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1// (C) Copyright John Maddock 2007.
2// Use, modification and distribution are subject to the
3// Boost Software License, Version 1.0. (See accompanying file
4// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
5
6#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
7#include <boost/math/concepts/real_concept.hpp>
8#define BOOST_TEST_MAIN
9#include <boost/test/unit_test.hpp>
10#include <boost/test/floating_point_comparison.hpp>
11#include <boost/math/special_functions/math_fwd.hpp>
12#include <boost/type_traits/is_floating_point.hpp>
13#include <boost/array.hpp>
14#include "functor.hpp"
15
16#include "handle_test_result.hpp"
17#include "table_type.hpp"
18
19#ifndef SC_
20# define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
21#endif
22
23template <class T>
24T cyl_bessel_i_int_wrapper(T v, T x)
25{
26#ifdef BESSEL_IN_FUNCTION_TO_TEST
27 return static_cast<T>(
28 BESSEL_IN_FUNCTION_TO_TEST(
29 boost::math::itrunc(v), x));
30#else
31 return static_cast<T>(
32 boost::math::cyl_bessel_i(
33 boost::math::itrunc(v), x));
34#endif
35}
36
37template <class Real, class T>
38void do_test_cyl_bessel_i(const T& data, const char* type_name, const char* test_name)
39{
40#if !(defined(ERROR_REPORTING_MODE) && !defined(BESSEL_I_FUNCTION_TO_TEST))
41 typedef Real value_type;
42
43 typedef value_type (*pg)(value_type, value_type);
44#ifdef BESSEL_I_FUNCTION_TO_TEST
45 pg funcp = BESSEL_I_FUNCTION_TO_TEST;
46#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
47 pg funcp = boost::math::cyl_bessel_i<value_type, value_type>;
48#else
49 pg funcp = boost::math::cyl_bessel_i;
50#endif
51
52 boost::math::tools::test_result<value_type> result;
53
54 std::cout << "Testing " << test_name << " with type " << type_name
55 << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
56
57 //
58 // test cyl_bessel_i against data:
59 //
60 result = boost::math::tools::test_hetero<Real>(
61 data,
62 bind_func<Real>(funcp, 0, 1),
63 extract_result<Real>(2));
64 handle_test_result(result, data[result.worst()], result.worst(), type_name, "cyl_bessel_i", test_name);
65 std::cout << std::endl;
66
67#endif
68}
69
70template <class Real, class T>
71void do_test_cyl_bessel_i_int(const T& data, const char* type_name, const char* test_name)
72{
73#if !(defined(ERROR_REPORTING_MODE) && !defined(BESSEL_IN_FUNCTION_TO_TEST))
74 typedef Real value_type;
75
76 typedef value_type (*pg)(value_type, value_type);
77#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
78 pg funcp = cyl_bessel_i_int_wrapper<value_type>;
79#else
80 pg funcp = cyl_bessel_i_int_wrapper;
81#endif
82
83 boost::math::tools::test_result<value_type> result;
84
85 std::cout << "Testing " << test_name << " with type " << type_name
86 << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
87
88 //
89 // test cyl_bessel_i against data:
90 //
91 result = boost::math::tools::test_hetero<Real>(
92 data,
93 bind_func<Real>(funcp, 0, 1),
94 extract_result<Real>(2));
95 handle_test_result(result, data[result.worst()], result.worst(), type_name, "cyl_bessel_i (integer orders)", test_name);
96 std::cout << std::endl;
97#endif
98}
99
100template <class T>
101void test_bessel(T, const char* name)
102{
103 // function values calculated on http://functions.wolfram.com/
104 static const boost::array<boost::array<typename table_type<T>::type, 3>, 10> i0_data = {{
