| // (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> |
| |
| #ifdef _MSC_VER |
| # pragma warning (disable : 4756) // overflow in constant arithmetic |
| #endif |
| |
| #include <boost/math/concepts/real_concept.hpp> |
| #include <boost/test/test_exec_monitor.hpp> |
| #include <boost/test/floating_point_comparison.hpp> |
| #include <boost/math/special_functions/legendre.hpp> |
| #include <boost/math/constants/constants.hpp> |
| #include <boost/array.hpp> |
| #include "functor.hpp" |
| |
| #include "handle_test_result.hpp" |
| #include "test_legendre_hooks.hpp" |
| |
| // |
| // DESCRIPTION: |
| // ~~~~~~~~~~~~ |
| // |
| // This file tests the legendre polynomials. |
| // 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: |
| // |
| if((std::numeric_limits<long double>::digits <= 64) |
| && (std::numeric_limits<long double>::digits != std::numeric_limits<double>::digits)) |
| { |
| #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "double", // test type(s) |
| ".*", // test data group |
| ".*", 10, 5); // test function |
| #endif |
| } |
| if(std::numeric_limits<long double>::digits == 64) |
| { |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| "Legendre Polynomials.*Large.*", // test data group |
| "boost::math::legendre_p", 1000, 200); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| "Legendre Polynomials.*Large.*", // test data group |
| "boost::math::legendre_q", 7000, 1000); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| "Legendre Polynomials.*Large.*", // test data group |
| "boost::math::legendre_p", 1000, 200); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| "Legendre Polynomials.*Large.*", // test data group |
| "boost::math::legendre_q", 7000, 1000); // test function |
| } |
| // |
| // Catch all cases come last: |
| // |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| "Legendre Polynomials.*Large.*", // test data group |
| "boost::math::legendre_p", 500, 200); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| "Legendre Polynomials.*Large.*", // test data group |
| "boost::math::legendre_q", 5400, 500); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| "Legendre Polynomials.*", // test data group |
| "boost::math::legendre_p", 300, 80); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| "Legendre Polynomials.*", // test data group |
| "boost::math::legendre_q", 100, 50); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| "Associated Legendre Polynomials.*", // test data group |
| ".*", 200, 20); // test function |
| |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| "Legendre Polynomials.*Large.*", // test data group |
| "boost::math::legendre_p", 500, 200); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| "Legendre Polynomials.*Large.*", // test data group |
| "boost::math::legendre_q", 5400, 500); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| "Legendre Polynomials.*", // test data group |
| "boost::math::legendre_p", 300, 80); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| "Legendre Polynomials.*", // test data group |
| "boost::math::legendre_q", 100, 50); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| "Associated Legendre Polynomials.*", // test data group |
| ".*", 200, 20); // 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_legendre_p(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)(int, value_type); |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| pg funcp = boost::math::legendre_p<value_type>; |
| #else |
| pg funcp = boost::math::legendre_p; |
| #endif |
| |
| boost::math::tools::test_result<value_type> result; |
| |
| std::cout << "Testing " << test_name << " with type " << type_name |
| << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"; |
| |
| // |
| // test legendre_p against data: |
| // |
| result = boost::math::tools::test( |
| data, |
| bind_func_int1(funcp, 0, 1), |
| extract_result(2)); |
| handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::legendre_p", test_name); |
| #ifdef TEST_OTHER |
| if(::boost::is_floating_point<value_type>::value){ |
| funcp = other::legendre_p; |
| result = boost::math::tools::test( |
| data, |
| bind_func_int1(funcp, 0, 1), |
| extract_result(2)); |
| print_test_result(result, data[result.worst()], result.worst(), type_name, "other::legendre_p"); |
| } |
| #endif |
| |
| typedef value_type (*pg2)(unsigned, value_type); |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| pg2 funcp2 = boost::math::legendre_q<value_type>; |
| #else |
| pg2 funcp2 = boost::math::legendre_q; |
| #endif |
| |
| // |
| // test legendre_q against data: |
| // |
| result = boost::math::tools::test( |
| data, |
| bind_func_int1(funcp2, 0, 1), |
| extract_result(3)); |
| handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::legendre_q", test_name); |
| #ifdef TEST_OTHER |
| if(::boost::is_floating_point<value_type>::value){ |
| funcp = other::legendre_q; |
| result = boost::math::tools::test( |
| data, |
| bind_func_int1(funcp2, 0, 1), |
| extract_result(3)); |
| print_test_result(result, data[result.worst()], result.worst(), type_name, "other::legendre_q"); |
| } |
| #endif |
| |
| |
| std::cout << std::endl; |
| } |
| |
| template <class T> |
| void do_test_assoc_legendre_p(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)(int, int, value_type); |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| pg funcp = boost::math::legendre_p<value_type>; |
| #else |
| pg funcp = boost::math::legendre_p; |
| #endif |
| |
| boost::math::tools::test_result<value_type> result; |
| |
| std::cout << "Testing " << test_name << " with type " << type_name |
| << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"; |
| |
| // |
| // test legendre_p against data: |
| // |
| result = boost::math::tools::test( |
| data, |
| bind_func_int2(funcp, 0, 1, 2), |
| extract_result(3)); |
| handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::legendre_p", test_name); |
| std::cout << std::endl; |
| } |
| |
| template <class T> |
