| // (C) Copyright John Maddock 2007. |
| // 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/expint.hpp> |
| #include <boost/math/special_functions/trunc.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_expint_hooks.hpp" |
| |
| // |
| // DESCRIPTION: |
| // ~~~~~~~~~~~~ |
| // |
| // This file tests the expint functions. 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 |
| |
| // |
| // On MacOS X erfc has much higher error levels than |
| // expected: given that the implementation is basically |
| // just a rational function evaluation combined with |
| // exponentiation, we conclude that exp and pow are less |
| // accurate on this platform, especially when the result |
| // is outside the range of a double. |
| // |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "Mac OS", // platform |
| "float|double|long double", // test type(s) |
| ".*E1.*", // test data group |
| ".*", 30, 10); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "Mac OS", // platform |
| "float|double|long double", // test type(s) |
| ".*Ei.*", // test data group |
| ".*", 300, 200); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "Mac OS", // platform |
| ".*", // test type(s) |
| ".*", // test data group |
| ".*", 40, 15); // test function |
| |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "float|double|long double", // test type(s) |
| ".*E1.*", // test data group |
| ".*", 2, 1); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "float|double|long double", // test type(s) |
| ".*Ei.*", // test data group |
| ".*", 6, 3); // test function |
| if(std::numeric_limits<long double>::digits > 100) |
| { |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| ".*Ei.*", // test data group |
| ".*", 150, 50); // test function |
| } |
| add_expected_result( |
| "Sun.*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| ".*Ei.*", // test data group |
| ".*", 150, 50); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| ".*Ei.*", // test data group |
| ".*", 50, 20); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| ".*", // test type(s) |
| ".*", // test data group |
| ".*", 25, 5); // test function |
| |
| std::cout << "Tests run with " << BOOST_COMPILER << ", " |
| << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; |
| } |
| |
| template <class T> |
| T expint_wrapper(T n, T z) |
| { |
| return boost::math::expint( |
| boost::math::itrunc(n), z); |
| } |
| |
| #ifdef TEST_OTHER |
| template <class T> |
| T other_expint_wrapper(T n, T z) |
| { |
| return other::expint( |
| boost::math::itrunc(n), z); |
| } |
| #endif |
| template <class T> |
| void do_test_expint(const T& data, const char* type_name, const char* test_name) |
| { |
| // |
| // test En(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, value_type); |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| pg funcp = expint_wrapper<value_type>; |
| #else |
| pg funcp = expint_wrapper; |
| #endif |
| |
| boost::math::tools::test_result<value_type> result; |
| // |
| // test expint against data: |
| // |
| result = boost::math::tools::test( |
| data, |
| bind_func(funcp, 0, 1), |
| extract_result(2)); |
| handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::expint", test_name); |
| #ifdef TEST_OTHER |
| if(boost::is_floating_point<value_type>::value && other::expint(2u, 2.0)) |
| { |
| funcp = other_expint_wrapper; |
| // |
| // test expint against data: |
| // |
| result = boost::math::tools::test( |
| data, |
| bind_func(funcp, 0, 1), |
| extract_result(2)); |
| handle_test_result(result, data[result.worst()], result.worst(), type_name, "other::expint", test_name); |
| } |
| #endif |
| std::cout << std::endl; |
| } |
| |
| template <class T> |
| void do_test_expint_Ei(const T& data, const char* type_name, const char* test_name) |
| { |
| // |
| // test Ei(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::expint<value_type>; |
| #else |
| pg funcp = boost::math::expint; |
| #endif |
| |
| boost::math::tools::test_result<value_type> result; |
| // |
| // test expint 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::expint", test_name); |
| #ifdef TEST_OTHER |
| if(boost::is_floating_point<value_type>::value && other::expint(2.0)) |
| { |
| funcp = other::expint; |
| // |
| // test expint 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, "other::expint", test_name); |
| } |
| #endif |
| } |
| |
| template <class T> |
| void test_expint(T, const char* name) |
| { |
| // |
| // The actual test data is rather verbose, so it's in a separate file |
| // |
| #include "expint_data.ipp" |
| do_test_expint(expint_data, name, "Exponential Integral En"); |
| #include "expint_small_data.ipp" |
| do_test_expint(expint_small_data, name, "Exponential Integral En: small z values"); |
| #include "expint_1_data.ipp" |
| do_test_expint(expint_1_data, name, "Exponential Integral E1"); |
| #include "expinti_data.ipp" |
| do_test_expint_Ei(expinti_data, name, "Exponential Integral Ei"); |
| |
| if(boost::math::tools::log_max_value<T>() > 100) |
| { |
| #include "expinti_data_double.ipp" |
| do_test_expint_Ei(expinti_data_double, name, "Exponential Integral Ei: double exponent range"); |
| } |
| #if defined(LDBL_MAX_10_EXP) && (LDBL_MAX_10_EXP > 2000) |
| if(boost::math::tools::log_max_value<T>() > 1000) |
| { |
| #include "expinti_data_long.ipp" |
| do_test_expint_Ei(expinti_data_long, name, "Exponential Integral Ei: long exponent range"); |
| } |
| #endif |
| } |
| |
| 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 |
| // expressed as a percentage: |
| // |
| T tolerance = boost::math::tools::epsilon<T>() * 100 * |
| (boost::is_floating_point<T>::value ? 500 : 500); |
| // |
| // En: |
| // |
