1 // { dg-do run { target c++11 } }
2 // { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" }
3 //
4 // Copyright (C) 2016-2018 Free Software Foundation, Inc.
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 // Test data for l=0, m=0.
41 // max(|f - f_GSL|): 0.0000000000000000 at index 0
42 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
43 // mean(f - f_GSL): 0.0000000000000000
44 // variance(f - f_GSL): 0.0000000000000000
45 // stddev(f - f_GSL): 0.0000000000000000
46 const testcase_sph_legendre<double>
47 data001[21] =
48 {
49 { 0.28209479177387814, 0, 0,
50 0.0000000000000000, 0.0 },
51 { 0.28209479177387814, 0, 0,
52 0.15707963267948966, 0.0 },
53 { 0.28209479177387814, 0, 0,
54 0.31415926535897931, 0.0 },
55 { 0.28209479177387814, 0, 0,
56 0.47123889803846897, 0.0 },
57 { 0.28209479177387814, 0, 0,
58 0.62831853071795862, 0.0 },
59 { 0.28209479177387814, 0, 0,
60 0.78539816339744828, 0.0 },
61 { 0.28209479177387814, 0, 0,
62 0.94247779607693793, 0.0 },
63 { 0.28209479177387814, 0, 0,
64 1.0995574287564276, 0.0 },
65 { 0.28209479177387814, 0, 0,
66 1.2566370614359172, 0.0 },
67 { 0.28209479177387814, 0, 0,
68 1.4137166941154069, 0.0 },
69 { 0.28209479177387814, 0, 0,
70 1.5707963267948966, 0.0 },
71 { 0.28209479177387814, 0, 0,
72 1.7278759594743862, 0.0 },
73 { 0.28209479177387814, 0, 0,
74 1.8849555921538759, 0.0 },
75 { 0.28209479177387814, 0, 0,
76 2.0420352248333655, 0.0 },
77 { 0.28209479177387814, 0, 0,
78 2.1991148575128552, 0.0 },
79 { 0.28209479177387814, 0, 0,
80 2.3561944901923448, 0.0 },
81 { 0.28209479177387814, 0, 0,
82 2.5132741228718345, 0.0 },
83 { 0.28209479177387814, 0, 0,
84 2.6703537555513241, 0.0 },
85 { 0.28209479177387814, 0, 0,
86 2.8274333882308138, 0.0 },
87 { 0.28209479177387814, 0, 0,
88 2.9845130209103035, 0.0 },
89 { 0.28209479177387814, 0, 0,
90 3.1415926535897931, 0.0 },
91 };
92 const double toler001 = 2.5000000000000020e-13;
93
94 // Test data for l=1, m=0.
95 // max(|f - f_GSL|): 0.0000000000000000 at index 0
96 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
97 // mean(f - f_GSL): 0.0000000000000000
98 // variance(f - f_GSL): 0.0000000000000000
99 // stddev(f - f_GSL): 0.0000000000000000
100 const testcase_sph_legendre<double>
101 data002[21] =
102 {
103 { 0.48860251190291992, 1, 0,
104 0.0000000000000000, 0.0 },
105 { 0.48258700419201095, 1, 0,
106 0.15707963267948966, 0.0 },
107 { 0.46468860282345237, 1, 0,
108 0.31415926535897931, 0.0 },
109 { 0.43534802584032634, 1, 0,
110 0.47123889803846897, 0.0 },
111 { 0.39528773562374969, 1, 0,
112 0.62831853071795862, 0.0 },
113 { 0.34549414947133550, 1, 0,
114 0.78539816339744828, 0.0 },
115 { 0.28719335072959395, 1, 0,
116 0.94247779607693793, 0.0 },
117 { 0.22182089855280449, 1, 0,
118 1.0995574287564276, 0.0 },
119 { 0.15098647967228981, 1, 0,
120 1.2566370614359172, 0.0 },
121 { 0.076434272566846345, 1, 0,
122 1.4137166941154069, 0.0 },
123 { 2.9918275112863332e-17, 1, 0,
124 1.5707963267948966, 0.0 },
125 { -0.076434272566846290, 1, 0,
126 1.7278759594743862, 0.0 },
127 { -0.15098647967228976, 1, 0,
128 1.8849555921538759, 0.0 },
129 { -0.22182089855280446, 1, 0,
130 2.0420352248333655, 0.0 },
131 { -0.28719335072959384, 1, 0,
132 2.1991148575128552, 0.0 },
133 { -0.34549414947133544, 1, 0,
134 2.3561944901923448, 0.0 },
135 { -0.39528773562374975, 1, 0,
136 2.5132741228718345, 0.0 },
137 { -0.43534802584032628, 1, 0,
138 2.6703537555513241, 0.0 },
139 { -0.46468860282345231, 1, 0,
140 2.8274333882308138, 0.0 },
141 { -0.48258700419201095, 1, 0,
142 2.9845130209103035, 0.0 },
143 { -0.48860251190291992, 1, 0,
144 3.1415926535897931, 0.0 },
145 };
146 const double toler002 = 2.5000000000000020e-13;
147
148 // Test data for l=1, m=1.
149 // max(|f - f_GSL|): 1.9984014443252818e-15 at index 9
150 // max(|f - f_GSL| / |f_GSL|): 5.9507621559271917e-15
151 // mean(f - f_GSL): 1.1981156807413147e-15
152 // variance(f - f_GSL): 7.5362762183006766e-32
153 // stddev(f - f_GSL): 2.7452278991553101e-16
154 const testcase_sph_legendre<double>
155 data003[21] =
156 {
157 { 0.0000000000000000, 1, 1,
158 0.0000000000000000, 0.0 },
159 { -0.054047192447078167, 1, 1,
160 0.15707963267948966, 0.0 },
161 { -0.10676356364376091, 1, 1,
162 0.31415926535897931, 0.0 },
163 { -0.15685106157558129, 1, 1,
164 0.47123889803846897, 0.0 },
165 { -0.20307636581258248, 1, 1,
166 0.62831853071795862, 0.0 },
167 { -0.24430125595146007, 1, 1,
168 0.78539816339744828, 0.0 },
169 { -0.27951063837942880, 1, 1,
170 0.94247779607693793, 0.0 },
171 { -0.30783754124787122, 1, 1,
172 1.0995574287564276, 0.0 },
173 { -0.32858446219656556, 1, 1,
174 1.2566370614359172, 0.0 },
175 { -0.34124054317667202, 1, 1,
176 1.4137166941154069, 0.0 },
177 { -0.34549414947133567, 1, 1,
178 1.5707963267948966, 0.0 },
179 { -0.34124054317667202, 1, 1,
180 1.7278759594743862, 0.0 },
181 { -0.32858446219656556, 1, 1,
182 1.8849555921538759, 0.0 },
183 { -0.30783754124787127, 1, 1,
184 2.0420352248333655, 0.0 },
185 { -0.27951063837942880, 1, 1,
186 2.1991148575128552, 0.0 },
187 { -0.24430125595146013, 1, 1,
188 2.3561944901923448, 0.0 },
189 { -0.20307636581258243, 1, 1,
190 2.5132741228718345, 0.0 },
191 { -0.15685106157558140, 1, 1,
192 2.6703537555513241, 0.0 },
193 { -0.10676356364376104, 1, 1,
194 2.8274333882308138, 0.0 },
195 { -0.054047192447078167, 1, 1,
196 2.9845130209103035, 0.0 },
197 { 0.0000000000000000, 1, 1,
198 3.1415926535897931, 0.0 },
199 };
200 const double toler003 = 5.0000000000000039e-13;
201
202 // Test data for l=2, m=0.
203 // max(|f - f_GSL|): 1.1102230246251565e-16 at index 0
204 // max(|f - f_GSL| / |f_GSL|): 3.1667226501700652e-15
205 // mean(f - f_GSL): -3.0233752009881492e-17
206 // variance(f - f_GSL): 3.4265646892248527e-34
207 // stddev(f - f_GSL): 1.8510982386747748e-17
208 const testcase_sph_legendre<double>
209 data004[21] =
210 {
211 { 0.63078313050504009, 2, 0,
212 0.0000000000000000, 0.0 },
213 { 0.60762858760316585, 2, 0,
214 0.15707963267948966, 0.0 },
215 { 0.54043148688396603, 2, 0,
216 0.31415926535897931, 0.0 },
217 { 0.43576954875556589, 2, 0,
218 0.47123889803846897, 0.0 },
219 { 0.30388781294457567, 2, 0,
220 0.62831853071795862, 0.0 },
221 { 0.15769578262626011, 2, 0,
222 0.78539816339744828, 0.0 },
223 { 0.011503752307944374, 2, 0,
224 0.94247779607693793, 0.0 },
225 { -0.12037798350304570, 2, 0,
226 1.0995574287564276, 0.0 },
227 { -0.22503992163144576, 2, 0,
228 1.2566370614359172, 0.0 },
229 { -0.29223702235064597, 2, 0,
230 1.4137166941154069, 0.0 },
231 { -0.31539156525252005, 2, 0,
232 1.5707963267948966, 0.0 },
233 { -0.29223702235064597, 2, 0,
234 1.7278759594743862, 0.0 },
235 { -0.22503992163144584, 2, 0,
236 1.8849555921538759, 0.0 },
237 { -0.12037798350304577, 2, 0,
238 2.0420352248333655, 0.0 },
239 { 0.011503752307944164, 2, 0,
240 2.1991148575128552, 0.0 },
241 { 0.15769578262625994, 2, 0,
242 2.3561944901923448, 0.0 },
243 { 0.30388781294457579, 2, 0,
244 2.5132741228718345, 0.0 },
245 { 0.43576954875556562, 2, 0,
246 2.6703537555513241, 0.0 },
247 { 0.54043148688396569, 2, 0,
248 2.8274333882308138, 0.0 },
249 { 0.60762858760316585, 2, 0,
250 2.9845130209103035, 0.0 },
251 { 0.63078313050504009, 2, 0,
252 3.1415926535897931, 0.0 },
253 };
254 const double toler004 = 2.5000000000000020e-13;
255
256 // Test data for l=2, m=1.
257 // max(|f - f_GSL|): 2.2204460492503131e-15 at index 5
258 // max(|f - f_GSL| / |f_GSL|): 5.9294218689659490e-15
259 // mean(f - f_GSL): 6.6084703846736834e-19
260 // variance(f - f_GSL): 2.2927737433182295e-38
261 // stddev(f - f_GSL): 1.5141907882820546e-19
262 const testcase_sph_legendre<double>
263 data005[21] =
264 {
265 { 0.0000000000000000, 2, 1,
266 0.0000000000000000, 0.0 },
267 { -0.11936529291378781, 2, 1,
268 0.15707963267948966, 0.0 },
269 { -0.22704627929027421, 2, 1,
270 0.31415926535897931, 0.0 },
271 { -0.31250239392538215, 2, 1,
272 0.47123889803846897, 0.0 },
273 { -0.36736859691086526, 2, 1,
274 0.62831853071795862, 0.0 },
275 { -0.38627420202318979, 2, 1,
276 0.78539816339744828, 0.0 },
277 { -0.36736859691086532, 2, 1,
278 0.94247779607693793, 0.0 },
279 { -0.31250239392538226, 2, 1,
280 1.0995574287564276, 0.0 },
281 { -0.22704627929027438, 2, 1,
282 1.2566370614359172, 0.0 },
283 { -0.11936529291378740, 2, 1,
284 1.4137166941154069, 0.0 },
285 { -4.7304946510089680e-17, 2, 1,
286 1.5707963267948966, 0.0 },
287 { 0.11936529291378731, 2, 1,
288 1.7278759594743862, 0.0 },
289 { 0.22704627929027429, 2, 1,
290 1.8849555921538759, 0.0 },
291 { 0.31250239392538226, 2, 1,
292 2.0420352248333655, 0.0 },
293 { 0.36736859691086521, 2, 1,
294 2.1991148575128552, 0.0 },
295 { 0.38627420202318979, 2, 1,
296 2.3561944901923448, 0.0 },
297 { 0.36736859691086526, 2, 1,
298 2.5132741228718345, 0.0 },
299 { 0.31250239392538232, 2, 1,
300 2.6703537555513241, 0.0 },
301 { 0.22704627929027449, 2, 1,
302 2.8274333882308138, 0.0 },
303 { 0.11936529291378781, 2, 1,
304 2.9845130209103035, 0.0 },
305 { 0.0000000000000000, 2, 1,
306 3.1415926535897931, 0.0 },
307 };
308 const double toler005 = 5.0000000000000039e-13;
309
310 // Test data for l=2, m=2.