| void test_legendre_p(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 a, input value b and erf(a, b): |
| // |
| # include "legendre_p.ipp" |
| |
| do_test_legendre_p(legendre_p, name, "Legendre Polynomials: Small Values"); |
| |
| # include "legendre_p_large.ipp" |
| |
| do_test_legendre_p(legendre_p_large, name, "Legendre Polynomials: Large Values"); |
| |
| # include "assoc_legendre_p.ipp" |
| |
| do_test_assoc_legendre_p(assoc_legendre_p, name, "Associated Legendre Polynomials: Small Values"); |
| |
| } |
| |
| template <class T> |
| void test_spots(T, const char* t) |
| { |
| std::cout << "Testing basic sanity checks for type " << t << std::endl; |
| // |
| // basic sanity checks, tolerance is 100 epsilon: |
| // |
| T tolerance = boost::math::tools::epsilon<T>() * 100; |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(1, static_cast<T>(0.5L)), static_cast<T>(0.5L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-1, static_cast<T>(0.5L)), static_cast<T>(1L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, static_cast<T>(0.5L)), static_cast<T>(-0.2890625000000000000000000000000000000000L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, static_cast<T>(0.5L)), static_cast<T>(-0.4375000000000000000000000000000000000000L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, static_cast<T>(0.5L)), static_cast<T>(0.2231445312500000000000000000000000000000L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, static_cast<T>(0.5L)), static_cast<T>(0.3232421875000000000000000000000000000000L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, static_cast<T>(0.5L)), static_cast<T>(-0.09542943523261546936538467572384923220258L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, static_cast<T>(0.5L)), static_cast<T>(-0.1316993126940266257030910566308990611306L), tolerance); |
| |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, 2, static_cast<T>(0.5L)), static_cast<T>(4.218750000000000000000000000000000000000L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, 2, static_cast<T>(0.5L)), static_cast<T>(5.625000000000000000000000000000000000000L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, 5, static_cast<T>(0.5L)), static_cast<T>(-5696.789530152175143607977274672800795328L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, 4, static_cast<T>(0.5L)), static_cast<T>(465.1171875000000000000000000000000000000L), tolerance); |
| if(std::numeric_limits<T>::max_exponent > std::numeric_limits<float>::max_exponent) |
| { |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, 30, static_cast<T>(0.5L)), static_cast<T>(-7.855722083232252643913331343916012143461e45L), tolerance); |
| } |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, 20, static_cast<T>(0.5L)), static_cast<T>(4.966634149702370788037088925152355134665e30L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, 2, static_cast<T>(-0.5L)), static_cast<T>(4.218750000000000000000000000000000000000L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, 2, static_cast<T>(-0.5L)), static_cast<T>(-5.625000000000000000000000000000000000000L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, 5, static_cast<T>(-0.5L)), static_cast<T>(-5696.789530152175143607977274672800795328L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, 4, static_cast<T>(-0.5L)), static_cast<T>(465.1171875000000000000000000000000000000L), tolerance); |
| if(std::numeric_limits<T>::max_exponent > std::numeric_limits<float>::max_exponent) |
| { |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, 30, static_cast<T>(-0.5L)), static_cast<T>(-7.855722083232252643913331343916012143461e45L), tolerance); |
| } |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, 20, static_cast<T>(-0.5L)), static_cast<T>(-4.966634149702370788037088925152355134665e30L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, -2, static_cast<T>(0.5L)), static_cast<T>(0.01171875000000000000000000000000000000000L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, -2, static_cast<T>(0.5L)), static_cast<T>(0.04687500000000000000000000000000000000000L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, -5, static_cast<T>(0.5L)), static_cast<T>(0.00002378609812640364935569308025139290054701L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, -4, static_cast<T>(0.5L)), static_cast<T>(0.0002563476562500000000000000000000000000000L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, -30, static_cast<T>(0.5L)), static_cast<T>(-2.379819988646847616996471299410611801239e-48L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, -20, static_cast<T>(0.5L)), static_cast<T>(4.356454600748202401657099008867502679122e-33L), tolerance); |
| |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(1, static_cast<T>(0.5L)), static_cast<T>(-0.7253469278329725771511886907693685738381L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(4, static_cast<T>(0.5L)), static_cast<T>(0.4401745259867706044988642951843745400835L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(7, static_cast<T>(0.5L)), static_cast<T>(-0.3439152932669753451878700644212067616780L), tolerance); |
| BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(40, static_cast<T>(0.5L)), static_cast<T>(0.1493671665503550095010454949479907886011L), tolerance); |
| } |
| |
| int test_main(int, char* []) |
| { |
| BOOST_MATH_CONTROL_FP; |
| test_spots(0.0F, "float"); |
| test_spots(0.0, "double"); |
| #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS |
| test_spots(0.0L, "long double"); |
| test_spots(boost::math::concepts::real_concept(0.1), "real_concept"); |
| #endif |
| |
| expected_results(); |
| |
| test_legendre_p(0.1F, "float"); |
| test_legendre_p(0.1, "double"); |
| #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS |
| test_legendre_p(0.1L, "long double"); |
| #ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS |
| test_legendre_p(boost::math::concepts::real_concept(0.1), "real_concept"); |
| #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; |
| } |
| |
| |
| |
