| // 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 |
| |
| #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 K 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|real_concept"; |
| #endif |
| // |
| // On MacOS X cyl_bessel_k has much higher error levels than |
| // expected: given that the implementation is basically |
| // just a continued fraction evaluation combined with |
| // exponentiation, we conclude that exp and pow are less |
| // accurate on this platform, especially when the result |
| // is outside the range of a double. |
| // |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "Mac OS", // platform |
| largest_type, // test type(s) |
| ".*", // test data group |
| ".*", 4000, 1300); // test function |
| |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*", // test data group |
| ".*", 35, 15); // 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_k_int_wrapper(T v, T x) |
| { |
| return static_cast<T>( |
| boost::math::cyl_bessel_k( |
| boost::math::itrunc(v), x)); |
| } |
| |
| template <class T> |
| void do_test_cyl_bessel_k(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_k<value_type, value_type>; |
| #else |
| pg funcp = boost::math::cyl_bessel_k; |
| #endif |
| |
| boost::math::tools::test_result<value_type> result; |
| |
| std::cout << "Testing " << test_name << " with type " << type_name |
| << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"; |
| |
| // |
| // test cyl_bessel_k 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_k", test_name); |
| std::cout << std::endl; |
| |
| #ifdef TEST_OTHER |
| if(boost::is_floating_point<value_type>::value) |
| { |
| funcp = other::cyl_bessel_k; |
| |
| // |
| // test other::cyl_bessel_k against data: |
| // |
| result = boost::math::tools::test( |
| data, |
| bind_func(funcp, 0, 1), |
| extract_result(2)); |
| print_test_result(result, data[result.worst()], result.worst(), type_name, "other::cyl_bessel_k"); |
| std::cout << std::endl; |
| } |
| #endif |
| } |
| |
| template <class T> |
| void do_test_cyl_bessel_k_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_k_int_wrapper<value_type>; |
| #else |
| pg funcp = cyl_bessel_k_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_k 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_k", 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>, 9> k0_data = {{ |
| SC_(0), SC_(1), SC_(0.421024438240708333335627379212609036136219748226660472298970), |
| SC_(0), SC_(2), SC_(0.113893872749533435652719574932481832998326624388808882892530), |
| SC_(0), SC_(4), SC_(0.0111596760858530242697451959798334892250090238884743405382553), |
| SC_(0), SC_(8), SC_(0.000146470705222815387096584408698677921967305368833759024089154), |
| SC_(0), T(std::ldexp(1.0, -15)), SC_(10.5131392267382037062459525561594822400447325776672021972753), |
| SC_(0), T(std::ldexp(1.0, -30)), SC_(20.9103469324567717360787328239372191382743831365906131108531), |
| SC_(0), T(std::ldexp(1.0, -60)), SC_(41.7047623492551310138446473188663682295952219631968830346918), |
| SC_(0), SC_(50), SC_(3.41016774978949551392067551235295223184502537762334808993276e-23), |
| SC_(0), SC_(100), SC_(4.65662822917590201893900528948388635580753948544211387402671e-45), |
| }}; |
| static const boost::array<boost::array<T, 3>, 9> k1_data = { |
| SC_(1), SC_(1), SC_(0.601907230197234574737540001535617339261586889968106456017768), |
| SC_(1), SC_(2), SC_(0.139865881816522427284598807035411023887234584841515530384442), |
| SC_(1), SC_(4), SC_(0.0124834988872684314703841799808060684838415849886258457917076), |
