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 * from: @(#)fdlibm.h 5.1 93/09/24
14 * $FreeBSD$
15 */
16
17 #ifndef _MATH_H_
18 #define _MATH_H_
19
20 #include <sys/cdefs.h>
21 #include <sys/_types.h>
22 #include <machine/_limits.h>
23
24 /*
25 * ANSI/POSIX
26 */
27 extern const union __infinity_un {
28 unsigned char __uc[8];
29 double __ud;
30 } __infinity;
31
32 extern const union __nan_un {
33 unsigned char __uc[sizeof(float)];
34 float __uf;
35 } __nan;
36
37 #if __GNUC_PREREQ__(3, 3) || (defined(__INTEL_COMPILER) && __INTEL_COMPILER >= 800)
38 #define __MATH_BUILTIN_CONSTANTS
39 #endif
40
41 #if __GNUC_PREREQ__(3, 0) && !defined(__INTEL_COMPILER)
42 #define __MATH_BUILTIN_RELOPS
43 #endif
44
45 #ifdef __MATH_BUILTIN_CONSTANTS
46 #define HUGE_VAL __builtin_huge_val()
47 #else
48 #define HUGE_VAL (__infinity.__ud)
49 #endif
50
51 #if __ISO_C_VISIBLE >= 1999
52 #define FP_ILOGB0 (-__INT_MAX)
53 #define FP_ILOGBNAN __INT_MAX
54
55 #ifdef __MATH_BUILTIN_CONSTANTS
56 #define HUGE_VALF __builtin_huge_valf()
57 #define HUGE_VALL __builtin_huge_vall()
58 #define INFINITY __builtin_inff()
59 #define NAN __builtin_nanf("")
60 #else
61 #define HUGE_VALF (float)HUGE_VAL
62 #define HUGE_VALL (long double)HUGE_VAL
63 #define INFINITY HUGE_VALF
64 #define NAN (__nan.__uf)
65 #endif /* __MATH_BUILTIN_CONSTANTS */
66
67 #define MATH_ERRNO 1
68 #define MATH_ERREXCEPT 2
69 #define math_errhandling MATH_ERREXCEPT
70
71 #define FP_FAST_FMAF 1
72
73 /* Symbolic constants to classify floating point numbers. */
74 #define FP_INFINITE 0x01
75 #define FP_NAN 0x02
76 #define FP_NORMAL 0x04
77 #define FP_SUBNORMAL 0x08
78 #define FP_ZERO 0x10
79
80 #if (__STDC_VERSION__ >= 201112L && defined(__clang__)) || \
81 __has_extension(c_generic_selections)
82 #define __fp_type_select(x, f, d, ld) _Generic((x), \
83 float: f(x), \
84 double: d(x), \
85 long double: ld(x), \
86 volatile float: f(x), \
87 volatile double: d(x), \
88 volatile long double: ld(x), \
89 volatile const float: f(x), \
90 volatile const double: d(x), \
91 volatile const long double: ld(x), \
92 const float: f(x), \
93 const double: d(x), \
94 const long double: ld(x))
95 #elif __GNUC_PREREQ__(3, 1) && !defined(__cplusplus)
96 #define __fp_type_select(x, f, d, ld) __builtin_choose_expr( \
97 __builtin_types_compatible_p(__typeof(x), long double), ld(x), \
98 __builtin_choose_expr( \
99 __builtin_types_compatible_p(__typeof(x), double), d(x), \
100 __builtin_choose_expr( \
101 __builtin_types_compatible_p(__typeof(x), float), f(x), (void)0)))
102 #else
103 #define __fp_type_select(x, f, d, ld) \
104 ((sizeof(x) == sizeof(float)) ? f(x) \
105 : (sizeof(x) == sizeof(double)) ? d(x) \
106 : ld(x))
107 #endif
108
109 #define fpclassify(x) \
110 __fp_type_select(x, __fpclassifyf, __fpclassifyd, __fpclassifyl)
111 #define isfinite(x) __fp_type_select(x, __isfinitef, __isfinite, __isfinitel)
112 #define isinf(x) __fp_type_select(x, __isinff, __isinf, __isinfl)
113 #define isnan(x) \
114 __fp_type_select(x, __inline_isnanf, __inline_isnan, __inline_isnanl)
115 #define isnormal(x) __fp_type_select(x, __isnormalf, __isnormal, __isnormall)
116
117 #ifdef __MATH_BUILTIN_RELOPS
118 #define isgreater(x, y) __builtin_isgreater((x), (y))
119 #define isgreaterequal(x, y) __builtin_isgreaterequal((x), (y))
120 #define isless(x, y) __builtin_isless((x), (y))
121 #define islessequal(x, y) __builtin_islessequal((x), (y))
122 #define islessgreater(x, y) __builtin_islessgreater((x), (y))
123 #define isunordered(x, y) __builtin_isunordered((x), (y))
124 #else
