| // (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/gamma.hpp> |
| #include <boost/test/test_exec_monitor.hpp> |
| #include <boost/test/results_collector.hpp> |
| #include <boost/test/unit_test.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" |
| |
| #if !defined(TEST_FLOAT) && !defined(TEST_DOUBLE) && !defined(TEST_LDOUBLE) && !defined(TEST_REAL_CONCEPT) |
| # define TEST_FLOAT |
| # define TEST_DOUBLE |
| # define TEST_LDOUBLE |
| # define TEST_REAL_CONCEPT |
| #endif |
| |
| // |
| // DESCRIPTION: |
| // ~~~~~~~~~~~~ |
| // |
| // This file tests the incomplete gamma function inverses |
| // gamma_p_inv and gamma_q_inv. There are three sets of tests: |
| // 1) Spot tests which compare our results with selected values |
| // computed using the online special function 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. |
| // 3) Round trip sanity checks, use the test data for the forward |
| // functions, and verify that we can get (approximately) back |
| // where we started. |
| // |
| // 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 |
| // |
| // 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) |
| "[^|]*small[^|]*", // test data group |
| "[^|]*", 200000, 10000); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "[^|]*", // platform |
| "real_concept", // test type(s) |
| "[^|]*small[^|]*", // test data group |
| "[^|]*", 70000, 8000); // test function |
| } |
| // |
| // These high error rates are seen on on some Linux |
| // architectures: |
| // |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "linux.*", // platform |
| largest_type, // test type(s) |
| "[^|]*medium[^|]*", // test data group |
| "[^|]*", 350, 5); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "linux.*", // platform |
| largest_type, // test type(s) |
| "[^|]*large[^|]*", // test data group |
| "[^|]*", 150, 5); // test function |
| |
| |
| // |
| // Catch all cases come last: |
| // |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "[^|]*", // platform |
| largest_type, // test type(s) |
| "[^|]*medium[^|]*", // test data group |
| "[^|]*", 20, 5); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "[^|]*", // platform |
| largest_type, // test type(s) |
| "[^|]*large[^|]*", // test data group |
| "[^|]*", 5, 2); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "[^|]*", // platform |
| largest_type, // test type(s) |
| "[^|]*small[^|]*", // test data group |
| "[^|]*", 2100, 500); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "[^|]*", // platform |
| "float|double", // test type(s) |
| "[^|]*small[^|]*", // test data group |
| "boost::math::gamma_p_inv", 500, 60); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "[^|]*", // platform |
| "float|double", // test type(s) |
| "[^|]*", // test data group |
| "boost::math::gamma_q_inv", 350, 60); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "[^|]*", // platform |
| "float|double", // test type(s) |
| "[^|]*", // test data group |
| "[^|]*", 4, 2); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "[^|]*", // platform |
| "real_concept", // test type(s) |
| "[^|]*medium[^|]*", // test data group |
| "[^|]*", 20, 5); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "[^|]*", // platform |
| "real_concept", // test type(s) |
| "[^|]*large[^|]*", // test data group |
| "[^|]*", 1000, 500); // test function |
| add_expected_result( |
| "[^|]*", // compiler |
| "[^|]*", // stdlib |
| "[^|]*", // platform |
| "real_concept", // test type(s) |
| "[^|]*small[^|]*", // test data group |
| "[^|]*", 3700, 500); // 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; |
| } |
| |
| #define BOOST_CHECK_CLOSE_EX(a, b, prec, i) \ |
| {\ |
| unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\ |
| BOOST_CHECK_CLOSE(a, b, prec); \ |
| if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\ |
| {\ |
| std::cerr << "Failure was at row " << i << std::endl;\ |
| std::cerr << std::setprecision(35); \ |
| std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\ |
| std::cerr << " , " << data[i][3] << " , " << data[i][4] << " , " << data[i][5] << " } " << std::endl;\ |
| }\ |
| } |
| |
| template <class T> |
| void do_test_gamma_2(const T& data, const char* type_name, const char* test_name) |
| { |
| // |
| // test gamma_p_inv(T, T) against data: |
| // |
| using namespace std; |
| typedef typename T::value_type row_type; |
| typedef typename row_type::value_type value_type; |
| |
| std::cout << test_name << " with type " << type_name << std::endl; |
| |
| // |
| // These sanity checks test for a round trip accuracy of one half |
| // of the bits in T, unless T is type float, in which case we check |
