math/math.h

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