mirror of
https://github.com/boostorg/math.git
synced 2026-01-27 07:02:08 +00:00
4bdf0dd8f0
Added new optimisation config options (still need documenting). Tidied up use of instrumentation code so they all use BOOST_MATH_INSTRUMENT now. Various tweaks to inverse incomplete beta and gamma to reduce number of iterations. Changed incomplete gamma and beta to calculate derivative at the same time as the function (performance optimisation for inverses). Fixed MinGW failures. Refactored and extended rational / polynomial test cases. [SVN r4172]
406 lines
18 KiB
C++
406 lines
18 KiB
C++
// (C) Copyright John Maddock 2006.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#include <boost/math/concepts/real_concept.hpp>
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#include <boost/test/included/test_exec_monitor.hpp>
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#include <boost/test/floating_point_comparison.hpp>
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#include <boost/math/special_functions/legendre.hpp>
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#include <boost/math/constants/constants.hpp>
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#include <boost/array.hpp>
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#include <boost/lambda/lambda.hpp>
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#include <boost/lambda/bind.hpp>
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#include "handle_test_result.hpp"
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#include "test_legendre_hooks.hpp"
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//
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// DESCRIPTION:
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// ~~~~~~~~~~~~
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//
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// This file tests the legendre polynomials.
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// There are two sets of tests, spot
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// tests which compare our results with selected values computed
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// using the online special function calculator at
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// functions.wolfram.com, while the bulk of the accuracy tests
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// use values generated with NTL::RR at 1000-bit precision
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// and our generic versions of these functions.
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//
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// Note that when this file is first run on a new platform many of
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// these tests will fail: the default accuracy is 1 epsilon which
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// is too tight for most platforms. In this situation you will
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// need to cast a human eye over the error rates reported and make
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// a judgement as to whether they are acceptable. Either way please
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// report the results to the Boost mailing list. Acceptable rates of
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// error are marked up below as a series of regular expressions that
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// identify the compiler/stdlib/platform/data-type/test-data/test-function
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// along with the maximum expected peek and RMS mean errors for that
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// test.
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//
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void expected_results()
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{
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//
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// Define the max and mean errors expected for
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// various compilers and platforms.
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//
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const char* largest_type;
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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if(boost::math::tools::digits<double>() == boost::math::tools::digits<long double>())
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{
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largest_type = "(long\\s+)?double";
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}
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else
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{
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largest_type = "long double";
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}
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#else
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largest_type = "(long\\s+)?double";
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#endif
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//
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// Linux:
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//
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if((std::numeric_limits<long double>::digits <= 64)
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&& (std::numeric_limits<long double>::digits != std::numeric_limits<double>::digits))
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{
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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".*", // platform
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"double", // test type(s)
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".*", // test data group
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".*", 10, 5); // test function
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#endif
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}
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if(std::numeric_limits<long double>::digits == 64)
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{
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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".*", // platform
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largest_type, // test type(s)
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"Legendre Polynomials.*Large.*", // test data group
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"boost::math::legendre_p", 1000, 200); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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".*", // platform
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largest_type, // test type(s)
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"Legendre Polynomials.*Large.*", // test data group
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"boost::math::legendre_q", 7000, 1000); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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".*", // platform
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"real_concept", // test type(s)
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"Legendre Polynomials.*Large.*", // test data group
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"boost::math::legendre_p", 1000, 200); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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".*", // platform
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"real_concept", // test type(s)
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"Legendre Polynomials.*Large.*", // test data group
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"boost::math::legendre_q", 7000, 1000); // test function
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}
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//
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// Catch all cases come last:
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//
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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".*", // platform
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largest_type, // test type(s)
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"Legendre Polynomials.*Large.*", // test data group
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"boost::math::legendre_p", 400, 200); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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".*", // platform
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largest_type, // test type(s)
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"Legendre Polynomials.*Large.*", // test data group
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"boost::math::legendre_q", 5400, 500); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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".*", // platform
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largest_type, // test type(s)
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"Legendre Polynomials.*", // test data group
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"boost::math::legendre_p", 300, 80); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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".*", // platform
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largest_type, // test type(s)
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"Legendre Polynomials.*", // test data group
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"boost::math::legendre_q", 100, 50); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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".*", // platform
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largest_type, // test type(s)
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"Associated Legendre Polynomials.*", // test data group
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".*", 200, 20); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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".*", // platform
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"real_concept", // test type(s)
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"Legendre Polynomials.*Large.*", // test data group
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"boost::math::legendre_p", 400, 200); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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".*", // platform
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"real_concept", // test type(s)
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"Legendre Polynomials.*Large.*", // test data group
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"boost::math::legendre_q", 5400, 500); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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".*", // platform
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"real_concept", // test type(s)
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"Legendre Polynomials.*", // test data group
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"boost::math::legendre_p", 300, 80); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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".*", // platform
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"real_concept", // test type(s)
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"Legendre Polynomials.*", // test data group
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"boost::math::legendre_q", 100, 50); // test function
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add_expected_result(
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".*", // compiler
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".*", // stdlib
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".*", // platform
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"real_concept", // test type(s)
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"Associated Legendre Polynomials.*", // test data group
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".*", 200, 20); // test function
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//
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// Finish off by printing out the compiler/stdlib/platform names,
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// we do this to make it easier to mark up expected error rates.
