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 #include <features.h>
  27
  28 __BEGIN_DECLS
  29
  30 /* Get machine-dependent vector math functions declarations.  */
  31 #include <bits/math-vector.h>
  32
  33 /* Get machine-dependent HUGE_VAL value (returned on overflow).
  34    On all IEEE754 machines, this is +Infinity.  */
  35 #include <bits/huge_val.h>
  36 #ifdef __USE_ISOC99
  37 # include <bits/huge_valf.h>
  38 # include <bits/huge_vall.h>
  39
  40 /* Get machine-dependent INFINITY value.  */
  41 # include <bits/inf.h>
  42
  43 /* Get machine-dependent NAN value (returned for some domain errors).  */
  44 # include <bits/nan.h>
  45 #endif /* __USE_ISOC99 */
  46
  47 /* Get general and ISO C99 specific information.  */
  48 #include <bits/mathdef.h>
  49
  50 /* The file <bits/mathcalls.h> contains the prototypes for all the
  51    actual math functions.  These macros are used for those prototypes,
  52    so we can easily declare each function as both `name' and `__name',
  53    and can declare the float versions `namef' and `__namef'.  */
  54
  55 #define __SIMD_DECL(function) __CONCAT (__DECL_SIMD_, function)
  56
  57 #define __MATHCALL_VEC(function, suffix, args)  \
  58   __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
  59   __MATHCALL (function, suffix, args)
  60
  61 #define __MATHDECL_VEC(type, function,suffix, args) \
  62   __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
  63   __MATHDECL(type, function,suffix, args)
  64
  65 #define __MATHCALL(function,suffix, args)       \
  66   __MATHDECL (_Mdouble_,function,suffix, args)
  67 #define __MATHDECL(type, function,suffix, args) \
  68   __MATHDECL_1(type, function,suffix, args); \
  69   __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
  70 #define __MATHCALLX(function,suffix, args, attrib)      \
  71   __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
  72 #define __MATHDECLX(type, function,suffix, args, attrib) \
  73   __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
  74   __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
  75 #define __MATHDECL_1(type, function,suffix, args) \
  76   extern type __MATH_PRECNAME(function,suffix) args __THROW
  77
  78 #define _Mdouble_               double
  79 #define __MATH_PRECNAME(name,r) __CONCAT(name,r)
  80 #define __MATH_DECLARING_DOUBLE  1
  81 #define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
  82 #define _Mdouble_END_NAMESPACE   __END_NAMESPACE_STD
  83 #include <bits/mathcalls.h>
  84 #undef  _Mdouble_
  85 #undef _Mdouble_BEGIN_NAMESPACE
  86 #undef _Mdouble_END_NAMESPACE
  87 #undef  __MATH_PRECNAME
  88 #undef __MATH_DECLARING_DOUBLE
  89
  90 #ifdef __USE_ISOC99
  91
  92
  93 /* Include the file of declarations again, this time using `float'
  94    instead of `double' and appending f to each function name.  */
  95
  96 # ifndef _Mfloat_
  97 #  define _Mfloat_              float
  98 # endif
  99 # define _Mdouble_              _Mfloat_
 100 # define __MATH_PRECNAME(name,r) name##f##r
 101 # define __MATH_DECLARING_DOUBLE  0
 102 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
 103 # define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
 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 # if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
 112      || defined __LDBL_COMPAT \
 113      || defined _LIBC_TEST
 114 #  ifdef __LDBL_COMPAT
 115
 116 #   ifdef __USE_ISOC99
 117 extern float __nldbl_nexttowardf (float __x, long double __y)
 118                                   __THROW __attribute__ ((__const__));
 119 #    ifdef __REDIRECT_NTH
 120 extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
 121                              __nldbl_nexttowardf)
 122      __attribute__ ((__const__));
 123 extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
 124                               nextafter) __attribute__ ((__const__));
 125 extern long double __REDIRECT_NTH (nexttowardl,
 126                                    (long double __x, long double __y),
 127                                    nextafter) __attribute__ ((__const__));
