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// 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_ENABLE_ASSERT_HANDLER
#define BOOST_MATH_MAX_SERIES_ITERATION_POLICY INT_MAX
// for consistent behaviour across compilers/platforms:
#define BOOST_MATH_PROMOTE_DOUBLE_POLICY false
// overflow to infinity is OK, we treat these as zero error as long as the sign is correct!
#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
#include <iostream>
#include <ctime>
#include <boost/multiprecision/mpfr.hpp>
#include <boost/multiprecision/cpp_bin_float.hpp>
#include <boost/math/special_functions/hypergeometric_1F1.hpp>
#include <boost/math/special_functions/hypergeometric_pFq.hpp>
#include <boost/math/special_functions/relative_difference.hpp>
#include <boost/random.hpp>
#include <set>
#include <fstream>
#include <boost/iostreams/tee.hpp>
#include <boost/iostreams/stream.hpp>
using boost::multiprecision::mpfr_float;
namespace boost {
//
// We convert assertions into exceptions, so we can log them and continue:
//
void assertion_failed(char const * expr, char const *, char const * file, long line)
{
std::ostringstream oss;
oss << file << ":" << line << " Assertion failed: " << expr;
throw std::runtime_error(oss.str());
}
}
typedef boost::multiprecision::cpp_bin_float_quad test_type;
int main()
{
using std::floor;
using std::ceil;
try {
test_type a_start, a_end;
test_type b_start, b_end;
test_type a_mult, b_mult;
std::cout << "Enter range for parameter a: ";
std::cin >> a_start >> a_end;
std::cout << "Enter range for parameter b: ";
std::cin >> b_start >> b_end;
std::cout << "Enter multiplier for a parameter: ";
std::cin >> a_mult;
std::cout << "Enter multiplier for b parameter: ";
std::cin >> b_mult;
double error_limit = 200;
double time_limit = 10.0;
for (test_type a = a_start; a < a_end; a_start < 0 ? a /= a_mult : a *= a_mult)
{
for (test_type b = b_start; b < b_end; b_start < 0 ? b /= b_mult : b *= b_mult)
{
test_type z_mult = 2;
test_type last_good = 0;
test_type bad = 0;
try {
for (test_type z = 1; z < 1e10; z *= z_mult, z_mult *= 2)
{
// std::cout << "z = " << z << std::endl;
std::uintmax_t max_iter = 1000;
test_type calc = boost::math::tools::function_ratio_from_forwards_recurrence(boost::math::detail::hypergeometric_1F1_recurrence_a_and_b_coefficients<test_type>(a, b, z), std::numeric_limits<test_type>::epsilon() * 2, max_iter);
test_type reference = (test_type)(boost::math::hypergeometric_pFq_precision({ mpfr_float(a) }, { mpfr_float(b) }, mpfr_float(z), 50, time_limit) / boost::math::hypergeometric_pFq_precision({ mpfr_float(a + 1) }, { mpfr_float(b + 1) }, mpfr_float(z), std::numeric_limits<test_type>::digits10 * 2, time_limit));
double err = (double)boost::math::epsilon_difference(reference, calc);
if (err < error_limit)
{
last_good = z;
break;
}
else
{
bad = z;
}
}
}
catch (const std::exception& e)
{
std::cout << "Unexpected exception: " << e.what() << std::endl;
std::cout << "For a = " << a << " b = " << b << " z = " << bad * z_mult / 2 << std::endl;
}
test_type z_limit;
if (0 == bad)
z_limit = 1; // Any z is large enough
else if (0 == last_good)
z_limit = std::numeric_limits<test_type > ::infinity();
else
{
//
// At this stage last_good and bad should bracket the edge of the domain, bisect to narrow things down:
//
z_limit = last_good == 0 ? 0 : boost::math::tools::bisect([&a, b, error_limit, time_limit](test_type z)
{
std::uintmax_t max_iter = 1000;
test_type calc = boost::math::tools::function_ratio_from_forwards_recurrence(boost::math::detail::hypergeometric_1F1_recurrence_a_and_b_coefficients<test_type>(a, b, z), std::numeric_limits<test_type>::epsilon() * 2, max_iter);
test_type reference = (test_type)(boost::math::hypergeometric_pFq_precision({ mpfr_float(a) }, { mpfr_float(b) }, mpfr_float(z), 50, time_limit + 20) / boost::math::hypergeometric_pFq_precision({ mpfr_float(a + 1) }, { mpfr_float(b + 1) }, mpfr_float(z), std::numeric_limits<test_type>::digits10 * 2, time_limit + 20));
test_type err = boost::math::epsilon_difference(reference, calc);
return err < error_limit ? 1 : -1;
}, bad, last_good, boost::math::tools::equal_floor()).first;
z_limit = floor(z_limit + 2); // Give ourselves some headroom!