| // for just one decimal digit. The problem here is the sensitivity |
| // of the functions, not their accuracy. This test data was generated |
| // for the forward functions, which means that when it is used as |
| // the input to the inverses then it is necessarily inexact. This rounding |
| // of the input is what makes the data unsuitable for use as an accuracy check, |
| // and also demonstrates that you can't in general round-trip these functions. |
| // It is however a useful sanity check. |
| // |
| value_type precision = static_cast<value_type>(ldexp(1.0, 1-boost::math::policies::digits<value_type, boost::math::policies::policy<> >()/2)) * 100; |
| if(boost::math::policies::digits<value_type, boost::math::policies::policy<> >() < 50) |
| precision = 1; // 1% or two decimal digits, all we can hope for when the input is truncated to float |
| |
| for(unsigned i = 0; i < data.size(); ++i) |
| { |
| // |
| // These inverse tests are thrown off if the output of the |
| // incomplete gamma is too close to 1: basically there is insuffient |
| // information left in the value we're using as input to the inverse |
| // to be able to get back to the original value. |
| // |
| if(data[i][5] == 0) |
| BOOST_CHECK_EQUAL(boost::math::gamma_p_inv(data[i][0], data[i][5]), value_type(0)); |
| else if((1 - data[i][5] > 0.001) |
| && (fabs(data[i][5]) > 2 * boost::math::tools::min_value<value_type>()) |
| && (fabs(data[i][5]) > 2 * boost::math::tools::min_value<double>())) |
| { |
| value_type inv = boost::math::gamma_p_inv(data[i][0], data[i][5]); |
| BOOST_CHECK_CLOSE_EX(data[i][1], inv, precision, i); |
| } |
| else if(1 == data[i][5]) |
| BOOST_CHECK_EQUAL(boost::math::gamma_p_inv(data[i][0], data[i][5]), boost::math::tools::max_value<value_type>()); |
| else |
| { |
| // not enough bits in our input to get back to x, but we should be in |
| // the same ball park: |
| value_type inv = boost::math::gamma_p_inv(data[i][0], data[i][5]); |
| BOOST_CHECK_CLOSE_EX(data[i][1], inv, 100000, i); |
| } |
| |
| if(data[i][3] == 0) |
| BOOST_CHECK_EQUAL(boost::math::gamma_q_inv(data[i][0], data[i][3]), boost::math::tools::max_value<value_type>()); |
| else if((1 - data[i][3] > 0.001) && (fabs(data[i][3]) > 2 * boost::math::tools::min_value<value_type>())) |
| { |
| value_type inv = boost::math::gamma_q_inv(data[i][0], data[i][3]); |
| BOOST_CHECK_CLOSE_EX(data[i][1], inv, precision, i); |
| } |
| else if(1 == data[i][3]) |
| BOOST_CHECK_EQUAL(boost::math::gamma_q_inv(data[i][0], data[i][3]), value_type(0)); |
| else if(fabs(data[i][3]) > 2 * boost::math::tools::min_value<value_type>()) |
| { |
| // not enough bits in our input to get back to x, but we should be in |
| // the same ball park: |
| value_type inv = boost::math::gamma_q_inv(data[i][0], data[i][3]); |
| BOOST_CHECK_CLOSE_EX(data[i][1], inv, 100, i); |
| } |
| } |
| std::cout << std::endl; |
| } |
| |
| template <class T> |
| void do_test_gamma_inv(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::gamma_p_inv<value_type, value_type>; |
| #else |
| pg funcp = boost::math::gamma_p_inv; |
| #endif |
| |
| boost::math::tools::test_result<value_type> result; |
| |
| std::cout << "Testing " << test_name << " with type " << type_name |
| << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"; |
| |
| // |
| // test gamma_p_inv(T, T) against data: |
| // |
| 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::gamma_p_inv", test_name); |
| // |
| // test gamma_q_inv(T, T) against data: |
| // |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| funcp = boost::math::gamma_q_inv<value_type, value_type>; |
| #else |
| funcp = boost::math::gamma_q_inv; |
| #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_inv", test_name); |
| #ifdef TEST_OTHER |
| if(boost::is_floating_point<value_type>::value) |
| { |
| funcp = other::gamma_p_inv; |
| // |
| // test gamma_p_inv(T, T) against data: |
| // |
| result = boost::math::tools::test( |
| data, |
| bind_func(funcp, 0, 1), |
| extract_result(2)); |
| print_test_result(result, data[result.worst()], result.worst(), type_name, "other::gamma_q"); |
| // |
| // test gamma_q_inv(T, T) against data: |
| // |
| funcp = other::gamma_q_inv; |
| 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 |
| } |
| |
| 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, "Running round trip sanity checks on incomplete gamma medium sized values"); |
| |
| # include "igamma_small_data.ipp" |
| |
| do_test_gamma_2(igamma_small_data, name, "Running round trip sanity checks on incomplete gamma small values"); |
| |
| # include "igamma_big_data.ipp" |
| |
