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///////////////////////////////////////////////////////////////
// Copyright 2021 John Maddock. Distributed under the Boost
// Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at https://www.boost.org/LICENSE_1_0.txt
//
#ifdef _MSC_VER
#define _SCL_SECURE_NO_WARNINGS
#endif
#include <thread>
#include <boost/detail/lightweight_test.hpp>
#include <array>
#include <boost/math/special_functions/relative_difference.hpp>
#include <boost/math/special_functions/gamma.hpp>
#include <boost/math/quadrature/tanh_sinh.hpp>
#include "test.hpp"
#if !defined(TEST_MPF_50) && !defined(TEST_MPFR_50)
#define TEST_MPF_50
#define TEST_MPFR_50
#ifdef _MSC_VER
#pragma message("CAUTION!!: No backend type specified so testing everything.... this will take some time!!")
#endif
#ifdef __GNUC__
#pragma warning "CAUTION!!: No backend type specified so testing everything.... this will take some time!!"
#endif
#endif
#include <boost/multiprecision/mpfr.hpp>
#if defined(TEST_MPF_50)
#include <boost/multiprecision/gmp.hpp>
#endif
template <class T>
void thread_test_proc(unsigned digits)
{
typedef boost::multiprecision::number<boost::multiprecision::mpfr_float_backend<1000> > mpfr_float_1000;
if (!mpfr_buildopt_tls_p())
return;
T::thread_default_precision(digits);
T result, value;
value = boost::math::constants::pi<T>();
result.assign(boost::math::constants::pi<mpfr_float_1000>().str());
BOOST_CHECK_LE(boost::math::epsilon_difference(value, result), 20);
BOOST_CHECK_EQUAL(value.precision(), digits);
for (unsigned i = 20; i < 500; ++i)
{
T arg(i);
arg /= 3;
value = boost::math::tgamma(arg);
BOOST_CHECK_EQUAL(value.precision(), digits);
result.assign(boost::math::tgamma(mpfr_float_1000(arg)).str());
BOOST_CHECK_LE(boost::math::epsilon_difference(value, result), 800);
}
//
// Try tanh_sinh integration:
//
using namespace boost::math::constants;
boost::math::quadrature::tanh_sinh<T> integrator;
T tol = 500;
// Example 1:
auto f1 = [](const T& t) { return static_cast<T>(t * boost::math::log1p(t)); };
T Q = integrator.integrate(f1, (T)0, (T)1);
T Q_expected = half<T>() * half<T>();
BOOST_CHECK_EQUAL(Q.precision(), digits);
BOOST_CHECK_EQUAL(Q_expected.precision(), digits);
BOOST_CHECK_LE(boost::math::epsilon_difference(Q, Q_expected), tol);
// Example 2:
auto f2 = [](const T& t) { return static_cast<T>(t * t * atan(t)); };
Q = integrator.integrate(f2, (T)0, (T)1);
Q_expected = (pi<T>() - 2 + 2 * ln_two<T>()) / 12;
BOOST_CHECK_EQUAL(Q.precision(), digits);
BOOST_CHECK_EQUAL(Q_expected.precision(), digits);
BOOST_CHECK_LE(boost::math::epsilon_difference(Q, Q_expected), tol);
// Example 3:
auto f3 = [](const T& t) { return static_cast<T>(exp(t) * cos(t)); };
Q = integrator.integrate(f3, (T)0, half_pi<T>());
Q_expected = boost::math::expm1(half_pi<T>()) * half<T>();
BOOST_CHECK_EQUAL(Q.precision(), digits);
BOOST_CHECK_EQUAL(Q_expected.precision(), digits);
BOOST_CHECK_LE(boost::math::epsilon_difference(Q, Q_expected), tol);
// Example 4:
auto f4 = [](T x) -> T { T t0 = sqrt(x*x + 2); return atan(t0)/(t0*(x*x+1)); };
Q = integrator.integrate(f4, (T)0, (T)1);
Q_expected = 5 * pi<T>() * pi<T>() / 96;
BOOST_CHECK_EQUAL(Q.precision(), digits);
BOOST_CHECK_EQUAL(Q_expected.precision(), digits);
BOOST_CHECK_LE(boost::math::epsilon_difference(Q, Q_expected), tol);
// Example 5:
auto f5 = [](const T& t)->T { return sqrt(t) * log(t); };
Q = integrator.integrate(f5, (T)0, (T)1);
Q_expected = -4 / (T)9;
BOOST_CHECK_EQUAL(Q.precision(), digits);
BOOST_CHECK_EQUAL(Q_expected.precision(), digits);
BOOST_CHECK_LE(boost::math::epsilon_difference(Q, Q_expected), tol);
// Example 6:
auto f6 = [](const T& t)->T { return sqrt(1 - t * t); };
Q = integrator.integrate(f6, (T)0, (T)1);
Q_expected = pi<T>() / 4;
BOOST_CHECK_EQUAL(Q.precision(), digits);
BOOST_CHECK_EQUAL(Q_expected.precision(), digits);
BOOST_CHECK_LE(boost::math::epsilon_difference(Q, Q_expected), tol);
}
int main()
{
#ifdef TEST_MPF_50
{
std::thread t1(thread_test_proc<boost::multiprecision::mpf_float>, 35);
std::thread t2(thread_test_proc<boost::multiprecision::mpf_float>, 55);
std::thread t3(thread_test_proc<boost::multiprecision::mpf_float>, 75);
std::thread t4(thread_test_proc<boost::multiprecision::mpf_float>, 105);
std::thread t5(thread_test_proc<boost::multiprecision::mpf_float>, 305);
t1.join();
t2.join();
t3.join();
t4.join();
t5.join();
}
#endif
#ifdef TEST_MPFR_50
{
std::thread t1(thread_test_proc<boost::multiprecision::mpfr_float>, 35);
std::thread t2(thread_test_proc<boost::multiprecision::mpfr_float>, 55);
std::thread t3(thread_test_proc<boost::multiprecision::mpfr_float>, 75);
std::thread t4(thread_test_proc<boost::multiprecision::mpfr_float>, 105);
std::thread t5(thread_test_proc<boost::multiprecision::mpfr_float>, 305);
t1.join();
t2.join();
t3.join();
t4.join();
t5.join();
}
#endif
return boost::report_errors();
}
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