d6b3171aa6845807f5871e895eadfeb6b95c00ff
1 // { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" }
3 // Copyright (C) 2016 Free Software Foundation, Inc.
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)
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.
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/>.
22 // This can take long on simulators, timing out the test.
23 // { dg-options "-DMAX_ITERATIONS=5" { target simulator } }
25 #ifndef MAX_ITERATIONS
26 #define MAX_ITERATIONS (sizeof(data001) / sizeof(testcase_riemann_zeta<double>))
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/
33 #if defined(__TEST_DEBUG)
38 std::cout << "line " << __LINE__ \
39 << " max_abs_frac = " << max_abs_frac \
43 # include <testsuite_hooks.h>
45 #include <specfun_testcase.h>
48 // max(|f - f_GSL|): 8.8817841970012523e-16
49 // max(|f - f_GSL| / |f_GSL|): 3.7349082148991403e-15
50 const testcase_riemann_zeta
<double>
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 },
109 const double toler001
= 2.5000000000000020e-13;
112 // This can take long on simulators, timing out the test.
113 // { dg-options "-DMAX_ITERATIONS=5" { target simulator } }
115 #ifndef MAX_ITERATIONS
116 #define MAX_ITERATIONS (sizeof(data001) / sizeof(testcase_riemann_zeta<double>))
121 // max(|f - f_GSL|): 2.6645352591003757e-15
122 // max(|f - f_GSL| / |f_GSL|): 1.1657079722157521e-15
123 const testcase_riemann_zeta
<double>
126 { 5.5915824411777502, 1.2000000000000000 },
127 { 3.1055472779775792, 1.3999999999999999 },
128 { 2.2857656656801324, 1.6000000000000001 },
129 { 1.8822296181028220, 1.8000000000000000 },
130 { 1.6449340668482275, 2.0000000000000000 },
131 { 1.4905432565068937, 2.2000000000000002 },
132 { 1.3833428588407359, 2.3999999999999999 },
133 { 1.3054778090727803, 2.6000000000000001 },
134 { 1.2470314223172541, 2.7999999999999998 },
135 { 1.2020569031595945, 3.0000000000000000 },
136 { 1.1667733709844674, 3.2000000000000002 },
137 { 1.1386637757280420, 3.3999999999999999 },
138 { 1.1159890791233376, 3.6000000000000001 },
139 { 1.0975105764590047, 3.7999999999999998 },
140 { 1.0823232337111381, 4.0000000000000000 },
141 { 1.0697514772338095, 4.2000000000000002 },
142 { 1.0592817259798355, 4.4000000000000004 },
143 { 1.0505173825665735, 4.5999999999999996 },
144 { 1.0431480133351789, 4.7999999999999998 },
145 { 1.0369277551433700, 5.0000000000000000 },
146 { 1.0316598766779168, 5.2000000000000002 },
147 { 1.0271855389203537, 5.4000000000000004 },
148 { 1.0233754792270300, 5.5999999999999996 },
149 { 1.0201237683883446, 5.7999999999999998 },
150 { 1.0173430619844492, 6.0000000000000000 },
151 { 1.0149609451852233, 6.2000000000000002 },
152 { 1.0129170887121841, 6.4000000000000004 },
153 { 1.0111610141542708, 6.5999999999999996 },
154 { 1.0096503223447120, 6.7999999999999998 },
155 { 1.0083492773819229, 7.0000000000000000 },
156 { 1.0072276664807169, 7.2000000000000002 },
157 { 1.0062598756930512, 7.4000000000000004 },
158 { 1.0054241359879634, 7.5999999999999996 },
159 { 1.0047019048164696, 7.7999999999999998 },
160 { 1.0040773561979444, 8.0000000000000000 },
