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[thirdparty/gcc.git] / libstdc++-v3 / testsuite / special_functions / 20_sph_legendre / check_value.cc
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196c9e7a 1// { dg-do run { target c++11 } }
2be75957
ESR		 2// { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" }
3//
cbe34bb5 4// Copyright (C) 2016-2017 Free Software Foundation, Inc.
2be75957
ESR		 5//
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)
10// any later version.
11//
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.
16//
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/>.
20
21// sph_legendre
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/
24#include <limits>
25#include <cmath>
26#if defined(__TEST_DEBUG)
27# include <iostream>
28# define VERIFY(A) \
29 if (!(A)) \
30 { \
31 std::cout << "line " << __LINE__ \
32 << " max_abs_frac = " << max_abs_frac \
33 << std::endl; \
34 }
35#else
36# include <testsuite_hooks.h>
37#endif
38#include <specfun_testcase.h>
39
40
41// Test data for l=0, m=0.
42// max(|f - f_GSL|): 0.0000000000000000
43// max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
44const testcase_sph_legendre<double>
45data001[21] =
46{
47 { 0.28209479177387814, 0, 0,
48 0.0000000000000000 },
49 { 0.28209479177387814, 0, 0,
50 0.15707963267948966 },
51 { 0.28209479177387814, 0, 0,
52 0.31415926535897931 },
53 { 0.28209479177387814, 0, 0,
54 0.47123889803846897 },
55 { 0.28209479177387814, 0, 0,
56 0.62831853071795862 },
57 { 0.28209479177387814, 0, 0,
58 0.78539816339744828 },
59 { 0.28209479177387814, 0, 0,
60 0.94247779607693793 },
61 { 0.28209479177387814, 0, 0,
62 1.0995574287564276 },
63 { 0.28209479177387814, 0, 0,
64 1.2566370614359172 },
65 { 0.28209479177387814, 0, 0,
66 1.4137166941154069 },
67 { 0.28209479177387814, 0, 0,
68 1.5707963267948966 },
69 { 0.28209479177387814, 0, 0,
70 1.7278759594743860 },
71 { 0.28209479177387814, 0, 0,
72 1.8849555921538759 },
73 { 0.28209479177387814, 0, 0,
74 2.0420352248333655 },
75 { 0.28209479177387814, 0, 0,
76 2.1991148575128552 },
77 { 0.28209479177387814, 0, 0,
78 2.3561944901923448 },
79 { 0.28209479177387814, 0, 0,
80 2.5132741228718345 },
81 { 0.28209479177387814, 0, 0,
82 2.6703537555513241 },
83 { 0.28209479177387814, 0, 0,
84 2.8274333882308138 },
85 { 0.28209479177387814, 0, 0,
86 2.9845130209103035 },
87 { 0.28209479177387814, 0, 0,
88 3.1415926535897931 },
89};
90const double toler001 = 2.5000000000000020e-13;
91
92// Test data for l=1, m=0.
93// max(|f - f_GSL|): 0.0000000000000000
94// max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
95const testcase_sph_legendre<double>
96data002[21] =
97{
98 { 0.48860251190291992, 1, 0,
99 0.0000000000000000 },
100 { 0.48258700419201100, 1, 0,
101 0.15707963267948966 },
102 { 0.46468860282345231, 1, 0,
103 0.31415926535897931 },
104 { 0.43534802584032634, 1, 0,
105 0.47123889803846897 },
106 { 0.39528773562374975, 1, 0,
107 0.62831853071795862 },
108 { 0.34549414947133550, 1, 0,
109 0.78539816339744828 },
110 { 0.28719335072959390, 1, 0,
111 0.94247779607693793 },
112 { 0.22182089855280449, 1, 0,
113 1.0995574287564276 },
114 { 0.15098647967228981, 1, 0,
115 1.2566370614359172 },
116 { 0.076434272566846345, 1, 0,
117 1.4137166941154069 },
118 { 2.9918275112863369e-17, 1, 0,
119 1.5707963267948966 },
120 { -0.076434272566846179, 1, 0,
121 1.7278759594743860 },
122 { -0.15098647967228976, 1, 0,
123 1.8849555921538759 },
124 { -0.22182089855280443, 1, 0,
125 2.0420352248333655 },
126 { -0.28719335072959384, 1, 0,
127 2.1991148575128552 },
128 { -0.34549414947133544, 1, 0,
129 2.3561944901923448 },
130 { -0.39528773562374969, 1, 0,
131 2.5132741228718345 },
132 { -0.43534802584032628, 1, 0,
133 2.6703537555513241 },
134 { -0.46468860282345231, 1, 0,
135 2.8274333882308138 },
136 { -0.48258700419201095, 1, 0,
137 2.9845130209103035 },
138 { -0.48860251190291992, 1, 0,
139 3.1415926535897931 },
140};
141const double toler002 = 2.5000000000000020e-13;
142
143// Test data for l=1, m=1.
144// max(|f - f_GSL|): 2.2204460492503131e-16
145// max(|f - f_GSL| / |f_GSL|): 7.7031500691196945e-16
146const testcase_sph_legendre<double>
147data003[21] =
148{
149 { 0.0000000000000000, 1, 1,
150 0.0000000000000000 },
151 { -0.054047192447077917, 1, 1,
152 0.15707963267948966 },
153 { -0.10676356364376104, 1, 1,
154 0.31415926535897931 },
155 { -0.15685106157558129, 1, 1,
156 0.47123889803846897 },
157 { -0.20307636581258243, 1, 1,
158 0.62831853071795862 },
159 { -0.24430125595146007, 1, 1,
160 0.78539816339744828 },
161 { -0.27951063837942880, 1, 1,
162 0.94247779607693793 },
163 { -0.30783754124787122, 1, 1,
164 1.0995574287564276 },
165 { -0.32858446219656556, 1, 1,
166 1.2566370614359172 },
167 { -0.34124054317667202, 1, 1,
168 1.4137166941154069 },
169 { -0.34549414947133567, 1, 1,
170 1.5707963267948966 },
171 { -0.34124054317667202, 1, 1,
172 1.7278759594743860 },
173 { -0.32858446219656556, 1, 1,
174 1.8849555921538759 },
175 { -0.30783754124787127, 1, 1,
176 2.0420352248333655 },
177 { -0.27951063837942880, 1, 1,
178 2.1991148575128552 },
179 { -0.24430125595146013, 1, 1,
180 2.3561944901923448 },
181 { -0.20307636581258248, 1, 1,
182 2.5132741228718345 },
183 { -0.15685106157558140, 1, 1,
184 2.6703537555513241 },
185 { -0.10676356364376104, 1, 1,
186 2.8274333882308138 },
187 { -0.054047192447078167, 1, 1,
188 2.9845130209103035 },
189 { 0.0000000000000000, 1, 1,
190 3.1415926535897931 },
191};
192const double toler003 = 2.5000000000000020e-13;
193
194// Test data for l=2, m=0.
195// max(|f - f_GSL|): 5.5511151231257827e-17
196// max(|f - f_GSL| / |f_GSL|): 3.0159263334953002e-15
197const testcase_sph_legendre<double>
198data004[21] =
199{
200 { 0.63078313050504009, 2, 0,
201 0.0000000000000000 },
202 { 0.60762858760316607, 2, 0,
203 0.15707963267948966 },
204 { 0.54043148688396569, 2, 0,
205 0.31415926535897931 },
206 { 0.43576954875556589, 2, 0,
207 0.47123889803846897 },
208 { 0.30388781294457579, 2, 0,
209 0.62831853071795862 },
210 { 0.15769578262626011, 2, 0,
211 0.78539816339744828 },
212 { 0.011503752307944235, 2, 0,
213 0.94247779607693793 },
214 { -0.12037798350304570, 2, 0,
215 1.0995574287564276 },
216 { -0.22503992163144576, 2, 0,
217 1.2566370614359172 },
218 { -0.29223702235064597, 2, 0,
219 1.4137166941154069 },
220 { -0.31539156525252005, 2, 0,
221 1.5707963267948966 },
222 { -0.29223702235064608, 2, 0,
223 1.7278759594743860 },
224 { -0.22503992163144584, 2, 0,
225 1.8849555921538759 },
226 { -0.12037798350304584, 2, 0,
227 2.0420352248333655 },
228 { 0.011503752307944164, 2, 0,
229 2.1991148575128552 },
230 { 0.15769578262625994, 2, 0,
231 2.3561944901923448 },
232 { 0.30388781294457567, 2, 0,
233 2.5132741228718345 },
234 { 0.43576954875556562, 2, 0,
235 2.6703537555513241 },
236 { 0.54043148688396569, 2, 0,
237 2.8274333882308138 },
238 { 0.60762858760316585, 2, 0,
239 2.9845130209103035 },
240 { 0.63078313050504009, 2, 0,
241 3.1415926535897931 },
242};
243const double toler004 = 2.5000000000000020e-13;
244
245// Test data for l=2, m=1.
