math/math.h

   1 /* Declarations for math functions.
   2    Copyright (C) 1991-1993, 1995-1999, 2001, 2002, 2004, 2006, 2009
   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, write to the Free
  18    Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
  19    02111-1307 USA.  */
  20
  21 /*
  22  *      ISO C99 Standard: 7.12 Mathematics      <math.h>
  23  */
  24
  25 #ifndef _MATH_H
  26 #define _MATH_H 1
  27
  28 #include <features.h>
  29
  30 __BEGIN_DECLS
  31
  32 /* Get machine-dependent HUGE_VAL value (returned on overflow).
  33    On all IEEE754 machines, this is +Infinity.  */
  34 #include <bits/huge_val.h>
  35 #ifdef __USE_ISOC99
  36 # include <bits/huge_valf.h>
  37 # include <bits/huge_vall.h>
  38
  39 /* Get machine-dependent INFINITY value.  */
  40 # include <bits/inf.h>
  41
  42 /* Get machine-dependent NAN value (returned for some domain errors).  */
  43 # include <bits/nan.h>
  44 #endif /* __USE_ISOC99 */
  45
  46 /* Get general and ISO C99 specific information.  */
  47 #include <bits/mathdef.h>
  48
  49 /* The file <bits/mathcalls.h> contains the prototypes for all the
  50    actual math functions.  These macros are used for those prototypes,
  51    so we can easily declare each function as both `name' and `__name',
  52    and can declare the float versions `namef' and `__namef'.  */
  53
  54 #define __MATHCALL(function,suffix, args)       \
  55   __MATHDECL (_Mdouble_,function,suffix, args)
  56 #define __MATHDECL(type, function,suffix, args) \
  57   __MATHDECL_1(type, function,suffix, args); \
  58   __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
  59 #define __MATHCALLX(function,suffix, args, attrib)      \
  60   __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
  61 #define __MATHDECLX(type, function,suffix, args, attrib) \
  62   __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
  63   __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
  64 #define __MATHDECL_1(type, function,suffix, args) \
  65   extern type __MATH_PRECNAME(function,suffix) args __THROW
  66
  67 #define _Mdouble_               double
  68 #define __MATH_PRECNAME(name,r) __CONCAT(name,r)
  69 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
  70 # define _Mdouble_END_NAMESPACE   __END_NAMESPACE_STD
  71 #include <bits/mathcalls.h>
  72 #undef  _Mdouble_
  73 #undef _Mdouble_BEGIN_NAMESPACE
  74 #undef _Mdouble_END_NAMESPACE
  75 #undef  __MATH_PRECNAME
  76
  77 #if defined __USE_MISC || defined __USE_ISOC99
  78
  79
  80 /* Include the file of declarations again, this time using `float'
  81    instead of `double' and appending f to each function name.  */
  82
  83 # ifndef _Mfloat_
  84 #  define _Mfloat_              float
  85 # endif
  86 # define _Mdouble_              _Mfloat_
  87 # ifdef __STDC__
  88 #  define __MATH_PRECNAME(name,r) name##f##r
  89 # else
  90 #  define __MATH_PRECNAME(name,r) name/**/f/**/r
  91 # endif
  92 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
  93 # define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
  94 # include <bits/mathcalls.h>
  95 # undef _Mdouble_
  96 # undef _Mdouble_BEGIN_NAMESPACE
  97 # undef _Mdouble_END_NAMESPACE
  98 # undef __MATH_PRECNAME
  99
 100 # if (__STDC__ - 0 || __GNUC__ - 0) \
 101      && (!defined __NO_LONG_DOUBLE_MATH || defined __LDBL_COMPAT)
 102 #  ifdef __LDBL_COMPAT
 103
 104 #   ifdef __USE_ISOC99
 105 extern float __nldbl_nexttowardf (float __x, long double __y)
 106                                   __THROW __attribute__ ((__const__));
 107 #    ifdef __REDIRECT_NTH
 108 extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
 109                              __nldbl_nexttowardf)
 110      __attribute__ ((__const__));
 111 extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
 112                               nextafter) __attribute__ ((__const__));
 113 extern long double __REDIRECT_NTH (nexttowardl,
 114                                    (long double __x, long double __y),
 115                                    nextafter) __attribute__ ((__const__));
 116 #    endif
 117 #   endif
 118
 119 /* Include the file of declarations again, this time using `long double'
 120    instead of `double' and appending l to each function name.  */
 121
 122 #   undef __MATHDECL_1
 123 #   define __MATHDECL_2(type, function,suffix, args, alias) \
 124   extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
 125                              args, alias)
 126 #   define __MATHDECL_1(type, function,suffix, args) \
 127   __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
 128 #  endif
 129
 130 #  ifndef _Mlong_double_
 131 #   define _Mlong_double_       long double
 132 #  endif
 133 #  define _Mdouble_             _Mlong_double_
 134 #  ifdef __STDC__
 135 #   define __MATH_PRECNAME(name,r) name##l##r
 136 #  else
 137 #   define __MATH_PRECNAME(name,r) name/**/l/**/r
 138 #  endif
 139 #  define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
 140 #  define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
 141 #  include <bits/mathcalls.h>
 142 #  undef _Mdouble_
 143 # undef _Mdouble_BEGIN_NAMESPACE
 144 # undef _Mdouble_END_NAMESPACE
 145 #  undef __MATH_PRECNAME
 146
 147 # endif /* __STDC__ || __GNUC__ */
 148
 149 #endif  /* Use misc or ISO C99.  */
 150 #undef  __MATHDECL_1
 151 #undef  __MATHDECL
 152 #undef  __MATHCALL
 153
 154
