1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
|
/* $OpenBSD: monotl.c,v 1.2 2011/07/08 16:49:05 martynas Exp $ */
/*
* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
*
* Permission to use, copy, modify, and distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*/
/* monotl.c
Floating point function test vectors.
Arguments and function values are synthesized for NPTS points in
the vicinity of each given tabulated test point. The points are
chosen to be near and on either side of the likely function algorithm
domain boundaries. Since the function programs change their methods
at these points, major coding errors or monotonicity failures might be
detected.
August, 1998
S. L. Moshier */
#include <float.h>
#if LDBL_MANT_DIG == 64
/* Unit of error tolerance in test[i].thresh. */
static long double MACHEPL =
5.42101086242752217003726400434970855712890625E-20L;
/* How many times the above error to allow before printing a complaint.
If TOL < 0, consider absolute error instead of relative error. */
#define TOL 8
/* Number of test points to generate on each side of tabulated point. */
#define NPTS 100
#include <stdio.h>
/* Avoid including math.h. */
long double frexpl (long double, int *);
long double ldexpl (long double, int);
/* Functions of one variable. */
long double expl (long double);
long double logl (long double);
long double sinl (long double);
long double cosl (long double);
long double tanl (long double);
long double atanl (long double);
long double asinl (long double);
long double acosl (long double);
long double sinhl (long double);
long double coshl (long double);
long double tanhl (long double);
long double asinhl (long double);
long double acoshl (long double);
long double atanhl (long double);
long double lgammal (long double);
long double tgammal (long double);
long double fabsl (long double);
long double floorl (long double);
long double j0l (long double);
long double y0l (long double);
long double j1l (long double);
long double y1l (long double);
/* Data structure of the test. */
struct oneargument
{
char *name; /* Name of the function. */
long double (*func) (long double); /* Function call. */
long double arg1; /* Function argument, assumed exact. */
long double answer1; /* Exact number, close to function value. */
long double answer2; /* answer1 + answer2 has extended precision. */
long double derivative; /* dy/dx evaluated at x = arg1. */
/* Error report threshold. 2 => 1 ulp approximately
if thresh < 0 then consider absolute error instead of relative error. */
int thresh;
};
static struct oneargument test1[] =
{
{"exp", expl, 1.0L, 2.7182769775390625L,
4.85091998273536028747e-6L, 2.71828182845904523536L, TOL},
{"exp", expl, -1.0L, 3.678741455078125e-1L,
5.29566362982159552377e-6L, 3.678794411714423215955e-1L, TOL},
{"exp", expl, 0.5L, 1.648712158203125L,
9.1124970031468486507878e-6L, 1.64872127070012814684865L, TOL},
{"exp", expl, -0.5L, 6.065216064453125e-1L,
9.0532673209236037995e-6L, 6.0653065971263342360e-1L, TOL},
{"exp", expl, 2.0L, 7.3890533447265625L,
2.75420408772723042746e-6L, 7.38905609893065022723L, TOL},