311 // max(|f - f_GSL|): 2.2759572004815709e-15 at index 10
312 // max(|f - f_GSL| / |f_GSL|): 6.0197685443914339e-15
313 // mean(f - f_GSL): -1.0489294618073093e-15
314 // variance(f - f_GSL): 5.7763283331987012e-32
315 // stddev(f - f_GSL): 2.4033993287006430e-16
316 const testcase_sph_legendre<double>
317 data006[21] =
318 {
319 { 0.0000000000000000, 2, 2,
320 0.0000000000000000, 0.0 },
321 { 0.0094528025561623485, 2, 2,
322 0.15707963267948966, 0.0 },
323 { 0.036885904048903732, 2, 2,
324 0.31415926535897931, 0.0 },
325 { 0.079613961366457681, 2, 2,
326 0.47123889803846897, 0.0 },
327 { 0.13345445455470126, 2, 2,
328 0.62831853071795862, 0.0 },
329 { 0.19313710101159490, 2, 2,
330 0.78539816339744828, 0.0 },
331 { 0.25281974746848851, 2, 2,
332 0.94247779607693793, 0.0 },
333 { 0.30666024065673209, 2, 2,
334 1.0995574287564276, 0.0 },
335 { 0.34938829797428600, 2, 2,
336 1.2566370614359172, 0.0 },
337 { 0.37682139946702753, 2, 2,
338 1.4137166941154069, 0.0 },
339 { 0.38627420202318985, 2, 2,
340 1.5707963267948966, 0.0 },
341 { 0.37682139946702753, 2, 2,
342 1.7278759594743862, 0.0 },
343 { 0.34938829797428606, 2, 2,
344 1.8849555921538759, 0.0 },
345 { 0.30666024065673214, 2, 2,
346 2.0420352248333655, 0.0 },
347 { 0.25281974746848856, 2, 2,
348 2.1991148575128552, 0.0 },
349 { 0.19313710101159498, 2, 2,
350 2.3561944901923448, 0.0 },
351 { 0.13345445455470123, 2, 2,
352 2.5132741228718345, 0.0 },
353 { 0.079613961366457764, 2, 2,
354 2.6703537555513241, 0.0 },
355 { 0.036885904048903809, 2, 2,
356 2.8274333882308138, 0.0 },
357 { 0.0094528025561623485, 2, 2,
358 2.9845130209103035, 0.0 },
359 { 0.0000000000000000, 2, 2,
360 3.1415926535897931, 0.0 },
361 };
362 const double toler006 = 5.0000000000000039e-13;
363
364 // Test data for l=5, m=0.
365 // max(|f - f_GSL|): 1.0547118733938987e-15 at index 18
366 // max(|f - f_GSL| / |f_GSL|): 2.9385557676213648e-15
367 // mean(f - f_GSL): -4.2955057500378082e-17
368 // variance(f - f_GSL): 9.6869690655191325e-35
369 // stddev(f - f_GSL): 9.8422401238331574e-18
370 const testcase_sph_legendre<double>
371 data007[21] =
372 {
373 { 0.93560257962738880, 5, 0,
374 0.0000000000000000, 0.0 },
375 { 0.77014422942079852, 5, 0,
376 0.15707963267948966, 0.0 },
377 { 0.35892185032365348, 5, 0,
378 0.31415926535897931, 0.0 },
379 { -0.090214932090594294, 5, 0,
380 0.47123889803846897, 0.0 },
381 { -0.36214460396518905, 5, 0,
382 0.62831853071795862, 0.0 },
383 { -0.35145955579226906, 5, 0,
384 0.78539816339744828, 0.0 },
385 { -0.11441703594725193, 5, 0,
386 0.94247779607693793, 0.0 },
387 { 0.17248966720808107, 5, 0,
388 1.0995574287564276, 0.0 },
389 { 0.32128384287200523, 5, 0,
390 1.2566370614359172, 0.0 },
391 { 0.24377632246714948, 5, 0,
392 1.4137166941154069, 0.0 },
393 { 1.0741712853887687e-16, 5, 0,
394 1.5707963267948966, 0.0 },
395 { -0.24377632246714936, 5, 0,
396 1.7278759594743862, 0.0 },
397 { -0.32128384287200534, 5, 0,
398 1.8849555921538759, 0.0 },
399 { -0.17248966720808118, 5, 0,
400 2.0420352248333655, 0.0 },
401 { 0.11441703594725151, 5, 0,
402 2.1991148575128552, 0.0 },
403 { 0.35145955579226895, 5, 0,
404 2.3561944901923448, 0.0 },
405 { 0.36214460396518883, 5, 0,
406 2.5132741228718345, 0.0 },
407 { 0.090214932090594752, 5, 0,
408 2.6703537555513241, 0.0 },
409 { -0.35892185032365165, 5, 0,
410 2.8274333882308138, 0.0 },
411 { -0.77014422942079852, 5, 0,
412 2.9845130209103035, 0.0 },
413 { -0.93560257962738880, 5, 0,
414 3.1415926535897931, 0.0 },
415 };
416 const double toler007 = 2.5000000000000020e-13;
417
418 // Test data for l=5, m=1.
419 // max(|f - f_GSL|): 3.3306690738754696e-15 at index 2
420 // max(|f - f_GSL| / |f_GSL|): 6.7265986294921411e-15
421 // mean(f - f_GSL): 6.3573485100559560e-16
422 // variance(f - f_GSL): 2.1218337041113107e-32
423 // stddev(f - f_GSL): 1.4566515383273072e-16
424 const testcase_sph_legendre<double>
425 data008[21] =
426 {
427 { 0.0000000000000000, 5, 1,
428 0.0000000000000000, 0.0 },
429 { -0.36712373713318402, 5, 1,
430 0.15707963267948966, 0.0 },
431 { -0.54610329010534708, 5, 1,
432 0.31415926535897931, 0.0 },
433 { -0.45381991493631763, 5, 1,
434 0.47123889803846897, 0.0 },
435 { -0.15679720635769906, 5, 1,
436 0.62831853071795862, 0.0 },
437 { 0.16985499419838601, 5, 1,
438 0.78539816339744828, 0.0 },
439 { 0.34468004499725169, 5, 1,
440 0.94247779607693793, 0.0 },
441 { 0.28349471119605985, 5, 1,
442 1.0995574287564276, 0.0 },
443 { 0.044286619339675815, 5, 1,
444 1.2566370614359172, 0.0 },
445 { -0.21193784177193470, 5, 1,
446 1.4137166941154069, 0.0 },
447 { -0.32028164857621527, 5, 1,
448 1.5707963267948966, 0.0 },
449 { -0.21193784177193487, 5, 1,
450 1.7278759594743862, 0.0 },
451 { 0.044286619339675592, 5, 1,
452 1.8849555921538759, 0.0 },
453 { 0.28349471119605973, 5, 1,
454 2.0420352248333655, 0.0 },
455 { 0.34468004499725174, 5, 1,
456 2.1991148575128552, 0.0 },
457 { 0.16985499419838640, 5, 1,
458 2.3561944901923448, 0.0 },
459 { -0.15679720635769961, 5, 1,
460 2.5132741228718345, 0.0 },
461 { -0.45381991493631768, 5, 1,
462 2.6703537555513241, 0.0 },
463 { -0.54610329010534753, 5, 1,
464 2.8274333882308138, 0.0 },
465 { -0.36712373713318402, 5, 1,
466 2.9845130209103035, 0.0 },
467 { 0.0000000000000000, 5, 1,
468 3.1415926535897931, 0.0 },
469 };
470 const double toler008 = 5.0000000000000039e-13;
471
472 // Test data for l=5, m=2.
473 // max(|f - f_GSL|): 2.6645352591003757e-15 at index 4
474 // max(|f - f_GSL| / |f_GSL|): 6.1144597746666128e-15
475 // mean(f - f_GSL): -4.3615904538845404e-17
476 // variance(f - f_GSL): 9.9873224258937960e-35
477 // stddev(f - f_GSL): 9.9936592026613535e-18
478 const testcase_sph_legendre<double>
479 data009[21] =
480 {
481 { 0.0000000000000000, 5, 2,
482 0.0000000000000000, 0.0 },
483 { 0.078919441745546909, 5, 2,
484 0.15707963267948966, 0.0 },
485 { 0.26373799140437948, 5, 2,
486 0.31415926535897931, 0.0 },
487 { 0.43002359842080096, 5, 2,
488 0.47123889803846897, 0.0 },
489 { 0.45642486439050983, 5, 2,
490 0.62831853071795862, 0.0 },
491 { 0.29959604906083298, 5, 2,
492 0.78539816339744828, 0.0 },
493 { 0.023781239849532509, 5, 2,
494 0.94247779607693793, 0.0 },
495 { -0.23313989334673826, 5, 2,
496 1.0995574287564276, 0.0 },
497 { -0.33799912776303714, 5, 2,
498 1.2566370614359172, 0.0 },
499 { -0.23964508489529746, 5, 2,
500 1.4137166941154069, 0.0 },
501 { -1.0377480524338157e-16, 5, 2,
502 1.5707963267948966, 0.0 },
503 { 0.23964508489529732, 5, 2,
504 1.7278759594743862, 0.0 },
505 { 0.33799912776303714, 5, 2,
506 1.8849555921538759, 0.0 },
507 { 0.23313989334673843, 5, 2,
508 2.0420352248333655, 0.0 },
509 { -0.023781239849531916, 5, 2,
510 2.1991148575128552, 0.0 },
511 { -0.29959604906083270, 5, 2,
512 2.3561944901923448, 0.0 },
513 { -0.45642486439050983, 5, 2,
514 2.5132741228718345, 0.0 },
515 { -0.43002359842080118, 5, 2,
516 2.6703537555513241, 0.0 },
517 { -0.26373799140437981, 5, 2,
518 2.8274333882308138, 0.0 },
519 { -0.078919441745546909, 5, 2,
520 2.9845130209103035, 0.0 },
521 { 0.0000000000000000, 5, 2,
522 3.1415926535897931, 0.0 },
523 };
524 const double toler009 = 5.0000000000000039e-13;
525
526 // Test data for l=5, m=5.
527 // max(|f - f_GSL|): 2.3869795029440866e-15 at index 10
528 // max(|f - f_GSL| / |f_GSL|): 5.4714279627676651e-15
529 // mean(f - f_GSL): 7.7966720691209837e-16
530 // variance(f - f_GSL): 3.1913750060540917e-32
531 // stddev(f - f_GSL): 1.7864419962747438e-16
532 const testcase_sph_legendre<double>
533 data010[21] =
534 {
535 { 0.0000000000000000, 5, 5,
536 0.0000000000000000, 0.0 },
537 { -4.3481439097910151e-05, 5, 5,
538 0.15707963267948966, 0.0 },
539 { -0.0013078367086431740, 5, 5,
540 0.31415926535897931, 0.0 },
541 { -0.0089510818191922761, 5, 5,
542 0.47123889803846897, 0.0 },
543 { -0.032563803777573910, 5, 5,
544 0.62831853071795862, 0.0 },
545 { -0.082047757105021241, 5, 5,
546 0.78539816339744828, 0.0 },
547 { -0.16085328164143806, 5, 5,
548 0.94247779607693793, 0.0 },
549 { -0.26064303436645381, 5, 5,
550 1.0995574287564276, 0.0 },
551 { -0.36113811790820571, 5, 5,
552 1.2566370614359172, 0.0 },
553 { -0.43625592459446139, 5, 5,
554 1.4137166941154069, 0.0 },
555 { -0.46413220344085809, 5, 5,
556 1.5707963267948966, 0.0 },
557 { -0.43625592459446144, 5, 5,
558 1.7278759594743862, 0.0 },
559 { -0.36113811790820577, 5, 5,
560 1.8849555921538759, 0.0 },
561 { -0.26064303436645381, 5, 5,
562 2.0420352248333655, 0.0 },
563 { -0.16085328164143822, 5, 5,
564 2.1991148575128552, 0.0 },
565 { -0.082047757105021310, 5, 5,
566 2.3561944901923448, 0.0 },
567 { -0.032563803777573896, 5, 5,
568 2.5132741228718345, 0.0 },
569 { -0.0089510818191923004, 5, 5,
570 2.6703537555513241, 0.0 },
571 { -0.0013078367086431812, 5, 5,
572 2.8274333882308138, 0.0 },
573 { -4.3481439097910151e-05, 5, 5,
574 2.9845130209103035, 0.0 },
575 { 0.0000000000000000, 5, 5,
576 3.1415926535897931, 0.0 },
577 };
578 const double toler010 = 5.0000000000000039e-13;
579
580 // Test data for l=10, m=0.
