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// (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)
#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
#include <boost/math/concepts/real_concept.hpp>
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp>
#include <boost/test/tools/floating_point_comparison.hpp>
#include <boost/math/special_functions/math_fwd.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 "table_type.hpp"
#ifndef SC_
# define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
#endif
template <class T>
T cyl_bessel_i_int_wrapper(T v, T x)
{
#ifdef BESSEL_IN_FUNCTION_TO_TEST
return static_cast<T>(
BESSEL_IN_FUNCTION_TO_TEST(
boost::math::itrunc(v), x));
#else
return static_cast<T>(
boost::math::cyl_bessel_i(
boost::math::itrunc(v), x));
#endif
}
template <class Real, class T>
void do_test_cyl_bessel_i(const T& data, const char* type_name, const char* test_name)
{
#if !(defined(ERROR_REPORTING_MODE) && !defined(BESSEL_I_FUNCTION_TO_TEST))
typedef Real value_type;
typedef value_type (*pg)(value_type, value_type);
#ifdef BESSEL_I_FUNCTION_TO_TEST
pg funcp = BESSEL_I_FUNCTION_TO_TEST;
#elif 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_hetero<Real>(
data,
bind_func<Real>(funcp, 0, 1),
extract_result<Real>(2));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "cyl_bessel_i", test_name);
std::cout << std::endl;
#endif
}
template <class Real, class T>
void do_test_cyl_bessel_i_int(const T& data, const char* type_name, const char* test_name)
{
#if !(defined(ERROR_REPORTING_MODE) && !defined(BESSEL_IN_FUNCTION_TO_TEST))
typedef Real 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_hetero<Real>(
data,
bind_func<Real>(funcp, 0, 1),
extract_result<Real>(2));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "cyl_bessel_i (integer orders)", test_name);
std::cout << std::endl;
#endif
}
template <class T>
void test_bessel(T, const char* name)
{
// function values calculated on http://functions.wolfram.com/
static const std::array<std::array<typename table_type<T>::type, 3>, 10> i0_data = {{
{{ SC_(0.0), SC_(0.0), SC_(1.0) }},
{{ SC_(0.0), SC_(1.0), SC_(1.26606587775200833559824462521471753760767031135496220680814) }},
{{ SC_(0.0), SC_(-2.0), SC_(2.27958530233606726743720444081153335328584110278545905407084) }},
{{ SC_(0.0), SC_(4.0), SC_(11.3019219521363304963562701832171024974126165944353377060065) }},
{{ SC_(0.0), SC_(-7.0), SC_(168.593908510289698857326627187500840376522679234531714193194) }},
{{ SC_(0.0), SC_(0.0009765625), SC_(1.00000023841859331241759166109699567801556273303717896447683) }},
{{ SC_(0.0), SC_(9.5367431640625e-7), SC_(1.00000000000022737367544324498417583090700894607432256476338) }},
{{ SC_(0.0), SC_(-1.0), SC_(1.26606587775200833559824462521471753760767031135496220680814) }},
{{ SC_(0.0), SC_(100.0), SC_(1.07375170713107382351972085760349466128840319332527279540154e42) }},
{{ SC_(0.0), SC_(200.0), SC_(2.03968717340972461954167312677945962233267573614834337894328e85) }},
}};
static const std::array<std::array<typename table_type<T>::type, 3>, 10> i1_data = {{
{{ SC_(1.0), SC_(0.0), SC_(0.0) }},
{{ SC_(1.0), SC_(1.0), SC_(0.565159103992485027207696027609863307328899621621092009480294) }},
{{ SC_(1.0), SC_(-2.0), SC_(-1.59063685463732906338225442499966624795447815949553664713229) }},
{{ SC_(1.0), SC_(4.0), SC_(9.75946515370444990947519256731268090005597033325296730692753) }},
{{ SC_(1.0), SC_(-8.0), SC_(-399.873136782560098219083086145822754889628443904067647306574) }},
{{ SC_(1.0), SC_(0.0009765625), SC_(0.000488281308207663226432087816784315537514225208473395063575150) }},
