| // (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> |
| |
| #define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error |
| #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/bessel.hpp> |
| #include <boost/type_traits/is_floating_point.hpp> |
| #include <boost/array.hpp> |
| #include "functor.hpp" |
| |
| #include "handle_test_result.hpp" |
| #include "test_bessel_hooks.hpp" |
| |
| // |
| // DESCRIPTION: |
| // ~~~~~~~~~~~~ |
| // |
| // This file tests the bessel Y function. 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|real_concept"; |
| } |
| else |
| { |
| largest_type = "long double|real_concept"; |
| } |
| #else |
| largest_type = "(long\\s+)?double"; |
| #endif |
| |
| // |
| // HP-UX and Solaris rates are very slightly higher: |
| // |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "HP-UX|Sun Solaris", // platform |
| largest_type, // test type(s) |
| ".*(Y[nv]|y).*Random.*", // test data group |
| ".*", 30000, 30000); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "HP-UX|Sun Solaris", // platform |
| largest_type, // test type(s) |
| ".*Y[01Nv].*", // test data group |
| ".*", 1300, 500); // test function |
| // |
| // Tru64: |
| // |
| add_expected_result( |
| ".*Tru64.*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*(Y[nv]|y).*Random.*", // test data group |
| ".*", 30000, 30000); // test function |
| add_expected_result( |
| ".*Tru64.*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*Y[01Nv].*", // test data group |
| ".*", 400, 200); // test function |
| |
| // |
| // Mac OS X rates are very slightly higher: |
| // |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "Mac OS", // platform |
| largest_type, // test type(s) |
| ".*(Y[nv1]).*", // test data group |
| ".*", 600000, 100000); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "Mac OS", // platform |
| "long double|real_concept", // test type(s) |
| ".*Y[0].*", // test data group |
| ".*", 1200, 1000); // test function |
| |
| // |
| // Linux: |
| // |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "linux", // platform |
| largest_type, // test type(s) |
| ".*Yv.*Random.*", // test data group |
| ".*", 200000, 200000); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "linux", // platform |
| largest_type, // test type(s) |
| ".*Y[01v].*", // test data group |
| ".*", 2000, 1000); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "linux", // platform |
| largest_type, // test type(s) |
| ".*Yn.*", // test data group |
| ".*", 30000, 30000); // test function |
| // |
| // MinGW: |
| // |
| add_expected_result( |
| ".*mingw.*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*Yv.*Random.*", // test data group |
| ".*", 200000, 200000); // test function |
| add_expected_result( |
| ".*mingw.*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*Y[01v].*", // test data group |
| ".*", 2000, 1000); // test function |
| add_expected_result( |
| ".*mingw.*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*Yn.*", // test data group |
| ".*", 30000, 30000); // test function |
| // |
| // Solaris version of long double has it's own error rates, |
| // again just a touch higher than msvc's 64-bit double: |
| // |
| add_expected_result( |
| "GNU.*", // compiler |
| ".*", // stdlib |
| "Sun.*", // platform |
| largest_type, // test type(s) |
| "Y[0N].*Mathworld.*", // test data group |
| ".*", 2000, 2000); // test function |
| |
| #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS |
| if((std::numeric_limits<double>::digits != std::numeric_limits<long double>::digits) |
| && (std::numeric_limits<long double>::digits < 90)) |
| { |
| // some errors spill over into type double as well: |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "double", // test type(s) |
| ".*Y[Nn].*", // test data group |
| ".*", 20, 20); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "double", // test type(s) |
| ".*Yv.*", // test data group |
| ".*", 80, 70); // test function |
| } |
| #endif |
| // |
| // defaults are based on MSVC-8 on Win32: |
| // |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*Y0.*Random.*", // test data group |
| ".*", 600, 400); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| ".*(Y[nv]|y).*Random.*", // test data group |
| ".*", 2000, 2000); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*(Y[nv]|y).*Random.*", // test data group |
| ".*", 1500, 1000); // test function |
| // |
| // Fallback for sun has to go after the general cases above: |
| // |
| add_expected_result( |
| "GNU.*", // compiler |
