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git.ipfire.org Git - thirdparty/gcc.git/blob - libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/12_ellint_1/check_value.cc
1 // { dg-do run { target c++11 } }
2 // { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" }
4 // Copyright (C) 2016-2024 Free Software Foundation, Inc.
6 // This file is part of the GNU ISO C++ Library. This library is free
7 // software; you can redistribute it and/or modify it under the
8 // terms of the GNU General Public License as published by the
9 // Free Software Foundation; either version 3, or (at your option)
12 // This library is distributed in the hope that it will be useful,
13 // but WITHOUT ANY WARRANTY; without even the implied warranty of
14 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 // GNU General Public License for more details.
17 // You should have received a copy of the GNU General Public License along
18 // with this library; see the file COPYING3. If not see
19 // <http://www.gnu.org/licenses/>.
22 // Compare against values generated by the GNU Scientific Library.
23 // The GSL can be found on the web: http://www.gnu.org/software/gsl/
26 #if defined(__TEST_DEBUG)
31 std::cout << "line " << __LINE__ \
32 << " max_abs_frac = " << max_abs_frac \
36 # include <testsuite_hooks.h>
38 #include <specfun_testcase.h>
40 // Test data for k=-0.90000000000000002.
41 // max(|f - f_Boost|): 8.8817841970012523e-16 at index 7
42 // max(|f - f_Boost| / |f_Boost|): 5.7842011620951154e-16
43 // mean(f - f_Boost): 5.8286708792820721e-17
44 // variance(f - f_Boost): 4.1942474344433133e-34
45 // stddev(f - f_Boost): 2.0479861900030756e-17
46 const testcase_ellint_1
<double>
49 { 0.0000000000000000, -0.90000000000000002, 0.0000000000000000, 0.0 },
50 { 0.17525427376115027, -0.90000000000000002, 0.17453292519943295, 0.0 },
51 { 0.35492464591297446, -0.90000000000000002, 0.34906585039886590, 0.0 },
52 { 0.54388221416157123, -0.90000000000000002, 0.52359877559829882, 0.0 },
53 { 0.74797400423532512, -0.90000000000000002, 0.69813170079773179, 0.0 },
54 { 0.97463898451966446, -0.90000000000000002, 0.87266462599716477, 0.0 },
55 { 1.2334463254523438, -0.90000000000000002, 1.0471975511965976, 0.0 },
56 { 1.5355247765594913, -0.90000000000000002, 1.2217304763960306, 0.0 },
57 { 1.8882928567775126, -0.90000000000000002, 1.3962634015954636, 0.0 },
58 { 2.2805491384227703, -0.90000000000000002, 1.5707963267948966, 0.0 },
60 const double toler001
= 2.5000000000000020e-13;
62 // Test data for k=-0.80000000000000004.
63 // max(|f - f_Boost|): 8.8817841970012523e-16 at index 8
64 // max(|f - f_Boost| / |f_Boost|): 5.2032670495747184e-16
65 // mean(f - f_Boost): 1.9428902930940239e-16
66 // variance(f - f_Boost): 2.7486111305082033e-32
67 // stddev(f - f_Boost): 1.6578935823834422e-16
68 const testcase_ellint_1
<double>
71 { 0.0000000000000000, -0.80000000000000004, 0.0000000000000000, 0.0 },
72 { 0.17510154241338899, -0.80000000000000004, 0.17453292519943295, 0.0 },
73 { 0.35365068839779396, -0.80000000000000004, 0.34906585039886590, 0.0 },
74 { 0.53926804409084550, -0.80000000000000004, 0.52359877559829882, 0.0 },
75 { 0.73587926028070372, -0.80000000000000004, 0.69813170079773179, 0.0 },
76 { 0.94770942970071170, -0.80000000000000004, 0.87266462599716477, 0.0 },
77 { 1.1789022995388236, -0.80000000000000004, 1.0471975511965976, 0.0 },
78 { 1.4323027881876012, -0.80000000000000004, 1.2217304763960306, 0.0 },
79 { 1.7069629739121677, -0.80000000000000004, 1.3962634015954636, 0.0 },
80 { 1.9953027776647294, -0.80000000000000004, 1.5707963267948966, 0.0 },
82 const double toler002
= 2.5000000000000020e-13;
84 // Test data for k=-0.69999999999999996.
