include/math.h

   1 /*      $NetBSD: math.h,v 1.63 2013/09/16 15:54:42 martin Exp $ */
   2
   3 /*
   4  * ====================================================
   5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   6  *
   7  * Developed at SunPro, a Sun Microsystems, Inc. business.
   8  * Permission to use, copy, modify, and distribute this
   9  * software is freely granted, provided that this notice
  10  * is preserved.
  11  * ====================================================
  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 <sys/featuretest.h>
  23
  24 union __float_u {
  25         unsigned char __dummy[sizeof(float)];
  26         float __val;
  27 };
  28
  29 union __double_u {
  30         unsigned char __dummy[sizeof(double)];
  31         double __val;
  32 };
  33
  34 union __long_double_u {
  35         unsigned char __dummy[sizeof(long double)];
  36         long double __val;
  37 };
  38
  39 #include <machine/math.h>               /* may use __float_u, __double_u,
  40                                            or __long_double_u */
  41 #include <limits.h>                     /* for INT_{MIN,MAX} */
  42
  43 #if ((_POSIX_C_SOURCE - 0) >= 200809L || defined(_NETBSD_SOURCE))
  44 #  if defined(__FLT_EVAL_METHOD__) && (__FLT_EVAL_METHOD__ - 0) == 0
  45 typedef double double_t;
  46 typedef float float_t;
  47 #  elif (__FLT_EVAL_METHOD__ - 0) == 1
  48 typedef double double_t;
  49 typedef double float_t;
  50 #  elif (__FLT_EVAL_METHOD__ - 0) == 2
  51 typedef long double double_t;
  52 typedef long double float_t;
  53 #  endif
  54 #endif
  55
  56 #ifdef __HAVE_LONG_DOUBLE
  57 #define __fpmacro_unary_floating(__name, __arg0)                        \
  58         /* LINTED */                                                    \
  59         ((sizeof (__arg0) == sizeof (float))                            \
  60         ?       __ ## __name ## f (__arg0)                              \
  61         : (sizeof (__arg0) == sizeof (double))                          \
  62         ?       __ ## __name ## d (__arg0)                              \
  63         :       __ ## __name ## l (__arg0))
  64 #else
  65 #define __fpmacro_unary_floating(__name, __arg0)                        \
  66         /* LINTED */                                                    \
  67         ((sizeof (__arg0) == sizeof (float))                            \
  68         ?       __ ## __name ## f (__arg0)                              \
  69         :       __ ## __name ## d (__arg0))
  70 #endif /* __HAVE_LONG_DOUBLE */
  71
  72 /*
  73  * ANSI/POSIX
  74  */
  75 /* 7.12#3 HUGE_VAL, HUGELF, HUGE_VALL */
  76 #if __GNUC_PREREQ__(3, 3)
  77 #define HUGE_VAL        __builtin_huge_val()
  78 #else
  79 extern const union __double_u __infinity;
  80 #define HUGE_VAL        __infinity.__val
  81 #endif
  82
  83 /*
  84  * ISO C99
  85  */
  86 #if !defined(_ANSI_SOURCE) && !defined(_POSIX_C_SOURCE) && \
  87     !defined(_XOPEN_SOURCE) || \
  88     ((__STDC_VERSION__ - 0) >= 199901L) || \
  89     ((_POSIX_C_SOURCE - 0) >= 200112L) || \
  90     ((_XOPEN_SOURCE  - 0) >= 600) || \
  91     defined(_ISOC99_SOURCE) || defined(_NETBSD_SOURCE)
  92 /* 7.12#3 HUGE_VAL, HUGELF, HUGE_VALL */
  93 #if __GNUC_PREREQ__(3, 3)
  94 #define HUGE_VALF       __builtin_huge_valf()
  95 #define HUGE_VALL       __builtin_huge_vall()
  96 #else
  97 extern const union __float_u __infinityf;
  98 #define HUGE_VALF       __infinityf.__val
  99
 100 extern const union __long_double_u __infinityl;
 101 #define HUGE_VALL       __infinityl.__val
 102 #endif
 103
 104 /* 7.12#4 INFINITY */
 105 #if defined(__INFINITY)
 106 #define INFINITY        __INFINITY      /* float constant which overflows */
 107 #elif __GNUC_PREREQ__(3, 3)
 108 #define INFINITY        __builtin_inff()
 109 #else