{"exp", expl, -2.0L, 1.353302001953125e-1L,
5.08304130019189399949e-6L, 1.3533528323661269189e-1L, TOL},
{"log", logl, 1.41421356237309492343L, 3.465728759765625e-1L,
7.1430341006605745676897e-7L, 7.0710678118654758708668e-1L, TOL},
{"log", logl, 7.07106781186547461715e-1L, -3.46588134765625e-1L,
1.45444856522566402246e-5L, 1.41421356237309517417L, TOL},
{"sin", sinl, 7.85398163397448278999e-1L, 7.0709228515625e-1L,
1.4496030297502751942956e-5L, 7.071067811865475460497e-1L, TOL},
{"sin", sinl, -7.85398163397448501044e-1L, -7.071075439453125e-1L,
7.62758764840238811175e-7L, 7.07106781186547389040e-1L, TOL},
{"sin", sinl, 1.570796326794896558L, 9.999847412109375e-1L,
1.52587890625e-5L, 6.12323399573676588613e-17L, TOL},
{"sin", sinl, -1.57079632679489678004L, -1.0L,
1.29302922820150306903e-32L, -1.60812264967663649223e-16L, TOL},
{"sin", sinl, 4.712388980384689674L, -1.0L,
1.68722975549458979398e-32L, -1.83697019872102976584e-16L, TOL},
{"sin", sinl, -4.71238898038468989604L, 9.999847412109375e-1L,
1.52587890625e-5L, 3.83475850529283315008e-17L, TOL},
{"cos", cosl, 3.92699081698724139500E-1L, 9.23873901367187500000E-1L,
5.63114409926198633370E-6L, -3.82683432365089757586E-1L, TOL},
{"cos", cosl, 7.85398163397448278999E-1L, 7.07092285156250000000E-1L,
1.44960302975460497458E-5L, -7.07106781186547502752E-1L, TOL},
{"cos", cosl, 1.17809724509617241850E0L, 3.82675170898437500000E-1L,
8.26146665231415693919E-6L, -9.23879532511286738554E-1L, TOL},
{"cos", cosl, 1.96349540849362069750E0L, -3.82690429687500000000E-1L,
6.99732241029898567203E-6L, -9.23879532511286785419E-1L, TOL},
{"cos", cosl, 2.35619449019234483700E0L, -7.07107543945312500000E-1L,
7.62758765040545859856E-7L, -7.07106781186547589348E-1L, TOL},
{"cos", cosl, 2.74889357189106897650E0L, -9.23889160156250000000E-1L,
9.62764496328487887036E-6L, -3.82683432365089870728E-1L, TOL},
{"cos", cosl, 3.14159265358979311600E0L, -1.00000000000000000000E0L,
7.49879891330928797323E-33L, -1.22464679914735317723E-16L, TOL},
{"tan", tanl, 7.85398163397448278999E-1L, 9.999847412109375e-1L,
1.52587890624387676600E-5L, 1.99999999999999987754E0L, TOL},
{"tan", tanl, 1.17809724509617241850E0L, 2.41419982910156250000E0L,
1.37332715322352112604E-5L, 6.82842712474618858345E0L, TOL},
{"tan", tanl, 1.96349540849362069750E0L, -2.41421508789062500000E0L,
1.52551752942854759743E-6L, 6.82842712474619262118E0L, TOL},
{"tan", tanl, 2.35619449019234483700E0L, -1.00001525878906250000E0L,
1.52587890623163029801E-5L, 2.00000000000000036739E0L, TOL},
{"tan", tanl, 2.74889357189106897650E0L, -4.14215087890625000000E-1L,
1.52551752982565655126E-6L, 1.17157287525381000640E0L, TOL},
{"atan", atanl, 4.14213562373094923430E-1L, 3.92684936523437500000E-1L,
1.41451752865477964149E-5L, 8.53553390593273837869E-1L, TOL},
{"atan", atanl, 1.0L, 7.85385131835937500000E-1L,
1.30315615108096156608E-5L, 0.5L, TOL},
{"atan", atanl, 2.41421356237309492343E0L, 1.17808532714843750000E0L,
1.19179477349460632350E-5L, 1.46446609406726250782E-1L, TOL},
{"atan", atanl, -2.41421356237309514547E0L, -1.17810058593750000000E0L,
