1 /*
2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4 *
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
8 * is preserved.
9 * ====================================================
10 */
11
12 /*
13 */
14
15 #ifndef _MATH_H_
16 #define _MATH_H_
17
18 #include <sys/_types.h>
19 #include <machine/_limits.h>
20
21 /*
22 * ANSI/POSIX
23 */
24 extern const union __infinity_un {
25 unsigned char __uc[8];
26 double __ud;
27 } __infinity;
28
29 extern const union __nan_un {
30 unsigned char __uc[sizeof(float)];
31 float __uf;
32 } __nan;
33
34 #if __GNUC_PREREQ__(3, 3)
35 #define __MATH_BUILTIN_CONSTANTS
36 #endif
37
38 #if __GNUC_PREREQ__(3, 0)
39 #define __MATH_BUILTIN_RELOPS
40 #endif
41
42 #ifdef __MATH_BUILTIN_CONSTANTS
43 #define HUGE_VAL __builtin_huge_val()
44 #else
45 #define HUGE_VAL (__infinity.__ud)
46 #endif
47
48 #if __ISO_C_VISIBLE >= 1999
49 #define FP_ILOGB0 (-__INT_MAX)
50 #define FP_ILOGBNAN __INT_MAX
51
52 #ifdef __MATH_BUILTIN_CONSTANTS
53 #define HUGE_VALF __builtin_huge_valf()
54 #define HUGE_VALL __builtin_huge_vall()
55 #define INFINITY __builtin_inff()
56 #define NAN __builtin_nanf("")
57 #else
58 #define HUGE_VALF (float)HUGE_VAL
59 #define HUGE_VALL (long double)HUGE_VAL
60 #define INFINITY HUGE_VALF
61 #define NAN (__nan.__uf)
62 #endif /* __MATH_BUILTIN_CONSTANTS */
63
64 #define MATH_ERRNO 1
65 #define MATH_ERREXCEPT 2
66 #define math_errhandling MATH_ERREXCEPT
67
68 #define FP_FAST_FMAF 1
69
70 /* Symbolic constants to classify floating point numbers. */
71 #define FP_INFINITE 0x01
72 #define FP_NAN 0x02
73 #define FP_NORMAL 0x04
74 #define FP_SUBNORMAL 0x08
75 #define FP_ZERO 0x10
76
77 #if __STDC_VERSION__ >= 201112L || __has_extension(c_generic_selections)
78 #define __fp_type_select(x, f, d, ld) __extension__ _Generic((x), \
79 float: f, \
80 double: d, \
81 long double: ld)(x)
82 #elif __GNUC_PREREQ__(3, 1) && !defined(__cplusplus)
83 #define __fp_type_select(x, f, d, ld) __builtin_choose_expr( \
84 __builtin_types_compatible_p(__typeof(x), long double), ld(x), \
85 __builtin_choose_expr( \
86 __builtin_types_compatible_p(__typeof(x), double), d(x), \
87 __builtin_choose_expr( \
88 __builtin_types_compatible_p(__typeof(x), float), f(x), (void)0)))
89 #else
90 #define __fp_type_select(x, f, d, ld) \
91 ((sizeof(x) == sizeof(float)) ? f(x) \
92 : (sizeof(x) == sizeof(double)) ? d(x) \
93 : ld(x))
94 #endif
95
96 #define fpclassify(x) \
97 __fp_type_select(x, __fpclassifyf, __fpclassifyd, __fpclassifyl)
98 #define isfinite(x) __fp_type_select(x, __isfinitef, __isfinite, __isfinitel)
99 #define isinf(x) __fp_type_select(x, __isinff, __isinf, __isinfl)
100 #define isnan(x) \
101 __fp_type_select(x, __inline_isnanf, __inline_isnan, __inline_isnanl)
102 #define isnormal(x) __fp_type_select(x, __isnormalf, __isnormal, __isnormall)
103
104 #ifdef __MATH_BUILTIN_RELOPS
105 #define isgreater(x, y) __builtin_isgreater((x), (y))
106 #define isgreaterequal(x, y) __builtin_isgreaterequal((x), (y))
107 #define isless(x, y) __builtin_isless((x), (y))
108 #define islessequal(x, y) __builtin_islessequal((x), (y))
109 #define islessgreater(x, y) __builtin_islessgreater((x), (y))
110 #define isunordered(x, y) __builtin_isunordered((x), (y))
111 #else
112 #define isgreater(x, y) (!isunordered((x), (y)) && (x) > (y))
113 #define isgreaterequal(x, y) (!isunordered((x), (y)) && (x) >= (y))
114 #define isless(x, y) (!isunordered((x), (y)) && (x) < (y))
115 #define islessequal(x, y) (!isunordered((x), (y)) && (x) <= (y))
116 #define islessgreater(x, y) (!isunordered((x), (y)) && \
117 ((x) > (y) || (y) > (x)))
118 #define isunordered(x, y) (isnan(x) || isnan(y))
119 #endif /* __MATH_BUILTIN_RELOPS */
120