 155 #if defined __USE_MISC || defined __USE_XOPEN
 156 /* This variable is used by `gamma' and `lgamma'.  */
 157 extern int signgam;
 158 #endif
 159
 160
 161 /* ISO C99 defines some generic macros which work on any data type.  */
 162 #ifdef __USE_ISOC99
 163
 164 /* Get the architecture specific values describing the floating-point
 165    evaluation.  The following symbols will get defined:
 166
 167     float_t     floating-point type at least as wide as `float' used
 168                 to evaluate `float' expressions
 169     double_t    floating-point type at least as wide as `double' used
 170                 to evaluate `double' expressions
 171
 172     FLT_EVAL_METHOD
 173                 Defined to
 174                   0     if `float_t' is `float' and `double_t' is `double'
 175                   1     if `float_t' and `double_t' are `double'
 176                   2     if `float_t' and `double_t' are `long double'
 177                   else  `float_t' and `double_t' are unspecified
 178
 179     INFINITY    representation of the infinity value of type `float'
 180
 181     FP_FAST_FMA
 182     FP_FAST_FMAF
 183     FP_FAST_FMAL
 184                 If defined it indicates that the `fma' function
 185                 generally executes about as fast as a multiply and an add.
 186                 This macro is defined only iff the `fma' function is
 187                 implemented directly with a hardware multiply-add instructions.
 188
 189     FP_ILOGB0   Expands to a value returned by `ilogb (0.0)'.
 190     FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
 191
 192     DECIMAL_DIG Number of decimal digits supported by conversion between
 193                 decimal and all internal floating-point formats.
 194
 195 */
 196
 197 /* All floating-point numbers can be put in one of these categories.  */
 198 enum
 199   {
 200     FP_NAN,
 201 # define FP_NAN FP_NAN
 202     FP_INFINITE,
 203 # define FP_INFINITE FP_INFINITE
 204     FP_ZERO,
 205 # define FP_ZERO FP_ZERO
 206     FP_SUBNORMAL,
 207 # define FP_SUBNORMAL FP_SUBNORMAL
 208     FP_NORMAL
 209 # define FP_NORMAL FP_NORMAL
 210   };
 211
 212 /* Return number of classification appropriate for X.  */
 213 # ifdef __NO_LONG_DOUBLE_MATH
 214 #  define fpclassify(x) \
 215      (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
 216 # else
 217 #  define fpclassify(x) \
 218      (sizeof (x) == sizeof (float)                                            \
 219       ? __fpclassifyf (x)                                                     \
 220       : sizeof (x) == sizeof (double)                                         \
 221       ? __fpclassify (x) : __fpclassifyl (x))
 222 # endif
 223
 224 /* Return nonzero value if sign of X is negative.  */
 225 # ifdef __NO_LONG_DOUBLE_MATH
 226 #  define signbit(x) \
 227      (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
 228 # else
 229 #  define signbit(x) \
 230      (sizeof (x) == sizeof (float)                                            \
 231       ? __signbitf (x)                                                        \
 232       : sizeof (x) == sizeof (double)                                         \
 233       ? __signbit (x) : __signbitl (x))
 234 # endif
 235
 236 /* Return nonzero value if X is not +-Inf or NaN.  */
 237 # ifdef __NO_LONG_DOUBLE_MATH
 238 #  define isfinite(x) \
 239      (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
 240 # else
 241 #  define isfinite(x) \
 242      (sizeof (x) == sizeof (float)                                            \
 243       ? __finitef (x)                                                         \
 244       : sizeof (x) == sizeof (double)                                         \
 245       ? __finite (x) : __finitel (x))
 246 # endif
 247
 248 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
 249 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
 250
 251 /* Return nonzero value if X is a NaN.  We could use `fpclassify' but
 252    we already have this functions `__isnan' and it is faster.  */
 253 # ifdef __NO_LONG_DOUBLE_MATH
 254 #  define isnan(x) \
 255      (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
 256 # else
 257 #  define isnan(x) \
 258      (sizeof (x) == sizeof (float)                                            \
 259       ? __isnanf (x)                                                          \
 260       : sizeof (x) == sizeof (double)                                         \
 261       ? __isnan (x) : __isnanl (x))
 262 # endif
 263
 264 /* Return nonzero value is X is positive or negative infinity.  */
 265 # ifdef __NO_LONG_DOUBLE_MATH
 266 #  define isinf(x) \
 267      (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
 268 # else
 269 #  define isinf(x) \
 270      (sizeof (x) == sizeof (float)                                            \
 271       ? __isinff (x)                                                          \
 272       : sizeof (x) == sizeof (double)                                         \
 273       ? __isinf (x) : __isinfl (x))
 274 # endif
 275
 276 /* Bitmasks for the math_errhandling macro.  */
 277 # define MATH_ERRNO     1       /* errno set by math functions.  */
 278 # define MATH_ERREXCEPT 2       /* Exceptions raised by math functions.  */
 279
 280 /* By default all functions support both errno and exception handling.
