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a2a2059f | 1 | /* Implementation of various C99 functions |
e3c063ce | 2 | Copyright (C) 2004-2013 Free Software Foundation, Inc. |
a2a2059f BD |
3 | |
4 | This file is part of the GNU Fortran 95 runtime library (libgfortran). | |
5 | ||
6 | Libgfortran is free software; you can redistribute it and/or | |
57dea9f6 | 7 | modify it under the terms of the GNU General Public |
a2a2059f | 8 | License as published by the Free Software Foundation; either |
748086b7 | 9 | version 3 of the License, or (at your option) any later version. |
a2a2059f BD |
10 | |
11 | Libgfortran is distributed in the hope that it will be useful, | |
12 | but WITHOUT ANY WARRANTY; without even the implied warranty of | |
13 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
57dea9f6 | 14 | GNU General Public License for more details. |
a2a2059f | 15 | |
748086b7 JJ |
16 | Under Section 7 of GPL version 3, you are granted additional |
17 | permissions described in the GCC Runtime Library Exception, version | |
18 | 3.1, as published by the Free Software Foundation. | |
19 | ||
20 | You should have received a copy of the GNU General Public License and | |
21 | a copy of the GCC Runtime Library Exception along with this program; | |
22 | see the files COPYING3 and COPYING.RUNTIME respectively. If not, see | |
23 | <http://www.gnu.org/licenses/>. */ | |
a2a2059f BD |
24 | |
25 | #include "config.h" | |
1409cd0b FXC |
26 | |
27 | #define C99_PROTOS_H WE_DONT_WANT_PROTOS_NOW | |
a2a2059f BD |
28 | #include "libgfortran.h" |
29 | ||
d08d4988 TB |
30 | /* On a C99 system "I" (with I*I = -1) should be defined in complex.h; |
31 | if not, we define a fallback version here. */ | |
32 | #ifndef I | |
33 | # if defined(_Imaginary_I) | |
34 | # define I _Imaginary_I | |
35 | # elif defined(_Complex_I) | |
36 | # define I _Complex_I | |
37 | # else | |
38 | # define I (1.0fi) | |
39 | # endif | |
40 | #endif | |
edf8dc34 | 41 | |
d08d4988 TB |
42 | /* Prototypes are included to silence -Wstrict-prototypes |
43 | -Wmissing-prototypes. */ | |
edf8dc34 | 44 | |
7afebb02 FXC |
45 | |
46 | /* Wrappers for systems without the various C99 single precision Bessel | |
47 | functions. */ | |
48 | ||
49 | #if defined(HAVE_J0) && ! defined(HAVE_J0F) | |
50 | #define HAVE_J0F 1 | |
d08d4988 | 51 | float j0f (float); |
7afebb02 FXC |
52 | |
53 | float | |
54 | j0f (float x) | |
55 | { | |
56 | return (float) j0 ((double) x); | |
57 | } | |
58 | #endif | |
59 | ||
60 | #if defined(HAVE_J1) && !defined(HAVE_J1F) | |
61 | #define HAVE_J1F 1 | |
d08d4988 | 62 | float j1f (float); |
7afebb02 FXC |
63 | |
64 | float j1f (float x) | |
65 | { | |
66 | return (float) j1 ((double) x); | |
67 | } | |
68 | #endif | |
69 | ||
70 | #if defined(HAVE_JN) && !defined(HAVE_JNF) | |
71 | #define HAVE_JNF 1 | |
d08d4988 | 72 | float jnf (int, float); |
7afebb02 FXC |
73 | |
74 | float | |
75 | jnf (int n, float x) | |
76 | { | |
77 | return (float) jn (n, (double) x); | |
78 | } | |
79 | #endif | |
80 | ||
81 | #if defined(HAVE_Y0) && !defined(HAVE_Y0F) | |
82 | #define HAVE_Y0F 1 | |
d08d4988 | 83 | float y0f (float); |
7afebb02 FXC |
84 | |
85 | float | |
86 | y0f (float x) | |
87 | { | |
88 | return (float) y0 ((double) x); | |
89 | } | |
90 | #endif | |
91 | ||
92 | #if defined(HAVE_Y1) && !defined(HAVE_Y1F) | |
93 | #define HAVE_Y1F 1 | |
d08d4988 | 94 | float y1f (float); |
7afebb02 FXC |
95 | |
96 | float | |
97 | y1f (float x) | |
98 | { | |
99 | return (float) y1 ((double) x); | |
100 | } | |
101 | #endif | |
102 | ||
103 | #if defined(HAVE_YN) && !defined(HAVE_YNF) | |
104 | #define HAVE_YNF 1 | |
d08d4988 | 105 | float ynf (int, float); |
7afebb02 FXC |
106 | |
107 | float | |
108 | ynf (int n, float x) | |
109 | { | |
110 | return (float) yn (n, (double) x); | |
111 | } | |
112 | #endif | |
113 | ||
114 | ||
115 | /* Wrappers for systems without the C99 erff() and erfcf() functions. */ | |
116 | ||
117 | #if defined(HAVE_ERF) && !defined(HAVE_ERFF) | |
118 | #define HAVE_ERFF 1 | |
d08d4988 | 119 | float erff (float); |
7afebb02 FXC |
120 | |
121 | float | |
122 | erff (float x) | |
123 | { | |
124 | return (float) erf ((double) x); | |
125 | } | |
126 | #endif | |
127 | ||
128 | #if defined(HAVE_ERFC) && !defined(HAVE_ERFCF) | |
129 | #define HAVE_ERFCF 1 | |
d08d4988 | 130 | float erfcf (float); |
7afebb02 FXC |
131 | |
132 | float | |
133 | erfcf (float x) | |
134 | { | |
135 | return (float) erfc ((double) x); | |
136 | } | |
137 | #endif | |
138 | ||
139 | ||
453310d8 | 140 | #ifndef HAVE_ACOSF |
2cdc88b6 | 141 | #define HAVE_ACOSF 1 |
d08d4988 TB |
142 | float acosf (float x); |
143 | ||
453310d8 | 144 | float |
d08d4988 | 145 | acosf (float x) |
453310d8 | 146 | { |
d08d4988 | 147 | return (float) acos (x); |
453310d8 RS |
148 | } |
149 | #endif | |
150 | ||
456d9b17 | 151 | #if HAVE_ACOSH && !HAVE_ACOSHF |
d08d4988 TB |
152 | float acoshf (float x); |
153 | ||
456d9b17 FXC |
154 | float |
155 | acoshf (float x) | |
156 | { | |
157 | return (float) acosh ((double) x); | |
158 | } | |
159 | #endif | |
160 | ||
453310d8 | 161 | #ifndef HAVE_ASINF |
2cdc88b6 | 162 | #define HAVE_ASINF 1 |
d08d4988 TB |
163 | float asinf (float x); |
164 | ||
453310d8 | 165 | float |
d08d4988 | 166 | asinf (float x) |
453310d8 | 167 | { |
d08d4988 | 168 | return (float) asin (x); |
453310d8 RS |
169 | } |
170 | #endif | |
171 | ||
456d9b17 | 172 | #if HAVE_ASINH && !HAVE_ASINHF |
d08d4988 TB |
173 | float asinhf (float x); |
174 | ||
456d9b17 FXC |
175 | float |
176 | asinhf (float x) | |
177 | { | |
178 | return (float) asinh ((double) x); | |
179 | } | |
180 | #endif | |
181 | ||
453310d8 | 182 | #ifndef HAVE_ATAN2F |
2cdc88b6 | 183 | #define HAVE_ATAN2F 1 |
d08d4988 TB |
184 | float atan2f (float y, float x); |
185 | ||
453310d8 | 186 | float |
d08d4988 | 187 | atan2f (float y, float x) |
453310d8 | 188 | { |
d08d4988 | 189 | return (float) atan2 (y, x); |
453310d8 RS |
190 | } |
191 | #endif | |
192 | ||
193 | #ifndef HAVE_ATANF | |
2cdc88b6 | 194 | #define HAVE_ATANF 1 |
d08d4988 TB |
195 | float atanf (float x); |
196 | ||
453310d8 | 197 | float |
d08d4988 | 198 | atanf (float x) |
453310d8 | 199 | { |
d08d4988 | 200 | return (float) atan (x); |
453310d8 RS |
201 | } |
202 | #endif | |
203 | ||
456d9b17 | 204 | #if HAVE_ATANH && !HAVE_ATANHF |
d08d4988 TB |
205 | float atanhf (float x); |
206 | ||
456d9b17 FXC |
207 | float |
208 | atanhf (float x) | |
209 | { | |
210 | return (float) atanh ((double) x); | |
211 | } | |
212 | #endif | |
213 | ||
453310d8 | 214 | #ifndef HAVE_CEILF |
2cdc88b6 | 215 | #define HAVE_CEILF 1 |
d08d4988 TB |
216 | float ceilf (float x); |
217 | ||
453310d8 | 218 | float |
d08d4988 | 219 | ceilf (float x) |
453310d8 | 220 | { |
d08d4988 | 221 | return (float) ceil (x); |
453310d8 RS |
222 | } |
223 | #endif | |
224 | ||
225 | #ifndef HAVE_COPYSIGNF | |
2cdc88b6 | 226 | #define HAVE_COPYSIGNF 1 |
d08d4988 TB |
227 | float copysignf (float x, float y); |
228 | ||
453310d8 | 229 | float |
d08d4988 | 230 | copysignf (float x, float y) |
453310d8 | 231 | { |
d08d4988 | 232 | return (float) copysign (x, y); |
453310d8 RS |
233 | } |
234 | #endif | |
235 | ||
236 | #ifndef HAVE_COSF | |
2cdc88b6 | 237 | #define HAVE_COSF 1 |
d08d4988 TB |
238 | float cosf (float x); |
239 | ||
453310d8 | 240 | float |
d08d4988 | 241 | cosf (float x) |
453310d8 | 242 | { |
d08d4988 | 243 | return (float) cos (x); |
453310d8 RS |
244 | } |
245 | #endif | |
246 | ||
247 | #ifndef HAVE_COSHF | |
2cdc88b6 | 248 | #define HAVE_COSHF 1 |
d08d4988 TB |
249 | float coshf (float x); |
250 | ||
453310d8 | 251 | float |
d08d4988 | 252 | coshf (float x) |
453310d8 | 253 | { |
d08d4988 | 254 | return (float) cosh (x); |
453310d8 RS |
255 | } |
256 | #endif | |
257 | ||
258 | #ifndef HAVE_EXPF | |
2cdc88b6 | 259 | #define HAVE_EXPF 1 |
d08d4988 TB |
260 | float expf (float x); |
261 | ||
453310d8 | 262 | float |
d08d4988 | 263 | expf (float x) |
453310d8 | 264 | { |
d08d4988 | 265 | return (float) exp (x); |
453310d8 RS |
266 | } |
267 | #endif | |
268 | ||
6e4d9244 | 269 | #ifndef HAVE_FABSF |
