math/math.h

   1 /* Declarations for math functions.
   2    Copyright (C) 1991-1993, 1995-1999, 2001, 2002, 2004, 2006
   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                                   __attribute__ ((__const__)) __THROW;
 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 #    endif
 114 #   endif
 115
 116 /* Include the file of declarations again, this time using `long double'
 117    instead of `double' and appending l to each function name.  */
 118
 119 #   undef __MATHDECL_1
 120 #   define __MATHDECL_2(type, function,suffix, args, alias) \
 121   extern type __REDIRECT(__MATH_PRECNAME(function,suffix), \
 122                          args, alias) __THROW
 123 #   define __MATHDECL_1(type, function,suffix, args) \
 124   __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
 125 #  endif
 126
 127 #  ifndef _Mlong_double_
 128 #   define _Mlong_double_       long double
 129 #  endif
 130 #  define _Mdouble_             _Mlong_double_
 131 #  ifdef __STDC__
 132 #   define __MATH_PRECNAME(name,r) name##l##r
 133 #  else
 134 #   define __MATH_PRECNAME(name,r) name/**/l/**/r
 135 #  endif
 136 #  define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
 137 #  define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
 138 #  include <bits/mathcalls.h>
 139 #  undef _Mdouble_
 140 # undef _Mdouble_BEGIN_NAMESPACE
 141 # undef _Mdouble_END_NAMESPACE
 142 #  undef __MATH_PRECNAME
 143
 144 # endif /* __STDC__ || __GNUC__ */
 145
 146 #endif  /* Use misc or ISO C99.  */
 147 #undef  __MATHDECL_1
 148 #undef  __MATHDECL
 149 #undef  __MATHCALL
 150
 151
 152 #if defined __USE_MISC || defined __USE_XOPEN
 153 /* This variable is used by `gamma' and `lgamma'.  */
 154 extern int signgam;
 155 #endif
 156
 157
 158 /* ISO C99 defines some generic macros which work on any data type.  */
 159 #ifdef __USE_ISOC99
 160
 161 /* Get the architecture specific values describing the floating-point
 162    evaluation.  The following symbols will get defined:
 163
 164     float_t     floating-point type at least as wide as `float' used
 165                 to evaluate `float' expressions
 166     double_t    floating-point type at least as wide as `double' used
 167                 to evaluate `double' expressions
 168
 169     FLT_EVAL_METHOD
 170                 Defined to
 171                   0     if `float_t' is `float' and `double_t' is `double'
 172                   1     if `float_t' and `double_t' are `double'
 173                   2     if `float_t' and `double_t' are `long double'
 174                   else  `float_t' and `double_t' are unspecified
 175
 176     INFINITY    representation of the infinity value of type `float'
 177
 178     FP_FAST_FMA
 179     FP_FAST_FMAF
 180     FP_FAST_FMAL
 181                 If defined it indicates that the `fma' function
 182                 generally executes about as fast as a multiply and an add.
 183                 This macro is defined only iff the `fma' function is
 184                 implemented directly with a hardware multiply-add instructions.
 185
 186     FP_ILOGB0   Expands to a value returned by `ilogb (0.0)'.
 187     FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
 188
 189     DECIMAL_DIG Number of decimal digits supported by conversion between
 190                 decimal and all internal floating-point formats.