581 // max(|f - f_GSL|): 9.9920072216264089e-16 at index 18
582 // max(|f - f_GSL| / |f_GSL|): 4.3176588435352323e-15
583 // mean(f - f_GSL): 5.6171998269725183e-18
584 // variance(f - f_GSL): 1.6565290295473546e-36
585 // stddev(f - f_GSL): 1.2870621700397205e-18
586 const testcase_sph_legendre<double>
587 data011[21] =
588 {
589 { 1.2927207364566027, 10, 0,
590 0.0000000000000000, 0.0 },
591 { 0.55288895150522011, 10, 0,
592 0.15707963267948966, 0.0 },
593 { -0.44874428379711329, 10, 0,
594 0.31415926535897931, 0.0 },
595 { -0.25532095827149687, 10, 0,
596 0.47123889803846897, 0.0 },
597 { 0.36625249688013994, 10, 0,
598 0.62831853071795862, 0.0 },
599 { 0.14880806329084206, 10, 0,
600 0.78539816339744828, 0.0 },
601 { -0.33533356797848740, 10, 0,
602 0.94247779607693793, 0.0 },
603 { -0.080639967662335665, 10, 0,
604 1.0995574287564276, 0.0 },
605 { 0.32197986450174521, 10, 0,
606 1.2566370614359172, 0.0 },
607 { 0.025713542103667848, 10, 0,
608 1.4137166941154069, 0.0 },
609 { -0.31813049373736707, 10, 0,
610 1.5707963267948966, 0.0 },
611 { 0.025713542103667528, 10, 0,
612 1.7278759594743862, 0.0 },
613 { 0.32197986450174543, 10, 0,
614 1.8849555921538759, 0.0 },
615 { -0.080639967662335416, 10, 0,
616 2.0420352248333655, 0.0 },
617 { -0.33533356797848757, 10, 0,
618 2.1991148575128552, 0.0 },
619 { 0.14880806329084156, 10, 0,
620 2.3561944901923448, 0.0 },
621 { 0.36625249688013961, 10, 0,
622 2.5132741228718345, 0.0 },
623 { -0.25532095827149576, 10, 0,
624 2.6703537555513241, 0.0 },
625 { -0.44874428379711545, 10, 0,
626 2.8274333882308138, 0.0 },
627 { 0.55288895150522011, 10, 0,
628 2.9845130209103035, 0.0 },
629 { 1.2927207364566027, 10, 0,
630 3.1415926535897931, 0.0 },
631 };
632 const double toler011 = 2.5000000000000020e-13;
633
634 // Test data for l=10, m=1.
635 // max(|f - f_GSL|): 6.2172489379008766e-15 at index 1
636 // max(|f - f_GSL| / |f_GSL|): 1.0515246092567303e-14
637 // mean(f - f_GSL): -3.3042351923367698e-17
638 // variance(f - f_GSL): 5.7319343582953255e-35
639 // stddev(f - f_GSL): 7.5709539414101082e-18
640 const testcase_sph_legendre<double>
641 data012[21] =
642 {
643 { 0.0000000000000000, 10, 1,
644 0.0000000000000000, 0.0 },
645 { -0.74373723919064050, 10, 1,
646 0.15707963267948966, 0.0 },
647 { -0.29035110456209651, 10, 1,
648 0.31415926535897931, 0.0 },
649 { 0.42219282075271530, 10, 1,
650 0.47123889803846897, 0.0 },
651 { 0.17109256898931161, 10, 1,
652 0.62831853071795862, 0.0 },
653 { -0.35583574648544281, 10, 1,
654 0.78539816339744828, 0.0 },
655 { -0.10089212303544023, 10, 1,
656 0.94247779607693793, 0.0 },
657 { 0.32997652649321085, 10, 1,
658 1.0995574287564276, 0.0 },
659 { 0.047416376890032939, 10, 1,
660 1.2566370614359172, 0.0 },
661 { -0.31999356750295660, 10, 1,
662 1.4137166941154069, 0.0 },
663 { -2.0430664782290742e-16, 10, 1,
664 1.5707963267948966, 0.0 },
665 { 0.31999356750295660, 10, 1,
666 1.7278759594743862, 0.0 },
667 { -0.047416376890032544, 10, 1,
668 1.8849555921538759, 0.0 },
669 { -0.32997652649321096, 10, 1,
670 2.0420352248333655, 0.0 },
671 { 0.10089212303543935, 10, 1,
672 2.1991148575128552, 0.0 },
673 { 0.35583574648544292, 10, 1,
674 2.3561944901923448, 0.0 },
675 { -0.17109256898931269, 10, 1,
676 2.5132741228718345, 0.0 },
677 { -0.42219282075271569, 10, 1,
678 2.6703537555513241, 0.0 },
679 { 0.29035110456209601, 10, 1,
680 2.8274333882308138, 0.0 },
681 { 0.74373723919064050, 10, 1,
682 2.9845130209103035, 0.0 },
683 { 0.0000000000000000, 10, 1,
684 3.1415926535897931, 0.0 },
685 };
686 const double toler012 = 1.0000000000000008e-12;
687
688 // Test data for l=10, m=2.
689 // max(|f - f_GSL|): 3.3306690738754696e-15 at index 2
690 // max(|f - f_GSL| / |f_GSL|): 7.9132043938587384e-15
691 // mean(f - f_GSL): -3.3504944850294902e-16
692 // variance(f - f_GSL): 5.8935519794618406e-33
693 // stddev(f - f_GSL): 7.6769472965898634e-17
694 const testcase_sph_legendre<double>
695 data013[21] =
696 {
697 { 0.0000000000000000, 10, 2,
698 0.0000000000000000, 0.0 },
699 { 0.34571695599980556, 10, 2,
700 0.15707963267948966, 0.0 },
701 { 0.62485535978198148, 10, 2,
702 0.31415926535897931, 0.0 },
703 { 0.098210039644716252, 10, 2,
704 0.47123889803846897, 0.0 },
705 { -0.41494799233049695, 10, 2,
706 0.62831853071795862, 0.0 },
707 { -0.081698973831472732, 10, 2,
708 0.78539816339744828, 0.0 },
709 { 0.35253132222271277, 10, 2,
710 0.94247779607693793, 0.0 },
711 { 0.049026298555980979, 10, 2,
712 1.0995574287564276, 0.0 },
713 { -0.32791246874130792, 10, 2,
714 1.2566370614359172, 0.0 },
715 { -0.016196782433946871, 10, 2,
716 1.4137166941154069, 0.0 },
717 { 0.32106263400438334, 10, 2,
718 1.5707963267948966, 0.0 },
719 { -0.016196782433946497, 10, 2,
720 1.7278759594743862, 0.0 },
721 { -0.32791246874130803, 10, 2,
722 1.8849555921538759, 0.0 },
723 { 0.049026298555980730, 10, 2,
724 2.0420352248333655, 0.0 },
725 { 0.35253132222271266, 10, 2,
726 2.1991148575128552, 0.0 },
727 { -0.081698973831472121, 10, 2,
728 2.3561944901923448, 0.0 },
729 { -0.41494799233049684, 10, 2,
730 2.5132741228718345, 0.0 },
731 { 0.098210039644715197, 10, 2,
732 2.6703537555513241, 0.0 },
733 { 0.62485535978198081, 10, 2,
734 2.8274333882308138, 0.0 },
735 { 0.34571695599980556, 10, 2,
736 2.9845130209103035, 0.0 },
737 { 0.0000000000000000, 10, 2,
738 3.1415926535897931, 0.0 },
739 };
740 const double toler013 = 5.0000000000000039e-13;
741
742 // Test data for l=10, m=5.
743 // max(|f - f_GSL|): 2.8310687127941492e-15 at index 4
744 // max(|f - f_GSL| / |f_GSL|): 6.7700052018114004e-15
745 // mean(f - f_GSL): 3.8329128231106644e-17
746 // variance(f - f_GSL): 7.7128908725222343e-35
747 // stddev(f - f_GSL): 8.7823065720357509e-18
748 const testcase_sph_legendre<double>
749 data014[21] =
750 {
751 { 0.0000000000000000, 10, 5,
752 0.0000000000000000, 0.0 },
753 { -0.0030300124052750873, 10, 5,
754 0.15707963267948966, 0.0 },
755 { -0.070348585248056511, 10, 5,
756 0.31415926535897931, 0.0 },
757 { -0.30055029290703639, 10, 5,
758 0.47123889803846897, 0.0 },
759 { -0.49987818144009138, 10, 5,
760 0.62831853071795862, 0.0 },
761 { -0.28108771757150108, 10, 5,
762 0.78539816339744828, 0.0 },
763 { 0.22068081187249255, 10, 5,
764 0.94247779607693793, 0.0 },
765 { 0.33689502212592121, 10, 5,
766 1.0995574287564276, 0.0 },
767 { -0.086095515520764110, 10, 5,
768 1.2566370614359172, 0.0 },
769 { -0.33935827318511558, 10, 5,
770 1.4137166941154069, 0.0 },
771 { -1.9213014340664546e-16, 10, 5,
772 1.5707963267948966, 0.0 },
773 { 0.33935827318511558, 10, 5,
774 1.7278759594743862, 0.0 },
775 { 0.086095515520764512, 10, 5,
776 1.8849555921538759, 0.0 },
777 { -0.33689502212592104, 10, 5,
778 2.0420352248333655, 0.0 },
779 { -0.22068081187249344, 10, 5,
780 2.1991148575128552, 0.0 },
781 { 0.28108771757150064, 10, 5,
782 2.3561944901923448, 0.0 },
783 { 0.49987818144009155, 10, 5,
784 2.5132741228718345, 0.0 },
785 { 0.30055029290703672, 10, 5,
786 2.6703537555513241, 0.0 },
787 { 0.070348585248056802, 10, 5,
788 2.8274333882308138, 0.0 },
789 { 0.0030300124052750873, 10, 5,
790 2.9845130209103035, 0.0 },
791 { 0.0000000000000000, 10, 5,
792 3.1415926535897931, 0.0 },
793 };
794 const double toler014 = 5.0000000000000039e-13;
795
796 // Test data for l=10, m=10.