85 // max(|f - f_Boost|): 8.8817841970012523e-16 at index 8
86 // max(|f - f_Boost| / |f_Boost|): 5.5425633303580569e-16
87 // mean(f - f_Boost): 3.3306690738754695e-17
88 // variance(f - f_Boost): 2.8136647641852830e-32
89 // stddev(f - f_Boost): 1.6773982127644239e-16
90 const testcase_ellint_1
<double>
93 { 0.0000000000000000, -0.69999999999999996, 0.0000000000000000, 0.0 },
94 { 0.17496737466916723, -0.69999999999999996, 0.17453292519943295, 0.0 },
95 { 0.35254687535677931, -0.69999999999999996, 0.34906585039886590, 0.0 },
96 { 0.53536740275997130, -0.69999999999999996, 0.52359877559829882, 0.0 },
97 { 0.72603797651684454, -0.69999999999999996, 0.69813170079773179, 0.0 },
98 { 0.92698296348313447, -0.69999999999999996, 0.87266462599716477, 0.0 },
99 { 1.1400447527693316, -0.69999999999999996, 1.0471975511965976, 0.0 },
100 { 1.3657668117194071, -0.69999999999999996, 1.2217304763960306, 0.0 },
101 { 1.6024686895959162, -0.69999999999999996, 1.3962634015954636, 0.0 },
102 { 1.8456939983747234, -0.69999999999999996, 1.5707963267948966, 0.0 },
104 const double toler003
= 2.5000000000000020e-13;
106 // Test data for k=-0.59999999999999998.
107 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 7
108 // max(|f - f_Boost| / |f_Boost|): 3.3664899092028927e-16
109 // mean(f - f_Boost): 5.2735593669694933e-17
110 // variance(f - f_Boost): 3.4333862218458872e-34
111 // stddev(f - f_Boost): 1.8529398861932589e-17
112 const testcase_ellint_1
<double>
115 { 0.0000000000000000, -0.59999999999999998, 0.0000000000000000, 0.0 },
116 { 0.17485154362988359, -0.59999999999999998, 0.17453292519943295, 0.0 },
117 { 0.35160509865544320, -0.59999999999999998, 0.34906585039886590, 0.0 },
118 { 0.53210652578446138, -0.59999999999999998, 0.52359877559829882, 0.0 },
119 { 0.71805304664485659, -0.59999999999999998, 0.69813170079773179, 0.0 },
120 { 0.91082759030195981, -0.59999999999999998, 0.87266462599716477, 0.0 },
121 { 1.1112333229323361, -0.59999999999999998, 1.0471975511965976, 0.0 },
122 { 1.3191461190365270, -0.59999999999999998, 1.2217304763960306, 0.0 },
123 { 1.5332022105084779, -0.59999999999999998, 1.3962634015954636, 0.0 },
124 { 1.7507538029157523, -0.59999999999999998, 1.5707963267948966, 0.0 },
126 const double toler004
= 2.5000000000000020e-13;
128 // Test data for k=-0.50000000000000000.
