Hypergeometric: start testing larger arguments to 1F1 and begin to fix the errors.

include/boost/math/special_functions/detail/hypergeometric_1f1_scaled_series.hpp

@@ -0,0 +1,54 @@
+
+///////////////////////////////////////////////////////////////////////////////
+//  Copyright 2017 John Maddock
+//  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)
+//
+#ifndef BOOST_MATH_HYPERGEOMETRIC_1F1_SCALED_SERIES_HPP
+  #define BOOST_MATH_HYPERGEOMETRIC_1F1_SCALED_SERIES_HPP
+
+  #include <boost/array.hpp>
+
+  namespace boost{ namespace math{ namespace detail{
+
+     template <class T, class Policy>
+     T hypergeometric_1f1_scaled_series(const T& a, const T& b, const T& z, const Policy& pol, const char* function)
+     {
+        BOOST_MATH_STD_USING_CORE
+        //
+        // Result is returned scaled by e^-z.
+        // Whenever the terms start becoming too large, we scale by some factor e^-n
+        // and keep track of the integer scaling factor n.  At the end we can perform
+        // an exact subtraction of n from z and scale the result:
+        //
+        T sum(0), term(1), upper_limit(sqrt(boost::math::tools::max_value<T>())), diff;
+        unsigned n = 0;
+        boost::intmax_t log_scaling_factor = -boost::math::itrunc(boost::math::tools::log_max_value<T>());
+        T scaling_factor = exp(log_scaling_factor);
+        boost::intmax_t current_scaling = 0;
+
+        do
+        {
+           sum += term;
+           if (sum >= upper_limit)
+           {
+              sum *= scaling_factor;
+              term *= scaling_factor;
+              current_scaling += log_scaling_factor;
+           }
+           term *= (((a + n) / ((b + n) * (n + 1))) * z);
+           if (n > boost::math::policies::get_max_series_iterations<Policy>())
+              return boost::math::policies::raise_evaluation_error(function, "Series did not converge, best value is %1%", sum, pol);
+           ++n;
+           diff = fabs(term / sum);
+        } while (diff > boost::math::policies::get_epsilon<T, Policy>());
+
+        return sum * exp(-z - current_scaling);
+     }
+
+
+
+  } } } // namespaces
+
+#endif // BOOST_MATH_HYPERGEOMETRIC_1F1_SCALED_SERIES_HPP

tools/hyp_1f1_big_data.cpp

@@ -0,0 +1,160 @@
+//  (C) Copyright John Maddock 2006.
+//  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)
+
+#define BOOST_MATH_MAX_SERIES_ITERATION_POLICY 10000000
+
+#include <boost/math/special_functions/hypergeometric_1f1.hpp>
+#include <boost/math/constants/constants.hpp>
+#include <boost/lexical_cast.hpp>
+#include <fstream>
+#include <map>
+#include <boost/math/tools/test_data.hpp>
+#include <boost/random.hpp>
+#define BOOST_MATH_USE_MPFR
+#include "mp_t.hpp"
+
+#include <boost/multiprecision/mpfi.hpp>
+
+using namespace boost::math::tools;
+using namespace boost::math;
+using namespace std;
+using namespace boost::multiprecision;
+
+typedef mpfi_float_1000 mpfi_type;
+
+mp_t hypergeometric_1f1_generic_series(mp_t a_, mp_t b_, mp_t z_)
+{
+   mpfi_type a(a_), b(b_), z(z_), sum(0), term(1), diff;
+   unsigned n = 0;
+
+   do
+   {
+      sum += term;
+      term *= (((a + n) / ((b + n) * (n + 1))) * z);
+      ++n;
+      diff = fabs(term / sum);
+      if (n > 10000000)
+      {
+         std::cout << "Aborting series evaluation due to too many iterations...\n";
+         throw evaluation_error("");
+      }
+      if (fabs(upper(sum)) > std::numeric_limits<double>::max())
+      {
+         std::cout << "Aborting series evaluation due to over large sum...\n";
+         throw evaluation_error("");
+      }
+   } while (upper(diff) > 1e-40);
+
+   mp_t r = mp_t(width(sum) / median(sum));
+   if (fabs(r) > 1e-40)
+   {
+      std::cout << "Aborting to to error in result of " << r << std::endl;
+         throw evaluation_error("");
+   }
+   std::cout << "Found error in sum was " << r << std::endl;
+
+   return mp_t(median(sum));
+}
+
+
+struct hypergeometric_1f1_gen
+{
+   mp_t operator()(mp_t a1, mp_t a2, mp_t z)
+   {
+      mp_t result;
+      try {
+         result = hypergeometric_1f1_generic_series(a1, a2, z);
+         std::cout << a1 << " " << a2 << " " << z << " " << result << std::endl;
+      }
+      catch (...)
+      {
+         throw std::domain_error("");
+      }
+      if (fabs(result) > std::numeric_limits<double>::max())
+      {
+         std::cout << "Rejecting over large value\n";
+         throw std::domain_error("");
+      }
+      return result;
+   }
+};
+
+
+int main(int, char* [])
+{
+   parameter_info<mp_t> arg1, arg2, arg3;
+   test_data<mp_t> data;
+
+   std::cout << "Welcome.\n"
+      "This program will generate spot tests for 1F1 (Yeh!!):\n";
+
+   std::string line;
+   bool cont;
+
+   std::vector<mp_t> v;
+   random_ns::mt19937 rnd;
+   random_ns::uniform_real_distribution<float> ur_a(0, 1);
+
+   mp_t p = ur_a(rnd);
+   p *= 1e6;
+   v.push_back(p);
+   v.push_back(-p);
+   p = ur_a(rnd);
+   p *= 1e5;
+   v.push_back(p);
+   v.push_back(-p);
+   p = ur_a(rnd);
+   p *= 1e4;
+   v.push_back(p);
+   v.push_back(-p);
+   p = ur_a(rnd);
+   p *= 1e3;
+   v.push_back(p);
+   v.push_back(-p);
+   p = ur_a(rnd);
+   p *= 1e2;
+   v.push_back(p);
+   v.push_back(-p);
+   p = ur_a(rnd);
+   p *= 1e-5;
+   v.push_back(p);
+   v.push_back(-p);
+   p = ur_a(rnd);
+   p *= 1e-12;
+   v.push_back(p);
+   v.push_back(-p);
+   p = ur_a(rnd);
+   p *= 1e-30;
+   v.push_back(p);
+   v.push_back(-p);
+
+   for (unsigned i = 0; i < v.size(); ++i)
+   {
+      for (unsigned j = 0; j < v.size(); ++j)
+      {
+         for (unsigned k = 0; k < v.size(); ++k)
+         {
+            arg1 = make_single_param(v[i]);
+            arg2 = make_single_param(mp_t(v[j] * 3 / 2));
+            arg3 = make_single_param(mp_t(v[k] * 5 / 4));
+            data.insert(hypergeometric_1f1_gen(), arg1, arg2, arg3);
+         }
+      }
+   }
+
+
+   std::cout << "Enter name of test data file [default=hypergeometric_1f1.ipp]";
+   std::getline(std::cin, line);
+   boost::algorithm::trim(line);
+   if(line == "")
+      line = "hypergeometric_1f1.ipp";
+   std::ofstream ofs(line.c_str());
+   ofs << std::scientific << std::setprecision(40);
+   write_code(ofs, data, line.c_str());
+   
+   return 0;
+}
+
+