usr/src/boot/include/math.h

   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
 197 __inline_isnan(__const double __x)
 198 {
 199
 200         return (__x != __x);
 201 }
 202
 203 static __inline int
 204 __inline_isnanf(__const float __x)
 205 {
 206
 207         return (__x != __x);
 208 }
 209
 210 static __inline int
 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_ */