 128 #    endif
 129 #   endif
 130
 131 #   undef __MATHDECL_1
 132 #   define __MATHDECL_2(type, function,suffix, args, alias) \
 133   extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
 134                              args, alias)
 135 #   define __MATHDECL_1(type, function,suffix, args) \
 136   __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
 137 #  endif
 138
 139 /* Include the file of declarations again, this time using `long double'
 140    instead of `double' and appending l to each function name.  */
 141
 142 #  ifndef _Mlong_double_
 143 #   define _Mlong_double_       long double
 144 #  endif
 145 #  define _Mdouble_             _Mlong_double_
 146 #  define __MATH_PRECNAME(name,r) name##l##r
 147 #  define __MATH_DECLARING_DOUBLE  0
 148 #  define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
 149 #  define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
 150 #  define __MATH_DECLARE_LDOUBLE   1
 151 #  include <bits/mathcalls.h>
 152 #  undef _Mdouble_
 153 #  undef _Mdouble_BEGIN_NAMESPACE
 154 #  undef _Mdouble_END_NAMESPACE
 155 #  undef __MATH_PRECNAME
 156 #  undef __MATH_DECLARING_DOUBLE
 157
 158 # endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */
 159
 160 #endif  /* Use ISO C99.  */
 161 #undef  __MATHDECL_1
 162 #undef  __MATHDECL
 163 #undef  __MATHCALL
 164
 165
 166 #if defined __USE_MISC || defined __USE_XOPEN
 167 /* This variable is used by `gamma' and `lgamma'.  */
 168 extern int signgam;
 169 #endif
 170
 171
 172 /* ISO C99 defines some generic macros which work on any data type.  */
 173 #ifdef __USE_ISOC99
 174
 175 /* Get the architecture specific values describing the floating-point
 176    evaluation.  The following symbols will get defined:
 177
 178     float_t     floating-point type at least as wide as `float' used
 179                 to evaluate `float' expressions
 180     double_t    floating-point type at least as wide as `double' used
 181                 to evaluate `double' expressions
 182
 183     FLT_EVAL_METHOD
 184                 Defined to
 185                   0     if `float_t' is `float' and `double_t' is `double'
 186                   1     if `float_t' and `double_t' are `double'
 187                   2     if `float_t' and `double_t' are `long double'
 188                   else  `float_t' and `double_t' are unspecified
 189
 190     INFINITY    representation of the infinity value of type `float'
 191
 192     FP_FAST_FMA
 193     FP_FAST_FMAF
 194     FP_FAST_FMAL
 195                 If defined it indicates that the `fma' function
 196                 generally executes about as fast as a multiply and an add.
 197                 This macro is defined only iff the `fma' function is
 198                 implemented directly with a hardware multiply-add instructions.
 199
 200     FP_ILOGB0   Expands to a value returned by `ilogb (0.0)'.
 201     FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
 202
 203     DECIMAL_DIG Number of decimal digits supported by conversion between
 204                 decimal and all internal floating-point formats.
 205
 206 */
 207
 208 /* All floating-point numbers can be put in one of these categories.  */
 209 enum
 210   {
 211     FP_NAN =
 212 # define FP_NAN 0
 213       FP_NAN,
 214     FP_INFINITE =
 215 # define FP_INFINITE 1
 216       FP_INFINITE,
 217     FP_ZERO =
 218 # define FP_ZERO 2
 219       FP_ZERO,
 220     FP_SUBNORMAL =
 221 # define FP_SUBNORMAL 3
 222       FP_SUBNORMAL,
 223     FP_NORMAL =
 224 # define FP_NORMAL 4
 225       FP_NORMAL
 226   };
 227
 228 /* GCC bug 66462 means we cannot use the math builtins with -fsignaling-nan,
 229    so disable builtins if this is enabled.  When fixed in a newer GCC,
 230    the __SUPPORT_SNAN__ check may be skipped for those versions.  */
 231
 232 /* Return number of classification appropriate for X.  */
 233 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__                         \
 234      && !defined __OPTIMIZE_SIZE__
 235 #  define fpclassify(x) __builtin_fpclassify (FP_NAN, FP_INFINITE,            \
