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- Committer: Bazaar Package Importer
- Author(s): Thomas Weber, Rafael Laboissiere, Thomas Weber
- Date: 2009-04-04 23:05:32 UTC
- mfrom: (3.1.1 experimental)
- Revision ID: james.westby@ubuntu.com-20090404230532-st3iredznjuhp02y
Tags: 1.0.7-2
[ Rafael Laboissiere ]
* debian/copyright: Add header
* debian/control: Bump build-dependency on octave-pkg-dev to >= 0.6.4,
such that the package is built with the versioned packages directory
[ Thomas Weber ]
* Upload to unstable
* debian/copyright: Add header
* debian/control: Bump build-dependency on octave-pkg-dev to >= 0.6.4,
such that the package is built with the versioned packages directory
[ Thomas Weber ]
* Upload to unstable
- files added:
- debian/clean
- doc
- inst
- files removed:
- src/config.log
- files modified:
- ChangeLog
added
removed
inst/test_sf.c
1
/* specfunc/test_sf.c
2
*
3
* Copyright (C) 2007 Brian Gough
4
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2004 Gerard Jungman
5
*
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* This program is free software; you can redistribute it and/or modify
7
* it under the terms of the GNU General Public License as published by
8
* the Free Software Foundation; either version 3 of the License, or (at
9
* your option) any later version.
10
*
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* This program is distributed in the hope that it will be useful, but
12
* WITHOUT ANY WARRANTY; without even the implied warranty of
13
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14
* General Public License for more details.
15
*
16
* You should have received a copy of the GNU General Public License
17
* along with this program; if not, write to the Free Software
18
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
19
*/
20
21
/* Author: G. Jungman */
22
23
#include <config.h>
24
#include <stdio.h>
25
#include <stdlib.h>
26
#include <string.h>
27
#include <gsl/gsl_math.h>
28
#include <gsl/gsl_errno.h>
29
#include <gsl/gsl_ieee_utils.h>
30
#include <gsl/gsl_test.h>
31
#include <gsl/gsl_sf.h>
32
#include "test_sf.h"
33
34
35
double
36
test_sf_frac_diff(double x1, double x2)
37
{
38
if(x1 == 0.0 && x2 == 0.0) {
39
return 0.0;
40
}
41
else if (x1 == 0.0) {
42
return fabs(x2);
43
} else if(x1 <= DBL_MAX && x2 <= DBL_MAX && (x1 + x2 != 0.0)) {
44
return fabs((x1-x2)/(x1+x2));
45
}
46
else {
47
return 1.0;
48
}
49
}
50
51
52
/* Check a result against a given value and tolerance.
53
*/
54
int
55
test_sf_check_result(char * message_buff, gsl_sf_result r, double val, double tol)
56
{
57
int s = 0;
58
double f = 0, d = 0;
59
60
if (gsl_isnan(r.val) || gsl_isnan(val))
61
{
62
s = (gsl_isnan(r.val) != gsl_isnan(val)) ? TEST_SF_INCONS : s;
63
}
64
else if (gsl_isinf(r.val) || gsl_isinf(val))
65
{
66
s = (gsl_isinf(r.val) != gsl_isinf(val)) ? TEST_SF_INCONS : s;
67
}
68
else
69
{
70
f = test_sf_frac_diff(val, r.val);
71
d = fabs(val - r.val);
72
73
if(d > 2.0 * TEST_SIGMA * r.err) s |= TEST_SF_INCONS;
74
if(r.err < 0.0) s |= TEST_SF_ERRNEG;
75
if(gsl_isinf(r.err)) s |= TEST_SF_ERRBAD;
76
#if TEST_EXCESSIVE_ERROR
77
if(d > 0 && r.err > 1e4 * fabs(val)*tol) s |= TEST_SF_ERRBIG;
78
#endif
79
if(f > TEST_FACTOR * tol) s |= TEST_SF_TOLBAD;
80
}
81
82
if(s != 0) {
83
char buff[2048];
84
sprintf(buff, " expected: %20.16e\n", val);
85
strcat(message_buff, buff);
86
sprintf(buff, " obtained: %20.16e +/- %.16e (rel=%g)\n", r.val, r.err, r.err/(fabs(r.val) + r.err));
87
strcat(message_buff, buff);
88
sprintf(buff, " fracdiff: %20.16e\n", f);
89
strcat(message_buff, buff);
90
sprintf(buff, " tolerance: %20.16e\n", tol);
91
strcat(message_buff, buff);
92
}
93
94
if(s & TEST_SF_INCONS) {
95
strcat(message_buff, " value/expected not consistent within reported error\n");
96
}
97
if(s & TEST_SF_ERRNEG) {
98
strcat(message_buff, " reported error negative\n");
99
}
100
if(s & TEST_SF_ERRBAD) {
101
strcat(message_buff, " reported error is bad\n");
102
}
103
if(s & TEST_SF_ERRBIG) {
104
strcat(message_buff, " reported error is much too big\n");
105
}
106
if(s & TEST_SF_TOLBAD) {
107
strcat(message_buff, " value not within tolerance of expected value\n");
108
}
109
110
return s;
111
}
112
113
/* Check a result against a given value and tolerance.
114
*/
115
int
116
test_sf_check_e10(char * message_buff, int e10, int e10_in)
117
{
118
int s = 0;
119
120
if (e10 != e10_in)
121
{
122
s = TEST_SF_EXPBAD;
123
}
124
125
if(s != 0) {
126
char buff[2048];
127
sprintf(buff, " expected exponent: 10^%d\n", e10_in);
128
strcat(message_buff, buff);
129
sprintf(buff, " obtained exponent: 10^%d", e10);
130
strcat(message_buff, buff);
131
}
132
133
if(s & TEST_SF_EXPBAD) {
134
strcat(message_buff, " exponent is incorrect\n");
135
}
136
137
return s;
138
}
139
140
int
141
test_sf_check_val(char * message_buff, double rval, double val, double tol)
142
{
143
int s = 0;
144
double f = test_sf_frac_diff(val, rval);
145
146
if(f > TEST_FACTOR * tol) s |= TEST_SF_TOLBAD;
147
148
if(s != 0) {
149
char buff[2048];
150
sprintf(buff, " expected: %20.16e\n", val);
151
strcat(message_buff, buff);
152
sprintf(buff, " obtained: %20.16e\n", rval);
153
strcat(message_buff, buff);
154
sprintf(buff, " fracdiff: %20.16e\n", f);
155
strcat(message_buff, buff);
156
}
157
158
if(s & TEST_SF_TOLBAD) {
159
strcat(message_buff, " value not within tolerance of expected value\n");
160
}
161
162
return s;
163
}
164
165
166
/* Relax the condition on the agreement and on the usefulness
167
* of the error estimate.
168
*/
169
int
170
test_sf_check_result_relax(char * message_buff, gsl_sf_result r, double val, double tol)
171
{
172
int s = 0;
173
double f = test_sf_frac_diff(val, r.val);
174
175
if(f > GSL_MAX_DBL(TEST_SNGL, TEST_FACTOR * tol)) s |= TEST_SF_INCONS;
176
if(r.err < 0.0) s |= TEST_SF_ERRNEG;
177
if(gsl_isinf(r.err)) s |= TEST_SF_ERRBAD;
178
if(f > TEST_FACTOR * tol) s |= TEST_SF_TOLBAD;
179
180
if(s != 0) {
181
char buff[2048];
182
sprintf(buff, " expected: %20.16e\n", val);
183
strcat(message_buff, buff);
184
sprintf(buff, " obtained: %20.16e +/- %.16e (rel=%g)\n", r.val, r.err, r.err/(fabs(r.val) + r.err));
185
strcat(message_buff, buff);
186
sprintf(buff, " fracdiff: %20.16e\n", f);
187
strcat(message_buff, buff);
188
}
189
190
if(s & TEST_SF_INCONS) {
191
strcat(message_buff, " value/expected not consistent MAX(tol,SINGLE_PREC)\n");
192
}
193
if(s & TEST_SF_ERRNEG) {
194
strcat(message_buff, " reported error negative\n");
195
}
196
if(s & TEST_SF_ERRBAD) {
197
strcat(message_buff, " reported error is bad\n");
198
}
199
if(s & TEST_SF_TOLBAD) {
200
strcat(message_buff, " value not within tolerance of expected value\n");
201
}
202
203
return s;
204
}
205
206
207
/* Check a return value.
208
*/
209
int
210
test_sf_check_return(char * message_buff, int val_return, int expected_return)
211
{
212
if(val_return != expected_return) {
213
char buff[256];
214
sprintf(buff, " unexpected return code: %d\n", val_return);
215
strcat(message_buff, buff);
216
return TEST_SF_RETBAD;
217
}
218
else {
219
return 0;
220
}
221
}
222
223
224
int
225
test_sf (gsl_sf_result r, double val_in, double tol, int status,
226
int expect_return, const char * desc)
227
{
228
char message_buff[4096];
229
int local_s = 0;
230
231
message_buff[0] = '\0';
232
233
local_s |= test_sf_check_result(message_buff, r, val_in, tol);
234
local_s |= test_sf_check_return(message_buff, status, expect_return);
235
236
gsl_test(local_s, desc);
237
if(local_s != 0) {
238
/* printf(" %s %d\n", __FILE__, __LINE__); */
239
printf("%s", message_buff);
240
printf(" %22.18e %22.18e\n", r.val, r.err);
241
}
242
return local_s;
243
}
244
245
int
246
test_sf_e10 (gsl_sf_result_e10 re, double val_in, int e10_in, double tol, int status,
247
int expect_return, const char * desc)
248
{
249
char message_buff[4096];
250
int local_s = 0;
251
gsl_sf_result r;
252
r.val = re.val; r.err = re.err;
253
254
message_buff[0] = '\0';
255
256
local_s |= test_sf_check_result(message_buff, r, val_in, tol);
257
local_s |= test_sf_check_e10(message_buff, re.e10, e10_in);
258
local_s |= test_sf_check_return(message_buff, status, expect_return);
259
260
gsl_test(local_s, desc);
261
if(local_s != 0) {
262
/* printf(" %s %d\n", __FILE__, __LINE__); */
263
printf("%s", message_buff);
264
printf(" %22.18e %22.18e 10^%d\n", re.val, re.err, re.e10);
265
}
266
return local_s;
267
}
268
269
270
int
271
test_sf_val (double val, double val_in, double tol, const char * desc)
272
{
273
char message_buff[4096];
274
int local_s = 0;
275
276
message_buff[0] = '\0';
277
278
local_s |= test_sf_check_val(message_buff, val, val_in, tol);
279
280
gsl_test(local_s, desc);
281
if(local_s != 0) {
282
/* printf(" %s %d\n", __FILE__, __LINE__); */
283
printf("%s", message_buff);
284
printf(" %22.18e\n", val);
285
}
286
return local_s;
287
}
288
289
290
int
291
test_sf_rlx (gsl_sf_result r, double val_in, double tol, int status,
292
int expect_return, const char * desc)
293
{
294
char message_buff[4096];
295
int local_s = 0;
296
297
message_buff[0] = '\0';
298
299
local_s |= test_sf_check_result_relax(message_buff, r, val_in, tol);
300
local_s |= test_sf_check_return(message_buff, status, expect_return);
301
302
gsl_test(local_s, desc);
303
if(local_s != 0) {
304
/* printf(" %s %d\n", __FILE__, __LINE__); */
305
printf("%s", message_buff);
306
printf(" %22.18e %22.18e\n", r.val, r.err);
307
}
308
return local_s;
309
}
310
311
312
int
313
test_sf_2 (gsl_sf_result r1, double val1, double tol1,
314
gsl_sf_result r2, double val2, double tol2,
315
int status, int expect_return, const char * desc)
316
{
317
char message_buff[4096];
318
int local_s = 0;
319
320
message_buff[0] = '\0';
321
322
local_s |= test_sf_check_result(message_buff, r1, val1, tol1);
323
local_s |= test_sf_check_result(message_buff, r2, val2, tol2);
324
local_s |= test_sf_check_return(message_buff, status, expect_return);
325
326
gsl_test(local_s, desc);
327
if(local_s != 0) {
328
/* printf(" %s %d\n", __FILE__, __LINE__); */
329
printf("%s", message_buff);
330
printf(" %22.18e %22.18e\n", r1.val, r1.err);
331
printf(" %22.18e %22.18e\n", r2.val, r2.err);
332
}
333
return local_s;
334
}
335
336
int
337
test_sf_sgn (gsl_sf_result r, double sgn, double val_in, double tol, double expect_sgn, int status,
338
int expect_return, const char * desc)
339
{
340
char message_buff[4096];
341
gsl_sf_result local_r;
342
int local_s = 0;
343
344
message_buff[0] = '\0';
345
346
local_r.val = sgn;
347
local_r.err = 0.0;
348
local_s |= test_sf_check_result(message_buff, r, val_in, tol);
349
local_s |= test_sf_check_result(message_buff, local_r, expect_sgn, 0.0);
350
local_s |= test_sf_check_return(message_buff, status, expect_return);
351
352
gsl_test(local_s, desc);
353
if(local_s != 0) {
354
/* printf(" %s %d\n", __FILE__, __LINE__); */
355
printf("%s", message_buff);
356
printf(" %22.18e %22.18e\n", r.val, r.err);
357
}
358
return local_s;
359
}
360
361
int test_clausen(void)
362
{
363
gsl_sf_result r;
364
int s = 0;
365
366
TEST_SF(s, gsl_sf_clausen_e, (M_PI/20.0, &r), 0.4478882448133546, TEST_TOL0, GSL_SUCCESS);
367
TEST_SF(s, gsl_sf_clausen_e, (M_PI/6.0, &r), 0.8643791310538927, TEST_TOL0, GSL_SUCCESS);
368
TEST_SF(s, gsl_sf_clausen_e, (M_PI/3.0, &r), 1.0149416064096535, TEST_TOL0, GSL_SUCCESS);
369
TEST_SF(s, gsl_sf_clausen_e, ( 2.0*M_PI + M_PI/3.0, &r), 1.0149416064096535, TEST_TOL0, GSL_SUCCESS);
370
TEST_SF(s, gsl_sf_clausen_e, (100.0*M_PI + M_PI/3.0, &r), 1.0149416064096535, TEST_TOL0, GSL_SUCCESS);
371
372
return s;
373
}
374
375
376
int test_coupling(void)
377
{
378
gsl_sf_result r;
379
int s = 0;
380
381
/* Test 3j */
382
383
TEST_SF(s, gsl_sf_coupling_3j_e, (0, 1, 1, 0, 1, -1, &r), sqrt(1.0/2.0), TEST_TOL0, GSL_SUCCESS);
384
TEST_SF(s, gsl_sf_coupling_3j_e, (1, 1, 2, 1, -1, 0, &r), sqrt(1.0/6.0), TEST_TOL0, GSL_SUCCESS);
385
TEST_SF(s, gsl_sf_coupling_3j_e, (2, 4, 6, 0, 2, -2, &r), sqrt(8.0/105.0), TEST_TOL0, GSL_SUCCESS);
386
TEST_SF(s, gsl_sf_coupling_3j_e, (4, 4, 8, 0, 0, 0, &r), sqrt(2.0/35.0), TEST_TOL0, GSL_SUCCESS);
387
TEST_SF(s, gsl_sf_coupling_3j_e, (4, 4, 8, 2, -2, 0, &r), 2.0/3.0*sqrt(2.0/35.0), TEST_TOL2, GSL_SUCCESS);
388
TEST_SF(s, gsl_sf_coupling_3j_e, (4, 4, 8, 4, -4, 0, &r), 1.0/(3.0*sqrt(70.0)), TEST_TOL2, GSL_SUCCESS);
389
390
/* Test 3j error checking */
391
392
TEST_SF(s, gsl_sf_coupling_3j_e, (-1, 1, 2, 1, -1, 0, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
393
TEST_SF(s, gsl_sf_coupling_3j_e, (1, -1, 2, 1, -1, 0, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
394
TEST_SF(s, gsl_sf_coupling_3j_e, (1, 1, -2, 1, -1, 0, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
395
396
/* Test |m_i|<=j_i */
397
398
TEST_SF(s, gsl_sf_coupling_3j_e, (1, 1, 2, 2, -1, 0, &r), 0, 0, GSL_SUCCESS);
399
TEST_SF(s, gsl_sf_coupling_3j_e, (1, 1, 2, 1, -2, 0, &r), 0, 0, GSL_SUCCESS);
400
TEST_SF(s, gsl_sf_coupling_3j_e, (1, 1, 2, 1, -1, 3, &r), 0, 0, GSL_SUCCESS);
401
402
/* Test triangle condition j1 + j2 >= j, j >= j2 - j1, j>= j1 - j2 */
403
404
TEST_SF(s, gsl_sf_coupling_3j_e, (1, 1, 3, 1, -1, 0, &r), 0, 0, GSL_SUCCESS);
405
TEST_SF(s, gsl_sf_coupling_3j_e, (1, 4, 2, 1, -1, 0, &r), 0, 0, GSL_SUCCESS);
406
TEST_SF(s, gsl_sf_coupling_3j_e, (4, 1, 2, 1, -1, 0, &r), 0, 0, GSL_SUCCESS);
407
408
/* Test 6j */
409
410
TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 4, 2, 2, 2, &r), 1.0/6.0, TEST_TOL0, GSL_SUCCESS);
411
TEST_SF(s, gsl_sf_coupling_6j_e, (4, 4, 2, 4, 4, 4, &r), -1.0/10.0, TEST_TOL0, GSL_SUCCESS);
412
TEST_SF(s, gsl_sf_coupling_6j_e, (4, 4, 2, 4, 4, 2, &r), 1.0/6.0, TEST_TOL0, GSL_SUCCESS);
413
TEST_SF(s, gsl_sf_coupling_6j_e, (4, 4, 2, 2, 2, 2, &r), -0.5/sqrt(5.0), TEST_TOL0, GSL_SUCCESS);
414
TEST_SF(s, gsl_sf_coupling_6j_e, (4, 4, 4, 2, 2, 2, &r), sqrt(7.0/3.0)/10.0, TEST_TOL0, GSL_SUCCESS);
415
TEST_SF(s, gsl_sf_coupling_6j_e, (6, 6, 6, 4, 4, 4, &r), -sqrt(3.0/5.0)/14.0, TEST_TOL0, GSL_SUCCESS);
416
TEST_SF(s, gsl_sf_coupling_6j_e, (6, 6, 6, 4, 4, 2, &r), -sqrt(3.0/5.0)/7.0, TEST_TOL0, GSL_SUCCESS);
417
418
/* Test 6j error checking */
419
420
TEST_SF(s, gsl_sf_coupling_6j_e, (-2, 2, 4, 2, 2, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
421
TEST_SF(s, gsl_sf_coupling_6j_e, (2, -2, 4, 2, 2, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
422
TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, -4, 2, 2, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
423
TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 4, -2, 2, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
424
TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 4, 2, -2, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
425
TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 4, 2, 2, -2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
426
427
/* Test 6j triangle conditions */
428
429
TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 4, 2, 2, 7, &r), 0, 0, GSL_SUCCESS);
430
TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 4, 2, 7, 2, &r), 0, 0, GSL_SUCCESS);
431
TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 4, 7, 2, 2, &r), 0, 0, GSL_SUCCESS);
432
TEST_SF(s, gsl_sf_coupling_6j_e, (2, 2, 7, 2, 2, 2, &r), 0, 0, GSL_SUCCESS);
433
TEST_SF(s, gsl_sf_coupling_6j_e, (2, 7, 4, 2, 2, 2, &r), 0, 0, GSL_SUCCESS);
434
TEST_SF(s, gsl_sf_coupling_6j_e, (7, 2, 4, 2, 2, 2, &r), 0, 0, GSL_SUCCESS);
435
436
/* Test 9j */
437
438
TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 2, 1, 1, 2, &r), -sqrt(1.0/6.0)/10.0, TEST_TOL2, GSL_SUCCESS);
439
TEST_SF(s, gsl_sf_coupling_9j_e, (8, 4, 10, 7, 3, 8, 1, 1, 2, &r), sqrt(7.0/3.0)/60.0, TEST_TOL2, GSL_SUCCESS);
440
441
/* Test 9j error checking */
442
443
TEST_SF(s, gsl_sf_coupling_9j_e, (-4, 2, 4, 3, 3, 2, 1, 1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
444
TEST_SF(s, gsl_sf_coupling_9j_e, (4, -2, 4, 3, 3, 2, 1, 1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
445
TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, -4, 3, 3, 2, 1, 1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
446
TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, -3, 3, 2, 1, 1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
447
TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, -3, 2, 1, 1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
448
TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, -2, 1, 1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
449
TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 2, -1, 1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
450
TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 2, 1, -1, 2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
451
TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 2, 1, 1, -2, &r), GSL_NAN, GSL_NAN, GSL_EDOM);
452
453
TEST_SF(s, gsl_sf_coupling_9j_e, (10, 2, 4, 3, 3, 2, 1, 1, 2, &r), 0, 0, GSL_SUCCESS);
454
TEST_SF(s, gsl_sf_coupling_9j_e, (4, 10, 4, 3, 3, 2, 1, 1, 2, &r), 0, 0, GSL_SUCCESS);
455
TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 10, 3, 3, 2, 1, 1, 2, &r), 0, 0, GSL_SUCCESS);
456
TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 10, 3, 2, 1, 1, 2, &r), 0, 0, GSL_SUCCESS);
457
TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 10, 2, 1, 1, 2, &r), 0, 0, GSL_SUCCESS);
458
TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 10, 1, 1, 2, &r), 0, 0, GSL_SUCCESS);
459
TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 2, 10, 1, 2, &r), 0, 0, GSL_SUCCESS);
460
TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 2, 1, 10, 2, &r), 0, 0, GSL_SUCCESS);
461
TEST_SF(s, gsl_sf_coupling_9j_e, (4, 2, 4, 3, 3, 2, 1, 1, 10, &r), 0, 0, GSL_SUCCESS);
462
return s;
463
}
464
465
int test_dawson(void)
466
{
467
gsl_sf_result r;
468
int s = 0;
469
470
TEST_SF(s, gsl_sf_dawson_e, (1.0e-15, &r), 1.0e-15, TEST_TOL0, GSL_SUCCESS);
471
TEST_SF(s, gsl_sf_dawson_e, (0.5, &r), 0.4244363835020222959, TEST_TOL0, GSL_SUCCESS);
472
TEST_SF(s, gsl_sf_dawson_e, (2.0, &r), 0.30134038892379196603, TEST_TOL0, GSL_SUCCESS);
473
TEST_SF(s, gsl_sf_dawson_e, (1000.0, &r), 0.0005000002500003750009, TEST_TOL0, GSL_SUCCESS);
474
475
return s;
476
}
477
478
int test_debye(void)
479
{
480
gsl_sf_result r;
481
int s = 0;
482
483
TEST_SF(s, gsl_sf_debye_1_e, (0.1, &r), 0.975277750004723276, TEST_TOL0, GSL_SUCCESS);
484
TEST_SF(s, gsl_sf_debye_1_e, (1.0, &r), 0.777504634112248239, TEST_TOL0, GSL_SUCCESS);
485
TEST_SF(s, gsl_sf_debye_1_e, (10.0, &r), 0.164443465679946027, TEST_TOL0, GSL_SUCCESS);
486
487
TEST_SF(s, gsl_sf_debye_2_e, (0.1, &r), 0.967083287045302664, TEST_TOL0, GSL_SUCCESS);
488
TEST_SF(s, gsl_sf_debye_2_e, (1.0, &r), 0.70787847562782924, TEST_TOL0, GSL_SUCCESS);
489
TEST_SF(s, gsl_sf_debye_2_e, (10.0, &r), 0.0479714980201218708, TEST_TOL0, GSL_SUCCESS);
490
491
TEST_SF(s, gsl_sf_debye_3_e, (0.1, &r), 0.962999940487211048, TEST_TOL0, GSL_SUCCESS);
492
TEST_SF(s, gsl_sf_debye_3_e, (1.0, &r), 0.674415564077814667, TEST_TOL0, GSL_SUCCESS);
493
TEST_SF(s, gsl_sf_debye_3_e, (10.0, &r), 0.0192957656903454886, TEST_TOL0, GSL_SUCCESS);
494
495
TEST_SF(s, gsl_sf_debye_4_e, (0.1, &r), 0.960555486124335944, TEST_TOL0, GSL_SUCCESS);
496
TEST_SF(s, gsl_sf_debye_4_e, (1.0, &r), 0.654874068886737049, TEST_TOL0, GSL_SUCCESS);
497
TEST_SF(s, gsl_sf_debye_4_e, (10.0, &r), 0.00967367556027115896, TEST_TOL0, GSL_SUCCESS);
498
499
TEST_SF(s, gsl_sf_debye_5_e, (0.1, &r), 0.95892849428310568745, TEST_TOL0, GSL_SUCCESS);
500
TEST_SF(s, gsl_sf_debye_5_e, (1.0, &r), 0.6421002580217790246, TEST_TOL0, GSL_SUCCESS);
501
TEST_SF(s, gsl_sf_debye_5_e, (10.0, &r), 0.005701535852992908538, TEST_TOL0, GSL_SUCCESS);
502
503
TEST_SF(s, gsl_sf_debye_6_e, (0.1, &r), 0.95776777382605465878, TEST_TOL0, GSL_SUCCESS);
504
TEST_SF(s, gsl_sf_debye_6_e, (1.0, &r), 0.63311142583495107588, TEST_TOL0, GSL_SUCCESS);
505
TEST_SF(s, gsl_sf_debye_6_e, (10.0, &r), 3.7938493294615955279e-3, TEST_TOL0, GSL_SUCCESS);
506
507
return s;
508
}
509
510
511
int test_elementary(void)
512
{
513
gsl_sf_result r;
514
double x = 0.2*DBL_MAX;
515
int s = 0;
516
517
TEST_SF(s, gsl_sf_multiply_e, (-3.0,2.0, &r), -6.0, TEST_TOL0, GSL_SUCCESS);
518
TEST_SF(s, gsl_sf_multiply_e, (x, 1.0/x, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
519
TEST_SF(s, gsl_sf_multiply_e, (x, 0.2, &r), 0.04*DBL_MAX, TEST_TOL1, GSL_SUCCESS);
520
TEST_SF(s, gsl_sf_multiply_e, (x, 4.0, &r), 0.8*DBL_MAX, TEST_TOL1, GSL_SUCCESS);
521
s += ( gsl_sf_multiply_e(DBL_MAX, 1.1, &r) != GSL_EOVRFLW);
522
s += ( gsl_sf_multiply_e(DBL_MIN, DBL_MIN, &r) != GSL_EUNDRFLW);
523
s += ( gsl_sf_multiply_e(DBL_MIN, -DBL_MIN, &r) != GSL_EUNDRFLW);
524