2cdc88b6 | 270 | #define HAVE_FABSF 1 |
d08d4988 TB |
271 | float fabsf (float x); |
272 | ||
6e4d9244 | 273 | float |
d08d4988 | 274 | fabsf (float x) |
6e4d9244 | 275 | { |
d08d4988 | 276 | return (float) fabs (x); |
6e4d9244 EB |
277 | } |
278 | #endif | |
279 | ||
453310d8 | 280 | #ifndef HAVE_FLOORF |
2cdc88b6 | 281 | #define HAVE_FLOORF 1 |
d08d4988 TB |
282 | float floorf (float x); |
283 | ||
453310d8 | 284 | float |
d08d4988 | 285 | floorf (float x) |
453310d8 | 286 | { |
d08d4988 | 287 | return (float) floor (x); |
453310d8 RS |
288 | } |
289 | #endif | |
290 | ||
eb647f7d FXC |
291 | #ifndef HAVE_FMODF |
292 | #define HAVE_FMODF 1 | |
d08d4988 TB |
293 | float fmodf (float x, float y); |
294 | ||
eb647f7d FXC |
295 | float |
296 | fmodf (float x, float y) | |
297 | { | |
298 | return (float) fmod (x, y); | |
299 | } | |
300 | #endif | |
301 | ||
453310d8 | 302 | #ifndef HAVE_FREXPF |
2cdc88b6 | 303 | #define HAVE_FREXPF 1 |
d08d4988 TB |
304 | float frexpf (float x, int *exp); |
305 | ||
453310d8 | 306 | float |
d08d4988 | 307 | frexpf (float x, int *exp) |
453310d8 | 308 | { |
d08d4988 | 309 | return (float) frexp (x, exp); |
453310d8 RS |
310 | } |
311 | #endif | |
312 | ||
313 | #ifndef HAVE_HYPOTF | |
2cdc88b6 | 314 | #define HAVE_HYPOTF 1 |
d08d4988 TB |
315 | float hypotf (float x, float y); |
316 | ||
453310d8 | 317 | float |
d08d4988 | 318 | hypotf (float x, float y) |
453310d8 | 319 | { |
d08d4988 | 320 | return (float) hypot (x, y); |
453310d8 RS |
321 | } |
322 | #endif | |
323 | ||
324 | #ifndef HAVE_LOGF | |
2cdc88b6 | 325 | #define HAVE_LOGF 1 |
d08d4988 TB |
326 | float logf (float x); |
327 | ||
453310d8 | 328 | float |
d08d4988 | 329 | logf (float x) |
453310d8 | 330 | { |
d08d4988 | 331 | return (float) log (x); |
453310d8 RS |
332 | } |
333 | #endif | |
334 | ||
335 | #ifndef HAVE_LOG10F | |
2cdc88b6 | 336 | #define HAVE_LOG10F 1 |
d08d4988 TB |
337 | float log10f (float x); |
338 | ||
453310d8 | 339 | float |
d08d4988 | 340 | log10f (float x) |
453310d8 | 341 | { |
d08d4988 | 342 | return (float) log10 (x); |
453310d8 RS |
343 | } |
344 | #endif | |
345 | ||
ae973d6a | 346 | #ifndef HAVE_SCALBN |
2cdc88b6 | 347 | #define HAVE_SCALBN 1 |
d08d4988 TB |
348 | double scalbn (double x, int y); |
349 | ||
ae973d6a | 350 | double |
d08d4988 | 351 | scalbn (double x, int y) |
ae973d6a | 352 | { |
b65d72ab FXC |
353 | #if (FLT_RADIX == 2) && defined(HAVE_LDEXP) |
354 | return ldexp (x, y); | |
355 | #else | |
d08d4988 | 356 | return x * pow (FLT_RADIX, y); |
b65d72ab | 357 | #endif |
ae973d6a FXC |
358 | } |
359 | #endif | |
360 | ||
453310d8 | 361 | #ifndef HAVE_SCALBNF |
2cdc88b6 | 362 | #define HAVE_SCALBNF 1 |
d08d4988 TB |
363 | float scalbnf (float x, int y); |
364 | ||
453310d8 | 365 | float |
d08d4988 | 366 | scalbnf (float x, int y) |
453310d8 | 367 | { |
d08d4988 | 368 | return (float) scalbn (x, y); |
453310d8 RS |
369 | } |
370 | #endif | |
371 | ||
372 | #ifndef HAVE_SINF | |
2cdc88b6 | 373 | #define HAVE_SINF 1 |
d08d4988 TB |
374 | float sinf (float x); |
375 | ||
453310d8 | 376 | float |
d08d4988 | 377 | sinf (float x) |
453310d8 | 378 | { |
d08d4988 | 379 | return (float) sin (x); |
453310d8 RS |
380 | } |
381 | #endif | |
382 | ||
383 | #ifndef HAVE_SINHF | |
2cdc88b6 | 384 | #define HAVE_SINHF 1 |
d08d4988 TB |
385 | float sinhf (float x); |
386 | ||
453310d8 | 387 | float |
d08d4988 | 388 | sinhf (float x) |
453310d8 | 389 | { |
d08d4988 | 390 | return (float) sinh (x); |
453310d8 RS |
391 | } |
392 | #endif | |
393 | ||
394 | #ifndef HAVE_SQRTF | |
2cdc88b6 | 395 | #define HAVE_SQRTF 1 |
d08d4988 TB |
396 | float sqrtf (float x); |
397 | ||
453310d8 | 398 | float |
d08d4988 | 399 | sqrtf (float x) |
453310d8 | 400 | { |
d08d4988 | 401 | return (float) sqrt (x); |
453310d8 RS |
402 | } |
403 | #endif | |
404 | ||
405 | #ifndef HAVE_TANF | |
2cdc88b6 | 406 | #define HAVE_TANF 1 |
d08d4988 TB |
407 | float tanf (float x); |
408 | ||
453310d8 | 409 | float |
d08d4988 | 410 | tanf (float x) |
453310d8 | 411 | { |
d08d4988 | 412 | return (float) tan (x); |
453310d8 RS |
413 | } |
414 | #endif | |
415 | ||
416 | #ifndef HAVE_TANHF | |
2cdc88b6 | 417 | #define HAVE_TANHF 1 |
d08d4988 TB |
418 | float tanhf (float x); |
419 | ||
453310d8 | 420 | float |
d08d4988 | 421 | tanhf (float x) |
453310d8 | 422 | { |
d08d4988 | 423 | return (float) tanh (x); |
453310d8 RS |
424 | } |
425 | #endif | |
426 | ||
69a2d125 | 427 | #ifndef HAVE_TRUNC |
2cdc88b6 | 428 | #define HAVE_TRUNC 1 |
d08d4988 TB |
429 | double trunc (double x); |
430 | ||
69a2d125 | 431 | double |
d08d4988 | 432 | trunc (double x) |
69a2d125 EB |
433 | { |
434 | if (!isfinite (x)) | |
435 | return x; | |
436 | ||
437 | if (x < 0.0) | |
438 | return - floor (-x); | |
439 | else | |
440 | return floor (x); | |
441 | } | |
442 | #endif | |
443 | ||
444 | #ifndef HAVE_TRUNCF | |
2cdc88b6 | 445 | #define HAVE_TRUNCF 1 |
d08d4988 TB |
446 | float truncf (float x); |
447 | ||
69a2d125 | 448 | float |
d08d4988 | 449 | truncf (float x) |
69a2d125 EB |
450 | { |
451 | return (float) trunc (x); | |
452 | } | |
453 | #endif | |
454 | ||
453310d8 | 455 | #ifndef HAVE_NEXTAFTERF |
2cdc88b6 | 456 | #define HAVE_NEXTAFTERF 1 |
453310d8 RS |
457 | /* This is a portable implementation of nextafterf that is intended to be |
458 | independent of the floating point format or its in memory representation. | |
067a5735 | 459 | This implementation works correctly with denormalized values. */ |
d08d4988 TB |
460 | float nextafterf (float x, float y); |
461 | ||
453310d8 | 462 | float |
d08d4988 | 463 | nextafterf (float x, float y) |
453310d8 | 464 | { |
067a5735 RS |
465 | /* This variable is marked volatile to avoid excess precision problems |
466 | on some platforms, including IA-32. */ | |
467 | volatile float delta; | |
468 | float absx, denorm_min; | |
453310d8 | 469 | |
d08d4988 | 470 | if (isnan (x) || isnan (y)) |
067a5735 | 471 | return x + y; |
453310d8 RS |
472 | if (x == y) |
473 | return x; | |
74421469 EB |
474 | if (!isfinite (x)) |
475 | return x > 0 ? __FLT_MAX__ : - __FLT_MAX__; | |
453310d8 | 476 | |
067a5735 RS |
477 | /* absx = fabsf (x); */ |
478 | absx = (x < 0.0) ? -x : x; | |
453310d8 | 479 | |
067a5735 RS |
480 | /* __FLT_DENORM_MIN__ is non-zero iff the target supports denormals. */ |
481 | if (__FLT_DENORM_MIN__ == 0.0f) | |
482 | denorm_min = __FLT_MIN__; | |
483 | else | |
484 | denorm_min = __FLT_DENORM_MIN__; | |
485 | ||
486 | if (absx < __FLT_MIN__) | |
487 | delta = denorm_min; | |
453310d8 RS |
488 | else |
489 | { | |
067a5735 RS |
490 | float frac; |
491 | int exp; | |
492 | ||
493 | /* Discard the fraction from x. */ | |
494 | frac = frexpf (absx, &exp); | |
495 | delta = scalbnf (0.5f, exp); | |
496 | ||
497 | /* Scale x by the epsilon of the representation. By rights we should | |
498 | have been able to combine this with scalbnf, but some targets don't | |
499 | get that correct with denormals. */ | |
500 | delta *= __FLT_EPSILON__; | |
501 | ||
502 | /* If we're going to be reducing the absolute value of X, and doing so | |
503 | would reduce the exponent of X, then the delta to be applied is | |
504 | one exponent smaller. */ | |
505 | if (frac == 0.5f && (y < x) == (x > 0)) | |
506 | delta *= 0.5f; | |
507 | ||
508 | /* If that underflows to zero, then we're back to the minimum. */ | |
509 | if (delta == 0.0f) | |
510 | delta = denorm_min; | |
453310d8 | 511 | } |
067a5735 RS |
512 | |
513 | if (y < x) | |
514 | delta = -delta; | |
515 | ||
516 | return x + delta; | |
453310d8 RS |
517 | } |
518 | #endif | |
519 | ||
bf4d99cf | 520 | |
c0c3c409 | 521 | #if !defined(HAVE_POWF) || defined(HAVE_BROKEN_POWF) |
bf4d99cf | 522 | #ifndef HAVE_POWF |
2cdc88b6 | 523 | #define HAVE_POWF 1 |
c0c3c409 | 524 | #endif |
d08d4988 TB |
525 | float powf (float x, float y); |
526 | ||
bf4d99cf | 527 | float |
d08d4988 | 528 | powf (float x, float y) |
bf4d99cf | 529 | { |
d08d4988 | 530 | return (float) pow (x, y); |
bf4d99cf TS |
531 | } |
532 | #endif | |
533 | ||
bc20e36d | 534 | |
287188ea FXC |
535 | #ifndef HAVE_ROUND |
536 | #define HAVE_ROUND 1 | |
