math/math.h

   1 /* Declarations for math functions.
   2    Copyright (C) 1991-2016 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4
   5    The GNU C Library is free software; you can redistribute it and/or
   6    modify it under the terms of the GNU Lesser General Public
   7    License as published by the Free Software Foundation; either
   8    version 2.1 of the License, or (at your option) any later version.
   9
  10    The GNU C Library is distributed in the hope that it will be useful,
  11    but WITHOUT ANY WARRANTY; without even the implied warranty of
  12    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13    Lesser General Public License for more details.
  14
  15    You should have received a copy of the GNU Lesser General Public
  16    License along with the GNU C Library; if not, see
  17    <http://www.gnu.org/licenses/>.  */
  18
  19 /*
  20  *      ISO C99 Standard: 7.12 Mathematics      <math.h>
  21  */
  22
  23 #ifndef _MATH_H
  24 #define _MATH_H 1
  25
  26 #define __GLIBC_INTERNAL_STARTING_HEADER_IMPLEMENTATION
  27 #include <bits/libc-header-start.h>
  28
  29 __BEGIN_DECLS
  30
  31 /* Get machine-dependent vector math functions declarations.  */
  32 #include <bits/math-vector.h>
  33
  34 /* Get machine-dependent HUGE_VAL value (returned on overflow).
  35    On all IEEE754 machines, this is +Infinity.  */
  36 #include <bits/huge_val.h>
  37 #ifdef __USE_ISOC99
  38 # include <bits/huge_valf.h>
  39 # include <bits/huge_vall.h>
  40
  41 /* Get machine-dependent INFINITY value.  */
  42 # include <bits/inf.h>
  43
  44 /* Get machine-dependent NAN value (returned for some domain errors).  */
  45 # include <bits/nan.h>
  46 #endif /* __USE_ISOC99 */
  47
  48 /* Get the architecture specific values describing the floating-point
  49    evaluation.  The following symbols will get defined:
  50
  51     float_t     floating-point type at least as wide as `float' used
  52                 to evaluate `float' expressions
  53     double_t    floating-point type at least as wide as `double' used
  54                 to evaluate `double' expressions
  55
  56     FP_FAST_FMA
  57     FP_FAST_FMAF
  58     FP_FAST_FMAL
  59                 If defined it indicates that the `fma' function
  60                 generally executes about as fast as a multiply and an add.
  61                 This macro is defined only iff the `fma' function is
  62                 implemented directly with a hardware multiply-add instructions.
  63
  64     FP_ILOGB0   Expands to a value returned by `ilogb (0.0)'.
  65     FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
  66
  67 */
  68
  69 #include <bits/mathdef.h>
  70
  71 /* The file <bits/mathcalls.h> contains the prototypes for all the
  72    actual math functions.  These macros are used for those prototypes,
  73    so we can easily declare each function as both `name' and `__name',
  74    and can declare the float versions `namef' and `__namef'.  */
  75
  76 #define __SIMD_DECL(function) __CONCAT (__DECL_SIMD_, function)
  77
  78 #define __MATHCALL_VEC(function, suffix, args)  \
  79   __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
  80   __MATHCALL (function, suffix, args)
  81
  82 #define __MATHDECL_VEC(type, function,suffix, args) \
  83   __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
  84   __MATHDECL(type, function,suffix, args)
  85
  86 #define __MATHCALL(function,suffix, args)       \
  87   __MATHDECL (_Mdouble_,function,suffix, args)
  88 #define __MATHDECL(type, function,suffix, args) \
  89   __MATHDECL_1(type, function,suffix, args); \
  90   __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
  91 #define __MATHCALLX(function,suffix, args, attrib)      \
  92   __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
  93 #define __MATHDECLX(type, function,suffix, args, attrib) \
  94   __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
  95   __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
  96 #define __MATHDECL_1(type, function,suffix, args) \
  97   extern type __MATH_PRECNAME(function,suffix) args __THROW
  98
  99 #define _Mdouble_               double
 100 #define __MATH_PRECNAME(name,r) __CONCAT(name,r)
 101 #define __MATH_DECLARING_DOUBLE  1
