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[Carlson Elliptic Integrals] Update RD to use Carlson's latest methods. Add more RD test cases. Update copyright info.
This commit is contained in:
jzmaddock
@@ -1,4 +1,4 @@
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// Copyright (c) 2006 Xiaogang Zhang
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// Copyright (c) 2006 Xiaogang Zhang, 2015 John Maddock
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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@@ -8,6 +8,7 @@
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// Summer of Code 2006. JM modified it to fit into the
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// Boost.Math conceptual framework better, and to correctly
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// handle the y < 0 case.
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// Updated 2015 to use Carlson's latest methods.
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//
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#ifndef BOOST_MATH_ELLINT_RC_HPP
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@@ -1,4 +1,4 @@
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// Copyright (c) 2006 Xiaogang Zhang
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// Copyright (c) 2006 Xiaogang Zhang, 2015 John Maddock.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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@@ -7,6 +7,7 @@
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// XZ wrote the original of this file as part of the Google
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// Summer of Code 2006. JM modified it slightly to fit into the
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// Boost.Math conceptual framework better.
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// Updated 2015 to use Carlson's latest methods.
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#ifndef BOOST_MATH_ELLINT_RD_HPP
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#define BOOST_MATH_ELLINT_RD_HPP
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@@ -28,78 +29,101 @@ namespace boost { namespace math { namespace detail{
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template <typename T, typename Policy>
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T ellint_rd_imp(T x, T y, T z, const Policy& pol)
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{
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T value, u, lambda, sigma, factor, tolerance;
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T X, Y, Z, EA, EB, EC, ED, EE, S1, S2;
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unsigned long k;
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BOOST_MATH_STD_USING
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using namespace boost::math;
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BOOST_MATH_STD_USING
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using namespace boost::math::tools;
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static const char* function = "boost::math::ellint_rd<%1%>(%1%,%1%,%1%)";
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static const char* function = "boost::math::ellint_rd<%1%>(%1%,%1%,%1%)";
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if(x < 0)
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{
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return policies::raise_domain_error<T>(function,
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"Argument x must be >= 0, but got %1%", x, pol);
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}
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if(y < 0)
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{
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return policies::raise_domain_error<T>(function,
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"Argument y must be >= 0, but got %1%", y, pol);
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}
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if(z <= 0)
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{
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return policies::raise_domain_error<T>(function,
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"Argument z must be > 0, but got %1%", z, pol);
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}
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if(x + y == 0)
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{
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return policies::raise_domain_error<T>(function,
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"At most one argument can be zero, but got, x + y = %1%", x + y, pol);
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}
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//
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// Special cases from http://dlmf.nist.gov/19.20#iv
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//
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using std::swap;
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if(x == z)
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swap(x, y);
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if(y == z)
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{
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if(x == y)
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{
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return 1 / (x * sqrt(x));
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}
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else if(x == 0)
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{
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return 3 * constants::pi<T>() / (4 * y * sqrt(y));
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}
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else
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{
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3 * (ellint_rc_imp(x, y, pol) - sqrt(x) / y) / (2 * (y - x));
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}
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}
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if(x == y)
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{
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return 3 * (ellint_rc_imp(z, x, pol) - 1 / sqrt(z)) / (z - x);
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}
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if (x < 0)
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{
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return policies::raise_domain_error<T>(function,
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"Argument x must be >= 0, but got %1%", x, pol);
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}
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if (y < 0)
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{
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return policies::raise_domain_error<T>(function,
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"Argument y must be >= 0, but got %1%", y, pol);
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}
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if (z <= 0)
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{
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return policies::raise_domain_error<T>(function,
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"Argument z must be > 0, but got %1%", z, pol);
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}
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if (x + y == 0)
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{
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return policies::raise_domain_error<T>(function,
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"At most one argument can be zero, but got, x + y = %1%", x+y, pol);
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}
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T xn = x;
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T yn = y;
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T zn = z;
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T An = (x + y + 3 * z) / 5;
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T A0 = An;
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T Q = pow(tools::epsilon<T>() / 4, -T(1) / 8) * (std::max)((std::max)(An - x, An - y), An - z);
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T lambda, rx, ry, rz;
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unsigned k = 0;
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T fn = 1;
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T RD_sum = 0;
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// error scales as the 6th power of tolerance
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tolerance = pow(tools::epsilon<T>() / 3, T(1)/6);
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for(; k < policies::get_max_series_iterations<Policy>(); ++k)
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{
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rx = sqrt(xn);
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ry = sqrt(yn);
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rz = sqrt(zn);
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lambda = rx * ry + rx * rz + ry * rz;
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RD_sum += fn / (rz * (zn + lambda));
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An = (An + lambda) / 4;
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xn = (xn + lambda) / 4;
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yn = (yn + lambda) / 4;
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zn = (zn + lambda) / 4;
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fn /= 4;
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Q /= 4;
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if(Q < An)
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break;
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}
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// duplication
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sigma = 0;
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factor = 1;
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k = 1;
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do
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{
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u = (x + y + z + z + z) / 5;
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X = (u - x) / u;
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Y = (u - y) / u;
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Z = (u - z) / u;
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if ((tools::max)(abs(X), abs(Y), abs(Z)) < tolerance)
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break;
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T sx = sqrt(x);
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T sy = sqrt(y);
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T sz = sqrt(z);
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lambda = sy * (sx + sz) + sz * sx; //sqrt(x * y) + sqrt(y * z) + sqrt(z * x);
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sigma += factor / (sz * (z + lambda));
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factor /= 4;
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x = (x + lambda) / 4;
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y = (y + lambda) / 4;
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z = (z + lambda) / 4;
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++k;
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}
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while(k < policies::get_max_series_iterations<Policy>());
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policies::check_series_iterations<T, Policy>(function, k, pol);
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// Check to see if we gave up too soon:
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policies::check_series_iterations<T>(function, k, pol);
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T X = fn * (A0 - x) / An;
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T Y = fn * (A0 - y) / An;
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T Z = -(X + Y) / 3;
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T E2 = X * Y - 6 * Z * Z;
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T E3 = (3 * X * Y - 8 * Z * Z) * Z;
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T E4 = 3 * (X * Y - Z * Z) * Z * Z;
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T E5 = X * Y * Z * Z * Z;
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// Taylor series expansion to the 5th order
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EA = X * Y;
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EB = Z * Z;
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EC = EA - EB;
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ED = EA - 6 * EB;
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EE = ED + EC + EC;
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S1 = ED * (ED * T(9) / 88 - Z * EE * T(9) / 52 - T(3) / 14);
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S2 = Z * (EE / 6 + Z * (-EC * T(9) / 22 + Z * EA * T(3) / 26));
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value = 3 * sigma + factor * (1 + S1 + S2) / (u * sqrt(u));
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T result = fn * pow(An, T(-3) / 2) *
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(1 - 3 * E2 / 14 + E3 / 6 + 9 * E2 * E2 / 88 - 3 * E4 / 22 - 9 * E2 * E3 / 52 + 3 * E5 / 26 - E2 * E2 * E2 / 16
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+ 3 * E3 * E3 / 40 + 3 * E2 * E4 / 20 + 45 * E2 * E2 * E3 / 272 - 9 * (E3 * E4 + E2 * E5) / 68);
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result += 3 * RD_sum;
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return value;
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return result;
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}
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} // namespace detail
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@@ -1,4 +1,4 @@
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// Copyright (c) 2006 Xiaogang Zhang
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// Copyright (c) 2006 Xiaogang Zhang, 2015 John Maddock
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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@@ -8,6 +8,7 @@
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// Summer of Code 2006. JM modified it to fit into the
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// Boost.Math conceptual framework better, and to handle
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// types longer than 80-bit reals.
