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1 | // Copyright (c) 2013 Anton Bikineev |
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> | |
92f5a8d4 | 10 | #include <boost/test/tools/floating_point_comparison.hpp> |
7c673cae FG |
11 | #include <boost/math/special_functions/math_fwd.hpp> |
12 | #include <boost/math/constants/constants.hpp> | |
13 | #include <boost/type_traits/is_floating_point.hpp> | |
14 | #include <boost/array.hpp> | |
15 | #include "functor.hpp" | |
16 | ||
17 | #include "handle_test_result.hpp" | |
18 | #include "table_type.hpp" | |
19 | ||
20 | #ifndef SC_ | |
21 | # define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L)) | |
22 | #endif | |
23 | ||
24 | template <class Real, class T> | |
25 | void do_test_cyl_bessel_j_prime(const T& data, const char* type_name, const char* test_name) | |
26 | { | |
27 | #if !(defined(ERROR_REPORTING_MODE) && !defined(BESSEL_JP_FUNCTION_TO_TEST)) | |
28 | typedef Real value_type; | |
29 | ||
30 | typedef value_type (*pg)(value_type, value_type); | |
31 | #ifdef BESSEL_JP_FUNCTION_TO_TEST | |
32 | pg funcp = BESSEL_JP_FUNCTION_TO_TEST; | |
33 | #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) | |
34 | pg funcp = boost::math::cyl_bessel_j_prime<value_type, value_type>; | |
35 | #else | |
36 | pg funcp = boost::math::cyl_bessel_j_prime; | |
37 | #endif | |
38 | ||
39 | boost::math::tools::test_result<value_type> result; | |
40 | ||
41 | std::cout << "Testing " << test_name << " with type " << type_name | |
42 | << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"; | |
43 | ||
44 | // | |
45 | // test cyl_bessel_j against data: | |
46 | // | |
47 | result = boost::math::tools::test_hetero<Real>( | |
48 | data, | |
49 | bind_func<Real>(funcp, 0, 1), | |
50 | extract_result<Real>(2)); | |
51 | handle_test_result(result, data[result.worst()], result.worst(), type_name, "cyl_bessel_j_prime", test_name); | |
52 | std::cout << std::endl; | |
53 | #endif | |
54 | } | |
55 | ||
56 | template <class T> | |
57 | T cyl_bessel_j_prime_int_wrapper(T v, T x) | |
58 | { | |
59 | #ifdef BESSEL_JPN_FUNCTION_TO_TEST | |
60 | return static_cast<T>(BESSEL_JPN_FUNCTION_TO_TEST(boost::math::itrunc(v), x)); | |
61 | #else | |
62 | return static_cast<T>(boost::math::cyl_bessel_j_prime(boost::math::itrunc(v), x)); | |
63 | #endif | |
64 | } | |
65 | ||
66 | ||
67 | template <class Real, class T> | |
68 | void do_test_cyl_bessel_j_prime_int(const T& data, const char* type_name, const char* test_name) | |
69 | { | |
70 | #if !(defined(ERROR_REPORTING_MODE) && !defined(BESSEL_JPN_FUNCTION_TO_TEST)) | |
71 | typedef Real value_type; | |
72 | ||
73 | typedef value_type (*pg)(value_type, value_type); | |
74 | #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) | |
75 | pg funcp = cyl_bessel_j_prime_int_wrapper<value_type>; | |
76 | #else | |
77 | pg funcp = cyl_bessel_j_prime_int_wrapper; | |
78 | #endif | |
79 | ||
80 | boost::math::tools::test_result<value_type> result; | |
81 | ||
82 | std::cout << "Testing " << test_name << " with type " << type_name | |
83 | << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"; | |