246// max(|f - f_GSL|): 2.2204460492503131e-16
247// max(|f - f_GSL| / |f_GSL|): 8.1384221730905279e-16
248const testcase_sph_legendre<double>
249data005[21] =
250{
251 { 0.0000000000000000, 2, 1,
252 0.0000000000000000 },
253 { -0.11936529291378727, 2, 1,
254 0.15707963267948966 },
255 { -0.22704627929027449, 2, 1,
256 0.31415926535897931 },
257 { -0.31250239392538215, 2, 1,
258 0.47123889803846897 },
259 { -0.36736859691086526, 2, 1,
260 0.62831853071795862 },
261 { -0.38627420202318979, 2, 1,
262 0.78539816339744828 },
263 { -0.36736859691086526, 2, 1,
264 0.94247779607693793 },
265 { -0.31250239392538226, 2, 1,
266 1.0995574287564276 },
267 { -0.22704627929027438, 2, 1,
268 1.2566370614359172 },
269 { -0.11936529291378740, 2, 1,
270 1.4137166941154069 },
271 { -4.7304946510089748e-17, 2, 1,
272 1.5707963267948966 },
273 { 0.11936529291378714, 2, 1,
274 1.7278759594743860 },
275 { 0.22704627929027429, 2, 1,
276 1.8849555921538759 },
277 { 0.31250239392538220, 2, 1,
278 2.0420352248333655 },
279 { 0.36736859691086521, 2, 1,
280 2.1991148575128552 },
281 { 0.38627420202318979, 2, 1,
282 2.3561944901923448 },
283 { 0.36736859691086526, 2, 1,
284 2.5132741228718345 },
285 { 0.31250239392538232, 2, 1,
286 2.6703537555513241 },
287 { 0.22704627929027449, 2, 1,
288 2.8274333882308138 },
289 { 0.11936529291378781, 2, 1,
290 2.9845130209103035 },
291 { 0.0000000000000000, 2, 1,
292 3.1415926535897931 },
293};
294const double toler005 = 2.5000000000000020e-13;
295
296// Test data for l=2, m=2.
297// max(|f - f_GSL|): 1.6653345369377348e-16
298// max(|f - f_GSL| / |f_GSL|): 6.2393366429561032e-16
299const testcase_sph_legendre<double>
300data006[21] =
301{
302 { 0.0000000000000000, 2, 2,
303 0.0000000000000000 },
304 { 0.0094528025561622549, 2, 2,
305 0.15707963267948966 },
306 { 0.036885904048903795, 2, 2,
307 0.31415926535897931 },
308 { 0.079613961366457681, 2, 2,
309 0.47123889803846897 },
310 { 0.13345445455470123, 2, 2,
311 0.62831853071795862 },
312 { 0.19313710101159484, 2, 2,
313 0.78539816339744828 },
314 { 0.25281974746848851, 2, 2,
315 0.94247779607693793 },
316 { 0.30666024065673209, 2, 2,
317 1.0995574287564276 },
318 { 0.34938829797428600, 2, 2,
319 1.2566370614359172 },
320 { 0.37682139946702747, 2, 2,
321 1.4137166941154069 },
322 { 0.38627420202318979, 2, 2,
323 1.5707963267948966 },
324 { 0.37682139946702753, 2, 2,
325 1.7278759594743860 },
326 { 0.34938829797428606, 2, 2,
327 1.8849555921538759 },
328 { 0.30666024065673209, 2, 2,
329 2.0420352248333655 },
330 { 0.25281974746848856, 2, 2,
331 2.1991148575128552 },
332 { 0.19313710101159492, 2, 2,
333 2.3561944901923448 },
334 { 0.13345445455470126, 2, 2,
335 2.5132741228718345 },
336 { 0.079613961366457764, 2, 2,
337 2.6703537555513241 },
338 { 0.036885904048903795, 2, 2,
339 2.8274333882308138 },
340 { 0.0094528025561623433, 2, 2,
341 2.9845130209103035 },
342 { 0.0000000000000000, 2, 2,
343 3.1415926535897931 },
344};
345const double toler006 = 2.5000000000000020e-13;
346
347// Test data for l=5, m=0.
348// max(|f - f_GSL|): 1.0547118733938987e-15
349// max(|f - f_GSL| / |f_GSL|): 2.9385557676213648e-15
350const testcase_sph_legendre<double>
351data007[21] =
352{
353 { 0.93560257962738880, 5, 0,
354 0.0000000000000000 },
355 { 0.77014422942079963, 5, 0,
356 0.15707963267948966 },
357 { 0.35892185032365165, 5, 0,
358 0.31415926535897931 },
359 { -0.090214932090594294, 5, 0,
360 0.47123889803846897 },
361 { -0.36214460396518883, 5, 0,
362 0.62831853071795862 },
363 { -0.35145955579226906, 5, 0,
364 0.78539816339744828 },
365 { -0.11441703594725168, 5, 0,
366 0.94247779607693793 },
367 { 0.17248966720808107, 5, 0,
368 1.0995574287564276 },
369 { 0.32128384287200523, 5, 0,
370 1.2566370614359172 },
371 { 0.24377632246714948, 5, 0,
372 1.4137166941154069 },
373 { 1.0741712853887702e-16, 5, 0,
374 1.5707963267948966 },
375 { -0.24377632246714911, 5, 0,
376 1.7278759594743860 },
377 { -0.32128384287200534, 5, 0,
378 1.8849555921538759 },
379 { -0.17248966720808132, 5, 0,
380 2.0420352248333655 },
381 { 0.11441703594725151, 5, 0,
382 2.1991148575128552 },
383 { 0.35145955579226895, 5, 0,
384 2.3561944901923448 },
385 { 0.36214460396518905, 5, 0,
386 2.5132741228718345 },
387 { 0.090214932090594752, 5, 0,
388 2.6703537555513241 },
389 { -0.35892185032365165, 5, 0,
390 2.8274333882308138 },
391 { -0.77014422942079852, 5, 0,
392 2.9845130209103035 },
393 { -0.93560257962738880, 5, 0,
394 3.1415926535897931 },
395};
396const double toler007 = 2.5000000000000020e-13;
397
398// Test data for l=5, m=1.
399// max(|f - f_GSL|): 4.4408920985006262e-16
400// max(|f - f_GSL| / |f_GSL|): 1.4161260272615034e-15
401const testcase_sph_legendre<double>
402data008[21] =
403{
404 { 0.0000000000000000, 5, 1,
405 0.0000000000000000 },
406 { -0.36712373713318258, 5, 1,
407 0.15707963267948966 },
408 { -0.54610329010534753, 5, 1,
409 0.31415926535897931 },
410 { -0.45381991493631763, 5, 1,
411 0.47123889803846897 },
412 { -0.15679720635769961, 5, 1,
413 0.62831853071795862 },
414 { 0.16985499419838601, 5, 1,
415 0.78539816339744828 },
416 { 0.34468004499725180, 5, 1,
417 0.94247779607693793 },
418 { 0.28349471119605985, 5, 1,
419 1.0995574287564276 },
420 { 0.044286619339675815, 5, 1,
421 1.2566370614359172 },
422 { -0.21193784177193470, 5, 1,
423 1.4137166941154069 },
424 { -0.32028164857621527, 5, 1,
425 1.5707963267948966 },
426 { -0.21193784177193514, 5, 1,
427 1.7278759594743860 },
428 { 0.044286619339675592, 5, 1,
429 1.8849555921538759 },
430 { 0.28349471119605968, 5, 1,
431 2.0420352248333655 },
432 { 0.34468004499725174, 5, 1,
433 2.1991148575128552 },
434 { 0.16985499419838640, 5, 1,
435 2.3561944901923448 },
436 { -0.15679720635769906, 5, 1,
437 2.5132741228718345 },
438 { -0.45381991493631768, 5, 1,
439 2.6703537555513241 },
440 { -0.54610329010534753, 5, 1,
441 2.8274333882308138 },
442 { -0.36712373713318402, 5, 1,
443 2.9845130209103035 },
444 { 0.0000000000000000, 5, 1,
445 3.1415926535897931 },
446};
447const double toler008 = 2.5000000000000020e-13;
448
449// Test data for l=5, m=2.
450// max(|f - f_GSL|): 1.6653345369377348e-16
451// max(|f - f_GSL| / |f_GSL|): 3.0636916515712721e-15
452const testcase_sph_legendre<double>
453data009[21] =
454{
455 { 0.0000000000000000, 5, 2,
456 0.0000000000000000 },
457 { 0.078919441745546146, 5, 2,
458 0.15707963267948966 },
459 { 0.26373799140437987, 5, 2,
460 0.31415926535897931 },
461 { 0.43002359842080096, 5, 2,
462 0.47123889803846897 },
463 { 0.45642486439050983, 5, 2,
464 0.62831853071795862 },
465 { 0.29959604906083293, 5, 2,
466 0.78539816339744828 },
467 { 0.023781239849532215, 5, 2,
468 0.94247779607693793 },
469 { -0.23313989334673826, 5, 2,
470 1.0995574287564276 },
471 { -0.33799912776303714, 5, 2,
472 1.2566370614359172 },
473 { -0.23964508489529743, 5, 2,
474 1.4137166941154069 },
475 { -1.0377480524338170e-16, 5, 2,
476 1.5707963267948966 },
477 { 0.23964508489529704, 5, 2,
478 1.7278759594743860 },
479 { 0.33799912776303714, 5, 2,
480 1.8849555921538759 },
481 { 0.23313989334673843, 5, 2,
482 2.0420352248333655 },
483 { -0.023781239849531916, 5, 2,
484 2.1991148575128552 },
485 { -0.29959604906083276, 5, 2,
486 2.3561944901923448 },
487 { -0.45642486439050983, 5, 2,
488 2.5132741228718345 },
489 { -0.43002359842080118, 5, 2,
490 2.6703537555513241 },
491 { -0.26373799140437987, 5, 2,
492 2.8274333882308138 },
493 { -0.078919441745546867, 5, 2,
494 2.9845130209103035 },
495 { 0.0000000000000000, 5, 2,
496 3.1415926535897931 },
497};
498const double toler009 = 2.5000000000000020e-13;
499
500// Test data for l=5, m=5.
