math/math.h

   1 /* Declarations for math functions.
   2    Copyright (C) 1991-1993, 1995-1999, 2001, 2002, 2004, 2006, 2009, 2011, 2012
   3    Free Software Foundation, Inc.
   4    This file is part of the GNU C Library.
   5
   6    The GNU C Library is free software; you can redistribute it and/or
   7    modify it under the terms of the GNU Lesser General Public
   8    License as published by the Free Software Foundation; either
   9    version 2.1 of the License, or (at your option) any later version.
  10
  11    The GNU C Library is distributed in the hope that it will be useful,
  12    but WITHOUT ANY WARRANTY; without even the implied warranty of
  13    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  14    Lesser General Public License for more details.
  15
  16    You should have received a copy of the GNU Lesser General Public
  17    License along with the GNU C Library; if not, see
  18    <http://www.gnu.org/licenses/>.  */
  19
  20 /*
  21  *      ISO C99 Standard: 7.12 Mathematics      <math.h>
  22  */
  23
  24 #ifndef _MATH_H
  25 #define _MATH_H 1
  26
  27 #include <features.h>
  28
  29 __BEGIN_DECLS
  30
  31 /* Get machine-dependent HUGE_VAL value (returned on overflow).
  32    On all IEEE754 machines, this is +Infinity.  */
  33 #include <bits/huge_val.h>
  34 #ifdef __USE_ISOC99
  35 # include <bits/huge_valf.h>
  36 # include <bits/huge_vall.h>
  37
  38 /* Get machine-dependent INFINITY value.  */
  39 # include <bits/inf.h>
  40
  41 /* Get machine-dependent NAN value (returned for some domain errors).  */
  42 # include <bits/nan.h>
  43 #endif /* __USE_ISOC99 */
  44
  45 /* Get general and ISO C99 specific information.  */
  46 #include <bits/mathdef.h>
  47
  48 /* The file <bits/mathcalls.h> contains the prototypes for all the
  49    actual math functions.  These macros are used for those prototypes,
  50    so we can easily declare each function as both `name' and `__name',
  51    and can declare the float versions `namef' and `__namef'.  */
  52
  53 #define __MATHCALL(function,suffix, args)       \
  54   __MATHDECL (_Mdouble_,function,suffix, args)
  55 #define __MATHDECL(type, function,suffix, args) \
  56   __MATHDECL_1(type, function,suffix, args); \
  57   __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
  58 #define __MATHCALLX(function,suffix, args, attrib)      \
  59   __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
  60 #define __MATHDECLX(type, function,suffix, args, attrib) \
  61   __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
  62   __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
  63 #define __MATHDECL_1(type, function,suffix, args) \
  64   extern type __MATH_PRECNAME(function,suffix) args __THROW
  65
  66 #define _Mdouble_               double
  67 #define __MATH_PRECNAME(name,r) __CONCAT(name,r)
  68 #define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
  69 #define _Mdouble_END_NAMESPACE   __END_NAMESPACE_STD
  70 #include <bits/mathcalls.h>
  71 #undef  _Mdouble_
  72 #undef _Mdouble_BEGIN_NAMESPACE
  73 #undef _Mdouble_END_NAMESPACE
  74 #undef  __MATH_PRECNAME
  75
  76 #if defined __USE_MISC || defined __USE_ISOC99
  77
  78
  79 /* Include the file of declarations again, this time using `float'
  80    instead of `double' and appending f to each function name.  */
  81
  82 # ifndef _Mfloat_
  83 #  define _Mfloat_              float
  84 # endif
  85 # define _Mdouble_              _Mfloat_
  86 # define __MATH_PRECNAME(name,r) name##f##r
  87 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
  88 # define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
  89 # include <bits/mathcalls.h>
  90 # undef _Mdouble_
  91 # undef _Mdouble_BEGIN_NAMESPACE
  92 # undef _Mdouble_END_NAMESPACE
  93 # undef __MATH_PRECNAME
  94