 191
 192 */
 193
 194 /* All floating-point numbers can be put in one of these categories.  */
 195 enum
 196   {
 197     FP_NAN,
 198 # define FP_NAN FP_NAN
 199     FP_INFINITE,
 200 # define FP_INFINITE FP_INFINITE
 201     FP_ZERO,
 202 # define FP_ZERO FP_ZERO
 203     FP_SUBNORMAL,
 204 # define FP_SUBNORMAL FP_SUBNORMAL
 205     FP_NORMAL
 206 # define FP_NORMAL 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 is 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 #endif /* Use ISO C99.  */
 278
 279 #ifdef  __USE_MISC
 280 /* Support for various different standard error handling behaviors.  */
 281 typedef enum
 282 {
 283   _IEEE_ = -1,  /* According to IEEE 754/IEEE 854.  */
 284   _SVID_,       /* According to System V, release 4.  */
 285   _XOPEN_,      /* Nowadays also Unix98.  */
 286   _POSIX_,
 287   _ISOC_        /* Actually this is ISO C99.  */
 288 } _LIB_VERSION_TYPE;
 289
 290 /* This variable can be changed at run-time to any of the values above to
 291    affect floating point error handling behavior (it may also be necessary
 292    to change the hardware FPU exception settings).  */
 293 extern _LIB_VERSION_TYPE _LIB_VERSION;
 294 #endif
 295
 296
 297 #ifdef __USE_SVID
 298 /* In SVID error handling, `matherr' is called with this description
 299    of the exceptional condition.
 300
 301    We have a problem when using C++ since `exception' is a reserved
 302    name in C++.  */
 303 # ifdef __cplusplus
 304 struct __exception
 305 # else
 306 struct exception
 307 # endif
 308   {
 309     int type;
 310     char *name;
 311     double arg1;
 312     double arg2;
 313     double retval;
 314   };
 315
 316 # ifdef __cplusplus
 317 extern int matherr (struct __exception *__exc) throw ();
 318 # else
 319 extern int matherr (struct exception *__exc);
 320 # endif
 321
 322 # define X_TLOSS        1.41484755040568800000e+16
 323
 324 /* Types of exceptions in the `type' field.  */
 325 # define DOMAIN         1
 326 # define SING           2
 327 # define OVERFLOW       3
 328 # define UNDERFLOW      4
 329 # define TLOSS          5
 330 # define PLOSS          6
 331
 332 /* SVID mode specifies returning this large value instead of infinity.  */
 333 # define HUGE           3.40282347e+38F
 334
 335 #else   /* !SVID */
 336
 337 # ifdef __USE_XOPEN
 338 /* X/Open wants another strange constant.  */
 339 #  define MAXFLOAT      3.40282347e+38F
 340 # endif
 341
 342 #endif  /* SVID */
 343
 344
 345 /* Some useful constants.  */
 346 #if defined __USE_BSD || defined __USE_XOPEN
 347 # define M_E            2.7182818284590452354   /* e */
 348 # define M_LOG2E        1.4426950408889634074   /* log_2 e */
 349 # define M_LOG10E       0.43429448190325182765  /* log_10 e */
 350 # define M_LN2          0.69314718055994530942  /* log_e 2 */
 351 # define M_LN10         2.30258509299404568402  /* log_e 10 */
 352 # define M_PI           3.14159265358979323846  /* pi */
 353 # define M_PI_2         1.57079632679489661923  /* pi/2 */
 354 # define M_PI_4         0.78539816339744830962  /* pi/4 */
 355 # define M_1_PI         0.31830988618379067154  /* 1/pi */
 356 # define M_2_PI         0.63661977236758134308  /* 2/pi */
 357 # define M_2_SQRTPI     1.12837916709551257390  /* 2/sqrt(pi) */
 358 # define M_SQRT2        1.41421356237309504880  /* sqrt(2) */
 359 # define M_SQRT1_2      0.70710678118654752440  /* 1/sqrt(2) */
 360 #endif
 361
 362 /* The above constants are not adequate for computation using `long double's.
