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 #ifdef __ia64__ 73 #define FP_FAST_FMA 1 74 #define FP_FAST_FMAL 1 75 #endif 76 77 /* Symbolic constants to classify floating point numbers. */ 78 #define FP_INFINITE 0x01 79 #define FP_NAN 0x02 80 #define FP_NORMAL 0x04 81 #define FP_SUBNORMAL 0x08 82 #define FP_ZERO 0x10 83 84 #if (__STDC_VERSION__ >= 201112L && defined(__clang__)) || \ 85 __has_extension(c_generic_selections) 86 #define __fp_type_select(x, f, d, ld) _Generic((x), \ 87 float: f(x), \ 88 double: d(x), \ 89 long double: ld(x), \ 90 volatile float: f(x), \ 91 volatile double: d(x), \ 92 volatile long double: ld(x), \ 93 volatile const float: f(x), \ 94 volatile const double: d(x), \ 95 volatile const long double: ld(x), \ 96 const float: f(x), \ 97 const double: d(x), \ 98 const long double: ld(x)) 99 #elif __GNUC_PREREQ__(3, 1) && !defined(__cplusplus) 100 #define __fp_type_select(x, f, d, ld) __builtin_choose_expr( \ 101 __builtin_types_compatible_p(__typeof(x), long double), ld(x), \ 102 __builtin_choose_expr( \ 103 __builtin_types_compatible_p(__typeof(x), double), d(x), \ 104 __builtin_choose_expr( \ 105 __builtin_types_compatible_p(__typeof(x), float), f(x), (void)0))) 106 #else 107 #define __fp_type_select(x, f, d, ld) \ 108 ((sizeof(x) == sizeof(float)) ? f(x) \ 109 : (sizeof(x) == sizeof(double)) ? d(x) \ 110 : ld(x)) 111 #endif 112 113 #define fpclassify(x) \ 114 __fp_type_select(x, __fpclassifyf, __fpclassifyd, __fpclassifyl) 115 #define isfinite(x) __fp_type_select(x, __isfinitef, __isfinite, __isfinitel) 116 #define isinf(x) __fp_type_select(x, __isinff, __isinf, __isinfl) 117 #define isnan(x) \ 118 __fp_type_select(x, __inline_isnanf, __inline_isnan, __inline_isnanl) 119 #define isnormal(x) __fp_type_select(x, __isnormalf, __isnormal, __isnormall) 120 121 #ifdef __MATH_BUILTIN_RELOPS 122 #define isgreater(x, y) __builtin_isgreater((x), (y)) 123 #define isgreaterequal(x, y) __builtin_isgreaterequal((x), (y)) 124 #define isless(x, y) __builtin_isless((x), (y)) 125 #define islessequal(x, y) __builtin_islessequal((x), (y)) 126 #define islessgreater(x, y) __builtin_islessgreater((x), (y)) 127 #define isunordered(x, y) __builtin_isunordered((x), (y)) 128 #else 129 #define isgreater(x, y) (!isunordered((x), (y)) && (x) > (y)) 130 #define isgreaterequal(x, y) (!isunordered((x), (y)) && (x) >= (y)) 131 #define isless(x, y) (!isunordered((x), (y)) && (x) < (y)) 132 #define islessequal(x, y) (!isunordered((x), (y)) && (x) <= (y)) 133 #define islessgreater(x, y) (!isunordered((x), (y)) && \ 134 ((x) > (y) || (y) > (x))) 135 #define isunordered(x, y) (isnan(x) || isnan(y)) 136 #endif /* __MATH_BUILTIN_RELOPS */ 137 138 #define signbit(x) __fp_type_select(x, __signbitf, __signbit, __signbitl) 139 140 typedef __double_t double_t; 141 typedef __float_t float_t; 142 #endif /* __ISO_C_VISIBLE >= 1999 */ 143 144 /* 145 * XOPEN/SVID 146 */ 147 #if __BSD_VISIBLE || __XSI_VISIBLE 148 #define M_E 2.7182818284590452354 /* e */ 149 #define M_LOG2E 1.4426950408889634074 /* log 2e */ 150 #define M_LOG10E 0.43429448190325182765 /* log 10e */ 151 #define M_LN2 0.69314718055994530942 /* log e2 */ 152 #define M_LN10 2.30258509299404568402 /* log e10 */ 153 #define M_PI 3.14159265358979323846 /* pi */ 154 #define M_PI_2 1.57079632679489661923 /* pi/2 */ 155 #define M_PI_4 0.78539816339744830962 /* pi/4 */ 156 #define M_1_PI 0.31830988618379067154 /* 1/pi */ 157 #define M_2_PI 0.63661977236758134308 /* 2/pi */ 158 #define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */ 159 #define M_SQRT2 1.41421356237309504880 /* sqrt(2) */ 160 #define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */ 161 162 #define MAXFLOAT ((float)3.40282346638528860e+38) 163 extern int signgam; 164 #endif /* __BSD_VISIBLE || __XSI_VISIBLE */ 165 166 #if __BSD_VISIBLE 167 #if 0 168 /* Old value from 4.4BSD-Lite math.h; this is probably better. */ 169 #define HUGE HUGE_VAL 170 #else 171 #define HUGE MAXFLOAT 172 #endif 173 #endif /* __BSD_VISIBLE */ 174 175 /* 176 * Most of these functions depend on the rounding mode and have the side 177 * effect of raising floating-point exceptions, so they are not declared 178 * as __pure2. In C99, FENV_ACCESS affects the purity of these functions. 179 */ 180 __BEGIN_DECLS 181 /* 182 * ANSI/POSIX 183 */ 184 int __fpclassifyd(double) __pure2; 185 int __fpclassifyf(float) __pure2; 186 int __fpclassifyl(long double) __pure2; 187 int __isfinitef(float) __pure2; 188 int __isfinite(double) __pure2; 189 int __isfinitel(long double) __pure2; 190 int __isinff(float) __pure2; 191 int __isinf(double) __pure2; 192 int __isinfl(long double) __pure2; 193 int __isnormalf(float) __pure2; 194 int __isnormal(double) __pure2; 195 int __isnormall(long double) __pure2; 196 int __signbit(double) __pure2; 197 int __signbitf(float) __pure2; 198 int __signbitl(long double) __pure2; 199 200 static __inline int 201 __inline_isnan(__const double __x) 202 { 203 204 return (__x != __x); 205 } 206 207 static __inline int 208 __inline_isnanf(__const float __x) 209 { 210 211 return (__x != __x); 212 } 213 214 static __inline int 215 __inline_isnanl(__const long double __x) 216 { 217 218 return (__x != __x); 219 } 220 221 /* 222 * Version 2 of the Single UNIX Specification (UNIX98) defined isnan() and 223 * isinf() as functions taking double. C99, and the subsequent POSIX revisions 224 * (SUSv3, POSIX.1-2001, define it as a macro that accepts any real floating 225 * point type. If we are targeting SUSv2 and C99 or C11 (or C++11) then we 226 * expose the newer definition, assuming that the language spec takes 227 * precedence over the operating system interface spec. 228 */ 229 #if __XSI_VISIBLE > 0 && __XSI_VISIBLE < 600 && __ISO_C_VISIBLE < 1999 230 #undef isinf 231 #undef isnan 232 int isinf(double); 233 int isnan(double); 234 #endif 235 236 double acos(double); 237 double asin(double); 238 double atan(double); 239 double atan2(double, double); 240 double cos(double); 241 double sin(double); 242 double tan(double); 243 244 double cosh(double); 245 double sinh(double); 246 double tanh(double); 247 248 double exp(double); 249 double frexp(double, int *); /* fundamentally !__pure2 */ 250 double ldexp(double, int); 251 double log(double); 252 double log10(double); 253 double modf(double, double *); /* fundamentally !__pure2 */ 254 255 double pow(double, double); 256 double sqrt(double); 257 258 double ceil(double); 259 double fabs(double) __pure2; 260 double floor(double); 261 double fmod(double, double); 262 263 /* 264 * These functions are not in C90. 