501// max(|f - f_GSL|): 1.1102230246251565e-16
502// max(|f - f_GSL| / |f_GSL|): 4.2617219728402347e-16
503const testcase_sph_legendre<double>
504data010[21] =
505{
506 { 0.0000000000000000, 5, 5,
507 0.0000000000000000 },
508 { -4.3481439097909148e-05, 5, 5,
509 0.15707963267948966 },
510 { -0.0013078367086431812, 5, 5,
511 0.31415926535897931 },
512 { -0.0089510818191922761, 5, 5,
513 0.47123889803846897 },
514 { -0.032563803777573896, 5, 5,
515 0.62831853071795862 },
516 { -0.082047757105021241, 5, 5,
517 0.78539816339744828 },
518 { -0.16085328164143814, 5, 5,
519 0.94247779607693793 },
520 { -0.26064303436645381, 5, 5,
521 1.0995574287564276 },
522 { -0.36113811790820571, 5, 5,
523 1.2566370614359172 },
524 { -0.43625592459446139, 5, 5,
525 1.4137166941154069 },
526 { -0.46413220344085809, 5, 5,
527 1.5707963267948966 },
528 { -0.43625592459446155, 5, 5,
529 1.7278759594743860 },
530 { -0.36113811790820577, 5, 5,
531 1.8849555921538759 },
532 { -0.26064303436645386, 5, 5,
533 2.0420352248333655 },
534 { -0.16085328164143822, 5, 5,
535 2.1991148575128552 },
536 { -0.082047757105021310, 5, 5,
537 2.3561944901923448 },
538 { -0.032563803777573910, 5, 5,
539 2.5132741228718345 },
540 { -0.0089510818191923004, 5, 5,
541 2.6703537555513241 },
542 { -0.0013078367086431812, 5, 5,
543 2.8274333882308138 },
544 { -4.3481439097910151e-05, 5, 5,
545 2.9845130209103035 },
546 { 0.0000000000000000, 5, 5,
547 3.1415926535897931 },
548};
549const double toler010 = 2.5000000000000020e-13;
550
551// Test data for l=10, m=0.
552// max(|f - f_GSL|): 9.9920072216264089e-16
553// max(|f - f_GSL| / |f_GSL|): 2.2266594990531305e-15
554const testcase_sph_legendre<double>
555data011[21] =
556{
557 { 1.2927207364566027, 10, 0,
558 0.0000000000000000 },
559 { 0.55288895150522555, 10, 0,
560 0.15707963267948966 },
561 { -0.44874428379711545, 10, 0,
562 0.31415926535897931 },
563 { -0.25532095827149687, 10, 0,
564 0.47123889803846897 },
565 { 0.36625249688013961, 10, 0,
566 0.62831853071795862 },
567 { 0.14880806329084206, 10, 0,
568 0.78539816339744828 },
569 { -0.33533356797848757, 10, 0,
570 0.94247779607693793 },
571 { -0.080639967662335665, 10, 0,
572 1.0995574287564276 },
573 { 0.32197986450174521, 10, 0,
574 1.2566370614359172 },
575 { 0.025713542103667848, 10, 0,
576 1.4137166941154069 },
577 { -0.31813049373736707, 10, 0,
578 1.5707963267948966 },
579 { 0.025713542103666699, 10, 0,
580 1.7278759594743860 },
581 { 0.32197986450174543, 10, 0,
582 1.8849555921538759 },
583 { -0.080639967662335096, 10, 0,
584 2.0420352248333655 },
585 { -0.33533356797848757, 10, 0,
586 2.1991148575128552 },
587 { 0.14880806329084156, 10, 0,
588 2.3561944901923448 },
589 { 0.36625249688013994, 10, 0,
590 2.5132741228718345 },
591 { -0.25532095827149576, 10, 0,
592 2.6703537555513241 },
593 { -0.44874428379711545, 10, 0,
594 2.8274333882308138 },
595 { 0.55288895150522011, 10, 0,
596 2.9845130209103035 },
597 { 1.2927207364566027, 10, 0,
598 3.1415926535897931 },
599};
600const double toler011 = 2.5000000000000020e-13;
601
602// Test data for l=10, m=1.
603// max(|f - f_GSL|): 1.4432899320127035e-15
604// max(|f - f_GSL| / |f_GSL|): 4.9708436073954521e-15
605const testcase_sph_legendre<double>
606data012[21] =
607{
608 { 0.0000000000000000, 10, 1,
609 0.0000000000000000 },
610 { -0.74373723919063894, 10, 1,
611 0.15707963267948966 },
612 { -0.29035110456209601, 10, 1,
613 0.31415926535897931 },
614 { 0.42219282075271530, 10, 1,
615 0.47123889803846897 },
616 { 0.17109256898931269, 10, 1,
617 0.62831853071795862 },
618 { -0.35583574648544281, 10, 1,
619 0.78539816339744828 },
620 { -0.10089212303543979, 10, 1,
621 0.94247779607693793 },
622 { 0.32997652649321085, 10, 1,
623 1.0995574287564276 },
624 { 0.047416376890032939, 10, 1,
625 1.2566370614359172 },
626 { -0.31999356750295660, 10, 1,
627 1.4137166941154069 },
628 { -2.0430664782290766e-16, 10, 1,
629 1.5707963267948966 },
630 { 0.31999356750295660, 10, 1,
631 1.7278759594743860 },
632 { -0.047416376890032544, 10, 1,
633 1.8849555921538759 },
634 { -0.32997652649321091, 10, 1,
635 2.0420352248333655 },
636 { 0.10089212303543935, 10, 1,
637 2.1991148575128552 },
638 { 0.35583574648544292, 10, 1,
639 2.3561944901923448 },
640 { -0.17109256898931161, 10, 1,
641 2.5132741228718345 },
642 { -0.42219282075271569, 10, 1,
643 2.6703537555513241 },
644 { 0.29035110456209601, 10, 1,
645 2.8274333882308138 },
646 { 0.74373723919064050, 10, 1,
647 2.9845130209103035 },
648 { 0.0000000000000000, 10, 1,
649 3.1415926535897931 },
650};
651const double toler012 = 2.5000000000000020e-13;
652
653// Test data for l=10, m=2.
654// max(|f - f_GSL|): 3.3306690738754696e-16
655// max(|f - f_GSL| / |f_GSL|): 3.3968188217108871e-15
656const testcase_sph_legendre<double>
657data013[21] =
658{
659 { 0.0000000000000000, 10, 2,
660 0.0000000000000000 },
661 { 0.34571695599980246, 10, 2,
662 0.15707963267948966 },
663 { 0.62485535978198059, 10, 2,
664 0.31415926535897931 },
665 { 0.098210039644716252, 10, 2,
666 0.47123889803846897 },
667 { -0.41494799233049684, 10, 2,
668 0.62831853071795862 },
669 { -0.081698973831472732, 10, 2,
670 0.78539816339744828 },
671 { 0.35253132222271277, 10, 2,
672 0.94247779607693793 },
673 { 0.049026298555980979, 10, 2,
674 1.0995574287564276 },
675 { -0.32791246874130792, 10, 2,
676 1.2566370614359172 },
677 { -0.016196782433946885, 10, 2,
678 1.4137166941154069 },
679 { 0.32106263400438328, 10, 2,
680 1.5707963267948966 },
681 { -0.016196782433945761, 10, 2,
682 1.7278759594743860 },
683 { -0.32791246874130803, 10, 2,
684 1.8849555921538759 },
685 { 0.049026298555980424, 10, 2,
686 2.0420352248333655 },
687 { 0.35253132222271266, 10, 2,
688 2.1991148575128552 },
689 { -0.081698973831472121, 10, 2,
690 2.3561944901923448 },
691 { -0.41494799233049695, 10, 2,
692 2.5132741228718345 },
693 { 0.098210039644715197, 10, 2,
694 2.6703537555513241 },
695 { 0.62485535978198059, 10, 2,
696 2.8274333882308138 },
697 { 0.34571695599980545, 10, 2,
698 2.9845130209103035 },
699 { 0.0000000000000000, 10, 2,
700 3.1415926535897931 },
701};
702const double toler013 = 2.5000000000000020e-13;
703
704// Test data for l=10, m=5.
705// max(|f - f_GSL|): 3.6082248300317588e-16
706// max(|f - f_GSL| / |f_GSL|): 1.6350423942234514e-15
707const testcase_sph_legendre<double>
708data014[21] =
709{
710 { 0.0000000000000000, 10, 5,
711 0.0000000000000000 },
712 { -0.0030300124052750196, 10, 5,
713 0.15707963267948966 },
714 { -0.070348585248056802, 10, 5,
715 0.31415926535897931 },
716 { -0.30055029290703639, 10, 5,
717 0.47123889803846897 },
718 { -0.49987818144009155, 10, 5,
719 0.62831853071795862 },
720 { -0.28108771757150108, 10, 5,
721 0.78539816339744828 },
722 { 0.22068081187249292, 10, 5,
723 0.94247779607693793 },
724 { 0.33689502212592121, 10, 5,
725 1.0995574287564276 },
726 { -0.086095515520764110, 10, 5,
727 1.2566370614359172 },
728 { -0.33935827318511558, 10, 5,
729 1.4137166941154069 },
730 { -1.9213014340664578e-16, 10, 5,
731 1.5707963267948966 },
732 { 0.33935827318511552, 10, 5,
733 1.7278759594743860 },
734 { 0.086095515520764512, 10, 5,
735 1.8849555921538759 },
736 { -0.33689502212592087, 10, 5,
737 2.0420352248333655 },
738 { -0.22068081187249344, 10, 5,
739 2.1991148575128552 },
740 { 0.28108771757150064, 10, 5,
741 2.3561944901923448 },
742 { 0.49987818144009138, 10, 5,
743 2.5132741228718345 },
744 { 0.30055029290703672, 10, 5,
745 2.6703537555513241 },
746 { 0.070348585248056802, 10, 5,
747 2.8274333882308138 },
748 { 0.0030300124052750873, 10, 5,
749 2.9845130209103035 },
750 { 0.0000000000000000, 10, 5,
751 3.1415926535897931 },
752};
753const double toler014 = 2.5000000000000020e-13;
754
755// Test data for l=10, m=10.