84 | ||
85 | // | |
86 | // test cyl_bessel_j against data: | |
87 | // | |
88 | result = boost::math::tools::test_hetero<Real>( | |
89 | data, | |
90 | bind_func<Real>(funcp, 0, 1), | |
91 | extract_result<Real>(2)); | |
92 | handle_test_result(result, data[result.worst()], result.worst(), type_name, "cyl_bessel_j_prime (integer orders)", test_name); | |
93 | std::cout << std::endl; | |
94 | #endif | |
95 | } | |
96 | ||
97 | template <class Real, class T> | |
98 | void do_test_sph_bessel_j_prime(const T& data, const char* type_name, const char* test_name) | |
99 | { | |
100 | #if !(defined(ERROR_REPORTING_MODE) && !defined(BESSEL_JPS_FUNCTION_TO_TEST)) | |
101 | typedef Real value_type; | |
102 | ||
103 | typedef value_type (*pg)(unsigned, value_type); | |
104 | #ifdef BESSEL_JPS_FUNCTION_TO_TEST | |
105 | pg funcp = BESSEL_JPS_FUNCTION_TO_TEST; | |
106 | #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS) | |
107 | pg funcp = boost::math::sph_bessel_prime<value_type>; | |
108 | #else | |
109 | pg funcp = boost::math::sph_bessel_prime; | |
110 | #endif | |
111 | ||
112 | boost::math::tools::test_result<value_type> result; | |
113 | ||
114 | std::cout << "Testing " << test_name << " with type " << type_name | |
115 | << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"; | |
116 | ||
117 | // | |
118 | // test sph_bessel against data: | |
119 | // | |
120 | result = boost::math::tools::test_hetero<Real>( | |
121 | data, | |
122 | bind_func_int1<Real>(funcp, 0, 1), | |
123 | extract_result<Real>(2)); | |
124 | handle_test_result(result, data[result.worst()], result.worst(), type_name, "sph_bessel_prime", test_name); | |
125 | std::cout << std::endl; | |
126 | #endif | |
127 | } | |
128 | ||
129 | template <class T> | |
130 | void test_bessel_prime(T, const char* name) | |
131 | { | |
132 | // | |
133 | // The actual test data is rather verbose, so it's in a separate file | |
134 | // | |
135 | // The contents are as follows, each row of data contains | |
136 | // three items, input value a, input value b and J'(a, b): | |
137 | // | |
138 | // function values calculated on http://functions.wolfram.com/ | |
1e59de90 | 139 | static const std::array<std::array<typename table_type<T>::type, 3>, 8> j0_data = {{ |
7c673cae FG |
140 | {{ SC_(0.0), SC_(0.0), SC_(0.0) }}, |
141 | {{ SC_(0.0), SC_(1.0), SC_(-0.440050585744933515959682203718914913127) }}, | |
142 | {{ SC_(0.0), SC_(-2.0), SC_(0.576724807756873387202448242269137086920) }}, | |
143 | {{ SC_(0.0), SC_(4.0), SC_(0.06604332802354913614318542080327502873) }}, | |
144 | {{ SC_(0.0), SC_(-8.0), SC_(0.2346363468539146243812766515904546115488) }}, | |
145 | {{ SC_(0.0), SC_(1e-05), SC_(-0.499999999993750000000026041666666612413194e-5) }}, | |
146 | {{ SC_(0.0), SC_(1e-10), SC_(-0.499999999999999999999375000000000000000000e-10) }}, | |
147 | {{ SC_(0.0), SC_(-1e+01), SC_(0.0434727461688614366697487680258592883062724) }}, | |
148 | }}; | |
1e59de90 | 149 | static const std::array<std::array<T, 3>, 6> j0_tricky = {{ |
7c673cae FG |
150 | // Big numbers make the accuracy of std::sin the limiting factor: |
