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 # include <bits/mathdef.h>
 136
 137 /* All floating-point numbers can be put in one of these categories.  */
 138 enum
 139   {
 140     FP_NAN,
 141 # define FP_NAN FP_NAN
 142     FP_INFINITE,
 143 # define FP_INFINITE FP_INFINITE
 144     FP_ZERO,
 145 # define FP_ZERO FP_ZERO
 146     FP_SUBNORMAL,
 147 # define FP_SUBNORMAL FP_SUBNORMAL
 148     FP_NORMAL
 149 # define FP_NORMAL FP_NORMAL
 150   };
 151
 152 /* Return number of classification appropriate for X.  */
 153 # define fpclassify(x) \
 154      (sizeof (x) == sizeof (float) ?                                          \
 155         __fpclassifyf (x)                                                     \
 156       : sizeof (x) == sizeof (double) ?                                       \
 157         __fpclassify (x) : __fpclassifyl (x))
 158
 159 /* Return nonzero value if sign of X is negative.  */
 160 # define signbit(x) \
 161      (sizeof (x) == sizeof (float) ?                                          \
 162         __signbitf (x)                                                        \
 163       : sizeof (x) == sizeof (double) ?                                       \
 164         __signbit (x) : __signbitl (x))
 165
 166 /* Return nonzero value if X is not +-Inf or NaN.  */
 167 # define isfinite(x) \
 168      (sizeof (x) == sizeof (float) ?                                          \
 169         __finitef (x)                                                         \
 170       : sizeof (x) == sizeof (double) ?                                       \
 171         __finite (x) : __finitel (x))
 172
 173 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
 174 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
 175
 176 /* Return nonzero value if X is a NaN.  We could use `fpclassify' but
 177    we already have this functions `__isnan' and it is faster.  */
 178 # define isnan(x) \
 179      (sizeof (x) == sizeof (float) ?                                          \
 180         __isnanf (x)                                                          \
 181       : sizeof (x) == sizeof (double) ?                                       \
 182         __isnan (x) : __isnanl (x))
 183
 184
 185 /* Conversion functions.  */
 186
 187 /* Round X to nearest integral value according to current rounding
 188    direction.  */
 189 extern long int lrint __P ((long double __x));
 190 extern long long int llrint __P ((long double __x));
 191
 192 /* Round X to nearest integral value, rounding halfway cases away from
 193    zero.  */
 194 extern long int lround __P ((long double __x));
 195 extern long long int llround __P ((long double __x));
 196
 197 #endif /* Use ISO C 9X.  */
 198
 199 #ifdef  __USE_MISC
 200 /* Support for various different standard error handling behaviors.  */
 201
 202 typedef enum { _IEEE_ = -1, _SVID_, _XOPEN_, _POSIX_ } _LIB_VERSION_TYPE;
 203
 204 /* This variable can be changed at run-time to any of the values above to
 205    affect floating point error handling behavior (it may also be necessary
 206    to change the hardware FPU exception settings).  */
 207 extern _LIB_VERSION_TYPE _LIB_VERSION;
 208 #endif
 209
 210
 211 #ifdef __USE_SVID
 212 /* In SVID error handling, `matherr' is called with this description
 213    of the exceptional condition.
 214
 215    We have a problem when using C++ since `exception' is reserved in
 216    C++.  */
 217 # ifdef __cplusplus
 218 struct __exception
 219 # else
 220 struct exception
 221 # endif
 222   {
 223     int type;
 224     char *name;
 225     double arg1;
 226     double arg2;
 227     double retval;
 228   };
 229
 230 # ifdef __cplusplus
 231 extern int __matherr __P ((struct __exception *__exc));
 232 extern int matherr __P ((struct __exception *__exc));
 233 # else
 234 extern int __matherr __P ((struct exception *__exc));
 235 extern int matherr __P ((struct exception *__exc));
 236 # endif
 237
 238 # define X_TLOSS        1.41484755040568800000e+16
 239
 240 /* Types of exceptions in the `type' field.  */
 241 # define DOMAIN         1
 242 # define SING           2
 243 # define OVERFLOW       3
 244 # define UNDERFLOW      4
 245 # define TLOSS          5
 246 # define PLOSS          6
 247
 248 /* SVID mode specifies returning this large value instead of infinity.  */
 249 # define HUGE           FLT_MAX
 250 # include <float.h>             /* Defines FLT_MAX.  */
 251
 252 #else   /* !SVID */
 253
 254 # ifdef __USE_XOPEN
 255 /* X/Open wants another strange constant.  */