| BOOST_CHECK_CLOSE(::boost::math::expint(0, static_cast<T>(1)/1024), static_cast<T>(1023.0004881223430781283448725609773366468629307172L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(0, static_cast<T>(0.125F)), static_cast<T>(7.0599752206767632229191371458324058897760385999252L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(0, static_cast<T>(0.5F)), static_cast<T>(1.2130613194252668472075990699823609068838362709744L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(0, static_cast<T>(1.5F)), static_cast<T>(0.14875344009895321928885364717600834756144775290739L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(0, static_cast<T>(4.5F)), static_cast<T>(0.0024686658973871792213651409526512283936753927790603L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(0, static_cast<T>(50.0F)), static_cast<T>(3.8574996959278355660346856330540251495056653024605e-24L), tolerance); |
| |
| BOOST_CHECK_CLOSE(::boost::math::expint(1, static_cast<T>(1)/1024), static_cast<T>(6.3552324648310718026144555193580322129376300855378L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(1, static_cast<T>(0.125F)), static_cast<T>(1.6234256405841687914563069246244088736331060573721L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(1, static_cast<T>(0.5F)), static_cast<T>(0.55977359477616081174679593931508523522684689031635L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(1, static_cast<T>(1.5F)), static_cast<T>(0.10001958240663265190190933991166697826173000614035L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(1, static_cast<T>(4.5F)), static_cast<T>(0.0020734007547146144328855938695797884889319725701443L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(1, static_cast<T>(50.0F)), static_cast<T>(3.7832640295504590186989678540212857803028931862511e-24L), tolerance); |
| |
| BOOST_CHECK_CLOSE(::boost::math::expint(2, static_cast<T>(1)/1024), static_cast<T>(0.99281763247803906867747111039220635198625517639812L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(2, static_cast<T>(0.125F)), static_cast<T>(0.67956869751157430393285377765099962701786656781914L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(2, static_cast<T>(0.5F)), static_cast<T>(0.32664386232455301773040156533363783582849469032901L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(2, static_cast<T>(1.5F)), static_cast<T>(0.073100786538480851080416460896512053949576620150553L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(2, static_cast<T>(4.5F)), static_cast<T>(0.0017786931420265415481579618738214795713453909401220L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(2, static_cast<T>(50.0F)), static_cast<T>(3.7117833188688273667858889516369684601386058104706e-24L), tolerance); |
| |
| BOOST_CHECK_CLOSE(::boost::math::expint(5, static_cast<T>(1)/1024), static_cast<T>(0.24967471743034509414923673526350536071348482068601L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(5, static_cast<T>(0.125F)), static_cast<T>(0.21195078838966585733668853784460504343264488743527L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(5, static_cast<T>(0.5F)), static_cast<T>(0.13097731169586484777931864012654136046214618229236L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(5, static_cast<T>(1.5F)), static_cast<T>(0.038529924425495155395971538166055731456940831714065L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(5, static_cast<T>(4.5F)), static_cast<T>(0.0012311157382296328534406162790653865883418172939975L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(5, static_cast<T>(50.0F)), static_cast<T>(3.5124400631332394056901125740903320085753990490695e-24L), tolerance); |
| |
| BOOST_CHECK_CLOSE(::boost::math::expint(22, static_cast<T>(1)/1024), static_cast<T>(0.047570244582119027573000641518739337055625638422014L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(22, static_cast<T>(0.125F)), static_cast<T>(0.041762730174712898120606793100375713866392079558609L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(22, static_cast<T>(0.5F)), static_cast<T>(0.028178840877963713109230354192609362941651630844684L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(22, static_cast<T>(1.5F)), static_cast<T>(0.0098864453561701486668317763826728620676449196215016L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(22, static_cast<T>(4.5F)), static_cast<T>(0.00043257793497205419001613830279995985617548506505159L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(22, static_cast<T>(50.0F)), static_cast<T>(2.6900194251201629500599598206345018300567305625080e-24L), tolerance); |
| // |
| // Ei: |
| // |
| BOOST_CHECK_CLOSE(::boost::math::expint(static_cast<T>(1)/1024), static_cast<T>(-6.35327933972759151358547423727042905862963067106751711596065L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(static_cast<T>(0.125)), static_cast<T>(-1.37320852494298333781545045921206470808223543321810480716122L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(static_cast<T>(0.5)), static_cast<T>(0.454219904863173579920523812662802365281405554352642045162818L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(static_cast<T>(1)), static_cast<T>(1.89511781635593675546652093433163426901706058173270759164623L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(static_cast<T>(50.5)), static_cast<T>(1.72763195602911805201155668940185673806099654090456049881069e20L), tolerance); |
| |
| BOOST_CHECK_CLOSE(::boost::math::expint(static_cast<T>(-1)/1024), static_cast<T>(-6.35523246483107180261445551935803221293763008553775821607264L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(static_cast<T>(-0.125)), static_cast<T>(-1.62342564058416879145630692462440887363310605737209536579267L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(static_cast<T>(-0.5)), static_cast<T>(-0.559773594776160811746795939315085235226846890316353515248293L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(static_cast<T>(-1)), static_cast<T>(-0.219383934395520273677163775460121649031047293406908207577979L), tolerance); |
| BOOST_CHECK_CLOSE(::boost::math::expint(static_cast<T>(-50.5)), static_cast<T>(-2.27237132932219350440719707268817831250090574830769670186618e-24L), tolerance); |
| } |
| |
| int test_main(int, char* []) |
| { |
| expected_results(); |
| BOOST_MATH_CONTROL_FP; |
| |
| boost::math::expint(114.7); |
| |
| 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_expint(0.1F, "float"); |
| test_expint(0.1, "double"); |
| #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS |
| test_expint(0.1L, "long double"); |
| test_expint(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; |
| } |
| |
