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1 | // { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" } |
2 | // | |
3 | // Copyright (C) 2016 Free Software Foundation, Inc. | |
4 | // | |
5 | // This file is part of the GNU ISO C++ Library. This library is free | |
6 | // software; you can redistribute it and/or modify it under the | |
7 | // terms of the GNU General Public License as published by the | |
8 | // Free Software Foundation; either version 3, or (at your option) | |
9 | // any later version. | |
10 | // | |
11 | // This library is distributed in the hope that it will be useful, | |
12 | // but WITHOUT ANY WARRANTY; without even the implied warranty of | |
13 | // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
14 | // GNU General Public License for more details. | |
15 | // | |
16 | // You should have received a copy of the GNU General Public License along | |
17 | // with this library; see the file COPYING3. If not see | |
18 | // <http://www.gnu.org/licenses/>. | |
19 | ||
20 | // riemann_zeta | |
21 | ||
22 | // This can take long on simulators, timing out the test. | |
82f0f789 | 23 | // { dg-additional-options "-DMAX_ITERATIONS=5" { target simulator } } |
2be75957 ESR |
24 | |
25 | #ifndef MAX_ITERATIONS | |
26 | #define MAX_ITERATIONS (sizeof(data001) / sizeof(testcase_riemann_zeta<double>)) | |
27 | #endif | |
28 | ||
29 | // Compare against values generated by the GNU Scientific Library. | |
30 | // The GSL can be found on the web: http://www.gnu.org/software/gsl/ | |
31 | #include <limits> | |
32 | #include <cmath> | |
33 | #if defined(__TEST_DEBUG) | |
34 | # include <iostream> | |
35 | # define VERIFY(A) \ | |
36 | if (!(A)) \ | |
37 | { \ | |
38 | std::cout << "line " << __LINE__ \ | |
39 | << " max_abs_frac = " << max_abs_frac \ | |
40 | << std::endl; \ | |
41 | } | |
42 | #else | |
43 | # include <testsuite_hooks.h> | |
44 | #endif | |
45 | #include <specfun_testcase.h> | |
46 | ||
47 | // Test data. | |
48 | // max(|f - f_GSL|): 8.8817841970012523e-16 | |
49 | // max(|f - f_GSL| / |f_GSL|): 3.7349082148991403e-15 | |
50 | const testcase_riemann_zeta<double> | |
51 | data001[55] = | |
52 | { | |
53 | { 0.0000000000000000, -10.000000000000000 }, | |
54 | { -0.0033669820451019579, -9.8000000000000007 }, | |
55 | { -0.0058129517767319039, -9.5999999999999996 }, | |
56 | { -0.0072908732290557004, -9.4000000000000004 }, | |
57 | { -0.0078420910654484442, -9.1999999999999993 }, | |
58 | { -0.0075757575757575803, -9.0000000000000000 }, | |
59 | { -0.0066476555677551898, -8.8000000000000007 }, | |
60 | { -0.0052400095350859429, -8.5999999999999996 }, | |
61 | { -0.0035434308017674959, -8.4000000000000004 }, | |
62 | { -0.0017417330388368585, -8.1999999999999993 }, | |
63 | { 0.0000000000000000, -8.0000000000000000 }, | |
64 | { 0.0015440036789213961, -7.7999999999999998 }, | |
65 | { 0.0027852131086497423, -7.5999999999999996 }, | |
66 | { 0.0036537321227995880, -7.4000000000000004 }, | |
67 | { 0.0041147930817053468, -7.2000000000000002 }, | |
68 | { 0.0041666666666666683, -7.0000000000000000 }, | |
69 | { 0.0038369975032738366, -6.7999999999999998 }, | |
70 | { 0.0031780270571782981, -6.5999999999999996 }, | |
71 | { 0.0022611282027338573, -6.4000000000000004 }, | |
72 | { 0.0011710237049390511, -6.2000000000000002 }, | |
73 | { 0.0000000000000000, -6.0000000000000000 }, | |
74 | { -0.0011576366649881879, -5.7999999999999998 }, | |
75 | { -0.0022106784318564345, -5.5999999999999996 }, | |
76 | { -0.0030755853460586891, -5.4000000000000004 }, | |
77 | { -0.0036804380477934787, -5.2000000000000002 }, | |
78 | { -0.0039682539682539698, -5.0000000000000000 }, | |
79 | { -0.0038996891301999797, -4.7999999999999998 }, | |