525
return s;
526
}
527
528
529
int test_ellint(void)
530
{
531
gsl_sf_result r;
532
gsl_mode_t mode = GSL_MODE_DEFAULT;
533
int s = 0;
534
535
TEST_SF(s, gsl_sf_ellint_Kcomp_e, ( 0.99, mode, &r), 3.3566005233611923760, TEST_TOL0, GSL_SUCCESS);
536
TEST_SF(s, gsl_sf_ellint_Kcomp_e, ( 0.50, mode, &r), 1.6857503548125960429, TEST_TOL0, GSL_SUCCESS);
537
TEST_SF(s, gsl_sf_ellint_Kcomp_e, (0.010, mode, &r), 1.5708355989121522360, TEST_TOL0, GSL_SUCCESS);
538
539
TEST_SF(s, gsl_sf_ellint_Ecomp_e, (0.99, mode, &r), 1.0284758090288040010, TEST_TOL0, GSL_SUCCESS);
540
TEST_SF(s, gsl_sf_ellint_Ecomp_e, (0.50, mode, &r), 1.4674622093394271555, TEST_TOL0, GSL_SUCCESS);
541
TEST_SF(s, gsl_sf_ellint_Ecomp_e, (0.01, mode, &r), 1.5707570561503852873, TEST_TOL0, GSL_SUCCESS);
542
543
TEST_SF(s, gsl_sf_ellint_Pcomp_e, (0.99, 0.1, mode, &r), 3.13792612351836506315593, TEST_TOL0, GSL_SUCCESS);
544
TEST_SF(s, gsl_sf_ellint_Pcomp_e, (0.50, 0.1, mode, &r), 1.60455249360848890075108, TEST_TOL0, GSL_SUCCESS);
545
TEST_SF(s, gsl_sf_ellint_Pcomp_e, (0.01, 0.1, mode, &r), 1.49773208536003801277453, TEST_TOL0, GSL_SUCCESS);
546
547
TEST_SF(s, gsl_sf_ellint_Dcomp_e, (0.99, mode, &r), 2.375395076351788975665323192, TEST_TOL0, GSL_SUCCESS);
548
TEST_SF(s, gsl_sf_ellint_Dcomp_e, (0.50, mode, &r), 0.8731525818926755496456335628, TEST_TOL0, GSL_SUCCESS);
549
TEST_SF(s, gsl_sf_ellint_Dcomp_e, (0.01, mode, &r), 0.7854276176694868932799393751, TEST_TOL0, GSL_SUCCESS);
550
551
TEST_SF(s, gsl_sf_ellint_F_e, (M_PI/3.0, 0.99, mode, &r), 1.3065333392738766762, TEST_TOL0, GSL_SUCCESS);
552
TEST_SF(s, gsl_sf_ellint_F_e, (M_PI/3.0, 0.50, mode, &r), 1.0895506700518854093, TEST_TOL0, GSL_SUCCESS);
553
TEST_SF(s, gsl_sf_ellint_F_e, (M_PI/3.0, 0.01, mode, &r), 1.0472129063770918952, TEST_TOL0, GSL_SUCCESS);
554
555
TEST_SF(s, gsl_sf_ellint_E_e, (M_PI/3.0, 0.99, mode, &r), 0.8704819220377943536, TEST_TOL0, GSL_SUCCESS);
556
TEST_SF(s, gsl_sf_ellint_E_e, (M_PI/3.0, 0.50, mode, &r), 1.0075555551444720293, TEST_TOL0, GSL_SUCCESS);
557
TEST_SF(s, gsl_sf_ellint_E_e, (M_PI/3.0, 0.01, mode, &r), 1.0471821963889481104, TEST_TOL0, GSL_SUCCESS);
558
559
TEST_SF(s, gsl_sf_ellint_P_e, (M_PI/3.0, 0.99, 0.5, mode, &r), 1.1288726598764099882, TEST_TOL0, GSL_SUCCESS);
560
TEST_SF(s, gsl_sf_ellint_P_e, (M_PI/3.0, 0.50, 0.5, mode, &r), 0.9570574331323584890, TEST_TOL0, GSL_SUCCESS);
561
TEST_SF(s, gsl_sf_ellint_P_e, (M_PI/3.0, 0.01, 0.5, mode, &r), 0.9228868127118118465, TEST_TOL0, GSL_SUCCESS);
562
563
TEST_SF(s, gsl_sf_ellint_RF_e, (5.0e-11, 1.0e-10, 1.0, mode, &r), 12.36441982979439, TEST_TOL0, GSL_SUCCESS);
564
565
TEST_SF(s, gsl_sf_ellint_RF_e, (1.0, 2.0, 3.0, mode, &r), 0.7269459354689082, TEST_TOL0, GSL_SUCCESS);
566
567
TEST_SF(s, gsl_sf_ellint_RD_e, (5.0e-11, 1.0e-10, 1.0, mode, &r), 34.0932594919337362, TEST_TOL0, GSL_SUCCESS);
568
569
TEST_SF(s, gsl_sf_ellint_RD_e, (1.0, 2.0, 3.0, mode, &r), 0.2904602810289906, TEST_TOL0, GSL_SUCCESS);
570
571
TEST_SF(s, gsl_sf_ellint_RC_e, (1.0, 2.0, mode, &r), 0.7853981633974482, TEST_TOL0, GSL_SUCCESS);
572
573
TEST_SF(s, gsl_sf_ellint_RJ_e, (2.0, 3.0, 4.0, 5.0, mode, &r), 0.1429757966715675, TEST_TOL0, GSL_SUCCESS);
574
575
/* E, argument phi > pi/2 */
576
577
TEST_SF(s, gsl_sf_ellint_E_e, (M_PI/2.0, 0.99, mode, &r), 1.02847580902880400098389, TEST_TOL0, GSL_SUCCESS);
578
TEST_SF(s, gsl_sf_ellint_E_e, (M_PI/2.0, 0.50, mode, &r), 1.46746220933942715545980, TEST_TOL0, GSL_SUCCESS);
579
TEST_SF(s, gsl_sf_ellint_E_e, (M_PI/2.0, 0.01, mode, &r), 1.57075705615038528733708, TEST_TOL0, GSL_SUCCESS);
580
581
TEST_SF(s, gsl_sf_ellint_E_e, (2*M_PI/3.0, 0.99, mode, &r), 1.18646969601981364833972, TEST_TOL1, GSL_SUCCESS);
582
TEST_SF(s, gsl_sf_ellint_E_e, (2*M_PI/3.0, 0.50, mode, &r), 1.92736886353438228163734, TEST_TOL0, GSL_SUCCESS);
583
TEST_SF(s, gsl_sf_ellint_E_e, (2*M_PI/3.0, 0.01, mode, &r), 2.09433191591182246425715, TEST_TOL0, GSL_SUCCESS);
584
585
TEST_SF(s, gsl_sf_ellint_E_e, (M_PI, 0.99, mode, &r), 2.05695161805760800196777, TEST_TOL0, GSL_SUCCESS);
586
TEST_SF(s, gsl_sf_ellint_E_e, (M_PI, 0.50, mode, &r), 2.93492441867885431091959, TEST_TOL0, GSL_SUCCESS);
587
TEST_SF(s, gsl_sf_ellint_E_e, (M_PI, 0.01, mode, &r), 3.14151411230077057467416, TEST_TOL0, GSL_SUCCESS);
588
589
TEST_SF(s, gsl_sf_ellint_E_e, (4*M_PI/3, 0.99, mode, &r), 2.92743354009540235559582, TEST_TOL0, GSL_SUCCESS);
590
TEST_SF(s, gsl_sf_ellint_E_e, (4*M_PI/3, 0.50, mode, &r), 3.94247997382332634020184, TEST_TOL0, GSL_SUCCESS);
591
TEST_SF(s, gsl_sf_ellint_E_e, (4*M_PI/3, 0.01, mode, &r), 4.18869630868971868509117, TEST_TOL0, GSL_SUCCESS);
592
593
TEST_SF(s, gsl_sf_ellint_E_e, (3*M_PI/2.0, 0.99, mode, &r), 3.08542742708641200295166, TEST_TOL0, GSL_SUCCESS);
594
TEST_SF(s, gsl_sf_ellint_E_e, (3*M_PI/2.0, 0.50, mode, &r), 4.40238662801828146637939, TEST_TOL0, GSL_SUCCESS);
595
TEST_SF(s, gsl_sf_ellint_E_e, (3*M_PI/2.0, 0.01, mode, &r), 4.71227116845115586201123, TEST_TOL0, GSL_SUCCESS);
596
597
TEST_SF(s, gsl_sf_ellint_E_e, (5*M_PI/3, 0.99, mode, &r), 3.24342131407742165030750, TEST_TOL1, GSL_SUCCESS);
598
TEST_SF(s, gsl_sf_ellint_E_e, (5*M_PI/3, 0.50, mode, &r), 4.86229328221323659255693, TEST_TOL0, GSL_SUCCESS);
599
TEST_SF(s, gsl_sf_ellint_E_e, (5*M_PI/3, 0.01, mode, &r), 5.23584602821259303893130, TEST_TOL0, GSL_SUCCESS);
600
601
TEST_SF(s, gsl_sf_ellint_E_e, (2*M_PI, 0.99, mode, &r), 4.11390323611521600393555, TEST_TOL0, GSL_SUCCESS);
602
TEST_SF(s, gsl_sf_ellint_E_e, (2*M_PI, 0.50, mode, &r), 5.86984883735770862183918, TEST_TOL0, GSL_SUCCESS);
603
TEST_SF(s, gsl_sf_ellint_E_e, (2*M_PI, 0.01, mode, &r), 6.28302822460154114934831, TEST_TOL0, GSL_SUCCESS);
604
605
TEST_SF(s, gsl_sf_ellint_E_e, (7*M_PI/3.0, 0.99, mode, &r), 4.98438515815301035756360, TEST_TOL0, GSL_SUCCESS);
606
TEST_SF(s, gsl_sf_ellint_E_e, (7*M_PI/3.0, 0.50, mode, &r), 6.87740439250218065112143, TEST_TOL0, GSL_SUCCESS);
607
TEST_SF(s, gsl_sf_ellint_E_e, (7*M_PI/3.0, 0.01, mode, &r), 7.33021042099048925976532, TEST_TOL0, GSL_SUCCESS);
608
609
/* Test some negative arguments, phi < 0 */
610
611
TEST_SF(s, gsl_sf_ellint_E_e, (-M_PI/2.0, 0.99, mode, &r), -1.02847580902880400098389, TEST_TOL0, GSL_SUCCESS);
612
TEST_SF(s, gsl_sf_ellint_E_e, (-M_PI/2.0, 0.50, mode, &r), -1.46746220933942715545980, TEST_TOL0, GSL_SUCCESS);
613
TEST_SF(s, gsl_sf_ellint_E_e, (-M_PI/2.0, 0.01, mode, &r), -1.57075705615038528733708, TEST_TOL0, GSL_SUCCESS);
614
615
TEST_SF(s, gsl_sf_ellint_E_e, (-2*M_PI/3.0, 0.99, mode, &r), -1.18646969601981364833972, TEST_TOL1, GSL_SUCCESS);
616
TEST_SF(s, gsl_sf_ellint_E_e, (-2*M_PI/3.0, 0.50, mode, &r), -1.92736886353438228163734, TEST_TOL0, GSL_SUCCESS);
617
TEST_SF(s, gsl_sf_ellint_E_e, (-2*M_PI/3.0, 0.01, mode, &r), -2.09433191591182246425715, TEST_TOL0, GSL_SUCCESS);
618
619
TEST_SF(s, gsl_sf_ellint_E_e, (-M_PI, 0.99, mode, &r), -2.05695161805760800196777, TEST_TOL0, GSL_SUCCESS);
620
TEST_SF(s, gsl_sf_ellint_E_e, (-M_PI, 0.50, mode, &r), -2.93492441867885431091959, TEST_TOL0, GSL_SUCCESS);
621
TEST_SF(s, gsl_sf_ellint_E_e, (-M_PI, 0.01, mode, &r), -3.14151411230077057467416, TEST_TOL0, GSL_SUCCESS);
622
623
TEST_SF(s, gsl_sf_ellint_E_e, (-4*M_PI/3, 0.99, mode, &r), -2.92743354009540235559582, TEST_TOL0, GSL_SUCCESS);
624
TEST_SF(s, gsl_sf_ellint_E_e, (-4*M_PI/3, 0.50, mode, &r), -3.94247997382332634020184, TEST_TOL0, GSL_SUCCESS);
625
TEST_SF(s, gsl_sf_ellint_E_e, (-4*M_PI/3, 0.01, mode, &r), -4.18869630868971868509117, TEST_TOL0, GSL_SUCCESS);
626
627
TEST_SF(s, gsl_sf_ellint_E_e, (-3*M_PI/2.0, 0.99, mode, &r), -3.08542742708641200295166, TEST_TOL0, GSL_SUCCESS);
628
TEST_SF(s, gsl_sf_ellint_E_e, (-3*M_PI/2.0, 0.50, mode, &r), -4.40238662801828146637939, TEST_TOL0, GSL_SUCCESS);
629
TEST_SF(s, gsl_sf_ellint_E_e, (-3*M_PI/2.0, 0.01, mode, &r), -4.71227116845115586201123, TEST_TOL0, GSL_SUCCESS);
630
631
TEST_SF(s, gsl_sf_ellint_E_e, (-5*M_PI/3, 0.99, mode, &r), -3.24342131407742165030750, TEST_TOL1, GSL_SUCCESS);
632
TEST_SF(s, gsl_sf_ellint_E_e, (-5*M_PI/3, 0.50, mode, &r), -4.86229328221323659255693, TEST_TOL0, GSL_SUCCESS);
633
TEST_SF(s, gsl_sf_ellint_E_e, (-5*M_PI/3, 0.01, mode, &r), -5.23584602821259303893130, TEST_TOL0, GSL_SUCCESS);
634
635
TEST_SF(s, gsl_sf_ellint_E_e, (-2*M_PI, 0.99, mode, &r), -4.11390323611521600393555, TEST_TOL0, GSL_SUCCESS);
636
TEST_SF(s, gsl_sf_ellint_E_e, (-2*M_PI, 0.50, mode, &r), -5.86984883735770862183918, TEST_TOL0, GSL_SUCCESS);
637
TEST_SF(s, gsl_sf_ellint_E_e, (-2*M_PI, 0.01, mode, &r), -6.28302822460154114934831, TEST_TOL0, GSL_SUCCESS);
638
639
TEST_SF(s, gsl_sf_ellint_E_e, (-7*M_PI/3.0, 0.99, mode, &r), -4.98438515815301035756360, TEST_TOL0, GSL_SUCCESS);
640
TEST_SF(s, gsl_sf_ellint_E_e, (-7*M_PI/3.0, 0.50, mode, &r), -6.87740439250218065112143, TEST_TOL0, GSL_SUCCESS);
641
TEST_SF(s, gsl_sf_ellint_E_e, (-7*M_PI/3.0, 0.01, mode, &r), -7.33021042099048925976532, TEST_TOL0, GSL_SUCCESS);
642
643
644
/* F, argument phi > pi/2 */
645
646
TEST_SF(s, gsl_sf_ellint_F_e, (M_PI/2.0, 0.99, mode, &r), 3.35660052336119237603347, TEST_TOL0, GSL_SUCCESS);
647
TEST_SF(s, gsl_sf_ellint_F_e, (M_PI/2.0, 0.50, mode, &r), 1.68575035481259604287120, TEST_TOL0, GSL_SUCCESS);
648
TEST_SF(s, gsl_sf_ellint_F_e, (M_PI/2.0, 0.01, mode, &r), 1.57083559891215223602641, TEST_TOL0, GSL_SUCCESS);
649
650
TEST_SF(s, gsl_sf_ellint_F_e, (2*M_PI/3.0, 0.99, mode, &r), 5.40666770744850807588478, TEST_TOL0, GSL_SUCCESS);
651
TEST_SF(s, gsl_sf_ellint_F_e, (2*M_PI/3.0, 0.50, mode, &r), 2.28195003957330667648585, TEST_TOL0, GSL_SUCCESS);
652
TEST_SF(s, gsl_sf_ellint_F_e, (2*M_PI/3.0, 0.01, mode, &r), 2.09445829144721257687207, TEST_TOL0, GSL_SUCCESS);
653
654
TEST_SF(s, gsl_sf_ellint_F_e, (M_PI, 0.99, mode, &r), 6.71320104672238475206694, TEST_TOL0, GSL_SUCCESS);
655
TEST_SF(s, gsl_sf_ellint_F_e, (M_PI, 0.50, mode, &r), 3.37150070962519208574241, TEST_TOL0, GSL_SUCCESS);
656
TEST_SF(s, gsl_sf_ellint_F_e, (M_PI, 0.01, mode, &r), 3.14167119782430447205281, TEST_TOL0, GSL_SUCCESS);
657
658
TEST_SF(s, gsl_sf_ellint_F_e, (4*M_PI/3, 0.99, mode, &r), 8.01973438599626142824910, TEST_TOL0, GSL_SUCCESS);
659
TEST_SF(s, gsl_sf_ellint_F_e, (4*M_PI/3, 0.50, mode, &r), 4.46105137967707749499897, TEST_TOL0, GSL_SUCCESS);
660
TEST_SF(s, gsl_sf_ellint_F_e, (4*M_PI/3, 0.01, mode, &r), 4.18888410420139636723356, TEST_TOL0, GSL_SUCCESS);
661
662
TEST_SF(s, gsl_sf_ellint_F_e, (3*M_PI/2.0, 0.99, mode, &r), 10.0698015700835771281004, TEST_TOL0, GSL_SUCCESS);
663
TEST_SF(s, gsl_sf_ellint_F_e, (3*M_PI/2.0, 0.50, mode, &r), 5.05725106443778812861361, TEST_TOL0, GSL_SUCCESS);
664
TEST_SF(s, gsl_sf_ellint_F_e, (3*M_PI/2.0, 0.01, mode, &r), 4.71250679673645670807922, TEST_TOL0, GSL_SUCCESS);
665
666
TEST_SF(s, gsl_sf_ellint_F_e, (5*M_PI/3, 0.99, mode, &r), 12.1198687541708928279517, TEST_TOL0, GSL_SUCCESS);
667
TEST_SF(s, gsl_sf_ellint_F_e, (5*M_PI/3, 0.50, mode, &r), 5.65345074919849876222825, TEST_TOL0, GSL_SUCCESS);
668
TEST_SF(s, gsl_sf_ellint_F_e, (5*M_PI/3, 0.01, mode, &r), 5.23612948927151704892488, TEST_TOL0, GSL_SUCCESS);
669
670
TEST_SF(s, gsl_sf_ellint_F_e, (2*M_PI, 0.99, mode, &r), 13.4264020934447695041339, TEST_TOL0, GSL_SUCCESS);
671
TEST_SF(s, gsl_sf_ellint_F_e, (2*M_PI, 0.50, mode, &r), 6.74300141925038417148481, TEST_TOL0, GSL_SUCCESS);
672
TEST_SF(s, gsl_sf_ellint_F_e, (2*M_PI, 0.01, mode, &r), 6.28334239564860894410562, TEST_TOL0, GSL_SUCCESS);
673
674
TEST_SF(s, gsl_sf_ellint_F_e, (7*M_PI/3.0, 0.99, mode, &r), 14.7329354327186461803160, TEST_TOL0, GSL_SUCCESS);
675
TEST_SF(s, gsl_sf_ellint_F_e, (7*M_PI/3.0, 0.50, mode, &r), 7.83255208930226958074138, TEST_TOL0, GSL_SUCCESS);
676
TEST_SF(s, gsl_sf_ellint_F_e, (7*M_PI/3.0, 0.01, mode, &r), 7.33055530202570083928637, TEST_TOL0, GSL_SUCCESS);
677
678
/* F, negative argument phi < 0 */
679
680
TEST_SF(s, gsl_sf_ellint_F_e, (-M_PI/2.0, 0.99, mode, &r), -3.35660052336119237603347, TEST_TOL0, GSL_SUCCESS);
681
TEST_SF(s, gsl_sf_ellint_F_e, (-M_PI/2.0, 0.50, mode, &r), -1.68575035481259604287120, TEST_TOL0, GSL_SUCCESS);
682
TEST_SF(s, gsl_sf_ellint_F_e, (-M_PI/2.0, 0.01, mode, &r), -1.57083559891215223602641, TEST_TOL0, GSL_SUCCESS);
683
684
TEST_SF(s, gsl_sf_ellint_F_e, (-2*M_PI/3.0, 0.99, mode, &r), -5.40666770744850807588478, TEST_TOL0, GSL_SUCCESS);
685
TEST_SF(s, gsl_sf_ellint_F_e, (-2*M_PI/3.0, 0.50, mode, &r), -2.28195003957330667648585, TEST_TOL0, GSL_SUCCESS);
686
TEST_SF(s, gsl_sf_ellint_F_e, (-2*M_PI/3.0, 0.01, mode, &r), -2.09445829144721257687207, TEST_TOL0, GSL_SUCCESS);
687
688
TEST_SF(s, gsl_sf_ellint_F_e, (-M_PI, 0.99, mode, &r), -6.71320104672238475206694, TEST_TOL0, GSL_SUCCESS);
689
TEST_SF(s, gsl_sf_ellint_F_e, (-M_PI, 0.50, mode, &r), -3.37150070962519208574241, TEST_TOL0, GSL_SUCCESS);
690
TEST_SF(s, gsl_sf_ellint_F_e, (-M_PI, 0.01, mode, &r), -3.14167119782430447205281, TEST_TOL0, GSL_SUCCESS);
691
692
TEST_SF(s, gsl_sf_ellint_F_e, (-4*M_PI/3, 0.99, mode, &r), -8.01973438599626142824910, TEST_TOL0, GSL_SUCCESS);
693
TEST_SF(s, gsl_sf_ellint_F_e, (-4*M_PI/3, 0.50, mode, &r), -4.46105137967707749499897, TEST_TOL0, GSL_SUCCESS);
694
TEST_SF(s, gsl_sf_ellint_F_e, (-4*M_PI/3, 0.01, mode, &r), -4.18888410420139636723356, TEST_TOL0, GSL_SUCCESS);
695
696
TEST_SF(s, gsl_sf_ellint_F_e, (-3*M_PI/2.0, 0.99, mode, &r), -10.0698015700835771281004, TEST_TOL0, GSL_SUCCESS);
697
TEST_SF(s, gsl_sf_ellint_F_e, (-3*M_PI/2.0, 0.50, mode, &r), -5.05725106443778812861361, TEST_TOL0, GSL_SUCCESS);
698
TEST_SF(s, gsl_sf_ellint_F_e, (-3*M_PI/2.0, 0.01, mode, &r), -4.71250679673645670807922, TEST_TOL0, GSL_SUCCESS);
699
700
TEST_SF(s, gsl_sf_ellint_F_e, (-5*M_PI/3, 0.99, mode, &r), -12.1198687541708928279517, TEST_TOL0, GSL_SUCCESS);
701
TEST_SF(s, gsl_sf_ellint_F_e, (-5*M_PI/3, 0.50, mode, &r), -5.65345074919849876222825, TEST_TOL0, GSL_SUCCESS);
702
TEST_SF(s, gsl_sf_ellint_F_e, (-5*M_PI/3, 0.01, mode, &r), -5.23612948927151704892488, TEST_TOL0, GSL_SUCCESS);
703
704
TEST_SF(s, gsl_sf_ellint_F_e, (-2*M_PI, 0.99, mode, &r), -13.4264020934447695041339, TEST_TOL0, GSL_SUCCESS);
705
TEST_SF(s, gsl_sf_ellint_F_e, (-2*M_PI, 0.50, mode, &r), -6.74300141925038417148481, TEST_TOL0, GSL_SUCCESS);
706
TEST_SF(s, gsl_sf_ellint_F_e, (-2*M_PI, 0.01, mode, &r), -6.28334239564860894410562, TEST_TOL0, GSL_SUCCESS);
707
708
TEST_SF(s, gsl_sf_ellint_F_e, (-7*M_PI/3.0, 0.99, mode, &r), -14.7329354327186461803160, TEST_TOL0, GSL_SUCCESS);
709
TEST_SF(s, gsl_sf_ellint_F_e, (-7*M_PI/3.0, 0.50, mode, &r), -7.83255208930226958074138, TEST_TOL0, GSL_SUCCESS);
710
TEST_SF(s, gsl_sf_ellint_F_e, (-7*M_PI/3.0, 0.01, mode, &r), -7.33055530202570083928637, TEST_TOL0, GSL_SUCCESS);
711
712
/* P, argument phi > pi/2 */
713
714
TEST_SF(s, gsl_sf_ellint_P_e, (M_PI/2.0, 0.99, -0.1, mode, &r), 3.61678162163246646783050, TEST_TOL0, GSL_SUCCESS);
715
TEST_SF(s, gsl_sf_ellint_P_e, (M_PI/2.0, 0.50, -0.1, mode, &r), 1.78030349465454812629168, TEST_TOL0, GSL_SUCCESS);
716
TEST_SF(s, gsl_sf_ellint_P_e, (M_PI/2.0, 0.01, -0.1, mode, &r), 1.65580719756898353270922, TEST_TOL0, GSL_SUCCESS);
717
718
TEST_SF(s, gsl_sf_ellint_P_e, (2*M_PI/3.0, 0.99, -0.1, mode, &r), 5.88008918207571119911983, TEST_TOL0, GSL_SUCCESS);
719
TEST_SF(s, gsl_sf_ellint_P_e, (2*M_PI/3.0, 0.50, -0.1, mode, &r), 2.43655207300356008717867, TEST_TOL0, GSL_SUCCESS);
720
TEST_SF(s, gsl_sf_ellint_P_e, (2*M_PI/3.0, 0.01, -0.1, mode, &r), 2.23211110528200554950903, TEST_TOL0, GSL_SUCCESS);
721
722
TEST_SF(s, gsl_sf_ellint_P_e, (M_PI, 0.99, -0.1, mode, &r), 7.23356324326493293566099, TEST_TOL0, GSL_SUCCESS);
723
TEST_SF(s, gsl_sf_ellint_P_e, (M_PI, 0.50, -0.1, mode, &r), 3.56060698930909625258336, TEST_TOL0, GSL_SUCCESS);
724
TEST_SF(s, gsl_sf_ellint_P_e, (M_PI, 0.01, -0.1, mode, &r), 3.31161439513796706541844, TEST_TOL0, GSL_SUCCESS);
725
726
TEST_SF(s, gsl_sf_ellint_P_e, (4*M_PI/3, 0.99, -0.1, mode, &r), 8.58703730445415467220216, TEST_TOL0, GSL_SUCCESS);
727
TEST_SF(s, gsl_sf_ellint_P_e, (4*M_PI/3, 0.50, -0.1, mode, &r), 4.68466190561463241798805, TEST_TOL0, GSL_SUCCESS);
728
TEST_SF(s, gsl_sf_ellint_P_e, (4*M_PI/3, 0.01, -0.1, mode, &r), 4.39111768499392858132786, TEST_TOL0, GSL_SUCCESS);
729
730
TEST_SF(s, gsl_sf_ellint_P_e, (3*M_PI/2.0, 0.99, -0.1, mode, &r), 10.8503448648973994034915, TEST_TOL0, GSL_SUCCESS);
731
TEST_SF(s, gsl_sf_ellint_P_e, (3*M_PI/2.0, 0.50, -0.1, mode, &r), 5.34091048396364437887504, TEST_TOL0, GSL_SUCCESS);
732
TEST_SF(s, gsl_sf_ellint_P_e, (3*M_PI/2.0, 0.01, -0.1, mode, &r), 4.96742159270695059812767, TEST_TOL0, GSL_SUCCESS);
733
734
TEST_SF(s, gsl_sf_ellint_P_e, (5*M_PI/3, 0.99, -0.1, mode, &r), 13.1136524253406441347808, TEST_TOL0, GSL_SUCCESS);
735
TEST_SF(s, gsl_sf_ellint_P_e, (5*M_PI/3, 0.50, -0.1, mode, &r), 5.99715906231265633976204, TEST_TOL0, GSL_SUCCESS);
736
TEST_SF(s, gsl_sf_ellint_P_e, (5*M_PI/3, 0.01, -0.1, mode, &r), 5.54372550041997261492747, TEST_TOL0, GSL_SUCCESS);
737
738
TEST_SF(s, gsl_sf_ellint_P_e, (2*M_PI, 0.99, -0.1, mode, &r), 14.4671264865298658713220, TEST_TOL0, GSL_SUCCESS);
739
TEST_SF(s, gsl_sf_ellint_P_e, (2*M_PI, 0.50, -0.1, mode, &r), 7.12121397861819250516672, TEST_TOL0, GSL_SUCCESS);
740
TEST_SF(s, gsl_sf_ellint_P_e, (2*M_PI, 0.01, -0.1, mode, &r), 6.62322879027593413083689, TEST_TOL0, GSL_SUCCESS);
741
742
TEST_SF(s, gsl_sf_ellint_P_e, (7*M_PI/3.0, 0.99, -0.1, mode, &r), 15.8206005477190876078631, TEST_TOL0, GSL_SUCCESS);
743
TEST_SF(s, gsl_sf_ellint_P_e, (7*M_PI/3.0, 0.50, -0.1, mode, &r), 8.24526889492372867057141, TEST_TOL0, GSL_SUCCESS);
744
TEST_SF(s, gsl_sf_ellint_P_e, (7*M_PI/3.0, 0.01, -0.1, mode, &r), 7.70273208013189564674630, TEST_TOL0, GSL_SUCCESS);
745
746
/* P, negative argument phi < 0 */
747
748
TEST_SF(s, gsl_sf_ellint_P_e, (-M_PI/2.0, 0.99, -0.1, mode, &r), -3.61678162163246646783050, TEST_TOL0, GSL_SUCCESS);
749
TEST_SF(s, gsl_sf_ellint_P_e, (-M_PI/2.0, 0.50, -0.1, mode, &r), -1.78030349465454812629168, TEST_TOL0, GSL_SUCCESS);
750
TEST_SF(s, gsl_sf_ellint_P_e, (-M_PI/2.0, 0.01, -0.1, mode, &r), -1.65580719756898353270922, TEST_TOL0, GSL_SUCCESS);
751
752
TEST_SF(s, gsl_sf_ellint_P_e, (-2*M_PI/3.0, 0.99, -0.1, mode, &r), -5.88008918207571119911983, TEST_TOL0, GSL_SUCCESS);
753
TEST_SF(s, gsl_sf_ellint_P_e, (-2*M_PI/3.0, 0.50, -0.1, mode, &r), -2.43655207300356008717867, TEST_TOL0, GSL_SUCCESS);
754
TEST_SF(s, gsl_sf_ellint_P_e, (-2*M_PI/3.0, 0.01, -0.1, mode, &r), -2.23211110528200554950903, TEST_TOL0, GSL_SUCCESS);
755
756
TEST_SF(s, gsl_sf_ellint_P_e, (-M_PI, 0.99, -0.1, mode, &r), -7.23356324326493293566099, TEST_TOL0, GSL_SUCCESS);
757
TEST_SF(s, gsl_sf_ellint_P_e, (-M_PI, 0.50, -0.1, mode, &r), -3.56060698930909625258336, TEST_TOL0, GSL_SUCCESS);
758
TEST_SF(s, gsl_sf_ellint_P_e, (-M_PI, 0.01, -0.1, mode, &r), -3.31161439513796706541844, TEST_TOL0, GSL_SUCCESS);
759
760
TEST_SF(s, gsl_sf_ellint_P_e, (-4*M_PI/3, 0.99, -0.1, mode, &r), -8.58703730445415467220216, TEST_TOL0, GSL_SUCCESS);
761
TEST_SF(s, gsl_sf_ellint_P_e, (-4*M_PI/3, 0.50, -0.1, mode, &r), -4.68466190561463241798805, TEST_TOL0, GSL_SUCCESS);
762
TEST_SF(s, gsl_sf_ellint_P_e, (-4*M_PI/3, 0.01, -0.1, mode, &r), -4.39111768499392858132786, TEST_TOL0, GSL_SUCCESS);
763
764
TEST_SF(s, gsl_sf_ellint_P_e, (-3*M_PI/2.0, 0.99, -0.1, mode, &r), -10.8503448648973994034915, TEST_TOL0, GSL_SUCCESS);
765
TEST_SF(s, gsl_sf_ellint_P_e, (-3*M_PI/2.0, 0.50, -0.1, mode, &r), -5.34091048396364437887504, TEST_TOL0, GSL_SUCCESS);
766
TEST_SF(s, gsl_sf_ellint_P_e, (-3*M_PI/2.0, 0.01, -0.1, mode, &r), -4.96742159270695059812767, TEST_TOL0, GSL_SUCCESS);
767
768
TEST_SF(s, gsl_sf_ellint_P_e, (-5*M_PI/3, 0.99, -0.1, mode, &r), -13.1136524253406441347808, TEST_TOL0, GSL_SUCCESS);
769
TEST_SF(s, gsl_sf_ellint_P_e, (-5*M_PI/3, 0.50, -0.1, mode, &r), -5.99715906231265633976204, TEST_TOL0, GSL_SUCCESS);
770
TEST_SF(s, gsl_sf_ellint_P_e, (-5*M_PI/3, 0.01, -0.1, mode, &r), -5.54372550041997261492747, TEST_TOL0, GSL_SUCCESS);
771
772
TEST_SF(s, gsl_sf_ellint_P_e, (-2*M_PI, 0.99, -0.1, mode, &r), -14.4671264865298658713220, TEST_TOL0, GSL_SUCCESS);
773
TEST_SF(s, gsl_sf_ellint_P_e, (-2*M_PI, 0.50, -0.1, mode, &r), -7.12121397861819250516672, TEST_TOL0, GSL_SUCCESS);
774
TEST_SF(s, gsl_sf_ellint_P_e, (-2*M_PI, 0.01, -0.1, mode, &r), -6.62322879027593413083689, TEST_TOL0, GSL_SUCCESS);
775
776
TEST_SF(s, gsl_sf_ellint_P_e, (-7*M_PI/3.0, 0.99, -0.1, mode, &r), -15.8206005477190876078631, TEST_TOL0, GSL_SUCCESS);
777
TEST_SF(s, gsl_sf_ellint_P_e, (-7*M_PI/3.0, 0.50, -0.1, mode, &r), -8.24526889492372867057141, TEST_TOL0, GSL_SUCCESS);
778
TEST_SF(s, gsl_sf_ellint_P_e, (-7*M_PI/3.0, 0.01, -0.1, mode, &r), -7.70273208013189564674630, TEST_TOL0, GSL_SUCCESS);
779
780
/* D, argument phi > pi/2 */