 110 #define INFINITY        HUGE_VALF       /* positive infinity */
 111 #endif /* __INFINITY */
 112
 113 /* 7.12#5 NAN: a quiet NaN, if supported */
 114 #ifdef __HAVE_NANF
 115 #if __GNUC_PREREQ__(3,3)
 116 #define NAN     __builtin_nanf("")
 117 #else
 118 extern const union __float_u __nanf;
 119 #define NAN             __nanf.__val
 120 #endif
 121 #endif /* __HAVE_NANF */
 122
 123 /* 7.12#6 number classification macros */
 124 #define FP_INFINITE     0x00
 125 #define FP_NAN          0x01
 126 #define FP_NORMAL       0x02
 127 #define FP_SUBNORMAL    0x03
 128 #define FP_ZERO         0x04
 129 /* NetBSD extensions */
 130 #define _FP_LOMD        0x80            /* range for machine-specific classes */
 131 #define _FP_HIMD        0xff
 132
 133 #define FP_ILOGB0       INT_MIN
 134 #define FP_ILOGBNAN     INT_MAX
 135
 136 #endif /* !_ANSI_SOURCE && ... */
 137
 138 /*
 139  * XOPEN/SVID
 140  */
 141 #if defined(_XOPEN_SOURCE) || defined(_NETBSD_SOURCE)
 142 #define M_E             2.7182818284590452354   /* e */
 143 #define M_LOG2E         1.4426950408889634074   /* log 2e */
 144 #define M_LOG10E        0.43429448190325182765  /* log 10e */
 145 #define M_LN2           0.69314718055994530942  /* log e2 */
 146 #define M_LN10          2.30258509299404568402  /* log e10 */
 147 #define M_PI            3.14159265358979323846  /* pi */
 148 #define M_PI_2          1.57079632679489661923  /* pi/2 */
 149 #define M_PI_4          0.78539816339744830962  /* pi/4 */
 150 #define M_1_PI          0.31830988618379067154  /* 1/pi */
 151 #define M_2_PI          0.63661977236758134308  /* 2/pi */
 152 #define M_2_SQRTPI      1.12837916709551257390  /* 2/sqrt(pi) */
 153 #define M_SQRT2         1.41421356237309504880  /* sqrt(2) */
 154 #define M_SQRT1_2       0.70710678118654752440  /* 1/sqrt(2) */
 155
 156 #define MAXFLOAT        ((float)3.40282346638528860e+38)
 157 extern int signgam;
 158 #endif /* _XOPEN_SOURCE || _NETBSD_SOURCE */
 159
 160 #if defined(_NETBSD_SOURCE)
 161 enum fdversion {fdlibm_ieee = -1, fdlibm_svid, fdlibm_xopen, fdlibm_posix};
 162
 163 #define _LIB_VERSION_TYPE enum fdversion
 164 #define _LIB_VERSION _fdlib_version
 165
 166 /* if global variable _LIB_VERSION is not desirable, one may
 167  * change the following to be a constant by:
 168  *      #define _LIB_VERSION_TYPE const enum version
 169  * In that case, after one initializes the value _LIB_VERSION (see
 170  * s_lib_version.c) during compile time, it cannot be modified
 171  * in the middle of a program
 172  */
 173 extern  _LIB_VERSION_TYPE  _LIB_VERSION;
 174
 175 #define _IEEE_  fdlibm_ieee
 176 #define _SVID_  fdlibm_svid
 177 #define _XOPEN_ fdlibm_xopen
 178 #define _POSIX_ fdlibm_posix
 179
 180 #ifndef __cplusplus
 181 struct exception {
 182         int type;
 183         const char *name;
 184         double arg1;
 185         double arg2;
 186         double retval;
 187 };
 188 #endif
 189
 190 #define HUGE            MAXFLOAT
 191
 192 /*
 193  * set X_TLOSS = pi*2**52, which is possibly defined in <values.h>
 194  * (one may replace the following line by "#include <values.h>")
 195  */
 196
 197 #define X_TLOSS         1.41484755040568800000e+16
 198
 199 #define DOMAIN          1
 200 #define SING            2
 201 #define OVERFLOW        3
 202 #define UNDERFLOW       4
 203 #define TLOSS           5
 204 #define PLOSS           6
 205
 206 #endif /* _NETBSD_SOURCE */
 207
 208 __BEGIN_DECLS
 209 /*
 210  * ANSI/POSIX
 211  */
 212 double  acos(double);
 213 double  asin(double);
 214 double  atan(double);
 215 double  atan2(double, double);
 216 double  cos(double);
 217 double  sin(double);
 218 double  tan(double);
 219
 220 double  cosh(double);
 221 double  sinh(double);
 222 double  tanh(double);
 223
 224 double  exp(double);
 225 double  exp2(double);
