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380 lines
17 KiB
C++
380 lines
17 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/math/special_functions/gamma.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/tools/stats.hpp>
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#include <boost/math/tools/test.hpp>
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#include <boost/math/constants/constants.hpp>
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#include <boost/type_traits/is_floating_point.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 "test_gamma_hooks.hpp"
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#include "handle_test_result.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 incomplete gamma functions tgamma,
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// tgamma_lower, gamma_P and gamma_Q. 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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add_expected_result(
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"[^|]*", // compiler
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"[^|]*", // stdlib
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"linux", // platform
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largest_type, // test type(s)
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"[^|]*medium[^|]*", // test data group
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"[^|]*", 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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"linux", // platform
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"real_concept", // test type(s)
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"[^|]*medium[^|]*", // test data group
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"[^|]*", 600, 200); // test function
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//
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// HP-UX:
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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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"HP-UX", // platform
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largest_type, // test type(s)
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"[^|]*medium[^|]*", // test data group
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"[^|]*", 500, 50); // test function
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add_expected_result(
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"[^|]*", // compiler
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"[^|]*", // stdlib
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"HP-UX", // platform
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"real_concept", // test type(s)
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"[^|]*medium[^|]*", // test data group
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"[^|]*", 500, 100); // test function
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//
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// Large exponent range causes more extreme test cases to be evaluated:
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//
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if(std::numeric_limits<long double>::max_exponent > std::numeric_limits<double>::max_exponent)
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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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"[^|]*large[^|]*", // test data group
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".*", 40000, 3000); // 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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"[^|]*medium[^|]*", // test data group
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"[^|]*", 50, 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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largest_type, // test type(s)
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"[^|]*small[^|]*", // test data group
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"[^|]*", 20, 10); // 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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"[^|]*large[^|]*", // test data group
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"boost::math::gamma_Q", 500, 50); // test function
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add_expected_result(
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"[^|]*", // compiler
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"[^|]*", // stdlib
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"Cygwin", // platform
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largest_type, // test type(s)
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"[^|]*large[^|]*", // test data group
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"boost::math::gamma_P", 700, 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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"[^|]*large[^|]*", // test data group
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"boost::math::gamma_P", 300, 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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"[^|]*integer[^|]*", // test data group
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".*", 20, 10); // 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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"[^|]*medium[^|]*", // test data group
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"[^|]*", 200, 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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"[^|]*small[^|]*", // test data group
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".*", 20, 10); // 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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"[^|]*large[^|]*", // test data group
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".*", 1000000, 100000); // 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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"[^|]*integer[^|]*", // test data group
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".*", 30, 10); // 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_gamma_2(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)(value_type, value_type);
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pg funcp = boost::math::tgamma;
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using namespace boost::lambda;
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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 tgamma(T, T) against data:
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//
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if(data[0][2] > 0)
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{
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result = boost::math::tools::test(
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data,
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bind(funcp, ret<value_type>(_1[0]), ret<value_type>(_1[1])),
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ret<value_type>(_1[2]));
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handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::tgamma", test_name);
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//
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// test tgamma_lower(T, T) against data:
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//
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funcp = boost::math::tgamma_lower;
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result = boost::math::tools::test(
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data,
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bind(funcp, ret<value_type>(_1[0]), ret<value_type>(_1[1])),
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ret<value_type>(_1[4]));
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handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::tgamma_lower", test_name);
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}
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//
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// test gamma_Q(T, T) against data:
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//
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funcp = boost::math::gamma_Q;
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result = boost::math::tools::test(
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data,
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bind(funcp, ret<value_type>(_1[0]), ret<value_type>(_1[1])),
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ret<value_type>(_1[3]));
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handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::gamma_Q", test_name);
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#if defined(TEST_CEPHES) || defined(TEST_GSL)
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//
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// test other gamma_Q(T, T) against data:
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//
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if(boost::is_floating_point<value_type>::value)
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{
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funcp = other::gamma_Q;
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result = boost::math::tools::test(
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data,
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bind(funcp, ret<value_type>(_1[0]), ret<value_type>(_1[1])),
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ret<value_type>(_1[3]));
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print_test_result(result, data[result.worst()], result.worst(), type_name, "other::gamma_Q");