 236      FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x)
 237 # elif defined __NO_LONG_DOUBLE_MATH
 238 #  define fpclassify(x) \
 239      (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
 240 # else
 241 #  define fpclassify(x) \
 242      (sizeof (x) == sizeof (float)                                            \
 243       ? __fpclassifyf (x)                                                     \
 244       : sizeof (x) == sizeof (double)                                         \
 245       ? __fpclassify (x) : __fpclassifyl (x))
 246 # endif
 247
 248 /* Return nonzero value if sign of X is negative.  */
 249 # if __GNUC_PREREQ (4,0)
 250 #  define signbit(x) \
 251      (sizeof (x) == sizeof (float)                                            \
 252       ? __builtin_signbitf (x)                                                        \
 253       : sizeof (x) == sizeof (double)                                         \
 254       ? __builtin_signbit (x) : __builtin_signbitl (x))
 255 # else
 256 #  ifdef __NO_LONG_DOUBLE_MATH
 257 #   define signbit(x) \
 258      (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
 259 #  else
 260 #   define signbit(x) \
 261      (sizeof (x) == sizeof (float)                                            \
 262       ? __signbitf (x)                                                        \
 263       : sizeof (x) == sizeof (double)                                         \
 264       ? __signbit (x) : __signbitl (x))
 265 #  endif
 266 # endif
 267
 268 /* Return nonzero value if X is not +-Inf or NaN.  */
 269 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
 270 #  define isfinite(x) __builtin_isfinite (x)
 271 # elif defined __NO_LONG_DOUBLE_MATH
 272 #  define isfinite(x) \
 273      (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
 274 # else
 275 #  define isfinite(x) \
 276      (sizeof (x) == sizeof (float)                                            \
 277       ? __finitef (x)                                                         \
 278       : sizeof (x) == sizeof (double)                                         \
 279       ? __finite (x) : __finitel (x))
 280 # endif
 281
 282 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
 283 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
 284 #  define isnormal(x) __builtin_isnormal (x)
 285 # else
 286 #  define isnormal(x) (fpclassify (x) == FP_NORMAL)
 287 # endif
 288
 289 /* Return nonzero value if X is a NaN.  We could use `fpclassify' but
 290    we already have this functions `__isnan' and it is faster.  */
 291 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
 292 #  define isnan(x) __builtin_isnan (x)
 293 # elif defined __NO_LONG_DOUBLE_MATH
 294 #  define isnan(x) \
 295      (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
 296 # else
 297 #  define isnan(x) \
 298      (sizeof (x) == sizeof (float)                                            \
 299       ? __isnanf (x)                                                          \
 300       : sizeof (x) == sizeof (double)                                         \
 301       ? __isnan (x) : __isnanl (x))
 302 # endif
 303
 304 /* Return nonzero value if X is positive or negative infinity.  */
 305 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
 306 #  define isinf(x) __builtin_isinf_sign (x)
 307 # elif defined __NO_LONG_DOUBLE_MATH
 308 #  define isinf(x) \
 309      (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
 310 # else
 311 #  define isinf(x) \
 312      (sizeof (x) == sizeof (float)                                            \
 313       ? __isinff (x)                                                          \
 314       : sizeof (x) == sizeof (double)                                         \
 315       ? __isinf (x) : __isinfl (x))
 316 # endif
 317
 318 /* Bitmasks for the math_errhandling macro.  */
 319 # define MATH_ERRNO     1       /* errno set by math functions.  */
 320 # define MATH_ERREXCEPT 2       /* Exceptions raised by math functions.  */
 321
 322 /* By default all functions support both errno and exception handling.