| ".*", // stdlib |
| "Sun.*", // platform |
| largest_type, // test type(s) |
| "Y[0N].*", // test data group |
| ".*", 200, 200); // test function |
| // |
| // General fallback: |
| // |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*", // test data group |
| ".*", 60, 40); // 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 <class T> |
| void do_test_cyl_neumann_y(const T& data, const char* type_name, const char* test_name) |
| { |
| typedef typename T::value_type row_type; |
| typedef typename row_type::value_type value_type; |
| |
| typedef value_type (*pg)(value_type, value_type); |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| pg funcp = boost::math::cyl_neumann<value_type, value_type>; |
| #else |
| pg funcp = boost::math::cyl_neumann; |
| #endif |
| |
| boost::math::tools::test_result<value_type> result; |
| |
| std::cout << "Testing " << test_name << " with type " << type_name |
| << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"; |
| |
| // |
| // test cyl_neumann 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::cyl_neumann", test_name); |
| std::cout << std::endl; |
| |
| #ifdef TEST_OTHER |
| if(boost::is_floating_point<value_type>::value) |
| { |
| funcp = other::cyl_neumann; |
| |
| // |
| // test other::cyl_neumann 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::cyl_neumann", test_name); |
| std::cout << std::endl; |
| } |
| #endif |
| } |
| |
| template <class T> |
| T cyl_neumann_int_wrapper(T v, T x) |
| { |
| return static_cast<T>(boost::math::cyl_neumann(boost::math::itrunc(v), x)); |
| } |
| |
| template <class T> |
| void do_test_cyl_neumann_y_int(const T& data, const char* type_name, const char* test_name) |
| { |
| typedef typename T::value_type row_type; |
| typedef typename row_type::value_type value_type; |
| |
| typedef value_type (*pg)(value_type, value_type); |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| pg funcp = cyl_neumann_int_wrapper<value_type>; |
| #else |
| pg funcp = cyl_neumann_int_wrapper; |
| #endif |
| |
| boost::math::tools::test_result<value_type> result; |
| |
| std::cout << "Testing " << test_name << " with type " << type_name |
| << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"; |
| |
| // |
| // test cyl_neumann 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::cyl_neumann", test_name); |
| std::cout << std::endl; |
| } |
| |
| template <class T> |
| void do_test_sph_neumann_y(const T& data, const char* type_name, const char* test_name) |
| { |
| typedef typename T::value_type row_type; |
| typedef typename row_type::value_type value_type; |
| |
| typedef value_type (*pg)(unsigned, value_type); |
| #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) |
| pg funcp = boost::math::sph_neumann<value_type>; |
| #else |
| pg funcp = boost::math::sph_neumann; |
| #endif |
| |
| typedef int (*cast_t)(value_type); |
| |
| boost::math::tools::test_result<value_type> result; |
| |
| std::cout << "Testing " << test_name << " with type " << type_name |
| << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"; |
| |
| // |
| // test sph_neumann against data: |
| // |
| result = boost::math::tools::test( |
| data, |
| bind_func_int1(funcp, 0, 1), |
| extract_result(2)); |
| handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::cyl_neumann", test_name); |
| std::cout << std::endl; |
| } |
| |
| template <class T> |
| void test_bessel(T, const char* name) |
| { |
| // |
| // The actual test data is rather verbose, so it's in a separate file |
| // |
| // The contents are as follows, each row of data contains |
| // three items, input value a, input value b and erf(a, b): |
| // |
| // 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> y0_data = {{ |
| SC_(0), SC_(1), SC_(0.0882569642156769579829267660235151628278175230906755467110438), |
| SC_(0), SC_(2), SC_(0.510375672649745119596606592727157873268139227085846135571839), |
| SC_(0), SC_(4), SC_(-0.0169407393250649919036351344471532182404925898980149027169321), |
| SC_(0), SC_(8), SC_(0.223521489387566220527323400498620359274814930781423577578334), |
| SC_(0), SC_(1e-05), SC_(-7.40316028370197013259676050746759072070960287586102867247159), |
| SC_(0), SC_(1e-10), SC_(-14.7325162726972420426916696426209144888762342592762415255386), |
| SC_(0), SC_(1e-20), SC_(-29.3912282502857968601858410375186700783698345615477536431464), |
| SC_(0), SC_(1e+03), SC_(0.00471591797762281339977326146566525500985900489680197718528000), |
| SC_(0), SC_(1e+05), SC_(0.00184676615886506410434074102431546125884886798090392516843524) |