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//
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std::cout << "Tests run with " << BOOST_COMPILER << ", "
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<< BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
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}
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template <class T>
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void do_test_legendre_p(const T& data, const char* type_name, const char* test_name)
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{
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typedef typename T::value_type row_type;
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typedef typename row_type::value_type value_type;
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typedef value_type (*pg)(int, value_type);
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pg funcp = boost::math::legendre_p;
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typedef int (*cast_t)(value_type);
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cast_t rc = &boost::math::tools::real_cast<int, value_type>;
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boost::math::tools::test_result<value_type> result;
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std::cout << "Testing " << test_name << " with type " << type_name
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<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
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//
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// test legendre_p against data:
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//
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(funcp,
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boost::lambda::ret<int>(
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boost::lambda::bind(
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rc,
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boost::lambda::ret<value_type>(boost::lambda::_1[0]))),
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boost::lambda::ret<value_type>(boost::lambda::_1[1])),
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boost::lambda::ret<value_type>(boost::lambda::_1[2]));
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handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::legendre_p", test_name);
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#ifdef TEST_OTHER
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if(::boost::is_floating_point<value_type>::value){
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funcp = other::legendre_p;
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(funcp,
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boost::lambda::ret<int>(
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boost::lambda::bind(
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rc,
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boost::lambda::ret<value_type>(boost::lambda::_1[0]))),
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boost::lambda::ret<value_type>(boost::lambda::_1[1])),
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boost::lambda::ret<value_type>(boost::lambda::_1[2]));
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print_test_result(result, data[result.worst()], result.worst(), type_name, "other::legendre_p");
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}
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#endif
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typedef value_type (*pg2)(unsigned, value_type);
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pg2 funcp2 = boost::math::legendre_q;
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//
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// test legendre_q against data:
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//
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(funcp2,
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boost::lambda::ret<int>(
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boost::lambda::bind(
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rc,
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boost::lambda::ret<value_type>(boost::lambda::_1[0]))),
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boost::lambda::ret<value_type>(boost::lambda::_1[1])),
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boost::lambda::ret<value_type>(boost::lambda::_1[3]));
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handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::legendre_q", test_name);
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#ifdef TEST_OTHER
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if(::boost::is_floating_point<value_type>::value){
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funcp = other::legendre_q;
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(funcp2,
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boost::lambda::ret<int>(
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boost::lambda::bind(
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rc,
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boost::lambda::ret<value_type>(boost::lambda::_1[0]))),
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boost::lambda::ret<value_type>(boost::lambda::_1[1])),
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boost::lambda::ret<value_type>(boost::lambda::_1[3]));
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print_test_result(result, data[result.worst()], result.worst(), type_name, "other::legendre_q");
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}
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#endif
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std::cout << std::endl;
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}
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template <class T>
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void do_test_assoc_legendre_p(const T& data, const char* type_name, const char* test_name)
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{
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typedef typename T::value_type row_type;
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typedef typename row_type::value_type value_type;
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typedef value_type (*pg)(int, int, value_type);
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pg funcp = boost::math::legendre_p;
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typedef int (*cast_t)(value_type);
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cast_t rc = &boost::math::tools::real_cast<int, value_type>;
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boost::math::tools::test_result<value_type> result;
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std::cout << "Testing " << test_name << " with type " << type_name
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<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
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//
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// test legendre_p against data:
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//
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result = boost::math::tools::test(
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data,
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boost::lambda::bind(funcp,
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boost::lambda::ret<int>(
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boost::lambda::bind(
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rc,
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boost::lambda::ret<value_type>(boost::lambda::_1[0]))),
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boost::lambda::ret<int>(
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boost::lambda::bind(
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rc,
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boost::lambda::ret<value_type>(boost::lambda::_1[1]))),
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boost::lambda::ret<value_type>(boost::lambda::_1[2])),
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boost::lambda::ret<value_type>(boost::lambda::_1[3]));
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handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::legendre_p", test_name);
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std::cout << std::endl;
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}
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template <class T>