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// Updated 2015 to use Carlson's latest methods.
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//
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#ifndef BOOST_MATH_ELLINT_RF_HPP
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#define BOOST_MATH_ELLINT_RF_HPP
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@@ -1,4 +1,4 @@
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// Copyright (c) 2006 Xiaogang Zhang
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// Copyright (c) 2006 Xiaogang Zhang, 2015 John Maddock
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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@@ -8,6 +8,7 @@
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// Summer of Code 2006. JM modified it to fit into the
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// Boost.Math conceptual framework better, and to correctly
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// handle the p < 0 case.
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// Updated 2015 to use Carlson's latest methods.
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//
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#ifndef BOOST_MATH_ELLINT_RJ_HPP
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228
test/ellint_rd_0yy.ipp
Normal file
228
test/ellint_rd_0yy.ipp
Normal file
@@ -0,0 +1,228 @@
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#ifndef SC_
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# define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
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#endif
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static const boost::array<boost::array<T, 4>, 221> ellint_rd_0yy = {{
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{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.3980121253550848455436022016469058470638e-33), SC_(1.3980121253550848455436022016469058470638e-33), SC_(4.5075933427301716232672795034855345692850e+49) },
|
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{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.7494794261211793309535608228238390754549e-33), SC_(1.7494794261211793309535608228238390754549e-33), SC_(3.2199407235554817226615307866947803938564e+49) },
|
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{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(5.8726742677921440789517852801186900989207e-33), SC_(5.8726742677921440789517852801186900989207e-33), SC_(5.2354891815381075869697810446193501064438e+48) },
|
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{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.1309113765786506096540062665750175659960e-32), SC_(1.1309113765786506096540062665750175659960e-32), SC_(1.9591526532522238800125709320252743161241e+48) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.3891181146915726390794029968681816070943e-32), SC_(1.3891181146915726390794029968681816070943e-32), SC_(1.4391377787499269400927485477485886768717e+48) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(4.8536338069604874547155326932387107373984e-32), SC_(4.8536338069604874547155326932387107373984e-32), SC_(2.2034876750953806189172437564774275736541e+47) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(9.4336713037670874919513419574389437932846e-32), SC_(9.4336713037670874919513419574389437932846e-32), SC_(8.1318624868386456742114211802159880281555e+46) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.2040325324738106751721983353783124694865e-31), SC_(1.2040325324738106751721983353783124694865e-31), SC_(5.6396714463599834543132107821392013656837e+46) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(3.2192605509133527499735325052444797920840e-31), SC_(3.2192605509133527499735325052444797920840e-31), SC_(1.2899620817873123488958262770226551475010e+46) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(5.1598089430474145704786096554063029578715e-31), SC_(5.1598089430474145704786096554063029578715e-31), SC_(6.3571243221039164981188237286935464910062e+45) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(8.6580669655578129845734803403304892059082e-31), SC_(8.6580669655578129845734803403304892059082e-31), SC_(2.9246892262678841512667853928021133305832e+45) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.4410831025899022881322276426055071978088e-30), SC_(2.4410831025899022881322276426055071978088e-30), SC_(6.1778490048502380351529857344675390759941e+44) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(4.0342289035474833635882447965222031649226e-30), SC_(4.0342289035474833635882447965222031649226e-30), SC_(2.9078388270756910613550920230806241035946e+44) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(7.4997427315795683999931409064612184484767e-30), SC_(7.4997427315795683999931409064612184484767e-30), SC_(1.1472064694021494573881450931960080790526e+44) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.9524385645124032915396812389852876697084e-29), SC_(1.9524385645124032915396812389852876697084e-29), SC_(2.7311469634494727792399520940657654512231e+43) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(5.0307396633271274021036423836193003824470e-29), SC_(5.0307396633271274021036423836193003824470e-29), SC_(6.6033356137966398138516962580399577046152e+42) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(9.8828830280863654554637712926778439923276e-29), SC_(9.8828830280863654554637712926778439923276e-29), SC_(2.3982014064068530283911440001042264840411e+42) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.0159108358364658025376430240459520615557e-28), SC_(2.0159108358364658025376430240459520615557e-28), SC_(8.2319771677314581385498523947797460816717e+41) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(3.9680608719690755813060883143357162268402e-28), SC_(3.9680608719690755813060883143357162268402e-28), SC_(2.9808741945019792609548473554157723415638e+41) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(7.9474558416608700456074110588635447509500e-28), SC_(7.9474558416608700456074110588635447509500e-28), SC_(1.0516444901620232783721998493769337461329e+41) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(9.3511217333788972162109341828680044038835e-28), SC_(9.3511217333788972162109341828680044038835e-28), SC_(8.2397791221868831084700129809818532631473e+40) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.7882427361992658143258966170331945402566e-27), SC_(2.7882427361992658143258966170331945402566e-27), SC_(1.6003510785687549140380943789426537461361e+40) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(6.3673277743463290223091457894565066834118e-27), SC_(6.3673277743463290223091457894565066834118e-27), SC_(4.6374082021103840466514853911190947500707e+39) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.2802620846058105842978295818115658417924e-26), SC_(1.2802620846058105842978295818115658