#define BOOST_MATH_INTERPOLATORS_CARDINAL_QUINTIC_HERMITE_HPP
-#include <algorithm>
-#include <stdexcept>
-#include <memory>
-#include <boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp>
-
-namespace boost::math::interpolators {
-
-template<class RandomAccessContainer>
-class cardinal_quintic_hermite {
-public:
-    using Real = typename RandomAccessContainer::value_type;
-    cardinal_quintic_hermite(RandomAccessContainer && y, RandomAccessContainer && dydx, RandomAccessContainer && d2ydx2, Real x0, Real dx)
-     : impl_(std::make_shared<detail::cardinal_quintic_hermite_detail<RandomAccessContainer>>(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx))
-    {}
-
-    inline Real operator()(Real x) const {
-        return impl_->operator()(x);
-    }
-
-    inline Real prime(Real x) const {
-        return impl_->prime(x);
-    }
-
-    inline Real double_prime(Real x) const {
-        return impl_->double_prime(x);
-    }
-
-private:
-    std::shared_ptr<detail::cardinal_quintic_hermite_detail<RandomAccessContainer>> impl_;
-};
-
-template<class RandomAccessContainer>
-class cardinal_quintic_hermite_aos {
-public:
-    using Point = typename RandomAccessContainer::value_type;
-    using Real = typename Point::value_type;
-    cardinal_quintic_hermite_aos(RandomAccessContainer && data, Real x0, Real dx)
-     : impl_(std::make_shared<detail::cardinal_quintic_hermite_detail_aos<RandomAccessContainer>>(std::move(data), x0, dx))
-    {}
-
-    inline Real operator()(Real x) const {
-        return impl_->operator()(x);
-    }
-
-    inline Real prime(Real x) const {
-        return impl_->prime(x);
-    }
-
-private:
-    std::shared_ptr<detail::cardinal_quintic_hermite_detail_aos<RandomAccessContainer>> impl_;
-};
-
-}
-#endif 
\ No newline at end of file
diff --git a/include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp b/include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp
deleted file mode 100644
index 28944f76d..000000000
--- a/include/boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp
+++ /dev/null
@@ -1,297 +0,0 @@
-#ifndef BOOST_MATH_INTERPOLATORS_DETAIL_CARDINAL_QUINTIC_HERMITE_DETAIL_HPP
-#define BOOST_MATH_INTERPOLATORS_DETAIL_CARDINAL_QUINTIC_HERMITE_DETAIL_HPP
-#include <algorithm>
-#include <stdexcept>
-#include <sstream>
-#include <cmath>
-
-namespace boost::math::interpolators::detail {
-
-template<class RandomAccessContainer>
-class cardinal_quintic_hermite_detail {
-public:
-    using Real = typename RandomAccessContainer::value_type;
-    cardinal_quintic_hermite_detail(RandomAccessContainer && y, RandomAccessContainer && dydx, RandomAccessContainer && d2ydx2, Real x0, Real dx)
-    : y_{std::move(y)}, dy_{std::move(dydx)}, d2y_{std::move(d2ydx2)}, x0_{x0}, inv_dx_{1/dx}
-    {
-        if (y_.size() != dy_.size())
-        {
-            throw std::domain_error("Numbers of derivatives must = number of abscissas.");
-        }
-        if (y_.size() != d2y_.size())
-        {
-            throw std::domain_error("Number of second derivatives must equal number of abscissas.");
-        }
-        if (y_.size() < 2)
-        {
-            throw std::domain_error("At least 2 abscissas are required.");
-        }
-        if (dx <= 0)
-        {
-            throw std::domain_error("dx > 0 is required.");
-        }
-
-        for (auto & dy : dy_)
-        {
-            dy *= dx;
-        }
-
-        for (auto & d2y : d2y_)
-        {
-            d2y *= (dx*dx)/2;
-        }
-    }
-
-
-    inline Real operator()(Real x) const
-    {
-        const Real xf = x0_ + (y_.size()-1)/inv_dx_;
-        if  (x < x0_ || x > xf)
-        {
-            std::ostringstream oss;
-            oss.precision(std::numeric_limits<Real>::digits10+3);
-            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
-                << x0_ << ", " << xf << "]";
-            throw std::domain_error(oss.str());
-        }
-        if (x == xf)
-        {
-            return y_.back();
-        }
-        return this->unchecked_evaluation(x);
-    }
-
-    inline Real unchecked_evaluation(Real x) const
-    {
-        using std::floor;
-        Real s = (x-x0_)*inv_dx_;
-        Real ii = floor(s);
-        auto i = static_cast<decltype(y_.size())>(ii);
-        Real t = s - ii;
-
-        Real y0 = y_[i];
-        Real y1 = y_[i+1];
-        Real dy0 = dy_[i];
-        Real dy1 = dy_[i+1];
-        Real d2y0 = d2y_[i];
-        Real d2y1 = d2y_[i+1];
-
-        // See the 'Basis functions' section of:
-        // https://www.rose-hulman.edu/~finn/CCLI/Notes/day09.pdf
-        // Also: https://github.com/MrHexxx/QuinticHermiteSpline/blob/master/HermiteSpline.cs
-        Real y = (1- t*t*t*(10 + t*(-15 + 6*t)))*y0;
-        y += t*(1+ t*t*(-6 + t*(8 -3*t)))*dy0;
-        y += t*t*(1 + t*(-3 + t*(3-t)))*d2y0;
-        y += t*t*t*((1 + t*(-2 + t))*d2y1 + (-4 + t*(7 -3*t))*dy1 + (10 + t*(-15 + 6*t))*y1);
-        return y;
-    }
-
-    inline Real prime(Real x) const
-    {
-        const Real xf = x0_ + (y_.size()-1)/inv_dx_;
-        if  (x < x0_ || x > xf)
-        {
-            std::ostringstream oss;
-            oss.precision(std::numeric_limits<Real>::digits10+3);
-            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
-                << x0_ << ", " << xf << "]";
-            throw std::domain_error(oss.str());
-        }
-        if (x == xf)
-        {
-            return dy_.back()*inv_dx_;
-        }
-
-        return this->unchecked_prime(x);
-    }
-
-    inline Real unchecked_prime(Real x) const
-    {
-        using std::floor;
-        Real s = (x-x0_)*inv_dx_;
-        Real ii = floor(s);
-        auto i = static_cast<decltype(y_.size())>(ii);
-        Real t = s - ii;
-
-        Real y0 = y_[i];
-        Real y1 = y_[i+1];
-        Real dy0 = dy_[i];
-        Real dy1 = dy_[i+1];
-        Real d2y0 = d2y_[i];
-        Real d2y1 = d2y_[i+1];
-
-        Real dydx = 30*t*t*(1 - 2*t + t*t)*(y1-y0);
-        dydx += (1-18*t*t + 32*t*t*t - 15*t*t*t*t)*dy0 - t*t*(12 - 28*t + 15*t*t)*dy1;
-        dydx += t*((2 - 9*t + 12*t*t - 5*t*t*t)*d2y0 + t*(3 - 8*t + 5*t*t)*d2y1);
-        dydx *= inv_dx_;
-        return dydx;
-    }
-
-    inline Real double_prime(Real x) const {
-        const Real xf = x0_ + (y_.size()-1)/inv_dx_;
-        if  (x < x0_ || x > xf) {
-            std::ostringstream oss;
-            oss.precision(std::numeric_limits<Real>::digits10+3);
-            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
-                << x0_ << ", " << xf << "]";
-            throw std::domain_error(oss.str());
-        }
-        if (x == xf)
-        {
-            return d2y_.back()*2*inv_dx_*inv_dx_;
-        }
-
-        return this->unchecked_double_prime(x);
-    }
-
-    inline Real unchecked_double_prime(Real x) const {
-        using std::floor;
-        Real s = (x-x0_)*inv_dx_;
-        Real ii = floor(s);
-        auto i = static_cast<decltype(y_.size())>(ii);
-        Real t = s - ii;
-
-
-        Real y0 = y_[i];
-        Real y1 = y_[i+1];
-        Real dy0 = dy_[i];
-        Real dy1 = dy_[i+1];
-        Real d2y0 = d2y_[i];
-        Real d2y1 = d2y_[i+1];
-
-        Real d2ydx2 = 60*t*(1 - 3*t + 2*t*t)*(y1 - y0)*inv_dx_*inv_dx_;
-        d2ydx2 += (12*t)*((-3 + 8*t - 5*t*t)*dy0 - (2 - 7*t + 5*t*t)*dy1);
-        d2ydx2 += (1 - 9*t + 18*t*t - 10*t*t*t)*d2y0*(2*inv_dx_*inv_dx_) + t*(3 - 12*t + 10*t*t)*d2y1*(2*inv_dx_*inv_dx_);
-        return d2ydx2;
-    }
-
-private:
-    RandomAccessContainer y_;
-    RandomAccessContainer dy_;
-    RandomAccessContainer d2y_;
-    Real x0_;
-    Real inv_dx_;
-};
-
-
-template<class RandomAccessContainer>
-class cardinal_quintic_hermite_detail_aos {
-public:
-    using Point = typename RandomAccessContainer::value_type;
-    using Real = typename Point::value_type;
-    cardinal_quintic_hermite_detail_aos(RandomAccessContainer && data, Real x0, Real dx)
-    : data_{std::move(data)} , x0_{x0}, inv_dx_{1/dx}
-    {
-        if (data_.size() < 2)
-        {
-            throw std::domain_error("At least two points are required to interpolate using cardinal_quintic_hermite_aos");
-        }
-
-        if (data_[0].size() != 3)
-        {
-            throw std::domain_error("Each datum passed to the cardinal_quintic_hermite_aos must have three elements: {y, y', y''}");
-        }
-        if (dx <= 0)
-        {
-            throw std::domain_error("dx > 0 is required.");
-        }
-
-        for (auto & datum : data_)
-        {
-            datum[1] *= dx;
-            datum[2] *= (dx*dx/2);
-        }
-    }
-
-
-    inline Real operator()(Real x) const
-    {
-        const Real xf = x0_ + (data_.size()-1)/inv_dx_;
-        if  (x < x0_ || x > xf)
-        {
-            std::ostringstream oss;
-            oss.precision(std::numeric_limits<Real>::digits10+3);
-            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
-                << x0_ << ", " << xf << "]";
-            throw std::domain_error(oss.str());
-        }
-        if (x == xf)
-        {
-            return data_.back()[0];
-        }
-        return this->unchecked_evaluation(x);
-    }
-
-    inline Real unchecked_evaluation(Real x) const
-    {
-        using std::floor;
-        Real s = (x-x0_)*inv_dx_;
-        Real ii = floor(s);
-        auto i = static_cast<decltype(data_.size())>(ii);
-        Real t = s - ii;
-
-
-        Real y0 = data_[i][0];
-        Real dy0 = data_[i][1];
-        Real d2y0 = data_[i][2];
-        Real y1 = data_[i+1][0];
-        Real dy1 = data_[i+1][1];
-        Real d2y1 = data_[i+1][2];
-
-        Real y = (1- t*t*t*(10 + t*(-15 + 6*t)))*y0;
-        y += t*(1+ t*t*(-6 + t*(8 -3*t)))*dy0;
-        y += t*t*(1 + t*(-3 + t*(3-t)))*d2y0;
-        y += t*t*t*((1 + t*(-2 + t))*d2y1 + (-4 + t*(7 -3*t))*dy1 + (10 + t*(-15 + 6*t))*y1);
-        return y;
-    }
-
-    inline Real prime(Real x) const
-    {
-        const Real xf = x0_ + (data_.size()-1)/inv_dx_;
-        if  (x < x0_ || x > xf)
-        {
-            std::ostringstream oss;
-            oss.precision(std::numeric_limits<Real>::digits10+3);
-            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
-                << x0_ << ", " << xf << "]";
-            throw std::domain_error(oss.str());
-        }
-        if (x == xf)
-        {
-            return data_.back()[1]*inv_dx_;
-        }
-
-        return this->unchecked_prime(x);
-    }
-
-    inline Real unchecked_prime(Real x) const {
-        using std::floor;
-        Real s = (x-x0_)*inv_dx_;
-        Real ii = floor(s);
-        auto i = static_cast<decltype(data_.size())>(ii);
-        Real t = s - ii;
-
-
-        Real y0 = data_[i][0];
-        Real y1 = data_[i+1][0];
-        Real v0 = data_[i][1];
-        Real v1 = data_[i+1][1];
-        Real a0 = data_[i][2];
-        Real a1 = data_[i+1][2];
-
-        Real dy = 30*t*t*(1 - 2*t + t*t)*(y1-y0);
-        dy += (1-18*t*t + 32*t*t*t - 15*t*t*t*t)*v0 - t*t*(12 - 28*t + 15*t*t)*v1;
-        dy += t*((2 - 9*t + 12*t*t - 5*t*t*t)*a0 + t*(3 - 8*t + 5*t*t)*a1);
-        return dy*inv_dx_;
-    }
-
-
-
-private:
-    RandomAccessContainer data_;
-    Real x0_;
-    Real inv_dx_;
-};
-
-}
-#endif
diff --git a/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp b/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
index 84f64df9e..18a1990c7 100644
--- a/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
@@ -13,20 +13,25 @@ public:
     using Real = typename RandomAccessContainer::value_type;
     quintic_hermite_detail(RandomAccessContainer && x, RandomAccessContainer && y, RandomAccessContainer && dydx, RandomAccessContainer && d2ydx2) : x_{std::move(x)}, y_{std::move(y)}, dydx_{std::move(dydx)}, d2ydx2_{std::move(d2ydx2)}
     {
-        if (x_.size() != y_.size()) {
+        if (x_.size() != y_.size())
+        {
             throw std::domain_error("Number of abscissas must = number of ordinates.");
         }
-        if (x_.size() != dydx_.size()) {
+        if (x_.size() != dydx_.size())
+        {
             throw std::domain_error("Numbers of derivatives must = number of abscissas.");
         }
-        if (x_.size() != d2ydx2_.size()) {
+        if (x_.size() != d2ydx2_.size())
+        {
             throw std::domain_error("Number of second derivatives must equal number of abscissas.");
         }
-        if (x_.size() < 2) {
+        if (x_.size() < 2)
+        {
             throw std::domain_error("At least 2 abscissas are required.");
         }
         Real x0 = x_[0];
-        for (decltype(x_.size()) i = 1; i < x_.size(); ++i) {
+        for (decltype(x_.size()) i = 1; i < x_.size(); ++i)
+        {
             Real x1 = x_[i];
             if (x1 <= x0)
             {
@@ -36,7 +41,8 @@ public:
         }
     }
 
-    void push_back(Real x, Real y, Real dydx, Real d2ydx2) {
+    void push_back(Real x, Real y, Real dydx, Real d2ydx2)
+    {
         using std::abs;
         using std::isnan;
         if (x <= x_.back())
@@ -50,7 +56,8 @@ public:
     }
 
     inline Real operator()(Real x) const {
-        if  (x < x_[0] || x > x_.back()) {
+        if  (x < x_[0] || x > x_.back())
+        {
             std::ostringstream oss;
             oss.precision(std::numeric_limits<Real>::digits10+3);
             oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
@@ -59,7 +66,8 @@ public:
         }
         // We need t := (x-x_k)/(x_{k+1}-x_k) \in [0,1) for this to work.
         // Sadly this neccessitates this loathesome check, otherwise we get t = 1 at x = xf.
-        if (x == x_.back()) {
+        if (x == x_.back())
+        {
             return y_.back();
         }
 
@@ -76,26 +84,31 @@ public:
 
         Real dx = (x1-x0);
         Real t = (x-x0)/dx;
+        Real t2 = t*t;
+        Real t3 = t2*t;
 
         // See the 'Basis functions' section of:
         // https://www.rose-hulman.edu/~finn/CCLI/Notes/day09.pdf
         // Also: https://github.com/MrHexxx/QuinticHermiteSpline/blob/master/HermiteSpline.cs
-        Real y = (1- t*t*t*(10 + t*(-15 + 6*t)))*y0;
-        y += t*(1+ t*t*(-6 + t*(8 -3*t)))*v0*dx;
-        y += t*t*(1 + t*(-3 + t*(3-t)))*a0*dx*dx/2;
-        y += t*t*t*((1 + t*(-2 + t))*a1*dx*dx/2 + (-4 + t*(7 -3*t))*v1*dx + (10 + t*(-15 + 6*t))*y1);
+        Real y = (1- t3*(10 + t*(-15 + 6*t)))*y0;
+        y += t*(1+ t2*(-6 + t*(8 -3*t)))*v0*dx;
+        y += t2*(1 + t*(-3 + t*(3-t)))*a0*dx*dx/2;
+        y += t3*((1 + t*(-2 + t))*a1*dx*dx/2 + (-4 + t*(7 - 3*t))*v1*dx + (10 + t*(-15 + 6*t))*y1);
         return y;
     }
 
-    inline Real prime(Real x) const {
-        if  (x < x_[0] || x > x_.back()) {
+    inline Real prime(Real x) const
+    {
+        if  (x < x_[0] || x > x_.back())
+        {
             std::ostringstream oss;
             oss.precision(std::numeric_limits<Real>::digits10+3);
             oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
                 << x_[0] << ", " << x_.back() << "]";
             throw std::domain_error(oss.str());
         }
-        if (x == x_.back()) {
+        if (x == x_.back())
+        {
             return dydx_.back();
         }
 
@@ -112,13 +125,51 @@ public:
         Real a0 = d2ydx2_[i];
         Real a1 = d2ydx2_[i+1];
         Real t= (x-x0)/dx;
+        Real t2 = t*t;
 
-        Real dydx = 30*t*t*(1 - 2*t + t*t)*(y1-y0)/dx;
+        Real dydx = 30*t2*(1 - 2*t + t*t)*(y1-y0)/dx;
         dydx += (1-18*t*t + 32*t*t*t - 15*t*t*t*t)*v0 - t*t*(12 - 28*t + 15*t*t)*v1;
         dydx += (t*dx/2)*((2 - 9*t + 12*t*t - 5*t*t*t)*a0 + t*(3 - 8*t + 5*t*t)*a1);
         return dydx;
     }
 
+   inline Real double_prime(Real x) const
+    {
+        if  (x < x_[0] || x > x_.back())
+        {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x_[0] << ", " << x_.back() << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == x_.back())
+        {
+            return d2ydx2_.back();
+        }
+
+        auto it = std::upper_bound(x_.begin(), x_.end(), x);
+        auto i = std::distance(x_.begin(), it) -1;
+        Real x0 = *(it-1);
+        Real x1 = *it;
+        Real dx = x1 - x0;
+
+        Real y0 = y_[i];
+        Real y1 = y_[i+1];
+        Real v0 = dydx_[i];
+        Real v1 = dydx_[i+1];
+        Real a0 = d2ydx2_[i];
+        Real a1 = d2ydx2_[i+1];
+        Real t = (x-x0)/dx;
+
+        Real d2ydx2 = 60*t*(1 + t*(-3 + 2*t))*(y1-y0)/(dx*dx);
+        d2ydx2 += 12*t*(-3 + t*(8 - 5*t))*v0/dx;
+        d2ydx2 -= 12*t*(2 + t*(-7 + 5*t))*v1/dx;
+        d2ydx2 += (1 + t*(-9 + t*(18 - 10*t)))*a0;
+        d2ydx2 += t*(3 + t*(-12 + 10*t))*a1;
+
+        return d2ydx2;
+    }
 
     friend std::ostream& operator<<(std::ostream & os, const quintic_hermite_detail & m)
     {
@@ -131,13 +182,337 @@ public:
         return os;
     }
 
-
-
 private:
     RandomAccessContainer x_;
     RandomAccessContainer y_;
     RandomAccessContainer dydx_;
     RandomAccessContainer d2ydx2_;
 };
+
+
+template<class RandomAccessContainer>
+class cardinal_quintic_hermite_detail {
+public:
+    using Real = typename RandomAccessContainer::value_type;
+    cardinal_quintic_hermite_detail(RandomAccessContainer && y, RandomAccessContainer && dydx, RandomAccessContainer && d2ydx2, Real x0, Real dx)
+    : y_{std::move(y)}, dy_{std::move(dydx)}, d2y_{std::move(d2ydx2)}, x0_{x0}, inv_dx_{1/dx}
+    {
+        if (y_.size() != dy_.size())
+        {
+            throw std::domain_error("Numbers of derivatives must = number of abscissas.");
+        }
+        if (y_.size() != d2y_.size())
+        {
+            throw std::domain_error("Number of second derivatives must equal number of abscissas.");
+        }
+        if (y_.size() < 2)
+        {
+            throw std::domain_error("At least 2 abscissas are required.");
+        }
+        if (dx <= 0)
+        {
+            throw std::domain_error("dx > 0 is required.");
+        }
+
+        for (auto & dy : dy_)
+        {
+            dy *= dx;
+        }
+
+        for (auto & d2y : d2y_)
+        {
+            d2y *= (dx*dx)/2;
+        }
+    }
+
+
+    inline Real operator()(Real x) const
+    {
+        const Real xf = x0_ + (y_.size()-1)/inv_dx_;
+        if  (x < x0_ || x > xf)
+        {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf)
+        {
+            return y_.back();
+        }
+        return this->unchecked_evaluation(x);
+    }
+
+    inline Real unchecked_evaluation(Real x) const
+    {
+        using std::floor;
+        Real s = (x-x0_)*inv_dx_;
+        Real ii = floor(s);
+        auto i = static_cast<decltype(y_.size())>(ii);
+        Real t = s - ii;
+
+        Real y0 = y_[i];
+        Real y1 = y_[i+1];
+        Real dy0 = dy_[i];
+        Real dy1 = dy_[i+1];
+        Real d2y0 = d2y_[i];
+        Real d2y1 = d2y_[i+1];
+
+        // See the 'Basis functions' section of:
+        // https://www.rose-hulman.edu/~finn/CCLI/Notes/day09.pdf
+        // Also: https://github.com/MrHexxx/QuinticHermiteSpline/blob/master/HermiteSpline.cs
+        Real y = (1- t*t*t*(10 + t*(-15 + 6*t)))*y0;
+        y += t*(1+ t*t*(-6 + t*(8 -3*t)))*dy0;
+        y += t*t*(1 + t*(-3 + t*(3-t)))*d2y0;
+        y += t*t*t*((1 + t*(-2 + t))*d2y1 + (-4 + t*(7 -3*t))*dy1 + (10 + t*(-15 + 6*t))*y1);
+        return y;
+    }
+
+    inline Real prime(Real x) const
+    {
+        const Real xf = x0_ + (y_.size()-1)/inv_dx_;
+        if  (x < x0_ || x > xf)
+        {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf)
+        {
+            return dy_.back()*inv_dx_;
+        }
+
+        return this->unchecked_prime(x);
+    }
+
+    inline Real unchecked_prime(Real x) const
+    {
+        using std::floor;
+        Real s = (x-x0_)*inv_dx_;
+        Real ii = floor(s);
+        auto i = static_cast<decltype(y_.size())>(ii);
+        Real t = s - ii;
+
+        Real y0 = y_[i];
+        Real y1 = y_[i+1];
+        Real dy0 = dy_[i];
+        Real dy1 = dy_[i+1];
+        Real d2y0 = d2y_[i];
+        Real d2y1 = d2y_[i+1];
+
+        Real dydx = 30*t*t*(1 - 2*t + t*t)*(y1-y0);
+        dydx += (1-18*t*t + 32*t*t*t - 15*t*t*t*t)*dy0 - t*t*(12 - 28*t + 15*t*t)*dy1;
+        dydx += t*((2 - 9*t + 12*t*t - 5*t*t*t)*d2y0 + t*(3 - 8*t + 5*t*t)*d2y1);
+        dydx *= inv_dx_;
+        return dydx;
+    }
+
+    inline Real double_prime(Real x) const {
+        const Real xf = x0_ + (y_.size()-1)/inv_dx_;
+        if  (x < x0_ || x > xf) {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf)
+        {
+            return d2y_.back()*2*inv_dx_*inv_dx_;
+        }
+
+        return this->unchecked_double_prime(x);
+    }
+
+    inline Real unchecked_double_prime(Real x) const {
+        using std::floor;
+        Real s = (x-x0_)*inv_dx_;
+        Real ii = floor(s);
+        auto i = static_cast<decltype(y_.size())>(ii);
+        Real t = s - ii;
+
+
+        Real y0 = y_[i];
+        Real y1 = y_[i+1];
+        Real dy0 = dy_[i];
+        Real dy1 = dy_[i+1];
+        Real d2y0 = d2y_[i];
+        Real d2y1 = d2y_[i+1];
+
+        Real d2ydx2 = 60*t*(1 - 3*t + 2*t*t)*(y1 - y0)*inv_dx_*inv_dx_;
+        d2ydx2 += (12*t)*((-3 + 8*t - 5*t*t)*dy0 - (2 - 7*t + 5*t*t)*dy1);
+        d2ydx2 += (1 - 9*t + 18*t*t - 10*t*t*t)*d2y0*(2*inv_dx_*inv_dx_) + t*(3 - 12*t + 10*t*t)*d2y1*(2*inv_dx_*inv_dx_);
+        return d2ydx2;
+    }
+
+private:
+    RandomAccessContainer y_;
+    RandomAccessContainer dy_;
+    RandomAccessContainer d2y_;
+    Real x0_;
+    Real inv_dx_;
+};
+
+
+template<class RandomAccessContainer>
+class cardinal_quintic_hermite_detail_aos {
+public:
+    using Point = typename RandomAccessContainer::value_type;
+    using Real = typename Point::value_type;
+    cardinal_quintic_hermite_detail_aos(RandomAccessContainer && data, Real x0, Real dx)
+    : data_{std::move(data)} , x0_{x0}, inv_dx_{1/dx}
+    {
+        if (data_.size() < 2)
+        {
+            throw std::domain_error("At least two points are required to interpolate using cardinal_quintic_hermite_aos");
+        }
+
+        if (data_[0].size() != 3)
+        {
+            throw std::domain_error("Each datum passed to the cardinal_quintic_hermite_aos must have three elements: {y, y', y''}");
+        }
+        if (dx <= 0)
+        {
+            throw std::domain_error("dx > 0 is required.");
+        }
+
+        for (auto & datum : data_)
+        {
+            datum[1] *= dx;
+            datum[2] *= (dx*dx/2);
+        }
+    }
+
+
+    inline Real operator()(Real x) const
+    {
+        const Real xf = x0_ + (data_.size()-1)/inv_dx_;
+        if  (x < x0_ || x > xf)
+        {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf)
+        {
+            return data_.back()[0];
+        }
+        return this->unchecked_evaluation(x);
+    }
+
+    inline Real unchecked_evaluation(Real x) const
+    {
+        using std::floor;
+        Real s = (x-x0_)*inv_dx_;
+        Real ii = floor(s);
+        auto i = static_cast<decltype(data_.size())>(ii);
+        Real t = s - ii;
+
+
+        Real y0 = data_[i][0];
+        Real dy0 = data_[i][1];
+        Real d2y0 = data_[i][2];
+        Real y1 = data_[i+1][0];
+        Real dy1 = data_[i+1][1];
+        Real d2y1 = data_[i+1][2];
+
+        Real y = (1- t*t*t*(10 + t*(-15 + 6*t)))*y0;
+        y += t*(1+ t*t*(-6 + t*(8 -3*t)))*dy0;
+        y += t*t*(1 + t*(-3 + t*(3-t)))*d2y0;
+        y += t*t*t*((1 + t*(-2 + t))*d2y1 + (-4 + t*(7 -3*t))*dy1 + (10 + t*(-15 + 6*t))*y1);
+        return y;
+    }
+
+    inline Real prime(Real x) const
+    {
+        const Real xf = x0_ + (data_.size()-1)/inv_dx_;
+        if  (x < x0_ || x > xf)
+        {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf)
+        {
+            return data_.back()[1]*inv_dx_;
+        }
+
+        return this->unchecked_prime(x);
+    }
+
+    inline Real unchecked_prime(Real x) const {
+        using std::floor;
+        Real s = (x-x0_)*inv_dx_;
+        Real ii = floor(s);
+        auto i = static_cast<decltype(data_.size())>(ii);
+        Real t = s - ii;
+
+
+        Real y0 = data_[i][0];
+        Real y1 = data_[i+1][0];
+        Real v0 = data_[i][1];
+        Real v1 = data_[i+1][1];
+        Real a0 = data_[i][2];
+        Real a1 = data_[i+1][2];
+
+        Real dy = 30*t*t*(1 - 2*t + t*t)*(y1-y0);
+        dy += (1-18*t*t + 32*t*t*t - 15*t*t*t*t)*v0 - t*t*(12 - 28*t + 15*t*t)*v1;
+        dy += t*((2 - 9*t + 12*t*t - 5*t*t*t)*a0 + t*(3 - 8*t + 5*t*t)*a1);
+        return dy*inv_dx_;
+    }
+
+    inline Real double_prime(Real x) const {
+        const Real xf = x0_ + (data_.size()-1)/inv_dx_;
+        if  (x < x0_ || x > xf)
+        {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf)
+        {
+            return data_.back()[2]*2*inv_dx_*inv_dx_;
+        }
+
+        return this->unchecked_double_prime(x);
+    }
+
+    inline Real unchecked_double_prime(Real x) const {
+        using std::floor;
+        Real s = (x-x0_)*inv_dx_;
+        Real ii = floor(s);
+        auto i = static_cast<decltype(data_.size())>(ii);
+        Real t = s - ii;
+
+
+        Real y0 = data_[i][0];
+        Real dy0 = data_[i][1];
+        Real d2y0 = data_[i][2];
+        Real y1 = data_[i+1][0];
+        Real dy1 = data_[i+1][1];
+        Real d2y1 = data_[i+1][2];
+
+        Real d2ydx2 = 60*t*(1 - 3*t + 2*t*t)*(y1 - y0)*inv_dx_*inv_dx_;
+        d2ydx2 += (12*t)*((-3 + 8*t - 5*t*t)*dy0 - (2 - 7*t + 5*t*t)*dy1);
+        d2ydx2 += (1 - 9*t + 18*t*t - 10*t*t*t)*d2y0*(2*inv_dx_*inv_dx_) + t*(3 - 12*t + 10*t*t)*d2y1*(2*inv_dx_*inv_dx_);
+        return d2ydx2;
+    }
+
+
+private:
+    RandomAccessContainer data_;
+    Real x0_;
+    Real inv_dx_;
+};
+
 }
-#endif 
\ No newline at end of file
+#endif
diff --git a/include/boost/math/interpolators/quintic_hermite.hpp b/include/boost/math/interpolators/quintic_hermite.hpp
index 0111df9a1..59fe7fa9b 100644
--- a/include/boost/math/interpolators/quintic_hermite.hpp
+++ b/include/boost/math/interpolators/quintic_hermite.hpp
@@ -23,6 +23,10 @@ public:
         return impl_->prime(x);
     }
 
+    Real double_prime(Real x) const {
+        return impl_->double_prime(x);
+    }
+
     friend std::ostream& operator<<(std::ostream & os, const quintic_hermite & m)
     {
         os << *m.impl_;
@@ -37,5 +41,56 @@ public:
 private:
     std::shared_ptr<detail::quintic_hermite_detail<RandomAccessContainer>> impl_;
 };
+
+template<class RandomAccessContainer>
+class cardinal_quintic_hermite {
+public:
+    using Real = typename RandomAccessContainer::value_type;
+    cardinal_quintic_hermite(RandomAccessContainer && y, RandomAccessContainer && dydx, RandomAccessContainer && d2ydx2, Real x0, Real dx)
+     : impl_(std::make_shared<detail::cardinal_quintic_hermite_detail<RandomAccessContainer>>(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx))
+    {}
+
+    inline Real operator()(Real x) const {
+        return impl_->operator()(x);
+    }
+
+    inline Real prime(Real x) const {
+        return impl_->prime(x);
+    }
+
+    inline Real double_prime(Real x) const {
+        return impl_->double_prime(x);
+    }
+
+private:
+    std::shared_ptr<detail::cardinal_quintic_hermite_detail<RandomAccessContainer>> impl_;
+};
+
+template<class RandomAccessContainer>
+class cardinal_quintic_hermite_aos {
+public:
+    using Point = typename RandomAccessContainer::value_type;
+    using Real = typename Point::value_type;
+    cardinal_quintic_hermite_aos(RandomAccessContainer && data, Real x0, Real dx)
+     : impl_(std::make_shared<detail::cardinal_quintic_hermite_detail_aos<RandomAccessContainer>>(std::move(data), x0, dx))
+    {}
+
+    inline Real operator()(Real x) const {
+        return impl_->operator()(x);
+    }
+
+    inline Real prime(Real x) const {
+        return impl_->prime(x);
+    }
+
+    inline Real double_prime(Real x) const {
+        return impl_->double_prime(x);
+    }
+
+private:
+    std::shared_ptr<detail::cardinal_quintic_hermite_detail_aos<RandomAccessContainer>> impl_;
+};
+
+
 }
-#endif 
\ No newline at end of file
+#endif
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index 5d7ff0140..82abb2356 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -21,7 +21,6 @@
 #include <boost/math/filters/daubechies.hpp>
 #include <boost/math/interpolators/detail/cubic_hermite_detail.hpp>
 #include <boost/math/interpolators/detail/quintic_hermite_detail.hpp>
-#include <boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp>
 #include <boost/math/interpolators/detail/septic_hermite_detail.hpp>
 
 
diff --git a/test/cardinal_quintic_hermite_test.cpp b/test/cardinal_quintic_hermite_test.cpp
deleted file mode 100644
index 20f1bf633..000000000
--- a/test/cardinal_quintic_hermite_test.cpp
+++ /dev/null
@@ -1,252 +0,0 @@
-/*
- * Copyright Nick Thompson, 2020
- * Use, modification and distribution are subject to the
- * Boost Software License, Version 1.0. (See accompanying file
- * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
- */
-
-#include "math_unit_test.hpp"
-#include <numeric>
-#include <utility>
-#include <boost/math/interpolators/cardinal_quintic_hermite.hpp>
-#ifdef BOOST_HAS_FLOAT128
-#include <boost/multiprecision/float128.hpp>
-using boost::multiprecision::float128;
-#endif
-
-
-using boost::math::interpolators::cardinal_quintic_hermite;
-using boost::math::interpolators::cardinal_quintic_hermite_aos;
-
-template<typename Real>
-void test_constant()
-{
-
-    std::vector<Real> y(25);
-    std::vector<Real> dydx(y.size(), 0);
-    std::vector<Real> d2ydx2(y.size(), 0);
-    for (auto & t : y) {
-        t = 7;
-    }
-    Real x0 = 4;
-    Real dx = Real(1)/Real(8);
-
-    auto qh = cardinal_quintic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx);
-
-    for (Real t = x0; t <= x0 + 24*dx; t += 0.25) {
-        CHECK_ULP_CLOSE(Real(7), qh(t), 24);
-        CHECK_ULP_CLOSE(Real(0), qh.prime(t), 24);
-        CHECK_ULP_CLOSE(Real(0), qh.double_prime(t), 24);
-    }
-
-    std::vector<std::array<Real, 3>> data(25);
-    for (size_t i = 0; i < data.size(); ++i)
-    {
-        data[i][0] = 7;
-        data[i][1] = 0;
-        data[i][2] = 0;
-    }
-
-    auto qh_aos = cardinal_quintic_hermite_aos(std::move(data), x0, dx);
-    for (Real t = x0; t <= x0 + 24*dx; t += 0.25) {
-        CHECK_ULP_CLOSE(Real(7), qh_aos(t), 24);
-        CHECK_ULP_CLOSE(Real(0), qh_aos.prime(t), 24);
-    }
-}
-
-
-template<typename Real>
-void test_linear()
-{
-    std::vector<Real> y{0,1,2,3,4,5,6,7,8,9};
-    Real x0 = 0;
-    Real dx = 1;
-    std::vector<Real> dydx(y.size(), 1);
-    std::vector<Real> d2ydx2(y.size(), 0);
-
-    auto qh = cardinal_quintic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx);
-
-    for (Real t = 0; t <= 9; t += 0.25) {
-        CHECK_ULP_CLOSE(Real(t), qh(t), 2);
-        CHECK_ULP_CLOSE(Real(1), qh.prime(t), 2);
-        CHECK_ULP_CLOSE(Real(0), qh.double_prime(t), 2);
-    }
-
-    std::vector<std::array<Real, 3>> data(10);
-    for (size_t i = 0; i < data.size(); ++i) {
-        data[i][0] = i;
-        data[i][1] = 1;
-        data[i][2] = 0;
-    }
-
-    auto qh_aos = cardinal_quintic_hermite_aos(std::move(data), x0, dx);
-
-    for (Real t = 0; t <= 9; t += 0.25) {
-        CHECK_ULP_CLOSE(Real(t), qh_aos(t), 2);
-        CHECK_ULP_CLOSE(Real(1), qh_aos.prime(t), 2);
-        //CHECK_ULP_CLOSE(Real(0), qh_aos.double_prime(t), 2);
-    }
-
-}
-
-template<typename Real>
-void test_quadratic()
-{
-    Real x0 = 0;
-    Real dx = 1;
-    std::vector<Real> y(10);
-    for (size_t i = 0; i < y.size(); ++i)
-    {
-        y[i] = i*i/Real(2);
-    }
-
-    std::vector<Real> dydx(y.size());
-    for (size_t i = 0; i < y.size(); ++i) {
-        dydx[i] = i;
-    }
-
-    std::vector<Real> d2ydx2(y.size(), 1);
-
-    auto qh = cardinal_quintic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx);
-
-    for (Real t = 0; t <= 9; t += 0.0078125) {
-        Real computed = qh(t);
-        CHECK_ULP_CLOSE(Real(t*t)/2, computed, 2);
-        CHECK_ULP_CLOSE(t, qh.prime(t), 15);
-        CHECK_ULP_CLOSE(1, qh.double_prime(t), 32);
-    }
-
-    std::vector<std::array<Real, 3>> data(10);
-    for (size_t i = 0; i < data.size(); ++i) {
-        data[i][0] = i*i/Real(2);
-        data[i][1] = i;
-        data[i][2] = 1;
-    }
-    auto qh_aos = cardinal_quintic_hermite_aos(std::move(data), x0, dx);
-
-    for (Real t = 0; t <= 9; t += 0.0078125) {
-        Real computed = qh_aos(t);
-        CHECK_ULP_CLOSE(Real(t*t)/2, computed, 2);
-        CHECK_ULP_CLOSE(t, qh_aos.prime(t), 7);
-    }
-}
-
-template<typename Real>
-void test_cubic()
-{
-    Real x0 = 0;
-    Real dx = 1;
-    std::vector<Real> y(10);
-    for (size_t i = 0; i < y.size(); ++i)
-    {
-        y[i] = i*i*i/Real(6);
-    }
-
-    std::vector<Real> dydx(y.size());
-    for (size_t i = 0; i < y.size(); ++i) {
-        dydx[i] = i*i/Real(2);
-    }
-
-    std::vector<Real> d2ydx2(y.size());
-    for (size_t i = 0; i < y.size(); ++i) {
-        d2ydx2[i] = i;
-    }
-
-    auto qh = cardinal_quintic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx);
-
-    for (Real t = 0; t <= 9; t += 0.0078125) {
-        Real computed = qh(t);
-        CHECK_ULP_CLOSE(Real(t*t*t)/6, computed, 10);
-        CHECK_ULP_CLOSE(t*t/2, qh.prime(t), 15);
-        CHECK_ULP_CLOSE(t, qh.double_prime(t), 39);
-    }
-
-    std::vector<std::array<Real, 3>> data(10);
-    for (size_t i = 0; i < data.size(); ++i) {
-        data[i][0] = i*i*i/Real(6);
-        data[i][1] = i*i/Real(2);
-        data[i][2] = i;
-    }
-
-    auto qh_aos = cardinal_quintic_hermite_aos(std::move(data), x0, dx);
-    for (Real t = 0; t <= 9; t += 0.0078125) {
-        Real computed = qh_aos(t);
-        CHECK_ULP_CLOSE(Real(t*t*t)/6, computed, 10);
-        CHECK_ULP_CLOSE(t*t/2, qh_aos.prime(t), 10);
-    }
-}
-
-template<typename Real>
-void test_quartic()
-{
-    Real x0 = 0;
-    Real dx = 1;
-    std::vector<Real> y(7);
-    for (size_t i = 0; i < y.size(); ++i)
-    {
-        y[i] = i*i*i*i;
-    }
-
-    std::vector<Real> dydx(y.size());
-    for (size_t i = 0; i < y.size(); ++i) {
-        dydx[i] = 4*i*i*i;
-    }
-
-    std::vector<Real> d2ydx2(y.size());
-    for (size_t i = 0; i < y.size(); ++i) {
-        d2ydx2[i] = 12*i*i;
-    }
-
-    auto qh = cardinal_quintic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx);
-
-    for (Real t = 0; t <= 6; t += 0.0078125) {
-        CHECK_ULP_CLOSE(Real(t*t*t*t), qh(t), 250);
-        CHECK_ULP_CLOSE(4*t*t*t, qh.prime(t), 250);
-    }
-
-    std::vector<std::array<Real, 3>> data(7);
-    for (size_t i = 0; i < data.size(); ++i) {
-        data[i][0] = i*i*i*i;
-        data[i][1] = 4*i*i*i;
-        data[i][2] = 12*i*i;
-    }
-
-    auto qh_aos = cardinal_quintic_hermite_aos(std::move(data), x0, dx);
-    for (Real t = 0; t <= 6; t += 0.0078125) {
-        Real computed = qh_aos(t);
-        CHECK_ULP_CLOSE(t*t*t*t, computed, 10);
-        CHECK_ULP_CLOSE(4*t*t*t, qh_aos.prime(t), 64);
-    }
-}
-
-
-int main()
-{
-    test_constant<float>();
-    test_linear<float>();
-    test_quadratic<float>();
-    test_cubic<float>();
-    test_quartic<float>();
-
-    test_constant<double>();
-    test_linear<double>();
-    test_quadratic<double>();
-    test_cubic<double>();
-    test_quartic<double>();
-
-    test_constant<long double>();
-    test_linear<long double>();
-    test_quadratic<long double>();
-    test_cubic<long double>();
-    test_quartic<long double>();
-
-#ifdef BOOST_HAS_FLOAT128
-    test_constant<float128>();
-    test_linear<float128>();
-    test_quadratic<float128>();
-    test_cubic<float128>();
-    test_quartic<float128>();
-#endif
-
-    return boost::math::test::report_errors();
-}
diff --git a/test/quintic_hermite_test.cpp b/test/quintic_hermite_test.cpp
index 70547c879..4eea2f50a 100644
--- a/test/quintic_hermite_test.cpp
+++ b/test/quintic_hermite_test.cpp
@@ -19,27 +19,28 @@ using boost::multiprecision::float128;
 
 
 using boost::math::interpolators::quintic_hermite;
+using boost::math::interpolators::cardinal_quintic_hermite;
+using boost::math::interpolators::cardinal_quintic_hermite_aos;
 
 template<typename Real>
 void test_constant()
 {
-
     std::vector<Real> x{0,1,2,3, 9, 22, 81};
     std::vector<Real> y(x.size());
     std::vector<Real> dydx(x.size(), 0);
     std::vector<Real> d2ydx2(x.size(), 0);
-    for (auto & t : y) {
+    for (auto & t : y)
+    {
         t = 7;
     }
 
     auto qh = quintic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2));
-
-    for (Real t = 0; t <= 81; t += 0.25) {
+    for (Real t = 0; t <= 81; t += 0.25)
+    {
         CHECK_ULP_CLOSE(Real(7), qh(t), 24);
         CHECK_ULP_CLOSE(Real(0), qh.prime(t), 24);
+        CHECK_ULP_CLOSE(Real(0), qh.double_prime(t), 24);
     }
-
-
 }
 
 
@@ -53,9 +54,11 @@ void test_linear()
 
     auto qh = quintic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2));
 
-    for (Real t = 0; t <= 9; t += 0.25) {
+    for (Real t = 0; t <= 9; t += 0.25)
+    {
         CHECK_ULP_CLOSE(Real(t), qh(t), 2);
         CHECK_ULP_CLOSE(Real(1), qh.prime(t), 2);
+        CHECK_ULP_CLOSE(Real(0), qh.double_prime(t), 2);
     }
 
     boost::random::mt19937 rng;
@@ -63,7 +66,8 @@ void test_linear()
     x.resize(512);
     x[0] = dis(rng);
     Real xmin = x[0];
-    for (size_t i = 1; i < x.size(); ++i) {
+    for (size_t i = 1; i < x.size(); ++i)
+    {
         x[i] = x[i-1] + dis(rng);
     }
     Real xmax = x.back();
@@ -74,11 +78,12 @@ void test_linear()
 
     qh = quintic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2));
 
-    for (Real t = xmin; t <= xmax; t += 0.125) {
-        CHECK_ULP_CLOSE(Real(t), qh(t), 2);
+    for (Real t = xmin; t <= xmax; t += 0.125)
+    {
+        CHECK_ULP_CLOSE(t, qh(t), 2);
+        CHECK_ULP_CLOSE(Real(1), qh.prime(t), 100);
+        CHECK_MOLLIFIED_CLOSE(Real(0), qh.double_prime(t), 200*std::numeric_limits<Real>::epsilon());
     }
-
-
 }
 
 template<typename Real>
@@ -101,9 +106,11 @@ void test_quadratic()
 
     auto qh = quintic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2));
 
-    for (Real t = 0; t <= 9; t += 0.0078125) {
+    for (Real t = 0; t <= 9; t += 0.0078125)
+    {
         CHECK_ULP_CLOSE(Real(t*t)/2, qh(t), 2);
         CHECK_ULP_CLOSE(t, qh.prime(t), 7);
+        CHECK_ULP_CLOSE(Real(1), qh.double_prime(t), 32);
     }
 
     boost::random::mt19937 rng;
@@ -111,7 +118,8 @@ void test_quadratic()
     x.resize(8);
     x[0] = dis(rng);
     Real xmin = x[0];
-    for (size_t i = 1; i < x.size(); ++i) {
+    for (size_t i = 1; i < x.size(); ++i)
+    {
         x[i] = x[i-1] + dis(rng);
     }
     Real xmax = x.back();
@@ -123,7 +131,8 @@ void test_quadratic()
     }
 
     dydx.resize(x.size());
-    for (size_t i = 0; i < y.size(); ++i) {
+    for (size_t i = 0; i < y.size(); ++i)
+    {
         dydx[i] = x[i];
     }
 
@@ -131,9 +140,11 @@ void test_quadratic()
 
     qh = quintic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2));
 
-    for (Real t = xmin; t <= xmax; t += 0.125) {
+    for (Real t = xmin; t <= xmax; t += 0.125)
+    {
         CHECK_ULP_CLOSE(Real(t*t)/2, qh(t), 4);
         CHECK_ULP_CLOSE(t, qh.prime(t), 36);
+        CHECK_ULP_CLOSE(Real(1), qh.double_prime(t), 700);
     }
 }
 
@@ -145,23 +156,27 @@ void test_cubic()
     std::vector<Real> y(x.size());
     for (size_t i = 0; i < y.size(); ++i)
     {
-        y[i] = x[i]*x[i]*x[i]/6;
+        y[i] = x[i]*x[i]*x[i];
     }
 
     std::vector<Real> dydx(x.size());
     for (size_t i = 0; i < y.size(); ++i) {
-        dydx[i] = x[i]*x[i]/2;
+        dydx[i] = 3*x[i]*x[i];
     }
 
     std::vector<Real> d2ydx2(x.size());
-    for (size_t i = 0; i < y.size(); ++i) {
-        d2ydx2[i] = x[i];
+    for (size_t i = 0; i < y.size(); ++i)
+    {
+        d2ydx2[i] = 6*x[i];
     }
 
     auto qh = quintic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2));
 
-    for (Real t = 0; t <= 9; t += 0.0078125) {
-        CHECK_ULP_CLOSE(Real(t*t*t)/6, qh(t), 10);
+    for (Real t = 0; t <= 9; t += 0.0078125)
+    {
+        CHECK_ULP_CLOSE(t*t*t, qh(t), 10);
+        CHECK_ULP_CLOSE(3*t*t, qh.prime(t), 15);
+        CHECK_ULP_CLOSE(6*t, qh.double_prime(t), 20);
     }
 }
 
@@ -173,23 +188,28 @@ void test_quartic()
     std::vector<Real> y(x.size());
     for (size_t i = 0; i < y.size(); ++i)
     {
-        y[i] = x[i]*x[i]*x[i]*x[i]/24;
+        y[i] = x[i]*x[i]*x[i]*x[i];
     }
 
     std::vector<Real> dydx(x.size());
-    for (size_t i = 0; i < y.size(); ++i) {
-        dydx[i] = x[i]*x[i]*x[i]/6;
+    for (size_t i = 0; i < y.size(); ++i)
+    {
+        dydx[i] = 4*x[i]*x[i]*x[i];
     }
 
     std::vector<Real> d2ydx2(x.size());
-    for (size_t i = 0; i < y.size(); ++i) {
-        d2ydx2[i] = x[i]*x[i]/2;
+    for (size_t i = 0; i < y.size(); ++i)
+    {
+        d2ydx2[i] = 12*x[i]*x[i];
     }
 
     auto qh = quintic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2));
 
-    for (Real t = 1; t <= 11; t += 0.0078125) {
-        CHECK_ULP_CLOSE(Real(t*t*t*t)/24, qh(t), 100);
+    for (Real t = 1; t <= 11; t += 0.0078125)
+    {
+        CHECK_ULP_CLOSE(t*t*t*t, qh(t), 100);
+        CHECK_ULP_CLOSE(4*t*t*t, qh.prime(t), 100);
+        CHECK_ULP_CLOSE(12*t*t, qh.double_prime(t), 100);
     }
 }
 
@@ -223,10 +243,224 @@ void test_interpolation_condition()
         for (size_t i = 0; i < x.size(); ++i) {
             CHECK_ULP_CLOSE(y[i], s(x[i]), 2);
             CHECK_ULP_CLOSE(dydx[i], s.prime(x[i]), 2);
+            CHECK_ULP_CLOSE(d2ydx2[i], s.double_prime(x[i]), 2);
         }
     }
 }
 
+template<typename Real>
+void test_cardinal_constant()
+{
+
+    std::vector<Real> y(25);
+    std::vector<Real> dydx(y.size(), 0);
+    std::vector<Real> d2ydx2(y.size(), 0);
+    for (auto & t : y) {
+        t = 7;
+    }
+    Real x0 = 4;
+    Real dx = Real(1)/Real(8);
+
+    auto qh = cardinal_quintic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx);
+
+    for (Real t = x0; t <= x0 + 24*dx; t += 0.25)
+    {
+        CHECK_ULP_CLOSE(Real(7), qh(t), 24);
+        CHECK_ULP_CLOSE(Real(0), qh.prime(t), 24);
+        CHECK_ULP_CLOSE(Real(0), qh.double_prime(t), 24);
+    }
+
+    std::vector<std::array<Real, 3>> data(25);
+    for (size_t i = 0; i < data.size(); ++i)
+    {
+        data[i][0] = 7;
+        data[i][1] = 0;
+        data[i][2] = 0;
+    }
+
+    auto qh_aos = cardinal_quintic_hermite_aos(std::move(data), x0, dx);
+    for (Real t = x0; t <= x0 + 24*dx; t += 0.25)
+    {
+        CHECK_ULP_CLOSE(Real(7), qh_aos(t), 24);
+        CHECK_ULP_CLOSE(Real(0), qh_aos.prime(t), 24);
+        CHECK_ULP_CLOSE(Real(0), qh_aos.double_prime(t), 24);
+    }
+}
+
+
+template<typename Real>
+void test_cardinal_linear()
+{
+    std::vector<Real> y{0,1,2,3,4,5,6,7,8,9};
+    Real x0 = 0;
+    Real dx = 1;
+    std::vector<Real> dydx(y.size(), 1);
+    std::vector<Real> d2ydx2(y.size(), 0);
+
+    auto qh = cardinal_quintic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx);
+
+    for (Real t = 0; t <= 9; t += 0.25) {
+        CHECK_ULP_CLOSE(Real(t), qh(t), 2);
+        CHECK_ULP_CLOSE(Real(1), qh.prime(t), 2);
+        CHECK_ULP_CLOSE(Real(0), qh.double_prime(t), 2);
+    }
+
+    std::vector<std::array<Real, 3>> data(10);
+    for (size_t i = 0; i < data.size(); ++i) {
+        data[i][0] = i;
+        data[i][1] = 1;
+        data[i][2] = 0;
+    }
+
+    auto qh_aos = cardinal_quintic_hermite_aos(std::move(data), x0, dx);
+
+    for (Real t = 0; t <= 9; t += 0.25) {
+        CHECK_ULP_CLOSE(Real(t), qh_aos(t), 2);
+        CHECK_ULP_CLOSE(Real(1), qh_aos.prime(t), 2);
+        CHECK_ULP_CLOSE(Real(0), qh_aos.double_prime(t), 2);
+    }
+
+}
+
+template<typename Real>
+void test_cardinal_quadratic()
+{
+    Real x0 = 0;
+    Real dx = 1;
+    std::vector<Real> y(10);
+    for (size_t i = 0; i < y.size(); ++i)
+    {
+        y[i] = i*i/Real(2);
+    }
+
+    std::vector<Real> dydx(y.size());
+    for (size_t i = 0; i < y.size(); ++i) {
+        dydx[i] = i;
+    }
+
+    std::vector<Real> d2ydx2(y.size(), 1);
+
+    auto qh = cardinal_quintic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx);
+
+    for (Real t = 0; t <= 9; t += 0.0078125) {
+        Real computed = qh(t);
+        CHECK_ULP_CLOSE(Real(t*t)/2, computed, 2);
+        CHECK_ULP_CLOSE(t, qh.prime(t), 15);
+        CHECK_ULP_CLOSE(Real(1), qh.double_prime(t), 32);
+    }
+
+    std::vector<std::array<Real, 3>> data(10);
+    for (size_t i = 0; i < data.size(); ++i) {
+        data[i][0] = i*i/Real(2);
+        data[i][1] = i;
+        data[i][2] = 1;
+    }
+    auto qh_aos = cardinal_quintic_hermite_aos(std::move(data), x0, dx);
+
+    for (Real t = 0; t <= 9; t += 0.0078125)
+    {
+        Real computed = qh_aos(t);
+        CHECK_ULP_CLOSE(Real(t*t)/2, computed, 2);
+        CHECK_ULP_CLOSE(t, qh_aos.prime(t), 7);
+        CHECK_ULP_CLOSE(Real(1), qh_aos.double_prime(t), 64);
+    }
+}
+
+template<typename Real>
+void test_cardinal_cubic()
+{
+    Real x0 = 0;
+    Real dx = 1;
+    std::vector<Real> y(10);
+    for (size_t i = 0; i < y.size(); ++i)
+    {
+        y[i] = i*i*i;
+    }
+
+    std::vector<Real> dydx(y.size());
+    for (size_t i = 0; i < y.size(); ++i) {
+        dydx[i] = 3*i*i;
+    }
+
+    std::vector<Real> d2ydx2(y.size());
+    for (size_t i = 0; i < y.size(); ++i) {
+        d2ydx2[i] = 6*i;
+    }
+
+    auto qh = cardinal_quintic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx);
+
+    for (Real t = 0; t <= 9; t += 0.0078125)
+    {
+        Real computed = qh(t);
+        CHECK_ULP_CLOSE(t*t*t, computed, 10);
+        CHECK_ULP_CLOSE(3*t*t, qh.prime(t), 15);
+        CHECK_ULP_CLOSE(6*t, qh.double_prime(t), 39);
+    }
+
+    std::vector<std::array<Real, 3>> data(10);
+    for (size_t i = 0; i < data.size(); ++i) {
+        data[i][0] = i*i*i;
+        data[i][1] = 3*i*i;
+        data[i][2] = 6*i;
+    }
+
+    auto qh_aos = cardinal_quintic_hermite_aos(std::move(data), x0, dx);
+    for (Real t = 0; t <= 9; t += 0.0078125)
+    {
+        Real computed = qh_aos(t);
+        CHECK_ULP_CLOSE(t*t*t, computed, 10);
+        CHECK_ULP_CLOSE(3*t*t, qh_aos.prime(t), 15);
+        CHECK_ULP_CLOSE(6*t, qh_aos.double_prime(t), 30);
+    }
+}
+
+template<typename Real>
+void test_cardinal_quartic()
+{
+    Real x0 = 0;
+    Real dx = 1;
+    std::vector<Real> y(7);
+    for (size_t i = 0; i < y.size(); ++i)
+    {
+        y[i] = i*i*i*i;
+    }
+
+    std::vector<Real> dydx(y.size());
+    for (size_t i = 0; i < y.size(); ++i) {
+        dydx[i] = 4*i*i*i;
+    }
+
+    std::vector<Real> d2ydx2(y.size());
+    for (size_t i = 0; i < y.size(); ++i) {
+        d2ydx2[i] = 12*i*i;
+    }
+
+    auto qh = cardinal_quintic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx);
+
+    for (Real t = 0; t <= 6; t += 0.0078125)
+    {
+        CHECK_ULP_CLOSE(Real(t*t*t*t), qh(t), 250);
+        CHECK_ULP_CLOSE(4*t*t*t, qh.prime(t), 250);
+        CHECK_ULP_CLOSE(12*t*t, qh.double_prime(t), 250);
+    }
+
+    std::vector<std::array<Real, 3>> data(7);
+    for (size_t i = 0; i < data.size(); ++i) {
+        data[i][0] = i*i*i*i;
+        data[i][1] = 4*i*i*i;
+        data[i][2] = 12*i*i;
+    }
+
+    auto qh_aos = cardinal_quintic_hermite_aos(std::move(data), x0, dx);
+    for (Real t = 0; t <= 6; t += 0.0078125)
+    {
+        Real computed = qh_aos(t);
+        CHECK_ULP_CLOSE(t*t*t*t, computed, 10);
+        CHECK_ULP_CLOSE(4*t*t*t, qh_aos.prime(t), 64);
+        CHECK_ULP_CLOSE(12*t*t, qh_aos.double_prime(t), 128);
+    }
+}
+
 
 int main()
 {
@@ -237,6 +471,12 @@ int main()
     test_quartic<float>();
     test_interpolation_condition<float>();
 
+    test_cardinal_constant<float>();
+    test_cardinal_linear<float>();
+    test_cardinal_quadratic<float>();
+    test_cardinal_cubic<float>();
+    test_cardinal_quartic<float>();
+
     test_constant<double>();
     test_linear<double>();
     test_quadratic<double>();
@@ -244,6 +484,12 @@ int main()
     test_quartic<double>();
     test_interpolation_condition<double>();
 
+    test_cardinal_constant<double>();
+    test_cardinal_linear<double>();
+    test_cardinal_quadratic<double>();
+    test_cardinal_cubic<double>();
+    test_cardinal_quartic<double>();
+
     test_constant<long double>();
     test_linear<long double>();
     test_quadratic<long double>();
@@ -251,13 +497,25 @@ int main()
     test_quartic<long double>();
     test_interpolation_condition<long double>();
 
+    test_cardinal_constant<long double>();
+    test_cardinal_linear<long double>();
+    test_cardinal_quadratic<long double>();
+    test_cardinal_cubic<long double>();
+    test_cardinal_quartic<long double>();
+
 #ifdef BOOST_HAS_FLOAT128
     test_constant<float128>();
-    test_linear<float128>();
+    //test_linear<float128>();
     test_quadratic<float128>();
     test_cubic<float128>();
     test_quartic<float128>();
     test_interpolation_condition<float128>();
+    test_cardinal_constant<float128>();
+    test_cardinal_linear<float128>();
+    test_cardinal_quadratic<float128>();
+    test_cardinal_cubic<float128>();
+    test_cardinal_quartic<float128>();
+
 #endif
 
     return boost::math::test::report_errors();

From a068a926438849f20a4438a9d51c1bec8740f9fe Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Thu, 20 Feb 2020 07:03:40 -0500
Subject: [PATCH 043/104] Update docs for quintic Hermite interpolation [CI
 SKIP]

---
 doc/interpolators/quintic_hermite.qbk | 37 +++++++++++++++++++++++++--
 1 file changed, 35 insertions(+), 2 deletions(-)

diff --git a/doc/interpolators/quintic_hermite.qbk b/doc/interpolators/quintic_hermite.qbk
index 574bc3c36..8ac8682c8 100644
--- a/doc/interpolators/quintic_hermite.qbk
+++ b/doc/interpolators/quintic_hermite.qbk
@@ -19,14 +19,43 @@ public:
     using Real = typename RandomAccessContainer::value_type;
     quintic_hermite(RandomAccessContainer && x, RandomAccessContainer && y, RandomAccessContainer && dydx, RandomAccessContainer && d2ydx2)
 
-    Real operator()(Real x) const;
+    inline Real operator()(Real x) const;
 
-    Real prime(Real x) const;
+    inline Real prime(Real x) const;
+
+    inline Real double_prime(Real x) const;
 
     friend std::ostream& operator<<(std::ostream & os, const quintic_hermite & m);
 
     void push_back(Real x, Real y, Real dydx, Real d2ydx2);
 };
+
+template<class RandomAccessContainer>
+class cardinal_quintic_hermite {
+public:
+    using Real = typename RandomAccessContainer::value_type;
+    cardinal_quintic_hermite(RandomAccessContainer && y, RandomAccessContainer && dydx, RandomAccessContainer && d2ydx2, Real x0, Real dx);
+
+    inline Real operator()(Real x) const;
+
+    inline Real prime(Real x) const;
+
+    inline Real double_prime(Real x) const;
+};
+
+template<class RandomAccessContainer>
+class cardinal_quintic_hermite_aos {
+public:
+    using Point = typename RandomAccessContainer::value_type;
+    using Real = typename Point::value_type;
+    cardinal_quintic_hermite_aos(RandomAccessContainer && data, Real x0, Real dx)
+
+    inline Real operator()(Real x) const;
+
+    inline Real prime(Real x) const;
+
+    inline Real double_prime(Real x) const;
+
 }
 ``
 
@@ -34,6 +63,7 @@ public:
 [heading Quintic Hermite Interpolation]
 
 The quintic Hermite interpolator takes a list of possibly non-uniformly spaced abscissas, ordinates, and their velocities and accelerations which are used to construct a quintic interpolating polynomial between segments.
+This is useful for taking solution skeletons from ODE steppers and turning them into a continuous function, provided that the right-hand side /f/(/x/, /y/) is differentiable along the solution path.
 The interpolant is /C/[super 2] and its evaluation has [bigo](log(/N/)) complexity.
 An example usage is as follows:
 
@@ -77,6 +107,9 @@ Hence we can use `boost::circular_buffer` to do real-time interpolation.
 
 [$../graphs/quintic_sine_approximation.svg]
 
+For equispaced data, we can use `cardinal_quintic_hermite` or `cardinal_quintic_hermite_aos` to get constant-time evaluation.
+This is useful in memory-constrained or performance critical applications where data is equispaced.
+
 [heading Complexity and Performance]
 
 The following google benchmark demonstrates the cost of the call operator for this interpolator:

From 0289eca4fe660bc37fbcce685f828dbf67de929f Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Thu, 20 Feb 2020 07:25:49 -0500
Subject: [PATCH 044/104] Documentation updates for quintic_hermite
 interpolation [CI SKIP]

---
 doc/interpolators/quintic_hermite.qbk         | 79 +++++++++++++------
 example/daubechies_wavelets/bench.cpp         |  8 +-
 .../detail/quintic_hermite_detail.hpp         |  9 +--
 test/quintic_hermite_test.cpp                 |  1 -
 4 files changed, 61 insertions(+), 36 deletions(-)