 281    In gcc's fast math mode and if inline functions are defined this
 282    might not be true.  */
 283 # ifndef __FAST_MATH__
 284 #  define math_errhandling      (MATH_ERRNO | MATH_ERREXCEPT)
 285 # endif
 286
 287 #endif /* Use ISO C99.  */
 288
 289 #ifdef  __USE_MISC
 290 /* Support for various different standard error handling behaviors.  */
 291 typedef enum
 292 {
 293   _IEEE_ = -1,  /* According to IEEE 754/IEEE 854.  */
 294   _SVID_,       /* According to System V, release 4.  */
 295   _XOPEN_,      /* Nowadays also Unix98.  */
 296   _POSIX_,
 297   _ISOC_        /* Actually this is ISO C99.  */
 298 } _LIB_VERSION_TYPE;
 299
 300 /* This variable can be changed at run-time to any of the values above to
 301    affect floating point error handling behavior (it may also be necessary
 302    to change the hardware FPU exception settings).  */
 303 extern _LIB_VERSION_TYPE _LIB_VERSION;
 304 #endif
 305
 306
 307 #ifdef __USE_SVID
 308 /* In SVID error handling, `matherr' is called with this description
 309    of the exceptional condition.
 310
 311    We have a problem when using C++ since `exception' is a reserved
 312    name in C++.  */
 313 # ifdef __cplusplus
 314 struct __exception
 315 # else
 316 struct exception
 317 # endif
 318   {
 319     int type;
 320     char *name;
 321     double arg1;
 322     double arg2;
 323     double retval;
 324   };
 325
 326 # ifdef __cplusplus
 327 extern int matherr (struct __exception *__exc) throw ();
 328 # else
 329 extern int matherr (struct exception *__exc);
 330 # endif
 331
 332 # define X_TLOSS        1.41484755040568800000e+16
 333
 334 /* Types of exceptions in the `type' field.  */
 335 # define DOMAIN         1
 336 # define SING           2
 337 # define OVERFLOW       3
 338 # define UNDERFLOW      4
 339 # define TLOSS          5
 340 # define PLOSS          6
 341
 342 /* SVID mode specifies returning this large value instead of infinity.  */
 343 # define HUGE           3.40282347e+38F
 344
 345 #else   /* !SVID */
 346
 347 # ifdef __USE_XOPEN
 348 /* X/Open wants another strange constant.  */
 349 #  define MAXFLOAT      3.40282347e+38F
 350 # endif
 351
 352 #endif  /* SVID */
 353
 354
 355 /* Some useful constants.  */
 356 #if defined __USE_BSD || defined __USE_XOPEN
 357 # define M_E            2.7182818284590452354   /* e */
 358 # define M_LOG2E        1.4426950408889634074   /* log_2 e */
 359 # define M_LOG10E       0.43429448190325182765  /* log_10 e */
 360 # define M_LN2          0.69314718055994530942  /* log_e 2 */
 361 # define M_LN10         2.30258509299404568402  /* log_e 10 */
 362 # define M_PI           3.14159265358979323846  /* pi */
 363 # define M_PI_2         1.57079632679489661923  /* pi/2 */
 364 # define M_PI_4         0.78539816339744830962  /* pi/4 */
 365 # define M_1_PI         0.31830988618379067154  /* 1/pi */
 366 # define M_2_PI         0.63661977236758134308  /* 2/pi */
 367 # define M_2_SQRTPI     1.12837916709551257390  /* 2/sqrt(pi) */
 368 # define M_SQRT2        1.41421356237309504880  /* sqrt(2) */
 369 # define M_SQRT1_2      0.70710678118654752440  /* 1/sqrt(2) */
 370 #endif
 371
 372 /* The above constants are not adequate for computation using `long double's.