  95 # if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
  96      || defined __LDBL_COMPAT
  97 #  ifdef __LDBL_COMPAT
  98
  99 #   ifdef __USE_ISOC99
 100 extern float __nldbl_nexttowardf (float __x, long double __y)
 101                                   __THROW __attribute__ ((__const__));
 102 #    ifdef __REDIRECT_NTH
 103 extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
 104                              __nldbl_nexttowardf)
 105      __attribute__ ((__const__));
 106 extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
 107                               nextafter) __attribute__ ((__const__));
 108 extern long double __REDIRECT_NTH (nexttowardl,
 109                                    (long double __x, long double __y),
 110                                    nextafter) __attribute__ ((__const__));
 111 #    endif
 112 #   endif
 113
 114 #   undef __MATHDECL_1
 115 #   define __MATHDECL_2(type, function,suffix, args, alias) \
 116   extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
 117                              args, alias)
 118 #   define __MATHDECL_1(type, function,suffix, args) \
 119   __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
 120 #  endif
 121
 122 /* Include the file of declarations again, this time using `long double'
 123    instead of `double' and appending l to each function name.  */
 124
 125 #  ifndef _Mlong_double_
 126 #   define _Mlong_double_       long double
 127 #  endif
 128 #  define _Mdouble_             _Mlong_double_
 129 #  define __MATH_PRECNAME(name,r) name##l##r
 130 #  define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
 131 #  define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
 132 #  define __MATH_DECLARE_LDOUBLE   1
 133 #  include <bits/mathcalls.h>
 134 #  undef _Mdouble_
 135 #  undef _Mdouble_BEGIN_NAMESPACE
 136 #  undef _Mdouble_END_NAMESPACE
 137 #  undef __MATH_PRECNAME
 138
 139 # endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */
 140
 141 #endif  /* Use misc or ISO C99.  */
 142 #undef  __MATHDECL_1
 143 #undef  __MATHDECL
 144 #undef  __MATHCALL
 145
 146
 147 #if defined __USE_MISC || defined __USE_XOPEN
 148 /* This variable is used by `gamma' and `lgamma'.  */
 149 extern int signgam;
 150 #endif
 151
 152
 153 /* ISO C99 defines some generic macros which work on any data type.  */
 154 #ifdef __USE_ISOC99
 155
 156 /* Get the architecture specific values describing the floating-point
 157    evaluation.  The following symbols will get defined:
 158
 159     float_t     floating-point type at least as wide as `float' used
 160                 to evaluate `float' expressions
 161     double_t    floating-point type at least as wide as `double' used
 162                 to evaluate `double' expressions
 163
 164     FLT_EVAL_METHOD
 165                 Defined to
 166                   0     if `float_t' is `float' and `double_t' is `double'
 167                   1     if `float_t' and `double_t' are `double'
 168                   2     if `float_t' and `double_t' are `long double'
 169                   else  `float_t' and `double_t' are unspecified
 170
 171     INFINITY    representation of the infinity value of type `float'
 172
 173     FP_FAST_FMA
 174     FP_FAST_FMAF
 175     FP_FAST_FMAL
 176                 If defined it indicates that the `fma' function
 177                 generally executes about as fast as a multiply and an add.
 178                 This macro is defined only iff the `fma' function is
 179                 implemented directly with a hardware multiply-add instructions.
 180
 181     FP_ILOGB0   Expands to a value returned by `ilogb (0.0)'.
 182     FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
 183
 184     DECIMAL_DIG Number of decimal digits supported by conversion between
 185                 decimal and all internal floating-point formats.