 256 #  define MAXFLOAT      FLT_MAX
 257 #  include <float.h>
 258 # endif
 259
 260 #endif  /* SVID */
 261
 262
 263 #ifdef __USE_BSD
 264
 265 /* Some useful constants.  */
 266 # define M_E            _Mldbl(2.7182818284590452354)   /* e */
 267 # define M_LOG2E        _Mldbl(1.4426950408889634074)   /* log_2 e */
 268 # define M_LOG10E       _Mldbl(0.43429448190325182765)  /* log_10 e */
 269 # define M_LN2          _Mldbl(0.69314718055994530942)  /* log_e 2 */
 270 # define M_LN10         _Mldbl(2.30258509299404568402)  /* log_e 10 */
 271 # define M_PI           _Mldbl(3.14159265358979323846)  /* pi */
 272 # define M_PI_2         _Mldbl(1.57079632679489661923)  /* pi/2 */
 273 # define M_PI_4         _Mldbl(0.78539816339744830962)  /* pi/4 */
 274 # define M_1_PI         _Mldbl(0.31830988618379067154)  /* 1/pi */
 275 # define M_2_PI         _Mldbl(0.63661977236758134308)  /* 2/pi */
 276 # define M_2_SQRTPI     _Mldbl(1.12837916709551257390)  /* 2/sqrt(pi) */
 277 # define M_SQRT2        _Mldbl(1.41421356237309504880)  /* sqrt(2) */
 278 # define M_SQRT1_2      _Mldbl(0.70710678118654752440)  /* 1/sqrt(2) */
 279
 280 #endif
 281
 282 /* Our constants might specify more precision than `double' can represent.
 283    Use `long double' constants in standard and GNU C, where they are
 284    supported and the cast to `double'.
 285
 286    If the constants are use in code which does not use prototypes, one
 287    might get problems if a function takes a `double' argument and any
 288    of the constants are provided as the argument.  In this case, cast
 289    the argument to `double'.
 290
 291    Please note we define the macro even if the constants are not defined.
 292    This helps us to use the macros in other places.  */
 293 #if __STDC__ - 0 || __GNUC__ - 0
 294 # define _Mldbl(x) x##L
 295 #else   /* Traditional C.  */
 296 # define _Mldbl(x) x
 297 #endif  /* Standard or GNU C.  */
 298
 299
 300 /* Get machine-dependent inline versions (if there are any).  */
 301 #ifdef __OPTIMIZE__
 302 # include <bits/mathinline.h>
 303 #endif
 304
 305
 306 #if __USE_ISOC9X
 307 /* ISO C 9X defines some macros to compare number while taking care
 308    for unordered numbers.  Since many FPUs provide special
 309    instructions to support these operations and these tests are
 310    defined in <bits/mathinline.h>, we define the generic macros at
 311    this late point.  */
 312
 313 /* Return nonzero value if X is greater than Y.  */
 314 # ifndef isgreater
 315 #  define isgreater(x, y) \
 316   (__extension__                                                              \
 317    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 318       !isunordered (__x, __y) && __x > __y; }))
 319 # endif
 320
 321 /* Return nonzero value if X is greater than or equal to Y.  */
 322 # ifndef isgreaterequal
 323 #  define isgreaterequal(x, y) \
 324   (__extension__                                                              \
 325    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 326       !isunordered (__x, __y) && __x >= __y; }))
 327 # endif
 328
 329 /* Return nonzero value if X is less than Y.  */
 330 # ifndef isless
 331 #  define isless(x, y) \
 332   (__extension__                                                              \
 333    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 334       !isunordered (__x, __y) && __x < __y; }))
 335 # endif
 336
 337 /* Return nonzero value if X is less than or equal to Y.  */
 338 # ifndef islessequal
 339 #  define islessequal(x, y) \
 340   (__extension__                                                              \
 341    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 342       !isunordered (__x, __y) && __x <= __y; }))
 343 # endif
 344
 345 /* Return nonzero value if either X is less than Y or Y is less than X.  */
 346 # ifndef islessgreater
 347 #  define islessgreater(x, y) \
 348   (__extension__                                                              \
 349    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 350       !isunordered (__x, __y) && (__x < __y || __y < __x); }))
 351 # endif
 352
 353 /* Return nonzero value if arguments are unordered.  */
 354 # ifndef isunordered
 355 #  define isunordered(x, y) \
 356   (__extension__                                                              \
 357    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 358       fpclassify (__x) == FP_NAN || fpclassify (__y) == FP_NAN; }))
 359 # endif
 360
 361 #endif
 362
 363 __END_DECLS
 364
 365
 366 #endif /* math.h  */