| // (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/math/special_functions/trunc.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 I 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"; |
| } |
| else |
| { |
| largest_type = "long double"; |
| } |
| #else |
| largest_type = "(long\\s+)?double"; |
| #endif |
| |
| // |
| // Mac OS has higher error rates, why? |
| // |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "Mac OS", // platform |
| largest_type, // test type(s) |
| ".*", // test data group |
| ".*", 100, 50); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "Mac OS", // platform |
| "real_concept", // test type(s) |
| ".*", // test data group |
| ".*", 100, 50); // test function |
| |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*", // test data group |
| ".*", 15, 10); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "real_concept", // test type(s) |
| ".*", // test data group |
| ".*", 15, 10); // 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> |
| T cyl_bessel_i_int_wrapper(T v, T x) |
| { |
| return static_cast<T>( |
| boost::math::cyl_bessel_i( |
| boost::math::itrunc(v), x)); |
| } |
| |
| template <class T> |
| void do_test_cyl_bessel_i(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_bessel_i<value_type, value_type>; |
| #else |
| pg funcp = boost::math::cyl_bessel_i; |
| #endif |
| |
| boost::math::tools::test_result<value_type> result; |
| |
| std::cout << "Testing " << test_name << " with type " << type_name |
| << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"; |
| |
| // |
| // test cyl_bessel_i 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_bessel_i", test_name); |
| std::cout << std::endl; |
| |
| #ifdef TEST_OTHER |
| if(boost::is_floating_point<value_type>::value) |
| { |
| funcp = other::cyl_bessel_i; |
| |
| // |
| // test other::cyl_bessel_i against data: |
| // |
| result = boost::math::tools::test( |
| data, |
| boost::lambda::bind(funcp, |
| boost::lambda::ret<value_type>(boost::lambda::_1[0]), |
| boost::lambda::ret<value_type>(boost::lambda::_1[1])), |
| boost::lambda::ret<value_type>(boost::lambda::_1[2])); |
| print_test_result(result, data[result.worst()], result.worst(), type_name, "other::cyl_bessel_i"); |
| std::cout << std::endl; |
| } |
| #endif |
| } |
| |
| template <class T> |
| void do_test_cyl_bessel_i_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_bessel_i_int_wrapper<value_type>; |
| #else |
| pg funcp = cyl_bessel_i_int_wrapper; |
| #endif |
| |
| boost::math::tools::test_result<value_type> result; |
| |
| std::cout << "Testing " << test_name << " with type " << type_name |
| << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"; |
| |
| // |
| // test cyl_bessel_i 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_bessel_i", test_name); |
| std::cout << std::endl; |
| } |
| |
| template <class T> |
| void test_bessel(T, const char* 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, 3>, 10> i0_data = {{ |
| SC_(0), SC_(0), SC_(1), |
| SC_(0), SC_(1), SC_(1.26606587775200833559824462521471753760767031135496220680814), |
| SC_(0), SC_(-2), SC_(2.27958530233606726743720444081153335328584110278545905407084), |
| SC_(0), SC_(4), SC_(11.3019219521363304963562701832171024974126165944353377060065), |
| SC_(0), SC_(-7), SC_(168.593908510289698857326627187500840376522679234531714193194), |
| SC_(0), SC_(1) / 1024, SC_(1.00000023841859331241759166109699567801556273303717896447683), |
| SC_(0), SC_(1) / (1024*1024), SC_(1.00000000000022737367544324498417583090700894607432256476338), |
| SC_(0), SC_(-1), SC_(1.26606587775200833559824462521471753760767031135496220680814), |
| SC_(0), SC_(100), SC_(1.07375170713107382351972085760349466128840319332527279540154e42), |
| SC_(0), SC_(200), SC_(2.03968717340972461954167312677945962233267573614834337894328e85), |
| }}; |
