math/math.h

   1 /* Declarations for math functions.
   2    Copyright (C) 1991, 92, 93, 95, 96, 97, 98 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 Library General Public License as
   7    published by the Free Software Foundation; either version 2 of the
   8    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    Library General Public License for more details.
  14
  15    You should have received a copy of the GNU Library General Public
  16    License along with the GNU C Library; see the file COPYING.LIB.  If not,
  17    write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
  18    Boston, MA 02111-1307, USA.  */
  19
  20 /*
  21  *      ISO C Standard: 4.5 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
  35 /* Get machine-dependent NAN value (returned for some domain errors).  */
  36 #ifdef   __USE_ISOC9X
  37 # include <bits/nan.h>
  38 #endif
  39
  40
  41 /* The file <bits/mathcalls.h> contains the prototypes for all the
  42    actual math functions.  These macros are used for those prototypes,
  43    so we can easily declare each function as both `name' and `__name',
  44    and can declare the float versions `namef' and `__namef'.  */
  45
  46 #define __MATHCALL(function,suffix, args)       \
  47   __MATHDECL (_Mdouble_,function,suffix, args)
  48 #define __MATHDECL(type, function,suffix, args) \
  49   __MATHDECL_1(type, function,suffix, args); \
  50   __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
  51 #define __MATHCALLX(function,suffix, args, attrib)      \
  52   __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
  53 #define __MATHDECLX(type, function,suffix, args, attrib) \
  54   __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
  55   __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
  56 #define __MATHDECL_1(type, function,suffix, args) \
  57   extern type __MATH_PRECNAME(function,suffix) args
  58
  59 #define _Mdouble_               double
  60 #define __MATH_PRECNAME(name,r) __CONCAT(name,r)
  61 #include <bits/mathcalls.h>
  62 #undef  _Mdouble_
  63 #undef  __MATH_PRECNAME
  64
  65 #if defined __USE_MISC || defined __USE_ISOC9X
  66
  67
  68 /* Include the file of declarations again, this time using `float'
  69    instead of `double' and appending f to each function name.  */
  70
  71 # ifndef _Mfloat_
  72 #  define _Mfloat_              float
  73 # endif
  74 # define _Mdouble_              _Mfloat_
  75 # ifdef __STDC__
  76 #  define __MATH_PRECNAME(name,r) name##f##r
  77 # else
  78 #  define __MATH_PRECNAME(name,r) name/**/f/**/r
  79 # endif
  80 # include <bits/mathcalls.h>
  81 # undef _Mdouble_
  82 # undef __MATH_PRECNAME
  83
  84 # if __STDC__ - 0 || __GNUC__ - 0
  85 /* Include the file of declarations again, this time using `long double'
  86    instead of `double' and appending l to each function name.  */
  87
  88 #  ifndef _Mlong_double_
  89 #   define _Mlong_double_       long double
  90 #  endif
  91 #  define _Mdouble_             _Mlong_double_
  92 #  ifdef __STDC__
  93 #   define __MATH_PRECNAME(name,r) name##l##r
  94 #  else
  95 #   define __MATH_PRECNAME(name,r) name/**/l/**/r
  96 #  endif
  97 #  include <bits/mathcalls.h>
  98 #  undef _Mdouble_
  99 #  undef __MATH_PRECNAME
 100
 101 # endif /* __STDC__ || __GNUC__ */
 102
 103 #endif  /* Use misc or ISO C 9X.  */
 104 #undef  __MATHDECL_1
 105 #undef  __MATHDECL
 106 #undef  __MATHCALL
 107
 108
 109 #if defined __USE_MISC || defined __USE_XOPEN || defined __USE_ISOC9X
 110 /* This variable is used by `gamma' and `lgamma'.  */
 111 extern int signgam;
 112 #endif
 113
 114
 115 /* ISO C 9X defines some generic macros which work on any data type.  */
 116 #if __USE_ISOC9X
 117
 118 /* Get the architecture specific values describing the floating-point
 119    evaluation.  The following symbols will get defined:
 120
 121     float_t     floating-point type at least as wide as `float' used
 122                 to evaluate `float' expressions
 123     double_t    floating-point type at least as wide as `double' used
 124                 to evaluate `double' expressions
 125
 126     FLT_EVAL_METHOD
 127                 Defined to
 128                   0     if `float_t' is `float' and `double_t' is `double'
 129                   1     if `float_t' and `double_t' are `double'
 130                   2     if `float_t' and `double_t' are `long double'
 131                   else  `float_t' and `double_t' are unspecified
 132
 133     INFINITY    representation of the infinity value of type `float'
 134
 135     FP_FAST_FMA
 136     FP_FAST_FMAF
 137     FP_FAST_FMAL
 138                 If defined it indicates that the `fma' function
 139                 generally executes about as fast as a multiply and an add.
 140                 This macro is defined only iff the `fma' function is
 141                 implemented directly with a hardware multiply-add instructions.
 142
 143     FP_ILOGB0   Expands to a value returned by `ilogb (0.0)'.
 144     FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
 145
 146     DECIMAL_DIG Number of decimal digits supported by conversion between
 147                 decimal and all internal floating-point formats.