| }}; |
| static const boost::array<boost::array<T, 3>, 9> y1_data = { |
| SC_(1), SC_(1), SC_(-0.781212821300288716547150000047964820549906390716444607843833), |
| SC_(1), SC_(2), SC_(-0.107032431540937546888370772277476636687480898235053860525795), |
| SC_(1), SC_(4), SC_(0.397925710557100005253979972450791852271189181622908340876586), |
| SC_(1), SC_(8), SC_(-0.158060461731247494255555266187483550327344049526705737651263), |
| SC_(1), SC_(1e-10), SC_(-6.36619772367581343150789184284462611709080831190542841855708e9), |
| SC_(1), SC_(1e-20), SC_(-6.36619772367581343075535053490057448139324059868649274367256e19), |
| SC_(1), SC_(1e+01), SC_(0.249015424206953883923283474663222803260416543069658461246944), |
| SC_(1), SC_(1e+03), SC_(-0.0247843312923517789148623560971412909386318548648705287583490), |
| SC_(1), SC_(1e+05), SC_(0.00171921035008825630099494523539897102954509504993494957572726) |
| }; |
| static const boost::array<boost::array<T, 3>, 9> yn_data = { |
| SC_(2), SC_(1e-20), SC_(-1.27323954473516268615107010698011489627570899691226996904849e40), |
| SC_(5), SC_(10), SC_(0.135403047689362303197029014762241709088405766746419538495983), |
| SC_(-5), SC_(1e+06), SC_(0.000331052088322609048503535570014688967096938338061796192422114), |
| SC_(10), SC_(10), SC_(-0.359814152183402722051986577343560609358382147846904467526222), |
| SC_(10), SC_(1e-10), SC_(-1.18280490494334933900960937719565669877576135140014365217993e108), |
| SC_(-10), SC_(1e+06), SC_(0.000725951969295187086245251366365393653610914686201194434805730), |
| SC_(1e+02), SC_(5), SC_(-5.08486391602022287993091563093082035595081274976837280338134e115), |
| SC_(1e+03), SC_(1e+05), SC_(0.00217254919137684037092834146629212647764581965821326561261181), |
| SC_(-1e+03), SC_(7e+02), SC_(-1.88753109980945889960843803284345261796244752396992106755091e77) |
| }; |
| static const boost::array<boost::array<T, 3>, 9> yv_data = { |
| //SC_(2.25), SC_(1) / 1024, SC_(-1.01759203636941035147948317764932151601257765988969544340275e7), |
| SC_(0.5), SC_(1) / (1024*1024), SC_(-817.033790261762580469303126467917092806755460418223776544122), |
| SC_(5.5), SC_(3.125), SC_(-2.61489440328417468776474188539366752698192046890955453259866), |
| SC_(-5.5), SC_(3.125), SC_(-0.0274994493896489729948109971802244976377957234563871795364056), |
| SC_(-5.5), SC_(1e+04), SC_(-0.00759343502722670361395585198154817047185480147294665270646578), |
| SC_(-10486074) / (1024*1024), SC_(1)/1024, SC_(-1.50382374389531766117868938966858995093408410498915220070230e38), |
| SC_(-10486074) / (1024*1024), SC_(1e+02), SC_(0.0583041891319026009955779707640455341990844522293730214223545), |
| SC_(141.75), SC_(1e+02), SC_(-5.38829231428696507293191118661269920130838607482708483122068e9), |
| SC_(141.75), SC_(2e+04), SC_(-0.00376577888677186194728129112270988602876597726657372330194186), |
| SC_(-141.75), SC_(1e+02), SC_(-3.81009803444766877495905954105669819951653361036342457919021e9), |
| }; |
| |
| do_test_cyl_neumann_y(y0_data, name, "Y0: Mathworld Data"); |
| do_test_cyl_neumann_y(y1_data, name, "Y1: Mathworld Data"); |
| do_test_cyl_neumann_y(yn_data, name, "Yn: Mathworld Data"); |
| do_test_cyl_neumann_y_int(y0_data, name, "Y0: Mathworld Data (Integer Version)"); |
| do_test_cyl_neumann_y_int(y1_data, name, "Y1: Mathworld Data (Integer Version)"); |
| do_test_cyl_neumann_y_int(yn_data, name, "Yn: Mathworld Data (Integer Version)"); |
| do_test_cyl_neumann_y(yv_data, name, "Yv: Mathworld Data"); |
| |
| #include "bessel_y01_data.ipp" |
| do_test_cyl_neumann_y(bessel_y01_data, name, "Y0 and Y1: Random Data"); |
| #include "bessel_yn_data.ipp" |
| do_test_cyl_neumann_y(bessel_yn_data, name, "Yn: Random Data"); |
| #include "bessel_yv_data.ipp" |
| do_test_cyl_neumann_y(bessel_yv_data, name, "Yv: Random Data"); |
| |
| #include "sph_neumann_data.ipp" |
| do_test_sph_neumann_y(sph_neumann_data, name, "y: Random Data"); |
| } |
| |
| int test_main(int, char* []) |
| { |
| #ifdef TEST_GSL |
| gsl_set_error_handler_off(); |
| #endif |
| expected_results(); |
| BOOST_MATH_CONTROL_FP; |
| |
| #ifndef BOOST_MATH_BUGGY_LARGE_FLOAT_CONSTANTS |
| test_bessel(0.1F, "float"); |
| #endif |
| test_bessel(0.1, "double"); |
| #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS |
| test_bessel(0.1L, "long double"); |
| #ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS |
| test_bessel(boost::math::concepts::real_concept(0.1), "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; |
| } |
| |
| |
| |
| |