781
782
TEST_SF(s, gsl_sf_ellint_D_e, (M_PI/2.0, 0.99, 0, mode, &r), 2.375395076351788975665323192, TEST_TOL0, GSL_SUCCESS);
783
TEST_SF(s, gsl_sf_ellint_D_e, (M_PI/2.0, 0.50, 0, mode, &r), 0.8731525818926755496456335628, TEST_TOL0, GSL_SUCCESS);
784
TEST_SF(s, gsl_sf_ellint_D_e, (M_PI/2.0, 0.01, 0, mode, &r), 0.7854276176694868932799393751, TEST_TOL0, GSL_SUCCESS);
785
786
TEST_SF(s, gsl_sf_ellint_D_e, (2*M_PI/3.0, 0.99, 0, mode, &r), 4.305885125424644860264320635, TEST_TOL0, GSL_SUCCESS);
787
TEST_SF(s, gsl_sf_ellint_D_e, (2*M_PI/3.0, 0.50, 0, mode, &r), 1.418324704155697579394036402, TEST_TOL0, GSL_SUCCESS);
788
TEST_SF(s, gsl_sf_ellint_D_e, (2*M_PI/3.0, 0.01, 0, mode, &r), 1.263755353901126149206022061, TEST_TOL0, GSL_SUCCESS);
789
790
TEST_SF(s, gsl_sf_ellint_D_e, (M_PI, 0.99, 0, mode, &r), 4.750790152703577951330646444, TEST_TOL0, GSL_SUCCESS);
791
TEST_SF(s, gsl_sf_ellint_D_e, (M_PI, 0.50, 0, mode, &r), 1.746305163785351099291267125, TEST_TOL0, GSL_SUCCESS);
792
TEST_SF(s, gsl_sf_ellint_D_e, (M_PI, 0.01, 0, mode, &r), 1.570855235338973786559878750, TEST_TOL0, GSL_SUCCESS);
793
794
TEST_SF(s, gsl_sf_ellint_D_e, (4*M_PI/3, 0.99, 0, mode, &r), 5.195695179982511042396972113, TEST_TOL0, GSL_SUCCESS);
795
TEST_SF(s, gsl_sf_ellint_D_e, (4*M_PI/3, 0.50, 0, mode, &r), 2.074285623415004619188497818, TEST_TOL0, GSL_SUCCESS);
796
TEST_SF(s, gsl_sf_ellint_D_e, (4*M_PI/3, 0.01, 0, mode, &r), 1.877955116776821423913735408, TEST_TOL0, GSL_SUCCESS);
797
798
TEST_SF(s, gsl_sf_ellint_D_e, (3*M_PI/2.0, 0.99, 0, mode, &r), 7.126185229055366926995969476, TEST_TOL0, GSL_SUCCESS);
799
TEST_SF(s, gsl_sf_ellint_D_e, (3*M_PI/2.0, 0.50, 0, mode, &r), 2.619457745678026648936900687, TEST_TOL0, GSL_SUCCESS);
800
TEST_SF(s, gsl_sf_ellint_D_e, (3*M_PI/2.0, 0.01, 0, mode, &r), 2.356282853008460679839818125, TEST_TOL0, GSL_SUCCESS);
801
802
TEST_SF(s, gsl_sf_ellint_D_e, (5*M_PI/3, 0.99, 0, mode, &r), 9.056675278128222811594967044, TEST_TOL0, GSL_SUCCESS);
803
TEST_SF(s, gsl_sf_ellint_D_e, (5*M_PI/3, 0.50, 0, mode, &r), 3.164629867941048678685303509, TEST_TOL0, GSL_SUCCESS);
804
TEST_SF(s, gsl_sf_ellint_D_e, (5*M_PI/3, 0.01, 0, mode, &r), 2.834610589240099935765900794, TEST_TOL0, GSL_SUCCESS);
805
806
TEST_SF(s, gsl_sf_ellint_D_e, (2*M_PI, 0.99, 0, mode, &r), 9.501580305407155902661292832, TEST_TOL0, GSL_SUCCESS);
807
TEST_SF(s, gsl_sf_ellint_D_e, (2*M_PI, 0.50, 0, mode, &r), 3.492610327570702198582534249, TEST_TOL0, GSL_SUCCESS);
808
TEST_SF(s, gsl_sf_ellint_D_e, (2*M_PI, 0.01, 0, mode, &r), 3.141710470677947573119757500, TEST_TOL0, GSL_SUCCESS);
809
810
TEST_SF(s, gsl_sf_ellint_D_e, (7*M_PI/3.0, 0.99, 0, mode, &r), 9.946485332686088993727618315, TEST_TOL0, GSL_SUCCESS);
811
TEST_SF(s, gsl_sf_ellint_D_e, (7*M_PI/3.0, 0.50, 0, mode, &r), 3.820590787200355718479764901, TEST_TOL0, GSL_SUCCESS);
812
TEST_SF(s, gsl_sf_ellint_D_e, (7*M_PI/3.0, 0.01, 0, mode, &r), 3.448810352115795210473614120, TEST_TOL0, GSL_SUCCESS);
813
814
/* P, negative argument phi < 0 */
815
816
TEST_SF(s, gsl_sf_ellint_D_e, (-M_PI/2.0, 0.99, 0, mode, &r), -2.375395076351788975665323192, TEST_TOL0, GSL_SUCCESS);
817
TEST_SF(s, gsl_sf_ellint_D_e, (-M_PI/2.0, 0.50, 0, mode, &r), -0.8731525818926755496456335628, TEST_TOL0, GSL_SUCCESS);
818
TEST_SF(s, gsl_sf_ellint_D_e, (-M_PI/2.0, 0.01, 0, mode, &r), -0.7854276176694868932799393751, TEST_TOL0, GSL_SUCCESS);
819
820
TEST_SF(s, gsl_sf_ellint_D_e, (-2*M_PI/3.0, 0.99, 0, mode, &r), -4.305885125424644860264320635, TEST_TOL0, GSL_SUCCESS);
821
TEST_SF(s, gsl_sf_ellint_D_e, (-2*M_PI/3.0, 0.50, 0, mode, &r), -1.418324704155697579394036402, TEST_TOL0, GSL_SUCCESS);
822
TEST_SF(s, gsl_sf_ellint_D_e, (-2*M_PI/3.0, 0.01, 0, mode, &r), -1.263755353901126149206022061, TEST_TOL0, GSL_SUCCESS);
823
824
TEST_SF(s, gsl_sf_ellint_D_e, (-M_PI, 0.99, 0, mode, &r), -4.750790152703577951330646444, TEST_TOL0, GSL_SUCCESS);
825
TEST_SF(s, gsl_sf_ellint_D_e, (-M_PI, 0.50, 0, mode, &r), -1.746305163785351099291267125, TEST_TOL0, GSL_SUCCESS);
826
TEST_SF(s, gsl_sf_ellint_D_e, (-M_PI, 0.01, 0, mode, &r), -1.570855235338973786559878750, TEST_TOL0, GSL_SUCCESS);
827
828
TEST_SF(s, gsl_sf_ellint_D_e, (-4*M_PI/3, 0.99, 0, mode, &r), -5.195695179982511042396972113, TEST_TOL0, GSL_SUCCESS);
829
TEST_SF(s, gsl_sf_ellint_D_e, (-4*M_PI/3, 0.50, 0, mode, &r), -2.074285623415004619188497818, TEST_TOL0, GSL_SUCCESS);
830
TEST_SF(s, gsl_sf_ellint_D_e, (-4*M_PI/3, 0.01, 0, mode, &r), -1.877955116776821423913735408, TEST_TOL0, GSL_SUCCESS);
831
832
TEST_SF(s, gsl_sf_ellint_D_e, (-3*M_PI/2.0, 0.99, 0, mode, &r), -7.126185229055366926995969476, TEST_TOL0, GSL_SUCCESS);
833
TEST_SF(s, gsl_sf_ellint_D_e, (-3*M_PI/2.0, 0.50, 0, mode, &r), -2.619457745678026648936900687, TEST_TOL0, GSL_SUCCESS);
834
TEST_SF(s, gsl_sf_ellint_D_e, (-3*M_PI/2.0, 0.01, 0, mode, &r), -2.356282853008460679839818125, TEST_TOL0, GSL_SUCCESS);
835
836
TEST_SF(s, gsl_sf_ellint_D_e, (-5*M_PI/3, 0.99, 0, mode, &r), -9.056675278128222811594967044, TEST_TOL0, GSL_SUCCESS);
837
TEST_SF(s, gsl_sf_ellint_D_e, (-5*M_PI/3, 0.50, 0, mode, &r), -3.164629867941048678685303509, TEST_TOL0, GSL_SUCCESS);
838
TEST_SF(s, gsl_sf_ellint_D_e, (-5*M_PI/3, 0.01, 0, mode, &r), -2.834610589240099935765900794, TEST_TOL0, GSL_SUCCESS);
839
840
TEST_SF(s, gsl_sf_ellint_D_e, (-2*M_PI, 0.99, 0, mode, &r), -9.501580305407155902661292832, TEST_TOL0, GSL_SUCCESS);
841
TEST_SF(s, gsl_sf_ellint_D_e, (-2*M_PI, 0.50, 0, mode, &r), -3.492610327570702198582534249, TEST_TOL0, GSL_SUCCESS);
842
TEST_SF(s, gsl_sf_ellint_D_e, (-2*M_PI, 0.01, 0, mode, &r), -3.141710470677947573119757500, TEST_TOL0, GSL_SUCCESS);
843
844
TEST_SF(s, gsl_sf_ellint_D_e, (-7*M_PI/3.0, 0.99, 0, mode, &r), -9.946485332686088993727618315, TEST_TOL0, GSL_SUCCESS);
845
TEST_SF(s, gsl_sf_ellint_D_e, (-7*M_PI/3.0, 0.50, 0, mode, &r), -3.820590787200355718479764901, TEST_TOL0, GSL_SUCCESS);
846
TEST_SF(s, gsl_sf_ellint_D_e, (-7*M_PI/3.0, 0.01, 0, mode, &r), -3.448810352115795210473614120, TEST_TOL0, GSL_SUCCESS);
847
848
return s;
849
}
850
851
852
int test_erf(void)
853
{
854
gsl_sf_result r;
855
int s = 0;
856
857
TEST_SF(s, gsl_sf_erfc_e, (-10.0, &r), 2.0, TEST_TOL0, GSL_SUCCESS);
858
TEST_SF(s, gsl_sf_erfc_e, (-5.0000002, &r), 1.9999999999984625433, TEST_TOL0, GSL_SUCCESS);
859
TEST_SF(s, gsl_sf_erfc_e, (-5.0, &r), 1.9999999999984625402, TEST_TOL0, GSL_SUCCESS);
860
TEST_SF(s, gsl_sf_erfc_e, (-1.0, &r), 1.8427007929497148693, TEST_TOL0, GSL_SUCCESS);
861
TEST_SF(s, gsl_sf_erfc_e, (-0.5, &r), 1.5204998778130465377, TEST_TOL0, GSL_SUCCESS);
862
TEST_SF(s, gsl_sf_erfc_e, (1.0, &r), 0.15729920705028513066, TEST_TOL0, GSL_SUCCESS);
863
TEST_SF(s, gsl_sf_erfc_e, (3.0, &r), 0.000022090496998585441373, TEST_TOL1, GSL_SUCCESS);
864
TEST_SF(s, gsl_sf_erfc_e, (7.0, &r), 4.183825607779414399e-23, TEST_TOL2, GSL_SUCCESS);
865
TEST_SF(s, gsl_sf_erfc_e, (10.0, &r), 2.0884875837625447570e-45, TEST_TOL2, GSL_SUCCESS);
866
867
TEST_SF(s, gsl_sf_log_erfc_e, (-1.0, &r), log(1.842700792949714869), TEST_TOL0, GSL_SUCCESS);
868
TEST_SF(s, gsl_sf_log_erfc_e, (-0.1, &r), 0.106576400586522485015, TEST_TOL0, GSL_SUCCESS);
869
TEST_SF(s, gsl_sf_log_erfc_e, (-1e-10, &r), 1.1283791670318505967e-10, TEST_TOL0, GSL_SUCCESS);
870
TEST_SF(s, gsl_sf_log_erfc_e, (0.0, &r), log(1.0), TEST_TOL0, GSL_SUCCESS);
871
TEST_SF(s, gsl_sf_log_erfc_e, (1e-10, &r), -1.128379167159174551e-10, TEST_TOL0, GSL_SUCCESS);
872
TEST_SF(s, gsl_sf_log_erfc_e, (0.001, &r), -0.0011290158896213548027, TEST_TOL0, GSL_SUCCESS);
873
TEST_SF(s, gsl_sf_log_erfc_e, (0.1, &r), -0.119304973737395598329, TEST_TOL0, GSL_SUCCESS);
874
TEST_SF(s, gsl_sf_log_erfc_e, (1.0, &r), log(0.15729920705028513066), TEST_TOL0, GSL_SUCCESS);
875
TEST_SF(s, gsl_sf_log_erfc_e, (10.0, &r), log(2.0884875837625447570e-45), TEST_TOL0, GSL_SUCCESS);
876
877
TEST_SF(s, gsl_sf_erf_e, (-10.0, &r), -1.0000000000000000000, TEST_TOL0, GSL_SUCCESS);
878
TEST_SF(s, gsl_sf_erf_e, (0.5, &r), 0.5204998778130465377, TEST_TOL0, GSL_SUCCESS);
879
TEST_SF(s, gsl_sf_erf_e, (1.0, &r), 0.8427007929497148693, TEST_TOL0, GSL_SUCCESS);
880
TEST_SF(s, gsl_sf_erf_e, (10.0, &r), 1.0000000000000000000, TEST_TOL0, GSL_SUCCESS);
881
882
TEST_SF(s, gsl_sf_erf_Z_e, (1.0, &r), 0.24197072451914334980, TEST_TOL0, GSL_SUCCESS);
883
TEST_SF(s, gsl_sf_erf_Q_e, (10.0, &r), 7.619853024160526066e-24, TEST_TOL2, GSL_SUCCESS);
884
885
TEST_SF(s, gsl_sf_hazard_e, (-20.0, &r), 5.5209483621597631896e-88, TEST_TOL2, GSL_SUCCESS);
886
TEST_SF(s, gsl_sf_hazard_e, (-10.0, &r), 7.6945986267064193463e-23, TEST_TOL2, GSL_SUCCESS);
887
TEST_SF(s, gsl_sf_hazard_e, (-1.0, &r), 0.28759997093917836123, TEST_TOL0, GSL_SUCCESS);
888
TEST_SF(s, gsl_sf_hazard_e, ( 0.0, &r), 0.79788456080286535588, TEST_TOL0, GSL_SUCCESS);
889
TEST_SF(s, gsl_sf_hazard_e, ( 1.0, &r), 1.5251352761609812091, TEST_TOL0, GSL_SUCCESS);
890
TEST_SF(s, gsl_sf_hazard_e, (10.0, &r), 10.098093233962511963, TEST_TOL2, GSL_SUCCESS);
891
TEST_SF(s, gsl_sf_hazard_e, (20.0, &r), 20.049753068527850542, TEST_TOL2, GSL_SUCCESS);
892
TEST_SF(s, gsl_sf_hazard_e, (30.0, &r), 30.033259667433677037, TEST_TOL2, GSL_SUCCESS);
893
TEST_SF(s, gsl_sf_hazard_e, (50.0, &r), 50.019984031905639809, TEST_TOL0, GSL_SUCCESS);
894
TEST_SF(s, gsl_sf_hazard_e, (80.0, &r), 80.012496096798234468, TEST_TOL0, GSL_SUCCESS);
895
TEST_SF(s, gsl_sf_hazard_e, (150.0, &r), 150.00666607420571802, TEST_TOL0, GSL_SUCCESS);
896
TEST_SF(s, gsl_sf_hazard_e, (300.0, &r), 300.00333325926337415, TEST_TOL0, GSL_SUCCESS);
897
TEST_SF(s, gsl_sf_hazard_e, (900.0, &r), 900.00111110836764382, TEST_TOL0, GSL_SUCCESS);
898
TEST_SF(s, gsl_sf_hazard_e, (1001.0, &r), 1001.0009989990049990, TEST_TOL0, GSL_SUCCESS);
899
TEST_SF(s, gsl_sf_hazard_e, (2000.0, &r), 2000.0004999997500003, TEST_TOL0, GSL_SUCCESS);
900
901
return s;
902
}
903
904
905
int test_exp(void)
906
{
907
gsl_sf_result r;
908
gsl_sf_result_e10 re;
909
double x;
910
int sa;
911
int s = 0;
912
913
TEST_SF(s, gsl_sf_exp_e, (-10.0, &r), exp(-10.0), TEST_TOL0, GSL_SUCCESS);
914
TEST_SF(s, gsl_sf_exp_e, ( 10.0, &r), exp( 10.0), TEST_TOL0, GSL_SUCCESS);
915
916
sa = 0;
917
sa += gsl_sf_exp_e10_e(1.0, &re);
918
sa += ( test_sf_frac_diff(re.val, M_E ) > TEST_TOL0 );
919
sa += ( re.err > TEST_TOL1 );
920
sa += ( re.e10 != 0 );
921
gsl_test(sa, " gsl_sf_exp_e10_e(1.0, &re)");
922
923
sa = 0;
924
sa += gsl_sf_exp_e10_e(2000.0, &re);
925
sa += ( test_sf_frac_diff(re.val, 3.88118019428363725 ) > TEST_TOL3 );
926
sa += ( re.err > TEST_TOL5 );
927
sa += ( re.e10 != 868 );
928
gsl_test(sa, " gsl_sf_exp_e10_e(2000.0, &re)");
929
930
931
TEST_SF(s, gsl_sf_exp_err_e, (-10.0, TEST_TOL1, &r), exp(-10.0), TEST_TOL1, GSL_SUCCESS);
932
TEST_SF(s, gsl_sf_exp_err_e, ( 10.0, TEST_TOL1, &r), exp( 10.0), TEST_TOL1, GSL_SUCCESS);
933
934
sa = 0;
935
sa += gsl_sf_exp_err_e10_e(1.0, TEST_SQRT_TOL0, &re);
936
sa += ( test_sf_frac_diff(re.val, M_E ) > TEST_TOL1 );
937
sa += ( re.err > 32.0 * TEST_SQRT_TOL0 );
938
sa += ( re.e10 != 0 );
939
gsl_test(sa, " gsl_sf_exp_err_e10_e(1.0, TEST_SQRT_TOL0, &re)");
940
941
sa = 0;
942
sa += gsl_sf_exp_err_e10_e(2000.0, 1.0e-10, &re);
943
sa += ( test_sf_frac_diff(re.val, 3.88118019428363725 ) > TEST_TOL3 );
944
sa += ( re.err > 1.0e-07 );
945
sa += ( re.e10 != 868 );
946
gsl_test(sa, " gsl_sf_exp_err_e10_e(2000.0, 1.0e-10, &re)");
947
948
949
x = 0.8*GSL_LOG_DBL_MAX;
950
TEST_SF(s, gsl_sf_exp_mult_e, (-10.0, 1.0e-06, &r), 1.0e-06*exp(-10.0), TEST_TOL0, GSL_SUCCESS);
951
TEST_SF(s, gsl_sf_exp_mult_e, (-10.0, 2.0, &r), 2.0*exp(-10.0), TEST_TOL0, GSL_SUCCESS);
952
TEST_SF(s, gsl_sf_exp_mult_e, (-10.0, -2.0, &r), -2.0*exp(-10.0), TEST_TOL0, GSL_SUCCESS);
953
TEST_SF(s, gsl_sf_exp_mult_e, ( 10.0, 1.0e-06, &r), 1.0e-06*exp( 10.0), TEST_TOL0, GSL_SUCCESS);
954
TEST_SF(s, gsl_sf_exp_mult_e, ( 10.0, -2.0, &r), -2.0*exp( 10.0), TEST_TOL0, GSL_SUCCESS);
955
TEST_SF(s, gsl_sf_exp_mult_e, (x, 1.00001, &r), 1.00001*exp(x), TEST_TOL3, GSL_SUCCESS);
956
TEST_SF(s, gsl_sf_exp_mult_e, (x, 1.000001, &r), 1.000001*exp(x), TEST_TOL3, GSL_SUCCESS);
957
TEST_SF(s, gsl_sf_exp_mult_e, (x, 1.000000001, &r), 1.000000001*exp(x), TEST_TOL3, GSL_SUCCESS);
958
TEST_SF(s, gsl_sf_exp_mult_e, (x, 100.0, &r), 100.0*exp(x), TEST_TOL3, GSL_SUCCESS);
959
TEST_SF(s, gsl_sf_exp_mult_e, (x, 1.0e+20, &r), 1.0e+20*exp(x), TEST_TOL3, GSL_SUCCESS);
960
TEST_SF(s, gsl_sf_exp_mult_e, (x, exp(-x)*exp(M_LN2), &r), 2.0, TEST_TOL4, GSL_SUCCESS );
961
962
TEST_SF(s, gsl_sf_exp_mult_err_e, (-10.0, TEST_SQRT_TOL0, 2.0, TEST_SQRT_TOL0, &r), 2.0*exp(-10.0), TEST_SQRT_TOL0, GSL_SUCCESS);
963
TEST_SF(s, gsl_sf_exp_mult_err_e, (x, TEST_SQRT_TOL0*x, exp(-x)*exp(M_LN2), TEST_SQRT_TOL0*exp(-x)*exp(M_LN2), &r), 2.0, TEST_SQRT_TOL0, GSL_SUCCESS );
964
965
sa = 0;
966
sa += gsl_sf_exp_mult_e10_e(1.0, 1.0, &re);
967
sa += ( test_sf_frac_diff(re.val, M_E ) > TEST_TOL0 );
968
sa += ( re.err > TEST_TOL2 );
969
sa += ( re.e10 != 0 );
970
gsl_test(sa, "gsl_sf_exp_mult_e10_e(1.0, 1.0, &re)");
971
TEST_SF_E10(s, gsl_sf_exp_mult_e10_e, (1.0, 1.0, &re), M_E, 0, TEST_TOL0, GSL_SUCCESS);
972
973
sa = 0;
974
sa += gsl_sf_exp_mult_e10_e(1000.0, 1.0e+200, &re);
975
sa += ( test_sf_frac_diff(re.val, 1.970071114017046993888879352) > TEST_TOL3 );
976
sa += ( re.err > 1.0e-11 );
977
sa += ( re.e10 != 634 );
978
gsl_test(sa, "gsl_sf_exp_mult_e10_e(1000.0, 1.0e+200, &re)");
979
TEST_SF_E10(s, gsl_sf_exp_mult_e10_e, (1000.0, 1.0e+200, &re), 1.970071114017046993888879352, 634, TEST_TOL3, GSL_SUCCESS);
980
981
sa = 0;
982
sa += gsl_sf_exp_mult_err_e10_e(1.0, TEST_TOL0, 1.0, TEST_TOL0, &re);
983
sa += ( test_sf_frac_diff(re.val, M_E ) > TEST_TOL0 );
984
sa += ( re.err > TEST_TOL2 );
985
sa += ( re.e10 != 0 );
986
gsl_test(sa, "gsl_sf_exp_mult_err_e10_e(1.0, TEST_TOL0, 1.0, TEST_TOL0, &re)");
987
TEST_SF_E10(s, gsl_sf_exp_mult_err_e10_e, (1.0, TEST_TOL0, 1.0, TEST_TOL0, &re), M_E, 0, TEST_TOL0, GSL_SUCCESS);
988
989
sa = 0;
990
sa += gsl_sf_exp_mult_err_e10_e(1000.0, 1.0e-12, 1.0e+200, 1.0e+190, &re);
991
sa += ( test_sf_frac_diff(re.val, 1.9700711140165661 ) > TEST_TOL3 );
992
sa += ( re.err > 1.0e-09 );
993
sa += ( re.e10 != 634 );
994
gsl_test(sa, "gsl_sf_exp_mult_err_e10_e(1.0e-12, 1.0e+200, &re)");
995
TEST_SF_E10(s, gsl_sf_exp_mult_err_e10_e, (1000.0, 1.0e-12, 1.0e+200, 1.0e+190, &re), 1.9700711140165661,634, TEST_TOL3, GSL_SUCCESS);
996
997
/* Test cases from Szymon Jaroszewicz */
998
999
TEST_SF_E10(s, gsl_sf_exp_mult_e10_e, (10000.0, 1.0, &re), 8.806818225662921587261496007, 4342, TEST_TOL5, GSL_SUCCESS);
1000
TEST_SF_E10(s, gsl_sf_exp_mult_e10_e, (100.0, 1.0, &re), 2.688117141816135448412625551e43, 0, TEST_TOL1, GSL_SUCCESS);
1001
TEST_SF_E10(s, gsl_sf_exp_e10_e, (100.0, &re), 2.688117141816135448412625551e43, 0, TEST_TOL1, GSL_SUCCESS);
1002
TEST_SF_E10(s, gsl_sf_exp_e10_e, (1000.0, &re), 1.970071114017046993888879352, 434, TEST_TOL1, GSL_SUCCESS);
1003
TEST_SF_E10(s, gsl_sf_exp_e10_e, (-100.0, &re), 3.720075976020835962959695803e-44, 0, TEST_TOL1, GSL_SUCCESS);
1004
TEST_SF_E10(s, gsl_sf_exp_e10_e, (-1000.0, &re), 5.075958897549456765291809479, -435, TEST_TOL1, GSL_SUCCESS);
1005
1006
TEST_SF(s, gsl_sf_expm1_e, (-10.0, &r), exp(-10.0)-1.0, TEST_TOL0, GSL_SUCCESS);
1007
TEST_SF(s, gsl_sf_expm1_e, (-0.001, &r), -0.00099950016662500845, TEST_TOL0, GSL_SUCCESS);
1008
TEST_SF(s, gsl_sf_expm1_e, (-1.0e-8, &r), -1.0e-08 + 0.5e-16, TEST_TOL0, GSL_SUCCESS);
1009
TEST_SF(s, gsl_sf_expm1_e, ( 1.0e-8, &r), 1.0e-08 + 0.5e-16, TEST_TOL0, GSL_SUCCESS);
1010
TEST_SF(s, gsl_sf_expm1_e, ( 0.001, &r), 0.0010005001667083417, TEST_TOL0, GSL_SUCCESS);
1011
TEST_SF(s, gsl_sf_expm1_e, ( 10.0, &r), exp(10.0)-1.0, TEST_TOL0, GSL_SUCCESS);
1012
1013
TEST_SF(s, gsl_sf_exprel_e, (-10.0, &r), 0.0999954600070237515, TEST_TOL0, GSL_SUCCESS);
1014
TEST_SF(s, gsl_sf_exprel_e, (-0.001, &r), 0.9995001666250084, TEST_TOL0, GSL_SUCCESS);
1015
TEST_SF(s, gsl_sf_exprel_e, (-1.0e-8, &r), 1.0 - 0.5e-08, TEST_TOL0, GSL_SUCCESS);
1016
TEST_SF(s, gsl_sf_exprel_e, ( 1.0e-8, &r), 1.0 + 0.5e-08, TEST_TOL0, GSL_SUCCESS);
1017
TEST_SF(s, gsl_sf_exprel_e, ( 0.001, &r), 1.0005001667083417, TEST_TOL0, GSL_SUCCESS);
1018
TEST_SF(s, gsl_sf_exprel_e, ( 10.0, &r), 2202.5465794806716517, TEST_TOL0, GSL_SUCCESS);
1019
1020
TEST_SF(s, gsl_sf_exprel_2_e, (-10.0, &r), 0.18000090799859524970, TEST_TOL0, GSL_SUCCESS);
1021
TEST_SF(s, gsl_sf_exprel_2_e, (-0.001, &r), 0.9996667499833361107, TEST_TOL0, GSL_SUCCESS);
1022
TEST_SF(s, gsl_sf_exprel_2_e, (-1.0e-8, &r), 0.9999999966666666750, TEST_TOL0, GSL_SUCCESS);
1023
TEST_SF(s, gsl_sf_exprel_2_e, ( 1.0e-8, &r), 1.0000000033333333417, TEST_TOL0, GSL_SUCCESS);
1024
TEST_SF(s, gsl_sf_exprel_2_e, ( 0.001, &r), 1.0003334166833361115, TEST_TOL0, GSL_SUCCESS);
1025
TEST_SF(s, gsl_sf_exprel_2_e, ( 10.0, &r), 440.3093158961343303, TEST_TOL0, GSL_SUCCESS);
1026
1027
TEST_SF(s, gsl_sf_exprel_n_e, (3, -1000.0, &r), 0.00299400600000000000, TEST_TOL0, GSL_SUCCESS);
1028
TEST_SF(s, gsl_sf_exprel_n_e, (3, -100.0, &r), 0.02940600000000000000, TEST_TOL0, GSL_SUCCESS);
1029
TEST_SF(s, gsl_sf_exprel_n_e, (3, -10.0, &r), 0.24599972760042142509, TEST_TOL0, GSL_SUCCESS);
1030
TEST_SF(s, gsl_sf_exprel_n_e, (3, -3.0, &r), 0.5444917625849191238, TEST_TOL0, GSL_SUCCESS);
1031
TEST_SF(s, gsl_sf_exprel_n_e, (3, -0.001, &r), 0.9997500499916678570, TEST_TOL0, GSL_SUCCESS);
1032
TEST_SF(s, gsl_sf_exprel_n_e, (3, -1.0e-8, &r), 0.9999999975000000050, TEST_TOL0, GSL_SUCCESS);
1033
TEST_SF(s, gsl_sf_exprel_n_e, (3, 1.0e-8, &r), 1.0000000025000000050, TEST_TOL0, GSL_SUCCESS);
1034
TEST_SF(s, gsl_sf_exprel_n_e, (3, 0.001, &r), 1.0002500500083345240, TEST_TOL0, GSL_SUCCESS);
1035
TEST_SF(s, gsl_sf_exprel_n_e, (3, 3.0, &r), 2.5745637607083706091, TEST_TOL0, GSL_SUCCESS);
1036
TEST_SF(s, gsl_sf_exprel_n_e, (3, 3.1, &r), 2.6772417068460206247, TEST_TOL0, GSL_SUCCESS);
1037
TEST_SF(s, gsl_sf_exprel_n_e, (3, 10.0, &r), 131.79279476884029910, TEST_TOL1, GSL_SUCCESS);
1038
TEST_SF(s, gsl_sf_exprel_n_e, (3, 100.0, &r), 1.6128702850896812690e+38, TEST_TOL2, GSL_SUCCESS);
1039
1040
TEST_SF(s, gsl_sf_exprel_n_e, (50, -1000.0, &r), 0.04766231609253975959, TEST_TOL0, GSL_SUCCESS);
1041
TEST_SF(s, gsl_sf_exprel_n_e, (50, -100.0, &r), 0.3348247572345889317, TEST_TOL0, GSL_SUCCESS);
1042
TEST_SF(s, gsl_sf_exprel_n_e, (50, -10.0, &r), 0.8356287051853286482, TEST_TOL0, GSL_SUCCESS);
1043
TEST_SF(s, gsl_sf_exprel_n_e, (50, -3.0, &r), 0.9443881609152163615, TEST_TOL0, GSL_SUCCESS);
1044
TEST_SF(s, gsl_sf_exprel_n_e, (50, -1.0, &r), 0.980762245565660617, TEST_TOL0, GSL_SUCCESS);
1045
TEST_SF(s, gsl_sf_exprel_n_e, (50, -1.0e-8, &r), 1.0 -1.0e-8/51.0, TEST_TOL0, GSL_SUCCESS);
1046
TEST_SF(s, gsl_sf_exprel_n_e, (50, 1.0e-8, &r), 1.0 +1.0e-8/51.0, TEST_TOL0, GSL_SUCCESS);
1047
TEST_SF(s, gsl_sf_exprel_n_e, (50, 1.0, &r), 1.01999216583666790, TEST_TOL0, GSL_SUCCESS);
1048
TEST_SF(s, gsl_sf_exprel_n_e, (50, 3.0, &r), 1.0624205757460368307, TEST_TOL0, GSL_SUCCESS);
1049
TEST_SF(s, gsl_sf_exprel_n_e, (50, 48.0, &r), 7.499573876877194416, TEST_TOL0, GSL_SUCCESS);
1050
TEST_SF(s, gsl_sf_exprel_n_e, (50, 50.1, &r), 9.311803306230992272, TEST_TOL4, GSL_SUCCESS);
1051
TEST_SF(s, gsl_sf_exprel_n_e, (50, 100.0, &r), 8.175664432485807634e+07, TEST_TOL4, GSL_SUCCESS);
1052
TEST_SF(s, gsl_sf_exprel_n_e, (50, 500.0, &r), 4.806352370663185330e+146, TEST_TOL3, GSL_SUCCESS);
1053
1054
TEST_SF(s, gsl_sf_exprel_n_e, (500, -1000.0, &r), 0.3334815803127619256, TEST_TOL0, GSL_SUCCESS);
1055
TEST_SF(s, gsl_sf_exprel_n_e, (500, -100.0, &r), 0.8335646217536183909, TEST_TOL0, GSL_SUCCESS);
1056
TEST_SF(s, gsl_sf_exprel_n_e, (500, -10.0, &r), 0.9804297803131823066, TEST_TOL0, GSL_SUCCESS);
1057
TEST_SF(s, gsl_sf_exprel_n_e, (500, -3.0, &r), 0.9940475488850672997, TEST_TOL0, GSL_SUCCESS);
1058
TEST_SF(s, gsl_sf_exprel_n_e, (500, -1.0, &r), 0.9980079602383488808, TEST_TOL0, GSL_SUCCESS);
1059
TEST_SF(s, gsl_sf_exprel_n_e, (500, -1.0e-8, &r), 1.0 -1.0e-8/501.0, TEST_TOL0, GSL_SUCCESS);
1060
TEST_SF(s, gsl_sf_exprel_n_e, (500, 1.0e-8, &r), 1.0 +1.0e-8/501.0, TEST_TOL0, GSL_SUCCESS);
1061
TEST_SF(s, gsl_sf_exprel_n_e, (500, 1.0, &r), 1.0019999920160634252, TEST_TOL0, GSL_SUCCESS);
1062
TEST_SF(s, gsl_sf_exprel_n_e, (500, 3.0, &r), 1.0060240236632444934, TEST_TOL0, GSL_SUCCESS);
1063
TEST_SF(s, gsl_sf_exprel_n_e, (500, 48.0, &r), 1.1059355517981272174, TEST_TOL0, GSL_SUCCESS);
1064
TEST_SF(s, gsl_sf_exprel_n_e, (500, 100.0, &r), 1.2492221464878287204, TEST_TOL1, GSL_SUCCESS);
1065
TEST_SF(s, gsl_sf_exprel_n_e, (500, 500.0, &r), 28.363019877927630858, TEST_TOL2, GSL_SUCCESS);
1066
TEST_SF(s, gsl_sf_exprel_n_e, (500, 1000.0, &r), 2.4037563160335300322e+68, TEST_TOL4, GSL_SUCCESS);
1067