537 | /* Round to nearest integral value. If the argument is halfway between two | |
538 | integral values then round away from zero. */ | |
539 | double round (double x); | |
540 | ||
541 | double | |
542 | round (double x) | |
543 | { | |
544 | double t; | |
545 | if (!isfinite (x)) | |
546 | return (x); | |
547 | ||
548 | if (x >= 0.0) | |
549 | { | |
550 | t = floor (x); | |
551 | if (t - x <= -0.5) | |
552 | t += 1.0; | |
553 | return (t); | |
554 | } | |
555 | else | |
556 | { | |
557 | t = floor (-x); | |
558 | if (t + x <= -0.5) | |
559 | t += 1.0; | |
560 | return (-t); | |
561 | } | |
562 | } | |
563 | #endif | |
564 | ||
565 | ||
a2a2059f BD |
566 | /* Algorithm by Steven G. Kargl. */ |
567 | ||
c120ef14 | 568 | #if !defined(HAVE_ROUNDL) |
94f548c2 | 569 | #define HAVE_ROUNDL 1 |
d08d4988 TB |
570 | long double roundl (long double x); |
571 | ||
c120ef14 | 572 | #if defined(HAVE_CEILL) |
94f548c2 FXC |
573 | /* Round to nearest integral value. If the argument is halfway between two |
574 | integral values then round away from zero. */ | |
575 | ||
576 | long double | |
d08d4988 | 577 | roundl (long double x) |
94f548c2 FXC |
578 | { |
579 | long double t; | |
580 | if (!isfinite (x)) | |
581 | return (x); | |
582 | ||
583 | if (x >= 0.0) | |
584 | { | |
d08d4988 | 585 | t = ceill (x); |
94f548c2 FXC |
586 | if (t - x > 0.5) |
587 | t -= 1.0; | |
588 | return (t); | |
589 | } | |
590 | else | |
591 | { | |
d08d4988 | 592 | t = ceill (-x); |
94f548c2 FXC |
593 | if (t + x > 0.5) |
594 | t -= 1.0; | |
595 | return (-t); | |
596 | } | |
597 | } | |
c120ef14 FXC |
598 | #else |
599 | ||
600 | /* Poor version of roundl for system that don't have ceill. */ | |
601 | long double | |
d08d4988 | 602 | roundl (long double x) |
c120ef14 FXC |
603 | { |
604 | if (x > DBL_MAX || x < -DBL_MAX) | |
605 | { | |
606 | #ifdef HAVE_NEXTAFTERL | |
1c4bc9ca | 607 | long double prechalf = nextafterl (0.5L, LDBL_MAX); |
c120ef14 FXC |
608 | #else |
609 | static long double prechalf = 0.5L; | |
610 | #endif | |
611 | return (GFC_INTEGER_LARGEST) (x + (x > 0 ? prechalf : -prechalf)); | |
612 | } | |
613 | else | |
614 | /* Use round(). */ | |
d08d4988 | 615 | return round ((double) x); |
c120ef14 FXC |
616 | } |
617 | ||
618 | #endif | |
94f548c2 FXC |
619 | #endif |
620 | ||
a2a2059f | 621 | #ifndef HAVE_ROUNDF |
2cdc88b6 | 622 | #define HAVE_ROUNDF 1 |
a2a2059f BD |
623 | /* Round to nearest integral value. If the argument is halfway between two |
624 | integral values then round away from zero. */ | |
d08d4988 | 625 | float roundf (float x); |
a2a2059f BD |
626 | |
627 | float | |
d08d4988 | 628 | roundf (float x) |
a2a2059f BD |
629 | { |
630 | float t; | |
118ea208 | 631 | if (!isfinite (x)) |
a2a2059f BD |
632 | return (x); |
633 | ||
634 | if (x >= 0.0) | |
635 | { | |
d08d4988 | 636 | t = floorf (x); |
63f90eb7 JDA |
637 | if (t - x <= -0.5) |
638 | t += 1.0; | |
a2a2059f BD |
639 | return (t); |
640 | } | |
641 | else | |
642 | { | |
d08d4988 | 643 | t = floorf (-x); |
63f90eb7 JDA |
644 | if (t + x <= -0.5) |
645 | t += 1.0; | |
a2a2059f BD |
646 | return (-t); |
647 | } | |
648 | } | |
649 | #endif | |
32aa3bff | 650 | |
94f548c2 FXC |
651 | |
652 | /* lround{f,,l} and llround{f,,l} functions. */ | |
653 | ||
654 | #if !defined(HAVE_LROUNDF) && defined(HAVE_ROUNDF) | |
655 | #define HAVE_LROUNDF 1 | |
d08d4988 TB |
656 | long int lroundf (float x); |
657 | ||
94f548c2 FXC |
658 | long int |
659 | lroundf (float x) | |
660 | { | |
661 | return (long int) roundf (x); | |
662 | } | |
663 | #endif | |
664 | ||
665 | #if !defined(HAVE_LROUND) && defined(HAVE_ROUND) | |
666 | #define HAVE_LROUND 1 | |
d08d4988 TB |
667 | long int lround (double x); |
668 | ||
94f548c2 FXC |
669 | long int |
670 | lround (double x) | |
671 | { | |
672 | return (long int) round (x); | |
673 | } | |
674 | #endif | |
675 | ||
676 | #if !defined(HAVE_LROUNDL) && defined(HAVE_ROUNDL) | |
677 | #define HAVE_LROUNDL 1 | |
d08d4988 TB |
678 | long int lroundl (long double x); |
679 | ||
94f548c2 FXC |
680 | long int |
681 | lroundl (long double x) | |
682 | { | |
683 | return (long long int) roundl (x); | |
684 | } | |
685 | #endif | |
686 | ||
687 | #if !defined(HAVE_LLROUNDF) && defined(HAVE_ROUNDF) | |
688 | #define HAVE_LLROUNDF 1 | |
d08d4988 TB |
689 | long long int llroundf (float x); |
690 | ||
94f548c2 FXC |
691 | long long int |
692 | llroundf (float x) | |
693 | { | |
694 | return (long long int) roundf (x); | |
695 | } | |
696 | #endif | |
697 | ||
698 | #if !defined(HAVE_LLROUND) && defined(HAVE_ROUND) | |
699 | #define HAVE_LLROUND 1 | |
d08d4988 TB |
700 | long long int llround (double x); |
701 | ||
94f548c2 FXC |
702 | long long int |
703 | llround (double x) | |
704 | { | |
705 | return (long long int) round (x); | |
706 | } | |
707 | #endif | |
708 | ||
709 | #if !defined(HAVE_LLROUNDL) && defined(HAVE_ROUNDL) | |
710 | #define HAVE_LLROUNDL 1 | |
d08d4988 TB |
711 | long long int llroundl (long double x); |
712 | ||
94f548c2 FXC |
713 | long long int |
714 | llroundl (long double x) | |
715 | { | |
716 | return (long long int) roundl (x); | |
717 | } | |
718 | #endif | |
719 | ||
720 | ||
32aa3bff | 721 | #ifndef HAVE_LOG10L |
2cdc88b6 | 722 | #define HAVE_LOG10L 1 |
32aa3bff FXC |
723 | /* log10 function for long double variables. The version provided here |
724 | reduces the argument until it fits into a double, then use log10. */ | |
d08d4988 TB |
725 | long double log10l (long double x); |
726 | ||
32aa3bff | 727 | long double |
d08d4988 | 728 | log10l (long double x) |
32aa3bff FXC |
729 | { |
730 | #if LDBL_MAX_EXP > DBL_MAX_EXP | |
731 | if (x > DBL_MAX) | |
732 | { | |
733 | double val; | |
734 | int p2_result = 0; | |
735 | if (x > 0x1p16383L) { p2_result += 16383; x /= 0x1p16383L; } | |
736 | if (x > 0x1p8191L) { p2_result += 8191; x /= 0x1p8191L; } | |
737 | if (x > 0x1p4095L) { p2_result += 4095; x /= 0x1p4095L; } | |
738 | if (x > 0x1p2047L) { p2_result += 2047; x /= 0x1p2047L; } | |
739 | if (x > 0x1p1023L) { p2_result += 1023; x /= 0x1p1023L; } | |
740 | val = log10 ((double) x); | |
741 | return (val + p2_result * .30102999566398119521373889472449302L); | |
742 | } | |
743 | #endif | |
744 | #if LDBL_MIN_EXP < DBL_MIN_EXP | |
745 | if (x < DBL_MIN) | |
746 | { | |
747 | double val; | |
748 | int p2_result = 0; | |
749 | if (x < 0x1p-16380L) { p2_result += 16380; x /= 0x1p-16380L; } | |
750 | if (x < 0x1p-8189L) { p2_result += 8189; x /= 0x1p-8189L; } | |
751 | if (x < 0x1p-4093L) { p2_result += 4093; x /= 0x1p-4093L; } | |
752 | if (x < 0x1p-2045L) { p2_result += 2045; x /= 0x1p-2045L; } | |
753 | if (x < 0x1p-1021L) { p2_result += 1021; x /= 0x1p-1021L; } | |
d08d4988 | 754 | val = fabs (log10 ((double) x)); |
32aa3bff FXC |
755 | return (- val - p2_result * .30102999566398119521373889472449302L); |
756 | } | |
757 | #endif | |
758 | return log10 (x); | |
759 | } | |
760 | #endif | |
1409cd0b FXC |
761 | |
762 | ||
eb647f7d FXC |
763 | #ifndef HAVE_FLOORL |
764 | #define HAVE_FLOORL 1 | |
d08d4988 TB |
765 | long double floorl (long double x); |
766 | ||
eb647f7d FXC |
767 | long double |
768 | floorl (long double x) | |
769 | { | |
770 | /* Zero, possibly signed. */ | |
771 | if (x == 0) | |
772 | return x; | |
773 | ||
774 | /* Large magnitude. */ | |
775 | if (x > DBL_MAX || x < (-DBL_MAX)) | |
776 | return x; | |
777 | ||
778 | /* Small positive values. */ | |
779 | if (x >= 0 && x < DBL_MIN) | |
780 | return 0; | |
781 | ||
782 | /* Small negative values. */ | |
783 | if (x < 0 && x > (-DBL_MIN)) | |
784 | return -1; | |
785 | ||
786 | return floor (x); | |
787 | } | |
788 | #endif | |
789 | ||
790 | ||
791 | #ifndef HAVE_FMODL | |
792 | #define HAVE_FMODL 1 | |
d08d4988 TB |
793 | long double fmodl (long double x, long double y); |
794 | ||
eb647f7d FXC |
795 | long double |
796 | fmodl (long double x, long double y) | |
797 | { | |
798 | if (y == 0.0L) | |
799 | return 0.0L; | |
800 | ||
801 | /* Need to check that the result has the same sign as x and magnitude | |
802 | less than the magnitude of y. */ | |
803 | return x - floorl (x / y) * y; | |
804 | } | |
805 | #endif | |
806 | ||
