| // 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_2.hpp> |
| #include <boost/array.hpp> |
| #include "functor.hpp" |
| |
| #include "handle_test_result.hpp" |
| // |
| // DESCRIPTION: |
| // ~~~~~~~~~~~~ |
| // |
| // This file tests the Elliptic Integrals of the second 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) |
| ".*", // test data group |
| ".*", 15, 6); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| ".*", // test data group |
| ".*", 15, 6); // 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_e2(const 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_2<value_type, value_type>; |
| #else |
| value_type (*fp2)(value_type, value_type) = boost::math::ellint_2; |
| #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_2", test); |
| |
| std::cout << std::endl; |
| } |
| |
| template <typename T> |
| void do_test_ellint_e1(T& data, const char* type_name, const char* test) |
| { |
| typedef typename T::value_type row_type; |
| typedef typename row_type::value_type value_type; |
| boost::math::tools::test_result<value_type> result; |
| |
| std::cout << "Testing: " << test << std::endl; |
| |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| value_type (*fp1)(value_type) = boost::math::ellint_2<value_type>; |
| #else |
| value_type (*fp1)(value_type) = boost::math::ellint_2; |
| #endif |
| result = boost::math::tools::test( |
| data, |
| bind_func(fp1, 0), |
| extract_result(1)); |
| handle_test_result(result, data[result.worst()], result.worst(), |
| type_name, "boost::math::ellint_2", test); |
| |
| std::cout << std::endl; |
| } |
| |
| template <typename T> |
| void test_spots(T, const char* type_name) |
| { |
| // Function values calculated on http://functions.wolfram.com/ |
| // Note that Mathematica's EllipticE accepts k^2 as the second parameter. |
| #define SC_(x) static_cast<T>(BOOST_JOIN(x, L)) |
| static const boost::array<boost::array<T, 3>, 10> data1 = { |
| SC_(0), SC_(0), SC_(0), |
| SC_(-10), SC_(0), SC_(-10), |
| SC_(-1), SC_(-1), SC_(-0.84147098480789650665250232163029899962256306079837), |
| SC_(-4), SC_(900) / 1024, SC_(-3.1756145986492562317862928524528520686391383168377), |
| SC_(8), SC_(-600) / 1024, SC_(7.2473147180505693037677015377802777959345489333465), |
| SC_(1e-05), SC_(800) / 1024, SC_(9.999999999898274739584436515967055859383969942432E-6), |
| SC_(1e+05), SC_(100) / 1024, SC_(99761.153306972066658135668386691227343323331995888), |
| SC_(1e+10), SC_(-0.5), SC_(9.3421545766487137036576748555295222252286528414669e9), |
| static_cast<T>(ldexp(SC_(1), 66)), SC_(400) / 1024, SC_(7.0886102721911705466476846969992069994308167515242e19), |
| static_cast<T>(ldexp(SC_(1), 166)), SC_(900) / 1024, SC_(7.1259011068364515942912094521783688927118026465790e49), |
| }; |
| #undef SC_ |
| |
| do_test_ellint_e2(data1, type_name, "Elliptic Integral E: Mathworld Data"); |
| |
| #include "ellint_e2_data.ipp" |
| |
| do_test_ellint_e2(ellint_e2_data, type_name, "Elliptic Integral E: Random Data"); |
| |
| // Function values calculated on http://functions.wolfram.com/ |
| // Note that Mathematica's EllipticE accepts k^2 as the second parameter. |
| #define SC_(x) static_cast<T>(BOOST_JOIN(x, L)) |
| static const boost::array<boost::array<T, 2>, 10> data2 = { |
| SC_(-1), SC_(1), |
| SC_(0), SC_(1.5707963267948966192313216916397514420985846996876), |
| SC_(100) / 1024, SC_(1.5670445330545086723323795143598956428788609133377), |
| SC_(200) / 1024, SC_(1.5557071588766556854463404816624361127847775545087), |
| SC_(300) / 1024, SC_(1.5365278991162754883035625322482669608948678755743), |
| SC_(400) / 1024, SC_(1.5090417763083482272165682786143770446401437564021), |
| SC_(-0.5), SC_(1.4674622093394271554597952669909161360253617523272), |
| SC_(-600) / 1024, SC_(1.4257538571071297192428217218834579920545946473778), |
| SC_(-800) / 1024, SC_(1.2927868476159125056958680222998765985004489572909), |
| SC_(-900) / 1024, SC_(1.1966864890248739524112920627353824133420353430982), |
| }; |
| #undef SC_ |
| |
| do_test_ellint_e1(data2, type_name, "Elliptic Integral E: Mathworld Data"); |
| |
| #include "ellint_e_data.ipp" |
| |
| do_test_ellint_e1(ellint_e_data, type_name, "Elliptic Integral E: Random Data"); |
| } |
| |
| int test_main(int, char* []) |
| { |
| expected_results(); |
| BOOST_MATH_CONTROL_FP; |
| #ifndef BOOST_MATH_BUGGY_LARGE_FLOAT_CONSTANTS |
| test_spots(0.0F, "float"); |
| #endif |
| 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; |
| } |