417924e-26), SC_(1.6265327427673199292492683523168879331831e+39) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.5295786350139981648664921989981478850189e-26), SC_(2.5295786350139981648664921989981478850189e-26), SC_(5.8565095970457391914797111441321805264607e+38) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.8689244097271181025975906229169039426616e-26), SC_(2.8689244097271181025975906229169039426616e-26), SC_(4.8487799776012116544026189428582000085828e+38) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(7.6792108552998581016945261284770797094792e-26), SC_(7.6792108552998581016945261284770797094792e-26), SC_(1.1072259281756202115081480962871127420943e+38) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.8591977352242616487743079115958899226631e-25), SC_(1.8591977352242616487743079115958899226631e-25), SC_(2.9391568532186769604057269025306538055943e+37) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(3.7228919776082830648394626760138917268353e-25), SC_(3.7228919776082830648394626760138917268353e-25), SC_(1.0372668142458025191836426570876594939768e+37) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(5.3643882618567678488066742377790444354368e-25), SC_(5.3643882618567678488066742377790444354368e-25), SC_(5.9969555633403996040304559961761339372739e+36) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(9.4454615474045197976285755041988786463725e-25), SC_(9.4454615474045197976285755041988786463725e-25), SC_(2.5667073814630641210346435302809237333871e+36) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.6622742888463273191629024333782773358015e-24), SC_(1.6622742888463273191629024333782773358015e-24), SC_(1.0994034736897091951482460793729684001915e+36) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(4.7042126583826492571881501298937085578378e-24), SC_(4.7042126583826492571881501298937085578378e-24), SC_(2.3093019207333082014680732641029849321245e+35) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(7.3616720556278283564328024996187890133248e-24), SC_(7.3616720556278283564328024996187890133248e-24), SC_(1.1796317031402849031779618673326472752225e+35) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.5354544851880595018243965945098708503203e-23), SC_(2.5354544851880595018243965945098708503203e-23), SC_(1.8455567662373838950133656611287719411634e+34) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(4.3404174612542203037430892437393593896733e-23), SC_(4.3404174612542203037430892437393593896733e-23), SC_(8.2397471174074355708481727744393670098703e+33) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(9.4878661342759511104190386438428025939196e-23), SC_(9.4878661342759511104190386438428025939196e-23), SC_(2.5495193547757707650015926055658627197772e+33) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.9888655119526487934053853251590432416052e-22), SC_(1.9888655119526487934053853251590432416052e-22), SC_(8.4004588879902697969624976614191462312147e+32) },
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{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(4.9568887500000000000000000000000000000000e+05), SC_(4.9568887500000000000000000000000000000000e+05), SC_(6.7514550135866210227659090372628434738153e-09) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(7.4614825000000000000000000000000000000000e+05), SC_(7.4614825000000000000000000000000000000000e+05), SC_(3.6557244129771091797512715583810805221466e-09) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.0544660000000000000000000000000000000000e+06), SC_(2.0544660000000000000000000000000000000000e+06), SC_(8.0013395078363534043556338337041169765456e-10) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(3.3155060000000000000000000000000000000000e+06), SC_(3.3155060000000000000000000000000000000000e+06), SC_(3.9028908772860887973647028521779308741608e-10) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(6.4894920000000000000000000000000000000000e+06), SC_(6.4894920000000000000000000000000000000000e+06), SC_(1.4252632397584000862191716526761712040234e-10) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(9.7144880000000000000000000000000000000000e+06), SC_(9.7144880000000000000000000000000000000000e+06), SC_(7.7818214492976104425809068828123683300226e-11) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.9102944000000000000000000000000000000000e+07), SC_(1.9102944000000000000000000000000000000000e+07), SC_(2.8220238657672161392200388968311941529244e-11) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(5.9113888000000000000000000000000000000000e+07), SC_(5.9113888000000000000000000000000000000000e+07), SC_(5.1841415293379107198281099443161527090192e-12) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(7.7127808000000000000000000000000000000000e+07), SC_(7.7127808000000000000000000000000000000000e+07), SC_(3.4785211876505007113126307050932323648480e-12) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.6510873600000000000000000000000000000000e+08), SC_(1.6510873600000000000000000000000000000000e+08), SC_(1.1105958776673761205941747441743925909257e-12) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(3.3755980800000000000000000000000000000000e+08), SC_(3.3755980800000000000000000000000000000000e+08), SC_(3.7991377387201342909393024807672376828521e-13) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(9.7159372800000000000000000000000000000000e+08), SC_(9.7159372800000000000000000000000000000000e+08), SC_(7.7800803484729872159615890961902299182403e-14) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.9764551680000000000000000000000000000000e+09), SC_(1.9764551680000000000000000000000000000000e+09), SC_(2.6815178025032209084857916637442357439588e-14) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(4.2703175680000000000000000000000000000000e+09), SC_(4.2703175680000000000000000000000000000000e+09), SC_(8.4434682840831492116613635121799845005006e-15) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(5.3871001600000000000000000000000000000000e+09), SC_(5.3871001600000000000000000000000000000000e+09), SC_(5.9590710106811630634114258223376320661736e-15) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.1445641216000000000000000000000000000000e+10), SC_(1.1445641216000000000000000000000000000000e+10), SC_(1.9242032507399093707745358747656568252613e-15) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(3.1169175552000000000000000000000000000000e+10), SC_(3.1169175552000000000000000000000000000000e+10), SC_(4.2817683100028441236074770957482909058314e-16) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(4.4661866496000000000000000000000000000000e+10), SC_(4.4661866496000000000000000000000000000000e+10), SC_(2.4963520528655146730005427407239493932124e-16) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(8.5454389248000000000000000000000000000000e+10), SC_(8.5454389248000000000000000000000000000000e+10), SC_(9.4321255772