265 */ 266 #if __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE 267 double acosh(double); 268 double asinh(double); 269 double atanh(double); 270 double cbrt(double); 271 double erf(double); 272 double erfc(double); 273 double exp2(double); 274 double expm1(double); 275 double fma(double, double, double); 276 double hypot(double, double); 277 int ilogb(double) __pure2; 278 double lgamma(double); 279 long long llrint(double); 280 long long llround(double); 281 double log1p(double); 282 double log2(double); 283 double logb(double); 284 long lrint(double); 285 long lround(double); 286 double nan(const char *) __pure2; 287 double nextafter(double, double); 288 double remainder(double, double); 289 double remquo(double, double, int *); 290 double rint(double); 291 #endif /* __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE */ 292 293 #if __BSD_VISIBLE || __XSI_VISIBLE 294 double j0(double); 295 double j1(double); 296 double jn(int, double); 297 double y0(double); 298 double y1(double); 299 double yn(int, double); 300 301 #if __XSI_VISIBLE <= 500 || __BSD_VISIBLE 302 double gamma(double); 303 #endif 304 305 #if __XSI_VISIBLE <= 600 || __BSD_VISIBLE 306 double scalb(double, double); 307 #endif 308 #endif /* __BSD_VISIBLE || __XSI_VISIBLE */ 309 310 #if __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 311 double copysign(double, double) __pure2; 312 double fdim(double, double); 313 double fmax(double, double) __pure2; 314 double fmin(double, double) __pure2; 315 double nearbyint(double); 316 double round(double); 317 double scalbln(double, long); 318 double scalbn(double, int); 319 double tgamma(double); 320 double trunc(double); 321 #endif 322 323 /* 324 * BSD math library entry points 325 */ 326 #if __BSD_VISIBLE 327 double drem(double, double); 328 int finite(double) __pure2; 329 int isnanf(float) __pure2; 330 331 /* 332 * Reentrant version of gamma & lgamma; passes signgam back by reference 333 * as the second argument; user must allocate space for signgam. 334 */ 335 double gamma_r(double, int *); 336 double lgamma_r(double, int *); 337 338 /* 339 * IEEE Test Vector 340 */ 341 double significand(double); 342 #endif /* __BSD_VISIBLE */ 343 344 /* float versions of ANSI/POSIX functions */ 345 #if __ISO_C_VISIBLE >= 1999 346 float acosf(float); 347 float asinf(float); 348 float atanf(float); 349 float atan2f(float, float); 350 float cosf(float); 351 float sinf(float); 352 float tanf(float); 353 354 float coshf(float); 355 float sinhf(float); 356 float tanhf(float); 357 358 float exp2f(float); 359 float expf(float); 360 float expm1f(float); 361 float frexpf(float, int *); /* fundamentally !__pure2 */ 362 int ilogbf(float) __pure2; 363 float ldexpf(float, int); 364 float log10f(float); 365 float log1pf(float); 366 float log2f(float); 367 float logf(float); 368 float modff(float, float *); /* fundamentally !__pure2 */ 369 370 float powf(float, float); 371 float sqrtf(float); 372 373 float ceilf(float); 374 float fabsf(float) __pure2; 375 float floorf(float); 376 float fmodf(float, float); 377 float roundf(float); 378 379 float erff(float); 380 float erfcf(float); 381 float hypotf(float, float); 382 float lgammaf(float); 383 float tgammaf(float); 384 385 float acoshf(float); 386 float asinhf(float); 387 float atanhf(float); 388 float cbrtf(float); 389 float logbf(float); 390 float copysignf(float, float) __pure2; 391 long long llrintf(float); 392 long long llroundf(float); 393 long lrintf(float); 394 long lroundf(float); 395 float nanf(const char *) __pure2; 396 float nearbyintf(float); 397 float nextafterf(float, float); 398 float remainderf(float, float); 399 float remquof(float, float, int *); 400 float rintf(float); 401 float scalblnf(float, long); 402 float scalbnf(float, int); 403 float truncf(float); 404 405 float fdimf(float, float); 406 float fmaf(float, float, float); 407 float