151 | {{ SC_(0.0), SC_(1e+03), SC_(-0.00472831190708952391757607190121691628542) }}, | |
152 | {{ SC_(0.0), SC_(1e+05), SC_(-0.0018467575628825677163621239671142157437) }}, | |
153 | // test at the regular Bessel roots: | |
154 | {{ SC_(0.0), T(2521642)/(1024 * 1024), SC_(-0.519147572225778564548541576612898453392794) }}, | |
155 | {{ SC_(0.0), T(5788221)/(1024 * 1024), SC_(0.34026483151709114336072749629487476476084) }}, | |
156 | {{ SC_(0.0), T(9074091)/(1024 * 1024), SC_(-0.271452311894657014854145327490965399410) }}, | |
157 | {{ SC_(0.0), T(12364320)/(1024 * 1024), SC_(0.2324598316641066033541448467171088144257742) }} | |
158 | }}; | |
159 | ||
1e59de90 | 160 | static const std::array<std::array<typename table_type<T>::type, 3>, 8> j1_data = {{ |
7c673cae FG |
161 | {{ SC_(1.0), SC_(0.0), SC_(0.5) }}, |
162 | {{ SC_(1.0), SC_(1.0), SC_(0.325147100813033035490035322383748307781902) }}, | |
163 | {{ SC_(1.0), SC_(-2.0), SC_(-0.064471624737201025549396666484619917634997) }}, | |
164 | {{ SC_(1.0), SC_(4.0), SC_(-0.38063897785796008825079441325087928479376) }}, | |
165 | {{ SC_(1.0), SC_(-8.0), SC_(0.1423212637808145780432098264031651746248) }}, | |
166 | {{ SC_(1.0), SC_(1e-05), SC_(0.499999999981250000000130208333332953559028) }}, | |
167 | {{ SC_(1.0), SC_(1e-10), SC_(0.499999999999999999998125000000000000000001) }}, | |
168 | {{ SC_(1.0), SC_(-1e+01), SC_(-0.250283039068234478864735739287914682660226) }}, | |
169 | }}; | |
1e59de90 | 170 | static const std::array<std::array<T, 3>, 5> j1_tricky = {{ |
7c673cae FG |
171 | // Big numbers make the accuracy of std::sin the limiting factor: |
172 | {{ SC_(1.0), SC_(1e+03), SC_(0.024781957840513085037413155043792491869881) }}, | |
173 | {{ SC_(1.0), SC_(1e+05), SC_(-0.0017192195838116010182477650983128728897) }}, | |
174 | // test at the regular Bessel roots: | |
175 | {{ SC_(1.0), T(4017834)/(1024*1024), SC_(-0.4027594878673806944036073218740057200193405151367) }}, | |
176 | {{ SC_(1.0), T(7356375)/(1024*1024), SC_(0.3001157854852247730548242543591186404228210449219) }}, | |
177 | {{ SC_(1.0), T(10667654)/(1024*1024), SC_(-0.2497048893045206718888096020236844196915626525879) }}, | |
178 | }}; | |
179 | ||
1e59de90 | 180 | static const std::array<std::array<typename table_type<T>::type, 3>, 17> jn_data = {{ |
7c673cae FG |
181 | {{ SC_(-1.0), SC_(1.25), SC_(-0.2374074770153809244011000600949046202003956) }}, |
182 | {{ SC_(2.0), SC_(0.0), SC_(0.0) }}, | |
183 | {{ SC_(-2.0), SC_(0.0), SC_(0.0) }}, | |
184 | {{ SC_(2.0), SC_(1e-02), SC_(0.00249995833352864539930612069540679799606337) }}, | |
185 | {{ SC_(5.0), SC_(10.0), SC_(-0.102571922008611714904101858221407144485) }}, | |
186 | {{ SC_(5.0), SC_(-10.0), SC_(-0.102571922008611714904101858221407144485) }}, | |
187 | {{ SC_(-5.0), SC_(1e+06), SC_(-0.0003310524513007044105585859534523271988) }}, | |
188 | {{ SC_(5.0), SC_(1e+06), SC_(0.0003310524513007044105585859534523271988) }}, | |
189 | {{ SC_(-5.0), SC_(-1.0), SC_(-0.001227850313053782886909720690402218190791576) }}, | |
190 | {{ SC_(10.0), SC_(10.0), SC_(0.08436957863176118824849051273337698304165) }}, | |