493191527939849265186549774193e-17) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.3929971712000000000000000000000000000000e+11), SC_(1.3929971712000000000000000000000000000000e+11), SC_(4.5319570396672945799633779540526596875336e-17) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(5.3031193804800000000000000000000000000000e+11), SC_(5.3031193804800000000000000000000000000000e+11), SC_(6.1011827035996025839064319743515775808041e-18) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(6.6918337740800000000000000000000000000000e+11), SC_(6.6918337740800000000000000000000000000000e+11), SC_(4.3042096746907435806042618825310417839570e-18) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.4843227668480000000000000000000000000000e+12), SC_(1.4843227668480000000000000000000000000000e+12), SC_(1.3029225868961457064838553318032260485440e-18) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(4.1943386030080000000000000000000000000000e+12), SC_(4.1943386030080000000000000000000000000000e+12), SC_(2.7429374547049133322395441219388040465550e-19) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(5.2626813091840000000000000000000000000000e+12), SC_(5.2626813091840000000000000000000000000000e+12), SC_(1.9516436777499619261945798028398024751089e-19) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.6259294953472000000000000000000000000000e+13), SC_(1.6259294953472000000000000000000000000000e+13), SC_(3.5938386238498959072625178440021092756251e-20) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.2009299861504000000000000000000000000000e+13), SC_(2.2009299861504000000000000000000000000000e+13), SC_(2.2819272519675800431951305861279162239509e-20) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(6.8786065506304000000000000000000000000000e+13), SC_(6.8786065506304000000000000000000000000000e+13), SC_(4.1300987211319311489897580110740712752178e-21) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.1371902350131200000000000000000000000000e+14), SC_(1.1371902350131200000000000000000000000000e+14), SC_(1.9429492342862758680684197436751902166073e-21) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.5035760310681600000000000000000000000000e+14), SC_(2.5035760310681600000000000000000000000000e+14), SC_(5.9479862865426145036643495194169053576632e-22) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(4.1469385637888000000000000000000000000000e+14), SC_(4.1469385637888000000000000000000000000000e+14), SC_(2.7900997742768856811230709366990755552635e-22) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.1188403227852800000000000000000000000000e+15), SC_(1.1188403227852800000000000000000000000000e+15), SC_(6.2959166703581510507427023891850640475674e-23) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.5218330776371200000000000000000000000000e+15), SC_(1.5218330776371200000000000000000000000000e+15), SC_(3.9688127291865771760534052034980278039998e-23) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.4040102334300160000000000000000000000000e+15), SC_(2.4040102334300160000000000000000000000000e+15), SC_(1.9989718025624541686455647924354864093254e-23) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(8.2453193010708480000000000000000000000000e+15), SC_(8.2453193010708480000000000000000000000000e+15), SC_(3.1470230108464078311689252897877097346046e-24) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.6155287555670016000000000000000000000000e+16), SC_(1.6155287555670016000000000000000000000000e+16), SC_(1.1474640741369548623445900822905912901507e-24) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.8557572558553088000000000000000000000000e+16), SC_(2.8557572558553088000000000000000000000000e+16), SC_(4.8823532977164457651971469379539455344943e-25) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(5.7448039442284544000000000000000000000000e+16), SC_(5.7448039442284544000000000000000000000000e+16), SC_(1.7111903335004092462021079073751565638677e-25) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.1166935585443020800000000000000000000000e+17), SC_(1.1166935585443020800000000000000000000000e+17), SC_(6.3140805736119643939308376323938502709515e-26) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.4972259272897331200000000000000000000000e+17), SC_(2.4972259272897331200000000000000000000000e+17), SC_(1.8880973518065091628213155256128506085821e-26) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(5.5259337852138291200000000000000000000000e+17), SC_(5.5259337852138291200000000000000000000000e+17), SC_(5.7359138663416932442576503782018173885376e-27) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(9.7723521452893798400000000000000000000000e+17), SC_(9.7723521452893798400000000000000000000000e+17), SC_(2.4390037811986451279834646752278514524585e-27) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.4824715277303808000000000000000000000000e+18), SC_(1.4824715277303808000000000000000000000000e+18), SC_(1.3053638892034804953553807066633295943717e-27) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(3.8734002442595205120000000000000000000000e+18), SC_(3.8734002442595205120000000000000000000000e+18), SC_(3.0908118787584867111563111840832332734625e-28) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(8.1036557834067640320000000000000000000000e+18), SC_(8.1036557834067640320000000000000000000000e+18), SC_(1.0213854292655262701303425728679526821507e-28) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.2841886794098147328000000000000000000000e+19), SC_(1.2841886794098147328000000000000000000000e+19), SC_(5.1199754714887938695239302653266843195455e-29) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(3.2350587576425381888000000000000000000000e+19), SC_(3.2350587576425381888000000000000000000000e+19), SC_(1.2805244538124277827397355937894229934702e-29) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(5.7611295478532538368000000000000000000000e+19), SC_(5.7611295478532538368000000000000000000000e+19), SC_(5.3882740300356636672484121699969957324696e-30) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.0185889793465699532800000000000000000000e+20), SC_(1.0185889793465699532800000000000000000000e+20), SC_(2.2919897789608940183657211549044838616924e-30) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.7827935411160009932800000000000000000000e+20), SC_(1.7827935411160009932800000000000000000000e+20), SC_(9.8982759706563146724882285943398528993460e-31) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(4.6273923221278425088000000000000000000000e+20), SC_(4.6273923221278425088000000000000000000000e+20), SC_(2.3670457587038131191455894984924187577553e-31) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(9.0160094215120355328000000000000000000000e+20), SC_(9.0160094215120355328000000000000000000000e+20), SC_(8.7034131673916872330608301334881918414135e-32) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.2701445