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700ea50732fb745e76cc0a917e04486858025990
math/test/test_gamma.cpp
John Maddock 700ea50732 Fixes for VC-7.1. 
[SVN r39478]
2007-09-22 17:00:29 +00:00

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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)
#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
#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>
#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
#include <boost/lambda/lambda.hpp>
#include <boost/lambda/bind.hpp>
#endif
#include "test_gamma_hooks.hpp"
#include "handle_test_result.hpp"
//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the functions tgamma and lgamma, and the
// function tgamma1pm1. 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::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >())
{
largest_type = "(long\\s+)?double";
}
else
{
largest_type = "long double";
}
#else
largest_type = "(long\\s+)?double";
#endif
//
// G++ on Darwin: results are just slightly worse than we might hope for
// but still pretty good:
//
add_expected_result(
".*", // compiler
".*", // stdlib
"Mac OS", // platform
largest_type, // test type(s)
"factorials", // test data group
"boost::math::tgamma", 100, 15); // test function
//
// G++ on Linux, result vary a bit by processor type,
// on Itanium results are *much* better than listed here,
// but x86 appears to have much less accurate std::pow
// that throws off the results:
//
add_expected_result(
".*", // compiler
".*", // stdlib
"linux", // platform
largest_type, // test type(s)
"factorials", // test data group
"boost::math::tgamma", 400, 200); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"linux", // platform
largest_type, // test type(s)
"factorials", // test data group
"boost::math::lgamma", 30, 10); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"linux", // platform
largest_type, // test type(s)
"near (1|2|-10)", // test data group
"boost::math::tgamma", 10, 5); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"linux", // platform
largest_type, // test type(s)
"near (1|2|-10)", // test data group
"boost::math::lgamma", 50, 30); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"linux", // platform
largest_type, // test type(s)
"tgamma1pm1.*", // test data group
"boost::math::tgamma1pm1", 50, 15); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"linux", // platform
"real_concept", // test type(s)
"factorials", // test data group
"boost::math::tgamma", 220, 70); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"linux", // platform
"real_concept", // test type(s)
"near (0|-55)", // test data group
"boost::math::(t|l)gamma", 130, 60); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"linux", // platform
"real_concept", // test type(s)
"tgamma1pm1.*", // test data group
"boost::math::tgamma1pm1", 40, 10); // test function
//
// HP-UX results:
//
add_expected_result(
".*", // compiler
".*", // stdlib
"HP-UX", // platform
largest_type, // test type(s)
"factorials", // test data group
"boost::math::tgamma", 5, 4); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"HP-UX", // platform
largest_type, // test type(s)
"near (0|-55)", // test data group
"boost::math::tgamma", 10, 5); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"HP-UX", // platform
largest_type, // test type(s)
"near (1|2|-10)", // test data group
"boost::math::lgamma", 250, 200); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"HP-UX", // platform
"real_concept", // test type(s)
"factorials", // test data group
"boost::math::lgamma", 50, 20); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"HP-UX", // platform
"real_concept", // test type(s)
"tgamma1pm1.*", // test data group
"boost::math::tgamma1pm1", 200, 60); // test function
//
// Catch all cases come last:
//
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
"factorials", // test data group
"boost::math::tgamma", 4, 1); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
"factorials", // test data group
"boost::math::lgamma", 9, 1); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
"near (0|-55)", // test data group
"boost::math::(t|l)gamma", 200, 100); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
"near (1|2|-10)", // test data group
"boost::math::tgamma", 10, 5); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
"near (1|2|-10)", // test data group
"boost::math::lgamma", 14, 7); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
"tgamma1pm1.*", // test data group
"boost::math::tgamma1pm1", 30, 9); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"real_concept", // test type(s)
"factorials", // test data group
"boost::math::tgamma", 70, 25); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"real_concept", // test type(s)
"factorials", // test data group
"boost::math::lgamma", 30, 4); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"real_concept", // test type(s)
"near.*", // test data group
"boost::math::tgamma", 60, 30); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"real_concept", // test type(s)
"near.*", // test data group
"boost::math::lgamma", 10000000, 10000000); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"real_concept", // test type(s)
"tgamma1pm1.*", // test data group
"boost::math::tgamma1pm1", 20, 5); // 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(const T& data, const char* type_name, const char* test_name)
{
#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
typedef typename T::value_type row_type;
typedef typename row_type::value_type value_type;
typedef value_type (*pg)(value_type);
pg funcp = boost::math::tgamma;
boost::math::tools::test_result<value_type> result;
std::cout << "Testing " << test_name << " with type " << type_name
<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
//
// test tgamma against data:
//
result = boost::math::tools::test(
data,
boost::lambda::bind(funcp, boost::lambda::ret<value_type>(boost::lambda::_1[0])),
