| // (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> |
| |
| #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 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::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 |
| // |
| // Linux: |
| // |
| // These should not really be needed, but on *some* Linux |
| // versions these error rates are quite large and appear to |
| // be related to the accuracy of powl and expl. On Itanium |
| // or Xeon machines the error rates are much lower than this. |
| // Worst cases appear to be AMD64 machines. |
| // |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "linux", // platform |
| largest_type, // test type(s) |
| "[^|]*medium[^|]*", // test data group |
| "[^|]*", 1000, 200); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "linux", // platform |
| largest_type, // test type(s) |
| "[^|]*integer[^|]*", // test data group |
| "[^|]*", 1000, 200); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "linux", // platform |
| "real_concept", // test type(s) |
| "[^|]*medium[^|]*", // test data group |
| "[^|]*", 1000, 200); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "linux", // platform |
| "real_concept", // test type(s) |
| "[^|]*integer[^|]*", // test data group |
| "[^|]*", 600, 200); // test function |
| |
| // |
| // Mac OS X: |
| // It's not clear why these should be required, but see notes above |
| // about Linux. |
| // |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "Mac OS", // platform |
| largest_type, // test type(s) |
| "[^|]*medium[^|]*", // test data group |
| "[^|]*", 5000, 1000); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "Mac OS", // platform |
| largest_type, // test type(s) |
| "[^|]*small[^|]*", // test data group |
| "[^|]*", 40, 15); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "Mac OS", // platform |
| largest_type, // test type(s) |
| "[^|]*integer[^|]*", // test data group |
| "[^|]*", 2000, 300); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "Mac OS", // platform |
| "real_concept", // test type(s) |
| "[^|]*medium[^|]*", // test data group |
| "[^|]*", 5000, 1000); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "Mac OS", // platform |
| "real_concept", // test type(s) |
| "[^|]*small[^|]*", // test data group |
| "[^|]*", 40, 15); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "Mac OS", // platform |
| "real_concept", // test type(s) |
| "[^|]*integer[^|]*", // test data group |
| "[^|]*", 2000, 300); // test function |
| // |
| // HP-UX: |
| // |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "HP-UX", // platform |
| largest_type, // test type(s) |
| "[^|]*medium[^|]*", // test data group |
| "[^|]*", 500, 50); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "HP-UX", // platform |
| "real_concept", // test type(s) |
| "[^|]*medium[^|]*", // test data group |
| "[^|]*", 500, 100); // test function |
| // |
| // Sun OS: |
| // |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "Sun.*", // platform |
| largest_type, // test type(s) |
| "[^|]*medium[^|]*", // test data group |
| "[^|]*", 500, 100); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "Sun.*", // platform |
| largest_type, // test type(s) |
| "[^|]*integer[^|]*", // test data group |
| "[^|]*", 100, 30); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "Sun.*", // platform |
| "real_concept", // test type(s) |
| "[^|]*medium[^|]*", // test data group |
| "[^|]*", 500, 100); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "Sun.*", // platform |
| "real_concept", // test type(s) |
| "[^|]*integer[^|]*", // test data group |
| "[^|]*", 100, 30); // test function |
| |
| // |
| // Mac OS X: |
| // |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "Mac OS", // platform |
| largest_type, // test type(s) |
| "[^|]*medium[^|]*", // test data group |
| "[^|]*", 100, 50); // test function |
| |
| // |
| // Large exponent range causes more extreme test cases to be evaluated: |
| // |
| if(std::numeric_limits<long double>::max_exponent > std::numeric_limits<double>::max_exponent) |
| { |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "[^|]*", // platform |
| largest_type, // test type(s) |
| "[^|]*large[^|]*", // test data group |
| ".*", 40000, 3000); // test function |
| } |
| |
| |
| // |
| // 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 |
| "[^|]*", 20, 10); // 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", 350, 50); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "[^|]*", // platform |
| largest_type, // test type(s) |
| "[^|]*integer[^|]*", // test data group |
| ".*", 20, 10); // 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 |
| ".*", 20, 10); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "[^|]*", // platform |
| "real_concept", // test type(s) |
| "[^|]*large[^|]*", // test data group |
| ".*", 1000000, 100000); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "[^|]*", // platform |
| "real_concept", // test type(s) |
| "[^|]*integer[^|]*", // test data group |
| ".*", 40, 10); // 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); |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| pg funcp = boost::math::tgamma<value_type, 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(T, T) against data: |
| // |
| if(data[0][2] > 0) |
| { |
| result = boost::math::tools::test( |
| data, |
| bind_func(funcp, 0, 1), |
| extract_result(2)); |
| handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::tgamma", test_name); |
| // |
| // test tgamma_lower(T, T) against data: |
| // |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| funcp = boost::math::tgamma_lower<value_type, value_type>; |
| #else |
| funcp = boost::math::tgamma_lower; |
| #endif |
| result = boost::math::tools::test( |
| data, |
| bind_func(funcp, 0, 1), |
| extract_result(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: |
| // |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| funcp = boost::math::gamma_q<value_type, value_type>; |
| #else |
| funcp = boost::math::gamma_q; |
| #endif |
| result = boost::math::tools::test( |
| data, |
| bind_func(funcp, 0, 1), |
| extract_result(3)); |
| handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::gamma_q", test_name); |
| #if defined(TEST_OTHER) |
| // |
| // 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_func(funcp, 0, 1), |
| extract_result(3)); |
| print_test_result(result, data[result.worst()], result.worst(), type_name, "other::gamma_q"); |
| } |
| #endif |
| // |
| // test gamma_p(T, T) against data: |
| // |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| funcp = boost::math::gamma_p<value_type, value_type>; |
| #else |
| funcp = boost::math::gamma_p; |
| #endif |
| result = boost::math::tools::test( |
| data, |
| bind_func(funcp, 0, 1), |
| extract_result(5)); |
| handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::gamma_p", test_name); |
| #if defined(TEST_OTHER) |
| // |
| // 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_func(funcp, 0, 1), |
| extract_result(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"); |
| |
| # include "igamma_int_data.ipp" |
| |
| do_test_gamma_2(igamma_int_data, name, "tgamma(a, z) integer and half integer 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; |
| #if (defined(macintosh) || defined(__APPLE__) || defined(__APPLE_CC__)) |
| tolerance *= 10; |
| #endif |
| 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>(9)/10), static_cast<T>(0.31853210360412109873859360390443790076576777747449L), tolerance*10); |
| 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); |
| |
| // naive check on derivative function: |
| using namespace std; // For ADL of std functions |
| tolerance = boost::math::tools::epsilon<T>() * 5000; // 50 eps |
| BOOST_CHECK_CLOSE(::boost::math::gamma_p_derivative(static_cast<T>(20.5), static_cast<T>(22)), |
| exp(static_cast<T>(-22)) * pow(static_cast<T>(22), static_cast<T>(19.5)) / boost::math::tgamma(static_cast<T>(20.5)), tolerance); |
| |
| } |
| |
| 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); |
| #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582)) |
| test_spots(boost::math::concepts::real_concept(0.1)); |
| #endif |
| #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; |
| } |
| |
| |
| |