fmaxf(float, float) __pure2; 408 float fminf(float, float) __pure2; 409 #endif 410 411 /* 412 * float versions of BSD math library entry points 413 */ 414 #if __BSD_VISIBLE 415 float dremf(float, float); 416 int finitef(float) __pure2; 417 float gammaf(float); 418 float j0f(float); 419 float j1f(float); 420 float jnf(int, float); 421 float scalbf(float, float); 422 float y0f(float); 423 float y1f(float); 424 float ynf(int, float); 425 426 /* 427 * Float versions of reentrant version of gamma & lgamma; passes 428 * signgam back by reference as the second argument; user must 429 * allocate space for signgam. 430 */ 431 float gammaf_r(float, int *); 432 float lgammaf_r(float, int *); 433 434 /* 435 * float version of IEEE Test Vector 436 */ 437 float significandf(float); 438 #endif /* __BSD_VISIBLE */ 439 440 /* 441 * long double versions of ISO/POSIX math functions 442 */ 443 #if __ISO_C_VISIBLE >= 1999 444 long double acoshl(long double); 445 long double acosl(long double); 446 long double asinhl(long double); 447 long double asinl(long double); 448 long double atan2l(long double, long double); 449 long double atanhl(long double); 450 long double atanl(long double); 451 long double cbrtl(long double); 452 long double ceill(long double); 453 long double copysignl(long double, long double) __pure2; 454 long double coshl(long double); 455 long double cosl(long double); 456 long double exp2l(long double); 457 long double expl(long double); 458 long double expm1l(long double); 459 long double fabsl(long double) __pure2; 460 long double fdiml(long double, long double); 461 long double floorl(long double); 462 long double fmal(long double, long double, long double); 463 long double fmaxl(long double, long double) __pure2; 464 long double fminl(long double, long double) __pure2; 465 long double fmodl(long double, long double); 466 long double frexpl(long double value, int *); /* fundamentally !__pure2 */ 467 long double hypotl(long double, long double); 468 int ilogbl(long double) __pure2; 469 long double ldexpl(long double, int); 470 long long llrintl(long double); 471 long long llroundl(long double); 472 long double log10l(long double); 473 long double log1pl(long double); 474 long double log2l(long double); 475 long double logbl(long double); 476 long double logl(long double); 477 long lrintl(long double); 478 long lroundl(long double); 479 long double modfl(long double, long double *); /* fundamentally !__pure2 */ 480 long double nanl(const char *) __pure2; 481 long double nearbyintl(long double); 482 long double nextafterl(long double, long double); 483 double nexttoward(double, long double); 484 float nexttowardf(float, long double); 485 long double nexttowardl(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 truncl(long double); 498 499 #endif /* __ISO_C_VISIBLE >= 1999 */ 500 __END_DECLS 501 502 #endif /* !_MATH_H_ */ 503 504 /* separate header for cmath */ 505 #ifndef _MATH_EXTRA_H_ 506 #if __ISO_C_VISIBLE >= 1999 507 #if _DECLARE_C99_LDBL_MATH 508 509 #define _MATH_EXTRA_H_ 510 511 /* 512 * extra long double versions of math functions for C99 and cmath 513 */ 514 __BEGIN_DECLS 515 516 long double erfcl(long double); 517 long double erfl(long double); 518 long double lgammal(long double); 519 long double powl(long double, long double); 520 long double tgammal(long double); 521 522 __END_DECLS 523 524 #endif /* !_DECLARE_C99_LDBL_MATH */ 525 #endif /* __ISO_C_VISIBLE >= 1999 */ 526 #endif /* !_MATH_EXTRA_H_ */ 527