TEST_SF(s, gsl_sf_exprel_n_e, (500, 1600.0, &r), 7.899293535320607403e+226, TEST_TOL4, GSL_SUCCESS);
1068
1069
return s;
1070
}
1071
1072
1073
int test_expint(void)
1074
{
1075
gsl_sf_result r;
1076
int s = 0;
1077
1078
TEST_SF(s, gsl_sf_expint_E1_e, (-1.0, &r), -1.8951178163559367555, TEST_TOL0, GSL_SUCCESS);
1079
TEST_SF(s, gsl_sf_expint_E1_e, (1.0e-10, &r), 22.448635265138923980, TEST_TOL0, GSL_SUCCESS);
1080
TEST_SF(s, gsl_sf_expint_E1_e, (1.0e-05, &r), 10.935719800043695615, TEST_TOL0, GSL_SUCCESS);
1081
TEST_SF(s, gsl_sf_expint_E1_e, (0.1, &r), 1.82292395841939066610, TEST_TOL0, GSL_SUCCESS);
1082
TEST_SF(s, gsl_sf_expint_E1_e, (1.0, &r), 0.21938393439552027368, TEST_TOL0, GSL_SUCCESS);
1083
TEST_SF(s, gsl_sf_expint_E1_e, (10.0, &r), 4.156968929685324277e-06, TEST_TOL1, GSL_SUCCESS);
1084
TEST_SF(s, gsl_sf_expint_E1_e, (50.0, &r), 3.783264029550459019e-24, TEST_TOL2, GSL_SUCCESS);
1085
TEST_SF(s, gsl_sf_expint_E1_e, (300.0, &r), 1.710384276804510115e-133, TEST_TOL2, GSL_SUCCESS);
1086
1087
TEST_SF(s, gsl_sf_expint_E2_e, (-1.0, &r), 0.8231640121031084799, TEST_TOL1, GSL_SUCCESS);
1088
TEST_SF(s, gsl_sf_expint_E2_e, (0.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
1089
TEST_SF(s, gsl_sf_expint_E2_e, (1.0/4294967296.0, &r), 0.9999999947372139168, TEST_TOL0, GSL_SUCCESS);
1090
TEST_SF(s, gsl_sf_expint_E2_e, (1.0/65536.0, &r), 0.9998243233207178845, TEST_TOL0, GSL_SUCCESS);
1091
TEST_SF(s, gsl_sf_expint_E2_e, (0.1, &r), 0.7225450221940205066, TEST_TOL0, GSL_SUCCESS);
1092
TEST_SF(s, gsl_sf_expint_E2_e, (1.0, &r), 0.14849550677592204792, TEST_TOL0, GSL_SUCCESS);
1093
TEST_SF(s, gsl_sf_expint_E2_e, (10.0, &r), 3.830240465631608762e-06, TEST_TOL1, GSL_SUCCESS);
1094
TEST_SF(s, gsl_sf_expint_E2_e, (50.0, &r), 3.711783318868827367e-24, TEST_TOL2, GSL_SUCCESS);
1095
TEST_SF(s, gsl_sf_expint_E2_e, (300.0, &r), 1.7047391998483433998e-133, TEST_TOL2, GSL_SUCCESS);
1096
1097
/* Tests for E_n(x) */
1098
1099
TEST_SF(s, gsl_sf_expint_En_e, (1,-1.0, &r), -1.8951178163559367555, TEST_TOL0, GSL_SUCCESS);
1100
TEST_SF(s, gsl_sf_expint_En_e, (1,1.0e-10, &r), 22.448635265138923980, TEST_TOL0, GSL_SUCCESS);
1101
TEST_SF(s, gsl_sf_expint_En_e, (1,1.0e-05, &r), 10.935719800043695615, TEST_TOL0, GSL_SUCCESS);
1102
TEST_SF(s, gsl_sf_expint_En_e, (1,0.1, &r), 1.82292395841939066610, TEST_TOL0, GSL_SUCCESS);
1103
TEST_SF(s, gsl_sf_expint_En_e, (1,1.0, &r), 0.21938393439552027368, TEST_TOL0, GSL_SUCCESS);
1104
TEST_SF(s, gsl_sf_expint_En_e, (1,10.0, &r), 4.156968929685324277e-06, TEST_TOL1, GSL_SUCCESS);
1105
TEST_SF(s, gsl_sf_expint_En_e, (1,50.0, &r), 3.783264029550459019e-24, TEST_TOL2, GSL_SUCCESS);
1106
TEST_SF(s, gsl_sf_expint_En_e, (1,300.0, &r), 1.710384276804510115e-133, TEST_TOL2, GSL_SUCCESS);
1107
1108
TEST_SF(s, gsl_sf_expint_En_e, (2,-1.0, &r), 0.8231640121031084799, TEST_TOL1, GSL_SUCCESS);
1109
TEST_SF(s, gsl_sf_expint_En_e, (2,0.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
1110
TEST_SF(s, gsl_sf_expint_En_e, (2,1.0/4294967296.0, &r), 0.9999999947372139168, TEST_TOL0, GSL_SUCCESS);
1111
TEST_SF(s, gsl_sf_expint_En_e, (2,1.0/65536.0, &r), 0.9998243233207178845, TEST_TOL0, GSL_SUCCESS);
1112
TEST_SF(s, gsl_sf_expint_En_e, (2,0.1, &r), 0.7225450221940205066, TEST_TOL0, GSL_SUCCESS);
1113
TEST_SF(s, gsl_sf_expint_En_e, (2,1.0, &r), 0.14849550677592204792, TEST_TOL0, GSL_SUCCESS);
1114
TEST_SF(s, gsl_sf_expint_En_e, (2,10.0, &r), 3.830240465631608762e-06, TEST_TOL1, GSL_SUCCESS);
1115
TEST_SF(s, gsl_sf_expint_En_e, (2,50.0, &r), 3.711783318868827367e-24, TEST_TOL2, GSL_SUCCESS);
1116
TEST_SF(s, gsl_sf_expint_En_e, (2,300.0, &r), 1.7047391998483433998e-133, TEST_TOL2, GSL_SUCCESS);
1117
1118
TEST_SF(s, gsl_sf_expint_En_e, (3,0.0, &r), 0.5, TEST_TOL0, GSL_SUCCESS);
1119
TEST_SF(s, gsl_sf_expint_En_e, (3,1.0/4294967296.0, &r), 0.499999999767169356972, TEST_TOL1, GSL_SUCCESS);
1120
TEST_SF(s, gsl_sf_expint_En_e, (3,1.0/65536.0, &r), 0.4999847426094515610, TEST_TOL0, GSL_SUCCESS);
1121
TEST_SF(s, gsl_sf_expint_En_e, (3,0.1, &r), 0.4162914579082787612543, TEST_TOL0, GSL_SUCCESS);
1122
TEST_SF(s, gsl_sf_expint_En_e, (3,1.0, &r), 0.10969196719776013683858, TEST_TOL1, GSL_SUCCESS);
1123
TEST_SF(s, gsl_sf_expint_En_e, (3,10.0, &r),0.000003548762553084381959981, TEST_TOL1, GSL_SUCCESS);
1124
TEST_SF(s, gsl_sf_expint_En_e, (3,50.0, &r), 3.6429094264752049812e-24, TEST_TOL2, GSL_SUCCESS);
1125
TEST_SF(s, gsl_sf_expint_En_e, (3,300.0, &r),1.699131143349179084e-133, TEST_TOL2, GSL_SUCCESS);
1126
1127
TEST_SF(s, gsl_sf_expint_En_e, (10,0.0, &r), 0.111111111111111111, TEST_TOL0, GSL_SUCCESS);
1128
TEST_SF(s, gsl_sf_expint_En_e, (10,1.0/4294967296.0, &r), 0.111111111082007280658, TEST_TOL2, GSL_SUCCESS);
1129
TEST_SF(s, gsl_sf_expint_En_e, (10,1.0/65536.0, &r), 0.11110920377910896018606, TEST_TOL1, GSL_SUCCESS);
1130
TEST_SF(s, gsl_sf_expint_En_e, (10,0.1, &r), 0.099298432000896813567905, TEST_TOL1, GSL_SUCCESS);
1131
TEST_SF(s, gsl_sf_expint_En_e, (10,1.0, &r), 0.036393994031416401634164534, TEST_TOL1, GSL_SUCCESS);
1132
TEST_SF(s, gsl_sf_expint_En_e, (10,10.0, &r), 0.00000232530265702821081778968, TEST_TOL1, GSL_SUCCESS);
1133
TEST_SF(s, gsl_sf_expint_En_e, (10,50.0, &r), 3.223296586749110919572e-24, TEST_TOL2, GSL_SUCCESS);
1134
TEST_SF(s, gsl_sf_expint_En_e, (10,300.0, &r), 1.6608815083360041367294736e-133, TEST_TOL2, GSL_SUCCESS);
1135
1136
/* Tests for Ei(x) */
1137
1138
TEST_SF(s, gsl_sf_expint_Ei_e, (-1.0, &r), -0.21938393439552027368, TEST_TOL0, GSL_SUCCESS);
1139
TEST_SF(s, gsl_sf_expint_Ei_e, (1.0/4294967296.0, &r), -21.603494112783886397, TEST_TOL0, GSL_SUCCESS);
1140
TEST_SF(s, gsl_sf_expint_Ei_e, (1.0, &r), 1.8951178163559367555, TEST_TOL0, GSL_SUCCESS);
1141
1142
TEST_SF(s, gsl_sf_expint_E1_scaled_e, (-10000.0, &r), -0.00010001000200060024012, TEST_TOL0, GSL_SUCCESS);
1143
TEST_SF(s, gsl_sf_expint_E1_scaled_e, (-1000.0, &r), -0.0010010020060241207251, TEST_TOL0, GSL_SUCCESS);
1144
TEST_SF(s, gsl_sf_expint_E1_scaled_e, (-10.0, &r), -0.11314702047341077803, TEST_TOL0, GSL_SUCCESS);
1145
TEST_SF(s, gsl_sf_expint_E1_scaled_e, (-1.0, &r), -0.69717488323506606877, TEST_TOL0, GSL_SUCCESS);
1146
TEST_SF(s, gsl_sf_expint_E1_scaled_e, (1.0e-10, &r), 22.448635267383787506, TEST_TOL0, GSL_SUCCESS);
1147
TEST_SF(s, gsl_sf_expint_E1_scaled_e, (1.0e-05, &r), 10.935829157788483865, TEST_TOL0, GSL_SUCCESS);
1148
TEST_SF(s, gsl_sf_expint_E1_scaled_e, (0.1, &r), 2.0146425447084516791, TEST_TOL0, GSL_SUCCESS);
1149
TEST_SF(s, gsl_sf_expint_E1_scaled_e, (1.0, &r), 0.59634736232319407434, TEST_TOL0, GSL_SUCCESS);
1150
TEST_SF(s, gsl_sf_expint_E1_scaled_e, (10.0, &r), 0.091563333939788081876, TEST_TOL0, GSL_SUCCESS);
1151
TEST_SF(s, gsl_sf_expint_E1_scaled_e, (50.0, &r), 0.019615109930114870365, TEST_TOL0, GSL_SUCCESS);
1152
TEST_SF(s, gsl_sf_expint_E1_scaled_e, (300.0, &r), 0.0033222955652707070644, TEST_TOL0, GSL_SUCCESS);
1153
TEST_SF(s, gsl_sf_expint_E1_scaled_e, (1000.0, &r), 0.00099900199402388071500, TEST_TOL0, GSL_SUCCESS);
1154
TEST_SF(s, gsl_sf_expint_E1_scaled_e, (10000.0, &r), 0.000099990001999400239880, TEST_TOL0, GSL_SUCCESS);
1155
1156
TEST_SF(s, gsl_sf_expint_E2_scaled_e, (-10000.0, &r), -0.00010002000600240120072, TEST_TOL3, GSL_SUCCESS);
1157
TEST_SF(s, gsl_sf_expint_E2_scaled_e, (-1000.0, &r), -0.0010020060241207250807, TEST_TOL3, GSL_SUCCESS);
1158
TEST_SF(s, gsl_sf_expint_E2_scaled_e, (-10.0, &r), -0.13147020473410778034, TEST_TOL1, GSL_SUCCESS);
1159
TEST_SF(s, gsl_sf_expint_E2_scaled_e, (-1.0, &r), 0.30282511676493393123, TEST_TOL1, GSL_SUCCESS);
1160
TEST_SF(s, gsl_sf_expint_E2_scaled_e, (0.0, &r), 1.0, TEST_TOL1, GSL_SUCCESS);
1161
TEST_SF(s, gsl_sf_expint_E2_scaled_e, (1.0/4294967296.0, &r), 0.99999999497004455927, TEST_TOL0, GSL_SUCCESS);
1162
TEST_SF(s, gsl_sf_expint_E2_scaled_e, (1.0/65536.0, &r), 0.99983957954556245453, TEST_TOL0, GSL_SUCCESS);
1163
TEST_SF(s, gsl_sf_expint_E2_scaled_e, (0.1, &r), 0.79853574552915483209, TEST_TOL0, GSL_SUCCESS);
1164
TEST_SF(s, gsl_sf_expint_E2_scaled_e, (1.0, &r), 0.40365263767680592566, TEST_TOL0, GSL_SUCCESS);
1165
TEST_SF(s, gsl_sf_expint_E2_scaled_e, (10.0, &r), 0.084366660602119181239, TEST_TOL1, GSL_SUCCESS);
1166
TEST_SF(s, gsl_sf_expint_E2_scaled_e, (50.0, &r), 0.019244503494256481735, TEST_TOL2, GSL_SUCCESS);
1167
TEST_SF(s, gsl_sf_expint_E2_scaled_e, (300.0, &r), 0.0033113304187878806691, TEST_TOL0, GSL_SUCCESS);
1168
TEST_SF(s, gsl_sf_expint_E2_scaled_e, (1000.0, &r), 0.00099800597611928500004, TEST_TOL0, GSL_SUCCESS);
1169
TEST_SF(s, gsl_sf_expint_E2_scaled_e, (10000.0, &r), 0.000099980005997601199281, TEST_TOL0, GSL_SUCCESS);
1170
1171
/* Tests for E_n(x) */
1172
1173
1174
TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,-10000.0, &r), -0.00010001000200060024012, TEST_TOL0, GSL_SUCCESS);
1175
TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,-1000.0, &r), -0.0010010020060241207251, TEST_TOL0, GSL_SUCCESS);
1176
TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,-10.0, &r), -0.11314702047341077803, TEST_TOL0, GSL_SUCCESS);
1177
TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,-1.0, &r), -0.69717488323506606877, TEST_TOL0, GSL_SUCCESS);
1178
TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,1.0e-10, &r), 22.448635267383787506, TEST_TOL0, GSL_SUCCESS);
1179
TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,1.0e-05, &r), 10.935829157788483865, TEST_TOL0, GSL_SUCCESS);
1180
TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,0.1, &r), 2.0146425447084516791, TEST_TOL0, GSL_SUCCESS);
1181
TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,1.0, &r), 0.59634736232319407434, TEST_TOL0, GSL_SUCCESS);
1182
TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,10.0, &r), 0.091563333939788081876, TEST_TOL0, GSL_SUCCESS);
1183
TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,50.0, &r), 0.019615109930114870365, TEST_TOL0, GSL_SUCCESS);
1184
TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,300.0, &r), 0.0033222955652707070644, TEST_TOL0, GSL_SUCCESS);
1185
TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,1000.0, &r), 0.00099900199402388071500, TEST_TOL0, GSL_SUCCESS);
1186
TEST_SF(s, gsl_sf_expint_En_scaled_e, (1,10000.0, &r), 0.000099990001999400239880, TEST_TOL0, GSL_SUCCESS);
1187
1188
TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,-10000.0, &r), -0.00010002000600240120072, TEST_TOL3, GSL_SUCCESS);
1189
TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,-1000.0, &r), -0.0010020060241207250807, TEST_TOL3, GSL_SUCCESS);
1190
TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,-10.0, &r), -0.13147020473410778034, TEST_TOL1, GSL_SUCCESS);
1191
TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,-1.0, &r), 0.30282511676493393123, TEST_TOL1, GSL_SUCCESS);
1192
TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,0.0, &r), 1.0, TEST_TOL1, GSL_SUCCESS);
1193
TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,1.0/4294967296.0, &r), 0.99999999497004455927, TEST_TOL0, GSL_SUCCESS);
1194
TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,1.0/65536.0, &r), 0.99983957954556245453, TEST_TOL0, GSL_SUCCESS);
1195
TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,0.1, &r), 0.79853574552915483209, TEST_TOL0, GSL_SUCCESS);
1196
TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,1.0, &r), 0.40365263767680592566, TEST_TOL0, GSL_SUCCESS);
1197
TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,10.0, &r), 0.084366660602119181239, TEST_TOL1, GSL_SUCCESS);
1198
TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,50.0, &r), 0.019244503494256481735, TEST_TOL2, GSL_SUCCESS);
1199
TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,300.0, &r), 0.0033113304187878806691, TEST_TOL0, GSL_SUCCESS);
1200
TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,1000.0, &r), 0.00099800597611928500004, TEST_TOL0, GSL_SUCCESS);
1201
TEST_SF(s, gsl_sf_expint_En_scaled_e, (2,10000.0, &r), 0.000099980005997601199281, TEST_TOL0, GSL_SUCCESS);
1202
1203
TEST_SF(s, gsl_sf_expint_En_scaled_e, (3,0.0, &r), 0.5, TEST_TOL0, GSL_SUCCESS);
1204
TEST_SF(s, gsl_sf_expint_En_scaled_e, (3,1.0/4294967296.0, &r), 0.4999999998835846787586, TEST_TOL1, GSL_SUCCESS);
1205
TEST_SF(s, gsl_sf_expint_En_scaled_e, (3,1.0/65536.0, &r), 0.4999923718293796877864492, TEST_TOL0, GSL_SUCCESS);
1206
TEST_SF(s, gsl_sf_expint_En_scaled_e, (3,0.1, &r), 0.4600732127235422583955, TEST_TOL0, GSL_SUCCESS);
1207
TEST_SF(s, gsl_sf_expint_En_scaled_e, (3,1.0, &r), 0.298173681161597037170539, TEST_TOL1, GSL_SUCCESS);
1208
TEST_SF(s, gsl_sf_expint_En_scaled_e, (3,10.0, &r), 0.07816669698940409380349, TEST_TOL1, GSL_SUCCESS);
1209
TEST_SF(s, gsl_sf_expint_En_scaled_e, (3,50.0, &r), 0.0188874126435879566345, TEST_TOL2, GSL_SUCCESS);
1210
TEST_SF(s, gsl_sf_expint_En_scaled_e, (3,300.0, &r), 0.00330043718181789963028657675, TEST_TOL2, GSL_SUCCESS);
1211
1212
TEST_SF(s, gsl_sf_expint_En_scaled_e, (10,0.0, &r), 0.111111111111111111, TEST_TOL0, GSL_SUCCESS);
1213
TEST_SF(s, gsl_sf_expint_En_scaled_e, (10,1.0/4294967296.0, &r), 0.11111111110787735217158, TEST_TOL2, GSL_SUCCESS);
1214
TEST_SF(s, gsl_sf_expint_En_scaled_e, (10,1.0/65536.0, &r), 0.1111108991839472074435, TEST_TOL1, GSL_SUCCESS);
1215
TEST_SF(s, gsl_sf_expint_En_scaled_e, (10,0.1, &r), 0.1097417392579033988025, TEST_TOL1, GSL_SUCCESS);
1216
TEST_SF(s, gsl_sf_expint_En_scaled_e, (10,1.0, &r), 0.09892913264064615521915, TEST_TOL1, GSL_SUCCESS);
1217
TEST_SF(s, gsl_sf_expint_En_scaled_e, (10,10.0, &r), 0.0512181994376050593314159875, TEST_TOL1, GSL_SUCCESS);
1218
TEST_SF(s, gsl_sf_expint_En_scaled_e, (10,50.0, &r), 0.0167118436335939556034579, TEST_TOL2, GSL_SUCCESS);
1219
TEST_SF(s, gsl_sf_expint_En_scaled_e, (10,300.0, &r), 0.0032261400811599644878615, TEST_TOL2, GSL_SUCCESS);
1220
1221
1222
TEST_SF(s, gsl_sf_expint_Ei_scaled_e, (-1000.0, &r), -0.00099900199402388071500, TEST_TOL0, GSL_SUCCESS);
1223
TEST_SF(s, gsl_sf_expint_Ei_scaled_e, (-1.0, &r), -0.59634736232319407434, TEST_TOL0, GSL_SUCCESS);
1224
TEST_SF(s, gsl_sf_expint_Ei_scaled_e, (1.0/4294967296.0, &r), -21.603494107753930958, TEST_TOL0, GSL_SUCCESS);
1225
TEST_SF(s, gsl_sf_expint_Ei_scaled_e, (1.0, &r), 0.69717488323506606877, TEST_TOL0, GSL_SUCCESS);
1226
TEST_SF(s, gsl_sf_expint_Ei_scaled_e, (1000.0, &r), 0.0010010020060241207251, TEST_TOL0, GSL_SUCCESS);
1227
1228
1229
TEST_SF(s, gsl_sf_Shi_e, (-1.0, &r), -1.0572508753757285146, TEST_TOL0, GSL_SUCCESS);
1230
TEST_SF(s, gsl_sf_Shi_e, (1.0/4294967296.0, &r), 2.3283064365386962891e-10, TEST_TOL0, GSL_SUCCESS);
1231
TEST_SF(s, gsl_sf_Shi_e, (1.0/65536.0, &r), 0.00001525878906269737298, TEST_TOL0, GSL_SUCCESS);
1232
TEST_SF(s, gsl_sf_Shi_e, (0.1, &r), 0.1000555722250569955, TEST_TOL0, GSL_SUCCESS);
1233
TEST_SF(s, gsl_sf_Shi_e, (1.0, &r), 1.0572508753757285146, TEST_TOL0, GSL_SUCCESS);
1234
TEST_SF(s, gsl_sf_Shi_e, (10.0, &r), 1246.1144901994233444, TEST_TOL1, GSL_SUCCESS);
1235
TEST_SF(s, gsl_sf_Shi_e, (50.0, &r), 5.292818448565845482e+19, TEST_TOL2, GSL_SUCCESS);
1236
TEST_SF(s, gsl_sf_Shi_e, (300.0, &r), 3.248241254044332895e+127, TEST_TOL2, GSL_SUCCESS);
1237
1238
TEST_SF(s, gsl_sf_Chi_e, (-1.0, &r), 0.8378669409802082409, TEST_TOL0, GSL_SUCCESS);
1239
TEST_SF(s, gsl_sf_Chi_e, (1.0/4294967296.0, &r), -21.603494113016717041, TEST_TOL0, GSL_SUCCESS);
1240
TEST_SF(s, gsl_sf_Chi_e, (1.0/65536.0, &r), -10.513139223999384429, TEST_TOL0, GSL_SUCCESS);
1241
TEST_SF(s, gsl_sf_Chi_e, (1.0/8.0, &r), -1.4983170827635760646, TEST_TOL0, GSL_SUCCESS);
1242
TEST_SF(s, gsl_sf_Chi_e, (1.0, &r), 0.8378669409802082409, TEST_TOL0, GSL_SUCCESS);
1243
TEST_SF(s, gsl_sf_Chi_e, (10.0, &r), 1246.1144860424544147, TEST_TOL1, GSL_SUCCESS);
1244
TEST_SF(s, gsl_sf_Chi_e, (50.0, &r), 5.292818448565845482e+19, TEST_TOL2, GSL_SUCCESS);
1245
TEST_SF(s, gsl_sf_Chi_e, (300.0, &r), 3.248241254044332895e+127, TEST_TOL2, GSL_SUCCESS);
1246
1247
TEST_SF(s, gsl_sf_expint_3_e, (1.0e-10, &r), 1.0e-10, TEST_TOL0, GSL_SUCCESS);
1248
TEST_SF(s, gsl_sf_expint_3_e, (1.0e-05, &r), 9.9999999999999975e-06, TEST_TOL0, GSL_SUCCESS);
1249
TEST_SF(s, gsl_sf_expint_3_e, (0.1, &r), 0.09997500714119079665122, TEST_TOL0, GSL_SUCCESS);
1250
TEST_SF(s, gsl_sf_expint_3_e, (0.5, &r), 0.48491714311363971332427, TEST_TOL0, GSL_SUCCESS);
1251
TEST_SF(s, gsl_sf_expint_3_e, (1.0, &r), 0.80751118213967145285833, TEST_TOL0, GSL_SUCCESS);
1252
TEST_SF(s, gsl_sf_expint_3_e, (2.0, &r), 0.89295351429387631138208, TEST_TOL0, GSL_SUCCESS);
1253
TEST_SF(s, gsl_sf_expint_3_e, (5.0, &r), 0.89297951156924921121856, TEST_TOL0, GSL_SUCCESS);
1254
TEST_SF(s, gsl_sf_expint_3_e, (10.0, &r), 0.89297951156924921121856, TEST_TOL0, GSL_SUCCESS);
1255
TEST_SF(s, gsl_sf_expint_3_e, (100.0, &r), 0.89297951156924921121856, TEST_TOL0, GSL_SUCCESS);
1256
1257
TEST_SF(s, gsl_sf_Si_e, (-1.0, &r), -0.9460830703671830149, TEST_TOL0, GSL_SUCCESS);
1258
TEST_SF(s, gsl_sf_Si_e, (1.0e-10, &r), 1.0e-10, TEST_TOL0, GSL_SUCCESS);
1259
TEST_SF(s, gsl_sf_Si_e, (1.0e-05, &r), 9.999999999944444444e-06, TEST_TOL0, GSL_SUCCESS);
1260
TEST_SF(s, gsl_sf_Si_e, (0.1, &r), 0.09994446110827695016, TEST_TOL0, GSL_SUCCESS);
1261
TEST_SF(s, gsl_sf_Si_e, (1.0, &r), 0.9460830703671830149, TEST_TOL0, GSL_SUCCESS);
1262
TEST_SF(s, gsl_sf_Si_e, (10.0, &r), 1.6583475942188740493, TEST_TOL0, GSL_SUCCESS);
1263
TEST_SF(s, gsl_sf_Si_e, (50.0, &r), 1.5516170724859358947, TEST_TOL0, GSL_SUCCESS);
1264
TEST_SF(s, gsl_sf_Si_e, (300.0, &r), 1.5708810882137495193, TEST_TOL0, GSL_SUCCESS);
1265
/*
1266
TEST_SF(s, gsl_sf_Si_e, (1.0e+20, &r), 1.5707963267948966192, TEST_TOL0, GSL_SUCCESS);
1267
*/
1268
1269
TEST_SF(s, gsl_sf_Ci_e, (1.0/4294967296.0, &r), -21.603494113016717041, TEST_TOL0, GSL_SUCCESS);
1270
TEST_SF(s, gsl_sf_Ci_e, (1.0/65536.0, &r), -10.513139224115799751, TEST_TOL0, GSL_SUCCESS);
1271
TEST_SF(s, gsl_sf_Ci_e, (1.0/8.0, &r), -1.5061295845296396649, TEST_TOL0, GSL_SUCCESS);
1272
TEST_SF(s, gsl_sf_Ci_e, (1.0, &r), 0.3374039229009681347, TEST_TOL0, GSL_SUCCESS);
1273
TEST_SF(s, gsl_sf_Ci_e, (10.0, &r), -0.04545643300445537263, TEST_TOL0, GSL_SUCCESS);
1274
TEST_SF(s, gsl_sf_Ci_e, (50.0, &r), -0.005628386324116305440, TEST_TOL0, GSL_SUCCESS);
1275
TEST_SF(s, gsl_sf_Ci_e, (300.0, &r), -0.003332199918592111780, TEST_TOL0, GSL_SUCCESS);
1276
TEST_SF(s, gsl_sf_Ci_e, (65536.0, &r), 0.000010560248837656279453, TEST_TOL0, GSL_SUCCESS);
1277
TEST_SF(s, gsl_sf_Ci_e, (4294967296.0, &r), -1.0756463261957757485e-10, TEST_SQRT_TOL0, GSL_SUCCESS);
1278
TEST_SF(s, gsl_sf_Ci_e, (1099511627776.0, &r), -3.689865584710764214e-13, 1024.0*TEST_SQRT_TOL0, GSL_SUCCESS);
1279
1280
TEST_SF(s, gsl_sf_atanint_e, (1.0e-10, &r), 1.0e-10, TEST_TOL0, GSL_SUCCESS);
1281
TEST_SF(s, gsl_sf_atanint_e, (1.0e-05, &r), 9.99999999988888888889e-06, TEST_TOL0, GSL_SUCCESS);
1282
TEST_SF(s, gsl_sf_atanint_e, (0.1, &r), 0.09988928686033618404, TEST_TOL0, GSL_SUCCESS);
1283
TEST_SF(s, gsl_sf_atanint_e, (1.0, &r), 0.91596559417721901505, TEST_TOL0, GSL_SUCCESS);
1284
TEST_SF(s, gsl_sf_atanint_e, (2.0, &r), 1.57601540344632342236, TEST_TOL0, GSL_SUCCESS);
1285
TEST_SF(s, gsl_sf_atanint_e, (10.0, &r), 3.71678149306806859029, TEST_TOL0, GSL_SUCCESS);
1286
TEST_SF(s, gsl_sf_atanint_e, (50.0, &r), 6.16499047850274874222, TEST_TOL0, GSL_SUCCESS);
1287
TEST_SF(s, gsl_sf_atanint_e, (300.0, &r), 8.96281388924518959990, TEST_TOL0, GSL_SUCCESS);
1288
TEST_SF(s, gsl_sf_atanint_e, (1.0e+5, &r), 18.084471031038661920, TEST_TOL0, GSL_SUCCESS);
1289
1290
return s;
1291
}
1292
1293
1294
int test_fermidirac(void)
1295
{
1296
gsl_sf_result r;
1297
int s = 0;
1298
1299
TEST_SF(s, gsl_sf_fermi_dirac_m1_e, (-10.0, &r), 0.00004539786870243439450, TEST_TOL0, GSL_SUCCESS);
1300
TEST_SF(s, gsl_sf_fermi_dirac_m1_e, ( -1.0, &r), 0.26894142136999512075, TEST_TOL0, GSL_SUCCESS);
1301
TEST_SF(s, gsl_sf_fermi_dirac_m1_e, ( 1.0, &r), 0.7310585786300048793, TEST_TOL0, GSL_SUCCESS);
1302
TEST_SF(s, gsl_sf_fermi_dirac_m1_e, ( 10.0, &r), 0.9999546021312975656, TEST_TOL0, GSL_SUCCESS);
1303
1304
TEST_SF(s, gsl_sf_fermi_dirac_0_e, (-10.0, &r), 0.00004539889921686464677, TEST_TOL0, GSL_SUCCESS);
1305
TEST_SF(s, gsl_sf_fermi_dirac_0_e, ( -1.0, &r), 0.31326168751822283405, TEST_TOL0, GSL_SUCCESS);
1306
TEST_SF(s, gsl_sf_fermi_dirac_0_e, ( 1.0, &r), 1.3132616875182228340, TEST_TOL0, GSL_SUCCESS);
1307
TEST_SF(s, gsl_sf_fermi_dirac_0_e, ( 10.0, &r), 10.000045398899216865, TEST_TOL0, GSL_SUCCESS);
1308
1309
TEST_SF(s, gsl_sf_fermi_dirac_1_e, (-10.0, &r), 0.00004539941448447633524, TEST_TOL0, GSL_SUCCESS);
1310
TEST_SF(s, gsl_sf_fermi_dirac_1_e, ( -2.0, &r), 0.13101248471442377127, TEST_TOL0, GSL_SUCCESS);
1311
TEST_SF(s, gsl_sf_fermi_dirac_1_e, ( -1.0, &r), 0.3386479964034521798, TEST_TOL0, GSL_SUCCESS);