105 {{ SC_(0.0), SC_(0.0), SC_(1.0) }},
106 {{ SC_(0.0), SC_(1.0), SC_(1.26606587775200833559824462521471753760767031135496220680814) }},
107 {{ SC_(0.0), SC_(-2.0), SC_(2.27958530233606726743720444081153335328584110278545905407084) }},
108 {{ SC_(0.0), SC_(4.0), SC_(11.3019219521363304963562701832171024974126165944353377060065) }},
109 {{ SC_(0.0), SC_(-7.0), SC_(168.593908510289698857326627187500840376522679234531714193194) }},
110 {{ SC_(0.0), SC_(0.0009765625), SC_(1.00000023841859331241759166109699567801556273303717896447683) }},
111 {{ SC_(0.0), SC_(9.5367431640625e-7), SC_(1.00000000000022737367544324498417583090700894607432256476338) }},
112 {{ SC_(0.0), SC_(-1.0), SC_(1.26606587775200833559824462521471753760767031135496220680814) }},
113 {{ SC_(0.0), SC_(100.0), SC_(1.07375170713107382351972085760349466128840319332527279540154e42) }},
114 {{ SC_(0.0), SC_(200.0), SC_(2.03968717340972461954167312677945962233267573614834337894328e85) }},
115 }};
116 static const boost::array<boost::array<typename table_type<T>::type, 3>, 10> i1_data = {{
117 {{ SC_(1.0), SC_(0.0), SC_(0.0) }},
118 {{ SC_(1.0), SC_(1.0), SC_(0.565159103992485027207696027609863307328899621621092009480294) }},
119 {{ SC_(1.0), SC_(-2.0), SC_(-1.59063685463732906338225442499966624795447815949553664713229) }},
120 {{ SC_(1.0), SC_(4.0), SC_(9.75946515370444990947519256731268090005597033325296730692753) }},
121 {{ SC_(1.0), SC_(-8.0), SC_(-399.873136782560098219083086145822754889628443904067647306574) }},
122 {{ SC_(1.0), SC_(0.0009765625), SC_(0.000488281308207663226432087816784315537514225208473395063575150) }},
123 {{ SC_(1.0), SC_(9.5367431640625e-7), SC_(4.76837158203179210108624277276025646653133998635956784292029E-7) }},
124 {{ SC_(1.0), SC_(-10.0), SC_(-2670.98830370125465434103196677215254914574515378753771310849) }},
125 {{ SC_(1.0), SC_(100.0), SC_(1.06836939033816248120614576322429526544612284405623226965918e42) }},
126 {{ SC_(1.0), SC_(200.0), SC_(2.03458154933206270342742797713906950389661161681122964159220e85) }},
127 }};
128 static const boost::array<boost::array<typename table_type<T>::type, 3>, 11> in_data = {{
129 {{ SC_(-2.0), SC_(0.0), SC_(0.0) }},
130 {{ SC_(2.0), SC_(9.5367431640625e-7), SC_(1.13686837721624646204093977095674566928522671779753217215467e-13) }},
131 {{ SC_(5.0), SC_(10.0), SC_(777.188286403259959907293484802339632852674154572666041953297) }},
132 {{ SC_(-5.0), SC_(100.0), SC_(9.47009387303558124618275555002161742321578485033007130107740e41) }},
133 {{ SC_(-5.0), SC_(-1.0), SC_(-0.000271463155956971875181073905153777342383564426758143634974124) }},
134 {{ SC_(10.0), SC_(20.0), SC_(3.54020020901952109905289138244985607057267103782948493874391e6) }},
135 {{ SC_(10.0), SC_(-5.0), SC_(0.00458004441917605126118647027872016953192323139337073320016447) }},
136 {{ SC_(1e+02), SC_(9.0), SC_(2.74306601746058997093587654668959071522869282506446891736820e-93) }},
137 {{ SC_(1e+02), SC_(80.0), SC_(4.65194832850610205318128191404145885093970505338730540776711e8) }},
138 {{ SC_(-100.0), SC_(-200.0), SC_(4.35275044972702191438729017441198257508190719030765213981307e74) }},
139 {{ SC_(10.0), SC_(1e-100), SC_(2.69114445546737213403880070546737213403880070546737213403880e-1010) }},
140 }};
141 static const boost::array<boost::array<typename table_type<T>::type, 3>, 10> iv_data = {{