129 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 7
130 // max(|f - f_Boost| / |f_Boost|): 3.4551389361831220e-16
131 // mean(f - f_Boost): -5.8286708792820721e-17
132 // variance(f - f_Boost): 4.1942474344433133e-34
133 // stddev(f - f_Boost): 2.0479861900030756e-17
134 const testcase_ellint_1
<double>
137 { 0.0000000000000000, -0.50000000000000000, 0.0000000000000000, 0.0 },
138 { 0.17475385514035785, -0.50000000000000000, 0.17453292519943295, 0.0 },
139 { 0.35081868470101579, -0.50000000000000000, 0.34906585039886590, 0.0 },
140 { 0.52942862705190574, -0.50000000000000000, 0.52359877559829882, 0.0 },
141 { 0.71164727562630326, -0.50000000000000000, 0.69813170079773179, 0.0 },
142 { 0.89824523594227768, -0.50000000000000000, 0.87266462599716477, 0.0 },
143 { 1.0895506700518853, -0.50000000000000000, 1.0471975511965976, 0.0 },
144 { 1.2853005857432933, -0.50000000000000000, 1.2217304763960306, 0.0 },
145 { 1.4845545520549488, -0.50000000000000000, 1.3962634015954636, 0.0 },
146 { 1.6857503548125961, -0.50000000000000000, 1.5707963267948966, 0.0 },
148 const double toler005
= 2.5000000000000020e-13;
150 // Test data for k=-0.39999999999999991.
151 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 9
152 // max(|f - f_Boost| / |f_Boost|): 3.1423314994346225e-16
153 // mean(f - f_Boost): -6.9388939039072284e-17
154 // variance(f - f_Boost): 1.7333369499485123e-32
155 // stddev(f - f_Boost): 1.3165625507162629e-16
156 const testcase_ellint_1
<double>
159 { 0.0000000000000000, -0.39999999999999991, 0.0000000000000000, 0.0 },
160 { 0.17467414669441528, -0.39999999999999991, 0.17453292519943295, 0.0 },
161 { 0.35018222772483443, -0.39999999999999991, 0.34906585039886590, 0.0 },
162 { 0.52729015917508748, -0.39999999999999991, 0.52359877559829882, 0.0 },
163 { 0.70662374407341244, -0.39999999999999991, 0.69813170079773179, 0.0 },
164 { 0.88859210497602159, -0.39999999999999991, 0.87266462599716477, 0.0 },
165 { 1.0733136290471381, -0.39999999999999991, 1.0471975511965976, 0.0 },
166 { 1.2605612170157066, -0.39999999999999991, 1.2217304763960306, 0.0 },
167 { 1.4497513956433439, -0.39999999999999991, 1.3962634015954636, 0.0 },
168 { 1.6399998658645112, -0.39999999999999991, 1.5707963267948966, 0.0 },
170 const double toler006
= 2.5000000000000020e-13;
172 // Test data for k=-0.29999999999999993.
173 // max(|f - f_Boost|): 6.6613381477509392e-16 at index 9
174 // max(|f - f_Boost| / |f_Boost|): 4.2241249691539529e-16
175 // mean(f - f_Boost): -8.3266726846886741e-17
176 // variance(f - f_Boost): 4.1942474344433135e-32
177 // stddev(f - f_Boost): 2.0479861900030756e-16
178 const testcase_ellint_1
<double>
181 { 0.0000000000000000, -0.29999999999999993, 0.0000000000000000, 0.0 },
182 { 0.17461228653000099, -0.29999999999999993, 0.17453292519943295, 0.0 },
183 { 0.34969146102798421, -0.29999999999999993, 0.34906585039886590, 0.0 },
184 { 0.52565822873726309, -0.29999999999999993, 0.52359877559829882, 0.0 },
185 { 0.70284226512408543, -0.29999999999999993, 0.69813170079773179, 0.0 },
186 { 0.88144139195111171, -0.29999999999999993, 0.87266462599716477, 0.0 },
187 { 1.0614897067260520, -0.29999999999999993, 1.0471975511965976, 0.0 },
188 { 1.2428416824174220, -0.29999999999999993, 1.2217304763960306, 0.0 },
189 { 1.4251795877015929, -0.29999999999999993, 1.3962634015954636, 0.0 },
190 { 1.6080486199305126, -0.29999999999999993, 1.5707963267948966, 0.0 },
192 const double toler007
= 2.5000000000000020e-13;
194 // Test data for k=-0.19999999999999996.