 102 #define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
 103 #define _Mdouble_END_NAMESPACE   __END_NAMESPACE_STD
 104 #include <bits/mathcalls.h>
 105 #undef  _Mdouble_
 106 #undef _Mdouble_BEGIN_NAMESPACE
 107 #undef _Mdouble_END_NAMESPACE
 108 #undef  __MATH_PRECNAME
 109 #undef __MATH_DECLARING_DOUBLE
 110
 111 #ifdef __USE_ISOC99
 112
 113
 114 /* Include the file of declarations again, this time using `float'
 115    instead of `double' and appending f to each function name.  */
 116
 117 # ifndef _Mfloat_
 118 #  define _Mfloat_              float
 119 # endif
 120 # define _Mdouble_              _Mfloat_
 121 # define __MATH_PRECNAME(name,r) name##f##r
 122 # define __MATH_DECLARING_DOUBLE  0
 123 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
 124 # define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
 125 # include <bits/mathcalls.h>
 126 # undef _Mdouble_
 127 # undef _Mdouble_BEGIN_NAMESPACE
 128 # undef _Mdouble_END_NAMESPACE
 129 # undef __MATH_PRECNAME
 130 # undef __MATH_DECLARING_DOUBLE
 131
 132 # if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
 133      || defined __LDBL_COMPAT \
 134      || defined _LIBC_TEST
 135 #  ifdef __LDBL_COMPAT
 136
 137 #   ifdef __USE_ISOC99
 138 extern float __nldbl_nexttowardf (float __x, long double __y)
 139                                   __THROW __attribute__ ((__const__));
 140 #    ifdef __REDIRECT_NTH
 141 extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
 142                              __nldbl_nexttowardf)
 143      __attribute__ ((__const__));
 144 extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
 145                               nextafter) __attribute__ ((__const__));
 146 extern long double __REDIRECT_NTH (nexttowardl,
 147                                    (long double __x, long double __y),
 148                                    nextafter) __attribute__ ((__const__));
 149 #    endif
 150 #   endif
 151
 152 #   undef __MATHDECL_1
 153 #   define __MATHDECL_2(type, function,suffix, args, alias) \
 154   extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
 155                              args, alias)
 156 #   define __MATHDECL_1(type, function,suffix, args) \
 157   __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
 158 #  endif
 159
 160 /* Include the file of declarations again, this time using `long double'
 161    instead of `double' and appending l to each function name.  */
 162
 163 #  ifndef _Mlong_double_
 164 #   define _Mlong_double_       long double
 165 #  endif
 166 #  define _Mdouble_             _Mlong_double_
 167 #  define __MATH_PRECNAME(name,r) name##l##r
 168 #  define __MATH_DECLARING_DOUBLE  0
 169 #  define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
 170 #  define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
 171 #  define __MATH_DECLARE_LDOUBLE   1
 172 #  include <bits/mathcalls.h>
 173 #  undef _Mdouble_
 174 #  undef _Mdouble_BEGIN_NAMESPACE
 175 #  undef _Mdouble_END_NAMESPACE
 176 #  undef __MATH_PRECNAME
 177 #  undef __MATH_DECLARING_DOUBLE
 178
 179 # endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */
 180
 181 #endif  /* Use ISO C99.  */
 182 #undef  __MATHDECL_1
 183 #undef  __MATHDECL
 184 #undef  __MATHCALL
 185
 186
 187 #if defined __USE_MISC || defined __USE_XOPEN
 188 /* This variable is used by `gamma' and `lgamma'.  */
 189 extern int signgam;
 190 #endif
 191
 192
 193 /* ISO C99 defines some generic macros which work on any data type.  */
 194 #ifdef __USE_ISOC99
 195
 196 /* All floating-point numbers can be put in one of these categories.  */
 197 enum
 198   {
 199     FP_NAN =
 200 # define FP_NAN 0
 201       FP_NAN,
 202     FP_INFINITE =
 203 # define FP_INFINITE 1
 204       FP_INFINITE,
 205     FP_ZERO =
 206 # define FP_ZERO 2
 207       FP_ZERO,
 208     FP_SUBNORMAL =
 209 # define FP_SUBNORMAL 3
 210       FP_SUBNORMAL,
 211     FP_NORMAL =
 212 # define FP_NORMAL 4
 213       FP_NORMAL
 214   };
 215
 216 /* GCC bug 66462 means we cannot use the math builtins with -fsignaling-nan,
 217    so disable builtins if this is enabled.  When fixed in a newer GCC,
 218    the __SUPPORT_SNAN__ check may be skipped for those versions.  */
 219
 220 /* Return number of classification appropriate for X.  */
 221 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__                         \