125 #define isgreater(x, y) (!isunordered((x), (y)) && (x) > (y))
126 #define isgreaterequal(x, y) (!isunordered((x), (y)) && (x) >= (y))
127 #define isless(x, y) (!isunordered((x), (y)) && (x) < (y))
128 #define islessequal(x, y) (!isunordered((x), (y)) && (x) <= (y))
129 #define islessgreater(x, y) (!isunordered((x), (y)) && \
130 ((x) > (y) || (y) > (x)))
131 #define isunordered(x, y) (isnan(x) || isnan(y))
132 #endif /* __MATH_BUILTIN_RELOPS */
133
134 #define signbit(x) __fp_type_select(x, __signbitf, __signbit, __signbitl)
135
136 typedef __double_t double_t;
137 typedef __float_t float_t;
138 #endif /* __ISO_C_VISIBLE >= 1999 */
139
140 /*
141 * XOPEN/SVID
142 */
143 #if __BSD_VISIBLE || __XSI_VISIBLE
144 #define M_E 2.7182818284590452354 /* e */
145 #define M_LOG2E 1.4426950408889634074 /* log 2e */
146 #define M_LOG10E 0.43429448190325182765 /* log 10e */
147 #define M_LN2 0.69314718055994530942 /* log e2 */
148 #define M_LN10 2.30258509299404568402 /* log e10 */
149 #define M_PI 3.14159265358979323846 /* pi */
150 #define M_PI_2 1.57079632679489661923 /* pi/2 */
151 #define M_PI_4 0.78539816339744830962 /* pi/4 */
152 #define M_1_PI 0.31830988618379067154 /* 1/pi */
153 #define M_2_PI 0.63661977236758134308 /* 2/pi */
154 #define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
155 #define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
156 #define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
157
158 #define MAXFLOAT ((float)3.40282346638528860e+38)
159 extern int signgam;
160 #endif /* __BSD_VISIBLE || __XSI_VISIBLE */
161
162 #if __BSD_VISIBLE
163 #if 0
164 /* Old value from 4.4BSD-Lite math.h; this is probably better. */
165 #define HUGE HUGE_VAL
166 #else
167 #define HUGE MAXFLOAT
168 #endif
169 #endif /* __BSD_VISIBLE */
170
171 /*
172 * Most of these functions depend on the rounding mode and have the side
173 * effect of raising floating-point exceptions, so they are not declared
174 * as __pure2. In C99, FENV_ACCESS affects the purity of these functions.
175 */
176 __BEGIN_DECLS
177 /*
178 * ANSI/POSIX
179 */
180 int __fpclassifyd(double) __pure2;
181 int __fpclassifyf(float) __pure2;
182 int __fpclassifyl(long double) __pure2;
183 int __isfinitef(float) __pure2;
184 int __isfinite(double) __pure2;
185 int __isfinitel(long double) __pure2;
186 int __isinff(float) __pure2;
187 int __isinf(double) __pure2;
188 int __isinfl(long double) __pure2;
189 int __isnormalf(float) __pure2;
190 int __isnormal(double) __pure2;
191 int __isnormall(long double) __pure2;
192 int __signbit(double) __pure2;
193 int __signbitf(float) __pure2;
194 int __signbitl(long double) __pure2;
195
196 static __inline int
__inline_isnan(__const double __x)197 __inline_isnan(__const double __x)
198 {
199
200 return (__x != __x);
201 }
202
203 static __inline int
__inline_isnanf(__const float __x)204 __inline_isnanf(__const float __x)
205 {
206
207 return (__x != __x);
208 }
209
210 static __inline int
__inline_isnanl(__const long double __x)211 __inline_isnanl(__const long double __x)
212 {
213
214 return (__x != __x);
215 }
216
217 /*
218 * Version 2 of the Single UNIX Specification (UNIX98) defined isnan() and
219 * isinf() as functions taking double. C99, and the subsequent POSIX revisions
220 * (SUSv3, POSIX.1-2001, define it as a macro that accepts any real floating
221 * point type. If we are targeting SUSv2 and C99 or C11 (or C++11) then we
222 * expose the newer definition, assuming that the language spec takes
223 * precedence over the operating system interface spec.