boost::lambda::ret<value_type>(boost::lambda::_1[1]));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::tgamma", test_name);
#ifdef TEST_OTHER
if(::boost::is_floating_point<value_type>::value){
funcp = other::tgamma;
result = boost::math::tools::test(
data,
boost::lambda::bind(funcp, boost::lambda::ret<value_type>(boost::lambda::_1[0])),
boost::lambda::ret<value_type>(boost::lambda::_1[1]));
print_test_result(result, data[result.worst()], result.worst(), type_name, "other::tgamma");
}
#endif
//
// test lgamma against data:
//
funcp = boost::math::lgamma;
result = boost::math::tools::test(
data,
boost::lambda::bind(funcp, boost::lambda::ret<value_type>(boost::lambda::_1[0])),
boost::lambda::ret<value_type>(boost::lambda::_1[2]));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::lgamma", test_name);
#ifdef TEST_OTHER
if(::boost::is_floating_point<value_type>::value){
funcp = other::lgamma;
result = boost::math::tools::test(
data,
boost::lambda::bind(funcp, boost::lambda::ret<value_type>(boost::lambda::_1[0])),
boost::lambda::ret<value_type>(boost::lambda::_1[2]));
print_test_result(result, data[result.worst()], result.worst(), type_name, "other::lgamma");
}
#endif
std::cout << std::endl;
#endif
}
template <class T>
void do_test_gammap1m1(const T& data, const char* type_name, const char* test_name)
{
#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
typedef typename T::value_type row_type;
typedef typename row_type::value_type value_type;
typedef value_type (*pg)(value_type);
pg funcp = boost::math::tgamma1pm1;
boost::math::tools::test_result<value_type> result;
std::cout << "Testing " << test_name << " with type " << type_name
<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
//
// test tgamma1pm1 against data:
//
result = boost::math::tools::test(
data,
boost::lambda::bind(funcp, boost::lambda::ret<value_type>(boost::lambda::_1[0])),
boost::lambda::ret<value_type>(boost::lambda::_1[1]));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::tgamma1pm1", test_name);
std::cout << std::endl;
#endif
}
template <class T>
void test_gamma(T, const char* name)
{
//
// The actual test data is rather verbose, so it's in a separate file
//
// The contents are as follows, each row of data contains
// three items, input value, gamma and lgamma:
//
// gamma and lgamma at integer and half integer values:
// boost::array<boost::array<T, 3>, N> factorials;
//
// gamma and lgamma for z near 0:
// boost::array<boost::array<T, 3>, N> near_0;
//
// gamma and lgamma for z near 1:
// boost::array<boost::array<T, 3>, N> near_1;
//
// gamma and lgamma for z near 2:
// boost::array<boost::array<T, 3>, N> near_2;
//
// gamma and lgamma for z near -10:
// boost::array<boost::array<T, 3>, N> near_m10;
//
// gamma and lgamma for z near -55:
// boost::array<boost::array<T, 3>, N> near_m55;
//
// The last two cases are chosen more or less at random,
// except that one is even and the other odd, and both are
// at negative poles. The data near zero also tests near
// a pole, the data near 1 and 2 are to probe lgamma as
// the result -> 0.
//
# include "test_gamma_data.ipp"
do_test_gamma(factorials, name, "factorials");
do_test_gamma(near_0, name, "near 0");
do_test_gamma(near_1, name, "near 1");
do_test_gamma(near_2, name, "near 2");
do_test_gamma(near_m10, name, "near -10");
do_test_gamma(near_m55, name, "near -55");
//
// And now tgamma1pm1 which computes gamma(1+dz)-1:
//
do_test_gammap1m1(gammap1m1_data, name, "tgamma1pm1(dz)");
}
template <class T>
void test_spots(T)
{
//
// basic sanity checks, tolerance is 50 epsilon expressed as a percentage:
//
T tolerance = boost::math::tools::epsilon<T>() * 5000;
BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(3.5)), static_cast<T>(3.3233509704478425511840640312646472177454052302295L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(0.125)), static_cast<T>(7.5339415987976119046992298412151336246104195881491L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(-0.125)), static_cast<T>(-8.7172188593831756100190140408231437691829605421405L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(-3.125)), static_cast<T>(1.1668538708507675587790157356605097019141636072094L), tolerance);
// Lower tolerance on this one, is only really needed on Linux x86 systems, result is mostly down to std lib accuracy:
BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(-53249.0/1024)), static_cast<T>(-1.2646559519067605488251406578743995122462767733517e-65L), tolerance * 3);
int sign = 1;
BOOST_CHECK_CLOSE(::boost::math::lgamma(static_cast<T>(3.5), &sign), static_cast<T>(1.2009736023470742248160218814507129957702389154682L), tolerance);
BOOST_CHECK(sign == 1);
BOOST_CHECK_CLOSE(::boost::math::lgamma(static_cast<T>(0.125), &sign), static_cast<T>(2.0194183575537963453202905211670995899482809521344L), tolerance);
BOOST_CHECK(sign == 1);
BOOST_CHECK_CLOSE(::boost::math::lgamma(static_cast<T>(-0.125), &sign), static_cast<T>(2.1653002489051702517540619481440174064962195287626L), tolerance);
BOOST_CHECK(sign == -1);
BOOST_CHECK_CLOSE(::boost::math::lgamma(static_cast<T>(-3.125), &sign), static_cast<T>(0.1543111276840418242676072830970532952413339012367L), tolerance);
BOOST_CHECK(sign == 1);
BOOST_CHECK_CLOSE(::boost::math::lgamma(static_cast<T>(-53249.0/1024), &sign), static_cast<T>(-149.43323093420259741100038126078721302600128285894L), tolerance);
BOOST_CHECK(sign == -1);
}
int test_main(int, char* [])
{
expected_results();
#ifndef BOOST_MATH_BUGGY_LARGE_FLOAT_CONSTANTS
test_spots(0.0F);
#endif
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
#ifndef BOOST_MATH_BUGGY_LARGE_FLOAT_CONSTANTS
test_gamma(0.1F, "float");
#endif
test_gamma(0.1, "double");
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_gamma(0.1L, "long double");
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
test_gamma(boost::math::concepts::real_concept(0.1), "real_concept");
#endif
#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::cout;
#endif
return 0;
}
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