195 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 6
196 // max(|f - f_Boost| / |f_Boost|): 4.2156475739151676e-16
197 // mean(f - f_Boost): -9.7144514654701197e-17
198 // variance(f - f_Boost): 1.1650687317898094e-33
199 // stddev(f - f_Boost): 3.4133103166717924e-17
200 const testcase_ellint_1
<double>
203 { 0.0000000000000000, -0.19999999999999996, 0.0000000000000000, 0.0 },
204 { 0.17456817290292806, -0.19999999999999996, 0.17453292519943295, 0.0 },
205 { 0.34934315932086796, -0.19999999999999996, 0.34906585039886590, 0.0 },
206 { 0.52450880529443988, -0.19999999999999996, 0.52359877559829882, 0.0 },
207 { 0.70020491009844887, -0.19999999999999996, 0.69813170079773179, 0.0 },
208 { 0.87651006649967977, -0.19999999999999996, 0.87266462599716477, 0.0 },
209 { 1.0534305870298994, -0.19999999999999996, 1.0471975511965976, 0.0 },
210 { 1.2308975521670789, -0.19999999999999996, 1.2217304763960306, 0.0 },
211 { 1.4087733584990738, -0.19999999999999996, 1.3962634015954636, 0.0 },
212 { 1.5868678474541662, -0.19999999999999996, 1.5707963267948966, 0.0 },
214 const double toler008
= 2.5000000000000020e-13;
216 // Test data for k=-0.099999999999999978.
217 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 8
218 // max(|f - f_Boost| / |f_Boost|): 3.1735566504509645e-16
219 // mean(f - f_Boost): -3.6082248300317589e-17
220 // variance(f - f_Boost): 8.2258607846939269e-33
221 // stddev(f - f_Boost): 9.0696531271564778e-17
222 const testcase_ellint_1
<double>
225 { 0.0000000000000000, -0.099999999999999978, 0.0000000000000000, 0.0 },
226 { 0.17454173353063662, -0.099999999999999978, 0.17453292519943295, 0.0 },
227 { 0.34913506721468096, -0.099999999999999978, 0.34906585039886590, 0.0 },
228 { 0.52382550016538953, -0.099999999999999978, 0.52359877559829882, 0.0 },
229 { 0.69864700854177020, -0.099999999999999978, 0.69813170079773179, 0.0 },
230 { 0.87361792586964859, -0.099999999999999978, 0.87266462599716477, 0.0 },
231 { 1.0487386319621685, -0.099999999999999978, 1.0471975511965976, 0.0 },
232 { 1.2239913752078759, -0.099999999999999978, 1.2217304763960306, 0.0 },
233 { 1.3993423113684051, -0.099999999999999978, 1.3962634015954636, 0.0 },
234 { 1.5747455615173558, -0.099999999999999978, 1.5707963267948966, 0.0 },
236 const double toler009
= 2.5000000000000020e-13;
238 // Test data for k=0.0000000000000000.
239 // max(|f - f_Boost|): 2.2204460492503131e-16 at index 7
240 // max(|f - f_Boost| / |f_Boost|): 2.1203697876423447e-16
241 // mean(f - f_Boost): -1.9428902930940238e-17
242 // variance(f - f_Boost): 4.6602749271592373e-35
243 // stddev(f - f_Boost): 6.8266206333435850e-18
244 const testcase_ellint_1
<double>
247 { 0.0000000000000000, 0.0000000000000000, 0.0000000000000000, 0.0 },
248 { 0.17453292519943295, 0.0000000000000000, 0.17453292519943295, 0.0 },
249 { 0.34906585039886590, 0.0000000000000000, 0.34906585039886590, 0.0 },
250 { 0.52359877559829882, 0.0000000000000000, 0.52359877559829882, 0.0 },
251 { 0.69813170079773179, 0.0000000000000000, 0.69813170079773179, 0.0 },
252 { 0.87266462599716477, 0.0000000000000000, 0.87266462599716477, 0.0 },
253 { 1.0471975511965976, 0.0000000000000000, 1.0471975511965976, 0.0 },
254 { 1.2217304763960306, 0.0000000000000000, 1.2217304763960306, 0.0 },
255 { 1.3962634015954636, 0.0000000000000000, 1.3962634015954636, 0.0 },
256 { 1.5707963267948966, 0.0000000000000000, 1.5707963267948966, 0.0 },
258 const double toler010
= 2.5000000000000020e-13;
260 // Test data for k=0.10000000000000009.