797 // max(|f - f_GSL|): 2.8865798640254070e-15 at index 10
798 // max(|f - f_GSL| / |f_GSL|): 5.5362170773729674e-15
799 // mean(f - f_GSL): -6.6245801611758948e-16
800 // variance(f - f_GSL): 2.3039657713718755e-32
801 // stddev(f - f_GSL): 1.5178820017945649e-16
802 const testcase_sph_legendre<double>
803 data015[21] =
804 {
805 { 0.0000000000000000, 10, 10,
806 0.0000000000000000, 0.0 },
807 { 4.7624282733345673e-09, 10, 10,
808 0.15707963267948966, 0.0 },
809 { 4.3085156534549315e-06, 10, 10,
810 0.31415926535897931, 0.0 },
811 { 0.00020182347649472387, 10, 10,
812 0.47123889803846897, 0.0 },
813 { 0.0026711045506511706, 10, 10,
814 0.62831853071795862, 0.0 },
815 { 0.016957196623256909, 10, 10,
816 0.78539816339744828, 0.0 },
817 { 0.065174916004990271, 10, 10,
818 0.94247779607693793, 0.0 },
819 { 0.17112476903017845, 10, 10,
820 1.0995574287564276, 0.0 },
821 { 0.32852414199733554, 10, 10,
822 1.2566370614359172, 0.0 },
823 { 0.47940582314838287, 10, 10,
824 1.4137166941154069, 0.0 },
825 { 0.54263029194422152, 10, 10,
826 1.5707963267948966, 0.0 },
827 { 0.47940582314838293, 10, 10,
828 1.7278759594743862, 0.0 },
829 { 0.32852414199733571, 10, 10,
830 1.8849555921538759, 0.0 },
831 { 0.17112476903017851, 10, 10,
832 2.0420352248333655, 0.0 },
833 { 0.065174916004990410, 10, 10,
834 2.1991148575128552, 0.0 },
835 { 0.016957196623256943, 10, 10,
836 2.3561944901923448, 0.0 },
837 { 0.0026711045506511684, 10, 10,
838 2.5132741228718345, 0.0 },
839 { 0.00020182347649472493, 10, 10,
840 2.6703537555513241, 0.0 },
841 { 4.3085156534549772e-06, 10, 10,
842 2.8274333882308138, 0.0 },
843 { 4.7624282733345673e-09, 10, 10,
844 2.9845130209103035, 0.0 },
845 { 0.0000000000000000, 10, 10,
846 3.1415926535897931, 0.0 },
847 };
848 const double toler015 = 5.0000000000000039e-13;
849
850 // Test data for l=20, m=0.
851 // max(|f - f_GSL|): 1.2212453270876722e-15 at index 1
852 // max(|f - f_GSL| / |f_GSL|): 2.0731910827878347e-15
853 // mean(f - f_GSL): 1.1102230246251565e-16
854 // variance(f - f_GSL): 6.4711246131411122e-34
855 // stddev(f - f_GSL): 2.5438405243138007e-17
856 const testcase_sph_legendre<double>
857 data016[21] =
858 {
859 { 1.8062879984608917, 20, 0,
860 0.0000000000000000, 0.0 },
861 { -0.58906549291416732, 20, 0,
862 0.15707963267948966, 0.0 },
863 { 0.45624611402342063, 20, 0,
864 0.31415926535897931, 0.0 },
865 { -0.39955402700466724, 20, 0,
866 0.47123889803846897, 0.0 },
867 { 0.36818552901640805, 20, 0,
868 0.62831853071795862, 0.0 },
869 { -0.34873131330857743, 20, 0,
870 0.78539816339744828, 0.0 },
871 { 0.33600882829186468, 20, 0,
872 0.94247779607693793, 0.0 },
873 { -0.32759286308122931, 20, 0,
874 1.0995574287564276, 0.0 },
875 { 0.32222458068091325, 20, 0,
876 1.2566370614359172, 0.0 },
877 { -0.31922731037135965, 20, 0,
878 1.4137166941154069, 0.0 },
879 { 0.31826262039531755, 20, 0,
880 1.5707963267948966, 0.0 },
881 { -0.31922731037135971, 20, 0,
882 1.7278759594743862, 0.0 },
883 { 0.32222458068091342, 20, 0,
884 1.8849555921538759, 0.0 },
885 { -0.32759286308122926, 20, 0,
886 2.0420352248333655, 0.0 },
887 { 0.33600882829186518, 20, 0,
888 2.1991148575128552, 0.0 },
889 { -0.34873131330857782, 20, 0,
890 2.3561944901923448, 0.0 },
891 { 0.36818552901640772, 20, 0,
892 2.5132741228718345, 0.0 },
893 { -0.39955402700466824, 20, 0,
894 2.6703537555513241, 0.0 },
895 { 0.45624611402342408, 20, 0,
896 2.8274333882308138, 0.0 },
897 { -0.58906549291416732, 20, 0,
898 2.9845130209103035, 0.0 },
899 { 1.8062879984608917, 20, 0,
900 3.1415926535897931, 0.0 },
901 };
902 const double toler016 = 2.5000000000000020e-13;
903
904 // Test data for l=20, m=1.
905 // max(|f - f_GSL|): 6.2727600891321345e-15 at index 1
906 // max(|f - f_GSL| / |f_GSL|): 1.3664592043119372e-14
907 // mean(f - f_GSL): 2.8416422654096149e-17
908 // variance(f - f_GSL): 4.2393386513952014e-35
909 // stddev(f - f_GSL): 6.5110203896126770e-18
910 const testcase_sph_legendre<double>
911 data017[21] =
912 {
913 { 0.0000000000000000, 20, 1,
914 0.0000000000000000, 0.0 },
915 { -0.45905213045059046, 20, 1,
916 0.15707963267948966, 0.0 },
917 { 0.31166370423309414, 20, 1,
918 0.31415926535897931, 0.0 },
919 { -0.23278757741246778, 20, 1,
920 0.47123889803846897, 0.0 },
921 { 0.17937240823503983, 20, 1,
922 0.62831853071795862, 0.0 },
923 { -0.13857299972299839, 20, 1,
924 0.78539816339744828, 0.0 },
925 { 0.10495324841927815, 20, 1,
926 0.94247779607693793, 0.0 },
927 { -0.075707774352163665, 20, 1,
928 1.0995574287564276, 0.0 },
929 { 0.049168697683476224, 20, 1,
930 1.2566370614359172, 0.0 },
931 { -0.024216050551253303, 20, 1,
932 1.4137166941154069, 0.0 },
933 { 3.9938443510694310e-16, 20, 1,
934 1.5707963267948966, 0.0 },
935 { 0.024216050551252380, 20, 1,
936 1.7278759594743862, 0.0 },
937 { -0.049168697683475482, 20, 1,
938 1.8849555921538759, 0.0 },
939 { 0.075707774352163346, 20, 1,
940 2.0420352248333655, 0.0 },
941 { -0.10495324841927638, 20, 1,
942 2.1991148575128552, 0.0 },
943 { 0.13857299972299741, 20, 1,
944 2.3561944901923448, 0.0 },
945 { -0.17937240823504172, 20, 1,
946 2.5132741228718345, 0.0 },
947 { 0.23278757741246703, 20, 1,
948 2.6703537555513241, 0.0 },
949 { -0.31166370423309253, 20, 1,
950 2.8274333882308138, 0.0 },
951 { 0.45905213045059046, 20, 1,
952 2.9845130209103035, 0.0 },
953 { 0.0000000000000000, 20, 1,
954 3.1415926535897931, 0.0 },
955 };
956 const double toler017 = 1.0000000000000008e-12;
957
958 // Test data for l=20, m=2.
959 // max(|f - f_GSL|): 3.2196467714129540e-15 at index 2
960 // max(|f - f_GSL| / |f_GSL|): 7.1072009465107655e-15
961 // mean(f - f_GSL): 9.2518585385429716e-17
962 // variance(f - f_GSL): 4.4938365369035506e-34
963 // stddev(f - f_GSL): 2.1198671035948340e-17
964 const testcase_sph_legendre<double>
965 data018[21] =
966 {
967 { 0.0000000000000000, 20, 2,
968 0.0000000000000000, 0.0 },
969 { 0.87399805141574205, 20, 2,
970 0.15707963267948966, 0.0 },
971 { -0.55116854080894906, 20, 2,
972 0.31415926535897931, 0.0 },
973 { 0.44520137308557572, 20, 2,
974 0.47123889803846897, 0.0 },
975 { -0.39321637877908278, 20, 2,
976 0.62831853071795862, 0.0 },
977 { 0.36312025711350954, 20, 2,
978 0.78539816339744828, 0.0 },
979 { -0.34427103004873089, 20, 2,
980 0.94247779607693793, 0.0 },
981 { 0.33214917638387642, 20, 2,
982 1.0995574287564276, 0.0 },
983 { -0.32455734448839091, 20, 2,
984 1.2566370614359172, 0.0 },
985 { 0.32036529628513255, 20, 2,
986 1.4137166941154069, 0.0 },
987 { -0.31902310563819986, 20, 2,
988 1.5707963267948966, 0.0 },
989 { 0.32036529628513261, 20, 2,
990 1.7278759594743862, 0.0 },
991 { -0.32455734448839102, 20, 2,
992 1.8849555921538759, 0.0 },
993 { 0.33214917638387659, 20, 2,
994 2.0420352248333655, 0.0 },
995 { -0.34427103004873105, 20, 2,
996 2.1991148575128552, 0.0 },
997 { 0.36312025711350981, 20, 2,
998 2.3561944901923448, 0.0 },
999 { -0.39321637877908228, 20, 2,
1000 2.5132741228718345, 0.0 },
1001 { 0.44520137308557650, 20, 2,
1002 2.6703537555513241, 0.0 },
1003 { -0.55116854080895039, 20, 2,
1004 2.8274333882308138, 0.0 },
1005 { 0.87399805141574205, 20, 2,
1006 2.9845130209103035, 0.0 },
1007 { 0.0000000000000000, 20, 2,
1008 3.1415926535897931, 0.0 },
1009 };
1010 const double toler018 = 5.0000000000000039e-13;
1011
1012 // Test data for l=20, m=5.
1013 // max(|f - f_GSL|): 3.7747582837255322e-15 at index 2
1014 // max(|f - f_GSL| / |f_GSL|): 2.9846361325102863e-14
1015 // mean(f - f_GSL): -1.9825411154020758e-17
1016 // variance(f - f_GSL): 2.0634963689863462e-35
1017 // stddev(f - f_GSL): 4.5425723648460969e-18
1018 const testcase_sph_legendre<double>
1019 data019[21] =
1020 {
1021 { 0.0000000000000000, 20, 5,
1022 0.0000000000000000, 0.0 },
1023 { -0.10024848623505046, 20, 5,
1024 0.15707963267948966, 0.0 },
1025 { -0.68115361075940650, 20, 5,
1026 0.31415926535897931, 0.0 },
1027 { 0.31774532551156298, 20, 5,
1028 0.47123889803846897, 0.0 },
1029 { -0.16011868165390658, 20, 5,
1030 0.62831853071795862, 0.0 },
1031 { 0.085844143304115578, 20, 5,
1032 0.78539816339744828, 0.0 },
1033 { -0.047467540840863798, 20, 5,
1034 0.94247779607693793, 0.0 },
1035 { 0.026283575189471796, 20, 5,
1036 1.0995574287564276, 0.0 },
1037 { -0.013891104052597688, 20, 5,
1038 1.2566370614359172, 0.0 },
1039 { 0.0059873308239496957, 20, 5,
1040 1.4137166941154069, 0.0 },
1041 { 3.9355286582083051e-16, 20, 5,
1042 1.5707963267948966, 0.0 },
1043 { -0.0059873308239503324, 20, 5,
1044 1.7278759594743862, 0.0 },
1045 { 0.013891104052598547, 20, 5,
1046 1.8849555921538759, 0.0 },
1047 { -0.026283575189472153, 20, 5,
1048 2.0420352248333655, 0.0 },
1049 { 0.047467540840865928, 20, 5,
1050 2.1991148575128552, 0.0 },
1051 { -0.085844143304117007, 20, 5,
1052 2.3561944901923448, 0.0 },
1053 { 0.16011868165390544, 20, 5,
1054 2.5132741228718345, 0.0 },
1055 { -0.31774532551156381, 20, 5,
1056 2.6703537555513241, 0.0 },
1057 { 0.68115361075940484, 20, 5,
1058 2.8274333882308138, 0.0 },
1059 { 0.10024848623505046, 20, 5,
1060 2.9845130209103035, 0.0 },
1061 { 0.0000000000000000, 20, 5,
1062 3.1415926535897931, 0.0 },
1063 };
1064 const double toler019 = 2.5000000000000015e-12;
1065
1066 // Test data for l=20, m=10.