3.34084132752141908545E-6L, 1.46446609406726227789E-1L, TOL},
{"atan", atanl, -1.0L, -7.85400390625000000000E-1L,
2.22722755169038433915E-6L, 0.5L, TOL},
{"atan", atanl, -4.14213562373095145475E-1L, -3.92700195312500000000E-1L,
1.11361377576267665972E-6L, 8.53553390593273703853E-1L, TOL},
{"asin", asinl, 3.82683432365089615246E-1L, 3.92684936523437500000E-1L,
1.41451752864854321970E-5L, 1.08239220029239389286E0L, TOL},
{"asin", asinl, 0.5L, 5.23590087890625000000E-1L,
8.68770767387307710723E-6L, 1.15470053837925152902E0L, TOL},
{"asin", asinl, 7.07106781186547461715E-1L, 7.85385131835937500000E-1L,
1.30315615107209645016E-5L, 1.41421356237309492343E0L, TOL},
{"asin", asinl, 9.23879532511286738483E-1L, 1.17808532714843750000E0L,
1.19179477349183147612E-5L, 2.61312592975275276483E0L, TOL},
{"asin", asinl, -0.5L, -5.23605346679687500000E-1L,
6.57108138862692289277E-6L, 1.15470053837925152902E0L, TOL},
{"asin", asinl, 1.16415321826934814453125e-10L,
1.16415321826934814453125e-10L, 2.629536350736706018055e-31L,
1.0000000000000000000067762L, TOL},
{"asin", asinl, 1.0000000000000000000183779E-10L,
9.9999999979890480394928431E-11L, 2.0109519607076028264987890E-20L,
1.0L, TOL},
{"asin", asinl, 1.0000000000000000000007074E-8L,
9.9999999999948220585910263E-9L, 5.1781080827147808155022014E-21L,
1.0L, TOL},
{"asin", asinl, 0.97499847412109375L, 1.346710205078125L,
3.969526822009922560999e-6L, 4.500216008585875735254L, TOL},
{"acos", acosl, 1.95090322016128192573E-1L, 1.37443542480468750000E0L,
1.13611408471185777914E-5L, -1.01959115820831832232E0L, TOL},
{"acos", acosl, 3.82683432365089615246E-1L, 1.17808532714843750000E0L,
1.19179477351337991247E-5L, -1.08239220029239389286E0L, TOL},
{"acos", acosl, 0.5L, 1.04719543457031250000E0L,
2.11662628524615421446E-6L, -1.15470053837925152902E0L, TOL},
{"acos", acosl, 7.07106781186547461715E-1L, 7.85385131835937500000E-1L,
1.30315615108982668201E-5L, -1.41421356237309492343E0L, TOL},
{"acos", acosl, 9.23879532511286738483E-1L, 3.92684936523437500000E-1L,
1.41451752867009165605E-5L, -2.61312592975275276483E0L, TOL},
{"acos", acosl, 9.80785280403230430579E-1L, 1.96334838867187500000E-1L,
1.47019821746724723933E-5L, -5.12583089548300990774E0L, TOL},
{"acos", acosl, -0.5L, 2.09439086914062500000E0L,
4.23325257049230842892E-6L, -1.15470053837925152902E0L, TOL},
{"sinh", sinhl, 1.0L, 1.17518615722656250000E0L,
1.50364172389568823819E-5L, 1.54308063481524377848E0L, TOL},
{"sinh", sinhl, 7.09089565712818057364E2L, 4.49423283712885057274E307L,
1.70878916528708958045E289L, 4.49423283712885057274E307L, TOL},
{"sinh", sinhl, 2.22044604925031308085E-16L, 0.00000000000000000000E0L,
2.22044604925031308085E-16L, 1.00000000000000000000E0L, TOL},
{"sinh", sinhl, 3.7252902984619140625e-9L, 3.7252902984619140625e-9L,
8.616464714094038285889380656847999229E-27L,
1.00000000000000000693889L, TOL},
{"sinh", sinhl, 2.3283064365386962890625e-10L, 2.3283064365386962890625e-10L,
2.103629080589364814436978072135626630E-30,
1.000000000000000000027105L, TOL},
{"cosh", coshl, 7.09089565712818057364E2L, 4.49423283712885057274E307L,