734077667737600000000000000000000e+21), SC_(1.2701445734077667737600000000000000000000e+21), SC_(5.2051278407785688074255931933669289656894e-32) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(3.3155928298666191749120000000000000000000e+21), SC_(3.3155928298666191749120000000000000000000e+21), SC_(1.2341539808816862521170317613391946510448e-32) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(4.9771373655898078576640000000000000000000e+21), SC_(4.9771373655898078576640000000000000000000e+21), SC_(6.7102962701127552801341429015075475398530e-33) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.2776477955669473886208000000000000000000e+22), SC_(1.2776477955669473886208000000000000000000e+22), SC_(1.6315275478998638830427112838892252504389e-33) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.8915946875483827732480000000000000000000e+22), SC_(2.8915946875483827732480000000000000000000e+22), SC_(4.7918697943460309562905327155954211448158e-34) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(6.0175170680284052979712000000000000000000e+22), SC_(6.0175170680284052979712000000000000000000e+22), SC_(1.5961920371007136112833933609990592988290e-34) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.3443007097640605397811200000000000000000e+23), SC_(1.3443007097640605397811200000000000000000e+23), SC_(4.7804248375722997628622077193023794814013e-35) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.0496508805231257269043200000000000000000e+23), SC_(2.0496508805231257269043200000000000000000e+23), SC_(2.5391671795527559896976819042656491284534e-35) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(5.8451880892949689322700800000000000000000e+23), SC_(5.8451880892949689322700800000000000000000e+23), SC_(5.2724612927599312901094304956968433167960e-36) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.1877492456483867611627520000000000000000e+24), SC_(1.1877492456483867611627520000000000000000e+24), SC_(1.8202204578416780911178524107925313786398e-36) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.3659727517469077458124800000000000000000e+24), SC_(1.3659727517469077458124800000000000000000e+24), SC_(1.4758699214387048154605529284228707494743e-36) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.7912598561413239479992320000000000000000e+24), SC_(2.7912598561413239479992320000000000000000e+24), SC_(5.0525512994012465727676763040305965712619e-37) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(7.5863641567366151374110720000000000000000e+24), SC_(7.5863641567366151374110720000000000000000e+24), SC_(1.1276143852004982402635329255328796693850e-37) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.3490721907030264366759936000000000000000e+25), SC_(1.3490721907030264366759936000000000000000e+25), SC_(4.7550857279740359683414401392355109918138e-38) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.8422143749589281569505280000000000000000e+25), SC_(2.8422143749589281569505280000000000000000e+25), SC_(1.5549838708278000161595879548914170697276e-38) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(5.3668403805728358185041920000000000000000e+25), SC_(5.3668403805728358185041920000000000000000e+25), SC_(5.9928460036854257851184826574163145043933e-39) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(7.8292113919495847997865984000000000000000e+25), SC_(7.8292113919495847997865984000000000000000e+25), SC_(3.4012151670138518589307069582271112442824e-39) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.6723325902934740461577830400000000000000e+26), SC_(2.6723325902934740461577830400000000000000e+26), SC_(5.3935582557398062230908772136375217746037e-40) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(4.1381935158038852363563827200000000000000e+26), SC_(4.1381935158038852363563827200000000000000e+26), SC_(2.7989487233600208620032657603051221740589e-40) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(8.5948309609429296171135795200000000000000e+26), SC_(8.5948309609429296171135795200000000000000e+26), SC_(9.3509369060078590761745876410319415141389e-41) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.4387120406003935998650613760000000000000e+27), SC_(1.4387120406003935998650613760000000000000e+27), SC_(4.3176786756284766864734496422796754986260e-41) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(4.7722405758868522542091468800000000000000e+27), SC_(4.7722405758868522542091468800000000000000e+27), SC_(7.1470635307930435762258201315587124165876e-42) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(8.8848657238129553346144501760000000000000e+27), SC_(8.8848657238129553346144501760000000000000e+27), SC_(2.8134217007743770084246644718535234373550e-42) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.4222615588981551190220210176000000000000e+28), SC_(1.4222615588981551190220210176000000000000e+28), SC_(1.3891269213879890840577193085919440628281e-42) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.5971287269650318385179787264000000000000e+28), SC_(2.5971287269650318385179787264000000000000e+28), SC_(5.6295142404326337602794867823487177132089e-43) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(7.3788279667987478486078980096000000000000e+28), SC_(7.3788279667987478486078980096000000000000e+28), SC_(1.1755200971350565530931192470231204451937e-43) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.2110285949621213703269305548800000000000e+29), SC_(1.2110285949621213703269305548800000000000e+29), SC_(5.5908718690751496153521322929883094013480e-44) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.5675627459944222489782622617600000000000e+29), SC_(2.5675627459944222489782622617600000000000e+29), SC_(1.8110462342888698713130034708115039083540e-44) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(3.6940874261654810399932311142400000000000e+29), SC_(3.6940874261654810399932311142400000000000e+29), SC_(1.0494225253714638031453061402424236164186e-44) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(7.0959714371010081353141059584000000000000e+29), SC_(7.0959714371010081353141059584000000000000e+29), SC_(3.9417887715248635810294861925054143971404e-45) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.0307529873257442803568470917120000000000e+30), SC_(2.0307529873257442803568470917120000000000e+30), SC_(8.1418947679419291958629669368504135508466e-46) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(3.7318536643073322480964646993920000000000e+30), SC_(3.7318536643073322480964646993920000000000e+30), SC_(3.2683174122867076063900066892540299647201e-46) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(6.4040234014314612931042308259840000000000e+30), SC_(6.4040234014314612931042308259840000000000e+30), SC_(1.4538907408092340225382513632512530627004e-46) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.3591440405379759208451461349376000000000e+31), SC_(1.3591440405379759208451461349376000000000e+31), SC_(4