math.h (14109B) - Raw
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 */ 15 16 #ifndef _MATH_H_ 17 #define _MATH_H_ 18 19 #include <sys/_types.h> 20 #include <machine/_limits.h> 21 22 /* 23 * ANSI/POSIX 24 */ 25 extern const union __infinity_un { 26 unsigned char __uc[8]; 27 double __ud; 28 } __infinity; 29 30 extern const union __nan_un { 31 unsigned char __uc[sizeof(float)]; 32 float __uf; 33 } __nan; 34 35 #if __GNUC_PREREQ__(3, 3) 36 #define __MATH_BUILTIN_CONSTANTS 37 #endif 38 39 #if __GNUC_PREREQ__(3, 0) 40 #define __MATH_BUILTIN_RELOPS 41 #endif 42 43 #ifdef __MATH_BUILTIN_CONSTANTS 44 #define HUGE_VAL __builtin_huge_val() 45 #else 46 #define HUGE_VAL (__infinity.__ud) 47 #endif 48 49 #if __ISO_C_VISIBLE >= 1999 50 #define FP_ILOGB0 (-__INT_MAX) 51 #define FP_ILOGBNAN __INT_MAX 52 53 #ifdef __MATH_BUILTIN_CONSTANTS 54 #define HUGE_VALF __builtin_huge_valf() 55 #define HUGE_VALL __builtin_huge_vall() 56 #define INFINITY __builtin_inff() 57 #define NAN __builtin_nanf("") 58 #else 59 #define HUGE_VALF (float)HUGE_VAL 60 #define HUGE_VALL (long double)HUGE_VAL 61 #define INFINITY HUGE_VALF 62 #define NAN (__nan.__uf) 63 #endif /* __MATH_BUILTIN_CONSTANTS */ 64 65 #define MATH_ERRNO 1 66 #define MATH_ERREXCEPT 2 67 #define math_errhandling MATH_ERREXCEPT 68 69 #define FP_FAST_FMAF 1 70 71 /* Symbolic constants to classify floating point numbers. */ 72 #define FP_INFINITE 0x01 73 #define FP_NAN 0x02 74 #define FP_NORMAL 0x04 75 #define FP_SUBNORMAL 0x08 76 #define FP_ZERO 0x10 77 78 #if __STDC_VERSION__ >= 201112L || __has_extension(c_generic_selections) 79 #define __fp_type_select(x, f, d, ld) __extension__ _Generic((x), \ 80 float: f(x), \ 81 double: d(x), \ 82 long double: ld(x)) 83 #elif __GNUC_PREREQ__(3, 1) && !defined(__cplusplus) 84 #define __fp_type_select(x, f, d, ld) __builtin_choose_expr( \ 85 __builtin_types_compatible_p(__typeof(x), long double), ld(x), \ 86 __builtin_choose_expr( \ 87 __builtin_types_compatible_p(__typeof(x), double), d(x), \ 88 __builtin_choose_expr( \ 89 __builtin_types_compatible_p(__typeof(x), float), f(x), (void)0))) 90 #else 91 #define __fp_type_select(x, f, d, ld) \ 92 ((sizeof(x) == sizeof(float)) ? f(x) \ 93 : (sizeof(x) == sizeof(double)) ? d(x) \ 94 : ld(x)) 95 #endif 96 97 #define fpclassify(x) \ 98 __fp_type_select(x, __fpclassifyf, __fpclassifyd, __fpclassifyl) 99 #define isfinite(x) __fp_type_select(x, __isfinitef, __isfinite, __isfinitel) 100 #define isinf(x) __fp_type_select(x, __isinff, __isinf, __isinfl) 101 #define isnan(x) \ 102 __fp_type_select(x, __inline_isnanf, __inline_isnan, __inline_isnanl) 103 #define isnormal(x) __fp_type_select(x, __isnormalf, __isnormal, __isnormall) 104 105 #ifdef __MATH_BUILTIN_RELOPS 106 #define isgreater(x, y) __builtin_isgreater((x), (y)) 107 #define isgreaterequal(x, y) __builtin_isgreaterequal((x), (y)) 108 #define isless(x, y) __builtin_isless((x), (y)) 109 #define islessequal(x, y) __builtin_islessequal((x), (y)) 110 #define islessgreater(x, y) __builtin_islessgreater((x), (y)) 111 #define isunordered(x, y) __builtin_isunordered((x), (y)) 112 #else 113 #define isgreater(x, y) (!isunordered((x), (y)) && (x) > (y)) 114 #define isgreaterequal(x, y) (!isunordered((x), (y)) && (x) >= (y)) 115 #define isless(x, y) (!isunordered((x), (y)) && (x) < (y)) 116 #define islessequal(x, y) (!isunordered((x), (y)) && (x) <= (y)) 117 #define islessgreater(x, y) (!isunordered((x), (y)) && \ 118 ((x) > (y) || (y) > (x))) 119 #define isunordered(x, y) (isnan(x) || isnan(y)) 120 #endif /* __MATH_BUILTIN_RELOPS */ 121 122 #define signbit(x) __fp_type_select(x, __signbitf, __signbit, __signbitl) 123 124 typedef __double_t double_t; 125 typedef __float_t float_t; 126 #endif /* __ISO_C_VISIBLE >= 1999 */ 127 128 /* 129 * XOPEN/SVID 130 */ 131 #if __BSD_VISIBLE || __XSI_VISIBLE 132 #define M_E 2.7182818284590452354 /* e */ 133 #define M_LOG2E 1.4426950408889634074 /* log 2e */ 134 #define M_LOG10E 0.43429448190325182765 /* log 10e */ 135 #define M_LN2 0.69314718055994530942 /* log e2 */ 136 #define M_LN10 2.30258509299404568402 /* log e10 */ 137 #define M_PI 3.14159265358979323846 /* pi */ 138 #define M_PI_2 1.57079632679489661923 /* pi/2 */ 139 #define M_PI_4 0.78539816339744830962 /* pi/4 */ 140 #define M_1_PI 0.31830988618379067154 /* 1/pi */ 141 #define M_2_PI 0.63661977236758134308 /* 2/pi */ 142 #define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */ 143 #define M_SQRT2 1.41421356237309504880 /* sqrt(2) */ 144 #define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */ 145 146 #define MAXFLOAT ((float)3.40282346638528860e+38) 147 extern int signgam; 148 #endif /* __BSD_VISIBLE || __XSI_VISIBLE */ 149 150 #if __BSD_VISIBLE 151 #if 0 152 /* Old value from 4.4BSD-Lite math.h; this is probably better. */ 153 #define HUGE HUGE_VAL 154 #else 155 #define HUGE MAXFLOAT 156 #endif 157 #endif /* __BSD_VISIBLE */ 158 159 /* 160 * Most of these functions depend on the rounding mode and have the side 161 * effect of raising floating-point exceptions, so they are not declared 162 * as __pure2. In C99, FENV_ACCESS affects the purity of these functions. 163 */ 164 __BEGIN_DECLS 165 /* 166 * ANSI/POSIX 167 */ 168 int __fpclassifyd(double) __pure2; 169 int __fpclassifyf(float) __pure2; 170 int __fpclassifyl(long double) __pure2; 171 int __isfinitef(float) __pure2; 172 int __isfinite(double) __pure2; 173 int __isfinitel(long double) __pure2; 174 int __isinff(float) __pure2; 175 int __isinf(double) __pure2; 176 int __isinfl(long double) __pure2; 177 int __isnormalf(float) __pure2; 178 int __isnormal(double) __pure2; 179 int __isnormall(long double) __pure2; 180 int __signbit(double) __pure2; 181 int __signbitf(float) __pure2; 182 int __signbitl(long double) __pure2; 183 184 static __inline int 185 __inline_isnan(__const double __x) 186 { 187 188 return (__x != __x); 189 } 190 191 static __inline int 192 __inline_isnanf(__const float __x) 193 { 194 195 return (__x != __x); 196 } 197 198 static __inline int 199 __inline_isnanl(__const long double __x) 200 { 201 202 return (__x != __x); 203 } 204 205 /* 206 * Define the following aliases, for compatibility with glibc and CUDA. 207 */ 208 #define __isnan __inline_isnan 209 #define __isnanf __inline_isnanf 210 211 /* 212 * Version 2 of the Single UNIX Specification (UNIX98) defined isnan() and 213 * isinf() as functions taking double. C99, and the subsequent POSIX revisions 214 * (SUSv3, POSIX.1-2001, define it as a macro that accepts any real floating 215 * point type. If we are targeting SUSv2 and C99 or C11 (or C++11) then we 216 * expose the newer definition, assuming that the language spec takes 217 * precedence over the operating system interface spec. 218 */ 219 #if __XSI_VISIBLE > 0 && __XSI_VISIBLE < 600 && __ISO_C_VISIBLE < 1999 220 #undef isinf 221 #undef isnan 222 int isinf(double); 223 int isnan(double); 224 #endif 225 226 double acos(double); 227 double asin(double); 228 double atan(double); 229 double atan2(double, double); 230 double cos(double); 231 double sin(double); 232 double tan(double); 233 234 double cosh(double); 235 double sinh(double); 236 double tanh(double); 237 238 double exp(double); 239 double frexp(double, int *); /* fundamentally !__pure2 */ 240 double ldexp(double, int); 241 double log(double); 242 double log10(double); 243 double modf(double, double *); /* fundamentally !__pure2 */ 244 245 double pow(double, double); 246 double sqrt(double); 247 248 double ceil(double); 249 double fabs(double) __pure2; 250 double floor(double); 251 double fmod(double, double); 252 253 /* 254 * These functions are not in C90. 