807 | ||
1409cd0b | 808 | #if !defined(HAVE_CABSF) |
2cdc88b6 | 809 | #define HAVE_CABSF 1 |
d08d4988 TB |
810 | float cabsf (float complex z); |
811 | ||
1409cd0b FXC |
812 | float |
813 | cabsf (float complex z) | |
814 | { | |
815 | return hypotf (REALPART (z), IMAGPART (z)); | |
816 | } | |
817 | #endif | |
818 | ||
819 | #if !defined(HAVE_CABS) | |
2cdc88b6 | 820 | #define HAVE_CABS 1 |
d08d4988 TB |
821 | double cabs (double complex z); |
822 | ||
1409cd0b FXC |
823 | double |
824 | cabs (double complex z) | |
825 | { | |
826 | return hypot (REALPART (z), IMAGPART (z)); | |
827 | } | |
828 | #endif | |
829 | ||
830 | #if !defined(HAVE_CABSL) && defined(HAVE_HYPOTL) | |
2cdc88b6 | 831 | #define HAVE_CABSL 1 |
d08d4988 TB |
832 | long double cabsl (long double complex z); |
833 | ||
1409cd0b FXC |
834 | long double |
835 | cabsl (long double complex z) | |
836 | { | |
837 | return hypotl (REALPART (z), IMAGPART (z)); | |
838 | } | |
839 | #endif | |
840 | ||
841 | ||
842 | #if !defined(HAVE_CARGF) | |
2cdc88b6 | 843 | #define HAVE_CARGF 1 |
d08d4988 TB |
844 | float cargf (float complex z); |
845 | ||
1409cd0b FXC |
846 | float |
847 | cargf (float complex z) | |
848 | { | |
849 | return atan2f (IMAGPART (z), REALPART (z)); | |
850 | } | |
851 | #endif | |
852 | ||
853 | #if !defined(HAVE_CARG) | |
2cdc88b6 | 854 | #define HAVE_CARG 1 |
d08d4988 TB |
855 | double carg (double complex z); |
856 | ||
1409cd0b FXC |
857 | double |
858 | carg (double complex z) | |
859 | { | |
860 | return atan2 (IMAGPART (z), REALPART (z)); | |
861 | } | |
862 | #endif | |
863 | ||
864 | #if !defined(HAVE_CARGL) && defined(HAVE_ATAN2L) | |
2cdc88b6 | 865 | #define HAVE_CARGL 1 |
d08d4988 TB |
866 | long double cargl (long double complex z); |
867 | ||
1409cd0b FXC |
868 | long double |
869 | cargl (long double complex z) | |
870 | { | |
871 | return atan2l (IMAGPART (z), REALPART (z)); | |
872 | } | |
873 | #endif | |
874 | ||
875 | ||
876 | /* exp(z) = exp(a)*(cos(b) + i sin(b)) */ | |
877 | #if !defined(HAVE_CEXPF) | |
2cdc88b6 | 878 | #define HAVE_CEXPF 1 |
d08d4988 TB |
879 | float complex cexpf (float complex z); |
880 | ||
1409cd0b FXC |
881 | float complex |
882 | cexpf (float complex z) | |
883 | { | |
884 | float a, b; | |
885 | float complex v; | |
886 | ||
887 | a = REALPART (z); | |
888 | b = IMAGPART (z); | |
889 | COMPLEX_ASSIGN (v, cosf (b), sinf (b)); | |
890 | return expf (a) * v; | |
891 | } | |
892 | #endif | |
893 | ||
894 | #if !defined(HAVE_CEXP) | |
2cdc88b6 | 895 | #define HAVE_CEXP 1 |
d08d4988 TB |
896 | double complex cexp (double complex z); |
897 | ||
1409cd0b FXC |
898 | double complex |
899 | cexp (double complex z) | |
900 | { | |
901 | double a, b; | |
902 | double complex v; | |
903 | ||
904 | a = REALPART (z); | |
905 | b = IMAGPART (z); | |
906 | COMPLEX_ASSIGN (v, cos (b), sin (b)); | |
907 | return exp (a) * v; | |
908 | } | |
909 | #endif | |
910 | ||
911 | #if !defined(HAVE_CEXPL) && defined(HAVE_COSL) && defined(HAVE_SINL) && defined(EXPL) | |
2cdc88b6 | 912 | #define HAVE_CEXPL 1 |
d08d4988 TB |
913 | long double complex cexpl (long double complex z); |
914 | ||
1409cd0b FXC |
915 | long double complex |
916 | cexpl (long double complex z) | |
917 | { | |
918 | long double a, b; | |
919 | long double complex v; | |
920 | ||
921 | a = REALPART (z); | |
922 | b = IMAGPART (z); | |
923 | COMPLEX_ASSIGN (v, cosl (b), sinl (b)); | |
924 | return expl (a) * v; | |
925 | } | |
926 | #endif | |
927 | ||
928 | ||
929 | /* log(z) = log (cabs(z)) + i*carg(z) */ | |
930 | #if !defined(HAVE_CLOGF) | |
2cdc88b6 | 931 | #define HAVE_CLOGF 1 |
d08d4988 TB |
932 | float complex clogf (float complex z); |
933 | ||
1409cd0b FXC |
934 | float complex |
935 | clogf (float complex z) | |
936 | { | |
937 | float complex v; | |
938 | ||
939 | COMPLEX_ASSIGN (v, logf (cabsf (z)), cargf (z)); | |
940 | return v; | |
941 | } | |
942 | #endif | |
943 | ||
944 | #if !defined(HAVE_CLOG) | |
2cdc88b6 | 945 | #define HAVE_CLOG 1 |
d08d4988 TB |
946 | double complex clog (double complex z); |
947 | ||
1409cd0b FXC |
948 | double complex |
949 | clog (double complex z) | |
950 | { | |
951 | double complex v; | |
952 | ||
953 | COMPLEX_ASSIGN (v, log (cabs (z)), carg (z)); | |
954 | return v; | |
955 | } | |
956 | #endif | |
957 | ||
958 | #if !defined(HAVE_CLOGL) && defined(HAVE_LOGL) && defined(HAVE_CABSL) && defined(HAVE_CARGL) | |
2cdc88b6 | 959 | #define HAVE_CLOGL 1 |
d08d4988 TB |
960 | long double complex clogl (long double complex z); |
961 | ||
1409cd0b FXC |
962 | long double complex |
963 | clogl (long double complex z) | |
964 | { | |
965 | long double complex v; | |
966 | ||
967 | COMPLEX_ASSIGN (v, logl (cabsl (z)), cargl (z)); | |
968 | return v; | |
969 | } | |
970 | #endif | |
971 | ||
972 | ||
973 | /* log10(z) = log10 (cabs(z)) + i*carg(z) */ | |
974 | #if !defined(HAVE_CLOG10F) | |
2cdc88b6 | 975 | #define HAVE_CLOG10F 1 |
d08d4988 TB |
976 | float complex clog10f (float complex z); |
977 | ||
1409cd0b FXC |
978 | float complex |
979 | clog10f (float complex z) | |
980 | { | |
981 | float complex v; | |
982 | ||
983 | COMPLEX_ASSIGN (v, log10f (cabsf (z)), cargf (z)); | |
984 | return v; | |
985 | } | |
986 | #endif | |
987 | ||
988 | #if !defined(HAVE_CLOG10) | |
2cdc88b6 | 989 | #define HAVE_CLOG10 1 |
d08d4988 TB |
990 | double complex clog10 (double complex z); |
991 | ||
1409cd0b FXC |
992 | double complex |
993 | clog10 (double complex z) | |
994 | { | |
995 | double complex v; | |
996 | ||
997 | COMPLEX_ASSIGN (v, log10 (cabs (z)), carg (z)); | |
998 | return v; | |
999 | } | |
1000 | #endif | |
1001 | ||
1002 | #if !defined(HAVE_CLOG10L) && defined(HAVE_LOG10L) && defined(HAVE_CABSL) && defined(HAVE_CARGL) | |
2cdc88b6 | 1003 | #define HAVE_CLOG10L 1 |
d08d4988 TB |
1004 | long double complex clog10l (long double complex z); |
1005 | ||
1409cd0b FXC |
1006 | long double complex |
1007 | clog10l (long double complex z) | |
1008 | { | |
1009 | long double complex v; | |
1010 | ||
1011 | COMPLEX_ASSIGN (v, log10l (cabsl (z)), cargl (z)); | |
1012 | return v; | |
1013 | } | |
1014 | #endif | |
1015 | ||
1016 | ||
1017 | /* pow(base, power) = cexp (power * clog (base)) */ | |
1018 | #if !defined(HAVE_CPOWF) | |
2cdc88b6 | 1019 | #define HAVE_CPOWF 1 |
d08d4988 TB |
1020 | float complex cpowf (float complex base, float complex power); |
1021 | ||
1409cd0b FXC |
1022 | float complex |
1023 | cpowf (float complex base, float complex power) | |
1024 | { | |
1025 | return cexpf (power * clogf (base)); | |
1026 | } | |
1027 | #endif | |
1028 | ||
1029 | #if !defined(HAVE_CPOW) | |
2cdc88b6 | 1030 | #define HAVE_CPOW 1 |
d08d4988 TB |
1031 | double complex cpow (double complex base, double complex power); |
1032 | ||
1409cd0b FXC |
1033 | double complex |
1034 | cpow (double complex base, double complex power) | |
1035 | { | |
1036 | return cexp (power * clog (base)); | |
1037 | } | |
1038 | #endif | |
1039 | ||
1040 | #if !defined(HAVE_CPOWL) && defined(HAVE_CEXPL) && defined(HAVE_CLOGL) | |
2cdc88b6 | 1041 | #define HAVE_CPOWL 1 |
d08d4988 TB |
1042 | long double complex cpowl (long double complex base, long double complex power); |
1043 | ||
1409cd0b FXC |
1044 | long double complex |
1045 | cpowl (long double complex base, long double complex power) | |
1046 | { | |
1047 | return cexpl (power * clogl (base)); | |
1048 | } | |
1049 | #endif | |
1050 | ||
1051 | ||
1052 | /* sqrt(z). Algorithm pulled from glibc. */ | |
1053 | #if !defined(HAVE_CSQRTF) | |
2cdc88b6 | 1054 | #define HAVE_CSQRTF 1 |
d08d4988 TB |
1055 | float complex csqrtf (float complex z); |
1056 | ||
1409cd0b FXC |
1057 | float complex |
1058 | csqrtf (float complex z) | |
1059 | { | |
1060 | float re, im; | |
1061 | float complex v; | |
1062 | ||
1063 | re = REALPART (z); | |
1064 | im = IMAGPART (z); | |
1065 | if (im == 0) | |
1066 | { | |
1067 | if (re < 0) | |
1068 | { | |
1069 | COMPLEX_ASSIGN (v, 0, copysignf (sqrtf (-re), im)); | |
1070 | } | |
1071 | else | |
1072 | { | |
1073 | COMPLEX_ASSIGN (v, fabsf (sqrtf (re)), copysignf (0, im)); | |
1074 | } | |
1075 | } | |
1076 | else if (re == 0) | |
