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  * $NetBSD: math.h,v 1.46 2007/02/22 22:08:19 drochner Exp $
  12  */
  13
  14 /*
  15  * @(#)fdlibm.h 5.1 93/09/24
  16  */
  17
  18 #ifndef _MATH_H_
  19 #define _MATH_H_
  20
  21 #include <sys/cdefs.h>
  22 #include <machine/limits.h>
  23
  24 #if __GNUC_PREREQ__(3, 3) || (defined(__INTEL_COMPILER) && __INTEL_COMPILER >= 800)
  25 #define __MATH_BUILTIN_CONSTANTS
  26 #endif
  27
  28 #if __GNUC_PREREQ__(3, 0) && !defined(__INTEL_COMPILER)
  29 #define __MATH_BUILTIN_RELOPS
  30 #endif
  31
  32 union __float_u {
  33         unsigned char __dummy[sizeof(float)];
  34         float __val;
  35 };
  36
  37 union __double_u {
  38         unsigned char __dummy[sizeof(double)];
  39         double __val;
  40 };
  41
  42 union __long_double_u {
  43         unsigned char __dummy[sizeof(long double)];
  44         long double __val;
  45 };
  46
  47 #include <machine/math.h>
  48
  49 #ifdef __HAVE_LONG_DOUBLE
  50 #define __fpmacro_unary_floating(__name, __arg0)                        \
  51         /* LINTED */                                                    \
  52         ((sizeof (__arg0) == sizeof (float))                            \
  53         ?       __ ## __name ## f (__arg0)                              \
  54         : (sizeof (__arg0) == sizeof (double))                          \
  55         ?       __ ## __name ## d (__arg0)                              \
  56         :       __ ## __name ## l (__arg0))
  57 #else
  58 #define __fpmacro_unary_floating(__name, __arg0)                        \
  59         /* LINTED */                                                    \
  60         ((sizeof (__arg0) == sizeof (float))                            \
  61         ?       __ ## __name ## f (__arg0)                              \
  62         :       __ ## __name ## d (__arg0))
  63 #endif /* __HAVE_LONG_DOUBLE */
  64
  65 /*
  66  * ANSI/POSIX
  67  */
  68 /* 7.12#3 HUGE_VAL, HUGELF, HUGE_VALL */
  69 extern const union __double_u __infinity;
  70 #ifdef __MATH_BUILTIN_CONSTANTS
  71 #define HUGE_VAL        __builtin_huge_val()
  72 #else
  73 #define HUGE_VAL        __infinity.__val
  74 #endif
  75
  76 /*
  77  * ISO C99
  78  */
  79 #if __ISO_C_VISIBLE >= 1999
  80 /* 7.12#3 HUGE_VAL, HUGELF, HUGE_VALL */
  81 extern const union __float_u __infinityf;
  82 #ifdef __MATH_BUILTIN_CONSTANTS
  83 #define HUGE_VALF       __builtin_huge_valf()
  84 #else
  85 #define HUGE_VALF       __infinityf.__val
  86 #endif
  87
  88 extern const union __long_double_u __infinityl;
  89 #ifdef __MATH_BUILTIN_CONSTANTS
  90 #define HUGE_VALL       __builtin_huge_vall()
  91 #else
  92 #define HUGE_VALL       __infinityl.__val
  93 #endif
  94
  95 /* 7.12#4 INFINITY */
  96 #ifdef __MATH_BUILTIN_CONSTANTS
  97 #define INFINITY        __builtin_inf()
  98 #elif defined(__INFINITY)
  99 #define INFINITY        __INFINITY      /* float constant which overflows */
 100 #else
 101 #define INFINITY        HUGE_VALF       /* positive infinity */
 102 #endif /* __INFINITY */
 103
 104 /* 7.12#5 NAN: a quiet NaN, if supported */
 105 #ifdef __MATH_BUILTIN_CONSTANTS
 106 #define NAN             __builtin_nan("")
 107 #elif defined(__HAVE_NANF)
 108 extern const union __float_u __nanf;
 109 #define NAN             __nanf.__val
 110 #endif /* __HAVE_NANF */
 111
 112 /* 7.12#6 number classification macros */
 113 #define FP_INFINITE     0x00
 114 #define FP_NAN          0x01
 115 #define FP_NORMAL       0x02
 116 #define FP_SUBNORMAL    0x03
 117 #define FP_ZERO         0x04
 118 /* NetBSD extensions */
 119 #define _FP_LOMD        0x80            /* range for machine-specific classes */
 120 #define _FP_HIMD        0xff
 121