 186
 187 */
 188
 189 /* All floating-point numbers can be put in one of these categories.  */
 190 enum
 191   {
 192     FP_NAN =
 193 # define FP_NAN 0
 194       FP_NAN,
 195     FP_INFINITE =
 196 # define FP_INFINITE 1
 197       FP_INFINITE,
 198     FP_ZERO =
 199 # define FP_ZERO 2
 200       FP_ZERO,
 201     FP_SUBNORMAL =
 202 # define FP_SUBNORMAL 3
 203       FP_SUBNORMAL,
 204     FP_NORMAL =
 205 # define FP_NORMAL 4
 206       FP_NORMAL
 207   };
 208
 209 /* Return number of classification appropriate for X.  */
 210 # ifdef __NO_LONG_DOUBLE_MATH
 211 #  define fpclassify(x) \
 212      (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
 213 # else
 214 #  define fpclassify(x) \
 215      (sizeof (x) == sizeof (float)                                            \
 216       ? __fpclassifyf (x)                                                     \
 217       : sizeof (x) == sizeof (double)                                         \
 218       ? __fpclassify (x) : __fpclassifyl (x))
 219 # endif
 220
 221 /* Return nonzero value if sign of X is negative.  */
 222 # ifdef __NO_LONG_DOUBLE_MATH
 223 #  define signbit(x) \
 224      (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
 225 # else
 226 #  define signbit(x) \
 227      (sizeof (x) == sizeof (float)                                            \
 228       ? __signbitf (x)                                                        \
 229       : sizeof (x) == sizeof (double)                                         \
 230       ? __signbit (x) : __signbitl (x))
 231 # endif
 232
 233 /* Return nonzero value if X is not +-Inf or NaN.  */
 234 # ifdef __NO_LONG_DOUBLE_MATH
 235 #  define isfinite(x) \
 236      (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
 237 # else
 238 #  define isfinite(x) \
 239      (sizeof (x) == sizeof (float)                                            \
 240       ? __finitef (x)                                                         \
 241       : sizeof (x) == sizeof (double)                                         \
 242       ? __finite (x) : __finitel (x))
 243 # endif
 244
 245 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
 246 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
 247
 248 /* Return nonzero value if X is a NaN.  We could use `fpclassify' but
 249    we already have this functions `__isnan' and it is faster.  */
 250 # ifdef __NO_LONG_DOUBLE_MATH
 251 #  define isnan(x) \
 252      (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
 253 # else
 254 #  define isnan(x) \
 255      (sizeof (x) == sizeof (float)                                            \
 256       ? __isnanf (x)                                                          \
 257       : sizeof (x) == sizeof (double)                                         \
 258       ? __isnan (x) : __isnanl (x))
 259 # endif
 260
 261 /* Return nonzero value if X is positive or negative infinity.  */
 262 # ifdef __NO_LONG_DOUBLE_MATH
 263 #  define isinf(x) \
 264      (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
 265 # else
 266 #  define isinf(x) \
 267      (sizeof (x) == sizeof (float)                                            \
 268       ? __isinff (x)                                                          \
 269       : sizeof (x) == sizeof (double)                                         \
 270       ? __isinf (x) : __isinfl (x))
 271 # endif
 272
 273 /* Bitmasks for the math_errhandling macro.  */
 274 # define MATH_ERRNO     1       /* errno set by math functions.  */
 275 # define MATH_ERREXCEPT 2       /* Exceptions raised by math functions.  */
 276
 277 /* By default all functions support both errno and exception handling.
 278    In gcc's fast math mode and if inline functions are defined this
 279    might not be true.  */
 280 # ifndef __FAST_MATH__
 281 #  define math_errhandling      (MATH_ERRNO | MATH_ERREXCEPT)
 282 # endif
 283
 284 #endif /* Use ISO C99.  */
 285
 286 #ifdef  __USE_MISC
 287 /* Support for various different standard error handling behaviors.  */
 288 typedef enum
 289 {
 290   _IEEE_ = -1,  /* According to IEEE 754/IEEE 854.  */
 291   _SVID_,       /* According to System V, release 4.  */
 292   _XOPEN_,      /* Nowadays also Unix98.  */
 293   _POSIX_,
 294   _ISOC_        /* Actually this is ISO C99.  */
 295 } _LIB_VERSION_TYPE;
 296
 297 /* This variable can be changed at run-time to any of the values above to
 298    affect floating point error handling behavior (it may also be necessary
 299    to change the hardware FPU exception settings).  */
 300 extern _LIB_VERSION_TYPE _LIB_VERSION;
 301 #endif
 302
 303
 304 #ifdef __USE_SVID
 305 /* In SVID error handling, `matherr' is called with this description
 306    of the exceptional condition.