1312
TEST_SF(s, gsl_sf_fermi_dirac_1_e, ( -0.4, &r), 0.5825520806897909028, TEST_TOL0, GSL_SUCCESS);
1313
TEST_SF(s, gsl_sf_fermi_dirac_1_e, ( 0.4, &r), 1.1423819861584355337, TEST_TOL0, GSL_SUCCESS);
1314
TEST_SF(s, gsl_sf_fermi_dirac_1_e, ( 1.0, &r), 1.8062860704447742567, TEST_TOL0, GSL_SUCCESS);
1315
TEST_SF(s, gsl_sf_fermi_dirac_1_e, ( 1.5, &r), 2.5581520872227806402, TEST_TOL0, GSL_SUCCESS);
1316
TEST_SF(s, gsl_sf_fermi_dirac_1_e, ( 2.5, &r), 4.689474797599761667, TEST_TOL0, GSL_SUCCESS);
1317
TEST_SF(s, gsl_sf_fermi_dirac_1_e, ( 10.0, &r), 51.64488866743374196, TEST_TOL0, GSL_SUCCESS);
1318
TEST_SF(s, gsl_sf_fermi_dirac_1_e, ( 12.0, &r), 73.64492792264531092, TEST_TOL0, GSL_SUCCESS);
1319
TEST_SF(s, gsl_sf_fermi_dirac_1_e, ( 20.0, &r), 201.64493406478707282, TEST_TOL0, GSL_SUCCESS);
1320
TEST_SF(s, gsl_sf_fermi_dirac_1_e, ( 50.0, &r), 1251.6449340668482264, TEST_TOL0, GSL_SUCCESS);
1321
1322
TEST_SF(s, gsl_sf_fermi_dirac_2_e, (-10.0, &r), 0.00004539967212174776662, TEST_TOL0, GSL_SUCCESS);
1323
TEST_SF(s, gsl_sf_fermi_dirac_2_e, ( -2.0, &r), 0.13313272938565030508, TEST_TOL0, GSL_SUCCESS);
1324
TEST_SF(s, gsl_sf_fermi_dirac_2_e, ( -1.0, &r), 0.3525648792978077590, TEST_TOL0, GSL_SUCCESS);
1325
TEST_SF(s, gsl_sf_fermi_dirac_2_e, ( -0.4, &r), 0.6229402647001272120, TEST_TOL0, GSL_SUCCESS);
1326
TEST_SF(s, gsl_sf_fermi_dirac_2_e, ( 0.4, &r), 1.2915805581060844533, TEST_TOL0, GSL_SUCCESS);
1327
TEST_SF(s, gsl_sf_fermi_dirac_2_e, ( 1.0, &r), 2.1641656128127008622, TEST_TOL0, GSL_SUCCESS);
1328
TEST_SF(s, gsl_sf_fermi_dirac_2_e, ( 1.5, &r), 3.247184513920792475, TEST_TOL0, GSL_SUCCESS);
1329
TEST_SF(s, gsl_sf_fermi_dirac_2_e, ( 2.5, &r), 6.797764392735056317, TEST_TOL0, GSL_SUCCESS);
1330
TEST_SF(s, gsl_sf_fermi_dirac_2_e, ( 10.0, &r), 183.11605273482105278, TEST_TOL0, GSL_SUCCESS);
1331
TEST_SF(s, gsl_sf_fermi_dirac_2_e, ( 12.0, &r), 307.73921494638635166, TEST_TOL0, GSL_SUCCESS);
1332
TEST_SF(s, gsl_sf_fermi_dirac_2_e, ( 20.0, &r), 1366.2320146723590157, TEST_TOL0, GSL_SUCCESS);
1333
TEST_SF(s, gsl_sf_fermi_dirac_2_e, ( 50.0, &r), 20915.580036675744655, TEST_TOL0, GSL_SUCCESS);
1334
TEST_SF(s, gsl_sf_fermi_dirac_2_e, (200.0, &r), 1.3336623201467029786e+06, TEST_TOL0, GSL_SUCCESS);
1335
1336
TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, (-10.0, &r), 0.00004539847236080549532, TEST_TOL0, GSL_SUCCESS);
1337
TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, ( -2.0, &r), 0.12366562180120994266, TEST_TOL0, GSL_SUCCESS);
1338
TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, ( -1.0, &r), 0.29402761761145122022, TEST_TOL0, GSL_SUCCESS);
1339
TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, ( -0.4, &r), 0.4631755336886027800, TEST_TOL0, GSL_SUCCESS);
1340
TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, ( 0.4, &r), 0.7654084737661656915, TEST_TOL0, GSL_SUCCESS);
1341
TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, ( 1.0, &r), 1.0270571254743506890, TEST_TOL0, GSL_SUCCESS);
1342
TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, ( 1.5, &r), 1.2493233478527122008, TEST_TOL0, GSL_SUCCESS);
1343
TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, ( 2.5, &r), 1.6663128834358313625, TEST_TOL0, GSL_SUCCESS);
1344
TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, ( 10.0, &r), 3.552779239536617160, TEST_TOL0, GSL_SUCCESS);
1345
TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, ( 12.0, &r), 3.897268231925439359, TEST_TOL0, GSL_SUCCESS);
1346
TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, ( 20.0, &r), 5.041018507535328603, TEST_TOL0, GSL_SUCCESS);
1347
TEST_SF(s, gsl_sf_fermi_dirac_mhalf_e, ( 50.0, &r), 7.977530858581869960, TEST_TOL1, GSL_SUCCESS);
1348
1349
TEST_SF(s, gsl_sf_fermi_dirac_half_e, (-10.0, &r), 0.00004539920105264132755, TEST_TOL1, GSL_SUCCESS);
1350
TEST_SF(s, gsl_sf_fermi_dirac_half_e, ( -2.0, &r), 0.12929851332007559106, TEST_TOL0, GSL_SUCCESS);
1351
TEST_SF(s, gsl_sf_fermi_dirac_half_e, ( -1.0, &r), 0.3277951592607115477, TEST_TOL0, GSL_SUCCESS);
1352
TEST_SF(s, gsl_sf_fermi_dirac_half_e, ( -0.4, &r), 0.5522452153690688947, TEST_TOL0, GSL_SUCCESS);
1353
TEST_SF(s, gsl_sf_fermi_dirac_half_e, ( 0.4, &r), 1.0386797503389389277, TEST_TOL0, GSL_SUCCESS);
1354
TEST_SF(s, gsl_sf_fermi_dirac_half_e, ( 1.0, &r), 1.5756407761513002308, TEST_TOL0, GSL_SUCCESS);
1355
TEST_SF(s, gsl_sf_fermi_dirac_half_e, ( 1.5, &r), 2.1448608775831140360, TEST_TOL0, GSL_SUCCESS);
1356
TEST_SF(s, gsl_sf_fermi_dirac_half_e, ( 2.5, &r), 3.606975377950373251, TEST_TOL0, GSL_SUCCESS);
1357
TEST_SF(s, gsl_sf_fermi_dirac_half_e, ( 10.0, &r), 24.084656964637653615, TEST_TOL0, GSL_SUCCESS);
1358
TEST_SF(s, gsl_sf_fermi_dirac_half_e, ( 12.0, &r), 31.540203287044242593, TEST_TOL0, GSL_SUCCESS);
1359
TEST_SF(s, gsl_sf_fermi_dirac_half_e, ( 20.0, &r), 67.49151222165892049, TEST_TOL0, GSL_SUCCESS);
1360
TEST_SF(s, gsl_sf_fermi_dirac_half_e, ( 50.0, &r), 266.09281252136259343, TEST_TOL1, GSL_SUCCESS);
1361
1362
TEST_SF(s, gsl_sf_fermi_dirac_3half_e, (-10.0, &r), 0.00004539956540456176333, TEST_TOL0, GSL_SUCCESS);
1363
TEST_SF(s, gsl_sf_fermi_dirac_3half_e, ( -2.0, &r), 0.13224678225177236685, TEST_TOL0, GSL_SUCCESS);
1364
TEST_SF(s, gsl_sf_fermi_dirac_3half_e, ( -1.0, &r), 0.3466747947990574170, TEST_TOL0, GSL_SUCCESS);
1365
TEST_SF(s, gsl_sf_fermi_dirac_3half_e, ( -0.4, &r), 0.6056120213305040910, TEST_TOL0, GSL_SUCCESS);
1366
TEST_SF(s, gsl_sf_fermi_dirac_3half_e, ( 0.4, &r), 1.2258236403963668282, TEST_TOL0, GSL_SUCCESS);
1367
TEST_SF(s, gsl_sf_fermi_dirac_3half_e, ( 1.0, &r), 2.0022581487784644573, TEST_TOL0, GSL_SUCCESS);
1368
TEST_SF(s, gsl_sf_fermi_dirac_3half_e, ( 1.5, &r), 2.9277494127932173068, TEST_TOL0, GSL_SUCCESS);
1369
TEST_SF(s, gsl_sf_fermi_dirac_3half_e, ( 2.5, &r), 5.768879312210516582, TEST_TOL0, GSL_SUCCESS);
1370
TEST_SF(s, gsl_sf_fermi_dirac_3half_e, ( 10.0, &r), 101.00510084332600020, TEST_TOL2, GSL_SUCCESS);
1371
TEST_SF(s, gsl_sf_fermi_dirac_3half_e, ( 12.0, &r), 156.51518642795728036, TEST_TOL1, GSL_SUCCESS);
1372
TEST_SF(s, gsl_sf_fermi_dirac_3half_e, ( 20.0, &r), 546.5630100657601959, TEST_TOL1, GSL_SUCCESS);
1373
TEST_SF(s, gsl_sf_fermi_dirac_3half_e, ( 50.0, &r), 5332.353566687145552, TEST_TOL1, GSL_SUCCESS);
1374
1375
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (3, -2.0, &r), 0.1342199155038680215, TEST_TOL0, GSL_SUCCESS);
1376
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (3, 0.0, &r), 0.9470328294972459176, TEST_TOL0, GSL_SUCCESS);
1377
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (3, 0.1, &r), 1.0414170610956165759, TEST_TOL0, GSL_SUCCESS);
1378
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (3, 1.0, &r), 2.3982260822489407070, TEST_TOL0, GSL_SUCCESS);
1379
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (3, 3.0, &r), 12.621635313399690724, TEST_TOL1, GSL_SUCCESS);
1380
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (3, 100.0, &r), 4.174893231066566793e+06, TEST_TOL1, GSL_SUCCESS);
1381
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (3, 500.0, &r), 2.604372285319088354e+09, TEST_TOL1, GSL_SUCCESS);
1382
1383
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (5, -2.0, &r), 0.13505242246823676478, TEST_TOL0, GSL_SUCCESS);
1384
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (5, 0.0, &r), 0.9855510912974351041, TEST_TOL0, GSL_SUCCESS);
1385
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (5, 0.1, &r), 1.0876519750101492782, TEST_TOL0, GSL_SUCCESS);
1386
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (5, 1.0, &r), 2.6222337848692390539, TEST_TOL0, GSL_SUCCESS);
1387
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (5, 3.0, &r), 17.008801618012113022, TEST_TOL1, GSL_SUCCESS);
1388
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (5, 100.0, &r), 1.3957522531334869874e+09, TEST_TOL1, GSL_SUCCESS);
1389
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (5, 500.0, &r), 2.1705672808114817955e+13, TEST_TOL2, GSL_SUCCESS);
1390
1391
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (7, -2.0, &r), 0.1352641105671255851, TEST_TOL0, GSL_SUCCESS);
1392
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (7, 0.0, &r), 0.9962330018526478992, TEST_TOL0, GSL_SUCCESS);
1393
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (7, 0.1, &r), 1.1005861815180315485, TEST_TOL0, GSL_SUCCESS);
1394
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (7, 1.0, &r), 2.6918878172003129203, TEST_TOL0, GSL_SUCCESS);
1395
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (7, 3.0, &r), 19.033338976999367642, TEST_TOL2, GSL_SUCCESS);
1396
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (7, 10.0, &r), 5654.530932873610014, TEST_TOL1, GSL_SUCCESS);
1397
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (7, 50.0, &r), 1.005005069985066278e+09, TEST_TOL2, GSL_SUCCESS);
1398
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (7, 500.0, &r), 9.691690268341569514e+16, TEST_TOL3, GSL_SUCCESS);
1399
1400
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (9, -2.0, &r), 0.1353174385330242691, TEST_TOL0, GSL_SUCCESS);
1401
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (9, 0.0, &r), 0.9990395075982715656, TEST_TOL0, GSL_SUCCESS);
1402
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (9, 0.1, &r), 1.1039997234712941212, TEST_TOL0, GSL_SUCCESS);
1403
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (9, 1.0, &r), 2.7113648898129249947, TEST_TOL0, GSL_SUCCESS);
1404
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (9, 3.0, &r), 19.768544008138602223, TEST_TOL2, GSL_SUCCESS);
1405
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (9, 10.0, &r), 10388.990167312912478, TEST_TOL2, GSL_SUCCESS);
1406
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (9, 50.0, &r), 2.85466960802601649e+10, TEST_TOL1, GSL_SUCCESS);
1407
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (9, 500.0, &r), 2.69273849842695876e+20, 2*TEST_TOL1, GSL_SUCCESS);
1408
1409
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (10, -2.0, &r), 0.13532635396712288092, TEST_TOL0, GSL_SUCCESS);
1410
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (10, 0.0, &r), 0.9995171434980607541, TEST_TOL0, GSL_SUCCESS);
1411
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (10, 0.1, &r), 1.1045818238852612296, TEST_TOL0, GSL_SUCCESS);
1412
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (10, 1.0, &r), 2.7147765350346120647, TEST_TOL0, GSL_SUCCESS);
1413
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (10, 3.0, &r), 19.917151938411675171, TEST_TOL1, GSL_SUCCESS);
1414
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (10, 10.0, &r), 12790.918595516495955, TEST_TOL2, GSL_SUCCESS);
1415
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (10, 50.0, &r), 1.3147703201869657654e+11, TEST_TOL2, GSL_SUCCESS);
1416
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (10, 500.0, &r), 1.2241331244469204398e+22, TEST_TOL2, GSL_SUCCESS);
1417
1418
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (11, -2.0, &r), 0.1353308162894847149, TEST_TOL0, GSL_SUCCESS);
1419
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (11, 0.0, &r), 0.9997576851438581909, TEST_TOL0, GSL_SUCCESS);
1420
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (11, 0.1, &r), 1.1048751811565850418, TEST_TOL0, GSL_SUCCESS);
1421
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (11, 1.0, &r), 2.7165128749007313436, TEST_TOL0, GSL_SUCCESS);
1422
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (11, 3.0, &r), 19.997483022044603065, TEST_TOL2, GSL_SUCCESS);
1423
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (11, 10.0, &r), 14987.996005901818036, TEST_TOL2, GSL_SUCCESS);
1424
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (11, 50.0, &r), 5.558322924078990628e+11, TEST_TOL2, GSL_SUCCESS);
1425
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (11, 500.0, &r), 5.101293089606198280e+23, TEST_TOL2, GSL_SUCCESS);
1426
1427
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (20, -2.0, &r), 0.13533527450327238373, TEST_TOL0, GSL_SUCCESS);
1428
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (20, 0.0, &r), 0.9999995232582155428, TEST_TOL0, GSL_SUCCESS);
1429
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (20, 0.1, &r), 1.1051703357941368203, TEST_TOL0, GSL_SUCCESS);
1430
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (20, 1.0, &r), 2.7182783069905721654, TEST_TOL0, GSL_SUCCESS);
1431
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (20, 3.0, &r), 20.085345296028242734, TEST_TOL2, GSL_SUCCESS);
1432
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (20, 10.0, &r), 21898.072920149606475, TEST_TOL2, GSL_SUCCESS);
1433
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (20, 50.0, &r), 1.236873256595717618e+16, TEST_TOL2, GSL_SUCCESS);
1434
TEST_SF(s, gsl_sf_fermi_dirac_int_e, (20, 500.0, &r), 9.358938204369557277e+36, TEST_TOL2, GSL_SUCCESS);
1435
1436
1437
return s;
1438
}
1439
1440
1441
int test_gegen(void)
1442
{
1443
gsl_sf_result r;
1444
double ga[100];
1445
int s = 0;
1446
int sa;
1447
1448
TEST_SF(s, gsl_sf_gegenpoly_1_e, (-0.2, 1.0, &r), -0.4, TEST_TOL0, GSL_SUCCESS);
1449
TEST_SF(s, gsl_sf_gegenpoly_1_e, ( 0.0, 1.0, &r), 2.0, TEST_TOL0, GSL_SUCCESS);
1450
TEST_SF(s, gsl_sf_gegenpoly_1_e, ( 1.0, 1.0, &r), 2.0, TEST_TOL0, GSL_SUCCESS);
1451
TEST_SF(s, gsl_sf_gegenpoly_1_e, ( 1.0, 0.5, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
1452
TEST_SF(s, gsl_sf_gegenpoly_1_e, ( 5.0, 1.0, &r), 10.0, TEST_TOL0, GSL_SUCCESS);
1453
TEST_SF(s, gsl_sf_gegenpoly_1_e, ( 100.0, 0.5, &r), 100.0, TEST_TOL0, GSL_SUCCESS);
1454
1455
TEST_SF(s, gsl_sf_gegenpoly_2_e, (-0.2, 0.5, &r), 0.12, TEST_TOL0, GSL_SUCCESS);
1456
TEST_SF(s, gsl_sf_gegenpoly_2_e, ( 0.0, 1.0, &r), 1.00, TEST_TOL0, GSL_SUCCESS);
1457
TEST_SF(s, gsl_sf_gegenpoly_2_e, ( 1.0, 1.0, &r), 3.00, TEST_TOL0, GSL_SUCCESS);
1458
TEST_SF(s, gsl_sf_gegenpoly_2_e, ( 1.0, 0.1, &r), -0.96, TEST_TOL0, GSL_SUCCESS);
1459
TEST_SF(s, gsl_sf_gegenpoly_2_e, ( 5.0, 1.0, &r), 55.0, TEST_TOL0, GSL_SUCCESS);
1460
TEST_SF(s, gsl_sf_gegenpoly_2_e, ( 100.0, 0.5, &r), 4950.0, TEST_TOL0, GSL_SUCCESS);
1461
1462
TEST_SF(s, gsl_sf_gegenpoly_3_e, (-0.2, 0.5, &r), 0.112, TEST_TOL0, GSL_SUCCESS);
1463
TEST_SF(s, gsl_sf_gegenpoly_3_e, ( 0.0, 1.0, &r), -2.0/3.0, TEST_TOL0, GSL_SUCCESS);
1464
TEST_SF(s, gsl_sf_gegenpoly_3_e, ( 1.0, 1.0, &r), 4.000, TEST_TOL0, GSL_SUCCESS);
1465
TEST_SF(s, gsl_sf_gegenpoly_3_e, ( 1.0, 0.1, &r), -0.392, TEST_TOL0, GSL_SUCCESS);
1466
TEST_SF(s, gsl_sf_gegenpoly_3_e, ( 5.0, 1.0, &r), 220.000, TEST_TOL0, GSL_SUCCESS);
1467
TEST_SF(s, gsl_sf_gegenpoly_3_e, ( 100.0, 0.5, &r), 161600.000, TEST_TOL0, GSL_SUCCESS);
1468
1469
TEST_SF(s, gsl_sf_gegenpoly_n_e, (1, 1.0, 1.0, &r), 2.000 , TEST_TOL0, GSL_SUCCESS);
1470
TEST_SF(s, gsl_sf_gegenpoly_n_e, (10, 1.0, 1.0, &r), 11.000 , TEST_TOL0, GSL_SUCCESS);
1471
TEST_SF(s, gsl_sf_gegenpoly_n_e, (10, 1.0, 0.1, &r), -0.4542309376 , TEST_TOL0, GSL_SUCCESS);
1472
TEST_SF(s, gsl_sf_gegenpoly_n_e, (10, 5.0, 1.0, &r), 9.23780e+4 , TEST_TOL0, GSL_SUCCESS);
1473
TEST_SF(s, gsl_sf_gegenpoly_n_e, (10, 100.0, 0.5, &r), 1.5729338392690000e+13, TEST_TOL0, GSL_SUCCESS);
1474
TEST_SF(s, gsl_sf_gegenpoly_n_e, (1000, 100.0, 1.0, &r), 3.3353666135627322e+232, TEST_TOL1, GSL_SUCCESS);
1475
TEST_SF(s, gsl_sf_gegenpoly_n_e, (100, 2000.0, 1.0, &r), 5.8753432034937579e+202, TEST_TOL0, GSL_SUCCESS);
1476
TEST_SF(s, gsl_sf_gegenpoly_n_e, (103, 207.0, 2.0, &r), 1.4210272202235983e+145, TEST_TOL0, GSL_SUCCESS);
1477
TEST_SF(s, gsl_sf_gegenpoly_n_e, (103, -0.4, 0.3, &r), -1.64527498094522e-04, TEST_TOL1, GSL_SUCCESS);
1478
1479
sa = 0;
1480
gsl_sf_gegenpoly_array(99, 5.0, 1.0, ga);
1481
sa += ( test_sf_frac_diff( ga[1], 10.0 ) > TEST_TOL0 );
1482
sa += ( test_sf_frac_diff( ga[10], 9.23780e+4 ) > TEST_TOL0 );
1483
gsl_test(sa, " gsl_sf_gegenpoly_array");
1484
s += sa;
1485
1486
return s;
1487
}
1488
1489
1490
int test_jac(void)
1491
{
1492
double u, m;
1493
double sn, cn, dn;
1494
int stat_ej;
1495
int s = 0;
1496
int sa;
1497
1498
u = 0.5;
1499
m = 0.5;
1500
sa = 0;
1501
stat_ej = gsl_sf_elljac_e(u, m, &sn, &cn, &dn);
1502
sa += test_sf_val(sn, 0.4707504736556572833, TEST_TOL0, "gsl_sf_elljac_e(0.5|0.5) sn");
1503
sa += test_sf_val(cn, 0.8822663948904402865, TEST_TOL0, "gsl_sf_elljac_e(0.5|0.5) cn");
1504
sa += test_sf_val(dn, 0.9429724257773856873, TEST_TOL0, "gsl_sf_elljac_e(0.5|0.5) dn");
1505
gsl_test(s, " gsl_sf_elljac_e(0.5|0.5)");
1506
s += sa;
1507
1508
u = 1.0;
1509
m = 0.3;
1510
sa = 0;
1511
stat_ej = gsl_sf_elljac_e(u, m, &sn, &cn, &dn);
1512
sa += test_sf_val(sn, 0.8187707145344889190, TEST_TOL0, "gsl_sf_elljac_e(1.0|0.3) sn");
1513
sa += test_sf_val(cn, 0.5741206467465548795, TEST_TOL0, "gsl_sf_elljac_e(1.0|0.3) cn");
1514
sa += test_sf_val(dn, 0.8938033089590823040, TEST_TOL0, "gsl_sf_elljac_e(1.0|0.3) dn");
1515
gsl_test(sa, " gsl_sf_elljac_e(1.0|0.3)");
1516
s += sa;
1517
1518
u = 1.0;
1519
m = 0.6;
1520
sa = 0;
1521
stat_ej = gsl_sf_elljac_e(u, m, &sn, &cn, &dn);
1522
sa += test_sf_val(sn, 0.7949388393365780943, TEST_TOL0, "gsl_sf_elljac_e(1.0|0.6) sn");
1523
sa += test_sf_val(cn, 0.6066895760718277578, TEST_TOL0, "gsl_sf_elljac_e(1.0|0.6) cn");
1524
sa += test_sf_val(dn, 0.7879361300438814425, TEST_TOL0, "gsl_sf_elljac_e(1.0|0.6) dn");
1525
gsl_test(sa, " gsl_sf_elljac_e(1.0|0.6)");
1526
s += sa;
1527
1528
u = 3.0;
1529
m = 0.6;
1530
sa = 0;
1531
stat_ej = gsl_sf_elljac_e(u, m, &sn, &cn, &dn);
1532
sa += test_sf_val(sn, 0.7432676860864044186, TEST_TOL0, " gsl_sf_elljac_e(3.0|0.6) sn");
1533
sa += test_sf_val(cn, -0.6689941306317733154, TEST_TOL0, " gsl_sf_elljac_e(3.0|0.6) cn");
1534
sa += test_sf_val(dn, 0.8176379933025723259, TEST_TOL0, " gsl_sf_elljac_e(3.0|0.6) dn");
1535
gsl_test(sa, " gsl_sf_elljac_e(3.0|0.6)");
1536
s += sa;
1537
1538
u = 2.0;
1539
m = 0.999999;
1540
sa = 0;
1541
stat_ej = gsl_sf_elljac_e(u, m, &sn, &cn, &dn);
1542
sa += test_sf_val(sn, 0.96402778575700186570, TEST_TOL1, "gsl_sf_elljac_e(2.0|0.999999) sn");
1543
sa += test_sf_val(cn, 0.26580148285600686381, TEST_TOL1, "gsl_sf_elljac_e(2.0|0.999999) cn");
1544
sa += test_sf_val(dn, 0.26580323105264131136, TEST_TOL1, "gsl_sf_elljac_e(2.0|0.999999) dn");
1545
gsl_test(sa, " gsl_sf_elljac_e(2.0|0.999999)");
1546
s += sa;
1547
1548
/* test supplied by Ivan Panchenko */
1549
u = 1.69695970624443;
1550
m = 0.270378013104138;
1551
sa = 0;
1552
stat_ej = gsl_sf_elljac_e(u, m, &sn, &cn, &dn);
1553
sa += test_sf_val(sn, 1.0, TEST_TOL0, "gsl_sf_elljac_e(1.69..|0.27..) sn");
1554
sa += test_sf_val(cn, 0.0, TEST_TOL1, "gsl_sf_elljac_e(1.69..|0.27..) cn");
1555
sa += test_sf_val(dn, 0.8541791304497336, TEST_TOL1, "gsl_sf_elljac_e(1.69..|0.27..) dn");
1556
gsl_test(sa, " gsl_sf_elljac_e(1.69695970624443|0.270378013104138)");
1557
s += sa;
1558
1559
1560
1561
/* Check known values from Abramowitz & Stegun, Table 16.5 */
1562
u = 0;
1563
m = 0.1;
1564
1565
{
1566
double mc = 1 - m;
1567
/* quarter period K is (pi/2)/agm(1,mc) */
1568
double K = (M_PI_2)/ 0.9741726903999478375938128316;
1569
1570
double A = 1.0 / sqrt(1+sqrt(mc));
1571
double B = pow(mc, 0.25) / sqrt(1+sqrt(mc));
1572
double C = pow(mc, 0.25);
1573
double C2 = sqrt(mc);
1574
1575
double eps = 1e-10;
1576
1577
sa = 0;
1578
stat_ej = gsl_sf_elljac_e(0.0, m, &sn, &cn, &dn);
1579
sa += test_sf_val(sn, 0.0, TEST_TOL0, "gsl_sf_elljac_e(0|0.1) sn");
1580
sa += test_sf_val(cn, 1.0, TEST_TOL0, "gsl_sf_elljac_e(0|0.1) cn");
1581
sa += test_sf_val(dn, 1.0, TEST_TOL0, "gsl_sf_elljac_e(0|0.1) dn");
1582
gsl_test(sa, " gsl_sf_elljac_e(0|0.1)");
1583
s += sa;
1584
1585
sa = 0;
1586
stat_ej = gsl_sf_elljac_e(-eps, m, &sn, &cn, &dn);
1587
sa += test_sf_val(sn, -eps, TEST_TOL0, "gsl_sf_elljac_e(-1e-10|0.1) sn");
1588
sa += test_sf_val(cn, 1.0, TEST_TOL0, "gsl_sf_elljac_e(-1e-10|0.1) cn");
1589
sa += test_sf_val(dn, 1.0, TEST_TOL0, "gsl_sf_elljac_e(-1e-10|0.1) dn");
1590
gsl_test(sa, " gsl_sf_elljac_e(-1e-10|0.1)");
1591
s += sa;
1592
1593
sa = 0;
1594
stat_ej = gsl_sf_elljac_e(eps, m, &sn, &cn, &dn);
1595
sa += test_sf_val(sn, eps, TEST_TOL0, "gsl_sf_elljac_e(1e-10|0.1) sn");
1596
sa += test_sf_val(cn, 1.0, TEST_TOL0, "gsl_sf_elljac_e(1e-10|0.1) cn");
1597
sa += test_sf_val(dn, 1.0, TEST_TOL0, "gsl_sf_elljac_e(1e-10|0.1) dn");
1598
gsl_test(sa, " gsl_sf_elljac_e(1e-10|0.1)");
1599
s += sa;
1600
1601
sa = 0;
1602
stat_ej = gsl_sf_elljac_e(1e-30, m, &sn, &cn, &dn);
1603
sa += test_sf_val(sn, 1e-30, TEST_TOL0, "gsl_sf_elljac_e(1e-30|0.1) sn");
1604
sa += test_sf_val(cn, 1.0, TEST_TOL0, "gsl_sf_elljac_e(1e-30|0.1) cn");
1605
sa += test_sf_val(dn, 1.0, TEST_TOL0, "gsl_sf_elljac_e(1e-30|0.1) dn");