 148
 149 */
 150 # include <bits/mathdef.h>
 151
 152 /* All floating-point numbers can be put in one of these categories.  */
 153 enum
 154   {
 155     FP_NAN,
 156 # define FP_NAN FP_NAN
 157     FP_INFINITE,
 158 # define FP_INFINITE FP_INFINITE
 159     FP_ZERO,
 160 # define FP_ZERO FP_ZERO
 161     FP_SUBNORMAL,
 162 # define FP_SUBNORMAL FP_SUBNORMAL
 163     FP_NORMAL
 164 # define FP_NORMAL FP_NORMAL
 165   };
 166
 167 /* Return number of classification appropriate for X.  */
 168 # define fpclassify(x) \
 169      (sizeof (x) == sizeof (float) ?                                          \
 170         __fpclassifyf (x)                                                     \
 171       : sizeof (x) == sizeof (double) ?                                       \
 172         __fpclassify (x) : __fpclassifyl (x))
 173
 174 /* Return nonzero value if sign of X is negative.  */
 175 # define signbit(x) \
 176      (sizeof (x) == sizeof (float) ?                                          \
 177         __signbitf (x)                                                        \
 178       : sizeof (x) == sizeof (double) ?                                       \
 179         __signbit (x) : __signbitl (x))
 180
 181 /* Return nonzero value if X is not +-Inf or NaN.  */
 182 # define isfinite(x) \
 183      (sizeof (x) == sizeof (float) ?                                          \
 184         __finitef (x)                                                         \
 185       : sizeof (x) == sizeof (double) ?                                       \
 186         __finite (x) : __finitel (x))
 187
 188 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
 189 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
 190
 191 /* Return nonzero value if X is a NaN.  We could use `fpclassify' but
 192    we already have this functions `__isnan' and it is faster.  */
 193 # define isnan(x) \
 194      (sizeof (x) == sizeof (float) ?                                          \
 195         __isnanf (x)                                                          \
 196       : sizeof (x) == sizeof (double) ?                                       \
 197         __isnan (x) : __isnanl (x))
 198
 199 /* Return nonzero value is X is positive or negative infinity.  */
 200 # define isinf(x) \
 201      (sizeof (x) == sizeof (float) ?                                          \
 202         __isinff (x)                                                          \
 203       : sizeof (x) == sizeof (double) ?                                       \
 204         __isinf (x) : __isinfl (x))
 205
 206 #endif /* Use ISO C 9X.  */
 207
 208 #ifdef  __USE_MISC
 209 /* Support for various different standard error handling behaviors.  */
 210 typedef enum
 211 {
 212   _IEEE_ = -1,  /* According to IEEE 754/IEEE 854.  */
 213   _SVID_,       /* According to System V, release 4.  */
 214   _XOPEN_,      /* Nowadays also Unix98.  */
 215   _POSIX_,
 216   _ISOC_        /* Actually this is ISO C 9X.  */
 217 } _LIB_VERSION_TYPE;
 218
 219 /* This variable can be changed at run-time to any of the values above to
 220    affect floating point error handling behavior (it may also be necessary
 221    to change the hardware FPU exception settings).  */
 222 extern _LIB_VERSION_TYPE _LIB_VERSION;
 223 #endif
 224
 225
 226 #ifdef __USE_SVID
 227 /* In SVID error handling, `matherr' is called with this description
 228    of the exceptional condition.
 229
 230    We have a problem when using C++ since `exception' is a reserved
 231    name in C++.  */
 232 # ifdef __cplusplus
 233 struct __exception
 234 # else
 235 struct exception
 236 # endif
 237   {
 238     int type;
 239     char *name;
 240     double arg1;
 241     double arg2;
 242     double retval;
 243   };
 244
 245 # ifdef __cplusplus
 246 extern int __matherr __P ((struct __exception *__exc));
 247 extern int matherr __P ((struct __exception *__exc));
 248 # else
 249 extern int __matherr __P ((struct exception *__exc));
 250 extern int matherr __P ((struct exception *__exc));
 251 # endif
 252
 253 # define X_TLOSS        1.41484755040568800000e+16
 254
 255 /* Types of exceptions in the `type' field.  */
 256 # define DOMAIN         1
 257 # define SING           2
 258 # define OVERFLOW       3
 259 # define UNDERFLOW      4
 260 # define TLOSS          5
 261 # define PLOSS          6
 262
 263 /* SVID mode specifies returning this large value instead of infinity.  */
 264 # define HUGE           FLT_MAX
 265 # include <float.h>             /* Defines FLT_MAX.  */
 266
 267 #else   /* !SVID */
 268
 269 # ifdef __USE_XOPEN
 270 /* X/Open wants another strange constant.  */
 271 #  define MAXFLOAT      FLT_MAX
 272 #  include <float.h>
 273 # endif
 274
 275 #endif  /* SVID */
 276
 277
 278 /* Some useful constants.  */
 279 #if defined __USE_BSD || defined __USE_XOPEN
 280 # define M_E            2.7182818284590452354   /* e */
 281 # define M_LOG2E        1.4426950408889634074   /* log_2 e */
 282 # define M_LOG10E       0.43429448190325182765  /* log_10 e */
 283 # define M_LN2          0.69314718055994530942  /* log_e 2 */
 284 # define M_LN10         2.30258509299404568402  /* log_e 10 */
 285 # define M_PI           3.14159265358979323846  /* pi */
 286 # define M_PI_2         1.57079632679489661923  /* pi/2 */
 287 # define M_PI_4         0.78539816339744830962  /* pi/4 */
 288 # define M_1_PI         0.31830988618379067154  /* 1/pi */
 289 # define M_2_PI         0.63661977236758134308  /* 2/pi */
 290 # define M_2_SQRTPI     1.12837916709551257390  /* 2/sqrt(pi) */
 291 # define M_SQRT2        1.41421356237309504880  /* sqrt(2) */
 292 # define M_SQRT1_2      0.70710678118654752440  /* 1/sqrt(2) */
 293 #endif
 294
 295 /* The above constants are not adequate for computation using `long double's.