1077 | { | |
1078 | float r; | |
1079 | ||
1080 | r = sqrtf (0.5 * fabsf (im)); | |
1081 | ||
a2694f68 | 1082 | COMPLEX_ASSIGN (v, r, copysignf (r, im)); |
1409cd0b FXC |
1083 | } |
1084 | else | |
1085 | { | |
1086 | float d, r, s; | |
1087 | ||
1088 | d = hypotf (re, im); | |
1089 | /* Use the identity 2 Re res Im res = Im x | |
1090 | to avoid cancellation error in d +/- Re x. */ | |
1091 | if (re > 0) | |
1092 | { | |
1093 | r = sqrtf (0.5 * d + 0.5 * re); | |
1094 | s = (0.5 * im) / r; | |
1095 | } | |
1096 | else | |
1097 | { | |
1098 | s = sqrtf (0.5 * d - 0.5 * re); | |
1099 | r = fabsf ((0.5 * im) / s); | |
1100 | } | |
1101 | ||
1102 | COMPLEX_ASSIGN (v, r, copysignf (s, im)); | |
1103 | } | |
1104 | return v; | |
1105 | } | |
1106 | #endif | |
1107 | ||
1108 | #if !defined(HAVE_CSQRT) | |
2cdc88b6 | 1109 | #define HAVE_CSQRT 1 |
d08d4988 TB |
1110 | double complex csqrt (double complex z); |
1111 | ||
1409cd0b FXC |
1112 | double complex |
1113 | csqrt (double complex z) | |
1114 | { | |
1115 | double re, im; | |
1116 | double complex v; | |
1117 | ||
1118 | re = REALPART (z); | |
1119 | im = IMAGPART (z); | |
1120 | if (im == 0) | |
1121 | { | |
1122 | if (re < 0) | |
1123 | { | |
1124 | COMPLEX_ASSIGN (v, 0, copysign (sqrt (-re), im)); | |
1125 | } | |
1126 | else | |
1127 | { | |
1128 | COMPLEX_ASSIGN (v, fabs (sqrt (re)), copysign (0, im)); | |
1129 | } | |
1130 | } | |
1131 | else if (re == 0) | |
1132 | { | |
1133 | double r; | |
1134 | ||
1135 | r = sqrt (0.5 * fabs (im)); | |
1136 | ||
a2694f68 | 1137 | COMPLEX_ASSIGN (v, r, copysign (r, im)); |
1409cd0b FXC |
1138 | } |
1139 | else | |
1140 | { | |
1141 | double d, r, s; | |
1142 | ||
1143 | d = hypot (re, im); | |
1144 | /* Use the identity 2 Re res Im res = Im x | |
1145 | to avoid cancellation error in d +/- Re x. */ | |
1146 | if (re > 0) | |
1147 | { | |
1148 | r = sqrt (0.5 * d + 0.5 * re); | |
1149 | s = (0.5 * im) / r; | |
1150 | } | |
1151 | else | |
1152 | { | |
1153 | s = sqrt (0.5 * d - 0.5 * re); | |
1154 | r = fabs ((0.5 * im) / s); | |
1155 | } | |
1156 | ||
1157 | COMPLEX_ASSIGN (v, r, copysign (s, im)); | |
1158 | } | |
1159 | return v; | |
1160 | } | |
1161 | #endif | |
1162 | ||
1163 | #if !defined(HAVE_CSQRTL) && defined(HAVE_COPYSIGNL) && defined(HAVE_SQRTL) && defined(HAVE_FABSL) && defined(HAVE_HYPOTL) | |
2cdc88b6 | 1164 | #define HAVE_CSQRTL 1 |
d08d4988 TB |
1165 | long double complex csqrtl (long double complex z); |
1166 | ||
1409cd0b FXC |
1167 | long double complex |
1168 | csqrtl (long double complex z) | |
1169 | { | |
1170 | long double re, im; | |
1171 | long double complex v; | |
1172 | ||
1173 | re = REALPART (z); | |
1174 | im = IMAGPART (z); | |
1175 | if (im == 0) | |
1176 | { | |
1177 | if (re < 0) | |
1178 | { | |
1179 | COMPLEX_ASSIGN (v, 0, copysignl (sqrtl (-re), im)); | |
1180 | } | |
1181 | else | |
1182 | { | |
1183 | COMPLEX_ASSIGN (v, fabsl (sqrtl (re)), copysignl (0, im)); | |
1184 | } | |
1185 | } | |
1186 | else if (re == 0) | |
1187 | { | |
1188 | long double r; | |
1189 | ||
1190 | r = sqrtl (0.5 * fabsl (im)); | |
1191 | ||
1192 | COMPLEX_ASSIGN (v, copysignl (r, im), r); | |
1193 | } | |
1194 | else | |
1195 | { | |
1196 | long double d, r, s; | |
1197 | ||
1198 | d = hypotl (re, im); | |
1199 | /* Use the identity 2 Re res Im res = Im x | |
1200 | to avoid cancellation error in d +/- Re x. */ | |
1201 | if (re > 0) | |
1202 | { | |
1203 | r = sqrtl (0.5 * d + 0.5 * re); | |
1204 | s = (0.5 * im) / r; | |
1205 | } | |
1206 | else | |
1207 | { | |
1208 | s = sqrtl (0.5 * d - 0.5 * re); | |
1209 | r = fabsl ((0.5 * im) / s); | |
1210 | } | |
1211 | ||
1212 | COMPLEX_ASSIGN (v, r, copysignl (s, im)); | |
1213 | } | |
1214 | return v; | |
1215 | } | |
1216 | #endif | |
1217 | ||
1218 | ||
1219 | /* sinh(a + i b) = sinh(a) cos(b) + i cosh(a) sin(b) */ | |
1220 | #if !defined(HAVE_CSINHF) | |
2cdc88b6 | 1221 | #define HAVE_CSINHF 1 |
d08d4988 TB |
1222 | float complex csinhf (float complex a); |
1223 | ||
1409cd0b FXC |
1224 | float complex |
1225 | csinhf (float complex a) | |
1226 | { | |
1227 | float r, i; | |
1228 | float complex v; | |
1229 | ||
1230 | r = REALPART (a); | |
1231 | i = IMAGPART (a); | |
1232 | COMPLEX_ASSIGN (v, sinhf (r) * cosf (i), coshf (r) * sinf (i)); | |
1233 | return v; | |
1234 | } | |
1235 | #endif | |
1236 | ||
1237 | #if !defined(HAVE_CSINH) | |
2cdc88b6 | 1238 | #define HAVE_CSINH 1 |
d08d4988 TB |
1239 | double complex csinh (double complex a); |
1240 | ||
1409cd0b FXC |
1241 | double complex |
1242 | csinh (double complex a) | |
1243 | { | |
1244 | double r, i; | |
1245 | double complex v; | |
1246 | ||
1247 | r = REALPART (a); | |
1248 | i = IMAGPART (a); | |
1249 | COMPLEX_ASSIGN (v, sinh (r) * cos (i), cosh (r) * sin (i)); | |
1250 | return v; | |
1251 | } | |
1252 | #endif | |
1253 | ||
1254 | #if !defined(HAVE_CSINHL) && defined(HAVE_COSL) && defined(HAVE_COSHL) && defined(HAVE_SINL) && defined(HAVE_SINHL) | |
2cdc88b6 | 1255 | #define HAVE_CSINHL 1 |
d08d4988 TB |
1256 | long double complex csinhl (long double complex a); |
1257 | ||
1409cd0b FXC |
1258 | long double complex |
1259 | csinhl (long double complex a) | |
1260 | { | |
1261 | long double r, i; | |
1262 | long double complex v; | |
1263 | ||
1264 | r = REALPART (a); | |
1265 | i = IMAGPART (a); | |
1266 | COMPLEX_ASSIGN (v, sinhl (r) * cosl (i), coshl (r) * sinl (i)); | |
1267 | return v; | |
1268 | } | |
1269 | #endif | |
1270 | ||
1271 | ||
5bde96d2 | 1272 | /* cosh(a + i b) = cosh(a) cos(b) + i sinh(a) sin(b) */ |
1409cd0b | 1273 | #if !defined(HAVE_CCOSHF) |
2cdc88b6 | 1274 | #define HAVE_CCOSHF 1 |
d08d4988 TB |
1275 | float complex ccoshf (float complex a); |
1276 | ||
1409cd0b FXC |
1277 | float complex |
1278 | ccoshf (float complex a) | |
1279 | { | |
1280 | float r, i; | |
1281 | float complex v; | |
1282 | ||
1283 | r = REALPART (a); | |
1284 | i = IMAGPART (a); | |
5bde96d2 | 1285 | COMPLEX_ASSIGN (v, coshf (r) * cosf (i), sinhf (r) * sinf (i)); |
1409cd0b FXC |
1286 | return v; |
1287 | } | |
1288 | #endif | |
1289 | ||
1290 | #if !defined(HAVE_CCOSH) | |
2cdc88b6 | 1291 | #define HAVE_CCOSH 1 |
d08d4988 TB |
1292 | double complex ccosh (double complex a); |
1293 | ||
1409cd0b FXC |
1294 | double complex |
1295 | ccosh (double complex a) | |
1296 | { | |
1297 | double r, i; | |
1298 | double complex v; | |
1299 | ||
1300 | r = REALPART (a); | |
1301 | i = IMAGPART (a); | |
5bde96d2 | 1302 | COMPLEX_ASSIGN (v, cosh (r) * cos (i), sinh (r) * sin (i)); |
1409cd0b FXC |
1303 | return v; |
1304 | } | |
1305 | #endif | |
1306 | ||
1307 | #if !defined(HAVE_CCOSHL) && defined(HAVE_COSL) && defined(HAVE_COSHL) && defined(HAVE_SINL) && defined(HAVE_SINHL) | |
2cdc88b6 | 1308 | #define HAVE_CCOSHL 1 |
d08d4988 TB |
1309 | long double complex ccoshl (long double complex a); |
1310 | ||
1409cd0b FXC |
1311 | long double complex |
1312 | ccoshl (long double complex a) | |
1313 | { | |
1314 | long double r, i; | |
1315 | long double complex v; | |
1316 | ||
1317 | r = REALPART (a); | |
1318 | i = IMAGPART (a); | |
5bde96d2 | 1319 | COMPLEX_ASSIGN (v, coshl (r) * cosl (i), sinhl (r) * sinl (i)); |
1409cd0b FXC |
1320 | return v; |
1321 | } | |
1322 | #endif | |
1323 | ||
1324 | ||
5bde96d2 | 1325 | /* tanh(a + i b) = (tanh(a) + i tan(b)) / (1 + i tanh(a) tan(b)) */ |
1409cd0b | 1326 | #if !defined(HAVE_CTANHF) |
2cdc88b6 | 1327 | #define HAVE_CTANHF 1 |
d08d4988 TB |
1328 | float complex ctanhf (float complex a); |
1329 | ||
1409cd0b FXC |
1330 | float complex |
1331 | ctanhf (float complex a) | |
1332 | { | |
1333 | float rt, it; | |
1334 | float complex n, d; | |
1335 | ||
1336 | rt = tanhf (REALPART (a)); | |
1337 | it = tanf (IMAGPART (a)); | |
1338 | COMPLEX_ASSIGN (n, rt, it); | |
5bde96d2 | 1339 | COMPLEX_ASSIGN (d, 1, rt * it); |
1409cd0b FXC |
1340 | |
1341 | return n / d; | |
1342 | } | |
1343 | #endif | |
1344 | ||
1345 | #if !defined(HAVE_CTANH) | |
2cdc88b6 | 1346 | #define HAVE_CTANH 1 |
d08d4988 | 1347 | double complex ctanh (double complex a); |
1409cd0b FXC |
1348 | double complex |
1349 | ctanh (double complex a) | |