121 #define signbit(x) __fp_type_select(x, __signbitf, __signbit, __signbitl)
122
123 typedef __double_t double_t;
124 typedef __float_t float_t;
125 #endif /* __ISO_C_VISIBLE >= 1999 */
126
127 /*
128 * XOPEN/SVID
129 */
130 #if __BSD_VISIBLE || __XSI_VISIBLE
131 #define M_E 2.7182818284590452354 /* e */
132 #define M_LOG2E 1.4426950408889634074 /* log 2e */
133 #define M_LOG10E 0.43429448190325182765 /* log 10e */
134 #define M_LN2 0.69314718055994530942 /* log e2 */
135 #define M_LN10 2.30258509299404568402 /* log e10 */
136 #define M_PI 3.14159265358979323846 /* pi */
137 #define M_PI_2 1.57079632679489661923 /* pi/2 */
138 #define M_PI_4 0.78539816339744830962 /* pi/4 */
139 #define M_1_PI 0.31830988618379067154 /* 1/pi */
140 #define M_2_PI 0.63661977236758134308 /* 2/pi */
141 #define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
142 #define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
143 #define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
144
145 #if __BSD_VISIBLE || __XSI_VISIBLE >= 800
146 #define M_El 2.718281828459045235360287471352662498L /* e */
147 #define M_LOG2El 1.442695040888963407359924681001892137L /* log_2 e */
148 #define M_LOG10El 0.434294481903251827651128918916605082L /* log_10 e */
149 #define M_LN2l 0.693147180559945309417232121458176568L /* log_e 2 */
150 #define M_LN10l 2.302585092994045684017991454684364208L /* log_e 10 */
151 #define M_PIl 3.141592653589793238462643383279502884L /* pi */
152 #define M_PI_2l 1.570796326794896619231321691639751442L /* pi/2 */
153 #define M_PI_4l 0.785398163397448309615660845819875721L /* pi/4 */
154 #define M_1_PIl 0.318309886183790671537767526745028724L /* 1/pi */
155 #define M_2_PIl 0.636619772367581343075535053490057448L /* 2/pi */
156 #define M_2_SQRTPIl 1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
157 #define M_SQRT2l 1.414213562373095048801688724209698079L /* sqrt(2) */
158 #define M_SQRT1_2l 0.707106781186547524400844362104849039L /* 1/sqrt(2) */
159 #endif /* __BSD_VISIBLE || __XSI_VISIBLE >= 800 */
160
161 #define MAXFLOAT ((float)3.40282346638528860e+38)
162 extern int signgam;
163 #endif /* __BSD_VISIBLE || __XSI_VISIBLE */
164
165 #if __BSD_VISIBLE
166 #if 0
167 /* Old value from 4.4BSD-Lite math.h; this is probably better. */
168 #define HUGE HUGE_VAL
169 #else
170 #define HUGE MAXFLOAT
171 #endif
172 #endif /* __BSD_VISIBLE */
173
174 /*
175 * Most of these functions depend on the rounding mode and have the side
176 * effect of raising floating-point exceptions, so they are not declared
177 * as __pure2. In C99, FENV_ACCESS affects the purity of these functions.
178 */
179 __BEGIN_DECLS
180 /*
181 * ANSI/POSIX
182 */
183 int __fpclassifyd(double) __pure2;
184 int __fpclassifyf(float) __pure2;
185 int __fpclassifyl(long double) __pure2;
186 int __isfinitef(float) __pure2;
187 int __isfinite(double) __pure2;
188 int __isfinitel(long double) __pure2;
189 int __isinff(float) __pure2;
190 int __isinf(double) __pure2;
191 int __isinfl(long double) __pure2;
192 int __isnormalf(float) __pure2;
193 int __isnormal(double) __pure2;
194 int __isnormall(long double) __pure2;
195 int __signbit(double) __pure2;
196 int __signbitf(float) __pure2;
197 int __signbitl(long double) __pure2;
198
199 static __inline int
__inline_isnan(const double __x)200 __inline_isnan(const double __x)
201 {
202
203 return (__x != __x);
204 }
205
206 static __inline int
__inline_isnanf(const float __x)207 __inline_isnanf(const float __x)
208 {
209
210 return (__x != __x);
211 }
212
213 static __inline int
__inline_isnanl(const long double __x)214 __inline_isnanl(const long double __x)
215 {
216
217 return (__x != __x);
218 }
219
220 /*
221 * Define the following aliases, for compatibility with glibc and CUDA.