261 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 8
262 // max(|f - f_Boost| / |f_Boost|): 3.1735566504509645e-16
263 // mean(f - f_Boost): -5.8286708792820721e-17
264 // variance(f - f_Boost): 4.1942474344433133e-34
265 // stddev(f - f_Boost): 2.0479861900030756e-17
266 const testcase_ellint_1
<double>
269 { 0.0000000000000000, 0.10000000000000009, 0.0000000000000000, 0.0 },
270 { 0.17454173353063662, 0.10000000000000009, 0.17453292519943295, 0.0 },
271 { 0.34913506721468096, 0.10000000000000009, 0.34906585039886590, 0.0 },
272 { 0.52382550016538953, 0.10000000000000009, 0.52359877559829882, 0.0 },
273 { 0.69864700854177020, 0.10000000000000009, 0.69813170079773179, 0.0 },
274 { 0.87361792586964859, 0.10000000000000009, 0.87266462599716477, 0.0 },
275 { 1.0487386319621685, 0.10000000000000009, 1.0471975511965976, 0.0 },
276 { 1.2239913752078759, 0.10000000000000009, 1.2217304763960306, 0.0 },
277 { 1.3993423113684051, 0.10000000000000009, 1.3962634015954636, 0.0 },
278 { 1.5747455615173560, 0.10000000000000009, 1.5707963267948966, 0.0 },
280 const double toler011
= 2.5000000000000020e-13;
282 // Test data for k=0.20000000000000018.
283 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 6
284 // max(|f - f_Boost| / |f_Boost|): 4.2156475739151676e-16
285 // mean(f - f_Boost): -9.7144514654701197e-17
286 // variance(f - f_Boost): 1.1650687317898094e-33
287 // stddev(f - f_Boost): 3.4133103166717924e-17
288 const testcase_ellint_1
<double>
291 { 0.0000000000000000, 0.20000000000000018, 0.0000000000000000, 0.0 },
292 { 0.17456817290292806, 0.20000000000000018, 0.17453292519943295, 0.0 },
293 { 0.34934315932086796, 0.20000000000000018, 0.34906585039886590, 0.0 },
294 { 0.52450880529443988, 0.20000000000000018, 0.52359877559829882, 0.0 },
295 { 0.70020491009844887, 0.20000000000000018, 0.69813170079773179, 0.0 },
296 { 0.87651006649967977, 0.20000000000000018, 0.87266462599716477, 0.0 },
297 { 1.0534305870298994, 0.20000000000000018, 1.0471975511965976, 0.0 },
298 { 1.2308975521670789, 0.20000000000000018, 1.2217304763960306, 0.0 },
299 { 1.4087733584990738, 0.20000000000000018, 1.3962634015954636, 0.0 },
300 { 1.5868678474541662, 0.20000000000000018, 1.5707963267948966, 0.0 },
302 const double toler012
= 2.5000000000000020e-13;
304 // Test data for k=0.30000000000000004.