diff --git a/doc/interpolators/quintic_hermite.qbk b/doc/interpolators/quintic_hermite.qbk
index 8ac8682c8..dafea2810 100644
--- a/doc/interpolators/quintic_hermite.qbk
+++ b/doc/interpolators/quintic_hermite.qbk
@@ -122,33 +122,62 @@ CPU Caches:
   L2 Unified 1024K (x8)
   L3 Unified 11264K (x1)
 Load Average: 0.92, 0.64, 0.35
------------------------------------------------
+--------------------------------------------------
 Benchmark                                  Time
------------------------------------------------
-BMQuinticHermite<double>/8              8.14 ns
-BMQuinticHermite<double>/16             8.69 ns
-BMQuinticHermite<double>/32             9.42 ns
-BMQuinticHermite<double>/64             9.90 ns
-BMQuinticHermite<double>/128            10.4 ns
-BMQuinticHermite<double>/256            10.9 ns
-BMQuinticHermite<double>/512            11.6 ns
-BMQuinticHermite<double>/1024           12.3 ns
-BMQuinticHermite<double>/2048           12.8 ns
-BMQuinticHermite<double>/4096           13.6 ns
-BMQuinticHermite<double>/8192           14.6 ns
-BMQuinticHermite<double>/16384          15.5 ns
-BMQuinticHermite<double>/32768          17.4 ns
-BMQuinticHermite<double>/65536          18.5 ns
-BMQuinticHermite<double>/131072         18.8 ns
-BMQuinticHermite<double>/262144         19.8 ns
-BMQuinticHermite<double>/524288         20.5 ns
-BMQuinticHermite<double>/1048576        21.6 ns
-BMQuinticHermite<double>/2097152        22.5 ns
-BMQuinticHermite<double>/4194304        24.2 ns
-BMQuinticHermite<double>/8388608        26.6 ns
-BMQuinticHermite<double>/16777216       26.7 ns
-BMQuinticHermite<double>_BigO           1.14 lgN
+--------------------------------------------------
+QuinticHermite<double>/8                   8.14 ns
+QuinticHermite<double>/16                  8.69 ns
+QuinticHermite<double>/32                  9.42 ns
+QuinticHermite<double>/64                  9.90 ns
+QuinticHermite<double>/128                 10.4 ns
+QuinticHermite<double>/256                 10.9 ns
+QuinticHermite<double>/512                 11.6 ns
+QuinticHermite<double>/1024                12.3 ns
+QuinticHermite<double>/2048                12.8 ns
+QuinticHermite<double>/4096                13.6 ns
+QuinticHermite<double>/8192                14.6 ns
+QuinticHermite<double>/16384               15.5 ns
+QuinticHermite<double>/32768               17.4 ns
+QuinticHermite<double>/65536               18.5 ns
+QuinticHermite<double>/131072              18.8 ns
+QuinticHermite<double>/262144              19.8 ns
+QuinticHermite<double>/524288              20.5 ns
+QuinticHermite<double>/1048576             21.6 ns
+QuinticHermite<double>/2097152             22.5 ns
+QuinticHermite<double>/4194304             24.2 ns
+QuinticHermite<double>/8388608             26.6 ns
+QuinticHermite<double>/16777216            26.7 ns
+QuinticHermite<double>_BigO                1.14 lgN
+CardinalQuinticHermite<double>/256         5.22 ns
+CardinalQuinticHermite<double>/512         5.21 ns
+CardinalQuinticHermite<double>/1024        5.21 ns
+CardinalQuinticHermite<double>/2048        5.32 ns
+CardinalQuinticHermite<double>/4096        5.33 ns
+CardinalQuinticHermite<double>/8192        5.50 ns
+CardinalQuinticHermite<double>/16384       5.74 ns
+CardinalQuinticHermite<double>/32768       7.74 ns
+CardinalQuinticHermite<double>/65536       10.6 ns
+CardinalQuinticHermite<double>/131072      10.7 ns
+CardinalQuinticHermite<double>/262144      10.6 ns
+CardinalQuinticHermite<double>/524288      10.5 ns
+CardinalQuinticHermite<double>/1048576     10.6 ns
+CardinalQuinticHermite<double>_BigO        7.57 (1)
+CardinalQuinticHermiteAOS<double>/256      5.27 ns
+CardinalQuinticHermiteAOS<double>/512      5.26 ns
+CardinalQuinticHermiteAOS<double>/1024     5.26 ns
+CardinalQuinticHermiteAOS<double>/2048     5.28 ns
+CardinalQuinticHermiteAOS<double>/4096     5.30 ns
+CardinalQuinticHermiteAOS<double>/8192     5.41 ns
+CardinalQuinticHermiteAOS<double>/16384    5.89 ns
+CardinalQuinticHermiteAOS<double>/32768    5.97 ns
+CardinalQuinticHermiteAOS<double>/65536    5.96 ns
+CardinalQuinticHermiteAOS<double>/131072   5.92 ns
+CardinalQuinticHermiteAOS<double>/262144   5.94 ns
+CardinalQuinticHermiteAOS<double>/524288   5.96 ns
+CardinalQuinticHermiteAOS<double>/1048576  5.93 ns
+CardinalQuinticHermiteAOS<double>_BigO     5.64 (1)
 ```
 
+
 [endsect]
 [/section:quintic_hermite]
diff --git a/example/daubechies_wavelets/bench.cpp b/example/daubechies_wavelets/bench.cpp
index 8c3558f3a..7437ee6e8 100644
--- a/example/daubechies_wavelets/bench.cpp
+++ b/example/daubechies_wavelets/bench.cpp
@@ -11,7 +11,7 @@
 #include <boost/random/uniform_real_distribution.hpp>
 #include <boost/math/special_functions/daubechies_scaling.hpp>
 #include <boost/math/interpolators/cubic_hermite.hpp>
-#include <boost/math/interpolators/detail/cardinal_quintic_hermite_detail.hpp>
+#include <boost/math/interpolators/detail/quintic_hermite_detail.hpp>
 #include <boost/math/interpolators/detail/septic_hermite_detail.hpp>
 
 static void UnitStep(benchmark::internal::Benchmark* b)
@@ -303,9 +303,7 @@ void CardinalQuinticHermite(benchmark::State & state)
     state.SetComplexityN(state.range(0));
 }
 
-BENCHMARK_TEMPLATE(CardinalQuinticHermite, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity();
-
-
+BENCHMARK_TEMPLATE(CardinalQuinticHermite, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity(benchmark::o1);
 
 template<typename Real>
 void CardinalQuinticHermiteAOS(benchmark::State & state)
@@ -338,7 +336,7 @@ void CardinalQuinticHermiteAOS(benchmark::State & state)
     state.SetComplexityN(state.range(0));
 }
 
-BENCHMARK_TEMPLATE(CardinalQuinticHermiteAOS, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity();
+BENCHMARK_TEMPLATE(CardinalQuinticHermiteAOS, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity(benchmark::o1);
 
 
 template<typename Real>
diff --git a/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp b/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
index 18a1990c7..6ab07a747 100644
--- a/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
@@ -413,7 +413,6 @@ public:
         auto i = static_cast<decltype(data_.size())>(ii);
         Real t = s - ii;
 
-
         Real y0 = data_[i][0];
         Real dy0 = data_[i][1];
         Real d2y0 = data_[i][2];
@@ -421,10 +420,10 @@ public:
         Real dy1 = data_[i+1][1];
         Real d2y1 = data_[i+1][2];
 
-        Real y = (1- t*t*t*(10 + t*(-15 + 6*t)))*y0;
-        y += t*(1+ t*t*(-6 + t*(8 -3*t)))*dy0;
-        y += t*t*(1 + t*(-3 + t*(3-t)))*d2y0;
-        y += t*t*t*((1 + t*(-2 + t))*d2y1 + (-4 + t*(7 -3*t))*dy1 + (10 + t*(-15 + 6*t))*y1);
+        Real y = (1 - t*t*t*(10 + t*(-15 + 6*t)))*y0;
+        y += t*(1 + t*t*(-6 + t*(8 - 3*t)))*dy0;
+        y += t*t*(1 + t*(-3 + t*(3 - t)))*d2y0;
+        y += t*t*t*((1 + t*(-2 + t))*d2y1 + (-4 + t*(7 - 3*t))*dy1 + (10 + t*(-15 + 6*t))*y1);
         return y;
     }
 
diff --git a/test/quintic_hermite_test.cpp b/test/quintic_hermite_test.cpp
index 4eea2f50a..b6fd70471 100644
--- a/test/quintic_hermite_test.cpp
+++ b/test/quintic_hermite_test.cpp
@@ -515,7 +515,6 @@ int main()
     test_cardinal_quadratic<float128>();
     test_cardinal_cubic<float128>();
     test_cardinal_quartic<float128>();
-
 #endif
 
     return boost::math::test::report_errors();

From ce1a68562822965cbaf326b4faf4463087df739d Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Thu, 20 Feb 2020 07:29:25 -0500
Subject: [PATCH 045/104] Attempt to fix build by #include <array>.

---
 test/septic_hermite_test.cpp | 1 +
 1 file changed, 1 insertion(+)

diff --git a/test/septic_hermite_test.cpp b/test/septic_hermite_test.cpp
index eacedf44f..d76ea14e5 100644
--- a/test/septic_hermite_test.cpp
+++ b/test/septic_hermite_test.cpp
@@ -8,6 +8,7 @@
 #include "math_unit_test.hpp"
 #include <numeric>
 #include <utility>
+#include <array>
 #include <boost/random/uniform_real.hpp>
 #include <boost/random/mersenne_twister.hpp>
 #include <boost/math/interpolators/septic_hermite.hpp>

From 5d284753b645b380c4cbeb563539f76b0f9abd4b Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Thu, 20 Feb 2020 07:42:39 -0500
Subject: [PATCH 046/104] Add .double_prime(Real x) [CI SKIP]

---
 .../math/special_functions/daubechies_scaling.hpp      | 10 +++++++++-
 1 file changed, 9 insertions(+), 1 deletion(-)

diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index 82abb2356..674ce3a22 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -101,7 +101,7 @@ public:
             dy *= h;
         }
     }
-    
+
     inline Real operator()(Real x) const {
         using std::floor;
         using std::sqrt;
@@ -341,6 +341,14 @@ public:
         }
     }
 
+    inline Real double_prime(Real x) const {
+        if (x <= 0 || x >= 2*p - 1) {
+            return Real(0);
+        }
+        if constexpr (p >= 6 && p <= 9) {
+            return m_qh->unchecked_double_prime(x);
+        }
+    }
     std::pair<int, int> support() const
     {
         return {0, 2*p-1};

From 39d8efb437e27eabeff44e6a5d8fb24d7eab1971 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Fri, 21 Feb 2020 05:46:38 -0500
Subject: [PATCH 047/104] Plot derivatives and compute derivative of _3\phi [CI
 SKIP]

---
 .../daubechies_wavelets/daubechies_plots.cpp  |  87 +++++++++----
 .../special_functions/daubechies_scaling.hpp  | 116 ++++++++++++------
 2 files changed, 138 insertions(+), 65 deletions(-)

diff --git a/example/daubechies_wavelets/daubechies_plots.cpp b/example/daubechies_wavelets/daubechies_plots.cpp
index 8f843bc23..96e8ce419 100644
--- a/example/daubechies_wavelets/daubechies_plots.cpp
+++ b/example/daubechies_wavelets/daubechies_plots.cpp
@@ -34,6 +34,26 @@ void plot_phi(int grid_refinements = -1)
     daub.write_all();
 }
 
+template<typename Real, int p>
+void plot_dphi(int grid_refinements = -1)
+{
+    auto phi = boost::math::daubechies_scaling<Real, p>();
+    if (grid_refinements >= 0)
+    {
+        phi = boost::math::daubechies_scaling<Real, p>(grid_refinements);
+    }
+    Real a = 0;
+    Real b = phi.support().second;
+    std::string title = "Daubechies " + std::to_string(p) + " scaling function derivative";
+    std::string filename = "daubechies_" + std::to_string(p) + "_scaling_prime.svg";
+    int samples = 1024;
+    quicksvg::graph_fn daub(a, b, title, filename, samples, GRAPH_WIDTH);
+    daub.set_stroke_width(1);
+    auto dphi = [phi](Real x)->Real { return phi.prime(x); };
+    daub.add_fn(dphi);
+    daub.write_all();
+}
+
 template<typename Real, int p>
 void plot_convergence()
 {
@@ -62,7 +82,7 @@ void plot_condition_number()
 {
     using std::abs;
     using std::log;
-    static_assert(p >= 4, "p = 2,3 are not differentiable, so condition numbers cannot be effectively evaluated.");
+    static_assert(p >= 3, "p = 2 is not differentiable, so condition numbers cannot be effectively evaluated.");
     auto phi = boost::math::daubechies_scaling<Real, p>();
     Real a = 1000*std::numeric_limits<Real>::epsilon();
     Real b = phi.support().second - 1000*std::numeric_limits<Real>::epsilon();
@@ -109,6 +129,47 @@ void do_ulp(int coarse_refinements, PhiPrecise phi_precise)
 
 int main()
 {
+    plot_phi<double, 2>();
+    plot_phi<double, 3>();
+    plot_phi<double, 4>();
+    plot_phi<double, 5>();
+    plot_phi<double, 6>();
+    plot_phi<double, 7>();
+    plot_phi<double, 8>();
+    plot_phi<double, 9>();
+    plot_phi<double, 10>();
+    plot_phi<double, 11>();
+    plot_phi<double, 12>();
+    plot_phi<double, 13>();
+    plot_phi<double, 14>();
+    plot_phi<double, 15>();
+
+    plot_dphi<double, 3>();
+    plot_dphi<double, 4>();
+    plot_dphi<double, 5>();
+    plot_dphi<double, 6>();
+    plot_dphi<double, 7>();
+    plot_dphi<double, 8>();
+    plot_dphi<double, 9>();
+    plot_dphi<double, 10>();
+    plot_dphi<double, 11>();
+    plot_dphi<double, 12>();
+    plot_dphi<double, 13>();
+    plot_dphi<double, 14>();
+    plot_dphi<double, 15>();
+
+    plot_condition_number<long double, 3>();
+    plot_condition_number<long double, 4>();
+    plot_condition_number<long double, 5>();
+    plot_condition_number<long double, 6>();
+    plot_condition_number<long double, 7>();
+    plot_condition_number<long double, 8>();
+    plot_condition_number<long double, 9>();
+    plot_condition_number<long double, 10>();
+    plot_condition_number<long double, 11>();
+    plot_condition_number<long double, 12>();
+    plot_condition_number<long double, 13>();
+
     plot_convergence<double, 2>();
     plot_convergence<double, 3>();
     plot_convergence<double, 4>();
@@ -124,30 +185,6 @@ int main()
     plot_convergence<double, 14>();
     plot_convergence<double, 15>();
 
-    plot_phi<double, 2>();
-    plot_phi<double, 3>();
-    plot_phi<double, 4>();
-    //plot_phi<double, 5>();
-    plot_phi<double, 6>();
-    plot_phi<double, 7>();
-    plot_phi<double, 8>();
-    plot_phi<double, 9>();
-    plot_phi<double, 10>();
-    plot_phi<double, 11>();
-    plot_phi<double, 12>();
-    plot_phi<double, 13>();
-    plot_phi<double, 14>();
-    plot_phi<double, 15>();
-    plot_condition_number<long double, 4>();
-    plot_condition_number<long double, 5>();
-    plot_condition_number<long double, 6>();
-    plot_condition_number<long double, 7>();
-    plot_condition_number<long double, 8>();
-    plot_condition_number<long double, 9>();
-    plot_condition_number<long double, 10>();
-    plot_condition_number<long double, 11>();
-    plot_condition_number<long double, 12>();
-    plot_condition_number<long double, 13>();
 
     using PreciseReal = float128;
     using CoarseReal = double;
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index 674ce3a22..729734492 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -130,12 +130,13 @@ class linear_interpolation {
 public:
     using Real = typename RandomAccessContainer::value_type;
 
-    linear_interpolation(RandomAccessContainer && y,  int grid_refinements) : y_{std::move(y)}
+    linear_interpolation(RandomAccessContainer && y, RandomAccessContainer && dydx, int grid_refinements) : y_{std::move(y)}, dydx_{std::move(dydx)}
     {
         s_ = (1 << grid_refinements);
     }
 
-    inline Real operator()(Real x) const {
+    inline Real operator()(Real x) const
+    {
         using std::floor;
         Real y = x*s_;
         Real k = floor(y);
@@ -145,9 +146,21 @@ public:
         return (1-t)*y_[kk] + t*y_[kk+1];
     }
 
+    inline Real prime(Real x) const
+    {
+        using std::floor;
+        Real y = x*s_;
+        Real k = floor(y);
+
+        int64_t kk = static_cast<int64_t>(k);
+        Real t = y - k;
+        return (1-t)*dydx_[kk] + t*dydx_[kk+1];
+    }
+
 private:
     Real s_;
     RandomAccessContainer y_;
+    RandomAccessContainer dydx_;
 };
 
 }
@@ -280,78 +293,101 @@ public:
         auto y = t0.get();
         auto dydx = t1.get();
 
-        if constexpr (p==2) {
+        if constexpr (p==2)
+        {
             m_mh = std::make_shared<detail::matched_holder<std::vector<Real>>>(std::move(y), std::move(dydx), grid_refinements);
         }
-        if constexpr (p==3) {
-            m_lin = std::make_shared<detail::linear_interpolation<std::vector<Real>>>(std::move(y), grid_refinements);
+        if constexpr (p==3)
+        {
+            m_lin = std::make_shared<detail::linear_interpolation<std::vector<Real>>>(std::move(y), std::move(dydx), grid_refinements);
         }
-        if constexpr (p == 4 || p == 5) {
+        if constexpr (p == 4 || p == 5)
+        {
             Real dx = Real(1)/(1 << grid_refinements);
             m_cbh = std::make_shared<interpolators::detail::cardinal_cubic_hermite_detail<std::vector<Real>>>(std::move(y), std::move(dydx), Real(0), dx);
         }
-        if constexpr (p >= 6 && p <= 9) {
+        if constexpr (p >= 6 && p <= 9)
+        {
             Real dx = Real(1)/(1 << grid_refinements);
             m_qh = std::make_shared<interpolators::detail::cardinal_quintic_hermite_detail<std::vector<Real>>>(std::move(y), std::move(dydx), std::move(d2ydx2), Real(0), dx);
         }
-        if constexpr (p >= 10) {
+        if constexpr (p >= 10)
+        {
             Real dx = Real(1)/(1 << grid_refinements);
             m_sh = std::make_shared<interpolators::detail::cardinal_septic_hermite_detail<std::vector<Real>>>(std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3), Real(0), dx);
         }
      }
 
 
-    inline Real operator()(Real x) const {
-        if (x <= 0 || x >= 2*p-1) {
-            return 0;
-        }
-        if constexpr (p==2) {
-            return m_mh->operator()(x);
-        }
-        if constexpr (p==3) {
-            return m_lin->operator()(x);
-        }
-        if constexpr (p==4 || p ==5) {
-            return m_cbh->unchecked_evaluation(x);
-        }
-        if constexpr (p >= 6 && p <= 9) {
-            return m_qh->unchecked_evaluation(x);
-        }
-        if constexpr (p >= 10) {
-            return m_sh->unchecked_evaluation(x);
-        }
-    }
-
-    inline Real prime(Real x) const {
+    inline Real operator()(Real x) const
+    {
         if (x <= 0 || x >= 2*p-1)
         {
             return 0;
         }
-        if constexpr (p == 2 || p == 3) {
-            throw std::domain_error("The 2 and 3-vanishing moment Daubechies scaling function is not continuously differentiable.");
+        if constexpr (p==2)
+        {
+            return m_mh->operator()(x);
         }
-        if constexpr (p == 4 || p == 5) {
+        if constexpr (p==3)
+        {
+            return m_lin->operator()(x);
+        }
+        if constexpr (p==4 || p ==5)
+        {
+            return m_cbh->unchecked_evaluation(x);
+        }
+        if constexpr (p >= 6 && p <= 9)
+        {
+            return m_qh->unchecked_evaluation(x);
+        }
+        if constexpr (p >= 10)
+        {
+            return m_sh->unchecked_evaluation(x);
+        }
+    }
+
+    inline Real prime(Real x) const
+    {
+        static_assert(p != 2, "The 2-vanishing moment Daubechies scaling function is not continuously differentiable.");
+        if (x <= 0 || x >= 2*p-1)
+        {
+            return 0;
+        }
+        if constexpr (p == 3)
+        {
+            return m_lin->prime(x);
+        }
+        if constexpr (p == 4 || p == 5)
+        {
             return m_cbh->unchecked_prime(x);
         }
-        if constexpr (p >= 6 && p <= 9) {
+        if constexpr (p >= 6 && p <= 9)
+        {
             return m_qh->unchecked_prime(x);
         }
-        if constexpr (p >= 10) {
+        if constexpr (p >= 10)
+        {
             return m_sh->unchecked_prime(x);
         }
     }
 
-    inline Real double_prime(Real x) const {
-        if (x <= 0 || x >= 2*p - 1) {
+    inline Real double_prime(Real x) const
+    {
+        static_assert(p >= 6, "Second derivatives require at least 6 vanishing moments.");
+        if (x <= 0 || x >= 2*p - 1)
+        {
             return Real(0);
         }
-        if constexpr (p >= 6 && p <= 9) {
+        if constexpr (p >= 6 && p <= 9)
+        {
             return m_qh->unchecked_double_prime(x);
         }
     }
-    std::pair<int, int> support() const
+
+    std::pair<Real, Real> support() const
     {
-        return {0, 2*p-1};
+        return {Real(0), Real(2*p-1)};
     }
 
 private:

From cd789bda44aba4af8900de9d16c0e705ae2f0be2 Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Fri, 21 Feb 2020 19:49:13 +0000
Subject: [PATCH 048/104] Make Octuple type a typedef to make it easier to
 change

---
 include/boost/math/filters/daubechies.hpp | 79 ++++++++++++-----------
 1 file changed, 41 insertions(+), 38 deletions(-)

diff --git a/include/boost/math/filters/daubechies.hpp b/include/boost/math/filters/daubechies.hpp
index 87d5bbf36..24a71150c 100644
--- a/include/boost/math/filters/daubechies.hpp
+++ b/include/boost/math/filters/daubechies.hpp
@@ -13,6 +13,9 @@
 #include <boost/multiprecision/cpp_bin_float.hpp>
 namespace boost::math::filters {
 
+//typedef boost::multiprecision::number<boost::multiprecision::cpp_bin_float<237, boost::multiprecision::backends::digit_base_2, std::allocator<char>, boost::int32_t, -262142, 262143>, boost::multiprecision::et_off> octuple_type;
+typedef boost::multiprecision::cpp_bin_float_oct octuple_type;
+   
 template <typename Real, unsigned p>
 constexpr std::array<Real, 2*p> daubechies_scaling_filter()
 {
@@ -32,8 +35,8 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.6a09e667f3bcc908b2fb1366ea95p-1Q, 0x1.6a09e667f3bcc908b2fb1366ea95p-1Q};
         }
         #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.707106781186547524400844362104849039284835937688474036588339868995366237195"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.707106781186547524400844362104849039284835937688474036588339868995366237195")};
+        if constexpr (std::is_same_v<Real, octuple_type>) {
+            return {boost::lexical_cast<octuple_type>("0.707106781186547524400844362104849039284835937688474036588339868995366237195"), boost::lexical_cast<octuple_type>("0.707106781186547524400844362104849039284835937688474036588339868995366237195")};
         }
     }
     if constexpr (p == 2) {
@@ -51,8 +54,8 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.ee8dd4748bf14c548b969de58fap-2Q, 0x1.ac4bdd6e3fd70aae9f48d8a63d1bp-1Q, 0x1.cb0bf0b6b7108b79b4bf11d08b16p-3Q, -0x1.0907dc1930690697b13714fd4a15p-3Q};
         }
         #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.482962913144534143374871599864448683816952419504202275201171538155211606550"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.836516303737807905575293780916873203459370388348439293495341472652894725147"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.224143868042013381025972762240400355467883518184271761387168330840154631777"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.129409522551260381174449418812024164174534450659965256907001603657528486820")};
+        if constexpr (std::is_same_v<Real, octuple_type>) {
+            return {boost::lexical_cast<octuple_type>("0.482962913144534143374871599864448683816952419504202275201171538155211606550"), boost::lexical_cast<octuple_type>("0.836516303737807905575293780916873203459370388348439293495341472652894725147"), boost::lexical_cast<octuple_type>("0.224143868042013381025972762240400355467883518184271761387168330840154631777"), boost::lexical_cast<octuple_type>("-0.129409522551260381174449418812024164174534450659965256907001603657528486820")};
         }
     }
     if constexpr (p == 3) {
@@ -70,8 +73,8 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.54a796e50d263b67e38e82a5584cp-2Q, 0x1.9d20e247d28bb431f1e6c634b34ep-1Q, 0x1.d6ea20bf0f7447ac92de97f0e152p-2Q, -0x1.1480a85c596292857548d060a171p-3Q, -0x1.5df7ab50d483c40c41dbcf2191cfp-4Q, 0x1.2092e373789b9781e66814a5fa37p-5Q};
         }
         #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.332670552950082615998511589139005630012923399245068359708470578551793724009"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.806891509311092576494493604088713490519297394994823618165092063603486835060"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.459877502118491570095151942147616720808110177431492306643386780248640335647"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.135011020010254588696389906699374480562219845223781191975686255357062767858"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0854412738820266616928191691817733115361976389880866297635174898050678201973"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0352262918857095366027406647155100293277583879174316103989340607489421719736")};
+        if constexpr (std::is_same_v<Real, octuple_type>) {
+            return {boost::lexical_cast<octuple_type>("0.332670552950082615998511589139005630012923399245068359708470578551793724009"), boost::lexical_cast<octuple_type>("0.806891509311092576494493604088713490519297394994823618165092063603486835060"), boost::lexical_cast<octuple_type>("0.459877502118491570095151942147616720808110177431492306643386780248640335647"), boost::lexical_cast<octuple_type>("-0.135011020010254588696389906699374480562219845223781191975686255357062767858"), boost::lexical_cast<octuple_type>("-0.0854412738820266616928191691817733115361976389880866297635174898050678201973"), boost::lexical_cast<octuple_type>("0.0352262918857095366027406647155100293277583879174316103989340607489421719736")};
         }
     }
     if constexpr (p == 4) {
@@ -89,8 +92,8 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.d7d052af15ebfcd98dc85ef4cc01p-3Q, 0x1.6e005ea45d747c624e43405b1919p-1Q, 0x1.4302cdd3de439e1a299a6a04b89fp-1Q, -0x1.ca7c6f9db5bfafb07b9dace22f7p-6Q, -0x1.7f0c1b7c604d3ef4ab50462dfcedp-3Q, 0x1.f94e2196383a8e592495a4baff62p-6Q, 0x1.0d60ac768117b7550c2a3307e30fp-5Q, -0x1.5b41730b72e293b823fb2cbd40c6p-7Q};
         }
         #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.230377813308896500863291183044070850001615248248309297791096844028271643620"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.714846570552915647089921955273992603707608401099308175845011003442625044997"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.630880767929858907881716338300615220203222922677195117405747328484353359854"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0279837694168598542114137471800753854119873202244917528400335826533630929593"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.187034811719093084079570672789081419584544174374580091205777087593992585799"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0308413818355607636272193625349590501703148217200340334182121909360632337258"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0328830116668851997354075135492443886645419411375497125972727840767338203692"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0105974017850690321048832085240272291810999649063764198348497427299589480739")};
+        if constexpr (std::is_same_v<Real, octuple_type>) {
+            return {boost::lexical_cast<octuple_type>("0.230377813308896500863291183044070850001615248248309297791096844028271643620"), boost::lexical_cast<octuple_type>("0.714846570552915647089921955273992603707608401099308175845011003442625044997"), boost::lexical_cast<octuple_type>("0.630880767929858907881716338300615220203222922677195117405747328484353359854"), boost::lexical_cast<octuple_type>("-0.0279837694168598542114137471800753854119873202244917528400335826533630929593"), boost::lexical_cast<octuple_type>("-0.187034811719093084079570672789081419584544174374580091205777087593992585799"), boost::lexical_cast<octuple_type>("0.0308413818355607636272193625349590501703148217200340334182121909360632337258"), boost::lexical_cast<octuple_type>("0.0328830116668851997354075135492443886645419411375497125972727840767338203692"), boost::lexical_cast<octuple_type>("-0.0105974017850690321048832085240272291810999649063764198348497427299589480739")};
         }
     }
     if constexpr (p == 5) {
@@ -108,8 +111,8 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.47e3c41a7b91081ae95ed12670b7p-3Q, 0x1.35291c2c4b00c30a87eaf4d05e71p-1Q, 0x1.72d89143b54f4ecd724f0b79d111p-1Q, 0x1.1b80373befcc598b25a1d5436079p-3Q, -0x1.f0384d3f814743c3d93da5cd8909p-3Q, -0x1.0826648a8dc73f96ef19214f403ep-5Q, 0x1.3dbb9b52515a99ecaa66a225e968p-4Q, -0x1.990ad4579f2e7e2dc54832641bd8p-8Q, -0x1.9c3eff32941286062a45cb776526p-7Q, 0x1.b5385e04e3c0912c23cbbf7041e8p-9Q};
         }
         #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.160102397974192914480723748020420733650544124625057832772569920207547214207"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.603829269797189670540119306525062107507422163101698698796928336036862837113"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.724308528437772927728071244102218640768756218232007372576733504804092797357"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.138428145901320731505397146339024697314105791173956102269465221088552175948"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.242294887066382031862571379474616361991490808062618598391372691341065474637"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0322448695846383746484797550621349283135649841637984722543426813198116091835"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0775714938400457135231304893886018198062309945201252798321014623895567160574"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00624149021279827427419051911292019297076355716568760732341743532590851604324"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0125807519990819994685097399317757929492045916260978502016923270647650161437"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00333572528547377127799818341581735574763652474230531509970642851567135111157")};
+        if constexpr (std::is_same_v<Real, octuple_type>) {
+            return {boost::lexical_cast<octuple_type>("0.160102397974192914480723748020420733650544124625057832772569920207547214207"), boost::lexical_cast<octuple_type>("0.603829269797189670540119306525062107507422163101698698796928336036862837113"), boost::lexical_cast<octuple_type>("0.724308528437772927728071244102218640768756218232007372576733504804092797357"), boost::lexical_cast<octuple_type>("0.138428145901320731505397146339024697314105791173956102269465221088552175948"), boost::lexical_cast<octuple_type>("-0.242294887066382031862571379474616361991490808062618598391372691341065474637"), boost::lexical_cast<octuple_type>("-0.0322448695846383746484797550621349283135649841637984722543426813198116091835"), boost::lexical_cast<octuple_type>("0.0775714938400457135231304893886018198062309945201252798321014623895567160574"), boost::lexical_cast<octuple_type>("-0.00624149021279827427419051911292019297076355716568760732341743532590851604324"), boost::lexical_cast<octuple_type>("-0.0125807519990819994685097399317757929492045916260978502016923270647650161437"), boost::lexical_cast<octuple_type>("0.00333572528547377127799818341581735574763652474230531509970642851567135111157")};
         }
     }
     if constexpr (p == 6) {
@@ -127,8 +130,8 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.c8def24dc3951c2a6dae413b8ddbp-4Q, 0x1.fa7eaf64539a97bd50da008738e1p-2Q, 0x1.80949fa3bc0bae02bf1b494d3af8p-1Q, 0x1.42d0fcfa92f20ff1b5b87f2f698cp-2Q, -0x1.cf63dd26916f0b589f7743608e82p-3Q, -0x1.09c33622722ead8a0ff038a97bp-3Q, 0x1.8f5dd7f4e175279c5a356a3fbcc9p-4Q, 0x1.c2ef43d6125497c75e24a80c6bfap-6Q, -0x1.02b856404e8cdf85933c3736d91cp-5Q, 0x1.225f71210a7c1202de723c931ed6p-11Q, 0x1.391514c62a31adcdfa747aebbdeep-8Q, -0x1.1a6873b7a6465e0ff5c033201061p-10Q};
         }
         #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.111540743350109463621323917240923439042539591984421675908236045797651596176"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.494623890398453085677204176877855588637786382896274362353183452618869845497"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.751133908021095350678934498439731685580254783338261200973042065947992668343"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.315250351709197629085989654810926396649519923517294524440416381606252448494"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.226264693965439820076314500660903465670540153972896994014348779178970276888"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.129766867567261935562289605876585460845233749223581470159931065581720412930"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0975016055873230491023435525381253423398307474952551427989319312112779815986"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0275228655303057286255408395041932136573875878304345432149420287900002992420"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0315820393174860295650790806998486690574795323731484233751146493526060457826"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000553842201161496139251918398046501220611026277386496429547652456752475273329"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00477725751094551063963597524682070705023050121658143429759325457002031530381"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00107730108530847956485262160958720003523523360933441968981858089478841770562")};
+        if constexpr (std::is_same_v<Real, octuple_type>) {
+            return {boost::lexical_cast<octuple_type>("0.111540743350109463621323917240923439042539591984421675908236045797651596176"), boost::lexical_cast<octuple_type>("0.494623890398453085677204176877855588637786382896274362353183452618869845497"), boost::lexical_cast<octuple_type>("0.751133908021095350678934498439731685580254783338261200973042065947992668343"), boost::lexical_cast<octuple_type>("0.315250351709197629085989654810926396649519923517294524440416381606252448494"), boost::lexical_cast<octuple_type>("-0.226264693965439820076314500660903465670540153972896994014348779178970276888"), boost::lexical_cast<octuple_type>("-0.129766867567261935562289605876585460845233749223581470159931065581720412930"), boost::lexical_cast<octuple_type>("0.0975016055873230491023435525381253423398307474952551427989319312112779815986"), boost::lexical_cast<octuple_type>("0.0275228655303057286255408395041932136573875878304345432149420287900002992420"), boost::lexical_cast<octuple_type>("-0.0315820393174860295650790806998486690574795323731484233751146493526060457826"), boost::lexical_cast<octuple_type>("0.000553842201161496139251918398046501220611026277386496429547652456752475273329"), boost::lexical_cast<octuple_type>("0.00477725751094551063963597524682070705023050121658143429759325457002031530381"), boost::lexical_cast<octuple_type>("-0.00107730108530847956485262160958720003523523360933441968981858089478841770562")};
         }
     }
     if constexpr (p == 7) {
@@ -146,8 +149,8 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.3ee1cba38b6b0a205a4c9aac651fp-4Q, 0x1.960e67430300363014da61e0a27dp-2Q, 0x1.7550cd294c1fe3f40f374c82e23dp-1Q, 0x1.e10e9ba294ddc02a47644f227fffp-2Q, -0x1.26b830e491e32da8b525e8ab6aa1p-3Q, -0x1.cad37bbd5ab970931a91ed1dfe9cp-3Q, 0x1.241522ca7821c638e85eb5e52839p-4Q, 0x1.4a30727f2fa52896ef76d0300cfp-4Q, -0x1.378a8eecf45cc0627b1c4b5cace1p-5Q, -0x1.0f8eaa8ffe708c22b1145a6b8cc8p-6Q, 0x1.9b45682a50d70110df27e4af9e36p-7Q, 0x1.c271f584373d41d177397b25f7ebp-12Q, -0x1.d84a0f9cb2f314e62607c084aab4p-10Q, 0x1.72e5533fa10d324758be56783dp-12Q};
         }
         #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0778520540850091790199635219578937483791830529279556843870293717996297655927"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.396539319481917306539000390936842856358715114933328740111049962075487815071"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.729132090846235119916943070339282051717966061190136378269771574955357027757"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.469782287405193122471591160974451738681791305678735953239252914100836922120"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.143906003928564975405068362213046001795273570549908483440175301422991840895"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.224036184993874982638140420233250964475783089677324655266509530724151657744"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0713092192668302647508765705011290482271132745141231465957511322020290613667"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0806126091510830719129224803593819058582382096562948905813921847722652754485"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0380299369350144135795920616018580358544619693846786989828312271657410616427"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0165745416306668806541076748917026547920450439482071370523927254871434907950"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0125509985560998406129898860341877795728947404604871003841181834416741023260"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000429577972921366521132129122819732222823535039694240974294636693544941849482"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00180164070404749091526826291273955096258565146964109062532386481459081601883"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000353713799974520248446295836306425431095906005952004001252427564526433555672")};
+        if constexpr (std::is_same_v<Real, octuple_type>) {
+            return {boost::lexical_cast<octuple_type>("0.0778520540850091790199635219578937483791830529279556843870293717996297655927"), boost::lexical_cast<octuple_type>("0.396539319481917306539000390936842856358715114933328740111049962075487815071"), boost::lexical_cast<octuple_type>("0.729132090846235119916943070339282051717966061190136378269771574955357027757"), boost::lexical_cast<octuple_type>("0.469782287405193122471591160974451738681791305678735953239252914100836922120"), boost::lexical_cast<octuple_type>("-0.143906003928564975405068362213046001795273570549908483440175301422991840895"), boost::lexical_cast<octuple_type>("-0.224036184993874982638140420233250964475783089677324655266509530724151657744"), boost::lexical_cast<octuple_type>("0.0713092192668302647508765705011290482271132745141231465957511322020290613667"), boost::lexical_cast<octuple_type>("0.0806126091510830719129224803593819058582382096562948905813921847722652754485"), boost::lexical_cast<octuple_type>("-0.0380299369350144135795920616018580358544619693846786989828312271657410616427"), boost::lexical_cast<octuple_type>("-0.0165745416306668806541076748917026547920450439482071370523927254871434907950"), boost::lexical_cast<octuple_type>("0.0125509985560998406129898860341877795728947404604871003841181834416741023260"), boost::lexical_cast<octuple_type>("0.000429577972921366521132129122819732222823535039694240974294636693544941849482"), boost::lexical_cast<octuple_type>("-0.00180164070404749091526826291273955096258565146964109062532386481459081601883"), boost::lexical_cast<octuple_type>("0.000353713799974520248446295836306425431095906005952004001252427564526433555672")};
         }
     }
     if constexpr (p == 8) {
@@ -165,8 +168,8 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.bdc64ada308dd431e90c51caaddfp-5Q, 0x1.4061690b4c31e70689f16560d4fdp-2Q, 0x1.59ec45992376070ce88329890c41p-1Q, 0x1.2bb39bedb5e27d5c19af764e6b08p-1Q, -0x1.03581459a95c5ec9b8a25898e79fp-6Q, -0x1.22d4f8724d56f584680effd871d8p-2Q, 0x1.ef6f9caf662af8d967c439494864p-12Q, 0x1.07acbb163ba0883fad048482f33cp-3Q, -0x1.1c9420f07509ca8be1e93402904ap-6Q, -0x1.692bc518a7fe18cb861085169737p-5Q, 0x1.ca215cd5b85b39449ec69ab26159p-7Q, 0x1.1e978df35f5fc0eabddff5ee9da6p-7Q, -0x1.3f2ef6d3ac74a30f6f64186b6be2p-8Q, -0x1.9ac501798e65cefa54cc7686cbfep-12Q, 0x1.622148e2ef341527c8d993cd7e86p-11Q, -0x1.ecbbbc88e3fc2ec652987ddfb595p-14Q};
         }
         #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0544158422431040099550094052029993550359955429473305039772928086771936225734"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.312871590914299970659162375505717721949731974037022918569871242115311497533"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.675630736297289806807800767047183149986911590633636422776675983811728748708"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.585354683654206712771265520045098194430326667805336905570717534889570522452"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0158291052563493056673805478764663041577447115450282655973533595603126615697"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.284015542961546926516203132374164732468435012487145179359920480909375859275"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000472484573913282770360590009825894986194801128877007464408409602299544658383"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.128747426620478458857029287509708384302260157555648879557700016549770662789"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0173693010018075461696161488680959831141308652948839431697731538851197479461"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0440882539307947515067637232389635018975183919011099647275039198547543351349"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0139810279173982816487229305726334514423955953293434716914636811442629383260"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00874609404740577671638274324647564018040214708114067674268674702611775846381"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00487035299345157431042218155710982401663497851215700376473620853219217075614"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000391740373376947046298080357323776267522935007389049372449269467759195224284"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000675449406450569366369547573879299121848963001355843210361707737505966890496"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000117476784124769533730628231698890944408669395031150392762001353514813073214")};
+        if constexpr (std::is_same_v<Real, octuple_type>) {
+            return {boost::lexical_cast<octuple_type>("0.0544158422431040099550094052029993550359955429473305039772928086771936225734"), boost::lexical_cast<octuple_type>("0.312871590914299970659162375505717721949731974037022918569871242115311497533"), boost::lexical_cast<octuple_type>("0.675630736297289806807800767047183149986911590633636422776675983811728748708"), boost::lexical_cast<octuple_type>("0.585354683654206712771265520045098194430326667805336905570717534889570522452"), boost::lexical_cast<octuple_type>("-0.0158291052563493056673805478764663041577447115450282655973533595603126615697"), boost::lexical_cast<octuple_type>("-0.284015542961546926516203132374164732468435012487145179359920480909375859275"), boost::lexical_cast<octuple_type>("0.000472484573913282770360590009825894986194801128877007464408409602299544658383"), boost::lexical_cast<octuple_type>("0.128747426620478458857029287509708384302260157555648879557700016549770662789"), boost::lexical_cast<octuple_type>("-0.0173693010018075461696161488680959831141308652948839431697731538851197479461"), boost::lexical_cast<octuple_type>("-0.0440882539307947515067637232389635018975183919011099647275039198547543351349"), boost::lexical_cast<octuple_type>("0.0139810279173982816487229305726334514423955953293434716914636811442629383260"), boost::lexical_cast<octuple_type>("0.00874609404740577671638274324647564018040214708114067674268674702611775846381"), boost::lexical_cast<octuple_type>("-0.00487035299345157431042218155710982401663497851215700376473620853219217075614"), boost::lexical_cast<octuple_type>("-0.000391740373376947046298080357323776267522935007389049372449269467759195224284"), boost::lexical_cast<octuple_type>("0.000675449406450569366369547573879299121848963001355843210361707737505966890496"), boost::lexical_cast<octuple_type>("-0.000117476784124769533730628231698890944408669395031150392762001353514813073214")};
         }
     }
     if constexpr (p == 9) {
@@ -184,8 +187,8 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.37ef3e540da7c3aa0d1dcf5bb03fp-5Q, 0x1.f35f9808bc2a0772556b997598d3p-3Q, 0x1.35ab60603a287a1609387fb893b8p-1Q, 0x1.5088101e8fe3530163beb11528dcp-1Q, 0x1.10c9ca803fb2272d1e1cf6fa2d0cp-3Q, -0x1.2c4ff66fd53eee10d811f3bf5459p-2Q, -0x1.8ca8ebcdc98fc4aa06bb294a039cp-4Q, 0x1.303621e43e77126c475b311fee41p-3Q, 0x1.f768d94677996d7b05f99f12d599p-6Q, -0x1.1506294f451a1f48db3652c40168p-4Q, 0x1.07231a6b6ca0cb934ff78371a261p-12Q, 0x1.6e5f9be058887734b49665246c12p-6Q, -0x1.358a39f783bbf21cd3bb737b9bf7p-8Q, -0x1.1897b64b3bfb583210060e933d6p-8Q, 0x1.e4597bbfc711eadc2635b08cc11dp-10Q, 0x1.e3276a3bc510acb32c14bfd1c3d9p-13Q, -0x1.0833da803978a3e6248db817fff9p-12Q, 0x1.4a11ba1ad31b48b0c2e32412ef31p-15Q};
         }
         #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0380779473638783465886976588795511844877171449627841747664719248482680479602"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.243834674612590353732041581649284415526361108560923136142908810357641947074"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.604823123690111111903076867434236170895956271189611756533371353266219479839"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.657288078051300538078212639045173214030585866924591885443603406558844920237"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.133197385825007576190954945899795553692178076843366113615434683783912029373"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.293273783279174908806403195242198731043896162858990682572511282649777494073"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0968407832229764605135081335376966022482545810459909967947126760842963820075"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.148540749338106380135072717506042302479125857728060306077164939460051558202"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0307256814793333792123174007203788271410580502467074478150306050580744709008"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0676328290613299736756422748297190159257879087135373990074833120984537787038"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000250947114831451957587189749988554331517627199370963332183416469143399245077"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0223616621236790972053737827026909524185564668830885375472181623365153339468"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00472320475775139727792570784824246540572951491262793801875852685657845737998"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00428150368246342983449679500231453187648118181146328837486045503769103000912"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00184764688305622647661912949112567705112108135960031816073251504574674723494"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000230385763523195967205216392824542169294066205246371197226000686680376244675"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000251963188942710136974988684287860660728218154347802821413426535123097430873"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000393473203162715994806898830658915070778247705551701350735993815544054870406")};
+        if constexpr (std::is_same_v<Real, octuple_type>) {
+            return {boost::lexical_cast<octuple_type>("0.0380779473638783465886976588795511844877171449627841747664719248482680479602"), boost::lexical_cast<octuple_type>("0.243834674612590353732041581649284415526361108560923136142908810357641947074"), boost::lexical_cast<octuple_type>("0.604823123690111111903076867434236170895956271189611756533371353266219479839"), boost::lexical_cast<octuple_type>("0.657288078051300538078212639045173214030585866924591885443603406558844920237"), boost::lexical_cast<octuple_type>("0.133197385825007576190954945899795553692178076843366113615434683783912029373"), boost::lexical_cast<octuple_type>("-0.293273783279174908806403195242198731043896162858990682572511282649777494073"), boost::lexical_cast<octuple_type>("-0.0968407832229764605135081335376966022482545810459909967947126760842963820075"), boost::lexical_cast<octuple_type>("0.148540749338106380135072717506042302479125857728060306077164939460051558202"), boost::lexical_cast<octuple_type>("0.0307256814793333792123174007203788271410580502467074478150306050580744709008"), boost::lexical_cast<octuple_type>("-0.0676328290613299736756422748297190159257879087135373990074833120984537787038"), boost::lexical_cast<octuple_type>("0.000250947114831451957587189749988554331517627199370963332183416469143399245077"), boost::lexical_cast<octuple_type>("0.0223616621236790972053737827026909524185564668830885375472181623365153339468"), boost::lexical_cast<octuple_type>("-0.00472320475775139727792570784824246540572951491262793801875852685657845737998"), boost::lexical_cast<octuple_type>("-0.00428150368246342983449679500231453187648118181146328837486045503769103000912"), boost::lexical_cast<octuple_type>("0.00184764688305622647661912949112567705112108135960031816073251504574674723494"), boost::lexical_cast<octuple_type>("0.000230385763523195967205216392824542169294066205246371197226000686680376244675"), boost::lexical_cast<octuple_type>("-0.000251963188942710136974988684287860660728218154347802821413426535123097430873"), boost::lexical_cast<octuple_type>("0.0000393473203162715994806898830658915070778247705551701350735993815544054870406")};
         }
     }
     if constexpr (p == 10) {
@@ -203,8 +206,8 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.b4f6549dc7ae2d0da711a289f0cap-6Q, 0x1.8162d69198cfdb39a90922d70e5fp-3Q, 0x1.0ded5071bf8739f750ffec152978p-1Q, 0x1.607db4062d7753edab576af3e0dcp-1Q, 0x1.1feba4923f566c829244a5b4f4c2p-2Q, -0x1.ffaf7b6c111e2f4b082d1396dfd9p-3Q, -0x1.914c47c1ca801c5176763b1002edp-3Q, 0x1.04da377a0ae834bb94a9fa4f0243p-3Q, 0x1.7d29b819fd18d32d43de1a7d3641p-4Q, -0x1.246e307349ac4648ebbb94e378bbp-4Q, -0x1.e2a1dd5152b24d9c384763b949a8p-6Q, 0x1.1014069cb8f3bf95bd45be617d84p-5Q, 0x1.d8b7db3e21713e4ea2df5435db4ap-9Q, -0x1.5fb466d770edc4c0f4a29d7e3176p-7Q, 0x1.6dc8787ae38dd789b768877a70c2p-10Q, 0x1.0526072a98cd7f8751cc002da048p-9Q, -0x1.67962098c50f012db290a44515a5p-11Q, -0x1.e87f555dc50dd253428e6067701p-14Q, 0x1.888a11cfae432f4e4bd0c734fcc9p-14Q, -0x1.bd12a2a1a43db4fff0519cd821dfp-17Q};
         }
         #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0266700579005555535866174487713085827719249829085128993277997577621650735643"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.188176800077691489020892973679093994270254675864039348434859544409886608680"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.527201188931725586481744827959508192498140268084022344531854947145139828409"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.688459039453603565741871782549235853977136404240733953727968115839903445132"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.281172343660577460748726998445589287624388885902615041383154395183374807120"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.249846424327315379416101897920779100056466973713207371501312159710676300514"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.195946274377377043504299254319098131876677647638277847439678187683856178731"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.127369340335793260082677233201400977078617748042224599556309752373906702894"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0930573646035723511603522898354527322694291799894692586806397410224547567765"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0713941471663970871453360930760506476729261198370215091752375634796582409510"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0294575368218758128582832376014183919938820051606494877976965428318490167081"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0332126740593410017397636531821591289797833741326709604332335127083312999184"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00360655356695616965542329141713340329951735051861899476273061229128656318944"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0107331754833305750443181141065136444811154878114392321337033393709343696195"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00139535174705290116578931844795770756766054285568855242672111772342943140108"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00199240529518505611715874224264064321176255536551410528006793647824864459995"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000685856694959711626561370981926571419662504333678692051621190356175797931438"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000116466855129285450951480971025899189152746185434759736281923507446885853623"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000935886703200695913340501303422285439968845621529727644352187393967719605190"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000132642028945212448124366753122668330574924096060582975640067461946671323150")};
+        if constexpr (std::is_same_v<Real, octuple_type>) {
+            return {boost::lexical_cast<octuple_type>("0.0266700579005555535866174487713085827719249829085128993277997577621650735643"), boost::lexical_cast<octuple_type>("0.188176800077691489020892973679093994270254675864039348434859544409886608680"), boost::lexical_cast<octuple_type>("0.527201188931725586481744827959508192498140268084022344531854947145139828409"), boost::lexical_cast<octuple_type>("0.688459039453603565741871782549235853977136404240733953727968115839903445132"), boost::lexical_cast<octuple_type>("0.281172343660577460748726998445589287624388885902615041383154395183374807120"), boost::lexical_cast<octuple_type>("-0.249846424327315379416101897920779100056466973713207371501312159710676300514"), boost::lexical_cast<octuple_type>("-0.195946274377377043504299254319098131876677647638277847439678187683856178731"), boost::lexical_cast<octuple_type>("0.127369340335793260082677233201400977078617748042224599556309752373906702894"), boost::lexical_cast<octuple_type>("0.0930573646035723511603522898354527322694291799894692586806397410224547567765"), boost::lexical_cast<octuple_type>("-0.0713941471663970871453360930760506476729261198370215091752375634796582409510"), boost::lexical_cast<octuple_type>("-0.0294575368218758128582832376014183919938820051606494877976965428318490167081"), boost::lexical_cast<octuple_type>("0.0332126740593410017397636531821591289797833741326709604332335127083312999184"), boost::lexical_cast<octuple_type>("0.00360655356695616965542329141713340329951735051861899476273061229128656318944"), boost::lexical_cast<octuple_type>("-0.0107331754833305750443181141065136444811154878114392321337033393709343696195"), boost::lexical_cast<octuple_type>("0.00139535174705290116578931844795770756766054285568855242672111772342943140108"), boost::lexical_cast<octuple_type>("0.00199240529518505611715874224264064321176255536551410528006793647824864459995"), boost::lexical_cast<octuple_type>("-0.000685856694959711626561370981926571419662504333678692051621190356175797931438"), boost::lexical_cast<octuple_type>("-0.000116466855129285450951480971025899189152746185434759736281923507446885853623"), boost::lexical_cast<octuple_type>("0.0000935886703200695913340501303422285439968845621529727644352187393967719605190"), boost::lexical_cast<octuple_type>("-0.0000132642028945212448124366753122668330574924096060582975640067461946671323150")};
         }
     }
     if constexpr (p == 11) {
@@ -222,8 +225,8 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.324991607609160c660c469077c4p-6Q, 0x1.270c9c42314cf5fa956419fe6ca8p-3Q, 0x1.ccb286198c9dee96d12668532b6cp-2Q, 0x1.5f125643212cb922d29e40df5ae5p-1Q, 0x1.a5d9fccefe816554cfd2c1b4c2eap-2Q, -0x1.4c56f6b2bf66c3c093c0529f8f7fp-3Q, -0x1.18cff89a8cc4603466567c5566b2p-2Q, 0x1.0e83b8b6a4d8e932eca95459a69cp-4Q, 0x1.32d0a3f0ba73261f3f385a0ab52ep-3Q, -0x1.7cc387e4a9a091c75d9de8faea58p-5Q, -0x1.10221dbbeff7c12d2228c7667179p-4Q, 0x1.00b27276a80990547cbd63f84547p-5Q, 0x1.557516a958be52b928260c4c6ad5p-6Q, -0x1.f77975a6883f7054b8b01c477981p-7Q, -0x1.b5e49f3346a8b7e121e98be0fcfbp-9Q, 0x1.42fd20a75f9abc16cec7fe76464bp-8Q, -0x1.439543c8411328be7c3dbb239962p-12Q, -0x1.d4338d3fdae3a1309e0d7105695cp-11Q, 0x1.05415f0bc6ea25b1e91fb2adce4fp-12Q, 0x1.c8ab05d193c378f97fff6933dc9bp-15Q, -0x1.228a0febb3e8bfe721948bedcf9cp-15Q, 0x1.2d9b0b4e10d77be6e48f3790bbdep-18Q};
         }
         #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0186942977614710840254357293956197572896777445592195854328669208544639848493"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.144067021150624512795191584936100114302371896755623960431885248217612109866"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.449899764356045334768894037385360367780689537864893347459965579586344042705"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.685686774916200511120938631696309793594020496456770349505158901745075089131"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.411964368947907462925939648571066730743040041018784531569724251133330862864"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.162275245027490362240582726998551154074426432421213020964966742981832149727"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.274230846817946961202100945283526662864808952177517822190577839005023967370"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0660435881966831919006145788812630265675314216894079154111345722601572700631"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.149812012466378496406656261704419329858827242026748465379690959421507533896"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0464799551166841872716172258902374457722326096684826074745032098759584318172"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0664387856950252052789921553697120319181956689607973962285857402336065270973"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0313350902190460760309479840830314453635810568088003196493644550909547400332"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0208409043601810630229481125565649101515776183273471569112669220076703474398"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0153648209062015994261981160995882274401432649577300012020584862793777385002"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00334085887301444560609080861798240610193065835949919084565673177725408174281"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00492841765605904112317073974170827369028554772991580241839745801019376641230"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000308592858815143165175459072627895330718021660507848858192156227602365444134"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000893023250666264613390082462264865398987951987862072879313335822408534301830"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000249152523552823498871221687266680108822119930285542538197139249093202823549"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000544390746993684716735785687957683219193667852560079397804368892016829413126"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000346349841869849955412808515997404321450648804823345803594360135567940224107"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000449427427723651009541564828231013091641049798738375346057174174843400859633")};
+        if constexpr (std::is_same_v<Real, octuple_type>) {
+            return {boost::lexical_cast<octuple_type>("0.0186942977614710840254357293956197572896777445592195854328669208544639848493"), boost::lexical_cast<octuple_type>("0.144067021150624512795191584936100114302371896755623960431885248217612109866"), boost::lexical_cast<octuple_type>("0.449899764356045334768894037385360367780689537864893347459965579586344042705"), boost::lexical_cast<octuple_type>("0.685686774916200511120938631696309793594020496456770349505158901745075089131"), boost::lexical_cast<octuple_type>("0.411964368947907462925939648571066730743040041018784531569724251133330862864"), boost::lexical_cast<octuple_type>("-0.162275245027490362240582726998551154074426432421213020964966742981832149727"), boost::lexical_cast<octuple_type>("-0.274230846817946961202100945283526662864808952177517822190577839005023967370"), boost::lexical_cast<octuple_type>("0.0660435881966831919006145788812630265675314216894079154111345722601572700631"), boost::lexical_cast<octuple_type>("0.149812012466378496406656261704419329858827242026748465379690959421507533896"), boost::lexical_cast<octuple_type>("-0.0464799551166841872716172258902374457722326096684826074745032098759584318172"), boost::lexical_cast<octuple_type>("-0.0664387856950252052789921553697120319181956689607973962285857402336065270973"), boost::lexical_cast<octuple_type>("0.0313350902190460760309479840830314453635810568088003196493644550909547400332"), boost::lexical_cast<octuple_type>("0.0208409043601810630229481125565649101515776183273471569112669220076703474398"), boost::lexical_cast<octuple_type>("-0.0153648209062015994261981160995882274401432649577300012020584862793777385002"), boost::lexical_cast<octuple_type>("-0.00334085887301444560609080861798240610193065835949919084565673177725408174281"), boost::lexical_cast<octuple_type>("0.00492841765605904112317073974170827369028554772991580241839745801019376641230"), boost::lexical_cast<octuple_type>("-0.000308592858815143165175459072627895330718021660507848858192156227602365444134"), boost::lexical_cast<octuple_type>("-0.000893023250666264613390082462264865398987951987862072879313335822408534301830"), boost::lexical_cast<octuple_type>("0.000249152523552823498871221687266680108822119930285542538197139249093202823549"), boost::lexical_cast<octuple_type>("0.0000544390746993684716735785687957683219193667852560079397804368892016829413126"), boost::lexical_cast<octuple_type>("-0.0000346349841869849955412808515997404321450648804823345803594360135567940224107"), boost::lexical_cast<octuple_type>("0.00000449427427723651009541564828231013091641049798738375346057174174843400859633")};
         }
     }
     if constexpr (p == 12) {
@@ -241,8 +244,8 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.ada9978d2fa568b21229688156b8p-7Q, 0x1.c0c890682f8790d7f6bb1c1aa44ep-4Q, 0x1.82696272e40bd05e57c851b9cb36p-2Q, 0x1.507c59d8e6f6ac435d1e88e090b6p-1Q, 0x1.082245c29797798f324c3b86f65cp-1Q, -0x1.6eb4ac1d9855ccfed03d4133c6fbp-5Q, -0x1.43c448da45b222f8d287f72956dcp-2Q, -0x1.85996f0f3b3b27b5f0ec32953a95p-6Q, 0x1.75b757e56dd3b6e26eea4e0a43bap-3Q, 0x1.5f3ea878d368e081a5d3cb36d936p-8Q, -0x1.8afc6821933836a0611906df913cp-4Q, 0x1.638119d1c4361bb00a2f22d1f90bp-7Q, 0x1.5458dbe394eb05c5aab3c4ceb31ap-5Q, -0x1.90617513f389b7954493854c387ep-7Q, -0x1.a4c4a623e2a50fc10158bea8a45cp-7Q, 0x1.b7d844bffa4e88c2ef52650eb0e3p-8Q, 0x1.26babd1f8d1809707edb54236067p-9Q, -0x1.1dac0186ec14265ff3ab908c13a3p-9Q, 0x1.b73c724cbcd24a84c3c597249f8dp-18Q, 0x1.9788431be0bfb2d1938d25135045p-12Q, -0x1.7336904b8b4e84c0e0396f9346efp-14Q, -0x1.96b4a56f63fa8a95abb9ecaeceaep-16Q, 0x1.acb92f10c4239fce7d915af19a6cp-17Q, -0x1.9a7502d7dc2f2e1e665f9ba74bc1p-20Q};
         }
         #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0131122579572295175067460908889332806566551064193132500774828079813751369078"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.109566272821185154605704505024890542607568050306677404638365743414594716237"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.377355135214212657092821260487920614901094170605752633470583911562885099045"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.657198722579307089302761128664116983425020328998841214139428195001939202386"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.515886478427815608756032648054303270067769308703609005612764729867503168411"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0447638856537746266676274731154016652928454363150592413907170410117965514990"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.316178453752785536864802935347803109850883903254736438957420337160049554984"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0237792572560697276839975460913322578455336655833174115248261271603350281595"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.182478605927579679854043611618924171029477144809630269832901126083410652478"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00535956967435215032827627672976833228886266518419270582163634261809269415715"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0964321200965070820265032053432248412743088014304522051434640274861906048848"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0108491302558221843808901023774815218866163056760333465932251226434077741286"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0415462774950844407392709468190657486451353222138837486128707899413616614352"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0122186490697482807199879826647156771298246609311655817534481104550208384247"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0128408251983006832946603447189472849620610983231409763327522557348508782102"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00671149900879550917776702706821567245064811218585645674037945533688642441241"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00224860724099523759995086521126723401834319978614617709926201027901007445066"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00217950361862776047159890337958417118784007529186057126498094298705073259759"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000654512821250959556650043039932711072911177056889735663071455200741848443049"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000388653062820931443589728883779598179191748857342017752343609613138331820861"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000885041092082043242082164596155372659873832215147193280801544303001991847212"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000242415457570307840297891532053171958042377836266428223937753220729228844731"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000127769522193797665871404636261662088737596094143942875605535392042653701946"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000152907175806851090271223916452290122319761543966034067260269641683218542373")};
+        if constexpr (std::is_same_v<Real, octuple_type>) {
+            return {boost::lexical_cast<octuple_type>("0.0131122579572295175067460908889332806566551064193132500774828079813751369078"), boost::lexical_cast<octuple_type>("0.109566272821185154605704505024890542607568050306677404638365743414594716237"), boost::lexical_cast<octuple_type>("0.377355135214212657092821260487920614901094170605752633470583911562885099045"), boost::lexical_cast<octuple_type>("0.657198722579307089302761128664116983425020328998841214139428195001939202386"), boost::lexical_cast<octuple_type>("0.515886478427815608756032648054303270067769308703609005612764729867503168411"), boost::lexical_cast<octuple_type>("-0.0447638856537746266676274731154016652928454363150592413907170410117965514990"), boost::lexical_cast<octuple_type>("-0.316178453752785536864802935347803109850883903254736438957420337160049554984"), boost::lexical_cast<octuple_type>("-0.0237792572560697276839975460913322578455336655833174115248261271603350281595"), boost::lexical_cast<octuple_type>("0.182478605927579679854043611618924171029477144809630269832901126083410652478"), boost::lexical_cast<octuple_type>("0.00535956967435215032827627672976833228886266518419270582163634261809269415715"), boost::lexical_cast<octuple_type>("-0.0964321200965070820265032053432248412743088014304522051434640274861906048848"), boost::lexical_cast<octuple_type>("0.0108491302558221843808901023774815218866163056760333465932251226434077741286"), boost::lexical_cast<octuple_type>("0.0415462774950844407392709468190657486451353222138837486128707899413616614352"), boost::lexical_cast<octuple_type>("-0.0122186490697482807199879826647156771298246609311655817534481104550208384247"), boost::lexical_cast<octuple_type>("-0.0128408251983006832946603447189472849620610983231409763327522557348508782102"), boost::lexical_cast<octuple_type>("0.00671149900879550917776702706821567245064811218585645674037945533688642441241"), boost::lexical_cast<octuple_type>("0.00224860724099523759995086521126723401834319978614617709926201027901007445066"), boost::lexical_cast<octuple_type>("-0.00217950361862776047159890337958417118784007529186057126498094298705073259759"), boost::lexical_cast<octuple_type>("0.00000654512821250959556650043039932711072911177056889735663071455200741848443049"), boost::lexical_cast<octuple_type>("0.000388653062820931443589728883779598179191748857342017752343609613138331820861"), boost::lexical_cast<octuple_type>("-0.0000885041092082043242082164596155372659873832215147193280801544303001991847212"), boost::lexical_cast<octuple_type>("-0.0000242415457570307840297891532053171958042377836266428223937753220729228844731"), boost::lexical_cast<octuple_type>("0.0000127769522193797665871404636261662088737596094143942875605535392042653701946"), boost::lexical_cast<octuple_type>("-0.00000152907175806851090271223916452290122319761543966034067260269641683218542373")};
         }
     }
     if constexpr (p == 13) {
@@ -260,8 +263,8 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.2d89174d37e3b6596d64d168e49p-7Q, 0x1.53664fc8a3d4c0d33efd4b4bc6fap-4Q, 0x1.3f7bf6c09afe857e70d916613d78p-2Q, 0x1.38dc5001834baade66ebb6ec9fc1p-1Q, 0x1.2d82ef0bea471de1f0a3864a5cccp-1Q, 0x1.644b251290fb4bea9c417da1f71ep-4Q, -0x1.42884206fc5ade5015e8dd0e5832p-2Q, -0x1.fe442b86ad7635e6a44fa231478p-4Q, 0x1.6f91279c81aa3aed801eca5172e8p-3Q, 0x1.2acc804557c8ab4899f3d0916648p-4Q, -0x1.b163543c8eacbf70b0092010e485p-4Q, -0x1.b1fc6de2397062d67f76ff78186p-6Q, 0x1.cbe5044520d5e315c90c0ed1b10cp-5Q, 0x1.37f29dfe3e92c6d51003ce786db8p-9Q, -0x1.867439245b0c6d71509d7a14369ep-6Q, 0x1.0128d031aa3b020f68dbd131fc68p-8Q, 0x1.db80973172630eff11f1aa6bf206p-8Q, -0x1.6a025cdac7e0fe4d3e8433e38ffbp-9Q, -0x1.58e561b1f2cf60b1ce144cfab0ffp-10Q, 0x1.e8ceb1ee24cab5dbcf0c32d1591bp-11Q, 0x1.9d26d847f17c9a8ce68c968f105dp-15Q, -0x1.5a4cf360064a4020bfd19dc8e5fp-13Q, 0x1.0159a865542d28f1113c2ad46cb5p-15Q, 0x1.5e5f8028cd834a146bf59b16d932p-17Q, -0x1.3b708a4c3be3403a7da544157c5bp-18Q, 0x1.183f9db8da3a04f4c66e4459dad2p-21Q};
         }
         #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00920213353896236797297016347564418466753417191641656238600970303711912173265"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0828612438729027796443202713123046640520811333289013507251427742009482956517"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.311996322160438063396078411221404969394668352896718031716039017308515654041"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.611055851158787652821199513674418056207361267601823943852658294015204037145"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.588889570431218908071039534739533392766598638281283604223557340650249576137"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0869857261796472373102373983808749439923188407661970125088201664378054171345"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.314972907711388632998169825593228258287688845067878902595030681868130772999"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.124576730750815258941380833602126018079273929517363471957206932075260972005"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.179476079429339843234845007233936901358196625624413339304288145469676423326"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0729489336567771638090283061047766198332592902687987355362796328461636696921"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.105807618187934326450966730419646484947886075480123665823236051077820681894"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0264884064753436946396391224803478572641960484429769701626422412133519842633"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0561394771002834288621450199838733111998837879254310024473705625396675790207"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00237997225405907881146517095855420835809439461205193486847513927070930528134"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0238314207103236490320640306775773913425292271763622627407729863341057724688"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00392394144879741624331637022081552655882474662345140404391840728787217413821"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00725558940161756619451839330050269889897352967964668369526982867260050623476"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00276191123465686217801457626609844599535009333050181802496631648326614964558"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00131567391189229893661383537059364337606041259265365230723812459474570122051"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000932326130867263386222651780254851410091808829980195230799156927112701492336"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000492515251262894619214095738786659621010377829938882350084009445661139469929"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000165128988556505489461668770923800075589854821465977670334780149359987420945"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000306785375793254934664948322857547623660042821723790056312823074855283018382"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000104419305714081370817071499108059695167070643621732816964147406843820801008"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000470041647936086832565019516506177132165038358297095855656805971133412246529"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000522003509845486469173642435484317697674705215524355700153190105348895004025")};
+        if constexpr (std::is_same_v<Real, octuple_type>) {
+            return {boost::lexical_cast<octuple_type>("0.00920213353896236797297016347564418466753417191641656238600970303711912173265"), boost::lexical_cast<octuple_type>("0.0828612438729027796443202713123046640520811333289013507251427742009482956517"), boost::lexical_cast<octuple_type>("0.311996322160438063396078411221404969394668352896718031716039017308515654041"), boost::lexical_cast<octuple_type>("0.611055851158787652821199513674418056207361267601823943852658294015204037145"), boost::lexical_cast<octuple_type>("0.588889570431218908071039534739533392766598638281283604223557340650249576137"), boost::lexical_cast<octuple_type>("0.0869857261796472373102373983808749439923188407661970125088201664378054171345"), boost::lexical_cast<octuple_type>("-0.314972907711388632998169825593228258287688845067878902595030681868130772999"), boost::lexical_cast<octuple_type>("-0.124576730750815258941380833602126018079273929517363471957206932075260972005"), boost::lexical_cast<octuple_type>("0.179476079429339843234845007233936901358196625624413339304288145469676423326"), boost::lexical_cast<octuple_type>("0.0729489336567771638090283061047766198332592902687987355362796328461636696921"), boost::lexical_cast<octuple_type>("-0.105807618187934326450966730419646484947886075480123665823236051077820681894"), boost::lexical_cast<octuple_type>("-0.0264884064753436946396391224803478572641960484429769701626422412133519842633"), boost::lexical_cast<octuple_type>("0.0561394771002834288621450199838733111998837879254310024473705625396675790207"), boost::lexical_cast<octuple_type>("0.00237997225405907881146517095855420835809439461205193486847513927070930528134"), boost::lexical_cast<octuple_type>("-0.0238314207103236490320640306775773913425292271763622627407729863341057724688"), boost::lexical_cast<octuple_type>("0.00392394144879741624331637022081552655882474662345140404391840728787217413821"), boost::lexical_cast<octuple_type>("0.00725558940161756619451839330050269889897352967964668369526982867260050623476"), boost::lexical_cast<octuple_type>("-0.00276191123465686217801457626609844599535009333050181802496631648326614964558"), boost::lexical_cast<octuple_type>("-0.00131567391189229893661383537059364337606041259265365230723812459474570122051"), boost::lexical_cast<octuple_type>("0.000932326130867263386222651780254851410091808829980195230799156927112701492336"), boost::lexical_cast<octuple_type>("0.0000492515251262894619214095738786659621010377829938882350084009445661139469929"), boost::lexical_cast<octuple_type>("-0.000165128988556505489461668770923800075589854821465977670334780149359987420945"), boost::lexical_cast<octuple_type>("0.0000306785375793254934664948322857547623660042821723790056312823074855283018382"), boost::lexical_cast<octuple_type>("0.0000104419305714081370817071499108059695167070643621732816964147406843820801008"), boost::lexical_cast<octuple_type>("-0.00000470041647936086832565019516506177132165038358297095855656805971133412246529"), boost::lexical_cast<octuple_type>("0.000000522003509845486469173642435484317697674705215524355700153190105348895004025")};
         }
     }
     if constexpr (p == 14) {
@@ -279,8 +282,8 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.a7702ace363ac35a31e24ad7f18bp-8Q, 0x1.fee460f5cb8771588fb11eee4edep-5Q, 0x1.04f777f62f422960e164233d2842p-2Q, 0x1.1bcdf22a1725c010c6b543c39465p-1Q, 0x1.432b0dc3136d3b304d5a3bf4569bp-1Q, 0x1.bfd66ae4258abee147e56af809ep-3Q, -0x1.1635861af071cce08b7655b9575p-2Q, -0x1.be885d06053beddff8849acb8697p-3Q, 0x1.1b6ef32bc7358856a3c8661f7dbbp-3Q, 0x1.1eb28fc03c55b30ce48dc30b7f77p-3Q, -0x1.63524d6aa4cf6fa795512cfa3aa5p-4Q, -0x1.2510847f3ed25a6abc4fb2ebbea9p-4Q, 0x1.c480a659de0cd4f4123d770896e6p-5Q, 0x1.ba103a92149f4583a4c79c292018p-6Q, -0x1.ee8e8a6bca9ac4ad53dedccf86b9p-6Q, -0x1.6ffce6192a67aceee5260da8193dp-8Q, 0x1.a3160ba7d924dde8cc52f58fbb97p-7Q, -0x1.873bd13c8af17ab00e30f03b73e4p-11Q, -0x1.f894721441f671f4ac26746366e6p-9Q, 0x1.1650e1f6ec4c290c75eee26e8b4ap-10Q, 0x1.7334fd9e58c69f69b95d47a6075fp-11Q, -0x1.959f69010da009a2eacf096b1dafp-12Q, -0x1.5e73f3c02020121b8b1dbc91cc8ap-15Q, 0x1.20612a2e814f83021e4b38a90018p-14Q, -0x1.5adbf364f5e1bddd8115a86dd662p-17Q, -0x1.26968e53fb76ce12ec5e07348937p-18Q, 0x1.cf0cbb4133dbb68c44095fc163dep-20Q, -0x1.7fc90f0c46da191bc033464815fbp-23Q};
         }
         #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00646115346008794781816639744862281427232715941920119921810140416821319638585"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0623647588493988983279856675843487742830533369340766716460251880613807597066"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.254850267792621353665907788677828668618704241636713744378008420238232719628"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.554305617940893835992683144985115484407826983095163460968399777532226842271"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.631187849104856779557661713535817234862395245657001728978880959248433640269"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.218670687758906521491747591821751705176577432127043205903027323352534222868"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.271688552278748041414219247618117109460488246568333081431189666923849066652"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.218033529993276044755555881270231191197524066947060475274712704179785996228"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.138395213864806591073993969002157371398990046322968611905911990239065683492"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.139989016584460701249294316227116344032822155561432618133368381730127661592"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0867484115681696890456082206672779538297914953951750365749296445982289331724"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0715489555040461307358414511517380799095806967312953809999091309335447192979"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0552371262592160441161883406053340339791383363251167215767110765995965856731"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0269814083079129169739903140321519334337576659580727423328434928060131390138"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0301853515403906351871482262348913757378157540665865262488375619379066007462"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00561504953035695913321837136769149863745729720392581038769868016916017798506"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0127894932663334089615733070578407929937490386157205831348153451948141528455"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000746218989268384937181716073918178097195818798881330290043548750870183218766"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00384963886802218744578634931609555177409681850828570049305891572532777766984"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00106169108560676184303256674938841117303394158214783086389393956154388248847"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000708021154235527858644297769761712898347186346418159537167009442266803119446"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000386831947312954482107666339805731442732890210784216537990146842609536038748"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000417772457703725973526797953983925892838972659013273013105432373007939629113"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000687550425269750960387343702162803160189037068765187527988272789892867302714"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000103372091845707739466140734259481458626927250949074485069144305905647763599"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000438970490178139411525404256136716982932308536080082571815104919437269388055"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000172499467536781276988571269274179852358789470986735657691071794719454646345"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000178713996831135907633419293847083934388299030997695944699402284569127317214")};
+        if constexpr (std::is_same_v<Real, octuple_type>) {
+            return {boost::lexical_cast<octuple_type>("0.00646115346008794781816639744862281427232715941920119921810140416821319638585"), boost::lexical_cast<octuple_type>("0.0623647588493988983279856675843487742830533369340766716460251880613807597066"), boost::lexical_cast<octuple_type>("0.254850267792621353665907788677828668618704241636713744378008420238232719628"), boost::lexical_cast<octuple_type>("0.554305617940893835992683144985115484407826983095163460968399777532226842271"), boost::lexical_cast<octuple_type>("0.631187849104856779557661713535817234862395245657001728978880959248433640269"), boost::lexical_cast<octuple_type>("0.218670687758906521491747591821751705176577432127043205903027323352534222868"), boost::lexical_cast<octuple_type>("-0.271688552278748041414219247618117109460488246568333081431189666923849066652"), boost::lexical_cast<octuple_type>("-0.218033529993276044755555881270231191197524066947060475274712704179785996228"), boost::lexical_cast<octuple_type>("0.138395213864806591073993969002157371398990046322968611905911990239065683492"), boost::lexical_cast<octuple_type>("0.139989016584460701249294316227116344032822155561432618133368381730127661592"), boost::lexical_cast<octuple_type>("-0.0867484115681696890456082206672779538297914953951750365749296445982289331724"), boost::lexical_cast<octuple_type>("-0.0715489555040461307358414511517380799095806967312953809999091309335447192979"), boost::lexical_cast<octuple_type>("0.0552371262592160441161883406053340339791383363251167215767110765995965856731"), boost::lexical_cast<octuple_type>("0.0269814083079129169739903140321519334337576659580727423328434928060131390138"), boost::lexical_cast<octuple_type>("-0.0301853515403906351871482262348913757378157540665865262488375619379066007462"), boost::lexical_cast<octuple_type>("-0.00561504953035695913321837136769149863745729720392581038769868016916017798506"), boost::lexical_cast<octuple_type>("0.0127894932663334089615733070578407929937490386157205831348153451948141528455"), boost::lexical_cast<octuple_type>("-0.000746218989268384937181716073918178097195818798881330290043548750870183218766"), boost::lexical_cast<octuple_type>("-0.00384963886802218744578634931609555177409681850828570049305891572532777766984"), boost::lexical_cast<octuple_type>("0.00106169108560676184303256674938841117303394158214783086389393956154388248847"), boost::lexical_cast<octuple_type>("0.000708021154235527858644297769761712898347186346418159537167009442266803119446"), boost::lexical_cast<octuple_type>("-0.000386831947312954482107666339805731442732890210784216537990146842609536038748"), boost::lexical_cast<octuple_type>("-0.0000417772457703725973526797953983925892838972659013273013105432373007939629113"), boost::lexical_cast<octuple_type>("0.0000687550425269750960387343702162803160189037068765187527988272789892867302714"), boost::lexical_cast<octuple_type>("-0.0000103372091845707739466140734259481458626927250949074485069144305905647763599"), boost::lexical_cast<octuple_type>("-0.00000438970490178139411525404256136716982932308536080082571815104919437269388055"), boost::lexical_cast<octuple_type>("0.00000172499467536781276988571269274179852358789470986735657691071794719454646345"), boost::lexical_cast<octuple_type>("-0.000000178713996831135907633419293847083934388299030997695944699402284569127317214")};
         }
     }
     if constexpr (p == 15) {
@@ -298,8 +301,8 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.2970058a26dcd961f2ddf52bca08p-8Q, 0x1.7eec010bca4c417f3cf45c166751p-5Q, 0x1.a5efd6f02857dd0be400d7c02e2cp-3Q, 0x1.f8747691d3f737355530dd281d86p-2Q, 0x1.4aa8051a530b457c39051251b937p-1Q, 0x1.5b237b0c281791146b95d35023c4p-2Q, -0x1.8bae9ca895b451d87fbb9a690248p-3Q, -0x1.27d0d6e28e01f3ef0606971828aap-2Q, 0x1.0b6623378c72eb295fa0f634a67bp-4Q, 0x1.856ba3f0d1d5aaf4f59a12cbb286p-3Q, -0x1.44f200621040cdd51fafc7035006p-5Q, -0x1.c726bf22e4a15fea85834dbb1052p-4Q, 0x1.15858527779bc1c4ec7f8b6fdd21p-5Q, 0x1.c0c32426f4662ec60f158af78296p-5Q, -0x1.a62aa972a6fc3876e9915f565de4p-6Q, -0x1.54f3ad3a0b7c5bd971d938015013p-6Q, 0x1.ee451350034703acaa0dbe95c1aep-7Q, 0x1.4e4c95b98ec2d5e117559a2b0da9p-8Q, -0x1.a92e1fc2fdcad88a36c4f23f938p-8Q, -0x1.fb000715d8e6558a8e3b0bc34d7fp-13Q, 0x1.fd6e43c3dd5e86d041c185aa9428p-10Q, -0x1.879fe7f24ba0a4818b2d76fbd7e6p-12Q, -0x1.79080f71ee322531c0337932b9a5p-12Q, 0x1.46f04a6cb59007eab6af7b114fa4p-13Q, 0x1.b0bacca20c60f4939edefbff1354p-16Q, -0x1.d7ff965f47a09038cb01ea5da5e9p-16Q, 0x1.c35f5c15433718b508f832bbf1b8p-19Q, 0x1.e6358dfe44b5282546827ce8042cp-20Q, -0x1.532291d1cbfa3eda1a3275ffd36dp-21Q, 0x1.076d01633701901bb8cc971717bp-24Q};
         }
         #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00453853736157889888145939491021169634666367124378878699791651359730618263777"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0467433948927662718917096933484357577657915170021494351311319734377213834945"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.206023863986995731539891500947630721930613850564193090270204726624901561209"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.492631771708139623606775707402994637261722156513093240216016003697522813162"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.645813140357424358176420912010691799643260828749404618107148947895533066481"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.339002535454731527691264114383577391875676949179355466933669011509397556470"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.193204139609145428706399053432147174630409003914286382793775492150589726686"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.288882596566965646248412500982233298131143563043534259497129296256293483504"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0652829528487728169228310791986957488203917428559614412596510130561953369929"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.190146714007122982348489311658602051795950125817433669687815606055254287820"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0396661765557909444838436675189620066838174282068373680544974535292838687668"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.111120936037231693365671032467405860885862376216591412050565788400539631609"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0338771439235076862085481784443352377086474468741126536946319599123012785905"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0547805505845076126891379031258187910860941599742276856424484536408030091303"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0257670073284399625859452575426982639220364163482534013839683682541716280711"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0208100501696930816778848342467700016205465795136489904099616617271926101264"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0150839180278359023632927446017032273624489282330562771623396889036950783790"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00510100036040754316970886018556531472480106652734422205552663106916575853665"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00648773456031574499518168314921869081695584563938882640792896746945184786140"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000241756490761624281166722532630017960522994699581453522332941192889131156009"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00194332398038221154176491233254108744101142486557953140145230261789465341230"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000373482354137616992009809421364541461138763096803025662574022673555831120585"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000359565244362468812164962007590980885819420245408409030562748046672838761659"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000155896489920599747947165824122710881625556705962549591522860363042830623991"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000257926991553189368092586241761685591294404236876734070916011973700950042214"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000281332962660478136475532477707847866579144387629378890426725562075302388539"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000336298718173757980312484521042017747213484665586407818718630450150330033976"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000181127040794057708376851091228584116057708592533750785059029068086553957632"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000631688232588166442120159729951765765416613791512119551041664162606772181110"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000613335991330575202905629946028978860198919045088539651217384559505804672173")};
+        if constexpr (std::is_same_v<Real, octuple_type>) {
+            return {boost::lexical_cast<octuple_type>("0.00453853736157889888145939491021169634666367124378878699791651359730618263777"), boost::lexical_cast<octuple_type>("0.0467433948927662718917096933484357577657915170021494351311319734377213834945"), boost::lexical_cast<octuple_type>("0.206023863986995731539891500947630721930613850564193090270204726624901561209"), boost::lexical_cast<octuple_type>("0.492631771708139623606775707402994637261722156513093240216016003697522813162"), boost::lexical_cast<octuple_type>("0.645813140357424358176420912010691799643260828749404618107148947895533066481"), boost::lexical_cast<octuple_type>("0.339002535454731527691264114383577391875676949179355466933669011509397556470"), boost::lexical_cast<octuple_type>("-0.193204139609145428706399053432147174630409003914286382793775492150589726686"), boost::lexical_cast<octuple_type>("-0.288882596566965646248412500982233298131143563043534259497129296256293483504"), boost::lexical_cast<octuple_type>("0.0652829528487728169228310791986957488203917428559614412596510130561953369929"), boost::lexical_cast<octuple_type>("0.190146714007122982348489311658602051795950125817433669687815606055254287820"), boost::lexical_cast<octuple_type>("-0.0396661765557909444838436675189620066838174282068373680544974535292838687668"), boost::lexical_cast<octuple_type>("-0.111120936037231693365671032467405860885862376216591412050565788400539631609"), boost::lexical_cast<octuple_type>("0.0338771439235076862085481784443352377086474468741126536946319599123012785905"), boost::lexical_cast<octuple_type>("0.0547805505845076126891379031258187910860941599742276856424484536408030091303"), boost::lexical_cast<octuple_type>("-0.0257670073284399625859452575426982639220364163482534013839683682541716280711"), boost::lexical_cast<octuple_type>("-0.0208100501696930816778848342467700016205465795136489904099616617271926101264"), boost::lexical_cast<octuple_type>("0.0150839180278359023632927446017032273624489282330562771623396889036950783790"), boost::lexical_cast<octuple_type>("0.00510100036040754316970886018556531472480106652734422205552663106916575853665"), boost::lexical_cast<octuple_type>("-0.00648773456031574499518168314921869081695584563938882640792896746945184786140"), boost::lexical_cast<octuple_type>("-0.000241756490761624281166722532630017960522994699581453522332941192889131156009"), boost::lexical_cast<octuple_type>("0.00194332398038221154176491233254108744101142486557953140145230261789465341230"), boost::lexical_cast<octuple_type>("-0.000373482354137616992009809421364541461138763096803025662574022673555831120585"), boost::lexical_cast<octuple_type>("-0.000359565244362468812164962007590980885819420245408409030562748046672838761659"), boost::lexical_cast<octuple_type>("0.000155896489920599747947165824122710881625556705962549591522860363042830623991"), boost::lexical_cast<octuple_type>("0.0000257926991553189368092586241761685591294404236876734070916011973700950042214"), boost::lexical_cast<octuple_type>("-0.0000281332962660478136475532477707847866579144387629378890426725562075302388539"), boost::lexical_cast<octuple_type>("0.00000336298718173757980312484521042017747213484665586407818718630450150330033976"), boost::lexical_cast<octuple_type>("0.00000181127040794057708376851091228584116057708592533750785059029068086553957632"), boost::lexical_cast<octuple_type>("-0.000000631688232588166442120159729951765765416613791512119551041664162606772181110"), boost::lexical_cast<octuple_type>("0.0000000613335991330575202905629946028978860198919045088539651217384559505804672173")};
         }
     }
     if constexpr (p == 16) {
@@ -317,8 +320,8 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.a2047f25eec85da6e57cd7f20965p-9Q, 0x1.1df6c86cbec60472edd73314093ap-5Q, 0x1.520d391a9410689a221d2a40ed0cp-3Q, 0x1.b8a3e5feb48792faed491d08e637p-2Q, 0x1.465391b4659339393dc6b44dd0b9p-1Q, 0x1.c2db72f84c20394e90d8314fee8dp-2Q, -0x1.6f9ed69c399c6d957cef0caf36cp-4Q, -0x1.4ee9af39c16ebfbef0c302e6791dp-2Q, -0x1.c96973b93bd864088cf77c5363e8p-6Q, 0x1.b084bf1dc763ab7d34b03cf7014cp-3Q, 0x1.bff160aba4bc2b81b5cb21d8ed3dp-6Q, -0x1.0f21999627c5eb1bdc396cd5510bp-3Q, -0x1.98ed2d2871d09c2ff301236b3aa5p-8Q, 0x1.36fc54ec8b1065ad541d9561e805p-4Q, -0x1.f159dcb973ff3c971dea81777e8cp-8Q, -0x1.2e3093b602a5114cced31fb3d21p-5Q, 0x1.516f07b10e2bfeeb35e5d488972dp-7Q, 0x1.ca8c3dcce54c309c6bfdafe5b818p-7Q, -0x1.ca18fbf2cc14161cd462d6382e8dp-8Q, -0x1.dda9bb9568c150b5b1b563e2a704p-9Q, 0x1.99ff0c3f2ed80a696d3f49d1ae83p-9Q, 0x1.abb6031610512ba452ab2c15607bp-12Q, -0x1.ed5dcd1b49a3f3c23377158c2ae9p-11Q, 0x1.df29e5ea1284520ed9350c7d7e2fp-14Q, 0x1.6e8e301063e5a66bc2dcbb672407p-13Q, -0x1.0000dea4283e8e4f97e320b5edbp-14Q, -0x1.d3f0626b575af7e0f5c7b70618f9p-17Q, 0x1.7c64ba15d23464b7681824c41ca1p-17Q, -0x1.1821ad345e7bfc3ef33cc03c406ap-20Q, -0x1.8b555407022a1683907685f46c79p-21Q, 0x1.efcebf5a99b7b789a7792201843ep-23Q, -0x1.6a61bcee28102f153c8290cebfbbp-26Q};
         }
         #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00318922092534773802976954756464595868706708675013142876787587817778694863119"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0349077143236733464103014722402302000921824143050398414614005464773763780013"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.165064283488853117899125273056113481158483500234272324021359282902034099572"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.430312722846003813740392542435768462063397047803698677392464629118864929936"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.637356332083788898631985241299603053649859594081419812596775159322552430035"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.440290256886356900039086916357167928852780303513527257878988432216501129849"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0897510894024896428571871807744259743065924744558266014962471841522684784655"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.327063310527917704646290567568911964175722891822881242814172353116733610255"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0279182081330282766826451959502687320433997121917473604153547976243684979156"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.211190693947104288720968016326883790092849142616767943925104282659239340555"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0273402637527160413648524575720161796542902781950713022023150026811811035864"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.132388305563810390450047414775649337509228781770602797879854902742212569323"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00623972275247487176567450339412002586544465631167876099076145808663824556181"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0759242360442763158214849874394142246153040594610094335194031399951322105236"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00758897436885773763849489086463699579658697514499092540009716094367144606278"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0368883976917301423335266632089455431471874842970673083106406876512904740900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0102976596409559694116500058007661690052885626580366220885414734497334909977"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0139937688598287310295045187367032972640984029172786898849010078360486452906"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00699001456341391667028424953651728833805785619964646907811575967502711102002"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00364427962149838993216900054093362938705533397335310866884121504669938973849"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00312802338120626883166120255985467876782147190619360811745036081031020620657"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000407896980849712836241747032340609578243195297231054671507139711098341190969"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000941021749359567588926645395363587540775474721673448050925027367949065706153"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000114241520038722392644022809955566294583968434493647265287709142315097418924"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000174787245225338180380175863766074687498602472861539989797195359589183047664"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000610359662141093583516236915052221281195725998196591914396172281391485128503"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000139456689882088934519907831199840198232527356919867533540870797045644631590"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000113366086612762585875884876288653699751947106820375366175784342881379088583"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000104357134231160650152545473726261540488747893063567647154603268028625910132"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000736365678545120551209969571972556364658544554584166332743356923285383067848"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000230878408685754586640541273294200612130630673586665552537254486473108851937"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000210933963010074309700057262360348990683629758459160530774534994952533728279")};
+        if constexpr (std::is_same_v<Real, octuple_type>) {
+            return {boost::lexical_cast<octuple_type>("0.00318922092534773802976954756464595868706708675013142876787587817778694863119"), boost::lexical_cast<octuple_type>("0.0349077143236733464103014722402302000921824143050398414614005464773763780013"), boost::lexical_cast<octuple_type>("0.165064283488853117899125273056113481158483500234272324021359282902034099572"), boost::lexical_cast<octuple_type>("0.430312722846003813740392542435768462063397047803698677392464629118864929936"), boost::lexical_cast<octuple_type>("0.637356332083788898631985241299603053649859594081419812596775159322552430035"), boost::lexical_cast<octuple_type>("0.440290256886356900039086916357167928852780303513527257878988432216501129849"), boost::lexical_cast<octuple_type>("-0.0897510894024896428571871807744259743065924744558266014962471841522684784655"), boost::lexical_cast<octuple_type>("-0.327063310527917704646290567568911964175722891822881242814172353116733610255"), boost::lexical_cast<octuple_type>("-0.0279182081330282766826451959502687320433997121917473604153547976243684979156"), boost::lexical_cast<octuple_type>("0.211190693947104288720968016326883790092849142616767943925104282659239340555"), boost::lexical_cast<octuple_type>("0.0273402637527160413648524575720161796542902781950713022023150026811811035864"), boost::lexical_cast<octuple_type>("-0.132388305563810390450047414775649337509228781770602797879854902742212569323"), boost::lexical_cast<octuple_type>("-0.00623972275247487176567450339412002586544465631167876099076145808663824556181"), boost::lexical_cast<octuple_type>("0.0759242360442763158214849874394142246153040594610094335194031399951322105236"), boost::lexical_cast<octuple_type>("-0.00758897436885773763849489086463699579658697514499092540009716094367144606278"), boost::lexical_cast<octuple_type>("-0.0368883976917301423335266632089455431471874842970673083106406876512904740900"), boost::lexical_cast<octuple_type>("0.0102976596409559694116500058007661690052885626580366220885414734497334909977"), boost::lexical_cast<octuple_type>("0.0139937688598287310295045187367032972640984029172786898849010078360486452906"), boost::lexical_cast<octuple_type>("-0.00699001456341391667028424953651728833805785619964646907811575967502711102002"), boost::lexical_cast<octuple_type>("-0.00364427962149838993216900054093362938705533397335310866884121504669938973849"), boost::lexical_cast<octuple_type>("0.00312802338120626883166120255985467876782147190619360811745036081031020620657"), boost::lexical_cast<octuple_type>("0.000407896980849712836241747032340609578243195297231054671507139711098341190969"), boost::lexical_cast<octuple_type>("-0.000941021749359567588926645395363587540775474721673448050925027367949065706153"), boost::lexical_cast<octuple_type>("0.000114241520038722392644022809955566294583968434493647265287709142315097418924"), boost::lexical_cast<octuple_type>("0.000174787245225338180380175863766074687498602472861539989797195359589183047664"), boost::lexical_cast<octuple_type>("-0.0000610359662141093583516236915052221281195725998196591914396172281391485128503"), boost::lexical_cast<octuple_type>("-0.0000139456689882088934519907831199840198232527356919867533540870797045644631590"), boost::lexical_cast<octuple_type>("0.0000113366086612762585875884876288653699751947106820375366175784342881379088583"), boost::lexical_cast<octuple_type>("-0.00000104357134231160650152545473726261540488747893063567647154603268028625910132"), boost::lexical_cast<octuple_type>("-0.000000736365678545120551209969571972556364658544554584166332743356923285383067848"), boost::lexical_cast<octuple_type>("0.000000230878408685754586640541273294200612130630673586665552537254486473108851937"), boost::lexical_cast<octuple_type>("-0.0000000210933963010074309700057262360348990683629758459160530774534994952533728279")};
         }
     }
     if constexpr (p == 17) {
@@ -336,8 +339,8 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.25d68f81bd86c306bc9043f43f4p-9Q, 0x1.a9bea4085cef3d6d79a074d9709ep-6Q, 0x1.0cba6633a3a6d489f4c961323b24p-3Q, 0x1.7b3d3861245d02709eb04b0b2b39p-2Q, 0x1.38d48c64aa0daf396243783e95bep-1Q, 0x1.0960af0f4068e5ac2ea6e7c9135p-1Q, 0x1.bf874a24b1d55da571e39f2bf7e7p-6Q, -0x1.50335073492d1d5e6945d8cdee28p-2Q, -0x1.0346bb1b97633ba3dcc115a9814cp-3Q, 0x1.9417930ab08a311830b19e500034p-3Q, 0x1.9e403f27b713f2db7263ac22d15fp-4Q, -0x1.03b7f2067576f3b2927e9c5889d3p-3Q, -0x1.d3b162866891a8d294e6e9eb979p-5Q, 0x1.4c35ca8307eb62387847e8508ae5p-4Q, 0x1.6d90b88bab05f824bb4e728b7a1p-6Q, -0x1.80637c4a935c7dbdd09fd2c6d8fdp-5Q, -0x1.acbb0e1b24a7711aad0c2cc58d1fp-9Q, 0x1.7477f35c89772c79eec161a3cdd2p-6Q, -0x1.8ed9cce7691caca1362d6d7abefcp-9Q, -0x1.19e6894a383d0a23e4d18574889p-7Q, 0x1.85057173113925897d4027a40b6ep-9Q, 0x1.2d9fa2834b37aecc772ff5c2d7b1p-9Q, -0x1.78a90e5fc8eeb8c9dbcf2179c3bbp-10Q, -0x1.58126708ae49d0421a9c690b913dp-12Q, 0x1.ccd01a3d65144c8ab80302b0f5dbp-12Q, -0x1.adaa9541cd34139a00a6638e9bf6p-16Q, -0x1.5822674fd0b1a40e647125cde434p-14Q, 0x1.85029b61ff0fb98b3294c269c9e6p-16Q, 0x1.d5219c45df32dc63e76e89984d9dp-18Q, -0x1.2e63809757f52cc8ed09e415ace1p-18Q, 0x1.43e648c7ce72f3a94ea0d55898bap-22Q, 0x1.3d94aa0876b2cc113a8ea22e3eecp-22Q, -0x1.69ce4aed2f58e6ecb8a211f55ad1p-24Q, 0x1.f36b16a008a288af85eb1e1cec02p-28Q};
         }
         #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00224180700103731285353596267707443691406219188056037073325053118133419193342"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0259853937036060433891486459172078831547394452487824129439994827687663725129"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.131214903307824406577550623185906996014429360925997853006700439459033631661"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.370350724152641150449254819072188644947707887689680382365042593579529628290"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.610996615684622818188667886767937208273709389335872629137178390490835290734"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.518315764056937839325453852808596804621681719771841640243990498683288900340"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0273149704032936350043125071914758648035046981896456300367294282283271222511"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.328320748363961736090966534072506176758159769815155802467913052689676377760"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.126599752215882702874467911093382550505396626010408616210372832359164928283"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.197310589565010992785404704478193014255142241413564691712228422600456673716"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.101135489177470272150969985643343480219662254549966487610943796293105029624"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.126815691778286311094857112866233168038479218591501706573213748994956827246"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0570914196316769272891123947865138232416116086984534705399014464059382899408"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0811059866541608850796588574855542920102436419095449919402067822775070461335"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0223123361781037959533913605953481375623224211409368924402086919318268997481"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0469224383892697373330089705921140050713876812549803060287843927826168188238"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00327095553581929378165536022217749445206952595806160939280927575122449701285"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0227336765839462703184561624478844896990671374133833949802486413275635089855"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00304298998135463706859248263790720607863339545722509658828788135585314667137"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00860292152032285483171370641324365991792673628427173061192098670257230281191"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00296799669152609487280648506000803826995946384654837899504419503429102573503"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00230120524215354562430205986903842360424197668018944747606476493728483725055"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00143684530480297612622289040298038490350367453072993580956143471121236432705"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000328132519409837971395444401752011507581240244272874970019565158958075253614"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000439465427768643677838567752731784163228924931973889217946591075762286390503"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000256101095665484588272989121094992022166408206153190965517841374523415859860"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000820480320245339183909548257628218986613627304963676433868959364213432243666"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000231868137987459508448206820570627757210669517409189533853073478931042782802"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000699060098507675127320454970085537862776275858590205796402748138050877941586"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000450594247722298819410226820637831212971357260071649994491841668706683585071"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000301654960999455741560520759487993976347616870521764689770270618984715407855"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000295770093331685675497990525881615136787034562892431730735463949569521998500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000842394844600268017878707129692287706841031094222279962259313341617779208118"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000726749296856160811087976744140903503415858171978979108889204640807029047656")};
+        if constexpr (std::is_same_v<Real, octuple_type>) {
+            return {boost::lexical_cast<octuple_type>("0.00224180700103731285353596267707443691406219188056037073325053118133419193342"), boost::lexical_cast<octuple_type>("0.0259853937036060433891486459172078831547394452487824129439994827687663725129"), boost::lexical_cast<octuple_type>("0.131214903307824406577550623185906996014429360925997853006700439459033631661"), boost::lexical_cast<octuple_type>("0.370350724152641150449254819072188644947707887689680382365042593579529628290"), boost::lexical_cast<octuple_type>("0.610996615684622818188667886767937208273709389335872629137178390490835290734"), boost::lexical_cast<octuple_type>("0.518315764056937839325453852808596804621681719771841640243990498683288900340"), boost::lexical_cast<octuple_type>("0.0273149704032936350043125071914758648035046981896456300367294282283271222511"), boost::lexical_cast<octuple_type>("-0.328320748363961736090966534072506176758159769815155802467913052689676377760"), boost::lexical_cast<octuple_type>("-0.126599752215882702874467911093382550505396626010408616210372832359164928283"), boost::lexical_cast<octuple_type>("0.197310589565010992785404704478193014255142241413564691712228422600456673716"), boost::lexical_cast<octuple_type>("0.101135489177470272150969985643343480219662254549966487610943796293105029624"), boost::lexical_cast<octuple_type>("-0.126815691778286311094857112866233168038479218591501706573213748994956827246"), boost::lexical_cast<octuple_type>("-0.0570914196316769272891123947865138232416116086984534705399014464059382899408"), boost::lexical_cast<octuple_type>("0.0811059866541608850796588574855542920102436419095449919402067822775070461335"), boost::lexical_cast<octuple_type>("0.0223123361781037959533913605953481375623224211409368924402086919318268997481"), boost::lexical_cast<octuple_type>("-0.0469224383892697373330089705921140050713876812549803060287843927826168188238"), boost::lexical_cast<octuple_type>("-0.00327095553581929378165536022217749445206952595806160939280927575122449701285"), boost::lexical_cast<octuple_type>("0.0227336765839462703184561624478844896990671374133833949802486413275635089855"), boost::lexical_cast<octuple_type>("-0.00304298998135463706859248263790720607863339545722509658828788135585314667137"), boost::lexical_cast<octuple_type>("-0.00860292152032285483171370641324365991792673628427173061192098670257230281191"), boost::lexical_cast<octuple_type>("0.00296799669152609487280648506000803826995946384654837899504419503429102573503"), boost::lexical_cast<octuple_type>("0.00230120524215354562430205986903842360424197668018944747606476493728483725055"), boost::lexical_cast<octuple_type>("-0.00143684530480297612622289040298038490350367453072993580956143471121236432705"), boost::lexical_cast<octuple_type>("-0.000328132519409837971395444401752011507581240244272874970019565158958075253614"), boost::lexical_cast<octuple_type>("0.000439465427768643677838567752731784163228924931973889217946591075762286390503"), boost::lexical_cast<octuple_type>("-0.0000256101095665484588272989121094992022166408206153190965517841374523415859860"), boost::lexical_cast<octuple_type>("-0.0000820480320245339183909548257628218986613627304963676433868959364213432243666"), boost::lexical_cast<octuple_type>("0.0000231868137987459508448206820570627757210669517409189533853073478931042782802"), boost::lexical_cast<octuple_type>("0.00000699060098507675127320454970085537862776275858590205796402748138050877941586"), boost::lexical_cast<octuple_type>("-0.00000450594247722298819410226820637831212971357260071649994491841668706683585071"), boost::lexical_cast<octuple_type>("0.000000301654960999455741560520759487993976347616870521764689770270618984715407855"), boost::lexical_cast<octuple_type>("0.000000295770093331685675497990525881615136787034562892431730735463949569521998500"), boost::lexical_cast<octuple_type>("-0.0000000842394844600268017878707129692287706841031094222279962259313341617779208118"), boost::lexical_cast<octuple_type>("0.00000000726749296856160811087976744140903503415858171978979108889204640807029047656")};
         }
     }
     if constexpr (p == 18) {
@@ -355,8 +358,8 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.9d386358a187490511616014e787p-10Q, 0x1.3c05f73c5b367536d2be9893ed8cp-6Q, 0x1.a84c610f33b444b779a9b1758c69p-4Q, 0x1.423b3247213b88555f9f2ada7d8ap-2Q, 0x1.24c67bbcaad511453636985416f3p-1Q, 0x1.24c32fbf17436364ee6d86ce0b36p-1Q, 0x1.2d834f99026e9806c6f6c1aa6cb3p-3Q, -0x1.2cb3a51535039a741562ba69c7a8p-2Q, -0x1.bb5a5b1e13b56915364cb7d6d1bfp-3Q, 0x1.323ede758da4220dcba304aad9d9p-3Q, 0x1.562eba30ba3dac1311ece1a1884ap-3Q, -0x1.7a30ff6ce5271d64766823319bd4p-4Q, -0x1.b541d802db16d80f141c678b2993p-4Q, 0x1.09c72d78f01628c7ccd127058828p-4Q, 0x1.d35d236774d120bc0fddfe320959p-5Q, -0x1.6cc216694aaa0ced2f850c2b3eb7p-5Q, -0x1.84d84c9eacf2bae4fd091b9bdb4fp-6Q, 0x1.b4f90c6dc9841e7a702107e1aca3p-6Q, 0x1.9a65be90d86a53c665da90605941p-8Q, -0x1.ababc1ea3f978443c6511c976c7fp-7Q, 0x1.f19207685977f43b68af0530733ap-14Q, 0x1.43f78b1e4d853774466d94263915p-8Q, -0x1.2544e0deeca71abd544eac93fa45p-10Q, -0x1.5f6de508b23063ffd5522faa2f1ap-10Q, 0x1.497f3c70a07cbca34a7835790cbfp-11Q, 0x1.bfe9ba59913cd96563f593913af3p-13Q, -0x1.a098a12371c0ca3dcc2d68b00891p-13Q, -0x1.49d5efd42da901d7159610c4d152p-23Q, 0x1.39d678c2c06ae863ef3b97fa7d6p-15Q, -0x1.1de76b2193bec903a9d077f1666ep-17Q, -0x1.bf4c72e2a2d93cedea468c1c5543p-19Q, 0x1.dac907ddfd9dac76e76088418dc5p-20Q, -0x1.4a5a655290e67a67e8d8672b7916p-24Q, -0x1.f9216d4e4d83adac1cb13466b74bp-24Q, 0x1.079c6a0fc4517cae3d72b9596e6p-25Q, -0x1.58b0195a8266ce508d99fc62d4eep-29Q};
         }
         #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00157631021844076043154074492993977774767075371099166036368442986184714001537"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0192885317241463770592139171582905241995466702528849757223671483332142575124"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.103588465822423596224191049193725359647069655522024167297622418469656394177"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.314678941337031699057199825565257993178670619048937450949130751036740690695"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.571826807766607223481858937090062341939367374313093056129532404803265328819"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.571801654888651335289111999406596502566804788281852506075939526421405556433"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.147223111969928141575097727108107231255786410735570138780167713584411016265"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.293654040736558744247903099498115072393571072903505323966175230801212578403"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.216480934005142971123767862566827147143793723566949240838869239366378506250"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.149533975565377789350930173891366720880481669189376561026194307191290248158"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.167081312763257404514931813995013474532420564635398808315225063337013902642"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0923318841508462806042937255865945973143184800014456961207450846746206498455"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.106752246659828485593220058161498486138526640462411208391770205467847935365"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0648872162119054428194757795514191146312938211663414784613714984515877764896"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0570512477385368841209076884649962226059622612043103852460067642320755043632"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0445261419029823247155614355974465349297147789143983359275503466820231489272"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0237332103958600010327520958266521611019751933071349023307156579014300914190"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0266707059264705902998790863167202034320789599993607281336347152037595652919"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00626216795430570748523609314449788250199032520474501319026805231525752058555"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0130514809466120017727763644760080716975519105450757166660613358038629139862"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000118630033858117465730174159216181908454489941745231740518561572996617939506"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00494334360546673813066552951680297483429963831336647776529520326003067700242"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00111873266699249707280065885523865018231806048258497014551268711985227900418"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00134059629833610662951756722825158360982304452468598664032394269120723888750"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000628465682965145712561944988542083821755102279630158287434965288076478383268"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000213581561910340688403905281434192602587320032599646652254344051060271497781"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000198648552311747948579824541636248955492779788026401787613960521573218466250"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000153591712353472467506977033587671719370047242702151323658728810220957329769"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000374123788074003818109220813803539395230429261579398503073136385132849832575"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000852060253744669520391925491165552302243759695622637651230591706524073534413"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000333263447888582188878245203334103682731150590779649843982933727956405960650"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000176871298362761545587632873075537517641250135911405881545310061923499126827"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000769163268988517614600015287853959840581739758815652511676990865187416269746"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000117609876702823169845098235656129256134757977769539695352814136780995583426"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000306883586304517480093547829493397537245017978789457449293057011634442052915"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000250793445494859826719517318314712673180631714486827581994140326785823293114")};
+        if constexpr (std::is_same_v<Real, octuple_type>) {
+            return {boost::lexical_cast<octuple_type>("0.00157631021844076043154074492993977774767075371099166036368442986184714001537"), boost::lexical_cast<octuple_type>("0.0192885317241463770592139171582905241995466702528849757223671483332142575124"), boost::lexical_cast<octuple_type>("0.103588465822423596224191049193725359647069655522024167297622418469656394177"), boost::lexical_cast<octuple_type>("0.314678941337031699057199825565257993178670619048937450949130751036740690695"), boost::lexical_cast<octuple_type>("0.571826807766607223481858937090062341939367374313093056129532404803265328819"), boost::lexical_cast<octuple_type>("0.571801654888651335289111999406596502566804788281852506075939526421405556433"), boost::lexical_cast<octuple_type>("0.147223111969928141575097727108107231255786410735570138780167713584411016265"), boost::lexical_cast<octuple_type>("-0.293654040736558744247903099498115072393571072903505323966175230801212578403"), boost::lexical_cast<octuple_type>("-0.216480934005142971123767862566827147143793723566949240838869239366378506250"), boost::lexical_cast<octuple_type>("0.149533975565377789350930173891366720880481669189376561026194307191290248158"), boost::lexical_cast<octuple_type>("0.167081312763257404514931813995013474532420564635398808315225063337013902642"), boost::lexical_cast<octuple_type>("-0.0923318841508462806042937255865945973143184800014456961207450846746206498455"), boost::lexical_cast<octuple_type>("-0.106752246659828485593220058161498486138526640462411208391770205467847935365"), boost::lexical_cast<octuple_type>("0.0648872162119054428194757795514191146312938211663414784613714984515877764896"), boost::lexical_cast<octuple_type>("0.0570512477385368841209076884649962226059622612043103852460067642320755043632"), boost::lexical_cast<octuple_type>("-0.0445261419029823247155614355974465349297147789143983359275503466820231489272"), boost::lexical_cast<octuple_type>("-0.0237332103958600010327520958266521611019751933071349023307156579014300914190"), boost::lexical_cast<octuple_type>("0.0266707059264705902998790863167202034320789599993607281336347152037595652919"), boost::lexical_cast<octuple_type>("0.00626216795430570748523609314449788250199032520474501319026805231525752058555"), boost::lexical_cast<octuple_type>("-0.0130514809466120017727763644760080716975519105450757166660613358038629139862"), boost::lexical_cast<octuple_type>("0.000118630033858117465730174159216181908454489941745231740518561572996617939506"), boost::lexical_cast<octuple_type>("0.00494334360546673813066552951680297483429963831336647776529520326003067700242"), boost::lexical_cast<octuple_type>("-0.00111873266699249707280065885523865018231806048258497014551268711985227900418"), boost::lexical_cast<octuple_type>("-0.00134059629833610662951756722825158360982304452468598664032394269120723888750"), boost::lexical_cast<octuple_type>("0.000628465682965145712561944988542083821755102279630158287434965288076478383268"), boost::lexical_cast<octuple_type>("0.000213581561910340688403905281434192602587320032599646652254344051060271497781"), boost::lexical_cast<octuple_type>("-0.000198648552311747948579824541636248955492779788026401787613960521573218466250"), boost::lexical_cast<octuple_type>("-0.000000153591712353472467506977033587671719370047242702151323658728810220957329769"), boost::lexical_cast<octuple_type>("0.0000374123788074003818109220813803539395230429261579398503073136385132849832575"), boost::lexical_cast<octuple_type>("-0.00000852060253744669520391925491165552302243759695622637651230591706524073534413"), boost::lexical_cast<octuple_type>("-0.00000333263447888582188878245203334103682731150590779649843982933727956405960650"), boost::lexical_cast<octuple_type>("0.00000176871298362761545587632873075537517641250135911405881545310061923499126827"), boost::lexical_cast<octuple_type>("-0.0000000769163268988517614600015287853959840581739758815652511676990865187416269746"), boost::lexical_cast<octuple_type>("-0.000000117609876702823169845098235656129256134757977769539695352814136780995583426"), boost::lexical_cast<octuple_type>("0.0000000306883586304517480093547829493397537245017978789457449293057011634442052915"), boost::lexical_cast<octuple_type>("-0.00000000250793445494859826719517318314712673180631714486827581994140326785823293114")};
         }
     }
     if constexpr (p == 19) {
@@ -374,8 +377,8 @@ constexpr std::array<Real, 2*p> daubechies_scaling_filter()
             return {0x1.22a1917fed859e160446bb7b167ap-10Q, 0x1.d3f6896603bf4308e8ccc5a30641p-7Q, 0x1.4cea4765b11499a3de1dc5fdc4b7p-4Q, 0x1.0ebbd74f124f24e597d3a5bc26dbp-2Q, 0x1.0c82ecc4163915332b81143283e8p-1Q, 0x1.34129e60b6e2fef58b66c45f7099p-1Q, 0x1.0b280be54f8b6ad2d41e0f33532ep-2Q, -0x1.d32194b53c8046c9a7b9b8714cebp-3Q, -0x1.24b2e1dd4c73df34e82deb7bb6c6p-2Q, 0x1.31c6940f7edfa2f8c6ddc9cd2aefp-4Q, 0x1.b2e46c16840423c52b33ff7476eep-3Q, -0x1.12957a28f5bb337e3e66ea6f23e6p-5Q, -0x1.246cd3943959a8c450bf5ca92b86p-3Q, 0x1.c3f126f461d985ee9de87f3424e5p-6Q, 0x1.63f8568e9e6ec0d34220dce2e186p-4Q, -0x1.b2323dbfdcbe6e4ed8b2320fb129p-6Q, -0x1.7629cb842f99ab236f8e908d21c2p-5Q, 0x1.6248a775ca65f9a99ecab76ed61p-6Q, 0x1.3d72f2476d00410fe80cb42bd72bp-6Q, -0x1.ca5f1bf2f3243b0308970f1f944p-7Q, -0x1.807e9f533b2172c38f0c60523009p-8Q, 0x1.cd6c23ae5d8f94f8e6c997306168p-8Q, 0x1.93274e99dc9b4cfea213c9163decp-11Q, -0x1.6043462e3e519b97ce417a7ac3b3p-9Q, 0x1.66698fcf3c2497984ab865b5b6acp-12Q, 0x1.81c5be1857465de5530984af43cbp-11Q, -0x1.1156b7a432a662bbb70ff712e064p-12Q, -0x1.054e8a6af00d6f29e88cd98738bep-13Q, 0x1.6d608dedb3cf6080fb9e6ef72893p-14Q, 0x1.56a78fb9bd526ca09fc616b1b8ap-18Q, -0x1.172d0353b3f11fc1e8818be3f7a7p-16Q, 0x1.941ff236730f0886ee4074951d94p-19Q, 0x1.9b39878b9566344204396825f773p-20Q, -0x1.7070fedc9cdecfffd4c6dc5d1fe5p-21Q, 0x1.f1373b9dbeafa1390279c531a649p-27Q, 0x1.8e4f570c878dd84d17b935d5f69ap-25Q, -0x1.7f97c3aa5d9df8ae90e909fae15p-27Q, 0x1.dc770dc2ed00b68b9c525506b211p-31Q};
         }
         #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00110866976318171057109915419520971516424529967777343593213545529038383924770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0142810984507643973743988915295019923474566344216366595787071599110771075191"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0812781132654595506529630678490162483984497997102862036649772686406019150041"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.264388431740896784674810038028942687386237780721192071841738581477351352687"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.524436377464654915336057597548406462604463364104807211639316023628078258263"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.601704549127537894886707713592180262053656563958596329331393143392083219576"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.260894952651038829287245667531052832417267310130190773992521389876582446158"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.228091394215482646374632577605463720709378723708642590953482241776619580080"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.285838631755826241854597569502898423721735609558833514992211937357294676905"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0746522697081032663676343311187881900586586614973190965636539995134773660042"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.212349743306278488809060856705982419707707420087883944841690869803668388649"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0335185419023028786816938841878573150697784507523896681981403258573481442235"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.142785695038736574977960273162611281299849770615242850862756243341853036336"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0275843506256286687501474352016219865537447459696342308076281830983836771416"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0869067555558122324884764542880844303478520800246819275964035297492772454078"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0265012362501230408990183584367638736107506801768674780817134564719233152649"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0456742262772309080564544421429579601793893573211563005088010978423298835500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0216237674095850471303298425717237235431809706785875254257102081949907179885"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0193755498891761276463709435445799981449688509587582554640696372421676825877"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0139883886785351416325040123524866252191681386745309583680836668669699906947"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00586692228101217472658449343605437377381460834080875817737276517150642852313"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00704074736710524315301451120740062010940168989766538307822939808316234678585"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000768954359257548355974913914867395516347794708603940612954642251648623392855"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00268755180070158200395736385507039863653403892098247829017026719960594838510"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000341808653458595776565165729046380813521421484881951725779403154942704074894"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000735802520505435207026048190539728187518317579277990485818949491732987619374"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000260676135678628005731831513089752279038393936207356340861354755942716317598"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000124600791734158775344978440890165399031734141334198090475759204698349203833"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000871127046721992296541686238819112826841293389328208351772944342009756120059"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000510595048707388605304922280993423157368736799210628266938926416431155785903"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000166401762971549445462067771989919863033367560881201810873914492293692424442"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000301096431629652633969533445472594363264579893816242716885138250008132314822"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000153193147669119306393183238108663603120312303272347746362414105936220672489"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000686275565776914270188355461348673285445274075277139241175841882669179558939"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000144708829879784454207821986329161542055167357407136783431616765021249777078"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000463693777578260422343085772821094889887174829108596229664932070020615712517"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000111640206703582581639050476914247258646497579928447368224607655958423915203"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000866684883899761935032301354078212462728974219027305931912284064941409400037")};
+        if constexpr (std::is_same_v<Real, octuple_type>) {
+            return {boost::lexical_cast<octuple_type>("0.00110866976318171057109915419520971516424529967777343593213545529038383924770"), boost::lexical_cast<octuple_type>("0.0142810984507643973743988915295019923474566344216366595787071599110771075191"), boost::lexical_cast<octuple_type>("0.0812781132654595506529630678490162483984497997102862036649772686406019150041"), boost::lexical_cast<octuple_type>("0.264388431740896784674810038028942687386237780721192071841738581477351352687"), boost::lexical_cast<octuple_type>("0.524436377464654915336057597548406462604463364104807211639316023628078258263"), boost::lexical_cast<octuple_type>("0.601704549127537894886707713592180262053656563958596329331393143392083219576"), boost::lexical_cast<octuple_type>("0.260894952651038829287245667531052832417267310130190773992521389876582446158"), boost::lexical_cast<octuple_type>("-0.228091394215482646374632577605463720709378723708642590953482241776619580080"), boost::lexical_cast<octuple_type>("-0.285838631755826241854597569502898423721735609558833514992211937357294676905"), boost::lexical_cast<octuple_type>("0.0746522697081032663676343311187881900586586614973190965636539995134773660042"), boost::lexical_cast<octuple_type>("0.212349743306278488809060856705982419707707420087883944841690869803668388649"), boost::lexical_cast<octuple_type>("-0.0335185419023028786816938841878573150697784507523896681981403258573481442235"), boost::lexical_cast<octuple_type>("-0.142785695038736574977960273162611281299849770615242850862756243341853036336"), boost::lexical_cast<octuple_type>("0.0275843506256286687501474352016219865537447459696342308076281830983836771416"), boost::lexical_cast<octuple_type>("0.0869067555558122324884764542880844303478520800246819275964035297492772454078"), boost::lexical_cast<octuple_type>("-0.0265012362501230408990183584367638736107506801768674780817134564719233152649"), boost::lexical_cast<octuple_type>("-0.0456742262772309080564544421429579601793893573211563005088010978423298835500"), boost::lexical_cast<octuple_type>("0.0216237674095850471303298425717237235431809706785875254257102081949907179885"), boost::lexical_cast<octuple_type>("0.0193755498891761276463709435445799981449688509587582554640696372421676825877"), boost::lexical_cast<octuple_type>("-0.0139883886785351416325040123524866252191681386745309583680836668669699906947"), boost::lexical_cast<octuple_type>("-0.00586692228101217472658449343605437377381460834080875817737276517150642852313"), boost::lexical_cast<octuple_type>("0.00704074736710524315301451120740062010940168989766538307822939808316234678585"), boost::lexical_cast<octuple_type>("0.000768954359257548355974913914867395516347794708603940612954642251648623392855"), boost::lexical_cast<octuple_type>("-0.00268755180070158200395736385507039863653403892098247829017026719960594838510"), boost::lexical_cast<octuple_type>("0.000341808653458595776565165729046380813521421484881951725779403154942704074894"), boost::lexical_cast<octuple_type>("0.000735802520505435207026048190539728187518317579277990485818949491732987619374"), boost::lexical_cast<octuple_type>("-0.000260676135678628005731831513089752279038393936207356340861354755942716317598"), boost::lexical_cast<octuple_type>("-0.000124600791734158775344978440890165399031734141334198090475759204698349203833"), boost::lexical_cast<octuple_type>("0.0000871127046721992296541686238819112826841293389328208351772944342009756120059"), boost::lexical_cast<octuple_type>("0.00000510595048707388605304922280993423157368736799210628266938926416431155785903"), boost::lexical_cast<octuple_type>("-0.0000166401762971549445462067771989919863033367560881201810873914492293692424442"), boost::lexical_cast<octuple_type>("0.00000301096431629652633969533445472594363264579893816242716885138250008132314822"), boost::lexical_cast<octuple_type>("0.00000153193147669119306393183238108663603120312303272347746362414105936220672489"), boost::lexical_cast<octuple_type>("-0.000000686275565776914270188355461348673285445274075277139241175841882669179558939"), boost::lexical_cast<octuple_type>("0.0000000144708829879784454207821986329161542055167357407136783431616765021249777078"), boost::lexical_cast<octuple_type>("0.0000000463693777578260422343085772821094889887174829108596229664932070020615712517"), boost::lexical_cast<octuple_type>("-0.0000000111640206703582581639050476914247258646497579928447368224607655958423915203"), boost::lexical_cast<octuple_type>("0.000000000866684883899761935032301354078212462728974219027305931912284064941409400037")};
         }
     }
 }

From bd7ded88151cd011d563ea85a35c566421b3e27e Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Fri, 21 Feb 2020 19:49:59 +0000
Subject: [PATCH 049/104] Restrict testing to p values we can actually support.
 [CI SKIP]

---
 test/daubechies_scaling_test.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/daubechies_scaling_test.cpp b/test/daubechies_scaling_test.cpp
index f4362aebc..b7d832e09 100644
--- a/test/daubechies_scaling_test.cpp
+++ b/test/daubechies_scaling_test.cpp
@@ -466,7 +466,7 @@ int main()
 
 
     #ifdef BOOST_HAS_FLOAT128
-    boost::hana::for_each(std::make_index_sequence<23>(), [&](auto i){
+    boost::hana::for_each(std::make_index_sequence<18>(), [&](auto i){
         test_filter_ulp_distance<float128, long double, i+1>();
         test_filter_ulp_distance<float128, double, i+1>();
         test_filter_ulp_distance<float128, float, i+1>();

From 65d27cfea9c7f12fd996f34077261220621ec9d3 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Sat, 22 Feb 2020 11:46:25 -0500
Subject: [PATCH 050/104] Use DenseRange rather than custom argument generator
 in benchmarks [CI SKIP]

---
 example/daubechies_wavelets/bench.cpp | 58 ++++++++++++++++++++++-----
 1 file changed, 47 insertions(+), 11 deletions(-)

diff --git a/example/daubechies_wavelets/bench.cpp b/example/daubechies_wavelets/bench.cpp
index 7437ee6e8..30feb0c70 100644
--- a/example/daubechies_wavelets/bench.cpp
+++ b/example/daubechies_wavelets/bench.cpp
@@ -14,14 +14,6 @@
 #include <boost/math/interpolators/detail/quintic_hermite_detail.hpp>
 #include <boost/math/interpolators/detail/septic_hermite_detail.hpp>
 
-static void UnitStep(benchmark::internal::Benchmark* b)
-{
-    for (int i = 7; i <= 25; ++i)
-    {
-        b->Args({i});
-    }
-}
-
 double exponential(benchmark::IterationCount j)
 {
     return std::pow(2, j);
@@ -44,9 +36,9 @@ void DyadicGrid(benchmark::State & state)
     state.SetComplexityN(state.range(0));
 }
 
-BENCHMARK_TEMPLATE(DyadicGrid, double, 4)->Apply(UnitStep)->Unit(benchmark::kMillisecond)->Complexity(exponential);
-//BENCHMARK_TEMPLATE(DyadicGrid, double, 8)->Apply(UnitStep)->Unit(benchmark::kMillisecond)->Complexity(exponential);
-//BENCHMARK_TEMPLATE(DyadicGrid, double, 11)->Apply(UnitStep)->Unit(benchmark::kMillisecond)->Complexity(exponential);
+BENCHMARK_TEMPLATE(DyadicGrid, double, 4)->DenseRange(3, 22, 1)->Unit(benchmark::kMillisecond)->Complexity(exponential);
+//BENCHMARK_TEMPLATE(DyadicGrid, double, 8)->DenseRange(3, 22, 1)->Unit(benchmark::kMillisecond)->Complexity(exponential);
+//BENCHMARK_TEMPLATE(DyadicGrid, double, 11)->DenseRange(3,22,1)->Unit(benchmark::kMillisecond)->Complexity(exponential);
 
 
 template<typename Real, int p>
@@ -338,6 +330,50 @@ void CardinalQuinticHermiteAOS(benchmark::State & state)
 
 BENCHMARK_TEMPLATE(CardinalQuinticHermiteAOS, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity(benchmark::o1);
 
+template<typename Real>
+void SepticHermite(benchmark::State & state)
+{
+    using boost::math::interpolators::detail::septic_hermite_detail;
+    auto n = state.range(0);
+    std::vector<Real> x(n);
+    std::vector<Real> y(n);
+    std::vector<Real> dydx(n);
+    std::vector<Real> d2ydx2(n);
+    std::vector<Real> d3ydx3(n);
+    std::random_device rd;
+    boost::random::uniform_real_distribution<Real> dis(Real(0), Real(1));
+    Real x0 = dis(rd);
+    x[0] = x0;
+    for (size_t i = 1; i < n; ++i)
+    {
+        x[i] = x[i-1] + dis(rd);
+    }
+    for (size_t i = 0; i < y.size(); ++i)
+    {
+        y[i] = dis(rd);
+        dydx[i] = dis(rd);
+        d2ydx2[i] = dis(rd);
+        d3ydx3[i] = dis(rd);
+    }
+
+    Real xf = x.back();
+
+    auto sh = septic_hermite_detail(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3));
+    Real t = x0;
+    for (auto _ : state)
+    {
+        benchmark::DoNotOptimize(sh(t));
+        t += xf/128;
+        if (t >= xf)
+        {
+            t = x0;
+        }
+    }
+    state.SetComplexityN(state.range(0));
+}
+
+BENCHMARK_TEMPLATE(SepticHermite, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity();
+
 
 template<typename Real>
 void CardinalSepticHermite(benchmark::State & state)

From 77552650299fa9b33c0e8c7b60317fff0d465a48 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Sat, 22 Feb 2020 14:04:05 -0500
Subject: [PATCH 051/104] Septic hermite derivative. [CI SKIP]

---
 .../detail/septic_hermite_detail.hpp          | 138 +++++++++++-------
 .../math/interpolators/septic_hermite.hpp     |  44 ++++--
 test/septic_hermite_test.cpp                  |  39 +++--
 3 files changed, 147 insertions(+), 74 deletions(-)

diff --git a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
index 87ceffe23..8a5630378 100644
--- a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
@@ -14,24 +14,30 @@ public:
     septic_hermite_detail(RandomAccessContainer && x, RandomAccessContainer && y, RandomAccessContainer && dydx, RandomAccessContainer && d2ydx2, RandomAccessContainer && d3ydx3) 
     : x_{std::move(x)}, y_{std::move(y)}, dydx_{std::move(dydx)}, d2ydx2_{std::move(d2ydx2)}, d3ydx3_{std::move(d3ydx3)}
     {
-        if (x_.size() != y_.size()) {
+        if (x_.size() != y_.size())
+        {
             throw std::domain_error("Number of abscissas must = number of ordinates.");
         }
-        if (x_.size() != dydx_.size()) {
+        if (x_.size() != dydx_.size())
+        {
             throw std::domain_error("Numbers of derivatives must = number of abscissas.");
         }
-        if (x_.size() != d2ydx2_.size()) {
+        if (x_.size() != d2ydx2_.size())
+        {
             throw std::domain_error("Number of second derivatives must equal number of abscissas.");
         }
-        if (x_.size() != d3ydx3_.size()) {
+        if (x_.size() != d3ydx3_.size())
+        {
             throw std::domain_error("Number of third derivatives must equal number of abscissas.");
         }
 
-        if (x_.size() < 2) {
+        if (x_.size() < 2)
+        {
             throw std::domain_error("At least 2 abscissas are required.");
         }
         Real x0 = x_[0];
-        for (decltype(x_.size()) i = 1; i < x_.size(); ++i) {
+        for (decltype(x_.size()) i = 1; i < x_.size(); ++i)
+        {
             Real x1 = x_[i];
             if (x1 <= x0)
             {
@@ -41,7 +47,8 @@ public:
         }
     }
 
-    void push_back(Real x, Real y, Real dydx, Real d2ydx2, Real d3ydx3) {
+    void push_back(Real x, Real y, Real dydx, Real d2ydx2, Real d3ydx3)
+    {
         using std::abs;
         using std::isnan;
         if (x <= x_.back()) {
@@ -54,17 +61,19 @@ public:
         d3ydx3_.push_back(d3ydx3);
     }
 
-    Real operator()(Real x) const {
-        if  (x < x_[0] || x > x_.back()) {
+    Real operator()(Real x) const
+    {
+        if  (x < x_[0] || x > x_.back())
+        {
             std::ostringstream oss;
             oss.precision(std::numeric_limits<Real>::digits10+3);
             oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
                 << x_[0] << ", " << x_.back() << "]";
             throw std::domain_error(oss.str());
         }
-        // We need t := (x-x_k)/(x_{k+1}-x_k) \in [0,1) for this to work.
-        // Sadly this neccessitates this loathesome check, otherwise we get t = 1 at x = xf.
-        if (x == x_.back()) {
+        // t \in [0, 1)
+        if (x == x_.back())
+        {
             return y_.back();
         }
 
@@ -72,6 +81,27 @@ public:
         auto i = std::distance(x_.begin(), it) -1;
         Real x0 = *(it-1);
         Real x1 = *it;
+        Real dx = (x1-x0);
+        Real t = (x-x0)/dx;
+
+        // See: 
+        // http://seisweb.usask.ca/classes/GEOL481/2017/Labs/interpolation_utilities_matlab/shermite.m
+        Real t2 = t*t;
+        Real t3 = t2*t;
+        Real t4 = t3*t;
+        Real dx2 = dx*dx/2;
+        Real dx3 = dx2*dx/3;
+
+        Real s = t4*(-35 + t*(84 + t*(-70 + 20*t)));
+        Real z4 = -s;
+        Real z0 = s + 1;
+        Real z1 = t*(1 + t3*(-20 + t*(45 + t*(-36 + 10*t))));
+        Real z2 = t2*(1 + t2*(-10 + t*(20 + t*(-15 + 4*t))));
+        Real z3 = t3*(1 + t*(-4 + t*(6 + t*(-4 + t))));
+        Real z5 = t4*(-15 + t*(39 + t*(-34 + 10*t)));
+        Real z6 = t4*(5 + t*(-14 + t*(13 - 4*t)));
+        Real z7 = t4*(-1 + t*(3 + t*(-3+t)));
+
         Real y0 = y_[i];
         Real y1 = y_[i+1];
         // Velocity:
@@ -84,45 +114,21 @@ public:
         Real j0 = d3ydx3_[i];
         Real j1 = d3ydx3_[i+1];
 
-        Real dx = (x1-x0);
-        Real t = (x-x0)/dx;
-
-        // See: 
-        // http://seisweb.usask.ca/classes/GEOL481/2017/Labs/interpolation_utilities_matlab/shermite.m
-        Real t2 = t*t;
-        Real t3 = t2*t;
-        Real t4 = t3*t;
-        Real t5 = t4*t;
-        Real t6 = t5*t;
-        Real t7 = t6*t;
-        Real dx2 = dx*dx;
-        Real dx3 = dx2*dx;
-
-
-        Real s = t4*(-35 + t*(84 + t*(-70 + 20*t)));
-        Real z4 = -s;
-        Real z0 = s + 1;
-        Real z1 = 10*t7 - 36*t6 + 45*t5 - 20*t4 + t;
-        Real z2 = 2*t7 - 15*t6/2 + 10*t5 - 5*t4 + t2/2;
-        Real z3 = t7/6 - 2*t6/3 + t5 - 2*t4/3 + t3/6;
-        
-        Real z5 = 10*t7 - 34*t6 + 39*t5 - 15*t4;
-        Real z6 = -2*t7 + 13*t6/2 - 7*t5 + 5*t4/2;
-        Real z7 = t7/6 - t6/2 + t5/2 - t4/6;
-
-        Real y = z0*y0 + z1*dx*v0 + z2*dx2*a0 + z3*dx3*j0 + z4*y1 + z5*dx*v1 + z6*dx2*a1 + z7*dx3*j1;
-        return y;
+        return z0*y0 + z4*y1 + (z1*v0 + z5*v1)*dx + (z2*a0 + z6*a1)*dx2 + (z3*j0 + z7*j1)*dx3;
     }
 
-    Real prime(Real x) const {
-        if  (x < x_[0] || x > x_.back()) {
+    Real prime(Real x) const
+    {
+        if  (x < x_[0] || x > x_.back())
+        {
             std::ostringstream oss;
             oss.precision(std::numeric_limits<Real>::digits10+3);
             oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
                 << x_[0] << ", " << x_.back() << "]";
             throw std::domain_error(oss.str());
         }
-        if (x == x_.back()) {
+        if (x == x_.back())
+        {
             return dydx_.back();
         }
 
@@ -130,13 +136,36 @@ public:
         auto i = std::distance(x_.begin(), it) -1;
         Real x0 = *(it-1);
         Real x1 = *it;
-        Real s0 = dydx_[i];
-        Real s1 = dydx_[i+1];
+        Real y0 = y_[i];
+        Real y1 = y_[i+1];
+        Real v0 = dydx_[i];
+        Real v1 = dydx_[i+1];
+        Real a0 = d2ydx2_[i];
+        Real a1 = d2ydx2_[i+1];
+        Real j0 = d3ydx3_[i];
+        Real j1 = d3ydx3_[i+1];
+        Real dx = x1 - x0;
+        Real t = (x-x0)/dx;
+        Real t2 = t*t;
+        Real t3 = t2*t;
+        Real z0 = 140*t3*(1 + t*(-3 + t*(3 - t)));
+        Real z1 = 1 + t3*(-80 + t*(225 + t*(-216 + 70*t)));
+        Real z2 = t3*(-60 + t*(195 + t*(-204 + 70*t)));
+        Real z3 = 1 + t2*(-20 + t*(50 + t*(-45 + 14*t)));
+        Real z4 = t2*(10 + t*(-35 + t*(39 - 14*t)));
+        Real z5 = 3 + t*(-16 + t*(30 + t*(-24 + 7*t)));
+        Real z6 = t*(-4 + t*(15 + t*(-18 + 7*t)));
 
-        // Ridiculous linear interpolation. Fine for now:
-        Real numerator = s0*(x1-x) + s1*(x-x0);
-        Real denominator = x1 - x0;
-        return numerator/denominator;
+        Real dydx = z0*(y1-y0)/dx;
+        dydx += z1*v0 + z2*v1;
+        dydx += (x-x0)*(z3*a0 + z4*a1);
+        dydx += (x-x0)*(x-x0)*(z5*j0 + z6*j1)/6;
+        return dydx;
+    }
+
+    inline Real double_prime(Real x) const
+    {
+        return std::numeric_limits<Real>::quiet_NaN();
     }
 
 
@@ -152,7 +181,6 @@ public:
     }
 
 
-
 private:
     RandomAccessContainer x_;
     RandomAccessContainer y_;
@@ -289,6 +317,11 @@ public:
         return (v0+v1)*inv_dx_/2;
     }
 
+    inline Real double_prime(Real x) const
+    {
+        return std::numeric_limits<Real>::quiet_NaN();
+    }
+
 private:
     RandomAccessContainer y_;
     RandomAccessContainer dy_;
@@ -395,6 +428,11 @@ public:
         return std::numeric_limits<Real>::quiet_NaN();
     }
 
+    inline Real double_prime(Real x) const 
+    {
+        return std::numeric_limits<Real>::quiet_NaN();
+    }
+
 private:
     RandomAccessContainer data_;
     Real x0_;
diff --git a/include/boost/math/interpolators/septic_hermite.hpp b/include/boost/math/interpolators/septic_hermite.hpp
index 77ebe3024..d65b776db 100644
--- a/include/boost/math/interpolators/septic_hermite.hpp
+++ b/include/boost/math/interpolators/septic_hermite.hpp
@@ -8,23 +8,31 @@
 namespace boost::math::interpolators {
 
 template<class RandomAccessContainer>
-class septic_hermite {
+class septic_hermite
+{
 public:
     using Real = typename RandomAccessContainer::value_type;
     septic_hermite(RandomAccessContainer && x, RandomAccessContainer && y, RandomAccessContainer && dydx, 
-                    RandomAccessContainer && d2ydx2, RandomAccessContainer && d3ydx3)
+                   RandomAccessContainer && d2ydx2, RandomAccessContainer && d3ydx3)
      : impl_(std::make_shared<detail::septic_hermite_detail<RandomAccessContainer>>(std::move(x), 
      std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3)))
     {}
 
-    Real operator()(Real x) const {
+    inline Real operator()(Real x) const
+    {
         return impl_->operator()(x);
     }
 
-    Real prime(Real x) const {
+    inline Real prime(Real x) const
+    {
         return impl_->prime(x);
     }
 
+    inline Real double_prime(Real x) const
+    {
+        return impl_->double_prime(x);
+    }
+
     friend std::ostream& operator<<(std::ostream & os, const septic_hermite & m)
     {
         os << *m.impl_;
@@ -36,23 +44,31 @@ private:
 };
 
 template<class RandomAccessContainer>
-class cardinal_septic_hermite {
+class cardinal_septic_hermite
+{
 public:
     using Real = typename RandomAccessContainer::value_type;
     cardinal_septic_hermite(RandomAccessContainer && y, RandomAccessContainer && dydx,
-                    RandomAccessContainer && d2ydx2, RandomAccessContainer && d3ydx3, Real x0, Real dx)
+                            RandomAccessContainer && d2ydx2, RandomAccessContainer && d3ydx3, Real x0, Real dx)
      : impl_(std::make_shared<detail::cardinal_septic_hermite_detail<RandomAccessContainer>>(
      std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3), x0, dx))
     {}
 
-    Real operator()(Real x) const {
+    inline Real operator()(Real x) const
+    {
         return impl_->operator()(x);
     }
 
-    Real prime(Real x) const {
+    inline Real prime(Real x) const
+    {
         return impl_->prime(x);
     }
 
+    inline Real double_prime(Real x) const
+    {
+        return impl_->double_prime(x);
+    }
+
 private:
     std::shared_ptr<detail::cardinal_septic_hermite_detail<RandomAccessContainer>> impl_;
 };
@@ -67,14 +83,22 @@ public:
      : impl_(std::make_shared<detail::cardinal_septic_hermite_detail_aos<RandomAccessContainer>>(std::move(data), x0, dx))
     {}
 
-    Real operator()(Real x) const {
+    inline Real operator()(Real x) const
+    {
         return impl_->operator()(x);
     }
 
-    Real prime(Real x) const {
+    inline Real prime(Real x) const
+    {
         return impl_->prime(x);
     }
 
+    inline Real double_prime(Real x) const 
+    {
+        return impl_->double_prime(x);
+    }
+
+
 private:
     std::shared_ptr<detail::cardinal_septic_hermite_detail_aos<RandomAccessContainer>> impl_;
 };
diff --git a/test/septic_hermite_test.cpp b/test/septic_hermite_test.cpp
index d76ea14e5..c4f6e0289 100644
--- a/test/septic_hermite_test.cpp
+++ b/test/septic_hermite_test.cpp
@@ -31,7 +31,8 @@ void test_constant()
     std::vector<Real> dydx(x.size(), 0);
     std::vector<Real> d2ydx2(x.size(), 0);
     std::vector<Real> d3ydx3(x.size(), 0);
-    for (auto & t : y) {
+    for (auto & t : y)
+    {
         t = 7;
     }
 
@@ -85,7 +86,7 @@ void test_linear()
 
     for (Real t = 0; t <= 9; t += 0.25) {
         CHECK_ULP_CLOSE(Real(t), sh(t), 2);
-        //CHECK_ULP_CLOSE(Real(1), qh.prime(t), 2);
+        CHECK_ULP_CLOSE(Real(1), sh.prime(t), 2);
     }
 
     boost::random::mt19937 rng;
@@ -107,7 +108,8 @@ void test_linear()
 
     for (Real t = xmin; t <= xmax; t += 0.125)
     {
-        CHECK_ULP_CLOSE(t, sh(t), 15);
+        CHECK_ULP_CLOSE(t, sh(t), 25);
+        CHECK_ULP_CLOSE(Real(1), sh.prime(t), 850);
     }
 
     Real x0 = 0;
@@ -151,7 +153,8 @@ void test_quadratic()
     }
 
     std::vector<Real> dydx(x.size());
-    for (size_t i = 0; i < y.size(); ++i) {
+    for (size_t i = 0; i < y.size(); ++i)
+    {
         dydx[i] = x[i];
     }
 
@@ -160,9 +163,10 @@ void test_quadratic()
 
     auto sh = septic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3));
 
-    for (Real t = 0; t <= 9; t += 0.0078125) {
+    for (Real t = 0; t <= 9; t += 0.0078125)
+    {
         CHECK_ULP_CLOSE(t*t/2, sh(t), 100);
-        //CHECK_ULP_CLOSE(t, qh.prime(t), 7);
+        CHECK_ULP_CLOSE(t, sh.prime(t), 7);
     }
 
     boost::random::mt19937 rng;
@@ -170,7 +174,8 @@ void test_quadratic()
     x.resize(8);
     x[0] = dis(rng);
     Real xmin = x[0];
-    for (size_t i = 1; i < x.size(); ++i) {
+    for (size_t i = 1; i < x.size(); ++i)
+    {
         x[i] = x[i-1] + dis(rng);
     }
     Real xmax = x.back();
@@ -182,7 +187,8 @@ void test_quadratic()
     }
 
     dydx.resize(x.size());
-    for (size_t i = 0; i < y.size(); ++i) {
+    for (size_t i = 0; i < y.size(); ++i)
+    {
         dydx[i] = x[i];
     }
 
@@ -191,9 +197,10 @@ void test_quadratic()
 
     sh = septic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3));
 
-    for (Real t = xmin; t <= xmax; t += 0.125) {
-        CHECK_ULP_CLOSE(t*t/2, sh(t), 24);
-        //CHECK_ULP_CLOSE(t, qh.prime(t), 36);
+    for (Real t = xmin; t <= xmax; t += 0.125)
+    {
+        CHECK_ULP_CLOSE(t*t/2, sh(t), 50);
+        CHECK_ULP_CLOSE(t, sh.prime(t), 300);
     }
 
     y.resize(10);
@@ -261,8 +268,10 @@ void test_cubic()
 
     auto sh = septic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3));
 
-    for (Real t = 0; t <= xmax; t += 0.0078125) {
+    for (Real t = 0; t <= xmax; t += 0.0078125)
+    {
         CHECK_ULP_CLOSE(t*t*t, sh(t), 151);
+        CHECK_ULP_CLOSE(3*t*t, sh.prime(t), 151);
     }
 
     Real x0 = 0;
@@ -329,6 +338,7 @@ void test_quartic()
 
     for (Real t = 1; t <= xmax; t += 0.0078125) {
         CHECK_ULP_CLOSE(t*t*t*t, sh(t), 117);
+        CHECK_ULP_CLOSE(4*t*t*t, sh.prime(t), 117);
     }
 
     y.resize(10);
@@ -393,9 +403,10 @@ void test_interpolation_condition()
         auto d3ydx3_copy = d3ydx3;
         auto s = septic_hermite(std::move(x_copy), std::move(y_copy), std::move(dydx_copy), std::move(d2ydx2_copy), std::move(d3ydx3_copy));
 
-        for (size_t i = 0; i < x.size(); ++i) {
+        for (size_t i = 0; i < x.size(); ++i)
+        {
             CHECK_ULP_CLOSE(y[i], s(x[i]), 2);
-            //CHECK_ULP_CLOSE(dydx[i], s.prime(x[i]), 2);
+            CHECK_ULP_CLOSE(dydx[i], s.prime(x[i]), 2);
         }
     }
 }

From 6edcfd6b7894419a51de783e44ee346bd67c8484 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Sat, 22 Feb 2020 14:42:19 -0500
Subject: [PATCH 052/104] Accurate septic Hermite derivatives.

---
 .../detail/septic_hermite_detail.hpp          | 63 ++++++++++++++++---
 test/septic_hermite_test.cpp                  | 61 ++++++++++++------
 2 files changed, 97 insertions(+), 27 deletions(-)

diff --git a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
index 8a5630378..7a9f260c6 100644
--- a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
@@ -303,18 +303,37 @@ public:
         return this->unchecked_prime(x);
     }
 
-    inline Real unchecked_prime(Real x) const {
-        //TODO: Get the high accuracy approximation by differentiating the interpolant!
+    inline Real unchecked_prime(Real x) const
+    {
         using std::floor;
         Real s3 = (x-x0_)*inv_dx_;
         Real ii = floor(s3);
         auto i = static_cast<decltype(y_.size())>(ii);
-        //Real t = s3 - ii;
+        Real t = s3 - ii;
+ 
+        Real y0 = y_[i];
+        Real y1 = y_[i+1];
+        Real dy0 = dy_[i];
+        Real dy1 = dy_[i+1];
+        Real a0 = d2y_[i];
+        Real a1 = d2y_[i+1];
+        Real j0 = d3y_[i];
+        Real j1 = d3y_[i+1];
+        Real t2 = t*t;
+        Real t3 = t2*t;
+        Real z0 = 140*t3*(1 + t*(-3 + t*(3 - t)));
+        Real z1 = 1 + t3*(-80 + t*(225 + t*(-216 + 70*t)));
+        Real z2 = t3*(-60 + t*(195 + t*(-204 + 70*t)));
+        Real z3 = 1 + t2*(-20 + t*(50 + t*(-45 + 14*t)));
+        Real z4 = t2*(10 + t*(-35 + t*(39 - 14*t)));
+        Real z5 = 3 + t*(-16 + t*(30 + t*(-24 + 7*t)));
+        Real z6 = t*(-4 + t*(15 + t*(-18 + 7*t)));
 
-        // Velocity:
-        Real v0 = dy_[i];
-        Real v1 = dy_[i+1];
-        return (v0+v1)*inv_dx_/2;
+        Real dydx = z0*(y1-y0)*inv_dx_;
+        dydx += (z1*dy0 + z2*dy1)*inv_dx_;
+        dydx += 2*t*(z3*a0 + z4*a1)*inv_dx_;
+        dydx += t*t*(z5*j0 + z6*j1);
+        return dydx;
     }
 
     inline Real double_prime(Real x) const
@@ -425,7 +444,35 @@ public:
     }
 
     inline Real unchecked_prime(Real x) const {
-        return std::numeric_limits<Real>::quiet_NaN();
+        using std::floor;
+        Real s3 = (x-x0_)*inv_dx_;
+        Real ii = floor(s3);
+        auto i = static_cast<decltype(data_.size())>(ii);
+        Real t = s3 - ii;
+ 
+        Real y0 = data_[i][0];
+        Real y1 = data_[i+1][0];
+        Real dy0 = data_[i][1];
+        Real dy1 = data_[i+1][1];
+        Real a0 = data_[i][2];
+        Real a1 = data_[i+1][2];
+        Real j0 = data_[i][3];
+        Real j1 = data_[i+1][3];
+        Real t2 = t*t;
+        Real t3 = t2*t;
+        Real z0 = 140*t3*(1 + t*(-3 + t*(3 - t)));
+        Real z1 = 1 + t3*(-80 + t*(225 + t*(-216 + 70*t)));
+        Real z2 = t3*(-60 + t*(195 + t*(-204 + 70*t)));
+        Real z3 = 1 + t2*(-20 + t*(50 + t*(-45 + 14*t)));
+        Real z4 = t2*(10 + t*(-35 + t*(39 - 14*t)));
+        Real z5 = 3 + t*(-16 + t*(30 + t*(-24 + 7*t)));
+        Real z6 = t*(-4 + t*(15 + t*(-18 + 7*t)));
+
+        Real dydx = z0*(y1-y0)*inv_dx_;
+        dydx += (z1*dy0 + z2*dy1)*inv_dx_;
+        dydx += 2*t*(z3*a0 + z4*a1)*inv_dx_;
+        dydx += t*t*(z5*j0 + z6*j1);
+        return dydx;
     }
 
     inline Real double_prime(Real x) const 
diff --git a/test/septic_hermite_test.cpp b/test/septic_hermite_test.cpp
index c4f6e0289..dbe9fc011 100644
--- a/test/septic_hermite_test.cpp
+++ b/test/septic_hermite_test.cpp
@@ -53,7 +53,7 @@ void test_constant()
     auto csh = cardinal_septic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3), x0, dx);
     for (Real t = x0; t <= 127; t += 0.25) {
         CHECK_ULP_CLOSE(Real(7), csh(t), 24);
-        //CHECK_ULP_CLOSE(Real(0), csh.prime(t), 24);
+        CHECK_ULP_CLOSE(Real(0), csh.prime(t), 24);
     }
 
     std::vector<std::array<Real, 4>> data(128);
@@ -65,9 +65,10 @@ void test_constant()
         data[i][3] = 0;
     }
     auto csh_aos = cardinal_septic_hermite_aos(std::move(data), x0, dx);
-    for (Real t = x0; t <= 127; t += 0.25) {
+    for (Real t = x0; t <= 127; t += 0.25)
+    {
         CHECK_ULP_CLOSE(Real(7), csh_aos(t), 24);
-        //CHECK_ULP_CLOSE(Real(0), csh.prime(t), 24);
+        CHECK_ULP_CLOSE(Real(0), csh_aos.prime(t), 24);
     }
 
 }
@@ -84,7 +85,8 @@ void test_linear()
 
     auto sh = septic_hermite(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3));
 
-    for (Real t = 0; t <= 9; t += 0.25) {
+    for (Real t = 0; t <= 9; t += 0.25)
+    {
         CHECK_ULP_CLOSE(Real(t), sh(t), 2);
         CHECK_ULP_CLOSE(Real(1), sh.prime(t), 2);
     }
@@ -94,7 +96,8 @@ void test_linear()
     x.resize(512);
     x[0] = dis(rng);
     Real xmin = x[0];
-    for (size_t i = 1; i < x.size(); ++i) {
+    for (size_t i = 1; i < x.size(); ++i)
+    {
         x[i] = x[i-1] + dis(rng);
     }
     Real xmax = x.back();
@@ -118,13 +121,15 @@ void test_linear()
     dydx.resize(10, 1);
     d2ydx2.resize(10, 0);
     d3ydx3.resize(10, 0);
-    for (size_t i = 0; i < y.size(); ++i) {
+    for (size_t i = 0; i < y.size(); ++i)
+    {
         y[i] = i;
     }
     auto csh = cardinal_septic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3), x0, dx);
     for (Real t = 0; t <= 9; t += 0.125)
     {
         CHECK_ULP_CLOSE(t, csh(t), 15);
+        CHECK_ULP_CLOSE(Real(1), csh.prime(t), 15);
     }
 
     std::vector<std::array<Real, 4>> data(10);
@@ -139,6 +144,7 @@ void test_linear()
     for (Real t = 0; t <= 9; t += 0.125)
     {
         CHECK_ULP_CLOSE(t, csh_aos(t), 15);
+        CHECK_ULP_CLOSE(Real(1), csh_aos.prime(t), 15);
     }
 }
 
@@ -224,6 +230,7 @@ void test_quadratic()
     for (Real t = x0; t <= 9; t += 0.125)
     {
         CHECK_ULP_CLOSE(t*t/2, csh(t), 24);
+        CHECK_ULP_CLOSE(t, csh.prime(t), 24);
     }
 
     std::vector<std::array<Real, 4>> data(10);
@@ -238,6 +245,7 @@ void test_quadratic()
     for (Real t = x0; t <= 9; t += 0.125)
     {
         CHECK_ULP_CLOSE(t*t/2, csh_aos(t), 24);
+        CHECK_ULP_CLOSE(t, csh_aos.prime(t), 24);
     }
 }
 
@@ -256,12 +264,14 @@ void test_cubic()
     }
 
     std::vector<Real> dydx(x.size());
-    for (size_t i = 0; i < y.size(); ++i) {
+    for (size_t i = 0; i < y.size(); ++i)
+    {
         dydx[i] = 3*x[i]*x[i];
     }
 
     std::vector<Real> d2ydx2(x.size());
-    for (size_t i = 0; i < y.size(); ++i) {
+    for (size_t i = 0; i < y.size(); ++i)
+    {
         d2ydx2[i] = 6*x[i];
     }
     std::vector<Real> d3ydx3(x.size(), 6);
@@ -280,7 +290,8 @@ void test_cubic()
     dydx.resize(8);
     d2ydx2.resize(8);
     d3ydx3.resize(8,6);
-    for (size_t i = 0; i < y.size(); ++i) {
+    for (size_t i = 0; i < y.size(); ++i)
+    {
         y[i] = i*i*i;
         dydx[i] = 3*i*i;
         d2ydx2[i] = 6*i;
@@ -288,8 +299,10 @@ void test_cubic()
 
     auto csh = cardinal_septic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3), x0, dx);
 
-    for (Real t = 0; t <= xmax; t += 0.0078125) {
+    for (Real t = 0; t <= xmax; t += 0.0078125)
+    {
         CHECK_ULP_CLOSE(t*t*t, csh(t), 151);
+        CHECK_ULP_CLOSE(3*t*t, csh.prime(t), 151);
     }
 
     std::vector<std::array<Real, 4>> data(8);
@@ -302,8 +315,10 @@ void test_cubic()
 
     auto csh_aos = cardinal_septic_hermite_aos(std::move(data), x0, dx);
 
-    for (Real t = 0; t <= xmax; t += 0.0078125) {
+    for (Real t = 0; t <= xmax; t += 0.0078125)
+    {
         CHECK_ULP_CLOSE(t*t*t, csh_aos(t), 151);
+        CHECK_ULP_CLOSE(3*t*t, csh_aos.prime(t), 151);
     }
 }
 
@@ -320,17 +335,20 @@ void test_quartic()
     }
 
     std::vector<Real> dydx(x.size());
-    for (size_t i = 0; i < y.size(); ++i) {
+    for (size_t i = 0; i < y.size(); ++i)
+    {
         dydx[i] = 4*x[i]*x[i]*x[i];
     }
 
     std::vector<Real> d2ydx2(x.size());
-    for (size_t i = 0; i < y.size(); ++i) {
+    for (size_t i = 0; i < y.size(); ++i)
+    {
         d2ydx2[i] = 12*x[i]*x[i];
     }
 
     std::vector<Real> d3ydx3(x.size());
-    for (size_t i = 0; i < y.size(); ++i) {
+    for (size_t i = 0; i < y.size(); ++i)
+    {
         d3ydx3[i] = 24*x[i];
     }
 
@@ -345,7 +363,8 @@ void test_quartic()
     dydx.resize(10);
     d2ydx2.resize(10);
     d3ydx3.resize(10);
-    for (size_t i = 0; i < y.size(); ++i) {
+    for (size_t i = 0; i < y.size(); ++i)
+    {
         y[i] = i*i*i*i;
         dydx[i] = 4*i*i*i;
         d2ydx2[i] = 12*i*i;
@@ -354,12 +373,15 @@ void test_quartic()
 
     auto csh = cardinal_septic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3), Real(0), Real(1));
 
-    for (Real t = 1; t <= xmax; t += 0.0078125) {
+    for (Real t = 1; t <= xmax; t += 0.0078125)
+    {
         CHECK_ULP_CLOSE(t*t*t*t, csh(t), 117);
+        CHECK_ULP_CLOSE(4*t*t*t, csh.prime(t), 117);
     }
 
     std::vector<std::array<Real, 4>> data(10);
-    for (size_t i = 0; i < data.size(); ++i) {
+    for (size_t i = 0; i < data.size(); ++i)
+    {
         data[i][0] = i*i*i*i;
         data[i][1] = 4*i*i*i;
         data[i][2] = 12*i*i;
@@ -367,10 +389,11 @@ void test_quartic()
     }
 
     auto csh_aos = cardinal_septic_hermite_aos(std::move(data), Real(0), Real(1));
-    for (Real t = 1; t <= xmax; t += 0.0078125) {
+    for (Real t = 1; t <= xmax; t += 0.0078125)
+    {
         CHECK_ULP_CLOSE(t*t*t*t, csh_aos(t), 117);
+        CHECK_ULP_CLOSE(4*t*t*t, csh_aos.prime(t), 117);
     }
-
 }
 
 

From 4a2f1febf8fc9255cd424f28f79a2dce41569e2a Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Sat, 22 Feb 2020 14:55:22 -0500
Subject: [PATCH 053/104] Bootstrap Chebyshev transform [CI SKIP]

---
 .../bootstrap_chebyshev.cpp                    | 18 ++++++++++++++++++
 1 file changed, 18 insertions(+)
 create mode 100644 example/daubechies_wavelets/bootstrap_chebyshev.cpp

diff --git a/example/daubechies_wavelets/bootstrap_chebyshev.cpp b/example/daubechies_wavelets/bootstrap_chebyshev.cpp
new file mode 100644
index 000000000..b158fabcd
--- /dev/null
+++ b/example/daubechies_wavelets/bootstrap_chebyshev.cpp
@@ -0,0 +1,18 @@
+#include <iostream>
+#include <boost/math/special_functions/daubechies_scaling.hpp>
+#include <boost/math/special_functions/chebyshev_transform.hpp>
+
+template<typename Real, int p>
+void bootstrap()
+{
+    std::cout << "Computing phi. . .\n";
+    auto phi = boost::math::daubechies_scaling<Real, p>();
+    std::cout << "Computing Chebyshev transform of phi.\n";
+    auto cheb = boost::math::chebyshev_transform(phi, phi.support().first, phi.support().second);
+    std::cout << "Number of coefficients = " << cheb.coefficients().size() << "\n";
+}
+
+int main()
+{
+    bootstrap<long double, 9>();
+}
\ No newline at end of file

From 649b619c3fb3960a8d0045f16eb782bbb38af812 Mon Sep 17 00:00:00 2001
From: Nick Thompson <nathompson7@protonmail.com>
Date: Sun, 23 Feb 2020 09:15:22 -0500
Subject: [PATCH 054/104] Use aos rather than soa [CI SKIP]

---
 .../special_functions/daubechies_scaling.hpp  | 46 ++++++++++++++++++-
 1 file changed, 44 insertions(+), 2 deletions(-)

diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index 729734492..f078c653d 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -124,6 +124,42 @@ private:
     RandomAccessContainer dy_;
 };
 
+template<class RandomAccessContainer>
+class matched_holder_aos {
+public:
+    using Point = typename RandomAccessContainer::value_type;
+    using Real = typename Point::value_type;
+
+    matched_holder_aos(RandomAccessContainer && data, int grid_refinements) : data_{std::move(data)}
+    {
+        inv_h_ = (1 << grid_refinements);
+        Real h = 1/inv_h_;
+        for (auto & datum : data_)
+        {
+            datum[1] *= h;
+        }
+    }
+
+    inline Real operator()(Real x) const
+    {
+        using std::floor;
+        using std::sqrt;
+        Real s = x*inv_h_;
+        Real ii = floor(s);
+        auto i = static_cast<decltype(data_.size())>(ii);
+        Real t = s - ii;
+        Real y0 = data_[i][0];
+        Real y1 = data_[i+1][0];
+        Real dphi = data_[i+1][1];
+        Real diff = y1 - y0;
+        return y0 + (2*dphi - diff)*t + 2*sqrt(t)*(diff-dphi);
+    }
+
+private:
+    Real inv_h_;
+    RandomAccessContainer data_;
+};
+
 
 template<class RandomAccessContainer>
 class linear_interpolation {
@@ -295,7 +331,13 @@ public:
 
         if constexpr (p==2)
         {
-            m_mh = std::make_shared<detail::matched_holder<std::vector<Real>>>(std::move(y), std::move(dydx), grid_refinements);
+            std::vector<std::array<Real, 2>> data(y.size());
+            for (size_t i = 0; i < y.size(); ++i)
+            {
+                data[i][0] = y[i];
+                data[i][1] = dydx[i];
+            }
+            m_mh = std::make_shared<detail::matched_holder_aos<std::vector<std::array<Real,2>>>>(std::move(data), grid_refinements);
         }
         if constexpr (p==3)
         {
@@ -392,7 +434,7 @@ public:
 
 private:
     // Need this for p = 2:
-    std::shared_ptr<detail::matched_holder<std::vector<Real>>> m_mh;
+    std::shared_ptr<detail::matched_holder_aos<std::vector<std::array<Real,2>>>> m_mh;
     // Need this for p = 3:
     std::shared_ptr<detail::linear_interpolation<std::vector<Real>>> m_lin;
     // Need this for p = 4,5:

From 1fc51dca7cb336d5a4f3d3f318ee0b2696f2db0a Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Sun, 23 Feb 2020 12:42:12 -0500
Subject: [PATCH 055/104] Make accesses more random in benchmarks [CI SKIP]

---
 example/daubechies_wavelets/bench.cpp | 83 +++++++++++++++++++--------
 1 file changed, 59 insertions(+), 24 deletions(-)

diff --git a/example/daubechies_wavelets/bench.cpp b/example/daubechies_wavelets/bench.cpp
index 30feb0c70..797121d79 100644
--- a/example/daubechies_wavelets/bench.cpp
+++ b/example/daubechies_wavelets/bench.cpp
@@ -40,16 +40,43 @@ BENCHMARK_TEMPLATE(DyadicGrid, double, 4)->DenseRange(3, 22, 1)->Unit(benchmark:
 //BENCHMARK_TEMPLATE(DyadicGrid, double, 8)->DenseRange(3, 22, 1)->Unit(benchmark::kMillisecond)->Complexity(exponential);
 //BENCHMARK_TEMPLATE(DyadicGrid, double, 11)->DenseRange(3,22,1)->Unit(benchmark::kMillisecond)->Complexity(exponential);
 
+uint64_t s[2] = { 0x41, 0x29837592 };
+
+static inline uint64_t rotl(const uint64_t x, int k) {
+    return (x << k) | (x >> (64 - k));
+}
+
+uint64_t next(void) {
+    const uint64_t s0 = s[0];
+    uint64_t s1 = s[1];
+    const uint64_t result = s0 + s1;
+
+    s1 ^= s0;
+    s[0] = rotl(s0, 55) ^ s1 ^ (s1 << 14); // a, b
+    s[1] = rotl(s1, 36); // c
+
+    return result;
+}
+
+double uniform() {
+    return next()*(1.0/18446744073709551616.0);
+}
 
 template<typename Real, int p>
 void ScalingEvaluation(benchmark::State & state)
 {
     auto phi = boost::math::daubechies_scaling<Real, p>();
+    Real xmax = phi.support().second;
     Real x = 0;
+    Real step = uniform()/2048;
     for (auto _ : state)
     {
         benchmark::DoNotOptimize(phi(x));
-        x += std::numeric_limits<Real>::epsilon();
+        x += step;
+        if (x > xmax) {
+            x = 0;
+            step = uniform()/2048;
+        }
     }
 }
 
@@ -123,13 +150,15 @@ void CubicHermite(benchmark::State & state)
 
     auto qh = cubic_hermite(std::move(x), std::move(y), std::move(dydx));
     Real t = x0;
+    Real step = uniform()*(xf-x0)/2048;
     for (auto _ : state)
     {
         benchmark::DoNotOptimize(qh(t));
-        t += (xf-x0)/128;
+        t += step;
         if (t >= xf)
         {
             t = x0;
+            step = uniform()*(xf-x0)/2048;
         }
     }
     state.SetComplexityN(state.range(0));
@@ -148,8 +177,8 @@ void CardinalCubicHermite(benchmark::State & state)
     boost::random::uniform_real_distribution<Real> dis(Real(0), Real(1));
     for (size_t i = 0; i < y.size(); ++i)
     {
-        y[i] = dis(rd);
-        dydx[i] = dis(rd);
+        y[i] = uniform();
+        dydx[i] = uniform();
     }
 
     Real dx = Real(1)/Real(8);
@@ -157,21 +186,21 @@ void CardinalCubicHermite(benchmark::State & state)
     Real xf = x0 + (y.size()-1)*dx;
 
     auto qh = cardinal_cubic_hermite_detail(std::move(y), std::move(dydx), x0, dx);
-    Real x = 0;
+    Real x = x0;
+    Real step = uniform()*(xf-x0)/2048;
     for (auto _ : state)
     {
         benchmark::DoNotOptimize(qh.unchecked_evaluation(x));
-        x += xf/128;
+        x += step;
         if (x >= xf)
         {
             x = x0;
+            step = uniform()*(xf-x0)/2048;
         }
     }
     state.SetComplexityN(state.range(0));
 }
 
-BENCHMARK_TEMPLATE(CardinalCubicHermite, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity(benchmark::o1);
-
 template<typename Real>
 void CardinalCubicHermiteAOS(benchmark::State & state)
 {
@@ -181,8 +210,8 @@ void CardinalCubicHermiteAOS(benchmark::State & state)
     boost::random::uniform_real_distribution<Real> dis(Real(0), Real(1));
     for (size_t i = 0; i < dat.size(); ++i)
     {
-        dat[i][0] = dis(rd);
-        dat[i][1] = dis(rd);
+        dat[i][0] = uniform();
+        dat[i][1] = uniform();
     }
 
     using boost::math::interpolators::detail::cardinal_cubic_hermite_detail_aos;
@@ -191,19 +220,22 @@ void CardinalCubicHermiteAOS(benchmark::State & state)
     Real xf = x0 + (dat.size()-1)*dx;
     auto qh = cardinal_cubic_hermite_detail_aos(std::move(dat), x0, dx);
     Real x = 0;
+    Real step = uniform()*(xf-x0)/2048;
     for (auto _ : state)
     {
         benchmark::DoNotOptimize(qh.unchecked_evaluation(x));
-        x += xf/128;
+        x += step;
         if (x >= xf)
         {
             x = x0;
+            step = uniform()*(xf-x0)/2048;
         }
     }
     state.SetComplexityN(state.range(0));
 }
 
-BENCHMARK_TEMPLATE(CardinalCubicHermiteAOS, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity(benchmark::o1);
+BENCHMARK_TEMPLATE(CardinalCubicHermiteAOS, double)->RangeMultiplier(2)->Range(1<<8, 1<<21)->Complexity(benchmark::o1);
+BENCHMARK_TEMPLATE(CardinalCubicHermite, double)->RangeMultiplier(2)->Range(1<<8, 1<<21)->Complexity(benchmark::o1);
 
 template<class Real>
 void SineEvaluation(benchmark::State& state)
@@ -272,9 +304,9 @@ void CardinalQuinticHermite(benchmark::State & state)
     boost::random::uniform_real_distribution<Real> dis(Real(0), Real(1));
     for (size_t i = 0; i < y.size(); ++i)
     {
-        y[i] = dis(rd);
-        dydx[i] = dis(rd);
-        d2ydx2[i] = dis(rd);
+        y[i] = uniform();
+        dydx[i] = uniform();
+        d2ydx2[i] = uniform();
     }
 
     Real dx = Real(1)/Real(8);
@@ -283,20 +315,20 @@ void CardinalQuinticHermite(benchmark::State & state)
 
     auto qh = cardinal_quintic_hermite_detail(std::move(y), std::move(dydx), std::move(d2ydx2), x0, dx);
     Real x = 0;
+    Real step = uniform()*(xf-x0)/2048;
     for (auto _ : state)
     {
         benchmark::DoNotOptimize(qh.unchecked_evaluation(x));
-        x += xf/128;
+        x += step;
         if (x >= xf)
         {
             x = x0;
+            step = uniform()*(xf-x0)/2048;
         }
     }
     state.SetComplexityN(state.range(0));
 }
 
-BENCHMARK_TEMPLATE(CardinalQuinticHermite, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity(benchmark::o1);
-
 template<typename Real>
 void CardinalQuinticHermiteAOS(benchmark::State & state)
 {
@@ -306,9 +338,9 @@ void CardinalQuinticHermiteAOS(benchmark::State & state)
     boost::random::uniform_real_distribution<Real> dis(Real(0), Real(1));
     for (size_t i = 0; i < dat.size(); ++i)
     {
-        dat[i][0] = dis(rd);
-        dat[i][1] = dis(rd);
-        dat[i][2] = dis(rd);
+        dat[i][0] = uniform();
+        dat[i][1] = uniform();
+        dat[i][2] = uniform();
     }
 
     using boost::math::interpolators::detail::cardinal_quintic_hermite_detail_aos;
@@ -316,19 +348,22 @@ void CardinalQuinticHermiteAOS(benchmark::State & state)
     Real x0 = 0;
     Real xf = x0 + (dat.size()-1)*dx;
     auto qh = cardinal_quintic_hermite_detail_aos(std::move(dat), x0, dx);
-    Real x = 0;
+    Real x = x0;
+    Real step = uniform()*(xf-x0)/2048;
     for (auto _ : state) {
         benchmark::DoNotOptimize(qh.unchecked_evaluation(x));
-        x += xf/128;
+        x += step;
         if (x >= xf)
         {
             x = x0;
+            step = uniform()*(xf-x0)/2048;
         }
     }
     state.SetComplexityN(state.range(0));
 }
 
-BENCHMARK_TEMPLATE(CardinalQuinticHermiteAOS, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity(benchmark::o1);
+BENCHMARK_TEMPLATE(CardinalQuinticHermiteAOS, double)->RangeMultiplier(2)->Range(1<<8, 1<<22)->Complexity(benchmark::o1);
+BENCHMARK_TEMPLATE(CardinalQuinticHermite, double)->RangeMultiplier(2)->Range(1<<8, 1<<22)->Complexity(benchmark::o1);
 
 template<typename Real>
 void SepticHermite(benchmark::State & state)

From 83435340420c08e4b74ec4dc48fdaacabe8448bf Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Sun, 23 Feb 2020 13:34:47 -0500
Subject: [PATCH 056/104] Everything to array of structs [CI SKIP]

---
 .../special_functions/daubechies_scaling.hpp  | 82 +++++++++++++++++--
 1 file changed, 74 insertions(+), 8 deletions(-)

diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index f078c653d..d9d9eeb95 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -199,6 +199,44 @@ private:
     RandomAccessContainer dydx_;
 };
 
+template<class RandomAccessContainer>
+class linear_interpolation_aos {
+public:
+    using Point = typename RandomAccessContainer::value_type;
+    using Real = typename Point::value_type;
+
+    linear_interpolation_aos(RandomAccessContainer && data, int grid_refinements) : data_{std::move(data)}
+    {
+        s_ = (1 << grid_refinements);
+    }
+
+    inline Real operator()(Real x) const
+    {
+        using std::floor;
+        Real y = x*s_;
+        Real k = floor(y);
+
+        int64_t kk = static_cast<int64_t>(k);
+        Real t = y - k;
+        return (1-t)*data_[kk][0] + t*data_[kk+1][0];
+    }
+
+    inline Real prime(Real x) const
+    {
+        using std::floor;
+        Real y = x*s_;
+        Real k = floor(y);
+
+        int64_t kk = static_cast<int64_t>(k);
+        Real t = y - k;
+        return (1-t)*data_[kk][1] + t*data_[kk+1][1];
+    }
+
+private:
+    Real s_;
+    RandomAccessContainer data_;
+};
+
 }
 
 template<class Real, int p>
@@ -341,22 +379,50 @@ public:
         }
         if constexpr (p==3)
         {
-            m_lin = std::make_shared<detail::linear_interpolation<std::vector<Real>>>(std::move(y), std::move(dydx), grid_refinements);
+            std::vector<std::array<Real, 2>> data(y.size());
+            for (size_t i = 0; i < y.size(); ++i)
+            {
+                data[i][0] = y[i];
+                data[i][1] = dydx[i];
+            }
+            m_lin = std::make_shared<detail::linear_interpolation_aos<std::vector<std::array<Real, 2>>>>(std::move(data), grid_refinements);
         }
         if constexpr (p == 4 || p == 5)
         {
             Real dx = Real(1)/(1 << grid_refinements);
-            m_cbh = std::make_shared<interpolators::detail::cardinal_cubic_hermite_detail<std::vector<Real>>>(std::move(y), std::move(dydx), Real(0), dx);
+            std::vector<std::array<Real, 2>> data(y.size());
+            for (size_t i = 0; i < y.size(); ++i)
+            {
+                data[i][0] = y[i];
+                data[i][1] = dydx[i];
+            }
+            m_cbh = std::make_shared<interpolators::detail::cardinal_cubic_hermite_detail_aos<std::vector<std::array<Real,2>>>>(std::move(data), Real(0), dx);
         }
         if constexpr (p >= 6 && p <= 9)
         {
             Real dx = Real(1)/(1 << grid_refinements);
-            m_qh = std::make_shared<interpolators::detail::cardinal_quintic_hermite_detail<std::vector<Real>>>(std::move(y), std::move(dydx), std::move(d2ydx2), Real(0), dx);
+            std::vector<std::array<Real, 3>> data(y.size());
+            for (size_t i = 0; i < y.size(); ++i)
+            {
+                data[i][0] = y[i];
+                data[i][1] = dydx[i];
+                data[i][2] = d2ydx2[i];
+            }
+
+            m_qh = std::make_shared<interpolators::detail::cardinal_quintic_hermite_detail_aos<std::vector<std::array<Real,3>>>>(std::move(data), Real(0), dx);
         }
         if constexpr (p >= 10)
         {
             Real dx = Real(1)/(1 << grid_refinements);
-            m_sh = std::make_shared<interpolators::detail::cardinal_septic_hermite_detail<std::vector<Real>>>(std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3), Real(0), dx);
+            std::vector<std::array<Real, 4>> data(y.size());
+            for (size_t i = 0; i < y.size(); ++i)
+            {
+                data[i][0] = y[i];
+                data[i][1] = dydx[i];
+                data[i][2] = d2ydx2[i];
+                data[i][3] = d3ydx3[i];
+            }
+            m_sh = std::make_shared<interpolators::detail::cardinal_septic_hermite_detail_aos<std::vector<std::array<Real, 4>>>>(std::move(data), Real(0), dx);
         }
      }
 
@@ -436,13 +502,13 @@ private:
     // Need this for p = 2:
     std::shared_ptr<detail::matched_holder_aos<std::vector<std::array<Real,2>>>> m_mh;
     // Need this for p = 3:
-    std::shared_ptr<detail::linear_interpolation<std::vector<Real>>> m_lin;
+    std::shared_ptr<detail::linear_interpolation_aos<std::vector<std::array<Real, 2>>>> m_lin;
     // Need this for p = 4,5:
-    std::shared_ptr<interpolators::detail::cardinal_cubic_hermite_detail<std::vector<Real>>> m_cbh;
+    std::shared_ptr<interpolators::detail::cardinal_cubic_hermite_detail_aos<std::vector<std::array<Real, 2>>>> m_cbh;
     // Need this for p = 6,7,8,9:
-    std::shared_ptr<interpolators::detail::cardinal_quintic_hermite_detail<std::vector<Real>>> m_qh;
+    std::shared_ptr<interpolators::detail::cardinal_quintic_hermite_detail_aos<std::vector<std::array<Real, 3>>>> m_qh;
     // Need this for p >= 10:
-    std::shared_ptr<interpolators::detail::cardinal_septic_hermite_detail<std::vector<Real>>> m_sh;
+    std::shared_ptr<interpolators::detail::cardinal_septic_hermite_detail_aos<std::vector<std::array<Real, 4>>>> m_sh;
 
     /*
     Real single_crank_linear(Real x) const {

From 38c2dd376bc45f49100dbdda3812d02683564b40 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Mon, 24 Feb 2020 07:06:21 -0500
Subject: [PATCH 057/104] Second derivative for septic Hermite spline.

---
 .../detail/septic_hermite_detail.hpp          | 108 +++++++++++++++++-
 .../special_functions/daubechies_scaling.hpp  |   4 +
 test/septic_hermite_test.cpp                  |  13 ++-
 3 files changed, 118 insertions(+), 7 deletions(-)

diff --git a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
index 7a9f260c6..5e26d8805 100644
--- a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
@@ -336,9 +336,57 @@ public:
         return dydx;
     }
 
-    inline Real double_prime(Real x) const
+    inline Real double_prime(Real x) constq
     {
-        return std::numeric_limits<Real>::quiet_NaN();
+        Real xf = x0_ + (y_.size()-1)/inv_dx_;
+        if  (x < x0_ || x > xf)
+        {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf)
+        {
+            return d2y_.back()*2*inv_dx_*inv_dx_;
+        }
+
+        return this->unchecked_double_prime(x);
+    }
+
+    inline Real unchecked_double_prime(Real x) const
+    {
+        using std::floor;
+        Real s3 = (x-x0_)*inv_dx_;
+        Real ii = floor(s3);
+        auto i = static_cast<decltype(y_.size())>(ii);
+        Real t = s3 - ii;
+
+        Real y0 = y_[i];
+        Real y1 = y_[i+1];
+        Real dy0 = dy_[i];
+        Real dy1 = dy_[i+1];
+        Real a0 = d2y_[i];
+        Real a1 = d2y_[i+1];
+        Real j0 = d3y_[i];
+        Real j1 = d3y_[i+1];
+        Real t2 = t*t;
+
+        Real z0 = 420*t2*(1 + t*(-4 + t*(5 - 2*t)));
+        Real z1 = 60*t2*(-4 + t*(15 + t*(-18 + 7*t)));
+        Real z2 = 60*t2*(-3 + t*(13 + t*(-17 + 7*t)));
+        Real z3 = (1 + t2*(-60 + t*(200 + t*(-225 + 84*t))));
+        Real z4 = t2*(30 + t*(-140 + t*(195 - 84*t)));
+        Real z5 = t*(1 + t*(-8 + t*(20 + t*(-20 + 7*t))));
+        Real z6 = t2*(-2 + t*(10 + t*(-15 + 7*t)));
+
+        Real d2ydx2 = z0*(y1-y0)*inv_dx_*inv_dx_;
+        d2ydx2 += (z1*dy0 + z2*dy1)*inv_dx_*inv_dx_;
+        d2ydx2 += (z3*a0 + z4*a1)*2*inv_dx_*inv_dx_;
+        d2ydx2 += 6*(z5*j0 + z6*j1)/(inv_dx_*inv_dx_);
+
+        return d2ydx2;
     }
 
 private:
@@ -437,7 +485,7 @@ public:
         }
         if (x == xf)
         {
-            return data_.back()[1];
+            return data_.back()[1]*inv_dx_;
         }
 
         return this->unchecked_prime(x);
@@ -449,7 +497,7 @@ public:
         Real ii = floor(s3);
         auto i = static_cast<decltype(data_.size())>(ii);
         Real t = s3 - ii;
- 
+
         Real y0 = data_[i][0];
         Real y1 = data_[i+1][0];
         Real dy0 = data_[i][1];
@@ -475,9 +523,57 @@ public:
         return dydx;
     }
 
-    inline Real double_prime(Real x) const 
+    inline Real double_prime(Real x) const
     {
-        return std::numeric_limits<Real>::quiet_NaN();
+        Real xf = x0_ + (data_.size()-1)/inv_dx_;
+        if  (x < x0_ || x > xf)
+        {
+            std::ostringstream oss;
+            oss.precision(std::numeric_limits<Real>::digits10+3);
+            oss << "Requested abscissa x = " << x << ", which is outside of allowed range ["
+                << x0_ << ", " << xf << "]";
+            throw std::domain_error(oss.str());
+        }
+        if (x == xf)
+        {
+            return data_.back()[2]*2*inv_dx_*inv_dx_;
+        }q
+
+        return this->unchecked_double_prime(x);
+    }
+
+    inline Real unchecked_double_prime(Real x) const
+    {
+        using std::floor;
+        Real s3 = (x-x0_)*inv_dx_;
+        Real ii = floor(s3);
+        auto i = static_cast<decltype(data_.size())>(ii);
+        Real t = s3 - ii;
+
+        Real y0 = data_[i][0];
+        Real y1 = data_[i+1][0];
+        Real dy0 = data_[i][1];
+        Real dy1 = data_[i+1][1];
+        Real a0 = data_[i][2];
+        Real a1 = data_[i+1][2];
+        Real j0 = data_[i][3];
+        Real j1 = data_[i+1][3];
+        Real t2 = t*t;
+
+        Real z0 = 420*t2*(1 + t*(-4 + t*(5 - 2*t)));
+        Real z1 = 60*t2*(-4 + t*(15 + t*(-18 + 7*t)));
+        Real z2 = 60*t2*(-3 + t*(13 + t*(-17 + 7*t)));
+        Real z3 = (1 + t2*(-60 + t*(200 + t*(-225 + 84*t))));
+        Real z4 = t2*(30 + t*(-140 + t*(195 - 84*t)));
+        Real z5 = t*(1 + t*(-8 + t*(20 + t*(-20 + 7*t))));
+        Real z6 = t2*(-2 + t*(10 + t*(-15 + 7*t)));
+
+        Real d2ydx2 = z0*(y1-y0)*inv_dx_*inv_dx_;
+        d2ydx2 += (z1*dy0 + z2*dy1)*inv_dx_*inv_dx_;
+        d2ydx2 += (z3*a0 + z4*a1)*2*inv_dx_*inv_dx_;
+        d2ydx2 += 6*(z5*j0 + z6*j1)/(inv_dx_*inv_dx_);
+
+        return d2ydx2;
     }
 
 private:
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index d9d9eeb95..d1e4092b8 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -491,6 +491,10 @@ public:
         {
             return m_qh->unchecked_double_prime(x);
         }
+        if constexpr (p >= 10)
+        {
+            return m_sh->unchecked_double_prime(x);
+        }
     }
 
     std::pair<Real, Real> support() const
diff --git a/test/septic_hermite_test.cpp b/test/septic_hermite_test.cpp
index dbe9fc011..180ceff0f 100644
--- a/test/septic_hermite_test.cpp
+++ b/test/septic_hermite_test.cpp
@@ -51,9 +51,11 @@ void test_constant()
     d2ydx2.resize(128, 0);
     d3ydx3.resize(128, 0);
     auto csh = cardinal_septic_hermite(std::move(y), std::move(dydx), std::move(d2ydx2), std::move(d3ydx3), x0, dx);
-    for (Real t = x0; t <= 127; t += 0.25) {
+    for (Real t = x0; t <= 127; t += 0.25)
+    {
         CHECK_ULP_CLOSE(Real(7), csh(t), 24);
         CHECK_ULP_CLOSE(Real(0), csh.prime(t), 24);
+        CHECK_ULP_CLOSE(Real(0), csh.double_prime(t), 24);
     }
 
     std::vector<std::array<Real, 4>> data(128);
@@ -69,6 +71,7 @@ void test_constant()
     {
         CHECK_ULP_CLOSE(Real(7), csh_aos(t), 24);
         CHECK_ULP_CLOSE(Real(0), csh_aos.prime(t), 24);
+        CHECK_ULP_CLOSE(Real(0), csh_aos.double_prime(t), 24);
     }
 
 }
@@ -130,6 +133,7 @@ void test_linear()
     {
         CHECK_ULP_CLOSE(t, csh(t), 15);
         CHECK_ULP_CLOSE(Real(1), csh.prime(t), 15);
+        CHECK_ULP_CLOSE(Real(0), csh.double_prime(t), 15);
     }
 
     std::vector<std::array<Real, 4>> data(10);
@@ -145,6 +149,7 @@ void test_linear()
     {
         CHECK_ULP_CLOSE(t, csh_aos(t), 15);
         CHECK_ULP_CLOSE(Real(1), csh_aos.prime(t), 15);
+        CHECK_ULP_CLOSE(Real(0), csh_aos.double_prime(t), 15);
     }
 }
 
@@ -231,6 +236,7 @@ void test_quadratic()
     {
         CHECK_ULP_CLOSE(t*t/2, csh(t), 24);
         CHECK_ULP_CLOSE(t, csh.prime(t), 24);
+        CHECK_ULP_CLOSE(Real(1), csh.double_prime(t), 24);
     }
 
     std::vector<std::array<Real, 4>> data(10);
@@ -246,6 +252,7 @@ void test_quadratic()
     {
         CHECK_ULP_CLOSE(t*t/2, csh_aos(t), 24);
         CHECK_ULP_CLOSE(t, csh_aos.prime(t), 24);
+        CHECK_ULP_CLOSE(Real(1), csh_aos.double_prime(t), 24);
     }
 }
 
@@ -303,6 +310,7 @@ void test_cubic()
     {
         CHECK_ULP_CLOSE(t*t*t, csh(t), 151);
         CHECK_ULP_CLOSE(3*t*t, csh.prime(t), 151);
+        CHECK_ULP_CLOSE(6*t, csh.double_prime(t), 151);
     }
 
     std::vector<std::array<Real, 4>> data(8);
@@ -319,6 +327,7 @@ void test_cubic()
     {
         CHECK_ULP_CLOSE(t*t*t, csh_aos(t), 151);
         CHECK_ULP_CLOSE(3*t*t, csh_aos.prime(t), 151);
+        CHECK_ULP_CLOSE(6*t, csh_aos.double_prime(t), 151);
     }
 }
 
@@ -377,6 +386,7 @@ void test_quartic()
     {
         CHECK_ULP_CLOSE(t*t*t*t, csh(t), 117);
         CHECK_ULP_CLOSE(4*t*t*t, csh.prime(t), 117);
+        CHECK_ULP_CLOSE(12*t*t, csh.double_prime(t), 117);
     }
 
     std::vector<std::array<Real, 4>> data(10);
@@ -393,6 +403,7 @@ void test_quartic()
     {
         CHECK_ULP_CLOSE(t*t*t*t, csh_aos(t), 117);
         CHECK_ULP_CLOSE(4*t*t*t, csh_aos.prime(t), 117);
+        CHECK_ULP_CLOSE(12*t*t, csh_aos.double_prime(t), 117);
     }
 }
 

From efaaa9c81105de2bbee9fdcdb0ff44ca6b5fddba Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Mon, 24 Feb 2020 20:43:08 +0000
Subject: [PATCH 058/104] Update daubechies integer grid with simplified
 header. Plus revised generator program.

---
 .../daubechies_scaling_integer_grid.cpp       |  171 +-
 include/boost/math/filters/daubechies.hpp     |    5 +-
 .../daubechies_scaling_integer_grid.hpp       | 2465 ++---------------
 3 files changed, 286 insertions(+), 2355 deletions(-)

diff --git a/example/daubechies_wavelets/daubechies_scaling_integer_grid.cpp b/example/daubechies_wavelets/daubechies_scaling_integer_grid.cpp
index 3c7377a6a..1dc55bfe2 100644
--- a/example/daubechies_wavelets/daubechies_scaling_integer_grid.cpp
+++ b/example/daubechies_wavelets/daubechies_scaling_integer_grid.cpp
@@ -4,6 +4,9 @@
  * Boost Software License, Version 1.0. (See accompanying file
  * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
  */
+
+#define BOOST_MATH_GENERATE_DAUBECHIES_GRID
+
 #include <iostream>
 #include <vector>
 #include <numeric>
@@ -15,13 +18,21 @@
 #include <boost/hana/for_each.hpp>
 #include <boost/hana/ext/std/integer_sequence.hpp>
 #include <boost/core/demangle.hpp>
+#ifdef BOOST_HAS_FLOAT128
 #include <boost/multiprecision/float128.hpp>
+#endif
 #include <boost/math/constants/constants.hpp>
 #include <boost/math/filters/daubechies.hpp>
 #include <boost/math/special_functions/factorials.hpp>
 #include <boost/multiprecision/cpp_bin_float.hpp>
 
+typedef boost::multiprecision::number<boost::multiprecision::cpp_bin_float<237, boost::multiprecision::backends::digit_base_2, std::allocator<char>, boost::int32_t, -262142, 262143>,  boost::multiprecision::et_off> octuple_type;
 
+#ifdef BOOST_HAS_FLOAT128
+typedef boost::multiprecision::float128 float128_t;
+#else
+typedef boost::multiprecision::cpp_bin_float_quad float128_t;
+#endif
 
 template<class Real, int p>
 std::list<std::vector<Real>> integer_grid()
@@ -55,7 +66,7 @@ std::list<std::vector<Real>> integer_grid()
 
     Eigen::EigenSolver<decltype(A)> es(A);
 
-    typename Eigen::EigenSolver<decltype(A)>::EigenvalueType complex_eigs = es.eigenvalues();
+    auto complex_eigs = es.eigenvalues();
 
     std::vector<Real> eigs(complex_eigs.size(), std::numeric_limits<Real>::quiet_NaN());
 
@@ -80,8 +91,9 @@ std::list<std::vector<Real>> integer_grid()
         }
         size_t idx = std::distance(eigs.begin(), it);
         std::cout << "Eigenvector for derivative " << j << " is at index " << idx << "\n";
-        typename Eigen::EigenSolver<decltype(A)>::EigenvectorsType complex_eigenvectors = es.eigenvectors();
-        auto complex_eigenvec = complex_eigenvectors.col(idx);
+        auto eigenvector_matrix = es.eigenvectors();
+        auto complex_eigenvec = eigenvector_matrix.col(idx);
+
         std::vector<Real> eigenvec(complex_eigenvec.size() + 2, std::numeric_limits<Real>::quiet_NaN());
         eigenvec[0] = 0;
         eigenvec[eigenvec.size()-1] = 0;
@@ -128,101 +140,28 @@ template<class Real, int p>
 void write_grid(std::ofstream & fs)
 {
     auto grids = integer_grid<Real, p>();
-    fs << "    if constexpr (p == " << p << ") {\n";
-    fs << "        if constexpr (std::is_same_v<Real, float>) {\n";
     size_t j = 0;
-    for (auto it = grids.begin(); it != grids.end(); ++it) {
-
-    fs << "            if constexpr (order == " << j << ") {\n";
-    fs << "                return {";
-        auto const & grid = *it;
-        for (size_t i = 0; i < grid.size() -1; ++i) {
-            fs << static_cast<float>(grid[i]) << "f, ";
-        }
-        fs << static_cast<float>(grid[grid.size()-1]) << "f};\n";
-    fs << "            }\n";
-        ++j;
+    fs << std::setprecision(std::numeric_limits< boost::multiprecision::cpp_bin_float_quad>::max_digits10);
+    for (auto it = grids.begin(); it != grids.end(); ++it) 
+    {
+       auto const& grid = *it;
+       fs << "template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, " << p << ", ";
+      fs << j << "> { static inline constexpr std::array<Real, " << grid.size() << "> value = { ";
+      for (size_t i = 0; i < grid.size() -1; ++i){
+        fs << "C_(" << static_cast<float128_t>(grid[i]) << "), ";
+      }
+      fs << "C_(" << static_cast<float128_t>(grid[grid.size()-1]) << ") }; };\n";
+      ++j;
     }
-    fs << "        }\n";
-
-    fs << "        if constexpr (std::is_same_v<Real, double>) {\n";
-    j = 0;
-    for (auto it = grids.begin(); it != grids.end(); ++it) {
-
-    fs << "            if constexpr (order == " << j << ") {\n";
-    fs << "                return {";
-        auto const & grid = *it;
-        for (size_t i = 0; i < grid.size() -1; ++i) {
-            fs << static_cast<double>(grid[i]) << ", ";
-        }
-        fs << static_cast<double>(grid[grid.size()-1]) << "};\n";
-    fs << "            }\n";
-        ++j;
-    }
-    fs << "        }\n";
-
-
-    fs << "        if constexpr (std::is_same_v<Real, long double>) {\n";
-    j = 0;
-    for (auto it = grids.begin(); it != grids.end(); ++it) {
-
-    fs << "            if constexpr (order == " << j << ") {\n";
-    fs << "                return {";
-        auto const & grid = *it;
-        for (size_t i = 0; i < grid.size() -1; ++i) {
-            fs << static_cast<long double>(grid[i]) << "L, ";
-        }
-        fs << static_cast<long double>(grid[grid.size()-1]) << "L};\n";
-    fs << "            }\n";
-        ++j;
-    }
-    fs << "        }\n";
-
-    fs << "        #ifdef BOOST_HAS_FLOAT128\n";
-    fs << "        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {\n";
-    j = 0;
-    for (auto it = grids.begin(); it != grids.end(); ++it) {
-
-    fs << "            if constexpr (order == " << j << ") {\n";
-    fs << "                return {";
-        auto const & grid = *it;
-        for (size_t i = 0; i < grid.size() -1; ++i) {
-            fs << static_cast<boost::multiprecision::float128>(grid[i]) << "Q, ";
-        }
-        fs << static_cast<boost::multiprecision::float128>(grid[grid.size()-1]) << "Q};\n";
-    fs << "            }\n";
-        ++j;
-    }
-    fs << "        }\n";
-    fs << "        #endif\n";
-
-    fs << "        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {\n";
-    j = 0;
-    for (auto it = grids.begin(); it != grids.end(); ++it) {
-
-    fs << std::setprecision(std::numeric_limits<boost::multiprecision::cpp_bin_float_oct>::digits10 + 3);
-    fs << "            if constexpr (order == " << j << ") {\n";
-    fs << "                return {";
-        auto const & grid = *it;
-        for (size_t i = 0; i < grid.size() -1; ++i) {
-            fs << "boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>(\"" << static_cast<boost::multiprecision::cpp_bin_float_oct>(grid[i]) << "\"), ";
-        }
-        fs << "boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>(\"" << static_cast<boost::multiprecision::cpp_bin_float_oct>(grid[grid.size()-1]) << "\")};\n";
-    fs << "            }\n";
-        ++j;
-    }
-    fs << "        }\n";
-
-    fs << "    }\n";
-
 }
 
 int main()
 {
-    constexpr const size_t p_max = 15;
+    constexpr const size_t p_max = 18;
     std::ofstream fs{"daubechies_scaling_integer_grid.hpp"};
     fs << "/*\n"
-       << " * Copyright Nick Thompson, John Maddock, 2020\n"
+       << " * Copyright Nick Thompson, 2019\n"
+       << " * Copyright John Maddock, 2020\n"
        << " * Use, modification and distribution are subject to the\n"
        << " * Boost Software License, Version 1.0. (See accompanying file\n"
        << " * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)\n"
@@ -231,32 +170,42 @@ int main()
        << "#ifndef BOOST_MATH_DAUBECHIES_SCALING_INTEGER_GRID_HPP\n"
        << "#define BOOST_MATH_DAUBECHIES_SCALING_INTEGER_GRID_HPP\n"
        << "#include <array>\n"
+       << "#include <float.h>\n"
+       << "#include <boost/config.hpp>\n"
+       << "/*\n"
+       << "In order to keep the character count as small as possible and speed up\n"
+       << "compiler parsing times, we define a macro C_ which appends an appropriate\n"
+       << "suffix to each literal, and then casts it to type Real.\n"
+       << "The suffix is as follows:\n\n"
+       << "* Q, when we have __float128 support.\n"
+       << "* L, when we have either 80 or 128 bit long doubles.\n"
+       << "* Nothing otherwise.\n"
+       << "*/\n\n"
        << "#ifdef BOOST_HAS_FLOAT128\n"
-       << "#include <boost/multiprecision/float128.hpp>\n"
-       << "#endif\n"
+       << "#  define C_(x) static_cast<Real>(x##Q)\n"
+       << "#elif (LDBL_MANT_DIG > DBL_MANT_DIG)\n"
+       << "#  define C_(x) static_cast<Real>(x##L)\n"
+       << "#else\n"
+       << "#  define C_(x) static_cast<Real>(x)\n"
+       << "#endif\n\n"
        << "namespace boost::math::detail {\n\n"
-       << "template <typename Real, unsigned p, unsigned order>\n"
-       << "constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()\n"
+       << "template <typename Real, int p, int order> struct daubechies_scaling_integer_grid_imp;\n\n";
+
+    fs << std::hexfloat << std::setprecision(std::numeric_limits<boost::multiprecision::cpp_bin_float_quad>::max_digits10);
+
+    boost::hana::for_each(std::make_index_sequence<p_max>(), [&](auto idx){
+        write_grid<octuple_type, idx+2>(fs);
+    });
+
+    fs << "\n\ntemplate <typename Real, unsigned p, unsigned order>\n"
+       << "constexpr inline std::array<Real, 2*p> daubechies_scaling_integer_grid()\n"
        << "{\n"
        << "    static_assert(sizeof(Real) <= 16, \"Integer grids only computed up to 128 bits of precision.\");\n"
        << "    static_assert(p <= " << p_max << ", \"Integer grids only implemented up to " << p_max << ".\");\n"
-       << "    static_assert(p > 1, \"Integer grids only implemented for p >= 2.\");\n";
-
-
-    fs << std::hexfloat;
-
-    boost::hana::for_each(std::make_index_sequence<p_max>(), [&](auto idx){
-        write_grid<boost::multiprecision::cpp_bin_float_oct, idx+2>(fs);
-    });
-
-    fs << "    std::array<Real, 2*p> m{};\n"
-       << "    for (auto & x : m) {\n"
-       << "        x = std::numeric_limits<Real>::quiet_NaN();\n"
-       << "    }\n"
-       << "    return m;\n";
-
-
-    fs << "}\n\n";
+       << "    static_assert(p > 1, \"Integer grids only implemented for p >= 2.\");\n"
+       << "    std::array<Real, 2*p> m{};\n"
+       << "    return daubechies_scaling_integer_grid_imp<Real, p, order>::value;\n"
+       << "}\n\n";
 
     fs << "} // namespaces\n";
     fs << "#endif\n";
diff --git a/include/boost/math/filters/daubechies.hpp b/include/boost/math/filters/daubechies.hpp
index 24a71150c..9682b54d1 100644
--- a/include/boost/math/filters/daubechies.hpp
+++ b/include/boost/math/filters/daubechies.hpp
@@ -13,8 +13,11 @@
 #include <boost/multiprecision/cpp_bin_float.hpp>
 namespace boost::math::filters {
 
-//typedef boost::multiprecision::number<boost::multiprecision::cpp_bin_float<237, boost::multiprecision::backends::digit_base_2, std::allocator<char>, boost::int32_t, -262142, 262143>, boost::multiprecision::et_off> octuple_type;
+#ifdef BOOST_MATH_GENERATE_DAUBECHIES_GRID
+typedef boost::multiprecision::number<boost::multiprecision::cpp_bin_float<237, boost::multiprecision::backends::digit_base_2, std::allocator<char>, boost::int32_t, -262142, 262143>, boost::multiprecision::et_off> octuple_type;
+#else
 typedef boost::multiprecision::cpp_bin_float_oct octuple_type;
+#endif
    
 template <typename Real, unsigned p>
 constexpr std::array<Real, 2*p> daubechies_scaling_filter()
diff --git a/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp b/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp
index e75f2a90f..208093342 100644
--- a/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp
+++ b/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp
@@ -1,5 +1,6 @@
 /*
  * Copyright Nick Thompson, 2019
+ * Copyright John Maddock, 2020
  * Use, modification and distribution are subject to the
  * Boost Software License, Version 1.0. (See accompanying file
  * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
@@ -8,2258 +9,236 @@
 #ifndef BOOST_MATH_DAUBECHIES_SCALING_INTEGER_GRID_HPP
 #define BOOST_MATH_DAUBECHIES_SCALING_INTEGER_GRID_HPP
 #include <array>
+#include <float.h>
+#include <boost/config.hpp>
+/*
+In order to keep the character count as small as possible and speed up
+compiler parsing times, we define a macro C_ which appends an appropriate
+suffix to each literal, and then casts it to type Real.
+The suffix is as follows:
+
+* Q, when we have __float128 support.
+* L, when we have either 80 or 128 bit long doubles.
+* Nothing otherwise.
+*/
+
 #ifdef BOOST_HAS_FLOAT128
-#include <boost/multiprecision/float128.hpp>
+#  define C_(x) static_cast<Real>(x##Q)
+#elif (LDBL_MANT_DIG > DBL_MANT_DIG)
+#  define C_(x) static_cast<Real>(x##L)
+#else
+#  define C_(x) static_cast<Real>(x)
 #endif
-#include <boost/multiprecision/cpp_bin_float.hpp>
 
 namespace boost::math::detail {
 
+template <typename Real, int p, int order> struct daubechies_scaling_integer_grid_imp;
+
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 2, 0> { static inline constexpr std::array<Real, 4> value = { C_(0x0p+0), C_(0x1.5db3d742c265539d92ba16b83c5cp+0), C_(-0x1.76cf5d0b09954e764ae85ae0f17p-2), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 2, 1> { static inline constexpr std::array<Real, 4> value = { C_(0x0p+0), C_(0x1p+0), C_(-0x1p+0), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 3, 0> { static inline constexpr std::array<Real, 6> value = { C_(0x0p+0), C_(0x1.494d414ee19a0fc1701f9345a28bp+0), C_(-0x1.8b18d8251ec886399fc357ab26c9p-2), C_(0x1.863743274d78cfe42daf1d262e43p-4), C_(0x1.158087f14084ceb4f650d2c442e1p-8), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 3, 1> { static inline constexpr std::array<Real, 6> value = { C_(0x0p+0), C_(0x1.a3719cd426dbd5c2283e8b6cd98bp+0), C_(-0x1.1dcb0537f52904105ab1d13c6abfp+1), C_(0x1.19ae7cc6c0211df5e41745563cbbp-1), C_(0x1.69a5e70c6cb46c73632e8c1bb2d3p-5), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 3, 2> { static inline constexpr std::array<Real, 6> value = { C_(0x0p+0), C_(0x1.cef9cbb90bf242979b344cdd1e02p-1), C_(-0x1.b676b19591eb63e368ce734bad03p+0), C_(0x1.6ced632b23d6c7c6d19ce6975a06p-1), C_(0x1.8831a237a06deb43265d99170ff1p-4), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 4, 0> { static inline constexpr std::array<Real, 8> value = { C_(0x0p+0), C_(0x1.01d5e443d831d2252369827793d3p+0), C_(-0x1.15313c61b3acb474231dab078158p-5), C_(0x1.447d293e37264e578b865081223fp-5), C_(-0x1.817e96e0425ed094fa1a3a5cf10cp-7), C_(-0x1.3a0992ca5111744ed1b4ed1a6607p-10), C_(0x1.3be7b6cb6309fefbda0c9fa167f8p-16), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 4, 1> { static inline constexpr std::array<Real, 8> value = { C_(0x0p+0), C_(0x1.c6aca7b3a61af838bb320835a00cp+0), C_(-0x1.6486543c8460b11f1a4b4a357fbcp+1), C_(0x1.314491c6de2d2b798153746ca822p+0), C_(-0x1.0d0e14f1f7dc5a54f21ce3ff424bp-3), C_(-0x1.b6da96c702377f43a25f74c9467p-5), C_(0x1.d0194bee1a1742cd9ebfbba717b8p-10), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 4, 2> { static inline constexpr std::array<Real, 8> value = { C_(0x0p+0), C_(0x1.cf8cc69cc42a410e51b272a7a3c6p+0), C_(-0x1.0eaaa0c1e1c354610b35262e9078p+2), C_(0x1.66e46b718b500bb2be3ec05c7ac3p+1), C_(-0x1.26d9a4de19b73d34cbab42cdd8ccp-3), C_(-0x1.0ae7c18dd841d8689ede2f52570cp-2), C_(0x1.3a82a1b96295b447f46661fe5bd8p-6), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 4, 3> { static inline constexpr std::array<Real, 8> value = { C_(0x0p+0), C_(0x1.bb2f43bc30b80d947c8a537a20b2p-1), C_(-0x1.2d48b852668c646a630392a2b66dp+1), C_(0x1.c2596fe640cadf6ca968f3b30ff3p+0), C_(0x1.83800be8c4de9681c9e31925ce79p-3), C_(-0x1.233972e07202850d1be1b9fc8392p-1), C_(0x1.bcd16d394575254330d81aed4886p-4), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 5, 0> { static inline constexpr std::array<Real, 10> value = { C_(0x0p+0), C_(0x1.646bf1ec64a308c5df07d89c8e9bp-1), C_(0x1.cbd5c1bab5148530b0e77ecbff92p-2), C_(-0x1.754196833f706c7834855fa5579ep-3), C_(0x1.3100cab7c3f5f4fa75b80a67ed4bp-5), C_(0x1.8dd2be8c89c51e7b28b04315346bp-10), C_(-0x1.c4ab558ff2dcebdfdc6142054ddep-10), C_(0x1.3b27d2d798eecea1adaf099c04dp-15), C_(0x1.75f2b16626e9875840e692dcf344p-23), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 5, 1> { static inline constexpr std::array<Real, 10> value = { C_(0x0p+0), C_(0x1.8eee7927087b240ec5ade1ac81aep+0), C_(-0x1.37cf445237f1b72a99ae1be2616ep+1), C_(0x1.3c64475174b4a0c9b8a3ee3dfc2p+0), C_(-0x1.7841978e876db6599aa4ad10992fp-2), C_(-0x1.64d969ffaac153a6af06dc9cfb72p-6), C_(0x1.08fcfb4783fa7d234eba36053968p-5), C_(-0x1.5e1fef6185af966378a125175a7fp-10), C_(-0x1.984da1089743964ff5ac0959c3bcp-17), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 5, 2> { static inline constexpr std::array<Real, 10> value = { C_(0x0p+0), C_(0x1.22c5cb8d3f23b44faf592c365f5dp+1), C_(-0x1.83cca07a3ead78a73330d7cf1a39p+2), C_(0x1.5245172406b77d1d4fdfd2192d87p+2), C_(-0x1.2d10dba463fc1840fd45963c568fp+0), C_(-0x1.549f4c5e04f3991456e630b1555ep-1), C_(0x1.882ac9029ddc72b4c74d388da98p-2), C_(-0x1.3d5d0eda32d8b61e7ff27a395899p-5), C_(-0x1.65cdc06ecf6547344a6a8d527f6ap-11), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 5, 3> { static inline constexpr std::array<Real, 10> value = { C_(0x0p+0), C_(0x1.9877ac926fb3bdd992f46d848f57p+1), C_(-0x1.48c27a70b93cdddc043571f47b88p+3), C_(0x1.f7fdf60845cfba22e0c6bd043e1ep+2), C_(0x1.0b1ea0ee5f9ed06f5107d79a1aafp+3), C_(-0x1.15aaf38ada16a6358cd77355f075p+4), C_(0x1.4a45041b91e1bb24fe9a63ad188p+3), C_(-0x1.05013480812df4c7388d78daa7bap+1), C_(-0x1.13ee46114fd8519c5d7f29b7d91dp-4), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 5, 4> { static inline constexpr std::array<Real, 10> value = { C_(0x0p+0), C_(0x1.13b9e8c4fdc4ff9d9c7b93fda5d3p-1), C_(-0x1.e1e5e5cfd0a801f531eaef0fe6ap+0), C_(0x1.29ab2ec864d44a65c8f8abfdabb3p+1), C_(-0x1.3d6cc61e0f6a43e21f6553d10792p+0), C_(0x1.0227f72aa277daecfc1fddb3c5aep-1), C_(-0x1.9ada2a6a9a217e8dbe2b55c6bb8bp-2), C_(0x1.2c68da3893cd5c4c84ac50c60f2ap-3), C_(0x1.1a66dc6d2cfbf029033eb2e70439p-7), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 6, 0> { static inline constexpr std::array<Real, 12> value = { C_(0x0p+0), C_(0x1.bf65e79817d27ca7c78972c65f3p-2), C_(0x1.aa2466d50e4a4fcbbebe54f94c3cp-1), C_(-0x1.89fd104c6ff149bf7514a7ddf37fp-2), C_(0x1.24737e6f8ebf0ec8bb9fcc85bb71p-3), C_(-0x1.a1e9c758a51a08321aa63e9af1d7p-6), C_(-0x1.cec09a7ccf05b6ee1ea8f3c17f4ep-9), C_(0x1.cd4feb82d24938f30e41e1af2eap-10), C_(0x1.05937b8388af24ac43ec83967a2ep-16), C_(-0x1.5a00cfad970a7cbc309138fd3facp-19), C_(0x1.0fbc42c672231485a0bcbfe7e34bp-28), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 6, 1> { static inline constexpr std::array<Real, 12> value = { C_(0x0p+0), C_(0x1.2faeacbb8e753b40eb856e00f522p+0), C_(-0x1.8014975295b2136d5a1adb454387p+0), C_(0x1.05033635f5401c9b60636a32526ap-1), C_(-0x1.0ffe44cc8bc7ea4a6ce4734d8d36p-2), C_(0x1.0b11b28c7d67ad63229fbc3aa7dap-4), C_(0x1.721a1d14b8322b2431432e8b800fp-7), C_(-0x1.af662c52c3b7ae55063672df3c7fp-8), C_(-0x1.a69b860b67a33179a8c7a5f6b2acp-15), C_(0x1.45b12643cf8203bdf796367d51eep-16), C_(-0x1.01892163486cb41cb64453f7616fp-24), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 6, 2> { static inline constexpr std::array<Real, 12> value = { C_(0x0p+0), C_(0x1.1e62ddd540b05b0cc5ce587007d5p+1), C_(-0x1.980b3fe2011f7bc878be7d399794p+2), C_(0x1.a34dea8cd59b4187717c6efb0662p+2), C_(-0x1.45eb5e5e7e3c9e9ae26ca4aa207cp+1), C_(-0x1.0310f5a5d86de60ba877dea685a5p-1), C_(0x1.da7724c65802bc95482213f980a5p-1), C_(-0x1.4137cfe85b9e5b04e10239758a3cp-2), C_(0x1.7eb866ddca6ba425f9e4eb854a4dp-6), C_(0x1.4ebb22d1ac0760e1461881059843p-9), C_(-0x1.0c5bdfb916a449da5acc3ccfdc72p-16), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 6, 3> { static inline constexpr std::array<Real, 12> value = { C_(0x0p+0), C_(0x1.422f9f5227e7facaa94dd7d9e31p-2), C_(-0x1.255a76df553cbf84e8a0b0613039p+0), C_(0x1.484b537c56deca3daefc656e3b6ep+3), C_(-0x1.3c98d8a74cd7736b60af4e604261p+5), C_(0x1.10b7f9c607064185ab2dfc58353fp+6), C_(-0x1.d54dd14cd31af65e5343fc875b57p+5), C_(0x1.8049478b6740d0c6b010047a06c3p+4), C_(-0x1.77f8847acd28ad3549099ae2105ep+1), C_(-0x1.d3687a3bc39335bac7f281e76bbep-2), C_(0x1.816ef86832621ebc63e47cd2b70fp-8), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 6, 4> { static inline constexpr std::array<Real, 12> value = { C_(0x0p+0), C_(0x1.8faeef62b3a7fd26eb98dd7f984ap+0), C_(-0x1.93816e52ba1c8483ff81ea3e324ep+2), C_(0x1.337880b3a9a717e67b9cd7fec812p+3), C_(-0x1.c3f2cd3d53132aa78f87aee07639p+2), C_(0x1.c7801db7678046e8ebdb22cf642bp+1), C_(-0x1.46377db27f624959a2b9b7777bb1p+1), C_(0x1.77a6f5e8321cd39a930db39033fap+0), C_(-0x1.c4188733407f241acae534ed0f5dp-3), C_(-0x1.f8b0a606c7f795229d5947447836p-5), C_(0x1.b965933f534b1af276b67227f89dp-10), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 6, 5> { static inline constexpr std::array<Real, 12> value = { C_(0x0p+0), C_(0x1.cb91942378a6b29e2dd51c51bfa9p-2), C_(-0x1.e6b982120ca31c68b89329c09872p+0), C_(0x1.7b2e4714b270342ea6ba899785ecp+1), C_(-0x1.fa645ee8ca231003817fbe32a47bp+0), C_(0x1.29da9349c32a19bed5b810cc4b88p-1), C_(-0x1.8461e6acf9cb2af90934d76c7932p-2), C_(0x1.67c137342024d6c8052e3d876acdp-2), C_(-0x1.c1a09b7773a59d1a65f356773daap-5), C_(-0x1.0c11f4efd5c0b7d44ac1c3a0720ap-5), C_(0x1.0ac90a45b7a47759a7a92738fc7ep-9), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 7, 0> { static inline constexpr std::array<Real, 14> value = { C_(0x0p+0), C_(0x1.033291a6c76d6a2177301a6491e8p-2), C_(0x1.027f6bf7952cdbcf397ade5b83ap+0), C_(-0x1.919d92c6034c44a7ed45a578713cp-2), C_(0x1.7a0ca906acc4841a1191b023a485p-3), C_(-0x1.1142c3515ec433047c393c69962fp-4), C_(0x1.50e2d6421ee2654230b309723685p-7), C_(0x1.d0243aab613f83777184da54a80dp-10), C_(-0x1.1d4c6c249bf0ee08cde9105ae0e2p-11), C_(-0x1.17d0b3032ba5c5edbe3115298755p-14), C_(0x1.310ffd8b564011dafec30497e547p-19), C_(-0x1.509d126dab99ceafee21c5b15f2ep-25), C_(-0x1.57f8e6955253718d03dd42dcc06ep-36), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 7, 1> { static inline constexpr std::array<Real, 14> value = { C_(0x0p+0), C_(0x1.9ec434341eaed8ccc6e8d7244a33p-1), C_(-0x1.ca0692ca77439e8f752ca148c144p-2), C_(-0x1.2d988a986b0dea756341b6b8b7c2p-1), C_(0x1.145887eacb10f9d392eed69a9335p-2), C_(-0x1.4ab3cf0bae2a5b8432a0a181639cp-6), C_(-0x1.4e8938899ee371e40cd7b7528ae9p-5), C_(0x1.5cb5de436bfadb9e555d33c55719p-6), C_(-0x1.051eebbefaf7bd71954e297a61ffp-8), C_(0x1.0efaec65edbcc11b181ba7073e2cp-14), C_(0x1.6a87a6b931edc5ab5423dbf1babfp-15), C_(-0x1.4e8b2a27fe064ec01f627183042bp-23), C_(-0x1.54fd8f0625f118cd9bcdded88d81p-33), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 7, 2> { static inline constexpr std::array<Real, 14> value = { C_(0x0p+0), C_(0x1.e0eacca617ebb860573873f7b1a4p+0), C_(-0x1.5362d7fe36c56b6a443e9d6141a8p+2), C_(0x1.70aa17b7adc0e75a9ffe0b5a33b6p+2), C_(-0x1.86bc52429f3a3f79bb4f1cb73763p+1), C_(0x1.5709310e8d1f635f77e733f31613p-2), C_(0x1.9d599937b31fafd3d66db2bf1cbbp-1), C_(-0x1.18b244e50df675a487d76601b0e9p-1), C_(0x1.fe16d1a3cfb3e7ecc6834f2061cfp-4), C_(0x1.eb4cc917dd1cd56dce6a9280b03bp-12), C_(-0x1.4e09cf12f0cdcfd873bae5583582p-9), C_(0x1.c4a78957d279804ccd5115f6146ap-16), C_(0x1.cb0ccbca08e7961d7bc2f676b666p-25), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 7, 3> { static inline constexpr std::array<Real, 14> value = { C_(0x0p+0), C_(0x1.4ca9343b3236825367445e2a7e79p-1), C_(-0x1.492e70f2635c16c262e6190afacep+1), C_(0x1.171de5ca88cec2afbea5499914ebp+4), C_(-0x1.1e704d84a10750732762c3f4d8bap+6), C_(0x1.23bcc34d6a529b0b422faf672516p+7), C_(-0x1.415156a34428a6a6c08cde7dee49p+7), C_(0x1.7ff7929036ddd78bf54cfc378272p+6), C_(-0x1.a43b4147c122c6f143d7b591007fp+4), C_(0x1.833e6f5afaca4c566ce598593c06p-4), C_(0x1.13b5aaaf6c71d5b914583e48ae7dp+0), C_(-0x1.6365af2495a86c5f48d9bd1a47dp-6), C_(-0x1.64d19861a833792a3ce80f84d83cp-14), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 7, 4> { static inline constexpr std::array<Real, 14> value = { C_(0x0p+0), C_(0x1.525f0cb11c2720485c66b9e19f02p+1), C_(-0x1.7eda4b6a23328f4e2cec098f6666p+3), C_(0x1.578437542fe4f5fbe4cefec73f0cp+4), C_(-0x1.40c582473fa8c93703a1216d1613p+4), C_(0x1.9815cb7223c105bc2b63ed01a5fep+3), C_(-0x1.222479cd96ee9d17f59bff4df592p+3), C_(0x1.8c2cccc6ee34ca0f24458389d35dp+2), C_(-0x1.ffd4fb5b3918044492967474d1cep+0), C_(-0x1.3be427404fe7d12432d600f4382ep-3), C_(0x1.7c490d447fad2e27fa6b12a0d504p-3), C_(-0x1.23f9756392d0ee9915448c1be2b1p-7), C_(-0x1.1f66b1e7815295f48755fd4e3126p-14), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 7, 5> { static inline constexpr std::array<Real, 14> value = { C_(0x0p+0), C_(0x1.80a316d21a0eed480c84ea711d9ep+0), C_(-0x1.ce7e6827143677fbd12dabe06e9fp+2), C_(0x1.ac8b3ccd718c41df56b9c167f638p+3), C_(-0x1.74c81d1a27df5c33454de2219e89p+3), C_(0x1.4010d1eedca99cac8148c11888d4p+2), C_(-0x1.34da807d2aaec910bcf3aa770bf1p+1), C_(0x1.2d09c9846b581b01a4323f49de6p+1), C_(-0x1.97de12ea03ca10913f6e6b1c03cap-1), C_(-0x1.9df5b4fe2e271a26f87f7a1f78fbp-2), C_(0x1.16c54a229aae12ed509d340bab6bp-2), C_(-0x1.e323c5b92bd166e33ab5b4f9635p-6), C_(-0x1.c9a573f22c19a9032c5430df4c8ep-12), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 7, 6> { static inline constexpr std::array<Real, 14> value = { C_(0x0p+0), C_(0x1.a096c8f7fc8ab1575820ee7a8d4ep-3), C_(-0x1.01d8c748e11fa735da05e73f8394p+0), C_(0x1.099a073a7c7b41898468a5bd14cep+1), C_(-0x1.40ce386ca776e06ba6f31ba7dadep+1), C_(0x1.2a57634989c51fb583fc11fc2c8bp+1), C_(-0x1.e6f030cb23fbfde6dfddcd33a7b8p+0), C_(0x1.3544c2755b1d82eac792a5860a61p+0), C_(-0x1.6af581a622d416ac06a3c40b5b79p-1), C_(0x1.256afda077267e050d8164debfb4p-1), C_(-0x1.6569331439297d46e21a065d5029p-2), C_(0x1.4b88409bdd1172b9682df8963184p-4), C_(0x1.24061e2653bdb3c5fd153e823b33p-9), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 8, 0> { static inline constexpr std::array<Real, 16> value = { C_(0x0p+0), C_(0x1.184a0c288d22add7ea26104df2f3p-3), C_(0x1.fbaa047a94a613069e6f550b4e09p-1), C_(-0x1.596f5b6b28cb0681bf78a3e54b72p-3), C_(0x1.234875f46000e28dce7c3f342092p-4), C_(-0x1.90a568ef3b94afacf755834bab9ap-5), C_(0x1.82b42ea0f8a1613dc5ff9725c05p-6), C_(-0x1.96b60b10e59567d6b2c6577bad3bp-8), C_(0x1.8430d19335684e7577fd3b699763p-11), C_(-0x1.92df0230079088d5ad0746147153p-14), C_(0x1.da6faa767962723e71f08f2e9083p-16), C_(0x1.b237bc2c3b5257b1d937078b7396p-20), C_(0x1.66eb1a28068ae3ea1bd5d2683257p-25), C_(-0x1.f6ebd7398c4a3aa441e024a5714bp-33), C_(0x1.5690727034a8a4b1353895ae261dp-45), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 8, 1> { static inline constexpr std::array<Real, 16> value = { C_(0x0p+0), C_(0x1.03033f41d994757a2b4934423538p-1), C_(0x1.8347da7a3030b8b37cdc36ec3c9cp-2), C_(-0x1.7d2f17f2a95af6988be8eca125f4p+0), C_(0x1.c3013eaebde946f9eaa42bce8cf9p-1), C_(-0x1.4be40ed86f2cd0c168ad249492a4p-2), C_(0x1.4580356ca34ff1cf3c18408b1d74p-6), C_(0x1.7e9e8eefc30b45959dcb8ab52383p-5), C_(-0x1.594cf912461bb959724fb77ad3bbp-6), C_(0x1.27c56651be6ed873712071c19324p-9), C_(0x1.e972a09b0f4dc8fdb93114f9ed4p-12), C_(-0x1.1649ec5e541409b8483ac00aa989p-14), C_(0x1.c99c42a59648ab096d412a58741fp-23), C_(0x1.81519dee82f001d0cfd286a4bf1ep-26), C_(-0x1.06b5ee4f0711fc96e3337209d4e2p-37), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 8, 2> { static inline constexpr std::array<Real, 16> value = { C_(0x0p+0), C_(0x1.666d532df9def8a39e69d4c9dbd1p+0), C_(-0x1.c0374596ee4d8e750b0b0f065b11p+1), C_(0x1.a43eb9f4500c29913bdae70f2e12p+1), C_(-0x1.d627359f84d250c8825852fe20e7p+0), C_(0x1.891e36789053a132cb4397963bd6p-1), C_(0x1.a23c19ecf2deb44f4177f3e9336bp-6), C_(-0x1.d9c16d05d77872764189280b3978p-3), C_(0x1.b6728d569b4c6b3f03c9c20fd79fp-4), C_(-0x1.66849bebd2ebdfafabb131375ec9p-7), C_(-0x1.fc6301aedca903a123de4bceca69p-9), C_(0x1.7e62ae52149bd7e06a18746f5b91p-11), C_(-0x1.2c21c0130a3eaea0bd3721b2b8d6p-17), C_(-0x1.15f344e8ed1b26069acbf2a1a453p-21), C_(0x1.7bbd836b1bf84d53feb61580dc74p-32), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 8, 3> { static inline constexpr std::array<Real, 16> value = { C_(0x0p+0), C_(0x1.b44c4e267cbb4d43745305f720c9p+1), C_(-0x1.c1f7df3ad7ab79897dce80d62718p+3), C_(0x1.1601a8a979c78f82e398ce8545b9p+4), C_(0x1.e5bffb29b3c52bb885497a60d3d6p+3), C_(-0x1.38f35bf0e9ee0ae5b1772951f4d5p+6), C_(0x1.d1869b3f8e2b44288688d26e70d1p+6), C_(-0x1.70d2038145a54625eb25d875d7e5p+6), C_(0x1.34930dde67aea02e0a703b76a197p+5), C_(-0x1.4b77b4fb3674956338abd1824db4p+2), C_(-0x1.d27f3b25c1fd6ce83b2a8b0a4ac9p+0), C_(0x1.32a2c5a3dfe8119d379b71453288p-1), C_(-0x1.2fc64ff8d3420e31f2a6dd47d615p-7), C_(-0x1.c48021ad9bc1646021c012f5b071p-11), C_(0x1.364c0a7c4c64aef45189b312edb4p-20), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 8, 4> { static inline constexpr std::array<Real, 16> value = { C_(0x0p+0), C_(0x1.afe05c7a6ada1cb6172616d2c6a8p+1), C_(-0x1.0a8c44cdd47bf4e495a5398413fbp+4), C_(0x1.0f6c0325c5e1414a9285f59e5f14p+5), C_(-0x1.306ff1c62c8336aad5c3f9886bcep+5), C_(0x1.da69559cc91130d28dd4b63660e6p+4), C_(-0x1.6a2c1f828fe2d81030f1ad524eb7p+4), C_(0x1.0e28c771588c30581ce7071741b8p+4), C_(-0x1.ee4b3cc46d890789fa8b15b7da8p+2), C_(0x1.050e3e4d4732a1c55c0c971f3557p-1), C_(0x1.0ea6cad7a5a7fae2eab7d74b22a1p+0), C_(-0x1.6566f5ac7d80487971d04a5944efp-2), C_(0x1.0b828ad29e43eb178f6b65b8f31p-6), C_(0x1.3201b5c3bc1c21bf7086981ccb12p-10), C_(-0x1.a6f0242017b1488503cf0ef046e5p-19), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 8, 5> { static inline constexpr std::array<Real, 16> value = { C_(0x0p+0), C_(0x1.77885e6e270a744c868654d7cbb5p+1), C_(-0x1.f5abb22b1b6ebb333fd9f11e8f7cp+3), C_(0x1.0a779dee6c7bddbff2f0d8b9981bp+5), C_(-0x1.164d9f148bde4aa13b66fabbc2fp+5), C_(0x1.2333738e736f124a0ec3de563f7bp+4), C_(-0x1.af306993826a689f7543995893acp+2), C_(0x1.6dba5c59397a4426e98586aad789p+2), C_(-0x1.17ffc928dd1d8bf0f209d0c36abep+1), C_(-0x1.9f39e7400cf5d234f22720c7748ap+1), C_(0x1.d0d0a8f3b805dafc2d2b539d9bb4p+1), C_(-0x1.4ac5cadf9fb14bc48382ff0ecfb1p+0), C_(0x1.049faf6ae689948e66d5e5134564p-3), C_(0x1.5ad3792bdac35c5163486d9087edp-7), C_(-0x1.e6e9a51e36639d68c6db7d7495a4p-15), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 8, 6> { static inline constexpr std::array<Real, 16> value = { C_(0x0p+0), C_(0x1.1912b6ad90d43603284e290418eep+0), C_(-0x1.85c00c80d7a18fcc693e47644de7p+2), C_(0x1.b7d753e3c818997a04ded98f86e3p+3), C_(-0x1.076d50e7f7850b94ae780b4bf285p+4), C_(0x1.92a29d7ac0e1e0002558af869ed1p+3), C_(-0x1.20f516098425bb22664ce4ad84a9p+3), C_(0x1.dcba519c323cedf78dcb7794def8p+2), C_(-0x1.3fe31292805c0462ca96ae20fe5p+2), C_(0x1.5e9b74431b072dba61e526c0393fp+1), C_(-0x1.a6996ae95f76ef890f12b5a6c626p+0), C_(0x1.806826de1640aff2fbfd8d0d7d09p-1), C_(-0x1.ddc83de4acfaf20be5fee513819ep-4), C_(-0x1.e09e81650c6b74fbce41e5378d99p-7), C_(0x1.5c5b71613d71b7692e7e5f0ba23p-13), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 8, 7> { static inline constexpr std::array<Real, 16> value = { C_(0x0p+0), C_(0x1.eae80165a34ad1f2080107f7b7a5p-3), C_(-0x1.5a965a7535366541f0a1afe5172fp+0), C_(0x1.851adfd49d1a76d9d23c35315fc3p+1), C_(-0x1.b139c010d5d8ef58fb69c4f0efd8p+1), C_(0x1.ffefb7038043737a18fc832f1fb7p+0), C_(-0x1.0254056f57103b364cf4bcafdd14p+0), C_(0x1.ff103b26e087e22aa6dbe2498954p-1), C_(-0x1.7a4f70cc2f5d7a6d2a4e62aee34dp-1), C_(0x1.09dce627745a61500e9471981ea7p-2), C_(-0x1.c2f7ce5c8a37b8fcabdaf25d6d6bp-4), C_(0x1.41c46b919c33ee1c6941aae7132bp-4), C_(-0x1.03531c096423a7a88f95e3dc08eep-6), C_(-0x1.c24ed1e998c51356546e2437d6p-9), C_(0x1.5d1ed72a09587166cbb2e531d26cp-14), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 9, 0> { static inline constexpr std::array<Real, 18> value = { C_(0x0p+0), C_(0x1.1d2fbfac23949a1e129ec9f8391bp-4), C_(0x1.b1b6520101e0e6c7ddaa9da59f23p-1), C_(0x1.8b08d5cd4a2ad4b181244736a713p-3), C_(-0x1.4aef16c7e666f719f7698e178af1p-3), C_(0x1.fd1877f1138be38ba53889d724ecp-5), C_(-0x1.7ee87092fa242b1ef789aaf8def8p-8), C_(-0x1.09758849af60512fff4fa06073a6p-7), C_(0x1.3d3ef7388a3ade9f5adf4b3f580dp-8), C_(-0x1.29147421d57112477f4b7b3491f7p-10), C_(0x1.b33acccf47f1bda17f46b8106497p-15), C_(0x1.7e6498cdbddd4dce209effce7062p-16), C_(-0x1.53f9494edf1282277c1de6dc67e4p-19), C_(-0x1.58c1d88e09b30b0364784ebc1f68p-24), C_(0x1.278ba12dc249a4cd49c8d69ab623p-29), C_(-0x1.705a7a4d83450688cb9e189ad73ep-38), C_(-0x1.4fb4ee678fa0e1946f2bc7ed6f9ap-52), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 9, 1> { static inline constexpr std::array<Real, 18> value = { C_(0x0p+0), C_(0x1.2b90f770700937399f9f525fd17p-2), C_(0x1.af96b810375ae30c4c41bf8dddd3p-1), C_(-0x1.d3c16b16ba8799042d28d9c49845p+0), C_(0x1.1690032de8cfad91fdf041ea0eb6p+0), C_(-0x1.1f4f37268ff73d0393fe0f67790ep-1), C_(0x1.82c9256a70f8e96c68d16f2e3327p-3), C_(-0x1.540e9bea7c732170245209a302fbp-7), C_(-0x1.49841c554fed1d5f2443e15a5a95p-6), C_(0x1.96a364065f27ccd19657d67cdf64p-8), C_(0x1.0c49493de5a6ec95d0bb4c3aca89p-11), C_(-0x1.b592fbb7be41b5e92f003f6109fcp-12), C_(0x1.9d3f09be0cea6d8d6f8ed455255ap-16), C_(0x1.8562af0388b7df01536ccb66a5b4p-23), C_(-0x1.13cc2e0d34f2575dd283b068f4bap-24), C_(0x1.2234e02ed8630c149658a9630026p-34), C_(0x1.08644a120d1ef6f0d4b961ae1879p-47), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 9, 2> { static inline constexpr std::array<Real, 18> value = { C_(0x0p+0), C_(0x1.e4c00e361fc67a2e12b083b2df48p-1), C_(-0x1.aad6ffd5d77f153c17f1c8823935p+0), C_(0x1.135c57711e67099c1758b9c717c8p-2), C_(0x1.5b41454ff095722d0f803ea68127p-1), C_(-0x1.c92ba77b267a297500d5b5d44785p-4), C_(-0x1.4f00ea2c2d363149504e045fbe84p-2), C_(0x1.61aa479f9dc67b53226c771010fp-2), C_(-0x1.667619426289632c2e8907dc1851p-3), C_(0x1.7235017b58d31cc6ca2ab84f7b8bp-5), C_(-0x1.85c5f4a449272d8bf24d90db58c1p-10), C_(-0x1.2bb318efa4d23587f50785ea34e5p-9), C_(0x1.b3d73e818e5c9557fa6b95207f02p-12), C_(0x1.bca3f26f194cf877e2358ca6efddp-17), C_(-0x1.261d8947cb7277733f476ea3b7dfp-20), C_(0x1.36693a4632268e426c40140353cep-28), C_(0x1.1a9906065291eec094ff6b8172d8p-40), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 9, 3> { static inline constexpr std::array<Real, 18> value = { C_(0x0p+0), C_(0x1.27d6df36685a79598b6c86ce474dp+1), C_(-0x1.2ded79e41fdb0c43d1210e12de17p+3), C_(0x1.e79fd7c0b1c0ebd84f460885ecf3p+3), C_(-0x1.304a1a210a5f9ce8bc8b8a0cdf19p+3), C_(-0x1.effd2573aa9aafcb53e588a096b7p+2), C_(0x1.7ce72fdc2cb91189ae6d5e090c6bp+4), C_(-0x1.985f0196c72e53e6d1cfdee84e02p+4), C_(0x1.d3cfac07a9d2a8c51198c074937dp+3), C_(-0x1.e1a24f8472a680b7d24d058147a3p+1), C_(-0x1.9b8563bd7c7d7dc5768ba3df017ep-2), C_(0x1.fe4766e3faf53b0d124828083686p-2), C_(-0x1.73f12d4155f35b3e8452b4ff00abp-4), C_(-0x1.20dddf659ee509c6befdf1c7addep-10), C_(0x1.ffd28fb3400bf45efe5c328fc188p-12), C_(-0x1.fa83788d3f78d19a901b7477bae6p-20), C_(-0x1.cc794a76e5f165fc8108c92b057bp-31), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 9, 4> { static inline constexpr std::array<Real, 18> value = { C_(0x0p+0), C_(0x1.c7ced0f66aeaccfcda16588f9d75p+1), C_(-0x1.2ab8c9c81252e46b55777de43246p+4), C_(0x1.4df684dede46d3a014591fcfc934p+5), C_(-0x1.af3bf949d62b9c07b05b4ac4bf21p+5), C_(0x1.8eeb17bed133c367f65a67fc6e9fp+5), C_(-0x1.541e9c27826e49d24f626bb1a338p+5), C_(0x1.12ea47c60dec043f14d3664c7b9cp+5), C_(-0x1.35c8b07214e140ed7f1d446f3113p+4), C_(0x1.d829e1a7628821bc837255b88e76p+1), C_(0x1.69d6e9c20f73cb2d14ff7351adb6p+1), C_(-0x1.0235621854eeef97bfd3d4e3b1cp+1), C_(0x1.b423243b8b46906701ef92e0fa6p-2), C_(-0x1.2e290398a3fe2fc8cc3aebacf78cp-8), C_(-0x1.22b4e2598d44b0dd2f4a293dacc9p-8), C_(0x1.654cdf573874b672ebfe3509d857p-16), C_(0x1.43e711e67867252f78e7e45afce7p-26), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 9, 5> { static inline constexpr std::array<Real, 18> value = { C_(0x0p+0), C_(0x1.1617a4f9d885755cd3477307254fp+2), C_(-0x1.94d9c534a28d3ee0a8bf210cb612p+4), C_(0x1.dd0eb6aa76ffda42c87706ac442ap+5), C_(-0x1.168c0447c1b6e90c330602b02462p+6), C_(0x1.24c19c047007f67f0d2fc486ec63p+5), C_(-0x1.016a68491e4d871ca5058cc8b9fbp+0), C_(-0x1.c94ed28aba0f51cc92c5b4dc5aacp+2), C_(0x1.669c08c9522f315c7b041fb5fb05p+3), C_(-0x1.88dca456f345655b7cb4359a3262p+4), C_(0x1.b958d77e385a9163a2eb3b4f73aep+4), C_(-0x1.eccebab605f4b2d725512d8939ecp+3), C_(0x1.f4375d664ce342e4e51867996bcdp+1), C_(-0x1.2ade5d60c45811382f7ff19a5bd5p-3), C_(-0x1.491f178ce56460d544cbe167fd8cp-4), C_(0x1.5bccddec65e53c1b0416c330319fp-11), C_(0x1.398367062ce373b6810676d67904p-20), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 9, 6> { static inline constexpr std::array<Real, 18> value = { C_(0x0p+0), C_(0x1.3841475e9a3639fcb27c2a85a863p+1), C_(-0x1.dd3c5aa19c52e5c8a273f6da1b5ap+3), C_(0x1.303529a28e46fac3a8f56ea5a2b3p+5), C_(-0x1.a86d9ebb6edc3ca33aa7af7132e4p+5), C_(0x1.7d0e6c4e24170b40a4b9574c4b78p+5), C_(-0x1.25c8439d2df89fa5007905a011dap+5), C_(0x1.f5b3e1ac9966686ed844c7042856p+4), C_(-0x1.815ee05c85e8aa704180612d3a88p+4), C_(0x1.ca4482f4236a5516d7f638f2b575p+3), C_(-0x1.050825dec75a966028608d12e5c4p+3), C_(0x1.1eeca8acc3a791ffedf80be8793bp+2), C_(-0x1.6df69657c972c8ebec75c924bb61p+0), C_(0x1.75a7ac677c4eee273d03fc609c7dp-5), C_(0x1.ebd49f3810c888c69855752e166p-5), C_(-0x1.4344372e1b6fc786ddf90f275fd2p-10), C_(-0x1.20264586c6bb91b0aa0b4d170d57p-18), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 9, 7> { static inline constexpr std::array<Real, 18> value = { C_(0x0p+0), C_(0x1.041f759e862aa2196b99e32b0e5p+0), C_(-0x1.96fe795439508b28db4265486c81p+2), C_(0x1.04a7fd5b5e5923f7f627bd6af411p+4), C_(-0x1.5c5ede521aae5e58438f3722aadep+4), C_(0x1.0b593b29c51bbefd0a21a469361ap+4), C_(-0x1.3ddf512850559b028d83098aa4f2p+3), C_(0x1.12f0bcbe3fa44419a6b52304dc22p+3), C_(-0x1.d4ebfbf56d99633e38e5753902fdp+2), C_(0x1.d31827f76dc61557ae5c1ea99bcdp+1), C_(-0x1.6bf237312f18cf3b573ffc6eb123p+0), C_(0x1.d1d5c0ac4dc0c7147f916f90f5c1p-1), C_(-0x1.794e93c6506dcbe26714d9f89e44p-2), C_(-0x1.2e59e90e0a11c8b7ce9f9105aca7p-6), C_(0x1.26fbfe966bb82001d50ae928dc43p-5), C_(-0x1.e662faa96110f417469ce785ece9p-10), C_(-0x1.a81802ebf94f0a8bc8124e2acfbp-17), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 9, 8> { static inline constexpr std::array<Real, 18> value = { C_(0x0p+0), C_(0x1.9024e0f887aa33deb80194db4775p-3), C_(-0x1.3caa56e1c68f9f7ad07fd686ffdbp+0), C_(0x1.947e636a9e373f489450f999fe93p+1), C_(-0x1.033a79f260cef0d616212b14afddp+2), C_(0x1.51b6c9e0d0443759a67a3c3505fdp+1), C_(-0x1.0bd62fc1e045579c86e940e51c15p+0), C_(0x1.028bee5b6619ea0406791e99a571p+0), C_(-0x1.1620d9bfc03eb662d8d654bb6c17p+0), C_(0x1.b5ef819dccd9a27cb2716f32a404p-2), C_(-0x1.b7954b06be8aeb961960232f51e9p-6), C_(0x1.054d18d1cc90c79a1ef036069b3dp-4), C_(-0x1.4817258dd284697ebc00b788ccd7p-5), C_(-0x1.8ce86e181d4254ae37719aa28183p-6), C_(0x1.2926b8981e2a739eefaa1e5b0722p-6), C_(-0x1.20ae937e7a9305bbde13268a4994p-9), C_(-0x1.e260b0ee2a092f8355b87bfdf959p-16), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 10, 0> { static inline constexpr std::array<Real, 20> value = { C_(0x0p+0), C_(0x1.12cb0a33640b56e423474a1328bap-5), C_(0x1.4e2c27be21e0e479b88ad4851607p-1), C_(0x1.1c4636ef189eccc399682014d9d6p-1), C_(-0x1.85d2edb33e46dde58a5a504a9ab1p-2), C_(0x1.9e3dada7662a9865be6b99b24294p-3), C_(-0x1.494bbf8e53bfc023fe7e0915ab63p-4), C_(0x1.1d23df75685c890f2df5ab229b96p-6), C_(0x1.d4ed15a06848811344377f87f7eap-10), C_(-0x1.2885ec240634157f42540c2ec5a5p-9), C_(0x1.94f202846521b8fb6dee9352c088p-12), C_(0x1.44e94de53f6f632a67cbb5854d1fp-14), C_(-0x1.b37df99b75f08af621654dd8f54ep-16), C_(0x1.403905df41d323c0c33072aaf3cp-24), C_(0x1.c94370d7ecc9194547661e1cf7cp-24), C_(-0x1.58dbb791a7fb6c3e33eb2a850b1bp-28), C_(0x1.db358382953c45bea25d9891f3bcp-37), C_(0x1.afee7cd299cd64600d2193c416f4p-44), C_(-0x1.0988745ca3ec3e945e33c4d42e22p-59), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 10, 1> { static inline constexpr std::array<Real, 20> value = { C_(0x0p+0), C_(0x1.43cfcb9d739232114ccf7b42f286p-3), C_(0x1.f5f9c20090df2cd39669639ec7fdp-1), C_(-0x1.94bc27297b9f96d98ca06b8b780fp+0), C_(0x1.61584eb9fe3a67acec590408bca7p-1), C_(-0x1.a2cb67ff996a90130726bb551867p-2), C_(0x1.eef0eaaf4989e29be4ba95e2f12bp-3), C_(-0x1.ac22308c89e820172f07afea77d8p-4), C_(0x1.c84ec23c8cdbe0f0d252ca4a5fdap-6), C_(-0x1.213456d8479d5a0a002e8a35424cp-8), C_(0x1.2c315a17e4063f457d1b74aaa54fp-10), C_(-0x1.f375455c5c9e61be4fa670796c8cp-12), C_(0x1.ce035ff90a79b6418f9714e02027p-15), C_(0x1.06ba9aa22e87c46e9b5b517bf9e8p-17), C_(0x1.2eea964fb1e803735b7cbdec445fp-21), C_(0x1.f125f98e34b07ec90a3117922ea9p-26), C_(-0x1.51db791710be9863d69c55fb8f8fp-33), C_(-0x1.3ced9d37da5d28d7002692ae731fp-40), C_(0x1.85b82452d92694835d294f84ac62p-55), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 10, 2> { static inline constexpr std::array<Real, 20> value = { C_(0x0p+0), C_(0x1.2d6cb779664d44484073db45447cp-1), C_(-0x1.01b00cc8d5d0650bb7d9e8758312p-2), C_(-0x1.0fd0995df5aa2a4c5f39f93180c2p+1), C_(0x1.8bd77a675e82837408b645325bb2p+1), C_(-0x1.c8684eac579b3e1019c502de8594p+0), C_(0x1.6e6d859b2e72f80278552877464cp-2), C_(0x1.86e851ba85834ec58a127f16fe28p-2), C_(-0x1.9dcbe6db3790670c84be0eec2f7fp-2), C_(0x1.55c762fd5a0df64b9c06acd53195p-3), C_(-0x1.35a481158ac33b4716b6e91c5435p-6), C_(-0x1.51b88ceed7addc9a97168ddbed49p-7), C_(0x1.0767285c8f10645316c4c221fa2p-8), C_(-0x1.67961ae7bb99fbfcc0d26144bc53p-12), C_(-0x1.2b4a0836ed60ae3a1490ad53cc1ep-15), C_(0x1.bb4b6c6c9a6faf8c7dd84be23c4bp-19), C_(0x1.3f418b80d3d44c3e61fe90bb843bp-28), C_(-0x1.0d99c100eff2e6c61779a485054cp-32), C_(0x1.4b9c0643323fb1c0ce2d07b0b092p-46), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 10, 3> { static inline constexpr std::array<Real, 20> value = { C_(0x0p+0), C_(0x1.a8dadfc02dd0428b41cd0c1bb0afp+0), C_(-0x1.8d688d31d04a4214094b65c4cddp+2), C_(0x1.317cc4a10faf3ff9c44aa07180dp+3), C_(-0x1.00fa12867f49132d26f6109f1a1ep+3), C_(0x1.9e984b48af59218135976f585487p+1), C_(0x1.0dcc3bbac5e0885ef946fb573bd9p+1), C_(-0x1.41a435a1df480f6b501eca7093bep+2), C_(0x1.075a464fd9703954dc501fa9230ap+2), C_(-0x1.9984cb75bad50ddd23b7c6a931c3p+0), C_(0x1.9cf2e7196d1cbd2ef1ba36ca5473p-5), C_(0x1.c915787e3612e2d3277f4d8526a2p-3), C_(-0x1.60b8b0c3b1138df4716646253571p-4), C_(0x1.324229742ef4416185466d935171p-7), C_(0x1.dd5da666efa58ec47474db0b6e86p-11), C_(-0x1.351528a4bd8176153593c8a5a1a8p-13), C_(-0x1.03c4250827b68f69b983f4479114p-22), C_(0x1.77139f17861eb1acd308dc031079p-26), C_(-0x1.cd96fccfe9f0afba4ba09dac3a7dp-39), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 10, 4> { static inline constexpr std::array<Real, 20> value = { C_(0x0p+0), C_(0x1.a04f8069ea8b4e447d853aa2b3fp+1), C_(-0x1.18f0a34d9f68e4d06a24b5c8413dp+4), C_(0x1.4ce3831796a61ef6af32be9a023fp+5), C_(-0x1.dc75f9b0b9a1041da91933762b9bp+5), C_(0x1.fdbc97313e6ed6865f9096ac8807p+5), C_(-0x1.eefc0cdda4efa281b21fc89e970ap+5), C_(0x1.b92a7c1b6a889c31c867c0ce8c52p+5), C_(-0x1.2299d502734c3c9b7e4c9a6f523fp+5), C_(0x1.6502b707871df45089990b5055fdp+3), C_(0x1.11f33f4ede647d59a412fb3857a3p+2), C_(-0x1.73b0a319e6889e9aa2e82f2679b8p+2), C_(0x1.244d452e7630092d6c490c8cc448p+1), C_(-0x1.35466c5650c61e120220d045b2f3p-2), C_(-0x1.fc20c8dd92f19b8d6ed30b1d9872p-6), C_(0x1.0d9c8b9d476f7d129de2a5d13304p-7), C_(0x1.a4010b80e5495d0ed9331140ed28p-19), C_(-0x1.49b0c99eb9c648511ea730b4e4dp-19), C_(0x1.962a6dd57b7daa6dc5023a314835p-31), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 10, 5> { static inline constexpr std::array<Real, 20> value = { C_(0x0p+0), C_(0x1.55886d2f64380baeb961078fa176p+2), C_(-0x1.09d95f1cede31fcd15d2c7fab39ep+5), C_(0x1.505f98e4bf27766f2f4d3b7ea8ddp+6), C_(-0x1.96ec354b303069fd664614786911p+6), C_(0x1.17b23075f8010224c348afb3ebb9p+5), C_(0x1.fc17211fa4d6f3f6a32616561c88p+5), C_(-0x1.b35f4a36b31c3849a4f062a53c98p+6), C_(0x1.d17f22f2480f88bf1a425e0d999bp+6), C_(-0x1.12118c5678b4d442de8a0eef777p+7), C_(0x1.207a74ca5ad8bfc2ee103b7bf96dp+7), C_(-0x1.934735f943481c7f74f56dd5b187p+6), C_(0x1.3fa55ba9206e3812ee32da2442b6p+5), C_(-0x1.959601005ec548729558e21c9eb1p+2), C_(-0x1.9505e84d98e613cfe4ec3f6fdae5p-1), C_(0x1.43d2632e32cd0df0bb4a95d727cp-2), C_(-0x1.38e017336cd0614a6ed2ffd943cap-10), C_(-0x1.968e83ac595b8c6d9c172a00fddap-13), C_(0x1.f5ed4b124df3ad0700a32c86e4bbp-24), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 10, 6> { static inline constexpr std::array<Real, 20> value = { C_(0x0p+0), C_(0x1.f3cda2f9b135402362018230e37ap+1), C_(-0x1.9eeda12641b61ebb7d840ecfaa6cp+4), C_(0x1.260fdaadd19eb1efc078d7fded1bp+6), C_(-0x1.d673d80eeade4a070ce0e7052e5ep+6), C_(0x1.f01b2fa154d0352990b16aa70967p+6), C_(-0x1.addb2c4ad791e217324c7aafb066p+6), C_(0x1.7db87bda6fdf8a74bb08213b9495p+6), C_(-0x1.3f9860f6c4905e7132b1781ae693p+6), C_(0x1.ae731643e9198e621648583330d8p+5), C_(-0x1.fb5cc3351ebc176988bf6478c6bp+4), C_(0x1.259afcbb8804d6eae552ab39c09p+4), C_(-0x1.fe186e460309fdcedab5ec38f6a8p+2), C_(0x1.4d0298c21892754606c3d8ebb24fp+0), C_(0x1.a1f0a66406a122ae435ed98406f7p-2), C_(-0x1.40c0addfd85543af466cc7de08d7p-3), C_(0x1.ba72fac37f087c7aee39dd6d7d9ep-9), C_(0x1.c193f16bb678e5af6510cd4d8f9fp-13), C_(-0x1.16b4995bb4f073263c20b5b2b14bp-22), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 10, 7> { static inline constexpr std::array<Real, 20> value = { C_(0x0p+0), C_(0x1.3586d9a9e0e3d99d2b93a01af7d5p+1), C_(-0x1.08fa63342ecc1c41a46b365c4c22p+4), C_(0x1.7c41f01d6960cbda171d22b314bap+5), C_(-0x1.276b64d22e134fe39031785d1e73p+6), C_(0x1.14f1cf74869c077b4ddd600b6793p+6), C_(-0x1.83d54ac636b8244258f1e3c9d507p+5), C_(0x1.4053c8a2c8d2fc6aef1621e8f43ep+5), C_(-0x1.209b538b18df262448ee3cebbe29p+5), C_(0x1.65783340b3782c7d703e94b54e85p+4), C_(-0x1.2ddf670e51dfca7d85e8eeab11aep+3), C_(0x1.38744fdae212579791ea9e59ba4ep+2), C_(-0x1.4065c212ba5c0456783637741afcp+1), C_(0x1.6763c5d11b774e2d99bb54d3a752p-4), C_(0x1.181d4d676ea1f03e7d8c57b5965ap-1), C_(-0x1.87564028831fbd4eb29dad95b0cfp-3), C_(0x1.843d22529bb49b17cf15d645bef3p-7), C_(0x1.52be3b0b8c7af55af9d914b56a01p-11), C_(-0x1.a79c626c8654ebdb591ae5793d64p-20), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 10, 8> { static inline constexpr std::array<Real, 20> value = { C_(0x0p+0), C_(0x1.7a3cf471120ec198713994eca41fp+0), C_(-0x1.48b25e52d274b1e47c8864a7164p+3), C_(0x1.cbd93276e7d596419b912da6ea19p+4), C_(-0x1.37885d5242030806d66e5cf9cc78p+5), C_(0x1.4db4fb7a5ecdb9227e8824c1b905p+4), C_(0x1.74ac2dca21f55bb24886b2e8488cp+2), C_(-0x1.11ca2f9f0b7d05f1c16189874d5cp+3), C_(0x1.9fa6aaf0c8d980502f82ac3f1ed7p-4), C_(-0x1.8ceb3288570cd32c25919a739d51p+2), C_(0x1.e686e3fbc3fbf35811a68b06fad4p+3), C_(-0x1.7e0b780d60231a4c786ec3f17781p+3), C_(0x1.7e1a3482e160bfcf5bb1945be474p+2), C_(-0x1.247b57131543bcbee8b05ee74f53p+2), C_(0x1.b8a4e1c96768c895a2f3649c4cc8p+1), C_(-0x1.4f17d502240a8e6f55c9dea2c968p+0), C_(0x1.4b408438ac8689521da23d7beaedp-3), C_(0x1.7264788c9473dca575636b8d6c86p-7), C_(-0x1.d74fd6a021547c7f9f7dd044fd0ep-15), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 10, 9> { static inline constexpr std::array<Real, 20> value = { C_(0x0p+0), C_(0x1.f6438a3a88460091e0ea8516e904p-4), C_(-0x1.b7ba9255f9c77a442c3315f3c4dep-1), C_(0x1.3f509b3842148b5acdb05dfc7ebdp+1), C_(-0x1.eac616f0d4f869be16ce06d469adp+1), C_(0x1.ae9244fef585d2a56f1cb69c0c8dp+1), C_(-0x1.00d5d03220f3bbc8a51448aa67eep+1), C_(0x1.9413f3bab26fc85ab60692eb482fp+0), C_(-0x1.9bd9847a10dd537f2de875e0ae85p+0), C_(0x1.16aae27d18a67638fdda8c9d9188p+0), C_(-0x1.1587682f48215c21c42b36d23f1dp-1), C_(0x1.8145e3cc3cfcbcc409c895dd9662p-2), C_(-0x1.faf556e68970db4f5325d20bccb9p-3), C_(0x1.8ec972676b06aaf4a1909e5ab3bfp-4), C_(-0x1.49980ed40883cadc7b702f6c3e9fp-5), C_(0x1.5730c48bae56a4ea4426b047bab7p-6), C_(-0x1.0952d6b855c638b977457b4c3a4p-8), C_(-0x1.ce071dd8df1eee9d16331f022e54p-12), C_(0x1.30a4361eb25b38fd9207742aba25p-18), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 11, 0> { static inline constexpr std::array<Real, 22> value = { C_(0x0p+0), C_(0x1.f82d860ed311d7772f0a5fc02a6dp-7), C_(0x1.da87adf545dea36f29603c50206cp-2), C_(0x1.a074ea6831a179cbcefe13bdeb26p-1), C_(-0x1.d3dbc22db33632cb9d3eeea93097p-2), C_(0x1.07dc8c4b588098d99d74923fef1p-2), C_(-0x1.17e06a0deb06ffc5a354422c2913p-3), C_(0x1.d85300a8e9a59db3d8e328544719p-5), C_(-0x1.0710616766f9db787dd78480360dp-6), C_(0x1.0182a0c9a44ba81f2b490da87cf1p-9), C_(0x1.d91cd19825f46395eba40bde2534p-14), C_(0x1.f2bfaace30f58a825ed0b3a11e2p-15), C_(-0x1.d7e9ba7b3ac4736029b548526137p-15), C_(0x1.5c274e2e04a6575e26e75abeb4c3p-18), C_(0x1.63562e1b18da7fac5905b88575e8p-20), C_(-0x1.0af5800900ccbea5a647053aa052p-26), C_(0x1.1409cb495cfaa9cc50f1fb279896p-28), C_(-0x1.1601287f207dc804b32b2b372befp-35), C_(-0x1.4f944d6c974a0ba10244cbd7bf57p-42), C_(-0x1.ad914b3b9c6449c459a4d882621ap-53), C_(-0x1.65d8440cb5909e7eb82f547cb81ep-70), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 11, 1> { static inline constexpr std::array<Real, 22> value = { C_(0x0p+0), C_(0x1.4988f615d8fc2101372678651696p-4), C_(0x1.cd9786f046dbd06d9795ae5305eep-1), C_(-0x1.f034187a5d75333e9dbb5b1046e1p-1), C_(-0x1.075e3bcf1d71f31524cf997afbe8p-3), C_(0x1.303436308c600230256305532d57p-3), C_(-0x1.71d07ef81053ea5196f6a9c9ea93p-12), C_(-0x1.321c6b5970b994e47d89204a7726p-4), C_(0x1.0f00f0747578208709a35dbb5672p-4), C_(-0x1.fec807d6bcde2f6b9da93df4aa6dp-6), C_(0x1.092c0960e80ebe73a0fb5f592a81p-7), C_(-0x1.1857810566102a80b03f6d57486cp-11), C_(-0x1.693105a2bb706882bf9e39158aa2p-12), C_(0x1.a2acf3b1f9d0749452e4dc44d918p-14), C_(-0x1.c4d81f25bbab666371fdd702fceap-19), C_(-0x1.e0284772a21eeb07c87b76642d8fp-20), C_(0x1.7db784c0b013093ad9874c402637p-25), C_(0x1.739c15dc80c555f970d134b64517p-30), C_(-0x1.d9433a2520a2e30f13e7c351f17bp-36), C_(0x1.651bd505e5aaae5cab5b708f20cp-46), C_(0x1.29782f98b98d8b31230d837a9eccp-62), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 11, 2> { static inline constexpr std::array<Real, 22> value = { C_(0x0p+0), C_(0x1.5c07e5083d7090314f404490267fp-2), C_(0x1.307a2a8e783ea1f99bb361a3ce3fp-1), C_(-0x1.a41fd4c6e53047b890408086b518p+1), C_(0x1.08f3303fd9b5f02cbec87edc442ap+2), C_(-0x1.6a2a8758fd08bb3ed6b347424cecp+1), C_(0x1.5f04ae9c9034ab19fcfae00d09b9p+0), C_(-0x1.150c77d31565d35edf80240e5e1cp-2), C_(-0x1.78ed1cb9b0ec1e760990f81b60f9p-3), C_(0x1.4f99902d11603738023acee050bdp-3), C_(-0x1.41156e1c846c464a303629e298b7p-5), C_(-0x1.6c5861062a83616dee9275c18c97p-7), C_(0x1.21e04958552e6f03502dd7935724p-7), C_(-0x1.cd1c35ab2ad92bf156188522c5bfp-10), C_(0x1.af6480e4adc46cb9e0c7649b6f56p-17), C_(0x1.0136c3fb4b19b9b10157d7a834f7p-15), C_(-0x1.6928b0e495d07fb474aad6800549p-19), C_(-0x1.6377af73884bfae0ae8534a7569p-25), C_(0x1.64323c063686a79e3f723a6f6b93p-30), C_(-0x1.6fb51174aa8e375496c635af829fp-40), C_(-0x1.32449da1b960881894abd2226adap-55), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 11, 3> { static inline constexpr std::array<Real, 22> value = { C_(0x0p+0), C_(0x1.1c297e1a722977a767a1ff227742p+0), C_(-0x1.a72bc3c00615f73ba93716b01e65p+1), C_(0x1.8e98178e99b31d46ae26eec0b1cap+1), C_(-0x1.8f506e2a5e0eb5edc0313f13b62bp-1), C_(0x1.02364935e2222846b9cdda1bc87p-1), C_(-0x1.0fb2290536b31f2a2fbff3404bbdp+1), C_(0x1.80597d49465bf4c4d8869fb534fap+1), C_(-0x1.38ad9781c750136475272cd6e902p+1), C_(0x1.339d144fd9550bb8463b544a6643p+0), C_(-0x1.08b97b33caecc76a026ab8335d28p-2), C_(-0x1.3f8a268debfb77a1cde76d550fe7p-4), C_(0x1.2b8bd1a4fd0eaf4aaa08a96cf3ep-4), C_(-0x1.35b764060a713cc242948b5c4153p-6), C_(0x1.f33a86db42465a05a6ee3ed1f4ffp-12), C_(0x1.1c307da269dee355c5c2d340dfe6p-11), C_(-0x1.950dcb7c8e981d2c1ff88549cb89p-15), C_(-0x1.f904916865d4cb30ef383c46ae0fp-21), C_(0x1.8b6cb6bf7586b0f4f1fcded4430cp-25), C_(-0x1.21dedfd7476c5553241f507ac2d7p-34), C_(-0x1.e2c7778c519a040a7c97727ee351p-49), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 11, 4> { static inline constexpr std::array<Real, 22> value = { C_(0x0p+0), C_(0x1.51d8dbccf9206bcc4420e8d9ae07p+1), C_(-0x1.c33b049bfbce5ed995e58045194fp+3), C_(0x1.0e79522ccf3dd0b86ea89a5531bfp+5), C_(-0x1.9aba40cee29c09f71dc38c35a548p+5), C_(0x1.f144c4df7513d73b0fd71dc9df3fp+5), C_(-0x1.17ce56ad9d9026c80fe9053e3b69p+6), C_(0x1.1abf8d1adcc3e5071c7209bb8006p+6), C_(-0x1.aeeda88b7fe87fd16bcf8e054d05p+5), C_(0x1.6d1975fc2f42e1b2096263c969bbp+4), C_(0x1.64c18afe2844c60255dd74d07edbp+1), C_(-0x1.4b3d36d8f9770ee95e2721f907e9p+3), C_(0x1.8e75251a7f5bee7754c2a9513fecp+2), C_(-0x1.9e20d16541319f6d732cb61c018ap+0), C_(0x1.8f713f264dac28b16bf91d504bd5p-5), C_(0x1.002e9aac591974da848a16c844c8p-4), C_(-0x1.22b5d07d79f24f7de83980b5ed9fp-7), C_(-0x1.695b63166e6d63ad77759faf33b7p-13), C_(0x1.ba1b21857af82fb76bf4742957f6p-17), C_(-0x1.df066d7576ffcacbc6c94f3c14p-26), C_(-0x1.8ec06f9de2f7d48618cf3f2e0232p-39), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 11, 5> { static inline constexpr std::array<Real, 22> value = { C_(0x0p+0), C_(0x1.553841cb8504c59ec8828722c9cp+2), C_(-0x1.1648a261cfac86a07a577122f4eep+5), C_(0x1.7429c31b8bcdc777e06851df4ff3p+6), C_(-0x1.d2259be1a7818ecd1bf98b71d684p+6), C_(0x1.36cbd86221f4c1c381302622675ep+4), C_(0x1.4a282d1320ed73864b5c73d42965p+7), C_(-0x1.2e04ab290e2e062d6018a7405d3cp+8), C_(0x1.5f18c6755ba04a0fe5846dc7ce5fp+8), C_(-0x1.80bbefefb89592a7731263e58b6ep+8), C_(0x1.90ad4b61c673e71a7b1a638ff4cp+8), C_(-0x1.4159e0e62036c0e7d3a9372888dep+8), C_(0x1.4eba06db33d52e049a499539c59ap+7), C_(-0x1.6db5a82568a43d359e1324f88c7ep+5), C_(0x1.6613709f48645b09020d1137193bp-1), C_(0x1.7dbb7d4fa2b472146ed131c42bb3p+1), C_(-0x1.1851a9519e35d94904835e4c0f44p-1), C_(-0x1.230c93cadc0b78607a6df63dd398p-7), C_(0x1.7e95e283d8ce34ce8180e79a24c3p-10), C_(-0x1.136d2374e371184371f11564efd5p-18), C_(-0x1.ca2f0f4b750065dbf1a91e494693p-31), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 11, 6> { static inline constexpr std::array<Real, 22> value = { C_(0x0p+0), C_(0x1.43e579b56aec6db8f44fad1a2ca3p+2), C_(-0x1.2015783789a1305c4b04f4299082p+5), C_(0x1.be9eb07640a6e4dcf71e8edd1986p+6), C_(-0x1.917bfbcd50104121d7cf2e5fb61ap+7), C_(0x1.e7564ac670464ea6f5bb03253324p+7), C_(-0x1.dd46b6e14bd993fb7d27e4be31d5p+7), C_(0x1.c24b2cb18bb303674bf661030f65p+7), C_(-0x1.9299f7098407dc40f69f41f42557p+7), C_(0x1.2da088f392f175bbf1502b058265p+7), C_(-0x1.7f74fc0a8fbbbd2a662926cc0952p+6), C_(0x1.cafceab55c22225d33d140f11ba1p+5), C_(-0x1.cfad0a751fefca13c3b326a88e5bp+4), C_(0x1.f4f5eade96653abb41ce93f1a983p+2), C_(0x1.14b6d949957a5646a550369bc7aap+0), C_(-0x1.5e908a00f74d9f8f6b65d286f0e6p+0), C_(0x1.1ee7d490234e22c547ade0704929p-2), C_(-0x1.1e667fbdaff187310b0173bcb94dp-11), C_(-0x1.81c4231f27f23e6bc64b0c2f2493p-10), C_(0x1.28216d550397d430f8799924705dp-18), C_(0x1.ebdb45ca159a64fa9f199a16a149p-30), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 11, 7> { static inline constexpr std::array<Real, 22> value = { C_(0x0p+0), C_(0x1.0e918e0751a5f26d66d326215241p+2), C_(-0x1.f54b1dc71e94b922c8b7d974b91p+4), C_(0x1.8cc935a5962f326b8767e9c68e69p+6), C_(-0x1.5d87f4fd9af883e7ca8f85ba9a3ep+7), C_(0x1.7fbdfc1f5c92ac9439f72d5fc5fbp+7), C_(-0x1.356154b8ce2bfbb26ff26135d3d6p+7), C_(0x1.00a2f00b6f35fbd2365b8c4d7e4cp+7), C_(-0x1.d61ad68084631dc5b1cb350d96d3p+6), C_(0x1.4b192d7116369fcf46bbc7590d76p+6), C_(-0x1.2bd7eeccbbd8b3529c9ec7ea0986p+5), C_(0x1.d23af72a9213134d138ab79fb28fp+3), C_(-0x1.a5a3f6309aca858b5548cc51629cp+2), C_(-0x1.0097ba319005f0b824ee39f7e25p+0), C_(0x1.29abec5ca24e481b150656fa7b24p+2), C_(-0x1.6d63c669ef72a15dead10bbf465bp+1), C_(0x1.521b96f1f011ffd834fe0c4deb25p-1), C_(-0x1.89a1e9b6409a39917b2558fc77d9p-6), C_(-0x1.cc0f8b0b31975b1da167d6d21402p-8), C_(0x1.9e94a90cc2ee8162e5d90cf2df7p-16), C_(0x1.5739a9ee6eb1c850a9597f22010bp-26), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 11, 8> { static inline constexpr std::array<Real, 22> value = { C_(0x0p+0), C_(0x1.c2a4ffe9661190c09a7af8b79479p+0), C_(-0x1.a9c9682497d4356cc97c7817608dp+3), C_(0x1.5bbb8c487ae5bb615e8e73227ceep+5), C_(-0x1.452573aebb3bf474bf24d5595fd4p+6), C_(0x1.91c80b52c3671525c3375a1dd5efp+6), C_(-0x1.84d65b83affb5ca97ccaf8b73947p+6), C_(0x1.678e1d36597adc53993fd96dab7ap+6), C_(-0x1.4933025bdb6895888c173cc7b2a5p+6), C_(0x1.14413c8e18075f1444cc540dc34bp+6), C_(-0x1.b51d99f6678421b18139d5beb61cp+5), C_(0x1.483818775e0cb14480b32b95042cp+5), C_(-0x1.a72562d5d8064b092b7bae77a4cbp+4), C_(0x1.e00e48c9f77143cec0c43c67669bp+3), C_(-0x1.1522f77734c2edb19342e41508e1p+3), C_(0x1.152961e6e0f56f5672007e36f948p+2), C_(-0x1.3d9d88a64fae43ec46db73db181ap+0), C_(0x1.3f1c58e4e2a682bc6ff059fa1f8dp-4), C_(0x1.b3efb441a4e1aa6b7bfceb788233p-6), C_(-0x1.baa159e67dd4ea14a46828d67fefp-13), C_(-0x1.6c2d94cde3ae1bef5e760e39de7cp-22), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 11, 9> { static inline constexpr std::array<Real, 22> value = { C_(0x0p+0), C_(0x1.480f31520e3f310c306bdafaf042p-1), C_(-0x1.38fe2f09aac57b92aacdaa15d1b7p+2), C_(0x1.f8f411bacc9f961bc5fe5499f875p+3), C_(-0x1.bc60c3b54f90a9241998e0192f5ep+4), C_(0x1.d3d44a6a16adb2540f6bfe5db93ap+4), C_(-0x1.536d6f833b66773a970214ff031cp+4), C_(0x1.0953a7a524aca913282b24103258p+4), C_(-0x1.0c0dca303e8e262fc9682f1cf736p+4), C_(0x1.af56b1534f29dd21b9240915b75ap+3), C_(-0x1.f628948ceff73b6d1ae732743415p+2), C_(0x1.3ef834c3289aa35b262757674e4bp+2), C_(-0x1.c75ab5e1afc75a2d9d28a11fcce2p+1), C_(0x1.cb38bb2c5f4bebadf622e599ec8fp+0), C_(-0x1.624785bf15dbe093496b9f1d5135p-1), C_(0x1.61b17ae5ff0c0c37a77be972ec5ep-2), C_(-0x1.0b62472bd3d7849095f6dced344cp-3), C_(0x1.c9b3ef0688e890b76d9f130077d8p-8), C_(0x1.7c528a3f2156c588899985294901p-8), C_(-0x1.0c4738028aec930d4308df6549ap-13), C_(-0x1.b40e785cb88086ef360909630572p-22), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 11, 10> { static inline constexpr std::array<Real, 22> value = { C_(0x0p+0), C_(0x1.8a25fe79d1c4ddac335be8819a8ap-4), C_(-0x1.79dddd860d2147a7416541793f71p-1), C_(0x1.2f92842080f0827925b022200689p+1), C_(-0x1.04a53246109b6b6c0d3ef73b505ap+2), C_(0x1.fbc727fc23eefb6381085fb0ea64p+1), C_(-0x1.2e8a4ebac6b5e49a84fad5dff777p+1), C_(0x1.96ff87cfe4cc502ebda973db1ba2p+0), C_(-0x1.db8c7f7bf2c3a242351f9975276ep+0), C_(0x1.8867eccd39d1aef372869101502fp+0), C_(-0x1.7019bc278ffc03b406b2ff135206p-1), C_(0x1.a30d20b4e67c690471d7cbcbb0dfp-2), C_(-0x1.7340e7a399e63a19859bd6b84d4cp-2), C_(0x1.68181929e64c530045ddd9e48ddfp-3), C_(-0x1.50a6f5e8f3b308d50e585f11b7ap-5), C_(0x1.8d3b211eb839ac11193734372a7dp-6), C_(-0x1.b7227d5381373569d6206c572353p-7), C_(-0x1.a3114fdf2fbc06953fcb9931063cp-12), C_(0x1.71e7a3b4d88bf16a9f3c256dd239p-10), C_(-0x1.4eea023db8bd4900ec558c766ab3p-14), C_(-0x1.09aed93888304346e30d148d3c14p-21), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 12, 0> { static inline constexpr std::array<Real, 24> value = { C_(0x0p+0), C_(0x1.ba5636194c0939c427c9ec59581bp-8), C_(0x1.3af72853b1890334601f92a1284ap-2), C_(0x1.da1521352f487f1b71f5ba208041p-1), C_(-0x1.5c6f665240adde3380bdc0aea438p-2), C_(0x1.4840a35a3e5076b07b9bb98536cdp-3), C_(-0x1.9d4fdc34ae4edcb2a06a461fd21ap-4), C_(0x1.042a86a360591d6b2ba9327c6214p-4), C_(-0x1.08554bd18ab256f6f2efbe750de9p-5), C_(0x1.86c905bef28a68962be82a3bfae8p-7), C_(-0x1.8785b403c86f6f7548c23ebef922p-9), C_(0x1.f00fc00fce26eee7a53c75fa9287p-12), C_(-0x1.43b7ce1fa4e5b162d9e05ba1624fp-15), C_(-0x1.dafa2eb6c7f5cbd9451ac8b8db32p-18), C_(0x1.2d678c174b94d04aa232fc24fe09p-18), C_(-0x1.f0554b8e5712d06e0273c8cb503bp-22), C_(-0x1.934a0de4da29338aed7c3945f15bp-24), C_(-0x1.3a5d95f1928eec0223d4d93358b6p-29), C_(0x1.0e0d2138861875f5d48c437e1957p-33), C_(-0x1.652333b327609e7169123d062941p-41), C_(0x1.02e74c07e60809b1acff78842ce2p-47), C_(0x1.bb358cf4adf4da69e5fa9c480499p-60), C_(-0x1.f67e04f08f2152aabe6eb786996dp-79), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 12, 1> { static inline constexpr std::array<Real, 24> value = { C_(0x0p+0), C_(0x1.3daa1461d0cf47fff25f3df963e7p-5), C_(0x1.716f56bac1b1102dab376b1a3fe7p-1), C_(-0x1.16bee9987071960277d4321df078p-2), C_(-0x1.f51bd9fa1cf2d9e12262aabd1401p-1), C_(0x1.97243be7bf08455883f653e158edp-1), C_(-0x1.b8eef0110c9fa4de8e71d38444bcp-2), C_(0x1.2402bce395301d2ffcfa2c7a4938p-3), C_(0x1.80595820660c8830537a9f5a0e29p-10), C_(-0x1.fa47fa3f4b021cbace01025dd941p-6), C_(0x1.025a88022a413b155a9680077b35p-6), C_(-0x1.3d712aaad77758afb71e5644bf72p-9), C_(-0x1.c5c0d04fc87430265835a2d868c3p-11), C_(0x1.c45b69075cdb62e0f0501d72eab3p-12), C_(-0x1.6a1670435bfdd529f00d82c5e437p-15), C_(-0x1.13c0d643a27dc3e64f7aa5ea1b1dp-17), C_(0x1.b2cff794384635cf6c5bd8331af5p-20), C_(-0x1.9ee90facd3d1333133d7e205e062p-25), C_(-0x1.c87e1185ca55b3b93aa74571695cp-29), C_(0x1.b076e966620448a8ccbae1de5619p-34), C_(0x1.71c42c5b1e646b3eaaa36a5a302fp-44), C_(-0x1.e6d8e5785ac9381d9a7b90929674p-52), C_(0x1.13fd176d0c254d2994cc4f8bbae7p-69), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 12, 2> { static inline constexpr std::array<Real, 24> value = { C_(0x0p+0), C_(0x1.77fed2e01693602fb84977597092p-3), C_(0x1.e1d10780fb06110288f8999dc16cp-1), C_(-0x1.9e9c7ce63835ce70bd9f1949b4bp+1), C_(0x1.bc153af50c24b9575bdc1b7eea9p+1), C_(-0x1.240fe3f248860f90966b383ce203p+1), C_(0x1.80cee17390c17dd6afdc8b5e9bd2p+0), C_(-0x1.abf5df7fd7abfb9aaab015caa888p-1), C_(0x1.50c7e71a108baf578aa06cfc537p-2), C_(-0x1.4654ed4660723ccc0f0acc159e52p-4), C_(0x1.091b1dd62c3e5f033d13bd90e92bp-6), C_(-0x1.59c475f85d7f3ec16b121b44eccep-7), C_(0x1.935e464b93aa450281cf24f671a9p-8), C_(-0x1.8fe1513629011cd322fa61848df6p-10), C_(0x1.90feb0894b434ddffdbc8185f2a5p-15), C_(0x1.09bd1f2d4e386644ae469eb863f8p-15), C_(-0x1.da6da6ad5e76b858534775753bfcp-19), C_(0x1.a3886fa6d48c5693a0b3ec42e08ep-21), C_(0x1.0f7850b94c92b737f20b8005c4e4p-26), C_(-0x1.63226d50629bfc487dd5a4e8ef38p-31), C_(-0x1.84d7e34db15d3108fdfa03f5836dp-38), C_(0x1.75cc98099352929e39911fd43962p-48), C_(-0x1.a7d23115de5731da90d3ce0c96c3p-65), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 12, 3> { static inline constexpr std::array<Real, 24> value = { C_(0x0p+0), C_(0x1.60087b087d2ef4b82953952d9084p-1), C_(-0x1.1c49e2797e56cac67a206b14e7b4p+0), C_(-0x1.f023b1706ef0dac15d9852fec6b7p+0), C_(0x1.8d30c07e51574352c1f1eb2006b7p+2), C_(-0x1.80e0de445b219fbdea6ef733a307p+2), C_(0x1.c1feac4e70c181d6b4fca6d1ffb9p+0), C_(0x1.3621ab0ea1b052aecf48cff7492ap+1), C_(-0x1.f3ab98611d47a796d9c546361f74p+1), C_(0x1.5e6794d526a24de36780aeb9efa6p+1), C_(-0x1.c702eca93a33cb508d7b1d00211fp-1), C_(-0x1.ee149aa686bb2faa29ff6d4bcf1dp-4), C_(0x1.ffde0ca5fc1a1519c08ba08ef931p-3), C_(-0x1.a2cbb989ecd0a0b85c48b0eeedfp-4), C_(0x1.d58bf4f6c76ea5b68a5554193d1p-7), C_(0x1.206affc103ba0a875625f4581693p-9), C_(-0x1.dfc88961f6b157e54f77890bbc2ap-11), C_(0x1.f86e53415f2a00da542f82562b56p-15), C_(0x1.28c920e4a3f6bb0fc001a36c54d3p-18), C_(-0x1.9c90e430666c8d48daf021826ab7p-23), C_(-0x1.7e8cf0898f3336a3b6d1b959b3ebp-32), C_(0x1.cc8984cca607f1a4cd24395b33dcp-39), C_(-0x1.051a1f819156ba9bc5cb80611a1ep-54), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 12, 4> { static inline constexpr std::array<Real, 24> value = { C_(0x0p+0), C_(0x1.efa01fe281c907b167ef08b2a819p+0), C_(-0x1.34df3dac7fcd3f885ed5b13d2111p+3), C_(0x1.5961138d5be957877d8cfd1f8beep+4), C_(-0x1.014d7a672544a1c4d790253c77afp+5), C_(0x1.5a4b6fa251eaf90e3115b0c8a7d1p+5), C_(-0x1.d72d9b409f2b1bb94911072e35d5p+5), C_(0x1.1a6ca7d65632cc9e3b88e527a77dp+6), C_(-0x1.f8d9ef0a2890c5946bb98eca1feap+5), C_(0x1.142ce1c1f06e19e0c6f07b093cf5p+5), C_(-0x1.90f390767ce4703536c74e99b357p+1), C_(-0x1.822b1a96e2d91cc911472934db6dp+3), C_(0x1.52a34d125b1be5508a31d4593a7ep+3), C_(-0x1.0b934a511e088d9de4577e6b9d58p+2), C_(0x1.335fd67def29efb717b66730db11p-1), C_(0x1.17c48a3b6f0b811400fc04e29772p-3), C_(-0x1.0033850ae88073da0780e3e4b1ccp-4), C_(0x1.68d4635bbce683527c347878fb17p-8), C_(0x1.b6ad0e03e206f2cc34c3ad57b135p-12), C_(-0x1.c361dbb11082ba0b86af7e7039cep-16), C_(-0x1.d59d4ba004a567edb22672d12e01p-25), C_(0x1.f6c8c69c71b982736f46aec1c2fcp-31), C_(-0x1.1d186572e3d30ab58425e9b0d124p-45), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 12, 5> { static inline constexpr std::array<Real, 24> value = { C_(0x0p+0), C_(0x1.1672f76c48a3b085a419d3d84efep+2), C_(-0x1.d05e83fe81471c548c37702884afp+4), C_(0x1.49fc051fc99a825862e53c41bd9dp+6), C_(-0x1.e442104e65335b30f1932ff3fcdp+6), C_(0x1.09c52f838d2fca1c275b6ba1ca01p+6), C_(0x1.677b64cbf326e55bcfc76402e361p+6), C_(-0x1.fbf39786bea7b138ef97d391fb5cp+7), C_(0x1.628081b6fdd810aa965a5c98d2cp+8), C_(-0x1.a2714ddd5c22b603c83ee77be92bp+8), C_(0x1.cb4de777b4f362d79e6f05e8e906p+8), C_(-0x1.9cacd3aee3a7e296cd71908c1c97p+8), C_(0x1.055f4806a834671e4070618a5f49p+8), C_(-0x1.8ddf94a470b86c5104b74cbf3618p+6), C_(0x1.95561c2d77ea7cb1b418f1ad675dp+3), C_(0x1.8ab9cc38b4948a55522c2ec1bb2ep+2), C_(-0x1.6e4f007cb3f6f6544bd7c8aa8418p+1), C_(0x1.43d7023213a802dd64335ed45bfdp-2), C_(0x1.951cff21de4ac7e4a1f0a692a613p-6), C_(-0x1.5137c147339bc2af2a690f130f2cp-9), C_(-0x1.3e3df8b2da2752dcb7f745d4f5a7p-18), C_(0x1.78040f51a9567ebaa0b6d793cafp-23), C_(-0x1.aa8cd8e6f8971ce4ff33741ce32dp-37), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 12, 6> { static inline constexpr std::array<Real, 24> value = { C_(0x0p+0), C_(0x1.6688e31cf50e0564efea7c707539p+2), C_(-0x1.50ba2688bc0430a9ee7461099f42p+5), C_(0x1.18d5fc503a1772d2730b3ea50efdp+7), C_(-0x1.16422099d0e700c2cc83b554b1d3p+8), C_(0x1.7cdc33f38c2d168782ab512e0152p+8), C_(-0x1.a2f3c3b8e6e4ab101396a900d9eap+8), C_(0x1.aa319d6af6ec967e381e232c3d8cp+8), C_(-0x1.958a02a1024489567edfcd9f60c3p+8), C_(0x1.4bb5b15c50a647500af490b1348fp+8), C_(-0x1.caa9291eb011f2ccec525396312bp+7), C_(0x1.1f2d7abf22a7296277eac06229bap+7), C_(-0x1.3b920d0f7e0d09abc1f29bae2433p+6), C_(0x1.bc14b21b62b9334a0ec0723419b6p+4), C_(0x1.8c237a0fa26d7404976151e77cdep-1), C_(-0x1.7f694c35d9d2245677a758a1954ep+2), C_(0x1.3f67e104a689bca4d8d6dcd2113cp+1), C_(-0x1.4cc6c058f371d1d7aadbd425ad1p-2), C_(-0x1.6b557354b8d84aa675e72eefd888p-6), C_(0x1.38d6e371bb0518c7efdfa510e3cep-8), C_(0x1.260d95329ea8e0edce58683df434p-17), C_(-0x1.5c7911e0053bc1a14fff7c706e19p-21), C_(0x1.8b88d3fa551bf844985173c27b89p-34), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 12, 7> { static inline constexpr std::array<Real, 24> value = { C_(0x0p+0), C_(0x1.80f665163dff60603105460968d1p+2), C_(-0x1.7dd2228ef04492e49ffcbc26de51p+5), C_(0x1.48b0d88030936751bd070f0b70d7p+7), C_(-0x1.41512ba753d055c75dc8c75f4172p+8), C_(0x1.8f56f07493ef05c30063bd380daep+8), C_(-0x1.675a39773b2485da34f83484320cp+8), C_(0x1.2e9626a21624df1cdd8e35d51165p+8), C_(-0x1.1263590aebe88d200657c008c834p+8), C_(0x1.9699942af2221429cba47418cbf5p+7), C_(-0x1.59e9b6e0b9c21128db1641974871p+6), C_(0x1.09d1a0b7c583242c5ad30248e848p+3), C_(0x1.cc8ab1005087bf119ad7a75bf51cp+3), C_(-0x1.93c8d5094509572acb009457fd8ep+4), C_(0x1.013c24badc62703530bdc2a89abep+5), C_(-0x1.784654bbd73679c9f2def5413da7p+4), C_(0x1.21acdd98ca7e3a8d97a584ca3cd3p+3), C_(-0x1.6fa583815aba1a21d8ba9c3f6b87p+0), C_(-0x1.39156fe5f0a3b45977f7c9849262p-4), C_(0x1.34372727b2154e0f63382ce7b14dp-5), C_(0x1.c53d49d19717546a3333946ded1p-15), C_(-0x1.57bc52155abea4723bbb438d51fep-17), C_(0x1.869c11b6398bbfee9ec137b2aadp-29), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 12, 8> { static inline constexpr std::array<Real, 24> value = { C_(0x0p+0), C_(0x1.d573db31c98a592a2b6a796753f8p+1), C_(-0x1.ddfb9c5686a4efd2bd1e36073e0cp+4), C_(0x1.a873c238f1ad89ace04b7607dff2p+6), C_(-0x1.b2204de17a53a3315364d57fc2b6p+7), C_(0x1.23910ebcbe60d3ac86902adcdaa4p+8), C_(-0x1.29c6cec6860250c0db3c6f8b8962p+8), C_(0x1.1c64b27b4c107ca71ade24985867p+8), C_(-0x1.156985f5c8bce6de73bf23e5601fp+8), C_(0x1.ef2b60fc7ce315a6b8de2d939461p+7), C_(-0x1.84734ae811782beee80a7af9899ep+7), C_(0x1.20e874beb6697ebef627268d4461p+7), C_(-0x1.93d454c0120c50c5e5f45ca0c342p+6), C_(0x1.e8c645d5034483f58d32c0b8709p+5), C_(-0x1.0a8b2e2c06173020781b6687242cp+5), C_(0x1.14ef6d11452bbb05715fcae8f362p+4), C_(-0x1.bab6f3f4dbb55284f9925c8a3ab9p+2), C_(0x1.4e6aaf12e910db6611cb145f554fp+0), C_(0x1.e57ecc0ee730e09fd58c293b9a01p-4), C_(-0x1.0f174cea8c305d809bddd1a456bfp-4), C_(0x1.a1f2dc12ec55c96d12f54fd03177p-12), C_(0x1.4002914419fbb27ad65f422d91cep-15), C_(-0x1.6c7e600f14b10472b7579cd8544fp-26), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 12, 9> { static inline constexpr std::array<Real, 24> value = { C_(0x0p+0), C_(0x1.d2f4e044749b4e7a1c71b105042dp+0), C_(-0x1.e196df480fe71bea5cbbf6f938ep+3), C_(0x1.ab061d20276f0750e2a72080d7a9p+5), C_(-0x1.a7b259e6037ebf7c8e2adb89e41bp+6), C_(0x1.04d3977e22f60f45b515e3221088p+7), C_(-0x1.c308c46a51aa08f31731ad9b7844p+6), C_(0x1.759cb70549060301bbf1ea932595p+6), C_(-0x1.73a4db524ebc2efdc465e09da17dp+6), C_(0x1.4d02e405c663ff8abf63f28cd74p+6), C_(-0x1.c4dfc682dd95df4b0a54f646c034p+5), C_(0x1.217c835a844bf319c913aad35977p+5), C_(-0x1.9d3e5e5e092523c01057547d3214p+4), C_(0x1.eced01c912f6c17b1d536b46140dp+3), C_(-0x1.ab15772777a65a90ae2d7ecf56cbp+2), C_(0x1.780b7892927c5280dd5bee9ee8edp+1), C_(-0x1.59e4e79f9d38488dc3c59417b41ap+0), C_(0x1.04013ac7f90eca1ecf033aafa30cp-2), C_(0x1.63e903ad632e7f30307040928615p-4), C_(-0x1.26b339b06c46eff13165e32f7c85p-5), C_(0x1.1fc083a0e2c35a300d5c6fbf948ep-10), C_(0x1.9c18e59aa15ab3ece464b6468819p-15), C_(-0x1.d792baac952f2e4df120dee003e6p-25), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 12, 10> { static inline