1.70878916528708958045E289L, 4.49423283712885057274E307L, TOL},
{"cosh", coshl, 1.0L, 1.54307556152343750000E0L,
5.07329180627847790562E-6L, 1.17520119364380145688E0L, TOL},
{"cosh", coshl, 0.5L, 1.12762451171875000000E0L,
1.45348763078522622516E-6L, 5.21095305493747361622E-1L, TOL},
{"tanh", tanhl, 0.5L, 4.62112426757812500000E-1L,
4.73050219725850231848E-6L, 7.86447732965927410150E-1L, TOL},
{"tanh", tanhl, 5.49306144334054780032E-1L, 4.99984741210937500000E-1L,
1.52587890624507506378E-5L, 7.50000000000000049249E-1L, TOL},
{"tanh", tanhl, 0.625L, 5.54595947265625000000E-1L,
3.77508375729399903910E-6L, 6.92419147969988069631E-1L, TOL},
{"asinh", asinhl, 0.5L, 4.81201171875000000000E-1L,
1.06531846034474977589E-5L, 8.94427190999915878564E-1L, TOL},
{"asinh", asinhl, 1.0L, 8.81362915039062500000E-1L,
1.06719804805252326093E-5L, 7.07106781186547524401E-1L, TOL},
{"asinh", asinhl, 2.0L, 1.44363403320312500000E0L,
1.44197568534249327674E-6L, 4.47213595499957939282E-1L, TOL},
{"acosh", acoshl, 2.0L, 1.31695556640625000000E0L,
2.33051856670862504635E-6L, 5.77350269189625764509E-1L, TOL},
{"acosh", acoshl, 1.5L, 9.62417602539062500000E-1L,
6.04758014439499551783E-6L, 8.94427190999915878564E-1L, TOL},
{"acosh", acoshl, 1.03125L, 2.49343872070312500000E-1L,
9.62177257298785143908E-6L, 3.96911150685467059809E0L, TOL},
{"atanh", atanhl, 0.5L, 5.49301147460937500000E-1L,
4.99687311734569762262E-6L, 1.33333333333333333333E0L, TOL},
#if 0
{"j0", j0l, 8.0L, 1.71646118164062500000E-1L,
4.68897349140609086941E-6L, -2.34636346853914624381E-1, -4},
{"j0", j0l, 4.54541015625L, -3.09783935546875000000E-1L,
7.07472668157686463367E-6L, 2.42993657373627558460E-1L, -4},
{"j0", j0l, 2.85711669921875L, -2.07901000976562500000E-1L,
1.15237285263902751582E-5L, -3.90402225324501311651E-1L, -4},
{"j0", j0l, 2.0L, 2.23876953125000000000E-1L,
1.38260162356680518275E-5L, -5.76724807756873387202E-1L, -4},
{"j0", j0l, 1.16415321826934814453125e-10L, 9.99984741210937500000E-1L,
1.52587890624999966119E-5L, 9.99999999999999999997E-1L, -4},
{"j0", j0l, -2.0L, 2.23876953125000000000E-1L,
1.38260162356680518275E-5L, 5.76724807756873387202E-1L, -4},
{"y0", y0l, 8.0L, 2.23510742187500000000E-1L,
1.07472000662205273234E-5L, 1.58060461731247494256E-1L, -4},
{"y0", y0l, 4.54541015625L, -2.08114624023437500000E-1L,
1.45018823856668874574E-5L, -2.88887645307401250876E-1L, -4},
{"y0", y0l, 2.85711669921875L, 4.20303344726562500000E-1L,
1.32781607563122276008E-5L, -2.82488638474982469213E-1, -4},
{"y0", y0l, 2.0L, 5.10360717773437500000E-1L,
1.49548763076195966066E-5L, 1.07032431540937546888E-1L, -4},
{"y0", y0l, 1.16415321826934814453125e-10L, -1.46357574462890625000E1L,
3.54110537011061127637E-6L, 5.46852220461145271913E9L, -4},
{"j1", j1l, 8.0L, 2.34634399414062500000E-1L,
1.94743985212438127665E-6L,1.42321263780814578043E-1, -4},
{"j1", j1l, 4.54541015625L, -2.42996215820312500000E-1L,
2.55844668494153980076E-6L, -2.56317734136211337012E-1, -4},
{"j1", j1l, 2.85711669921875L, 3.90396118164062500000E-1L,
6.10716043881165077013E-6L, -3.44531507106757980441E-1L, -4},
{"j1", j1l, 2.0L, 5.76721191406250000000E-1L,