1606
gsl_test(sa, " gsl_sf_elljac_e(1e-30|0.1)");
1607
s += sa;
1608
1609
sa = 0;
1610
stat_ej = gsl_sf_elljac_e(K / 2.0 - eps, m, &sn, &cn, &dn);
1611
sa += test_sf_val(sn, A - eps*B*C, TEST_TOL2, "gsl_sf_elljac_e(K/2-1e-10|0.1) sn");
1612
sa += test_sf_val(cn, B + eps*A*C, TEST_TOL2, "gsl_sf_elljac_e(K/2-1e-10|0.1) cn");
1613
sa += test_sf_val(dn, C + m*eps*A*B, TEST_TOL2, "gsl_sf_elljac_e(K/2-1e-10|0.1) dn");
1614
gsl_test(sa, " gsl_sf_elljac_e(K/2-1e-10|0.1)");
1615
s += sa;
1616
1617
sa = 0;
1618
stat_ej = gsl_sf_elljac_e(K / 2.0, m, &sn, &cn, &dn);
1619
sa += test_sf_val(sn, A, TEST_TOL2, "gsl_sf_elljac_e(K/2|0.1) sn");
1620
sa += test_sf_val(cn, B, TEST_TOL2, "gsl_sf_elljac_e(K/2|0.1) cn");
1621
sa += test_sf_val(dn, C, TEST_TOL2, "gsl_sf_elljac_e(K/2|0.1) dn");
1622
gsl_test(sa, " gsl_sf_elljac_e(K/2|0.1)");
1623
s += sa;
1624
1625
sa = 0;
1626
stat_ej = gsl_sf_elljac_e(K / 2.0 + eps, m, &sn, &cn, &dn);
1627
sa += test_sf_val(sn, A + eps*B*C, TEST_TOL2, "gsl_sf_elljac_e(K/2+1e-10|0.1) sn");
1628
sa += test_sf_val(cn, B - eps*A*C, TEST_TOL2, "gsl_sf_elljac_e(K/2+1e-10|0.1) cn");
1629
sa += test_sf_val(dn, C - m*eps*A*B, TEST_TOL2, "gsl_sf_elljac_e(K/2+1e-10|0.1) dn");
1630
gsl_test(sa, " gsl_sf_elljac_e(K/2+1e-10|0.1)");
1631
s += sa;
1632
1633
sa = 0;
1634
stat_ej = gsl_sf_elljac_e(K - eps, m, &sn, &cn, &dn);
1635
sa += test_sf_val(sn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(K-1e-10|0.1) sn");
1636
sa += test_sf_val(cn, eps*C2, 10*TEST_SNGL, "gsl_sf_elljac_e(K-1e-10|0.1) cn");
1637
sa += test_sf_val(dn, C2, TEST_TOL2, "gsl_sf_elljac_e(K-1e-10|0.1) dn");
1638
gsl_test(sa, " gsl_sf_elljac_e(K-1e-10|0.1)");
1639
s += sa;
1640
1641
sa = 0;
1642
stat_ej = gsl_sf_elljac_e(K, m, &sn, &cn, &dn);
1643
sa += test_sf_val(sn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(K|0.1) sn");
1644
sa += test_sf_val(cn, 0.0, TEST_TOL1, "gsl_sf_elljac_e(K|0.1) cn");
1645
sa += test_sf_val(dn, C2, TEST_TOL2, "gsl_sf_elljac_e(K|0.1) dn");
1646
gsl_test(sa, " gsl_sf_elljac_e(K|0.1)");
1647
s += sa;
1648
1649
sa = 0;
1650
stat_ej = gsl_sf_elljac_e(K + eps, m, &sn, &cn, &dn);
1651
sa += test_sf_val(sn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(K+1e-10|0.1) sn");
1652
sa += test_sf_val(cn, -eps*C2, 10*TEST_SNGL, "gsl_sf_elljac_e(K+1e-10|0.1) cn");
1653
sa += test_sf_val(dn, C2, TEST_TOL2, "gsl_sf_elljac_e(K+1e-10|0.1) dn");
1654
gsl_test(sa, " gsl_sf_elljac_e(K+1e-10|0.1)");
1655
s += sa;
1656
1657
sa = 0;
1658
stat_ej = gsl_sf_elljac_e(3.0*K / 2.0, m, &sn, &cn, &dn);
1659
sa += test_sf_val(sn, A, TEST_TOL2, "gsl_sf_elljac_e(3K/2|0.1) sn");
1660
sa += test_sf_val(cn, -B, TEST_TOL2, "gsl_sf_elljac_e(3K/2|0.1) cn");
1661
sa += test_sf_val(dn, C, TEST_TOL2, "gsl_sf_elljac_e(3K/2|0.1) dn");
1662
gsl_test(sa, " gsl_sf_elljac_e(3K/2|0.1)");
1663
s += sa;
1664
1665
1666
sa = 0;
1667
stat_ej = gsl_sf_elljac_e(2.0*K - eps, m, &sn, &cn, &dn);
1668
sa += test_sf_val(sn, eps, 10*TEST_SNGL, "gsl_sf_elljac_e(2K-1e-10|0.1) sn");
1669
sa += test_sf_val(cn, -1.0, TEST_TOL1, "gsl_sf_elljac_e(2K-1e-10|0.1) cn");
1670
sa += test_sf_val(dn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(2K-1e-10|0.1) dn");
1671
gsl_test(sa, " gsl_sf_elljac_e(2K-1e-10|0.1)");
1672
s += sa;
1673
1674
sa = 0;
1675
stat_ej = gsl_sf_elljac_e(2.0*K, m, &sn, &cn, &dn);
1676
sa += test_sf_val(sn, 0.0, TEST_TOL1, "gsl_sf_elljac_e(2K|0.1) sn");
1677
sa += test_sf_val(cn, -1.0, TEST_TOL1, "gsl_sf_elljac_e(2K|0.1) cn");
1678
sa += test_sf_val(dn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(2K|0.1) dn");
1679
gsl_test(sa, " gsl_sf_elljac_e(2K|0.1)");
1680
s += sa;
1681
1682
sa = 0;
1683
stat_ej = gsl_sf_elljac_e(2.0*K + eps, m, &sn, &cn, &dn);
1684
sa += test_sf_val(sn, -eps, 10*TEST_SNGL, "gsl_sf_elljac_e(2K+1e-10|0.1) sn");
1685
sa += test_sf_val(cn, -1.0, TEST_TOL1, "gsl_sf_elljac_e(2K+1e-10|0.1) cn");
1686
sa += test_sf_val(dn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(2K+1e-10|0.1) dn");
1687
gsl_test(sa, " gsl_sf_elljac_e(2K+1e-10|0.1)");
1688
s += sa;
1689
1690
sa = 0;
1691
stat_ej = gsl_sf_elljac_e(5.0*K / 2.0, m, &sn, &cn, &dn);
1692
sa += test_sf_val(sn, -A, TEST_TOL2, "gsl_sf_elljac_e(5K/2|0.1) sn");
1693
sa += test_sf_val(cn, -B, TEST_TOL2, "gsl_sf_elljac_e(5K/2|0.1) cn");
1694
sa += test_sf_val(dn, C, TEST_TOL2, "gsl_sf_elljac_e(5K/2|0.1) dn");
1695
gsl_test(sa, " gsl_sf_elljac_e(5K/2|0.1)");
1696
s += sa;
1697
1698
sa = 0;
1699
stat_ej = gsl_sf_elljac_e(3.0*K - eps, m, &sn, &cn, &dn);
1700
sa += test_sf_val(sn, -1.0, TEST_TOL1, "gsl_sf_elljac_e(3K-1e-10|0.1) sn");
1701
sa += test_sf_val(cn, -C2 * eps, 10*TEST_SNGL, "gsl_sf_elljac_e(3K-1e-10|0.1) cn");
1702
sa += test_sf_val(dn, C2, TEST_TOL2, "gsl_sf_elljac_e(3K-1e-10|0.1) dn");
1703
gsl_test(sa, " gsl_sf_elljac_e(3K-1e-10|0.1)");
1704
s += sa;
1705
1706
sa = 0;
1707
stat_ej = gsl_sf_elljac_e(3.0*K, m, &sn, &cn, &dn);
1708
sa += test_sf_val(sn, -1.0, TEST_TOL1, "gsl_sf_elljac_e(3K|0.1) sn");
1709
sa += test_sf_val(cn, 0.0, TEST_TOL1, "gsl_sf_elljac_e(3K|0.1) cn");
1710
sa += test_sf_val(dn, C2, TEST_TOL2, "gsl_sf_elljac_e(3K|0.1) dn");
1711
gsl_test(sa, " gsl_sf_elljac_e(3K|0.1)");
1712
s += sa;
1713
1714
sa = 0;
1715
stat_ej = gsl_sf_elljac_e(3.0*K + eps, m, &sn, &cn, &dn);
1716
sa += test_sf_val(sn, -1.0, TEST_TOL1, "gsl_sf_elljac_e(3K+1e-10|0.1) sn");
1717
sa += test_sf_val(cn, +C2 * eps, 10*TEST_SNGL, "gsl_sf_elljac_e(3K+1e-10|0.1) cn");
1718
sa += test_sf_val(dn, C2, TEST_TOL2, "gsl_sf_elljac_e(3K+1e-10|0.1) dn");
1719
gsl_test(sa, " gsl_sf_elljac_e(3K+1e-10|0.1)");
1720
s += sa;
1721
1722
sa = 0;
1723
stat_ej = gsl_sf_elljac_e(7.0*K / 2.0, m, &sn, &cn, &dn);
1724
sa += test_sf_val(sn, -A, TEST_TOL2, "gsl_sf_elljac_e(7K/2|0.1) sn");
1725
sa += test_sf_val(cn, B, TEST_TOL2, "gsl_sf_elljac_e(7K/2|0.1) cn");
1726
sa += test_sf_val(dn, C, TEST_TOL2, "gsl_sf_elljac_e(7K/2|0.1) dn");
1727
gsl_test(sa, " gsl_sf_elljac_e(7K/2|0.1)");
1728
s += sa;
1729
1730
sa = 0;
1731
stat_ej = gsl_sf_elljac_e(4.0*K - eps, m, &sn, &cn, &dn);
1732
sa += test_sf_val(sn, -eps, 10*TEST_SNGL, "gsl_sf_elljac_e(4K-1e-10|0.1) sn");
1733
sa += test_sf_val(cn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(4K-1e-10|0.1) cn");
1734
sa += test_sf_val(dn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(4K-1e-10|0.1) dn");
1735
gsl_test(sa, " gsl_sf_elljac_e(4K-1e-10|0.1)");
1736
s += sa;
1737
1738
sa = 0;
1739
stat_ej = gsl_sf_elljac_e(4.0*K, m, &sn, &cn, &dn);
1740
sa += test_sf_val(sn, 0.0, TEST_TOL1, "gsl_sf_elljac_e(4K|0.1) sn");
1741
sa += test_sf_val(cn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(4K|0.1) cn");
1742
sa += test_sf_val(dn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(4K|0.1) dn");
1743
gsl_test(sa, " gsl_sf_elljac_e(4K|0.1)");
1744
s += sa;
1745
1746
sa = 0;
1747
stat_ej = gsl_sf_elljac_e(9.0 * K / 2.0, m, &sn, &cn, &dn);
1748
sa += test_sf_val(sn, A, TEST_TOL2, "gsl_sf_elljac_e(9K/2|0.1) sn");
1749
sa += test_sf_val(cn, B, TEST_TOL2, "gsl_sf_elljac_e(9K/2|0.1) cn");
1750
sa += test_sf_val(dn, C, TEST_TOL2, "gsl_sf_elljac_e(9K/2|0.1) dn");
1751
gsl_test(sa, " gsl_sf_elljac_e(9K/2|0.1)");
1752
s += sa;
1753
1754
sa = 0;
1755
stat_ej = gsl_sf_elljac_e(-K / 2.0, m, &sn, &cn, &dn);
1756
sa += test_sf_val(sn, -A, TEST_TOL2, "gsl_sf_elljac_e(-K/2|0.1) sn");
1757
sa += test_sf_val(cn, B, TEST_TOL2, "gsl_sf_elljac_e(-K/2|0.1) cn");
1758
sa += test_sf_val(dn, C, TEST_TOL2, "gsl_sf_elljac_e(-K/2|0.1) dn");
1759
gsl_test(sa, " gsl_sf_elljac_e(-K/2|0.1)");
1760
s += sa;
1761
1762
sa = 0;
1763
stat_ej = gsl_sf_elljac_e(-K, m, &sn, &cn, &dn);
1764
sa += test_sf_val(sn, -1.0, TEST_TOL1, "gsl_sf_elljac_e(-K|0.1) sn");
1765
sa += test_sf_val(cn, 0.0, TEST_TOL1, "gsl_sf_elljac_e(-K|0.1) cn");
1766
sa += test_sf_val(dn, C2, TEST_TOL2, "gsl_sf_elljac_e(-K|0.1) dn");
1767
gsl_test(sa, " gsl_sf_elljac_e(-K|0.1)");
1768
s += sa;
1769
1770
sa = 0;
1771
stat_ej = gsl_sf_elljac_e(-3.0*K / 2.0, m, &sn, &cn, &dn);
1772
sa += test_sf_val(sn, -A, TEST_TOL2, "gsl_sf_elljac_e(-3K/2|0.1) sn");
1773
sa += test_sf_val(cn, -B, TEST_TOL2, "gsl_sf_elljac_e(-3K/2|0.1) cn");
1774
sa += test_sf_val(dn, C, TEST_TOL2, "gsl_sf_elljac_e(-3K/2|0.1) dn");
1775
gsl_test(sa, " gsl_sf_elljac_e(-3K/2|0.1)");
1776
s += sa;
1777
1778
sa = 0;
1779
stat_ej = gsl_sf_elljac_e(-2.0*K, m, &sn, &cn, &dn);
1780
sa += test_sf_val(sn, 0.0, TEST_TOL1, "gsl_sf_elljac_e(-2K|0.1) sn");
1781
sa += test_sf_val(cn, -1.0, TEST_TOL1, "gsl_sf_elljac_e(-2K|0.1) cn");
1782
sa += test_sf_val(dn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(-2K|0.1) dn");
1783
gsl_test(sa, " gsl_sf_elljac_e(-2K|0.1)");
1784
s += sa;
1785
1786
sa = 0;
1787
stat_ej = gsl_sf_elljac_e(-5.0*K / 2.0, m, &sn, &cn, &dn);
1788
sa += test_sf_val(sn, A, TEST_TOL2, "gsl_sf_elljac_e(-5K/2|0.1) sn");
1789
sa += test_sf_val(cn, -B, TEST_TOL2, "gsl_sf_elljac_e(-5K/2|0.1) cn");
1790
sa += test_sf_val(dn, C, TEST_TOL2, "gsl_sf_elljac_e(-5K/2|0.1) dn");
1791
gsl_test(sa, " gsl_sf_elljac_e(-5K/2|0.1)");
1792
s += sa;
1793
1794
sa = 0;
1795
stat_ej = gsl_sf_elljac_e(-3.0*K, m, &sn, &cn, &dn);
1796
sa += test_sf_val(sn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(-3K|0.1) sn");
1797
sa += test_sf_val(cn, 0.0, TEST_TOL1, "gsl_sf_elljac_e(-3K|0.1) cn");
1798
sa += test_sf_val(dn, C2, TEST_TOL2, "gsl_sf_elljac_e(-3K|0.1) dn");
1799
gsl_test(sa, " gsl_sf_elljac_e(-3K|0.1)");
1800
s += sa;
1801
1802
sa = 0;
1803
stat_ej = gsl_sf_elljac_e(-7.0*K / 2.0, m, &sn, &cn, &dn);
1804
sa += test_sf_val(sn, A, TEST_TOL2, "gsl_sf_elljac_e(-7K/2|0.1) sn");
1805
sa += test_sf_val(cn, B, TEST_TOL2, "gsl_sf_elljac_e(-7K/2|0.1) cn");
1806
sa += test_sf_val(dn, C, TEST_TOL2, "gsl_sf_elljac_e(-7K/2|0.1) dn");
1807
gsl_test(sa, " gsl_sf_elljac_e(-7K/2|0.1)");
1808
s += sa;
1809
1810
sa = 0;
1811
stat_ej = gsl_sf_elljac_e(-4.0*K, m, &sn, &cn, &dn);
1812
sa += test_sf_val(sn, 0.0, TEST_TOL1, "gsl_sf_elljac_e(-4K|0.1) sn");
1813
sa += test_sf_val(cn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(-4K|0.1) cn");
1814
sa += test_sf_val(dn, 1.0, TEST_TOL1, "gsl_sf_elljac_e(-4K|0.1) dn");
1815
gsl_test(sa, " gsl_sf_elljac_e(-4K|0.1)");
1816
s += sa;
1817
}
1818
1819
1820
return s;
1821
}
1822
1823
1824
int test_laguerre(void)
1825
{
1826
gsl_sf_result r;
1827
int s = 0;
1828
1829
TEST_SF(s, gsl_sf_laguerre_1_e, (0.5, -1.0, &r), 2.5, TEST_TOL0, GSL_SUCCESS);
1830
TEST_SF(s, gsl_sf_laguerre_1_e, (0.5, 1.0, &r), 0.5, TEST_TOL0, GSL_SUCCESS);
1831
TEST_SF(s, gsl_sf_laguerre_1_e, (1.0, 1.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
1832
1833
TEST_SF(s, gsl_sf_laguerre_2_e, ( 0.5, -1.0, &r), 4.875, TEST_TOL0, GSL_SUCCESS);
1834
TEST_SF(s, gsl_sf_laguerre_2_e, ( 0.5, 1.0, &r), -0.125, TEST_TOL0, GSL_SUCCESS);
1835
TEST_SF(s, gsl_sf_laguerre_2_e, ( 1.0, 1.0, &r), 0.5, TEST_TOL0, GSL_SUCCESS);
1836
TEST_SF(s, gsl_sf_laguerre_2_e, (-1.0, 1.0, &r), -0.5, TEST_TOL0, GSL_SUCCESS);
1837
TEST_SF(s, gsl_sf_laguerre_2_e, (-2.0, 1.0, &r), 0.5, TEST_TOL0, GSL_SUCCESS);
1838
TEST_SF(s, gsl_sf_laguerre_2_e, (-3.0, 1.0, &r), 2.5, TEST_TOL0, GSL_SUCCESS);
1839
1840
TEST_SF(s, gsl_sf_laguerre_3_e, (0.5, -1.0, &r), 8.479166666666666667, TEST_TOL0, GSL_SUCCESS);
1841
TEST_SF(s, gsl_sf_laguerre_3_e, (0.5, 1.0, &r), -0.6041666666666666667, TEST_TOL0, GSL_SUCCESS);
1842
TEST_SF(s, gsl_sf_laguerre_3_e, (1.0, 1.0, &r), -0.16666666666666666667, TEST_TOL1, GSL_SUCCESS);
1843
TEST_SF(s, gsl_sf_laguerre_3_e, ( 2.0, 1.0, &r), 2.3333333333333333333, TEST_TOL0, GSL_SUCCESS);
1844
TEST_SF(s, gsl_sf_laguerre_3_e, (-2.0, 1.0, &r), 1.0/3.0, TEST_TOL0, GSL_SUCCESS);
1845
TEST_SF(s, gsl_sf_laguerre_3_e, (-3.0, 1.0, &r), -1.0/6.0, TEST_TOL0, GSL_SUCCESS);
1846
TEST_SF(s, gsl_sf_laguerre_3_e, (-4.0, 1.0, &r), -8.0/3.0, TEST_TOL0, GSL_SUCCESS);
1847
1848
TEST_SF(s, gsl_sf_laguerre_n_e, (1, 0.5, 1.0, &r), 0.5, TEST_TOL0, GSL_SUCCESS);
1849
TEST_SF(s, gsl_sf_laguerre_n_e, (2, 1.0, 1.0, &r), 0.5, TEST_TOL1, GSL_SUCCESS);
1850
TEST_SF(s, gsl_sf_laguerre_n_e, (3, 2.0, 1.0, &r), 2.3333333333333333333, TEST_TOL1, GSL_SUCCESS);
1851
TEST_SF(s, gsl_sf_laguerre_n_e, (4, 2.0, 0.5, &r), 6.752604166666666667, TEST_TOL1, GSL_SUCCESS);
1852
TEST_SF(s, gsl_sf_laguerre_n_e, (90, 2.0, 0.5, &r), -48.79047157201507897, TEST_TOL1, GSL_SUCCESS);
1853
TEST_SF(s, gsl_sf_laguerre_n_e, (90, 2.0, -100.0, &r), 2.5295879275042410902e+63, TEST_TOL2, GSL_SUCCESS);
1854
TEST_SF(s, gsl_sf_laguerre_n_e, (90, 2.0, 100.0, &r), -2.0929042259546928670e+20, TEST_TOL1, GSL_SUCCESS);
1855
TEST_SF(s, gsl_sf_laguerre_n_e, (100, 2.0, -0.5, &r), 2.2521795545919391405e+07, TEST_TOL2, GSL_SUCCESS);
1856
TEST_SF(s, gsl_sf_laguerre_n_e, (100, 2.0, 0.5, &r), -28.764832945909097418, TEST_TOL2, GSL_SUCCESS);
1857
TEST_SF(s, gsl_sf_laguerre_n_e, (1000, 2.0, -0.5, &r), 2.4399915170947549589e+21, TEST_TOL3, GSL_SUCCESS);
1858
TEST_SF(s, gsl_sf_laguerre_n_e, (1000, 2.0, 0.5, &r), -306.77440254315317525, TEST_TOL2, GSL_SUCCESS); /**/
1859
TEST_SF(s, gsl_sf_laguerre_n_e, (100000, 2.0, 1.0, &r), 5107.73491348319, TEST_TOL4, GSL_SUCCESS);
1860
1861
/* Compute these with the recurrence
1862
* L(0,alpha,x)=1;
1863
* L(1,alpha,x)=1+alpha-x;
1864
* L(n,alpha,x)=((2*n-1+alpha-x)*L(n-1,alpha,x)-(n+alpha-1)*L(n-2,alpha,x))/k
1865
*/
1866
1867
TEST_SF(s, gsl_sf_laguerre_n_e, (1e5, 2.5, 2.5, &r), -0.41491680394598644969113795e5, TEST_TOL4, GSL_SUCCESS);
1868
TEST_SF(s, gsl_sf_laguerre_n_e, (1e5+1, 2.5, 2.5, &r), -0.41629446949552321027514888e5, TEST_TOL4, GSL_SUCCESS);
1869
TEST_SF(s, gsl_sf_laguerre_n_e, (1e6+1, 2.5, 2.5, &r), -0.48017961545391273151977118e6, TEST_TOL4, GSL_SUCCESS);
1870
TEST_SF(s, gsl_sf_laguerre_n_e, (5e6+1, 2.5, 2.5, &r), -0.15174037401611122446089494e7, TEST_TOL6, GSL_SUCCESS);
1871
TEST_SF(s, gsl_sf_laguerre_n_e, (8e6+1, 2.5, 2.5, &r), 0.63251509472091810994286362e6, TEST_SNGL, GSL_SUCCESS);
1872
TEST_SF(s, gsl_sf_laguerre_n_e, (1e7+1, 2.5, 2.5, &r), 0.15299484685632983178033887e7, TEST_SNGL, GSL_SUCCESS);
1873
TEST_SF(s, gsl_sf_laguerre_n_e, (1e8+1, 2.5, 2.5, &r), 0.23645341644922756725290777e8, TEST_SNGL, GSL_SUCCESS);
1874
TEST_SF(s, gsl_sf_laguerre_n_e, (1e9+1, 2.5, 2.5, &r), -0.17731002248958790286185878e8, 100*TEST_SNGL, GSL_SUCCESS);
1875
1876
TEST_SF(s, gsl_sf_laguerre_n_e, (1, -2.0, 1.0, &r), -2.0, TEST_TOL0, GSL_SUCCESS);
1877
TEST_SF(s, gsl_sf_laguerre_n_e, (2, -2.0, 1.0, &r), 0.5, TEST_TOL0, GSL_SUCCESS);
1878
TEST_SF(s, gsl_sf_laguerre_n_e, (3, -2.0, 1.0, &r), 1.0/3.0, TEST_TOL0, GSL_SUCCESS);
1879
TEST_SF(s, gsl_sf_laguerre_n_e, (10, -2.0, 1.0, &r), -0.04654954805996472663, TEST_TOL2, GSL_SUCCESS);
1880
TEST_SF(s, gsl_sf_laguerre_n_e, (10, -5.0, 1.0, &r), -0.0031385030864197530864, TEST_TOL2, GSL_SUCCESS);
1881
TEST_SF(s, gsl_sf_laguerre_n_e, (10, -9.0, 1.0, &r), -2.480158730158730159e-06, TEST_TOL5, GSL_SUCCESS);
1882
TEST_SF(s, gsl_sf_laguerre_n_e, (10, -11.0, 1.0, &r), 2.7182818011463844797, TEST_TOL2, GSL_SUCCESS);
1883
TEST_SF(s, gsl_sf_laguerre_n_e, (10, -11.0, -1.0, &r), 0.3678794642857142857, TEST_TOL2, GSL_SUCCESS);
1884
TEST_SF(s, gsl_sf_laguerre_n_e, (100, -2.0, 1.0, &r), -0.0027339992019526273866, TEST_SQRT_TOL0, GSL_SUCCESS);
1885
TEST_SF(s, gsl_sf_laguerre_n_e, (100, -2.0, -1.0, &r), 229923.09193402028290, TEST_TOL5, GSL_SUCCESS);
1886
TEST_SF(s, gsl_sf_laguerre_n_e, (100, -10.0, 1.0, &r), 3.25966665871244092e-11, TEST_TOL6, GSL_SUCCESS);
1887
TEST_SF(s, gsl_sf_laguerre_n_e, (100, -10.0, -1.0, &r), 0.00016484365618205810025, TEST_TOL6, GSL_SUCCESS);
1888
TEST_SF(s, gsl_sf_laguerre_n_e, (100, -20.0, 1.0, &r), 5.09567630343671251e-21, TEST_TOL3, GSL_SUCCESS);
1889
TEST_SF(s, gsl_sf_laguerre_n_e, (100, -30.0, 1.0, &r), 3.46063150272466192e-34, TEST_TOL1, GSL_SUCCESS);
1890
TEST_SF(s, gsl_sf_laguerre_n_e, (100, -50.0, 1.0, &r), 1.20981872933162889e-65, TEST_TOL1, GSL_SUCCESS);
1891
TEST_SF(s, gsl_sf_laguerre_n_e, (100, -50.0, -1.0, &r), 8.60763477742332922e-65, TEST_TOL1, GSL_SUCCESS);
1892
TEST_SF(s, gsl_sf_laguerre_n_e, (100, -50.5, 1.0, &r), 4.84021010426688393e-31, TEST_TOL1, GSL_SUCCESS);
1893
TEST_SF(s, gsl_sf_laguerre_n_e, (100, -50.5, -1.0, &r), 8.49861345212160618e-33, TEST_TOL1, GSL_SUCCESS);
1894
TEST_SF(s, gsl_sf_laguerre_n_e, (100, -101.0, 1.0, &r), 2.7182818284590452354, TEST_TOL1, GSL_SUCCESS);
1895
TEST_SF(s, gsl_sf_laguerre_n_e, (100, -101.0, -1.0, &r), 0.3678794411714423216, TEST_TOL1, GSL_SUCCESS);
1896
TEST_SF(s, gsl_sf_laguerre_n_e, (100, -102.0, 1.0, &r), 271.8281828459045235, TEST_TOL1, GSL_SUCCESS);
1897
TEST_SF(s, gsl_sf_laguerre_n_e, (100, -102.0, -1.0, &r), 37.52370299948711680, TEST_TOL1, GSL_SUCCESS);
1898
TEST_SF(s, gsl_sf_laguerre_n_e, (100, -110.0, 1.0, &r), 1.0666955248998831554e+13, TEST_TOL1, GSL_SUCCESS);
1899
TEST_SF(s, gsl_sf_laguerre_n_e, (100, -110.0, -1.0, &r), 1.7028306108058225871e+12, TEST_TOL1, GSL_SUCCESS);
1900
TEST_SF(s, gsl_sf_laguerre_n_e, (100, -200.0, 1.0, &r), 7.47851889721356628e+58, TEST_TOL1, GSL_SUCCESS);
1901
TEST_SF(s, gsl_sf_laguerre_n_e, (100, -200.0, -1.0, &r), 2.73740299754732273e+58, TEST_TOL1, GSL_SUCCESS);
1902
TEST_SF(s, gsl_sf_laguerre_n_e, (100, -50.0, 10.0, &r), 4.504712811317745591e-21, TEST_SQRT_TOL0, GSL_SUCCESS);
1903
TEST_SF(s, gsl_sf_laguerre_n_e, (100, -50.0, -10.0, &r), 1.475165520610679937e-11, TEST_TOL1, GSL_SUCCESS);
1904
1905
/* test cases for Ed Smith-Rowland */
1906
1907
TEST_SF(s, gsl_sf_laguerre_n_e, (100, 0.0, 0.5, &r), 0.18682260367692278801, TEST_TOL2, GSL_SUCCESS);
1908
TEST_SF(s, gsl_sf_laguerre_n_e, (100, 0.0, 10.5, &r), 9.1796907354050059874, TEST_TOL2, GSL_SUCCESS);
1909
TEST_SF(s, gsl_sf_laguerre_n_e, (100, 0.0, -10.5, &r), 5.6329215744170606488e24, TEST_TOL2, GSL_SUCCESS);
1910
TEST_SF(s, gsl_sf_laguerre_n_e, (100, 0.0, 100.5, &r), -3.9844782875811907525e20, TEST_TOL2, GSL_SUCCESS);
1911
TEST_SF(s, gsl_sf_laguerre_n_e, (100, 0.0, 150, &r), -1.4463204337261709595e31, TEST_TOL2, GSL_SUCCESS);
1912
1913
return s;
1914
}
1915
1916
1917
int test_lambert(void)
1918
{
1919
gsl_sf_result r;
1920
int s = 0;
1921
1922
TEST_SF(s, gsl_sf_lambert_W0_e, (0.0, &r), 0.0, TEST_TOL0, GSL_SUCCESS);
1923
TEST_SF(s, gsl_sf_lambert_W0_e, (1.0, &r), 0.567143290409783872999969, TEST_TOL0, GSL_SUCCESS);
1924
TEST_SF(s, gsl_sf_lambert_W0_e, (2.0, &r), 0.852605502013725491346472, TEST_TOL0, GSL_SUCCESS);
1925
TEST_SF(s, gsl_sf_lambert_W0_e, (20.0, &r), 2.205003278024059970493066, TEST_TOL0, GSL_SUCCESS);
1926
TEST_SF(s, gsl_sf_lambert_W0_e, (1000.0, &r), 5.24960285240159622712606, TEST_TOL0, GSL_SUCCESS);
1927
TEST_SF(s, gsl_sf_lambert_W0_e, (1.0e+6, &r), 11.38335808614005262200016, TEST_TOL0, GSL_SUCCESS);
1928
TEST_SF(s, gsl_sf_lambert_W0_e, (1.0e+12, &r), 24.43500440493491313826305, TEST_TOL0, GSL_SUCCESS);
1929
TEST_SF(s, gsl_sf_lambert_W0_e, (1.0e+308, &r), 702.641362034106812081125, TEST_TOL0, GSL_SUCCESS);
1930
1931
/* Test case from Katrin Wolff <katrin_wolff@gmx.de> fails under
1932
double-precision */
1933
1934
TEST_SF(s, gsl_sf_lambert_W0_e, (1.6849341956993852953416990, &r), 0.775706963944252869680440, TEST_TOL0, GSL_SUCCESS);
1935
1936
TEST_SF(s, gsl_sf_lambert_W0_e, (-1.0/M_E - GSL_DBL_EPSILON, &r), -1.0, TEST_TOL0, GSL_EDOM);
1937
TEST_SF(s, gsl_sf_lambert_W0_e, (-1.0/M_E + 1.0/(1024.0*1024.0*1024.0), &r), -0.999928845560308370714970, TEST_TOL0, GSL_SUCCESS);
1938
TEST_SF(s, gsl_sf_lambert_W0_e, (-1.0/M_E + 1.0/(1024.0*1024.0), &r), -0.997724730359774141620354, TEST_TOL0, GSL_SUCCESS);
1939
TEST_SF(s, gsl_sf_lambert_W0_e, (-1.0/M_E + 1.0/512.0, &r), -0.900335676696088773044678, TEST_TOL0, GSL_SUCCESS);
1940
TEST_SF(s, gsl_sf_lambert_W0_e, (-1.0/M_E + 0.25, &r), -0.1349044682661213545487599, TEST_TOL0, GSL_SUCCESS);
1941
1942
TEST_SF(s, gsl_sf_lambert_Wm1_e, (0.0, &r), 0.0, TEST_TOL0, GSL_SUCCESS);
1943
TEST_SF(s, gsl_sf_lambert_Wm1_e, (1.0, &r), 0.567143290409783872999969, TEST_TOL0, GSL_SUCCESS);
1944
TEST_SF(s, gsl_sf_lambert_Wm1_e, (2.0, &r), 0.852605502013725491346472, TEST_TOL0, GSL_SUCCESS);
1945
TEST_SF(s, gsl_sf_lambert_Wm1_e, (20.0, &r), 2.205003278024059970493066, TEST_TOL0, GSL_SUCCESS);
1946
1947
TEST_SF(s, gsl_sf_lambert_Wm1_e, (-1.0/M_E - GSL_DBL_EPSILON, &r), -1.0, TEST_TOL0, GSL_EDOM);
1948
TEST_SF(s, gsl_sf_lambert_Wm1_e, (-1.0/M_E + 1.0/(1024.0*1024.0*1024.0), &r), -1.000071157815154608049055, TEST_TOL1, GSL_SUCCESS);
1949
TEST_SF(s, gsl_sf_lambert_Wm1_e, (-1.0/M_E + 1.0/(1024.0*1024.0), &r), -1.002278726118593023934693, TEST_TOL1, GSL_SUCCESS);
1950
TEST_SF(s, gsl_sf_lambert_Wm1_e, (-1.0/M_E + 1.0/512.0, &r), -1.106761200865743124599130, TEST_TOL1, GSL_SUCCESS);
1951
TEST_SF(s, gsl_sf_lambert_Wm1_e, (-1.0/M_E + 1.0/64.0, &r), -1.324240940341812125489772, TEST_TOL1, GSL_SUCCESS);
1952