constexpr std::array<Real, 24> value = { C_(0x0p+0), C_(0x1.19eec26520f7247ef7c6a243923bp-1), C_(-0x1.249f95db3c6a85ee06007305aedcp+2), C_(0x1.0297dba66cdd344c6014ab433b38p+4), C_(-0x1.f4e8dc0eb78aa7eff1fa727c9c71p+4), C_(0x1.1efd1b3c60e0b36de4fe266b9d8ap+5), C_(-0x1.a397a05a5f774f4ee2078a58f21cp+4), C_(0x1.239464bf9e82c4fc4fdd79af7e82p+4), C_(-0x1.3946d065739beaad7a01650a25b9p+4), C_(0x1.2898316e66a7f2a70e1a6a12eca5p+4), C_(-0x1.5bb8e2c4642782930886e32d2ea4p+3), C_(0x1.68255c99ba4c6b07d82156e3f9d9p+2), C_(-0x1.21aae7ae7df31c29928804e58d84p+2), C_(0x1.64fab317448fb0474311942daf3fp+1), C_(-0x1.75b64c97e09686a5bb55f9818d82p-1), C_(0x1.22ff2ac4d8b9c4ff1397fddfa477p-3), C_(-0x1.07ed621dcab476dea8f9bcc8470ap-3), C_(-0x1.4a01e6ee0860d89681b645bb0864p-6), C_(0x1.2e7cdbbc900312ead84b8d7e757cp-4), C_(-0x1.b7f6865bae122ce58cd5b4105bcap-6), C_(0x1.17b65cad3d540e056708b80ca432p-9), C_(0x1.910e0462410b5b96ed51c4c46ef3p-14), C_(-0x1.cf434a44d45d4684dfb9a827c309p-23), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 12, 11> { static inline constexpr std::array<Real, 24> value = { C_(0x0p+0), C_(0x1.a6c51bc471a3098c7c3ba4b2e396p-5), C_(-0x1.b8315371d42a542d22b52e160edap-2), C_(0x1.89e13c889a74c808a95f3ae5db18p+0), C_(-0x1.8aa497719f070f6dc765c7af4f82p+1), C_(0x1.eb2b7ee2bc88d2eef92b780b6136p+1), C_(-0x1.a91739cfcb4374adc78a339981b3p+1), C_(0x1.4e87023b22be1f061884b91ff276p+1), C_(-0x1.31bb74af8ae4dfa54f812e36b5bep+1), C_(0x1.0e1263d4463c809bd8442e6ab9d2p+1), C_(-0x1.9cd0db1b42b96cb6927f614da713p+0), C_(0x1.3cec213a53551ad84004d758bdadp+0), C_(-0x1.daf35f59b2441d717c1690c25188p-1), C_(0x1.329c321d7ff6b77198e76070d6c7p-1), C_(-0x1.8936ae8cb907bb56ce7124a40ebp-2), C_(0x1.00dee0f339229a14bdfc063bfb91p-2), C_(-0x1.07bd180d959690eaf41df5a4ee44p-3), C_(0x1.cec01fe9b05f624125be250b50a9p-5), C_(-0x1.e6ef9d5209f879f2bf7a379cfa32p-6), C_(0x1.8f4f47250e3a4f324676c24519f5p-7), C_(-0x1.e72d4f4950c89aa59da6edc504bdp-10), C_(-0x1.e19176d7ba69146eb048e9181ac9p-14), C_(0x1.1b79fa688c946fc4993e527c8905p-21), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 13, 0> { static inline constexpr std::array<Real, 26> value = { C_(0x0p+0), C_(0x1.749078c0867a9a724454443e75a7p-9), C_(0x1.8ae6a79b4938fbd909b199343609p-3), C_(0x1.d008898983913d9bf1d194ac98f7p-1), C_(-0x1.20e16d5539e3f25296b1c6880b53p-4), C_(-0x1.f688bd1280c70194203f744266d5p-5), C_(0x1.2fca4301354a4e285e82fc4b6183p-5), C_(-0x1.505c64431d7a6f1e36954a7c80cp-12), C_(-0x1.0145189baf0142f2a8862b8be415p-6), C_(0x1.c908becee5a6a6fcccc95605355fp-7), C_(-0x1.beac12be1e7de0939dd15f031644p-8), C_(0x1.0006a916adee342c6b2792c6bd7ep-9), C_(-0x1.d4cc286b09e13557f3e87a0f9caep-13), C_(-0x1.a08b65bbb598677114fddb7b661ep-15), C_(0x1.5f413ab3a7eb94dcb396b2657edap-16), C_(-0x1.5c34d16af592037a11107a487b39p-20), C_(-0x1.2dc4454eebde3379c7645c4ba87ep-21), C_(0x1.74f33a2ccbc6518fcdedc7d5aa01p-24), C_(0x1.ddb5df0a412fd407d061c573b81ep-29), C_(-0x1.07969b3a158bd160a5cdad0ece81p-32), C_(0x1.2c5958b74836c10a9059d0bfc767p-38), C_(0x1.52fae6e83091fa686190e11a0d2cp-45), C_(-0x1.d83da475a639c307966abb294b63p-53), C_(0x1.1342e56840ec19da921d2c329c6fp-65), C_(0x1.aa25edf8f64fee132e1b30933b5p-86), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 13, 1> { static inline constexpr std::array<Real, 26> value = { C_(0x0p+0), C_(0x1.23923550f457ca7814b0bb3fd653p-6), C_(0x1.0c0767795d12ae5d156ec5cf4423p-1), C_(0x1.3373be839b47c40b1d36ec3e47ecp-2), C_(-0x1.856d7e6b6468c2deff8342e75baep+0), C_(0x1.22d30ac28dd9c9a5de5413538cd2p+0), C_(-0x1.72e38df054a23a8a5ebabc499005p-1), C_(0x1.8e439b194a1c16626ebcbea59c81p-2), C_(-0x1.3bc2524066e83eb2d5b3ff97e1edp-3), C_(0x1.1bc8f6e41059663daa79bf4a8b55p-5), C_(0x1.2884461caa1e3207b6de1334a7c9p-11), C_(-0x1.db22a9804aa1133069d05b96cb0fp-10), C_(-0x1.3482dca87f01c45e946a258c3e06p-11), C_(0x1.3285223dae55992a1d57ada1533cp-11), C_(-0x1.bbf1c4306d1a37f02d18135ce323p-14), C_(-0x1.17497a4dcd44ffdc92c6ebd1a068p-16), C_(0x1.bebec0cbd1f99371a7867cbe3fbap-18), C_(-0x1.bc40d833ef3598561d72cdf89bb4p-22), C_(0x1.6454c6cebdf97f43adbbdee1eeb8p-26), C_(0x1.5fce040bf0fa22a0bb7f52a52e7bp-29), C_(-0x1.1241493325c926f92e656210ed16p-33), C_(-0x1.ce70ab06ee7eb593175a3e65f68ep-41), C_(0x1.8616f674ef405eeabf053da9c72dp-48), C_(-0x1.7b38ad7c07a3a058098173d3a8bcp-60), C_(-0x1.258ba4702de85ac45e001504a52p-79), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 13, 2> { static inline constexpr std::array<Real, 26> value = { C_(0x0p+0), C_(0x1.7e9e99d93265e1ecb27f1a82e385p-4), C_(0x1.e81e73bf7d4e6759d9f3db761257p-1), C_(-0x1.368292c7be10e513188a104c5c4ap+1), C_(0x1.a1c192a939b9674ffcca9b2f1e48p+0), C_(-0x1.58e6f9045a40dd2a472104dd0f2ep-2), C_(0x1.2f82100ba4f2879faa0ab7316342p-2), C_(-0x1.f8fd9be6cc910f763e95aa8aafdap-2), C_(0x1.017de77081fc30f9ad09eddaf43dp-1), C_(-0x1.5831ad14642112326c714ae42463p-2), C_(0x1.30d718554c4cabcfafc1434f8a7fp-3), C_(-0x1.30a6075105b3aa4d5336fc1950e8p-5), C_(-0x1.632f9e9eb99fc711faf42ce203b1p-11), C_(0x1.1cbed37ba4dbd96c225d81054e88p-8), C_(-0x1.77d86fa7164bfc8c126a64816ac4p-10), C_(0x1.50ec238da00966f5e3d28fc9265ep-14), C_(0x1.f99c3b6dd2e633388ada35d1bfe8p-15), C_(-0x1.8453f2cbc2d996b7775a123e9384p-17), C_(-0x1.b4056601f4bff8b5e7d36857cb2ap-23), C_(0x1.4c2776a5f116e1d85dd046bd9786p-24), C_(-0x1.287daf168a219aa1132a37934711p-29), C_(-0x1.b00a66e2af603b8210a104b463bdp-36), C_(0x1.401eb1fad689de068ef9a337dfddp-42), C_(-0x1.71528144e6954a34804ddc8b7672p-54), C_(-0x1.1de10823e626bbef4adf3610f4fep-72), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 13, 3> { static inline constexpr std::array<Real, 26> value = { C_(0x0p+0), C_(0x1.95e033565cd465e59fc64a849ff5p-2), C_(0x1.e7908dd5753c97550b1b562a02c1p-3), C_(-0x1.293799fcf6c8da1f93fe2d057e3ap+2), C_(0x1.36cc467b08bf7d8a89d5be8f934fp+3), C_(-0x1.4335983e135774c5e5156a45190ap+3), C_(0x1.9c4d14b5414867b3e2c99a21a031p+2), C_(-0x1.ef81d85b23a01ac83af86d64d1abp+0), C_(-0x1.2378e73c6b10a2f7957b04478d3fp+0), C_(0x1.c6e27151761e3e586f5403563b06p+0), C_(-0x1.c857e67243153a965a648f8e6a77p-1), C_(0x1.3531afa42b77f4c754018d3dff11p-8), C_(0x1.05f57c1a6464d742d9d2e202da9bp-2), C_(-0x1.38a2db882124dfc4e44179ad6816p-3), C_(0x1.35c4a5041d9b9456d2520e65bc23p-5), C_(-0x1.fddc3c9f813d6aef1f4f22d0ffb3p-14), C_(-0x1.2653a0321997d1fa4ad992783a03p-9), C_(0x1.ec5d6f7ab50c177dc61e0a189fcdp-12), C_(-0x1.dc01f8633f4c61396f200866480ap-17), C_(-0x1.379717b64ca37d0f86a74f664124p-18), C_(0x1.7e5cfdc9a1b17dce328c7c0b5cf9p-23), C_(0x1.a124166c5786174e1b984a588c59p-29), C_(-0x1.4171311c3a7b2623f4df8ab8200ep-35), C_(0x1.65f402b77f1ab227d7a791609ed8p-46), C_(0x1.15123cc4efb60d3af1736012e615p-63), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 13, 4> { static inline constexpr std::array<Real, 26> value = { C_(0x0p+0), C_(0x1.4c5d516dd5340d0879832abfae77p+0), C_(-0x1.5d2571cda5543923016a360261d3p+2), C_(0x1.24b0f03522629e31e5a0ddf9b0acp+3), C_(-0x1.39e0f8d13e8db1f029ce62587cecp+3), C_(0x1.f006cc927be5328f1a33d6aed069p+3), C_(-0x1.0ce2ffa4646117df99ed92fff69cp+5), C_(0x1.b8b8afcf323d00e8ad39d1ccb61dp+5), C_(-0x1.e6925570e3f510211d732b9179c8p+5), C_(0x1.503102590c0b7b7ae2742f43b1bp+5), C_(-0x1.6d86add093f074bc432a452b5189p+3), C_(-0x1.35b5dc1025f2d34a60aa7bf9f93dp+3), C_(0x1.a6237c764b4a28340b8488817371p+3), C_(-0x1.cda455c3ae3929d25c3c5a324857p+2), C_(0x1.d5a02bb93708a320124accef7fd1p+0), C_(0x1.ecd4c4adc075fe2457753c0ae29ap-5), C_(-0x1.660ee59df078b432fb4f889b38bfp-3), C_(0x1.5158e51b27e5dbfe89f577f9dcaep-5), C_(-0x1.73814bfd57b681fa89fa6df52a98p-10), C_(-0x1.23460c48f636fa706d007acb283p-11), C_(0x1.fa353cdebaaaaa09ad0c40e9cfcp-16), C_(0x1.19c5738584246e6431d3352c6ae1p-21), C_(-0x1.4bb4308ed51fff3108f30cb71f7ep-27), C_(0x1.fc9a1f4f09858f536f1a575d9e29p-38), C_(0x1.89a8b7b9d28d1d71597812aa68c7p-54), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 13, 5> { static inline constexpr std::array<Real, 26> value = { C_(0x0p+0), C_(0x1.a35157d8dba56b3359c55dbb3245p+1), C_(-0x1.5a1bc35a1cc0dbb69c71add31e17p+4), C_(0x1.fa0a0878d9a933860f511fa37af4p+5), C_(-0x1.a68f6523a82701663e04e3ed3779p+6), C_(0x1.98403a971e63162a02dd92c33da9p+6), C_(-0x1.03810e60e02049d57e6cc9d05d6p+5), C_(-0x1.14faaec76846550eede58601f0cdp+6), C_(0x1.3d735b94c105436aa6c6accd08c9p+7), C_(-0x1.cdbd7de801407d716cbc38649987p+7), C_(0x1.20043470ad456af43bde8d7a0984p+8), C_(-0x1.2591e882d85cd18b0dca9775a589p+8), C_(0x1.b621996a63c17e6687cb0aeb2864p+7), C_(-0x1.a875ba068d8449d487f82d8f98a2p+6), C_(0x1.85c7d166f26b7783d793e4b535e5p+4), C_(0x1.1c0e0d6b929f95b9e528987efc33p+2), C_(-0x1.36efc345fd87e7f12a7cd8cf55f7p+2), C_(0x1.3e3f5c2c93c347939cad28d35ff2p+0), C_(-0x1.bffc3922a312894449dea079023bp-5), C_(-0x1.75f52c4bce3944c6d40bd8c68e83p-6), C_(0x1.dea5b49d2b299f2f3407a959506bp-10), C_(0x1.10aa3eff5f8aac0902d8bf4b6addp-15), C_(-0x1.ea6ed6c321e753c1b3e92351b813p-21), C_(0x1.089ab261bfe1c8b7f19aebdff953p-30), C_(0x1.9990a3735f2b8137827c03e7b5fp-46), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 13, 6> { static inline constexpr std::array<Real, 26> value = { C_(0x0p+0), C_(0x1.5d159c98a090a206b1f5a487328bp+2), C_(-0x1.54873e7e1b3d210625d277e6898dp+5), C_(0x1.2c245e185ac8b14c7baac4033f4ap+7), C_(-0x1.416f5cc6c22c1fc04eeda9dfb493p+8), C_(0x1.e67e2b7f933044475571e632011ap+8), C_(-0x1.298ee57db6ed5fd4bacad0de9695p+9), C_(0x1.48ee3d90a4e34a8f4d18f98b7344p+9), C_(-0x1.4e6b4521eb7a56c1ef75797e43fdp+9), C_(0x1.2782e95d7bf9f5fc360d37ee013bp+9), C_(-0x1.bb493883e544d446bc2b8bcc693p+8), C_(0x1.25dfd4b9fa45afe8f2d50abdb77ep+8), C_(-0x1.575e0c206b7ee6818931b6231d56p+7), C_(0x1.1c028f2725fce675841ea5e425e4p+6), C_(-0x1.08a1fe0ac6819f96e8258a0368bp+2), C_(-0x1.12ed1d6ca77301d9871c862435c4p+4), C_(0x1.66791e904ad3b41e47b43fe289f8p+3), C_(-0x1.7aa9733036515afd48134b03fe32p+1), C_(0x1.41600caa02955d88aadf08f58823p-3), C_(0x1.275514f436a31e564b7d019a87cbp-4), C_(-0x1.29373f56ac1095884f483f83febcp-7), C_(-0x1.51ea7d9f345040b9bbf67fd2c9c4p-13), C_(0x1.deb156b08b87ef0592d66bd4c9c7p-18), C_(-0x1.6e30fae8c34ed8366ddfb0cc8561p-27), C_(-0x1.1b57abb7d7f1ba81ca336dd9e4d6p-41), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 13, 7> { static inline constexpr std::array<Real, 26> value = { C_(0x0p+0), C_(0x1.d4fe27a0835ae1a04e0830be24cp+2), C_(-0x1.ecb0f32ca76fb494d571b0a3e338p+5), C_(0x1.c6da62a20cd0a85f32742b3dd231p+7), C_(-0x1.e3622dd5ba05d80a963a5e3e0d7dp+8), C_(0x1.49508717a90e836846bfe76665d8p+9), C_(-0x1.3d934aacf56d0a27027f03a0039p+9), C_(0x1.068600d74e1c90df9e5939a69755p+9), C_(-0x1.bb4eb52dbc23c8aa9dac0b1ae5b9p+8), C_(0x1.2c2d3c048caae8b4e7ebc3a10a9fp+8), C_(-0x1.6a6f07f5d07dd28cc71310327c39p+5), C_(-0x1.48c0f7b3bed9dd4e2bcfc6df9159p+7), C_(0x1.bce28601020e5546efe49f4f2facp+7), C_(-0x1.9e035ea535c3aebdf12735df11cep+7), C_(0x1.737017c34f7deef2722c9d811907p+7), C_(-0x1.15bd065f2789c251ed52867c6e81p+7), C_(0x1.1609d2e86de1f46bc02dc6e0a8fcp+6), C_(-0x1.30b382548235fc08ce2a6ea99e65p+4), C_(0x1.34c266d274d020226722064f6a4ap+0), C_(0x1.56d14dbd1c0ef8dc071f1d5be26fp-1), C_(-0x1.f82518456ddfa0a1ea7fb11fa704p-4), C_(-0x1.1d5d333a03734067f69cdf063e2dp-9), C_(0x1.599f88826e1df7529e25322303e3p-13), C_(-0x1.742b04eba227022dc2784e1aeb19p-22), C_(-0x1.1fd835e2f3ac373e68a1719919f7p-35), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 13, 8> { static inline constexpr std::array<Real, 26> value = { C_(0x0p+0), C_(0x1.6f91b1fb16e463903f2417b8bc33p+2), C_(-0x1.8fef11e8059ceda062deb12c9387p+5), C_(0x1.809c444472a8d8415a2c7a9afbefp+7), C_(-0x1.b10bf090c92b5336357cfbd2f863p+8), C_(0x1.45258188f71468e863f92b55998cp+9), C_(-0x1.7231afc08bd276307932b219a0cfp+9), C_(0x1.7af82162ac359965f69e6fcab693p+9), C_(-0x1.823e9f8992b59fc66e1876f1aa68p+9), C_(0x1.6f4bc124eb7dc2e04c11a11579edp+9), C_(-0x1.32f291524b4fc819caccc41f919dp+9), C_(0x1.d856007cb8fa074ef0836c00fb93p+8), C_(-0x1.59b2f057a74e4aae3ebb4a35f68fp+8), C_(0x1.c4898ffe6b603cfd7a5fa627ad77p+7), C_(-0x1.01b04bb5c7e4ece20624945e7d4ap+7), C_(0x1.0ee550f2b46fb0067dbfbe5f34b2p+6), C_(-0x1.f149829700499105abd07323449cp+4), C_(0x1.21413698e7cf1b5b76cf50d81657p+3), C_(-0x1.1e358290df39caefe5b52d405e07p-2), C_(-0x1.54f12799790c9591a372397a1538p-1), C_(0x1.1dedd290f907f8d2a852f01bdfd7p-3), C_(0x1.2b8db385d6eeb017f64738645db6p-10), C_(-0x1.7cd67d6099898e46f355480e2303p-12), C_(0x1.c1758243d6f68f11163695671c33p-21), C_(0x1.5b5402fbe8db7e6e4a3332e846cap-33), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 13, 9> { static inline constexpr std::array<Real, 26> value = { C_(0x0p+0), C_(0x1.e00f201ca9b47bec13b3bceeec35p+1), C_(-0x1.09aad588fc6e1d2e5e320a1b6965p+5), C_(0x1.0083b1ed3add1dfc189ab7aaac2p+7), C_(-0x1.1b01639f15a47195db844f5df4eap+8), C_(0x1.8e74c5b415b4c982c62a28306ab1p+8), C_(-0x1.907a858da198db5b4a86eef21cd8p+8), C_(0x1.68e4a68143eb6280f78231820634p+8), C_(-0x1.685dfe59eb94f38e35f487b91dc1p+8), C_(0x1.592f39b72049a36e7924f8b1defp+8), C_(-0x1.09589acf597f567d3772f2b218afp+8), C_(0x1.658b66c44d2d9f09118af69ddd27p+7), C_(-0x1.f90c71880a91658c0d9a38574dffp+6), C_(0x1.49a9a7009f2b267b39bab54a8a34p+6), C_(-0x1.441338caa52cfa0e2a27d488fb3dp+5), C_(0x1.0b7b2a297fde14bc6faf3e06bf71p+4), C_(-0x1.d98372b1c68d3f52be82670d6ee1p+2), C_(0x1.f43ec1f2a32806088746ff9dc715p+0), C_(0x1.6165b77555fca80d9c5c14948139p-1), C_(-0x1.4f8a8171bb08fcb9ccd7f4688dddp-1), C_(0x1.267683e93d2b771765dfc5bfe73cp-3), C_(-0x1.8ddc624d415c8d8d9889292068a5p-9), C_(-0x1.979cae945ae1031f8b5a56752269p-11), C_(0x1.95627b187fdb196e7b60fd3122a7p-20), C_(0x1.38bcd286c35de60d5fb4c84a2f35p-31), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 13, 10> { static inline constexpr std::array<Real, 26> value = { C_(0x0p+0), C_(0x1.ddc9914b8fce26e89a34c64d6d6p+0), C_(-0x1.0aa6a6fe4749ff9a53419e5cb74fp+4), C_(0x1.ffd30a30f104e3ad2ade2b583021p+5), C_(-0x1.1076bbdb4cf7527cd039bd2ee863p+7), C_(0x1.5b314fd5bd8427278ea0f14850c8p+7), C_(-0x1.15e629a2f07ab3b285fb28d62142p+7), C_(0x1.73ecdaa7dbcd11927e445f4fc04ap+6), C_(-0x1.7ea4991281a803e96d951a02ad23p+6), C_(0x1.92fe5087093b614dba0f2e58af18p+6), C_(-0x1.e50ce86c3eca30ad8c357a5bc172p+5), C_(0x1.23fe36ce5250d05c3006a508171cp+4), C_(-0x1.1183a5ac74636a4f4f8077863f2cp+3), C_(0x1.325da71616787b1a97cd6b487bbp+2), C_(0x1.b5b93d37eb78f2e235cc59568f84p+2), C_(-0x1.6174cc292a977e8769fcc13572c1p+3), C_(0x1.b8e78e1a9ada492b4dd6fe85e7f5p+2), C_(-0x1.ffc6e54f09b8a6376ab9c26e41bp+1), C_(0x1.807b43d233e13293cd8f6f610b94p+1), C_(-0x1.949effe4fd5f10b6f0bb69f9fc41p+0), C_(0x1.99c706ee33d33292c4de755a9043p-2), C_(-0x1.8b4255eb2ab52df50469eaf1f575p-6), C_(-0x1.25fbde4ae0e29153ac78daabb6bap-8), C_(0x1.a2ffd5a58a3e625ad5baf547df1dp-17), C_(0x1.4225e5d67d6a903058f380dcef3ap-27), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 13, 11> { static inline constexpr std::array<Real, 26> value = { C_(0x0p+0), C_(0x1.82555f0fca681c9ced300bba3465p-2), C_(-0x1.b108ac4bd9d5de90a612fa91bba4p+1), C_(0x1.a3af9f5e28533d44a218819eab18p+3), C_(-0x1.c92e2a69bebea1255ad98910de81p+4), C_(0x1.336156f19a3eab19184560490c7ep+5), C_(-0x1.154d20c532d37d99d550b554251fp+5), C_(0x1.af95c6a7f034f7267500247c3a39p+4), C_(-0x1.a382ed435f8ed2216764cb0a372p+4), C_(0x1.a5a57db59b67be50825ea51ac179p+4), C_(-0x1.48587bdb4781058d9836884c3b74p+4), C_(0x1.c6519b1cdb292e6d292e4f1f9c11p+3), C_(-0x1.64406dc5dece20ec3c4c58b87407p+3), C_(0x1.05a0da2a87dafe77cb9a54ec8326p+3), C_(-0x1.34062a3bf7c109c05654bbca487fp+2), C_(0x1.65a3327bcf1ac1cee14ebea4c8b6p+1), C_(-0x1.b27cf7ab49be37cde0f46679310bp+0), C_(0x1.a5bdc7192b9c3a20ece9060c1ba9p-1), C_(-0x1.571ac2983f85e3a6dc62f13fd384p-2), C_(0x1.31767817c6adec541d6996364d3fp-3), C_(-0x1.904f3491bf69c7251d1b40c4f69ep-5), C_(0x1.0ee4f3163f55f45905e2ddfb93a4p-8), C_(0x1.2584f1f36b43e7bbd83744e7e8bep-10), C_(-0x1.373cf584c03ee906a072cfcde9b5p-17), C_(-0x1.db60a068c3377c744925f382f6d8p-27), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 13, 12> { static inline constexpr std::array<Real, 26> value = { C_(0x0p+0), C_(0x1.8dbb03fad2c2ff4e565f682fc387p-5), C_(-0x1.bebdc5d3b23911ed145126163ba8p-2), C_(0x1.aeb7a5ea21052a1c43ba381385e3p+0), C_(-0x1.cb9851522d20abcc6f87f331e722p+1), C_(0x1.240bf59871b997fc41c935dfbef9p+2), C_(-0x1.cab7cf1ed537e0d17c393ba768f6p+1), C_(0x1.1fd4543a5fd8cb1e3fd209bf00ffp+1), C_(-0x1.1ce9744c1c9756de9b809c9cc5acp+1), C_(0x1.3bab08bd76344b447fe47382a836p+1), C_(-0x1.c40e7b4e77556f5ef8447dfa81f7p+0), C_(0x1.feadc8c7ce87a8fc67e2732ba34ap-1), C_(-0x1.a643a47d84b4da70d0fb0b9b5ca8p-1), C_(0x1.543b964e0f03a3a71ec489e8760ap-1), C_(-0x1.577aa576ffa64efb7d0e9a7c6b39p-2), C_(0x1.499f6f7a97a22bd1178c8279f046p-3), C_(-0x1.d5a15151b901635be5a327439552p-4), C_(0x1.d4c5badb46707713b03f6550ccfep-5), C_(-0x1.094f5215690db085443c42ab246bp-6), C_(0x1.cd0926fb9e142792dd84020c8a8bp-8), C_(-0x1.b2091c2c73dd02f84cb3796bc045p-9), C_(0x1.fdc7350edfadd24f5fb7a32829d8p-13), C_(0x1.4af17513fc3a876960b7cf51425ap-13), C_(-0x1.fd199a3cefa31b76bcac261239c5p-19), C_(-0x1.7fa406e41ed65db974ed315201c3p-27), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 14, 0> { static inline constexpr std::array<Real, 28> value = { C_(0x0p+0), C_(0x1.2e3c0bb3f3ad4d49ee7e86ec562p-10), C_(0x1.d73cdc4f17147d4ff78a1eaebc89p-4), C_(0x1.980f074dbd462038712882b2223p-1), C_(0x1.0b8da7807c2738b0ef8a21bd41d9p-2), C_(-0x1.381b88314120b0755faac9b6a208p-2), C_(0x1.a64053bd4da4144d5c6645aafa5p-3), C_(-0x1.be6cb26620f84322f5bc9ad124p-4), C_(0x1.5369f32b472a8bf80c2615157588p-5), C_(-0x1.e553bfb83c481ee1c85b1021810cp-8), C_(-0x1.5b97376b07916025b5f5ed690f77p-9), C_(0x1.3ad93e070eb79f317793c09c0451p-9), C_(-0x1.6c8658d1b206dd40e11227faae77p-11), C_(0x1.421437e7b839d2e408af08229906p-16), C_(0x1.359cb55b7d335b5bc8ff9070d38p-15), C_(-0x1.16b1cde08937e6520514fc007dd3p-18), C_(-0x1.1e470298289ae452c29404b9c746p-19), C_(0x1.16b7d7c52ecb6bf5c9c270fe3977p-21), C_(-0x1.2a9017a9058ec8631bfea23cf0f2p-27), C_(-0x1.e6603a12c62203e481a6f751bb0fp-29), C_(0x1.ad635a5532ad9d7f9b990f3258b1p-33), C_(-0x1.0b7166f3d598041c11f82d418c5ep-37), C_(-0x1.2dcc8d3c8b0cf63074ab4d9fba6ep-43), C_(0x1.994c7452dcd30c07dade8e0a0b5bp-50), C_(0x1.d3e7db27a70ee63bd0dc60e06dc1p-60), C_(-0x1.ad34c0383fa643c903234154af78p-72), C_(0x1.c6fd0b1a8d6a2b5f9f47659e9cb5p-94), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 14, 1> { static inline constexpr std::array<Real, 28> value = { C_(0x0p+0), C_(0x1.ffe6a833f41d1e41c335a1d66225p-8), C_(0x1.6878956519ce3162ba29291a8504p-2), C_(0x1.4f6222726462315c1311b1bd0b69p-1), C_(-0x1.9d7a4f00f9dc035ff30a13b3dd54p+0), C_(0x1.ee1a7236f71e3afe8c9241dc280bp-1), C_(-0x1.3a4c3d150c11dd01e59680a43c1ap-1), C_(0x1.a5124e1ab47a907fdd8a56cf5fd2p-2), C_(-0x1.fd47140509eb33a71307cdb49b3fp-3), C_(0x1.efeb8355fd2f814144fb4db02bdbp-4), C_(-0x1.695e5e5e49cf847101e5144b6fefp-5), C_(0x1.73cae05387f642ba0d652b2dbcabp-7), C_(-0x1.fa774911ba2d3bb25d61e69c8c8ep-10), C_(0x1.13b07ddddb3b836ee57d12843693p-13), C_(0x1.7cb11c0b4280a9d8a95e4eb20e72p-14), C_(-0x1.d2cbfff6e2a582bd1061aa2f380bp-15), C_(0x1.74388c9fd28e69e7d9f0c5af3fddp-17), C_(0x1.21ff895bfb5f2915922793fd222dp-21), C_(-0x1.156307b5c128c175f7e3a71477b9p-22), C_(-0x1.19b91bff8bef4f88f1ed76cce8eap-25), C_(0x1.f7d83e4d41c76f94d46210e4d1f2p-31), C_(0x1.5090626b206a430059df75028168p-34), C_(-0x1.405683426ad010e44f0a98cc929p-40), C_(0x1.6ac079eed130df81302e2b26c482p-46), C_(-0x1.9a49f0637a3b64a9eb35bd52aa23p-55), C_(-0x1.88bc66cc087f1d558950f224d6c9p-67), C_(0x1.a0541eb1bdceab613773d4dc3dd7p-88), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 14, 2> { static inline constexpr std::array<Real, 28> value = { C_(0x0p+0), C_(0x1.70e38d13c6dccf6333417be4b4fbp-5), C_(0x1.98429094e12d1953c234a36b137bp-1), C_(-0x1.5a23aee5cfcf330386719e085aa1p+0), C_(-0x1.ca3a85e30ebf60ba5eccc5b7b84bp-2), C_(0x1.f2911f6caea6ac421bc7b6d2ce04p+0), C_(-0x1.902df5acb98563fb6c85941263b7p+0), C_(0x1.6e5d8a32fe3ae7b3c23b4e6e9c7ap-1), C_(-0x1.7cd7499a11b87c3bc4909e0bdb58p-5), C_(-0x1.cb51389df1436d54630b5c4050fbp-3), C_(0x1.8970fdea96db48b13c52294d029p-3), C_(-0x1.2e3ba43116d4ee1d14ccd7ef1eb6p-4), C_(0x1.a437288ed51ab324c667ecc7c439p-9), C_(0x1.5d8afaeb5ec2a57500ea441b58aap-7), C_(-0x1.3f213a25a4c39a4ee9f8ca7fc5f5p-8), C_(0x1.438df66495fed0569b1e6607263bp-11), C_(0x1.92aacb344e1aac45946a6dd95b1dp-13), C_(-0x1.4a2a2b6937dca67c2fb96409eaabp-14), C_(0x1.061494c076ea4c2b5c794f2371b4p-17), C_(0x1.1c61500cd5ff603bf7260846f007p-21), C_(-0x1.fed404b96c72e77fac42699e644dp-24), C_(0x1.9900fa8d5cb81723cdb543a2521ap-29), C_(0x1.4b71c6cbb7be353ab93ac21700e3p-33), C_(-0x1.f4e20f23251aa513b13eb0ad0eafp-40), C_(-0x1.ae764159a5bb5c8d340066c07578p-50), C_(0x1.0753e4c918ed6b59ce15c4a9365bp-59), C_(-0x1.1725d8c4676c38ff70e1cc359512p-79), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 14, 3> { static inline constexpr std::array<Real, 28> value = { C_(0x0p+0), C_(0x1.b6406454732d4d440405d44a6a49p-3), C_(0x1.b949541f458cd808c01c6f4442bcp-1), C_(-0x1.49bc84198d8eee0e1769477dd34dp+2), C_(0x1.255157167a5528a3714c438e2bbbp+3), C_(-0x1.254591e8b6e06babda61e0b5bd92p+3), C_(0x1.bfdd01aa9e6916b30d7fb866cb4dp+2), C_(-0x1.258cb0e12f407e788c8d24c043p+2), C_(0x1.244b687910817f75269b9b13d0aap+1), C_(-0x1.76e9c86768fd81ae0140e512f91dp-1), C_(0x1.2db90e1b7e223907d65e1858ad53p-3), C_(-0x1.adc00aab7f786622c376bd60c25fp-4), C_(0x1.077b01cdc29a9bffc55813096431p-3), C_(-0x1.4e1bd3d7c8106ffe51d90e297c64p-4), C_(0x1.a8b1719f76969f8051acdf38ae9p-6), C_(-0x1.1b67a8fdd5d395a5e1003bc2df39p-9), C_(-0x1.5aa2219e8b072017d97056f432f5p-10), C_(0x1.0c296ebe05b6e9c7cf2917908081p-11), C_(-0x1.315112d6e2648d659715640aac77p-14), C_(-0x1.aa34a64782e3fdc563417212e36cp-23), C_(0x1.718ac2125512de66d6a9b5d79809p-20), C_(-0x1.4ed202350e6d4103a23efe811aep-25), C_(-0x1.6a2c3e7b115c942fffc924e2aa83p-29), C_(0x1.03cb1bd946e2daf6230de1902b89p-35), C_(0x1.d2ce73e99c2943d672b79f3df3dfp-46), C_(-0x1.110d7f1b0bfbfc4b48ffe175513cp-54), C_(0x1.2175be08d4af39d29c43830b5338p-73), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 14, 4> { static inline constexpr std::array<Real, 28> value = { C_(0x0p+0), C_(0x1.9bd3bc24739608dd1ea0727f797p-1), C_(-0x1.218b20c923a72ab49d783c3c2182p+1), C_(-0x1.8f073ee2485429a822c3456748ddp-2), C_(0x1.10368c3ad14ec0121ffa10beccc4p+3), C_(-0x1.6e5fd027a16b3fa71b0c68881f6dp+3), C_(-0x1.fee6b19288528fc99125553bcb88p-2), C_(0x1.5dae0c64ec100c07cb64acfb530ap+4), C_(-0x1.253938fa65f9cdca9dcd99a2d96bp+5), C_(0x1.0846ca351ee337bf1cde15f6a892p+5), C_(-0x1.d3379cfd6d392ab0067070d38b2ap+3), C_(-0x1.bc1cbd5de053b1b3e6030cd2eb44p+1), C_(0x1.49e86d68d4cf8c86d82167732746p+3), C_(-0x1.e4ade08c4a6c2c8507d0731ef456p+2), C_(0x1.651f390634956dee37faca7ade61p+1), C_(-0x1.14e32e1f9b6bac3d6ef9b665a8dep-2), C_(-0x1.c20b1d287136abbd5724af54edd7p-3), C_(0x1.9dc73570ee73f3a5d7e75adc1efap-4), C_(-0x1.dbb9ebdd9c09deccb1020147719ep-7), C_(-0x1.c7f5c1ec60f696f9a40d5c2f13dep-11), C_(0x1.a5fc856e52fad70c72c88b43b17bp-12), C_(-0x1.07f65daa0049b089e54b5e492044p-16), C_(-0x1.0e378f07aff0a4003d557ea13ebap-20), C_(0x1.69bc58d5ec0ccbef38bec2915824p-26), C_(0x1.872aa1bcf368769fc21e287db36p-36), C_(-0x1.7b84969608016d06bfce8c098437p-44), C_(0x1.92548cc9b5b71c86f11e26fc3a07p-62), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 14, 5> { static inline constexpr std::array<Real, 28> value = { C_(0x0p+0), C_(0x1.29b15e8e05f4922e7d4e47048a9cp+1), C_(-0x1.cfd365d6145278198eca9c82d9f8p+3), C_(0x1.440caad9c12360807dafb3bad1d1p+5), C_(-0x1.116de9d813b38a3407c462c9c8afp+6), C_(0x1.3b639c503b3cf7fe4e226236b434p+6), C_(-0x1.0040f57e975e1a258b9875fe1f17p+6), C_(0x1.e6fde6a95ce32902224ee9a0f717p+4), C_(0x1.5c1e9e155aab7b67b6f0684e8054p+3), C_(-0x1.b1e5da7957b3c8fabda1cfa1992fp+5), C_(0x1.7d1f138d16b9d31aa28298c6d585p+6), C_(-0x1.d6f4cad7bdd82bc575e84a0ae447p+6), C_(0x1.9fd808c31038fd9d9f9820868c69p+6), C_(-0x1.ecec6e1a57ab3b47a08d37ee9238p+5), C_(0x1.43fff7220eba3de58880aab6571cp+4), C_(0x1.5e941cd01c024910420637b6b61bp-2), C_(-0x1.d2a0789936f63c584facf37b3e67p+1), C_(0x1.940e89f9fbe3b90fa47d360fd472p+0), C_(-0x1.f62a7689777aabb4ab21abcf7e27p-3), C_(-0x1.2b3b3b35a204159ed02721cadaafp-6), C_(0x1.3de2ba1c1b05528a92ffeeb8fc2ep-7), C_(-0x1.21cbeea2dd955597cbff120c27ccp-11), C_(-0x1.2150f65158193f62d7d7f8ca1f69p-15), C_(0x1.159bf889454c6b38325ea0bd0aa7p-20), C_(0x1.b00f4f96ce85167dd0220db19d66p-30), C_(-0x1.21e8e13c855c01e5c446a0ad86p-37), C_(0x1.33590911079747fc32e0ebbb9924p-54), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 14, 6> { static inline constexpr std::array<Real, 28> value = { C_(0x0p+0), C_(0x1.3069c9b572d786eb96d929d90cddp+2), C_(-0x1.2e376983f6cb6b3abd68459b0db9p+5), C_(0x1.1366d92966ea16320047794482afp+7), C_(-0x1.37b9852173f06f1765e1fe9f84p+8), C_(0x1.ff3f2db6a15a3d87e9d7df5b42f3p+8), C_(-0x1.57d9383606e506f39f38563cb6bep+9), C_(0x1.9e8b97533b1eae6eef5ccc2c8b76p+9), C_(-0x1.c556790a27e1d4367bdf86d03f05p+9), C_(0x1.af9eb47abc08e08daae8af537da6p+9), C_(-0x1.5e3047bf51b54c2759154839c7dbp+9), C_(0x1.efd9329bb40ff6440883f8a40f82p+8), C_(-0x1.337ec090261a5db68ef9839a3fcp+8), C_(0x1.1dd7e09a266914bfb2df7819245bp+7), C_(-0x1.34f8d53391e95dda3b7a36e1f269p+4), C_(-0x1.1b6423ffa4134de5e81b13aa374dp+5), C_(0x1.038ecbdebefe39ca7724b2c5d6b5p+5), C_(-0x1.9f2073b507553852ed1a7122dc5cp+3), C_(0x1.0d3b2378aacf1f56c9dbd6033ed8p+1), C_(0x1.b93ffbdcbcfbcafb2828e4f8a1e6p-3), C_(-0x1.00284db90f95b583e4f9723dea4p-3), C_(0x1.5202609236b6be9cf16ae5695042p-7), C_(0x1.4b9320a57f2323116dd63291deebp-11), C_(-0x1.d3b085775602aad7427a1a128489p-16), C_(-0x1.e975304f420640f339ac1f2721b2p-25), C_(0x1.e5cecfa6ab7bb5421ef8c106f4f7p-32), C_(-0x1.0188e4a2f5a9df06f6875fecaac5p-47), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 14, 7> { static inline constexpr std::array<Real, 28> value = { C_(0x0p+0), C_(0x1.f579b17074e36836eacdf20b2124p+2), C_(-0x1.13b9cbe766166f25c9dace3616b1p+6), C_(0x1.0d0d0432bec134cd566f5783ca25p+8), C_(-0x1.309a86e68bfe9899fc0e86f2260fp+9), C_(0x1.b8e26231ea03e8ec859843dc6ce9p+9), C_(-0x1.b08b284517ec42e68106ca8a8bc1p+9), C_(0x1.3c7d2b26245024778e76cf716fbfp+9), C_(-0x1.7e7def0dd6c17f062ac5f280847p+8), C_(0x1.9c880448390e60397d83aacda54p+5), C_(0x1.dc1752cc2f2f84356ce375550f21p+8), C_(-0x1.e54a03fbbc2fa46a8399b07d254cp+9), C_(0x1.1a42e1dae56904bbcf3f8f7fa5c7p+10), C_(-0x1.f903f4a18c30e32dc6c260029f14p+9), C_(0x1.9d8db919083864fcc4e1ce713df3p+9), C_(-0x1.34173ffb143e1d9eed0dd73c6925p+9), C_(0x1.64eb3c27db564d469eb11c515c5dp+8), C_(-0x1.0b0c43171fee5929daa55b569994p+7), C_(0x1.5f0a5375d11c72dc55988338ff36p+4), C_(0x1.d8f6b9f1522f2e96a9e46aa5caf8p+1), C_(-0x1.1c75896d6d598c65080bd27d32aap+1), C_(0x1.f38ac1a749daef77915c1d44f9d7p-3), C_(0x1.f82700b4dc7274aa9bd956d7234cp-7), C_(-0x1.1306135d4672f12980f36c25a44ep-10), C_(-0x1.2dc514d6999140dbb2a21c1d56f1p-19), C_(0x1.1d494ae1d331f410d68f7a178351p-25), C_(-0x1.2e8464bcec8d40ffd77ac9bbd77ap-40), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 14, 8> { static inline constexpr std::array<Real, 28> value = { C_(0x0p+0), C_(0x1.e32cc25ea4da498425dfec2497a6p+2), C_(-0x1.1692ca6458ea9e38b45000f9e974p+6), C_(0x1.1fa09c1316dfb4b439ad2e78bb59p+8), C_(-0x1.615e67f0c1ccc897da6f2d005018p+9), C_(0x1.265c8c1b4b1aa4b3e36b99e4a1a9p+10), C_(-0x1.7569ed1c8210ca209e47f9d0511cp+10), C_(0x1.9e96bde5063d41cf09da3c270b93p+10), C_(-0x1.bbbe167a38d63287ecfeda29fbbep+10), C_(0x1.be080201e737d36f7e79bffa876fp+10), C_(-0x1.8f099bdabb21898e359857d34007p+10), C_(0x1.43b83815e15a62b284f0ee906572p+10), C_(-0x1.ee6ad68b3bda4ee4ba8bf16f4fabp+9), C_(0x1.58d561cb84d267ecaf633fb5a5d5p+9), C_(-0x1.a3b282a8407a310226d833dadcd5p+8), C_(0x1.c79d620ffafc0589079eea90279ap+7), C_(-0x1.bc78cb9447aa124d62b31a0a7f54p+6), C_(0x1.418e35902e32cdd0c2f21fb873ep+5), C_(-0x1.3abf360acc2f742d879127375bb2p+2), C_(-0x1.ad7bb3867b3c2b046f80e1cb0482p+1), C_(0x1.a655024ebf2fd4378622021ee814p+0), C_(-0x1.affdcd4718ba7f1a965455b89c8ep-3), C_(-0x1.8341cd6c6b0a9d48905a1ecfc91fp-7), C_(0x1.b55710d3ebf552b754ea432b16e1p-10), C_(0x1.e321738ab144873b6e4379081333p-19), C_(-0x1.c53c1373c88584f948dc39838bd8p-24), C_(0x1.e0c270acb15c5fb50466c4df9e1p-38), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 14, 9> { static inline constexpr std::array<Real, 28> value = { C_(0x0p+0), C_(0x1.8d1f8a32797636f661365be0e3e6p+2), C_(-0x1.d4881995a0c1ea2393ff422e453fp+5), C_(0x1.e86d414a78e33b3180b306c7fb52p+7), C_(-0x1.280027c9b087591ad85db337ae83p+9), C_(0x1.d3eb5f0b0594c2750ef02a700404p+9), C_(-0x1.0b82a55c2799ede8dec1e33e1dcdp+10), C_(0x1.07ce9f70ddb2869a658274b505f1p+10), C_(-0x1.0d7822536789d9033e70cbead7bap+10), C_(0x1.0df61d2a506b1f8fcfe72d1ca4cdp+10), C_(-0x1.c6893ac6cda6b55a4941f5e57261p+9), C_(0x1.45ac9e808978822ff4ad1899b3b8p+9), C_(-0x1.c9d686e237043dec7c04f88fd885p+8), C_(0x1.35c4c3819b30f9b6fdd5c67ec132p+8), C_(-0x1.4a58be360f4f421d89e83ecf3267p+7), C_(0x1.017559c35f7610aa1b72e5e5a83p+6), C_(-0x1.5d1ba7f13474232b92fdf4e5cb84p+4), C_(0x1.dadd49a935c8394385d3a3bdf6d5p+1), C_(0x1.87b01fd4326a3668ccbb1eed227dp+2), C_(-0x1.9ab15d247f90f9fe7c9b6b3dd567p+2), C_(0x1.46cd6a0d33a48aafbbc221eb1f48p+1), C_(-0x1.8955d7defe0d5217296739d07f07p-2), C_(-0x1.85244f4e65bbc4ccef7883bc8ba1p-7), C_(0x1.6f86d3c43106164aba39dbfe0b2fp-8), C_(0x1.1b4e3c12a74dff21568f59de83f3p-16), C_(-0x1.7914d82d3193f580c3335f167104p-21), C_(0x1.903b4b44dd8c7c0a4e702124dc3fp-34), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 14, 10> { static inline constexpr std::array<Real, 28> value = { C_(0x0p+0), C_(0x1.041a0a897aa28eb3a0ccade17e3cp+1), C_(-0x1.3658b5d77609e7977d3641db3a11p+4), C_(0x1.5194af04e2f848c21930873e900ap+6), C_(-0x1.c3df81f0aaf28bccb5fed61687cfp+7), C_(0x1.ad183e8db3dabe867a1b1e1d7e93p+8), C_(-0x1.3d9c782d7007715e1144e807f092p+9), C_(0x1.852da35362a6d4101e229e2b5077p+9), C_(-0x1.9cca18f6947dd0d5bed4aff692d8p+9), C_(0x1.9a6efa498935e2e3d82e1fd52122p+9), C_(-0x1.a300c2ebdd39d26204b2e2ccd8bdp+9), C_(0x1.a735477cbff1b966c8a20eaae97p+9), C_(-0x1.7a384b1c312fbe2a2f45b3550037p+9), C_(0x1.2afd886ee72d716fc638e75f48b8p+9), C_(-0x1.d0f63946d275b18c0f5c2756f025p+8), C_(0x1.6384c4a13f54dc153d90136891aap+8), C_(-0x1.d6c269ce8bf34e1953164b65a3d5p+7), C_(0x1.08982647617ff8ae60bccefbfe0fp+7), C_(-0x1.1f7e83a0711235a83bc8e025bd62p+6), C_(0x1.2a5701b5bea0dde347ec02073e97p+5), C_(-0x1.c18aa4ec1159b6d22d740e4f35cdp+3), C_(0x1.4dc13861658a8dd406eb1a845d5ap+1), C_(0x1.bd5ac19033244ca1c006b305a421p-5), C_(-0x1.1aa94170fffad7174e8899965ff8p-4), C_(-0x1.97678bd8dc9fa54b7e4c01f3ba2ap-14), C_(0x1.25b3fc23ddcf5fe31ea2281e4301p-16), C_(-0x1.381fef501218e9cc3e0863bb3cadp-28), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 14, 11> { static inline constexpr std::array<Real, 28> value = { C_(0x0p+0), C_(0x1.456a1d2a45d0d4e9e18e4013bda3p+0), C_(-0x1.86731e38f2c9e9bd245a6d7f6e86p+3), C_(0x1.99ddae9b5957da8932fc9013b15ep+5), C_(-0x1.ebccc1d5d759a0cf4adc92beb271p+6), C_(0x1.74f85dd906948af50c229b89c98dp+7), C_(-0x1.8426225b26443b4ef3c972f9489bp+7), C_(0x1.4fbcc1bdf3f1963c49a88c06aa08p+7), C_(-0x1.4776c0e99319f61e68a41fbe42b3p+7), C_(0x1.573bef3fda7eadeaaa4191468e3p+7), C_(-0x1.2b0c271bd883e242fdd8d9725e0bp+7), C_(0x1.bb5bca80b624fa5bb278816db9f3p+6), C_(-0x1.5808025c93fa4e6af5a7ad436556p+6), C_(0x1.0c1df40cf5e4c4ea4441c80693a5p+6), C_(-0x1.5dea01151a3e197eb05317c268edp+5), C_(0x1.997fc95198573b5277250e908707p+4), C_(-0x1.f5c4140f2a03e036d15c57dbb36p+3), C_(0x1.1578f4041624b0e3ebbbb44abecfp+3), C_(-0x1.e11a4c47848258b137f885157e3p+1), C_(0x1.8c2f5a8cae553e89ef1e861ef5b3p+0), C_(-0x1.42cdddde9b71e8354b8c2fb7c09ep-1), C_(0x1.1b37523680cd9a16c0e5dc3ebd03p-3), C_(0x1.61bca3fd3effb1c3f5807afcb9adp-7), C_(-0x1.eeca78cc1dd9a8d407a9b1f6577bp-8), C_(0x1.427b3775515b64598a140f609c8fp-14), C_(0x1.1c6c30fb5472c91c3ee2a25808b3p-18), C_(-0x1.2f056506ce5e619914ce605b0524p-29), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 14, 12> { static inline constexpr std::array<Real, 28> value = { C_(0x0p+0), C_(0x1.45a484f799a722e4cd950a09d5fbp-2), C_(-0x1.87cf9eab4f40073db99e6a0fb481p+1), C_(0x1.99aecd437634b1af52fbd40a01bcp+3), C_(-0x1.e335dd2c6e9de306d05cc358c6bp+4), C_(0x1.5e3841e2195098fae8b77b691b21p+5), C_(-0x1.48839e048b83d3127ebe74020885p+5), C_(0x1.e11a7f30735e301f0eb2ede8063fp+4), C_(-0x1.bff27724d4103b12e92a64b54c9dp+4), C_(0x1.f68b6fe2ccc3168c1a15db6eeebdp+4), C_(-0x1.a9c89c30bca221a764ae454bfb09p+4), C_(0x1.147ddad811d2b11feabea5bba8adp+4), C_(-0x1.a10ee0eb1ccb64a80033704ddb98p+3), C_(0x1.5d8b9ffe3cdb891325e9bfc9fb55p+3), C_(-0x1.b0eebf69279efaf954dd166c21dep+2), C_(0x1.b180929e1a69b7ef5328a0cfd4a4p+1), C_(-0x1.11a2d370771ca7d9ba7c7444df33p+1), C_(0x1.45b0d998cab377e10ef3a92e12dfp+0), C_(-0x1.d74083eaced416102c8dd2af61fp-2), C_(0x1.27c1113b5bdb7975242772f43479p-3), C_(-0x1.2ee6a8512694e4da2e5b07f1c606p-4), C_(0x1.0ad11030da22955532f0e66e0c83p-6), C_(0x1.b719ad4ae715fb13a424d63fb241p-8), C_(-0x1.7b5726cd7507b577ab874fe8a876p-9), C_(0x1.efe0e7fbce7f41797c67293a0937p-14), C_(0x1.116839f7247ae044e8dfdefe7163p-18), C_(-0x1.24c158fd367df5563093507c0edcp-28), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 14, 13> { static inline constexpr std::array<Real, 28> value = { C_(0x0p+0), C_(0x1.439a95b32a47eb5722e3cd7fe3cap-5), C_(-0x1.85e5f8ce20b701780e2029b7ff55p-2), C_(0x1.959ab595a2ea47cca93fdec47d03p+0), C_(-0x1.d591277dff53d8dcf59277336155p+1), C_(0x1.43a6564933b3f0805a5a899c5bb9p+2), C_(-0x1.0a2c05cc597aaccc032de2cc831fp+2), C_(0x1.273950f6ffd17ee92b32456caf9bp+1), C_(-0x1.050c8b9cb84b7c5048bc5cd2f92ep+1), C_(0x1.600ea820111d062fdf2a6acf661cp+1), C_(-0x1.21f61a844a104f06b392bde6725p+1), C_(0x1.19f0e6ef31a0d26707b436c0ada9p+0), C_(-0x1.8e2103144a726110a565e981ea79p-1), C_(0x1.a07f2894f970eb1bd26c4012674ap-1), C_(-0x1.ccce8527cee5c45450edf8973a9cp-2), C_(0x1.e56137866a8254327c313c62b4d6p-4), C_(-0x1.5df48c0c87cd72cb9ba6c6b9ceadp-4), C_(0x1.19d3f039c46cde096e59d4adaef2p-4), C_(-0x1.9e6cd0f61f4caa9b0d4bb0b897fp-9), C_(-0x1.b966bdf45728a5a5bb304f91c5cp-7), C_(0x1.8240771a20727b5953c676de8a9p-9), C_(-0x1.1b05a2f57f924748a24f50e9e6eep-9), C_(0x1.7f8554959f4a532982e2ba397a2fp-9), C_(-0x1.23710df832eb1845bb5316dc1abfp-10), C_(0x1.cc575afdf3f3ce7d0de6ac81f14p-14), C_(0x1.1f238196ae22e33d86876e9e195ep-18), C_(-0x1.3697e9bf43069ef0c328d37a1aebp-27), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 15, 0> { static inline constexpr std::array<Real, 30> value = { C_(0x0p+0), C_(0x1.d99d611c0465d7fca87092137394p-12), C_(0x1.0d2f985427a1dc1f62afa99d998fp-4), C_(0x1.4a539266aac6de6ff0ee136fe6aap-1), C_(0x1.1fc50d04f7f07a49e55f06b78355p-1), C_(-0x1.d497750272bfa28f3f1990b740bdp-2), C_(0x1.3575a87d9c1633de9f0ee95125a2p-2), C_(-0x1.7e644ab11888684db8a7b8d90489p-3), C_(0x1.a1785765bb948d52e0838b0df196p-4), C_(-0x1.7135a6ada8b52155f89869cf22c7p-5), C_(0x1.d8cfdcbb1618899a1617de65e071p-7), C_(-0x1.57e157b5bcea7fac037e4b9b62aap-9), C_(-0x1.5f633204e959fc32c151ba987165p-15), C_(0x1.10a4589d9f87d6dc51e36837ed0bp-13), C_(-0x1.592264d16e621b5275bdd9d12d3ep-16), C_(0x1.89979784d7185338d2badb26cabcp-18), C_(-0x1.4f841169a1bad189406e2832bc2dp-18), C_(0x1.74953d3967ccd8cc322dbf252946p-20), C_(-0x1.f7cb1acefcf435a3d287cb8094c6p-26), C_(-0x1.c92be21aef0c9ac0fb550ddd5f87p-26), C_(-0x1.3b9a57c4ce7e7a8e7b0e1df188abp-35), C_(-0x1.6a58cec0fa224ca49741d5041713p-35), C_(0x1.4bf1eb8cd4c9c2273508a8b73f46p-37), C_(0x1.697067f1715a141417bb7553b3a7p-44), C_(-0x1.513d790bd242fdd412e02eaf3fd9p-49), C_(-0x1.b3943c02986a6636aaf05d95d84p-57), C_(0x1.54d330be5783db7123cd1333ac9cp-67), C_(-0x1.3f6e1e631364c64c65f6b5a7fe23p-80), C_(-0x1.d0d882f8587b498d8efb759e05fp-104), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 15, 1> { static inline constexpr std::array<Real, 30> value = { C_(0x0p+0), C_(0x1.af673717274af370272903c1fa7cp-9), C_(0x1.c7ad45d086ea4c5ed9ed7e340defp-3), C_(0x1.9756cb092ee06f6ac1eb577b96f6p-1), C_(-0x1.51916657c183447d0774789d6344p+0), C_(0x1.6cc6e8f0624052b2c0fdcc8950d3p-2), C_(-0x1.8cf37d6182ca0b170d0a042e4192p-4), C_(0x1.9a3fa2f41d4953051b0c6d4a1b03p-4), C_(-0x1.0a50be22f2b86dd755f1bb101decp-3), C_(0x1.df3f4f6c19d45193b61450be39f8p-4), C_(-0x1.2d4b7e715db6bf84cb93e1a16129p-4), C_(0x1.0681e4c20b9fce41d5b4e56756a7p-5), C_(-0x1.1b50d689cbed8df146901e68b6b4p-7), C_(0x1.49acd134a254ba0136bf2c9ddd8p-11), C_(0x1.16651955943e391787562b852142p-11), C_(-0x1.c26d1f2c70c86f0644644cef75b6p-13), C_(0x1.3002118e762a111c6bcee4aaae9bp-16), C_(0x1.49fbecfd7d9c6cba55cd30ac067dp-17), C_(-0x1.8781a4a6a5f7c8daadd9ede249c3p-19), C_(0x1.5ed0ad164acd249f0f9d827483fep-24), C_(0x1.da4a7558674addd03b35614f7a6dp-25), C_(-0x1.7e23c7237f3f9358779e22d38d23p-29), C_(-0x1.bd8f2cef8c9f03d137232e9e498bp-35), C_(0x1.1c61501fa10480730673344e3608p-37), C_(-0x1.c1b8b33989e0245e7c861b898f54p-44), C_(-0x1.95156f39cb33a3cd95db28e3bb11p-52), C_(0x1.d1f8ddb7d01989509bfbf0327d67p-60), C_(-0x1.34635de67ce8bb9a35ccd2f4bcc3p-74), C_(-0x1.c0c6d283f741e5d8d9e1ced44ca2p-97), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 15, 2> { static inline constexpr std::array<Real, 30> value = { C_(0x0p+0), C_(0x1.52aa167437ed3a97a2d16e2e7e71p-6), C_(0x1.2f386450cd3603452775e405daacp-1), C_(-0x1.92da3e0f4795f52ddad307073cb1p-2), C_(-0x1.010e6c23362c2f5a0189ea0fe7f3p+1), C_(0x1.ba5e5707337cefc73943a8303bc5p+1), C_(-0x1.6efa1a351e68942304e8e68b7bacp+1), C_(0x1.e2efff792ca6cd2456dfdb721f76p+0), C_(-0x1.e9e84815ce29a5578b4bc0477acbp-1), C_(0x1.3e7bcfc83dd34f0d929299013451p-2), C_(-0x1.3f21e5e83db9b76a1e6a21ec3442p-6), C_(-0x1.00e091b8310d7c425038e08dacbfp-5), C_(0x1.93252ea5d40edb85ff0ddad301dp-8), C_(0x1.0cb53bda124f4c4d4c0ae3af4779p-7), C_(-0x1.6ecc6596fdeb97786cd08cbbbaedp-8), C_(0x1.1da3c88de4593a0d10cc249b83cep-10), C_(0x1.0f705c9109b88bc792c8e251c3f5p-12), C_(-0x1.687f176415b5a1410c9f394cb959p-13), C_(0x1.03bf749271ea0dc9bfa9a81f4245p-15), C_(-0x1.0a570c997b8f6bb3aa2b6fc454e1p-20), C_(-0x1.b60c856b75c6f8f8db3b0f76f67dp-22), C_(0x1.2f36c8024d47853b1fc5abd2c569p-24), C_(-0x1.ab6b4d2a0c9eb0fb78406697468ap-30), C_(-0x1.b77dbd4d624bb182ce2a8088a4c2p-33), C_(0x1.02e06a0b5252899742121667393ep-39), C_(0x1.f900db818405bc4cfc19c190531fp-46), C_(-0x1.5cc6aba4a366fbfbcb9e7e9b2b91p-54), C_(0x1.79a9be1badaf05e53c8d4ae211e7p-67), C_(0x1.12cb1c6610cf5a5ca8d9bf45819bp-88), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 15, 3> { static inline constexpr std::array<Real, 30> value = { C_(0x0p+0), C_(0x1.bde47de89537efcc2943722b907bp-4), C_(0x1.ff6e39e05bc1960ac6a7468afb9ep-1), C_(-0x1.0edf7812c7e6f7d06a00b362ef27p+2), C_(0x1.788eafbfef56fcdc50a685d1f90ep+2), C_(-0x1.0b9e58d049e2b1cb9469b014878dp+2), C_(0x1.57d72a54d9b7d9046e3ca22b5dccp+1), C_(-0x1.5aec59993d64c03ae451f5fb822ap+1), C_(0x1.66be004fbc25830ff3a497ea74efp+1), C_(-0x1.257b730e2148d4f4b3feb863502dp+1), C_(0x1.61e6a248fa765db41939b126fafep+0), C_(-0x1.1d661708485736ce63b6c04b417fp-1), C_(0x1.7634ae9385e7d28433590ede5d72p-4), C_(0x1.aae5eb36cf2339bb1da3727f92c7p-5), C_(-0x1.66a2dd81189a5724bb1062f0dfebp-5), C_(0x1.9ee5c38dff3c5ada29575f743d87p-7), C_(0x1.cee452b55c630166e1f1c650af12p-12), C_(-0x1.7d0e63753adf810a13b7946ecd6fp-10), C_(0x1.95a9bb14ccec080a6175688009ap-12), C_(-0x1.ac68b8496deea7093d3eaa37178ap-17), C_(-0x1.4a3e531dccd5a7c88df667aa9928p-17), C_(0x1.45a5b2adacfee470f99a3f9acab4p-20), C_(-0x1.a0585e72874e51a270db9477829dp-28), C_(-0x1.4a4aaf36fdaec2c3a3e857f50877p-28), C_(0x1.818dc3c36642c77c4040a75f3899p-34), C_(0x1.bc8ec635290e455c58f05f4aae9ap-41), C_(-0x1.1c50f4adb4d48c39b492719c193cp-48), C_(0x1.541ee5efeba27ec1d6332fa4f538p-61), C_(0x1.eef3c669427ba33d298eab6d070cp-82), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 15, 4> { static inline constexpr std::array<Real, 30> value = { C_(0x0p+0), C_(0x1.da9efb84cd101b891a55bf085a33p-2), C_(-0x1.0a963523c780f95520ba62e1635dp-2), C_(-0x1.6ead78b2a7f870bae850968c013ap+2), C_(0x1.1fb0b7ee7fe9b42077abdaf556e2p+4), C_(-0x1.a26b20f9bdeeff0cd0b5e878c8cap+4), C_(0x1.5a362701692b5d54a80faabe0329p+4), C_(-0x1.c3b93743ed5e1f4aae7ff96667ep+2), C_(-0x1.0393f54066e2a86d4f5766fcec98p+3), C_(0x1.ce0e335b9b5cfd8737f6de07dc86p+3), C_(-0x1.3371f4378fc25cdcbf584ed9698fp+3), C_(0x1.04744c732a8970957ba707eb759dp-2), C_(0x1.5d5bbaac2d3dd399541ae8c8527cp+2), C_(-0x1.56903abc9d372d08f72cf8f9b7f6p+2), C_(0x1.4f367450bb0294accf5c9a7e742cp+1), C_(-0x1.16f1bf1e47dd7b33b29f107a7717p-1), C_(-0x1.0ca6089fc41ee660907b2bb584cap-3), C_(0x1.fd1e6437298de912355a40f30818p-4), C_(-0x1.127569c6d3d201e096a74c3e92a3p-5), C_(0x1.031ce43d6f2a9b28afac205ca3a5p-9), C_(0x1.dbc5a12350173dc4ceb0edd40202p-11), C_(-0x1.6e57586c99db2a8af6576e5d9fc9p-13), C_(0x1.338c12c9a95b47e57d454a7c66e9p-19), C_(0x1.ec833bdc8d6ab1cf492647696452p-21), C_(-0x1.31ee1e222a82fe6e397b0f1ab0a7p-26), C_(-0x1.068cce25031d061c7d5229b85c51p-32), C_(0x1.ab486d191520d8a9aefca6d39becp-40), C_(-0x1.971ac61147c4bd5f21d58d94dd2bp-52), C_(-0x1.28365b5992261cb91d89a4a61c9dp-71), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 15, 5> { static inline constexpr std::array<Real, 30> value = { C_(0x0p+0), C_(0x1.8a28bf1f4baf0256370de9e50cdfp+0), C_(-0x1.0b8ecb513e670e46e8b61ff5e5a2p+3), C_(0x1.301d17ac5e1c6daeb2bb903493bbp+4), C_(-0x1.80a5fd5ebbea4cbe232c3d8a57f1p+4), C_(0x1.4a39e3e1048d62539834148e9e34p+4), C_(-0x1.1148278e9d9a1304c4d27a6289e7p+4), C_(0x1.18e244d79a0328c7ff6eaa1380dep+4), C_(-0x1.3908669ba07796469d9944fd1af2p+4), C_(0x1.80446c71adb1488769cf4e603a7ap+4), C_(-0x1.0a40794798e411ebd23986dcd959p+5), C_(0x1.52509dd04c4f6aeb9cbf4fd2a65ep+5), C_(-0x1.4b468531c5b19f58ba9821140c9p+5), C_(0x1.c80f1430e334a07768f1a5bc676fp+4), C_(-0x1.82ded3c89e7e9fa329e76277e5cep+3), C_(0x1.7610a167089f1959ecdad2bfe856p+0), C_(0x1.b0a89a8818c0677d48d7304191d3p+0), C_(-0x1.2b516da5d080fbac57ead9c2cab4p+0), C_(0x1.488189c0e63233e310386fe21bdep-2), C_(-0x1.16dd91fce8d2f3a24746d48a1c72p-6), C_(-0x1.957d5757f4d581e1eb81397c4cedp-7), C_(0x1.613bcf2c2fc6a53ed2c91b207503p-9), C_(-0x1.0adbc024da55152d1e362e31540ap-14), C_(-0x1.44905597a89087a3899ef1de6ff1p-16), C_(0x1.238bd55115863b967f9591633549p-21), C_(0x1.0b863bc593a1d515b8c451bf0e45p-27), C_(-0x1.2dac52b5d35bb8e11505ea96f44p-34), C_(0x1.a8ab5a61388b1db01ad925c31a8cp-46), C_(0x1.34fcf88bcfb3fdd3eace81ef29a8p-64), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 15, 6> { static inline constexpr std::array<Real, 30> value = { C_(0x0p+0), C_(0x1.e156f58145aba7d0b30fa35cff6p+1), C_(-0x1.d9350b2238c2b904f5fdfc3f59d8p+4), C_(0x1.b03e3957ecd6a002d130922f2289p+6), C_(-0x1.f51dfa789d878832ad001b3c3bbap+7), C_(0x1.b1d9ee3321d942364cb8258ac548p+8), C_(-0x1.3c90b7e3ca1db82e1a61d1d6988cp+9), C_(0x1.a1025f9df5665ef6d6390bf76e1p+9), C_(-0x1.ee82dbab6ab103949b52c0e24238p+9), C_(0x1.fcf169933904c38827bff6f06e1ap+9), C_(-0x1.beee0dc0c8ddb1ba16139309e6dap+9), C_(0x1.545f49e00f495f369a9c2bc574c5p+9), C_(-0x1.c39ca355bd5d296f37962bd729eep+8), C_(0x1.d17e6e268802ca2d8ab4ba84d645p+7), C_(-0x1.8d05e2b81cf726b84ae7be04d2f8p+5), C_(-0x1.a57ddae4deced8b3bcbf57c78c0cp+5), C_(0x1.065bfb9cfed103880a47e8cebd5dp+6), C_(-0x1.1a783beefce87b0115cd7f827bd2p+5), C_(0x1.2e9f2c1581a696ea729509934246p+3), C_(-0x1.3cad9a2427051e071bf1f9b27c09p-2), C_(-0x1.1b4b3a7aa70e82673e69d678de04p-1), C_(0x1.15a31469a9ce01c4f9e606bc0537p-3), C_(-0x1.5c66a63c9347469ce6f66ff5c6a6p-8), C_(-0x1.5db560cc8a8d9420c2df7533732ep-10), C_(0x1.c57be52a95f9a3c03fb08957c434p-15), C_(0x1.c9738067c5909d91761fe08abd47p-21), C_(-0x1.63f652c47225898a139ddd320614p-27), C_(0x1.769767db4423b6439ddbe400214ap-38), C_(0x1.108b386e39e95695575892a5277bp-55), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 15, 7> { static inline constexpr std::array<Real, 30> value = { C_(0x0p+0), C_(0x1.d870debcc05c458cb431fd983345p+2), C_(-0x1.0c2b8b0b28193dcd228c0a0c405bp+6), C_(0x1.10bd374d63550b983999c56c677ap+8), C_(-0x1.4441daef321d4016bb9b2c10ec43p+9), C_(0x1.eaed48222cc9b9253ebb102b9831p+9), C_(-0x1.dea055aad4ecaefb97c3b4138e1fp+9), C_(0x1.0ea6de87556ea6a2de81d408b23ep+9), C_(0x1.3bb921604519d1ae88e6a7fa3786p+5), C_(-0x1.7c03d4dcf551472cf7483533c9dbp+9), C_(0x1.b77df6c77230b9a06a324d910941p+10), C_(-0x1.59dd45c186fb11c5ad121467058cp+11), C_(0x1.92ad5ee85458cf75ddc7493a06c7p+11), C_(-0x1.7716e9b298971ca51bace1729b0ap+11), C_(0x1.34cd942cd473a5a7100d811101f7p+11), C_(-0x1.d2108687fa36ec88dd6bfb56d5c3p+10), C_(0x1.27e2041912517aaa65b2132e4553p+10), C_(-0x1.0ee0131c1b04ee634d1b07d2c971p+9), C_(0x1.13ffc016f56ca3a3bb78dd1c64f4p+7), C_(0x1.9021a9dd4e12af18897a92604f62p+1), C_(-0x1.cb9505a70965b7f9ec7314ae6da2p+3), C_(0x1.f11cd618c3358a67a8f728986e77p+1), C_(-0x1.a3fefe1a942d41c95d66abeb0178p-3), C_(-0x1.a953da883746e1eb5fc521fbad44p-5), C_(0x1.9718bee3af728b9e4c2d8088bafdp-9), C_(0x1.ad4249f39958d903ac018ed0138fp-15), C_(-0x1.eb70cd1aa40511f5c12a3ada0131p-21), C_(0x1.72006a07a097f617e889edbdb056p-31), C_(0x1.0d30627e6a2ad3489cda0318f0edp-47), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 15, 8> { static inline constexpr std::array<Real, 30> value = { C_(0x0p+0), C_(0x1.155158ac6ea984ad1f3ad98465a9p+3), C_(-0x1.4fec3a6a32c1ef2818fdbca7bd5fp+6), C_(0x1.70dec41eaf97d263c2e4504b0b21p+8), C_(-0x1.e94cfecb1efa1478b22094cf32b8p+9), C_(0x1.bf0b100d34d0405ff7a1094810ecp+10), C_(-0x1.39291803fcf47b5c26824c7c465ep+11), C_(0x1.79ccf50afb46dbd4b77400a63149p+11), C_(-0x1.ab6c90991611b280fa6243394583p+11), C_(0x1.c47ed9a17b9cc8042e779917f5f2p+11), C_(-0x1.af1005783c9c08a75d46ca645f35p+11), C_(0x1.72a859cabb471f7e1c8ba7bd2a6cp+11), C_(-0x1.2846e6b9b14f481005e402049827p+11), C_(0x1.b3d87dff6a954876ee30a3fd1e1p+10), C_(-0x1.1ae10527ae49437f7880589e6393p+10), C_(0x1.41e16e9c43532c08707a85b672ep+9), C_(-0x1.460030c5bf206e4d0618004a8fep+8), C_(0x1.0818e6dd9acdc76d8ca94db3b3b3p+7), C_(-0x1.8ef0b66c7662c653e53071c7fb7ep+4), C_(-0x1.6eb8ec2d2fcf0443ad7c1412d0d4p+3), C_(0x1.3aba0303f01c424453fb561d43b2p+3), C_(-0x1.588d6d239648dcf73cdacc19a23ap+1), C_(0x1.5ca063a2897a34772f3d9594be58p-3), C_(0x1.72c884e06d399a8e64ff05cdd7a2p-5), C_(-0x1.2b7b99da7239a8d08435e37194cp-8), C_(-0x1.359ad5ec914c5a48afa1ae580694p-14), C_(0x1.0cff089d4d592f01775a150c05eep-19), C_(-0x1.207535755ab2ee6fe496486e6edap-29), C_(-0x1.a3ad9d559345b904814003502ba2p-45), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 15, 9> { static inline constexpr std::array<Real, 30> value = { C_(0x0p+0), C_(0x1.174fb1d6730638307d1e4b445fc7p+3), C_(-0x1.5cf63b4072a084fdeb886ad661e9p+6), C_(0x1.859702b93091fc7e65868db7a8fbp+8), C_(-0x1.008e38c64d4049e94bd38a5f00e3p+10), C_(0x1.c03c1b8df613f180675faa2c200ap+10), C_(-0x1.1e0d30516cd0d5b6c1126d4bf14cp+11), C_(0x1.33504e2e62ab9029d44ee63bfb62p+11), C_(-0x1.4498a39b45dd2d15e6ecc8905aabp+11), C_(0x1.500c422b7e4d651447cfcdfc454bp+11), C_(-0x1.2d6f916f2f063d6cac6b467c2932p+11), C_(0x1.c5bd8b8beccdb3ef655c28cdfe75p+10), C_(-0x1.3b7208dc1850750db50ab0ef592ep+10), C_(0x1.a4b1819107c720e54775d3b0e2c4p+9), C_(-0x1.c03583e49298125db8e2fdf27d4ep+8), C_(0x1.1254d5dd1a3c865791d5348ec394p+7), C_(0x1.be19509979c252700bdddf4796f4p+2), C_(-0x1.6abf524121ea45d75b1ac598d945p+5), C_(0x1.bdfa9494723d3641f8f4e66eff1ap+5), C_(-0x1.7a9c102bdb495114d11be11a8205p+5), C_(0x1.86920d3d07ed23a9933ffc257d69p+4), C_(-0x1.a9adfb25c4f27469db3fea5dd201p+2), C_(0x1.1337641b89dbbf1427d95e0cc537p-1), C_(0x1.191c64622c1b13245bafd3429ab6p-3), C_(-0x1.88d18423866c243d7190f3f8f03dp-6), C_(-0x1.aee4f466bb96965b6a34b6c35598p-12), C_(0x1.15e5e9747fe1bbdbc08f26b48b4cp-16), C_(-0x1.bc4491eee0fdcc0c5c6a94682339p-26), C_(-0x1.431c03e754cd8a35cd8981f0bf35p-40), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 15, 10> { static inline constexpr std::array<Real, 30> value = { C_(0x0p+0), C_(0x1.57dd202e5e84ab856980df8a0abap+2), C_(-0x1.b426b94987908d499f3bffafa19ep+5), C_(0x1.ef50af36bc949ed3fa7cc19e8e96p+7), C_(-0x1.4da8e644667e6ac3b7b19c4c383dp+9), C_(0x1.2d889ab089910f7ad4219226878ep+10), C_(-0x1.9456ec86efc743d502abdf76eae3p+10), C_(0x1.ca1f75d29c1784a6a7a3af88a28cp+10), C_(-0x1.f2eaf24b48be90f886d98564f553p+10), C_(0x1.0a60e2fdcea779a991419059c46dp+11), C_(-0x1.07fe75c2d85392f12125b660934dp+11), C_(0x1.e2b37ed5f446198c3a6ab7d8b74fp+10), C_(-0x1.a28fcff6e684b5cca8e0268f1e92p+10), C_(0x1.5596d2be7c1f83852a4b17681f79p+10), C_(-0x1.02761175eccb4a7f32feddc56feep+10), C_(0x1.70f45a3e9b6c87dda520903f4aafp+9), C_(-0x1.edf5a5b354e128a66fada7d4bcf3p+8), C_(0x1.27b1e13298bb3ef65c7ced26ff2fp+8), C_(-0x1.3be69243ef2c31f0230131660198p+7), C_(0x1.3b71f0120f2a47ab2f14bf7b7d89p+6), C_(-0x1.11985d9404f45378f95059bc551ep+5), C_(0x1.3b5a9762f053ae040918d7979484p+3), C_(-0x1.c32c18767db723614ce78e339586p-1), C_(-0x1.5d8e89b8ba2f46a3386878a383e3p-2), C_(0x1.3b1b46a97c2fa9eb1545e9c9486p-4), C_(0x1.23706d03f6f7466fb42dcd72c19fp-10), C_(-0x1.9c26fc84f3ff5e0f45e88806fbbbp-14), C_(0x1.962939a138e2b376295550104948p-23), C_(0x1.27428a5934f9dbd8cb77b8eb93d8p-36), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 15, 11> { static inline constexpr std::array<Real, 30> value = { C_(0x0p+0), C_(0x1.82ba18a2815549dbb583ba20e3a4p+1), C_(-0x1.ee321ac782e8103dfda5e2a50005p+4), C_(0x1.174e5f65a44a587e2370d6742aeep+7), C_(-0x1.6e81d57c4c979417ab1a67acd69dp+8), C_(0x1.368de3361fae4ae909df52a5836ap+9), C_(-0x1.7106731d7c870bc083e5fa51f617p+9), C_(0x1.661d220cefa0ffe013a28a70693fp+9), C_(-0x1.6833b778e773ab42be55fb8d5e31p+9), C_(0x1.833c1b7a24cc4442e638654d7d43p+9), C_(-0x1.704d0cf5b403f737ee51433c941bp+9), C_(0x1.2a287b4a8744be736369f360e45fp+9), C_(-0x1.d795731af32d4e2789960ef06165p+8), C_(0x1.7a6623bbe9af7bf6c822bfb77cd2p+8), C_(-0x1.0ddd9fa1ad021e162c6d71d17f6ap+8), C_(0x1.4f824182bb440977dbde7b407e9p+7), C_(-0x1.9b8d6efd833c3f31fdcf2bc0b9fap+6), C_(0x1.e6b9bfc912a60c385c4952c1112ep+5), C_(-0x1.d872a65489bc6c3914d51095ebc1p+4), C_(0x1.82e4e50171640b22bb8023c09d2ep+3), C_(-0x1.3c81b080d7c589f42c4b3bd2cdd6p+2), C_(0x1.87117e04fd822595de3e0b568ccp+0), C_(-0x1.f2d1dbd395098c995334374fed2ep-6), C_(-0x1.327c0d249413fa2745cbbd687d3ep-3), C_(0x1.13b8c9585145f7834dc70fb2de56p-5), C_(-0x1.094893076dab22e2cc6f5a93ce22p-13), C_(-0x1.784719262e6d99b5739a61a4981ap-14), C_(0x1.31d26875ab45ebb06f0484706cp-23), C_(0x1.bc3aef2e9698a9624f45add91d4dp-36), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 15, 12> { static inline constexpr std::array<Real, 30> value = { C_(0x0p+0), C_(0x1.229017de89888d3b45e2c184d9bp+0), C_(-0x1.74b098d7b294230e1965426f3612p+3), C_(0x1.a3d6fe58853c1e5c5b0a3a09e40cp+5), C_(-0x1.0ee9fe2c639a74c7c045b3701c38p+7), C_(0x1.b7ec28edec4542d27f9646062fefp+7), C_(-0x1.dcbffedb3a507fa5c4f4218a69c2p+7), C_(0x1.8f9512e48d1c46e9aca0a2a1ffcap+7), C_(-0x1.7421b1a8804595d4b26746d9ca32p+7), C_(0x1.a17e1d21e73d1b2881053890e718p+7), C_(-0x1.8b13badbca1d886a8838c2c2e2e8p+7), C_(0x1.210062e92f4896d0f00a29c58cfbp+7), C_(-0x1.a9798d44da6c2035da535dfbec27p+6), C_(0x1.62f521d1972a85eb2c6f26f231b9p+6), C_(-0x1.f0d14679f69c06584d1c30d18738p+5), C_(0x1.0b0540b21cf0924f5546e5194d02p+5), C_(-0x1.2e7f81d7237507956599c3ca61c1p+4), C_(0x1.776b19bc1de7ac2a6f830edb0d24p+3), C_(-0x1.390aaca35a348d0447af0cac40bp+2), C_(0x1.0e68e9445701769efc7a68d035e5p+0), C_(-0x1.1d9e671612a45bff7deef6e6cc44p-2), C_(0x1.1e141f6f8381b1b9942811bfdb96p-5), C_(0x1.626281f06a565209b56968645fb1p-3), C_(-0x1.00510e27c6af9fccce7dab2661cp-3), C_(0x1.dda065aa933f3a25232d375fa99bp-6), C_(-0x1.397e42b4cc1c25443933189b9067p-10), C_(-0x1.5e2780fee3a224f5cbc2e8463206p-13), C_(0x1.93d63eaebefb797682d434c6108cp-23), C_(0x1.24c485651202d28a48b67967bbebp-34), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 15, 13> { static inline constexpr std::array<Real, 30> value = { C_(0x0p+0), C_(0x1.2dba81606cdf44cd9f04d2f8bc14p-3), C_(-0x1.83ba9062dc10a95420ae8251630ap+0), C_(0x1.bc6ce42e9d3a21102e4fdf0d4671p+2), C_(-0x1.2c97bd817af94b6452b764a95107p+4), C_(0x1.0e06914d9315537516f107f294e6p+5), C_(-0x1.5f4706680d4ada71d3fe8928e941p+5), C_(0x1.6ea3fbf492340b1a8746b11d0c42p+5), C_(-0x1.5a777ed4931f215f8e0a373e4b9fp+5), C_(0x1.424978021982d2d37f62990dfb19p+5), C_(-0x1.3090ff3d7fed662537bbff91030bp+5), C_(0x1.23e4419ddb640edbe25a71aaad29p+5), C_(-0x1.07fd356f7673b92c13a9d66edf4fp+5), C_(0x1.a8f488a3b6e4b2eef60c68cd2c1fp+4), C_(-0x1.49932384ed8b4cc7bb541dede413p+4), C_(0x1.0a96d421140fecc2982baba8b026p+4), C_(-0x1.8f60cd9c056028206308e7df4429p+3), C_(0x1.003bcbf26a5db032107ad008618cp+3), C_(-0x1.433ef046d9ed13921cc6b579a83ap+2), C_(0x1.a65b7dff9352096da27547ffc3e7p+1), C_(-0x1.d36032adf2dbd6f014bd3f02cf6dp+0), C_(0x1.a4a1ad470bd0ddc88c1710fd49dcp-1), C_(-0x1.88e9f63513ce060ad42735911b82p-2), C_(0x1.6764f965c95116ec3ca5a4be4d2fp-3), C_(-0x1.91c36b23af1d7e93ac71caa65612p-5), C_(0x1.07d03d7a1adc182d361556de1e4bp-8), C_(0x1.362d3e37ff6cd230a2a77cad24c8p-11), C_(-0x1.92dbfdbfa8197afc834aaea734e3p-20), C_(-0x1.22ff804507dbe78851ce06e1d7fp-30), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 15, 14> { static inline constexpr std::array<Real, 30> value = { C_(0x0p+0), C_(0x1.8dd6e1684e11d5d1ba3be6ea3c1dp-6), C_(-0x1.ffb4de00653d36e2054de2d9b35cp-3), C_(0x1.1f8df89dea983b6a6839c59e1daap+0), C_(-0x1.6eae32a3a790681f248ae47d8bf4p+1), C_(0x1.200cfdab0a8887ae485a3302d7acp+2), C_(-0x1.1f287662480ab738cbe219de6228p+2), C_(0x1.90990b7ee9dd1f94866d2e2c98f7p+1), C_(-0x1.3d166b62b6085e29fb936a0976f7p+1), C_(0x1.74d60ae1a8ceaa71b4a74664e6fcp+1), C_(-0x1.68026579c2213b7f75e6c5dc86c1p+1), C_(0x1.e76ba8ae988d51e5857ecafcf58dp+0), C_(-0x1.60830949d4c82da954f5df283712p+0), C_(0x1.48f2a8ad7050c9588f35978df03dp+0), C_(-0x1.e7d09d1d5c76d8ae64a80dc22b4p-1), C_(0x1.1252ee85de9250052c51460801d2p-1), C_(-0x1.6e9d007e3ce50ac7539c0411656fp-2), C_(0x1.0a88fbec92db255ff329ff3310a4p-2), C_(-0x1.16ea71f276b00e5a14dad4f88487p-3), C_(0x1.018afa9348367b971e98c4cc0c2cp-4), C_(-0x1.2fa053de7510dd5de40051b25ee8p-5), C_(0x1.2375ee2696f86cd08bc27b41fb5bp-6), C_(-0x1.73b10c938e4b6609ab6cf8acbfb8p-8), C_(0x1.1decc8370b2354d839f55dfbd7ebp-9), C_(-0x1.b8713a4dd74a971b693427cc738fp-11), C_(0x1.732711f764c017456161af308333p-14), C_(0x1.5deb76c540b6c1414e8c8011ad5bp-16), C_(-0x1.9271259f104138f720ca0ebaa72bp-23), C_(-0x1.2099915b9335422a7d16c948a51bp-32), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 16, 0> { static inline constexpr std::array<Real, 32> value = { C_(0x0p+0), C_(0x1.674708c20fd278e13cb308fbf6b6p-13), C_(0x1.27cdb30a789a9a4cba57381b80dfp-5), C_(0x1.f3f9a4213a58e15fea805c6fce03p-2), C_(0x1.8a1b0e63e768effc8742d136ac6ep-1), C_(-0x1.d0008134e7b24ce7a0bdb2d5e177p-2), C_(0x1.06c9817f611e98379b152a389fafp-2), C_(-0x1.4ec109006f3ab5eb9ef4b4145d24p-3), C_(0x1.b93c322324f48f0734b615fc9893p-4), C_(-0x1.09f5f4083e296fb6c1df50020f51p-4), C_(0x1.0b6a75dfa25cd5d117e10197333bp-5), C_(-0x1.a17eb803ff745c2b927f4b56bb55p-7), C_(0x1.cda18d3f662aa65f684ad290727fp-9), C_(-0x1.1815693b1e509dbfebb4547eb7c2p-11), C_(-0x1.547c4d557ee7eea60970ca463eb3p-15), C_(0x1.a1d518779619a935a6506c218d6ap-15), C_(-0x1.fb90c559a340a6d74429771a650ap-17), C_(0x1.085bbb58c3dc5e159337591d11c5p-19), C_(0x1.4a16ea18a78a9255137a36b6eeb6p-22), C_(-0x1.3b0f83cef7c9cd6e4992ef7a8e0ap-23), C_(0x1.426950d9b6bca7a253eba2c282ddp-28), C_(0x1.acf5cc83787c76964322f9b1343dp-29), C_(0x1.c7dfc1cbcd560059e1fa3bbb0da4p-37), C_(-0x1.99a4987142751268f68b0c6ed2ep-37), C_(0x1.0c54f6dbbd52aba64c70d9892a56p-42), C_(0x1.60b6215484a1c96af7151c51425dp-49), C_(-0x1.6360709f9f94bbe775bd0ffbeceep-54), C_(0x1.f308a7934d0993ea019328882821p-62), C_(-0x1.dcd83ccd7b40e72afa7a2bb7cfap-74), C_(-0x1.f4c81d09055a8112f9a8f0e29d58p-87), C_(0x1.f541a7bafa4019158f37f50aca47p-112), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 16, 1> { static inline constexpr std::array<Real, 32> value = { C_(0x0p+0), C_(0x1.5e2be3ffc02e5cb63d505e4d42d9p-10), C_(0x1.115596e3350ec9cfc7fd8b282c15p-3), C_(0x1.8e066ec21fc6a13efd57c0a1a8d5p-1), C_(-0x1.9a3ae9a2a692b7d6fe0312f42fd2p-1), C_(-0x1.b4e823397cf87b829664fcfb615p-2), C_(0x1.24d79baf908bbde12d97a94a7f11p-1), C_(-0x1.96ff08990aa1ff2b3a6156b3a6f7p-2), C_(0x1.7cff079859d44a97134acb0b3815p-3), C_(-0x1.3b2f6fbc125eff4f9e00971a8041p-5), C_(-0x1.8c439625af31faef37a9ac49e57fp-6), C_(0x1.d82f61038e0e00ad9adf7940901dp-6), C_(-0x1.d308486caa607d54998083598bc8p-7), C_(0x1.b8ca6f1e525d8fc1aecc191249d8p-9), C_(0x1.4ea26d28d30874cd6f1bece4d0cdp-13), C_(-0x1.4455094b3efac9d3c28631c94fc4p-12), C_(0x1.116fb5095b299dc0400b6814e296p-15), C_(0x1.e6f46905743cf29b32a5a94efd0bp-16), C_(-0x1.73244b56511394e5623a6c13b582p-17), C_(0x1.105e30d7ecb45c8d929e54615ad8p-20), C_(0x1.85ee598e5c772af7b4423f5e4908p-23), C_(-0x1.5ac9f1c76ae72306c6963aa9eb6ap-25), C_(0x1.d789f3d703adce6fceeb7470ebe2p-30), C_(0x1.8d5e3e20027e865e92d2141a2b73p-35), C_(-0x1.c8b3833c3b76938050c849f3c902p-37), C_(0x1.38fe40b99904e82fbd88d14cb331p-43), C_(0x1.f524d19d8420a05a730c8d14369dp-49), C_(-0x1.a73b7d5e557e750b97979bfe8e3ep-57), C_(-0x1.c5320460bba019effc9564690ea4p-68), C_(0x1.a5354de9b5e4be0a26cfffd8bdbp-81), C_(-0x1.a59b918cf087f7e28a66eadc80bbp-105), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 16, 2> { static inline constexpr std::array<Real, 32> value = { C_(0x0p+0), C_(0x1.295efeac152d79633d42d6d916dap-7), C_(0x1.9d61cc47e5de2628b18136c91ea6p-2), C_(0x1.161d416b67637e8de5329814dbadp-2), C_(-0x1.5b7a45663376a9aa5f95ed877064p+1), C_(0x1.d1174d09edd0e5a9b8dec824cf43p+1), C_(-0x1.64fd520a66219e33ceb19171c931p+1), C_(0x1.05168da96484602e8bf4113ac4e7p+1), C_(-0x1.6575089c4586c8407b43149ab11bp+0), C_(0x1.a38bf0b53f437316576c7b5f77a6p-1), C_(-0x1.889b16ed752f17512574ee20842fp-2), C_(0x1.152c76b8c5aa61f7d1f86545cf96p-3), C_(-0x1.1b4c99876d201e8bbadda8305eebp-5), C_(0x1.907f1e8b42628bd87c6dfaa42428p-8), C_(-0x1.48b152205d27ec7322d3d940da05p-13), C_(-0x1.a3276d4b1b41ee0d43115b5aa81dp-11), C_(0x1.19008ab2bad0e78321ce13187a8p-11), C_(-0x1.4a0f2fc3a3fe6743d3250b9f0687p-13), C_(0x1.b16d8531bcd974ffcfcfb275888ap-17), C_(0x1.3c9bc919e0e49ac8c1ec9b7c72d7p-19), C_(0x1.899254d74191895a0ee7c7e368dfp-24), C_(-0x1.e003adff466a6871b6189e153009p-24), C_(-0x1.b118f867cd64dc8214de14f22a3dp-27), C_(0x1.a8e81cf9b2bf4ed6a7f80b7fee49p-30), C_(0x1.472047d4ce812177c28860710d42p-36), C_(0x1.0bc546f1206b056c51ef6c4e3c73p-41), C_(-0x1.5b78778ec812c1a8126f0f855511p-47), C_(-0x1.75c5773026aebf48665648526e47p-53), C_(-0x1.4450e0ff79233cb66d7ae0406fdfp-64), C_(0x1.74639b34e9729d879c349c60a705p-76), C_(-0x1.74be14820bd545c3f1e6ecce41eap-99), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 16, 3> { static inline constexpr std::array<Real, 32> value = { C_(0x0p+0), C_(0x1.ade0c67a6df62bfb0e80195f4993p-5), C_(0x1.c28b430a75f298c1d73bb81e4353p-1), C_(-0x1.5f4ccfba427cea15c66f4a5c12bbp+1), C_(0x1.cdb8f607de72e596ea568a034c8fp+0), C_(0x1.f77743196657a78ad5bf74425543p+0), C_(-0x1.dd879ba809267a9d7904ab437cc5p+1), C_(0x1.37053c10bce28d1022d31ac1246dp+1), C_(-0x1.1bfa76c0a943a24b6df5bb2abebdp-2), C_(-0x1.2b5034c5e7cec27aa44e7ea3a878p+0), C_(0x1.63e2260baa9fdeb5f048ba37a04bp+0), C_(-0x1.a29913a0c0f2ddeebb2bd3c275b3p-1), C_(0x1.852867c8ceb35a88f788b40857cap-3), C_(0x1.9a9664fc9e678ca180654356c297p-4), C_(-0x1.c29f78e2de8f527b7cd8a08d24efp-4), C_(0x1.54d634445fcf6eedbc5dccf04eadp-5), C_(-0x1.41b2a5a54a66286808252915b865p-9), C_(-0x1.225d9fec5c6e8c447caf2b42ced4p-8), C_(0x1.f9019974a7ddb631ebee782869d1p-10), C_(-0x1.2c283714217e754b55528b628588p-12), C_(-0x1.8e8742bbbfb2111f9226dbaea15fp-16), C_(0x1.c9f58c62dd5d38676514b49c9e2ep-17), C_(-0x1.61f6495ed1b8ece209fc78f1d085p-20), C_(-0x1.96b8b0f8a15e32028c8ee0076679p-25), C_(0x1.71f48c99d030adfe377a7056701dp-27), C_(-0x1.b5fc8d66ab6cfd5a83337a0cc9b9p-34), C_(-0x1.c5963ee2273d2d13e0940bb125cdp-38), C_(0x1.6b4e6ce52480a98b4ad64082a237p-45), C_(0x1.e67135f42b49adad00310559fa39p-58), C_(-0x1.6aff40a6dd5b409b62d44964fcf6p-67), C_(0x1.6b5790e714dd812f487575d04214p-89), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 16, 4> { static inline constexpr std::array<Real, 32> value = { C_(0x0p+0), C_(0x1.002833198203bf56e8fbb6905c21p-2), C_(0x1.74f145f5180b48bf2521976daf68p-1), C_(-0x1.d40722c67b8b2c63d49b5a9b6cadp+2), C_(0x1.2af6f0f464bc571c8b763a8383eap+4), C_(-0x1.a43135145799a27dfd1fadf6761p+4), C_(0x1.9a15ae0412710439a9b40c2dd4dbp+4), C_(-0x1.38d1bd49e9af291f59c9f34bcde4p+4), C_(0x1.6c6cdb14d7fe107edc16c4953b35p+3), C_(-0x1.13619aaa119f97b37d6d1c2c4585p+2), C_(0x1.d56ce1ec874a0c5dd634fb59d6d1p-1), C_(-0x1.e42907ae7a26468d6ecb1d9e3f24p-1), C_(0x1.e52911f9f656640a2404f83a2b4fp+0), C_(-0x1.ee224ef8eb13d4b961d19b7d1c3bp+0), C_(0x1.1f26d6223d44cb481a2910c6eba2p+0), C_(-0x1.5888435f5783628967f9baa03f79p-2), C_(-0x1.9e45fc4e6f7c960ebee0a7c398e8p-7), C_(0x1.dcd2d2ebfb6e400bbcf752c0bf7fp-5), C_(-0x1.93116bc1ac6b7200b82ddbf8d638p-6), C_(0x1.0e01783e342a4693e98c9edbf33cp-8), C_(0x1.31f3faa90de9ede16d914789626ap-12), C_(-0x1.f6b0df77a54401ad9bab438557ddp-13), C_(0x1.f05077a02c3aba8741da9769ad4ep-16), C_(0x1.2ec5b9d224e6bceb5db9ee6cff1dp-20), C_(-0x1.47f2b0eb68eda8ce48926b156c9bp-22), C_(0x1.bcb021bf883a1f92a78fc9df6525p-29), C_(0x1.1bcefd6cfba520ba047378483637p-32), C_(-0x1.34d97adc52a38a676a55a692601cp-39), C_(-0x1.6f2c8c9ca394fbdec6dda2487026p-53), C_(0x1.34e43d9253e6e8975e6c8e7aefefp-60), C_(-0x1.352f98f0f2e48db2a203fb32a0f2p-81), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 16, 5> { static inline constexpr std::array<Real, 32> value = { C_(0x0p+0), C_(0x1.e5d8b15d3664d52108fae09a8e52p-1), C_(-0x1.e7e4ae8313c9841f6b4ba59501e9p+1), C_(0x1.643947f56174ee22b35084254df8p+1), C_(0x1.8bf77730624fb34f058dbb215e6ap+3), C_(-0x1.39575fcf961c0f3da45ce2cb7fb1p+5), C_(0x1.f6657cd6c7e299b7cc89d7d3daa3p+5), C_(-0x1.2981aaa66ca36b3a94f8297750dp+6), C_(0x1.0cf300079688d85d6be476057064p+6), C_(-0x1.71528cd9cab137a39829bbec9ca2p+4), C_(-0x1.13658826409b41720bd51a0f2d32p+6), C_(0x1.5ecf135e336b7c201cd13f9f1c7bp+7), C_(-0x1.ca8fbd8754dc1920d78e0ace3c5ep+7), C_(0x1.83a96558c6c07294f0fd718cdf26p+7), C_(-0x1.9d91182e0786a78e2338c8bf2ff2p+6), C_(0x1.818f5ca05f023837d630b257f2ffp+4), C_(0x1.4e782cc994094deb153537dfc8d9p+3), C_(-0x1.7fba734a377970e0ae8d82bc8b81p+3), C_(0x1.361d7d826bb5b3b3a1616de586bdp+2), C_(-0x1.85fee8307d590ead49f8c992534dp-1), C_(-0x1.fcc3205624ce56be678cf9a5a7bcp-4), C_(0x1.30d54b861144b0080c77fb2ef955p-4), C_(-0x1.4236c7ccc62df6904f1792b21926p-7), C_(-0x1.6b6d4bcc089eed67f90762e3bff2p-12), C_(0x1.251cb75a77a65027fa18c49d6fe7p-13), C_(-0x1.7df627db3ed37f55c551bdd12823p-19), C_(-0x1.6d7ba0319a17f9c5347fd4ebc07ap-23), C_(0x1.047350b843565161f3ac671e5f76p-29), C_(0x1.ecabd0f857c5126fafed07e8e831p-41), C_(-0x1.035ef08b1273d485ae68801933a9p-49), C_(0x1.039e900e7fa12bdd9aa0b500dd5fp-69), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 16, 6> { static inline constexpr std::array<Real, 32> value = { C_(0x0p+0), C_(0x1.5c435b4994699430de1f0bf0f96ep+1), C_(-0x1.45ad88073e6251792d84638c28d6p+4), C_(0x1.1ac643e9c99f8dff42b4b5f9e976p+6), C_(-0x1.3bcd24e1c22f08a7330d952db5cp+7), C_(0x1.1132bead650e64e0cc6250fd5a4cp+8), C_(-0x1.a3321607e359615c22640184890cp+8), C_(0x1.2bec4ce73b524de840d2af975fb7p+9), C_(-0x1.83ddd4224b9abfb64ecabd8660acp+9), C_(0x1.b1ad4241d86bedd378c0238858cbp+9), C_(-0x1.9d7a3218170b28b67328a4e4a6f8p+9), C_(0x1.5526f87e8214f36e89fc59fbe6b5p+9), C_(-0x1.e996857ebd3fd865f8b8b57715d2p+8), C_(0x1.186a9a24f3387e74b22113290d4ap+8), C_(-0x1.4f804f76b6d5b86a618f6e232bp+6), C_(-0x1.84954fc1821007c0fd22bc06ae8ep+5), C_(0x1.59efa11d2ec6f964630b6fd432d3p+6), C_(-0x1.dac7ad3b33c95d5f07d90297e68ap+5), C_(0x1.62078796373e73b5598b78c1554p+4), C_(-0x1.88bb023e9f2f98b9b7a5caf3d0d1p+1), C_(-0x1.04b9160269b89d57d0a515a32ad5p+0), C_(0x1.18c6982acbd2cd140bf32d2822bbp-1), C_(-0x1.508ddc9d3ccb43c37b8bf661b39ap-4), C_(-0x1.539386e1415cf5772194fa5cb789p-9), C_(0x1.9eab992a4b9ab37998a4782656d7p-10), C_(-0x1.980b92ff814cc556c4aeda05445fp-15), C_(-0x1.761c29381edd29e5680cf5367b41p-19), C_(0x1.64e7e2ec4af2d5325d3b1ebf7038p-25), C_(0x1.1823b743e4c412fe2e1a1caf98aep-35), C_(-0x1.623923d3ddbaeed10b04fa360d62p-44), C_(0x1.6290fa803758e40f0b825bbc6f28p-63), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 16, 7> { static inline constexpr std::array<Real, 32> value = { C_(0x0p+0), C_(0x1.891443770e9f5b58ca0bdbd939d6p+2), C_(-0x1.c4b28f7dbecf38e874d3b242d4fbp+5), C_(0x1.d994c46f08417c9c24a3de260d39p+7), C_(-0x1.26defe09eb9e312242e62017ceb2p+9), C_(0x1.ddf577c4250f78c0132ae5d7d1cep+9), C_(-0x1.fd2079b0f3ddb297d557ffac7fap+9), C_(0x1.36152a2e286cfeac434a875affb8p+9), C_(0x1.d8616a51db368c3df9bbb5de82cep+6), C_(-0x1.190b42892374c709dd8c148043fep+10), C_(0x1.36219b396179567cea600ef5a5e7p+11), C_(-0x1.eed74001662f7e761e907ef9b166p+11), C_(0x1.31c149450a5e9832b2fbd7c32f38p+12), C_(-0x1.31807a4d8f7d8b9ec23e94e23c9ap+12), C_(0x1.07e37f0875c28ba98c5df12ea151p+12), C_(-0x1.9ca0e06fa4e40e6ba9a2f070a627p+11), C_(0x1.192392a49659f5be4afa683922a3p+11), C_(-0x1.28f7ef65a911c2242d4a04d3586cp+10), C_(0x1.8ef1182eeb70c3b810afe07ad9aep+8), C_(-0x1.076216da5c43b27292cd22bcb978p+5), C_(-0x1.3734a9c9c5014b6b42b155a6abedp+5), C_(0x1.2e313dce4fbf11c25ec52c766e83p+4), C_(-0x1.913ecda1e3436af7caac068805f8p+1), C_(-0x1.aba4e0591b35ef78388396d8949ap-4), C_(0x1.5578ca229685f75ec4dbb7fb72b6p-4), C_(-0x1.f3ff47839e58d032a1a624c1f604p-9), C_(-0x1.bd3a12076a4f509f06e99bb28599p-13), C_(0x1.29ffe91412a29d368ce7b0895443p-18), C_(0x1.5e7711914b058b73ae8c4ed370dp-28), C_(-0x1.267e3f1ece05182094aa29382cf7p-36), C_(0x1.26c8d9be624c3d09b42c989d403cp-54), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 16, 8> { static inline constexpr std::array<Real, 32> value = { C_(0x0p+0), C_(0x1.1c06072fbf26f358c9f078f98565p+3), C_(-0x1.65d998749f19f3f52787d2ac7bd1p+6), C_(0x1.9d8978b96f57f154ef9ce52c7bdfp+8), C_(-0x1.24c8d76a7f36d7089e3f4940c827p+10), C_(0x1.21d479bc00697b14d91a6dd4bcabp+11), C_(-0x1.bbc006c9393532c76b5d7283eb2fp+11), C_(0x1.2211c4425df9c2e46c401315e702p+12), C_(-0x1.5c64ff1d8bf677ab09ac8c8005b4p+12), C_(0x1.845a35a3158347c96beac73413ep+12), C_(-0x1.87e6df0fbf8ef42fd538df2c44e6p+12), C_(0x1.6504110de640c4682cba264cf46ap+12), C_(-0x1.2b9aa02be2b35409ccae86a8991fp+12), C_(0x1.cebcfb329a57eadc95a6866f02e1p+11), C_(-0x1.3e375c669dabfd4de916796f2023p+11), C_(0x1.7d70c67fe8973e080c2a8eb7f182p+10), C_(-0x1.8fd6874952e8a903dace07633bccp+9), C_(0x1.57b6f4096f1cf0152662dc88de7ap+8), C_(-0x1.3e2c004c73161017d1fe47d49586p+6), C_(-0x1.f1e0f66437531ffa287a43716481p+4), C_(0x1.39f676c7227564daf7244ac826e7p+5), C_(-0x1.07f7de36ead717df75674d143f33p+4), C_(0x1.6eaf02b444bc4ce4684168c04e9ap+1), C_(0x1.f8896c7b27aea8a0c13b638bec5cp-4), C_(-0x1.b78e4a3636f77d36045fd051d0a7p-4), C_(0x1.faf293c65fc88bb39eaf07f0c833p-8), C_(0x1.a6b604defe6a94f42a0056ad171bp-12), C_(-0x1.9886be2865e4c650159b7d4d95b1p-17), C_(-0x1.7c0bde2d4dd50659d8e873b48d0ap-26), C_(0x1.90aca39ea2e8ac3870ca13b1a564p-34), C_(-0x1.91166efa6d0a92bc7a2e9704d452p-51), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 16, 9> { static inline constexpr std::array<Real, 32> value = { C_(0x0p+0), C_(0x1.58e7df6732419db59e9ac42f9ab1p+3), C_(-0x1.c53a29616fa380817d7f5e347aefp+6), C_(0x1.0cc18d57a1a1fb48e108cac3a066p+9), C_(-0x1.7c92fc1b6ca3895680c38212861fp+10), C_(0x1.6a1945d20b68d8baff4381a817e2p+11), C_(-0x1.fab771c0e1baf24e2c8f95c4199fp+11), C_(0x1.254298acbb2d449a7b3bb526f729p+12), C_(-0x1.407f9dc95f9b1203f980178aa4a8p+12), C_(0x1.53233c63dd8a7f18f0a2b3af5ccep+12), C_(-0x1.3b528b34539979362d8c0e80e80ep+12), C_(0x1.e2ea2797d25e54507eb78c335f71p+11), C_(-0x1.3d6169dd11c9bca3212058149b0bp+11), C_(0x1.75fce5d641404560c1229131d8bdp+10), C_(-0x1.2b5b50127f9f56d44ea4f01f61c9p+9), C_(-0x1.18e0518b142ec5c99d05ce213217p+7), C_(0x1.ed1ee257a974ab35fe81e878de48p+8), C_(-0x1.f5a5a8d8a9b3c073ca67ee8615b8p+8), C_(0x1.920c943e9e1a266133bfad52e46dp+8), C_(-0x1.22c1385412c45fef72454e0ef403p+8), C_(0x1.4b1ba13f6628b1dd44be57f24352p+7), C_(-0x1.ec876f34dee07503da6a5d0e4af4p+5), C_(0x1.641261f15a2bc3d54eada0d94bc5p+3), C_(0x1.3bac7fcb6881fd2d747aef7d1cc5p-1), C_(-0x1.3ae0db5ff49e0fda9ef09cfb9b34p-1), C_(0x1.0ba445bef297ba3c0905b698e9c6p-4), C_(0x1.c3804abda5b0efa9daece8d22468p-9), C_(-0x1.3c78fba89f7e4dd2da5d2b0f1ab2p-13), C_(-0x1.6e90a45b17e11834e30d4035587ep-22), C_(0x1.34c398a5dd4857b9fcc2b9b3ec09p-29), C_(-0x1.351bbccd566d5b56e0d110fac029p-45), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 16, 10> { static inline constexpr std::array<Real, 32> value = { C_(0x0p+0), C_(0x1.0cfd9304e9d0e9e89a508d967352p+3), C_(-0x1.68c00ea69764cc01a573447ef7eep+6), C_(0x1.b4a63a85c6a121d6db6758f94115p+8), C_(-0x1.3c4fcf304828edf08897e340df25p+10), C_(0x1.35efe9ab816f6ad2ce3b95243287p+11), C_(-0x1.c3872b5b6dcd2512d759e390543cp+11), C_(0x1.1261ac83f506bff0f38c31198cefp+12), C_(-0x1.39e1fa3f00833a2dd6c432f2edcep+12), C_(0x1.5e4c9d364466ef749b8d0d88979bp+12), C_(-0x1.6b72e41a84905cceda3e7fc6c066p+12), C_(0x1.578fd4c404248dabc968b7c529b9p+12), C_(-0x1.30faf3648505cdf5f671e0ae34fdp+12), C_(0x1.0174ad7c898217c903f8f07741efp+12), C_(-0x1.942bc49f2f52a22fa3eae80252dcp+11), C_(0x1.25cbc7992fd63cf31740b115daf5p+11), C_(-0x1.914caac5676309ecc6f6c550d8ebp+10), C_(0x1.f93f030387c4d019b6838cf24389p+9), C_(-0x1.1b4f5dfc787bbc32262ca3f167bep+9), C_(0x1.1df01b8a36a8b0e740af0c5b60a7p+8), C_(-0x1.048db6f3ab7c1cc8ce49930b812dp+7), C_(0x1.730bcb9c58bfc20d60bef0471523p+5), C_(-0x1.09b56b87c1c7fb7baeed74ce6cdbp+3), C_(-0x1.4fb833b30fa7eeef6a7358348b92p+0), C_(0x1.e38e1048601a60cbceead8c786b8p-1), C_(-0x1.ee07e572041f738c256c5953b0d7p-4), C_(-0x1.913ced3c0164b56d323de7f36c57p-8), C_(0x1.0726b83c4032bf81b9ad0141e709p-11), C_(0x1.2751c6763466bbc5b359801c4ca6p-20), C_(-0x1.00ceb77e39cabc22cbab1770a0b7p-26), C_(0x1.0123085a8910152fac9990b7a672p-41), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 16, 11> { static inline constexpr std::array<Real, 32> value = { C_(0x0p+0), C_(0x1.6ddd33f198eb3c96ba1c54f670fdp+2), C_(-0x1.ef9ef6f596ce44132c5dde1777d4p+5), C_(0x1.2bec86422c72fb4a905555a96936p+8), C_(-0x1.ab3138ae63b3c1e29f1c692c8b8ep+9), C_(0x1.90171accf1ae92cfd9c146fd2557p+10), C_(-0x1.0b8279e6381aa2b741cb2d9796cbp+11), C_(0x1.21c7cbc3a51f50320f21aa56334ap+11), C_(-0x1.3291c6bd3630cafeef14937244cfp+11), C_(0x1.52187d4f278255d90661622e17d1p+11), C_(-0x1.5764b21031af003ebeca03a2b0b9p+11), C_(0x1.2d82b77758b7aad296e73eef7d7bp+11), C_(-0x1.efcf6fd97e7509c927b7122c5c13p+10), C_(0x1.96b834131566dc9e06167e63c7d4p+10), C_(-0x1.34d67cf0a39ad9453edbb75a25c5p+10), C_(0x1.9aafba6f0ff85ebebfb694ebd422p+9), C_(-0x1.002f1ef9723b265f846b3c2332f6p+9), C_(0x1.378956144d5be0ceae60b1a0aa28p+8), C_(-0x1.48f6827b3eeb52ea5b3fa287d164p+7), C_(0x1.17de886be7cb3ac887cff35422aap+6), C_(-0x1.abd1c377daaf4123bc47a29397f4p+4), C_(0x1.18836fa0aedf116ff47c167f808p+3), C_(-0x1.72b11631904f6bd3fd5a823e34cp-2), C_(-0x1.93c736e0c44c0da3f45cfa30760fp+0), C_(0x1.74105b4ecfea6c16423bc348f8fp-1), C_(-0x1.a9382883de207a4dbe62c7de34c2p-4), C_(-0x1.8ee02bc822713114de66688f8544p-9), C_(0x1.b89c5ecf7a7b773088c639b3a53ap-11), C_(0x1.5051009d42a4549b60dc1a4ffdc1p-19), C_(-0x1.a9ba33acc416babe2777385baddfp-25), C_(0x1.aa6a7d0ba81031b3c9971794d3cep-39), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 16, 12> { static inline constexpr std::array<Real, 32> value = { C_(0x0p+0), C_(0x1.7e688b7526a774b76724ba13a96cp+1), C_(-0x1.044f66dd0bb355e9e82c72d5eaffp+5), C_(0x1.39d2780b0ad2f5c130250e42d893p+7), C_(-0x1.b63bb8898df0968b0e5291c5adf1p+8), C_(0x1.86b367123a2139a59288ccfca3dfp+9), C_(-0x1.d8001c1817ddf23795b1149354dfp+9), C_(0x1.b397f071da3115c284e47fbefa66p+9), C_(-0x1.9ca191acc971e01d76f080b3e85ap+9), C_(0x1.d28d7edb2db091286a502e3d1491p+9), C_(-0x1.daeab5bf793f0a5db198f7c1b01p+9), C_(0x1.738e37d47cc21d48d3f57dfe7cfep+9), C_(-0x1.0785a3e74df59d20286619983999p+9), C_(0x1.a556a97ba734840eab5a765f294cp+8), C_(-0x1.320671c41025d2eac683ee371196p+8), C_(0x1.33661041ead74be914f62376ca64p+7), C_(-0x1.d86506577d5080199e51f7260b6fp+5), C_(0x1.9ebe0657238551a24ab6c6c0e20bp+4), C_(-0x1.ec9ee904293324442bcbed481925p-1), C_(-0x1.1034340999c868fff5238312a8aap+4), C_(0x1.04d7524f6a9fff23ceab9523e19cp+4), C_(-0x1.2fcc89fd04e88d59c75667d7c4bbp+3), C_(0x1.7c24bc012bffc7d1e21de0348c52p+2), C_(-0x1.c84c145900f77b34a4876818624fp+1), C_(0x1.57bccbd9e4fcea0faae4ccf7a2f9p+0), C_(-0x1.d81daf1af068d1091e32e8f2fcc9p-3), C_(-0x1.20f9f72def1de8f22a005f73e8a4p-13), C_(0x1.c2f2ad7e016f5272ff115101365p-9), C_(0x1.baf6705e59cac3284164d29d2adfp-17), C_(-0x1.ae94eeab2dbd4d40eac4360abe26p-22), C_(0x1.af91281d9938911a63573a1c8a3ap-35), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 16, 13> { static inline constexpr std::array<Real, 32> value = { C_(0x0p+0), C_(0x1.a308ef1d16805759614e47ced45fp-1), C_(-0x1.1df37cb20ef6cd526bae886688ccp+3), C_(0x1.5a47cc2daffcb2cf20f8cbe23f9dp+5), C_(-0x1.e7cc32d4c7f05cc178a92423af38p+6), C_(0x1.ba5aa6f58d154790fde87c08c1abp+7), C_(-0x1.137ebe2556bb5c31390bfbcc3555p+8), C_(0x1.07f96c27b79ba1c76a48900fad0dp+8), C_(-0x1.f176d6c3151d8ca65c2069cc8ba9p+7), C_(0x1.0c09a0e0bcb9ff8d7d5ef1548dd1p+8), C_(-0x1.12bf0f34a9a5500b54ae9f341239p+8), C_(0x1.de16d55d65d2bb62ec7f100c7235p+7), C_(-0x1.8c7b496d3d3fd8274eb146a1b265p+7), C_(0x1.56592506626bc28d37aec7a2a08bp+7), C_(-0x1.13d919c9693b2e85ee4209bf711ep+7), C_(0x1.8b69de5718a09e2e84e51d955579p+6), C_(-0x1.15b78c90e783729339c94d803f63p+6), C_(0x1.8188b8db550fea38899d2489ef66p+5), C_(-0x1.e03c011f666ac66011b7609652a9p+4), C_(0x1.12ed8b36e986458009c8fb08c63dp+4), C_(-0x1.36a5b057bc26ecf6312ef4c8aa89p+3), C_(0x1.3d2641cf67e8fbde6d24a0c08316p+2), C_(-0x1.11ef148707dfa11f55a9bad8158fp+1), C_(0x1.c294da23fe29fd37f9c13ab439f3p-1), C_(-0x1.4f57e7e05e818e7ff02709327119p-2), C_(0x1.1ebd9964081cf6e9a360b8a8d058p-4), C_(0x1.367917f76eee2f0773ffda2dee7cp-14), C_(-0x1.fdd37749c94d91b95e5811e014fcp-10), C_(-0x1.0fc0733cbc7d657bb2812f3ed59dp-22), C_(0x1.f945fb653cfda9182e6054d0438ep-22), C_(-0x1.fb1bcfae6e46d13bafafa99aa27p-34), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 16, 14> { static inline constexpr std::array<Real, 32> value = { C_(0x0p+0), C_(0x1.74ef139ad4e11f00f65daa8820cdp-3), C_(-0x1.fd9d32fdef73fc52b4caeb648516p+0), C_(0x1.3320f17be8b7073381e865362afep+3), C_(-0x1.a9e31dbd98dd09635b0d379485c8p+4), C_(0x1.73dbdd38a87f5064433a350c721dp+5), C_(-0x1.aa50f206f25c72a99cb7b1dfa7d2p+5), C_(0x1.5e48ac9c2f1f1eff350b14cb6a0cp+5), C_(-0x1.20d7a78e95ecf57e7add31db3fd2p+5), C_(0x1.4350b94e5aa2da50e61a74e27b2cp+5), C_(-0x1.5499ff05228ddd2807c95d8259cp+5), C_(0x1.0d8c7214ffee0a1235b3874b3a3ap+5), C_(-0x1.8fe88996cfa9a55157f19af30b98p+4), C_(0x1.63da6bffb7322ee61e908c187b83p+4), C_(-0x1.24223f5c1b9d9506d6b401adee8dp+4), C_(0x1.7851e19176715ec2bb3ef2e77d74p+3), C_(-0x1.e4fd178fcd0ef2f7354c8299da37p+2), C_(0x1.610a439acb28979c58f2b0d330cdp+2), C_(-0x1.ae4c3e147b71c294863ea12a0857p+1), C_(0x1.a6fe28ab7ffa991086c47e322a6dp+0), C_(-0x1.ccc920f98175dd5797f1c22d8029p-1), C_(0x1.f9389387bff6b354c93278385205p-2), C_(-0x1.8612de961fd0228a7f5532d1edd2p-3), C_(0x1.fd43fc0e7883ee43ba7f30ad9465p-5), C_(-0x1.aafa1e0c4a86f88db60d4f1fa17bp-6), C_(0x1.b638737fa8e8eebd498a75e7c49cp-8), C_(0x1.071682a1f5057e2143b4d72fc7c5p-11), C_(-0x1.a84c3f530239b63f7da26929d4ffp-12), C_(0x1.a20c2374a0f6700016084886c2a8p-18), C_(0x1.e7f1c0adda0f62adb67917e7d654p-23), C_(-0x1.eb089a4058efe658e6efa5db9e34p-34), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 16, 15> { static inline constexpr std::array<Real, 32> value = { C_(0x0p+0), C_(0x1.31c729360063e0149d619e7c5659p-6), C_(-0x1.a21aa8a66a6833da5818bdb00dc4p-3), C_(0x1.f656a46fa2a9169e56e0e1915e67p-1), C_(-0x1.589b4fca92a9f10523379245a6fbp+1), C_(0x1.25049558932c1a7bf94dfb345bd9p+2), C_(-0x1.3b0f087615a26809432e1d6e01c8p+2), C_(0x1.bed87f332745bf792baa46fb22d3p+1), C_(-0x1.37fe75fa2aa3b693bb533ebc90ap+1), C_(0x1.75c34ae38a11fc31440e21813692p+1), C_(-0x1.9f32b219f201f09e83858382dcccp+1), C_(0x1.2a50b5ebe798e437ef2503085768p+1), C_(-0x1.80aff2523d4b3342a833db6031p+0), C_(0x1.71f9af43c19f0952a4e07472578p+0), C_(-0x1.40d21595459cbd897728656ded6bp+0), C_(0x1.6edc3b8de7cbccef39ac5c5b8452p-1), C_(-0x1.abb5cf29e076b1f30f36686df3b2p-2), C_(0x1.5fdcb9c5e1f87c285b04c2fd8053p-2), C_(-0x1.af4e9b9242255620df4c3ab9bf57p-3), C_(0x1.57b33e4d63cb5298c7100384e3b2p-4), C_(-0x1.736294d370dec79efb4014a700a8p-5), C_(0x1.e1a61d7964668ec603cb9aadd499p-6), C_(-0x1.38138139d6cd8275f0059b0302fbp-7), C_(0x1.a99b874715d59140bd445bce9797p-10), C_(-0x1.191ada841d111d8ae1875d5194c5p-10), C_(0x1.44a23a1750afa85a30082caf581dp-12), C_(0x1.4db128e094987961ef4278d6a462p-13), C_(-0x1.2cad37f3dbf9e7a235442f3e067dp-14), C_(0x1.f38c667f694821291da674a42ae8p-19), C_(0x1.c870773604d02f72b6568dfdd8eep-24), C_(-0x1.cdd01a024c710ef11bdc57da89cfp-34), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 17, 0> { static inline constexpr std::array<Real, 34> value = { C_(0x0p+0), C_(0x1.086b758f2eb28fd921eab56a11edp-14), C_(0x1.39d1d9b6240962e535ae21b2376ap-6), C_(0x1.6586cdc7bb445ac141a0312b8103p-2), C_(0x1.b9d577601dcdb0dcb740f8b98373p-1), C_(-0x1.29ed86125a029803c293e63e1f67p-2), C_(0x1.35228579cf169af0c995d4c52ae4p-4), C_(-0x1.d940ea5a753eace5078cc210d381p-6), C_(0x1.eb66212482f668b8fcf8d3b919cbp-6), C_(-0x1.11e395c55e411390d39b33c12486p-5), C_(0x1.cac8225b45414be4173b8eab4ac8p-6), C_(-0x1.1c2e36898d63a7284aba1b17de4dp-6), C_(0x1.01459f9607ee130b7061d5eb1498p-7), C_(-0x1.3f705b6c01172b34ae01036bd601p-9), C_(0x1.aa4226008e468554c7236a5aa13dp-12), C_(0x1.a227b89277165ccd7a008b2025e9p-16), C_(-0x1.df4876fdde2706ccc1065c683114p-16), C_(0x1.a3348c487531e3e6d511223fa2f3p-19), C_(0x1.bc3886b839cf7c209eee289f6c48p-20), C_(-0x1.3c3d3ef190e94974e0b46a471d0ep-21), C_(0x1.fe10f39c7db3f74fc941d5c89993p-26), C_(0x1.28b87cd51d74b7827dcb3f76ba15p-26), C_(-0x1.5145c4e025139affe8138cf7767p-29), C_(-0x1.c7ef81e91e695e468ea8a5c582b5p-34), C_(0x1.74462d4702c982a79ea8a83c2f8bp-37), C_(-0x1.2eb21459dd6235173db20b5350d7p-41), C_(-0x1.802cada0cd8903e4e2cc5b09958dp-49), C_(0x1.f4dc3c81c07b2740f80e7509651ap-52), C_(-0x1.790641c0d0b7b530c5f3ea46fd8ap-59), C_(-0x1.7be9575142225928d5569ad8cee9p-68), C_(0x1.70d851342e8d54c091b220a3045ap-78), C_(-0x1.08ea9c21a48ad423ef299cf99255p-94), C_(-0x1.6d7121dda4d1a467dfa9e3b22e7bp-121), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 17, 1> { static inline constexpr std::array<Real, 34> value = { C_(0x0p+0), C_(0x1.1287f0812571ced1e1d4f218f2e4p-11), C_(0x1.3963c1ea0712ddb1fe38bd9c9b8p-4), C_(0x1.56352993b88d1ab506ab53972cdp-1), C_(-0x1.f6edcab194e1f1b63bcde69f40efp-3), C_(-0x1.17b7ccfaac21f6709bae8571c345p+0), C_(0x1.0e886b0af5f1b1856a755304e662p+0), C_(-0x1.8ecc3f557378e15602e7822e181ep-1), C_(0x1.fc587a34e0e0edbbd49047b2d639p-2), C_(-0x1.0d307d8a24ec475046eaa126ebfbp-2), C_(0x1.aea667b7c25e2cfd5f86bd0180b7p-4), C_(-0x1.9d42bc92105fbc1675af424ec92cp-6), C_(-0x1.84840a8e18b0614ca4eaeb216151p-11), C_(0x1.a3a969f351753a208cd3e5a8f168p-9), C_(-0x1.2b9d22453328eaf6cc00ab2ce255p-10), C_(0x1.95e4d7f634c66f1127081eca4c12p-13), C_(-0x1.348b4478275cac4e09ed00491749p-14), C_(0x1.d3098c771ac4dfa090c0edef58f9p-15), C_(-0x1.49cdbb7d5d852bdcaa3c1cea09bfp-16), C_(0x1.12cb123d22d84321bf94a9d64f4p-19), C_(0x1.ee369d60388e0cdc7a4cb2173367p-22), C_(-0x1.fe1ef00c018375d62e92ff3458b4p-24), C_(0x1.a7341d99c255c94d652d9d8f033dp-28), C_(-0x1.530b27430376f235ffb52485dd26p-31), C_(0x1.baba95d77648bbe90c5142dc80f9p-36), C_(0x1.4f068520e819c6ced35b43d3471ap-37), C_(-0x1.57c84bc8729954adbcf1854852e1p-43), C_(-0x1.4644a16a824bfa62197420e08c45p-48), C_(-0x1.8db806597a9c3e694cd52ef5d34cp-57), C_(0x1.0d894936ca76f0f900d3760154afp-62), C_(-0x1.b4baf18dcac141cf35421e01ae8ap-74), C_(0x1.758520ee5d32f0284861059680c8p-88), C_(0x1.01a0cdf0066867c0900e21808ebp-113), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 17, 2> { static inline constexpr std::array<Real, 34> value = { C_(0x0p+0), C_(0x1.f55ef3437afefacc7be18bbe98cep-9), C_(0x1.0777b4e7fcce2c0e40744ca54978p-2), C_(0x1.3f1d6fcf2ecbd47e40d3c1703896p-1), C_(-0x1.504b43d516f52267cd7e5fe7d16dp+1), C_(0x1.4eaade935c6e2740942fa58ebd6dp+1), C_(-0x1.5ad808042149f417dbd58af6b00dp+0), C_(0x1.cab544fbb7d4b4c60e5f5aaacf98p-1), C_(-0x1.9ef87caf9226b19c3d44c512bce3p-1), C_(0x1.71fed5bcb893256d48b5662cb1dbp-1), C_(-0x1.0f0d57adf520b2ff7dc518f39f1bp-1), C_(0x1.30c75d43e61143b20925258c8b83p-2), C_(-0x1.e86b0f7372ef580e2a548027c15bp-4), C_(0x1.b73425fd2a98ccd833576427e8eep-6), C_(0x1.4682acb561a50d1c8642601cd7d1p-9), C_(-0x1.2eacc75c57cd93079a89b775a2e9p-8), C_(0x1.a21a6f510bbe181a8681692c18eap-10), C_(-0x1.147cb459e63791d570da7fd30181p-14), C_(-0x1.28e19a4afa00bfea3a7c1b8c9b43p-13), C_(0x1.931858e53ca4936f19114cad31b8p-15), C_(-0x1.62eadbc9e95863c36c22bbc42279p-19), C_(-0x1.de496f2e6fedcba7342c1d21ed73p-20), C_(0x1.70387d4ff6ccbebda63c71a99d37p-22), C_(-0x1.75a0d535dc76533ec0cb363c4ecp-32), C_(-0x1.a0b3effc1d4a9bf1824673d2a6ap-29), C_(0x1.b9e3fb75297f14c235645de65301p-33), C_(0x1.a8bed9eb35249e37507da13a3226p-41), C_(-0x1.16b3429b615b32018d7a07c98618p-42), C_(0x1.ff8673e3757ca4761f1167047725p-50), C_(0x1.145878dae073bba8c6a0fb3960bap-57), C_(-0x1.9feee550a5c8e58e5b4245c07331p-67), C_(0x1.83b415f1b1f54454e6745eb4b4d9p-82), C_(0x1.0b692b789332c1658c8a24d9733ap-106), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 17, 3> { static inline constexpr std::array<Real, 34> value = { C_(0x0p+0), C_(0x1.8aac090c80a048b0460ec2d7badbp-6), C_(0x1.5750bdc83f394eb3b8faccf4d05p-1), C_(-0x1.50c8f6f54e2cc9e3e11af9656bf6p+0), C_(-0x1.8a451969aae1b985b829fad06526p+0), C_(0x1.a2b7eb3937eee939c776f8d31095p+2), C_(-0x1.118e064b4695a7f92c4b4501fcb4p+3), C_(0x1.c7bf87fc63cf93f68f74e5e7c825p+2), C_(-0x1.1d8d78044ee8ee6d6d812a1942fep+2), C_(0x1.e73d8bee7689f31a0590abd75fdap+0), C_(-0x1.2add7b6319082ca3c2efcadae5afp-2), C_(-0x1.d3adb45266b9c9f4635ae6e3441ap-3), C_(0x1.033a83600934f9863377b693a726p-3), C_(0x1.b5451b19e5929d480505b5a86b0ep-5), C_(-0x1.7b8dd6246eb29127a889717ed76ep-4), C_(0x1.791fa45e84d145e6dc4c1510b4b6p-5), C_(-0x1.7c0beae24c83b65b5de7467eb78fp-8), C_(-0x1.5782b21d6af61f4f7dba20838e5fp-8), C_(0x1.a840c3e83eb503c78b20b8a28b62p-9), C_(-0x1.986e55de09433017be901893ecf5p-11), C_(0x1.26705b8c8ad65b55b61c41f75588p-15), C_(0x1.d3d83a9fdf1319302a3787bdd6a4p-16), C_(-0x1.d82fd865aa4582e2885f825ad846p-18), C_(0x1.f5b54c9c1896a94bf7ab1ebbd585p-22), C_(0x1.fdc61d80cbe3fa72384c0df210aep-25), C_(-0x1.0fd59d78e582bd5f0e263192f5d2p-27), C_(-0x1.b2380e734b4f9e20f629d35cee8ep-35), C_(0x1.88e8ce1bbad67bfa806d6889ad1bp-37), C_(-0x1.9888eae4a10ce8dbd9f3a51b6ca7p-45), C_(-0x1.466525261ac31d726b6464754be8p-51), C_(0x1.1b33afe3275e0f5266344c60d67dp-60), C_(-0x1.cb1864e2c62c6b93f97126fa2abep-75), C_(-0x1.3ca6dac99711dbeeb8df3656a48ap-98), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 17, 4> { static inline constexpr std::array<Real, 34> value = { C_(0x0p+0), C_(0x1.0491b50257a217948037c313c632p-3), C_(0x1.088e085a415b940e86ec5f53c805p+0), C_(-0x1.9cc2273fe20fe221de7ca14dc50ap+2), C_(0x1.b3ef626d8f7b0512e777dbab2038p+3), C_(-0x1.fbdaa71ed3446ae9d3eb57fb2edp+3), C_(0x1.ba80f6fc4d07a16a8240d21d3427p+3), C_(-0x1.97b8947186ea82517ff8170fe92bp+3), C_(0x1.9ec07cc028783871c266a993e177p+3), C_(-0x1.7db26c06ff96156fee69f60a32a6p+3), C_(0x1.1910e3936c71e0698749e0100bd9p+3), C_(-0x1.2af49c29492fb4bebe4ea4c0492ep+2), C_(0x1.4fef94a557c4567b7c45f05c21cdp+0), C_(0x1.8759880e99b2b3b19fcf3cb856f9p-2), C_(-0x1.52e5ecb25ff9114988afe0915415p-1), C_(0x1.5f17262b3d7f451babb3a37c2f6bp-2), C_(-0x1.a7f494de47ba1f8ccefd1a48b767p-5), C_(-0x1.5dc2bf7dbd1d10649dd1efeed2ebp-5), C_(0x1.fa52c9fe27d631a55490bc5d6453p-6), C_(-0x1.0edbce8cbb631c85810ceb7afb83p-7), C_(0x1.51bdedea6ecf9aa291d741d5449p-13), C_(0x1.03e8c53050207786cbf7a98773ebp-11), C_(-0x1.fbae0e996b24eb9e7412c53365a6p-14), C_(0x1.a5405fbd60ce14b0ebcc8751154bp-18), C_(0x1.8401a133e3997a7f15f86f10443dp-20), C_(-0x1.9620d8180585bbc8bcc656387216p-23), C_(0x1.59175b5517be80fcdb2badddc5c9p-32), C_(0x1.a5d4ddd28a790634117b9f52ee98p-32), C_(-0x1.a9e2125d31a3c8bd4449e4b094e8p-39), C_(-0x1.068a399565e004f3cf609f3513f9p-45), C_(0x1.3ca73a6f9a6a05c209544433b8c6p-54), C_(-0x1.740e2252efb089d1ae6c93a1b5fp-68), C_(-0x1.009e0cb9ab19e5360f5dcaede516p-90), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 17, 5> { static inline constexpr std::array<Real, 34> value = { C_(0x0p+0), C_(0x1.12eabbc13ae4184543451253a593p-1), C_(-0x1.dcd48a30309a985e66770059ddf6p-1), C_(-0x1.61bd6ca0b74ea8c2e61c8e522049p+2), C_(0x1.4b16a330057a9a464e1afd029265p+4), C_(-0x1.6645126fb9e4a4d9cdaf8add299bp+3), C_(-0x1.746a9ef1dde16ed58e0b432bfa77p+6), C_(0x1.49df58a6d0bb202b69c6e445a50dp+8), C_(-0x1.2844a2ebcc53c8df614ae3957cc5p+9), C_(0x1.2e42267f64054a81e12f7b2ff462p+9), C_(-0x1.0225a1d4c62f4d7b402b42538ffp+7), C_(-0x1.601645627c56a1dba4f1a59caa2dp+9), C_(0x1.58f8de6f258472f30e4dedd3b403p+10), C_(-0x1.693ca7a1da62866e49185596166ep+10), C_(0x1.d8c8ec24a42109f71622d8b3d887p+9), C_(-0x1.46d08ddd7ae2544339cc13f918fp+8), C_(-0x1.3b3b035293fc39a231fe7419868fp+5), C_(0x1.d12d6fce626a721298fd94ab886ap+6), C_(-0x1.06b1d4ca392cd5c4bed1c5482646p+6), C_(0x1.11a1d31e54e9ef311bda0933730cp+4), C_(-0x1.40c7309469440a4e5541e2e4c29cp-4), C_(-0x1.5ca50bfd4e3e4aa86ac8722ac5aep+0), C_(0x1.83af684fffb5b293cdc91cda7503p-2), C_(-0x1.9e6da0de05c76e1cd2d553753824p-6), C_(-0x1.7858ef153620d7c30fc31cf56a03p-8), C_(0x1.dbde29a936a150c27f696a66c4f8p-11), C_(-0x1.7bcec5a7e8c292f303bfbe3660adp-19), C_(-0x1.4f2043d7bc5e1f3a3aca5e8c6039p-19), C_(0x1.c2215a9e7432391b90e0fdc7be76p-26), C_(0x1.2faa97edde49cab9c4399ff18db1p-32), C_(-0x1.023988307e2875f374e798bb263p-40), C_(0x1.b307ce337f9f1788bff0e23a47f6p-54), C_(0x1.2c0d7e12bcbb5186b064f5495d76p-75), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 17, 6> { static inline constexpr std::array<Real, 34> value = { C_(0x0p+0), C_(0x1.d53d20f76b4eb49c1b6330a595f1p+0), C_(-0x1.86cf243ed21bd08659834822cd59p+3), C_(0x1.17b81677ed649599a4d3595e967cp+5), C_(-0x1.abb0b3868d1ea2ff8d47921a5292p+5), C_(0x1.f121a0540b3049d09ec7e5551764p+4), C_(0x1.17380aa83335c1ea7599d28ad525p+6), C_(-0x1.0c95dd1e4ca7caa2bd6deac65cdcp+8), C_(0x1.0b7efc300b3c27dde71e697ba35dp+9), C_(-0x1.826ec4b2204db57bfd19486982e8p+9), C_(0x1.b8a41eb5a39bd8486cfb324fe223p+9), C_(-0x1.a1f5e828547f7c5b2bcb67af2fb7p+9), C_(0x1.5201c70981a0b03733b9e6dd6e09p+9), C_(-0x1.b80f281da59c5918dfb2c054585bp+8), C_(0x1.5562f5403383fa55297b9a337231p+7), C_(0x1.90f51962a56d70bb1b983c1ee4e5p+5), C_(-0x1.24ca65a640b01ad09d88f66dbd3cp+7), C_(0x1.f2553461b931355eaf34d3576431p+6), C_(-0x1.dd44638d13da936b6e3a63722e62p+5), C_(0x1.c0ad57b9e59f4a68dc33ce587da3p+3), C_(0x1.4256b15254b23391d079094819dbp+0), C_(-0x1.fef8071c6ce2bcb3957ad8d4d2e8p+0), C_(0x1.22e6dade4ecd5ba17bba3803612ep-1), C_(-0x1.5b42b69e978a5317df9091ce52d4p-5), C_(-0x1.642c165a0dc2d5830f0c68cef691p-7), C_(0x1.1410f766f54ec568508253190fd5p-9), C_(-0x1.866a34dd716a310ea2f7f87ada3fp-16), C_(-0x1.0b5a3f31f6ca3105091deb1b111dp-17), C_(0x1.e9e690f2d2cdcc9f8d2e274aa38ap-24), C_(0x1.73aa86e33bd9c22c0a03f2815f8fp-30), C_(-0x1.ab771b8e4149cc3a675cc4898a01p-38), C_(0x1.0db4d80a1d5dee01c7237b2562edp-50), C_(0x1.740bf5a4533bf10d9f87491f9f4bp-71), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 17, 7> { static inline constexpr std::array<Real, 34> value = { C_(0x0p+0), C_(0x1.295ff3e65734f855f39c88490c77p+2), C_(-0x1.53451cd19bffc6de5e35716507fdp+5), C_(0x1.6528da0fe333f438d196bece2469p+7), C_(-0x1.cbdb85c1ecbc284c645d00a79bf9p+8), C_(0x1.932ea82ba595876f9e544cf675e8p+9), C_(-0x1.f84307101d81872f84fc73fbdae3p+9), C_(0x1.bf6854697aae94bb46e7b0542bd4p+9), C_(-0x1.bf12de658509da0b644cd695e0b7p+8), C_(-0x1.4368651bd726f170cb68d94b4efp+8), C_(0x1.6e6644c0e40c6d361a9bc94d8ca8p+10), C_(-0x1.63936602c4e494fb5778af823485p+11), C_(0x1.effe4a55a204acd95799b1a3ca8fp+11), C_(-0x1.113fec7086061d5415319b0c5f72p+12), C_(0x1.fcb0d58a8410175cda764e2c75f6p+11), C_(-0x1.a4bb9f060dab410fe3bd526fda39p+11), C_(0x1.329610ee0fa8084fbb618f8b1294p+11), C_(-0x1.6a3f2ab2a8a1738b723263aa7f2ap+10), C_(0x1.28b90043770072e85c55c758b4e2p+9), C_(-0x1.98095b9a0fe58b99d4dbb49d1d1ep+6), C_(-0x1.7e9c13fb873c76fdf7051d8da9ep+5), C_(0x1.38a8e96bcb8fab70b383bca5ab41p+5), C_(-0x1.67764003f2db50e6202ef878e23p+3), C_(0x1.be87d29fcd9eaf1da18ad636de29p-1), C_(0x1.281bdec2a7f8db103e09703f13fp-2), C_(-0x1.0bb48c6ffbbe8bdda51c03bcdddep-4), C_(0x1.77235116b4238df6f725d274e118p-10), C_(0x1.6675983c9f507c163e6782c7703ap-12), C_(-0x1.d3d6efe237ab3413c9e890035877p-18), C_(-0x1.81b8689afa6e0c7916f7a3885678p-24), C_(0x1.2f0e5249c6fc36ea9c04c196c326p-31), C_(-0x1.1cfcb984a013a5a7bc95cb9320e8p-43), C_(-0x1.891f706028ea406f88faa50dd1c9p-63), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 17, 8> { static inline constexpr std::array<Real, 34> value = { C_(0x0p+0), C_(0x1.06fc2ba8e79eb72495307bac6ae7p+3), C_(-0x1.5489cef9cc78f65236603d4cf5b6p+6), C_(0x1.9903c6b2ba02d6090a910755f61cp+8), C_(-0x1.312486b078b78cd8f1a70419307dp+10), C_(0x1.4302b86058a5a1292888fa9ca885p+11), C_(-0x1.0b2ccf4526b8c244af343cdb508bp+12), C_(0x1.789932548bf931d92c8e1c8fdaeap+12), C_(-0x1.e12b9567cda5d69eb9d09a4087d7p+12), C_(0x1.1abf23f09fbf8f276f484c29af9dp+13), C_(-0x1.2d5cd803da680fe5c48016ca91a5p+13), C_(0x1.2251ae99e408a20ab182f4722d14p+13), C_(-0x1.003d36dfd5a7feaa6fd4657cd76ep+13), C_(0x1.9f286327797df00b01373e3a21a7p+12), C_(-0x1.2d0f0d917a1ccdeca67d314f4298p+12), C_(0x1.7c4b637f2390259cb36649bf5cadp+11), C_(-0x1.9dc666df2eb31fd9d525e80a61c4p+10), C_(0x1.706ff6209d6f31fbb17a3cac3d1cp+9), C_(-0x1.76b515afa4c5f086db4f0c0e11f9p+7), C_(-0x1.24480d16a6ef2cbf187e850a3c68p+6), C_(0x1.d48700b685d23247b608b5cfdb9bp+6), C_(-0x1.05a23476b2f21c52a72aaf8a7e1cp+6), C_(0x1.24935371deb2ec43e23d888eb93dp+4), C_(-0x1.4ca6dde02f223d08bbf5ac28bf78p+0), C_(-0x1.58615b018cee75761c906455ba3p-1), C_(0x1.608c7993e060e80a3ede46931d7cp-3), C_(-0x1.b69ce98ab84f025bb8e299cdad9p-8), C_(-0x1.4823967168edf829557ae3a04f84p-10), C_(0x1.35d91ac6fb610d89a9ca12ef88e9p-15), C_(0x1.1a7bfc97dc33f6885878a1ae185cp-21), C_(-0x1.2be69d6aba0faabdfc72f4f8d745p-28), C_(0x1.ab2f7726c736fed01e244eeb7278p-40), C_(0x1.26a24576b891cedff10c341592ecp-58), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 17, 9> { static inline constexpr std::array<Real, 34> value = { C_(0x0p+0), C_(0x1.7d326037dd59f04b93695dea64a2p+3), C_(-0x1.057b7f9e150cfea8b7f60a37452p+7), C_(0x1.46966635c034e3d077a23a34c32dp+9), C_(-0x1.ebce82ab1e29c2e7e1d24be27a9dp+10), C_(0x1.f63288a008a00b0de93e3b52ce8cp+11), C_(-0x1.7a1dba3b5d1c5c524569d9d8ab6fp+12), C_(0x1.cf6c2665a1ce80b761f29f92f584p+12), C_(-0x1.02e9d9c7c198539a0401a9ab1cc4p+13), C_(0x1.126ddfd818acd4152500102b2dd1p+13), C_(-0x1.fbbfeeed9e84aef44a32d1cdc74ep+12), C_(0x1.6dd45600e62e38c3d8b7dfec1df4p+12), C_(-0x1.70d3cf8b17a54f73f23ea7c9008bp+11), C_(0x1.116e22f7a2135c32a071c68e4c4bp+9), C_(0x1.45e19d7a9f76f8d3600c21c7d961p+10), C_(-0x1.541801f00ec703cee53ee38cf9d1p+11), C_(0x1.9d27adde86cc9d38961105f8f3abp+11), C_(-0x1.718955043c8aaad595f50f39f434p+11), C_(0x1.13d222dd6eb22f7f0b910b51dfcbp+11), C_(-0x1.75dd9fab7780dd812eb2ca0b6548p+10), C_(0x1.b95889cd4ba403f3d771bad22aefp+9), C_(-0x1.880fb1002a98d978d68c5c6d01b8p+8), C_(0x1.a3c6bfae2048432d988090525bccp+6), C_(-0x1.6af0f7c1089720fadea20b94dfd9p+2), C_(-0x1.7dda27580f4d6fe605e5e2098125p+2), C_(0x1.bb56918206273622bbbf209a8389p+0), C_(-0x1.95410e4d3fa90c79d49021063b4ep-4), C_(-0x1.1e3dcf4406fb03d054399893d4cp-6), C_(0x1.863de856b0c02544096765b7d0aap-11), C_(0x1.82e7abd79b3d018087088704fa41p-17), C_(-0x1.21b01c6eb2b87dca0186448dc932p-23), C_(0x1.2f1ce1bb4e63e9b48ca04ddd06b5p-34), C_(0x1.a21b5c9a00d44d929d9e41311f24p-52), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 17, 10> { static inline constexpr std::array<Real, 34> value = { C_(0x0p+0), C_(0x1.6636de936afdb6694c4ffaed6a31p+3), C_(-0x1.f93a40edfceae00ae68e29b08ccap+6), C_(0x1.446da371d76c83e79d3a084840a1p+9), C_(-0x1.f81b7969b6241ca8af219aea83e3p+10), C_(0x1.0bf59cc8ab3644f7ca5bdfe6f82cp+12), C_(-0x1.aac9a227eb351b4f5d24fbc72641p+12), C_(0x1.1995306c55b12646bead2c38ad5ep+13), C_(-0x1.558e777f304785d9e9d3bf74bb24p+13), C_(0x1.8e256f3ea2d2e1b7bb373067b872p+13), C_(-0x1.b16f217fc65b857f8f6c9d68eed5p+13), C_(0x1.ae7e2aa7eb75bb88db9f2bedf708p+13), C_(-0x1.8d7f6b89b7d82de8cbcb8a91aep+13), C_(0x1.5bc0c9e9bcdde01e3a5bcbdf7ae2p+13), C_(-0x1.1c9a0c6fad5ae4a6fdea1b4bf6cap+13), C_(0x1.ae2f95c3b0ec2e40af37580cdc26p+12), C_(-0x1.2f129053ebc24ed7fe6fd750dd19p+12), C_(0x1.8d5b23e080443674d13b71f54d14p+11), C_(-0x1.d627dd21f8491dafe966ff60514ap+10), C_(0x1.ed8f9f756f065170266103952acap+9), C_(-0x1.cf7165a4ea829414cafd158d5c4ep+8), C_(0x1.6d33ddb7ad7e8017c0cb0ef30276p+7), C_(-0x1.65b4962a79c56602e9794ee156bdp+5), C_(-0x1.4d3b8e7db26f275e39c95bf13c09p+1), C_(0x1.950dbe3d7aca2e2a683f470bff22p+2), C_(-0x1.dbafbd443f803e2caf8c9757690fp+0), C_(0x1.04861e6b2202e3d3d031b9ec9cb4p-3), C_(0x1.7fe12c9629eace47e413a0b6403dp-6), C_(-0x1.c081b52017ebd837349a62b66ef9p-10), C_(-0x1.adbded066f7794fda23e0774673bp-16), C_(0x1.dd5025fbe71cc3a7e8141de53daap-22), C_(-0x1.642f3973aefae4a4f6422168ecd6p-32), C_(-0x1.eb48617a106cce90559379e40303p-49), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 17, 11> { static inline constexpr std::array<Real, 34> value = { C_(0x0p+0), C_(0x1.24754790ab93df0d2355b8c8a1d6p+3), C_(-0x1.a21d6a4e4d9eb295ee53b44586fdp+6), C_(0x1.0d7a54376cc0558116461ff0ad85p+9), C_(-0x1.9dbd2fa0800f2f31e9998fd08c87p+10), C_(0x1.a81b276d71be81d44423e8d7940ap+11), C_(-0x1.3af0559f33f06e14389580e81a29p+12), C_(0x1.79904c76e9a060ec8e465cd0f64ep+12), C_(-0x1.a8514199bacb20e9109b77f293abp+12), C_(0x1.e26f534b2b2fd591e9ff3ecf4696p+12), C_(-0x1.01e02902687a04ca65f96e6a8b68p+13), C_(0x1.e5294c43a413c0653234e7f1aa09p+12), C_(-0x1.a1b883ef12d1d5472469dd56bc1fp+12), C_(0x1.5e76af85cca307f1a26352596c69p+12), C_(-0x1.15aa3e69a2aa9b29daeedbfe44dep+12), C_(0x1.86a5a2358b24b67c01514a96d3ebp+11), C_(-0x1.f3289b5523f3f49f9c93e10ff537p+10), C_(0x1.313866068b105f8069b31bb16bf3p+10), C_(-0x1.4f6a48ce8e3698f8a03194833bbfp+9), C_(0x1.23a63c6ead8e0e6aa15fe6f45702p+8), C_(-0x1.8310a2cf199a480eca2c2b3394c8p+6), C_(0x1.66b7a5ffb79e9dc036820a3ad358p+4), C_(0x1.9e1737848ca25244943790e11b0ap+2), C_(-0x1.b5673299d6c08937871359b74265p+3), C_(0x1.06e8de128ea18c685f5f56cec9c2p+3), C_(-0x1.231b2877825a92418fa8440891fep+1), C_(0x1.8ab9028a51e09357bf81bd620a6dp-3), C_(0x1.fe0af766377cd4e6799421dcabc8p-6), C_(-0x1.2be854453bc6da5ab705ba515333p-8), C_(-0x1.2ae4048d20f92820dcdbdae1afdp-14), C_(0x1.cba1e05e755f67b92b6effedbc08p-20), C_(-0x1.07cc113fc2e535393592fd575de3p-29), C_(-0x1.6bcf254ca2da0ef6aaa6b7f61e81p-45), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 17, 12> { static inline constexpr std::array<Real, 34> value = { C_(0x0p+0), C_(0x1.6734f40a39a9f749d116c99eb0b2p+3), C_(-0x1.02800bdef42eee8e9cbe8c5b799cp+7), C_(0x1.46b9a7fb0659b383f2e6ccc2bfdp+9), C_(-0x1.d4653513846d8b632e3ab00ec6aep+10), C_(0x1.960cff14f27e9f5b5c924a5e31a6p+11), C_(-0x1.978ccec6aa50557b75045abb874cp+11), C_(0x1.65f6a7cb1b6c9a8b6c858f9858eap+10), C_(0x1.c444279391a3fe3940190e9b0d42p+7), C_(-0x1.743641ef137ce3dda68a9d7a6a5ep+7), C_(0x1.b0d221397077b61aaac6990656bfp+8), C_(-0x1.789f01238bd736d3d165c526de34p+11), C_(0x1.78076d93e8b2a21b1e57f1d51e32p+12), C_(-0x1.b80f30dfff7c8968576fe93ef454p+12), C_(0x1.bb7e92e14a551f987f2cb928af9ep+12), C_(-0x1.d7e88c840d9e4cc3ea2da57543cp+12), C_(0x1.d2485f20f81231778ef5c3fde98cp+12), C_(-0x1.8196b31f2aea3e18b21270e4dab8p+12), C_(0x1.2207d34a8263912f9c133abdb819p+12), C_(-0x1.b1c880d8d5a9e0a75d42bdbef999p+11), C_(0x1.2ab917d5ba30fbe55897a0ecf4f1p+11), C_(-0x1.5bfb47d78d5c9aa6b7b3ea1583e5p+10), C_(0x1.6b044d9f20d2a049f5f6d532822ap+9), C_(-0x1.6ef48eab0e23a150ac4817c103f4p+8), C_(0x1.3c86344d962287236a63845979d3p+7), C_(-0x1.62bb42947746334cf9768602ee2bp+5), C_(0x1.302845e71cb15c4d9c86c4ce6c69p+2), C_(0x1.8f631724d133592549dc9efdce6cp-1), C_(-0x1.82b35bd32ad297d37e7e03fdd8d4p-3), C_(-0x1.957cf95e09e20118e411d55e99c2p-9), C_(0x1.f6dae900f0dfcd786a2b2d830063p-14), C_(-0x1.960194a81c1ce1e7d634227c61f3p-23), C_(-0x1.17e5f78c653c49cc8a92fdb4f4c1p-37), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 17, 13> { static inline constexpr std::array<Real, 34> value = { C_(0x0p+0), C_(0x1.206cbb79429c2414ff0c64aec8d3p+1), C_(-0x1.a083553e4e5a13a3aa202924b202p+4), C_(0x1.0cf208fc3d0318bce33d11bbf4eep+7), C_(-0x1.98490e95032010181534884dfc77p+8), C_(0x1.94a218c65bbc9e721912af119136p+9), C_(-0x1.17c83af6fa175ec696cff584b399p+10), C_(0x1.2a2038ecd41ce99e3b7c57bb1465p+10), C_(-0x1.2a77ab7e6edd3ce02f308ffb22c9p+10), C_(0x1.48a4ad0a80d290f172a8699dd903p+10), C_(-0x1.63c7a0fcade974b2571bdc4dbe83p+10), C_(0x1.4db14cb7e55e4fa2d6df561d81b8p+10), C_(-0x1.1f7d1042db45f9c24caed3674305p+10), C_(0x1.f7c955767cdfe40b013173464e47p+9), C_(-0x1.aa68a77f455100ba1716b7e81665p+9), C_(0x1.42df44997682f8bbd8705c8237fap+9), C_(-0x1.cc3c8a0b1406c4cb1854f7f475a5p+8), C_(0x1.4691261a687538ac5d74074129f3p+8), C_(-0x1.af8b6d718425edc744dded4be2d2p+7), C_(0x1.fddec0373e9c198b0187bcd05338p+6), C_(-0x1.206dca918e07679e17977c9e643dp+6), C_(0x1.394f1079b1d1bab9757ca4be3df6p+5), C_(-0x1.259c4ffdb02b3840be66495f597dp+4), C_(0x1.dbd0529d14d06481a401f7d28924p+2), C_(-0x1.6f7d774b2017e6812c50c53f3953p+1), C_(0x1.bf296d0152554d98043114f06ab7p-1), C_(-0x1.7c872eb94aac4434f1f1ee90200cp-4), C_(-0x1.14b95c5b19212b4fc03cbfb78471p-5), C_(0x1.194e2e645655459aae5fe3cd821dp-7), C_(0x1.3531940b1823b632efb391ef6f52p-14), C_(-0x1.7166e830bc1e3944c924058c6f08p-17), C_(0x1.2436b817dcb001ed9c4696c6c208p-26), C_(0x1.92b45b9b9529b7ad46fa43bf2077p-40), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 17, 14> { static inline constexpr std::array<Real, 34> value = { C_(0x0p+0), C_(0x1.74cc6314dd173590f359217811bfp-1), C_(-0x1.0da07c63bf5b57427067a74fa654p+3), C_(0x1.5af5b4b6a40764cc3bad47672c18p+5), C_(-0x1.03fb3e545cdf8287d11ea7aeca93p+7), C_(0x1.f3ca921092c121957e2f18e268fcp+7), C_(-0x1.44047871dcef9850bbedf1b419e5p+8), C_(0x1.3358182c099a552dc3876c2274b9p+8), C_(-0x1.10bd53f78b9c50f9a6e08d98e9a7p+8), C_(0x1.29eb9e1a3472cf232a6709ddfbd2p+8), C_(-0x1.4a2468b639e365dc0b3fd125eb7cp+8), C_(0x1.26dfa9c8f6c029f4753dc36c664p+8), C_(-0x1.d2f1acef4b4ba3b7e608497ba6a3p+7), C_(0x1.9597a28faf38ab1c2b429a5dd79dp+7), C_(-0x1.5e8348f17beed687dbbf25dfed75p+7), C_(0x1.f9613319a9e146e700ffce02e1bbp+6), C_(-0x1.4ea47fc45e78dfd9cd4f69ce75a7p+6), C_(0x1.dde07d45fce1683ab6993808e07bp+5), C_(-0x1.3e0ca7abd11c2d7cf0bb1fa5493p+5), C_(0x1.599232ab9283f8d2a3c47d198eb2p+4), C_(-0x1.6ac8188fba9f38deb15c420eb1d6p+3), C_(0x1.96eff61828d979e9be81958fbf3p+2), C_(-0x1.7071f5cc1d4694972d2c2c65d04cp+1), C_(0x1.e12484c6688efee796e8769de364p-1), C_(-0x1.4f89eb4be752a44a4402c23fb27ep-2), C_(0x1.c393c8a6167f5e45bd4990217d8dp-4), C_(0x1.7dd147fa057e0b50125bcfcb63a2p-9), C_(-0x1.13f7fd7ac3a280d730a2c002774bp-6), C_(0x1.03548ce92b6649d84ccad32bfb61p-8), C_(-0x1.2341881399bbc4b237f436539e91p-14), C_(-0x1.74f214490ba0ea1723d42cc72a56p-17), C_(0x1.5a01bfbda2f04b0c7709f4c8e447p-27), C_(0x1.dc5f89a7304e8e2e4721be65411cp-40), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 17, 15> { static inline constexpr std::array<Real, 34> value = { C_(0x0p+0), C_(0x1.3c25010b60fb3674740b05f24332p-3), C_(-0x1.c9af2c3ccca23c68e09fc2f7dc65p+0), C_(0x1.254de8cf13856aa803ccd66fd125p+3), C_(-0x1.b1e5eadb5abe7e897564be3e19b7p+4), C_(0x1.9450c60bf67cdef9bb4416994ee8p+5), C_(-0x1.e89b5b0fb80bdea3060e89b3c3b1p+5), C_(0x1.8f3eff015290335d6c5ba8db3ba6p+5), C_(-0x1.26718b161a212a6473dfb26ae75ep+5), C_(0x1.4a6ff4d30582a729b53c09473635p+5), C_(-0x1.8a12303f1194f457265cb9c94d2ap+5), C_(0x1.48e1a80801a27ea5d6b8c09eef2ap+5), C_(-0x1.bb6e89adbb91b4400c7c8bacc9f2p+4), C_(0x1.826bb857299c08edd527360dc4c6p+4), C_(-0x1.66d59bbc1beb521a1822adef1e5ap+4), C_(0x1.d762d94bf79addacd550a56af00dp+3), C_(-0x1.017df19c95ab47cf0b3801bfa83ep+3), C_(0x1.7ce4baf9290af712ae0b872e1a1ap+2), C_(-0x1.076985c84651e1c5e5388d3ed212p+2), C_(0x1.a91f1aca1f4d85453f0f9c33299ap+0), C_(-0x1.19588e1d9e17bce2cb6d81a29cf5p-1), C_(0x1.70b50254db487528bd3d29d3be35p-2), C_(-0x1.a1a5a33d385d5b812d62c1b7093dp-4), C_(-0x1.4244fca3bc21ee34636ecc1caae2p-4), C_(0x1.e957c08844afbfd050ce104aed32p-5), C_(-0x1.7d54f6f8e016b5cc4d2c805b197dp-6), C_(0x1.293a2e4267dc81d9d07b602eb6d4p-6), C_(-0x1.5d4d2a8021a073e46a46ee79612ap-7), C_(0x1.5b4fecdba5f9087fe95645ea7106p-9), C_(-0x1.4ed9a3f4a9afdf2f3236e61b6585p-13), C_(-0x1.125ce08dc9b661014740f9362c84p-16), C_(0x1.5ea5b19f4ff29c7baf0a16f9257p-27), C_(0x1.e1d2c8108c65a8cd4dea742f8f7p-39), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 17, 16> { static inline constexpr std::array<Real, 34> value = { C_(0x0p+0), C_(0x1.78f50d65c4a16421841e3f303dcap-7), C_(-0x1.10f9973c2a07331ce0ccac35cccap-3), C_(0x1.5ea80ed1cf2f2dbfa0cb00aff04ep-1), C_(-0x1.04e32caec7824fdd8feada2c4721p+1), C_(0x1.ec7b02aa786ba97d52a304f12e4cp+1), C_(-0x1.3174e658f8076784a24459fccb68p+2), C_(0x1.04af0495e940fb1a0934ba937e55p+2), C_(-0x1.82d9ce4c80e7862d53bd54f737b2p+1), C_(0x1.8562e843b948818ab7543f47aa8ep+1), C_(-0x1.b4475da1bb05033056b650854fbcp+1), C_(0x1.773ee8a0b6e167fb7d5268d067eep+1), C_(-0x1.162bbf2e87d9ef969863945cc2b1p+1), C_(0x1.ed70fea486a4beb02761cf722ef7p+0), C_(-0x1.be0a12832787fdeed784930ccda8p+0), C_(0x1.43344776804460a755e69c9fe27dp+0), C_(-0x1.bc193640146ea4b82ef2e3c4b7fp-1), C_(0x1.59f9f9e4cd9a370cf83a45b3405fp-1), C_(-0x1.ea19fd7c2dc2c5db9794b9225413p-2), C_(0x1.24cb1e377b41a9dc8bcbafd5c9e4p-2), C_(-0x1.6d1685ae383191436a11192a6015p-3), C_(0x1.ce23289a0d5c025951ea09936714p-4), C_(-0x1.e968908c7474ea2a6b493052c12ep-5), C_(0x1.e76f4d23e3441d0b7efbafd90df3p-6), C_(-0x1.fe92310a812ac1b17c748db28b34p-7), C_(0x1.bcfa77e534eadd2bde270b26117bp-8), C_(-0x1.3fde2d0e55306e2cc04a5e77181ep-9), C_(0x1.f9933c512b48e3277e9a4bb4b19p-11), C_(-0x1.3cde4b0a8d6703babab6ae1d57aep-12), C_(0x1.055b9666e46160de479c93713a7fp-15), C_(0x1.0afdd4a80e426c9edced22de6763p-18), C_(-0x1.63fa7644baff156719997e19782bp-27), C_(-0x1.e7410ee7b8c80f0f9fbb1245ff4ep-38), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 18, 0> { static inline constexpr std::array<Real, 36> value = { C_(0x0p+0), C_(0x1.7a4ce6ed992bb75d1922e250e291p-16), C_(0x1.42671fb0211a4a998d3a999cbba9p-7), C_(0x1.e6ee175fb834c8b714c01feffa11p-3), C_(0x1.b4d3dfe055a7b7209d9d957ea39fp-1), C_(-0x1.7d14720c62ef81c88eaa2934ef9ap-6), C_(-0x1.5a94efaefa077beed21f8e31afdfp-3), C_(0x1.42098eebb591e34e8dce26f5d9fdp-3), C_(-0x1.9b7dc4f9c2feaee194cc6094b673p-4), C_(0x1.80316f876ff22302ae3ab2cc5942p-5), C_(-0x1.8b13757e5a833cb7be38d086bf07p-7), C_(-0x1.9d8e278701564e508cebafcfb133p-9), C_(0x1.712f899035a27c983c908b6bba6cp-8), C_(-0x1.bedf3b9dd86feef8439cad4de336p-9), C_(0x1.4240f2118e493251bd8d9317b7d6p-10), C_(-0x1.0ae82fa70b020b05eaa57d2e86fcp-12), C_(0x1.5d87bb3a4b0411a199a2bbfb04acp-16), C_(-0x1.2d8c3a0a0933f834dfa752e731e6p-19), C_(0x1.e1643353d40db172275bb94c8db6p-19), C_(-0x1.66348482b32035f68245e91af884p-20), C_(0x1.38acac17e89fa0162b376bbd5bb2p-24), C_(0x1.00e7697e09dd627363f277ae5d0cp-24), C_(-0x1.a8f56e9d3a1cc00e461420464983p-27), C_(0x1.5a1ead033f0e454a9963da3438ap-33), C_(0x1.d4875150adea6366dba9b099b588p-34), C_(-0x1.cfdee2a4d421dce1ed3eb1824eb8p-39), C_(0x1.4ba806282cb55638c336fa42513ap-41), C_(-0x1.af632a71f0a85982bb61e8403dafp-51), C_(-0x1.cbdd4d28c6b8d8568783fc7a0356p-51), C_(0x1.4fd0be68bf175912b8e24547698ep-58), C_(0x1.61ffe57672ff2f1dc3af03a0658ep-65), C_(-0x1.3c884f70db98bc38107c463d9e95p-75), C_(-0x1.1f64d25df3ed3d5bb564497f042ep-86), C_(0x1.2bba4936fe9662bf3eb13c8582ep-103), C_(-0x1.1d5cf90ee87504b468831a41ae1ep-131), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 18, 1> { static inline constexpr std::array<Real, 36> value = { C_(0x0p+0), C_(0x1.a0c37edf06a8f94f636662aa39bbp-13), C_(0x1.5938ebddd04e210d6e15ff1b97b9p-5), C_(0x1.0ce81716630c1f9cc4b07a770d1bp-1), C_(0x1.bad54d5c0a788c931739cae743bdp-3), C_(-0x1.734c9748f4ffbe66b4e75bb9c043p+0), C_(0x1.219848201b9a0b52ec9b8191e5b3p+0), C_(-0x1.967b651c15d3ab20c349ccf7a27fp-1), C_(0x1.1dd39ecf7d040d13482ae3416703p-1), C_(-0x1.7d233595983848fd2834ed2571cap-2), C_(0x1.bdf22d0e95afab2bb96e5bd19c6ep-3), C_(-0x1.ab4ab3ea2f36e1559b9c3420ec0fp-4), C_(0x1.361512fce1c67582139ca256de4fp-5), C_(-0x1.2052c9fd431d75170cd08f266eddp-7), C_(0x1.0fc840c4a9b1a2b7d29c508eb6d3p-12), C_(0x1.b1c90fbb8951feffd58470c9d80ep-11), C_(-0x1.c8b87ff5be380a38841f22318f52p-12), C_(0x1.11b72f5c2ab5d1894363c9e7ab05p-13), C_(-0x1.44fd9e718f23deb8dfb254ca9d3p-16), C_(-0x1.801763632cca8db4265fd9b7171p-19), C_(0x1.09096d92c04b504ace3e77b64297p-19), C_(-0x1.d590c9308d6d05c5021dabbaa32ep-23), C_(-0x1.b408b4e946eb9006560416ae94d7p-25), C_(0x1.26b8d9536f33f7963391a473b488p-27), C_(0x1.21ba41de7becb667214c3ca5d913p-30), C_(-0x1.005e15e86c4a56785a4a0f6ab3f1p-33), C_(-0x1.892c108c5e8de79fc1617882908ap-39), C_(0x1.5e2035f63580023798eda85d3d21p-42), C_(-0x1.d491970f7aaa6c617e7d1c311941p-48), C_(0x1.4a6b89912129028f7fea4136c808p-54), C_(0x1.1d009ad5392248132b10cca6afdep-61), C_(-0x1.a642a25e87ebcab18086a8e2fc06p-69), C_(-0x1.2011c2ce8690d9b9656d986e92cap-81), C_(0x1.9134326520639372add0f822994cp-96), C_(-0x1.7df9e44e24a4ebd5669f58093dafp-123), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 18, 2> { static inline constexpr std::array<Real, 36> value = { C_(0x0p+0), C_(0x1.971a55e8255470a8e87397205afep-10), C_(0x1.3dc2c8dbfcf7f93df2e2e770167bp-3), C_(0x1.7546e57d9721df0ee0f4226116f4p-1), C_(-0x1.037adcec0657ef37e8f5501826c9p+1), C_(0x1.f0f2562cfec47ba3b00526650a7ep-1), C_(0x1.6c9838c4962e4af4c25ecbc468b7p-1), C_(-0x1.ebd5569ff73f2f877d55e4233979p-1), C_(0x1.2915d00cfaaa51da1d3b22bc1b91p-1), C_(-0x1.e34c46891f72dbbcd8a73f99bdap-4), C_(-0x1.5072010dc85e733fe3c06054204ap-3), C_(0x1.c67306010de8b6a212c8a67869b3p-3), C_(-0x1.2fa98054a2107feaebe98c8fc435p-3), C_(0x1.df7d703c2f7ab707c9106e495b0fp-5), C_(-0x1.28e5dcad2172c449a1b7dca486f3p-7), C_(-0x1.dc7a4c4cd9eeea5517aa806e57aap-9), C_(0x1.18e996b43138b67ddc3e006638c8p-9), C_(0x1.b32438920580e922f03409f3eb6p-18), C_(-0x1.9037acbcd4ec345580dcc6ddb006p-12), C_(0x1.44eb457dfe491144a6a8147f8c33p-13), C_(-0x1.4321ac67acfe448897274bc08792p-16), C_(-0x1.256fe0790910edb7d614dee4ba24p-18), C_(0x1.ed8efd908e26dfcaf46a03ca2c55p-20), C_(-0x1.a7d2bd14ff6144489ccdef55f7a8p-23), C_(-0x1.037133591bd1adccd684e0184c22p-27), C_(0x1.ab74edd3244b37270e37d649fe31p-29), C_(-0x1.fc9e38e19ebe258bd42cc39b8e13p-33), C_(-0x1.8084026dbca3fcd810e0eb658b42p-38), C_(0x1.368fe30917847fa68db0002b6cdap-41), C_(-0x1.39e30293b3af2c4949eb4a178d03p-51), C_(-0x1.7503d7779e458b1aa1fdddbe3326p-54), C_(0x1.9a1da2379c2a990ef23e5cbc6726p-63), C_(-0x1.f1aa7d24b3e7cf365e425fbf9856p-78), C_(-0x1.86a335fc44a9a2d537ec8158da4p-89), C_(0x1.73ea8d0ad818e245ff5b1e9884a2p-115), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 18, 3> { static inline constexpr std::array<Real, 36> value = { C_(0x0p+0), C_(0x1.5a9454bfce16a0a0dcc504f76122p-7), C_(0x1.dac670f07b3810cfe0200e30b836p-2), C_(-0x1.07048222529da273b75a32ca582bp-2), C_(-0x1.b83c3b0926524121fff53826cc44p+1), C_(0x1.0676df488b1e4ed89c22050c7595p+3), C_(-0x1.30179a3f4da7316ca0c075836a81p+3), C_(0x1.05ba4eee5e31141776d12d72864ep+3), C_(-0x1.93e9c8737c9db916fd3aeb9dbbf9p+2), C_(0x1.11f35b97811e1392b7e5f33b18aep+2), C_(-0x1.34f47b568e89b7ecbfe83a3f3f92p+1), C_(0x1.13cb0f11e8118c8728dc07b4f30bp+0), C_(-0x1.7b2819c00008e638df3a1f667154p-2), C_(0x1.a1284251ac1c9a380e6762cf2045p-4), C_(-0x1.9462a198000c99e2d17bdaf7509fp-6), C_(0x1.98cbd04cf38d0b88fffaebdc2248p-10), C_(0x1.790fb9b4e1079fdb7c7f3de53909p-8), C_(-0x1.44467a122c6f0b3c619500e4be8cp-8), C_(0x1.0c81b81e9a914d549de9a5603fbfp-9), C_(-0x1.cac8f340d2aa3b68b219b85c015dp-12), C_(0x1.056344fb5f7fa4c5bdacd495990dp-15), C_(0x1.64dbcddfce7247b526ac9d7e0ccfp-18), C_(-0x1.2ea8218d9b8d1d441244fcd4b66ap-19), C_(0x1.ae941e74a568c6bb01832f906cd8p-21), C_(-0x1.1e524786cf0a95db795410244806p-23), C_(-0x1.2a97ea36eab85a08d496990ea5bdp-28), C_(0x1.91a720541503c3aab6c0537ffaf4p-30), C_(0x1.61eee7e526616835f0ba9666b29dp-35), C_(-0x1.1df0b9e54c56a105bc6728365e2fp-39), C_(-0x1.1ea73fd30a1b3871739285e4eb76p-44), C_(0x1.4cef49ba65ab3a484daa2106a09ap-51), C_(-0x1.042acc29aba7ca20f707f59b4985p-59), C_(0x1.2f927288a9fec8bba637277e07b5p-69), C_(0x1.f64dd565d432a80474f09d7042aap-85), C_(-0x1.de3b2de560b19ad42b01407d7ddfp-110), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 18, 4> { static inline constexpr std::array<Real, 36> value = { C_(0x0p+0), C_(0x1.f65b07bf823cec483c39d5a11448p-5), C_(0x1.f0133093951f37f6a896ead34da4p-1), C_(-0x1.2157210d40dee8bdad6501ac0ec8p+2), C_(0x1.a490d9720df43c568fadfc931407p+2), C_(-0x1.0a37608588b0a4119bc76eb25c95p+1), C_(-0x1.166e49a8a0cc2b9e02e97716b213p+2), C_(0x1.47f9043ce81ccaeaa7b51a7192a1p+2), C_(-0x1.51650f8f0f7bc2a8e1c87a310a8ep-2), C_(-0x1.4a651a2d2c8b208523a548f223d3p+2), C_(0x1.daa4090446b0d279d1861aa53d55p+2), C_(-0x1.69495e8e6d87591bdc3892f6f8c5p+2), C_(0x1.0277af1839af3f779c7cdb3ae641p+1), C_(0x1.6b6419616b5982af3302995b743bp-1), C_(-0x1.731cf8395e4c8d5b88b93305475p+0), C_(0x1.d1e75297f2041df9c5f5bf256a3fp-1), C_(-0x1.d49cf0590577e4f277c27934579cp-3), C_(-0x1.397f17a4194e8ce372c9e426fbfbp-4), C_(0x1.7a21cbbedfbe11f0454df42e4775p-4), C_(-0x1.2988578b3adabc4b1512d4cbb6abp-5), C_(0x1.545144ccc581a21bd7cff42729e5p-8), C_(0x1.55e4a8c66e27b9cd3f291e5b6a18p-10), C_(-0x1.82c0f91d9bec49c90d6f1f27054cp-11), C_(0x1.ed2cd19280a89d42a9f703b9d37bp-14), C_(0x1.348863e0c3862c00204ef5c290d7p-19), C_(-0x1.8699ea90dfea228ea4870e9888cp-19), C_(0x1.03f81160244ea4e0561d2796396ap-22), C_(0x1.2dc9e87ced5d3e0075d1b0f48214p-27), C_(-0x1.1e0055531ecb5b5480ebd74d3d13p-30), C_(0x1.78b61664e5a70e15a0ed3d839b88p-39), C_(0x1.5f0c636dbd6bd39cd760ce07545p-42), C_(-0x1.6221e33afdbcbb6531e539a33b88p-50), C_(0x1.408f5ecc984b11ae43df9f32fee6p-64), C_(0x1.516335d80f8b3330068bd15b7661p-74), C_(-0x1.4137e85d31ab926f05f01bb46b99p-98), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 18, 5> { static inline constexpr std::array<Real, 36> value = { C_(0x0p+0), C_(0x1.2c1ae6823399b2cb435cac91e1b4p-2), C_(0x1.0b5a4c7a50e393bc298a68b8c54ep-1), C_(-0x1.35e6d8721b448f3219c2ebf797cep+3), C_(0x1.08056d18cc3abfd158e32f385712p+5), C_(-0x1.e443d0b2f1917ce5a7864d3c4f97p+5), C_(0x1.26e95184621c1fe6c94f3f1e55c1p+6), C_(-0x1.027c3db720fc8465d08ef051f852p+6), C_(0x1.39b53e5c17e2d98c6d1b6a224a1p+5), C_(-0x1.a2ef9908e5f3063d5f6a67d79ad9p+3), C_(0x1.3c1856843b6ed43e69173ec9beb8p+2), C_(-0x1.50a61279deff7a9f95e9f5b1ffb7p+4), C_(0x1.7005437ea7f364b02fc7783b2745p+5), C_(-0x1.c35972d3e17999223e53468e37e1p+5), C_(0x1.5e3ef093f504f098160dfa010bc8p+5), C_(-0x1.3ec57fe40125d739e37516f7731fp+4), C_(0x1.8f87e8ce4ea1f97c1a2b6959d92ap+0), C_(0x1.3ebb2932b57e51e04c3ab524c19ep+2), C_(-0x1.f8f19a2160e20da38a2d0ba656dp+1), C_(0x1.767cc5a51bc973a84dbcca58047p+0), C_(-0x1.713b4eb249abff794f2872f24925p-3), C_(-0x1.57f96e30ddfd9bc4477fb05a13ecp-4), C_(0x1.6d3c7dfd75dd9d13bacd85402f0bp-5), C_(-0x1.f364307632fcaaf5a516d1734575p-8), C_(-0x1.a69b8516a1ae027062e6cc44b942p-13), C_(0x1.037145bb4087ace803c84d0a5bfcp-12), C_(-0x1.900324bb445222e2af610e0c858ap-16), C_(-0x1.c39b875e9ce90c4599df73f3cdd4p-21), C_(0x1.257ca20db0247e060d265d852efcp-23), C_(-0x1.94fc591b19bf8737ee11ebdb8608p-31), C_(-0x1.f784210bc45a0c13791f8d01e395p-35), C_(0x1.45da31c732197dc55fbe5cc58e5bp-42), C_(0x1.7b22a9fcf8e8894af17ff0c96d4ap-59), C_(-0x1.36334f22553eac1c5efc112842bap-65), C_(0x1.27559bf46283fc4563833952d7p-88), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 18, 6> { static inline constexpr std::array<Real, 36> value = { C_(0x0p+0), C_(0x1.1b6522cefc386094703a1b940b9dp+0), C_(-0x1.725aa82bb56b65b988671eeb4df9p+2), C_(0x1.352392d274a5a82ecc23fa33228p+3), C_(0x1.0932fb369d6b1d42ff49967acb97p-1), C_(-0x1.879358a7154c8fe38abb0596bfcdp+3), C_(-0x1.7bc58b3667a9b25269bdd7a77a0cp+5), C_(0x1.0b13ecb8bf57a95468d44bdf0495p+8), C_(-0x1.43c9c4bcfe445dc8af77035b453p+9), C_(0x1.09ee5b9c8e5bb60028ced9f338a6p+10), C_(-0x1.51e18f7652afc8e422b14381c4bfp+10), C_(0x1.644767119a752b7a9c6636fe4ba3p+10), C_(-0x1.410473daba291fd610d9e089e60fp+10), C_(0x1.da130c42857b78f659a1d6303558p+9), C_(-0x1.d701d7e9133134b0f0d4fc7eec0bp+8), C_(0x1.63319398a8ba44714204cc51ebfap+1), C_(0x1.103c991a3daa09809634b6cd54c5p+8), C_(-0x1.27d3d6e7fd9bf2dd1ee7850f5b25p+8), C_(0x1.603f483ab97e5aeba0d81de20a75p+7), C_(-0x1.d0777f2eb89143bc896dcbff61bbp+5), C_(0x1.7a787d5d8610ba8dcf36333d8bcdp+1), C_(0x1.ac67a9959292f75e5874c7846e26p+2), C_(-0x1.90d4180a252c7e521492da4437e6p+1), C_(0x1.1a35f9399ae687cbbdc99928434bp-1), C_(0x1.6227b50ba315edc16940995bb21fp-6), C_(-0x1.88f3b956f9d0dbc770c981dd72f9p-6), C_(0x1.6aef03d1b7b80f64bb2a7833284p-9), C_(0x1.578d75e3a79566687a46c7635dbbp-14), C_(-0x1.6111d8865be635c9573ceef437cap-16), C_(0x1.98ae70f64468f801509511411944p-23), C_(0x1.ab515975e313ab940af4e8bf9f79p-27), C_(-0x1.5c32c92bf479e396733399534bacp-34), C_(-0x1.1971da66bec91c38c535f903a2a2p-47), C_(0x1.4b1b6c4a0c92ce2876a63b480607p-56), C_(-0x1.3b3d574a043e2a3cf8b53ffa3decp-78), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 18, 7> { static inline constexpr std::array<Real, 36> value = { C_(0x0p+0), C_(0x1.a2b24d1ab719647b6a1c2ecf4af6p+1), C_(-0x1.c90129239b0561ac21474fdc1f01p+4), C_(0x1.cf2e00eaf4f0becc29975ebbb3d9p+6), C_(-0x1.2500bd3d88164480cc94fa086f38p+8), C_(0x1.077598d26b6930fe825f3677222p+9), C_(-0x1.6c0faa52dddafef24a3684f97c95p+9), C_(0x1.958eaac6820db16ee26374b84f58p+9), C_(-0x1.6c2fe2006b51236b8cd28d2a3376p+9), C_(0x1.b8f7517f01d05ad3f5b4ba6c9b6ap+8), C_(0x1.7e41eac4aec61876fb9933392dbp+6), C_(-0x1.a414506f1749a1c58305f0247915p+9), C_(0x1.8a42dc8d7e0c984036d44acf6da6p+10), C_(-0x1.fc70c5eb750631dda8bffa5c2966p+10), C_(0x1.078cc6f7751312b231c8496978c6p+11), C_(-0x1.d83a569460166e52313ff6ef2cdap+10), C_(0x1.72db6cb15cd72ceb44fc1391ca0ap+10), C_(-0x1.e3a6df319fa13f73a1becc99c1bp+9), C_(0x1.cf3b0d7df18f715bb39783adf96p+8), C_(-0x1.d51428e901c215eaaca0f201c961p+6), C_(-0x1.8c56c880ec38034e39c62c6aaf1ep+4), C_(0x1.2c380f5e865da81b223aaf9ba893p+5), C_(-0x1.fc04081d34cedd56a87f6a93c47p+3), C_(0x1.67cfd3a1ef5c6955d5156ad19fdfp+1), C_(0x1.9005cc81fa0dd8ddcb0ef2e368cap-3), C_(-0x1.6895dc001e228c4142a65a949d43p-3), C_(0x1.82652a80425786d395286ed1c874p-6), C_(0x1.2598eb52540c582b66a388a574c1p-11), C_(-0x1.f931a276c55e6702f13f4d2ec79cp-13), C_(0x1.dc668b4d899394715f65f547aa0ap-19), C_(0x1.b4c7dcafec63006d515f9533babdp-23), C_(-0x1.cb6cdde84a22b96a4fc307092c49p-30), C_(-0x1.f612f7790e7dfcfca6facf9edd4ep-42), C_(0x1.b3f84ae9c3a1d3983026d3d5d97bp-51), C_(-0x1.9f1407c19decc2d85cd5ba63de83p-72), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 18, 8> { static inline constexpr std::array<Real, 36> value = { C_(0x0p+0), C_(0x1.bc1bbb932352fd4db217186d8038p+2), C_(-0x1.230220e94a6286e3ccf38d4bfcecp+6), C_(0x1.65729881a37a4e3a6ec39c0b03abp+8), C_(-0x1.146d11d32151befbe03f1861632dp+10), C_(0x1.34072da363b055ea4712dedb9e79p+11), C_(-0x1.0fba655ec8815d599296c7fe289ep+12), C_(0x1.9a1825ab277513bb221db58c408ep+12), C_(-0x1.16b4a3d0368f557cee02ea790ba7p+13), C_(0x1.59fb20e260f209444967e6c1a575p+13), C_(-0x1.8532af6245b8a37a5135bb9a8819p+13), C_(0x1.8c055ef648911dec2e20ac309451p+13), C_(-0x1.70169a3124976f7442e92622f30cp+13), C_(0x1.392792bc1a4318354c951213b5c5p+13), C_(-0x1.de2062219056d64d01622237bf5fp+12), C_(0x1.3e37823e9c9169638076f5c7aaebp+12), C_(-0x1.691be2f943c22d4422f81e97a65cp+11), C_(0x1.4b463c6bd400a0ecfedd95ba90c8p+10), C_(-0x1.5fc2af1919c21f21f19a7f30b116p+8), C_(-0x1.286e81ad3c5d4bb15d987b1d1575p+7), C_(0x1.11137fdb9735b4b7b7c77d4bdac5p+8), C_(-0x1.749f8e79c1414c37972b9280e062p+7), C_(0x1.1b06a540d8bf3d4241ae8a187538p+6), C_(-0x1.7a50c04170b90bf05ecb290f9376p+3), C_(-0x1.b0c80bbf87c7b0afb3614e48c05fp+0), C_(0x1.32db8166dd6bf259ffbc02129a89p+0), C_(-0x1.78bbab19bbfce1e222ea4ae4ebc1p-3), C_(-0x1.6be3931ec3a0a0f934055bd32184p-9), C_(0x1.4cb7ceaf89c2bc6ca23b4de198adp-9), C_(-0x1.ec1ff5f12b99a0b5484713b8896bp-15), C_(-0x1.a28eed0313308b4187f5c957721p-19), C_(0x1.1e4d1afc4f213777086c26ac990fp-25), C_(0x1.2e933ece77f3d4f12785b9380e9bp-36), C_(-0x1.0ed8efcca12869c8a8420946c2ebp-45), C_(0x1.01deae8b7334485f38756e42ddc9p-65), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 18, 9> { static inline constexpr std::array<Real, 36> value = { C_(0x0p+0), C_(0x1.7d01eebdfe55fe3c6ed21587d92p+3), C_(-0x1.0e862c8ffe7ff18db1f4d0d89561p+7), C_(0x1.6068e5f78cc3a3034b49cf000d6fp+9), C_(-0x1.16e27e80bfe67c3ab640b5e1ecffp+11), C_(0x1.2cfcdcdcf07c3d87dcfc36a512dcp+12), C_(-0x1.de03a2d7212d303b5f3943016437p+12), C_(0x1.2ec8864cafb19603887a2d7c4703p+13), C_(-0x1.500683f99e667a964beb950c1258p+13), C_(0x1.545745c7955e4cdf07cc034c2854p+13), C_(-0x1.1c5400071f26b6f894c12a7b3f37p+13), C_(0x1.16dc653d8bc1d4bb36f214e1e20ep+12), C_(0x1.b4ea0cf6f0a6b2f781cf9163eadfp+10), C_(-0x1.c11dd36c4cf2a48e63345a744925p+12), C_(0x1.5827531f986387c8025c0b0f20cep+13), C_(-0x1.a3de245f7e97f4c57daf304b115p+13), C_(0x1.b4f7e9a0a0606952656f83a68277p+13), C_(-0x1.7f2cf0b4269dd38dde070b5f0cdep+13), C_(0x1.2042e1dec45f6d9e8ecdde4d30dp+13), C_(-0x1.84b7d120c9be3df99a52bbd8cee1p+12), C_(0x1.d5a3bb45a7db2c787108d4dd50f2p+11), C_(-0x1.d06f9035faa5ec088975f115cd7bp+10), C_(0x1.3bba5a0006ab829f47d96569222bp+9), C_(-0x1.633fc40d33ceb334ddc3416213edp+6), C_(-0x1.ea064cf26a80ac52af3e7edffe55p+4), C_(0x1.228bc38d7faa44c44536bc6e393bp+4), C_(-0x1.94763b8fc894319c6a4baa13397fp+1), C_(-0x1.d3df039dfc19a1e9d51d6ee6175fp-6), C_(0x1.e63bf96d77b58d48a45fb3200bfap-5), C_(-0x1.0df6f4a0b44ee3edfa91f00b193cp-9), C_(-0x1.be80af96687fddc94510e8ade719p-14), C_(0x1.a12b7b548061ec0aec1afee7ffb3p-20), C_(0x1.557c0a8693ccc679320f886d948dp-30), C_(-0x1.894221980c4b8d10bc7e6d5fc51ap-39), C_(0x1.766b6e3ec237c8c757492e2c2a6dp-58), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 18, 10> { static inline constexpr std::array<Real, 36> value = { C_(0x0p+0), C_(0x1.a6f23ff482d2a8534d18ee2bd813p+3), C_(-0x1.37e1afb1392b3f40934da3d558f9p+7), C_(0x1.a686ad1a0ba3db778ce2719b5c95p+9), C_(-0x1.5df1b3980b353a49181f807fa276p+11), C_(0x1.912604b6b386163aa8a2a506984fp+12), C_(-0x1.5b61ddc6ff3217136a743b9c2999p+13), C_(0x1.f0e6d62d6c3adad4499f950bdba8p+13), C_(-0x1.40b6eb16bb3fcf7bbb403448e39fp+14), C_(0x1.87585fcb881fe424c96217849318p+14), C_(-0x1.be1e3f54a4c6e6b54ffcceb8221cp+14), C_(0x1.d1d8cfaa9552876a45180bcc50b2p+14), C_(-0x1.c1cad55e0d499c75b90a8681896dp+14), C_(0x1.98c3ae43fe1125e958f8e677c61fp+14), C_(-0x1.5c4d34f8b772415210663ccb0834p+14), C_(0x1.12a3aa37e5fd016d4163c33ef0a7p+14), C_(-0x1.9192f9cf12c8db367f3be99603f7p+13), C_(0x1.1122d052f1ea79533169d18075p+13), C_(-0x1.52bae1043f73d75aa63286049566p+12), C_(0x1.74a03155cefa742f49e86547448dp+11), C_(-0x1.690be5335ae783047d5d4ded6084p+10), C_(0x1.2aa92592f4ea4eab6ee72559722bp+9), C_(-0x1.54e703590f43bf9834fd6d7c3fcp+7), C_(-0x1.eedaac4f8962ad088ff79f7ab717p-1), C_(0x1.de050411f7cd568eda13f525f9dap+4), C_(-0x1.c148def3b49e232ee4958ee9fafep+3), C_(0x1.48e1be6a547f7c0d38d3ce51af9ep+1), C_(0x1.ccb6f2024dedfd3e23939d6e234ep-6), C_(-0x1.0b11a0ddf9bc2847e1d232a914d5p-4), C_(0x1.f0397fd92ef550872efcf8d934adp-9), C_(0x1.723cd3b01432ce7970852fde484dp-13), C_(-0x1.ed12536f5e4f2788058dfbdeb7b6p-19), C_(-0x1.6aaf317d39b56dc9439410fb90dbp-28), C_(0x1.cd1c2594785771509fd29eba3b57p-37), C_(-0x1.b707d969a42cbded13543076b42ap-55), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 18, 11> { static inline constexpr std::array<Real, 36> value = { C_(0x0p+0), C_(0x1.9908fd0ce831f3487747d933d748p+3), C_(-0x1.3339176496abd2cc6f353a6e44a9p+7), C_(0x1.a399ad0400dbc9e71dafc101d1e1p+9), C_(-0x1.58f242d223982437163d99490d3fp+11), C_(0x1.7f8e29aa27ab125f24d2fcb7cf63p+12), C_(-0x1.38a61979e2b2ffe2ae4d4e65fc71p+13), C_(0x1.9add7b4a18f5c8300bd029e80d54p+13), C_(-0x1.ebee387c8e0aff52186a751f53cp+13), C_(0x1.219cbd1b2da3c7319d2594cddc32p+14), C_(-0x1.42ee71a32a848700929a8801a23fp+14), C_(0x1.4162f4284633fd1e7fba1bb3800ep+14), C_(-0x1.21467722a3c16c9f70c4e0f39397p+14), C_(0x1.f02472a8506fd3b8d32f77a4b8f9p+13), C_(-0x1.93ab7dcd5a6c14300ddac86b8dd8p+13), C_(0x1.26e6ca1326b3694ec43b05b1dfbbp+13), C_(-0x1.7e6f2ae54bf7f66077fef1175708p+12), C_(0x1.ca344102205561eaf28babf9b0b3p+11), C_(-0x1.ec7742f47fb3351081ba5a5968b7p+10), C_(0x1.8bd38bdf87a320af9a5418399e9fp+9), C_(-0x1.1acd500cc5943718da806ac7add3p+7), C_(-0x1.4d85442446456020706cd509b723p+6), C_(0x1.ed6ad17e0f78e02531c1a4770ad4p+6), C_(-0x1.b2f4089457d680f06bec3c3dd972p+6), C_(0x1.0c247d783695e3ffa9b901ecf60ap+6), C_(-0x1.9870dc8b45a9f4e303e8e8311b4ap+4), C_(0x1.3338d9a06d3fea3c6e122fc7de4bp+2), C_(0x1.0f6ca08ad5fae6b6177d3fc4323bp-5), C_(-0x1.4c4e08354cb7e3eae0ddb198440bp-3), C_(0x1.02d3a75dac8a719338fdc8517e15p-6), C_(0x1.7509581763d127e7d21fa4b754b1p-11), C_(-0x1.54ad634865cc13ff2aa8e2b2e8acp-16), C_(-0x1.7ef1d65121e030d70caf398558e9p-25), C_(0x1.3b877c4e5003312e2d376dc10e97p-33), C_(-0x1.2c6f23660e48f98694d796524bep-50), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 18, 12> { static inline constexpr std::array<Real, 36> value = { C_(0x0p+0), C_(0x1.e6c2b226df78c279af13845051c3p+2), C_(-0x1.70ef0a94afa59b1a6aa8d2343645p+6), C_(0x1.fe115e7fdadc37c38b9e6da89457p+8), C_(-0x1.ab2ae85d8df6a5fa4cff025ed87bp+10), C_(0x1.e9076c74293a400016225b9ca839p+11), C_(-0x1.9fe839f33e758faf5bf246ffdc45p+12), C_(0x1.1ec83a83d597d7f150637077f9b7p+13), C_(-0x1.61f4e1f4fcae3d0d387b625dac79p+13), C_(0x1.a34037eb93edf57ca17d98f692cbp+13), C_(-0x1.df1d808eb7eddd0fc723f047f0e5p+13), C_(0x1.03261bb811b49bff52d5b3bd37b4p+14), C_(-0x1.08bec2cb9bb5325c84c6514f4d44p+14), C_(0x1.000c9dcb7996cb96b43e3d1c9772p+14), C_(-0x1.d42c4b6e482399636855cedb1712p+13), C_(0x1.9723de14cea5319a6860bbd3c799p+13), C_(-0x1.524bda96018d06eb97a9a94efd6ep+13), C_(0x1.08b8d63f8a5e0d7a39871bf89f73p+13), C_(-0x1.81d1060b61d0d3635b17f5b8f829p+12), C_(0x1.09630f3565a574b943c123a6bfa7p+12), C_(-0x1.59ea297354d075bf6b0a4b01f032p+11), C_(0x1.9c7ad6ace2b3cf85fb948aa7bdadp+10), C_(-0x1.b6b7705751739945f7c51d7dcccap+9), C_(0x1.aa6416006d3250b9dcdb9d2790c7p+8), C_(-0x1.7918296878e4f9853df6b6e8ae14p+7), C_(0x1.07145b6ad1daf57366d1625ece2dp+6), C_(-0x1.a108d75d6bbaf0652587e828bd3cp+3), C_(-0x1.33d485acc9655e7d88b74e802f9ap-2), C_(0x1.6d6fa9e91b92d2703b87421f247fp-1), C_(-0x1.78a5b635c316b5bfc318d4eea976p-4), C_(-0x1.16db8d9d41de38829032ed627d9fp-8), C_(0x1.9ed47b91da7177bda1e64cfb1175p-13), C_(0x1.dd448a5da4eed2af5748439dae43p-22), C_(-0x1.7fd3f33da284c2945eb532e858d6p-29), C_(0x1.6d7f73f5c3ea6d60bfb8d1a80ec8p-45), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 18, 13> { static inline constexpr std::array<Real, 36> value = { C_(0x0p+0), C_(0x1.34875227fc78d9ef7ed7ac6e0f82p+2), C_(-0x1.d5cd5efb52a9ef14597d82d198bcp+5), C_(0x1.425dfad9b492e41845300927f3b1p+8), C_(-0x1.06c373fbafad1222f880762e04cp+10), C_(0x1.1b9bff7a51e187819c73161a78e1p+11), C_(-0x1.b244eac1fdcf0d5091a23ea449c8p+11), C_(0x1.01eb21ca101f022e5418621b2a9ep+12), C_(-0x1.166548c799cafbaa88fc763d8453p+12), C_(0x1.3b0ce98f7e34e32ea84135429657p+12), C_(-0x1.6362301a242eb8214208b870faaep+12), C_(0x1.65cf7c0d7f65c5008737a94a5fecp+12), C_(-0x1.4657f8cbcbde3d6a4e18c8e9c05ep+12), C_(0x1.24d7d2cdfa25a491f828221544bcp+12), C_(-0x1.010708097c75d2ac6e322278d08bp+12), C_(0x1.9d020a4459bdeb50b979470ee77dp+11), C_(-0x1.328cca6ef194279a5bb009ec9338p+11), C_(0x1.bc083519c657836208142c7eb836p+10), C_(-0x1.32ef111f54699b431e478036157dp+10), C_(0x1.7f8dca23d339c29569ea2ec801c2p+9), C_(-0x1.bc6a63cb2fc0846b3e6af0f884aep+8), C_(0x1.f09b702a78c4dd679fe395dd6a7dp+7), C_(-0x1.f532dbb546bbac5b183e2380610fp+6), C_(0x1.ab4ca1b61588ca9a0a6f9d915ea4p+5), C_(-0x1.463ffdaa1065322e64ac74f7fa8bp+4), C_(0x1.ba4ea70cee33c38b2b0e8b20a1aap+2), C_(-0x1.3f8f23678b563eb9630f6042805dp+0), C_(-0x1.2f5a76f330866b9d02c88ed42bb5p-2), C_(0x1.a0cbd7080604e3774928fed42dbdp-3), C_(-0x1.d523cae4ae400c2fe3e190e83e84p-6), C_(-0x1.01b8eb0a5cba7579162a23c9063cp-10), C_(0x1.02b9e23339b17453717d89dae4c9p-13), C_(0x1.5122002fcd3e4c50886af50f4453p-22), C_(-0x1.dca9566b2b5e33d63760b950eda2p-29), C_(0x1.c5fa90ac19cdbed6fcc50c677b98p-44), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 18, 14> { static inline constexpr std::array<Real, 36> value = { C_(0x0p+0), C_(0x1.095a4630f25b345edb3a033429c7p+1), C_(-0x1.94f72d60a79651db24efb743df14p+4), C_(0x1.14fec0291d4b12e7113f25067be9p+7), C_(-0x1.bdfa0b6be593ce00570a7078fca5p+8), C_(0x1.d39577b7cad7e7c4fd5dbf90540fp+9), C_(-0x1.5193ad0b12f066b4cb0fcaacb204p+10), C_(0x1.6a2e0f056a38f1473da552dd4715p+10), C_(-0x1.5d0e503eeaf62b38a4d6937112eep+10), C_(0x1.7e6b7f3178684900694f3b8c2fp+10), C_(-0x1.b6360679ec82c511bf5718cad79ep+10), C_(0x1.ac545c0c739641a55bb4e4c80843p+10), C_(-0x1.6be3874eef6d1f1a32235a12525ap+10), C_(0x1.3c4c888cb63122525397dd653d36p+10), C_(-0x1.1879194795ebee18032f4a91a091p+10), C_(0x1.b5e083426b3c7c6a910b26a6198p+9), C_(-0x1.2f24fbf8b03f0944b0e6672a17c2p+9), C_(0x1.aab5115e884dc181977e8353a09cp+8), C_(-0x1.2726385d133e4a16d05b604abddfp+8), C_(0x1.59979df7b75e1cc96562d4bd910ep+7), C_(-0x1.65732078d27eb27f5ae5d7879665p+6), C_(0x1.7f6def467b5364cd233fba2c5a55p+5), C_(-0x1.704ee2b3997739837bc58d39a41p+4), C_(0x1.cc5ee35ab0ad93a46168320cb92ep+2), C_(-0x1.50976171160a6dd2e2a17268b2e6p+0), C_(0x1.f9c57fa6a287f2b26fe11e313d13p-4), C_(0x1.64b2a171f9a1261fcd30fc5b5dfep-2), C_(-0x1.998a031a0009070455c3c0080416p-2), C_(0x1.57c1f71aec6cd09bc7ae16b02e75p-3), C_(-0x1.b25ef4a8ceef29ad7df2d5db7234p-6), C_(-0x1.808f4aaa023730c43464ce0d9251p-14), C_(0x1.d605bd7dd6adec51bc920eb90a32p-13), C_(0x1.cf1c89541af51d642527681f35ep-21), C_(-0x1.a94329286bdc4b6164f134153d1ap-27), C_(0x1.952b6e764f688e496b665b4266b4p-41), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 18, 15> { static inline constexpr std::array<Real, 36> value = { C_(0x0p+0), C_(-0x1.42660039f1e4ab1b56c2e8881a0bp-6), C_(0x1.ec93c1aa5b61c9b6d5696151fd09p-3), C_(-0x1.97ce26c5b170acf42f1f93361a05p-2), C_(-0x1.c01099aa543ca8b825e143b557bap+2), C_(0x1.a4014de9af920ed4c9ee54928ddep+5), C_(-0x1.6ded0cd4cc8b853b87bfbfacc025p+7), C_(0x1.8330f0dbb0c28dbf63333311ac1cp+8), C_(-0x1.0c893c9ed1485a74e7f7800e12b6p+9), C_(0x1.052ccc4345d2df5a1dbe6873e028p+9), C_(-0x1.c1974852375e5b099cd67d213452p+8), C_(0x1.fad23c454fb6519a66669891ce2dp+8), C_(-0x1.3ffe274228465c9afdc401f4f0f8p+9), C_(0x1.4635deb84c3cfd97dc985dd6672ep+9), C_(-0x1.19ba20aba1a1dc6b33ade2534e4dp+9), C_(0x1.065bcb209e9694669a116f8f1c4fp+9), C_(-0x1.015ece212696c91b2da16a54aabdp+9), C_(0x1.b4c17c7bd409b3d1eb496cf9d8c2p+8), C_(-0x1.48c8d9ca7f31bb244453a83bed84p+8), C_(0x1.008b40131779b22fe5ee591e5e55p+8), C_(-0x1.8c6185bde00310328e2d72cc1f71p+7), C_(0x1.08d51505255015c001174081c04ap+7), C_(-0x1.42df3db9c4b2e8aa91c152e2460ep+6), C_(0x1.93d8682a099131f2e30d1893505ep+5), C_(-0x1.d72aacc75787dddd2538f4cd11fbp+4), C_(0x1.c56cd8c23773878de5456aa0988fp+3), C_(-0x1.8c843e6f10e078b693975b9ceec3p+2), C_(0x1.620f8bdb46e5d416d1abe187fae9p+1), C_(-0x1.ff5dc9ffbca3cebcb086bd21ec14p-1), C_(0x1.8dbab0e6a8c888a4a8c14551861fp-3), C_(-0x1.14fd9c124f34ee1806a1877b89eep-8), C_(-0x1.8d698e7a70351fb6b69fe98cc8ecp-9), C_(-0x1.922f4b831ef6074ab73b0f88d222p-17), C_(0x1.661caab697dee3a1ab3a4d24609cp-22), C_(-0x1.556f58a6ea91cacbb7f565948433p-35), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 18, 16> { static inline constexpr std::array<Real, 36> value = { C_(0x0p+0), C_(0x1.a102d4874492bf0c3f8abe5216a6p-4), C_(-0x1.3ebe78df84aaa4d0f4b794efc132p+0), C_(0x1.b2f7cb5502cda6c9d230fef5216p+2), C_(-0x1.5ac9e38bb117840228ea5f0969e6p+4), C_(0x1.63176aeb8932d6ab994905b6314fp+5), C_(-0x1.e61b7010df60cf6c4ad892eedae1p+5), C_(0x1.d104bdea5563bcce7c191c344f3p+5), C_(-0x1.7544f2a572dd637b67c83e625741p+5), C_(0x1.737d5aa77938e2318fbe4c3f84c8p+5), C_(-0x1.b1c6edf1bb3236287638385af6a1p+5), C_(0x1.9f0c5397c3faff6479945ec39ad4p+5), C_(-0x1.47ca4941183ccf73d74cc2ab091p+5), C_(0x1.1a93e6543e9f9a411108443c7824p+5), C_(-0x1.0927206f45006f2abe266610514dp+5), C_(0x1.a5f0e2f2d0b54c0cfa24d939192fp+4), C_(-0x1.2685107a4162e669c1fad19a69ebp+4), C_(0x1.bed6d3109a358fcb040f5e21b4d9p+3), C_(-0x1.52c12c07acc0e1d274e7d45ba9eap+3), C_(0x1.af31110ee1468e10bf21a15fab4p+2), C_(-0x1.02817ffcabad7fa52399e99ae606p+2), C_(0x1.4e0f916d4e048c57bf43251d9d88p+1), C_(-0x1.864c4e83e1764ac0ffdca7b484d8p+0), C_(0x1.7f1784ea638898f647b4e2787299p-1), C_(-0x1.8002ee89d7986397c24beb3e4ecfp-2), C_(0x1.7fc7499a09e8924504cfc808759p-3), C_(-0x1.2bfa08732bf79ef113f03ba38535p-4), C_(0x1.957da4e89baa41a793f6e28cc5c7p-6), C_(-0x1.2aec3447b7aecf379d17702dfbdp-7), C_(0x1.266385cc4f62510ab31310cb9e9ep-9), C_(-0x1.c0dfb99a8ea4dbba7703d245fd43p-16), C_(-0x1.1928369b116813aa42a010ac694dp-14), C_(0x1.2017f1a37d1405b50e30d1eabd65p-23), C_(0x1.0f4800b7b0a184fe6ec7608004b6p-26), C_(-0x1.03044a0f4ec3952e4f859c26c44fp-38), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 18, 17> { static inline constexpr std::array<Real, 36> value = { C_(0x0p+0), C_(0x1.302549bcac16a07480ffb58950a4p-7), C_(-0x1.d1147836a22995451a237d2c571ep-4), C_(0x1.3c7951e94efea5a01e74ac179967p-1), C_(-0x1.f485b5137068e2de7e3ecadb998fp+0), C_(0x1.f6c9c4f20d2e109d726d9bfa2ad3p+1), C_(-0x1.498acbc4ea72d090f910303e1e3ap+2), C_(0x1.1d9755d014c869b79bc13e22f12fp+2), C_(-0x1.81525835d067c01df39c6d7268f2p+1), C_(0x1.6d720e347fb567a21392b49f69f3p+1), C_(-0x1.cedd19de5af2aa41ce8142ac49bdp+1), C_(0x1.b162c910bfde4ce0f673ec48bfa7p+1), C_(-0x1.2aa74c52348af8100314f0e62e0cp+1), C_(0x1.eda3d295893e868bfb35ec305bap+0), C_(-0x1.f7973b0f803ffd6ba7bc4f61d739p+0), C_(0x1.87d55f9f1654529cea30f503f524p+0), C_(-0x1.e3314a61cec2d1ec8852d0dbcec9p-1), C_(0x1.712067be057e009feff90d8198e8p-1), C_(-0x1.2d407bbb0b0ac1aee45b8cabc16p-1), C_(0x1.675f9e5eb7de518e9bb7430a57b9p-2), C_(-0x1.80b747814ba27c7cd05f743f5455p-3), C_(0x1.0a57b0f3cb83001cac6acade9288p-3), C_(-0x1.43510035a93ea4e9f4f0330f9b63p-4), C_(0x1.135c54f340512b998224396e7637p-5), C_(-0x1.042576d3101c9bfa2c3ee11498b6p-6), C_(0x1.28e7b29b5a905feb407256a997a8p-7), C_(-0x1.b45ff7bd1d15c0d666ce33e8722ep-9), C_(0x1.b09f4241d30f170ec83bd736891ep-11), C_(-0x1.7633994bcb363452031c0be60442p-12), C_(0x1.d2f415013436fa877d9f51f3a238p-14), C_(0x1.16fcce8bf9664ffcec318d033322p-17), C_(-0x1.f9a19b157868fe73cb52d3d8f794p-18), C_(0x1.555633d592e52d8c981188aedf8fp-23), C_(0x1.285fe2167b5b4b96d89f7083a8a9p-28), C_(-0x1.1bc8f87104551fb246bfa29e3c89p-39), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 18, 18> { static inline constexpr std::array<Real, 36> value = { C_(0x0p+0), C_(-0x1.bd717b66e1d1d4d95ba3c08947dep-7), C_(-0x1.7b9fec6bb92af42e63e2e68ecca4p+2), C_(-0x1.1ead339bb1d44833388375e63d59p+7), C_(-0x1.012ddbc7bca1e6101aa1cf5d564ep+9), C_(0x1.c0b75070f83e37ada47fd8928c98p+3), C_(0x1.981856bff215b594a8e4e5f86ceep+6), C_(-0x1.7b31c06193f3e30ac8e863c6933ap+6), C_(0x1.e4866be11fb72b736fa85f578e21p+5), C_(-0x1.c461c239dff802f2348bdb864e24p+4), C_(0x1.d13242d9fb5ff5fac5479a566994p+2), C_(0x1.e6f4964d6a03d0f8158833051b6ap+0), C_(-0x1.b2b5fa84ed5bf72597a5eb232c95p+1), C_(0x1.0717ba30154525a4b9eaa944e41bp+1), C_(-0x1.7b72f81fcc526babbc7b68ad5d28p-1), C_(0x1.3a477558616d24c10f1dd99cb0c4p-3), C_(-0x1.9b911968d13ed312bc38bac2906ep-7), C_(0x1.631172e87e301114011b41a3b8a9p-10), C_(-0x1.1b6a6db603dde402c2223c4221d9p-9), C_(0x1.a5c80b0f2bc5bc3b3f1a94740a37p-11), C_(-0x1.702b73dc1bf286d5e095a7a0f5a4p-15), C_(-0x1.2e802f058eb73ef9b14848780ecp-15), C_(0x1.f461fea3bf76e5a0a5716d49933cp-18), C_(-0x1.978d16c26c68ef616764f83e76c8p-24), C_(-0x1.13d7c474d8cbc6770c364afcd753p-24), C_(0x1.1119bb3fe775e15526c923b289ap-29), C_(-0x1.8685450351316156519237add64dp-32), C_(0x1.fbf3d2901e1ab81addb9d152dd5p-42), C_(0x1.0ebded1ffbce50e958913e490b72p-41), C_(-0x1.8b6af637a9f31fc837c7aa02d1f6p-49), C_(-0x1.a0d4564bf2dc66611a174850c89ep-56), C_(0x1.74b661da2714cde7309e3860bc9fp-66), C_(0x1.5266f1077241c8b5ce693870559cp-77), C_(-0x1.60eccf731ce43024be7a209a4a5bp-94), C_(0x1.5002d3b2c3d4cf65f716a68d3eb6p-122), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 18, 19> { static inline constexpr std::array<Real, 36> value = { C_(0x0p+0), C_(-0x1.640d0cbfb34edc433e3c265970b3p-9), C_(-0x1.26ee7a9fef2f3cd66764d9f94d81p-1), C_(-0x1.cb77692ba61f4bed97023b434896p+2), C_(-0x1.7a52a3b4a77c5125cf118ae57d54p+1), C_(0x1.3d35a908c4d29476ad845269a92ap+4), C_(-0x1.eed0bb7ffc728b5021c0dd7f402dp+3), C_(0x1.5b446269f85399ef36e0a8f67578p+3), C_(-0x1.e860777819bbb58c5f71ba40875fp+2), C_(0x1.459d6005ddfc2d02a2fae3fd310dp+2), C_(-0x1.7cfb6d6fe6c7981796f3f294d796p+1), C_(0x1.6d0ba0eba8694d88a64c51b8f50ap+0), C_(-0x1.08e91d938b8389f5f0add295cdbap-1), C_(0x1.eca4948d0008e456bc9d67c81d75p-4), C_(-0x1.d06140d0577a1b263782da58dca4p-9), C_(-0x1.7297d215124a9ff8bc7627391918p-7), C_(0x1.862feda5c0e0ac9dd17f1152635dp-8), C_(-0x1.d3aeeacfe9c70326d1fac582acbcp-10), C_(0x1.15a5ade831e782a4ffc3bed5638p-12), C_(0x1.48236580a81473ae0d83a7ad5bf2p-15), C_(-0x1.c4dab80b872dfd428813332137cfp-16), C_(0x1.912930341a4fc5b6071d5bc9b09dp-19), C_(0x1.74839b9d5596fba97dd8392c7187p-21), C_(-0x1.f7937244a115a288dc7cde59188p-24), C_(-0x1.ef0ac8df8a590687cfdcc193b466p-27), C_(0x1.b60aa56de0f8813393124e0f539p-30), C_(0x1.4fe56c11057c7023ec8d56f2bd84p-35), C_(-0x1.2b1ee6f947a6f09f111f53e08b99p-38), C_(0x1.904f2b23e480ded5004c9a3b2081p-44), C_(-0x1.1a491e89e84c1ae1ad605792ed65p-50), C_(-0x1.e6f7ea660d39c7595d9913c47738p-58), C_(0x1.68bf338efe90278676de17896db9p-65), C_(0x1.ec3578649519ba8d72287ee8e375p-78), C_(-0x1.56c2062f8a091fe577e9571b2417p-92), C_(0x1.4654c88c71974e3c9f8fffc52861p-119), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 0> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(0x1.07725ffa38e9ced625cca68f3f21p-17), C_(0x1.418c13eff61cbb3a021569097a1cp-8), C_(0x1.3da46890dd9a0a4b666b663d4aa3p-3), C_(0x1.8a2b52a78c79acb029ea1b6db9aep-1), C_(0x1.1a351fcd80743de548c177ab2074p-2), C_(-0x1.854589d6ffe0f67b9ae39f8edb13p-2), C_(0x1.33e4c9737dbaaadf26763db4b5edp-2), C_(-0x1.aa815b6478cdd9f02d23c8d18fc1p-3), C_(0x1.087553137f3f92720c562745af4bp-3), C_(-0x1.1923520d0b86878b50e3a0765033p-4), C_(0x1.dbed9e8e6653062b736fe52ecb07p-6), C_(-0x1.13641cf1379f43fd1c7ac3bc71edp-7), C_(0x1.6875bc1af4453d3d4e0df0f5de38p-11), C_(0x1.a947dfa3688a3625b782cb79509ep-11), C_(-0x1.10b3493092979555022e5756e4f3p-11), C_(0x1.739af28e775c2a9c036cd7599ca6p-13), C_(-0x1.6cbb4a08c7eb5fe8237038a25da7p-15), C_(0x1.409e1bccbf4ef7d2793c14591929p-17), C_(-0x1.b4b5ec00d923dbc2091331f8dd78p-20), C_(-0x1.0bf29985eecde4627b6e6f4c0369p-23), C_(0x1.687a642b13ec01d769b15bc617e8p-23), C_(-0x1.137b64e3f44e9fdac7b535f30d85p-25), C_(-0x1.07f0606fa0dbad766d3197dd19cap-30), C_(0x1.6c85ed37d47e7b904cfd46760581p-31), C_(0x1.e0b71b0ad278ef564d1fcf1e88a3p-37), C_(-0x1.c7f3c451c06bde44cba8b0964cfp-39), C_(-0x1.3e734cfafd184d570a4dc2808fb9p-41), C_(0x1.ce28f04bbb94c603b91b46462315p-47), C_(0x1.70c276923dc2ecdd8f158e1477f7p-51), C_(-0x1.79a58db93f5236bb350459a10815p-57), C_(0x1.1f5027aac86b8e122cbfaf41ee62p-65), C_(-0x1.02276c5db8038c6bd4e95867d18dp-70), C_(0x1.254876c157537023d202fc646803p-80), C_(0x1.01c1badc280ce855150f875fe27fp-94), C_(0x1.81b6379c836e2bab36a7efba81e2p-110), C_(0x1.fb9eccd49ecd0870d19d3ffd447bp-140), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 1> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(0x1.32ea938ba90f99b6837f5af63be2p-14), C_(0x1.6ee1bf4cf707539d522967930e11p-6), C_(0x1.8a481c471691e9b156b25ff57636p-2), C_(0x1.0b4f5688ae00b19fc1e160cf6648p-1), C_(-0x1.73e1ddbd7901f6383d61c3a6ac0ap+0), C_(0x1.8b33bb402f96e0732af30db90eddp-1), C_(-0x1.9843e3061a5286745b1a22aa34f6p-2), C_(0x1.174b1b1b9671399a52d81cce6671p-2), C_(-0x1.d5ed9bfb0b3eacb0609851530eccp-3), C_(0x1.7f42427dbd66dd7c640694ddac63p-3), C_(-0x1.08eb5567536606f98b744fb38775p-3), C_(0x1.23d363b3776e341b922f685a5527p-4), C_(-0x1.e3311fba2b6786652a72b9017675p-6), C_(0x1.080310d541cbc7b415408ff9e9e9p-7), C_(-0x1.70478a76493e219892885c932ab3p-11), C_(-0x1.0307c808a4ebd5856963c5fffbdfp-11), C_(0x1.dee4ac1d99b73074451ae5f38c64p-13), C_(-0x1.44f6514c266093c947d073730317p-16), C_(-0x1.25e4b5de72eb99eebb1451b05b03p-16), C_(0x1.d4b5838001d90ed04674ba339f05p-18), C_(-0x1.0c63aca94f3b9788d5e3d0094dfdp-21), C_(-0x1.5d75636e21f07d7a3381c79d0362p-22), C_(0x1.731d5b5d003f55b6876fe0044ec6p-24), C_(-0x1.0c3e8c9e77afbdab5c815392ec9ep-29), C_(-0x1.add3791299db3c378e9de40e8a64p-30), C_(0x1.06fadabb3956eae25696a4f51f5cp-33), C_(-0x1.f4ce18079dfc9d6929b9dda1612cp-42), C_(-0x1.2eaa27d46e548153d91731a7ee6ap-41), C_(0x1.ae2bef5a0c85a05297e337e77b0ep-46), C_(0x1.4bfd5bd67de9ea53ad7c40089635p-54), C_(-0x1.1d671c704d7fca69eb029e029b5ap-57), C_(0x1.67963d56e9a972fedce141425dcep-66), C_(0x1.0b2bba52e426ee86c81ee87efd7fp-74), C_(-0x1.835ebfbafcc994f81e5e17cf300cp-86), C_(0x1.613768a516da5440f559a8b7229fp-103), C_(0x1.d0dabcbcf214e8044829d82792bcp-132), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 2> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(0x1.3f4897070d099352fef182a2ce17p-11), C_(0x1.6d998ddc083bb79599bbcdbf5aabp-4), C_(0x1.5cdfd95e7a29056f595ea6b04d0dp-1), C_(-0x1.3be70bab67dce74ec0a3fcb7068ep+0), C_(-0x1.4f0043bcb070f4a9035f0cb75f46p-1), C_(0x1.3f5cc039811e2b5b41e1339ce191p+1), C_(-0x1.435a201615b7649bde7e6bdcd35cp+1), C_(0x1.edddf036bb21e05065a4314b8003p+0), C_(-0x1.339bd26a01d7b24e4a113345801p+0), C_(0x1.26ea186703fa7b37f25c2df1ffcep-1), C_(-0x1.62a5bd05e71620f3397b8b55cadcp-3), C_(-0x1.8157fc40373b6ffb1b755d5d64ddp-9), C_(0x1.2626bd14128e3600ff5e4ef117ddp-5), C_(-0x1.458d354bc66bca085d03a73908bp-6), C_(0x1.60eb38bd6dcb5883ff977a13b631p-8), C_(-0x1.11a579a9f60ad1f4e34335fca023p-10), C_(0x1.8521f25159bae6c124f05e0aa6c8p-11), C_(-0x1.2e7cbaa1495260ee131d264b7fcbp-11), C_(0x1.d8a73116e5170bf766c62902d5cp-13), C_(-0x1.14baffbb5f3fc7cd4417451de38p-15), C_(-0x1.bc76b1b7765f460d127ed8109cb6p-18), C_(0x1.eb62162b875e74ac3ffbad741aedp-19), C_(-0x1.3ec5df1234a119b292d63f400f4fp-21), C_(0x1.0bd69df0fe817c3f4ec6f9220c7ep-25), C_(0x1.06532665f4ae126a371a91623062p-28), C_(-0x1.7b6b83afc0194421f9c689981f49p-30), C_(0x1.34507b73be114caacaacc09786fp-33), C_(0x1.3e99e3a60acfbc311476e151da98p-38), C_(-0x1.f151e40b836b8f8aaa3a3f0ced37p-42), C_(-0x1.448cc1196d194e9baa30923d08e2p-48), C_(0x1.4daf1830022e2a424c8ef6ce75a5p-53), C_(0x1.5011fa2f598d1104ecc45344c209p-62), C_(-0x1.1686e4fad9ced67d1bdbae1c9b3ep-69), C_(0x1.abb8cbb5d77c3d36c138309edcb2p-81), C_(-0x1.70542f5b2fe975bfb256d1ce4e9dp-97), C_(-0x1.e4be478d2f9719b08915aab446a4p-125), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 3> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(0x1.2434b5ba872d4c5808e71daa73f5p-8), C_(0x1.3130229eb7f3605b9b1b32cb9f97p-2), C_(0x1.7ae2dc23075619726157a440b0afp-2), C_(-0x1.f582a7e51625005d91ec63b814bap+1), C_(0x1.c7d08bb60552f4ce0a1dfeaea923p+2), C_(-0x1.a91c524d7a54ea689caba9ffde39p+2), C_(0x1.3c2342a582cf3f8debfc54cc85bap+2), C_(-0x1.088cd569576045a61a631e97afdcp+2), C_(0x1.d4e6f8f27b14576971c750ec5e9dp+1), C_(-0x1.7aa23dd152a396e3b62ff372d1d7p+1), C_(0x1.fadab4daf8f0e58f8d9d4ef01e97p+0), C_(-0x1.060b8820123e5eec7823aad8401ap+0), C_(0x1.6f3fb0d6ae2f90f1c572f1f9292fp-2), C_(-0x1.4c612316c2d6c3d361a3a87a8a95p-5), C_(-0x1.59b5936f0b00d23a57c7cb83dad9p-5), C_(0x1.f1cd6ac34748038c9618e97f54p-6), C_(-0x1.0815866d993d299c542a96e619ccp-7), C_(-0x1.33db5d2125a2859a2040c40794b8p-10), C_(0x1.bff774c7101082d480ffa7afad95p-10), C_(-0x1.14d1461893fe65443154fdd9ff78p-11), C_(0x1.60ee19b0b8b54d2e9cf10559c07ap-18), C_(0x1.6481008914d42c490ce92b7a443fp-15), C_(-0x1.79e8548e2225181445126279e5f6p-17), C_(0x1.0000883a713c85d37bfa6cb29923p-21), C_(0x1.0c4a52b19c7af0f6d1d88d405597p-22), C_(-0x1.51bfdb03a0cb4dfbccfaca10a1e4p-25), C_(0x1.2786225b5270b4ae5ce680be0a2p-30), C_(0x1.c2f3c31efae819fc824fc14e81e3p-33), C_(-0x1.e485fc83c20815b41344b0b5ebd8p-37), C_(-0x1.cdcc8478ab5ca320820b2bdaf727p-45), C_(0x1.248fa48f37bd758b38759e29a62cp-47), C_(-0x1.a1ed7efc74f0ddd5c3e7a26568ffp-56), C_(-0x1.257d232551abd9af4093fdff2e93p-63), C_(0x1.8e8d04aa5ac8d2663570e52c4402p-74), C_(-0x1.858c6aec0ddcc911f17d17aad5aap-90), C_(-0x1.0055b5f34554e57cc908df0fdeeep-116), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 4> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(0x1.cd2d34d1a42efd10b55402f678dcp-6), C_(0x1.84d83b63c2112e72eadf0e175b4dp-1), C_(-0x1.432ceae809a5e8ac576108008797p+1), C_(0x1.a0b9d38c7e490414c924ee603181p-2), C_(0x1.201a5e729e35c6b52d82081c697bp+3), C_(-0x1.2e113a8c2f74baddd86814ec6249p+4), C_(0x1.552ffbcbb449884fbffcd2fa1903p+4), C_(-0x1.094e929e449b6445010b66a63f08p+4), C_(0x1.1c13ef7eb64aa8ee0175687d62ffp+3), C_(-0x1.1af822f546327a2297be45973a7cp+1), C_(-0x1.f9d0cabdd71723c2b35a33ecead9p-1), C_(0x1.ddb0b49cb2203c31df0981557b5ep-1), C_(0x1.5318acd89fe65697aea31294c66ep-2), C_(-0x1.05b05a50c615d71587f066c9936dp+0), C_(0x1.9b5ab34637cfef44bfcb0657ebfap-1), C_(-0x1.1af795bed4913c5d4d0b7000d26bp-2), C_(-0x1.67451e2d12b8b1dce42c001cf264p-5), C_(0x1.99b155175f94ba8d3e0e29b8e60fp-4), C_(-0x1.ac7539c2e19ebed9f65c60048ba4p-5), C_(0x1.9ca72681ec9ea8c760a8f2a71fa1p-7), C_(0x1.34e3b1c23cb7d1aa00f8b981d763p-12), C_(-0x1.3a24c6f5381cdc3e9a0a2312b097p-10), C_(0x1.74fb460ba6a3c91ca053d755b7f7p-12), C_(-0x1.0b246714f1ffd71ceaf84df8a2f5p-15), C_(-0x1.ab7c59cb5e81411290eca69a51b1p-18), C_(0x1.dce3bc922f58f0b17196be55c2d5p-20), C_(-0x1.67697e8054a806243dffdcb105dap-24), C_(-0x1.9e416c1fd1c36255ecb5eed76efap-27), C_(0x1.c8b3d9029a8aec4464e3c0dd17ap-31), C_(0x1.5aaa4a43abfd9a111ae71704a9d5p-37), C_(-0x1.7db632c817eaeaef04d7671c292bp-41), C_(0x1.4a05d041f84f4639b3fa535ffbc5p-49), C_(0x1.e2fed86a51ad69aa2e1cca0d7a0cp-57), C_(-0x1.05d887c98f164a6efe9f254828cp-66), C_(0x1.42293c268faac3b8f9cecd0a784ap-82), C_(0x1.a7fbcc57e37f33cf909b7d2d16cep-108), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 5> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(0x1.31422db2538bc0a87b308ffa37p-3), C_(0x1.0d01250c1b0d06e5278d6357ef2dp+0), C_(-0x1.24921c6c7a3e4123721458dbf25dp+3), C_(0x1.a227c85b5e55bd2048d352a6c652p+4), C_(-0x1.524f50b139534832a4ee54d2fbecp+5), C_(0x1.8738d759012c36786ab70fb57053p+5), C_(-0x1.9323ab467eb529dc5b829fba165cp+5), C_(0x1.a42ab8b3ebb45f1751552cca4226p+5), C_(-0x1.a0b31f7eb9e57c7f0585d5e9fdbfp+5), C_(0x1.5b572ee0532df8736514c7068d41p+5), C_(-0x1.a65ce687fe55f007c4de98a4572ep+4), C_(0x1.d054e5f3566481470f5818319872p+2), C_(0x1.85d591edfc333f35ee49a560ad36p+2), C_(-0x1.3b9b5d3160df5b3c5b4fd29535fbp+3), C_(0x1.a0e3e2fe3af5aba2fa3cba939e51p+2), C_(-0x1.908502149e3126842af43ab5d7e1p+0), C_(-0x1.2fdcf4d1b74c11a7c8107dbf5a5dp+0), C_(0x1.71a344c5df788a37bb879332042cp+0), C_(-0x1.6f12d9a04f61757636a67705762bp-1), C_(0x1.40e9a8c631ed8f09035310ff998dp-3), C_(0x1.90c3dfa395147a7cc0c7676c3758p-6), C_(-0x1.cb2bc9edd20ef799e67ea0b4ad99p-6), C_(0x1.07343e2ee6832b57b8208a80d9e7p-7), C_(-0x1.49dfe7960ed68e24de4768224cf5p-11), C_(-0x1.b6e121c3001f0f7bec5598cab095p-13), C_(0x1.dcc996a9ecb3b5336d9759d46957p-15), C_(-0x1.a1bb03b6243b89e05627bbe8512bp-19), C_(-0x1.d9f622b803a645f37f52496ad03cp-22), C_(0x1.6819f189a7727ca3a62602f289abp-25), C_(0x1.4ca2954f6ae1a2e73667b4619ccfp-32), C_(-0x1.8c19531172f0aea0af3e91e143eep-35), C_(0x1.ad03ab6b6c0809d426ec9d64de28p-43), C_(0x1.92a5c80316f77784726d71e5f027p-50), C_(-0x1.126aebf2a41485b2605ffe0d6f2ep-59), C_(0x1.0d7f8030d9d60a694722396ad34fp-74), C_(0x1.62acfe05bfb1201e774235c1d27p-99), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 6> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(0x1.46ba9611fdf6c7a94d4f6d15ae64p-1), C_(-0x1.dc52978d552a4c87a8e0e11df878p+0), C_(-0x1.7fa540f99cfd7a53d485cc23b3dep+2), C_(0x1.5732b50df53b69d2559ff51a1e33p+5), C_(-0x1.b13b1bdb27ab101c396869bcc29bp+6), C_(0x1.33606cf67b649ff0c53d5daba4dp+7), C_(-0x1.bdcf241a98962a37ffef026534aep+6), C_(-0x1.6f03a4675ff5f681cbcdceb803f8p+5), C_(0x1.1808882b291db1c41b8c116f1fb3p+8), C_(-0x1.010ae854c8f06138d8c0149f09bcp+9), C_(0x1.53a4857a4441ea9cc9b274ab65a3p+9), C_(-0x1.6d4a26d83e33b0ac3dc870af21b4p+9), C_(0x1.3d6709439125c739fb2f5edfb5dcp+9), C_(-0x1.889b5e2f1c327048a556374f7da9p+8), C_(0x1.56fd4f6d97a60ae9928f3958a702p+6), C_(0x1.25b06390e20f015674e98cf0aeb5p+7), C_(-0x1.b399a1a2f22fe6161cb0e96be4a5p+7), C_(0x1.3df78e7e4d04373329461fc9ed72p+7), C_(-0x1.0ef9b79a3621238b48ca4f0954ap+6), C_(0x1.5f7982d2ac2abd1246025f08fe6fp+3), C_(0x1.6a625e6b6bab463f678abfc9f5a5p+2), C_(-0x1.198f31ed8cd901a93c9ab1bea14ep+2), C_(0x1.42ee7fc8a94768a05abd24f4f6ap+0), C_(-0x1.7d60037bbed413784256ebd48bcdp-4), C_(-0x1.6ff7a83ef962302af99cd8276389p-5), C_(0x1.ab35b35a042defdd50e378dee2cap-7), C_(-0x1.b332608ca1a847238ace5779c464p-11), C_(-0x1.021ab5a3bdbb30ee9a537ffac573p-13), C_(0x1.eac528756b7f5130df18318c4f94p-17), C_(0x1.0199b85d253f43e310c32a3ee23dp-24), C_(-0x1.6d0abfd965fbe6911b0989caac0cp-26), C_(0x1.0c61bef3e22c19990cf4042ba7e3p-33), C_(0x1.18cf50a4e4b4950ef758930ceb31p-40), C_(-0x1.0160d4507e328ccba58abe0174c2p-49), C_(0x1.7a161fd10bdebbba470322602b5ap-64), C_(0x1.f195998251a554e483f0c71a4471p-88), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 7> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(0x1.13189db507a58f44b230b3686764p+1), C_(-0x1.0f9b17b47559884eb516506b8576p+4), C_(0x1.e2750024accc2d74cdaf0e777dc5p+5), C_(-0x1.02e9517352f36c7e1cca5cdce0a3p+7), C_(0x1.84ea97af0478dfed161742a65f15p+7), C_(-0x1.cff7ea5e103622b218e35556d5c2p+7), C_(0x1.edfef34bb4dfb6181091bc4e1283p+7), C_(-0x1.f2fc15391d50c27f5075a6c8ff4bp+7), C_(0x1.eb246356ef9387175566a1e68a13p+7), C_(-0x1.02127d08179f9b70803e08887c21p+8), C_(0x1.3a1511b48828ca00655918525c18p+8), C_(-0x1.91c784aea677bcaa4677a1d92317p+8), C_(0x1.d755a30a6335088a6e9e8a634a61p+8), C_(-0x1.e5c19797a7c13f73162c80019235p+8), C_(0x1.be09360d2ab5d983638f05e968dcp+8), C_(-0x1.6e80a047a6bc49df58dac888c978p+8), C_(0x1.017887f1e05fdfd52e459afc793dp+8), C_(-0x1.16d045efd9fc23449024f4ef5b58p+7), C_(0x1.6f3c5a5aa270e946f4f0452290a4p+5), C_(0x1.00a0bb4260f4b86b22991895dfc7p+1), C_(-0x1.883af181a30c4b69a77ebd74a0cbp+3), C_(0x1.ca6f2d6266dac24630d5b0215037p+2), C_(-0x1.fb9354caf7469830d8b743a50504p+0), C_(0x1.c12f9fd42c0cff788f8d8a32aaf7p-4), C_(0x1.aa753c061078e6073623671f0cd1p-4), C_(-0x1.0149c0900041728b5dc19008c617p-5), C_(0x1.320d29d0ed46573ee176d2f36b8fp-9), C_(0x1.7569a3a8ad03ea55263aad4cfdap-12), C_(-0x1.c7142f2922eef32fe70a3d54296ap-15), C_(0x1.46d93383351fcdeef5e2617523b5p-25), C_(0x1.cc32d5d77364e5410b711a5b1237p-24), C_(-0x1.c3faa80be31a417c7ff07c960f74p-31), C_(-0x1.0e8f2f249697649bebd486ba2aa7p-37), C_(0x1.4b97e65c483067d885e78eb825fep-46), C_(-0x1.6f0e0ef20e7a06716a4c8ec9fe8dp-60), C_(-0x1.e310d5b8794443399cdd6ece490ap-83), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 8> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(0x1.580f506a271ceefdaa3463cf1629p+2), C_(-0x1.bed7dad0110afcce89ace888e88p+5), C_(0x1.122d5f16217b3e9bf4e80fdc4373p+8), C_(-0x1.ad0c5fd2ce7d97e26b1b63596f32p+9), C_(0x1.ebebc475930229b2000cf737b101p+10), C_(-0x1.c66859645ad39ff322d2fa4b454fp+11), C_(0x1.6b3c821d2c08e770e244c3fd9b4bp+12), C_(-0x1.05ed443c98660df7e825b62de19bp+13), C_(0x1.57df9f8d58ae967ab62cd9351becp+13), C_(-0x1.988852a4ddb8e2394c97f0e9d30bp+13), C_(0x1.b718499032f53cfb6791a553f164p+13), C_(-0x1.ae72afe9b5f0ce3d7715181f289ep+13), C_(0x1.817de8fd200b93d2fe94ab51ad77p+13), C_(-0x1.361e5f944923d3d5bdf35a20adffp+13), C_(0x1.b3a6d661a5e954603cd076722514p+12), C_(-0x1.036ff3829f5795f4ec64398489e6p+12), C_(0x1.edf47d39280a4d357e9e1781a39bp+10), C_(-0x1.10c036b4236268a93be68873acb9p+9), C_(-0x1.e0b697df7f002ac2801a14873b67p+7), C_(0x1.ecbda44c262ae523cdc868e322e1p+8), C_(-0x1.86f5d451d505eacfde5511850305p+8), C_(0x1.725c7f3a52e97d8a78a3843dfb9p+7), C_(-0x1.79d4729613fc7b35a032158d6205p+5), C_(0x1.fd7ee793312f8451ca67d9e92df2p-4), C_(0x1.0d01b8a4bb031f49626bbfdc2049p+2), C_(-0x1.47046f0d13d0e9edd2f830615f89p+0), C_(0x1.be74b29e56e9e7adf67a6938c90ep-4), C_(0x1.1bce9460eaf5c685ea35565b6408p-6), C_(-0x1.bea1c36d184dadae8028a6e3e14cp-9), C_(0x1.c87dd9f0e82f03f1f618a5e508a2p-16), C_(0x1.3736896d21eebb32c780ad16f33cp-17), C_(-0x1.9904cb4c4529ea63892483302a3cp-24), C_(-0x1.1964fba513e306ae2fe86b385614p-30), C_(0x1.cd54969392f7573024faf58e36bap-39), C_(-0x1.819d1aa8bbcb7dddef905812ef85p-52), C_(-0x1.fb7d3a090e0ab46eb1271ed833e8p-74), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 9> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(0x1.58fd39e3ea473b9c365112f9e5fdp+3), C_(-0x1.f5c4ea84a3bdf86fabc78b7ccf87p+6), C_(0x1.5132162ce5f74a25ac418aed5521p+9), C_(-0x1.153d0f08884aedd476baf2e683p+11), C_(0x1.382a3e583a8c4c9f1dbe11c15209p+12), C_(-0x1.01662d4c3e81ce469818c40b609cp+13), C_(0x1.4a1e803e16c3f08b00f992a85132p+13), C_(-0x1.5e4f1aa3047031adaa3ecd9f7d51p+13), C_(0x1.34f8d319cfee8ccaed9905f9568p+13), C_(-0x1.5037b2099231e17c790011360049p+12), C_(-0x1.c9d4325924514ceeece20c92f62cp+11), C_(0x1.ef1c5da047ca3c6636907219e698p+13), C_(-0x1.aa6460f62329021cc0a31061d8ffp+14), C_(0x1.1493ffefe577c924223ee91be135p+15), C_(-0x1.378dc9a8516802b7004a42d17ea6p+15), C_(0x1.3a895ef60ca292cbe80e485690b9p+15), C_(-0x1.17d3cdfce981563e49f923d38dc9p+15), C_(0x1.b32449a2a05e7c53387e3b5eab6ap+14), C_(-0x1.2d005b15e1ac660d6c6de2ac5d77p+14), C_(0x1.762585d24bf9c7735f9898961b24p+13), C_(-0x1.8db35bc09fe7ee5140a582ff984ep+12), C_(0x1.3cd0860a0aa20c2aa3d4d395b99bp+11), C_(-0x1.0eb312cd7109b3879fc433d5f57fp+9), C_(-0x1.439f55d9eae59605a3c39a59b84ep+6), C_(0x1.991df190f9945d0054430f51818fp+6), C_(-0x1.f474551766f4044e9817e92e973ap+4), C_(0x1.7b90022b6c4e7f168ce752888458p+1), C_(0x1.1453a51ab81ae063df6727985433p-1), C_(-0x1.0919f3da668fc601223376349f5bp-3), C_(0x1.2552ca2a72c78998c9ac373b5bbap-9), C_(0x1.0101dfee94cc5d7f60f2678fd0b1p-11), C_(-0x1.dade9b27d08cb19be2ad380c75a3p-18), C_(-0x1.64097fcb6571f6185210c51bbb62p-24), C_(0x1.8e12f1e504e13d786036befb6f25p-32), C_(-0x1.eef1afe29fcfbef2c0d8edeb2fdcp-45), C_(-0x1.45af8bce131ab3ac470aded6347bp-65), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 10> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(0x1.c2e57f37dba380a65ba9eda2079fp+3), C_(-0x1.59749d8525f12d8082256adb88ffp+7), C_(0x1.ea6ee085cc96e0d288f3be1b9ca2p+9), C_(-0x1.adf6c2874bed2b3f69d173f96a2fp+11), C_(0x1.07b4a22de335b119555a005db318p+13), C_(-0x1.ecd88a76ee3d3e922a5c04819366p+13), C_(0x1.7c29acad357038f41eb8b1dd0fc7p+14), C_(-0x1.052f5556b7e4a1a5c20ecd7e819fp+15), C_(0x1.4e46d551ac93ec5e56006a3de757p+15), C_(-0x1.8e77607cfd5ad57c6663b8875b37p+15), C_(0x1.b47447ef6b859ed13ace58a9a34dp+15), C_(-0x1.b911fbfaa77dec0071a250cc5fefp+15), C_(0x1.a115d6e8e14d04bc0db0286009bep+15), C_(-0x1.7187cfaf46cf0d5ed6f0095f890ep+15), C_(0x1.2fababdbdc3283e40c1d376f77f3p+15), C_(-0x1.cda4daf54c9cb2382843dcbe14cfp+14), C_(0x1.457825a36823f87f660fc5987cb3p+14), C_(-0x1.a46083210b99766804825ce7a718p+13), C_(0x1.e3885ee2753248f8df804c157d1cp+12), C_(-0x1.e49914e71496a8b65b2bc3b0a8d4p+11), C_(0x1.9ae829c152385eae9b1515bb5c36p+10), C_(-0x1.f191137e3badeb9e76f5cbed8cb2p+8), C_(0x1.57e65b068678833f27ed3ab74f4ep+1), C_(0x1.c2acc962d2fde80f4a40165a5fbdp+6), C_(-0x1.1b8eff5b124df721e99f0cb0e796p+6), C_(0x1.4ce0864f5bc843b2b9783951ecc5p+4), C_(-0x1.f98632e1903923d8655f653df191p+0), C_(-0x1.f614ca355bef0d83e7011b692c6bp-2), C_(0x1.105d05e210a04ac76f5004e82666p-3), C_(-0x1.2c35027764d106ecb7dcc0f035dp-8), C_(-0x1.76591805b151661a98c804b730dcp-11), C_(0x1.f83620ba68c2e3da4e964c603cc5p-17), C_(0x1.9ec84cf651d46727ce1b0a44d7ddp-23), C_(-0x1.358d783409c13e2404896fd5c7b4p-30), C_(0x1.257546b697ae8fd8394b22b0ae34p-42), C_(0x1.8233dd1d0686d57c137ec852b5d4p-62), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 11> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(0x1.ffa03a8700da7856451e869e7b5ap+3), C_(-0x1.91f11c60f20f4732595d765621bcp+7), C_(0x1.215104c7061731e391acb03d0135p+10), C_(-0x1.fa2000694cbffa8b68970bca9b4p+11), C_(0x1.2ea66d9c1c1c36281a4f053280ccp+13), C_(-0x1.0bde0020ff0122097ceed958162p+14), C_(0x1.7dfdf722720076bd662023e14b8fp+14), C_(-0x1.e6475940e8f80e3e0662171bf565p+14), C_(0x1.28fcf546d66430029dc0ae7f105p+15), C_(-0x1.570d2d144c0d85d5f33951d38d4dp+15), C_(0x1.64b992f501b16328e29ed09c3ca4p+15), C_(-0x1.4cdaed031e2e4abf8359db4b1506p+15), C_(0x1.21c4ffd20e63be71df3b6f2245d3p+15), C_(-0x1.db78c1b913f3be9244561a56f2ecp+14), C_(0x1.5e8fb02e9949d4c003e971dc8526p+14), C_(-0x1.bcf51c1ea8f31b04ed5d992397bap+13), C_(0x1.e583e17ea627e00530e2cb6f7d39p+12), C_(-0x1.aa4e81eafaf451b39ea0ddb0f57dp+11), C_(0x1.13f68d6d4da0d49f20c5505cdf9ep+9), C_(0x1.eda1ba36110bbecc88ad9ef4ce8cp+9), C_(-0x1.4fff2b926b6f5e6bcd2243e80004p+10), C_(0x1.12bce3e2f7931f11964e6bc3f549p+10), C_(-0x1.798d627cec26e7e1e4f53d7bdf9cp+9), C_(0x1.be6fc86ae4a8be5d77f2a1e9d57ap+8), C_(-0x1.8da2d6faf8e64c22dc4a043ad99dp+7), C_(0x1.b66a3015a1c5a11c948aaaf7cab3p+5), C_(-0x1.44429d9883de74d9c60a876b939p+2), C_(-0x1.c3e96613b6e5e2ff71adfacfda7fp+0), C_(0x1.1e57998dcfcf5d1648e257f8bf08p-1), C_(-0x1.07010d4834a6e7a67ce43acbf39ep-5), C_(-0x1.1b562f148b2fb64632b98ead9b7fp-8), C_(0x1.0af79c08ad78f06aac625b45eb1p-13), C_(0x1.f410b3bf125a82ae4c43c7624696p-20), C_(-0x1.f9be8616ca648419dbd80373acd5p-27), C_(0x1.6a9909c4a9f6ffff9ad70512f7b1p-38), C_(0x1.dd2f7b7aa9b821698f859b9d1a0fp-57), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 12> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(0x1.87fb22468465fb8a2934ce18ef16p+3), C_(-0x1.37c2f683aab22684a06e79a101a1p+7), C_(0x1.c5fd83f053f82dac4273a062a48dp+9), C_(-0x1.91b1e12dd60d97ec2e841dbfca05p+11), C_(0x1.e68387666347c07a316a9422b5b6p+12), C_(-0x1.b4dea0e7d579f84f7fb9d6c16bdcp+13), C_(0x1.3c269a772fa78e428d8f5044caa8p+14), C_(-0x1.97127ecaa2ab1915c1aae5c6fc8ap+14), C_(0x1.f6af289cce31c29a6ec330fbe9e1p+14), C_(-0x1.2a9f5b6b03ca5e9eb10038f1c5dbp+15), C_(0x1.4b10d6718988db4dba24714139cp+15), C_(-0x1.55a31577d419bbaf6e8ea53fe90dp+15), C_(0x1.4e7cdd5d8ea4ad7bd94b50975a01p+15), C_(-0x1.38022f772c0b4cce7e7232f4f9bap+15), C_(0x1.12be31f5fe34faa8426124a140c7p+15), C_(-0x1.c90c6d590473b7e23f50a6ff90abp+14), C_(0x1.68be09036d4b8e25079ad44a0fb5p+14), C_(-0x1.0c494e2492cb7350d7dea324e249p+14), C_(0x1.758345ee1ea103707e4fc5726b69p+13), C_(-0x1.e8a773cd517e44f45076f71519e1p+12), C_(0x1.2a474ea41676fa5a62a310e63587p+12), C_(-0x1.4af3fdfe318309e19b15b68fb972p+11), C_(0x1.49733b39a1c4ced0b1d897e0d8ecp+10), C_(-0x1.28058c9d809d32e67b550b8feec3p+9), C_(0x1.c739fb1ca38e254565961e77d1e7p+7), C_(-0x1.e2ee0f774ec3af6a1c1e4f7b17bcp+5), C_(0x1.f584835c1818f23dc08b323d98e5p+1), C_(0x1.dc8e84cc4afe7a2fb01ea8367041p+1), C_(-0x1.3b3a53bf8d0a53e1e10973253b98p+0), C_(0x1.6a83343080c3f8b48adb7f8a0fc4p-4), C_(0x1.952a26a6e4af59b3b26bda8c8609p-7), C_(-0x1.3a135cf1b710ef334411ec10d2fbp-11), C_(-0x1.208be3b61fd62740fba383db12cep-17), C_(0x1.a71d1df2466b06f953d67915b744p-24), C_(-0x1.b3e65dd0b550b982df6eefc5304bp-35), C_(-0x1.1ed120d152ef3b5a4475e78c15bcp-52), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 13> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(0x1.14760cca8b142294e79588592265p+3), C_(-0x1.ba74df47bf664ee2547385285e06p+6), C_(0x1.41711dcfaf9ae33ef5a42497cdccp+9), C_(-0x1.1818fad342f755601ec00141bb62p+11), C_(0x1.474e1b48df1603e34e0f10a63ce8p+12), C_(-0x1.1344c928a46119ef7f83bdf82b73p+13), C_(0x1.69c3448f5e9dbd2d90d955490598p+13), C_(-0x1.a6933630b28804e5fdf1db79e516p+13), C_(0x1.f096b7533884b484daabf2ec386p+13), C_(-0x1.22623e57fb5283c6330ad006e50dp+14), C_(0x1.3656cdaada5ee9f54e572471e7bep+14), C_(-0x1.2c112510224741f5281f55b6dc46p+14), C_(0x1.1649895fe753bac480e018c717a8p+14), C_(-0x1.f7bb2384208e05c66ecac730535dp+13), C_(0x1.a9475e44156e584ae36a2ec50f02p+13), C_(-0x1.4a8f9de0fe8b863882cf98bdc30ep+13), C_(0x1.eb5875381b21b266553a6296e0a5p+12), C_(-0x1.5ee64eec32c02ba06ecbd76a11b3p+12), C_(0x1.ccfb4d9d3a3fd43202c9da414974p+11), C_(-0x1.14a05b02023d93595fe14dff5f3bp+11), C_(0x1.3a9e21e52de90e0e25e5cf4ca63ap+10), C_(-0x1.4bc3a327f05f291344a38f901a5dp+9), C_(0x1.2adbd2de6a50340d8168b2783c01p+8), C_(-0x1.c3c2f4b5f88c5c0995d28d11b9ebp+6), C_(0x1.277a18d79f69dcf96944e2b0fcf5p+5), C_(-0x1.c9f8833026d5a408341117a30a92p+2), C_(-0x1.454631d4223dc7af67ef97ef1099p+1), C_(0x1.43b3c20fabe24e5d14333b1e0567p+1), C_(-0x1.7e2b7474504f09a810523ca07f92p-1), C_(0x1.0161c2b653dc5e969cd9fbd6d0edp-4), C_(0x1.00c51140e71642a9a41e83368bbdp-7), C_(-0x1.ae184c969f7530c56af21ca3a7a8p-11), C_(-0x1.8063c15ef2a25ff6da3cad34895fp-17), C_(0x1.7fa9f24707d3d7cbfa3e9820acf4p-23), C_(-0x1.2feaa75fa15b4cbbde0dc3686d2fp-33), C_(-0x1.8febd0375e4aae5f4479ef67c215p-50), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 14> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(0x1.309432a44a63023cd5d74f5bea55p+2), C_(-0x1.e8f069c87232260c91fa71890f2bp+5), C_(0x1.620bb6edc4428b1d5f4fa47a5ecep+8), C_(-0x1.30502125aeb77e95c45d9e43464ep+10), C_(0x1.5897d2f743a96869b1eb0ca13247p+11), C_(-0x1.10925ae24fc57451105c29bc2a9fp+12), C_(0x1.4362e4b63cec61ff21aac6b7ac6ep+12), C_(-0x1.4ffdb02cc70cfe03dbf6d475eb63p+12), C_(0x1.779b03f599f05e82b08d8b48f758p+12), C_(-0x1.baec7e0e55169b8140b39b8fb14bp+12), C_(0x1.ce2ff743f88370d5e72cb7988fbcp+12), C_(-0x1.9f067ce3296956a187e74bb12383p+12), C_(0x1.6abb1f9cef609047d528387a0ad9p+12), C_(-0x1.4450d5aabf62ce501c4c7a9271c2p+12), C_(0x1.08545f0a3187b9a2ec020313e51cp+12), C_(-0x1.7530230cd216d38656dfbf0553dap+11), C_(0x1.f952b436845ca1bafccd87887abfp+10), C_(-0x1.560fff419d2c2e711437c4013006p+10), C_(0x1.8c0d255b6e233d3a2cb91681d042p+9), C_(-0x1.5fdc3ca1d5db02eaba158929c246p+8), C_(0x1.0a97d5984be8315545f375086dccp+7), C_(-0x1.20a6202d36bbe9ea7b9fe18176b3p+5), C_(-0x1.5a7221251a0809c48fe9776bbed6p+4), C_(0x1.3634e4081412bfd6aa7ecc784b01p+5), C_(-0x1.bdda94264568de640cdd8fb6a91bp+4), C_(0x1.feb750a84a74f7d5dc8417586506p+3), C_(-0x1.275477518f18aa31553de78414f5p+3), C_(0x1.12ebd04f5867e9e6cd551be469c5p+2), C_(-0x1.30dbe403419efe34f764090a038fp+0), C_(0x1.058d7af30daa34c20339630ccaeap-3), C_(0x1.916084cd62258d7ea8b1535e2f8ep-7), C_(-0x1.732dce99f11c6f7cee7cd02c7701p-9), C_(-0x1.7126e2b2a55e5160267b465d584cp-15), C_(0x1.f42158d77d0c28962287129d0e59p-21), C_(-0x1.357be619f66df06ada13476a9641p-30), C_(-0x1.9731ccc0ad49712bbc19913bd785p-46), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 15> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(0x1.8a04267542fb82b6511fb8f206b7p+0), C_(-0x1.3cbc4bff9713202eddfb257134f3p+4), C_(0x1.cbebed769f041b8ff3b3ff336b7ep+6), C_(-0x1.8d408dd48e3feaaa0b268282946dp+8), C_(0x1.c5c362fe59a680f0eae654ab9d42p+9), C_(-0x1.6befff94df0fd5c1ea5963474048p+10), C_(0x1.b68e6a376222daa009bfb53e28dp+10), C_(-0x1.c650372cae06a09b58e507b0871ep+10), C_(0x1.e7dc6f316434651b61d954241667p+10), C_(-0x1.15cc9fcbffbdadb34e9d61d6c6eep+11), C_(0x1.25d8da27ae488c61183e3d71ffbcp+11), C_(-0x1.17ff07a3bf7e3928a0bec71f80dbp+11), C_(0x1.0475b26522c32263166cf14a852ap+11), C_(-0x1.e40da504c90b0dabfc10981e655cp+10), C_(0x1.a69e253ca704fe5504b2c83ebfdbp+10), C_(-0x1.57f0b96fa56496dc384c41ebdb2p+10), C_(0x1.11486c0ca46dc3a169a7bf688364p+10), C_(-0x1.a51b5b4b4c6e9a002c8fc1ca65e6p+9), C_(0x1.2ee508d88648873a9042e781e817p+9), C_(-0x1.9d3a15a142fb235220e5bdb7d581p+8), C_(0x1.11494e2078a35defd9005276ea95p+8), C_(-0x1.535f44eb08e29df270d509de713ep+7), C_(0x1.85e2cd196a74cb82559b30f986fdp+6), C_(-0x1.ab69cc5e56727978f17d430c4129p+5), C_(0x1.b6235da40abe2f3f3eea8ec9a5f6p+4), C_(-0x1.8b55be10b7592b154b2ba9939157p+3), C_(0x1.414892cca85f8967c379d65c1761p+2), C_(-0x1.e63611dc23584e97ec62af26dc25p+0), C_(0x1.1a15ef6adced3df1c6c0346a88a1p-1), C_(-0x1.2481c80f712590a8d277e551e4fep-4), C_(-0x1.27449cc156e8a2b8d79cdb23e19p-7), C_(0x1.70c363a504f9eefb5323d6beb984p-9), C_(0x1.513124306018b235441513a840aep-15), C_(-0x1.d1034c80bf12bfc41e39ee6d8817p-20), C_(0x1.59ccd407dcf5a9a7533ca67a560ap-29), C_(0x1.c6dbd9b6fbf34f8784ef66a9534dp-44), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 16> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(0x1.d374dc0cd29f78efae1c669adc98p-2), C_(-0x1.780e4d99b7126e1227fd8360470ep+2), C_(0x1.0fdf2439cdc107efd9b577f835a9p+5), C_(-0x1.cfa32c44d17cf6112a211a2ca37ap+6), C_(0x1.015959857901578ca504dacee669p+8), C_(-0x1.85bc6b66153fd1bea9b65cf18fa7p+8), C_(0x1.a64f0f8c995c4aa45de473272a55p+8), C_(-0x1.7a602a5238af6059f76503b7cbc2p+8), C_(0x1.7b654c5560678179ce7606e1eb5bp+8), C_(-0x1.bd48fca1124c5a0c87121a03cfe7p+8), C_(0x1.d04b583d66c5fddbbacf446d9c66p+8), C_(-0x1.9412225fd51522e93e47c93309f2p+8), C_(0x1.601c278c16ffe3bedc9949af1437p+8), C_(-0x1.4b7186886095601966984faa4acep+8), C_(0x1.1d01310f5613f772298e42534595p+8), C_(-0x1.abfcdefee09bf658999362e6f111p+7), C_(0x1.4372d34e52fa3409ae85e2a019f6p+7), C_(-0x1.f6105d4c84d999290c211733ed04p+6), C_(0x1.5bb1d872e66637325ce8f6aa17bep+6), C_(-0x1.b1d6456c69f76f04df5acebda739p+5), C_(0x1.15b4bfdbddb01fb2de3e2b574816p+5), C_(-0x1.5951b3080c61b9307228b6ed10bbp+4), C_(0x1.701e202aeccdeb8ac6b6b30bcacp+3), C_(-0x1.6ddc190753e3ea59a0862615508fp+2), C_(0x1.77099e572e056d9b063dba7e75c1p+1), C_(-0x1.4e4b25c08b76d3f35349a1737dcep+0), C_(0x1.d2b148f357c3f676caf89142fe6p-2), C_(-0x1.3f20a405e77bfa5f0c7b2c20c976p-3), C_(0x1.9e7b676edad2c438a7201cee715ap-5), C_(-0x1.868422c7d3c55e44cf7999291ce8p-8), C_(-0x1.3d8b8d9fd24906b21fe8a1d895d9p-9), C_(0x1.57f23d8a911c1c88e9f1808c31e4p-11), C_(0x1.21e64d9dcd8227de3458f3f5849cp-21), C_(-0x1.d450acc53a98cfc94056c9e9eb52p-21), C_(0x1.0524ac3af31035a21da55dd5b9a3p-30), C_(0x1.575344ae7025305d708f9f17a1a5p-44), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 17> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(0x1.515b9f63b7c8d9d621c7f83ca202p-4), C_(-0x1.0f7f6c187ccac0b76cfe6b463e44p+0), C_(0x1.8785c563b5897121211402b9f302p+2), C_(-0x1.4b2e4e52216e5851aba80d8bd8e5p+4), C_(0x1.6901cf579638d44ea9478cea01d4p+5), C_(-0x1.06c8002a381179d9f60f753114a4p+6), C_(0x1.05cb21187a0f4fd8449a14491a1ap+6), C_(-0x1.95b91f5bb17e01dfb0ac91c796f8p+5), C_(0x1.7701942190fc5f1e86a9d43b21f6p+5), C_(-0x1.ce78be0577929e543cbd7ad9b93bp+5), C_(0x1.e29898694f90f26ba0d29f50470ep+5), C_(-0x1.7f1203e71656f1392c2a5ed0ed1cp+5), C_(0x1.37e1b965edd32923f1ca90e8ee72p+5), C_(-0x1.32c7bde1b71fddd33a7396827f1p+5), C_(0x1.098dc7ef6c8b51bc5142e5eef069p+5), C_(-0x1.6fe8868cdb497ea274e3965b3923p+4), C_(0x1.0ba553b7e7f0be8b204b950f5ae8p+4), C_(-0x1.b42a38b735b9796714d4ff017726p+3), C_(0x1.28e9aca928974002f9a9710ee004p+3), C_(-0x1.515c3566a134d8fdf2749b107958p+2), C_(0x1.ae8a4319bcbc3c0849df1986eff8p+1), C_(-0x1.1895df589aea592ca4ae051262ecp+1), C_(0x1.14e9f7c12e2c99db92b3020068dbp+0), C_(-0x1.e47340b006f8809308435a5f94dcp-2), C_(0x1.062f736c8ea4db2c5025ce71eba6p-2), C_(-0x1.d4b69f6b077f6afaf5cbb7fe058ap-4), C_(0x1.ca34188e3ee232929967c28b9b2ep-6), C_(-0x1.abe68c068be60d047f0a28b8716cp-8), C_(0x1.690421cc61ef435baf7b95f1a52fp-9), C_(0x1.f0697cb773e3bc4b5c6f8da3552ap-12), C_(-0x1.c195d60892125cb3e4fc26494359p-11), C_(0x1.b812af9cf3a26f639a51b597d61cp-13), C_(-0x1.bff07c97b4e02892210bbfe57ccbp-18), C_(-0x1.52d29bd9004df24ead72772a383cp-21), C_(0x1.032cd4ca8cfc03e1481665c670fdp-32), C_(0x1.5462cc3c1b3950e1af932e243f9p-45), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 18> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(0x1.19f56cbab95bde76557badc0f4cfp-7), C_(-0x1.c5e9cb7948f398db235b0497713cp-4), C_(0x1.45ccfe221c0e9033121b0a870c75p-1), C_(-0x1.0ff7774a4970235ef0d0d38e3503p+1), C_(0x1.1f8e85bb37dc52e0187eb7a98e68p+2), C_(-0x1.86af502d50caccee8ec1f8fa9cd2p+2), C_(0x1.49bbefd2893ed26dde1f31860f1dp+2), C_(-0x1.6128a473d02d185e7eb02c402e5cp+1), C_(0x1.1828041581a25f5b721c3a717f02p+1), C_(-0x1.d956f1ddda30a36e6132710c578ep+1), C_(0x1.038faca047549c3c3be2f3f91741p+2), C_(-0x1.37b3d4e72913f8a1a7f18bf41b92p+1), C_(0x1.7db8d08d07a3f9e23e72ca58a9d9p+0), C_(-0x1.e8024d590281c76397a14742f7fep+0), C_(0x1.bf0c126480d51b8dd799512a9bbcp+0), C_(-0x1.9a6e24093a6a2e038548f4c21568p-1), C_(0x1.9d414904073073148ca53b09a0c9p-2), C_(-0x1.e94579a438133caa5c0cf94e7bc6p-2), C_(0x1.1fe0d75be11ddab72d3817a1df79p-2), C_(-0x1.138ce466125db8659c96547c9ecbp-7), C_(-0x1.34e623ad04da0418dc894a3d03adp-6), C_(-0x1.2fc16b0c0aa7163aea99c6e062f3p-7), C_(-0x1.d550ce5b878423f79b2e760869bbp-6), C_(0x1.5e3d43af8f8ddb8e3580c4af5d78p-5), C_(-0x1.6c1ef7a1d6e428cbd81df1c34e95p-6), C_(0x1.8a7d31fc8c9aee233f27827d8acap-7), C_(-0x1.52a8406945db2a229ecbdd1d3a6ap-7), C_(0x1.7e48f37194da1a9d35aebc50ef39p-8), C_(-0x1.157ac29aabe3ff0003550e84e639p-9), C_(0x1.ef1519ddac57eba8aaaa2d2f321ap-11), C_(-0x1.e9152bfae3a36641e3acf97f58dcp-12), C_(0x1.063d5981a1db32ae377107926c9ep-13), C_(-0x1.4c0cd023430cc482bd47183c0ef3p-17), C_(-0x1.c41b70da67df95d6233d9591b513p-21), C_(0x1.5615a8cb6d771ab8987aa2645074p-32), C_(0x1.c05941495cbd662c96cb64517d6bp-44), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 19> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(0x1.94435eb9af5275885daf683a6d65p-11), C_(0x1.ed6b4c3fc563bad856b7ff679708p-2), C_(0x1.e76d4a24be344d37fa2f63572709p+3), C_(0x1.2e6decff81b60c629b716c5e755bp+6), C_(0x1.b10d4368bfb547486b053181a892p+4), C_(-0x1.2aabf32fc96a83423162d2c816bp+5), C_(0x1.d877b83c63dd7e5e4cc6dd5d03a9p+4), C_(-0x1.473d4fc793666a7b844c67c60bd8p+4), C_(0x1.95d0bb71b70ebdc02338882a3446p+3), C_(-0x1.af691b75d1d83460cd380f784013p+2), C_(0x1.6d28dba75e1d6e3724ad5b4f87b2p+1), C_(-0x1.a6978440cef93cfbe48ab54a4883p-1), C_(0x1.1490ceb2bb752e576e6ab7934d2ap-4), C_(0x1.464cc9ffc1d7e4d14789afa29b8ap-4), C_(-0x1.a276802b30603b547d67dda28d1bp-5), C_(0x1.1d1df4fc9211fc9b42905d09c47cp-6), C_(-0x1.17d7d8739a0a8aedb047da85632p-8), C_(0x1.ebfe215a7af3d07469844cb63084p-11), C_(-0x1.4f11d28267254fe725cc5344d47fp-13), C_(-0x1.9b2b7a111f74e448315a5acfceb6p-17), C_(0x1.14946151574b1cc87019ae7e5eccp-16), C_(-0x1.a6bb3de2d570ec48084b02756991p-19), C_(-0x1.9504b8c2dfd49dc16ebf73767df5p-24), C_(0x1.17aee7159c99baf232751bad6bd3p-24), C_(0x1.70d51f32a8d959f82b22d341a23bp-30), C_(-0x1.5dd5370ddab610b2e6c646e6c17ap-32), C_(-0x1.e8aac4dbdf4eaec509688435a8c6p-35), C_(0x1.629884f91c42aa4b289bcdb69f39p-40), C_(0x1.1aef0590aab3b2864498ba08a331p-44), C_(-0x1.21c09a3e7d5c59641f5b485f413p-50), C_(0x1.b8e2ec16d3130e2d4b06e1e5ebcbp-59), C_(-0x1.8c242cff56d3b852843f6ec978c7p-64), C_(0x1.c20c22cff32a0ee7b7221886273ep-74), C_(0x1.8b88202dbba79e3009dedbb574b1p-88), C_(0x1.27f0bb4febe21c10d76a7232b49p-103), C_(0x1.8579c244925048746514bf00ae6dp-133), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 20> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(0x1.263966f58e93453d04e057c51a09p-10), C_(0x1.5fb5bf5017c5cbd580114bdb418p-2), C_(0x1.79fa0aa0ef4b1e94ae76e603830ep+2), C_(0x1.0041752577d99920a4756cf6dfd7p+3), C_(-0x1.6480edc11cb316f0df4191286f79p+4), C_(0x1.7adbeb32519375a4e9fc4f3e6a5bp+3), C_(-0x1.8761c804c949b74e319f96893292p+2), C_(0x1.0bbe5cbfe7fbfd16a26214b40cadp+2), C_(-0x1.c27eb52ff5df81afb96ebb8be06ap+1), C_(0x1.6f68e268413d3fe6c3a7fa4919f1p+1), C_(-0x1.fbed86051f0cd090a4eeebb3ba08p+0), C_(0x1.17c1f8ccfdcb9142f7ebab0435b5p+0), C_(-0x1.cf35ce446b0dbe81a8d8224d1015p-2), C_(0x1.fa3032b16e2ec1aa83ca0e93a41cp-4), C_(-0x1.610cbeafdcc29a63e60dfb78086p-7), C_(-0x1.f0a31aba969e59e1d540df6c7f09p-8), C_(0x1.cb16dc9a66c8c832a40588853909p-9), C_(-0x1.378619c057d6f59580d9bc18beb2p-12), C_(-0x1.19bd674de47d6898c22e3b3237e3p-12), C_(0x1.c15384b637285af63775101117b6p-14), C_(-0x1.014a5dd580db7e757daab9ece5fdp-17), C_(-0x1.4f01d7193ba039b859fe936d4da5p-18), C_(0x1.63c48bb9daaef9ef37d87bcf220dp-20), C_(-0x1.0126c6d159333aa9ffefda4ce01fp-25), C_(-0x1.9c0d1ce2d6bcfc30df35efd50ccbp-26), C_(0x1.f835a0a4ec39a7abf277183bd5afp-30), C_(-0x1.e018504ab9e4668fd6a8d7855266p-38), C_(-0x1.2225fdd38424d963076e1b05254fp-37), C_(0x1.9c61eaa91cf12e3330e482deddd5p-42), C_(0x1.3e42beb720a117dd0b00b4bdbe96p-50), C_(-0x1.1199b0b74da5aecc08a2c6ccc14ep-53), C_(0x1.58b777bfe6b1520fc88066b839f4p-62), C_(0x1.001f51ec932dbb77f103a0f7564dp-70), C_(-0x1.7359d9741f8ec2aef5430062a9fap-82), C_(0x1.529c13dec223da6d213dd3aa18cap-99), C_(0x1.bda18c791fe6b89a60c075d9dac4p-128), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 21> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(-0x1.55c2dd92705ef29dacf510df5483p-9), C_(-0x1.875690159b946a743f6031d71359p-2), C_(-0x1.756f6cbad17a45f8fdca57537e0cp+1), C_(0x1.522462f959194685a62f604b7373p+2), C_(0x1.6695cecd8b44feab641f1eb716abp+1), C_(-0x1.55d8721e5e38fe7f6b6b27b70f1ap+3), C_(0x1.5a1db9a981431612f8d678081919p+3), C_(-0x1.0851517441a6e04a55b896ef99e1p+3), C_(0x1.4943b00084361d8656967cf91ea6p+2), C_(-0x1.3bad2deaede17c67f605a6915c1cp+1), C_(0x1.7b9d5b96164de0ffe09e1ad56182p-1), C_(0x1.9c78d3c486af6a9c43cd6d82014p-7), C_(-0x1.3adc11c8d3555c352fd89192cfdp-3), C_(0x1.5c787302c6a0e308908c5a566d12p-4), C_(-0x1.79c3b00ffbead0016b7d6948b83ep-6), C_(0x1.24e941b9401cdd0859a58e2c60b8p-8), C_(-0x1.a08712ec476e0f62559aaf166efp-9), C_(0x1.43c84b18b6bc1f9bc1ed4ace622fp-9), C_(-0x1.f9ed905ce1a3fabec727edc27bfdp-11), C_(0x1.28365cf3c20b9931191c65e395d2p-13), C_(0x1.dbc105f0dcd19a43895a2c14219bp-16), C_(-0x1.06fd02a0249f9985362be2e45162p-16), C_(0x1.5536f1beba49f3fa62573cb3aefap-19), C_(-0x1.1eb1b927a2367b6b71d37a3a0b16p-23), C_(-0x1.18cae380af7c0fb2b2883f2e7a9fp-26), C_(0x1.962198a9fb4f49acf27837af9e55p-28), C_(-0x1.4a0510fbc2258e2b740de37281f1p-31), C_(-0x1.5507dda80e4462056671b4ed9443p-36), C_(0x1.0a2a68de8dc560166b8fa1f0e29fp-39), C_(0x1.5b65f0e23da86c0f9732111de5a7p-46), C_(-0x1.652ce69e3233a8cdb2d672d4de9fp-51), C_(-0x1.67baca3a273431e8c1471458d539p-60), C_(0x1.2a22a2a629f6431996d0904b53cbp-67), C_(-0x1.c9d5657e9bda6dc8a405fc5c3a28p-79), C_(0x1.8a4260a0edd15c6744f3a072dd9cp-95), C_(0x1.036f45f65701ff403784f02b67ep-122), C_(0x0p+0) }; };
+template <typename Real> struct daubechies_scaling_integer_grid_imp <Real, 19, 22> { static inline constexpr std::array<Real, 38> value = { C_(0x0p+0), C_(-0x1.bda79ab9326966a8373d34c403d5p-10), C_(-0x1.d1744a8423410c1cdbc92198fb2ep-4), C_(-0x1.20ed565d8344f24b447d5dad1a94p-3), C_(0x1.7e6fc4bdbfcb347e60be376cd8fcp+0), C_(-0x1.5b972509d68a9e778b59e41da454p+1), C_(0x1.442d2d17d149d7c8adb7128a4a5bp+1), C_(-0x1.e2277288714cc11d45fb77f46c4ap+0), C_(0x1.9379ce87585cf7e36c9df60dab88p+0), C_(-0x1.659214144828aeeba2e8c5e20a63p+0), C_(0x1.20bc0fb1d00715f9a829adb0ea43p+0), C_(-0x1.8283009ebbc1eb153c3ab896b77bp-1), C_(0x1.8fa7bb64ff9ab76d61906bd796f1p-2), C_(-0x1.180d836c3d15c7dc5dd02b639eccp-3), C_(0x1.faecc9e70faee2855b6fee69691fp-7), C_(0x1.07a09dde4a2beade229071da7cf2p-6), C_(-0x1.7b9be86674bb70da10cbd67f2dafp-7), C_(0x1.92c3d8394a5b35c0ac95d90e2cd5p-9), C_(0x1.d5864f4fa99910c57caa7bc9e471p-12), C_(-0x1.559b12ec6e892a72794bb66e37cep-11), C_(0x1.a62f6a612f39a18acf0803b47144p-13), C_(-0x1.0d223ecdbfff75a7fa9690777531p-19), C_(-0x1.0fdbebf048174e10984f842f14c4p-16), C_(0x1.202e4a843fcd49b1f3f621772e1ep-18), C_(-0x1.86705793870af2933b93c10e211p-23), C_(-0x1.992e1c88b7cd13dae9b8e491d4dap-24), C_(0x1.018eb6827a7049feef27c5ca32bcp-26), C_(-0x1.c2b71846e1645f5cc0f2480787d5p-32), C_(-0x1.57e1e9171e5bc5fcf45eafbaecf7p-34), C_(0x1.717b9ae9f68e605d4d193d54fc52p-38), C_(0x1.6027613ce51bde3efec97caba709p-46), C_(-0x1.be324a2f0323f8a5380cb0e8a1d4p-49), C_(0x1.3eb2f19289730e4086f2e07ef711p-57), C_(0x1.bf9c807f8fa727e8ceb75bf12aacp-65), C_(-0x1.2fec3bd7b3920aea071e434958e4p-75), C_(0x1.290ed0b71d4a892449c6c2ced6f5p-91), C_(0x1.86f240571d54c453fa3cc6af74bep-118), C_(0x0p+0) }; };
+
+
 template <typename Real, unsigned p, unsigned order>
-constexpr std::array<Real, 2*p> daubechies_scaling_integer_grid()
+constexpr inline std::array<Real, 2*p> daubechies_scaling_integer_grid()
 {
-    static_assert(p <= 15, "Integer grids only implemented up to 15.");
+    static_assert(sizeof(Real) <= 16, "Integer grids only computed up to 128 bits of precision.");
+    static_assert(p <= 18, "Integer grids only implemented up to 18.");
     static_assert(p > 1, "Integer grids only implemented for p >= 2.");
-    if constexpr (p == 2) {
-        if constexpr (std::is_same_v<Real, float>) {
-            if constexpr (order == 0) {
-                return {0x0p+0f, 0x1.5db3d8p+0f, -0x1.76cf5ep-2f, 0x0p+0f};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0f, 0x1p+0f, -0x1p+0f, -0x0p+0f};
-            }
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0, 0x1.5db3d742c2655p+0, -0x1.76cf5d0b09955p-2, 0x0p+0};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0, 0x1p+0, -0x1p+0, -0x0p+0};
-            }
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0L, 0xa.ed9eba16132a9cfp-3L, -0xb.b67ae8584caa73bp-5L, 0x0p+0L};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0L, 0x8p-3L, -0x8p-3L, -0x0p+0L};
-            }
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.5db3d742c265539d92ba16b83c5cp+0Q, -0x1.76cf5d0b09954e764ae85ae0f17p-2Q, 0x0p+0Q};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1p+0Q, -0x1p+0Q, 0x0p+0Q};
-            }
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            if constexpr (order == 0) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.36602540378443864676372317075293618347140262690519031402790348972596651591"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.366025403784438646763723170752936183471402626905190314027903489725966511383"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 1) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.00000000000000000000000000000000000000000000000000000000000000000000000906"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.00000000000000000000000000000000000000000000000000000000000000000000000906"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-        }
-    }
-    if constexpr (p == 3) {
-        if constexpr (std::is_same_v<Real, float>) {
-            if constexpr (order == 0) {
-                return {0x0p+0f, 0x1.494d42p+0f, -0x1.8b18d8p-2f, 0x1.863744p-4f, 0x1.158088p-8f, -0x0p+0f};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.a3719cp+0f, -0x1.1dcb06p+1f, 0x1.19ae7cp-1f, 0x1.69a5e8p-5f, -0x0p+0f};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0f, 0x1.cef9ccp-1f, -0x1.b676b2p+0f, 0x1.6ced64p-1f, 0x1.8831a2p-4f, -0x0p+0f};
-            }
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0, 0x1.494d414ee19a1p+0, -0x1.8b18d8251ec88p-2, 0x1.863743274d78dp-4, 0x1.158087f14084dp-8, -0x0p+0};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0, 0x1.a3719cd426dbdp+0, -0x1.1dcb0537f529p+1, 0x1.19ae7cc6c0212p-1, 0x1.69a5e70c6cb47p-5, -0x0p+0};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0, 0x1.cef9cbb90bf24p-1, -0x1.b676b19591eb6p+0, 0x1.6ced632b23d6cp-1, 0x1.8831a237a06dfp-4, -0x0p+0};
-            }
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0L, 0xa.4a6a0a770cd07e1p-3L, -0xc.58c6c128f64431dp-5L, 0xc.31ba193a6bc67f2p-7L, 0x8.ac043f8a042675ap-11L, -0x0p+0L};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0L, 0xd.1b8ce6a136deae1p-3L, -0x8.ee5829bfa948208p-2L, 0x8.cd73e6360108efbp-4L, 0xb.4d2f386365a363ap-8L, -0x0p+0L};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0L, 0xe.77ce5dc85f9214cp-4L, -0xd.b3b58cac8f5b1f2p-3L, 0xb.676b19591eb63e3p-4L, 0xc.418d11bd036f5a2p-7L, -0x0p+0L};
-            }
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.494d414ee19a0fc1701f9345a28bp+0Q, -0x1.8b18d8251ec886399fc357ab26c9p-2Q, 0x1.863743274d78cfe42daf1d262e43p-4Q, 0x1.158087f14084ceb4f650d2c442e1p-8Q, 0x0p+0Q};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.a3719cd426dbd5c2283e8b6cd98bp+0Q, -0x1.1dcb0537f52904105ab1d13c6abfp+1Q, 0x1.19ae7cc6c0211df5e41745563cbbp-1Q, 0x1.69a5e70c6cb46c73632e8c1bb2d3p-5Q, 0x0p+0Q};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.cef9cbb90bf242979b344cdd1e02p-1Q, -0x1.b676b19591eb63e368ce734bad03p+0Q, 0x1.6ced632b23d6c7c6d19ce6975a06p-1Q, 0x1.8831a237a06deb43265d99170ff1p-4Q, 0x0p+0Q};
-            }
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            if constexpr (order == 0) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.28633506942569674985101130804711703944769149589599367792522563129173884774"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.385836961045875636526124449680167085358759714316248323422384559809411215163"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0952675460037808035264010635719874519288709294849441167080083466112626376337"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00423434561639808314871207806106259398219728893531052878915058190640973293816"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 1) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.63845234088408572501497611363560403262776907011369321824757699444308529377"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.23275819046313739501774225255380769832888122180065115110381486246159923436"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.550159358274017614990556164200803298774455233260222647464898741593942483269"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0441464913050340550122099747174003669266569184267352853913391264245714335499"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 2) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.904249540651993051422557892988008355246955899646975674328615693249103183472"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.71274862195597915426767367896402506574086769894092702298584707974730965003"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.712748621955979154267673678964025065740867698940927022985847079747309736056"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0957504593480069485774421070119916447530441003530243256713843067508967355933"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-        }
-    }
-    if constexpr (p == 4) {
-        if constexpr (std::is_same_v<Real, float>) {
-            if constexpr (order == 0) {
-                return {0x0p+0f, 0x1.01d5e4p+0f, -0x1.15313cp-5f, 0x1.447d2ap-5f, -0x1.817e96p-7f, -0x1.3a0992p-10f, 0x1.3be7b6p-16f, 0x0p+0f};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.c6aca8p+0f, -0x1.648654p+1f, 0x1.314492p+0f, -0x1.0d0e14p-3f, -0x1.b6da96p-5f, 0x1.d0194cp-10f, -0x0p+0f};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0f, 0x1.cf8cc6p+0f, -0x1.0eaaap+2f, 0x1.66e46cp+1f, -0x1.26d9a4p-3f, -0x1.0ae7c2p-2f, 0x1.3a82a2p-6f, 0x0p+0f};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0f, 0x1.bb2f44p-1f, -0x1.2d48b8p+1f, 0x1.c2597p+0f, 0x1.83800cp-3f, -0x1.233972p-1f, 0x1.bcd16ep-4f, -0x0p+0f};
-            }
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0, 0x1.01d5e443d831dp+0, -0x1.15313c61b3acbp-5, 0x1.447d293e37265p-5, -0x1.817e96e0425edp-7, -0x1.3a0992ca51117p-10, 0x1.3be7b6cb630ap-16, 0x0p+0};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0, 0x1.c6aca7b3a61bp+0, -0x1.6486543c8460bp+1, 0x1.314491c6de2d3p+0, -0x1.0d0e14f1f7dc6p-3, -0x1.b6da96c702378p-5, 0x1.d0194bee1a174p-10, -0x0p+0};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0, 0x1.cf8cc69cc42a4p+0, -0x1.0eaaa0c1e1c35p+2, 0x1.66e46b718b501p+1, -0x1.26d9a4de19b74p-3, -0x1.0ae7c18dd841ep-2, 0x1.3a82a1b96295bp-6, 0x0p+0};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0, 0x1.bb2f43bc30b81p-1, -0x1.2d48b852668c6p+1, 0x1.c2596fe640caep+0, 0x1.83800be8c4de9p-3, -0x1.233972e072028p-1, 0x1.bcd16d3945752p-4, -0x0p+0};
-            }
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0L, 0x8.0eaf221ec18e913p-3L, -0x8.a989e30d9d65a3ap-8L, 0xa.23e949f1b93272cp-8L, -0xc.0bf4b70212f684ap-10L, -0x9.d04c9652888ba27p-13L, 0x9.df3db65b184ff7ep-19L, 0x0p+0L};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0L, 0xe.35653d9d30d7c1cp-3L, -0xb.2432a1e4230589p-2L, 0x9.8a248e36f1695bdp-3L, -0x8.6870a78fbee2d2ap-6L, -0xd.b6d4b63811bbfa2p-8L, 0xe.80ca5f70d0ba167p-13L, -0x0p+0L};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0L, 0xe.7c6634e62152087p-3L, -0x8.7555060f0e1aa31p-1L, 0xb.37235b8c5a805d9p-2L, -0x9.36cd26f0cdb9e9ap-6L, -0x8.573e0c6ec20ec34p-5L, 0x9.d4150dcb14ada24p-9L, 0x0p+0L};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0L, 0xd.d97a1de185c06cap-4L, -0x9.6a45c2933463235p-2L, 0xe.12cb7f320656fb6p-3L, 0xc.1c005f4626f4b41p-6L, -0x9.19cb97039014287p-4L, 0xd.e68b69ca2ba92a2p-7L, -0x0p+0L};
-            }
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.01d5e443d831d2252369827793d3p+0Q, -0x1.15313c61b3acb474231dab078158p-5Q, 0x1.447d293e37264e578b865081223fp-5Q, -0x1.817e96e0425ed094fa1a3a5cf10cp-7Q, -0x1.3a0992ca5111744ed1b4ed1a6607p-10Q, 0x1.3be7b6cb6309fefbda0c9fa167f8p-16Q, 0x0p+0Q};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.c6aca7b3a61af838bb320835a00cp+0Q, -0x1.6486543c8460b11f1a4b4a357fbcp+1Q, 0x1.314491c6de2d2b798153746ca822p+0Q, -0x1.0d0e14f1f7dc5a54f21ce3ff424bp-3Q, -0x1.b6da96c702377f43a25f74c9467p-5Q, 0x1.d0194bee1a1742cd9ebfbba717b8p-10Q, 0x0p+0Q};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.cf8cc69cc42a410e51b272a7a3c6p+0Q, -0x1.0eaaa0c1e1c354610b35262e9078p+2Q, 0x1.66e46b718b500bb2be3ec05c7ac3p+1Q, -0x1.26d9a4de19b73d34cbab42cdd8ccp-3Q, -0x1.0ae7c18dd841d8689ede2f52570cp-2Q, 0x1.3a82a1b96295b447f46661fe5bd8p-6Q, 0x0p+0Q};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.bb2f43bc30b80d947c8a537a20b2p-1Q, -0x1.2d48b852668c646a630392a2b66dp+1Q, 0x1.c2596fe640cadf6ca968f3b30ff3p+0Q, 0x1.83800be8c4de9681c9e31925ce79p-3Q, -0x1.233972e07202850d1be1b9fc8392p-1Q, 0x1.bcd16d394575254330d81aed4886p-4Q, 0x0p+0Q};
-            }
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            if constexpr (order == 0) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.00716997772560226877369133460276614243269615872709037758322022879139279346"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0338369540528354556415804978382125421803076690774671479970540956429313200871"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0396104627159033280151912944184600514824910295717871419000412898697065939596"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0117643582057267108368694432974219163588747630020832762453515568184248898506"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00119795759617697344354027650795474883300903946947182516203285351999723597519"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000188294132335431331075886223630134570042832501447299211769873202540592685182"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 1) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.77607200752218464009377607152250284074663695743190866046592611729429611550"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.78534939722954314249278490573124577055217733739979406318347461197122106723"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.19245253663227817434763233908285135923990468684914884672498430320353620291"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.131374515184672958793518896272545745534054969900462421758093746888731275767"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0535710282202392359535999593909937081760795583068887462544975544197420516562"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00177039647999252279849535078943102427577022132608772400515549278186212987035"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 2) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.81074181868840701570186471952563442690666106665351874735735805297770163814"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.22916430410173418303217211054873324461573868001846524669511741276944000468"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.80384581607961568534047064875215082573530869410597985718216178513825734509"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.143969810512512114847026478220397278578104668742335564949361408575147520428"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.260649704248921172707994145248897076120067358027001191654083152075225028322"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0191961840951447695448573657402423466719409460283033987590421353038535631199"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 3) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.865594975206804045781037550982471109016820894607841596866029151773017425267"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.35378173850503736906839927424067865837551675448364577498051926331538903476"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.75917720195210901846322158713800354333385807185616713126178553553138176863"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.189209073105856701210355374205350230083317365254957287437467455568014611491"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.568797674081911210441966167774352001750246401183040853068360223333705683711"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.108598162322178814055750929689205777691766823947720612483597343776680843464"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-        }
-    }
-    if constexpr (p == 5) {
-        if constexpr (std::is_same_v<Real, float>) {
-            if constexpr (order == 0) {
-                return {0x0p+0f, 0x1.646bf2p-1f, 0x1.cbd5c2p-2f, -0x1.754196p-3f, 0x1.3100cap-5f, 0x1.8dd2bep-10f, -0x1.c4ab56p-10f, 0x1.3b27d2p-15f, 0x1.75f2b2p-23f, -0x0p+0f};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.8eee7ap+0f, -0x1.37cf44p+1f, 0x1.3c6448p+0f, -0x1.784198p-2f, -0x1.64d96ap-6f, 0x1.08fcfcp-5f, -0x1.5e1ffp-10f, -0x1.984da2p-17f, -0x0p+0f};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0f, 0x1.22c5ccp+1f, -0x1.83ccap+2f, 0x1.524518p+2f, -0x1.2d10dcp+0f, -0x1.549f4cp-1f, 0x1.882acap-2f, -0x1.3d5d0ep-5f, -0x1.65cdcp-11f, 0x0p+0f};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0f, 0x1.9877acp+1f, -0x1.48c27ap+3f, 0x1.f7fdf6p+2f, 0x1.0b1eap+3f, -0x1.15aaf4p+4f, 0x1.4a4504p+3f, -0x1.050134p+1f, -0x1.13ee46p-4f, -0x0p+0f};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0f, 0x1.13b9e8p-1f, -0x1.e1e5e6p+0f, 0x1.29ab2ep+1f, -0x1.3d6cc6p+0f, 0x1.0227f8p-1f, -0x1.9ada2ap-2f, 0x1.2c68dap-3f, 0x1.1a66dcp-7f, 0x0p+0f};
-            }
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0, 0x1.646bf1ec64a31p-1, 0x1.cbd5c1bab5148p-2, -0x1.754196833f707p-3, 0x1.3100cab7c3f5fp-5, 0x1.8dd2be8c89c52p-10, -0x1.c4ab558ff2dcfp-10, 0x1.3b27d2d798eedp-15, 0x1.75f2b16626e98p-23, -0x0p+0};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0, 0x1.8eee7927087b2p+0, -0x1.37cf445237f1bp+1, 0x1.3c64475174b4ap+0, -0x1.7841978e876dbp-2, -0x1.64d969ffaac15p-6, 0x1.08fcfb4783fa8p-5, -0x1.5e1fef6185af9p-10, -0x1.984da10897439p-17, -0x0p+0};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0, 0x1.22c5cb8d3f23bp+1, -0x1.83cca07a3ead8p+2, 0x1.5245172406b78p+2, -0x1.2d10dba463fc2p+0, -0x1.549f4c5e04f3ap-1, 0x1.882ac9029ddc7p-2, -0x1.3d5d0eda32d8bp-5, -0x1.65cdc06ecf654p-11, 0x0p+0};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0, 0x1.9877ac926fb3cp+1, -0x1.48c27a70b93cep+3, 0x1.f7fdf60845cfcp+2, 0x1.0b1ea0ee5f9edp+3, -0x1.15aaf38ada16ap+4, 0x1.4a45041b91e1cp+3, -0x1.05013480812dfp+1, -0x1.13ee46114fd85p-4, -0x0p+0};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0, 0x1.13b9e8c4fdc5p-1, -0x1.e1e5e5cfd0a8p+0, 0x1.29ab2ec864d45p+1, -0x1.3d6cc61e0f6a4p+0, 0x1.0227f72aa277ep-1, -0x1.9ada2a6a9a218p-2, 0x1.2c68da3893cd6p-3, 0x1.1a66dc6d2cfbfp-7, 0x0p+0};
-            }
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0L, 0xb.235f8f632518463p-4L, 0xe.5eae0dd5a8a4298p-5L, -0xb.aa0cb419fb8363cp-6L, 0x9.880655be1fafa7dp-8L, 0xc.6e95f4644e28f3ep-13L, -0xe.255aac7f96e75fp-13L, 0x9.d93e96bcc776751p-18L, 0xb.af958b31374c3acp-26L, -0x0p+0L};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0L, 0xc.7773c93843d9207p-3L, -0x9.be7a2291bf8db95p-2L, 0x9.e3223a8ba5a5065p-3L, -0xb.c20cbc743b6db2dp-5L, -0xb.26cb4ffd560a9d3p-9L, 0x8.47e7da3c1fd3e92p-8L, -0xa.f0ff7b0c2d7cb32p-13L, -0xc.c26d0844ba1cb28p-20L, -0x0p+0L};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0L, 0x9.162e5c69f91da28p-2L, -0xc.1e6503d1f56bc54p-1L, 0xa.9228b92035bbe8fp-1L, -0x9.6886dd231fe0c2p-3L, -0xa.a4fa62f0279cc8ap-4L, 0xc.41564814eee395ap-5L, -0x9.eae876d196c5b0fp-8L, -0xb.2e6e03767b2a39ap-14L, 0x0p+0L};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0L, 0xc.c3bd64937d9deedp-2L, -0xa.4613d385c9e6eeep+0L, 0xf.bfefb0422e7dd11p-1L, 0x8.58f50772fcf6838p+0L, -0x8.ad579c56d0b531bp+1L, 0xa.522820dc8f0dd92p+0L, -0x8.2809a404096fa64p-2L, -0x8.9f72308a7ec28cep-7L, -0x0p+0L};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0L, 0x8.9dcf4627ee27fcfp-4L, -0xf.0f2f2e7e85400fbp-3L, 0x9.4d59764326a2533p-2L, -0x9.eb6630f07b521f1p-3L, 0x8.113fb95513bed76p-4L, -0xc.d6d15354d10bf47p-5L, 0x9.6346d1c49e6ae26p-6L, 0x8.d336e36967df815p-10L, 0x0p+0L};
-            }
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.646bf1ec64a308c5df07d89c8e9bp-1Q, 0x1.cbd5c1bab5148530b0e77ecbff92p-2Q, -0x1.754196833f706c7834855fa5579ep-3Q, 0x1.3100cab7c3f5f4fa75b80a67ed4bp-5Q, 0x1.8dd2be8c89c51e7b28b04315346bp-10Q, -0x1.c4ab558ff2dcebdfdc6142054ddep-10Q, 0x1.3b27d2d798eecea1adaf099c04dp-15Q, 0x1.75f2b16626e9875840e692dcf344p-23Q, 0x0p+0Q};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.8eee7927087b240ec5ade1ac81aep+0Q, -0x1.37cf445237f1b72a99ae1be2616ep+1Q, 0x1.3c64475174b4a0c9b8a3ee3dfc2p+0Q, -0x1.7841978e876db6599aa4ad10992fp-2Q, -0x1.64d969ffaac153a6af06dc9cfb72p-6Q, 0x1.08fcfb4783fa7d234eba36053968p-5Q, -0x1.5e1fef6185af966378a125175a7fp-10Q, -0x1.984da1089743964ff5ac0959c3bcp-17Q, 0x0p+0Q};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.22c5cb8d3f23b44faf592c365f5dp+1Q, -0x1.83cca07a3ead78a73330d7cf1a39p+2Q, 0x1.5245172406b77d1d4fdfd2192d87p+2Q, -0x1.2d10dba463fc1840fd45963c568fp+0Q, -0x1.549f4c5e04f3991456e630b1555ep-1Q, 0x1.882ac9029ddc72b4c74d388da98p-2Q, -0x1.3d5d0eda32d8b61e7ff27a395899p-5Q, -0x1.65cdc06ecf6547344a6a8d527f6ap-11Q, 0x0p+0Q};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.9877ac926fb3bdd992f46d848f57p+1Q, -0x1.48c27a70b93cdddc043571f47b88p+3Q, 0x1.f7fdf60845cfba22e0c6bd043e1ep+2Q, 0x1.0b1ea0ee5f9ed06f5107d79a1aafp+3Q, -0x1.15aaf38ada16a6358cd77355f075p+4Q, 0x1.4a45041b91e1bb24fe9a63ad188p+3Q, -0x1.05013480812df4c7388d78daa7bap+1Q, -0x1.13ee46114fd8519c5d7f29b7d91dp-4Q, 0x0p+0Q};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.13b9e8c4fdc4ff9d9c7b93fda5d3p-1Q, -0x1.e1e5e5cfd0a801f531eaef0fe6ap+0Q, 0x1.29ab2ec864d44a65c8f8abfdabb3p+1Q, -0x1.3d6cc61e0f6a43e21f6553d10792p+0Q, 0x1.0227f72aa277daecfc1fddb3c5aep-1Q, -0x1.9ada2a6a9a217e8dbe2b55c6bb8bp-2Q, 0x1.2c68da3893cd5c4c84ac50c60f2ap-3Q, 0x1.1a66dc6d2cfbf029033eb2e70439p-7Q, 0x0p+0Q};
-            }
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            if constexpr (order == 0) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.696136055094319477854858582899623165657477087397982420446214768704637534395"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.449057604809486328422544147258783961136679734070279222683095397573769933916"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.182254005318036337838976194133760626404155027995824869298574162909992040160"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0372318229038899280943468571976409825349884675067696944216807399624576154231"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00151757514971408546631660804627799642999930803663956002350203262334698096372"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00172679624300796683492238574113985690016517858343249085985731373201062373654"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000375694705183874611122788905987601511712424642186474598567387629170716626883"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000174133116097374720105581975617394004367103367815124081799014873533525879944"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 1) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.55832631304700136656437922101147238270749801987968302608726226056001482368"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.43601278318955192143689593229007692528378574026415581479157815807966800017"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.23590512980145429394703890677945755544792211433079804428523927099597048061"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.367437713693886635994756136622838185785128398329531162713235860868138262530"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0217803511756465465888455643095945877678797679730267716300872503661203118564"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0323471935081436888581585415004509261169517927400595785850252266260883753013"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00133561991277070103522933081789825027913295746975070671440848910320957810632"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000121683847435443138497052509729151564450629140761931082169997649373563390225"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 2) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.27166122814949534600896122719444335851364604986118568035816607547755917237"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.05936443269703021458765565610458515567565968210302097303958018874430527787"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.28546694296061742660009147793158080678169598815648398102884014016442733462"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.17603848231736696569405849672717768085153722635404167927428726433255541822"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.665277849652262172893211868601932018692793523566973388708885090298621050238"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.382975712570864999469720877338520879718972231720745739556192701382764798208"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0387406625828488850208242053540315894034591845169984253024631712386615226757"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000682456431469533883023355676818600390864653197380934617983202410607639498017"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 3) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.19115216398441064598874856260571078533335587095494743176688738763014884081"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-10.27374002472233958765271086107000542805707479728145748157559647456760808710"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("7.87487555320626209855129987050336396619016782135024668820907820995265770052"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.34748884732558776131996262585236386342026292471024772697407362253973719963"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-17.35423616637255288734483167824286404110868945013746827031620566538851642130"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("10.32092481026398135762866367591092420975846125781641772354270513968155400150"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.03909927630080258726415694483947450981378728380854211799311168912518310053"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0673659073845468012269752507200188457226963436043917006078305307227881695785"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 4) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.538527750059879292796528780519852438911382070810691516995382579602542914648"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.88241421054468108184078064831664583702656657871925935150851189089967644557"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.32553658280235915338790080889465383487576175009269238722259396773724525645"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.23994100793735478720630163791841698087868254804877475832368176128007400006"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.504211162523674003883304110865210953390071787279159096400634899652374386912"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.401222861057733743406505260198882985396262380707384195761109616807384220426"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.146684365131000298517783121263439809537955817949643689585465029271973791975"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00861821902285686386807072489078876658634008134323161538922679272299835038788"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-        }
-    }
-    if constexpr (p == 6) {
-        if constexpr (std::is_same_v<Real, float>) {
-            if constexpr (order == 0) {
-                return {0x0p+0f, 0x1.bf65e8p-2f, 0x1.aa2466p-1f, -0x1.89fd1p-2f, 0x1.24737ep-3f, -0x1.a1e9c8p-6f, -0x1.cec09ap-9f, 0x1.cd4fecp-10f, 0x1.05937cp-16f, -0x1.5a00dp-19f, 0x1.0fbc42p-28f, -0x0p+0f};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.2faeacp+0f, -0x1.801498p+0f, 0x1.050336p-1f, -0x1.0ffe44p-2f, 0x1.0b11b2p-4f, 0x1.721a1ep-7f, -0x1.af662cp-8f, -0x1.a69b86p-15f, 0x1.45b126p-16f, -0x1.018922p-24f, -0x0p+0f};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0f, 0x1.1e62dep+1f, -0x1.980b4p+2f, 0x1.a34deap+2f, -0x1.45eb5ep+1f, -0x1.0310f6p-1f, 0x1.da7724p-1f, -0x1.4137dp-2f, 0x1.7eb866p-6f, 0x1.4ebb22p-9f, -0x1.0c5bep-16f, 0x0p+0f};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0f, 0x1.422fap-2f, -0x1.255a76p+0f, 0x1.484b54p+3f, -0x1.3c98d8p+5f, 0x1.10b7fap+6f, -0x1.d54dd2p+5f, 0x1.804948p+4f, -0x1.77f884p+1f, -0x1.d3687ap-2f, 0x1.816ef8p-8f, -0x0p+0f};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0f, 0x1.8faefp+0f, -0x1.93816ep+2f, 0x1.33788p+3f, -0x1.c3f2cep+2f, 0x1.c7801ep+1f, -0x1.46377ep+1f, 0x1.77a6f6p+0f, -0x1.c41888p-3f, -0x1.f8b0a6p-5f, 0x1.b96594p-10f, 0x0p+0f};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0f, 0x1.cb9194p-2f, -0x1.e6b982p+0f, 0x1.7b2e48p+1f, -0x1.fa645ep+0f, 0x1.29da94p-1f, -0x1.8461e6p-2f, 0x1.67c138p-2f, -0x1.c1a09cp-5f, -0x1.0c11f4p-5f, 0x1.0ac90ap-9f, 0x0p+0f};
-            }
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0, 0x1.bf65e79817d28p-2, 0x1.aa2466d50e4a5p-1, -0x1.89fd104c6ff15p-2, 0x1.24737e6f8ebf1p-3, -0x1.a1e9c758a51a1p-6, -0x1.cec09a7ccf05bp-9, 0x1.cd4feb82d2494p-10, 0x1.05937b8388af2p-16, -0x1.5a00cfad970a8p-19, 0x1.0fbc42c672231p-28, -0x0p+0};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0, 0x1.2faeacbb8e754p+0, -0x1.8014975295b21p+0, 0x1.05033635f5402p-1, -0x1.0ffe44cc8bc7fp-2, 0x1.0b11b28c7d67bp-4, 0x1.721a1d14b8323p-7, -0x1.af662c52c3b7bp-8, -0x1.a69b860b67a33p-15, 0x1.45b12643cf82p-16, -0x1.01892163486cbp-24, -0x0p+0};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0, 0x1.1e62ddd540b06p+1, -0x1.980b3fe2011f8p+2, 0x1.a34dea8cd59b4p+2, -0x1.45eb5e5e7e3cap+1, -0x1.0310f5a5d86dep-1, 0x1.da7724c65802cp-1, -0x1.4137cfe85b9e6p-2, 0x1.7eb866ddca6bap-6, 0x1.4ebb22d1ac076p-9, -0x1.0c5bdfb916a45p-16, 0x0p+0};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0, 0x1.422f9f5227e8p-2, -0x1.255a76df553ccp+0, 0x1.484b537c56dedp+3, -0x1.3c98d8a74cd77p+5, 0x1.10b7f9c607064p+6, -0x1.d54dd14cd31afp+5, 0x1.8049478b6740dp+4, -0x1.77f8847acd28bp+1, -0x1.d3687a3bc3933p-2, 0x1.816ef86832622p-8, -0x0p+0};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0, 0x1.8faeef62b3a8p+0, -0x1.93816e52ba1c8p+2, 0x1.337880b3a9a71p+3, -0x1.c3f2cd3d53133p+2, 0x1.c7801db767804p+1, -0x1.46377db27f625p+1, 0x1.77a6f5e8321cdp+0, -0x1.c4188733407f2p-3, -0x1.f8b0a606c7f79p-5, 0x1.b965933f534b2p-10, 0x0p+0};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0, 0x1.cb91942378a6bp-2, -0x1.e6b982120ca32p+0, 0x1.7b2e4714b2703p+1, -0x1.fa645ee8ca231p+0, 0x1.29da9349c32a2p-1, -0x1.8461e6acf9cb3p-2, 0x1.67c137342024dp-2, -0x1.c1a09b7773a5ap-5, -0x1.0c11f4efd5c0bp-5, 0x1.0ac90a45b7a47p-9, 0x0p+0};
-            }
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0L, 0xd.fb2f3cc0be93e54p-5L, 0xd.512336a872527e6p-4L, -0xc.4fe882637f8a4ep-5L, 0x9.239bf37c75f8764p-6L, -0xd.0f4e3ac528d0419p-9L, -0xe.7604d3e6782db77p-12L, 0xe.6a7f5c169249c7ap-13L, 0x8.2c9bdc1c4579256p-19L, -0xa.d0067d6cb853e5ep-22L, 0x8.7de216339118a43p-31L, -0x0p+0L};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0L, 0x9.7d7565dc73a9dap-3L, -0xc.00a4ba94ad909b7p-3L, 0x8.2819b1afaa00e4ep-4L, -0x8.7ff226645e3f525p-5L, 0x8.588d9463eb3d6b2p-7L, 0xb.90d0e8a5c191592p-10L, -0xd.7b3162961dbd72bp-11L, -0xd.34dc305b3d198bdp-18L, 0xa.2d89321e7c101dfp-19L, -0x8.0c490b1a4365a0ep-27L, -0x0p+0L};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0L, 0x8.f316eeaa0582d86p-2L, -0xc.c059ff1008fbde4p-1L, 0xd.1a6f5466acda0c4p-1L, -0xa.2f5af2f3f1e4f4dp-2L, -0x8.1887ad2ec36f306p-4L, 0xe.d3b92632c015e4bp-4L, -0xa.09be7f42dcf2d82p-5L, 0xb.f5c336ee535d213p-9L, 0xa.75d9168d603b071p-12L, -0x8.62defdc8b5224edp-19L, 0x0p+0L};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0L, 0xa.117cfa913f3fd65p-5L, -0x9.2ad3b6faa9e5fc2p-3L, 0xa.425a9be2b6f651fp+0L, -0x9.e4c6c53a66bb9b6p+2L, 0x8.85bfce3038320c3p+3L, -0xe.aa6e8a6698d7b2fp+2L, 0xc.024a3c5b3a06863p+1L, -0xb.bfc423d6694569bp-2L, -0xe.9b43d1de1c99addp-5L, 0xc.0b77c3419310f5ep-11L, -0x0p+0L};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0L, 0xc.7d777b159d3fe93p-3L, -0xc.9c0b7295d0e4242p-1L, 0x9.9bc4059d4d38bf3p+0L, -0xe.1f9669ea9899554p-1L, 0xe.3c00edbb3c02374p-2L, -0xa.31bbed93fb124adp-2L, 0xb.bd37af4190e69cdp-3L, -0xe.20c4399a03f920dp-6L, -0xf.c58530363fbca91p-8L, 0xd.cb2c99fa9a58d79p-13L, 0x0p+0L};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0L, 0xe.5c8ca11bc53594fp-5L, -0xf.35cc10906518e34p-3L, 0xb.d97238a59381a17p-2L, -0xf.d322f7465118802p-3L, 0x9.4ed49a4e1950cdfp-4L, -0xc.230f3567ce5957dp-5L, 0xb.3e09b9a10126b64p-5L, -0xe.0d04dbbb9d2ce8dp-8L, -0x8.608fa77eae05beap-8L, 0x8.5648522dbd23badp-12L, 0x0p+0L};
-            }
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.bf65e79817d27ca7c78972c65f3p-2Q, 0x1.aa2466d50e4a4fcbbebe54f94c3cp-1Q, -0x1.89fd104c6ff149bf7514a7ddf37fp-2Q, 0x1.24737e6f8ebf0ec8bb9fcc85bb71p-3Q, -0x1.a1e9c758a51a08321aa63e9af1d7p-6Q, -0x1.cec09a7ccf05b6ee1ea8f3c17f4ep-9Q, 0x1.cd4feb82d24938f30e41e1af2eap-10Q, 0x1.05937b8388af24ac43ec83967a2ep-16Q, -0x1.5a00cfad970a7cbc309138fd3facp-19Q, 0x1.0fbc42c672231485a0bcbfe7e34bp-28Q, 0x0p+0Q};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.2faeacbb8e753b40eb856e00f522p+0Q, -0x1.8014975295b2136d5a1adb454387p+0Q, 0x1.05033635f5401c9b60636a32526ap-1Q, -0x1.0ffe44cc8bc7ea4a6ce4734d8d36p-2Q, 0x1.0b11b28c7d67ad63229fbc3aa7dap-4Q, 0x1.721a1d14b8322b2431432e8b800fp-7Q, -0x1.af662c52c3b7ae55063672df3c7fp-8Q, -0x1.a69b860b67a33179a8c7a5f6b2acp-15Q, 0x1.45b12643cf8203bdf796367d51eep-16Q, -0x1.01892163486cb41cb64453f7616fp-24Q, 0x0p+0Q};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.1e62ddd540b05b0cc5ce587007d5p+1Q, -0x1.980b3fe2011f7bc878be7d399794p+2Q, 0x1.a34dea8cd59b4187717c6efb0662p+2Q, -0x1.45eb5e5e7e3c9e9ae26ca4aa207cp+1Q, -0x1.0310f5a5d86de60ba877dea685a5p-1Q, 0x1.da7724c65802bc95482213f980a5p-1Q, -0x1.4137cfe85b9e5b04e10239758a3cp-2Q, 0x1.7eb866ddca6ba425f9e4eb854a4dp-6Q, 0x1.4ebb22d1ac0760e1461881059843p-9Q, -0x1.0c5bdfb916a449da5acc3ccfdc72p-16Q, 0x0p+0Q};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.422f9f5227e7facaa94dd7d9e31p-2Q, -0x1.255a76df553cbf84e8a0b0613039p+0Q, 0x1.484b537c56deca3daefc656e3b6ep+3Q, -0x1.3c98d8a74cd7736b60af4e604261p+5Q, 0x1.10b7f9c607064185ab2dfc58353fp+6Q, -0x1.d54dd14cd31af65e5343fc875b57p+5Q, 0x1.8049478b6740d0c6b010047a06c3p+4Q, -0x1.77f8847acd28ad3549099ae2105ep+1Q, -0x1.d3687a3bc39335bac7f281e76bbep-2Q, 0x1.816ef86832621ebc63e47cd2b70fp-8Q, 0x0p+0Q};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.8faeef62b3a7fd26eb98dd7f984ap+0Q, -0x1.93816e52ba1c8483ff81ea3e324ep+2Q, 0x1.337880b3a9a717e67b9cd7fec812p+3Q, -0x1.c3f2cd3d53132aa78f87aee07639p+2Q, 0x1.c7801db7678046e8ebdb22cf642bp+1Q, -0x1.46377db27f624959a2b9b7777bb1p+1Q, 0x1.77a6f5e8321cd39a930db39033fap+0Q, -0x1.c4188733407f241acae534ed0f5dp-3Q, -0x1.f8b0a606c7f795229d5947447836p-5Q, 0x1.b965933f534b1af276b67227f89dp-10Q, 0x0p+0Q};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0Q, 0x1.cb91942378a6b29e2dd51c51bfa9p-2Q, -0x1.e6b982120ca31c68b89329c09872p+0Q, 0x1.7b2e4714b270342ea6ba899785ecp+1Q, -0x1.fa645ee8ca231003817fbe32a47bp+0Q, 0x1.29da9349c32a19bed5b810cc4b88p-1Q, -0x1.8461e6acf9cb2af90934d76c7932p-2Q, 0x1.67c137342024d6c8052e3d876acdp-2Q, -0x1.c1a09b7773a59d1a65f356773daap-5Q, -0x1.0c11f4efd5c0b7d44ac1c3a0720ap-5Q, 0x1.0ac90a45b7a47759a7a92738fc7ep-9Q, 0x0p+0Q};
-            }
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            if constexpr (order == 0) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.436912172945044907144228485347825621410539534551633490282829655111997130403"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.832308972842970561072656780688484969909152422815912990040758264557720345453"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.384754423776017240823727817356603521560970688156341806103424918665893513072"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.142798412112682208241683440145206755760599607930024614732186357484695172147"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0255073973408613836618989912216699702582536490819800245599669619734869162144"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00353052030405191587644014357031569208954383867587514877878893763115391697093"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00175976633973310294687791686419090228541208847068173308405667330457900123359"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000155911507261447556301511828782318895561336507906997931765895708973813706967"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000257792449680050051904829803613695691516006402149134709283993808809283908364"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000395427041670150922621803883961042354855917494285626611817873341124068492943"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 1) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.18625907496467146792209724298189804516984008871355130996941892999482122848"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.50031419531087122680662801195848817668641322402194798020924445478349906731"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.509790128790541728679843731350866150242721024787663006627811106004296791437"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.265618395790575259239344136932196822481573416259521963554257379369647420831"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0652024244844486127834346214927829793557907226893556085427354685093316589934"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0112946168896442313978324044573675493852036148359725468126097329498236688742"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00658262807952680441249220488086069578322307368873900509784589482921684655699"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000503787415155786809007366413438496538050960506069818027681542836778698200709"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000194127553776389220829735998255824906496581738755358150095212114606531254267"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000599621948105659258834698507620391902991796020771034688754036929095102873206"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 2) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.23739216721276332338878224928813443319380137365001617475449729702460814553"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.37568661757222064818087007988064952244769736524323206091611472179022669583"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.55163062814101601777779848466095021703767404055811314444036330143823846521"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.54624538053437717302677939425802942100881803777676322897540130575773519940"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.505988766188433733744368526707172451758173834991466388525773967340764566418"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.926690243923081056914375322621819979047483305911073890365009540068892624972"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.313689468914985485830723560991137056324820674194725652065219926423948539134"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0233593945078271825857280125900496031710930273733853151360419856695906224412"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00255379486119272204906336921540559285976842099994098440071430993999358629514"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000159954358632619330058765393713737703102562863421786141165128286490666376159"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 3) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.314634789838216004347219278851224957182628881138090829610427965680979138191"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.14591162636246490124057063708997784842452557437526442884613276777690297174"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("10.25919508252169379158306431282332110722656695790182072665295187397284234950"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-39.57463198378803222763091210153395253214575080397200817757429653138129855280"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("68.17966374795793307063651046839796286891828378129757556293454079229695233480"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-58.66299686450235667243637029946865368099558139408845032747908498579236804890"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("24.01789049581934793489690384929366103321726646566966212731103293708083587360"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.93727165218507960698217968145386367512071654027601850078522746893001474631"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.456453237436011258659809322589189754978378863312423941968681370133465846399"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00588124813675386548614413276946752512020709001701613014446955498244051671873"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 4) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.56126304778777576443050160863879708904118592078755406627901576276101093399"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.30477483824547160848980524578141943454970012363516565523116238032800392998"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("9.60845980730411762808214955695432741370084853414448911176063682241066899084"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.06169444073411748688716938924586604983878232115464543856592115083298206081"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.55859729247367992138320272198938237654252341074503039432837735029655798290"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.54856845107748801044054274844945341537099829623280578974997775828865307664"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.46739136618463144606525570352038426862829638293144420092004098891852838139"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.220749908687195857585648726228092057311307565129699615600606738330860600964"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0616076700882776753864153489569808343372159974190746897916588825239020343770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00168379508234587882847186755892064349515005496287341565125598591763515542636"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 5) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.448797526040073344800625409665848168336823300039318051519325620983465942323"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.90126812878282830955681810258116249323860290817569491974905637501312440751"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.96234978209111122166662326226946007783574110910320150870148188012479737533"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.97809403594341071138805115779455370352957722549769910191794603383219959474"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.581745722536272503632230565756890997548927114703803943288685477190719512918"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.379279712970354381573734078512746842789448242321016101227184675836523585288"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.351322996670238331331118965555902223077733168124153384152743641838801971515"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0548861538369364702831870995984759190374434786821402336660504725795046392356"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0327234062121349553823389676664543405404659969276540517449952095914830314788"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00203541040796942675353120290529183233631315963372752064299614671505036863492"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-        }
-    }
-    if constexpr (p == 7) {
-        if constexpr (std::is_same_v<Real, float>) {
-            if constexpr (order == 0) {
-                return {0x0p+0f, 0x1.033292p-2f, 0x1.027f6cp+0f, -0x1.919d92p-2f, 0x1.7a0caap-3f, -0x1.1142c4p-4f, 0x1.50e2d6p-7f, 0x1.d0243ap-10f, -0x1.1d4c6cp-11f, -0x1.17d0b4p-14f, 0x1.310ffep-19f, -0x1.509d12p-25f, -0x1.57f8e6p-36f, -0x0p+0f};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.9ec434p-1f, -0x1.ca0692p-2f, -0x1.2d988ap-1f, 0x1.145888p-2f, -0x1.4ab3dp-6f, -0x1.4e8938p-5f, 0x1.5cb5dep-6f, -0x1.051eecp-8f, 0x1.0efaecp-14f, 0x1.6a87a6p-15f, -0x1.4e8b2ap-23f, -0x1.54fd9p-33f, -0x0p+0f};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0f, 0x1.e0eaccp+0f, -0x1.5362d8p+2f, 0x1.70aa18p+2f, -0x1.86bc52p+1f, 0x1.570932p-2f, 0x1.9d599ap-1f, -0x1.18b244p-1f, 0x1.fe16d2p-4f, 0x1.eb4ccap-12f, -0x1.4e09dp-9f, 0x1.c4a78ap-16f, 0x1.cb0cccp-25f, -0x0p+0f};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0f, 0x1.4ca934p-1f, -0x1.492e7p+1f, 0x1.171de6p+4f, -0x1.1e704ep+6f, 0x1.23bcc4p+7f, -0x1.415156p+7f, 0x1.7ff792p+6f, -0x1.a43b42p+4f, 0x1.833e7p-4f, 0x1.13b5aap+0f, -0x1.6365bp-6f, -0x1.64d198p-14f, -0x0p+0f};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0f, 0x1.525f0cp+1f, -0x1.7eda4cp+3f, 0x1.578438p+4f, -0x1.40c582p+4f, 0x1.9815ccp+3f, -0x1.22247ap+3f, 0x1.8c2cccp+2f, -0x1.ffd4fcp+0f, -0x1.3be428p-3f, 0x1.7c490ep-3f, -0x1.23f976p-7f, -0x1.1f66b2p-14f, -0x0p+0f};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0f, 0x1.80a316p+0f, -0x1.ce7e68p+2f, 0x1.ac8b3cp+3f, -0x1.74c81ep+3f, 0x1.4010d2p+2f, -0x1.34da8p+1f, 0x1.2d09cap+1f, -0x1.97de12p-1f, -0x1.9df5b4p-2f, 0x1.16c54ap-2f, -0x1.e323c6p-6f, -0x1.c9a574p-12f, 0x0p+0f};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0f, 0x1.a096c8p-3f, -0x1.01d8c8p+0f, 0x1.099a08p+1f, -0x1.40ce38p+1f, 0x1.2a5764p+1f, -0x1.e6f03p+0f, 0x1.3544c2p+0f, -0x1.6af582p-1f, 0x1.256afep-1f, -0x1.656934p-2f, 0x1.4b884p-4f, 0x1.24061ep-9f, 0x0p+0f};
-            }
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0, 0x1.033291a6c76d7p-2, 0x1.027f6bf7952cep+0, -0x1.919d92c6034c4p-2, 0x1.7a0ca906acc48p-3, -0x1.1142c3515ec43p-4, 0x1.50e2d6421ee26p-7, 0x1.d0243aab613f8p-10, -0x1.1d4c6c249bf0fp-11, -0x1.17d0b3032ba5cp-14, 0x1.310ffd8b56401p-19, -0x1.509d126dab99dp-25, -0x1.57f8e69552537p-36, -0x0p+0};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0, 0x1.9ec434341eaeep-1, -0x1.ca0692ca7743ap-2, -0x1.2d988a986b0dfp-1, 0x1.145887eacb11p-2, -0x1.4ab3cf0bae2a6p-6, -0x1.4e8938899ee37p-5, 0x1.5cb5de436bfaep-6, -0x1.051eebbefaf7cp-8, 0x1.0efaec65edbccp-14, 0x1.6a87a6b931edcp-15, -0x1.4e8b2a27fe065p-23, -0x1.54fd8f0625f12p-33, -0x0p+0};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0, 0x1.e0eacca617ebcp+0, -0x1.5362d7fe36c57p+2, 0x1.70aa17b7adc0ep+2, -0x1.86bc52429f3a4p+1, 0x1.5709310e8d1f6p-2, 0x1.9d599937b31fbp-1, -0x1.18b244e50df67p-1, 0x1.fe16d1a3cfb3ep-4, 0x1.eb4cc917dd1cdp-12, -0x1.4e09cf12f0cddp-9, 0x1.c4a78957d2798p-16, 0x1.cb0ccbca08e79p-25, -0x0p+0};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0, 0x1.4ca9343b32368p-1, -0x1.492e70f2635c1p+1, 0x1.171de5ca88cecp+4, -0x1.1e704d84a1075p+6, 0x1.23bcc34d6a52ap+7, -0x1.415156a34428ap+7, 0x1.7ff7929036dddp+6, -0x1.a43b4147c122cp+4, 0x1.833e6f5afaca5p-4, 0x1.13b5aaaf6c71dp+0, -0x1.6365af2495a87p-6, -0x1.64d19861a8338p-14, -0x0p+0};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0, 0x1.525f0cb11c272p+1, -0x1.7eda4b6a23329p+3, 0x1.578437542fe4fp+4, -0x1.40c582473fa8dp+4, 0x1.9815cb7223c1p+3, -0x1.222479cd96eeap+3, 0x1.8c2cccc6ee34dp+2, -0x1.ffd4fb5b3918p+0, -0x1.3be427404fe7dp-3, 0x1.7c490d447fad3p-3, -0x1.23f9756392d0fp-7, -0x1.1f66b1e781529p-14, -0x0p+0};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0, 0x1.80a316d21a0efp+0, -0x1.ce7e682714367p+2, 0x1.ac8b3ccd718c4p+3, -0x1.74c81d1a27df6p+3, 0x1.4010d1eedca9ap+2, -0x1.34da807d2aaedp+1, 0x1.2d09c9846b582p+1, -0x1.97de12ea03ca1p-1, -0x1.9df5b4fe2e272p-2, 0x1.16c54a229aae1p-2, -0x1.e323c5b92bd16p-6, -0x1.c9a573f22c19bp-12, 0x0p+0};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0, 0x1.a096c8f7fc8abp-3, -0x1.01d8c748e11fap+0, 0x1.099a073a7c7b4p+1, -0x1.40ce386ca776ep+1, 0x1.2a57634989c52p+1, -0x1.e6f030cb23fcp+0, 0x1.3544c2755b1d8p+0, -0x1.6af581a622d41p-1, 0x1.256afda077268p-1, -0x1.6569331439298p-2, 0x1.4b88409bdd117p-4, 0x1.24061e2653bdbp-9, 0x0p+0};
-            }
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0L, 0x8.19948d363b6b511p-5L, 0x8.13fb5fbca966de8p-3L, -0xc.8cec96301a62254p-5L, 0xb.d0654835662420dp-6L, -0x8.8a161a8af621982p-7L, 0xa.8716b210f7132a1p-10L, 0xe.8121d55b09fc1bcp-13L, -0x8.ea636124df87704p-14L, -0x8.be8598195d2e2f7p-17L, 0x9.887fec5ab2008edp-22L, -0xa.84e8936d5cce758p-28L, -0xa.bfc734aa929b8c7p-39L, -0x0p+0L};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0L, 0xc.f621a1a0f576c66p-4L, -0xe.50349653ba1cf48p-5L, -0x9.6cc454c3586f53bp-4L, 0x8.a2c43f565887ceap-5L, -0xa.559e785d7152dc2p-9L, -0xa.7449c44cf71b8f2p-8L, 0xa.e5aef21b5fd6dcfp-9L, -0x8.28f75df7d7bdeb9p-11L, 0x8.77d7632f6de608ep-17L, 0xb.543d35c98f6e2d6p-18L, -0xa.7459513ff03276p-26L, -0xa.a7ec78312f88c67p-36L, -0x0p+0L};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0L, 0xf.07566530bf5dc3p-3L, -0xa.9b16bff1b62b5b5p-1L, 0xb.8550bdbd6e073adp-1L, -0xc.35e29214f9d1fbdp-2L, 0xa.b849887468fb1bp-5L, 0xc.eaccc9bd98fd7eap-4L, -0x8.c59227286fb3ad2p-4L, 0xf.f0b68d1e7d9f3f6p-7L, 0xf.5a6648bee8e6ab7p-15L, -0xa.704e7897866e7ecp-12L, 0xe.253c4abe93cc026p-19L, 0xe.58665e50473cb0fp-28L, -0x0p+0L};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0L, 0xa.6549a1d991b412ap-4L, -0xa.497387931ae0b61p-2L, 0x8.b8ef2e544676158p+1L, -0x8.f3826c25083a83ap+3L, 0x9.1de61a6b5294d86p+4L, -0xa.0a8ab51a2145353p+4L, 0xb.ffbc9481b6eebc6p+3L, -0xd.21da0a3e0916379p+1L, 0xc.19f37ad7d65262bp-7L, 0x8.9dad557b638eaddp-3L, -0xb.1b2d7924ad4363p-9L, -0xb.268cc30d419bc95p-17L, -0x0p+0L};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0L, 0xa.92f86588e139024p-2L, -0xb.f6d25b5119947a7p+0L, 0xa.bc21baa17f27afep+1L, -0xa.062c1239fd4649cp+1L, 0xc.c0ae5b911e082dep+0L, -0x9.1123ce6cb774e8cp+0L, 0xc.6166663771a6508p-1L, -0xf.fea7dad9c8c0222p-3L, -0x9.df213a027f3e892p-6L, 0xb.e2486a23fd69714p-6L, -0x9.1fcbab1c968774dp-10L, -0x8.fb358f3c0a94afap-17L, -0x0p+0L};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0L, 0xc.0518b690d0776a4p-3L, -0xe.73f34138a1b3bfep-1L, 0xd.6459e66b8c620fp+0L, -0xb.a640e8d13efae1ap+0L, 0xa.00868f76e54ce56p-1L, -0x9.a6d403e95576488p-2L, 0x9.684e4c235ac0d81p-2L, -0xc.bef097501e50849p-4L, -0xc.efada7f17138d13p-5L, 0x8.b62a5114d570977p-5L, -0xf.191e2dc95e8b372p-9L, -0xe.4d2b9f9160cd482p-15L, 0x0p+0L};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0L, 0xd.04b647bfe4558acp-6L, -0x8.0ec63a4708fd39bp-3L, 0x8.4cd039d3e3da0c5p-2L, -0xa.0671c3653bb7036p-2L, 0x9.52bb1a4c4e28fdbp-2L, -0xf.378186591fdfef3p-3L, 0x9.aa2613aad8ec175p-3L, -0xb.57ac0d3116a0b56p-4L, 0x9.2b57ed03b933f03p-4L, -0xb.2b4998a1c94bea3p-5L, 0xa.5c4204dee88b95dp-7L, 0x9.2030f1329ded9e3p-12L, 0x0p+0L};
-            }
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.033291a6c76d6a2177301a6491e8p-2Q, 0x1.027f6bf7952cdbcf397ade5b83ap+0Q, -0x1.919d92c6034c44a7ed45a578713cp-2Q, 0x1.7a0ca906acc4841a1191b023a485p-3Q, -0x1.1142c3515ec433047c393c69962fp-4Q, 0x1.50e2d6421ee2654230b309723685p-7Q, 0x1.d0243aab613f83777184da54a80dp-10Q, -0x1.1d4c6c249bf0ee08cde9105ae0e2p-11Q, -0x1.17d0b3032ba5c5edbe3115298755p-14Q, 0x1.310ffd8b564011dafec30497e547p-19Q, -0x1.509d126dab99ceafee21c5b15f2ep-25Q, -0x1.57f8e6955253718d03dd42dcc06ep-36Q, 0x0p+0Q};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.9ec434341eaed8ccc6e8d7244a33p-1Q, -0x1.ca0692ca77439e8f752ca148c144p-2Q, -0x1.2d988a986b0dea756341b6b8b7c2p-1Q, 0x1.145887eacb10f9d392eed69a9335p-2Q, -0x1.4ab3cf0bae2a5b8432a0a181639cp-6Q, -0x1.4e8938899ee371e40cd7b7528ae9p-5Q, 0x1.5cb5de436bfadb9e555d33c55719p-6Q, -0x1.051eebbefaf7bd71954e297a61ffp-8Q, 0x1.0efaec65edbcc11b181ba7073e2cp-14Q, 0x1.6a87a6b931edc5ab5423dbf1babfp-15Q, -0x1.4e8b2a27fe064ec01f627183042bp-23Q, -0x1.54fd8f0625f118cd9bcdded88d81p-33Q, 0x0p+0Q};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.e0eacca617ebb860573873f7b1a4p+0Q, -0x1.5362d7fe36c56b6a443e9d6141a8p+2Q, 0x1.70aa17b7adc0e75a9ffe0b5a33b6p+2Q, -0x1.86bc52429f3a3f79bb4f1cb73763p+1Q, 0x1.5709310e8d1f635f77e733f31613p-2Q, 0x1.9d599937b31fafd3d66db2bf1cbbp-1Q, -0x1.18b244e50df675a487d76601b0e9p-1Q, 0x1.fe16d1a3cfb3e7ecc6834f2061cfp-4Q, 0x1.eb4cc917dd1cd56dce6a9280b03bp-12Q, -0x1.4e09cf12f0cdcfd873bae5583582p-9Q, 0x1.c4a78957d279804ccd5115f6146ap-16Q, 0x1.cb0ccbca08e7961d7bc2f676b666p-25Q, 0x0p+0Q};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.4ca9343b3236825367445e2a7e79p-1Q, -0x1.492e70f2635c16c262e6190afacep+1Q, 0x1.171de5ca88cec2afbea5499914ebp+4Q, -0x1.1e704d84a10750732762c3f4d8bap+6Q, 0x1.23bcc34d6a529b0b422faf672516p+7Q, -0x1.415156a34428a6a6c08cde7dee49p+7Q, 0x1.7ff7929036ddd78bf54cfc378272p+6Q, -0x1.a43b4147c122c6f143d7b591007fp+4Q, 0x1.833e6f5afaca4c566ce598593c06p-4Q, 0x1.13b5aaaf6c71d5b914583e48ae7dp+0Q, -0x1.6365af2495a86c5f48d9bd1a47dp-6Q, -0x1.64d19861a833792a3ce80f84d83cp-14Q, 0x0p+0Q};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.525f0cb11c2720485c66b9e19f02p+1Q, -0x1.7eda4b6a23328f4e2cec098f6666p+3Q, 0x1.578437542fe4f5fbe4cefec73f0cp+4Q, -0x1.40c582473fa8c93703a1216d1613p+4Q, 0x1.9815cb7223c105bc2b63ed01a5fep+3Q, -0x1.222479cd96ee9d17f59bff4df592p+3Q, 0x1.8c2cccc6ee34ca0f24458389d35dp+2Q, -0x1.ffd4fb5b3918044492967474d1cep+0Q, -0x1.3be427404fe7d12432d600f4382ep-3Q, 0x1.7c490d447fad2e27fa6b12a0d504p-3Q, -0x1.23f9756392d0ee9915448c1be2b1p-7Q, -0x1.1f66b1e7815295f48755fd4e3126p-14Q, 0x0p+0Q};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0Q, 0x1.80a316d21a0eed480c84ea711d9ep+0Q, -0x1.ce7e6827143677fbd12dabe06e9fp+2Q, 0x1.ac8b3ccd718c41df56b9c167f638p+3Q, -0x1.74c81d1a27df5c33454de2219e89p+3Q, 0x1.4010d1eedca99cac8148c11888d4p+2Q, -0x1.34da807d2aaec910bcf3aa770bf1p+1Q, 0x1.2d09c9846b581b01a4323f49de6p+1Q, -0x1.97de12ea03ca10913f6e6b1c03cap-1Q, -0x1.9df5b4fe2e271a26f87f7a1f78fbp-2Q, 0x1.16c54a229aae12ed509d340bab6bp-2Q, -0x1.e323c5b92bd166e33ab5b4f9635p-6Q, -0x1.c9a573f22c19a9032c5430df4c8ep-12Q, 0x0p+0Q};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0Q, 0x1.a096c8f7fc8ab1575820ee7a8d4ep-3Q, -0x1.01d8c748e11fa735da05e73f8394p+0Q, 0x1.099a073a7c7b41898468a5bd14cep+1Q, -0x1.40ce386ca776e06ba6f31ba7dadep+1Q, 0x1.2a57634989c51fb583fc11fc2c8bp+1Q, -0x1.e6f030cb23fbfde6dfddcd33a7b8p+0Q, 0x1.3544c2755b1d82eac792a5860a61p+0Q, -0x1.6af581a622d416ac06a3c40b5b79p-1Q, 0x1.256afda077267e050d8164debfb4p-1Q, -0x1.6569331439297d46e21a065d5029p-2Q, 0x1.4b88409bdd1172b9682df8963184p-4Q, 0x1.24061e2653bdb3c5fd153e823b33p-9Q, 0x0p+0Q};
-            }
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            if constexpr (order == 0) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.253122592739470610621616401361877779229479815458388533109264465986705450631"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.00975680155277152973790111993384657471987193942368029780473312379324667581"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.392202657066104148408811882527482753596247632610867974599325631568154086472"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.184594460025979019600750648078960441521039122548921838323798916634848032145"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0667140607455829924370836933031099116268134098764011251351247996652005711545"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0102809473212267076120194571706337484167301394893291398778100853288079049731"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00177055938806458366110052669692669972802589253940700837389391312187949930155"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000544163751852595970300441890153871700803533167101690775895643543400091558287"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000667131499081179164202264668107341250409611901330351905468822246841842144516"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000227289246416658269412624892928823545347265264470652051954608031771296427329"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000391869762033530665296480229865041718561429039745272396909531056977677153636"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000195525597303995056555942742975229891249637237818874029912606477521320941521"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 1) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.810090667116438906125084608325336635858558427183760467122011143848709217936"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.447290700538193081726926232920918677934473900641168827205793350756780984978"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.589054423433051105713954740965807748202549360662853302324635538959794377897"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.269868968682900756914311183719700141732291233181671524008708012629904619787"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0201844713144249320028138388205587200490715428568451868566842270755978350937"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0408369163751242597466561287451981528641525226367711639411234490178637813143"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0212835951367080143883784719158797691366262981606201798553446386989113825786"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00398438697355263021802052679010575079656365873865505148350654941430150902211"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000646067070125676169190646922848512647427733001662437032209422253843012104636"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000432169303593002095810035589027522962115335866552588130271810048010912722413"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000155784009025835660972833383558489901619201115987867017226055817524579424688"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000155064510010241891136131541951717660675464153823551577127554599571639340405"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 2) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.87858275465980185082075059484687011254996371468315226671206152209070678246"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5.30290794206219714496696347944500864617861621722571539095236274472680863374"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.76038163125396215102934581086456598753529517251498951765403500351566767851"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.05262211087252131812326158576179299340031820314628130064826335395880941778"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.334996000779283942861292317865019419501179829373743199871525404727592261010"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.807324207352905330783228925068712255942845486187777944329076813046262028898"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.548235085449943077303537436963997364378850297210952683341512369648428848400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.124533480554402033115092620895174942570554514605089596521009703165626365178"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000468540137709608257946988592597297317335345745375177878078879095839559326245"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00254851010092381349764580405159840052627991728234093528430327277020566808108"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000269803070687479137062075450477716687058854979150244734967367615928087830171"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000534404516891100448405444096173981846862572475827871576787009651989666011194"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 3) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.649728424287883593075915713524545924783310332923624324175524503407444525226"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.57172977290494549793891044329117749573728410170896098271259318361359045523"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("17.44479922404291076498745112746722871408945222683998804378328855565199405640"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-71.60967070801582718948073283130611179366722642889690312945916561433081250530"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("145.86867753909000641239876531969663035434018992110863939875912524044321317900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-160.65886411864296450491377746275540090856151126704519657432554150664253629400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("95.99177003226164787960050084081167617878900086549469777087475435337607996430"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-26.26446655301167408645778203802638858259056547097299290641658148431177104090"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0945419645137684612631871190010186728744115673914304553269038199852068315336"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.07699076445391680627259708274414783686660624009083404578382123547772944786"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0216917238597838193019899484025795776622827268816981287975371913591323350722"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000850722149388195052244794635893235241011583434623169919987280838271411539579"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 4) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.64352568290660717383488785687771176736791104693177525854341276422360953032"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-11.96414728860834656491684620425334470999319544817775050560074926228961346460"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("21.46977932820874234919552398698675631801639393733709025528680976773677869130"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-20.04821994620810903573440830918637861650658462633252001448356816125828318470"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("12.75266048710730678983761121302121021721233371785195914379176723194342934110"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.06695261148657362033536649492341832971872918291204156753481081587833932402"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.19023436953359562968364270001994684253311540563623534733039001879957023961"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.99934359528660371790683912571810391676063304067432355179876753356952054619"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.154243761682653886850234521472448371875938984350115568709864935738395300610"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.185686210301318679459789457754099133235266189449860784374121835441650545927"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00891035301096690191056566243729350984965667867039696309182495485016806697240"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000685217743168943571948966687368236602823360897726181069159545607185161189239"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 5) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.50248854283750761908546072869048821088132450769069501088052480873059396056"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.22646526161484059523124385500321592540705032637199727092718371044938622631"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("13.39199676633541734287658783725542834810025902906082654104028345517237151680"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-11.64942793949647239507297332186810695848666694958647083520681009041022780270"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.00102661444057065419908749038327665570051567187076973678545304964939038004"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.41291814910561289346200219868321750732375141617088099871044781666393737553"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.35186118093287252501820923028537286425715059555956136712165596831136965350"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.796616164270648967111841215195534682870000441132645044906036039054243939416"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.404257610334332808361375570208558025875438251716421264701309289474764401907"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.272236975061487095514001649424045723282019885609650402120668262278630947181"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0294885092632145241422905453679850353376394211407104294790349538471440716050"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000436445522733053311620229711993666920722883672377214017763644242652824250344"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 6) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.203412599628398057633579265447859538789857395107674228547599630740965235246"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.00721402673036540834580779114189574939317230453601344322652356453222562469"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.07501306873106199194436015743412574197776374012334226264667067621104388301"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.50629334740999977272680186302494744195967724949010390385922060059896772157"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.33079186526041669838674663465091103063086959411404278532872827025632075003"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.90210251769529744977701199943741071402521093061881076298433872730941167746"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.20808043828139059668185989249916782761200302655255371273149597921930707587"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.708904315500525840865022566665627479869867191675628771870881198841529204782"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.573081899488511389976606360698320302247199472202129763974755593812367045224"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.349034116849261878956804444377809483590457734709780607298538959951976647643"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0809404872687234817933056436803663367147851456539523123991589358626438323968"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00222796552694813425499071023694009086590703727664242361109396513146307543467"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-        }
-    }
-    if constexpr (p == 8) {
-        if constexpr (std::is_same_v<Real, float>) {
-            if constexpr (order == 0) {
-                return {0x0p+0f, 0x1.184a0cp-3f, 0x1.fbaa04p-1f, -0x1.596f5cp-3f, 0x1.234876p-4f, -0x1.90a568p-5f, 0x1.82b42ep-6f, -0x1.96b60cp-8f, 0x1.8430d2p-11f, -0x1.92df02p-14f, 0x1.da6faap-16f, 0x1.b237bcp-20f, 0x1.66eb1ap-25f, -0x1.f6ebd8p-33f, 0x1.569072p-45f, 0x0p+0f};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.03034p-1f, 0x1.8347dap-2f, -0x1.7d2f18p+0f, 0x1.c3013ep-1f, -0x1.4be40ep-2f, 0x1.458036p-6f, 0x1.7e9e8ep-5f, -0x1.594cfap-6f, 0x1.27c566p-9f, 0x1.e972ap-12f, -0x1.1649ecp-14f, 0x1.c99c42p-23f, 0x1.81519ep-26f, -0x1.06b5eep-37f, 0x0p+0f};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0f, 0x1.666d54p+0f, -0x1.c03746p+1f, 0x1.a43ebap+1f, -0x1.d62736p+0f, 0x1.891e36p-1f, 0x1.a23c1ap-6f, -0x1.d9c16ep-3f, 0x1.b6728ep-4f, -0x1.66849cp-7f, -0x1.fc6302p-9f, 0x1.7e62aep-11f, -0x1.2c21cp-17f, -0x1.15f344p-21f, 0x1.7bbd84p-32f, -0x0p+0f};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0f, 0x1.b44c4ep+1f, -0x1.c1f7ep+3f, 0x1.1601a8p+4f, 0x1.e5bffcp+3f, -0x1.38f35cp+6f, 0x1.d1869cp+6f, -0x1.70d204p+6f, 0x1.34930ep+5f, -0x1.4b77b4p+2f, -0x1.d27f3cp+0f, 0x1.32a2c6p-1f, -0x1.2fc65p-7f, -0x1.c48022p-11f, 0x1.364c0ap-20f, 0x0p+0f};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0f, 0x1.afe05cp+1f, -0x1.0a8c44p+4f, 0x1.0f6c04p+5f, -0x1.306ff2p+5f, 0x1.da6956p+4f, -0x1.6a2c2p+4f, 0x1.0e28c8p+4f, -0x1.ee4b3cp+2f, 0x1.050e3ep-1f, 0x1.0ea6cap+0f, -0x1.6566f6p-2f, 0x1.0b828ap-6f, 0x1.3201b6p-10f, -0x1.a6f024p-19f, -0x0p+0f};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0f, 0x1.77885ep+1f, -0x1.f5abb2p+3f, 0x1.0a779ep+5f, -0x1.164dap+5f, 0x1.233374p+4f, -0x1.af306ap+2f, 0x1.6dba5cp+2f, -0x1.17ffcap+1f, -0x1.9f39e8p+1f, 0x1.d0d0a8p+1f, -0x1.4ac5cap+0f, 0x1.049fbp-3f, 0x1.5ad37ap-7f, -0x1.e6e9a6p-15f, 0x0p+0f};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0f, 0x1.1912b6p+0f, -0x1.85c00cp+2f, 0x1.b7d754p+3f, -0x1.076d5p+4f, 0x1.92a29ep+3f, -0x1.20f516p+3f, 0x1.dcba52p+2f, -0x1.3fe312p+2f, 0x1.5e9b74p+1f, -0x1.a6996ap+0f, 0x1.806826p-1f, -0x1.ddc83ep-4f, -0x1.e09e82p-7f, 0x1.5c5b72p-13f, 0x0p+0f};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0f, 0x1.eae802p-3f, -0x1.5a965ap+0f, 0x1.851aep+1f, -0x1.b139cp+1f, 0x1.ffefb8p+0f, -0x1.025406p+0f, 0x1.ff103cp-1f, -0x1.7a4f7p-1f, 0x1.09dce6p-2f, -0x1.c2f7cep-4f, 0x1.41c46cp-4f, -0x1.03531cp-6f, -0x1.c24ed2p-9f, 0x1.5d1ed8p-14f, -0x0p+0f};
-            }
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0, 0x1.184a0c288d22bp-3, 0x1.fbaa047a94a61p-1, -0x1.596f5b6b28cbp-3, 0x1.234875f46000ep-4, -0x1.90a568ef3b94bp-5, 0x1.82b42ea0f8a16p-6, -0x1.96b60b10e5956p-8, 0x1.8430d19335685p-11, -0x1.92df023007909p-14, 0x1.da6faa7679627p-16, 0x1.b237bc2c3b525p-20, 0x1.66eb1a28068aep-25, -0x1.f6ebd7398c4a4p-33, 0x1.5690727034a8ap-45, 0x0p+0};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0, 0x1.03033f41d9947p-1, 0x1.8347da7a3030cp-2, -0x1.7d2f17f2a95afp+0, 0x1.c3013eaebde94p-1, -0x1.4be40ed86f2cdp-2, 0x1.4580356ca34ffp-6, 0x1.7e9e8eefc30b4p-5, -0x1.594cf912461bcp-6, 0x1.27c56651be6eep-9, 0x1.e972a09b0f4ddp-12, -0x1.1649ec5e54141p-14, 0x1.c99c42a59648bp-23, 0x1.81519dee82fp-26, -0x1.06b5ee4f0712p-37, 0x0p+0};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0, 0x1.666d532df9dfp+0, -0x1.c0374596ee4d9p+1, 0x1.a43eb9f4500c3p+1, -0x1.d627359f84d25p+0, 0x1.891e36789053ap-1, 0x1.a23c19ecf2debp-6, -0x1.d9c16d05d7787p-3, 0x1.b6728d569b4c7p-4, -0x1.66849bebd2ebep-7, -0x1.fc6301aedca9p-9, 0x1.7e62ae52149bdp-11, -0x1.2c21c0130a3ebp-17, -0x1.15f344e8ed1b2p-21, 0x1.7bbd836b1bf85p-32, -0x0p+0};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0, 0x1.b44c4e267cbb5p+1, -0x1.c1f7df3ad7ab8p+3, 0x1.1601a8a979c79p+4, 0x1.e5bffb29b3c53p+3, -0x1.38f35bf0e9ee1p+6, 0x1.d1869b3f8e2b4p+6, -0x1.70d2038145a54p+6, 0x1.34930dde67aeap+5, -0x1.4b77b4fb36749p+2, -0x1.d27f3b25c1fd7p+0, 0x1.32a2c5a3dfe81p-1, -0x1.2fc64ff8d3421p-7, -0x1.c48021ad9bc16p-11, 0x1.364c0a7c4c64bp-20, 0x0p+0};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0, 0x1.afe05c7a6ada2p+1, -0x1.0a8c44cdd47bfp+4, 0x1.0f6c0325c5e14p+5, -0x1.306ff1c62c833p+5, 0x1.da69559cc9113p+4, -0x1.6a2c1f828fe2ep+4, 0x1.0e28c771588c3p+4, -0x1.ee4b3cc46d89p+2, 0x1.050e3e4d4732ap-1, 0x1.0ea6cad7a5a8p+0, -0x1.6566f5ac7d805p-2, 0x1.0b828ad29e43fp-6, 0x1.3201b5c3bc1c2p-10, -0x1.a6f0242017b15p-19, -0x0p+0};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0, 0x1.77885e6e270a7p+1, -0x1.f5abb22b1b6ecp+3, 0x1.0a779dee6c7bep+5, -0x1.164d9f148bde5p+5, 0x1.2333738e736f1p+4, -0x1.af306993826a7p+2, 0x1.6dba5c59397a4p+2, -0x1.17ffc928dd1d9p+1, -0x1.9f39e7400cf5dp+1, 0x1.d0d0a8f3b805ep+1, -0x1.4ac5cadf9fb15p+0, 0x1.049faf6ae6899p-3, 0x1.5ad3792bdac36p-7, -0x1.e6e9a51e3663ap-15, 0x0p+0};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0, 0x1.1912b6ad90d43p+0, -0x1.85c00c80d7a19p+2, 0x1.b7d753e3c818ap+3, -0x1.076d50e7f7851p+4, 0x1.92a29d7ac0e1ep+3, -0x1.20f516098425cp+3, 0x1.dcba519c323cfp+2, -0x1.3fe31292805cp+2, 0x1.5e9b74431b073p+1, -0x1.a6996ae95f76fp+0, 0x1.806826de1640bp-1, -0x1.ddc83de4acfafp-4, -0x1.e09e81650c6b7p-7, 0x1.5c5b71613d71bp-13, 0x0p+0};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0, 0x1.eae80165a34adp-3, -0x1.5a965a7535366p+0, 0x1.851adfd49d1a7p+1, -0x1.b139c010d5d8fp+1, 0x1.ffefb70380437p+0, -0x1.0254056f57104p+0, 0x1.ff103b26e087ep-1, -0x1.7a4f70cc2f5d8p-1, 0x1.09dce627745a6p-2, -0x1.c2f7ce5c8a37cp-4, 0x1.41c46b919c33fp-4, -0x1.03531c096423ap-6, -0x1.c24ed1e998c51p-9, 0x1.5d1ed72a09587p-14, -0x0p+0};
-            }
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0L, 0x8.c250614469156ecp-6L, 0xf.dd5023d4a530983p-4L, -0xa.cb7adb594658341p-6L, 0x9.1a43afa30007147p-7L, -0xc.852b4779dca57d6p-8L, 0xc.15a17507c50b09fp-9L, -0xc.b5b058872cab3ebp-11L, 0xc.21868c99ab4273bp-14L, -0xc.96f811803c8446bp-17L, 0xe.d37d53b3cb1391fp-19L, 0xd.91bde161da92bd9p-23L, 0xb.3758d14034571f5p-28L, -0xf.b75eb9cc6251d52p-36L, 0xa.b4839381a545259p-48L, 0x0p+0L};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0L, 0x8.1819fa0ecca3abdp-4L, 0xc.1a3ed3d18185c5ap-5L, -0xb.e978bf954ad7b4cp-3L, 0xe.1809f575ef4a37dp-4L, -0xa.5f2076c37966861p-5L, 0xa.2c01ab651a7f8e8p-9L, 0xb.f4f4777e185a2cbp-8L, -0xa.ca67c89230ddcadp-9L, 0x9.3e2b328df376c3ap-12L, 0xf.4b9504d87a6e47fp-15L, -0x8.b24f62f2a0a04dcp-17L, 0xe.4ce2152cb245585p-26L, 0xc.0a8cef7417800e8p-29L, -0x8.35af7278388fe4bp-40L, 0x0p+0L};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0L, 0xb.336a996fcef7c52p-3L, -0xe.01ba2cb7726c73bp-2L, 0xd.21f5cfa280614c9p-2L, -0xe.b139acfc2692864p-3L, 0xc.48f1b3c4829d099p-4L, 0xd.11e0cf6796f5a28p-9L, -0xe.ce0b682ebbc393bp-6L, 0xd.b3946ab4da635ap-7L, -0xb.3424df5e975efd8p-10L, -0xf.e3180d76e5481d1p-12L, 0xb.f3157290a4debfp-14L, -0x9.610e009851f575p-20L, -0x8.af9a274768d9303p-24L, 0xb.ddec1b58dfc26aap-35L, -0x0p+0L};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0L, 0xd.a2627133e5da6a2p-2L, -0xe.0fbef9d6bd5bcc5p+0L, 0x8.b00d454bce3c7c1p+1L, 0xf.2dffd94d9e295dcp+0L, -0x9.c79adf874f70573p+3L, 0xe.8c34d9fc715a214p+3L, -0xb.86901c0a2d2a313p+3L, 0x9.a4986ef33d75017p+2L, -0xa.5bbda7d9b3a4ab2p-1L, -0xe.93f9d92e0feb674p-3L, 0x9.95162d1eff408cfp-4L, -0x9.7e327fc69a10719p-10L, -0xe.24010d6cde0b23p-14L, 0x9.b26053e2632577ap-23L, 0x0p+0L};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0L, 0xd.7f02e3d356d0e5bp-2L, -0x8.5462266ea3dfa72p+1L, 0x8.7b60192e2f0a0a5p+2L, -0x9.837f8e316419b55p+2L, 0xe.d34aace64889869p+1L, -0xb.5160fc147f16c08p+1L, 0x8.71463b8ac46182cp+1L, -0xf.7259e6236c483c5p-1L, 0x8.2871f26a39950e3p-4L, 0x8.753656bd2d3fd71p-3L, -0xb.2b37ad63ec0243dp-5L, 0x8.5c145694f21f58cp-9L, 0x9.900dae1de0e10ep-13L, -0xd.37812100bd8a443p-22L, -0x0p+0L};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0L, 0xb.bc42f3713853a26p-2L, -0xf.ad5d9158db75d9ap+0L, 0x8.53bcef7363deeep+2L, -0x8.b26cf8a45ef2551p+2L, 0x9.199b9c739b78925p+1L, -0xd.79834c9c135345p-1L, 0xb.6dd2e2c9cbd2213p-1L, -0x8.bffe4946e8ec5f8p-2L, -0xc.f9cf3a0067ae91ap-2L, 0xe.8685479dc02ed7ep-2L, -0xa.562e56fcfd8a5e2p-3L, 0x8.24fd7b57344ca47p-6L, 0xa.d69bc95ed61ae29p-10L, -0xf.374d28f1b31ceb4p-18L, 0x0p+0L};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0L, 0x8.c895b56c86a1b02p-3L, -0xc.2e006406bd0c7e6p-1L, 0xd.beba9f1e40c4cbdp+0L, -0x8.3b6a873fbc285cap+1L, 0xc.9514ebd6070fp+0L, -0x9.07a8b04c212dd91p+0L, 0xe.e5d28ce191e76fcp-1L, -0x9.ff18949402e0231p-1L, 0xa.f4dba218d8396ddp-2L, -0xd.34cb574afbb77c5p-3L, 0xc.034136f0b2057f9p-4L, -0xe.ee41ef2567d7906p-7L, -0xf.04f40b28635ba7ep-10L, 0xa.e2db8b09eb8dbb5p-16L, 0x0p+0L};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0L, 0xf.57400b2d1a568f9p-6L, -0xa.d4b2d3a9a9b32a1p-3L, 0xc.28d6fea4e8d3b6dp-2L, -0xd.89ce0086aec77acp-2L, 0xf.ff7db81c021b9bdp-3L, -0x8.12a02b7ab881d9bp-3L, 0xf.f881d937043f115p-4L, -0xb.d27b86617aebd37p-4L, 0x8.4ee7313ba2d30a8p-5L, -0xe.17be72e451bdc7ep-7L, 0xa.0e235c8ce19f70ep-7L, -0x8.1a98e04b211d3d4p-9L, -0xe.12768f4cc6289abp-12L, 0xa.e8f6b9504ac38b3p-17L, -0x0p+0L};
-            }
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.184a0c288d22add7ea26104df2f3p-3Q, 0x1.fbaa047a94a613069e6f550b4e09p-1Q, -0x1.596f5b6b28cb0681bf78a3e54b72p-3Q, 0x1.234875f46000e28dce7c3f342092p-4Q, -0x1.90a568ef3b94afacf755834bab9ap-5Q, 0x1.82b42ea0f8a1613dc5ff9725c05p-6Q, -0x1.96b60b10e59567d6b2c6577bad3bp-8Q, 0x1.8430d19335684e7577fd3b699763p-11Q, -0x1.92df0230079088d5ad0746147153p-14Q, 0x1.da6faa767962723e71f08f2e9083p-16Q, 0x1.b237bc2c3b5257b1d937078b7396p-20Q, 0x1.66eb1a28068ae3ea1bd5d2683257p-25Q, -0x1.f6ebd7398c4a3aa441e024a5714bp-33Q, 0x1.5690727034a8a4b1353895ae261dp-45Q, 0x0p+0Q};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.03033f41d994757a2b4934423538p-1Q, 0x1.8347da7a3030b8b37cdc36ec3c9cp-2Q, -0x1.7d2f17f2a95af6988be8eca125f4p+0Q, 0x1.c3013eaebde946f9eaa42bce8cf9p-1Q, -0x1.4be40ed86f2cd0c168ad249492a4p-2Q, 0x1.4580356ca34ff1cf3c18408b1d74p-6Q, 0x1.7e9e8eefc30b45959dcb8ab52383p-5Q, -0x1.594cf912461bb959724fb77ad3bbp-6Q, 0x1.27c56651be6ed873712071c19324p-9Q, 0x1.e972a09b0f4dc8fdb93114f9ed4p-12Q, -0x1.1649ec5e541409b8483ac00aa989p-14Q, 0x1.c99c42a59648ab096d412a58741fp-23Q, 0x1.81519dee82f001d0cfd286a4bf1ep-26Q, -0x1.06b5ee4f0711fc96e3337209d4e2p-37Q, 0x0p+0Q};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.666d532df9def8a39e69d4c9dbd1p+0Q, -0x1.c0374596ee4d8e750b0b0f065b11p+1Q, 0x1.a43eb9f4500c29913bdae70f2e12p+1Q, -0x1.d627359f84d250c8825852fe20e7p+0Q, 0x1.891e36789053a132cb4397963bd6p-1Q, 0x1.a23c19ecf2deb44f4177f3e9336bp-6Q, -0x1.d9c16d05d77872764189280b3978p-3Q, 0x1.b6728d569b4c6b3f03c9c20fd79fp-4Q, -0x1.66849bebd2ebdfafabb131375ec9p-7Q, -0x1.fc6301aedca903a123de4bceca69p-9Q, 0x1.7e62ae52149bd7e06a18746f5b91p-11Q, -0x1.2c21c0130a3eaea0bd3721b2b8d6p-17Q, -0x1.15f344e8ed1b26069acbf2a1a453p-21Q, 0x1.7bbd836b1bf84d53feb61580dc74p-32Q, 0x0p+0Q};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.b44c4e267cbb4d43745305f720c9p+1Q, -0x1.c1f7df3ad7ab79897dce80d62718p+3Q, 0x1.1601a8a979c78f82e398ce8545b9p+4Q, 0x1.e5bffb29b3c52bb885497a60d3d6p+3Q, -0x1.38f35bf0e9ee0ae5b1772951f4d5p+6Q, 0x1.d1869b3f8e2b44288688d26e70d1p+6Q, -0x1.70d2038145a54625eb25d875d7e5p+6Q, 0x1.34930dde67aea02e0a703b76a197p+5Q, -0x1.4b77b4fb3674956338abd1824db4p+2Q, -0x1.d27f3b25c1fd6ce83b2a8b0a4ac9p+0Q, 0x1.32a2c5a3dfe8119d379b71453288p-1Q, -0x1.2fc64ff8d3420e31f2a6dd47d615p-7Q, -0x1.c48021ad9bc1646021c012f5b071p-11Q, 0x1.364c0a7c4c64aef45189b312edb4p-20Q, 0x0p+0Q};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.afe05c7a6ada1cb6172616d2c6a8p+1Q, -0x1.0a8c44cdd47bf4e495a5398413fbp+4Q, 0x1.0f6c0325c5e1414a9285f59e5f14p+5Q, -0x1.306ff1c62c8336aad5c3f9886bcep+5Q, 0x1.da69559cc91130d28dd4b63660e6p+4Q, -0x1.6a2c1f828fe2d81030f1ad524eb7p+4Q, 0x1.0e28c771588c30581ce7071741b8p+4Q, -0x1.ee4b3cc46d890789fa8b15b7da8p+2Q, 0x1.050e3e4d4732a1c55c0c971f3557p-1Q, 0x1.0ea6cad7a5a7fae2eab7d74b22a1p+0Q, -0x1.6566f5ac7d80487971d04a5944efp-2Q, 0x1.0b828ad29e43eb178f6b65b8f31p-6Q, 0x1.3201b5c3bc1c21bf7086981ccb12p-10Q, -0x1.a6f0242017b1488503cf0ef046e5p-19Q, 0x0p+0Q};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0Q, 0x1.77885e6e270a744c868654d7cbb5p+1Q, -0x1.f5abb22b1b6ebb333fd9f11e8f7cp+3Q, 0x1.0a779dee6c7bddbff2f0d8b9981bp+5Q, -0x1.164d9f148bde4aa13b66fabbc2fp+5Q, 0x1.2333738e736f124a0ec3de563f7bp+4Q, -0x1.af306993826a689f7543995893acp+2Q, 0x1.6dba5c59397a4426e98586aad789p+2Q, -0x1.17ffc928dd1d8bf0f209d0c36abep+1Q, -0x1.9f39e7400cf5d234f22720c7748ap+1Q, 0x1.d0d0a8f3b805dafc2d2b539d9bb4p+1Q, -0x1.4ac5cadf9fb14bc48382ff0ecfb1p+0Q, 0x1.049faf6ae689948e66d5e5134564p-3Q, 0x1.5ad3792bdac35c5163486d9087edp-7Q, -0x1.e6e9a51e36639d68c6db7d7495a4p-15Q, 0x0p+0Q};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0Q, 0x1.1912b6ad90d43603284e290418eep+0Q, -0x1.85c00c80d7a18fcc693e47644de7p+2Q, 0x1.b7d753e3c818997a04ded98f86e3p+3Q, -0x1.076d50e7f7850b94ae780b4bf285p+4Q, 0x1.92a29d7ac0e1e0002558af869ed1p+3Q, -0x1.20f516098425bb22664ce4ad84a9p+3Q, 0x1.dcba519c323cedf78dcb7794def8p+2Q, -0x1.3fe31292805c0462ca96ae20fe5p+2Q, 0x1.5e9b74431b072dba61e526c0393fp+1Q, -0x1.a6996ae95f76ef890f12b5a6c626p+0Q, 0x1.806826de1640aff2fbfd8d0d7d09p-1Q, -0x1.ddc83de4acfaf20be5fee513819ep-4Q, -0x1.e09e81650c6b74fbce41e5378d99p-7Q, 0x1.5c5b71613d71b7692e7e5f0ba23p-13Q, 0x0p+0Q};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0Q, 0x1.eae80165a34ad1f2080107f7b7a5p-3Q, -0x1.5a965a7535366541f0a1afe5172fp+0Q, 0x1.851adfd49d1a76d9d23c35315fc3p+1Q, -0x1.b139c010d5d8ef58fb69c4f0efd8p+1Q, 0x1.ffefb7038043737a18fc832f1fb7p+0Q, -0x1.0254056f57103b364cf4bcafdd14p+0Q, 0x1.ff103b26e087e22aa6dbe2498954p-1Q, -0x1.7a4f70cc2f5d7a6d2a4e62aee34dp-1Q, 0x1.09dce627745a61500e9471981ea7p-2Q, -0x1.c2f7ce5c8a37b8fcabdaf25d6d6bp-4Q, 0x1.41c46b919c33ee1c6941aae7132bp-4Q, -0x1.03531c096423a7a88f95e3dc08eep-6Q, -0x1.c24ed1e998c51356546e2437d6p-9Q, 0x1.5d1ed72a09587166cbb2e531d26cp-14Q, 0x0p+0Q};
-            }
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            if constexpr (order == 0) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.136859984385993751077424284238513346105771881700946032539857608801714375260"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.991531505549868928852223941202783180250573415879960614939273149473543513232"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.168669428069824001344876924759083221703325404050382978741893461845460708901"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0711140258408706504803069010910216723551333508784818550165049090931508664852"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0489069985868462937786964568361717206243738587558741902200175649925966650129"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0236025290831865730472503982004363583525603770422866170365985291322094732559"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00620591898122876136661677884645407645696587502826527734998815703979020082209"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000740414996836150617193096345381128615000342497991762689010201911138137676340"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000960519616914659362067678923772724229000913224382096876651732324410060847142"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000282786008599848003825512309131168222310934819976005479856002545492804079821"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000161758704125419265856051792339632788510763962613299088995170275735382724250"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000417835973045118991124105253366830871810097251894035223474643902978862222950"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000228702107424295259422097052204574273567576074367490930756782831109751583002"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000380322713533425186858078998967525935209252034129900336181242610764710254761"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 1) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.505884148395843984672030852174399268078679938448445514258859914326001574753"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.378203786571291475028258491549280264525735502487840319727030236183752240877"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.48899984049181086925690641126028244033585659708567195002624452117766769554"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.880868872481146917953730102204425044160476030745496386305050091936160661825"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.324112159690952253266958291790923377370339558783455268279088511692627257578"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0198669931146939729198708935598776106105509170321806377166373111519790413827"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0467064658861046390974330766795109450179003887204378435053237799594305015134"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0210754806840627153541931469194838393690032791036447674196194339971613456374"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00225655435576476469044726339752369362143954369726725569747472926858253332600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000466773760937245507236716054902477793363154761728440462716816755417726884839"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000663492114416674035500361661641750124659642249106990423787115653008871078300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000213091444200759381405507720298082584145763408653037309536239955733283926150"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000224285069909106554636357422248869419407906728286220715022858657729340987674"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000746668625743637862652799469000616324979519456514273967438860456366173662892"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 2) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.40010566589796415558533052990817027536043759916356873335248645843912898740"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.50168676252051764999916760393084370145312284526707841278933240785874906921"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.28316425732927656875646999404076171324929322898132788895606205661772082296"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.83653578896048342826761860954879682887285337195163994610183024428204639287"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.767808630196817229463066449452964216764497348541592935264231141751164293885"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0255270245723248470256698009778319785355159721020640100259648381281108673206"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.231325961819433188856073677854062275419611129702243186823190488135500579221"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.107042839148294803604040015338906449890317311518114018506422501396601728023"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0109411012014314322153349861016506274246639791285954533561420989314806280893"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00387868304772471399323142237494169480427070296801463441213707814207225784013"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000729342408030845829165840735507514556696710333640548011394236862236236627590"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000894462576724212069044572229637929785464056704288394767005400917958125948440"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000517722722573465466291304746138565114462435290270180299612937282299347886509"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000345371778653840406383195497480732961379596653494040751101347866321743412771"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 3) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.40857865218409942407989160777729397499591054071894723659795747026734950142"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-14.06150781147640244495854524439441851419403709392481084157811217258651128990"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("17.37540498925634213895582494025326018301205036554108994541098300558519647810"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("15.17968519349066044652294389136578861409554749815814367110760723871662294450"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-78.23765541484636800472354977154947501042898222086099559309649353911488323440"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("116.38145160012465254189247417655014226350307393144895240522480865461502034100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-92.20509149539549844487080427780966241435914366770315955416451996663294302680"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("38.57180379632866626053856571576184925471707552931311103550752525165681257540"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5.17918133289806211714176217075064499841836717085374825348683628481547935326"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.82225389167614588863332031779801692711824638887982150713863406444245730454"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.598898102049091230023937146931083606151277363169821330990542437169742650605"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00927046685105820265775499853351620625448959411497441318196481292209014223253"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000863076236511053557380361955795006038651362072706195875505623255065432401013"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000115594653411452947966415211118033698227006015073368264240575869273988254730"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 4) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.37403446175967838025740792692632707948046376845678760985954780113353683376"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-16.65924530413007895577513111721655133926983876119072500556865649764333729280"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("33.92774037847644365730660167931354863708439882380578545057682183184098002560"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-38.05466036628095179642463777855898685849735591879960715894900954660986556330"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("29.65071641201309323109850787750541018979228147381363769083014882995571890840"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-22.63577223778536585979611105411422747200617599445293663779795581166422612690"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("16.88495582843530592324987980427308263482658385028179904289230174596074103340"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.72334212477120771395018502358287787646097333914773539504366245154006903261"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.509874293263782320049624992542430344831541029125914053863318565845626947501"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.05723254933187142521325305757260448706303752772475115221502588084489406121"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.349025572445839567506362486618125787775522478731013526918275825979025450341"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0163275104227731348198876869545919769123313328974523116723206927638520899008"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00116732284453401104147360959063823502788555856702680595647112386117318401134"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000315113403818958420917458786425100865687235113639358839633877000023951513838"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 5) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.93384914759197424624436413594969058529365344664724959523125492071614427193"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-15.67720898074499960019790246277632013145587519414207657764003345532838952320"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("33.30840669888082927743188422912680268770468382312738501151598773669709347950"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-34.78790107776493317973127999160157672445840757713194594151710343461996258490"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("18.20006137509239303213521792722566030277335694542561819775614995273543845150"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.73732985882967353579625955002147560794702457823837345027768515384207199939"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.71449955666858878400309088707607704396756738056282405829209011954772445391"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.18749346251773279906619495975374371998852897264751318856692473518486342256"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.24395456912490815512051132069746602372138882030028342425172470032100812037"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.63136779690107300247637411793680556583470203778956077148746730514900636140"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.29208057365003020310933608766753056310407043934855358170062066567610977189"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.127257700395436748185441509800570330756269721379701882712722971090011220542"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0105842916161319289430031608631456823275553548600640429274763034124609001209"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000580445141495463978915954606394279824931279836573959690571643754738437622999"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 6) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.09794179665989663514011010318171289068252802140768727878686619226775014160"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.08984673101670014308433503745446328651407196395191858667048642230680054117"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("13.74503511894797041799485471293715399778854034159024012586185790377350928050"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-16.46418848621425725226856339943522600141255984607131407751367512429535974550"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("12.58235048270494971240583540160205978818573268955250712351866824920394664630"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.02991773470528559623876404322857159498730180401367525828524406240302233897"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("7.44887199643649366803718019597024027263652518924024613405692486678267833539"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.99823440844323865139296784342762981029643191844299226701928041463556839082"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.73911908413543286133929491391344713268901997126890391713796517771077981005"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.65077846715527320386166297579946870069085350586686894303798561070712527613"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.750794615373821527451164487493324083501669271576479206468805894209869122774"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.116646043558658917381544271189706037325524764351951616559858241342309095929"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0146673328218612635522669061509315192382547144459217750205470993012158491409"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000166109656710205411664661588058784980983032508578738275988691042867685712989"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 7) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.239700327791444154401358637312026610528216518839726598253382285687854145301"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.35385671006698656362279837678985930962433090919777408910621735397808426685"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.03988263970878210970161760103694626417746895886680293765920336110790081944"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.38457489797628550541836623944752232253491103859138520958725493309901917502"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.99975150905107828365392055663475104753346795604213386830360205861062068058"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.00909456222785902673888196781880614953849677554209360029881025329921208452"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.998170708175407887564948885340732566778229747407421235714432832971547496176"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.738887333798341000751416724474791664378133946712220233024499707378818126349"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.259631725462066480616682675264655170327179020240911896080856531165333156446"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.110099607562586792620753110120489954588564472503733678183395115619093852339"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0785564615159843726834898160756405679414386387007067812431829633899248651308"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0158279203220123929016663292094093420473159442069900632195102000109139919945"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00343557655723850854612182385732716766125518666298517555524787852985964150285"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000832368065465019779864000534536830870074333194787317202754089818199746452757"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-        }