142 {{ SC_(2.25), SC_(9.5367431640625e-7), SC_(2.34379212133481347189068464680335815256364262507955635911656e-15) }},
143 {{ SC_(5.5), SC_(3.125), SC_(0.0583514045989371500460946536220735787163510569634133670181210) }},
144 {{ SC_(-4.9990234375), SC_(2.125), SC_(0.0267920938009571023702933210070984416052633027166975342895062) }},
145 {{ SC_(-5.5), SC_(10.0), SC_(597.577606961369169607937419869926705730305175364662688426534) }},
146 {{ SC_(-5.5), SC_(100.0), SC_(9.22362906144706871737354069133813819358704200689067071415379e41) }},
147 {{ SC_(-10.0002994537353515625), SC_(0.0009765625), SC_(1.41474005665181350367684623930576333542989766867888186478185e35) }},
148 {{ SC_(-10.0002994537353515625), SC_(50.0), SC_(1.07153277202900671531087024688681954238311679648319534644743e20) }},
149 {{ SC_(141.400390625), SC_(100.0), SC_(2066.27694757392660413922181531984160871678224178890247540320) }},
150 {{ SC_(141.400390625), SC_(200.0), SC_(2.23699739472246928794922868978337381373643889659337595319774e64) }},
151 {{ SC_(-141.400390625), SC_(100.0), SC_(2066.27694672763190927440969155740243346136463461655104698748) }},
152 }};
153 static const boost::array<boost::array<typename table_type<T>::type, 3>, 5> iv_large_data = {{
154 // Bug report https://svn.boost.org/trac/boost/ticket/5560:
155 {{ SC_(-1.0), SC_(3.7291703656001033716454826577314669186882357673002034471357591666031391925350591524680874452002139016807558e-155), SC_(1.86458518280005168582274132886573345934411788365010172356788e-155) }},
156 {{ SC_(1.0), SC_(3.7291703656001033716454826577314669186882357673002034471357591666031391925350591524680874452002139016807558e-155), SC_(1.86458518280005168582274132886573345934411788365010172356788e-155) }},
157 {{ SC_(-1.125), SC_(3.7291703656001033716454826577314669186882357673002034471357591666031391925350591524680874452002139016807558e-155), SC_(-1.34963720853101363690381585556234820027343435206156667634081e173) }},
158 {{ SC_(1.125), SC_(3.7291703656001033716454826577314669186882357673002034471357591666031391925350591524680874452002139016807558e-155), SC_(8.02269390325932403421158766283366891170783955777638875887348e-175) }},
159 {{ SC_(0.5), SC_(1.2458993688871959419388378518880931736878259938089494331010226962863582408064841833232475731084062642684629e-206), SC_(8.90597649117647254543282704099383321071493400182381039079219e-104) }},
160 }};
161
162 do_test_cyl_bessel_i<T>(i0_data, name, "Bessel I0: Mathworld Data");
163 do_test_cyl_bessel_i<T>(i1_data, name, "Bessel I1: Mathworld Data");
164 do_test_cyl_bessel_i<T>(in_data, name, "Bessel In: Mathworld Data");
165
166 do_test_cyl_bessel_i_int<T>(i0_data, name, "Bessel I0: Mathworld Data (Integer Version)");
167 do_test_cyl_bessel_i_int<T>(i1_data, name, "Bessel I1: Mathworld Data (Integer Version)");
168 do_test_cyl_bessel_i_int<T>(in_data, name, "Bessel In: Mathworld Data (Integer Version)");
169
170 do_test_cyl_bessel_i<T>(iv_data, name, "Bessel Iv: Mathworld Data");
171
172#include "bessel_i_int_data.ipp"
173 do_test_cyl_bessel_i<T>(bessel_i_int_data, name, "Bessel In: Random Data");
174#include "bessel_i_data.ipp"
175 do_test_cyl_bessel_i<T>(bessel_i_data, name, "Bessel Iv: Random Data");
176
177 if(0 != static_cast<T>(ldexp(0.5, -700)))
178 do_test_cyl_bessel_i<T>(iv_large_data, name, "Bessel Iv: Mathworld Data (large values)");
179}
180