{{ SC_(1.0), SC_(9.5367431640625e-7), SC_(4.76837158203179210108624277276025646653133998635956784292029E-7) }},
{{ SC_(1.0), SC_(-10.0), SC_(-2670.98830370125465434103196677215254914574515378753771310849) }},
{{ SC_(1.0), SC_(100.0), SC_(1.06836939033816248120614576322429526544612284405623226965918e42) }},
{{ SC_(1.0), SC_(200.0), SC_(2.03458154933206270342742797713906950389661161681122964159220e85) }},
}};
static const std::array<std::array<typename table_type<T>::type, 3>, 11> in_data = {{
{{ SC_(-2.0), SC_(0.0), SC_(0.0) }},
{{ SC_(2.0), SC_(9.5367431640625e-7), SC_(1.13686837721624646204093977095674566928522671779753217215467e-13) }},
{{ SC_(5.0), SC_(10.0), SC_(777.188286403259959907293484802339632852674154572666041953297) }},
{{ SC_(-5.0), SC_(100.0), SC_(9.47009387303558124618275555002161742321578485033007130107740e41) }},
{{ SC_(-5.0), SC_(-1.0), SC_(-0.000271463155956971875181073905153777342383564426758143634974124) }},
{{ SC_(10.0), SC_(20.0), SC_(3.54020020901952109905289138244985607057267103782948493874391e6) }},
{{ SC_(10.0), SC_(-5.0), SC_(0.00458004441917605126118647027872016953192323139337073320016447) }},
{{ SC_(1e+02), SC_(9.0), SC_(2.74306601746058997093587654668959071522869282506446891736820e-93) }},
{{ SC_(1e+02), SC_(80.0), SC_(4.65194832850610205318128191404145885093970505338730540776711e8) }},
{{ SC_(-100.0), SC_(-200.0), SC_(4.35275044972702191438729017441198257508190719030765213981307e74) }},
{{ SC_(10.0), SC_(1e-100), SC_(2.69114445546737213403880070546737213403880070546737213403880e-1010) }},
}};
static const std::array<std::array<typename table_type<T>::type, 3>, 10> iv_data = {{
{{ SC_(2.25), SC_(9.5367431640625e-7), SC_(2.34379212133481347189068464680335815256364262507955635911656e-15) }},
{{ SC_(5.5), SC_(3.125), SC_(0.0583514045989371500460946536220735787163510569634133670181210) }},
{{ SC_(-4.9990234375), SC_(2.125), SC_(0.0267920938009571023702933210070984416052633027166975342895062) }},
{{ SC_(-5.5), SC_(10.0), SC_(597.577606961369169607937419869926705730305175364662688426534) }},
{{ SC_(-5.5), SC_(100.0), SC_(9.22362906144706871737354069133813819358704200689067071415379e41) }},
{{ SC_(-10.0002994537353515625), SC_(0.0009765625), SC_(1.41474005665181350367684623930576333542989766867888186478185e35) }},
{{ SC_(-10.0002994537353515625), SC_(50.0), SC_(1.07153277202900671531087024688681954238311679648319534644743e20) }},
{{ SC_(141.400390625), SC_(100.0), SC_(2066.27694757392660413922181531984160871678224178890247540320) }},
{{ SC_(141.400390625), SC_(200.0), SC_(2.23699739472246928794922868978337381373643889659337595319774e64) }},
{{ SC_(-141.400390625), SC_(100.0), SC_(2066.27694672763190927440969155740243346136463461655104698748) }},
}};
static const std::array<std::array<typename table_type<T>::type, 3>, 5> iv_large_data = {{
// Bug report https://svn.boost.org/trac/boost/ticket/5560:
{{ SC_(-1.0), SC_(3.7291703656001033716454826577314669186882357673002034471357591666031391925350591524680874452002139016807558e-155), SC_(1.86458518280005168582274132886573345934411788365010172356788e-155) }},
{{ SC_(1.0), SC_(3.7291703656001033716454826577314669186882357673002034471357591666031391925350591524680874452002139016807558e-155), SC_(1.86458518280005168582274132886573345934411788365010172356788e-155) }},
{{ SC_(-1.125), SC_(3.7291703656001033716454826577314669186882357673002034471357591666031391925350591524680874452002139016807558e-155), SC_(-1.34963720853101363690381585556234820027343435206156667634081e173) }},