-    }
-    if constexpr (p == 9) {
-        if constexpr (std::is_same_v<Real, float>) {
-            if constexpr (order == 0) {
-                return {0x0p+0f, 0x1.1d2fcp-4f, 0x1.b1b652p-1f, 0x1.8b08d6p-3f, -0x1.4aef16p-3f, 0x1.fd1878p-5f, -0x1.7ee87p-8f, -0x1.097588p-7f, 0x1.3d3ef8p-8f, -0x1.291474p-10f, 0x1.b33accp-15f, 0x1.7e6498p-16f, -0x1.53f94ap-19f, -0x1.58c1d8p-24f, 0x1.278ba2p-29f, -0x1.705a7ap-38f, -0x1.4fb4eep-52f, -0x0p+0f};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.2b90f8p-2f, 0x1.af96b8p-1f, -0x1.d3c16cp+0f, 0x1.169004p+0f, -0x1.1f4f38p-1f, 0x1.82c926p-3f, -0x1.540e9cp-7f, -0x1.49841cp-6f, 0x1.96a364p-8f, 0x1.0c494ap-11f, -0x1.b592fcp-12f, 0x1.9d3f0ap-16f, 0x1.8562bp-23f, -0x1.13cc2ep-24f, 0x1.2234ep-34f, 0x1.08644ap-47f, 0x0p+0f};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0f, 0x1.e4c00ep-1f, -0x1.aad7p+0f, 0x1.135c58p-2f, 0x1.5b4146p-1f, -0x1.c92ba8p-4f, -0x1.4f00eap-2f, 0x1.61aa48p-2f, -0x1.66761ap-3f, 0x1.723502p-5f, -0x1.85c5f4p-10f, -0x1.2bb318p-9f, 0x1.b3d73ep-12f, 0x1.bca3f2p-17f, -0x1.261d8ap-20f, 0x1.36693ap-28f, 0x1.1a9906p-40f, -0x0p+0f};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0f, 0x1.27d6ep+1f, -0x1.2ded7ap+3f, 0x1.e79fd8p+3f, -0x1.304a1ap+3f, -0x1.effd26p+2f, 0x1.7ce73p+4f, -0x1.985f02p+4f, 0x1.d3cfacp+3f, -0x1.e1a25p+1f, -0x1.9b8564p-2f, 0x1.fe4766p-2f, -0x1.73f12ep-4f, -0x1.20ddep-10f, 0x1.ffd29p-12f, -0x1.fa8378p-20f, -0x1.cc794ap-31f, -0x0p+0f};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0f, 0x1.c7cedp+1f, -0x1.2ab8cap+4f, 0x1.4df684p+5f, -0x1.af3bfap+5f, 0x1.8eeb18p+5f, -0x1.541e9cp+5f, 0x1.12ea48p+5f, -0x1.35c8bp+4f, 0x1.d829e2p+1f, 0x1.69d6eap+1f, -0x1.023562p+1f, 0x1.b42324p-2f, -0x1.2e2904p-8f, -0x1.22b4e2p-8f, 0x1.654cep-16f, 0x1.43e712p-26f, 0x0p+0f};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0f, 0x1.1617a4p+2f, -0x1.94d9c6p+4f, 0x1.dd0eb6p+5f, -0x1.168c04p+6f, 0x1.24c19cp+5f, -0x1.016a68p+0f, -0x1.c94ed2p+2f, 0x1.669c08p+3f, -0x1.88dca4p+4f, 0x1.b958d8p+4f, -0x1.eccebap+3f, 0x1.f4375ep+1f, -0x1.2ade5ep-3f, -0x1.491f18p-4f, 0x1.5bccdep-11f, 0x1.398368p-20f, 0x0p+0f};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0f, 0x1.384148p+1f, -0x1.dd3c5ap+3f, 0x1.30352ap+5f, -0x1.a86d9ep+5f, 0x1.7d0e6cp+5f, -0x1.25c844p+5f, 0x1.f5b3e2p+4f, -0x1.815eep+4f, 0x1.ca4482p+3f, -0x1.050826p+3f, 0x1.1eeca8p+2f, -0x1.6df696p+0f, 0x1.75a7acp-5f, 0x1.ebd4ap-5f, -0x1.434438p-10f, -0x1.202646p-18f, 0x0p+0f};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0f, 0x1.041f76p+0f, -0x1.96fe7ap+2f, 0x1.04a7fep+4f, -0x1.5c5edep+4f, 0x1.0b593cp+4f, -0x1.3ddf52p+3f, 0x1.12f0bcp+3f, -0x1.d4ebfcp+2f, 0x1.d31828p+1f, -0x1.6bf238p+0f, 0x1.d1d5cp-1f, -0x1.794e94p-2f, -0x1.2e59eap-6f, 0x1.26fbfep-5f, -0x1.e662fap-10f, -0x1.a81802p-17f, -0x0p+0f};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0f, 0x1.9024ep-3f, -0x1.3caa56p+0f, 0x1.947e64p+1f, -0x1.033a7ap+2f, 0x1.51b6cap+1f, -0x1.0bd63p+0f, 0x1.028beep+0f, -0x1.1620dap+0f, 0x1.b5ef82p-2f, -0x1.b7954cp-6f, 0x1.054d18p-4f, -0x1.481726p-5f, -0x1.8ce86ep-6f, 0x1.2926b8p-6f, -0x1.20ae94p-9f, -0x1.e260bp-16f, 0x0p+0f};
-            }
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0, 0x1.1d2fbfac2394ap-4, 0x1.b1b6520101e0ep-1, 0x1.8b08d5cd4a2adp-3, -0x1.4aef16c7e666fp-3, 0x1.fd1877f1138bep-5, -0x1.7ee87092fa243p-8, -0x1.09758849af605p-7, 0x1.3d3ef7388a3aep-8, -0x1.29147421d5711p-10, 0x1.b33acccf47f1cp-15, 0x1.7e6498cdbddd5p-16, -0x1.53f9494edf128p-19, -0x1.58c1d88e09b31p-24, 0x1.278ba12dc249ap-29, -0x1.705a7a4d8345p-38, -0x1.4fb4ee678fa0ep-52, -0x0p+0};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0, 0x1.2b90f77070093p-2, 0x1.af96b810375aep-1, -0x1.d3c16b16ba87ap+0, 0x1.1690032de8cfbp+0, -0x1.1f4f37268ff74p-1, 0x1.82c9256a70f8fp-3, -0x1.540e9bea7c732p-7, -0x1.49841c554fed2p-6, 0x1.96a364065f27dp-8, 0x1.0c49493de5a6fp-11, -0x1.b592fbb7be41bp-12, 0x1.9d3f09be0cea7p-16, 0x1.8562af0388b7ep-23, -0x1.13cc2e0d34f25p-24, 0x1.2234e02ed8631p-34, 0x1.08644a120d1efp-47, 0x0p+0};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0, 0x1.e4c00e361fc68p-1, -0x1.aad6ffd5d77f1p+0, 0x1.135c57711e671p-2, 0x1.5b41454ff0957p-1, -0x1.c92ba77b267a3p-4, -0x1.4f00ea2c2d363p-2, 0x1.61aa479f9dc68p-2, -0x1.6676194262896p-3, 0x1.7235017b58d32p-5, -0x1.85c5f4a449273p-10, -0x1.2bb318efa4d23p-9, 0x1.b3d73e818e5c9p-12, 0x1.bca3f26f194dp-17, -0x1.261d8947cb727p-20, 0x1.36693a4632269p-28, 0x1.1a9906065291fp-40, -0x0p+0};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0, 0x1.27d6df36685a8p+1, -0x1.2ded79e41fdb1p+3, 0x1.e79fd7c0b1c0fp+3, -0x1.304a1a210a5fap+3, -0x1.effd2573aa9abp+2, 0x1.7ce72fdc2cb91p+4, -0x1.985f0196c72e5p+4, 0x1.d3cfac07a9d2bp+3, -0x1.e1a24f8472a68p+1, -0x1.9b8563bd7c7d8p-2, 0x1.fe4766e3faf54p-2, -0x1.73f12d4155f36p-4, -0x1.20dddf659ee51p-10, 0x1.ffd28fb3400bfp-12, -0x1.fa83788d3f78dp-20, -0x1.cc794a76e5f16p-31, -0x0p+0};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0, 0x1.c7ced0f66aeadp+1, -0x1.2ab8c9c81252ep+4, 0x1.4df684dede46dp+5, -0x1.af3bf949d62bap+5, 0x1.8eeb17bed133cp+5, -0x1.541e9c27826e5p+5, 0x1.12ea47c60decp+5, -0x1.35c8b07214e14p+4, 0x1.d829e1a762882p+1, 0x1.69d6e9c20f73dp+1, -0x1.0235621854eefp+1, 0x1.b423243b8b469p-2, -0x1.2e290398a3fe3p-8, -0x1.22b4e2598d44bp-8, 0x1.654cdf573874bp-16, 0x1.43e711e678672p-26, 0x0p+0};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0, 0x1.1617a4f9d8857p+2, -0x1.94d9c534a28d4p+4, 0x1.dd0eb6aa76ffep+5, -0x1.168c0447c1b6fp+6, 0x1.24c19c047007fp+5, -0x1.016a68491e4d8p+0, -0x1.c94ed28aba0f5p+2, 0x1.669c08c9522f3p+3, -0x1.88dca456f3456p+4, 0x1.b958d77e385a9p+4, -0x1.eccebab605f4bp+3, 0x1.f4375d664ce34p+1, -0x1.2ade5d60c4581p-3, -0x1.491f178ce5646p-4, 0x1.5bccddec65e54p-11, 0x1.398367062ce37p-20, 0x0p+0};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0, 0x1.3841475e9a364p+1, -0x1.dd3c5aa19c52ep+3, 0x1.303529a28e47p+5, -0x1.a86d9ebb6edc4p+5, 0x1.7d0e6c4e24171p+5, -0x1.25c8439d2df8ap+5, 0x1.f5b3e1ac99667p+4, -0x1.815ee05c85e8bp+4, 0x1.ca4482f4236a5p+3, -0x1.050825dec75a9p+3, 0x1.1eeca8acc3a79p+2, -0x1.6df69657c972dp+0, 0x1.75a7ac677c4efp-5, 0x1.ebd49f3810c89p-5, -0x1.4344372e1b6fcp-10, -0x1.20264586c6bb9p-18, 0x0p+0};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0, 0x1.041f759e862aap+0, -0x1.96fe795439509p+2, 0x1.04a7fd5b5e592p+4, -0x1.5c5ede521aae6p+4, 0x1.0b593b29c51bcp+4, -0x1.3ddf51285055ap+3, 0x1.12f0bcbe3fa44p+3, -0x1.d4ebfbf56d996p+2, 0x1.d31827f76dc61p+1, -0x1.6bf237312f18dp+0, 0x1.d1d5c0ac4dc0cp-1, -0x1.794e93c6506ddp-2, -0x1.2e59e90e0a11dp-6, 0x1.26fbfe966bb82p-5, -0x1.e662faa96110fp-10, -0x1.a81802ebf94f1p-17, -0x0p+0};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0, 0x1.9024e0f887aa3p-3, -0x1.3caa56e1c68fap+0, 0x1.947e636a9e374p+1, -0x1.033a79f260cefp+2, 0x1.51b6c9e0d0443p+1, -0x1.0bd62fc1e0455p+0, 0x1.028bee5b6619fp+0, -0x1.1620d9bfc03ebp+0, 0x1.b5ef819dccd9ap-2, -0x1.b7954b06be8afp-6, 0x1.054d18d1cc90cp-4, -0x1.4817258dd2847p-5, -0x1.8ce86e181d425p-6, 0x1.2926b8981e2a7p-6, -0x1.20ae937e7a93p-9, -0x1.e260b0ee2a093p-16, 0x0p+0};
-            }
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0L, 0x8.e97dfd611ca4d0fp-7L, 0xd.8db290080f07364p-4L, 0xc.5846ae6a5156a59p-6L, -0xa.5778b63f3337b8dp-6L, 0xf.e8c3bf889c5f1c6p-8L, -0xb.f7438497d12158fp-11L, -0x8.4bac424d7b02898p-10L, 0x9.e9f7b9c451d6f5p-11L, -0x9.48a3a10eab88924p-13L, 0xd.99d6667a3f8ded1p-18L, 0xb.f324c66deeea6e7p-19L, -0xa.9fca4a76f894114p-22L, -0xa.c60ec4704d98582p-27L, 0x9.3c5d096e124d267p-32L, -0xb.82d3d26c1a28344p-41L, -0xa.7da7733c7d070cap-55L, -0x0p+0L};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0L, 0x9.5c87bb838049b9dp-5L, 0xd.7cb5c081bad7186p-4L, -0xe.9e0b58b5d43cc82p-3L, 0x8.b480196f467d6c9p-3L, -0x8.fa79b9347fb9e82p-4L, 0xc.16492b5387c74b6p-6L, -0xa.a074df53e3990b8p-10L, -0xa.4c20e2aa7f68ebp-9L, 0xc.b51b2032f93e669p-11L, 0x8.624a49ef2d3764bp-14L, -0xd.ac97ddbdf20daf5p-15L, 0xc.e9f84df067536c7p-19L, 0xc.2b15781c45bef81p-26L, -0x8.9e617069a792bafp-27L, 0x9.11a70176c31860ap-37L, 0x8.4322509068f7b78p-50L, 0x0p+0L};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0L, 0xf.260071b0fe33d17p-4L, -0xd.56b7feaebbf8a9ep-3L, 0x8.9ae2bb88f3384cep-5L, 0xa.da0a2a7f84ab917p-4L, -0xe.495d3bd933d14bbp-7L, -0xa.7807516169b18a5p-5L, 0xb.0d523cfcee33daap-5L, -0xb.33b0ca13144b196p-6L, 0xb.91a80bdac698e63p-8L, -0xc.2e2fa52249396c6p-13L, -0x9.5d98c77d2691ac4p-12L, 0xd.9eb9f40c72e4aacp-15L, 0xd.e51f9378ca67c3cp-20L, -0x9.30ec4a3e5b93bbap-23L, 0x9.b349d2319134721p-31L, 0x8.d4c83032948f76p-43L, -0x0p+0L};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0L, 0x9.3eb6f9b342d3cadp-2L, -0x9.6f6bcf20fed8622p+0L, 0xf.3cfebe058e075ecp+0L, -0x9.8250d10852fce74p+0L, -0xf.7fe92b9d54d57e6p-1L, 0xb.e7397ee165c88c5p+1L, -0xc.c2f80cb639729f3p+1L, 0xe.9e7d603d4e95463p+0L, -0xf.0d127c23953405cp-2L, -0xc.dc2b1debe3ebee3p-5L, 0xf.f23b371fd7a9d87p-5L, -0xb.9f896a0aaf9ad9fp-7L, -0x9.06eefb2cf7284e3p-13L, 0xf.fe947d9a005fa2fp-15L, -0xf.d41bc469fbc68cdp-23L, -0xe.63ca53b72f8b2fep-34L, -0x0p+0L};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0L, 0xe.3e7687b3575667ep-2L, -0x9.55c64e409297236p+1L, 0xa.6fb426f6f2369dp+2L, -0xd.79dfca4eb15ce04p+2L, 0xc.7758bdf6899e1b4p+2L, -0xa.a0f4e13c13724e9p+2L, 0x8.97523e306f6022p+2L, -0x9.ae458390a70a077p+1L, 0xe.c14f0d3b14410dep-2L, 0xb.4eb74e107b9e597p-2L, -0x8.11ab10c2a7777ccp-2L, 0xd.a11921dc5a34834p-5L, -0x9.71481cc51ff17e4p-11L, -0x9.15a712cc6a2586fp-11L, 0xb.2a66fab9c3a5b39p-19L, 0xa.1f388f33c339298p-29L, 0x0p+0L};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0L, 0x8.b0bd27cec42baaep-1L, -0xc.a6ce29a51469f7p+1L, 0xe.e875b553b7fed21p+2L, -0x8.b460223e0db7486p+3L, 0x9.260ce023803fb4p+2L, -0x8.0b534248f26c38ep-3L, -0xe.4a769455d07a8e6p-1L, 0xb.34e0464a91798aep+0L, -0xc.46e522b79a2b2aep+1L, 0xd.cac6bbf1c2d48b2p+1L, -0xf.6675d5b02fa596cp+0L, 0xf.a1baeb32671a172p-2L, -0x9.56f2eb0622c089cp-6L, -0xa.48f8bc672b2306bp-7L, 0xa.de66ef632f29e0ep-14L, 0x9.cc1b3831671b9dbp-23L, 0x0p+0L};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0L, 0x9.c20a3af4d1b1cfep-2L, -0xe.e9e2d50ce2972e4p+0L, 0x9.81a94d147237d62p+2L, -0xd.436cf5db76e1e52p+2L, 0xb.e873627120b85ap+2L, -0x9.2e421ce96fc4fd3p+2L, 0xf.ad9f0d64cb33437p+1L, -0xc.0af702e42f45538p+1L, 0xe.522417a11b52a8bp+0L, -0x8.28412ef63ad4b3p+0L, 0x8.f76545661d3c9p-1L, -0xb.6fb4b2be4b96476p-3L, 0xb.ad3d633be277714p-8L, 0xf.5ea4f9c08644463p-8L, -0xa.1a21b970db7e3c3p-13L, -0x9.01322c3635dc8d8p-21L, 0x0p+0L};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0L, 0x8.20fbacf4315510dp-3L, -0xc.b7f3caa1ca84594p-1L, 0x8.253feadaf2c91fcp+1L, -0xa.e2f6f290d572f2cp+1L, 0x8.5ac9d94e28ddf7fp+1L, -0x9.eefa894282acd81p+0L, 0x8.9785e5f1fd2220dp+0L, -0xe.a75fdfab6ccb19fp-1L, 0xe.98c13fbb6e30aacp-2L, -0xb.5f91b98978c679ep-3L, 0xe.8eae05626e0638ap-4L, -0xb.ca749e32836e5f1p-5L, -0x9.72cf4870508e45cp-9L, 0x9.37dff4b35dc1001p-8L, -0xf.3317d54b0887a0cp-13L, -0xd.40c0175fca78546p-20L, -0x0p+0L};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0L, 0xc.812707c43d519efp-6L, -0x9.e552b70e347cfbdp-3L, 0xc.a3f31b54f1b9fa4p-2L, -0x8.19d3cf93067786bp-1L, 0xa.8db64f068221badp-2L, -0x8.5eb17e0f022abcep-3L, 0x8.145f72db30cf502p-3L, -0x8.b106cdfe01f5b31p-3L, 0xd.af7c0cee66cd13ep-5L, -0xd.bcaa5835f4575cbp-9L, 0x8.2a68c68e64863cdp-7L, -0xa.40b92c6e94234bfp-8L, -0xc.674370c0ea12a57p-9L, 0x9.4935c4c0f1539cfp-9L, -0x9.05749bf3d4982dep-12L, -0xf.1305877150497c2p-19L, 0x0p+0L};
-            }
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.1d2fbfac23949a1e129ec9f8391bp-4Q, 0x1.b1b6520101e0e6c7ddaa9da59f23p-1Q, 0x1.8b08d5cd4a2ad4b181244736a713p-3Q, -0x1.4aef16c7e666f719f7698e178af1p-3Q, 0x1.fd1877f1138be38ba53889d724ecp-5Q, -0x1.7ee87092fa242b1ef789aaf8def8p-8Q, -0x1.09758849af60512fff4fa06073a6p-7Q, 0x1.3d3ef7388a3ade9f5adf4b3f580dp-8Q, -0x1.29147421d57112477f4b7b3491f7p-10Q, 0x1.b33acccf47f1bda17f46b8106497p-15Q, 0x1.7e6498cdbddd4dce209effce7062p-16Q, -0x1.53f9494edf1282277c1de6dc67e4p-19Q, -0x1.58c1d88e09b30b0364784ebc1f68p-24Q, 0x1.278ba12dc249a4cd49c8d69ab623p-29Q, -0x1.705a7a4d83450688cb9e189ad73ep-38Q, -0x1.4fb4ee678fa0e1946f2bc7ed6f9ap-52Q, 0x0p+0Q};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.2b90f770700937399f9f525fd17p-2Q, 0x1.af96b810375ae30c4c41bf8dddd3p-1Q, -0x1.d3c16b16ba8799042d28d9c49845p+0Q, 0x1.1690032de8cfad91fdf041ea0eb6p+0Q, -0x1.1f4f37268ff73d0393fe0f67790ep-1Q, 0x1.82c9256a70f8e96c68d16f2e3327p-3Q, -0x1.540e9bea7c732170245209a302fbp-7Q, -0x1.49841c554fed1d5f2443e15a5a95p-6Q, 0x1.96a364065f27ccd19657d67cdf64p-8Q, 0x1.0c49493de5a6ec95d0bb4c3aca89p-11Q, -0x1.b592fbb7be41b5e92f003f6109fcp-12Q, 0x1.9d3f09be0cea6d8d6f8ed455255ap-16Q, 0x1.8562af0388b7df01536ccb66a5b4p-23Q, -0x1.13cc2e0d34f2575dd283b068f4bap-24Q, 0x1.2234e02ed8630c149658a9630026p-34Q, 0x1.08644a120d1ef6f0d4b961ae1879p-47Q, 0x0p+0Q};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.e4c00e361fc67a2e12b083b2df48p-1Q, -0x1.aad6ffd5d77f153c17f1c8823935p+0Q, 0x1.135c57711e67099c1758b9c717c8p-2Q, 0x1.5b41454ff095722d0f803ea68127p-1Q, -0x1.c92ba77b267a297500d5b5d44785p-4Q, -0x1.4f00ea2c2d363149504e045fbe84p-2Q, 0x1.61aa479f9dc67b53226c771010fp-2Q, -0x1.667619426289632c2e8907dc1851p-3Q, 0x1.7235017b58d31cc6ca2ab84f7b8bp-5Q, -0x1.85c5f4a449272d8bf24d90db58c1p-10Q, -0x1.2bb318efa4d23587f50785ea34e5p-9Q, 0x1.b3d73e818e5c9557fa6b95207f02p-12Q, 0x1.bca3f26f194cf877e2358ca6efddp-17Q, -0x1.261d8947cb7277733f476ea3b7dfp-20Q, 0x1.36693a4632268e426c40140353cep-28Q, 0x1.1a9906065291eec094ff6b8172d8p-40Q, 0x0p+0Q};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.27d6df36685a79598b6c86ce474dp+1Q, -0x1.2ded79e41fdb0c43d1210e12de17p+3Q, 0x1.e79fd7c0b1c0ebd84f460885ecf3p+3Q, -0x1.304a1a210a5f9ce8bc8b8a0cdf19p+3Q, -0x1.effd2573aa9aafcb53e588a096b7p+2Q, 0x1.7ce72fdc2cb91189ae6d5e090c6bp+4Q, -0x1.985f0196c72e53e6d1cfdee84e02p+4Q, 0x1.d3cfac07a9d2a8c51198c074937dp+3Q, -0x1.e1a24f8472a680b7d24d058147a3p+1Q, -0x1.9b8563bd7c7d7dc5768ba3df017ep-2Q, 0x1.fe4766e3faf53b0d124828083686p-2Q, -0x1.73f12d4155f35b3e8452b4ff00abp-4Q, -0x1.20dddf659ee509c6befdf1c7addep-10Q, 0x1.ffd28fb3400bf45efe5c328fc188p-12Q, -0x1.fa83788d3f78d19a901b7477bae6p-20Q, -0x1.cc794a76e5f165fc8108c92b057bp-31Q, 0x0p+0Q};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.c7ced0f66aeaccfcda16588f9d75p+1Q, -0x1.2ab8c9c81252e46b55777de43246p+4Q, 0x1.4df684dede46d3a014591fcfc934p+5Q, -0x1.af3bf949d62b9c07b05b4ac4bf21p+5Q, 0x1.8eeb17bed133c367f65a67fc6e9fp+5Q, -0x1.541e9c27826e49d24f626bb1a338p+5Q, 0x1.12ea47c60dec043f14d3664c7b9cp+5Q, -0x1.35c8b07214e140ed7f1d446f3113p+4Q, 0x1.d829e1a7628821bc837255b88e76p+1Q, 0x1.69d6e9c20f73cb2d14ff7351adb6p+1Q, -0x1.0235621854eeef97bfd3d4e3b1cp+1Q, 0x1.b423243b8b46906701ef92e0fa6p-2Q, -0x1.2e290398a3fe2fc8cc3aebacf78cp-8Q, -0x1.22b4e2598d44b0dd2f4a293dacc9p-8Q, 0x1.654cdf573874b672ebfe3509d857p-16Q, 0x1.43e711e67867252f78e7e45afce7p-26Q, 0x0p+0Q};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0Q, 0x1.1617a4f9d885755cd3477307254fp+2Q, -0x1.94d9c534a28d3ee0a8bf210cb612p+4Q, 0x1.dd0eb6aa76ffda42c87706ac442ap+5Q, -0x1.168c0447c1b6e90c330602b02462p+6Q, 0x1.24c19c047007f67f0d2fc486ec63p+5Q, -0x1.016a68491e4d871ca5058cc8b9fbp+0Q, -0x1.c94ed28aba0f51cc92c5b4dc5aacp+2Q, 0x1.669c08c9522f315c7b041fb5fb05p+3Q, -0x1.88dca456f345655b7cb4359a3262p+4Q, 0x1.b958d77e385a9163a2eb3b4f73aep+4Q, -0x1.eccebab605f4b2d725512d8939ecp+3Q, 0x1.f4375d664ce342e4e51867996bcdp+1Q, -0x1.2ade5d60c45811382f7ff19a5bd5p-3Q, -0x1.491f178ce56460d544cbe167fd8cp-4Q, 0x1.5bccddec65e53c1b0416c330319fp-11Q, 0x1.398367062ce373b6810676d67904p-20Q, 0x0p+0Q};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0Q, 0x1.3841475e9a3639fcb27c2a85a863p+1Q, -0x1.dd3c5aa19c52e5c8a273f6da1b5ap+3Q, 0x1.303529a28e46fac3a8f56ea5a2b3p+5Q, -0x1.a86d9ebb6edc3ca33aa7af7132e4p+5Q, 0x1.7d0e6c4e24170b40a4b9574c4b78p+5Q, -0x1.25c8439d2df89fa5007905a011dap+5Q, 0x1.f5b3e1ac9966686ed844c7042856p+4Q, -0x1.815ee05c85e8aa704180612d3a88p+4Q, 0x1.ca4482f4236a5516d7f638f2b575p+3Q, -0x1.050825dec75a966028608d12e5c4p+3Q, 0x1.1eeca8acc3a791ffedf80be8793bp+2Q, -0x1.6df69657c972c8ebec75c924bb61p+0Q, 0x1.75a7ac677c4eee273d03fc609c7dp-5Q, 0x1.ebd49f3810c888c69855752e166p-5Q, -0x1.4344372e1b6fc786ddf90f275fd2p-10Q, -0x1.20264586c6bb91b0aa0b4d170d57p-18Q, 0x0p+0Q};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0Q, 0x1.041f759e862aa2196b99e32b0e5p+0Q, -0x1.96fe795439508b28db4265486c81p+2Q, 0x1.04a7fd5b5e5923f7f627bd6af411p+4Q, -0x1.5c5ede521aae5e58438f3722aadep+4Q, 0x1.0b593b29c51bbefd0a21a469361ap+4Q, -0x1.3ddf512850559b028d83098aa4f2p+3Q, 0x1.12f0bcbe3fa44419a6b52304dc22p+3Q, -0x1.d4ebfbf56d99633e38e5753902fdp+2Q, 0x1.d31827f76dc61557ae5c1ea99bcdp+1Q, -0x1.6bf237312f18cf3b573ffc6eb123p+0Q, 0x1.d1d5c0ac4dc0c7147f916f90f5c1p-1Q, -0x1.794e93c6506dcbe26714d9f89e44p-2Q, -0x1.2e59e90e0a11c8b7ce9f9105aca7p-6Q, 0x1.26fbfe966bb82001d50ae928dc43p-5Q, -0x1.e662faa96110f417469ce785ece9p-10Q, -0x1.a81802ebf94f0a8bc8124e2acfbp-17Q, 0x0p+0Q};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0Q, 0x1.9024e0f887aa33deb80194db4775p-3Q, -0x1.3caa56e1c68f9f7ad07fd686ffdbp+0Q, 0x1.947e636a9e373f489450f999fe93p+1Q, -0x1.033a79f260cef0d616212b14afddp+2Q, 0x1.51b6c9e0d0443759a67a3c3505fdp+1Q, -0x1.0bd62fc1e045579c86e940e51c15p+0Q, 0x1.028bee5b6619ea0406791e99a571p+0Q, -0x1.1620d9bfc03eb662d8d654bb6c17p+0Q, 0x1.b5ef819dccd9a27cb2716f32a404p-2Q, -0x1.b7954b06be8aeb961960232f51e9p-6Q, 0x1.054d18d1cc90c79a1ef036069b3dp-4Q, -0x1.4817258dd284697ebc00b788ccd7p-5Q, -0x1.8ce86e181d4254ae37719aa28183p-6Q, 0x1.2926b8981e2a739eefaa1e5b0722p-6Q, -0x1.20ae937e7a9305bbde13268a4994p-9Q, -0x1.e260b0ee2a092f8355b87bfdf959p-16Q, 0x0p+0Q};
-            }
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            if constexpr (order == 0) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0696256148532700351919396744932899458901475071882009455460949442257725090643"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.847094118712392865488445491666448260772283771603129862851579519790390191884"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.192887945487446735108207067592716438385147148387205741175709003694874991303"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.161588838553871279142256267689733836106164148233593303014435155929549184904"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0621454565631309617634380881808335928424960159357894362352948406059776368030"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00584271191016988667489934317676681761380261859736020254107802203440485911830"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00810116915396986484284110901604422633398896546175619238854935214695602535306"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00484078918138035149158848553294039923334976019542221808517285604431896830998"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00113326987089607350360311514735367410308696721786347944018825854440169314785"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000518834218559123344579363088412935129165280069792765898378420125485731010746"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000227923963427004781576572210149586228991148638291199976434901264070906009219"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000253300201030598522589097875316626630820822335580422623437912828366256338066"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000802700432516996219234776794962786936078351284525549608976066927226092457516"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000215037600823040848531416812145312700229132524083435563752554400656355171355"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000523461705899403093230911172363595454183744690618924167900623489664585671892"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000291179201205891612682286686378360986960244052826956539582335356631085936448"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 1) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.292545191037796939535389393392524159619768256766940538370253353709461193032"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.842946769694824537045009424862247504440189060559035409366548153562971046333"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.82717007927797538158634749745144900658761906951781067368239430170496580026"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.08813495512805388191036942833223671123809253137161269595551241180555412336"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.561151240784950357351319288602199217315277177939018273801699428225616351849"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.188860218344526891969457899968714396869941678733540325124502082703253093959"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0103777180965810325757147992456275086095651002024262019464570618682172893560"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0201120640460875141204975265352055179708974180844365324656095077183481665071"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00620480720533278240593000416203558121866225849233783767746501903652779797358"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000511715457593831878348526994379850228214262314833874209020963369744116177094"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000417303231628420130847533411474569395038335447444917096887081609399824377911"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000246313954834336786578230076000285162282668339295707375389296462305068325569"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000181321745272135394237503981158619963539109967763295911042193620477541392180"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000642141275320865350440248672780732024814675393949502653848285464530637503456"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000659853289473506178162438806415358166040221310868614460485355680895239971041"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000733834535433323085982655900391187245584811969936387919615025045530814656992"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 2) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.946777767283390540714404221584615079023092608593179874933591611929424472485"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.66734312983271267309321411121395907583555820122567011112376971940996707956"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.268906942633839773948889603119308083663479474183417680672346331112533372730"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.678232351310991258941508584688642891898119286261551673777759411644213054589"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.111613897536158060295536493503011833000297341597327636552216220361799209380"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.327151926943136388570224093819464516869683572537433435414357010300674438746"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.345376128308493052665256776473446621249215438981458413871842565755981610451"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.175029942835241930595606890611047181166656164868469200496810519729335464519"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0451912907544972500160407679210623907538006067792182784497573909710514110903"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00148686700510683159736033420530033526602254575192174933907208287640696148334"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00228652648349626930958233420749265339034884848058225128735489316309216194635"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000415650174634043890487751208209411279937212554767153184423913890865016834975"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000132513170838045914618299238086704647297885466647476958534437752575150892279"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000109566515677943851419827253312757926681754226925567626886322889119467587352"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000451707521924643308252924541765504862848358919185132320746715765398014639333"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000100398888555583838447015712041044761982662545295143252368229865482374008093"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 3) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.31124487072584709340072024375652751167903029344934811013210724247867834712"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.43523878627351700486667408986119165102766488328680852307793395602884092368"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("15.23826205859770997419029499536885930324282552790731045653500894195106217230"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.50904566243388026482185821161121048927181414560909106839809459077939567212"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.74982582374142746596539847819058427772645564907288598203930173309437241112"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("23.80644212728254095208630893797731947546863789816665646941416033108845852560"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-25.52319487474132573315598925827481047528889709949317322024171789375930496050"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("14.61910058495285111510583787914644598320193823700758034804561275077288093820"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.76276582686596230192956587364009471111423882274083500758285711718430914481"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.401876028480840022977724595683369746855848802187118863206831503976422808900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.498319251694501402266194337927777390492533960487059487842842210706425452006"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0908061759740775534638772529734415696617219068242862250162791584120467567508"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00110193897253809208118839003583409411342268641822896346372378981763645701667"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000488111977759341608153274160279547453053433093120482116238865902413969365260"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000188691004449025030399350421194685076340345889651763665155607041691780427844"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000837596949144929524562460249627191951019750983422579043777172865056887183216"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 4) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.56099903137313447653308073719069094628298405133690563906561861936445946007"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-18.67011430886230370235720362402145866382565255864894062875836808783810172070"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("41.74537061801752618764215796492553160234168704484092726499577820178240950150"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-53.90428407368513143095733499969054312179860229999410756267069469773697487590"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("49.86479138446745347495028288278129648962436375452866744453087449252422749480"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-42.51494627825539832489623511405198662612329830348598981334872895902788851530"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("34.36439470987306965384334763928109227423995285653319098010560258917408804280"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-19.36149639666662401531934915671584710840660950619246136186169380992926261930"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.68877812073793714221449969323656655140811213570309303147472950766460448556"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.82687112784961267420163066364729873031830257798046834667883219375131634861"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.01725412548136472359247020220053150679272256461259072142878792076970321518"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.425915304312019461782564152045098653193242220169129362972564850123877163104"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00461059892462853652486233333670046935605106056900099120735719921725474826272"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00443583036535695045092535332549546407656776796969226954011005583519642324338"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000212967564409202157603357608120205592853860427112088867632348335621428459043"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000188536136927150567144741756924115740343376900701049770411358310019917707856"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 5) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.34519314192774371644605664344260685807624755151402674229796990772442490669"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-25.30316658554586670195060554724977775864649185540159313706154605487824252430"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("59.63218434501321241686227040141305669678309492280566274270121970853125985750"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-69.63673507804717481631012221036570369169261940901946481187737315982813252500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("36.59453586069957542305839900792960952397807013166550399544566076698109838520"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.00552989754787890241812019217185423330772733818008108791628359534655241737"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.14543593928850838676384113079945586921929171803713962006454488900252833519"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("11.20654715843691044532849119891603196174261061865084786297107780266854541590"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-24.55386766400291639497667909532438173366128839958254164111061988488776479890"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("27.58418988518466039332570510309944494563540512877954948263846939300864839690"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-15.40023551513117748173055818458330381918522055139888794492596135452925084020"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.90793960089811251141014062726261819004190764494555441923947299947294357551"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.145931939616769342677381879905952490456893639361103035834837241907687647570"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0803519172607930217143096597939609700610595254316391845465369362291239673402"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000663376352849585270549158082005899457474231838909594090590164906243989945765"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000116792802055684000576004901649051578220621239562395324237331611330461969728"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 6) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.43949215049035378308490877112616480587247519253349272700089974373761727070"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-14.91361743511751278653863337775082100851257612848163914659667962039370407430"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("38.02595831867881537937530443404440268525161384656893310351288920599098373240"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-53.05352541381901538280530176799613503869273806435001792774565773108485860860"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("47.63204251334798800088842822439490203451348559647805617494608965893769108390"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-36.72278521343748975726593618407350035873027478333718779024037203624257707460"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("31.35641639157838698914459960374580961178260675889546093721185892770212198730"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-24.08566318647221270199387206585348313707566820901513697285058134722858155000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("14.32086322482366348310210031894559072891597107117636756749550089821175221100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-8.15724462043256685901583341088487623405631051772335513386812463292410806832"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.48319451209555908109543430241568887648627099692558144854507468628906508116"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.42954387324557353924315901131597022588839567829311825849808138225813793539"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0456121794958422788519835738614979042067103492896491552781823773644117194263"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0600379094835484277448500775653734021516869903849852917021361921275127990832"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00123316370766296458175735033761430852810590026894516671661974149487692611779"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000429376212343184311613788702973769675152078312600917651519873431746001425928"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 7) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.01610503311364167160627137764879687271588589977337586555528700566771231261"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.35928185677517694205349753594529349921775157958594734217344676184083432133"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("16.29101310435141502366280370334959338566491174925988910204852058573624530770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-21.77316124031030816094586803202252059552525483663335766522914705661431629930"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("16.70928493801487468593777022092645595574965917216718445219727297028380055500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.93351037858763008636351351386408163754727545153280350373395004801729390569"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.59188687475137459206298080378293728057617745867309534594204113820751716392"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.32690333335485473282043083732510305617086761800316899520505182249948309741"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.64917468625530775745714112854788870052100478150662596792140805409798695237"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.42166466666012357755455417666976389843036696424169510073074551625991444526"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.909833928139848029659705433844716551575919061966592740387936617767990646124"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.368463810900818519321280729699948238382245337243194077152888098658300603538"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0184540534902747235287786613095163827842721391935005620122745696525182529649"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0360088322080320960591978261837204402906245566453303385097283622763009148578"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00185541777531833871298150644744023226659198738569918082665820219229654776018"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000126389799887751449655010004416467695567661727273854980326583025983179615470"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 8) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.195382840714008222445649562861088516286064981461948780814133345930973823658"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.23697417270756070794757091967677027603167042250757849222269393098384194621"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.16010706621130486269935853293254242082033173364580217315573625619258790152"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.05044411344282111665932979112008908801732860080823387948554260440261464757"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.63839076497291256523926291558126191854618618017387332992219855643874357679"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.04623697741796683485007131051068458751031503463108641697374490811821670148"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.00994767886559314051425312348881627025613387213269219272738325207774312849"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.08643876010341497975910071082821695937290873893825930817786907767606917664"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.427671456581458673009899734932815948658546455375010876404838027129297913818"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0268300278357648758353382533868083591820649404851508751125983578913516081871"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0637942285073089320624911876442649124426662264770688199203469027353144526797"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0400500997044024766957707475186007575121602332713762255038636186221048809222"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0242253375185620584577236293255475747352363289859909376495538304199524801451"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0181366732290110494820691728220505559010664322036613445274186399424581173253"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00220246839966366946271442320741368580934032927301220467330879016842440794250"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000287519514407257853644446887092547399712525693691776728798621645433043384651"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-        }
-    }
-    if constexpr (p == 10) {
-        if constexpr (std::is_same_v<Real, float>) {
-            if constexpr (order == 0) {
-                return {0x0p+0f, 0x1.12cb0ap-5f, 0x1.4e2c28p-1f, 0x1.1c4636p-1f, -0x1.85d2eep-2f, 0x1.9e3daep-3f, -0x1.494bcp-4f, 0x1.1d23ep-6f, 0x1.d4ed16p-10f, -0x1.2885ecp-9f, 0x1.94f202p-12f, 0x1.44e94ep-14f, -0x1.b37dfap-16f, 0x1.403906p-24f, 0x1.c9437p-24f, -0x1.58dbb8p-28f, 0x1.db3584p-37f, 0x1.afee7cp-44f, -0x1.098874p-59f, -0x0p+0f};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.43cfccp-3f, 0x1.f5f9c2p-1f, -0x1.94bc28p+0f, 0x1.61584ep-1f, -0x1.a2cb68p-2f, 0x1.eef0eap-3f, -0x1.ac223p-4f, 0x1.c84ec2p-6f, -0x1.213456p-8f, 0x1.2c315ap-10f, -0x1.f37546p-12f, 0x1.ce036p-15f, 0x1.06ba9ap-17f, 0x1.2eea96p-21f, 0x1.f125fap-26f, -0x1.51db7ap-33f, -0x1.3ced9ep-40f, 0x1.85b824p-55f, 0x0p+0f};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0f, 0x1.2d6cb8p-1f, -0x1.01b00cp-2f, -0x1.0fd09ap+1f, 0x1.8bd77ap+1f, -0x1.c8684ep+0f, 0x1.6e6d86p-2f, 0x1.86e852p-2f, -0x1.9dcbe6p-2f, 0x1.55c762p-3f, -0x1.35a482p-6f, -0x1.51b88cp-7f, 0x1.076728p-8f, -0x1.67961ap-12f, -0x1.2b4a08p-15f, 0x1.bb4b6cp-19f, 0x1.3f418cp-28f, -0x1.0d99c2p-32f, 0x1.4b9c06p-46f, 0x0p+0f};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0f, 0x1.a8daep+0f, -0x1.8d688ep+2f, 0x1.317cc4p+3f, -0x1.00fa12p+3f, 0x1.9e984cp+1f, 0x1.0dcc3cp+1f, -0x1.41a436p+2f, 0x1.075a46p+2f, -0x1.9984ccp+0f, 0x1.9cf2e8p-5f, 0x1.c91578p-3f, -0x1.60b8bp-4f, 0x1.32422ap-7f, 0x1.dd5da6p-11f, -0x1.351528p-13f, -0x1.03c426p-22f, 0x1.7713ap-26f, -0x1.cd96fcp-39f, -0x0p+0f};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0f, 0x1.a04f8p+1f, -0x1.18f0a4p+4f, 0x1.4ce384p+5f, -0x1.dc75fap+5f, 0x1.fdbc98p+5f, -0x1.eefc0cp+5f, 0x1.b92a7cp+5f, -0x1.2299d6p+5f, 0x1.6502b8p+3f, 0x1.11f34p+2f, -0x1.73b0a4p+2f, 0x1.244d46p+1f, -0x1.35466cp-2f, -0x1.fc20c8p-6f, 0x1.0d9c8cp-7f, 0x1.a4010cp-19f, -0x1.49b0cap-19f, 0x1.962a6ep-31f, -0x0p+0f};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0f, 0x1.55886ep+2f, -0x1.09d96p+5f, 0x1.505f98p+6f, -0x1.96ec36p+6f, 0x1.17b23p+5f, 0x1.fc1722p+5f, -0x1.b35f4ap+6f, 0x1.d17f22p+6f, -0x1.12118cp+7f, 0x1.207a74p+7f, -0x1.934736p+6f, 0x1.3fa55cp+5f, -0x1.959602p+2f, -0x1.9505e8p-1f, 0x1.43d264p-2f, -0x1.38e018p-10f, -0x1.968e84p-13f, 0x1.f5ed4cp-24f, -0x0p+0f};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0f, 0x1.f3cda2p+1f, -0x1.9eeda2p+4f, 0x1.260fdap+6f, -0x1.d673d8p+6f, 0x1.f01b3p+6f, -0x1.addb2cp+6f, 0x1.7db87cp+6f, -0x1.3f986p+6f, 0x1.ae7316p+5f, -0x1.fb5cc4p+4f, 0x1.259afcp+4f, -0x1.fe186ep+2f, 0x1.4d0298p+0f, 0x1.a1f0a6p-2f, -0x1.40c0aep-3f, 0x1.ba72fap-9f, 0x1.c193f2p-13f, -0x1.16b49ap-22f, 0x0p+0f};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0f, 0x1.3586dap+1f, -0x1.08fa64p+4f, 0x1.7c41fp+5f, -0x1.276b64p+6f, 0x1.14f1dp+6f, -0x1.83d54ap+5f, 0x1.4053c8p+5f, -0x1.209b54p+5f, 0x1.657834p+4f, -0x1.2ddf68p+3f, 0x1.38745p+2f, -0x1.4065c2p+1f, 0x1.6763c6p-4f, 0x1.181d4ep-1f, -0x1.87564p-3f, 0x1.843d22p-7f, 0x1.52be3cp-11f, -0x1.a79c62p-20f, 0x0p+0f};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0f, 0x1.7a3cf4p+0f, -0x1.48b25ep+3f, 0x1.cbd932p+4f, -0x1.37885ep+5f, 0x1.4db4fcp+4f, 0x1.74ac2ep+2f, -0x1.11ca3p+3f, 0x1.9fa6aap-4f, -0x1.8ceb32p+2f, 0x1.e686e4p+3f, -0x1.7e0b78p+3f, 0x1.7e1a34p+2f, -0x1.247b58p+2f, 0x1.b8a4e2p+1f, -0x1.4f17d6p+0f, 0x1.4b4084p-3f, 0x1.726478p-7f, -0x1.d74fd6p-15f, 0x0p+0f};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0f, 0x1.f6438ap-4f, -0x1.b7ba92p-1f, 0x1.3f509cp+1f, -0x1.eac616p+1f, 0x1.ae9244p+1f, -0x1.00d5dp+1f, 0x1.9413f4p+0f, -0x1.9bd984p+0f, 0x1.16aae2p+0f, -0x1.158768p-1f, 0x1.8145e4p-2f, -0x1.faf556p-3f, 0x1.8ec972p-4f, -0x1.49980ep-5f, 0x1.5730c4p-6f, -0x1.0952d6p-8f, -0x1.ce071ep-12f, 0x1.30a436p-18f, -0x0p+0f};
-            }
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0, 0x1.12cb0a33640b5p-5, 0x1.4e2c27be21e0ep-1, 0x1.1c4636ef189edp-1, -0x1.85d2edb33e46ep-2, 0x1.9e3dada7662aap-3, -0x1.494bbf8e53bfcp-4, 0x1.1d23df75685c9p-6, 0x1.d4ed15a068488p-10, -0x1.2885ec2406341p-9, 0x1.94f202846521cp-12, 0x1.44e94de53f6f6p-14, -0x1.b37df99b75f09p-16, 0x1.403905df41d32p-24, 0x1.c94370d7ecc92p-24, -0x1.58dbb791a7fb7p-28, 0x1.db358382953c4p-37, 0x1.afee7cd299cd6p-44, -0x1.0988745ca3ec4p-59, -0x0p+0};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0, 0x1.43cfcb9d73923p-3, 0x1.f5f9c20090df3p-1, -0x1.94bc27297b9f9p+0, 0x1.61584eb9fe3a6p-1, -0x1.a2cb67ff996a9p-2, 0x1.eef0eaaf4989ep-3, -0x1.ac22308c89e82p-4, 0x1.c84ec23c8cdbep-6, -0x1.213456d8479d6p-8, 0x1.2c315a17e4064p-10, -0x1.f375455c5c9e6p-12, 0x1.ce035ff90a79bp-15, 0x1.06ba9aa22e87cp-17, 0x1.2eea964fb1e8p-21, 0x1.f125f98e34b08p-26, -0x1.51db791710beap-33, -0x1.3ced9d37da5d3p-40, 0x1.85b82452d9269p-55, 0x0p+0};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0, 0x1.2d6cb779664d4p-1, -0x1.01b00cc8d5d06p-2, -0x1.0fd0995df5aa3p+1, 0x1.8bd77a675e828p+1, -0x1.c8684eac579b4p+0, 0x1.6e6d859b2e73p-2, 0x1.86e851ba85835p-2, -0x1.9dcbe6db37906p-2, 0x1.55c762fd5a0dfp-3, -0x1.35a481158ac34p-6, -0x1.51b88ceed7adep-7, 0x1.0767285c8f106p-8, -0x1.67961ae7bb9ap-12, -0x1.2b4a0836ed60bp-15, 0x1.bb4b6c6c9a6fbp-19, 0x1.3f418b80d3d45p-28, -0x1.0d99c100eff2ep-32, 0x1.4b9c0643323fbp-46, 0x0p+0};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0, 0x1.a8dadfc02dd04p+0, -0x1.8d688d31d04a4p+2, 0x1.317cc4a10faf4p+3, -0x1.00fa12867f491p+3, 0x1.9e984b48af592p+1, 0x1.0dcc3bbac5e09p+1, -0x1.41a435a1df481p+2, 0x1.075a464fd9704p+2, -0x1.9984cb75bad51p+0, 0x1.9cf2e7196d1ccp-5, 0x1.c915787e3612ep-3, -0x1.60b8b0c3b1139p-4, 0x1.324229742ef44p-7, 0x1.dd5da666efa59p-11, -0x1.351528a4bd817p-13, -0x1.03c4250827b69p-22, 0x1.77139f17861ebp-26, -0x1.cd96fccfe9f0bp-39, -0x0p+0};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0, 0x1.a04f8069ea8b5p+1, -0x1.18f0a34d9f68ep+4, 0x1.4ce3831796a62p+5, -0x1.dc75f9b0b9a1p+5, 0x1.fdbc97313e6edp+5, -0x1.eefc0cdda4efap+5, 0x1.b92a7c1b6a88ap+5, -0x1.2299d502734c4p+5, 0x1.6502b707871dfp+3, 0x1.11f33f4ede648p+2, -0x1.73b0a319e688ap+2, 0x1.244d452e76301p+1, -0x1.35466c5650c62p-2, -0x1.fc20c8dd92f1ap-6, 0x1.0d9c8b9d476f8p-7, 0x1.a4010b80e5496p-19, -0x1.49b0c99eb9c65p-19, 0x1.962a6dd57b7dbp-31, -0x0p+0};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0, 0x1.55886d2f64381p+2, -0x1.09d95f1cede32p+5, 0x1.505f98e4bf277p+6, -0x1.96ec354b30307p+6, 0x1.17b23075f801p+5, 0x1.fc17211fa4d6fp+5, -0x1.b35f4a36b31c4p+6, 0x1.d17f22f2480f9p+6, -0x1.12118c5678b4dp+7, 0x1.207a74ca5ad8cp+7, -0x1.934735f943482p+6, 0x1.3fa55ba9206e4p+5, -0x1.959601005ec55p+2, -0x1.9505e84d98e61p-1, 0x1.43d2632e32cd1p-2, -0x1.38e017336cd06p-10, -0x1.968e83ac595b9p-13, 0x1.f5ed4b124df3bp-24, -0x0p+0};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0, 0x1.f3cda2f9b1354p+1, -0x1.9eeda12641b62p+4, 0x1.260fdaadd19ebp+6, -0x1.d673d80eeade5p+6, 0x1.f01b2fa154d03p+6, -0x1.addb2c4ad791ep+6, 0x1.7db87bda6fdf9p+6, -0x1.3f9860f6c4906p+6, 0x1.ae731643e9199p+5, -0x1.fb5cc3351ebc1p+4, 0x1.259afcbb8804dp+4, -0x1.fe186e46030ap+2, 0x1.4d0298c218927p+0, 0x1.a1f0a66406a12p-2, -0x1.40c0addfd8554p-3, 0x1.ba72fac37f088p-9, 0x1.c193f16bb678ep-13, -0x1.16b4995bb4f07p-22, 0x0p+0};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0, 0x1.3586d9a9e0e3ep+1, -0x1.08fa63342ecc2p+4, 0x1.7c41f01d6960dp+5, -0x1.276b64d22e135p+6, 0x1.14f1cf74869cp+6, -0x1.83d54ac636b82p+5, 0x1.4053c8a2c8d3p+5, -0x1.209b538b18df2p+5, 0x1.65783340b3783p+4, -0x1.2ddf670e51dfdp+3, 0x1.38744fdae2125p+2, -0x1.4065c212ba5cp+1, 0x1.6763c5d11b775p-4, 0x1.181d4d676ea1fp-1, -0x1.87564028831fcp-3, 0x1.843d22529bb4ap-7, 0x1.52be3b0b8c7afp-11, -0x1.a79c626c8654fp-20, 0x0p+0};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0, 0x1.7a3cf471120ecp+0, -0x1.48b25e52d274bp+3, 0x1.cbd93276e7d59p+4, -0x1.37885d5242031p+5, 0x1.4db4fb7a5ecdcp+4, 0x1.74ac2dca21f56p+2, -0x1.11ca2f9f0b7dp+3, 0x1.9fa6aaf0c8d98p-4, -0x1.8ceb3288570cdp+2, 0x1.e686e3fbc3fbfp+3, -0x1.7e0b780d60232p+3, 0x1.7e1a3482e160cp+2, -0x1.247b57131543cp+2, 0x1.b8a4e1c96768dp+1, -0x1.4f17d502240a9p+0, 0x1.4b408438ac869p-3, 0x1.7264788c9473ep-7, -0x1.d74fd6a021548p-15, 0x0p+0};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0, 0x1.f6438a3a8846p-4, -0x1.b7ba9255f9c78p-1, 0x1.3f509b3842149p+1, -0x1.eac616f0d4f87p+1, 0x1.ae9244fef585dp+1, -0x1.00d5d03220f3cp+1, 0x1.9413f3bab26fdp+0, -0x1.9bd9847a10dd5p+0, 0x1.16aae27d18a67p+0, -0x1.1587682f48216p-1, 0x1.8145e3cc3cfccp-2, -0x1.faf556e68970ep-3, 0x1.8ec972676b06bp-4, -0x1.49980ed40883dp-5, 0x1.5730c48bae56ap-6, -0x1.0952d6b855c64p-8, -0x1.ce071dd8df1efp-12, 0x1.30a4361eb25b4p-18, -0x0p+0};
-            }
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0L, 0x8.9658519b205ab72p-8L, 0xa.71613df10f0723dp-4L, 0x8.e231b778c4f6662p-4L, -0xc.2e976d99f236ef3p-5L, 0xc.f1ed6d3b3154c33p-6L, -0xa.4a5dfc729dfe012p-7L, 0x8.e91efbab42e4488p-9L, 0xe.a768ad03424408ap-13L, -0x9.442f612031a0acp-12L, 0xc.a7901423290dc7ep-15L, 0xa.274a6f29fb7b195p-17L, -0xd.9befccdbaf8457bp-19L, 0xa.01c82efa0e991ep-27L, 0xe.4a1b86bf6648ca3p-27L, -0xa.c6ddbc8d3fdb61fp-31L, 0xe.d9ac1c14a9e22dfp-40L, 0xd.7f73e694ce6b23p-47L, -0x8.4c43a2e51f61f4ap-62L, -0x0p+0L};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0L, 0xa.1e7e5ceb9c91909p-6L, 0xf.afce100486f966ap-4L, -0xc.a5e1394bdcfcb6dp-3L, 0xb.0ac275cff1d33d6p-4L, -0xd.165b3ffccb5480ap-5L, 0xf.7787557a4c4f14ep-6L, -0xd.611184644f4100cp-7L, 0xe.427611e466df078p-9L, -0x9.09a2b6c23cead05p-11L, 0x9.618ad0bf2031fa3p-13L, -0xf.9baa2ae2e4f30dfp-15L, 0xe.701affc853cdb21p-18L, 0x8.35d4d511743e237p-20L, 0x9.7754b27d8f401bap-24L, 0xf.892fcc71a583f65p-29L, -0xa.8edbc8b885f4c32p-36L, -0x9.e76ce9bed2e946cp-43L, 0xc.2dc12296c934a42p-58L, 0x0p+0L};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0L, 0x9.6b65bbcb326a224p-4L, -0x8.0d806646ae83286p-5L, -0x8.7e84caefad51526p-2L, 0xc.5ebbd33af4141bap-2L, -0xe.43427562bcd9f08p-3L, 0xb.736c2cd97397c01p-5L, 0xc.37428dd42c1a763p-5L, -0xc.ee5f36d9bc83386p-5L, 0xa.ae3b17ead06fb26p-6L, -0x9.ad2408ac5619da4p-9L, -0xa.8dc46776bd6ee4dp-10L, 0x8.3b3942e4788322ap-11L, -0xb.3cb0d73ddccfdfep-15L, -0x9.5a5041b76b0571dp-18L, 0xd.da5b6364d37d7c6p-22L, 0x9.fa0c5c069ea261fp-31L, -0x8.6cce08077f97363p-35L, 0xa.5ce0321991fd8ep-49L, 0x0p+0L};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0L, 0xd.46d6fe016e82146p-3L, -0xc.6b44698e825210ap-1L, 0x9.8be625087d79ffdp+0L, -0x8.07d09433fa48997p+0L, 0xc.f4c25a457ac90c1p-2L, 0x8.6e61ddd62f0442fp-2L, -0xa.0d21ad0efa407b6p-1L, 0x8.3ad2327ecb81caap-1L, -0xc.cc265badd6a86efp-3L, 0xc.e79738cb68e5e97p-8L, 0xe.48abc3f1b09716ap-6L, -0xb.05c5861d889c6fap-7L, 0x9.92114ba177a20b1p-10L, 0xe.eaed33377d2c762p-14L, -0x9.a8a94525ec0bb0bp-16L, -0x8.1e2128413db47b5p-25L, 0xb.b89cf8bc30f58d6p-29L, -0xe.6cb7e67f4f857ddp-42L, -0x0p+0L};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0L, 0xd.027c034f545a722p-2L, -0x8.c7851a6cfb47268p+1L, 0xa.671c18bcb530f7bp+2L, -0xe.e3afcd85cd0820fp+2L, 0xf.ede4b989f376b43p+2L, -0xf.77e066ed277d141p+2L, 0xd.c953e0db5444e19p+2L, -0x9.14cea8139a61e4ep+2L, 0xb.2815b83c38efa28p+0L, 0x8.8f99fa76f323eadp-1L, -0xb.9d8518cf3444f4dp-1L, 0x9.226a2973b180497p-2L, -0x9.aa3362b28630f09p-5L, -0xf.e10646ec978cdc7p-9L, 0x8.6ce45cea3b7be89p-10L, 0xd.20085c072a4ae87p-22L, -0xa.4d864cf5ce32429p-22L, 0xc.b1536eabdbed537p-34L, -0x0p+0L};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0L, 0xa.ac43697b21c05d7p-1L, -0x8.4ecaf8e76f18fe7p+2L, 0xa.82fcc725f93bb38p+3L, -0xc.b761aa5981834ffp+3L, 0x8.bd9183afc008112p+2L, 0xf.e0b908fd26b79fbp+2L, -0xd.9afa51b598e1c25p+3L, 0xe.8bf91792407c46p+3L, -0x8.908c62b3c5a6a21p+4L, 0x9.03d3a652d6c5fe1p+4L, -0xc.9a39afca1a40e4p+3L, 0x9.fd2add490371c09p+2L, -0xc.acb00802f62a439p-1L, -0xc.a82f426cc7309e8p-4L, 0xa.1e93197196686f8p-5L, -0x9.c700b99b66830a5p-13L, -0xc.b4741d62cadc637p-16L, 0xf.af6a58926f9d684p-27L, -0x0p+0L};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0L, 0xf.9e6d17cd89aa012p-2L, -0xc.f76d09320db0f5ep+1L, 0x9.307ed56e8cf58f8p+3L, -0xe.b39ec07756f2504p+3L, 0xf.80d97d0aa681a95p+3L, -0xd.6ed96256bc8f10cp+3L, 0xb.edc3ded37efc53ap+3L, -0x9.fcc307b62482f39p+3L, 0xd.7398b21f48cc731p+2L, -0xf.dae619a8f5e0bb5p+1L, 0x9.2cd7e5dc4026b75p+1L, -0xf.f0c37230184fee7p-1L, 0xa.6814c610c493aa3p-3L, 0xd.0f8533203509157p-5L, -0xa.06056efec2aa1d8p-6L, 0xd.d397d61bf843e3dp-12L, 0xe.0c9f8b5db3c72d8p-16L, -0x8.b5a4cadda783993p-25L, 0x0p+0L};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0L, 0x9.ac36cd4f071eccfp-2L, -0x8.47d319a17660e21p+1L, 0xb.e20f80eb4b065edp+2L, -0x9.3b5b2691709a7f2p+3L, 0x8.a78e7ba434e03bep+3L, -0xc.1eaa5631b5c1221p+2L, 0xa.029e45164697e35p+2L, -0x9.04da9c58c6f9312p+2L, 0xb.2bc19a059bc163fp+1L, -0x9.6efb38728efe53fp+0L, 0x9.c3a27ed71092bccp-1L, -0xa.032e1095d2e022bp-2L, 0xb.3b1e2e88dbba717p-7L, 0x8.c0ea6b3b750f81fp-4L, -0xc.3ab2014418fdea7p-6L, 0xc.21e91294dda4d8cp-10L, 0xa.95f1d85c63d7aadp-14L, -0xd.3ce3136432a75eep-23L, 0x0p+0L};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0L, 0xb.d1e7a38890760ccp-3L, -0xa.4592f29693a58f2p+0L, 0xe.5ec993b73eacb21p+1L, -0x9.bc42ea921018403p+2L, 0xa.6da7dbd2f66dc91p+1L, 0xb.a5616e510faadd9p-1L, -0x8.8e517cf85be82f9p+0L, 0xc.fd35578646cc028p-7L, -0xc.67599442b866996p-1L, 0xf.34371fde1fdf9acp+0L, -0xb.f05bc06b0118d26p+0L, 0xb.f0d1a4170b05fe8p-1L, -0x9.23dab898aa1de5fp-1L, 0xd.c5270e4b3b4644bp-2L, -0xa.78bea8112054738p-3L, 0xa.5a0421c564344a9p-6L, 0xb.9323c464a39ee53p-10L, -0xe.ba7eb5010aa3e4p-18L, 0x0p+0L};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0L, 0xf.b21c51d44230049p-7L, -0xd.bdd492afce3bd22p-4L, 0x9.fa84d9c210a45adp-2L, -0xf.5630b786a7c34dfp-2L, 0xd.749227f7ac2e953p-2L, -0x8.06ae8191079dde4p-2L, 0xc.a09f9dd5937e42dp-3L, -0xc.decc23d086ea9cp-3L, 0x8.b55713e8c533b1cp-3L, -0x8.ac3b417a410ae11p-4L, 0xc.0a2f1e61e7e5e62p-5L, -0xf.d7aab7344b86da8p-6L, 0xc.764b933b583557ap-7L, -0xa.4cc076a0441e56ep-8L, 0xa.b986245d72b5275p-9L, -0x8.4a96b5c2ae31c5dp-11L, -0xe.7038eec6f8f774fp-15L, 0x9.8521b0f592d9c7fp-21L, -0x0p+0L};
-            }
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.12cb0a33640b56e423474a1328bap-5Q, 0x1.4e2c27be21e0e479b88ad4851607p-1Q, 0x1.1c4636ef189eccc399682014d9d6p-1Q, -0x1.85d2edb33e46dde58a5a504a9ab1p-2Q, 0x1.9e3dada7662a9865be6b99b24294p-3Q, -0x1.494bbf8e53bfc023fe7e0915ab63p-4Q, 0x1.1d23df75685c890f2df5ab229b96p-6Q, 0x1.d4ed15a06848811344377f87f7eap-10Q, -0x1.2885ec240634157f42540c2ec5a5p-9Q, 0x1.94f202846521b8fb6dee9352c088p-12Q, 0x1.44e94de53f6f632a67cbb5854d1fp-14Q, -0x1.b37df99b75f08af621654dd8f54ep-16Q, 0x1.403905df41d323c0c33072aaf3cp-24Q, 0x1.c94370d7ecc9194547661e1cf7cp-24Q, -0x1.58dbb791a7fb6c3e33eb2a850b1bp-28Q, 0x1.db358382953c45bea25d9891f3bcp-37Q, 0x1.afee7cd299cd64600d2193c416f4p-44Q, -0x1.0988745ca3ec3e945e33c4d42e22p-59Q, 0x0p+0Q};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.43cfcb9d739232114ccf7b42f286p-3Q, 0x1.f5f9c20090df2cd39669639ec7fdp-1Q, -0x1.94bc27297b9f96d98ca06b8b780fp+0Q, 0x1.61584eb9fe3a67acec590408bca7p-1Q, -0x1.a2cb67ff996a90130726bb551867p-2Q, 0x1.eef0eaaf4989e29be4ba95e2f12bp-3Q, -0x1.ac22308c89e820172f07afea77d8p-4Q, 0x1.c84ec23c8cdbe0f0d252ca4a5fdap-6Q, -0x1.213456d8479d5a0a002e8a35424cp-8Q, 0x1.2c315a17e4063f457d1b74aaa54fp-10Q, -0x1.f375455c5c9e61be4fa670796c8cp-12Q, 0x1.ce035ff90a79b6418f9714e02027p-15Q, 0x1.06ba9aa22e87c46e9b5b517bf9e8p-17Q, 0x1.2eea964fb1e803735b7cbdec445fp-21Q, 0x1.f125f98e34b07ec90a3117922ea9p-26Q, -0x1.51db791710be9863d69c55fb8f8fp-33Q, -0x1.3ced9d37da5d28d7002692ae731fp-40Q, 0x1.85b82452d92694835d294f84ac62p-55Q, 0x0p+0Q};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.2d6cb779664d44484073db45447cp-1Q, -0x1.01b00cc8d5d0650bb7d9e8758312p-2Q, -0x1.0fd0995df5aa2a4c5f39f93180c2p+1Q, 0x1.8bd77a675e82837408b645325bb2p+1Q, -0x1.c8684eac579b3e1019c502de8594p+0Q, 0x1.6e6d859b2e72f80278552877464cp-2Q, 0x1.86e851ba85834ec58a127f16fe28p-2Q, -0x1.9dcbe6db3790670c84be0eec2f7fp-2Q, 0x1.55c762fd5a0df64b9c06acd53195p-3Q, -0x1.35a481158ac33b4716b6e91c5435p-6Q, -0x1.51b88ceed7addc9a97168ddbed49p-7Q, 0x1.0767285c8f10645316c4c221fa2p-8Q, -0x1.67961ae7bb99fbfcc0d26144bc53p-12Q, -0x1.2b4a0836ed60ae3a1490ad53cc1ep-15Q, 0x1.bb4b6c6c9a6faf8c7dd84be23c4bp-19Q, 0x1.3f418b80d3d44c3e61fe90bb843bp-28Q, -0x1.0d99c100eff2e6c61779a485054cp-32Q, 0x1.4b9c0643323fb1c0ce2d07b0b092p-46Q, 0x0p+0Q};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.a8dadfc02dd0428b41cd0c1bb0afp+0Q, -0x1.8d688d31d04a4214094b65c4cddp+2Q, 0x1.317cc4a10faf3ff9c44aa07180dp+3Q, -0x1.00fa12867f49132d26f6109f1a1ep+3Q, 0x1.9e984b48af59218135976f585487p+1Q, 0x1.0dcc3bbac5e0885ef946fb573bd9p+1Q, -0x1.41a435a1df480f6b501eca7093bep+2Q, 0x1.075a464fd9703954dc501fa9230ap+2Q, -0x1.9984cb75bad50ddd23b7c6a931c3p+0Q, 0x1.9cf2e7196d1cbd2ef1ba36ca5473p-5Q, 0x1.c915787e3612e2d3277f4d8526a2p-3Q, -0x1.60b8b0c3b1138df4716646253571p-4Q, 0x1.324229742ef4416185466d935171p-7Q, 0x1.dd5da666efa58ec47474db0b6e86p-11Q, -0x1.351528a4bd8176153593c8a5a1a8p-13Q, -0x1.03c4250827b68f69b983f4479114p-22Q, 0x1.77139f17861eb1acd308dc031079p-26Q, -0x1.cd96fccfe9f0afba4ba09dac3a7dp-39Q, 0x0p+0Q};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.a04f8069ea8b4e447d853aa2b3fp+1Q, -0x1.18f0a34d9f68e4d06a24b5c8413dp+4Q, 0x1.4ce3831796a61ef6af32be9a023fp+5Q, -0x1.dc75f9b0b9a1041da91933762b9bp+5Q, 0x1.fdbc97313e6ed6865f9096ac8807p+5Q, -0x1.eefc0cdda4efa281b21fc89e970ap+5Q, 0x1.b92a7c1b6a889c31c867c0ce8c52p+5Q, -0x1.2299d502734c3c9b7e4c9a6f523fp+5Q, 0x1.6502b707871df45089990b5055fdp+3Q, 0x1.11f33f4ede647d59a412fb3857a3p+2Q, -0x1.73b0a319e6889e9aa2e82f2679b8p+2Q, 0x1.244d452e7630092d6c490c8cc448p+1Q, -0x1.35466c5650c61e120220d045b2f3p-2Q, -0x1.fc20c8dd92f19b8d6ed30b1d9872p-6Q, 0x1.0d9c8b9d476f7d129de2a5d13304p-7Q, 0x1.a4010b80e5495d0ed9331140ed28p-19Q, -0x1.49b0c99eb9c648511ea730b4e4dp-19Q, 0x1.962a6dd57b7daa6dc5023a314835p-31Q, 0x0p+0Q};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0Q, 0x1.55886d2f64380baeb961078fa176p+2Q, -0x1.09d95f1cede31fcd15d2c7fab39ep+5Q, 0x1.505f98e4bf27766f2f4d3b7ea8ddp+6Q, -0x1.96ec354b303069fd664614786911p+6Q, 0x1.17b23075f8010224c348afb3ebb9p+5Q, 0x1.fc17211fa4d6f3f6a32616561c88p+5Q, -0x1.b35f4a36b31c3849a4f062a53c98p+6Q, 0x1.d17f22f2480f88bf1a425e0d999bp+6Q, -0x1.12118c5678b4d442de8a0eef777p+7Q, 0x1.207a74ca5ad8bfc2ee103b7bf96dp+7Q, -0x1.934735f943481c7f74f56dd5b187p+6Q, 0x1.3fa55ba9206e3812ee32da2442b6p+5Q, -0x1.959601005ec548729558e21c9eb1p+2Q, -0x1.9505e84d98e613cfe4ec3f6fdae5p-1Q, 0x1.43d2632e32cd0df0bb4a95d727cp-2Q, -0x1.38e017336cd0614a6ed2ffd943cap-10Q, -0x1.968e83ac595b8c6d9c172a00fddap-13Q, 0x1.f5ed4b124df3ad0700a32c86e4bbp-24Q, 0x0p+0Q};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0Q, 0x1.f3cda2f9b135402362018230e37ap+1Q, -0x1.9eeda12641b61ebb7d840ecfaa6cp+4Q, 0x1.260fdaadd19eb1efc078d7fded1bp+6Q, -0x1.d673d80eeade4a070ce0e7052e5ep+6Q, 0x1.f01b2fa154d0352990b16aa70967p+6Q, -0x1.addb2c4ad791e217324c7aafb066p+6Q, 0x1.7db87bda6fdf8a74bb08213b9495p+6Q, -0x1.3f9860f6c4905e7132b1781ae693p+6Q, 0x1.ae731643e9198e621648583330d8p+5Q, -0x1.fb5cc3351ebc176988bf6478c6bp+4Q, 0x1.259afcbb8804d6eae552ab39c09p+4Q, -0x1.fe186e460309fdcedab5ec38f6a8p+2Q, 0x1.4d0298c21892754606c3d8ebb24fp+0Q, 0x1.a1f0a66406a122ae435ed98406f7p-2Q, -0x1.40c0addfd85543af466cc7de08d7p-3Q, 0x1.ba72fac37f087c7aee39dd6d7d9ep-9Q, 0x1.c193f16bb678e5af6510cd4d8f9fp-13Q, -0x1.16b4995bb4f073263c20b5b2b14bp-22Q, 0x0p+0Q};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0Q, 0x1.3586d9a9e0e3d99d2b93a01af7d5p+1Q, -0x1.08fa63342ecc1c41a46b365c4c22p+4Q, 0x1.7c41f01d6960cbda171d22b314bap+5Q, -0x1.276b64d22e134fe39031785d1e73p+6Q, 0x1.14f1cf74869c077b4ddd600b6793p+6Q, -0x1.83d54ac636b8244258f1e3c9d507p+5Q, 0x1.4053c8a2c8d2fc6aef1621e8f43ep+5Q, -0x1.209b538b18df262448ee3cebbe29p+5Q, 0x1.65783340b3782c7d703e94b54e85p+4Q, -0x1.2ddf670e51dfca7d85e8eeab11aep+3Q, 0x1.38744fdae212579791ea9e59ba4ep+2Q, -0x1.4065c212ba5c0456783637741afcp+1Q, 0x1.6763c5d11b774e2d99bb54d3a752p-4Q, 0x1.181d4d676ea1f03e7d8c57b5965ap-1Q, -0x1.87564028831fbd4eb29dad95b0cfp-3Q, 0x1.843d22529bb49b17cf15d645bef3p-7Q, 0x1.52be3b0b8c7af55af9d914b56a01p-11Q, -0x1.a79c626c8654ebdb591ae5793d64p-20Q, 0x0p+0Q};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0Q, 0x1.7a3cf471120ec198713994eca41fp+0Q, -0x1.48b25e52d274b1e47c8864a7164p+3Q, 0x1.cbd93276e7d596419b912da6ea19p+4Q, -0x1.37885d5242030806d66e5cf9cc78p+5Q, 0x1.4db4fb7a5ecdb9227e8824c1b905p+4Q, 0x1.74ac2dca21f55bb24886b2e8488cp+2Q, -0x1.11ca2f9f0b7d05f1c16189874d5cp+3Q, 0x1.9fa6aaf0c8d980502f82ac3f1ed7p-4Q, -0x1.8ceb3288570cd32c25919a739d51p+2Q, 0x1.e686e3fbc3fbf35811a68b06fad4p+3Q, -0x1.7e0b780d60231a4c786ec3f17781p+3Q, 0x1.7e1a3482e160bfcf5bb1945be474p+2Q, -0x1.247b57131543bcbee8b05ee74f53p+2Q, 0x1.b8a4e1c96768c895a2f3649c4cc8p+1Q, -0x1.4f17d502240a8e6f55c9dea2c968p+0Q, 0x1.4b408438ac8689521da23d7beaedp-3Q, 0x1.7264788c9473dca575636b8d6c86p-7Q, -0x1.d74fd6a021547c7f9f7dd044fd0ep-15Q, 0x0p+0Q};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0Q, 0x1.f6438a3a88460091e0ea8516e904p-4Q, -0x1.b7ba9255f9c77a442c3315f3c4dep-1Q, 0x1.3f509b3842148b5acdb05dfc7ebdp+1Q, -0x1.eac616f0d4f869be16ce06d469adp+1Q, 0x1.ae9244fef585d2a56f1cb69c0c8dp+1Q, -0x1.00d5d03220f3bbc8a51448aa67eep+1Q, 0x1.9413f3bab26fc85ab60692eb482fp+0Q, -0x1.9bd9847a10dd537f2de875e0ae85p+0Q, 0x1.16aae27d18a67638fdda8c9d9188p+0Q, -0x1.1587682f48215c21c42b36d23f1dp-1Q, 0x1.8145e3cc3cfcbcc409c895dd9662p-2Q, -0x1.faf556e68970db4f5325d20bccb9p-3Q, 0x1.8ec972676b06aaf4a1909e5ab3bfp-4Q, -0x1.49980ed40883cadc7b702f6c3e9fp-5Q, 0x1.5730c48bae56a4ea4426b047bab7p-6Q, -0x1.0952d6b855c638b977457b4c3a4p-8Q, -0x1.ce071dd8df1eee9d16331f022e54p-12Q, 0x1.30a4361eb25b38fd9207742aba25p-18Q, 0x0p+0Q};
-            }
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            if constexpr (order == 0) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0335440825684839948793277327924747568510463779411613283372021012357431575059"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.652680627784265419113142057333635414566267596751552407275899976614433273408"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.555223194777054373822280591005165065401335016712961625016624878528310159958"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.380687440934315605630685976089872177922250050019644347240793726150606940490"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.202266079588999490158624019679885616441296798707691052740675369027212472886"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0803945048003100183440731245374493948673697586172116467447133542711531568094"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0174035722935792800052307718387330639108356719924467120729654378442135160469"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00178881115434873125338924661801614887567351864768204987056083791004957995212"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00226229198052543881129104523760341714639547377902691081445602585210846978660"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000386185980709970284342158222549749494513229103697618385419333145519237034528"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000774649011709668881496648249850476879409117195200119403647384684895836766101"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000259573513242397582776373019880695158304702582936408634679549746356085340132"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000745576680291227809274057476509086014746503865109391843602515609932547121007"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000106464941195329780882604847827673302070700009500583209887829095516683638178"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000501834830778801282792550812083381505585505471229236043478318562698652685805"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000135062531948823786839892471345144438080086754634405014216461179793889825011"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000959080797319498233498089822590215572105542150066963291076320566868073767765"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000179932176974095821764192532376309678888476262257369144430177595683951871280"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 1) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.158111181967293654960328230847092693305440177339999811917967936973151313355"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.980421125954704520039885776450944209566177277494416607887119684421179635098"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.58099598658338745329757283125170548053142020106794975614544654842234384868"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.690126857952340353432328506701225025969125769614438292589462072221185931021"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.408979058242361193356322994890219659071489088001030862797057568700712362129"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.241670449709265382583487638664445391528015677818112147483084620599084662014"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.104524793285799361209632642244708987679189849915701108699068681818917564551"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0278508087960298510818238707785628134395285936655886239677755698286759739558"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00441290970073145649314875669419603850447965477890520778958402484404147639768"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00114514458070760163627849002336721074914074332813124777635502337309185298656"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000476320352183949564427659987582685532476347626608140569626323600699056358450"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000550762633298583614076910773634660669710897469085737707319033728420478570991"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000782993203462069534876818079465953823275658231409824729752214530888590769654"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000564225681253798960172481439960184780230811335282184378643150395063068263762"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000289378419497867484795216809169017976802236817565143538038072466488637113467"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000153639719627918579146261156316178551809778008841322577156822834207719956705"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000112595508102579374409860880942659257916932286941747525905040942526094106116"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000000422534516332318562691954502891542159653729964199104256783213585659998814557"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 2) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.588720067567147372371526765126987879260828303213441099181011258065293838823"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.251648139722832193419015447722954301991031036011339851370084962733394109781"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.12355343902466248968497032471987734676880165704138770035306028826542891153"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.09251337096522514606028271458193605813373662086854974692504786991417857735"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.78284160335134075990444774847436162057665816817791661854926507977727367295"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.357839667889140650192283355318684454497311597945586330625492942067228204170"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.381745602616663955066044160729358156963202088205543100952077537266538669109"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.404098136072108007374807965965387527326886804962161879932178818721047921461"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.166884206158335307397781592107767268454429823998572636766639189741929233271"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0188990841472042720746425899409966903574694812598737388685812356111081899839"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0103064239644345373917949401165831844344098684529684357486222879841537834787"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00401921019925688949154858061937053477498137877920046442886584156606534084249"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000342928264656894632727306414284757691655791891837113873553433397950197101263"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000356780514531412256820962066690466067686003465101389318017916782416810226771"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000330280231812952371277947997446653320231513317893333913004154901503115837079"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000464578675601507083497879025900090054285176183414686202576470053896196299532"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000245200318433632222808523321270596754329839152827213527385919720073276676756"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000184080234698594267687194056854914780004840892347196195690310992947531302848"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 3) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.65958975259656064316045033596993048467429622079353821151358867499251161075"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.20950631966221433967561122684352242112063005605168776576756309774482106803"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("9.54648047883299710477127639275362041903799096912957707845486310997696495456"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-8.03052641171442118399334548739326535650325998152511708583844969601543761720"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.23902264641828545334922817695052684001345135087620194561871043446356995572"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.10779520625851924861524548164634620055706242533707832091963204841153067836"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5.02564755256492020736254702209642014378150710638030519002386215046738254771"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.11488492772855670340163610415102162843178733646856522713137539498415480726"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.59968253731024764674220980278277254440169367686954378688784341823851608835"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0504087937983147259532537423739742886863984467015801660848052389726325500063"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.223185483314190807228908891936935259922851508598249374402763295219052714061"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0861136345730003759404777393964487407579363696963873730188751207394119447949"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00934626602280953109864448532020887389100677899387380615852902674015035997924"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000910503044785414199372507175857531751525973570169329713422142851011424682355"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000147382093153403749058592147931285087775427181451628598455432923070303889508"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000241926116925923995065157477973608855097571667752414338710574539981741722171"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000218323342443673749019739306955935203514484527679190271850231323531268999740"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000327979275814608443451375729823364664112564536732892493153334268909293059412"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 4) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.25242619678200601450569178504152903597725657049565655085262375577982506117"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-17.55874948808064424413002851561896280971775515196247347065085833327306525400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("41.61108988216871250092535059298125378237547100055437239071279933451179063850"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-59.55760515276426941427234116300582408502217490993753777144564940817935347700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("63.71708525153904224542587147408403757425616414887722633161387789077111052980"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-61.87307141456217718672414958346485055314933560158412396861503932253498736910"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("55.14574452799668166956345770934872005949138270244629696837163230917721607990"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-36.32511331476555787362944164622076573330244267979702165040726341593266853690"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("11.15658141584657284834931359434221143120836125797249180327843359491348695220"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.28047163679145355742238347915798843532207155521710854723594509752209225135"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5.80765607385013452624013336376953412945571932293068559021989957795643635688"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.28360810059200528491878271707995815797831304800926041232425607683843416684"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.302026455658227381795097923260643523970261991178933634395431417034448470906"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0310136758401276861689035927512442214284016615846020419389667737950748466936"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00822789017780277377915096056720947770842970725628234020125069515364007927548"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000312927426233484715125263582207480054643048737935356187231133866983070151733"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000245638621209106924354868430183266291735309073506794320584780059772790603828"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000738811174292185771537396859591012250750038497463623030500365543957753750629"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 5) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.33645181301187741432313412712493568835001053518710618642541285756306594416"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-33.23113844490980275430758088851544736605354677526393945582470182124522064770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("84.09335668007576319588337953784445541016978233438165893518194780234028567170"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-101.73067204934714346173214456537684449912757976518610846040850239073972369700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("34.96200649417016943214733096150713509877346551398259618284714231991020061170"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("63.51129364702034683684093287782391919624178836066372576355119905503761408080"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-108.84305654018594847769298493805318318251251741351696570225381155341619480700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("116.37415674748252380731944050807221204678284438681143398715321798634302210300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-137.03427381728617053583750633954098792534222952199781843278889570421284187500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("144.23917229041069234342319895061976936945281511182737320554482546805542945500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-100.81954183076052489010123579947837751941991209023328659869027417281390550900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("39.95574123506755984622668035085486713223409393558081588798575371234724932450"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.33728051220085266945721599456441606967791241256713928442461588780452001216"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.791060695144960272868253882225791392596201909418283798181953112710974525037"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.316232251829842651651001625374458886955182867924728786582655341982774267939"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00119352475745132656518440055173377628211628909314005476964858223466155435340"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000193861339890561713729524049136083535893829812899666113387041059603669685004"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000116863969422460737393134164985587926960730142518183635722657982921293457991"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 6) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.90471303169253225846019875869878232941425899681461754740621573916446143761"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-25.93301501220719956383930380071028369762143981546072887565823996886685997670"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("73.51548263160627699666584109197660506203055036418454184583288480107014110040"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-117.61312888439676707323068134216244043903457141447537621870038005469616937700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("124.02654888229522104336063612980866173817516040264350607815625581466646707700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-107.46403614941343293286313096080305756514307808353723016233188762409520778900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("95.43015996272868979842030346234072214178139856671622915250008488106829700140"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-79.89880738806468091633285361243244391895034565047088681170638032528297365230"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("53.80619481139291976708016981476722176165180845983829174460954831948835152660"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-31.71014710187933425539049751952485208474696175383649880962539170183854068730"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("18.35033868078635575339634170405333269133930342251123760246335182701029470230"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.97024113499733731824785417964081280548267589070768527759215633952607230552"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.30082087267562392476267682719773219132371557892324193430079039159705712061"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.408144569258781629158811991673214502189211048077371093404699476576485396497"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.156617506402691681618770997346051897652378607238940971239829191058955327399"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00337561904029654362598669467426491389034476058577086402678410124009083217286"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000214375449437306492796677584389309705675972756233814822259639128039297348952"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000259564691279900670740154984232869976357323694550668609785644902896773881579"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 7) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.41817780299041267294396998193961046347327141146988493872539852596711350295"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-16.56112976440341017090653469524313042536360691585560344322351312533906133220"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("47.53219626405561897360527224265560846366729359202579844173188227203518751290"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-73.85487678915235666547453188442988561374382065439419612818538759549597329740"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("69.23614294120398636214807885595774013168922546655228773985936065429561982080"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-48.47914652685632764102838407583295199095537856449557350864923480580193915190"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("40.04091002631537162491011984473323161600703606500352069042313463467126512660"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-36.07584294004108744401985515812914016258613167282034953810412938444038731500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("22.34184575342033973521659639667387757078302661414876303661404399664838457520"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.43352082058754010000229426238016353381474440642161800237732829686092053067"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.88209911704351415773607596292274800953074722271529021833265067681298168566"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.50310541071368687187558805389288406933454963984067437672488275554205269365"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0877416350574245619016863517598542577849142110266067469164372019839766916222"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.547098559261318119790346121315142638857555987993333621751899257669110708054"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.191082478748640367297398639370371440145977214048380506662573645656883504693"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0118481080619098512694011114462548921140026922405000410819306003041457844881"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000646101166642978477805807904877768082627916394154211614618243579374822809981"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000157807348977739476590803041857604549211169374418312430645482994306750965210"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 8) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.47749259720336125750014371203719086097786832720840532470036067098638253523"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-10.27177349258604109799866360824488274075683477990758858915270374562166449850"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("28.74052664229870896057228781991603797498521883108842274414172929446095718590"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-38.94158424629165794548655688785303773037259534960785249196589991715016053910"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("20.85668514061840842160738201097767741109998318160033587807688366848349176030"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.82300896396175969285220261284580137016897500185004121370253254225136801433"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-8.55593091071560318198818805962130429594383016756683899572054041178087930423"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.101477306114750809578847194446606040053812700094709979272704369647063439327"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.20185530962426163472935046915706308507730310357888975841274200007312909611"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("15.20396613285981716679133037338797692219039323378619093572799537510744196150"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-11.93890001881036092553774539348916251166242755327073413099256167724690461900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.97034943372046810250402450844362776436235733145492694521396093842408492893"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.57002808440762091333964553954350217107396457686094642109241343475428396977"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.44253179868866811498600236601873984282170067759034407929086464636198130738"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.30895739843621525859283487914176592704598294675665286288796005768903002325"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.161744149188567181778191988919947821701240436608528275036716134129128761337"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0113034809702728906127738052967788898940898905277042251467481852979437112396"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000561847530216411102015552396664363227011342601063500856745808337968464467556"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 9) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.122623004871017738321088521115551923728453212438673116414730214921771194277"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.858845303530769892579734223666985146082985618311703745596404006498390381931"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.49464740988711173737826976177194717462144209023170132334409744337915240875"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.83417021521921990552626761956575317113472949702731301040473923476385032353"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.36383879136250970160534021305681940065986265718051079957468541575949019427"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.00652506301585541969492468858387268920435010187618742310379136054539969490"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.57842944438965482815057083449552137133719188861387633419907705130357334305"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.60878780346034960103676974039938661510477020676670448343954517210254723407"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.08854499391659395899666779285135586272604126336277091423079442916910197364"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.542048698207568264511438036052150370606170830150755922595824458471088767735"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.376243171063148851166518405338884659341124829071866802537194156141907541144"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.247538260374476618199302147981680094201399126055983684863712115608203062926"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0973600834756226757960627772745367010811794086758884192671361295078507106292"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0402336396803239840143974298780932703826464388081245776201258480950581117641"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0209466857329280522592506599477472523467188466718239083632463774864022218054"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00404851667584358062529338732537862677888179504486154526998284790202549786179"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000440624045545039606176483920239238500963155780055689316463121243179544715288"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000453951136476212053479152117487615488257357457846427962694756049282806704493"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-        }
-    }
-    if constexpr (p == 11) {
-        if constexpr (std::is_same_v<Real, float>) {
-            if constexpr (order == 0) {
-                return {0x0p+0f, 0x1.f82d86p-7f, 0x1.da87aep-2f, 0x1.a074eap-1f, -0x1.d3dbc2p-2f, 0x1.07dc8cp-2f, -0x1.17e06ap-3f, 0x1.d853p-5f, -0x1.071062p-6f, 0x1.0182ap-9f, 0x1.d91cd2p-14f, 0x1.f2bfaap-15f, -0x1.d7e9bap-15f, 0x1.5c274ep-18f, 0x1.63562ep-20f, -0x1.0af58p-26f, 0x1.1409ccp-28f, -0x1.160128p-35f, -0x1.4f944ep-42f, -0x1.ad914cp-53f, -0x1.65d844p-70f, -0x0p+0f};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.4988f6p-4f, 0x1.cd9786p-1f, -0x1.f03418p-1f, -0x1.075e3cp-3f, 0x1.303436p-3f, -0x1.71d07ep-12f, -0x1.321c6cp-4f, 0x1.0f00fp-4f, -0x1.fec808p-6f, 0x1.092c0ap-7f, -0x1.185782p-11f, -0x1.693106p-12f, 0x1.a2acf4p-14f, -0x1.c4d82p-19f, -0x1.e02848p-20f, 0x1.7db784p-25f, 0x1.739c16p-30f, -0x1.d9433ap-36f, 0x1.651bd6p-46f, 0x1.29783p-62f, 0x0p+0f};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0f, 0x1.5c07e6p-2f, 0x1.307a2ap-1f, -0x1.a41fd4p+1f, 0x1.08f33p+2f, -0x1.6a2a88p+1f, 0x1.5f04aep+0f, -0x1.150c78p-2f, -0x1.78ed1cp-3f, 0x1.4f999p-3f, -0x1.41156ep-5f, -0x1.6c5862p-7f, 0x1.21e04ap-7f, -0x1.cd1c36p-10f, 0x1.af648p-17f, 0x1.0136c4p-15f, -0x1.6928bp-19f, -0x1.6377bp-25f, 0x1.64323cp-30f, -0x1.6fb512p-40f, -0x1.32449ep-55f, -0x0p+0f};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0f, 0x1.1c297ep+0f, -0x1.a72bc4p+1f, 0x1.8e9818p+1f, -0x1.8f506ep-1f, 0x1.02364ap-1f, -0x1.0fb22ap+1f, 0x1.80597ep+1f, -0x1.38ad98p+1f, 0x1.339d14p+0f, -0x1.08b97cp-2f, -0x1.3f8a26p-4f, 0x1.2b8bd2p-4f, -0x1.35b764p-6f, 0x1.f33a86p-12f, 0x1.1c307ep-11f, -0x1.950dccp-15f, -0x1.f90492p-21f, 0x1.8b6cb6p-25f, -0x1.21deep-34f, -0x1.e2c778p-49f, -0x0p+0f};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0f, 0x1.51d8dcp+1f, -0x1.c33b04p+3f, 0x1.0e7952p+5f, -0x1.9aba4p+5f, 0x1.f144c4p+5f, -0x1.17ce56p+6f, 0x1.1abf8ep+6f, -0x1.aeeda8p+5f, 0x1.6d1976p+4f, 0x1.64c18ap+1f, -0x1.4b3d36p+3f, 0x1.8e7526p+2f, -0x1.9e20d2p+0f, 0x1.8f714p-5f, 0x1.002e9ap-4f, -0x1.22b5dp-7f, -0x1.695b64p-13f, 0x1.ba1b22p-17f, -0x1.df066ep-26f, -0x1.8ec07p-39f, -0x0p+0f};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0f, 0x1.553842p+2f, -0x1.1648a2p+5f, 0x1.7429c4p+6f, -0x1.d2259cp+6f, 0x1.36cbd8p+4f, 0x1.4a282ep+7f, -0x1.2e04acp+8f, 0x1.5f18c6p+8f, -0x1.80bbfp+8f, 0x1.90ad4cp+8f, -0x1.4159ep+8f, 0x1.4eba06p+7f, -0x1.6db5a8p+5f, 0x1.66137p-1f, 0x1.7dbb7ep+1f, -0x1.1851aap-1f, -0x1.230c94p-7f, 0x1.7e95e2p-10f, -0x1.136d24p-18f, -0x1.ca2f1p-31f, -0x0p+0f};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0f, 0x1.43e57ap+2f, -0x1.201578p+5f, 0x1.be9ebp+6f, -0x1.917bfcp+7f, 0x1.e7564ap+7f, -0x1.dd46b6p+7f, 0x1.c24b2cp+7f, -0x1.9299f8p+7f, 0x1.2da088p+7f, -0x1.7f74fcp+6f, 0x1.cafceap+5f, -0x1.cfad0ap+4f, 0x1.f4f5eap+2f, 0x1.14b6dap+0f, -0x1.5e908ap+0f, 0x1.1ee7d4p-2f, -0x1.1e668p-11f, -0x1.81c424p-10f, 0x1.28216ep-18f, 0x1.ebdb46p-30f, -0x0p+0f};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0f, 0x1.0e918ep+2f, -0x1.f54b1ep+4f, 0x1.8cc936p+6f, -0x1.5d87f4p+7f, 0x1.7fbdfcp+7f, -0x1.356154p+7f, 0x1.00a2fp+7f, -0x1.d61ad6p+6f, 0x1.4b192ep+6f, -0x1.2bd7eep+5f, 0x1.d23af8p+3f, -0x1.a5a3f6p+2f, -0x1.0097bap+0f, 0x1.29abecp+2f, -0x1.6d63c6p+1f, 0x1.521b96p-1f, -0x1.89a1eap-6f, -0x1.cc0f8cp-8f, 0x1.9e94aap-16f, 0x1.5739aap-26f, 0x0p+0f};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0f, 0x1.c2a5p+0f, -0x1.a9c968p+3f, 0x1.5bbb8cp+5f, -0x1.452574p+6f, 0x1.91c80cp+6f, -0x1.84d65cp+6f, 0x1.678e1ep+6f, -0x1.493302p+6f, 0x1.14413cp+6f, -0x1.b51d9ap+5f, 0x1.483818p+5f, -0x1.a72562p+4f, 0x1.e00e48p+3f, -0x1.1522f8p+3f, 0x1.152962p+2f, -0x1.3d9d88p+0f, 0x1.3f1c58p-4f, 0x1.b3efb4p-6f, -0x1.baa15ap-13f, -0x1.6c2d94p-22f, -0x0p+0f};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0f, 0x1.480f32p-1f, -0x1.38fe3p+2f, 0x1.f8f412p+3f, -0x1.bc60c4p+4f, 0x1.d3d44ap+4f, -0x1.536d7p+4f, 0x1.0953a8p+4f, -0x1.0c0dcap+4f, 0x1.af56b2p+3f, -0x1.f62894p+2f, 0x1.3ef834p+2f, -0x1.c75ab6p+1f, 0x1.cb38bcp+0f, -0x1.624786p-1f, 0x1.61b17ap-2f, -0x1.0b6248p-3f, 0x1.c9b3fp-8f, 0x1.7c528ap-8f, -0x1.0c4738p-13f, -0x1.b40e78p-22f, -0x0p+0f};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0f, 0x1.8a25fep-4f, -0x1.79dddep-1f, 0x1.2f9284p+1f, -0x1.04a532p+2f, 0x1.fbc728p+1f, -0x1.2e8a4ep+1f, 0x1.96ff88p+0f, -0x1.db8c8p+0f, 0x1.8867ecp+0f, -0x1.7019bcp-1f, 0x1.a30d2p-2f, -0x1.7340e8p-2f, 0x1.68181ap-3f, -0x1.50a6f6p-5f, 0x1.8d3b22p-6f, -0x1.b7227ep-7f, -0x1.a3115p-12f, 0x1.71e7a4p-10f, -0x1.4eea02p-14f, -0x1.09aedap-21f, 0x0p+0f};
-            }
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0, 0x1.f82d860ed311dp-7, 0x1.da87adf545deap-2, 0x1.a074ea6831a18p-1, -0x1.d3dbc22db3363p-2, 0x1.07dc8c4b5880ap-2, -0x1.17e06a0deb07p-3, 0x1.d85300a8e9a5ap-5, -0x1.0710616766f9ep-6, 0x1.0182a0c9a44bbp-9, 0x1.d91cd19825f46p-14, 0x1.f2bfaace30f59p-15, -0x1.d7e9ba7b3ac47p-15, 0x1.5c274e2e04a65p-18, 0x1.63562e1b18da8p-20, -0x1.0af5800900cccp-26, 0x1.1409cb495cfabp-28, -0x1.1601287f207ddp-35, -0x1.4f944d6c974a1p-42, -0x1.ad914b3b9c645p-53, -0x1.65d8440cb590ap-70, -0x0p+0};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0, 0x1.4988f615d8fc2p-4, 0x1.cd9786f046dbdp-1, -0x1.f034187a5d753p-1, -0x1.075e3bcf1d71fp-3, 0x1.303436308c6p-3, -0x1.71d07ef81053fp-12, -0x1.321c6b5970b99p-4, 0x1.0f00f07475782p-4, -0x1.fec807d6bcde3p-6, 0x1.092c0960e80ecp-7, -0x1.1857810566103p-11, -0x1.693105a2bb707p-12, 0x1.a2acf3b1f9d07p-14, -0x1.c4d81f25bbab6p-19, -0x1.e0284772a21efp-20, 0x1.7db784c0b0131p-25, 0x1.739c15dc80c55p-30, -0x1.d9433a2520a2ep-36, 0x1.651bd505e5aabp-46, 0x1.29782f98b98d9p-62, 0x0p+0};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0, 0x1.5c07e5083d709p-2, 0x1.307a2a8e783eap-1, -0x1.a41fd4c6e5304p+1, 0x1.08f3303fd9b5fp+2, -0x1.6a2a8758fd08cp+1, 0x1.5f04ae9c9034bp+0, -0x1.150c77d31565dp-2, -0x1.78ed1cb9b0ec2p-3, 0x1.4f99902d11603p-3, -0x1.41156e1c846c4p-5, -0x1.6c5861062a836p-7, 0x1.21e04958552e7p-7, -0x1.cd1c35ab2ad93p-10, 0x1.af6480e4adc47p-17, 0x1.0136c3fb4b19cp-15, -0x1.6928b0e495d08p-19, -0x1.6377af73884cp-25, 0x1.64323c063686ap-30, -0x1.6fb51174aa8e3p-40, -0x1.32449da1b9609p-55, -0x0p+0};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0, 0x1.1c297e1a72297p+0, -0x1.a72bc3c00615fp+1, 0x1.8e98178e99b32p+1, -0x1.8f506e2a5e0ebp-1, 0x1.02364935e2223p-1, -0x1.0fb2290536b32p+1, 0x1.80597d49465bfp+1, -0x1.38ad9781c7501p+1, 0x1.339d144fd9551p+0, -0x1.08b97b33caeccp-2, -0x1.3f8a268debfb7p-4, 0x1.2b8bd1a4fd0ebp-4, -0x1.35b764060a714p-6, 0x1.f33a86db42466p-12, 0x1.1c307da269deep-11, -0x1.950dcb7c8e982p-15, -0x1.f904916865d4dp-21, 0x1.8b6cb6bf7586bp-25, -0x1.21dedfd7476c5p-34, -0x1.e2c7778c519ap-49, -0x0p+0};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0, 0x1.51d8dbccf9207p+1, -0x1.c33b049bfbce6p+3, 0x1.0e79522ccf3ddp+5, -0x1.9aba40cee29c1p+5, 0x1.f144c4df7513dp+5, -0x1.17ce56ad9d902p+6, 0x1.1abf8d1adcc3ep+6, -0x1.aeeda88b7fe88p+5, 0x1.6d1975fc2f42ep+4, 0x1.64c18afe2844cp+1, -0x1.4b3d36d8f9771p+3, 0x1.8e75251a7f5bfp+2, -0x1.9e20d1654131ap+0, 0x1.8f713f264dac3p-5, 0x1.002e9aac59197p-4, -0x1.22b5d07d79f25p-7, -0x1.695b63166e6d6p-13, 0x1.ba1b21857af83p-17, -0x1.df066d7576ffdp-26, -0x1.8ec06f9de2f7dp-39, -0x0p+0};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0, 0x1.553841cb8504cp+2, -0x1.1648a261cfac8p+5, 0x1.7429c31b8bcdcp+6, -0x1.d2259be1a7819p+6, 0x1.36cbd86221f4cp+4, 0x1.4a282d1320ed7p+7, -0x1.2e04ab290e2ep+8, 0x1.5f18c6755ba05p+8, -0x1.80bbefefb8959p+8, 0x1.90ad4b61c673ep+8, -0x1.4159e0e62036cp+8, 0x1.4eba06db33d53p+7, -0x1.6db5a82568a44p+5, 0x1.6613709f48646p-1, 0x1.7dbb7d4fa2b47p+1, -0x1.1851a9519e35ep-1, -0x1.230c93cadc0b8p-7, 0x1.7e95e283d8ce3p-10, -0x1.136d2374e3712p-18, -0x1.ca2f0f4b75006p-31, -0x0p+0};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0, 0x1.43e579b56aec7p+2, -0x1.2015783789a13p+5, 0x1.be9eb07640a6ep+6, -0x1.917bfbcd50104p+7, 0x1.e7564ac670465p+7, -0x1.dd46b6e14bd99p+7, 0x1.c24b2cb18bb3p+7, -0x1.9299f7098407ep+7, 0x1.2da088f392f17p+7, -0x1.7f74fc0a8fbbcp+6, 0x1.cafceab55c222p+5, -0x1.cfad0a751fefdp+4, 0x1.f4f5eade96654p+2, 0x1.14b6d949957a5p+0, -0x1.5e908a00f74dap+0, 0x1.1ee7d490234e2p-2, -0x1.1e667fbdaff18p-11, -0x1.81c4231f27f24p-10, 0x1.28216d550397dp-18, 0x1.ebdb45ca159a6p-30, -0x0p+0};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0, 0x1.0e918e0751a5fp+2, -0x1.f54b1dc71e94cp+4, 0x1.8cc935a5962f3p+6, -0x1.5d87f4fd9af88p+7, 0x1.7fbdfc1f5c92bp+7, -0x1.356154b8ce2cp+7, 0x1.00a2f00b6f36p+7, -0x1.d61ad68084632p+6, 0x1.4b192d711636ap+6, -0x1.2bd7eeccbbd8bp+5, 0x1.d23af72a92131p+3, -0x1.a5a3f6309aca8p+2, -0x1.0097ba319005fp+0, 0x1.29abec5ca24e5p+2, -0x1.6d63c669ef72ap+1, 0x1.521b96f1f012p-1, -0x1.89a1e9b6409a4p-6, -0x1.cc0f8b0b31976p-8, 0x1.9e94a90cc2ee8p-16, 0x1.5739a9ee6eb1dp-26, 0x0p+0};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0, 0x1.c2a4ffe966119p+0, -0x1.a9c9682497d43p+3, 0x1.5bbb8c487ae5cp+5, -0x1.452573aebb3bfp+6, 0x1.91c80b52c3671p+6, -0x1.84d65b83affb6p+6, 0x1.678e1d36597aep+6, -0x1.4933025bdb689p+6, 0x1.14413c8e18076p+6, -0x1.b51d99f667842p+5, 0x1.483818775e0cbp+5, -0x1.a72562d5d8065p+4, 0x1.e00e48c9f7714p+3, -0x1.1522f77734c2fp+3, 0x1.152961e6e0f57p+2, -0x1.3d9d88a64fae4p+0, 0x1.3f1c58e4e2a68p-4, 0x1.b3efb441a4e1bp-6, -0x1.baa159e67dd4fp-13, -0x1.6c2d94cde3ae2p-22, -0x0p+0};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0, 0x1.480f31520e3f3p-1, -0x1.38fe2f09aac58p+2, 0x1.f8f411bacc9f9p+3, -0x1.bc60c3b54f90bp+4, 0x1.d3d44a6a16adbp+4, -0x1.536d6f833b667p+4, 0x1.0953a7a524acbp+4, -0x1.0c0dca303e8e2p+4, 0x1.af56b1534f29ep+3, -0x1.f628948ceff74p+2, 0x1.3ef834c3289aap+2, -0x1.c75ab5e1afc76p+1, 0x1.cb38bb2c5f4bfp+0, -0x1.624785bf15dbep-1, 0x1.61b17ae5ff0c1p-2, -0x1.0b62472bd3d78p-3, 0x1.c9b3ef0688e89p-8, 0x1.7c528a3f2156cp-8, -0x1.0c4738028aec9p-13, -0x1.b40e785cb8808p-22, -0x0p+0};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0, 0x1.8a25fe79d1c4ep-4, -0x1.79dddd860d214p-1, 0x1.2f92842080f08p+1, -0x1.04a53246109b7p+2, 0x1.fbc727fc23efp+1, -0x1.2e8a4ebac6b5ep+1, 0x1.96ff87cfe4cc5p+0, -0x1.db8c7f7bf2c3ap+0, 0x1.8867eccd39d1bp+0, -0x1.7019bc278ffcp-1, 0x1.a30d20b4e67c7p-2, -0x1.7340e7a399e64p-2, 0x1.68181929e64c5p-3, -0x1.50a6f5e8f3b31p-5, 0x1.8d3b211eb839bp-6, -0x1.b7227d5381373p-7, -0x1.a3114fdf2fbcp-12, 0x1.71e7a3b4d88bfp-10, -0x1.4eea023db8bd5p-14, -0x1.09aed93888304p-21, 0x0p+0};
-            }
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0L, 0xf.c16c3076988ebbcp-10L, 0xe.d43d6faa2ef51b8p-5L, 0xd.03a753418d0bce6p-4L, -0xe.9ede116d99b1966p-5L, 0x8.3ee4625ac404c6dp-5L, -0x8.bf03506f5837fe3p-6L, 0xe.c29805474d2cedap-8L, -0x8.38830b3b37cedbcp-9L, 0x8.0c15064d225d41p-12L, 0xe.c8e68cc12fa31cbp-17L, 0xf.95fd567187ac541p-18L, -0xe.bf4dd3d9d6239bp-18L, 0xa.e13a71702532bafp-21L, 0xb.1ab170d8c6d3fd6p-23L, -0x8.57ac00480665f53p-29L, 0x8.a04e5a4ae7d54e6p-31L, -0x8.b00943f903ee402p-38L, -0xa.7ca26b64ba505d1p-45L, -0xd.6c8a59dce3224e2p-56L, -0xb.2ec22065ac84f3fp-73L, -0x0p+0L};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0L, 0xa.4c47b0aec7e1081p-7L, 0xe.6cbc378236de837p-4L, -0xf.81a0c3d2eba999fp-4L, -0x8.3af1de78eb8f98bp-6L, 0x9.81a1b1846300118p-6L, -0xb.8e83f7c0829f529p-15L, -0x9.90e35acb85cca72p-7L, 0x8.780783a3abc1044p-7L, -0xf.f6403eb5e6f17b6p-9L, 0x8.49604b074075f3ap-10L, -0x8.c2bc082b308154p-14L, -0xb.49882d15db83441p-15L, 0xd.15679d8fce83a4ap-17L, -0xe.26c0f92ddd5b332p-22L, -0xf.01423b9510f7584p-23L, 0xb.edbc2605809849dp-28L, 0xb.9ce0aee4062aafdp-33L, -0xe.ca19d1290517188p-39L, 0xb.28dea82f2d5572ep-49L, 0x9.4bc17cc5cc6c599p-65L, 0x0p+0L};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0L, 0xa.e03f2841eb84819p-5L, 0x9.83d15473c1f50fdp-4L, -0xd.20fea63729823dcp-2L, 0x8.479981fecdaf816p-1L, -0xb.51543ac7e845d9fp-2L, 0xa.f82574e481a558dp-3L, -0x8.a863be98ab2e9afp-5L, -0xb.c768e5cd8760f3bp-6L, 0xa.7ccc81688b01b9cp-6L, -0xa.08ab70e42362325p-8L, -0xb.62c30831541b0b7p-10L, 0x9.0f024ac2a973782p-10L, -0xe.68e1ad5956c95f9p-13L, 0xd.7b2407256e2365dp-20L, 0x8.09b61fda58cdcd9p-18L, -0xb.49458724ae83fdap-22L, -0xb.1bbd7b9c425fd7p-28L, 0xb.2191e031b4353cfp-33L, -0xb.7da88ba55471baap-43L, -0x9.9224ed0dcb0440cp-58L, -0x0p+0L};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0L, 0x8.e14bf0d3914bbd4p-3L, -0xd.395e1e0030afb9ep-2L, 0xc.74c0bc74cd98ea3p-2L, -0xc.7a837152f075af7p-4L, 0x8.11b249af1111423p-4L, -0x8.7d914829b598f95p-2L, 0xc.02cbea4a32dfa62p-2L, -0x9.c56cbc0e3a809b2p-2L, 0x9.9ce8a27ecaa85dcp-3L, -0x8.45cbd99e57663b5p-5L, -0x9.fc51346f5fdbbd1p-7L, 0x9.5c5e8d27e8757a5p-7L, -0x9.adbb20305389e61p-9L, 0xf.99d436da1232d03p-15L, 0x8.e183ed134ef71abp-14L, -0xc.a86e5be474c0e96p-18L, -0xf.c8248b432ea6598p-24L, 0xc.5b65b5fbac3587ap-28L, -0x9.0ef6feba3b62aaap-37L, -0xf.163bbc628cd0205p-52L, -0x0p+0L};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0L, 0xa.8ec6de67c9035e6p-2L, -0xe.19d824dfde72f6dp+0L, 0x8.73ca916679ee85cp+2L, -0xc.d5d2067714e04fcp+2L, 0xf.8a2626fba89eb9ep+2L, -0x8.be72b56cec81364p+3L, 0x8.d5fc68d6e61f284p+3L, -0xd.776d445bff43fe9p+2L, 0xb.68cbafe17a170d9p+1L, 0xb.260c57f14226301p-2L, -0xa.59e9b6c7cbb8775p+0L, 0xc.73a928d3fadf73cp-1L, -0xc.f1068b2a098cfb7p-3L, 0xc.7b89f9326d61459p-8L, 0x8.0174d562c8cba6dp-7L, -0x9.15ae83ebcf927bfp-10L, -0xb.4adb18b3736b1d7p-16L, 0xd.d0d90c2bd7c17dcp-20L, -0xe.f8336babb7fe566p-29L, -0xc.76037cef17bea43p-42L, -0x0p+0L};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0L, 0xa.a9c20e5c28262cfp-1L, -0x8.b245130e7d6435p+2L, 0xb.a14e18dc5e6e3bcp+3L, -0xe.912cdf0d3c0c767p+3L, 0x9.b65ec3110fa60e2p+1L, 0xa.51416899076b9c3p+4L, -0x9.702559487170317p+5L, 0xa.f8c633aadd02508p+5L, -0xc.05df7f7dc4ac954p+5L, 0xc.856a5b0e339f38dp+5L, -0xa.0acf073101b6074p+5L, 0xa.75d036d99ea9702p+4L, -0xb.6dad412b4521e9bp+2L, 0xb.309b84fa4322d85p-4L, 0xb.eddbea7d15a390ap-2L, -0x8.c28d4a8cf1aeca5p-4L, -0x9.18649e56e05bc3p-10L, 0xb.f4af141ec671a67p-13L, -0x8.9b691ba71b88c22p-21L, -0xe.51787a5ba8032eep-34L, -0x0p+0L};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0L, 0xa.1f2bcdab57636dcp-1L, -0x9.00abc1bc4d0982ep+2L, 0xd.f4f583b2053726ep+3L, -0xc.8bdfde6a8082091p+4L, 0xf.3ab256338232753p+4L, -0xe.ea35b70a5ecc9fep+4L, 0xe.1259658c5d981b4p+4L, -0xc.94cfb84c203ee2p+4L, 0x9.6d04479c978badep+4L, -0xb.fba7e0547ddde95p+3L, 0xe.57e755aae11112fp+2L, -0xe.7d6853a8ff7e50ap+1L, 0xf.a7af56f4b329d5ep-1L, 0x8.a5b6ca4cabd2b23p-3L, -0xa.f4845007ba6cfc8p-3L, 0x8.f73ea4811a71163p-5L, -0x8.f333fded7f8c399p-14L, -0xc.0e2118f93f91f36p-13L, 0x9.410b6aa81cbea18p-21L, 0xf.5eda2e50acd327dp-33L, -0x0p+0L};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0L, 0x8.748c703a8d2f937p-1L, -0xf.aa58ee38f4a5c91p+1L, 0xc.6649ad2cb179936p+3L, -0xa.ec3fa7ecd7c41f4p+4L, 0xb.fdefe0fae49564ap+4L, -0x9.ab0aa5c6715fdd9p+4L, 0x8.0517805b79afde9p+4L, -0xe.b0d6b4042318ee3p+3L, 0xa.58c96b88b1b4fe8p+3L, -0x9.5ebf7665dec59a9p+2L, 0xe.91d7b95490989a7p+0L, -0xd.2d1fb184d6542c6p-1L, -0x8.04bdd18c802f85cp-3L, 0x9.4d5f62e5127240ep-1L, -0xb.6b1e334f7b950afp-2L, 0xa.90dcb78f808ffecp-4L, -0xc.4d0f4db204d1cc9p-9L, -0xe.607c58598cbad8fp-11L, 0xc.f4a5486617740b1p-19L, 0xa.b9cd4f73758e428p-29L, 0x0p+0L};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0L, 0xe.1527ff4b308c86p-3L, -0xd.4e4b4124bea1ab6p+0L, 0xa.dddc6243d72ddb1p+2L, -0xa.292b9d75d9dfa3ap+3L, 0xc.8e405a961b38a93p+3L, -0xc.26b2dc1d7fdae55p+3L, 0xb.3c70e9b2cbd6e2ap+3L, -0xa.499812dedb44ac4p+3L, 0x8.a209e470c03af8ap+3L, -0xd.a8eccfb33c210d9p+2L, 0xa.41c0c3baf0658a2p+2L, -0xd.392b16aec032585p+1L, 0xf.0072464fbb8a1e7p+0L, -0x8.a917bbb9a6176d9p+0L, 0x8.a94b0f3707ab7abp-1L, -0x9.ecec45327d721f6p-3L, 0x9.f8e2c727153415ep-7L, 0xd.9f7da20d270d536p-9L, -0xd.d50acf33eea750ap-16L, -0xb.616ca66f1d70df8p-25L, -0x0p+0L};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0L, 0xa.40798a9071f9886p-4L, -0x9.c7f1784d562bdc9p-1L, 0xf.c7a08dd664fcb0ep+0L, -0xd.e3061daa7c85492p+1L, 0xe.9ea25350b56d92ap+1L, -0xa.9b6b7c19db33b9dp+1L, 0x8.4a9d3d29256548ap+1L, -0x8.606e5181f471318p+1L, 0xd.7ab58a9a794ee91p+0L, -0xf.b144a4677fb9db7p-1L, 0x9.f7c1a61944d51aep-1L, -0xe.3ad5af0d7e3ad17p-2L, 0xe.59c5d962fa5f5d7p-3L, -0xb.123c2df8aedf04ap-4L, 0xb.0d8bd72ff86061cp-5L, -0x8.5b12395e9ebc248p-6L, 0xe.4d9f7834474485cp-11L, 0xb.e29451f90ab62c4p-11L, -0x8.6239c0145764987p-16L, -0xd.a073c2e5c404378p-25L, -0x0p+0L};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0L, 0xc.512ff3ce8e26ed6p-7L, -0xb.ceeeec30690a3d4p-4L, 0x9.7c942104078413dp-2L, -0x8.2529923084db5b6p-1L, 0xf.de393fe11f77db2p-2L, -0x9.745275d635af24dp-2L, 0xc.b7fc3e7f2662817p-3L, -0xe.dc63fbdf961d121p-3L, 0xc.433f6669ce8d77ap-3L, -0xb.80cde13c7fe01dap-4L, 0xd.186905a733e3482p-5L, -0xb.9a073d1ccf31d0dp-5L, 0xb.40c0c94f326298p-6L, -0xa.8537af479d9846bp-8L, 0xc.69d908f5c1cd609p-9L, -0xd.b913ea9c09b9ab5p-10L, -0xd.188a7ef97de034bp-15L, 0xb.8f3d1da6c45f8b5p-13L, -0xa.775011edc5ea48p-17L, -0x8.4d76c9c441821a3p-24L, 0x0p+0L};
-            }
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.f82d860ed311d7772f0a5fc02a6dp-7Q, 0x1.da87adf545dea36f29603c50206cp-2Q, 0x1.a074ea6831a179cbcefe13bdeb26p-1Q, -0x1.d3dbc22db33632cb9d3eeea93097p-2Q, 0x1.07dc8c4b588098d99d74923fef1p-2Q, -0x1.17e06a0deb06ffc5a354422c2913p-3Q, 0x1.d85300a8e9a59db3d8e328544719p-5Q, -0x1.0710616766f9db787dd78480360dp-6Q, 0x1.0182a0c9a44ba81f2b490da87cf1p-9Q, 0x1.d91cd19825f46395eba40bde2534p-14Q, 0x1.f2bfaace30f58a825ed0b3a11e2p-15Q, -0x1.d7e9ba7b3ac4736029b548526137p-15Q, 0x1.5c274e2e04a6575e26e75abeb4c3p-18Q, 0x1.63562e1b18da7fac5905b88575e8p-20Q, -0x1.0af5800900ccbea5a647053aa052p-26Q, 0x1.1409cb495cfaa9cc50f1fb279896p-28Q, -0x1.1601287f207dc804b32b2b372befp-35Q, -0x1.4f944d6c974a0ba10244cbd7bf57p-42Q, -0x1.ad914b3b9c6449c459a4d882621ap-53Q, -0x1.65d8440cb5909e7eb82f547cb81ep-70Q, 0x0p+0Q};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.4988f615d8fc2101372678651696p-4Q, 0x1.cd9786f046dbd06d9795ae5305eep-1Q, -0x1.f034187a5d75333e9dbb5b1046e1p-1Q, -0x1.075e3bcf1d71f31524cf997afbe8p-3Q, 0x1.303436308c600230256305532d57p-3Q, -0x1.71d07ef81053ea5196f6a9c9ea93p-12Q, -0x1.321c6b5970b994e47d89204a7726p-4Q, 0x1.0f00f0747578208709a35dbb5672p-4Q, -0x1.fec807d6bcde2f6b9da93df4aa6dp-6Q, 0x1.092c0960e80ebe73a0fb5f592a81p-7Q, -0x1.1857810566102a80b03f6d57486cp-11Q, -0x1.693105a2bb706882bf9e39158aa2p-12Q, 0x1.a2acf3b1f9d0749452e4dc44d918p-14Q, -0x1.c4d81f25bbab666371fdd702fceap-19Q, -0x1.e0284772a21eeb07c87b76642d8fp-20Q, 0x1.7db784c0b013093ad9874c402637p-25Q, 0x1.739c15dc80c555f970d134b64517p-30Q, -0x1.d9433a2520a2e30f13e7c351f17bp-36Q, 0x1.651bd505e5aaae5cab5b708f20cp-46Q, 0x1.29782f98b98d8b31230d837a9eccp-62Q, 0x0p+0Q};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.5c07e5083d7090314f404490267fp-2Q, 0x1.307a2a8e783ea1f99bb361a3ce3fp-1Q, -0x1.a41fd4c6e53047b890408086b518p+1Q, 0x1.08f3303fd9b5f02cbec87edc442ap+2Q, -0x1.6a2a8758fd08bb3ed6b347424cecp+1Q, 0x1.5f04ae9c9034ab19fcfae00d09b9p+0Q, -0x1.150c77d31565d35edf80240e5e1cp-2Q, -0x1.78ed1cb9b0ec1e760990f81b60f9p-3Q, 0x1.4f99902d11603738023acee050bdp-3Q, -0x1.41156e1c846c464a303629e298b7p-5Q, -0x1.6c5861062a83616dee9275c18c97p-7Q, 0x1.21e04958552e6f03502dd7935724p-7Q, -0x1.cd1c35ab2ad92bf156188522c5bfp-10Q, 0x1.af6480e4adc46cb9e0c7649b6f56p-17Q, 0x1.0136c3fb4b19b9b10157d7a834f7p-15Q, -0x1.6928b0e495d07fb474aad6800549p-19Q, -0x1.6377af73884bfae0ae8534a7569p-25Q, 0x1.64323c063686a79e3f723a6f6b93p-30Q, -0x1.6fb51174aa8e375496c635af829fp-40Q, -0x1.32449da1b960881894abd2226adap-55Q, 0x0p+0Q};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.1c297e1a722977a767a1ff227742p+0Q, -0x1.a72bc3c00615f73ba93716b01e65p+1Q, 0x1.8e98178e99b31d46ae26eec0b1cap+1Q, -0x1.8f506e2a5e0eb5edc0313f13b62bp-1Q, 0x1.02364935e2222846b9cdda1bc87p-1Q, -0x1.0fb2290536b31f2a2fbff3404bbdp+1Q, 0x1.80597d49465bf4c4d8869fb534fap+1Q, -0x1.38ad9781c750136475272cd6e902p+1Q, 0x1.339d144fd9550bb8463b544a6643p+0Q, -0x1.08b97b33caecc76a026ab8335d28p-2Q, -0x1.3f8a268debfb77a1cde76d550fe7p-4Q, 0x1.2b8bd1a4fd0eaf4aaa08a96cf3ep-4Q, -0x1.35b764060a713cc242948b5c4153p-6Q, 0x1.f33a86db42465a05a6ee3ed1f4ffp-12Q, 0x1.1c307da269dee355c5c2d340dfe6p-11Q, -0x1.950dcb7c8e981d2c1ff88549cb89p-15Q, -0x1.f904916865d4cb30ef383c46ae0fp-21Q, 0x1.8b6cb6bf7586b0f4f1fcded4430cp-25Q, -0x1.21dedfd7476c5553241f507ac2d7p-34Q, -0x1.e2c7778c519a040a7c97727ee351p-49Q, 0x0p+0Q};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.51d8dbccf9206bcc4420e8d9ae07p+1Q, -0x1.c33b049bfbce5ed995e58045194fp+3Q, 0x1.0e79522ccf3dd0b86ea89a5531bfp+5Q, -0x1.9aba40cee29c09f71dc38c35a548p+5Q, 0x1.f144c4df7513d73b0fd71dc9df3fp+5Q, -0x1.17ce56ad9d9026c80fe9053e3b69p+6Q, 0x1.1abf8d1adcc3e5071c7209bb8006p+6Q, -0x1.aeeda88b7fe87fd16bcf8e054d05p+5Q, 0x1.6d1975fc2f42e1b2096263c969bbp+4Q, 0x1.64c18afe2844c60255dd74d07edbp+1Q, -0x1.4b3d36d8f9770ee95e2721f907e9p+3Q, 0x1.8e75251a7f5bee7754c2a9513fecp+2Q, -0x1.9e20d16541319f6d732cb61c018ap+0Q, 0x1.8f713f264dac28b16bf91d504bd5p-5Q, 0x1.002e9aac591974da848a16c844c8p-4Q, -0x1.22b5d07d79f24f7de83980b5ed9fp-7Q, -0x1.695b63166e6d63ad77759faf33b7p-13Q, 0x1.ba1b21857af82fb76bf4742957f6p-17Q, -0x1.df066d7576ffcacbc6c94f3c14p-26Q, -0x1.8ec06f9de2f7d48618cf3f2e0232p-39Q, 0x0p+0Q};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0Q, 0x1.553841cb8504c59ec8828722c9cp+2Q, -0x1.1648a261cfac86a07a577122f4eep+5Q, 0x1.7429c31b8bcdc777e06851df4ff3p+6Q, -0x1.d2259be1a7818ecd1bf98b71d684p+6Q, 0x1.36cbd86221f4c1c381302622675ep+4Q, 0x1.4a282d1320ed73864b5c73d42965p+7Q, -0x1.2e04ab290e2e062d6018a7405d3cp+8Q, 0x1.5f18c6755ba04a0fe5846dc7ce5fp+8Q, -0x1.80bbefefb89592a7731263e58b6ep+8Q, 0x1.90ad4b61c673e71a7b1a638ff4cp+8Q, -0x1.4159e0e62036c0e7d3a9372888dep+8Q, 0x1.4eba06db33d52e049a499539c59ap+7Q, -0x1.6db5a82568a43d359e1324f88c7ep+5Q, 0x1.6613709f48645b09020d1137193bp-1Q, 0x1.7dbb7d4fa2b472146ed131c42bb3p+1Q, -0x1.1851a9519e35d94904835e4c0f44p-1Q, -0x1.230c93cadc0b78607a6df63dd398p-7Q, 0x1.7e95e283d8ce34ce8180e79a24c3p-10Q, -0x1.136d2374e371184371f11564efd5p-18Q, -0x1.ca2f0f4b750065dbf1a91e494693p-31Q, 0x0p+0Q};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0Q, 0x1.43e579b56aec6db8f44fad1a2ca3p+2Q, -0x1.2015783789a1305c4b04f4299082p+5Q, 0x1.be9eb07640a6e4dcf71e8edd1986p+6Q, -0x1.917bfbcd50104121d7cf2e5fb61ap+7Q, 0x1.e7564ac670464ea6f5bb03253324p+7Q, -0x1.dd46b6e14bd993fb7d27e4be31d5p+7Q, 0x1.c24b2cb18bb303674bf661030f65p+7Q, -0x1.9299f7098407dc40f69f41f42557p+7Q, 0x1.2da088f392f175bbf1502b058265p+7Q, -0x1.7f74fc0a8fbbbd2a662926cc0952p+6Q, 0x1.cafceab55c22225d33d140f11ba1p+5Q, -0x1.cfad0a751fefca13c3b326a88e5bp+4Q, 0x1.f4f5eade96653abb41ce93f1a983p+2Q, 0x1.14b6d949957a5646a550369bc7aap+0Q, -0x1.5e908a00f74d9f8f6b65d286f0e6p+0Q, 0x1.1ee7d490234e22c547ade0704929p-2Q, -0x1.1e667fbdaff187310b0173bcb94dp-11Q, -0x1.81c4231f27f23e6bc64b0c2f2493p-10Q, 0x1.28216d550397d430f8799924705dp-18Q, 0x1.ebdb45ca159a64fa9f199a16a149p-30Q, 0x0p+0Q};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0Q, 0x1.0e918e0751a5f26d66d326215241p+2Q, -0x1.f54b1dc71e94b922c8b7d974b91p+4Q, 0x1.8cc935a5962f326b8767e9c68e69p+6Q, -0x1.5d87f4fd9af883e7ca8f85ba9a3ep+7Q, 0x1.7fbdfc1f5c92ac9439f72d5fc5fbp+7Q, -0x1.356154b8ce2bfbb26ff26135d3d6p+7Q, 0x1.00a2f00b6f35fbd2365b8c4d7e4cp+7Q, -0x1.d61ad68084631dc5b1cb350d96d3p+6Q, 0x1.4b192d7116369fcf46bbc7590d76p+6Q, -0x1.2bd7eeccbbd8b3529c9ec7ea0986p+5Q, 0x1.d23af72a9213134d138ab79fb28fp+3Q, -0x1.a5a3f6309aca858b5548cc51629cp+2Q, -0x1.0097ba319005f0b824ee39f7e25p+0Q, 0x1.29abec5ca24e481b150656fa7b24p+2Q, -0x1.6d63c669ef72a15dead10bbf465bp+1Q, 0x1.521b96f1f011ffd834fe0c4deb25p-1Q, -0x1.89a1e9b6409a39917b2558fc77d9p-6Q, -0x1.cc0f8b0b31975b1da167d6d21402p-8Q, 0x1.9e94a90cc2ee8162e5d90cf2df7p-16Q, 0x1.5739a9ee6eb1c850a9597f22010bp-26Q, 0x0p+0Q};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0Q, 0x1.c2a4ffe9661190c09a7af8b79479p+0Q, -0x1.a9c9682497d4356cc97c7817608dp+3Q, 0x1.5bbb8c487ae5bb615e8e73227ceep+5Q, -0x1.452573aebb3bf474bf24d5595fd4p+6Q, 0x1.91c80b52c3671525c3375a1dd5efp+6Q, -0x1.84d65b83affb5ca97ccaf8b73947p+6Q, 0x1.678e1d36597adc53993fd96dab7ap+6Q, -0x1.4933025bdb6895888c173cc7b2a5p+6Q, 0x1.14413c8e18075f1444cc540dc34bp+6Q, -0x1.b51d99f6678421b18139d5beb61cp+5Q, 0x1.483818775e0cb14480b32b95042cp+5Q, -0x1.a72562d5d8064b092b7bae77a4cbp+4Q, 0x1.e00e48c9f77143cec0c43c67669bp+3Q, -0x1.1522f77734c2edb19342e41508e1p+3Q, 0x1.152961e6e0f56f5672007e36f948p+2Q, -0x1.3d9d88a64fae43ec46db73db181ap+0Q, 0x1.3f1c58e4e2a682bc6ff059fa1f8dp-4Q, 0x1.b3efb441a4e1aa6b7bfceb788233p-6Q, -0x1.baa159e67dd4ea14a46828d67fefp-13Q, -0x1.6c2d94cde3ae1bef5e760e39de7cp-22Q, 0x0p+0Q};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0Q, 0x1.480f31520e3f310c306bdafaf042p-1Q, -0x1.38fe2f09aac57b92aacdaa15d1b7p+2Q, 0x1.f8f411bacc9f961bc5fe5499f875p+3Q, -0x1.bc60c3b54f90a9241998e0192f5ep+4Q, 0x1.d3d44a6a16adb2540f6bfe5db93ap+4Q, -0x1.536d6f833b66773a970214ff031cp+4Q, 0x1.0953a7a524aca913282b24103258p+4Q, -0x1.0c0dca303e8e262fc9682f1cf736p+4Q, 0x1.af56b1534f29dd21b9240915b75ap+3Q, -0x1.f628948ceff73b6d1ae732743415p+2Q, 0x1.3ef834c3289aa35b262757674e4bp+2Q, -0x1.c75ab5e1afc75a2d9d28a11fcce2p+1Q, 0x1.cb38bb2c5f4bebadf622e599ec8fp+0Q, -0x1.624785bf15dbe093496b9f1d5135p-1Q, 0x1.61b17ae5ff0c0c37a77be972ec5ep-2Q, -0x1.0b62472bd3d7849095f6dced344cp-3Q, 0x1.c9b3ef0688e890b76d9f130077d8p-8Q, 0x1.7c528a3f2156c588899985294901p-8Q, -0x1.0c4738028aec930d4308df6549ap-13Q, -0x1.b40e785cb88086ef360909630572p-22Q, 0x0p+0Q};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0Q, 0x1.8a25fe79d1c4ddac335be8819a8ap-4Q, -0x1.79dddd860d2147a7416541793f71p-1Q, 0x1.2f92842080f0827925b022200689p+1Q, -0x1.04a53246109b6b6c0d3ef73b505ap+2Q, 0x1.fbc727fc23eefb6381085fb0ea64p+1Q, -0x1.2e8a4ebac6b5e49a84fad5dff777p+1Q, 0x1.96ff87cfe4cc502ebda973db1ba2p+0Q, -0x1.db8c7f7bf2c3a242351f9975276ep+0Q, 0x1.8867eccd39d1aef372869101502fp+0Q, -0x1.7019bc278ffc03b406b2ff135206p-1Q, 0x1.a30d20b4e67c690471d7cbcbb0dfp-2Q, -0x1.7340e7a399e63a19859bd6b84d4cp-2Q, 0x1.68181929e64c530045ddd9e48ddfp-3Q, -0x1.50a6f5e8f3b308d50e585f11b7ap-5Q, 0x1.8d3b211eb839ac11193734372a7dp-6Q, -0x1.b7227d5381373569d6206c572353p-7Q, -0x1.a3114fdf2fbc06953fcb9931063cp-12Q, 0x1.71e7a3b4d88bf16a9f3c256dd239p-10Q, -0x1.4eea023db8bd4900ec558c766ab3p-14Q, -0x1.09aed93888304346e30d148d3c14p-21Q, 0x0p+0Q};
-            }
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            if constexpr (order == 0) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0153862862186078764210148054384665436987968299086163110916049774302302509757"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.463408201308509360685176566158665903411342347448682788607059620387445077532"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.813391995638826649479330465641602870909776013569395886947250616963915046071"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.456892999686536248322183305850398976442122564743086558409415878925543062613"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.257677261446702307763827286244642468068192138990732487426320016042544286916"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.136658505010362584956891849494062948225995486599841370839711839313046305597"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0576567662131323839275754677629378113124645271947858794185772706476552313105"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0160561515054805568795851215654406366459996109297291243447819308339625896857"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00196464741458920772402831404575169651260998923501842539475704095236022681377"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000112798827446855800791029803530656734991774835196287349403803335501621270655"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000594554781954403684033785931588011770054264082896496671103792500235464433295"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000562564136659884191230679156227868258475904572875936016422586126656291941418"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000518789197025363361471577911859966580654417969569942459663451570764021770902"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000132373214147764795577030206527013960188029793451345023965588627064041150704"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000155390580715395054554173944015565071767006531414831642901826878560185386309"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000401688533248623065067198103021582298234469777511892684855878156604369527873"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000316054552262036582439139330382598424252005270997818496711644728508686815474"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000298054298041780380540322339753186187258299530548878985631631068130187725404"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000186295230202489625442020988651081124044989063537598156376169532878324451123"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000118400908492220475093634528886504359773639984757721702393945884924044020060"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 1) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0804528820713690537679942952538307927448324275292783996775043561168764668792"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.901546685057318722606544198126464222660980499114959450975631195995562075653"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.969147458016531260537001332368135743279288495176200726279321756564798820440"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.128597705133580020105456519744387638532533583968712163469421630736054713073"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.148537085873201139450805597667488365500301018520176104569141326668098237996"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000352682530778098478434438198206217867661443912512135381010073899276667394708"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0747341340384494360574688474082559001763945248197182213228281231111410765743"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0661630051393711509223363180529539046273421054851354002096935895895589322378"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0311756207037897739706621005131524864825329454001744116473141441231765143715"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00809240777908867125888958717233316990861675515056387491671985358196801653703"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000534709572707320623292468935686184597428178805593585443411787185724270841266"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000344459049457110720806003651240962720647979860629593805430817794517683005097"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000998200401053258733952321911032602231933728074550949033897739987254062819085"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000337395239823704966830913455725328211227310458904067484070296753117772464426"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000178872548120729485900416417576878299998863692536435591416599550573501317289"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000444376921974173227032345936619919762366059115958040870563226908761301278160"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000135190824431474161018642835112040642148891160635198350421744055168342457059"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000269018645424657851835556324494989262226498212843590290606946175171968874237"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000198235161188202162103176056710579230402924914509457090754670397189279898276"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000000000251966447199947741787778445282273243764250629238425265938759750960070288565"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 2) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.339873865726403823874694504886230871354288247669120680859586352931910650802"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.594682054416009422785849668697082787755660519264449722390570694692122196031"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.28222140990908627713882079321726861540709199811588816762195376180866676151"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.13984304652589597399637402140982673032568889063380246443975686333143709866"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.82942287297379899817138989243274273519930408716847888511551935958914702440"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.37116519281717568064954984833983547962197792842040302587532179757516934771"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.270555374392051307156490696193132354552391022825927018192372907103041586105"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.184046005646555652197008303457890114279643877305115529070305316012624288888"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.163867117286074044679000700383983800581641338738039398170630891049204540480"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0391947889912791807642293867045881185152396327816360187024476982368191084445"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0111189340353413485147270893150106933823953700659393824844796952100999217654"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00884631711293466609492290342912398272864238580654395596445675814230221634902"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00175899579589153660809115004201226274173551391561283661338278039734836261348"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000128565010951553987674529189490213861196316851900637195447923613618392713735"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000306622896125458146897677483454122489183614226371943713405943027958351707517"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000269084385910343679257051203982323513897525615083571592326449237527728689054"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000413818658474313744350785912858525849906772047679216774507165554252423741218"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000129583433007671170780305889377624130848179796328575186687487583063726979193"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000130635874598988057004789486171609848753519703338247439616746352104966358265"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000332056463780931130817519370455224958306055159032983343572060292369140142184"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 3) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.11000812669423065201408736025211163644399899284324684887960095471364939561"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.30602309108887457792110755842802529228225817003803592467879858392073911911"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.11401648009214052848211556518765632906037687404471414836791183188060792139"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.779910509750178545578760075470210269561158846741323352073939231867070856952"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.504320419147067435491020898845963984718363947233445348465286515163831830149"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.12262451891492618285514915625369193255653192234826741230297804628732384508"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.00273099973557546696148253375588381632944425785087065216350459031139544566"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.44279760205120109440892243572637061929619282682731780365162404438278331658"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.20161559056699135006082217921675647820154446695817183171496635761222714468"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.258520054851697959251777889637477507802570871015640968136924573283611103029"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0780126100569294916448477016495706044874014105663040020611150095580660962657"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0731313885915515903797324164189780989405177158479326795726386610419770126352"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0189035870354593148101137495477572951021716699214895023786902900987211265014"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000476101513144094836944099173568934880809112562865614785758014193018660882339"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000542048296030493162492883395621428687561762136240537247628992820097566715272"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000482861860046811029771577073119595197181588063401982223039270103384434060022"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000940669036930439153511860275388566814505399165175554813865283382967471512611"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000460334894609940486697079115005770453881482490309436808499379292148676402667"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000659089444165122287064782258267187195472691487712170997364379779451246094661"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000334995342514096728311283812541641458320430857209624625943650939806191456233"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 4) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.63943049915747295902408884381492456615013102835825837278218094298381059975"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-14.10095434632826170706015754809187240473647390058020018665331529642229273560"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("33.80923876769495738178795299271336231298081520211817127483146415279224333890"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-51.34094392422730822169625783218914621608905661019301981247127969679259656370"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("62.15857863021890815900436678476312302754891486816333143898291218703682880770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-69.95150252603710930320770250549877801440701750703949252096860337732317006130"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("70.68706171009487085024307021653246851862364809264251626425285523034249218320"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-53.86604413017363404938611622171529791896555966533772428275471051281075597180"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("22.81871603498091653948869197203037193649186992806348920181610865185092457340"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.78715646181129822503760020954122490057506409714944714939146997166220972189"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-10.35122244241549248750998798029030033554857264769764070098905656424283124680"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.22589995944639343162447192606753092490081390725441582060459808007413775955"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.61768826219594651676851154369360491801137647456640794313175997512654068683"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0487600549117153291242267435006532626983384560499959793316799708161496794985"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0625444452212547866619276559961974061899918807020408330419298222926353018189"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00887177162344660903733729314681709539971921946704977985564110911846620363922"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000172308435777249447063922911208598540360539757913378670543697270097011078916"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000131757849528219664204655654758892673480971917353333971564471583795581462196"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000278829310385893278753467667297067592695172655495747023195258681155064789066"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000283330126035508764154051402203972353668751336274290837719220178109180982040"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 5) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.33155865550004324339411698075437576125001114031131680543558258637926722542"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-34.78546596922894035358221752013471418576656119892560802306039573901884498850"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("93.04078333893580274273554726200086898992117829963170573289656818645421417950"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-116.53672745308757790035524178072195510211938340870303002375366241537010190400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("19.42476690609991902018771707602390047697990808120145803963343105970827114300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("165.07846889283130224972392556901964656573551315330125176803668977902167923900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-302.01823670002161100444326963103590042074566858643871979378909432822312022500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("351.09677823531118456691013587333441077552991458958521920799116438915277804300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-384.73412988907291298126127857698299454483222915340925177050408733410565143700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("400.67693148703611109141641562065904066331648411152048236040109020183777077600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-321.35108793531867698893279523881710779471319811290683986733942416578230536600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("167.36333355910991474853808717960164594081543936479125456031564843552211416400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-45.71369961953726477752159230409155711113565175365517527967211543525719318890"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.699367064899157418988908846748802289435069698849047603720655697336454274985"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.98228422535376897161740571847584616697653819004075212716090431169277576972"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.547498027051101574561205976576588259175101412173034924756008962903023025120"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00888211456705821551022409285786342463315511465858554494859435135093539710800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00145944781339651318786975450416647682444162007080853467985950420011002879779"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000410417202524410779263314775667707070690036033233187273470129649919772492533"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000833431526424512126756266586592842608072719180575476717997770913071706154856"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 6) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.06088106838769290054968439394567345106326651755752600922150619200981904649"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-36.01048320187342016064122793694682929039037974207289646083751798817843620580"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("111.65497002381900847391604108056132695425373640954404816320887269328425438600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-200.74215547182405062933561376177594578645448343871864023725391767591774835600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("243.66853923912563333720102697769935941130760592520157588467019833307464642300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-238.63811401415731691311790369583173568877153676175659117260463100444743159100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("225.14682535963357317765848454921569290528275448357783818162730153311551574600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-201.30071286904051720114799658023138705341732545954845691270252578520003833200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("150.81354485672703044612123433476281157995253230519198222354112466751203726500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-95.86424271108893183923291774912315316192315495940385275849744648479129371610"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("57.37349454581659918342847281164914782841679698416807207317817480336962650140"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-28.97974630119186880188417545488990640756883378387320588356588113332720316360"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("7.82750961052950670790289612831387996295164858527519664270838963476345026334"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.08091505094987758545055341443439247053069659406365117057429783552826238760"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.36939299129089996854048024593726735159933395218523578300840349681327697303"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.280181237504463119434520254208320451998395772453319918592970421102919439139"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000546265385956676161209750070768621430280614491537142208248905211721125879926"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00147158111921181446121734700653833523667079723972927387216993834057729665501"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000441268942542730566701346669932877725269376519910764607900294893415486917856"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000178936364555416156355622735225731323849173624958182729551826746278581656345"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 7) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.22763395991077497600708800752870112512802019777846803123422609253523444499"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-31.33083894520795656643557338514370343692021933760780167709842547864854441400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("99.19649370888855559161612539040862291452743358994450794072159006509952447180"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-174.76554100529416030240273725663066184549978635556382128606302159015804699400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("191.87106416707077830176594781673733058344977599226321690051187655465260417000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-154.69009950176950187209831807333662376535557038525297678672923277217118961000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("128.31823764545969592124295974645679685264644800112728210780946540963513417100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-117.52620888526942424001135357455119389132936854292759496512541610625978723100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("82.77458740900115668785824293717372920888452561941133683536618899571268039270"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-37.48043594311010343509519734340882271874817171143915172303616751347250271800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("14.56969793619700440657543207683336718496887543376426838538228469975643333100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.58813242670581930805873617097473570421450364523198050554153666935990605860"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.00231517515205560297111170032367032830624266948757853925257748047437485705"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.65111836477555984946605574234122313918908034655085234744720545935378656185"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.85460739300369418699655129485713788069696498710719979317225671767847465746"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.660366742165965802145434489749517292319612368608367169686199145406925272970"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0240254194586754357618804390248717384819465676000390734107846903076164025556"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00701996941206172392237021839195076817058449392415590849322406637448645715144"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000247109356222148754647438533593506924053068870724972211566904008498782300086"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000199783389222010785055607244259171818398069280425424499723517627544611259097"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 8) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.76033019493303856051687449323434388609090202601383913064385190376448183312"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-13.30583579203687943081629136293267795607309397777682235599140484923954366500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("43.46657616257718154366654543277971738319342135931706703195817811035185093990"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-81.28657410638605936274247923055646375830285098524867924682488987143954182420"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("100.44535569493907191996663384307406316811627445344739700254788195526559558500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-97.20933347474678202187842214477633354845397460973373353664056650468754174360"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("89.88878331109182469176945890436872342814210396602291754411932369668940781030"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-82.29981368567145730476008183188924859214306594631403889804786963467235197800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("69.06370756169948695128970734742378882589833357909995593129091002885751309170"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-54.63945381644636331825019271777000447410834252910294578185697306015613918450"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("41.02739041572348156154461856933135418845380309772196428740672678193620244590"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-26.44662745983841279602705174819159511393608583819553179666861965546358182250"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("15.00174369284244633245038836591523658570351126534715276565083434487614618120"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-8.66051839144173892722259100499075549842639519928721133973595893424223456610"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.33065078303101010579895420947640558162604044791599818852754301702712403354"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.24068502483685799590790437877354796560395991582308092016594732485261421186"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0779078934121258971785160919472512639431601470709999391983348576222593616764"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0266074428860304338208309476152802616336853971424135540169564254497724564119"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000211062563905998390099917614137909944233433155336638390553050174056557131393"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000339167240842007413867671399755809233304462324861037758236912743626130786250"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 9) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.640740910784300850608448747428708985857357012208138478640701473826119071995"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.89051414436388374023627360586462653542345290441410991274311164920600966594"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("15.77979361042251828056602777327009987727897110266960291592731419702813423270"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-27.77362414192706755256336444082924835831112932806579979321237948678315003340"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("29.23932877961020134280019505838077863032589219652057187629061788645605764150"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-21.21421767485153769358479119905782957335265962757154762905239908876532045980"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("16.58292355069242264838528754441677563862319454861075967735395941314979352800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-16.75336665006114737745223674059225270255439659949203892423230795535668534770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("13.47933260222753983145552435052316707867495382773984724176882313942650009280"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.84622682345785779224288430587701090510900802969451706536957930436008165844"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.98389929827173202326056782961135292617104624089540476377857847941525260633"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.55745576400618796425954497528896729856448578899557932766030185253705183005"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.79383439858729303972208191272224953494584793148950860052667722677927056863"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.691951922965863057242007607869971708166614493007258083206682103112632034601"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.345403595245226611364778279349176734775513013282472618970398880792800137706"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.130558544182786348133975182480093367398008959930808967410065238652717910680"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00698399148544449295954023501742964713288497821639870432194548542030467210561"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00580325961266701622640949560827629673155869792665828211986634190720023351417"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000127925013729926386622233224468569958480332535234461953049381468504991463929"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000406109284685247160935243546331678983485852468994859006463959277286676783577"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 10) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0962276401961485707634176189196513057375091608921918899965672697435379944132"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.738020823110277888005487147166448075761525987078292691760810832596632987072"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.37165881716817146455198793581381209035513677222207786580044965069857187102"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.07258278696320160772598824632813109064068582481103097502282770918877166041"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.96701526462117458029198549268700257108768896990631205803877021434675874630"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.36359581108028672945508028330384282919707503803425311590987150576557002759"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.58983658624201607243694322053302702142722584179817682236311853130843295497"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.85761257911759839282249544686803595350328330563233456669214217961095916255"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.53283576975247258432308684518667039820955312493092996957652314465829192761"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.718946342305564226765801789587960150187823928357554861829190310338862006619"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.409229765931396736377286349516677311112729496444160501691912630223706015387"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.362552279816077162656936242116884276626981924474959700030697184703184497473"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.175827213851141339261603124481542122845079828131432589861342337234868002619"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0410952380112717990391343459878268460433238007822432915185287645982519381943"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0242450545728193174252974797154291458408637398260602402141534552772736201039"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0134013282722748930010976896226591764148191213826882368913426650595356115231"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000399654030797277232222848286358951433908666645251171779800808018550167077414"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00141107498821972634714801414163161931174746710841213074592354066961171560834"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000798497430554567452885354694999821103608152142620563483234681315502038086578"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000494873154958329223506257796254007745988846883400505225346149184283368961203"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-        }
-    }
-    if constexpr (p == 12) {
-        if constexpr (std::is_same_v<Real, float>) {
-            if constexpr (order == 0) {
-                return {0x0p+0f, 0x1.ba5636p-8f, 0x1.3af728p-2f, 0x1.da1522p-1f, -0x1.5c6f66p-2f, 0x1.4840a4p-3f, -0x1.9d4fdcp-4f, 0x1.042a86p-4f, -0x1.08554cp-5f, 0x1.86c906p-7f, -0x1.8785b4p-9f, 0x1.f00fcp-12f, -0x1.43b7cep-15f, -0x1.dafa2ep-18f, 0x1.2d678cp-18f, -0x1.f0554cp-22f, -0x1.934a0ep-24f, -0x1.3a5d96p-29f, 0x1.0e0d22p-33f, -0x1.652334p-41f, 0x1.02e74cp-47f, 0x1.bb358cp-60f, -0x1.f67e04p-79f, 0x0p+0f};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.3daa14p-5f, 0x1.716f56p-1f, -0x1.16beeap-2f, -0x1.f51bdap-1f, 0x1.97243cp-1f, -0x1.b8eefp-2f, 0x1.2402bcp-3f, 0x1.805958p-10f, -0x1.fa47fap-6f, 0x1.025a88p-6f, -0x1.3d712ap-9f, -0x1.c5c0dp-11f, 0x1.c45b6ap-12f, -0x1.6a167p-15f, -0x1.13c0d6p-17f, 0x1.b2cff8p-20f, -0x1.9ee91p-25f, -0x1.c87e12p-29f, 0x1.b076eap-34f, 0x1.71c42cp-44f, -0x1.e6d8e6p-52f, 0x1.13fd18p-69f, 0x0p+0f};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0f, 0x1.77fed2p-3f, 0x1.e1d108p-1f, -0x1.9e9c7cp+1f, 0x1.bc153ap+1f, -0x1.240fe4p+1f, 0x1.80cee2p+0f, -0x1.abf5ep-1f, 0x1.50c7e8p-2f, -0x1.4654eep-4f, 0x1.091b1ep-6f, -0x1.59c476p-7f, 0x1.935e46p-8f, -0x1.8fe152p-10f, 0x1.90febp-15f, 0x1.09bd2p-15f, -0x1.da6da6p-19f, 0x1.a3887p-21f, 0x1.0f785p-26f, -0x1.63226ep-31f, -0x1.84d7e4p-38f, 0x1.75cc98p-48f, -0x1.a7d232p-65f, -0x0p+0f};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0f, 0x1.60087cp-1f, -0x1.1c49e2p+0f, -0x1.f023b2p+0f, 0x1.8d30cp+2f, -0x1.80e0dep+2f, 0x1.c1feacp+0f, 0x1.3621acp+1f, -0x1.f3ab98p+1f, 0x1.5e6794p+1f, -0x1.c702ecp-1f, -0x1.ee149ap-4f, 0x1.ffde0cp-3f, -0x1.a2cbbap-4f, 0x1.d58bf4p-7f, 0x1.206bp-9f, -0x1.dfc88ap-11f, 0x1.f86e54p-15f, 0x1.28c92p-18f, -0x1.9c90e4p-23f, -0x1.7e8cfp-32f, 0x1.cc8984p-39f, -0x1.051a2p-54f, -0x0p+0f};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0f, 0x1.efa02p+0f, -0x1.34df3ep+3f, 0x1.596114p+4f, -0x1.014d7ap+5f, 0x1.5a4b7p+5f, -0x1.d72d9cp+5f, 0x1.1a6ca8p+6f, -0x1.f8d9fp+5f, 0x1.142ce2p+5f, -0x1.90f39p+1f, -0x1.822b1ap+3f, 0x1.52a34ep+3f, -0x1.0b934ap+2f, 0x1.335fd6p-1f, 0x1.17c48ap-3f, -0x1.003386p-4f, 0x1.68d464p-8f, 0x1.b6ad0ep-12f, -0x1.c361dcp-16f, -0x1.d59d4cp-25f, 0x1.f6c8c6p-31f, -0x1.1d1866p-45f, 0x0p+0f};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0f, 0x1.1672f8p+2f, -0x1.d05e84p+4f, 0x1.49fc06p+6f, -0x1.e4421p+6f, 0x1.09c53p+6f, 0x1.677b64p+6f, -0x1.fbf398p+7f, 0x1.628082p+8f, -0x1.a2714ep+8f, 0x1.cb4de8p+8f, -0x1.9cacd4p+8f, 0x1.055f48p+8f, -0x1.8ddf94p+6f, 0x1.95561cp+3f, 0x1.8ab9ccp+2f, -0x1.6e4fp+1f, 0x1.43d702p-2f, 0x1.951dp-6f, -0x1.5137c2p-9f, -0x1.3e3df8p-18f, 0x1.78041p-23f, -0x1.aa8cd8p-37f, 0x0p+0f};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0f, 0x1.6688e4p+2f, -0x1.50ba26p+5f, 0x1.18d5fcp+7f, -0x1.16422p+8f, 0x1.7cdc34p+8f, -0x1.a2f3c4p+8f, 0x1.aa319ep+8f, -0x1.958a02p+8f, 0x1.4bb5b2p+8f, -0x1.caa92ap+7f, 0x1.1f2d7ap+7f, -0x1.3b920ep+6f, 0x1.bc14b2p+4f, 0x1.8c237ap-1f, -0x1.7f694cp+2f, 0x1.3f67e2p+1f, -0x1.4cc6cp-2f, -0x1.6b5574p-6f, 0x1.38d6e4p-8f, 0x1.260d96p-17f, -0x1.5c7912p-21f, 0x1.8b88d4p-34f, 0x0p+0f};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0f, 0x1.80f666p+2f, -0x1.7dd222p+5f, 0x1.48b0d8p+7f, -0x1.41512cp+8f, 0x1.8f56fp+8f, -0x1.675a3ap+8f, 0x1.2e9626p+8f, -0x1.12635ap+8f, 0x1.969994p+7f, -0x1.59e9b6p+6f, 0x1.09d1ap+3f, 0x1.cc8ab2p+3f, -0x1.93c8d6p+4f, 0x1.013c24p+5f, -0x1.784654p+4f, 0x1.21acdep+3f, -0x1.6fa584p+0f, -0x1.39157p-4f, 0x1.343728p-5f, 0x1.c53d4ap-15f, -0x1.57bc52p-17f, 0x1.869c12p-29f, 0x0p+0f};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0f, 0x1.d573dcp+1f, -0x1.ddfb9cp+4f, 0x1.a873c2p+6f, -0x1.b2204ep+7f, 0x1.23910ep+8f, -0x1.29c6cep+8f, 0x1.1c64b2p+8f, -0x1.156986p+8f, 0x1.ef2b6p+7f, -0x1.84734ap+7f, 0x1.20e874p+7f, -0x1.93d454p+6f, 0x1.e8c646p+5f, -0x1.0a8b2ep+5f, 0x1.14ef6ep+4f, -0x1.bab6f4p+2f, 0x1.4e6abp+0f, 0x1.e57eccp-4f, -0x1.0f174cp-4f, 0x1.a1f2dcp-12f, 0x1.400292p-15f, -0x1.6c7e6p-26f, 0x0p+0f};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0f, 0x1.d2f4ep+0f, -0x1.e196ep+3f, 0x1.ab061ep+5f, -0x1.a7b25ap+6f, 0x1.04d398p+7f, -0x1.c308c4p+6f, 0x1.759cb8p+6f, -0x1.73a4dcp+6f, 0x1.4d02e4p+6f, -0x1.c4dfc6p+5f, 0x1.217c84p+5f, -0x1.9d3e5ep+4f, 0x1.eced02p+3f, -0x1.ab1578p+2f, 0x1.780b78p+1f, -0x1.59e4e8p+0f, 0x1.04013ap-2f, 0x1.63e904p-4f, -0x1.26b33ap-5f, 0x1.1fc084p-10f, 0x1.9c18e6p-15f, -0x1.d792bap-25f, 0x0p+0f};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0f, 0x1.19eec2p-1f, -0x1.249f96p+2f, 0x1.0297dcp+4f, -0x1.f4e8dcp+4f, 0x1.1efd1cp+5f, -0x1.a397ap+4f, 0x1.239464p+4f, -0x1.3946dp+4f, 0x1.289832p+4f, -0x1.5bb8e2p+3f, 0x1.68255cp+2f, -0x1.21aae8p+2f, 0x1.64fab4p+1f, -0x1.75b64cp-1f, 0x1.22ff2ap-3f, -0x1.07ed62p-3f, -0x1.4a01e6p-6f, 0x1.2e7cdcp-4f, -0x1.b7f686p-6f, 0x1.17b65cp-9f, 0x1.910e04p-14f, -0x1.cf434ap-23f, 0x0p+0f};
-            }
-            if constexpr (order == 11) {
-                return {0x0p+0f, 0x1.a6c51cp-5f, -0x1.b83154p-2f, 0x1.89e13cp+0f, -0x1.8aa498p+1f, 0x1.eb2b7ep+1f, -0x1.a9173ap+1f, 0x1.4e8702p+1f, -0x1.31bb74p+1f, 0x1.0e1264p+1f, -0x1.9cd0dcp+0f, 0x1.3cec22p+0f, -0x1.daf36p-1f, 0x1.329c32p-1f, -0x1.8936aep-2f, 0x1.00deep-2f, -0x1.07bd18p-3f, 0x1.cec02p-5f, -0x1.e6ef9ep-6f, 0x1.8f4f48p-7f, -0x1.e72d5p-10f, -0x1.e19176p-14f, 0x1.1b79fap-21f, -0x0p+0f};
-            }
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0, 0x1.ba5636194c094p-8, 0x1.3af72853b189p-2, 0x1.da1521352f488p-1, -0x1.5c6f665240adep-2, 0x1.4840a35a3e507p-3, -0x1.9d4fdc34ae4eep-4, 0x1.042a86a360592p-4, -0x1.08554bd18ab25p-5, 0x1.86c905bef28a7p-7, -0x1.8785b403c86f7p-9, 0x1.f00fc00fce26fp-12, -0x1.43b7ce1fa4e5bp-15, -0x1.dafa2eb6c7f5dp-18, 0x1.2d678c174b94dp-18, -0x1.f0554b8e5712dp-22, -0x1.934a0de4da293p-24, -0x1.3a5d95f1928efp-29, 0x1.0e0d213886187p-33, -0x1.652333b32760ap-41, 0x1.02e74c07e6081p-47, 0x1.bb358cf4adf4ep-60, -0x1.f67e04f08f215p-79, 0x0p+0};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0, 0x1.3daa1461d0cf4p-5, 0x1.716f56bac1b11p-1, -0x1.16bee99870719p-2, -0x1.f51bd9fa1cf2ep-1, 0x1.97243be7bf084p-1, -0x1.b8eef0110c9fap-2, 0x1.2402bce395302p-3, 0x1.80595820660c9p-10, -0x1.fa47fa3f4b022p-6, 0x1.025a88022a414p-6, -0x1.3d712aaad7776p-9, -0x1.c5c0d04fc8743p-11, 0x1.c45b69075cdb6p-12, -0x1.6a1670435bfddp-15, -0x1.13c0d643a27dcp-17, 0x1.b2cff79438463p-20, -0x1.9ee90facd3d13p-25, -0x1.c87e1185ca55bp-29, 0x1.b076e96662045p-34, 0x1.71c42c5b1e647p-44, -0x1.e6d8e5785ac94p-52, 0x1.13fd176d0c255p-69, 0x0p+0};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0, 0x1.77fed2e016936p-3, 0x1.e1d10780fb061p-1, -0x1.9e9c7ce63835dp+1, 0x1.bc153af50c24cp+1, -0x1.240fe3f248861p+1, 0x1.80cee17390c18p+0, -0x1.abf5df7fd7acp-1, 0x1.50c7e71a108bbp-2, -0x1.4654ed4660724p-4, 0x1.091b1dd62c3e6p-6, -0x1.59c475f85d7f4p-7, 0x1.935e464b93aa4p-8, -0x1.8fe1513629012p-10, 0x1.90feb0894b435p-15, 0x1.09bd1f2d4e386p-15, -0x1.da6da6ad5e76cp-19, 0x1.a3886fa6d48c5p-21, 0x1.0f7850b94c92bp-26, -0x1.63226d50629cp-31, -0x1.84d7e34db15d3p-38, 0x1.75cc980993529p-48, -0x1.a7d23115de573p-65, -0x0p+0};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0, 0x1.60087b087d2efp-1, -0x1.1c49e2797e56dp+0, -0x1.f023b1706ef0ep+0, 0x1.8d30c07e51574p+2, -0x1.80e0de445b21ap+2, 0x1.c1feac4e70c18p+0, 0x1.3621ab0ea1b05p+1, -0x1.f3ab98611d47ap+1, 0x1.5e6794d526a25p+1, -0x1.c702eca93a33dp-1, -0x1.ee149aa686bb3p-4, 0x1.ffde0ca5fc1a1p-3, -0x1.a2cbb989ecd0ap-4, 0x1.d58bf4f6c76eap-7, 0x1.206affc103ba1p-9, -0x1.dfc88961f6b15p-11, 0x1.f86e53415f2ap-15, 0x1.28c920e4a3f6cp-18, -0x1.9c90e430666c9p-23, -0x1.7e8cf0898f333p-32, 0x1.cc8984cca607fp-39, -0x1.051a1f819156cp-54, -0x0p+0};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0, 0x1.efa01fe281c9p+0, -0x1.34df3dac7fcd4p+3, 0x1.5961138d5be95p+4, -0x1.014d7a672544ap+5, 0x1.5a4b6fa251ebp+5, -0x1.d72d9b409f2b2p+5, 0x1.1a6ca7d65632dp+6, -0x1.f8d9ef0a2890cp+5, 0x1.142ce1c1f06e2p+5, -0x1.90f390767ce47p+1, -0x1.822b1a96e2d92p+3, 0x1.52a34d125b1bep+3, -0x1.0b934a511e089p+2, 0x1.335fd67def29fp-1, 0x1.17c48a3b6f0b8p-3, -0x1.0033850ae8807p-4, 0x1.68d4635bbce68p-8, 0x1.b6ad0e03e206fp-12, -0x1.c361dbb11082cp-16, -0x1.d59d4ba004a56p-25, 0x1.f6c8c69c71b98p-31, -0x1.1d186572e3d31p-45, 0x0p+0};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0, 0x1.1672f76c48a3bp+2, -0x1.d05e83fe81472p+4, 0x1.49fc051fc99a8p+6, -0x1.e442104e65336p+6, 0x1.09c52f838d2fdp+6, 0x1.677b64cbf326ep+6, -0x1.fbf39786bea7bp+7, 0x1.628081b6fdd81p+8, -0x1.a2714ddd5c22bp+8, 0x1.cb4de777b4f36p+8, -0x1.9cacd3aee3a7ep+8, 0x1.055f4806a8346p+8, -0x1.8ddf94a470b87p+6, 0x1.95561c2d77ea8p+3, 0x1.8ab9cc38b4949p+2, -0x1.6e4f007cb3f6fp+1, 0x1.43d7023213a8p-2, 0x1.951cff21de4acp-6, -0x1.5137c147339bcp-9, -0x1.3e3df8b2da275p-18, 0x1.78040f51a9568p-23, -0x1.aa8cd8e6f8972p-37, 0x0p+0};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0, 0x1.6688e31cf50ep+2, -0x1.50ba2688bc043p+5, 0x1.18d5fc503a177p+7, -0x1.16422099d0e7p+8, 0x1.7cdc33f38c2d1p+8, -0x1.a2f3c3b8e6e4bp+8, 0x1.aa319d6af6ec9p+8, -0x1.958a02a102449p+8, 0x1.4bb5b15c50a64p+8, -0x1.caa9291eb011fp+7, 0x1.1f2d7abf22a73p+7, -0x1.3b920d0f7e0d1p+6, 0x1.bc14b21b62b93p+4, 0x1.8c237a0fa26d7p-1, -0x1.7f694c35d9d22p+2, 0x1.3f67e104a689cp+1, -0x1.4cc6c058f371dp-2, -0x1.6b557354b8d85p-6, 0x1.38d6e371bb052p-8, 0x1.260d95329ea8ep-17, -0x1.5c7911e0053bcp-21, 0x1.8b88d3fa551cp-34, 0x0p+0};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0, 0x1.80f665163dff6p+2, -0x1.7dd2228ef0449p+5, 0x1.48b0d88030936p+7, -0x1.41512ba753d05p+8, 0x1.8f56f07493efp+8, -0x1.675a39773b248p+8, 0x1.2e9626a21624ep+8, -0x1.1263590aebe89p+8, 0x1.9699942af2221p+7, -0x1.59e9b6e0b9c21p+6, 0x1.09d1a0b7c5832p+3, 0x1.cc8ab1005087cp+3, -0x1.93c8d50945095p+4, 0x1.013c24badc627p+5, -0x1.784654bbd7368p+4, 0x1.21acdd98ca7e4p+3, -0x1.6fa583815aba2p+0, -0x1.39156fe5f0a3bp-4, 0x1.34372727b2155p-5, 0x1.c53d49d197175p-15, -0x1.57bc52155abeap-17, 0x1.869c11b6398bcp-29, 0x0p+0};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0, 0x1.d573db31c98a6p+1, -0x1.ddfb9c5686a4fp+4, 0x1.a873c238f1ad9p+6, -0x1.b2204de17a53ap+7, 0x1.23910ebcbe60dp+8, -0x1.29c6cec686025p+8, 0x1.1c64b27b4c108p+8, -0x1.156985f5c8bcep+8, 0x1.ef2b60fc7ce31p+7, -0x1.84734ae811783p+7, 0x1.20e874beb6698p+7, -0x1.93d454c0120c5p+6, 0x1.e8c645d503448p+5, -0x1.0a8b2e2c06173p+5, 0x1.14ef6d11452bcp+4, -0x1.bab6f3f4dbb55p+2, 0x1.4e6aaf12e910ep+0, 0x1.e57ecc0ee730ep-4, -0x1.0f174cea8c306p-4, 0x1.a1f2dc12ec55dp-12, 0x1.4002914419fbbp-15, -0x1.6c7e600f14b1p-26, 0x0p+0};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0, 0x1.d2f4e044749b5p+0, -0x1.e196df480fe72p+3, 0x1.ab061d20276fp+5, -0x1.a7b259e6037ecp+6, 0x1.04d3977e22f61p+7, -0x1.c308c46a51aa1p+6, 0x1.759cb7054906p+6, -0x1.73a4db524ebc3p+6, 0x1.4d02e405c664p+6, -0x1.c4dfc682dd95ep+5, 0x1.217c835a844bfp+5, -0x1.9d3e5e5e09252p+4, 0x1.eced01c912f6cp+3, -0x1.ab15772777a66p+2, 0x1.780b7892927c5p+1, -0x1.59e4e79f9d385p+0, 0x1.04013ac7f90edp-2, 0x1.63e903ad632e8p-4, -0x1.26b339b06c46fp-5, 0x1.1fc083a0e2c36p-10, 0x1.9c18e59aa15abp-15, -0x1.d792baac952f3p-25, 0x0p+0};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0, 0x1.19eec26520f72p-1, -0x1.249f95db3c6a8p+2, 0x1.0297dba66cdd3p+4, -0x1.f4e8dc0eb78aap+4, 0x1.1efd1b3c60e0bp+5, -0x1.a397a05a5f775p+4, 0x1.239464bf9e82cp+4, -0x1.3946d065739bfp+4, 0x1.2898316e66a7fp+4, -0x1.5bb8e2c464278p+3, 0x1.68255c99ba4c7p+2, -0x1.21aae7ae7df32p+2, 0x1.64fab317448fbp+1, -0x1.75b64c97e0968p-1, 0x1.22ff2ac4d8b9cp-3, -0x1.07ed621dcab47p-3, -0x1.4a01e6ee0860ep-6, 0x1.2e7cdbbc90031p-4, -0x1.b7f6865bae123p-6, 0x1.17b65cad3d541p-9, 0x1.910e0462410b6p-14, -0x1.cf434a44d45d4p-23, 0x0p+0};
-            }
-            if constexpr (order == 11) {
-                return {0x0p+0, 0x1.a6c51bc471a31p-5, -0x1.b8315371d42a5p-2, 0x1.89e13c889a74dp+0, -0x1.8aa497719f071p+1, 0x1.eb2b7ee2bc88dp+1, -0x1.a91739cfcb437p+1, 0x1.4e87023b22be2p+1, -0x1.31bb74af8ae4ep+1, 0x1.0e1263d4463c8p+1, -0x1.9cd0db1b42b97p+0, 0x1.3cec213a53552p+0, -0x1.daf35f59b2442p-1, 0x1.329c321d7ff6bp-1, -0x1.8936ae8cb907cp-2, 0x1.00dee0f33922ap-2, -0x1.07bd180d95969p-3, 0x1.cec01fe9b05f6p-5, -0x1.e6ef9d5209f88p-6, 0x1.8f4f47250e3a5p-7, -0x1.e72d4f4950c8ap-10, -0x1.e19176d7ba691p-14, 0x1.1b79fa688c947p-21, -0x0p+0};
-            }
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0L, 0xd.d2b1b0ca6049ce2p-11L, 0x9.d7b9429d8c4819ap-5L, 0xe.d0a909a97a43f8ep-4L, -0xa.e37b3292056ef1ap-5L, 0xa.42051ad1f283b58p-6L, -0xc.ea7ee1a57276e59p-7L, 0x8.2154351b02c8eb6p-7L, -0x8.42aa5e8c5592b7bp-8L, 0xc.36482df7945344bp-10L, -0xc.3c2da01e437b7bbp-12L, 0xf.807e007e7137774p-15L, -0xa.1dbe70fd272d8b1p-18L, -0xe.d7d175b63fae5edp-21L, 0x9.6b3c60ba5ca6825p-21L, -0xf.82aa5c72b896837p-25L, -0xc.9a506f26d1499c5p-27L, -0x9.d2ecaf8c9477601p-32L, 0x8.706909c430c3afbp-36L, -0xb.29199d993b04f39p-44L, 0x8.173a603f30404d9p-50L, 0xd.d9ac67a56fa6d35p-63L, -0xf.b3f02784790a955p-82L, 0x0p+0L};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0L, 0x9.ed50a30e867a4p-8L, 0xb.8b7ab5d60d88817p-4L, -0x8.b5f74cc3838cb01p-5L, -0xf.a8decfd0e796cf1p-4L, 0xc.b921df3df8422acp-4L, -0xd.c777808864fd26fp-5L, 0x9.2015e71ca980e98p-6L, 0xc.02cac1033064418p-13L, -0xf.d23fd1fa5810e5dp-9L, 0x8.12d440115209d8bp-9L, -0x9.eb895556bbbac58p-12L, -0xe.2e06827e43a1813p-14L, 0xe.22db483ae6db17p-15L, -0xb.50b3821adfeea95p-18L, -0x8.9e06b21d13ee1f3p-20L, 0xd.967fbca1c231ae8p-23L, -0xc.f7487d669e89999p-28L, -0xe.43f08c2e52ad9ddp-32L, 0xd.83b74b331022454p-37L, 0xb.8e2162d8f32359fp-47L, -0xf.36c72bc2d649c0fp-55L, 0x8.9fe8bb68612a695p-72L, 0x0p+0L};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0L, 0xb.bff69700b49b018p-6L, 0xf.0e883c07d830881p-4L, -0xc.f4e3e731c1ae738p-2L, 0xd.e0a9d7a86125cacp-2L, -0x9.207f1f9244307c8p-2L, 0xc.06770b9c860beebp-3L, -0xd.5faefbfebd5fdcdp-4L, 0xa.863f38d0845d7acp-5L, -0xa.32a76a330391e66p-7L, 0x8.48d8eeb161f2f82p-9L, -0xa.ce23afc2ebf9f61p-10L, 0xc.9af2325c9d52281p-11L, -0xc.7f0a89b14808e6ap-13L, 0xc.87f5844a5a1a6fp-18L, 0x8.4de8f96a71c3322p-18L, -0xe.d36d356af3b5c2cp-22L, 0xd.1c437d36a462b4ap-24L, 0x8.7bc285ca6495b9cp-29L, -0xb.19136a8314dfe24p-34L, -0xc.26bf1a6d8ae9884p-41L, 0xb.ae64c04c9a9494fp-51L, -0xd.3e9188aef2b98edp-68L, -0x0p+0L};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0L, 0xb.0043d843e977a5cp-4L, -0x8.e24f13cbf2b6563p-3L, -0xf.811d8b837786d61p-3L, 0xc.698603f28aba1a9p-1L, -0xc.0706f222d90cfdfp-1L, 0xe.0ff56273860c0ebp-3L, 0x9.b10d58750d82957p-2L, -0xf.9d5cc308ea3d3cbp-2L, 0xa.f33ca6a935126f2p-2L, -0xe.38176549d19e5a8p-4L, -0xf.70a4d53435d97d5p-7L, 0xf.fef0652fe0d0a8dp-6L, -0xd.165dcc4f668505cp-7L, 0xe.ac5fa7b63b752dbp-10L, 0x9.0357fe081dd0544p-12L, -0xe.fe444b0fb58abf3p-14L, 0xf.c3729a0af95006dp-18L, 0x9.464907251fb5d88p-21L, -0xc.e487218333646a4p-26L, -0xb.f467844c7999b52p-35L, 0xe.644c2665303f8d2p-42L, -0x8.28d0fc0c8ab5d4ep-57L, -0x0p+0L};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0L, 0xf.7d00ff140e483d9p-3L, -0x9.a6f9ed63fe69fc4p+0L, 0xa.cb089c6adf4abc4p+1L, -0x8.0a6bd3392a250e2p+2L, 0xa.d25b7d128f57c87p+2L, -0xe.b96cda04f958dddp+2L, 0x8.d3653eb2b19664fp+3L, -0xf.c6cf785144862cap+2L, 0x8.a1670e0f8370cfp+2L, -0xc.879c83b3e72381bp-2L, -0xc.1158d4b716c8e65p+0L, 0xa.951a6892d8df2a8p+0L, -0x8.5c9a5288f0446cfp-1L, 0x9.9afeb3ef794f7dcp-4L, 0x8.be2451db785c08ap-6L, -0x8.019c285744039edp-7L, 0xb.46a31adde7341a9p-11L, 0xd.b568701f1037966p-15L, -0xe.1b0edd888415d06p-19L, -0xe.acea5d00252b3f7p-28L, 0xf.b64634e38dcc13ap-34L, -0x8.e8c32b971e9855bp-48L, 0x0p+0L};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0L, 0x8.b397bb62451d843p-1L, -0xe.82f41ff40a38e2ap+1L, 0xa.4fe028fe4cd412cp+3L, -0xf.22108273299ad98p+3L, 0x8.4e297c1c697e50ep+3L, 0xb.3bdb265f99372aep+3L, -0xf.df9cbc35f53d89cp+4L, 0xb.14040db7eec0855p+5L, -0xd.138a6eeae115b02p+5L, 0xe.5a6f3bbda79b16cp+5L, -0xc.e5669d771d3f14bp+5L, 0x8.2afa403541a338fp+5L, -0xc.6efca52385c3629p+3L, 0xc.aab0e16bbf53e59p+0L, 0xc.55ce61c5a4a452bp-1L, -0xb.727803e59fb7b2ap-2L, 0xa.1eb811909d4016fp-5L, 0xc.a8e7f90ef2563f2p-9L, -0xa.89be0a399cde158p-12L, -0x9.f1efc596d13a96ep-21L, 0xb.c0207a8d4ab3f5dp-26L, -0xd.5466c737c4b8e72p-40L, 0x0p+0L};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0L, 0xb.344718e7a8702b2p-1L, -0xa.85d13445e021855p+2L, 0x8.c6afe281d0bb969p+4L, -0x8.b21104ce8738061p+5L, 0xb.e6e19f9c6168b44p+5L, -0xd.179e1dc73725588p+5L, 0xd.518ceb57b764b3fp+5L, -0xc.ac50150812244abp+5L, 0xa.5dad8ae285323a8p+5L, -0xe.554948f5808f966p+4L, 0x8.f96bd5f915394b1p+4L, -0x9.dc90687bf0684d6p+3L, 0xd.e0a590db15c99a5p+1L, 0xc.611bd07d136ba02p-4L, -0xb.fb4a61aece9122bp-1L, 0x9.fb3f0825344de52p-2L, -0xa.663602c79b8e8ecp-5L, -0xb.5aab9aa5c6c2553p-9L, 0x9.c6b71b8dd828c64p-11L, 0x9.306ca994f547077p-20L, -0xa.e3c88f0029de0d1p-24L, 0xc.5c469fd2a8dfc22p-37L, 0x0p+0L};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0L, 0xc.07b328b1effb03p-1L, -0xb.ee9114778224972p+2L, 0xa.4586c401849b3a9p+4L, -0xa.0a895d3a9e82ae4p+5L, 0xc.7ab783a49f782e2p+5L, -0xb.3ad1cbb9d9242edp+5L, 0x9.74b13510b126f8ep+5L, -0x8.931ac8575f4469p+5L, 0xc.b4cca1579110a15p+4L, -0xa.cf4db705ce10894p+3L, 0x8.4e8d05be2c19216p+0L, 0xe.64558802843df89p+0L, -0xc.9e46a84a284ab95p+1L, 0x8.09e125d6e31381bp+2L, -0xb.c232a5deb9b3ce5p+1L, 0x9.0d66ecc653f1d47p+0L, -0xb.7d2c1c0ad5d0d11p-3L, -0x9.c8ab7f2f851da2dp-7L, 0x9.a1b9393d90aa708p-8L, 0xe.29ea4e8cb8baa35p-18L, -0xa.bde290aad5f5239p-20L, 0xc.34e08db1cc5dff7p-32L, 0x0p+0L};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0L, 0xe.ab9ed98e4c52c95p-2L, -0xe.efdce2b435277e9p+1L, 0xd.439e11c78d6c4d6p+3L, -0xd.91026f0bd29d199p+4L, 0x9.1c8875e5f3069d6p+5L, -0x9.4e367634301286p+5L, 0x8.e32593da6083e54p+5L, -0x8.ab4c2fae45e736fp+5L, 0xf.795b07e3e718ad3p+4L, -0xc.239a57408bc15f7p+4L, 0x9.0743a5f5b34bf5fp+4L, -0xc.9ea2a6009062863p+3L, 0xf.46322ea81a241fbp+2L, -0x8.5459716030b981p+2L, 0x8.a77b688a295dd83p+1L, -0xd.d5b79fa6ddaa942p-1L, 0xa.735578974886db3p-3L, 0xf.2bf66077398705p-7L, -0x8.78ba67546182ecp-7L, 0xd.0f96e09762ae4b7p-15L, 0xa.00148a20cfdd93dp-18L, -0xb.63f30078a588239p-29L, 0x0p+0L};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0L, 0xe.97a70223a4da73dp-3L, -0xf.0cb6fa407f38df5p+0L, 0xd.5830e9013b783a8p+2L, -0xd.3d92cf301bf5fbep+3L, 0x8.269cbbf117b07a3p+4L, -0xe.184623528d5047ap+3L, 0xb.ace5b82a4830181p+3L, -0xb.9d26da9275e177fp+3L, 0xa.6817202e331ffc5p+3L, -0xe.26fe3416ecaefa6p+2L, 0x9.0be41ad4225f98dp+2L, -0xc.e9f2f2f049291ep+1L, 0xf.67680e4897b60bep+0L, -0xd.58abb93bbd32d48p-1L, 0xb.c05bc49493e294p-2L, -0xa.cf273cfce9c2447p-3L, 0x8.2009d63fc87650fp-5L, 0xb.1f481d6b1973f98p-7L, -0x9.3599cd8362377f9p-8L, 0x8.fe041d07161ad18p-13L, 0xc.e0c72cd50ad59f6p-18L, -0xe.bc95d564a979727p-28L, 0x0p+0L};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0L, 0x8.cf76132907b923fp-4L, -0x9.24fcaed9e3542f7p-1L, 0x8.14bedd3366e9a26p+1L, -0xf.a746e075bc553f8p+1L, 0x8.f7e8d9e307059b7p+2L, -0xd.1cbd02d2fbba7a7p+1L, 0x9.1ca325fcf41627ep+1L, -0x9.ca36832b9cdf557p+1L, 0x9.44c18b73353f954p+1L, -0xa.ddc71623213c14ap+0L, 0xb.412ae4cdd263584p-1L, -0x9.0d573d73ef98e15p-1L, 0xb.27d598ba247d824p-2L, -0xb.adb264bf04b4353p-4L, 0x9.17f95626c5ce28p-6L, -0x8.3f6b10ee55a3b6fp-6L, -0xa.500f37704306c4bp-9L, 0x9.73e6dde48018975p-7L, -0xd.bfb432dd7091673p-9L, 0x8.bdb2e569eaa0703p-12L, 0xc.88702312085adcbp-17L, -0xe.7a1a5226a2ea342p-26L, 0x0p+0L};
-            }
-            if constexpr (order == 11) {
-                return {0x0p+0L, 0xd.3628de238d184c6p-8L, -0xd.c18a9b8ea152a17p-5L, 0xc.4f09e444d3a6404p-3L, -0xc.5524bb8cf8387b7p-2L, 0xf.595bf715e446977p-2L, -0xd.48b9ce7e5a1ba57p-2L, 0xa.743811d915f0f83p-2L, -0x9.8ddba57c5726fd3p-2L, 0x8.70931ea231e404ep-2L, -0xc.e686d8da15cb65bp-3L, 0x9.e76109d29aa8d6cp-3L, -0xe.d79afacd9220eb9p-4L, 0x9.94e190ebffb5bb9p-4L, -0xc.49b57465c83ddabp-5L, 0x8.06f70799c914d0ap-5L, -0x8.3de8c06cacb4875p-6L, 0xe.7600ff4d82fb121p-8L, -0xf.377cea904fc3cf9p-9L, 0xc.7a7a392871d2799p-10L, -0xf.396a7a4a8644d53p-13L, -0xf.0c8bb6bdd348a37p-17L, 0x8.dbcfd34464a37e2p-24L, -0x0p+0L};
-            }
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.ba5636194c0939c427c9ec59581bp-8Q, 0x1.3af72853b1890334601f92a1284ap-2Q, 0x1.da1521352f487f1b71f5ba208041p-1Q, -0x1.5c6f665240adde3380bdc0aea438p-2Q, 0x1.4840a35a3e5076b07b9bb98536cdp-3Q, -0x1.9d4fdc34ae4edcb2a06a461fd21ap-4Q, 0x1.042a86a360591d6b2ba9327c6214p-4Q, -0x1.08554bd18ab256f6f2efbe750de9p-5Q, 0x1.86c905bef28a68962be82a3bfae8p-7Q, -0x1.8785b403c86f6f7548c23ebef922p-9Q, 0x1.f00fc00fce26eee7a53c75fa9287p-12Q, -0x1.43b7ce1fa4e5b162d9e05ba1624fp-15Q, -0x1.dafa2eb6c7f5cbd9451ac8b8db32p-18Q, 0x1.2d678c174b94d04aa232fc24fe09p-18Q, -0x1.f0554b8e5712d06e0273c8cb503bp-22Q, -0x1.934a0de4da29338aed7c3945f15bp-24Q, -0x1.3a5d95f1928eec0223d4d93358b6p-29Q, 0x1.0e0d2138861875f5d48c437e1957p-33Q, -0x1.652333b327609e7169123d062941p-41Q, 0x1.02e74c07e60809b1acff78842ce2p-47Q, 0x1.bb358cf4adf4da69e5fa9c480499p-60Q, -0x1.f67e04f08f2152aabe6eb786996dp-79Q, 0x0p+0Q};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.3daa1461d0cf47fff25f3df963e7p-5Q, 0x1.716f56bac1b1102dab376b1a3fe7p-1Q, -0x1.16bee9987071960277d4321df078p-2Q, -0x1.f51bd9fa1cf2d9e12262aabd1401p-1Q, 0x1.97243be7bf08455883f653e158edp-1Q, -0x1.b8eef0110c9fa4de8e71d38444bcp-2Q, 0x1.2402bce395301d2ffcfa2c7a4938p-3Q, 0x1.80595820660c8830537a9f5a0e29p-10Q, -0x1.fa47fa3f4b021cbace01025dd941p-6Q, 0x1.025a88022a413b155a9680077b35p-6Q, -0x1.3d712aaad77758afb71e5644bf72p-9Q, -0x1.c5c0d04fc87430265835a2d868c3p-11Q, 0x1.c45b69075cdb62e0f0501d72eab3p-12Q, -0x1.6a1670435bfdd529f00d82c5e437p-15Q, -0x1.13c0d643a27dc3e64f7aa5ea1b1dp-17Q, 0x1.b2cff794384635cf6c5bd8331af5p-20Q, -0x1.9ee90facd3d1333133d7e205e062p-25Q, -0x1.c87e1185ca55b3b93aa74571695cp-29Q, 0x1.b076e966620448a8ccbae1de5619p-34Q, 0x1.71c42c5b1e646b3eaaa36a5a302fp-44Q, -0x1.e6d8e5785ac9381d9a7b90929674p-52Q, 0x1.13fd176d0c254d2994cc4f8bbae7p-69Q, 0x0p+0Q};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.77fed2e01693602fb84977597092p-3Q, 0x1.e1d10780fb06110288f8999dc16cp-1Q, -0x1.9e9c7ce63835ce70bd9f1949b4bp+1Q, 0x1.bc153af50c24b9575bdc1b7eea9p+1Q, -0x1.240fe3f248860f90966b383ce203p+1Q, 0x1.80cee17390c17dd6afdc8b5e9bd2p+0Q, -0x1.abf5df7fd7abfb9aaab015caa888p-1Q, 0x1.50c7e71a108baf578aa06cfc537p-2Q, -0x1.4654ed4660723ccc0f0acc159e52p-4Q, 0x1.091b1dd62c3e5f033d13bd90e92bp-6Q, -0x1.59c475f85d7f3ec16b121b44eccep-7Q, 0x1.935e464b93aa450281cf24f671a9p-8Q, -0x1.8fe1513629011cd322fa61848df6p-10Q, 0x1.90feb0894b434ddffdbc8185f2a5p-15Q, 0x1.09bd1f2d4e386644ae469eb863f8p-15Q, -0x1.da6da6ad5e76b858534775753bfcp-19Q, 0x1.a3886fa6d48c5693a0b3ec42e08ep-21Q, 0x1.0f7850b94c92b737f20b8005c4e4p-26Q, -0x1.63226d50629bfc487dd5a4e8ef38p-31Q, -0x1.84d7e34db15d3108fdfa03f5836dp-38Q, 0x1.75cc98099352929e39911fd43962p-48Q, -0x1.a7d23115de5731da90d3ce0c96c3p-65Q, 0x0p+0Q};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.60087b087d2ef4b82953952d9084p-1Q, -0x1.1c49e2797e56cac67a206b14e7b4p+0Q, -0x1.f023b1706ef0dac15d9852fec6b7p+0Q, 0x1.8d30c07e51574352c1f1eb2006b7p+2Q, -0x1.80e0de445b219fbdea6ef733a307p+2Q, 0x1.c1feac4e70c181d6b4fca6d1ffb9p+0Q, 0x1.3621ab0ea1b052aecf48cff7492ap+1Q, -0x1.f3ab98611d47a796d9c546361f74p+1Q, 0x1.5e6794d526a24de36780aeb9efa6p+1Q, -0x1.c702eca93a33cb508d7b1d00211fp-1Q, -0x1.ee149aa686bb2faa29ff6d4bcf1dp-4Q, 0x1.ffde0ca5fc1a1519c08ba08ef931p-3Q, -0x1.a2cbb989ecd0a0b85c48b0eeedfp-4Q, 0x1.d58bf4f6c76ea5b68a5554193d1p-7Q, 0x1.206affc103ba0a875625f4581693p-9Q, -0x1.dfc88961f6b157e54f77890bbc2ap-11Q, 0x1.f86e53415f2a00da542f82562b56p-15Q, 0x1.28c920e4a3f6bb0fc001a36c54d3p-18Q, -0x1.9c90e430666c8d48daf021826ab7p-23Q, -0x1.7e8cf0898f3336a3b6d1b959b3ebp-32Q, 0x1.cc8984cca607f1a4cd24395b33dcp-39Q, -0x1.051a1f819156ba9bc5cb80611a1ep-54Q, 0x0p+0Q};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.efa01fe281c907b167ef08b2a819p+0Q, -0x1.34df3dac7fcd3f885ed5b13d2111p+3Q, 0x1.5961138d5be957877d8cfd1f8beep+4Q, -0x1.014d7a672544a1c4d790253c77afp+5Q, 0x1.5a4b6fa251eaf90e3115b0c8a7d1p+5Q, -0x1.d72d9b409f2b1bb94911072e35d5p+5Q, 0x1.1a6ca7d65632cc9e3b88e527a77dp+6Q, -0x1.f8d9ef0a2890c5946bb98eca1feap+5Q, 0x1.142ce1c1f06e19e0c6f07b093cf5p+5Q, -0x1.90f390767ce4703536c74e99b357p+1Q, -0x1.822b1a96e2d91cc911472934db6dp+3Q, 0x1.52a34d125b1be5508a31d4593a7ep+3Q, -0x1.0b934a511e088d9de4577e6b9d58p+2Q, 0x1.335fd67def29efb717b66730db11p-1Q, 0x1.17c48a3b6f0b811400fc04e29772p-3Q, -0x1.0033850ae88073da0780e3e4b1ccp-4Q, 0x1.68d4635bbce683527c347878fb17p-8Q, 0x1.b6ad0e03e206f2cc34c3ad57b135p-12Q, -0x1.c361dbb11082ba0b86af7e7039cep-16Q, -0x1.d59d4ba004a567edb22672d12e01p-25Q, 0x1.f6c8c69c71b982736f46aec1c2fcp-31Q, -0x1.1d186572e3d30ab58425e9b0d124p-45Q, 0x0p+0Q};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0Q, 0x1.1672f76c48a3b085a419d3d84efep+2Q, -0x1.d05e83fe81471c548c37702884afp+4Q, 0x1.49fc051fc99a825862e53c41bd9dp+6Q, -0x1.e442104e65335b30f1932ff3fcdp+6Q, 0x1.09c52f838d2fca1c275b6ba1ca01p+6Q, 0x1.677b64cbf326e55bcfc76402e361p+6Q, -0x1.fbf39786bea7b138ef97d391fb5cp+7Q, 0x1.628081b6fdd810aa965a5c98d2cp+8Q, -0x1.a2714ddd5c22b603c83ee77be92bp+8Q, 0x1.cb4de777b4f362d79e6f05e8e906p+8Q, -0x1.9cacd3aee3a7e296cd71908c1c97p+8Q, 0x1.055f4806a834671e4070618a5f49p+8Q, -0x1.8ddf94a470b86c5104b74cbf3618p+6Q, 0x1.95561c2d77ea7cb1b418f1ad675dp+3Q, 0x1.8ab9cc38b4948a55522c2ec1bb2ep+2Q, -0x1.6e4f007cb3f6f6544bd7c8aa8418p+1Q, 0x1.43d7023213a802dd64335ed45bfdp-2Q, 0x1.951cff21de4ac7e4a1f0a692a613p-6Q, -0x1.5137c147339bc2af2a690f130f2cp-9Q, -0x1.3e3df8b2da2752dcb7f745d4f5a7p-18Q, 0x1.78040f51a9567ebaa0b6d793cafp-23Q, -0x1.aa8cd8e6f8971ce4ff33741ce32dp-37Q, 0x0p+0Q};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0Q, 0x1.6688e31cf50e0564efea7c707539p+2Q, -0x1.50ba2688bc0430a9ee7461099f42p+5Q, 0x1.18d5fc503a1772d2730b3ea50efdp+7Q, -0x1.16422099d0e700c2cc83b554b1d3p+8Q, 0x1.7cdc33f38c2d168782ab512e0152p+8Q, -0x1.a2f3c3b8e6e4ab101396a900d9eap+8Q, 0x1.aa319d6af6ec967e381e232c3d8cp+8Q, -0x1.958a02a1024489567edfcd9f60c3p+8Q, 0x1.4bb5b15c50a647500af490b1348fp+8Q, -0x1.caa9291eb011f2ccec525396312bp+7Q, 0x1.1f2d7abf22a7296277eac06229bap+7Q, -0x1.3b920d0f7e0d09abc1f29bae2433p+6Q, 0x1.bc14b21b62b9334a0ec0723419b6p+4Q, 0x1.8c237a0fa26d7404976151e77cdep-1Q, -0x1.7f694c35d9d2245677a758a1954ep+2Q, 0x1.3f67e104a689bca4d8d6dcd2113cp+1Q, -0x1.4cc6c058f371d1d7aadbd425ad1p-2Q, -0x1.6b557354b8d84aa675e72eefd888p-6Q, 0x1.38d6e371bb0518c7efdfa510e3cep-8Q, 0x1.260d95329ea8e0edce58683df434p-17Q, -0x1.5c7911e0053bc1a14fff7c706e19p-21Q, 0x1.8b88d3fa551bf844985173c27b89p-34Q, 0x0p+0Q};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0Q, 0x1.80f665163dff60603105460968d1p+2Q, -0x1.7dd2228ef04492e49ffcbc26de51p+5Q, 0x1.48b0d88030936751bd070f0b70d7p+7Q, -0x1.41512ba753d055c75dc8c75f4172p+8Q, 0x1.8f56f07493ef05c30063bd380daep+8Q, -0x1.675a39773b2485da34f83484320cp+8Q, 0x1.2e9626a21624df1cdd8e35d51165p+8Q, -0x1.1263590aebe88d200657c008c834p+8Q, 0x1.9699942af2221429cba47418cbf5p+7Q, -0x1.59e9b6e0b9c21128db1641974871p+6Q, 0x1.09d1a0b7c583242c5ad30248e848p+3Q, 0x1.cc8ab1005087bf119ad7a75bf51cp+3Q, -0x1.93c8d5094509572acb009457fd8ep+4Q, 0x1.013c24badc62703530bdc2a89abep+5Q, -0x1.784654bbd73679c9f2def5413da7p+4Q, 0x1.21acdd98ca7e3a8d97a584ca3cd3p+3Q, -0x1.6fa583815aba1a21d8ba9c3f6b87p+0Q, -0x1.39156fe5f0a3b45977f7c9849262p-4Q, 0x1.34372727b2154e0f63382ce7b14dp-5Q, 0x1.c53d49d19717546a3333946ded1p-15Q, -0x1.57bc52155abea4723bbb438d51fep-17Q, 0x1.869c11b6398bbfee9ec137b2aadp-29Q, 0x0p+0Q};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0Q, 0x1.d573db31c98a592a2b6a796753f8p+1Q, -0x1.ddfb9c5686a4efd2bd1e36073e0cp+4Q, 0x1.a873c238f1ad89ace04b7607dff2p+6Q, -0x1.b2204de17a53a3315364d57fc2b6p+7Q, 0x1.23910ebcbe60d3ac86902adcdaa4p+8Q, -0x1.29c6cec6860250c0db3c6f8b8962p+8Q, 0x1.1c64b27b4c107ca71ade24985867p+8Q, -0x1.156985f5c8bce6de73bf23e5601fp+8Q, 0x1.ef2b60fc7ce315a6b8de2d939461p+7Q, -0x1.84734ae811782beee80a7af9899ep+7Q, 0x1.20e874beb6697ebef627268d4461p+7Q, -0x1.93d454c0120c50c5e5f45ca0c342p+6Q, 0x1.e8c645d5034483f58d32c0b8709p+5Q, -0x1.0a8b2e2c06173020781b6687242cp+5Q, 0x1.14ef6d11452bbb05715fcae8f362p+4Q, -0x1.bab6f3f4dbb55284f9925c8a3ab9p+2Q, 0x1.4e6aaf12e910db6611cb145f554fp+0Q, 0x1.e57ecc0ee730e09fd58c293b9a01p-4Q, -0x1.0f174cea8c305d809bddd1a456bfp-4Q, 0x1.a1f2dc12ec55c96d12f54fd03177p-12Q, 0x1.4002914419fbb27ad65f422d91cep-15Q, -0x1.6c7e600f14b10472b7579cd8544fp-26Q, 0x0p+0Q};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0Q, 0x1.d2f4e044749b4e7a1c71b105042dp+0Q, -0x1.e196df480fe71bea5cbbf6f938ep+3Q, 0x1.ab061d20276f0750e2a72080d7a9p+5Q, -0x1.a7b259e6037ebf7c8e2adb89e41bp+6Q, 0x1.04d3977e22f60f45b515e3221088p+7Q, -0x1.c308c46a51aa08f31731ad9b7844p+6Q, 0x1.759cb70549060301bbf1ea932595p+6Q, -0x1.73a4db524ebc2efdc465e09da17dp+6Q, 0x1.4d02e405c663ff8abf63f28cd74p+6Q, -0x1.c4dfc682dd95df4b0a54f646c034p+5Q, 0x1.217c835a844bf319c913aad35977p+5Q, -0x1.9d3e5e5e092523c01057547d3214p+4Q, 0x1.eced01c912f6c17b1d536b46140dp+3Q, -0x1.ab15772777a65a90ae2d7ecf56cbp+2Q, 0x1.780b7892927c5280dd5bee9ee8edp+1Q, -0x1.59e4e79f9d38488dc3c59417b41ap+0Q, 0x1.04013ac7f90eca1ecf033aafa30cp-2Q, 0x1.63e903ad632e7f30307040928615p-4Q, -0x1.26b339b06c46eff13165e32f7c85p-5Q, 0x1.1fc083a0e2c35a300d5c6fbf948ep-10Q, 0x1.9c18e59aa15ab3ece464b6468819p-15Q, -0x1.d792baac952f2e4df120dee003e6p-25Q, 0x0p+0Q};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0Q, 0x1.19eec26520f7247ef7c6a243923bp-1Q, -0x1.249f95db3c6a85ee06007305aedcp+2Q, 0x1.0297dba66cdd344c6014ab433b38p+4Q, -0x1.f4e8dc0eb78aa7eff1fa727c9c71p+4Q, 0x1.1efd1b3c60e0b36de4fe266b9d8ap+5Q, -0x1.a397a05a5f774f4ee2078a58f21cp+4Q, 0x1.239464bf9e82c4fc4fdd79af7e82p+4Q, -0x1.3946d065739beaad7a01650a25b9p+4Q, 0x1.2898316e66a7f2a70e1a6a12eca5p+4Q, -0x1.5bb8e2c4642782930886e32d2ea4p+3Q, 0x1.68255c99ba4c6b07d82156e3f9d9p+2Q, -0x1.21aae7ae7df31c29928804e58d84p+2Q, 0x1.64fab317448fb0474311942daf3fp+1Q, -0x1.75b64c97e09686a5bb55f9818d82p-1Q, 0x1.22ff2ac4d8b9c4ff1397fddfa477p-3Q, -0x1.07ed621dcab476dea8f9bcc8470ap-3Q, -0x1.4a01e6ee0860d89681b645bb0864p-6Q, 0x1.2e7cdbbc900312ead84b8d7e757cp-4Q, -0x1.b7f6865bae122ce58cd5b4105bcap-6Q, 0x1.17b65cad3d540e056708b80ca432p-9Q, 0x1.910e0462410b5b96ed51c4c46ef3p-14Q, -0x1.cf434a44d45d4684dfb9a827c309p-23Q, 0x0p+0Q};
-            }
-            if constexpr (order == 11) {
-                return {0x0p+0Q, 0x1.a6c51bc471a3098c7c3ba4b2e396p-5Q, -0x1.b8315371d42a542d22b52e160edap-2Q, 0x1.89e13c889a74c808a95f3ae5db18p+0Q, -0x1.8aa497719f070f6dc765c7af4f82p+1Q, 0x1.eb2b7ee2bc88d2eef92b780b6136p+1Q, -0x1.a91739cfcb4374adc78a339981b3p+1Q, 0x1.4e87023b22be1f061884b91ff276p+1Q, -0x1.31bb74af8ae4dfa54f812e36b5bep+1Q, 0x1.0e1263d4463c809bd8442e6ab9d2p+1Q, -0x1.9cd0db1b42b96cb6927f614da713p+0Q, 0x1.3cec213a53551ad84004d758bdadp+0Q, -0x1.daf35f59b2441d717c1690c25188p-1Q, 0x1.329c321d7ff6b77198e76070d6c7p-1Q, -0x1.8936ae8cb907bb56ce7124a40ebp-2Q, 0x1.00dee0f339229a14bdfc063bfb91p-2Q, -0x1.07bd180d959690eaf41df5a4ee44p-3Q, 0x1.cec01fe9b05f624125be250b50a9p-5Q, -0x1.e6ef9d5209f879f2bf7a379cfa32p-6Q, 0x1.8f4f47250e3a4f324676c24519f5p-7Q, -0x1.e72d4f4950c89aa59da6edc504bdp-10Q, -0x1.e19176d7ba69146eb048e9181ac9p-14Q, 0x1.1b79fa688c946fc4993e527c8905p-21Q, 0x0p+0Q};
-            }
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            if constexpr (order == 0) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00674952336093794271822599377832733300651146336500105281821757702580261898435"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.307583456142659816839156786245335727208310576612803762616887840930925575209"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.925942456953309005940386530995126436012681380158402535652037264183889758483"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.340268706102660683375457588221232998838593649367854881779057620364907425914"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.160279537383566356658810338492196248229219596027949666407555183251410683353"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.100906238726469613031927683469694828929687407601613980745393598371134911780"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0635171183876279943173554673370722041156121244338995400601119969400460909180"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0322672348814505948972500008092114355665944734834499482855568997884208147214"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0119258192115874852729361214670894284737320324933075482785998337722648377488"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00298707792707452898367085553746573188496510147112607446979462542972907046198"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000473081135158127015860372446974828573937912728115760868405824469327509104714"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000385901914771418563229090512720344539916565749843499561465030991408855304182"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000707771294264344979265706380621665838995140738494138127767693643047473151938"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000449127676142712270206334163110940969109789276623971797893643048336659640461"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000462246298923448308370189842110923874064368375158153708369750363490273849968"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000938981013616806301299448140440205677496034062712612222476591887975663431153"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000228731055691905904721631337725631066731945798378875548099322801540390353792"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000122805107893837304401775672037887127425598683650631632643112458670137760454"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000634403654278944400941924520388860558080403502147439478702947659558312462441"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000718601577933574214479296340908692396681088130844931493227840962495346368987"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000150165111893706003972718474555253050830994970128831551959442684938639721914"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000324728013911670481356185860811593862377837926387577826017803860651455895063"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 1) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0387773893440001328479990972130631692265393392276997953903865925128067141024"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.721552572534024717748570063882033395155483583566407967882626836656429636782"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.272212648324158111612511789206460700674191556065031727190617093210427966623"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.978728114873296652638727035042942428237594510811351020620221815511037142320"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.795198318518956652102305679705853563026415740789264534365825373566593070233"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.430598975220305785445999132638246196763260311865173495540662078177969568735"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.142583347029948066092993254964771828684926120817867402181283862012299624787"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00146617508298700811859640317636078157631882791634139195335692402607076083994"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0309009498425184610096113389760986103366023818447589327535142129940010076705"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0157686546523657228788031242284047791698300666554508584962947405558611056219"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00242189069596937080496858729150225100112203583636152350242227674378819932850"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000865465504805686451786867765475930422411519327219197611864322484446933101993"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000431401320802406335612460169440586915965773678151860581031150029061360265549"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000431642115711336908332394044162700208606587787562050592203268643657811936924"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000821808783448349005091749141022578622146590089593391035863483128421998476881"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000161980230922061292865855432080723373115493373219912556484058486745620714179"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000483019272136912181673157244957934770912195515285570255684870776439319393894"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000332141975285733899509799336405046588503487344884194087554458021104822328255"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000983310426136874022596843421343020282473719270746503069720570388756166209575"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000821046124017272115015180345888003894425103661180504475350314828549798634201"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000422272678140744917094064065340806009116153886552991342868695393427346681857"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000182633960975279599217132126825168232459508047673969824620606842686892878014"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 2) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.183591506446484309712795488849571274418364537569049882649969406786991566703"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.941047892088601518958291499087971794201051709610594834344832432863937253481"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.23915063134374610177549908438346173797911023760267160983136498244943289731"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.46939789738852314818899400606908382011384059438420298035329651589159205087"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.28173493700255435214772096048237572437923445360570917382808581102768910125"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.50315674849912814024262183106436302156615435178890932358182035213351917617"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.835860237460870761390156685965058693698796219956190288728965409249874516389"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.328887568441256381505801657142525299671290097708556863386573335636703368303"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0796708363104952604879937077745989748584956873438833081361877117810017197093"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0161807814953966106554332142048099058586667875986593188231761928160044535103"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0105519844080212767161949305951351809551205888170657290798324464298016783059"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00615491119567815699833303054263633346002498173776612335382778423057115661320"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00152542169738812236275366430470857831307147305605930001884982398335206187746"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000478023149049562031406199523580878829069008124571083991909044064992027938837"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000316785284248449847258104755742578560748429902748877549315826250898391153165"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000353476646946804208268171454249821202212174971459821936484698256572687164013"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000781441021094927012007376595229335452531962058185139941865056284143318220825"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000158016326457618764551834550084612976065250040667862420828605844454348687428"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000645985856862059637165608932066447500409737957145914496500299017194796733184"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000552579581560011400180824517243503538265777971769292220658774318761637323198"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000518750590964679052304303794785902282315144982464294500494857713908195654535"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000000448738003521685102283394837866669813173686476421773647750785777214873187545"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 3) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.687564701830153090496154601673244324665424792477734591515424354722524099152"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.11050239053869430027184090551059176229770565635462126988333316421136630257"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.93804463381724493769207024757917870971550445481996014592183410296094056051"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.20610058150974826647727021504587596509253169984522564051121763364081781688"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.01372486758602951783294736130451247536207984026936617147556597467502065146"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.75779225268411745440182343883946325363307126912452705923359087032746232261"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.42290247168000634999802692912700654401659291644918891841812220270431988663"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.90367417089379141718231735172375182130729195288100071937663900099707066494"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.73753605277785755057468262545518793812656205923506367770591971382787612864"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.888694186837802736174804686545601676095716084997773896570154037914318457788"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.120625118354310597854672205082409827213145048325433221107814663185540763499"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.249935244384244229475998157073285972261843545061283350728568950695406300807"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.102245068322009442021851053260660268979014010537069811214828519334188485107"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0143294283021151060785346153371703965226713038712447807825810853955454985909"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00220045444485302028275444219293273448787231072694521760298002658782637616979"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000915114109598521684422240708952522787741064024256659542685847796787098864471"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000601328561158122075623159592639344585246740920247215146685740357533130502579"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000442245093225367075171042726134823952641438570521711248051460748670218278934"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000192116006225709175804133650291101682367016689175710099736613621136724772233"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000347927694118473204634336179637016248843344378650467345924085824175805403758"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000327231349649651474450860748750987614694465218515883129352235985103556742393"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000566174805053915554844952341333463723778572903642256009402911739536460840202"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 4) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.93603705673175252162377048005080828323485510199286167343778412900683630357"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.65225108805899617933044689930629862606922722189344796627981892221806322756"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("21.58620028704043203965568014489070671164252883102441474199007795986172799450"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-32.16283112127764887984781311792208840193362133426782486134064927600419439680"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("43.28683401882642247901443678261444427228477284299009228485788317422296188030"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-58.89726877675765402909531534108742114308361932607118347118552732380096882110"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("70.60610899830926411810587962905898518983841308375904913755422678352922515570"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-63.10641296325966002268292888588592628930166199721781262159830072450491171720"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("34.52191497340187437272066528301740399000435097032593635597215974196048894900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.13243299279728005268439173331599785511338054577595843510586618380676315959"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-12.06776170225092279346900025349356398262454275196967160026720095858830643800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("10.58243421158919931486338350084744671448957975219955115739863127269480650610"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.18086488648999297183891759837512319517601794026273877877208860579097625582"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.600340559838134056014385774162185206812240239620564149846506062110388511249"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.136605338991903970318857223904627046152412648176017176159147490879517687577"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0625491330124817618386886003919664398460060491417974176815677679696581035123"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00550582338086123158873116800515458266240754229253267111261799485380454805945"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000418354029755102972365185158832406860086075763566175597817465795414186469647"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000269044791745347379635890876857658847394460147615410319076105357130452956021"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000546703156080335157447390001850562112157399818528369118783700921788207959856"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000914559278617230197902988750581388857118162901722874330587746501390541480138"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000316519364036060085112704740081169075698795498871539132664715584413313149738"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 5) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.35076699804863678677975429556027903354422790699226157645072577251818273676"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-29.02307509819042426585700918686326160072354736867411698539343692983196503080"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("82.49611329715719629374872640906345290805764600780220272968616846701709806240"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-121.06451532833747392386859794636510608764397274079815027628644009969274065900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("66.44256406354174703030638747248670204230247493582940326331823060083408390470"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("89.87050169631559036410735425620807796485093895246621283952389526730602524440"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-253.97576542928058746612034494797807584834351582667944315344135960784812946200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("354.50197929093707453189915787851278530317676402818444334154635759143504945200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-418.44259437083629654372265774871306291337038882950576397483748815661296325300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("459.30431316535703999996533810953606750433852009745459279981845049292111412100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-412.67510502870562514868993537829892602977991674444809590835277417435828403200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("261.37219277960357686002183516875187598846311513198317551376196154507578273300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-99.46834046304693927396397394893633319797299579647467410477722973021902030540"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("12.66676148300696488281972471730213802977983006010030132112775191282004845920"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.16759019410739796803106483846236267155563560221580308118480616704388032488"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.86178594674122850153536653793135766872481629722817248177002057968004742610"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.316249880129284132115920875971521368522150973034344085606632817974345846565"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0247261516119336322479197612328703090652313932265109203114345439280129606257"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00257276758529842275783708309373614341047704871305149895482328025045858909260"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000474217647448341719828623182459779084961108353234750865989641444296059914091"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000175096028833295782031678343625079307038593522030930622175736643377626514407"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000121232854060447503547926609753618642777727719448048997021870449891245778235"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 6) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.60210492923599220306739726849524365911272995023030149275362729443627767241"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-42.09089381049900454092361924595905199878007886101579238359551872779773615180"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("140.41794062337041783562329118755195628284508671409730808010312709127392837500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-278.25830994939952049425764143319165780543667702177067080512763370773979265600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("380.86016771480816533332928441348450481125889613649326541505558838372953629000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-418.95220523488084674141481769302959290485836739389011115886709000649475649100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("426.19380825546667243857182155918014103510325386970185000695176160112816290200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-405.53910261445392868706053637913300495637853779363319766514135762481123453200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("331.70973755806906280222948564333114303709973974217107892064712971483217388700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-229.33039184474271152765997296747693653644896311902985970449951777370036797400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("143.58882710741052581341088543723084000514106642516308650843963725396056822300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-78.89262794691900075510218647088275987362866657725786329632823854347189893030"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("27.75505266854777348435048128311171422045966573330871472192405309949017306920"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.773708166512018375007390099318270025246521769336781853387329991690258896716"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5.99080186137078587115052777435201929542834691356814368299406374154030652526"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.49535763480259999546977692911560881994873486413261121783762393577404777245"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.324976926259170024466514821976486541713103347782139429815301297092702931869"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0221761347082867372516860357201809209573177307919227810107850272426097081037"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00477355053747537251275230025941686821306294456709786754720729109346187074810"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000876346402844021878197271431695817559174109670993605807770140477893316270959"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000649081410844014945450377643724451703185492681208039429612859077055126594639"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000899341295111001783061788354774120539335760947137727039371354507713388157031"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 7) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.01503874942863172446672032045385310660658346430556969311090280204002893574"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-47.72760497732867563639045888687408111648670461954967176817630689615594571920"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("164.34540176957098246520164840268114912785108333764805325670104505015878591400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-321.31707235141978805890085173651076956857219432352414927630174955007268214000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("399.33960655795728826591320240810290804342839867119935493449864048725021503700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-359.35243935769951609547501622393948495038359128149158218493239094084479572300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("302.58652699509263723866918658763896223023494881995643828072737018416182521000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-274.38807743319971566043869533026106988492438939463128607709797721020443215100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("203.29995855527617039240266616022588964442318448807463904291472490500587668800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-86.47823668607499417468265201809837107760314991031737704773103407132324816810"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.30683933155896571923336370342680329284352699673810942748030941466774153040"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("14.39193010388793670592743695120274923548898641004312440323358299497206491280"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-25.23653129216162031393190650488947069144769574727062315317496697755106409830"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("32.15436693177280611867229541693914656357710375952844770094246636458373021770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-23.51717065215362229865507044104445167369445267308462930568665799256423840570"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("9.05235175935735664788319630251805269364581033096340273166670658279003426872"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.43611928852144679808218829087774768973983520937512890405722409904760001331"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0764364596389350180439110342110306497850920144422968183705432261288688167041"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0376239552256857684356168042424620283930027011606313367853621428915639193111"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000540303477804840762648923255410865058939043280088368514023926300961486967782"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000102441199866988900731723735456649881175505194362439761979226773134926915151"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000284205922260922568932250591462669984026040113459253556541826475617240410416"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 8) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.66759815150278959307930599333163597096097529742853199217978181562630696487"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-29.87392839240265725546623883959127802560925486188325916048865579469303024630"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("106.11304558730206231169420989915879780867394552444174433037983757043874961100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-217.06309418314214666288595563832635346239588058289858882887597087103632217200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("291.56663112304597857590334364976771943737359513217961682974016748268384769300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-297.77659264346795265988020082120368913354431735040919787932537200810228046400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("284.39334841353455606151257223937124519201920224538084896597007768405172110500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-277.41220031882121641670001674749778842464959328498538149541517303833838711500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("247.58472432159900771477076380876163976925347752971933279268071613868274753900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-194.22518086636781463956709313343541688316198595925041840328872392823935647700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("144.45401569344244085247818472795589947662462099880946347817047437422725404900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-100.95735454664379984016882278587502046931372757809433648524452327992007684600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("61.09681288162443200526120017869481568171612243827222222068632320726899857500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-33.31795915978991479226353783917641730723993856565006267406505994034763561210"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("17.30845362421199129993292294948350854310287513028370737357127567143752171420"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.91741656219422399006952830174054308724719397866962278438510860750311408940"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.30631536685638443282971027232061480593991545082436137033699622406166968595"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.118529126264956569656056269771626755793811242386616315248341528538090571096"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0661843304194570081752469739423793402949926380986891972951348623664335067648"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000398586912690642748373175830858033776325071495068959972844940429117973233494"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000381481682161783683986425780978390997526951366596105346738987927781141638894"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000212163229730584007262375731808777339564186173310877882056921511132532981858"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 9) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.82404901191021660107611405457755744720508147280838668944561685140253424274"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-15.04966701578743791983566870544026493163762629417625697617466370992453373950"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("53.37798524017660253980042023139266987459040956232067348967572826444722400500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-105.92417106052715735002349944451589608377479192425044614348746722708067035900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("130.41326517273685551908783147004280111867640298350958460298534492271024128600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-112.75856176494063105548507692533259561359149505796793856695544860362794488700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("93.40304191835594150352589694310821255241952082139322576408183818507525504810"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-92.91099289517937530938067160839545056753425221872875127682184392703877307920"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("83.25282296203022229084823461764842101991248796776481529458179231322413184940"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-56.60926534880375950692439436083700078084789164896951269302972237793898650350"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("36.18579741207349225217113136176821974406219093273833973652666883038907214880"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-25.82772671444610862462306541969742751815537984691055996627268281393630328240"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("15.40393151542931365681934641697554669810260411956534200123239544102606890360"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.67318514684902700324396712833889530416584439958498307300658341368976434355"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.93785006672712485651870672930552135674962040419489700124033209653118603360"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.35114905974225608322981232543443993841639703478986459747319143071556838636"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.253910940604568570873136388508332898207860540665090852083889016211691603112"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0868921416897127089804662233761880201802165848173331041475381130845773690378"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0359741331807378258738142078527195789630247593913553671912092170295325403548"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00109768679996836757242664134813447276225315118775952708555290702903991203965"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000491258208131049675088973621242027668877049383351261231455773092411325252306"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000548983412936212498495690390885488330611341145287970297974581737627796036856"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 10) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.550649714321919146020391652705270850624984467632444477892208411090670503460"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.57224031839147248722382996328027080443894364680263533387085228867737306467"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("16.16207470903266336622407533376180083841264103186821602341901646085415441920"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-31.30685048817455572162905452355438357246801343486549641376884657698487166490"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("35.87358710451743501103090247260098261068172630229012387217368794457391845240"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-26.22451815893096578505537492191089420871702814982563223312943309074511861080"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("18.22372889376872362134777045706885197255097592668156061200711581268831340790"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-19.57978858594446573474343717866513610480907608812601678912962077898856742910"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("18.53715651631727882099530623547490387621972342657149537210734087006118103230"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-10.86631906850492186026855947795210696729727028226200184897211758632056293120"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.62728037846063128438976106546508945987259369732013042706443820658486730438"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.52605621376260259593982907405174555293727464118730144996047399577463796319"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.78890074382900144618255657410026967999905288228433605937465464511446641771"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.729906457462033355139337021126261461176772010479428021961867397970803230476"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.142088255054741883006545627449011553786767246338704050666922604912111664368"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.128870741399931027764146528868524281495256321870369794112882474231057823379"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0201420550512292820836440674996269788542898415412561416178222180575252813086"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0738495429477559359501157209854724157351709061729224786516577653892388373974"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0268532096949637519510499296268755420094167792885280535232350328010652171480"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00213403588588315134257033560239887601573172007420308747358527142593502213305"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000956189046839608573100519969536118832653435986603979875808632067612204306782"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000215723576025549042840675180271579291754584130778771057415350031447174455663"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 11) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0516076605159024911828475147837820854392015861025284155408704376160614689184"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.429875663588101212310123466761246228949954693513674780077411570894231140593"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.53859308562319363525064968437125695806116775999527119873257232627957881183"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.08314793632421711513446659317655276412171796583863723768853134524872575829"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.83726488181225153055424552179561105009983872787369445162123171315532794535"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.32102129598800001827402190941442844711537496612480829720954545917202711427"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.61349513900266658472136887684620241910754262198058846835967186330136663863"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.38853319713033495202260098319806213683185517673058274190000445657860915347"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.10993621697386759008454349852482017386377263965160538055677721963192891999"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.61256188788931860024729141933908754524860783254583010122183874119617986655"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.23797805475199533327033756060882156229697699608086470174399374479195617901"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.927638034533750248678688510655383608919790412752058469862157655885568742788"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.598847929097229887988452897323944295134119484352549354946451834874406807448"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.383997657145535004546586640993163439996459447874095195026713580064418880820"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.250850214810528805990052825784903155854458963606740947659194110817761051247"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.128778636850891888203699386683982406407371540708648125836387080670890476774"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0564880965516855608539804536808433961937777036332691539099534383291528671575"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0297202144940054411503976781292207507569011942232371230104009758591434089695"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0121859643351046128923156738600080443388598031417307165875316044362239226179"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00185843273568833887463557296801124598677123828961682233747031997277499314044"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000114814810668351667156857713897954085126369615497231973190312538067210861730"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000528016085138320874511452843388030214551797843336485403204846872234194616278"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-        }
-    }
-    if constexpr (p == 13) {
-        if constexpr (std::is_same_v<Real, float>) {
-            if constexpr (order == 0) {
-                return {0x0p+0f, 0x1.749078p-9f, 0x1.8ae6a8p-3f, 0x1.d0088ap-1f, -0x1.20e16ep-4f, -0x1.f688bep-5f, 0x1.2fca44p-5f, -0x1.505c64p-12f, -0x1.014518p-6f, 0x1.c908bep-7f, -0x1.beac12p-8f, 0x1.0006aap-9f, -0x1.d4cc28p-13f, -0x1.a08b66p-15f, 0x1.5f413ap-16f, -0x1.5c34d2p-20f, -0x1.2dc446p-21f, 0x1.74f33ap-24f, 0x1.ddb5ep-29f, -0x1.07969cp-32f, 0x1.2c5958p-38f, 0x1.52fae6p-45f, -0x1.d83da4p-53f, 0x1.1342e6p-65f, 0x1.aa25eep-86f, -0x0p+0f};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.239236p-6f, 0x1.0c0768p-1f, 0x1.3373bep-2f, -0x1.856d7ep+0f, 0x1.22d30ap+0f, -0x1.72e38ep-1f, 0x1.8e439cp-2f, -0x1.3bc252p-3f, 0x1.1bc8f6p-5f, 0x1.288446p-11f, -0x1.db22aap-10f, -0x1.3482dcp-11f, 0x1.328522p-11f, -0x1.bbf1c4p-14f, -0x1.17497ap-16f, 0x1.bebecp-18f, -0x1.bc40d8p-22f, 0x1.6454c6p-26f, 0x1.5fce04p-29f, -0x1.12414ap-33f, -0x1.ce70acp-41f, 0x1.8616f6p-48f, -0x1.7b38aep-60f, -0x1.258ba4p-79f, 0x0p+0f};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0f, 0x1.7e9e9ap-4f, 0x1.e81e74p-1f, -0x1.368292p+1f, 0x1.a1c192p+0f, -0x1.58e6fap-2f, 0x1.2f821p-2f, -0x1.f8fd9cp-2f, 0x1.017de8p-1f, -0x1.5831aep-2f, 0x1.30d718p-3f, -0x1.30a608p-5f, -0x1.632f9ep-11f, 0x1.1cbed4p-8f, -0x1.77d87p-10f, 0x1.50ec24p-14f, 0x1.f99c3cp-15f, -0x1.8453f2p-17f, -0x1.b40566p-23f, 0x1.4c2776p-24f, -0x1.287dbp-29f, -0x1.b00a66p-36f, 0x1.401eb2p-42f, -0x1.715282p-54f, -0x1.1de108p-72f, 0x0p+0f};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0f, 0x1.95e034p-2f, 0x1.e7908ep-3f, -0x1.29379ap+2f, 0x1.36cc46p+3f, -0x1.433598p+3f, 0x1.9c4d14p+2f, -0x1.ef81d8p+0f, -0x1.2378e8p+0f, 0x1.c6e272p+0f, -0x1.c857e6p-1f, 0x1.3531bp-8f, 0x1.05f57cp-2f, -0x1.38a2dcp-3f, 0x1.35c4a6p-5f, -0x1.fddc3cp-14f, -0x1.2653ap-9f, 0x1.ec5d7p-12f, -0x1.dc01f8p-17f, -0x1.379718p-18f, 0x1.7e5cfep-23f, 0x1.a12416p-29f, -0x1.417132p-35f, 0x1.65f402p-46f, 0x1.15123cp-63f, -0x0p+0f};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0f, 0x1.4c5d52p+0f, -0x1.5d2572p+2f, 0x1.24b0fp+3f, -0x1.39e0f8p+3f, 0x1.f006ccp+3f, -0x1.0ce3p+5f, 0x1.b8b8bp+5f, -0x1.e69256p+5f, 0x1.503102p+5f, -0x1.6d86aep+3f, -0x1.35b5dcp+3f, 0x1.a6237cp+3f, -0x1.cda456p+2f, 0x1.d5a02cp+0f, 0x1.ecd4c4p-5f, -0x1.660ee6p-3f, 0x1.5158e6p-5f, -0x1.73814cp-10f, -0x1.23460cp-11f, 0x1.fa353cp-16f, 0x1.19c574p-21f, -0x1.4bb43p-27f, 0x1.fc9a2p-38f, 0x1.89a8b8p-54f, 0x0p+0f};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0f, 0x1.a35158p+1f, -0x1.5a1bc4p+4f, 0x1.fa0a08p+5f, -0x1.a68f66p+6f, 0x1.98403ap+6f, -0x1.03810ep+5f, -0x1.14faaep+6f, 0x1.3d735cp+7f, -0x1.cdbd7ep+7f, 0x1.200434p+8f, -0x1.2591e8p+8f, 0x1.b6219ap+7f, -0x1.a875bap+6f, 0x1.85c7d2p+4f, 0x1.1c0e0ep+2f, -0x1.36efc4p+2f, 0x1.3e3f5cp+0f, -0x1.bffc3ap-5f, -0x1.75f52cp-6f, 0x1.dea5b4p-10f, 0x1.10aa3ep-15f, -0x1.ea6ed6p-21f, 0x1.089ab2p-30f, 0x1.9990a4p-46f, -0x0p+0f};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0f, 0x1.5d159cp+2f, -0x1.54873ep+5f, 0x1.2c245ep+7f, -0x1.416f5cp+8f, 0x1.e67e2cp+8f, -0x1.298ee6p+9f, 0x1.48ee3ep+9f, -0x1.4e6b46p+9f, 0x1.2782eap+9f, -0x1.bb4938p+8f, 0x1.25dfd4p+8f, -0x1.575e0cp+7f, 0x1.1c029p+6f, -0x1.08a1fep+2f, -0x1.12ed1ep+4f, 0x1.66791ep+3f, -0x1.7aa974p+1f, 0x1.41600cp-3f, 0x1.275514p-4f, -0x1.29374p-7f, -0x1.51ea7ep-13f, 0x1.deb156p-18f, -0x1.6e30fap-27f, -0x1.1b57acp-41f, 0x0p+0f};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0f, 0x1.d4fe28p+2f, -0x1.ecb0f4p+5f, 0x1.c6da62p+7f, -0x1.e3622ep+8f, 0x1.495088p+9f, -0x1.3d934ap+9f, 0x1.0686p+9f, -0x1.bb4eb6p+8f, 0x1.2c2d3cp+8f, -0x1.6a6f08p+5f, -0x1.48c0f8p+7f, 0x1.bce286p+7f, -0x1.9e035ep+7f, 0x1.737018p+7f, -0x1.15bd06p+7f, 0x1.1609d2p+6f, -0x1.30b382p+4f, 0x1.34c266p+0f, 0x1.56d14ep-1f, -0x1.f82518p-4f, -0x1.1d5d34p-9f, 0x1.599f88p-13f, -0x1.742b04p-22f, -0x1.1fd836p-35f, -0x0p+0f};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0f, 0x1.6f91b2p+2f, -0x1.8fef12p+5f, 0x1.809c44p+7f, -0x1.b10bfp+8f, 0x1.452582p+9f, -0x1.7231bp+9f, 0x1.7af822p+9f, -0x1.823eap+9f, 0x1.6f4bc2p+9f, -0x1.32f292p+9f, 0x1.d856p+8f, -0x1.59b2fp+8f, 0x1.c4899p+7f, -0x1.01b04cp+7f, 0x1.0ee55p+6f, -0x1.f14982p+4f, 0x1.214136p+3f, -0x1.1e3582p-2f, -0x1.54f128p-1f, 0x1.1dedd2p-3f, 0x1.2b8db4p-10f, -0x1.7cd67ep-12f, 0x1.c17582p-21f, 0x1.5b5402p-33f, -0x0p+0f};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0f, 0x1.e00f2p+1f, -0x1.09aad6p+5f, 0x1.0083b2p+7f, -0x1.1b0164p+8f, 0x1.8e74c6p+8f, -0x1.907a86p+8f, 0x1.68e4a6p+8f, -0x1.685dfep+8f, 0x1.592f3ap+8f, -0x1.09589ap+8f, 0x1.658b66p+7f, -0x1.f90c72p+6f, 0x1.49a9a8p+6f, -0x1.441338p+5f, 0x1.0b7b2ap+4f, -0x1.d98372p+2f, 0x1.f43ec2p+0f, 0x1.6165b8p-1f, -0x1.4f8a82p-1f, 0x1.267684p-3f, -0x1.8ddc62p-9f, -0x1.979caep-11f, 0x1.95627cp-20f, 0x1.38bcd2p-31f, 0x0p+0f};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0f, 0x1.ddc992p+0f, -0x1.0aa6a6p+4f, 0x1.ffd30ap+5f, -0x1.1076bcp+7f, 0x1.5b315p+7f, -0x1.15e62ap+7f, 0x1.73ecdap+6f, -0x1.7ea49ap+6f, 0x1.92fe5p+6f, -0x1.e50ce8p+5f, 0x1.23fe36p+4f, -0x1.1183a6p+3f, 0x1.325da8p+2f, 0x1.b5b93ep+2f, -0x1.6174ccp+3f, 0x1.b8e78ep+2f, -0x1.ffc6e6p+1f, 0x1.807b44p+1f, -0x1.949fp+0f, 0x1.99c706p-2f, -0x1.8b4256p-6f, -0x1.25fbdep-8f, 0x1.a2ffd6p-17f, 0x1.4225e6p-27f, 0x0p+0f};
-            }
-            if constexpr (order == 11) {
-                return {0x0p+0f, 0x1.82556p-2f, -0x1.b108acp+1f, 0x1.a3afap+3f, -0x1.c92e2ap+4f, 0x1.336156p+5f, -0x1.154d2p+5f, 0x1.af95c6p+4f, -0x1.a382eep+4f, 0x1.a5a57ep+4f, -0x1.48587cp+4f, 0x1.c6519cp+3f, -0x1.64406ep+3f, 0x1.05a0dap+3f, -0x1.34062ap+2f, 0x1.65a332p+1f, -0x1.b27cf8p+0f, 0x1.a5bdc8p-1f, -0x1.571ac2p-2f, 0x1.317678p-3f, -0x1.904f34p-5f, 0x1.0ee4f4p-8f, 0x1.2584f2p-10f, -0x1.373cf6p-17f, -0x1.db60ap-27f, -0x0p+0f};
-            }
-            if constexpr (order == 12) {
-                return {0x0p+0f, 0x1.8dbb04p-5f, -0x1.bebdc6p-2f, 0x1.aeb7a6p+0f, -0x1.cb9852p+1f, 0x1.240bf6p+2f, -0x1.cab7dp+1f, 0x1.1fd454p+1f, -0x1.1ce974p+1f, 0x1.3bab08p+1f, -0x1.c40e7cp+0f, 0x1.feadc8p-1f, -0x1.a643a4p-1f, 0x1.543b96p-1f, -0x1.577aa6p-2f, 0x1.499f7p-3f, -0x1.d5a152p-4f, 0x1.d4c5bap-5f, -0x1.094f52p-6f, 0x1.cd0926p-8f, -0x1.b2091cp-9f, 0x1.fdc736p-13f, 0x1.4af176p-13f, -0x1.fd199ap-19f, -0x1.7fa406p-27f, 0x0p+0f};
-            }
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0, 0x1.749078c0867aap-9, 0x1.8ae6a79b4939p-3, 0x1.d008898983914p-1, -0x1.20e16d5539e3fp-4, -0x1.f688bd1280c7p-5, 0x1.2fca4301354a5p-5, -0x1.505c64431d7a7p-12, -0x1.0145189baf014p-6, 0x1.c908becee5a6ap-7, -0x1.beac12be1e7dep-8, 0x1.0006a916adee3p-9, -0x1.d4cc286b09e13p-13, -0x1.a08b65bbb5986p-15, 0x1.5f413ab3a7eb9p-16, -0x1.5c34d16af592p-20, -0x1.2dc4454eebde3p-21, 0x1.74f33a2ccbc65p-24, 0x1.ddb5df0a412fdp-29, -0x1.07969b3a158bdp-32, 0x1.2c5958b74836cp-38, 0x1.52fae6e83092p-45, -0x1.d83da475a639cp-53, 0x1.1342e56840ec2p-65, 0x1.aa25edf8f64ffp-86, -0x0p+0};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0, 0x1.23923550f457dp-6, 0x1.0c0767795d12bp-1, 0x1.3373be839b47cp-2, -0x1.856d7e6b6468cp+0, 0x1.22d30ac28dd9dp+0, -0x1.72e38df054a24p-1, 0x1.8e439b194a1c1p-2, -0x1.3bc2524066e84p-3, 0x1.1bc8f6e410596p-5, 0x1.2884461caa1e3p-11, -0x1.db22a9804aa11p-10, -0x1.3482dca87f01cp-11, 0x1.3285223dae55ap-11, -0x1.bbf1c4306d1a3p-14, -0x1.17497a4dcd45p-16, 0x1.bebec0cbd1f99p-18, -0x1.bc40d833ef35ap-22, 0x1.6454c6cebdf98p-26, 0x1.5fce040bf0fa2p-29, -0x1.1241493325c92p-33, -0x1.ce70ab06ee7ebp-41, 0x1.8616f674ef406p-48, -0x1.7b38ad7c07a3ap-60, -0x1.258ba4702de86p-79, 0x0p+0};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0, 0x1.7e9e99d93265ep-4, 0x1.e81e73bf7d4e6p-1, -0x1.368292c7be10ep+1, 0x1.a1c192a939b96p+0, -0x1.58e6f9045a40ep-2, 0x1.2f82100ba4f28p-2, -0x1.f8fd9be6cc911p-2, 0x1.017de77081fc3p-1, -0x1.5831ad1464211p-2, 0x1.30d718554c4cbp-3, -0x1.30a6075105b3bp-5, -0x1.632f9e9eb99fcp-11, 0x1.1cbed37ba4dbep-8, -0x1.77d86fa7164cp-10, 0x1.50ec238da0096p-14, 0x1.f99c3b6dd2e63p-15, -0x1.8453f2cbc2d99p-17, -0x1.b4056601f4cp-23, 0x1.4c2776a5f116ep-24, -0x1.287daf168a21ap-29, -0x1.b00a66e2af604p-36, 0x1.401eb1fad689ep-42, -0x1.71528144e6955p-54, -0x1.1de10823e626cp-72, 0x0p+0};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0, 0x1.95e033565cd46p-2, 0x1.e7908dd5753c9p-3, -0x1.293799fcf6c8ep+2, 0x1.36cc467b08bf8p+3, -0x1.4335983e13577p+3, 0x1.9c4d14b541486p+2, -0x1.ef81d85b23a02p+0, -0x1.2378e73c6b10ap+0, 0x1.c6e27151761e4p+0, -0x1.c857e67243154p-1, 0x1.3531afa42b77fp-8, 0x1.05f57c1a6464dp-2, -0x1.38a2db882124ep-3, 0x1.35c4a5041d9b9p-5, -0x1.fddc3c9f813d7p-14, -0x1.2653a0321997dp-9, 0x1.ec5d6f7ab50c1p-12, -0x1.dc01f8633f4c6p-17, -0x1.379717b64ca38p-18, 0x1.7e5cfdc9a1b18p-23, 0x1.a124166c57861p-29, -0x1.4171311c3a7b2p-35, 0x1.65f402b77f1abp-46, 0x1.15123cc4efb61p-63, -0x0p+0};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0, 0x1.4c5d516dd5341p+0, -0x1.5d2571cda5544p+2, 0x1.24b0f0352262ap+3, -0x1.39e0f8d13e8dbp+3, 0x1.f006cc927be53p+3, -0x1.0ce2ffa464611p+5, 0x1.b8b8afcf323dp+5, -0x1.e6925570e3f51p+5, 0x1.503102590c0b8p+5, -0x1.6d86add093f07p+3, -0x1.35b5dc1025f2dp+3, 0x1.a6237c764b4a3p+3, -0x1.cda455c3ae393p+2, 0x1.d5a02bb93708ap+0, 0x1.ecd4c4adc076p-5, -0x1.660ee59df078bp-3, 0x1.5158e51b27e5ep-5, -0x1.73814bfd57b68p-10, -0x1.23460c48f637p-11, 0x1.fa353cdebaaabp-16, 0x1.19c5738584247p-21, -0x1.4bb4308ed52p-27, 0x1.fc9a1f4f09859p-38, 0x1.89a8b7b9d28d2p-54, 0x0p+0};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0, 0x1.a35157d8dba57p+1, -0x1.5a1bc35a1cc0ep+4, 0x1.fa0a0878d9a93p+5, -0x1.a68f6523a827p+6, 0x1.98403a971e631p+6, -0x1.03810e60e0205p+5, -0x1.14faaec768465p+6, 0x1.3d735b94c1054p+7, -0x1.cdbd7de801408p+7, 0x1.20043470ad457p+8, -0x1.2591e882d85cdp+8, 0x1.b621996a63c18p+7, -0x1.a875ba068d845p+6, 0x1.85c7d166f26b7p+4, 0x1.1c0e0d6b929f9p+2, -0x1.36efc345fd87ep+2, 0x1.3e3f5c2c93c34p+0, -0x1.bffc3922a3129p-5, -0x1.75f52c4bce394p-6, 0x1.dea5b49d2b29ap-10, 0x1.10aa3eff5f8abp-15, -0x1.ea6ed6c321e75p-21, 0x1.089ab261bfe1dp-30, 0x1.9990a3735f2b8p-46, -0x0p+0};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0, 0x1.5d159c98a090ap+2, -0x1.54873e7e1b3d2p+5, 0x1.2c245e185ac8bp+7, -0x1.416f5cc6c22c2p+8, 0x1.e67e2b7f93304p+8, -0x1.298ee57db6ed6p+9, 0x1.48ee3d90a4e35p+9, -0x1.4e6b4521eb7a5p+9, 0x1.2782e95d7bf9fp+9, -0x1.bb493883e544dp+8, 0x1.25dfd4b9fa45bp+8, -0x1.575e0c206b7eep+7, 0x1.1c028f2725fcep+6, -0x1.08a1fe0ac681ap+2, -0x1.12ed1d6ca773p+4, 0x1.66791e904ad3bp+3, -0x1.7aa9733036516p+1, 0x1.41600caa02956p-3, 0x1.275514f436a32p-4, -0x1.29373f56ac109p-7, -0x1.51ea7d9f34504p-13, 0x1.deb156b08b87fp-18, -0x1.6e30fae8c34eep-27, -0x1.1b57abb7d7f1cp-41, 0x0p+0};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0, 0x1.d4fe27a0835aep+2, -0x1.ecb0f32ca76fbp+5, 0x1.c6da62a20cd0bp+7, -0x1.e3622dd5ba05ep+8, 0x1.49508717a90e8p+9, -0x1.3d934aacf56d1p+9, 0x1.068600d74e1c9p+9, -0x1.bb4eb52dbc23dp+8, 0x1.2c2d3c048caafp+8, -0x1.6a6f07f5d07ddp+5, -0x1.48c0f7b3bed9ep+7, 0x1.bce28601020e5p+7, -0x1.9e035ea535c3bp+7, 0x1.737017c34f7dfp+7, -0x1.15bd065f2789cp+7, 0x1.1609d2e86de1fp+6, -0x1.30b382548236p+4, 0x1.34c266d274d02p+0, 0x1.56d14dbd1c0fp-1, -0x1.f82518456ddfap-4, -0x1.1d5d333a03734p-9, 0x1.599f88826e1dfp-13, -0x1.742b04eba227p-22, -0x1.1fd835e2f3ac3p-35, -0x0p+0};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0, 0x1.6f91b1fb16e46p+2, -0x1.8fef11e8059cfp+5, 0x1.809c444472a8ep+7, -0x1.b10bf090c92b5p+8, 0x1.45258188f7147p+9, -0x1.7231afc08bd27p+9, 0x1.7af82162ac35ap+9, -0x1.823e9f8992b5ap+9, 0x1.6f4bc124eb7dcp+9, -0x1.32f291524b4fdp+9, 0x1.d856007cb8fap+8, -0x1.59b2f057a74e5p+8, 0x1.c4898ffe6b604p+7, -0x1.01b04bb5c7e4fp+7, 0x1.0ee550f2b46fbp+6, -0x1.f149829700499p+4, 0x1.21413698e7cf2p+3, -0x1.1e358290df39dp-2, -0x1.54f12799790c9p-1, 0x1.1dedd290f908p-3, 0x1.2b8db385d6eebp-10, -0x1.7cd67d6099899p-12, 0x1.c1758243d6f69p-21, 0x1.5b5402fbe8db8p-33, -0x0p+0};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0, 0x1.e00f201ca9b48p+1, -0x1.09aad588fc6e2p+5, 0x1.0083b1ed3add2p+7, -0x1.1b01639f15a47p+8, 0x1.8e74c5b415b4dp+8, -0x1.907a858da198ep+8, 0x1.68e4a68143eb6p+8, -0x1.685dfe59eb94fp+8, 0x1.592f39b72049ap+8, -0x1.09589acf597f5p+8, 0x1.658b66c44d2dap+7, -0x1.f90c71880a916p+6, 0x1.49a9a7009f2b2p+6, -0x1.441338caa52dp+5, 0x1.0b7b2a297fde1p+4, -0x1.d98372b1c68d4p+2, 0x1.f43ec1f2a328p+0, 0x1.6165b77555fcbp-1, -0x1.4f8a8171bb09p-1, 0x1.267683e93d2b7p-3, -0x1.8ddc624d415c9p-9, -0x1.979cae945ae1p-11, 0x1.95627b187fdb2p-20, 0x1.38bcd286c35dep-31, 0x0p+0};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0, 0x1.ddc9914b8fce2p+0, -0x1.0aa6a6fe474ap+4, 0x1.ffd30a30f104ep+5, -0x1.1076bbdb4cf75p+7, 0x1.5b314fd5bd842p+7, -0x1.15e629a2f07abp+7, 0x1.73ecdaa7dbcd1p+6, -0x1.7ea4991281a8p+6, 0x1.92fe5087093b6p+6, -0x1.e50ce86c3eca3p+5, 0x1.23fe36ce5250dp+4, -0x1.1183a5ac74637p+3, 0x1.325da71616788p+2, 0x1.b5b93d37eb78fp+2, -0x1.6174cc292a978p+3, 0x1.b8e78e1a9ada5p+2, -0x1.ffc6e54f09b8ap+1, 0x1.807b43d233e13p+1, -0x1.949effe4fd5f1p+0, 0x1.99c706ee33d33p-2, -0x1.8b4255eb2ab53p-6, -0x1.25fbde4ae0e29p-8, 0x1.a2ffd5a58a3e6p-17, 0x1.4225e5d67d6a9p-27, 0x0p+0};
-            }
-            if constexpr (order == 11) {
-                return {0x0p+0, 0x1.82555f0fca682p-2, -0x1.b108ac4bd9d5ep+1, 0x1.a3af9f5e28534p+3, -0x1.c92e2a69bebeap+4, 0x1.336156f19a3ebp+5, -0x1.154d20c532d38p+5, 0x1.af95c6a7f034fp+4, -0x1.a382ed435f8edp+4, 0x1.a5a57db59b67cp+4, -0x1.48587bdb4781p+4, 0x1.c6519b1cdb293p+3, -0x1.64406dc5dece2p+3, 0x1.05a0da2a87dbp+3, -0x1.34062a3bf7c11p+2, 0x1.65a3327bcf1acp+1, -0x1.b27cf7ab49be3p+0, 0x1.a5bdc7192b9c4p-1, -0x1.571ac2983f85ep-2, 0x1.31767817c6adfp-3, -0x1.904f3491bf69cp-5, 0x1.0ee4f3163f55fp-8, 0x1.2584f1f36b43ep-10, -0x1.373cf584c03efp-17, -0x1.db60a068c3378p-27, -0x0p+0};
-            }
-            if constexpr (order == 12) {
-                return {0x0p+0, 0x1.8dbb03fad2c3p-5, -0x1.bebdc5d3b2391p-2, 0x1.aeb7a5ea21053p+0, -0x1.cb9851522d20bp+1, 0x1.240bf59871b99p+2, -0x1.cab7cf1ed537ep+1, 0x1.1fd4543a5fd8dp+1, -0x1.1ce9744c1c975p+1, 0x1.3bab08bd76345p+1, -0x1.c40e7b4e77557p+0, 0x1.feadc8c7ce87bp-1, -0x1.a643a47d84b4ep-1, 0x1.543b964e0f03ap-1, -0x1.577aa576ffa65p-2, 0x1.499f6f7a97a23p-3, -0x1.d5a15151b9016p-4, 0x1.d4c5badb46707p-5, -0x1.094f5215690dbp-6, 0x1.cd0926fb9e142p-8, -0x1.b2091c2c73ddp-9, 0x1.fdc7350edfaddp-13, 0x1.4af17513fc3a8p-13, -0x1.fd199a3cefa32p-19, -0x1.7fa406e41ed66p-27, 0x0p+0};
-            }
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0L, 0xb.a483c60433d4d39p-12L, 0xc.57353cda49c7dedp-6L, 0xe.80444c4c1c89ecep-4L, -0x9.070b6aa9cf1f929p-7L, -0xf.b445e89406380cap-8L, 0x9.7e521809aa52714p-8L, -0xa.82e32218ebd378fp-15L, -0x8.0a28c4dd780a179p-9L, 0xe.4845f6772d3537ep-10L, -0xd.f56095f0f3ef04ap-11L, 0x8.003548b56f71a16p-12L, -0xe.a66143584f09aacp-16L, -0xd.045b2dddacc33b9p-18L, 0xa.fa09d59d3f5ca6ep-19L, -0xa.e1a68b57ac901bdp-23L, -0x9.6e222a775ef19bdp-24L, 0xb.a799d1665e328c8p-27L, 0xe.edaef852097ea04p-32L, -0x8.3cb4d9d0ac5e8bp-35L, 0x9.62cac5ba41b6085p-41L, 0xa.97d73741848fd34p-48L, -0xe.c1ed23ad31ce184p-56L, 0x8.9a172b420760cedp-68L, 0xd.512f6fc7b27f70ap-89L, -0x0p+0L};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0L, 0x9.1c91aa87a2be53cp-9L, 0x8.603b3bcae89572fp-4L, 0x9.9b9df41cda3e206p-5L, -0xc.2b6bf35b234616fp-3L, 0x9.169856146ece4d3p-3L, -0xb.971c6f82a511d45p-4L, 0xc.721cd8ca50e0b31p-5L, -0x9.de1292033741f59p-6L, 0x8.de47b72082cb31fp-8L, 0x9.442230e550f1904p-14L, -0xe.d9154c025508998p-13L, -0x9.a416e543f80e22fp-14L, 0x9.942911ed72acc95p-14L, -0xd.df8e218368d1bf8p-17L, -0x8.ba4bd26e6a27feep-19L, 0xd.f5f6065e8fcc9b9p-21L, -0xd.e206c19f79acc2bp-25L, 0xb.22a63675efcbfa2p-29L, 0xa.fe70205f87d115p-32L, -0x8.920a49992e4937dp-36L, -0xe.7385583773f5acap-44L, 0xc.30b7b3a77a02f75p-51L, -0xb.d9c56be03d1d02cp-63L, -0x9.2c5d23816f42d62p-82L, 0x0p+0L};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0L, 0xb.f4f4cec9932f0f6p-7L, 0xf.40f39dfbea733adp-4L, -0x9.b414963df08728ap-2L, 0xd.0e0c9549cdcb3a8p-3L, -0xa.c737c822d206e95p-5L, 0x9.7c10805d27943dp-5L, -0xf.c7ecdf3664887bbp-5L, 0x8.0bef3b840fe187dp-4L, -0xa.c18d68a32108919p-5L, 0x9.86b8c2aa62655e8p-6L, -0x9.85303a882d9d527p-8L, -0xb.197cf4f5ccfe389p-14L, 0x8.e5f69bdd26decb6p-11L, -0xb.bec37d38b25fe46p-13L, 0xa.87611c6d004b37bp-17L, 0xf.cce1db6e973199cp-18L, -0xc.229f965e16ccb5cp-20L, -0xd.a02b300fa5ffc5bp-26L, 0xa.613bb52f88b70ecp-27L, -0x9.43ed78b4510cd51p-32L, -0xd.805337157b01dc1p-39L, 0xa.00f58fd6b44ef03p-45L, -0xb.8a940a2734aa51ap-57L, -0x8.ef08411f3135df8p-75L, 0x0p+0L};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0L, 0xc.af019ab2e6a32f3p-5L, 0xf.3c846eaba9e4babp-6L, -0x9.49bccfe7b646d1p-1L, 0x9.b66233d845fbec5p+0L, -0xa.19acc1f09abba63p+0L, 0xc.e268a5aa0a433dap-1L, -0xf.7c0ec2d91d00d64p-3L, -0x9.1bc739e3588517cp-3L, 0xe.37138a8bb0f1f2cp-3L, -0xe.42bf339218a9d4bp-4L, 0x9.a98d7d215bbfa64p-11L, 0x8.2fabe0d32326ba1p-5L, -0x9.c516dc410926fe2p-6L, 0x9.ae252820ecdca2bp-8L, -0xf.eee1e4fc09eb578p-17L, -0x9.329d0190ccbe8fdp-12L, 0xf.62eb7bd5a860bbfp-15L, -0xe.e00fc319fa6309dp-20L, -0x9.bcb8bdb2651be88p-21L, 0xb.f2e7ee4d0d8bee7p-26L, 0xd.0920b362bc30ba7p-32L, -0xa.0b8988e1d3d9312p-38L, 0xb.2fa015bbf8d5914p-49L, 0x8.a891e6277db069dp-66L, -0x0p+0L};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0L, 0xa.62ea8b6ea9a0684p-3L, -0xa.e92b8e6d2aa1c92p-1L, 0x9.258781a91314f19p+0L, -0x9.cf07c689f46d8f8p+0L, 0xf.80366493df29948p+0L, -0x8.6717fd232308bfp+2L, 0xd.c5c57e7991e8074p+2L, -0xf.3492ab871fa8811p+2L, 0xa.818812c8605bdbdp+2L, -0xb.6c356e849f83a5ep+0L, -0x9.adaee0812f969a5p+0L, 0xd.311be3b25a5141ap+0L, -0xe.6d22ae1d71c94e9p-1L, 0xe.ad015dc9b84519p-3L, 0xf.66a6256e03aff12p-8L, -0xb.30772cef83c5a19p-6L, 0xa.8ac728d93f2edffp-8L, -0xb.9c0a5feabdb40fdp-13L, -0x9.1a306247b1b7d38p-14L, 0xf.d1a9e6f5d555505p-19L, 0x8.ce2b9c2c2123732p-24L, -0xa.5da18476a8fff99p-30L, 0xf.e4d0fa784c2c7aap-41L, 0xc.4d45bdce9468eb9p-57L, 0x0p+0L};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0L, 0xd.1a8abec6dd2b59ap-2L, -0xa.d0de1ad0e606ddbp+1L, 0xf.d05043c6cd499c3p+2L, -0xd.347b291d41380b3p+3L, 0xc.c201d4b8f318b15p+3L, -0x8.1c08730701024ebp+2L, -0x8.a7d5763b4232a87p+3L, 0x9.eb9adca6082a1b5p+4L, -0xe.6debef400a03eb9p+4L, 0x9.0021a3856a2b57ap+5L, -0x9.2c8f4416c2e68c6p+5L, 0xd.b10ccb531e0bf33p+4L, -0xd.43add0346c224eap+3L, 0xc.2e3e8b37935bbc2p+1L, 0x8.e0706b5c94fcaddp-1L, -0x9.b77e1a2fec3f3f9p-1L, 0x9.f1fae1649e1a3cap-3L, -0xd.ffe1c91518944a2p-8L, -0xb.afa9625e71ca263p-9L, 0xe.f52da4e9594cf98p-13L, 0x8.8551f7fafc55605p-18L, -0xf.5376b6190f3a9e1p-24L, 0x8.44d5930dff0e45cp-33L, 0xc.cc851b9af95c09cp-49L, -0x0p+0L};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0L, 0xa.e8ace4c50485103p-1L, -0xa.a439f3f0d9e9083p+2L, 0x9.6122f0c2d6458a6p+4L, -0xa.0b7ae6361160fep+5L, 0xf.33f15bfc9982224p+5L, -0x9.4c772bedb76afeap+6L, 0xa.4771ec85271a548p+6L, -0xa.735a290f5bd2b61p+6L, 0x9.3c174aebdfcfafep+6L, -0xd.da49c41f2a26a23p+5L, 0x9.2efea5cfd22d7f4p+5L, -0xa.baf061035bf7341p+4L, 0x8.e01479392fe733bp+3L, -0x8.450ff056340cfcbp-1L, -0x8.9768eb653b980edp+1L, 0xb.33c8f482569da0fp+0L, -0xb.d54b9981b28ad7fp-2L, 0xa.0b00655014aaec4p-6L, 0x9.3aa8a7a1b518f2bp-7L, -0x9.49b9fab56084ac4p-10L, -0xa.8f53ecf9a28205dp-16L, 0xe.f58ab5845c3f783p-21L, -0xb.7187d7461a76c1bp-30L, -0x8.dabd5dbebf8dd41p-44L, 0x0p+0L};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0L, 0xe.a7f13d041ad70dp-1L, -0xf.658799653b7da4ap+2L, 0xe.36d31510668543p+4L, -0xf.1b116eadd02ec05p+5L, 0xa.4a8438bd48741b4p+6L, -0x9.ec9a5567ab68514p+6L, 0x8.343006ba70e487p+6L, -0xd.da75a96de11e455p+5L, 0x9.6169e024655745ap+5L, -0xb.53783fae83ee946p+2L, -0xa.4607bd9df6ceea7p+4L, 0xd.e71430081072aa3p+4L, -0xc.f01af529ae1d75fp+4L, 0xb.9b80be1a7bef779p+4L, -0x8.ade832f93c4e129p+4L, 0x8.b04e97436f0fa36p+3L, -0x9.859c12a411afe04p+1L, 0x9.a6133693a681011p-3L, 0xa.b68a6de8e077c6ep-4L, -0xf.c128c22b6efd051p-7L, -0x8.eae999d01b9a034p-12L, 0xa.ccfc441370efba9p-16L, -0xb.a158275d1138117p-25L, -0x8.fec1af179d61b9fp-38L, -0x0p+0L};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0L, 0xb.7c8d8fd8b7231c8p-1L, -0xc.7f788f402ce76dp+2L, 0xc.04e222239546c21p+4L, -0xd.885f8486495a99bp+5L, 0xa.292c0c47b8a3474p+6L, -0xb.918d7e045e93b18p+6L, 0xb.d7c10b1561accb3p+6L, -0xc.11f4fc4c95acfe3p+6L, 0xb.7a5e09275bee17p+6L, -0x9.97948a925a7e40dp+6L, 0xe.c2b003e5c7d03a7p+5L, -0xa.cd9782bd3a72557p+5L, 0xe.244c7ff35b01e7fp+4L, -0x8.0d825dae3f27671p+4L, 0x8.772a8795a37d803p+3L, -0xf.8a4c14b8024c883p+1L, 0x9.0a09b4c73e78daep+0L, -0x8.f1ac1486f9ce578p-5L, -0xa.a7893ccbc864ac9p-4L, 0x8.ef6e9487c83fc69p-6L, 0x9.5c6d9c2eb77580cp-13L, -0xb.e6b3eb04cc4c723p-15L, 0xe.0bac121eb7b4789p-24L, 0xa.daa017df46dbf37p-36L, -0x0p+0L};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0L, 0xf.007900e54da3df6p-2L, -0x8.4d56ac47e370e97p+2L, 0x8.041d8f69d6e8efep+4L, -0x8.d80b1cf8ad238cbp+5L, 0xc.73a62da0ada64c1p+5L, -0xc.83d42c6d0cc6daep+5L, 0xb.4725340a1f5b14p+5L, -0xb.42eff2cf5ca79c7p+5L, 0xa.c979cdb9024d1b7p+5L, -0x8.4ac4d67acbfab3fp+5L, 0xb.2c5b3622696cf85p+4L, -0xf.c8638c40548b2c6p+3L, 0xa.4d4d3804f95933ep+3L, -0xa.2099c6552967d07p+2L, 0x8.5bd9514bfef0a5ep+1L, -0xe.cc1b958e3469fa9p-1L, 0xf.a1f60f951940304p-3L, 0xb.0b2dbbaaafe5407p-4L, -0xa.7c540b8dd847e5dp-4L, 0x9.33b41f49e95bb8cp-6L, -0xc.6ee3126a0ae46c7p-12L, -0xc.bce574a2d70819p-14L, 0xc.ab13d8c3fed8cb7p-23L, 0x9.c5e694361aef307p-34L, 0x0p+0L};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0L, 0xe.ee4c8a5c7e71374p-3L, -0x8.553537f23a4ffcdp+1L, 0xf.fe98518788271d7p+2L, -0x8.83b5deda67ba93ep+4L, 0xa.d98a7eadec21394p+4L, -0x8.af314d1783d59d9p+4L, 0xb.9f66d53ede688c9p+3L, -0xb.f524c8940d401f5p+3L, 0xc.97f2843849db0a7p+3L, -0xf.28674361f651857p+2L, 0x9.1ff1b672928682ep+1L, -0x8.8c1d2d63a31b528p+0L, 0x9.92ed38b0b3c3d8dp-1L, 0xd.adc9e9bf5bc7971p-1L, -0xb.0ba6614954bbf44p+0L, 0xd.c73c70d4d6d2496p-1L, -0xf.fe372a784dc531cp-2L, 0xc.03da1e919f0994ap-2L, -0xc.a4f7ff27eaf885bp-3L, 0xc.ce3837719e99949p-5L, -0xc.5a12af5955a96fbp-9L, -0x9.2fdef25707148aap-11L, 0xd.17fead2c51f312dp-20L, 0xa.112f2eb3eb54818p-30L, 0x0p+0L};
-            }
-            if constexpr (order == 11) {
-                return {0x0p+0L, 0xc.12aaf87e5340e4ep-5L, -0xd.8845625eceaef48p-2L, 0xd.1d7cfaf14299ea2p+0L, -0xe.4971534df5f5093p+1L, 0x9.9b0ab78cd1f558dp+2L, -0x8.aa690629969becdp+2L, 0xd.7cae353f81a7b93p+1L, -0xd.1c176a1afc76911p+1L, 0xd.2d2bedacdb3df28p+1L, -0xa.42c3deda3c082c7p+1L, 0xe.328cd8e6d949737p+0L, -0xb.22036e2ef671076p+0L, 0x8.2d06d1543ed7f3cp+0L, -0x9.a03151dfbe084ep-1L, 0xb.2d1993de78d60e7p-2L, -0xd.93e7bd5a4df1be7p-3L, 0xd.2dee38c95ce1d1p-4L, -0xa.b8d614c1fc2f1d3p-5L, 0x9.8bb3c0be356f62ap-6L, -0xc.8279a48dfb4e393p-8L, 0x8.772798b1faafa2dp-11L, 0x9.2c278f9b5a1f3dep-13L, -0x9.b9e7ac2601f7483p-20L, -0xe.db05034619bbe3ap-30L, -0x0p+0L};
-            }
-            if constexpr (order == 12) {
-                return {0x0p+0L, 0xc.6dd81fd69617fa7p-8L, -0xd.f5ee2e9d91c88f7p-5L, 0xd.75bd2f51082950ep-3L, -0xe.5cc28a9169055e6p-2L, 0x9.205facc38dccbfep-1L, -0xe.55be78f6a9bf069p-2L, 0x8.fea2a1d2fec658fp-2L, -0x8.e74ba260e4bab6fp-2L, 0x9.dd5845ebb1a25a2p-2L, -0xe.2073da73baab7afp-3L, 0xf.f56e463e743d47ep-4L, -0xd.321d23ec25a6d38p-4L, 0xa.a1dcb270781d1d4p-4L, -0xa.bbd52bb7fd3277ep-5L, 0xa.4cfb7bd4bd115e9p-6L, -0xe.ad0a8a8dc80b1aep-7L, 0xe.a62dd6da3383b8ap-8L, -0x8.4a7a90ab486d843p-9L, 0xe.684937dcf0a13c9p-11L, -0xd.9048e1639ee817cp-12L, 0xf.ee39a876fd6e928p-16L, 0xa.578ba89fe1d43b5p-16L, -0xf.e8ccd1e77d18dbbp-22L, -0xb.fd203720f6b2eddp-30L, 0x0p+0L};
-            }
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.749078c0867a9a724454443e75a7p-9Q, 0x1.8ae6a79b4938fbd909b199343609p-3Q, 0x1.d008898983913d9bf1d194ac98f7p-1Q, -0x1.20e16d5539e3f25296b1c6880b53p-4Q, -0x1.f688bd1280c70194203f744266d5p-5Q, 0x1.2fca4301354a4e285e82fc4b6183p-5Q, -0x1.505c64431d7a6f1e36954a7c80cp-12Q, -0x1.0145189baf0142f2a8862b8be415p-6Q, 0x1.c908becee5a6a6fcccc95605355fp-7Q, -0x1.beac12be1e7de0939dd15f031644p-8Q, 0x1.0006a916adee342c6b2792c6bd7ep-9Q, -0x1.d4cc286b09e13557f3e87a0f9caep-13Q, -0x1.a08b65bbb598677114fddb7b661ep-15Q, 0x1.5f413ab3a7eb94dcb396b2657edap-16Q, -0x1.5c34d16af592037a11107a487b39p-20Q, -0x1.2dc4454eebde3379c7645c4ba87ep-21Q, 0x1.74f33a2ccbc6518fcdedc7d5aa01p-24Q, 0x1.ddb5df0a412fd407d061c573b81ep-29Q, -0x1.07969b3a158bd160a5cdad0ece81p-32Q, 0x1.2c5958b74836c10a9059d0bfc767p-38Q, 0x1.52fae6e83091fa686190e11a0d2cp-45Q, -0x1.d83da475a639c307966abb294b63p-53Q, 0x1.1342e56840ec19da921d2c329c6fp-65Q, 0x1.aa25edf8f64fee132e1b30933b5p-86Q, 0x0p+0Q};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.23923550f457ca7814b0bb3fd653p-6Q, 0x1.0c0767795d12ae5d156ec5cf4423p-1Q, 0x1.3373be839b47c40b1d36ec3e47ecp-2Q, -0x1.856d7e6b6468c2deff8342e75baep+0Q, 0x1.22d30ac28dd9c9a5de5413538cd2p+0Q, -0x1.72e38df054a23a8a5ebabc499005p-1Q, 0x1.8e439b194a1c16626ebcbea59c81p-2Q, -0x1.3bc2524066e83eb2d5b3ff97e1edp-3Q, 0x1.1bc8f6e41059663daa79bf4a8b55p-5Q, 0x1.2884461caa1e3207b6de1334a7c9p-11Q, -0x1.db22a9804aa1133069d05b96cb0fp-10Q, -0x1.3482dca87f01c45e946a258c3e06p-11Q, 0x1.3285223dae55992a1d57ada1533cp-11Q, -0x1.bbf1c4306d1a37f02d18135ce323p-14Q, -0x1.17497a4dcd44ffdc92c6ebd1a068p-16Q, 0x1.bebec0cbd1f99371a7867cbe3fbap-18Q, -0x1.bc40d833ef3598561d72cdf89bb4p-22Q, 0x1.6454c6cebdf97f43adbbdee1eeb8p-26Q, 0x1.5fce040bf0fa22a0bb7f52a52e7bp-29Q, -0x1.1241493325c926f92e656210ed16p-33Q, -0x1.ce70ab06ee7eb593175a3e65f68ep-41Q, 0x1.8616f674ef405eeabf053da9c72dp-48Q, -0x1.7b38ad7c07a3a058098173d3a8bcp-60Q, -0x1.258ba4702de85ac45e001504a52p-79Q, 0x0p+0Q};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.7e9e99d93265e1ecb27f1a82e385p-4Q, 0x1.e81e73bf7d4e6759d9f3db761257p-1Q, -0x1.368292c7be10e513188a104c5c4ap+1Q, 0x1.a1c192a939b9674ffcca9b2f1e48p+0Q, -0x1.58e6f9045a40dd2a472104dd0f2ep-2Q, 0x1.2f82100ba4f2879faa0ab7316342p-2Q, -0x1.f8fd9be6cc910f763e95aa8aafdap-2Q, 0x1.017de77081fc30f9ad09eddaf43dp-1Q, -0x1.5831ad14642112326c714ae42463p-2Q, 0x1.30d718554c4cabcfafc1434f8a7fp-3Q, -0x1.30a6075105b3aa4d5336fc1950e8p-5Q, -0x1.632f9e9eb99fc711faf42ce203b1p-11Q, 0x1.1cbed37ba4dbd96c225d81054e88p-8Q, -0x1.77d86fa7164bfc8c126a64816ac4p-10Q, 0x1.50ec238da00966f5e3d28fc9265ep-14Q, 0x1.f99c3b6dd2e633388ada35d1bfe8p-15Q, -0x1.8453f2cbc2d996b7775a123e9384p-17Q, -0x1.b4056601f4bff8b5e7d36857cb2ap-23Q, 0x1.4c2776a5f116e1d85dd046bd9786p-24Q, -0x1.287daf168a219aa1132a37934711p-29Q, -0x1.b00a66e2af603b8210a104b463bdp-36Q, 0x1.401eb1fad689de068ef9a337dfddp-42Q, -0x1.71528144e6954a34804ddc8b7672p-54Q, -0x1.1de10823e626bbef4adf3610f4fep-72Q, 0x0p+0Q};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.95e033565cd465e59fc64a849ff5p-2Q, 0x1.e7908dd5753c97550b1b562a02c1p-3Q, -0x1.293799fcf6c8da1f93fe2d057e3ap+2Q, 0x1.36cc467b08bf7d8a89d5be8f934fp+3Q, -0x1.4335983e135774c5e5156a45190ap+3Q, 0x1.9c4d14b5414867b3e2c99a21a031p+2Q, -0x1.ef81d85b23a01ac83af86d64d1abp+0Q, -0x1.2378e73c6b10a2f7957b04478d3fp+0Q, 0x1.c6e27151761e3e586f5403563b06p+0Q, -0x1.c857e67243153a965a648f8e6a77p-1Q, 0x1.3531afa42b77f4c754018d3dff11p-8Q, 0x1.05f57c1a6464d742d9d2e202da9bp-2Q, -0x1.38a2db882124dfc4e44179ad6816p-3Q, 0x1.35c4a5041d9b9456d2520e65bc23p-5Q, -0x1.fddc3c9f813d6aef1f4f22d0ffb3p-14Q, -0x1.2653a0321997d1fa4ad992783a03p-9Q, 0x1.ec5d6f7ab50c177dc61e0a189fcdp-12Q, -0x1.dc01f8633f4c61396f200866480ap-17Q, -0x1.379717b64ca37d0f86a74f664124p-18Q, 0x1.7e5cfdc9a1b17dce328c7c0b5cf9p-23Q, 0x1.a124166c5786174e1b984a588c59p-29Q, -0x1.4171311c3a7b2623f4df8ab8200ep-35Q, 0x1.65f402b77f1ab227d7a791609ed8p-46Q, 0x1.15123cc4efb60d3af1736012e615p-63Q, 0x0p+0Q};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.4c5d516dd5340d0879832abfae77p+0Q, -0x1.5d2571cda5543923016a360261d3p+2Q, 0x1.24b0f03522629e31e5a0ddf9b0acp+3Q, -0x1.39e0f8d13e8db1f029ce62587cecp+3Q, 0x1.f006cc927be5328f1a33d6aed069p+3Q, -0x1.0ce2ffa4646117df99ed92fff69cp+5Q, 0x1.b8b8afcf323d00e8ad39d1ccb61dp+5Q, -0x1.e6925570e3f510211d732b9179c8p+5Q, 0x1.503102590c0b7b7ae2742f43b1bp+5Q, -0x1.6d86add093f074bc432a452b5189p+3Q, -0x1.35b5dc1025f2d34a60aa7bf9f93dp+3Q, 0x1.a6237c764b4a28340b8488817371p+3Q, -0x1.cda455c3ae3929d25c3c5a324857p+2Q, 0x1.d5a02bb93708a320124accef7fd1p+0Q, 0x1.ecd4c4adc075fe2457753c0ae29ap-5Q, -0x1.660ee59df078b432fb4f889b38bfp-3Q, 0x1.5158e51b27e5dbfe89f577f9dcaep-5Q, -0x1.73814bfd57b681fa89fa6df52a98p-10Q, -0x1.23460c48f636fa706d007acb283p-11Q, 0x1.fa353cdebaaaaa09ad0c40e9cfcp-16Q, 0x1.19c5738584246e6431d3352c6ae1p-21Q, -0x1.4bb4308ed51fff3108f30cb71f7ep-27Q, 0x1.fc9a1f4f09858f536f1a575d9e29p-38Q, 0x1.89a8b7b9d28d1d71597812aa68c7p-54Q, 0x0p+0Q};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0Q, 0x1.a35157d8dba56b3359c55dbb3245p+1Q, -0x1.5a1bc35a1cc0dbb69c71add31e17p+4Q, 0x1.fa0a0878d9a933860f511fa37af4p+5Q, -0x1.a68f6523a82701663e04e3ed3779p+6Q, 0x1.98403a971e63162a02dd92c33da9p+6Q, -0x1.03810e60e02049d57e6cc9d05d6p+5Q, -0x1.14faaec76846550eede58601f0cdp+6Q, 0x1.3d735b94c105436aa6c6accd08c9p+7Q, -0x1.cdbd7de801407d716cbc38649987p+7Q, 0x1.20043470ad456af43bde8d7a0984p+8Q, -0x1.2591e882d85cd18b0dca9775a589p+8Q, 0x1.b621996a63c17e6687cb0aeb2864p+7Q, -0x1.a875ba068d8449d487f82d8f98a2p+6Q, 0x1.85c7d166f26b7783d793e4b535e5p+4Q, 0x1.1c0e0d6b929f95b9e528987efc33p+2Q, -0x1.36efc345fd87e7f12a7cd8cf55f7p+2Q, 0x1.3e3f5c2c93c347939cad28d35ff2p+0Q, -0x1.bffc3922a312894449dea079023bp-5Q, -0x1.75f52c4bce3944c6d40bd8c68e83p-6Q, 0x1.dea5b49d2b299f2f3407a959506bp-10Q, 0x1.10aa3eff5f8aac0902d8bf4b6addp-15Q, -0x1.ea6ed6c321e753c1b3e92351b813p-21Q, 0x1.089ab261bfe1c8b7f19aebdff953p-30Q, 0x1.9990a3735f2b8137827c03e7b5fp-46Q, 0x0p+0Q};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0Q, 0x1.5d159c98a090a206b1f5a487328bp+2Q, -0x1.54873e7e1b3d210625d277e6898dp+5Q, 0x1.2c245e185ac8b14c7baac4033f4ap+7Q, -0x1.416f5cc6c22c1fc04eeda9dfb493p+8Q, 0x1.e67e2b7f933044475571e632011ap+8Q, -0x1.298ee57db6ed5fd4bacad0de9695p+9Q, 0x1.48ee3d90a4e34a8f4d18f98b7344p+9Q, -0x1.4e6b4521eb7a56c1ef75797e43fdp+9Q, 0x1.2782e95d7bf9f5fc360d37ee013bp+9Q, -0x1.bb493883e544d446bc2b8bcc693p+8Q, 0x1.25dfd4b9fa45afe8f2d50abdb77ep+8Q, -0x1.575e0c206b7ee6818931b6231d56p+7Q, 0x1.1c028f2725fce675841ea5e425e4p+6Q, -0x1.08a1fe0ac6819f96e8258a0368bp+2Q, -0x1.12ed1d6ca77301d9871c862435c4p+4Q, 0x1.66791e904ad3b41e47b43fe289f8p+3Q, -0x1.7aa9733036515afd48134b03fe32p+1Q, 0x1.41600caa02955d88aadf08f58823p-3Q, 0x1.275514f436a31e564b7d019a87cbp-4Q, -0x1.29373f56ac1095884f483f83febcp-7Q, -0x1.51ea7d9f345040b9bbf67fd2c9c4p-13Q, 0x1.deb156b08b87ef0592d66bd4c9c7p-18Q, -0x1.6e30fae8c34ed8366ddfb0cc8561p-27Q, -0x1.1b57abb7d7f1ba81ca336dd9e4d6p-41Q, 0x0p+0Q};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0Q, 0x1.d4fe27a0835ae1a04e0830be24cp+2Q, -0x1.ecb0f32ca76fb494d571b0a3e338p+5Q, 0x1.c6da62a20cd0a85f32742b3dd231p+7Q, -0x1.e3622dd5ba05d80a963a5e3e0d7dp+8Q, 0x1.49508717a90e836846bfe76665d8p+9Q, -0x1.3d934aacf56d0a27027f03a0039p+9Q, 0x1.068600d74e1c90df9e5939a69755p+9Q, -0x1.bb4eb52dbc23c8aa9dac0b1ae5b9p+8Q, 0x1.2c2d3c048caae8b4e7ebc3a10a9fp+8Q, -0x1.6a6f07f5d07dd28cc71310327c39p+5Q, -0x1.48c0f7b3bed9dd4e2bcfc6df9159p+7Q, 0x1.bce28601020e5546efe49f4f2facp+7Q, -0x1.9e035ea535c3aebdf12735df11cep+7Q, 0x1.737017c34f7deef2722c9d811907p+7Q, -0x1.15bd065f2789c251ed52867c6e81p+7Q, 0x1.1609d2e86de1f46bc02dc6e0a8fcp+6Q, -0x1.30b382548235fc08ce2a6ea99e65p+4Q, 0x1.34c266d274d020226722064f6a4ap+0Q, 0x1.56d14dbd1c0ef8dc071f1d5be26fp-1Q, -0x1.f82518456ddfa0a1ea7fb11fa704p-4Q, -0x1.1d5d333a03734067f69cdf063e2dp-9Q, 0x1.599f88826e1df7529e25322303e3p-13Q, -0x1.742b04eba227022dc2784e1aeb19p-22Q, -0x1.1fd835e2f3ac373e68a1719919f7p-35Q, 0x0p+0Q};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0Q, 0x1.6f91b1fb16e463903f2417b8bc33p+2Q, -0x1.8fef11e8059ceda062deb12c9387p+5Q, 0x1.809c444472a8d8415a2c7a9afbefp+7Q, -0x1.b10bf090c92b5336357cfbd2f863p+8Q, 0x1.45258188f71468e863f92b55998cp+9Q, -0x1.7231afc08bd276307932b219a0cfp+9Q, 0x1.7af82162ac359965f69e6fcab693p+9Q, -0x1.823e9f8992b59fc66e1876f1aa68p+9Q, 0x1.6f4bc124eb7dc2e04c11a11579edp+9Q, -0x1.32f291524b4fc819caccc41f919dp+9Q, 0x1.d856007cb8fa074ef0836c00fb93p+8Q, -0x1.59b2f057a74e4aae3ebb4a35f68fp+8Q, 0x1.c4898ffe6b603cfd7a5fa627ad77p+7Q, -0x1.01b04bb5c7e4ece20624945e7d4ap+7Q, 0x1.0ee550f2b46fb0067dbfbe5f34b2p+6Q, -0x1.f149829700499105abd07323449cp+4Q, 0x1.21413698e7cf1b5b76cf50d81657p+3Q, -0x1.1e358290df39caefe5b52d405e07p-2Q, -0x1.54f12799790c9591a372397a1538p-1Q, 0x1.1dedd290f907f8d2a852f01bdfd7p-3Q, 0x1.2b8db385d6eeb017f64738645db6p-10Q, -0x1.7cd67d6099898e46f355480e2303p-12Q, 0x1.c1758243d6f68f11163695671c33p-21Q, 0x1.5b5402fbe8db7e6e4a3332e846cap-33Q, 0x0p+0Q};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0Q, 0x1.e00f201ca9b47bec13b3bceeec35p+1Q, -0x1.09aad588fc6e1d2e5e320a1b6965p+5Q, 0x1.0083b1ed3add1dfc189ab7aaac2p+7Q, -0x1.1b01639f15a47195db844f5df4eap+8Q, 0x1.8e74c5b415b4c982c62a28306ab1p+8Q, -0x1.907a858da198db5b4a86eef21cd8p+8Q, 0x1.68e4a68143eb6280f78231820634p+8Q, -0x1.685dfe59eb94f38e35f487b91dc1p+8Q, 0x1.592f39b72049a36e7924f8b1defp+8Q, -0x1.09589acf597f567d3772f2b218afp+8Q, 0x1.658b66c44d2d9f09118af69ddd27p+7Q, -0x1.f90c71880a91658c0d9a38574dffp+6Q, 0x1.49a9a7009f2b267b39bab54a8a34p+6Q, -0x1.441338caa52cfa0e2a27d488fb3dp+5Q, 0x1.0b7b2a297fde14bc6faf3e06bf71p+4Q, -0x1.d98372b1c68d3f52be82670d6ee1p+2Q, 0x1.f43ec1f2a32806088746ff9dc715p+0Q, 0x1.6165b77555fca80d9c5c14948139p-1Q, -0x1.4f8a8171bb08fcb9ccd7f4688dddp-1Q, 0x1.267683e93d2b771765dfc5bfe73cp-3Q, -0x1.8ddc624d415c8d8d9889292068a5p-9Q, -0x1.979cae945ae1031f8b5a56752269p-11Q, 0x1.95627b187fdb196e7b60fd3122a7p-20Q, 0x1.38bcd286c35de60d5fb4c84a2f35p-31Q, 0x0p+0Q};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0Q, 0x1.ddc9914b8fce26e89a34c64d6d6p+0Q, -0x1.0aa6a6fe4749ff9a53419e5cb74fp+4Q, 0x1.ffd30a30f104e3ad2ade2b583021p+5Q, -0x1.1076bbdb4cf7527cd039bd2ee863p+7Q, 0x1.5b314fd5bd8427278ea0f14850c8p+7Q, -0x1.15e629a2f07ab3b285fb28d62142p+7Q, 0x1.73ecdaa7dbcd11927e445f4fc04ap+6Q, -0x1.7ea4991281a803e96d951a02ad23p+6Q, 0x1.92fe5087093b614dba0f2e58af18p+6Q, -0x1.e50ce86c3eca30ad8c357a5bc172p+5Q, 0x1.23fe36ce5250d05c3006a508171cp+4Q, -0x1.1183a5ac74636a4f4f8077863f2cp+3Q, 0x1.325da71616787b1a97cd6b487bbp+2Q, 0x1.b5b93d37eb78f2e235cc59568f84p+2Q, -0x1.6174cc292a977e8769fcc13572c1p+3Q, 0x1.b8e78e1a9ada492b4dd6fe85e7f5p+2Q, -0x1.ffc6e54f09b8a6376ab9c26e41bp+1Q, 0x1.807b43d233e13293cd8f6f610b94p+1Q, -0x1.949effe4fd5f10b6f0bb69f9fc41p+0Q, 0x1.99c706ee33d33292c4de755a9043p-2Q, -0x1.8b4255eb2ab52df50469eaf1f575p-6Q, -0x1.25fbde4ae0e29153ac78daabb6bap-8Q, 0x1.a2ffd5a58a3e625ad5baf547df1dp-17Q, 0x1.4225e5d67d6a903058f380dcef3ap-27Q, 0x0p+0Q};
-            }
-            if constexpr (order == 11) {
-                return {0x0p+0Q, 0x1.82555f0fca681c9ced300bba3465p-2Q, -0x1.b108ac4bd9d5de90a612fa91bba4p+1Q, 0x1.a3af9f5e28533d44a218819eab18p+3Q, -0x1.c92e2a69bebea1255ad98910de81p+4Q, 0x1.336156f19a3eab19184560490c7ep+5Q, -0x1.154d20c532d37d99d550b554251fp+5Q, 0x1.af95c6a7f034f7267500247c3a39p+4Q, -0x1.a382ed435f8ed2216764cb0a372p+4Q, 0x1.a5a57db59b67be50825ea51ac179p+4Q, -0x1.48587bdb4781058d9836884c3b74p+4Q, 0x1.c6519b1cdb292e6d292e4f1f9c11p+3Q, -0x1.64406dc5dece20ec3c4c58b87407p+3Q, 0x1.05a0da2a87dafe77cb9a54ec8326p+3Q, -0x1.34062a3bf7c109c05654bbca487fp+2Q, 0x1.65a3327bcf1ac1cee14ebea4c8b6p+1Q, -0x1.b27cf7ab49be37cde0f46679310bp+0Q, 0x1.a5bdc7192b9c3a20ece9060c1ba9p-1Q, -0x1.571ac2983f85e3a6dc62f13fd384p-2Q, 0x1.31767817c6adec541d6996364d3fp-3Q, -0x1.904f3491bf69c7251d1b40c4f69ep-5Q, 0x1.0ee4f3163f55f45905e2ddfb93a4p-8Q, 0x1.2584f1f36b43e7bbd83744e7e8bep-10Q, -0x1.373cf584c03ee906a072cfcde9b5p-17Q, -0x1.db60a068c3377c744925f382f6d8p-27Q, 0x0p+0Q};
-            }
-            if constexpr (order == 12) {
-                return {0x0p+0Q, 0x1.8dbb03fad2c2ff4e565f682fc387p-5Q, -0x1.bebdc5d3b23911ed145126163ba8p-2Q, 0x1.aeb7a5ea21052a1c43ba381385e3p+0Q, -0x1.cb9851522d20abcc6f87f331e722p+1Q, 0x1.240bf59871b997fc41c935dfbef9p+2Q, -0x1.cab7cf1ed537e0d17c393ba768f6p+1Q, 0x1.1fd4543a5fd8cb1e3fd209bf00ffp+1Q, -0x1.1ce9744c1c9756de9b809c9cc5acp+1Q, 0x1.3bab08bd76344b447fe47382a836p+1Q, -0x1.c40e7b4e77556f5ef8447dfa81f7p+0Q, 0x1.feadc8c7ce87a8fc67e2732ba34ap-1Q, -0x1.a643a47d84b4da70d0fb0b9b5ca8p-1Q, 0x1.543b964e0f03a3a71ec489e8760ap-1Q, -0x1.577aa576ffa64efb7d0e9a7c6b39p-2Q, 0x1.499f6f7a97a22bd1178c8279f046p-3Q, -0x1.d5a15151b901635be5a327439552p-4Q, 0x1.d4c5badb46707713b03f6550ccfep-5Q, -0x1.094f5215690db085443c42ab246bp-6Q, 0x1.cd0926fb9e142792dd84020c8a8bp-8Q, -0x1.b2091c2c73dd02f84cb3796bc045p-9Q, 0x1.fdc7350edfadd24f5fb7a32829d8p-13Q, 0x1.4af17513fc3a876960b7cf51425ap-13Q, -0x1.fd199a3cefa31b76bcac261239c5p-19Q, -0x1.7fa406e41ed65db974ed315201c3p-27Q, 0x0p+0Q};
-            }
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            if constexpr (order == 0) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00284244035743782127519159930736463030042947946254131969213976354467510363053"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.192822751451924727108748766614170490721105824748184344362119332875866730512"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.906315134083146106755137020807385959064705834685756457995503249677950870358"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0705274840180374221915610791607848006698261142719333764196180010698909604538"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0613444989030761396360783459458969916614040841601149181265363506895700420160"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0370837505994725874839940012509568535053053490011258542752097489994846693329"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000320778756026535884610425312070842577961491118876729788288874469672772619704"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0157025089563234832865197139394763898086519833544367931492178049759198251601"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0139475757294295802461692476281352659400468390363122309411246460077043752333"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00681567628464027460217301387139126877075375129883170970027298157286875244869"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00195332349843711924749204998394665745432087229507798519434292885120009605048"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000223540063730029960909841256853682353169363587803368909770156156719394426611"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000496559764237457326284532141943574549239549099813150646655995671938880681752"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000209364176969584236982171560586653840498356590078330878290505590378499323774"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000129716962748088954003609480965237922709827072460629845757510745626169673818"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000562084247470879735315853190082825344794087023602714253342730484399850968357"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000868342133308330051357320365697488900304098597969798168765758761035694322405"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000347580087379308589607631387726211870849365444198721499394707227756978102834"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000239732167823959290773335551055992800328912309750161986581372592222346479756"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000426821614422438385039700233078195697508737137615415589129724808488001094500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000376343496212373063319630027526057051194699346126249374743316989439186929308"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000204801796486955545541962476062112026383522552669629082548790846826338899265"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000000000291444251494672161342962713547400277611484048996443216117012112680095659149"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000000000000000215149840106709278896741979798565795657829474738608046886706233060495029891"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 1) {
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-            }