 373    Therefore we provide as an extension constants with similar names as a
 374    GNU extension.  Provide enough digits for the 128-bit IEEE quad.  */
 375 #ifdef __USE_GNU
 376 # define M_El           2.7182818284590452353602874713526625L  /* e */
 377 # define M_LOG2El       1.4426950408889634073599246810018921L  /* log_2 e */
 378 # define M_LOG10El      0.4342944819032518276511289189166051L  /* log_10 e */
 379 # define M_LN2l         0.6931471805599453094172321214581766L  /* log_e 2 */
 380 # define M_LN10l        2.3025850929940456840179914546843642L  /* log_e 10 */
 381 # define M_PIl          3.1415926535897932384626433832795029L  /* pi */
 382 # define M_PI_2l        1.5707963267948966192313216916397514L  /* pi/2 */
 383 # define M_PI_4l        0.7853981633974483096156608458198757L  /* pi/4 */
 384 # define M_1_PIl        0.3183098861837906715377675267450287L  /* 1/pi */
 385 # define M_2_PIl        0.6366197723675813430755350534900574L  /* 2/pi */
 386 # define M_2_SQRTPIl    1.1283791670955125738961589031215452L  /* 2/sqrt(pi) */
 387 # define M_SQRT2l       1.4142135623730950488016887242096981L  /* sqrt(2) */
 388 # define M_SQRT1_2l     0.7071067811865475244008443621048490L  /* 1/sqrt(2) */
 389 #endif
 390
 391
 392 /* When compiling in strict ISO C compatible mode we must not use the
 393    inline functions since they, among other things, do not set the
 394    `errno' variable correctly.  */
 395 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
 396 # define __NO_MATH_INLINES      1
 397 #endif
 398
 399 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
 400 /* ISO C99 defines some macros to compare number while taking care for
 401    unordered numbers.  Many FPUs provide special instructions to support
 402    these operations.  Generic support in GCC for these as builtins went
 403    in before 3.0.0, but not all cpus added their patterns.  We define
 404    versions that use the builtins here, and <bits/mathinline.h> will
 405    undef/redefine as appropriate for the specific GCC version in use.  */
 406 # define isgreater(x, y)        __builtin_isgreater(x, y)
 407 # define isgreaterequal(x, y)   __builtin_isgreaterequal(x, y)
 408 # define isless(x, y)           __builtin_isless(x, y)
 409 # define islessequal(x, y)      __builtin_islessequal(x, y)
 410 # define islessgreater(x, y)    __builtin_islessgreater(x, y)
 411 # define isunordered(u, v)      __builtin_isunordered(u, v)
 412 #endif
 413
 414 /* Get machine-dependent inline versions (if there are any).  */
 415 #ifdef __USE_EXTERN_INLINES
 416 # include <bits/mathinline.h>
 417 #endif
 418
 419 #ifdef __USE_ISOC99
 420 /* If we've still got undefined comparison macros, provide defaults.  */
 421
 422 /* Return nonzero value if X is greater than Y.  */
 423 # ifndef isgreater
 424 #  define isgreater(x, y) \
 425   (__extension__                                                              \
 426    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 427       !isunordered (__x, __y) && __x > __y; }))
 428 # endif
 429
 430 /* Return nonzero value if X is greater than or equal to Y.  */
 431 # ifndef isgreaterequal
 432 #  define isgreaterequal(x, y) \
 433   (__extension__                                                              \
 434    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 435       !isunordered (__x, __y) && __x >= __y; }))
 436 # endif
 437
 438 /* Return nonzero value if X is less than Y.  */
 439 # ifndef isless
 440 #  define isless(x, y) \
 441   (__extension__                                                              \
 442    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 443       !isunordered (__x, __y) && __x < __y; }))
 444 # endif
 445
 446 /* Return nonzero value if X is less than or equal to Y.  */
 447 # ifndef islessequal
 448 #  define islessequal(x, y) \
 449   (__extension__                                                              \
 450    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 451       !isunordered (__x, __y) && __x <= __y; }))
 452 # endif
 453
 454 /* Return nonzero value if either X is less than Y or Y is less than X.  */
 455 # ifndef islessgreater
 456 #  define islessgreater(x, y) \
 457   (__extension__                                                              \
 458    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 459       !isunordered (__x, __y) && (__x < __y || __y < __x); }))
 460 # endif
 461
 462 /* Return nonzero value if arguments are unordered.  */
 463 # ifndef isunordered
 464 #  define isunordered(u, v) \
 465   (__extension__                                                              \
 466    ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v);                       \
 467       fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
 468 # endif
 469
 470 #endif
 471
 472 __END_DECLS
 473
 474
 475 #endif /* math.h  */