1350 | { | |
1351 | double rt, it; | |
1352 | double complex n, d; | |
1353 | ||
1354 | rt = tanh (REALPART (a)); | |
1355 | it = tan (IMAGPART (a)); | |
1356 | COMPLEX_ASSIGN (n, rt, it); | |
5bde96d2 | 1357 | COMPLEX_ASSIGN (d, 1, rt * it); |
1409cd0b FXC |
1358 | |
1359 | return n / d; | |
1360 | } | |
1361 | #endif | |
1362 | ||
1363 | #if !defined(HAVE_CTANHL) && defined(HAVE_TANL) && defined(HAVE_TANHL) | |
2cdc88b6 | 1364 | #define HAVE_CTANHL 1 |
d08d4988 TB |
1365 | long double complex ctanhl (long double complex a); |
1366 | ||
1409cd0b FXC |
1367 | long double complex |
1368 | ctanhl (long double complex a) | |
1369 | { | |
1370 | long double rt, it; | |
1371 | long double complex n, d; | |
1372 | ||
1373 | rt = tanhl (REALPART (a)); | |
1374 | it = tanl (IMAGPART (a)); | |
1375 | COMPLEX_ASSIGN (n, rt, it); | |
5bde96d2 | 1376 | COMPLEX_ASSIGN (d, 1, rt * it); |
1409cd0b FXC |
1377 | |
1378 | return n / d; | |
1379 | } | |
1380 | #endif | |
1381 | ||
1382 | ||
1383 | /* sin(a + i b) = sin(a) cosh(b) + i cos(a) sinh(b) */ | |
1384 | #if !defined(HAVE_CSINF) | |
2cdc88b6 | 1385 | #define HAVE_CSINF 1 |
d08d4988 TB |
1386 | float complex csinf (float complex a); |
1387 | ||
1409cd0b FXC |
1388 | float complex |
1389 | csinf (float complex a) | |
1390 | { | |
1391 | float r, i; | |
1392 | float complex v; | |
1393 | ||
1394 | r = REALPART (a); | |
1395 | i = IMAGPART (a); | |
1396 | COMPLEX_ASSIGN (v, sinf (r) * coshf (i), cosf (r) * sinhf (i)); | |
1397 | return v; | |
1398 | } | |
1399 | #endif | |
1400 | ||
1401 | #if !defined(HAVE_CSIN) | |
2cdc88b6 | 1402 | #define HAVE_CSIN 1 |
d08d4988 TB |
1403 | double complex csin (double complex a); |
1404 | ||
1409cd0b FXC |
1405 | double complex |
1406 | csin (double complex a) | |
1407 | { | |
1408 | double r, i; | |
1409 | double complex v; | |
1410 | ||
1411 | r = REALPART (a); | |
1412 | i = IMAGPART (a); | |
1413 | COMPLEX_ASSIGN (v, sin (r) * cosh (i), cos (r) * sinh (i)); | |
1414 | return v; | |
1415 | } | |
1416 | #endif | |
1417 | ||
1418 | #if !defined(HAVE_CSINL) && defined(HAVE_COSL) && defined(HAVE_COSHL) && defined(HAVE_SINL) && defined(HAVE_SINHL) | |
2cdc88b6 | 1419 | #define HAVE_CSINL 1 |
d08d4988 TB |
1420 | long double complex csinl (long double complex a); |
1421 | ||
1409cd0b FXC |
1422 | long double complex |
1423 | csinl (long double complex a) | |
1424 | { | |
1425 | long double r, i; | |
1426 | long double complex v; | |
1427 | ||
1428 | r = REALPART (a); | |
1429 | i = IMAGPART (a); | |
1430 | COMPLEX_ASSIGN (v, sinl (r) * coshl (i), cosl (r) * sinhl (i)); | |
1431 | return v; | |
1432 | } | |
1433 | #endif | |
1434 | ||
1435 | ||
1436 | /* cos(a + i b) = cos(a) cosh(b) - i sin(a) sinh(b) */ | |
1437 | #if !defined(HAVE_CCOSF) | |
2cdc88b6 | 1438 | #define HAVE_CCOSF 1 |
d08d4988 TB |
1439 | float complex ccosf (float complex a); |
1440 | ||
1409cd0b FXC |
1441 | float complex |
1442 | ccosf (float complex a) | |
1443 | { | |
1444 | float r, i; | |
1445 | float complex v; | |
1446 | ||
1447 | r = REALPART (a); | |
1448 | i = IMAGPART (a); | |
1449 | COMPLEX_ASSIGN (v, cosf (r) * coshf (i), - (sinf (r) * sinhf (i))); | |
1450 | return v; | |
1451 | } | |
1452 | #endif | |
1453 | ||
1454 | #if !defined(HAVE_CCOS) | |
2cdc88b6 | 1455 | #define HAVE_CCOS 1 |
d08d4988 TB |
1456 | double complex ccos (double complex a); |
1457 | ||
1409cd0b FXC |
1458 | double complex |
1459 | ccos (double complex a) | |
1460 | { | |
1461 | double r, i; | |
1462 | double complex v; | |
1463 | ||
1464 | r = REALPART (a); | |
1465 | i = IMAGPART (a); | |
1466 | COMPLEX_ASSIGN (v, cos (r) * cosh (i), - (sin (r) * sinh (i))); | |
1467 | return v; | |
1468 | } | |
1469 | #endif | |
1470 | ||
1471 | #if !defined(HAVE_CCOSL) && defined(HAVE_COSL) && defined(HAVE_COSHL) && defined(HAVE_SINL) && defined(HAVE_SINHL) | |
2cdc88b6 | 1472 | #define HAVE_CCOSL 1 |
d08d4988 TB |
1473 | long double complex ccosl (long double complex a); |
1474 | ||
1409cd0b FXC |
1475 | long double complex |
1476 | ccosl (long double complex a) | |
1477 | { | |
1478 | long double r, i; | |
1479 | long double complex v; | |
1480 | ||
1481 | r = REALPART (a); | |
1482 | i = IMAGPART (a); | |
1483 | COMPLEX_ASSIGN (v, cosl (r) * coshl (i), - (sinl (r) * sinhl (i))); | |
1484 | return v; | |
1485 | } | |
1486 | #endif | |
1487 | ||
1488 | ||
1489 | /* tan(a + i b) = (tan(a) + i tanh(b)) / (1 - i tan(a) tanh(b)) */ | |
1490 | #if !defined(HAVE_CTANF) | |
2cdc88b6 | 1491 | #define HAVE_CTANF 1 |
d08d4988 TB |
1492 | float complex ctanf (float complex a); |
1493 | ||
1409cd0b FXC |
1494 | float complex |
1495 | ctanf (float complex a) | |
1496 | { | |
1497 | float rt, it; | |
1498 | float complex n, d; | |
1499 | ||
1500 | rt = tanf (REALPART (a)); | |
1501 | it = tanhf (IMAGPART (a)); | |
1502 | COMPLEX_ASSIGN (n, rt, it); | |
1503 | COMPLEX_ASSIGN (d, 1, - (rt * it)); | |
1504 | ||
1505 | return n / d; | |
1506 | } | |
1507 | #endif | |
1508 | ||
1509 | #if !defined(HAVE_CTAN) | |
2cdc88b6 | 1510 | #define HAVE_CTAN 1 |
d08d4988 TB |
1511 | double complex ctan (double complex a); |
1512 | ||
1409cd0b FXC |
1513 | double complex |
1514 | ctan (double complex a) | |
1515 | { | |
1516 | double rt, it; | |
1517 | double complex n, d; | |
1518 | ||
1519 | rt = tan (REALPART (a)); | |
1520 | it = tanh (IMAGPART (a)); | |
1521 | COMPLEX_ASSIGN (n, rt, it); | |
1522 | COMPLEX_ASSIGN (d, 1, - (rt * it)); | |
1523 | ||
1524 | return n / d; | |
1525 | } | |
1526 | #endif | |
1527 | ||
1528 | #if !defined(HAVE_CTANL) && defined(HAVE_TANL) && defined(HAVE_TANHL) | |
2cdc88b6 | 1529 | #define HAVE_CTANL 1 |
d08d4988 TB |
1530 | long double complex ctanl (long double complex a); |
1531 | ||
1409cd0b FXC |
1532 | long double complex |
1533 | ctanl (long double complex a) | |
1534 | { | |
1535 | long double rt, it; | |
1536 | long double complex n, d; | |
1537 | ||
1538 | rt = tanl (REALPART (a)); | |
1539 | it = tanhl (IMAGPART (a)); | |
1540 | COMPLEX_ASSIGN (n, rt, it); | |
1541 | COMPLEX_ASSIGN (d, 1, - (rt * it)); | |
1542 | ||
1543 | return n / d; | |
1544 | } | |
1545 | #endif | |
1546 | ||
fb0a0e15 | 1547 | |
504ed63a TB |
1548 | /* Complex ASIN. Returns wrongly NaN for infinite arguments. |
1549 | Algorithm taken from Abramowitz & Stegun. */ | |
1550 | ||
1551 | #if !defined(HAVE_CASINF) && defined(HAVE_CLOGF) && defined(HAVE_CSQRTF) | |
1552 | #define HAVE_CASINF 1 | |
d08d4988 TB |
1553 | complex float casinf (complex float z); |
1554 | ||
504ed63a TB |
1555 | complex float |
1556 | casinf (complex float z) | |
1557 | { | |
1558 | return -I*clogf (I*z + csqrtf (1.0f-z*z)); | |
1559 | } | |
1560 | #endif | |
1561 | ||
1562 | ||
1563 | #if !defined(HAVE_CASIN) && defined(HAVE_CLOG) && defined(HAVE_CSQRT) | |
1564 | #define HAVE_CASIN 1 | |
d08d4988 TB |
1565 | complex double casin (complex double z); |
1566 | ||
504ed63a TB |
1567 | complex double |
1568 | casin (complex double z) | |
1569 | { | |
1570 | return -I*clog (I*z + csqrt (1.0-z*z)); | |
1571 | } | |
1572 | #endif | |
1573 | ||
1574 | ||
1575 | #if !defined(HAVE_CASINL) && defined(HAVE_CLOGL) && defined(HAVE_CSQRTL) | |
1576 | #define HAVE_CASINL 1 | |
d08d4988 TB |
1577 | complex long double casinl (complex long double z); |
1578 | ||
504ed63a TB |
1579 | complex long double |
1580 | casinl (complex long double z) | |
1581 | { | |
1582 | return -I*clogl (I*z + csqrtl (1.0L-z*z)); | |
1583 | } | |
1584 | #endif | |
1585 | ||
1586 | ||
1587 | /* Complex ACOS. Returns wrongly NaN for infinite arguments. | |
1588 | Algorithm taken from Abramowitz & Stegun. */ | |
1589 | ||
1590 | #if !defined(HAVE_CACOSF) && defined(HAVE_CLOGF) && defined(HAVE_CSQRTF) | |
1591 | #define HAVE_CACOSF 1 | |
d08d4988 TB |
1592 | complex float cacosf (complex float z); |
1593 | ||
504ed63a TB |
1594 | complex float |
1595 | cacosf (complex float z) | |
1596 | { | |
d08d4988 | 1597 | return -I*clogf (z + I*csqrtf (1.0f-z*z)); |
504ed63a TB |
1598 | } |
1599 | #endif | |
1600 | ||
1601 | ||
504ed63a TB |
1602 | #if !defined(HAVE_CACOS) && defined(HAVE_CLOG) && defined(HAVE_CSQRT) |
1603 | #define HAVE_CACOS 1 | |
d08d4988 TB |