 307
 308    We have a problem when using C++ since `exception' is a reserved
 309    name in C++.  */
 310 # ifdef __cplusplus
 311 struct __exception
 312 # else
 313 struct exception
 314 # endif
 315   {
 316     int type;
 317     char *name;
 318     double arg1;
 319     double arg2;
 320     double retval;
 321   };
 322
 323 # ifdef __cplusplus
 324 extern int matherr (struct __exception *__exc) throw ();
 325 # else
 326 extern int matherr (struct exception *__exc);
 327 # endif
 328
 329 # define X_TLOSS        1.41484755040568800000e+16
 330
 331 /* Types of exceptions in the `type' field.  */
 332 # define DOMAIN         1
 333 # define SING           2
 334 # define OVERFLOW       3
 335 # define UNDERFLOW      4
 336 # define TLOSS          5
 337 # define PLOSS          6
 338
 339 /* SVID mode specifies returning this large value instead of infinity.  */
 340 # define HUGE           3.40282347e+38F
 341
 342 #else   /* !SVID */
 343
 344 # ifdef __USE_XOPEN
 345 /* X/Open wants another strange constant.  */
 346 #  define MAXFLOAT      3.40282347e+38F
 347 # endif
 348
 349 #endif  /* SVID */
 350
 351
 352 /* Some useful constants.  */
 353 #if defined __USE_BSD || defined __USE_XOPEN
 354 # define M_E            2.7182818284590452354   /* e */
 355 # define M_LOG2E        1.4426950408889634074   /* log_2 e */
 356 # define M_LOG10E       0.43429448190325182765  /* log_10 e */
 357 # define M_LN2          0.69314718055994530942  /* log_e 2 */
 358 # define M_LN10         2.30258509299404568402  /* log_e 10 */
 359 # define M_PI           3.14159265358979323846  /* pi */
 360 # define M_PI_2         1.57079632679489661923  /* pi/2 */
 361 # define M_PI_4         0.78539816339744830962  /* pi/4 */
 362 # define M_1_PI         0.31830988618379067154  /* 1/pi */
 363 # define M_2_PI         0.63661977236758134308  /* 2/pi */
 364 # define M_2_SQRTPI     1.12837916709551257390  /* 2/sqrt(pi) */
 365 # define M_SQRT2        1.41421356237309504880  /* sqrt(2) */
 366 # define M_SQRT1_2      0.70710678118654752440  /* 1/sqrt(2) */
 367 #endif
 368
 369 /* The above constants are not adequate for computation using `long double's.