756// max(|f - f_GSL|): 9.9920072216264089e-16
757// max(|f - f_GSL| / |f_GSL|): 1.9163828344752537e-15
758const testcase_sph_legendre<double>
759data015[21] =
760{
761 { 0.0000000000000000, 10, 10,
762 0.0000000000000000 },
763 { 4.7624282733343473e-09, 10, 10,
764 0.15707963267948966 },
765 { 4.3085156534549772e-06, 10, 10,
766 0.31415926535897931 },
767 { 0.00020182347649472387, 10, 10,
768 0.47123889803846897 },
769 { 0.0026711045506511684, 10, 10,
770 0.62831853071795862 },
771 { 0.016957196623256909, 10, 10,
772 0.78539816339744828 },
773 { 0.065174916004990341, 10, 10,
774 0.94247779607693793 },
775 { 0.17112476903017845, 10, 10,
776 1.0995574287564276 },
777 { 0.32852414199733554, 10, 10,
778 1.2566370614359172 },
779 { 0.47940582314838287, 10, 10,
780 1.4137166941154069 },
781 { 0.54263029194422152, 10, 10,
782 1.5707963267948966 },
783 { 0.47940582314838309, 10, 10,
784 1.7278759594743860 },
785 { 0.32852414199733571, 10, 10,
786 1.8849555921538759 },
787 { 0.17112476903017856, 10, 10,
788 2.0420352248333655 },
789 { 0.065174916004990410, 10, 10,
790 2.1991148575128552 },
791 { 0.016957196623256943, 10, 10,
792 2.3561944901923448 },
793 { 0.0026711045506511706, 10, 10,
794 2.5132741228718345 },
795 { 0.00020182347649472493, 10, 10,
796 2.6703537555513241 },
797 { 4.3085156534549772e-06, 10, 10,
798 2.8274333882308138 },
799 { 4.7624282733345673e-09, 10, 10,
800 2.9845130209103035 },
801 { 0.0000000000000000, 10, 10,
802 3.1415926535897931 },
803};
804const double toler015 = 2.5000000000000020e-13;
805
806// Test data for l=20, m=0.
807// max(|f - f_GSL|): 1.2212453270876722e-15
808// max(|f - f_GSL| / |f_GSL|): 2.1900476331757668e-15
809const testcase_sph_legendre<double>
810data016[21] =
811{
812 { 1.8062879984608917, 20, 0,
813 0.0000000000000000 },
814 { -0.58906549291415933, 20, 0,
815 0.15707963267948966 },
816 { 0.45624611402342408, 20, 0,
817 0.31415926535897931 },
818 { -0.39955402700466724, 20, 0,
819 0.47123889803846897 },
820 { 0.36818552901640772, 20, 0,
821 0.62831853071795862 },
822 { -0.34873131330857743, 20, 0,
823 0.78539816339744828 },
824 { 0.33600882829186507, 20, 0,
825 0.94247779607693793 },
826 { -0.32759286308122931, 20, 0,
827 1.0995574287564276 },
828 { 0.32222458068091325, 20, 0,
829 1.2566370614359172 },
830 { -0.31922731037135965, 20, 0,
831 1.4137166941154069 },
832 { 0.31826262039531755, 20, 0,
833 1.5707963267948966 },
834 { -0.31922731037135987, 20, 0,
835 1.7278759594743860 },
836 { 0.32222458068091342, 20, 0,
837 1.8849555921538759 },
838 { -0.32759286308122942, 20, 0,
839 2.0420352248333655 },
840 { 0.33600882829186518, 20, 0,
841 2.1991148575128552 },
842 { -0.34873131330857782, 20, 0,
843 2.3561944901923448 },
844 { 0.36818552901640805, 20, 0,
845 2.5132741228718345 },
846 { -0.39955402700466824, 20, 0,
847 2.6703537555513241 },
848 { 0.45624611402342408, 20, 0,
849 2.8274333882308138 },
850 { -0.58906549291416732, 20, 0,
851 2.9845130209103035 },
852 { 1.8062879984608917, 20, 0,
853 3.1415926535897931 },
854};
855const double toler016 = 2.5000000000000020e-13;
856
857// Test data for l=20, m=1.
858// max(|f - f_GSL|): 2.8310687127941492e-15
859// max(|f - f_GSL| / |f_GSL|): 9.0837292708194213e-15
860const testcase_sph_legendre<double>
861data017[21] =
862{
863 { 0.0000000000000000, 20, 1,
864 0.0000000000000000 },
865 { -0.45905213045060256, 20, 1,
866 0.15707963267948966 },
867 { 0.31166370423309253, 20, 1,
868 0.31415926535897931 },
869 { -0.23278757741246778, 20, 1,
870 0.47123889803846897 },
871 { 0.17937240823504172, 20, 1,
872 0.62831853071795862 },
873 { -0.13857299972299839, 20, 1,
874 0.78539816339744828 },
875 { 0.10495324841927722, 20, 1,
876 0.94247779607693793 },
877 { -0.075707774352163665, 20, 1,
878 1.0995574287564276 },
879 { 0.049168697683476224, 20, 1,
880 1.2566370614359172 },
881 { -0.024216050551253303, 20, 1,
882 1.4137166941154069 },
883 { 3.9938443510694349e-16, 20, 1,
884 1.5707963267948966 },
885 { 0.024216050551250919, 20, 1,
886 1.7278759594743860 },
887 { -0.049168697683475482, 20, 1,
888 1.8849555921538759 },
889 { 0.075707774352163068, 20, 1,
890 2.0420352248333655 },
891 { -0.10495324841927638, 20, 1,
892 2.1991148575128552 },
893 { 0.13857299972299741, 20, 1,
894 2.3561944901923448 },
895 { -0.17937240823503983, 20, 1,
896 2.5132741228718345 },
897 { 0.23278757741246703, 20, 1,
898 2.6703537555513241 },
899 { -0.31166370423309253, 20, 1,
900 2.8274333882308138 },
901 { 0.45905213045059046, 20, 1,
902 2.9845130209103035 },
903 { 0.0000000000000000, 20, 1,
904 3.1415926535897931 },
905};
906const double toler017 = 5.0000000000000039e-13;
907
908// Test data for l=20, m=2.
909// max(|f - f_GSL|): 2.3314683517128287e-15
910// max(|f - f_GSL| / |f_GSL|): 2.6675898738403374e-15
911const testcase_sph_legendre<double>
912data018[21] =
913{
914 { 0.0000000000000000, 20, 2,
915 0.0000000000000000 },
916 { 0.87399805141574394, 20, 2,
917 0.15707963267948966 },
918 { -0.55116854080895061, 20, 2,
919 0.31415926535897931 },
920 { 0.44520137308557572, 20, 2,
921 0.47123889803846897 },
922 { -0.39321637877908228, 20, 2,
923 0.62831853071795862 },
924 { 0.36312025711350937, 20, 2,
925 0.78539816339744828 },
926 { -0.34427103004873116, 20, 2,
927 0.94247779607693793 },
928 { 0.33214917638387642, 20, 2,
929 1.0995574287564276 },
930 { -0.32455734448839091, 20, 2,
931 1.2566370614359172 },
932 { 0.32036529628513238, 20, 2,
933 1.4137166941154069 },
934 { -0.31902310563819986, 20, 2,
935 1.5707963267948966 },
936 { 0.32036529628513266, 20, 2,
937 1.7278759594743860 },
938 { -0.32455734448839102, 20, 2,
939 1.8849555921538759 },
940 { 0.33214917638387659, 20, 2,
941 2.0420352248333655 },
942 { -0.34427103004873105, 20, 2,
943 2.1991148575128552 },
944 { 0.36312025711350981, 20, 2,
945 2.3561944901923448 },
946 { -0.39321637877908278, 20, 2,
947 2.5132741228718345 },
948 { 0.44520137308557650, 20, 2,
949 2.6703537555513241 },
950 { -0.55116854080895061, 20, 2,
951 2.8274333882308138 },
952 { 0.87399805141574527, 20, 2,
953 2.9845130209103035 },
954 { 0.0000000000000000, 20, 2,
955 3.1415926535897931 },
956};
957const double toler018 = 2.5000000000000020e-13;
958
959// Test data for l=20, m=5.
960// max(|f - f_GSL|): 3.5388358909926865e-16
961// max(|f - f_GSL| / |f_GSL|): 1.2458491381272207e-14
962const testcase_sph_legendre<double>
963data019[21] =
964{
965 { 0.0000000000000000, 20, 5,
966 0.0000000000000000 },
967 { -0.10024848623504863, 20, 5,
968 0.15707963267948966 },
969 { -0.68115361075940484, 20, 5,
970 0.31415926535897931 },
971 { 0.31774532551156298, 20, 5,
972 0.47123889803846897 },
973 { -0.16011868165390544, 20, 5,
974 0.62831853071795862 },
975 { 0.085844143304115578, 20, 5,
976 0.78539816339744828 },
977 { -0.047467540840864568, 20, 5,
978 0.94247779607693793 },
979 { 0.026283575189471796, 20, 5,
980 1.0995574287564276 },
981 { -0.013891104052597688, 20, 5,
982 1.2566370614359172 },
983 { 0.0059873308239496957, 20, 5,
984 1.4137166941154069 },
985 { 3.9355286582083095e-16, 20, 5,
986 1.5707963267948966 },
987 { -0.0059873308239519014, 20, 5,
988 1.7278759594743860 },
989 { 0.013891104052598547, 20, 5,
990 1.8849555921538759 },
991 { -0.026283575189472864, 20, 5,
992 2.0420352248333655 },
993 { 0.047467540840865928, 20, 5,
994 2.1991148575128552 },
995 { -0.085844143304117007, 20, 5,
996 2.3561944901923448 },
997 { 0.16011868165390658, 20, 5,
998 2.5132741228718345 },
999 { -0.31774532551156381, 20, 5,
1000 2.6703537555513241 },
1001 { 0.68115361075940484, 20, 5,
1002 2.8274333882308138 },
1003 { 0.10024848623505046, 20, 5,
1004 2.9845130209103035 },
1005 { 0.0000000000000000, 20, 5,
1006 3.1415926535897931 },
1007};
1008const double toler019 = 1.0000000000000008e-12;
1009
1010// Test data for l=20, m=10.