80 | { -0.0034551830834302711, -4.5999999999999996 }, | |
81 | { -0.0026366345018725115, -4.4000000000000004 }, | |
82 | { -0.0014687209305056974, -4.2000000000000002 }, | |
83 | { 0.0000000000000000, -4.0000000000000000 }, | |
84 | { 0.0016960463875825202, -3.7999999999999998 }, | |
85 | { 0.0035198355903356747, -3.5999999999999996 }, | |
86 | { 0.0053441503206513421, -3.4000000000000004 }, | |
87 | { 0.0070119720770910540, -3.2000000000000002 }, | |
88 | { 0.0083333333333333350, -3.0000000000000000 }, | |
89 | { 0.0090807294856852811, -2.7999999999999998 }, | |
90 | { 0.0089824623788396681, -2.5999999999999996 }, | |
91 | { 0.0077130239874243630, -2.4000000000000004 }, | |
92 | { 0.0048792123593036068, -2.2000000000000002 }, | |
93 | { 0.0000000000000000, -2.0000000000000000 }, | |
94 | { -0.0075229347765968010, -1.8000000000000007 }, | |
95 | { -0.018448986678963775, -1.5999999999999996 }, | |
96 | { -0.033764987694047593, -1.4000000000000004 }, | |
97 | { -0.054788441243880631, -1.1999999999999993 }, | |
98 | { -0.083333333333333398, -1.0000000000000000 }, | |
99 | { -0.12198707766977103, -0.80000000000000071 }, | |
100 | { -0.17459571193801401, -0.59999999999999964 }, | |
101 | { -0.24716546083171492, -0.40000000000000036 }, | |
102 | { -0.34966628059831484, -0.19999999999999929 }, | |
103 | { -0.49999999999999994, 0.0000000000000000 }, | |
104 | { -0.73392092489633953, 0.19999999999999929 }, | |
105 | { -1.1347977838669825, 0.40000000000000036 }, | |
106 | { -1.9526614482239983, 0.59999999999999964 }, | |
107 | { -4.4375384158955677, 0.80000000000000071 }, | |
108 | }; | |
109 | const double toler001 = 2.5000000000000020e-13; | |
110 | // riemann_zeta | |
111 | ||
2be75957 ESR |
112 | #ifndef MAX_ITERATIONS |
113 | #define MAX_ITERATIONS (sizeof(data001) / sizeof(testcase_riemann_zeta<double>)) | |
114 | #endif | |
115 | ||
116 | ||
117 | // Test data. | |
118 | // max(|f - f_GSL|): 2.6645352591003757e-15 | |
119 | // max(|f - f_GSL| / |f_GSL|): 1.1657079722157521e-15 | |
120 | const testcase_riemann_zeta<double> | |
121 | data002[145] = | |
122 | { | |
123 | { 5.5915824411777502, 1.2000000000000000 }, | |
124 | { 3.1055472779775792, 1.3999999999999999 }, | |
125 | { 2.2857656656801324, 1.6000000000000001 }, | |
126 | { 1.8822296181028220, 1.8000000000000000 }, | |
127 | { 1.6449340668482275, 2.0000000000000000 }, | |
128 | { 1.4905432565068937, 2.2000000000000002 }, | |
129 | { 1.3833428588407359, 2.3999999999999999 }, | |
130 | { 1.3054778090727803, 2.6000000000000001 }, | |
131 | { 1.2470314223172541, 2.7999999999999998 }, | |
132 | { 1.2020569031595945, 3.0000000000000000 }, | |
133 | { 1.1667733709844674, 3.2000000000000002 }, | |
134 | { 1.1386637757280420, 3.3999999999999999 }, | |
135 | { 1.1159890791233376, 3.6000000000000001 }, | |
136 | { 1.0975105764590047, 3.7999999999999998 }, | |
137 | { 1.0823232337111381, 4.0000000000000000 }, | |
138 | { 1.0697514772338095, 4.2000000000000002 }, | |
139 | { 1.0592817259798355, 4.4000000000000004 }, | |
140 | { 1.0505173825665735, 4.5999999999999996 }, | |
141 | { 1.0431480133351789, 4.7999999999999998 }, | |
142 | { 1.0369277551433700, 5.0000000000000000 }, | |
143 | { 1.0316598766779168, 5.2000000000000002 }, | |
144 | { 1.0271855389203537, 5.4000000000000004 }, | |
145 | { 1.0233754792270300, 5.5999999999999996 }, | |
146 | { 1.0201237683883446, 5.7999999999999998 }, | |
147 | { 1.0173430619844492, 6.0000000000000000 }, | |
148 | { 1.0149609451852233, 6.2000000000000002 }, | |
149 | { 1.0129170887121841, 6.4000000000000004 }, | |
150 | { 1.0111610141542708, 6.5999999999999996 }, | |
151 | { 1.0096503223447120, 6.7999999999999998 }, | |
152 | { 1.0083492773819229, 7.0000000000000000 }, | |