3.61635062338720244824E-6L, -6.44716247372010255494E-2L, -4},
{"j1", j1l, 1.16415321826934814453125e-10L,
5.820677273504770710133016109466552734375e-11L,
8.881784197001251337312921818461805735896e-16L,
4.99999999999999999997E-1L, -4},
{"j1", j1l, -2.0L, -5.76721191406250000000E-1L,
-3.61635062338720244824E-6L, -6.44716247372010255494E-2L, -4},
{"y1", y1l, 8.0L, -1.58065795898437500000E-1L,
5.33416719000574444473E-6L, 2.43279047103972157309E-1L, -4},
{"y1", y1l, 4.54541015625L, 2.88879394531250000000E-1L,
8.25077615125087585195E-6L, -2.71656024771791736625E-1L, -4},
{"y1", y1l, 2.85711669921875L, 2.82485961914062500000E-1,
2.67656091996921314433E-6L, 3.21444694221532719737E-1, -4},
{"y1", y1l, 2.0L, -1.07040405273437500000E-1L,
7.97373249995311162923E-6L, 5.63891888420213893041E-1, -4},
{"y1", y1l, 1.16415321826934814453125e-10L, -5.46852220500000000000E9L,
3.88547280871200700671E-1L, 4.69742480525120196168E19L, -4},
#endif
{"tgamma", tgammal, 1.0L, 1.0L,
0.0L, -5.772156649015328606e-1L, TOL},
{"tgamma", tgammal, 2.0L, 1.0L,
0.0L, 4.2278433509846713939e-1L, TOL},
{"tgamma", tgammal, 3.0L, 2.0L,
0.0L, 1.845568670196934279L, TOL},
{"tgamma", tgammal, 4.0L, 6.0L,
0.0L, 7.536706010590802836L, TOL},
{"lgamma", lgammal, 8.0L, 8.525146484375L,
1.48766904143001655310E-5, 2.01564147795560999654E0L, TOL},
{"lgamma", lgammal, 8.99993896484375e-1L, 6.6375732421875e-2L,
5.11505711292524166220E-6L, -7.54938684259372234258E-1, -TOL},
{"lgamma", lgammal, 7.31597900390625e-1L, 2.2369384765625e-1L,
5.21506341809849792422E-6L,-1.13355566660398608343E0L, -TOL},
{"lgamma", lgammal, 2.31639862060546875e-1L, 1.3686676025390625L,
1.12609441752996145670E-5L, -4.56670961813812679012E0, -TOL},
{"lgamma", lgammal, 1.73162841796875L, -8.88214111328125e-2L,
3.36207740803753034508E-6L, 2.33339034686200586920E-1L, -TOL},
{"lgamma", lgammal, 1.23162841796875L,-9.3902587890625e-2L,
1.28765089229009648104E-5L, -2.49677345775751390414E-1L, -TOL},
{"lgamma", lgammal, 7.3786976294838206464e19L, 3.301798506038663053312e21L,
-1.656137564136932662487046269677E5L, 4.57477139169563904215E1L, TOL},
{"lgamma", lgammal, 1.0L, 0.0L,
0.0L, -5.77215664901532860607E-1L, -TOL},
{"lgamma", lgammal, 2.0L, 0.0L,
0.0L, 4.22784335098467139393E-1L, -TOL},
{"lgamma", lgammal, 1.08420217248550443401E-19L,4.36682586669921875e1L,
1.37082843669932230418E-5L, -9.22337203685477580858E18L, TOL},
{"lgamma", lgammal, -0.5L, 1.2655029296875L,
9.19379714539648894580E-6L, 3.64899739785765205590E-2L, TOL},
{"lgamma", lgammal, -1.5L, 8.6004638671875e-1L,
6.28657731014510932682E-7L, 7.03156640645243187226E-1L, TOL},
{"lgamma", lgammal, -2.5L, -5.6243896484375E-2L,
1.79986700949327405470E-7, 1.10315664064524318723E0L, -TOL},
{"lgamma", lgammal, -3.5L, -1.30902099609375L,
1.43111007079536392848E-5L, 1.38887092635952890151E0L, TOL},
{"null", NULL, 0.0L, 0.0L, 0.0L, 1},
};
/* These take care of extra-precise floating point register problems. */
static volatile long double volat1;
static volatile long double volat2;
/* Return the next nearest floating point value to X
in the direction of UPDOWN (+1 or -1).