 222      && !defined __OPTIMIZE_SIZE__
 223 #  define fpclassify(x) __builtin_fpclassify (FP_NAN, FP_INFINITE,            \
 224      FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x)
 225 # elif defined __NO_LONG_DOUBLE_MATH
 226 #  define fpclassify(x) \
 227      (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
 228 # else
 229 #  define fpclassify(x) \
 230      (sizeof (x) == sizeof (float)                                            \
 231       ? __fpclassifyf (x)                                                     \
 232       : sizeof (x) == sizeof (double)                                         \
 233       ? __fpclassify (x) : __fpclassifyl (x))
 234 # endif
 235
 236 /* Return nonzero value if sign of X is negative.  */
 237 # if __GNUC_PREREQ (4,0)
 238 #  define signbit(x) \
 239      (sizeof (x) == sizeof (float)                                            \
 240       ? __builtin_signbitf (x)                                                        \
 241       : sizeof (x) == sizeof (double)                                         \
 242       ? __builtin_signbit (x) : __builtin_signbitl (x))
 243 # else
 244 #  ifdef __NO_LONG_DOUBLE_MATH
 245 #   define signbit(x) \
 246      (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
 247 #  else
 248 #   define signbit(x) \
 249      (sizeof (x) == sizeof (float)                                            \
 250       ? __signbitf (x)                                                        \
 251       : sizeof (x) == sizeof (double)                                         \
 252       ? __signbit (x) : __signbitl (x))
 253 #  endif
 254 # endif
 255
 256 /* Return nonzero value if X is not +-Inf or NaN.  */
 257 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
 258 #  define isfinite(x) __builtin_isfinite (x)
 259 # elif defined __NO_LONG_DOUBLE_MATH
 260 #  define isfinite(x) \
 261      (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
 262 # else
 263 #  define isfinite(x) \
 264      (sizeof (x) == sizeof (float)                                            \
 265       ? __finitef (x)                                                         \
 266       : sizeof (x) == sizeof (double)                                         \
 267       ? __finite (x) : __finitel (x))
 268 # endif
 269
 270 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
 271 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
 272 #  define isnormal(x) __builtin_isnormal (x)
 273 # else
 274 #  define isnormal(x) (fpclassify (x) == FP_NORMAL)
 275 # endif
 276
 277 /* Return nonzero value if X is a NaN.  We could use `fpclassify' but
 278    we already have this functions `__isnan' and it is faster.  */
 279 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
 280 #  define isnan(x) __builtin_isnan (x)
 281 # elif defined __NO_LONG_DOUBLE_MATH
 282 #  define isnan(x) \
 283      (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
 284 # else
 285 #  define isnan(x) \
 286      (sizeof (x) == sizeof (float)                                            \
 287       ? __isnanf (x)                                                          \
 288       : sizeof (x) == sizeof (double)                                         \
 289       ? __isnan (x) : __isnanl (x))
 290 # endif
 291
 292 /* Return nonzero value if X is positive or negative infinity.  */
 293 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
 294 #  define isinf(x) __builtin_isinf_sign (x)
 295 # elif defined __NO_LONG_DOUBLE_MATH
 296 #  define isinf(x) \
 297      (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
 298 # else
 299 #  define isinf(x) \
 300      (sizeof (x) == sizeof (float)                                            \
 301       ? __isinff (x)                                                          \
 302       : sizeof (x) == sizeof (double)                                         \
 303       ? __isinf (x) : __isinfl (x))
 304 # endif
 305
 306 /* Bitmasks for the math_errhandling macro.  */
 307 # define MATH_ERRNO     1       /* errno set by math functions.  */
 308 # define MATH_ERREXCEPT 2       /* Exceptions raised by math functions.  */
 309
 310 /* By default all functions support both errno and exception handling.