TEST_SF(s, gsl_sf_lambert_Wm1_e, (-1.0/M_E + 0.25, &r), -3.345798131120112, TEST_TOL1, GSL_SUCCESS);
1953
1954
return s;
1955
}
1956
1957
1958
int test_log(void)
1959
{
1960
gsl_sf_result r;
1961
gsl_sf_result r1, r2;
1962
int s = 0;
1963
1964
TEST_SF(s, gsl_sf_log_e, (0.1, &r), -2.3025850929940456840, TEST_TOL0, GSL_SUCCESS);
1965
TEST_SF(s, gsl_sf_log_e, (1.1, &r), 0.09531017980432486004, TEST_TOL1, GSL_SUCCESS);
1966
TEST_SF(s, gsl_sf_log_e, (1000.0, &r), 6.907755278982137052, TEST_TOL0, GSL_SUCCESS);
1967
1968
TEST_SF(s, gsl_sf_log_abs_e, (-0.1, &r), -2.3025850929940456840, TEST_TOL0, GSL_SUCCESS);
1969
TEST_SF(s, gsl_sf_log_abs_e, (-1.1, &r), 0.09531017980432486004, TEST_TOL1, GSL_SUCCESS);
1970
TEST_SF(s, gsl_sf_log_abs_e, (-1000.0, &r), 6.907755278982137052, TEST_TOL0, GSL_SUCCESS);
1971
TEST_SF(s, gsl_sf_log_abs_e, (0.1, &r), -2.3025850929940456840, TEST_TOL0, GSL_SUCCESS);
1972
TEST_SF(s, gsl_sf_log_abs_e, (1.1, &r), 0.09531017980432486004, TEST_TOL1, GSL_SUCCESS);
1973
TEST_SF(s, gsl_sf_log_abs_e, (1000.0, &r), 6.907755278982137052, TEST_TOL0, GSL_SUCCESS);
1974
1975
TEST_SF_2(s, gsl_sf_complex_log_e, (1.0, 1.0, &r1, &r2),
1976
0.3465735902799726547, TEST_TOL0,
1977
0.7853981633974483096, TEST_TOL0,
1978
GSL_SUCCESS);
1979
1980
TEST_SF_2(s, gsl_sf_complex_log_e, (1.0, -1.0, &r1, &r2),
1981
0.3465735902799726547, TEST_TOL0,
1982
-0.7853981633974483096, TEST_TOL0,
1983
GSL_SUCCESS);
1984
1985
TEST_SF_2(s, gsl_sf_complex_log_e, (1.0, 100.0, &r1, &r2),
1986
4.605220183488258022, TEST_TOL0,
1987
1.560796660108231381, TEST_TOL0,
1988
GSL_SUCCESS);
1989
1990
TEST_SF_2(s, gsl_sf_complex_log_e, (-1000.0, -1.0, &r1, &r2),
1991
6.907755778981887052, TEST_TOL0,
1992
-3.1405926539231263718, TEST_TOL0,
1993
GSL_SUCCESS);
1994
1995
TEST_SF_2(s, gsl_sf_complex_log_e, (-1.0, 0.0, &r1, &r2),
1996
0.0, TEST_TOL0,
1997
3.1415926535897932385, TEST_TOL0,
1998
GSL_SUCCESS);
1999
2000
2001
TEST_SF(s, gsl_sf_log_1plusx_e, (1.0e-10, &r), 9.999999999500000000e-11, TEST_TOL0, GSL_SUCCESS);
2002
TEST_SF(s, gsl_sf_log_1plusx_e, (1.0e-8, &r), 9.999999950000000333e-09, TEST_TOL0, GSL_SUCCESS);
2003
TEST_SF(s, gsl_sf_log_1plusx_e, (1.0e-4, &r), 0.00009999500033330833533, TEST_TOL0, GSL_SUCCESS);
2004
TEST_SF(s, gsl_sf_log_1plusx_e, (0.1, &r), 0.09531017980432486004, TEST_TOL0, GSL_SUCCESS);
2005
TEST_SF(s, gsl_sf_log_1plusx_e, (0.49, &r), 0.3987761199573677730, TEST_TOL0, GSL_SUCCESS);
2006
2007
TEST_SF(s, gsl_sf_log_1plusx_e, (-0.49, &r), -0.6733445532637655964, TEST_TOL0, GSL_SUCCESS);
2008
TEST_SF(s, gsl_sf_log_1plusx_e, (1.0, &r), M_LN2, TEST_TOL0, GSL_SUCCESS);
2009
TEST_SF(s, gsl_sf_log_1plusx_e, (-0.99, &r), -4.605170185988091368, TEST_TOL0, GSL_SUCCESS);
2010
2011
TEST_SF(s, gsl_sf_log_1plusx_mx_e, (1.0e-10, &r), -4.999999999666666667e-21, TEST_TOL0, GSL_SUCCESS);
2012
TEST_SF(s, gsl_sf_log_1plusx_mx_e, (1.0e-8, &r), -4.999999966666666917e-17, TEST_TOL0, GSL_SUCCESS);
2013
TEST_SF(s, gsl_sf_log_1plusx_mx_e, (1.0e-4, &r), -4.999666691664666833e-09, TEST_TOL0, GSL_SUCCESS);
2014
TEST_SF(s, gsl_sf_log_1plusx_mx_e, (0.1, &r), -0.004689820195675139956, TEST_TOL0, GSL_SUCCESS);
2015
TEST_SF(s, gsl_sf_log_1plusx_mx_e, (0.49, &r), -0.09122388004263222704, TEST_TOL0, GSL_SUCCESS);
2016
2017
TEST_SF(s, gsl_sf_log_1plusx_mx_e, (-0.49, &r), -0.18334455326376559639, TEST_TOL0, GSL_SUCCESS);
2018
TEST_SF(s, gsl_sf_log_1plusx_mx_e, (1.0, &r), M_LN2-1.0, TEST_TOL0, GSL_SUCCESS);
2019
TEST_SF(s, gsl_sf_log_1plusx_mx_e, (-0.99, &r), -3.615170185988091368, TEST_TOL0, GSL_SUCCESS);
2020
2021
return s;
2022
}
2023
2024
2025
int test_pow_int(void)
2026
{
2027
gsl_sf_result r;
2028
int status = 0;
2029
int s = 0;
2030
2031
TEST_SF(s, gsl_sf_pow_int_e, (2.0, 3, &r), 8.0, TEST_TOL0, GSL_SUCCESS);
2032
TEST_SF(s, gsl_sf_pow_int_e, (-2.0, 3, &r), -8.0, TEST_TOL0, GSL_SUCCESS);
2033
TEST_SF(s, gsl_sf_pow_int_e, (2.0, -3, &r), 1.0/8.0, TEST_TOL0, GSL_SUCCESS);
2034
TEST_SF(s, gsl_sf_pow_int_e, (-2.0, -3, &r), -1.0/8.0, TEST_TOL0, GSL_SUCCESS);
2035
2036
2037
TEST_SF(s, gsl_sf_pow_int_e, (10.0, 4, &r), 1.0e+4, TEST_TOL0, GSL_SUCCESS);
2038
TEST_SF(s, gsl_sf_pow_int_e, (10.0, -4, &r), 1.0e-4, TEST_TOL0, GSL_SUCCESS);
2039
TEST_SF(s, gsl_sf_pow_int_e, (-10.0, 4, &r), 1.0e+4, TEST_TOL0, GSL_SUCCESS);
2040
TEST_SF(s, gsl_sf_pow_int_e, (-10.0, -4, &r), 1.0e-4, TEST_TOL0, GSL_SUCCESS);
2041
2042
TEST_SF(s, gsl_sf_pow_int_e, (10.0, 40, &r), 1.0e+40, TEST_TOL0, GSL_SUCCESS);
2043
TEST_SF(s, gsl_sf_pow_int_e, (8.0, -40, &r), 7.523163845262640051e-37, TEST_TOL0, GSL_SUCCESS);
2044
TEST_SF(s, gsl_sf_pow_int_e, (-10.0, 40, &r), 1.0e+40, TEST_TOL0, GSL_SUCCESS);
2045
TEST_SF(s, gsl_sf_pow_int_e, (-8.0, -40, &r), 7.523163845262640051e-37, TEST_TOL0, GSL_SUCCESS);
2046
2047
TEST_SF(s, gsl_sf_pow_int_e, (10.0, 41, &r), 1.0e+41, TEST_TOL0, GSL_SUCCESS);
2048
TEST_SF(s, gsl_sf_pow_int_e, (8.0, -41, &r), 9.403954806578300064e-38, TEST_TOL0, GSL_SUCCESS);
2049
TEST_SF(s, gsl_sf_pow_int_e, (-10.0, 41, &r), -1.0e+41, TEST_TOL0, GSL_SUCCESS);
2050
TEST_SF(s, gsl_sf_pow_int_e, (-8.0, -41, &r), -9.403954806578300064e-38, TEST_TOL0, GSL_SUCCESS);
2051
2052
return status;
2053
}
2054
2055
int test_psi(void)
2056
{
2057
gsl_sf_result r;
2058
int s = 0;
2059
2060
/* Test values taken 1-4 from gp-pari */
2061
2062
TEST_SF(s, gsl_sf_psi_int_e, (1, &r), -0.57721566490153286060, TEST_TOL0, GSL_SUCCESS);
2063
TEST_SF(s, gsl_sf_psi_int_e, (2, &r), 0.42278433509846713939, TEST_TOL0, GSL_SUCCESS);
2064
TEST_SF(s, gsl_sf_psi_int_e, (3, &r), 0.92278433509846713939, TEST_TOL0, GSL_SUCCESS);
2065
TEST_SF(s, gsl_sf_psi_int_e, (4, &r), 1.2561176684318004727, TEST_TOL0, GSL_SUCCESS);
2066
2067
TEST_SF(s, gsl_sf_psi_int_e, (5, &r), 1.5061176684318004727, TEST_TOL0, GSL_SUCCESS);
2068
TEST_SF(s, gsl_sf_psi_int_e, (100, &r), 4.600161852738087400, TEST_TOL0, GSL_SUCCESS);
2069
TEST_SF(s, gsl_sf_psi_int_e, (110, &r), 4.695928024251535633, TEST_TOL0, GSL_SUCCESS);
2070
TEST_SF(s, gsl_sf_psi_int_e, (5000, &r), 8.517093188082904107, TEST_TOL0, GSL_SUCCESS);
2071
2072
TEST_SF(s, gsl_sf_psi_e, (5000.0, &r), 8.517093188082904107, TEST_TOL0, GSL_SUCCESS);
2073
TEST_SF(s, gsl_sf_psi_e, (5.0, &r), 1.5061176684318004727, TEST_TOL0, GSL_SUCCESS);
2074
TEST_SF(s, gsl_sf_psi_e, (-10.5, &r), 2.3982391295357816134, TEST_TOL0, GSL_SUCCESS);
2075
TEST_SF(s, gsl_sf_psi_e, (-100.5, &r), 4.615124601338064117, TEST_TOL2, GSL_SUCCESS);
2076
TEST_SF(s, gsl_sf_psi_e, (-1.0e+5-0.5, &r), 11.512935464924395337, 4.0*TEST_TOL4, GSL_SUCCESS);
2077
TEST_SF(s, gsl_sf_psi_e, (-262144.0-0.5, &r), 12.476653064769611581, 4.0*TEST_TOL4, GSL_SUCCESS);
2078
2079
TEST_SF(s, gsl_sf_psi_1piy_e, (0.8, &r), -0.07088340212750589223, TEST_TOL1, GSL_SUCCESS);
2080
TEST_SF(s, gsl_sf_psi_1piy_e, (1.0, &r), 0.09465032062247697727, TEST_TOL0, GSL_SUCCESS);
2081
TEST_SF(s, gsl_sf_psi_1piy_e, (5.0, &r), 1.6127848446157465854, TEST_TOL2, GSL_SUCCESS);
2082
TEST_SF(s, gsl_sf_psi_1piy_e, (100.0, &r), 4.605178519404762003, TEST_TOL0, GSL_SUCCESS);
2083
TEST_SF(s, gsl_sf_psi_1piy_e, (2000.0, &r), 7.600902480375416216, TEST_TOL0, GSL_SUCCESS);
2084
2085
TEST_SF(s, gsl_sf_psi_1piy_e, (-0.8, &r), -0.07088340212750589223, TEST_TOL1, GSL_SUCCESS);
2086
TEST_SF(s, gsl_sf_psi_1piy_e, (-1.0, &r), 0.09465032062247697727, TEST_TOL0, GSL_SUCCESS);
2087
TEST_SF(s, gsl_sf_psi_1piy_e, (-5.0, &r), 1.6127848446157465854, TEST_TOL2, GSL_SUCCESS);
2088
TEST_SF(s, gsl_sf_psi_1piy_e, (-100.0, &r), 4.605178519404762003, TEST_TOL0, GSL_SUCCESS);
2089
TEST_SF(s, gsl_sf_psi_1piy_e, (-2000.0, &r), 7.600902480375416216, TEST_TOL0, GSL_SUCCESS);
2090
2091
/* Additional test values 1-4 computed using gp-pari and
2092
Abramowitz & Stegun 6.4.6 */
2093
2094
TEST_SF(s, gsl_sf_psi_1_int_e, (1, &r), 1.6449340668482264364, TEST_TOL0, GSL_SUCCESS);
2095
TEST_SF(s, gsl_sf_psi_1_int_e, (2, &r), 0.64493406684822643647, TEST_TOL0, GSL_SUCCESS);
2096
TEST_SF(s, gsl_sf_psi_1_int_e, (3, &r), 0.39493406684822643647, TEST_TOL0, GSL_SUCCESS);
2097
TEST_SF(s, gsl_sf_psi_1_int_e, (4, &r), 0.28382295573711532536, TEST_TOL0, GSL_SUCCESS);
2098
2099
TEST_SF(s, gsl_sf_psi_1_int_e, (1, &r), 1.6449340668482264365, TEST_TOL0, GSL_SUCCESS);
2100
TEST_SF(s, gsl_sf_psi_1_int_e, (5, &r), 0.22132295573711532536, TEST_TOL0, GSL_SUCCESS);
2101
TEST_SF(s, gsl_sf_psi_1_int_e, (100, &r), 0.010050166663333571395, TEST_TOL0, GSL_SUCCESS);
2102
TEST_SF(s, gsl_sf_psi_1_int_e, (110, &r), 0.009132356622022545705, TEST_TOL0, GSL_SUCCESS);
2103
TEST_SF(s, gsl_sf_psi_1_int_e, (500, &r), 0.0020020013333322666697, TEST_TOL0, GSL_SUCCESS);
2104
2105
TEST_SF(s, gsl_sf_psi_1_e, (1.0/32.0, &r), 1025.5728544782377089, TEST_TOL0, GSL_SUCCESS);
2106
TEST_SF(s, gsl_sf_psi_1_e, (1.0, &r), 1.6449340668482264365, TEST_TOL0, GSL_SUCCESS);
2107
TEST_SF(s, gsl_sf_psi_1_e, (5.0, &r), 0.22132295573711532536, TEST_TOL0, GSL_SUCCESS);
2108
TEST_SF(s, gsl_sf_psi_1_e, (100.0, &r), 0.010050166663333571395, TEST_TOL0, GSL_SUCCESS);
2109
TEST_SF(s, gsl_sf_psi_1_e, (110.0, &r), 0.009132356622022545705, TEST_TOL0, GSL_SUCCESS);
2110
TEST_SF(s, gsl_sf_psi_1_e, (500.0, &r), 0.0020020013333322666697, TEST_TOL0, GSL_SUCCESS);
2111
2112
TEST_SF(s, gsl_sf_psi_1_e, (-1.0 - 1.0/128.0, &r), 16386.648472598746587, TEST_TOL0, GSL_SUCCESS);
2113
TEST_SF(s, gsl_sf_psi_1_e, (-1.50, &r), 9.3792466449891237539, TEST_TOL0, GSL_SUCCESS);
2114
TEST_SF(s, gsl_sf_psi_1_e, (-10.5, &r), 9.7787577398148123845, TEST_TOL0, GSL_SUCCESS);
2115
TEST_SF(s, gsl_sf_psi_1_e, (-15.5, &r), 9.8071247184113896201, TEST_TOL0, GSL_SUCCESS);
2116
TEST_SF(s, gsl_sf_psi_1_e, (-50.5, &r), 9.8499971860824842274, TEST_TOL0, GSL_SUCCESS);
2117
TEST_SF(s, gsl_sf_psi_1_e, (-1000.5, &r), 9.8686054001734414233, TEST_TOL0, GSL_SUCCESS);
2118
2119
TEST_SF(s, gsl_sf_psi_n_e, (1, 1, &r), 1.6449340668482264364, TEST_TOL0, GSL_SUCCESS);
2120
TEST_SF(s, gsl_sf_psi_n_e, (1, 2, &r), 0.64493406684822643647, TEST_TOL0, GSL_SUCCESS);
2121
TEST_SF(s, gsl_sf_psi_n_e, (1, 3, &r), 0.39493406684822643647, TEST_TOL0, GSL_SUCCESS);
2122
TEST_SF(s, gsl_sf_psi_n_e, (1, 4, &r), 0.28382295573711532536, TEST_TOL0, GSL_SUCCESS);
2123
2124
TEST_SF(s, gsl_sf_psi_n_e, (1, 5, &r), 0.22132295573711532536, TEST_TOL0, GSL_SUCCESS);
2125
TEST_SF(s, gsl_sf_psi_n_e, (1, 100, &r), 0.010050166663333571395, TEST_TOL0, GSL_SUCCESS);
2126
TEST_SF(s, gsl_sf_psi_n_e, (1, 110, &r), 0.009132356622022545705, TEST_TOL0, GSL_SUCCESS);
2127
TEST_SF(s, gsl_sf_psi_n_e, (1, 500, &r), 0.0020020013333322666697, TEST_TOL0, GSL_SUCCESS);
2128
2129
TEST_SF(s, gsl_sf_psi_n_e, (3, 5.0, &r), 0.021427828192755075022, TEST_TOL0, GSL_SUCCESS);
2130
TEST_SF(s, gsl_sf_psi_n_e, (3, 500.0, &r), 1.6048063999872000683e-08, TEST_TOL0, GSL_SUCCESS);
2131
TEST_SF(s, gsl_sf_psi_n_e, (10, 5.0, &r), -0.08675107579196581317, TEST_TOL1, GSL_SUCCESS);
2132
TEST_SF(s, gsl_sf_psi_n_e, (10, 50.0, &r), -4.101091112731268288e-12, TEST_TOL0, GSL_SUCCESS);
2133
2134
TEST_SF(s, gsl_sf_psi_n_e, (0, -1.5, &r), 0.70315664064524318723, TEST_TOL0, GSL_SUCCESS);
2135
TEST_SF(s, gsl_sf_psi_n_e, (1, -1.5, &r), 9.3792466449891237539, TEST_TOL0, GSL_SUCCESS);
2136
2137
return s;
2138
}
2139
2140
2141
int test_psi_complex(void)
2142
{
2143
gsl_sf_result r1;
2144
gsl_sf_result r2;
2145
int s = 0;
2146
2147
TEST_SF_2(s, gsl_sf_complex_psi_e, (1.0e+07, 1.0e+06, &r1, &r2),
2148
16.1230707668799525, TEST_TOL0,
2149
0.09966865744165720, TEST_TOL0,
2150
GSL_SUCCESS);
2151
2152
TEST_SF_2(s, gsl_sf_complex_psi_e, (10.0, 50.0, &r1, &r2),
2153
3.92973987174863660, TEST_TOL0,
2154
1.38302847985210276, TEST_TOL0,
2155
GSL_SUCCESS);
2156
2157
TEST_SF_2(s, gsl_sf_complex_psi_e, (2.0, 21.0, &r1, &r2),
2158
3.04697388853248195, TEST_TOL0,
2159
1.49947549076817824, TEST_TOL0,
2160
GSL_SUCCESS);
2161
2162
TEST_SF_2(s, gsl_sf_complex_psi_e, (1.5, 0.0, &r1, &r2),
2163
0.0364899739785765206, TEST_TOL2,
2164
0.0, TEST_TOL1,
2165
GSL_SUCCESS);
2166
2167
TEST_SF_2(s, gsl_sf_complex_psi_e, (1.0, 5.0, &r1, &r2),
2168
1.612784844615747, TEST_TOL1,
2169
1.470796326794968, TEST_TOL1,
2170
GSL_SUCCESS);
2171
2172
TEST_SF_2(s, gsl_sf_complex_psi_e, (-1.5, 5.0, &r1, &r2),
2173
1.68260717336484070, TEST_TOL0,
2174
1.95230236730713338, TEST_TOL0,
2175
GSL_SUCCESS);
2176
2177
TEST_SF_2(s, gsl_sf_complex_psi_e, (-20.5, -20.5, &r1, &r2),
2178
3.37919358657933066, TEST_TOL0,
2179
-2.36829046481731091, TEST_TOL0,
2180
GSL_SUCCESS);
2181
2182
return s;
2183
}
2184
2185
2186
2187
2188
int test_synch(void)
2189
{
2190
gsl_sf_result r;
2191
int s = 0;
2192
2193
TEST_SF(s, gsl_sf_synchrotron_1_e, (0.01, &r), 0.444972504114210632, TEST_TOL0, GSL_SUCCESS);
2194
TEST_SF(s, gsl_sf_synchrotron_1_e, (1.0, &r), 0.651422815355364504, TEST_TOL1, GSL_SUCCESS);
2195
TEST_SF(s, gsl_sf_synchrotron_1_e, (10.0, &r), 0.000192238264300868882, TEST_TOL1, GSL_SUCCESS);
2196
TEST_SF(s, gsl_sf_synchrotron_1_e, (100.0, &r), 4.69759366592220221e-43, TEST_TOL1, GSL_SUCCESS);
2197
2198
TEST_SF(s, gsl_sf_synchrotron_2_e, (0.01, &r), 0.23098077342226277732, TEST_TOL2, GSL_SUCCESS);
2199
TEST_SF(s, gsl_sf_synchrotron_2_e, (1.0, &r), 0.4944750621042082670, TEST_TOL1, GSL_SUCCESS);
2200
TEST_SF(s, gsl_sf_synchrotron_2_e, (10.0, &r), 0.00018161187569530204281, TEST_TOL1, GSL_SUCCESS);
2201
TEST_SF(s, gsl_sf_synchrotron_2_e, (256.0, &r), 1.3272635474353774058e-110, TEST_TOL4, GSL_SUCCESS); /* exp()... not my fault */
2202
2203
return s;
2204
}
2205
2206
2207
int test_transport(void)
2208
{
2209
gsl_sf_result r;
2210
int s = 0;
2211
2212
TEST_SF(s, gsl_sf_transport_2_e, (1.0e-10, &r), 9.9999999999999999999e-11, TEST_TOL0, GSL_SUCCESS);
2213
TEST_SF(s, gsl_sf_transport_2_e, (1.0, &r), 0.97303256135517012845, TEST_TOL0, GSL_SUCCESS);
2214
TEST_SF(s, gsl_sf_transport_2_e, (3.0, &r), 2.41105004901695346199, TEST_TOL0, GSL_SUCCESS);
2215
TEST_SF(s, gsl_sf_transport_2_e, (10.0, &r), 3.28432911449795173575, TEST_TOL0, GSL_SUCCESS);
2216
TEST_SF(s, gsl_sf_transport_2_e, (100.0, &r), 3.28986813369645287294, TEST_TOL0, GSL_SUCCESS);
2217
TEST_SF(s, gsl_sf_transport_2_e, (1.0e+05, &r), 3.28986813369645287294, TEST_TOL0, GSL_SUCCESS);
2218
2219
TEST_SF(s, gsl_sf_transport_3_e, (1.0e-10, &r), 4.999999999999999999997e-21, TEST_TOL0, GSL_SUCCESS);
2220
TEST_SF(s, gsl_sf_transport_3_e, (1.0, &r), 0.479841006572417499939, TEST_TOL0, GSL_SUCCESS);
2221
TEST_SF(s, gsl_sf_transport_3_e, (3.0, &r), 3.210604662942246772338, TEST_TOL0, GSL_SUCCESS);
2222
TEST_SF(s, gsl_sf_transport_3_e, (5.0, &r), 5.614386613842273228585, TEST_TOL0, GSL_SUCCESS);
2223
TEST_SF(s, gsl_sf_transport_3_e, (10.0, &r), 7.150322712008592975030, TEST_TOL0, GSL_SUCCESS);
2224
TEST_SF(s, gsl_sf_transport_3_e, (30.0, &r), 7.212341416160946511930, TEST_TOL0, GSL_SUCCESS);
2225
TEST_SF(s, gsl_sf_transport_3_e, (100.0, &r), 7.212341418957565712398, TEST_TOL0, GSL_SUCCESS);
2226
TEST_SF(s, gsl_sf_transport_3_e, (1.0e+05, &r), 7.212341418957565712398, TEST_TOL0, GSL_SUCCESS);
2227
2228
TEST_SF(s, gsl_sf_transport_4_e, (1.0e-10, &r), 3.33333333333333333333e-31, TEST_TOL0, GSL_SUCCESS);
2229
TEST_SF(s, gsl_sf_transport_4_e, (1.0e-07, &r), 3.33333333333333166666e-22, TEST_TOL0, GSL_SUCCESS);
2230
TEST_SF(s, gsl_sf_transport_4_e, (1.0e-04, &r), 3.33333333166666666726e-13, TEST_TOL0, GSL_SUCCESS);
2231
TEST_SF(s, gsl_sf_transport_4_e, (0.1, &r), 0.000333166726172109903824, TEST_TOL0, GSL_SUCCESS);
2232
TEST_SF(s, gsl_sf_transport_4_e, (1.0, &r), 0.31724404523442648241, TEST_TOL0, GSL_SUCCESS);
2233
TEST_SF(s, gsl_sf_transport_4_e, (3.0, &r), 5.96482239737147652446, TEST_TOL0, GSL_SUCCESS);
2234
TEST_SF(s, gsl_sf_transport_4_e, (5.0, &r), 15.3597843168821829816, TEST_TOL0, GSL_SUCCESS);
2235
TEST_SF(s, gsl_sf_transport_4_e, (10.0, &r), 25.2736676770304417334, TEST_TOL0, GSL_SUCCESS);
2236
TEST_SF(s, gsl_sf_transport_4_e, (30.0, &r), 25.9757575220840937469, TEST_TOL0, GSL_SUCCESS);
2237
TEST_SF(s, gsl_sf_transport_4_e, (100.0, &r), 25.9757576090673165963, TEST_TOL1, GSL_SUCCESS);
2238
TEST_SF(s, gsl_sf_transport_4_e, (1.0e+05, &r), 25.9757576090673165963, TEST_TOL2, GSL_SUCCESS);
2239
2240
TEST_SF(s, gsl_sf_transport_5_e, (1.0e-10, &r), 2.49999999999999999999e-41, TEST_TOL0, GSL_SUCCESS);
2241
TEST_SF(s, gsl_sf_transport_5_e, (1.0e-07, &r), 2.49999999999999861111e-29, TEST_TOL0, GSL_SUCCESS);
2242
TEST_SF(s, gsl_sf_transport_5_e, (1.0e-04, &r), 2.49999999861111111163e-17, TEST_TOL0, GSL_SUCCESS);
2243
TEST_SF(s, gsl_sf_transport_5_e, (0.1, &r), 0.000024986116317791487410, TEST_TOL0, GSL_SUCCESS);
2244
TEST_SF(s, gsl_sf_transport_5_e, (1.0, &r), 0.236615879239094789259153, TEST_TOL0, GSL_SUCCESS);
2245
TEST_SF(s, gsl_sf_transport_5_e, (3.0, &r), 12.77055769104415951115760, TEST_TOL0, GSL_SUCCESS);
2246
TEST_SF(s, gsl_sf_transport_5_e, (5.0, &r), 50.26309221817518778543615, TEST_TOL0, GSL_SUCCESS);
2247
TEST_SF(s, gsl_sf_transport_5_e, (10.0, &r), 116.3807454024207107698556, TEST_TOL0, GSL_SUCCESS);
2248
TEST_SF(s, gsl_sf_transport_5_e, (30.0, &r), 124.4313279083858954839911, TEST_TOL0, GSL_SUCCESS);
2249
TEST_SF(s, gsl_sf_transport_5_e, (100.0, &r), 124.4313306172043911597639, TEST_TOL0, GSL_SUCCESS);
2250
TEST_SF(s, gsl_sf_transport_5_e, (1.0e+05, &r), 124.43133061720439115976, TEST_TOL0, GSL_SUCCESS);
2251
2252
return s;
2253
}
2254
2255
2256
int test_trig(void)
2257
{
2258
gsl_sf_result r;
2259
gsl_sf_result r1, r2;
2260
double theta;
2261
int s = 0;
2262
int sa;
2263
2264
TEST_SF(s, gsl_sf_sin_e, (-10.0, &r), 0.5440211108893698134, TEST_TOL0, GSL_SUCCESS);
2265
TEST_SF(s, gsl_sf_sin_e, (1.0, &r), 0.8414709848078965067, TEST_TOL0, GSL_SUCCESS);
2266
TEST_SF(s, gsl_sf_sin_e, (1000.0, &r), 0.8268795405320025603, TEST_TOL0, GSL_SUCCESS);
2267
TEST_SF(s, gsl_sf_sin_e, (1048576.75, &r), 0.8851545351115651914, TEST_TOL1, GSL_SUCCESS);
2268
TEST_SF(s, gsl_sf_sin_e, (62831853.75, &r), 0.6273955953485000827, TEST_TOL3, GSL_SUCCESS);
2269
TEST_SF(s, gsl_sf_sin_e, (1073741822.5, &r), -0.8284043541754465988, TEST_SQRT_TOL0, GSL_SUCCESS);
2270
TEST_SF(s, gsl_sf_sin_e, (1073741824.0, &r), -0.6173264150460421708, TEST_SQRT_TOL0, GSL_SUCCESS);
2271
TEST_SF(s, gsl_sf_sin_e, (1073741825.5, &r), 0.7410684679436226926, TEST_SQRT_TOL0, GSL_SUCCESS);
2272
/*
2273
TEST_SF(s, gsl_sf_sin_e, (1099511627776.0, &r), -0.4057050115328287198, 32.0*TEST_SQRT_TOL0, GSL_SUCCESS);
2274
*/
2275
2276
TEST_SF(s, gsl_sf_cos_e, (-10.0, &r), -0.8390715290764524523, TEST_TOL0, GSL_SUCCESS);
2277
TEST_SF(s, gsl_sf_cos_e, (1.0, &r), 0.5403023058681397174, TEST_TOL0, GSL_SUCCESS);
2278
TEST_SF(s, gsl_sf_cos_e, (1000.0, &r), 0.5623790762907029911, TEST_TOL1, GSL_SUCCESS);
2279
TEST_SF(s, gsl_sf_cos_e, (1048576.75, &r), 0.4652971620066351799, TEST_TOL2, GSL_SUCCESS);
2280
TEST_SF(s, gsl_sf_cos_e, (62831853.75, &r), 0.7787006914966116436, TEST_TOL2, GSL_SUCCESS);
2281
TEST_SF(s, gsl_sf_cos_e, (1073741822.5, &r), -0.5601305436977716102, TEST_SQRT_TOL0, GSL_SUCCESS);
2282
TEST_SF(s, gsl_sf_cos_e, (1073741824.0, &r), 0.7867071229411881196, TEST_SQRT_TOL0, GSL_SUCCESS);
2283
/*
2284
TEST_SF(s, gsl_sf_cos_e, (1099511627776.0, &r), -0.9140040719915570023, 128.0*TEST_SQRT_TOL0, GSL_SUCCESS);
2285
*/
2286
2287
TEST_SF(s, gsl_sf_sinc_e, (1.0/1024.0, &r), 0.9999984312693665404, TEST_TOL0, GSL_SUCCESS);
2288
TEST_SF(s, gsl_sf_sinc_e, (1.0/2.0, &r), 2.0/M_PI, TEST_TOL0, GSL_SUCCESS);
2289
TEST_SF(s, gsl_sf_sinc_e, (80.5, &r), 0.0039541600768172754, TEST_TOL0, GSL_SUCCESS);
2290
TEST_SF(s, gsl_sf_sinc_e, (100.5, &r), 0.0031672625490924445, TEST_TOL0, GSL_SUCCESS);
2291
TEST_SF(s, gsl_sf_sinc_e, (1.0e+06 + 0.5, &r), 3.18309727028927157e-07, TEST_TOL0, GSL_SUCCESS);
2292
2293
/*
2294
TEST_SF(s, gsl_sf_sin_pi_x_e, (1000.5, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
2295
TEST_SF(s, gsl_sf_sin_pi_x_e, (10000.0 + 1.0/65536.0, &r), 0.00004793689960306688455, TEST_TOL0, GSL_SUCCESS);
2296
TEST_SF(s, gsl_sf_sin_pi_x_e, (1099511627776.0 + 1 + 0.125, &r), -0.3826834323650897717, TEST_TOL0, GSL_SUCCESS);
2297
*/
2298
2299
TEST_SF_2(s, gsl_sf_complex_sin_e, (1.0, 5.0, &r1, &r2),
2300
62.44551846769653403, TEST_TOL0,
2301
40.09216577799840254, TEST_TOL0,
2302
GSL_SUCCESS);
2303
2304
TEST_SF_2(s, gsl_sf_complex_cos_e, (1.0, 5.0, &r1, &r2),
2305
40.09580630629882573, TEST_TOL0,
2306
-62.43984868079963017, TEST_TOL0,
2307
GSL_SUCCESS);
2308
2309
TEST_SF_2(s, gsl_sf_complex_logsin_e, (1.0, 100.0, &r1, &r2),
2310
99.3068528194400546900, TEST_TOL0,
2311
0.5707963267948966192, TEST_TOL0,
2312
GSL_SUCCESS);
2313
2314
TEST_SF_2(s, gsl_sf_complex_logsin_e, (1.0, -100.0, &r1, &r2),
2315
99.3068528194400546900, TEST_TOL1,
2316
-0.5707963267948966192, TEST_TOL1,
2317
GSL_SUCCESS);
2318
2319
TEST_SF_2(s, gsl_sf_complex_logsin_e, (5.0, 5.0, &r1, &r2),
2320
4.3068909128079757420, TEST_TOL0,
2321
2.8540063315538773952, TEST_TOL0,