 122 /* 7.12#8 values returned by ilogb(0) or ilogb(NAN), respectively */
 123 #define FP_ILOGB0       INT_MIN
 124 #define FP_ILOGBNAN     INT_MIN
 125
 126 #endif /* ISO C99 */
 127
 128 /*
 129  * XOPEN/SVID
 130  */
 131 #if __XSI_VISIBLE > 0
 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 /* _XSI_VISIBLE */
 149
 150 #if __DF_VISIBLE
 151 #define HUGE            MAXFLOAT
 152
 153 /*
 154  * set X_TLOSS = pi*2**52, which is possibly defined in <values.h>
 155  * (one may replace the following line by "#include <values.h>")
 156  */
 157
 158 #define X_TLOSS         1.41484755040568800000e+16
 159
 160 #define DOMAIN          1
 161 #define SING            2
 162 #define OVERFLOW        3
 163 #define UNDERFLOW       4
 164 #define TLOSS           5
 165 #define PLOSS           6
 166
 167 #endif /* __DF_VISIBLE */
 168
 169 __BEGIN_DECLS
 170 /*
 171  * ANSI/POSIX
 172  */
 173 double  acos(double);
 174 double  asin(double);
 175 double  atan(double);
 176 double  atan2(double, double);
 177 double  cos(double);
 178 double  sin(double);
 179 double  tan(double);
 180
 181 double  cosh(double);
 182 double  sinh(double);
 183 double  tanh(double);
 184
 185 double  exp(double);
 186 double  exp2(double);
 187 double  frexp(double, int *);
 188 double  ldexp(double, int);
 189 double  log(double);
 190 double  log2(double);
 191 double  log10(double);
 192 double  modf(double, double *);
 193
 194 double  pow(double, double);
 195 double  sqrt(double);
 196
 197 double  ceil(double);
 198 double  fabs(double);
 199 double  floor(double);
 200 double  fmod(double, double);
 201
 202 #if __XSI_VISIBLE > 0
 203 double  erf(double);
 204 double  erfc(double);
 205 double  gamma(double);
 206 double  hypot(double, double);
 207 int     finite(double);
 208 double  j0(double);
 209 double  j1(double);
 210 double  jn(int, double);
 211 double  lgamma(double);
 212 double  tgamma(double);
 213 double  y0(double);
 214 double  y1(double);
 215 double  yn(int, double);
 216 #endif /* __XSI_VISIBLE */
 217
 218 #if __XSI_VISIBLE >= 500
 219 double  acosh(double);
 220 double  asinh(double);
 221 double  atanh(double);
 222 double  cbrt(double);
 223 double  expm1(double);
 224 int     ilogb(double);
 225 double  log1p(double);
 226 double  logb(double);
 227 double  nextafter(double, double);
 228 double  remainder(double, double);
 229 double  rint(double);
 230 double  scalb(double, double);
 231 #endif /* __XSI_VISIBLE >= 500 */
 232
 233 /*
 234  * ISO C99
 235  */
 236 #if __ISO_C_VISIBLE >= 1999
 237 /* 7.12.3.1 int fpclassify(real-floating x) */
 238 #define fpclassify(__x) __fpmacro_unary_floating(fpclassify, __x)
 239
 240 /* 7.12.3.2 int isfinite(real-floating x) */
 241 #define isfinite(__x)   __fpmacro_unary_floating(isfinite, __x)
 242
 243 /* 7.12.3.5 int isnormal(real-floating x) */
 244 #define isnormal(__x)   (fpclassify(__x) == FP_NORMAL)
 245
 246 /* 7.12.3.6 int signbit(real-floating x) */
 247 #define signbit(__x)    __fpmacro_unary_floating(signbit, __x)
 248
 249 /* 7.12.4 trigonometric */
 250
 251 float   acosf(float);
 252 float   asinf(float);
 253 float   atanf(float);
 254 float   atan2f(float, float);
 255 float   cosf(float);
 256 float   sinf(float);
 257 float   tanf(float);
 258
 259 /* 7.12.5 hyperbolic */
 260
 261 float   acoshf(float);
 262 float   asinhf(float);
 263 float   atanhf(float);
 264 float   coshf(float);
 265 float   sinhf(float);
 266 float   tanhf(float);
 267
 268 /* 7.12.6 exp / log */
 269
 270 float   expf(float);
 271 float   exp2f(float);
 272 float   expm1f(float);
 273 float   frexpf(float, int *);
 274 int     ilogbf(float);
 275 float   ldexpf(float, int);
 276 float   logf(float);
 277 float   log2f(float);
 278 float   log10f(float);
 279 float   log1pf(float);