.7023278833342860065376684855651586923174e-47) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(3.3548706991994435886603137187840000000000e+31), SC_(3.3548706991994435886603137187840000000000e+31), SC_(1.2125438583023261721596118356642995944174e-47) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(6.2057760084058088674091939659776000000000e+31), SC_(6.2057760084058088674091939659776000000000e+31), SC_(4.8196665441053827803014265044521328436745e-48) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.3704533965093724230190214466764800000000e+32), SC_(1.3704533965093724230190214466764800000000e+32), SC_(1.4686378906513292112999070481163903409364e-48) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.7845325737156862002881598429593600000000e+32), SC_(2.7845325737156862002881598429593600000000e+32), SC_(5.0708723963212168362133117338203669626452e-49) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(5.6730753221070809445480004793139200000000e+32), SC_(5.6730753221070809445480004793139200000000e+32), SC_(1.7437463494176452573758584103072608457383e-49) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.2905320649443607278078011679703040000000e+33), SC_(1.2905320649443607278078011679703040000000e+33), SC_(5.0822723761830381176597034725085270215632e-50) },
|
||||
{ SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.8829105135731812542623926420766720000000e+33), SC_(1.8829105135731812542623926420766720000000e+33), SC_(2.8838098141007479934327118196252617895602e-50) }
|
||||
}};
|
||||
//#undef SC_
|
||||
|
||||
228
test/ellint_rd_xxx.ipp
Normal file
228
test/ellint_rd_xxx.ipp
Normal file
@@ -0,0 +1,228 @@
|
||||
#ifndef SC_
|
||||
# define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
|
||||
#endif
|
||||
static const boost::array<boost::array<T, 4>, 221> ellint_rd_xxx = {{
|
||||
{ SC_(1.3980121253550848455436022016469058470638e-33), SC_(1.3980121253550848455436022016469058470638e-33), SC_(1.3980121253550848455436022016469058470638e-33), SC_(1.9130820318496712875229216324832408264587e+49) },
|
||||
{ SC_(1.7494794261211793309535608228238390754549e-33), SC_(1.7494794261211793309535608228238390754549e-33), SC_(1.7494794261211793309535608228238390754549e-33), SC_(1.3665852869779972929460567093420455622924e+49) },
|
||||
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|
||||
{ SC_(2.8557572558553088000000000000000000000000e+16), SC_(2.8557572558553088000000000000000000000000e+16), SC_(2.8557572558553088000000000000000000000000e+16), SC_(2.0721350966735692041560346691659593278158e-25) },
|
||||
{ SC_(5.7448039442284544000000000000000000000000e+16), SC_(5.7448039442284544000000000000000000000000e+16), SC_(5.7448039442284544000000000000000000000000e+16), SC_(7.2625173372709075817988731803585361348306e-26) },
|
||||
{ SC_(1.1166935585443020800000000000000000000000e+17), SC_(1.1166935585443020800000000000000000000000e+17), SC_(1.1166935585443020800000000000000000000000e+17), SC_(2.6797790249889441376478657893074556432642e-26) },
|
||||
{ SC_(2.4972259272897331200000000000000000000000e+17), SC_(2.4972259272897331200000000000000000000000e+17), SC_(2.4972259272897331200000000000000000000000e+17), SC_(8.0133340420992867452374294355367895337196e-27) },
|
||||
{ SC_(5.5259337852138291200000000000000000000000e+17), SC_(5.5259337852138291200000000000000000000000e+17), SC_(5.5259337852138291200000000000000000000000e+17), SC_(2.4343974532736681000058069022355272982086e-27) },
|
||||
{ SC_(9.7723521452893798400000000000000000000000e+17), SC_(9.7723521452893798400000000000000000000000e+17), SC_(9.7723521452893798400000000000000000000000e+17), SC_(1.0351453546602344224967003388756464660737e-27) },
|
||||
{ SC_(1.4824715277303808000000000000000000000000e+18), SC_(1.4824715277303808000000000000000000000000e+18), SC_(1.4824715277303808000000000000000000000000e+18), SC_(5.5401364133438695077020587760081212866457e-28) },
|
||||
{ SC_(3.8734002442595205120000000000000000000000e+18), SC_(3.8734002442595205120000000000000000000000e+18), SC_(3.8734002442595205120000000000000000000000e+18), SC_(1.3117813031241628231394820272642234623008e-28) },
|
||||
{ SC_(8.1036557834067640320000000000000000000000e+18), SC_(8.1036557834067640320000000000000000000000e+18), SC_(8.1036557834067640320000000000000000000000e+18), SC_(4.3348943965238912629172876802061223034712e-29) },
|
||||
{ SC_(1.2841886794098147328000000000000000000000e+19), SC_(1.2841886794098147328000000000000000000000e+19), SC_(1.2841886794098147328000000000000000000000e+19), SC_(2.1729850794578639427299792767817563216792e-29) },
|
||||
{ SC_(3.2350587576425381888000000000000000000000e+19), SC_(3.2350587576425381888000000000000000000000e+19), SC_(3.2350587576425381888000000000000000000000e+19), SC_(5.4347145753145946959178277776169309459060e-30) },
|
||||
{ SC_(5.7611295478532538368000000000000000000000e+19), SC_(5.7611295478532538368000000000000000000000e+19), SC_(5.7611295478532538368000000000000000000000e+19), SC_(2.2868545243036362403546021192045469279848e-30) },
|
||||
{ SC_(1.0185889793465699532800000000000000000000e+20), SC_(1.0185889793465699532800000000000000000000e+20), SC_(1.0185889793465699532800000000000000000000e+20), SC_(9.7275067423393828543599556836992248128789e-31) },
|
||||
{ SC_(1.7827935411160009932800000000000000000000e+20), SC_(1.7827935411160009932800000000000000000000e+20), SC_(1.7827935411160009932800000000000000000000e+20), SC_(4.2009587968471488750572362027061472656058e-31) },
|
||||
{ SC_(4.6273923221278425088000000000000000000000e+20), SC_(4.6273923221278425088000000000000000000000e+20), SC_(4.6273923221278425088000000000000000000000e+20), SC_(1.0046054213931135883644470099263326087106e-31) },
|
||||
{ SC_(9.0160094215120355328000000000000000000000e+20), SC_(9.0160094215120355328000000000000000000000e+20), SC_(9.0160094215120355328000000000000000000000e+20), SC_(3.6938432729639373749450863473476250731635e-32) },
|
||||
{ SC_(1.2701445734077667737600000000000000000000e+21), SC_(1.2701445734077667737600000000000000000000e+21), SC_(1.2701445734077667737600000000000000000000e+21), SC_(2.2091248674270751061752260956354737147220e-32) },
|
||||
{ SC_(3.3155928298666191749120000000000000000000e+21), SC_(3.3155928298666191749120000000000000000000e+21), SC_(3.3155928298666191749120000000000000000000e+21), SC_(5.2379121758362895910185848055946476645437e-33) },
|
||||
{ SC_(4.9771373655898078576640000000000000000000e+21), SC_(4.9771373655898078576640000000000000000000e+21), SC_(4.9771373655898078576640000000000000000000e+21), SC_(2.8479381893321415974223960789148685276211e-33) },
|
||||
{ SC_(1.2776477955669473886208000000000000000000e+22), SC_(1.2776477955669473886208000000000000000000e+22), SC_(1.2776477955669473886208000000000000000000e+22), SC_(6.9244179743696634091696789337235938404876e-34) },
|
||||