| static const boost::array<boost::array<T, 3>, 10> i1_data = { |
| SC_(1), SC_(0), SC_(0), |
| SC_(1), SC_(1), SC_(0.565159103992485027207696027609863307328899621621092009480294), |
| SC_(1), SC_(-2), SC_(-1.59063685463732906338225442499966624795447815949553664713229), |
| SC_(1), SC_(4), SC_(9.75946515370444990947519256731268090005597033325296730692753), |
| SC_(1), SC_(-8), SC_(-399.873136782560098219083086145822754889628443904067647306574), |
| SC_(1), SC_(1)/1024, SC_(0.000488281308207663226432087816784315537514225208473395063575150), |
| SC_(1), SC_(1)/(1024*1024), SC_(4.76837158203179210108624277276025646653133998635956784292029E-7), |
| SC_(1), SC_(-10), SC_(-2670.98830370125465434103196677215254914574515378753771310849), |
| SC_(1), SC_(100), SC_(1.06836939033816248120614576322429526544612284405623226965918e42), |
| SC_(1), SC_(200), SC_(2.03458154933206270342742797713906950389661161681122964159220e85), |
| }; |
| static const boost::array<boost::array<T, 3>, 10> in_data = { |
| SC_(-2), SC_(0), SC_(0), |
| SC_(2), SC_(1)/(1024*1024), SC_(1.13686837721624646204093977095674566928522671779753217215467e-13), |
| SC_(5), SC_(10), SC_(777.188286403259959907293484802339632852674154572666041953297), |
| SC_(-5), SC_(100), SC_(9.47009387303558124618275555002161742321578485033007130107740e41), |
| SC_(-5), SC_(-1), SC_(-0.000271463155956971875181073905153777342383564426758143634974124), |
| SC_(10), SC_(20), SC_(3.54020020901952109905289138244985607057267103782948493874391e6), |
| SC_(10), SC_(-5), SC_(0.00458004441917605126118647027872016953192323139337073320016447), |
| SC_(1e+02), SC_(9), SC_(2.74306601746058997093587654668959071522869282506446891736820e-93), |
| SC_(1e+02), SC_(80), SC_(4.65194832850610205318128191404145885093970505338730540776711e8), |
| SC_(-100), SC_(-200), SC_(4.35275044972702191438729017441198257508190719030765213981307e74), |
| }; |
| static const boost::array<boost::array<T, 3>, 10> iv_data = { |
| SC_(2.25), SC_(1)/(1024*1024), SC_(2.34379212133481347189068464680335815256364262507955635911656e-15), |
| SC_(5.5), SC_(3.125), SC_(0.0583514045989371500460946536220735787163510569634133670181210), |
| SC_(-5) + T(1)/1024, SC_(2.125), SC_(0.0267920938009571023702933210070984416052633027166975342895062), |
| SC_(-5.5), SC_(10), SC_(597.577606961369169607937419869926705730305175364662688426534), |
| SC_(-5.5), SC_(100), SC_(9.22362906144706871737354069133813819358704200689067071415379e41), |
| SC_(-10486074)/(1024*1024), SC_(1)/1024, SC_(1.41474005665181350367684623930576333542989766867888186478185e35), |
| SC_(-10486074)/(1024*1024), SC_(50), SC_(1.07153277202900671531087024688681954238311679648319534644743e20), |
| SC_(144794)/1024, SC_(100), SC_(2066.27694757392660413922181531984160871678224178890247540320), |
| SC_(144794)/1024, SC_(200), SC_(2.23699739472246928794922868978337381373643889659337595319774e64), |
| SC_(-144794)/1024, SC_(100), SC_(2066.27694672763190927440969155740243346136463461655104698748), |
| }; |
| #undef SC_ |
| |
| do_test_cyl_bessel_i(i0_data, name, "Bessel I0: Mathworld Data"); |
| do_test_cyl_bessel_i(i1_data, name, "Bessel I1: Mathworld Data"); |
| do_test_cyl_bessel_i(in_data, name, "Bessel In: Mathworld Data"); |
| |
| do_test_cyl_bessel_i_int(i0_data, name, "Bessel I0: Mathworld Data (Integer Version)"); |
| do_test_cyl_bessel_i_int(i1_data, name, "Bessel I1: Mathworld Data (Integer Version)"); |
| do_test_cyl_bessel_i_int(in_data, name, "Bessel In: Mathworld Data (Integer Version)"); |
| |
| do_test_cyl_bessel_i(iv_data, name, "Bessel Iv: Mathworld Data"); |
| |
| #include "bessel_i_int_data.ipp" |
| do_test_cyl_bessel_i(bessel_i_int_data, name, "Bessel In: Random Data"); |
| #include "bessel_i_data.ipp" |
| do_test_cyl_bessel_i(bessel_i_data, name, "Bessel Iv: 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; |
| } |
| |
| |
| |
| |