 226 double  frexp(double, int *);
 227 double  ldexp(double, int);
 228 double  log(double);
 229 double  log2(double);
 230 double  log10(double);
 231 double  modf(double, double *);
 232
 233 double  pow(double, double);
 234 double  sqrt(double);
 235
 236 double  ceil(double);
 237 double  fabs(double);
 238 double  floor(double);
 239 double  fmod(double, double);
 240
 241 #if defined(_XOPEN_SOURCE) || defined(_NETBSD_SOURCE)
 242 double  erf(double);
 243 double  erfc(double);
 244 double  gamma(double);
 245 double  hypot(double, double);
 246 int     finite(double);
 247 double  j0(double);
 248 double  j1(double);
 249 double  jn(int, double);
 250 double  lgamma(double);
 251 double  y0(double);
 252 double  y1(double);
 253 double  yn(int, double);
 254
 255 #if (_XOPEN_SOURCE - 0) >= 500 || defined(_NETBSD_SOURCE)
 256 double  acosh(double);
 257 double  asinh(double);
 258 double  atanh(double);
 259 double  cbrt(double);
 260 double  expm1(double);
 261 int     ilogb(double);
 262 double  log1p(double);
 263 double  logb(double);
 264 double  nextafter(double, double);
 265 double  remainder(double, double);
 266 double  rint(double);
 267 double  scalb(double, double);
 268 #endif /* (_XOPEN_SOURCE - 0) >= 500 || defined(_NETBSD_SOURCE)*/
 269 #endif /* _XOPEN_SOURCE || _NETBSD_SOURCE */
 270
 271 /*
 272  * ISO C99
 273  */
 274 #if !defined(_ANSI_SOURCE) && !defined(_POSIX_C_SOURCE) && \
 275     !defined(_XOPEN_SOURCE) || \
 276     ((__STDC_VERSION__ - 0) >= 199901L) || \
 277     ((_POSIX_C_SOURCE - 0) >= 200112L) || \
 278     ((_XOPEN_SOURCE  - 0) >= 600) || \
 279     defined(_ISOC99_SOURCE) || defined(_NETBSD_SOURCE)
 280 /* 7.12.3.1 int fpclassify(real-floating x) */
 281 #define fpclassify(__x) __fpmacro_unary_floating(fpclassify, __x)
 282
 283 /* 7.12.3.2 int isfinite(real-floating x) */
 284 #define isfinite(__x)   __fpmacro_unary_floating(isfinite, __x)
 285
 286 /* 7.12.3.5 int isnormal(real-floating x) */
 287 #define isnormal(__x)   (fpclassify(__x) == FP_NORMAL)
 288
 289 /* 7.12.3.6 int signbit(real-floating x) */
 290 #define signbit(__x)    __fpmacro_unary_floating(signbit, __x)
 291
 292 /* 7.12.4 trigonometric */
 293
 294 float   acosf(float);
 295 float   asinf(float);
 296 float   atanf(float);
 297 float   atan2f(float, float);
 298 float   cosf(float);
 299 float   sinf(float);
 300 float   tanf(float);
 301
 302 long double     acosl(long double);
 303 long double     asinl(long double);
 304 long double     atanl(long double);
 305 long double     atan2l(long double, long double);
 306 long double     cosl(long double);
 307 long double     sinl(long double);
 308 long double     tanl(long double);
 309
 310 /* 7.12.5 hyperbolic */
 311
 312 float   acoshf(float);
 313 float   asinhf(float);
 314 float   atanhf(float);
 315 float   coshf(float);
 316 float   sinhf(float);
 317 float   tanhf(float);
 318 long double     acoshl(long double);
 319 long double     asinhl(long double);
 320 long double     atanhl(long double);
 321 long double     coshl(long double);
 322 long double     sinhl(long double);
 323 long double     tanhl(long double);
 324
 325 /* 7.12.6 exp / log */
 326
 327 float   expf(float);
 328 float   exp2f(float);
 329 float   expm1f(float);
 330 float   frexpf(float, int *);
 331 int     ilogbf(float);
 332 float   ldexpf(float, int);
 333 float   logf(float);
 334 float   log2f(float);
 335 float   log10f(float);
 336 float   log1pf(float);
 337 float   logbf(float);
 338 float   modff(float, float *);
 339 float   scalbnf(float, int);
 340 float   scalblnf(float, long);
 341
 342 long double     expl(long double);
 343 long double     exp2l(long double);
 344 long double     expm1l(long double);
 345 long double     frexpl(long double, int *);
 346 int             ilogbl(long double);
