| // (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> |
| |
| #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 functions. 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 specific rates: |
| // |
| // Error rate for double precision are limited by the accuracy of |
| // the approximations use, which bracket rather than preserve the root. |
| // |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "HP-UX", // platform |
| largest_type, // test type(s) |
| ".*J0.*Tricky.*", // test data group |
| ".*", 80000000000LL, 80000000000LL); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "HP-UX", // platform |
| largest_type, // test type(s) |
| ".*J1.*Tricky.*", // test data group |
| ".*", 3000000, 2000000); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "HP-UX", // platform |
| "double", // test type(s) |
| ".*Tricky.*", // test data group |
| ".*", 100000, 100000); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "HP-UX", // platform |
| largest_type, // test type(s) |
| ".*J.*Tricky.*", // test data group |
| ".*", 3000, 500); // test function |
| // |
| // HP Tru64: |
| // |
| add_expected_result( |
| ".*Tru64.*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "double", // test type(s) |
| ".*Tricky.*", // test data group |
| ".*", 100000, 100000); // test function |
| add_expected_result( |
| ".*Tru64.*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*Tricky large.*", // test data group |
| ".*", 3000, 1000); // test function |
| // |
| // Solaris specific rates: |
| // |
| // Error rate for double precision are limited by the accuracy of |
| // the approximations use, which bracket rather than preserve the root. |
| // |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "Sun Solaris", // platform |
| largest_type, // test type(s) |
| "Bessel J: Random Data.*Tricky.*", // test data group |
| ".*", 3000, 500); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "Sun Solaris", // platform |
| "double", // test type(s) |
| ".*Tricky.*", // test data group |
| ".*", 200000, 100000); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "Sun Solaris", // platform |
| largest_type, // test type(s) |
| ".*J.*tricky.*", // test data group |
| ".*", 400000000, 200000000); // test function |
| // |
| // Mac OS X: |
| // |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "Mac OS", // platform |
| largest_type, // test type(s) |
| ".*J0.*Tricky.*", // test data group |
| ".*", 400000000, 400000000); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "Mac OS", // platform |
| largest_type, // test type(s) |
| ".*J1.*Tricky.*", // test data group |
| ".*", 3000000, 2000000); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "Mac OS", // platform |
| largest_type, // test type(s) |
| "Bessel JN.*", // test data group |
| ".*", 40000, 20000); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "Mac OS", // platform |
| largest_type, // test type(s) |
| "Bessel J:.*", // test data group |
| ".*", 50000, 20000); // test function |
| |
| |
| |
| // |
| // Linux specific results: |
| // |
| // sin and cos appear to have only double precision for large |
| // arguments on some linux distros: |
| // |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| "linux", // platform |
| largest_type, // test type(s) |
| ".*J:.*", // test data group |
| ".*", 40000, 30000); // 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) |
| ".*J0.*Tricky.*", // test data group |
| ".*", 400000, 400000); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "double", // test type(s) |
| ".*J1.*Tricky.*", // test data group |