1604 | complex double cacos (complex double z); |
1605 | ||
1606 | complex double | |
504ed63a TB |
1607 | cacos (complex double z) |
1608 | { | |
1609 | return -I*clog (z + I*csqrt (1.0-z*z)); | |
1610 | } | |
1611 | #endif | |
1612 | ||
1613 | ||
1614 | #if !defined(HAVE_CACOSL) && defined(HAVE_CLOGL) && defined(HAVE_CSQRTL) | |
1615 | #define HAVE_CACOSL 1 | |
d08d4988 TB |
1616 | complex long double cacosl (complex long double z); |
1617 | ||
504ed63a TB |
1618 | complex long double |
1619 | cacosl (complex long double z) | |
1620 | { | |
1621 | return -I*clogl (z + I*csqrtl (1.0L-z*z)); | |
1622 | } | |
1623 | #endif | |
1624 | ||
1625 | ||
1626 | /* Complex ATAN. Returns wrongly NaN for infinite arguments. | |
1627 | Algorithm taken from Abramowitz & Stegun. */ | |
1628 | ||
1629 | #if !defined(HAVE_CATANF) && defined(HAVE_CLOGF) | |
1630 | #define HAVE_CACOSF 1 | |
d08d4988 TB |
1631 | complex float catanf (complex float z); |
1632 | ||
504ed63a TB |
1633 | complex float |
1634 | catanf (complex float z) | |
1635 | { | |
1636 | return I*clogf ((I+z)/(I-z))/2.0f; | |
1637 | } | |
1638 | #endif | |
1639 | ||
1640 | ||
1641 | #if !defined(HAVE_CATAN) && defined(HAVE_CLOG) | |
1642 | #define HAVE_CACOS 1 | |
d08d4988 TB |
1643 | complex double catan (complex double z); |
1644 | ||
504ed63a TB |
1645 | complex double |
1646 | catan (complex double z) | |
1647 | { | |
1648 | return I*clog ((I+z)/(I-z))/2.0; | |
1649 | } | |
1650 | #endif | |
1651 | ||
1652 | ||
1653 | #if !defined(HAVE_CATANL) && defined(HAVE_CLOGL) | |
1654 | #define HAVE_CACOSL 1 | |
d08d4988 TB |
1655 | complex long double catanl (complex long double z); |
1656 | ||
504ed63a TB |
1657 | complex long double |
1658 | catanl (complex long double z) | |
1659 | { | |
1660 | return I*clogl ((I+z)/(I-z))/2.0L; | |
1661 | } | |
1662 | #endif | |
1663 | ||
1664 | ||
1665 | /* Complex ASINH. Returns wrongly NaN for infinite arguments. | |
1666 | Algorithm taken from Abramowitz & Stegun. */ | |
1667 | ||
1668 | #if !defined(HAVE_CASINHF) && defined(HAVE_CLOGF) && defined(HAVE_CSQRTF) | |
1669 | #define HAVE_CASINHF 1 | |
d08d4988 TB |
1670 | complex float casinhf (complex float z); |
1671 | ||
504ed63a TB |
1672 | complex float |
1673 | casinhf (complex float z) | |
1674 | { | |
1675 | return clogf (z + csqrtf (z*z+1.0f)); | |
1676 | } | |
1677 | #endif | |
1678 | ||
1679 | ||
1680 | #if !defined(HAVE_CASINH) && defined(HAVE_CLOG) && defined(HAVE_CSQRT) | |
1681 | #define HAVE_CASINH 1 | |
d08d4988 TB |
1682 | complex double casinh (complex double z); |
1683 | ||
504ed63a TB |
1684 | complex double |
1685 | casinh (complex double z) | |
1686 | { | |
1687 | return clog (z + csqrt (z*z+1.0)); | |
1688 | } | |
1689 | #endif | |
1690 | ||
1691 | ||
1692 | #if !defined(HAVE_CASINHL) && defined(HAVE_CLOGL) && defined(HAVE_CSQRTL) | |
1693 | #define HAVE_CASINHL 1 | |
d08d4988 TB |
1694 | complex long double casinhl (complex long double z); |
1695 | ||
504ed63a TB |
1696 | complex long double |
1697 | casinhl (complex long double z) | |
1698 | { | |
1699 | return clogl (z + csqrtl (z*z+1.0L)); | |
1700 | } | |
1701 | #endif | |
1702 | ||
1703 | ||
1704 | /* Complex ACOSH. Returns wrongly NaN for infinite arguments. | |
1705 | Algorithm taken from Abramowitz & Stegun. */ | |
1706 | ||
1707 | #if !defined(HAVE_CACOSHF) && defined(HAVE_CLOGF) && defined(HAVE_CSQRTF) | |
1708 | #define HAVE_CACOSHF 1 | |
d08d4988 TB |
1709 | complex float cacoshf (complex float z); |
1710 | ||
504ed63a TB |
1711 | complex float |
1712 | cacoshf (complex float z) | |
1713 | { | |
1714 | return clogf (z + csqrtf (z-1.0f) * csqrtf (z+1.0f)); | |
1715 | } | |
1716 | #endif | |
1717 | ||
1718 | ||
1719 | #if !defined(HAVE_CACOSH) && defined(HAVE_CLOG) && defined(HAVE_CSQRT) | |
1720 | #define HAVE_CACOSH 1 | |
d08d4988 TB |
1721 | complex double cacosh (complex double z); |
1722 | ||
504ed63a TB |
1723 | complex double |
1724 | cacosh (complex double z) | |
1725 | { | |
1726 | return clog (z + csqrt (z-1.0) * csqrt (z+1.0)); | |
1727 | } | |
1728 | #endif | |
1729 | ||
1730 | ||
1731 | #if !defined(HAVE_CACOSHL) && defined(HAVE_CLOGL) && defined(HAVE_CSQRTL) | |
1732 | #define HAVE_CACOSHL 1 | |
d08d4988 TB |
1733 | complex long double cacoshl (complex long double z); |
1734 | ||
504ed63a TB |
1735 | complex long double |
1736 | cacoshl (complex long double z) | |
1737 | { | |
1738 | return clogl (z + csqrtl (z-1.0L) * csqrtl (z+1.0L)); | |
1739 | } | |
1740 | #endif | |
1741 | ||
1742 | ||
1743 | /* Complex ATANH. Returns wrongly NaN for infinite arguments. | |
1744 | Algorithm taken from Abramowitz & Stegun. */ | |
1745 | ||
1746 | #if !defined(HAVE_CATANHF) && defined(HAVE_CLOGF) | |
1747 | #define HAVE_CATANHF 1 | |
d08d4988 TB |
1748 | complex float catanhf (complex float z); |
1749 | ||
504ed63a TB |
1750 | complex float |
1751 | catanhf (complex float z) | |
1752 | { | |
1753 | return clogf ((1.0f+z)/(1.0f-z))/2.0f; | |
1754 | } | |
1755 | #endif | |
1756 | ||
1757 | ||
1758 | #if !defined(HAVE_CATANH) && defined(HAVE_CLOG) | |
1759 | #define HAVE_CATANH 1 | |
d08d4988 TB |
1760 | complex double catanh (complex double z); |
1761 | ||
504ed63a TB |
1762 | complex double |
1763 | catanh (complex double z) | |
1764 | { | |
1765 | return clog ((1.0+z)/(1.0-z))/2.0; | |
1766 | } | |
1767 | #endif | |
1768 | ||
1769 | #if !defined(HAVE_CATANHL) && defined(HAVE_CLOGL) | |
1770 | #define HAVE_CATANHL 1 | |
d08d4988 TB |
1771 | complex long double catanhl (complex long double z); |
1772 | ||
504ed63a TB |
1773 | complex long double |
1774 | catanhl (complex long double z) | |
1775 | { | |
1776 | return clogl ((1.0L+z)/(1.0L-z))/2.0L; | |
1777 | } | |
1778 | #endif | |
1779 | ||
1780 | ||
fb0a0e15 FXC |
1781 | #if !defined(HAVE_TGAMMA) |
1782 | #define HAVE_TGAMMA 1 | |
d08d4988 | 1783 | double tgamma (double); |
fb0a0e15 FXC |
1784 | |
1785 | /* Fallback tgamma() function. Uses the algorithm from | |
1786 | http://www.netlib.org/specfun/gamma and references therein. */ | |
1787 | ||
1788 | #undef SQRTPI | |
1789 | #define SQRTPI 0.9189385332046727417803297 | |
1790 | ||
1791 | #undef PI | |
1792 | #define PI 3.1415926535897932384626434 | |
1793 | ||
1794 | double | |
1795 | tgamma (double x) | |
1796 | { | |
1797 | int i, n, parity; | |
1798 | double fact, res, sum, xden, xnum, y, y1, ysq, z; | |
1799 | ||
1800 | static double p[8] = { | |
1801 | -1.71618513886549492533811e0, 2.47656508055759199108314e1, | |
1802 | -3.79804256470945635097577e2, 6.29331155312818442661052e2, | |
1803 | 8.66966202790413211295064e2, -3.14512729688483675254357e4, | |
1804 | -3.61444134186911729807069e4, 6.64561438202405440627855e4 }; | |
1805 | ||
1806 | static double q[8] = { | |
1807 | -3.08402300119738975254353e1, 3.15350626979604161529144e2, | |
1808 | -1.01515636749021914166146e3, -3.10777167157231109440444e3, | |
1809 | 2.25381184209801510330112e4, 4.75584627752788110767815e3, | |
1810 | -1.34659959864969306392456e5, -1.15132259675553483497211e5 }; | |
1811 | ||
1812 | static double c[7] = { -1.910444077728e-03, | |
1813 | 8.4171387781295e-04, -5.952379913043012e-04, | |
1814 | 7.93650793500350248e-04, -2.777777777777681622553e-03, | |
1815 | 8.333333333333333331554247e-02, 5.7083835261e-03 }; | |
1816 | ||
1817 | static const double xminin = 2.23e-308; | |
1818 | static const double xbig = 171.624; | |
1819 | static const double xnan = __builtin_nan ("0x0"), xinf = __builtin_inf (); | |
1820 | static double eps = 0; | |
1821 | ||
1822 | if (eps == 0) | |
d08d4988 | 1823 | eps = nextafter (1., 2.) - 1.; |
fb0a0e15 FXC |
1824 | |
1825 | parity = 0; | |
1826 | fact = 1; | |
1827 | n = 0; | |
1828 | y = x; | |
1829 | ||
b1012ca4 | 1830 | if (isnan (x)) |
fb0a0e15 FXC |
1831 | return x; |
1832 | ||
1833 | if (y <= 0) | |
1834 | { | |
1835 | y = -x; | |
d08d4988 | 1836 | y1 = trunc (y); |
fb0a0e15 FXC |
1837 | res = y - y1; |
1838 | ||
1839 | if (res != 0) | |
1840 | { | |
d08d4988 | 1841 | if (y1 != trunc (y1*0.5l)*2) |
fb0a0e15 | 1842 | parity = 1; |
d08d4988 | 1843 | fact = -PI / sin (PI*res); |
fb0a0e15 FXC |
1844 | y = y + 1; |
1845 | } | |
1846 | else | |
