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// (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)
#include <pch.hpp>
#include <boost/math/concepts/real_concept.hpp>
#include <boost/math/special_functions/acosh.hpp>
#include <boost/math/special_functions/asinh.hpp>
#include <boost/math/special_functions/atanh.hpp>
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp>
#include <boost/test/tools/floating_point_comparison.hpp>
#include <boost/math/tools/stats.hpp>
#include <boost/math/tools/test.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/type_traits/is_floating_point.hpp>
#include <boost/array.hpp>
#include "functor.hpp"
#include "handle_test_result.hpp"
#include "table_type.hpp"
#include <iostream>
#include <iomanip>
//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the inverse hyperbolic functions. There are two sets of tests:
// 1) Sanity checks: comparison to test values created with the
// online calculator at functions.wolfram.com
// 2) Accuracy tests use values generated with NTL::RR at
// 1000-bit precision and our generic versions of these functions.
//
// Note that when this file is first run on a new platform many of
// these tests will fail: the default accuracy is 1 epsilon which
// is too tight for most platforms. In this situation you will
// need to cast a human eye over the error rates reported and make
// a judgement as to whether they are acceptable. Either way please
// report the results to the Boost mailing list. Acceptable rates of
// error are marked up below as a series of regular expressions that
// identify the compiler/stdlib/platform/data-type/test-data/test-function
// along with the maximum expected peek and RMS mean errors for that
// test.
//
void expected_results()
{
//
// Define the max and mean errors expected for
// various compilers and platforms.
//
const char* largest_type;
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
if(boost::math::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >())
{
largest_type = "(long\\s+)?double|real_concept";
}
else
{
largest_type = "long double|real_concept";
}
#else
largest_type = "(long\\s+)?double";
#endif
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
"atanh.*", // test data group
".*", 6, 1); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"real_concept", // test type(s)
".*", // test data group
".*", 4, 2); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*", // test data group
".*", 4, 1); // test function
std::cout << "Tests run with " << BOOST_COMPILER << ", "
<< BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
}
template <class Real, class T>
void do_test_asinh(const T& data, const char* type_name, const char* test_name)
{
//
// test asinh(T) against data:
//
using namespace std;
typedef Real value_type;
std::cout << test_name << " with type " << type_name << std::endl;
typedef value_type (*pg)(value_type);
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
pg funcp = boost::math::asinh<value_type>;
#else
pg funcp = boost::math::asinh;
#endif
boost::math::tools::test_result<value_type> result;
//
// test asinh against data:
//
result = boost::math::tools::test_hetero<Real>(
data,
bind_func<Real>(funcp, 0),
extract_result<Real>(1));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::asinh", test_name);
std::cout << std::endl;
}
template <class Real, class T>
void do_test_acosh(const T& data, const char* type_name, const char* test_name)
{
//
// test acosh(T) against data:
//
using namespace std;
typedef Real value_type;
std::cout << test_name << " with type " << type_name << std::endl;
typedef value_type (*pg)(value_type);
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
pg funcp = boost::math::acosh<value_type>;
#else
pg funcp = boost::math::acosh;
#endif
boost::math::tools::test_result<value_type> result;
//
// test acosh against data:
//
result = boost::math::tools::test_hetero<Real>(
data,
bind_func<Real>(funcp, 0),
extract_result<Real>(1));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::acosh", test_name);
std::cout << std::endl;
}
template <class Real, class T>
void do_test_atanh(const T& data, const char* type_name, const char* test_name)
{
//
// test atanh(T) against data:
//
using namespace std;
typedef Real value_type;
std::cout << test_name << " with type " << type_name << std::endl;
typedef value_type (*pg)(value_type);
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
pg funcp = boost::math::atanh<value_type>;
#else
pg funcp = boost::math::atanh;
#endif
boost::math::tools::test_result<value_type> result;
//
// test atanh against data:
//
result = boost::math::tools::test_hetero<Real>(
data,
bind_func<Real>(funcp, 0),
extract_result<Real>(1));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::atanh", test_name);
std::cout << std::endl;
}
template <class T>
void test_inv_hyperbolics(T, const char* name)
{
// function values calculated on http://functions.wolfram.com/
#define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
static const std::array<std::array<typename table_type<T>::type, 2>, 16> data1 = {{
{{ SC_(1.0), SC_(0.0) }},
{{ SC_(18014398509481985.0)/SC_(18014398509481984.0), (SC_(18014398509481985.0)/SC_(18014398509481984.0) == 1 ? 0 : SC_(1.05367121277235078980001569764860129317209081216314559121044e-8)) }},
{{ SC_(140737488355329.0)/SC_(140737488355328.0), (SC_(140737488355329.0)/SC_(140737488355328.0) == 1 ? 0 : SC_(1.19209289550781179413921062141751258430803882725295121500042e-7)) }},