191 | {{ SC_(10.0), SC_(-10.0), SC_(-0.08436957863176118824849051273337698304165) }}, | |
192 | {{ SC_(10.0), SC_(-5.0), SC_(-0.00258467784485473925206548854676116157568106) }}, | |
193 | {{ SC_(-10.0), SC_(1e+06), SC_(-0.0007259518037193243350387875733893635962) }}, | |
194 | {{ SC_(10.0), SC_(1e+06), SC_(-0.0007259518037193243350387875733893635962) }}, | |
195 | {{ SC_(1e+02), SC_(8e+01), SC_(3.5036060582489177538508950593467499997755e-06) }}, | |
196 | {{ SC_(1e+03), SC_(1e+05), SC_(-0.0021724469777608393409850758227465776486) }}, | |
197 | {{ SC_(10.0), SC_(1e-100), SC_(2.69114445546737213403880070546737213403880070547e-909) }}, | |
198 | }}; | |
199 | do_test_cyl_bessel_j_prime<T>(j0_data, name, "Bessel J0': Mathworld Data"); | |
200 | do_test_cyl_bessel_j_prime<T>(j0_tricky, name, "Bessel J0': Mathworld Data (Tricky cases)"); | |
201 | do_test_cyl_bessel_j_prime<T>(j1_data, name, "Bessel J1': Mathworld Data"); | |
202 | do_test_cyl_bessel_j_prime<T>(j1_tricky, name, "Bessel J1': Mathworld Data (tricky cases)"); | |
203 | do_test_cyl_bessel_j_prime<T>(jn_data, name, "Bessel JN': Mathworld Data"); | |
204 | ||
205 | do_test_cyl_bessel_j_prime_int<T>(j0_data, name, "Bessel J0': Mathworld Data (Integer Version)"); | |
206 | do_test_cyl_bessel_j_prime_int<T>(j0_tricky, name, "Bessel J0': Mathworld Data (Tricky cases) (Integer Version)"); | |
207 | do_test_cyl_bessel_j_prime_int<T>(j1_data, name, "Bessel J1': Mathworld Data (Integer Version)"); | |
208 | do_test_cyl_bessel_j_prime_int<T>(j1_tricky, name, "Bessel J1': Mathworld Data (tricky cases) (Integer Version)"); | |
209 | do_test_cyl_bessel_j_prime_int<T>(jn_data, name, "Bessel JN': Mathworld Data (Integer Version)"); | |
210 | ||
1e59de90 | 211 | static const std::array<std::array<T, 3>, 21> jv_data = {{ |
7c673cae FG |
212 | {{ T(22.5), T(0), SC_(0.0) }}, |
213 | {{ T(2457)/1024, T(1)/1024, SC_(9.35477929043111040277363766198320562099360690e-6) }}, | |
214 | {{ SC_(5.5), T(3217)/1024, SC_(0.042165579369684463582791278988393873) }}, | |
215 | {{ SC_(-5.5), T(3217)/1024, SC_(3.361570113176257957139775812778503494) }}, | |
216 | {{ SC_(-5.5), SC_(1e+04), SC_(0.007593311396019034252155600098309836289) }}, | |
217 | {{ SC_(5.5), SC_(1e+04), SC_(-0.00245022241637437956702428797044365092) }}, | |
218 | {{ SC_(5.5), SC_(1e+06), SC_(-0.000279242826717266554062248256927185394) }}, | |
219 | {{ SC_(5.125), SC_(1e+06), SC_(0.0001830632695189459708211614700642271) }}, | |
220 | {{ SC_(5.875), SC_(1e+06), SC_(-0.0006474276718101871487286860109203539) }}, | |
221 | {{ SC_(0.5), SC_(101.0), SC_(0.070640819172197226936337703929857171981702865) }}, | |
222 | {{ SC_(-5.5), SC_(1e+04), SC_(0.007593311396019034252155600098309836289) }}, | |
223 | {{ SC_(-5.5), SC_(1e+06), SC_(-0.0007474243882060190346457525218941411076) }}, | |
224 | {{ SC_(-0.5), SC_(101.0), SC_(-0.036238035321276062532981494694583591262302408) }}, | |
225 | {{ T(-10486074) / (1024*1024), T(1)/512, SC_(-7.0724447469115535625316241941528969321944e35) }}, | |
226 | {{ T(-10486074) / (1024*1024), SC_(15.0), SC_(-0.15994088796049823354364759206656917967697690) }}, | |