1847 | return x == 0 ? copysign (xinf, x) : xnan; | |
1848 | } | |
1849 | ||
1850 | if (y < eps) | |
1851 | { | |
1852 | if (y >= xminin) | |
1853 | res = 1 / y; | |
1854 | else | |
1855 | return xinf; | |
1856 | } | |
1857 | else if (y < 13) | |
1858 | { | |
1859 | y1 = y; | |
1860 | if (y < 1) | |
1861 | { | |
1862 | z = y; | |
1863 | y = y + 1; | |
1864 | } | |
1865 | else | |
1866 | { | |
1867 | n = (int)y - 1; | |
1868 | y = y - n; | |
1869 | z = y - 1; | |
1870 | } | |
1871 | ||
1872 | xnum = 0; | |
1873 | xden = 1; | |
1874 | for (i = 0; i < 8; i++) | |
1875 | { | |
1876 | xnum = (xnum + p[i]) * z; | |
1877 | xden = xden * z + q[i]; | |
1878 | } | |
1879 | ||
1880 | res = xnum / xden + 1; | |
1881 | ||
1882 | if (y1 < y) | |
1883 | res = res / y1; | |
1884 | else if (y1 > y) | |
1885 | for (i = 1; i <= n; i++) | |
1886 | { | |
1887 | res = res * y; | |
1888 | y = y + 1; | |
1889 | } | |
1890 | } | |
1891 | else | |
1892 | { | |
1893 | if (y < xbig) | |
1894 | { | |
1895 | ysq = y * y; | |
1896 | sum = c[6]; | |
1897 | for (i = 0; i < 6; i++) | |
1898 | sum = sum / ysq + c[i]; | |
1899 | ||
1900 | sum = sum/y - y + SQRTPI; | |
d08d4988 TB |
1901 | sum = sum + (y - 0.5) * log (y); |
1902 | res = exp (sum); | |
fb0a0e15 FXC |
1903 | } |
1904 | else | |
1905 | return x < 0 ? xnan : xinf; | |
1906 | } | |
1907 | ||
1908 | if (parity) | |
1909 | res = -res; | |
1910 | if (fact != 1) | |
1911 | res = fact / res; | |
1912 | ||
1913 | return res; | |
1914 | } | |
1915 | #endif | |
1916 | ||
1917 | ||
1918 | ||
1919 | #if !defined(HAVE_LGAMMA) | |
1920 | #define HAVE_LGAMMA 1 | |
d08d4988 | 1921 | double lgamma (double); |
fb0a0e15 FXC |
1922 | |
1923 | /* Fallback lgamma() function. Uses the algorithm from | |
1924 | http://www.netlib.org/specfun/algama and references therein, | |
1925 | except for negative arguments (where netlib would return +Inf) | |
1926 | where we use the following identity: | |
1927 | lgamma(y) = log(pi/(|y*sin(pi*y)|)) - lgamma(-y) | |
1928 | */ | |
1929 | ||
1930 | double | |
1931 | lgamma (double y) | |
1932 | { | |
1933 | ||
1934 | #undef SQRTPI | |
1935 | #define SQRTPI 0.9189385332046727417803297 | |
1936 | ||
1937 | #undef PI | |
1938 | #define PI 3.1415926535897932384626434 | |
1939 | ||
1940 | #define PNT68 0.6796875 | |
1941 | #define D1 -0.5772156649015328605195174 | |
1942 | #define D2 0.4227843350984671393993777 | |
1943 | #define D4 1.791759469228055000094023 | |
1944 | ||
1945 | static double p1[8] = { | |
1946 | 4.945235359296727046734888e0, 2.018112620856775083915565e2, | |
1947 | 2.290838373831346393026739e3, 1.131967205903380828685045e4, | |
1948 | 2.855724635671635335736389e4, 3.848496228443793359990269e4, | |
1949 | 2.637748787624195437963534e4, 7.225813979700288197698961e3 }; | |
1950 | static double q1[8] = { | |
1951 | 6.748212550303777196073036e1, 1.113332393857199323513008e3, | |
1952 | 7.738757056935398733233834e3, 2.763987074403340708898585e4, | |
1953 | 5.499310206226157329794414e4, 6.161122180066002127833352e4, | |
1954 | 3.635127591501940507276287e4, 8.785536302431013170870835e3 }; | |
1955 | static double p2[8] = { | |
1956 | 4.974607845568932035012064e0, 5.424138599891070494101986e2, | |
1957 | 1.550693864978364947665077e4, 1.847932904445632425417223e5, | |
1958 | 1.088204769468828767498470e6, 3.338152967987029735917223e6, | |
1959 | 5.106661678927352456275255e6, 3.074109054850539556250927e6 }; | |
1960 | static double q2[8] = { | |
1961 | 1.830328399370592604055942e2, 7.765049321445005871323047e3, | |
1962 | 1.331903827966074194402448e5, 1.136705821321969608938755e6, | |
1963 | 5.267964117437946917577538e6, 1.346701454311101692290052e7, | |
1964 | 1.782736530353274213975932e7, 9.533095591844353613395747e6 }; | |
1965 | static double p4[8] = { | |
1966 | 1.474502166059939948905062e4, 2.426813369486704502836312e6, | |
1967 | 1.214755574045093227939592e8, 2.663432449630976949898078e9, | |
1968 | 2.940378956634553899906876e10, 1.702665737765398868392998e11, | |
1969 | 4.926125793377430887588120e11, 5.606251856223951465078242e11 }; | |
1970 | static double q4[8] = { | |
1971 | 2.690530175870899333379843e3, 6.393885654300092398984238e5, | |
1972 | 4.135599930241388052042842e7, 1.120872109616147941376570e9, | |
1973 | 1.488613728678813811542398e10, 1.016803586272438228077304e11, | |
1974 | 3.417476345507377132798597e11, 4.463158187419713286462081e11 }; | |
1975 | static double c[7] = { | |
1976 | -1.910444077728e-03, 8.4171387781295e-04, | |
1977 | -5.952379913043012e-04, 7.93650793500350248e-04, | |
1978 | -2.777777777777681622553e-03, 8.333333333333333331554247e-02, | |
1979 | 5.7083835261e-03 }; | |
1980 | ||
1981 | static double xbig = 2.55e305, xinf = __builtin_inf (), eps = 0, | |
1982 | frtbig = 2.25e76; | |
1983 | ||
1984 | int i; | |
1985 | double corr, res, xden, xm1, xm2, xm4, xnum, ysq; | |
1986 | ||
1987 | if (eps == 0) | |
d08d4988 | 1988 | eps = __builtin_nextafter (1., 2.) - 1.; |
fb0a0e15 FXC |
1989 | |
1990 | if ((y > 0) && (y <= xbig)) | |
1991 | { | |
1992 | if (y <= eps) | |
d08d4988 | 1993 | res = -log (y); |
fb0a0e15 FXC |
1994 | else if (y <= 1.5) |
1995 | { | |
1996 | if (y < PNT68) | |
1997 | { | |
d08d4988 | 1998 | corr = -log (y); |
fb0a0e15 FXC |
1999 | xm1 = y; |
2000 | } | |
2001 | else | |
2002 | { | |
2003 | corr = 0; | |
2004 | xm1 = (y - 0.5) - 0.5; | |
2005 | } | |
2006 | ||
2007 | if ((y <= 0.5) || (y >= PNT68)) | |
2008 | { | |
2009 | xden = 1; | |
2010 | xnum = 0; | |
2011 | for (i = 0; i < 8; i++) | |
2012 | { | |
2013 | xnum = xnum*xm1 + p1[i]; | |
2014 | xden = xden*xm1 + q1[i]; | |
2015 | } | |
2016 | res = corr + (xm1 * (D1 + xm1*(xnum/xden))); | |
2017 | } | |
2018 | else | |
2019 | { | |
2020 | xm2 = (y - 0.5) - 0.5; | |
2021 | xden = 1; | |
2022 | xnum = 0; | |
2023 | for (i = 0; i < 8; i++) | |
2024 | { | |
2025 | xnum = xnum*xm2 + p2[i]; | |
2026 | xden = xden*xm2 + q2[i]; | |
2027 | } | |
2028 | res = corr + xm2 * (D2 + xm2*(xnum/xden)); | |
2029 | } | |
2030 | } | |
2031 | else if (y <= 4) | |
2032 | { | |
2033 | xm2 = y - 2; | |
2034 | xden = 1; | |
2035 | xnum = 0; | |
2036 | for (i = 0; i < 8; i++) | |
2037 | { | |
2038 | xnum = xnum*xm2 + p2[i]; | |
2039 | xden = xden*xm2 + q2[i]; | |
2040 | } | |
2041 | res = xm2 * (D2 + xm2*(xnum/xden)); | |
2042 | } | |
2043 | else if (y <= 12) | |
2044 | { | |
2045 | xm4 = y - 4; | |
2046 | xden = -1; | |
2047 | xnum = 0; | |
2048 | for (i = 0; i < 8; i++) | |
2049 | { | |
2050 | xnum = xnum*xm4 + p4[i]; | |
2051 | xden = xden*xm4 + q4[i]; | |
2052 | } | |
2053 | res = D4 + xm4*(xnum/xden); | |
2054 | } | |
2055 | else | |
2056 | { | |
2057 | res = 0; | |
2058 | if (y <= frtbig) | |
2059 | { | |
2060 | res = c[6]; | |
2061 | ysq = y * y; | |
2062 | for (i = 0; i < 6; i++) | |
2063 | res = res / ysq + c[i]; | |
2064 | } | |
2065 | res = res/y; | |
d08d4988 | 2066 | corr = log (y); |
fb0a0e15 FXC |
2067 | res = res + SQRTPI - 0.5*corr; |
2068 | res = res + y*(corr-1); | |
2069 | } | |
2070 | } | |
2071 | else if (y < 0 && __builtin_floor (y) != y) | |
2072 | { | |
2073 | /* lgamma(y) = log(pi/(|y*sin(pi*y)|)) - lgamma(-y) | |
2074 | For abs(y) very close to zero, we use a series expansion to | |
2075 | the first order in y to avoid overflow. */ | |
2076 | if (y > -1.e-100) | |
2077 | res = -2 * log (fabs (y)) - lgamma (-y); | |
2078 | else | |
2079 | res = log (PI / fabs (y * sin (PI * y))) - lgamma (-y); | |
2080 | } | |
2081 | else | |
2082 | res = xinf; | |
2083 | ||
2084 | return res; | |
2085 | } | |
2086 | #endif | |
2087 | ||
2088 | ||
2089 | #if defined(HAVE_TGAMMA) && !defined(HAVE_TGAMMAF) | |
2090 | #define HAVE_TGAMMAF 1 | |
d08d4988 | 2091 | float tgammaf (float); |
fb0a0e15 FXC |
2092 | |
2093 | float | |
2094 | tgammaf (float x) | |
2095 | { | |
2096 | return (float) tgamma ((double) x); | |
2097 | } | |
2098 | #endif | |
2099 | ||
2100 | #if defined(HAVE_LGAMMA) && !defined(HAVE_LGAMMAF) | |
2101 | #define HAVE_LGAMMAF 1 | |
d08d4988 | 2102 | float lgammaf (float); |
fb0a0e15 FXC |
2103 | |
2104 | float | |
2105 | lgammaf (float x) | |
2106 | { | |
2107 | return (float) lgamma ((double) x); | |
2108 | } | |
2109 | #endif |