1067 // max(|f - f_GSL|): 2.3314683517128287e-15 at index 4
1068 // max(|f - f_GSL| / |f_GSL|): 1.0575432165608034e-14
1069 // mean(f - f_GSL): -1.4002922808555493e-16
1070 // variance(f - f_GSL): 1.0294296977074090e-33
1071 // stddev(f - f_GSL): 3.2084726860414586e-17
1072 const testcase_sph_legendre<double>
1073 data020[21] =
1074 {
1075 { 0.0000000000000000, 20, 10,
1076 0.0000000000000000, 0.0 },
1077 { 3.0595797603707888e-05, 20, 10,
1078 0.15707963267948966, 0.0 },
1079 { 0.015924453916396863, 20, 10,
1080 0.31415926535897931, 0.0 },
1081 { 0.26588079118745744, 20, 10,
1082 0.47123889803846897, 0.0 },
1083 { 0.54045081420686736, 20, 10,
1084 0.62831853071795862, 0.0 },
1085 { -0.28215279394285531, 20, 10,
1086 0.78539816339744828, 0.0 },
1087 { 0.0085297337582239223, 20, 10,
1088 0.94247779607693793, 0.0 },
1089 { 0.16930127953533738, 20, 10,
1090 1.0995574287564276, 0.0 },
1091 { -0.27215134048018325, 20, 10,
1092 1.2566370614359172, 0.0 },
1093 { 0.32456597088029526, 20, 10,
1094 1.4137166941154069, 0.0 },
1095 { -0.34057893241353715, 20, 10,
1096 1.5707963267948966, 0.0 },
1097 { 0.32456597088029493, 20, 10,
1098 1.7278759594743862, 0.0 },
1099 { -0.27215134048018291, 20, 10,
1100 1.8849555921538759, 0.0 },
1101 { 0.16930127953533702, 20, 10,
1102 2.0420352248333655, 0.0 },
1103 { 0.0085297337582257438, 20, 10,
1104 2.1991148575128552, 0.0 },
1105 { -0.28215279394285619, 20, 10,
1106 2.3561944901923448, 0.0 },
1107 { 0.54045081420686869, 20, 10,
1108 2.5132741228718345, 0.0 },
1109 { 0.26588079118745828, 20, 10,
1110 2.6703537555513241, 0.0 },
1111 { 0.015924453916397002, 20, 10,
1112 2.8274333882308138, 0.0 },
1113 { 3.0595797603707888e-05, 20, 10,
1114 2.9845130209103035, 0.0 },
1115 { 0.0000000000000000, 20, 10,
1116 3.1415926535897931, 0.0 },
1117 };
1118 const double toler020 = 1.0000000000000008e-12;
1119
1120 // Test data for l=20, m=20.
1121 // max(|f - f_GSL|): 2.6645352591003757e-15 at index 10
1122 // max(|f - f_GSL| / |f_GSL|): 4.5133454703584717e-15
1123 // mean(f - f_GSL): -4.3857545834694365e-16
1124 // variance(f - f_GSL): 1.0098292714872165e-32
1125 // stddev(f - f_GSL): 1.0049026179124106e-16
1126 const testcase_sph_legendre<double>
1127 data021[21] =
1128 {
1129 { 0.0000000000000000, 20, 20,
1130 0.0000000000000000, 0.0 },
1131 { 4.9264471419250786e-17, 20, 20,
1132 0.15707963267948966, 0.0 },
1133 { 4.0321091681530921e-11, 20, 20,
1134 0.31415926535897931, 0.0 },
1135 { 8.8474944184471664e-08, 20, 20,
1136 0.47123889803846897, 0.0 },
1137 { 1.5497395129387791e-05, 20, 20,
1138 0.62831853071795862, 0.0 },
1139 { 0.00062457564282984495, 20, 20,
1140 0.78539816339744828, 0.0 },
1141 { 0.0092265192458967308, 20, 20,
1142 0.94247779607693793, 0.0 },
1143 { 0.063606673236323297, 20, 20,
1144 1.0995574287564276, 0.0 },
1145 { 0.23442909509776316, 20, 20,
1146 1.2566370614359172, 0.0 },
1147 { 0.49921030481087009, 20, 20,
1148 1.4137166941154069, 0.0 },
1149 { 0.63956545825776223, 20, 20,
1150 1.5707963267948966, 0.0 },
1151 { 0.49921030481087025, 20, 20,
1152 1.7278759594743862, 0.0 },
1153 { 0.23442909509776336, 20, 20,
1154 1.8849555921538759, 0.0 },
1155 { 0.063606673236323324, 20, 20,
1156 2.0420352248333655, 0.0 },
1157 { 0.0092265192458967742, 20, 20,
1158 2.1991148575128552, 0.0 },
1159 { 0.00062457564282984766, 20, 20,
1160 2.3561944901923448, 0.0 },
1161 { 1.5497395129387764e-05, 20, 20,
1162 2.5132741228718345, 0.0 },
1163 { 8.8474944184472617e-08, 20, 20,
1164 2.6703537555513241, 0.0 },
1165 { 4.0321091681531780e-11, 20, 20,
1166 2.8274333882308138, 0.0 },
1167 { 4.9264471419250786e-17, 20, 20,
1168 2.9845130209103035, 0.0 },
1169 { 0.0000000000000000, 20, 20,
1170 3.1415926535897931, 0.0 },
1171 };
1172 const double toler021 = 2.5000000000000020e-13;
1173
1174 // Test data for l=50, m=0.
1175 // max(|f - f_GSL|): 4.8849813083506888e-15 at index 1
1176 // max(|f - f_GSL| / |f_GSL|): 9.1896305557688689e-15
1177 // mean(f - f_GSL): -4.0592529337857286e-16
1178 // variance(f - f_GSL): 8.6507055497352237e-33
1179 // stddev(f - f_GSL): 9.3009169170223341e-17
1180 const testcase_sph_legendre<double>
1181 data022[21] =
1182 {
1183 { 2.8350175706934717, 50, 0,
1184 0.0000000000000000, 0.0 },
1185 { 0.53157537495172758, 50, 0,
1186 0.15707963267948966, 0.0 },
1187 { -0.46056183476300561, 50, 0,
1188 0.31415926535897931, 0.0 },
1189 { -0.24876032079677909, 50, 0,
1190 0.47123889803846897, 0.0 },
1191 { 0.36926172901532667, 50, 0,
1192 0.62831853071795862, 0.0 },
1193 { 0.14571730283563575, 50, 0,
1194 0.78539816339744828, 0.0 },
1195 { -0.33636199170850750, 50, 0,
1196 0.94247779607693793, 0.0 },
1197 { -0.079132716267091507, 50, 0,
1198 1.0995574287564276, 0.0 },
1199 { 0.32232921941301451, 50, 0,
1200 1.2566370614359172, 0.0 },
1201 { 0.025253991969481544, 50, 0,
1202 1.4137166941154069, 0.0 },
1203 { -0.31830208724152359, 50, 0,
1204 1.5707963267948966, 0.0 },
1205 { 0.025253991969479882, 50, 0,
1206 1.7278759594743862, 0.0 },
1207 { 0.32232921941301479, 50, 0,
1208 1.8849555921538759, 0.0 },
1209 { -0.079132716267090064, 50, 0,
1210 2.0420352248333655, 0.0 },
1211 { -0.33636199170850883, 50, 0,
1212 2.1991148575128552, 0.0 },
1213 { 0.14571730283563347, 50, 0,
1214 2.3561944901923448, 0.0 },
1215 { 0.36926172901532522, 50, 0,
1216 2.5132741228718345, 0.0 },
1217 { -0.24876032079677354, 50, 0,
1218 2.6703537555513241, 0.0 },
1219 { -0.46056183476301255, 50, 0,
1220 2.8274333882308138, 0.0 },
1221 { 0.53157537495172758, 50, 0,
1222 2.9845130209103035, 0.0 },
1223 { 2.8350175706934717, 50, 0,
1224 3.1415926535897931, 0.0 },
1225 };
1226 const double toler022 = 5.0000000000000039e-13;
1227
1228 // Test data for l=50, m=1.
1229 // max(|f - f_GSL|): 7.8825834748386114e-15 at index 1
1230 // max(|f - f_GSL| / |f_GSL|): 1.6168319946399610e-14
1231 // mean(f - f_GSL): -8.8223079635391627e-17
1232 // variance(f - f_GSL): 4.0862386846851427e-34
1233 // stddev(f - f_GSL): 2.0214447023564960e-17
1234 const testcase_sph_legendre<double>
1235 data023[21] =
1236 {
1237 { 0.0000000000000000, 50, 1,
1238 0.0000000000000000, 0.0 },
1239 { -0.63751752155228247, 50, 1,
1240 0.15707963267948966, 0.0 },
1241 { -0.32616619317605133, 50, 1,
1242 0.31415926535897931, 0.0 },
1243 { 0.40649930826162850, 50, 1,
1244 0.47123889803846897, 0.0 },
1245 { 0.18473991408343635, 50, 1,
1246 0.62831853071795862, 0.0 },
1247 { -0.35083930302013117, 50, 1,
1248 0.78539816339744828, 0.0 },
1249 { -0.10755382110947342, 50, 1,
1250 0.94247779607693793, 0.0 },
1251 { 0.32822568316499900, 50, 1,
1252 1.0995574287564276, 0.0 },
1253 { 0.050286056609797389, 50, 1,
1254 1.2566370614359172, 0.0 },
1255 { -0.31935368562159644, 50, 1,
1256 1.4137166941154069, 0.0 },
1257 { -9.8421602686195843e-16, 50, 1,
1258 1.5707963267948966, 0.0 },
1259 { 0.31935368562159649, 50, 1,
1260 1.7278759594743862, 0.0 },
1261 { -0.050286056609795446, 50, 1,
1262 1.8849555921538759, 0.0 },
1263 { -0.32822568316499923, 50, 1,
1264 2.0420352248333655, 0.0 },
1265 { 0.10755382110946902, 50, 1,
1266 2.1991148575128552, 0.0 },
1267 { 0.35083930302013205, 50, 1,
1268 2.3561944901923448, 0.0 },
1269 { -0.18473991408344057, 50, 1,
1270 2.5132741228718345, 0.0 },
1271 { -0.40649930826163011, 50, 1,
1272 2.6703537555513241, 0.0 },
1273 { 0.32616619317604606, 50, 1,
1274 2.8274333882308138, 0.0 },
1275 { 0.63751752155228247, 50, 1,
1276 2.9845130209103035, 0.0 },
1277 { 0.0000000000000000, 50, 1,
1278 3.1415926535897931, 0.0 },
1279 };
1280 const double toler023 = 1.0000000000000008e-12;
1281
1282 // Test data for l=50, m=2.