153 | { 1.0072276664807169, 7.2000000000000002 }, | |
154 | { 1.0062598756930512, 7.4000000000000004 }, | |
155 | { 1.0054241359879634, 7.5999999999999996 }, | |
156 | { 1.0047019048164696, 7.7999999999999998 }, | |
157 | { 1.0040773561979444, 8.0000000000000000 }, | |
158 | { 1.0035369583062013, 8.1999999999999993 }, | |
159 | { 1.0030691220374448, 8.4000000000000004 }, | |
160 | { 1.0026639074861505, 8.5999999999999996 }, | |
161 | { 1.0023127779098220, 8.8000000000000007 }, | |
162 | { 1.0020083928260823, 9.0000000000000000 }, | |
163 | { 1.0017444334995897, 9.1999999999999993 }, | |
164 | { 1.0015154553480514, 9.4000000000000004 }, | |
165 | { 1.0013167628052648, 9.5999999999999996 }, | |
166 | { 1.0011443029840295, 9.8000000000000007 }, | |
167 | { 1.0009945751278182, 10.000000000000000 }, | |
168 | { 1.0008645533615086, 10.199999999999999 }, | |
169 | { 1.0007516206744649, 10.400000000000000 }, | |
170 | { 1.0006535124140847, 10.600000000000000 }, | |
171 | { 1.0005682678503411, 10.800000000000001 }, | |
172 | { 1.0004941886041194, 11.000000000000000 }, | |
173 | { 1.0004298029239944, 11.199999999999999 }, | |
174 | { 1.0003738349551168, 11.400000000000000 }, | |
175 | { 1.0003251782761946, 11.600000000000000 }, | |
176 | { 1.0002828730909989, 11.800000000000001 }, | |
177 | { 1.0002460865533080, 12.000000000000000 }, | |
178 | { 1.0002140957818750, 12.199999999999999 }, | |
179 | { 1.0001862731874056, 12.400000000000000 }, | |
180 | { 1.0001620737887460, 12.600000000000000 }, | |
181 | { 1.0001410242422089, 12.800000000000001 }, | |
182 | { 1.0001227133475783, 13.000000000000000 }, | |
183 | { 1.0001067838280169, 13.199999999999999 }, | |
184 | { 1.0000929252097515, 13.400000000000000 }, | |
185 | { 1.0000808676518718, 13.600000000000000 }, | |
186 | { 1.0000703765974504, 13.800000000000001 }, | |
187 | { 1.0000612481350588, 14.000000000000000 }, | |
188 | { 1.0000533049750668, 14.199999999999999 }, | |
189 | { 1.0000463929582293, 14.400000000000000 }, | |
190 | { 1.0000403780253397, 14.600000000000000 }, | |
191 | { 1.0000351435864272, 14.800000000000001 }, | |
192 | { 1.0000305882363070, 15.000000000000000 }, | |
193 | { 1.0000266237704787, 15.199999999999999 }, | |
194 | { 1.0000231734615617, 15.400000000000000 }, | |
195 | { 1.0000201705617975, 15.600000000000000 }, | |
196 | { 1.0000175570017611, 15.800000000000001 }, | |
197 | { 1.0000152822594086, 16.000000000000000 }, | |
198 | { 1.0000133023770337, 16.199999999999999 }, | |
199 | { 1.0000115791066830, 16.399999999999999 }, | |
200 | { 1.0000100791671644, 16.600000000000001 }, | |
201 | { 1.0000087735980010, 16.800000000000001 }, | |
202 | { 1.0000076371976379, 17.000000000000000 }, | |
203 | { 1.0000066480348633, 17.199999999999999 }, | |
204 | { 1.0000057870238734, 17.399999999999999 }, | |
205 | { 1.0000050375546607, 17.600000000000001 }, | |
206 | { 1.0000043851715013, 17.800000000000001 }, | |
207 | { 1.0000038172932648, 18.000000000000000 }, | |
208 | { 1.0000033229700953, 18.199999999999999 }, | |
209 | { 1.0000028926717153, 18.399999999999999 }, | |
210 | { 1.0000025181032419, 18.600000000000001 }, | |
211 | { 1.0000021920449287, 18.800000000000001 }, | |
212 | { 1.0000019082127167, 19.000000000000000 }, | |
213 | { 1.0000016611368951, 19.199999999999999 }, | |
214 | { 1.0000014460565094, 19.399999999999999 }, | |
215 | { 1.0000012588274738, 19.600000000000001 }, | |
216 | { 1.0000010958426055, 19.800000000000001 }, | |
217 | { 1.0000009539620338, 20.000000000000000 }, | |
218 | { 1.0000008304526344, 20.199999999999999 }, | |
219 | { 1.0000007229353187, 20.399999999999999 }, | |
220 | { 1.0000006293391575, 20.600000000000001 }, | |