 311    In gcc's fast math mode and if inline functions are defined this
 312    might not be true.  */
 313 # ifndef __FAST_MATH__
 314 #  define math_errhandling      (MATH_ERRNO | MATH_ERREXCEPT)
 315 # endif
 316
 317 #endif /* Use ISO C99.  */
 318
 319 #if __GLIBC_USE (IEC_60559_BFP_EXT)
 320 /* Return nonzero value if X is a signaling NaN.  */
 321 # ifdef __NO_LONG_DOUBLE_MATH
 322 #  define issignaling(x) \
 323      (sizeof (x) == sizeof (float) ? __issignalingf (x) : __issignaling (x))
 324 # else
 325 #  define issignaling(x) \
 326      (sizeof (x) == sizeof (float)                                            \
 327       ? __issignalingf (x)                                                    \
 328       : sizeof (x) == sizeof (double)                                         \
 329       ? __issignaling (x) : __issignalingl (x))
 330 # endif
 331
 332 /* Return nonzero value if X is subnormal.  */
 333 # define issubnormal(x) (fpclassify (x) == FP_SUBNORMAL)
 334
 335 /* Return nonzero value if X is zero.  */
 336 # ifdef __SUPPORT_SNAN__
 337 #  define iszero(x) (fpclassify (x) == FP_ZERO)
 338 # else
 339 #  define iszero(x) ((x) == 0)
 340 # endif
 341 #endif /* Use IEC_60559_BFP_EXT.  */
 342
 343 #ifdef  __USE_MISC
 344 /* Support for various different standard error handling behaviors.  */
 345 typedef enum
 346 {
 347   _IEEE_ = -1,  /* According to IEEE 754/IEEE 854.  */
 348   _SVID_,       /* According to System V, release 4.  */
 349   _XOPEN_,      /* Nowadays also Unix98.  */
 350   _POSIX_,
 351   _ISOC_        /* Actually this is ISO C99.  */
 352 } _LIB_VERSION_TYPE;
 353
 354 /* This variable can be changed at run-time to any of the values above to
 355    affect floating point error handling behavior (it may also be necessary
 356    to change the hardware FPU exception settings).  */
 357 extern _LIB_VERSION_TYPE _LIB_VERSION;
 358 #endif
 359
 360
 361 #ifdef __USE_MISC
 362 /* In SVID error handling, `matherr' is called with this description
 363    of the exceptional condition.
 364
 365    We have a problem when using C++ since `exception' is a reserved
 366    name in C++.  */
 367 # ifdef __cplusplus
 368 struct __exception
 369 # else
 370 struct exception
 371 # endif
 372   {
 373     int type;
 374     char *name;
 375     double arg1;
 376     double arg2;
 377     double retval;
 378   };
 379
 380 # ifdef __cplusplus
 381 extern int matherr (struct __exception *__exc) throw ();
 382 # else
 383 extern int matherr (struct exception *__exc);
 384 # endif
 385
 386 # define X_TLOSS        1.41484755040568800000e+16
 387
 388 /* Types of exceptions in the `type' field.  */
 389 # define DOMAIN         1
 390 # define SING           2
 391 # define OVERFLOW       3
 392 # define UNDERFLOW      4
 393 # define TLOSS          5
 394 # define PLOSS          6
 395
 396 /* SVID mode specifies returning this large value instead of infinity.  */
 397 # define HUGE           3.40282347e+38F
 398
 399 #else   /* !Misc.  */
 400
 401 # ifdef __USE_XOPEN
 402 /* X/Open wants another strange constant.  */
 403 #  define MAXFLOAT      3.40282347e+38F
 404 # endif
 405
 406 #endif  /* Misc.  */
 407
 408
 409 /* Some useful constants.  */
 410 #if defined __USE_MISC || defined __USE_XOPEN
 411 # define M_E            2.7182818284590452354   /* e */
 412 # define M_LOG2E        1.4426950408889634074   /* log_2 e */
 413 # define M_LOG10E       0.43429448190325182765  /* log_10 e */
 414 # define M_LN2          0.69314718055994530942  /* log_e 2 */
 415 # define M_LN10         2.30258509299404568402  /* log_e 10 */
 416 # define M_PI           3.14159265358979323846  /* pi */
 417 # define M_PI_2         1.57079632679489661923  /* pi/2 */
 418 # define M_PI_4         0.78539816339744830962  /* pi/4 */
 419 # define M_1_PI         0.31830988618379067154  /* 1/pi */
 420 # define M_2_PI         0.63661977236758134308  /* 2/pi */
 421 # define M_2_SQRTPI     1.12837916709551257390  /* 2/sqrt(pi) */
 422 # define M_SQRT2        1.41421356237309504880  /* sqrt(2) */
 423 # define M_SQRT1_2      0.70710678118654752440  /* 1/sqrt(2) */
 424 #endif
 425
 426 /* The above constants are not adequate for computation using `long double's.
