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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)
- #include <pch_light.hpp>
- #include "test_legendre.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
- "legendre_p", 1000, 200); // test function
- add_expected_result(
- "Intel.*", // compiler
- ".*", // stdlib
- ".*", // platform
- largest_type, // test type(s)
- "Legendre Polynomials.*Large.*", // test data group
- "legendre_q", 10000, 1000); // test function
- add_expected_result(
- ".*", // compiler
- ".*", // stdlib
- ".*", // platform
- largest_type, // test type(s)
- "Legendre Polynomials.*Large.*", // test data group
- "legendre_q", 7000, 1000); // test function
- add_expected_result(
- ".*", // compiler
- ".*", // stdlib
- ".*", // platform
- "real_concept", // test type(s)
- "Legendre Polynomials.*Large.*", // test data group
- "legendre_p", 1000, 200); // test function
- add_expected_result(
- ".*", // compiler
- ".*", // stdlib
- ".*", // platform
- "real_concept", // test type(s)
- "Legendre Polynomials.*Large.*", // test data group
- "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
- "legendre_p", 500, 200); // test function
- add_expected_result(
- ".*", // compiler
- ".*", // stdlib
- ".*", // platform
- largest_type, // test type(s)
- "Legendre Polynomials.*Large.*", // test data group
- "legendre_q", 5400, 500); // test function
- add_expected_result(
- ".*", // compiler
- ".*", // stdlib
- ".*", // platform
- largest_type, // test type(s)
- "Legendre Polynomials.*", // test data group
- "legendre_p", 300, 80); // test function
- add_expected_result(
- ".*", // compiler
- ".*", // stdlib
- ".*", // platform
- largest_type, // test type(s)
- "Legendre Polynomials.*", // test data group
- "legendre_q", 100, 50); // test function
- add_expected_result(
- "Intel.*", // compiler
- ".*", // stdlib
- ".*", // platform
- largest_type, // test type(s)
- "Associated Legendre Polynomials.*", // test data group
- ".*", 300, 20); // 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
- "legendre_p", 500, 200); // test function
- add_expected_result(
- ".*", // compiler
- ".*", // stdlib
- ".*", // platform
- "real_concept", // test type(s)
- "Legendre Polynomials.*Large.*", // test data group
- "legendre_q", 5400, 500); // test function
- add_expected_result(
- ".*", // compiler
- ".*", // stdlib
- ".*", // platform
- "real_concept", // test type(s)
- "Legendre Polynomials.*", // test data group
- "legendre_p", 300, 80); // test function
- add_expected_result(
- ".*", // compiler
- ".*", // stdlib
- ".*", // platform
- "real_concept", // test type(s)
- "Legendre Polynomials.*", // test data group
- "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;
- }
- BOOST_AUTO_TEST_CASE( test_main )
- {
- 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::endl;
- #endif
- test_legendre_p_prime<float>();
- test_legendre_p_prime<double>();
- test_legendre_p_prime<long double>();
- int ulp_distance = test_legendre_p_zeros_double_ulp(1, 100);
- BOOST_CHECK(ulp_distance <= 2);
- test_legendre_p_zeros<float>();
- test_legendre_p_zeros<double>();
- test_legendre_p_zeros<long double>();
- }
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