| ".*", 5000, 5000); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "double", // test type(s) |
| ".*(JN|j).*|.*Tricky.*", // test data group |
| ".*", 50, 50); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| "double", // test type(s) |
| ".*", // test data group |
| ".*", 30, 30); // test function |
| // |
| // and we have a few cases with higher limits as well: |
| // |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*J0.*Tricky.*", // test data group |
| ".*", 400000000, 400000000); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*J1.*Tricky.*", // test data group |
| ".*", 5000000, 5000000); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*(JN|j).*|.*Tricky.*", // test data group |
| ".*", 33000, 20000); // test function |
| } |
| #endif |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*J0.*Tricky.*", // test data group |
| ".*", 400000000, 400000000); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*J1.*Tricky.*", // test data group |
| ".*", 5000000, 5000000); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*JN.*Integer.*", // test data group |
| ".*", 30000, 10000); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*(JN|j).*|.*Tricky.*", // test data group |
| ".*", 1500, 700); // test function |
| add_expected_result( |
| ".*", // compiler |
| ".*", // stdlib |
| ".*", // platform |
| largest_type, // test type(s) |
| ".*", // test data group |
| ".*", 40, 20); // 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_bessel_j(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_j<value_type, value_type>; |
| #else |
| pg funcp = boost::math::cyl_bessel_j; |
| #endif |
| |
| boost::math::tools::test_result<value_type> result; |
| |
| std::cout << "Testing " << test_name << " with type " << type_name |
| << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"; |
| |
| // |
| // test cyl_bessel_j 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_j", test_name); |
| std::cout << std::endl; |
| |
| #ifdef TEST_OTHER |
| if(boost::is_floating_point<value_type>::value) |
| { |
| funcp = other::cyl_bessel_j; |
| |
| // |
| // test other::cyl_bessel_j 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_bessel_j", test_name); |
| std::cout << std::endl; |
| } |
| #endif |
| } |
| |
| template <class T> |
| T cyl_bessel_j_int_wrapper(T v, T x) |
| { |
| return static_cast<T>(boost::math::cyl_bessel_j(boost::math::itrunc(v), x)); |
| } |
| |
| |
| template <class T> |
| void do_test_cyl_bessel_j_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_j_int_wrapper<value_type>; |
| #else |
| pg funcp = cyl_bessel_j_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_j 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_j", test_name); |
| std::cout << std::endl; |
| } |
| |
| template <class T> |
| void do_test_sph_bessel_j(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_bessel<value_type>; |
| #else |
| pg funcp = boost::math::sph_bessel; |
| #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_bessel 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::sph_bessel", 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>, 8> j0_data = {{ |
| { SC_(0), SC_(0), SC_(1) }, |
| { SC_(0), SC_(1), SC_(0.7651976865579665514497175261026632209093) }, |
| { SC_(0), SC_(-2), SC_(0.2238907791412356680518274546499486258252) }, |
| { SC_(0), SC_(4), SC_(-0.3971498098638473722865907684516980419756) }, |
| { SC_(0), SC_(-8), SC_(0.1716508071375539060908694078519720010684) }, |
| { SC_(0), SC_(1e-05), SC_(0.999999999975000000000156249999999565972) }, |