227 | {{ T(10486074) / (1024*1024), SC_(1e+02), SC_(-0.05778764167290516644655950658602424434253) }}, | |
228 | {{ T(10486074) / (1024*1024), SC_(2e+04), SC_(-0.00091101010794789360775314125410690740803) }}, | |
229 | {{ T(-10486074) / (1024*1024), SC_(1e+02), SC_(-0.057736130385111563671838499496767877709471701) }}, | |
230 | {{ SC_(1.5), T(8034)/1024, SC_(0.2783550354042687982259490073096357) }}, | |
231 | {{ SC_(8.5), boost::math::constants::pi<T>() * 4, SC_(-0.194590144622675911618596506265006877277074) }}, | |
232 | {{ SC_(-8.5), boost::math::constants::pi<T>() * 4, SC_(-0.014516314554743677558496402742690038592728) }}, | |
233 | }}; | |
234 | do_test_cyl_bessel_j_prime<T>(jv_data, name, "Bessel J': Mathworld Data"); | |
1e59de90 | 235 | static const std::array<std::array<T, 3>, 4> jv_large_data = {{ |
7c673cae FG |
236 | #if LDBL_MAX_10_EXP > 308 |
237 | {{ SC_(-0.5), static_cast<T>(std::ldexp(0.5, -683)), SC_(-2.8687031947358902542073388638943588627056993e308) }}, | |
238 | #else | |
239 | {{ SC_(-0.5), static_cast<T>(std::ldexp(0.5, -450)), SC_(-1.7688953183288445554095310240218576026580197125814e203) }}, | |
240 | #endif | |
241 | {{ SC_(256.0), SC_(512.0), SC_(0.032286467266411904239327492993951594201583145) }}, | |
242 | {{ SC_(-256.0), SC_(8.0), SC_(4.6974301387555891979202431551474684165419e-352) }}, | |
243 | {{ SC_(-2.5), SC_(4.0), SC_(-0.3580070651681080294136741901878543615958139) }}, | |
244 | }}; | |
245 | if(jv_large_data[0][1] != 0) | |
246 | do_test_cyl_bessel_j_prime<T>(jv_large_data, name, "Bessel J': Mathworld Data (large values)"); | |
247 | ||
248 | #include "bessel_j_prime_int_data.ipp" | |
249 | do_test_cyl_bessel_j_prime<T>(bessel_j_prime_int_data, name, "Bessel JN': Random Data"); | |
250 | ||
251 | #include "bessel_j_prime_data.ipp" | |
252 | do_test_cyl_bessel_j_prime<T>(bessel_j_prime_data, name, "Bessel J': Random Data"); | |
253 | ||
254 | #include "bessel_j_prime_large_data.ipp" | |
255 | do_test_cyl_bessel_j_prime<T>(bessel_j_prime_large_data, name, "Bessel J': Random Data (Tricky large values)"); | |
256 | ||
257 | #include "sph_bessel_prime_data.ipp" | |
258 | do_test_sph_bessel_j_prime<T>(sph_bessel_prime_data, name, "Bessel j': Random Data"); | |
259 | ||
260 | // | |
261 | // Some special cases: | |
262 | // | |
263 | BOOST_CHECK_EQUAL(boost::math::cyl_bessel_j_prime(T(1), T(0)), T(0.5)); | |
264 | BOOST_CHECK_EQUAL(boost::math::cyl_bessel_j_prime(T(-1), T(0)), T(-0.5)); | |
265 | BOOST_CHECK_EQUAL(boost::math::cyl_bessel_j_prime(T(2), T(0)), T(0)); | |
266 | ||
267 | // | |
268 | // Special cases that are errors: | |
269 | // | |
270 | BOOST_MATH_CHECK_THROW(boost::math::sph_bessel_prime(1, T(0)), std::domain_error); | |
271 | BOOST_MATH_CHECK_THROW(boost::math::sph_bessel_prime(100000, T(0)), std::domain_error); | |
272 | BOOST_MATH_CHECK_THROW(boost::math::cyl_bessel_j_prime(T(-2.5), T(0)), std::domain_error); | |
273 | BOOST_MATH_CHECK_THROW(boost::math::cyl_bessel_j_prime(T(-2.5), T(-2)), std::domain_error); | |
274 | BOOST_MATH_CHECK_THROW(boost::math::cyl_bessel_j_prime(T(2.5), T(-2)), std::domain_error); | |
275 | } | |
276 |