161 { 1.0035369583062013, 8.1999999999999993 },
162 { 1.0030691220374448, 8.4000000000000004 },
163 { 1.0026639074861505, 8.5999999999999996 },
164 { 1.0023127779098220, 8.8000000000000007 },
165 { 1.0020083928260823, 9.0000000000000000 },
166 { 1.0017444334995897, 9.1999999999999993 },
167 { 1.0015154553480514, 9.4000000000000004 },
168 { 1.0013167628052648, 9.5999999999999996 },
169 { 1.0011443029840295, 9.8000000000000007 },
170 { 1.0009945751278182, 10.000000000000000 },
171 { 1.0008645533615086, 10.199999999999999 },
172 { 1.0007516206744649, 10.400000000000000 },
173 { 1.0006535124140847, 10.600000000000000 },
174 { 1.0005682678503411, 10.800000000000001 },
175 { 1.0004941886041194, 11.000000000000000 },
176 { 1.0004298029239944, 11.199999999999999 },
177 { 1.0003738349551168, 11.400000000000000 },
178 { 1.0003251782761946, 11.600000000000000 },
179 { 1.0002828730909989, 11.800000000000001 },
180 { 1.0002460865533080, 12.000000000000000 },
181 { 1.0002140957818750, 12.199999999999999 },
182 { 1.0001862731874056, 12.400000000000000 },
183 { 1.0001620737887460, 12.600000000000000 },
184 { 1.0001410242422089, 12.800000000000001 },
185 { 1.0001227133475783, 13.000000000000000 },
186 { 1.0001067838280169, 13.199999999999999 },
187 { 1.0000929252097515, 13.400000000000000 },
188 { 1.0000808676518718, 13.600000000000000 },
189 { 1.0000703765974504, 13.800000000000001 },
190 { 1.0000612481350588, 14.000000000000000 },
191 { 1.0000533049750668, 14.199999999999999 },
192 { 1.0000463929582293, 14.400000000000000 },
193 { 1.0000403780253397, 14.600000000000000 },
194 { 1.0000351435864272, 14.800000000000001 },
195 { 1.0000305882363070, 15.000000000000000 },
196 { 1.0000266237704787, 15.199999999999999 },
197 { 1.0000231734615617, 15.400000000000000 },
198 { 1.0000201705617975, 15.600000000000000 },
199 { 1.0000175570017611, 15.800000000000001 },
200 { 1.0000152822594086, 16.000000000000000 },
201 { 1.0000133023770337, 16.199999999999999 },
202 { 1.0000115791066830, 16.399999999999999 },
203 { 1.0000100791671644, 16.600000000000001 },
204 { 1.0000087735980010, 16.800000000000001 },
205 { 1.0000076371976379, 17.000000000000000 },
206 { 1.0000066480348633, 17.199999999999999 },
207 { 1.0000057870238734, 17.399999999999999 },
208 { 1.0000050375546607, 17.600000000000001 },
209 { 1.0000043851715013, 17.800000000000001 },
210 { 1.0000038172932648, 18.000000000000000 },
211 { 1.0000033229700953, 18.199999999999999 },
212 { 1.0000028926717153, 18.399999999999999 },
213 { 1.0000025181032419, 18.600000000000001 },
214 { 1.0000021920449287, 18.800000000000001 },
215 { 1.0000019082127167, 19.000000000000000 },
216 { 1.0000016611368951, 19.199999999999999 },
217 { 1.0000014460565094, 19.399999999999999 },
218 { 1.0000012588274738, 19.600000000000001 },
219 { 1.0000010958426055, 19.800000000000001 },
220 { 1.0000009539620338, 20.000000000000000 },
221 { 1.0000008304526344, 20.199999999999999 },
222 { 1.0000007229353187, 20.399999999999999 },
223 { 1.0000006293391575, 20.600000000000001 },
224 { 1.0000005478614529, 20.800000000000001 },