 323    In gcc's fast math mode and if inline functions are defined this
 324    might not be true.  */
 325 # ifndef __FAST_MATH__
 326 #  define math_errhandling      (MATH_ERRNO | MATH_ERREXCEPT)
 327 # endif
 328
 329 #endif /* Use ISO C99.  */
 330
 331 #ifdef __USE_GNU
 332 /* Return nonzero value if X is a signaling NaN.  */
 333 # ifdef __NO_LONG_DOUBLE_MATH
 334 #  define issignaling(x) \
 335      (sizeof (x) == sizeof (float) ? __issignalingf (x) : __issignaling (x))
 336 # else
 337 #  define issignaling(x) \
 338      (sizeof (x) == sizeof (float)                                            \
 339       ? __issignalingf (x)                                                    \
 340       : sizeof (x) == sizeof (double)                                         \
 341       ? __issignaling (x) : __issignalingl (x))
 342 # endif
 343 #endif /* Use GNU.  */
 344
 345 #ifdef  __USE_MISC
 346 /* Support for various different standard error handling behaviors.  */
 347 typedef enum
 348 {
 349   _IEEE_ = -1,  /* According to IEEE 754/IEEE 854.  */
 350   _SVID_,       /* According to System V, release 4.  */
 351   _XOPEN_,      /* Nowadays also Unix98.  */
 352   _POSIX_,
 353   _ISOC_        /* Actually this is ISO C99.  */
 354 } _LIB_VERSION_TYPE;
 355
 356 /* This variable can be changed at run-time to any of the values above to
 357    affect floating point error handling behavior (it may also be necessary
 358    to change the hardware FPU exception settings).  */
 359 extern _LIB_VERSION_TYPE _LIB_VERSION;
 360 #endif
 361
 362
 363 #ifdef __USE_MISC
 364 /* In SVID error handling, `matherr' is called with this description
 365    of the exceptional condition.
 366
 367    We have a problem when using C++ since `exception' is a reserved
 368    name in C++.  */
 369 # ifdef __cplusplus
 370 struct __exception
 371 # else
 372 struct exception
 373 # endif
 374   {
 375     int type;
 376     char *name;
 377     double arg1;
 378     double arg2;
 379     double retval;
 380   };
 381
 382 # ifdef __cplusplus
 383 extern int matherr (struct __exception *__exc) throw ();
 384 # else
 385 extern int matherr (struct exception *__exc);
 386 # endif
 387
 388 # define X_TLOSS        1.41484755040568800000e+16
 389
 390 /* Types of exceptions in the `type' field.  */
 391 # define DOMAIN         1
 392 # define SING           2
 393 # define OVERFLOW       3
 394 # define UNDERFLOW      4
 395 # define TLOSS          5
 396 # define PLOSS          6
 397
 398 /* SVID mode specifies returning this large value instead of infinity.  */
 399 # define HUGE           3.40282347e+38F
 400
 401 #else   /* !Misc.  */
 402
 403 # ifdef __USE_XOPEN
 404 /* X/Open wants another strange constant.  */
 405 #  define MAXFLOAT      3.40282347e+38F
 406 # endif
 407
 408 #endif  /* Misc.  */
 409
 410
 411 /* Some useful constants.  */
 412 #if defined __USE_MISC || defined __USE_XOPEN
 413 # define M_E            2.7182818284590452354   /* e */
 414 # define M_LOG2E        1.4426950408889634074   /* log_2 e */
 415 # define M_LOG10E       0.43429448190325182765  /* log_10 e */
 416 # define M_LN2          0.69314718055994530942  /* log_e 2 */
 417 # define M_LN10         2.30258509299404568402  /* log_e 10 */
 418 # define M_PI           3.14159265358979323846  /* pi */
 419 # define M_PI_2         1.57079632679489661923  /* pi/2 */
 420 # define M_PI_4         0.78539816339744830962  /* pi/4 */
 421 # define M_1_PI         0.31830988618379067154  /* 1/pi */
 422 # define M_2_PI         0.63661977236758134308  /* 2/pi */
 423 # define M_2_SQRTPI     1.12837916709551257390  /* 2/sqrt(pi) */
 424 # define M_SQRT2        1.41421356237309504880  /* sqrt(2) */
 425 # define M_SQRT1_2      0.70710678118654752440  /* 1/sqrt(2) */
 426 #endif
 427
 428 /* The above constants are not adequate for computation using `long double's.