305 // max(|f - f_Boost|): 8.8817841970012523e-16 at index 9
306 // max(|f - f_Boost| / |f_Boost|): 5.5233306300061082e-16
307 // mean(f - f_Boost): -1.0547118733938987e-16
308 // variance(f - f_Boost): 7.5633408838247182e-32
309 // stddev(f - f_Boost): 2.7501528837184157e-16
310 const testcase_ellint_1
<double>
313 { 0.0000000000000000, 0.30000000000000004, 0.0000000000000000, 0.0 },
314 { 0.17461228653000099, 0.30000000000000004, 0.17453292519943295, 0.0 },
315 { 0.34969146102798421, 0.30000000000000004, 0.34906585039886590, 0.0 },
316 { 0.52565822873726309, 0.30000000000000004, 0.52359877559829882, 0.0 },
317 { 0.70284226512408543, 0.30000000000000004, 0.69813170079773179, 0.0 },
318 { 0.88144139195111171, 0.30000000000000004, 0.87266462599716477, 0.0 },
319 { 1.0614897067260520, 0.30000000000000004, 1.0471975511965976, 0.0 },
320 { 1.2428416824174220, 0.30000000000000004, 1.2217304763960306, 0.0 },
321 { 1.4251795877015929, 0.30000000000000004, 1.3962634015954636, 0.0 },
322 { 1.6080486199305128, 0.30000000000000004, 1.5707963267948966, 0.0 },
324 const double toler013
= 2.5000000000000020e-13;
326 // Test data for k=0.40000000000000013.
327 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 9
328 // max(|f - f_Boost| / |f_Boost|): 3.1423314994346225e-16
329 // mean(f - f_Boost): -4.7184478546569152e-17
330 // variance(f - f_Boost): 1.9448563670505968e-32
331 // stddev(f - f_Boost): 1.3945810722401896e-16
332 const testcase_ellint_1
<double>
335 { 0.0000000000000000, 0.40000000000000013, 0.0000000000000000, 0.0 },
336 { 0.17467414669441528, 0.40000000000000013, 0.17453292519943295, 0.0 },
337 { 0.35018222772483443, 0.40000000000000013, 0.34906585039886590, 0.0 },
338 { 0.52729015917508748, 0.40000000000000013, 0.52359877559829882, 0.0 },
339 { 0.70662374407341244, 0.40000000000000013, 0.69813170079773179, 0.0 },
340 { 0.88859210497602159, 0.40000000000000013, 0.87266462599716477, 0.0 },
341 { 1.0733136290471381, 0.40000000000000013, 1.0471975511965976, 0.0 },
342 { 1.2605612170157066, 0.40000000000000013, 1.2217304763960306, 0.0 },
343 { 1.4497513956433439, 0.40000000000000013, 1.3962634015954636, 0.0 },
344 { 1.6399998658645112, 0.40000000000000013, 1.5707963267948966, 0.0 },
346 const double toler014
= 2.5000000000000020e-13;
348 // Test data for k=0.50000000000000000.
349 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 7
350 // max(|f - f_Boost| / |f_Boost|): 3.4551389361831220e-16
351 // mean(f - f_Boost): -5.8286708792820721e-17
352 // variance(f - f_Boost): 4.1942474344433133e-34
353 // stddev(f - f_Boost): 2.0479861900030756e-17
354 const testcase_ellint_1
<double>
357 { 0.0000000000000000, 0.50000000000000000, 0.0000000000000000, 0.0 },
358 { 0.17475385514035785, 0.50000000000000000, 0.17453292519943295, 0.0 },
359 { 0.35081868470101579, 0.50000000000000000, 0.34906585039886590, 0.0 },
360 { 0.52942862705190574, 0.50000000000000000, 0.52359877559829882, 0.0 },
361 { 0.71164727562630326, 0.50000000000000000, 0.69813170079773179, 0.0 },
362 { 0.89824523594227768, 0.50000000000000000, 0.87266462599716477, 0.0 },
363 { 1.0895506700518853, 0.50000000000000000, 1.0471975511965976, 0.0 },
364 { 1.2853005857432933, 0.50000000000000000, 1.2217304763960306, 0.0 },
365 { 1.4845545520549488, 0.50000000000000000, 1.3962634015954636, 0.0 },
366 { 1.6857503548125961, 0.50000000000000000, 1.5707963267948966, 0.0 },
368 const double toler015
= 2.5000000000000020e-13;
370 // Test data for k=0.60000000000000009.