{{ SC_(1073741825.0)/SC_(1073741824.0), (SC_(1073741825.0)/SC_(1073741824.0) == 1 ? 0 : SC_(0.0000431583728718059579720327225039166883356735150941350459126580)) }},
{{ SC_(32769.0)/32768, (SC_(32769.0)/32768 == 1 ? 0 : SC_(0.00781248013192149783598227588546120945538554063153555218442060)) }},
{{ SC_(1025.0)/1024, SC_(0.0441905780831100944299637635287994671116916497867872322058681) }},
{{ SC_(513.0)/512, SC_(0.0624898319417098609694799246056217361555882834152944713872228) }},
{{ SC_(129.0)/128, SC_(0.124918762511080617606418193883982155828039646714882611321039) }},
{{ SC_(33.0)/32, SC_(0.249353493842885487851439075410018843027071727873456825299808) }},
{{ SC_(5.0)/4, SC_(0.693147180559945309417232121458176568075500134360255254120680) }},
{{ SC_(3.0)/2, SC_(0.962423650119206894995517826848736846270368668771321039322036) }},
{{ SC_(1.75), SC_(1.15881036042994681173087299087873019318368454205435905403767) }},
{{ SC_(2.0), SC_(1.31695789692481670862504634730796844402698197146751647976847) }},
{{ SC_(20.0), SC_(3.68825386736129666761816757203235188783315569765587425882926) }},
{{ SC_(200.0), SC_(5.99145829704938742305501213819154333467246121857058747847273) }},
{{ SC_(2000.0), SC_(8.29404957760202181151262480475259799729149903827743516943515) }},
}};
#undef SC_
//
// The actual test data is rather verbose, so it's in a separate file
//
#include "asinh_data.ipp"
do_test_asinh<T>(asinh_data, name, "asinh");
#include "acosh_data.ipp"
do_test_acosh<T>(data1, name, "acosh: Mathworld Data");
do_test_acosh<T>(acosh_data, name, "acosh");
#include "atanh_data.ipp"
do_test_atanh<T>(atanh_data, name, "atanh");
}
extern "C" double zetac(double);
template <class T>
void test_spots(T, const char* t)
{
std::cout << "Testing basic sanity checks for type " << t << std::endl;
//
// Basic sanity checks, tolerance is either 5 or 10 epsilon
// expressed as a percentage:
//
T tolerance = boost::math::tools::epsilon<T>() * 100 *
(boost::is_floating_point<T>::value ? 5 : 10);
BOOST_CHECK_CLOSE(::boost::math::acosh(static_cast<T>(262145)/262144L), static_cast<T>(0.00276213498595136093375633956331651432309750291610866833462649L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::acosh(static_cast<T>(2)), static_cast<T>(1.31695789692481670862504634730796844402698197146751647976847L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::acosh(static_cast<T>(40)), static_cast<T>(4.38187034804006698696313269586603717076961771721038534547948L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::acosh(static_cast<T>(262145L)), static_cast<T>(13.1698002453253126137651962522659827810753786944786303017757L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T>(0)), static_cast<T>(0), tolerance);
BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T>(1)/262145L), static_cast<T>(3.81468271375603081996185039385472561751449912305225962381803e-6L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T>(0.25)), static_cast<T>(0.247466461547263452944781549788359289253766903098567696469117L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T>(1)), static_cast<T>(0.881373587019543025232609324979792309028160328261635410753296L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T>(10)), static_cast<T>(2.99822295029796973884659553759645347660705805487730365573446L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T>(262145L)), static_cast<T>(13.1698002453325885158685460826511173257938039316922010439486L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::atanh(static_cast<T>(0)), static_cast<T>(0), tolerance);
BOOST_CHECK_CLOSE(::boost::math::atanh(static_cast<T>(1)/262145L), static_cast<T>(3.81468271378378607794264842456613940280945630999769224301574e-6L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::atanh(static_cast<T>(-1)/262145L), static_cast<T>(-3.81468271378378607794264842456613940280945630999769224301574e-6L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::atanh(static_cast<T>(0.5)), static_cast<T>(0.549306144334054845697622618461262852323745278911374725867347L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::atanh(static_cast<T>(-0.5)), static_cast<T>(-0.549306144334054845697622618461262852323745278911374725867347L), tolerance);
}
BOOST_AUTO_TEST_CASE( test_main )
{
expected_results();
BOOST_MATH_CONTROL_FP;
test_spots(0.0f, "float");
test_spots(0.0, "double");
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_spots(0.0L, "long double");
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
test_spots(boost::math::concepts::real_concept(0.1), "real_concept");
#endif
#else
std::cout << "<note>The long double tests have been disabled on this platform "
"either because the long double overloads of the usual math functions are "
"not available at all, or because they are too inaccurate for these tests "
"to pass.</note>" << std::endl;
#endif
test_inv_hyperbolics(0.1F, "float");
test_inv_hyperbolics(0.1, "double");
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_inv_hyperbolics(0.1L, "long double");
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
test_inv_hyperbolics(boost::math::concepts::real_concept(0.1), "real_concept");
#endif
#else
std::cout << "<note>The long double tests have been disabled on this platform "
"either because the long double overloads of the usual math functions are "
"not available at all, or because they are too inaccurate for these tests "
"to pass.</note>" << std::endl;
#endif
}
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