 363    Therefore we provide as an extension constants with similar names as a
 364    GNU extension.  Provide enough digits for the 128-bit IEEE quad.  */
 365 #ifdef __USE_GNU
 366 # define M_El           2.7182818284590452353602874713526625L  /* e */
 367 # define M_LOG2El       1.4426950408889634073599246810018921L  /* log_2 e */
 368 # define M_LOG10El      0.4342944819032518276511289189166051L  /* log_10 e */
 369 # define M_LN2l         0.6931471805599453094172321214581766L  /* log_e 2 */
 370 # define M_LN10l        2.3025850929940456840179914546843642L  /* log_e 10 */
 371 # define M_PIl          3.1415926535897932384626433832795029L  /* pi */
 372 # define M_PI_2l        1.5707963267948966192313216916397514L  /* pi/2 */
 373 # define M_PI_4l        0.7853981633974483096156608458198757L  /* pi/4 */
 374 # define M_1_PIl        0.3183098861837906715377675267450287L  /* 1/pi */
 375 # define M_2_PIl        0.6366197723675813430755350534900574L  /* 2/pi */
 376 # define M_2_SQRTPIl    1.1283791670955125738961589031215452L  /* 2/sqrt(pi) */
 377 # define M_SQRT2l       1.4142135623730950488016887242096981L  /* sqrt(2) */
 378 # define M_SQRT1_2l     0.7071067811865475244008443621048490L  /* 1/sqrt(2) */
 379 #endif
 380
 381
 382 /* When compiling in strict ISO C compatible mode we must not use the
 383    inline functions since they, among other things, do not set the
 384    `errno' variable correctly.  */
 385 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
 386 # define __NO_MATH_INLINES      1
 387 #endif
 388
 389 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
 390 /* ISO C99 defines some macros to compare number while taking care for
 391    unordered numbers.  Many FPUs provide special instructions to support
 392    these operations.  Generic support in GCC for these as builtins went
 393    in before 3.0.0, but not all cpus added their patterns.  We define
 394    versions that use the builtins here, and <bits/mathinline.h> will
 395    undef/redefine as appropriate for the specific GCC version in use.  */
 396 # define isgreater(x, y)        __builtin_isgreater(x, y)
 397 # define isgreaterequal(x, y)   __builtin_isgreaterequal(x, y)
 398 # define isless(x, y)           __builtin_isless(x, y)
 399 # define islessequal(x, y)      __builtin_islessequal(x, y)
 400 # define islessgreater(x, y)    __builtin_islessgreater(x, y)
 401 # define isunordered(u, v)      __builtin_isunordered(u, v)
 402 #endif
 403
 404 /* Get machine-dependent inline versions (if there are any).  */
 405 #ifdef __USE_EXTERN_INLINES
 406 # include <bits/mathinline.h>
 407 #endif
 408
 409 #ifdef __USE_ISOC99
 410 /* If we've still got undefined comparison macros, provide defaults.  */
 411
 412 /* Return nonzero value if X is greater than Y.  */
 413 # ifndef isgreater
 414 #  define isgreater(x, y) \
 415   (__extension__                                                              \
 416    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 417       !isunordered (__x, __y) && __x > __y; }))
 418 # endif
 419
 420 /* Return nonzero value if X is greater than or equal to Y.  */
 421 # ifndef isgreaterequal
 422 #  define isgreaterequal(x, y) \
 423   (__extension__                                                              \
 424    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 425       !isunordered (__x, __y) && __x >= __y; }))
 426 # endif
 427
 428 /* Return nonzero value if X is less than Y.  */
 429 # ifndef isless
 430 #  define isless(x, y) \
 431   (__extension__                                                              \
 432    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 433       !isunordered (__x, __y) && __x < __y; }))
 434 # endif
 435
 436 /* Return nonzero value if X is less than or equal to Y.  */
 437 # ifndef islessequal
 438 #  define islessequal(x, y) \
 439   (__extension__                                                              \
 440    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 441       !isunordered (__x, __y) && __x <= __y; }))
 442 # endif
 443
 444 /* Return nonzero value if either X is less than Y or Y is less than X.  */
 445 # ifndef islessgreater
 446 #  define islessgreater(x, y) \
 447   (__extension__                                                              \
 448    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 449       !isunordered (__x, __y) && (__x < __y || __y < __x); }))
 450 # endif
 451
 452 /* Return nonzero value if arguments are unordered.  */
 453 # ifndef isunordered
 454 #  define isunordered(u, v) \
 455   (__extension__                                                              \
 456    ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v);                       \
 457       fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
 458 # endif
 459
 460 #endif
 461
 462 __END_DECLS
 463
 464
 465 #endif /* math.h  */