 427    Therefore we provide as an extension constants with similar names as a
 428    GNU extension.  Provide enough digits for the 128-bit IEEE quad.  */
 429 #ifdef __USE_GNU
 430 # define M_El           2.718281828459045235360287471352662498L /* e */
 431 # define M_LOG2El       1.442695040888963407359924681001892137L /* log_2 e */
 432 # define M_LOG10El      0.434294481903251827651128918916605082L /* log_10 e */
 433 # define M_LN2l         0.693147180559945309417232121458176568L /* log_e 2 */
 434 # define M_LN10l        2.302585092994045684017991454684364208L /* log_e 10 */
 435 # define M_PIl          3.141592653589793238462643383279502884L /* pi */
 436 # define M_PI_2l        1.570796326794896619231321691639751442L /* pi/2 */
 437 # define M_PI_4l        0.785398163397448309615660845819875721L /* pi/4 */
 438 # define M_1_PIl        0.318309886183790671537767526745028724L /* 1/pi */
 439 # define M_2_PIl        0.636619772367581343075535053490057448L /* 2/pi */
 440 # define M_2_SQRTPIl    1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
 441 # define M_SQRT2l       1.414213562373095048801688724209698079L /* sqrt(2) */
 442 # define M_SQRT1_2l     0.707106781186547524400844362104849039L /* 1/sqrt(2) */
 443 #endif
 444
 445
 446 /* When compiling in strict ISO C compatible mode we must not use the
 447    inline functions since they, among other things, do not set the
 448    `errno' variable correctly.  */
 449 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
 450 # define __NO_MATH_INLINES      1
 451 #endif
 452
 453 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
 454 /* ISO C99 defines some macros to compare number while taking care for
 455    unordered numbers.  Many FPUs provide special instructions to support
 456    these operations.  Generic support in GCC for these as builtins went
 457    in before 3.0.0, but not all cpus added their patterns.  We define
 458    versions that use the builtins here, and <bits/mathinline.h> will
 459    undef/redefine as appropriate for the specific GCC version in use.  */
 460 # define isgreater(x, y)        __builtin_isgreater(x, y)
 461 # define isgreaterequal(x, y)   __builtin_isgreaterequal(x, y)
 462 # define isless(x, y)           __builtin_isless(x, y)
 463 # define islessequal(x, y)      __builtin_islessequal(x, y)
 464 # define islessgreater(x, y)    __builtin_islessgreater(x, y)
 465 # define isunordered(u, v)      __builtin_isunordered(u, v)
 466 #endif
 467
 468 /* Get machine-dependent inline versions (if there are any).  */
 469 #ifdef __USE_EXTERN_INLINES
 470 # include <bits/mathinline.h>
 471 #endif
 472
 473 /* Define special entry points to use when the compiler got told to
 474    only expect finite results.  */
 475 #if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0
 476 # include <bits/math-finite.h>
 477 #endif
 478
 479 #ifdef __USE_ISOC99
 480 /* If we've still got undefined comparison macros, provide defaults.  */
 481
 482 /* Return nonzero value if X is greater than Y.  */
 483 # ifndef isgreater
 484 #  define isgreater(x, y) \
 485   (__extension__                                                              \
 486    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 487       !isunordered (__x, __y) && __x > __y; }))
 488 # endif
 489
 490 /* Return nonzero value if X is greater than or equal to Y.  */
 491 # ifndef isgreaterequal
 492 #  define isgreaterequal(x, y) \
 493   (__extension__                                                              \
 494    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 495       !isunordered (__x, __y) && __x >= __y; }))
 496 # endif
 497
 498 /* Return nonzero value if X is less than Y.  */
 499 # ifndef isless
 500 #  define isless(x, y) \
 501   (__extension__                                                              \
 502    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 503       !isunordered (__x, __y) && __x < __y; }))
 504 # endif
 505
 506 /* Return nonzero value if X is less than or equal to Y.  */
 507 # ifndef islessequal
 508 #  define islessequal(x, y) \
 509   (__extension__                                                              \
 510    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 511       !isunordered (__x, __y) && __x <= __y; }))
 512 # endif
 513
 514 /* Return nonzero value if either X is less than Y or Y is less than X.  */
 515 # ifndef islessgreater
 516 #  define islessgreater(x, y) \
 517   (__extension__                                                              \
 518    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 519       !isunordered (__x, __y) && (__x < __y || __y < __x); }))
 520 # endif
 521
 522 /* Return nonzero value if arguments are unordered.  */
 523 # ifndef isunordered
 524 #  define isunordered(u, v) \
 525   (__extension__                                                              \
 526    ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v);                       \
 527       fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
 528 # endif
 529
 530 #endif
 531
 532 __END_DECLS
 533
 534
 535 #endif /* math.h  */