math/math.h

   1 /* Declarations for math functions.
   2    Copyright (C) 1991, 92, 93, 95, 96, 97 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_GNU
  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_t'
 134
 135      FP_FAST_FMA
 136      FP_FAST_FMAF
 137      FP_FAST_FMAL
 138                 If defined it indicates that the 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 */
 147 # include <bits/mathdef.h>
 148
 149 /* All floating-point numbers can be put in one of these categories.  */
 150 enum
 151   {
 152     FP_NAN,
 153 # define FP_NAN FP_NAN
 154     FP_INFINITE,
 155 # define FP_INFINITE FP_INFINITE
 156     FP_ZERO,
 157 # define FP_ZERO FP_ZERO
 158     FP_SUBNORMAL,
 159 # define FP_SUBNORMAL FP_SUBNORMAL
 160     FP_NORMAL
 161 # define FP_NORMAL FP_NORMAL
 162   };
 163
 164 /* Return number of classification appropriate for X.  */
 165 # define fpclassify(x) \
 166      (sizeof (x) == sizeof (float) ?                                          \
 167         __fpclassifyf (x)                                                     \
 168       : sizeof (x) == sizeof (double) ?                                       \
 169         __fpclassify (x) : __fpclassifyl (x))
 170
 171 /* Return nonzero value if sign of X is negative.  */
 172 # define signbit(x) \
 173      (sizeof (x) == sizeof (float) ?                                          \
 174         __signbitf (x)                                                        \
 175       : sizeof (x) == sizeof (double) ?                                       \
 176         __signbit (x) : __signbitl (x))
 177
 178 /* Return nonzero value if X is not +-Inf or NaN.  */
 179 # define isfinite(x) \
 180      (sizeof (x) == sizeof (float) ?                                          \
 181         __finitef (x)                                                         \
 182       : sizeof (x) == sizeof (double) ?                                       \
 183         __finite (x) : __finitel (x))
 184
 185 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
 186 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
 187
 188 /* Return nonzero value if X is a NaN.  We could use `fpclassify' but
 189    we already have this functions `__isnan' and it is faster.  */
 190 # define isnan(x) \
 191      (sizeof (x) == sizeof (float) ?                                          \
 192         __isnanf (x)                                                          \
 193       : sizeof (x) == sizeof (double) ?                                       \
 194         __isnan (x) : __isnanl (x))
 195
 196 #endif /* Use ISO C 9X.  */
 197
 198 #ifdef  __USE_MISC
 199 /* Support for various different standard error handling behaviors.  */
 200
 201 typedef enum { _IEEE_ = -1, _SVID_, _XOPEN_, _POSIX_ } _LIB_VERSION_TYPE;
 202
 203 /* This variable can be changed at run-time to any of the values above to
 204    affect floating point error handling behavior (it may also be necessary
 205    to change the hardware FPU exception settings).  */
 206 extern _LIB_VERSION_TYPE _LIB_VERSION;
 207 #endif
 208
 209
 210 #ifdef __USE_SVID
 211 /* In SVID error handling, `matherr' is called with this description
 212    of the exceptional condition.
 213
 214    We have a problem when using C++ since `exception' is reserved in
 215    C++.  */
 216 # ifdef __cplusplus
 217 struct __exception
 218 # else
 219 struct exception
 220 # endif
 221   {
 222     int type;
 223     char *name;
 224     double arg1;
 225     double arg2;
 226     double retval;
 227   };
 228
 229 # ifdef __cplusplus
 230 extern int __matherr __P ((struct __exception *__exc));
 231 extern int matherr __P ((struct __exception *__exc));
 232 # else
 233 extern int __matherr __P ((struct exception *__exc));
 234 extern int matherr __P ((struct exception *__exc));
 235 # endif
 236
 237 # define X_TLOSS        1.41484755040568800000e+16
 238
 239 /* Types of exceptions in the `type' field.  */
 240 # define DOMAIN         1
 241 # define SING           2
 242 # define OVERFLOW       3
 243 # define UNDERFLOW      4
 244 # define TLOSS          5
 245 # define PLOSS          6
 246
 247 /* SVID mode specifies returning this large value instead of infinity.  */
 248 # define HUGE           FLT_MAX
 249 # include <float.h>             /* Defines FLT_MAX.  */
 250
 251 #else   /* !SVID */
 252
 253 # ifdef __USE_XOPEN
 254 /* X/Open wants another strange constant.  */
 255 #  define MAXFLOAT      FLT_MAX
 256 #  include <float.h>