{{ SC_(1.125), SC_(3.7291703656001033716454826577314669186882357673002034471357591666031391925350591524680874452002139016807558e-155), SC_(8.02269390325932403421158766283366891170783955777638875887348e-175) }},
{{ SC_(0.5), SC_(1.2458993688871959419388378518880931736878259938089494331010226962863582408064841833232475731084062642684629e-206), SC_(8.90597649117647254543282704099383321071493400182381039079219e-104) }},
}};
do_test_cyl_bessel_i<T>(i0_data, name, "Bessel I0: Mathworld Data");
do_test_cyl_bessel_i<T>(i1_data, name, "Bessel I1: Mathworld Data");
do_test_cyl_bessel_i<T>(in_data, name, "Bessel In: Mathworld Data");
do_test_cyl_bessel_i_int<T>(i0_data, name, "Bessel I0: Mathworld Data (Integer Version)");
do_test_cyl_bessel_i_int<T>(i1_data, name, "Bessel I1: Mathworld Data (Integer Version)");
do_test_cyl_bessel_i_int<T>(in_data, name, "Bessel In: Mathworld Data (Integer Version)");
do_test_cyl_bessel_i<T>(iv_data, name, "Bessel Iv: Mathworld Data");
#include "bessel_i_int_data.ipp"
do_test_cyl_bessel_i<T>(bessel_i_int_data, name, "Bessel In: Random Data");
#include "bessel_i_data.ipp"
do_test_cyl_bessel_i<T>(bessel_i_data, name, "Bessel Iv: Random Data");
if(0 != static_cast<T>(ldexp(0.5, -700)))
do_test_cyl_bessel_i<T>(iv_large_data, name, "Bessel Iv: Mathworld Data (large values)");
//
// Special cases for full coverage:
//
#ifndef BOOST_MATH_NO_EXCEPTIONS
BOOST_CHECK_THROW(boost::math::cyl_bessel_i(T(-2.5), T(-2.5)), std::domain_error);
#endif
BOOST_CHECK_EQUAL(boost::math::cyl_bessel_i(T(0), T(0)), T(1));
BOOST_CHECK_EQUAL(boost::math::cyl_bessel_i(T(10), T(0)), T(0));
BOOST_CHECK_EQUAL(boost::math::cyl_bessel_i(T(-10), T(0)), T(0));
BOOST_IF_CONSTEXPR (std::numeric_limits<T>::has_infinity)
{
BOOST_CHECK_EQUAL(boost::math::cyl_bessel_i(T(-10.5), T(0)), std::numeric_limits<T>::infinity());
BOOST_IF_CONSTEXPR(std::numeric_limits<T>::max_exponent < 11356)
{
BOOST_CHECK_EQUAL(boost::math::cyl_bessel_i(T(0.25), T(8000)), std::numeric_limits<T>::infinity());
}
else BOOST_IF_CONSTEXPR(std::numeric_limits<T>::max_exponent10 < 9200)
{
BOOST_CHECK_EQUAL(boost::math::cyl_bessel_i(T(0.25), T(21000)), std::numeric_limits<T>::infinity());
}
}
T tolerance = boost::math::tools::epsilon<T>() * 100;
#ifndef SYCL_LANGUAGE_VERSION
if ((boost::math::tools::digits<T>() <= std::numeric_limits<double>::digits) && (std::numeric_limits<T>::max_exponent > 1000))
{
BOOST_CHECK_CLOSE_FRACTION(boost::math::cyl_bessel_i(T(0.5), T(710)), SC_(3.3447452278080108123142599104927325061327359278058601201179e306), tolerance);
}
#endif
#if LDBL_MAX_EXP >= 11356
BOOST_IF_CONSTEXPR (std::numeric_limits<T>::max_exponent >= 11356)
{
T mul = std::is_floating_point<T>::value ? 1 : 10;
BOOST_CHECK_CLOSE_FRACTION(boost::math::cyl_bessel_i(T(0.5), T(11357)), SC_(7.173138695269929329584326974917488634629578339622112563648e4929), tolerance * mul);
}
#endif
BOOST_IF_CONSTEXPR (std::numeric_limits<T>::max_exponent10 > 304)
{
BOOST_IF_CONSTEXPR(std::is_floating_point<T>::value == false)
tolerance *= 4; // multiprecision type.
BOOST_CHECK_CLOSE_FRACTION(boost::math::cyl_bessel_i(0, T(700)), SC_(1.5295933476718737363162072288904508649662689614661164851272e302), tolerance);
BOOST_CHECK_CLOSE_FRACTION(boost::math::cyl_bessel_i(1, T(600)), SC_(6.1411813450668919369004006361519512681603654557478168763761e258), tolerance);
}
else BOOST_IF_CONSTEXPR(std::numeric_limits<T>::is_specialized)
{
BOOST_CHECK_EQUAL(boost::math::cyl_bessel_i(0, T(700)), std::numeric_limits<T>::infinity());
BOOST_CHECK_EQUAL(boost::math::cyl_bessel_i(1, T(600)), std::numeric_limits<T>::infinity());
}
}
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