{ SC_(2.8915946875483827732480000000000000000000e+22), SC_(2.8915946875483827732480000000000000000000e+22), SC_(2.8915946875483827732480000000000000000000e+22), SC_(2.0337327051277727008982819400180427993931e-34) },
|
||||
{ SC_(6.0175170680284052979712000000000000000000e+22), SC_(6.0175170680284052979712000000000000000000e+22), SC_(6.0175170680284052979712000000000000000000e+22), SC_(6.7744494087600150203765673017484711578262e-35) },
|
||||
{ SC_(1.3443007097640605397811200000000000000000e+23), SC_(1.3443007097640605397811200000000000000000e+23), SC_(1.3443007097640605397811200000000000000000e+23), SC_(2.0288753146104063272103101319477436751656e-35) },
|
||||
{ SC_(2.0496508805231257269043200000000000000000e+23), SC_(2.0496508805231257269043200000000000000000e+23), SC_(2.0496508805231257269043200000000000000000e+23), SC_(1.0776560212334060415241952783961381215531e-35) },
|
||||
{ SC_(5.8451880892949689322700800000000000000000e+23), SC_(5.8451880892949689322700800000000000000000e+23), SC_(5.8451880892949689322700800000000000000000e+23), SC_(2.2377020720091407413010659087995982032280e-36) },
|
||||
{ SC_(1.1877492456483867611627520000000000000000e+24), SC_(1.1877492456483867611627520000000000000000e+24), SC_(1.1877492456483867611627520000000000000000e+24), SC_(7.7252555568665586603456786042795749256475e-37) },
|
||||
{ SC_(1.3659727517469077458124800000000000000000e+24), SC_(1.3659727517469077458124800000000000000000e+24), SC_(1.3659727517469077458124800000000000000000e+24), SC_(6.2637864895364561301401520132953130469257e-37) },
|
||||
{ SC_(2.7912598561413239479992320000000000000000e+24), SC_(2.7912598561413239479992320000000000000000e+24), SC_(2.7912598561413239479992320000000000000000e+24), SC_(2.1443693720668992815087263609302554517038e-37) },
|
||||
{ SC_(7.5863641567366151374110720000000000000000e+24), SC_(7.5863641567366151374110720000000000000000e+24), SC_(7.5863641567366151374110720000000000000000e+24), SC_(4.7857440881650091612417628752981254574601e-38) },
|
||||
{ SC_(1.3490721907030264366759936000000000000000e+25), SC_(1.3490721907030264366759936000000000000000e+25), SC_(1.3490721907030264366759936000000000000000e+25), SC_(2.0181210624874437322755542031848925852443e-38) },
|
||||
{ SC_(2.8422143749589281569505280000000000000000e+25), SC_(2.8422143749589281569505280000000000000000e+25), SC_(2.8422143749589281569505280000000000000000e+25), SC_(6.5995565192110303816586016066095847879993e-39) },
|
||||
{ SC_(5.3668403805728358185041920000000000000000e+25), SC_(5.3668403805728358185041920000000000000000e+25), SC_(5.3668403805728358185041920000000000000000e+25), SC_(2.5434428391334568706163940836113767799054e-39) },
|
||||
{ SC_(7.8292113919495847997865984000000000000000e+25), SC_(7.8292113919495847997865984000000000000000e+25), SC_(7.8292113919495847997865984000000000000000e+25), SC_(1.4435205502650156869693831753504925796075e-39) },
|
||||
{ SC_(2.6723325902934740461577830400000000000000e+26), SC_(2.6723325902934740461577830400000000000000e+26), SC_(2.6723325902934740461577830400000000000000e+26), SC_(2.2890972193469096777795156856123092483278e-40) },
|
||||
{ SC_(4.1381935158038852363563827200000000000000e+26), SC_(4.1381935158038852363563827200000000000000e+26), SC_(4.1381935158038852363563827200000000000000e+26), SC_(1.1879107327559925906773287960526392067809e-40) },
|
||||
{ SC_(8.5948309609429296171135795200000000000000e+26), SC_(8.5948309609429296171135795200000000000000e+26), SC_(8.5948309609429296171135795200000000000000e+26), SC_(3.9686608830175590814715691622534817404011e-41) },
|
||||
{ SC_(1.4387120406003935998650613760000000000000e+27), SC_(1.4387120406003935998650613760000000000000e+27), SC_(1.4387120406003935998650613760000000000000e+27), SC_(1.8324797437566406076041039429974310120006e-41) },
|
||||
{ SC_(4.7722405758868522542091468800000000000000e+27), SC_(4.7722405758868522542091468800000000000000e+27), SC_(4.7722405758868522542091468800000000000000e+27), SC_(3.0333079720467397282520192477118791550916e-42) },
|
||||
{ SC_(8.8848657238129553346144501760000000000000e+27), SC_(8.8848657238129553346144501760000000000000e+27), SC_(8.8848657238129553346144501760000000000000e+27), SC_(1.1940532551473316279692357164340213043762e-42) },
|
||||
{ SC_(1.4222615588981551190220210176000000000000e+28), SC_(1.4222615588981551190220210176000000000000e+28), SC_(1.4222615588981551190220210176000000000000e+28), SC_(5.8956377632246711579832955264973200436422e-43) },
|
||||
{ SC_(2.5971287269650318385179787264000000000000e+28), SC_(2.5971287269650318385179787264000000000000e+28), SC_(2.5971287269650318385179787264000000000000e+28), SC_(2.3892400495228539274598050730404314792108e-43) },
|
||||
{ SC_(7.3788279667987478486078980096000000000000e+28), SC_(7.3788279667987478486078980096000000000000e+28), SC_(7.3788279667987478486078980096000000000000e+28), SC_(4.9890622443442454143628998892754947824020e-44) },
|
||||
{ SC_(1.2110285949621213703269305548800000000000e+29), SC_(1.2110285949621213703269305548800000000000e+29), SC_(1.2110285949621213703269305548800000000000e+29), SC_(2.3728397177512905263928217528665158827501e-44) },
|
||||
{ SC_(2.5675627459944222489782622617600000000000e+29), SC_(2.5675627459944222489782622617600000000000e+29), SC_(2.5675627459944222489782622617600000000000e+29), SC_(7.6863189428009715118983101443511744090196e-45) },
|
||||
{ SC_(3.6940874261654810399932311142400000000000e+29), SC_(3.6940874261654810399932311142400000000000e+29), SC_(3.6940874261654810399932311142400000000000e+29), SC_(4.4538875281292909532958673539665046029890e-45) },
|
||||
{ SC_(7.0959714371010081353141059584000000000000e+29), SC_(7.0959714371010081353141059584000000000000e+29), SC_(7.0959714371010081353141059584000000000000e+29), SC_(1.6729471136328311706955118425734608582646e-45) },
|
||||
{ SC_(2.0307529873257442803568470917120000000000e+30), SC_(2.0307529873257442803568470917120000000000e+30), SC_(2.0307529873257442803568470917120000000000e+30), SC_(3.4555274625386616585934609941429203994493e-46) },
|
||||
{ SC_(3.7318536643073322480964646993920000000000e+30), SC_(3.7318536643073322480964646993920000000000e+30), SC_(3.7318536643073322480964646993920000000000e+30), SC_(1.3871169913566441993441180101040613652334e-46) },
|
||||
{ SC_(6.4040234014314612931042308259840000000000e+30), SC_(6.4040234014314612931042308259840000000000e+30), SC_(6.4040234014314612931042308259840000000000e+30), SC_(6.1705039497420584674312487188888623304008e-47) },
|
||||
{ SC_(1.3591440405379759208451461349376000000000e+31), SC_(1.3591440405379759208451461349376000000000e+31), SC_(1.3591440405379759208451461349376000000000e+31), SC_(1.9957299377906691708015705180778289952633e-47) },
|
||||
{ SC_(3.3548706991994435886603137187840000000000e+31), SC_(3.3548706991994435886603137187840000000000e+31), SC_(3.3548706991994435886603137187840000000000e+31), SC_(5.1461959670542379650843010267432936776139e-48) },
|
||||
