| // (C) Copyright John Maddock 2006. |
| // Use, modification and distribution are subject to the |
| // Boost Software License, Version 1.0. (See accompanying file |
| // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) |
| |
| #include <pch.hpp> |
| |
| #include <boost/math/concepts/real_concept.hpp> |
| #include <boost/math/special_functions/zeta.hpp> |
| #include <boost/test/test_exec_monitor.hpp> |
| #include <boost/test/floating_point_comparison.hpp> |
| #include <boost/math/tools/stats.hpp> |
| #include <boost/math/tools/test.hpp> |
| #include <boost/math/constants/constants.hpp> |
| #include <boost/type_traits/is_floating_point.hpp> |
| #include <boost/array.hpp> |
| #include "functor.hpp" |
| |
| #include "handle_test_result.hpp" |
| #include "test_zeta_hooks.hpp" |
| |
| // |
| // DESCRIPTION: |
| // ~~~~~~~~~~~~ |
| // |
| // This file tests the zeta function. There are two sets of tests: |
| // 1) Sanity checks: comparison to test values created with the |
| // online calculator at functions.wolfram.com |
| // 2) Accuracy tests use values generated with NTL::RR at |
| // 1000-bit precision and our generic versions of these functions. |
| // |
| // 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 |
| |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*Random values less than 1", // test data group |
| ".*", 1200, 500); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| ".*Random values less than 1", // test data group |
| ".*", 1200, 500); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*", // test data group |
| ".*", 3, 1); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| ".*", // test data group |
| ".*", 16, 5); // test function |
| |
| std::cout << "Tests run with " << BOOST_COMPILER << ", " |
| << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; |
| } |
| |
| template <class T> |
| void do_test_zeta(const T& data, const char* type_name, const char* test_name) |
| { |
| // |
| // test zeta(T) against data: |
| // |
| using namespace std; |
| typedef typename T::value_type row_type; |
| typedef typename row_type::value_type value_type; |
| |
| std::cout << test_name << " with type " << type_name << std::endl; |
| |
| typedef value_type (*pg)(value_type); |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| pg funcp = boost::math::zeta<value_type>; |
| #else |
| pg funcp = boost::math::zeta; |
| #endif |
| |
| boost::math::tools::test_result<value_type> result; |
| // |
| // test zeta against data: |
| // |
| result = boost::math::tools::test( |
| data, |
| bind_func(funcp, 0), |
| extract_result(1)); |
| handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::zeta", test_name); |
| #ifdef TEST_OTHER |
| if(boost::is_floating_point<value_type>::value) |
| { |
| funcp = other::zeta; |
| |
| result = boost::math::tools::test( |
| data, |
| bind_func(funcp, 0), |
| extract_result(1)); |
| handle_test_result(result, data[result.worst()], result.worst(), type_name, "other::zeta", test_name); |
| } |
| #endif |
| std::cout << std::endl; |
| } |
| template <class T> |
| void test_zeta(T, const char* name) |
| { |
| // |
| // The actual test data is rather verbose, so it's in a separate file |
| // |
| #include "zeta_data.ipp" |
| do_test_zeta(zeta_data, name, "Zeta: Random values greater than 1"); |
| #include "zeta_neg_data.ipp" |
| do_test_zeta(zeta_neg_data, name, "Zeta: Random values less than 1"); |
| #include "zeta_1_up_data.ipp" |
| do_test_zeta(zeta_1_up_data, name, "Zeta: Values close to and greater than 1"); |
| #include "zeta_1_below_data.ipp" |
| do_test_zeta(zeta_1_below_data, name, "Zeta: Values close to and less than 1"); |
| } |
| |
| extern "C" double zetac(double); |
| |
| 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 either 5 or 10 epsilon |
| // expressed as a percentage: |
| // |
| T tolerance = boost::math::tools::epsilon<T>() * 100 * |
| (boost::is_floating_point<T>::value ? 5 : 10); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(0.125)), static_cast<T>(-0.63277562349869525529352526763564627152686379131122L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(1023) / static_cast<T>(1024)), static_cast<T>(-1023.4228554489429786541032870895167448906103303056L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(1025) / static_cast<T>(1024)), static_cast<T>(1024.5772867695045940578681624248887776501597556226L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(0.5)), static_cast<T>(-1.46035450880958681288949915251529801246722933101258149054289L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(1.125)), static_cast<T>(8.5862412945105752999607544082693023591996301183069L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(2)), static_cast<T>(1.6449340668482264364724151666460251892189499012068L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(3.5)), static_cast<T>(1.1267338673170566464278124918549842722219969574036L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(4)), static_cast<T>(1.08232323371113819151600369654116790277475095191872690768298L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(4 + static_cast<T>(1) / 1024), static_cast<T>(1.08225596856391369799036835439238249195298434901488518878804L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(4.5)), static_cast<T>(1.05470751076145426402296728896028011727249383295625173068468L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(6.5)), static_cast<T>(1.01200589988852479610078491680478352908773213619144808841031L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(7.5)), static_cast<T>(1.00582672753652280770224164440459408011782510096320822989663L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(8.125)), static_cast<T>(1.0037305205308161603183307711439385250181080293472L), 2 * tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(16.125)), static_cast<T>(1.0000140128224754088474783648500235958510030511915L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(0)), static_cast<T>(-0.5L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(-0.125)), static_cast<T>(-0.39906966894504503550986928301421235400280637468895L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(-1)), static_cast<T>(-0.083333333333333333333333333333333333333333333333333L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(-2)), static_cast<T>(0L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(-2.5)), static_cast<T>(0.0085169287778503305423585670283444869362759902200745L), tolerance * 3); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(-3)), static_cast<T>(0.0083333333333333333333333333333333333333333333333333L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(-4)), static_cast<T>(0), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(-20)), static_cast<T>(0), tolerance * 100); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(-21)), static_cast<T>(-281.46014492753623188405797101449275362318840579710L), tolerance * 100); |
| BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast<T>(-30.125)), static_cast<T>(2.2762941726834511267740045451463455513839970804578e7L), tolerance * 100); |
| } |
| |
| int test_main(int, char* []) |
| { |
| expected_results(); |
| 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"); |
| #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 |
| |
| test_zeta(0.1F, "float"); |
| test_zeta(0.1, "double"); |
| #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS |
| test_zeta(0.1L, "long double"); |
| test_zeta(boost::math::concepts::real_concept(0.1), "real_concept"); |
| #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; |
| } |
| |
| |
| |