 280 float   logbf(float);
 281 float   modff(float, float *);
 282 float   scalblnf(float, long);
 283 float   scalbnf(float, int);
 284
 285 /* 7.12.7 power / absolute */
 286
 287 float   cbrtf(float);
 288 float   fabsf(float);
 289 float   hypotf(float, float);
 290 float   powf(float, float);
 291 float   sqrtf(float);
 292
 293 /* 7.12.8 error / gamma */
 294
 295 float   erff(float);
 296 float   erfcf(float);
 297 float   lgammaf(float);
 298 float   tgammaf(float);
 299
 300 /* 7.12.9 nearest integer */
 301
 302 float   ceilf(float);
 303 float   floorf(float);
 304 float   nearbyintf(float);
 305 double  nearbyint(double);
 306 float   rintf(float);
 307 double  round(double);
 308 float   roundf(float);
 309 double  trunc(double);
 310 float   truncf(float);
 311 long int        lrint(double);
 312 long int        lrintf(float);
 313 /* LONGLONG */
 314 long long int   llrint(double);
 315 /* LONGLONG */
 316 long long int   llrintf(float);
 317 long int        lround(double);
 318 long int        lroundf(float);
 319 /* LONGLONG */
 320 long long int   llround(double);
 321 /* LONGLONG */
 322 long long int   llroundf(float);
 323
 324 /* 7.12.10 remainder */
 325
 326 float   fmodf(float, float);
 327 float   remainderf(float, float);
 328
 329 /* 7.12.10.3 The remquo functions */
 330 double remquo(double, double, int *);
 331 float  remquof(float, float, int *);
 332
 333 /* 7.12.11 manipulation */
 334
 335 float   copysignf(float, float);
 336 double  nan(const char *);
 337 float   nanf(const char *);
 338 float   nextafterf(float, float);
 339
 340 /* 7.12.12 maximum, minimum, positive difference */
 341 double  fdim(double, double);
 342 float   fdimf(float, float);
 343
 344 double  fmax(double, double);
 345 float   fmaxf(float, float);
 346
 347 double  fmin(double, double);
 348 float   fminf(float, float);
 349
 350
 351 /* isoC99 */
 352 double fma  (double, double, double);
 353 float  fmaf (float,  float,  float);
 354
 355
 356
 357
 358 #endif /* __ISO_C_VISIBLE >= 1999 */
 359
 360 #if __ISO_C_VISIBLE >= 1999
 361 /* 7.12.3.3 int isinf(real-floating x) */
 362 #ifdef __isinf
 363 #define isinf(__x)      __isinf(__x)
 364 #else
 365 #define isinf(__x)      __fpmacro_unary_floating(isinf, __x)
 366 #endif
 367
 368 /* 7.12.3.4 int isnan(real-floating x) */
 369 #ifdef __isnan
 370 #define isnan(__x)      __isnan(__x)
 371 #else
 372 #define isnan(__x)      __fpmacro_unary_floating(isnan, __x)
 373 #endif
 374
 375 /* 7.12.14 Comparision macros */
 376 #ifdef __MATH_BUILTIN_RELOPS
 377 #define isgreater(x, y)         __builtin_isgreater((x), (y))
 378 #define isgreaterequal(x, y)    __builtin_isgreaterequal((x), (y))
 379 #define isless(x, y)            __builtin_isless((x), (y))
 380 #define islessequal(x, y)       __builtin_islessequal((x), (y))
 381 #define islessgreater(x, y)     __builtin_islessgreater((x), (y))
 382 #define isunordered(x, y)       __builtin_isunordered((x), (y))
 383 #else
 384 #define isgreater(x, y)         (!isunordered((x), (y)) && (x) > (y))
 385 #define isgreaterequal(x, y)    (!isunordered((x), (y)) && (x) >= (y))
 386 #define isless(x, y)            (!isunordered((x), (y)) && (x) < (y))
 387 #define islessequal(x, y)       (!isunordered((x), (y)) && (x) <= (y))
 388 #define islessgreater(x, y)     (!isunordered((x), (y)) && \
 389                                         ((x) > (y) || (y) > (x)))
 390 #define isunordered(x, y)       (isnan(x) || isnan(y))
 391 #endif /* __MATH_BUILTIN_RELOPS */
 392
 393 #endif /* __ISO_C_VISIBLE >= 1999 */
 394
 395 #if __DF_VISIBLE
 396 /*
 397  * IEEE Test Vector
 398  */
 399 double  significand(double);
 400
 401 /*
 402  * Functions callable from C, intended to support IEEE arithmetic.