1011// max(|f - f_GSL|): 1.6653345369377348e-15
1012// max(|f - f_GSL| / |f_GSL|): 2.0744116940226714e-14
1013const testcase_sph_legendre<double>
1014data020[21] =
1015{
1016 { 0.0000000000000000, 20, 10,
1017 0.0000000000000000 },
1018 { 3.0595797603706485e-05, 20, 10,
1019 0.15707963267948966 },
1020 { 0.015924453916397002, 20, 10,
1021 0.31415926535897931 },
1022 { 0.26588079118745744, 20, 10,
1023 0.47123889803846897 },
1024 { 0.54045081420686869, 20, 10,
1025 0.62831853071795862 },
1026 { -0.28215279394285531, 20, 10,
1027 0.78539816339744828 },
1028 { 0.0085297337582245884, 20, 10,
1029 0.94247779607693793 },
1030 { 0.16930127953533738, 20, 10,
1031 1.0995574287564276 },
1032 { -0.27215134048018325, 20, 10,
1033 1.2566370614359172 },
1034 { 0.32456597088029526, 20, 10,
1035 1.4137166941154069 },
1036 { -0.34057893241353715, 20, 10,
1037 1.5707963267948966 },
1038 { 0.32456597088029449, 20, 10,
1039 1.7278759594743860 },
1040 { -0.27215134048018291, 20, 10,
1041 1.8849555921538759 },
1042 { 0.16930127953533675, 20, 10,
1043 2.0420352248333655 },
1044 { 0.0085297337582257438, 20, 10,
1045 2.1991148575128552 },
1046 { -0.28215279394285619, 20, 10,
1047 2.3561944901923448 },
1048 { 0.54045081420686736, 20, 10,
1049 2.5132741228718345 },
1050 { 0.26588079118745828, 20, 10,
1051 2.6703537555513241 },
1052 { 0.015924453916397002, 20, 10,
1053 2.8274333882308138 },
1054 { 3.0595797603707888e-05, 20, 10,
1055 2.9845130209103035 },
1056 { 0.0000000000000000, 20, 10,
1057 3.1415926535897931 },
1058};
1059const double toler020 = 2.5000000000000015e-12;
1060
1061// Test data for l=20, m=20.
1062// max(|f - f_GSL|): 3.3306690738754696e-16
1063// max(|f - f_GSL| / |f_GSL|): 8.6795105199201385e-16
1064const testcase_sph_legendre<double>
1065data021[21] =
1066{
1067 { 0.0000000000000000, 20, 20,
1068 0.0000000000000000 },
1069 { 4.9264471419246231e-17, 20, 20,
1070 0.15707963267948966 },
1071 { 4.0321091681531780e-11, 20, 20,
1072 0.31415926535897931 },
1073 { 8.8474944184471664e-08, 20, 20,
1074 0.47123889803846897 },
1075 { 1.5497395129387764e-05, 20, 20,
1076 0.62831853071795862 },
1077 { 0.00062457564282984495, 20, 20,
1078 0.78539816339744828 },
1079 { 0.0092265192458967568, 20, 20,
1080 0.94247779607693793 },
1081 { 0.063606673236323297, 20, 20,
1082 1.0995574287564276 },
1083 { 0.23442909509776316, 20, 20,
1084 1.2566370614359172 },
1085 { 0.49921030481087009, 20, 20,
1086 1.4137166941154069 },
1087 { 0.63956545825776223, 20, 20,
1088 1.5707963267948966 },
1089 { 0.49921030481087064, 20, 20,
1090 1.7278759594743860 },
1091 { 0.23442909509776336, 20, 20,
1092 1.8849555921538759 },
1093 { 0.063606673236323380, 20, 20,
1094 2.0420352248333655 },
1095 { 0.0092265192458967742, 20, 20,
1096 2.1991148575128552 },
1097 { 0.00062457564282984766, 20, 20,
1098 2.3561944901923448 },
1099 { 1.5497395129387791e-05, 20, 20,
1100 2.5132741228718345 },
1101 { 8.8474944184472617e-08, 20, 20,
1102 2.6703537555513241 },
1103 { 4.0321091681531780e-11, 20, 20,
1104 2.8274333882308138 },
1105 { 4.9264471419250786e-17, 20, 20,
1106 2.9845130209103035 },
1107 { 0.0000000000000000, 20, 20,
1108 3.1415926535897931 },
1109};
1110const double toler021 = 2.5000000000000020e-13;
1111
1112// Test data for l=50, m=0.
1113// max(|f - f_GSL|): 4.8849813083506888e-15
1114// max(|f - f_GSL| / |f_GSL|): 9.2046020313085697e-15
1115const testcase_sph_legendre<double>
1116data022[21] =
1117{
1118 { 2.8350175706934717, 50, 0,
1119 0.0000000000000000 },
1120 { 0.53157537495174900, 50, 0,
1121 0.15707963267948966 },
1122 { -0.46056183476301255, 50, 0,
1123 0.31415926535897931 },
1124 { -0.24876032079677909, 50, 0,
1125 0.47123889803846897 },
1126 { 0.36926172901532522, 50, 0,
1127 0.62831853071795862 },
1128 { 0.14571730283563575, 50, 0,
1129 0.78539816339744828 },
1130 { -0.33636199170850806, 50, 0,
1131 0.94247779607693793 },
1132 { -0.079132716267091507, 50, 0,
1133 1.0995574287564276 },
1134 { 0.32232921941301451, 50, 0,
1135 1.2566370614359172 },
1136 { 0.025253991969481544, 50, 0,
1137 1.4137166941154069 },
1138 { -0.31830208724152359, 50, 0,
1139 1.5707963267948966 },
1140 { 0.025253991969476332, 50, 0,
1141 1.7278759594743860 },
1142 { 0.32232921941301479, 50, 0,
1143 1.8849555921538759 },
1144 { -0.079132716267088510, 50, 0,
1145 2.0420352248333655 },
1146 { -0.33636199170850883, 50, 0,
1147 2.1991148575128552 },
1148 { 0.14571730283563347, 50, 0,
1149 2.3561944901923448 },
1150 { 0.36926172901532667, 50, 0,
1151 2.5132741228718345 },
1152 { -0.24876032079677354, 50, 0,
1153 2.6703537555513241 },
1154 { -0.46056183476301255, 50, 0,
1155 2.8274333882308138 },
1156 { 0.53157537495172758, 50, 0,
1157 2.9845130209103035 },
1158 { 2.8350175706934717, 50, 0,
1159 3.1415926535897931 },
1160};
1161const double toler022 = 5.0000000000000039e-13;
1162
1163// Test data for l=50, m=1.
1164// max(|f - f_GSL|): 4.2743586448068527e-15
1165// max(|f - f_GSL| / |f_GSL|): 1.3104848798660735e-14
1166const testcase_sph_legendre<double>
1167data023[21] =
1168{
1169 { 0.0000000000000000, 50, 1,
1170 0.0000000000000000 },
1171 { -0.63751752155226260, 50, 1,
1172 0.15707963267948966 },
1173 { -0.32616619317604606, 50, 1,
1174 0.31415926535897931 },
1175 { 0.40649930826162850, 50, 1,
1176 0.47123889803846897 },
1177 { 0.18473991408344057, 50, 1,
1178 0.62831853071795862 },
1179 { -0.35083930302013117, 50, 1,
1180 0.78539816339744828 },
1181 { -0.10755382110947125, 50, 1,
1182 0.94247779607693793 },
1183 { 0.32822568316499900, 50, 1,
1184 1.0995574287564276 },
1185 { 0.050286056609797389, 50, 1,
1186 1.2566370614359172 },
1187 { -0.31935368562159644, 50, 1,
1188 1.4137166941154069 },
1189 { -9.8421602686195941e-16, 50, 1,
1190 1.5707963267948966 },
1191 { 0.31935368562159716, 50, 1,
1192 1.7278759594743860 },
1193 { -0.050286056609795446, 50, 1,
1194 1.8849555921538759 },
1195 { -0.32822568316499912, 50, 1,
1196 2.0420352248333655 },
1197 { 0.10755382110946902, 50, 1,
1198 2.1991148575128552 },
1199 { 0.35083930302013205, 50, 1,
1200 2.3561944901923448 },
1201 { -0.18473991408343635, 50, 1,
1202 2.5132741228718345 },
1203 { -0.40649930826163011, 50, 1,
1204 2.6703537555513241 },
1205 { 0.32616619317604606, 50, 1,
1206 2.8274333882308138 },
1207 { 0.63751752155228247, 50, 1,
1208 2.9845130209103035 },
1209 { 0.0000000000000000, 50, 1,
1210 3.1415926535897931 },
1211};
1212const double toler023 = 1.0000000000000008e-12;
1213
1214// Test data for l=50, m=2.
1215// max(|f - f_GSL|): 7.5495165674510645e-15
1216// max(|f - f_GSL| / |f_GSL|): 2.0277903864891892e-14
1217const testcase_sph_legendre<double>
1218data024[21] =
1219{
1220 { 0.0000000000000000, 50, 2,
1221 0.0000000000000000 },
1222 { -0.37230261163838724, 50, 2,
1223 0.15707963267948966 },
1224 { 0.50051599680316194, 50, 2,
1225 0.31415926535897931 },
1226 { 0.21724795180329495, 50, 2,
1227 0.47123889803846897 },
1228 { -0.37948127307610924, 50, 2,
1229 0.62831853071795862 },
1230 { -0.13187372121003396, 50, 2,
1231 0.78539816339744828 },
1232 { 0.33959009162400228, 50, 2,
1233 0.94247779607693793 },
1234 { 0.072537503112489563, 50, 2,
1235 1.0995574287564276 },
1236 { -0.32310306941855266, 50, 2,
1237 1.2566370614359172 },
1238 { -0.023259822816436588, 50, 2,
1239 1.4137166941154069 },
1240 { 0.31842698506357275, 50, 2,
1241 1.5707963267948966 },
1242 { -0.023259822816431196, 50, 2,
1243 1.7278759594743860 },
1244 { -0.32310306941855316, 50, 2,
1245 1.8849555921538759 },
1246 { 0.072537503112487453, 50, 2,
1247 2.0420352248333655 },
1248 { 0.33959009162400267, 50, 2,
1249 2.1991148575128552 },
1250 { -0.13187372121003124, 50, 2,
1251 2.3561944901923448 },
1252 { -0.37948127307611107, 50, 2,
1253 2.5132741228718345 },
1254 { 0.21724795180329090, 50, 2,
1255 2.6703537555513241 },
1256 { 0.50051599680316194, 50, 2,
1257 2.8274333882308138 },
1258 { -0.37230261163837081, 50, 2,
1259 2.9845130209103035 },
1260 { 0.0000000000000000, 50, 2,
1261 3.1415926535897931 },
1262};
1263const double toler024 = 2.5000000000000015e-12;
1264
1265// Test data for l=50, m=5.