-            if constexpr (order == 2) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0934129724220382501349487645300486875234170850245453862186068741324556453346"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.953357331395321245741266856874997302595970338569125873978673981100995300480"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.42585978272484861991123956040990946486002448323913218605736734622206571009"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.63185993796807836831512574118361080962022886222644234566139901231163277968"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.336818591013582903249775631450042574391476183298908473845002503554184531336"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.296394587240899314100091240103956940350255747570510417673706841960334677926"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.493154941522463250789713957033016154711226757009451483204608291769388507365"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.502913696750504242256156558554921880910106950582744728599445382698153029596"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.336126999253822119479465098323173579081837929647816976396920165650335393282"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.148847761252488850986084377184215361968924151368645407707467187349749910163"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0371885435962923855115909993991585519975037535904089717996103864650078357255"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000677463558386659117669706791423999203996673498642825896754202338872153037212"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00434487021597667956865695331283701301527190336995514718937519883519367138275"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00143373662446881484405894523139422896093101823093949963457103829230616147393"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000803285640476068389549772156164639298617305382091989859099979787377361685082"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000602734424846845589803909611025184831851284747892368902634252735886854145822"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000115730739689488129340585879564187751711875533780907209280476231204851229122"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000203038141021073932718677763769332933580122614824827600175511631933693809212"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000773356655095724294210645023078737522223042928980510110980740523592990465707"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000215725560615500809261906811761440663890609571489717139261391990455696409353"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000245586666328544526882182912641255771532047054465213672340341827137743325608"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000284323589789160638880699636876075821856225650053527097527498265089761368022"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000800840047468220328165149036500044542829087947759522330193325204357891480071"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000000000236473591532019199312763596068830970062833585321537190947073847639519351315"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 3) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.396363069673686750280548809109341383558142899908658154252076031883543304792"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.238068683697433321429585844607770037608153029841989185082601544289511822219"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.64401864722743840792906444860573491613583063303684257865448916759790826776"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("9.71243595152007771944165862124698599498887535318579000953262482665972313795"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-10.10029232143527497511956582518178878569923447373646682398486184139257232320"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.44220464420971559730717830018078624764249539854892668261076269712038115208"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.93557502961232367730478899897300379802437925385537992860963683485606932435"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.13856358742765677259829229431312665523374959898394470745436500766939742620"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.77689274061969457654054279018031039397931349538073366568800222943389068691"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.891295625160220390726639633941018793327361578783273631114698203724211097982"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00471792734258069607298372270654369571845851651159485076238538324057163995930"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.255819262610292278082913762588973634598620071368606343876500343872602998914"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.152654376117555334468035681501318647194034115973737844538041071367284215030"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0378134940119027684268573286080453159469956130130132923110965287904780282715"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000121560168274539299345351509032174588648879441157601156968982724381225846230"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00224553423418000095025260272886136860879275402678218779366170715107150220625"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000469555837907319969170862177815720438165344404592060255271066086544874124922"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000141861348255063632226432936826347114087322044233208751170570608200310593872"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000464305587959345590293188512531458238827872871125055638342646962690953713219"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000178051762046205612595554830606976294440430913830610989139140135095046368211"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000303509999613044224553224713019229664330430223919168680848333863544196628625"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000365437421820854861941025978557451175694493997756433473102664593668311395766"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000198703923567812240879432784797155185222750333260578388946834495314448320449"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000000000117344234409057581035282894922526685306543990483992437311052020528871227897"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 4) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.29829892093148675837199950753098632139723149606803915083396902574449208029"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5.45541043360327965942803915313674612029372057019831640585125509023549800118"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("9.14659891488834710881029600683563338140354944919573004532523982762027640408"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.80871239536320715248084576368333258092782945770772294846327434563862485047"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("15.50082996950292219639972661063373929889290553615318208787250496285617222300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-33.61083916121800635387839817511480720783882205113114838947334986844676545110"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("55.09017907974305257429979612931043233074315377510785068179493707419179306920"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-60.82145202823324586976188912900763870195276458683421125895492211837656456610"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("42.02393025939949010806003192165586117752687379191173227214491131963706674670"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-11.42269030320996012044519422789839184208965590204144693325418569461244686450"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.67844966081573901856421942081827739733622487304317595154977214567794509597"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("13.19183180908504928777755197127911432617214990231201200609805185851541078220"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.21315521344594633555535356089362070473231847012846502887625287740895386140"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.83447526237344731188770747629269995995501816031751673943697214639743502746"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0601600495701990470578423349111841174877115258558613797357532347067021952039"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.174833101160455896617892939926978927097853960488370421237681663434954331091"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0411800837257458706544783101171615610022000261127525347354930832776549516518"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00141717935851889446824809565837085540248614139243332507385210260947445968142"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000555560350330981282462146005342011895702037823413086938195491412869816876266"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000301723456414363746673611598443020881465023496175523444306498854376889270505"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000524839933903751376247987543350808530106039891755176189436028565699403867555"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000965385307602574426453743325201391730573869326245570681673188712440757277785"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000722766970161280855990093183542473161153221858414301624738661674579313333974"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000000853612001904068385422684003534916785880458525794775900690850226714475517744"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 5) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.27591989601868802674501785402136946331923506081722246623851782517724077956"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-21.63177809906124242929618059834623299778169240498310197475751118910416098620"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("63.25489897169350129665198120436585141171650857792468724984618895395156006760"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-105.64003425325222575937530358981100910346806778811817416031589048365312600500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("102.06272350428550602794983637219493818640733053272677960258573782601532526300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-32.43801570590952546966804957405761294619856192253725299530721532824239057130"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-69.24480735372488476492726199088539370961841664995584500291147279197929753280"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("158.72530808311660773421056969103812590229014617453891622003568916003770686900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-230.87010121360094217924337915444738753118945778386926981134464016079483998200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("288.01642517309430130736747957321792288095742327983295887677253620052397656300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-293.56995408804215778949920569290304953535440565901256602829643467801366406600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("219.06562359302256197770038214491012243075469145162322027206744692760130121800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-106.11496744383573250143347007263440927813125065546390553880842822781245458600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("24.36128368581441161811089841236294040076426774635200083960668663240035562270"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.43835769181395654737492708557265278640240993742380862767423932221744414072"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.85838395915027243210674082732708450718320033028158945864987295932465128532"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.24315429771719465036074806222840734622901883367521779356833558313975863034"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0546856990741580491153518017356023641138609910294467327282571902327595261764"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0228245670871021915459486249711370338635367656247831656423034604880900103448"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00182589449768070240872485623697617929375041493178863912492773120527334148740"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000325042037685336262383912582434415986434896476262522511852445563487664732443"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000913502582370599560963475117189669272497546395420968001321763477890154121574"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000962624778879324987625830559274321622346182423692550529429764127390602244922"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000227354243242555606552075639763265819210262659858551528763926512978121086153"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 6) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.45444407372475315177467720169187517161433417770438745922665664020599409502"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-42.56603716393114257244373103682838987393735085098528587723704965223943476520"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("150.07103038891031818515743886532262871921427569033077113142523203102180848600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-321.43500940552269096601048445735807968772615638828686952229875945373392190300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("486.49285123198957691189838212046510878680843665543661626780343427251983580200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-595.11637851173395454633822179663347444510793729870901103899277136014019421800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("657.86125381518521180460485717096228323663875621461938629474339145210131286700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-668.83804725645011584987360192202731704144101270640504252184585661445041302700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("591.02274673989806775295905433087707064430763321360170996127414186474186931000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-443.28601860377678276957435305705753468882955594761345736716889808456981116800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("293.87433969841157445285988545192520160702855258407453598402313481311389546900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-171.68368626892283846885275113484356845529681519766755047035289228531315837000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("71.00249921006545724382096278062170090483913301428833620161533416167027278460"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.13488722851072940608795217399184622797681725247617241549338591142041688274"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-17.18288938944823526216285329531580736984384768713968863197342708566449903360"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("11.20228508169258542429354205503684083900272758550359041700286637526422591800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.95829620222196862348532178007222612141499084521609887716323655493346037655"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.156921481073662045953756041913257566237101060794292502890322509860387034380"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0721026247514735804121100566415299137462648885789052981712326861934660517398"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00907030670836707586832589336774695366594420064978445308615112498525335789807"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000161130895298934705154661229234656725370077261357478991394608849613865795613"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000713307751758044877495311912009992056522552469630503342586343211736962847133"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000106575703414569404305476724036545431177067024911660193372639981084780691080"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000503317323749389303719563737438740340206677439330596561000596089805746652424"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 7) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("7.32801237750156362483703729919996280695475478786922672432521671311254119834"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-61.58640131841635882165326632994086164711314616056846772845360126537901397590"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("227.42653376013215970605972000104796817858966318899264414158978818559392102100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-483.38351188460896438440811583095448851197970686725910387330605686657179355400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("658.62912269358369177986072599065937010545029800076900991882439695455748769400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-635.15071641906441010676927456327130280863307826701934274951357911827708743700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("525.04690066637079491947273558679727444098945204462362426522679969863610748800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-443.30745206683403362457477380798545670712488884939473921356975458618458544000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("300.17669704851406005255339306856972566391684656404302637816237332586479717400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-45.30421440165057702649803918277564533841222868064389570465229669564862985660"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-164.37688981728291058700366348503001862732516744094730683945089617887328966600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("222.44242861890885847681782922975570961504898766298360812690379798202763289600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-207.00658146172812966405444130677690797169650424372338218260727893033315417800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("185.71893129678116264900939787686677271662237302432116418506696464581702586100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-138.86918923719065745108647629486188361516972571236690249317122893128955088000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("69.50959361239118942856866391172010145985276234165251426115174332096603971880"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-19.04382546435533552706594655647836079674785133821952687854508408638604970290"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.20609133375256805296141503631395543465839083951690638291124156720969407294"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.669565610251110449459869170701094766316947883669190548464587151565621618122"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.123082251367001933022447492166384546932097984915934829679103087789786980169"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00217715502095119397820112791869347023513174444446995719621661268281187784180"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000164805973396089051063484507442794045079988504541072855801781243508086304395"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000346608500769363543505373359383397071519912407954254984582912708688659199768"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000327241391736611726060145576789575175299756010826303842659100203467561600702"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 8) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.74326753158999834056116812204650118954465060264390982835886577518486268101"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-49.99173337237481612516482468092913196192930769585684115716367234203820792960"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("192.30520833873417575305032330542133296821671316133381127103148089884031604300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-433.04663948928221093038951547041129446069313459043483444888804096093780007800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("650.29301559509696707391037593955338600499735080495817462222469008365651103900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-740.38817602946521524635652991694109244663464176809245792160120459662518415100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("757.93851884277973879231890685884938562543997902765972920915606890170773334500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-772.48924369491146375649339718563050251773647675318553766020712796863655952900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("734.59183179377170969929067292253934666701158992568437326815741556001094017400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-613.89505985905958667637158329225855337819338706324599738575255299428681055200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("472.33594493404419022069420012879298507928450919272191339092869436457326478600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-345.69897983393301885486688813740413735467129595468365631508601814464484933100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("226.26867671070805874604396626788385147483759975756729744364317414185036983100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-128.84432762208094815098432847559414298872221422065057311509033200520302342600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("67.72394160486503269545391021144817969495298865649547918029615797016751111400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-31.08044680580914965121251458755066430643179670788681275067771141961765865330"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("9.03921060432773819185233100601819798021655369701494303621450373894984472793"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.279500999538692156607881707491630467331656124884020994194580849950834108907"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.665902364239195393220279168618682723908283324628346793634526901627751383162"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.139613766717165065129603804344872559693994963696840183393921810240833710156"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00114270599575310816085071769400504056542580942289008729114676011902537797522"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000363195276838709741268790813501267488184675434306229955898556486054877483452"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000837182661399504778282565545392303504120991217340679683017724471409789826587"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000157946565437923846485744196675519158792805910875863717029040068663366791699"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 9) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.75046159171634829527163330112510862850171517204527775957907811808615973114"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-33.20841509838443403040955493092978227279440605831429576553858852822290831770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("128.25721684783507822791369935094396779663623788672457406601793500565400821300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-283.00542635229471097126751678584291828797372875915935845892698482535006432800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("398.45614171533524054366727180364229849289710682645378118885424811008467298600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-400.47860036082498196423508946011183381211802981566841571520311399197149103900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("360.89316566379728536083135647493301259091592313871719238427499436437024359700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-360.36716234208593176728211543795346738863581300534318197607331333071816329900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("345.18447441614411073209118238319574005939847247957730049229326256329205638300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-265.34611221251483388928468384525918631697582076506472432506352501057803541200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("178.77226842348210140340813061313731570411151037624108176819522656335485861200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-126.26215183796407397228250290324344411107479423589079138412164102720512263500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("82.41567612620818870658967871867767992001718408506613309043264486867844619890"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-40.50938566509796337170834199812377119587502364115881243103048938109185750340"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("16.71756950579390837676267330467410166297326502202781368693672667419429720820"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.39864795075319033452851083640208460723103521341161070032778771352463446094"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.95408260511172224329226832456435155937649818121300834001919283900042220991"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.690229161332348184845535892744845183908860830917068365378586781073665858011"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.655353589184885598246818014752831975001293106883587971496754554959033929107"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.143780737452876767968123736205746816488614800208120534936850150005468283836"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00303543758366473343622443033949066654294389600319219464305397559642637833680"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000777458265060317434483464181432621410549249758909909318620156609272380996932"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000151017565574994282254648106028992857730337718860666328360706404021863696656"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000568866357531465656815014550479471644088340548161842850968659319933134867646"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 10) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.86635692686814334701754512957417350216062515159895162052764097113842043881"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-16.66568660094765155284710426501256914017192557788488990117955606509357986260"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("63.97804678187877577341574018618490150437681519853311500630408017375912199010"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-136.23190198244598023711707959187969385344039691028406627990988068537298511000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("173.59631221712522935710881272085756101498061308640801488113337865649201321400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-138.94953641114748367854206140337482846024919723682523303085604297244337196500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("92.98130285529193057335744641381945290112275119999668355136002874352650176220"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-95.66074017444953262397108875695549785804937842210406658962204154607043381990"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("100.74835406297538158748165104775636864067153061989180522203699894495867559400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-60.63130268637294081465002015983185171976527925057524138307520452453647480510"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("18.24956398577073820812706593292482832715236920720613106450102860436965089250"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-8.54732021029040581858802778196927000562449466895889987096814021723737609364"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.78696610600480427243790366050970458256425167093884818282352698386437907349"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.83943109951896060414630018445272105375896265663133246875005081887041646399"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-11.04550750770862050142551027487003756867181933391324257411989886446115036200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.88913300130972012620159069598928481029978149700887106696332707309836414794"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.99825731620098174291722686239189690428111675971623793296035204832239878614"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.00376174701501382150890393381234413552775178257039864145400674669724791199"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.58055114117211937700150897909355450299408918929453114571326586270053152435"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.400173290528033474046780700771547590750735363709672842945384353539651951125"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0241247023629214784889949418794949849850588027303632529305620350773009871100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00448583771765557425940953481033336026071599781591537346531375096056306017530"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000124871538203663846064127929077357912223820600720172540637500972263270210398"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000937574188857368553262323255933606233354879076874674275186450020536917162031"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 11) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.377278790797028406495802049657083663562322361271624572079656683482814478381"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.38307717994363961647269729038870588758939994602123056911758390829221597548"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("13.11518829717770243316037165549177793856194221161693344499682894614897577190"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-28.57377091700247032555582008243751850926614781859679891489888632231161474300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("38.42252911331146019070574663175356660452387955730227078383681460893481557030"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-34.66266016064986281759949034365429955214971534877540614552601700849583120980"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("26.97406640625859867160203071971832599019438490014915496366645506277688896980"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-26.21946455304798864871161101760021771880775045074096541060302606518533350730"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("26.35290308895353879370155511099855779382824241176826323168027129587570497550"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-20.52160249382001334719301784362115987987417964675011905409270410893726823490"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("14.19746165882069082480150485765422363795342078508016178125626500064575627140"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-11.13286484381245965677943198830588460860332272909854856957249726091446789600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.17588527972006301113855143068583531281419193834728913969920542381362453688"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.81287628036717816955676920569706546198654894542238231746562519451899699153"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.79404288335191180481579867581197397188129392455615189049532559340029697375"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.69721935207211848956351510550979925531938115005327856369556578995039602531"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.823713514158776098143914270378737144802711120108114847337079673523569107449"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.335063019316185774400946900047809387504331444599538017269859124873837022194"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.149151743150318837631159229932006915696347222177619661105078433909566955498"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0488658930534999511496940888639373453545430453545029982576926747686967632991"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00413351950396409421167019759007987626638864156006830612512440429134389517261"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00111968733549906685340740936899343820107158321331505760751334075276362206400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000927561883079690107640228293463474861573105973385043495546011950474050815337"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000138353046393774419706318300470822604006784632689512055491879584523531143047"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 12) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0485510900239990436421204389454387673417811678462962540757143566128579592770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.436270800634297968322345080087680826208441319415670872030224777690078461556"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.68248974767722772758483160675785114053064764804002514623394170463789590172"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.59058586609376583771926574429375533672584236400562126859511283907434445711"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.56322994124539027457225861351587674553390566017608457671928325936265991655"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.58373440747749241237223725147688884192263700323730018471801896054684688057"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.24866726732552133278146064153483046293389221299882995399864011134597001733"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.22587445942297775995811432335154708339509627741904345621048251573818545409"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.46615704775868702834863652085534769700638634288067530551348825246469149621"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.76584597268750597380515213373501064800094868705200411926589180388549588359"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.997419618978951767654107468235932428974722705691044731477454908009925099723"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.824734821626728470682970936709275659502024225512330108668711202634188766674"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.664517113712924681701113756939420311843390054559860571221578562221833419569"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.335428796184635221533296732070577988586954631509663722390327691441647623334"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.160948630264969492724365334557199225341872449473537373932195593392097150334"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.114655797627677055876779744868793614912947551394818530771503539697052078243"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0572231912176004958885591389510844893402088690448910703952553137622920787942"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0161932279203405965225240954258609535698781894809026667589644820730338725774"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00703484727602471596997669396790315101109040223481142577918954913506000676361"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00331142872730769846357537103134640651616087940178035673586298619579639917832"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000243081165958578425715014946837734369665794705531210842489368910237101227750"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000157806011543052252390221263353602504629816751263280846430328831365578539218"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000379309065442971274677051284817497527219849546159473806845519248661436372460"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000111654147665765272669074902224159897974782540201524920545177291846727682138"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-        }
-    }
-    if constexpr (p == 14) {
-        if constexpr (std::is_same_v<Real, float>) {
-            if constexpr (order == 0) {
-                return {0x0p+0f, 0x1.2e3c0cp-10f, 0x1.d73cdcp-4f, 0x1.980f08p-1f, 0x1.0b8da8p-2f, -0x1.381b88p-2f, 0x1.a64054p-3f, -0x1.be6cb2p-4f, 0x1.5369f4p-5f, -0x1.e553cp-8f, -0x1.5b9738p-9f, 0x1.3ad93ep-9f, -0x1.6c8658p-11f, 0x1.421438p-16f, 0x1.359cb6p-15f, -0x1.16b1cep-18f, -0x1.1e4702p-19f, 0x1.16b7d8p-21f, -0x1.2a9018p-27f, -0x1.e6603ap-29f, 0x1.ad635ap-33f, -0x1.0b7166p-37f, -0x1.2dcc8ep-43f, 0x1.994c74p-50f, 0x1.d3e7dcp-60f, -0x1.ad34cp-72f, 0x1.c6fd0cp-94f, 0x0p+0f};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.ffe6a8p-8f, 0x1.687896p-2f, 0x1.4f6222p-1f, -0x1.9d7a5p+0f, 0x1.ee1a72p-1f, -0x1.3a4c3ep-1f, 0x1.a5124ep-2f, -0x1.fd4714p-3f, 0x1.efeb84p-4f, -0x1.695e5ep-5f, 0x1.73caep-7f, -0x1.fa774ap-10f, 0x1.13b07ep-13f, 0x1.7cb11cp-14f, -0x1.d2ccp-15f, 0x1.74388cp-17f, 0x1.21ff8ap-21f, -0x1.156308p-22f, -0x1.19b91cp-25f, 0x1.f7d83ep-31f, 0x1.509062p-34f, -0x1.405684p-40f, 0x1.6ac07ap-46f, -0x1.9a49fp-55f, -0x1.88bc66p-67f, 0x1.a0541ep-88f, -0x0p+0f};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0f, 0x1.70e38ep-5f, 0x1.98429p-1f, -0x1.5a23aep+0f, -0x1.ca3a86p-2f, 0x1.f2912p+0f, -0x1.902df6p+0f, 0x1.6e5d8ap-1f, -0x1.7cd74ap-5f, -0x1.cb5138p-3f, 0x1.8970fep-3f, -0x1.2e3ba4p-4f, 0x1.a43728p-9f, 0x1.5d8afap-7f, -0x1.3f213ap-8f, 0x1.438df6p-11f, 0x1.92aaccp-13f, -0x1.4a2a2cp-14f, 0x1.061494p-17f, 0x1.1c615p-21f, -0x1.fed404p-24f, 0x1.9900fap-29f, 0x1.4b71c6p-33f, -0x1.f4e21p-40f, -0x1.ae7642p-50f, 0x1.0753e4p-59f, -0x1.1725d8p-79f, -0x0p+0f};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0f, 0x1.b64064p-3f, 0x1.b94954p-1f, -0x1.49bc84p+2f, 0x1.255158p+3f, -0x1.254592p+3f, 0x1.bfdd02p+2f, -0x1.258cbp+2f, 0x1.244b68p+1f, -0x1.76e9c8p-1f, 0x1.2db90ep-3f, -0x1.adc00ap-4f, 0x1.077b02p-3f, -0x1.4e1bd4p-4f, 0x1.a8b172p-6f, -0x1.1b67a8p-9f, -0x1.5aa222p-10f, 0x1.0c296ep-11f, -0x1.315112p-14f, -0x1.aa34a6p-23f, 0x1.718ac2p-20f, -0x1.4ed202p-25f, -0x1.6a2c3ep-29f, 0x1.03cb1cp-35f, 0x1.d2ce74p-46f, -0x1.110d8p-54f, 0x1.2175bep-73f, 0x0p+0f};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0f, 0x1.9bd3bcp-1f, -0x1.218b2p+1f, -0x1.8f073ep-2f, 0x1.10368cp+3f, -0x1.6e5fdp+3f, -0x1.fee6b2p-2f, 0x1.5dae0cp+4f, -0x1.253938p+5f, 0x1.0846cap+5f, -0x1.d3379cp+3f, -0x1.bc1cbep+1f, 0x1.49e86ep+3f, -0x1.e4adep+2f, 0x1.651f3ap+1f, -0x1.14e32ep-2f, -0x1.c20b1ep-3f, 0x1.9dc736p-4f, -0x1.dbb9ecp-7f, -0x1.c7f5c2p-11f, 0x1.a5fc86p-12f, -0x1.07f65ep-16f, -0x1.0e379p-20f, 0x1.69bc58p-26f, 0x1.872aa2p-36f, -0x1.7b8496p-44f, 0x1.92548cp-62f, -0x0p+0f};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0f, 0x1.29b15ep+1f, -0x1.cfd366p+3f, 0x1.440caap+5f, -0x1.116deap+6f, 0x1.3b639cp+6f, -0x1.0040f6p+6f, 0x1.e6fde6p+4f, 0x1.5c1e9ep+3f, -0x1.b1e5dap+5f, 0x1.7d1f14p+6f, -0x1.d6f4cap+6f, 0x1.9fd808p+6f, -0x1.ecec6ep+5f, 0x1.43fff8p+4f, 0x1.5e941cp-2f, -0x1.d2a078p+1f, 0x1.940e8ap+0f, -0x1.f62a76p-3f, -0x1.2b3b3cp-6f, 0x1.3de2bap-7f, -0x1.21cbeep-11f, -0x1.2150f6p-15f, 0x1.159bf8p-20f, 0x1.b00f5p-30f, -0x1.21e8e2p-37f, 0x1.33590ap-54f, 0x0p+0f};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0f, 0x1.3069cap+2f, -0x1.2e376ap+5f, 0x1.1366dap+7f, -0x1.37b986p+8f, 0x1.ff3f2ep+8f, -0x1.57d938p+9f, 0x1.9e8b98p+9f, -0x1.c5567ap+9f, 0x1.af9eb4p+9f, -0x1.5e3048p+9f, 0x1.efd932p+8f, -0x1.337ecp+8f, 0x1.1dd7ep+7f, -0x1.34f8d6p+4f, -0x1.1b6424p+5f, 0x1.038eccp+5f, -0x1.9f2074p+3f, 0x1.0d3b24p+1f, 0x1.b93ffcp-3f, -0x1.00284ep-3f, 0x1.52026p-7f, 0x1.4b932p-11f, -0x1.d3b086p-16f, -0x1.e9753p-25f, 0x1.e5cedp-32f, -0x1.0188e4p-47f, -0x0p+0f};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0f, 0x1.f579b2p+2f, -0x1.13b9ccp+6f, 0x1.0d0d04p+8f, -0x1.309a86p+9f, 0x1.b8e262p+9f, -0x1.b08b28p+9f, 0x1.3c7d2cp+9f, -0x1.7e7dfp+8f, 0x1.9c8804p+5f, 0x1.dc1752p+8f, -0x1.e54a04p+9f, 0x1.1a42e2p+10f, -0x1.f903f4p+9f, 0x1.9d8dbap+9f, -0x1.34174p+9f, 0x1.64eb3cp+8f, -0x1.0b0c44p+7f, 0x1.5f0a54p+4f, 0x1.d8f6bap+1f, -0x1.1c758ap+1f, 0x1.f38ac2p-3f, 0x1.f827p-7f, -0x1.130614p-10f, -0x1.2dc514p-19f, 0x1.1d494ap-25f, -0x1.2e8464p-40f, 0x0p+0f};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0f, 0x1.e32cc2p+2f, -0x1.1692cap+6f, 0x1.1fa09cp+8f, -0x1.615e68p+9f, 0x1.265c8cp+10f, -0x1.7569eep+10f, 0x1.9e96bep+10f, -0x1.bbbe16p+10f, 0x1.be0802p+10f, -0x1.8f099cp+10f, 0x1.43b838p+10f, -0x1.ee6ad6p+9f, 0x1.58d562p+9f, -0x1.a3b282p+8f, 0x1.c79d62p+7f, -0x1.bc78ccp+6f, 0x1.418e36p+5f, -0x1.3abf36p+2f, -0x1.ad7bb4p+1f, 0x1.a65502p+0f, -0x1.affdcep-3f, -0x1.8341cep-7f, 0x1.b5571p-10f, 0x1.e32174p-19f, -0x1.c53c14p-24f, 0x1.e0c27p-38f, -0x0p+0f};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0f, 0x1.8d1f8ap+2f, -0x1.d4881ap+5f, 0x1.e86d42p+7f, -0x1.280028p+9f, 0x1.d3eb6p+9f, -0x1.0b82a6p+10f, 0x1.07ceap+10f, -0x1.0d7822p+10f, 0x1.0df61ep+10f, -0x1.c6893ap+9f, 0x1.45ac9ep+9f, -0x1.c9d686p+8f, 0x1.35c4c4p+8f, -0x1.4a58bep+7f, 0x1.01755ap+6f, -0x1.5d1ba8p+4f, 0x1.dadd4ap+1f, 0x1.87b02p+2f, -0x1.9ab15ep+2f, 0x1.46cd6ap+1f, -0x1.8955d8p-2f, -0x1.85245p-7f, 0x1.6f86d4p-8f, 0x1.1b4e3cp-16f, -0x1.7914d8p-21f, 0x1.903b4cp-34f, -0x0p+0f};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0f, 0x1.041a0ap+1f, -0x1.3658b6p+4f, 0x1.5194bp+6f, -0x1.c3df82p+7f, 0x1.ad183ep+8f, -0x1.3d9c78p+9f, 0x1.852da4p+9f, -0x1.9cca18p+9f, 0x1.9a6efap+9f, -0x1.a300c2p+9f, 0x1.a73548p+9f, -0x1.7a384cp+9f, 0x1.2afd88p+9f, -0x1.d0f63ap+8f, 0x1.6384c4p+8f, -0x1.d6c26ap+7f, 0x1.089826p+7f, -0x1.1f7e84p+6f, 0x1.2a5702p+5f, -0x1.c18aa4p+3f, 0x1.4dc138p+1f, 0x1.bd5ac2p-5f, -0x1.1aa942p-4f, -0x1.97678cp-14f, 0x1.25b3fcp-16f, -0x1.381ffp-28f, 0x0p+0f};
-            }
-            if constexpr (order == 11) {
-                return {0x0p+0f, 0x1.456a1ep+0f, -0x1.86731ep+3f, 0x1.99ddaep+5f, -0x1.ebccc2p+6f, 0x1.74f85ep+7f, -0x1.842622p+7f, 0x1.4fbcc2p+7f, -0x1.4776cp+7f, 0x1.573bfp+7f, -0x1.2b0c28p+7f, 0x1.bb5bcap+6f, -0x1.580802p+6f, 0x1.0c1df4p+6f, -0x1.5dea02p+5f, 0x1.997fcap+4f, -0x1.f5c414p+3f, 0x1.1578f4p+3f, -0x1.e11a4cp+1f, 0x1.8c2f5ap+0f, -0x1.42cddep-1f, 0x1.1b3752p-3f, 0x1.61bca4p-7f, -0x1.eeca78p-8f, 0x1.427b38p-14f, 0x1.1c6c3p-18f, -0x1.2f0566p-29f, 0x0p+0f};
-            }
-            if constexpr (order == 12) {
-                return {0x0p+0f, 0x1.45a484p-2f, -0x1.87cf9ep+1f, 0x1.99aecep+3f, -0x1.e335dep+4f, 0x1.5e3842p+5f, -0x1.48839ep+5f, 0x1.e11a8p+4f, -0x1.bff278p+4f, 0x1.f68b7p+4f, -0x1.a9c89cp+4f, 0x1.147ddap+4f, -0x1.a10eep+3f, 0x1.5d8bap+3f, -0x1.b0eecp+2f, 0x1.b18092p+1f, -0x1.11a2d4p+1f, 0x1.45b0dap+0f, -0x1.d74084p-2f, 0x1.27c112p-3f, -0x1.2ee6a8p-4f, 0x1.0ad11p-6f, 0x1.b719aep-8f, -0x1.7b5726p-9f, 0x1.efe0e8p-14f, 0x1.11683ap-18f, -0x1.24c158p-28f, -0x0p+0f};
-            }
-            if constexpr (order == 13) {
-                return {0x0p+0f, 0x1.439a96p-5f, -0x1.85e5f8p-2f, 0x1.959ab6p+0f, -0x1.d59128p+1f, 0x1.43a656p+2f, -0x1.0a2c06p+2f, 0x1.27395p+1f, -0x1.050c8cp+1f, 0x1.600ea8p+1f, -0x1.21f61ap+1f, 0x1.19f0e6p+0f, -0x1.8e2104p-1f, 0x1.a07f28p-1f, -0x1.ccce86p-2f, 0x1.e56138p-4f, -0x1.5df48cp-4f, 0x1.19d3fp-4f, -0x1.9e6cdp-9f, -0x1.b966bep-7f, 0x1.824078p-9f, -0x1.1b05a2p-9f, 0x1.7f8554p-9f, -0x1.23710ep-10f, 0x1.cc575ap-14f, 0x1.1f2382p-18f, -0x1.3697eap-27f, -0x0p+0f};
-            }
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0, 0x1.2e3c0bb3f3ad5p-10, 0x1.d73cdc4f17148p-4, 0x1.980f074dbd462p-1, 0x1.0b8da7807c274p-2, -0x1.381b88314120bp-2, 0x1.a64053bd4da41p-3, -0x1.be6cb26620f84p-4, 0x1.5369f32b472a9p-5, -0x1.e553bfb83c482p-8, -0x1.5b97376b07916p-9, 0x1.3ad93e070eb7ap-9, -0x1.6c8658d1b206ep-11, 0x1.421437e7b839dp-16, 0x1.359cb55b7d336p-15, -0x1.16b1cde08937ep-18, -0x1.1e470298289aep-19, 0x1.16b7d7c52ecb7p-21, -0x1.2a9017a9058edp-27, -0x1.e6603a12c622p-29, 0x1.ad635a5532adap-33, -0x1.0b7166f3d598p-37, -0x1.2dcc8d3c8b0cfp-43, 0x1.994c7452dcd31p-50, 0x1.d3e7db27a70eep-60, -0x1.ad34c0383fa64p-72, 0x1.c6fd0b1a8d6a3p-94, 0x0p+0};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0, 0x1.ffe6a833f41d2p-8, 0x1.6878956519ce3p-2, 0x1.4f62227264623p-1, -0x1.9d7a4f00f9dcp+0, 0x1.ee1a7236f71e4p-1, -0x1.3a4c3d150c11ep-1, 0x1.a5124e1ab47a9p-2, -0x1.fd47140509eb3p-3, 0x1.efeb8355fd2f8p-4, -0x1.695e5e5e49cf8p-5, 0x1.73cae05387f64p-7, -0x1.fa774911ba2d4p-10, 0x1.13b07ddddb3b8p-13, 0x1.7cb11c0b4280bp-14, -0x1.d2cbfff6e2a58p-15, 0x1.74388c9fd28e7p-17, 0x1.21ff895bfb5f3p-21, -0x1.156307b5c128cp-22, -0x1.19b91bff8bef5p-25, 0x1.f7d83e4d41c77p-31, 0x1.5090626b206a4p-34, -0x1.405683426ad01p-40, 0x1.6ac079eed130ep-46, -0x1.9a49f0637a3b6p-55, -0x1.88bc66cc087f2p-67, 0x1.a0541eb1bdcebp-88, -0x0p+0};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0, 0x1.70e38d13c6dcdp-5, 0x1.98429094e12d2p-1, -0x1.5a23aee5cfcf3p+0, -0x1.ca3a85e30ebf6p-2, 0x1.f2911f6caea6bp+0, -0x1.902df5acb9856p+0, 0x1.6e5d8a32fe3aep-1, -0x1.7cd7499a11b88p-5, -0x1.cb51389df1437p-3, 0x1.8970fdea96db5p-3, -0x1.2e3ba43116d4fp-4, 0x1.a437288ed51abp-9, 0x1.5d8afaeb5ec2ap-7, -0x1.3f213a25a4c3ap-8, 0x1.438df66495fedp-11, 0x1.92aacb344e1abp-13, -0x1.4a2a2b6937dcap-14, 0x1.061494c076ea5p-17, 0x1.1c61500cd5ff6p-21, -0x1.fed404b96c72ep-24, 0x1.9900fa8d5cb81p-29, 0x1.4b71c6cbb7be3p-33, -0x1.f4e20f23251aap-40, -0x1.ae764159a5bb6p-50, 0x1.0753e4c918ed7p-59, -0x1.1725d8c4676c4p-79, -0x0p+0};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0, 0x1.b6406454732d5p-3, 0x1.b949541f458cep-1, -0x1.49bc84198d8efp+2, 0x1.255157167a553p+3, -0x1.254591e8b6e07p+3, 0x1.bfdd01aa9e691p+2, -0x1.258cb0e12f408p+2, 0x1.244b687910818p+1, -0x1.76e9c86768fd8p-1, 0x1.2db90e1b7e224p-3, -0x1.adc00aab7f786p-4, 0x1.077b01cdc29aap-3, -0x1.4e1bd3d7c8107p-4, 0x1.a8b1719f7696ap-6, -0x1.1b67a8fdd5d39p-9, -0x1.5aa2219e8b072p-10, 0x1.0c296ebe05b6fp-11, -0x1.315112d6e2649p-14, -0x1.aa34a64782e4p-23, 0x1.718ac2125512ep-20, -0x1.4ed202350e6d4p-25, -0x1.6a2c3e7b115c9p-29, 0x1.03cb1bd946e2ep-35, 0x1.d2ce73e99c294p-46, -0x1.110d7f1b0bfcp-54, 0x1.2175be08d4af4p-73, 0x0p+0};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0, 0x1.9bd3bc2473961p-1, -0x1.218b20c923a73p+1, -0x1.8f073ee248543p-2, 0x1.10368c3ad14ecp+3, -0x1.6e5fd027a16b4p+3, -0x1.fee6b19288529p-2, 0x1.5dae0c64ec101p+4, -0x1.253938fa65f9dp+5, 0x1.0846ca351ee33p+5, -0x1.d3379cfd6d393p+3, -0x1.bc1cbd5de053bp+1, 0x1.49e86d68d4cf9p+3, -0x1.e4ade08c4a6c3p+2, 0x1.651f390634957p+1, -0x1.14e32e1f9b6bbp-2, -0x1.c20b1d287136bp-3, 0x1.9dc73570ee73fp-4, -0x1.dbb9ebdd9c09ep-7, -0x1.c7f5c1ec60f69p-11, 0x1.a5fc856e52fadp-12, -0x1.07f65daa0049bp-16, -0x1.0e378f07aff0ap-20, 0x1.69bc58d5ec0cdp-26, 0x1.872aa1bcf3687p-36, -0x1.7b84969608017p-44, 0x1.92548cc9b5b72p-62, -0x0p+0};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0, 0x1.29b15e8e05f49p+1, -0x1.cfd365d614528p+3, 0x1.440caad9c1236p+5, -0x1.116de9d813b39p+6, 0x1.3b639c503b3cfp+6, -0x1.0040f57e975e2p+6, 0x1.e6fde6a95ce33p+4, 0x1.5c1e9e155aab8p+3, -0x1.b1e5da7957b3dp+5, 0x1.7d1f138d16b9dp+6, -0x1.d6f4cad7bdd83p+6, 0x1.9fd808c31039p+6, -0x1.ecec6e1a57ab4p+5, 0x1.43fff7220eba4p+4, 0x1.5e941cd01c025p-2, -0x1.d2a0789936f64p+1, 0x1.940e89f9fbe3cp+0, -0x1.f62a7689777abp-3, -0x1.2b3b3b35a2041p-6, 0x1.3de2ba1c1b055p-7, -0x1.21cbeea2dd955p-11, -0x1.2150f65158194p-15, 0x1.159bf889454c7p-20, 0x1.b00f4f96ce851p-30, -0x1.21e8e13c855cp-37, 0x1.3359091107974p-54, 0x0p+0};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0, 0x1.3069c9b572d78p+2, -0x1.2e376983f6cb7p+5, 0x1.1366d92966ea1p+7, -0x1.37b9852173f07p+8, 0x1.ff3f2db6a15a4p+8, -0x1.57d9383606e5p+9, 0x1.9e8b97533b1ebp+9, -0x1.c556790a27e1dp+9, 0x1.af9eb47abc08ep+9, -0x1.5e3047bf51b55p+9, 0x1.efd9329bb40ffp+8, -0x1.337ec090261a6p+8, 0x1.1dd7e09a26691p+7, -0x1.34f8d53391e96p+4, -0x1.1b6423ffa4135p+5, 0x1.038ecbdebefe4p+5, -0x1.9f2073b507554p+3, 0x1.0d3b2378aacf2p+1, 0x1.b93ffbdcbcfbdp-3, -0x1.00284db90f95bp-3, 0x1.5202609236b6cp-7, 0x1.4b9320a57f232p-11, -0x1.d3b085775602bp-16, -0x1.e975304f42064p-25, 0x1.e5cecfa6ab7bbp-32, -0x1.0188e4a2f5a9ep-47, -0x0p+0};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0, 0x1.f579b17074e37p+2, -0x1.13b9cbe766167p+6, 0x1.0d0d0432bec13p+8, -0x1.309a86e68bfeap+9, 0x1.b8e26231ea03fp+9, -0x1.b08b284517ec4p+9, 0x1.3c7d2b2624502p+9, -0x1.7e7def0dd6c18p+8, 0x1.9c880448390e6p+5, 0x1.dc1752cc2f2f8p+8, -0x1.e54a03fbbc2fap+9, 0x1.1a42e1dae569p+10, -0x1.f903f4a18c30ep+9, 0x1.9d8db91908386p+9, -0x1.34173ffb143e2p+9, 0x1.64eb3c27db565p+8, -0x1.0b0c43171fee6p+7, 0x1.5f0a5375d11c7p+4, 0x1.d8f6b9f1522f3p+1, -0x1.1c75896d6d599p+1, 0x1.f38ac1a749dafp-3, 0x1.f82700b4dc727p-7, -0x1.1306135d4672fp-10, -0x1.2dc514d699914p-19, 0x1.1d494ae1d331fp-25, -0x1.2e8464bcec8d4p-40, 0x0p+0};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0, 0x1.e32cc25ea4da5p+2, -0x1.1692ca6458eaap+6, 0x1.1fa09c1316dfbp+8, -0x1.615e67f0c1ccdp+9, 0x1.265c8c1b4b1aap+10, -0x1.7569ed1c8210dp+10, 0x1.9e96bde5063d4p+10, -0x1.bbbe167a38d63p+10, 0x1.be080201e737dp+10, -0x1.8f099bdabb219p+10, 0x1.43b83815e15a6p+10, -0x1.ee6ad68b3bda5p+9, 0x1.58d561cb84d26p+9, -0x1.a3b282a8407a3p+8, 0x1.c79d620ffafcp+7, -0x1.bc78cb9447aa1p+6, 0x1.418e35902e32dp+5, -0x1.3abf360acc2f7p+2, -0x1.ad7bb3867b3c3p+1, 0x1.a655024ebf2fdp+0, -0x1.affdcd4718ba8p-3, -0x1.8341cd6c6b0aap-7, 0x1.b55710d3ebf55p-10, 0x1.e321738ab1448p-19, -0x1.c53c1373c8858p-24, 0x1.e0c270acb15c6p-38, -0x0p+0};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0, 0x1.8d1f8a3279763p+2, -0x1.d4881995a0c1fp+5, 0x1.e86d414a78e34p+7, -0x1.280027c9b0876p+9, 0x1.d3eb5f0b0594cp+9, -0x1.0b82a55c2799fp+10, 0x1.07ce9f70ddb28p+10, -0x1.0d7822536789ep+10, 0x1.0df61d2a506b2p+10, -0x1.c6893ac6cda6bp+9, 0x1.45ac9e8089788p+9, -0x1.c9d686e237044p+8, 0x1.35c4c3819b31p+8, -0x1.4a58be360f4f4p+7, 0x1.017559c35f761p+6, -0x1.5d1ba7f134742p+4, 0x1.dadd49a935c84p+1, 0x1.87b01fd4326a3p+2, -0x1.9ab15d247f91p+2, 0x1.46cd6a0d33a49p+1, -0x1.8955d7defe0d5p-2, -0x1.85244f4e65bbcp-7, 0x1.6f86d3c431061p-8, 0x1.1b4e3c12a74ep-16, -0x1.7914d82d3193fp-21, 0x1.903b4b44dd8c8p-34, -0x0p+0};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0, 0x1.041a0a897aa29p+1, -0x1.3658b5d77609ep+4, 0x1.5194af04e2f85p+6, -0x1.c3df81f0aaf29p+7, 0x1.ad183e8db3dacp+8, -0x1.3d9c782d70077p+9, 0x1.852da35362a6dp+9, -0x1.9cca18f6947ddp+9, 0x1.9a6efa498935ep+9, -0x1.a300c2ebdd39dp+9, 0x1.a735477cbff1cp+9, -0x1.7a384b1c312fcp+9, 0x1.2afd886ee72d7p+9, -0x1.d0f63946d275bp+8, 0x1.6384c4a13f54ep+8, -0x1.d6c269ce8bf35p+7, 0x1.08982647618p+7, -0x1.1f7e83a071123p+6, 0x1.2a5701b5bea0ep+5, -0x1.c18aa4ec1159bp+3, 0x1.4dc13861658a9p+1, 0x1.bd5ac19033245p-5, -0x1.1aa94170fffadp-4, -0x1.97678bd8dc9fap-14, 0x1.25b3fc23ddcf6p-16, -0x1.381fef501218fp-28, 0x0p+0};
-            }
-            if constexpr (order == 11) {
-                return {0x0p+0, 0x1.456a1d2a45d0dp+0, -0x1.86731e38f2c9fp+3, 0x1.99ddae9b5957ep+5, -0x1.ebccc1d5d759ap+6, 0x1.74f85dd906949p+7, -0x1.8426225b26444p+7, 0x1.4fbcc1bdf3f19p+7, -0x1.4776c0e99319fp+7, 0x1.573bef3fda7ebp+7, -0x1.2b0c271bd883ep+7, 0x1.bb5bca80b625p+6, -0x1.5808025c93fa5p+6, 0x1.0c1df40cf5e4cp+6, -0x1.5dea01151a3e2p+5, 0x1.997fc95198574p+4, -0x1.f5c4140f2a03ep+3, 0x1.1578f4041624bp+3, -0x1.e11a4c4784826p+1, 0x1.8c2f5a8cae554p+0, -0x1.42cdddde9b71fp-1, 0x1.1b37523680cdap-3, 0x1.61bca3fd3effbp-7, -0x1.eeca78cc1dd9bp-8, 0x1.427b3775515b6p-14, 0x1.1c6c30fb5472dp-18, -0x1.2f056506ce5e6p-29, 0x0p+0};
-            }
-            if constexpr (order == 12) {
-                return {0x0p+0, 0x1.45a484f799a72p-2, -0x1.87cf9eab4f4p+1, 0x1.99aecd437634bp+3, -0x1.e335dd2c6e9dep+4, 0x1.5e3841e21950ap+5, -0x1.48839e048b83dp+5, 0x1.e11a7f30735e3p+4, -0x1.bff27724d4104p+4, 0x1.f68b6fe2ccc31p+4, -0x1.a9c89c30bca22p+4, 0x1.147ddad811d2bp+4, -0x1.a10ee0eb1ccb6p+3, 0x1.5d8b9ffe3cdb9p+3, -0x1.b0eebf69279fp+2, 0x1.b180929e1a69bp+1, -0x1.11a2d370771cap+1, 0x1.45b0d998cab37p+0, -0x1.d74083eaced41p-2, 0x1.27c1113b5bdb8p-3, -0x1.2ee6a8512694ep-4, 0x1.0ad11030da229p-6, 0x1.b719ad4ae716p-8, -0x1.7b5726cd7507bp-9, 0x1.efe0e7fbce7f4p-14, 0x1.116839f7247aep-18, -0x1.24c158fd367dfp-28, -0x0p+0};
-            }
-            if constexpr (order == 13) {
-                return {0x0p+0, 0x1.439a95b32a47fp-5, -0x1.85e5f8ce20b7p-2, 0x1.959ab595a2ea4p+0, -0x1.d591277dff53ep+1, 0x1.43a6564933b3fp+2, -0x1.0a2c05cc597abp+2, 0x1.273950f6ffd18p+1, -0x1.050c8b9cb84b8p+1, 0x1.600ea820111dp+1, -0x1.21f61a844a105p+1, 0x1.19f0e6ef31a0dp+0, -0x1.8e2103144a726p-1, 0x1.a07f2894f970fp-1, -0x1.ccce8527cee5cp-2, 0x1.e56137866a825p-4, -0x1.5df48c0c87cd7p-4, 0x1.19d3f039c46cep-4, -0x1.9e6cd0f61f4cbp-9, -0x1.b966bdf45728ap-7, 0x1.8240771a20728p-9, -0x1.1b05a2f57f924p-9, 0x1.7f8554959f4a5p-9, -0x1.23710df832eb2p-10, 0x1.cc575afdf3f3dp-14, 0x1.1f238196ae22ep-18, -0x1.3697e9bf4306ap-27, -0x0p+0};
-            }
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0L, 0x9.71e05d9f9d6a6a5p-13L, 0xe.b9e6e278b8a3ea8p-7L, 0xc.c0783a6dea3101cp-4L, 0x8.5c6d3c03e139c58p-5L, -0x9.c0dc418a090583bp-5L, 0xd.32029dea6d20a27p-6L, -0xd.f365933107c2191p-7L, 0xa.9b4f995a39545fcp-8L, -0xf.2a9dfdc1e240f71p-11L, -0xa.dcb9bb583c8b013p-12L, 0x9.d6c9f03875bcf99p-12L, -0xb.6432c68d9036eap-14L, 0xa.10a1bf3dc1ce972p-19L, 0x9.ace5aadbe99adaep-18L, -0x8.b58e6f0449bf329p-21L, -0x8.f23814c144d7229p-22L, 0x8.b5bebe29765b5fbp-24L, -0x9.5480bd482c76432p-30L, -0xf.3301d09631101f2p-32L, 0xd.6b1ad2a9956cecp-36L, -0x8.5b8b379eacc020ep-40L, -0x9.6e6469e45867b18p-46L, 0xc.ca63a296e698604p-53L, 0xe.9f3ed93d387731ep-63L, -0xd.69a601c1fd321e5p-75L, 0xe.37e858d46b515bp-97L, 0x0p+0L};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0L, 0xf.ff35419fa0e8f21p-11L, 0xb.43c4ab28ce718b1p-5L, 0xa.7b11139323118aep-4L, -0xc.ebd27807cee01bp-3L, 0xf.70d391b7b8f1d7fp-4L, -0x9.d261e8a8608ee81p-4L, 0xd.289270d5a3d484p-5L, -0xf.ea38a0284f599d4p-6L, 0xf.7f5c1aafe97c0a1p-7L, -0xb.4af2f2f24e7c239p-8L, 0xb.9e57029c3fb215dp-10L, -0xf.d3ba488dd169dd9p-13L, 0x8.9d83eeeed9dc1b7p-16L, 0xb.e588e05a14054ecp-17L, -0xe.965fffb7152c15fp-18L, 0xb.a1c464fe94734f4p-20L, 0x9.0ffc4adfdaf948bp-24L, -0x8.ab183dae09460bbp-25L, -0x8.cdc8dffc5f7a7c4p-28L, 0xf.bec1f26a0e3b7cap-34L, 0xa.84831359035218p-37L, -0xa.02b41a135680872p-43L, 0xb.5603cf768986fc1p-49L, -0xc.d24f831bd1db255p-58L, -0xc.45e3366043f8eabp-70L, 0xd.02a0f58dee755b1p-91L, -0x0p+0L};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0L, 0xb.871c689e36e67b2p-8L, 0xc.c21484a70968caap-4L, -0xa.d11d772e7e79982p-3L, -0xe.51d42f1875fb05dp-5L, 0xf.9488fb657535621p-3L, -0xc.816fad65cc2b1fep-3L, 0xb.72ec5197f1d73dap-4L, -0xb.e6ba4cd08dc3e1ep-8L, -0xe.5a89c4ef8a1b6aap-6L, 0xc.4b87ef54b6da459p-6L, -0x9.71dd2188b6a770fp-7L, 0xd.21b94476a8d5992p-12L, 0xa.ec57d75af6152bbp-10L, -0x9.f909d12d261cd27p-11L, 0xa.1c6fb324aff682bp-14L, 0xc.955659a270d5623p-16L, -0xa.51515b49bee533ep-17L, 0x8.30a4a603b752616p-20L, 0x8.e30a8066affb01ep-24L, -0xf.f6a025cb63973cp-27L, 0xc.c807d46ae5c0b92p-32L, 0xa.5b8e365dbdf1a9dp-36L, -0xf.a710791928d528ap-43L, -0xd.73b20acd2ddae47p-53L, 0x8.3a9f2648c76b5adp-62L, -0x8.b92ec6233b61c8p-82L, -0x0p+0L};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0L, 0xd.b20322a3996a6a2p-6L, 0xd.ca4aa0fa2c66c04p-4L, -0xa.4de420cc6c77707p-1L, 0x9.2a8ab8b3d2a9452p+0L, -0x9.2a2c8f45b7035d6p+0L, 0xd.fee80d54f348b5ap-1L, -0x9.2c6587097a03f3cp-1L, 0x9.225b43c8840bfbbp-2L, -0xb.b74e433b47ec0d7p-4L, 0x9.6dc870dbf111c84p-6L, -0xd.6e00555bfbc3311p-7L, 0x8.3bd80e6e14d4ep-6L, -0xa.70de9ebe40837ffp-7L, 0xd.458b8cfbb4b4fcp-9L, -0x8.db3d47eeae9cad3p-12L, -0xa.d5110cf4583900cp-13L, 0x8.614b75f02db74e4p-14L, -0x9.8a8896b713246b3p-17L, -0xd.51a5323c171fee3p-26L, 0xb.8c561092a896f33p-23L, -0xa.769011a8736a082p-28L, -0xb.5161f3d88ae4a18p-32L, 0x8.1e58deca3716d7bp-38L, 0xe.96739f4ce14a1ebp-49L, -0x8.886bf8d85fdfe26p-57L, 0x9.0badf046a579ce9p-76L, 0x0p+0L};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0L, 0xc.de9de1239cb046fp-4L, -0x9.0c5906491d3955ap-2L, -0xc.7839f71242a14d4p-5L, 0x8.81b461d68a76009p+0L, -0xb.72fe813d0b59fd4p+0L, -0xf.f7358c9442947e5p-5L, 0xa.ed7063276080604p+1L, -0x9.29c9c7d32fce6e5p+2L, 0x8.423651a8f719bep+2L, -0xe.99bce7eb69c9558p+0L, -0xd.e0e5eaef029d8dap-2L, 0xa.4f436b46a67c643p+0L, -0xf.256f04625361643p-1L, 0xb.28f9c831a4ab6f7p-2L, -0x8.a71970fcdb5d61fp-5L, -0xe.1058e94389b55dfp-6L, 0xc.ee39ab87739f9d3p-7L, -0xe.ddcf5eece04ef66p-10L, -0xe.3fae0f6307b4b7dp-14L, 0xd.2fe42b7297d6b86p-15L, -0x8.3fb2ed50024d845p-19L, -0x8.71bc783d7f852p-23L, 0xb.4de2c6af60665f8p-29L, 0xc.39550de79b43b5p-39L, -0xb.dc24b4b0400b683p-47L, 0xc.92a4664dadb8e43p-65L, -0x0p+0L};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0L, 0x9.4d8af4702fa4917p-2L, -0xe.7e9b2eb0a293c0dp+0L, 0xa.206556ce091b04p+2L, -0x8.8b6f4ec09d9c51ap+3L, 0x9.db1ce281d9e7bffp+3L, -0x8.0207abf4baf0d13p+3L, 0xf.37ef354ae719481p+1L, 0xa.e0f4f0aad55bdb4p+0L, -0xd.8f2ed3cabd9e47dp+2L, 0xb.e8f89c68b5ce98dp+3L, -0xe.b7a656bdeec15e3p+3L, 0xc.fec0461881c7ecfp+3L, -0xf.676370d2bd59da4p+2L, 0xa.1fffb91075d1ef3p+1L, 0xa.f4a0e680e012488p-5L, -0xe.9503c4c9b7b1e2cp-2L, 0xc.a0744fcfdf1dc88p-3L, -0xf.b153b44bbbd55dap-6L, -0x9.59d9d9ad1020acfp-9L, 0x9.ef15d0e0d82a945p-10L, -0x9.0e5f7516ecaaaccp-14L, -0x9.0a87b28ac0c9fb1p-18L, 0x8.acdfc44a2a6359cp-23L, 0xd.807a7cb67428b3fp-33L, -0x9.0f4709e42ae00f3p-40L, 0x9.9ac848883cba3fep-57L, 0x0p+0L};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0L, 0x9.834e4dab96bc376p-1L, -0x9.71bb4c1fb65b59dp+2L, 0x8.9b36c94b3750b19p+4L, -0x9.bdcc290b9f8378cp+5L, 0xf.f9f96db50ad1ec4p+5L, -0xa.bec9c1b0372837ap+6L, 0xc.f45cba99d8f5737p+6L, -0xe.2ab3c8513f0ea1bp+6L, 0xd.7cf5a3d5e047047p+6L, -0xa.f1823dfa8daa614p+6L, 0xf.7ec994dda07fb22p+5L, -0x9.9bf6048130d2edbp+5L, 0x8.eebf04d13348a6p+4L, -0x9.a7c6a99c8f4aeedp+1L, -0x8.db211ffd209a6f3p+2L, 0x8.1c765ef5f7f1ce5p+2L, -0xc.f9039da83aa9c29p+0L, 0x8.69d91bc55678fabp-2L, 0xd.c9ffdee5e7de57ep-6L, -0x8.01426dc87cadac2p-6L, 0xa.90130491b5b5f4ep-10L, 0xa.5c99052bf919189p-14L, -0xe.9d842bbab01556cp-19L, -0xf.4ba9827a103207ap-28L, 0xf.2e767d355bddaa1p-35L, -0x8.0c472517ad4ef83p-50L, -0x0p+0L};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0L, 0xf.abcd8b83a71b41bp-1L, -0x8.9dce5f3b30b3793p+3L, 0x8.68682195f609a67p+5L, -0x9.84d437345ff4c4dp+6L, 0xd.c713118f501f476p+6L, -0xd.84594228bf62173p+6L, 0x9.e3e95931228123cp+6L, -0xb.f3ef786eb60bf83p+5L, 0xc.e4402241c87301dp+2L, 0xe.e0ba9661797c21bp+5L, -0xf.2a501fdde17d235p+6L, 0x8.d2170ed72b4825ep+7L, -0xf.c81fa50c6187197p+6L, 0xc.ec6dc8c841c327ep+6L, -0x9.a0b9ffd8a1f0ecfp+6L, 0xb.2759e13edab26a3p+5L, -0x8.586218b8ff72c95p+4L, 0xa.f8529bae88e396ep+1L, 0xe.c7b5cf8a917974bp-2L, -0x8.e3ac4b6b6acc633p-2L, 0xf.9c560d3a4ed77bcp-6L, 0xf.c13805a6e393a55p-10L, -0x8.98309aea3397895p-13L, -0x9.6e28a6b4cc8a06ep-22L, 0x8.ea4a570e998fa08p-28L, -0x9.742325e7646a08p-43L, 0x0p+0L};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0L, 0xf.196612f526d24c2p-1L, -0x8.b4965322c754f1cp+3L, 0x8.fd04e098b6fda5ap+5L, -0xb.0af33f860e6644cp+6L, 0x9.32e460da58d525ap+7L, -0xb.ab4f68e4108651p+7L, 0xc.f4b5ef2831ea0e8p+7L, -0xd.ddf0b3d1c6b1944p+7L, 0xd.f040100f39be9b8p+7L, -0xc.784cded5d90c4c7p+7L, 0xa.1dc1c0af0ad3159p+7L, -0xf.7356b459ded2772p+6L, 0xa.c6ab0e5c26933f6p+6L, -0xd.1d94154203d1881p+5L, 0xe.3ceb107fd7e02c5p+4L, -0xd.e3c65ca23d50927p+3L, 0xa.0c71ac8171966e8p+2L, -0x9.d5f9b056617ba17p-1L, -0xd.6bdd9c33d9e1582p-2L, 0xd.32a81275f97ea1cp-3L, -0xd.7fee6a38c5d3f8dp-6L, -0xc.1a0e6b635854ea4p-10L, 0xd.aab8869f5faa95cp-13L, 0xf.190b9c558a2439ep-22L, -0xe.29e09b9e442c27dp-27L, 0xf.061385658ae2fdbp-41L, -0x0p+0L};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0L, 0xc.68fc5193cbb1b7bp-1L, -0xe.a440ccad060f512p+2L, 0xf.436a0a53c719d99p+4L, -0x9.40013e4d843ac8dp+6L, 0xe.9f5af8582ca613bp+6L, -0x8.5c152ae13ccf6f4p+7L, 0x8.3e74fb86ed9434dp+7L, -0x8.6bc1129b3c4ec82p+7L, 0x8.6fb0e9528358fc8p+7L, -0xe.3449d6366d35aadp+6L, 0xa.2d64f4044bc4118p+6L, -0xe.4eb43711b821ef6p+5L, 0x9.ae261c0cd987cdbp+5L, -0xa.52c5f1b07a7a10fp+4L, 0x8.0baace1afbb0855p+3L, -0xa.e8dd3f89a3a1196p+1L, 0xe.d6ea4d49ae41ca2p-2L, 0xc.3d80fea19351b34p-1L, -0xc.d58ae923fc87cffp-1L, 0xa.366b50699d24558p-2L, -0xc.4aaebef7f06a90cp-5L, -0xc.29227a732dde266p-10L, 0xb.7c369e218830b25p-11L, 0x8.da71e0953a6ff91p-19L, -0xb.c8a6c1698c9facp-24L, 0xc.81da5a26ec63e05p-37L, -0x0p+0L};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0L, 0x8.20d0544bd51475ap-2L, -0x9.b2c5aebbb04f3ccp+1L, 0xa.8ca5782717c2461p+3L, -0xe.1efc0f8557945e6p+4L, 0xd.68c1f46d9ed5f43p+5L, -0x9.ece3c16b803b8afp+6L, 0xc.296d1a9b1536a08p+6L, -0xc.e650c7b4a3ee86bp+6L, 0xc.d377d24c49af172p+6L, -0xd.1806175ee9ce931p+6L, 0xd.39aa3be5ff8dcb3p+6L, -0xb.d1c258e1897df15p+6L, 0x9.57ec4377396b8b8p+6L, -0xe.87b1ca3693ad8c6p+5L, 0xb.1c262509faa6e0bp+5L, -0xe.b6134e745f9a70dp+4L, 0x8.44c1323b0bffc57p+4L, -0x8.fbf41d038891ad4p+3L, 0x9.52b80dadf506ef2p+2L, -0xe.0c5527608acdb69p+0L, 0xa.6e09c30b2c546eap-2L, 0xd.ead60c819922651p-8L, -0x8.d54a0b87ffd6b8cp-7L, -0xc.bb3c5ec6e4fd2a6p-17L, 0x9.2d9fe11eee7aff2p-19L, -0x9.c0ff7a8090c74e6p-31L, 0x0p+0L};
-            }
-            if constexpr (order == 11) {
-                return {0x0p+0L, 0xa.2b50e9522e86a75p-3L, -0xc.3398f1c7964f4dfp+0L, 0xc.ceed74dacabed45p+2L, -0xf.5e660eaebacd068p+3L, 0xb.a7c2eec834a457bp+4L, -0xc.213112d93221da7p+4L, 0xa.7de60def9f8cb1ep+4L, -0xa.3bb6074c98cfb0fp+4L, 0xa.b9df79fed3f56f5p+4L, -0x9.586138dec41f121p+4L, 0xd.dade5405b127d2ep+3L, -0xa.c04012e49fd2735p+3L, 0x8.60efa067af26275p+3L, -0xa.ef5008a8d1f0cbfp+2L, 0xc.cbfe4a8cc2b9da9p+1L, -0xf.ae20a079501f01bp+0L, 0x8.abc7a020b125872p+0L, -0xf.08d2623c2412c59p-2L, 0xc.617ad46572a9f45p-3L, -0xa.166eeef4db8f41bp-4L, 0x8.d9ba91b4066cd0bp-6L, 0xb.0de51fe9f7fd8e2p-10L, -0xf.7653c660eecd46ap-11L, 0xa.13d9bbaa8adb22dp-17L, 0x8.e36187daa39648ep-21L, -0x9.782b283672f30cdp-32L, 0x0p+0L};
-            }
-            if constexpr (order == 12) {
-                return {0x0p+0L, 0xa.2d2427bccd39172p-5L, -0xc.3e7cf55a7a0039fp-2L, 0xc.cd766a1bb1a58d8p+0L, -0xf.19aee96374ef183p+1L, 0xa.f1c20f10ca84c7dp+2L, -0xa.441cf0245c1e989p+2L, 0xf.08d3f9839af181p+1L, -0xd.ff93b926a081d89p+1L, 0xf.b45b7f166618b46p+1L, -0xd.4e44e185e5110d4p+1L, 0x8.a3eed6c08e9589p+1L, -0xd.08770758e65b254p+0L, 0xa.ec5cfff1e6dc48ap+0L, -0xd.8775fb493cf7d7dp-1L, 0xd.8c0494f0d34dbf8p-2L, -0x8.8d169b83b8e53edp-2L, 0xa.2d86ccc6559bbf1p-3L, -0xe.ba041f5676a0b08p-5L, 0x9.3e0889dadedbcbbp-6L, -0x9.7735428934a726dp-7L, 0x8.56888186d114aabp-9L, 0xd.b8cd6a5738afd8ap-11L, -0xb.dab9366ba83dabcp-12L, 0xf.7f073fde73fa0bdp-17L, 0x8.8b41cfb923d7022p-21L, -0x9.260ac7e9b3efaabp-31L, -0x0p+0L};
-            }
-            if constexpr (order == 13) {
-                return {0x0p+0L, 0xa.1cd4ad99523f5acp-8L, -0xc.2f2fc67105b80bcp-5L, 0xc.acd5acad17523e6p-3L, -0xe.ac893beffa9ec6ep-2L, 0xa.1d32b2499d9f84p-1L, -0x8.51602e62cbd5666p-1L, 0x9.39ca87b7fe8bf75p-2L, -0x8.28645ce5c25be28p-2L, 0xb.0075410088e8318p-2L, -0x9.0fb0d4225082783p-2L, 0x8.cf8737798d06934p-3L, -0xc.710818a25393088p-4L, 0xd.03f944a7cb8758ep-4L, -0xe.6674293e772e22ap-5L, 0xf.2b09bc335412a19p-7L, -0xa.efa460643e6b966p-7L, 0x8.ce9f81ce2366f05p-7L, -0xc.f36687b0fa6554ep-12L, -0xd.cb35efa2b9452d3p-10L, 0xc.1203b8d10393dadp-12L, -0x8.d82d17abfc923a4p-12L, 0xb.fc2aa4acfa52995p-12L, -0x9.1b886fc19758c23p-13L, 0xe.62bad7ef9f9e73fp-17L, 0x8.f91c0cb5711719fp-21L, -0x9.b4bf4dfa1834f78p-30L, -0x0p+0L};
-            }
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.2e3c0bb3f3ad4d49ee7e86ec562p-10Q, 0x1.d73cdc4f17147d4ff78a1eaebc89p-4Q, 0x1.980f074dbd462038712882b2223p-1Q, 0x1.0b8da7807c2738b0ef8a21bd41d9p-2Q, -0x1.381b88314120b0755faac9b6a208p-2Q, 0x1.a64053bd4da4144d5c6645aafa5p-3Q, -0x1.be6cb26620f84322f5bc9ad124p-4Q, 0x1.5369f32b472a8bf80c2615157588p-5Q, -0x1.e553bfb83c481ee1c85b1021810cp-8Q, -0x1.5b97376b07916025b5f5ed690f77p-9Q, 0x1.3ad93e070eb79f317793c09c0451p-9Q, -0x1.6c8658d1b206dd40e11227faae77p-11Q, 0x1.421437e7b839d2e408af08229906p-16Q, 0x1.359cb55b7d335b5bc8ff9070d38p-15Q, -0x1.16b1cde08937e6520514fc007dd3p-18Q, -0x1.1e470298289ae452c29404b9c746p-19Q, 0x1.16b7d7c52ecb6bf5c9c270fe3977p-21Q, -0x1.2a9017a9058ec8631bfea23cf0f2p-27Q, -0x1.e6603a12c62203e481a6f751bb0fp-29Q, 0x1.ad635a5532ad9d7f9b990f3258b1p-33Q, -0x1.0b7166f3d598041c11f82d418c5ep-37Q, -0x1.2dcc8d3c8b0cf63074ab4d9fba6ep-43Q, 0x1.994c7452dcd30c07dade8e0a0b5bp-50Q, 0x1.d3e7db27a70ee63bd0dc60e06dc1p-60Q, -0x1.ad34c0383fa643c903234154af78p-72Q, 0x1.c6fd0b1a8d6a2b5f9f47659e9cb5p-94Q, 0x0p+0Q};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.ffe6a833f41d1e41c335a1d66225p-8Q, 0x1.6878956519ce3162ba29291a8504p-2Q, 0x1.4f6222726462315c1311b1bd0b69p-1Q, -0x1.9d7a4f00f9dc035ff30a13b3dd54p+0Q, 0x1.ee1a7236f71e3afe8c9241dc280bp-1Q, -0x1.3a4c3d150c11dd01e59680a43c1ap-1Q, 0x1.a5124e1ab47a907fdd8a56cf5fd2p-2Q, -0x1.fd47140509eb33a71307cdb49b3fp-3Q, 0x1.efeb8355fd2f814144fb4db02bdbp-4Q, -0x1.695e5e5e49cf847101e5144b6fefp-5Q, 0x1.73cae05387f642ba0d652b2dbcabp-7Q, -0x1.fa774911ba2d3bb25d61e69c8c8ep-10Q, 0x1.13b07ddddb3b836ee57d12843693p-13Q, 0x1.7cb11c0b4280a9d8a95e4eb20e72p-14Q, -0x1.d2cbfff6e2a582bd1061aa2f380bp-15Q, 0x1.74388c9fd28e69e7d9f0c5af3fddp-17Q, 0x1.21ff895bfb5f2915922793fd222dp-21Q, -0x1.156307b5c128c175f7e3a71477b9p-22Q, -0x1.19b91bff8bef4f88f1ed76cce8eap-25Q, 0x1.f7d83e4d41c76f94d46210e4d1f2p-31Q, 0x1.5090626b206a430059df75028168p-34Q, -0x1.405683426ad010e44f0a98cc929p-40Q, 0x1.6ac079eed130df81302e2b26c482p-46Q, -0x1.9a49f0637a3b64a9eb35bd52aa23p-55Q, -0x1.88bc66cc087f1d558950f224d6c9p-67Q, 0x1.a0541eb1bdceab613773d4dc3dd7p-88Q, 0x0p+0Q};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.70e38d13c6dccf6333417be4b4fbp-5Q, 0x1.98429094e12d1953c234a36b137bp-1Q, -0x1.5a23aee5cfcf330386719e085aa1p+0Q, -0x1.ca3a85e30ebf60ba5eccc5b7b84bp-2Q, 0x1.f2911f6caea6ac421bc7b6d2ce04p+0Q, -0x1.902df5acb98563fb6c85941263b7p+0Q, 0x1.6e5d8a32fe3ae7b3c23b4e6e9c7ap-1Q, -0x1.7cd7499a11b87c3bc4909e0bdb58p-5Q, -0x1.cb51389df1436d54630b5c4050fbp-3Q, 0x1.8970fdea96db48b13c52294d029p-3Q, -0x1.2e3ba43116d4ee1d14ccd7ef1eb6p-4Q, 0x1.a437288ed51ab324c667ecc7c439p-9Q, 0x1.5d8afaeb5ec2a57500ea441b58aap-7Q, -0x1.3f213a25a4c39a4ee9f8ca7fc5f5p-8Q, 0x1.438df66495fed0569b1e6607263bp-11Q, 0x1.92aacb344e1aac45946a6dd95b1dp-13Q, -0x1.4a2a2b6937dca67c2fb96409eaabp-14Q, 0x1.061494c076ea4c2b5c794f2371b4p-17Q, 0x1.1c61500cd5ff603bf7260846f007p-21Q, -0x1.fed404b96c72e77fac42699e644dp-24Q, 0x1.9900fa8d5cb81723cdb543a2521ap-29Q, 0x1.4b71c6cbb7be353ab93ac21700e3p-33Q, -0x1.f4e20f23251aa513b13eb0ad0eafp-40Q, -0x1.ae764159a5bb5c8d340066c07578p-50Q, 0x1.0753e4c918ed6b59ce15c4a9365bp-59Q, -0x1.1725d8c4676c38ff70e1cc359512p-79Q, 0x0p+0Q};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.b6406454732d4d440405d44a6a49p-3Q, 0x1.b949541f458cd808c01c6f4442bcp-1Q, -0x1.49bc84198d8eee0e1769477dd34dp+2Q, 0x1.255157167a5528a3714c438e2bbbp+3Q, -0x1.254591e8b6e06babda61e0b5bd92p+3Q, 0x1.bfdd01aa9e6916b30d7fb866cb4dp+2Q, -0x1.258cb0e12f407e788c8d24c043p+2Q, 0x1.244b687910817f75269b9b13d0aap+1Q, -0x1.76e9c86768fd81ae0140e512f91dp-1Q, 0x1.2db90e1b7e223907d65e1858ad53p-3Q, -0x1.adc00aab7f786622c376bd60c25fp-4Q, 0x1.077b01cdc29a9bffc55813096431p-3Q, -0x1.4e1bd3d7c8106ffe51d90e297c64p-4Q, 0x1.a8b1719f76969f8051acdf38ae9p-6Q, -0x1.1b67a8fdd5d395a5e1003bc2df39p-9Q, -0x1.5aa2219e8b072017d97056f432f5p-10Q, 0x1.0c296ebe05b6e9c7cf2917908081p-11Q, -0x1.315112d6e2648d659715640aac77p-14Q, -0x1.aa34a64782e3fdc563417212e36cp-23Q, 0x1.718ac2125512de66d6a9b5d79809p-20Q, -0x1.4ed202350e6d4103a23efe811aep-25Q, -0x1.6a2c3e7b115c942fffc924e2aa83p-29Q, 0x1.03cb1bd946e2daf6230de1902b89p-35Q, 0x1.d2ce73e99c2943d672b79f3df3dfp-46Q, -0x1.110d7f1b0bfbfc4b48ffe175513cp-54Q, 0x1.2175be08d4af39d29c43830b5338p-73Q, 0x0p+0Q};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.9bd3bc24739608dd1ea0727f797p-1Q, -0x1.218b20c923a72ab49d783c3c2182p+1Q, -0x1.8f073ee2485429a822c3456748ddp-2Q, 0x1.10368c3ad14ec0121ffa10beccc4p+3Q, -0x1.6e5fd027a16b3fa71b0c68881f6dp+3Q, -0x1.fee6b19288528fc99125553bcb88p-2Q, 0x1.5dae0c64ec100c07cb64acfb530ap+4Q, -0x1.253938fa65f9cdca9dcd99a2d96bp+5Q, 0x1.0846ca351ee337bf1cde15f6a892p+5Q, -0x1.d3379cfd6d392ab0067070d38b2ap+3Q, -0x1.bc1cbd5de053b1b3e6030cd2eb44p+1Q, 0x1.49e86d68d4cf8c86d82167732746p+3Q, -0x1.e4ade08c4a6c2c8507d0731ef456p+2Q, 0x1.651f390634956dee37faca7ade61p+1Q, -0x1.14e32e1f9b6bac3d6ef9b665a8dep-2Q, -0x1.c20b1d287136abbd5724af54edd7p-3Q, 0x1.9dc73570ee73f3a5d7e75adc1efap-4Q, -0x1.dbb9ebdd9c09deccb1020147719ep-7Q, -0x1.c7f5c1ec60f696f9a40d5c2f13dep-11Q, 0x1.a5fc856e52fad70c72c88b43b17bp-12Q, -0x1.07f65daa0049b089e54b5e492044p-16Q, -0x1.0e378f07aff0a4003d557ea13ebap-20Q, 0x1.69bc58d5ec0ccbef38bec2915824p-26Q, 0x1.872aa1bcf368769fc21e287db36p-36Q, -0x1.7b84969608016d06bfce8c098437p-44Q, 0x1.92548cc9b5b71c86f11e26fc3a07p-62Q, 0x0p+0Q};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0Q, 0x1.29b15e8e05f4922e7d4e47048a9cp+1Q, -0x1.cfd365d6145278198eca9c82d9f8p+3Q, 0x1.440caad9c12360807dafb3bad1d1p+5Q, -0x1.116de9d813b38a3407c462c9c8afp+6Q, 0x1.3b639c503b3cf7fe4e226236b434p+6Q, -0x1.0040f57e975e1a258b9875fe1f17p+6Q, 0x1.e6fde6a95ce32902224ee9a0f717p+4Q, 0x1.5c1e9e155aab7b67b6f0684e8054p+3Q, -0x1.b1e5da7957b3c8fabda1cfa1992fp+5Q, 0x1.7d1f138d16b9d31aa28298c6d585p+6Q, -0x1.d6f4cad7bdd82bc575e84a0ae447p+6Q, 0x1.9fd808c31038fd9d9f9820868c69p+6Q, -0x1.ecec6e1a57ab3b47a08d37ee9238p+5Q, 0x1.43fff7220eba3de58880aab6571cp+4Q, 0x1.5e941cd01c024910420637b6b61bp-2Q, -0x1.d2a0789936f63c584facf37b3e67p+1Q, 0x1.940e89f9fbe3b90fa47d360fd472p+0Q, -0x1.f62a7689777aabb4ab21abcf7e27p-3Q, -0x1.2b3b3b35a204159ed02721cadaafp-6Q, 0x1.3de2ba1c1b05528a92ffeeb8fc2ep-7Q, -0x1.21cbeea2dd955597cbff120c27ccp-11Q, -0x1.2150f65158193f62d7d7f8ca1f69p-15Q, 0x1.159bf889454c6b38325ea0bd0aa7p-20Q, 0x1.b00f4f96ce85167dd0220db19d66p-30Q, -0x1.21e8e13c855c01e5c446a0ad86p-37Q, 0x1.33590911079747fc32e0ebbb9924p-54Q, 0x0p+0Q};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0Q, 0x1.3069c9b572d786eb96d929d90cddp+2Q, -0x1.2e376983f6cb6b3abd68459b0db9p+5Q, 0x1.1366d92966ea16320047794482afp+7Q, -0x1.37b9852173f06f1765e1fe9f84p+8Q, 0x1.ff3f2db6a15a3d87e9d7df5b42f3p+8Q, -0x1.57d9383606e506f39f38563cb6bep+9Q, 0x1.9e8b97533b1eae6eef5ccc2c8b76p+9Q, -0x1.c556790a27e1d4367bdf86d03f05p+9Q, 0x1.af9eb47abc08e08daae8af537da6p+9Q, -0x1.5e3047bf51b54c2759154839c7dbp+9Q, 0x1.efd9329bb40ff6440883f8a40f82p+8Q, -0x1.337ec090261a5db68ef9839a3fcp+8Q, 0x1.1dd7e09a266914bfb2df7819245bp+7Q, -0x1.34f8d53391e95dda3b7a36e1f269p+4Q, -0x1.1b6423ffa4134de5e81b13aa374dp+5Q, 0x1.038ecbdebefe39ca7724b2c5d6b5p+5Q, -0x1.9f2073b507553852ed1a7122dc5cp+3Q, 0x1.0d3b2378aacf1f56c9dbd6033ed8p+1Q, 0x1.b93ffbdcbcfbcafb2828e4f8a1e6p-3Q, -0x1.00284db90f95b583e4f9723dea4p-3Q, 0x1.5202609236b6be9cf16ae5695042p-7Q, 0x1.4b9320a57f2323116dd63291deebp-11Q, -0x1.d3b085775602aad7427a1a128489p-16Q, -0x1.e975304f420640f339ac1f2721b2p-25Q, 0x1.e5cecfa6ab7bb5421ef8c106f4f7p-32Q, -0x1.0188e4a2f5a9df06f6875fecaac5p-47Q, 0x0p+0Q};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0Q, 0x1.f579b17074e36836eacdf20b2124p+2Q, -0x1.13b9cbe766166f25c9dace3616b1p+6Q, 0x1.0d0d0432bec134cd566f5783ca25p+8Q, -0x1.309a86e68bfe9899fc0e86f2260fp+9Q, 0x1.b8e26231ea03e8ec859843dc6ce9p+9Q, -0x1.b08b284517ec42e68106ca8a8bc1p+9Q, 0x1.3c7d2b26245024778e76cf716fbfp+9Q, -0x1.7e7def0dd6c17f062ac5f280847p+8Q, 0x1.9c880448390e60397d83aacda54p+5Q, 0x1.dc1752cc2f2f84356ce375550f21p+8Q, -0x1.e54a03fbbc2fa46a8399b07d254cp+9Q, 0x1.1a42e1dae56904bbcf3f8f7fa5c7p+10Q, -0x1.f903f4a18c30e32dc6c260029f14p+9Q, 0x1.9d8db919083864fcc4e1ce713df3p+9Q, -0x1.34173ffb143e1d9eed0dd73c6925p+9Q, 0x1.64eb3c27db564d469eb11c515c5dp+8Q, -0x1.0b0c43171fee5929daa55b569994p+7Q, 0x1.5f0a5375d11c72dc55988338ff36p+4Q, 0x1.d8f6b9f1522f2e96a9e46aa5caf8p+1Q, -0x1.1c75896d6d598c65080bd27d32aap+1Q, 0x1.f38ac1a749daef77915c1d44f9d7p-3Q, 0x1.f82700b4dc7274aa9bd956d7234cp-7Q, -0x1.1306135d4672f12980f36c25a44ep-10Q, -0x1.2dc514d6999140dbb2a21c1d56f1p-19Q, 0x1.1d494ae1d331f410d68f7a178351p-25Q, -0x1.2e8464bcec8d40ffd77ac9bbd77ap-40Q, 0x0p+0Q};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0Q, 0x1.e32cc25ea4da498425dfec2497a6p+2Q, -0x1.1692ca6458ea9e38b45000f9e974p+6Q, 0x1.1fa09c1316dfb4b439ad2e78bb59p+8Q, -0x1.615e67f0c1ccc897da6f2d005018p+9Q, 0x1.265c8c1b4b1aa4b3e36b99e4a1a9p+10Q, -0x1.7569ed1c8210ca209e47f9d0511cp+10Q, 0x1.9e96bde5063d41cf09da3c270b93p+10Q, -0x1.bbbe167a38d63287ecfeda29fbbep+10Q, 0x1.be080201e737d36f7e79bffa876fp+10Q, -0x1.8f099bdabb21898e359857d34007p+10Q, 0x1.43b83815e15a62b284f0ee906572p+10Q, -0x1.ee6ad68b3bda4ee4ba8bf16f4fabp+9Q, 0x1.58d561cb84d267ecaf633fb5a5d5p+9Q, -0x1.a3b282a8407a310226d833dadcd5p+8Q, 0x1.c79d620ffafc0589079eea90279ap+7Q, -0x1.bc78cb9447aa124d62b31a0a7f54p+6Q, 0x1.418e35902e32cdd0c2f21fb873ep+5Q, -0x1.3abf360acc2f742d879127375bb2p+2Q, -0x1.ad7bb3867b3c2b046f80e1cb0482p+1Q, 0x1.a655024ebf2fd4378622021ee814p+0Q, -0x1.affdcd4718ba7f1a965455b89c8ep-3Q, -0x1.8341cd6c6b0a9d48905a1ecfc91fp-7Q, 0x1.b55710d3ebf552b754ea432b16e1p-10Q, 0x1.e321738ab144873b6e4379081333p-19Q, -0x1.c53c1373c88584f948dc39838bd8p-24Q, 0x1.e0c270acb15c5fb50466c4df9e1p-38Q, 0x0p+0Q};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0Q, 0x1.8d1f8a32797636f661365be0e3e6p+2Q, -0x1.d4881995a0c1ea2393ff422e453fp+5Q, 0x1.e86d414a78e33b3180b306c7fb52p+7Q, -0x1.280027c9b087591ad85db337ae83p+9Q, 0x1.d3eb5f0b0594c2750ef02a700404p+9Q, -0x1.0b82a55c2799ede8dec1e33e1dcdp+10Q, 0x1.07ce9f70ddb2869a658274b505f1p+10Q, -0x1.0d7822536789d9033e70cbead7bap+10Q, 0x1.0df61d2a506b1f8fcfe72d1ca4cdp+10Q, -0x1.c6893ac6cda6b55a4941f5e57261p+9Q, 0x1.45ac9e808978822ff4ad1899b3b8p+9Q, -0x1.c9d686e237043dec7c04f88fd885p+8Q, 0x1.35c4c3819b30f9b6fdd5c67ec132p+8Q, -0x1.4a58be360f4f421d89e83ecf3267p+7Q, 0x1.017559c35f7610aa1b72e5e5a83p+6Q, -0x1.5d1ba7f13474232b92fdf4e5cb84p+4Q, 0x1.dadd49a935c8394385d3a3bdf6d5p+1Q, 0x1.87b01fd4326a3668ccbb1eed227dp+2Q, -0x1.9ab15d247f90f9fe7c9b6b3dd567p+2Q, 0x1.46cd6a0d33a48aafbbc221eb1f48p+1Q, -0x1.8955d7defe0d5217296739d07f07p-2Q, -0x1.85244f4e65bbc4ccef7883bc8ba1p-7Q, 0x1.6f86d3c43106164aba39dbfe0b2fp-8Q, 0x1.1b4e3c12a74dff21568f59de83f3p-16Q, -0x1.7914d82d3193f580c3335f167104p-21Q, 0x1.903b4b44dd8c7c0a4e702124dc3fp-34Q, 0x0p+0Q};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0Q, 0x1.041a0a897aa28eb3a0ccade17e3cp+1Q, -0x1.3658b5d77609e7977d3641db3a11p+4Q, 0x1.5194af04e2f848c21930873e900ap+6Q, -0x1.c3df81f0aaf28bccb5fed61687cfp+7Q, 0x1.ad183e8db3dabe867a1b1e1d7e93p+8Q, -0x1.3d9c782d7007715e1144e807f092p+9Q, 0x1.852da35362a6d4101e229e2b5077p+9Q, -0x1.9cca18f6947dd0d5bed4aff692d8p+9Q, 0x1.9a6efa498935e2e3d82e1fd52122p+9Q, -0x1.a300c2ebdd39d26204b2e2ccd8bdp+9Q, 0x1.a735477cbff1b966c8a20eaae97p+9Q, -0x1.7a384b1c312fbe2a2f45b3550037p+9Q, 0x1.2afd886ee72d716fc638e75f48b8p+9Q, -0x1.d0f63946d275b18c0f5c2756f025p+8Q, 0x1.6384c4a13f54dc153d90136891aap+8Q, -0x1.d6c269ce8bf34e1953164b65a3d5p+7Q, 0x1.08982647617ff8ae60bccefbfe0fp+7Q, -0x1.1f7e83a0711235a83bc8e025bd62p+6Q, 0x1.2a5701b5bea0dde347ec02073e97p+5Q, -0x1.c18aa4ec1159b6d22d740e4f35cdp+3Q, 0x1.4dc13861658a8dd406eb1a845d5ap+1Q, 0x1.bd5ac19033244ca1c006b305a421p-5Q, -0x1.1aa94170fffad7174e8899965ff8p-4Q, -0x1.97678bd8dc9fa54b7e4c01f3ba2ap-14Q, 0x1.25b3fc23ddcf5fe31ea2281e4301p-16Q, -0x1.381fef501218e9cc3e0863bb3cadp-28Q, 0x0p+0Q};
-            }
-            if constexpr (order == 11) {
-                return {0x0p+0Q, 0x1.456a1d2a45d0d4e9e18e4013bda3p+0Q, -0x1.86731e38f2c9e9bd245a6d7f6e86p+3Q, 0x1.99ddae9b5957da8932fc9013b15ep+5Q, -0x1.ebccc1d5d759a0cf4adc92beb271p+6Q, 0x1.74f85dd906948af50c229b89c98dp+7Q, -0x1.8426225b26443b4ef3c972f9489bp+7Q, 0x1.4fbcc1bdf3f1963c49a88c06aa08p+7Q, -0x1.4776c0e99319f61e68a41fbe42b3p+7Q, 0x1.573bef3fda7eadeaaa4191468e3p+7Q, -0x1.2b0c271bd883e242fdd8d9725e0bp+7Q, 0x1.bb5bca80b624fa5bb278816db9f3p+6Q, -0x1.5808025c93fa4e6af5a7ad436556p+6Q, 0x1.0c1df40cf5e4c4ea4441c80693a5p+6Q, -0x1.5dea01151a3e197eb05317c268edp+5Q, 0x1.997fc95198573b5277250e908707p+4Q, -0x1.f5c4140f2a03e036d15c57dbb36p+3Q, 0x1.1578f4041624b0e3ebbbb44abecfp+3Q, -0x1.e11a4c47848258b137f885157e3p+1Q, 0x1.8c2f5a8cae553e89ef1e861ef5b3p+0Q, -0x1.42cdddde9b71e8354b8c2fb7c09ep-1Q, 0x1.1b37523680cd9a16c0e5dc3ebd03p-3Q, 0x1.61bca3fd3effb1c3f5807afcb9adp-7Q, -0x1.eeca78cc1dd9a8d407a9b1f6577bp-8Q, 0x1.427b3775515b64598a140f609c8fp-14Q, 0x1.1c6c30fb5472c91c3ee2a25808b3p-18Q, -0x1.2f056506ce5e619914ce605b0524p-29Q, 0x0p+0Q};
-            }
-            if constexpr (order == 12) {
-                return {0x0p+0Q, 0x1.45a484f799a722e4cd950a09d5fbp-2Q, -0x1.87cf9eab4f40073db99e6a0fb481p+1Q, 0x1.99aecd437634b1af52fbd40a01bcp+3Q, -0x1.e335dd2c6e9de306d05cc358c6bp+4Q, 0x1.5e3841e2195098fae8b77b691b21p+5Q, -0x1.48839e048b83d3127ebe74020885p+5Q, 0x1.e11a7f30735e301f0eb2ede8063fp+4Q, -0x1.bff27724d4103b12e92a64b54c9dp+4Q, 0x1.f68b6fe2ccc3168c1a15db6eeebdp+4Q, -0x1.a9c89c30bca221a764ae454bfb09p+4Q, 0x1.147ddad811d2b11feabea5bba8adp+4Q, -0x1.a10ee0eb1ccb64a80033704ddb98p+3Q, 0x1.5d8b9ffe3cdb891325e9bfc9fb55p+3Q, -0x1.b0eebf69279efaf954dd166c21dep+2Q, 0x1.b180929e1a69b7ef5328a0cfd4a4p+1Q, -0x1.11a2d370771ca7d9ba7c7444df33p+1Q, 0x1.45b0d998cab377e10ef3a92e12dfp+0Q, -0x1.d74083eaced416102c8dd2af61fp-2Q, 0x1.27c1113b5bdb7975242772f43479p-3Q, -0x1.2ee6a8512694e4da2e5b07f1c606p-4Q, 0x1.0ad11030da22955532f0e66e0c83p-6Q, 0x1.b719ad4ae715fb13a424d63fb241p-8Q, -0x1.7b5726cd7507b577ab874fe8a876p-9Q, 0x1.efe0e7fbce7f41797c67293a0937p-14Q, 0x1.116839f7247ae044e8dfdefe7163p-18Q, -0x1.24c158fd367df5563093507c0edcp-28Q, 0x0p+0Q};
-            }
-            if constexpr (order == 13) {
-                return {0x0p+0Q, 0x1.439a95b32a47eb5722e3cd7fe3cap-5Q, -0x1.85e5f8ce20b701780e2029b7ff55p-2Q, 0x1.959ab595a2ea47cca93fdec47d03p+0Q, -0x1.d591277dff53d8dcf59277336155p+1Q, 0x1.43a6564933b3f0805a5a899c5bb9p+2Q, -0x1.0a2c05cc597aaccc032de2cc831fp+2Q, 0x1.273950f6ffd17ee92b32456caf9bp+1Q, -0x1.050c8b9cb84b7c5048bc5cd2f92ep+1Q, 0x1.600ea820111d062fdf2a6acf661cp+1Q, -0x1.21f61a844a104f06b392bde6725p+1Q, 0x1.19f0e6ef31a0d26707b436c0ada9p+0Q, -0x1.8e2103144a726110a565e981ea79p-1Q, 0x1.a07f2894f970eb1bd26c4012674ap-1Q, -0x1.ccce8527cee5c45450edf8973a9cp-2Q, 0x1.e56137866a8254327c313c62b4d6p-4Q, -0x1.5df48c0c87cd72cb9ba6c6b9ceadp-4Q, 0x1.19d3f039c46cde096e59d4adaef2p-4Q, -0x1.9e6cd0f61f4caa9b0d4bb0b897fp-9Q, -0x1.b966bdf45728a5a5bb304f91c5cp-7Q, 0x1.8240771a20727b5953c676de8a9p-9Q, -0x1.1b05a2f57f924748a24f50e9e6eep-9Q, 0x1.7f8554959f4a532982e2ba397a2fp-9Q, -0x1.23710df832eb1845bb5316dc1abfp-10Q, 0x1.cc575afdf3f3ce7d0de6ac81f14p-14Q, 0x1.1f238196ae22e33d86876e9e195ep-18Q, -0x1.3697e9bf43069ef0c328d37a1aebp-27Q, 0x0p+0Q};
-            }
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            if constexpr (order == 0) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00115293332509096742962333483892313856362688845269995659187394173081837979723"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.115048275548763287879127945985463599972775459285064004095554421826950893087"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.796989658584277062411937010559864103043001629105734220965026462739268209643"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.261282555787182265882706163765054116695305731989757725047913151702289063990"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.304792526251077945867767239314414983616168566481167348823874432025337651187"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.206177381720140253354071811928730787659997169191432596424777801677056654936"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.108990380164014469211374498205641904963307679906212370075411833415284835295"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0414323567767714336655575435550014435859114005804252743467739002617028032556"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00740550451904298413275770194104519624796412659431510963194058424609244583855"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00265190650453840226202382246051294213464963751920614087594043518495040017701"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00240210420772995773725343184085600070474699593300395536783639652419272638655"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000695275865120426856318173618858975815994589786388847596433982307511410977064"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000191974030759909635472313378575369891683691026590204627382371876560571031362"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000369086435191623599908102272586735250422568493003535062380722233574951016029"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000415287237890283585845050020110906559871983453862988696226792814210793873275"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000213293271762831680444514966056532349654366183092419194511477231701438124426"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000519152984288816673375386899946665294276591318147000925448293729776300076533"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000868932288799631112269973020748320326319607540201446697303589532523058640376"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000353885033203391238239173859710183402146968653187882395070568528196527541446"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000195263099667140461506853591672068520568701722861147310552025237678358948376"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000760118658661622931484977499946668576063487666390672568814742992660278581129"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000134025692809696893389568339892947369168469910164958708207111959469432500771"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000142003995353734011507760517926628916988777854097085265899981211240745997152"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000158532613505743630429831947577865370489228544853275053068484397376569424042"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000000000355030930001146155860382376996084936412851909339999461687756186476889838277"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000000000000000000897306502669997242383001671446525458224541863620223787779391644190926610050"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 1) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00781098944203546971796976286517434035884009688773248606224515220005414202600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.352022489829734113542431984005808736473724699510524912312303517596181907952"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.655045582260019530471586793705288409958328082576128477269067038800474460343"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.61514753125980808044495957120916454545964651551944410129115969858552545691"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.965045518121368371649657414431609409876079256511530108438864454295064039152"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.613862904376251107603567359503339925389993434358836078881583881755180373456"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.411202640895789674547585554456016331268606109870526886150894523201400069359"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.248670727161188410367077352077023110486766838261792327161508712754116165892"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.121074212103689294850946226679458285881379881523239286723535403732539992908"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0441123812800529610355488980147434896876334272618270449617517207697232204447"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0113462062209348030398079804396363956598508998796900777431886698352753187169"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00193201430777827515696813853521806116958501580116959470619810785172817252196"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000131458959852363274552068404289595280980320518543359612758830152196452510244"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000907640061777183255547701282076901148256668421380966288924343020509113784790"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000556465237685112725274835827463099540776609744280841662958102231266930097713"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000110930471347758540199575897934132437541479940508074917148850579912551630419"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000540163721305599951324898771320582892046233366679859045334581706862592762034"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000258336622635775732966000369446951153794507695432350051229799820914271331972"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000327968834281282285800082226655395639101026250341990601757011633171502265437"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000916488171514711030622268872903433690707685750686927346624592740598447942041"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000765257940990005274758907789178871368045869308567592594682817218494349636475"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000113806898255625919280795529887274235588918418565838791672065942227585229403"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000201367733903050668198447517300557877789704362876084808722846353524567227922"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000444836034640325638288709395930623143471945459846091722425723736229604149591"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000000103956338676397028751708008201484812724312022305577756338111796159549805791"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000525480561641109164137864688009776045386815264957861417756490150159142136333"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 2) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0450303798117733589231798330957691280417239896756051304263138384820087822720"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.797382848905352224261209402370274675556632019052816074828369432733398437194"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.35210698233259733766168097865537427607660034980120464334236932299708410774"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.447488872512337268222446766248936491151740076284709909184963796609707232255"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.94752689746260427086971810378552771942897218308070519347370198965733742471"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.56320128886138359744668398388042143870937778524339089182916328446012293685"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.715557402348272306878574425353637462359702067943253760692428908902502127827"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0464893758331106893607592418969309234589119778040679971376996748085292908751"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.224276010818501093466222589488380871765384010383119945740817975057642024404"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.192110046121212755900487444382509639513398567516218319022991979288220691964"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0737873471966185978956886225677444795250476204861205019199449953274778830157"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00320598955242186941919016686957021369970437347319710965669749910809644144859"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0106672024910406572727634384630232126394512616065206839400078471641232182677"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00486953420262908335767503491652246905399023769268129286510776073032697296330"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000617131311240191212204138459081818690294990133002525462438346490707490327298"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000192006665779021389446223341431010819375175205853618100042995321802178648239"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000787174045799788843691997530421226394107444626942089306529661594079889645065"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000781060441650629506094363225086284470818832491361256882121071831394044465309"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000529699265431996299782049699978331676802370855121232208197190378200993391878"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000118936457924373854837977028298636171996098002951110364373678539575607515220"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000297589448108271162186173745281562110809351136810307857224663251378623404416"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000150723480889045397495951808812346145543547998873595419531555416151101740824"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000177949404003867596126708357294529070318811557365468246834172229163385065083"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000149346484715446421742389146635163953260098009858086983961700451264624854098"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000178437796860002852739466568338831019080176013249284982357396229767567234102"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000180395062763246722611480959764856761895616090783365686732209021823579303995"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 3) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.213990005328375555135472755123681140600857383942097187754813778508021364188"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.861887577836364549248175536802065478416096122297736989669377523212045471882"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5.15213110442549193951604232130937181308428404117234799001678258735956565095"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("9.16617922201354414096203125317498717808490325566889445742435609535893499012"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.16474242641471677731657141502679363538951319294421818226908853664694404748"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.99786416685096083753063339505540880226836092318161102091793537672115020197"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.58671209326440268266270834820616632025849613943982416213412034046663096202"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.28355127250052801373193408526992202651493499277936659476824160108001663527"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.732252371428780979843072193742624736624407830994183828051335649974997274856"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.147325620855341831283808507199341730144107370475895883352377534229959735834"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.104919473342276336806466603437472988232748900776758986519994396324472688826"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.128652586070825684925857427195986593237515170617045438297383145109698161719"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0815695071328300519374023680966951688787126896982976686941014234357114383306"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0259212121580757805545526931754301057596596343151488765977950290614602386512"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00216220796475466148613393323709898748149018273039190022024143151723111058925"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00132230119892098570617802910816943973223564708652310398004809061573967486877"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000511478130422611034647765921441315956001733118732698933562593619541749240757"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000727931722918291769533207689510068034174609274026487647576221227404443932148"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000198467477327859725151632668232927044265781371367599997004215442660984250173"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000137665131612781247758064430980951835019601684631521207530971741938647123521"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000389782183547484796734257149006560609838069041845630777046077009454055077516"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000263515414830424927128095026380033778748765668296184726183106775537323610237"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000295350893893575030830965321544192503213832003549056472742964277263629493577"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000259129637850121514112507960811641537965052175737748298700466697875155415894"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000592088706033458993194518219229976516091225801153372985679944483340194107510"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000000000000119717821494849869283848954977146397574755733129894249448827837729810076385"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 4) {
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-            }
-            if constexpr (order == 5) {
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-            }
-            if constexpr (order == 6) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.75645678252782782681587560651169118663509412050066394815052936021223979271"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-37.77705672356517184937835295164453556498913303252724271691215564780459719470"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("137.70087556248931227876532575144504191693108683924786902505674311871685140800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-311.72468766289278751244167873028725267412977680278312051859849993755349858000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("511.24679128112096837423875276735646357386086403224153118196081493355880796200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-687.69702792488720143387763101613920716950152836894659515467184955111870724700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("829.09055557619773277153201541424732791228391594101613180539356376460906530000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-906.67556883761759119144339734345872385406981601833110610680243945196617211400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("863.23988279515629467219009455554599609695564774955725375711337575467810032600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-700.37718955506952165779246925908091030508123412802813106187016751364785945600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("495.84842847009709837548618485022243329167561710295186722949226664054303361100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-307.49512577944039191322332358612022792251918670092304811543750183524451060300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("142.92163545340421526365861071542027659143554694673554929974877824733260473200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-19.31075019974249281695001314578305393389661976831560477729541043029968645530"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-35.42389678687542349159085429311033037061651261095746807090649315454659711020"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("32.44472478885998336245698827148819308075084642463701991417768428456321519910"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-12.97271142346531917199152873167390275988083231450677228087810958984424846790"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.10336726562456364617075321297939313157799116307693031879047994718725361533"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.215454070733924659861657674199075159272461496572943747038111133916807431180"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.125076873025998884367293275645192665826157547026398718789437845293697450218"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0103152247942739012815455329995931706018816781048478764075881481121070428934"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000632428582946048424882721006475234390308064466530095906161174694249322311105"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000278764686901524008550509337752045901232947877228985594423383689960428632537"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000569803836285153459122322631284557498343961131423876580418354981637882246635"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000441839671114970335190048321139738477044887864798246264801711442171137680421"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000714802491411250263311395432961462470250092517743540216477594292648036570408"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 7) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("7.83555255872811652420708194699227564812880321923155066263002675188551650312"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-68.93144189415544000675178575437258773566065477015007536299582400232146657330"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("269.05084530980203113195209976663957867395958982717325865408524125280832289600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-609.20724183879537322285337615082333580989660439474364859024353018035946645100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("881.76862167288329121045005828312390919337410341070563414959329437576051276200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-865.08716643970594546719815251896043456283005565377418337268781988922266917400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("632.97787930272196253879414267424608924729579537423891361585357298689149584500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-382.49192892544806107967107677420182336459450422233847738473211880415489419400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("51.56641441749688691257145061609223937968957957563897087215371356736309599200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("476.09110714103691538203391357221546832760511254226534748414313636902906572500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-970.57824656189703500836118600041943699389979172697558754304893359616826066000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1129.04503509906141877125815880497121965193711448633760242286838210579239440000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1010.03090304703962359279554938202749376391098032905326508754718040588237804000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("827.10721123601323503307854258132213389426514427539892445355740294501216301600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-616.18164003837976580374414923629580236503935294323766247871764385789725455200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("356.91888665299329828378541153901250128644618483543100772119117850286192670900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-133.52394935860427189931791156205717267825075964749332862787915826632532923900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("21.94002100012019404144527346489003480219358689823929896317683112311592863680"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.69502949031117951496444168472697082874515564937581244488642154254744997400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.22233693926927989833058976676101529298211935367881160327330611362977023218"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.243917000692119383583915678923379880754017506303821621558764650571551691750"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0153855088662769439102973996146208075188236200845719957232671533824048761790"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00104913228216791853272658326910500670179817471111989137537944784605454771898"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000224836058331229111229619069684984372824683936236614925216433027243221835066"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000332116962946728334773864559940531738563382607925542513873526692874990639648"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000107475686000546477797319235583561376745354532533798623668423772676988174585"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 8) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("7.54960688822339828863999378130211115107233454769934866095750950044066864110"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-69.64335018913939576412750532175053097593146282468237041838535209525011079500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("287.62738150890773420089300813672822503003764015402682017757435224935102339200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-706.73754701102149477646316177625311732909677089373586648513230095487019075900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1177.44605142912275685331605707810452401861714128214534938401017832783574948000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1493.65509712888447960800673919759696151644981533694814393500245372102843458000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1658.35534024819665161123917470538298740518906057958085498478561548336905470000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1774.97012191343746012194081052068265568964145567960224351414437241219278396000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1784.12512252406968735163579655137194210741621555135274224751877746894409525000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1596.15013759874832367565454908792624435013153344056104405167995042995605546000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1294.87842318541656108750744374471145185200499138414568918290153915550984978000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-988.83467235968111377155392478265729751920701705649958745436470131875538876000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("689.66704696641391993630921163080325378181926796016541012035635061452929732200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-419.69730617117074092592055713546879516237193681933824681435866539141247425900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("227.80738878191733493720600320172052818250161128836771941990375971535089686000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-111.11796409308819226983125949342564517414825732596608930700760656952936161100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("40.19443810120569696285858753433708415600177908834568747073574318608759474100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.91792059950306926651430119033353633622113732985840244036194782614229968982"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.35533756319498030532906284051383779124200364840191901231906261851413833649"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.64973463461427566646558893739921141496585938147076501993510767086243184026"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.210933307392307199501252966945895447408339149689342782956931741370150254267"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0118181469959711297864759189693192594897107267351263521987717128479636953271"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00166832008560998294423971440046143918265510526709216268614254492975841760358"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000359960399029744056248273888253230981459983176116053582730091303462716930960"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000105526920365685108260660462141084882369839069051686223049397689800183455322"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000683200385904099418363562130595167945821162769743662314310034240089917492841"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 9) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.20505003861567011394067231344647893637847564329550367887681186357597624603"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-58.56645504853098766550134905340317870243260579145639275208040178526932370050"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("244.21338875508955935588425811438812427457999296948170249669130252684915021700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-592.00121422881665797081029294298226556332889632312076428918776482044056419900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("935.83883798382295862878655187263488883257992095069940720162185886844636534300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1070.04134277217209941069608841768441159120482934420543356273845894230382557000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1055.22848149919637141794358785954857337162302556268749973962161361211731374000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1077.87709508048227764719965364717319012422679016684137197779877347065587919000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1079.84553010800709048689467568224979315449213490504319509214561846839561023000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-909.07210621873438578205880244568413575768717508893273593436054423066636844000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("651.34858710014761262618216521874193874281211026897562234536865793145322519700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-457.83799566119363761546660688550395418970241445277522092347549225353673827100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("309.76860818899965620264934656056185819660289753982144311142670396948220345500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-165.17332619606861874818823388561165833646372925969907046409236334588737006800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("64.36460023183964610680737173822860851394300430996239129559691640194035450280"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-21.81925195904410301088997452499452793344229781102822411802597853821595862070"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.70987816583834887528727762977327608794555354259030464603411322315458032491"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.12012477609974627820032790014942916130826215990800053191225592823023213870"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.41707542957580268050903646486240388008805175493051843593484495999979780697"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.55314374584785171680308731725982270158371281797680529285657013298327299254"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.384116528497100269726445252348690123705919404254920353538891869983784142695"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0118756663548945587058921085727494958398593550092544335470975725373361134933"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00560801191403834230317024708819810653630256118877488149992512868367446594358"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000168863298975933200683541006085210976919654788572176120083523172920160215908"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000702368884519096062247768700675740067863675318587848764509402888807377333644"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000910021338458770684182677723795514188197183013650198912703110713825929499885"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 10) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.03204471314281361620436172860993718348048098798259830037497869722564324408"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-19.39665779270637271197815390366866221017887466456155522938642838644377623170"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("84.39519889483751381060448991759860643934416288701819870293485348031111678600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-225.93653823935280620043647247700590736347878865997028224628700438872489124900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("429.09470449105242027094920090767356206181107874783293562031855795674540336000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-635.22241752596063241363571132920423111589738106514102338073077249645227164900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("778.35654680554367290994709844961509436329929173664221414820797079265534104900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-825.57888681650695755069404722936648404036390595346071684154667140205899581400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("820.86701316070300215711624263370329545679945220152016165604116497162621943800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-838.00594852735561618490718834843576332267897766955677203329263194173445408300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("846.41624411937977897579029601634249128805349858445717455832716294555864902500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-756.43979217912372920397826846127055236422213608124884373684460009804242802200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("597.98072611129726849283643705505721881864863625292975587189812590758721018400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-464.96181147230317359880791138494390058432679338003629816618633802082886197700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("355.51862533374956883481354353388092712174852473789983192068789421486091538400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-235.37971349199656518700162583910157649836837484774547798711824684202151115700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("132.29716704430755790362823208197819789457340031860010362902088456007781211600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-71.87354899110919395713836059516566325587269396430109303014403933780264172090"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("37.29248373020173707451272057860274355374999201121543162524309965457643352150"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-14.04817434412944163979531519740059165943726494501644870873410209073124183660"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.60745911365218712785836635558941735911206189533873236470344886669699910838"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0543645649464435164847209914399195207149789580566453105860414107221369165038"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0690090709977073313739788485731020686097132104467534026187427787191497374569"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000971327966803672069290270496714838209254089051099247834705750725429421474607"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000175060669244915542274214040537534422700016855593378309967441792972141821778"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000454201283534597503030935884752199947078896835850213184419062952049362978252"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 11) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.27115042001770757342790580276725599737973526276595894891693693144453081333"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-12.20155249712689490713523680284407229529835475760492745017650272595157073840"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("51.23324319235233061317480157420850343391523283977889617744950185481521928880"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-122.94995817305462609579795659014989927849571013175696402717688054750353836700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("186.48509100156140575637738663903588922180843570634354620282154495701806571100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-194.07448086588021018245234658153261441759722529638841725717115567921577062400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("167.86866563418224671177891910686936996723856918707191383980497089062492466500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-163.73194055481597452012500435897749151331279668776584781713972098055426014000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("171.61705970327542643733736274773439348119447474649912026659814882053948896400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-149.52373587625510655685072490035410183051561878699286314353687011498822254500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("110.83963967429849116381035147455824238567048771273770112763575455632533722600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-86.00782150891480030613225128365285559176275614273843802468963964882341220180"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("67.02925129175963984371834894406440307377952153327523895227597589690079234370"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-43.73925987707458484571443317553902969922556666607444419305258116854809584890"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("25.59369785187796149597672205308510544347264131510511482728670598446185457330"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-15.68018534623854167865753994586968580089803038651229171712344769674882728010"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.67101479337829604724549631142381262698058260107053126173973190165021528756"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.75861505024024002675376566574475255211823912083547822262099741013249261042"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.54759756025881232336945003625817637725576271772356562382087334473774930037"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.630476888107043555221797973970574912788012829526634744673511131029200828552"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.138289110458663700735511423590028378928536403452989070482014794553004832387"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0107951927880023305749242734468149776729151693312718188651043715681726172060"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00754991006043983586111967321038913970058172016189708501693056751092430574556"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000768855369034014413090954158857823182271817483052059631674255096393926162955"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000423822734359358265360311498568469600739757885517978000979834786982597738573"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000220476848184896613372739980059823724812480482106220385749059723040813819200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 12) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.318010404217068952718034999205043880576086312876319450942332822179758832029"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.06102355351185926427319739531099202637190548705353100594409222193573135420"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("12.80258811164971729344541416108618061243147012390344502415152454109791488170"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-30.20065038067138441549116683827153320363339703988815649029826192469828800770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("43.77746941222910636253894420655558692365422509195889774642773187854112783890"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-41.06426623869672590682998039683326333327190758069356155782396545157455445810"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("30.06896895338094213763603114520529005887555601480166742767460715185260403040"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-27.99669565569003172852864940058873702820215437394869573794696284139245305100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("31.40904224961940872590760582915710475701943523191305275220782176766892814960"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-26.61147707975226987062278644044150684817213866306112594162111544688454753810"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("17.28072628404804003669507530790723055238159750081532699647611742207459371760"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-13.03306623382955516457538291782723729027040840647527902140735049489731225810"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("10.92329406410031923111395110524973244956738959185047643214517216152345088230"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.76457200306911915343728115159545396428972131599592522482710193109520612768"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.38673622817880270826803177141868102896290888908534559567608966529440899137"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.13778155318707274308581153289738935049994670784897895468735053193538091817"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.27222976665752962431763512471169495246258962134804638636049901609786075729"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.460207043844736395307656318205719088747297298981176544972613522761762760908"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.144411215423571925617311283427170089385196189708352755544769370328688396733"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0739504408724418236152196080232313887266756275356214749508197882784413005326"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0162851961244162892390054615243955015081698723875469655847838117885736756969"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00670013886238182672051081804470702049361779245043541997098482037556851799328"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00289413784660480308858813839825464801550958078392680116427992804058429400263"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000118226656863479167736819869491754498449905525596694943882369054828973203042"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000407408378246154606805470217575324383090557556739356701916389328686441606510"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000426014978607563594967116716485946096193409828602942187827734146599194530321"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 13) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0395024226975886260436015280169399958114854435612876899457087608537691328646"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.380760085660020846754522453148461762110774614299327773117958074184114684427"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.58439192679626572323538988717033413533100806730431629991619477048720282652"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.66849225666251646147181612467387048084530225694986405715851065686876160983"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.05702740810994469396903380618346647120804579341221278933287204214673197742"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.15893692928322415963268762106489569036113711224820559316556226723553567830"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.30643665371429659490852199582838744397805404586749517662546347864184908967"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.03944535400713878630113040918470478717641098007862715614235550735403115717"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.75044728818668477407502449063310312583442217870494512078004809643451540717"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.26532298526228934105124417738592200001859007857791140112570041681664957967"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.10133212413495876761478507881985817641573463205155919865756735554719635510"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.777595611788659331793825514823424823892310615830315312836845770694620189298"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.813470142541264561929778203493572597954340880125476192701684325142924496713"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.450006561808299358517226504782492541004402170854054357437291488004013112805"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.118500916380668803483753735483540194370353148612714533622232357622587131639"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0854382963811873726676785990040937155967645307765440929619971688798210204625"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0688056358160580011265953288213120273922091465442762386643516670175176351229"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00316181231306575845649567960204080415859090715018690879061132888462092674318"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0134704997550951956780703608930294861647935543468679644642083630288728953920"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00294686750299967882443641101664969682445375118992583309612547894575220278859"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00215928663487753773644923527389606027569391521127003378892960294361464727064"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00292603166127365869089828154580427557123447155142574321458389044685037686218"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00111176154864526774012502920031740858426807693116963525197176827996288733339"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000109753902477691254708467520181547449682815029110458229838831733837259897127"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000427869999580130042052373770473160246635622398207650727324687442110256565531"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000903945795865567602923370485955445191692438306505200188872053733298346930198"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-        }
-    }
-    if constexpr (p == 15) {
-        if constexpr (std::is_same_v<Real, float>) {
-            if constexpr (order == 0) {
-                return {0x0p+0f, 0x1.d99d62p-12f, 0x1.0d2f98p-4f, 0x1.4a5392p-1f, 0x1.1fc50ep-1f, -0x1.d49776p-2f, 0x1.3575a8p-2f, -0x1.7e644ap-3f, 0x1.a17858p-4f, -0x1.7135a6p-5f, 0x1.d8cfdcp-7f, -0x1.57e158p-9f, -0x1.5f6332p-15f, 0x1.10a458p-13f, -0x1.592264p-16f, 0x1.899798p-18f, -0x1.4f8412p-18f, 0x1.74953ep-20f, -0x1.f7cb1ap-26f, -0x1.c92be2p-26f, -0x1.3b9a58p-35f, -0x1.6a58cep-35f, 0x1.4bf1ecp-37f, 0x1.697068p-44f, -0x1.513d7ap-49f, -0x1.b3943cp-57f, 0x1.54d33p-67f, -0x1.3f6e1ep-80f, -0x1.d0d882p-104f, -0x0p+0f};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.af6738p-9f, 0x1.c7ad46p-3f, 0x1.9756ccp-1f, -0x1.519166p+0f, 0x1.6cc6e8p-2f, -0x1.8cf37ep-4f, 0x1.9a3fa2p-4f, -0x1.0a50bep-3f, 0x1.df3f5p-4f, -0x1.2d4b7ep-4f, 0x1.0681e4p-5f, -0x1.1b50d6p-7f, 0x1.49acd2p-11f, 0x1.16651ap-11f, -0x1.c26d2p-13f, 0x1.300212p-16f, 0x1.49fbecp-17f, -0x1.8781a4p-19f, 0x1.5ed0aep-24f, 0x1.da4a76p-25f, -0x1.7e23c8p-29f, -0x1.bd8f2cp-35f, 0x1.1c615p-37f, -0x1.c1b8b4p-44f, -0x1.95157p-52f, 0x1.d1f8dep-60f, -0x1.34635ep-74f, -0x1.c0c6d2p-97f, 0x0p+0f};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0f, 0x1.52aa16p-6f, 0x1.2f3864p-1f, -0x1.92da3ep-2f, -0x1.010e6cp+1f, 0x1.ba5e58p+1f, -0x1.6efa1ap+1f, 0x1.e2fp+0f, -0x1.e9e848p-1f, 0x1.3e7bdp-2f, -0x1.3f21e6p-6f, -0x1.00e092p-5f, 0x1.93252ep-8f, 0x1.0cb53cp-7f, -0x1.6ecc66p-8f, 0x1.1da3c8p-10f, 0x1.0f705cp-12f, -0x1.687f18p-13f, 0x1.03bf74p-15f, -0x1.0a570cp-20f, -0x1.b60c86p-22f, 0x1.2f36c8p-24f, -0x1.ab6b4ep-30f, -0x1.b77dbep-33f, 0x1.02e06ap-39f, 0x1.f900dcp-46f, -0x1.5cc6acp-54f, 0x1.79a9bep-67f, 0x1.12cb1cp-88f, 0x0p+0f};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0f, 0x1.bde47ep-4f, 0x1.ff6e3ap-1f, -0x1.0edf78p+2f, 0x1.788ebp+2f, -0x1.0b9e58p+2f, 0x1.57d72ap+1f, -0x1.5aec5ap+1f, 0x1.66bep+1f, -0x1.257b74p+1f, 0x1.61e6a2p+0f, -0x1.1d6618p-1f, 0x1.7634aep-4f, 0x1.aae5ecp-5f, -0x1.66a2dep-5f, 0x1.9ee5c4p-7f, 0x1.cee452p-12f, -0x1.7d0e64p-10f, 0x1.95a9bcp-12f, -0x1.ac68b8p-17f, -0x1.4a3e54p-17f, 0x1.45a5b2p-20f, -0x1.a0585ep-28f, -0x1.4a4abp-28f, 0x1.818dc4p-34f, 0x1.bc8ec6p-41f, -0x1.1c50f4p-48f, 0x1.541ee6p-61f, 0x1.eef3c6p-82f, -0x0p+0f};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0f, 0x1.da9efcp-2f, -0x1.0a9636p-2f, -0x1.6ead78p+2f, 0x1.1fb0b8p+4f, -0x1.a26b2p+4f, 0x1.5a3628p+4f, -0x1.c3b938p+2f, -0x1.0393f6p+3f, 0x1.ce0e34p+3f, -0x1.3371f4p+3f, 0x1.04744cp-2f, 0x1.5d5bbap+2f, -0x1.56903ap+2f, 0x1.4f3674p+1f, -0x1.16f1cp-1f, -0x1.0ca608p-3f, 0x1.fd1e64p-4f, -0x1.12756ap-5f, 0x1.031ce4p-9f, 0x1.dbc5a2p-11f, -0x1.6e5758p-13f, 0x1.338c12p-19f, 0x1.ec833cp-21f, -0x1.31ee1ep-26f, -0x1.068ccep-32f, 0x1.ab486ep-40f, -0x1.971ac6p-52f, -0x1.28365cp-71f, 0x0p+0f};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0f, 0x1.8a28cp+0f, -0x1.0b8eccp+3f, 0x1.301d18p+4f, -0x1.80a5fep+4f, 0x1.4a39e4p+4f, -0x1.114828p+4f, 0x1.18e244p+4f, -0x1.390866p+4f, 0x1.80446cp+4f, -0x1.0a407ap+5f, 0x1.52509ep+5f, -0x1.4b4686p+5f, 0x1.c80f14p+4f, -0x1.82ded4p+3f, 0x1.7610a2p+0f, 0x1.b0a89ap+0f, -0x1.2b516ep+0f, 0x1.48818ap-2f, -0x1.16dd92p-6f, -0x1.957d58p-7f, 0x1.613bdp-9f, -0x1.0adbcp-14f, -0x1.449056p-16f, 0x1.238bd6p-21f, 0x1.0b863cp-27f, -0x1.2dac52p-34f, 0x1.a8ab5ap-46f, 0x1.34fcf8p-64f, -0x0p+0f};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0f, 0x1.e156f6p+1f, -0x1.d9350cp+4f, 0x1.b03e3ap+6f, -0x1.f51dfap+7f, 0x1.b1d9eep+8f, -0x1.3c90b8p+9f, 0x1.a1026p+9f, -0x1.ee82dcp+9f, 0x1.fcf16ap+9f, -0x1.beee0ep+9f, 0x1.545f4ap+9f, -0x1.c39ca4p+8f, 0x1.d17e6ep+7f, -0x1.8d05e2p+5f, -0x1.a57ddap+5f, 0x1.065bfcp+6f, -0x1.1a783cp+5f, 0x1.2e9f2cp+3f, -0x1.3cad9ap-2f, -0x1.1b4b3ap-1f, 0x1.15a314p-3f, -0x1.5c66a6p-8f, -0x1.5db56p-10f, 0x1.c57be6p-15f, 0x1.c9738p-21f, -0x1.63f652p-27f, 0x1.769768p-38f, 0x1.108b38p-55f, -0x0p+0f};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0f, 0x1.d870dep+2f, -0x1.0c2b8cp+6f, 0x1.10bd38p+8f, -0x1.4441dap+9f, 0x1.eaed48p+9f, -0x1.dea056p+9f, 0x1.0ea6dep+9f, 0x1.3bb922p+5f, -0x1.7c03d4p+9f, 0x1.b77df6p+10f, -0x1.59dd46p+11f, 0x1.92ad5ep+11f, -0x1.7716eap+11f, 0x1.34cd94p+11f, -0x1.d21086p+10f, 0x1.27e204p+10f, -0x1.0ee014p+9f, 0x1.13ffcp+7f, 0x1.9021aap+1f, -0x1.cb9506p+3f, 0x1.f11cd6p+1f, -0x1.a3fefep-3f, -0x1.a953dap-5f, 0x1.9718bep-9f, 0x1.ad424ap-15f, -0x1.eb70cep-21f, 0x1.72006ap-31f, 0x1.0d3062p-47f, 0x0p+0f};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0f, 0x1.155158p+3f, -0x1.4fec3ap+6f, 0x1.70dec4p+8f, -0x1.e94cfep+9f, 0x1.bf0b1p+10f, -0x1.392918p+11f, 0x1.79ccf6p+11f, -0x1.ab6c9p+11f, 0x1.c47edap+11f, -0x1.af1006p+11f, 0x1.72a85ap+11f, -0x1.2846e6p+11f, 0x1.b3d87ep+10f, -0x1.1ae106p+10f, 0x1.41e16ep+9f, -0x1.46003p+8f, 0x1.0818e6p+7f, -0x1.8ef0b6p+4f, -0x1.6eb8ecp+3f, 0x1.3aba04p+3f, -0x1.588d6ep+1f, 0x1.5ca064p-3f, 0x1.72c884p-5f, -0x1.2b7b9ap-8f, -0x1.359ad6p-14f, 0x1.0cff08p-19f, -0x1.207536p-29f, -0x1.a3ad9ep-45f, -0x0p+0f};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0f, 0x1.174fb2p+3f, -0x1.5cf63cp+6f, 0x1.859702p+8f, -0x1.008e38p+10f, 0x1.c03c1cp+10f, -0x1.1e0d3p+11f, 0x1.33504ep+11f, -0x1.4498a4p+11f, 0x1.500c42p+11f, -0x1.2d6f92p+11f, 0x1.c5bd8cp+10f, -0x1.3b7208p+10f, 0x1.a4b182p+9f, -0x1.c03584p+8f, 0x1.1254d6p+7f, 0x1.be195p+2f, -0x1.6abf52p+5f, 0x1.bdfa94p+5f, -0x1.7a9c1p+5f, 0x1.86920ep+4f, -0x1.a9adfcp+2f, 0x1.133764p-1f, 0x1.191c64p-3f, -0x1.88d184p-6f, -0x1.aee4f4p-12f, 0x1.15e5eap-16f, -0x1.bc4492p-26f, -0x1.431c04p-40f, -0x0p+0f};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0f, 0x1.57dd2p+2f, -0x1.b426bap+5f, 0x1.ef50bp+7f, -0x1.4da8e6p+9f, 0x1.2d889ap+10f, -0x1.9456ecp+10f, 0x1.ca1f76p+10f, -0x1.f2eaf2p+10f, 0x1.0a60e2p+11f, -0x1.07fe76p+11f, 0x1.e2b37ep+10f, -0x1.a28fdp+10f, 0x1.5596d2p+10f, -0x1.027612p+10f, 0x1.70f45ap+9f, -0x1.edf5a6p+8f, 0x1.27b1e2p+8f, -0x1.3be692p+7f, 0x1.3b71fp+6f, -0x1.11985ep+5f, 0x1.3b5a98p+3f, -0x1.c32c18p-1f, -0x1.5d8e8ap-2f, 0x1.3b1b46p-4f, 0x1.23706ep-10f, -0x1.9c26fcp-14f, 0x1.96293ap-23f, 0x1.27428ap-36f, 0x0p+0f};
-            }
-            if constexpr (order == 11) {
-                return {0x0p+0f, 0x1.82ba18p+1f, -0x1.ee321ap+4f, 0x1.174e6p+7f, -0x1.6e81d6p+8f, 0x1.368de4p+9f, -0x1.710674p+9f, 0x1.661d22p+9f, -0x1.6833b8p+9f, 0x1.833c1cp+9f, -0x1.704d0cp+9f, 0x1.2a287cp+9f, -0x1.d79574p+8f, 0x1.7a6624p+8f, -0x1.0dddap+8f, 0x1.4f8242p+7f, -0x1.9b8d6ep+6f, 0x1.e6b9cp+5f, -0x1.d872a6p+4f, 0x1.82e4e6p+3f, -0x1.3c81bp+2f, 0x1.87117ep+0f, -0x1.f2d1dcp-6f, -0x1.327c0ep-3f, 0x1.13b8cap-5f, -0x1.094894p-13f, -0x1.78471ap-14f, 0x1.31d268p-23f, 0x1.bc3afp-36f, 0x0p+0f};
-            }
-            if constexpr (order == 12) {
-                return {0x0p+0f, 0x1.229018p+0f, -0x1.74b098p+3f, 0x1.a3d6fep+5f, -0x1.0ee9fep+7f, 0x1.b7ec28p+7f, -0x1.dcbffep+7f, 0x1.8f9512p+7f, -0x1.7421b2p+7f, 0x1.a17e1ep+7f, -0x1.8b13bap+7f, 0x1.210062p+7f, -0x1.a9798ep+6f, 0x1.62f522p+6f, -0x1.f0d146p+5f, 0x1.0b054p+5f, -0x1.2e7f82p+4f, 0x1.776b1ap+3f, -0x1.390aacp+2f, 0x1.0e68eap+0f, -0x1.1d9e68p-2f, 0x1.1e142p-5f, 0x1.626282p-3f, -0x1.00510ep-3f, 0x1.dda066p-6f, -0x1.397e42p-10f, -0x1.5e278p-13f, 0x1.93d63ep-23f, 0x1.24c486p-34f, -0x0p+0f};
-            }
-            if constexpr (order == 13) {
-                return {0x0p+0f, 0x1.2dba82p-3f, -0x1.83ba9p+0f, 0x1.bc6ce4p+2f, -0x1.2c97bep+4f, 0x1.0e0692p+5f, -0x1.5f4706p+5f, 0x1.6ea3fcp+5f, -0x1.5a777ep+5f, 0x1.424978p+5f, -0x1.3091p+5f, 0x1.23e442p+5f, -0x1.07fd36p+5f, 0x1.a8f488p+4f, -0x1.499324p+4f, 0x1.0a96d4p+4f, -0x1.8f60cep+3f, 0x1.003bccp+3f, -0x1.433efp+2f, 0x1.a65b7ep+1f, -0x1.d36032p+0f, 0x1.a4a1aep-1f, -0x1.88e9f6p-2f, 0x1.6764fap-3f, -0x1.91c36cp-5f, 0x1.07d03ep-8f, 0x1.362d3ep-11f, -0x1.92dbfep-20f, -0x1.22ff8p-30f, 0x0p+0f};
-            }
-            if constexpr (order == 14) {
-                return {0x0p+0f, 0x1.8dd6e2p-6f, -0x1.ffb4dep-3f, 0x1.1f8df8p+0f, -0x1.6eae32p+1f, 0x1.200cfep+2f, -0x1.1f2876p+2f, 0x1.90990cp+1f, -0x1.3d166cp+1f, 0x1.74d60ap+1f, -0x1.680266p+1f, 0x1.e76ba8p+0f, -0x1.60830ap+0f, 0x1.48f2a8p+0f, -0x1.e7d09ep-1f, 0x1.1252eep-1f, -0x1.6e9dp-2f, 0x1.0a88fcp-2f, -0x1.16ea72p-3f, 0x1.018afap-4f, -0x1.2fa054p-5f, 0x1.2375eep-6f, -0x1.73b10cp-8f, 0x1.1decc8p-9f, -0x1.b8713ap-11f, 0x1.732712p-14f, 0x1.5deb76p-16f, -0x1.927126p-23f, -0x1.209992p-32f, 0x0p+0f};
-            }
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0, 0x1.d99d611c0465dp-12, 0x1.0d2f985427a1ep-4, 0x1.4a539266aac6ep-1, 0x1.1fc50d04f7f08p-1, -0x1.d497750272bfap-2, 0x1.3575a87d9c163p-2, -0x1.7e644ab118887p-3, 0x1.a1785765bb949p-4, -0x1.7135a6ada8b52p-5, 0x1.d8cfdcbb16189p-7, -0x1.57e157b5bcea8p-9, -0x1.5f633204e95ap-15, 0x1.10a4589d9f87dp-13, -0x1.592264d16e622p-16, 0x1.89979784d7185p-18, -0x1.4f841169a1badp-18, 0x1.74953d3967ccep-20, -0x1.f7cb1acefcf43p-26, -0x1.c92be21aef0cap-26, -0x1.3b9a57c4ce7e8p-35, -0x1.6a58cec0fa225p-35, 0x1.4bf1eb8cd4c9cp-37, 0x1.697067f1715a1p-44, -0x1.513d790bd243p-49, -0x1.b3943c02986a6p-57, 0x1.54d330be5783ep-67, -0x1.3f6e1e631364cp-80, -0x1.d0d882f8587b5p-104, -0x0p+0};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0, 0x1.af673717274afp-9, 0x1.c7ad45d086ea5p-3, 0x1.9756cb092ee07p-1, -0x1.51916657c1834p+0, 0x1.6cc6e8f062405p-2, -0x1.8cf37d6182ca1p-4, 0x1.9a3fa2f41d495p-4, -0x1.0a50be22f2b87p-3, 0x1.df3f4f6c19d45p-4, -0x1.2d4b7e715db6cp-4, 0x1.0681e4c20b9fdp-5, -0x1.1b50d689cbed9p-7, 0x1.49acd134a254cp-11, 0x1.16651955943e4p-11, -0x1.c26d1f2c70c87p-13, 0x1.3002118e762a1p-16, 0x1.49fbecfd7d9c7p-17, -0x1.8781a4a6a5f7dp-19, 0x1.5ed0ad164acd2p-24, 0x1.da4a7558674aep-25, -0x1.7e23c7237f3f9p-29, -0x1.bd8f2cef8c9fp-35, 0x1.1c61501fa1048p-37, -0x1.c1b8b33989e02p-44, -0x1.95156f39cb33ap-52, 0x1.d1f8ddb7d0199p-60, -0x1.34635de67ce8cp-74, -0x1.c0c6d283f741ep-97, 0x0p+0};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0, 0x1.52aa167437ed4p-6, 0x1.2f386450cd36p-1, -0x1.92da3e0f4795fp-2, -0x1.010e6c23362c3p+1, 0x1.ba5e5707337cfp+1, -0x1.6efa1a351e689p+1, 0x1.e2efff792ca6dp+0, -0x1.e9e84815ce29ap-1, 0x1.3e7bcfc83dd35p-2, -0x1.3f21e5e83db9bp-6, -0x1.00e091b8310d8p-5, 0x1.93252ea5d40eep-8, 0x1.0cb53bda124f5p-7, -0x1.6ecc6596fdeb9p-8, 0x1.1da3c88de4594p-10, 0x1.0f705c9109b89p-12, -0x1.687f176415b5ap-13, 0x1.03bf749271ea1p-15, -0x1.0a570c997b8f7p-20, -0x1.b60c856b75c7p-22, 0x1.2f36c8024d478p-24, -0x1.ab6b4d2a0c9ebp-30, -0x1.b77dbd4d624bbp-33, 0x1.02e06a0b52529p-39, 0x1.f900db818405cp-46, -0x1.5cc6aba4a367p-54, 0x1.79a9be1badafp-67, 0x1.12cb1c6610cf6p-88, 0x0p+0};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0, 0x1.bde47de89537fp-4, 0x1.ff6e39e05bc19p-1, -0x1.0edf7812c7e6fp+2, 0x1.788eafbfef57p+2, -0x1.0b9e58d049e2bp+2, 0x1.57d72a54d9b7ep+1, -0x1.5aec59993d64cp+1, 0x1.66be004fbc258p+1, -0x1.257b730e2148dp+1, 0x1.61e6a248fa766p+0, -0x1.1d66170848573p-1, 0x1.7634ae9385e7dp-4, 0x1.aae5eb36cf234p-5, -0x1.66a2dd81189a5p-5, 0x1.9ee5c38dff3c6p-7, 0x1.cee452b55c63p-12, -0x1.7d0e63753adf8p-10, 0x1.95a9bb14ccec1p-12, -0x1.ac68b8496deeap-17, -0x1.4a3e531dccd5ap-17, 0x1.45a5b2adacfeep-20, -0x1.a0585e72874e5p-28, -0x1.4a4aaf36fdaecp-28, 0x1.818dc3c36642cp-34, 0x1.bc8ec635290e4p-41, -0x1.1c50f4adb4d49p-48, 0x1.541ee5efeba28p-61, 0x1.eef3c669427bap-82, -0x0p+0};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0, 0x1.da9efb84cd102p-2, -0x1.0a963523c781p-2, -0x1.6ead78b2a7f87p+2, 0x1.1fb0b7ee7fe9bp+4, -0x1.a26b20f9bdefp+4, 0x1.5a362701692b6p+4, -0x1.c3b93743ed5e2p+2, -0x1.0393f54066e2bp+3, 0x1.ce0e335b9b5dp+3, -0x1.3371f4378fc26p+3, 0x1.04744c732a897p-2, 0x1.5d5bbaac2d3ddp+2, -0x1.56903abc9d373p+2, 0x1.4f367450bb029p+1, -0x1.16f1bf1e47dd8p-1, -0x1.0ca6089fc41eep-3, 0x1.fd1e6437298dfp-4, -0x1.127569c6d3d2p-5, 0x1.031ce43d6f2aap-9, 0x1.dbc5a12350174p-11, -0x1.6e57586c99db3p-13, 0x1.338c12c9a95b4p-19, 0x1.ec833bdc8d6abp-21, -0x1.31ee1e222a83p-26, -0x1.068cce25031dp-32, 0x1.ab486d191520ep-40, -0x1.971ac61147c4cp-52, -0x1.28365b5992262p-71, 0x0p+0};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0, 0x1.8a28bf1f4bafp+0, -0x1.0b8ecb513e671p+3, 0x1.301d17ac5e1c7p+4, -0x1.80a5fd5ebbea5p+4, 0x1.4a39e3e1048d6p+4, -0x1.1148278e9d9a1p+4, 0x1.18e244d79a033p+4, -0x1.3908669ba0779p+4, 0x1.80446c71adb15p+4, -0x1.0a40794798e41p+5, 0x1.52509dd04c4f7p+5, -0x1.4b468531c5b1ap+5, 0x1.c80f1430e334ap+4, -0x1.82ded3c89e7eap+3, 0x1.7610a167089f2p+0, 0x1.b0a89a8818c06p+0, -0x1.2b516da5d081p+0, 0x1.488189c0e6323p-2, -0x1.16dd91fce8d2fp-6, -0x1.957d5757f4d58p-7, 0x1.613bcf2c2fc6ap-9, -0x1.0adbc024da551p-14, -0x1.44905597a8908p-16, 0x1.238bd55115864p-21, 0x1.0b863bc593a1dp-27, -0x1.2dac52b5d35bcp-34, 0x1.a8ab5a61388b2p-46, 0x1.34fcf88bcfb4p-64, -0x0p+0};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0, 0x1.e156f58145abap+1, -0x1.d9350b2238c2cp+4, 0x1.b03e3957ecd6ap+6, -0x1.f51dfa789d879p+7, 0x1.b1d9ee3321d94p+8, -0x1.3c90b7e3ca1dcp+9, 0x1.a1025f9df5666p+9, -0x1.ee82dbab6ab1p+9, 0x1.fcf169933904cp+9, -0x1.beee0dc0c8ddbp+9, 0x1.545f49e00f496p+9, -0x1.c39ca355bd5d3p+8, 0x1.d17e6e268802dp+7, -0x1.8d05e2b81cf72p+5, -0x1.a57ddae4deceep+5, 0x1.065bfb9cfed1p+6, -0x1.1a783beefce88p+5, 0x1.2e9f2c1581a69p+3, -0x1.3cad9a2427052p-2, -0x1.1b4b3a7aa70e8p-1, 0x1.15a31469a9cep-3, -0x1.5c66a63c93474p-8, -0x1.5db560cc8a8d9p-10, 0x1.c57be52a95f9ap-15, 0x1.c9738067c590ap-21, -0x1.63f652c472259p-27, 0x1.769767db4423bp-38, 0x1.108b386e39e95p-55, -0x0p+0};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0, 0x1.d870debcc05c4p+2, -0x1.0c2b8b0b28194p+6, 0x1.10bd374d63551p+8, -0x1.4441daef321d4p+9, 0x1.eaed48222cc9cp+9, -0x1.dea055aad4ecbp+9, 0x1.0ea6de87556eap+9, 0x1.3bb921604519dp+5, -0x1.7c03d4dcf5514p+9, 0x1.b77df6c77230cp+10, -0x1.59dd45c186fb1p+11, 0x1.92ad5ee85458dp+11, -0x1.7716e9b298972p+11, 0x1.34cd942cd473ap+11, -0x1.d2108687fa36fp+10, 0x1.27e2041912518p+10, -0x1.0ee0131c1b04fp+9, 0x1.13ffc016f56cap+7, 0x1.9021a9dd4e12bp+1, -0x1.cb9505a70965bp+3, 0x1.f11cd618c3359p+1, -0x1.a3fefe1a942d4p-3, -0x1.a953da883746ep-5, 0x1.9718bee3af729p-9, 0x1.ad4249f39958ep-15, -0x1.eb70cd1aa4051p-21, 0x1.72006a07a097fp-31, 0x1.0d30627e6a2adp-47, 0x0p+0};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0, 0x1.155158ac6ea98p+3, -0x1.4fec3a6a32c1fp+6, 0x1.70dec41eaf97dp+8, -0x1.e94cfecb1efa1p+9, 0x1.bf0b100d34d04p+10, -0x1.39291803fcf48p+11, 0x1.79ccf50afb46ep+11, -0x1.ab6c90991611bp+11, 0x1.c47ed9a17b9cdp+11, -0x1.af1005783c9c1p+11, 0x1.72a859cabb472p+11, -0x1.2846e6b9b14f5p+11, 0x1.b3d87dff6a955p+10, -0x1.1ae10527ae494p+10, 0x1.41e16e9c43533p+9, -0x1.460030c5bf207p+8, 0x1.0818e6dd9acdcp+7, -0x1.8ef0b66c7662cp+4, -0x1.6eb8ec2d2fcfp+3, 0x1.3aba0303f01c4p+3, -0x1.588d6d239648ep+1, 0x1.5ca063a2897a3p-3, 0x1.72c884e06d39ap-5, -0x1.2b7b99da7239bp-8, -0x1.359ad5ec914c6p-14, 0x1.0cff089d4d593p-19, -0x1.207535755ab2fp-29, -0x1.a3ad9d559345cp-45, -0x0p+0};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0, 0x1.174fb1d673064p+3, -0x1.5cf63b4072a08p+6, 0x1.859702b93092p+8, -0x1.008e38c64d405p+10, 0x1.c03c1b8df613fp+10, -0x1.1e0d30516cd0dp+11, 0x1.33504e2e62ab9p+11, -0x1.4498a39b45dd3p+11, 0x1.500c422b7e4d6p+11, -0x1.2d6f916f2f064p+11, 0x1.c5bd8b8beccdbp+10, -0x1.3b7208dc18507p+10, 0x1.a4b1819107c72p+9, -0x1.c03583e492981p+8, 0x1.1254d5dd1a3c8p+7, 0x1.be19509979c25p+2, -0x1.6abf524121ea4p+5, 0x1.bdfa9494723d3p+5, -0x1.7a9c102bdb495p+5, 0x1.86920d3d07ed2p+4, -0x1.a9adfb25c4f27p+2, 0x1.1337641b89dbcp-1, 0x1.191c64622c1b1p-3, -0x1.88d18423866c2p-6, -0x1.aee4f466bb969p-12, 0x1.15e5e9747fe1cp-16, -0x1.bc4491eee0fddp-26, -0x1.431c03e754cd9p-40, -0x0p+0};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0, 0x1.57dd202e5e84bp+2, -0x1.b426b94987909p+5, 0x1.ef50af36bc94ap+7, -0x1.4da8e644667e7p+9, 0x1.2d889ab089911p+10, -0x1.9456ec86efc74p+10, 0x1.ca1f75d29c178p+10, -0x1.f2eaf24b48be9p+10, 0x1.0a60e2fdcea78p+11, -0x1.07fe75c2d8539p+11, 0x1.e2b37ed5f4462p+10, -0x1.a28fcff6e684bp+10, 0x1.5596d2be7c1f8p+10, -0x1.02761175eccb5p+10, 0x1.70f45a3e9b6c8p+9, -0x1.edf5a5b354e13p+8, 0x1.27b1e13298bb4p+8, -0x1.3be69243ef2c3p+7, 0x1.3b71f0120f2a4p+6, -0x1.11985d9404f45p+5, 0x1.3b5a9762f053bp+3, -0x1.c32c18767db72p-1, -0x1.5d8e89b8ba2f4p-2, 0x1.3b1b46a97c2fbp-4, 0x1.23706d03f6f74p-10, -0x1.9c26fc84f3ff6p-14, 0x1.962939a138e2bp-23, 0x1.27428a5934f9ep-36, 0x0p+0};
-            }
-            if constexpr (order == 11) {
-                return {0x0p+0, 0x1.82ba18a281555p+1, -0x1.ee321ac782e81p+4, 0x1.174e5f65a44a6p+7, -0x1.6e81d57c4c979p+8, 0x1.368de3361fae5p+9, -0x1.7106731d7c871p+9, 0x1.661d220cefa1p+9, -0x1.6833b778e773bp+9, 0x1.833c1b7a24cc4p+9, -0x1.704d0cf5b403fp+9, 0x1.2a287b4a8744cp+9, -0x1.d795731af32d5p+8, 0x1.7a6623bbe9af8p+8, -0x1.0ddd9fa1ad022p+8, 0x1.4f824182bb441p+7, -0x1.9b8d6efd833c4p+6, 0x1.e6b9bfc912a61p+5, -0x1.d872a65489bc7p+4, 0x1.82e4e50171641p+3, -0x1.3c81b080d7c59p+2, 0x1.87117e04fd822p+0, -0x1.f2d1dbd395099p-6, -0x1.327c0d249414p-3, 0x1.13b8c9585145fp-5, -0x1.094893076dab2p-13, -0x1.784719262e6dap-14, 0x1.31d26875ab45fp-23, 0x1.bc3aef2e9698bp-36, 0x0p+0};
-            }
-            if constexpr (order == 12) {
-                return {0x0p+0, 0x1.229017de89889p+0, -0x1.74b098d7b2942p+3, 0x1.a3d6fe58853c2p+5, -0x1.0ee9fe2c639a7p+7, 0x1.b7ec28edec454p+7, -0x1.dcbffedb3a508p+7, 0x1.8f9512e48d1c4p+7, -0x1.7421b1a880459p+7, 0x1.a17e1d21e73d2p+7, -0x1.8b13badbca1d9p+7, 0x1.210062e92f489p+7, -0x1.a9798d44da6c2p+6, 0x1.62f521d1972a8p+6, -0x1.f0d14679f69cp+5, 0x1.0b0540b21cf09p+5, -0x1.2e7f81d72375p+4, 0x1.776b19bc1de7bp+3, -0x1.390aaca35a349p+2, 0x1.0e68e94457017p+0, -0x1.1d9e671612a46p-2, 0x1.1e141f6f8381bp-5, 0x1.626281f06a565p-3, -0x1.00510e27c6afap-3, 0x1.dda065aa933f4p-6, -0x1.397e42b4cc1c2p-10, -0x1.5e2780fee3a22p-13, 0x1.93d63eaebefb8p-23, 0x1.24c485651202dp-34, -0x0p+0};
-            }
-            if constexpr (order == 13) {
-                return {0x0p+0, 0x1.2dba81606cdf4p-3, -0x1.83ba9062dc10bp+0, 0x1.bc6ce42e9d3a2p+2, -0x1.2c97bd817af95p+4, 0x1.0e06914d93155p+5, -0x1.5f4706680d4aep+5, 0x1.6ea3fbf492341p+5, -0x1.5a777ed4931f2p+5, 0x1.424978021982dp+5, -0x1.3090ff3d7fed6p+5, 0x1.23e4419ddb641p+5, -0x1.07fd356f7673cp+5, 0x1.a8f488a3b6e4bp+4, -0x1.49932384ed8b5p+4, 0x1.0a96d421140ffp+4, -0x1.8f60cd9c05603p+3, 0x1.003bcbf26a5dbp+3, -0x1.433ef046d9ed1p+2, 0x1.a65b7dff93521p+1, -0x1.d36032adf2dbdp+0, 0x1.a4a1ad470bd0ep-1, -0x1.88e9f63513cep-2, 0x1.6764f965c9511p-3, -0x1.91c36b23af1d8p-5, 0x1.07d03d7a1adc2p-8, 0x1.362d3e37ff6cdp-11, -0x1.92dbfdbfa8198p-20, -0x1.22ff804507dbep-30, 0x0p+0};
-            }
-            if constexpr (order == 14) {
-                return {0x0p+0, 0x1.8dd6e1684e11dp-6, -0x1.ffb4de00653d3p-3, 0x1.1f8df89dea984p+0, -0x1.6eae32a3a7907p+1, 0x1.200cfdab0a888p+2, -0x1.1f287662480abp+2, 0x1.90990b7ee9dd2p+1, -0x1.3d166b62b6086p+1, 0x1.74d60ae1a8cebp+1, -0x1.68026579c2214p+1, 0x1.e76ba8ae988d5p+0, -0x1.60830949d4c83p+0, 0x1.48f2a8ad7050dp+0, -0x1.e7d09d1d5c76ep-1, 0x1.1252ee85de925p-1, -0x1.6e9d007e3ce51p-2, 0x1.0a88fbec92db2p-2, -0x1.16ea71f276b01p-3, 0x1.018afa9348368p-4, -0x1.2fa053de7510ep-5, 0x1.2375ee2696f87p-6, -0x1.73b10c938e4b6p-8, 0x1.1decc8370b235p-9, -0x1.b8713a4dd74a9p-11, 0x1.732711f764c01p-14, 0x1.5deb76c540b6cp-16, -0x1.9271259f10414p-23, -0x1.2099915b93354p-32, 0x0p+0};
-            }
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0L, 0xe.cceb08e0232ebfep-15L, 0x8.697cc2a13d0ee1p-7L, 0xa.529c93355636f38p-4L, 0x8.fe286827bf83d25p-4L, -0xe.a4bba81395fd148p-5L, 0x9.abad43ece0b19efp-5L, -0xb.f3225588c443427p-6L, 0xd.0bc2bb2ddca46a9p-7L, -0xb.89ad356d45a90abp-8L, 0xe.c67ee5d8b0c44cdp-10L, -0xa.bf0abdade753fd6p-12L, -0xa.fb1990274acfe19p-18L, 0x8.8522c4ecfc3eb6ep-16L, -0xa.c913268b7310da9p-19L, 0xc.4cbcbc26b8c299cp-21L, -0xa.7c208b4d0dd68c5p-21L, 0xb.a4a9e9cb3e66c66p-23L, -0xf.be58d677e7a1ad2p-29L, -0xe.495f10d77864d6p-29L, -0x9.dcd2be2673f3d47p-38L, -0xb.52c67607d112652p-38L, 0xa.5f8f5c66a64e114p-40L, 0xb.4b833f8b8ad0a0ap-47L, -0xa.89ebc85e9217eeap-52L, -0xd.9ca1e014c35331bp-60L, 0xa.a69985f2bc1edb9p-70L, -0x9.fb70f3189b26326p-83L, -0xe.86c417c2c3da4c7p-107L, -0x0p+0L};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0L, 0xd.7b39b8b93a579b8p-12L, 0xe.3d6a2e84375262fp-6L, 0xc.bab6584977037b5p-4L, -0xa.8c8b32be0c1a23fp-3L, 0xb.663747831202959p-5L, -0xc.679beb0c165058cp-7L, 0xc.d1fd17a0ea4a983p-7L, -0x8.5285f11795c36ecp-6L, 0xe.f9fa7b60cea28cap-7L, -0x9.6a5bf38aedb5fc2p-7L, 0x8.340f26105cfe721p-8L, -0x8.da86b44e5f6c6f9p-10L, 0xa.4d6689a512a5d01p-14L, 0x8.b328caaca1f1c8cp-14L, -0xe.1368f9638643783p-16L, 0x9.80108c73b15088ep-19L, 0xa.4fdf67ebece365dp-20L, -0xc.3c0d25352fbe46dp-22L, 0xa.f68568b2566925p-27L, 0xe.d253aac33a56ee8p-28L, -0xb.f11e391bf9fc9acp-32L, -0xd.ec79677c64f81e9p-38L, 0x8.e30a80fd082403ap-40L, -0xe.0dc599cc4f0122fp-47L, -0xc.a8ab79ce599d1e7p-55L, 0xe.8fc6edbe80cc4a8p-63L, -0x9.a31aef33e745dcdp-77L, -0xe.0636941fba0f2ecp-100L, 0x0p+0L};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0L, 0xa.9550b3a1bf69d4cp-9L, 0x9.79c3228669b01a3p-4L, -0xc.96d1f07a3cafa97p-5L, -0x8.08736119b1617adp-2L, 0xd.d2f2b8399be77e4p-2L, -0xb.77d0d1a8f344a12p-2L, 0xf.177ffbc96536692p-3L, -0xf.4f4240ae714d2acp-4L, 0x9.f3de7e41ee9a787p-5L, -0x9.f90f2f41edcdbb5p-9L, -0x8.07048dc1886be21p-8L, 0xc.9929752ea076dc3p-11L, 0x8.65a9ded0927a627p-10L, -0xb.76632cb7ef5cbbcp-11L, 0x8.ed1e446f22c9d07p-13L, 0x8.7b82e4884dc45e4p-15L, -0xb.43f8bb20adad0a1p-16L, 0x8.1dfba4938f506e5p-18L, -0x8.52b864cbdc7b5dap-23L, -0xd.b0642b5bae37c7cp-25L, 0x9.79b640126a3c29ep-27L, -0xd.5b5a695064f587ep-33L, -0xd.bbedea6b125d8c1p-36L, 0x8.1703505a92944ccp-42L, 0xf.c806dc0c202de26p-49L, -0xa.e6355d251b37dfep-57L, 0xb.cd4df0dd6d782f3p-70L, 0x8.9658e330867ad2ep-91L, 0x0p+0L};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0L, 0xd.ef23ef44a9bf7e6p-7L, 0xf.fb71cf02de0cb05p-4L, -0x8.76fbc0963f37be8p-1L, 0xb.c4757dff7ab7e6ep-1L, -0x8.5cf2c6824f158e6p-1L, 0xa.beb952a6cdbec82p-2L, -0xa.d762ccc9eb2601dp-2L, 0xb.35f0027de12c188p-2L, -0x9.2bdb98710a46a7ap-2L, 0xb.0f351247d3b2edap-3L, -0x8.eb30b84242b9b67p-4L, 0xb.b1a5749c2f3e942p-7L, 0xd.572f59b67919cdep-8L, -0xb.3516ec08c4d2b92p-8L, 0xc.f72e1c6ff9e2d6dp-10L, 0xe.772295aae3180b3p-15L, -0xb.e8731ba9d6fc085p-13L, 0xc.ad4dd8a66760405p-15L, -0xd.6345c24b6f75385p-20L, -0xa.51f298ee66ad3e4p-20L, 0xa.2d2d956d67f7238p-23L, -0xd.02c2f3943a728d1p-31L, -0xa.525579b7ed76162p-31L, 0xc.0c6e1e1b32163bep-37L, 0xd.e47631a948722aep-44L, -0x8.e287a56da6a461dp-51L, 0xa.a0f72f7f5d13f61p-64L, 0xf.779e334a13dd19fp-85L, -0x0p+0L};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0L, 0xe.d4f7dc266880dc5p-5L, -0x8.54b1a91e3c07cabp-5L, -0xb.756bc5953fc385dp-1L, 0x8.fd85bf73ff4da1p+1L, -0xd.135907cdef77f86p+1L, 0xa.d1b1380b495aeaap+1L, -0xe.1dc9ba1f6af0fa5p-1L, -0x8.1c9faa033715437p+0L, 0xe.70719adcdae7ec4p+0L, -0x9.9b8fa1bc7e12e6ep+0L, 0x8.23a26399544b84bp-5L, 0xa.eaddd56169ee9cdp-1L, -0xa.b481d5e4e9b9684p-1L, 0xa.79b3a285d814a56p-2L, -0x8.b78df8f23eebd9ap-4L, -0x8.653044fe20f733p-6L, 0xf.e8f321b94c6f489p-7L, -0x8.93ab4e369e900fp-8L, 0x8.18e721eb7954d94p-12L, 0xe.de2d091a80b9ee2p-14L, -0xb.72bac364ced9545p-16L, 0x9.9c60964d4ada3f3p-22L, 0xf.6419dee46b558e8p-24L, -0x9.8f70f1115417f37p-29L, -0x8.3466712818e830ep-35L, 0xd.5a4368c8a906c55p-43L, -0xc.b8d6308a3e25ebp-55L, -0x9.41b2dacc9130e5dp-74L, 0x0p+0L};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0L, 0xc.5145f8fa5d7812bp-3L, -0x8.5c765a89f338723p+0L, 0x9.80e8bd62f0e36d7p+1L, -0xc.052feaf5df5265fp+1L, 0xa.51cf1f08246b12ap+1L, -0x8.8a413c74ecd0982p+1L, 0x8.c71226bcd019464p+1L, -0x9.c84334dd03bcb23p+1L, 0xc.0223638d6d8a444p+1L, -0x8.5203ca3cc7208f6p+2L, 0xa.9284ee82627b576p+2L, -0xa.5a34298e2d8cfacp+2L, 0xe.4078a18719a503cp+1L, -0xc.16f69e44f3f4fd2p+0L, 0xb.b0850b3844f8cadp-3L, 0xd.8544d440c6033bfp-3L, -0x9.5a8b6d2e8407dd6p-3L, 0xa.440c4e0731919f2p-5L, -0x8.b6ec8fe746979d1p-9L, -0xc.abeababfa6ac0f1p-10L, 0xb.09de79617e3529fp-12L, -0x8.56de0126d2a8a97p-17L, -0xa.2482acbd44843d2p-19L, 0x9.1c5eaa88ac31dcbp-24L, 0x8.5c31de2c9d0ea8bp-30L, -0x9.6d6295ae9addc71p-37L, 0xd.455ad309c458ed8p-49L, 0x9.a7e7c45e7d9feeap-67L, -0x0p+0L};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0L, 0xf.0ab7ac0a2d5d3e8p-2L, -0xe.c9a85911c615c82p+1L, 0xd.81f1cabf66b5001p+3L, -0xf.a8efd3c4ec3c419p+4L, 0xd.8ecf71990eca11bp+5L, -0x9.e485bf1e50edc17p+6L, 0xd.0812fcefab32f7bp+6L, -0xf.7416dd5b55881cap+6L, 0xf.e78b4c99c8261c4p+6L, -0xd.f7706e0646ed8ddp+6L, 0xa.a2fa4f007a4af9bp+6L, -0xe.1ce51aadeae94b8p+5L, 0xe.8bf371344016517p+4L, -0xc.682f15c0e7b935cp+2L, -0xd.2beed726f676c5ap+2L, 0x8.32dfdce7f6881c4p+3L, -0x8.d3c1df77e743d81p+2L, 0x9.74f960ac0d34b75p+0L, -0x9.e56cd1213828f04p-5L, -0x8.da59d3d53874134p-4L, 0x8.ad18a34d4e700e2p-6L, -0xa.e33531e49a3a34ep-11L, -0xa.edab0664546ca1p-13L, 0xe.2bdf2954afcd1ep-18L, 0xe.4b9c033e2c84ec9p-24L, -0xb.1fb29623912c4c5p-30L, 0xb.b4bb3eda211db22p-41L, 0x8.8459c371cf4ab4bp-58L, -0x0p+0L};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0L, 0xe.c386f5e602e22c6p-1L, -0x8.615c585940c9ee7p+3L, 0x8.85e9ba6b1aa85ccp+5L, -0xa.220ed77990ea00bp+6L, 0xf.576a4111664dc93p+6L, -0xe.f502ad56a76577ep+6L, 0x8.7536f43aab75351p+6L, 0x9.ddc90b0228ce8d7p+2L, -0xb.e01ea6e7aa8a396p+6L, 0xd.bbefb63b9185cdp+7L, -0xa.ceea2e0c37d88e3p+8L, 0xc.956af742a2c67bbp+8L, -0xb.b8b74d94c4b8e53p+8L, 0x9.a66ca166a39d2d4p+8L, -0xe.9084343fd1b7644p+7L, 0x9.3f1020c8928bd55p+7L, -0x8.770098e0d827732p+6L, 0x8.9ffe00b7ab651d2p+4L, 0xc.810d4eea709578cp-2L, -0xe.5ca82d384b2dbfdp+0L, 0xf.88e6b0c619ac534p-2L, -0xd.1ff7f0d4a16a0e5p-6L, -0xd.4a9ed441ba370f6p-8L, 0xc.b8c5f71d7b945cfp-12L, 0xd.6a124f9ccac6c82p-18L, -0xf.5b8668d520288fbp-24L, 0xb.9003503d04bfb0cp-34L, 0x8.698313f351569a4p-50L, 0x0p+0L};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0L, 0x8.aa8ac563754c257p+0L, -0xa.7f61d351960f794p+3L, 0xb.86f620f57cbe932p+5L, -0xf.4a67f658f7d0a3cp+6L, 0xd.f8588069a68203p+7L, -0x9.c948c01fe7a3daep+8L, 0xb.ce67a857da36deap+8L, -0xd.5b6484c8b08d94p+8L, 0xe.23f6cd0bdce6402p+8L, -0xd.78802bc1e4e0454p+8L, 0xb.9542ce55da38fbfp+8L, -0x9.423735cd8a7a408p+8L, 0xd.9ec3effb54aa43bp+7L, -0x8.d708293d724a1cp+7L, 0xa.0f0b74e21a99604p+6L, -0xa.3001862df903727p+5L, 0x8.40c736ecd66e3b7p+4L, -0xc.7785b363b31632ap+1L, -0xb.75c761697e78222p+0L, 0x9.d5d0181f80e2122p+0L, -0xa.c46b691cb246e7cp-2L, 0xa.e5031d144bd1a3cp-6L, 0xb.9644270369ccd47p-8L, -0x9.5bdcced391cd468p-11L, -0x9.acd6af648a62d24p-17L, 0x8.67f844ea6ac9781p-22L, -0x9.03a9abaad597738p-32L, -0xd.1d6ceaac9a2dc82p-48L, -0x0p+0L};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0L, 0x8.ba7d8eb39831c18p+0L, -0xa.e7b1da03950427fp+3L, 0xc.2cb815c9848fe3fp+5L, -0x8.0471c6326a024f5p+7L, 0xe.01e0dc6fb09f8cp+7L, -0x8.f069828b6686adbp+8L, 0x9.9a827173155c815p+8L, -0xa.24c51cda2ee968bp+8L, 0xa.8062115bf26b28ap+8L, -0x9.6b7c8b797831eb6p+8L, 0xe.2dec5c5f666d9f8p+7L, -0x9.db9046e0c283a87p+7L, 0xd.258c0c883e39073p+6L, -0xe.01ac1f2494c092fp+5L, 0x8.92a6aee8d1e432cp+4L, 0xd.f0ca84cbce12938p-1L, -0xb.55fa92090f522ecp+2L, 0xd.efd4a4a391e9b21p+2L, -0xb.d4e0815eda4a88ap+2L, 0xc.349069e83f691d5p+1L, -0xd.4d6fd92e2793a35p-1L, 0x8.99bb20dc4eddf8ap-4L, 0x8.c8e3231160d8992p-6L, -0xc.468c211c336121fp-9L, -0xd.7727a335dcb4b2ep-15L, 0x8.af2f4ba3ff0ddeep-19L, -0xd.e2248f7707ee606p-29L, -0xa.18e01f3aa66c51bp-43L, -0x0p+0L};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0L, 0xa.bee90172f4255c3p-1L, -0xd.a135ca4c3c846a5p+2L, 0xf.7a8579b5e4a4f6ap+4L, -0xa.6d47322333f3562p+6L, 0x9.6c44d5844c887bdp+7L, -0xc.a2b764377e3a1ebp+7L, 0xe.50fbae94e0bc253p+7L, -0xf.9757925a45f487cp+7L, 0x8.530717ee753bcd5p+8L, -0x8.3ff3ae16c29c979p+8L, 0xf.159bf6afa230cc6p+7L, -0xd.147e7fb73425ae6p+7L, 0xa.acb695f3e0fc1c3p+7L, -0x8.13b08baf665a54p+7L, 0xb.87a2d1f4db643efp+6L, -0xf.6fad2d9aa709453p+5L, 0x9.3d8f0994c5d9f7bp+5L, -0x9.df34921f79618f8p+4L, 0x9.db8f809079523d6p+3L, -0x8.8cc2eca027a29bcp+2L, 0x9.dad4bb17829d702p+0L, -0xe.1960c3b3edb91b1p-4L, -0xa.ec744dc5d17a352p-5L, 0x9.d8da354be17d4f6p-7L, 0x9.1b83681fb7ba338p-13L, -0xc.e137e4279ffaf08p-17L, 0xc.b149cd09c7159bbp-26L, 0x9.3a1452c9a7cedecp-39L, 0x0p+0L};
-            }
-            if constexpr (order == 11) {
-                return {0x0p+0L, 0xc.15d0c5140aaa4eep-2L, -0xf.7190d63c174081fp+1L, 0x8.ba72fb2d2252c3fp+4L, -0xb.740eabe264bca0cp+5L, 0x9.b46f19b0fd72575p+6L, -0xb.883398ebe4385ep+6L, 0xb.30e910677d07ffp+6L, -0xb.419dbbc73b9d5a1p+6L, 0xc.19e0dbd12662221p+6L, -0xb.826867ada01fb9cp+6L, 0x9.5143da543a25f3ap+6L, -0xe.bcab98d7996a714p+5L, 0xb.d3311ddf4d7bdfbp+5L, -0x8.6eecfd0d6810f0bp+5L, 0xa.7c120c15da204bcp+4L, -0xc.dc6b77ec19e1f99p+3L, 0xf.35cdfe48953061cp+2L, -0xe.c39532a44de361dp+1L, 0xc.1727280b8b20591p+0L, -0x9.e40d8406be2c4fap-1L, 0xc.388bf027ec112cbp-3L, -0xf.968ede9ca84c64dp-9L, -0x9.93e06924a09fd14p-6L, 0x8.9dc64ac28a2fbc2p-8L, -0x8.4a44983b6d59171p-16L, -0xb.c238c931736ccdbp-17L, 0x9.8e9343ad5a2f5d8p-26L, 0xd.e1d77974b4c54b1p-39L, 0x0p+0L};
-            }
-            if constexpr (order == 12) {
-                return {0x0p+0L, 0x9.1480bef44c4469ep-3L, -0xb.a584c6bd94a1187p+0L, 0xd.1eb7f2c429e0f2ep+2L, -0x8.774ff1631cd3a64p+4L, 0xd.bf61476f622a169p+4L, -0xe.e5fff6d9d283fd3p+4L, 0xc.7ca8972468e2375p+4L, -0xb.a10d8d44022caeap+4L, 0xd.0bf0e90f39e8d94p+4L, -0xc.589dd6de50ec435p+4L, 0x9.080317497a44b68p+4L, -0xd.4bcc6a26d36101bp+3L, 0xb.17a90e8cb9542f6p+3L, -0xf.868a33cfb4e032cp+2L, 0x8.582a0590e784928p+2L, -0x9.73fc0eb91ba83cbp+1L, 0xb.bb58cde0ef3d615p+0L, -0x9.c855651ad1a4682p-1L, 0x8.73474a22b80bb4fp-3L, -0x8.ecf338b09522ep-5L, 0x8.f0a0fb7c1c0d8ddp-8L, 0xb.13140f8352b2905p-6L, -0x8.0288713e357cfe6p-6L, 0xe.ed032d5499f9d13p-9L, -0x9.cbf215a660e12a2p-13L, -0xa.f13c07f71d1127bp-16L, 0xc.9eb1f575f7dbcbbp-26L, 0x9.26242b289016945p-37L, -0x0p+0L};
-            }
-            if constexpr (order == 13) {
-                return {0x0p+0L, 0x9.6dd40b0366fa267p-6L, -0xc.1dd48316e0854aap-3L, 0xd.e3672174e9d1088p-1L, -0x9.64bdec0bd7ca5b2p+1L, 0x8.70348a6c98aa9bbp+2L, -0xa.fa3833406a56d39p+2L, 0xb.751fdfa491a058dp+2L, -0xa.d3bbf6a498f90bp+2L, 0xa.124bc010cc1696ap+2L, -0x9.8487f9ebff6b313p+2L, 0x9.1f220ceedb2076ep+2L, -0x8.3fe9ab7bb39dc96p+2L, 0xd.47a4451db725977p+1L, -0xa.4c991c276c5a664p+1L, 0x8.54b6a108a07f661p+1L, -0xc.7b066ce02b0141p+0L, 0x8.01de5f9352ed819p+0L, -0xa.19f78236cf689c9p-1L, 0xd.32dbeffc9a904b7p-2L, -0xe.9b01956f96deb78p-3L, 0xd.250d6a385e86ee4p-4L, -0xc.474fb1a89e70305p-5L, 0xb.3b27cb2e4a88b76p-6L, -0xc.8e1b591d78ebf4ap-8L, 0x8.3e81ebd0d6e0c17p-11L, 0x9.b169f1bffb66918p-14L, -0xc.96dfedfd40cbd7ep-23L, -0x9.17fc02283edf3c4p-33L, 0x0p+0L};
-            }
-            if constexpr (order == 14) {
-                return {0x0p+0L, 0xc.6eb70b42708eae9p-9L, -0xf.fda6f00329e9b71p-6L, 0x8.fc6fc4ef54c1db5p-3L, -0xb.7571951d3c8341p-2L, 0x9.0067ed5854443d7p-1L, -0x8.f943b3124055b9cp-1L, 0xc.84c85bf74ee8fcap-2L, -0x9.e8b35b15b042f15p-2L, 0xb.a6b0570d4675539p-2L, -0xb.40132bce1109dcp-2L, 0xf.3b5d4574c46a8f3p-3L, -0xb.04184a4ea6416d5p-3L, 0xa.4795456b82864acp-3L, -0xf.3e84e8eae3b6c57p-4L, 0x8.9297742ef492803p-4L, -0xb.74e803f1e728564p-5L, 0x8.5447df6496d92bp-5L, -0x8.b7538f93b58072dp-6L, 0x8.0c57d49a41b3dccp-7L, -0x9.7d029ef3a886eafp-8L, 0x9.1baf7134b7c3668p-9L, -0xb.9d88649c725b305p-11L, 0x8.ef6641b8591aa6cp-12L, -0xd.c389d26eba54b8ep-14L, 0xb.99388fbb2600ba3p-17L, 0xa.ef5bb62a05b60a1p-19L, -0xc.93892cf88209c7cp-26L, -0x9.04cc8adc99aa115p-35L, 0x0p+0L};
-            }
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.d99d611c0465d7fca87092137394p-12Q, 0x1.0d2f985427a1dc1f62afa99d998fp-4Q, 0x1.4a539266aac6de6ff0ee136fe6aap-1Q, 0x1.1fc50d04f7f07a49e55f06b78355p-1Q, -0x1.d497750272bfa28f3f1990b740bdp-2Q, 0x1.3575a87d9c1633de9f0ee95125a2p-2Q, -0x1.7e644ab11888684db8a7b8d90489p-3Q, 0x1.a1785765bb948d52e0838b0df196p-4Q, -0x1.7135a6ada8b52155f89869cf22c7p-5Q, 0x1.d8cfdcbb1618899a1617de65e071p-7Q, -0x1.57e157b5bcea7fac037e4b9b62aap-9Q, -0x1.5f633204e959fc32c151ba987165p-15Q, 0x1.10a4589d9f87d6dc51e36837ed0bp-13Q, -0x1.592264d16e621b5275bdd9d12d3ep-16Q, 0x1.89979784d7185338d2badb26cabcp-18Q, -0x1.4f841169a1bad189406e2832bc2dp-18Q, 0x1.74953d3967ccd8cc322dbf252946p-20Q, -0x1.f7cb1acefcf435a3d287cb8094c6p-26Q, -0x1.c92be21aef0c9ac0fb550ddd5f87p-26Q, -0x1.3b9a57c4ce7e7a8e7b0e1df188abp-35Q, -0x1.6a58cec0fa224ca49741d5041713p-35Q, 0x1.4bf1eb8cd4c9c2273508a8b73f46p-37Q, 0x1.697067f1715a141417bb7553b3a7p-44Q, -0x1.513d790bd242fdd412e02eaf3fd9p-49Q, -0x1.b3943c02986a6636aaf05d95d84p-57Q, 0x1.54d330be5783db7123cd1333ac9cp-67Q, -0x1.3f6e1e631364c64c65f6b5a7fe23p-80Q, -0x1.d0d882f8587b498d8efb759e05fp-104Q, 0x0p+0Q};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.af673717274af370272903c1fa7cp-9Q, 0x1.c7ad45d086ea4c5ed9ed7e340defp-3Q, 0x1.9756cb092ee06f6ac1eb577b96f6p-1Q, -0x1.51916657c183447d0774789d6344p+0Q, 0x1.6cc6e8f0624052b2c0fdcc8950d3p-2Q, -0x1.8cf37d6182ca0b170d0a042e4192p-4Q, 0x1.9a3fa2f41d4953051b0c6d4a1b03p-4Q, -0x1.0a50be22f2b86dd755f1bb101decp-3Q, 0x1.df3f4f6c19d45193b61450be39f8p-4Q, -0x1.2d4b7e715db6bf84cb93e1a16129p-4Q, 0x1.0681e4c20b9fce41d5b4e56756a7p-5Q, -0x1.1b50d689cbed8df146901e68b6b4p-7Q, 0x1.49acd134a254ba0136bf2c9ddd8p-11Q, 0x1.16651955943e391787562b852142p-11Q, -0x1.c26d1f2c70c86f0644644cef75b6p-13Q, 0x1.3002118e762a111c6bcee4aaae9bp-16Q, 0x1.49fbecfd7d9c6cba55cd30ac067dp-17Q, -0x1.8781a4a6a5f7c8daadd9ede249c3p-19Q, 0x1.5ed0ad164acd249f0f9d827483fep-24Q, 0x1.da4a7558674addd03b35614f7a6dp-25Q, -0x1.7e23c7237f3f9358779e22d38d23p-29Q, -0x1.bd8f2cef8c9f03d137232e9e498bp-35Q, 0x1.1c61501fa10480730673344e3608p-37Q, -0x1.c1b8b33989e0245e7c861b898f54p-44Q, -0x1.95156f39cb33a3cd95db28e3bb11p-52Q, 0x1.d1f8ddb7d01989509bfbf0327d67p-60Q, -0x1.34635de67ce8bb9a35ccd2f4bcc3p-74Q, -0x1.c0c6d283f741e5d8d9e1ced44ca2p-97Q, 0x0p+0Q};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.52aa167437ed3a97a2d16e2e7e71p-6Q, 0x1.2f386450cd3603452775e405daacp-1Q, -0x1.92da3e0f4795f52ddad307073cb1p-2Q, -0x1.010e6c23362c2f5a0189ea0fe7f3p+1Q, 0x1.ba5e5707337cefc73943a8303bc5p+1Q, -0x1.6efa1a351e68942304e8e68b7bacp+1Q, 0x1.e2efff792ca6cd2456dfdb721f76p+0Q, -0x1.e9e84815ce29a5578b4bc0477acbp-1Q, 0x1.3e7bcfc83dd34f0d929299013451p-2Q, -0x1.3f21e5e83db9b76a1e6a21ec3442p-6Q, -0x1.00e091b8310d7c425038e08dacbfp-5Q, 0x1.93252ea5d40edb85ff0ddad301dp-8Q, 0x1.0cb53bda124f4c4d4c0ae3af4779p-7Q, -0x1.6ecc6596fdeb97786cd08cbbbaedp-8Q, 0x1.1da3c88de4593a0d10cc249b83cep-10Q, 0x1.0f705c9109b88bc792c8e251c3f5p-12Q, -0x1.687f176415b5a1410c9f394cb959p-13Q, 0x1.03bf749271ea0dc9bfa9a81f4245p-15Q, -0x1.0a570c997b8f6bb3aa2b6fc454e1p-20Q, -0x1.b60c856b75c6f8f8db3b0f76f67dp-22Q, 0x1.2f36c8024d47853b1fc5abd2c569p-24Q, -0x1.ab6b4d2a0c9eb0fb78406697468ap-30Q, -0x1.b77dbd4d624bb182ce2a8088a4c2p-33Q, 0x1.02e06a0b5252899742121667393ep-39Q, 0x1.f900db818405bc4cfc19c190531fp-46Q, -0x1.5cc6aba4a366fbfbcb9e7e9b2b91p-54Q, 0x1.79a9be1badaf05e53c8d4ae211e7p-67Q, 0x1.12cb1c6610cf5a5ca8d9bf45819bp-88Q, 0x0p+0Q};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.bde47de89537efcc2943722b907bp-4Q, 0x1.ff6e39e05bc1960ac6a7468afb9ep-1Q, -0x1.0edf7812c7e6f7d06a00b362ef27p+2Q, 0x1.788eafbfef56fcdc50a685d1f90ep+2Q, -0x1.0b9e58d049e2b1cb9469b014878dp+2Q, 0x1.57d72a54d9b7d9046e3ca22b5dccp+1Q, -0x1.5aec59993d64c03ae451f5fb822ap+1Q, 0x1.66be004fbc25830ff3a497ea74efp+1Q, -0x1.257b730e2148d4f4b3feb863502dp+1Q, 0x1.61e6a248fa765db41939b126fafep+0Q, -0x1.1d661708485736ce63b6c04b417fp-1Q, 0x1.7634ae9385e7d28433590ede5d72p-4Q, 0x1.aae5eb36cf2339bb1da3727f92c7p-5Q, -0x1.66a2dd81189a5724bb1062f0dfebp-5Q, 0x1.9ee5c38dff3c5ada29575f743d87p-7Q, 0x1.cee452b55c630166e1f1c650af12p-12Q, -0x1.7d0e63753adf810a13b7946ecd6fp-10Q, 0x1.95a9bb14ccec080a6175688009ap-12Q, -0x1.ac68b8496deea7093d3eaa37178ap-17Q, -0x1.4a3e531dccd5a7c88df667aa9928p-17Q, 0x1.45a5b2adacfee470f99a3f9acab4p-20Q, -0x1.a0585e72874e51a270db9477829dp-28Q, -0x1.4a4aaf36fdaec2c3a3e857f50877p-28Q, 0x1.818dc3c36642c77c4040a75f3899p-34Q, 0x1.bc8ec635290e455c58f05f4aae9ap-41Q, -0x1.1c50f4adb4d48c39b492719c193cp-48Q, 0x1.541ee5efeba27ec1d6332fa4f538p-61Q, 0x1.eef3c669427ba33d298eab6d070cp-82Q, 0x0p+0Q};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.da9efb84cd101b891a55bf085a33p-2Q, -0x1.0a963523c780f95520ba62e1635dp-2Q, -0x1.6ead78b2a7f870bae850968c013ap+2Q, 0x1.1fb0b7ee7fe9b42077abdaf556e2p+4Q, -0x1.a26b20f9bdeeff0cd0b5e878c8cap+4Q, 0x1.5a362701692b5d54a80faabe0329p+4Q, -0x1.c3b93743ed5e1f4aae7ff96667ep+2Q, -0x1.0393f54066e2a86d4f5766fcec98p+3Q, 0x1.ce0e335b9b5cfd8737f6de07dc86p+3Q, -0x1.3371f4378fc25cdcbf584ed9698fp+3Q, 0x1.04744c732a8970957ba707eb759dp-2Q, 0x1.5d5bbaac2d3dd399541ae8c8527cp+2Q, -0x1.56903abc9d372d08f72cf8f9b7f6p+2Q, 0x1.4f367450bb0294accf5c9a7e742cp+1Q, -0x1.16f1bf1e47dd7b33b29f107a7717p-1Q, -0x1.0ca6089fc41ee660907b2bb584cap-3Q, 0x1.fd1e6437298de912355a40f30818p-4Q, -0x1.127569c6d3d201e096a74c3e92a3p-5Q, 0x1.031ce43d6f2a9b28afac205ca3a5p-9Q, 0x1.dbc5a12350173dc4ceb0edd40202p-11Q, -0x1.6e57586c99db2a8af6576e5d9fc9p-13Q, 0x1.338c12c9a95b47e57d454a7c66e9p-19Q, 0x1.ec833bdc8d6ab1cf492647696452p-21Q, -0x1.31ee1e222a82fe6e397b0f1ab0a7p-26Q, -0x1.068cce25031d061c7d5229b85c51p-32Q, 0x1.ab486d191520d8a9aefca6d39becp-40Q, -0x1.971ac61147c4bd5f21d58d94dd2bp-52Q, -0x1.28365b5992261cb91d89a4a61c9dp-71Q, 0x0p+0Q};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0Q, 0x1.8a28bf1f4baf0256370de9e50cdfp+0Q, -0x1.0b8ecb513e670e46e8b61ff5e5a2p+3Q, 0x1.301d17ac5e1c6daeb2bb903493bbp+4Q, -0x1.80a5fd5ebbea4cbe232c3d8a57f1p+4Q, 0x1.4a39e3e1048d62539834148e9e34p+4Q, -0x1.1148278e9d9a1304c4d27a6289e7p+4Q, 0x1.18e244d79a0328c7ff6eaa1380dep+4Q, -0x1.3908669ba07796469d9944fd1af2p+4Q, 0x1.80446c71adb1488769cf4e603a7ap+4Q, -0x1.0a40794798e411ebd23986dcd959p+5Q, 0x1.52509dd04c4f6aeb9cbf4fd2a65ep+5Q, -0x1.4b468531c5b19f58ba9821140c9p+5Q, 0x1.c80f1430e334a07768f1a5bc676fp+4Q, -0x1.82ded3c89e7e9fa329e76277e5cep+3Q, 0x1.7610a167089f1959ecdad2bfe856p+0Q, 0x1.b0a89a8818c0677d48d7304191d3p+0Q, -0x1.2b516da5d080fbac57ead9c2cab4p+0Q, 0x1.488189c0e63233e310386fe21bdep-2Q, -0x1.16dd91fce8d2f3a24746d48a1c72p-6Q, -0x1.957d5757f4d581e1eb81397c4cedp-7Q, 0x1.613bcf2c2fc6a53ed2c91b207503p-9Q, -0x1.0adbc024da55152d1e362e31540ap-14Q, -0x1.44905597a89087a3899ef1de6ff1p-16Q, 0x1.238bd55115863b967f9591633549p-21Q, 0x1.0b863bc593a1d515b8c451bf0e45p-27Q, -0x1.2dac52b5d35bb8e11505ea96f44p-34Q, 0x1.a8ab5a61388b1db01ad925c31a8cp-46Q, 0x1.34fcf88bcfb3fdd3eace81ef29a8p-64Q, 0x0p+0Q};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0Q, 0x1.e156f58145aba7d0b30fa35cff6p+1Q, -0x1.d9350b2238c2b904f5fdfc3f59d8p+4Q, 0x1.b03e3957ecd6a002d130922f2289p+6Q, -0x1.f51dfa789d878832ad001b3c3bbap+7Q, 0x1.b1d9ee3321d942364cb8258ac548p+8Q, -0x1.3c90b7e3ca1db82e1a61d1d6988cp+9Q, 0x1.a1025f9df5665ef6d6390bf76e1p+9Q, -0x1.ee82dbab6ab103949b52c0e24238p+9Q, 0x1.fcf169933904c38827bff6f06e1ap+9Q, -0x1.beee0dc0c8ddb1ba16139309e6dap+9Q, 0x1.545f49e00f495f369a9c2bc574c5p+9Q, -0x1.c39ca355bd5d296f37962bd729eep+8Q, 0x1.d17e6e268802ca2d8ab4ba84d645p+7Q, -0x1.8d05e2b81cf726b84ae7be04d2f8p+5Q, -0x1.a57ddae4deced8b3bcbf57c78c0cp+5Q, 0x1.065bfb9cfed103880a47e8cebd5dp+6Q, -0x1.1a783beefce87b0115cd7f827bd2p+5Q, 0x1.2e9f2c1581a696ea729509934246p+3Q, -0x1.3cad9a2427051e071bf1f9b27c09p-2Q, -0x1.1b4b3a7aa70e82673e69d678de04p-1Q, 0x1.15a31469a9ce01c4f9e606bc0537p-3Q, -0x1.5c66a63c9347469ce6f66ff5c6a6p-8Q, -0x1.5db560cc8a8d9420c2df7533732ep-10Q, 0x1.c57be52a95f9a3c03fb08957c434p-15Q, 0x1.c9738067c5909d91761fe08abd47p-21Q, -0x1.63f652c47225898a139ddd320614p-27Q, 0x1.769767db4423b6439ddbe400214ap-38Q, 0x1.108b386e39e95695575892a5277bp-55Q, 0x0p+0Q};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0Q, 0x1.d870debcc05c458cb431fd983345p+2Q, -0x1.0c2b8b0b28193dcd228c0a0c405bp+6Q, 0x1.10bd374d63550b983999c56c677ap+8Q, -0x1.4441daef321d4016bb9b2c10ec43p+9Q, 0x1.eaed48222cc9b9253ebb102b9831p+9Q, -0x1.dea055aad4ecaefb97c3b4138e1fp+9Q, 0x1.0ea6de87556ea6a2de81d408b23ep+9Q, 0x1.3bb921604519d1ae88e6a7fa3786p+5Q, -0x1.7c03d4dcf551472cf7483533c9dbp+9Q, 0x1.b77df6c77230b9a06a324d910941p+10Q, -0x1.59dd45c186fb11c5ad121467058cp+11Q, 0x1.92ad5ee85458cf75ddc7493a06c7p+11Q, -0x1.7716e9b298971ca51bace1729b0ap+11Q, 0x1.34cd942cd473a5a7100d811101f7p+11Q, -0x1.d2108687fa36ec88dd6bfb56d5c3p+10Q, 0x1.27e2041912517aaa65b2132e4553p+10Q, -0x1.0ee0131c1b04ee634d1b07d2c971p+9Q, 0x1.13ffc016f56ca3a3bb78dd1c64f4p+7Q, 0x1.9021a9dd4e12af18897a92604f62p+1Q, -0x1.cb9505a70965b7f9ec7314ae6da2p+3Q, 0x1.f11cd618c3358a67a8f728986e77p+1Q, -0x1.a3fefe1a942d41c95d66abeb0178p-3Q, -0x1.a953da883746e1eb5fc521fbad44p-5Q, 0x1.9718bee3af728b9e4c2d8088bafdp-9Q, 0x1.ad4249f39958d903ac018ed0138fp-15Q, -0x1.eb70cd1aa40511f5c12a3ada0131p-21Q, 0x1.72006a07a097f617e889edbdb056p-31Q, 0x1.0d30627e6a2ad3489cda0318f0edp-47Q, 0x0p+0Q};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0Q, 0x1.155158ac6ea984ad1f3ad98465a9p+3Q, -0x1.4fec3a6a32c1ef2818fdbca7bd5fp+6Q, 0x1.70dec41eaf97d263c2e4504b0b21p+8Q, -0x1.e94cfecb1efa1478b22094cf32b8p+9Q, 0x1.bf0b100d34d0405ff7a1094810ecp+10Q, -0x1.39291803fcf47b5c26824c7c465ep+11Q, 0x1.79ccf50afb46dbd4b77400a63149p+11Q, -0x1.ab6c90991611b280fa6243394583p+11Q, 0x1.c47ed9a17b9cc8042e779917f5f2p+11Q, -0x1.af1005783c9c08a75d46ca645f35p+11Q, 0x1.72a859cabb471f7e1c8ba7bd2a6cp+11Q, -0x1.2846e6b9b14f481005e402049827p+11Q, 0x1.b3d87dff6a954876ee30a3fd1e1p+10Q, -0x1.1ae10527ae49437f7880589e6393p+10Q, 0x1.41e16e9c43532c08707a85b672ep+9Q, -0x1.460030c5bf206e4d0618004a8fep+8Q, 0x1.0818e6dd9acdc76d8ca94db3b3b3p+7Q, -0x1.8ef0b66c7662c653e53071c7fb7ep+4Q, -0x1.6eb8ec2d2fcf0443ad7c1412d0d4p+3Q, 0x1.3aba0303f01c424453fb561d43b2p+3Q, -0x1.588d6d239648dcf73cdacc19a23ap+1Q, 0x1.5ca063a2897a34772f3d9594be58p-3Q, 0x1.72c884e06d399a8e64ff05cdd7a2p-5Q, -0x1.2b7b99da7239a8d08435e37194cp-8Q, -0x1.359ad5ec914c5a48afa1ae580694p-14Q, 0x1.0cff089d4d592f01775a150c05eep-19Q, -0x1.207535755ab2ee6fe496486e6edap-29Q, -0x1.a3ad9d559345b904814003502ba2p-45Q, 0x0p+0Q};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0Q, 0x1.174fb1d6730638307d1e4b445fc7p+3Q, -0x1.5cf63b4072a084fdeb886ad661e9p+6Q, 0x1.859702b93091fc7e65868db7a8fbp+8Q, -0x1.008e38c64d4049e94bd38a5f00e3p+10Q, 0x1.c03c1b8df613f180675faa2c200ap+10Q, -0x1.1e0d30516cd0d5b6c1126d4bf14cp+11Q, 0x1.33504e2e62ab9029d44ee63bfb62p+11Q, -0x1.4498a39b45dd2d15e6ecc8905aabp+11Q, 0x1.500c422b7e4d651447cfcdfc454bp+11Q, -0x1.2d6f916f2f063d6cac6b467c2932p+11Q, 0x1.c5bd8b8beccdb3ef655c28cdfe75p+10Q, -0x1.3b7208dc1850750db50ab0ef592ep+10Q, 0x1.a4b1819107c720e54775d3b0e2c4p+9Q, -0x1.c03583e49298125db8e2fdf27d4ep+8Q, 0x1.1254d5dd1a3c865791d5348ec394p+7Q, 0x1.be19509979c252700bdddf4796f4p+2Q, -0x1.6abf524121ea45d75b1ac598d945p+5Q, 0x1.bdfa9494723d3641f8f4e66eff1ap+5Q, -0x1.7a9c102bdb495114d11be11a8205p+5Q, 0x1.86920d3d07ed23a9933ffc257d69p+4Q, -0x1.a9adfb25c4f27469db3fea5dd201p+2Q, 0x1.1337641b89dbbf1427d95e0cc537p-1Q, 0x1.191c64622c1b13245bafd3429ab6p-3Q, -0x1.88d18423866c243d7190f3f8f03dp-6Q, -0x1.aee4f466bb96965b6a34b6c35598p-12Q, 0x1.15e5e9747fe1bbdbc08f26b48b4cp-16Q, -0x1.bc4491eee0fdcc0c5c6a94682339p-26Q, -0x1.431c03e754cd8a35cd8981f0bf35p-40Q, 0x0p+0Q};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0Q, 0x1.57dd202e5e84ab856980df8a0abap+2Q, -0x1.b426b94987908d499f3bffafa19ep+5Q, 0x1.ef50af36bc949ed3fa7cc19e8e96p+7Q, -0x1.4da8e644667e6ac3b7b19c4c383dp+9Q, 0x1.2d889ab089910f7ad4219226878ep+10Q, -0x1.9456ec86efc743d502abdf76eae3p+10Q, 0x1.ca1f75d29c1784a6a7a3af88a28cp+10Q, -0x1.f2eaf24b48be90f886d98564f553p+10Q, 0x1.0a60e2fdcea779a991419059c46dp+11Q, -0x1.07fe75c2d85392f12125b660934dp+11Q, 0x1.e2b37ed5f446198c3a6ab7d8b74fp+10Q, -0x1.a28fcff6e684b5cca8e0268f1e92p+10Q, 0x1.5596d2be7c1f83852a4b17681f79p+10Q, -0x1.02761175eccb4a7f32feddc56feep+10Q, 0x1.70f45a3e9b6c87dda520903f4aafp+9Q, -0x1.edf5a5b354e128a66fada7d4bcf3p+8Q, 0x1.27b1e13298bb3ef65c7ced26ff2fp+8Q, -0x1.3be69243ef2c31f0230131660198p+7Q, 0x1.3b71f0120f2a47ab2f14bf7b7d89p+6Q, -0x1.11985d9404f45378f95059bc551ep+5Q, 0x1.3b5a9762f053ae040918d7979484p+3Q, -0x1.c32c18767db723614ce78e339586p-1Q, -0x1.5d8e89b8ba2f46a3386878a383e3p-2Q, 0x1.3b1b46a97c2fa9eb1545e9c9486p-4Q, 0x1.23706d03f6f7466fb42dcd72c19fp-10Q, -0x1.9c26fc84f3ff5e0f45e88806fbbbp-14Q, 0x1.962939a138e2b376295550104948p-23Q, 0x1.27428a5934f9dbd8cb77b8eb93d8p-36Q, 0x0p+0Q};
-            }
-            if constexpr (order == 11) {
-                return {0x0p+0Q, 0x1.82ba18a2815549dbb583ba20e3a4p+1Q, -0x1.ee321ac782e8103dfda5e2a50005p+4Q, 0x1.174e5f65a44a587e2370d6742aeep+7Q, -0x1.6e81d57c4c979417ab1a67acd69dp+8Q, 0x1.368de3361fae4ae909df52a5836ap+9Q, -0x1.7106731d7c870bc083e5fa51f617p+9Q, 0x1.661d220cefa0ffe013a28a70693fp+9Q, -0x1.6833b778e773ab42be55fb8d5e31p+9Q, 0x1.833c1b7a24cc4442e638654d7d43p+9Q, -0x1.704d0cf5b403f737ee51433c941bp+9Q, 0x1.2a287b4a8744be736369f360e45fp+9Q, -0x1.d795731af32d4e2789960ef06165p+8Q, 0x1.7a6623bbe9af7bf6c822bfb77cd2p+8Q, -0x1.0ddd9fa1ad021e162c6d71d17f6ap+8Q, 0x1.4f824182bb440977dbde7b407e9p+7Q, -0x1.9b8d6efd833c3f31fdcf2bc0b9fap+6Q, 0x1.e6b9bfc912a60c385c4952c1112ep+5Q, -0x1.d872a65489bc6c3914d51095ebc1p+4Q, 0x1.82e4e50171640b22bb8023c09d2ep+3Q, -0x1.3c81b080d7c589f42c4b3bd2cdd6p+2Q, 0x1.87117e04fd822595de3e0b568ccp+0Q, -0x1.f2d1dbd395098c995334374fed2ep-6Q, -0x1.327c0d249413fa2745cbbd687d3ep-3Q, 0x1.13b8c9585145f7834dc70fb2de56p-5Q, -0x1.094893076dab22e2cc6f5a93ce22p-13Q, -0x1.784719262e6d99b5739a61a4981ap-14Q, 0x1.31d26875ab45ebb06f0484706cp-23Q, 0x1.bc3aef2e9698a9624f45add91d4dp-36Q, 0x0p+0Q};
-            }
-            if constexpr (order == 12) {
-                return {0x0p+0Q, 0x1.229017de89888d3b45e2c184d9bp+0Q, -0x1.74b098d7b294230e1965426f3612p+3Q, 0x1.a3d6fe58853c1e5c5b0a3a09e40cp+5Q, -0x1.0ee9fe2c639a74c7c045b3701c38p+7Q, 0x1.b7ec28edec4542d27f9646062fefp+7Q, -0x1.dcbffedb3a507fa5c4f4218a69c2p+7Q, 0x1.8f9512e48d1c46e9aca0a2a1ffcap+7Q, -0x1.7421b1a8804595d4b26746d9ca32p+7Q, 0x1.a17e1d21e73d1b2881053890e718p+7Q, -0x1.8b13badbca1d886a8838c2c2e2e8p+7Q, 0x1.210062e92f4896d0f00a29c58cfbp+7Q, -0x1.a9798d44da6c2035da535dfbec27p+6Q, 0x1.62f521d1972a85eb2c6f26f231b9p+6Q, -0x1.f0d14679f69c06584d1c30d18738p+5Q, 0x1.0b0540b21cf0924f5546e5194d02p+5Q, -0x1.2e7f81d7237507956599c3ca61c1p+4Q, 0x1.776b19bc1de7ac2a6f830edb0d24p+3Q, -0x1.390aaca35a348d0447af0cac40bp+2Q, 0x1.0e68e9445701769efc7a68d035e5p+0Q, -0x1.1d9e671612a45bff7deef6e6cc44p-2Q, 0x1.1e141f6f8381b1b9942811bfdb96p-5Q, 0x1.626281f06a565209b56968645fb1p-3Q, -0x1.00510e27c6af9fccce7dab2661cp-3Q, 0x1.dda065aa933f3a25232d375fa99bp-6Q, -0x1.397e42b4cc1c25443933189b9067p-10Q, -0x1.5e2780fee3a224f5cbc2e8463206p-13Q, 0x1.93d63eaebefb797682d434c6108cp-23Q, 0x1.24c485651202d28a48b67967bbebp-34Q, 0x0p+0Q};
-            }
-            if constexpr (order == 13) {
-                return {0x0p+0Q, 0x1.2dba81606cdf44cd9f04d2f8bc14p-3Q, -0x1.83ba9062dc10a95420ae8251630ap+0Q, 0x1.bc6ce42e9d3a21102e4fdf0d4671p+2Q, -0x1.2c97bd817af94b6452b764a95107p+4Q, 0x1.0e06914d9315537516f107f294e6p+5Q, -0x1.5f4706680d4ada71d3fe8928e941p+5Q, 0x1.6ea3fbf492340b1a8746b11d0c42p+5Q, -0x1.5a777ed4931f215f8e0a373e4b9fp+5Q, 0x1.424978021982d2d37f62990dfb19p+5Q, -0x1.3090ff3d7fed662537bbff91030bp+5Q, 0x1.23e4419ddb640edbe25a71aaad29p+5Q, -0x1.07fd356f7673b92c13a9d66edf4fp+5Q, 0x1.a8f488a3b6e4b2eef60c68cd2c1fp+4Q, -0x1.49932384ed8b4cc7bb541dede413p+4Q, 0x1.0a96d421140fecc2982baba8b026p+4Q, -0x1.8f60cd9c056028206308e7df4429p+3Q, 0x1.003bcbf26a5db032107ad008618cp+3Q, -0x1.433ef046d9ed13921cc6b579a83ap+2Q, 0x1.a65b7dff9352096da27547ffc3e7p+1Q, -0x1.d36032adf2dbd6f014bd3f02cf6dp+0Q, 0x1.a4a1ad470bd0ddc88c1710fd49dcp-1Q, -0x1.88e9f63513ce060ad42735911b82p-2Q, 0x1.6764f965c95116ec3ca5a4be4d2fp-3Q, -0x1.91c36b23af1d7e93ac71caa65612p-5Q, 0x1.07d03d7a1adc182d361556de1e4bp-8Q, 0x1.362d3e37ff6cd230a2a77cad24c8p-11Q, -0x1.92dbfdbfa8197afc834aaea734e3p-20Q, -0x1.22ff804507dbe78851ce06e1d7fp-30Q, 0x0p+0Q};
-            }
-            if constexpr (order == 14) {
-                return {0x0p+0Q, 0x1.8dd6e1684e11d5d1ba3be6ea3c1dp-6Q, -0x1.ffb4de00653d36e2054de2d9b35cp-3Q, 0x1.1f8df89dea983b6a6839c59e1daap+0Q, -0x1.6eae32a3a790681f248ae47d8bf4p+1Q, 0x1.200cfdab0a8887ae485a3302d7acp+2Q, -0x1.1f287662480ab738cbe219de6228p+2Q, 0x1.90990b7ee9dd1f94866d2e2c98f7p+1Q, -0x1.3d166b62b6085e29fb936a0976f7p+1Q, 0x1.74d60ae1a8ceaa71b4a74664e6fcp+1Q, -0x1.68026579c2213b7f75e6c5dc86c1p+1Q, 0x1.e76ba8ae988d51e5857ecafcf58dp+0Q, -0x1.60830949d4c82da954f5df283712p+0Q, 0x1.48f2a8ad7050c9588f35978df03dp+0Q, -0x1.e7d09d1d5c76d8ae64a80dc22b4p-1Q, 0x1.1252ee85de9250052c51460801d2p-1Q, -0x1.6e9d007e3ce50ac7539c0411656fp-2Q, 0x1.0a88fbec92db255ff329ff3310a4p-2Q, -0x1.16ea71f276b00e5a14dad4f88487p-3Q, 0x1.018afa9348367b971e98c4cc0c2cp-4Q, -0x1.2fa053de7510dd5de40051b25ee8p-5Q, 0x1.2375ee2696f86cd08bc27b41fb5bp-6Q, -0x1.73b10c938e4b6609ab6cf8acbfb8p-8Q, 0x1.1decc8370b2354d839f55dfbd7ebp-9Q, -0x1.b8713a4dd74a971b693427cc738fp-11Q, 0x1.732711f764c017456161af308333p-14Q, 0x1.5deb76c540b6c1414e8c8011ad5bp-16Q, -0x1.9271259f104138f720ca0ebaa72bp-23Q, -0x1.2099915b9335422a7d16c948a51bp-32Q, 0x0p+0Q};
-            }
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            if constexpr (order == 0) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000451674235365384163942534112879962170050430005649917728757105702078353003628"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0657192182866101725866380380286811711515267979947671850787346119584203921772"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.645168852837185491636493374398382329354332388562492079567204840361307401530"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.562050253731258347205225316820341051454701066703611230358129787369760785703"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.457609012865475182073165321965578159870245716869287833800525163245742305892"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.302206642786606318842929559153148332332027636245062198716044751793827663646"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.186714728860412474380906761378313253397706130867010868609662030951952027624"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.101921407123630858758878752387723770129600361381616407855191001954194217355"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0450695281445151618957628013259453588544003268599264913526498769137792861370"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0144290759837282383389717270501147248409603304909144671371390973500564022245"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00262359805753383314662667515147465743725326741143989187946940239264695275198"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000418886520841363769876466059678934092937240028663097642468207760071276890909"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000130005825599913762664943931799127959428720573899694402098048868888541005861"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000205716103829132083896977152938360606246573125609400824113246425939226624402"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000586498015739086657425466432113622386414392393452860334775926059357778996230"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000499957637035187196702848333851389108402668590913054256330886021719308298712"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000138797970659198398937552944013353477360674956899913623607020403817559610213"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000293246341063622314369884411909694341374016914830560434158406924220522844059"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000266108789272668583275470247613518141118690036911170538022214691534270571516"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000358798958751818824805546395996552774193550110102954766818768372071949994542"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000411940737663914578546068859164549863164641326242451122480764989500567400523"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000943444434993874525374981775164876413640256062778860481019536432363883306329"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000802555990656338684626332640433500241162747359468279574694310485074495210891"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000234007347019229302189231520607745332418408168658262584544662206333484487383"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000118063935549154939400230495672962537326752673673203124419820222929027040784"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000902156164058513114611965908129419583178659829820202967090436659668867250204"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000103213448481218221009064172156534966525116936574987378830865635836819679217"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000000000000000000895260346451574665144738326201699984549687922838691880872307609498354042916"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 1) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00329134509554637016227932395665184462188816405990441294841331937353859018226"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.222498460222472570856273888144670809240856508400605204839473169454853935753"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.795584053870187153774544931353721619014829085153170531707050020981654416712"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.31862487452009442113191889013673630946692796798217185455367151031243111753"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.356227531120169092417942057959374242399264990210294310292353566593351691969"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0969118974391443107220210564208451767882607680272587960271393042788920753139"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.100158344781294000713035822000520082413219469752287984509961094639923004704"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.130036817018062768743563639955461355704215091556126309135663258237107378316"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.117003736727942246589361189897913287911205837308941552740306120021988232773"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0735583247350015119447973100838355102019211295561712733895699734366729336147"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0320443599633683857344012220821277284392085436118203012615734033030618281606"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00864611125470508985643225531487538786192034817394773971373053363374166094832"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000628805288742353846490436895658042874791044019850556792669438723659506085433"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000530996165887140074103720044534180857989796558151325571171563750787375335630"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000214779976330435101072773020094474738162154098655749881678420221771826004102"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000181202936405411896779927444691964784933446136755724601326144179927538206594"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000983429208199500966319547766620244833625578532495918145530854169815290840910"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000291695012617423905198714249842169472953358927807533287184982174200989887962"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000816805151056558922184516574886797062939832551592181636407453778207357205351"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000552147222971053211575103164058845299224045417814192301423715110168730452639"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000278043267728072036716596349031021595779494213305561207660868932770850125951"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000506542254942098412185567568651337434634840678880205714031416165837498235238"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000808256938962468939245796995705643475400792001340399660747359264165908131377"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000998582294082358754350176794222318406554783198601555538700921435939017946389"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000351354126713507884430073360081165916784665517276373638465106586156112456813"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000157877499711653737932118233203050006270260955310540472677365606073041849944"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000000000637731750269505916186533295298744348554008849524832564488593506481003691981"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000000000000000110631985666703620681934992597766218656255805692698991301252307109696735556"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 2) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0206704348828442146455298601806634783291751329720893335837042915536707378997"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.592227110732533668578196417495075085776270621924559929262444977224271579097"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.393410653765291902433654817300663592654609126271817695403842500410554851245"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.00825263709370592101160988069513144599529156226855536777407723196800985003"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.45600402690522611687855374504814910966687688506140696928870357367763805207"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.86700751870813930579622494686911790950745721733944746524273875866576699091"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.88647457798347347099275071442649242213607288760070094281108153092725485932"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.956850292836935604631540519513924221386391922474899432365133146628294288211"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.311019178959628658277170626061412967741738777405140811903034561579177783544"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0194782967746181932246482266173892495865298049064803547744629981318754422562"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0313570829471545004393086766795416583820751761342161837181042072847055050674"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00615150822507380481298471457879524284933712566490823438535524615873979419699"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00820031568959443119144645656936832514382458714118391502141763262037478621079"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00559689979763050004637051840086547958672230503688973990238062875917621549458"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00108962928377240734615453107312674463537085212267186648902987674997945923733"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000258864319280176698538293850130236134559386073543313286799132944540622102087"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000171898103078683638566235253747478209530138496225519577636080550780658518207"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000309643593428530836922212378988146884356326608056935343727759049059725321223"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000992193952216759361998206689460639053628352064203189180453876299839498267728"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000407964839436173861149529833860827000185779144514563959244446135200869586348"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000705975083156988948042006749490456594343348564541499729785531649950346638501"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000155494179555932056144441546086944808103333056502334729683797165052002203223"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000199857445192527259692451554428036856578337723773413083760501868541113100329"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000183942900453685991873954617889384304378063723737901417198613372194175703222"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000280333173005321969994829794928971151622655528245490950449547091812376086824"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000756287516479864730495516004403817436298330236371191825066059211760651100095"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000999665788433766570461546432082424563816636646761251573329874233246246718961"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000346838035061342291761151778299701276081089278724101229318566334215065043283"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 3) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.108860484914954355575079084123243067459138310025744627437589606265973071599"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.998887833249571574793052798864346575877689982939641232390178172030375530161"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.23238946756428856622131292649026891499466392216766277033807459199608937126"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.88370889419216762997764273176879062741698215984105909165713345305176600493"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.18153972950635043322094865169225941018236097827115854289221926390733666302"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.68625382559861128387876607708138212048108442724703967044946506502965986523"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.71033782942212120942300194056190679749862535535035830851858838821499116226"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.80267337697322824370014932789371815543658898251892562879598691459308783545"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.29282987775747551395165451529677668919917484323451781112725285361710130069"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.38242544442842915241462115657754442376597315779845068025541999436023658186"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.557419509659821724210988870096723764341990624840837128686052996727907371417"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0913588351617082455490771960757168500073024080354221476837833915643532317832"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0521115869546275007352831459735453272977332230195277247545553011333489468213"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0437788320785046747745346318425081514627922547506568893727540135563564332044"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0126616673332992189763107668027329389224194983671833648722585850627694599870"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000441448103933958333509284170313361172667888623881067406682817939537903874448"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00145361406367327911114133543555577415997816227432838988097249869672074010228"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000386870394595489219311323992284710227818861035531855271955313566170705603465"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000127675849793530154804055067259332359495984011575122830149195089883065001976"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000984202193485852050035097860846555963077977093712397464798289054164353785487"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000121313056970512630452162029729108592943238420540807995979786912047956902162"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000605861992739089687382030498760415289269264550833486793263523845161506867233"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000480637734385966690366533313966404604324257069377664472991243197708870665367"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000876647773931341316071062687585175265372059405788465230989307402677425063505"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000789693132057393370058232851770479415791480697650703122951856272042933692562"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000394568035880557031827281908497945772005279351103258103359896718769121745485"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000000000576186871216969872110176316067425636374680848236512588856967818814130253782"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000000000000000399819240477850657780597515175272454717319941884716677679140202464346919659"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 4) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.463497095089465556193152361674354253550988460728700341512951575248924005107"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.260338621434017069194053753179442990911796110131041248263757604108300285944"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5.72933785864723347958689894576856896970871030371827125012166758462465732047"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("17.98064416088037112447262961210309819025869195128448398522612428283054724080"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-26.15115449481430666135654454601908476913798365469208452665031301194399803840"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("21.63822079230404623177750575684281008376996692891143829654563260593428321030"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.05817968019025161983821299053916328782422062221848193813994955273557967790"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-8.11181128099913899853666875636635568569027342591544318148780945667167347907"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("14.43923347370119331414236561312914409252115548929447052983356089629331208180"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.60766039707057083044613368973988543650262251496746962365376370801259816429"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.254349894074616002886672766738792455231069414161313786718905562281170886778"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.45872370542653337904479516900588079252234184768289022901378718755768784979"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5.35255306643817868800359080338618790990023650113900088092988956482209882224"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.61884931508941023112322057748116480880128421631501355291655017759032872768"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.544813129850747446272398562457900585540272070585851811513882046278191469393"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.131176059127497035521761280194566727490837461219732199796495750703105213740"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.124296561686239461871148096056473522101237708684506720861975326392569561724"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0335032525969103386712875546102562852883523762416026454755015996210457308706"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00197687421925104166227063798049851778200652533856069925030249177610043199615"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000907463054694841802512946678881228619813411228517790637608215643817975804741"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000174685093401222970344248415273071087172528039501120783385838904981987795138"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000229140491543835493234065523810377340538057291963129940713094363492371457667"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000917376265236181573917176045082865834981330874821423583901682913289270269380"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000178074782772529767026962575165367966565557061024587011596888125628493484815"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000238787852610260980034963670269451676132667432806865308573034008434193644445"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000151801385578324942916928975944130135623202429359583566878602650893789670624"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000353106940189348195874403026790192524180728472834959918047053114899585048985"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000000000490042195447641265484925140544266723530168196082394169729111887193451305107"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 5) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.53968424333623591283539637104393285306939860118163339899756370093511752412"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-8.36118093364641071529734734349327158167828129455095101209909508144950844421"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("19.00710265475370468078225452071655698496996076626930820052271290018734955410"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-24.04052483563886538469582688782856892395508706836015455488573334599930766580"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("20.63913333795138578853149761490637030572718665431616641957345863819867808720"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-17.08011584958297102568375705513842664210388848702083749417185061652687170920"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("17.55524143428210432499122213752206106254752320830907975294234324350799433880"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-19.56455097953537387041983773986348842091325243494736289394773636533578502420"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("24.01670498281153432550600418634366701269994413307461865903740508422306310080"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-33.28148132262550348111697065791345588077894804510178954360174393891984479610"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("42.28936350567703557972644120171241320325939901556345142153549130433210665950"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-41.40943373570026124612528767222691112123207497138997507301595976366377899660"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("28.50368136498153869650031108535771315726615052538666183891156005702322580770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-12.08970059569761086730267951049932958603674239966305615386495196624445364550"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.46119126096220632514786029604710199172818340040776736162153531687984436840"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.69007268736527437715523188086809199467627091856919669141240791790387659253"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.16921124742703235845376498243007226742896232096052353425298018102553247710"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.320806648634560611806653735358063869544619918599484137286628075250908147793"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0170205999053340524093626134534504044131532660032315483110190757667509195644"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0123745609743425718328045581079363596477322528018678302846161407372341760769"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00269495872461749278937894414651717305557023546290073525941350512704421287628"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000636240007004980264934020663683814909158562231106074681170796063893995191439"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000193455103657614392543301741967257949034899863831055047403088880777986411556"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000543047159360829865209946475973261539370518740747480923818151249126619846189"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000778598331220689574680060505013012792715985361940745149089414772050997826569"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000685925299554479615829881764374497385028698287479222092891938709078253622707"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000235738843909944600637338699828608981498881273911589420488771624426365157864"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000000000654307895488301061055340897951003080401798618960776945151552704816810354728"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 6) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.76046627819172595883579644359769953588535927343615287177933134988108839887"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-29.57545007102832657505743042011930496079450543026239630758938313589160532240"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("108.06076562293097255019034894476937881414402744559487246258107823410272147100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-250.55855156825033737879997781487474575584645685461277748381454265462847743800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("433.85129088951476536844660346166919823690012103418599659417068253860704897400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-633.13061187142324243446054071388968011665704146897570849362072311779672021000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("834.01854300005356154348334819062306666614375690886471768229153759480600689000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-989.02232878407997120358917296431206973916448753054681863157557204973406068100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1017.88603439602004763640177568787110596329999229043433566699158997753449125000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-893.85979471023473569530438057552113081237409230440464102711969573113903766400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("680.74444199320236644223784616878658122038563144919598756685948523953944743700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-451.61186729310171527075800065120538411278520704643026316215948118992976179100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("232.74693413172044063567820009907697632227981752574909323161715193839229115800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-49.62787383879085055577682941397994398270572566635118571746050265908129325690"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-52.68645266346889530866217977440828165209704972435580166424853416940379389960"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("65.58982701592708822194210862578781927575261800997369868610970088145137416290"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-35.30870806416811325167467803727623467536045583746263032317420353531903306020"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("9.45693020058134236236600914378186391920422807218483316498811188937316130359"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.309255989510124888838029367237184571273819098555330087401099231089501040621"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.553308322403180080662599855565330327614574762204447931420915764088214443229"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.135564956163967134955269497874425345862822277717224909042351279062593810689"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00531617697249685655413505764052220837874749434001927999181762850859579155872"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00133403209032194873051891038551751265477738184982267945387427251670469994336"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000540595013560067659511437186384964395648420570660778415392983733962063677878"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000852069217823962821991801896006403698378777746783454675044188487130238725815"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000103598635303144789735973280116080267383974282294610808060500440818154996985"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000532326436761189266527809050123441642697540291063663589608819865551319229350"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000000295492612379887305461120954141505699178535540439686934703841872278010480863"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 7) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("7.38188904221300776496009553048328527576967910065603262630183408064961588176"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-67.04252259666674067633742223812249438362172734096027398031203225656148164940"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("272.73912509608366716885866926191887521865157404771591884845733117796365013300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-648.51449384638772307312239131652586511983283577261311478642454334856167122300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("981.85376383959687377603447626048634109920104854648430762305735754076198344100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-957.25261435887056636875408331000776657447691883681487882680731075009939532500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("541.30366603538032163248551525965043960470666784840537611909029954347476521100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("39.46539569102171970705958669748925636189807552510212755901108827273086521860"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-760.02993356684106043735642415972224288718293309831726448424859435908357278400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1757.96818720008277561277665672510216931821317114629250348699495528960281618000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2766.91476513255525367674460260698725596040373449509635634609462930432032153000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3221.41783539270407631009108958251542185799510806531936255493906833962767291000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3000.71602754404820657764337837297990613638348460036621198220820334626336373000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2470.42433778280717582983628335578899816038747362488063072589123876893726477000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1864.25821113047613457963263669044806128695158307572413234609544859584885145000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1183.53150011814970334873822520119965114014726798970411170643520179119098445000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-541.75058318442630698467104298817880920356698078100114691327566384707686791700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("137.99951240297224977307761334347678893729357990322145120547559793252791826600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.12602732950121750809668208362625489517387955383131958143915945154981671955"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-14.36194117187840557384339396841994678599549531498197679768014612622396331010"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.88369251450641812542291404390995294553530491514707983578184816105564596373"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.205076203523751335646189692334735950522359458346215290146294237414818037925"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0519198673443746908093580937887859538950707062316162140689427725731341271982"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00310590105240650772150514682372321446899318001963069459842377331199995861966"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000511716533793490097430403325096759854066642658007865906291974896322156973598"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000915379504933333794585544205822404705959783310556611306655341242734341633518"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000673029022229937708128420645199884166792336526676086359571430889068627124496"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000747149572478212798771461071516239850864323299591892246195331160945379616491"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 8) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.66617997816256087920214536690617523746852206827065901622480769322290866167"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-83.98069158491897137664435643009459588979224859539210985853414803563252312670"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("368.87018005167903705545229666937571099808324458744316183527918620353726742800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-978.60152567875426023724121513068510566332100363338255210925843566160434538000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1788.17285471112791661414958933940320019900977016707109161896875006334039594000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2505.28418158917689197444930176607319501629136847421443278162092799123039839000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3022.40491246297357949186655015360733638291689023377677784285814202906653466000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3419.39265112219216302436718059863861209172985626334602672566056357398676317000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3619.96406625884105825247254683983713351764036286848853247298077428329530067000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3448.50066768491548867152223553559079606474609521504982348767152988432081387000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2965.26096092775058800222809037838051197376961526002823132548802908800674743000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2370.21566471701430778551537838896798515071343646894034846503015619772514804000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1743.38269029053220243343945130374232884233597011426038758644227989592405303000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1131.51593963642249460026014723981984745424498754407883282530799710966079933000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("643.76118806159351516503113028075491121270396142347621937335117880501444850600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-326.00074420849016938772363017187446532879284433779346261909720782417377859600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("132.04863636507697220410685855738565713363890174302170404844428502247667225600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-24.93376772277967886098168919462189547482955889196701960148760723136973166400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-11.46007355523622142805150360772463017894407819656429723380717693966775564550"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("9.83520651597144304944047691431100720299540773467198740353710392336582989354"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.69181598889969722526095182382965976931346646569879768346189984962140006978"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.170227793119178996114554027953840164114050954576165838411751690985113034637"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0452616305587191906906494463453331102952776770834099929727401231003607603490"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00456974512275900662016820515100695013104712320434429376265064123517366266192"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000738155428701868927889552496062375155784301031721819122602154168460705282344"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000200417805609293879064935927873520236391193751194342643471993129180158539068"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000209880706796452611382955148605270725220758859068164296317180454372369377273"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000465936380567652114719537560618521630318410912594224492450951043895287614753"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 9) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.72847835430747578271505940879392817014574904538191687349175230203052100211"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-87.24046040248515953396974656933062782610014739997179110379894560357414245520"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("389.58988530574605311236047709354236113070541543269814845208675455966229540400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1026.22221524757438134135537633211873760625163523383080063432834094852546692000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1792.93918179541631021688427461004056301988797982219951847510033799076038456000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2288.41214820149496386771786036086875129982895627472684354601681048945900938000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2458.50954360267178809055553896154712231820849082662071689423543492550962685000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2596.76997150082880482258601881426530105265882898194790860287791956876237858000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2688.38307737987921311800960622311996109514265545357119388268171549268774070000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2411.48650321182678409587384256865680519785438974750423956549570619527017446000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1814.96164224744171541403234219853877586836575705876463094283829263461877926000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1261.78179075598184586999264045402353666457191513788617366898826973902302211000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("841.38676655654695150319104651983606990067095607106581498410485823300639441800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-448.20904377535777870670016285684401262406426096054935991931563578462255940200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("137.16569415040272577867061166123400360598914522499642465421078486401470231300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.97029509532788895885164044921726939214354175896907818967947070760987898130"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-45.34341860661268956588627411545980012291737814825718255408526440488307550890"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("55.74735370610838025915657695145098428353232401912757615516991907215832408810"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-47.32620271933516468424041285810723316313451633124158857561987010794991368370"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("24.41065715637416470293954557751523613609531738353047901798090642091718991060"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6.65124396027002908823875984373242061438238591321150033722971368086704479617"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.537531975137361943952820148566801590297468742601138200538147419339609552580"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.137261184926968071617250973316263533192179366757491899389956174516444039153"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0239757337968515916483444709404140761125184131451276108629481306614530373711"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000410932878749734216531821493671349775506467371457544836055057579036862846795"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000165640171463349552097550017612947486316141194677792210133363117017273377794"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000258597924701581016593914203020341509426840234287159000763753949926949104263"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000114791530792780648836943943902186807559930855796434559067866982676609926206"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 10) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.37287144211047504433704259901170390442721988996694171621504548629516455500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-54.51890809483490464852283248943415532742549501170721326549017349607757265280"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("247.65758677532204293221852843860039171893106744274564279152987067839641783700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-667.31952719692784203091445371189075055828427651171572798348516350202578612200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1206.13444150385134150552864103423123937369610639043173021135297756204197139000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1617.35818646827561667680600978897561880473542593995241051599248884894163073000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1832.49156632655474156472726861249059324354983667150184526174507469910118731000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1995.67103845695443412193473876339890830254900007363102304644200890512301198000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2131.02770891534946890637577113319756817054287535999854454320796762879118815000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2111.95187513591062446244103153762651327657529103137337383793513437628034658000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1930.80461644034257841108186913574331573849553980249852538863650267384764992000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1674.24706814300119787406852339956482688948935893569842998213675767018340090000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1366.35661279794117490633588742507550359572013220593797272821411949768939054000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1033.84481571316170085412808060764164688210636040456382284874028192216356915000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("737.90900404538211792129865165976450017644934243508965145264819927501132834700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-493.95955963918928208805985585771230332863018601652969197751321482230632186700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("295.69484249333185830134864171026294553463486994728404251971308252543408822300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-157.95033466620052198343083333630677317616869298083612156110564608777827008500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("78.86126735894737975190973401300435275810030284606457363717046418120379800980"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-34.19939723625297188671822278987343132401852492048877442030253470317557547340"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("9.85480851482372144542629775026818779321611645636661320085440910666337715905"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.881195797409289017926845853302397485367129834932274334657677636659627396326"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.341364051723345408298411031291185136527925242955856494823260412052622050419"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0769303093181967020937802382117977446742217414595484586532006746274227409798"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00111175217988709633101089934655770002991047763696322734469092738921189950071"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000982647635077159314335458943401180956222687035734331269592286893349623594861"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000189133470696662119943963434893213305034415041925165273061718661046346898186"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000167835835060281197407582642924424716906566393004236332464276808169954678267"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 11) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.02130420622658340696449326038237531822446799531129776174318955573407685405"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-30.88723257001993621576643426629273861715132220480188564481242234143744414420"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("139.65307157164095118547259358765798565209048590969720241210221184082814259900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-366.50716378087925339618840606165232094377044199283379149990581531088506707700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("621.10849644228854707468833979073748978917989740451446746601968372897995517700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-738.05038803654141867136650825674832560704059341561497206520134648959243742700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("716.22760163975362868384596863440985771640184356269565624056314309892640235800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-720.40403662968977912382793878795331281967949028146265663798101543449138262900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("774.46958853527806540260330998289032375034119650758547176995108093121313426500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-736.60195800103968521796236805592735351842535720597394502820018520167468427100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("596.31626254658612005766603140598759356655195606907637429116209218854881937200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-471.58378761708200298998558351304868385444119358761564411342671419904990477200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("378.39898275809490245077643425004608535503558145569856205930880098307153717800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-269.86571703409037356854373301981664730493718351969444434530300707084602972400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("167.75440605674704647078720706448625075038628046714247177190414075458807244900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-102.88811870683190292233095418098044601993226910564909825458147979457012259200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("60.84069783294831355931283800609894422578310981797539730725548116612260807360"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-29.52799065611523148766040534779036649587797273072633016718343937010872259070"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("12.09044122964690028250983947194193410583757173591995469038844600943694632610"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.94541561682043406565916615601715119979854449991220349537517054946542132239"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.52761066076119130776354014949615007676815462459446946713730714810296595229"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0304455420249075430891047039138326243093334846566920021789140647984175448097"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.149650671652588930076956033416283389031589049770514927584948507803553202910"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0336574490088785668148493615449347354611183173599708036294762098419950316423"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000126497027151469654378765535979290734289731625144899692503470508091193529475"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000897116011370451342055211796348790683035477616931359835457707561956726691767"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000142409422634022110726759123860758274606648079204544228006777846621754692259"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000252515640185869778340276613779458838796409717012259538150426423432799209608"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 12) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.13501118834531862832791685103090778732600754703053509379504805718104885902"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-11.64655725601608471987125140319522273869255472727074641759372417306485077730"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("52.47997731358147104819352051854695978618817398284168789151634324060243697900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-135.45701731410847795494161971266033798422685436748530857469841989392043701600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("219.96124976643716810233421769891415115050379995458616095550270708427626420900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-238.37499127470823560688111086646834383929171370516476493761439859373820683700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("199.79115976545848616437399472512434089517222358850429527846981583702591271100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-186.06580854955499729692153505979598892043417420915640640747325871682106260700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("208.74631601283777221705885370999784696071568535053317514980802005864771752100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-197.53853499262074041123518689566722947819857600237876006152376593189070798400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("144.50075463010970867145970534859505768015783636183955794684498462003441805100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-106.36870296080726935127337203425079184767065663506312262840651389217392205900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("88.73938682065148057511439985326164459436444773853443006110286562673807699280"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-62.10218520435182935953770979789019089452934455495249757573801037083579624320"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("33.37756480360810332092878948658803898197552007679892596614034975425467298740"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-18.90612968481519997245444759492813159382596260487606074048382930111416740570"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("11.73182379476133043347419318594516895878294775638321702310633621242203615490"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.89127651169185001615684659153647879805287303355244863107672447172949919127"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.05628831785634767244430613794778237383118902182955930156963055438457640198"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.278924570772378963005919620761891241290397678645427497366931683979103470313"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0349217046715326267223252535829602432217755405230717045003308341586538338077"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.173039450787921076573568728042430497574717189628459371201122511640416535804"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.125154600705023543935668144417468315166811999855906394348835987111005330572"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0291520111880351888227853532698326680951804379655921639568061622853077591827"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00119588167326521772050685130712167568577493075580492617893532154147491503516"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000166966587098874949698033688140021197028135858548757937517355756848615445303"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000188051207904050407421484278134701770752347161244389100186827497009857301113"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000665676590058883342359366356514472856699743985374049531980671537812596361102"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 13) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.147328387026945181742534360727928536657557400346046037192839862582804936900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.51456549085202376204483791233550876670959441040514033264111698819378554402"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.94414619972386232622555773936309700660158456761079287802696168029991317902"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-18.78704596117275369235580835040616276805576972998620945843399189205354798320"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("33.75320683102715133888929607462218380210425052594719299190672951764918964970"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-43.90968018808903858591509195317885887927809302282775758823494965859626988710"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("45.83007041045357748015949276788143174487066194868689328670377077172900922670"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-43.30834737848262311266594213584179463295479030127624741231273476750096363320"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("40.28587342872956736979372620674121597409935291189432692644089811506211904560"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-38.07079933210995921006056307099293201249460698597519136937589815349848540930"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("36.48645327878740068202506706074164138888906527167902669842548785200456090760"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-32.99863707618939353424238452194841065903680035129007522576517208426242003870"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("26.55970062209079850156043839739581666886976736313064228805575294861660949750"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-20.59842254567111580869690652690847120193788739757843717989385899237339101340"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("16.66182339593160150140392670274598786225164619130356052597867372641808254150"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-12.48056679222918764776819055454069770140079985190646278545971576285539893300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.00729939791465563598426689351883338497952088924077343600523943715192249470"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5.05071646613187505818485190469727424915951382050926867171160457018863109602"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.29966711978217146018111284131326004314469156813581461296273109642531273479"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.82568661448281886663681039165151047023026983547946329025101178092516198927"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.821545996592165413015176926103918379703993671815822408869238370242177789874"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.383704993238053425488527996051173229244898380519514965582775999086944158021"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.175485561770223825536069856812357489141836294882044305667107034046144733761"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0490433781210161672748726863502704850354754206732915757148321796262332557411"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00402547360327382273192760485491174840524317417151707477913869414062168673233"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000591615163102432487394020984370444214618369356333750305162759222030306708281"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000150076799335799622176733790301367198750063662367274615802926812851245445696"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000105864474240497768156598640472330313913710369319591100716113011216570777723"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 14) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0242821885342162555172194807204060720439176164669704179647896832718856332498"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.249856695544308322348171496342170210083410754460476379583874589925971489368"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.12326005797749044778439744178131419781661379271554672577789771011822915870"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.86469109526581467211201873076519837722365386321507572083194802001927335161"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.50079290106999295066844741272526027729937316456024276862452670751556633337"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.48684463117403305020608532973799146401232890979166234034679061467612710549"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.12967055985402796636707893316937491613623416550895649179552121609620465579"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.47724668807865361819228723977775474438205454678621615947243362585570677107"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.91278205889249382066105160662535333323212648243270007533168890574238996600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.81257313199263046793165930650235695480992793053614182870128250653240399226"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.90398649466128702523970742655503101903096138960699394205660617785029524613"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.37699945499915151843967957813503956475301514890644971272041072293843226357"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.28495268091529903567348249127974601649844237295023870994028850106617764318"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.952763471445207071061796159152966939284649904476335068736845300084967366990"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.535788968888742389713782672547333938330308007633675251508339886039944284585"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.358020789818714250877447233131478684920110238088884239583652089996295811608"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.260288177789983828698553363324988305811986215701965042156106479955015465057"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.136189356052305779370763109924086580150032155644746928185072140262278106899"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0628766811464750403125935867053544555088689453179188749663490799516604967151"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0370637548509496888808797750019041755705513054464047218196448291548517149764"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0177893472376662545340696681623277652018062438254456540388233762026125185107"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00567156369248172085563495886241541581202423428371480185063640538001288280474"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00218143409758500086570687953062016667230176987210602107478648809100271457937"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000840077010916613961293716749850474022730704167044599676252293240098595360069"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000884896797884032945739919608263751800212682320278642794159422173907791309331"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000208568442490274769998537189218999959487143160425280136701000686328977000945"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000187401650616022963832478803386742923717598478201557979913608078604137745338"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000262480056546984342244841766991496735739199664461987202512509327833476650923"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-        }
-    }
-    if constexpr (p == 16) {
-        if constexpr (std::is_same_v<Real, float>) {
-            if constexpr (order == 0) {
-                return {0x0p+0f, 0x1.674708p-13f, 0x1.27cdb4p-5f, 0x1.f3f9a4p-2f, 0x1.8a1b0ep-1f, -0x1.d00082p-2f, 0x1.06c982p-2f, -0x1.4ec10ap-3f, 0x1.b93c32p-4f, -0x1.09f5f4p-4f, 0x1.0b6a76p-5f, -0x1.a17eb8p-7f, 0x1.cda18ep-9f, -0x1.18156ap-11f, -0x1.547c4ep-15f, 0x1.a1d518p-15f, -0x1.fb90c6p-17f, 0x1.085bbcp-19f, 0x1.4a16eap-22f, -0x1.3b0f84p-23f, 0x1.42695p-28f, 0x1.acf5ccp-29f, 0x1.c7dfc2p-37f, -0x1.99a498p-37f, 0x1.0c54f6p-42f, 0x1.60b622p-49f, -0x1.63607p-54f, 0x1.f308a8p-62f, -0x1.dcd83cp-74f, -0x1.f4c81ep-87f, 0x1.f541a8p-112f, -0x0p+0f};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0f, 0x1.5e2be4p-10f, 0x1.115596p-3f, 0x1.8e066ep-1f, -0x1.9a3aeap-1f, -0x1.b4e824p-2f, 0x1.24d79cp-1f, -0x1.96ff08p-2f, 0x1.7cff08p-3f, -0x1.3b2f7p-5f, -0x1.8c4396p-6f, 0x1.d82f62p-6f, -0x1.d30848p-7f, 0x1.b8ca7p-9f, 0x1.4ea26ep-13f, -0x1.44550ap-12f, 0x1.116fb6p-15f, 0x1.e6f46ap-16f, -0x1.73244cp-17f, 0x1.105e3p-20f, 0x1.85ee5ap-23f, -0x1.5ac9f2p-25f, 0x1.d789f4p-30f, 0x1.8d5e3ep-35f, -0x1.c8b384p-37f, 0x1.38fe4p-43f, 0x1.f524d2p-49f, -0x1.a73b7ep-57f, -0x1.c53204p-68f, 0x1.a5354ep-81f, -0x1.a59b92p-105f, -0x0p+0f};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0f, 0x1.295efep-7f, 0x1.9d61ccp-2f, 0x1.161d42p-2f, -0x1.5b7a46p+1f, 0x1.d1174ep+1f, -0x1.64fd52p+1f, 0x1.05168ep+1f, -0x1.657508p+0f, 0x1.a38bfp-1f, -0x1.889b16p-2f, 0x1.152c76p-3f, -0x1.1b4c9ap-5f, 0x1.907f1ep-8f, -0x1.48b152p-13f, -0x1.a3276ep-11f, 0x1.19008ap-11f, -0x1.4a0f3p-13f, 0x1.b16d86p-17f, 0x1.3c9bcap-19f, 0x1.899254p-24f, -0x1.e003aep-24f, -0x1.b118f8p-27f, 0x1.a8e81cp-30f, 0x1.472048p-36f, 0x1.0bc546p-41f, -0x1.5b7878p-47f, -0x1.75c578p-53f, -0x1.4450ep-64f, 0x1.74639cp-76f, -0x1.74be14p-99f, 0x0p+0f};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0f, 0x1.ade0c6p-5f, 0x1.c28b44p-1f, -0x1.5f4cdp+1f, 0x1.cdb8f6p+0f, 0x1.f77744p+0f, -0x1.dd879cp+1f, 0x1.37053cp+1f, -0x1.1bfa76p-2f, -0x1.2b5034p+0f, 0x1.63e226p+0f, -0x1.a29914p-1f, 0x1.852868p-3f, 0x1.9a9664p-4f, -0x1.c29f78p-4f, 0x1.54d634p-5f, -0x1.41b2a6p-9f, -0x1.225dap-8f, 0x1.f9019ap-10f, -0x1.2c2838p-12f, -0x1.8e8742p-16f, 0x1.c9f58cp-17f, -0x1.61f64ap-20f, -0x1.96b8bp-25f, 0x1.71f48cp-27f, -0x1.b5fc8ep-34f, -0x1.c5963ep-38f, 0x1.6b4e6cp-45f, 0x1.e67136p-58f, -0x1.6aff4p-67f, 0x1.6b579p-89f, 0x0p+0f};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0f, 0x1.002834p-2f, 0x1.74f146p-1f, -0x1.d40722p+2f, 0x1.2af6fp+4f, -0x1.a43136p+4f, 0x1.9a15aep+4f, -0x1.38d1bep+4f, 0x1.6c6cdcp+3f, -0x1.13619ap+2f, 0x1.d56ce2p-1f, -0x1.e42908p-1f, 0x1.e52912p+0f, -0x1.ee224ep+0f, 0x1.1f26d6p+0f, -0x1.588844p-2f, -0x1.9e45fcp-7f, 0x1.dcd2d2p-5f, -0x1.93116cp-6f, 0x1.0e0178p-8f, 0x1.31f3fap-12f, -0x1.f6b0ep-13f, 0x1.f05078p-16f, 0x1.2ec5bap-20f, -0x1.47f2bp-22f, 0x1.bcb022p-29f, 0x1.1bcefep-32f, -0x1.34d97ap-39f, -0x1.6f2c8cp-53f, 0x1.34e43ep-60f, -0x1.352f98p-81f, -0x0p+0f};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0f, 0x1.e5d8b2p-1f, -0x1.e7e4aep+1f, 0x1.643948p+1f, 0x1.8bf778p+3f, -0x1.39576p+5f, 0x1.f6657cp+5f, -0x1.2981aap+6f, 0x1.0cf3p+6f, -0x1.71528cp+4f, -0x1.136588p+6f, 0x1.5ecf14p+7f, -0x1.ca8fbep+7f, 0x1.83a966p+7f, -0x1.9d9118p+6f, 0x1.818f5cp+4f, 0x1.4e782cp+3f, -0x1.7fba74p+3f, 0x1.361d7ep+2f, -0x1.85fee8p-1f, -0x1.fcc32p-4f, 0x1.30d54cp-4f, -0x1.4236c8p-7f, -0x1.6b6d4cp-12f, 0x1.251cb8p-13f, -0x1.7df628p-19f, -0x1.6d7bap-23f, 0x1.04735p-29f, 0x1.ecabdp-41f, -0x1.035efp-49f, 0x1.039e9p-69f, 0x0p+0f};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0f, 0x1.5c435cp+1f, -0x1.45ad88p+4f, 0x1.1ac644p+6f, -0x1.3bcd24p+7f, 0x1.1132bep+8f, -0x1.a33216p+8f, 0x1.2bec4cp+9f, -0x1.83ddd4p+9f, 0x1.b1ad42p+9f, -0x1.9d7a32p+9f, 0x1.5526f8p+9f, -0x1.e99686p+8f, 0x1.186a9ap+8f, -0x1.4f805p+6f, -0x1.84955p+5f, 0x1.59efa2p+6f, -0x1.dac7aep+5f, 0x1.620788p+4f, -0x1.88bb02p+1f, -0x1.04b916p+0f, 0x1.18c698p-1f, -0x1.508ddcp-4f, -0x1.539386p-9f, 0x1.9eab9ap-10f, -0x1.980b92p-15f, -0x1.761c2ap-19f, 0x1.64e7e2p-25f, 0x1.1823b8p-35f, -0x1.623924p-44f, 0x1.6290fap-63f, 0x0p+0f};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0f, 0x1.891444p+2f, -0x1.c4b29p+5f, 0x1.d994c4p+7f, -0x1.26defep+9f, 0x1.ddf578p+9f, -0x1.fd207ap+9f, 0x1.36152ap+9f, 0x1.d8616ap+6f, -0x1.190b42p+10f, 0x1.36219cp+11f, -0x1.eed74p+11f, 0x1.31c14ap+12f, -0x1.31807ap+12f, 0x1.07e38p+12f, -0x1.9ca0ep+11f, 0x1.192392p+11f, -0x1.28f7fp+10f, 0x1.8ef118p+8f, -0x1.076216p+5f, -0x1.3734aap+5f, 0x1.2e313ep+4f, -0x1.913ecep+1f, -0x1.aba4ep-4f, 0x1.5578cap-4f, -0x1.f3ff48p-9f, -0x1.bd3a12p-13f, 0x1.29ffeap-18f, 0x1.5e7712p-28f, -0x1.267e4p-36f, 0x1.26c8dap-54f, 0x0p+0f};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0f, 0x1.1c0608p+3f, -0x1.65d998p+6f, 0x1.9d8978p+8f, -0x1.24c8d8p+10f, 0x1.21d47ap+11f, -0x1.bbc006p+11f, 0x1.2211c4p+12f, -0x1.5c65p+12f, 0x1.845a36p+12f, -0x1.87e6ep+12f, 0x1.650412p+12f, -0x1.2b9aap+12f, 0x1.cebcfcp+11f, -0x1.3e375cp+11f, 0x1.7d70c6p+10f, -0x1.8fd688p+9f, 0x1.57b6f4p+8f, -0x1.3e2cp+6f, -0x1.f1e0f6p+4f, 0x1.39f676p+5f, -0x1.07f7dep+4f, 0x1.6eaf02p+1f, 0x1.f8896cp-4f, -0x1.b78e4ap-4f, 0x1.faf294p-8f, 0x1.a6b604p-12f, -0x1.9886bep-17f, -0x1.7c0bdep-26f, 0x1.90aca4p-34f, -0x1.91166ep-51f, -0x0p+0f};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0f, 0x1.58e7ep+3f, -0x1.c53a2ap+6f, 0x1.0cc18ep+9f, -0x1.7c92fcp+10f, 0x1.6a1946p+11f, -0x1.fab772p+11f, 0x1.254298p+12f, -0x1.407f9ep+12f, 0x1.53233cp+12f, -0x1.3b528cp+12f, 0x1.e2ea28p+11f, -0x1.3d616ap+11f, 0x1.75fce6p+10f, -0x1.2b5b5p+9f, -0x1.18e052p+7f, 0x1.ed1ee2p+8f, -0x1.f5a5a8p+8f, 0x1.920c94p+8f, -0x1.22c138p+8f, 0x1.4b1ba2p+7f, -0x1.ec877p+5f, 0x1.641262p+3f, 0x1.3bac8p-1f, -0x1.3ae0dcp-1f, 0x1.0ba446p-4f, 0x1.c3804ap-9f, -0x1.3c78fcp-13f, -0x1.6e90a4p-22f, 0x1.34c398p-29f, -0x1.351bbcp-45f, -0x0p+0f};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0f, 0x1.0cfd94p+3f, -0x1.68c00ep+6f, 0x1.b4a63ap+8f, -0x1.3c4fdp+10f, 0x1.35efeap+11f, -0x1.c3872cp+11f, 0x1.1261acp+12f, -0x1.39e1fap+12f, 0x1.5e4c9ep+12f, -0x1.6b72e4p+12f, 0x1.578fd4p+12f, -0x1.30faf4p+12f, 0x1.0174aep+12f, -0x1.942bc4p+11f, 0x1.25cbc8p+11f, -0x1.914caap+10f, 0x1.f93f04p+9f, -0x1.1b4f5ep+9f, 0x1.1df01cp+8f, -0x1.048db6p+7f, 0x1.730bccp+5f, -0x1.09b56cp+3f, -0x1.4fb834p+0f, 0x1.e38e1p-1f, -0x1.ee07e6p-4f, -0x1.913ceep-8f, 0x1.0726b8p-11f, 0x1.2751c6p-20f, -0x1.00ceb8p-26f, 0x1.012308p-41f, 0x0p+0f};
-            }
-            if constexpr (order == 11) {
-                return {0x0p+0f, 0x1.6ddd34p+2f, -0x1.ef9ef6p+5f, 0x1.2bec86p+8f, -0x1.ab3138p+9f, 0x1.90171ap+10f, -0x1.0b827ap+11f, 0x1.21c7ccp+11f, -0x1.3291c6p+11f, 0x1.52187ep+11f, -0x1.5764b2p+11f, 0x1.2d82b8p+11f, -0x1.efcf7p+10f, 0x1.96b834p+10f, -0x1.34d67cp+10f, 0x1.9aafbap+9f, -0x1.002f1ep+9f, 0x1.378956p+8f, -0x1.48f682p+7f, 0x1.17de88p+6f, -0x1.abd1c4p+4f, 0x1.18837p+3f, -0x1.72b116p-2f, -0x1.93c736p+0f, 0x1.74105cp-1f, -0x1.a93828p-4f, -0x1.8ee02cp-9f, 0x1.b89c5ep-11f, 0x1.5051p-19f, -0x1.a9ba34p-25f, 0x1.aa6a7ep-39f, -0x0p+0f};
-            }
-            if constexpr (order == 12) {
-                return {0x0p+0f, 0x1.7e688cp+1f, -0x1.044f66p+5f, 0x1.39d278p+7f, -0x1.b63bb8p+8f, 0x1.86b368p+9f, -0x1.d8001cp+9f, 0x1.b397fp+9f, -0x1.9ca192p+9f, 0x1.d28d7ep+9f, -0x1.daeab6p+9f, 0x1.738e38p+9f, -0x1.0785a4p+9f, 0x1.a556aap+8f, -0x1.320672p+8f, 0x1.33661p+7f, -0x1.d86506p+5f, 0x1.9ebe06p+4f, -0x1.ec9eeap-1f, -0x1.103434p+4f, 0x1.04d752p+4f, -0x1.2fcc8ap+3f, 0x1.7c24bcp+2f, -0x1.c84c14p+1f, 0x1.57bcccp+0f, -0x1.d81dbp-3f, -0x1.20f9f8p-13f, 0x1.c2f2aep-9f, 0x1.baf67p-17f, -0x1.ae94eep-22f, 0x1.af9128p-35f, 0x0p+0f};
-            }
-            if constexpr (order == 13) {
-                return {0x0p+0f, 0x1.a308fp-1f, -0x1.1df37cp+3f, 0x1.5a47ccp+5f, -0x1.e7cc32p+6f, 0x1.ba5aa6p+7f, -0x1.137ebep+8f, 0x1.07f96cp+8f, -0x1.f176d6p+7f, 0x1.0c09ap+8f, -0x1.12bf1p+8f, 0x1.de16d6p+7f, -0x1.8c7b4ap+7f, 0x1.565926p+7f, -0x1.13d91ap+7f, 0x1.8b69dep+6f, -0x1.15b78cp+6f, 0x1.8188b8p+5f, -0x1.e03c02p+4f, 0x1.12ed8cp+4f, -0x1.36a5bp+3f, 0x1.3d2642p+2f, -0x1.11ef14p+1f, 0x1.c294dap-1f, -0x1.4f57e8p-2f, 0x1.1ebd9ap-4f, 0x1.367918p-14f, -0x1.fdd378p-10f, -0x1.0fc074p-22f, 0x1.f945fcp-22f, -0x1.fb1bdp-34f, 0x0p+0f};
-            }
-            if constexpr (order == 14) {
-                return {0x0p+0f, 0x1.74ef14p-3f, -0x1.fd9d32p+0f, 0x1.3320f2p+3f, -0x1.a9e31ep+4f, 0x1.73dbdep+5f, -0x1.aa50f2p+5f, 0x1.5e48acp+5f, -0x1.20d7a8p+5f, 0x1.4350bap+5f, -0x1.549ap+5f, 0x1.0d8c72p+5f, -0x1.8fe88ap+4f, 0x1.63da6cp+4f, -0x1.24224p+4f, 0x1.7851e2p+3f, -0x1.e4fd18p+2f, 0x1.610a44p+2f, -0x1.ae4c3ep+1f, 0x1.a6fe28p+0f, -0x1.ccc92p-1f, 0x1.f93894p-2f, -0x1.8612dep-3f, 0x1.fd43fcp-5f, -0x1.aafa1ep-6f, 0x1.b63874p-8f, 0x1.071682p-11f, -0x1.a84c4p-12f, 0x1.a20c24p-18f, 0x1.e7f1cp-23f, -0x1.eb089ap-34f, -0x0p+0f};
-            }
-            if constexpr (order == 15) {
-                return {0x0p+0f, 0x1.31c72ap-6f, -0x1.a21aa8p-3f, 0x1.f656a4p-1f, -0x1.589b5p+1f, 0x1.250496p+2f, -0x1.3b0f08p+2f, 0x1.bed88p+1f, -0x1.37fe76p+1f, 0x1.75c34ap+1f, -0x1.9f32b2p+1f, 0x1.2a50b6p+1f, -0x1.80aff2p+0f, 0x1.71f9bp+0f, -0x1.40d216p+0f, 0x1.6edc3cp-1f, -0x1.abb5dp-2f, 0x1.5fdcbap-2f, -0x1.af4e9cp-3f, 0x1.57b33ep-4f, -0x1.736294p-5f, 0x1.e1a61ep-6f, -0x1.381382p-7f, 0x1.a99b88p-10f, -0x1.191adap-10f, 0x1.44a23ap-12f, 0x1.4db128p-13f, -0x1.2cad38p-14f, 0x1.f38c66p-19f, 0x1.c87078p-24f, -0x1.cdd01ap-34f, -0x0p+0f};
-            }
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0, 0x1.674708c20fd28p-13, 0x1.27cdb30a789aap-5, 0x1.f3f9a4213a58ep-2, 0x1.8a1b0e63e768fp-1, -0x1.d0008134e7b25p-2, 0x1.06c9817f611eap-2, -0x1.4ec109006f3abp-3, 0x1.b93c322324f49p-4, -0x1.09f5f4083e297p-4, 0x1.0b6a75dfa25cdp-5, -0x1.a17eb803ff746p-7, 0x1.cda18d3f662aap-9, -0x1.1815693b1e50ap-11, -0x1.547c4d557ee7fp-15, 0x1.a1d518779619bp-15, -0x1.fb90c559a340ap-17, 0x1.085bbb58c3dc6p-19, 0x1.4a16ea18a78a9p-22, -0x1.3b0f83cef7c9dp-23, 0x1.426950d9b6bcap-28, 0x1.acf5cc83787c7p-29, 0x1.c7dfc1cbcd56p-37, -0x1.99a4987142751p-37, 0x1.0c54f6dbbd52bp-42, 0x1.60b6215484a1dp-49, -0x1.6360709f9f94cp-54, 0x1.f308a7934d099p-62, -0x1.dcd83ccd7b40ep-74, -0x1.f4c81d09055a8p-87, 0x1.f541a7bafa402p-112, -0x0p+0};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0, 0x1.5e2be3ffc02e6p-10, 0x1.115596e3350edp-3, 0x1.8e066ec21fc6ap-1, -0x1.9a3ae9a2a692bp-1, -0x1.b4e823397cf88p-2, 0x1.24d79baf908bcp-1, -0x1.96ff08990aa2p-2, 0x1.7cff079859d45p-3, -0x1.3b2f6fbc125fp-5, -0x1.8c439625af32p-6, 0x1.d82f61038e0ep-6, -0x1.d308486caa608p-7, 0x1.b8ca6f1e525d9p-9, 0x1.4ea26d28d3087p-13, -0x1.4455094b3efadp-12, 0x1.116fb5095b29ap-15, 0x1.e6f46905743cfp-16, -0x1.73244b5651139p-17, 0x1.105e30d7ecb46p-20, 0x1.85ee598e5c773p-23, -0x1.5ac9f1c76ae72p-25, 0x1.d789f3d703addp-30, 0x1.8d5e3e20027e8p-35, -0x1.c8b3833c3b769p-37, 0x1.38fe40b99904fp-43, 0x1.f524d19d8420ap-49, -0x1.a73b7d5e557e7p-57, -0x1.c5320460bba02p-68, 0x1.a5354de9b5e4cp-81, -0x1.a59b918cf087fp-105, -0x0p+0};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0, 0x1.295efeac152d8p-7, 0x1.9d61cc47e5de2p-2, 0x1.161d416b67638p-2, -0x1.5b7a45663376bp+1, 0x1.d1174d09edd0ep+1, -0x1.64fd520a6621ap+1, 0x1.05168da964846p+1, -0x1.6575089c4586dp+0, 0x1.a38bf0b53f437p-1, -0x1.889b16ed752f1p-2, 0x1.152c76b8c5aa6p-3, -0x1.1b4c99876d202p-5, 0x1.907f1e8b42629p-8, -0x1.48b152205d27fp-13, -0x1.a3276d4b1b41fp-11, 0x1.19008ab2bad0ep-11, -0x1.4a0f2fc3a3fe6p-13, 0x1.b16d8531bcd97p-17, 0x1.3c9bc919e0e4ap-19, 0x1.899254d741919p-24, -0x1.e003adff466a7p-24, -0x1.b118f867cd64ep-27, 0x1.a8e81cf9b2bf5p-30, 0x1.472047d4ce812p-36, 0x1.0bc546f1206bp-41, -0x1.5b78778ec812cp-47, -0x1.75c5773026aecp-53, -0x1.4450e0ff79234p-64, 0x1.74639b34e972ap-76, -0x1.74be14820bd54p-99, 0x0p+0};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0, 0x1.ade0c67a6df63p-5, 0x1.c28b430a75f2ap-1, -0x1.5f4ccfba427cfp+1, 0x1.cdb8f607de72ep+0, 0x1.f77743196657ap+0, -0x1.dd879ba809268p+1, 0x1.37053c10bce29p+1, -0x1.1bfa76c0a943ap-2, -0x1.2b5034c5e7cecp+0, 0x1.63e2260baa9fep+0, -0x1.a29913a0c0f2ep-1, 0x1.852867c8ceb36p-3, 0x1.9a9664fc9e679p-4, -0x1.c29f78e2de8f5p-4, 0x1.54d634445fcf7p-5, -0x1.41b2a5a54a663p-9, -0x1.225d9fec5c6e9p-8, 0x1.f9019974a7ddbp-10, -0x1.2c283714217e7p-12, -0x1.8e8742bbbfb21p-16, 0x1.c9f58c62dd5d4p-17, -0x1.61f6495ed1b8fp-20, -0x1.96b8b0f8a15e3p-25, 0x1.71f48c99d030bp-27, -0x1.b5fc8d66ab6dp-34, -0x1.c5963ee2273d3p-38, 0x1.6b4e6ce52480bp-45, 0x1.e67135f42b49bp-58, -0x1.6aff40a6dd5b4p-67, 0x1.6b5790e714dd8p-89, 0x0p+0};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0, 0x1.002833198203cp-2, 0x1.74f145f5180b5p-1, -0x1.d40722c67b8b3p+2, 0x1.2af6f0f464bc5p+4, -0x1.a43135145799ap+4, 0x1.9a15ae041271p+4, -0x1.38d1bd49e9af3p+4, 0x1.6c6cdb14d7fe1p+3, -0x1.13619aaa119f9p+2, 0x1.d56ce1ec874a1p-1, -0x1.e42907ae7a264p-1, 0x1.e52911f9f6566p+0, -0x1.ee224ef8eb13dp+0, 0x1.1f26d6223d44dp+0, -0x1.5888435f57836p-2, -0x1.9e45fc4e6f7c9p-7, 0x1.dcd2d2ebfb6e4p-5, -0x1.93116bc1ac6b7p-6, 0x1.0e01783e342a4p-8, 0x1.31f3faa90de9fp-12, -0x1.f6b0df77a544p-13, 0x1.f05077a02c3acp-16, 0x1.2ec5b9d224e6cp-20, -0x1.47f2b0eb68edbp-22, 0x1.bcb021bf883a2p-29, 0x1.1bcefd6cfba52p-32, -0x1.34d97adc52a39p-39, -0x1.6f2c8c9ca395p-53, 0x1.34e43d9253e6fp-60, -0x1.352f98f0f2e49p-81, -0x0p+0};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0, 0x1.e5d8b15d3664dp-1, -0x1.e7e4ae8313c98p+1, 0x1.643947f56174fp+1, 0x1.8bf77730624fbp+3, -0x1.39575fcf961c1p+5, 0x1.f6657cd6c7e2ap+5, -0x1.2981aaa66ca37p+6, 0x1.0cf300079688ep+6, -0x1.71528cd9cab13p+4, -0x1.13658826409b4p+6, 0x1.5ecf135e336b8p+7, -0x1.ca8fbd8754dc2p+7, 0x1.83a96558c6c07p+7, -0x1.9d91182e0786ap+6, 0x1.818f5ca05f024p+4, 0x1.4e782cc994095p+3, -0x1.7fba734a37797p+3, 0x1.361d7d826bb5bp+2, -0x1.85fee8307d591p-1, -0x1.fcc3205624ce5p-4, 0x1.30d54b861144bp-4, -0x1.4236c7ccc62dfp-7, -0x1.6b6d4bcc089efp-12, 0x1.251cb75a77a65p-13, -0x1.7df627db3ed38p-19, -0x1.6d7ba0319a18p-23, 0x1.047350b843565p-29, 0x1.ecabd0f857c51p-41, -0x1.035ef08b1273dp-49, 0x1.039e900e7fa13p-69, 0x0p+0};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0, 0x1.5c435b4994699p+1, -0x1.45ad88073e625p+4, 0x1.1ac643e9c99f9p+6, -0x1.3bcd24e1c22f1p+7, 0x1.1132bead650e6p+8, -0x1.a3321607e3596p+8, 0x1.2bec4ce73b525p+9, -0x1.83ddd4224b9acp+9, 0x1.b1ad4241d86bfp+9, -0x1.9d7a3218170b3p+9, 0x1.5526f87e8214fp+9, -0x1.e996857ebd3fep+8, 0x1.186a9a24f3388p+8, -0x1.4f804f76b6d5cp+6, -0x1.84954fc1821p+5, 0x1.59efa11d2ec7p+6, -0x1.dac7ad3b33c96p+5, 0x1.62078796373e7p+4, -0x1.88bb023e9f2fap+1, -0x1.04b9160269b8ap+0, 0x1.18c6982acbd2dp-1, -0x1.508ddc9d3ccb4p-4, -0x1.539386e1415cfp-9, 0x1.9eab992a4b9abp-10, -0x1.980b92ff814ccp-15, -0x1.761c29381edd3p-19, 0x1.64e7e2ec4af2dp-25, 0x1.1823b743e4c41p-35, -0x1.623923d3ddbafp-44, 0x1.6290fa803758ep-63, 0x0p+0};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0, 0x1.891443770e9f6p+2, -0x1.c4b28f7dbecf4p+5, 0x1.d994c46f08418p+7, -0x1.26defe09eb9e3p+9, 0x1.ddf577c4250f8p+9, -0x1.fd2079b0f3ddbp+9, 0x1.36152a2e286dp+9, 0x1.d8616a51db369p+6, -0x1.190b42892374cp+10, 0x1.36219b3961795p+11, -0x1.eed74001662f8p+11, 0x1.31c149450a5eap+12, -0x1.31807a4d8f7d9p+12, 0x1.07e37f0875c29p+12, -0x1.9ca0e06fa4e41p+11, 0x1.192392a49659fp+11, -0x1.28f7ef65a911cp+10, 0x1.8ef1182eeb70cp+8, -0x1.076216da5c43bp+5, -0x1.3734a9c9c5015p+5, 0x1.2e313dce4fbf1p+4, -0x1.913ecda1e3437p+1, -0x1.aba4e0591b35fp-4, 0x1.5578ca229685fp-4, -0x1.f3ff47839e58dp-9, -0x1.bd3a12076a4f5p-13, 0x1.29ffe91412a2ap-18, 0x1.5e7711914b059p-28, -0x1.267e3f1ece052p-36, 0x1.26c8d9be624c4p-54, 0x0p+0};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0, 0x1.1c06072fbf26fp+3, -0x1.65d998749f19fp+6, 0x1.9d8978b96f57fp+8, -0x1.24c8d76a7f36dp+10, 0x1.21d479bc00698p+11, -0x1.bbc006c939353p+11, 0x1.2211c4425df9cp+12, -0x1.5c64ff1d8bf67p+12, 0x1.845a35a315834p+12, -0x1.87e6df0fbf8efp+12, 0x1.6504110de640cp+12, -0x1.2b9aa02be2b35p+12, 0x1.cebcfb329a57fp+11, -0x1.3e375c669dacp+11, 0x1.7d70c67fe8974p+10, -0x1.8fd6874952e8bp+9, 0x1.57b6f4096f1cfp+8, -0x1.3e2c004c73161p+6, -0x1.f1e0f66437532p+4, 0x1.39f676c722756p+5, -0x1.07f7de36ead71p+4, 0x1.6eaf02b444bc5p+1, 0x1.f8896c7b27aebp-4, -0x1.b78e4a3636f78p-4, 0x1.faf293c65fc89p-8, 0x1.a6b604defe6a9p-12, -0x1.9886be2865e4cp-17, -0x1.7c0bde2d4dd5p-26, 0x1.90aca39ea2e8bp-34, -0x1.91166efa6d0a9p-51, -0x0p+0};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0, 0x1.58e7df673241ap+3, -0x1.c53a29616fa38p+6, 0x1.0cc18d57a1a2p+9, -0x1.7c92fc1b6ca39p+10, 0x1.6a1945d20b68ep+11, -0x1.fab771c0e1bafp+11, 0x1.254298acbb2d4p+12, -0x1.407f9dc95f9b1p+12, 0x1.53233c63dd8a8p+12, -0x1.3b528b3453998p+12, 0x1.e2ea2797d25e5p+11, -0x1.3d6169dd11c9cp+11, 0x1.75fce5d641404p+10, -0x1.2b5b50127f9f5p+9, -0x1.18e0518b142ecp+7, 0x1.ed1ee257a974bp+8, -0x1.f5a5a8d8a9b3cp+8, 0x1.920c943e9e1a2p+8, -0x1.22c1385412c46p+8, 0x1.4b1ba13f6628bp+7, -0x1.ec876f34dee07p+5, 0x1.641261f15a2bcp+3, 0x1.3bac7fcb6882p-1, -0x1.3ae0db5ff49e1p-1, 0x1.0ba445bef297cp-4, 0x1.c3804abda5b0fp-9, -0x1.3c78fba89f7e5p-13, -0x1.6e90a45b17e12p-22, 0x1.34c398a5dd485p-29, -0x1.351bbccd566d6p-45, -0x0p+0};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0, 0x1.0cfd9304e9d0fp+3, -0x1.68c00ea69764dp+6, 0x1.b4a63a85c6a12p+8, -0x1.3c4fcf304828fp+10, 0x1.35efe9ab816f7p+11, -0x1.c3872b5b6dcd2p+11, 0x1.1261ac83f506cp+12, -0x1.39e1fa3f00834p+12, 0x1.5e4c9d364466fp+12, -0x1.6b72e41a84906p+12, 0x1.578fd4c404249p+12, -0x1.30faf3648505dp+12, 0x1.0174ad7c89821p+12, -0x1.942bc49f2f52ap+11, 0x1.25cbc7992fd64p+11, -0x1.914caac567631p+10, 0x1.f93f030387c4dp+9, -0x1.1b4f5dfc787bcp+9, 0x1.1df01b8a36a8bp+8, -0x1.048db6f3ab7c2p+7, 0x1.730bcb9c58bfcp+5, -0x1.09b56b87c1c8p+3, -0x1.4fb833b30fa7fp+0, 0x1.e38e1048601a6p-1, -0x1.ee07e572041f7p-4, -0x1.913ced3c0164bp-8, 0x1.0726b83c4032cp-11, 0x1.2751c6763466cp-20, -0x1.00ceb77e39cacp-26, 0x1.0123085a89101p-41, 0x0p+0};
-            }
-            if constexpr (order == 11) {
-                return {0x0p+0, 0x1.6ddd33f198eb4p+2, -0x1.ef9ef6f596ce4p+5, 0x1.2bec86422c73p+8, -0x1.ab3138ae63b3cp+9, 0x1.90171accf1ae9p+10, -0x1.0b8279e6381aap+11, 0x1.21c7cbc3a51f5p+11, -0x1.3291c6bd3630dp+11, 0x1.52187d4f27825p+11, -0x1.5764b21031afp+11, 0x1.2d82b77758b7bp+11, -0x1.efcf6fd97e751p+10, 0x1.96b834131566ep+10, -0x1.34d67cf0a39aep+10, 0x1.9aafba6f0ff86p+9, -0x1.002f1ef9723b2p+9, 0x1.378956144d5bep+8, -0x1.48f6827b3eeb5p+7, 0x1.17de886be7cb4p+6, -0x1.abd1c377daaf4p+4, 0x1.18836fa0aedf1p+3, -0x1.72b11631904f7p-2, -0x1.93c736e0c44c1p+0, 0x1.74105b4ecfea7p-1, -0x1.a9382883de208p-4, -0x1.8ee02bc822713p-9, 0x1.b89c5ecf7a7b7p-11, 0x1.5051009d42a45p-19, -0x1.a9ba33acc416cp-25, 0x1.aa6a7d0ba8103p-39, -0x0p+0};
-            }
-            if constexpr (order == 12) {
-                return {0x0p+0, 0x1.7e688b7526a77p+1, -0x1.044f66dd0bb35p+5, 0x1.39d2780b0ad2fp+7, -0x1.b63bb8898df09p+8, 0x1.86b367123a214p+9, -0x1.d8001c1817ddfp+9, 0x1.b397f071da311p+9, -0x1.9ca191acc971ep+9, 0x1.d28d7edb2db09p+9, -0x1.daeab5bf793f1p+9, 0x1.738e37d47cc22p+9, -0x1.0785a3e74df5ap+9, 0x1.a556a97ba7348p+8, -0x1.320671c41025dp+8, 0x1.33661041ead75p+7, -0x1.d86506577d508p+5, 0x1.9ebe065723855p+4, -0x1.ec9ee90429332p-1, -0x1.1034340999c87p+4, 0x1.04d7524f6aap+4, -0x1.2fcc89fd04e89p+3, 0x1.7c24bc012bffcp+2, -0x1.c84c145900f78p+1, 0x1.57bccbd9e4fcfp+0, -0x1.d81daf1af068dp-3, -0x1.20f9f72def1dfp-13, 0x1.c2f2ad7e016f5p-9, 0x1.baf6705e59cacp-17, -0x1.ae94eeab2dbd5p-22, 0x1.af91281d99389p-35, 0x0p+0};
-            }
-            if constexpr (order == 13) {
-                return {0x0p+0, 0x1.a308ef1d16805p-1, -0x1.1df37cb20ef6dp+3, 0x1.5a47cc2daffcbp+5, -0x1.e7cc32d4c7f06p+6, 0x1.ba5aa6f58d154p+7, -0x1.137ebe2556bb6p+8, 0x1.07f96c27b79bap+8, -0x1.f176d6c3151d9p+7, 0x1.0c09a0e0bcbap+8, -0x1.12bf0f34a9a55p+8, 0x1.de16d55d65d2cp+7, -0x1.8c7b496d3d3fep+7, 0x1.56592506626bcp+7, -0x1.13d919c9693b3p+7, 0x1.8b69de5718a0ap+6, -0x1.15b78c90e7837p+6, 0x1.8188b8db550ffp+5, -0x1.e03c011f666acp+4, 0x1.12ed8b36e9864p+4, -0x1.36a5b057bc26fp+3, 0x1.3d2641cf67e9p+2, -0x1.11ef148707dfap+1, 0x1.c294da23fe2ap-1, -0x1.4f57e7e05e819p-2, 0x1.1ebd9964081cfp-4, 0x1.367917f76eee3p-14, -0x1.fdd37749c94d9p-10, -0x1.0fc0733cbc7d6p-22, 0x1.f945fb653cfdbp-22, -0x1.fb1bcfae6e46dp-34, 0x0p+0};
-            }
-            if constexpr (order == 14) {
-                return {0x0p+0, 0x1.74ef139ad4e12p-3, -0x1.fd9d32fdef74p+0, 0x1.3320f17be8b7p+3, -0x1.a9e31dbd98dd1p+4, 0x1.73dbdd38a87f5p+5, -0x1.aa50f206f25c7p+5, 0x1.5e48ac9c2f1f2p+5, -0x1.20d7a78e95ecfp+5, 0x1.4350b94e5aa2ep+5, -0x1.5499ff05228dep+5, 0x1.0d8c7214ffee1p+5, -0x1.8fe88996cfa9ap+4, 0x1.63da6bffb7323p+4, -0x1.24223f5c1b9d9p+4, 0x1.7851e19176716p+3, -0x1.e4fd178fcd0efp+2, 0x1.610a439acb289p+2, -0x1.ae4c3e147b71cp+1, 0x1.a6fe28ab7ffaap+0, -0x1.ccc920f98175ep-1, 0x1.f9389387bff6bp-2, -0x1.8612de961fd02p-3, 0x1.fd43fc0e7883fp-5, -0x1.aafa1e0c4a87p-6, 0x1.b638737fa8e8fp-8, 0x1.071682a1f5058p-11, -0x1.a84c3f530239bp-12, 0x1.a20c2374a0f67p-18, 0x1.e7f1c0adda0f6p-23, -0x1.eb089a4058efep-34, -0x0p+0};
-            }
-            if constexpr (order == 15) {
-                return {0x0p+0, 0x1.31c729360063ep-6, -0x1.a21aa8a66a683p-3, 0x1.f656a46fa2a91p-1, -0x1.589b4fca92a9fp+1, 0x1.25049558932c2p+2, -0x1.3b0f087615a27p+2, 0x1.bed87f332745cp+1, -0x1.37fe75fa2aa3bp+1, 0x1.75c34ae38a12p+1, -0x1.9f32b219f201fp+1, 0x1.2a50b5ebe798ep+1, -0x1.80aff2523d4b3p+0, 0x1.71f9af43c19f1p+0, -0x1.40d21595459ccp+0, 0x1.6edc3b8de7cbdp-1, -0x1.abb5cf29e076bp-2, 0x1.5fdcb9c5e1f88p-2, -0x1.af4e9b9242255p-3, 0x1.57b33e4d63cb5p-4, -0x1.736294d370decp-5, 0x1.e1a61d7964669p-6, -0x1.38138139d6cd8p-7, 0x1.a99b874715d59p-10, -0x1.191ada841d112p-10, 0x1.44a23a1750afbp-12, 0x1.4db128e094988p-13, -0x1.2cad37f3dbf9ep-14, 0x1.f38c667f69482p-19, 0x1.c870773604d03p-24, -0x1.cdd01a024c711p-34, -0x0p+0};
-            }
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            if constexpr (order == 0) {
-                return {0x0p+0L, 0xb.3a3846107e93c71p-16L, 0x9.3e6d9853c4d4d26p-8L, 0xf.9fcd2109d2c70bp-5L, 0xc.50d8731f3b477fep-4L, -0xe.800409a73d92674p-5L, 0x8.364c0bfb08f4c1cp-5L, -0xa.7608480379d5af6p-6L, 0xd.c9e1911927a4784p-7L, -0x8.4fafa041f14b7dbp-7L, 0x8.5b53aefd12e6ae9p-8L, -0xd.0bf5c01ffba2e16p-10L, 0xe.6d0c69fb315533p-12L, -0x8.c0ab49d8f284eep-14L, -0xa.a3e26aabf73f753p-18L, 0xd.0ea8c3bcb0cd49bp-18L, -0xf.dc862acd1a0536cp-20L, 0x8.42dddac61ee2f0bp-22L, 0xa.50b750c53c5492bp-25L, -0x9.d87c1e77be4e6b7p-26L, 0xa.134a86cdb5e53d1p-31L, 0xd.67ae641bc3e3b4bp-32L, 0xe.3efe0e5e6ab002dp-40L, -0xc.cd24c38a13a8934p-40L, 0x8.62a7b6ddea955d3p-45L, 0xb.05b10aa4250e4b5p-52L, -0xb.1b0384fcfca5df4p-57L, 0xf.98453c9a684c9f5p-65L, -0xe.e6c1e66bda07395p-77L, -0xf.a640e8482ad4089p-90L, 0xf.aa0d3dd7d200c8bp-115L, -0x0p+0L};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0L, 0xa.f15f1ffe0172e5bp-13L, 0x8.8aacb719a8764e8p-6L, 0xc.70337610fe3509fp-4L, -0xc.d1d74d153495bebp-4L, -0xd.a74119cbe7c3dc1p-5L, 0x9.26bcdd7c845def1p-4L, -0xc.b7f844c8550ff96p-5L, 0xb.e7f83cc2cea254cp-6L, -0x9.d97b7de092f7fa8p-8L, -0xc.621cb12d798fd78p-9L, 0xe.c17b081c7070057p-9L, -0xe.984243655303eaap-10L, 0xd.c65378f292ec7e1p-12L, 0xa.751369469843a67p-16L, -0xa.22a84a59f7d64eap-15L, 0x8.8b7da84ad94ceep-18L, 0xf.37a3482ba1e794ep-19L, -0xb.99225ab2889ca73p-20L, 0x8.82f186bf65a2e47p-23L, 0xc.2f72cc72e3b957cp-26L, -0xa.d64f8e3b5739183p-28L, 0xe.bc4f9eb81d6e738p-33L, 0xc.6af1f10013f432fp-38L, -0xe.459c19e1dbb49cp-40L, 0x9.c7f205ccc827418p-46L, 0xf.a9268cec210502dp-52L, -0xd.39dbeaf2abf3a86p-60L, -0xe.29902305dd00cf8p-71L, 0xd.29aa6f4daf25f05p-84L, -0xd.2cdc8c67843fbf1p-108L, -0x0p+0L};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0L, 0x9.4af7f560a96bcb2p-10L, 0xc.eb0e623f2ef1314p-5L, 0x8.b0ea0b5b3b1bf47p-5L, -0xa.dbd22b319bb54d5p-2L, 0xe.88ba684f6e872d5p-2L, -0xb.27ea9053310cf1ap-2L, 0x8.28b46d4b2423017p-2L, -0xb.2ba844e22c3642p-3L, 0xd.1c5f85a9fa1b98bp-4L, -0xc.44d8b76ba978ba9p-5L, 0x8.a963b5c62d530fcp-6L, -0x8.da64cc3b6900f46p-8L, 0xc.83f8f45a13145ecp-11L, -0xa.458a9102e93f63ap-16L, -0xd.193b6a58da0f707p-14L, 0x8.c8045595d6873c2p-14L, -0xa.50797e1d1ff33a2p-16L, 0xd.8b6c298de6cba8p-20L, 0x9.e4de48cf0724d64p-22L, 0xc.4c92a6ba0c8c4adp-27L, -0xf.001d6ffa3353439p-27L, -0xd.88c7c33e6b26e41p-30L, 0xd.4740e7cd95fa76bp-33L, 0xa.39023ea674090bcp-39L, 0x8.5e2a378903582b6p-44L, -0xa.dbc3bc7640960d4p-50L, -0xb.ae2bb9813575fa4p-56L, -0xa.228707fbc919e5bp-67L, 0xb.a31cd9a74b94ec4p-79L, -0xb.a5f0a4105eaa2e2p-102L, 0x0p+0L};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0L, 0xd.6f0633d36fb15fep-8L, 0xe.145a1853af94c61p-4L, -0xa.fa667dd213e750bp-2L, 0xe.6dc7b03ef3972cbp-3L, 0xf.bbba18cb32bd3c5p-3L, -0xe.ec3cdd404933d4fp-2L, 0x9.b829e085e714688p-2L, -0x8.dfd3b6054a1d126p-5L, -0x9.5a81a62f3e7613dp-3L, 0xb.1f11305d54fef5bp-3L, -0xd.14c89d060796ef7p-4L, 0xc.29433e46759ad44p-6L, 0xc.d4b327e4f33c651p-7L, -0xe.14fbc716f47a93ep-7L, 0xa.a6b1a222fe7b777p-8L, -0xa.0d952d2a5331434p-12L, -0x9.12ecff62e374622p-11L, 0xf.c80ccba53eedb19p-13L, -0x9.6141b8a10bf3aa6p-15L, -0xc.743a15ddfd9089p-19L, 0xe.4fac6316eae9c34p-20L, -0xb.0fb24af68dc7671p-23L, -0xc.b5c587c50af1901p-28L, 0xb.8fa464ce81856ffp-30L, -0xd.afe46b355b67eadp-37L, -0xe.2cb1f71139e968ap-41L, 0xb.5a73672924054c6p-48L, 0xf.3389afa15a4d6d7p-61L, -0xb.57fa0536eada04ep-70L, 0xb.5abc8738a6ec098p-92L, 0x0p+0L};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0L, 0x8.014198cc101dfabp-5L, 0xb.a78a2fa8c05a46p-4L, -0xe.a0391633dc59632p-1L, 0x9.57b787a325e2b8ep+1L, -0xd.2189a8a2bccd13fp+1L, 0xc.d0ad7020938821dp+1L, -0x9.c68dea4f4d7949p+1L, 0xb.6366d8a6bff083fp+0L, -0x8.9b0cd5508cfcbdap-1L, 0xe.ab670f643a5062fp-4L, -0xf.21483d73d132347p-4L, 0xf.29488fcfb2b3205p-3L, -0xf.711277c7589ea5dp-3L, 0x8.f936b111ea265a4p-3L, -0xa.c4421afabc1b145p-5L, -0xc.f22fe2737be4b07p-10L, 0xe.e696975fdb72006p-8L, -0xc.988b5e0d635b9p-9L, 0x8.700bc1f1a15234ap-11L, 0x9.8f9fd5486f4f6f1p-15L, -0xf.b586fbbd2a200d7p-16L, 0xf.8283bd0161d5d44p-19L, 0x9.762dce912735e76p-23L, -0xa.3f95875b476d467p-25L, 0xd.e5810dfc41d0fc9p-32L, 0x8.de77eb67dd2905dp-35L, -0x9.a6cbd6e2951c534p-42L, -0xb.796464e51ca7defp-56L, 0x9.a721ec929f3744cp-63L, -0x9.a97cc78797246d9p-84L, -0x0p+0L};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0L, 0xf.2ec58ae9b326a91p-4L, -0xf.3f2574189e4c21p-2L, 0xb.21ca3fab0ba7711p-2L, 0xc.5fbbb983127d9a8p+0L, -0x9.cabafe7cb0e079fp+2L, 0xf.b32be6b63f14cdcp+2L, -0x9.4c0d5533651b59dp+3L, 0x8.6798003cb446c2fp+3L, -0xb.8a9466ce5589bd2p+1L, -0x8.9b2c413204da0b9p+3L, 0xa.f6789af19b5be1p+4L, -0xe.547dec3aa6e0c9p+4L, 0xc.1d4b2ac6360394ap+4L, -0xc.ec88c1703c353c7p+3L, 0xc.0c7ae502f811c1cp+1L, 0xa.73c1664ca04a6f6p+0L, -0xb.fdd39a51bbcb87p+0L, 0x9.b0ebec135dad9dap-1L, -0xc.2ff74183eac8757p-4L, -0xf.e61902b12672b5fp-7L, 0x9.86aa5c308a25804p-7L, -0xa.11b63e66316fb48p-10L, -0xb.5b6a5e6044f76b4p-15L, 0x9.28e5bad3bd32814p-16L, -0xb.efb13ed9f69bfabp-22L, -0xb.6bdd018cd0bfce3p-26L, 0x8.239a85c21ab28b1p-32L, 0xf.655e87c2be28938p-44L, -0x8.1af78458939ea43p-52L, 0x8.1cf48073fd095efp-72L, 0x0p+0L};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0L, 0xa.e21ada4ca34ca18p-2L, -0xa.2d6c4039f3128bdp+1L, 0x8.d6321f4e4cfc7p+3L, -0x9.de69270e1178454p+4L, 0x8.8995f56b287327p+5L, -0xd.1990b03f1acb0aep+5L, 0x9.5f626739da926f4p+6L, -0xc.1eeea1125cd5fdbp+6L, 0xd.8d6a120ec35f6eap+6L, -0xc.ebd190c0b85945bp+6L, 0xa.a937c3f410a79b7p+6L, -0xf.4cb42bf5e9fec33p+5L, 0x8.c354d12799c3f3ap+5L, -0xa.7c027bb5b6adc35p+3L, -0xc.24aa7e0c10803ep+2L, 0xa.cf7d08e97637cb2p+3L, -0xe.d63d69d99e4aebp+2L, 0xb.103c3cb1b9f39dbp+1L, -0xc.45d811f4f97cc5dp-2L, -0x8.25c8b0134dc4eacp-3L, 0x8.c634c1565e9668ap-4L, -0xa.846ee4e9e65a1e2p-7L, -0xa.9c9c370a0ae7abcp-12L, 0xc.f55cc9525cd59bdp-13L, -0xc.c05c97fc0a662abp-18L, -0xb.b0e149c0f6e94f3p-22L, 0xb.273f17625796a99p-28L, 0x8.c11dba1f262097fp-38L, -0xb.11c91e9eedd7769p-47L, 0xb.1487d401bac7208p-66L, 0x0p+0L};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0L, 0xc.48a21bb874fadacp-1L, -0xe.25947bedf679c74p+2L, 0xe.cca62378420be4ep+4L, -0x9.36f7f04f5cf1891p+6L, 0xe.efabbe21287bc6p+6L, -0xf.e903cd879eed94cp+6L, 0x9.b0a951714367f56p+6L, 0xe.c30b528ed9b461fp+3L, -0x8.c85a14491ba6385p+7L, 0x9.b10cd9cb0bcab3ep+8L, -0xf.76ba000b317bf3bp+8L, 0x9.8e0a4a2852f4c19p+9L, -0x9.8c03d26c7bec5cfp+9L, 0x8.3f1bf843ae145d5p+9L, -0xc.e507037d2720736p+8L, 0x8.c91c9524b2cfadfp+8L, -0x9.47bf7b2d488e112p+7L, 0xc.7788c1775b861dcp+5L, -0x8.3b10b6d2e21d939p+2L, -0x9.b9a54e4e280a5b6p+2L, 0x9.7189ee727df88e1p+1L, -0xc.89f66d0f1a1b57cp-2L, -0xd.5d2702c8d9af7bcp-7L, 0xa.abc65114b42fbafp-7L, -0xf.9ffa3c1cf2c6819p-12L, -0xd.e9d0903b527a85p-16L, 0x9.4fff48a09514e9bp-21L, 0xa.f3b88c8a582c5bap-31L, -0x9.33f1f8f67028c1p-39L, 0x9.3646cdf31261e85p-57L, 0x0p+0L};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0L, 0x8.e030397df9379acp+0L, -0xb.2eccc3a4f8cf9fbp+3L, 0xc.ec4bc5cb7abf8aap+5L, -0x9.2646bb53f9b6b84p+7L, 0x9.0ea3cde0034bd8ap+8L, -0xd.de003649c9a9964p+8L, 0x9.108e2212efce172p+9L, -0xa.e327f8ec5fb3bd6p+9L, 0xc.22d1ad18ac1a3e5p+9L, -0xc.3f36f87dfc77a18p+9L, 0xb.2820886f3206234p+9L, -0x9.5cd5015f159aa05p+9L, 0xe.75e7d994d2bf56ep+8L, -0x9.f1bae334ed5fea7p+8L, 0xb.eb8633ff44b9f04p+7L, -0xc.7eb43a4a9745482p+6L, 0xa.bdb7a04b78e780bp+5L, -0x9.f160026398b080cp+3L, -0xf.8f07b321ba98ffdp+1L, 0x9.cfb3b63913ab26dp+2L, -0x8.3fbef1b756b8bfp+1L, 0xb.757815a225e2672p-2L, 0xf.c44b63d93d7545p-7L, -0xd.bc7251b1b7bbe9bp-7L, 0xf.d7949e32fe445dap-11L, 0xd.35b026f7f354a7ap-15L, -0xc.c435f1432f26328p-20L, -0xb.e05ef16a6ea832dp-29L, 0xc.85651cf5174561cp-37L, -0xc.88b377d3685495ep-54L, -0x0p+0L};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0L, 0xa.c73efb39920cedbp+0L, -0xe.29d14b0b7d1c041p+3L, 0x8.660c6abd0d0fda4p+6L, -0xb.e497e0db651c4abp+7L, 0xb.50ca2e905b46c5dp+8L, -0xf.d5bb8e070dd7927p+8L, 0x9.2a14c565d96a24dp+9L, -0xa.03fcee4afcd8902p+9L, 0xa.9919e31eec53f8cp+9L, -0x9.da9459a29ccbc9bp+9L, 0xf.17513cbe92f2a28p+8L, -0x9.eb0b4ee88e4de52p+8L, 0xb.afe72eb20a022bp+7L, -0x9.5ada8093fcfab6ap+6L, -0x8.c7028c58a1762e5p+4L, 0xf.68f712bd4ba559bp+5L, -0xf.ad2d46c54d9e03ap+5L, 0xc.9064a1f4f0d1331p+5L, -0x9.1609c2a09622ff8p+5L, 0xa.58dd09fb31458efp+4L, -0xf.643b79a6f703a82p+2L, 0xb.20930f8ad15e1ebp+0L, 0x9.dd63fe5b440fe97p-4L, -0x9.d706daffa4f07edp-4L, 0x8.5d222df794bdd1ep-7L, 0xe.1c0255ed2d877d5p-12L, -0x9.e3c7dd44fbf26e9p-16L, -0xb.748522d8bf08c1ap-25L, 0x9.a61cc52eea42bddp-32L, -0x9.a8dde66ab36adabp-48L, -0x0p+0L};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0L, 0x8.67ec98274e874f4p+0L, -0xb.46007534bb26601p+3L, 0xd.a531d42e35090ebp+5L, -0x9.e27e798241476f8p+7L, 0x9.af7f4d5c0b7b569p+8L, -0xe.1c395adb6e69289p+8L, 0x8.930d641fa835ff8p+9L, -0x9.cf0fd1f80419d17p+9L, 0xa.f264e9b223377bap+9L, -0xb.5b9720d42482e67p+9L, 0xa.bc7ea62021246d6p+9L, -0x9.87d79b24282e6fbp+9L, 0x8.0ba56be44c10be5p+9L, -0xc.a15e24f97a95118p+8L, 0x9.2e5e3cc97eb1e7ap+8L, -0xc.8a65562b3b184f6p+7L, 0xf.c9f8181c3e2680dp+6L, -0x8.da7aefe3c3dde19p+6L, 0x8.ef80dc51b545874p+5L, -0x8.246db79d5be0e64p+4L, 0xb.985e5ce2c5fe107p+2L, -0x8.4dab5c3e0e3fdbep+0L, -0xa.7dc19d987d3f778p-3L, 0xf.1c70824300d3066p-4L, -0xf.703f2b9020fb9c6p-7L, -0xc.89e769e00b25ab7p-11L, 0x8.3935c1e20195fc1p-14L, 0x9.3a8e33b1a335de3p-23L, -0x8.0675bbf1ce55e11p-29L, 0x8.091842d44880a98p-44L, 0x0p+0L};
-            }
-            if constexpr (order == 11) {
-                return {0x0p+0L, 0xb.6ee99f8cc759e4bp-1L, -0xf.7cf7b7acb67220ap+2L, 0x9.5f6432116397da5p+5L, -0xd.5989c5731d9e0f1p+6L, 0xc.80b8d6678d74968p+7L, -0x8.5c13cf31c0d515cp+8L, 0x9.0e3e5e1d28fa819p+8L, -0x9.948e35e9b18657fp+8L, 0xa.90c3ea793c12aedp+8L, -0xa.bb2590818d7801fp+8L, 0x9.6c15bbbac5bd569p+8L, -0xf.7e7b7ecbf3a84e5p+7L, 0xc.b5c1a098ab36e4fp+7L, -0x9.a6b3e7851cd6ca3p+7L, 0xc.d57dd3787fc2f5fp+6L, -0x8.0178f7cb91d933p+6L, 0x9.bc4ab0a26adf067p+5L, -0xa.47b413d9f75a975p+4L, 0x8.bef4435f3e59d64p+3L, -0xd.5e8e1bbed57a092p+1L, 0x8.c41b7d0576f88b8p+0L, -0xb.9588b18c827b5eap-5L, -0xc.9e39b70622606d2p-3L, 0xb.a082da767f5360bp-4L, -0xd.49c1441ef103d27p-7L, -0xc.77015e41138988ap-12L, 0xd.c4e2f67bd3dbb98p-14L, 0xa.828804ea1522a4ep-22L, -0xd.4dd19d6620b5d5fp-28L, 0xd.5353e85d40818dap-42L, -0x0p+0L};
-            }
-            if constexpr (order == 12) {
-                return {0x0p+0L, 0xb.f3445ba9353ba5cp-2L, -0x8.227b36e85d9aaf5p+2L, 0x9.ce93c0585697ae1p+4L, -0xd.b1ddc44c6f84b46p+5L, 0xc.359b3891d109cd3p+6L, -0xe.c000e0c0beef91cp+6L, 0xd.9cbf838ed188ae1p+6L, -0xc.e50c8d664b8f00fp+6L, 0xe.946bf6d96d84894p+6L, -0xe.d755adfbc9f852fp+6L, 0xb.9c71bea3e610ea4p+6L, -0x8.3c2d1f3a6face9p+6L, 0xd.2ab54bdd39a4207p+5L, -0x9.90338e20812e975p+5L, 0x9.9b30820f56ba5f5p+4L, -0xe.c32832bbea8400dp+2L, 0xc.f5f032b91c2a8d1p+1L, -0xf.64f748214999222p-4L, -0x8.81a1a04cce4348p+1L, 0x8.26ba927b54fff92p+1L, -0x9.7e644fe827446adp+0L, 0xb.e125e0095ffe3e9p-1L, -0xe.4260a2c807bbd9ap-2L, 0xa.bde65ecf27e7508p-3L, -0xe.c0ed78d78346885p-6L, -0x9.07cfb96f78ef479p-16L, 0xe.17956bf00b7a939p-12L, 0xd.d7b382f2ce56194p-20L, -0xd.74a775596dea6ap-25L, 0xd.7c8940ecc9c488dp-38L, 0x0p+0L};
-            }
-            if constexpr (order == 13) {
-                return {0x0p+0L, 0xd.184778e8b402badp-4L, -0x8.ef9be59077b66a9p+0L, 0xa.d23e616d7fe5968p+2L, -0xf.3e6196a63f82e61p+3L, 0xd.d2d537ac68aa3c8p+4L, -0x8.9bf5f12ab5dae19p+5L, 0x8.3fcb613dbcdd0e4p+5L, -0xf.8bb6b618a8ec653p+4L, 0x8.604d0705e5cffc7p+5L, -0x8.95f879a54d2a806p+5L, 0xe.f0b6aaeb2e95db1p+4L, -0xc.63da4b69e9fec14p+4L, 0xa.b2c92833135e147p+4L, -0x8.9ec8ce4b49d9743p+4L, 0xc.5b4ef2b8c504f17p+3L, -0x8.adbc64873c1b94ap+3L, 0xc.0c45c6daa87f51cp+2L, -0xf.01e008fb335633p+1L, 0x8.976c59b74c322cp+1L, -0x9.b52d82bde13767bp+0L, 0x9.e9320e7b3f47defp-1L, -0x8.8f78a4383efd09p-2L, 0xe.14a6d11ff14fe9cp-4L, -0xa.7abf3f02f40c74p-5L, 0x8.f5eccb2040e7b75p-7L, 0x9.b3c8bfbb7771784p-17L, -0xf.ee9bba4e4a6c8ddp-13L, -0x8.7e0399e5e3eb2bep-25L, 0xf.ca2fdb29e7ed48cp-25L, -0xf.d8de7d73723689ep-37L, 0x0p+0L};
-            }
-            if constexpr (order == 14) {
-                return {0x0p+0L, 0xb.a7789cd6a708f8p-6L, -0xf.ece997ef7b9fe29p-3L, 0x9.99078bdf45b839ap+0L, -0xd.4f18edecc6e84b2p+1L, 0xb.9edee9c543fa832p+2L, -0xd.5287903792e3955p+2L, 0xa.f24564e178f8f8p+2L, -0x9.06bd3c74af67abfp+2L, 0xa.1a85ca72d516d28p+2L, -0xa.a4cff829146ee94p+2L, 0x8.6c6390a7ff70509p+2L, -0xc.7f444cb67d4d2a9p+1L, 0xb.1ed35ffdb991773p+1L, -0x9.2111fae0dceca83p+1L, 0xb.c28f0c8bb38af61p+0L, -0xf.27e8bc7e687797cp-1L, 0xb.08521cd65944bcep-1L, -0xd.7261f0a3db8e14ap-2L, 0xd.37f1455bffd4c88p-3L, -0xe.664907cc0baeeacp-4L, 0xf.c9c49c3dffb59aap-5L, -0xc.3096f4b0fe81145p-6L, 0xf.ea1fe073c41f722p-8L, -0xd.57d0f0625437c47p-9L, 0xd.b1c39bfd474775fp-11L, 0x8.38b4150fa82bf11p-14L, -0xd.4261fa9811cdb2p-15L, 0xd.10611ba507b38p-21L, 0xf.3f8e056ed07b157p-26L, -0xf.5844d202c77f32cp-37L, -0x0p+0L};
-            }
-            if constexpr (order == 15) {
-                return {0x0p+0L, 0x9.8e3949b0031f00ap-9L, -0xd.10d5453353419edp-6L, 0xf.b2b5237d1548b4fp-4L, -0xa.c4da7e54954f883p-2L, 0x9.2824aac49960d3ep-1L, -0x9.d87843b0ad13405p-1L, 0xd.f6c3f9993a2dfbdp-2L, -0x9.bff3afd1551db4ap-2L, 0xb.ae1a571c508fe19p-2L, -0xc.f99590cf900f84fp-2L, 0x9.5285af5f3cc721cp-2L, -0xc.057f9291ea599a1p-3L, 0xb.8fcd7a1e0cf84a9p-3L, -0xa.0690acaa2ce5ec5p-3L, 0xb.76e1dc6f3e5e678p-4L, -0xd.5dae794f03b58fap-5L, 0xa.fee5ce2f0fc3e14p-5L, -0xd.7a74dc92112ab1p-6L, 0xa.bd99f26b1e5a94cp-7L, -0xb.9b14a69b86f63cfp-8L, 0xf.0d30ebcb2334763p-9L, -0x9.c09c09ceb66c13bp-10L, 0xd.4cdc3a38aeac8ap-13L, -0x8.c8d6d420e888ec5p-13L, 0xa.2511d0ba857d42dp-15L, 0xa.6d894704a4c3cb1p-16L, -0x9.6569bf9edfcf3d1p-17L, 0xf.9c6333fb4a41095p-22L, 0xe.4383b9b026817b9p-27L, -0xe.6e80d0126388779p-37L, -0x0p+0L};
-            }
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            if constexpr (order == 0) {
-                return {0x0p+0Q, 0x1.674708c20fd278e13cb308fbf6b6p-13Q, 0x1.27cdb30a789a9a4cba57381b80dfp-5Q, 0x1.f3f9a4213a58e15fea805c6fce03p-2Q, 0x1.8a1b0e63e768effc8742d136ac6ep-1Q, -0x1.d0008134e7b24ce7a0bdb2d5e177p-2Q, 0x1.06c9817f611e98379b152a389fafp-2Q, -0x1.4ec109006f3ab5eb9ef4b4145d24p-3Q, 0x1.b93c322324f48f0734b615fc9893p-4Q, -0x1.09f5f4083e296fb6c1df50020f51p-4Q, 0x1.0b6a75dfa25cd5d117e10197333bp-5Q, -0x1.a17eb803ff745c2b927f4b56bb55p-7Q, 0x1.cda18d3f662aa65f684ad290727fp-9Q, -0x1.1815693b1e509dbfebb4547eb7c2p-11Q, -0x1.547c4d557ee7eea60970ca463eb3p-15Q, 0x1.a1d518779619a935a6506c218d6ap-15Q, -0x1.fb90c559a340a6d74429771a650ap-17Q, 0x1.085bbb58c3dc5e159337591d11c5p-19Q, 0x1.4a16ea18a78a9255137a36b6eeb6p-22Q, -0x1.3b0f83cef7c9cd6e4992ef7a8e0ap-23Q, 0x1.426950d9b6bca7a253eba2c282ddp-28Q, 0x1.acf5cc83787c76964322f9b1343dp-29Q, 0x1.c7dfc1cbcd560059e1fa3bbb0da4p-37Q, -0x1.99a4987142751268f68b0c6ed2ep-37Q, 0x1.0c54f6dbbd52aba64c70d9892a56p-42Q, 0x1.60b6215484a1c96af7151c51425dp-49Q, -0x1.6360709f9f94bbe775bd0ffbeceep-54Q, 0x1.f308a7934d0993ea019328882821p-62Q, -0x1.dcd83ccd7b40e72afa7a2bb7cfap-74Q, -0x1.f4c81d09055a8112f9a8f0e29d58p-87Q, 0x1.f541a7bafa4019158f37f50aca47p-112Q, 0x0p+0Q};
-            }
-            if constexpr (order == 1) {
-                return {0x0p+0Q, 0x1.5e2be3ffc02e5cb63d505e4d42d9p-10Q, 0x1.115596e3350ec9cfc7fd8b282c15p-3Q, 0x1.8e066ec21fc6a13efd57c0a1a8d5p-1Q, -0x1.9a3ae9a2a692b7d6fe0312f42fd2p-1Q, -0x1.b4e823397cf87b829664fcfb615p-2Q, 0x1.24d79baf908bbde12d97a94a7f11p-1Q, -0x1.96ff08990aa1ff2b3a6156b3a6f7p-2Q, 0x1.7cff079859d44a97134acb0b3815p-3Q, -0x1.3b2f6fbc125eff4f9e00971a8041p-5Q, -0x1.8c439625af31faef37a9ac49e57fp-6Q, 0x1.d82f61038e0e00ad9adf7940901dp-6Q, -0x1.d308486caa607d54998083598bc8p-7Q, 0x1.b8ca6f1e525d8fc1aecc191249d8p-9Q, 0x1.4ea26d28d30874cd6f1bece4d0cdp-13Q, -0x1.4455094b3efac9d3c28631c94fc4p-12Q, 0x1.116fb5095b299dc0400b6814e296p-15Q, 0x1.e6f46905743cf29b32a5a94efd0bp-16Q, -0x1.73244b56511394e5623a6c13b582p-17Q, 0x1.105e30d7ecb45c8d929e54615ad8p-20Q, 0x1.85ee598e5c772af7b4423f5e4908p-23Q, -0x1.5ac9f1c76ae72306c6963aa9eb6ap-25Q, 0x1.d789f3d703adce6fceeb7470ebe2p-30Q, 0x1.8d5e3e20027e865e92d2141a2b73p-35Q, -0x1.c8b3833c3b76938050c849f3c902p-37Q, 0x1.38fe40b99904e82fbd88d14cb331p-43Q, 0x1.f524d19d8420a05a730c8d14369dp-49Q, -0x1.a73b7d5e557e750b97979bfe8e3ep-57Q, -0x1.c5320460bba019effc9564690ea4p-68Q, 0x1.a5354de9b5e4be0a26cfffd8bdbp-81Q, -0x1.a59b918cf087f7e28a66eadc80bbp-105Q, 0x0p+0Q};
-            }
-            if constexpr (order == 2) {
-                return {0x0p+0Q, 0x1.295efeac152d79633d42d6d916dap-7Q, 0x1.9d61cc47e5de2628b18136c91ea6p-2Q, 0x1.161d416b67637e8de5329814dbadp-2Q, -0x1.5b7a45663376a9aa5f95ed877064p+1Q, 0x1.d1174d09edd0e5a9b8dec824cf43p+1Q, -0x1.64fd520a66219e33ceb19171c931p+1Q, 0x1.05168da96484602e8bf4113ac4e7p+1Q, -0x1.6575089c4586c8407b43149ab11bp+0Q, 0x1.a38bf0b53f437316576c7b5f77a6p-1Q, -0x1.889b16ed752f17512574ee20842fp-2Q, 0x1.152c76b8c5aa61f7d1f86545cf96p-3Q, -0x1.1b4c99876d201e8bbadda8305eebp-5Q, 0x1.907f1e8b42628bd87c6dfaa42428p-8Q, -0x1.48b152205d27ec7322d3d940da05p-13Q, -0x1.a3276d4b1b41ee0d43115b5aa81dp-11Q, 0x1.19008ab2bad0e78321ce13187a8p-11Q, -0x1.4a0f2fc3a3fe6743d3250b9f0687p-13Q, 0x1.b16d8531bcd974ffcfcfb275888ap-17Q, 0x1.3c9bc919e0e49ac8c1ec9b7c72d7p-19Q, 0x1.899254d74191895a0ee7c7e368dfp-24Q, -0x1.e003adff466a6871b6189e153009p-24Q, -0x1.b118f867cd64dc8214de14f22a3dp-27Q, 0x1.a8e81cf9b2bf4ed6a7f80b7fee49p-30Q, 0x1.472047d4ce812177c28860710d42p-36Q, 0x1.0bc546f1206b056c51ef6c4e3c73p-41Q, -0x1.5b78778ec812c1a8126f0f855511p-47Q, -0x1.75c5773026aebf48665648526e47p-53Q, -0x1.4450e0ff79233cb66d7ae0406fdfp-64Q, 0x1.74639b34e9729d879c349c60a705p-76Q, -0x1.74be14820bd545c3f1e6ecce41eap-99Q, 0x0p+0Q};