(Might fail if X is denormalized.) */
static long double
nextval (x, updown)
long double x;
int updown;
{
long double m;
int i;
volat1 = x;
m = 0.25L * MACHEPL * volat1 * updown;
volat2 = volat1 + m;
if (volat2 != volat1)
printf ("successor failed\n");
for (i = 2; i < 10; i++)
{
volat2 = volat1 + i * m;
if (volat1 != volat2)
return volat2;
}
printf ("nextval failed\n");
return volat1;
}
int
monotl ()
{
long double (*fun1) (long double);
int i, j, errs, tests, err_thresh;
long double x, x0, dy, err;
errs = 0;
tests = 0;
i = 0;
for (;;)
{
/* Function call reference. */
fun1 = test1[i].func;
if (fun1 == NULL)
break;
/* Function argument. */
volat1 = test1[i].arg1;
/* x0 is the given argument, x scans from slightly below to above x0. */
x0 = volat1;
x = volat1;
for (j = 0; j <= NPTS; j++)
{
/* delta x */
volat1 = x - x0;
/* delta y */
dy = volat1 * test1[i].derivative;
/* y + delta y */
dy = test1[i].answer2 + dy;
volat1 = test1[i].answer1 + dy;
/* Run the function under test. */
volat2 = (*(fun1)) (x);
if (volat2 != volat1)
{
/* Estimate difference between program result
and extended precision function value. */
err = volat2 - test1[i].answer1;
err = err - dy;
/* Compare difference with reporting threshold. */
err_thresh = test1[i].thresh;
if (err_thresh >= 0)
err = err / volat1; /* relative error */
else
{
err_thresh = -err_thresh; /* absolute error */
/* ...but relative error if function value > 1 */
if (fabsl(volat1) > 1.0L)
err = err / volat1;
}
if (fabsl (err) > (err_thresh * MACHEPL))
{
printf ("%d %s(%.19Le) = %.19Le, rel err = %.3Le\n",
j, test1[i].name, x, volat2, err);
errs += 1;
}
}
x = nextval (x, 1);
tests += 1;
}
x = x0;
x = nextval (x, -1);
for (j = 1; j < NPTS; j++)
{
volat1 = x - x0;
dy = volat1 * test1[i].derivative;
dy = test1[i].answer2 + dy;
volat1 = test1[i].answer1 + dy;
volat2 = (*(fun1)) (x);
if (volat2 != volat1)
{
err = volat2 - test1[i].answer1;
err = err - dy;
err_thresh = test1[i].thresh;
if (err_thresh >= 0)
err = err / volat1; /* relative error */
else
{
err_thresh = -err_thresh;
if (fabsl(volat1) > 1.0L)
err = err / volat1;
}
if (fabsl (err) > (err_thresh * MACHEPL))
{
printf ("%d %s(%.19Le) = %.19Le, rel err = %.3Le\n",
j, test1[i].name, x, volat2, err);
errs += 1;
}
}
x = nextval (x, -1);
tests += 1;
}
i += 1;
}
printf ("%d errors in %d tests\n", errs, tests);
return (errs);
}
#endif /* LDBL_MANT_DIG == 64 */
|