 296    Therefore we provide as an extension constants with similar names as a
 297    GNU extension.  Provide enough digits for the 128-bit IEEE quad.  */
 298 #ifdef __USE_GNU
 299 # define M_El           2.7182818284590452353602874713526625L  /* e */
 300 # define M_LOG2El       1.4426950408889634073599246810018922L  /* log_2 e */
 301 # define M_LOG10El      0.4342944819032518276511289189166051L  /* log_10 e */
 302 # define M_LN2l         0.6931471805599453094172321214581766L  /* log_e 2 */
 303 # define M_LN10l        2.3025850929940456840179914546843642L  /* log_e 10 */
 304 # define M_PIl          3.1415926535897932384626433832795029L  /* pi */
 305 # define M_PI_2l        1.5707963267948966192313216916397514L  /* pi/2 */
 306 # define M_PI_4l        0.7853981633974483096156608458198757L  /* pi/4 */
 307 # define M_1_PIl        0.3183098861837906715377675267450287L  /* 1/pi */
 308 # define M_2_PIl        0.6366197723675813430755350534900574L  /* 2/pi */
 309 # define M_2_SQRTPIl    1.1283791670955125738961589031215452L  /* 2/sqrt(pi) */
 310 # define M_SQRT2l       1.4142135623730950488016887242096981L  /* sqrt(2) */
 311 # define M_SQRT1_2l     0.7071067811865475244008443621048490L  /* 1/sqrt(2) */
 312 #endif
 313
 314
 315 /* When compiling in strict ISO C compatible mode we must not use the
 316    inline functions since they, among other things, do not set the
 317    `errno' variable correctly.  */
 318 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
 319 # define __NO_MATH_INLINES      1
 320 #endif
 321
 322 /* Get machine-dependent inline versions (if there are any).  */
 323 #ifdef __USE_EXTERN_INLINES
 324 # include <bits/mathinline.h>
 325 #endif
 326
 327
 328 #if __USE_ISOC9X
 329 /* ISO C 9X defines some macros to compare number while taking care
 330    for unordered numbers.  Since many FPUs provide special
 331    instructions to support these operations and these tests are
 332    defined in <bits/mathinline.h>, we define the generic macros at
 333    this late point and only if they are not defined yet.  */
 334
 335 /* Return nonzero value if X is greater than Y.  */
 336 # ifndef isgreater
 337 #  define isgreater(x, y) \
 338   (__extension__                                                              \
 339    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 340       !isunordered (__x, __y) && __x > __y; }))
 341 # endif
 342
 343 /* Return nonzero value if X is greater than or equal to Y.  */
 344 # ifndef isgreaterequal
 345 #  define isgreaterequal(x, y) \
 346   (__extension__                                                              \
 347    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 348       !isunordered (__x, __y) && __x >= __y; }))
 349 # endif
 350
 351 /* Return nonzero value if X is less than Y.  */
 352 # ifndef isless
 353 #  define isless(x, y) \
 354   (__extension__                                                              \
 355    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 356       !isunordered (__x, __y) && __x < __y; }))
 357 # endif
 358
 359 /* Return nonzero value if X is less than or equal to Y.  */
 360 # ifndef islessequal
 361 #  define islessequal(x, y) \
 362   (__extension__                                                              \
 363    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 364       !isunordered (__x, __y) && __x <= __y; }))
 365 # endif
 366
 367 /* Return nonzero value if either X is less than Y or Y is less than X.  */
 368 # ifndef islessgreater
 369 #  define islessgreater(x, y) \
 370   (__extension__                                                              \
 371    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 372       !isunordered (__x, __y) && (__x < __y || __y < __x); }))
 373 # endif
 374
 375 /* Return nonzero value if arguments are unordered.  */
 376 # ifndef isunordered
 377 #  define isunordered(u, v) \
 378   (__extension__                                                              \
 379    ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v);                       \
 380       fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
 381 # endif
 382
 383 #endif
 384
 385 __END_DECLS
 386
 387
 388 #endif /* math.h  */