}
// std::cout << "z_limit = " << z_limit << std::endl;
//
// Now over again for backwards recurrence domain at the same points:
//
bad = z_limit > 1e10 ? 1e10 : z_limit;
last_good = 0;
z_mult = 1.1;
for (test_type z = bad; z > 1; z /= z_mult, z_mult *= 2)
{
// std::cout << "z = " << z << std::endl;
try {
std::uintmax_t max_iter = 1000;
test_type calc = boost::math::tools::function_ratio_from_backwards_recurrence(boost::math::detail::hypergeometric_1F1_recurrence_a_and_b_coefficients<test_type>(a, b, z), std::numeric_limits<test_type>::epsilon() * 2, max_iter);
test_type reference = (test_type)(boost::math::hypergeometric_pFq_precision({ mpfr_float(a) }, { mpfr_float(b) }, mpfr_float(z), 50, time_limit) / boost::math::hypergeometric_pFq_precision({ mpfr_float(a - 1) }, { mpfr_float(b - 1) }, mpfr_float(z), std::numeric_limits<test_type>::digits10 * 2, time_limit));
test_type err = boost::math::epsilon_difference(reference, calc);
if (err < error_limit)
{
last_good = z;
break;
}
else
{
bad = z;
}
}
catch (const std::exception& e)
{
bad = z;
std::cout << "Unexpected exception: " << e.what() << std::endl;
std::cout << "For a = " << a << " b = " << b << " z = " << z << std::endl;
}
}
test_type lower_z_limit;
if (last_good < 1)
lower_z_limit = 0;
else if (last_good >= bad)
{
std::uintmax_t max_iter = 1000;
test_type z = bad;
test_type calc = boost::math::tools::function_ratio_from_forwards_recurrence(boost::math::detail::hypergeometric_1F1_recurrence_a_and_b_coefficients<test_type>(a, b, z), std::numeric_limits<test_type>::epsilon() * 2, max_iter);
test_type reference = (test_type)(boost::math::hypergeometric_pFq_precision({ mpfr_float(a) }, { mpfr_float(b) }, mpfr_float(z), 50, time_limit) / boost::math::hypergeometric_pFq_precision({ mpfr_float(a + 1) }, { mpfr_float(b + 1) }, mpfr_float(z), std::numeric_limits<test_type>::digits10 * 2, time_limit));
test_type err = boost::math::epsilon_difference(reference, calc);
if (err < error_limit)
{
lower_z_limit = bad; // Both forwards and backwards iteration work!!!
}
else
throw std::runtime_error("Internal logic failed!");
}
else
{
//
// At this stage last_good and bad should bracket the edge of the domain, bisect to narrow things down:
//
lower_z_limit = last_good == 0 ? 0 : boost::math::tools::bisect([&a, b, error_limit, time_limit](test_type z)
{
std::uintmax_t max_iter = 1000;
test_type calc = boost::math::tools::function_ratio_from_backwards_recurrence(boost::math::detail::hypergeometric_1F1_recurrence_a_and_b_coefficients<test_type>(a, b, z), std::numeric_limits<test_type>::epsilon() * 2, max_iter);
test_type reference = (test_type)(boost::math::hypergeometric_pFq_precision({ mpfr_float(a) }, { mpfr_float(b) }, mpfr_float(z), 50, time_limit + 20) / boost::math::hypergeometric_pFq_precision({ mpfr_float(a - 1) }, { mpfr_float(b - 1) }, mpfr_float(z), std::numeric_limits<test_type>::digits10 * 2, time_limit + 20));
test_type err = boost::math::epsilon_difference(reference, calc);
return err < error_limit ? 1 : -1;
}, last_good, bad, boost::math::tools::equal_floor()).first;
z_limit = ceil(z_limit - 2); // Give ourselves some headroom!
}
std::cout << std::setprecision(std::numeric_limits<test_type>::max_digits10) << "{ " << a << ", " << b << ", " << lower_z_limit << ", " << z_limit << "}," << std::endl;
}
}
}
catch (const std::exception& e)
{
std::cout << "Unexpected exception: " << e.what() << std::endl;
}
return 0;
}
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