222 */
223 #define __isnan __inline_isnan
224 #define __isnanf __inline_isnanf
225
226 /*
227 * Version 2 of the Single UNIX Specification (UNIX98) defined isnan() and
228 * isinf() as functions taking double. C99, and the subsequent POSIX revisions
229 * (SUSv3, POSIX.1-2001, define it as a macro that accepts any real floating
230 * point type. If we are targeting SUSv2 and C99 or C11 (or C++11) then we
231 * expose the newer definition, assuming that the language spec takes
232 * precedence over the operating system interface spec.
233 */
234 #if __XSI_VISIBLE > 0 && __XSI_VISIBLE < 600 && __ISO_C_VISIBLE < 1999
235 #undef isinf
236 #undef isnan
237 int isinf(double);
238 int isnan(double);
239 #endif
240
241 double acos(double);
242 double asin(double);
243 double atan(double);
244 double atan2(double, double);
245 double cos(double);
246 double sin(double);
247 double tan(double);
248
249 double cosh(double);
250 double sinh(double);
251 double tanh(double);
252
253 double exp(double);
254 double frexp(double, int *); /* fundamentally !__pure2 */
255 double ldexp(double, int);
256 double log(double);
257 double log10(double);
258 double modf(double, double *); /* fundamentally !__pure2 */
259
260 double pow(double, double);
261 double sqrt(double);
262
263 double ceil(double);
264 double fabs(double) __pure2;
265 double floor(double);
266 double fmod(double, double);
267
268 /*
269 * These functions are not in C90.
270 */
271 #if __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE
272 double acosh(double);
273 double asinh(double);
274 double atanh(double);
275 double cbrt(double);
276 double erf(double);
277 double erfc(double);
278 double exp2(double);
279 double expm1(double);
280 double fma(double, double, double);
281 double hypot(double, double);
282 int ilogb(double) __pure2;
283 double lgamma(double);
284 long long llrint(double);
285 long long llround(double);
286 double log1p(double);
287 double log2(double);
288 double logb(double);
289 long lrint(double);
290 long lround(double);
291 double nan(const char *) __pure2;
292 double nextafter(double, double);
293 double remainder(double, double);
294 double remquo(double, double, int *);
295 double rint(double);
296 #endif /* __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE */
297
298 #if __BSD_VISIBLE || __XSI_VISIBLE
299 double j0(double);
300 double j1(double);
301 double jn(int, double);
302 double y0(double);
303 double y1(double);
304 double yn(int, double);
305
306 #if __XSI_VISIBLE <= 500 || __BSD_VISIBLE
307 double gamma(double);
308 #endif
309
310 #if __XSI_VISIBLE <= 600 || __BSD_VISIBLE
311 double scalb(double, double);
312 #endif
313 #endif /* __BSD_VISIBLE || __XSI_VISIBLE */
314
315 #if __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999
316 double copysign(double, double) __pure2;
317 double fdim(double, double);
318 double fmax(double, double) __pure2;
319 double fmin(double, double) __pure2;
320 double nearbyint(double);
321 double round(double);
322 double scalbln(double, long);
323 double scalbn(double, int);
324 double tgamma(double);
325 double trunc(double);
326 #endif
327
328 /*
329 * BSD math library entry points
330 */
331 #if __BSD_VISIBLE
332 double drem(double, double);
333 int finite(double) __pure2;
334 int isnanf(float) __pure2;
335
336 /*
337 * Reentrant version of gamma & lgamma; passes signgam back by reference
338 * as the second argument; user must allocate space for signgam.