{ SC_(6.2057760084058088674091939659776000000000e+31), SC_(6.2057760084058088674091939659776000000000e+31), SC_(6.2057760084058088674091939659776000000000e+31), SC_(2.0455300121306774873511328924430576723673e-48) },
|
||||
{ SC_(1.3704533965093724230190214466764800000000e+32), SC_(1.3704533965093724230190214466764800000000e+32), SC_(1.3704533965093724230190214466764800000000e+32), SC_(6.2330927975790268155461535096378223350591e-49) },
|
||||
{ SC_(2.7845325737156862002881598429593600000000e+32), SC_(2.7845325737156862002881598429593600000000e+32), SC_(2.7845325737156862002881598429593600000000e+32), SC_(2.1521450871007098580247264140643505142883e-49) },
|
||||
{ SC_(5.6730753221070809445480004793139200000000e+32), SC_(5.6730753221070809445480004793139200000000e+32), SC_(5.6730753221070809445480004793139200000000e+32), SC_(7.4006893602204152108633305656949585309562e-50) },
|
||||
{ SC_(1.2905320649443607278078011679703040000000e+33), SC_(1.2905320649443607278078011679703040000000e+33), SC_(1.2905320649443607278078011679703040000000e+33), SC_(2.1569833888237949750965877861010398088413e-50) },
|
||||
{ SC_(1.8829105135731812542623926420766720000000e+33), SC_(1.8829105135731812542623926420766720000000e+33), SC_(1.8829105135731812542623926420766720000000e+33), SC_(1.2239268982694768381667683394968955347577e-50) }
|
||||
}};
|
||||
//#undef SC_
|
||||
|
||||
2217
test/ellint_rd_xxz.ipp
Normal file
2217
test/ellint_rd_xxz.ipp
Normal file
File diff suppressed because it is too large
Load Diff
4427
test/ellint_rd_xyy.ipp
Normal file
4427
test/ellint_rd_xyy.ipp
Normal file
File diff suppressed because it is too large
Load Diff
@@ -229,5 +229,21 @@ void test_spots(T, const char* type_name)
|
||||
#include "ellint_rd_data.ipp"
|
||||
|
||||
do_test_ellint_rd<T>(ellint_rd_data, type_name, "RD: Random data");
|
||||
|
||||
#include "ellint_rd_xyy.ipp"
|
||||
|
||||
do_test_ellint_rd<T>(ellint_rd_xyy, type_name, "RD: y = z");
|
||||
|
||||
#include "ellint_rd_xxz.ipp"
|
||||
|
||||
do_test_ellint_rd<T>(ellint_rd_xxz, type_name, "RD: x = y");
|
||||
|
||||
#include "ellint_rd_0yy.ipp"
|
||||
|
||||
do_test_ellint_rd<T>(ellint_rd_0yy, type_name, "RD: x = 0, y = z");
|
||||
|
||||
#include "ellint_rd_xxx.ipp"
|
||||
|
||||
do_test_ellint_rd<T>(ellint_rd_xxx, type_name, "RD: x = y = z");
|
||||
}
|
||||
|
||||
|
||||
@@ -146,6 +146,83 @@ T ellint_rj_old(T x, T y, T z, T p, const Policy& pol)
|
||||
return value;
|
||||
}
|
||||
|
||||
template <typename T, typename Policy>
|
||||
T ellint_rd_imp_old(T x, T y, T z, const Policy& pol)
|
||||
{
|
||||
T value, u, lambda, sigma, factor, tolerance;
|
||||
T X, Y, Z, EA, EB, EC, ED, EE, S1, S2;
|
||||
unsigned long k;
|
||||
|
||||
BOOST_MATH_STD_USING
|
||||
using namespace boost::math;
|
||||
|
||||
static const char* function = "boost::math::ellint_rd<%1%>(%1%,%1%,%1%)";
|
||||
|
||||
if(x < 0)
|
||||
{
|
||||
return policies::raise_domain_error<T>(function,
|
||||
"Argument x must be >= 0, but got %1%", x, pol);
|
||||
}
|
||||
if(y < 0)
|
||||
{
|
||||
return policies::raise_domain_error<T>(function,
|
||||
"Argument y must be >= 0, but got %1%", y, pol);
|
||||
}
|
||||
if(z <= 0)
|
||||
{
|
||||
return policies::raise_domain_error<T>(function,
|
||||
"Argument z must be > 0, but got %1%", z, pol);
|
||||
}
|
||||
if(x + y == 0)
|
||||
{
|
||||
return policies::raise_domain_error<T>(function,
|
||||
"At most one argument can be zero, but got, x + y = %1%", x + y, pol);
|
||||
}
|
||||
|
||||
// error scales as the 6th power of tolerance
|
||||
tolerance = pow(tools::epsilon<T>() / 3, T(1) / 6);
|
||||
|
||||
// duplication
|
||||
sigma = 0;
|
||||
factor = 1;
|
||||
k = 1;
|
||||
do
|
||||
{
|
||||
u = (x + y + z + z + z) / 5;
|
||||
X = (u - x) / u;
|
||||
Y = (u - y) / u;
|
||||
Z = (u - z) / u;
|
||||
if((tools::max)(abs(X), abs(Y), abs(Z)) < tolerance)
|
||||
break;
|
||||
T sx = sqrt(x);
|
||||
T sy = sqrt(y);
|
||||
T sz = sqrt(z);
|
||||
lambda = sy * (sx + sz) + sz * sx; //sqrt(x * y) + sqrt(y * z) + sqrt(z * x);
|
||||
sigma += factor / (sz * (z + lambda));
|
||||
factor /= 4;
|
||||
x = (x + lambda) / 4;
|
||||
y = (y + lambda) / 4;
|
||||
z = (z + lambda) / 4;
|
||||
++k;
|
||||
} while(k < policies::get_max_series_iterations<Policy>());
|
||||
|
||||
// Check to see if we gave up too soon:
|
||||
policies::check_series_iterations<T>(function, k, pol);
|
||||
|
||||
// Taylor series expansion to the 5th order
|
||||
EA = X * Y;
|
||||
EB = Z * Z;
|
||||
EC = EA - EB;
|
||||
ED = EA - 6 * EB;
|
||||
EE = ED + EC + EC;
|
||||
S1 = ED * (ED * T(9) / 88 - Z * EE * T(9) / 52 - T(3) / 14);
|
||||
S2 = Z * (EE / 6 + Z * (-EC * T(9) / 22 + Z * EA * T(3) / 26));
|
||||
value = 3 * sigma + factor * (1 + S1 + S2) / (u * sqrt(u));
|
||||
|
||||
return value;
|
||||
}
|
||||
|
||||
|
||||
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rj_data_4e(mp_t n)
|
||||
{
|
||||
mp_t result = ellint_rj_old(n, n, n, n, boost::math::policies::policy<>());
|
||||
@@ -182,6 +259,30 @@ boost::math::tuple<mp_t, mp_t, mp_t, mp_t, mp_t> generate_rj_data_2e_4(mp_t x, m
|
||||
return boost::math::make_tuple(x, y, p, p, r);
|
||||
}
|
||||
|
||||
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rd_data_2e_1(mp_t x, mp_t y)
|
||||
{
|
||||
mp_t r = ellint_rd_imp_old(x, y, y, boost::math::policies::policy<>());
|
||||
return boost::math::make_tuple(x, y, y, r);
|
||||
}
|
||||
|
||||
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rd_data_2e_2(mp_t x, mp_t y)
|
||||
{
|
||||
mp_t r = ellint_rd_imp_old(x, x, y, boost::math::policies::policy<>());
|
||||
return boost::math::make_tuple(x, x, y, r);
|
||||
}
|
||||
|
||||
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rd_data_2e_3(mp_t x)
|
||||
{
|
||||
mp_t r = ellint_rd_imp_old(mp_t(0), x, x, boost::math::policies::policy<>());
|
||||
return boost::math::make_tuple(0, x, x, r);
|
||||
}
|
||||
|
||||
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rd_data_3e(mp_t x)
|
||||
{
|
||||
mp_t r = ellint_rd_imp_old(x, x, x, boost::math::policies::policy<>());
|
||||
return boost::math::make_tuple(x, x, x, r);
|
||||
}
|
||||
|
||||
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rf_data(mp_t n)
|
||||
{
|
||||
static boost::mt19937 r;
|
||||
@@ -294,12 +395,12 @@ int cpp_main(int argc, char*argv [])
|
||||
cont = (line == "y");
|
||||
#else
|
||||
get_user_parameter_info(arg1, "x");
|
||||
get_user_parameter_info(arg2, "y");
|
||||
get_user_parameter_info(arg3, "p");
|
||||
//get_user_parameter_info(arg2, "y");
|
||||
//get_user_parameter_info(arg3, "p");
|
||||
arg1.type |= dummy_param;
|
||||
arg2.type |= dummy_param;
|
||||
arg3.type |= dummy_param;
|
||||
data.insert(generate_rj_data_2e_4, arg1, arg2, arg3);
|
||||
//arg2.type |= dummy_param;
|
||||
//arg3.type |= dummy_param;
|
||||
data.insert(generate_rd_data_3e, arg1);
|
||||
|
||||
std::cout << "Any more data [y/n]?";
|
||||
std::getline(std::cin, line);
|
||||
|
||||
Reference in New Issue
Block a user