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}
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#endif
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//
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// test gamma_P(T, T) against data:
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//
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funcp = boost::math::gamma_P;
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result = boost::math::tools::test(
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data,
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bind(funcp, ret<value_type>(_1[0]), ret<value_type>(_1[1])),
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ret<value_type>(_1[5]));
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handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::gamma_P", test_name);
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#if defined(TEST_CEPHES) || defined(TEST_GSL)
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//
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// test other gamma_P(T, T) against data:
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//
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if(boost::is_floating_point<value_type>::value)
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{
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funcp = other::gamma_P;
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result = boost::math::tools::test(
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data,
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bind(funcp, ret<value_type>(_1[0]), ret<value_type>(_1[1])),
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ret<value_type>(_1[5]));
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print_test_result(result, data[result.worst()], result.worst(), type_name, "other::gamma_P");
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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 test_gamma(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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// First the data for the incomplete gamma function, each
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// row has the following 6 entries:
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// Parameter a, parameter z,
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// Expected tgamma(a, z), Expected gamma_Q(a, z)
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// Expected tgamma_lower(a, z), Expected gamma_P(a, z)
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//
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# include "igamma_med_data.ipp"
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do_test_gamma_2(igamma_med_data, name, "tgamma(a, z) medium values");
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# include "igamma_small_data.ipp"
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do_test_gamma_2(igamma_small_data, name, "tgamma(a, z) small values");
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# include "igamma_big_data.ipp"
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do_test_gamma_2(igamma_big_data, name, "tgamma(a, z) large values");
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# include "igamma_int_data.ipp"
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do_test_gamma_2(igamma_int_data, name, "tgamma(a, z) integer and half integer values");
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}
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template <class T>
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void test_spots(T)
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{
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//
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// basic sanity checks, tolerance is 10 epsilon expressed as a percentage:
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//
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T tolerance = boost::math::tools::epsilon<T>() * 1000;
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(5), static_cast<T>(1)), static_cast<T>(23.912163676143750903709045060494956383977723517065L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(5), static_cast<T>(5)), static_cast<T>(10.571838841565097874621959975919877646444998907920L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(5), static_cast<T>(10)), static_cast<T>(0.70206451384706574414638719662835463671916532623256L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(5), static_cast<T>(100)), static_cast<T>(3.8734332808745531496973774140085644548465762343719e-36L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(0.5), static_cast<T>(0.5)), static_cast<T>(0.56241823159440712427949495730204306902676756479651L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(0.5), static_cast<T>(9)/10), static_cast<T>(0.31853210360412109873859360390443790076576777747449L), tolerance*10);
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(0.5), static_cast<T>(5)), static_cast<T>(0.0027746032604128093194908357272603294120210079791437L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma(static_cast<T>(0.5), static_cast<T>(100)), static_cast<T>(3.7017478604082789202535664481339075721362102520338e-45L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma_lower(static_cast<T>(5), static_cast<T>(1)), static_cast<T>(0.087836323856249096290954939505043616022276482935091L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma_lower(static_cast<T>(5), static_cast<T>(5)), static_cast<T>(13.428161158434902125378040024080122353555001092080L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma_lower(static_cast<T>(5), static_cast<T>(10)), static_cast<T>(23.297935486152934255853612803371645363280834673767L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::tgamma_lower(static_cast<T>(5), static_cast<T>(100)), static_cast<T>(23.999999999999999999999999999999999996126566719125L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_Q(static_cast<T>(5), static_cast<T>(1)), static_cast<T>(0.99634015317265628765454354418728984933240514654437L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_Q(static_cast<T>(5), static_cast<T>(5)), static_cast<T>(0.44049328506521241144258166566332823526854162116334L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_Q(static_cast<T>(5), static_cast<T>(10)), static_cast<T>(0.029252688076961072672766133192848109863298555259690L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_Q(static_cast<T>(5), static_cast<T>(100)), static_cast<T>(1.6139305336977304790405739225035685228527400976549e-37L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_Q(static_cast<T>(1.5), static_cast<T>(2)), static_cast<T>(0.26146412994911062220282207597592120190281060919079L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_Q(static_cast<T>(20.5), static_cast<T>(22)), static_cast<T>(0.34575332043467326814971590879658406632570278929072L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_P(static_cast<T>(5), static_cast<T>(1)), static_cast<T>(0.0036598468273437123454564558127101506675948534556288L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_P(static_cast<T>(5), static_cast<T>(5)), static_cast<T>(0.55950671493478758855741833433667176473145837883666L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_P(static_cast<T>(5), static_cast<T>(10)), static_cast<T>(0.97074731192303892732723386680715189013670144474031L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_P(static_cast<T>(5), static_cast<T>(100)), static_cast<T>(0.9999999999999999999999999999999999998386069466302L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_P(static_cast<T>(1.5), static_cast<T>(2)), static_cast<T>(0.73853587005088937779717792402407879809718939080921L), tolerance);
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BOOST_CHECK_CLOSE(::boost::math::gamma_P(static_cast<T>(20.5), static_cast<T>(22)), static_cast<T>(0.65424667956532673185028409120341593367429721070928L), tolerance);
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// naive check on derivative function:
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using namespace std; // For ADL of std functions
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tolerance = boost::math::tools::epsilon<T>() * 5000; // 50 eps
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BOOST_CHECK_CLOSE(::boost::math::gamma_P_derivative(static_cast<T>(20.5), static_cast<T>(22)),
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exp(static_cast<T>(-22)) * pow(static_cast<T>(22), static_cast<T>(19.5)) / boost::math::tgamma(static_cast<T>(20.5)), tolerance);
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}
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int test_main(int, char* [])
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{
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expected_results();
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test_spots(0.0F);
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test_spots(0.0);
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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test_spots(0.0L);
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test_spots(boost::math::concepts::real_concept(0.1));
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#endif
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test_gamma(0.1F, "float");
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test_gamma(0.1, "double");
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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test_gamma(0.1L, "long double");
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test_gamma(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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