| // 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 <pch.hpp> |
| |
| #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 <boost/math/concepts/real_concept.hpp> |
| #include <boost/test/test_exec_monitor.hpp> |
| #include <boost/test/floating_point_comparison.hpp> |
| #include <boost/math/special_functions/ellint_3.hpp> |
| #include <boost/array.hpp> |
| #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<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 |
| |
| // |
| // 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 <typename T> |
| 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<value_type, value_type, value_type>; |
| #else |
| value_type (*fp2)(value_type, value_type, value_type) = boost::math::ellint_3; |
| #endif |
| boost::math::tools::test_result<value_type> 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 <typename T> |
| 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<value_type, value_type>; |
| #else |
| value_type (*fp2)(value_type, value_type) = boost::math::ellint_3; |
| #endif |
| boost::math::tools::test_result<value_type> 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 <typename T> |
| void test_spots(T, const char* type_name) |
| { |
| // function values calculated on http://functions.wolfram.com/ |
| #define SC_(x) static_cast<T>(BOOST_JOIN(x, L)) |
| static const boost::array<boost::array<T, 4>, 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<T>(BOOST_JOIN(x, L)) |
| static const boost::array<boost::array<T, 3>, 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 << "<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; |
| } |