1283 // max(|f - f_GSL|): 3.7747582837255322e-15 at index 1
1284 // max(|f - f_GSL| / |f_GSL|): 1.3049193367556654e-14
1285 // mean(f - f_GSL): 2.4038311024250043e-16
1286 // variance(f - f_GSL): 3.0336620837175507e-33
1287 // stddev(f - f_GSL): 5.5078689923758629e-17
1288 const testcase_sph_legendre<double>
1289 data024[21] =
1290 {
1291 { 0.0000000000000000, 50, 2,
1292 0.0000000000000000, 0.0 },
1293 { -0.37230261163836259, 50, 2,
1294 0.15707963267948966, 0.0 },
1295 { 0.50051599680315517, 50, 2,
1296 0.31415926535897931, 0.0 },
1297 { 0.21724795180329495, 50, 2,
1298 0.47123889803846897, 0.0 },
1299 { -0.37948127307611107, 50, 2,
1300 0.62831853071795862, 0.0 },
1301 { -0.13187372121003413, 50, 2,
1302 0.78539816339744828, 0.0 },
1303 { 0.33959009162400128, 50, 2,
1304 0.94247779607693793, 0.0 },
1305 { 0.072537503112489563, 50, 2,
1306 1.0995574287564276, 0.0 },
1307 { -0.32310306941855266, 50, 2,
1308 1.2566370614359172, 0.0 },
1309 { -0.023259822816436636, 50, 2,
1310 1.4137166941154069, 0.0 },
1311 { 0.31842698506357275, 50, 2,
1312 1.5707963267948966, 0.0 },
1313 { -0.023259822816434638, 50, 2,
1314 1.7278759594743862, 0.0 },
1315 { -0.32310306941855316, 50, 2,
1316 1.8849555921538759, 0.0 },
1317 { 0.072537503112488411, 50, 2,
1318 2.0420352248333655, 0.0 },
1319 { 0.33959009162400267, 50, 2,
1320 2.1991148575128552, 0.0 },
1321 { -0.13187372121003124, 50, 2,
1322 2.3561944901923448, 0.0 },
1323 { -0.37948127307610924, 50, 2,
1324 2.5132741228718345, 0.0 },
1325 { 0.21724795180329090, 50, 2,
1326 2.6703537555513241, 0.0 },
1327 { 0.50051599680316095, 50, 2,
1328 2.8274333882308138, 0.0 },
1329 { -0.37230261163836259, 50, 2,
1330 2.9845130209103035, 0.0 },
1331 { 0.0000000000000000, 50, 2,
1332 3.1415926535897931, 0.0 },
1333 };
1334 const double toler024 = 1.0000000000000008e-12;
1335
1336 // Test data for l=50, m=5.
1337 // max(|f - f_GSL|): 6.4254157550180935e-15 at index 18
1338 // max(|f - f_GSL| / |f_GSL|): 8.3058098108785765e-14
1339 // mean(f - f_GSL): 3.9419525844577751e-16
1340 // variance(f - f_GSL): 8.1579698435094999e-33
1341 // stddev(f - f_GSL): 9.0321480521022794e-17
1342 const testcase_sph_legendre<double>
1343 data025[21] =
1344 {
1345 { 0.0000000000000000, 50, 5,
1346 0.0000000000000000, 0.0 },
1347 { -0.57750385903191603, 50, 5,
1348 0.15707963267948966, 0.0 },
1349 { 0.077360497065570286, 50, 5,
1350 0.31415926535897931, 0.0 },
1351 { 0.47707267400540226, 50, 5,
1352 0.47123889803846897, 0.0 },
1353 { 0.055370615126626811, 50, 5,
1354 0.62831853071795862, 0.0 },
1355 { -0.37629451847202833, 50, 5,
1356 0.78539816339744828, 0.0 },
1357 { -0.048042277801963115, 50, 5,
1358 0.94247779607693793, 0.0 },
1359 { 0.33619379362228718, 50, 5,
1360 1.0995574287564276, 0.0 },
1361 { 0.025265227185718764, 50, 5,
1362 1.2566370614359172, 0.0 },
1363 { -0.32083679430964535, 50, 5,
1364 1.4137166941154069, 0.0 },
1365 { -9.8189201019751726e-16, 50, 5,
1366 1.5707963267948966, 0.0 },
1367 { 0.32083679430964546, 50, 5,
1368 1.7278759594743862, 0.0 },
1369 { -0.025265227185716790, 50, 5,
1370 1.8849555921538759, 0.0 },
1371 { -0.33619379362228730, 50, 5,
1372 2.0420352248333655, 0.0 },
1373 { 0.048042277801958064, 50, 5,
1374 2.1991148575128552, 0.0 },
1375 { 0.37629451847202872, 50, 5,
1376 2.3561944901923448, 0.0 },
1377 { -0.055370615126630517, 50, 5,
1378 2.5132741228718345, 0.0 },
1379 { -0.47707267400540176, 50, 5,
1380 2.6703537555513241, 0.0 },
1381 { -0.077360497065588632, 50, 5,
1382 2.8274333882308138, 0.0 },
1383 { 0.57750385903191603, 50, 5,
1384 2.9845130209103035, 0.0 },
1385 { 0.0000000000000000, 50, 5,
1386 3.1415926535897931, 0.0 },
1387 };
1388 const double toler025 = 5.0000000000000029e-12;
1389
1390 // Test data for l=50, m=10.
1391 // max(|f - f_GSL|): 4.2188474935755949e-15 at index 17
1392 // max(|f - f_GSL| / |f_GSL|): 8.5566462271658482e-15
1393 // mean(f - f_GSL): 2.1378401694418937e-16
1394 // variance(f - f_GSL): 2.3994393097916561e-33
1395 // stddev(f - f_GSL): 4.8984072000923484e-17
1396 const testcase_sph_legendre<double>
1397 data026[21] =
1398 {
1399 { 0.0000000000000000, 50, 10,
1400 0.0000000000000000, 0.0 },
1401 { 0.15606941844801256, 50, 10,
1402 0.15707963267948966, 0.0 },
1403 { -0.53748868836814168, 50, 10,
1404 0.31415926535897931, 0.0 },
1405 { -0.49304919025183969, 50, 10,
1406 0.47123889803846897, 0.0 },
1407 { -0.26267582750427920, 50, 10,
1408 0.62831853071795862, 0.0 },
1409 { 0.22058983666314153, 50, 10,
1410 0.78539816339744828, 0.0 },
1411 { 0.32936725160671843, 50, 10,
1412 0.94247779607693793, 0.0 },
1413 { -0.092053311559447959, 50, 10,
1414 1.0995574287564276, 0.0 },
1415 { -0.32542913495935522, 50, 10,
1416 1.2566370614359172, 0.0 },
1417 { 0.025673223789103351, 50, 10,
1418 1.4137166941154069, 0.0 },
1419 { 0.32150019350255743, 50, 10,
1420 1.5707963267948966, 0.0 },
1421 { 0.025673223789105259, 50, 10,
1422 1.7278759594743862, 0.0 },
1423 { -0.32542913495935510, 50, 10,
1424 1.8849555921538759, 0.0 },
1425 { -0.092053311559449028, 50, 10,
1426 2.0420352248333655, 0.0 },
1427 { 0.32936725160671687, 50, 10,
1428 2.1991148575128552, 0.0 },
1429 { 0.22058983666314380, 50, 10,
1430 2.3561944901923448, 0.0 },
1431 { -0.26267582750428364, 50, 10,
1432 2.5132741228718345, 0.0 },
1433 { -0.49304919025184135, 50, 10,
1434 2.6703537555513241, 0.0 },
1435 { -0.53748868836814501, 50, 10,
1436 2.8274333882308138, 0.0 },
1437 { 0.15606941844801256, 50, 10,
1438 2.9845130209103035, 0.0 },
1439 { 0.0000000000000000, 50, 10,
1440 3.1415926535897931, 0.0 },
1441 };
1442 const double toler026 = 5.0000000000000039e-13;
1443
1444 // Test data for l=50, m=20.
1445 // max(|f - f_GSL|): 5.3290705182007514e-15 at index 17
1446 // max(|f - f_GSL| / |f_GSL|): 8.3091988651062939e-15
1447 // mean(f - f_GSL): -6.3705667112909982e-16
1448 // variance(f - f_GSL): 2.1306663117079729e-32
1449 // stddev(f - f_GSL): 1.4596802087128444e-16
1450 const testcase_sph_legendre<double>
1451 data027[21] =
1452 {
1453 { 0.0000000000000000, 50, 20,
1454 0.0000000000000000, 0.0 },
1455 { 3.0409598712835887e-07, 50, 20,
1456 0.15707963267948966, 0.0 },
1457 { 0.030940518122881844, 50, 20,
1458 0.31415926535897931, 0.0 },
1459 { 0.64134588721659802, 50, 20,
1460 0.47123889803846897, 0.0 },
1461 { 0.29895244392136594, 50, 20,
1462 0.62831853071795862, 0.0 },
1463 { 0.25309324781873871, 50, 20,
1464 0.78539816339744828, 0.0 },
1465 { 0.34368634714931567, 50, 20,
1466 0.94247779607693793, 0.0 },
1467 { 0.33996764360663945, 50, 20,
1468 1.0995574287564276, 0.0 },
1469 { 0.12866267745104024, 50, 20,
1470 1.2566370614359172, 0.0 },
1471 { -0.18201114398922874, 50, 20,
1472 1.4137166941154069, 0.0 },
1473 { -0.33216683431510857, 50, 20,
1474 1.5707963267948966, 0.0 },
1475 { -0.18201114398923010, 50, 20,
1476 1.7278759594743862, 0.0 },
1477 { 0.12866267745103857, 50, 20,
1478 1.8849555921538759, 0.0 },
1479 { 0.33996764360663895, 50, 20,
1480 2.0420352248333655, 0.0 },
1481 { 0.34368634714931812, 50, 20,
1482 2.1991148575128552, 0.0 },
1483 { 0.25309324781874126, 50, 20,
1484 2.3561944901923448, 0.0 },
1485 { 0.29895244392136405, 50, 20,
1486 2.5132741228718345, 0.0 },
1487 { 0.64134588721659869, 50, 20,
1488 2.6703537555513241, 0.0 },
1489 { 0.030940518122882274, 50, 20,
1490 2.8274333882308138, 0.0 },
1491 { 3.0409598712835887e-07, 50, 20,
1492 2.9845130209103035, 0.0 },
1493 { 0.0000000000000000, 50, 20,
1494 3.1415926535897931, 0.0 },
1495 };
1496 const double toler027 = 5.0000000000000039e-13;
1497
1498 // Test data for l=50, m=50.
1499 // max(|f - f_GSL|): 8.8817841970012523e-16 at index 10
1500 // max(|f - f_GSL| / |f_GSL|): 1.6947090122367552e-15
1501 // mean(f - f_GSL): 8.9876810627650302e-17
1502 // variance(f - f_GSL): 4.2408665715142198e-34
1503 // stddev(f - f_GSL): 2.0593364396120950e-17
1504 const testcase_sph_legendre<double>
1505 data028[21] =
1506 {
1507 { 0.0000000000000000, 50, 50,
1508 0.0000000000000000, 0.0 },
1509 { 4.1649039898161316e-41, 50, 50,
1510 0.15707963267948966, 0.0 },
1511 { 2.5240684647722935e-26, 50, 50,
1512 0.31415926535897931, 0.0 },
1513 { 5.6927376423967334e-18, 50, 50,
1514 0.47123889803846897, 0.0 },
1515 { 2.3116239814797222e-12, 50, 50,
1516 0.62831853071795862, 0.0 },
1517 { 2.3835981241325056e-08, 50, 50,
1518 0.78539816339744828, 0.0 },
1519 { 1.9992410287270217e-05, 50, 50,
1520 0.94247779607693793, 0.0 },
1521 { 0.0024947505670829830, 50, 50,
1522 1.0995574287564276, 0.0 },
1523 { 0.065057774647971231, 50, 50,
1524 1.2566370614359172, 0.0 },
1525 { 0.43050607056732243, 50, 50,
1526 1.4137166941154069, 0.0 },
1527 { 0.79980281171531975, 50, 50,
1528 1.5707963267948966, 0.0 },
1529 { 0.43050607056732287, 50, 50,
1530 1.7278759594743862, 0.0 },
1531 { 0.065057774647971398, 50, 50,
1532 1.8849555921538759, 0.0 },
1533 { 0.0024947505670829878, 50, 50,
1534 2.0420352248333655, 0.0 },
1535 { 1.9992410287270430e-05, 50, 50,
1536 2.1991148575128552, 0.0 },
1537 { 2.3835981241325311e-08, 50, 50,
1538 2.3561944901923448, 0.0 },
1539 { 2.3116239814797057e-12, 50, 50,
1540 2.5132741228718345, 0.0 },
1541 { 5.6927376423968952e-18, 50, 50,
1542 2.6703537555513241, 0.0 },
1543 { 2.5240684647724192e-26, 50, 50,
1544 2.8274333882308138, 0.0 },
1545 { 4.1649039898161316e-41, 50, 50,
1546 2.9845130209103035, 0.0 },
1547 { 0.0000000000000000, 50, 50,
1548 3.1415926535897931, 0.0 },
1549 };
1550 const double toler028 = 2.5000000000000020e-13;
1551
1552 // Test data for l=100, m=0.