| { SC_(0), SC_(1e-10), SC_(0.999999999999999999997500000000000000000) }, |
| { SC_(0), SC_(-1e+01), SC_(-0.2459357644513483351977608624853287538296) }, |
| }}; |
| static const boost::array<boost::array<T, 3>, 6> j0_tricky = {{ |
| // Big numbers make the accuracy of std::sin the limiting factor: |
| { SC_(0), SC_(1e+03), SC_(0.02478668615242017456133073111569370878617) }, |
| { SC_(0), SC_(1e+05), SC_(-0.001719201116235972192570601477073201747532) }, |
| // test at the roots: |
| { SC_(0), SC_(2521642)/(1024 * 1024), SC_(1.80208819970046790002973759410972422387259992955354630042138e-7) }, |
| { SC_(0), SC_(5788221)/(1024 * 1024), SC_(-1.37774249380686777043369399806210229535671843632174587432454e-7) }, |
| { SC_(0), SC_(9074091)/(1024 * 1024), SC_(1.03553057441100845081018471279571355857520645127532785991335e-7) }, |
| { SC_(0), SC_(12364320)/(1024 * 1024), SC_(-3.53017140778223781420794006033810387155048392363051866610931e-9) } |
| }}; |
| |
| static const boost::array<boost::array<T, 3>, 8> j1_data = { |
| SC_(1), SC_(0), SC_(0), |
| SC_(1), SC_(1), SC_(0.4400505857449335159596822037189149131274), |
| SC_(1), SC_(-2), SC_(-0.5767248077568733872024482422691370869203), |
| SC_(1), SC_(4), SC_(-6.604332802354913614318542080327502872742e-02), |
| SC_(1), SC_(-8), SC_(-0.2346363468539146243812766515904546115488), |
| SC_(1), SC_(1e-05), SC_(4.999999999937500000000260416666666124132e-06), |
| SC_(1), SC_(1e-10), SC_(4.999999999999999999993750000000000000000e-11), |
| SC_(1), SC_(-1e+01), SC_(-4.347274616886143666974876802585928830627e-02), |
| }; |
| static const boost::array<boost::array<T, 3>, 5> j1_tricky = { |
| // Big numbers make the accuracy of std::sin the limiting factor: |
| SC_(1), SC_(1e+03), SC_(4.728311907089523917576071901216916285418e-03), |
| SC_(1), SC_(1e+05), SC_(1.846757562882567716362123967114215743694e-03), |
| // test zeros: |
| SC_(1), SC_(4017834)/(1024*1024), SC_(3.53149033321258645807835062770856949751958513973522222203044e-7), |
| SC_(1), SC_(7356375)/(1024*1024), SC_(-2.31227973111067286051984021150135526024117175836722748404342e-7), |
| SC_(1), SC_(10667654)/(1024*1024), SC_(1.24591331097191900488116495350277530373473085499043086981229e-7), |
| }; |
| |
| static const boost::array<boost::array<T, 3>, 15> jn_data = { |
| // This first one is a modified test case from https://svn.boost.org/trac/boost/ticket/2733 |
| SC_(-1), SC_(1.25), SC_(-0.510623260319880467069474837274910375352924050139633057168856), |
| SC_(2), SC_(0), SC_(0), |
| SC_(2), SC_(1e-02), SC_(1.249989583365885362413250958437642113452e-05), |
| SC_(5), SC_(10), SC_(-0.2340615281867936404436949416457777864635), |
| SC_(5), SC_(-10), SC_(0.2340615281867936404436949416457777864635), |
| SC_(-5), SC_(1e+06), SC_(7.259643842453285052375779970433848914846e-04), |
| SC_(5), SC_(1e+06), SC_(-0.000725964384245328505237577997043384891484649290328285235308619), |
| SC_(-5), SC_(-1), SC_(2.497577302112344313750655409880451981584e-04), |
| SC_(10), SC_(10), SC_(0.2074861066333588576972787235187534280327), |
| SC_(10), SC_(-10), SC_(0.2074861066333588576972787235187534280327), |
| SC_(10), SC_(-5), SC_(1.467802647310474131107532232606627020895e-03), |
| SC_(-10), SC_(1e+06), SC_(-3.310793117604488741264958559035744460210e-04), |
| SC_(10), SC_(1e+06), SC_(-0.000331079311760448874126495855903574446020957243277028930713243), |
| SC_(1e+02), SC_(8e+01), SC_(4.606553064823477354141298259169874909670e-06), |
| SC_(1e+03), SC_(1e+05), SC_(1.283178112502480365195139312635384057363e-03), |
| }; |
| do_test_cyl_bessel_j(j0_data, name, "Bessel J0: Mathworld Data"); |