221 | { 1.0000005478614529, 20.800000000000001 }, | |
222 | { 1.0000004769329869, 21.000000000000000 }, | |
223 | { 1.0000004151877719, 21.199999999999999 }, | |
224 | { 1.0000003614367254, 21.399999999999999 }, | |
225 | { 1.0000003146447527, 21.600000000000001 }, | |
226 | { 1.0000002739108020, 21.800000000000001 }, | |
227 | { 1.0000002384505029, 22.000000000000000 }, | |
228 | { 1.0000002075810521, 22.199999999999999 }, | |
229 | { 1.0000001807080625, 22.399999999999999 }, | |
230 | { 1.0000001573141093, 22.600000000000001 }, | |
231 | { 1.0000001369487659, 22.800000000000001 }, | |
232 | { 1.0000001192199262, 23.000000000000000 }, | |
233 | { 1.0000001037862520, 23.199999999999999 }, | |
234 | { 1.0000000903506006, 23.399999999999999 }, | |
235 | { 1.0000000786543011, 23.600000000000001 }, | |
236 | { 1.0000000684721728, 23.800000000000001 }, | |
237 | { 1.0000000596081891, 24.000000000000000 }, | |
238 | { 1.0000000518917020, 24.199999999999999 }, | |
239 | { 1.0000000451741575, 24.399999999999999 }, | |
240 | { 1.0000000393262332, 24.600000000000001 }, | |
241 | { 1.0000000342353501, 24.800000000000001 }, | |
242 | { 1.0000000298035037, 25.000000000000000 }, | |
243 | { 1.0000000259453767, 25.199999999999999 }, | |
244 | { 1.0000000225866978, 25.399999999999999 }, | |
245 | { 1.0000000196628109, 25.600000000000001 }, | |
246 | { 1.0000000171174297, 25.800000000000001 }, | |
247 | { 1.0000000149015549, 26.000000000000000 }, | |
248 | { 1.0000000129725304, 26.199999999999999 }, | |
249 | { 1.0000000112932221, 26.399999999999999 }, | |
250 | { 1.0000000098313035, 26.600000000000001 }, | |
251 | { 1.0000000085586331, 26.800000000000001 }, | |
252 | { 1.0000000074507118, 27.000000000000000 }, | |
253 | { 1.0000000064862125, 27.199999999999999 }, | |
254 | { 1.0000000056465688, 27.399999999999999 }, | |
255 | { 1.0000000049156179, 27.600000000000001 }, | |
256 | { 1.0000000042792894, 27.800000000000001 }, | |
257 | { 1.0000000037253340, 28.000000000000000 }, | |
258 | { 1.0000000032430887, 28.199999999999999 }, | |
259 | { 1.0000000028232703, 28.399999999999999 }, | |
260 | { 1.0000000024577977, 28.600000000000001 }, | |
261 | { 1.0000000021396356, 28.800000000000001 }, | |
262 | { 1.0000000018626598, 29.000000000000000 }, | |
263 | { 1.0000000016215385, 29.199999999999999 }, | |
264 | { 1.0000000014116306, 29.399999999999999 }, | |
265 | { 1.0000000012288952, 29.600000000000001 }, | |
266 | { 1.0000000010698147, 29.800000000000001 }, | |
267 | { 1.0000000009313275, 30.000000000000000 }, | |
268 | }; | |
269 | const double toler002 = 2.5000000000000020e-13; | |
270 | ||
271 | template<typename Tp, unsigned int Num> | |
272 | void | |
273 | test(const testcase_riemann_zeta<Tp> (&data)[Num], Tp toler) | |
274 | { | |
275 | bool test __attribute__((unused)) = true; | |
276 | const Tp eps = std::numeric_limits<Tp>::epsilon(); | |
277 | Tp max_abs_diff = -Tp(1); | |
278 | Tp max_abs_frac = -Tp(1); | |
279 | unsigned int num_datum = MAX_ITERATIONS; | |
280 | for (unsigned int i = 0; i < num_datum; ++i) | |
281 | { | |
282 | const Tp f = std::riemann_zeta(data[i].s); | |
283 | const Tp f0 = data[i].f0; | |
284 | const Tp diff = f - f0; | |
285 | if (std::abs(diff) > max_abs_diff) | |
286 | max_abs_diff = std::abs(diff); | |
287 | if (std::abs(f0) > Tp(10) * eps | |
288 | && std::abs(f) > Tp(10) * eps) | |
289 | { | |
290 | const Tp frac = diff / f0; | |
291 | if (std::abs(frac) > max_abs_frac) | |
292 | max_abs_frac = std::abs(frac); | |
293 | } | |
294 | } | |
295 | VERIFY(max_abs_frac < toler); | |
296 | } | |
297 | ||
298 | int | |
299 | main() | |
300 | { | |
301 | test(data001, toler001); | |
302 | test(data002, toler002); | |
303 | return 0; | |
304 | } |