mirror of
https://github.com/boostorg/math.git
synced 2026-01-27 19:12:08 +00:00
4ecb968fc7
Added code for extracting the sign of a number. Fixed a few bugs and tidied up the code a little in places. Changed test_result to properly encapsulate it's contents. [SVN r3106]
306 lines
14 KiB
C++
306 lines
14 KiB
C++
// (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 <boost/math/concepts/real_concept.hpp>
|
|
#include <boost/math/special_functions/gamma.hpp>
|
|
#include <boost/test/included/test_exec_monitor.hpp>
|
|
#include <boost/test/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 <boost/lambda/lambda.hpp>
|
|
#include <boost/lambda/bind.hpp>
|
|
|
|
#include "test_gamma_hooks.hpp"
|
|
#include "handle_test_result.hpp"
|
|
|
|
//
|
|
// DESCRIPTION:
|
|
// ~~~~~~~~~~~~
|
|
//
|
|
// This file tests the incomplete gamma functions tgamma,
|
|
// tgamma_lower, gamma_P and gamma_Q. There are two sets of tests, spot
|
|
// tests which compare our results with selected values computed
|
|
// using the online special function calculator at
|
|
// functions.wolfram.com, while the bulk of the 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::tools::digits<double>() == boost::math::tools::digits<long double>())
|
|
{
|
|
largest_type = "(long\\s+)?double";
|
|
}
|
|
else
|
|
{
|
|
largest_type = "long double";
|
|
}
|
|
#else
|
|
largest_type = "(long\\s+)?double";
|
|
#endif
|
|
|
|
|
|
//
|
|
// Catch all cases come last:
|
|
//
|
|
add_expected_result(
|
|
"[^|]*", // compiler
|
|
"[^|]*", // stdlib
|
|
"[^|]*", // platform
|
|
largest_type, // test type(s)
|
|
"[^|]*medium[^|]*", // test data group
|
|
"[^|]*", 50, 20); // test function
|
|
add_expected_result(
|
|
"[^|]*", // compiler
|
|
"[^|]*", // stdlib
|
|
"[^|]*", // platform
|
|
largest_type, // test type(s)
|
|
"[^|]*small[^|]*", // test data group
|
|
"[^|]*", 10, 5); // test function
|
|
add_expected_result(
|
|
"[^|]*", // compiler
|
|
"[^|]*", // stdlib
|
|
"[^|]*", // platform
|
|
largest_type, // test type(s)
|
|
"[^|]*large[^|]*", // test data group
|
|
"boost::math::gamma_Q", 500, 50); // test function
|
|
add_expected_result(
|
|
"[^|]*", // compiler
|
|
"[^|]*", // stdlib
|
|
"Cygwin", // platform
|
|
largest_type, // test type(s)
|
|
"[^|]*large[^|]*", // test data group
|
|
"boost::math::gamma_P", 700, 50); // test function
|
|
add_expected_result(
|
|
"[^|]*", // compiler
|
|
"[^|]*", // stdlib
|
|
"[^|]*", // platform
|
|
largest_type, // test type(s)
|
|
"[^|]*large[^|]*", // test data group
|
|
"boost::math::gamma_P", 300, 50); // test function
|
|
add_expected_result(
|
|
"[^|]*", // compiler
|
|
"[^|]*", // stdlib
|
|
"[^|]*", // platform
|
|
"real_concept", // test type(s)
|
|
"[^|]*medium[^|]*", // test data group
|
|
"[^|]*", 200, 50); // test function
|
|
add_expected_result(
|
|
"[^|]*", // compiler
|
|
"[^|]*", // stdlib
|
|
"[^|]*", // platform
|
|
"real_concept", // test type(s)
|
|
"[^|]*small[^|]*", // test data group
|
|
".*", 10, 5); // test function
|
|
add_expected_result(
|
|
"[^|]*", // compiler
|
|
"[^|]*", // stdlib
|
|
"[^|]*", // platform
|
|
"real_concept", // test type(s)
|
|
"[^|]*large[^|]*", // test data group
|
|
".*", 1000000, 100000); // test function
|
|
|
|
//
|
|
// Finish off by printing out the compiler/stdlib/platform names,
|
|
// we do this to make it easier to mark up expected error rates.