 403  */
 404 double  copysign(double, double);
 405 double  scalbln(double, long);
 406 double  scalbn(double, int);
 407
 408 /*
 409  * BSD math library entry points
 410  */
 411 double  drem(double, double);
 412
 413 /*
 414  * Reentrant version of gamma & lgamma; passes signgam back by reference
 415  * as the second argument; user must allocate space for signgam.
 416  */
 417 double  gamma_r(double, int *);
 418 double  lgamma_r(double, int *);
 419 #endif /* __DF_VISIBLE */
 420
 421
 422 #if __DF_VISIBLE
 423
 424 /* float versions of ANSI/POSIX functions */
 425
 426 float   gammaf(float);
 427 int     finitef(float);
 428 float   j0f(float);
 429 float   j1f(float);
 430 float   jnf(int, float);
 431 float   y0f(float);
 432 float   y1f(float);
 433 float   ynf(int, float);
 434
 435 float   scalbf(float, float);
 436
 437 /*
 438  * float version of IEEE Test Vector
 439  */
 440 float   significandf(float);
 441
 442 /*
 443  * float versions of BSD math library entry points
 444  */
 445 float   dremf(float, float);
 446
 447 /*
 448  * Float versions of reentrant version of gamma & lgamma; passes
 449  * signgam back by reference as the second argument; user must
 450  * allocate space for signgam.
 451  */
 452 float   gammaf_r(float, int *);
 453 float   lgammaf_r(float, int *);
 454 #endif /* __DF_VISIBLE */
 455
 456 /*
 457  * Library implementation
 458  */
 459 int     __fpclassifyf(float);
 460 int     __fpclassifyd(double);
 461 int     __isfinitef(float);
 462 int     __isfinited(double);
 463 int     __isinff(float);
 464 int     __isinfd(double);
 465 int     __isnanf(float);
 466 int     __isnand(double);
 467 int     __signbitf(float);
 468 int     __signbitd(double);
 469
 470 #ifdef __HAVE_LONG_DOUBLE
 471 int     __fpclassifyl       (long double);
 472 int     __isfinitel         (long double);
 473 int     __isinfl            (long double);
 474 int     __isnanl            (long double);
 475 int     __signbitl          (long double);
 476
 477 long double     acosl       (long double);
 478 long double     asinl       (long double);
 479 long double     atan2l      (long double, long double);
 480 long double     atanl       (long double);
 481 long double     ceill       (long double);
 482 long double     cosl        (long double);
 483 long double     cbrtl       (long double);
 484 long double     copysignl   (long double, long double);
 485 long double     fdiml       (long double, long double);
 486 long double     exp2l       (long double);
 487 long double     fabsl       (long double);
 488 long double     floorl      (long double);
 489 long double     fmal        (long double, long double, long double);
 490 long double     frexpl      (long double, int *);
 491 long double     fmaxl       (long double, long double);
 492 long double     fminl       (long double, long double);
 493 long double     fmodl       (long double, long double);
 494 long double     hypotl      (long double, long double);
 495 int             ilogbl      (long double);
 496 long double     ldexpl      (long double, int);
 497 long long       llrintl     (long double);
 498 long long       llroundl    (long double);
 499 long double     logbl       (long double);
 500 long            lrintl      (long double);
 501 long            lroundl     (long double);
 502 long double     modfl       (long double, long double *);
 503 long double     nanl        (const char *);
 504 long double     nearbyintl  (long double);
 505 long double     nextafterl  (long double, long double);
 506 double          nexttoward  (double,      long double);
 507 float           nexttowardf (float,       long double);
 508 long double     remainderl  (long double, long double);
 509 long double     remquol     (long double, long double, int *);
 510 long double     rintl       (long double);
 511 long double     roundl      (long double);
 512 long double     scalblnl    (long double, long);
 513 long double     scalbnl     (long double, int);
 514 long double     sinl        (long double);
 515 long double     sqrtl       (long double);
 516 long double     tanl        (long double);
 517 long double     truncl      (long double);
 518 #endif
 519 __END_DECLS
 520
 521 #endif /* _MATH_H_ */