224 */
225 #if __XSI_VISIBLE > 0 && __XSI_VISIBLE < 600 && __ISO_C_VISIBLE < 1999
226 #undef isinf
227 #undef isnan
228 int isinf(double);
229 int isnan(double);
230 #endif
231
232 double acos(double);
233 double asin(double);
234 double atan(double);
235 double atan2(double, double);
236 double cos(double);
237 double sin(double);
238 double tan(double);
239
240 double cosh(double);
241 double sinh(double);
242 double tanh(double);
243
244 double exp(double);
245 double frexp(double, int *); /* fundamentally !__pure2 */
246 double ldexp(double, int);
247 double log(double);
248 double log10(double);
249 double modf(double, double *); /* fundamentally !__pure2 */
250
251 double pow(double, double);
252 double sqrt(double);
253
254 double ceil(double);
255 double fabs(double) __pure2;
256 double floor(double);
257 double fmod(double, double);
258
259 /*
260 * These functions are not in C90.
261 */
262 #if __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE
263 double acosh(double);
264 double asinh(double);
265 double atanh(double);
266 double cbrt(double);
267 double erf(double);
268 double erfc(double);
269 double exp2(double);
270 double expm1(double);
271 double fma(double, double, double);
272 double hypot(double, double);
273 int ilogb(double) __pure2;
274 double lgamma(double);
275 long long llrint(double);
276 long long llround(double);
277 double log1p(double);
278 double log2(double);
279 double logb(double);
280 long lrint(double);
281 long lround(double);
282 double nan(const char *) __pure2;
283 double nextafter(double, double);
284 double remainder(double, double);
285 double remquo(double, double, int *);
286 double rint(double);
287 #endif /* __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE */
288
289 #if __BSD_VISIBLE || __XSI_VISIBLE
290 double j0(double);
291 double j1(double);
292 double jn(int, double);
293 double y0(double);
294 double y1(double);
295 double yn(int, double);
296
297 #if __XSI_VISIBLE <= 500 || __BSD_VISIBLE
298 double gamma(double);
299 #endif
300
301 #if __XSI_VISIBLE <= 600 || __BSD_VISIBLE
302 double scalb(double, double);
303 #endif
304 #endif /* __BSD_VISIBLE || __XSI_VISIBLE */
305
306 #if __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999
307 double copysign(double, double) __pure2;
308 double fdim(double, double);
309 double fmax(double, double) __pure2;
310 double fmin(double, double) __pure2;
311 double nearbyint(double);
312 double round(double);
313 double scalbln(double, long);
314 double scalbn(double, int);
315 double tgamma(double);
316 double trunc(double);
317 #endif
318
319 /*
320 * BSD math library entry points
321 */
322 #if __BSD_VISIBLE
323 double drem(double, double);
324 int finite(double) __pure2;
325 int isnanf(float) __pure2;
326
327 /*
328 * Reentrant version of gamma & lgamma; passes signgam back by reference
329 * as the second argument; user must allocate space for signgam.