1266// max(|f - f_GSL|): 4.3021142204224816e-16
1267// max(|f - f_GSL| / |f_GSL|): 8.9548506383410822e-15
1268const testcase_sph_legendre<double>
1269data025[21] =
1270{
1271 { 0.0000000000000000, 50, 5,
1272 0.0000000000000000 },
1273 { -0.57750385903193124, 50, 5,
1274 0.15707963267948966 },
1275 { 0.077360497065588632, 50, 5,
1276 0.31415926535897931 },
1277 { 0.47707267400540226, 50, 5,
1278 0.47123889803846897 },
1279 { 0.055370615126630517, 50, 5,
1280 0.62831853071795862 },
1281 { -0.37629451847202833, 50, 5,
1282 0.78539816339744828 },
1283 { -0.048042277801960784, 50, 5,
1284 0.94247779607693793 },
1285 { 0.33619379362228718, 50, 5,
1286 1.0995574287564276 },
1287 { 0.025265227185718764, 50, 5,
1288 1.2566370614359172 },
1289 { -0.32083679430964535, 50, 5,
1290 1.4137166941154069 },
1291 { -9.8189201019751884e-16, 50, 5,
1292 1.5707963267948966 },
1293 { 0.32083679430964579, 50, 5,
1294 1.7278759594743860 },
1295 { -0.025265227185716790, 50, 5,
1296 1.8849555921538759 },
1297 { -0.33619379362228752, 50, 5,
1298 2.0420352248333655 },
1299 { 0.048042277801958064, 50, 5,
1300 2.1991148575128552 },
1301 { 0.37629451847202872, 50, 5,
1302 2.3561944901923448 },
1303 { -0.055370615126626811, 50, 5,
1304 2.5132741228718345 },
1305 { -0.47707267400540176, 50, 5,
1306 2.6703537555513241 },
1307 { -0.077360497065588632, 50, 5,
1308 2.8274333882308138 },
1309 { 0.57750385903191603, 50, 5,
1310 2.9845130209103035 },
1311 { 0.0000000000000000, 50, 5,
1312 3.1415926535897931 },
1313};
1314const double toler025 = 5.0000000000000039e-13;
1315
1316// Test data for l=50, m=10.
1317// max(|f - f_GSL|): 1.3322676295501878e-15
1318// max(|f - f_GSL| / |f_GSL|): 6.0812430149180488e-15
1319const testcase_sph_legendre<double>
1320data026[21] =
1321{
1322 { 0.0000000000000000, 50, 10,
1323 0.0000000000000000 },
1324 { 0.15606941844800776, 50, 10,
1325 0.15707963267948966 },
1326 { -0.53748868836814501, 50, 10,
1327 0.31415926535897931 },
1328 { -0.49304919025183969, 50, 10,
1329 0.47123889803846897 },
1330 { -0.26267582750428364, 50, 10,
1331 0.62831853071795862 },
1332 { 0.22058983666314153, 50, 10,
1333 0.78539816339744828 },
1334 { 0.32936725160671754, 50, 10,
1335 0.94247779607693793 },
1336 { -0.092053311559447959, 50, 10,
1337 1.0995574287564276 },
1338 { -0.32542913495935522, 50, 10,
1339 1.2566370614359172 },
1340 { 0.025673223789103351, 50, 10,
1341 1.4137166941154069 },
1342 { 0.32150019350255743, 50, 10,
1343 1.5707963267948966 },
1344 { 0.025673223789108836, 50, 10,
1345 1.7278759594743860 },
1346 { -0.32542913495935510, 50, 10,
1347 1.8849555921538759 },
1348 { -0.092053311559449819, 50, 10,
1349 2.0420352248333655 },
1350 { 0.32936725160671687, 50, 10,
1351 2.1991148575128552 },
1352 { 0.22058983666314380, 50, 10,
1353 2.3561944901923448 },
1354 { -0.26267582750427920, 50, 10,
1355 2.5132741228718345 },
1356 { -0.49304919025184135, 50, 10,
1357 2.6703537555513241 },
1358 { -0.53748868836814501, 50, 10,
1359 2.8274333882308138 },
1360 { 0.15606941844801256, 50, 10,
1361 2.9845130209103035 },
1362 { 0.0000000000000000, 50, 10,
1363 3.1415926535897931 },
1364};
1365const double toler026 = 5.0000000000000039e-13;
1366
1367// Test data for l=50, m=20.
1368// max(|f - f_GSL|): 4.4408920985006262e-16
1369// max(|f - f_GSL| / |f_GSL|): 6.0930911637998029e-15
1370const testcase_sph_legendre<double>
1371data027[21] =
1372{
1373 { 0.0000000000000000, 50, 20,
1374 0.0000000000000000 },
1375 { 3.0409598712833246e-07, 50, 20,
1376 0.15707963267948966 },
1377 { 0.030940518122882274, 50, 20,
1378 0.31415926535897931 },
1379 { 0.64134588721659802, 50, 20,
1380 0.47123889803846897 },
1381 { 0.29895244392136405, 50, 20,
1382 0.62831853071795862 },
1383 { 0.25309324781873871, 50, 20,
1384 0.78539816339744828 },
1385 { 0.34368634714931717, 50, 20,
1386 0.94247779607693793 },
1387 { 0.33996764360663945, 50, 20,
1388 1.0995574287564276 },
1389 { 0.12866267745104024, 50, 20,
1390 1.2566370614359172 },
1391 { -0.18201114398922874, 50, 20,
1392 1.4137166941154069 },
1393 { -0.33216683431510857, 50, 20,
1394 1.5707963267948966 },
1395 { -0.18201114398923302, 50, 20,
1396 1.7278759594743860 },
1397 { 0.12866267745103857, 50, 20,
1398 1.8849555921538759 },
1399 { 0.33996764360663895, 50, 20,
1400 2.0420352248333655 },
1401 { 0.34368634714931812, 50, 20,
1402 2.1991148575128552 },
1403 { 0.25309324781874126, 50, 20,
1404 2.3561944901923448 },
1405 { 0.29895244392136594, 50, 20,
1406 2.5132741228718345 },
1407 { 0.64134588721659869, 50, 20,
1408 2.6703537555513241 },
1409 { 0.030940518122882274, 50, 20,
1410 2.8274333882308138 },
1411 { 3.0409598712835887e-07, 50, 20,
1412 2.9845130209103035 },
1413 { 0.0000000000000000, 50, 20,
1414 3.1415926535897931 },
1415};
1416const double toler027 = 5.0000000000000039e-13;
1417
1418// Test data for l=50, m=50.
1419// max(|f - f_GSL|): 1.2323475573339238e-14
1420// max(|f - f_GSL| / |f_GSL|): 1.6099735616249234e-14
1421const testcase_sph_legendre<double>
1422data028[21] =
1423{
1424 { 0.0000000000000000, 50, 50,
1425 0.0000000000000000 },
1426 { 4.1649039898151844e-41, 50, 50,
1427 0.15707963267948966 },
1428 { 2.5240684647724192e-26, 50, 50,
1429 0.31415926535897931 },
1430 { 5.6927376423967334e-18, 50, 50,
1431 0.47123889803846897 },
1432 { 2.3116239814797057e-12, 50, 50,
1433 0.62831853071795862 },
1434 { 2.3835981241325056e-08, 50, 50,
1435 0.78539816339744828 },
1436 { 1.9992410287270356e-05, 50, 50,
1437 0.94247779607693793 },
1438 { 0.0024947505670829834, 50, 50,
1439 1.0995574287564276 },
1440 { 0.065057774647971231, 50, 50,
1441 1.2566370614359172 },
1442 { 0.43050607056732243, 50, 50,
1443 1.4137166941154069 },
1444 { 0.79980281171531975, 50, 50,
1445 1.5707963267948966 },
1446 { 0.43050607056732360, 50, 50,
1447 1.7278759594743860 },
1448 { 0.065057774647971398, 50, 50,
1449 1.8849555921538759 },
1450 { 0.0024947505670829899, 50, 50,
1451 2.0420352248333655 },
1452 { 1.9992410287270427e-05, 50, 50,
1453 2.1991148575128552 },
1454 { 2.3835981241325311e-08, 50, 50,
1455 2.3561944901923448 },
1456 { 2.3116239814797222e-12, 50, 50,
1457 2.5132741228718345 },
1458 { 5.6927376423968952e-18, 50, 50,
1459 2.6703537555513241 },
1460 { 2.5240684647724192e-26, 50, 50,
1461 2.8274333882308138 },
1462 { 4.1649039898161316e-41, 50, 50,
1463 2.9845130209103035 },
1464 { 0.0000000000000000, 50, 50,
1465 3.1415926535897931 },
1466};
1467const double toler028 = 1.0000000000000008e-12;
1468
1469// Test data for l=100, m=0.