1553 // max(|f - f_GSL|): 2.2759572004815709e-15 at index 18
1554 // max(|f - f_GSL| / |f_GSL|): 4.9270578369513465e-15
1555 // mean(f - f_GSL): -2.0618427600181479e-16
1556 // variance(f - f_GSL): 2.2318776726956083e-33
1557 // stddev(f - f_GSL): 4.7242752594399153e-17
1558 const testcase_sph_legendre<double>
1559 data029[21] =
1560 {
1561 { 3.9993839251484076, 100, 0,
1562 0.0000000000000000, 0.0 },
1563 { -0.60770160285939456, 100, 0,
1564 0.15707963267948966, 0.0 },
1565 { 0.46193027883954441, 100, 0,
1566 0.31415926535897931, 0.0 },
1567 { -0.40218718869815234, 100, 0,
1568 0.47123889803846897, 0.0 },
1569 { 0.36960201406911097, 100, 0,
1570 0.62831853071795862, 0.0 },
1571 { -0.34953726547378389, 100, 0,
1572 0.78539816339744828, 0.0 },
1573 { 0.33646959352497730, 100, 0,
1574 0.94247779607693793, 0.0 },
1575 { -0.32784733067663224, 100, 0,
1576 1.0995574287564276, 0.0 },
1577 { 0.32235624474047969, 100, 0,
1578 1.2566370614359172, 0.0 },
1579 { -0.31929330706601350, 100, 0,
1580 1.4137166941154069, 0.0 },
1581 { 0.31830791662110325, 100, 0,
1582 1.5707963267948966, 0.0 },
1583 { -0.31929330706601333, 100, 0,
1584 1.7278759594743862, 0.0 },
1585 { 0.32235624474048036, 100, 0,
1586 1.8849555921538759, 0.0 },
1587 { -0.32784733067663291, 100, 0,
1588 2.0420352248333655, 0.0 },
1589 { 0.33646959352498013, 100, 0,
1590 2.1991148575128552, 0.0 },
1591 { -0.34953726547378589, 100, 0,
1592 2.3561944901923448, 0.0 },
1593 { 0.36960201406910725, 100, 0,
1594 2.5132741228718345, 0.0 },
1595 { -0.40218718869815723, 100, 0,
1596 2.6703537555513241, 0.0 },
1597 { 0.46193027883955923, 100, 0,
1598 2.8274333882308138, 0.0 },
1599 { -0.60770160285939456, 100, 0,
1600 2.9845130209103035, 0.0 },
1601 { 3.9993839251484076, 100, 0,
1602 3.1415926535897931, 0.0 },
1603 };
1604 const double toler029 = 2.5000000000000020e-13;
1605
1606 // Test data for l=100, m=1.
1607 // max(|f - f_GSL|): 4.7184478546569153e-15 at index 18
1608 // max(|f - f_GSL| / |f_GSL|): 1.6136152688198031e-14
1609 // mean(f - f_GSL): 1.7347234759767562e-17
1610 // variance(f - f_GSL): 1.5798644075050619e-35
1611 // stddev(f - f_GSL): 3.9747508192401971e-18
1612 const testcase_sph_legendre<double>
1613 data030[21] =
1614 {
1615 { 0.0000000000000000, 100, 1,
1616 0.0000000000000000, 0.0 },
1617 { -0.50851949013714159, 100, 1,
1618 0.15707963267948966, 0.0 },
1619 { 0.33129641402223092, 100, 1,
1620 0.31415926535897931, 0.0 },
1621 { -0.24390405750942512, 100, 1,
1622 0.47123889803846897, 0.0 },
1623 { 0.18659755088413388, 100, 1,
1624 0.62831853071795862, 0.0 },
1625 { -0.14355908970517178, 100, 1,
1626 0.78539816339744828, 0.0 },
1627 { 0.10844906813251505, 100, 1,
1628 0.94247779607693793, 0.0 },
1629 { -0.078100088690857675, 100, 1,
1630 1.0995574287564276, 0.0 },
1631 { 0.050670002998302717, 100, 1,
1632 1.2566370614359172, 0.0 },
1633 { -0.024941251747138900, 100, 1,
1634 1.4137166941154069, 0.0 },
1635 { 1.9587949830851608e-15, 100, 1,
1636 1.5707963267948966, 0.0 },
1637 { 0.024941251747135025, 100, 1,
1638 1.7278759594743862, 0.0 },
1639 { -0.050670002998298824, 100, 1,
1640 1.8849555921538759, 0.0 },
1641 { 0.078100088690855773, 100, 1,
1642 2.0420352248333655, 0.0 },
1643 { -0.10844906813250622, 100, 1,
1644 2.1991148575128552, 0.0 },
1645 { 0.14355908970516626, 100, 1,
1646 2.3561944901923448, 0.0 },
1647 { -0.18659755088414104, 100, 1,
1648 2.5132741228718345, 0.0 },
1649 { 0.24390405750941679, 100, 1,
1650 2.6703537555513241, 0.0 },
1651 { -0.33129641402221749, 100, 1,
1652 2.8274333882308138, 0.0 },
1653 { 0.50851949013714159, 100, 1,
1654 2.9845130209103035, 0.0 },
1655 { 0.0000000000000000, 100, 1,
1656 3.1415926535897931, 0.0 },
1657 };
1658 const double toler030 = 1.0000000000000008e-12;
1659
1660 // Test data for l=100, m=2.
1661 // max(|f - f_GSL|): 9.3258734068513149e-15 at index 1
1662 // max(|f - f_GSL| / |f_GSL|): 1.3884756158405121e-14
1663 // mean(f - f_GSL): 1.1049362483174177e-15
1664 // variance(f - f_GSL): 6.4096415924402929e-32
1665 // stddev(f - f_GSL): 2.5317269980075443e-16
1666 const testcase_sph_legendre<double>
1667 data031[21] =
1668 {
1669 { 0.0000000000000000, 100, 2,
1670 0.0000000000000000, 0.0 },
1671 { 0.67166274297196848, 100, 2,
1672 0.15707963267948966, 0.0 },
1673 { -0.48226933687994433, 100, 2,
1674 0.31415926535897931, 0.0 },
1675 { 0.41175421895715525, 100, 2,
1676 0.47123889803846897, 0.0 },
1677 { -0.37475021787822776, 100, 2,
1678 0.62831853071795862, 0.0 },
1679 { 0.35242909383605286, 100, 2,
1680 0.78539816339744828, 0.0 },
1681 { -0.33807110409159863, 100, 2,
1682 0.94247779607693793, 0.0 },
1683 { 0.32867180390710077, 100, 2,
1684 1.0995574287564276, 0.0 },
1685 { -0.32271583790278502, 100, 2,
1686 1.2566370614359172, 0.0 },
1687 { 0.31940354677687466, 100, 2,
1688 1.4137166941154069, 0.0 },
1689 { -0.31833943693772526, 100, 2,
1690 1.5707963267948966, 0.0 },
1691 { 0.31940354677687455, 100, 2,
1692 1.7278759594743862, 0.0 },
1693 { -0.32271583790278552, 100, 2,
1694 1.8849555921538759, 0.0 },
1695 { 0.32867180390710116, 100, 2,
1696 2.0420352248333655, 0.0 },
1697 { -0.33807110409160157, 100, 2,
1698 2.1991148575128552, 0.0 },
1699 { 0.35242909383605503, 100, 2,
1700 2.3561944901923448, 0.0 },
1701 { -0.37475021787822438, 100, 2,
1702 2.5132741228718345, 0.0 },
1703 { 0.41175421895716052, 100, 2,
1704 2.6703537555513241, 0.0 },
1705 { -0.48226933687995360, 100, 2,
1706 2.8274333882308138, 0.0 },
1707 { 0.67166274297196848, 100, 2,
1708 2.9845130209103035, 0.0 },
1709 { 0.0000000000000000, 100, 2,
1710 3.1415926535897931, 0.0 },
1711 };
1712 const double toler031 = 1.0000000000000008e-12;
1713
1714 // Test data for l=100, m=5.
1715 // max(|f - f_GSL|): 1.5432100042289676e-14 at index 1
1716 // max(|f - f_GSL| / |f_GSL|): 2.4665959612621893e-13
1717 // mean(f - f_GSL): -8.4885802091131797e-16
1718 // variance(f - f_GSL): 3.7829396832437676e-32
1719 // stddev(f - f_GSL): 1.9449780675482609e-16
1720 const testcase_sph_legendre<double>
1721 data032[21] =
1722 {
1723 { 0.0000000000000000, 100, 5,
1724 0.0000000000000000, 0.0 },
1725 { 0.062564361105954577, 100, 5,
1726 0.15707963267948966, 0.0 },
1727 { 0.14179554455882706, 100, 5,
1728 0.31415926535897931, 0.0 },
1729 { -0.14356866942905960, 100, 5,
1730 0.47123889803846897, 0.0 },
1731 { 0.12355483388447824, 100, 5,
1732 0.62831853071795862, 0.0 },
1733 { -0.10090029999681642, 100, 5,
1734 0.78539816339744828, 0.0 },
1735 { 0.078905134460235241, 100, 5,
1736 0.94247779607693793, 0.0 },
1737 { -0.058040182398185071, 100, 5,
1738 1.0995574287564276, 0.0 },
1739 { 0.038142759389482424, 100, 5,
1740 1.2566370614359172, 0.0 },
1741 { -0.018906264170660478, 100, 5,
1742 1.4137166941154069, 0.0 },
1743 { 1.9576303042914504e-15, 100, 5,
1744 1.5707963267948966, 0.0 },
1745 { 0.018906264170657019, 100, 5,
1746 1.7278759594743862, 0.0 },
1747 { -0.038142759389478365, 100, 5,
1748 1.8849555921538759, 0.0 },
1749 { 0.058040182398183086, 100, 5,
1750 2.0420352248333655, 0.0 },
1751 { -0.078905134460225707, 100, 5,
1752 2.1991148575128552, 0.0 },
1753 { 0.10090029999681013, 100, 5,
1754 2.3561944901923448, 0.0 },
1755 { -0.12355483388448550, 100, 5,
1756 2.5132741228718345, 0.0 },
1757 { 0.14356866942904906, 100, 5,
1758 2.6703537555513241, 0.0 },
1759 { -0.14179554455879767, 100, 5,
1760 2.8274333882308138, 0.0 },
1761 { -0.062564361105954577, 100, 5,
1762 2.9845130209103035, 0.0 },
1763 { 0.0000000000000000, 100, 5,
1764 3.1415926535897931, 0.0 },
1765 };
1766 const double toler032 = 2.5000000000000014e-11;
1767
1768 // Test data for l=100, m=10.
