| // 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_1.hpp> |
| #include <boost/array.hpp> |
| #include "functor.hpp" |
| |
| #include "handle_test_result.hpp" |
| // |
| // DESCRIPTION: |
| // ~~~~~~~~~~~~ |
| // |
| // This file tests the Elliptic Integrals of the first 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 |
| ".*", 5, 3); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| ".*", // test data group |
| ".*", 5, 3); // 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_f(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_1<value_type, value_type>; |
| #else |
| value_type (*fp2)(value_type, value_type) = boost::math::ellint_1; |
| #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_1", test); |
| |
| std::cout << std::endl; |
| |
| } |
| |
| template <typename T> |
| void do_test_ellint_k(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_1<value_type>; |
| #else |
| value_type (*fp1)(value_type) = boost::math::ellint_1; |
| #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_1", 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 EllipticF 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>, 19> data1 = { |
| SC_(0), SC_(0), SC_(0), |
| SC_(-10), SC_(0), SC_(-10), |
| SC_(-1), SC_(-1), SC_(-1.2261911708835170708130609674719067527242483502207), |
| SC_(-4), SC_(0.875), SC_(-5.3190556182262405182189463092940736859067548232647), |
| SC_(8), SC_(-0.625), SC_(9.0419973860310100524448893214394562615252527557062), |
| SC_(1e-05), SC_(0.875), SC_(0.000010000000000127604166668510945638036143355898993088), |
| SC_(1e+05), SC_(10)/1024, SC_(100002.38431454899771096037307519328741455615271038), |
| SC_(1e-20), SC_(1), SC_(1.0000000000000000000000000000000000000000166666667e-20), |
| SC_(1e-20), SC_(1e-20), SC_(1.000000000000000e-20), |
| SC_(1e+20), SC_(400)/1024, SC_(1.0418143796499216839719289963154558027005142709763e20), |
| SC_(1e+50), SC_(0.875), SC_(1.3913251718238765549409892714295358043696028445944e50), |
| SC_(2), SC_(0.5), SC_(2.1765877052210673672479877957388515321497888026770), |
| SC_(4), SC_(0.5), SC_(4.2543274975235836861894752787874633017836785640477), |
| SC_(6), SC_(0.5), SC_(6.4588766202317746302999080620490579800463614807916), |
| SC_(10), SC_(0.5), SC_(10.697409951222544858346795279378531495869386960090), |
| SC_(-2), SC_(0.5), SC_(-2.1765877052210673672479877957388515321497888026770), |
| SC_(-4), SC_(0.5), SC_(-4.2543274975235836861894752787874633017836785640477), |
| SC_(-6), SC_(0.5), SC_(-6.4588766202317746302999080620490579800463614807916), |
| SC_(-10), SC_(0.5), SC_(-10.697409951222544858346795279378531495869386960090), |
| }; |
| #undef SC_ |
| |
| do_test_ellint_f(data1, type_name, "Elliptic Integral F: Mathworld Data"); |
| |
| #include "ellint_f_data.ipp" |
| |
| do_test_ellint_f(ellint_f_data, type_name, "Elliptic Integral F: Random Data"); |
| |
| // Function values calculated on http://functions.wolfram.com/ |
| // Note that Mathematica's EllipticK 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>, 9> data2 = { |
| SC_(0), SC_(1.5707963267948966192313216916397514420985846996876), |
| SC_(0.125), SC_(1.5769867712158131421244030532288080803822271060839), |
| SC_(0.25), SC_(1.5962422221317835101489690714979498795055744578951), |
| SC_(300)/1024, SC_(1.6062331054696636704261124078746600894998873503208), |
| SC_(400)/1024, SC_(1.6364782007562008756208066125715722889067992997614), |
| SC_(-0.5), SC_(1.6857503548125960428712036577990769895008008941411), |
| SC_(-0.75), SC_(1.9109897807518291965531482187613425592531451316788), |
| 1-SC_(1)/8, SC_(2.185488469278223686913080323730158689730428415766), |
| 1-SC_(1)/1024, SC_(4.5074135978990422666372495313621124487894807327687), |
| }; |
| #undef SC_ |
| |
| do_test_ellint_k(data2, type_name, "Elliptic Integral K: Mathworld Data"); |
| |
| #include "ellint_k_data.ipp" |
| |
| do_test_ellint_k(ellint_k_data, type_name, "Elliptic Integral K: Random Data"); |
| } |
| |
| 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; |
| } |