2322
GSL_SUCCESS);
2323
2324
TEST_SF(s, gsl_sf_lnsinh_e, (0.1, &r), -2.3009189815304652235, TEST_TOL0, GSL_SUCCESS);
2325
TEST_SF(s, gsl_sf_lnsinh_e, (1.0, &r), 0.16143936157119563361, TEST_TOL0, GSL_SUCCESS);
2326
TEST_SF(s, gsl_sf_lnsinh_e, (5.0, &r), 4.306807418479684201, TEST_TOL0, GSL_SUCCESS);
2327
TEST_SF(s, gsl_sf_lnsinh_e, (100.0, &r), 99.30685281944005469, TEST_TOL0, GSL_SUCCESS);
2328
2329
TEST_SF(s, gsl_sf_lncosh_e, (0.125, &r), 0.007792239318898252791, TEST_TOL0, GSL_SUCCESS);
2330
TEST_SF(s, gsl_sf_lncosh_e, (1.0, &r), 0.4337808304830271870, TEST_TOL0, GSL_SUCCESS);
2331
TEST_SF(s, gsl_sf_lncosh_e, (5.0, &r), 4.306898218339271555, TEST_TOL0, GSL_SUCCESS);
2332
TEST_SF(s, gsl_sf_lncosh_e, (100.0, &r), 99.30685281944005469, TEST_TOL0, GSL_SUCCESS);
2333
2334
TEST_SF_2(s, gsl_sf_polar_to_rect, (10.0, M_PI/6.0, &r1, &r2),
2335
(10.0 * sqrt(3) / 2.0), TEST_TOL0,
2336
(10.0 * 0.5), TEST_TOL0,
2337
GSL_SUCCESS);
2338
2339
TEST_SF_2(s, gsl_sf_polar_to_rect, (10.0, -2.0/3.0*M_PI, &r1, &r2),
2340
(10.0 * (-0.5)), TEST_TOL1,
2341
(10.0 * (-sqrt(3.0)/2.0)), TEST_TOL1,
2342
GSL_SUCCESS);
2343
2344
/* In double precision M_PI = \pi - 1.2246467991473531772e-16,
2345
i.e. the nearest machine number is slightly below the exact value
2346
of \pi. The true value of \pi satisfies
2347
2348
M_PI < \pi < nextafter(M_PI,+Inf)
2349
2350
where nextafter(M_PI,+Inf) = M_PI + 2*DBL_EPSILON
2351
2352
This also means that 2*M_PI is less than \pi by 2.449e-16. The
2353
true value of 2\pi satisfies
2354
2355
2*M_PI < 2\pi < nextafter(2*M_PI,+Inf)
2356
2357
where nextafter(2*M_PI,+Inf) = 2*M_PI + 4*DBL_EPSILON
2358
2359
BJG 25/9/06
2360
*/
2361
2362
#define DELTA (1.2246467991473531772e-16)
2363
2364
TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (2.0*M_PI), 2*M_PI, TEST_TOL1);
2365
TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (-2.0*M_PI), 2*DELTA, TEST_TOL1);
2366
2367
TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (2.0*M_PI+4*GSL_DBL_EPSILON), 4*GSL_DBL_EPSILON-2*DELTA, TEST_TOL1);
2368
TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (-2.0*M_PI-4*GSL_DBL_EPSILON), 2*M_PI-4*GSL_DBL_EPSILON+2*DELTA, TEST_TOL1);
2369
2370
TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (4.0*M_PI+8*GSL_DBL_EPSILON), 8*GSL_DBL_EPSILON-4*DELTA, TEST_TOL1);
2371
TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (-4.0*M_PI-8*GSL_DBL_EPSILON), 2*M_PI-8*GSL_DBL_EPSILON+4*DELTA, TEST_TOL1);
2372
2373
TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (1e9), 0.5773954235013851694, TEST_TOL1);
2374
TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (1e12), 5.625560548042800009446, TEST_SNGL);
2375
2376
TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (-1e9), 5.7057898836782013075, TEST_TOL1);
2377
TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (-1e12), 0.6576247591367864674792517289, 100*TEST_SNGL);
2378
2379
#ifdef EXTENDED
2380
TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (1e15), 2.1096981170701125979, TEST_TOL1);
2381
TEST_SF_THETA(s, gsl_sf_angle_restrict_pos_e, (-1e15), 4.1734871901094738790, TEST_TOL1);
2382
#endif
2383
2384
TEST_SF(s, gsl_sf_angle_restrict_pos_err_e, (2.0*M_PI, &r), 2*M_PI, TEST_TOL1, GSL_SUCCESS);
2385
TEST_SF(s, gsl_sf_angle_restrict_pos_err_e, (-2.0*M_PI, &r), 2*DELTA, TEST_TOL1, GSL_SUCCESS);
2386
2387
TEST_SF(s, gsl_sf_angle_restrict_pos_err_e, (1e9, &r), 0.5773954235013851694, TEST_TOL1, GSL_SUCCESS);
2388
TEST_SF(s, gsl_sf_angle_restrict_pos_err_e, (1e12, &r), 5.625560548042800009446, TEST_SNGL, GSL_SUCCESS);
2389
2390
TEST_SF(s, gsl_sf_angle_restrict_pos_err_e, (-1e9, &r), 5.7057898836782013075, TEST_TOL1, GSL_SUCCESS);
2391
TEST_SF(s, gsl_sf_angle_restrict_pos_err_e, (-1e12, &r), 0.6576247591367864674792517289, 100*TEST_SNGL, GSL_SUCCESS);
2392
2393
TEST_SF (s, gsl_sf_angle_restrict_pos_err_e, (1e15, &r), GSL_NAN, TEST_TOL1, GSL_ELOSS);
2394
TEST_SF (s, gsl_sf_angle_restrict_pos_err_e, (-1e15, &r), GSL_NAN, TEST_TOL1, GSL_ELOSS);
2395
2396
TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (2.0*M_PI), -2*DELTA, TEST_TOL1);
2397
TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (-2.0*M_PI), 2*DELTA, TEST_TOL1);
2398
2399
TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (M_PI), M_PI, TEST_TOL1);
2400
TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (-M_PI), -M_PI, TEST_TOL1);
2401
2402
TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (M_PI+2*GSL_DBL_EPSILON), -M_PI+2*(GSL_DBL_EPSILON-DELTA), TEST_TOL1);
2403
TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (-M_PI-2*GSL_DBL_EPSILON), M_PI-2*(GSL_DBL_EPSILON-DELTA), TEST_TOL1);
2404
2405
TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (3*M_PI+6*GSL_DBL_EPSILON), -M_PI+6*GSL_DBL_EPSILON-4*DELTA, TEST_TOL1);
2406
TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (-3*M_PI-6*GSL_DBL_EPSILON), M_PI-6*GSL_DBL_EPSILON+4*DELTA, TEST_TOL1);
2407
2408
2409
TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (1e9), 0.5773954235013851694, TEST_TOL1);
2410
TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (1e12), -0.6576247591367864674792517289, 100*TEST_SNGL);
2411
2412
TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (-1e9), -0.5773954235013851694, TEST_TOL1);
2413
TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (-1e12), 0.6576247591367864674792517289, 100*TEST_SNGL);
2414
2415
#ifdef EXTENDED
2416
TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (1e15), 2.1096981170701125979, TEST_TOL1);
2417
TEST_SF_THETA(s, gsl_sf_angle_restrict_symm_e, (-1e15), -2.1096981170701125979, TEST_TOL1);
2418
#endif
2419
2420
TEST_SF (s, gsl_sf_angle_restrict_symm_err_e, (2.0*M_PI, &r), -2*DELTA, TEST_TOL1, GSL_SUCCESS);
2421
TEST_SF (s, gsl_sf_angle_restrict_symm_err_e, (-2.0*M_PI, &r), 2*DELTA, TEST_TOL1, GSL_SUCCESS);
2422
2423
2424
TEST_SF(s, gsl_sf_angle_restrict_symm_err_e, (1e9, &r), 0.5773954235013851694, TEST_TOL1, GSL_SUCCESS);
2425
TEST_SF(s, gsl_sf_angle_restrict_symm_err_e, (1e12, &r), -0.6576247591367864674792517289, 100*TEST_SNGL, GSL_SUCCESS);
2426
2427
TEST_SF(s, gsl_sf_angle_restrict_symm_err_e, (-1e9, &r), -0.5773954235013851694, TEST_TOL1, GSL_SUCCESS);
2428
TEST_SF(s, gsl_sf_angle_restrict_symm_err_e, (-1e12, &r), 0.6576247591367864674792517289, 100*TEST_SNGL, GSL_SUCCESS);
2429
2430
TEST_SF (s, gsl_sf_angle_restrict_symm_err_e, (1e15, &r), GSL_NAN, TEST_TOL1, GSL_ELOSS);
2431
TEST_SF (s, gsl_sf_angle_restrict_symm_err_e, (-1e15, &r), GSL_NAN, TEST_TOL1, GSL_ELOSS);
2432
2433
theta = 5.0*M_PI + 5*DELTA + M_PI/2.0;
2434
gsl_sf_angle_restrict_pos_e(&theta);
2435
sa = 0;
2436
sa += ( test_sf_frac_diff( theta, 3.0/2.0*M_PI ) > TEST_TOL0 );
2437
gsl_test(sa, " gsl_angle_restrict_pos_e: theta = 11/2 Pi");
2438
s += sa;
2439
2440
theta = -5.0*M_PI - 5*DELTA - M_PI/2.0;
2441
gsl_sf_angle_restrict_pos_e(&theta);
2442
sa = 0;
2443
sa += ( test_sf_frac_diff( theta, M_PI/2.0 ) > 2.0*TEST_TOL0 );
2444
gsl_test(sa, " gsl_angle_restrict_pos_e: theta = -11/2 Pi");
2445
s += sa;
2446
2447
theta = 50000.0 + 1.0/65536.0;
2448
gsl_sf_angle_restrict_pos_e(&theta);
2449
sa = 0;
2450
sa += ( test_sf_frac_diff( theta, 4.6945260308194656055 ) > TEST_TOL0 );
2451
gsl_test(sa, " gsl_angle_restrict_pos_e: theta = 50000.0 + 1.0/65536.0");
2452
s += sa;
2453
2454
theta = 5000000.0 + 1.0/65536.0;
2455
gsl_sf_angle_restrict_pos_e(&theta);
2456
sa = 0;
2457
sa += ( test_sf_frac_diff( theta, 4.49537973053997376 ) > TEST_TOL0 );
2458
gsl_test(sa, " gsl_angle_restrict_pos_e: theta = 5000000.0 + 1.0/65536.0");
2459
s += sa;
2460
2461
/*
2462
theta = 140737488355328.0;
2463
gsl_sf_angle_restrict_pos_e(&theta);
2464
sa = 0;
2465
sa += ( test_sf_frac_diff( theta, 3.20652300406795792638 ) > TEST_TOL0 );
2466
gsl_test(sa, " gsl_angle_restrict_pos_e: theta = 2^47");
2467
s += sa;
2468
*/
2469
2470
theta = 5.0*M_PI + (5.5*DELTA + M_PI/2.0);
2471
gsl_sf_angle_restrict_symm_e(&theta);
2472
sa = 0;
2473
sa += ( test_sf_frac_diff( theta, -M_PI/2.0 ) > 2.0*TEST_TOL0 );
2474
gsl_test(sa, " gsl_angle_restrict_symm_e: theta = 11/2 Pi");
2475
s += sa;
2476
2477
theta = -5.0*M_PI - (5.5*DELTA + M_PI/2.0);
2478
gsl_sf_angle_restrict_symm_e(&theta);
2479
sa = 0;
2480
sa += ( test_sf_frac_diff( theta, M_PI/2.0 ) > 2.0*TEST_TOL0 );
2481
gsl_test(sa, " gsl_angle_restrict_symm_e: theta = -11/2 Pi");
2482
s += sa;
2483
2484
theta = 5.0*M_PI + 5*DELTA - M_PI/2.0;
2485
gsl_sf_angle_restrict_symm_e(&theta);
2486
sa = 0;
2487
sa += ( test_sf_frac_diff( theta, M_PI/2.0 ) > TEST_TOL0 );
2488
gsl_test(sa, " gsl_angle_restrict_symm_e: theta = -9/2 Pi");
2489
s += sa;
2490
2491
theta = 3.0/2.0*M_PI + 3.0/2.0*DELTA;
2492
gsl_sf_angle_restrict_symm_e(&theta);
2493
sa = 0;
2494
sa += ( test_sf_frac_diff( theta, -M_PI/2.0 ) > TEST_TOL0 );
2495
gsl_test(sa, " gsl_angle_restrict_symm_e: theta = 3/2 Pi");
2496
s += sa;
2497
2498
theta = -3.0/2.0*M_PI;
2499
gsl_sf_angle_restrict_symm_e(&theta);
2500
sa = 0;
2501
sa += ( test_sf_frac_diff( theta, M_PI/2.0 ) > TEST_TOL0 );
2502
gsl_test(sa, " gsl_angle_restrict_symm_e: theta = -3/2 Pi");
2503
s += sa;
2504
2505
theta = 50000.0 + 1.0/65536.0;
2506
gsl_sf_angle_restrict_symm_e(&theta);
2507
sa = 0;
2508
sa += ( test_sf_frac_diff( theta, -1.5886592763601208714 ) > TEST_TOL0 );
2509
gsl_test(sa, " gsl_angle_restrict_symm_e: theta = 50000.0 + 1.0/65536.0");
2510
s += sa;
2511
2512
return s;
2513
}
2514
2515
2516
/* I computed the values of zeta for s = -1e-10, 0, 1e-10 using the
2517
Jensen formula,
2518
2519
zeta(s) = -1/2 + 1/(1-s)
2520
+ integ(sin(s arctan(t))/((1+t^2)^(s/2)(exp(2pi*t)-1)), t, 0, inf)
2521
2522
transforming the integral from a semi-infinite range to the range
2523
[0,pi/2] using the substitution t = tan(u). After Taylor expansion
2524
in s and numerical evaluation of the integrals this gave,
2525
2526
zeta(s) = 1/2 + 1/(1-s)
2527
+ (0.0810614667944862 +/- 2e-16) s
2528
+ (-3.17822795429232e-3 +/- 2e-17) s^2
2529
+ ....
2530
2531
for an expansion about s = 0 [BJG 7/01]
2532
*/
2533
2534
int test_zeta(void)
2535
{
2536
gsl_sf_result r;
2537
int s = 0;
2538
2539
TEST_SF(s, gsl_sf_zeta_int_e, (-61.0, &r), -3.30660898765775767257e+34, TEST_TOL0, GSL_SUCCESS);
2540
2541
TEST_SF(s, gsl_sf_zeta_int_e, (-8, &r), 0.0, TEST_TOL0, GSL_SUCCESS);
2542
TEST_SF(s, gsl_sf_zeta_int_e, (-6, &r), 0.0, TEST_TOL0, GSL_SUCCESS);
2543
TEST_SF(s, gsl_sf_zeta_int_e, (-5.0, &r), -0.003968253968253968253968, TEST_TOL0, GSL_SUCCESS);
2544
2545
TEST_SF(s, gsl_sf_zeta_int_e, (-4, &r), 0.0, TEST_TOL0, GSL_SUCCESS);
2546
TEST_SF(s, gsl_sf_zeta_int_e, (-3, &r), 1.0/120.0, TEST_TOL0, GSL_SUCCESS);
2547
TEST_SF(s, gsl_sf_zeta_int_e, (-2, &r), 0.0, TEST_TOL0, GSL_SUCCESS);
2548
TEST_SF(s, gsl_sf_zeta_int_e, (-1, &r), -1.0/12.0, TEST_TOL0, GSL_SUCCESS);
2549
2550
TEST_SF(s, gsl_sf_zeta_int_e, ( 5.0, &r), 1.0369277551433699263313655, TEST_TOL0, GSL_SUCCESS);
2551
TEST_SF(s, gsl_sf_zeta_int_e, (31.0, &r), 1.0000000004656629065033784, TEST_TOL0, GSL_SUCCESS);
2552
2553
TEST_SF(s, gsl_sf_zetam1_int_e, (-61.0, &r), -3.30660898765775767257e+34, TEST_TOL0, GSL_SUCCESS);
2554
TEST_SF(s, gsl_sf_zetam1_int_e, (-5.0, &r), -1.003968253968253968253968, TEST_TOL0, GSL_SUCCESS);
2555
2556
TEST_SF(s, gsl_sf_zetam1_int_e, (-8, &r), -1.0, TEST_TOL0, GSL_SUCCESS);
2557
TEST_SF(s, gsl_sf_zetam1_int_e, (-6, &r), -1.0, TEST_TOL0, GSL_SUCCESS);
2558
TEST_SF(s, gsl_sf_zetam1_int_e, (-4, &r), -1.0, TEST_TOL0, GSL_SUCCESS);
2559
TEST_SF(s, gsl_sf_zetam1_int_e, (-3, &r), -119.0/120.0, TEST_TOL0, GSL_SUCCESS);
2560
TEST_SF(s, gsl_sf_zetam1_int_e, (-2, &r), -1.0, TEST_TOL0, GSL_SUCCESS);
2561
TEST_SF(s, gsl_sf_zetam1_int_e, (-1, &r), -13.0/12.0, TEST_TOL0, GSL_SUCCESS);
2562
2563
TEST_SF(s, gsl_sf_zetam1_int_e, ( 5.0, &r), 0.0369277551433699263313655, TEST_TOL0, GSL_SUCCESS);
2564
TEST_SF(s, gsl_sf_zetam1_int_e, (31.0, &r), 0.0000000004656629065033784, TEST_TOL0, GSL_SUCCESS);
2565
2566
TEST_SF(s, gsl_sf_zeta_e, (-151, &r), 8.195215221831378294e+143, TEST_TOL2, GSL_SUCCESS);
2567
TEST_SF(s, gsl_sf_zeta_e, (-51, &r), 9.68995788746359406565e+24, TEST_TOL1, GSL_SUCCESS);
2568
TEST_SF(s, gsl_sf_zeta_e, (-5, &r), -0.003968253968253968253968, TEST_TOL1, GSL_SUCCESS);
2569
2570
TEST_SF(s, gsl_sf_zeta_e, (-8, &r), 0.0, TEST_TOL1, GSL_SUCCESS);
2571
TEST_SF(s, gsl_sf_zeta_e, (-6, &r), 0.0, TEST_TOL1, GSL_SUCCESS);
2572
TEST_SF(s, gsl_sf_zeta_e, (-4, &r), 0.0, TEST_TOL1, GSL_SUCCESS);
2573
TEST_SF(s, gsl_sf_zeta_e, (-3, &r), 1.0/120.0, TEST_TOL1, GSL_SUCCESS);
2574
TEST_SF(s, gsl_sf_zeta_e, (-2, &r), 0.0, TEST_TOL1, GSL_SUCCESS);
2575
TEST_SF(s, gsl_sf_zeta_e, (-1, &r), -1.0/12.0, TEST_TOL1, GSL_SUCCESS);
2576
2577
TEST_SF(s, gsl_sf_zeta_e, (-0.5, &r), -0.207886224977354566017307, TEST_TOL1, GSL_SUCCESS);
2578
2579
TEST_SF(s, gsl_sf_zeta_e, (-1e-10, &r), -0.49999999990810614668948, TEST_TOL1, GSL_SUCCESS);
2580
TEST_SF(s, gsl_sf_zeta_e, (0.0, &r), -0.5, TEST_TOL0, GSL_SUCCESS);
2581
TEST_SF(s, gsl_sf_zeta_e, (1e-10, &r), -0.50000000009189385333058, TEST_TOL0, GSL_SUCCESS);
2582
2583
TEST_SF(s, gsl_sf_zeta_e, (0.5, &r), -1.460354508809586812889499, TEST_TOL0, GSL_SUCCESS);
2584
TEST_SF(s, gsl_sf_zeta_e, (1.0-1.0/1024.0, &r), -1023.4228554489429787, TEST_TOL0, GSL_SUCCESS);
2585
TEST_SF(s, gsl_sf_zeta_e, (1.0+1.0/1048576, &r), 1.0485765772157343441e+06, TEST_TOL0, GSL_SUCCESS);
2586
TEST_SF(s, gsl_sf_zeta_e, (5.0, &r), 1.036927755143369926331365, TEST_TOL0, GSL_SUCCESS);
2587
TEST_SF(s, gsl_sf_zeta_e, (25.5, &r), 1.000000021074106110269959, TEST_TOL0, GSL_SUCCESS);
2588
2589
TEST_SF(s, gsl_sf_zetam1_e, (-8, &r), -1.0, TEST_TOL1, GSL_SUCCESS);
2590
TEST_SF(s, gsl_sf_zetam1_e, (-6, &r), -1.0, TEST_TOL1, GSL_SUCCESS);
2591
TEST_SF(s, gsl_sf_zetam1_e, (-4, &r), -1.0, TEST_TOL1, GSL_SUCCESS);
2592
TEST_SF(s, gsl_sf_zetam1_e, (-3, &r), -119.0/120.0, TEST_TOL1, GSL_SUCCESS);
2593
TEST_SF(s, gsl_sf_zetam1_e, (-2, &r), -1.0, TEST_TOL1, GSL_SUCCESS);
2594
TEST_SF(s, gsl_sf_zetam1_e, (-1, &r), -13.0/12.0, TEST_TOL1, GSL_SUCCESS);
2595
TEST_SF(s, gsl_sf_zetam1_e, (-0.5, &r), -1.207886224977354566017307, TEST_TOL1, GSL_SUCCESS);
2596
TEST_SF(s, gsl_sf_zetam1_e, (-1e-10, &r), -1.49999999990810614668948, TEST_TOL1, GSL_SUCCESS);
2597
TEST_SF(s, gsl_sf_zetam1_e, (0.0, &r), -1.5, TEST_TOL0, GSL_SUCCESS);
2598
TEST_SF(s, gsl_sf_zetam1_e, (1e-10, &r), -1.50000000009189385333058, TEST_TOL0, GSL_SUCCESS);
2599
2600
TEST_SF(s, gsl_sf_zetam1_e, (0.5, &r), -2.460354508809586812889499, TEST_TOL0, GSL_SUCCESS);
2601
TEST_SF(s, gsl_sf_zetam1_e, (2.0, &r), 0.64493406684822643647, TEST_TOL1, GSL_SUCCESS);
2602
TEST_SF(s, gsl_sf_zetam1_e, (3.0, &r), 0.20205690315959428540, TEST_TOL1, GSL_SUCCESS);
2603
TEST_SF(s, gsl_sf_zetam1_e, (5.0, &r), 0.0369277551433699263314, TEST_TOL1, GSL_SUCCESS);
2604
TEST_SF(s, gsl_sf_zetam1_e, (9.5, &r), 0.0014125906121736622712, TEST_TOL1, GSL_SUCCESS);
2605
TEST_SF(s, gsl_sf_zetam1_e, (10.5, &r), 0.000700842641736155219500, TEST_TOL1, GSL_SUCCESS);
2606
TEST_SF(s, gsl_sf_zetam1_e, (12.5, &r), 0.000173751733643178193390, TEST_TOL1, GSL_SUCCESS);
2607
TEST_SF(s, gsl_sf_zetam1_e, (13.5, &r), 0.000086686727462338155188, TEST_TOL1, GSL_SUCCESS);
2608
TEST_SF(s, gsl_sf_zetam1_e, (15.5, &r), 0.000021619904246069108133, TEST_TOL1, GSL_SUCCESS);
2609
TEST_SF(s, gsl_sf_zetam1_e, (16.5, &r), 0.000010803124900178547671, TEST_TOL0, GSL_SUCCESS);
2610
TEST_SF(s, gsl_sf_zetam1_e, (25.5, &r), 0.000000021074106110269959, TEST_TOL0, GSL_SUCCESS);
2611
2612
TEST_SF(s, gsl_sf_hzeta_e, (2, 1.0, &r), 1.6449340668482264365, TEST_TOL0, GSL_SUCCESS);
2613
TEST_SF(s, gsl_sf_hzeta_e, (2, 10.0, &r), 0.1051663356816857461, TEST_TOL0, GSL_SUCCESS);
2614
TEST_SF(s, gsl_sf_hzeta_e, (5, 1.0, &r), 1.0369277551433699263, TEST_TOL0, GSL_SUCCESS);
2615
TEST_SF(s, gsl_sf_hzeta_e, (5, 10.0, &r), 0.000030413798676470276, TEST_TOL0, GSL_SUCCESS);
2616
TEST_SF(s, gsl_sf_hzeta_e, (9, 0.1, &r), 1.0000000004253980e+09, TEST_TOL0, GSL_SUCCESS);
2617
TEST_SF(s, gsl_sf_hzeta_e, (30, 0.5, &r), 1.0737418240000053e+09, TEST_TOL0, GSL_SUCCESS);
2618
TEST_SF(s, gsl_sf_hzeta_e, (30, 0.9, &r), 2.3589824880264765e+01, TEST_TOL1, GSL_SUCCESS);
2619
TEST_SF(s, gsl_sf_hzeta_e, (75, 0.25, &r), 1.4272476927059599e+45, TEST_TOL1, GSL_SUCCESS);
2620
2621
TEST_SF(s, gsl_sf_eta_int_e, (-91, &r), -4.945598888750002040e+94, TEST_TOL0, GSL_SUCCESS);
2622
TEST_SF(s, gsl_sf_eta_int_e, (-51, &r), -4.363969073121683116e+40, TEST_TOL0, GSL_SUCCESS);
2623
TEST_SF(s, gsl_sf_eta_int_e, (-5, &r), 0.25, TEST_TOL0, GSL_SUCCESS);
2624
TEST_SF(s, gsl_sf_eta_int_e, (-1, &r), 0.25, TEST_TOL0, GSL_SUCCESS);
2625
TEST_SF(s, gsl_sf_eta_int_e, ( 0, &r), 0.5, TEST_TOL0, GSL_SUCCESS);
2626
TEST_SF(s, gsl_sf_eta_int_e, ( 5, &r), 0.9721197704469093059, TEST_TOL0, GSL_SUCCESS);
2627
TEST_SF(s, gsl_sf_eta_int_e, ( 6, &r), 0.9855510912974351041, TEST_TOL0, GSL_SUCCESS);
2628
TEST_SF(s, gsl_sf_eta_int_e, ( 20, &r), 0.9999990466115815221, TEST_TOL0, GSL_SUCCESS);
2629
TEST_SF(s, gsl_sf_eta_int_e, ( 1000, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
2630
2631
TEST_SF(s, gsl_sf_eta_e, (-51.5, &r), -1.2524184036924703656e+41, TEST_TOL2, GSL_SUCCESS);
2632
TEST_SF(s, gsl_sf_eta_e, (-5, &r), 0.25, TEST_TOL0, GSL_SUCCESS);
2633
TEST_SF(s, gsl_sf_eta_e, (0.5, &r), 0.6048986434216303702, TEST_TOL0, GSL_SUCCESS);
2634
TEST_SF(s, gsl_sf_eta_e, (0.999, &r), 0.6929872789683383574, TEST_TOL0, GSL_SUCCESS);
2635
TEST_SF(s, gsl_sf_eta_e, (1.0, &r), 0.6931471805599453094, TEST_TOL0, GSL_SUCCESS);
2636
TEST_SF(s, gsl_sf_eta_e, (1.0+1.0e-10, &r), 0.6931471805759321998, TEST_TOL0, GSL_SUCCESS);
2637
TEST_SF(s, gsl_sf_eta_e, ( 5, &r), 0.9721197704469093059, TEST_TOL0, GSL_SUCCESS);
2638
TEST_SF(s, gsl_sf_eta_e, ( 5.2, &r), 0.9755278712546684682, TEST_TOL0, GSL_SUCCESS);
2639
TEST_SF(s, gsl_sf_eta_e, ( 6, &r), 0.9855510912974351041, TEST_TOL0, GSL_SUCCESS);
2640
TEST_SF(s, gsl_sf_eta_e, ( 20, &r), 0.9999990466115815221, TEST_TOL0, GSL_SUCCESS);
2641
2642
return s;
2643
}
2644
2645
int test_results(void)
2646
{
2647
int s = 0;
2648
2649
gsl_sf_result_e10 re;
2650
gsl_sf_result r;
2651
2652
re.val = -1.0;
2653
re.err = 0.5;
2654
re.e10 = 0;
2655
gsl_sf_result_smash_e(&re, &r);
2656
s += ( test_sf_frac_diff(r.val, -1.0) > TEST_TOL0 );
2657
s += ( test_sf_frac_diff(r.err, 0.5) > TEST_TOL0 );
2658
2659
re.val = -1.0;
2660
re.err = 0.5;
2661
re.e10 = 10;
2662
gsl_sf_result_smash_e(&re, &r);
2663
s += ( test_sf_frac_diff(r.val, -1.0e+10) > TEST_TOL1 );
2664
s += ( test_sf_frac_diff(r.err, 0.5e+10) > TEST_TOL1 );
2665
2666
re.val = 1.0;
2667
re.err = 0.5;
2668
re.e10 = 10000;
2669
s += ( gsl_sf_result_smash_e(&re, &r) != GSL_EOVRFLW );
2670
2671
re.val = 1.0;
2672
re.err = 0.5;
2673
re.e10 = -10000;
2674
s += ( gsl_sf_result_smash_e(&re, &r) != GSL_EUNDRFLW );
2675
2676
return s;
2677
}
2678
2679
2680
int main(int argc, char * argv[])
2681
{
2682
gsl_ieee_env_setup ();
2683
gsl_set_error_handler_off ();
2684
2685
gsl_test(test_airy(), "Airy Functions");
2686
gsl_test(test_bessel(), "Bessel Functions");
2687
gsl_test(test_clausen(), "Clausen Integral");
2688
gsl_test(test_coulomb(), "Coulomb Wave Functions");
2689
gsl_test(test_coupling(), "Coupling Coefficients");
2690
gsl_test(test_dawson(), "Dawson Integral");
2691
gsl_test(test_debye(), "Debye Functions");
2692
gsl_test(test_dilog(), "Dilogarithm");
2693
gsl_test(test_elementary(), "Elementary Functions (Misc)");
2694
gsl_test(test_ellint(), "Elliptic Integrals");
2695
gsl_test(test_jac(), "Elliptic Functions (Jacobi)");
2696
gsl_test(test_erf(), "Error Functions");
2697
gsl_test(test_exp(), "Exponential Functions");
2698
gsl_test(test_expint(), "Exponential/Sine/Cosine Integrals");
2699
gsl_test(test_fermidirac(), "Fermi-Dirac Functions");
2700
gsl_test(test_gamma(), "Gamma Functions");
2701
gsl_test(test_gegen(), "Gegenbauer Polynomials");
2702
gsl_test(test_hyperg(), "Hypergeometric Functions");
2703
gsl_test(test_laguerre(), "Laguerre Polynomials");
2704
gsl_test(test_lambert(), "Lambert W Functions");
2705
gsl_test(test_legendre(), "Legendre Functions");
2706
gsl_test(test_log(), "Logarithm");
2707
gsl_test(test_mathieu(), "Mathieu Functions");
2708
gsl_test(test_pow_int(), "Integer Powers");
2709
gsl_test(test_psi(), "Psi Functions");
2710
gsl_test(test_psi_complex(), "Psi Function for complex argument");
2711
gsl_test(test_synch(), "Synchrotron Functions");
2712
gsl_test(test_transport(), "Transport Functions");
2713
gsl_test(test_trig(), "Trigonometric and Related Functions");
2714
gsl_test(test_zeta(), "Zeta Functions");
2715
2716
gsl_test(test_results(), "Result Methods");
2717
2718
exit (gsl_test_summary());
2719
}
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Version: 2.0.1