1470// max(|f - f_GSL|): 7.5495165674510645e-15
1471// max(|f - f_GSL| / |f_GSL|): 1.2423065089723510e-14
1472const testcase_sph_legendre<double>
1473data029[21] =
1474{
1475 { 3.9993839251484076, 100, 0,
1476 0.0000000000000000 },
1477 { -0.60770160285935426, 100, 0,
1478 0.15707963267948966 },
1479 { 0.46193027883955923, 100, 0,
1480 0.31415926535897931 },
1481 { -0.40218718869815234, 100, 0,
1482 0.47123889803846897 },
1483 { 0.36960201406910725, 100, 0,
1484 0.62831853071795862 },
1485 { -0.34953726547378389, 100, 0,
1486 0.78539816339744828 },
1487 { 0.33646959352497829, 100, 0,
1488 0.94247779607693793 },
1489 { -0.32784733067663224, 100, 0,
1490 1.0995574287564276 },
1491 { 0.32235624474047969, 100, 0,
1492 1.2566370614359172 },
1493 { -0.31929330706601350, 100, 0,
1494 1.4137166941154069 },
1495 { 0.31830791662110325, 100, 0,
1496 1.5707963267948966 },
1497 { -0.31929330706601405, 100, 0,
1498 1.7278759594743860 },
1499 { 0.32235624474048036, 100, 0,
1500 1.8849555921538759 },
1501 { -0.32784733067663357, 100, 0,
1502 2.0420352248333655 },
1503 { 0.33646959352498013, 100, 0,
1504 2.1991148575128552 },
1505 { -0.34953726547378589, 100, 0,
1506 2.3561944901923448 },
1507 { 0.36960201406911097, 100, 0,
1508 2.5132741228718345 },
1509 { -0.40218718869815723, 100, 0,
1510 2.6703537555513241 },
1511 { 0.46193027883955923, 100, 0,
1512 2.8274333882308138 },
1513 { -0.60770160285939456, 100, 0,
1514 2.9845130209103035 },
1515 { 3.9993839251484076, 100, 0,
1516 3.1415926535897931 },
1517};
1518const double toler029 = 1.0000000000000008e-12;
1519
1520// Test data for l=100, m=1.
1521// max(|f - f_GSL|): 4.1078251911130792e-15
1522// max(|f - f_GSL| / |f_GSL|): 1.5162419336330716e-14
1523const testcase_sph_legendre<double>
1524data030[21] =
1525{
1526 { 0.0000000000000000, 100, 1,
1527 0.0000000000000000 },
1528 { -0.50851949013719866, 100, 1,
1529 0.15707963267948966 },
1530 { 0.33129641402221749, 100, 1,
1531 0.31415926535897931 },
1532 { -0.24390405750942512, 100, 1,
1533 0.47123889803846897 },
1534 { 0.18659755088414104, 100, 1,
1535 0.62831853071795862 },
1536 { -0.14355908970517178, 100, 1,
1537 0.78539816339744828 },
1538 { 0.10844906813251107, 100, 1,
1539 0.94247779607693793 },
1540 { -0.078100088690857675, 100, 1,
1541 1.0995574287564276 },
1542 { 0.050670002998302717, 100, 1,
1543 1.2566370614359172 },
1544 { -0.024941251747138900, 100, 1,
1545 1.4137166941154069 },
1546 { 1.9587949830851623e-15, 100, 1,
1547 1.5707963267948966 },
1548 { 0.024941251747127875, 100, 1,
1549 1.7278759594743860 },
1550 { -0.050670002998298824, 100, 1,
1551 1.8849555921538759 },
1552 { 0.078100088690853664, 100, 1,
1553 2.0420352248333655 },
1554 { -0.10844906813250622, 100, 1,
1555 2.1991148575128552 },
1556 { 0.14355908970516626, 100, 1,
1557 2.3561944901923448 },
1558 { -0.18659755088413388, 100, 1,
1559 2.5132741228718345 },
1560 { 0.24390405750941679, 100, 1,
1561 2.6703537555513241 },
1562 { -0.33129641402221749, 100, 1,
1563 2.8274333882308138 },
1564 { 0.50851949013714159, 100, 1,
1565 2.9845130209103035 },
1566 { 0.0000000000000000, 100, 1,
1567 3.1415926535897931 },
1568};
1569const double toler030 = 1.0000000000000008e-12;
1570
1571// Test data for l=100, m=2.
1572// max(|f - f_GSL|): 2.7755575615628914e-15
1573// max(|f - f_GSL| / |f_GSL|): 5.7552022268705475e-15
1574const testcase_sph_legendre<double>
1575data031[21] =
1576{
1577 { 0.0000000000000000, 100, 2,
1578 0.0000000000000000 },
1579 { 0.67166274297193962, 100, 2,
1580 0.15707963267948966 },
1581 { -0.48226933687995360, 100, 2,
1582 0.31415926535897931 },
1583 { 0.41175421895715525, 100, 2,
1584 0.47123889803846897 },
1585 { -0.37475021787822438, 100, 2,
1586 0.62831853071795862 },
1587 { 0.35242909383605225, 100, 2,
1588 0.78539816339744828 },
1589 { -0.33807110409160063, 100, 2,
1590 0.94247779607693793 },
1591 { 0.32867180390710077, 100, 2,
1592 1.0995574287564276 },
1593 { -0.32271583790278502, 100, 2,
1594 1.2566370614359172 },
1595 { 0.31940354677687444, 100, 2,
1596 1.4137166941154069 },
1597 { -0.31833943693772526, 100, 2,
1598 1.5707963267948966 },
1599 { 0.31940354677687555, 100, 2,
1600 1.7278759594743860 },
1601 { -0.32271583790278552, 100, 2,
1602 1.8849555921538759 },
1603 { 0.32867180390710193, 100, 2,
1604 2.0420352248333655 },
1605 { -0.33807110409160157, 100, 2,
1606 2.1991148575128552 },
1607 { 0.35242909383605503, 100, 2,
1608 2.3561944901923448 },
1609 { -0.37475021787822776, 100, 2,
1610 2.5132741228718345 },
1611 { 0.41175421895716052, 100, 2,
1612 2.6703537555513241 },
1613 { -0.48226933687995360, 100, 2,
1614 2.8274333882308138 },
1615 { 0.67166274297196660, 100, 2,
1616 2.9845130209103035 },
1617 { 0.0000000000000000, 100, 2,
1618 3.1415926535897931 },
1619};
1620const double toler031 = 5.0000000000000039e-13;
1621
1622// Test data for l=100, m=5.
1623// max(|f - f_GSL|): 5.9674487573602164e-16
1624// max(|f - f_GSL| / |f_GSL|): 8.4413588189215985e-15
1625const testcase_sph_legendre<double>
1626data032[21] =
1627{
1628 { 0.0000000000000000, 100, 5,
1629 0.0000000000000000 },
1630 { 0.062564361105902272, 100, 5,
1631 0.15707963267948966 },
1632 { 0.14179554455879767, 100, 5,
1633 0.31415926535897931 },
1634 { -0.14356866942905960, 100, 5,
1635 0.47123889803846897 },
1636 { 0.12355483388448550, 100, 5,
1637 0.62831853071795862 },
1638 { -0.10090029999681642, 100, 5,
1639 0.78539816339744828 },
1640 { 0.078905134460230675, 100, 5,
1641 0.94247779607693793 },
1642 { -0.058040182398185071, 100, 5,
1643 1.0995574287564276 },
1644 { 0.038142759389482424, 100, 5,
1645 1.2566370614359172 },
1646 { -0.018906264170660478, 100, 5,
1647 1.4137166941154069 },
1648 { 1.9576303042914544e-15, 100, 5,
1649 1.5707963267948966 },
1650 { 0.018906264170649455, 100, 5,
1651 1.7278759594743860 },
1652 { -0.038142759389478365, 100, 5,
1653 1.8849555921538759 },
1654 { 0.058040182398180429, 100, 5,
1655 2.0420352248333655 },
1656 { -0.078905134460225707, 100, 5,
1657 2.1991148575128552 },
1658 { 0.10090029999681013, 100, 5,
1659 2.3561944901923448 },
1660 { -0.12355483388447824, 100, 5,
1661 2.5132741228718345 },
1662 { 0.14356866942904906, 100, 5,
1663 2.6703537555513241 },
1664 { -0.14179554455879767, 100, 5,
1665 2.8274333882308138 },
1666 { -0.062564361105954577, 100, 5,
1667 2.9845130209103035 },
1668 { 0.0000000000000000, 100, 5,
1669 3.1415926535897931 },
1670};
1671const double toler032 = 5.0000000000000039e-13;
1672
1673// Test data for l=100, m=10.
1674// max(|f - f_GSL|): 1.7763568394002505e-15
1675// max(|f - f_GSL| / |f_GSL|): 4.0853922061744651e-15
1676const testcase_sph_legendre<double>
1677data033[21] =
1678{
1679 { 0.0000000000000000, 100, 10,
1680 0.0000000000000000 },
1681 { -0.75366545187996004, 100, 10,
1682 0.15707963267948966 },
1683 { -0.35914570017276798, 100, 10,
1684 0.31415926535897931 },
1685 { 0.43480692911578295, 100, 10,
1686 0.47123889803846897 },
1687 { -0.40862111080315755, 100, 10,
1688 0.62831853071795862 },
1689 { 0.37832688692909411, 100, 10,
1690 0.78539816339744828 },
1691 { -0.35484056194773445, 100, 10,
1692 0.94247779607693793 },
1693 { 0.33821981171196341, 100, 10,
1694 1.0995574287564276 },
1695 { -0.32729120767830594, 100, 10,
1696 1.2566370614359172 },
1697 { 0.32110336937091438, 100, 10,
1698 1.4137166941154069 },
1699 { -0.31910064020036194, 100, 10,
1700 1.5707963267948966 },
1701 { 0.32110336937091460, 100, 10,
1702 1.7278759594743860 },
1703 { -0.32729120767830605, 100, 10,
1704 1.8849555921538759 },
1705 { 0.33821981171196341, 100, 10,
1706 2.0420352248333655 },
1707 { -0.35484056194773461, 100, 10,
1708 2.1991148575128552 },
1709 { 0.37832688692909372, 100, 10,
1710 2.3561944901923448 },
1711 { -0.40862111080315500, 100, 10,
1712 2.5132741228718345 },
1713 { 0.43480692911577751, 100, 10,
1714 2.6703537555513241 },
1715 { -0.35914570017276798, 100, 10,
1716 2.8274333882308138 },
1717 { -0.75366545187997991, 100, 10,
1718 2.9845130209103035 },
1719 { 0.0000000000000000, 100, 10,
1720 3.1415926535897931 },
1721};
1722const double toler033 = 2.5000000000000020e-13;
1723
1724// Test data for l=100, m=20.