|
|
//
|
|
std::cout << "Tests run with " << BOOST_COMPILER << ", "
|
|
<< BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
|
|
}
|
|
|
|
template <class T>
|
|
void do_test_gamma_2(const T& data, const char* type_name, const char* test_name)
|
|
{
|
|
typedef typename T::value_type row_type;
|
|
typedef typename row_type::value_type value_type;
|
|
|
|
typedef value_type (*pg)(value_type, value_type);
|
|
pg funcp = boost::math::tgamma;
|
|
|
|
using namespace boost::lambda;
|
|
|
|
boost::math::tools::test_result<value_type> result;
|
|
|
|
std::cout << "Testing " << test_name << " with type " << type_name
|
|
<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
|
|
|
|
//
|
|
// test tgamma(T, T) against data:
|
|
//
|
|
if(data[0][2] > 0)
|
|
{
|
|
result = boost::math::tools::test(
|
|
data,
|
|
bind(funcp, ret<value_type>(_1[0]), ret<value_type>(_1[1])),
|
|
ret<value_type>(_1[2]));
|
|
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::tgamma", test_name);
|
|
//
|
|
// test tgamma_lower(T, T) against data:
|
|
//
|
|
funcp = boost::math::tgamma_lower;
|
|
result = boost::math::tools::test(
|
|
data,
|
|
bind(funcp, ret<value_type>(_1[0]), ret<value_type>(_1[1])),
|
|
ret<value_type>(_1[4]));
|
|
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::tgamma_lower", test_name);
|
|
}
|
|
//
|
|
// test gamma_Q(T, T) against data:
|
|
//
|
|
funcp = boost::math::gamma_Q;
|
|
result = boost::math::tools::test(
|
|
data,
|
|
bind(funcp, ret<value_type>(_1[0]), ret<value_type>(_1[1])),
|
|
ret<value_type>(_1[3]));
|
|
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::gamma_Q", test_name);
|
|
#if defined(TEST_CEPHES) || defined(TEST_GSL)
|
|
//
|
|
// test other gamma_Q(T, T) against data:
|
|
//
|
|
if(boost::is_floating_point<value_type>::value)
|
|
{
|
|
funcp = other::gamma_Q;
|
|
result = boost::math::tools::test(
|
|
data,
|
|
bind(funcp, ret<value_type>(_1[0]), ret<value_type>(_1[1])),
|
|
ret<value_type>(_1[3]));
|
|
print_test_result(result, data[result.worst()], result.worst(), type_name, "other::gamma_Q");
|
|
}
|
|
#endif
|
|
//
|
|
// test gamma_P(T, T) against data:
|
|
//
|
|
funcp = boost::math::gamma_P;
|
|
result = boost::math::tools::test(
|
|
data,
|
|
bind(funcp, ret<value_type>(_1[0]), ret<value_type>(_1[1])),
|
|
ret<value_type>(_1[5]));
|
|
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::gamma_P", test_name);
|
|
#if defined(TEST_CEPHES) || defined(TEST_GSL)
|
|
//
|
|
// test other gamma_P(T, T) against data:
|
|
//
|
|
if(boost::is_floating_point<value_type>::value)
|
|
{
|
|
funcp = other::gamma_P;
|
|
result = boost::math::tools::test(
|
|
data,
|
|
bind(funcp, ret<value_type>(_1[0]), ret<value_type>(_1[1])),
|
|
ret<value_type>(_1[5]));
|
|
print_test_result(result, data[result.worst()], result.worst(), type_name, "other::gamma_P");
|
|
}
|
|
#endif
|
|
std::cout << std::endl;
|
|
}
|
|
|
|
template <class T>
|
|
void test_gamma(T, const char* name)
|
|
{
|
|
//
|
|
// The actual test data is rather verbose, so it's in a separate file
|
|
//
|
|
// First the data for the incomplete gamma function, each
|
|
// row has the following 6 entries:
|
|
// Parameter a, parameter z,
|
|
// Expected tgamma(a, z), Expected gamma_Q(a, z)
|
|
// Expected tgamma_lower(a, z), Expected gamma_P(a, z)
|
|
//
|
|
# include "igamma_med_data.ipp"
|
|
|
|
do_test_gamma_2(igamma_med_data, name, "tgamma(a, z) medium values");
|
|
|
|
# include "igamma_small_data.ipp"
|
|
|
|
do_test_gamma_2(igamma_small_data, name, "tgamma(a, z) small values");
|
|
|
|
# include "igamma_big_data.ipp"
|
|
|
|
do_test_gamma_2(igamma_big_data, name, "tgamma(a, z) large values");
|
|
}
|
|
|
|
template <class T>
|
|
void test_spots(T)
|
|
{
|
|
//
|
|
// basic sanity checks, tolerance is 10 epsilon expressed as a percentage:
|
|
//
|
|
T tolerance = boost::math::tools::epsilon<T>() * 1000;
|
|
BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(5), static_cast<T>(1)), static_cast<T>(23.912163676143750903709045060494956383977723517065L), tolerance);
|
|
BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(5), static_cast<T>(5)), static_cast<T>(10.571838841565097874621959975919877646444998907920L), tolerance);
|
|
BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(5), static_cast<T>(10)), static_cast<T>(0.70206451384706574414638719662835463671916532623256L), tolerance);
|
|
BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(5), static_cast<T>(100)), static_cast<T>(3.8734332808745531496973774140085644548465762343719e-36L), tolerance);
|
|
BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(0.5), static_cast<T>(0.5)), static_cast<T>(0.56241823159440712427949495730204306902676756479651L), tolerance);
|
|
BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(0.5), static_cast<T>(0.9)), static_cast<T>(0.31853210360412109873859360390443790076576777747449L), tolerance);
|
|
BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(0.5), static_cast<T>(5)), static_cast<T>(0.0027746032604128093194908357272603294120210079791437L), tolerance);
|
|
BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(0.5), static_cast<T>(100)), static_cast<T>(3.7017478604082789202535664481339075721362102520338e-45L), tolerance);
|
|
|
|
BOOST_CHECK_CLOSE(::boost::math::tgamma_lower(static_cast<T>(5), static_cast<T>(1)), static_cast<T>(0.087836323856249096290954939505043616022276482935091L), tolerance);
|
|
BOOST_CHECK_CLOSE(::boost::math::tgamma_lower(static_cast<T>(5), static_cast<T>(5)), static_cast<T>(13.428161158434902125378040024080122353555001092080L), tolerance);
|
|
BOOST_CHECK_CLOSE(::boost::math::tgamma_lower(static_cast<T>(5), static_cast<T>(10)), static_cast<T>(23.297935486152934255853612803371645363280834673767L), tolerance);
|
|
BOOST_CHECK_CLOSE(::boost::math::tgamma_lower(static_cast<T>(5), static_cast<T>(100)), static_cast<T>(23.999999999999999999999999999999999996126566719125L), tolerance);
|
|
|
|
BOOST_CHECK_CLOSE(::boost::math::gamma_Q(static_cast<T>(5), static_cast<T>(1)), static_cast<T>(0.99634015317265628765454354418728984933240514654437L), tolerance);
|
|
BOOST_CHECK_CLOSE(::boost::math::gamma_Q(static_cast<T>(5), static_cast<T>(5)), static_cast<T>(0.44049328506521241144258166566332823526854162116334L), tolerance);
|
|
BOOST_CHECK_CLOSE(::boost::math::gamma_Q(static_cast<T>(5), static_cast<T>(10)), static_cast<T>(0.029252688076961072672766133192848109863298555259690L), tolerance);
|
|
BOOST_CHECK_CLOSE(::boost::math::gamma_Q(static_cast<T>(5), static_cast<T>(100)), static_cast<T>(1.6139305336977304790405739225035685228527400976549e-37L), tolerance);
|
|
BOOST_CHECK_CLOSE(::boost::math::gamma_Q(static_cast<T>(1.5), static_cast<T>(2)), static_cast<T>(0.26146412994911062220282207597592120190281060919079L), tolerance);
|
|
BOOST_CHECK_CLOSE(::boost::math::gamma_Q(static_cast<T>(20.5), static_cast<T>(22)), static_cast<T>(0.34575332043467326814971590879658406632570278929072L), tolerance);
|
|
|
|
BOOST_CHECK_CLOSE(::boost::math::gamma_P(static_cast<T>(5), static_cast<T>(1)), static_cast<T>(0.0036598468273437123454564558127101506675948534556288L), tolerance);
|
|
BOOST_CHECK_CLOSE(::boost::math::gamma_P(static_cast<T>(5), static_cast<T>(5)), static_cast<T>(0.55950671493478758855741833433667176473145837883666L), tolerance);
|
|
BOOST_CHECK_CLOSE(::boost::math::gamma_P(static_cast<T>(5), static_cast<T>(10)), static_cast<T>(0.97074731192303892732723386680715189013670144474031L), tolerance);
|
|
BOOST_CHECK_CLOSE(::boost::math::gamma_P(static_cast<T>(5), static_cast<T>(100)), static_cast<T>(0.9999999999999999999999999999999999998386069466302L), tolerance);
|
|
BOOST_CHECK_CLOSE(::boost::math::gamma_P(static_cast<T>(1.5), static_cast<T>(2)), static_cast<T>(0.73853587005088937779717792402407879809718939080921L), tolerance);
|
|
BOOST_CHECK_CLOSE(::boost::math::gamma_P(static_cast<T>(20.5), static_cast<T>(22)), static_cast<T>(0.65424667956532673185028409120341593367429721070928L), tolerance);
|
|
}
|
|
|
|
int test_main(int, char* [])
|
|
{
|
|
expected_results();
|
|
|
|
test_spots(0.0F);
|
|
test_spots(0.0);
|
|
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
|
|
test_spots(0.0L);
|
|
test_spots(boost::math::concepts::real_concept(0.1));
|
|
#endif
|
|
|
|
test_gamma(0.1F, "float");
|
|
test_gamma(0.1, "double");
|
|
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
|
|
test_gamma(0.1L, "long double");
|
|
test_gamma(boost::math::concepts::real_concept(0.1), "real_concept");
|
|
#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::cout;
|
|
#endif
|
|
return 0;
|
|
}
|
|
|
|
|