371 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 7
372 // max(|f - f_Boost| / |f_Boost|): 3.3664899092028927e-16
373 // mean(f - f_Boost): 7.4940054162198071e-17
374 // variance(f - f_Boost): 2.6715739327327140e-33
375 // stddev(f - f_Boost): 5.1687270509601433e-17
376 const testcase_ellint_1
<double>
379 { 0.0000000000000000, 0.60000000000000009, 0.0000000000000000, 0.0 },
380 { 0.17485154362988359, 0.60000000000000009, 0.17453292519943295, 0.0 },
381 { 0.35160509865544320, 0.60000000000000009, 0.34906585039886590, 0.0 },
382 { 0.53210652578446138, 0.60000000000000009, 0.52359877559829882, 0.0 },
383 { 0.71805304664485659, 0.60000000000000009, 0.69813170079773179, 0.0 },
384 { 0.91082759030195981, 0.60000000000000009, 0.87266462599716477, 0.0 },
385 { 1.1112333229323361, 0.60000000000000009, 1.0471975511965976, 0.0 },
386 { 1.3191461190365270, 0.60000000000000009, 1.2217304763960306, 0.0 },
387 { 1.5332022105084779, 0.60000000000000009, 1.3962634015954636, 0.0 },
388 { 1.7507538029157526, 0.60000000000000009, 1.5707963267948966, 0.0 },
390 const double toler016
= 2.5000000000000020e-13;
392 // Test data for k=0.70000000000000018.
393 // max(|f - f_Boost|): 6.6613381477509392e-16 at index 8
394 // max(|f - f_Boost| / |f_Boost|): 4.1569224977685422e-16
395 // mean(f - f_Boost): -1.1102230246251566e-17
396 // variance(f - f_Boost): 2.3145398087213714e-32
397 // stddev(f - f_Boost): 1.5213611697165703e-16
398 const testcase_ellint_1
<double>
401 { 0.0000000000000000, 0.70000000000000018, 0.0000000000000000, 0.0 },
402 { 0.17496737466916723, 0.70000000000000018, 0.17453292519943295, 0.0 },
403 { 0.35254687535677931, 0.70000000000000018, 0.34906585039886590, 0.0 },
404 { 0.53536740275997130, 0.70000000000000018, 0.52359877559829882, 0.0 },
405 { 0.72603797651684454, 0.70000000000000018, 0.69813170079773179, 0.0 },
406 { 0.92698296348313447, 0.70000000000000018, 0.87266462599716477, 0.0 },
407 { 1.1400447527693318, 0.70000000000000018, 1.0471975511965976, 0.0 },
408 { 1.3657668117194073, 0.70000000000000018, 1.2217304763960306, 0.0 },
409 { 1.6024686895959164, 0.70000000000000018, 1.3962634015954636, 0.0 },
410 { 1.8456939983747236, 0.70000000000000018, 1.5707963267948966, 0.0 },
412 const double toler017
= 2.5000000000000020e-13;
414 // Test data for k=0.80000000000000004.
415 // max(|f - f_Boost|): 8.8817841970012523e-16 at index 8
416 // max(|f - f_Boost| / |f_Boost|): 5.2032670495747184e-16
417 // mean(f - f_Boost): 1.9428902930940239e-16
418 // variance(f - f_Boost): 2.7486111305082033e-32
419 // stddev(f - f_Boost): 1.6578935823834422e-16
420 const testcase_ellint_1
<double>
423 { 0.0000000000000000, 0.80000000000000004, 0.0000000000000000, 0.0 },
424 { 0.17510154241338899, 0.80000000000000004, 0.17453292519943295, 0.0 },
425 { 0.35365068839779396, 0.80000000000000004, 0.34906585039886590, 0.0 },
426 { 0.53926804409084550, 0.80000000000000004, 0.52359877559829882, 0.0 },
427 { 0.73587926028070372, 0.80000000000000004, 0.69813170079773179, 0.0 },
428 { 0.94770942970071170, 0.80000000000000004, 0.87266462599716477, 0.0 },
429 { 1.1789022995388236, 0.80000000000000004, 1.0471975511965976, 0.0 },
430 { 1.4323027881876012, 0.80000000000000004, 1.2217304763960306, 0.0 },
431 { 1.7069629739121677, 0.80000000000000004, 1.3962634015954636, 0.0 },
432 { 1.9953027776647294, 0.80000000000000004, 1.5707963267948966, 0.0 },
434 const double toler018
= 2.5000000000000020e-13;
436 // Test data for k=0.90000000000000013.