1769 // max(|f - f_GSL|): 6.9944050551384862e-15 at index 1
1770 // max(|f - f_GSL| / |f_GSL|): 9.2805170220968737e-15
1771 // mean(f - f_GSL): -9.1725568939268895e-16
1772 // variance(f - f_GSL): 4.4171294985470989e-32
1773 // stddev(f - f_GSL): 2.1016968141354497e-16
1774 const testcase_sph_legendre<double>
1775 data033[21] =
1776 {
1777 { 0.0000000000000000, 100, 10,
1778 0.0000000000000000, 0.0 },
1779 { -0.75366545187997991, 100, 10,
1780 0.15707963267948966, 0.0 },
1781 { -0.35914570017278186, 100, 10,
1782 0.31415926535897931, 0.0 },
1783 { 0.43480692911578295, 100, 10,
1784 0.47123889803846897, 0.0 },
1785 { -0.40862111080315500, 100, 10,
1786 0.62831853071795862, 0.0 },
1787 { 0.37832688692909411, 100, 10,
1788 0.78539816339744828, 0.0 },
1789 { -0.35484056194773494, 100, 10,
1790 0.94247779607693793, 0.0 },
1791 { 0.33821981171196341, 100, 10,
1792 1.0995574287564276, 0.0 },
1793 { -0.32729120767830594, 100, 10,
1794 1.2566370614359172, 0.0 },
1795 { 0.32110336937091438, 100, 10,
1796 1.4137166941154069, 0.0 },
1797 { -0.31910064020036194, 100, 10,
1798 1.5707963267948966, 0.0 },
1799 { 0.32110336937091460, 100, 10,
1800 1.7278759594743862, 0.0 },
1801 { -0.32729120767830605, 100, 10,
1802 1.8849555921538759, 0.0 },
1803 { 0.33821981171196364, 100, 10,
1804 2.0420352248333655, 0.0 },
1805 { -0.35484056194773461, 100, 10,
1806 2.1991148575128552, 0.0 },
1807 { 0.37832688692909372, 100, 10,
1808 2.3561944901923448, 0.0 },
1809 { -0.40862111080315755, 100, 10,
1810 2.5132741228718345, 0.0 },
1811 { 0.43480692911577751, 100, 10,
1812 2.6703537555513241, 0.0 },
1813 { -0.35914570017276798, 100, 10,
1814 2.8274333882308138, 0.0 },
1815 { -0.75366545187997991, 100, 10,
1816 2.9845130209103035, 0.0 },
1817 { 0.0000000000000000, 100, 10,
1818 3.1415926535897931, 0.0 },
1819 };
1820 const double toler033 = 5.0000000000000039e-13;
1821
1822 // Test data for l=100, m=20.
1823 // max(|f - f_GSL|): 5.2180482157382357e-15 at index 2
1824 // max(|f - f_GSL| / |f_GSL|): 3.3114331221145530e-14
1825 // mean(f - f_GSL): -1.7066374768419445e-16
1826 // variance(f - f_GSL): 1.5291210256147554e-33
1827 // stddev(f - f_GSL): 3.9103977107383276e-17
1828 const testcase_sph_legendre<double>
1829 data034[21] =
1830 {
1831 { 0.0000000000000000, 100, 20,
1832 0.0000000000000000, 0.0 },
1833 { 0.053569660841557079, 100, 20,
1834 0.15707963267948966, 0.0 },
1835 { 0.57154926874731338, 100, 20,
1836 0.31415926535897931, 0.0 },
1837 { 0.47536909969585633, 100, 20,
1838 0.47123889803846897, 0.0 },
1839 { -0.28882554564109575, 100, 20,
1840 0.62831853071795862, 0.0 },
1841 { 0.020116179014043743, 100, 20,
1842 0.78539816339744828, 0.0 },
1843 { 0.14752195931707024, 100, 20,
1844 0.94247779607693793, 0.0 },
1845 { -0.24069428588868366, 100, 20,
1846 1.0995574287564276, 0.0 },
1847 { 0.29031796025014306, 100, 20,
1848 1.2566370614359172, 0.0 },
1849 { -0.31437256851143458, 100, 20,
1850 1.4137166941154069, 0.0 },
1851 { 0.32153954851141792, 100, 20,
1852 1.5707963267948966, 0.0 },
1853 { -0.31437256851143375, 100, 20,
1854 1.7278759594743862, 0.0 },
1855 { 0.29031796025014139, 100, 20,
1856 1.8849555921538759, 0.0 },
1857 { -0.24069428588868241, 100, 20,
1858 2.0420352248333655, 0.0 },
1859 { 0.14752195931706186, 100, 20,
1860 2.1991148575128552, 0.0 },
1861 { 0.020116179014049562, 100, 20,
1862 2.3561944901923448, 0.0 },
1863 { -0.28882554564109075, 100, 20,
1864 2.5132741228718345, 0.0 },
1865 { 0.47536909969585545, 100, 20,
1866 2.6703537555513241, 0.0 },
1867 { 0.57154926874732348, 100, 20,
1868 2.8274333882308138, 0.0 },
1869 { 0.053569660841557079, 100, 20,
1870 2.9845130209103035, 0.0 },
1871 { 0.0000000000000000, 100, 20,
1872 3.1415926535897931, 0.0 },
1873 };
1874 const double toler034 = 2.5000000000000015e-12;
1875
1876 // Test data for l=100, m=50.
1877 // max(|f - f_GSL|): 2.4980018054066022e-15 at index 15
1878 // max(|f - f_GSL| / |f_GSL|): 7.4927901205617944e-15
1879 // mean(f - f_GSL): 1.5662074559583175e-16
1880 // variance(f - f_GSL): 1.2878280424271984e-33
1881 // stddev(f - f_GSL): 3.5886321104666028e-17
1882 const testcase_sph_legendre<double>
1883 data035[21] =
1884 {
1885 { 0.0000000000000000, 100, 50,
1886 0.0000000000000000, 0.0 },
1887 { 3.3047910392597822e-21, 100, 50,
1888 0.15707963267948966, 0.0 },
1889 { 1.0592655372554564e-07, 100, 50,
1890 0.31415926535897931, 0.0 },
1891 { 0.080418744223952773, 100, 50,
1892 0.47123889803846897, 0.0 },
1893 { -0.56450600580392973, 100, 50,
1894 0.62831853071795862, 0.0 },
1895 { 0.33338739844742110, 100, 50,
1896 0.78539816339744828, 0.0 },
1897 { 0.39741714816514678, 100, 50,
1898 0.94247779607693793, 0.0 },
1899 { 0.35223993750972243, 100, 50,
1900 1.0995574287564276, 0.0 },
1901 { 0.17885891940721577, 100, 50,
1902 1.2566370614359172, 0.0 },
1903 { -0.15341660126461967, 100, 50,
1904 1.4137166941154069, 0.0 },
1905 { -0.34175924303503102, 100, 50,
1906 1.5707963267948966, 0.0 },
1907 { -0.15341660126462270, 100, 50,
1908 1.7278759594743862, 0.0 },
1909 { 0.17885891940721302, 100, 50,
1910 1.8849555921538759, 0.0 },
1911 { 0.35223993750972227, 100, 50,
1912 2.0420352248333655, 0.0 },
1913 { 0.39741714816514595, 100, 50,
1914 2.1991148575128552, 0.0 },
1915 { 0.33338739844741666, 100, 50,
1916 2.3561944901923448, 0.0 },
1917 { -0.56450600580393095, 100, 50,
1918 2.5132741228718345, 0.0 },
1919 { 0.080418744223953911, 100, 50,
1920 2.6703537555513241, 0.0 },
1921 { 1.0592655372554981e-07, 100, 50,
1922 2.8274333882308138, 0.0 },
1923 { 3.3047910392597822e-21, 100, 50,
1924 2.9845130209103035, 0.0 },
1925 { 0.0000000000000000, 100, 50,
1926 3.1415926535897931, 0.0 },
1927 };
1928 const double toler035 = 5.0000000000000039e-13;
1929
1930 // Test data for l=100, m=100.
1931 // max(|f - f_GSL|): 3.6637359812630166e-15 at index 10
1932 // max(|f - f_GSL| / |f_GSL|): 3.8591350247394187e-15
1933 // mean(f - f_GSL): 2.7412914496899967e-16
1934 // variance(f - f_GSL): 3.9452063763753292e-33
1935 // stddev(f - f_GSL): 6.2810877850698192e-17
1936 const testcase_sph_legendre<double>
1937 data036[21] =
1938 {
1939 { 0.0000000000000000, 100, 100,
1940 0.0000000000000000, 0.0 },
1941 { 2.5744136608873899e-81, 100, 100,
1942 0.15707963267948966, 0.0 },
1943 { 9.4551974868947092e-52, 100, 100,
1944 0.31415926535897931, 0.0 },
1945 { 4.8096190703397596e-35, 100, 100,
1946 0.47123889803846897, 0.0 },
1947 { 7.9305393636344023e-24, 100, 100,
1948 0.62831853071795862, 0.0 },
1949 { 8.4320740610944858e-16, 100, 100,
1950 0.78539816339744828, 0.0 },
1951 { 5.9319660146026674e-10, 100, 100,
1952 0.94247779607693793, 0.0 },
1953 { 9.2368225946797243e-06, 100, 100,
1954 1.0995574287564276, 0.0 },
1955 { 0.0062815489742044095, 100, 100,
1956 1.2566370614359172, 0.0 },
1957 { 0.27505966018176986, 100, 100,
1958 1.4137166941154069, 0.0 },
1959 { 0.94936713998764621, 100, 100,
1960 1.5707963267948966, 0.0 },
1961 { 0.27505966018177036, 100, 100,
1962 1.7278759594743862, 0.0 },
1963 { 0.0062815489742044433, 100, 100,
1964 1.8849555921538759, 0.0 },
1965 { 9.2368225946797582e-06, 100, 100,
1966 2.0420352248333655, 0.0 },
1967 { 5.9319660146027946e-10, 100, 100,
1968 2.1991148575128552, 0.0 },
1969 { 8.4320740610946652e-16, 100, 100,
1970 2.3561944901923448, 0.0 },
1971 { 7.9305393636342891e-24, 100, 100,
1972 2.5132741228718345, 0.0 },
1973 { 4.8096190703400333e-35, 100, 100,
1974 2.6703537555513241, 0.0 },
1975 { 9.4551974868956498e-52, 100, 100,
1976 2.8274333882308138, 0.0 },
1977 { 2.5744136608873899e-81, 100, 100,
1978 2.9845130209103035, 0.0 },
1979 { 0.0000000000000000, 100, 100,
1980 3.1415926535897931, 0.0 },
1981 };
1982 const double toler036 = 2.5000000000000020e-13;
1983
1984 template<typename Ret, unsigned int Num>
1985 void
test(const testcase_sph_legendre<Ret> (& data)[Num],Ret toler)1986 test(const testcase_sph_legendre<Ret> (&data)[Num], Ret toler)
1987 {
1988 bool test __attribute__((unused)) = true;
1989 const Ret eps = std::numeric_limits<Ret>::epsilon();
1990 Ret max_abs_diff = -Ret(1);
1991 Ret max_abs_frac = -Ret(1);
1992 unsigned int num_datum = Num;
1993 for (unsigned int i = 0; i < num_datum; ++i)
1994 {
1995 const Ret f = std::sph_legendre(data[i].l, data[i].m,
1996 data[i].theta);
1997 const Ret f0 = data[i].f0;
1998 const Ret diff = f - f0;
1999 if (std::abs(diff) > max_abs_diff)
2000 max_abs_diff = std::abs(diff);
2001 if (std::abs(f0) > Ret(10) * eps
2002 && std::abs(f) > Ret(10) * eps)
2003 {
2004 const Ret frac = diff / f0;
2005 if (std::abs(frac) > max_abs_frac)
2006 max_abs_frac = std::abs(frac);
2007 }
2008 }
2009 VERIFY(max_abs_frac < toler);
2010 }
2011
2012 int
main()2013 main()
2014 {
2015 test(data001, toler001);
2016 test(data002, toler002);
2017 test(data003, toler003);
2018 test(data004, toler004);
2019 test(data005, toler005);
2020 test(data006, toler006);
2021 test(data007, toler007);
2022 test(data008, toler008);
2023 test(data009, toler009);
2024 test(data010, toler010);
2025 test(data011, toler011);
2026 test(data012, toler012);
2027 test(data013, toler013);
2028 test(data014, toler014);
2029 test(data015, toler015);
2030 test(data016, toler016);
2031 test(data017, toler017);
2032 test(data018, toler018);
2033 test(data019, toler019);
2034 test(data020, toler020);
2035 test(data021, toler021);
2036 test(data022, toler022);
2037 test(data023, toler023);
2038 test(data024, toler024);
2039 test(data025, toler025);
2040 test(data026, toler026);
2041 test(data027, toler027);
2042 test(data028, toler028);
2043 test(data029, toler029);
2044 test(data030, toler030);
2045 test(data031, toler031);
2046 test(data032, toler032);
2047 test(data033, toler033);
2048 test(data034, toler034);
2049 test(data035, toler035);
2050 test(data036, toler036);
2051 return 0;
2052 }
2053