 347 long double     ldexpl(long double, int);
 348 long double     logl(long double);
 349 long double     log2l(long double);
 350 long double     log10l(long double);
 351 long double     log1pl(long double);
 352 long double     logbl(long double);
 353 long double     modfl(long double, long double *);
 354 long double     scalbnl(long double, int);
 355 long double     scalblnl(long double, long);
 356
 357
 358 /* 7.12.7 power / absolute */
 359
 360 float   cbrtf(float);
 361 float   fabsf(float);
 362 float   hypotf(float, float);
 363 float   powf(float, float);
 364 float   sqrtf(float);
 365 long double     cbrtl(long double);
 366 long double     fabsl(long double);
 367 long double     hypotl(long double, long double);
 368 long double     powl(long double, long double);
 369 long double     sqrtl(long double);
 370
 371 /* 7.12.8 error / gamma */
 372
 373 double  tgamma(double);
 374 float   erff(float);
 375 float   erfcf(float);
 376 float   lgammaf(float);
 377 float   tgammaf(float);
 378 long double     erfl(long double);
 379 long double     erfcl(long double);
 380 long double     lgammal(long double);
 381 long double     tgammal(long double);
 382
 383 /* 7.12.9 nearest integer */
 384
 385 /* LONGLONG */
 386 long long int   llrint(double);
 387 long int        lround(double);
 388 /* LONGLONG */
 389 long long int   llround(double);
 390 long int        lrint(double);
 391 double  round(double);
 392 double  trunc(double);
 393
 394 float   ceilf(float);
 395 float   floorf(float);
 396 /* LONGLONG */
 397 long long int   llrintf(float);
 398 long int        lroundf(float);
 399 /* LONGLONG */
 400 long long int   llroundf(float);
 401 long int        lrintf(float);
 402 float   rintf(float);
 403 float   roundf(float);
 404 float   truncf(float);
 405 long double     ceill(long double);
 406 long double     floorl(long double);
 407 /* LONGLONG */
 408 long long int   llrintl(long double);
 409 long int        lroundl(long double);
 410 /* LONGLONG */
 411 long long int   llroundl(long double);
 412 long int        lrintl(long double);
 413 long double     rintl(long double);
 414 long double     roundl(long double);
 415 long double     truncl(long double);
 416
 417 /* 7.12.10 remainder */
 418
 419 float   fmodf(float, float);
 420 float   remainderf(float, float);
 421 long double     fmodl(long double, long double);
 422 long double     remainderl(long double, long double);
 423
 424 /* 7.12.10.3 The remquo functions */
 425 double  remquo(double, double, int *);
 426 float   remquof(float, float, int *);
 427 long double     remquol(long double, long double, int *);
 428
 429 /* 7.12.11 manipulation */
 430
 431 double  nan(const char *);
 432 double  nearbyint(double);
 433 double  nexttoward(double, long double);
 434 float   copysignf(float, float);
 435 float   nanf(const char *);
 436 float   nearbyintf(float);
 437 float   nextafterf(float, float);
 438 float   nexttowardf(float, long double);
 439 long double     copysignl(long double, long double);
 440 long double     nanl(const char *);
 441 long double     nearbyintl(long double);
 442 long double     nextafterl(long double, long double);
 443 long double     nexttowardl(long double, long double);
 444
 445 /* 7.12.14 comparison */
 446
 447 #define isunordered(x, y)       (isnan(x) || isnan(y))
 448 #define isgreater(x, y)         (!isunordered((x), (y)) && (x) > (y))
 449 #define isgreaterequal(x, y)    (!isunordered((x), (y)) && (x) >= (y))
 450 #define isless(x, y)            (!isunordered((x), (y)) && (x) < (y))
 451 #define islessequal(x, y)       (!isunordered((x), (y)) && (x) <= (y))
 452 #define islessgreater(x, y)     (!isunordered((x), (y)) && \
 453                                  ((x) > (y) || (y) > (x)))
 454 double  fdim(double, double);
 455 double  fma(double, double, double);
