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
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
|
diff --git a/fdlibm.h b/fdlibm.h
--- a/fdlibm.h
+++ b/fdlibm.h
@@ -12,504 +12,66 @@
/*
* from: @(#)fdlibm.h 5.1 93/09/24
* $FreeBSD$
*/
#ifndef _MATH_H_
#define _MATH_H_
-#include <sys/cdefs.h>
-#include <sys/_types.h>
-#include <machine/_limits.h>
-
-/*
- * ANSI/POSIX
- */
-extern const union __infinity_un {
- unsigned char __uc[8];
- double __ud;
-} __infinity;
-
-extern const union __nan_un {
- unsigned char __uc[sizeof(float)];
- float __uf;
-} __nan;
-
-#if __GNUC_PREREQ__(3, 3)
-#define __MATH_BUILTIN_CONSTANTS
-#endif
-
-#if __GNUC_PREREQ__(3, 0)
-#define __MATH_BUILTIN_RELOPS
-#endif
-
-#ifdef __MATH_BUILTIN_CONSTANTS
-#define HUGE_VAL __builtin_huge_val()
-#else
-#define HUGE_VAL (__infinity.__ud)
-#endif
-
-#if __ISO_C_VISIBLE >= 1999
-#define FP_ILOGB0 (-__INT_MAX)
-#define FP_ILOGBNAN __INT_MAX
-
-#ifdef __MATH_BUILTIN_CONSTANTS
-#define HUGE_VALF __builtin_huge_valf()
-#define HUGE_VALL __builtin_huge_vall()
-#define INFINITY __builtin_inff()
-#define NAN __builtin_nanf("")
-#else
-#define HUGE_VALF (float)HUGE_VAL
-#define HUGE_VALL (long double)HUGE_VAL
-#define INFINITY HUGE_VALF
-#define NAN (__nan.__uf)
-#endif /* __MATH_BUILTIN_CONSTANTS */
-
-#define MATH_ERRNO 1
-#define MATH_ERREXCEPT 2
-#define math_errhandling MATH_ERREXCEPT
-
-#define FP_FAST_FMAF 1
-
-/* Symbolic constants to classify floating point numbers. */
-#define FP_INFINITE 0x01
-#define FP_NAN 0x02
-#define FP_NORMAL 0x04
-#define FP_SUBNORMAL 0x08
-#define FP_ZERO 0x10
-
-#if __STDC_VERSION__ >= 201112L || __has_extension(c_generic_selections)
-#define __fp_type_select(x, f, d, ld) __extension__ _Generic((x), \
- float: f(x), \
- double: d(x), \
- long double: ld(x))
-#elif __GNUC_PREREQ__(3, 1) && !defined(__cplusplus)
-#define __fp_type_select(x, f, d, ld) __builtin_choose_expr( \
- __builtin_types_compatible_p(__typeof(x), long double), ld(x), \
- __builtin_choose_expr( \
- __builtin_types_compatible_p(__typeof(x), double), d(x), \
- __builtin_choose_expr( \
- __builtin_types_compatible_p(__typeof(x), float), f(x), (void)0)))
-#else
-#define __fp_type_select(x, f, d, ld) \
- ((sizeof(x) == sizeof(float)) ? f(x) \
- : (sizeof(x) == sizeof(double)) ? d(x) \
- : ld(x))
-#endif
-
-#define fpclassify(x) \
- __fp_type_select(x, __fpclassifyf, __fpclassifyd, __fpclassifyl)
-#define isfinite(x) __fp_type_select(x, __isfinitef, __isfinite, __isfinitel)
-#define isinf(x) __fp_type_select(x, __isinff, __isinf, __isinfl)
-#define isnan(x) \
- __fp_type_select(x, __inline_isnanf, __inline_isnan, __inline_isnanl)
-#define isnormal(x) __fp_type_select(x, __isnormalf, __isnormal, __isnormall)
-
-#ifdef __MATH_BUILTIN_RELOPS
-#define isgreater(x, y) __builtin_isgreater((x), (y))
-#define isgreaterequal(x, y) __builtin_isgreaterequal((x), (y))
-#define isless(x, y) __builtin_isless((x), (y))
-#define islessequal(x, y) __builtin_islessequal((x), (y))
-#define islessgreater(x, y) __builtin_islessgreater((x), (y))
-#define isunordered(x, y) __builtin_isunordered((x), (y))
-#else
-#define isgreater(x, y) (!isunordered((x), (y)) && (x) > (y))
-#define isgreaterequal(x, y) (!isunordered((x), (y)) && (x) >= (y))
