// Copyright Xiaogang Zhang 2006 // Copyright John Maddock 2006, 2007 // Copyright Paul A. Bristow 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 #ifdef _MSC_VER # pragma warning(disable : 4756) // overflow in constant arithmetic // Constants are too big for float case, but this doesn't matter for test. #endif #include #include #include #include #include #include "functor.hpp" #include "handle_test_result.hpp" // // DESCRIPTION: // ~~~~~~~~~~~~ // // This file tests the Elliptic Integrals of the third kind. // There are two sets of tests, spot // tests which compare our results with selected values computed // using the online special function calculator at // functions.wolfram.com, while the bulk of the accuracy tests // use values generated with NTL::RR at 1000-bit precision // and our generic versions of these functions. // // Note that when this file is first run on a new platform many of // these tests will fail: the default accuracy is 1 epsilon which // is too tight for most platforms. In this situation you will // need to cast a human eye over the error rates reported and make // a judgement as to whether they are acceptable. Either way please // report the results to the Boost mailing list. Acceptable rates of // error are marked up below as a series of regular expressions that // identify the compiler/stdlib/platform/data-type/test-data/test-function // along with the maximum expected peek and RMS mean errors for that // test. // void expected_results() { // // Define the max and mean errors expected for // various compilers and platforms. // const char* largest_type; #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS if(boost::math::policies::digits >() == boost::math::policies::digits >()) { largest_type = "(long\\s+)?double"; } else { largest_type = "long double"; } #else largest_type = "(long\\s+)?double"; #endif // // Catch all cases come last: // add_expected_result( ".*", // compiler ".*", // stdlib ".*", // platform largest_type, // test type(s) ".*Large.*", // test data group ".*", 50, 20); // test function add_expected_result( ".*", // compiler ".*", // stdlib ".*", // platform "real_concept", // test type(s) ".*Large.*", // test data group ".*", 50, 20); // test function add_expected_result( ".*", // compiler ".*", // stdlib ".*", // platform largest_type, // test type(s) ".*", // test data group ".*", 15, 8); // test function add_expected_result( ".*", // compiler ".*", // stdlib ".*", // platform "real_concept", // test type(s) ".*", // test data group ".*", 15, 8); // test function // // Finish off by printing out the compiler/stdlib/platform names, // we do this to make it easier to mark up expected error rates. // std::cout << "Tests run with " << BOOST_COMPILER << ", " << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl; } template void do_test_ellint_pi3(T& data, const char* type_name, const char* test) { typedef typename T::value_type row_type; typedef typename row_type::value_type value_type; std::cout << "Testing: " << test << std::endl; #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) value_type (*fp2)(value_type, value_type, value_type) = boost::math::ellint_3; #else value_type (*fp2)(value_type, value_type, value_type) = boost::math::ellint_3; #endif boost::math::tools::test_result result; result = boost::math::tools::test( data, bind_func(fp2, 2, 0, 1), extract_result(3)); handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::ellint_3", test); std::cout << std::endl; } template void do_test_ellint_pi2(T& data, const char* type_name, const char* test) { typedef typename T::value_type row_type; typedef typename row_type::value_type value_type; std::cout << "Testing: " << test << std::endl; #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) value_type (*fp2)(value_type, value_type) = boost::math::ellint_3; #else value_type (*fp2)(value_type, value_type) = boost::math::ellint_3; #endif boost::math::tools::test_result result; result = boost::math::tools::test( data, bind_func(fp2, 1, 0), extract_result(2)); handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::ellint_3", test); std::cout << std::endl; } template void test_spots(T, const char* type_name) { // function values calculated on http://functions.wolfram.com/ #define SC_(x) static_cast(BOOST_JOIN(x, L)) static const boost::array, 25> data1 = { SC_(1), SC_(-1), SC_(0), SC_(-1.557407724654902230506974807458360173087), SC_(0), SC_(-4), SC_(0.4), SC_(-4.153623371196831087495427530365430979011), SC_(0), SC_(8), SC_(-0.6), SC_(8.935930619078575123490612395578518914416), SC_(0), SC_(0.5), SC_(0.25), SC_(0.501246705365439492445236118603525029757890291780157969500480), SC_(0), SC_(0.5), SC_(0), SC_(0.5), SC_(-2), SC_(0.5), SC_(0), SC_(0.437501067017546278595664813509803743009132067629603474488486), SC_(0.25), SC_(0.5), SC_(0), SC_(0.510269830229213412212501938035914557628394166585442994564135), SC_(0.75), SC_(0.5), SC_(0), SC_(0.533293253875952645421201146925578536430596894471541312806165), SC_(0.75), SC_(0.75), SC_(0), SC_(0.871827580412760575085768367421866079353646112288567703061975), SC_(1), SC_(0.25), SC_(0), SC_(0.255341921221036266504482236490473678204201638800822621740476), SC_(2), SC_(0.25), SC_(0), SC_(0.261119051639220165094943572468224137699644963125853641716219), SC_(1023)/1024, SC_(1.5), SC_(0), SC_(13.2821612239764190363647953338544569682942329604483733197131), SC_(0.5), SC_(-1), SC_(0.5), SC_(-1.228014414316220642611298946293865487807), SC_(0.5), SC_(1e+10), SC_(0.5), SC_(1.536591003599172091573590441336982730551e+10), SC_(-1e+05), SC_(10), SC_(0.75), SC_(0.0347926099493147087821620459290460547131012904008557007934290), SC_(-1e+10), SC_(10), SC_(0.875), SC_(0.000109956202759561502329123384755016959364346382187364656768212), SC_(-1e+10), SC_(1e+20), SC_(0.875), SC_(1.00000626665567332602765201107198822183913978895904937646809e15), SC_(-1e+10), SC_(1608)/1024, SC_(0.875), SC_(0.0000157080616044072676127333183571107873332593142625043567690379), 1-SC_(1) / 1024, SC_(1e+20), SC_(0.875), SC_(6.43274293944380717581167058274600202023334985100499739678963e21), SC_(50), SC_(0.1), SC_(0.25), SC_(0.124573770342749525407523258569507331686458866564082916835900), SC_(1.125), SC_(1), SC_(0.25), SC_(1.77299767784815770192352979665283069318388205110727241629752), SC_(1.125), SC_(10), SC_(0.25), SC_(0.662467818678976949597336360256848770217429434745967677192487), SC_(1.125), SC_(3), SC_(0.25), SC_(-0.142697285116693775525461312178015106079842313950476205580178), SC_(257)/256, SC_(1.5), SC_(0.1), SC_(22.2111124684047142809404895720078056163182744133864821626782), SC_(257)/256, SC_(21.5), SC_(0.1), SC_(-0.535282720703701002972775208780096689181320029073372524045546), }; #undef SC_ do_test_ellint_pi3(data1, type_name, "Elliptic Integral PI: Mathworld Data"); #include "ellint_pi3_data.ipp" do_test_ellint_pi3(ellint_pi3_data, type_name, "Elliptic Integral PI: Random Data"); #include "ellint_pi3_large_data.ipp" do_test_ellint_pi3(ellint_pi3_large_data, type_name, "Elliptic Integral PI: Large Random Data"); // function values calculated on http://functions.wolfram.com/ #define SC_(x) static_cast(BOOST_JOIN(x, L)) static const boost::array, 9> data2 = { SC_(0), SC_(0.2), SC_(1.586867847454166237308008033828114192951), SC_(0), SC_(0.4), SC_(1.639999865864511206865258329748601457626), SC_(0), SC_(0), SC_(1.57079632679489661923132169163975144209858469968755291048747), SC_(0.5), SC_(0), SC_(2.221441469079183123507940495030346849307), SC_(-4), SC_(0.3), SC_(0.712708870925620061597924858162260293305195624270730660081949), SC_(-1e+05), SC_(-0.5), SC_(0.00496944596485066055800109163256108604615568144080386919012831), SC_(-1e+10), SC_(-0.75), SC_(0.0000157080225184890546939710019277357161497407143903832703317801), SC_(1) / 1024, SC_(-0.875), SC_(2.18674503176462374414944618968850352696579451638002110619287), SC_(1023)/1024, SC_(-0.875), SC_(101.045289804941384100960063898569538919135722087486350366997), }; #undef SC_ do_test_ellint_pi2(data2, type_name, "Complete Elliptic Integral PI: Mathworld Data"); #include "ellint_pi2_data.ipp" do_test_ellint_pi2(ellint_pi2_data, type_name, "Complete Elliptic Integral PI: Random Data"); // Special cases, exceptions etc: BOOST_CHECK_THROW(boost::math::ellint_3(T(1.0001), T(-1), T(0)), std::domain_error); BOOST_CHECK_THROW(boost::math::ellint_3(T(0.5), T(20), T(1.5)), std::domain_error); BOOST_CHECK_THROW(boost::math::ellint_3(T(1.0001), T(-1)), std::domain_error); BOOST_CHECK_THROW(boost::math::ellint_3(T(0.5), T(1)), std::domain_error); BOOST_CHECK_THROW(boost::math::ellint_3(T(0.5), T(2)), std::domain_error); } 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"); #ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS test_spots(boost::math::concepts::real_concept(0), "real_concept"); #endif #else std::cout << "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." << std::cout; #endif return 0; }