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void test_legendre_p(T, const char* name)
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{
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//
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// The actual test data is rather verbose, so it's in a separate file
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//
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// The contents are as follows, each row of data contains
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// three items, input value a, input value b and erf(a, b):
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//
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# include "legendre_p.ipp"
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do_test_legendre_p(legendre_p, name, "Legendre Polynomials: Small Values");
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# include "legendre_p_large.ipp"
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do_test_legendre_p(legendre_p_large, name, "Legendre Polynomials: Large Values");
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# include "assoc_legendre_p.ipp"
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do_test_assoc_legendre_p(assoc_legendre_p, name, "Associated Legendre Polynomials: Small Values");
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}
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template <class T>
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void test_spots(T, const char* t)
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{
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std::cout << "Testing basic sanity checks for type " << t << std::endl;
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//
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// basic sanity checks, tolerance is 100 epsilon:
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//
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T tolerance = boost::math::tools::epsilon<T>() * 100;
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(1, static_cast<T>(0.5L)), static_cast<T>(0.5L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-1, static_cast<T>(0.5L)), static_cast<T>(1L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, static_cast<T>(0.5L)), static_cast<T>(-0.2890625000000000000000000000000000000000L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, static_cast<T>(0.5L)), static_cast<T>(-0.4375000000000000000000000000000000000000L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, static_cast<T>(0.5L)), static_cast<T>(0.2231445312500000000000000000000000000000L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, static_cast<T>(0.5L)), static_cast<T>(0.3232421875000000000000000000000000000000L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, static_cast<T>(0.5L)), static_cast<T>(-0.09542943523261546936538467572384923220258L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, static_cast<T>(0.5L)), static_cast<T>(-0.1316993126940266257030910566308990611306L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, 2, static_cast<T>(0.5L)), static_cast<T>(4.218750000000000000000000000000000000000L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, 2, static_cast<T>(0.5L)), static_cast<T>(5.625000000000000000000000000000000000000L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, 5, static_cast<T>(0.5L)), static_cast<T>(-5696.789530152175143607977274672800795328L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, 4, static_cast<T>(0.5L)), static_cast<T>(465.1171875000000000000000000000000000000L), tolerance);
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if(std::numeric_limits<T>::max_exponent > std::numeric_limits<float>::max_exponent)
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{
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, 30, static_cast<T>(0.5L)), static_cast<T>(-7.855722083232252643913331343916012143461e45L), tolerance);
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}
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, 20, static_cast<T>(0.5L)), static_cast<T>(4.966634149702370788037088925152355134665e30L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, 2, static_cast<T>(-0.5L)), static_cast<T>(4.218750000000000000000000000000000000000L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, 2, static_cast<T>(-0.5L)), static_cast<T>(-5.625000000000000000000000000000000000000L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, 5, static_cast<T>(-0.5L)), static_cast<T>(-5696.789530152175143607977274672800795328L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, 4, static_cast<T>(-0.5L)), static_cast<T>(465.1171875000000000000000000000000000000L), tolerance);
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if(std::numeric_limits<T>::max_exponent > std::numeric_limits<float>::max_exponent)
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{
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, 30, static_cast<T>(-0.5L)), static_cast<T>(-7.855722083232252643913331343916012143461e45L), tolerance);
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}
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, 20, static_cast<T>(-0.5L)), static_cast<T>(-4.966634149702370788037088925152355134665e30L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, -2, static_cast<T>(0.5L)), static_cast<T>(0.01171875000000000000000000000000000000000L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, -2, static_cast<T>(0.5L)), static_cast<T>(0.04687500000000000000000000000000000000000L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, -5, static_cast<T>(0.5L)), static_cast<T>(0.00002378609812640364935569308025139290054701L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, -4, static_cast<T>(0.5L)), static_cast<T>(0.0002563476562500000000000000000000000000000L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, -30, static_cast<T>(0.5L)), static_cast<T>(-2.379819988646847616996471299410611801239e-48L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, -20, static_cast<T>(0.5L)), static_cast<T>(4.356454600748202401657099008867502679122e-33L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(1, static_cast<T>(0.5L)), static_cast<T>(-0.7253469278329725771511886907693685738381L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(4, static_cast<T>(0.5L)), static_cast<T>(0.4401745259867706044988642951843745400835L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(7, static_cast<T>(0.5L)), static_cast<T>(-0.3439152932669753451878700644212067616780L), tolerance);
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BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(40, static_cast<T>(0.5L)), static_cast<T>(0.1493671665503550095010454949479907886011L), tolerance);
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}
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int test_main(int, char* [])
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{
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test_spots(0.0F, "float");
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test_spots(0.0, "double");
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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test_spots(0.0L, "long double");
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test_spots(boost::math::concepts::real_concept(0.1), "real_concept");
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#endif
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expected_results();
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test_legendre_p(0.1F, "float");
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test_legendre_p(0.1, "double");
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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test_legendre_p(0.1L, "long double");
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test_legendre_p(boost::math::concepts::real_concept(0.1), "real_concept");
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#else
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std::cout << "<note>The long double tests have been disabled on this platform "
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|
"either because the long double overloads of the usual math functions are "
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|
"not available at all, or because they are too inaccurate for these tests "
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|
"to pass.</note>" << std::cout;
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|
#endif
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return 0;
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}
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