| do_test_cyl_bessel_j(j0_tricky, name, "Bessel J0: Mathworld Data (Tricky cases)"); |
| do_test_cyl_bessel_j(j1_data, name, "Bessel J1: Mathworld Data"); |
| do_test_cyl_bessel_j(j1_tricky, name, "Bessel J1: Mathworld Data (tricky cases)"); |
| do_test_cyl_bessel_j(jn_data, name, "Bessel JN: Mathworld Data"); |
| |
| do_test_cyl_bessel_j_int(j0_data, name, "Bessel J0: Mathworld Data (Integer Version)"); |
| do_test_cyl_bessel_j_int(j0_tricky, name, "Bessel J0: Mathworld Data (Tricky cases) (Integer Version)"); |
| do_test_cyl_bessel_j_int(j1_data, name, "Bessel J1: Mathworld Data (Integer Version)"); |
| do_test_cyl_bessel_j_int(j1_tricky, name, "Bessel J1: Mathworld Data (tricky cases) (Integer Version)"); |
| do_test_cyl_bessel_j_int(jn_data, name, "Bessel JN: Mathworld Data (Integer Version)"); |
| |
| static const boost::array<boost::array<T, 3>, 17> jv_data = { |
| //SC_(-2.4), SC_(0), std::numeric_limits<T>::infinity(), |
| SC_(2457)/1024, SC_(1)/1024, SC_(3.80739920118603335646474073457326714709615200130620574875292e-9), |
| SC_(5.5), SC_(3217)/1024, SC_(0.0281933076257506091621579544064767140470089107926550720453038), |
| SC_(-5.5), SC_(3217)/1024, SC_(-2.55820064470647911823175836997490971806135336759164272675969), |
| SC_(-5.5), SC_(1e+04), SC_(2.449843111985605522111159013846599118397e-03), |
| SC_(5.5), SC_(1e+04), SC_(0.00759343502722670361395585198154817047185480147294665270646578), |
| SC_(5.5), SC_(1e+06), SC_(-0.000747424248595630177396350688505919533097973148718960064663632), |
| SC_(5.125), SC_(1e+06), SC_(-0.000776600124835704280633640911329691642748783663198207360238214), |
| SC_(5.875), SC_(1e+06), SC_(-0.000466322721115193071631008581529503095819705088484386434589780), |
| SC_(0.5), SC_(101), SC_(0.0358874487875643822020496677692429287863419555699447066226409), |
| SC_(-5.5), SC_(1e+04), SC_(0.00244984311198560552211115901384659911839737686676766460822577), |
| SC_(-5.5), SC_(1e+06), SC_(0.000279243200433579511095229508894156656558211060453622750659554), |
| SC_(-0.5), SC_(101), SC_(0.0708184798097594268482290389188138201440114881159344944791454), |
| SC_(-10486074) / (1024*1024), SC_(1)/1024, SC_(1.41474013160494695750009004222225969090304185981836460288562e35), |
| SC_(-10486074) / (1024*1024), SC_(15), SC_(-0.0902239288885423309568944543848111461724911781719692852541489), |
| SC_(10486074) / (1024*1024), SC_(1e+02), SC_(-0.0547064914615137807616774867984047583596945624129838091326863), |
| SC_(10486074) / (1024*1024), SC_(2e+04), SC_(-0.00556783614400875611650958980796060611309029233226596737701688), |
| SC_(-10486074) / (1024*1024), SC_(1e+02), SC_(-0.0547613660316806551338637153942604550779513947674222863858713), |
| }; |
| do_test_cyl_bessel_j(jv_data, name, "Bessel J: Mathworld Data"); |
| |
| #undef SC_ |
| |
| #include "bessel_j_int_data.ipp" |
| do_test_cyl_bessel_j(bessel_j_int_data, name, "Bessel JN: Random Data"); |
| |
| #include "bessel_j_data.ipp" |
| do_test_cyl_bessel_j(bessel_j_data, name, "Bessel J: Random Data"); |
| |
| #include "bessel_j_large_data.ipp" |
| do_test_cyl_bessel_j(bessel_j_large_data, name, "Bessel J: Random Data (Tricky large values)"); |
| |
| #include "sph_bessel_data.ipp" |
| do_test_sph_bessel_j(sph_bessel_data, name, "Bessel j: Random Data"); |
| } |
| |
| int test_main(int, char* []) |
| { |
| #ifdef TEST_GSL |
| gsl_set_error_handler_off(); |
| #endif |
| expected_results(); |
| BOOST_MATH_CONTROL_FP; |
| |
| test_bessel(0.1F, "float"); |
| 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; |
| } |
| |
| |
| |
| |