437 // max(|f - f_Boost|): 8.8817841970012523e-16 at index 9
438 // max(|f - f_Boost| / |f_Boost|): 4.3381508715713360e-16
439 // mean(f - f_Boost): 1.4710455076283324e-16
440 // variance(f - f_Boost): 6.7801293731072419e-32
441 // stddev(f - f_Boost): 2.6038681558610532e-16
442 const testcase_ellint_1
<double>
445 { 0.0000000000000000, 0.90000000000000013, 0.0000000000000000, 0.0 },
446 { 0.17525427376115027, 0.90000000000000013, 0.17453292519943295, 0.0 },
447 { 0.35492464591297446, 0.90000000000000013, 0.34906585039886590, 0.0 },
448 { 0.54388221416157123, 0.90000000000000013, 0.52359877559829882, 0.0 },
449 { 0.74797400423532512, 0.90000000000000013, 0.69813170079773179, 0.0 },
450 { 0.97463898451966446, 0.90000000000000013, 0.87266462599716477, 0.0 },
451 { 1.2334463254523440, 0.90000000000000013, 1.0471975511965976, 0.0 },
452 { 1.5355247765594915, 0.90000000000000013, 1.2217304763960306, 0.0 },
453 { 1.8882928567775128, 0.90000000000000013, 1.3962634015954636, 0.0 },
454 { 2.2805491384227707, 0.90000000000000013, 1.5707963267948966, 0.0 },
456 const double toler019
= 2.5000000000000020e-13;
458 template<typename Ret
, unsigned int Num
>
460 test(const testcase_ellint_1
<Ret
> (&data
)[Num
], Ret toler
)
462 bool test
__attribute__((unused
)) = true;
463 const Ret eps
= std::numeric_limits
<Ret
>::epsilon();
464 Ret max_abs_diff
= -Ret(1);
465 Ret max_abs_frac
= -Ret(1);
466 unsigned int num_datum
= Num
;
467 for (unsigned int i
= 0; i
< num_datum
; ++i
)
469 const Ret f
= std::tr1::ellint_1(data
[i
].k
, data
[i
].phi
);
470 const Ret f0
= data
[i
].f0
;
471 const Ret diff
= f
- f0
;
472 if (std::abs(diff
) > max_abs_diff
)
473 max_abs_diff
= std::abs(diff
);
474 if (std::abs(f0
) > Ret(10) * eps
475 && std::abs(f
) > Ret(10) * eps
)
477 const Ret frac
= diff
/ f0
;
478 if (std::abs(frac
) > max_abs_frac
)
479 max_abs_frac
= std::abs(frac
);
482 VERIFY(max_abs_frac
< toler
);
488 test(data001
, toler001
);
489 test(data002
, toler002
);
490 test(data003
, toler003
);
491 test(data004
, toler004
);
492 test(data005
, toler005
);
493 test(data006
, toler006
);
494 test(data007
, toler007
);
495 test(data008
, toler008
);
496 test(data009
, toler009
);
497 test(data010
, toler010
);
498 test(data011
, toler011
);
499 test(data012
, toler012
);
500 test(data013
, toler013
);
501 test(data014
, toler014
);
502 test(data015
, toler015
);
503 test(data016
, toler016
);
504 test(data017
, toler017
);
505 test(data018
, toler018
);
506 test(data019
, toler019
);