330 */
331 double gamma_r(double, int *);
332 double lgamma_r(double, int *);
333
334 /*
335 * IEEE Test Vector
336 */
337 double significand(double);
338 #endif /* __BSD_VISIBLE */
339
340 /* float versions of ANSI/POSIX functions */
341 #if __ISO_C_VISIBLE >= 1999
342 float acosf(float);
343 float asinf(float);
344 float atanf(float);
345 float atan2f(float, float);
346 float cosf(float);
347 float sinf(float);
348 float tanf(float);
349
350 float coshf(float);
351 float sinhf(float);
352 float tanhf(float);
353
354 float exp2f(float);
355 float expf(float);
356 float expm1f(float);
357 float frexpf(float, int *); /* fundamentally !__pure2 */
358 int ilogbf(float) __pure2;
359 float ldexpf(float, int);
360 float log10f(float);
361 float log1pf(float);
362 float log2f(float);
363 float logf(float);
364 float modff(float, float *); /* fundamentally !__pure2 */
365
366 float powf(float, float);
367 float sqrtf(float);
368
369 float ceilf(float);
370 float fabsf(float) __pure2;
371 float floorf(float);
372 float fmodf(float, float);
373 float roundf(float);
374
375 float erff(float);
376 float erfcf(float);
377 float hypotf(float, float);
378 float lgammaf(float);
379 float tgammaf(float);
380
381 float acoshf(float);
382 float asinhf(float);
383 float atanhf(float);
384 float cbrtf(float);
385 float logbf(float);
386 float copysignf(float, float) __pure2;
387 long long llrintf(float);
388 long long llroundf(float);
389 long lrintf(float);
390 long lroundf(float);
391 float nanf(const char *) __pure2;
392 float nearbyintf(float);
393 float nextafterf(float, float);
394 float remainderf(float, float);
395 float remquof(float, float, int *);
396 float rintf(float);
397 float scalblnf(float, long);
398 float scalbnf(float, int);
399 float truncf(float);
400
401 float fdimf(float, float);
402 float fmaf(float, float, float);
403 float fmaxf(float, float) __pure2;
404 float fminf(float, float) __pure2;
405 #endif
406
407 /*
408 * float versions of BSD math library entry points
409 */
410 #if __BSD_VISIBLE
411 float dremf(float, float);
412 int finitef(float) __pure2;
413 float gammaf(float);
414 float j0f(float);
415 float j1f(float);
416 float jnf(int, float);
417 float scalbf(float, float);
418 float y0f(float);
419 float y1f(float);
420 float ynf(int, float);
421
422 /*
423 * Float versions of reentrant version of gamma & lgamma; passes
424 * signgam back by reference as the second argument; user must
425 * allocate space for signgam.
426 */
427 float gammaf_r(float, int *);
428 float lgammaf_r(float, int *);
429
430 /*
431 * float version of IEEE Test Vector
432 */
433 float significandf(float);
434 #endif /* __BSD_VISIBLE */
435
436 /*
437 * long double versions of ISO/POSIX math functions
438 */
439 #if __ISO_C_VISIBLE >= 1999
440 long double acoshl(long double);
441 long double acosl(long double);
442 long double asinhl(long double);
443 long double asinl(long double);
444 long double atan2l(long double, long double);
445 long double atanhl(long double);
446 long double atanl(long double);
447 long double cbrtl(long double);
448 long double ceill(long double);
449 long double copysignl(long double, long double) __pure2;
450 long double coshl(long double);
451 long double cosl(long double);
452 long double erfcl(long double);
453 long double erfl(long double);
454 long double exp2l(long double);
455 long double expl(long double);
456 long double expm1l(long double);
457 long double fabsl(long double) __pure2;
458 long double fdiml(long double, long double);
459 long double floorl(long double);
460 long double fmal(long double, long double, long double);
461 long double fmaxl(long double, long double) __pure2;
462 long double fminl(long double, long double) __pure2;
463 long double fmodl(long double, long double);
464 long double frexpl(long double value, int *); /* fundamentally !__pure2 */
465 long double hypotl(long double, long double);
466 int ilogbl(long double) __pure2;
467 long double ldexpl(long double, int);
468 long double lgammal(long double);
469 long long llrintl(long double);
470 long long llroundl(long double);
471 long double log10l(long double);
472 long double log1pl(long double);
473 long double log2l(long double);
474 long double logbl(long double);
475 long double logl(long double);
476 long lrintl(long double);
477 long lroundl(long double);
478 long double modfl(long double, long double *); /* fundamentally !__pure2 */
479 long double nanl(const char *) __pure2;
480 long double nearbyintl(long double);
481 long double nextafterl(long double, long double);
482 double nexttoward(double, long double);
483 float nexttowardf(float, long double);
484 long double nexttowardl(long double, long double);
485 long double powl(long double, long double);
486 long double remainderl(long double, long double);
487 long double remquol(long double, long double, int *);
488 long double rintl(long double);
489 long double roundl(long double);
490 long double scalblnl(long double, long);
491 long double scalbnl(long double, int);
492 long double sinhl(long double);
493 long double sinl(long double);
494 long double sqrtl(long double);
495 long double tanhl(long double);
496 long double tanl(long double);
497 long double tgammal(long double);
498 long double truncl(long double);
499 #endif /* __ISO_C_VISIBLE >= 1999 */
500
501 #if __BSD_VISIBLE
502 long double lgammal_r(long double, int *);
503 #endif
504
505 __END_DECLS
506
507 #endif /* !_MATH_H_ */
508