225 { 1.0000004769329869, 21.000000000000000 },
226 { 1.0000004151877719, 21.199999999999999 },
227 { 1.0000003614367254, 21.399999999999999 },
228 { 1.0000003146447527, 21.600000000000001 },
229 { 1.0000002739108020, 21.800000000000001 },
230 { 1.0000002384505029, 22.000000000000000 },
231 { 1.0000002075810521, 22.199999999999999 },
232 { 1.0000001807080625, 22.399999999999999 },
233 { 1.0000001573141093, 22.600000000000001 },
234 { 1.0000001369487659, 22.800000000000001 },
235 { 1.0000001192199262, 23.000000000000000 },
236 { 1.0000001037862520, 23.199999999999999 },
237 { 1.0000000903506006, 23.399999999999999 },
238 { 1.0000000786543011, 23.600000000000001 },
239 { 1.0000000684721728, 23.800000000000001 },
240 { 1.0000000596081891, 24.000000000000000 },
241 { 1.0000000518917020, 24.199999999999999 },
242 { 1.0000000451741575, 24.399999999999999 },
243 { 1.0000000393262332, 24.600000000000001 },
244 { 1.0000000342353501, 24.800000000000001 },
245 { 1.0000000298035037, 25.000000000000000 },
246 { 1.0000000259453767, 25.199999999999999 },
247 { 1.0000000225866978, 25.399999999999999 },
248 { 1.0000000196628109, 25.600000000000001 },
249 { 1.0000000171174297, 25.800000000000001 },
250 { 1.0000000149015549, 26.000000000000000 },
251 { 1.0000000129725304, 26.199999999999999 },
252 { 1.0000000112932221, 26.399999999999999 },
253 { 1.0000000098313035, 26.600000000000001 },
254 { 1.0000000085586331, 26.800000000000001 },
255 { 1.0000000074507118, 27.000000000000000 },
256 { 1.0000000064862125, 27.199999999999999 },
257 { 1.0000000056465688, 27.399999999999999 },
258 { 1.0000000049156179, 27.600000000000001 },
259 { 1.0000000042792894, 27.800000000000001 },
260 { 1.0000000037253340, 28.000000000000000 },
261 { 1.0000000032430887, 28.199999999999999 },
262 { 1.0000000028232703, 28.399999999999999 },
263 { 1.0000000024577977, 28.600000000000001 },
264 { 1.0000000021396356, 28.800000000000001 },
265 { 1.0000000018626598, 29.000000000000000 },
266 { 1.0000000016215385, 29.199999999999999 },
267 { 1.0000000014116306, 29.399999999999999 },
268 { 1.0000000012288952, 29.600000000000001 },
269 { 1.0000000010698147, 29.800000000000001 },
270 { 1.0000000009313275, 30.000000000000000 },
272 const double toler002
= 2.5000000000000020e-13;
274 template<typename Tp
, unsigned int Num
>
276 test(const testcase_riemann_zeta
<Tp
> (&data
)[Num
], Tp toler
)
278 bool test
__attribute__((unused
)) = true;
279 const Tp eps
= std::numeric_limits
<Tp
>::epsilon();
280 Tp max_abs_diff
= -Tp(1);
281 Tp max_abs_frac
= -Tp(1);
282 unsigned int num_datum
= MAX_ITERATIONS
;
283 for (unsigned int i
= 0; i
< num_datum
; ++i
)
285 const Tp f
= std::riemann_zeta(data
[i
].s
);
286 const Tp f0
= data
[i
].f0
;
287 const Tp diff
= f
- f0
;
288 if (std::abs(diff
) > max_abs_diff
)
289 max_abs_diff
= std::abs(diff
);
290 if (std::abs(f0
) > Tp(10) * eps
291 && std::abs(f
) > Tp(10) * eps
)
293 const Tp frac
= diff
/ f0
;
294 if (std::abs(frac
) > max_abs_frac
)
295 max_abs_frac
= std::abs(frac
);
298 VERIFY(max_abs_frac
< toler
);
304 test(data001
, toler001
);
305 test(data002
, toler002
);