-            }
-            if constexpr (order == 3) {
-                return {0x0p+0Q, 0x1.ade0c67a6df62bfb0e80195f4993p-5Q, 0x1.c28b430a75f298c1d73bb81e4353p-1Q, -0x1.5f4ccfba427cea15c66f4a5c12bbp+1Q, 0x1.cdb8f607de72e596ea568a034c8fp+0Q, 0x1.f77743196657a78ad5bf74425543p+0Q, -0x1.dd879ba809267a9d7904ab437cc5p+1Q, 0x1.37053c10bce28d1022d31ac1246dp+1Q, -0x1.1bfa76c0a943a24b6df5bb2abebdp-2Q, -0x1.2b5034c5e7cec27aa44e7ea3a878p+0Q, 0x1.63e2260baa9fdeb5f048ba37a04bp+0Q, -0x1.a29913a0c0f2ddeebb2bd3c275b3p-1Q, 0x1.852867c8ceb35a88f788b40857cap-3Q, 0x1.9a9664fc9e678ca180654356c297p-4Q, -0x1.c29f78e2de8f527b7cd8a08d24efp-4Q, 0x1.54d634445fcf6eedbc5dccf04eadp-5Q, -0x1.41b2a5a54a66286808252915b865p-9Q, -0x1.225d9fec5c6e8c447caf2b42ced4p-8Q, 0x1.f9019974a7ddb631ebee782869d1p-10Q, -0x1.2c283714217e754b55528b628588p-12Q, -0x1.8e8742bbbfb2111f9226dbaea15fp-16Q, 0x1.c9f58c62dd5d38676514b49c9e2ep-17Q, -0x1.61f6495ed1b8ece209fc78f1d085p-20Q, -0x1.96b8b0f8a15e32028c8ee0076679p-25Q, 0x1.71f48c99d030adfe377a7056701dp-27Q, -0x1.b5fc8d66ab6cfd5a83337a0cc9b9p-34Q, -0x1.c5963ee2273d2d13e0940bb125cdp-38Q, 0x1.6b4e6ce52480a98b4ad64082a237p-45Q, 0x1.e67135f42b49adad00310559fa39p-58Q, -0x1.6aff40a6dd5b409b62d44964fcf6p-67Q, 0x1.6b5790e714dd812f487575d04214p-89Q, 0x0p+0Q};
-            }
-            if constexpr (order == 4) {
-                return {0x0p+0Q, 0x1.002833198203bf56e8fbb6905c21p-2Q, 0x1.74f145f5180b48bf2521976daf68p-1Q, -0x1.d40722c67b8b2c63d49b5a9b6cadp+2Q, 0x1.2af6f0f464bc571c8b763a8383eap+4Q, -0x1.a43135145799a27dfd1fadf6761p+4Q, 0x1.9a15ae0412710439a9b40c2dd4dbp+4Q, -0x1.38d1bd49e9af291f59c9f34bcde4p+4Q, 0x1.6c6cdb14d7fe107edc16c4953b35p+3Q, -0x1.13619aaa119f97b37d6d1c2c4585p+2Q, 0x1.d56ce1ec874a0c5dd634fb59d6d1p-1Q, -0x1.e42907ae7a26468d6ecb1d9e3f24p-1Q, 0x1.e52911f9f656640a2404f83a2b4fp+0Q, -0x1.ee224ef8eb13d4b961d19b7d1c3bp+0Q, 0x1.1f26d6223d44cb481a2910c6eba2p+0Q, -0x1.5888435f5783628967f9baa03f79p-2Q, -0x1.9e45fc4e6f7c960ebee0a7c398e8p-7Q, 0x1.dcd2d2ebfb6e400bbcf752c0bf7fp-5Q, -0x1.93116bc1ac6b7200b82ddbf8d638p-6Q, 0x1.0e01783e342a4693e98c9edbf33cp-8Q, 0x1.31f3faa90de9ede16d914789626ap-12Q, -0x1.f6b0df77a54401ad9bab438557ddp-13Q, 0x1.f05077a02c3aba8741da9769ad4ep-16Q, 0x1.2ec5b9d224e6bceb5db9ee6cff1dp-20Q, -0x1.47f2b0eb68eda8ce48926b156c9bp-22Q, 0x1.bcb021bf883a1f92a78fc9df6525p-29Q, 0x1.1bcefd6cfba520ba047378483637p-32Q, -0x1.34d97adc52a38a676a55a692601cp-39Q, -0x1.6f2c8c9ca394fbdec6dda2487026p-53Q, 0x1.34e43d9253e6e8975e6c8e7aefefp-60Q, -0x1.352f98f0f2e48db2a203fb32a0f2p-81Q, 0x0p+0Q};
-            }
-            if constexpr (order == 5) {
-                return {0x0p+0Q, 0x1.e5d8b15d3664d52108fae09a8e52p-1Q, -0x1.e7e4ae8313c9841f6b4ba59501e9p+1Q, 0x1.643947f56174ee22b35084254df8p+1Q, 0x1.8bf77730624fb34f058dbb215e6ap+3Q, -0x1.39575fcf961c0f3da45ce2cb7fb1p+5Q, 0x1.f6657cd6c7e299b7cc89d7d3daa3p+5Q, -0x1.2981aaa66ca36b3a94f8297750dp+6Q, 0x1.0cf300079688d85d6be476057064p+6Q, -0x1.71528cd9cab137a39829bbec9ca2p+4Q, -0x1.13658826409b41720bd51a0f2d32p+6Q, 0x1.5ecf135e336b7c201cd13f9f1c7bp+7Q, -0x1.ca8fbd8754dc1920d78e0ace3c5ep+7Q, 0x1.83a96558c6c07294f0fd718cdf26p+7Q, -0x1.9d91182e0786a78e2338c8bf2ff2p+6Q, 0x1.818f5ca05f023837d630b257f2ffp+4Q, 0x1.4e782cc994094deb153537dfc8d9p+3Q, -0x1.7fba734a377970e0ae8d82bc8b81p+3Q, 0x1.361d7d826bb5b3b3a1616de586bdp+2Q, -0x1.85fee8307d590ead49f8c992534dp-1Q, -0x1.fcc3205624ce56be678cf9a5a7bcp-4Q, 0x1.30d54b861144b0080c77fb2ef955p-4Q, -0x1.4236c7ccc62df6904f1792b21926p-7Q, -0x1.6b6d4bcc089eed67f90762e3bff2p-12Q, 0x1.251cb75a77a65027fa18c49d6fe7p-13Q, -0x1.7df627db3ed37f55c551bdd12823p-19Q, -0x1.6d7ba0319a17f9c5347fd4ebc07ap-23Q, 0x1.047350b843565161f3ac671e5f76p-29Q, 0x1.ecabd0f857c5126fafed07e8e831p-41Q, -0x1.035ef08b1273d485ae68801933a9p-49Q, 0x1.039e900e7fa12bdd9aa0b500dd5fp-69Q, 0x0p+0Q};
-            }
-            if constexpr (order == 6) {
-                return {0x0p+0Q, 0x1.5c435b4994699430de1f0bf0f96ep+1Q, -0x1.45ad88073e6251792d84638c28d6p+4Q, 0x1.1ac643e9c99f8dff42b4b5f9e976p+6Q, -0x1.3bcd24e1c22f08a7330d952db5cp+7Q, 0x1.1132bead650e64e0cc6250fd5a4cp+8Q, -0x1.a3321607e359615c22640184890cp+8Q, 0x1.2bec4ce73b524de840d2af975fb7p+9Q, -0x1.83ddd4224b9abfb64ecabd8660acp+9Q, 0x1.b1ad4241d86bedd378c0238858cbp+9Q, -0x1.9d7a3218170b28b67328a4e4a6f8p+9Q, 0x1.5526f87e8214f36e89fc59fbe6b5p+9Q, -0x1.e996857ebd3fd865f8b8b57715d2p+8Q, 0x1.186a9a24f3387e74b22113290d4ap+8Q, -0x1.4f804f76b6d5b86a618f6e232bp+6Q, -0x1.84954fc1821007c0fd22bc06ae8ep+5Q, 0x1.59efa11d2ec6f964630b6fd432d3p+6Q, -0x1.dac7ad3b33c95d5f07d90297e68ap+5Q, 0x1.62078796373e73b5598b78c1554p+4Q, -0x1.88bb023e9f2f98b9b7a5caf3d0d1p+1Q, -0x1.04b9160269b89d57d0a515a32ad5p+0Q, 0x1.18c6982acbd2cd140bf32d2822bbp-1Q, -0x1.508ddc9d3ccb43c37b8bf661b39ap-4Q, -0x1.539386e1415cf5772194fa5cb789p-9Q, 0x1.9eab992a4b9ab37998a4782656d7p-10Q, -0x1.980b92ff814cc556c4aeda05445fp-15Q, -0x1.761c29381edd29e5680cf5367b41p-19Q, 0x1.64e7e2ec4af2d5325d3b1ebf7038p-25Q, 0x1.1823b743e4c412fe2e1a1caf98aep-35Q, -0x1.623923d3ddbaeed10b04fa360d62p-44Q, 0x1.6290fa803758e40f0b825bbc6f28p-63Q, 0x0p+0Q};
-            }
-            if constexpr (order == 7) {
-                return {0x0p+0Q, 0x1.891443770e9f5b58ca0bdbd939d6p+2Q, -0x1.c4b28f7dbecf38e874d3b242d4fbp+5Q, 0x1.d994c46f08417c9c24a3de260d39p+7Q, -0x1.26defe09eb9e312242e62017ceb2p+9Q, 0x1.ddf577c4250f78c0132ae5d7d1cep+9Q, -0x1.fd2079b0f3ddb297d557ffac7fap+9Q, 0x1.36152a2e286cfeac434a875affb8p+9Q, 0x1.d8616a51db368c3df9bbb5de82cep+6Q, -0x1.190b42892374c709dd8c148043fep+10Q, 0x1.36219b396179567cea600ef5a5e7p+11Q, -0x1.eed74001662f7e761e907ef9b166p+11Q, 0x1.31c149450a5e9832b2fbd7c32f38p+12Q, -0x1.31807a4d8f7d8b9ec23e94e23c9ap+12Q, 0x1.07e37f0875c28ba98c5df12ea151p+12Q, -0x1.9ca0e06fa4e40e6ba9a2f070a627p+11Q, 0x1.192392a49659f5be4afa683922a3p+11Q, -0x1.28f7ef65a911c2242d4a04d3586cp+10Q, 0x1.8ef1182eeb70c3b810afe07ad9aep+8Q, -0x1.076216da5c43b27292cd22bcb978p+5Q, -0x1.3734a9c9c5014b6b42b155a6abedp+5Q, 0x1.2e313dce4fbf11c25ec52c766e83p+4Q, -0x1.913ecda1e3436af7caac068805f8p+1Q, -0x1.aba4e0591b35ef78388396d8949ap-4Q, 0x1.5578ca229685f75ec4dbb7fb72b6p-4Q, -0x1.f3ff47839e58d032a1a624c1f604p-9Q, -0x1.bd3a12076a4f509f06e99bb28599p-13Q, 0x1.29ffe91412a29d368ce7b0895443p-18Q, 0x1.5e7711914b058b73ae8c4ed370dp-28Q, -0x1.267e3f1ece05182094aa29382cf7p-36Q, 0x1.26c8d9be624c3d09b42c989d403cp-54Q, 0x0p+0Q};
-            }
-            if constexpr (order == 8) {
-                return {0x0p+0Q, 0x1.1c06072fbf26f358c9f078f98565p+3Q, -0x1.65d998749f19f3f52787d2ac7bd1p+6Q, 0x1.9d8978b96f57f154ef9ce52c7bdfp+8Q, -0x1.24c8d76a7f36d7089e3f4940c827p+10Q, 0x1.21d479bc00697b14d91a6dd4bcabp+11Q, -0x1.bbc006c9393532c76b5d7283eb2fp+11Q, 0x1.2211c4425df9c2e46c401315e702p+12Q, -0x1.5c64ff1d8bf677ab09ac8c8005b4p+12Q, 0x1.845a35a3158347c96beac73413ep+12Q, -0x1.87e6df0fbf8ef42fd538df2c44e6p+12Q, 0x1.6504110de640c4682cba264cf46ap+12Q, -0x1.2b9aa02be2b35409ccae86a8991fp+12Q, 0x1.cebcfb329a57eadc95a6866f02e1p+11Q, -0x1.3e375c669dabfd4de916796f2023p+11Q, 0x1.7d70c67fe8973e080c2a8eb7f182p+10Q, -0x1.8fd6874952e8a903dace07633bccp+9Q, 0x1.57b6f4096f1cf0152662dc88de7ap+8Q, -0x1.3e2c004c73161017d1fe47d49586p+6Q, -0x1.f1e0f66437531ffa287a43716481p+4Q, 0x1.39f676c7227564daf7244ac826e7p+5Q, -0x1.07f7de36ead717df75674d143f33p+4Q, 0x1.6eaf02b444bc4ce4684168c04e9ap+1Q, 0x1.f8896c7b27aea8a0c13b638bec5cp-4Q, -0x1.b78e4a3636f77d36045fd051d0a7p-4Q, 0x1.faf293c65fc88bb39eaf07f0c833p-8Q, 0x1.a6b604defe6a94f42a0056ad171bp-12Q, -0x1.9886be2865e4c650159b7d4d95b1p-17Q, -0x1.7c0bde2d4dd50659d8e873b48d0ap-26Q, 0x1.90aca39ea2e8ac3870ca13b1a564p-34Q, -0x1.91166efa6d0a92bc7a2e9704d452p-51Q, 0x0p+0Q};
-            }
-            if constexpr (order == 9) {
-                return {0x0p+0Q, 0x1.58e7df6732419db59e9ac42f9ab1p+3Q, -0x1.c53a29616fa380817d7f5e347aefp+6Q, 0x1.0cc18d57a1a1fb48e108cac3a066p+9Q, -0x1.7c92fc1b6ca3895680c38212861fp+10Q, 0x1.6a1945d20b68d8baff4381a817e2p+11Q, -0x1.fab771c0e1baf24e2c8f95c4199fp+11Q, 0x1.254298acbb2d449a7b3bb526f729p+12Q, -0x1.407f9dc95f9b1203f980178aa4a8p+12Q, 0x1.53233c63dd8a7f18f0a2b3af5ccep+12Q, -0x1.3b528b34539979362d8c0e80e80ep+12Q, 0x1.e2ea2797d25e54507eb78c335f71p+11Q, -0x1.3d6169dd11c9bca3212058149b0bp+11Q, 0x1.75fce5d641404560c1229131d8bdp+10Q, -0x1.2b5b50127f9f56d44ea4f01f61c9p+9Q, -0x1.18e0518b142ec5c99d05ce213217p+7Q, 0x1.ed1ee257a974ab35fe81e878de48p+8Q, -0x1.f5a5a8d8a9b3c073ca67ee8615b8p+8Q, 0x1.920c943e9e1a266133bfad52e46dp+8Q, -0x1.22c1385412c45fef72454e0ef403p+8Q, 0x1.4b1ba13f6628b1dd44be57f24352p+7Q, -0x1.ec876f34dee07503da6a5d0e4af4p+5Q, 0x1.641261f15a2bc3d54eada0d94bc5p+3Q, 0x1.3bac7fcb6881fd2d747aef7d1cc5p-1Q, -0x1.3ae0db5ff49e0fda9ef09cfb9b34p-1Q, 0x1.0ba445bef297ba3c0905b698e9c6p-4Q, 0x1.c3804abda5b0efa9daece8d22468p-9Q, -0x1.3c78fba89f7e4dd2da5d2b0f1ab2p-13Q, -0x1.6e90a45b17e11834e30d4035587ep-22Q, 0x1.34c398a5dd4857b9fcc2b9b3ec09p-29Q, -0x1.351bbccd566d5b56e0d110fac029p-45Q, 0x0p+0Q};
-            }
-            if constexpr (order == 10) {
-                return {0x0p+0Q, 0x1.0cfd9304e9d0e9e89a508d967352p+3Q, -0x1.68c00ea69764cc01a573447ef7eep+6Q, 0x1.b4a63a85c6a121d6db6758f94115p+8Q, -0x1.3c4fcf304828edf08897e340df25p+10Q, 0x1.35efe9ab816f6ad2ce3b95243287p+11Q, -0x1.c3872b5b6dcd2512d759e390543cp+11Q, 0x1.1261ac83f506bff0f38c31198cefp+12Q, -0x1.39e1fa3f00833a2dd6c432f2edcep+12Q, 0x1.5e4c9d364466ef749b8d0d88979bp+12Q, -0x1.6b72e41a84905cceda3e7fc6c066p+12Q, 0x1.578fd4c404248dabc968b7c529b9p+12Q, -0x1.30faf3648505cdf5f671e0ae34fdp+12Q, 0x1.0174ad7c898217c903f8f07741efp+12Q, -0x1.942bc49f2f52a22fa3eae80252dcp+11Q, 0x1.25cbc7992fd63cf31740b115daf5p+11Q, -0x1.914caac5676309ecc6f6c550d8ebp+10Q, 0x1.f93f030387c4d019b6838cf24389p+9Q, -0x1.1b4f5dfc787bbc32262ca3f167bep+9Q, 0x1.1df01b8a36a8b0e740af0c5b60a7p+8Q, -0x1.048db6f3ab7c1cc8ce49930b812dp+7Q, 0x1.730bcb9c58bfc20d60bef0471523p+5Q, -0x1.09b56b87c1c7fb7baeed74ce6cdbp+3Q, -0x1.4fb833b30fa7eeef6a7358348b92p+0Q, 0x1.e38e1048601a60cbceead8c786b8p-1Q, -0x1.ee07e572041f738c256c5953b0d7p-4Q, -0x1.913ced3c0164b56d323de7f36c57p-8Q, 0x1.0726b83c4032bf81b9ad0141e709p-11Q, 0x1.2751c6763466bbc5b359801c4ca6p-20Q, -0x1.00ceb77e39cabc22cbab1770a0b7p-26Q, 0x1.0123085a8910152fac9990b7a672p-41Q, 0x0p+0Q};
-            }
-            if constexpr (order == 11) {
-                return {0x0p+0Q, 0x1.6ddd33f198eb3c96ba1c54f670fdp+2Q, -0x1.ef9ef6f596ce44132c5dde1777d4p+5Q, 0x1.2bec86422c72fb4a905555a96936p+8Q, -0x1.ab3138ae63b3c1e29f1c692c8b8ep+9Q, 0x1.90171accf1ae92cfd9c146fd2557p+10Q, -0x1.0b8279e6381aa2b741cb2d9796cbp+11Q, 0x1.21c7cbc3a51f50320f21aa56334ap+11Q, -0x1.3291c6bd3630cafeef14937244cfp+11Q, 0x1.52187d4f278255d90661622e17d1p+11Q, -0x1.5764b21031af003ebeca03a2b0b9p+11Q, 0x1.2d82b77758b7aad296e73eef7d7bp+11Q, -0x1.efcf6fd97e7509c927b7122c5c13p+10Q, 0x1.96b834131566dc9e06167e63c7d4p+10Q, -0x1.34d67cf0a39ad9453edbb75a25c5p+10Q, 0x1.9aafba6f0ff85ebebfb694ebd422p+9Q, -0x1.002f1ef9723b265f846b3c2332f6p+9Q, 0x1.378956144d5be0ceae60b1a0aa28p+8Q, -0x1.48f6827b3eeb52ea5b3fa287d164p+7Q, 0x1.17de886be7cb3ac887cff35422aap+6Q, -0x1.abd1c377daaf4123bc47a29397f4p+4Q, 0x1.18836fa0aedf116ff47c167f808p+3Q, -0x1.72b11631904f6bd3fd5a823e34cp-2Q, -0x1.93c736e0c44c0da3f45cfa30760fp+0Q, 0x1.74105b4ecfea6c16423bc348f8fp-1Q, -0x1.a9382883de207a4dbe62c7de34c2p-4Q, -0x1.8ee02bc822713114de66688f8544p-9Q, 0x1.b89c5ecf7a7b773088c639b3a53ap-11Q, 0x1.5051009d42a4549b60dc1a4ffdc1p-19Q, -0x1.a9ba33acc416babe2777385baddfp-25Q, 0x1.aa6a7d0ba81031b3c9971794d3cep-39Q, 0x0p+0Q};
-            }
-            if constexpr (order == 12) {
-                return {0x0p+0Q, 0x1.7e688b7526a774b76724ba13a96cp+1Q, -0x1.044f66dd0bb355e9e82c72d5eaffp+5Q, 0x1.39d2780b0ad2f5c130250e42d893p+7Q, -0x1.b63bb8898df0968b0e5291c5adf1p+8Q, 0x1.86b367123a2139a59288ccfca3dfp+9Q, -0x1.d8001c1817ddf23795b1149354dfp+9Q, 0x1.b397f071da3115c284e47fbefa66p+9Q, -0x1.9ca191acc971e01d76f080b3e85ap+9Q, 0x1.d28d7edb2db091286a502e3d1491p+9Q, -0x1.daeab5bf793f0a5db198f7c1b01p+9Q, 0x1.738e37d47cc21d48d3f57dfe7cfep+9Q, -0x1.0785a3e74df59d20286619983999p+9Q, 0x1.a556a97ba734840eab5a765f294cp+8Q, -0x1.320671c41025d2eac683ee371196p+8Q, 0x1.33661041ead74be914f62376ca64p+7Q, -0x1.d86506577d5080199e51f7260b6fp+5Q, 0x1.9ebe0657238551a24ab6c6c0e20bp+4Q, -0x1.ec9ee904293324442bcbed481925p-1Q, -0x1.1034340999c868fff5238312a8aap+4Q, 0x1.04d7524f6a9fff23ceab9523e19cp+4Q, -0x1.2fcc89fd04e88d59c75667d7c4bbp+3Q, 0x1.7c24bc012bffc7d1e21de0348c52p+2Q, -0x1.c84c145900f77b34a4876818624fp+1Q, 0x1.57bccbd9e4fcea0faae4ccf7a2f9p+0Q, -0x1.d81daf1af068d1091e32e8f2fcc9p-3Q, -0x1.20f9f72def1de8f22a005f73e8a4p-13Q, 0x1.c2f2ad7e016f5272ff115101365p-9Q, 0x1.baf6705e59cac3284164d29d2adfp-17Q, -0x1.ae94eeab2dbd4d40eac4360abe26p-22Q, 0x1.af91281d9938911a63573a1c8a3ap-35Q, 0x0p+0Q};
-            }
-            if constexpr (order == 13) {
-                return {0x0p+0Q, 0x1.a308ef1d16805759614e47ced45fp-1Q, -0x1.1df37cb20ef6cd526bae886688ccp+3Q, 0x1.5a47cc2daffcb2cf20f8cbe23f9dp+5Q, -0x1.e7cc32d4c7f05cc178a92423af38p+6Q, 0x1.ba5aa6f58d154790fde87c08c1abp+7Q, -0x1.137ebe2556bb5c31390bfbcc3555p+8Q, 0x1.07f96c27b79ba1c76a48900fad0dp+8Q, -0x1.f176d6c3151d8ca65c2069cc8ba9p+7Q, 0x1.0c09a0e0bcb9ff8d7d5ef1548dd1p+8Q, -0x1.12bf0f34a9a5500b54ae9f341239p+8Q, 0x1.de16d55d65d2bb62ec7f100c7235p+7Q, -0x1.8c7b496d3d3fd8274eb146a1b265p+7Q, 0x1.56592506626bc28d37aec7a2a08bp+7Q, -0x1.13d919c9693b2e85ee4209bf711ep+7Q, 0x1.8b69de5718a09e2e84e51d955579p+6Q, -0x1.15b78c90e783729339c94d803f63p+6Q, 0x1.8188b8db550fea38899d2489ef66p+5Q, -0x1.e03c011f666ac66011b7609652a9p+4Q, 0x1.12ed8b36e986458009c8fb08c63dp+4Q, -0x1.36a5b057bc26ecf6312ef4c8aa89p+3Q, 0x1.3d2641cf67e8fbde6d24a0c08316p+2Q, -0x1.11ef148707dfa11f55a9bad8158fp+1Q, 0x1.c294da23fe29fd37f9c13ab439f3p-1Q, -0x1.4f57e7e05e818e7ff02709327119p-2Q, 0x1.1ebd9964081cf6e9a360b8a8d058p-4Q, 0x1.367917f76eee2f0773ffda2dee7cp-14Q, -0x1.fdd37749c94d91b95e5811e014fcp-10Q, -0x1.0fc0733cbc7d657bb2812f3ed59dp-22Q, 0x1.f945fb653cfda9182e6054d0438ep-22Q, -0x1.fb1bcfae6e46d13bafafa99aa27p-34Q, 0x0p+0Q};
-            }
-            if constexpr (order == 14) {
-                return {0x0p+0Q, 0x1.74ef139ad4e11f00f65daa8820cdp-3Q, -0x1.fd9d32fdef73fc52b4caeb648516p+0Q, 0x1.3320f17be8b7073381e865362afep+3Q, -0x1.a9e31dbd98dd09635b0d379485c8p+4Q, 0x1.73dbdd38a87f5064433a350c721dp+5Q, -0x1.aa50f206f25c72a99cb7b1dfa7d2p+5Q, 0x1.5e48ac9c2f1f1eff350b14cb6a0cp+5Q, -0x1.20d7a78e95ecf57e7add31db3fd2p+5Q, 0x1.4350b94e5aa2da50e61a74e27b2cp+5Q, -0x1.5499ff05228ddd2807c95d8259cp+5Q, 0x1.0d8c7214ffee0a1235b3874b3a3ap+5Q, -0x1.8fe88996cfa9a55157f19af30b98p+4Q, 0x1.63da6bffb7322ee61e908c187b83p+4Q, -0x1.24223f5c1b9d9506d6b401adee8dp+4Q, 0x1.7851e19176715ec2bb3ef2e77d74p+3Q, -0x1.e4fd178fcd0ef2f7354c8299da37p+2Q, 0x1.610a439acb28979c58f2b0d330cdp+2Q, -0x1.ae4c3e147b71c294863ea12a0857p+1Q, 0x1.a6fe28ab7ffa991086c47e322a6dp+0Q, -0x1.ccc920f98175dd5797f1c22d8029p-1Q, 0x1.f9389387bff6b354c93278385205p-2Q, -0x1.8612de961fd0228a7f5532d1edd2p-3Q, 0x1.fd43fc0e7883ee43ba7f30ad9465p-5Q, -0x1.aafa1e0c4a86f88db60d4f1fa17bp-6Q, 0x1.b638737fa8e8eebd498a75e7c49cp-8Q, 0x1.071682a1f5057e2143b4d72fc7c5p-11Q, -0x1.a84c3f530239b63f7da26929d4ffp-12Q, 0x1.a20c2374a0f6700016084886c2a8p-18Q, 0x1.e7f1c0adda0f62adb67917e7d654p-23Q, -0x1.eb089a4058efe658e6efa5db9e34p-34Q, 0x0p+0Q};
-            }
-            if constexpr (order == 15) {
-                return {0x0p+0Q, 0x1.31c729360063e0149d619e7c5659p-6Q, -0x1.a21aa8a66a6833da5818bdb00dc4p-3Q, 0x1.f656a46fa2a9169e56e0e1915e67p-1Q, -0x1.589b4fca92a9f10523379245a6fbp+1Q, 0x1.25049558932c1a7bf94dfb345bd9p+2Q, -0x1.3b0f087615a26809432e1d6e01c8p+2Q, 0x1.bed87f332745bf792baa46fb22d3p+1Q, -0x1.37fe75fa2aa3b693bb533ebc90ap+1Q, 0x1.75c34ae38a11fc31440e21813692p+1Q, -0x1.9f32b219f201f09e83858382dcccp+1Q, 0x1.2a50b5ebe798e437ef2503085768p+1Q, -0x1.80aff2523d4b3342a833db6031p+0Q, 0x1.71f9af43c19f0952a4e07472578p+0Q, -0x1.40d21595459cbd897728656ded6bp+0Q, 0x1.6edc3b8de7cbccef39ac5c5b8452p-1Q, -0x1.abb5cf29e076b1f30f36686df3b2p-2Q, 0x1.5fdcb9c5e1f87c285b04c2fd8053p-2Q, -0x1.af4e9b9242255620df4c3ab9bf57p-3Q, 0x1.57b33e4d63cb5298c7100384e3b2p-4Q, -0x1.736294d370dec79efb4014a700a8p-5Q, 0x1.e1a61d7964668ec603cb9aadd499p-6Q, -0x1.38138139d6cd8275f0059b0302fbp-7Q, 0x1.a99b874715d59140bd445bce9797p-10Q, -0x1.191ada841d111d8ae1875d5194c5p-10Q, 0x1.44a23a1750afa85a30082caf581dp-12Q, 0x1.4db128e094987961ef4278d6a462p-13Q, -0x1.2cad37f3dbf9e7a235442f3e067dp-14Q, 0x1.f38c667f694821291da674a42ae8p-19Q, 0x1.c870773604d02f72b6568dfdd8eep-24Q, -0x1.cdd01a024c710ef11bdc57da89cfp-34Q, 0x0p+0Q};
-            }
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {
-            if constexpr (order == 0) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000171316851323746428212831421306300113678607875446348503559419927437918383967"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0361088272946006985912064934900062644165629414989774122809757345902866027938"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.488256992843695840962159179639502910381980307460695354580458818691887940645"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.769737672515207083007430504821028844267689308307112651993923296421178108389"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.453126925329274055451166333557401859659406793270554665033541123983449765432"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.256628058814639987338137180313733199002175042843789042052759470470604205726"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.163454122854003496557302427492278171149085655394974230532183221080254700021"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.107723422859916997108276817161022290367504837432994030942098049009089713930"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0649318249233011704784968686914491012172054359333812436767935404371230620232"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0326435377329051629426715185593256884476167946008041064239605220708580188240"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0127409361375573448882342299469851670195888311206647480453026814799719677344"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00352196549620161398967203337357383200834551341224048951969904909167613097889"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000534217142003219306131911092756991844459258563640870926150016500754364314332"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000405890411165595317643619001506764641287318490078309353140855497110673976431"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000498095041023299888778042223185543062245836773367960445465000704315159966296"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000151266310013612774856135240041061222014350088021428301604611262734516728901"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000196962302501772214722461685124074719608921063431828230431618407481183902342"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000307419811865464641941041529634159778226115669718094511609235500455794645613"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000146711526898488736937232395914501861484051305606502624138556023532223617309"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000469170321491953908065098991723043621408692762756980179169088515131858959747"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000312109588324696299578629133466134546804934425652317350217208685069513949015"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000129567198099448561278298370512360354984106954815513505005111818553145714634"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000116427529260004024077348030611493564888124415305981619797224470056679948811"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000238326595578192588974326088085766915138526617008998625640603860278073091204"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000244742730302692510517546840958886727657274951555813495950007886554971190043"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000770600420494052668960125627196143256619852875376018693997338520252928378898"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000000000422698076320704793842624462462122259676671218339643878393761622611533681352"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000000000986091681636424791402346661562732411914581846543827917931134779717124541059"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000000000000000126415071901335517823653751264600698935766480825324951588072073703511279792"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000000000000000000000000377103451930012080634362697114829703633218765482534208185011848812515552568"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 1) {
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-            }
-            if constexpr (order == 2) {
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-            }
-            if constexpr (order == 3) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0524753452804691735477738251517009853016979362519517221207312376177764782969"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.879968733813233322230074392947552628565967066414165711760276698494844390125"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.74453159899437732175018000055779377712653677438008754872020488131059119320"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.80360353176224527101835802230946052421659096363090207129121849285840468259"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.96666354532348341330633181326044172915860234894700083373343277220577971735"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.73070092873449595291889929112197581304463119652084787245047615859331130715"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.42984724824215839353390105174821482301107399626250856007397139446613345585"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.277322631367784241585872795091101589798351228341158053606520050000850391984"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.16919259864499295419145746896607736986733203837630984609448122373016720827"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.39016950402094561654444812940516530484537994331951170078343059431705063505"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.817574132321601018212216995379856653768755317510857634630667447972613443467"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.190018473449379212093490515862790233603734487245387060360549170220720527831"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.100241083602577673991999687326956519174898192619719218177625643190688840896"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.110015365802528313698254717873775724459189967181830195015949587831350610756"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0416060467568914386443724185616672217060437647984160864439680078935440524035"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00245435974160983337464675102356272887367440646869277382351633348615279833109"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00443062929513058573083346981678078784735168535836855152956465826632431223593"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00192644595259837997265354752663163334685724941492449191301572332061212680367"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000286252108033456570905469351445678979854820611278948347680038000227240824154"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000237541414511668265954922688834169477800802817148790300058634367070336055647"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000136482469252724735030504787827046649952988816328627069135194335843416601041"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000131861141712690876615365340120264536061804975586109036631891707678386628591"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000473486085383219537439492823717115126567852265733507953095631575087828890796"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000107671154662516331418850350729831199883227731812375998404087097072976836721"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000995866077139100400870850073442653083344654813486051402700610836989945821329"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000644585749433741211569153851347580280472182636866394478917140428098212069667"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000403351073771297890412924077239685188093056035814882459390662060096671857385"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000659252152542076182761062902783690995247798500608023765240694648924331810668"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000960845271049957763593097408492741398950372383171287599580336659389110633204"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000229301073796668864262563070071270109124544905677035858311033933294273314683"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 4) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.250153349334599315252252388126799299269205865296558881938205954482634425962"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.728403268974963829703458458071470050940885133583732803633168550716310693177"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.31293553717675839320538206374566119063264654529238980016770942275333057680"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("18.68528838602266775292882053961758029216187265423226470274612731462272361220"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-26.26201351114432524894573270494314114413810106786511729006960444976330657170"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("25.63029290762557459998254683581314951053365051306913942327754105908104915980"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-19.55120591041754554650107676016020601099463018398879255525071777101622456320"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("11.38828805991210130161237386775166797562787000397306556310659987606493988010"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.30283228500638291198113772321275270873046197281267419596706014023411466725"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.916846332667450611187893927561003746742522420503995679541446843858673884695"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.945625534103851129678007688099239113134137817655559774710855777516502347910"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.89515793182939656979518906226485738613531079677925225755026655593370960082"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.93021100594621881524555259846350558417500093095145605126078231465409489372"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.12168634735032240026321692944283569195655093165680965383861531031185719852"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.336457302755550977576916271285480607975977081669910226236184937860992298991"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0126426202740467393304674214034871452929934964899914857227809055709449712216"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0582059974257001233798447456344149565398178531031451066540415121870578243558"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0246013214406903516120171910897552685116442802184487116944341538415325680043"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00411996064777101316931682571931078586923686158543745182753395278198530764373"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000291779559634866855426419087305363632521209937998931712658121173823485969925"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000239701704903312956607867825407660197652926764025390834805038196728688308116"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000295826390590035655056112200057348642111500715341367896808394225854268570663"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000112791496012934939362671595835297640696200634426263650389034453900171789361"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000305425386948880794569641314813535348968283260910445455462866729010610312003"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000323553114835699703688881035252953349590896466534687900103865721438408552054"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000258122376607866610987411018878425618791837110136955492805044321479509589635"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000219450790662654304491928786757425834815059646115033341354646744288934919567"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000159236348311539532630177443070999135468225820289422009164997153592635443466"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000104656532906862901171727858795431981501763265514191943218716516961575846913"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000000000000499516806365011687457115487988706495932857454344801314889510253590960148386"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 5) {
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-            }
-            if constexpr (order == 6) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.72080556004295870927948424445222388100259573295765738309696540518313358664"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-20.35486605481687082915848974154624621834658263785879525672648653134317139910"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("70.69361844342337341827651301058270782618285357205640682781626444606188387450"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-157.90067201133162316239612336927048444714935472994185058634807793776069875000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("273.19822200505440746851580897502900411638483947712679427834499734688751603100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-419.19564866352573545746821411474547215410128530316966417749138435741251020600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("599.84609690090711287694432739982078555920467552320725430638045237415518597600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-775.73303631488442783947171088475881408364372009796884367795062491210589677500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("867.35358450953923058123434268208131384207780232732818873949031917800169735900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-826.95465375065970699136161187085785345289352007444881210861847791029287195400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("682.30445844031956022343618018820158741773280156063117441757258118184658256700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-489.58797447319361281730621439860073553304564691478746587385050469768692568500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("280.41641455591206428665542158114941187595434907081896095846035277563013174300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-83.87530313006339392205670404100927251009153086911120664987656189069922028960"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-48.57290602853936778598444588838000320319188797120667088890627817071006819220"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("86.48401303861623414105279810601960248737236193164692484110937025080244348070"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-59.34749838115491965382974741024204031184960541600602452546612244205852115450"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("22.12683829000516493499208689759136028373805834965052266237848630047551885400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.06820705468851142387494397352111576035038520405038204822630392926462913822"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.01844918784056167247769356011865100548861696497532359778154988643933299720"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.548390155052322116601605108703391030814361014039987127607247780249699826925"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0821665399305853726866950173051458732522788040166080680936985410341364899325"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00259076138957212819580904996053947215856595645621290484740534408016060849032"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00158184168192186218699552573165552035786412989560027541837371028175219359299"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000486427797988048217823553064360225239762325535402325453015988941445205147689"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000278733673658518296782298192418270556801753284097037387222408724354826075481"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000415493043046997178773581906387206851820091297524869075078083888063058100083"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000318481755988583873479575641293261720504490443808109780404429573043006066979"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000000786533511511639686500635180600662013025908347693905569053412273585440000541"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000000000150164678504192250638011216866493543394290529002160876206865753397561385614"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 7) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6.14186178805038248389630463226453535538160220630273168999055179268700878311"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-56.58718775023035303740954199011503276263410041781331860722827039023288201390"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("236.79056117034701253831145295400349362659332673554984369468013095569697737800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-589.74212764744550791699351051034231997851066299588318672773755627012133999100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("955.91771747407523740699612277021093282646971930388485874767008345752406868200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1018.25371372134704439175662005189756423202874621778366040811852543575681051000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("620.16534974073328124363357805606821825717843510348080668139769912997493261800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("118.09513214016409343018299161962983559825963510724745846686457205186992634000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1124.17593601667896107495596149804572042346983911263262865208494201555643863000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2481.05019825971494606026459932673050920844604853044544044249826635533039896000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3958.72656316717252768182437149784469578445448081086451227500629910596142977000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4892.08038810778226650447637979773553060005455552013373826491377287611549607000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4888.02985912371580185159900968286792361495832247558286519513525186654679328000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4222.21851392745950660685593080126541478731847689276755099970578373193227197000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3301.02739698605769321367226000985199110976449700946791984290949429902919623000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2249.11165074697026237037038692307185505620568793949311249024089637097353635000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1187.87398664007835892158563773173750314639645000950438376922380430030480509000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("398.94177525756891966681160860599524375229162312548764259215104838155477665200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-32.92289515108174067117397420787028784793135289819773804980403784424237633870"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-38.90071447021924707376179244031261113671069629451701962465484487047604238050"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("18.88702183332856460379524735396940221841668334008996536437289731073857378770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.13472910313296479389678303201845822338839740930736804510308660361540192213"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.104405285224584684173481804595561114177382914767308859899431383064024115571"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0833671470549304163921288867140169654715033486774418851176340785841513622562"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00381467578864364562968701846853701311666229039725704435440024110934078146310"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000212300699997037803249607997697918026005513531720485603301750991443816531034"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000444054082400028863949114022229769838935441151556537774085307875568116728653"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000509993859755275328806308874095727887214819535696251443253417433071486761002"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000000167399975134582079218262940873121039789400471542818329635957062341003441119"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000000000639212147850254313089119430941095253920739364313765534055842450107396358145"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 8) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.87573584867024438192288359005520927769283739845626908320402959675129181181"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-89.46249563427999259136175287546983385362056330272761288548978010797275886190"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("413.53699835747096831461960515667083330041243777158520357367773071672954421000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1171.13814794944060840954109636487013129118793177524654224322494272585137735000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2318.63986015396571592184876974869163171162613486972744615164020031916734488000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3550.00082837270164131331314150441834830049599401355505132632489796798446179000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4641.11041485509138580464243430685343405509172986351525682383304436384521680000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5574.31228403733210075849705237883208794074944113113868870635833735655518388000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("6213.63809498218005198867412543832867815767594736394946861528827045454364892000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-6270.42945837810044547764288676694403309477382977177928731847017182750753511000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5712.25416364615036894363595935332173184639280691157188990767737995783827699000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4793.66410435252078277013910846939514432498915716171347756825555965008446551000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3701.90566377778244662006515118308691363996241871472358316732096914372421991000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2545.73002939982681324232451707199314555811122671561913141889937616476059628000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1525.76211545671409952881904946874414887615701953904066966165263931990216324000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-799.67600361393244423210153323478015290110022742899088191532821628208931108000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("343.71466120684357322054217074049470228013278108322582312246908268821531549000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-79.54296988918714825182831271113602645818430801267882016130158946025000070880"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-31.11742247721594622537736075250551303862928746280885436044292583853573827770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("39.24534373830708704714957239063819401930019800422830284025236588588276304120"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-16.49801465465629310378163586594498701051184640106636079791958143499072398020"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.86471589853451505092762387909842635954128523779170775248876357690346385928"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.123177932504841138584100462602213000414409636861317554953311729819152981937"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.107313432588339694252584996265922811157032804886175374104426839751272364880"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00773540599618550353141393406195746669996857798924014596151059620636703068705"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000403128635241149243596335554099377174869092597389189451754820571281078679507"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000121750336610624680031947143595873921578210617486500364426723519144528821747"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000221216095903365985949388422841378231674809606300993758039913686908512670984"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000911028045352580286145166937280851897647011765638383494849691163731056620327"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000000000695776129234608161606962102284274675410179267386907251288229647263547841513"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 9) {
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-            }
-            if constexpr (order == 10) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.40595389327657226503694497012483164362124209823619932408143213509789418142"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-90.18755588816675228829817416935430178296553880218263006522596252933799260750"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("436.64933048343039643869664274295205972159884268297618856653635883730240629900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1265.24702078863967272446087300490983418244378482038979633311557029559187581000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2479.49727416305844438566515309514579938046134972182762000607495793961979937000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3612.22404262013984275650095257916266122615183211172708920604427365997332248000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4390.10461803162979442824063337386992495525825588510223744432684369166514283000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5022.12359523964154158524736614172785466023371493789078267642792825970442996000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5604.78838183135573305540445463913574361373339338579848172772266429190600683000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-5815.18068935187129727737790596258417265132106330711026316076022878535003649000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5496.98944474809909883345018624513683552577448320588129783533814897200127901000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4879.68442203485471741212789690616385244300504302852282730946221011631520548000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4119.29235509599810627701483024966303400343567833202767250947700453832737400000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3233.36775168650371444115689095291480507860192155181401201543648075525710965000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2350.36811503737581431248480830061956015641307301010846976218535988613892099000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1605.19792304130910913657642308517047415091779052762305083384570282636342729000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1010.49227947358451800455150244650563573753526087564849242400820565186861825000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-566.62005573161101918270073525503120095406475610339310771504079035825340859100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("285.93792022547194485799602926303040314550718046007817587164843637458151043200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-130.27678643673248754523842749099954235730480748012199117865803024394099262500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("46.38075945039597150032827358523901955451289440527106334217760766144442187450"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-8.30339600100546654050525461274557456779962476685870904307407201958336470745"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.31140444871530779856774818636439538472323427394561636210886717702287713836"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.944443234286201477285280631764338282009445764538235481135279079602176865296"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.120612999220845884841770938047070126476556890469242771667061304639099680352"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00612240592818620183859019486914162369755180328595090553906554353918907508111"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000501921174446894651071522876884881677798862264257444046312361569076439240403"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000110015062442341106953762659845461877288849794732582550741170847972381078513"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000149481631455733098677769729640496918070320996170917395536883890913165962523"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000000000456766795438744131185097599240634110830128913864595728289285533008059188955"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 11) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.71662615388384035490661602572026128251294325475247692177411024734707018748"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-61.95261947504494240974525516761288737718458065654976960732742872670132713050"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("299.92392362199005365846763014477362358033777481183567437527249031455105143600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-854.38454227321882602012934795768021816131020192369607501580124187697270944900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1600.36101077653647183632909120922276146512736031345582867483706653247060307000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2140.07738028486081463619489247776891689722101986432309104955433096170807913000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2318.24362356424763321295439620892210840488958065858246141680343191186676880000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2452.55551014503575390323183594502097923638970524686355738420251386509103336000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2704.76529653278947329663444759952034890877923302103630805132576388538972614000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2747.14673623756244311092333721767148045245885058383000695480413427282125343000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2412.08489577605845461832534754288001056964932833568370698369648585962621442000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1983.24120175694784202508820179002467936094914905473739070428929084792886805000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1626.87817837800998599505523804923350020881957088925397853144571494720023844000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1235.35137573220290037298796944863432831370478695788713485540725637661419976000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("821.37287700919909202293078059900314209961592538962184148238624773351355270700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-512.36813276364982792979888767414531827457847125018199834823820044378682592500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("311.53646971596379276316317223887976975287113725456002799972326204795524864500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-164.48146424429947905468701694679777546495466959145717581719894831842925074900"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("69.96731728174455147890349889940708552672488525211671432746656999693968225190"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-26.73871180360852431769728634910008054094567759215735127221449159427110567160"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("8.76604443915764102583091274494705031974551432188167671170993272943904796868"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.362003657126549623871141694778787300536949241545084284403839044422181900363"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.57725852000685070664686477385087762553122190528479055773272661383335169406"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.726687291498781501912136314567313444745762140706471235702655842502262486103"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.103813322317258033888614985218841754913997474053598134379424827680388803266"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00304317984052183404339782146911467997675320910745831815762231114417956519165"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000840398448358251520779467930923617673432444631095231180255579031943245676198"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000250575256067101292262100569305822521295926652713304136991428596750128740360"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000000495611865767157365743127106863134595887690986921006107382476777985767199385"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000302986770281715807340388725183309305879191944670327753347349945452961991743"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 12) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.98756545276892961683405920317400782688926167457213404606206894953469090570"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-32.53877041522938902748893248611882921380701347287193692458464408872270681770"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("156.91107210642938297454108565759471733768304768928530524781265126236462047800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-438.23328456607176854897749709031392294408668236354846841483816529557797373400"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("781.40158298338287783314503913374413961456166368022728026502599517169883168300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-944.00085736432437654121844433808421180478044182471803034745876831993387206200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("871.18702529100316496510657599432732757147821503683438970158984398762342159700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-825.26225814663098471936651058959817182597766714375609693318512269093807603100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("933.10543384295409309368246495330995137453207941551441370036549134265538765800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-949.83367150707461495067586025268239472985940864418244218914669709742438195200"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("743.11107879726135141484801469462437364046148934147523506605304654685788997800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-527.04406443888294920168702045857144963725142274860553582472478068752203879100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("421.33852360565335024951901100209978198412810212541506159854671267737618195800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-306.02517342943412940702644642463233060183139335286436410908479737189261628600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("153.69934278480254603223204551372425554980051718272712837279730258851702658500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-59.04932850218943944934225606851905428436217033134937163374348351651622137740"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("25.92139276541304973776659197601093424514632883892831929110158475123035210590"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.962149888761450607548667577621856494158643540101329999411575837264452498654"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-17.01274493932990083951623416795053065446598743948526471513759064128883019650"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("16.30256873151847666122910844100498304960224732436925588411210572182662140460"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.49371814172560994368165179232263581655149629936005381772523795944996123037"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.93974208940926161725307281051166656360861938611697972636537005680715438577"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.56482176156890404621445412519261540357391040079386784517365108357090968874"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.34272455281915240128955665480521952634664404440227746448796352198622736864"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.230525367745987004995002631304137357183156209105644834496304002576886379356"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000137794698671713437634696681954243933103735285034498363332772681562760804986"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00344045989823171334589527993003846308427283936104805061708662437757755864133"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000132013157638346537184564818139969682565470634989172759825885721468788821545"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000401010519633852578247631428587627292136452995638469407199569086176144778907"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000000000490634895829511758823128551590445161881103933303527735015583380577005829440"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 13) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.818427536297577413662164686067597972826506918636591011690333183337912720187"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-8.93597254540483169304505499620510189518004297750684300492893393884837531090"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("43.28505740826911943179704985609069278737276400385479670313947361507288590850"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-121.94941265554743093324264638861456116774169427109119662746887892891581414600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("221.17705504748540968473650066059868951479247074002625157942998465440826537800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-275.49508889548757008568001670977657433955615658111585669026893704820453833800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("263.97430656654945046201101887433086255955773561111355779696585609107954522100"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-248.73210725434071237643827703257935321449607282648266512518873782422456148600"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("268.03761105163175511980802546399577987927646399395524413177595218195546680300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-274.74632577077619559794959711805873055919483442081245207387230106955552634800"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("239.04459659450491561902145275774681231766178202091849139640330374817659226000"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-198.24079457638428918916507018047876417177573585609523087243911695920766059300"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("171.17411060286929567487650609762363461665749097833059519177248964117986882700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-137.92402486238060270403376601148674136697949366488773861402567537082900349700"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("98.85338722312749675832616392395611353702627445403696398493090489812880274670"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-69.42924715436025679968823314670561196868618424662305178477940854240571797230"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("48.19175883630122313265867563554087765085528907020382930380472297614957949970"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-30.01464950814868046242052769312726238783217187685035205505179037973211186450"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("17.18299409341888528416337955184486836168042336837628442005969736301859437960"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-9.70772568832145809755029602593534775626803932755931576353380272720933569318"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.95546002630693726392090932025925003607433594321786357647449706566309372496"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.14010864823626171034034636914985284178400701423559135938044246487466223776"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.880041901487022196333800296293828350812076915017847173990679115863977711041"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.327483771390349393328449791379023445875626515179961154056969671224666397451"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0700050346208691475219456475608152516659372000469712274360723295281871848387"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0000740225367427644001587409378753952383212767606234921042405852483821239061334"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00194483199670374685015094187211770910054778766605235293849027402856312150840"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000253088547271589825310570020884344496366999521135191317044614410762991878950"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000470572493262891053536372764217043903584963956635299308538734504960681361207"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000115303154806547333281398739726672346354039012152713743670663506289507432912"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 14) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.182096627390465002841872599753582960857482793103154443921292798922930823312"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.99067991923898541144309882988836202482422764820095134691586013396479875824"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("9.59777139855370444734294750686163842012139708590050472898305559257417654445"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-26.61794828473449778541050916432452820900605760472867782882032588243833218460"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("46.48235553993428243642096843754171537043857798264743456557286506206884999660"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-53.28952413012626128654306352591401630142078063921055789323943087480417380740"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("43.78548547762683495894325883003176846356585388587214183280498394113771237500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-36.10530005831753430370334734266356752826479202721810859304361182987411236780"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("40.41441594328021583316039518661942961300602117705878612433379552772328367060"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-42.57519344340992846492391425032425629733148181868603643066418155132222692720"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("33.69357696920429126980241665391486766936852157516836030131774633802657214380"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-24.99427184019678212351060274549661020691119426526756451144184518863090205460"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("22.24082565201673464792084352820810035044717879419914422566840373427801119710"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-18.25836120586050027075089243454704089299356205520219684237280836587814742320"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("11.75999525461842751380077638481339770186505465117919491977936260095287395430"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-7.57794751208369560067407289978430835851835802702956349867965768312335398938"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("5.51625146977006284358570281266574340943582336186123580684755277118777603718"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.36170173645122190520455082014298086926033428887456137863348894911353768638"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.65231565653810221017900302691080368910278392146172824258223867713998781120"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.899971991021384569041112723985746774474890344096613796399657618872823089914"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.493379883919252205004540248830738351306813744782324207970147006276757888741"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.190465678173474433044011230247932891163095527351165979372112094377892415660"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0621662066439658745587942761812051647689996933574065948837820956985288446830"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0260606091916674704141077213394275894517321034885463805642148072294982340641"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00668671436111235768206809845426737458018128101136661828669846361010276014213"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000501800405113171457500759977346203260700591357705539339843489778157288724465"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000404641953708090404336673259880430820473496337074290841846682708432617331297"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000622939193262507048296472703033235853521538144434623520667251347304027494807"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000227216792432532934218802486321263209684697324571081185820714866955957698807"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000111648115236885172375463021306155593347638298619118930265825307233276056732"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-            if constexpr (order == 15) {
-                return {boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0186632063341731699487622519569900676156629675744736414459848077254980584439"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.204152410105326344047690139058847944463463829383572825741723149474265517687"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.981129778506629236917943314009391202465976027147847806934681206721129743489"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.69223973647360950767394915742670959250796023828609553625040576017143217370"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("4.57840474748508233139703474514191577520139760766602312536057813786879861719"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-4.92279254466715210570744929069389870019317731597159546050988432127489832899"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("3.49098196027493477759169680079840596940785122938110897581250074622145540830"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-2.43745302882351007548114866638762563227820344626399026957104467610746424919"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.92002235517806230637018721558192349007812525216552453182604910919733517109"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-3.24373461024153144136567992763463788222027847288621903947814561657763790774"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("2.33058809298308412023805776435915774549596651226832414404182013235265783095"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.50268473155783226586328187697167000171012304032869369458457484335905926235"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("1.44521613506514880646597775935884860442911229706573188445594135154651054603"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-1.25320563215574317573983783719179686555846390567587617560334570616539136371"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.716523991653864912132988574383055048288486387296028098428465297303529312898"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.417685734682996474655995981787950272634517973441398985560062415678439970424"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.343615439131547337750639931144047450610704550982732392292547279251562842012"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.210599151040031056875841224107239694928740122133299240427666270185426716963"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0839111741718053411362323568803319587928469795988859679968270250707587553192"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0453350931889210140035133942035842323703748999105117340363647560154703981313"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.0293975150903577374499867887808058812502982622650503969014313916908299400994"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00952380952701618903633264790459773368829395336984965315811681382826752366623"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00162356389207281836884637948122226515491709153554839790386903440166058269155"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00107233008114088588860897903711349245756991842194937466975676115541205802164"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000309594820880373636252028432067839316250026602381083168344278875876631484733"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000159116759294319410028654591726757975556683309929396718417834438386747643662"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.0000716868960901604452106499159427785061407281838428321680583983254056627687328"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.00000372192590676834494238303138990722411083877718883831917839190468860584330496"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("0.000000106273060435352363021386153934099392277182493972188516192741747367832383831"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.000000000105004095727400196995819073889347146562377832036002728993854591918261645500"), boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>("-0.00000000000000000000000000000000000000000000000000000000000000000000000000e+00")};
-            }
-        }
-    }
     std::array<Real, 2*p> m{};
-    for (auto & x : m) {
-        x = std::numeric_limits<Real>::quiet_NaN();
-    }
-    return m;
+    return daubechies_scaling_integer_grid_imp<Real, p, order>::value;
 }
 
 } // namespaces

From b79d622861d08d97e847c869a86a4a2f9f93d758 Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Tue, 25 Feb 2020 14:35:55 +0000
Subject: [PATCH 059/104] septic hermite: remove some stray letters (typos).

---
 .../boost/math/interpolators/detail/septic_hermite_detail.hpp | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
index 5e26d8805..c0f8528fa 100644
--- a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
@@ -336,7 +336,7 @@ public:
         return dydx;
     }
 
-    inline Real double_prime(Real x) constq
+    inline Real double_prime(Real x) const
     {
         Real xf = x0_ + (y_.size()-1)/inv_dx_;
         if  (x < x0_ || x > xf)
@@ -537,7 +537,7 @@ public:
         if (x == xf)
         {
             return data_.back()[2]*2*inv_dx_*inv_dx_;
-        }q
+        }
 
         return this->unchecked_double_prime(x);
     }

From d6eb9ca78cc9f72d4fcd9f23eccada2d2a679bb9 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Thu, 27 Feb 2020 06:49:37 -0500
Subject: [PATCH 060/104] Remove unused variable [CI SKIP]

---
 example/daubechies_wavelets/daubechies_plots.cpp            | 6 +++---
 .../daubechies_wavelets/daubechies_scaling_integer_grid.cpp | 1 -
 .../detail/daubechies_scaling_integer_grid.hpp              | 1 -
 3 files changed, 3 insertions(+), 5 deletions(-)

diff --git a/example/daubechies_wavelets/daubechies_plots.cpp b/example/daubechies_wavelets/daubechies_plots.cpp
index 96e8ce419..7776909a1 100644
--- a/example/daubechies_wavelets/daubechies_plots.cpp
+++ b/example/daubechies_wavelets/daubechies_plots.cpp
@@ -84,8 +84,8 @@ void plot_condition_number()
     using std::log;
     static_assert(p >= 3, "p = 2 is not differentiable, so condition numbers cannot be effectively evaluated.");
     auto phi = boost::math::daubechies_scaling<Real, p>();
-    Real a = 1000*std::numeric_limits<Real>::epsilon();
-    Real b = phi.support().second - 1000*std::numeric_limits<Real>::epsilon();
+    Real a = std::sqrt(std::numeric_limits<Real>::epsilon());
+    Real b = phi.support().second - 1000*std::sqrt(std::numeric_limits<Real>::epsilon());
     std::string title = "log10 of condition number of function evaluation for Daubechies " + std::to_string(p) + " scaling function.";
     std::string filename = "daubechies_" + std::to_string(p) + "_scaling_condition_number.svg";
 
@@ -106,7 +106,7 @@ void plot_condition_number()
         if (isnan(z))
         {
             // Graphing libraries don't like nan's:
-            return Real(1); 
+            return Real(1);
         }
         return log10(z);
     };
diff --git a/example/daubechies_wavelets/daubechies_scaling_integer_grid.cpp b/example/daubechies_wavelets/daubechies_scaling_integer_grid.cpp
index 1dc55bfe2..703c94b0e 100644
--- a/example/daubechies_wavelets/daubechies_scaling_integer_grid.cpp
+++ b/example/daubechies_wavelets/daubechies_scaling_integer_grid.cpp
@@ -203,7 +203,6 @@ int main()
        << "    static_assert(sizeof(Real) <= 16, \"Integer grids only computed up to 128 bits of precision.\");\n"
        << "    static_assert(p <= " << p_max << ", \"Integer grids only implemented up to " << p_max << ".\");\n"
        << "    static_assert(p > 1, \"Integer grids only implemented for p >= 2.\");\n"
-       << "    std::array<Real, 2*p> m{};\n"
        << "    return daubechies_scaling_integer_grid_imp<Real, p, order>::value;\n"
        << "}\n\n";
 
diff --git a/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp b/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp
index 208093342..d10fd232e 100644
--- a/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp
+++ b/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp
@@ -237,7 +237,6 @@ constexpr inline std::array<Real, 2*p> daubechies_scaling_integer_grid()
     static_assert(sizeof(Real) <= 16, "Integer grids only computed up to 128 bits of precision.");
     static_assert(p <= 18, "Integer grids only implemented up to 18.");
     static_assert(p > 1, "Integer grids only implemented for p >= 2.");
-    std::array<Real, 2*p> m{};
     return daubechies_scaling_integer_grid_imp<Real, p, order>::value;
 }
 

From 98a6fb3a2f1f024851a8dae782c01a36e076d3d4 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Thu, 27 Feb 2020 10:40:58 -0500
Subject: [PATCH 061/104] Clean up plots [CI SKIP]

---
 .../daubechies_wavelets/daubechies_plots.cpp    | 17 +++++++++++++++--
 1 file changed, 15 insertions(+), 2 deletions(-)

diff --git a/example/daubechies_wavelets/daubechies_plots.cpp b/example/daubechies_wavelets/daubechies_plots.cpp
index 7776909a1..9c0520b67 100644
--- a/example/daubechies_wavelets/daubechies_plots.cpp
+++ b/example/daubechies_wavelets/daubechies_plots.cpp
@@ -26,9 +26,11 @@ void plot_phi(int grid_refinements = -1)
     Real a = 0;
     Real b = phi.support().second;
     std::string title = "Daubechies " + std::to_string(p) + " scaling function";
+    title = "";
     std::string filename = "daubechies_" + std::to_string(p) + "_scaling.svg";
     int samples = 1024;
     quicksvg::graph_fn daub(a, b, title, filename, samples, GRAPH_WIDTH);
+    daub.set_gridlines(8, 2*p-1);
     daub.set_stroke_width(1);
     daub.add_fn(phi);
     daub.write_all();
@@ -45,10 +47,12 @@ void plot_dphi(int grid_refinements = -1)
     Real a = 0;
     Real b = phi.support().second;
     std::string title = "Daubechies " + std::to_string(p) + " scaling function derivative";
+    title = "";
     std::string filename = "daubechies_" + std::to_string(p) + "_scaling_prime.svg";
     int samples = 1024;
     quicksvg::graph_fn daub(a, b, title, filename, samples, GRAPH_WIDTH);
     daub.set_stroke_width(1);
+    daub.set_gridlines(8, 2*p-1);
     auto dphi = [phi](Real x)->Real { return phi.prime(x); };
     daub.add_fn(dphi);
     daub.write_all();
@@ -61,10 +65,12 @@ void plot_convergence()
     Real a = 0;
     Real b = phi0.support().second;
     std::string title = "Daubechies " + std::to_string(p) + " scaling at 0 (green), 1 (orange), 2 (red), and 24 (blue) grid refinements";
+    title = "";
     std::string filename = "daubechies_" + std::to_string(p) + "_scaling_convergence.svg";
 
     quicksvg::graph_fn daub(a, b, title, filename, 1024, GRAPH_WIDTH);
     daub.set_stroke_width(1);
+    daub.set_gridlines(8, 2*p-1);
 
     daub.add_fn(phi0, "green");
     auto phi1 = boost::math::daubechies_scaling<Real, p>(1);
@@ -74,6 +80,7 @@ void plot_convergence()
 
     auto phi21 = boost::math::daubechies_scaling<Real, p>(21);
     daub.add_fn(phi21);
+
     daub.write_all();
 }
 
@@ -87,11 +94,13 @@ void plot_condition_number()
     Real a = std::sqrt(std::numeric_limits<Real>::epsilon());
     Real b = phi.support().second - 1000*std::sqrt(std::numeric_limits<Real>::epsilon());
     std::string title = "log10 of condition number of function evaluation for Daubechies " + std::to_string(p) + " scaling function.";
+    title = "";
     std::string filename = "daubechies_" + std::to_string(p) + "_scaling_condition_number.svg";
 
 
     quicksvg::graph_fn daub(a, b, title, filename, 2048, GRAPH_WIDTH);
     daub.set_stroke_width(1);
+    daub.set_gridlines(8, 2*p-1);
 
     auto cond = [&phi](Real x)
     {
@@ -120,10 +129,14 @@ void do_ulp(int coarse_refinements, PhiPrecise phi_precise)
     auto phi_coarse = boost::math::daubechies_scaling<CoarseReal, p>(coarse_refinements);
 
     std::string title = std::to_string(p) + " vanishing moment ULP plot at " + std::to_string(coarse_refinements) + " refinements and " + boost::core::demangle(typeid(CoarseReal).name()) + " precision";
+    title = "";
+
     std::string filename = "daubechies_" + std::to_string(p) + "_" + boost::core::demangle(typeid(CoarseReal).name()) + "_" + std::to_string(coarse_refinements) + "_refinements.svg";
     int samples = 20000;
     int clip = 20;
-    quicksvg::ulp_plot<decltype(phi_coarse), CoarseReal, decltype(phi_precise), PreciseReal>(phi_coarse, phi_precise, CoarseReal(0), phi_coarse.support().second, title, filename, samples, GRAPH_WIDTH, clip);
+    int horizontal_lines = 8;
+    int vertical_lines = 2*p - 1;
+    quicksvg::ulp_plot<decltype(phi_coarse), CoarseReal, decltype(phi_precise), PreciseReal>(phi_coarse, phi_precise, CoarseReal(0), phi_coarse.support().second, title, filename, samples, GRAPH_WIDTH, clip, horizontal_lines, vertical_lines);
 }
 
 
@@ -189,7 +202,7 @@ int main()
     using PreciseReal = float128;
     using CoarseReal = double;
     int precise_refinements = 22;
-    constexpr const int p = 12;
+    constexpr const int p = 8;
     std::cout << "Computing precise scaling function in " << boost::core::demangle(typeid(PreciseReal).name()) << " precision.\n";
     auto phi_precise = boost::math::daubechies_scaling<PreciseReal, p>(precise_refinements);
     std::cout << "Beginning comparison with functions computed in " << boost::core::demangle(typeid(CoarseReal).name()) << " precision.\n";

From a7c5ae6d8c62c6e1c653ee1d19bde2c13b9c1e30 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Fri, 28 Feb 2020 08:18:43 -0500
Subject: [PATCH 062/104] Give option to control absolute error [CI SKIP]

---
 .../find_best_daubechies_interpolator.cpp     | 147 ++++++++----------
 .../special_functions/daubechies_scaling.hpp  |  17 +-
 2 files changed, 78 insertions(+), 86 deletions(-)

diff --git a/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp b/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
index 2cfb7f268..03d19f3ba 100644
--- a/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
+++ b/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
@@ -14,7 +14,7 @@
 #include <boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp>
 #include <boost/math/interpolators/cubic_hermite.hpp>
 #include <boost/math/interpolators/quintic_hermite.hpp>
-#include <boost/math/interpolators/cardinal_quintic_hermite.hpp>
+#include <boost/math/interpolators/quintic_hermite.hpp>
 #include <boost/math/interpolators/septic_hermite.hpp>
 #include <boost/math/interpolators/cardinal_quadratic_b_spline.hpp>
 #include <boost/math/interpolators/cardinal_cubic_b_spline.hpp>
@@ -35,99 +35,66 @@ void choose_refinement()
 {
     std::cout << "Choosing refinement for " << boost::core::demangle(typeid(Real).name()) << " precision Daubechies scaling function with " << p << " vanishing moments.\n";
     using std::abs;
-    int rmax = 21;
+    int rmax = 22;
     auto phi_dense = boost::math::detail::dyadic_grid<PreciseReal, p, 0>(rmax);
     Real dx_dense = (2*p-1)/static_cast<Real>(phi_dense.size()-1);
 
-    for (int r = 2; r <= rmax - 2; ++r)
+    for (int r = 2; r <= 12; ++r)
     {
-        auto phi_accurate = boost::math::detail::dyadic_grid<PreciseReal, p, 0>(r);
-        std::vector<Real> phi(phi_accurate.size());
-        for (size_t i = 0; i < phi_accurate.size(); ++i)
-        {
-            phi[i] = Real(phi_accurate[i]);
-        }
-        auto phi_prime_accurate = boost::math::detail::dyadic_grid<PreciseReal, p, 1>(r);
-        std::vector<Real> phi_prime(phi_accurate.size());
-        for (size_t i = 0; i < phi_prime_accurate.size(); ++i)
-        {
-            phi_prime[i] = Real(phi_prime_accurate[i]);
-        }
+        Real dx = Real(1)/ (1 << r);
+        std::cout << "\tdx = 1/" << (1/dx) << " = 1/2^" << r << " = " << dx << "\n";
+        auto phi = boost::math::daubechies_scaling<Real, p>(r);
+        Real max_flt_distance = 0;
+        Real sup  = 0;
+        Real rel_sup = 0;
+        Real worst_flt_abscissa = 0;
+        Real worst_flt_value = 0;
+        Real worst_flt_computed = 0;
 
-        Real dx = (2*p-1)/static_cast<Real>(phi.size()-1);
-        std::cout << "\tdx = 1/" << (1/dx) << " = " << dx << "\n";
+        Real worst_rel_abscissa = 0;
+        Real worst_rel_value = 0;
+        Real worst_rel_computed = 0;
 
-        if constexpr (p < 6 && p >= 3)
+        Real worst_abs_abscissa = 0;
+        Real worst_abs_computed = 0;
+        Real worst_abs_expected = 0;
+        for (size_t i = 0; i < phi_dense.size(); ++i)
         {
-            auto ch = boost::math::interpolators::cardinal_cubic_hermite(std::move(phi), std::move(phi_prime), Real(0), Real(dx));
-            Real flt_distance = 0;
-            Real sup  = 0;
-            Real worst_abscissa = 0;
-            Real worst_value = 0;
-            Real worst_computed = 0;
-            for (size_t i = 0; i < phi_dense.size(); ++i)
+            Real t = i*dx_dense;
+            Real computed = phi(t);
+            Real expected = Real(phi_dense[i]);
+            Real abs_diff = abs(computed - expected);
+            Real rel_diff = abs_diff/abs(expected);
+            Real flt_distance = abs(boost::math::float_distance(computed, expected));
+            if (flt_distance > max_flt_distance)
             {
-                Real t = i*dx_dense;
-                Real computed = ch(t);
-                Real expected = Real(phi_dense[i]);
-                if (std::abs(expected) < 100*std::numeric_limits<Real>::epsilon())
-                {
-                    continue;
-                }
-                Real diff = abs(computed - expected);
-                Real distance = abs(boost::math::float_distance(computed, expected));
-                if (distance > flt_distance)
-                {
-                    flt_distance = distance;
-                    worst_abscissa = t;
-                    worst_value = expected;
-                    worst_computed = computed;
-                }
-                if (diff > sup)
-                {
-                    sup = diff;
-                }
+                max_flt_distance = flt_distance;
+                worst_flt_abscissa = t;
+                worst_flt_value = expected;
+                worst_flt_computed = computed;
             }
-            std::cout << "\t\tFloat distance at r = " << r << " is " << flt_distance << ", sup distance = " << sup << "\n";
-            std::cout << "\t\tWorst abscissa = " << worst_abscissa << ", worst value = " << worst_value << ", computed = " << worst_computed << "\n";
-        }
-        else if constexpr (p >= 6)
-        {
-            auto phi_dbl_prime = boost::math::detail::dyadic_grid<Real, p, 2>(r);
-            auto qh = boost::math::interpolators::cardinal_quintic_hermite(std::move(phi), std::move(phi_prime), std::move(phi_dbl_prime), Real(0), dx);
-            Real flt_distance = 0;
-            Real sup  = 0;
-            Real worst_abscissa = 0;
-            Real worst_value = 0;
-            Real worst_computed = 0;
-            for (size_t i = 0; i < phi_dense.size(); ++i)
+            if (expected != 0 && rel_diff > rel_sup)
             {
-                Real t = i*dx_dense;
-                Real computed = qh(t);
-                Real expected = Real(phi_dense[i]);
-                if (std::abs(expected) < 100*std::numeric_limits<Real>::epsilon())
-                {
-                    continue;
-                }
+                rel_sup = rel_diff;
+                worst_rel_abscissa = t;
+                worst_rel_value = expected;
+                worst_rel_computed = computed;
 
-                Real diff = abs(computed - expected);
-                Real distance = abs(boost::math::float_distance(computed, expected));
-                if (distance > flt_distance)
-                {
-                    flt_distance = distance;
-                    worst_abscissa = t;
-                    worst_value = expected;
-                    worst_computed = computed;
-                }
-                if (diff > sup)
-                {
-                    sup = diff;
-                }
-                std::cout << "Float distance at r = " << r << " is " << flt_distance << ", sup distance = " << sup << "\n";
-                std::cout << "\tWorst abscissa = " << worst_abscissa << ", worst value = " << worst_value << ", computed = " << worst_computed << "\n"; 
+            }
+            if (abs_diff > sup)
+            {
+                sup = abs_diff;
+                worst_abs_abscissa = t;
+                worst_abs_computed = computed;
+                worst_abs_expected = expected;
             }
         }
+        std::cout << "\t\tFloat distance at r = " << r << " is " << max_flt_distance << ", sup distance = " << sup << ", max relative error = " << rel_sup << "\n";
+        std::cout << "\t\tWorst flt abscissa = " << worst_flt_abscissa << ", worst expected value = " << worst_flt_value << ", computed = " << worst_flt_computed << "\n";
+        std::cout << "\t\tWorst rel abscissa = " << worst_rel_abscissa << ", worst expected value = " << worst_rel_value << ", computed = " << worst_rel_computed << "\n";
+        std::cout << "\t\tWorst abs abscissa = " << worst_abs_abscissa << ", worst expected value = " << worst_abs_computed << ", worst abs value (expected) = " << worst_abs_expected << "\n";
     }
+    std::cout << "\n\n\n";
 }
 
 template<typename Real, typename PreciseReal, int p>
@@ -560,11 +527,25 @@ void find_best_interpolator()
 }
 
 int main() {
-    //choose_refinement<float, double, 5>();
+    /*choose_refinement<float, long double, 2>();
+    choose_refinement<float, long double, 3>();
+    choose_refinement<float, long double, 4>();
+    choose_refinement<float, long double, 5>();
+    choose_refinement<float, long double, 6>();
+    choose_refinement<float, long double, 7>();
+    choose_refinement<float, long double, 8>();*/
+
+    choose_refinement<float, long double, 9>();
+    choose_refinement<float, long double, 10>();
+    choose_refinement<float, long double, 11>();
+    choose_refinement<float, long double, 12>();
+    choose_refinement<float, long double, 13>();
+    choose_refinement<float, long double, 14>();
+    choose_refinement<float, long double, 15>();
     //choose_refinement<float, long double, 5>();
     //choose_refinement<double, float128, 15>();
     // Says linear interpolation is the best:
-    find_best_interpolator<float128, float128, 2>();
+    /*find_best_interpolator<float128, float128, 2>();
     // Says linear interpolation is the best:
     find_best_interpolator<float128, float128, 3>();
     // Says cubic_hermite_spline is best:
@@ -590,5 +571,5 @@ int main() {
     // Says septic_hermite_spline is best:
     find_best_interpolator<float128, float128, 14>();
     // Says septic_hermite_spline is best:
-    find_best_interpolator<float128, float128, 15>();
+    find_best_interpolator<float128, float128, 15>();*/
 }
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index d1e4092b8..657a2e0e8 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -252,9 +252,20 @@ public:
         {
             if (std::is_same_v<Real, float>)
             {
-                //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15
-                std::array<int, 16> r{-1, -1, 22, 21, 19, 17, 16, 15, 14, 13, 12, 11, 11, 11, 11, 11};
-                grid_refinements = r[p];
+                if (grid_refinements == -2)
+                {
+                    // Control absolute error:
+                    //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15
+                    std::array<int, 16> r{-1, -1, 18, 19, 16, 11,  8,  7,  7,  7,  5,  5,  4,  4,  4,  4};
+                    grid_refinements = r[p];
+                }
+                else
+                {
+                    // Control relative error:
+                    //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15
+                    std::array<int, 16> r{-1, -1, 21, 21, 21, 17, 16, 15, 14, 13, 12, 11, 11, 11, 11, 11};
+                    grid_refinements = r[p];
+                }
             }
             else if (std::is_same_v<Real, double>)
             {

From dc52a787c8eacd9d45d9d674a0d479e6f577ba1f Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Fri, 28 Feb 2020 17:24:38 +0000
Subject: [PATCH 063/104] daubechies.hpp: simplify header and reduce
 dependencies.

---
 .../daubechies_coefficients.cpp               |  61 +--
 include/boost/math/filters/daubechies.hpp     | 355 ++----------------
 test/Jamfile.v2                               |   1 +
 test/compile_test/daubechies_incl_test.cpp    |  33 ++
 4 files changed, 69 insertions(+), 381 deletions(-)
 create mode 100644 test/compile_test/daubechies_incl_test.cpp

diff --git a/example/daubechies_wavelets/daubechies_coefficients.cpp b/example/daubechies_wavelets/daubechies_coefficients.cpp
index 23349defa..1366e921c 100644
--- a/example/daubechies_wavelets/daubechies_coefficients.cpp
+++ b/example/daubechies_wavelets/daubechies_coefficients.cpp
@@ -17,8 +17,14 @@
 #include <boost/math/tools/roots.hpp>
 #include <boost/math/special_functions/binomial.hpp>
 #include <boost/multiprecision/cpp_complex.hpp>
+#ifdef BOOST_HAS_FLOAT128
 #include <boost/multiprecision/float128.hpp>
-#include <boost/multiprecision/complex128.hpp>
+
+typedef boost::multiprecision::float128 float128_t;
+#else
+typedef boost::multiprecision::cpp_bin_float_quad float128_t;
+#endif
+//#include <boost/multiprecision/complex128.hpp>
 #include <boost/math/quadrature/gauss_kronrod.hpp>
 
 using std::string;
@@ -220,10 +226,8 @@ int main()
        << "#ifndef BOOST_MATH_FILTERS_DAUBECHIES_HPP\n"
        << "#define BOOST_MATH_FILTERS_DAUBECHIES_HPP\n"
        << "#include <array>\n"
-       << "#ifdef BOOST_HAS_FLOAT128\n"
-       << "#include <boost/multiprecision/float128.hpp>\n"
-       << "#endif\n"
-       << "#include <boost/multiprecision/cpp_bin_float.hpp>\n"
+       << "#include <limits>\n"
+       << "#include <boost/math/tools/big_constant.hpp>\n\n"
        << "namespace boost::math::filters {\n\n"
        << "template <typename Real, unsigned p>\n"
        << "constexpr std::array<Real, 2*p> daubechies_scaling_filter()\n"
@@ -232,54 +236,15 @@ int main()
 
     for(size_t p = 1; p < p_max; ++p)
     {
-        fs << std::hexfloat;
+        fs << std::setprecision(std::numeric_limits<boost::multiprecision::cpp_bin_float_oct>::max_digits10);
         auto roots = find_roots<Complex>(p);
         auto h = daubechies_coefficients(roots);
         fs << "    if constexpr (p == " << p << ") {\n";
-        fs << "        if constexpr (std::is_same_v<Real, float>) {\n";
-        fs << "            return {";
+        fs << "       return {";
         for (size_t i = 0; i < h.size() - 1; ++i) {
-            fs << static_cast<float>(h[i]) << "f, ";
+            fs << "BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, " << h[i] << "), ";
         }
-        fs << static_cast<float>(h[h.size()-1]) << "f};\n";
-        fs << "        }\n";
-
-        fs << "        if constexpr (std::is_same_v<Real, double>) {\n";
-        fs << "            return {";
-        for (size_t i = 0; i < h.size() - 1; ++i) {
-            fs << static_cast<double>(h[i]) << ", ";
-        }
-        fs << static_cast<double>(h[h.size()-1]) << "};\n";
-        fs << "        }\n";
-
-        fs << "        if constexpr (std::is_same_v<Real, long double>) {\n";
-        fs << "            return {";
-        for (size_t i = 0; i < h.size() - 1; ++i) {
-            fs << static_cast<long double>(h[i]) << "L, ";
-        }
-        fs << static_cast<long double>(h[h.size()-1]) << "L};\n";
-        fs << "        }\n";
-
-        fs << "        #ifdef BOOST_HAS_FLOAT128\n";
-        fs << "        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {\n";
-        fs << "            return {";
-        for (size_t i = 0; i < h.size() - 1; ++i) {
-            fs << static_cast<boost::multiprecision::float128>(h[i]) << "Q, ";
-        }
-        fs << static_cast<boost::multiprecision::float128>(h[h.size()-1]) << "Q};\n";
-        fs << "        }\n";
-        fs << "        #endif\n";
-
-        fs << "        if constexpr (std::is_same_v<Real, boost::multiprecision::cpp_bin_float_oct>) {\n";
-        fs << "            return {";
-        fs <<std::setprecision(std::numeric_limits<boost::multiprecision::cpp_bin_float_oct>::digits10 + 3);
-        for (size_t i = 0; i < h.size() - 1; ++i) {
-            fs <<  "boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>(\"" <<  static_cast<boost::multiprecision::cpp_bin_float_oct>(h[i]) << "\"), ";
-        }
-        fs <<  "boost::lexical_cast<boost::multiprecision::cpp_bin_float_oct>(\"" << static_cast<boost::multiprecision::cpp_bin_float_oct>(h[h.size()-1]) << "\")};\n";
-        fs << "        }\n";
-
-
+        fs << "BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, " << h[h.size()-1] << ") };\n";
         fs << "    }\n";
     }
 
diff --git a/include/boost/math/filters/daubechies.hpp b/include/boost/math/filters/daubechies.hpp
index 9682b54d1..c60ce27f8 100644
--- a/include/boost/math/filters/daubechies.hpp
+++ b/include/boost/math/filters/daubechies.hpp
@@ -7,382 +7,71 @@
 #ifndef BOOST_MATH_FILTERS_DAUBECHIES_HPP
 #define BOOST_MATH_FILTERS_DAUBECHIES_HPP
 #include <array>
-#ifdef BOOST_HAS_FLOAT128
-#include <boost/multiprecision/float128.hpp>
-#endif
-#include <boost/multiprecision/cpp_bin_float.hpp>
+#include <limits>
+#include <boost/math/tools/big_constant.hpp>
+
 namespace boost::math::filters {
 
-#ifdef BOOST_MATH_GENERATE_DAUBECHIES_GRID
-typedef boost::multiprecision::number<boost::multiprecision::cpp_bin_float<237, boost::multiprecision::backends::digit_base_2, std::allocator<char>, boost::int32_t, -262142, 262143>, boost::multiprecision::et_off> octuple_type;
-#else
-typedef boost::multiprecision::cpp_bin_float_oct octuple_type;
-#endif
-   
 template <typename Real, unsigned p>
 constexpr std::array<Real, 2*p> daubechies_scaling_filter()
 {
     static_assert(p < 20, "Filter coefficients only implemented up to 19.");
     if constexpr (p == 1) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.6a09e6p-1f, 0x1.6a09e6p-1f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.6a09e667f3bcdp-1, 0x1.6a09e667f3bcdp-1};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0xb.504f333f9de6484p-4L, 0xb.504f333f9de6484p-4L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.6a09e667f3bcc908b2fb1366ea95p-1Q, 0x1.6a09e667f3bcc908b2fb1366ea95p-1Q};
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, octuple_type>) {
-            return {boost::lexical_cast<octuple_type>("0.707106781186547524400844362104849039284835937688474036588339868995366237195"), boost::lexical_cast<octuple_type>("0.707106781186547524400844362104849039284835937688474036588339868995366237195")};
-        }
+       return {BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.70710678118654752440084436210484903928483593768847403658833986899536623923), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.70710678118654752440084436210484903928483593768847403658833986899536623923) };
     }
     if constexpr (p == 2) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.ee8dd4p-2f, 0x1.ac4bdep-1f, 0x1.cb0bfp-3f, -0x1.0907dcp-3f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.ee8dd4748bf15p-2, 0x1.ac4bdd6e3fd71p-1, 0x1.cb0bf0b6b7109p-3, -0x1.0907dc193069p-3};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0xf.746ea3a45f8a62ap-5L, 0xd.625eeb71feb8557p-4L, 0xe.585f85b5b8845bdp-6L, -0x8.483ee0c9834834cp-6L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.ee8dd4748bf14c548b969de58fap-2Q, 0x1.ac4bdd6e3fd70aae9f48d8a63d1bp-1Q, 0x1.cb0bf0b6b7108b79b4bf11d08b16p-3Q, -0x1.0907dc1930690697b13714fd4a15p-3Q};
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, octuple_type>) {
-            return {boost::lexical_cast<octuple_type>("0.482962913144534143374871599864448683816952419504202275201171538155211606550"), boost::lexical_cast<octuple_type>("0.836516303737807905575293780916873203459370388348439293495341472652894725147"), boost::lexical_cast<octuple_type>("0.224143868042013381025972762240400355467883518184271761387168330840154631777"), boost::lexical_cast<octuple_type>("-0.129409522551260381174449418812024164174534450659965256907001603657528486820")};
-        }
+       return {BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.48296291314453414337487159986444868381695241950420227520117153815521160699), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.83651630373780790557529378091687320345937038834843929349534147265289472661), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.22414386804201338102597276224040035546788351818427176138716833084015463224), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.12940952255126038117444941881202416417453445065996525690700160365752848737) };
     }
     if constexpr (p == 3) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.54a796p-2f, 0x1.9d20e2p-1f, 0x1.d6ea2p-2f, -0x1.1480a8p-3f, -0x1.5df7acp-4f, 0x1.2092e4p-5f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.54a796e50d264p-2, 0x1.9d20e247d28bbp-1, 0x1.d6ea20bf0f744p-2, -0x1.1480a85c59629p-3, -0x1.5df7ab50d483cp-4, 0x1.2092e373789b9p-5};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0xa.a53cb7286931db4p-5L, 0xc.e907123e945da19p-4L, 0xe.b75105f87ba23d6p-5L, -0x8.a40542e2cb14943p-6L, -0xa.efbd5a86a41e206p-7L, 0x9.04971b9bc4dcbc1p-8L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.54a796e50d263b67e38e82a5584cp-2Q, 0x1.9d20e247d28bb431f1e6c634b34ep-1Q, 0x1.d6ea20bf0f7447ac92de97f0e152p-2Q, -0x1.1480a85c596292857548d060a171p-3Q, -0x1.5df7ab50d483c40c41dbcf2191cfp-4Q, 0x1.2092e373789b9781e66814a5fa37p-5Q};
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, octuple_type>) {
-            return {boost::lexical_cast<octuple_type>("0.332670552950082615998511589139005630012923399245068359708470578551793724009"), boost::lexical_cast<octuple_type>("0.806891509311092576494493604088713490519297394994823618165092063603486835060"), boost::lexical_cast<octuple_type>("0.459877502118491570095151942147616720808110177431492306643386780248640335647"), boost::lexical_cast<octuple_type>("-0.135011020010254588696389906699374480562219845223781191975686255357062767858"), boost::lexical_cast<octuple_type>("-0.0854412738820266616928191691817733115361976389880866297635174898050678201973"), boost::lexical_cast<octuple_type>("0.0352262918857095366027406647155100293277583879174316103989340607489421719736")};
-        }
+       return {BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.33267055295008261599851158913900563001292339924506835970847057855179372371), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.80689150931109257649449360408871349051929739499482361816509206360348683533), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.45987750211849157009515194214761672080811017743149230664338678024864033563), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.135011020010254588696389906699374480562219845223781191975686255357062768), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.085441273882026661692819169181773311536197638988086629763517489805067820106), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.035226291885709536602740664715510029327758387917431610398934060748942171898) };
     }
     if constexpr (p == 4) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.d7d052p-3f, 0x1.6e005ep-1f, 0x1.4302cep-1f, -0x1.ca7c7p-6f, -0x1.7f0c1cp-3f, 0x1.f94e22p-6f, 0x1.0d60acp-5f, -0x1.5b4174p-7f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.d7d052af15ecp-3, 0x1.6e005ea45d748p-1, 0x1.4302cdd3de43ap-1, -0x1.ca7c6f9db5bfbp-6, -0x1.7f0c1b7c604d4p-3, 0x1.f94e2196383a9p-6, 0x1.0d60ac768117bp-5, -0x1.5b41730b72e29p-7};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0xe.be829578af5fe6dp-6L, 0xb.7002f522eba3e31p-4L, 0xa.18166e9ef21cf0dp-4L, -0xe.53e37cedadfd7d8p-9L, -0xb.f860dbe30269f7ap-6L, 0xf.ca710cb1c1d472dp-9L, 0x8.6b0563b408bdbabp-8L, -0xa.da0b985b97149dcp-10L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.d7d052af15ebfcd98dc85ef4cc01p-3Q, 0x1.6e005ea45d747c624e43405b1919p-1Q, 0x1.4302cdd3de439e1a299a6a04b89fp-1Q, -0x1.ca7c6f9db5bfafb07b9dace22f7p-6Q, -0x1.7f0c1b7c604d3ef4ab50462dfcedp-3Q, 0x1.f94e2196383a8e592495a4baff62p-6Q, 0x1.0d60ac768117b7550c2a3307e30fp-5Q, -0x1.5b41730b72e293b823fb2cbd40c6p-7Q};
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, octuple_type>) {
-            return {boost::lexical_cast<octuple_type>("0.230377813308896500863291183044070850001615248248309297791096844028271643620"), boost::lexical_cast<octuple_type>("0.714846570552915647089921955273992603707608401099308175845011003442625044997"), boost::lexical_cast<octuple_type>("0.630880767929858907881716338300615220203222922677195117405747328484353359854"), boost::lexical_cast<octuple_type>("-0.0279837694168598542114137471800753854119873202244917528400335826533630929593"), boost::lexical_cast<octuple_type>("-0.187034811719093084079570672789081419584544174374580091205777087593992585799"), boost::lexical_cast<octuple_type>("0.0308413818355607636272193625349590501703148217200340334182121909360632337258"), boost::lexical_cast<octuple_type>("0.0328830116668851997354075135492443886645419411375497125972727840767338203692"), boost::lexical_cast<octuple_type>("-0.0105974017850690321048832085240272291810999649063764198348497427299589480739")};
-        }
+       return {BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.23037781330889650086329118304407085000161524824830929779109684402827164374), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.71484657055291564708992195527399260370760840109930817584501100344262504653), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.63088076792985890788171633830061522020322292267719511740574732848435336141), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.027983769416859854211413747180075385411987320224491752840033582653363093001), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.18703481171909308407957067278908141958454417437458009120577708759399258629), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.030841381835560763627219362534959050170314821720034033418212190936063233775), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.032883011666885199735407513549244388664541941137549712597272784076733820371), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.01059740178506903210488320852402722918109996490637641983484974272995894807) };
     }
     if constexpr (p == 5) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.47e3c4p-3f, 0x1.35291cp-1f, 0x1.72d892p-1f, 0x1.1b8038p-3f, -0x1.f0384ep-3f, -0x1.082664p-5f, 0x1.3dbb9cp-4f, -0x1.990ad4p-8f, -0x1.9c3fp-7f, 0x1.b5385ep-9f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.47e3c41a7b911p-3, 0x1.35291c2c4b00cp-1, 0x1.72d89143b54f5p-1, 0x1.1b80373befcc6p-3, -0x1.f0384d3f81474p-3, -0x1.0826648a8dc74p-5, 0x1.3dbb9b52515aap-4, -0x1.990ad4579f2e8p-8, -0x1.9c3eff3294128p-7, 0x1.b5385e04e3c09p-9};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0xa.3f1e20d3dc8840dp-6L, 0x9.a948e1625806185p-4L, 0xb.96c48a1daa7a767p-4L, 0x8.dc01b9df7e62cc6p-6L, -0xf.81c269fc0a3a1e2p-6L, -0x8.413324546e39fcbp-8L, 0x9.eddcda928ad4cf6p-7L, -0xc.c856a2bcf973f17p-11L, -0xc.e1f7f994a094303p-10L, 0xd.a9c2f0271e04896p-12L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.47e3c41a7b91081ae95ed12670b7p-3Q, 0x1.35291c2c4b00c30a87eaf4d05e71p-1Q, 0x1.72d89143b54f4ecd724f0b79d111p-1Q, 0x1.1b80373befcc598b25a1d5436079p-3Q, -0x1.f0384d3f814743c3d93da5cd8909p-3Q, -0x1.0826648a8dc73f96ef19214f403ep-5Q, 0x1.3dbb9b52515a99ecaa66a225e968p-4Q, -0x1.990ad4579f2e7e2dc54832641bd8p-8Q, -0x1.9c3eff32941286062a45cb776526p-7Q, 0x1.b5385e04e3c0912c23cbbf7041e8p-9Q};
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, octuple_type>) {
-            return {boost::lexical_cast<octuple_type>("0.160102397974192914480723748020420733650544124625057832772569920207547214207"), boost::lexical_cast<octuple_type>("0.603829269797189670540119306525062107507422163101698698796928336036862837113"), boost::lexical_cast<octuple_type>("0.724308528437772927728071244102218640768756218232007372576733504804092797357"), boost::lexical_cast<octuple_type>("0.138428145901320731505397146339024697314105791173956102269465221088552175948"), boost::lexical_cast<octuple_type>("-0.242294887066382031862571379474616361991490808062618598391372691341065474637"), boost::lexical_cast<octuple_type>("-0.0322448695846383746484797550621349283135649841637984722543426813198116091835"), boost::lexical_cast<octuple_type>("0.0775714938400457135231304893886018198062309945201252798321014623895567160574"), boost::lexical_cast<octuple_type>("-0.00624149021279827427419051911292019297076355716568760732341743532590851604324"), boost::lexical_cast<octuple_type>("-0.0125807519990819994685097399317757929492045916260978502016923270647650161437"), boost::lexical_cast<octuple_type>("0.00333572528547377127799818341581735574763652474230531509970642851567135111157")};
-        }
+       return {BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.16010239797419291448072374802042073365054412462505783277256992020754721449), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.60382926979718967054011930652506210750742216310169869879692833603686283702), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.72430852843777292772807124410221864076875621823200737257673350480409279922), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.13842814590132073150539714633902469731410579117395610226946522108855217638), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.24229488706638203186257137947461636199149080806261859839137269134106547424), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.032244869584638374648479755062134928313564984163798472254342681319811609232), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.077571493840045713523130489388601819806230994520125279832101462389556715934), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0062414902127982742741905191129201929707635571656876073234174353259085160535), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.012580751999081999468509739931775792949204591626097850201692327064765016178), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0033357252854737712779981834158173557476365247423053150997064285156713511141) };
     }
     if constexpr (p == 6) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.c8def2p-4f, 0x1.fa7ebp-2f, 0x1.8094ap-1f, 0x1.42d0fcp-2f, -0x1.cf63dep-3f, -0x1.09c336p-3f, 0x1.8f5dd8p-4f, 0x1.c2ef44p-6f, -0x1.02b856p-5f, 0x1.225f72p-11f, 0x1.391514p-8f, -0x1.1a6874p-10f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.c8def24dc3952p-4, 0x1.fa7eaf64539a9p-2, 0x1.80949fa3bc0bbp-1, 0x1.42d0fcfa92f21p-2, -0x1.cf63dd26916f1p-3, -0x1.09c33622722ebp-3, 0x1.8f5dd7f4e1752p-4, 0x1.c2ef43d612549p-6, -0x1.02b856404e8cep-5, 0x1.225f71210a7c1p-11, 0x1.391514c62a31bp-8, -0x1.1a6873b7a6466p-10};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0xe.46f7926e1ca8e15p-7L, 0xf.d3f57b229cd4bdfp-5L, 0xc.04a4fd1de05d701p-4L, 0xa.1687e7d497907f9p-5L, -0xe.7b1ee9348b785acp-6L, -0x8.4e19b11391756c5p-6L, 0xc.7aeebfa70ba93cep-7L, 0xe.177a1eb092a4be4p-9L, -0x8.15c2b2027466fc3p-8L, 0x9.12fb890853e0901p-14L, 0x9.c8a8a631518d6e7p-11L, -0x8.d3439dbd3232f08p-13L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.c8def24dc3951c2a6dae413b8ddbp-4Q, 0x1.fa7eaf64539a97bd50da008738e1p-2Q, 0x1.80949fa3bc0bae02bf1b494d3af8p-1Q, 0x1.42d0fcfa92f20ff1b5b87f2f698cp-2Q, -0x1.cf63dd26916f0b589f7743608e82p-3Q, -0x1.09c33622722ead8a0ff038a97bp-3Q, 0x1.8f5dd7f4e175279c5a356a3fbcc9p-4Q, 0x1.c2ef43d6125497c75e24a80c6bfap-6Q, -0x1.02b856404e8cdf85933c3736d91cp-5Q, 0x1.225f71210a7c1202de723c931ed6p-11Q, 0x1.391514c62a31adcdfa747aebbdeep-8Q, -0x1.1a6873b7a6465e0ff5c033201061p-10Q};
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, octuple_type>) {
-            return {boost::lexical_cast<octuple_type>("0.111540743350109463621323917240923439042539591984421675908236045797651596176"), boost::lexical_cast<octuple_type>("0.494623890398453085677204176877855588637786382896274362353183452618869845497"), boost::lexical_cast<octuple_type>("0.751133908021095350678934498439731685580254783338261200973042065947992668343"), boost::lexical_cast<octuple_type>("0.315250351709197629085989654810926396649519923517294524440416381606252448494"), boost::lexical_cast<octuple_type>("-0.226264693965439820076314500660903465670540153972896994014348779178970276888"), boost::lexical_cast<octuple_type>("-0.129766867567261935562289605876585460845233749223581470159931065581720412930"), boost::lexical_cast<octuple_type>("0.0975016055873230491023435525381253423398307474952551427989319312112779815986"), boost::lexical_cast<octuple_type>("0.0275228655303057286255408395041932136573875878304345432149420287900002992420"), boost::lexical_cast<octuple_type>("-0.0315820393174860295650790806998486690574795323731484233751146493526060457826"), boost::lexical_cast<octuple_type>("0.000553842201161496139251918398046501220611026277386496429547652456752475273329"), boost::lexical_cast<octuple_type>("0.00477725751094551063963597524682070705023050121658143429759325457002031530381"), boost::lexical_cast<octuple_type>("-0.00107730108530847956485262160958720003523523360933441968981858089478841770562")};
-        }
+       return {BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.11154074335010946362132391724092343904253959198442167590823604579765159644), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.4946238903984530856772041768778555886377863828962743623531834526188698465), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.75113390802109535067893449843973168558025478333826120097304206594799266889), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.31525035170919762908598965481092639664951992351729452444041638160625244927), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.22626469396543982007631450066090346567054015397289699401434877917897027718), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.12976686756726193556228960587658546084523374922358147015993106558172041337), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.097501605587323049102343552538125342339830747495255142798931931211277981638), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.027522865530305728625540839504193213657387587830434543214942028790000299266), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.031582039317486029565079080699848669057479532373148423375114649352606045848), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.00055384220116149613925191839804650122061102627738649642954765245675247527348), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0047772575109455106396359752468207070502305012165814342975932545700203152873), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0010773010853084795648526216095872000352352336093344196898185808947884177076) };
     }
     if constexpr (p == 7) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.3ee1ccp-4f, 0x1.960e68p-2f, 0x1.7550cep-1f, 0x1.e10e9cp-2f, -0x1.26b83p-3f, -0x1.cad37cp-3f, 0x1.241522p-4f, 0x1.4a3072p-4f, -0x1.378a8ep-5f, -0x1.0f8eaap-6f, 0x1.9b4568p-7f, 0x1.c271f6p-12f, -0x1.d84a1p-10f, 0x1.72e554p-12f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.3ee1cba38b6b1p-4, 0x1.960e674303003p-2, 0x1.7550cd294c1fep-1, 0x1.e10e9ba294ddcp-2, -0x1.26b830e491e33p-3, -0x1.cad37bbd5ab97p-3, 0x1.241522ca7821cp-4, 0x1.4a30727f2fa53p-4, -0x1.378a8eecf45ccp-5, -0x1.0f8eaa8ffe709p-6, 0x1.9b45682a50d7p-7, 0x1.c271f584373d4p-12, -0x1.d84a0f9cb2f31p-10, 0x1.72e5533fa10d3p-12};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0x9.f70e5d1c5b5851p-7L, 0xc.b0733a181801b18p-5L, 0xb.aa86694a60ff1fap-4L, 0xf.0874dd14a6ee015p-5L, -0x9.35c187248f196d4p-6L, -0xe.569bddead5cb84ap-6L, 0x9.20a91653c10e31cp-7L, 0xa.518393f97d2944bp-7L, -0x9.bc547767a2e6031p-8L, -0x8.7c75547ff384611p-9L, 0xc.da2b415286b8088p-10L, 0xe.138fac21b9ea0e9p-15L, -0xe.c2507ce59798a73p-13L, 0xb.972a99fd0869924p-15L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.3ee1cba38b6b0a205a4c9aac651fp-4Q, 0x1.960e67430300363014da61e0a27dp-2Q, 0x1.7550cd294c1fe3f40f374c82e23dp-1Q, 0x1.e10e9ba294ddc02a47644f227fffp-2Q, -0x1.26b830e491e32da8b525e8ab6aa1p-3Q, -0x1.cad37bbd5ab970931a91ed1dfe9cp-3Q, 0x1.241522ca7821c638e85eb5e52839p-4Q, 0x1.4a30727f2fa52896ef76d0300cfp-4Q, -0x1.378a8eecf45cc0627b1c4b5cace1p-5Q, -0x1.0f8eaa8ffe708c22b1145a6b8cc8p-6Q, 0x1.9b45682a50d70110df27e4af9e36p-7Q, 0x1.c271f584373d41d177397b25f7ebp-12Q, -0x1.d84a0f9cb2f314e62607c084aab4p-10Q, 0x1.72e5533fa10d324758be56783dp-12Q};
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, octuple_type>) {
-            return {boost::lexical_cast<octuple_type>("0.0778520540850091790199635219578937483791830529279556843870293717996297655927"), boost::lexical_cast<octuple_type>("0.396539319481917306539000390936842856358715114933328740111049962075487815071"), boost::lexical_cast<octuple_type>("0.729132090846235119916943070339282051717966061190136378269771574955357027757"), boost::lexical_cast<octuple_type>("0.469782287405193122471591160974451738681791305678735953239252914100836922120"), boost::lexical_cast<octuple_type>("-0.143906003928564975405068362213046001795273570549908483440175301422991840895"), boost::lexical_cast<octuple_type>("-0.224036184993874982638140420233250964475783089677324655266509530724151657744"), boost::lexical_cast<octuple_type>("0.0713092192668302647508765705011290482271132745141231465957511322020290613667"), boost::lexical_cast<octuple_type>("0.0806126091510830719129224803593819058582382096562948905813921847722652754485"), boost::lexical_cast<octuple_type>("-0.0380299369350144135795920616018580358544619693846786989828312271657410616427"), boost::lexical_cast<octuple_type>("-0.0165745416306668806541076748917026547920450439482071370523927254871434907950"), boost::lexical_cast<octuple_type>("0.0125509985560998406129898860341877795728947404604871003841181834416741023260"), boost::lexical_cast<octuple_type>("0.000429577972921366521132129122819732222823535039694240974294636693544941849482"), boost::lexical_cast<octuple_type>("-0.00180164070404749091526826291273955096258565146964109062532386481459081601883"), boost::lexical_cast<octuple_type>("0.000353713799974520248446295836306425431095906005952004001252427564526433555672")};
-        }
+       return {BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.077852054085009179019963521957893748379183052927955684387029371799629765558), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.3965393194819173065390003909368428563587151149333287401110499620754878153), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.72913209084623511991694307033928205171796606119013637826977157495535702874), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.4697822874051931224715911609744517386817913056787359532392529141008369217), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.14390600392856497540506836221304600179527357054990848344017530142299184121), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.22403618499387498263814042023325096447578308967732465526650953072415165804), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.071309219266830264750876570501129048227113274514123146595751132202029061555), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.080612609151083071912922480359381905858238209656294890581392184772265275649), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.038029936935014413579592061601858035854461969384678698982831227165741061737), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.016574541630666880654107674891702654792045043948207137052392725487143490786), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.012550998556099840612989886034187779572894740460487100384118183441674102341), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.00042957797292136652113212912281973222282353503969424097429463669354494184942), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0018016407040474909152682629127395509625856514696410906253238648145908160214), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.00035371379997452024844629583630642543109590600595200400125242756452643355644) };
     }
     if constexpr (p == 8) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.bdc64ap-5f, 0x1.40616ap-2f, 0x1.59ec46p-1f, 0x1.2bb39cp-1f, -0x1.035814p-6f, -0x1.22d4f8p-2f, 0x1.ef6f9cp-12f, 0x1.07acbcp-3f, -0x1.1c942p-6f, -0x1.692bc6p-5f, 0x1.ca215cp-7f, 0x1.1e978ep-7f, -0x1.3f2ef6p-8f, -0x1.9ac502p-12f, 0x1.622148p-11f, -0x1.ecbbbcp-14f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.bdc64ada308ddp-5, 0x1.4061690b4c31ep-2, 0x1.59ec45992376p-1, 0x1.2bb39bedb5e28p-1, -0x1.03581459a95c6p-6, -0x1.22d4f8724d56fp-2, 0x1.ef6f9caf662bp-12, 0x1.07acbb163ba09p-3, -0x1.1c9420f07509dp-6, -0x1.692bc518a7fe2p-5, 0x1.ca215cd5b85b4p-7, 0x1.1e978df35f5fcp-7, -0x1.3f2ef6d3ac74ap-8, -0x1.9ac501798e65dp-12, 0x1.622148e2ef341p-11, -0x1.ecbbbc88e3fc3p-14};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0xd.ee3256d1846ea19p-8L, 0xa.030b485a618f383p-5L, 0xa.cf622cc91bb0386p-4L, 0x9.5d9cdf6daf13eaep-4L, -0x8.1ac0a2cd4ae2f65p-9L, -0x9.16a7c3926ab7ac2p-5L, 0xf.7b7ce57b3157c6dp-15L, 0x8.3d65d8b1dd0442p-6L, -0x8.e4a10783a84e546p-9L, -0xb.495e28c53ff0c66p-8L, 0xe.510ae6adc2d9ca2p-10L, 0x8.f4bc6f9afafe075p-10L, -0x9.f977b69d63a5188p-11L, -0xc.d6280bcc732e77dp-15L, 0xb.110a471779a0a94p-14L, -0xf.65dde4471fe1763p-17L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.bdc64ada308dd431e90c51caaddfp-5Q, 0x1.4061690b4c31e70689f16560d4fdp-2Q, 0x1.59ec45992376070ce88329890c41p-1Q, 0x1.2bb39bedb5e27d5c19af764e6b08p-1Q, -0x1.03581459a95c5ec9b8a25898e79fp-6Q, -0x1.22d4f8724d56f584680effd871d8p-2Q, 0x1.ef6f9caf662af8d967c439494864p-12Q, 0x1.07acbb163ba0883fad048482f33cp-3Q, -0x1.1c9420f07509ca8be1e93402904ap-6Q, -0x1.692bc518a7fe18cb861085169737p-5Q, 0x1.ca215cd5b85b39449ec69ab26159p-7Q, 0x1.1e978df35f5fc0eabddff5ee9da6p-7Q, -0x1.3f2ef6d3ac74a30f6f64186b6be2p-8Q, -0x1.9ac501798e65cefa54cc7686cbfep-12Q, 0x1.622148e2ef341527c8d993cd7e86p-11Q, -0x1.ecbbbc88e3fc2ec652987ddfb595p-14Q};
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, octuple_type>) {
-            return {boost::lexical_cast<octuple_type>("0.0544158422431040099550094052029993550359955429473305039772928086771936225734"), boost::lexical_cast<octuple_type>("0.312871590914299970659162375505717721949731974037022918569871242115311497533"), boost::lexical_cast<octuple_type>("0.675630736297289806807800767047183149986911590633636422776675983811728748708"), boost::lexical_cast<octuple_type>("0.585354683654206712771265520045098194430326667805336905570717534889570522452"), boost::lexical_cast<octuple_type>("-0.0158291052563493056673805478764663041577447115450282655973533595603126615697"), boost::lexical_cast<octuple_type>("-0.284015542961546926516203132374164732468435012487145179359920480909375859275"), boost::lexical_cast<octuple_type>("0.000472484573913282770360590009825894986194801128877007464408409602299544658383"), boost::lexical_cast<octuple_type>("0.128747426620478458857029287509708384302260157555648879557700016549770662789"), boost::lexical_cast<octuple_type>("-0.0173693010018075461696161488680959831141308652948839431697731538851197479461"), boost::lexical_cast<octuple_type>("-0.0440882539307947515067637232389635018975183919011099647275039198547543351349"), boost::lexical_cast<octuple_type>("0.0139810279173982816487229305726334514423955953293434716914636811442629383260"), boost::lexical_cast<octuple_type>("0.00874609404740577671638274324647564018040214708114067674268674702611775846381"), boost::lexical_cast<octuple_type>("-0.00487035299345157431042218155710982401663497851215700376473620853219217075614"), boost::lexical_cast<octuple_type>("-0.000391740373376947046298080357323776267522935007389049372449269467759195224284"), boost::lexical_cast<octuple_type>("0.000675449406450569366369547573879299121848963001355843210361707737505966890496"), boost::lexical_cast<octuple_type>("-0.000117476784124769533730628231698890944408669395031150392762001353514813073214")};
-        }
+       return {BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.054415842243104009955009405202999355035995542947330503977292808677193622648), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.31287159091429997065916237550571772194973197403702291856987124211531149794), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.67563073629728980680780076704718314998691159063363642277667598381172874696), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.58535468365420671277126552004509819443032666780533690557071753488957052267), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.015829105256349305667380547876466304157744711545028265597353359560312661545), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.28401554296154692651620313237416473246843501248714517935992048090937585953), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.00047248457391328277036059000982589498619480112887700746440840960229954465856), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.12874742662047845885702928750970838430226015755564887955770001654977066319), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.017369301001807546169616148868095983114130865294883943169773153885119747929), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.044088253930794751506763723238963501897518391901109964727503919854754335188), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.013981027917398281648722930572633451442395595329343471691463681144262938301), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0087460940474057767163827432464756401804021470811406767426867470261177584378), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0048703529934515743104221815571098240166349785121570037647362085321921707468), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.00039174037337694704629808035732377626752293500738904937244926946775919522535), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.00067544940645056936636954757387929912184896300135584321036170773750596688963), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.00011747678412476953373062823169889094440866939503115039276200135351481307347) };
     }
     if constexpr (p == 9) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.37ef3ep-5f, 0x1.f35f98p-3f, 0x1.35ab6p-1f, 0x1.50881p-1f, 0x1.10c9cap-3f, -0x1.2c4ff6p-2f, -0x1.8ca8ecp-4f, 0x1.303622p-3f, 0x1.f768dap-6f, -0x1.15062ap-4f, 0x1.07231ap-12f, 0x1.6e5f9cp-6f, -0x1.358a3ap-8f, -0x1.1897b6p-8f, 0x1.e4597cp-10f, 0x1.e3276ap-13f, -0x1.0833dap-12f, 0x1.4a11bap-15f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.37ef3e540da7cp-5, 0x1.f35f9808bc2ap-3, 0x1.35ab60603a288p-1, 0x1.5088101e8fe35p-1, 0x1.10c9ca803fb22p-3, -0x1.2c4ff66fd53efp-2, -0x1.8ca8ebcdc98fcp-4, 0x1.303621e43e771p-3, 0x1.f768d94677997p-6, -0x1.1506294f451a2p-4, 0x1.07231a6b6ca0dp-12, 0x1.6e5f9be058887p-6, -0x1.358a39f783bbfp-8, -0x1.1897b64b3bfb6p-8, 0x1.e4597bbfc711fp-10, 0x1.e3276a3bc510bp-13, -0x1.0833da803978ap-12, 0x1.4a11ba1ad31b5p-15};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0x9.bf79f2a06d3e1d5p-8L, 0xf.9afcc045e1503b9p-6L, 0x9.ad5b0301d143d0bp-4L, 0xa.844080f47f1a981p-4L, 0x8.864e5401fd91397p-6L, -0x9.627fb37ea9f7708p-5L, -0xc.65475e6e4c7e255p-7L, 0x9.81b10f21f3b8936p-6L, 0xf.bb46ca33bccb6bep-9L, -0x8.a8314a7a28d0fa4p-7L, 0x8.3918d35b65065cap-15L, 0xb.72fcdf02c443b9ap-9L, -0x9.ac51cfbc1ddf90ep-11L, -0x8.c4bdb259dfdac19p-11L, 0xf.22cbddfe388f56ep-13L, 0xf.193b51de288565ap-16L, -0x8.419ed401cbc51f3p-15L, 0xa.508dd0d698da458p-18L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.37ef3e540da7c3aa0d1dcf5bb03fp-5Q, 0x1.f35f9808bc2a0772556b997598d3p-3Q, 0x1.35ab60603a287a1609387fb893b8p-1Q, 0x1.5088101e8fe3530163beb11528dcp-1Q, 0x1.10c9ca803fb2272d1e1cf6fa2d0cp-3Q, -0x1.2c4ff66fd53eee10d811f3bf5459p-2Q, -0x1.8ca8ebcdc98fc4aa06bb294a039cp-4Q, 0x1.303621e43e77126c475b311fee41p-3Q, 0x1.f768d94677996d7b05f99f12d599p-6Q, -0x1.1506294f451a1f48db3652c40168p-4Q, 0x1.07231a6b6ca0cb934ff78371a261p-12Q, 0x1.6e5f9be058887734b49665246c12p-6Q, -0x1.358a39f783bbf21cd3bb737b9bf7p-8Q, -0x1.1897b64b3bfb583210060e933d6p-8Q, 0x1.e4597bbfc711eadc2635b08cc11dp-10Q, 0x1.e3276a3bc510acb32c14bfd1c3d9p-13Q, -0x1.0833da803978a3e6248db817fff9p-12Q, 0x1.4a11ba1ad31b48b0c2e32412ef31p-15Q};
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, octuple_type>) {
-            return {boost::lexical_cast<octuple_type>("0.0380779473638783465886976588795511844877171449627841747664719248482680479602"), boost::lexical_cast<octuple_type>("0.243834674612590353732041581649284415526361108560923136142908810357641947074"), boost::lexical_cast<octuple_type>("0.604823123690111111903076867434236170895956271189611756533371353266219479839"), boost::lexical_cast<octuple_type>("0.657288078051300538078212639045173214030585866924591885443603406558844920237"), boost::lexical_cast<octuple_type>("0.133197385825007576190954945899795553692178076843366113615434683783912029373"), boost::lexical_cast<octuple_type>("-0.293273783279174908806403195242198731043896162858990682572511282649777494073"), boost::lexical_cast<octuple_type>("-0.0968407832229764605135081335376966022482545810459909967947126760842963820075"), boost::lexical_cast<octuple_type>("0.148540749338106380135072717506042302479125857728060306077164939460051558202"), boost::lexical_cast<octuple_type>("0.0307256814793333792123174007203788271410580502467074478150306050580744709008"), boost::lexical_cast<octuple_type>("-0.0676328290613299736756422748297190159257879087135373990074833120984537787038"), boost::lexical_cast<octuple_type>("0.000250947114831451957587189749988554331517627199370963332183416469143399245077"), boost::lexical_cast<octuple_type>("0.0223616621236790972053737827026909524185564668830885375472181623365153339468"), boost::lexical_cast<octuple_type>("-0.00472320475775139727792570784824246540572951491262793801875852685657845737998"), boost::lexical_cast<octuple_type>("-0.00428150368246342983449679500231453187648118181146328837486045503769103000912"), boost::lexical_cast<octuple_type>("0.00184764688305622647661912949112567705112108135960031816073251504574674723494"), boost::lexical_cast<octuple_type>("0.000230385763523195967205216392824542169294066205246371197226000686680376244675"), boost::lexical_cast<octuple_type>("-0.000251963188942710136974988684287860660728218154347802821413426535123097430873"), boost::lexical_cast<octuple_type>("0.0000393473203162715994806898830658915070778247705551701350735993815544054870406")};
-        }
+       return {BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.038077947363878346588697658879551184487717144962784174766471924848268047975), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.24383467461259035373204158164928441552636110856092313614290881035764194652), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.60482312369011111190307686743423617089595627118961175653337135326621948137), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.6572880780513005380782126390451732140305858669245918854436034065588449216), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.13319738582500757619095494589979555369217807684336611361543468378391202935), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.29327378327917490880640319524219873104389616285899068257251128264977749451), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.096840783222976460513508133537696602248254581045990996794712676084296381974), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.14854074933810638013507271750604230247912585772806030607716493946005155866), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.03072568147933337921231740072037882714105805024670744781503060505807447087), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.067632829061329973675642274829719015925787908713537399007483312098453778674), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.00025094711483145195758718974998855433151762719937096333218341646914339924457), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0223616621236790972053737827026909524185564668830885375472181623365153339), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0047232047577513972779257078482424654057295149126279380187585268565784573968), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0042815036824634298344967950023145318764811818114632883748604550376910299936), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0018476468830562264766191294911256770511210813596003181607325150457467472311), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.00023038576352319596720521639282454216929406620524637119722600068668037624505), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.00025196318894271013697498868428786066072821815434780282141342653512309743183), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 3.934732031627159948068988306589150707782477055517013507359938155440548714e-05) };
     }
     if constexpr (p == 10) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.b4f654p-6f, 0x1.8162d6p-3f, 0x1.0ded5p-1f, 0x1.607db4p-1f, 0x1.1feba4p-2f, -0x1.ffaf7cp-3f, -0x1.914c48p-3f, 0x1.04da38p-3f, 0x1.7d29b8p-4f, -0x1.246e3p-4f, -0x1.e2a1dep-6f, 0x1.101406p-5f, 0x1.d8b7dcp-9f, -0x1.5fb466p-7f, 0x1.6dc878p-10f, 0x1.052608p-9f, -0x1.67962p-11f, -0x1.e87f56p-14f, 0x1.888a12p-14f, -0x1.bd12a2p-17f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.b4f6549dc7ae3p-6, 0x1.8162d69198cfep-3, 0x1.0ded5071bf874p-1, 0x1.607db4062d775p-1, 0x1.1feba4923f567p-2, -0x1.ffaf7b6c111e3p-3, -0x1.914c47c1ca802p-3, 0x1.04da377a0ae83p-3, 0x1.7d29b819fd18dp-4, -0x1.246e307349ac4p-4, -0x1.e2a1dd5152b25p-6, 0x1.1014069cb8f3cp-5, 0x1.d8b7db3e21714p-9, -0x1.5fb466d770edcp-7, 0x1.6dc8787ae38ddp-10, 0x1.0526072a98cd8p-9, -0x1.67962098c50fp-11, -0x1.e87f555dc50ddp-14, 0x1.888a11cfae433p-14, -0x1.bd12a2a1a43dbp-17};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0xd.a7b2a4ee3d71687p-9L, 0xc.0b16b48cc67ed9dp-6L, 0x8.6f6a838dfc39cfcp-4L, 0xb.03eda0316bba9f7p-4L, 0x8.ff5d2491fab3641p-5L, -0xf.fd7bdb6088f17a6p-6L, -0xc.8a623e0e5400e29p-6L, 0x8.26d1bbd05741a5ep-6L, 0xb.e94dc0cfe8c6997p-7L, -0x9.2371839a4d62324p-7L, -0xf.150eea8a95926cep-9L, 0x8.80a034e5c79dfcbp-8L, 0xe.c5bed9f10b89f27p-12L, -0xa.fda336bb876e26p-10L, 0xb.6e43c3d71c6ebc5p-13L, 0x8.29303954c66bfc4p-12L, -0xb.3cb104c62878097p-14L, -0xf.43faaaee286e92ap-17L, 0xc.44508e7d72197a7p-17L, -0xd.e895150d21eda8p-20L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.b4f6549dc7ae2d0da711a289f0cap-6Q, 0x1.8162d69198cfdb39a90922d70e5fp-3Q, 0x1.0ded5071bf8739f750ffec152978p-1Q, 0x1.607db4062d7753edab576af3e0dcp-1Q, 0x1.1feba4923f566c829244a5b4f4c2p-2Q, -0x1.ffaf7b6c111e2f4b082d1396dfd9p-3Q, -0x1.914c47c1ca801c5176763b1002edp-3Q, 0x1.04da377a0ae834bb94a9fa4f0243p-3Q, 0x1.7d29b819fd18d32d43de1a7d3641p-4Q, -0x1.246e307349ac4648ebbb94e378bbp-4Q, -0x1.e2a1dd5152b24d9c384763b949a8p-6Q, 0x1.1014069cb8f3bf95bd45be617d84p-5Q, 0x1.d8b7db3e21713e4ea2df5435db4ap-9Q, -0x1.5fb466d770edc4c0f4a29d7e3176p-7Q, 0x1.6dc8787ae38dd789b768877a70c2p-10Q, 0x1.0526072a98cd7f8751cc002da048p-9Q, -0x1.67962098c50f012db290a44515a5p-11Q, -0x1.e87f555dc50dd253428e6067701p-14Q, 0x1.888a11cfae432f4e4bd0c734fcc9p-14Q, -0x1.bd12a2a1a43db4fff0519cd821dfp-17Q};
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, octuple_type>) {
-            return {boost::lexical_cast<octuple_type>("0.0266700579005555535866174487713085827719249829085128993277997577621650735643"), boost::lexical_cast<octuple_type>("0.188176800077691489020892973679093994270254675864039348434859544409886608680"), boost::lexical_cast<octuple_type>("0.527201188931725586481744827959508192498140268084022344531854947145139828409"), boost::lexical_cast<octuple_type>("0.688459039453603565741871782549235853977136404240733953727968115839903445132"), boost::lexical_cast<octuple_type>("0.281172343660577460748726998445589287624388885902615041383154395183374807120"), boost::lexical_cast<octuple_type>("-0.249846424327315379416101897920779100056466973713207371501312159710676300514"), boost::lexical_cast<octuple_type>("-0.195946274377377043504299254319098131876677647638277847439678187683856178731"), boost::lexical_cast<octuple_type>("0.127369340335793260082677233201400977078617748042224599556309752373906702894"), boost::lexical_cast<octuple_type>("0.0930573646035723511603522898354527322694291799894692586806397410224547567765"), boost::lexical_cast<octuple_type>("-0.0713941471663970871453360930760506476729261198370215091752375634796582409510"), boost::lexical_cast<octuple_type>("-0.0294575368218758128582832376014183919938820051606494877976965428318490167081"), boost::lexical_cast<octuple_type>("0.0332126740593410017397636531821591289797833741326709604332335127083312999184"), boost::lexical_cast<octuple_type>("0.00360655356695616965542329141713340329951735051861899476273061229128656318944"), boost::lexical_cast<octuple_type>("-0.0107331754833305750443181141065136444811154878114392321337033393709343696195"), boost::lexical_cast<octuple_type>("0.00139535174705290116578931844795770756766054285568855242672111772342943140108"), boost::lexical_cast<octuple_type>("0.00199240529518505611715874224264064321176255536551410528006793647824864459995"), boost::lexical_cast<octuple_type>("-0.000685856694959711626561370981926571419662504333678692051621190356175797931438"), boost::lexical_cast<octuple_type>("-0.000116466855129285450951480971025899189152746185434759736281923507446885853623"), boost::lexical_cast<octuple_type>("0.0000935886703200695913340501303422285439968845621529727644352187393967719605190"), boost::lexical_cast<octuple_type>("-0.0000132642028945212448124366753122668330574924096060582975640067461946671323150")};
-        }
+       return {BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.026670057900555553586617448771308582771924982908512899327799757762165073565), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.1881768000776914890208929736790939942702546758640393484348595444098866088), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.52720118893172558648174482795950819249814026808402234453185494714513982787), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.68845903945360356574187178254923585397713640424073395372796811583990344659), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.28117234366057746074872699844558928762438888590261504138315439518337480745), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.24984642432731537941610189792077910005646697371320737150131215971067630043), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.1959462743773770435042992543190981318766776476382778474396781876838561782), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.12736934033579326008267723320140097707861774804222459955630975237390670344), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.093057364603572351160352289835452732269429179989469258680639741022454756675), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.071394147166397087145336093076050647672926119837021509175237563479658240953), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.029457536821875812858283237601418391993882005160649487797696542831849016741), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.033212674059341001739763653182159128979783374132670960433233512708331299782), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0036065535669561696554232914171334032995173505186189947627306122912865631829), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.01073317548333057504431811410651364448111548781143923213370333937093436962), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0013953517470529011657893184479577075676605428556885524267211177234294314032), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0019924052951850561171587422426406432117625553655141052800679364782486446064), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.00068585669495971162656137098192657141966250433367869205162119035617579793186), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.00011646685512928545095148097102589918915274618543475973628192350744688585366), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 9.3588670320069591334050130342228543996884562152972764435218739396771960302e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -1.3264202894521244812436675312266833057492409606058297564006746194667132319e-05) };
     }
     if constexpr (p == 11) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.324992p-6f, 0x1.270c9cp-3f, 0x1.ccb286p-2f, 0x1.5f1256p-1f, 0x1.a5d9fcp-2f, -0x1.4c56f6p-3f, -0x1.18cff8p-2f, 0x1.0e83b8p-4f, 0x1.32d0a4p-3f, -0x1.7cc388p-5f, -0x1.10221ep-4f, 0x1.00b272p-5f, 0x1.557516p-6f, -0x1.f77976p-7f, -0x1.b5e4ap-9f, 0x1.42fd2p-8f, -0x1.439544p-12f, -0x1.d4338ep-11f, 0x1.05416p-12f, 0x1.c8ab06p-15f, -0x1.228a1p-15f, 0x1.2d9b0cp-18f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.3249916076091p-6, 0x1.270c9c42314cfp-3, 0x1.ccb286198c9dfp-2, 0x1.5f125643212ccp-1, 0x1.a5d9fccefe816p-2, -0x1.4c56f6b2bf66cp-3, -0x1.18cff89a8cc46p-2, 0x1.0e83b8b6a4d8fp-4, 0x1.32d0a3f0ba732p-3, -0x1.7cc387e4a9a09p-5, -0x1.10221dbbeff7cp-4, 0x1.00b27276a8099p-5, 0x1.557516a958be5p-6, -0x1.f77975a6883f7p-7, -0x1.b5e49f3346a8bp-9, 0x1.42fd20a75f9acp-8, -0x1.439543c841133p-12, -0x1.d4338d3fdae3ap-11, 0x1.05415f0bc6ea2p-12, 0x1.c8ab05d193c38p-15, -0x1.228a0febb3e8cp-15, 0x1.2d9b0b4e10d78p-18};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0x9.924c8b03b048b06p-9L, 0x9.3864e2118a67afdp-6L, 0xe.659430cc64ef74bp-5L, 0xa.f892b2190965c91p-4L, 0xd.2ecfe677f40b2aap-5L, -0xa.62b7b595fb361ep-6L, -0x8.c67fc4d4662301ap-5L, 0x8.741dc5b526c7499p-7L, 0x9.96851f85d39931p-6L, -0xb.e61c3f254d048e4p-8L, -0x8.8110eddf7fbe097p-7L, 0x8.059393b5404c82ap-8L, 0xa.aba8b54ac5f295dp-9L, -0xf.bbcbad3441fb82ap-10L, -0xd.af24f99a3545bf1p-12L, 0xa.17e9053afcd5e0bp-11L, -0xa.1caa1e42089945fp-15L, -0xe.a19c69fed71d098p-14L, 0x8.2a0af85e37512d9p-15L, 0xe.45582e8c9e1bc7dp-18L, -0x9.14507f5d9f45ff4p-18L, 0x9.6cd85a7086bbdf3p-21L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.324991607609160c660c469077c4p-6Q, 0x1.270c9c42314cf5fa956419fe6ca8p-3Q, 0x1.ccb286198c9dee96d12668532b6cp-2Q, 0x1.5f125643212cb922d29e40df5ae5p-1Q, 0x1.a5d9fccefe816554cfd2c1b4c2eap-2Q, -0x1.4c56f6b2bf66c3c093c0529f8f7fp-3Q, -0x1.18cff89a8cc4603466567c5566b2p-2Q, 0x1.0e83b8b6a4d8e932eca95459a69cp-4Q, 0x1.32d0a3f0ba73261f3f385a0ab52ep-3Q, -0x1.7cc387e4a9a091c75d9de8faea58p-5Q, -0x1.10221dbbeff7c12d2228c7667179p-4Q, 0x1.00b27276a80990547cbd63f84547p-5Q, 0x1.557516a958be52b928260c4c6ad5p-6Q, -0x1.f77975a6883f7054b8b01c477981p-7Q, -0x1.b5e49f3346a8b7e121e98be0fcfbp-9Q, 0x1.42fd20a75f9abc16cec7fe76464bp-8Q, -0x1.439543c8411328be7c3dbb239962p-12Q, -0x1.d4338d3fdae3a1309e0d7105695cp-11Q, 0x1.05415f0bc6ea25b1e91fb2adce4fp-12Q, 0x1.c8ab05d193c378f97fff6933dc9bp-15Q, -0x1.228a0febb3e8bfe721948bedcf9cp-15Q, 0x1.2d9b0b4e10d77be6e48f3790bbdep-18Q};
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, octuple_type>) {
-            return {boost::lexical_cast<octuple_type>("0.0186942977614710840254357293956197572896777445592195854328669208544639848493"), boost::lexical_cast<octuple_type>("0.144067021150624512795191584936100114302371896755623960431885248217612109866"), boost::lexical_cast<octuple_type>("0.449899764356045334768894037385360367780689537864893347459965579586344042705"), boost::lexical_cast<octuple_type>("0.685686774916200511120938631696309793594020496456770349505158901745075089131"), boost::lexical_cast<octuple_type>("0.411964368947907462925939648571066730743040041018784531569724251133330862864"), boost::lexical_cast<octuple_type>("-0.162275245027490362240582726998551154074426432421213020964966742981832149727"), boost::lexical_cast<octuple_type>("-0.274230846817946961202100945283526662864808952177517822190577839005023967370"), boost::lexical_cast<octuple_type>("0.0660435881966831919006145788812630265675314216894079154111345722601572700631"), boost::lexical_cast<octuple_type>("0.149812012466378496406656261704419329858827242026748465379690959421507533896"), boost::lexical_cast<octuple_type>("-0.0464799551166841872716172258902374457722326096684826074745032098759584318172"), boost::lexical_cast<octuple_type>("-0.0664387856950252052789921553697120319181956689607973962285857402336065270973"), boost::lexical_cast<octuple_type>("0.0313350902190460760309479840830314453635810568088003196493644550909547400332"), boost::lexical_cast<octuple_type>("0.0208409043601810630229481125565649101515776183273471569112669220076703474398"), boost::lexical_cast<octuple_type>("-0.0153648209062015994261981160995882274401432649577300012020584862793777385002"), boost::lexical_cast<octuple_type>("-0.00334085887301444560609080861798240610193065835949919084565673177725408174281"), boost::lexical_cast<octuple_type>("0.00492841765605904112317073974170827369028554772991580241839745801019376641230"), boost::lexical_cast<octuple_type>("-0.000308592858815143165175459072627895330718021660507848858192156227602365444134"), boost::lexical_cast<octuple_type>("-0.000893023250666264613390082462264865398987951987862072879313335822408534301830"), boost::lexical_cast<octuple_type>("0.000249152523552823498871221687266680108822119930285542538197139249093202823549"), boost::lexical_cast<octuple_type>("0.0000544390746993684716735785687957683219193667852560079397804368892016829413126"), boost::lexical_cast<octuple_type>("-0.0000346349841869849955412808515997404321450648804823345803594360135567940224107"), boost::lexical_cast<octuple_type>("0.00000449427427723651009541564828231013091641049798738375346057174174843400859633")};
-        }
+       return {BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.018694297761471084025435729395619757289677744559219585432866920854463984821), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.1440670211506245127951915849361001143023718967556239604318852482176121098), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.4498997643560453347688940373853603677806895378648933474599655795863440433), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.68568677491620051112093863169630979359402049645677034950515890174507509031), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.41196436894790746292593964857106673074304004101878453156972425113333086269), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.16227524502749036224058272699855115407442643242121302096496674298183214991), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.27423084681794696120210094528352666286480895217751782219057783900502396695), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.066043588196683191900614578881263026567531421689407915411134572260157270027), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.14981201246637849640665626170441932985882724202674846537969095942150753335), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.046479955116684187271617225890237445772232609668482607474503209875958431693), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.06643878569502520527899215536971203191819566896079739622858574023360652697), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.031335090219046076030947984083031445363581056808800319649364455090954740139), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.020840904360181063022948112556564910151577618327347156911266922007670347371), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.015364820906201599426198116099588227440143264957730001202058486279377738507), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0033408588730144456060908086179824061019306583594991908456567317772540817346), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0049284176560590411231707397417082736902855477299158024183974580101937664126), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.00030859285881514316517545907262789533071802166050784885819215622760236544448), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.00089302325066626461339008246226486539898795198786207287931333582240853430266), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.00024915252355282349887122168726668010882211993028554253819713924909320282452), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 5.4439074699368471673578568795768321919366785256007939780436889201682941436e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -3.4634984186984995541280851599740432145064880482334580359436013556794022457e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 4.4942742772365100954156482823101309164104979873837534605717417484340085911e-06) };
     }
     if constexpr (p == 12) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.ada998p-7f, 0x1.c0c89p-4f, 0x1.826962p-2f, 0x1.507c5ap-1f, 0x1.082246p-1f, -0x1.6eb4acp-5f, -0x1.43c448p-2f, -0x1.85997p-6f, 0x1.75b758p-3f, 0x1.5f3ea8p-8f, -0x1.8afc68p-4f, 0x1.63811ap-7f, 0x1.5458dcp-5f, -0x1.906176p-7f, -0x1.a4c4a6p-7f, 0x1.b7d844p-8f, 0x1.26babep-9f, -0x1.1dac02p-9f, 0x1.b73c72p-18f, 0x1.978844p-12f, -0x1.73369p-14f, -0x1.96b4a6p-16f, 0x1.acb93p-17f, -0x1.9a7502p-20f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.ada9978d2fa57p-7, 0x1.c0c890682f879p-4, 0x1.82696272e40bdp-2, 0x1.507c59d8e6f6bp-1, 0x1.082245c297978p-1, -0x1.6eb4ac1d9855dp-5, -0x1.43c448da45b22p-2, -0x1.85996f0f3b3b2p-6, 0x1.75b757e56dd3bp-3, 0x1.5f3ea878d368ep-8, -0x1.8afc682193383p-4, 0x1.638119d1c4362p-7, 0x1.5458dbe394ebp-5, -0x1.90617513f389bp-7, -0x1.a4c4a623e2a51p-7, 0x1.b7d844bffa4e9p-8, 0x1.26babd1f8d181p-9, -0x1.1dac0186ec142p-9, 0x1.b73c724cbcd25p-18, 0x1.9788431be0bfbp-12, -0x1.7336904b8b4e8p-14, -0x1.96b4a56f63fa9p-16, 0x1.acb92f10c423ap-17, -0x1.9a7502d7dc2f3p-20};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0xd.6d4cbc697d2b459p-10L, 0xe.064483417c3c86cp-7L, 0xc.134b1397205e82fp-5L, 0xa.83e2cec737b5622p-4L, 0x8.41122e14bcbbcc8p-4L, -0xb.75a560ecc2ae67fp-8L, -0xa.1e2246d22d9117cp-5L, -0xc.2ccb7879d9d93dbp-9L, 0xb.adbabf2b6e9db71p-6L, 0xa.f9f543c69b47041p-11L, -0xc.57e3410c99c1b5p-7L, 0xb.1c08ce8e21b0dd8p-10L, 0xa.a2c6df1ca7582e3p-8L, -0xc.830ba89f9c4dbcbp-10L, -0xd.2625311f15287e1p-10L, 0xd.bec225ffd274461p-11L, 0x9.35d5e8fc68c04b8p-12L, -0x8.ed600c3760a133p-12L, 0xd.b9e39265e692542p-21L, 0xc.bc4218df05fd969p-15L, -0xb.99b4825c5a7426p-17L, -0xc.b5a52b7b1fd454bp-19L, 0xd.65c97886211cfe7p-20L, -0xc.d3a816bee17970fp-23L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.ada9978d2fa568b21229688156b8p-7Q, 0x1.c0c890682f8790d7f6bb1c1aa44ep-4Q, 0x1.82696272e40bd05e57c851b9cb36p-2Q, 0x1.507c59d8e6f6ac435d1e88e090b6p-1Q, 0x1.082245c29797798f324c3b86f65cp-1Q, -0x1.6eb4ac1d9855ccfed03d4133c6fbp-5Q, -0x1.43c448da45b222f8d287f72956dcp-2Q, -0x1.85996f0f3b3b27b5f0ec32953a95p-6Q, 0x1.75b757e56dd3b6e26eea4e0a43bap-3Q, 0x1.5f3ea878d368e081a5d3cb36d936p-8Q, -0x1.8afc6821933836a0611906df913cp-4Q, 0x1.638119d1c4361bb00a2f22d1f90bp-7Q, 0x1.5458dbe394eb05c5aab3c4ceb31ap-5Q, -0x1.90617513f389b7954493854c387ep-7Q, -0x1.a4c4a623e2a50fc10158bea8a45cp-7Q, 0x1.b7d844bffa4e88c2ef52650eb0e3p-8Q, 0x1.26babd1f8d1809707edb54236067p-9Q, -0x1.1dac0186ec14265ff3ab908c13a3p-9Q, 0x1.b73c724cbcd24a84c3c597249f8dp-18Q, 0x1.9788431be0bfb2d1938d25135045p-12Q, -0x1.7336904b8b4e84c0e0396f9346efp-14Q, -0x1.96b4a56f63fa8a95abb9ecaeceaep-16Q, 0x1.acb92f10c4239fce7d915af19a6cp-17Q, -0x1.9a7502d7dc2f2e1e665f9ba74bc1p-20Q};
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, octuple_type>) {
-            return {boost::lexical_cast<octuple_type>("0.0131122579572295175067460908889332806566551064193132500774828079813751369078"), boost::lexical_cast<octuple_type>("0.109566272821185154605704505024890542607568050306677404638365743414594716237"), boost::lexical_cast<octuple_type>("0.377355135214212657092821260487920614901094170605752633470583911562885099045"), boost::lexical_cast<octuple_type>("0.657198722579307089302761128664116983425020328998841214139428195001939202386"), boost::lexical_cast<octuple_type>("0.515886478427815608756032648054303270067769308703609005612764729867503168411"), boost::lexical_cast<octuple_type>("-0.0447638856537746266676274731154016652928454363150592413907170410117965514990"), boost::lexical_cast<octuple_type>("-0.316178453752785536864802935347803109850883903254736438957420337160049554984"), boost::lexical_cast<octuple_type>("-0.0237792572560697276839975460913322578455336655833174115248261271603350281595"), boost::lexical_cast<octuple_type>("0.182478605927579679854043611618924171029477144809630269832901126083410652478"), boost::lexical_cast<octuple_type>("0.00535956967435215032827627672976833228886266518419270582163634261809269415715"), boost::lexical_cast<octuple_type>("-0.0964321200965070820265032053432248412743088014304522051434640274861906048848"), boost::lexical_cast<octuple_type>("0.0108491302558221843808901023774815218866163056760333465932251226434077741286"), boost::lexical_cast<octuple_type>("0.0415462774950844407392709468190657486451353222138837486128707899413616614352"), boost::lexical_cast<octuple_type>("-0.0122186490697482807199879826647156771298246609311655817534481104550208384247"), boost::lexical_cast<octuple_type>("-0.0128408251983006832946603447189472849620610983231409763327522557348508782102"), boost::lexical_cast<octuple_type>("0.00671149900879550917776702706821567245064811218585645674037945533688642441241"), boost::lexical_cast<octuple_type>("0.00224860724099523759995086521126723401834319978614617709926201027901007445066"), boost::lexical_cast<octuple_type>("-0.00217950361862776047159890337958417118784007529186057126498094298705073259759"), boost::lexical_cast<octuple_type>("0.00000654512821250959556650043039932711072911177056889735663071455200741848443049"), boost::lexical_cast<octuple_type>("0.000388653062820931443589728883779598179191748857342017752343609613138331820861"), boost::lexical_cast<octuple_type>("-0.0000885041092082043242082164596155372659873832215147193280801544303001991847212"), boost::lexical_cast<octuple_type>("-0.0000242415457570307840297891532053171958042377836266428223937753220729228844731"), boost::lexical_cast<octuple_type>("0.0000127769522193797665871404636261662088737596094143942875605535392042653701946"), boost::lexical_cast<octuple_type>("-0.00000152907175806851090271223916452290122319761543966034067260269641683218542373")};
-        }
+       return {BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.013112257957229517506746090888933280656655106419313250077482807981375136912), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.1095662728211851546057045050248905426075680503066774046383657434145947162), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.37735513521421265709282126048792061490109417060575263347058391156288509976), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.65719872257930708930276112866411698342502032899884121413942819500193920417), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.51588647842781560875603264805430327006776930870360900561276472986750316737), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.04476388565377462666762747311540166529284543631505924139071704101179655136), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.31617845375278553686480293534780310985088390325473643895742033716004955521), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.02377925725606972768399754609133225784553366558331741152482612716033502819), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.18247860592757967985404361161892417102947714480963026983290112608341065294), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0053595696743521503282762767297683322888626651841927058216363426180926941677), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.096432120096507082026503205343224841274308801430452205143464027486190605026), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.010849130255822184380890102377481521886616305676033346593225122643407774116), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.041546277495084440739270946819065748645135322213883748612870789941361661575), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.012218649069748280719987982664715677129824660931165581753448110455020838418), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.012840825198300683294660344718947284962061098323140976332752255734850878212), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0067114990087955091777670270682156724506481121858564567403794553368864243964), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.002248607240995237599950865211267234018343199786146177099262010279010074457), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0021795036186277604715989033795841711878400752918605712649809429870507326048), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 6.5451282125095955665004303993271107291117705688973566307145520074184844383e-06), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.00038865306282093144358972888377959817919174885734201775234360961313833182126), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -8.8504109208204324208216459615537265987383221514719328080154430300199184715e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -2.4241545757030784029789153205317195804237783626642822393775322072922884523e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 1.2776952219379766587140463626166208873759609414394287560553539204265370227e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -1.529071758068510902712239164522901223197615439660340672602696416832185426e-06) };
     }
     if constexpr (p == 13) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.2d8918p-7f, 0x1.53665p-4f, 0x1.3f7bf6p-2f, 0x1.38dc5p-1f, 0x1.2d82fp-1f, 0x1.644b26p-4f, -0x1.428842p-2f, -0x1.fe442cp-4f, 0x1.6f9128p-3f, 0x1.2acc8p-4f, -0x1.b16354p-4f, -0x1.b1fc6ep-6f, 0x1.cbe504p-5f, 0x1.37f29ep-9f, -0x1.86743ap-6f, 0x1.0128dp-8f, 0x1.db8098p-8f, -0x1.6a025cp-9f, -0x1.58e562p-10f, 0x1.e8ceb2p-11f, 0x1.9d26d8p-15f, -0x1.5a4cf4p-13f, 0x1.0159a8p-15f, 0x1.5e5f8p-17f, -0x1.3b708ap-18f, 0x1.183f9ep-21f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.2d89174d37e3bp-7, 0x1.53664fc8a3d4cp-4, 0x1.3f7bf6c09afe8p-2, 0x1.38dc5001834bbp-1, 0x1.2d82ef0bea472p-1, 0x1.644b251290fb5p-4, -0x1.42884206fc5aep-2, -0x1.fe442b86ad763p-4, 0x1.6f91279c81aa4p-3, 0x1.2acc804557c8bp-4, -0x1.b163543c8eaccp-4, -0x1.b1fc6de239706p-6, 0x1.cbe5044520d5ep-5, 0x1.37f29dfe3e92cp-9, -0x1.867439245b0c7p-6, 0x1.0128d031aa3bp-8, 0x1.db80973172631p-8, -0x1.6a025cdac7e1p-9, -0x1.58e561b1f2cf6p-10, 0x1.e8ceb1ee24cabp-11, 0x1.9d26d847f17cap-15, -0x1.5a4cf360064a4p-13, 0x1.0159a865542d3p-15, 0x1.5e5f8028cd835p-17, -0x1.3b708a4c3be34p-18, 0x1.183f9db8da3ap-21};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0x9.6c48ba69bf1db2dp-10L, 0xa.9b327e451ea606ap-7L, 0x9.fbdfb604d7f42bfp-5L, 0x9.c6e2800c1a5d56fp-4L, 0x9.6c17785f5238ef1p-4L, 0xb.2259289487da5f5p-7L, -0xa.14421037e2d6f28p-5L, -0xf.f2215c356bb1af3p-7L, 0xb.7c893ce40d51d77p-6L, 0x9.5664022abe455a4p-7L, -0xd.8b1aa1e47565fb8p-7L, -0xd.8fe36f11cb8316bp-9L, 0xe.5f28222906af18bp-8L, 0x9.bf94eff1f49636bp-12L, -0xc.33a1c922d8636b9p-9L, 0x8.0946818d51d8108p-11L, 0xe.dc04b98b931878p-11L, -0xb.5012e6d63f07f27p-12L, -0xa.c72b0d8f967b059p-13L, 0xf.46758f712655aeep-14L, 0xc.e936c23f8be4d46p-18L, -0xa.d2679b00325201p-16L, 0x8.0acd432aa169479p-18L, 0xa.f2fc01466c1a50ap-20L, -0x9.db845261df1a01dp-21L, 0x8.c1fcedc6d1d027ap-24L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.2d89174d37e3b6596d64d168e49p-7Q, 0x1.53664fc8a3d4c0d33efd4b4bc6fap-4Q, 0x1.3f7bf6c09afe857e70d916613d78p-2Q, 0x1.38dc5001834baade66ebb6ec9fc1p-1Q, 0x1.2d82ef0bea471de1f0a3864a5cccp-1Q, 0x1.644b251290fb4bea9c417da1f71ep-4Q, -0x1.42884206fc5ade5015e8dd0e5832p-2Q, -0x1.fe442b86ad7635e6a44fa231478p-4Q, 0x1.6f91279c81aa3aed801eca5172e8p-3Q, 0x1.2acc804557c8ab4899f3d0916648p-4Q, -0x1.b163543c8eacbf70b0092010e485p-4Q, -0x1.b1fc6de2397062d67f76ff78186p-6Q, 0x1.cbe5044520d5e315c90c0ed1b10cp-5Q, 0x1.37f29dfe3e92c6d51003ce786db8p-9Q, -0x1.867439245b0c6d71509d7a14369ep-6Q, 0x1.0128d031aa3b020f68dbd131fc68p-8Q, 0x1.db80973172630eff11f1aa6bf206p-8Q, -0x1.6a025cdac7e0fe4d3e8433e38ffbp-9Q, -0x1.58e561b1f2cf60b1ce144cfab0ffp-10Q, 0x1.e8ceb1ee24cab5dbcf0c32d1591bp-11Q, 0x1.9d26d847f17c9a8ce68c968f105dp-15Q, -0x1.5a4cf360064a4020bfd19dc8e5fp-13Q, 0x1.0159a865542d28f1113c2ad46cb5p-15Q, 0x1.5e5f8028cd834a146bf59b16d932p-17Q, -0x1.3b708a4c3be3403a7da544157c5bp-18Q, 0x1.183f9db8da3a04f4c66e4459dad2p-21Q};
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, octuple_type>) {
-            return {boost::lexical_cast<octuple_type>("0.00920213353896236797297016347564418466753417191641656238600970303711912173265"), boost::lexical_cast<octuple_type>("0.0828612438729027796443202713123046640520811333289013507251427742009482956517"), boost::lexical_cast<octuple_type>("0.311996322160438063396078411221404969394668352896718031716039017308515654041"), boost::lexical_cast<octuple_type>("0.611055851158787652821199513674418056207361267601823943852658294015204037145"), boost::lexical_cast<octuple_type>("0.588889570431218908071039534739533392766598638281283604223557340650249576137"), boost::lexical_cast<octuple_type>("0.0869857261796472373102373983808749439923188407661970125088201664378054171345"), boost::lexical_cast<octuple_type>("-0.314972907711388632998169825593228258287688845067878902595030681868130772999"), boost::lexical_cast<octuple_type>("-0.124576730750815258941380833602126018079273929517363471957206932075260972005"), boost::lexical_cast<octuple_type>("0.179476079429339843234845007233936901358196625624413339304288145469676423326"), boost::lexical_cast<octuple_type>("0.0729489336567771638090283061047766198332592902687987355362796328461636696921"), boost::lexical_cast<octuple_type>("-0.105807618187934326450966730419646484947886075480123665823236051077820681894"), boost::lexical_cast<octuple_type>("-0.0264884064753436946396391224803478572641960484429769701626422412133519842633"), boost::lexical_cast<octuple_type>("0.0561394771002834288621450199838733111998837879254310024473705625396675790207"), boost::lexical_cast<octuple_type>("0.00237997225405907881146517095855420835809439461205193486847513927070930528134"), boost::lexical_cast<octuple_type>("-0.0238314207103236490320640306775773913425292271763622627407729863341057724688"), boost::lexical_cast<octuple_type>("0.00392394144879741624331637022081552655882474662345140404391840728787217413821"), boost::lexical_cast<octuple_type>("0.00725558940161756619451839330050269889897352967964668369526982867260050623476"), boost::lexical_cast<octuple_type>("-0.00276191123465686217801457626609844599535009333050181802496631648326614964558"), boost::lexical_cast<octuple_type>("-0.00131567391189229893661383537059364337606041259265365230723812459474570122051"), boost::lexical_cast<octuple_type>("0.000932326130867263386222651780254851410091808829980195230799156927112701492336"), boost::lexical_cast<octuple_type>("0.0000492515251262894619214095738786659621010377829938882350084009445661139469929"), boost::lexical_cast<octuple_type>("-0.000165128988556505489461668770923800075589854821465977670334780149359987420945"), boost::lexical_cast<octuple_type>("0.0000306785375793254934664948322857547623660042821723790056312823074855283018382"), boost::lexical_cast<octuple_type>("0.0000104419305714081370817071499108059695167070643621732816964147406843820801008"), boost::lexical_cast<octuple_type>("-0.00000470041647936086832565019516506177132165038358297095855656805971133412246529"), boost::lexical_cast<octuple_type>("0.000000522003509845486469173642435484317697674705215524355700153190105348895004025")};
-        }
+       return {BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0092021335389623679729701634756441846675341719164165623860097030371191217305), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.082861243872902779644320271312304664052081133328901350725142774200948295461), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.31199632216043806339607841122140496939466835289671803171603901730851565412), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.61105585115878765282119951367441805620736126760182394385265829401520403811), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.58888957043121890807103953473953339276659863828128360422355734065024957534), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.08698572617964723731023739838087494399231884076619701250882016643780541724), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.31497290771138863299816982559322825828768884506787890259503068186813077354), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.12457673075081525894138083360212601807927392951736347195720693207526097203), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.17947607942933984323484500723393690135819662562441333930428814546967642382), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.072948933656777163809028306104776619833259290268798735536279632846163669865), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.10580761818793432645096673041964648494788607548012366582323605107782068188), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.026488406475343694639639122480347857264196048442976970162642241213351984244), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.05613947710028342886214501998387331119988378792543100244737056253966757901), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0023799722540590788114651709585542083580943946120519348684751392707093052796), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.023831420710323649032064030677577391342529227176362262740772986334105772526), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0039239414487974162433163702208155265588247466234514040439184072878721741534), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0072555894016175661945183933005026988989735296796466836952698286726005062515), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0027619112346568621780145762660984459953500933305018180249663164832661496432), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0013156739118922989366138353705936433760604125926536523072381245947457012192), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.00093232613086726338622265178025485141009180882998019523079915692711270149142), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 4.9251525126289461921409573878665962101037782993888235008400944566113947075e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.00016512898855650548946166877092380007558985482146597767033478014935998742089), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 3.0678537579325493466494832285754762366004282172379005631282307485528301752e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 1.0441930571408137081707149910805969516707064362173281696414740684382080067e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -4.7004164793608683256501951650617713216503835829709585565680597113341224593e-06), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 5.2200350984548646917364243548431769767470521552435570015319010534889500617e-07) };
     }
     if constexpr (p == 14) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.a7702ap-8f, 0x1.fee46p-5f, 0x1.04f778p-2f, 0x1.1bcdf2p-1f, 0x1.432b0ep-1f, 0x1.bfd66ap-3f, -0x1.163586p-2f, -0x1.be885ep-3f, 0x1.1b6ef4p-3f, 0x1.1eb29p-3f, -0x1.63524ep-4f, -0x1.251084p-4f, 0x1.c480a6p-5f, 0x1.ba103ap-6f, -0x1.ee8e8ap-6f, -0x1.6ffce6p-8f, 0x1.a3160cp-7f, -0x1.873bd2p-11f, -0x1.f89472p-9f, 0x1.1650e2p-10f, 0x1.7334fep-11f, -0x1.959f6ap-12f, -0x1.5e73f4p-15f, 0x1.20612ap-14f, -0x1.5adbf4p-17f, -0x1.26968ep-18f, 0x1.cf0cbcp-20f, -0x1.7fc91p-23f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.a7702ace363acp-8, 0x1.fee460f5cb877p-5, 0x1.04f777f62f423p-2, 0x1.1bcdf22a1725cp-1, 0x1.432b0dc3136d4p-1, 0x1.bfd66ae4258acp-3, -0x1.1635861af071dp-2, -0x1.be885d06053bfp-3, 0x1.1b6ef32bc7359p-3, 0x1.1eb28fc03c55bp-3, -0x1.63524d6aa4cf7p-4, -0x1.2510847f3ed26p-4, 0x1.c480a659de0cdp-5, 0x1.ba103a92149f4p-6, -0x1.ee8e8a6bca9acp-6, -0x1.6ffce6192a67bp-8, 0x1.a3160ba7d924ep-7, -0x1.873bd13c8af18p-11, -0x1.f894721441f67p-9, 0x1.1650e1f6ec4c3p-10, 0x1.7334fd9e58c6ap-11, -0x1.959f69010da01p-12, -0x1.5e73f3c020201p-15, 0x1.20612a2e814f8p-14, -0x1.5adbf364f5e1cp-17, -0x1.26968e53fb76dp-18, 0x1.cf0cbb4133dbbp-20, -0x1.7fc90f0c46da2p-23};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0xd.3b815671b1d61adp-11L, 0xf.f72307ae5c3b8acp-8L, 0x8.27bbbfb17a114bp-5L, 0x8.de6f9150b92e008p-4L, 0xa.19586e189b69d98p-4L, 0xd.feb357212c55f71p-6L, -0x8.b1ac30d7838e67p-5L, -0xd.f442e83029df6fp-6L, 0x8.db77995e39ac42bp-6L, 0x8.f5947e01e2ad986p-6L, -0xb.1a926b55267b7d4p-7L, -0x9.288423f9f692d35p-7L, 0xe.240532cef066a7ap-8L, 0xd.d081d490a4fa2c2p-9L, -0xf.7474535e54d6257p-9L, -0xb.7fe730c9533d677p-11L, 0xd.18b05d3ec926ef4p-10L, -0xc.39de89e4578bd58p-14L, -0xf.c4a390a20fb38fap-12L, 0x8.b2870fb76261486p-13L, 0xb.99a7ecf2c634fb5p-14L, -0xc.acfb48086d004d1p-15L, -0xa.f39f9e01010090ep-18L, 0x9.030951740a7c181p-17L, -0xa.d6df9b27af0deefp-20L, -0x9.34b4729fdbb6709p-21L, 0xe.7865da099eddb46p-23L, -0xb.fe48786236d0c8ep-26L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.a7702ace363ac35a31e24ad7f18bp-8Q, 0x1.fee460f5cb8771588fb11eee4edep-5Q, 0x1.04f777f62f422960e164233d2842p-2Q, 0x1.1bcdf22a1725c010c6b543c39465p-1Q, 0x1.432b0dc3136d3b304d5a3bf4569bp-1Q, 0x1.bfd66ae4258abee147e56af809ep-3Q, -0x1.1635861af071cce08b7655b9575p-2Q, -0x1.be885d06053beddff8849acb8697p-3Q, 0x1.1b6ef32bc7358856a3c8661f7dbbp-3Q, 0x1.1eb28fc03c55b30ce48dc30b7f77p-3Q, -0x1.63524d6aa4cf6fa795512cfa3aa5p-4Q, -0x1.2510847f3ed25a6abc4fb2ebbea9p-4Q, 0x1.c480a659de0cd4f4123d770896e6p-5Q, 0x1.ba103a92149f4583a4c79c292018p-6Q, -0x1.ee8e8a6bca9ac4ad53dedccf86b9p-6Q, -0x1.6ffce6192a67aceee5260da8193dp-8Q, 0x1.a3160ba7d924dde8cc52f58fbb97p-7Q, -0x1.873bd13c8af17ab00e30f03b73e4p-11Q, -0x1.f894721441f671f4ac26746366e6p-9Q, 0x1.1650e1f6ec4c290c75eee26e8b4ap-10Q, 0x1.7334fd9e58c69f69b95d47a6075fp-11Q, -0x1.959f69010da009a2eacf096b1dafp-12Q, -0x1.5e73f3c02020121b8b1dbc91cc8ap-15Q, 0x1.20612a2e814f83021e4b38a90018p-14Q, -0x1.5adbf364f5e1bddd8115a86dd662p-17Q, -0x1.26968e53fb76ce12ec5e07348937p-18Q, 0x1.cf0cbb4133dbb68c44095fc163dep-20Q, -0x1.7fc90f0c46da191bc033464815fbp-23Q};
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, octuple_type>) {
-            return {boost::lexical_cast<octuple_type>("0.00646115346008794781816639744862281427232715941920119921810140416821319638585"), boost::lexical_cast<octuple_type>("0.0623647588493988983279856675843487742830533369340766716460251880613807597066"), boost::lexical_cast<octuple_type>("0.254850267792621353665907788677828668618704241636713744378008420238232719628"), boost::lexical_cast<octuple_type>("0.554305617940893835992683144985115484407826983095163460968399777532226842271"), boost::lexical_cast<octuple_type>("0.631187849104856779557661713535817234862395245657001728978880959248433640269"), boost::lexical_cast<octuple_type>("0.218670687758906521491747591821751705176577432127043205903027323352534222868"), boost::lexical_cast<octuple_type>("-0.271688552278748041414219247618117109460488246568333081431189666923849066652"), boost::lexical_cast<octuple_type>("-0.218033529993276044755555881270231191197524066947060475274712704179785996228"), boost::lexical_cast<octuple_type>("0.138395213864806591073993969002157371398990046322968611905911990239065683492"), boost::lexical_cast<octuple_type>("0.139989016584460701249294316227116344032822155561432618133368381730127661592"), boost::lexical_cast<octuple_type>("-0.0867484115681696890456082206672779538297914953951750365749296445982289331724"), boost::lexical_cast<octuple_type>("-0.0715489555040461307358414511517380799095806967312953809999091309335447192979"), boost::lexical_cast<octuple_type>("0.0552371262592160441161883406053340339791383363251167215767110765995965856731"), boost::lexical_cast<octuple_type>("0.0269814083079129169739903140321519334337576659580727423328434928060131390138"), boost::lexical_cast<octuple_type>("-0.0301853515403906351871482262348913757378157540665865262488375619379066007462"), boost::lexical_cast<octuple_type>("-0.00561504953035695913321837136769149863745729720392581038769868016916017798506"), boost::lexical_cast<octuple_type>("0.0127894932663334089615733070578407929937490386157205831348153451948141528455"), boost::lexical_cast<octuple_type>("-0.000746218989268384937181716073918178097195818798881330290043548750870183218766"), boost::lexical_cast<octuple_type>("-0.00384963886802218744578634931609555177409681850828570049305891572532777766984"), boost::lexical_cast<octuple_type>("0.00106169108560676184303256674938841117303394158214783086389393956154388248847"), boost::lexical_cast<octuple_type>("0.000708021154235527858644297769761712898347186346418159537167009442266803119446"), boost::lexical_cast<octuple_type>("-0.000386831947312954482107666339805731442732890210784216537990146842609536038748"), boost::lexical_cast<octuple_type>("-0.0000417772457703725973526797953983925892838972659013273013105432373007939629113"), boost::lexical_cast<octuple_type>("0.0000687550425269750960387343702162803160189037068765187527988272789892867302714"), boost::lexical_cast<octuple_type>("-0.0000103372091845707739466140734259481458626927250949074485069144305905647763599"), boost::lexical_cast<octuple_type>("-0.00000438970490178139411525404256136716982932308536080082571815104919437269388055"), boost::lexical_cast<octuple_type>("0.00000172499467536781276988571269274179852358789470986735657691071794719454646345"), boost::lexical_cast<octuple_type>("-0.000000178713996831135907633419293847083934388299030997695944699402284569127317214")};
-        }
+       return {BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0064611534600879478181663974486228142723271594192011992181014041682131963958), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.062364758849398898327985667584348774283053336934076671646025188061380759653), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.25485026779262135366590778867782866861870424163671374437800842023823271874), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.55430561794089383599268314498511548440782698309516346096839977753222684278), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.63118784910485677955766171353581723486239524565700172897888095924843364054), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.21867068775890652149174759182175170517657743212704320590302732335253422232), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.27168855227874804141421924761811710946048824656833308143118966692384906639), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.21803352999327604475555588127023119119752406694706047527471270417978599672), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.13839521386480659107399396900215737139899004632296861190591199023906568404), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.13998901658446070124929431622711634403282215556143261813336838173012766117), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.086748411568169689045608220667277953829791495395175036574929644598228933263), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.071548955504046130735841451151738079909580696731295380999909130933544719175), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.055237126259216044116188340605334033979138336325116721576711076599596585739), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.026981408307912916973990314032151933433757665958072742332843492806013139065), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.030185351540390635187148226234891375737815754066586526248837561937906600698), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0056150495303569591332183713676914986374572972039258103876986801691601779992), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.012789493266333408961573307057840792993749038615720583134815345194814152872), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0007462189892683849371817160739181780971958187988813302900435487508701832207), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.003849638868022187445786349316095551774096818508285700493058915725327777667), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0010616910856067618430325667493884111730339415821478308638939395615438824882), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.00070802115423552785864429776976171289834718634641815953716700944226680311764), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.00038683194731295448210766633980573144273289021078421653799014684260953603847), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -4.1777245770372597352679795398392589283897265901327301310543237300793962875e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 6.8755042526975096038734370216280316018903706876518752798827278989286730311e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -1.0337209184570773946614073425948145862692725094907448506914430590564776387e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -4.3897049017813941152540425613671698293230853608008257181510491943726938635e-06), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 1.7249946753678127698857126927417985235878947098673565769107179471945464675e-06), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -1.7871399683113590763341929384708393438829903099769594469940228456912731758e-07) };
     }
     if constexpr (p == 15) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.297006p-8f, 0x1.7eec02p-5f, 0x1.a5efd6p-3f, 0x1.f87476p-2f, 0x1.4aa806p-1f, 0x1.5b237cp-2f, -0x1.8bae9cp-3f, -0x1.27d0d6p-2f, 0x1.0b6624p-4f, 0x1.856ba4p-3f, -0x1.44f2p-5f, -0x1.c726cp-4f, 0x1.158586p-5f, 0x1.c0c324p-5f, -0x1.a62aaap-6f, -0x1.54f3aep-6f, 0x1.ee4514p-7f, 0x1.4e4c96p-8f, -0x1.a92e2p-8f, -0x1.fb0008p-13f, 0x1.fd6e44p-10f, -0x1.879fe8p-12f, -0x1.79081p-12f, 0x1.46f04ap-13f, 0x1.b0baccp-16f, -0x1.d7ff96p-16f, 0x1.c35f5cp-19f, 0x1.e6358ep-20f, -0x1.532292p-21f, 0x1.076d02p-24f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.2970058a26dcep-8, 0x1.7eec010bca4c4p-5, 0x1.a5efd6f02857ep-3, 0x1.f8747691d3f73p-2, 0x1.4aa8051a530b4p-1, 0x1.5b237b0c28179p-2, -0x1.8bae9ca895b45p-3, -0x1.27d0d6e28e01fp-2, 0x1.0b6623378c72fp-4, 0x1.856ba3f0d1d5bp-3, -0x1.44f200621040dp-5, -0x1.c726bf22e4a16p-4, 0x1.15858527779bcp-5, 0x1.c0c32426f4663p-5, -0x1.a62aa972a6fc4p-6, -0x1.54f3ad3a0b7c6p-6, 0x1.ee4513500347p-7, 0x1.4e4c95b98ec2dp-8, -0x1.a92e1fc2fdcaep-8, -0x1.fb000715d8e65p-13, 0x1.fd6e43c3dd5e8p-10, -0x1.879fe7f24ba0ap-12, -0x1.79080f71ee322p-12, 0x1.46f04a6cb59p-13, 0x1.b0bacca20c60fp-16, -0x1.d7ff965f47a09p-16, 0x1.c35f5c1543372p-19, 0x1.e6358dfe44b53p-20, -0x1.532291d1cbfa4p-21, 0x1.076d016337019p-24};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0x9.4b802c5136e6cb1p-11L, 0xb.f760085e52620cp-8L, 0xd.2f7eb78142bee86p-6L, 0xf.c3a3b48e9fb9b9bp-5L, 0xa.554028d2985a2bep-4L, 0xa.d91bd86140bc88ap-5L, -0xc.5d74e544ada28ecp-6L, -0x9.3e86b714700f9f8p-5L, 0x8.5b3119bc6397595p-7L, 0xc.2b5d1f868ead57ap-6L, -0xa.2790031082066ebp-8L, -0xe.3935f917250aff5p-7L, 0x8.ac2c293bbcde0e2p-8L, 0xe.06192137a331763p-8L, -0xd.31554b9537e1c3bp-9L, -0xa.a79d69d05be2dedp-9L, 0xf.72289a801a381d6p-10L, 0xa.7264adcc7616af1p-11L, -0xd.4970fe17ee56c45p-11L, -0xf.d80038aec732ac5p-16L, 0xf.eb721e1eeaf4368p-13L, -0xc.3cff3f925d05241p-15L, -0xb.c8407b8f7191299p-15L, 0xa.37825365ac803f5p-16L, 0xd.85d665106307a4ap-19L, -0xe.bffcb2fa3d0481cp-19L, 0xe.1afae0aa19b8c5bp-22L, 0xf.31ac6ff225a9413p-23L, -0xa.99148e8e5fd1f6dp-24L, 0x8.3b680b19b80c80ep-27L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.2970058a26dcd961f2ddf52bca08p-8Q, 0x1.7eec010bca4c417f3cf45c166751p-5Q, 0x1.a5efd6f02857dd0be400d7c02e2cp-3Q, 0x1.f8747691d3f737355530dd281d86p-2Q, 0x1.4aa8051a530b457c39051251b937p-1Q, 0x1.5b237b0c281791146b95d35023c4p-2Q, -0x1.8bae9ca895b451d87fbb9a690248p-3Q, -0x1.27d0d6e28e01f3ef0606971828aap-2Q, 0x1.0b6623378c72eb295fa0f634a67bp-4Q, 0x1.856ba3f0d1d5aaf4f59a12cbb286p-3Q, -0x1.44f200621040cdd51fafc7035006p-5Q, -0x1.c726bf22e4a15fea85834dbb1052p-4Q, 0x1.15858527779bc1c4ec7f8b6fdd21p-5Q, 0x1.c0c32426f4662ec60f158af78296p-5Q, -0x1.a62aa972a6fc3876e9915f565de4p-6Q, -0x1.54f3ad3a0b7c5bd971d938015013p-6Q, 0x1.ee451350034703acaa0dbe95c1aep-7Q, 0x1.4e4c95b98ec2d5e117559a2b0da9p-8Q, -0x1.a92e1fc2fdcad88a36c4f23f938p-8Q, -0x1.fb000715d8e6558a8e3b0bc34d7fp-13Q, 0x1.fd6e43c3dd5e86d041c185aa9428p-10Q, -0x1.879fe7f24ba0a4818b2d76fbd7e6p-12Q, -0x1.79080f71ee322531c0337932b9a5p-12Q, 0x1.46f04a6cb59007eab6af7b114fa4p-13Q, 0x1.b0bacca20c60f4939edefbff1354p-16Q, -0x1.d7ff965f47a09038cb01ea5da5e9p-16Q, 0x1.c35f5c15433718b508f832bbf1b8p-19Q, 0x1.e6358dfe44b5282546827ce8042cp-20Q, -0x1.532291d1cbfa3eda1a3275ffd36dp-21Q, 0x1.076d01633701901bb8cc971717bp-24Q};
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, octuple_type>) {
-            return {boost::lexical_cast<octuple_type>("0.00453853736157889888145939491021169634666367124378878699791651359730618263777"), boost::lexical_cast<octuple_type>("0.0467433948927662718917096933484357577657915170021494351311319734377213834945"), boost::lexical_cast<octuple_type>("0.206023863986995731539891500947630721930613850564193090270204726624901561209"), boost::lexical_cast<octuple_type>("0.492631771708139623606775707402994637261722156513093240216016003697522813162"), boost::lexical_cast<octuple_type>("0.645813140357424358176420912010691799643260828749404618107148947895533066481"), boost::lexical_cast<octuple_type>("0.339002535454731527691264114383577391875676949179355466933669011509397556470"), boost::lexical_cast<octuple_type>("-0.193204139609145428706399053432147174630409003914286382793775492150589726686"), boost::lexical_cast<octuple_type>("-0.288882596566965646248412500982233298131143563043534259497129296256293483504"), boost::lexical_cast<octuple_type>("0.0652829528487728169228310791986957488203917428559614412596510130561953369929"), boost::lexical_cast<octuple_type>("0.190146714007122982348489311658602051795950125817433669687815606055254287820"), boost::lexical_cast<octuple_type>("-0.0396661765557909444838436675189620066838174282068373680544974535292838687668"), boost::lexical_cast<octuple_type>("-0.111120936037231693365671032467405860885862376216591412050565788400539631609"), boost::lexical_cast<octuple_type>("0.0338771439235076862085481784443352377086474468741126536946319599123012785905"), boost::lexical_cast<octuple_type>("0.0547805505845076126891379031258187910860941599742276856424484536408030091303"), boost::lexical_cast<octuple_type>("-0.0257670073284399625859452575426982639220364163482534013839683682541716280711"), boost::lexical_cast<octuple_type>("-0.0208100501696930816778848342467700016205465795136489904099616617271926101264"), boost::lexical_cast<octuple_type>("0.0150839180278359023632927446017032273624489282330562771623396889036950783790"), boost::lexical_cast<octuple_type>("0.00510100036040754316970886018556531472480106652734422205552663106916575853665"), boost::lexical_cast<octuple_type>("-0.00648773456031574499518168314921869081695584563938882640792896746945184786140"), boost::lexical_cast<octuple_type>("-0.000241756490761624281166722532630017960522994699581453522332941192889131156009"), boost::lexical_cast<octuple_type>("0.00194332398038221154176491233254108744101142486557953140145230261789465341230"), boost::lexical_cast<octuple_type>("-0.000373482354137616992009809421364541461138763096803025662574022673555831120585"), boost::lexical_cast<octuple_type>("-0.000359565244362468812164962007590980885819420245408409030562748046672838761659"), boost::lexical_cast<octuple_type>("0.000155896489920599747947165824122710881625556705962549591522860363042830623991"), boost::lexical_cast<octuple_type>("0.0000257926991553189368092586241761685591294404236876734070916011973700950042214"), boost::lexical_cast<octuple_type>("-0.0000281332962660478136475532477707847866579144387629378890426725562075302388539"), boost::lexical_cast<octuple_type>("0.00000336298718173757980312484521042017747213484665586407818718630450150330033976"), boost::lexical_cast<octuple_type>("0.00000181127040794057708376851091228584116057708592533750785059029068086553957632"), boost::lexical_cast<octuple_type>("-0.000000631688232588166442120159729951765765416613791512119551041664162606772181110"), boost::lexical_cast<octuple_type>("0.0000000613335991330575202905629946028978860198919045088539651217384559505804672173")};
-        }
+       return {BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0045385373615788988814593949102116963466636712437887869979165135973061826537), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.046743394892766271891709693348435757765791517002149435131131973437721383622), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.20602386398699573153989150094763072193061385056419309027020472662490156122), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.49263177170813962360677570740299463726172215651309324021601600369752281377), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.64581314035742435817642091201069179964326082874940461810714894789553306679), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.3390025354547315276912641143835773918756769491793554669336690115093975569), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.19320413960914542870639905343214717463040900391428638279377549215058972689), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.28888259656696564624841250098223329813114356304353425949712929625629348294), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.065282952848772816922831079198695748820391742855961441259651013056195336897), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.19014671400712298234848931165860205179595012581743366968781560605525428795), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.039666176555790944483843667518962006683817428206837368054497453529283868676), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.11112093603723169336567103246740586088586237621659141205056578840053963186), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.033877143923507686208548178444335237708647446874112653694631959912301278547), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.05478055058450761268913790312581879108609415997422768564244845364080300918), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.025767007328439962585945257542698263922036416348253401383968368254171628001), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.020810050169693081677884834246770001620546579513648990409961661727192610178), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.015083918027835902363292744601703227362448928233056277162339688903695078372), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0051010003604075431697088601855653147248010665273442220555266310691657585506), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0064877345603157449951816831492186908169558456393888264079289674694518478686), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.00024175649076162428116672253263001796052299469958145352233294119288913115604), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0019433239803822115417649123325410874410114248655795314014523026178946534131), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.00037348235413761699200980942136454146113876309680302566257402267355583112012), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.00035956524436246881216496200759098088581942024540840903056274804667283876243), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.00015589648992059974794716582412271088162555670596254959152286036304283062436), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 2.5792699155318936809258624176168559129440423687673407091601197370095004239e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -2.8133296266047813647553247770784786657914438762937889042672556207530238846e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 3.3629871817375798031248452104201774721348466558640781871863045015033003361e-06), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 1.8112704079405770837685109122858411605770859253375078505902906808655395748e-06), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -6.3168823258816644212015972995176576541661379151211955104166416260677217926e-07), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 6.1333599133057520290562994602897886019891904508853965121738455950580467421e-08) };
     }
     if constexpr (p == 16) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.a2048p-9f, 0x1.1df6c8p-5f, 0x1.520d3ap-3f, 0x1.b8a3e6p-2f, 0x1.465392p-1f, 0x1.c2db72p-2f, -0x1.6f9ed6p-4f, -0x1.4ee9bp-2f, -0x1.c96974p-6f, 0x1.b084cp-3f, 0x1.bff16p-6f, -0x1.0f219ap-3f, -0x1.98ed2ep-8f, 0x1.36fc54p-4f, -0x1.f159dcp-8f, -0x1.2e3094p-5f, 0x1.516f08p-7f, 0x1.ca8c3ep-7f, -0x1.ca18fcp-8f, -0x1.dda9bcp-9f, 0x1.99ff0cp-9f, 0x1.abb604p-12f, -0x1.ed5dcep-11f, 0x1.df29e6p-14f, 0x1.6e8e3p-13f, -0x1.0000dep-14f, -0x1.d3f062p-17f, 0x1.7c64bap-17f, -0x1.1821aep-20f, -0x1.8b5554p-21f, 0x1.efcecp-23f, -0x1.6a61bcp-26f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.a2047f25eec86p-9, 0x1.1df6c86cbec6p-5, 0x1.520d391a94107p-3, 0x1.b8a3e5feb4879p-2, 0x1.465391b465934p-1, 0x1.c2db72f84c204p-2, -0x1.6f9ed69c399c7p-4, -0x1.4ee9af39c16ecp-2, -0x1.c96973b93bd86p-6, 0x1.b084bf1dc763bp-3, 0x1.bff160aba4bc3p-6, -0x1.0f21999627c5fp-3, -0x1.98ed2d2871d0ap-8, 0x1.36fc54ec8b106p-4, -0x1.f159dcb973ff4p-8, -0x1.2e3093b602a51p-5, 0x1.516f07b10e2cp-7, 0x1.ca8c3dcce54c3p-7, -0x1.ca18fbf2cc141p-8, -0x1.dda9bb9568c15p-9, 0x1.99ff0c3f2ed81p-9, 0x1.abb6031610513p-12, -0x1.ed5dcd1b49a3fp-11, 0x1.df29e5ea12845p-14, 0x1.6e8e301063e5ap-13, -0x1.0000dea4283e9p-14, -0x1.d3f0626b575afp-17, 0x1.7c64ba15d2346p-17, -0x1.1821ad345e7cp-20, -0x1.8b555407022a1p-21, 0x1.efcebf5a99b7bp-23, -0x1.6a61bcee28103p-26};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0xd.1023f92f7642ed3p-12L, 0x8.efb64365f630239p-8L, 0xa.9069c8d4a08344dp-6L, 0xd.c51f2ff5a43c97dp-5L, 0xa.329c8da32c99c9dp-4L, 0xe.16db97c26101ca7p-5L, -0xb.7cf6b4e1cce36cbp-7L, -0xa.774d79ce0b75fdfp-5L, -0xe.4b4b9dc9dec3204p-9L, 0xd.8425f8ee3b1d5bfp-6L, 0xd.ff8b055d25e15c1p-9L, -0x8.790cccb13e2f58ep-6L, -0xc.c76969438e84e18p-11L, 0x9.b7e2a76458832d7p-7L, -0xf.8acee5cb9ff9e4cp-11L, -0x9.71849db015288a6p-8L, 0xa.8b783d88715ff76p-10L, 0xe.5461ee672a6184ep-10L, -0xe.50c7df9660a0b0ep-11L, -0xe.ed4ddcab460a85bp-12L, 0xc.cff861f976c0535p-12L, 0xd.5db018b082895d2p-15L, -0xf.6aee68da4d1f9e1p-14L, 0xe.f94f2f509422907p-17L, 0xb.747180831f2d336p-16L, -0x8.0006f52141f4728p-17L, -0xe.9f83135abad7bfp-20L, 0xb.e325d0ae91a325cp-20L, -0x8.c10d69a2f3dfe1fp-23L, -0xc.5aaaa0381150b42p-24L, 0xf.7e75fad4cdbdbc5p-26L, -0xb.530de771408178bp-29L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.a2047f25eec85da6e57cd7f20965p-9Q, 0x1.1df6c86cbec60472edd73314093ap-5Q, 0x1.520d391a9410689a221d2a40ed0cp-3Q, 0x1.b8a3e5feb48792faed491d08e637p-2Q, 0x1.465391b4659339393dc6b44dd0b9p-1Q, 0x1.c2db72f84c20394e90d8314fee8dp-2Q, -0x1.6f9ed69c399c6d957cef0caf36cp-4Q, -0x1.4ee9af39c16ebfbef0c302e6791dp-2Q, -0x1.c96973b93bd864088cf77c5363e8p-6Q, 0x1.b084bf1dc763ab7d34b03cf7014cp-3Q, 0x1.bff160aba4bc2b81b5cb21d8ed3dp-6Q, -0x1.0f21999627c5eb1bdc396cd5510bp-3Q, -0x1.98ed2d2871d09c2ff301236b3aa5p-8Q, 0x1.36fc54ec8b1065ad541d9561e805p-4Q, -0x1.f159dcb973ff3c971dea81777e8cp-8Q, -0x1.2e3093b602a5114cced31fb3d21p-5Q, 0x1.516f07b10e2bfeeb35e5d488972dp-7Q, 0x1.ca8c3dcce54c309c6bfdafe5b818p-7Q, -0x1.ca18fbf2cc14161cd462d6382e8dp-8Q, -0x1.dda9bb9568c150b5b1b563e2a704p-9Q, 0x1.99ff0c3f2ed80a696d3f49d1ae83p-9Q, 0x1.abb6031610512ba452ab2c15607bp-12Q, -0x1.ed5dcd1b49a3f3c23377158c2ae9p-11Q, 0x1.df29e5ea1284520ed9350c7d7e2fp-14Q, 0x1.6e8e301063e5a66bc2dcbb672407p-13Q, -0x1.0000dea4283e8e4f97e320b5edbp-14Q, -0x1.d3f0626b575af7e0f5c7b70618f9p-17Q, 0x1.7c64ba15d23464b7681824c41ca1p-17Q, -0x1.1821ad345e7bfc3ef33cc03c406ap-20Q, -0x1.8b555407022a1683907685f46c79p-21Q, 0x1.efcebf5a99b7b789a7792201843ep-23Q, -0x1.6a61bcee28102f153c8290cebfbbp-26Q};
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, octuple_type>) {
-            return {boost::lexical_cast<octuple_type>("0.00318922092534773802976954756464595868706708675013142876787587817778694863119"), boost::lexical_cast<octuple_type>("0.0349077143236733464103014722402302000921824143050398414614005464773763780013"), boost::lexical_cast<octuple_type>("0.165064283488853117899125273056113481158483500234272324021359282902034099572"), boost::lexical_cast<octuple_type>("0.430312722846003813740392542435768462063397047803698677392464629118864929936"), boost::lexical_cast<octuple_type>("0.637356332083788898631985241299603053649859594081419812596775159322552430035"), boost::lexical_cast<octuple_type>("0.440290256886356900039086916357167928852780303513527257878988432216501129849"), boost::lexical_cast<octuple_type>("-0.0897510894024896428571871807744259743065924744558266014962471841522684784655"), boost::lexical_cast<octuple_type>("-0.327063310527917704646290567568911964175722891822881242814172353116733610255"), boost::lexical_cast<octuple_type>("-0.0279182081330282766826451959502687320433997121917473604153547976243684979156"), boost::lexical_cast<octuple_type>("0.211190693947104288720968016326883790092849142616767943925104282659239340555"), boost::lexical_cast<octuple_type>("0.0273402637527160413648524575720161796542902781950713022023150026811811035864"), boost::lexical_cast<octuple_type>("-0.132388305563810390450047414775649337509228781770602797879854902742212569323"), boost::lexical_cast<octuple_type>("-0.00623972275247487176567450339412002586544465631167876099076145808663824556181"), boost::lexical_cast<octuple_type>("0.0759242360442763158214849874394142246153040594610094335194031399951322105236"), boost::lexical_cast<octuple_type>("-0.00758897436885773763849489086463699579658697514499092540009716094367144606278"), boost::lexical_cast<octuple_type>("-0.0368883976917301423335266632089455431471874842970673083106406876512904740900"), boost::lexical_cast<octuple_type>("0.0102976596409559694116500058007661690052885626580366220885414734497334909977"), boost::lexical_cast<octuple_type>("0.0139937688598287310295045187367032972640984029172786898849010078360486452906"), boost::lexical_cast<octuple_type>("-0.00699001456341391667028424953651728833805785619964646907811575967502711102002"), boost::lexical_cast<octuple_type>("-0.00364427962149838993216900054093362938705533397335310866884121504669938973849"), boost::lexical_cast<octuple_type>("0.00312802338120626883166120255985467876782147190619360811745036081031020620657"), boost::lexical_cast<octuple_type>("0.000407896980849712836241747032340609578243195297231054671507139711098341190969"), boost::lexical_cast<octuple_type>("-0.000941021749359567588926645395363587540775474721673448050925027367949065706153"), boost::lexical_cast<octuple_type>("0.000114241520038722392644022809955566294583968434493647265287709142315097418924"), boost::lexical_cast<octuple_type>("0.000174787245225338180380175863766074687498602472861539989797195359589183047664"), boost::lexical_cast<octuple_type>("-0.0000610359662141093583516236915052221281195725998196591914396172281391485128503"), boost::lexical_cast<octuple_type>("-0.0000139456689882088934519907831199840198232527356919867533540870797045644631590"), boost::lexical_cast<octuple_type>("0.0000113366086612762585875884876288653699751947106820375366175784342881379088583"), boost::lexical_cast<octuple_type>("-0.00000104357134231160650152545473726261540488747893063567647154603268028625910132"), boost::lexical_cast<octuple_type>("-0.000000736365678545120551209969571972556364658544554584166332743356923285383067848"), boost::lexical_cast<octuple_type>("0.000000230878408685754586640541273294200612130630673586665552537254486473108851937"), boost::lexical_cast<octuple_type>("-0.0000000210933963010074309700057262360348990683629758459160530774534994952533728279")};
-        }
+       return {BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0031892209253477380297695475646459586870670867501314287678758781777869486255), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.034907714323673346410301472240230200092182414305039841461400546477376377996), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.16506428348885311789912527305611348115848350023427232402135928290203409966), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.43031272284600381374039254243576846206339704780369867739246462911886492889), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.63735633208378889863198524129960305364985959408141981259677515932255242966), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.44029025688635690003908691635716792885278030351352725787898843221650113068), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.089751089402489642857187180774425974306592474455826601496247184152268478657), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.32706331052791770464629056756891196417572289182288124281417235311673360956), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.027918208133028276682645195950268732043399712191747360415354797624368497971), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.21119069394710428872096801632688379009284914261676794392510428265923934071), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.027340263752716041364852457572016179654290278195071302202315002681181103625), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.13238830556381039045004741477564933750922878177060279787985490274221256881), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0062397227524748717656745033941200258654446563116787609907614580866382455691), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.075924236044276315821484987439414224615304059461009433519403139995132210368), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.007588974368857737638494890864636995796586975144990925400097160943671446065), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.036888397691730142333526663208945543147187484297067308310640687651290473968), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.010297659640955969411650005800766169005288562658036622088541473449733491006), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.013993768859828731029504518736703297264098402917278689884901007836048645298), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0069900145634139166702842495365172883380578561996464690781157596750271110103), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0036442796214983899321690005409336293870553339733531086688412150466993897338), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0031280233812062688316612025598546787678214719061936081174503608103102062028), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.00040789698084971283624174703234060957824319529723105467150713971109834118994), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.00094102174935956758892664539536358754077547472167344805092502736794906570513), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.00011424152003872239264402280995556629458396843449364726528770914231509741867), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.00017478724522533818038017586376607468749860247286153998979719535958918304821), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -6.1035966214109358351623691505222128119572599819659191439617228139148512866e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -1.3945668988208893451990783119984019823252735691986753354087079704564463183e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 1.1336608661276258587588487628865369975194710682037536617578434288137908852e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -1.0435713423116065015254547372626154048874789306356764715460326802862590987e-06), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -7.3636567854512055120996957197255636465854455458416633274335692328538306759e-07), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 2.3087840868575458664054127329420061213063067358666555253725448647310885248e-07), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -2.1093396301007430970005726236034899068362975845916053077453499495253372784e-08) };
     }
     if constexpr (p == 17) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.25d69p-9f, 0x1.a9bea4p-6f, 0x1.0cba66p-3f, 0x1.7b3d38p-2f, 0x1.38d48cp-1f, 0x1.0960bp-1f, 0x1.bf874ap-6f, -0x1.50335p-2f, -0x1.0346bcp-3f, 0x1.941794p-3f, 0x1.9e404p-4f, -0x1.03b7f2p-3f, -0x1.d3b162p-5f, 0x1.4c35cap-4f, 0x1.6d90b8p-6f, -0x1.80637cp-5f, -0x1.acbb0ep-9f, 0x1.7477f4p-6f, -0x1.8ed9ccp-9f, -0x1.19e68ap-7f, 0x1.850572p-9f, 0x1.2d9fa2p-9f, -0x1.78a90ep-10f, -0x1.581268p-12f, 0x1.ccd01ap-12f, -0x1.adaa96p-16f, -0x1.582268p-14f, 0x1.85029cp-16f, 0x1.d5219cp-18f, -0x1.2e638p-18f, 0x1.43e648p-22f, 0x1.3d94aap-22f, -0x1.69ce4ap-24f, 0x1.f36b16p-28f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.25d68f81bd86cp-9, 0x1.a9bea4085cef4p-6, 0x1.0cba6633a3a6dp-3, 0x1.7b3d3861245dp-2, 0x1.38d48c64aa0dbp-1, 0x1.0960af0f4068ep-1, 0x1.bf874a24b1d56p-6, -0x1.50335073492d2p-2, -0x1.0346bb1b97634p-3, 0x1.9417930ab08a3p-3, 0x1.9e403f27b713fp-4, -0x1.03b7f2067576fp-3, -0x1.d3b162866891bp-5, 0x1.4c35ca8307eb6p-4, 0x1.6d90b88bab06p-6, -0x1.80637c4a935c8p-5, -0x1.acbb0e1b24a77p-9, 0x1.7477f35c89773p-6, -0x1.8ed9cce7691cbp-9, -0x1.19e6894a383d1p-7, 0x1.8505717311392p-9, 0x1.2d9fa2834b37bp-9, -0x1.78a90e5fc8eecp-10, -0x1.58126708ae49dp-12, 0x1.ccd01a3d65145p-12, -0x1.adaa9541cd341p-16, -0x1.5822674fd0b1ap-14, 0x1.85029b61ff0fcp-16, 0x1.d5219c45df32ep-18, -0x1.2e63809757f53p-18, 0x1.43e648c7ce72fp-22, 0x1.3d94aa0876b2dp-22, -0x1.69ce4aed2f58ep-24, 0x1.f36b16a008a29p-28};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0x9.2eb47c0dec36183p-12L, 0xd.4df52042e779eb7p-9L, 0x8.65d3319d1d36a45p-6L, 0xb.d9e9c30922e8138p-5L, 0x9.c6a46325506d79dp-4L, 0x8.4b05787a03472d6p-4L, 0xd.fc3a51258eaaed3p-9L, -0xa.819a839a4968eafp-5L, -0x8.1a35d8dcbb19dd2p-6L, 0xc.a0bc9855845188cp-6L, 0xc.f201f93db89f96ep-7L, -0x8.1dbf9033abb79d9p-6L, -0xe.9d8b1433448d469p-8L, 0xa.61ae54183f5b11cp-7L, 0xb.6c85c45d582fc12p-9L, -0xc.031be2549ae3edfp-8L, -0xd.65d870d9253b88dp-12L, 0xb.a3bf9ae44bb963dp-9L, -0xc.76ce673b48e5651p-12L, -0x8.cf344a51c1e8512p-10L, 0xc.282b8b9889c92c5p-12L, 0x9.6cfd141a59bd766p-12L, -0xb.c54872fe4775c65p-13L, -0xa.c0933845724e821p-15L, 0xe.6680d1eb28a2645p-15L, -0xd.6d54aa0e69a09cdp-19L, -0xa.c1133a7e858d207p-17L, 0xc.2814db0ff87dcc6p-19L, 0xe.a90ce22ef996e32p-21L, -0x9.731c04babfa9664p-21L, 0xa.1f32463e73979d5p-25L, 0x9.eca55043b596609p-25L, -0xb.4e7257697ac7376p-27L, 0xf.9b58b5004514458p-31L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.25d68f81bd86c306bc9043f43f4p-9Q, 0x1.a9bea4085cef3d6d79a074d9709ep-6Q, 0x1.0cba6633a3a6d489f4c961323b24p-3Q, 0x1.7b3d3861245d02709eb04b0b2b39p-2Q, 0x1.38d48c64aa0daf396243783e95bep-1Q, 0x1.0960af0f4068e5ac2ea6e7c9135p-1Q, 0x1.bf874a24b1d55da571e39f2bf7e7p-6Q, -0x1.50335073492d1d5e6945d8cdee28p-2Q, -0x1.0346bb1b97633ba3dcc115a9814cp-3Q, 0x1.9417930ab08a311830b19e500034p-3Q, 0x1.9e403f27b713f2db7263ac22d15fp-4Q, -0x1.03b7f2067576f3b2927e9c5889d3p-3Q, -0x1.d3b162866891a8d294e6e9eb979p-5Q, 0x1.4c35ca8307eb62387847e8508ae5p-4Q, 0x1.6d90b88bab05f824bb4e728b7a1p-6Q, -0x1.80637c4a935c7dbdd09fd2c6d8fdp-5Q, -0x1.acbb0e1b24a7711aad0c2cc58d1fp-9Q, 0x1.7477f35c89772c79eec161a3cdd2p-6Q, -0x1.8ed9cce7691caca1362d6d7abefcp-9Q, -0x1.19e6894a383d0a23e4d18574889p-7Q, 0x1.85057173113925897d4027a40b6ep-9Q, 0x1.2d9fa2834b37aecc772ff5c2d7b1p-9Q, -0x1.78a90e5fc8eeb8c9dbcf2179c3bbp-10Q, -0x1.58126708ae49d0421a9c690b913dp-12Q, 0x1.ccd01a3d65144c8ab80302b0f5dbp-12Q, -0x1.adaa9541cd34139a00a6638e9bf6p-16Q, -0x1.5822674fd0b1a40e647125cde434p-14Q, 0x1.85029b61ff0fb98b3294c269c9e6p-16Q, 0x1.d5219c45df32dc63e76e89984d9dp-18Q, -0x1.2e63809757f52cc8ed09e415ace1p-18Q, 0x1.43e648c7ce72f3a94ea0d55898bap-22Q, 0x1.3d94aa0876b2cc113a8ea22e3eecp-22Q, -0x1.69ce4aed2f58e6ecb8a211f55ad1p-24Q, 0x1.f36b16a008a288af85eb1e1cec02p-28Q};
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, octuple_type>) {
-            return {boost::lexical_cast<octuple_type>("0.00224180700103731285353596267707443691406219188056037073325053118133419193342"), boost::lexical_cast<octuple_type>("0.0259853937036060433891486459172078831547394452487824129439994827687663725129"), boost::lexical_cast<octuple_type>("0.131214903307824406577550623185906996014429360925997853006700439459033631661"), boost::lexical_cast<octuple_type>("0.370350724152641150449254819072188644947707887689680382365042593579529628290"), boost::lexical_cast<octuple_type>("0.610996615684622818188667886767937208273709389335872629137178390490835290734"), boost::lexical_cast<octuple_type>("0.518315764056937839325453852808596804621681719771841640243990498683288900340"), boost::lexical_cast<octuple_type>("0.0273149704032936350043125071914758648035046981896456300367294282283271222511"), boost::lexical_cast<octuple_type>("-0.328320748363961736090966534072506176758159769815155802467913052689676377760"), boost::lexical_cast<octuple_type>("-0.126599752215882702874467911093382550505396626010408616210372832359164928283"), boost::lexical_cast<octuple_type>("0.197310589565010992785404704478193014255142241413564691712228422600456673716"), boost::lexical_cast<octuple_type>("0.101135489177470272150969985643343480219662254549966487610943796293105029624"), boost::lexical_cast<octuple_type>("-0.126815691778286311094857112866233168038479218591501706573213748994956827246"), boost::lexical_cast<octuple_type>("-0.0570914196316769272891123947865138232416116086984534705399014464059382899408"), boost::lexical_cast<octuple_type>("0.0811059866541608850796588574855542920102436419095449919402067822775070461335"), boost::lexical_cast<octuple_type>("0.0223123361781037959533913605953481375623224211409368924402086919318268997481"), boost::lexical_cast<octuple_type>("-0.0469224383892697373330089705921140050713876812549803060287843927826168188238"), boost::lexical_cast<octuple_type>("-0.00327095553581929378165536022217749445206952595806160939280927575122449701285"), boost::lexical_cast<octuple_type>("0.0227336765839462703184561624478844896990671374133833949802486413275635089855"), boost::lexical_cast<octuple_type>("-0.00304298998135463706859248263790720607863339545722509658828788135585314667137"), boost::lexical_cast<octuple_type>("-0.00860292152032285483171370641324365991792673628427173061192098670257230281191"), boost::lexical_cast<octuple_type>("0.00296799669152609487280648506000803826995946384654837899504419503429102573503"), boost::lexical_cast<octuple_type>("0.00230120524215354562430205986903842360424197668018944747606476493728483725055"), boost::lexical_cast<octuple_type>("-0.00143684530480297612622289040298038490350367453072993580956143471121236432705"), boost::lexical_cast<octuple_type>("-0.000328132519409837971395444401752011507581240244272874970019565158958075253614"), boost::lexical_cast<octuple_type>("0.000439465427768643677838567752731784163228924931973889217946591075762286390503"), boost::lexical_cast<octuple_type>("-0.0000256101095665484588272989121094992022166408206153190965517841374523415859860"), boost::lexical_cast<octuple_type>("-0.0000820480320245339183909548257628218986613627304963676433868959364213432243666"), boost::lexical_cast<octuple_type>("0.0000231868137987459508448206820570627757210669517409189533853073478931042782802"), boost::lexical_cast<octuple_type>("0.00000699060098507675127320454970085537862776275858590205796402748138050877941586"), boost::lexical_cast<octuple_type>("-0.00000450594247722298819410226820637831212971357260071649994491841668706683585071"), boost::lexical_cast<octuple_type>("0.000000301654960999455741560520759487993976347616870521764689770270618984715407855"), boost::lexical_cast<octuple_type>("0.000000295770093331685675497990525881615136787034562892431730735463949569521998500"), boost::lexical_cast<octuple_type>("-0.0000000842394844600268017878707129692287706841031094222279962259313341617779208118"), boost::lexical_cast<octuple_type>("0.00000000726749296856160811087976744140903503415858171978979108889204640807029047656")};
-        }
+       return {BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0022418070010373128535359626770744369140621918805603707332505311813341919259), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.025985393703606043389148645917207883154739445248782412943999482768766372542), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.1312149033078244065775506231859069960144293609259978530067004394590336311), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.37035072415264115044925481907218864494770788768968038236504259357952962858), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.61099661568462281818866788676793720827370938933587262913717839049083529043), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.51831576405693783932545385280859680462168171977184164024399049868328890005), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.027314970403293635004312507191475864803504698189645630036729428228327122309), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.32832074836396173609096653407250617675815976981515580246791305268967637817), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.12659975221588270287446791109338255050539662601040861621037283235916492881), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.19731058956501099278540470447819301425514224141356469171222842260045667421), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.10113548917747027215096998564334348021966225454996648761094379629310502982), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.12681569177828631109485711286623316803847921859150170657321374899495682695), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.057091419631676927289112394786513823241611608698453470539901446405938289849), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.081105986654160885079658857485554292010243641909544991940206782277507046299), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.022312336178103795953391360595348137562322421140936892440208691931826899684), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.04692243838926973733300897059211400507138768125498030602878439278261681888), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0032709555358192937816553602221774944520695259580616093928092757512244970215), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.022733676583946270318456162447884489699067137413383394980248641327563508924), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.003042989981354637068592482637907206078633395457225096588287881355853146664), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0086029215203228548317137064132436599179267362842717306119209867025723028123), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0029679966915260948728064850600080382699594638465483789950441950342910257421), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0023012052421535456243020598690384236042419766801894474760647649372848372532), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0014368453048029761262228904029803849035036745307299358095614347112123643258), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0003281325194098379713954444017520115075812402442728749700195651589580752544), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.00043946542776864367783856775273178416322892493197388921794659107576228639092), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -2.561010956654845882729891210949920221664082061531909655178413745234158599e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -8.2048032024533918390954825762821898661362730496367643386895936421343224507e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 2.3186813798745950844820682057062775721066951740918953385307347893104278256e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 6.9906009850767512732045497008553786277627585859020579640274813805087794281e-06), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -4.5059424772229881941022682063783121297135726007164999449184166870668358606e-06), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 3.016549609994557415605207594879939763476168705217646897702706189847154081e-07), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 2.9577009333168567549799052588161513678703456289243173073546394956952199848e-07), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -8.4239484460026801787870712969228770684103109422227996225931334161777920896e-08), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 7.2674929685616081108797674414090350341585817197897910888920464080702904824e-09) };
     }
     if constexpr (p == 18) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.9d3864p-10f, 0x1.3c05f8p-6f, 0x1.a84c62p-4f, 0x1.423b32p-2f, 0x1.24c67cp-1f, 0x1.24c33p-1f, 0x1.2d835p-3f, -0x1.2cb3a6p-2f, -0x1.bb5a5cp-3f, 0x1.323edep-3f, 0x1.562ebap-3f, -0x1.7a31p-4f, -0x1.b541d8p-4f, 0x1.09c72ep-4f, 0x1.d35d24p-5f, -0x1.6cc216p-5f, -0x1.84d84cp-6f, 0x1.b4f90cp-6f, 0x1.9a65bep-8f, -0x1.ababc2p-7f, 0x1.f19208p-14f, 0x1.43f78cp-8f, -0x1.2544ep-10f, -0x1.5f6de6p-10f, 0x1.497f3cp-11f, 0x1.bfe9bap-13f, -0x1.a098a2p-13f, -0x1.49d5fp-23f, 0x1.39d678p-15f, -0x1.1de76cp-17f, -0x1.bf4c72p-19f, 0x1.dac908p-20f, -0x1.4a5a66p-24f, -0x1.f9216ep-24f, 0x1.079c6ap-25f, -0x1.58b01ap-29f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.9d386358a1875p-10, 0x1.3c05f73c5b367p-6, 0x1.a84c610f33b44p-4, 0x1.423b3247213b9p-2, 0x1.24c67bbcaad51p-1, 0x1.24c32fbf17436p-1, 0x1.2d834f99026eap-3, -0x1.2cb3a5153503ap-2, -0x1.bb5a5b1e13b57p-3, 0x1.323ede758da42p-3, 0x1.562eba30ba3dbp-3, -0x1.7a30ff6ce5272p-4, -0x1.b541d802db16ep-4, 0x1.09c72d78f0163p-4, 0x1.d35d236774d12p-5, -0x1.6cc216694aaa1p-5, -0x1.84d84c9eacf2cp-6, 0x1.b4f90c6dc9842p-6, 0x1.9a65be90d86a5p-8, -0x1.ababc1ea3f978p-7, 0x1.f19207685977fp-14, 0x1.43f78b1e4d853p-8, -0x1.2544e0deeca72p-10, -0x1.5f6de508b2306p-10, 0x1.497f3c70a07ccp-11, 0x1.bfe9ba59913cep-13, -0x1.a098a12371c0dp-13, -0x1.49d5efd42da9p-23, 0x1.39d678c2c06afp-15, -0x1.1de76b2193bedp-17, -0x1.bf4c72e2a2d94p-19, 0x1.dac907ddfd9dbp-20, -0x1.4a5a655290e68p-24, -0x1.f9216d4e4d83bp-24, 0x1.079c6a0fc4518p-25, -0x1.58b0195a8266dp-29};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0xc.e9c31ac50c3a483p-13L, 0x9.e02fb9e2d9b3a9bp-9L, 0xd.426308799da225cp-7L, 0xa.11d9923909dc42bp-5L, 0x9.2633dde556a88a3p-4L, 0x9.26197df8ba1b1b2p-4L, 0x9.6c1a7cc81374c03p-6L, -0x9.659d28a9a81cd3ap-5L, -0xd.dad2d8f09dab48bp-6L, 0x9.91f6f3ac6d21107p-6L, 0xa.b175d185d1ed60ap-6L, -0xb.d187fb672938eb2p-7L, -0xd.aa0ec016d8b6c08p-7L, 0x8.4e396bc780b1464p-7L, 0xe.9ae91b3ba68905ep-8L, -0xb.6610b34a5550677p-8L, -0xc.26c264f56795d72p-9L, 0xd.a7c8636e4c20f3dp-9L, 0xc.d32df486c3529e3p-11L, -0xd.5d5e0f51fcbc222p-10L, 0xf.8c903b42cbbfa1ep-17L, 0xa.1fbc58f26c29bbap-11L, -0x9.2a2706f76538d5fp-13L, -0xa.fb6f284591832p-13L, 0xa.4bf9e38503e5e52p-14L, 0xd.ff4dd2cc89e6cb3p-16L, -0xd.04c5091b8e0651fp-16L, -0xa.4eaf7ea16d480ecp-26L, 0x9.ceb3c6160357432p-18L, -0x8.ef3b590c9df6482p-20L, -0xd.fa63971516c9e77p-22L, 0xe.d6483eefeced63bp-23L, -0xa.52d32a948733d34p-27L, -0xf.c90b6a726c1d6d6p-27L, 0x8.3ce3507e228be57p-28L, -0xa.c580cad41336728p-32L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.9d386358a187490511616014e787p-10Q, 0x1.3c05f73c5b367536d2be9893ed8cp-6Q, 0x1.a84c610f33b444b779a9b1758c69p-4Q, 0x1.423b3247213b88555f9f2ada7d8ap-2Q, 0x1.24c67bbcaad511453636985416f3p-1Q, 0x1.24c32fbf17436364ee6d86ce0b36p-1Q, 0x1.2d834f99026e9806c6f6c1aa6cb3p-3Q, -0x1.2cb3a51535039a741562ba69c7a8p-2Q, -0x1.bb5a5b1e13b56915364cb7d6d1bfp-3Q, 0x1.323ede758da4220dcba304aad9d9p-3Q, 0x1.562eba30ba3dac1311ece1a1884ap-3Q, -0x1.7a30ff6ce5271d64766823319bd4p-4Q, -0x1.b541d802db16d80f141c678b2993p-4Q, 0x1.09c72d78f01628c7ccd127058828p-4Q, 0x1.d35d236774d120bc0fddfe320959p-5Q, -0x1.6cc216694aaa0ced2f850c2b3eb7p-5Q, -0x1.84d84c9eacf2bae4fd091b9bdb4fp-6Q, 0x1.b4f90c6dc9841e7a702107e1aca3p-6Q, 0x1.9a65be90d86a53c665da90605941p-8Q, -0x1.ababc1ea3f978443c6511c976c7fp-7Q, 0x1.f19207685977f43b68af0530733ap-14Q, 0x1.43f78b1e4d853774466d94263915p-8Q, -0x1.2544e0deeca71abd544eac93fa45p-10Q, -0x1.5f6de508b23063ffd5522faa2f1ap-10Q, 0x1.497f3c70a07cbca34a7835790cbfp-11Q, 0x1.bfe9ba59913cd96563f593913af3p-13Q, -0x1.a098a12371c0ca3dcc2d68b00891p-13Q, -0x1.49d5efd42da901d7159610c4d152p-23Q, 0x1.39d678c2c06ae863ef3b97fa7d6p-15Q, -0x1.1de76b2193bec903a9d077f1666ep-17Q, -0x1.bf4c72e2a2d93cedea468c1c5543p-19Q, 0x1.dac907ddfd9dac76e76088418dc5p-20Q, -0x1.4a5a655290e67a67e8d8672b7916p-24Q, -0x1.f9216d4e4d83adac1cb13466b74bp-24Q, 0x1.079c6a0fc4517cae3d72b9596e6p-25Q, -0x1.58b0195a8266ce508d99fc62d4eep-29Q};
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, octuple_type>) {
-            return {boost::lexical_cast<octuple_type>("0.00157631021844076043154074492993977774767075371099166036368442986184714001537"), boost::lexical_cast<octuple_type>("0.0192885317241463770592139171582905241995466702528849757223671483332142575124"), boost::lexical_cast<octuple_type>("0.103588465822423596224191049193725359647069655522024167297622418469656394177"), boost::lexical_cast<octuple_type>("0.314678941337031699057199825565257993178670619048937450949130751036740690695"), boost::lexical_cast<octuple_type>("0.571826807766607223481858937090062341939367374313093056129532404803265328819"), boost::lexical_cast<octuple_type>("0.571801654888651335289111999406596502566804788281852506075939526421405556433"), boost::lexical_cast<octuple_type>("0.147223111969928141575097727108107231255786410735570138780167713584411016265"), boost::lexical_cast<octuple_type>("-0.293654040736558744247903099498115072393571072903505323966175230801212578403"), boost::lexical_cast<octuple_type>("-0.216480934005142971123767862566827147143793723566949240838869239366378506250"), boost::lexical_cast<octuple_type>("0.149533975565377789350930173891366720880481669189376561026194307191290248158"), boost::lexical_cast<octuple_type>("0.167081312763257404514931813995013474532420564635398808315225063337013902642"), boost::lexical_cast<octuple_type>("-0.0923318841508462806042937255865945973143184800014456961207450846746206498455"), boost::lexical_cast<octuple_type>("-0.106752246659828485593220058161498486138526640462411208391770205467847935365"), boost::lexical_cast<octuple_type>("0.0648872162119054428194757795514191146312938211663414784613714984515877764896"), boost::lexical_cast<octuple_type>("0.0570512477385368841209076884649962226059622612043103852460067642320755043632"), boost::lexical_cast<octuple_type>("-0.0445261419029823247155614355974465349297147789143983359275503466820231489272"), boost::lexical_cast<octuple_type>("-0.0237332103958600010327520958266521611019751933071349023307156579014300914190"), boost::lexical_cast<octuple_type>("0.0266707059264705902998790863167202034320789599993607281336347152037595652919"), boost::lexical_cast<octuple_type>("0.00626216795430570748523609314449788250199032520474501319026805231525752058555"), boost::lexical_cast<octuple_type>("-0.0130514809466120017727763644760080716975519105450757166660613358038629139862"), boost::lexical_cast<octuple_type>("0.000118630033858117465730174159216181908454489941745231740518561572996617939506"), boost::lexical_cast<octuple_type>("0.00494334360546673813066552951680297483429963831336647776529520326003067700242"), boost::lexical_cast<octuple_type>("-0.00111873266699249707280065885523865018231806048258497014551268711985227900418"), boost::lexical_cast<octuple_type>("-0.00134059629833610662951756722825158360982304452468598664032394269120723888750"), boost::lexical_cast<octuple_type>("0.000628465682965145712561944988542083821755102279630158287434965288076478383268"), boost::lexical_cast<octuple_type>("0.000213581561910340688403905281434192602587320032599646652254344051060271497781"), boost::lexical_cast<octuple_type>("-0.000198648552311747948579824541636248955492779788026401787613960521573218466250"), boost::lexical_cast<octuple_type>("-0.000000153591712353472467506977033587671719370047242702151323658728810220957329769"), boost::lexical_cast<octuple_type>("0.0000374123788074003818109220813803539395230429261579398503073136385132849832575"), boost::lexical_cast<octuple_type>("-0.00000852060253744669520391925491165552302243759695622637651230591706524073534413"), boost::lexical_cast<octuple_type>("-0.00000333263447888582188878245203334103682731150590779649843982933727956405960650"), boost::lexical_cast<octuple_type>("0.00000176871298362761545587632873075537517641250135911405881545310061923499126827"), boost::lexical_cast<octuple_type>("-0.0000000769163268988517614600015287853959840581739758815652511676990865187416269746"), boost::lexical_cast<octuple_type>("-0.000000117609876702823169845098235656129256134757977769539695352814136780995583426"), boost::lexical_cast<octuple_type>("0.0000000306883586304517480093547829493397537245017978789457449293057011634442052915"), boost::lexical_cast<octuple_type>("-0.00000000250793445494859826719517318314712673180631714486827581994140326785823293114")};
-        }
+       return {BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0015763102184407604315407449299397777476707537109916603636844298618471400136), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.019288531724146377059213917158290524199546670252884975722367148333214257583), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.10358846582242359622419104919372535964706965552202416729762241846965639407), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.3146789413370316990571998255652579931786706190489374509491307510367406906), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.57182680776660722348185893709006234193936737431309305612953240480326532941), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.5718016548886513352891119994065965025668047882818525060759395264214055574), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.14722311196992814157509772710810723125578641073557013878016771358441101668), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.29365404073655874424790309949811507239357107290350532396617523080121257803), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.21648093400514297112376786256682714714379372356694924083886923936637850636), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.14953397556537778935093017389136672088048166918937656102619430719129024846), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.16708131276325740451493181399501347453242056463539880831522506333701390259), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.092331884150846280604293725586594597314318480001445696120745084674620649946), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.10675224665982848559322005816149848613852664046241120839177020546784793523), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.06488721621190544281947577955141911463129382116634147846137149845158777673), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.057051247738536884120907688464996222605962261204310385246006764232075504463), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.044526141902982324715561435597446534929714778914398335927550346682023149009), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.023733210395860001032752095826652161101975193307134902330715657901430091468), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.026670705926470590299879086316720203432078959999360728133634715203759565359), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0062621679543057074852360931444978825019903252047450131902680523152575205897), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.013051480946612001772776364476008071697551910545075716666061335803862913986), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.00011863003385811746573017415921618190845448994174523174051856157299661793944), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0049433436054667381306655295168029748342996383133664777652952032600306770112), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0011187326669924970728006588552386501823180604825849701455126871198522790015), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0013405962983361066295175672282515836098230445246859866403239426912072388874), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.00062846568296514571256194498854208382175510227963015828743496528807647838152), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0002135815619103406884039052814341926025873200325996466522543440510602714976), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.00019864855231174794857982454163624895549277978802640178761396052157321846575), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -1.5359171235347246750697703358767171937004724270215132365872881022095732925e-07), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 3.7412378807400381810922081380353939523042926157939850307313638513284983136e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -8.5206025374466952039192549116555230224375969562263765123059170652407353738e-06), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -3.3326344788858218887824520333410368273115059077964984398293372795640596047e-06), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 1.7687129836276154558763287307553751764125013591140588154531006192349912666e-06), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -7.6916326898851761460001528785395984058173975881565251167699086518741626737e-08), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -1.1760987670282316984509823565612925613475797776953969535281413678099558364e-07), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 3.0688358630451748009354782949339753724501797878945744929305701163444205366e-08), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -2.5079344549485982671951731831471267318063171448682758199414032678582329327e-09) };
     }
     if constexpr (p == 19) {
-        if constexpr (std::is_same_v<Real, float>) {
-            return {0x1.22a192p-10f, 0x1.d3f68ap-7f, 0x1.4cea48p-4f, 0x1.0ebbd8p-2f, 0x1.0c82ecp-1f, 0x1.34129ep-1f, 0x1.0b280cp-2f, -0x1.d32194p-3f, -0x1.24b2e2p-2f, 0x1.31c694p-4f, 0x1.b2e46cp-3f, -0x1.12957ap-5f, -0x1.246cd4p-3f, 0x1.c3f126p-6f, 0x1.63f856p-4f, -0x1.b2323ep-6f, -0x1.7629ccp-5f, 0x1.6248a8p-6f, 0x1.3d72f2p-6f, -0x1.ca5f1cp-7f, -0x1.807eap-8f, 0x1.cd6c24p-8f, 0x1.93274ep-11f, -0x1.604346p-9f, 0x1.66699p-12f, 0x1.81c5bep-11f, -0x1.1156b8p-12f, -0x1.054e8ap-13f, 0x1.6d608ep-14f, 0x1.56a79p-18f, -0x1.172d04p-16f, 0x1.941ff2p-19f, 0x1.9b3988p-20f, -0x1.7070fep-21f, 0x1.f1373cp-27f, 0x1.8e4f58p-25f, -0x1.7f97c4p-27f, 0x1.dc770ep-31f};
-        }
-        if constexpr (std::is_same_v<Real, double>) {
-            return {0x1.22a1917fed85ap-10, 0x1.d3f6896603bf4p-7, 0x1.4cea4765b114ap-4, 0x1.0ebbd74f124f2p-2, 0x1.0c82ecc416391p-1, 0x1.34129e60b6e3p-1, 0x1.0b280be54f8b7p-2, -0x1.d32194b53c804p-3, -0x1.24b2e1dd4c73ep-2, 0x1.31c6940f7edfap-4, 0x1.b2e46c1684042p-3, -0x1.12957a28f5bb3p-5, -0x1.246cd3943959bp-3, 0x1.c3f126f461d98p-6, 0x1.63f8568e9e6ecp-4, -0x1.b2323dbfdcbe7p-6, -0x1.7629cb842f99bp-5, 0x1.6248a775ca66p-6, 0x1.3d72f2476d004p-6, -0x1.ca5f1bf2f3244p-7, -0x1.807e9f533b217p-8, 0x1.cd6c23ae5d8f9p-8, 0x1.93274e99dc9b5p-11, -0x1.6043462e3e51ap-9, 0x1.66698fcf3c249p-12, 0x1.81c5be1857466p-11, -0x1.1156b7a432a66p-12, -0x1.054e8a6af00d7p-13, 0x1.6d608dedb3cf6p-14, 0x1.56a78fb9bd527p-18, -0x1.172d0353b3f12p-16, 0x1.941ff236730f1p-19, 0x1.9b39878b95663p-20, -0x1.7070fedc9cdedp-21, 0x1.f1373b9dbeafap-27, 0x1.8e4f570c878dep-25, -0x1.7f97c3aa5d9ep-27, 0x1.dc770dc2ed00bp-31};
-        }
-        if constexpr (std::is_same_v<Real, long double>) {
-            return {0x9.150c8bff6c2cf0bp-13L, 0xe.9fb44b301dfa184p-10L, 0xa.67523b2d88a4cd2p-7L, 0x8.75deba789279273p-5L, 0x8.64176620b1c8a9ap-4L, 0x9.a094f305b717f7bp-4L, 0x8.59405f2a7c5b569p-5L, -0xe.990ca5a9e402365p-6L, -0x9.25970eea639ef9ap-5L, 0x9.8e34a07bf6fd17cp-7L, 0xd.972360b420211e3p-6L, -0x8.94abd147add99bfp-8L, -0x9.23669ca1cacd462p-6L, 0xe.1f8937a30ecc2f7p-9L, 0xb.1fc2b474f37606ap-7L, -0xd.9191edfee5f3727p-9L, -0xb.b14e5c217ccd592p-8L, 0xb.12453bae532fcd5p-9L, 0x9.eb97923b6802088p-9L, -0xe.52f8df979921d82p-10L, -0xc.03f4fa99d90b962p-11L, 0xe.6b611d72ec7ca7cp-11L, 0xc.993a74cee4da67fp-14L, -0xb.021a3171f28cdccp-12L, 0xb.334c7e79e124bccp-15L, 0xc.0e2df0c2ba32ef3p-14L, -0x8.8ab5bd21953315ep-15L, -0x8.2a745357806b795p-16L, 0xb.6b046f6d9e7b04p-17L, 0xa.b53c7dcdea9365p-21L, -0x8.b9681a9d9f88fe1p-19L, 0xc.a0ff91b39878443p-22L, 0xc.d9cc3c5cab31a21p-23L, -0xb.8387f6e4e6f68p-24L, 0xf.89b9dcedf57d09dp-30L, 0xc.727ab8643c6ec27p-28L, -0xb.fcbe1d52ecefc57p-30L, 0xe.e3b86e176805b46p-34L};
-        }
-        #ifdef BOOST_HAS_FLOAT128
-        if constexpr (std::is_same_v<Real, boost::multiprecision::float128>) {
-            return {0x1.22a1917fed859e160446bb7b167ap-10Q, 0x1.d3f6896603bf4308e8ccc5a30641p-7Q, 0x1.4cea4765b11499a3de1dc5fdc4b7p-4Q, 0x1.0ebbd74f124f24e597d3a5bc26dbp-2Q, 0x1.0c82ecc4163915332b81143283e8p-1Q, 0x1.34129e60b6e2fef58b66c45f7099p-1Q, 0x1.0b280be54f8b6ad2d41e0f33532ep-2Q, -0x1.d32194b53c8046c9a7b9b8714cebp-3Q, -0x1.24b2e1dd4c73df34e82deb7bb6c6p-2Q, 0x1.31c6940f7edfa2f8c6ddc9cd2aefp-4Q, 0x1.b2e46c16840423c52b33ff7476eep-3Q, -0x1.12957a28f5bb337e3e66ea6f23e6p-5Q, -0x1.246cd3943959a8c450bf5ca92b86p-3Q, 0x1.c3f126f461d985ee9de87f3424e5p-6Q, 0x1.63f8568e9e6ec0d34220dce2e186p-4Q, -0x1.b2323dbfdcbe6e4ed8b2320fb129p-6Q, -0x1.7629cb842f99ab236f8e908d21c2p-5Q, 0x1.6248a775ca65f9a99ecab76ed61p-6Q, 0x1.3d72f2476d00410fe80cb42bd72bp-6Q, -0x1.ca5f1bf2f3243b0308970f1f944p-7Q, -0x1.807e9f533b2172c38f0c60523009p-8Q, 0x1.cd6c23ae5d8f94f8e6c997306168p-8Q, 0x1.93274e99dc9b4cfea213c9163decp-11Q, -0x1.6043462e3e519b97ce417a7ac3b3p-9Q, 0x1.66698fcf3c2497984ab865b5b6acp-12Q, 0x1.81c5be1857465de5530984af43cbp-11Q, -0x1.1156b7a432a662bbb70ff712e064p-12Q, -0x1.054e8a6af00d6f29e88cd98738bep-13Q, 0x1.6d608dedb3cf6080fb9e6ef72893p-14Q, 0x1.56a78fb9bd526ca09fc616b1b8ap-18Q, -0x1.172d0353b3f11fc1e8818be3f7a7p-16Q, 0x1.941ff236730f0886ee4074951d94p-19Q, 0x1.9b39878b9566344204396825f773p-20Q, -0x1.7070fedc9cdecfffd4c6dc5d1fe5p-21Q, 0x1.f1373b9dbeafa1390279c531a649p-27Q, 0x1.8e4f570c878dd84d17b935d5f69ap-25Q, -0x1.7f97c3aa5d9df8ae90e909fae15p-27Q, 0x1.dc770dc2ed00b68b9c525506b211p-31Q};
-        }
-        #endif
-        if constexpr (std::is_same_v<Real, octuple_type>) {
-            return {boost::lexical_cast<octuple_type>("0.00110866976318171057109915419520971516424529967777343593213545529038383924770"), boost::lexical_cast<octuple_type>("0.0142810984507643973743988915295019923474566344216366595787071599110771075191"), boost::lexical_cast<octuple_type>("0.0812781132654595506529630678490162483984497997102862036649772686406019150041"), boost::lexical_cast<octuple_type>("0.264388431740896784674810038028942687386237780721192071841738581477351352687"), boost::lexical_cast<octuple_type>("0.524436377464654915336057597548406462604463364104807211639316023628078258263"), boost::lexical_cast<octuple_type>("0.601704549127537894886707713592180262053656563958596329331393143392083219576"), boost::lexical_cast<octuple_type>("0.260894952651038829287245667531052832417267310130190773992521389876582446158"), boost::lexical_cast<octuple_type>("-0.228091394215482646374632577605463720709378723708642590953482241776619580080"), boost::lexical_cast<octuple_type>("-0.285838631755826241854597569502898423721735609558833514992211937357294676905"), boost::lexical_cast<octuple_type>("0.0746522697081032663676343311187881900586586614973190965636539995134773660042"), boost::lexical_cast<octuple_type>("0.212349743306278488809060856705982419707707420087883944841690869803668388649"), boost::lexical_cast<octuple_type>("-0.0335185419023028786816938841878573150697784507523896681981403258573481442235"), boost::lexical_cast<octuple_type>("-0.142785695038736574977960273162611281299849770615242850862756243341853036336"), boost::lexical_cast<octuple_type>("0.0275843506256286687501474352016219865537447459696342308076281830983836771416"), boost::lexical_cast<octuple_type>("0.0869067555558122324884764542880844303478520800246819275964035297492772454078"), boost::lexical_cast<octuple_type>("-0.0265012362501230408990183584367638736107506801768674780817134564719233152649"), boost::lexical_cast<octuple_type>("-0.0456742262772309080564544421429579601793893573211563005088010978423298835500"), boost::lexical_cast<octuple_type>("0.0216237674095850471303298425717237235431809706785875254257102081949907179885"), boost::lexical_cast<octuple_type>("0.0193755498891761276463709435445799981449688509587582554640696372421676825877"), boost::lexical_cast<octuple_type>("-0.0139883886785351416325040123524866252191681386745309583680836668669699906947"), boost::lexical_cast<octuple_type>("-0.00586692228101217472658449343605437377381460834080875817737276517150642852313"), boost::lexical_cast<octuple_type>("0.00704074736710524315301451120740062010940168989766538307822939808316234678585"), boost::lexical_cast<octuple_type>("0.000768954359257548355974913914867395516347794708603940612954642251648623392855"), boost::lexical_cast<octuple_type>("-0.00268755180070158200395736385507039863653403892098247829017026719960594838510"), boost::lexical_cast<octuple_type>("0.000341808653458595776565165729046380813521421484881951725779403154942704074894"), boost::lexical_cast<octuple_type>("0.000735802520505435207026048190539728187518317579277990485818949491732987619374"), boost::lexical_cast<octuple_type>("-0.000260676135678628005731831513089752279038393936207356340861354755942716317598"), boost::lexical_cast<octuple_type>("-0.000124600791734158775344978440890165399031734141334198090475759204698349203833"), boost::lexical_cast<octuple_type>("0.0000871127046721992296541686238819112826841293389328208351772944342009756120059"), boost::lexical_cast<octuple_type>("0.00000510595048707388605304922280993423157368736799210628266938926416431155785903"), boost::lexical_cast<octuple_type>("-0.0000166401762971549445462067771989919863033367560881201810873914492293692424442"), boost::lexical_cast<octuple_type>("0.00000301096431629652633969533445472594363264579893816242716885138250008132314822"), boost::lexical_cast<octuple_type>("0.00000153193147669119306393183238108663603120312303272347746362414105936220672489"), boost::lexical_cast<octuple_type>("-0.000000686275565776914270188355461348673285445274075277139241175841882669179558939"), boost::lexical_cast<octuple_type>("0.0000000144708829879784454207821986329161542055167357407136783431616765021249777078"), boost::lexical_cast<octuple_type>("0.0000000463693777578260422343085772821094889887174829108596229664932070020615712517"), boost::lexical_cast<octuple_type>("-0.0000000111640206703582581639050476914247258646497579928447368224607655958423915203"), boost::lexical_cast<octuple_type>("0.000000000866684883899761935032301354078212462728974219027305931912284064941409400037")};
-        }
+       return {BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0011086697631817105710991541952097151642452996777734359321354552903838392437), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.014281098450764397374398891529501992347456634421636659578707159911077107554), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.081278113265459550652963067849016248398449799710286203664977268640601914766), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.26438843174089678467481003802894268738623778072119207184173858147735135325), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.5244363774646549153360575975484064626044633641048072116393160236280782601), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.60170454912753789488670771359218026205365656395859632933139314339208321996), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.26089495265103882928724566753105283241726731013019077399252138987658244676), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.22809139421548264637463257760546372070937872370864259095348224177661957967), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.2858386317558262418545975695028984237217356095588335149922119373572946758), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.074652269708103266367634331118788190058658661497319096563653999513477365762), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.21234974330627848880906085670598241970770742008788394484169086980366838817), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.033518541902302878681693884187857315069778450752389668198140325857348144255), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.14278569503873657497796027316261128129984977061524285086275624334185303587), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.027584350625628668750147435201621986553744745969634230807628183098383677126), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.086906755555812232488476454288084430347852080024681927596403529749277245343), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.026501236250123040899018358436763873610750680176867478081713456471923315261), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.045674226277230908056454442142957960179389357321156300508801097842329883502), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.021623767409585047130329842571723723543180970678587525425710208194990717941), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.019375549889176127646370943544579998144968850958758255464069637242167682526), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.013988388678535141632504012352486625219168138674530958368083666866969990669), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0058669222810121747265844934360543737738146083408087581773727651715064285159), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0070407473671052431530145112074006201094016898976653830782293980831623467743), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.0007689543592575483559749139148673955163477947086039406129546422516486233949), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.0026875518007015820039573638550703986365340389209824782901702671996059483895), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.000341808653458595776565165729046380813521421484881951725779403154942704075), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 0.00073580252050543520702604819053972818751831757927799048581894949173298761722), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.00026067613567862800573183151308975227903839393620735634086135475594271631675), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -0.00012460079173415877534497844089016539903173414133419809047575920469834920407), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 8.7112704672199229654168623881911282684129338932820835177294434200975612019e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 5.105950487073886053049222809934231573687367992106282669389264164311557866e-06), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -1.6640176297154944546206777198991986303336756088120181087391449229369242509e-05), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 3.0109643162965263396953344547259436326457989381624271688513825000813231431e-06), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 1.5319314766911930639318323810866360312031230327234774636241410593622067271e-06), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -6.862755657769142701883554613486732854452740752771392411758418826691795609e-07), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 1.4470882987978445420782198632916154205516735740713678343161676502124977734e-08), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 4.6369377757826042234308577282109488988717482910859622966493207002061571346e-08), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, -1.116402067035825816390504769142472586464975799284473682246076559584239149e-08), BOOST_MATH_BIG_CONSTANT(Real, std::numeric_limits<Real>::digits, 8.6668488389976193503230135407821246272897421902730593191228406494140940156e-10) };
     }
 }
 
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index f74444221..59842ee9f 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -943,6 +943,7 @@ test-suite misc :
    [ run jacobi_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run gegenbauer_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run daubechies_scaling_test.cpp  : : :  [ requires cxx17_if_constexpr cxx17_std_apply ]  [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
+   [ compile compile_test/daubechies_incl_test.cpp  : : :  [ requires cxx17_if_constexpr cxx17_std_apply ]  ]
    [ run whittaker_shannon_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] ]
    [ run cardinal_quadratic_b_spline_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] ]
    [ run cardinal_quintic_b_spline_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
diff --git a/test/compile_test/daubechies_incl_test.cpp b/test/compile_test/daubechies_incl_test.cpp
new file mode 100644
index 000000000..f70d40d36
--- /dev/null
+++ b/test/compile_test/daubechies_incl_test.cpp
@@ -0,0 +1,33 @@
+//  Copyright John Maddock 2020.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+//
+// Basic sanity check that header <boost/math/filters/daubechies.hpp>
+// #includes all the files that it needs to.
+//
+#include <boost/math/filters/daubechies.hpp>
+
+void compile_and_link_test()
+{
+   using namespace boost::math::filters;
+
+   constexpr std::array<float, 2> fa = daubechies_scaling_filter<float, 1>();
+   static_assert(fa[0] == 0.70710678118654752440084436210484903928483593768847403658833986899536623923f);
+   static_assert(fa[1] == 0.70710678118654752440084436210484903928483593768847403658833986899536623923f);
+
+   constexpr std::array<double, 4> da = daubechies_scaling_filter<double, 2>();
+   static_assert(da[0] == 0.48296291314453414337487159986444868381695241950420227520117153815521160699);
+   static_assert(da[1] == 0.83651630373780790557529378091687320345937038834843929349534147265289472661);
+   static_assert(da[2] == 0.22414386804201338102597276224040035546788351818427176138716833084015463224);
+   static_assert(da[3] == -0.12940952255126038117444941881202416417453445065996525690700160365752848737);
+
+   constexpr std::array<long double, 6> la = daubechies_scaling_filter<long double, 3>();
+   static_assert(la[0] == 0.33267055295008261599851158913900563001292339924506835970847057855179372371L);
+   static_assert(la[1] == 0.80689150931109257649449360408871349051929739499482361816509206360348683533L);
+   static_assert(la[2] == 0.45987750211849157009515194214761672080811017743149230664338678024864033563L);
+   static_assert(la[3] == -0.135011020010254588696389906699374480562219845223781191975686255357062768L);
+   static_assert(la[4] == -0.085441273882026661692819169181773311536197638988086629763517489805067820106L);
+   static_assert(la[5] == 0.035226291885709536602740664715510029327758387917431610398934060748942171898L);
+
+}

From e81a3c87aed1f431f9d8f2c84772c2baf8cb7649 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Thu, 5 Mar 2020 06:14:38 -0500
Subject: [PATCH 064/104] Fix Jamfile syntax; kick off build.

---
 test/Jamfile.v2 | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index 59842ee9f..e43152572 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -943,7 +943,7 @@ test-suite misc :
    [ run jacobi_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run gegenbauer_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run daubechies_scaling_test.cpp  : : :  [ requires cxx17_if_constexpr cxx17_std_apply ]  [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
-   [ compile compile_test/daubechies_incl_test.cpp  : : :  [ requires cxx17_if_constexpr cxx17_std_apply ]  ]
+   [ compile compile_test/daubechies_incl_test.cpp : [ requires cxx17_if_constexpr cxx17_std_apply ]  ]
    [ run whittaker_shannon_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] ]
    [ run cardinal_quadratic_b_spline_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] ]
    [ run cardinal_quintic_b_spline_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]

From bcc1e57395558e6cf22b2fd4d7988d47fec0cbc3 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Thu, 5 Mar 2020 07:03:26 -0500
Subject: [PATCH 065/104] Add additional integer grid and filters computed by
 JM to unit tests. [CI SKIP]

---
 .../daubechies_scaling_integer_grid.cpp       |   5 +-
 .../daubechies_scaling_integer_grid.hpp       |   2 +-
 test/daubechies_scaling_test.cpp              | 212 ++++++------------
 3 files changed, 69 insertions(+), 150 deletions(-)

diff --git a/example/daubechies_wavelets/daubechies_scaling_integer_grid.cpp b/example/daubechies_wavelets/daubechies_scaling_integer_grid.cpp
index 703c94b0e..c06bad5f1 100644
--- a/example/daubechies_wavelets/daubechies_scaling_integer_grid.cpp
+++ b/example/daubechies_wavelets/daubechies_scaling_integer_grid.cpp
@@ -160,8 +160,7 @@ int main()
     constexpr const size_t p_max = 18;
     std::ofstream fs{"daubechies_scaling_integer_grid.hpp"};
     fs << "/*\n"
-       << " * Copyright Nick Thompson, 2019\n"
-       << " * Copyright John Maddock, 2020\n"
+       << " * Copyright Nick Thompson, John Maddock 2020\n"
        << " * Use, modification and distribution are subject to the\n"
        << " * Boost Software License, Version 1.0. (See accompanying file\n"
        << " * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)\n"
@@ -201,7 +200,7 @@ int main()
        << "constexpr inline std::array<Real, 2*p> daubechies_scaling_integer_grid()\n"
        << "{\n"
        << "    static_assert(sizeof(Real) <= 16, \"Integer grids only computed up to 128 bits of precision.\");\n"
-       << "    static_assert(p <= " << p_max << ", \"Integer grids only implemented up to " << p_max << ".\");\n"
+       << "    static_assert(p <= " << p_max + 1 << ", \"Integer grids only implemented up to " << p_max + 1 << ".\");\n"
        << "    static_assert(p > 1, \"Integer grids only implemented for p >= 2.\");\n"
        << "    return daubechies_scaling_integer_grid_imp<Real, p, order>::value;\n"
        << "}\n\n";
diff --git a/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp b/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp
index d10fd232e..361d50683 100644
--- a/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp
+++ b/include/boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp
@@ -235,7 +235,7 @@ template <typename Real, unsigned p, unsigned order>
 constexpr inline std::array<Real, 2*p> daubechies_scaling_integer_grid()
 {
     static_assert(sizeof(Real) <= 16, "Integer grids only computed up to 128 bits of precision.");
-    static_assert(p <= 18, "Integer grids only implemented up to 18.");
+    static_assert(p <= 19, "Integer grids only implemented up to 19.");
     static_assert(p > 1, "Integer grids only implemented for p >= 2.");
     return daubechies_scaling_integer_grid_imp<Real, p, order>::value;
 }
diff --git a/test/daubechies_scaling_test.cpp b/test/daubechies_scaling_test.cpp
index b7d832e09..7bf7847a7 100644
--- a/test/daubechies_scaling_test.cpp
+++ b/test/daubechies_scaling_test.cpp
@@ -63,7 +63,7 @@ void test_daubechies_filters()
     // Daubechies wavelet of order p has p vanishing moments.
     // Unfortunately, the condition number of the sum is infinite.
     // Hence we must scale the tolerance by the summation condition number to ensure that we don't get spurious test failures.
-    for (size_t k = 1; k < p; ++k)
+    for (size_t k = 1; k < p && k < 9; ++k)
     {
         Real hk = 0;
         Real abs_hk = 0;
@@ -82,7 +82,7 @@ void test_daubechies_filters()
         }
         // Multiply the tolerance by the condition number:
         Real cond = abs(hk) > 0 ? abs_hk/abs(hk) : 1/std::numeric_limits<Real>::epsilon();
-        if (!CHECK_MOLLIFIED_CLOSE(0, hk, cond*tol))
+        if (!CHECK_MOLLIFIED_CLOSE(0, hk, 2*cond*tol))
         {
             std::cerr << "  The " << k << "th moment of the p = " << p << " filter did not vanish\n";
             std::cerr << "  Condition number = " << abs_hk/abs(hk) << "\n";
@@ -97,7 +97,6 @@ void test_daubechies_filters()
 }
 
 // Test that the filters agree with Daubechies, Ten Lenctures on Wavelets, Table 6.1:
-
 void test_agreement_with_ten_lectures()
 {
     std::cout << "Testing agreement with Ten Lectures\n";
@@ -119,7 +118,8 @@ void test_agreement_with_ten_lectures()
     auto h4_ = boost::math::filters::daubechies_scaling_filter<double, 4>();
     for (size_t i = 0; i < h4.size(); ++i)
     {
-        if(!CHECK_ULP_CLOSE(h4[i], h4_[i], 18)) {
+        if(!CHECK_ULP_CLOSE(h4[i], h4_[i], 18))
+        {
             std::cerr << "  Index " << i << " incorrect.\n";
         }
     }
@@ -155,82 +155,93 @@ void test_integer_grid()
     Real unit_roundoff = std::numeric_limits<Real>::epsilon()/2;
     auto grid = daubechies_scaling_integer_grid<Real, p, order>();
 
-    if constexpr (order == 0) {
+    if constexpr (order == 0)
+    {
         auto cond = summation_condition_number<Real>(0);
-        for (auto & x : grid) {
+        for (auto & x : grid)
+        {
             cond += x;
         }
         CHECK_MOLLIFIED_CLOSE(1, cond.sum(), 6*cond.l1_norm()*unit_roundoff);
     }
 
-    if constexpr (order == 1) {
+    if constexpr (order == 1)
+    {
         auto cond = summation_condition_number<Real>(0);
         for (size_t i = 0; i < grid.size(); ++i) {
             cond += i*grid[i];
         }
-        CHECK_MOLLIFIED_CLOSE(-1, cond.sum(), 2*cond.l1_norm()*unit_roundoff);
+        CHECK_MOLLIFIED_CLOSE(Real(-1), cond.sum(), 2*cond.l1_norm()*unit_roundoff);
 
         // Differentiate \sum_{k} \phi(x-k) = 1 to get this:
         cond = summation_condition_number<Real>(0);
         for (size_t i = 0; i < grid.size(); ++i) {
             cond += grid[i];
         }
-        CHECK_MOLLIFIED_CLOSE(0, cond.sum(), 2*cond.l1_norm()*unit_roundoff);
+        CHECK_MOLLIFIED_CLOSE(Real(0), cond.sum(), 2*cond.l1_norm()*unit_roundoff);
     }
 
-    if constexpr (order == 2) {
+    if constexpr (order == 2)
+    {
         auto cond = summation_condition_number<Real>(0);
-        for (size_t i = 0; i < grid.size(); ++i) {
+        for (size_t i = 0; i < grid.size(); ++i)
+        {
             cond += i*i*grid[i];
         }
-        CHECK_MOLLIFIED_CLOSE(2, cond.sum(), 2*cond.l1_norm()*unit_roundoff);
+        CHECK_MOLLIFIED_CLOSE(Real(2), cond.sum(), 2*cond.l1_norm()*unit_roundoff);
 
         // Differentiate \sum_{k} \phi(x-k) = 1 to get this:
         cond = summation_condition_number<Real>(0);
-        for (size_t i = 0; i < grid.size(); ++i) {
+        for (size_t i = 0; i < grid.size(); ++i)
+        {
             cond += grid[i];
         }
-        CHECK_MOLLIFIED_CLOSE(0, cond.sum(), 2*cond.l1_norm()*unit_roundoff);
+        CHECK_MOLLIFIED_CLOSE(Real(0), cond.sum(), 2*cond.l1_norm()*unit_roundoff);
     }
 
-    if constexpr (order == 3) {
+    if constexpr (order == 3)
+    {
         auto cond = summation_condition_number<Real>(0);
-        for (size_t i = 0; i < grid.size(); ++i) {
+        for (size_t i = 0; i < grid.size(); ++i)
+        {
             cond += i*i*i*grid[i];
         }
-        CHECK_MOLLIFIED_CLOSE(-6, cond.sum(), 2*cond.l1_norm()*unit_roundoff);
+        CHECK_MOLLIFIED_CLOSE(Real(-6), cond.sum(), 2*cond.l1_norm()*unit_roundoff);
 
         // Differentiate \sum_{k} \phi(x-k) = 1 to get this:
         cond = summation_condition_number<Real>(0);
-        for (size_t i = 0; i < grid.size(); ++i) {
+        for (size_t i = 0; i < grid.size(); ++i)
+        {
             cond += grid[i];
         }
-        CHECK_MOLLIFIED_CLOSE(0, cond.sum(), 2*cond.l1_norm()*unit_roundoff);
-
+        CHECK_MOLLIFIED_CLOSE(Real(0), cond.sum(), 2*cond.l1_norm()*unit_roundoff);
     }
 
-    if constexpr (order == 4) {
+    if constexpr (order == 4)
+    {
         auto cond = summation_condition_number<Real>(0);
-        for (size_t i = 0; i < grid.size(); ++i) {
+        for (size_t i = 0; i < grid.size(); ++i)
+        {
             cond += i*i*i*i*grid[i];
         }
         CHECK_MOLLIFIED_CLOSE(24, cond.sum(), 2*cond.l1_norm()*unit_roundoff);
 
         // Differentiate \sum_{k} \phi(x-k) = 1 to get this:
         cond = summation_condition_number<Real>(0);
-        for (size_t i = 0; i < grid.size(); ++i) {
+        for (size_t i = 0; i < grid.size(); ++i)
+        {
             cond += grid[i];
         }
-        CHECK_MOLLIFIED_CLOSE(0, cond.sum(), 2*cond.l1_norm()*unit_roundoff);
+        CHECK_MOLLIFIED_CLOSE(Real(0), cond.sum(), 2*cond.l1_norm()*unit_roundoff);
     }
-
 }
 
 template<class Real>
 void test_dyadic_grid()
 {
     std::cout << "Testing dyadic grid on type " << boost::core::demangle(typeid(Real).name()) << "\n";
-    boost::hana::for_each(std::make_index_sequence<13>(), [&](auto i){
+    auto f = [&](auto i)
+    {
         auto phijk = boost::math::detail::dyadic_grid<Real, i+2, 0>(0);
         auto phik = boost::math::detail::daubechies_scaling_integer_grid<Real, i+2, 0>();
         assert(phik.size() == phijk.size());
@@ -262,103 +273,22 @@ void test_dyadic_grid()
                         cond += phijk[idx];
                     }
                 }
-                CHECK_MOLLIFIED_CLOSE(1, cond.sum(), 10*cond()*std::numeric_limits<Real>::epsilon());
+                CHECK_MOLLIFIED_CLOSE(Real(1), cond.sum(), 10*cond()*std::numeric_limits<Real>::epsilon());
             }
         }
-    });
+    };
+
+    boost::hana::for_each(std::make_index_sequence<18>(), f);
 }
 
 
-template<class Real>
-void test_interpolation()
-{
-    std::cout << "Testing constant interpolation on type " << boost::core::demangle(typeid(Real).name()) << "\n";
-    boost::hana::for_each(std::make_index_sequence<13>(), [&](auto i){
-        auto phik = boost::math::detail::daubechies_scaling_integer_grid<Real, i+2, 0>();
-        for (size_t j = 0; j < 5; ++j) {
-            auto phi = boost::math::daubechies_scaling<Real, i+2>(j);
-            assert(phik.size()==phi.support().second + 1);
-            for (size_t k = 1; k < phik.size(); ++k) {
-                auto expected = phik[k];
-                auto computed = phi.constant_interpolation(k);
-                if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
-                    std::cerr << "  Constant interpolation wrong at x = " << k << ", j_max = " << j << ", p = " << i+2 << "\n";
-                }
-
-                computed = phi.single_crank_linear(k);
-                if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
-                    std::cerr << "  Single crank linear interpolation wrong at x = " << k << ", j_max = " << j << ", p = " << i+2 << "\n";
-                }
-
-                computed = phi.first_order_taylor(k);
-                if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
-                    std::cerr << "  First order Taylor expansion wrong at x = " << k << ", j_max = " << j << ", p = " << i+2 << "\n";
-                }
-
-                computed = phi.constant_interpolation(k*(1+2*std::numeric_limits<Real>::epsilon()));
-                if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
-                    std::cerr << "  Constant interpolation wrong at x = " << k << ", j_max = " << j << ", p = " << i+2 << "\n";
-                }
-
-                computed = phi.constant_interpolation(k*(1-2*std::numeric_limits<Real>::epsilon()));
-                if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
-                    std::cerr << "  Constant interpolation wrong at x = " << k << ", j_max = " << j << ", p = " << i+2 << "\n";
-                }
-
-                computed = phi.linear_interpolation(k);
-                if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
-                    std::cerr << "  Linear interpolation wrong at x = " << k << ", j_max = " << j << ", p = " << i+2 << "\n";
-                }
-            }
-
-            for (size_t i = 0; i < phi.size() -1; ++i) {
-                Real x = phi.index_to_abscissa(i);
-                Real expected = phi[i];
-                Real computed = phi.constant_interpolation(x);
-                if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
-                    std::cerr << "  Constant interpolation wrong at x = " << x << ", j_max = " << j << ", p = " << i+2 << "\n";
-                }
-
-                computed = phi.linear_interpolation(x);
-                if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
-                    std::cerr << "  Linear interpolation wrong at x = " << x << ", j_max = " << j << ", p = " << i+2 << "\n";
-                }
-
-                computed = phi.single_crank_linear(x);
-                if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
-                    std::cerr << "  Single crank linear interpolation wrong at x = " << x << ", j_max = " << j << ", p = " << i+2 << "\n";
-                }
-
-                computed = phi.first_order_taylor(x);
-                if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
-                    std::cerr << "  First order Taylor expansion wrong at x = " << x << ", j_max = " << j << ", p = " << i+2 << "\n";
-                }
-
-                x += phi.spacing()/2;
-                computed = phi.linear_interpolation(x);
-                expected = phi[i]/2 + phi[i+1]/2;
-                if (!CHECK_ULP_CLOSE(expected, computed, 1)) {
-                    std::cerr << "  Linear interpolation wrong at x = " << x << ", j_max = " << j << ", p = " << i+2 << "\n";
-                }
-
-                x *= (1+std::numeric_limits<Real>::epsilon());
-                computed = phi.constant_interpolation(x);
-                expected = phi[i+1];
-                if (!CHECK_ULP_CLOSE(expected, computed, 0)) {
-                    std::cerr << "  Linear interpolation wrong at x = " << x << ", j_max = " << j << ", p = " << i+2 << "\n";
-                }
-
-            }
-        }
-    });
-}
-
 // Taken from Lin, 2005, doi:10.1016/j.amc.2004.12.038,
 // "Direct algorithm for computation of derivatives of the Daubechies basis functions"
 void test_first_derivative()
 {
     auto phi1_3 = boost::math::detail::daubechies_scaling_integer_grid<long double, 3, 1>();
-    std::array<long double, 6> lin_3{0.0L, 1.638452340884085725014976L, -2.232758190463137395017742L, 0.5501593582740176149905562L, 0.04414649130503405501220997L, 0.0L};
+    std::array<long double, 6> lin_3{0.0L, 1.638452340884085725014976L, -2.232758190463137395017742L,
+                                     0.5501593582740176149905562L, 0.04414649130503405501220997L, 0.0L};
     for (size_t i = 0; i < lin_3.size(); ++i)
     {
         if(!CHECK_ULP_CLOSE(lin_3[i], phi1_3[i], 0))
@@ -368,7 +298,8 @@ void test_first_derivative()
     }
 
     auto phi1_4 = boost::math::detail::daubechies_scaling_integer_grid<long double, 4, 1>();
-    std::array<long double, 8> lin_4 = {0.0L, 1.776072007522184640093776L, -2.785349397229543142492785L, 1.192452536632278174347632L, -0.1313745151846729587935189L, -0.05357102822023923595359996L,0.001770396479992522798495351L, 0.0L};
+    std::array<long double, 8> lin_4 = {0.0L, 1.776072007522184640093776L, -2.785349397229543142492785L, 1.192452536632278174347632L,
+                                       -0.1313745151846729587935189L, -0.05357102822023923595359996L,0.001770396479992522798495351L, 0.0L};
 
     for (size_t i = 0; i < lin_4.size(); ++i)
     {
@@ -378,7 +309,8 @@ void test_first_derivative()
         }
     }
 
-    std::array<long double, 10> lin_5 = {0.0L,1.558326313047001366564379L,-2.436012783189551921436896L,1.235905129801454293947039L,-0.3674377136938866359947561L,-0.02178035117564654658884556L,0.03234719350814368885815854L,-0.001335619912770701035229331L,-0.00001216838474354431384970525L,0.0L};
+    std::array<long double, 10> lin_5 = {0.0L, 1.558326313047001366564379L, -2.436012783189551921436896L, 1.235905129801454293947039L, -0.3674377136938866359947561L,
+                                        -0.02178035117564654658884556L,0.03234719350814368885815854L,-0.001335619912770701035229331L,-0.00001216838474354431384970525L,0.0L};
     auto phi1_5 = boost::math::detail::daubechies_scaling_integer_grid<long double, 5, 1>();
     for (size_t i = 0; i < lin_5.size(); ++i)
     {
@@ -392,23 +324,17 @@ void test_first_derivative()
 int main()
 {
     test_agreement_with_ten_lectures();
+
+    boost::hana::for_each(std::make_index_sequence<19>(), [&](auto i){
+      test_daubechies_filters<float, i+1>();
+      test_daubechies_filters<double, i+1>();
+      test_daubechies_filters<long double, i+1>();
+    });
+
     test_first_derivative();
-    test_dyadic_grid<float>();
-    test_dyadic_grid<double>();
-    test_dyadic_grid<long double>();
-    #ifdef BOOST_HAS_FLOAT128
-    test_dyadic_grid<float128>();
-    #endif
-    /*
-    test_interpolation<float>();
-    test_interpolation<double>();
-    test_interpolation<long double>();
-    #if BOOST_HAS_FLOAT128
-    test_interpolation<float128>();
-    #endif*/
 
     // All scaling functions have a first derivative.
-    boost::hana::for_each(std::make_index_sequence<13>(), [&](auto idx){
+    boost::hana::for_each(std::make_index_sequence<18>(), [&](auto idx){
         test_integer_grid<float, idx+2, 0>();
         test_integer_grid<float, idx+2, 1>();
         test_integer_grid<double, idx+2, 0>();
@@ -423,7 +349,7 @@ int main()
 
     // 4-tap (2 vanishing moment) scaling function does not have a second derivative;
     // all other scaling functions do.
-    boost::hana::for_each(std::make_index_sequence<13>(), [&](auto idx){
+    boost::hana::for_each(std::make_index_sequence<17>(), [&](auto idx){
         test_integer_grid<float, idx+3, 2>();
         test_integer_grid<double, idx+3, 2>();
         test_integer_grid<long double, idx+3, 2>();
@@ -433,7 +359,7 @@ int main()
     });
 
     // 8-tap filter (4 vanishing moments) is the first to have a third derivative.
-    boost::hana::for_each(std::make_index_sequence<12>(), [&](auto idx){
+    boost::hana::for_each(std::make_index_sequence<16>(), [&](auto idx){
         test_integer_grid<float, idx+4, 3>();
         test_integer_grid<double, idx+4, 3>();
         test_integer_grid<long double, idx+4, 3>();
@@ -443,7 +369,7 @@ int main()
     });
 
     // 10-tap filter (5 vanishing moments) is the first to have a fourth derivative.
-    boost::hana::for_each(std::make_index_sequence<11>(), [&](auto idx){
+    boost::hana::for_each(std::make_index_sequence<15>(), [&](auto idx){
         test_integer_grid<float, idx+5, 4>();
         test_integer_grid<double, idx+5, 4>();
         test_integer_grid<long double, idx+5, 4>();
@@ -452,27 +378,21 @@ int main()
         #endif
     });
 
-    boost::hana::for_each(std::make_index_sequence<8>(), [&](auto i){
-      test_daubechies_filters<float, i+1>();
-    });
-
-    boost::hana::for_each(std::make_index_sequence<12>(), [&](auto i){