 429    Therefore we provide as an extension constants with similar names as a
 430    GNU extension.  Provide enough digits for the 128-bit IEEE quad.  */
 431 #ifdef __USE_GNU
 432 # define M_El           2.718281828459045235360287471352662498L /* e */
 433 # define M_LOG2El       1.442695040888963407359924681001892137L /* log_2 e */
 434 # define M_LOG10El      0.434294481903251827651128918916605082L /* log_10 e */
 435 # define M_LN2l         0.693147180559945309417232121458176568L /* log_e 2 */
 436 # define M_LN10l        2.302585092994045684017991454684364208L /* log_e 10 */
 437 # define M_PIl          3.141592653589793238462643383279502884L /* pi */
 438 # define M_PI_2l        1.570796326794896619231321691639751442L /* pi/2 */
 439 # define M_PI_4l        0.785398163397448309615660845819875721L /* pi/4 */
 440 # define M_1_PIl        0.318309886183790671537767526745028724L /* 1/pi */
 441 # define M_2_PIl        0.636619772367581343075535053490057448L /* 2/pi */
 442 # define M_2_SQRTPIl    1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
 443 # define M_SQRT2l       1.414213562373095048801688724209698079L /* sqrt(2) */
 444 # define M_SQRT1_2l     0.707106781186547524400844362104849039L /* 1/sqrt(2) */
 445 #endif
 446
 447
 448 /* When compiling in strict ISO C compatible mode we must not use the
 449    inline functions since they, among other things, do not set the
 450    `errno' variable correctly.  */
 451 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
 452 # define __NO_MATH_INLINES      1
 453 #endif
 454
 455 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
 456 /* ISO C99 defines some macros to compare number while taking care for
 457    unordered numbers.  Many FPUs provide special instructions to support
 458    these operations.  Generic support in GCC for these as builtins went
 459    in before 3.0.0, but not all cpus added their patterns.  We define
 460    versions that use the builtins here, and <bits/mathinline.h> will
 461    undef/redefine as appropriate for the specific GCC version in use.  */
 462 # define isgreater(x, y)        __builtin_isgreater(x, y)
 463 # define isgreaterequal(x, y)   __builtin_isgreaterequal(x, y)
 464 # define isless(x, y)           __builtin_isless(x, y)
 465 # define islessequal(x, y)      __builtin_islessequal(x, y)
 466 # define islessgreater(x, y)    __builtin_islessgreater(x, y)
 467 # define isunordered(u, v)      __builtin_isunordered(u, v)
 468 #endif
 469
 470 /* Get machine-dependent inline versions (if there are any).  */
 471 #ifdef __USE_EXTERN_INLINES
 472 # include <bits/mathinline.h>
 473 #endif
 474
 475 /* Define special entry points to use when the compiler got told to
 476    only expect finite results.  */
 477 #if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0
 478 # include <bits/math-finite.h>
 479 #endif
 480
 481 #ifdef __USE_ISOC99
 482 /* If we've still got undefined comparison macros, provide defaults.  */
 483
 484 /* Return nonzero value if X is greater than Y.  */
 485 # ifndef isgreater
 486 #  define isgreater(x, y) \
 487   (__extension__                                                              \
 488    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 489       !isunordered (__x, __y) && __x > __y; }))
 490 # endif
 491
 492 /* Return nonzero value if X is greater than or equal to Y.  */
 493 # ifndef isgreaterequal
 494 #  define isgreaterequal(x, y) \
 495   (__extension__                                                              \
 496    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 497       !isunordered (__x, __y) && __x >= __y; }))
 498 # endif
 499
 500 /* Return nonzero value if X is less than Y.  */
 501 # ifndef isless
 502 #  define isless(x, y) \
 503   (__extension__                                                              \
 504    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 505       !isunordered (__x, __y) && __x < __y; }))
 506 # endif
 507
 508 /* Return nonzero value if X is less than or equal to Y.  */
 509 # ifndef islessequal
 510 #  define islessequal(x, y) \
 511   (__extension__                                                              \
 512    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 513       !isunordered (__x, __y) && __x <= __y; }))
 514 # endif
 515
 516 /* Return nonzero value if either X is less than Y or Y is less than X.  */
 517 # ifndef islessgreater
 518 #  define islessgreater(x, y) \
 519   (__extension__                                                              \
 520    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 521       !isunordered (__x, __y) && (__x < __y || __y < __x); }))
 522 # endif
 523
 524 /* Return nonzero value if arguments are unordered.  */
 525 # ifndef isunordered
 526 #  define isunordered(u, v) \
 527   (__extension__                                                              \
 528    ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v);                       \
 529       fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
 530 # endif
 531
 532 #endif
 533
 534 __END_DECLS
 535
 536
 537 #endif /* math.h  */