 456 double  fmax(double, double);
 457 double  fmin(double, double);
 458 float   fdimf(float, float);
 459 float   fmaf(float, float, float);
 460 float   fmaxf(float, float);
 461 float   fminf(float, float);
 462 long double fdiml(long double, long double);
 463 long double fmal(long double, long double, long double);
 464 long double fmaxl(long double, long double);
 465 long double fminl(long double, long double);
 466
 467 #endif /* !_ANSI_SOURCE && ... */
 468
 469 #if !defined(_ANSI_SOURCE) && !defined(_POSIX_C_SOURCE) || \
 470     !defined(_XOPEN_SOURCE) || \
 471     ((__STDC_VERSION__ - 0) >= 199901L) || \
 472     ((_POSIX_C_SOURCE - 0) >= 200112L) || \
 473     defined(_ISOC99_SOURCE) || defined(_NETBSD_SOURCE)
 474 /* 7.12.3.3 int isinf(real-floating x) */
 475 #if defined(__isinf) || defined(__HAVE_INLINE___ISINF)
 476 #define isinf(__x)      __isinf(__x)
 477 #else
 478 #define isinf(__x)      __fpmacro_unary_floating(isinf, __x)
 479 #endif
 480
 481 /* 7.12.3.4 int isnan(real-floating x) */
 482 #if defined(__isnan) || defined(__HAVE_INLINE___ISNAN)
 483 #define isnan(__x)      __isnan(__x)
 484 #else
 485 #define isnan(__x)      __fpmacro_unary_floating(isnan, __x)
 486 #endif
 487 #endif /* !_ANSI_SOURCE && ... */
 488
 489 #if defined(_NETBSD_SOURCE)
 490 #ifndef __cplusplus
 491 int     matherr(struct exception *);
 492 #endif
 493
 494 /*
 495  * IEEE Test Vector
 496  */
 497 double  significand(double);
 498
 499 /*
 500  * Functions callable from C, intended to support IEEE arithmetic.
 501  */
 502 double  copysign(double, double);
 503 double  scalbn(double, int);
 504 double  scalbln(double, long);
 505
 506 /*
 507  * BSD math library entry points
 508  */
 509 double  drem(double, double);
 510
 511 #endif /* _NETBSD_SOURCE */
 512
 513 #if defined(_NETBSD_SOURCE) || defined(_REENTRANT)
 514 /*
 515  * Reentrant version of gamma & lgamma; passes signgam back by reference
 516  * as the second argument; user must allocate space for signgam.
 517  */
 518 double  gamma_r(double, int *);
 519 double  lgamma_r(double, int *);
 520 #endif /* _NETBSD_SOURCE || _REENTRANT */
 521
 522
 523 #if defined(_NETBSD_SOURCE)
 524
 525 /* float versions of ANSI/POSIX functions */
 526
 527 float   gammaf(float);
 528 int     isinff(float);
 529 int     isnanf(float);
 530 int     finitef(float);
 531 float   j0f(float);
 532 float   j1f(float);
 533 float   jnf(int, float);
 534 float   y0f(float);
 535 float   y1f(float);
 536 float   ynf(int, float);
 537
 538 float   scalbf(float, float);
 539
 540 /*
 541  * float version of IEEE Test Vector
 542  */
 543 float   significandf(float);
 544
 545 /*
 546  * float versions of BSD math library entry points
 547  */
 548 float   dremf(float, float);
 549 #endif /* _NETBSD_SOURCE */
 550
 551 #if defined(_NETBSD_SOURCE) || defined(_REENTRANT)
 552 /*
 553  * Float versions of reentrant version of gamma & lgamma; passes
 554  * signgam back by reference as the second argument; user must
 555  * allocate space for signgam.
 556  */
 557 float   gammaf_r(float, int *);
 558 float   lgammaf_r(float, int *);
 559 #endif /* !... || _REENTRANT */
 560
 561 /*
 562  * Library implementation
 563  */
 564 int     __fpclassifyf(float);
 565 int     __fpclassifyd(double);
 566 int     __isfinitef(float);
 567 int     __isfinited(double);
 568 int     __isinff(float);
 569 int     __isinfd(double);
 570 int     __isnanf(float);
 571 int     __isnand(double);
 572 int     __signbitf(float);
 573 int     __signbitd(double);
 574
 575 #ifdef __HAVE_LONG_DOUBLE
 576 int     __fpclassifyl(long double);
 577 int     __isfinitel(long double);
 578 int     __isinfl(long double);
 579 int     __isnanl(long double);
 580 int     __signbitl(long double);
 581 #endif
 582
 583 __END_DECLS
 584
 585 #endif /* _MATH_H_ */