| SC_(1), SC_(8), SC_(0.000155369211805001133916862450622474621117065122872616157079566), |
| SC_(1), T(std::ldexp(1.0, -15)), SC_(32767.9998319528316432647441316539139725104728341577594326513), |
| SC_(1), T(std::ldexp(1.0, -30)), SC_(1.07374182399999999003003028572687332810353799544215073362305e9), |
| SC_(1), T(std::ldexp(1.0, -60)), SC_(1.15292150460684697599999999999999998169660198868126604634036e18), |
| SC_(1), SC_(50), SC_(3.44410222671755561259185303591267155099677251348256880221927e-23), |
| SC_(1), SC_(100), SC_(4.67985373563690928656254424202433530797494354694335352937465e-45), |
| }; |
| static const boost::array<boost::array<T, 3>, 9> kn_data = { |
| SC_(2), T(std::ldexp(1.0, -30)), SC_(2.30584300921369395150000000000000000234841952009593636868109e18), |
| SC_(5), SC_(10), SC_(0.0000575418499853122792763740236992723196597629124356739596921536), |
| SC_(-5), SC_(100), SC_(5.27325611329294989461777188449044716451716555009882448801072e-45), |
| SC_(10), SC_(10), SC_(0.00161425530039067002345725193091329085443750382929208307802221), |
| SC_(10), T(std::ldexp(1.0, -30)), SC_(3.78470202927236255215249281534478864916684072926050665209083e98), |
| SC_(-10), SC_(1), SC_(1.80713289901029454691597861302340015908245782948536080022119e8), |
| SC_(100), SC_(5), SC_(7.03986019306167654653386616796116726248616158936088056952477e115), |
| SC_(100), SC_(80), SC_(8.39287107246490782848985384895907681748152272748337807033319e-12), |
| SC_(-1000), SC_(700), SC_(6.51561979144735818903553852606383312984409361984128221539405e-31), |
| }; |
| static const boost::array<boost::array<T, 3>, 11> kv_data = { |
| SC_(0.5), SC_(0.875), SC_(0.558532231646608646115729767013630967055657943463362504577189), |
| SC_(0.5), SC_(1.125), SC_(0.383621010650189547146769320487006220295290256657827220786527), |
| SC_(2.25), T(std::ldexp(1.0, -30)), SC_(5.62397392719283271332307799146649700147907612095185712015604e20), |
| SC_(5.5), SC_(3217)/1024, SC_(1.30623288775012596319554857587765179889689223531159532808379), |
| SC_(-5.5), SC_(10), SC_(0.0000733045300798502164644836879577484533096239574909573072142667), |
| SC_(-5.5), SC_(100), SC_(5.41274555306792267322084448693957747924412508020839543293369e-45), |
| SC_(10240)/1024, SC_(1)/1024, SC_(2.35522579263922076203415803966825431039900000000993410734978e38), |
| SC_(10240)/1024, SC_(10), SC_(0.00161425530039067002345725193091329085443750382929208307802221), |
| SC_(144793)/1024, SC_(100), SC_(1.39565245860302528069481472855619216759142225046370312329416e-6), |
| SC_(144793)/1024, SC_(200), SC_(9.11950412043225432171915100042647230802198254567007382956336e-68), |
| SC_(-144793)/1024, SC_(50), SC_(1.30185229717525025165362673848737761549946548375142378172956e42), |
| }; |
| #undef SC_ |
| |
| do_test_cyl_bessel_k(k0_data, name, "Bessel K0: Mathworld Data"); |
| do_test_cyl_bessel_k(k1_data, name, "Bessel K1: Mathworld Data"); |
| do_test_cyl_bessel_k(kn_data, name, "Bessel Kn: Mathworld Data"); |
| |
| do_test_cyl_bessel_k_int(k0_data, name, "Bessel K0: Mathworld Data (Integer Version)"); |
| do_test_cyl_bessel_k_int(k1_data, name, "Bessel K1: Mathworld Data (Integer Version)"); |
| do_test_cyl_bessel_k_int(kn_data, name, "Bessel Kn: Mathworld Data (Integer Version)"); |
| |
| do_test_cyl_bessel_k(kv_data, name, "Bessel Kv: Mathworld Data"); |
| |
| #include "bessel_k_int_data.ipp" |
| do_test_cyl_bessel_k(bessel_k_int_data, name, "Bessel Kn: Random Data"); |
| #include "bessel_k_data.ipp" |
| do_test_cyl_bessel_k(bessel_k_data, name, "Bessel Kv: 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; |
| } |
| |
| |
| |
| |