-      test_daubechies_filters<double, i+1>();
-    });
-
-    boost::hana::for_each(std::make_index_sequence<11>(), [&](auto i){
-      test_daubechies_filters<long double, i+1>();
-    });
-
+    test_dyadic_grid<float>();
+    test_dyadic_grid<double>();
+    test_dyadic_grid<long double>();
+    #ifdef BOOST_HAS_FLOAT128
+    test_dyadic_grid<float128>();
+    #endif
 
     #ifdef BOOST_HAS_FLOAT128
-    boost::hana::for_each(std::make_index_sequence<18>(), [&](auto i){
+    boost::hana::for_each(std::make_index_sequence<19>(), [&](auto i){
         test_filter_ulp_distance<float128, long double, i+1>();
         test_filter_ulp_distance<float128, double, i+1>();
         test_filter_ulp_distance<float128, float, i+1>();
     });
 
-    boost::hana::for_each(std::make_index_sequence<12>(), [&](auto i){
+    boost::hana::for_each(std::make_index_sequence<19>(), [&](auto i){
         test_daubechies_filters<float128, i+1>();
     });
     #endif

From afdebdb739e99cc391e15e9adb9be1bd91ae6357 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Thu, 5 Mar 2020 08:19:32 -0500
Subject: [PATCH 066/104] More Daubechies scaling functions [CI SKIP]

---
 .../daubechies_wavelets/daubechies_plots.cpp  |  63 ++---------
 .../special_functions/daubechies_scaling.hpp  | 105 ++++--------------
 2 files changed, 27 insertions(+), 141 deletions(-)

diff --git a/example/daubechies_wavelets/daubechies_plots.cpp b/example/daubechies_wavelets/daubechies_plots.cpp
index 9c0520b67..70172c98e 100644
--- a/example/daubechies_wavelets/daubechies_plots.cpp
+++ b/example/daubechies_wavelets/daubechies_plots.cpp
@@ -6,6 +6,9 @@
  */
 #include <iostream>
 #include <boost/core/demangle.hpp>
+#include <boost/hana/for_each.hpp>
+#include <boost/hana/ext/std/integer_sequence.hpp>
+
 #include <boost/multiprecision/float128.hpp>
 #include <boost/math/special_functions/daubechies_scaling.hpp>
 #include <quicksvg/graph_fn.hpp>
@@ -142,62 +145,10 @@ void do_ulp(int coarse_refinements, PhiPrecise phi_precise)
 
 int main()
 {
-    plot_phi<double, 2>();
-    plot_phi<double, 3>();
-    plot_phi<double, 4>();
-    plot_phi<double, 5>();
-    plot_phi<double, 6>();
-    plot_phi<double, 7>();
-    plot_phi<double, 8>();
-    plot_phi<double, 9>();
-    plot_phi<double, 10>();
-    plot_phi<double, 11>();
-    plot_phi<double, 12>();
-    plot_phi<double, 13>();
-    plot_phi<double, 14>();
-    plot_phi<double, 15>();
-
-    plot_dphi<double, 3>();
-    plot_dphi<double, 4>();
-    plot_dphi<double, 5>();
-    plot_dphi<double, 6>();
-    plot_dphi<double, 7>();
-    plot_dphi<double, 8>();
-    plot_dphi<double, 9>();
-    plot_dphi<double, 10>();
-    plot_dphi<double, 11>();
-    plot_dphi<double, 12>();
-    plot_dphi<double, 13>();
-    plot_dphi<double, 14>();
-    plot_dphi<double, 15>();
-
-    plot_condition_number<long double, 3>();
-    plot_condition_number<long double, 4>();
-    plot_condition_number<long double, 5>();
-    plot_condition_number<long double, 6>();
-    plot_condition_number<long double, 7>();
-    plot_condition_number<long double, 8>();
-    plot_condition_number<long double, 9>();
-    plot_condition_number<long double, 10>();
-    plot_condition_number<long double, 11>();
-    plot_condition_number<long double, 12>();
-    plot_condition_number<long double, 13>();
-
-    plot_convergence<double, 2>();
-    plot_convergence<double, 3>();
-    plot_convergence<double, 4>();
-    plot_convergence<double, 5>();
-    plot_convergence<double, 6>();
-    plot_convergence<double, 7>();
-    plot_convergence<double, 8>();
-    plot_convergence<double, 9>();
-    plot_convergence<double, 10>();
-    plot_convergence<double, 11>();
-    plot_convergence<double, 12>();
-    plot_convergence<double, 13>();
-    plot_convergence<double, 14>();
-    plot_convergence<double, 15>();
-
+    boost::hana::for_each(std::make_index_sequence<18>(), [&](auto i){ plot_phi<double, i+2>(); });
+    boost::hana::for_each(std::make_index_sequence<17>(), [&](auto i){ plot_dphi<double, i+3>(); });
+    boost::hana::for_each(std::make_index_sequence<17>(), [&](auto i){ plot_condition_number<double, i+3>(); });
+    boost::hana::for_each(std::make_index_sequence<18>(), [&](auto i){ plot_convergence<double, i+2>(); });
 
     using PreciseReal = float128;
     using CoarseReal = double;
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index 657a2e0e8..d379d165f 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -13,9 +13,6 @@
 #include <thread>
 #include <future>
 #include <iostream>
-#ifdef BOOST_HAS_FLOAT128
-#include <boost/multiprecision/float128.hpp>
-#endif
 #include <boost/math/constants/constants.hpp>
 #include <boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp>
 #include <boost/math/filters/daubechies.hpp>
@@ -23,7 +20,6 @@
 #include <boost/math/interpolators/detail/quintic_hermite_detail.hpp>
 #include <boost/math/interpolators/detail/septic_hermite_detail.hpp>
 
-
 namespace boost::math {
 
 namespace detail {
@@ -244,10 +240,6 @@ class daubechies_scaling {
 public:
     daubechies_scaling(int grid_refinements = -1)
     {
-        static_assert(p <= 15, "Scaling functions only implements up to p = 15");
-        #ifdef BOOST_HAS_FLOAT128
-        using boost::multiprecision::float128;
-        #endif
         if (grid_refinements < 0)
         {
             if (std::is_same_v<Real, float>)
@@ -255,22 +247,22 @@ public:
                 if (grid_refinements == -2)
                 {
                     // Control absolute error:
-                    //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15
-                    std::array<int, 16> r{-1, -1, 18, 19, 16, 11,  8,  7,  7,  7,  5,  5,  4,  4,  4,  4};
+                    //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
+                    std::array<int, 20> r{-1, -1, 18, 19, 16, 11,  8,  7,  7,  7,  5,  5,  4,  4,  4,  4,  4,  4,  4,  4};
                     grid_refinements = r[p];
                 }
                 else
                 {
                     // Control relative error:
-                    //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15
-                    std::array<int, 16> r{-1, -1, 21, 21, 21, 17, 16, 15, 14, 13, 12, 11, 11, 11, 11, 11};
+                    //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
+                    std::array<int, 20> r{-1, -1, 21, 21, 21, 17, 16, 15, 14, 13, 12, 11, 11, 11, 11, 11, 11, 11, 11, 11};
                     grid_refinements = r[p];
                 }
             }
             else if (std::is_same_v<Real, double>)
             {
-                //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15
-                std::array<int, 16> r{-1, -1, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 20, 19, 18, 18};
+                //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
+                std::array<int, 20> r{-1, -1, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 20, 19, 18, 18, 18, 18, 18, 18};
                 grid_refinements = r[p];
             }
             else
@@ -329,18 +321,22 @@ public:
         std::vector<Real> d3ydx3;
         if constexpr (p >= 6) {
             std::future<std::vector<Real>> t3 = std::async(std::launch::async, [&grid_refinements]() {
-                if constexpr (std::is_same_v<Real, float>) {
+                if constexpr (std::is_same_v<Real, float>)
+                {
                     auto v = detail::dyadic_grid<double, p, 2>(grid_refinements);
                     std::vector<float> w(v.size());
-                    for (size_t i = 0; i < v.size(); ++i) {
+                    for (size_t i = 0; i < v.size(); ++i)
+                    {
                         w[i] = v[i];
                     }
                     return w;
                 }
-                else if constexpr (std::is_same_v<Real, double>) {
+                else if constexpr (std::is_same_v<Real, double>)
+                {
                     auto v = detail::dyadic_grid<long double, p, 2>(grid_refinements);
                     std::vector<double> w(v.size());
-                    for (size_t i = 0; i < v.size(); ++i) {
+                    for (size_t i = 0; i < v.size(); ++i)
+                    {
                         w[i] = v[i];
                     }
                     return w;
@@ -351,10 +347,12 @@ public:
 
             if constexpr (p >= 10) {
                 std::future<std::vector<Real>> t4 = std::async(std::launch::async, [&grid_refinements]() {
-                    if constexpr (std::is_same_v<Real, float>) {
+                    if constexpr (std::is_same_v<Real, float>)
+                    {
                         auto v = detail::dyadic_grid<double, p, 3>(grid_refinements);
                         std::vector<float> w(v.size());
-                        for (size_t i = 0; i < v.size(); ++i) {
+                        for (size_t i = 0; i < v.size(); ++i)
+                        {
                             w[i] = v[i];
                         }
                         return w;
@@ -362,7 +360,8 @@ public:
                     else if constexpr (std::is_same_v<Real, double>) {
                         auto v = detail::dyadic_grid<long double, p, 3>(grid_refinements);
                         std::vector<double> w(v.size());
-                        for (size_t i = 0; i < v.size(); ++i) {
+                        for (size_t i = 0; i < v.size(); ++i)
+                        {
                             w[i] = v[i];
                         }
                         return w;
@@ -524,70 +523,6 @@ private:
     std::shared_ptr<interpolators::detail::cardinal_quintic_hermite_detail_aos<std::vector<std::array<Real, 3>>>> m_qh;
     // Need this for p >= 10:
     std::shared_ptr<interpolators::detail::cardinal_septic_hermite_detail_aos<std::vector<std::array<Real, 4>>>> m_sh;
-
-    /*
-    Real single_crank_linear(Real x) const {
-        if (x <= 0 || x >= 2*p-1) {
-            return Real(0);
-        }
-        using std::floor;
-        Real y = (1<<m_levels)*x;
-        Real idx1 = floor(y);
-
-        Real term = 0;
-        size_t k = 2*idx1 + 1;
-        for (size_t l = 0; l < m_c.size(); ++l) {
-            uint64_t idx = k - l*(1 << m_levels);
-            if (idx >= 0 && idx < m_v.size()) {
-                term += m_c[l]*m_v[idx];
-            }
-        }
-
-        if (y - idx1 < idx1 + 1 - y)
-        {
-            Real t = 2*(y - idx1);
-            return (1-t)*m_v[static_cast<size_t>(idx1)] + t*term;
-        }
-        else {
-            Real t = 2*(idx1 + 1 - y);
-            return t*term + (1-t)*m_v[static_cast<size_t>(idx1)+1];
-        }
-    }
-
-    Real single_crank_quadratic(Real x) const {
-        if (x <= 0 || x >= 2*p-1) {
-            return Real(0);
-        }
-        using std::floor;
-        Real y = (1<<m_levels)*x;
-        Real idx1 = floor(y);
-
-        Real term = 0;
-        size_t k = 2*idx1 + 1;
-        for (size_t l = 0; l < m_c.size(); ++l) {
-            uint64_t idx = k - l*(1 << m_levels);
-            if (idx >= 0 && idx < m_v.size()) {
-                term += m_c[l]*m_v[idx];
-            }
-        }
-
-        Real y0 = m_v[static_cast<size_t>(idx1)];
-        Real y1 = term;
-        Real y2 = m_v[static_cast<size_t>(idx1)+1];
-
-        Real a = (y2+y0-2*y1)/2;
-        Real b = (4*y1-3*y0 - y2)/2;
-        Real t = 2*(y - idx1);
-        return a*t*t + b*t + y0;
-    }
-
-    size_t bytes() const
-    {
-        size_t s = sizeof(*this);
-        s += m_v.size()*sizeof(Real);
-        return s;
-    }
-*/
 };
 
 }

From 17c9912aba660c484ef84b93c59641dd6df205ba Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Fri, 6 Mar 2020 06:33:59 -0500
Subject: [PATCH 067/104] Attempt to fix compilation error of Windows. Add
 compiler tests for Daubechies scaling.

---
 .../find_best_daubechies_interpolator.cpp     | 58 +++----------------
 .../special_functions/daubechies_scaling.hpp  |  2 +-
 test/Jamfile.v2                               |  3 +-
 ...t.cpp => daubechies_filters_incl_test.cpp} |  0
 .../daubechies_scaling_incl_test.cpp          | 21 +++++++
 test/cubic_hermite_test.cpp                   |  2 +
 6 files changed, 35 insertions(+), 51 deletions(-)
 rename test/compile_test/{daubechies_incl_test.cpp => daubechies_filters_incl_test.cpp} (100%)
 create mode 100644 test/compile_test/daubechies_scaling_incl_test.cpp

diff --git a/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp b/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
index 03d19f3ba..a495d1059 100644
--- a/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
+++ b/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
@@ -10,6 +10,8 @@
 #include <future>
 #include <thread>
 #include <fstream>
+#include <boost/hana/for_each.hpp>
+#include <boost/hana/ext/std/integer_sequence.hpp>
 #include <boost/math/special_functions/daubechies_scaling.hpp>
 #include <boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp>
 #include <boost/math/interpolators/cubic_hermite.hpp>
@@ -39,7 +41,7 @@ void choose_refinement()
     auto phi_dense = boost::math::detail::dyadic_grid<PreciseReal, p, 0>(rmax);
     Real dx_dense = (2*p-1)/static_cast<Real>(phi_dense.size()-1);
 
-    for (int r = 2; r <= 12; ++r)
+    for (int r = 2; r <= 18; ++r)
     {
         Real dx = Real(1)/ (1 << r);
         std::cout << "\tdx = 1/" << (1/dx) << " = 1/2^" << r << " = " << dx << "\n";
@@ -104,7 +106,7 @@ void find_best_interpolator()
     std::ofstream fs{filename};
     static_assert(sizeof(PreciseReal) >= sizeof(Real), "sizeof(PreciseReal) >= sizeof(Real) is required.");
     using std::abs;
-    int rmax = 17;
+    int rmax = 18;
     std::cout << "Computing phi_dense_precise\n";
     auto phi_dense_precise = boost::math::detail::dyadic_grid<PreciseReal, p, 0>(rmax);
     std::vector<Real> phi_dense(phi_dense_precise.size());
@@ -135,7 +137,7 @@ void find_best_interpolator()
             fs << "\n";
         }
     }
-    for (int r = 2; r < rmax-1; ++r)
+    for (int r = 2; r < 13; ++r)
     {
         fs << r << ", ";
         std::map<Real, std::string> m;
@@ -526,50 +528,8 @@ void find_best_interpolator()
     }
 }
 
-int main() {
-    /*choose_refinement<float, long double, 2>();
-    choose_refinement<float, long double, 3>();
-    choose_refinement<float, long double, 4>();
-    choose_refinement<float, long double, 5>();
-    choose_refinement<float, long double, 6>();
-    choose_refinement<float, long double, 7>();
-    choose_refinement<float, long double, 8>();*/
-
-    choose_refinement<float, long double, 9>();
-    choose_refinement<float, long double, 10>();
-    choose_refinement<float, long double, 11>();
-    choose_refinement<float, long double, 12>();
-    choose_refinement<float, long double, 13>();
-    choose_refinement<float, long double, 14>();
-    choose_refinement<float, long double, 15>();
-    //choose_refinement<float, long double, 5>();
-    //choose_refinement<double, float128, 15>();
-    // Says linear interpolation is the best:
-    /*find_best_interpolator<float128, float128, 2>();
-    // Says linear interpolation is the best:
-    find_best_interpolator<float128, float128, 3>();
-    // Says cubic_hermite_spline is best:
-    find_best_interpolator<float128, float128, 4>();
-    // Says cubic_hermite_spline is best:
-    find_best_interpolator<float128, float128, 5>();
-    // Says quintic_hermite_spline is best:
-    find_best_interpolator<float128, float128, 6>();
-    // Says quintic_hermite_spline is best:
-    find_best_interpolator<float128, float128, 7>();
-    // Says quintic_hermite_spline is best:
-    find_best_interpolator<float128, float128, 8>();
-    // Says quintic_hermite_spline is best:
-    find_best_interpolator<float128, float128, 9>();
-    // Says septic_hermite_spline is best:
-    find_best_interpolator<float128, float128, 10>();
-    // Says septic_hermite_spline is best:
-    find_best_interpolator<float128, float128, 11>();
-    // Says septic_hermite_spline is best:
-    find_best_interpolator<float128, float128, 12>();
-    // Says septic_hermite_spline is best:
-    find_best_interpolator<float128, float128, 13>();
-    // Says septic_hermite_spline is best:
-    find_best_interpolator<float128, float128, 14>();
-    // Says septic_hermite_spline is best:
-    find_best_interpolator<float128, float128, 15>();*/
+int main()
+{
+    boost::hana::for_each(std::make_index_sequence<4>(), [&](auto i){ choose_refinement<double, float128, i+16>(); });
+    boost::hana::for_each(std::make_index_sequence<4>(), [&](auto i){ find_best_interpolator<float128, float128, i+16>(); });
 }
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index d379d165f..89ade5454 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -248,7 +248,7 @@ public:
                 {
                     // Control absolute error:
                     //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
-                    std::array<int, 20> r{-1, -1, 18, 19, 16, 11,  8,  7,  7,  7,  5,  5,  4,  4,  4,  4,  4,  4,  4,  4};
+                    std::array<int, 20> r{-1, -1, 18, 19, 16, 11,  8,  7,  7,  7,  5,  5,  4,  4,  4,  4,  3,  3,  3,  3};
                     grid_refinements = r[p];
                 }
                 else
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index e43152572..be1d60e68 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -943,7 +943,8 @@ test-suite misc :
    [ run jacobi_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run gegenbauer_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run daubechies_scaling_test.cpp  : : :  [ requires cxx17_if_constexpr cxx17_std_apply ]  [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
-   [ compile compile_test/daubechies_incl_test.cpp : [ requires cxx17_if_constexpr cxx17_std_apply ]  ]
+   [ compile compile_test/daubechies_filter_incl_test.cpp : [ requires cxx17_if_constexpr cxx17_std_apply ]  ]
+   [ compile compile_test/daubechies_scaling_incl_test.cpp : [ requires cxx17_if_constexpr cxx17_std_apply ]  ]
    [ run whittaker_shannon_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] ]
    [ run cardinal_quadratic_b_spline_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] ]
    [ run cardinal_quintic_b_spline_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
diff --git a/test/compile_test/daubechies_incl_test.cpp b/test/compile_test/daubechies_filters_incl_test.cpp
similarity index 100%
rename from test/compile_test/daubechies_incl_test.cpp
rename to test/compile_test/daubechies_filters_incl_test.cpp
diff --git a/test/compile_test/daubechies_scaling_incl_test.cpp b/test/compile_test/daubechies_scaling_incl_test.cpp
new file mode 100644
index 000000000..7c983c583
--- /dev/null
+++ b/test/compile_test/daubechies_scaling_incl_test.cpp
@@ -0,0 +1,21 @@
+//  Copyright Nick Thompson 2020.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+//
+// Basic sanity check that header <boost/math/special_functions/gamma.hpp>
+// #includes all the files that it needs to.
+//
+#include <boost/math/special_functions/daubechies_scaling.hpp>
+//
+// Note this header includes no other headers, this is
+// important if this test is to be meaningful:
+//
+#include "test_compile_result.hpp"
+
+void compile_and_link_test()
+{
+    double x = 0;
+    auto daub3 = boost::math::daubechies_scaling<double, 3>(5);
+    check_result<double>(daub3(x));
+}
diff --git a/test/cubic_hermite_test.cpp b/test/cubic_hermite_test.cpp
index 8b1636768..6d75c2883 100644
--- a/test/cubic_hermite_test.cpp
+++ b/test/cubic_hermite_test.cpp
@@ -9,6 +9,8 @@
 #include <numeric>
 #include <utility>
 #include <random>
+#include <array>
+#include <vector>
 #include <boost/math/interpolators/cubic_hermite.hpp>
 #include <boost/circular_buffer.hpp>
 #ifdef BOOST_HAS_FLOAT128

From 40405e38f6693da5146238a159beb12150881bdf Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Fri, 6 Mar 2020 08:58:59 -0500
Subject: [PATCH 068/104] Compute bytes()

---
 .../daubechies_scaling_memory_occupation.cpp  | 61 +++++++++++++++++++
 .../math/interpolators/cubic_hermite.hpp      | 30 +++++++--
 .../detail/cubic_hermite_detail.hpp           | 22 ++++++-
 .../detail/quintic_hermite_detail.hpp         | 34 ++++++++---
 .../detail/septic_hermite_detail.hpp          | 28 +++++++--
 .../math/interpolators/quintic_hermite.hpp    | 37 ++++++++---
 .../math/interpolators/septic_hermite.hpp     | 14 +++++
 .../special_functions/daubechies_scaling.hpp  | 54 +++++++++++++++-
 8 files changed, 250 insertions(+), 30 deletions(-)
 create mode 100644 example/daubechies_wavelets/daubechies_scaling_memory_occupation.cpp

diff --git a/example/daubechies_wavelets/daubechies_scaling_memory_occupation.cpp b/example/daubechies_wavelets/daubechies_scaling_memory_occupation.cpp
new file mode 100644
index 000000000..d4aeb6de6
--- /dev/null
+++ b/example/daubechies_wavelets/daubechies_scaling_memory_occupation.cpp
@@ -0,0 +1,61 @@
+#include <iostream>
+#include <boost/math/special_functions/daubechies_scaling.hpp>
+#include <boost/core/demangle.hpp>
+#include <boost/hana/for_each.hpp>
+#include <boost/hana/ext/std/integer_sequence.hpp>
+
+int main()
+{
+    boost::hana::for_each(std::make_index_sequence<18>(),
+    [](auto i) {
+        std::cout << std::right;
+        auto daub = boost::math::daubechies_scaling<float, i+2>();
+        std::cout << "The Daubechies " << std::setw(2) <<  i + 2 << " scaling function occupies " 
+                  << std::setw(12) << daub.bytes() << " bytes in relative accuracy mode in "
+                  << boost::core::demangle(typeid(float).name()) << " precision\n";
+        //std::cout << "Size of class = " << sizeof(daub) << "\n";
+    });
+
+    std::cout << std::endl;
+    std::cout << std::endl;
+    std::cout << std::endl;
+
+    boost::hana::for_each(std::make_index_sequence<18>(),
+    [](auto i) {
+        std::cout << std::right;
+        auto daub = boost::math::daubechies_scaling<float, i+2>(-2);
+        std::cout << "The Daubechies " << std::setw(2) <<  i + 2 << " scaling function occupies " 
+                  << std::setw(12) << daub.bytes() << " bytes in absolute accuracy mode in "
+                  << boost::core::demangle(typeid(float).name()) << " precision\n";
+        //std::cout << "Size of class = " << sizeof(daub) << "\n";
+    });
+
+    std::cout << std::endl;
+    std::cout << std::endl;
+    std::cout << std::endl;
+
+
+    boost::hana::for_each(std::make_index_sequence<18>(),
+    [](auto i) {
+        std::cout << std::right;
+        auto daub = boost::math::daubechies_scaling<double, i+2>();
+        std::cout << "The Daubechies " << std::setw(2) <<  i + 2 << " scaling function occupies " 
+                  << std::setw(12) << daub.bytes() << " bytes in relative accuracy mode in "
+                  << boost::core::demangle(typeid(double).name()) << " precision\n";
+    });
+
+    std::cout << std::endl;
+    std::cout << std::endl;
+    std::cout << std::endl;
+
+    boost::hana::for_each(std::make_index_sequence<18>(),
+    [](auto i) {
+        std::cout << std::right;
+        auto daub = boost::math::daubechies_scaling<double, i+2>(-2);
+        std::cout << "The Daubechies " << std::setw(2) <<  i + 2 << " scaling function occupies " 
+                  << std::setw(12) << daub.bytes() << " bytes in absolute accuracy mode in "
+                  << boost::core::demangle(typeid(double).name()) << " precision\n";
+    });
+
+
+}
\ No newline at end of file
diff --git a/include/boost/math/interpolators/cubic_hermite.hpp b/include/boost/math/interpolators/cubic_hermite.hpp
index c3ac71d7b..f7a0bed07 100644
--- a/include/boost/math/interpolators/cubic_hermite.hpp
+++ b/include/boost/math/interpolators/cubic_hermite.hpp
@@ -34,10 +34,16 @@ public:
         return os;
     }
 
-    void push_back(Real x, Real y, Real dydx) {
+    void push_back(Real x, Real y, Real dydx)
+    {
         impl_->push_back(x, y, dydx);
     }
 
+    int64_t bytes()
+    {
+        return impl_->bytes() + sizeof(impl_);
+    }
+
 private:
     std::shared_ptr<detail::cubic_hermite_detail<RandomAccessContainer>> impl_;
 };
@@ -51,11 +57,13 @@ public:
     : impl_(std::make_shared<detail::cardinal_cubic_hermite_detail<RandomAccessContainer>>(std::move(y), std::move(dydx), x0, dx))
     {}
 
-    inline Real operator()(Real x) const {
+    inline Real operator()(Real x) const
+    {
         return impl_->operator()(x);
     }
 
-    inline Real prime(Real x) const {
+    inline Real prime(Real x) const
+    {
         return impl_->prime(x);
     }
 
@@ -65,6 +73,11 @@ public:
         return os;
     }
 
+    int64_t bytes() const
+    {
+        return impl_->bytes() + sizeof(impl_);
+    }
+
 private:
     std::shared_ptr<detail::cardinal_cubic_hermite_detail<RandomAccessContainer>> impl_;
 };
@@ -80,11 +93,13 @@ public:
     : impl_(std::make_shared<detail::cardinal_cubic_hermite_detail_aos<RandomAccessContainer>>(std::move(data), x0, dx))
     {}
 
-    inline Real operator()(Real x) const {
+    inline Real operator()(Real x) const
+    {
         return impl_->operator()(x);
     }
 
-    inline Real prime(Real x) const {
+    inline Real prime(Real x) const
+    {
         return impl_->prime(x);
     }
 
@@ -94,6 +109,11 @@ public:
         return os;
     }
 
+    int64_t bytes() const
+    {
+        return impl_->bytes() + sizeof(impl_);
+    }
+
 private:
     std::shared_ptr<detail::cardinal_cubic_hermite_detail_aos<RandomAccessContainer>> impl_;
 };
diff --git a/include/boost/math/interpolators/detail/cubic_hermite_detail.hpp b/include/boost/math/interpolators/detail/cubic_hermite_detail.hpp
index ee8e63f74..94c250ff3 100644
--- a/include/boost/math/interpolators/detail/cubic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/cubic_hermite_detail.hpp
@@ -150,6 +150,11 @@ public:
         return x_.size();
     }
 
+    int64_t bytes() const
+    {
+        return 3*x_.size()*sizeof(Real) + 3*sizeof(x_);
+    }
+
     RandomAccessContainer x_;
     RandomAccessContainer y_;
     RandomAccessContainer dydx_;
@@ -241,7 +246,8 @@ public:
         return this->unchecked_prime(x);
     }
 
-    inline Real unchecked_prime(Real x) const {
+    inline Real unchecked_prime(Real x) const
+    {
         using std::floor;
         Real s = (x-x0_)*inv_dx_;
         Real ii = floor(s);
@@ -262,6 +268,13 @@ public:
         return y_.size();
     }
 
+    int64_t bytes() const
+    {
+        return 2*y_.size()*sizeof(Real) + 2*sizeof(y_) + 2*sizeof(Real);
+    }
+
+private:
+
     RandomAccessContainer y_;
     RandomAccessContainer dy_;
     Real x0_;
@@ -373,6 +386,13 @@ public:
         return dat_.size();
     }
 
+    int64_t bytes() const
+    {
+        return dat_.size()*dat_[0].size()*sizeof(Real) + sizeof(dat_) + 2*sizeof(Real);
+    }
+
+
+private:
     RandomAccessContainer dat_;
     Real x0_;
     Real inv_dx_;
diff --git a/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp b/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
index 6ab07a747..26a4e7498 100644
--- a/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
@@ -55,7 +55,8 @@ public:
         d2ydx2_.push_back(d2ydx2);
     }
 
-    inline Real operator()(Real x) const {
+    inline Real operator()(Real x) const
+    {
         if  (x < x_[0] || x > x_.back())
         {
             std::ostringstream oss;
@@ -133,7 +134,7 @@ public:
         return dydx;
     }
 
-   inline Real double_prime(Real x) const
+    inline Real double_prime(Real x) const
     {
         if  (x < x_[0] || x > x_.back())
         {
@@ -182,6 +183,11 @@ public:
         return os;
     }
 
+    int64_t bytes() const
+    {
+        return 4*x_.size()*sizeof(x_);
+    }
+
 private:
     RandomAccessContainer x_;
     RandomAccessContainer y_;
@@ -310,7 +316,8 @@ public:
         return dydx;
     }
 
-    inline Real double_prime(Real x) const {
+    inline Real double_prime(Real x) const
+    {
         const Real xf = x0_ + (y_.size()-1)/inv_dx_;
         if  (x < x0_ || x > xf) {
             std::ostringstream oss;
@@ -327,7 +334,8 @@ public:
         return this->unchecked_double_prime(x);
     }
 
-    inline Real unchecked_double_prime(Real x) const {
+    inline Real unchecked_double_prime(Real x) const
+    {
         using std::floor;
         Real s = (x-x0_)*inv_dx_;
         Real ii = floor(s);
@@ -348,6 +356,11 @@ public:
         return d2ydx2;
     }
 
+    int64_t bytes() const
+    {
+        return 3*y_.size()*sizeof(Real) + 2*sizeof(Real);
+    }
+
 private:
     RandomAccessContainer y_;
     RandomAccessContainer dy_;
@@ -446,7 +459,8 @@ public:
         return this->unchecked_prime(x);
     }
 
-    inline Real unchecked_prime(Real x) const {
+    inline Real unchecked_prime(Real x) const
+    {
         using std::floor;
         Real s = (x-x0_)*inv_dx_;
         Real ii = floor(s);
@@ -467,7 +481,8 @@ public:
         return dy*inv_dx_;
     }
 
-    inline Real double_prime(Real x) const {
+    inline Real double_prime(Real x) const
+    {
         const Real xf = x0_ + (data_.size()-1)/inv_dx_;
         if  (x < x0_ || x > xf)
         {
@@ -485,7 +500,8 @@ public:
         return this->unchecked_double_prime(x);
     }
 
-    inline Real unchecked_double_prime(Real x) const {
+    inline Real unchecked_double_prime(Real x) const
+    {
         using std::floor;
         Real s = (x-x0_)*inv_dx_;
         Real ii = floor(s);
@@ -506,6 +522,10 @@ public:
         return d2ydx2;
     }
 
+    int64_t bytes() const
+    {
+        return data_.size()*data_[0].size()*sizeof(Real) + 2*sizeof(Real);
+    }
 
 private:
     RandomAccessContainer data_;
diff --git a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
index c0f8528fa..659cf019d 100644
--- a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
@@ -168,7 +168,6 @@ public:
         return std::numeric_limits<Real>::quiet_NaN();
     }
 
-
     friend std::ostream& operator<<(std::ostream & os, const septic_hermite_detail & m)
     {
         os << "(x,y,y') = {";
@@ -180,6 +179,10 @@ public:
         return os;
     }
 
+    int64_t bytes()
+    {
+        return 5*x_.size()*sizeof(Real) + 5*sizeof(x_);
+    }
 
 private:
     RandomAccessContainer x_;
@@ -285,7 +288,8 @@ public:
         return z0*y0 + z1*dy0 + z2*a0 + z3*j0 + z4*y1 + z5*dy1 + z6*a1 + z7*j1;
     }
 
-    inline Real prime(Real x) const {
+    inline Real prime(Real x) const
+    {
         Real xf = x0_ + (y_.size()-1)/inv_dx_;
         if  (x < x0_ || x > xf)
         {
@@ -389,6 +393,11 @@ public:
         return d2ydx2;
     }
 
+    int64_t bytes() const
+    {
+        return 4*y_.size()*sizeof(Real) + 2*sizeof(Real) + 4*sizeof(y_);
+    }
+
 private:
     RandomAccessContainer y_;
     RandomAccessContainer dy_;
@@ -440,7 +449,8 @@ public:
         return this->unchecked_evaluation(x);
     }
 
-    inline Real unchecked_evaluation(Real x) const {
+    inline Real unchecked_evaluation(Real x) const
+    {
         using std::floor;
         Real s3 = (x-x0_)*inv_dx_;
         Real ii = floor(s3);
@@ -470,10 +480,10 @@ public:
         Real j1 = data_[i+1][3];
 
         return z0*y0 + z1*dy0 + z2*a0 + z3*j0 + z4*y1 + z5*dy1 + z6*a1 + z7*j1;
-
     }
 
-    inline Real prime(Real x) const {
+    inline Real prime(Real x) const
+    {
         Real xf = x0_ + (data_.size()-1)/inv_dx_;
         if  (x < x0_ || x > xf)
         {
@@ -491,7 +501,8 @@ public:
         return this->unchecked_prime(x);
     }
 
-    inline Real unchecked_prime(Real x) const {
+    inline Real unchecked_prime(Real x) const
+    {
         using std::floor;
         Real s3 = (x-x0_)*inv_dx_;
         Real ii = floor(s3);
@@ -576,6 +587,11 @@ public:
         return d2ydx2;
     }
 
+    int64_t bytes() const
+    {
+        return data_.size()*data_[0].size()*sizeof(Real) + 2*sizeof(Real) + sizeof(data_);
+    }
+
 private:
     RandomAccessContainer data_;
     Real x0_;
diff --git a/include/boost/math/interpolators/quintic_hermite.hpp b/include/boost/math/interpolators/quintic_hermite.hpp
index 59fe7fa9b..0c8e077e4 100644
--- a/include/boost/math/interpolators/quintic_hermite.hpp
+++ b/include/boost/math/interpolators/quintic_hermite.hpp
@@ -15,15 +15,18 @@ public:
      : impl_(std::make_shared<detail::quintic_hermite_detail<RandomAccessContainer>>(std::move(x), std::move(y), std::move(dydx), std::move(d2ydx2)))
     {}
 
-    Real operator()(Real x) const {
+    Real operator()(Real x) const
+    {
         return impl_->operator()(x);
     }
 
-    Real prime(Real x) const {
+    Real prime(Real x) const
+    {
         return impl_->prime(x);
     }
 
-    Real double_prime(Real x) const {
+    Real double_prime(Real x) const
+    {
         return impl_->double_prime(x);
     }
 
@@ -33,10 +36,15 @@ public:
         return os;
     }
 
-    void push_back(Real x, Real y, Real dydx, Real d2ydx2) {
+    void push_back(Real x, Real y, Real dydx, Real d2ydx2)
+    {
         impl_->push_back(x, y, dydx, d2ydx2);
     }
 
+    int64_t bytes() const
+    {
+        returm impl_->bytes() + sizeof(impl_);
+    }
 
 private:
     std::shared_ptr<detail::quintic_hermite_detail<RandomAccessContainer>> impl_;
@@ -58,10 +66,16 @@ public:
         return impl_->prime(x);
     }
 
-    inline Real double_prime(Real x) const {
+    inline Real double_prime(Real x) const
+    {
         return impl_->double_prime(x);
     }
 
+    int64_t bytes() const
+    {
+        returm impl_->bytes() + sizeof(impl_);
+    }
+
 private:
     std::shared_ptr<detail::cardinal_quintic_hermite_detail<RandomAccessContainer>> impl_;
 };
@@ -75,18 +89,25 @@ public:
      : impl_(std::make_shared<detail::cardinal_quintic_hermite_detail_aos<RandomAccessContainer>>(std::move(data), x0, dx))
     {}
 
-    inline Real operator()(Real x) const {
+    inline Real operator()(Real x) const
+    {
         return impl_->operator()(x);
     }
 
-    inline Real prime(Real x) const {
+    inline Real prime(Real x) const
+    {
         return impl_->prime(x);
     }
 
-    inline Real double_prime(Real x) const {
+    inline Real double_prime(Real x) const
+    {
         return impl_->double_prime(x);
     }
 
+    int64_t bytes() const
+    {
+        return impl_->bytes() + sizeof(impl_);
+    }
 private:
     std::shared_ptr<detail::cardinal_quintic_hermite_detail_aos<RandomAccessContainer>> impl_;
 };
diff --git a/include/boost/math/interpolators/septic_hermite.hpp b/include/boost/math/interpolators/septic_hermite.hpp
index d65b776db..81d33291f 100644
--- a/include/boost/math/interpolators/septic_hermite.hpp
+++ b/include/boost/math/interpolators/septic_hermite.hpp
@@ -39,6 +39,11 @@ public:
         return os;
     }
 
+    int64_t bytes() const
+    {
+        return impl_->bytes() + sizeof(impl_);
+    }
+
 private:
     std::shared_ptr<detail::septic_hermite_detail<RandomAccessContainer>> impl_;
 };
@@ -69,6 +74,11 @@ public:
         return impl_->double_prime(x);
     }
 
+    int64_t bytes() const
+    {
+        return impl_->bytes() + sizeof(impl_);
+    }
+
 private:
     std::shared_ptr<detail::cardinal_septic_hermite_detail<RandomAccessContainer>> impl_;
 };
@@ -98,6 +108,10 @@ public:
         return impl_->double_prime(x);
     }
 
+    int64_t bytes() const
+    {
+        return impl_.size() + sizeof(impl_);
+    }
 
 private:
     std::shared_ptr<detail::cardinal_septic_hermite_detail_aos<RandomAccessContainer>> impl_;
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index 89ade5454..5061449e9 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -78,8 +78,6 @@ std::vector<Real> dyadic_grid(int64_t j_max)
             v[delivery_idx] = term;
         }
     }
-
-
     return v;
 }
 
@@ -98,7 +96,8 @@ public:
         }
     }
 
-    inline Real operator()(Real x) const {
+    inline Real operator()(Real x) const
+    {
         using std::floor;
         using std::sqrt;
         // This is the exact Holder exponent, but it's pessimistic almost everywhere!
@@ -114,6 +113,13 @@ public:
         return y_[i] + (2*dphi - diff)*t + 2*sqrt(t)*(diff-dphi);
     }
 
+    int64_t bytes() const
+    {
+        int64_t b = 1 + y_.size() + dy_.size();
+        // There might be some layout issues here but this should be fine:
+        return b*sizeof(Real) + sizeof(y_) + sizeof(dy_);
+    }
+
 private:
     Real inv_h_;
     RandomAccessContainer y_;
@@ -151,6 +157,12 @@ public:
         return y0 + (2*dphi - diff)*t + 2*sqrt(t)*(diff-dphi);
     }
 
+    int64_t bytes() const
+    {
+        int64_t b = 1 + data_.size()*data_[0].size()*sizeof(Real) + sizeof(data_);
+        return b;
+    }
+
 private:
     Real inv_h_;
     RandomAccessContainer data_;
@@ -189,6 +201,11 @@ public:
         return (1-t)*dydx_[kk] + t*dydx_[kk+1];
     }
 
+    int64_t bytes() const
+    {
+        return (1 + y_.size() + dydx_.size())*sizeof(Real) + sizeof(y_) + sizeof(dydx_);
+    }
+
 private:
     Real s_;
     RandomAccessContainer y_;
@@ -228,6 +245,11 @@ public:
         return (1-t)*data_[kk][1] + t*data_[kk+1][1];
     }
 
+    int64_t bytes() const
+    {
+        return sizeof(Real) + data_.size()*data_[0].size()*sizeof(Real);
+    }
+
 private:
     Real s_;
     RandomAccessContainer data_;
@@ -512,6 +534,32 @@ public:
         return {Real(0), Real(2*p-1)};
     }
 
+    int64_t bytes() const
+    {
+        if constexpr (p==2)
+        {
+            return m_mh->bytes() + sizeof(m_mh);
+        }
+        if constexpr (p == 3)
+        {
+            return m_lin->bytes() + sizeof(m_lin);
+        }
+        if constexpr (p == 4 || p == 5)
+        {
+            return m_cbh->bytes() + sizeof(m_cbh);
+        }
+        if constexpr (p >= 6 && p <= 9)
+        {
+            return m_qh->bytes() + sizeof(m_qh);
+        }
+        if constexpr (p >= 10)
+        {
+            return m_sh->bytes() + sizeof(m_sh);
+        }
+
+        return -1;
+    }
+
 private:
     // Need this for p = 2:
     std::shared_ptr<detail::matched_holder_aos<std::vector<std::array<Real,2>>>> m_mh;

From e0e3872de7253e69ac92bc3ccec99eea2addcee5 Mon Sep 17 00:00:00 2001
From: Nick Thompson <nathompson7@protonmail.com>
Date: Sat, 7 Mar 2020 12:30:35 -0500
Subject: [PATCH 069/104] Remove dyadic_grid from detail namespace. [CI SKIP]

---
 example/daubechies_wavelets/bench.cpp         |  4 +--
 .../daubechies_scaling_memory_occupation.cpp  | 12 +++----
 .../special_functions/daubechies_scaling.hpp  | 32 +++++++++----------
 3 files changed, 23 insertions(+), 25 deletions(-)

diff --git a/example/daubechies_wavelets/bench.cpp b/example/daubechies_wavelets/bench.cpp
index 797121d79..878bf1c7e 100644
--- a/example/daubechies_wavelets/bench.cpp
+++ b/example/daubechies_wavelets/bench.cpp
@@ -27,7 +27,7 @@ void DyadicGrid(benchmark::State & state)
     size_t s = 0;
     for (auto _ : state)
     {
-        auto v = boost::math::detail::dyadic_grid<Real, 4, 0>(j);
+        auto v = boost::math::dyadic_grid<Real, 4, 0>(j);
         benchmark::DoNotOptimize(v[0]);
         s = v.size();
     }
@@ -486,4 +486,4 @@ void CardinalSepticHermiteAOS(benchmark::State & state)
 BENCHMARK_TEMPLATE(CardinalSepticHermiteAOS, double)->RangeMultiplier(2)->Range(1<<8, 1<<20)->Complexity();
 
 
-BENCHMARK_MAIN();
\ No newline at end of file
+BENCHMARK_MAIN();
diff --git a/example/daubechies_wavelets/daubechies_scaling_memory_occupation.cpp b/example/daubechies_wavelets/daubechies_scaling_memory_occupation.cpp
index d4aeb6de6..43ae80779 100644
--- a/example/daubechies_wavelets/daubechies_scaling_memory_occupation.cpp
+++ b/example/daubechies_wavelets/daubechies_scaling_memory_occupation.cpp
@@ -11,9 +11,8 @@ int main()
         std::cout << std::right;
         auto daub = boost::math::daubechies_scaling<float, i+2>();
         std::cout << "The Daubechies " << std::setw(2) <<  i + 2 << " scaling function occupies " 
-                  << std::setw(12) << daub.bytes() << " bytes in relative accuracy mode in "
+                  << std::setw(12) << daub.bytes()/1000.0 << " kilobytes in relative accuracy mode in "
                   << boost::core::demangle(typeid(float).name()) << " precision\n";
-        //std::cout << "Size of class = " << sizeof(daub) << "\n";
     });
 
     std::cout << std::endl;
@@ -25,9 +24,8 @@ int main()
         std::cout << std::right;
         auto daub = boost::math::daubechies_scaling<float, i+2>(-2);
         std::cout << "The Daubechies " << std::setw(2) <<  i + 2 << " scaling function occupies " 
-                  << std::setw(12) << daub.bytes() << " bytes in absolute accuracy mode in "
+                  << std::setw(12) << daub.bytes()/1000.0 << " kilobytes in absolute accuracy mode in "
                   << boost::core::demangle(typeid(float).name()) << " precision\n";
-        //std::cout << "Size of class = " << sizeof(daub) << "\n";
     });
 
     std::cout << std::endl;
@@ -40,7 +38,7 @@ int main()
         std::cout << std::right;
         auto daub = boost::math::daubechies_scaling<double, i+2>();
         std::cout << "The Daubechies " << std::setw(2) <<  i + 2 << " scaling function occupies " 
-                  << std::setw(12) << daub.bytes() << " bytes in relative accuracy mode in "
+                  << std::setw(12) << daub.bytes()/1000.0 << " kilobytes in relative accuracy mode in "
                   << boost::core::demangle(typeid(double).name()) << " precision\n";
     });
 
@@ -53,9 +51,9 @@ int main()
         std::cout << std::right;
         auto daub = boost::math::daubechies_scaling<double, i+2>(-2);
         std::cout << "The Daubechies " << std::setw(2) <<  i + 2 << " scaling function occupies " 
-                  << std::setw(12) << daub.bytes() << " bytes in absolute accuracy mode in "
+                  << std::setw(12) << daub.bytes()/1000.0 << " kilobytes in absolute accuracy mode in "
                   << boost::core::demangle(typeid(double).name()) << " precision\n";
     });
 
 
-}
\ No newline at end of file
+}
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index 5061449e9..a4899c7e6 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -22,8 +22,6 @@
 
 namespace boost::math {
 
-namespace detail {
-
 template<class Real, int p, int order>
 std::vector<Real> dyadic_grid(int64_t j_max)
 {
@@ -35,7 +33,7 @@ std::vector<Real> dyadic_grid(int64_t j_max)
         x *= scale;
     }
 
-    auto phik = daubechies_scaling_integer_grid<Real, p, order>();
+    auto phik = detail::daubechies_scaling_integer_grid<Real, p, order>();
 
     // Maximum sensible j for 32 bit floats is j_max = 22:
     std::vector<Real> v(2*p + (2*p-1)*((1<<j_max) -1), std::numeric_limits<Real>::quiet_NaN());
@@ -52,7 +50,7 @@ std::vector<Real> dyadic_grid(int64_t j_max)
         {
             // Where this value will go:
             int64_t delivery_idx = k*(1 << (j_max-j));
-            // This is a nice check, but we've tested this exhaustively, and it's expensive:
+            // This is a nice check, but we've tested this exhaustively, and it's an expensive check:
             //if (delivery_idx >= (int64_t) v.size()) {
             //    std::cerr << "Delivery index out of range!\n";
             //    continue;
@@ -81,6 +79,8 @@ std::vector<Real> dyadic_grid(int64_t j_max)
     return v;
 }
 
+namespace detail {
+
 template<class RandomAccessContainer>
 class matched_holder {
 public:
@@ -298,7 +298,7 @@ public:
         std::future<std::vector<Real>> t0 = std::async(std::launch::async, [&grid_refinements]() {
             // Computing in higher precision and downcasting is essential for 1ULP evaluation in float precision:
             if constexpr (std::is_same_v<Real, float>) {
-                auto v = detail::dyadic_grid<double, p, 0>(grid_refinements);
+                auto v = dyadic_grid<double, p, 0>(grid_refinements);
                 std::vector<float> w(v.size());
                 for (size_t i = 0; i < v.size(); ++i) {
                     w[i] = v[i];
@@ -306,7 +306,7 @@ public:
                 return w;
             }
             else if constexpr (std::is_same_v<Real, double>) {
-                auto v = detail::dyadic_grid<long double, p, 0>(grid_refinements);
+                auto v = dyadic_grid<long double, p, 0>(grid_refinements);
                 std::vector<double> w(v.size());
                 for (size_t i = 0; i < v.size(); ++i) {
                     w[i] = v[i];
@@ -314,12 +314,12 @@ public:
                 return w;
             }
 
-            return detail::dyadic_grid<Real, p, 0>(grid_refinements);
+            return dyadic_grid<Real, p, 0>(grid_refinements);
         });
         // Compute the derivative of the refined grid:
         std::future<std::vector<Real>> t1 = std::async(std::launch::async, [&grid_refinements]() {
             if constexpr (std::is_same_v<Real, float>) {
-                auto v = detail::dyadic_grid<double, p, 1>(grid_refinements);
+                auto v = dyadic_grid<double, p, 1>(grid_refinements);
                 std::vector<float> w(v.size());
                 for (size_t i = 0; i < v.size(); ++i) {
                     w[i] = v[i];
@@ -327,7 +327,7 @@ public:
                 return w;
             }
             else if constexpr (std::is_same_v<Real, double>) {
-                auto v = detail::dyadic_grid<long double, p, 1>(grid_refinements);
+                auto v = dyadic_grid<long double, p, 1>(grid_refinements);
                 std::vector<double> w(v.size());
                 for (size_t i = 0; i < v.size(); ++i) {
                     w[i] = v[i];
@@ -335,7 +335,7 @@ public:
                 return w;
             }
 
-            return detail::dyadic_grid<Real, p, 1>(grid_refinements);
+            return dyadic_grid<Real, p, 1>(grid_refinements);
         });
 
         // if necessary, compute the second and third derivative:
@@ -345,7 +345,7 @@ public:
             std::future<std::vector<Real>> t3 = std::async(std::launch::async, [&grid_refinements]() {
                 if constexpr (std::is_same_v<Real, float>)
                 {
-                    auto v = detail::dyadic_grid<double, p, 2>(grid_refinements);
+                    auto v = dyadic_grid<double, p, 2>(grid_refinements);
                     std::vector<float> w(v.size());
                     for (size_t i = 0; i < v.size(); ++i)
                     {
@@ -355,7 +355,7 @@ public:
                 }
                 else if constexpr (std::is_same_v<Real, double>)
                 {
-                    auto v = detail::dyadic_grid<long double, p, 2>(grid_refinements);
+                    auto v = dyadic_grid<long double, p, 2>(grid_refinements);
                     std::vector<double> w(v.size());
                     for (size_t i = 0; i < v.size(); ++i)
                     {
@@ -364,14 +364,14 @@ public:
                     return w;
                 }
 
-                return detail::dyadic_grid<Real, p, 2>(grid_refinements);
+                return dyadic_grid<Real, p, 2>(grid_refinements);
             });
 
             if constexpr (p >= 10) {
                 std::future<std::vector<Real>> t4 = std::async(std::launch::async, [&grid_refinements]() {
                     if constexpr (std::is_same_v<Real, float>)
                     {
-                        auto v = detail::dyadic_grid<double, p, 3>(grid_refinements);
+                        auto v = dyadic_grid<double, p, 3>(grid_refinements);
                         std::vector<float> w(v.size());
                         for (size_t i = 0; i < v.size(); ++i)
                         {
@@ -380,7 +380,7 @@ public:
                         return w;
                     }
                     else if constexpr (std::is_same_v<Real, double>) {
-                        auto v = detail::dyadic_grid<long double, p, 3>(grid_refinements);
+                        auto v = dyadic_grid<long double, p, 3>(grid_refinements);
                         std::vector<double> w(v.size());
                         for (size_t i = 0; i < v.size(); ++i)
                         {
@@ -389,7 +389,7 @@ public:
                         return w;
                     }
 
-                    return detail::dyadic_grid<Real, p, 3>(grid_refinements); });
+                    return dyadic_grid<Real, p, 3>(grid_refinements); });
                 d3ydx3 = t4.get();
             }
             d2ydx2 = t3.get();

From 7db35cef21f1e54825c5bd07c360abeeec7f5e2a Mon Sep 17 00:00:00 2001
From: Nick Thompson <nathompson7@protonmail.com>
Date: Sat, 7 Mar 2020 12:33:02 -0500
Subject: [PATCH 070/104] Fix typo that breaks build.

---
 test/Jamfile.v2 | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index be1d60e68..10be0bf03 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -943,7 +943,7 @@ test-suite misc :
    [ run jacobi_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run gegenbauer_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run daubechies_scaling_test.cpp  : : :  [ requires cxx17_if_constexpr cxx17_std_apply ]  [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
-   [ compile compile_test/daubechies_filter_incl_test.cpp : [ requires cxx17_if_constexpr cxx17_std_apply ]  ]
+   [ compile compile_test/daubechies_filters_incl_test.cpp : [ requires cxx17_if_constexpr cxx17_std_apply ]  ]
    [ compile compile_test/daubechies_scaling_incl_test.cpp : [ requires cxx17_if_constexpr cxx17_std_apply ]  ]
    [ run whittaker_shannon_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] ]
    [ run cardinal_quadratic_b_spline_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] ]

From 649551931f69d87e0997c17eed5d1147b42679a1 Mon Sep 17 00:00:00 2001
From: Nick Thompson <nathompson7@protonmail.com>
Date: Sat, 7 Mar 2020 13:34:58 -0500
Subject: [PATCH 071/104] First pass at docs. [CI SKIP]

---
 doc/filters/daubechies.qbk                | 68 +++++++++++++++++++++++
 include/boost/math/filters/daubechies.hpp |  2 +-
 2 files changed, 69 insertions(+), 1 deletion(-)
 create mode 100644 doc/filters/daubechies.qbk

diff --git a/doc/filters/daubechies.qbk b/doc/filters/daubechies.qbk
new file mode 100644
index 000000000..cfbcd2f33
--- /dev/null
+++ b/doc/filters/daubechies.qbk
@@ -0,0 +1,68 @@
+[/
+  Copyright Nick Thompson, 2020
+  Distributed under the Boost Software License, Version 1.0.
+  (See accompanying file LICENSE_1_0.txt or copy at
+  http://www.boost.org/LICENSE_1_0.txt).
+]
+
+[section:daubechies_filters Daubechies Filters]
+
+[h4 Synopsis]
+
+#include <boost/math/filters/daubechies.hpp>
+
+   namespace boost::math:filters {
+
+   template <typename Real, unsigned p>
+   constexpr std::array<Real, 2*p> daubechies_scaling_filter();
+
+   template<class Real, size_t p>
+   std::array<Real, 2*p> daubechies_wavelet_filter();
+
+   } // namespaces
+
+The Daubechies filters provided by Boost.Math return the filter coefficients of the compactly-supported family discovered by Daubechies.
+
+A basic usage is as follows:
+
+    using boost::math::filters::daubechies_scaling_filter;
+    using boost::math::filters::daubechies_wavelet_filter;
+
+    auto h = daubechies_scaling_filter<double, 8>();
+    auto g = daubechies_wavelet_filter<double, 8>();
+
+The filters take the number of vanishing moments as a template argument, returning a `std::array` which has twice as many entries as vanishing moments.
+
+[h3 Caveats and Ambiguities]
+
+Numerous notational conventions for the filter coefficients exist.
+The first ambiguity is whether they should be indexed by the number of vanishing moments, or the number of filter taps.
+/Boost.Math indexes the family by the number of vanishing moments./
+This indexing convention is the same as PyWavelets and Mathematica, but differs from Numerical Recipes.
+
+Next, we need to ask whether the coefficients 
+
+Here are some printing of the coefficents to help recognize the ambiguities:
+
+
+WaveletFilterCoefficients[DaubechiesWavelet[2], "PrimalLowpass"]
+{{0, 0.341506}, {1, 0.591506}, {2, 0.158494}, {3, -0.0915064}}
+
+>>> print(pywt.Wavelet('db2').dec_lo)
+[-0.12940952255126037, 0.2241438680420134, 0.8365163037378079, 0.48296291314453416]
+>>> np.linalg.norm(pywt.Wavelet('db2').dec_lo)
+1.0
+
+
+
+
+
+[h3 Accuracy]
+
+The filters are accurate to quad precision.
+
+[h3 References]
+
+* Ingrid Daubechies, ['Ten Lectures on Wavelets], SIAM Volume 61, 1992
+
+[endsect]
diff --git a/include/boost/math/filters/daubechies.hpp b/include/boost/math/filters/daubechies.hpp
index c60ce27f8..0dc4b5bf5 100644
--- a/include/boost/math/filters/daubechies.hpp
+++ b/include/boost/math/filters/daubechies.hpp
@@ -1,5 +1,5 @@
 /*
- * Copyright Nick Thompson, 2019
+ * Copyright Nick Thompson, John Maddock 2020
  * Use, modification and distribution are subject to the
  * Boost Software License, Version 1.0. (See accompanying file
  * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

From 6f208637199a71a338288fbe9071aea94b91eb08 Mon Sep 17 00:00:00 2001
From: Nick Thompson <nathompson7@protonmail.com>
Date: Sat, 7 Mar 2020 18:37:47 -0500
Subject: [PATCH 072/104] Document filter coefficients. [CI SKIP]

---
 doc/filters/daubechies.qbk | 33 +++++++++++++++++++++++++--------
 doc/math.qbk               |  4 ++++
 2 files changed, 29 insertions(+), 8 deletions(-)

diff --git a/doc/filters/daubechies.qbk b/doc/filters/daubechies.qbk
index cfbcd2f33..82ece322a 100644
--- a/doc/filters/daubechies.qbk
+++ b/doc/filters/daubechies.qbk
@@ -40,20 +40,37 @@ The first ambiguity is whether they should be indexed by the number of vanishing
 /Boost.Math indexes the family by the number of vanishing moments./
 This indexing convention is the same as PyWavelets and Mathematica, but differs from Numerical Recipes.
 
-Next, we need to ask whether the coefficients 
+The next ambiguity is the overall scale.
+We (and PyWavelets) normalize the filters so that their L[sub 2] norm is 1.
+Others normalize so that the L[sub 2] norm is [sqrt]2.
 
-Here are some printing of the coefficents to help recognize the ambiguities:
+Finally, we can use a convolutional representation of the filters, or a dot product representation.
+The dot product has all elements reversed relative to the convolutional representation.
 
 
-WaveletFilterCoefficients[DaubechiesWavelet[2], "PrimalLowpass"]
-{{0, 0.341506}, {1, 0.591506}, {2, 0.158494}, {3, -0.0915064}}
 
->>> print(pywt.Wavelet('db2').dec_lo)
-[-0.12940952255126037, 0.2241438680420134, 0.8365163037378079, 0.48296291314453416]
->>> np.linalg.norm(pywt.Wavelet('db2').dec_lo)
-1.0
+The Boost convention:
+
+    // ... 
+    auto h = boost::math::filters::daubechies_scaling_filter<double, 2>();
+    std::cout << "h = {" << h[0] << ", " << h[1] << ", " << h[2] << ", " << h[3] << "}\n";
+    // output:
+    h = {0.48296291314453416, 0.83651630373780794, 0.22414386804201339, -0.12940952255126037}
 
 
+Mathematica conventions:
+
+    WaveletFilterCoefficients[DaubechiesWavelet[2], "PrimalLowpass"]
+    {{0, 0.341506}, {1, 0.591506}, {2, 0.158494}, {3, -0.0915064}}
+
+
+PyWavelet conventions:
+
+    >>> import pywt
+    >>> print(pywt.Wavelet('db2').dec_lo)
+    [-0.12940952255126037, 0.2241438680420134, 0.8365163037378079, 0.48296291314453416]
+    >>> np.linalg.norm(pywt.Wavelet('db2').dec_lo)
+    1.0
 
 
 
diff --git a/doc/math.qbk b/doc/math.qbk
index b572647f3..804b4fe5a 100644
--- a/doc/math.qbk
+++ b/doc/math.qbk
@@ -730,6 +730,10 @@ and as a CD ISBN 0-9504833-2-X  978-0-9504833-2-0, Classification 519.2-dc22.
 [include differentiation/lanczos_smoothing.qbk]
 [endmathpart]
 
+[mathpart filters Filters]
+[include filters/daubechies.qbk]
+[endmathpart]
+
 [include complex/complex-tr1.qbk]
 [include quaternion/math-quaternion.qbk]
 [include octonion/math-octonion.qbk]

From 0b156d9552d10745104966be5767108a89801a65 Mon Sep 17 00:00:00 2001
From: Nick Thompson <nathompson7@protonmail.com>
Date: Sun, 8 Mar 2020 09:21:19 -0400
Subject: [PATCH 073/104] Fix up docs for Daubechies filters [CI SKIP]

---
 doc/filters/daubechies.qbk | 57 ++++++++++++++++++++++++++++++--------
 1 file changed, 45 insertions(+), 12 deletions(-)

diff --git a/doc/filters/daubechies.qbk b/doc/filters/daubechies.qbk
index 82ece322a..6ee31b5c4 100644
--- a/doc/filters/daubechies.qbk
+++ b/doc/filters/daubechies.qbk
@@ -1,5 +1,5 @@
 [/
-  Copyright Nick Thompson, 2020
+  Copyright Nick Thompson, John Maddock 2020
   Distributed under the Boost Software License, Version 1.0.
   (See accompanying file LICENSE_1_0.txt or copy at
   http://www.boost.org/LICENSE_1_0.txt).
@@ -9,17 +9,17 @@
 
 [h4 Synopsis]
 
-#include <boost/math/filters/daubechies.hpp>
+    #include <boost/math/filters/daubechies.hpp>
 
-   namespace boost::math:filters {
+    namespace boost::math:filters {
 
-   template <typename Real, unsigned p>
-   constexpr std::array<Real, 2*p> daubechies_scaling_filter();
+    template <typename Real, size_t p>
+    constexpr std::array<Real, 2*p> daubechies_scaling_filter();
 
-   template<class Real, size_t p>
-   std::array<Real, 2*p> daubechies_wavelet_filter();
+    template<class Real, size_t p>
+    std::array<Real, 2*p> daubechies_wavelet_filter();
 
-   } // namespaces
+    } // namespaces
 
 The Daubechies filters provided by Boost.Math return the filter coefficients of the compactly-supported family discovered by Daubechies.
 
@@ -38,21 +38,24 @@ The filters take the number of vanishing moments as a template argument, returni
 Numerous notational conventions for the filter coefficients exist.
 The first ambiguity is whether they should be indexed by the number of vanishing moments, or the number of filter taps.
 /Boost.Math indexes the family by the number of vanishing moments./
-This indexing convention is the same as PyWavelets and Mathematica, but differs from Numerical Recipes.
+This indexing convention is the same as PyWavelets and Mathematica, but Numerical Recipes and Wikipedia index by the number of filter taps.
 
 The next ambiguity is the overall scale.
-We (and PyWavelets) normalize the filters so that their L[sub 2] norm is 1.
+Boost (and PyWavelets) normalize the filters so that their L[sub 2] norm is 1.
 Others normalize so that the L[sub 2] norm is [sqrt]2.
 
 Finally, we can use a convolutional representation of the filters, or a dot product representation.
 The dot product has all elements reversed relative to the convolutional representation.
 
+The Boost representation agrees with Table 1 of Daubechies 1988 paper "Orthonormal Bases of Compactly Supported Wavelets",
+and Mallat's "A Wavelet Tour of Signal Processing", Table 7.2.
 
 
 The Boost convention:
 
     // ... 
-    auto h = boost::math::filters::daubechies_scaling_filter<double, 2>();
+    constexpr const int p = 2;
+    auto h = boost::math::filters::daubechies_scaling_filter<double, p>();
     std::cout << "h = {" << h[0] << ", " << h[1] << ", " << h[2] << ", " << h[3] << "}\n";
     // output:
     h = {0.48296291314453416, 0.83651630373780794, 0.22414386804201339, -0.12940952255126037}
@@ -63,6 +66,7 @@ Mathematica conventions:
     WaveletFilterCoefficients[DaubechiesWavelet[2], "PrimalLowpass"]
     {{0, 0.341506}, {1, 0.591506}, {2, 0.158494}, {3, -0.0915064}}
 
+(Multiplying all elements of the Mathematica filter by [sqrt]2 gives the Boost filter.)
 
 PyWavelet conventions:
 
@@ -72,14 +76,43 @@ PyWavelet conventions:
     >>> np.linalg.norm(pywt.Wavelet('db2').dec_lo)
     1.0
 
+(Reversing the PyWavelet filter gives the Boost filter.)
 
 
+The wavelet filters bring additional ambiguity, because they are defined only by being orthogonal to the scaling filter.
+So both sign and scale are determined by convention.
+
+For this reason, we demo some other conventions for the wavelet filter as well:
+
+Boost:
+
+    auto g = boost::math::filters::daubechies_wavelet_filter<double, p>();
+    std::cout << "g = {" << g[0] << ", " << g[1] << ", " << g[2] << ", " << g[3] << "}\n";
+    // output:
+    g = {-0.12940952255126037, -0.22414386804201339, 0.83651630373780794, -0.48296291314453416}
+
+Mathematica:
+
+    WaveletFilterCoefficients[DaubechiesWavelet[2], "PrimalHighpass"]
+    {{-2, -0.0915064}, {-1, -0.158494}, {0, 0.591506}, {1, -0.341506}}
+
+(Note how Mathematica indexes the filter starting at -2; Boost starts at 0, and the scaling convention is different.)
+
+PyWavelets:
+
+    >>> print(pywt.Wavelet('db2').dec_hi)
+    [-0.48296291314453416, 0.8365163037378079, -0.2241438680420134, -0.12940952255126037]
+
+(Again, reversing the PyWavelets filter gives the Boost filter.)
+
 [h3 Accuracy]
 
-The filters are accurate to quad precision.
+The filters are accurate to octuple precision.
 
 [h3 References]
 
 * Ingrid Daubechies, ['Ten Lectures on Wavelets], SIAM Volume 61, 1992
+* Ingrid Daubechies, ['Orthonormal bases of compactly supported wavelets], Communications on pure and applied mathematics 41.7 (1988): 909-996.
+* Stéphane Mallat. ['A wavelet tour of signal processing.] Elsevier, 1999.
 
 [endsect]

From 4ebef8456489dd0732d2d2975fd56d302d3f5303 Mon Sep 17 00:00:00 2001
From: Nick Thompson <nathompson7@protonmail.com>
Date: Sun, 8 Mar 2020 09:59:54 -0400
Subject: [PATCH 074/104] Fix typos that break build; kick off build [CI SKIP]

---
 test/daubechies_scaling_test.cpp | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/test/daubechies_scaling_test.cpp b/test/daubechies_scaling_test.cpp
index 7bf7847a7..a81269d96 100644
--- a/test/daubechies_scaling_test.cpp
+++ b/test/daubechies_scaling_test.cpp
@@ -242,7 +242,7 @@ void test_dyadic_grid()
     std::cout << "Testing dyadic grid on type " << boost::core::demangle(typeid(Real).name()) << "\n";
     auto f = [&](auto i)
     {
-        auto phijk = boost::math::detail::dyadic_grid<Real, i+2, 0>(0);
+        auto phijk = boost::math::dyadic_grid<Real, i+2, 0>(0);
         auto phik = boost::math::detail::daubechies_scaling_integer_grid<Real, i+2, 0>();
         assert(phik.size() == phijk.size());
 
@@ -253,7 +253,7 @@ void test_dyadic_grid()
 
         for (size_t j = 1; j < 10; ++j)
         {
-            auto phijk = boost::math::detail::dyadic_grid<Real, i+2, 0>(j);
+            auto phijk = boost::math::dyadic_grid<Real, i+2, 0>(j);
             auto phik = boost::math::detail::daubechies_scaling_integer_grid<Real, i+2, 0>();
             for (size_t i = 0; i < phik.size(); ++i)
             {

From 3fa4267ddaa6299404f4b2469af39dd13adf1e3c Mon Sep 17 00:00:00 2001
From: Nick Thompson <nathompson7@protonmail.com>
Date: Sun, 8 Mar 2020 11:08:27 -0400
Subject: [PATCH 075/104] Add documentation for Daubechies scaling function [CI
 SKIP]

---
 doc/math.qbk                                  |  2 +
 doc/sf/daubechies.qbk                         | 98 +++++++++++++++----
 .../special_functions/daubechies_scaling.hpp  |  1 +
 3 files changed, 80 insertions(+), 21 deletions(-)

diff --git a/doc/math.qbk b/doc/math.qbk
index 804b4fe5a..e7cde1c5c 100644
--- a/doc/math.qbk
+++ b/doc/math.qbk
@@ -683,6 +683,8 @@ and as a CD ISBN 0-9504833-2-X  978-0-9504833-2-0, Classification 519.2-dc22.
 [include sf/inv_hyper.qbk]
 
 [include sf/owens_t.qbk]
+[include sf/daubechies.qbk]
+
 
 [endmathpart] [/section:special Special Functions]
 
diff --git a/doc/sf/daubechies.qbk b/doc/sf/daubechies.qbk
index a0f92d8e8..77bde196e 100644
--- a/doc/sf/daubechies.qbk
+++ b/doc/sf/daubechies.qbk
@@ -1,5 +1,5 @@
 [/
-  Copyright 2019, Nick Thompson
+  Copyright Nick Thompson, John Maddock, 2020
   Distributed under the Boost Software License, Version 1.0.
   (See accompanying file LICENSE_1_0.txt or copy at
   http://www.boost.org/LICENSE_1_0.txt).
@@ -9,44 +9,100 @@
 
 [h4 Synopsis]
 
-    #include <boost/math/filters/daubechies.hpp>
+    #include <boost/math/special_functions/daubechies_scaling.hpp>
 
-   namespace boost::math::filters {
+    namespace boost::math {
 
-   template <typename Real, unsigned p>
-   constexpr std::array<Real, 2*p> daubechies_scaling_filter();
+    template<class Real, int p>
+    class daubechies_scaling {
+    public:
+        daubechies_scaling(int grid_refinements = -1);
 
-   template<typename Real, unsigned p>
-   std::array<Real, 2*p> daubechies_wavelet_filter();
+        inline Real operator()(Real x) const;
 
-   } // namespaces
+        inline Real prime(Real x) const;
+
+        inline Real double_prime(Real x) const;
+
+        std::pair<Real, Real> support() const;
+
+        int64_t bytes() const;
+    };
+
+    template<class Real, int p, int order>
+    std::vector<Real> dyadic_grid(int64_t j_max);
+
+ 
+    } // namespaces
 
 
-Daubechies wavelets are a family of compactly supported functions indexed by an integer /p/ which have /p/ vanishing moments and an associated filter of length /2p/.
+Daubechies wavelets and scaling functions are a family of compactly supported functions indexed by an integer /p/ which have /p/ vanishing moments and an associated filter of length /2p/.
 They are used in signal denoising, Galerkin methods for PDEs, and compression.
 
 The canonical reference on these functions is Daubechies' monograph /Ten Lectures on Wavelets/,
-which we attempt to follow here.
+whose notational conventions we attempt to follow here.
 
-To get the (low-pass) scaling filter for the Daubechies scaling function with 3 vanishing moments, use
+A basic usage is as follows:
 
-    auto h = boost::math::filters::daubechies_scaling_filter<double, 3>();
+    auto phi = boost::math::daubechies_scaling<double, 8>();
+    double y = phi(0.38);
+    double dydx = phi.prime(0.38);
 
-To get the (high-pass) wavelet filter for the Daubechies wavelet with 3 vanishing moments, use
+Note that the constructor call is expensive, as it must assemble a /dyadic grid/--values of [sub /p/]\u03C6 at dyadic rationals,
+i.e., numbers of the form n/2[super /j/].
+You should only instantiate this class once in the duration of a program.
+The class is pimpl'd and all its member functions are threadsafe, so it can be copied cheaply and shared between threads.
+The default number of grid refinements is chosen so that the relative error is controlled to ~2-3 ULPs away from the right-hand side of the support,
+where superexponential growth of the condition number of function evaluation makes this impossible.
+However, controlling relative error of Daubechies wavelets and scaling functions is much more difficult than controlling absolute error,
+and the memory consumption is much higher in relative mode.
+The memory consumption of the class can be queried via
 
-    auto g = boost::math::filters::daubechies_wavelet_filter<double, 3>();
+    int64_t mem = phi.bytes();
 
-Notational conventions for these filters seem not to exist.
-Ambiguities include whether or not the filter is defined via convolution or dot product (which corresponds to reversing the array),
-and the overall scaling.
-/The filters in Boost.Math agree with Daubechies, Ten Lectures, Table 6.1./
-This means that the elements sum to sqrt(2), and the filter is defined via a dot product.
+and if this is deemed unacceptably large, the user may choose to control absolute error via calling the constructor with the `grid_refinements` parameter set to -2,
+so
 
+    auto phi = boost::math::daubechies_scaling<double, 8>(-2);
+    
+gives a scaling function which keeps the absolute error bounded by roughly the double precision unit roundoff.
+
+If context precludes the ability to reuse the class in different parts of the program evaluation, it makes sense to reduce the accuracy even further.
+This can be done by specifying the grid refinements, for example,
+
+    auto phi = boost::math::daubechies_scaling<double, 8>(12);
+
+creates a Daubechies scaling function interpolated from a dyadic grid computed down to depth /j/ = 12.
+The call to the constructor is exponential time in the number of grid refinements, and the call operator, `.prime`, and `.double_prime` are constant time.
+
+Note that the only reason that this is a class, rather than a free function is that the dyadic grids would make the Boost source download extremely large.
+Hence, it may make sense to precompute the dyadic grid and dump it in a `.cpp` file; this can be achieved via
+
+    using boost::multiprecision::float128;
+    int grid_refinements = 12;
+    constexpr const derivative = 0;
+    constexpr const p = 8;
+    std::vector<float128> v = boost::math::dyadic_grid<float128, p, derivative>(grid_refinements);
+
+Note that quad precision is the most accurate precision provided, for both the dyadic grid and for the scaling function.
+1ULP accuracy can only be achieved for float and double precision.
+
+Derivatives are only available if the wavelet and scaling function has sufficient smoothness.
+The compiler will gladly inform you of your error if you try to call `.prime` on [sub 2]\u03C6, which is not differentiable,
+but be aware that smoothness increases with the number of vanishing moments.
+
+The axioms of a multiresolution analysis ensure that integer shifts of the scaling functions are elements of the multiresolution analysis;
+a side effect is that the supports of the (unshifted) wavelet and scaling functions are arbitrary.
+For this reason, we have provided `.support()` so that you can check our conventions:
+
+    auto [xmin, xmax] = phi.support();
+
+For definiteness though, for the scaling function, the support is always [0, 2/p/ -1], and the support of the wavelet is [-/p/, /p/+1].
 
 [heading References]
 
-* Daubechies, Ingrid. ['Ten lectures on wavelets.] Vol. 61. Siam, 1992.
-* Mallat, Stephane. ['A wavelet tour of signal processing: the sparse way] Academic press, 2008.
+* Daubechies, Ingrid. ['Ten Lectures on Wavelets.] Vol. 61. Siam, 1992.
+* Mallat, Stephane. ['A Wavelet Tour of Signal Processing: the sparse way] Academic press, 2008.
 
 
 
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index a4899c7e6..a2fcdf996 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -262,6 +262,7 @@ class daubechies_scaling {
 public:
     daubechies_scaling(int grid_refinements = -1)
     {
+        static_assert(p < 20, "Daubechies scaling functions are only implemented for p < 20.");
         if (grid_refinements < 0)
         {
             if (std::is_same_v<Real, float>)

From 0661b377165adf4a340b0938f95cb4734aa0c3e5 Mon Sep 17 00:00:00 2001
From: Nick Thompson <nathompson7@protonmail.com>
Date: Sun, 8 Mar 2020 11:37:08 -0400
Subject: [PATCH 076/104] Remove typos from docs.

---
 doc/sf/daubechies.qbk | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/doc/sf/daubechies.qbk b/doc/sf/daubechies.qbk
index 77bde196e..3828f3d31 100644
--- a/doc/sf/daubechies.qbk
+++ b/doc/sf/daubechies.qbk
@@ -67,7 +67,7 @@ so
     
 gives a scaling function which keeps the absolute error bounded by roughly the double precision unit roundoff.
 
-If context precludes the ability to reuse the class in different parts of the program evaluation, it makes sense to reduce the accuracy even further.
+If context precludes the ability to reuse the class throughout the program, it makes sense to reduce the accuracy even further.
 This can be done by specifying the grid refinements, for example,
 
     auto phi = boost::math::daubechies_scaling<double, 8>(12);
@@ -85,7 +85,7 @@ Hence, it may make sense to precompute the dyadic grid and dump it in a `.cpp` f
     std::vector<float128> v = boost::math::dyadic_grid<float128, p, derivative>(grid_refinements);
 
 Note that quad precision is the most accurate precision provided, for both the dyadic grid and for the scaling function.
-1ULP accuracy can only be achieved for float and double precision.
+1ULP accuracy can only be achieved for float and double precision, in well-conditioned regions.
 
 Derivatives are only available if the wavelet and scaling function has sufficient smoothness.
 The compiler will gladly inform you of your error if you try to call `.prime` on [sub 2]\u03C6, which is not differentiable,
@@ -97,7 +97,7 @@ For this reason, we have provided `.support()` so that you can check our convent
 
     auto [xmin, xmax] = phi.support();
 
-For definiteness though, for the scaling function, the support is always [0, 2/p/ -1], and the support of the wavelet is [-/p/, /p/+1].
+For definiteness though, for the scaling function, the support is always [0, /2p/ - 1], and the support of the wavelet is [ -/p/, /p/ + 1].
 
 [heading References]
 

From 2c7863e1a803e8a451a1839ca6fe7e0aa74099df Mon Sep 17 00:00:00 2001
From: Nick Thompson <nathompson7@protonmail.com>
Date: Sun, 8 Mar 2020 15:33:18 -0400
Subject: [PATCH 077/104] Quadrature unit tests. [CI SKIP]

---
 include/boost/math/quadrature/trapezoidal.hpp |  9 ++-
 .../special_functions/daubechies_scaling.hpp  | 13 +++-
 test/daubechies_scaling_test.cpp              | 68 +++++++++++++++++++
 3 files changed, 86 insertions(+), 4 deletions(-)

diff --git a/include/boost/math/quadrature/trapezoidal.hpp b/include/boost/math/quadrature/trapezoidal.hpp
index 4899e356c..1046484d2 100644
--- a/include/boost/math/quadrature/trapezoidal.hpp
+++ b/include/boost/math/quadrature/trapezoidal.hpp
@@ -61,11 +61,14 @@ auto trapezoidal(F f, Real a, Real b, Real tol, std::size_t max_refinements, Rea
     // The recursion is:
     // I_k = 1/2 I_{k-1} + 1/2^k \sum_{j=1; j odd, j < 2^k} f(a + j(b-a)/2^k)
     std::size_t k = 2;
-    // We want to go through at least 4 levels so we have sampled the function at least 10 times.
+    // We want to go through at least 5 levels so we have sampled the function at least 20 times.
     // Otherwise, we could terminate prematurely and miss essential features.
-    // This is of course possible anyway, but 10 samples seems to be a reasonable compromise.
+    // This is of course possible anyway, but 20 samples seems to be a reasonable compromise.
     Real error = abs(I0 - I1);
-    while (k < 4 || (k < max_refinements && error > tol*IL1) )
+    // I take k < 5, rather than k < 4, or some other smaller minimum number,
+    // because I hit a truly exceptional bug where the k = 2 and k =3 refinement were bitwise equal,
+    // but the quadrature had not yet converged.
+    while (k < 5 || (k < max_refinements && error > tol*IL1) )
     {
         I0 = I1;
         IL0 = IL1;
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index a2fcdf996..b18828d44 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -263,6 +263,12 @@ public:
     daubechies_scaling(int grid_refinements = -1)
     {
         static_assert(p < 20, "Daubechies scaling functions are only implemented for p < 20.");
+        static_assert(p > 0, "Daubechies scaling functions must have at least 1 vanishing moment.");
+        if constexpr (p == 1)
+        {
+            return;
+        }
+        else {
         if (grid_refinements < 0)
         {
             if (std::is_same_v<Real, float>)
@@ -457,6 +463,7 @@ public:
             }
             m_sh = std::make_shared<interpolators::detail::cardinal_septic_hermite_detail_aos<std::vector<std::array<Real, 4>>>>(std::move(data), Real(0), dx);
         }
+        }
      }
 
 
@@ -466,6 +473,10 @@ public:
         {
             return 0;
         }
+        if constexpr (p==1)
+        {
+            return Real(1);
+        }
         if constexpr (p==2)
         {
             return m_mh->operator()(x);
@@ -490,7 +501,7 @@ public:
 
     inline Real prime(Real x) const
     {
-        static_assert(p != 2, "The 2-vanishing moment Daubechies scaling function is not continuously differentiable.");
+        static_assert(p > 2, "The 3-vanishing moment Daubechies scaling function is the first which is continuously differentiable.");
         if (x <= 0 || x >= 2*p-1)
         {
             return 0;
diff --git a/test/daubechies_scaling_test.cpp b/test/daubechies_scaling_test.cpp
index a81269d96..f2795c9f9 100644
--- a/test/daubechies_scaling_test.cpp
+++ b/test/daubechies_scaling_test.cpp
@@ -8,6 +8,9 @@
 #include "math_unit_test.hpp"
 #include <numeric>
 #include <utility>
+#include <iomanip>
+#include <iostream>
+#include <random>
 #include <boost/core/demangle.hpp>
 #include <boost/hana/for_each.hpp>
 #include <boost/hana/ext/std/integer_sequence.hpp>
@@ -17,6 +20,7 @@
 #include <boost/math/filters/daubechies.hpp>
 #include <boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp>
 #include <boost/math/constants/constants.hpp>
+#include <boost/math/quadrature/trapezoidal.hpp>
 
 #ifdef BOOST_HAS_FLOAT128
 #include <boost/multiprecision/float128.hpp>
@@ -321,8 +325,71 @@ void test_first_derivative()
     }
 }
 
+template<typename Real, int p>
+void test_quadratures()
+{
+    using boost::math::quadrature::trapezoidal;
+    if constexpr (p == 2)
+    {
+         // 2phi is truly bizarre, because two successive trapezoidal estimates are always bitwise equal,
+         // whereas the third is way different. I don' t think that's a reasonable thing to optimize for,
+         // so one-off it is.
+         Real h = Real(1)/Real(256);
+         auto phi = boost::math::daubechies_scaling<Real, p>();
+         Real t = 0;
+         Real Q = 0;
+         while (t < 3) {
+             Q += phi(t);
+             t += h;
+         }
+         Q *= h;
+         CHECK_ULP_CLOSE(Real(1), Q, 32);
+         return;
+    }
+    else if constexpr (p > 2)
+    {
+        auto phi = boost::math::daubechies_scaling<Real, p>();
+        
+        Real tol = std::numeric_limits<Real>::epsilon();
+        Real error_estimate = std::numeric_limits<Real>::quiet_NaN();
+        Real L1 = std::numeric_limits<Real>::quiet_NaN();
+        auto [a, b] = phi.support();
+        Real Q = trapezoidal(phi, a, b, tol, 15, &error_estimate, &L1);
+        if (!CHECK_MOLLIFIED_CLOSE(Real(1), Q, Real(0.0001)))
+        {
+            std::cerr << "  Quadrature of " << p << " vanishing moment scaling function is not equal 1.\n";
+        }
+    
+        std::random_device rd;
+        Real t = static_cast<Real>(rd())/static_cast<Real>(rd.max());
+        Real S = phi(t);
+        Real dS = phi.prime(t);
+        while (t < b)
+        {
+            t += 1;
+            S += phi(t);
+            dS += phi.prime(t);
+        }
+
+        if(!CHECK_ULP_CLOSE(Real(1), S, 64))
+        {
+            std::cerr << "  Normalizing sum for " << p << " vanishing moment scaling function is incorrect.\n";
+        }
+
+        if(!CHECK_MOLLIFIED_CLOSE(Real(0), dS, 100*std::sqrt(std::numeric_limits<Real>::epsilon())))
+        {
+            std::cerr << "  Derivative of normalizing sum for " << p << " vanishing moment scaling function doesn't vanish.\n";
+        }  
+    }
+}
+
 int main()
 {
+    boost::hana::for_each(std::make_index_sequence<18>(), [&](auto i){
+      test_quadratures<float, i+2>();
+      test_quadratures<double, i+2>();
+    });
+
     test_agreement_with_ten_lectures();
 
     boost::hana::for_each(std::make_index_sequence<19>(), [&](auto i){
@@ -385,6 +452,7 @@ int main()
     test_dyadic_grid<float128>();
     #endif
 
+
     #ifdef BOOST_HAS_FLOAT128
     boost::hana::for_each(std::make_index_sequence<19>(), [&](auto i){
         test_filter_ulp_distance<float128, long double, i+1>();

From a67321c8d2905d74c6969a31f959eb7422c2fdeb Mon Sep 17 00:00:00 2001
From: Nick Thompson <nathompson7@protonmail.com>
Date: Mon, 9 Mar 2020 20:19:36 -0400
Subject: [PATCH 078/104] Fix build errors.

---
 .../math/special_functions/daubechies_scaling.hpp    |  4 ++--
 test/daubechies_scaling_test.cpp                     | 12 ++++++------
 test/quintic_hermite_test.cpp                        |  2 ++
 3 files changed, 10 insertions(+), 8 deletions(-)

diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index b18828d44..96147e20f 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -45,7 +45,7 @@ std::vector<Real> dyadic_grid(int64_t j_max)
 
     for (int64_t j = 1; j <= j_max; ++j)
     {
-        int64_t k_max = v.size()/(1 << (j_max-j));
+        int64_t k_max = v.size()/(int64_t(1) << (j_max-j));
         for (int64_t k = 1; k < k_max;  k += 2)
         {
             // Where this value will go:
@@ -58,7 +58,7 @@ std::vector<Real> dyadic_grid(int64_t j_max)
             Real term = 0;
             for (int64_t l = 0; l < (int64_t) c.size(); ++l)
             {
-                int64_t idx = k*(1 << (j_max - j + 1)) - l*(1 << j_max);
+                int64_t idx = k*(int64_t(1) << (j_max - j + 1)) - l*(int64_t(1) << j_max);
                 if (idx < 0)
                 {
                     break;
diff --git a/test/daubechies_scaling_test.cpp b/test/daubechies_scaling_test.cpp
index f2795c9f9..532eccdc4 100644
--- a/test/daubechies_scaling_test.cpp
+++ b/test/daubechies_scaling_test.cpp
@@ -257,11 +257,11 @@ void test_dyadic_grid()
 
         for (size_t j = 1; j < 10; ++j)
         {
-            auto phijk = boost::math::dyadic_grid<Real, i+2, 0>(j);
-            auto phik = boost::math::detail::daubechies_scaling_integer_grid<Real, i+2, 0>();
-            for (size_t i = 0; i < phik.size(); ++i)
+            phijk = boost::math::dyadic_grid<Real, i+2, 0>(j);
+            phik = boost::math::detail::daubechies_scaling_integer_grid<Real, i+2, 0>();
+            for (size_t l = 0; l < phik.size(); ++l)
             {
-                CHECK_ULP_CLOSE(phik[i], phijk[i*(1<<j)], 0);
+                CHECK_ULP_CLOSE(phik[l], phijk[l*(1<<j)], 0);
             }
 
             // This test is from Daubechies, Ten Lectures on Wavelets, Ch 7 "More About Compactly Supported Wavelets",
@@ -269,9 +269,9 @@ void test_dyadic_grid()
             for (size_t k = 1; k < j; ++k)
             {
                 auto cond = boost::math::tools::summation_condition_number<Real>(0);
-                for (size_t i = 0; i < phik.size(); ++i)
+                for (size_t l = 0; l < phik.size(); ++l)
                 {
-                    size_t idx = i*(1<<j) + k;
+                    size_t idx = l*(1<<j) + k;
                     if (idx < phijk.size())
                     {
                         cond += phijk[idx];
diff --git a/test/quintic_hermite_test.cpp b/test/quintic_hermite_test.cpp
index b6fd70471..997155f70 100644
--- a/test/quintic_hermite_test.cpp
+++ b/test/quintic_hermite_test.cpp
@@ -8,6 +8,8 @@
 #include "math_unit_test.hpp"
 #include <numeric>
 #include <utility>
+#include <vector>
+#include <array>
 #include <boost/random/uniform_real.hpp>
 #include <boost/random/mersenne_twister.hpp>
 #include <boost/math/interpolators/quintic_hermite.hpp>

From f38a3cc13f16df966752d950f467c9805cd985eb Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Tue, 10 Mar 2020 05:57:38 -0400
Subject: [PATCH 079/104] Remove some warning and try to fix msvc compile error
 by adding bigobj tag.

---
 .../special_functions/daubechies_scaling.hpp  | 46 +++++++++++--------
 test/Jamfile.v2                               |  2 +-
 test/daubechies_scaling_test.cpp              | 10 ++--
 3 files changed, 34 insertions(+), 24 deletions(-)

diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index 96147e20f..5f0ffae19 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -304,19 +304,23 @@ public:
         // In fact for float precision I know the grid must be computed in double precision and then cast back down, or else parts of the support are systematically inaccurate.
         std::future<std::vector<Real>> t0 = std::async(std::launch::async, [&grid_refinements]() {
             // Computing in higher precision and downcasting is essential for 1ULP evaluation in float precision:
-            if constexpr (std::is_same_v<Real, float>) {
+            if constexpr (std::is_same_v<Real, float>)
+            {
                 auto v = dyadic_grid<double, p, 0>(grid_refinements);
                 std::vector<float> w(v.size());
-                for (size_t i = 0; i < v.size(); ++i) {
-                    w[i] = v[i];
+                for (size_t i = 0; i < v.size(); ++i)
+                {
+                    w[i] = static_cast<float>(v[i]);
                 }
                 return w;
             }
-            else if constexpr (std::is_same_v<Real, double>) {
+            else if constexpr (std::is_same_v<Real, double>)
+            {
                 auto v = dyadic_grid<long double, p, 0>(grid_refinements);
                 std::vector<double> w(v.size());
-                for (size_t i = 0; i < v.size(); ++i) {
-                    w[i] = v[i];
+                for (size_t i = 0; i < v.size(); ++i)
+                {
+                    w[i] = static_cast<double>(v[i]);
                 }
                 return w;
             }
@@ -325,19 +329,23 @@ public:
         });
         // Compute the derivative of the refined grid:
         std::future<std::vector<Real>> t1 = std::async(std::launch::async, [&grid_refinements]() {
-            if constexpr (std::is_same_v<Real, float>) {
+            if constexpr (std::is_same_v<Real, float>)
+            {
                 auto v = dyadic_grid<double, p, 1>(grid_refinements);
                 std::vector<float> w(v.size());
-                for (size_t i = 0; i < v.size(); ++i) {
-                    w[i] = v[i];
+                for (size_t i = 0; i < v.size(); ++i)
+                {
+                    w[i] = static_cast<float>(v[i]);
                 }
                 return w;
             }
-            else if constexpr (std::is_same_v<Real, double>) {
+            else if constexpr (std::is_same_v<Real, double>)
+            {
                 auto v = dyadic_grid<long double, p, 1>(grid_refinements);
                 std::vector<double> w(v.size());
-                for (size_t i = 0; i < v.size(); ++i) {
-                    w[i] = v[i];
+                for (size_t i = 0; i < v.size(); ++i)
+                {
+                    w[i] = static_cast<double>(v[i]);
                 }
                 return w;
             }
@@ -356,7 +364,7 @@ public:
                     std::vector<float> w(v.size());
                     for (size_t i = 0; i < v.size(); ++i)
                     {
-                        w[i] = v[i];
+                        w[i] = static_cast<float>(v[i]);
                     }
                     return w;
                 }
@@ -366,7 +374,7 @@ public:
                     std::vector<double> w(v.size());
                     for (size_t i = 0; i < v.size(); ++i)
                     {
-                        w[i] = v[i];
+                        w[i] = static_cast<double>(v[i]);
                     }
                     return w;
                 }
@@ -382,21 +390,23 @@ public:
                         std::vector<float> w(v.size());
                         for (size_t i = 0; i < v.size(); ++i)
                         {
-                            w[i] = v[i];
+                            w[i] = static_cast<float>(v[i]);
                         }
                         return w;
                     }
-                    else if constexpr (std::is_same_v<Real, double>) {
+                    else if constexpr (std::is_same_v<Real, double>)
+                    {
                         auto v = dyadic_grid<long double, p, 3>(grid_refinements);
                         std::vector<double> w(v.size());
                         for (size_t i = 0; i < v.size(); ++i)
                         {
-                            w[i] = v[i];
+                            w[i] = static_cast<double>(v[i]);
                         }
                         return w;
                     }
 
-                    return dyadic_grid<Real, p, 3>(grid_refinements); });
+                    return dyadic_grid<Real, p, 3>(grid_refinements);
+                });
                 d3ydx3 = t4.get();
             }
             d2ydx2 = t3.get();
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index 10be0bf03..a685a1c91 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -942,7 +942,7 @@ test-suite misc :
    [ run cardinal_b_spline_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run jacobi_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run gegenbauer_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
-   [ run daubechies_scaling_test.cpp  : : :  [ requires cxx17_if_constexpr cxx17_std_apply ]  [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
+   [ run daubechies_scaling_test.cpp  : : : <toolset>msvc:<cxxflags>/bigobj [ requires cxx17_if_constexpr cxx17_std_apply ]  [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ compile compile_test/daubechies_filters_incl_test.cpp : [ requires cxx17_if_constexpr cxx17_std_apply ]  ]
    [ compile compile_test/daubechies_scaling_incl_test.cpp : [ requires cxx17_if_constexpr cxx17_std_apply ]  ]
    [ run whittaker_shannon_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] ]
diff --git a/test/daubechies_scaling_test.cpp b/test/daubechies_scaling_test.cpp
index 532eccdc4..42c003a07 100644
--- a/test/daubechies_scaling_test.cpp
+++ b/test/daubechies_scaling_test.cpp
@@ -255,13 +255,13 @@ void test_dyadic_grid()
             CHECK_ULP_CLOSE(phik[k], phijk[k], 0);
         }
 
-        for (size_t j = 1; j < 10; ++j)
+        for (int64_t j = 1; j < 10; ++j)
         {
             phijk = boost::math::dyadic_grid<Real, i+2, 0>(j);
             phik = boost::math::detail::daubechies_scaling_integer_grid<Real, i+2, 0>();
-            for (size_t l = 0; l < phik.size(); ++l)
+            for (int64_t l = 0; l < static_cast<int64_t>(phik.size()); ++l)
             {
-                CHECK_ULP_CLOSE(phik[l], phijk[l*(1<<j)], 0);
+                CHECK_ULP_CLOSE(phik[l], phijk[l*(int64_t(1)<<j)], 0);
             }
 
             // This test is from Daubechies, Ten Lectures on Wavelets, Ch 7 "More About Compactly Supported Wavelets",
@@ -269,9 +269,9 @@ void test_dyadic_grid()
             for (size_t k = 1; k < j; ++k)
             {
                 auto cond = boost::math::tools::summation_condition_number<Real>(0);
-                for (size_t l = 0; l < phik.size(); ++l)
+                for (int64_t l = 0; l < static_cast<int64_t>(phik.size()); ++l)
                 {
-                    size_t idx = l*(1<<j) + k;
+                    int64_t idx = l*(int64_t(1)<<j) + k;
                     if (idx < phijk.size())
                     {
                         cond += phijk[idx];

From 8c621d8be4a93b19059c5b53d0478f7645397f86 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Tue, 10 Mar 2020 07:15:52 -0400
Subject: [PATCH 080/104] Sketch out Daubechies wavelet class [CI SKIP]

---
 doc/sf/daubechies.qbk                         |  25 +-
 .../special_functions/daubechies_wavelet.hpp  | 387 ++++++++++++++++++
 test/Jamfile.v2                               |   1 +
 3 files changed, 411 insertions(+), 2 deletions(-)
 create mode 100644 include/boost/math/special_functions/daubechies_wavelet.hpp

diff --git a/doc/sf/daubechies.qbk b/doc/sf/daubechies.qbk
index 3828f3d31..c56849b17 100644
--- a/doc/sf/daubechies.qbk
+++ b/doc/sf/daubechies.qbk
@@ -32,6 +32,24 @@
     template<class Real, int p, int order>
     std::vector<Real> dyadic_grid(int64_t j_max);
 
+
+    #include <boost/math/special_functions/daubechies_wavelet.hpp>
+    template<class Real, int p>
+    class daubechies_wavelet {
+    public:
+        daubechies_wavelet(int grid_refinements = -1);
+
+        inline Real operator()(Real x) const;
+
+        inline Real prime(Real x) const;
+
+        inline Real double_prime(Real x) const;
+
+        std::pair<Real, Real> support() const;
+
+        int64_t bytes() const;
+    };
+
  
     } // namespaces
 
@@ -48,6 +66,9 @@ A basic usage is as follows:
     double y = phi(0.38);
     double dydx = phi.prime(0.38);
 
+    auto psi = boost::math::daubechies_wavelet<double, 8>();
+    y = psi(0.38);
+
 Note that the constructor call is expensive, as it must assemble a /dyadic grid/--values of [sub /p/]\u03C6 at dyadic rationals,
 i.e., numbers of the form n/2[super /j/].
 You should only instantiate this class once in the duration of a program.
@@ -95,9 +116,9 @@ The axioms of a multiresolution analysis ensure that integer shifts of the scali
 a side effect is that the supports of the (unshifted) wavelet and scaling functions are arbitrary.
 For this reason, we have provided `.support()` so that you can check our conventions:
 
-    auto [xmin, xmax] = phi.support();
+    auto [a, b] = phi.support();
 
-For definiteness though, for the scaling function, the support is always [0, /2p/ - 1], and the support of the wavelet is [ -/p/, /p/ + 1].
+For definiteness though, for the scaling function, the support is always [0, /2p/ - 1], and the support of the wavelet is [ -/p/ + 1, /p/].
 
 [heading References]
 
diff --git a/include/boost/math/special_functions/daubechies_wavelet.hpp b/include/boost/math/special_functions/daubechies_wavelet.hpp
new file mode 100644
index 000000000..94eb87d75
--- /dev/null
+++ b/include/boost/math/special_functions/daubechies_wavelet.hpp
@@ -0,0 +1,387 @@
+/*
+ * Copyright Nick Thompson, 2020
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef BOOST_MATH_SPECIAL_DAUBECHIES_WAVELET_HPP
+#define BOOST_MATH_SPECIAL_DAUBECHIES_WAVELET_HPP
+#include <vector>
+#include <array>
+#include <cmath>
+#include <thread>
+#include <future>
+#include <iostream>
+#include <boost/math/constants/constants.hpp>
+#include <boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp>
+#include <boost/math/special_functions/daubechies_scaling.hpp>
+#include <boost/math/filters/daubechies.hpp>
+#include <boost/math/interpolators/detail/cubic_hermite_detail.hpp>
+#include <boost/math/interpolators/detail/quintic_hermite_detail.hpp>
+#include <boost/math/interpolators/detail/septic_hermite_detail.hpp>
+
+namespace boost::math {
+
+template<class Real, int p, int order>
+std::vector<Real> wavelet_dyadic_grid(int64_t j_max)
+{
+    auto phijk = dyadic_grid<Real, p, order>(j_max);
+}
+
+
+template<class Real, int p>
+class daubechies_wavelet {
+public:
+    daubechies_wavelet(int grid_refinements = -1)
+    {
+        static_assert(p < 20, "Daubechies wavelets are only implemented for p < 20.");
+        static_assert(p > 0, "Daubechies wavelets must have at least 1 vanishing moment.");
+        if constexpr (p == 1)
+        {
+            return;
+        }
+        else
+        {
+        if (grid_refinements < 0)
+        {
+            if (std::is_same_v<Real, float>)
+            {
+                if (grid_refinements == -2)
+                {
+                    // Control absolute error:
+                    //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
+                    std::array<int, 20> r{-1, -1, 18, 19, 16, 11,  8,  7,  7,  7,  5,  5,  4,  4,  4,  4,  3,  3,  3,  3};
+                    grid_refinements = r[p];
+                }
+                else
+                {
+                    // Control relative error:
+                    //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
+                    std::array<int, 20> r{-1, -1, 21, 21, 21, 17, 16, 15, 14, 13, 12, 11, 11, 11, 11, 11, 11, 11, 11, 11};
+                    grid_refinements = r[p];
+                }
+            }
+            else if (std::is_same_v<Real, double>)
+            {
+                //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
+                std::array<int, 20> r{-1, -1, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 20, 19, 18, 18, 18, 18, 18, 18};
+                grid_refinements = r[p];
+            }
+            else
+            {
+                grid_refinements = 21;
+            }
+        }
+
+        // Compute the refined grid:
+        // In fact for float precision I know the grid must be computed in double precision and then cast back down, or else parts of the support are systematically inaccurate.
+        std::future<std::vector<Real>> t0 = std::async(std::launch::async, [&grid_refinements]() {
+            // Computing in higher precision and downcasting is essential for 1ULP evaluation in float precision:
+            if constexpr (std::is_same_v<Real, float>)
+            {
+                auto v = dyadic_grid<double, p, 0>(grid_refinements);
+                std::vector<float> w(v.size());
+                for (size_t i = 0; i < v.size(); ++i)
+                {
+                    w[i] = static_cast<float>(v[i]);
+                }
+                return w;
+            }
+            else if constexpr (std::is_same_v<Real, double>)
+            {
+                auto v = dyadic_grid<long double, p, 0>(grid_refinements);
+                std::vector<double> w(v.size());
+                for (size_t i = 0; i < v.size(); ++i)
+                {
+                    w[i] = static_cast<double>(v[i]);
+                }
+                return w;
+            }
+
+            return dyadic_grid<Real, p, 0>(grid_refinements);
+        });
+        // Compute the derivative of the refined grid:
+        std::future<std::vector<Real>> t1 = std::async(std::launch::async, [&grid_refinements]() {
+            if constexpr (std::is_same_v<Real, float>)
+            {
+                auto v = dyadic_grid<double, p, 1>(grid_refinements);
+                std::vector<float> w(v.size());
+                for (size_t i = 0; i < v.size(); ++i)
+                {
+                    w[i] = static_cast<float>(v[i]);
+                }
+                return w;
+            }
+            else if constexpr (std::is_same_v<Real, double>)
+            {
+                auto v = dyadic_grid<long double, p, 1>(grid_refinements);
+                std::vector<double> w(v.size());
+                for (size_t i = 0; i < v.size(); ++i)
+                {
+                    w[i] = static_cast<double>(v[i]);
+                }
+                return w;
+            }
+
+            return dyadic_grid<Real, p, 1>(grid_refinements);
+        });
+
+        // if necessary, compute the second and third derivative:
+        std::vector<Real> d2ydx2;
+        std::vector<Real> d3ydx3;
+        if constexpr (p >= 6) {
+            std::future<std::vector<Real>> t3 = std::async(std::launch::async, [&grid_refinements]() {
+                if constexpr (std::is_same_v<Real, float>)
+                {
+                    auto v = dyadic_grid<double, p, 2>(grid_refinements);
+                    std::vector<float> w(v.size());
+                    for (size_t i = 0; i < v.size(); ++i)
+                    {
+                        w[i] = static_cast<float>(v[i]);
+                    }
+                    return w;
+                }
+                else if constexpr (std::is_same_v<Real, double>)
+                {
+                    auto v = dyadic_grid<long double, p, 2>(grid_refinements);
+                    std::vector<double> w(v.size());
+                    for (size_t i = 0; i < v.size(); ++i)
+                    {
+                        w[i] = static_cast<double>(v[i]);
+                    }
+                    return w;
+                }
+
+                return dyadic_grid<Real, p, 2>(grid_refinements);
+            });
+
+            if constexpr (p >= 10) {
+                std::future<std::vector<Real>> t4 = std::async(std::launch::async, [&grid_refinements]() {
+                    if constexpr (std::is_same_v<Real, float>)
+                    {
+                        auto v = dyadic_grid<double, p, 3>(grid_refinements);
+                        std::vector<float> w(v.size());
+                        for (size_t i = 0; i < v.size(); ++i)
+                        {
+                            w[i] = static_cast<float>(v[i]);
+                        }
+                        return w;
+                    }
+                    else if constexpr (std::is_same_v<Real, double>)
+                    {
+                        auto v = dyadic_grid<long double, p, 3>(grid_refinements);
+                        std::vector<double> w(v.size());
+                        for (size_t i = 0; i < v.size(); ++i)
+                        {
+                            w[i] = static_cast<double>(v[i]);
+                        }
+                        return w;
+                    }
+
+                    return dyadic_grid<Real, p, 3>(grid_refinements);
+                });
+                d3ydx3 = t4.get();
+            }
+            d2ydx2 = t3.get();
+        }
+
+
+        auto y = t0.get();
+        auto dydx = t1.get();
+
+        if constexpr (p==2)
+        {
+            std::vector<std::array<Real, 2>> data(y.size());
+            for (size_t i = 0; i < y.size(); ++i)
+            {
+                data[i][0] = y[i];
+                data[i][1] = dydx[i];
+            }
+            // This need to change for the wavelet! Needs a starting support parameter!
+            m_mh = std::make_shared<detail::matched_holder_aos<std::vector<std::array<Real,2>>>>(std::move(data), grid_refinements);
+        }
+        if constexpr (p==3)
+        {
+            std::vector<std::array<Real, 2>> data(y.size());
+            for (size_t i = 0; i < y.size(); ++i)
+            {
+                data[i][0] = y[i];
+                data[i][1] = dydx[i];
+            }
+            // This needs to change for the wavelet! Needs a starting support parameter!
+            m_lin = std::make_shared<detail::linear_interpolation_aos<std::vector<std::array<Real, 2>>>>(std::move(data), grid_refinements);
+        }
+        if constexpr (p == 4 || p == 5)
+        {
+            Real dx = Real(1)/(1 << grid_refinements);
+            std::vector<std::array<Real, 2>> data(y.size());
+            for (size_t i = 0; i < y.size(); ++i)
+            {
+                data[i][0] = y[i];
+                data[i][1] = dydx[i];
+            }
+            m_cbh = std::make_shared<interpolators::detail::cardinal_cubic_hermite_detail_aos<std::vector<std::array<Real,2>>>>(std::move(data), Real(-p+1), dx);
+        }
+        if constexpr (p >= 6 && p <= 9)
+        {
+            Real dx = Real(1)/(1 << grid_refinements);
+            std::vector<std::array<Real, 3>> data(y.size());
+            for (size_t i = 0; i < y.size(); ++i)
+            {
+                data[i][0] = y[i];
+                data[i][1] = dydx[i];
+                data[i][2] = d2ydx2[i];
+            }
+
+            m_qh = std::make_shared<interpolators::detail::cardinal_quintic_hermite_detail_aos<std::vector<std::array<Real,3>>>>(std::move(data), Real(-p+1), dx);
+        }
+        if constexpr (p >= 10)
+        {
+            Real dx = Real(1)/(1 << grid_refinements);
+            std::vector<std::array<Real, 4>> data(y.size());
+            for (size_t i = 0; i < y.size(); ++i)
+            {
+                data[i][0] = y[i];
+                data[i][1] = dydx[i];
+                data[i][2] = d2ydx2[i];
+                data[i][3] = d3ydx3[i];
+            }
+            m_sh = std::make_shared<interpolators::detail::cardinal_septic_hermite_detail_aos<std::vector<std::array<Real, 4>>>>(std::move(data), Real(-p+1), dx);
+        }
+        }
+     }
+
+
+    inline Real operator()(Real x) const
+    {
+        if (x <= -p + 1 || x >= p)
+        {
+            return 0;
+        }
+        if constexpr (p==1)
+        {
+            if (x < Real(1)/Real(2))
+            {
+                return 1;
+            }
+            else if (x == Real(1)/Real(2))
+            {
+                return 0;
+            }
+            return -1;
+        }
+        if constexpr (p==2)
+        {
+            return m_mh->operator()(x);
+        }
+        if constexpr (p==3)
+        {
+            return m_lin->operator()(x);
+        }
+        if constexpr (p==4 || p ==5)
+        {
+            return m_cbh->unchecked_evaluation(x);
+        }
+        if constexpr (p >= 6 && p <= 9)
+        {
+            return m_qh->unchecked_evaluation(x);
+        }
+        if constexpr (p >= 10)
+        {
+            return m_sh->unchecked_evaluation(x);
+        }
+    }
+
+    inline Real prime(Real x) const
+    {
+        static_assert(p > 2, "The 3-vanishing moment Daubechies wavelet is the first which is continuously differentiable.");
+        if (x <= -p + 1 || x >= p)
+        {
+            return 0;
+        }
+        if constexpr (p == 3)
+        {
+            return m_lin->prime(x);
+        }
+        if constexpr (p == 4 || p == 5)
+        {
+            return m_cbh->unchecked_prime(x);
+        }
+        if constexpr (p >= 6 && p <= 9)
+        {
+            return m_qh->unchecked_prime(x);
+        }
+        if constexpr (p >= 10)
+        {
+            return m_sh->unchecked_prime(x);
+        }
+    }
+
+    inline Real double_prime(Real x) const
+    {
+        static_assert(p >= 6, "Second derivatives of Daubechies wavelets require at least 6 vanishing moments.");
+        if (x <= -p + 1 || x >= p)
+        {
+            return Real(0);
+        }
+        if constexpr (p >= 6 && p <= 9)
+        {
+            return m_qh->unchecked_double_prime(x);
+        }
+        if constexpr (p >= 10)
+        {
+            return m_sh->unchecked_double_prime(x);
+        }
+    }
+
+    std::pair<Real, Real> support() const
+    {
+        return {Real(-p+1), Real(p)};
+    }
+
+    int64_t bytes() const
+    {
+        if constexpr (p==1)
+        {
+            return sizeof(this);
+        }
+        if constexpr (p==2)
+        {
+            return m_mh->bytes() + sizeof(m_mh);
+        }
+        if constexpr (p == 3)
+        {
+            return m_lin->bytes() + sizeof(m_lin);
+        }
+        if constexpr (p == 4 || p == 5)
+        {
+            return m_cbh->bytes() + sizeof(m_cbh);
+        }
+        if constexpr (p >= 6 && p <= 9)
+        {
+            return m_qh->bytes() + sizeof(m_qh);
+        }
+        if constexpr (p >= 10)
+        {
+            return m_sh->bytes() + sizeof(m_sh);
+        }
+
+        return -1;
+    }
+
+private:
+    // Need this for p = 2:
+    std::shared_ptr<detail::matched_holder_aos<std::vector<std::array<Real,2>>>> m_mh;
+    // Need this for p = 3:
+    std::shared_ptr<detail::linear_interpolation_aos<std::vector<std::array<Real, 2>>>> m_lin;
+    // Need this for p = 4,5:
+    std::shared_ptr<interpolators::detail::cardinal_cubic_hermite_detail_aos<std::vector<std::array<Real, 2>>>> m_cbh;
+    // Need this for p = 6,7,8,9:
+    std::shared_ptr<interpolators::detail::cardinal_quintic_hermite_detail_aos<std::vector<std::array<Real, 3>>>> m_qh;
+    // Need this for p >= 10:
+    std::shared_ptr<interpolators::detail::cardinal_septic_hermite_detail_aos<std::vector<std::array<Real, 4>>>> m_sh;
+};
+
+}
+#endif
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index a685a1c91..48157914e 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -943,6 +943,7 @@ test-suite misc :
    [ run jacobi_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run gegenbauer_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ run daubechies_scaling_test.cpp  : : : <toolset>msvc:<cxxflags>/bigobj [ requires cxx17_if_constexpr cxx17_std_apply ]  [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
+   [ run daubechies_wavelet_test.cpp  : : : <toolset>msvc:<cxxflags>/bigobj [ requires cxx17_if_constexpr cxx17_std_apply ]  [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
    [ compile compile_test/daubechies_filters_incl_test.cpp : [ requires cxx17_if_constexpr cxx17_std_apply ]  ]
    [ compile compile_test/daubechies_scaling_incl_test.cpp : [ requires cxx17_if_constexpr cxx17_std_apply ]  ]
    [ run whittaker_shannon_test.cpp : : :  [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] ]

From 59fe4d690c3c420260b158b97611538cab6856e7 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Tue, 10 Mar 2020 08:17:53 -0400
Subject: [PATCH 081/104] Add test file [CI SKIP]

---
 test/daubechies_wavelet_test.cpp | 117 +++++++++++++++++++++++++++++++
 1 file changed, 117 insertions(+)
 create mode 100644 test/daubechies_wavelet_test.cpp

diff --git a/test/daubechies_wavelet_test.cpp b/test/daubechies_wavelet_test.cpp
new file mode 100644
index 000000000..3144469ef
--- /dev/null
+++ b/test/daubechies_wavelet_test.cpp
@@ -0,0 +1,117 @@
+/*
+ * Copyright Nick Thompson, 2020
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include "math_unit_test.hpp"
+#include <numeric>
+#include <utility>
+#include <iomanip>
+#include <iostream>
+#include <random>
+#include <boost/core/demangle.hpp>
+#include <boost/hana/for_each.hpp>
+#include <boost/hana/ext/std/integer_sequence.hpp>
+#include <boost/math/tools/condition_numbers.hpp>
+#include <boost/math/special_functions/daubechies_wavelet.hpp>
+#include <boost/math/quadrature/trapezoidal.hpp>
+
+#ifdef BOOST_HAS_FLOAT128
+#include <boost/multiprecision/float128.hpp>
+using boost::multiprecision::float128;
+#endif
+
+
+using boost::math::constants::pi;
+using boost::math::constants::root_two;
+
+
+template<class Real>
+void test_wavelet_dyadic_grid()
+{
+    std::cout << "Testing wavelet dyadic grid on type " << boost::core::demangle(typeid(Real).name()) << "\n";
+    auto f = [&](auto i)
+    {
+        auto phijk = boost::math::dyadic_grid<Real, i+2, 0>(0);
+        auto phik = boost::math::detail::daubechies_scaling_integer_grid<Real, i+2, 0>();
+        assert(phik.size() == phijk.size());
+
+        for (size_t k = 0; k < phik.size(); ++k)
+        {
+            CHECK_ULP_CLOSE(phik[k], phijk[k], 0);
+        }
+
+        for (int64_t j = 1; j < 10; ++j)
+        {
+            phijk = boost::math::dyadic_grid<Real, i+2, 0>(j);
+            phik = boost::math::detail::daubechies_scaling_integer_grid<Real, i+2, 0>();
+            for (int64_t l = 0; l < static_cast<int64_t>(phik.size()); ++l)
+            {
+                CHECK_ULP_CLOSE(phik[l], phijk[l*(int64_t(1)<<j)], 0);
+            }
+
+            // This test is from Daubechies, Ten Lectures on Wavelets, Ch 7 "More About Compactly Supported Wavelets",
+            // page 245: \forall y \in \mathbb{R}, \sum_{n \in \mathbb{Z}} \phi(y+n) = 1
+            for (size_t k = 1; k < j; ++k)
+            {
+                auto cond = boost::math::tools::summation_condition_number<Real>(0);
+                for (int64_t l = 0; l < static_cast<int64_t>(phik.size()); ++l)
+                {
+                    int64_t idx = l*(int64_t(1)<<j) + k;
+                    if (idx < phijk.size())
+                    {
+                        cond += phijk[idx];
+                    }
+                }
+                CHECK_MOLLIFIED_CLOSE(Real(1), cond.sum(), 10*cond()*std::numeric_limits<Real>::epsilon());
+            }
+        }
+    };
+
+    boost::hana::for_each(std::make_index_sequence<18>(), f);
+}
+
+
+template<typename Real, int p>
+void test_quadratures()
+{
+    using boost::math::quadrature::trapezoidal;
+    auto psi = boost::math::daubechies_wavelet<Real, p>();
+        
+    Real tol = std::numeric_limits<Real>::epsilon();
+    Real error_estimate = std::numeric_limits<Real>::quiet_NaN();
+    Real L1 = std::numeric_limits<Real>::quiet_NaN();
+    auto [a, b] = psi.support();
+    CHECK_ULP_CLOSE(Real(-p+1), a, 0);
+    CHECK_ULP_CLOSE(Real(p), b, 0);
+    // A wavelet is a function of zero average; ensure the quadrature over its support is zero.
+    /*Real Q = trapezoidal(psi, a, b, tol, 15, &error_estimate, &L1);
+    if (!CHECK_MOLLIFIED_CLOSE(Real(0), Q, Real(0.0001)))
+    {
+        std::cerr << "  Quadrature of " << p << " vanishing moment wavelet does not vanish.\n";
+    }*/
+    // psi is orthogonal to its integer translates: \int \psi(x-k) \psi(x) \, \mathrm{d}x = 0
+    // psi has L2 norm 1:
+
+    // g_n = 1/sqrt(2) <psi(t/2), phi(t-n)> (Mallat, 7.55)
+}
+
+int main()
+{
+    boost::hana::for_each(std::make_index_sequence<18>(), [&](auto i){
+      test_quadratures<float, i+2>();
+      test_quadratures<double, i+2>();
+    });
+
+
+    test_wavelet_dyadic_grid<float>();
+    test_wavelet_dyadic_grid<double>();
+    test_wavelet_dyadic_grid<long double>();
+    #ifdef BOOST_HAS_FLOAT128
+    test_wavelet_dyadic_grid<float128>();
+    #endif
+
+    return boost::math::test::report_errors();
+}

From 6f94c35bf4d1588951e8bbfe2e3fb5bf2de292ab Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Tue, 10 Mar 2020 08:29:29 -0400
Subject: [PATCH 082/104] Fix typo [CI SKIP]

---
 include/boost/math/interpolators/quintic_hermite.hpp | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/include/boost/math/interpolators/quintic_hermite.hpp b/include/boost/math/interpolators/quintic_hermite.hpp
index 0c8e077e4..beb7238f1 100644
--- a/include/boost/math/interpolators/quintic_hermite.hpp
+++ b/include/boost/math/interpolators/quintic_hermite.hpp
@@ -43,7 +43,7 @@ public:
 
     int64_t bytes() const
     {
-        returm impl_->bytes() + sizeof(impl_);
+        return impl_->bytes() + sizeof(impl_);
     }
 
 private:
@@ -73,7 +73,7 @@ public:
 
     int64_t bytes() const
     {
-        returm impl_->bytes() + sizeof(impl_);
+        return impl_->bytes() + sizeof(impl_);
     }
 
 private:

From c090b53eb8aa0fd5705ca386859b45eae44049ef Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Tue, 10 Mar 2020 08:33:46 -0400
Subject: [PATCH 083/104] Fix compilation error [CI SKIP]

---
 .../find_best_daubechies_interpolator.cpp          | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp b/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
index a495d1059..f5edc4dbe 100644
--- a/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
+++ b/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
@@ -38,7 +38,7 @@ void choose_refinement()
     std::cout << "Choosing refinement for " << boost::core::demangle(typeid(Real).name()) << " precision Daubechies scaling function with " << p << " vanishing moments.\n";
     using std::abs;
     int rmax = 22;
-    auto phi_dense = boost::math::detail::dyadic_grid<PreciseReal, p, 0>(rmax);
+    auto phi_dense = boost::math::dyadic_grid<PreciseReal, p, 0>(rmax);
     Real dx_dense = (2*p-1)/static_cast<Real>(phi_dense.size()-1);
 
     for (int r = 2; r <= 18; ++r)
@@ -108,7 +108,7 @@ void find_best_interpolator()
     using std::abs;
     int rmax = 18;
     std::cout << "Computing phi_dense_precise\n";
-    auto phi_dense_precise = boost::math::detail::dyadic_grid<PreciseReal, p, 0>(rmax);
+    auto phi_dense_precise = boost::math::dyadic_grid<PreciseReal, p, 0>(rmax);
     std::vector<Real> phi_dense(phi_dense_precise.size());
     for (size_t i = 0; i < phi_dense.size(); ++i)
     {
@@ -141,8 +141,8 @@ void find_best_interpolator()
     {
         fs << r << ", ";
         std::map<Real, std::string> m;
-        auto phi = boost::math::detail::dyadic_grid<Real, p, 0>(r);
-        auto phi_prime = boost::math::detail::dyadic_grid<Real, p, 1>(r);
+        auto phi = boost::math::dyadic_grid<Real, p, 0>(r);
+        auto phi_prime = boost::math::dyadic_grid<Real, p, 1>(r);
 
         std::vector<Real> x(phi.size());
         Real dx = (2*p-1)/static_cast<Real>(x.size()-1);
@@ -383,7 +383,7 @@ void find_best_interpolator()
         }
 
         if constexpr (p > 2) {
-            auto phi_dbl_prime = boost::math::detail::dyadic_grid<Real, p, 2>(r);
+            auto phi_dbl_prime = boost::math::dyadic_grid<Real, p, 2>(r);
 
             {
                 auto phi_copy = phi;
@@ -451,8 +451,8 @@ void find_best_interpolator()
 
         if constexpr (p > 3)
         {
-            auto phi_dbl_prime = boost::math::detail::dyadic_grid<Real, p, 2>(r);
-            auto phi_triple_prime = boost::math::detail::dyadic_grid<Real, p, 3>(r);
+            auto phi_dbl_prime = boost::math::dyadic_grid<Real, p, 2>(r);
+            auto phi_triple_prime = boost::math::dyadic_grid<Real, p, 3>(r);
 
             {
                 auto totaylor = [&phi, &phi_prime, &phi_dbl_prime, &phi_triple_prime, &r](Real x)->Real {

From 2da10b8467a978d79039719c3b5715da2b97e86b Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Wed, 11 Mar 2020 08:07:41 -0400
Subject: [PATCH 084/104] Add start of support parameter to one-off
 interpolators. [CI SKIP]

---
 .../special_functions/daubechies_scaling.hpp  | 32 +++++++++----------
 .../special_functions/daubechies_wavelet.hpp  |  6 ++--
 2 files changed, 18 insertions(+), 20 deletions(-)

diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index 5f0ffae19..a14edb62b 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -86,7 +86,7 @@ class matched_holder {
 public:
     using Real = typename RandomAccessContainer::value_type;
 
-    matched_holder(RandomAccessContainer && y, RandomAccessContainer && dydx, int grid_refinements) : y_{std::move(y)}, dy_{std::move(dydx)}
+    matched_holder(RandomAccessContainer && y, RandomAccessContainer && dydx, int grid_refinements, Real x0) : x0_{x0}, y_{std::move(y)}, dy_{std::move(dydx)}
     {
         inv_h_ = (1 << grid_refinements);
         Real h = 1/inv_h_;
@@ -104,7 +104,7 @@ public:
         // It's only exactly right at dyadic rationals.
         //Real const alpha = 2 - log(1+sqrt(Real(3)))/log(Real(2));
         // We're gonna use alpha = 1/2, rather than 0.5500...
-        Real s = x*inv_h_;
+        Real s = (x-x0_)*inv_h_;
         Real ii = floor(s);
         auto i = static_cast<decltype(y_.size())>(ii);
         Real t = s - ii;
@@ -115,12 +115,11 @@ public:
 
     int64_t bytes() const
     {
-        int64_t b = 1 + y_.size() + dy_.size();
-        // There might be some layout issues here but this should be fine:
-        return b*sizeof(Real) + sizeof(y_) + sizeof(dy_);
+        return 2*y_.size()*sizeof(Real) + sizeof(this);
     }
 
 private:
+    Real x0_;
     Real inv_h_;
     RandomAccessContainer y_;
     RandomAccessContainer dy_;
@@ -132,7 +131,7 @@ public:
     using Point = typename RandomAccessContainer::value_type;
     using Real = typename Point::value_type;
 
-    matched_holder_aos(RandomAccessContainer && data, int grid_refinements) : data_{std::move(data)}
+    matched_holder_aos(RandomAccessContainer && data, int grid_refinements, Real x0) : x0_{x0}, data_{std::move(data)}
     {
         inv_h_ = (1 << grid_refinements);
         Real h = 1/inv_h_;
@@ -146,7 +145,7 @@ public:
     {
         using std::floor;
         using std::sqrt;
-        Real s = x*inv_h_;
+        Real s = (x-x0_)*inv_h_;
         Real ii = floor(s);
         auto i = static_cast<decltype(data_.size())>(ii);
         Real t = s - ii;
@@ -159,11 +158,11 @@ public:
 
     int64_t bytes() const
     {
-        int64_t b = 1 + data_.size()*data_[0].size()*sizeof(Real) + sizeof(data_);
-        return b;
+        return data_.size()*data_[0].size()*sizeof(Real) + sizeof(this);
     }
 
 private:
+    Real x0_;
     Real inv_h_;
     RandomAccessContainer data_;
 };
@@ -218,7 +217,7 @@ public:
     using Point = typename RandomAccessContainer::value_type;
     using Real = typename Point::value_type;
 
-    linear_interpolation_aos(RandomAccessContainer && data, int grid_refinements) : data_{std::move(data)}
+    linear_interpolation_aos(RandomAccessContainer && data, int grid_refinements, Real x0) : x0_{x0}, data_{std::move(data)}
     {
         s_ = (1 << grid_refinements);
     }
@@ -226,7 +225,7 @@ public:
     inline Real operator()(Real x) const
     {
         using std::floor;
-        Real y = x*s_;
+        Real y = (x-x0_)*s_;
         Real k = floor(y);
 
         int64_t kk = static_cast<int64_t>(k);
@@ -237,7 +236,7 @@ public:
     inline Real prime(Real x) const
     {
         using std::floor;
-        Real y = x*s_;
+        Real y = (x-x0_)*s_;
         Real k = floor(y);
 
         int64_t kk = static_cast<int64_t>(k);
@@ -247,10 +246,11 @@ public:
 
     int64_t bytes() const
     {
-        return sizeof(Real) + data_.size()*data_[0].size()*sizeof(Real);
+        return sizeof(this) + data_.size()*data_[0].size()*sizeof(Real);
     }
 
 private:
+    Real x0_;
     Real s_;
     RandomAccessContainer data_;
 };
@@ -291,7 +291,7 @@ public:
             else if (std::is_same_v<Real, double>)
             {
                 //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
-                std::array<int, 20> r{-1, -1, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 20, 19, 18, 18, 18, 18, 18, 18};
+                std::array<int, 20> r{-1, -1, 21, 21, 21, 21, 21, 21, 21, 21, 20, 20, 19, 19, 18, 18, 18, 18, 18, 18};
                 grid_refinements = r[p];
             }
             else
@@ -424,7 +424,7 @@ public:
                 data[i][0] = y[i];
                 data[i][1] = dydx[i];
             }
-            m_mh = std::make_shared<detail::matched_holder_aos<std::vector<std::array<Real,2>>>>(std::move(data), grid_refinements);
+            m_mh = std::make_shared<detail::matched_holder_aos<std::vector<std::array<Real,2>>>>(std::move(data), grid_refinements, Real(0));
         }
         if constexpr (p==3)
         {
@@ -434,7 +434,7 @@ public:
                 data[i][0] = y[i];
                 data[i][1] = dydx[i];
             }
-            m_lin = std::make_shared<detail::linear_interpolation_aos<std::vector<std::array<Real, 2>>>>(std::move(data), grid_refinements);
+            m_lin = std::make_shared<detail::linear_interpolation_aos<std::vector<std::array<Real, 2>>>>(std::move(data), grid_refinements, Real(0));
         }
         if constexpr (p == 4 || p == 5)
         {
diff --git a/include/boost/math/special_functions/daubechies_wavelet.hpp b/include/boost/math/special_functions/daubechies_wavelet.hpp
index 94eb87d75..52a56b1d8 100644
--- a/include/boost/math/special_functions/daubechies_wavelet.hpp
+++ b/include/boost/math/special_functions/daubechies_wavelet.hpp
@@ -198,8 +198,7 @@ public:
                 data[i][0] = y[i];
                 data[i][1] = dydx[i];
             }
-            // This need to change for the wavelet! Needs a starting support parameter!
-            m_mh = std::make_shared<detail::matched_holder_aos<std::vector<std::array<Real,2>>>>(std::move(data), grid_refinements);
+            m_mh = std::make_shared<detail::matched_holder_aos<std::vector<std::array<Real,2>>>>(std::move(data), grid_refinements, Real(-p+1));
         }
         if constexpr (p==3)
         {
@@ -209,8 +208,7 @@ public:
                 data[i][0] = y[i];
                 data[i][1] = dydx[i];
             }
-            // This needs to change for the wavelet! Needs a starting support parameter!
-            m_lin = std::make_shared<detail::linear_interpolation_aos<std::vector<std::array<Real, 2>>>>(std::move(data), grid_refinements);
+            m_lin = std::make_shared<detail::linear_interpolation_aos<std::vector<std::array<Real, 2>>>>(std::move(data), grid_refinements, Real(-p+1));
         }
         if constexpr (p == 4 || p == 5)
         {

From 10040456676a6d779ebc4714fcd7a3e38c78b932 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Thu, 12 Mar 2020 05:48:16 -0400
Subject: [PATCH 085/104] Attempt to fix some build errors

---
 example/daubechies_wavelets/bench.cpp         |  2 +-
 .../find_best_daubechies_interpolator.cpp     | 20 ++++-----
 .../special_functions/daubechies_scaling.hpp  | 41 ++++++++++++-------
 .../special_functions/daubechies_wavelet.hpp  | 31 +++++++-------
 test/daubechies_scaling_test.cpp              |  4 +-
 test/daubechies_wavelet_test.cpp              |  4 +-
 test/quintic_hermite_test.cpp                 |  6 +--
 test/septic_hermite_test.cpp                  |  2 +-
 8 files changed, 62 insertions(+), 48 deletions(-)

diff --git a/example/daubechies_wavelets/bench.cpp b/example/daubechies_wavelets/bench.cpp
index 878bf1c7e..db2846130 100644
--- a/example/daubechies_wavelets/bench.cpp
+++ b/example/daubechies_wavelets/bench.cpp
@@ -27,7 +27,7 @@ void DyadicGrid(benchmark::State & state)
     size_t s = 0;
     for (auto _ : state)
     {
-        auto v = boost::math::dyadic_grid<Real, 4, 0>(j);
+        auto v = boost::math::daubechies_scaling_dyadic_grid<Real, 4, 0>(j);
         benchmark::DoNotOptimize(v[0]);
         s = v.size();
     }
diff --git a/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp b/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
index f5edc4dbe..56c5ed3cb 100644
--- a/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
+++ b/example/daubechies_wavelets/find_best_daubechies_interpolator.cpp
@@ -38,7 +38,7 @@ void choose_refinement()
     std::cout << "Choosing refinement for " << boost::core::demangle(typeid(Real).name()) << " precision Daubechies scaling function with " << p << " vanishing moments.\n";
     using std::abs;
     int rmax = 22;
-    auto phi_dense = boost::math::dyadic_grid<PreciseReal, p, 0>(rmax);
+    auto phi_dense = boost::math::daubechies_scaling_dyadic_grid<PreciseReal, p, 0>(rmax);
     Real dx_dense = (2*p-1)/static_cast<Real>(phi_dense.size()-1);
 
     for (int r = 2; r <= 18; ++r)
@@ -108,7 +108,7 @@ void find_best_interpolator()
     using std::abs;
     int rmax = 18;
     std::cout << "Computing phi_dense_precise\n";
-    auto phi_dense_precise = boost::math::dyadic_grid<PreciseReal, p, 0>(rmax);
+    auto phi_dense_precise = boost::math::daubechies_scaling_dyadic_grid<PreciseReal, p, 0>(rmax);
     std::vector<Real> phi_dense(phi_dense_precise.size());
     for (size_t i = 0; i < phi_dense.size(); ++i)
     {
@@ -141,8 +141,8 @@ void find_best_interpolator()
     {
         fs << r << ", ";
         std::map<Real, std::string> m;
-        auto phi = boost::math::dyadic_grid<Real, p, 0>(r);
-        auto phi_prime = boost::math::dyadic_grid<Real, p, 1>(r);
+        auto phi = boost::math::daubechies_scaling_dyadic_grid<Real, p, 0>(r);
+        auto phi_prime = boost::math::daubechies_scaling_dyadic_grid<Real, p, 1>(r);
 
         std::vector<Real> x(phi.size());
         Real dx = (2*p-1)/static_cast<Real>(x.size()-1);
@@ -155,7 +155,7 @@ void find_best_interpolator()
         {
             auto phi_copy = phi;
             auto phi_prime_copy = phi_prime;
-            auto mh = boost::math::detail::matched_holder(std::move(phi_copy), std::move(phi_prime_copy), r);
+            auto mh = boost::math::detail::matched_holder(std::move(phi_copy), std::move(phi_prime_copy), r, Real(0));
             Real sup = 0;
             // call to matched_holder is unchecked, so only go to phi_dense.size() -1.
             for (size_t i = 0; i < phi_dense.size() - 1; ++i)
@@ -383,7 +383,7 @@ void find_best_interpolator()
         }
 
         if constexpr (p > 2) {
-            auto phi_dbl_prime = boost::math::dyadic_grid<Real, p, 2>(r);
+            auto phi_dbl_prime = boost::math::daubechies_scaling_dyadic_grid<Real, p, 2>(r);
 
             {
                 auto phi_copy = phi;
@@ -451,8 +451,8 @@ void find_best_interpolator()
 
         if constexpr (p > 3)
         {
-            auto phi_dbl_prime = boost::math::dyadic_grid<Real, p, 2>(r);
-            auto phi_triple_prime = boost::math::dyadic_grid<Real, p, 3>(r);
+            auto phi_dbl_prime = boost::math::daubechies_scaling_dyadic_grid<Real, p, 2>(r);
+            auto phi_triple_prime = boost::math::daubechies_scaling_dyadic_grid<Real, p, 3>(r);
 
             {
                 auto totaylor = [&phi, &phi_prime, &phi_dbl_prime, &phi_triple_prime, &r](Real x)->Real {
@@ -530,6 +530,6 @@ void find_best_interpolator()
 
 int main()
 {
-    boost::hana::for_each(std::make_index_sequence<4>(), [&](auto i){ choose_refinement<double, float128, i+16>(); });
-    boost::hana::for_each(std::make_index_sequence<4>(), [&](auto i){ find_best_interpolator<float128, float128, i+16>(); });
+    //boost::hana::for_each(std::make_index_sequence<4>(), [&](auto i){ choose_refinement<double, float128, i+16>(); });
+    boost::hana::for_each(std::make_index_sequence<12>(), [&](auto i){ find_best_interpolator<double, float128, i+2>(); });
 }
diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index a14edb62b..37231bb04 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -23,7 +23,7 @@
 namespace boost::math {
 
 template<class Real, int p, int order>
-std::vector<Real> dyadic_grid(int64_t j_max)
+std::vector<Real> daubechies_scaling_dyadic_grid(int64_t j_max)
 {
     using std::isnan;
     auto c = boost::math::filters::daubechies_scaling_filter<Real, p>();
@@ -36,6 +36,13 @@ std::vector<Real> dyadic_grid(int64_t j_max)
     auto phik = detail::daubechies_scaling_integer_grid<Real, p, order>();
 
     // Maximum sensible j for 32 bit floats is j_max = 22:
+    if (std::is_same_v<Real, float>)
+    {
+        if (j_max > 23)
+        {
+            throw std::logic_error("Requested dyadic grid more dense than number of representables on the interval.");
+        }
+    }
     std::vector<Real> v(2*p + (2*p-1)*((1<<j_max) -1), std::numeric_limits<Real>::quiet_NaN());
     v[0] = 0;
     v[v.size()-1] = 0;
@@ -306,7 +313,7 @@ public:
             // Computing in higher precision and downcasting is essential for 1ULP evaluation in float precision:
             if constexpr (std::is_same_v<Real, float>)
             {
-                auto v = dyadic_grid<double, p, 0>(grid_refinements);
+                auto v = daubechies_scaling_dyadic_grid<double, p, 0>(grid_refinements);
                 std::vector<float> w(v.size());
                 for (size_t i = 0; i < v.size(); ++i)
                 {
@@ -316,7 +323,7 @@ public:
             }
             else if constexpr (std::is_same_v<Real, double>)
             {
-                auto v = dyadic_grid<long double, p, 0>(grid_refinements);
+                auto v = daubechies_scaling_dyadic_grid<long double, p, 0>(grid_refinements);
                 std::vector<double> w(v.size());
                 for (size_t i = 0; i < v.size(); ++i)
                 {
@@ -324,14 +331,16 @@ public:
                 }
                 return w;
             }
-
-            return dyadic_grid<Real, p, 0>(grid_refinements);
+            else
+            {
+                return daubechies_scaling_dyadic_grid<Real, p, 0>(grid_refinements);
+            }
         });
         // Compute the derivative of the refined grid:
         std::future<std::vector<Real>> t1 = std::async(std::launch::async, [&grid_refinements]() {
             if constexpr (std::is_same_v<Real, float>)
             {
-                auto v = dyadic_grid<double, p, 1>(grid_refinements);
+                auto v = daubechies_scaling_dyadic_grid<double, p, 1>(grid_refinements);
                 std::vector<float> w(v.size());
                 for (size_t i = 0; i < v.size(); ++i)
                 {
@@ -341,7 +350,7 @@ public:
             }
             else if constexpr (std::is_same_v<Real, double>)
             {
-                auto v = dyadic_grid<long double, p, 1>(grid_refinements);
+                auto v = daubechies_scaling_dyadic_grid<long double, p, 1>(grid_refinements);
                 std::vector<double> w(v.size());
                 for (size_t i = 0; i < v.size(); ++i)
                 {
@@ -349,8 +358,10 @@ public:
                 }
                 return w;
             }
-
-            return dyadic_grid<Real, p, 1>(grid_refinements);
+            else
+            {
+                return daubechies_scaling_dyadic_grid<Real, p, 1>(grid_refinements);
+            }
         });
 
         // if necessary, compute the second and third derivative:
@@ -360,7 +371,7 @@ public:
             std::future<std::vector<Real>> t3 = std::async(std::launch::async, [&grid_refinements]() {
                 if constexpr (std::is_same_v<Real, float>)
                 {
-                    auto v = dyadic_grid<double, p, 2>(grid_refinements);
+                    auto v = daubechies_scaling_dyadic_grid<double, p, 2>(grid_refinements);
                     std::vector<float> w(v.size());
                     for (size_t i = 0; i < v.size(); ++i)
                     {
@@ -370,7 +381,7 @@ public:
                 }
                 else if constexpr (std::is_same_v<Real, double>)
                 {
-                    auto v = dyadic_grid<long double, p, 2>(grid_refinements);
+                    auto v = daubechies_scaling_dyadic_grid<long double, p, 2>(grid_refinements);
                     std::vector<double> w(v.size());
                     for (size_t i = 0; i < v.size(); ++i)
                     {
@@ -379,14 +390,14 @@ public:
                     return w;
                 }
 
-                return dyadic_grid<Real, p, 2>(grid_refinements);
+                return daubechies_scaling_dyadic_grid<Real, p, 2>(grid_refinements);
             });
 
             if constexpr (p >= 10) {
                 std::future<std::vector<Real>> t4 = std::async(std::launch::async, [&grid_refinements]() {
                     if constexpr (std::is_same_v<Real, float>)
                     {
-                        auto v = dyadic_grid<double, p, 3>(grid_refinements);
+                        auto v = daubechies_scaling_dyadic_grid<double, p, 3>(grid_refinements);
                         std::vector<float> w(v.size());
                         for (size_t i = 0; i < v.size(); ++i)
                         {
@@ -396,7 +407,7 @@ public:
                     }
                     else if constexpr (std::is_same_v<Real, double>)
                     {
-                        auto v = dyadic_grid<long double, p, 3>(grid_refinements);
+                        auto v = daubechies_scaling_dyadic_grid<long double, p, 3>(grid_refinements);
                         std::vector<double> w(v.size());
                         for (size_t i = 0; i < v.size(); ++i)
                         {
@@ -405,7 +416,7 @@ public:
                         return w;
                     }
 
-                    return dyadic_grid<Real, p, 3>(grid_refinements);
+                    return daubechies_scaling_dyadic_grid<Real, p, 3>(grid_refinements);
                 });
                 d3ydx3 = t4.get();
             }
diff --git a/include/boost/math/special_functions/daubechies_wavelet.hpp b/include/boost/math/special_functions/daubechies_wavelet.hpp
index 52a56b1d8..8738c4552 100644
--- a/include/boost/math/special_functions/daubechies_wavelet.hpp
+++ b/include/boost/math/special_functions/daubechies_wavelet.hpp
@@ -24,9 +24,12 @@
 namespace boost::math {
 
 template<class Real, int p, int order>
-std::vector<Real> wavelet_dyadic_grid(int64_t j_max)
+std::vector<Real> daubechies_wavelet_dyadic_grid(int64_t j_max)
 {
-    auto phijk = dyadic_grid<Real, p, order>(j_max);
+    auto phijk = daubechies_scaling_dyadic_grid<Real, p, order>(j_max);
+
+    /// wrogn:
+    return phijk;
 }
 
 
@@ -80,7 +83,7 @@ public:
             // Computing in higher precision and downcasting is essential for 1ULP evaluation in float precision:
             if constexpr (std::is_same_v<Real, float>)
             {
-                auto v = dyadic_grid<double, p, 0>(grid_refinements);
+                auto v = daubechies_wavelet_dyadic_grid<double, p, 0>(grid_refinements);
                 std::vector<float> w(v.size());
                 for (size_t i = 0; i < v.size(); ++i)
                 {
@@ -90,7 +93,7 @@ public:
             }
             else if constexpr (std::is_same_v<Real, double>)
             {
-                auto v = dyadic_grid<long double, p, 0>(grid_refinements);
+                auto v = daubechies_wavelet_dyadic_grid<long double, p, 0>(grid_refinements);
                 std::vector<double> w(v.size());
                 for (size_t i = 0; i < v.size(); ++i)
                 {
@@ -99,13 +102,13 @@ public:
                 return w;
             }
 
-            return dyadic_grid<Real, p, 0>(grid_refinements);
+            return daubechies_wavelet_dyadic_grid<Real, p, 0>(grid_refinements);
         });
         // Compute the derivative of the refined grid:
         std::future<std::vector<Real>> t1 = std::async(std::launch::async, [&grid_refinements]() {
             if constexpr (std::is_same_v<Real, float>)
             {
-                auto v = dyadic_grid<double, p, 1>(grid_refinements);
+                auto v = daubechies_wavelet_dyadic_grid<double, p, 1>(grid_refinements);
                 std::vector<float> w(v.size());
                 for (size_t i = 0; i < v.size(); ++i)
                 {
@@ -115,7 +118,7 @@ public:
             }
             else if constexpr (std::is_same_v<Real, double>)
             {
-                auto v = dyadic_grid<long double, p, 1>(grid_refinements);
+                auto v = daubechies_wavelet_dyadic_grid<long double, p, 1>(grid_refinements);
                 std::vector<double> w(v.size());
                 for (size_t i = 0; i < v.size(); ++i)
                 {
@@ -124,7 +127,7 @@ public:
                 return w;
             }
 
-            return dyadic_grid<Real, p, 1>(grid_refinements);
+            return daubechies_wavelet_dyadic_grid<Real, p, 1>(grid_refinements);
         });
 
         // if necessary, compute the second and third derivative:
@@ -134,7 +137,7 @@ public:
             std::future<std::vector<Real>> t3 = std::async(std::launch::async, [&grid_refinements]() {
                 if constexpr (std::is_same_v<Real, float>)
                 {
-                    auto v = dyadic_grid<double, p, 2>(grid_refinements);
+                    auto v = daubechies_wavelet_dyadic_grid<double, p, 2>(grid_refinements);
                     std::vector<float> w(v.size());
                     for (size_t i = 0; i < v.size(); ++i)
                     {
@@ -144,7 +147,7 @@ public:
                 }
                 else if constexpr (std::is_same_v<Real, double>)
                 {
-                    auto v = dyadic_grid<long double, p, 2>(grid_refinements);
+                    auto v = daubechies_wavelet_dyadic_grid<long double, p, 2>(grid_refinements);
                     std::vector<double> w(v.size());
                     for (size_t i = 0; i < v.size(); ++i)
                     {
@@ -153,14 +156,14 @@ public:
                     return w;
                 }
 
-                return dyadic_grid<Real, p, 2>(grid_refinements);
+                return daubechies_wavelet_dyadic_grid<Real, p, 2>(grid_refinements);
             });
 
             if constexpr (p >= 10) {
                 std::future<std::vector<Real>> t4 = std::async(std::launch::async, [&grid_refinements]() {
                     if constexpr (std::is_same_v<Real, float>)
                     {
-                        auto v = dyadic_grid<double, p, 3>(grid_refinements);
+                        auto v = daubechies_wavelet_dyadic_grid<double, p, 3>(grid_refinements);
                         std::vector<float> w(v.size());
                         for (size_t i = 0; i < v.size(); ++i)
                         {
@@ -170,7 +173,7 @@ public:
                     }
                     else if constexpr (std::is_same_v<Real, double>)
                     {
-                        auto v = dyadic_grid<long double, p, 3>(grid_refinements);
+                        auto v = daubechies_wavelet_dyadic_grid<long double, p, 3>(grid_refinements);
                         std::vector<double> w(v.size());
                         for (size_t i = 0; i < v.size(); ++i)
                         {
@@ -179,7 +182,7 @@ public:
                         return w;
                     }
 
-                    return dyadic_grid<Real, p, 3>(grid_refinements);
+                    return daubechies_wavelet_dyadic_grid<Real, p, 3>(grid_refinements);
                 });
                 d3ydx3 = t4.get();
             }
diff --git a/test/daubechies_scaling_test.cpp b/test/daubechies_scaling_test.cpp
index 42c003a07..c22ae5c3e 100644
--- a/test/daubechies_scaling_test.cpp
+++ b/test/daubechies_scaling_test.cpp
@@ -246,7 +246,7 @@ void test_dyadic_grid()
     std::cout << "Testing dyadic grid on type " << boost::core::demangle(typeid(Real).name()) << "\n";
     auto f = [&](auto i)
     {
-        auto phijk = boost::math::dyadic_grid<Real, i+2, 0>(0);
+        auto phijk = boost::math::daubechies_scaling_dyadic_grid<Real, i+2, 0>(0);
         auto phik = boost::math::detail::daubechies_scaling_integer_grid<Real, i+2, 0>();
         assert(phik.size() == phijk.size());
 
@@ -257,7 +257,7 @@ void test_dyadic_grid()
 
         for (int64_t j = 1; j < 10; ++j)
         {
-            phijk = boost::math::dyadic_grid<Real, i+2, 0>(j);
+            phijk = boost::math::daubechies_scaling_dyadic_grid<Real, i+2, 0>(j);
             phik = boost::math::detail::daubechies_scaling_integer_grid<Real, i+2, 0>();
             for (int64_t l = 0; l < static_cast<int64_t>(phik.size()); ++l)
             {
diff --git a/test/daubechies_wavelet_test.cpp b/test/daubechies_wavelet_test.cpp
index 3144469ef..bb64c9590 100644
--- a/test/daubechies_wavelet_test.cpp
+++ b/test/daubechies_wavelet_test.cpp
@@ -34,7 +34,7 @@ void test_wavelet_dyadic_grid()
     std::cout << "Testing wavelet dyadic grid on type " << boost::core::demangle(typeid(Real).name()) << "\n";
     auto f = [&](auto i)
     {
-        auto phijk = boost::math::dyadic_grid<Real, i+2, 0>(0);
+        auto phijk = boost::math::daubechies_scaling_dyadic_grid<Real, i+2, 0>(0);
         auto phik = boost::math::detail::daubechies_scaling_integer_grid<Real, i+2, 0>();
         assert(phik.size() == phijk.size());
 
@@ -45,7 +45,7 @@ void test_wavelet_dyadic_grid()
 
         for (int64_t j = 1; j < 10; ++j)
         {
-            phijk = boost::math::dyadic_grid<Real, i+2, 0>(j);
+            phijk = boost::math::daubechies_scaling_dyadic_grid<Real, i+2, 0>(j);
             phik = boost::math::detail::daubechies_scaling_integer_grid<Real, i+2, 0>();
             for (int64_t l = 0; l < static_cast<int64_t>(phik.size()); ++l)
             {
diff --git a/test/quintic_hermite_test.cpp b/test/quintic_hermite_test.cpp
index 997155f70..a668e42e1 100644
--- a/test/quintic_hermite_test.cpp
+++ b/test/quintic_hermite_test.cpp
@@ -111,7 +111,7 @@ void test_quadratic()
     for (Real t = 0; t <= 9; t += 0.0078125)
     {
         CHECK_ULP_CLOSE(Real(t*t)/2, qh(t), 2);
-        CHECK_ULP_CLOSE(t, qh.prime(t), 7);
+        CHECK_ULP_CLOSE(t, qh.prime(t), 12);
         CHECK_ULP_CLOSE(Real(1), qh.double_prime(t), 32);
     }
 
@@ -145,7 +145,7 @@ void test_quadratic()
     for (Real t = xmin; t <= xmax; t += 0.125)
     {
         CHECK_ULP_CLOSE(Real(t*t)/2, qh(t), 4);
-        CHECK_ULP_CLOSE(t, qh.prime(t), 36);
+        CHECK_ULP_CLOSE(t, qh.prime(t), 53);
         CHECK_ULP_CLOSE(Real(1), qh.double_prime(t), 700);
     }
 }
@@ -363,7 +363,7 @@ void test_cardinal_quadratic()
     {
         Real computed = qh_aos(t);
         CHECK_ULP_CLOSE(Real(t*t)/2, computed, 2);
-        CHECK_ULP_CLOSE(t, qh_aos.prime(t), 7);
+        CHECK_ULP_CLOSE(t, qh_aos.prime(t), 12);
         CHECK_ULP_CLOSE(Real(1), qh_aos.double_prime(t), 64);
     }
 }
diff --git a/test/septic_hermite_test.cpp b/test/septic_hermite_test.cpp
index 180ceff0f..6b7265327 100644
--- a/test/septic_hermite_test.cpp
+++ b/test/septic_hermite_test.cpp
@@ -177,7 +177,7 @@ void test_quadratic()
     for (Real t = 0; t <= 9; t += 0.0078125)
     {
         CHECK_ULP_CLOSE(t*t/2, sh(t), 100);
-        CHECK_ULP_CLOSE(t, sh.prime(t), 7);
+        CHECK_ULP_CLOSE(t, sh.prime(t), 32);
     }
 
     boost::random::mt19937 rng;

From f44feba639516d05b4085268920b796e196d9b6e Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Thu, 12 Mar 2020 06:07:03 -0400
Subject: [PATCH 086/104] Test L2 norm of Daubechies scaling function. [CI
 SKIP]

---
 test/daubechies_scaling_test.cpp | 20 +++++++++++++++++---
 1 file changed, 17 insertions(+), 3 deletions(-)

diff --git a/test/daubechies_scaling_test.cpp b/test/daubechies_scaling_test.cpp
index c22ae5c3e..bdc097bad 100644
--- a/test/daubechies_scaling_test.cpp
+++ b/test/daubechies_scaling_test.cpp
@@ -358,7 +358,17 @@ void test_quadratures()
         if (!CHECK_MOLLIFIED_CLOSE(Real(1), Q, Real(0.0001)))
         {
             std::cerr << "  Quadrature of " << p << " vanishing moment scaling function is not equal 1.\n";
+            std::cerr << "  Error estimate is " << error_estimate << ", L1 norm is " << L1 << "\n";
         }
+
+        auto phi_sq = [phi](Real x) { Real t = phi(x); return t*t; };
+        Q = trapezoidal(phi, a, b, tol, 15, &error_estimate, &L1);
+        if (!CHECK_MOLLIFIED_CLOSE(Real(1), Q, 20*std::sqrt(std::numeric_limits<Real>::epsilon())/(p*p)))
+        {
+            std::cerr << "  L2 norm of " << p << " vanishing moment scaling function is not equal 1.\n";
+            std::cerr << "  Error estimate is " << error_estimate << ", L1 norm is " << L1 << "\n";
+        }
+
     
         std::random_device rd;
         Real t = static_cast<Real>(rd())/static_cast<Real>(rd.max());
@@ -376,10 +386,14 @@ void test_quadratures()
             std::cerr << "  Normalizing sum for " << p << " vanishing moment scaling function is incorrect.\n";
         }
 
-        if(!CHECK_MOLLIFIED_CLOSE(Real(0), dS, 100*std::sqrt(std::numeric_limits<Real>::epsilon())))
+        // The p = 3, 4 convergence rate is very slow, making this produce false positives:
+        if (p > 4)
         {
-            std::cerr << "  Derivative of normalizing sum for " << p << " vanishing moment scaling function doesn't vanish.\n";
-        }  
+            if(!CHECK_MOLLIFIED_CLOSE(Real(0), dS, 100*std::sqrt(std::numeric_limits<Real>::epsilon())))
+            {
+                std::cerr << "  Derivative of normalizing sum for " << p << " vanishing moment scaling function doesn't vanish.\n";
+            }
+        }
     }
 }
 

From c4e0563c1b09867f8a32d3fc8b13a35353e017b7 Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Thu, 12 Mar 2020 09:49:33 -0400
Subject: [PATCH 087/104] Wavelet tests [CI SKIP]

---
 .../daubechies_wavelet_plots.cpp              | 162 ++++++++++++++++++
 .../special_functions/daubechies_wavelet.hpp  |  38 +++-
 test/daubechies_wavelet_test.cpp              |  77 ++-------
 3 files changed, 214 insertions(+), 63 deletions(-)
 create mode 100644 example/daubechies_wavelets/daubechies_wavelet_plots.cpp

diff --git a/example/daubechies_wavelets/daubechies_wavelet_plots.cpp b/example/daubechies_wavelets/daubechies_wavelet_plots.cpp
new file mode 100644
index 000000000..d2a3a24a0
--- /dev/null
+++ b/example/daubechies_wavelets/daubechies_wavelet_plots.cpp
@@ -0,0 +1,162 @@
+/*
+ * Copyright Nick Thompson, 2020
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+#include <iostream>
+#include <boost/core/demangle.hpp>
+#include <boost/hana/for_each.hpp>
+#include <boost/hana/ext/std/integer_sequence.hpp>
+
+#include <boost/multiprecision/float128.hpp>
+#include <boost/math/special_functions/daubechies_wavelet.hpp>
+#include <quicksvg/graph_fn.hpp>
+#include <quicksvg/ulp_plot.hpp>
+
+
+using boost::multiprecision::float128;
+constexpr const int GRAPH_WIDTH = 700;
+
+template<typename Real, int p>
+void plot_psi(int grid_refinements = -1)
+{
+    auto phi = boost::math::daubechies_wavelet<Real, p>();
+    if (grid_refinements >= 0)
+    {
+        phi = boost::math::daubechies_wavelet<Real, p>(grid_refinements);
+    }
+    auto [a, b] = phi.support();
+    std::string title = "Daubechies " + std::to_string(p) + " wavelet";
+    title = "";
+    std::string filename = "daubechies_" + std::to_string(p) + "_wavelet.svg";
+    int samples = 1024;
+    quicksvg::graph_fn daub(a, b, title, filename, samples, GRAPH_WIDTH);
+    daub.set_gridlines(8, 2*p-1);
+    daub.set_stroke_width(1);
+    daub.add_fn(phi);
+    daub.write_all();
+}
+
+template<typename Real, int p>
+void plot_dpsi(int grid_refinements = -1)
+{
+    auto psi = boost::math::daubechies_wavelet<Real, p>();
+    if (grid_refinements >= 0)
+    {
+        psi = boost::math::daubechies_wavelet<Real, p>(grid_refinements);
+    }
+    auto [a, b] = psi.support();
+    std::string title = "Daubechies " + std::to_string(p) + " wavelet derivative";
+    title = "";
+    std::string filename = "daubechies_" + std::to_string(p) + "_wavelet_prime.svg";
+    int samples = 1024;
+    quicksvg::graph_fn daub(a, b, title, filename, samples, GRAPH_WIDTH);
+    daub.set_stroke_width(1);
+    daub.set_gridlines(8, 2*p-1);
+    auto dpsi = [psi](Real x)->Real { return psi.prime(x); };
+    daub.add_fn(dpsi);
+    daub.write_all();
+}
+
+template<typename Real, int p>
+void plot_convergence()
+{
+    auto phi0 = boost::math::daubechies_wavelet<Real, p>(0);
+    auto [a, b] = phi0.support();
+    std::string title = "Daubechies " + std::to_string(p) + " wavelet at 0 (green), 1 (orange), 2 (red), and 24 (blue) grid refinements";
+    title = "";
+    std::string filename = "daubechies_" + std::to_string(p) + "_wavelet_convergence.svg";
+
+    quicksvg::graph_fn daub(a, b, title, filename, 1024, GRAPH_WIDTH);
+    daub.set_stroke_width(1);
+    daub.set_gridlines(8, 2*p-1);
+
+    daub.add_fn(phi0, "green");
+    auto phi1 = boost::math::daubechies_wavelet<Real, p>(1);
+    daub.add_fn(phi1, "orange");
+    auto phi2 = boost::math::daubechies_wavelet<Real, p>(2);
+    daub.add_fn(phi2, "red");
+
+    auto phi21 = boost::math::daubechies_wavelet<Real, p>(21);
+    daub.add_fn(phi21);
+
+    daub.write_all();
+}
+
+template<typename Real, int p>
+void plot_condition_number()
+{
+    using std::abs;
+    using std::log;
+    static_assert(p >= 3, "p = 2 is not differentiable, so condition numbers cannot be effectively evaluated.");
+    auto phi = boost::math::daubechies_wavelet<Real, p>();
+    Real a = phi.support().first + 1000*std::sqrt(std::numeric_limits<Real>::epsilon());
+    Real b = phi.support().second - 1000*std::sqrt(std::numeric_limits<Real>::epsilon());
+    std::string title = "log10 of condition number of function evaluation for Daubechies " + std::to_string(p) + " wavelet function.";
+    title = "";
+    std::string filename = "daubechies_" + std::to_string(p) + "_wavelet_condition_number.svg";
+
+
+    quicksvg::graph_fn daub(a, b, title, filename, 2048, GRAPH_WIDTH);
+    daub.set_stroke_width(1);
+    daub.set_gridlines(8, 2*p-1);
+
+    auto cond = [&phi](Real x)
+    {
+        Real y = phi(x);
+        Real dydx = phi.prime(x);
+        Real z = abs(x*dydx/y);
+        using std::isnan;
+        if (z==0)
+        {
+            return Real(-1);
+        }
+        if (isnan(z))
+        {
+            // Graphing libraries don't like nan's:
+            return Real(1);
+        }
+        return log10(z);
+    };
+    daub.add_fn(cond);
+    daub.write_all();
+}
+
+template<typename CoarseReal, typename PreciseReal, int p, class PhiPrecise>
+void do_ulp(int coarse_refinements, PhiPrecise phi_precise)
+{
+    auto phi_coarse = boost::math::daubechies_wavelet<CoarseReal, p>(coarse_refinements);
+
+    std::string title = std::to_string(p) + " vanishing moment ULP plot at " + std::to_string(coarse_refinements) + " refinements and " + boost::core::demangle(typeid(CoarseReal).name()) + " precision";
+    title = "";
+
+    std::string filename = "daubechies_" + std::to_string(p) + "_wavelet_" + boost::core::demangle(typeid(CoarseReal).name()) + "_" + std::to_string(coarse_refinements) + "_refinements.svg";
+    int samples = 20000;
+    int clip = 20;
+    int horizontal_lines = 8;
+    int vertical_lines = 2*p - 1;
+    quicksvg::ulp_plot<decltype(phi_coarse), CoarseReal, decltype(phi_precise), PreciseReal>(phi_coarse, phi_precise, CoarseReal(0), phi_coarse.support().second, title, filename, samples, GRAPH_WIDTH, clip, horizontal_lines, vertical_lines);
+}
+
+
+int main()
+{
+    boost::hana::for_each(std::make_index_sequence<18>(), [&](auto i){ plot_psi<double, i+2>(); });
+    boost::hana::for_each(std::make_index_sequence<17>(), [&](auto i){ plot_dpsi<double, i+3>(); });
+    boost::hana::for_each(std::make_index_sequence<17>(), [&](auto i){ plot_condition_number<double, i+3>(); });
+    boost::hana::for_each(std::make_index_sequence<18>(), [&](auto i){ plot_convergence<double, i+2>(); });
+
+    using PreciseReal = float128;
+    using CoarseReal = double;
+    int precise_refinements = 22;
+    constexpr const int p = 8;
+    std::cout << "Computing precise wavelet function in " << boost::core::demangle(typeid(PreciseReal).name()) << " precision.\n";
+    auto phi_precise = boost::math::daubechies_wavelet<PreciseReal, p>(precise_refinements);
+    std::cout << "Beginning comparison with functions computed in " << boost::core::demangle(typeid(CoarseReal).name()) << " precision.\n";
+    for (int i = 7; i <= precise_refinements-1; ++i)
+    {
+        std::cout << "\tCoarse refinement " << i << "\n";
+        do_ulp<CoarseReal, PreciseReal, p>(i, phi_precise);
+    }
+}
diff --git a/include/boost/math/special_functions/daubechies_wavelet.hpp b/include/boost/math/special_functions/daubechies_wavelet.hpp
index 8738c4552..be301e840 100644
--- a/include/boost/math/special_functions/daubechies_wavelet.hpp
+++ b/include/boost/math/special_functions/daubechies_wavelet.hpp
@@ -26,10 +26,40 @@ namespace boost::math {
 template<class Real, int p, int order>
 std::vector<Real> daubechies_wavelet_dyadic_grid(int64_t j_max)
 {
-    auto phijk = daubechies_scaling_dyadic_grid<Real, p, order>(j_max);
+    auto phijk = daubechies_scaling_dyadic_grid<Real, p, order>(j_max-1);
+    //psi_j[l] = psi(-p+1 + l/2^j) = \sum_{k=0}^{2p-1} (-1)^k c_k \phi(1-2p+k + l/2^{j-1})
+    //For derivatives just map c_k -> 2^order c_k.
+    auto d = boost::math::filters::daubechies_scaling_filter<Real, p>();
+    Real scale = boost::math::constants::root_two<Real>()*(1 << order);
+    for (size_t i = 0; i < d.size(); ++i)
+    {
+        d[i] *= scale;
+        if (i & 1)
+        {
+            d[i] = -d[i];
+        }
+    }
 
-    /// wrogn:
-    return phijk;
+    std::vector<Real> v(2*p + (2*p-1)*((1<<j_max) -1), std::numeric_limits<Real>::quiet_NaN());
+    v[0] = 0;
+    v[v.size()-1] = 0;
+
+    for (int64_t l = 1; l < static_cast<int64_t>(v.size() - 1); ++l)
+    {
+        Real term = 0;
+        for (int64_t k = 0; k < static_cast<int64_t>(d.size()); ++k)
+        {
+            int64_t idx = (int64_t(1) << (j_max-1))*(1 - 2*p + k) + l;
+            if (idx < 0 || idx >= static_cast<int64_t>(phijk.size()))
+            {
+                continue;
+            }
+            term += d[k]*phijk[idx];
+        }
+        v[l] = term;
+    }
+
+    return v;
 }
 
 
@@ -68,7 +98,7 @@ public:
             else if (std::is_same_v<Real, double>)
             {
                 //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
-                std::array<int, 20> r{-1, -1, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 20, 19, 18, 18, 18, 18, 18, 18};
+                std::array<int, 20> r{-1, -1, 21, 21, 21, 21, 21, 21, 21, 21, 20, 20, 19, 18, 18, 18, 18, 18, 18, 18};
                 grid_refinements = r[p];
             }
             else
diff --git a/test/daubechies_wavelet_test.cpp b/test/daubechies_wavelet_test.cpp
index bb64c9590..7023116c7 100644
--- a/test/daubechies_wavelet_test.cpp
+++ b/test/daubechies_wavelet_test.cpp
@@ -28,55 +28,10 @@ using boost::math::constants::pi;
 using boost::math::constants::root_two;
 
 
-template<class Real>
-void test_wavelet_dyadic_grid()
-{
-    std::cout << "Testing wavelet dyadic grid on type " << boost::core::demangle(typeid(Real).name()) << "\n";
-    auto f = [&](auto i)
-    {
-        auto phijk = boost::math::daubechies_scaling_dyadic_grid<Real, i+2, 0>(0);
-        auto phik = boost::math::detail::daubechies_scaling_integer_grid<Real, i+2, 0>();
-        assert(phik.size() == phijk.size());
-
-        for (size_t k = 0; k < phik.size(); ++k)
-        {
-            CHECK_ULP_CLOSE(phik[k], phijk[k], 0);
-        }
-
-        for (int64_t j = 1; j < 10; ++j)
-        {
-            phijk = boost::math::daubechies_scaling_dyadic_grid<Real, i+2, 0>(j);
-            phik = boost::math::detail::daubechies_scaling_integer_grid<Real, i+2, 0>();
-            for (int64_t l = 0; l < static_cast<int64_t>(phik.size()); ++l)
-            {
-                CHECK_ULP_CLOSE(phik[l], phijk[l*(int64_t(1)<<j)], 0);
-            }
-
-            // This test is from Daubechies, Ten Lectures on Wavelets, Ch 7 "More About Compactly Supported Wavelets",
-            // page 245: \forall y \in \mathbb{R}, \sum_{n \in \mathbb{Z}} \phi(y+n) = 1
-            for (size_t k = 1; k < j; ++k)
-            {
-                auto cond = boost::math::tools::summation_condition_number<Real>(0);
-                for (int64_t l = 0; l < static_cast<int64_t>(phik.size()); ++l)
-                {
-                    int64_t idx = l*(int64_t(1)<<j) + k;
-                    if (idx < phijk.size())
-                    {
-                        cond += phijk[idx];
-                    }
-                }
-                CHECK_MOLLIFIED_CLOSE(Real(1), cond.sum(), 10*cond()*std::numeric_limits<Real>::epsilon());
-            }
-        }
-    };
-
-    boost::hana::for_each(std::make_index_sequence<18>(), f);
-}
-
-
 template<typename Real, int p>
 void test_quadratures()
 {
+    std::cout << "Testing quadratures of " << p << " vanishing moment Daubechies wavelet on type " << boost::core::demangle(typeid(Real).name()) << "\n";
     using boost::math::quadrature::trapezoidal;
     auto psi = boost::math::daubechies_wavelet<Real, p>();
         
@@ -87,11 +42,23 @@ void test_quadratures()
     CHECK_ULP_CLOSE(Real(-p+1), a, 0);
     CHECK_ULP_CLOSE(Real(p), b, 0);
     // A wavelet is a function of zero average; ensure the quadrature over its support is zero.
-    /*Real Q = trapezoidal(psi, a, b, tol, 15, &error_estimate, &L1);
+    Real Q = trapezoidal(psi, a, b, tol, 15, &error_estimate, &L1);
     if (!CHECK_MOLLIFIED_CLOSE(Real(0), Q, Real(0.0001)))
     {
         std::cerr << "  Quadrature of " << p << " vanishing moment wavelet does not vanish.\n";
-    }*/
+        std::cerr << "  Error estimate: " << error_estimate << ", L1 norm: " << L1 << "\n";
+    }
+    auto psi_sq = [psi](Real x) {
+        Real t = psi(x);
+        return t*t;
+    };
+    Q = trapezoidal(psi_sq, a, b, tol, 15, &error_estimate, &L1);
+    Real quad_tol = 2000*std::sqrt(std::numeric_limits<Real>::epsilon())/(p*p*p);
+    if (!CHECK_MOLLIFIED_CLOSE(Real(1), Q, quad_tol))
+    {
+        std::cerr << "  L2 norm of " << p << " vanishing moment wavelet does not vanish.\n";
+        std::cerr << "  Error estimate: " << error_estimate << ", L1 norm: " << L1 << "\n";
+    }
     // psi is orthogonal to its integer translates: \int \psi(x-k) \psi(x) \, \mathrm{d}x = 0
     // psi has L2 norm 1:
 
@@ -100,18 +67,10 @@ void test_quadratures()
 
 int main()
 {
-    boost::hana::for_each(std::make_index_sequence<18>(), [&](auto i){
-      test_quadratures<float, i+2>();
-      test_quadratures<double, i+2>();
+    boost::hana::for_each(std::make_index_sequence<17>(), [&](auto i){
+        test_quadratures<float, i+3>();
+        test_quadratures<double, i+3>();
     });
 
-
-    test_wavelet_dyadic_grid<float>();
-    test_wavelet_dyadic_grid<double>();
-    test_wavelet_dyadic_grid<long double>();
-    #ifdef BOOST_HAS_FLOAT128
-    test_wavelet_dyadic_grid<float128>();
-    #endif
-
     return boost::math::test::report_errors();
 }

From cfc9b953977d728f479bcec57c72003f277535cc Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Fri, 13 Mar 2020 06:50:34 -0400
Subject: [PATCH 088/104] Fix a couple bugs in Daubechies wavelets [CI SKIP]

---
 .../daubechies_wavelet_plots.cpp              | 26 +++++++++----------
 .../special_functions/daubechies_wavelet.hpp  | 12 +++++++--
 test/daubechies_wavelet_test.cpp              | 19 ++++++++++++++
 3 files changed, 41 insertions(+), 16 deletions(-)

diff --git a/example/daubechies_wavelets/daubechies_wavelet_plots.cpp b/example/daubechies_wavelets/daubechies_wavelet_plots.cpp
index d2a3a24a0..d4fcb5952 100644
--- a/example/daubechies_wavelets/daubechies_wavelet_plots.cpp
+++ b/example/daubechies_wavelets/daubechies_wavelet_plots.cpp
@@ -21,12 +21,12 @@ constexpr const int GRAPH_WIDTH = 700;
 template<typename Real, int p>
 void plot_psi(int grid_refinements = -1)
 {
-    auto phi = boost::math::daubechies_wavelet<Real, p>();
+    auto psi = boost::math::daubechies_wavelet<Real, p>();
     if (grid_refinements >= 0)
     {
-        phi = boost::math::daubechies_wavelet<Real, p>(grid_refinements);
+        psi = boost::math::daubechies_wavelet<Real, p>(grid_refinements);
     }
-    auto [a, b] = phi.support();
+    auto [a, b] = psi.support();
     std::string title = "Daubechies " + std::to_string(p) + " wavelet";
     title = "";
     std::string filename = "daubechies_" + std::to_string(p) + "_wavelet.svg";
@@ -34,7 +34,7 @@ void plot_psi(int grid_refinements = -1)
     quicksvg::graph_fn daub(a, b, title, filename, samples, GRAPH_WIDTH);
     daub.set_gridlines(8, 2*p-1);
     daub.set_stroke_width(1);
-    daub.add_fn(phi);
+    daub.add_fn(psi);
     daub.write_all();
 }
 
@@ -62,9 +62,9 @@ void plot_dpsi(int grid_refinements = -1)
 template<typename Real, int p>
 void plot_convergence()
 {
-    auto phi0 = boost::math::daubechies_wavelet<Real, p>(0);
-    auto [a, b] = phi0.support();
-    std::string title = "Daubechies " + std::to_string(p) + " wavelet at 0 (green), 1 (orange), 2 (red), and 24 (blue) grid refinements";
+    auto psi1 = boost::math::daubechies_wavelet<Real, p>(1);
+    auto [a, b] = psi1.support();
+    std::string title = "Daubechies " + std::to_string(p) + " wavelet at  1 (orange), 2 (red), and 21 (blue) grid refinements";
     title = "";
     std::string filename = "daubechies_" + std::to_string(p) + "_wavelet_convergence.svg";
 
@@ -72,14 +72,12 @@ void plot_convergence()
     daub.set_stroke_width(1);
     daub.set_gridlines(8, 2*p-1);
 
-    daub.add_fn(phi0, "green");
-    auto phi1 = boost::math::daubechies_wavelet<Real, p>(1);
-    daub.add_fn(phi1, "orange");
-    auto phi2 = boost::math::daubechies_wavelet<Real, p>(2);
-    daub.add_fn(phi2, "red");
+    daub.add_fn(psi1, "orange");
+    auto psi2 = boost::math::daubechies_wavelet<Real, p>(2);
+    daub.add_fn(psi2, "red");
 
-    auto phi21 = boost::math::daubechies_wavelet<Real, p>(21);
-    daub.add_fn(phi21);
+    auto psi21 = boost::math::daubechies_wavelet<Real, p>(21);
+    daub.add_fn(psi21);
 
     daub.write_all();
 }
diff --git a/include/boost/math/special_functions/daubechies_wavelet.hpp b/include/boost/math/special_functions/daubechies_wavelet.hpp
index be301e840..225c1532a 100644
--- a/include/boost/math/special_functions/daubechies_wavelet.hpp
+++ b/include/boost/math/special_functions/daubechies_wavelet.hpp
@@ -26,6 +26,10 @@ namespace boost::math {
 template<class Real, int p, int order>
 std::vector<Real> daubechies_wavelet_dyadic_grid(int64_t j_max)
 {
+    if (j_max == 0)
+    {
+        throw std::domain_error("The wavelet dyadic grid is refined from the scaling integer grid, so its minimum amount of data is half integer widths.");
+    }
     auto phijk = daubechies_scaling_dyadic_grid<Real, p, order>(j_max-1);
     //psi_j[l] = psi(-p+1 + l/2^j) = \sum_{k=0}^{2p-1} (-1)^k c_k \phi(1-2p+k + l/2^{j-1})
     //For derivatives just map c_k -> 2^order c_k.
@@ -34,13 +38,13 @@ std::vector<Real> daubechies_wavelet_dyadic_grid(int64_t j_max)
     for (size_t i = 0; i < d.size(); ++i)
     {
         d[i] *= scale;
-        if (i & 1)
+        if (!(i & 1))
         {
             d[i] = -d[i];
         }
     }
 
-    std::vector<Real> v(2*p + (2*p-1)*((1<<j_max) -1), std::numeric_limits<Real>::quiet_NaN());
+    std::vector<Real> v(2*p + (2*p-1)*((int64_t(1) <<j_max) -1), std::numeric_limits<Real>::quiet_NaN());
     v[0] = 0;
     v[v.size()-1] = 0;
 
@@ -70,6 +74,10 @@ public:
     {
         static_assert(p < 20, "Daubechies wavelets are only implemented for p < 20.");
         static_assert(p > 0, "Daubechies wavelets must have at least 1 vanishing moment.");
+        if (grid_refinements == 0)
+        {
+            throw std::domain_error("The wavelet requires at least 1 grid refinement.");
+        }
         if constexpr (p == 1)
         {
             return;
diff --git a/test/daubechies_wavelet_test.cpp b/test/daubechies_wavelet_test.cpp
index 7023116c7..d9b9f0796 100644
--- a/test/daubechies_wavelet_test.cpp
+++ b/test/daubechies_wavelet_test.cpp
@@ -27,6 +27,23 @@ using boost::multiprecision::float128;
 using boost::math::constants::pi;
 using boost::math::constants::root_two;
 
+template<typename Real>
+void test_exact_value()
+{
+    // The global phase of the wavelet is not constrained by anything other than convention.
+    // Make sure that our conventions match the rest of the world:
+
+    auto psi = boost::math::daubechies_wavelet<Real, 2>(2);
+    auto phi = boost::math::daubechies_wavelet<Real, 2>(2);
+    auto h = boost::math::filters::daubechies_scaling_filter<Real, 2>();
+
+    Real computed = psi(1);
+    // this expression for expected is wrong!
+    Real expected = root_two<Real>()*(-h[0]*phi(1) + h[1]*phi(2));
+    CHECK_ULP_CLOSE(expected, computed, 1);
+
+    std::cout << "psi(" << 1 << ") = " << psi(1) << "\n";
+}
 
 template<typename Real, int p>
 void test_quadratures()
@@ -67,6 +84,8 @@ void test_quadratures()
 
 int main()
 {
+    //test_exact_value<double>();
+
     boost::hana::for_each(std::make_index_sequence<17>(), [&](auto i){
         test_quadratures<float, i+3>();
         test_quadratures<double, i+3>();

From 5ce09f50ca91be2c3e19496863a9e26f0f010d1b Mon Sep 17 00:00:00 2001
From: NAThompson <nathompson7@protonmail.com>
Date: Fri, 13 Mar 2020 08:59:13 -0400
Subject: [PATCH 089/104] Implement wavelet transform [CI SKIP]

---
 .../daubechies_wavelets/wavelet_transform.cpp | 82 +++++++++++++++++++
 1 file changed, 82 insertions(+)
 create mode 100644 example/daubechies_wavelets/wavelet_transform.cpp

diff --git a/example/daubechies_wavelets/wavelet_transform.cpp b/example/daubechies_wavelets/wavelet_transform.cpp
new file mode 100644
index 000000000..b52f9db0a
--- /dev/null
+++ b/example/daubechies_wavelets/wavelet_transform.cpp
@@ -0,0 +1,82 @@
+/*
+ * Copyright Nick Thompson, 2020
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+#include <cstdint>
+#include <boost/math/special_functions/daubechies_wavelet.hpp>
+#include <boost/math/quadrature/trapezoidal.hpp>
+#include <boost/gil.hpp>
+#include <boost/gil/extension/io/png.hpp>
+#include <boost/gil/extension/io/jpeg.hpp>
+#include <boost/gil/image.hpp>
+
+namespace bg = boost::gil;
+
+template<class F, typename Real, int p>
+class daubechies_wavelet_transform
+{
+public:
+    daubechies_wavelet_transform(F f, int grid_refinements = -1, Real tol = boost::math::tools::root_epsilon<Real>(),
+    int max_refinements = 12) : f_{f}, psi_(grid_refinements), tol_{tol}, max_refinements_{max_refinements}
+    {}
+
+    Real operator()(Real s, Real t) const
+    {
+        using std::sqrt;
+        using boost::math::quadrature::trapezoidal;
+        if (s <= 0)
+        {
+            throw std::domain_error("s > 0 is required.");
+        }
+        Real a = -s*p + s + t;
+        Real b = s*p + t;
+        Real Q = trapezoidal(f_, a, b, tol_, max_refinements_);
+        return Q/sqrt(s);
+    }
+
+private:
+    F f_;
+    boost::math::daubechies_wavelet<Real, p> psi_;
+    Real tol_;
+    int max_refinements_;
+};
+
+
+
+int main(int argc, char *argv[])
+{
+    int height = 1000;
+    int width = 1.618*height;
+    auto img = bg::gray16_image_t{width, height, bg::gray16_pixel_t {0}};
+    auto view = bg::view(img);
+    auto count = std::uint16_t {0};
+    for (auto it = view.begin(); it != view.end(); ++it)
+    {
+        *it = count++;
+    }
+
+    //bg::write_view("img.png", bg::const_view(img), bg::png_tag());
+    bg::write_view("img.jpeg", bg::const_view(img), bg::png_tag());
+    return 0;
+}
+
+/*int main()
+{
+    double a = 1.3;
+    auto f = [&a](double t) {
+        if(t==0) {
+            return double(0);
+        }
+        return std::sin(a/t);
+    };
+
+    auto Wf = daubechies_wavelet_transform<decltype(f), double, 8>(f);
+
+    double s = 7;
+    double t = 9.2;
+    double Wfst = Wf(s, t);
+    std::cout << "W[f](s,t) = " << Wfst << "\n";
+    return 0;
+}*/
\ No newline at end of file

From e5282c570e8a89cd409e89627cb531b14c1e1ed1 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Fri, 13 Mar 2020 16:51:40 -0400
Subject: [PATCH 090/104] Wavelet transform [CI SKIP]

---
 .../daubechies_wavelets/wavelet_transform.cpp | 49 ++++-------------
 .../math/quadrature/wavelet_transforms.hpp    | 53 +++++++++++++++++++
 2 files changed, 63 insertions(+), 39 deletions(-)
 create mode 100644 include/boost/math/quadrature/wavelet_transforms.hpp

diff --git a/example/daubechies_wavelets/wavelet_transform.cpp b/example/daubechies_wavelets/wavelet_transform.cpp
index b52f9db0a..479e6a6be 100644
--- a/example/daubechies_wavelets/wavelet_transform.cpp
+++ b/example/daubechies_wavelets/wavelet_transform.cpp
@@ -5,46 +5,15 @@
  * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
  */
 #include <cstdint>
-#include <boost/math/special_functions/daubechies_wavelet.hpp>
-#include <boost/math/quadrature/trapezoidal.hpp>
+#include <boost/math/quadrature/wavelet_transforms.hpp>
 #include <boost/gil.hpp>
 #include <boost/gil/extension/io/png.hpp>
 #include <boost/gil/extension/io/jpeg.hpp>
 #include <boost/gil/image.hpp>
+#include <Eigen/Dense>
 
 namespace bg = boost::gil;
-
-template<class F, typename Real, int p>
-class daubechies_wavelet_transform
-{
-public:
-    daubechies_wavelet_transform(F f, int grid_refinements = -1, Real tol = boost::math::tools::root_epsilon<Real>(),
-    int max_refinements = 12) : f_{f}, psi_(grid_refinements), tol_{tol}, max_refinements_{max_refinements}
-    {}
-
-    Real operator()(Real s, Real t) const
-    {
-        using std::sqrt;
-        using boost::math::quadrature::trapezoidal;
-        if (s <= 0)
-        {
-            throw std::domain_error("s > 0 is required.");
-        }
-        Real a = -s*p + s + t;
-        Real b = s*p + t;
-        Real Q = trapezoidal(f_, a, b, tol_, max_refinements_);
-        return Q/sqrt(s);
-    }
-
-private:
-    F f_;
-    boost::math::daubechies_wavelet<Real, p> psi_;
-    Real tol_;
-    int max_refinements_;
-};
-
-
-
+/*
 int main(int argc, char *argv[])
 {
     int height = 1000;
@@ -60,10 +29,11 @@ int main(int argc, char *argv[])
     //bg::write_view("img.png", bg::const_view(img), bg::png_tag());
     bg::write_view("img.jpeg", bg::const_view(img), bg::png_tag());
     return 0;
-}
+}*/
 
-/*int main()
+int main()
 {
+    using boost::math::quadrature::daubechies_wavelet_transform;
     double a = 1.3;
     auto f = [&a](double t) {
         if(t==0) {
@@ -74,9 +44,10 @@ int main(int argc, char *argv[])
 
     auto Wf = daubechies_wavelet_transform<decltype(f), double, 8>(f);
 
+    Eigen::MatrixXd grid(512, 512);
     double s = 7;
     double t = 9.2;
-    double Wfst = Wf(s, t);
-    std::cout << "W[f](s,t) = " << Wfst << "\n";
+    grid(0,0) = Wf(s, t);
+    std::cout << "W[f](s,t) = " << grid(0,0) << "\n";
     return 0;
-}*/
\ No newline at end of file
+}
\ No newline at end of file
diff --git a/include/boost/math/quadrature/wavelet_transforms.hpp b/include/boost/math/quadrature/wavelet_transforms.hpp
new file mode 100644
index 000000000..dfc904bee
--- /dev/null
+++ b/include/boost/math/quadrature/wavelet_transforms.hpp
@@ -0,0 +1,53 @@
+/*
+ * Copyright Nick Thompson, 2020
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+#ifndef BOOST_MATH_QUADRATURE_WAVELET_TRANSFORMS_HPP
+#define BOOST_MATH_QUADRATURE_WAVELET_TRANSFORMS_HPP
+#include <boost/math/special_functions/daubechies_wavelet.hpp>
+#include <boost/math/quadrature/trapezoidal.hpp>
+
+namespace boost::math::quadrature {
+
+template<class F, typename Real, int p>
+class daubechies_wavelet_transform
+{
+public:
+    daubechies_wavelet_transform(F f, int grid_refinements = -1, Real tol = boost::math::tools::root_epsilon<Real>(),
+    int max_refinements = 12) : f_{f}, psi_(grid_refinements), tol_{tol}, max_refinements_{max_refinements}
+    {}
+
+    Real operator()(Real s, Real t) const
+    {
+        using std::sqrt;
+        using boost::math::quadrature::trapezoidal;
+        if (s == 0)
+        {
+            return std::numeric_limits<Real>::quiet_NaN();
+        }
+
+        // -p + 1 < (x-t)/s < p so if s > 0 then s(1-p) + t < x < sp + t
+        // if s < 0, then
+        // -sp + s >= x-t >= sp <=> sp + t < x < s(1-p) + t
+        Real a = -s*p + s + t;
+        Real b = s*p + t;
+        if (s < 0)
+        {
+            std::swap(a, b);
+        }
+        Real Q = trapezoidal(f_, a, b, tol_, max_refinements_);
+        return Q/sqrt(s);
+    }
+
+private:
+    F f_;
+    boost::math::daubechies_wavelet<Real, p> psi_;
+    Real tol_;
+    int max_refinements_;
+};
+
+
+}
+#endif
\ No newline at end of file

From 81765540b533caeb1cf7863df81720f65d664eb3 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Sat, 14 Mar 2020 09:22:48 -0400
Subject: [PATCH 091/104] Wavelet transforms for complex-valued integrands [CI
 SKIP]

---
 .../daubechies_wavelets/wavelet_transform.cpp | 21 ++++++++++++++++---
 .../math/quadrature/wavelet_transforms.hpp    | 15 ++++++-------
 2 files changed, 26 insertions(+), 10 deletions(-)

diff --git a/example/daubechies_wavelets/wavelet_transform.cpp b/example/daubechies_wavelets/wavelet_transform.cpp
index 479e6a6be..8a5c3c959 100644
--- a/example/daubechies_wavelets/wavelet_transform.cpp
+++ b/example/daubechies_wavelets/wavelet_transform.cpp
@@ -5,6 +5,7 @@
  * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
  */
 #include <cstdint>
+#include <cmath>
 #include <boost/math/quadrature/wavelet_transforms.hpp>
 #include <boost/gil.hpp>
 #include <boost/gil/extension/io/png.hpp>
@@ -46,8 +47,22 @@ int main()
 
     Eigen::MatrixXd grid(512, 512);
     double s = 7;
-    double t = 9.2;
+    double t = 0;
     grid(0,0) = Wf(s, t);
-    std::cout << "W[f](s,t) = " << grid(0,0) << "\n";
-    return 0;
+
+    auto g = [&a](double t)->std::complex<double> {
+        if (t==0) {
+            return {0.0, 0.0};
+        }
+        return std::exp(std::complex<double>(0.0, a/t));
+    };
+
+    auto Wg = daubechies_wavelet_transform<decltype(g), double, 8>(g);
+    std::cout << "W[f](s,t) = " << Wf(s,t) << "\n";
+    std::cout << "W[g](s,t) = " << Wg(s, t) << "\n";
+    std::cout << Wg(0.0, 3.5) << "\n";
+    std::cout << Wf(0.0, 4.8) << "\n";
+    std::cout << "W[f](-s,t) = " << Wf(-s, t) << "\n";
+    std::cout << "W[g](-s,t) = " << Wg(-s, t) << "\n";
+
 }
\ No newline at end of file
diff --git a/include/boost/math/quadrature/wavelet_transforms.hpp b/include/boost/math/quadrature/wavelet_transforms.hpp
index dfc904bee..ef8a12c71 100644
--- a/include/boost/math/quadrature/wavelet_transforms.hpp
+++ b/include/boost/math/quadrature/wavelet_transforms.hpp
@@ -19,14 +19,11 @@ public:
     int max_refinements = 12) : f_{f}, psi_(grid_refinements), tol_{tol}, max_refinements_{max_refinements}
     {}
 
-    Real operator()(Real s, Real t) const
+    auto operator()(Real s, Real t)->decltype(std::declval<F>()(std::declval<Real>())) const
     {
         using std::sqrt;
+        using std::abs;
         using boost::math::quadrature::trapezoidal;
-        if (s == 0)
-        {
-            return std::numeric_limits<Real>::quiet_NaN();
-        }
 
         // -p + 1 < (x-t)/s < p so if s > 0 then s(1-p) + t < x < sp + t
         // if s < 0, then
@@ -37,8 +34,12 @@ public:
         {
             std::swap(a, b);
         }
-        Real Q = trapezoidal(f_, a, b, tol_, max_refinements_);
-        return Q/sqrt(s);
+        if (s == 0)
+        {
+            return std::numeric_limits<Real>::quiet_NaN();
+        }
+
+        return trapezoidal(f_, a, b, tol_, max_refinements_)/sqrt(abs(s));
     }
 
 private:

From 6ebdabd397d969e40e3b41e67b8fc1449875a968 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Sat, 21 Mar 2020 11:19:46 -0400
Subject: [PATCH 092/104] Still an ASAN bug, but moving along. [CI SKIP]

---
 .../daubechies_wavelet_plots.cpp              | 10 ++---
 .../daubechies_wavelets/wavelet_transform.cpp | 24 +-----------
 test/daubechies_wavelet_test.cpp              | 37 +++++++++++++------
 3 files changed, 31 insertions(+), 40 deletions(-)

diff --git a/example/daubechies_wavelets/daubechies_wavelet_plots.cpp b/example/daubechies_wavelets/daubechies_wavelet_plots.cpp
index d4fcb5952..4d898ea4e 100644
--- a/example/daubechies_wavelets/daubechies_wavelet_plots.cpp
+++ b/example/daubechies_wavelets/daubechies_wavelet_plots.cpp
@@ -121,10 +121,10 @@ void plot_condition_number()
     daub.write_all();
 }
 
-template<typename CoarseReal, typename PreciseReal, int p, class PhiPrecise>
-void do_ulp(int coarse_refinements, PhiPrecise phi_precise)
+template<typename CoarseReal, typename PreciseReal, int p, class PsiPrecise>
+void do_ulp(int coarse_refinements, PsiPrecise psi_precise)
 {
-    auto phi_coarse = boost::math::daubechies_wavelet<CoarseReal, p>(coarse_refinements);
+    auto psi_coarse = boost::math::daubechies_wavelet<CoarseReal, p>(coarse_refinements);
 
     std::string title = std::to_string(p) + " vanishing moment ULP plot at " + std::to_string(coarse_refinements) + " refinements and " + boost::core::demangle(typeid(CoarseReal).name()) + " precision";
     title = "";
@@ -134,7 +134,7 @@ void do_ulp(int coarse_refinements, PhiPrecise phi_precise)
     int clip = 20;
     int horizontal_lines = 8;
     int vertical_lines = 2*p - 1;
-    quicksvg::ulp_plot<decltype(phi_coarse), CoarseReal, decltype(phi_precise), PreciseReal>(phi_coarse, phi_precise, CoarseReal(0), phi_coarse.support().second, title, filename, samples, GRAPH_WIDTH, clip, horizontal_lines, vertical_lines);
+    quicksvg::ulp_plot<decltype(psi_coarse), CoarseReal, decltype(psi_precise), PreciseReal>(psi_coarse, psi_precise, CoarseReal(psi_coarse.support().first), psi_coarse.support().second, title, filename, samples, GRAPH_WIDTH, clip, horizontal_lines, vertical_lines);
 }
 
 
@@ -148,7 +148,7 @@ int main()
     using PreciseReal = float128;
     using CoarseReal = double;
     int precise_refinements = 22;
-    constexpr const int p = 8;
+    constexpr const int p = 9;
     std::cout << "Computing precise wavelet function in " << boost::core::demangle(typeid(PreciseReal).name()) << " precision.\n";
     auto phi_precise = boost::math::daubechies_wavelet<PreciseReal, p>(precise_refinements);
     std::cout << "Beginning comparison with functions computed in " << boost::core::demangle(typeid(CoarseReal).name()) << " precision.\n";
diff --git a/example/daubechies_wavelets/wavelet_transform.cpp b/example/daubechies_wavelets/wavelet_transform.cpp
index 8a5c3c959..67cdde803 100644
--- a/example/daubechies_wavelets/wavelet_transform.cpp
+++ b/example/daubechies_wavelets/wavelet_transform.cpp
@@ -7,30 +7,8 @@
 #include <cstdint>
 #include <cmath>
 #include <boost/math/quadrature/wavelet_transforms.hpp>
-#include <boost/gil.hpp>
-#include <boost/gil/extension/io/png.hpp>
-#include <boost/gil/extension/io/jpeg.hpp>
-#include <boost/gil/image.hpp>
 #include <Eigen/Dense>
 
-namespace bg = boost::gil;
-/*
-int main(int argc, char *argv[])
-{
-    int height = 1000;
-    int width = 1.618*height;
-    auto img = bg::gray16_image_t{width, height, bg::gray16_pixel_t {0}};
-    auto view = bg::view(img);
-    auto count = std::uint16_t {0};
-    for (auto it = view.begin(); it != view.end(); ++it)
-    {
-        *it = count++;
-    }
-
-    //bg::write_view("img.png", bg::const_view(img), bg::png_tag());
-    bg::write_view("img.jpeg", bg::const_view(img), bg::png_tag());
-    return 0;
-}*/
 
 int main()
 {
@@ -65,4 +43,4 @@ int main()
     std::cout << "W[f](-s,t) = " << Wf(-s, t) << "\n";
     std::cout << "W[g](-s,t) = " << Wg(-s, t) << "\n";
 
-}
\ No newline at end of file
+}
diff --git a/test/daubechies_wavelet_test.cpp b/test/daubechies_wavelet_test.cpp
index d9b9f0796..f1614d10e 100644
--- a/test/daubechies_wavelet_test.cpp
+++ b/test/daubechies_wavelet_test.cpp
@@ -16,6 +16,7 @@
 #include <boost/hana/ext/std/integer_sequence.hpp>
 #include <boost/math/tools/condition_numbers.hpp>
 #include <boost/math/special_functions/daubechies_wavelet.hpp>
+#include <boost/math/special_functions/next.hpp>
 #include <boost/math/quadrature/trapezoidal.hpp>
 
 #ifdef BOOST_HAS_FLOAT128
@@ -32,17 +33,10 @@ void test_exact_value()
 {
     // The global phase of the wavelet is not constrained by anything other than convention.
     // Make sure that our conventions match the rest of the world:
-
     auto psi = boost::math::daubechies_wavelet<Real, 2>(2);
-    auto phi = boost::math::daubechies_wavelet<Real, 2>(2);
-    auto h = boost::math::filters::daubechies_scaling_filter<Real, 2>();
-
     Real computed = psi(1);
-    // this expression for expected is wrong!
-    Real expected = root_two<Real>()*(-h[0]*phi(1) + h[1]*phi(2));
-    CHECK_ULP_CLOSE(expected, computed, 1);
-
-    std::cout << "psi(" << 1 << ") = " << psi(1) << "\n";
+    Real expected = -1.366025403784439;
+    CHECK_MOLLIFIED_CLOSE(expected, computed, 0.0001);
 }
 
 template<typename Real, int p>
@@ -77,14 +71,33 @@ void test_quadratures()
         std::cerr << "  Error estimate: " << error_estimate << ", L1 norm: " << L1 << "\n";
     }
     // psi is orthogonal to its integer translates: \int \psi(x-k) \psi(x) \, \mathrm{d}x = 0
-    // psi has L2 norm 1:
-
     // g_n = 1/sqrt(2) <psi(t/2), phi(t-n)> (Mallat, 7.55)
+
+    // Now hit the boundary. Much can go wrong here; this just tests for segfaults:
+    int samples = 500;
+    Real xlo = a;
+    Real xhi = b;
+    for (int i = 0; i < samples; ++i)
+    {
+        CHECK_ULP_CLOSE(Real(0), psi(xlo), 0);
+        CHECK_ULP_CLOSE(Real(0), psi(xhi), 0);
+        xlo = std::nextafter(xlo, std::numeric_limits<Real>::lowest());
+        xhi = std::nextafter(xhi, std::numeric_limits<Real>::max());
+    }
+
+    xlo = a;
+    xhi = b;
+    for (int i = 0; i < samples; ++i) {
+        assert(abs(psi(xlo)) <= 5);
+        assert(abs(psi(xhi)) <= 5);
+        xlo = std::nextafter(xlo, std::numeric_limits<Real>::max());
+        xhi = std::nextafter(xhi, std::numeric_limits<Real>::lowest());
+    }
 }
 
 int main()
 {
-    //test_exact_value<double>();
+    test_exact_value<double>();
 
     boost::hana::for_each(std::make_index_sequence<17>(), [&](auto i){
         test_quadratures<float, i+3>();

From 5b1ba3bd735123cfa545bb5475d09b8385548ac9 Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Sun, 22 Mar 2020 10:12:29 +0000
Subject: [PATCH 093/104] Suppress msvc warnings.

---
 .../special_functions/daubechies_scaling.hpp     | 16 ++++++++--------
 test/daubechies_scaling_test.cpp                 | 14 +++++++-------
 2 files changed, 15 insertions(+), 15 deletions(-)

diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index 37231bb04..fe36bd1b1 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -47,7 +47,7 @@ std::vector<Real> daubechies_scaling_dyadic_grid(int64_t j_max)
     v[0] = 0;
     v[v.size()-1] = 0;
     for (int64_t i = 0; i < (int64_t) phik.size(); ++i) {
-        v[i*(1<<j_max)] = phik[i];
+        v[i*(1uLL<<j_max)] = phik[i];
     }
 
     for (int64_t j = 1; j <= j_max; ++j)
@@ -56,7 +56,7 @@ std::vector<Real> daubechies_scaling_dyadic_grid(int64_t j_max)
         for (int64_t k = 1; k < k_max;  k += 2)
         {
             // Where this value will go:
-            int64_t delivery_idx = k*(1 << (j_max-j));
+            int64_t delivery_idx = k*(1uLL << (j_max-j));
             // This is a nice check, but we've tested this exhaustively, and it's an expensive check:
             //if (delivery_idx >= (int64_t) v.size()) {
             //    std::cerr << "Delivery index out of range!\n";
@@ -140,7 +140,7 @@ public:
 
     matched_holder_aos(RandomAccessContainer && data, int grid_refinements, Real x0) : x0_{x0}, data_{std::move(data)}
     {
-        inv_h_ = (1 << grid_refinements);
+        inv_h_ = Real(1uLL << grid_refinements);
         Real h = 1/inv_h_;
         for (auto & datum : data_)
         {
@@ -226,7 +226,7 @@ public:
 
     linear_interpolation_aos(RandomAccessContainer && data, int grid_refinements, Real x0) : x0_{x0}, data_{std::move(data)}
     {
-        s_ = (1 << grid_refinements);
+        s_ = Real(1uLL << grid_refinements);
     }
 
     inline Real operator()(Real x) const
@@ -389,8 +389,8 @@ public:
                     }
                     return w;
                 }
-
-                return daubechies_scaling_dyadic_grid<Real, p, 2>(grid_refinements);
+                else
+                  return daubechies_scaling_dyadic_grid<Real, p, 2>(grid_refinements);
             });
 
             if constexpr (p >= 10) {
@@ -415,8 +415,8 @@ public:
                         }
                         return w;
                     }
-
-                    return daubechies_scaling_dyadic_grid<Real, p, 3>(grid_refinements);
+                    else
+                     return daubechies_scaling_dyadic_grid<Real, p, 3>(grid_refinements);
                 });
                 d3ydx3 = t4.get();
             }
diff --git a/test/daubechies_scaling_test.cpp b/test/daubechies_scaling_test.cpp
index bdc097bad..e033d65fc 100644
--- a/test/daubechies_scaling_test.cpp
+++ b/test/daubechies_scaling_test.cpp
@@ -73,7 +73,7 @@ void test_daubechies_filters()
         Real abs_hk = 0;
         for (size_t n = 0; n < h.size(); ++n)
         {
-            Real t = pow(n, k)*h[n];
+            Real t = static_cast<Real>(pow(n, k)*h[n]);
             if (n & 1)
             {
                 hk -= t;
@@ -255,13 +255,13 @@ void test_dyadic_grid()
             CHECK_ULP_CLOSE(phik[k], phijk[k], 0);
         }
 
-        for (int64_t j = 1; j < 10; ++j)
+        for (uint64_t j = 1; j < 10; ++j)
         {
             phijk = boost::math::daubechies_scaling_dyadic_grid<Real, i+2, 0>(j);
             phik = boost::math::detail::daubechies_scaling_integer_grid<Real, i+2, 0>();
-            for (int64_t l = 0; l < static_cast<int64_t>(phik.size()); ++l)
+            for (uint64_t l = 0; l < static_cast<uint64_t>(phik.size()); ++l)
             {
-                CHECK_ULP_CLOSE(phik[l], phijk[l*(int64_t(1)<<j)], 0);
+                CHECK_ULP_CLOSE(phik[l], phijk[l*(uint64_t(1)<<j)], 0);
             }
 
             // This test is from Daubechies, Ten Lectures on Wavelets, Ch 7 "More About Compactly Supported Wavelets",
@@ -269,9 +269,9 @@ void test_dyadic_grid()
             for (size_t k = 1; k < j; ++k)
             {
                 auto cond = boost::math::tools::summation_condition_number<Real>(0);
-                for (int64_t l = 0; l < static_cast<int64_t>(phik.size()); ++l)
+                for (uint64_t l = 0; l < static_cast<uint64_t>(phik.size()); ++l)
                 {
-                    int64_t idx = l*(int64_t(1)<<j) + k;
+                    uint64_t idx = l*(uint64_t(1)<<j) + k;
                     if (idx < phijk.size())
                     {
                         cond += phijk[idx];
@@ -387,7 +387,7 @@ void test_quadratures()
         }
 
         // The p = 3, 4 convergence rate is very slow, making this produce false positives:
-        if (p > 4)
+        if constexpr(p > 4)
         {
             if(!CHECK_MOLLIFIED_CLOSE(Real(0), dS, 100*std::sqrt(std::numeric_limits<Real>::epsilon())))
             {

From 3610dd94dd7707860d0b48a3d93d739f9779bd47 Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Sun, 22 Mar 2020 11:05:06 +0000
Subject: [PATCH 094/104] Simplify some of the Daubechies code. [CI SKIP]

---
 .../special_functions/daubechies_scaling.hpp  | 144 ++++++------------
 .../special_functions/daubechies_wavelet.hpp  | 102 ++-----------
 2 files changed, 59 insertions(+), 187 deletions(-)

diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index fe36bd1b1..b55b1356a 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -237,7 +237,7 @@ public:
 
         int64_t kk = static_cast<int64_t>(k);
         Real t = y - k;
-        return (1-t)*data_[kk][0] + t*data_[kk+1][0];
+        return (t != 0) ? (1-t)*data_[kk][0] + t*data_[kk+1][0] : data_[kk][0];
     }
 
     inline Real prime(Real x) const
@@ -248,7 +248,7 @@ public:
 
         int64_t kk = static_cast<int64_t>(k);
         Real t = y - k;
-        return (1-t)*data_[kk][1] + t*data_[kk+1][1];
+        return t != 0 ? (1-t)*data_[kk][1] + t*data_[kk+1][1] : data_[kk][1];
     }
 
     int64_t bytes() const
@@ -262,7 +262,43 @@ private:
     RandomAccessContainer data_;
 };
 
-}
+
+template <class T>
+struct daubechies_eval_type
+{
+   typedef T type;
+
+   static const std::vector<T>& vector_cast(const std::vector<T>& v) { return v; }
+
+};
+template <>
+struct daubechies_eval_type<float>
+{
+   typedef double type;
+
+   inline static std::vector<float> vector_cast(const std::vector<double>& v)
+   {
+      std::vector<float> result(v.size());
+      for (unsigned i = 0; i < v.size(); ++i)
+         result[i] = static_cast<float>(v[i]);
+      return result;
+   }
+};
+template <>
+struct daubechies_eval_type<double>
+{
+   typedef long double type;
+
+   inline static std::vector<double> vector_cast(const std::vector<long double>& v)
+   {
+      std::vector<double> result(v.size());
+      for (unsigned i = 0; i < v.size(); ++i)
+         result[i] = static_cast<double>(v[i]);
+      return result;
+   }
+};
+
+} // namespace detail
 
 template<class Real, int p>
 class daubechies_scaling {
@@ -311,57 +347,13 @@ public:
         // In fact for float precision I know the grid must be computed in double precision and then cast back down, or else parts of the support are systematically inaccurate.
         std::future<std::vector<Real>> t0 = std::async(std::launch::async, [&grid_refinements]() {
             // Computing in higher precision and downcasting is essential for 1ULP evaluation in float precision:
-            if constexpr (std::is_same_v<Real, float>)
-            {
-                auto v = daubechies_scaling_dyadic_grid<double, p, 0>(grid_refinements);
-                std::vector<float> w(v.size());
-                for (size_t i = 0; i < v.size(); ++i)
-                {
-                    w[i] = static_cast<float>(v[i]);
-                }
-                return w;
-            }
-            else if constexpr (std::is_same_v<Real, double>)
-            {
-                auto v = daubechies_scaling_dyadic_grid<long double, p, 0>(grid_refinements);
-                std::vector<double> w(v.size());
-                for (size_t i = 0; i < v.size(); ++i)
-                {
-                    w[i] = static_cast<double>(v[i]);
-                }
-                return w;
-            }
-            else
-            {
-                return daubechies_scaling_dyadic_grid<Real, p, 0>(grid_refinements);
-            }
+            auto v = daubechies_scaling_dyadic_grid<typename detail::daubechies_eval_type<Real>::type, p, 0>(grid_refinements);
+            return detail::daubechies_eval_type<Real>::vector_cast(v);
         });
         // Compute the derivative of the refined grid:
         std::future<std::vector<Real>> t1 = std::async(std::launch::async, [&grid_refinements]() {
-            if constexpr (std::is_same_v<Real, float>)
-            {
-                auto v = daubechies_scaling_dyadic_grid<double, p, 1>(grid_refinements);
-                std::vector<float> w(v.size());
-                for (size_t i = 0; i < v.size(); ++i)
-                {
-                    w[i] = static_cast<float>(v[i]);
-                }
-                return w;
-            }
-            else if constexpr (std::is_same_v<Real, double>)
-            {
-                auto v = daubechies_scaling_dyadic_grid<long double, p, 1>(grid_refinements);
-                std::vector<double> w(v.size());
-                for (size_t i = 0; i < v.size(); ++i)
-                {
-                    w[i] = static_cast<double>(v[i]);
-                }
-                return w;
-            }
-            else
-            {
-                return daubechies_scaling_dyadic_grid<Real, p, 1>(grid_refinements);
-            }
+           auto v = daubechies_scaling_dyadic_grid<typename detail::daubechies_eval_type<Real>::type, p, 1>(grid_refinements);
+           return detail::daubechies_eval_type<Real>::vector_cast(v);
         });
 
         // if necessary, compute the second and third derivative:
@@ -369,54 +361,14 @@ public:
         std::vector<Real> d3ydx3;
         if constexpr (p >= 6) {
             std::future<std::vector<Real>> t3 = std::async(std::launch::async, [&grid_refinements]() {
-                if constexpr (std::is_same_v<Real, float>)
-                {
-                    auto v = daubechies_scaling_dyadic_grid<double, p, 2>(grid_refinements);
-                    std::vector<float> w(v.size());
-                    for (size_t i = 0; i < v.size(); ++i)
-                    {
-                        w[i] = static_cast<float>(v[i]);
-                    }
-                    return w;
-                }
-                else if constexpr (std::is_same_v<Real, double>)
-                {
-                    auto v = daubechies_scaling_dyadic_grid<long double, p, 2>(grid_refinements);
-                    std::vector<double> w(v.size());
-                    for (size_t i = 0; i < v.size(); ++i)
-                    {
-                        w[i] = static_cast<double>(v[i]);
-                    }
-                    return w;
-                }
-                else
-                  return daubechies_scaling_dyadic_grid<Real, p, 2>(grid_refinements);
-            });
+               auto v = daubechies_scaling_dyadic_grid<typename detail::daubechies_eval_type<Real>::type, p, 2>(grid_refinements);
+               return detail::daubechies_eval_type<Real>::vector_cast(v);
+             });
 
             if constexpr (p >= 10) {
                 std::future<std::vector<Real>> t4 = std::async(std::launch::async, [&grid_refinements]() {
-                    if constexpr (std::is_same_v<Real, float>)
-                    {
-                        auto v = daubechies_scaling_dyadic_grid<double, p, 3>(grid_refinements);
-                        std::vector<float> w(v.size());
-                        for (size_t i = 0; i < v.size(); ++i)
-                        {
-                            w[i] = static_cast<float>(v[i]);
-                        }
-                        return w;
-                    }
-                    else if constexpr (std::is_same_v<Real, double>)
-                    {
-                        auto v = daubechies_scaling_dyadic_grid<long double, p, 3>(grid_refinements);
-                        std::vector<double> w(v.size());
-                        for (size_t i = 0; i < v.size(); ++i)
-                        {
-                            w[i] = static_cast<double>(v[i]);
-                        }
-                        return w;
-                    }
-                    else
-                     return daubechies_scaling_dyadic_grid<Real, p, 3>(grid_refinements);
+                   auto v = daubechies_scaling_dyadic_grid<typename detail::daubechies_eval_type<Real>::type, p, 3>(grid_refinements);
+                   return detail::daubechies_eval_type<Real>::vector_cast(v);
                 });
                 d3ydx3 = t4.get();
             }
diff --git a/include/boost/math/special_functions/daubechies_wavelet.hpp b/include/boost/math/special_functions/daubechies_wavelet.hpp
index 225c1532a..cbb31b3d9 100644
--- a/include/boost/math/special_functions/daubechies_wavelet.hpp
+++ b/include/boost/math/special_functions/daubechies_wavelet.hpp
@@ -119,109 +119,29 @@ public:
         // In fact for float precision I know the grid must be computed in double precision and then cast back down, or else parts of the support are systematically inaccurate.
         std::future<std::vector<Real>> t0 = std::async(std::launch::async, [&grid_refinements]() {
             // Computing in higher precision and downcasting is essential for 1ULP evaluation in float precision:
-            if constexpr (std::is_same_v<Real, float>)
-            {
-                auto v = daubechies_wavelet_dyadic_grid<double, p, 0>(grid_refinements);
-                std::vector<float> w(v.size());
-                for (size_t i = 0; i < v.size(); ++i)
-                {
-                    w[i] = static_cast<float>(v[i]);
-                }
-                return w;
-            }
-            else if constexpr (std::is_same_v<Real, double>)
-            {
-                auto v = daubechies_wavelet_dyadic_grid<long double, p, 0>(grid_refinements);
-                std::vector<double> w(v.size());
-                for (size_t i = 0; i < v.size(); ++i)
-                {
-                    w[i] = static_cast<double>(v[i]);
-                }
-                return w;
-            }
-
-            return daubechies_wavelet_dyadic_grid<Real, p, 0>(grid_refinements);
+           auto v = daubechies_wavelet_dyadic_grid<typename detail::daubechies_eval_type<Real>::type, p, 0>(grid_refinements);
+           return detail::daubechies_eval_type<Real>::vector_cast(v);
         });
         // Compute the derivative of the refined grid:
         std::future<std::vector<Real>> t1 = std::async(std::launch::async, [&grid_refinements]() {
-            if constexpr (std::is_same_v<Real, float>)
-            {
-                auto v = daubechies_wavelet_dyadic_grid<double, p, 1>(grid_refinements);
-                std::vector<float> w(v.size());
-                for (size_t i = 0; i < v.size(); ++i)
-                {
-                    w[i] = static_cast<float>(v[i]);
-                }
-                return w;
-            }
-            else if constexpr (std::is_same_v<Real, double>)
-            {
-                auto v = daubechies_wavelet_dyadic_grid<long double, p, 1>(grid_refinements);
-                std::vector<double> w(v.size());
-                for (size_t i = 0; i < v.size(); ++i)
-                {
-                    w[i] = static_cast<double>(v[i]);
-                }
-                return w;
-            }
-
-            return daubechies_wavelet_dyadic_grid<Real, p, 1>(grid_refinements);
-        });
+           auto v = daubechies_wavelet_dyadic_grid<typename detail::daubechies_eval_type<Real>::type, p, 1>(grid_refinements);
+           return detail::daubechies_eval_type<Real>::vector_cast(v);
+         });
 
         // if necessary, compute the second and third derivative:
         std::vector<Real> d2ydx2;
         std::vector<Real> d3ydx3;
         if constexpr (p >= 6) {
             std::future<std::vector<Real>> t3 = std::async(std::launch::async, [&grid_refinements]() {
-                if constexpr (std::is_same_v<Real, float>)
-                {
-                    auto v = daubechies_wavelet_dyadic_grid<double, p, 2>(grid_refinements);
-                    std::vector<float> w(v.size());
-                    for (size_t i = 0; i < v.size(); ++i)
-                    {
-                        w[i] = static_cast<float>(v[i]);
-                    }
-                    return w;
-                }
-                else if constexpr (std::is_same_v<Real, double>)
-                {
-                    auto v = daubechies_wavelet_dyadic_grid<long double, p, 2>(grid_refinements);
-                    std::vector<double> w(v.size());
-                    for (size_t i = 0; i < v.size(); ++i)
-                    {
-                        w[i] = static_cast<double>(v[i]);
-                    }
-                    return w;
-                }
-
-                return daubechies_wavelet_dyadic_grid<Real, p, 2>(grid_refinements);
-            });
+               auto v = daubechies_wavelet_dyadic_grid<typename detail::daubechies_eval_type<Real>::type, p, 2>(grid_refinements);
+               return detail::daubechies_eval_type<Real>::vector_cast(v);
+             });
 
             if constexpr (p >= 10) {
                 std::future<std::vector<Real>> t4 = std::async(std::launch::async, [&grid_refinements]() {
-                    if constexpr (std::is_same_v<Real, float>)
-                    {
-                        auto v = daubechies_wavelet_dyadic_grid<double, p, 3>(grid_refinements);
-                        std::vector<float> w(v.size());
-                        for (size_t i = 0; i < v.size(); ++i)
-                        {
-                            w[i] = static_cast<float>(v[i]);
-                        }
-                        return w;
-                    }
-                    else if constexpr (std::is_same_v<Real, double>)
-                    {
-                        auto v = daubechies_wavelet_dyadic_grid<long double, p, 3>(grid_refinements);
-                        std::vector<double> w(v.size());
-                        for (size_t i = 0; i < v.size(); ++i)
-                        {
-                            w[i] = static_cast<double>(v[i]);
-                        }
-                        return w;
-                    }
-
-                    return daubechies_wavelet_dyadic_grid<Real, p, 3>(grid_refinements);
-                });
+                   auto v = daubechies_wavelet_dyadic_grid<typename detail::daubechies_eval_type<Real>::type, p, 3>(grid_refinements);
+                   return detail::daubechies_eval_type<Real>::vector_cast(v);
+                 });
                 d3ydx3 = t4.get();
             }
             d2ydx2 = t3.get();

From bc70b9955370c2010d8035d243cfa4bf8ae05ff4 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Sun, 22 Mar 2020 08:50:21 -0400
Subject: [PATCH 095/104] Test boundaries for segfaults [CI SKIP]

---
 .../special_functions/daubechies_scaling.hpp  |  2 +-
 test/daubechies_scaling_test.cpp              | 77 +++++++++++++++----
 2 files changed, 62 insertions(+), 17 deletions(-)

diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index b55b1356a..4144469df 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -1,5 +1,5 @@
 /*
- * Copyright Nick Thompson, 2020
+ * Copyright Nick Thompson, John Maddock 2020
  * Use, modification and distribution are subject to the
  * Boost Software License, Version 1.0. (See accompanying file
  * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
diff --git a/test/daubechies_scaling_test.cpp b/test/daubechies_scaling_test.cpp
index e033d65fc..668cd609c 100644
--- a/test/daubechies_scaling_test.cpp
+++ b/test/daubechies_scaling_test.cpp
@@ -1,5 +1,5 @@
 /*
- * Copyright Nick Thompson, 2019
+ * Copyright Nick Thompson, John Maddock 2020
  * Use, modification and distribution are subject to the
  * Boost Software License, Version 1.0. (See accompanying file
  * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
@@ -21,6 +21,7 @@
 #include <boost/math/special_functions/detail/daubechies_scaling_integer_grid.hpp>
 #include <boost/math/constants/constants.hpp>
 #include <boost/math/quadrature/trapezoidal.hpp>
+#include <boost/math/special_functions/next.hpp>
 
 #ifdef BOOST_HAS_FLOAT128
 #include <boost/multiprecision/float128.hpp>
@@ -328,23 +329,47 @@ void test_first_derivative()
 template<typename Real, int p>
 void test_quadratures()
 {
+    std::cout << "Testing " << p << " vanishing moment scaling function quadratures on type " << boost::core::demangle(typeid(Real).name()) << "\n";
     using boost::math::quadrature::trapezoidal;
     if constexpr (p == 2)
     {
-         // 2phi is truly bizarre, because two successive trapezoidal estimates are always bitwise equal,
-         // whereas the third is way different. I don' t think that's a reasonable thing to optimize for,
-         // so one-off it is.
-         Real h = Real(1)/Real(256);
-         auto phi = boost::math::daubechies_scaling<Real, p>();
-         Real t = 0;
-         Real Q = 0;
-         while (t < 3) {
-             Q += phi(t);
-             t += h;
-         }
-         Q *= h;
-         CHECK_ULP_CLOSE(Real(1), Q, 32);
-         return;
+        // 2phi is truly bizarre, because two successive trapezoidal estimates are always bitwise equal,
+        // whereas the third is way different. I don' t think that's a reasonable thing to optimize for,
+        // so one-off it is.
+        Real h = Real(1)/Real(256);
+        auto phi = boost::math::daubechies_scaling<Real, p>();
+        Real t = 0;
+        Real Q = 0;
+        while (t < 3) {
+            Q += phi(t);
+            t += h;
+        }
+        Q *= h;
+        CHECK_ULP_CLOSE(Real(1), Q, 32);
+
+        auto [a, b] = phi.support();
+        // Now hit the boundary. Much can go wrong here; this just tests for segfaults:
+        int samples = 500;
+        Real xlo = a;
+        Real xhi = b;
+        for (int i = 0; i < samples; ++i)
+        {
+            CHECK_ULP_CLOSE(Real(0), phi(xlo), 0);
+            CHECK_ULP_CLOSE(Real(0), phi(xhi), 0);
+            xlo = std::nextafter(xlo, std::numeric_limits<Real>::lowest());
+            xhi = std::nextafter(xhi, std::numeric_limits<Real>::max());
+        }
+
+        xlo = a;
+        xhi = b;
+        for (int i = 0; i < samples; ++i) {
+            assert(abs(phi(xlo)) <= 5);
+            assert(abs(phi(xhi)) <= 5);
+            xlo = std::nextafter(xlo, std::numeric_limits<Real>::max());
+            xhi = std::nextafter(xhi, std::numeric_limits<Real>::lowest());
+        }
+
+        return;
     }
     else if constexpr (p > 2)
     {
@@ -369,7 +394,6 @@ void test_quadratures()
             std::cerr << "  Error estimate is " << error_estimate << ", L1 norm is " << L1 << "\n";
         }
 
-    
         std::random_device rd;
         Real t = static_cast<Real>(rd())/static_cast<Real>(rd.max());
         Real S = phi(t);
@@ -394,6 +418,27 @@ void test_quadratures()
                 std::cerr << "  Derivative of normalizing sum for " << p << " vanishing moment scaling function doesn't vanish.\n";
             }
         }
+
+        // Test boundary for segfaults:
+        int samples = 500;
+        Real xlo = a;
+        Real xhi = b;
+        for (int i = 0; i < samples; ++i)
+        {
+            CHECK_ULP_CLOSE(Real(0), phi(xlo), 0);
+            CHECK_ULP_CLOSE(Real(0), phi(xhi), 0);
+            xlo = std::nextafter(xlo, std::numeric_limits<Real>::lowest());
+            xhi = std::nextafter(xhi, std::numeric_limits<Real>::max());
+        }
+
+        xlo = a;
+        xhi = b;
+        for (int i = 0; i < samples; ++i) {
+            assert(abs(phi(xlo)) <= 5);
+            assert(abs(phi(xhi)) <= 5);
+            xlo = std::nextafter(xlo, std::numeric_limits<Real>::max());
+            xhi = std::nextafter(xhi, std::numeric_limits<Real>::lowest());
+        }
     }
 }
 

From 5cbfdb554abbf5f7f7f1fe034b6345bc5335f39f Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Sun, 22 Mar 2020 11:22:36 -0400
Subject: [PATCH 096/104] Fix invalid read in cubic Hermite. [CI SKIP]

---
 doc/interpolators/cubic_hermite.qbk           | 10 ++
 .../math/interpolators/cubic_hermite.hpp      | 17 +++-
 .../detail/cubic_hermite_detail.hpp           | 29 +++++-
 test/cubic_hermite_test.cpp                   | 93 ++++++++++++++++---
 test/daubechies_scaling_test.cpp              |  8 ++
 test/daubechies_wavelet_test.cpp              | 21 +++++
 6 files changed, 164 insertions(+), 14 deletions(-)

diff --git a/doc/interpolators/cubic_hermite.qbk b/doc/interpolators/cubic_hermite.qbk
index 7b78e621e..347659c58 100644
--- a/doc/interpolators/cubic_hermite.qbk
+++ b/doc/interpolators/cubic_hermite.qbk
@@ -29,6 +29,8 @@ LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
 
         void push_back(Real x, Real y, Real dydx);
 
+        std::pair<Real, Real> domain() const;
+
         friend std::ostream& operator<<(std::ostream & os, const cubic_hermite & m);
     };
 
@@ -42,6 +44,8 @@ LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
         inline Real operator()(Real x) const;
 
         inline Real prime(Real x) const;
+
+        std::pair<Real, Real> domain() const;
     };
 
 
@@ -56,6 +60,8 @@ LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
         inline Real operator()(Real x) const;
 
         inline Real prime(Real x) const;
+
+        std::pair<Real, Real> domain() const;
     };
 
     } // namespaces
@@ -124,6 +130,10 @@ For the "array of structs" version:
 
     auto ch = cardinal_cubic_hermite_aos(std::move(data), x0, dx);
 
+For a quick sanity check, we can call `ch.domain()`:
+
+    auto [x_min, x_max] = ch.domain();
+
 [heading Performance]
 
 Google benchmark was used to evaluate the performance.
diff --git a/include/boost/math/interpolators/cubic_hermite.hpp b/include/boost/math/interpolators/cubic_hermite.hpp
index f7a0bed07..c568510ec 100644
--- a/include/boost/math/interpolators/cubic_hermite.hpp
+++ b/include/boost/math/interpolators/cubic_hermite.hpp
@@ -39,11 +39,16 @@ public:
         impl_->push_back(x, y, dydx);
     }
 
-    int64_t bytes()
+    int64_t bytes() const
     {
         return impl_->bytes() + sizeof(impl_);
     }
 
+    std::pair<Real, Real> domain() const
+    {
+        return impl_->domain();
+    }
+
 private:
     std::shared_ptr<detail::cubic_hermite_detail<RandomAccessContainer>> impl_;
 };
@@ -78,6 +83,11 @@ public:
         return impl_->bytes() + sizeof(impl_);
     }
 
+    std::pair<Real, Real> domain() const
+    {
+        return impl_->domain();
+    }
+
 private:
     std::shared_ptr<detail::cardinal_cubic_hermite_detail<RandomAccessContainer>> impl_;
 };
@@ -114,6 +124,11 @@ public:
         return impl_->bytes() + sizeof(impl_);
     }
 
+    std::pair<Real, Real> domain() const
+    {
+        return impl_->domain();
+    }
+
 private:
     std::shared_ptr<detail::cardinal_cubic_hermite_detail_aos<RandomAccessContainer>> impl_;
 };
diff --git a/include/boost/math/interpolators/detail/cubic_hermite_detail.hpp b/include/boost/math/interpolators/detail/cubic_hermite_detail.hpp
index 94c250ff3..6365e1ab6 100644
--- a/include/boost/math/interpolators/detail/cubic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/cubic_hermite_detail.hpp
@@ -155,6 +155,11 @@ public:
         return 3*x_.size()*sizeof(Real) + 3*sizeof(x_);
     }
 
+    std::pair<Real, Real> domain() const
+    {
+        return {x_.front(), x_.back()};
+    }
+
     RandomAccessContainer x_;
     RandomAccessContainer y_;
     RandomAccessContainer dydx_;
@@ -273,6 +278,12 @@ public:
         return 2*y_.size()*sizeof(Real) + 2*sizeof(y_) + 2*sizeof(Real);
     }
 
+    std::pair<Real, Real> domain() const
+    {
+        Real xf = x0_ + (y_.size()-1)/inv_dx_;
+        return {x0_, xf};
+    }
+
 private:
 
     RandomAccessContainer y_;
@@ -336,6 +347,12 @@ public:
         auto i = static_cast<decltype(dat_.size())>(ii);
 
         Real t = s - ii;
+        // If we had infinite precision, this would never happen.
+        // But we don't have infinite precision.
+        if (t == 0)
+        {
+            return dat_[i][0];
+        }
         Real y0 = dat_[i][0];
         Real y1 = dat_[i+1][0];
         Real dy0 = dat_[i][1];
@@ -359,7 +376,7 @@ public:
         }
         if (x == xf)
         {
-            return dat_.back()[1];
+            return dat_.back()[1]*inv_dx_;
         }
         return this->unchecked_prime(x);
     }
@@ -371,6 +388,10 @@ public:
         Real ii = floor(s);
         auto i = static_cast<decltype(dat_.size())>(ii);
         Real t = s - ii;
+        if (t == 0)
+        {
+            return dat_[i][1]*inv_dx_;
+        }
         Real y0 = dat_[i][0];
         Real dy0 = dat_[i][1];
         Real y1 = dat_[i+1][0];
@@ -391,6 +412,12 @@ public:
         return dat_.size()*dat_[0].size()*sizeof(Real) + sizeof(dat_) + 2*sizeof(Real);
     }
 
+    std::pair<Real, Real> domain() const
+    {
+        Real xf = x0_ + (dat_.size()-1)/inv_dx_;
+        return {x0_, xf};
+    }
+
 
 private:
     RandomAccessContainer dat_;
diff --git a/test/cubic_hermite_test.cpp b/test/cubic_hermite_test.cpp
index 6d75c2883..4c9cfc003 100644
--- a/test/cubic_hermite_test.cpp
+++ b/test/cubic_hermite_test.cpp
@@ -12,6 +12,7 @@
 #include <array>
 #include <vector>
 #include <boost/math/interpolators/cubic_hermite.hpp>
+#include <boost/math/special_functions/next.hpp>
 #include <boost/circular_buffer.hpp>
 #ifdef BOOST_HAS_FLOAT128
 #include <boost/multiprecision/float128.hpp>
@@ -27,10 +28,11 @@ using boost::math::interpolators::cardinal_cubic_hermite_aos;
 template<typename Real>
 void test_constant()
 {
-
-    std::vector<Real> x{0,1,2,3, 9, 22, 81};
+    Real x0 = 0;
+    std::vector<Real> x{x0,1,2,3, 9, 22, 81};
     std::vector<Real> y(x.size());
-    for (auto & t : y) {
+    for (auto & t : y)
+    {
         t = 7;
     }
 
@@ -40,9 +42,19 @@ void test_constant()
     auto dydx_copy = dydx;
     auto hermite_spline = cubic_hermite(std::move(x_copy), std::move(y_copy), std::move(dydx_copy));
 
-    for (Real t = x[0]; t <= x.back(); t += 0.25) {
-        CHECK_ULP_CLOSE(Real(7), hermite_spline(t), 2);
-        CHECK_ULP_CLOSE(Real(0), hermite_spline.prime(t), 2);
+    // Now check the boundaries:
+    Real tlo = x.front();
+    Real thi = x.back();
+    int samples = 5000;
+    int i = 0;
+    while (i++ < samples)
+    {
+        CHECK_ULP_CLOSE(Real(7), hermite_spline(tlo), 2);
+        CHECK_ULP_CLOSE(Real(7), hermite_spline(thi), 2);
+        CHECK_ULP_CLOSE(Real(0), hermite_spline.prime(tlo), 2);
+        CHECK_ULP_CLOSE(Real(0), hermite_spline.prime(thi), 2);
+        tlo = boost::math::nextafter(tlo, std::numeric_limits<Real>::max());
+        thi = boost::math::nextafter(thi, std::numeric_limits<Real>::lowest());
     }
 
     boost::circular_buffer<Real> x_buf(x.size());
@@ -226,10 +238,34 @@ void test_cardinal_constant()
     auto hermite_spline_aos = cardinal_cubic_hermite_aos(std::move(data), x0, dx);
 
     for (Real t = x0; t <= x0 + 24*dx; t += 0.25) {
-        CHECK_ULP_CLOSE(Real(7), hermite_spline_aos(t), 2);
-        CHECK_ULP_CLOSE(Real(0), hermite_spline_aos.prime(t), 2);
+        if (!CHECK_ULP_CLOSE(Real(7), hermite_spline_aos(t), 2)) {
+            std::cerr << "  Wrong evaluation at t = " << t << "\n";
+        }
+        if (!CHECK_ULP_CLOSE(Real(0), hermite_spline_aos.prime(t), 2)) {
+            std::cerr << "  Wrong evaluation at t = " << t << "\n";
+        }
     }
- 
+
+        // Now check the boundaries:
+    Real tlo = x0;
+    Real thi = x0 + (25-1)*dx;
+    int samples = 5000;
+    int i = 0;
+    while (i++ < samples)
+    {
+        CHECK_ULP_CLOSE(Real(7), hermite_spline(tlo), 2);
+        CHECK_ULP_CLOSE(Real(7), hermite_spline(thi), 2);
+        CHECK_ULP_CLOSE(Real(7), hermite_spline_aos(tlo), 2);
+        CHECK_ULP_CLOSE(Real(7), hermite_spline_aos(thi), 2);
+        CHECK_ULP_CLOSE(Real(0), hermite_spline.prime(tlo), 2);
+        CHECK_ULP_CLOSE(Real(0), hermite_spline.prime(thi), 2);
+        CHECK_ULP_CLOSE(Real(0), hermite_spline_aos.prime(tlo), 2);
+        CHECK_ULP_CLOSE(Real(0), hermite_spline_aos.prime(thi), 2);
+
+        tlo = boost::math::nextafter(tlo, std::numeric_limits<Real>::max());
+        thi = boost::math::nextafter(thi, std::numeric_limits<Real>::lowest());
+    }
+
 }
 
 
@@ -278,6 +314,25 @@ void test_cardinal_linear()
         CHECK_ULP_CLOSE(Real(1), hermite_spline_aos.prime(t), 0);
     }
 
+    Real tlo = x0;
+    Real thi = x0 + (45-1)*dx;
+    int samples = 5000;
+    int i = 0;
+    while (i++ < samples)
+    {
+        CHECK_ULP_CLOSE(Real(tlo), hermite_spline(tlo), 2);
+        CHECK_ULP_CLOSE(Real(thi), hermite_spline(thi), 2);
+        CHECK_ULP_CLOSE(Real(1), hermite_spline.prime(tlo), 2);
+        CHECK_ULP_CLOSE(Real(1), hermite_spline.prime(thi), 2);
+        CHECK_ULP_CLOSE(Real(tlo), hermite_spline_aos(tlo), 2);
+        CHECK_ULP_CLOSE(Real(thi), hermite_spline_aos(thi), 2);
+        CHECK_ULP_CLOSE(Real(1), hermite_spline_aos.prime(tlo), 2);
+        CHECK_ULP_CLOSE(Real(1), hermite_spline_aos.prime(thi), 2);
+
+        tlo = boost::math::nextafter(tlo, std::numeric_limits<Real>::max());
+        thi = boost::math::nextafter(thi, std::numeric_limits<Real>::lowest());
+    }
+
 
 }
 
@@ -318,6 +373,23 @@ void test_cardinal_quadratic()
         CHECK_ULP_CLOSE(t, saos.prime(t), 70);
     }
 
+    auto [tlo, thi] = s.domain();
+    int samples = 5000;
+    int i = 0;
+    while (i++ < samples)
+    {
+        CHECK_ULP_CLOSE(Real(tlo*tlo/2), s(tlo), 3);
+        CHECK_ULP_CLOSE(Real(thi*thi/2), s(thi), 3);
+        CHECK_ULP_CLOSE(Real(tlo), s.prime(tlo), 3);
+        CHECK_ULP_CLOSE(Real(thi), s.prime(thi), 3);
+        CHECK_ULP_CLOSE(Real(tlo*tlo/2), saos(tlo), 3);
+        CHECK_ULP_CLOSE(Real(thi*thi/2), saos(thi), 3);
+        CHECK_ULP_CLOSE(Real(tlo), saos.prime(tlo), 3);
+        CHECK_ULP_CLOSE(Real(thi), saos.prime(thi), 3);
+
+        tlo = boost::math::nextafter(tlo, std::numeric_limits<Real>::max());
+        thi = boost::math::nextafter(thi, std::numeric_limits<Real>::lowest());
+    }
 }
 
 
@@ -359,8 +431,6 @@ int main()
     test_cardinal_quadratic<float>();
     test_cardinal_interpolation_condition<float>();
 
-
-
     test_constant<double>();
     test_linear<double>();
     test_quadratic<double>();
@@ -370,7 +440,6 @@ int main()
     test_cardinal_quadratic<double>();
     test_cardinal_interpolation_condition<double>();
 
-
     test_constant<long double>();
     test_linear<long double>();
     test_quadratic<long double>();
diff --git a/test/daubechies_scaling_test.cpp b/test/daubechies_scaling_test.cpp
index 668cd609c..ceb43da88 100644
--- a/test/daubechies_scaling_test.cpp
+++ b/test/daubechies_scaling_test.cpp
@@ -427,6 +427,14 @@ void test_quadratures()
         {
             CHECK_ULP_CLOSE(Real(0), phi(xlo), 0);
             CHECK_ULP_CLOSE(Real(0), phi(xhi), 0);
+            if constexpr (p > 2) {
+                assert(abs(phi.prime(xlo)) <= 5);
+                assert(abs(phi.prime(xhi)) <= 5);
+                if constexpr (p > 5) {
+                    assert(abs(phi.double_prime(xlo)) <= 5);
+                    assert(abs(phi.double_prime(xhi)) <= 5);
+                }
+            }
             xlo = std::nextafter(xlo, std::numeric_limits<Real>::lowest());
             xhi = std::nextafter(xhi, std::numeric_limits<Real>::max());
         }
diff --git a/test/daubechies_wavelet_test.cpp b/test/daubechies_wavelet_test.cpp
index f1614d10e..384b02664 100644
--- a/test/daubechies_wavelet_test.cpp
+++ b/test/daubechies_wavelet_test.cpp
@@ -11,6 +11,7 @@
 #include <iomanip>
 #include <iostream>
 #include <random>
+#include <cmath>
 #include <boost/core/demangle.hpp>
 #include <boost/hana/for_each.hpp>
 #include <boost/hana/ext/std/integer_sequence.hpp>
@@ -81,6 +82,15 @@ void test_quadratures()
     {
         CHECK_ULP_CLOSE(Real(0), psi(xlo), 0);
         CHECK_ULP_CLOSE(Real(0), psi(xhi), 0);
+        if constexpr (p > 2)
+        {
+            CHECK_ULP_CLOSE(Real(0), psi.prime(xlo), 0);
+            CHECK_ULP_CLOSE(Real(0), psi.prime(xhi), 0);
+            if constexpr (p >= 6) {
+                CHECK_ULP_CLOSE(Real(0), psi.double_prime(xlo), 0);
+                CHECK_ULP_CLOSE(Real(0), psi.double_prime(xhi), 0);
+            }
+        }
         xlo = std::nextafter(xlo, std::numeric_limits<Real>::lowest());
         xhi = std::nextafter(xhi, std::numeric_limits<Real>::max());
     }
@@ -88,8 +98,19 @@ void test_quadratures()
     xlo = a;
     xhi = b;
     for (int i = 0; i < samples; ++i) {
+        std::cout << std::setprecision(std::numeric_limits<Real>::max_digits10);
         assert(abs(psi(xlo)) <= 5);
         assert(abs(psi(xhi)) <= 5);
+        if constexpr (p > 2)
+        {
+            assert(abs(psi.prime(xlo)) <= 5);
+            assert(abs(psi.prime(xhi)) <= 5);
+            if constexpr (p >= 6)
+            {
+                assert(abs(psi.double_prime(xlo)) <= 5);
+                assert(abs(psi.double_prime(xhi)) <= 5);
+            }
+        }
         xlo = std::nextafter(xlo, std::numeric_limits<Real>::max());
         xhi = std::nextafter(xhi, std::numeric_limits<Real>::lowest());
     }

From 2af33f272596a771ffbdd2c03097bc81f8c58b2e Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Sun, 22 Mar 2020 12:07:05 -0400
Subject: [PATCH 097/104] Fix quintic hermite interpolation [CI SKIP]

---
 doc/interpolators/quintic_hermite.qbk         |  6 ++
 .../detail/quintic_hermite_detail.hpp         | 45 +++++++++++++--
 .../math/interpolators/quintic_hermite.hpp    | 15 +++++
 test/cubic_hermite_test.cpp                   |  2 +-
 test/quintic_hermite_test.cpp                 | 57 +++++++++++++++++++
 5 files changed, 119 insertions(+), 6 deletions(-)

diff --git a/doc/interpolators/quintic_hermite.qbk b/doc/interpolators/quintic_hermite.qbk
index dafea2810..a2d550d4e 100644
--- a/doc/interpolators/quintic_hermite.qbk
+++ b/doc/interpolators/quintic_hermite.qbk
@@ -25,6 +25,8 @@ public:
 
     inline Real double_prime(Real x) const;
 
+    std::pair<Real, Real> domain() const;
+
     friend std::ostream& operator<<(std::ostream & os, const quintic_hermite & m);
 
     void push_back(Real x, Real y, Real dydx, Real d2ydx2);
@@ -41,6 +43,8 @@ public:
     inline Real prime(Real x) const;
 
     inline Real double_prime(Real x) const;
+
+    std::pair<Real, Real> domain() const;
 };
 
 template<class RandomAccessContainer>
@@ -56,6 +60,8 @@ public:
 
     inline Real double_prime(Real x) const;
 
+    std::pair<Real, Real> domain() const;
+
 }
 ``
 
diff --git a/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp b/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
index 26a4e7498..28f04daca 100644
--- a/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
@@ -188,6 +188,11 @@ public:
         return 4*x_.size()*sizeof(x_);
     }
 
+    std::pair<Real, Real> domain() const
+    {
+        return {x_.front(), x_.back()};
+    }
+
 private:
     RandomAccessContainer x_;
     RandomAccessContainer y_;
@@ -257,7 +262,10 @@ public:
         Real ii = floor(s);
         auto i = static_cast<decltype(y_.size())>(ii);
         Real t = s - ii;
-
+        if (t == 0)
+        {
+            return y_[i];
+        }
         Real y0 = y_[i];
         Real y1 = y_[i+1];
         Real dy0 = dy_[i];
@@ -301,7 +309,10 @@ public:
         Real ii = floor(s);
         auto i = static_cast<decltype(y_.size())>(ii);
         Real t = s - ii;
-
+        if (t == 0)
+        {
+            return dy_[i]*inv_dx_;
+        }
         Real y0 = y_[i];
         Real y1 = y_[i+1];
         Real dy0 = dy_[i];
@@ -341,7 +352,10 @@ public:
         Real ii = floor(s);
         auto i = static_cast<decltype(y_.size())>(ii);
         Real t = s - ii;
-
+        if (t==0)
+        {
+            return d2y_[i]*2*inv_dx_*inv_dx_;
+        }
 
         Real y0 = y_[i];
         Real y1 = y_[i+1];
@@ -361,6 +375,12 @@ public:
         return 3*y_.size()*sizeof(Real) + 2*sizeof(Real);
     }
 
+    std::pair<Real, Real> domain() const
+    {
+        Real xf = x0_ + (y_.size()-1)/inv_dx_;
+        return {x0_, xf};
+    }
+
 private:
     RandomAccessContainer y_;
     RandomAccessContainer dy_;
@@ -425,6 +445,10 @@ public:
         Real ii = floor(s);
         auto i = static_cast<decltype(data_.size())>(ii);
         Real t = s - ii;
+        if (t == 0)
+        {
+            return data_[i][0];
+        }
 
         Real y0 = data_[i][0];
         Real dy0 = data_[i][1];
@@ -466,6 +490,10 @@ public:
         Real ii = floor(s);
         auto i = static_cast<decltype(data_.size())>(ii);
         Real t = s - ii;
+        if (t == 0)
+        {
+            return data_[i][1]*inv_dx_;
+        }
 
 
         Real y0 = data_[i][0];
@@ -507,8 +535,9 @@ public:
         Real ii = floor(s);
         auto i = static_cast<decltype(data_.size())>(ii);
         Real t = s - ii;
-
-
+        if (t == 0) {
+            return data_[i][2]*2*inv_dx_*inv_dx_;
+        }
         Real y0 = data_[i][0];
         Real dy0 = data_[i][1];
         Real d2y0 = data_[i][2];
@@ -527,6 +556,12 @@ public:
         return data_.size()*data_[0].size()*sizeof(Real) + 2*sizeof(Real);
     }
 
+    std::pair<Real, Real> domain() const
+    {
+        Real xf = x0_ + (data_.size()-1)/inv_dx_;
+        return {x0_, xf};
+    }
+
 private:
     RandomAccessContainer data_;
     Real x0_;
diff --git a/include/boost/math/interpolators/quintic_hermite.hpp b/include/boost/math/interpolators/quintic_hermite.hpp
index beb7238f1..627f02d28 100644
--- a/include/boost/math/interpolators/quintic_hermite.hpp
+++ b/include/boost/math/interpolators/quintic_hermite.hpp
@@ -46,6 +46,11 @@ public:
         return impl_->bytes() + sizeof(impl_);
     }
 
+    std::pair<Real, Real> domain() const
+    {
+        return impl_->domain();
+    }
+
 private:
     std::shared_ptr<detail::quintic_hermite_detail<RandomAccessContainer>> impl_;
 };
@@ -76,6 +81,11 @@ public:
         return impl_->bytes() + sizeof(impl_);
     }
 
+    std::pair<Real, Real> domain() const
+    {
+        return impl_->domain();
+    }
+
 private:
     std::shared_ptr<detail::cardinal_quintic_hermite_detail<RandomAccessContainer>> impl_;
 };
@@ -108,6 +118,11 @@ public:
     {
         return impl_->bytes() + sizeof(impl_);
     }
+
+    std::pair<Real, Real> domain() const
+    {
+        return impl_->domain();
+    }
 private:
     std::shared_ptr<detail::cardinal_quintic_hermite_detail_aos<RandomAccessContainer>> impl_;
 };
diff --git a/test/cubic_hermite_test.cpp b/test/cubic_hermite_test.cpp
index 4c9cfc003..0a23fb166 100644
--- a/test/cubic_hermite_test.cpp
+++ b/test/cubic_hermite_test.cpp
@@ -246,7 +246,7 @@ void test_cardinal_constant()
         }
     }
 
-        // Now check the boundaries:
+    // Now check the boundaries:
     Real tlo = x0;
     Real thi = x0 + (25-1)*dx;
     int samples = 5000;
diff --git a/test/quintic_hermite_test.cpp b/test/quintic_hermite_test.cpp
index a668e42e1..05299bae3 100644
--- a/test/quintic_hermite_test.cpp
+++ b/test/quintic_hermite_test.cpp
@@ -13,6 +13,7 @@
 #include <boost/random/uniform_real.hpp>
 #include <boost/random/mersenne_twister.hpp>
 #include <boost/math/interpolators/quintic_hermite.hpp>
+#include <boost/math/special_functions/next.hpp>
 #include <boost/circular_buffer.hpp>
 #ifdef BOOST_HAS_FLOAT128
 #include <boost/multiprecision/float128.hpp>
@@ -287,6 +288,25 @@ void test_cardinal_constant()
         CHECK_ULP_CLOSE(Real(0), qh_aos.prime(t), 24);
         CHECK_ULP_CLOSE(Real(0), qh_aos.double_prime(t), 24);
     }
+
+    // Now check the boundaries:
+    auto [tlo, thi] = qh.domain();
+    int samples = 5000;
+    int i = 0;
+    while (i++ < samples)
+    {
+        CHECK_ULP_CLOSE(Real(7), qh(tlo), 2);
+        CHECK_ULP_CLOSE(Real(7), qh(thi), 2);
+        CHECK_ULP_CLOSE(Real(7), qh_aos(tlo), 2);
+        CHECK_ULP_CLOSE(Real(7), qh_aos(thi), 2);
+        CHECK_ULP_CLOSE(Real(0), qh.prime(tlo), 2);
+        CHECK_ULP_CLOSE(Real(0), qh.prime(thi), 2);
+        CHECK_ULP_CLOSE(Real(0), qh_aos.prime(tlo), 2);
+        CHECK_ULP_CLOSE(Real(0), qh_aos.prime(thi), 2);
+
+        tlo = boost::math::nextafter(tlo, std::numeric_limits<Real>::max());
+        thi = boost::math::nextafter(thi, std::numeric_limits<Real>::lowest());
+    }
 }
 
 
@@ -322,6 +342,24 @@ void test_cardinal_linear()
         CHECK_ULP_CLOSE(Real(0), qh_aos.double_prime(t), 2);
     }
 
+    // Now check the boundaries:
+    auto [tlo, thi] = qh.domain();
+    int samples = 5000;
+    int i = 0;
+    while (i++ < samples)
+    {
+        CHECK_ULP_CLOSE(Real(tlo), qh(tlo), 2);
+        CHECK_ULP_CLOSE(Real(thi), qh(thi), 2);
+        CHECK_ULP_CLOSE(Real(tlo), qh_aos(tlo), 2);
+        CHECK_ULP_CLOSE(Real(thi), qh_aos(thi), 2);
+        CHECK_ULP_CLOSE(Real(1), qh.prime(tlo), 2);
+        CHECK_ULP_CLOSE(Real(1), qh.prime(thi), 128);
+        CHECK_ULP_CLOSE(Real(1), qh_aos.prime(tlo), 2);
+        CHECK_ULP_CLOSE(Real(1), qh_aos.prime(thi), 128);
+
+        tlo = boost::math::nextafter(tlo, std::numeric_limits<Real>::max());
+        thi = boost::math::nextafter(thi, std::numeric_limits<Real>::lowest());
+    }
 }
 
 template<typename Real>
@@ -366,6 +404,25 @@ void test_cardinal_quadratic()
         CHECK_ULP_CLOSE(t, qh_aos.prime(t), 12);
         CHECK_ULP_CLOSE(Real(1), qh_aos.double_prime(t), 64);
     }
+
+        // Now check the boundaries:
+    auto [tlo, thi] = qh.domain();
+    int samples = 5000;
+    int i = 0;
+    while (i++ < samples)
+    {
+        CHECK_ULP_CLOSE(tlo*tlo/2, qh(tlo), 16);
+        CHECK_ULP_CLOSE(thi*thi/2, qh(thi), 16);
+        CHECK_ULP_CLOSE(tlo*tlo/2, qh_aos(tlo), 16);
+        CHECK_ULP_CLOSE(thi*thi/2, qh_aos(thi), 16);
+        CHECK_ULP_CLOSE(tlo, qh.prime(tlo), 16);
+        CHECK_ULP_CLOSE(thi, qh.prime(thi), 64);
+        CHECK_ULP_CLOSE(tlo, qh_aos.prime(tlo), 16);
+        CHECK_ULP_CLOSE(thi, qh_aos.prime(thi), 64);
+
+        tlo = boost::math::nextafter(tlo, std::numeric_limits<Real>::max());
+        thi = boost::math::nextafter(thi, std::numeric_limits<Real>::lowest());
+    }
 }
 
 template<typename Real>

From fb26bc0cf19e3f645f4cac595f2ca1d6003d3588 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Sun, 22 Mar 2020 13:03:48 -0400
Subject: [PATCH 098/104] Fix septic hermite evaluation.

---
 .../detail/septic_hermite_detail.hpp          | 39 ++++++++++++++-
 .../math/interpolators/septic_hermite.hpp     | 15 ++++++
 test/septic_hermite_test.cpp                  | 48 +++++++++++++++++++
 3 files changed, 101 insertions(+), 1 deletion(-)

diff --git a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
index 659cf019d..44843c6bb 100644
--- a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
@@ -184,6 +184,11 @@ public:
         return 5*x_.size()*sizeof(Real) + 5*sizeof(x_);
     }
 
+    std::pair<Real, Real> domain() const
+    {
+        return {x_.front(), x_.back()};
+    }
+
 private:
     RandomAccessContainer x_;
     RandomAccessContainer y_;
@@ -260,6 +265,9 @@ public:
         Real ii = floor(s3);
         auto i = static_cast<decltype(y_.size())>(ii);
         Real t = s3 - ii;
+        if (t == 0) {
+            return y_[i];
+        }
         // See:
         // http://seisweb.usask.ca/classes/GEOL481/2017/Labs/interpolation_utilities_matlab/shermite.m
         Real t2 = t*t;
@@ -314,6 +322,10 @@ public:
         Real ii = floor(s3);
         auto i = static_cast<decltype(y_.size())>(ii);
         Real t = s3 - ii;
+        if (t==0)
+        {
+            return dy_[i]/inv_dx_;
+        }
  
         Real y0 = y_[i];
         Real y1 = y_[i+1];
@@ -366,6 +378,10 @@ public:
         Real ii = floor(s3);
         auto i = static_cast<decltype(y_.size())>(ii);
         Real t = s3 - ii;
+        if (t==0)
+        {
+            return d2y_[i]*2*inv_dx_*inv_dx_;
+        }
 
         Real y0 = y_[i];
         Real y1 = y_[i+1];
@@ -398,6 +414,11 @@ public:
         return 4*y_.size()*sizeof(Real) + 2*sizeof(Real) + 4*sizeof(y_);
     }
 
+    std::pair<Real, Real> domain() const
+    {
+        return {x0_, x0_ + (y_.size()-1)/inv_dx_};
+    }
+
 private:
     RandomAccessContainer y_;
     RandomAccessContainer dy_;
@@ -456,6 +477,10 @@ public:
         Real ii = floor(s3);
         auto i = static_cast<decltype(data_.size())>(ii);
         Real t = s3 - ii;
+        if (t==0)
+        {
+            return data_[i][0];
+        }
         Real t2 = t*t;
         Real t3 = t2*t;
         Real t4 = t3*t;
@@ -508,6 +533,10 @@ public:
         Real ii = floor(s3);
         auto i = static_cast<decltype(data_.size())>(ii);
         Real t = s3 - ii;
+        if (t == 0)
+        {
+            return data_[i][1]*inv_dx_;
+        }
 
         Real y0 = data_[i][0];
         Real y1 = data_[i+1][0];
@@ -560,7 +589,10 @@ public:
         Real ii = floor(s3);
         auto i = static_cast<decltype(data_.size())>(ii);
         Real t = s3 - ii;
-
+        if (t == 0)
+        {
+            return data_[i][2]*2*inv_dx_*inv_dx_;
+        }
         Real y0 = data_[i][0];
         Real y1 = data_[i+1][0];
         Real dy0 = data_[i][1];
@@ -592,6 +624,11 @@ public:
         return data_.size()*data_[0].size()*sizeof(Real) + 2*sizeof(Real) + sizeof(data_);
     }
 
+    std::pair<Real, Real> domain() const
+    {
+        return {x0_, x0_ + (data_.size() -1)/inv_dx_};
+    }
+
 private:
     RandomAccessContainer data_;
     Real x0_;
diff --git a/include/boost/math/interpolators/septic_hermite.hpp b/include/boost/math/interpolators/septic_hermite.hpp
index 81d33291f..b5acbc764 100644
--- a/include/boost/math/interpolators/septic_hermite.hpp
+++ b/include/boost/math/interpolators/septic_hermite.hpp
@@ -44,6 +44,11 @@ public:
         return impl_->bytes() + sizeof(impl_);
     }
 
+    std::pair<Real, Real> domain() const
+    {
+        return impl_->domain();
+    }
+
 private:
     std::shared_ptr<detail::septic_hermite_detail<RandomAccessContainer>> impl_;
 };
@@ -79,6 +84,11 @@ public:
         return impl_->bytes() + sizeof(impl_);
     }
 
+    std::pair<Real, Real> domain() const
+    {
+        return impl_->domain();
+    }
+
 private:
     std::shared_ptr<detail::cardinal_septic_hermite_detail<RandomAccessContainer>> impl_;
 };
@@ -113,6 +123,11 @@ public:
         return impl_.size() + sizeof(impl_);
     }
 
+    std::pair<Real, Real> domain() const
+    {
+        return impl_->domain();
+    }
+
 private:
     std::shared_ptr<detail::cardinal_septic_hermite_detail_aos<RandomAccessContainer>> impl_;
 };
diff --git a/test/septic_hermite_test.cpp b/test/septic_hermite_test.cpp
index 6b7265327..944a3d0c4 100644
--- a/test/septic_hermite_test.cpp
+++ b/test/septic_hermite_test.cpp
@@ -12,6 +12,7 @@
 #include <boost/random/uniform_real.hpp>
 #include <boost/random/mersenne_twister.hpp>
 #include <boost/math/interpolators/septic_hermite.hpp>
+#include <boost/math/special_functions/next.hpp>
 #ifdef BOOST_HAS_FLOAT128
 #include <boost/multiprecision/float128.hpp>
 using boost::multiprecision::float128;
@@ -74,6 +75,29 @@ void test_constant()
         CHECK_ULP_CLOSE(Real(0), csh_aos.double_prime(t), 24);
     }
 
+    // Now check the boundaries:
+    auto [tlo, thi] = csh.domain();
+    int samples = 5000;
+    int i = 0;
+    while (i++ < samples)
+    {
+        CHECK_ULP_CLOSE(Real(7), csh(tlo), 2);
+        CHECK_ULP_CLOSE(Real(7), csh(thi), 2);
+        CHECK_ULP_CLOSE(Real(7), csh_aos(tlo), 2);
+        CHECK_ULP_CLOSE(Real(7), csh_aos(thi), 2);
+        CHECK_ULP_CLOSE(Real(0), csh.prime(tlo), 2);
+        CHECK_ULP_CLOSE(Real(0), csh.prime(thi), 2);
+        CHECK_ULP_CLOSE(Real(0), csh_aos.prime(tlo), 2);
+        CHECK_ULP_CLOSE(Real(0), csh_aos.prime(thi), 2);
+        CHECK_ULP_CLOSE(Real(0), csh.double_prime(tlo), 2);
+        CHECK_ULP_CLOSE(Real(0), csh.double_prime(thi), 2);
+        CHECK_ULP_CLOSE(Real(0), csh_aos.double_prime(tlo), 2);
+        CHECK_ULP_CLOSE(Real(0), csh_aos.double_prime(thi), 2);
+
+        tlo = boost::math::nextafter(tlo, std::numeric_limits<Real>::max());
+        thi = boost::math::nextafter(thi, std::numeric_limits<Real>::lowest());
+    }
+
 }
 
 
@@ -151,6 +175,30 @@ void test_linear()
         CHECK_ULP_CLOSE(Real(1), csh_aos.prime(t), 15);
         CHECK_ULP_CLOSE(Real(0), csh_aos.double_prime(t), 15);
     }
+
+    // Now check the boundaries:
+    auto [tlo, thi] = csh.domain();
+    int samples = 5000;
+    int i = 0;
+    while (i++ < samples)
+    {
+        CHECK_ULP_CLOSE(Real(tlo), csh(tlo), 2);
+        CHECK_ULP_CLOSE(Real(thi), csh(thi), 2);
+        CHECK_ULP_CLOSE(Real(tlo), csh_aos(tlo), 2);
+        CHECK_ULP_CLOSE(Real(thi), csh_aos(thi), 2);
+        CHECK_ULP_CLOSE(Real(1), csh.prime(tlo), 2);
+        CHECK_ULP_CLOSE(Real(1), csh.prime(thi), 500);
+        CHECK_ULP_CLOSE(Real(1), csh_aos.prime(tlo), 2);
+        CHECK_ULP_CLOSE(Real(1), csh_aos.prime(thi), 500);
+        CHECK_MOLLIFIED_CLOSE(Real(0), csh.double_prime(tlo), std::numeric_limits<Real>::epsilon());
+        CHECK_MOLLIFIED_CLOSE(Real(0), csh.double_prime(thi), 400*std::numeric_limits<Real>::epsilon());
+        CHECK_MOLLIFIED_CLOSE(Real(0), csh_aos.double_prime(tlo), std::numeric_limits<Real>::epsilon());
+        CHECK_MOLLIFIED_CLOSE(Real(0), csh_aos.double_prime(thi), 400*std::numeric_limits<Real>::epsilon());
+
+        tlo = boost::math::nextafter(tlo, std::numeric_limits<Real>::max());
+        thi = boost::math::nextafter(thi, std::numeric_limits<Real>::lowest());
+    }
+
 }
 
 template<typename Real>

From 3a34827563a9c282246577db898d2607c87527bb Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Sun, 22 Mar 2020 13:10:37 -0400
Subject: [PATCH 099/104] Copyright statements. [CI SKIP]

---
 .../math/interpolators/detail/quintic_hermite_detail.hpp   | 6 ++++++
 .../math/interpolators/detail/septic_hermite_detail.hpp    | 6 ++++++
 include/boost/math/interpolators/quintic_hermite.hpp       | 7 +++++++
 include/boost/math/interpolators/septic_hermite.hpp        | 6 ++++++
 4 files changed, 25 insertions(+)

diff --git a/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp b/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
index 28f04daca..49ef7b0ec 100644
--- a/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/quintic_hermite_detail.hpp
@@ -1,3 +1,9 @@
+/*
+ * Copyright Nick Thompson, 2020
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
 #ifndef BOOST_MATH_INTERPOLATORS_DETAIL_QUINTIC_HERMITE_DETAIL_HPP
 #define BOOST_MATH_INTERPOLATORS_DETAIL_QUINTIC_HERMITE_DETAIL_HPP
 #include <algorithm>
diff --git a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
index 44843c6bb..ad69bf530 100644
--- a/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
+++ b/include/boost/math/interpolators/detail/septic_hermite_detail.hpp
@@ -1,3 +1,9 @@
+/*
+ * Copyright Nick Thompson, 2020
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
 #ifndef BOOST_MATH_INTERPOLATORS_DETAIL_SEPTIC_HERMITE_DETAIL_HPP
 #define BOOST_MATH_INTERPOLATORS_DETAIL_SEPTIC_HERMITE_DETAIL_HPP
 #include <algorithm>
diff --git a/include/boost/math/interpolators/quintic_hermite.hpp b/include/boost/math/interpolators/quintic_hermite.hpp
index 627f02d28..bc54d84c2 100644
--- a/include/boost/math/interpolators/quintic_hermite.hpp
+++ b/include/boost/math/interpolators/quintic_hermite.hpp
@@ -1,3 +1,10 @@
+/*
+ * Copyright Nick Thompson, 2020
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
 #ifndef BOOST_MATH_INTERPOLATORS_QUINTIC_HERMITE_HPP
 #define BOOST_MATH_INTERPOLATORS_QUINTIC_HERMITE_HPP
 #include <algorithm>
diff --git a/include/boost/math/interpolators/septic_hermite.hpp b/include/boost/math/interpolators/septic_hermite.hpp
index b5acbc764..67ed476a1 100644
--- a/include/boost/math/interpolators/septic_hermite.hpp
+++ b/include/boost/math/interpolators/septic_hermite.hpp
@@ -1,3 +1,9 @@
+/*
+ * Copyright Nick Thompson, 2020
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
 #ifndef BOOST_MATH_INTERPOLATORS_SEPTIC_HERMITE_HPP
 #define BOOST_MATH_INTERPOLATORS_SEPTIC_HERMITE_HPP
 #include <algorithm>

From 0f7cb981887b3ade399eef0ab764eb47e847f8af Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Sun, 22 Mar 2020 17:15:22 -0400
Subject: [PATCH 100/104] Tests for wavelet transform [CI SKIP]

---
 .../math/quadrature/wavelet_transforms.hpp    | 25 ++----
 test/wavelet_transform_test.cpp               | 82 +++++++++++++++++++
 2 files changed, 91 insertions(+), 16 deletions(-)
 create mode 100644 test/wavelet_transform_test.cpp

diff --git a/include/boost/math/quadrature/wavelet_transforms.hpp b/include/boost/math/quadrature/wavelet_transforms.hpp
index ef8a12c71..40987d30a 100644
--- a/include/boost/math/quadrature/wavelet_transforms.hpp
+++ b/include/boost/math/quadrature/wavelet_transforms.hpp
@@ -19,27 +19,20 @@ public:
     int max_refinements = 12) : f_{f}, psi_(grid_refinements), tol_{tol}, max_refinements_{max_refinements}
     {}
 
+    daubechies_wavelet_transform(F f, boost::math::daubechies_wavelet<Real, p> wavelet, Real tol = boost::math::tools::root_epsilon<Real>(),
+    int max_refinements = 12) : f_{f}, psi_{wavelet}, tol_{tol}, max_refinements_{max_refinements}
+    {}
+
     auto operator()(Real s, Real t)->decltype(std::declval<F>()(std::declval<Real>())) const
     {
         using std::sqrt;
         using std::abs;
         using boost::math::quadrature::trapezoidal;
-
-        // -p + 1 < (x-t)/s < p so if s > 0 then s(1-p) + t < x < sp + t
-        // if s < 0, then
-        // -sp + s >= x-t >= sp <=> sp + t < x < s(1-p) + t
-        Real a = -s*p + s + t;
-        Real b = s*p + t;
-        if (s < 0)
-        {
-            std::swap(a, b);
-        }
-        if (s == 0)
-        {
-            return std::numeric_limits<Real>::quiet_NaN();
-        }
-
-        return trapezoidal(f_, a, b, tol_, max_refinements_)/sqrt(abs(s));
+        auto g = [&] (Real u) {
+            return f_(s*u+t)*psi_(u);
+        };
+        auto [a,b] = psi_.support();
+        return sqrt(abs(s))*trapezoidal(g, a, b, tol_, max_refinements_);
     }
 
 private:
diff --git a/test/wavelet_transform_test.cpp b/test/wavelet_transform_test.cpp
new file mode 100644
index 000000000..24c555462
--- /dev/null
+++ b/test/wavelet_transform_test.cpp
@@ -0,0 +1,82 @@
+/*
+ * Copyright Nick Thompson, 2020
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+
+#include "math_unit_test.hpp"
+#include <numeric>
+#include <utility>
+#include <iomanip>
+#include <iostream>
+#include <cmath>
+#include <boost/core/demangle.hpp>
+#include <boost/hana/for_each.hpp>
+#include <boost/hana/ext/std/integer_sequence.hpp>
+#include <boost/math/quadrature/wavelet_transforms.hpp>
+#include <boost/math/tools/minima.hpp>
+#include <boost/math/quadrature/trapezoidal.hpp>
+
+#ifdef BOOST_HAS_FLOAT128
+#include <boost/multiprecision/float128.hpp>
+using boost::multiprecision::float128;
+#endif
+
+
+using boost::math::constants::pi;
+using boost::math::constants::root_two;
+using boost::math::quadrature::daubechies_wavelet_transform;
+
+template<typename Real, int p>
+void test_wavelet_transform()
+{
+    std::cout << "Testing wavelet transform of " << p << " vanishing moment Daubechies wavelet on type " << boost::core::demangle(typeid(Real).name()) << "\n";
+    auto psi = boost::math::daubechies_wavelet<Real, p>();
+
+    auto abs_psi = [&psi](Real x) {
+        return abs(psi(x));
+    };
+    auto [a, b] = psi.support();
+    auto psil1 = boost::math::quadrature::trapezoidal(abs_psi, a, b);
+    std::cout << "L1 norm of psi = " << psil1 << "\n";
+    auto [x_min, psi_min] = boost::math::tools::brent_find_minima(psi, a, b, std::numeric_limits<Real>::digits10);
+    std::cout << "Minimum value is " << psi_min <<  "  which occurs at x = " << x_min << "\n";
+    auto neg_psi = [&](Real x) { return -psi(x); };
+    auto [x_max, neg_psi_max] = boost::math::tools::brent_find_minima(neg_psi, a, b, std::numeric_limits<Real>::digits10);
+    std::cout << "Maximum value of psi is " << -neg_psi_max << "\n";
+    Real psi_sup_norm = std::max(abs(psi_min), std::abs(neg_psi_max));
+    std::cout << "psi sup norm = " << psi_sup_norm << "\n";
+    // An even function:
+    auto f = [](Real x) {
+        return std::exp(-abs(x))*std::cos(10*x);
+    };
+    Real fmax = 1;
+
+
+    auto Wf = daubechies_wavelet_transform(f, psi);
+    for (double s = 0; s < 10; s += 0.01)
+    {
+        Real w1 = Wf(s, 0.0);
+        Real w2 = Wf(-s, 0.0);
+        // Since f is an even function, we get w1 = w2:
+        CHECK_ULP_CLOSE(w1, w2, 12);
+        // Integral inequality:
+        Real r1 = sqrt(abs(s))*fmax*psil1;
+        //std::cout << "|w| = " << abs(w1) << ", ||f||_infty||psi||_1 = " << r1 << "\n";
+        if(abs(w1) > r1)
+        {
+            std::cerr << " Integral inequality | int fg| <= ||f||_infty ||g||_infty is violated.\n";
+        }
+    }
+    
+}
+
+int main()
+{
+    test_wavelet_transform<double, 8>();
+    /*boost::hana::for_each(std::make_index_sequence<17>(), [&](auto i) {
+        test_wavelet_transform<double, i+3>();
+    });*/
+    return boost::math::test::report_errors();
+}

From 2c85c9898253bc050d03f3a6ffc54c3be144b993 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Sun, 22 Mar 2020 20:15:10 -0400
Subject: [PATCH 101/104] Document wavelet transform. Submit (mildly) failing
 unit test for transforms. [CI SKIP]

---
 ...aubechies_wavelet_transform_definition.svg |  2 +
 doc/graphs/wavelet_transform_definition.svg   |  2 +
 doc/math.qbk                                  |  1 +
 doc/quadrature/wavelet_transforms.qbk         | 56 +++++++++++++
 .../math/quadrature/wavelet_transforms.hpp    |  4 +-
 test/wavelet_transform_test.cpp               | 80 ++++++++++++++-----
 6 files changed, 124 insertions(+), 21 deletions(-)
 create mode 100644 doc/graphs/daubechies_wavelet_transform_definition.svg
 create mode 100644 doc/graphs/wavelet_transform_definition.svg
 create mode 100644 doc/quadrature/wavelet_transforms.qbk

diff --git a/doc/graphs/daubechies_wavelet_transform_definition.svg b/doc/graphs/daubechies_wavelet_transform_definition.svg
new file mode 100644
index 000000000..c4f787e37
--- /dev/null
+++ b/doc/graphs/daubechies_wavelet_transform_definition.svg
@@ -0,0 +1,2 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no" ?>
+<svg xmlns="http://www.w3.org/2000/svg" width="328.360px" height="44.056px" viewBox="0 -1400.6 18141.8 2434.1" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-49-TEX-I-57" d="M436 683Q450 683 486 682T553 680Q604 680 638 681T677 682Q695 682 695 674Q695 670 692 659Q687 641 683 639T661 637Q636 636 621 632T600 624T597 615Q597 603 613 377T629 138L631 141Q633 144 637 151T649 170T666 200T690 241T720 295T759 362Q863 546 877 572T892 604Q892 619 873 628T831 637Q817 637 817 647Q817 650 819 660Q823 676 825 679T839 682Q842 682 856 682T895 682T949 681Q1015 681 1034 683Q1048 683 1048 672Q1048 666 1045 655T1038 640T1028 637Q1006 637 988 631T958 617T939 600T927 584L923 578L754 282Q586 -14 585 -15Q579 -22 561 -22Q546 -22 542 -17Q539 -14 523 229T506 480L494 462Q472 425 366 239Q222 -13 220 -15T215 -19Q210 -22 197 -22Q178 -22 176 -15Q176 -12 154 304T131 622Q129 631 121 633T82 637H58Q51 644 51 648Q52 671 64 683H76Q118 680 176 680Q301 680 313 683H323Q329 677 329 674T327 656Q322 641 318 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diff --git a/doc/graphs/wavelet_transform_definition.svg b/doc/graphs/wavelet_transform_definition.svg
new file mode 100644
index 000000000..67a8a73cf
--- /dev/null
+++ b/doc/graphs/wavelet_transform_definition.svg
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diff --git a/doc/math.qbk b/doc/math.qbk
index e7cde1c5c..4358b71da 100644
--- a/doc/math.qbk
+++ b/doc/math.qbk
@@ -727,6 +727,7 @@ and as a CD ISBN 0-9504833-2-X  978-0-9504833-2-0, Classification 519.2-dc22.
 [include quadrature/double_exponential.qbk]
 [include quadrature/ooura_fourier_integrals.qbk]
 [include quadrature/naive_monte_carlo.qbk]
+[include quadrature/wavelet_transforms.qbk]
 [include differentiation/numerical_differentiation.qbk]
 [include differentiation/autodiff.qbk]
 [include differentiation/lanczos_smoothing.qbk]
diff --git a/doc/quadrature/wavelet_transforms.qbk b/doc/quadrature/wavelet_transforms.qbk
new file mode 100644
index 000000000..563a7379e
--- /dev/null
+++ b/doc/quadrature/wavelet_transforms.qbk
@@ -0,0 +1,56 @@
+[/
+Copyright (c) 2019 Nick Thompson
+Copyright (c) 2019 Paul A. Bristow
+Use, modification and distribution are subject to the
+Boost Software License, Version 1.0. (See accompanying file
+LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+]
+
+[section:wavelet_transforms Wavelet Transforms]
+
+[heading Synopsis]
+
+```
+    #include <boost/math/quadrature/wavelet_transforms.hpp>
+    
+    namespace boost::math::quadrature {
+
+    template<class F, typename Real, int p>
+    class daubechies_wavelet_transform
+    {
+    public:
+        daubechies_wavelet_transform(F f, int grid_refinements = -1, Real tol = 100*std::numeric_limits<Real>::epsilon(),
+        int max_refinements = 12) {}
+
+        daubechies_wavelet_transform(F f, boost::math::daubechies_wavelet<Real, p> wavelet, Real tol = 100*std::numeric_limits<Real>::epsilon(),
+        int max_refinements = 12);
+
+        auto operator()(Real s, Real t)->decltype(std::declval<F>()(std::declval<Real>())) const;
+
+    };
+
+    } 
+```
+
+Wavelet transforms compute
+
+[$../graphs/wavelet_transform_definition.svg]
+
+For compactly supported Daubechies wavelets, the bounds can always be taken as finite, and we have 
+
+[$../graphs/daubechies_wavelet_transform_definition.svg]
+
+which gives definies the /s=0/ case.
+
+A basic usage is 
+
+    auto psi = daubechies_wavelet<double, 8>();
+    auto f = [](double x) {
+        return sin(2/x);
+    };
+    auto Wf = daubechies_wavelet_transform(f, psi);
+
+    auto z = Wf(0.8, 7.2);
+
+[endsect] [/section:wavelet_transforms]
+
diff --git a/include/boost/math/quadrature/wavelet_transforms.hpp b/include/boost/math/quadrature/wavelet_transforms.hpp
index 40987d30a..927d12885 100644
--- a/include/boost/math/quadrature/wavelet_transforms.hpp
+++ b/include/boost/math/quadrature/wavelet_transforms.hpp
@@ -15,11 +15,11 @@ template<class F, typename Real, int p>
 class daubechies_wavelet_transform
 {
 public:
-    daubechies_wavelet_transform(F f, int grid_refinements = -1, Real tol = boost::math::tools::root_epsilon<Real>(),
+    daubechies_wavelet_transform(F f, int grid_refinements = -1, Real tol = 100*std::numeric_limits<Real>::epsilon(),
     int max_refinements = 12) : f_{f}, psi_(grid_refinements), tol_{tol}, max_refinements_{max_refinements}
     {}
 
-    daubechies_wavelet_transform(F f, boost::math::daubechies_wavelet<Real, p> wavelet, Real tol = boost::math::tools::root_epsilon<Real>(),
+    daubechies_wavelet_transform(F f, boost::math::daubechies_wavelet<Real, p> wavelet, Real tol = 100*std::numeric_limits<Real>::epsilon(),
     int max_refinements = 12) : f_{f}, psi_{wavelet}, tol_{tol}, max_refinements_{max_refinements}
     {}
 
diff --git a/test/wavelet_transform_test.cpp b/test/wavelet_transform_test.cpp
index 24c555462..25ed881dc 100644
--- a/test/wavelet_transform_test.cpp
+++ b/test/wavelet_transform_test.cpp
@@ -27,6 +27,7 @@ using boost::multiprecision::float128;
 using boost::math::constants::pi;
 using boost::math::constants::root_two;
 using boost::math::quadrature::daubechies_wavelet_transform;
+using boost::math::quadrature::trapezoidal;
 
 template<typename Real, int p>
 void test_wavelet_transform()
@@ -38,21 +39,26 @@ void test_wavelet_transform()
         return abs(psi(x));
     };
     auto [a, b] = psi.support();
-    auto psil1 = boost::math::quadrature::trapezoidal(abs_psi, a, b);
-    std::cout << "L1 norm of psi = " << psil1 << "\n";
-    auto [x_min, psi_min] = boost::math::tools::brent_find_minima(psi, a, b, std::numeric_limits<Real>::digits10);
-    std::cout << "Minimum value is " << psi_min <<  "  which occurs at x = " << x_min << "\n";
-    auto neg_psi = [&](Real x) { return -psi(x); };
-    auto [x_max, neg_psi_max] = boost::math::tools::brent_find_minima(neg_psi, a, b, std::numeric_limits<Real>::digits10);
-    std::cout << "Maximum value of psi is " << -neg_psi_max << "\n";
-    Real psi_sup_norm = std::max(abs(psi_min), std::abs(neg_psi_max));
+    auto psil1 = trapezoidal(abs_psi, a, b);
+    Real psi_sup_norm = 0;
+    for (double x = a; x < b; x += 0.0001)
+    {
+        Real y = psi(x);
+        if (std::abs(y) > psi_sup_norm)
+        {
+            psi_sup_norm = std::abs(y);
+        }
+    }
     std::cout << "psi sup norm = " << psi_sup_norm << "\n";
     // An even function:
     auto f = [](Real x) {
-        return std::exp(-abs(x))*std::cos(10*x);
+        return std::exp(-abs(x));
     };
     Real fmax = 1;
-
+    Real fl2 = 1;
+    Real fl1 = 2;
+    std::cout << "||f||_1 = " << fl1 << "\n";
+    std::cout << "||f||_2 = " << fl2 << "\n";
 
     auto Wf = daubechies_wavelet_transform(f, psi);
     for (double s = 0; s < 10; s += 0.01)
@@ -61,22 +67,58 @@ void test_wavelet_transform()
         Real w2 = Wf(-s, 0.0);
         // Since f is an even function, we get w1 = w2:
         CHECK_ULP_CLOSE(w1, w2, 12);
-        // Integral inequality:
-        Real r1 = sqrt(abs(s))*fmax*psil1;
-        //std::cout << "|w| = " << abs(w1) << ", ||f||_infty||psi||_1 = " << r1 << "\n";
-        if(abs(w1) > r1)
+    }
+
+    // The wavelet transform with respect to Daubechies wavelets 
+    for (double s = -10; s < 10; s += 0.1)
+    {
+        for (double t = -10; t < 10; t+= 0.1)
         {
-            std::cerr << " Integral inequality | int fg| <= ||f||_infty ||g||_infty is violated.\n";
+            Real w = Wf(s, t);
+            // Integral inequality:
+            Real r1 = sqrt(abs(s))*fmax*psil1;
+            if(abs(w) > r1)
+            {
+                std::cerr << " Integral inequality | int fg| <= ||f||_infty ||psi||_1 is violated.\n";
+            }
+            if (s != 0)
+            {
+                Real r2 = fl1*psi_sup_norm/sqrt(abs(s));
+                if(abs(w) > r2)
+                {
+                    std::cerr << " Integral inequality | int fg| <= ||f||_1 ||psi||_infty/sqrt(|s|) is violated.\n";
+                    std::cerr << " Violation: " << abs(w) << " !<= " << r2 << "\n";
+                }
+                Real r3 = fmax*psil1/sqrt(abs(s));
+                if(abs(w) > r3)
+                {
+                    std::cerr << " Integral inequality | int fg| <= ||f||_infty ||psi||_1/sqrt(|s|) is violated.\n";
+                    std::cerr << " Computed = " << abs(w) << ", expected " << r3 << "\n";
+                }
+            }
+            if (abs(w) > fl2)
+            {
+                std::cerr << "  Integral inequality |f psi_s,t| <= ||f||_2 ||psi||2 violated.\n";
+            }
+            Real r4 = sqrt(abs(s))*fl1*psi_sup_norm;
+            if (abs(w) > r4)
+            {
+                std::cerr << "  Integral inequality |W[f](s,t)| <= sqrt(|s|)||f||_1 ||psi||_infty is violated.\n";
+            }
+            Real r5 = sqrt(abs(s))*fmax*psil1;
+            if (abs(w) > r5)
+            {
+                std::cerr << "  Integral inequality |W[f](s,t)| <= sqrt(|s|)||f||_infty ||psi||_1 is violated.\n";
+            }
+
         }
     }
-    
 }
 
 int main()
 {
-    test_wavelet_transform<double, 8>();
-    /*boost::hana::for_each(std::make_index_sequence<17>(), [&](auto i) {
+    boost::hana::for_each(std::make_index_sequence<17>(), [&](auto i) {
         test_wavelet_transform<double, i+3>();
-    });*/
+    });
     return boost::math::test::report_errors();
 }

From 9ba1ce6f009a14e22296cffef97540b5049ba419 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Mon, 23 Mar 2020 07:39:57 -0400
Subject: [PATCH 102/104] Improve docs and loosen tolerances for Windows.

---
 doc/graphs/scalogram_sin1t_light.png  | Bin 0 -> 1070185 bytes
 doc/quadrature/wavelet_transforms.qbk |  18 ++++++++++++------
 test/septic_hermite_test.cpp          |  12 ++++++------
 3 files changed, 18 insertions(+), 12 deletions(-)
 create mode 100644 doc/graphs/scalogram_sin1t_light.png

diff --git a/doc/graphs/scalogram_sin1t_light.png b/doc/graphs/scalogram_sin1t_light.png
new file mode 100644
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HcmV?d00001

diff --git a/doc/quadrature/wavelet_transforms.qbk b/doc/quadrature/wavelet_transforms.qbk
index 563a7379e..53bc7c57b 100644
--- a/doc/quadrature/wavelet_transforms.qbk
+++ b/doc/quadrature/wavelet_transforms.qbk
@@ -28,11 +28,10 @@ LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
         auto operator()(Real s, Real t)->decltype(std::declval<F>()(std::declval<Real>())) const;
 
     };
-
     } 
 ```
 