255 */ 256 #if __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE 257 double acosh(double); 258 double asinh(double); 259 double atanh(double); 260 double cbrt(double); 261 double erf(double); 262 double erfc(double); 263 double exp2(double); 264 double expm1(double); 265 double fma(double, double, double); 266 double hypot(double, double); 267 int ilogb(double) __pure2; 268 double lgamma(double); 269 long long llrint(double); 270 long long llround(double); 271 double log1p(double); 272 double log2(double); 273 double logb(double); 274 long lrint(double); 275 long lround(double); 276 double nan(const char *) __pure2; 277 double nextafter(double, double); 278 double remainder(double, double); 279 double remquo(double, double, int *); 280 double rint(double); 281 #endif /* __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE */ 282 283 #if __BSD_VISIBLE || __XSI_VISIBLE 284 double j0(double); 285 double j1(double); 286 double jn(int, double); 287 double y0(double); 288 double y1(double); 289 double yn(int, double); 290 291 #if __XSI_VISIBLE <= 500 || __BSD_VISIBLE 292 double gamma(double); 293 #endif 294 295 #if __XSI_VISIBLE <= 600 || __BSD_VISIBLE 296 double scalb(double, double); 297 #endif 298 #endif /* __BSD_VISIBLE || __XSI_VISIBLE */ 299 300 #if __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 301 double copysign(double, double) __pure2; 302 double fdim(double, double); 303 double fmax(double, double) __pure2; 304 double fmin(double, double) __pure2; 305 double nearbyint(double); 306 double round(double); 307 double scalbln(double, long); 308 double scalbn(double, int); 309 double tgamma(double); 310 double trunc(double); 311 #endif 312 313 /* 314 * BSD math library entry points 315 */ 316 #if __BSD_VISIBLE 317 double drem(double, double); 318 int finite(double) __pure2; 319 int isnanf(float) __pure2; 320 321 /* 322 * Reentrant version of gamma & lgamma; passes signgam back by reference 323 * as the second argument; user must allocate space for signgam. 324 */ 325 double gamma_r(double, int *); 326 double lgamma_r(double, int *); 327 328 /* 329 * IEEE Test Vector 330 */ 331 double significand(double); 332 #endif /* __BSD_VISIBLE */ 333 334 /* float versions of ANSI/POSIX functions */ 335 #if __ISO_C_VISIBLE >= 1999 336 float acosf(float); 337 float asinf(float); 338 float atanf(float); 339 float atan2f(float, float); 340 float cosf(float); 341 float sinf(float); 342 float tanf(float); 343 344 float coshf(float); 345 float sinhf(float); 346 float tanhf(float); 347 348 float exp2f(float); 349 float expf(float); 350 float expm1f(float); 351 float frexpf(float, int *); /* fundamentally !__pure2 */ 352 int ilogbf(float) __pure2; 353 float ldexpf(float, int); 354 float log10f(float); 355 float log1pf(float); 356 float log2f(float); 357 float logf(float); 358 float modff(float, float *); /* fundamentally !__pure2 */ 359 360 float powf(float, float); 361 float sqrtf(float); 362 363 float ceilf(float); 364 float fabsf(float) __pure2; 365 float floorf(float); 366 float fmodf(float, float); 367 float roundf(float); 368 369 float erff(float); 370 float erfcf(float); 371 float hypotf(float, float); 372 float lgammaf(float); 373 float tgammaf(float); 374 375 float acoshf(float); 376 float asinhf(float); 377 float atanhf(float); 378 float cbrtf(float); 379 float logbf(float); 380 float copysignf(float, float) __pure2; 381 long long llrintf(float); 382 long long llroundf(float); 383 long lrintf(float); 384 long lroundf(float); 385 float nanf(const char *) __pure2; 386 float nearbyintf(float); 387 float nextafterf(float, float); 388 float remainderf(float, float); 389 float remquof(float, float, int *); 390 float rintf(float); 391 float scalblnf(float, long); 392 float scalbnf(float, int); 393 float truncf(float); 394 395 float fdimf(float, float); 396 float fmaf(float, float, float); 397 float fmaxf(float, float) __pure2; 398 float fminf(float, float) __pure2; 399 #endif 400 401 /* 402 * float versions of BSD math library entry points 403 */ 404 #if __BSD_VISIBLE 405 float dremf(float, float); 406 int finitef(float) __pure2; 407 float gammaf(float); 408 float j0f(float); 409 float j1f(float); 410 float jnf(int, float); 411 float scalbf(float, float); 412 float y0f(float); 413 float y1f(float); 414 float ynf(int, float); 415 416 /* 417 * Float versions of reentrant version of gamma & lgamma; passes 418 * signgam back by reference as the second argument; user must 419 * allocate space for signgam. 