| // (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> |
| // Need to compile in IDE PAB 31 Oct 2008 |
| |
| #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/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 "functor.hpp" |
| |
| #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, 50); // 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, 80); // 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, 80); // test function |
| // |
| // Tru64: |
| // |
| add_expected_result( |
| ".*Tru64.*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| "factorials", // test data group |
| "boost::math::lgamma", 50, 20); // test function |
| // |
| // Sun OS: |
| // |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "Sun.*", // platform |
| largest_type, // test type(s) |
| "factorials", // test data group |
| "boost::math::tgamma", 300, 50); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "Sun.*", // platform |
| "real_concept", // test type(s) |
| "factorials", // test data group |
| "boost::math::tgamma", 300, 50); // 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", 40, 4); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| "near.*", // test data group |
| "boost::math::tgamma", 80, 60); // 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) |
| { |
| typedef typename T::value_type row_type; |
| typedef typename row_type::value_type value_type; |
| |
| typedef value_type (*pg)(value_type); |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| pg funcp = boost::math::tgamma<value_type>; |
| #else |
| pg funcp = boost::math::tgamma; |
| #endif |
| |
| 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, |
| bind_func(funcp, 0), |
| extract_result(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, |
| bind_func(funcp, 0), |
| extract_result(1)); |
| print_test_result(result, data[result.worst()], result.worst(), type_name, "other::tgamma"); |
| } |
| #endif |
| // |
| // test lgamma against data: |
| // |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| funcp = boost::math::lgamma<value_type>; |
| #else |
| funcp = boost::math::lgamma; |
| #endif |
| result = boost::math::tools::test( |
| data, |
| bind_func(funcp, 0), |
| extract_result(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, |
| bind_func(funcp, 0), |
| extract_result(2)); |
| print_test_result(result, data[result.worst()], result.worst(), type_name, "other::lgamma"); |
| } |
| #endif |
| |
| std::cout << std::endl; |
| } |
| |
| template <class T> |
| void do_test_gammap1m1(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); |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| pg funcp = boost::math::tgamma1pm1<value_type>; |
| #else |
| pg funcp = boost::math::tgamma1pm1; |
| #endif |
| |
| 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, |
| bind_func(funcp, 0), |
| extract_result(1)); |
| handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::tgamma1pm1", test_name); |
| 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 |
| // |
| // 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(); |
| BOOST_MATH_CONTROL_FP; |
| |
| #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; |
| } |
| |
| |
| |