-#define isless(x, y) (!isunordered((x), (y)) && (x) < (y))
-#define islessequal(x, y) (!isunordered((x), (y)) && (x) <= (y))
-#define islessgreater(x, y) (!isunordered((x), (y)) && \
- ((x) > (y) || (y) > (x)))
-#define isunordered(x, y) (isnan(x) || isnan(y))
-#endif /* __MATH_BUILTIN_RELOPS */
-
-#define signbit(x) __fp_type_select(x, __signbitf, __signbit, __signbitl)
-
-typedef __double_t double_t;
-typedef __float_t float_t;
-#endif /* __ISO_C_VISIBLE >= 1999 */
-
-/*
- * XOPEN/SVID
- */
-#if __BSD_VISIBLE || __XSI_VISIBLE
-#define M_E 2.7182818284590452354 /* e */
-#define M_LOG2E 1.4426950408889634074 /* log 2e */
-#define M_LOG10E 0.43429448190325182765 /* log 10e */
-#define M_LN2 0.69314718055994530942 /* log e2 */
-#define M_LN10 2.30258509299404568402 /* log e10 */
-#define M_PI 3.14159265358979323846 /* pi */
#define M_PI_2 1.57079632679489661923 /* pi/2 */
-#define M_PI_4 0.78539816339744830962 /* pi/4 */
-#define M_1_PI 0.31830988618379067154 /* 1/pi */
-#define M_2_PI 0.63661977236758134308 /* 2/pi */
-#define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
-#define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
-#define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
-
-#define MAXFLOAT ((float)3.40282346638528860e+38)
-extern int signgam;
-#endif /* __BSD_VISIBLE || __XSI_VISIBLE */
-
-#if __BSD_VISIBLE
-#if 0
-/* Old value from 4.4BSD-Lite math.h; this is probably better. */
-#define HUGE HUGE_VAL
-#else
-#define HUGE MAXFLOAT
-#endif
-#endif /* __BSD_VISIBLE */
-
-/*
- * Most of these functions depend on the rounding mode and have the side
- * effect of raising floating-point exceptions, so they are not declared
- * as __pure2. In C99, FENV_ACCESS affects the purity of these functions.
- */
-__BEGIN_DECLS
-/*
- * ANSI/POSIX
- */
-int __fpclassifyd(double) __pure2;
-int __fpclassifyf(float) __pure2;
-int __fpclassifyl(long double) __pure2;
-int __isfinitef(float) __pure2;
-int __isfinite(double) __pure2;
-int __isfinitel(long double) __pure2;
-int __isinff(float) __pure2;
-int __isinf(double) __pure2;
-int __isinfl(long double) __pure2;
-int __isnormalf(float) __pure2;
-int __isnormal(double) __pure2;
-int __isnormall(long double) __pure2;
-int __signbit(double) __pure2;
-int __signbitf(float) __pure2;
-int __signbitl(long double) __pure2;
-
-static __inline int
-__inline_isnan(__const double __x)
-{
-
- return (__x != __x);
-}
-
-static __inline int
-__inline_isnanf(__const float __x)
-{
-
- return (__x != __x);
-}
-
-static __inline int
-__inline_isnanl(__const long double __x)
-{
-
- return (__x != __x);
-}
-
-/*
- * Define the following aliases, for compatibility with glibc and CUDA.
- */
-#define __isnan __inline_isnan
-#define __isnanf __inline_isnanf
-
-/*
- * Version 2 of the Single UNIX Specification (UNIX98) defined isnan() and
- * isinf() as functions taking double. C99, and the subsequent POSIX revisions
- * (SUSv3, POSIX.1-2001, define it as a macro that accepts any real floating
- * point type. If we are targeting SUSv2 and C99 or C11 (or C++11) then we
- * expose the newer definition, assuming that the language spec takes
- * precedence over the operating system interface spec.