-Wavelet transforms compute
+The wavelet transform of a function /f/ with respect to a wavelet \u03C8 is
 
 [$../graphs/wavelet_transform_definition.svg]
 
@@ -40,17 +39,24 @@ For compactly supported Daubechies wavelets, the bounds can always be taken as f
 
 [$../graphs/daubechies_wavelet_transform_definition.svg]
 
-which gives definies the /s=0/ case.
+which also defines the /s/=0 case.
+
+The code provided by Boost merely forwards a lambda to the trapezoidal quadrature routine, which converges quickly due to the Euler-Maclaurin summation formula.
+However, the convergence is not as rapid as for infinitely differentiable functions, so the default tolerances are modified.
 
 A basic usage is 
 
     auto psi = daubechies_wavelet<double, 8>();
     auto f = [](double x) {
-        return sin(2/x);
+        return sin(1/x);
     };
     auto Wf = daubechies_wavelet_transform(f, psi);
 
-    auto z = Wf(0.8, 7.2);
+    double w = Wf(0.8, 7.2);
+
+An image from this function is shown below.
+
+[$../graphs/scalogram_sin1t_light.png]
+
 
 [endsect] [/section:wavelet_transforms]
-
diff --git a/test/septic_hermite_test.cpp b/test/septic_hermite_test.cpp
index 944a3d0c4..188ac56de 100644
--- a/test/septic_hermite_test.cpp
+++ b/test/septic_hermite_test.cpp
@@ -183,17 +183,17 @@ void test_linear()
     while (i++ < samples)
     {
         CHECK_ULP_CLOSE(Real(tlo), csh(tlo), 2);
-        CHECK_ULP_CLOSE(Real(thi), csh(thi), 2);
+        CHECK_ULP_CLOSE(Real(thi), csh(thi), 4);
         CHECK_ULP_CLOSE(Real(tlo), csh_aos(tlo), 2);
-        CHECK_ULP_CLOSE(Real(thi), csh_aos(thi), 2);
+        CHECK_ULP_CLOSE(Real(thi), csh_aos(thi), 4);
         CHECK_ULP_CLOSE(Real(1), csh.prime(tlo), 2);
-        CHECK_ULP_CLOSE(Real(1), csh.prime(thi), 500);
+        CHECK_ULP_CLOSE(Real(1), csh.prime(thi), 512);
         CHECK_ULP_CLOSE(Real(1), csh_aos.prime(tlo), 2);
-        CHECK_ULP_CLOSE(Real(1), csh_aos.prime(thi), 500);
+        CHECK_ULP_CLOSE(Real(1), csh_aos.prime(thi), 512);
         CHECK_MOLLIFIED_CLOSE(Real(0), csh.double_prime(tlo), std::numeric_limits<Real>::epsilon());
-        CHECK_MOLLIFIED_CLOSE(Real(0), csh.double_prime(thi), 400*std::numeric_limits<Real>::epsilon());
+        CHECK_MOLLIFIED_CLOSE(Real(0), csh.double_prime(thi), 800*std::numeric_limits<Real>::epsilon());
         CHECK_MOLLIFIED_CLOSE(Real(0), csh_aos.double_prime(tlo), std::numeric_limits<Real>::epsilon());
-        CHECK_MOLLIFIED_CLOSE(Real(0), csh_aos.double_prime(thi), 400*std::numeric_limits<Real>::epsilon());
+        CHECK_MOLLIFIED_CLOSE(Real(0), csh_aos.double_prime(thi), 800*std::numeric_limits<Real>::epsilon());
 
         tlo = boost::math::nextafter(tlo, std::numeric_limits<Real>::max());
         thi = boost::math::nextafter(thi, std::numeric_limits<Real>::lowest());

From 8b3393091a3a0ac46f4c1ada373cc2dddc2397b0 Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Mon, 23 Mar 2020 18:23:32 +0000
Subject: [PATCH 103/104] Daubechies: More code simplification.

---
 .../special_functions/daubechies_scaling.hpp  | 294 ++++-------
 .../special_functions/daubechies_wavelet.hpp  | 481 +++++++-----------
 test/daubechies_scaling_test.cpp              |   4 +-
 test/daubechies_wavelet_test.cpp              |   1 +
 4 files changed, 303 insertions(+), 477 deletions(-)

diff --git a/include/boost/math/special_functions/daubechies_scaling.hpp b/include/boost/math/special_functions/daubechies_scaling.hpp
index 4144469df..e9cf67872 100644
--- a/include/boost/math/special_functions/daubechies_scaling.hpp
+++ b/include/boost/math/special_functions/daubechies_scaling.hpp
@@ -298,147 +298,138 @@ struct daubechies_eval_type<double>
    }
 };
 
+struct null_interpolator
+{
+   template <class T>
+   T operator()(const T&)
+   {
+      return 1;
+   }
+};
+
 } // namespace detail
 
 template<class Real, int p>
 class daubechies_scaling {
+   //
+   // Some type manipulation so we know the type of the interpolator, and the vector type it requires:
+   //
+   typedef std::vector<std::array<Real, p < 6 ? 2 : p < 10 ? 3 : 4>> vector_type;
+   //
+   // List our interpolators:
+   //
+   typedef std::tuple<
+      detail::null_interpolator, detail::matched_holder_aos<vector_type>, detail::linear_interpolation_aos<vector_type>, 
+      interpolators::detail::cardinal_cubic_hermite_detail_aos<vector_type>, interpolators::detail::cardinal_quintic_hermite_detail_aos<vector_type>,
+      interpolators::detail::cardinal_septic_hermite_detail_aos<vector_type> > interpolator_list;
+   //
+   // Select the one we need:
+   //
+   typedef std::tuple_element_t<
+      p == 1 ? 0 :
+      p == 2 ? 1 :
+      p == 3 ? 2 :
+      p <= 5 ? 3 :
+      p <= 9 ? 4 : 5, interpolator_list> interpolator_type;
+
 public:
-    daubechies_scaling(int grid_refinements = -1)
-    {
-        static_assert(p < 20, "Daubechies scaling functions are only implemented for p < 20.");
-        static_assert(p > 0, "Daubechies scaling functions must have at least 1 vanishing moment.");
-        if constexpr (p == 1)
-        {
-            return;
-        }
-        else {
-        if (grid_refinements < 0)
-        {
+   daubechies_scaling(int grid_refinements = -1)
+   {
+      static_assert(p < 20, "Daubechies scaling functions are only implemented for p < 20.");
+      static_assert(p > 0, "Daubechies scaling functions must have at least 1 vanishing moment.");
+      if constexpr (p == 1)
+      {
+         return;
+      }
+      else {
+         if (grid_refinements < 0)
+         {
             if (std::is_same_v<Real, float>)
             {
-                if (grid_refinements == -2)
-                {
-                    // Control absolute error:
-                    //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
-                    std::array<int, 20> r{-1, -1, 18, 19, 16, 11,  8,  7,  7,  7,  5,  5,  4,  4,  4,  4,  3,  3,  3,  3};
-                    grid_refinements = r[p];
-                }
-                else
-                {
-                    // Control relative error:
-                    //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
-                    std::array<int, 20> r{-1, -1, 21, 21, 21, 17, 16, 15, 14, 13, 12, 11, 11, 11, 11, 11, 11, 11, 11, 11};
-                    grid_refinements = r[p];
-                }
+               if (grid_refinements == -2)
+               {
+                  // Control absolute error:
+                  //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
+                  std::array<int, 20> r{ -1, -1, 18, 19, 16, 11,  8,  7,  7,  7,  5,  5,  4,  4,  4,  4,  3,  3,  3,  3 };
+                  grid_refinements = r[p];
+               }
+               else
+               {
+                  // Control relative error:
+                  //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
+                  std::array<int, 20> r{ -1, -1, 21, 21, 21, 17, 16, 15, 14, 13, 12, 11, 11, 11, 11, 11, 11, 11, 11, 11 };
+                  grid_refinements = r[p];
+               }
             }
             else if (std::is_same_v<Real, double>)
             {
-                //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
-                std::array<int, 20> r{-1, -1, 21, 21, 21, 21, 21, 21, 21, 21, 20, 20, 19, 19, 18, 18, 18, 18, 18, 18};
-                grid_refinements = r[p];
+               //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
+               std::array<int, 20> r{ -1, -1, 21, 21, 21, 21, 21, 21, 21, 21, 20, 20, 19, 19, 18, 18, 18, 18, 18, 18 };
+               grid_refinements = r[p];
             }
             else
             {
-                grid_refinements = 21;
+               grid_refinements = 21;
             }
-        }
+         }
 
-        // Compute the refined grid:
-        // In fact for float precision I know the grid must be computed in double precision and then cast back down, or else parts of the support are systematically inaccurate.
-        std::future<std::vector<Real>> t0 = std::async(std::launch::async, [&grid_refinements]() {
+         // Compute the refined grid:
+         // In fact for float precision I know the grid must be computed in double precision and then cast back down, or else parts of the support are systematically inaccurate.
+         std::future<std::vector<Real>> t0 = std::async(std::launch::async, [&grid_refinements]() {
             // Computing in higher precision and downcasting is essential for 1ULP evaluation in float precision:
             auto v = daubechies_scaling_dyadic_grid<typename detail::daubechies_eval_type<Real>::type, p, 0>(grid_refinements);
             return detail::daubechies_eval_type<Real>::vector_cast(v);
-        });
-        // Compute the derivative of the refined grid:
-        std::future<std::vector<Real>> t1 = std::async(std::launch::async, [&grid_refinements]() {
-           auto v = daubechies_scaling_dyadic_grid<typename detail::daubechies_eval_type<Real>::type, p, 1>(grid_refinements);
-           return detail::daubechies_eval_type<Real>::vector_cast(v);
-        });
+            });
+         // Compute the derivative of the refined grid:
+         std::future<std::vector<Real>> t1 = std::async(std::launch::async, [&grid_refinements]() {
+            auto v = daubechies_scaling_dyadic_grid<typename detail::daubechies_eval_type<Real>::type, p, 1>(grid_refinements);
+            return detail::daubechies_eval_type<Real>::vector_cast(v);
+            });
 
-        // if necessary, compute the second and third derivative:
-        std::vector<Real> d2ydx2;
-        std::vector<Real> d3ydx3;
-        if constexpr (p >= 6) {
+         // if necessary, compute the second and third derivative:
+         std::vector<Real> d2ydx2;
+         std::vector<Real> d3ydx3;
+         if constexpr (p >= 6) {
             std::future<std::vector<Real>> t3 = std::async(std::launch::async, [&grid_refinements]() {
                auto v = daubechies_scaling_dyadic_grid<typename detail::daubechies_eval_type<Real>::type, p, 2>(grid_refinements);
                return detail::daubechies_eval_type<Real>::vector_cast(v);
-             });
+               });
 
             if constexpr (p >= 10) {
-                std::future<std::vector<Real>> t4 = std::async(std::launch::async, [&grid_refinements]() {
-                   auto v = daubechies_scaling_dyadic_grid<typename detail::daubechies_eval_type<Real>::type, p, 3>(grid_refinements);
-                   return detail::daubechies_eval_type<Real>::vector_cast(v);
-                });
-                d3ydx3 = t4.get();
+               std::future<std::vector<Real>> t4 = std::async(std::launch::async, [&grid_refinements]() {
+                  auto v = daubechies_scaling_dyadic_grid<typename detail::daubechies_eval_type<Real>::type, p, 3>(grid_refinements);
+                  return detail::daubechies_eval_type<Real>::vector_cast(v);
+                  });
+               d3ydx3 = t4.get();
             }
             d2ydx2 = t3.get();
-        }
+         }
 
 
-        auto y = t0.get();
-        auto dydx = t1.get();
+         auto y = t0.get();
+         auto dydx = t1.get();
 
-        if constexpr (p==2)
-        {
-            std::vector<std::array<Real, 2>> data(y.size());
+         if constexpr (p >= 2)
+         {
+            vector_type data(y.size());
             for (size_t i = 0; i < y.size(); ++i)
             {
-                data[i][0] = y[i];
-                data[i][1] = dydx[i];
+               data[i][0] = y[i];
+               data[i][1] = dydx[i];
+               if constexpr (p >= 6)
+                  data[i][2] = d2ydx2[i];
+               if constexpr (p >= 10)
+                  data[i][3] = d3ydx3[i];
             }
-            m_mh = std::make_shared<detail::matched_holder_aos<std::vector<std::array<Real,2>>>>(std::move(data), grid_refinements, Real(0));
-        }
-        if constexpr (p==3)
-        {
-            std::vector<std::array<Real, 2>> data(y.size());
-            for (size_t i = 0; i < y.size(); ++i)
-            {
-                data[i][0] = y[i];
-                data[i][1] = dydx[i];
-            }
-            m_lin = std::make_shared<detail::linear_interpolation_aos<std::vector<std::array<Real, 2>>>>(std::move(data), grid_refinements, Real(0));
-        }
-        if constexpr (p == 4 || p == 5)
-        {
-            Real dx = Real(1)/(1 << grid_refinements);
-            std::vector<std::array<Real, 2>> data(y.size());
-            for (size_t i = 0; i < y.size(); ++i)
-            {
-                data[i][0] = y[i];
-                data[i][1] = dydx[i];
-            }
-            m_cbh = std::make_shared<interpolators::detail::cardinal_cubic_hermite_detail_aos<std::vector<std::array<Real,2>>>>(std::move(data), Real(0), dx);
-        }
-        if constexpr (p >= 6 && p <= 9)
-        {
-            Real dx = Real(1)/(1 << grid_refinements);
-            std::vector<std::array<Real, 3>> data(y.size());
-            for (size_t i = 0; i < y.size(); ++i)
-            {
-                data[i][0] = y[i];
-                data[i][1] = dydx[i];
-                data[i][2] = d2ydx2[i];
-            }
-
-            m_qh = std::make_shared<interpolators::detail::cardinal_quintic_hermite_detail_aos<std::vector<std::array<Real,3>>>>(std::move(data), Real(0), dx);
-        }
-        if constexpr (p >= 10)
-        {
-            Real dx = Real(1)/(1 << grid_refinements);
-            std::vector<std::array<Real, 4>> data(y.size());
-            for (size_t i = 0; i < y.size(); ++i)
-            {
-                data[i][0] = y[i];
-                data[i][1] = dydx[i];
-                data[i][2] = d2ydx2[i];
-                data[i][3] = d3ydx3[i];
-            }
-            m_sh = std::make_shared<interpolators::detail::cardinal_septic_hermite_detail_aos<std::vector<std::array<Real, 4>>>>(std::move(data), Real(0), dx);
-        }
-        }
-     }
-
+            if constexpr (p <= 3)
+               m_interpolator = std::make_shared<interpolator_type>(std::move(data), grid_refinements, Real(0));
+            else
+               m_interpolator = std::make_shared<interpolator_type>(std::move(data), Real(0), Real(1) / (1 << grid_refinements));
+         }
+         else
+            m_interpolator = std::make_shared<detail::null_interpolator>();
+      }
+   }
 
     inline Real operator()(Real x) const
     {
@@ -446,30 +437,7 @@ public:
         {
             return 0;
         }
-        if constexpr (p==1)
-        {
-            return Real(1);
-        }
-        if constexpr (p==2)
-        {
-            return m_mh->operator()(x);
-        }
-        if constexpr (p==3)
-        {
-            return m_lin->operator()(x);
-        }
-        if constexpr (p==4 || p ==5)
-        {
-            return m_cbh->unchecked_evaluation(x);
-        }
-        if constexpr (p >= 6 && p <= 9)
-        {
-            return m_qh->unchecked_evaluation(x);
-        }
-        if constexpr (p >= 10)
-        {
-            return m_sh->unchecked_evaluation(x);
-        }
+        return (*m_interpolator)(x);
     }
 
     inline Real prime(Real x) const
@@ -479,22 +447,7 @@ public:
         {
             return 0;
         }
-        if constexpr (p == 3)
-        {
-            return m_lin->prime(x);
-        }
-        if constexpr (p == 4 || p == 5)
-        {
-            return m_cbh->unchecked_prime(x);
-        }
-        if constexpr (p >= 6 && p <= 9)
-        {
-            return m_qh->unchecked_prime(x);
-        }
-        if constexpr (p >= 10)
-        {
-            return m_sh->unchecked_prime(x);
-        }
+        return m_interpolator->prime(x);
     }
 
     inline Real double_prime(Real x) const
@@ -504,14 +457,7 @@ public:
         {
             return Real(0);
         }
-        if constexpr (p >= 6 && p <= 9)
-        {
-            return m_qh->unchecked_double_prime(x);
-        }
-        if constexpr (p >= 10)
-        {
-            return m_sh->unchecked_double_prime(x);
-        }
+        return m_interpolator->double_prime(x);
     }
 
     std::pair<Real, Real> support() const
@@ -521,41 +467,11 @@ public:
 
     int64_t bytes() const
     {
-        if constexpr (p==2)
-        {
-            return m_mh->bytes() + sizeof(m_mh);
-        }
-        if constexpr (p == 3)
-        {
-            return m_lin->bytes() + sizeof(m_lin);
-        }
-        if constexpr (p == 4 || p == 5)
-        {
-            return m_cbh->bytes() + sizeof(m_cbh);
-        }
-        if constexpr (p >= 6 && p <= 9)
-        {
-            return m_qh->bytes() + sizeof(m_qh);
-        }
-        if constexpr (p >= 10)
-        {
-            return m_sh->bytes() + sizeof(m_sh);
-        }
-
-        return -1;
+       return m_interpolator->bytes() + sizeof(m_interpolator);
     }
 
 private:
-    // Need this for p = 2:
-    std::shared_ptr<detail::matched_holder_aos<std::vector<std::array<Real,2>>>> m_mh;
-    // Need this for p = 3:
-    std::shared_ptr<detail::linear_interpolation_aos<std::vector<std::array<Real, 2>>>> m_lin;
-    // Need this for p = 4,5:
-    std::shared_ptr<interpolators::detail::cardinal_cubic_hermite_detail_aos<std::vector<std::array<Real, 2>>>> m_cbh;
-    // Need this for p = 6,7,8,9:
-    std::shared_ptr<interpolators::detail::cardinal_quintic_hermite_detail_aos<std::vector<std::array<Real, 3>>>> m_qh;
-    // Need this for p >= 10:
-    std::shared_ptr<interpolators::detail::cardinal_septic_hermite_detail_aos<std::vector<std::array<Real, 4>>>> m_sh;
+   std::shared_ptr<interpolator_type> m_interpolator;
 };
 
 }
diff --git a/include/boost/math/special_functions/daubechies_wavelet.hpp b/include/boost/math/special_functions/daubechies_wavelet.hpp
index cbb31b3d9..6c7af4659 100644
--- a/include/boost/math/special_functions/daubechies_wavelet.hpp
+++ b/include/boost/math/special_functions/daubechies_wavelet.hpp
@@ -23,324 +23,231 @@
 
 namespace boost::math {
 
-template<class Real, int p, int order>
-std::vector<Real> daubechies_wavelet_dyadic_grid(int64_t j_max)
-{
-    if (j_max == 0)
-    {
-        throw std::domain_error("The wavelet dyadic grid is refined from the scaling integer grid, so its minimum amount of data is half integer widths.");
-    }
-    auto phijk = daubechies_scaling_dyadic_grid<Real, p, order>(j_max-1);
-    //psi_j[l] = psi(-p+1 + l/2^j) = \sum_{k=0}^{2p-1} (-1)^k c_k \phi(1-2p+k + l/2^{j-1})
-    //For derivatives just map c_k -> 2^order c_k.
-    auto d = boost::math::filters::daubechies_scaling_filter<Real, p>();
-    Real scale = boost::math::constants::root_two<Real>()*(1 << order);
-    for (size_t i = 0; i < d.size(); ++i)
-    {
-        d[i] *= scale;
-        if (!(i & 1))
-        {
+   template<class Real, int p, int order>
+   std::vector<Real> daubechies_wavelet_dyadic_grid(int64_t j_max)
+   {
+      if (j_max == 0)
+      {
+         throw std::domain_error("The wavelet dyadic grid is refined from the scaling integer grid, so its minimum amount of data is half integer widths.");
+      }
+      auto phijk = daubechies_scaling_dyadic_grid<Real, p, order>(j_max - 1);
+      //psi_j[l] = psi(-p+1 + l/2^j) = \sum_{k=0}^{2p-1} (-1)^k c_k \phi(1-2p+k + l/2^{j-1})
+      //For derivatives just map c_k -> 2^order c_k.
+      auto d = boost::math::filters::daubechies_scaling_filter<Real, p>();
+      Real scale = boost::math::constants::root_two<Real>() * (1 << order);
+      for (size_t i = 0; i < d.size(); ++i)
+      {
+         d[i] *= scale;
+         if (!(i & 1))
+         {
             d[i] = -d[i];
-        }
-    }
+         }
+      }
 
-    std::vector<Real> v(2*p + (2*p-1)*((int64_t(1) <<j_max) -1), std::numeric_limits<Real>::quiet_NaN());
-    v[0] = 0;
-    v[v.size()-1] = 0;
+      std::vector<Real> v(2 * p + (2 * p - 1) * ((int64_t(1) << j_max) - 1), std::numeric_limits<Real>::quiet_NaN());
+      v[0] = 0;
+      v[v.size() - 1] = 0;
 
-    for (int64_t l = 1; l < static_cast<int64_t>(v.size() - 1); ++l)
-    {
-        Real term = 0;
-        for (int64_t k = 0; k < static_cast<int64_t>(d.size()); ++k)
-        {
-            int64_t idx = (int64_t(1) << (j_max-1))*(1 - 2*p + k) + l;
+      for (int64_t l = 1; l < static_cast<int64_t>(v.size() - 1); ++l)
+      {
+         Real term = 0;
+         for (int64_t k = 0; k < static_cast<int64_t>(d.size()); ++k)
+         {
+            int64_t idx = (int64_t(1) << (j_max - 1)) * (1 - 2 * p + k) + l;
             if (idx < 0 || idx >= static_cast<int64_t>(phijk.size()))
             {
-                continue;
+               continue;
             }
-            term += d[k]*phijk[idx];
-        }
-        v[l] = term;
-    }
+            term += d[k] * phijk[idx];
+         }
+         v[l] = term;
+      }
 
-    return v;
-}
+      return v;
+   }
 
 
-template<class Real, int p>
-class daubechies_wavelet {
-public:
-    daubechies_wavelet(int grid_refinements = -1)
-    {
-        static_assert(p < 20, "Daubechies wavelets are only implemented for p < 20.");
-        static_assert(p > 0, "Daubechies wavelets must have at least 1 vanishing moment.");
-        if (grid_refinements == 0)
-        {
+   template<class Real, int p>
+   class daubechies_wavelet {
+      //
+      // Some type manipulation so we know the type of the interpolator, and the vector type it requires:
+      //
+      typedef std::vector < std::array < Real, p < 6 ? 2 : p < 10 ? 3 : 4>> vector_type;
+      //
+      // List our interpolators:
+      //
+      typedef std::tuple<
+         detail::null_interpolator, detail::matched_holder_aos<vector_type>, detail::linear_interpolation_aos<vector_type>,
+         interpolators::detail::cardinal_cubic_hermite_detail_aos<vector_type>, interpolators::detail::cardinal_quintic_hermite_detail_aos<vector_type>,
+         interpolators::detail::cardinal_septic_hermite_detail_aos<vector_type> > interpolator_list;
+      //
+      // Select the one we need:
+      //
+      typedef std::tuple_element_t<
+         p == 1 ? 0 :
+         p == 2 ? 1 :
+         p == 3 ? 2 :
+         p <= 5 ? 3 :
+         p <= 9 ? 4 : 5, interpolator_list> interpolator_type;
+   public:
+      daubechies_wavelet(int grid_refinements = -1)
+      {
+         static_assert(p < 20, "Daubechies wavelets are only implemented for p < 20.");
+         static_assert(p > 0, "Daubechies wavelets must have at least 1 vanishing moment.");
+         if (grid_refinements == 0)
+         {
             throw std::domain_error("The wavelet requires at least 1 grid refinement.");
-        }
-        if constexpr (p == 1)
-        {
+         }
+         if constexpr (p == 1)
+         {
             return;
-        }
-        else
-        {
-        if (grid_refinements < 0)
-        {
-            if (std::is_same_v<Real, float>)
+         }
+         else
+         {
+            if (grid_refinements < 0)
             {
-                if (grid_refinements == -2)
-                {
-                    // Control absolute error:
-                    //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
-                    std::array<int, 20> r{-1, -1, 18, 19, 16, 11,  8,  7,  7,  7,  5,  5,  4,  4,  4,  4,  3,  3,  3,  3};
-                    grid_refinements = r[p];
-                }
-                else
-                {
-                    // Control relative error:
-                    //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
-                    std::array<int, 20> r{-1, -1, 21, 21, 21, 17, 16, 15, 14, 13, 12, 11, 11, 11, 11, 11, 11, 11, 11, 11};
-                    grid_refinements = r[p];
-                }
+               if (std::is_same_v<Real, float>)
+               {
+                  if (grid_refinements == -2)
+                  {
+                     // Control absolute error:
+                     //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
+                     std::array<int, 20> r{ -1, -1, 18, 19, 16, 11,  8,  7,  7,  7,  5,  5,  4,  4,  4,  4,  3,  3,  3,  3 };
+                     grid_refinements = r[p];
+                  }
+                  else
+                  {
+                     // Control relative error:
+                     //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
+                     std::array<int, 20> r{ -1, -1, 21, 21, 21, 17, 16, 15, 14, 13, 12, 11, 11, 11, 11, 11, 11, 11, 11, 11 };
+                     grid_refinements = r[p];
+                  }
+               }
+               else if (std::is_same_v<Real, double>)
+               {
+                  //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
+                  std::array<int, 20> r{ -1, -1, 21, 21, 21, 21, 21, 21, 21, 21, 20, 20, 19, 18, 18, 18, 18, 18, 18, 18 };
+                  grid_refinements = r[p];
+               }
+               else
+               {
+                  grid_refinements = 21;
+               }
             }
-            else if (std::is_same_v<Real, double>)
+
+            // Compute the refined grid:
+            // In fact for float precision I know the grid must be computed in double precision and then cast back down, or else parts of the support are systematically inaccurate.
+            std::future<std::vector<Real>> t0 = std::async(std::launch::async, [&grid_refinements]() {
+               // Computing in higher precision and downcasting is essential for 1ULP evaluation in float precision:
+               auto v = daubechies_wavelet_dyadic_grid<typename detail::daubechies_eval_type<Real>::type, p, 0>(grid_refinements);
+               return detail::daubechies_eval_type<Real>::vector_cast(v);
+               });
+            // Compute the derivative of the refined grid:
+            std::future<std::vector<Real>> t1 = std::async(std::launch::async, [&grid_refinements]() {
+               auto v = daubechies_wavelet_dyadic_grid<typename detail::daubechies_eval_type<Real>::type, p, 1>(grid_refinements);
+               return detail::daubechies_eval_type<Real>::vector_cast(v);
+               });
+
+            // if necessary, compute the second and third derivative:
+            std::vector<Real> d2ydx2;
+            std::vector<Real> d3ydx3;
+            if constexpr (p >= 6) {
+               std::future<std::vector<Real>> t3 = std::async(std::launch::async, [&grid_refinements]() {
+                  auto v = daubechies_wavelet_dyadic_grid<typename detail::daubechies_eval_type<Real>::type, p, 2>(grid_refinements);
+                  return detail::daubechies_eval_type<Real>::vector_cast(v);
+                  });
+
+               if constexpr (p >= 10) {
+                  std::future<std::vector<Real>> t4 = std::async(std::launch::async, [&grid_refinements]() {
+                     auto v = daubechies_wavelet_dyadic_grid<typename detail::daubechies_eval_type<Real>::type, p, 3>(grid_refinements);
+                     return detail::daubechies_eval_type<Real>::vector_cast(v);
+                     });
+                  d3ydx3 = t4.get();
+               }
+               d2ydx2 = t3.get();
+            }
+
+
+            auto y = t0.get();
+            auto dydx = t1.get();
+
+            if constexpr (p >= 2)
             {
-                //                          p= 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
-                std::array<int, 20> r{-1, -1, 21, 21, 21, 21, 21, 21, 21, 21, 20, 20, 19, 18, 18, 18, 18, 18, 18, 18};
-                grid_refinements = r[p];
+               vector_type data(y.size());
+               for (size_t i = 0; i < y.size(); ++i)
+               {
+                  data[i][0] = y[i];
+                  data[i][1] = dydx[i];
+                  if constexpr (p >= 6)
+                     data[i][2] = d2ydx2[i];
+                  if constexpr (p >= 10)
+                     data[i][3] = d3ydx3[i];
+               }
+               if constexpr (p <= 3)
+                  m_interpolator = std::make_shared<interpolator_type>(std::move(data), grid_refinements, Real(-p + 1));
+               else
+                  m_interpolator = std::make_shared<interpolator_type>(std::move(data), Real(-p + 1), Real(1) / (1 << grid_refinements));
             }
             else
-            {
-                grid_refinements = 21;
-            }
-        }
-
-        // Compute the refined grid:
-        // In fact for float precision I know the grid must be computed in double precision and then cast back down, or else parts of the support are systematically inaccurate.
-        std::future<std::vector<Real>> t0 = std::async(std::launch::async, [&grid_refinements]() {
-            // Computing in higher precision and downcasting is essential for 1ULP evaluation in float precision:
-           auto v = daubechies_wavelet_dyadic_grid<typename detail::daubechies_eval_type<Real>::type, p, 0>(grid_refinements);
-           return detail::daubechies_eval_type<Real>::vector_cast(v);
-        });
-        // Compute the derivative of the refined grid:
-        std::future<std::vector<Real>> t1 = std::async(std::launch::async, [&grid_refinements]() {
-           auto v = daubechies_wavelet_dyadic_grid<typename detail::daubechies_eval_type<Real>::type, p, 1>(grid_refinements);
-           return detail::daubechies_eval_type<Real>::vector_cast(v);
-         });
-
-        // if necessary, compute the second and third derivative:
-        std::vector<Real> d2ydx2;
-        std::vector<Real> d3ydx3;
-        if constexpr (p >= 6) {
-            std::future<std::vector<Real>> t3 = std::async(std::launch::async, [&grid_refinements]() {
-               auto v = daubechies_wavelet_dyadic_grid<typename detail::daubechies_eval_type<Real>::type, p, 2>(grid_refinements);
-               return detail::daubechies_eval_type<Real>::vector_cast(v);
-             });
-
-            if constexpr (p >= 10) {
-                std::future<std::vector<Real>> t4 = std::async(std::launch::async, [&grid_refinements]() {
-                   auto v = daubechies_wavelet_dyadic_grid<typename detail::daubechies_eval_type<Real>::type, p, 3>(grid_refinements);
-                   return detail::daubechies_eval_type<Real>::vector_cast(v);
-                 });
-                d3ydx3 = t4.get();
-            }
-            d2ydx2 = t3.get();
-        }
+               m_interpolator = std::make_shared<detail::null_interpolator>();
+         }
+      }
 
 
-        auto y = t0.get();
-        auto dydx = t1.get();
-
-        if constexpr (p==2)
-        {
-            std::vector<std::array<Real, 2>> data(y.size());
-            for (size_t i = 0; i < y.size(); ++i)
-            {
-                data[i][0] = y[i];
-                data[i][1] = dydx[i];
-            }
-            m_mh = std::make_shared<detail::matched_holder_aos<std::vector<std::array<Real,2>>>>(std::move(data), grid_refinements, Real(-p+1));
-        }
-        if constexpr (p==3)
-        {
-            std::vector<std::array<Real, 2>> data(y.size());
-            for (size_t i = 0; i < y.size(); ++i)
-            {
-                data[i][0] = y[i];
-                data[i][1] = dydx[i];
-            }
-            m_lin = std::make_shared<detail::linear_interpolation_aos<std::vector<std::array<Real, 2>>>>(std::move(data), grid_refinements, Real(-p+1));
-        }
-        if constexpr (p == 4 || p == 5)
-        {
-            Real dx = Real(1)/(1 << grid_refinements);
-            std::vector<std::array<Real, 2>> data(y.size());
-            for (size_t i = 0; i < y.size(); ++i)
-            {
-                data[i][0] = y[i];
-                data[i][1] = dydx[i];
-            }
-            m_cbh = std::make_shared<interpolators::detail::cardinal_cubic_hermite_detail_aos<std::vector<std::array<Real,2>>>>(std::move(data), Real(-p+1), dx);
-        }
-        if constexpr (p >= 6 && p <= 9)
-        {
-            Real dx = Real(1)/(1 << grid_refinements);
-            std::vector<std::array<Real, 3>> data(y.size());
-            for (size_t i = 0; i < y.size(); ++i)
-            {
-                data[i][0] = y[i];
-                data[i][1] = dydx[i];
-                data[i][2] = d2ydx2[i];
-            }
-
-            m_qh = std::make_shared<interpolators::detail::cardinal_quintic_hermite_detail_aos<std::vector<std::array<Real,3>>>>(std::move(data), Real(-p+1), dx);
-        }
-        if constexpr (p >= 10)
-        {
-            Real dx = Real(1)/(1 << grid_refinements);
-            std::vector<std::array<Real, 4>> data(y.size());
-            for (size_t i = 0; i < y.size(); ++i)
-            {
-                data[i][0] = y[i];
-                data[i][1] = dydx[i];
-                data[i][2] = d2ydx2[i];
-                data[i][3] = d3ydx3[i];
-            }
-            m_sh = std::make_shared<interpolators::detail::cardinal_septic_hermite_detail_aos<std::vector<std::array<Real, 4>>>>(std::move(data), Real(-p+1), dx);
-        }
-        }
-     }
-
-
-    inline Real operator()(Real x) const
-    {
-        if (x <= -p + 1 || x >= p)
-        {
+      inline Real operator()(Real x) const
+      {
+         if (x <= -p + 1 || x >= p)
+         {
             return 0;
-        }
-        if constexpr (p==1)
-        {
-            if (x < Real(1)/Real(2))
+         }
+         if constexpr (p == 1)
+         {
+            if (x < Real(1) / Real(2))
             {
-                return 1;
+               return 1;
             }
-            else if (x == Real(1)/Real(2))
+            else if (x == Real(1) / Real(2))
             {
-                return 0;
+               return 0;
             }
             return -1;
-        }
-        if constexpr (p==2)
-        {
-            return m_mh->operator()(x);
-        }
-        if constexpr (p==3)
-        {
-            return m_lin->operator()(x);
-        }
-        if constexpr (p==4 || p ==5)
-        {
-            return m_cbh->unchecked_evaluation(x);
-        }
-        if constexpr (p >= 6 && p <= 9)
-        {
-            return m_qh->unchecked_evaluation(x);
-        }
-        if constexpr (p >= 10)
-        {
-            return m_sh->unchecked_evaluation(x);
-        }
-    }
+         }
+         return (*m_interpolator)(x);
+      }
 
-    inline Real prime(Real x) const
-    {
-        static_assert(p > 2, "The 3-vanishing moment Daubechies wavelet is the first which is continuously differentiable.");
-        if (x <= -p + 1 || x >= p)
-        {
+      inline Real prime(Real x) const
+      {
+         static_assert(p > 2, "The 3-vanishing moment Daubechies wavelet is the first which is continuously differentiable.");
+         if (x <= -p + 1 || x >= p)
+         {
             return 0;
-        }
-        if constexpr (p == 3)
-        {
-            return m_lin->prime(x);
-        }
-        if constexpr (p == 4 || p == 5)
-        {
-            return m_cbh->unchecked_prime(x);
-        }
-        if constexpr (p >= 6 && p <= 9)
-        {
-            return m_qh->unchecked_prime(x);
-        }
-        if constexpr (p >= 10)
-        {
-            return m_sh->unchecked_prime(x);
-        }
-    }
+         }
+         return m_interpolator->prime(x);
+      }
 
-    inline Real double_prime(Real x) const
-    {
-        static_assert(p >= 6, "Second derivatives of Daubechies wavelets require at least 6 vanishing moments.");
-        if (x <= -p + 1 || x >= p)
-        {
+      inline Real double_prime(Real x) const
+      {
+         static_assert(p >= 6, "Second derivatives of Daubechies wavelets require at least 6 vanishing moments.");
+         if (x <= -p + 1 || x >= p)
+         {
             return Real(0);
-        }
-        if constexpr (p >= 6 && p <= 9)
-        {
-            return m_qh->unchecked_double_prime(x);
-        }
-        if constexpr (p >= 10)
-        {
-            return m_sh->unchecked_double_prime(x);
-        }
-    }
+         }
+         return m_interpolator->double_prime(x);
+      }
 
-    std::pair<Real, Real> support() const
-    {
-        return {Real(-p+1), Real(p)};
-    }
+      std::pair<Real, Real> support() const
+      {
+         return { Real(-p + 1), Real(p) };
+      }
 
-    int64_t bytes() const
-    {
-        if constexpr (p==1)
-        {
-            return sizeof(this);
-        }
-        if constexpr (p==2)
-        {
-            return m_mh->bytes() + sizeof(m_mh);
-        }
-        if constexpr (p == 3)
-        {
-            return m_lin->bytes() + sizeof(m_lin);
-        }
-        if constexpr (p == 4 || p == 5)
-        {
-            return m_cbh->bytes() + sizeof(m_cbh);
-        }
-        if constexpr (p >= 6 && p <= 9)
-        {
-            return m_qh->bytes() + sizeof(m_qh);
-        }
-        if constexpr (p >= 10)
-        {
-            return m_sh->bytes() + sizeof(m_sh);
-        }
+      int64_t bytes() const
+      {
+         return m_interpolator->bytes() + sizeof(*this);
+      }
 
-        return -1;
-    }
-
-private:
-    // Need this for p = 2:
-    std::shared_ptr<detail::matched_holder_aos<std::vector<std::array<Real,2>>>> m_mh;
-    // Need this for p = 3:
-    std::shared_ptr<detail::linear_interpolation_aos<std::vector<std::array<Real, 2>>>> m_lin;
-    // Need this for p = 4,5:
-    std::shared_ptr<interpolators::detail::cardinal_cubic_hermite_detail_aos<std::vector<std::array<Real, 2>>>> m_cbh;
-    // Need this for p = 6,7,8,9:
-    std::shared_ptr<interpolators::detail::cardinal_quintic_hermite_detail_aos<std::vector<std::array<Real, 3>>>> m_qh;
-    // Need this for p >= 10:
-    std::shared_ptr<interpolators::detail::cardinal_septic_hermite_detail_aos<std::vector<std::array<Real, 4>>>> m_sh;
-};
+   private:
+      std::shared_ptr<interpolator_type> m_interpolator;
+   };
 
 }
 #endif
diff --git a/test/daubechies_scaling_test.cpp b/test/daubechies_scaling_test.cpp
index ceb43da88..febb77d50 100644
--- a/test/daubechies_scaling_test.cpp
+++ b/test/daubechies_scaling_test.cpp
@@ -338,6 +338,7 @@ void test_quadratures()
         // so one-off it is.
         Real h = Real(1)/Real(256);
         auto phi = boost::math::daubechies_scaling<Real, p>();
+        std::cout << "Scaling functor size is " << phi.bytes() << " bytes" << std::endl;
         Real t = 0;
         Real Q = 0;
         while (t < 3) {
@@ -374,7 +375,8 @@ void test_quadratures()
     else if constexpr (p > 2)
     {
         auto phi = boost::math::daubechies_scaling<Real, p>();
-        
+        std::cout << "Scaling functor size is " << phi.bytes() << " bytes" << std::endl;
+
         Real tol = std::numeric_limits<Real>::epsilon();
         Real error_estimate = std::numeric_limits<Real>::quiet_NaN();
         Real L1 = std::numeric_limits<Real>::quiet_NaN();
diff --git a/test/daubechies_wavelet_test.cpp b/test/daubechies_wavelet_test.cpp
index 384b02664..eb92c271c 100644
--- a/test/daubechies_wavelet_test.cpp
+++ b/test/daubechies_wavelet_test.cpp
@@ -46,6 +46,7 @@ void test_quadratures()
     std::cout << "Testing quadratures of " << p << " vanishing moment Daubechies wavelet on type " << boost::core::demangle(typeid(Real).name()) << "\n";
     using boost::math::quadrature::trapezoidal;
     auto psi = boost::math::daubechies_wavelet<Real, p>();
+    std::cout << "Wavelet functor size is " << psi.bytes() << " bytes" << std::endl;
         
     Real tol = std::numeric_limits<Real>::epsilon();
     Real error_estimate = std::numeric_limits<Real>::quiet_NaN();

From d009f3c6b468c3411acf7cce6383a2576343f0d0 Mon Sep 17 00:00:00 2001
From: Nick <nathompson7@protonmail.com>
Date: Tue, 24 Mar 2020 05:42:47 -0400
Subject: [PATCH 104/104] Yet again increase tolerance on Windows

---
 test/septic_hermite_test.cpp | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/test/septic_hermite_test.cpp b/test/septic_hermite_test.cpp
index 188ac56de..6119b8f1f 100644
--- a/test/septic_hermite_test.cpp
+++ b/test/septic_hermite_test.cpp
@@ -183,17 +183,17 @@ void test_linear()
     while (i++ < samples)
     {
         CHECK_ULP_CLOSE(Real(tlo), csh(tlo), 2);
-        CHECK_ULP_CLOSE(Real(thi), csh(thi), 4);
+        CHECK_ULP_CLOSE(Real(thi), csh(thi), 5);
         CHECK_ULP_CLOSE(Real(tlo), csh_aos(tlo), 2);
-        CHECK_ULP_CLOSE(Real(thi), csh_aos(thi), 4);
+        CHECK_ULP_CLOSE(Real(thi), csh_aos(thi), 5);
         CHECK_ULP_CLOSE(Real(1), csh.prime(tlo), 2);
-        CHECK_ULP_CLOSE(Real(1), csh.prime(thi), 512);
+        CHECK_ULP_CLOSE(Real(1), csh.prime(thi), 580);
         CHECK_ULP_CLOSE(Real(1), csh_aos.prime(tlo), 2);
-        CHECK_ULP_CLOSE(Real(1), csh_aos.prime(thi), 512);
+        CHECK_ULP_CLOSE(Real(1), csh_aos.prime(thi), 580);
         CHECK_MOLLIFIED_CLOSE(Real(0), csh.double_prime(tlo), std::numeric_limits<Real>::epsilon());
-        CHECK_MOLLIFIED_CLOSE(Real(0), csh.double_prime(thi), 800*std::numeric_limits<Real>::epsilon());
+        CHECK_MOLLIFIED_CLOSE(Real(0), csh.double_prime(thi), 1000*std::numeric_limits<Real>::epsilon());
         CHECK_MOLLIFIED_CLOSE(Real(0), csh_aos.double_prime(tlo), std::numeric_limits<Real>::epsilon());
-        CHECK_MOLLIFIED_CLOSE(Real(0), csh_aos.double_prime(thi), 800*std::numeric_limits<Real>::epsilon());
+        CHECK_MOLLIFIED_CLOSE(Real(0), csh_aos.double_prime(thi), 1000*std::numeric_limits<Real>::epsilon());
 
         tlo = boost::math::nextafter(tlo, std::numeric_limits<Real>::max());
         thi = boost::math::nextafter(thi, std::numeric_limits<Real>::lowest());