 257 # endif
 258
 259 #endif  /* SVID */
 260
 261
 262 #ifdef __USE_BSD
 263
 264 /* Some useful constants.  */
 265 # define M_E            _Mldbl(2.7182818284590452354)   /* e */
 266 # define M_LOG2E        _Mldbl(1.4426950408889634074)   /* log_2 e */
 267 # define M_LOG10E       _Mldbl(0.43429448190325182765)  /* log_10 e */
 268 # define M_LN2          _Mldbl(0.69314718055994530942)  /* log_e 2 */
 269 # define M_LN10         _Mldbl(2.30258509299404568402)  /* log_e 10 */
 270 # define M_PI           _Mldbl(3.14159265358979323846)  /* pi */
 271 # define M_PI_2         _Mldbl(1.57079632679489661923)  /* pi/2 */
 272 # define M_PI_4         _Mldbl(0.78539816339744830962)  /* pi/4 */
 273 # define M_1_PI         _Mldbl(0.31830988618379067154)  /* 1/pi */
 274 # define M_2_PI         _Mldbl(0.63661977236758134308)  /* 2/pi */
 275 # define M_2_SQRTPI     _Mldbl(1.12837916709551257390)  /* 2/sqrt(pi) */
 276 # define M_SQRT2        _Mldbl(1.41421356237309504880)  /* sqrt(2) */
 277 # define M_SQRT1_2      _Mldbl(0.70710678118654752440)  /* 1/sqrt(2) */
 278
 279 #endif
 280
 281 /* Our constants might specify more precision than `double' can represent.
 282    Use `long double' constants in standard and GNU C, where they are
 283    supported and the cast to `double'.
 284
 285    If the constants are use in code which does not use prototypes, one
 286    might get problems if a function takes a `double' argument and any
 287    of the constants are provided as the argument.  In this case, cast
 288    the argument to `double'.
 289
 290    Please note we define the macro even if the constants are not defined.
 291    This helps us to use the macros in other places.  */
 292 #if __STDC__ - 0 || __GNUC__ - 0
 293 # define _Mldbl(x) x##L
 294 #else   /* Traditional C.  */
 295 # define _Mldbl(x) x
 296 #endif  /* Standard or GNU C.  */
 297
 298
 299 /* Get machine-dependent inline versions (if there are any).  */
 300 #ifdef __OPTIMIZE__
 301 # include <bits/mathinline.h>
 302 #endif
 303
 304
 305 #if __USE_ISOC9X
 306 /* ISO C 9X defines some macros to compare number while taking care
 307    for unordered numbers.  Since many FPUs provide special
 308    instructions to support these operations and these tests are
 309    defined in <bits/mathinline.h>, we define the generic macros at
 310    this late point.  */
 311
 312 /* Return nonzero value if X is greater than Y.  */
 313 # ifndef isgreater
 314 #  define isgreater(x, y) \
 315   (__extension__                                                              \
 316    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 317       !isunordered (__x, __y) && __x > __y; }))
 318 # endif
 319
 320 /* Return nonzero value if X is greater than or equal to Y.  */
 321 # ifndef isgreaterequal
 322 #  define isgreaterequal(x, y) \
 323   (__extension__                                                              \
 324    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 325       !isunordered (__x, __y) && __x >= __y; }))
 326 # endif
 327
 328 /* Return nonzero value if X is less than Y.  */
 329 # ifndef isless
 330 #  define isless(x, y) \
 331   (__extension__                                                              \
 332    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 333       !isunordered (__x, __y) && __x < __y; }))
 334 # endif
 335
 336 /* Return nonzero value if X is less than or equal to Y.  */
 337 # ifndef islessequal
 338 #  define islessequal(x, y) \
 339   (__extension__                                                              \
 340    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 341       !isunordered (__x, __y) && __x <= __y; }))
 342 # endif
 343
 344 /* Return nonzero value if either X is less than Y or Y is less than X.  */
 345 # ifndef islessgreater
 346 #  define islessgreater(x, y) \
 347   (__extension__                                                              \
 348    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 349       !isunordered (__x, __y) && (__x < __y || __y < __x); }))
 350 # endif
 351
 352 /* Return nonzero value if arguments are unordered.  */
 353 # ifndef isunordered
 354 #  define isunordered(x, y) \
 355   (__extension__                                                              \
 356    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 357       fpclassify (__x) == FP_NAN || fpclassify (__y) == FP_NAN; }))
 358 # endif
 359
 360 #endif
 361
 362 __END_DECLS
 363
 364
 365 #endif /* math.h  */