- */
-#if __XSI_VISIBLE > 0 && __XSI_VISIBLE < 600 && __ISO_C_VISIBLE < 1999
-#undef isinf
-#undef isnan
-int isinf(double);
-int isnan(double);
-#endif
-
double acos(double);
double asin(double);
double atan(double);
double atan2(double, double);
double cos(double);
double sin(double);
double tan(double);
double cosh(double);
double sinh(double);
double tanh(double);
double exp(double);
-double frexp(double, int *); /* fundamentally !__pure2 */
-double ldexp(double, int);
double log(double);
double log10(double);
-double modf(double, double *); /* fundamentally !__pure2 */
double pow(double, double);
-double sqrt(double);
double ceil(double);
-double fabs(double) __pure2;
+double fabs(double);
double floor(double);
-double fmod(double, double);
-/*
- * These functions are not in C90.
- */
-#if __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE
double acosh(double);
double asinh(double);
double atanh(double);
double cbrt(double);
-double erf(double);
-double erfc(double);
double exp2(double);
double expm1(double);
-double fma(double, double, double);
double hypot(double, double);
-int ilogb(double) __pure2;
-double lgamma(double);
-long long llrint(double);
-long long llround(double);
double log1p(double);
double log2(double);
-double logb(double);
-long lrint(double);
-long lround(double);
-double nan(const char *) __pure2;
-double nextafter(double, double);
-double remainder(double, double);
-double remquo(double, double, int *);
double rint(double);
-#endif /* __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE */
-
-#if __BSD_VISIBLE || __XSI_VISIBLE
-double j0(double);
-double j1(double);
-double jn(int, double);
-double y0(double);
-double y1(double);
-double yn(int, double);
-
-#if __XSI_VISIBLE <= 500 || __BSD_VISIBLE
-double gamma(double);
-#endif
-
-#if __XSI_VISIBLE <= 600 || __BSD_VISIBLE
-double scalb(double, double);
-#endif
-#endif /* __BSD_VISIBLE || __XSI_VISIBLE */
-
-#if __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999
-double copysign(double, double) __pure2;
-double fdim(double, double);
-double fmax(double, double) __pure2;
-double fmin(double, double) __pure2;
+double copysign(double, double);
double nearbyint(double);
-double round(double);
-double scalbln(double, long);
double scalbn(double, int);
-double tgamma(double);
double trunc(double);
-#endif
-
-/*
- * BSD math library entry points
- */
-#if __BSD_VISIBLE
-double drem(double, double);
-int finite(double) __pure2;
-int isnanf(float) __pure2;
-
-/*
- * Reentrant version of gamma & lgamma; passes signgam back by reference
- * as the second argument; user must allocate space for signgam.
- */
-double gamma_r(double, int *);
-double lgamma_r(double, int *);
-
-/*
- * IEEE Test Vector
- */
-double significand(double);
-#endif /* __BSD_VISIBLE */
-
-/* float versions of ANSI/POSIX functions */
-#if __ISO_C_VISIBLE >= 1999
float acosf(float);
float asinf(float);
float atanf(float);
-float atan2f(float, float);
float cosf(float);
float sinf(float);
float tanf(float);
-
-float coshf(float);
-float sinhf(float);
-float tanhf(float);
-
float exp2f(float);
float expf(float);
-float expm1f(float);
-float frexpf(float, int *); /* fundamentally !__pure2 */
-int ilogbf(float) __pure2;
-float ldexpf(float, int);
-float log10f(float);
-float log1pf(float);
-float log2f(float);
float logf(float);
-float modff(float, float *); /* fundamentally !__pure2 */
-
float powf(float, float);
float sqrtf(float);
float ceilf(float);
-float fabsf(float) __pure2;
+float fabsf(float);
float floorf(float);
-float fmodf(float, float);
-float roundf(float);
-
-float erff(float);
-float erfcf(float);
-float hypotf(float, float);
-float lgammaf(float);
-float tgammaf(float);
-
-float acoshf(float);
-float asinhf(float);
-float atanhf(float);
-float cbrtf(float);
-float logbf(float);
-float copysignf(float, float) __pure2;
-long long llrintf(float);
-long long llroundf(float);
-long lrintf(float);
-long lroundf(float);
-float nanf(const char *) __pure2;
float nearbyintf(float);
-float nextafterf(float, float);
-float remainderf(float, float);
-float remquof(float, float, int *);
float rintf(float);
-float scalblnf(float, long);
float scalbnf(float, int);
float truncf(float);
-float fdimf(float, float);
-float fmaf(float, float, float);
-float fmaxf(float, float) __pure2;
-float fminf(float, float) __pure2;
-#endif
-
-/*
- * float versions of BSD math library entry points
- */
-#if __BSD_VISIBLE
-float dremf(float, float);
-int finitef(float) __pure2;
-float gammaf(float);
-float j0f(float);
-float j1f(float);
-float jnf(int, float);
-float scalbf(float, float);
-float y0f(float);
-float y1f(float);
-float ynf(int, float);
-
-/*
- * Float versions of reentrant version of gamma & lgamma; passes
- * signgam back by reference as the second argument; user must
- * allocate space for signgam.