 370    Therefore we provide as an extension constants with similar names as a
 371    GNU extension.  Provide enough digits for the 128-bit IEEE quad.  */
 372 #ifdef __USE_GNU
 373 # define M_El           2.718281828459045235360287471352662498L /* e */
 374 # define M_LOG2El       1.442695040888963407359924681001892137L /* log_2 e */
 375 # define M_LOG10El      0.434294481903251827651128918916605082L /* log_10 e */
 376 # define M_LN2l         0.693147180559945309417232121458176568L /* log_e 2 */
 377 # define M_LN10l        2.302585092994045684017991454684364208L /* log_e 10 */
 378 # define M_PIl          3.141592653589793238462643383279502884L /* pi */
 379 # define M_PI_2l        1.570796326794896619231321691639751442L /* pi/2 */
 380 # define M_PI_4l        0.785398163397448309615660845819875721L /* pi/4 */
 381 # define M_1_PIl        0.318309886183790671537767526745028724L /* 1/pi */
 382 # define M_2_PIl        0.636619772367581343075535053490057448L /* 2/pi */
 383 # define M_2_SQRTPIl    1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
 384 # define M_SQRT2l       1.414213562373095048801688724209698079L /* sqrt(2) */
 385 # define M_SQRT1_2l     0.707106781186547524400844362104849039L /* 1/sqrt(2) */
 386 #endif
 387
 388
 389 /* When compiling in strict ISO C compatible mode we must not use the
 390    inline functions since they, among other things, do not set the
 391    `errno' variable correctly.  */
 392 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
 393 # define __NO_MATH_INLINES      1
 394 #endif
 395
 396 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
 397 /* ISO C99 defines some macros to compare number while taking care for
 398    unordered numbers.  Many FPUs provide special instructions to support
 399    these operations.  Generic support in GCC for these as builtins went
 400    in before 3.0.0, but not all cpus added their patterns.  We define
 401    versions that use the builtins here, and <bits/mathinline.h> will
 402    undef/redefine as appropriate for the specific GCC version in use.  */
 403 # define isgreater(x, y)        __builtin_isgreater(x, y)
 404 # define isgreaterequal(x, y)   __builtin_isgreaterequal(x, y)
 405 # define isless(x, y)           __builtin_isless(x, y)
 406 # define islessequal(x, y)      __builtin_islessequal(x, y)
 407 # define islessgreater(x, y)    __builtin_islessgreater(x, y)
 408 # define isunordered(u, v)      __builtin_isunordered(u, v)
 409 #endif
 410
 411 /* Get machine-dependent inline versions (if there are any).  */
 412 #ifdef __USE_EXTERN_INLINES
 413 # include <bits/mathinline.h>
 414 #endif
 415
 416 /* Define special entry points to use when the compiler got told to
 417    only expect finite results.  */
 418 #if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0
 419 # include <bits/math-finite.h>
 420 #endif
 421
 422 #ifdef __USE_ISOC99
 423 /* If we've still got undefined comparison macros, provide defaults.  */
 424
 425 /* Return nonzero value if X is greater than Y.  */
 426 # ifndef isgreater
 427 #  define isgreater(x, y) \
 428   (__extension__                                                              \
 429    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 430       !isunordered (__x, __y) && __x > __y; }))
 431 # endif
 432
 433 /* Return nonzero value if X is greater than or equal to Y.  */
 434 # ifndef isgreaterequal
 435 #  define isgreaterequal(x, y) \
 436   (__extension__                                                              \
 437    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 438       !isunordered (__x, __y) && __x >= __y; }))
 439 # endif
 440
 441 /* Return nonzero value if X is less than Y.  */
 442 # ifndef isless
 443 #  define isless(x, y) \
 444   (__extension__                                                              \
 445    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 446       !isunordered (__x, __y) && __x < __y; }))
 447 # endif
 448
 449 /* Return nonzero value if X is less than or equal to Y.  */
 450 # ifndef islessequal
 451 #  define islessequal(x, y) \
 452   (__extension__                                                              \
 453    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 454       !isunordered (__x, __y) && __x <= __y; }))
 455 # endif
 456
 457 /* Return nonzero value if either X is less than Y or Y is less than X.  */
 458 # ifndef islessgreater
 459 #  define islessgreater(x, y) \
 460   (__extension__                                                              \
 461    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 462       !isunordered (__x, __y) && (__x < __y || __y < __x); }))
 463 # endif
 464
 465 /* Return nonzero value if arguments are unordered.  */
 466 # ifndef isunordered
 467 #  define isunordered(u, v) \
 468   (__extension__                                                              \
 469    ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v);                       \
 470       fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
 471 # endif
 472
 473 #endif
 474
 475 __END_DECLS
 476
 477
 478 #endif /* math.h  */