339 */
340 double gamma_r(double, int *);
341 double lgamma_r(double, int *);
342
343 /*
344 * IEEE Test Vector
345 */
346 double significand(double);
347 #endif /* __BSD_VISIBLE */
348
349 /* float versions of ANSI/POSIX functions */
350 #if __ISO_C_VISIBLE >= 1999
351 float acosf(float);
352 float asinf(float);
353 float atanf(float);
354 float atan2f(float, float);
355 float cosf(float);
356 float sinf(float);
357 float tanf(float);
358
359 float coshf(float);
360 float sinhf(float);
361 float tanhf(float);
362
363 float exp2f(float);
364 float expf(float);
365 float expm1f(float);
366 float frexpf(float, int *); /* fundamentally !__pure2 */
367 int ilogbf(float) __pure2;
368 float ldexpf(float, int);
369 float log10f(float);
370 float log1pf(float);
371 float log2f(float);
372 float logf(float);
373 float modff(float, float *); /* fundamentally !__pure2 */
374
375 float powf(float, float);
376 float sqrtf(float);
377
378 float ceilf(float);
379 float fabsf(float) __pure2;
380 float floorf(float);
381 float fmodf(float, float);
382 float roundf(float);
383
384 float erff(float);
385 float erfcf(float);
386 float hypotf(float, float);
387 float lgammaf(float);
388 float tgammaf(float);
389
390 float acoshf(float);
391 float asinhf(float);
392 float atanhf(float);
393 float cbrtf(float);
394 float logbf(float);
395 float copysignf(float, float) __pure2;
396 long long llrintf(float);
397 long long llroundf(float);
398 long lrintf(float);
399 long lroundf(float);
400 float nanf(const char *) __pure2;
401 float nearbyintf(float);
402 float nextafterf(float, float);
403 float remainderf(float, float);
404 float remquof(float, float, int *);
405 float rintf(float);
406 float scalblnf(float, long);
407 float scalbnf(float, int);
408 float truncf(float);
409
410 float fdimf(float, float);
411 float fmaf(float, float, float);
412 float fmaxf(float, float) __pure2;
413 float fminf(float, float) __pure2;
414 #endif
415
416 /*
417 * float versions of BSD math library entry points
418 */
419 #if __BSD_VISIBLE
420 float dremf(float, float);
421 int finitef(float) __pure2;
422 float gammaf(float);
423 float j0f(float);
424 float j1f(float);
425 float jnf(int, float);
426 float scalbf(float, float);
427 float y0f(float);
428 float y1f(float);
429 float ynf(int, float);
430
431 /*
432 * Float versions of reentrant version of gamma & lgamma; passes
433 * signgam back by reference as the second argument; user must
434 * allocate space for signgam.
435 */
436 float gammaf_r(float, int *);
437 float lgammaf_r(float, int *);
438
439 /*
440 * float version of IEEE Test Vector
441 */
442 float significandf(float);
443 #endif /* __BSD_VISIBLE */
444
445 /*
446 * long double versions of ISO/POSIX math functions
447 */
448 #if __ISO_C_VISIBLE >= 1999
449 long double acoshl(long double);
450 long double acosl(long double);
451 long double asinhl(long double);
452 long double asinl(long double);
453 long double atan2l(long double, long double);
454 long double atanhl(long double);
455 long double atanl(long double);
456 long double cbrtl(long double);
457 long double ceill(long double);
458 long double copysignl(long double, long double) __pure2;
459 long double coshl(long double);
460 long double cosl(long double);
461 long double erfcl(long double);
462 long double erfl(long double);
463 long double exp2l(long double);
464 long double expl(long double);
465 long double expm1l(long double);
466 long double fabsl(long double) __pure2;
467 long double fdiml(long double, long double);
468 long double floorl(long double);
469 long double fmal(long double, long double, long double);
470 long double fmaxl(long double, long double) __pure2;
471 long double fminl(long double, long double) __pure2;
472 long double fmodl(long double, long double);
473 long double frexpl(long double, int *); /* fundamentally !__pure2 */
474 long double hypotl(long double, long double);
475 int ilogbl(long double) __pure2;
476 long double ldexpl(long double, int);
477 long double lgammal(long double);
478 long long llrintl(long double);
479 long long llroundl(long double);
480 long double log10l(long double);
481 long double log1pl(long double);
482 long double log2l(long double);
483 long double logbl(long double);
484 long double logl(long double);
485 long lrintl(long double);
486 long lroundl(long double);
487 long double modfl(long double, long double *); /* fundamentally !__pure2 */
488 long double nanl(const char *) __pure2;
489 long double nearbyintl(long double);
490 long double nextafterl(long double, long double);
491 double nexttoward(double, long double);
492 float nexttowardf(float, long double);
493 long double nexttowardl(long double, long double);
494 long double powl(long double, long double);
495 long double remainderl(long double, long double);
496 long double remquol(long double, long double, int *);
497 long double rintl(long double);
498 long double roundl(long double);
499 long double scalblnl(long double, long);
500 long double scalbnl(long double, int);
501 long double sinhl(long double);
502 long double sinl(long double);
503 long double sqrtl(long double);
504 long double tanhl(long double);
505 long double tanl(long double);
506 long double tgammal(long double);
507 long double truncl(long double);
508 #endif /* __ISO_C_VISIBLE >= 1999 */
509
510 #if __BSD_VISIBLE
511 long double lgammal_r(long double, int *);
512 void sincos(double, double *, double *);
513 void sincosf(float, float *, float *);
514 void sincosl(long double, long double *, long double *);
515 double cospi(double);
516 float cospif(float);
517 long double cospil(long double);
518 double sinpi(double);
519 float sinpif(float);
520 long double sinpil(long double);
521 double tanpi(double);
522 float tanpif(float);
523 long double tanpil(long double);
524 #endif
525
526 __END_DECLS
527
528 #endif /* !_MATH_H_ */
529