- */
-float gammaf_r(float, int *);
-float lgammaf_r(float, int *);
-
-/*
- * float version of IEEE Test Vector
- */
-float significandf(float);
-#endif /* __BSD_VISIBLE */
-
-/*
- * long double versions of ISO/POSIX math functions
- */
-#if __ISO_C_VISIBLE >= 1999
-long double acoshl(long double);
-long double acosl(long double);
-long double asinhl(long double);
-long double asinl(long double);
-long double atan2l(long double, long double);
-long double atanhl(long double);
-long double atanl(long double);
-long double cbrtl(long double);
-long double ceill(long double);
-long double copysignl(long double, long double) __pure2;
-long double coshl(long double);
-long double cosl(long double);
-long double erfcl(long double);
-long double erfl(long double);
-long double exp2l(long double);
-long double expl(long double);
-long double expm1l(long double);
-long double fabsl(long double) __pure2;
-long double fdiml(long double, long double);
-long double floorl(long double);
-long double fmal(long double, long double, long double);
-long double fmaxl(long double, long double) __pure2;
-long double fminl(long double, long double) __pure2;
-long double fmodl(long double, long double);
-long double frexpl(long double, int *); /* fundamentally !__pure2 */
-long double hypotl(long double, long double);
-int ilogbl(long double) __pure2;
-long double ldexpl(long double, int);
-long double lgammal(long double);
-long long llrintl(long double);
-long long llroundl(long double);
-long double log10l(long double);
-long double log1pl(long double);
-long double log2l(long double);
-long double logbl(long double);
-long double logl(long double);
-long lrintl(long double);
-long lroundl(long double);
-long double modfl(long double, long double *); /* fundamentally !__pure2 */
-long double nanl(const char *) __pure2;
-long double nearbyintl(long double);
-long double nextafterl(long double, long double);
-double nexttoward(double, long double);
-float nexttowardf(float, long double);
-long double nexttowardl(long double, long double);
-long double powl(long double, long double);
-long double remainderl(long double, long double);
-long double remquol(long double, long double, int *);
-long double rintl(long double);
-long double roundl(long double);
-long double scalblnl(long double, long);
-long double scalbnl(long double, int);
-long double sinhl(long double);
-long double sinl(long double);
-long double sqrtl(long double);
-long double tanhl(long double);
-long double tanl(long double);
-long double tgammal(long double);
-long double truncl(long double);
-#endif /* __ISO_C_VISIBLE >= 1999 */
-
-#if __BSD_VISIBLE
-long double lgammal_r(long double, int *);
-void sincos(double, double *, double *);
-void sincosf(float, float *, float *);
-void sincosl(long double, long double *, long double *);
-double cospi(double);
-float cospif(float);
-long double cospil(long double);
-double sinpi(double);
-float sinpif(float);
-long double sinpil(long double);
-double tanpi(double);
-float tanpif(float);
-long double tanpil(long double);
-#endif
-
-__END_DECLS
-
#endif /* !_MATH_H_ */
|