1725// max(|f - f_GSL|): 9.7144514654701197e-16
1726// max(|f - f_GSL| / |f_GSL|): 2.8802569343392205e-14
1727const testcase_sph_legendre<double>
1728data034[21] =
1729{
1730 { 0.0000000000000000, 100, 20,
1731 0.0000000000000000 },
1732 { 0.053569660841553700, 100, 20,
1733 0.15707963267948966 },
1734 { 0.57154926874732348, 100, 20,
1735 0.31415926535897931 },
1736 { 0.47536909969585633, 100, 20,
1737 0.47123889803846897 },
1738 { -0.28882554564109075, 100, 20,
1739 0.62831853071795862 },
1740 { 0.020116179014043743, 100, 20,
1741 0.78539816339744828 },
1742 { 0.14752195931706563, 100, 20,
1743 0.94247779607693793 },
1744 { -0.24069428588868366, 100, 20,
1745 1.0995574287564276 },
1746 { 0.29031796025014306, 100, 20,
1747 1.2566370614359172 },
1748 { -0.31437256851143458, 100, 20,
1749 1.4137166941154069 },
1750 { 0.32153954851141792, 100, 20,
1751 1.5707963267948966 },
1752 { -0.31437256851143169, 100, 20,
1753 1.7278759594743860 },
1754 { 0.29031796025014139, 100, 20,
1755 1.8849555921538759 },
1756 { -0.24069428588868083, 100, 20,
1757 2.0420352248333655 },
1758 { 0.14752195931706186, 100, 20,
1759 2.1991148575128552 },
1760 { 0.020116179014049562, 100, 20,
1761 2.3561944901923448 },
1762 { -0.28882554564109575, 100, 20,
1763 2.5132741228718345 },
1764 { 0.47536909969585545, 100, 20,
1765 2.6703537555513241 },
1766 { 0.57154926874732348, 100, 20,
1767 2.8274333882308138 },
1768 { 0.053569660841557079, 100, 20,
1769 2.9845130209103035 },
1770 { 0.0000000000000000, 100, 20,
1771 3.1415926535897931 },
1772};
1773const double toler034 = 2.5000000000000015e-12;
1774
1775// Test data for l=100, m=50.
1776// max(|f - f_GSL|): 8.3266726846886741e-15
1777// max(|f - f_GSL| / |f_GSL|): 1.8981734972089879e-14
1778const testcase_sph_legendre<double>
1779data035[21] =
1780{
1781 { 0.0000000000000000, 100, 50,
1782 0.0000000000000000 },
1783 { 3.3047910392590615e-21, 100, 50,
1784 0.15707963267948966 },
1785 { 1.0592655372554981e-07, 100, 50,
1786 0.31415926535897931 },
1787 { 0.080418744223952773, 100, 50,
1788 0.47123889803846897 },
1789 { -0.56450600580393095, 100, 50,
1790 0.62831853071795862 },
1791 { 0.33338739844742110, 100, 50,
1792 0.78539816339744828 },
1793 { 0.39741714816514706, 100, 50,
1794 0.94247779607693793 },
1795 { 0.35223993750972243, 100, 50,
1796 1.0995574287564276 },
1797 { 0.17885891940721577, 100, 50,
1798 1.2566370614359172 },
1799 { -0.15341660126461967, 100, 50,
1800 1.4137166941154069 },
1801 { -0.34175924303503102, 100, 50,
1802 1.5707963267948966 },
1803 { -0.15341660126462869, 100, 50,
1804 1.7278759594743860 },
1805 { 0.17885891940721302, 100, 50,
1806 1.8849555921538759 },
1807 { 0.35223993750972105, 100, 50,
1808 2.0420352248333655 },
1809 { 0.39741714816514595, 100, 50,
1810 2.1991148575128552 },
1811 { 0.33338739844741666, 100, 50,
1812 2.3561944901923448 },
1813 { -0.56450600580392973, 100, 50,
1814 2.5132741228718345 },
1815 { 0.080418744223953911, 100, 50,
1816 2.6703537555513241 },
1817 { 1.0592655372554981e-07, 100, 50,
1818 2.8274333882308138 },
1819 { 3.3047910392597822e-21, 100, 50,
1820 2.9845130209103035 },
1821 { 0.0000000000000000, 100, 50,
1822 3.1415926535897931 },
1823};
1824const double toler035 = 1.0000000000000008e-12;
1825
1826// Test data for l=100, m=100.
1827// max(|f - f_GSL|): 2.3314683517128287e-14
1828// max(|f - f_GSL| / |f_GSL|): 2.6593512237122742e-14
1829const testcase_sph_legendre<double>
1830data036[21] =
1831{
1832 { 0.0000000000000000, 100, 100,
1833 0.0000000000000000 },
1834 { 2.5744136608862186e-81, 100, 100,
1835 0.15707963267948966 },
1836 { 9.4551974868956498e-52, 100, 100,
1837 0.31415926535897931 },
1838 { 4.8096190703397596e-35, 100, 100,
1839 0.47123889803846897 },
1840 { 7.9305393636342891e-24, 100, 100,
1841 0.62831853071795862 },
1842 { 8.4320740610944858e-16, 100, 100,
1843 0.78539816339744828 },
1844 { 5.9319660146027522e-10, 100, 100,
1845 0.94247779607693793 },
1846 { 9.2368225946797243e-06, 100, 100,
1847 1.0995574287564276 },
1848 { 0.0062815489742044095, 100, 100,
1849 1.2566370614359172 },
1850 { 0.27505966018176986, 100, 100,
1851 1.4137166941154069 },
1852 { 0.94936713998764621, 100, 100,
1853 1.5707963267948966 },
1854 { 0.27505966018177130, 100, 100,
1855 1.7278759594743860 },
1856 { 0.0062815489742044433, 100, 100,
1857 1.8849555921538759 },
1858 { 9.2368225946797734e-06, 100, 100,
1859 2.0420352248333655 },
1860 { 5.9319660146027946e-10, 100, 100,
1861 2.1991148575128552 },
1862 { 8.4320740610946652e-16, 100, 100,
1863 2.3561944901923448 },
1864 { 7.9305393636344023e-24, 100, 100,
1865 2.5132741228718345 },
1866 { 4.8096190703400333e-35, 100, 100,
1867 2.6703537555513241 },
1868 { 9.4551974868956498e-52, 100, 100,
1869 2.8274333882308138 },
1870 { 2.5744136608873895e-81, 100, 100,
1871 2.9845130209103035 },
1872 { 0.0000000000000000, 100, 100,
1873 3.1415926535897931 },
1874};
1875const double toler036 = 2.5000000000000015e-12;
1876
1877template<typename Tp, unsigned int Num>
1878 void
1879 test(const testcase_sph_legendre<Tp> (&data)[Num], Tp toler)
1880 {
2be75957
ESR		 1881 const Tp eps = std::numeric_limits<Tp>::epsilon();
1882 Tp max_abs_diff = -Tp(1);
1883 Tp max_abs_frac = -Tp(1);
1884 unsigned int num_datum = Num;
1885 for (unsigned int i = 0; i < num_datum; ++i)
1886 {
1887 const Tp f = std::sph_legendre(data[i].l, data[i].m,
1888 data[i].theta);
1889 const Tp f0 = data[i].f0;
1890 const Tp diff = f - f0;
1891 if (std::abs(diff) > max_abs_diff)
1892 max_abs_diff = std::abs(diff);
1893 if (std::abs(f0) > Tp(10) * eps
1894 && std::abs(f) > Tp(10) * eps)
1895 {
1896 const Tp frac = diff / f0;
1897 if (std::abs(frac) > max_abs_frac)
1898 max_abs_frac = std::abs(frac);
1899 }
1900 }
1901 VERIFY(max_abs_frac < toler);
1902 }
1903
1904int
1905main()
1906{
1907 test(data001, toler001);
1908 test(data002, toler002);
1909 test(data003, toler003);
1910 test(data004, toler004);
1911 test(data005, toler005);
1912 test(data006, toler006);
1913 test(data007, toler007);
1914 test(data008, toler008);
1915 test(data009, toler009);
1916 test(data010, toler010);
1917 test(data011, toler011);
1918 test(data012, toler012);
1919 test(data013, toler013);
1920 test(data014, toler014);
1921 test(data015, toler015);
1922 test(data016, toler016);
1923 test(data017, toler017);
1924 test(data018, toler018);
1925 test(data019, toler019);
1926 test(data020, toler020);
1927 test(data021, toler021);
1928 test(data022, toler022);
1929 test(data023, toler023);
1930 test(data024, toler024);
1931 test(data025, toler025);
1932 test(data026, toler026);
1933 test(data027, toler027);
1934 test(data028, toler028);
1935 test(data029, toler029);
1936 test(data030, toler030);
1937 test(data031, toler031);
1938 test(data032, toler032);
1939 test(data033, toler033);
1940 test(data034, toler034);
1941 test(data035, toler035);
1942 test(data036, toler036);
1943 return 0;
1944}
Mirror of https://gcc.gnu.org/git/gcc.git