| do_test_gamma_2(igamma_big_data, name, "Running round trip sanity checks on incomplete gamma large values"); |
| |
| # include "gamma_inv_data.ipp" |
| |
| do_test_gamma_inv(gamma_inv_data, name, "incomplete gamma inverse(a, z) medium values"); |
| |
| # include "gamma_inv_big_data.ipp" |
| |
| do_test_gamma_inv(gamma_inv_big_data, name, "incomplete gamma inverse(a, z) large values"); |
| |
| # include "gamma_inv_small_data.ipp" |
| |
| do_test_gamma_inv(gamma_inv_small_data, name, "incomplete gamma inverse(a, z) small values"); |
| } |
| |
| template <class T> |
| void test_spots(T, const char* type_name) |
| { |
| std::cout << "Running spot checks for type " << type_name << std::endl; |
| // |
| // basic sanity checks, tolerance is 150 epsilon expressed as a percentage: |
| // |
| T tolerance = boost::math::tools::epsilon<T>() * 15000; |
| if(tolerance < 1e-25f) |
| tolerance = 1e-25f; // limit of test data? |
| BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(1)/100, static_cast<T>(1.0/128)), static_cast<T>(0.35767144525455121503672919307647515332256996883787L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(1)/100, static_cast<T>(0.5)), static_cast<T>(4.4655350189103486773248562646452806745879516124613e-31L), tolerance*10); |
| // |
| // We can't test in this region against Mathworld's data as the results produced |
| // by functions.wolfram.com appear to be in error, and do *not* round trip with |
| // their own version of gamma_q. Using our output from the inverse as input to |
| // their version of gamma_q *does* round trip however. It should be pointed out |
| // that the functions in this area are very sensitive with nearly infinite |
| // first derivatives, it's also questionable how useful these functions are |
| // in this part of the domain. |
| // |
| //BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(1e-2), static_cast<T>(1.0-1.0/128)), static_cast<T>(3.8106736649978161389878528903698068142257930575497e-181L), tolerance); |
| // |
| BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(0.5), static_cast<T>(1.0/128)), static_cast<T>(3.5379794687984498627918583429482809311448951189097L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(0.5), static_cast<T>(1.0/2)), static_cast<T>(0.22746821155978637597125832348982469815821055329511L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(0.5), static_cast<T>(1.0-1.0/128)), static_cast<T>(0.000047938431649305382237483273209405461203600840052182L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(10), static_cast<T>(1.0/128)), static_cast<T>(19.221865946801723949866005318845155649972164294057L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(10), static_cast<T>(1.0/2)), static_cast<T>(9.6687146147141311517500637401166726067778162022664L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(10), static_cast<T>(1.0-1.0/128)), static_cast<T>(3.9754602513640844712089002210120603689809432130520L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(10000), static_cast<T>(1.0/128)), static_cast<T>(10243.369973939134157953734588122880006091919872879L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(10000), static_cast<T>(1.0/2)), static_cast<T>(9999.6666686420474237369661574633153551436435884101L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::gamma_q_inv(static_cast<T>(10000), static_cast<T>(1.0-1.0/128)), static_cast<T>(9759.8597223369324083191194574874497413261589080204L), tolerance); |
| } |
| |
| int test_main(int, char* []) |
| { |
| expected_results(); |
| BOOST_MATH_CONTROL_FP; |
| |
| #ifndef BOOST_MATH_BUGGY_LARGE_FLOAT_CONSTANTS |
| #ifdef TEST_FLOAT |
| test_spots(0.0F, "float"); |
| #endif |
| #endif |
| #ifdef TEST_DOUBLE |
| test_spots(0.0, "double"); |
| #endif |
| #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS |
| #ifdef TEST_LDOUBLE |
| test_spots(0.0L, "long double"); |
| #endif |
| #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582)) |
| #ifdef TEST_REAL_CONCEPT |
| test_spots(boost::math::concepts::real_concept(0.1), "real_concept"); |
| #endif |
| #endif |
| #endif |
| |
| #ifndef BOOST_MATH_BUGGY_LARGE_FLOAT_CONSTANTS |
| #ifdef TEST_FLOAT |
| test_gamma(0.1F, "float"); |
| #endif |
| #endif |
| #ifdef TEST_DOUBLE |
| test_gamma(0.1, "double"); |
| #endif |
| #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS |
| #ifdef TEST_LDOUBLE |
| test_gamma(0.1L, "long double"); |
| #endif |
| #ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS |
| #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582)) |
| #ifdef TEST_REAL_CONCEPT |
| test_gamma(boost::math::concepts::real_concept(0.1), "real_concept"); |
| #endif |
| #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; |
| } |
| |
| |
| |