420 */ 421 float gammaf_r(float, int *); 422 float lgammaf_r(float, int *); 423 424 /* 425 * float version of IEEE Test Vector 426 */ 427 float significandf(float); 428 #endif /* __BSD_VISIBLE */ 429 430 /* 431 * long double versions of ISO/POSIX math functions 432 */ 433 #if __ISO_C_VISIBLE >= 1999 434 long double acoshl(long double); 435 long double acosl(long double); 436 long double asinhl(long double); 437 long double asinl(long double); 438 long double atan2l(long double, long double); 439 long double atanhl(long double); 440 long double atanl(long double); 441 long double cbrtl(long double); 442 long double ceill(long double); 443 long double copysignl(long double, long double) __pure2; 444 long double coshl(long double); 445 long double cosl(long double); 446 long double erfcl(long double); 447 long double erfl(long double); 448 long double exp2l(long double); 449 long double expl(long double); 450 long double expm1l(long double); 451 long double fabsl(long double) __pure2; 452 long double fdiml(long double, long double); 453 long double floorl(long double); 454 long double fmal(long double, long double, long double); 455 long double fmaxl(long double, long double) __pure2; 456 long double fminl(long double, long double) __pure2; 457 long double fmodl(long double, long double); 458 long double frexpl(long double, int *); /* fundamentally !__pure2 */ 459 long double hypotl(long double, long double); 460 int ilogbl(long double) __pure2; 461 long double ldexpl(long double, int); 462 long double lgammal(long double); 463 long long llrintl(long double); 464 long long llroundl(long double); 465 long double log10l(long double); 466 long double log1pl(long double); 467 long double log2l(long double); 468 long double logbl(long double); 469 long double logl(long double); 470 long lrintl(long double); 471 long lroundl(long double); 472 long double modfl(long double, long double *); /* fundamentally !__pure2 */ 473 long double nanl(const char *) __pure2; 474 long double nearbyintl(long double); 475 long double nextafterl(long double, long double); 476 double nexttoward(double, long double); 477 float nexttowardf(float, long double); 478 long double nexttowardl(long double, long double); 479 long double powl(long double, long double); 480 long double remainderl(long double, long double); 481 long double remquol(long double, long double, int *); 482 long double rintl(long double); 483 long double roundl(long double); 484 long double scalblnl(long double, long); 485 long double scalbnl(long double, int); 486 long double sinhl(long double); 487 long double sinl(long double); 488 long double sqrtl(long double); 489 long double tanhl(long double); 490 long double tanl(long double); 491 long double tgammal(long double); 492 long double truncl(long double); 493 #endif /* __ISO_C_VISIBLE >= 1999 */ 494 495 #if __BSD_VISIBLE 496 long double lgammal_r(long double, int *); 497 void sincos(double, double *, double *); 498 void sincosf(float, float *, float *); 499 void sincosl(long double, long double *, long double *); 500 double cospi(double); 501 float cospif(float); 502 long double cospil(long double); 503 double sinpi(double); 504 float sinpif(float); 505 long double sinpil(long double); 506 double tanpi(double); 507 float tanpif(float); 508 long double tanpil(long double); 509 #endif 510 511 __END_DECLS 512 513 #endif /* !_MATH_H_ */