math/math.h

   1 /* Declarations for math functions.
   2    Copyright (C) 1991,92,93,95,96,97,98,99,2001 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
  35 /* Get machine-dependent NAN value (returned for some domain errors).  */
  36 #ifdef   __USE_ISOC99
  37 # include <bits/nan.h>
  38 #endif
  39 /* Get general and ISO C99 specific information.  */
  40 #include <bits/mathdef.h>
  41
  42
  43 /* The file <bits/mathcalls.h> contains the prototypes for all the
  44    actual math functions.  These macros are used for those prototypes,
  45    so we can easily declare each function as both `name' and `__name',
  46    and can declare the float versions `namef' and `__namef'.  */
  47
  48 #define __MATHCALL(function,suffix, args)       \
  49   __MATHDECL (_Mdouble_,function,suffix, args)
  50 #define __MATHDECL(type, function,suffix, args) \
  51   __MATHDECL_1(type, function,suffix, args); \
  52   __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
  53 #define __MATHCALLX(function,suffix, args, attrib)      \
  54   __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
  55 #define __MATHDECLX(type, function,suffix, args, attrib) \
  56   __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
  57   __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
  58 #define __MATHDECL_1(type, function,suffix, args) \
  59   extern type __MATH_PRECNAME(function,suffix) args __THROW
  60
  61 #define _Mdouble_               double
  62 #define __MATH_PRECNAME(name,r) __CONCAT(name,r)
  63 #include <bits/mathcalls.h>
  64 #undef  _Mdouble_
  65 #undef  __MATH_PRECNAME
  66
  67 #if defined __USE_MISC || defined __USE_ISOC99
  68
  69
  70 /* Include the file of declarations again, this time using `float'
  71    instead of `double' and appending f to each function name.  */
  72
  73 # ifndef _Mfloat_
  74 #  define _Mfloat_              float
  75 # endif
  76 # define _Mdouble_              _Mfloat_
  77 # ifdef __STDC__
  78 #  define __MATH_PRECNAME(name,r) name##f##r
  79 # else
  80 #  define __MATH_PRECNAME(name,r) name/**/f/**/r
  81 # endif
  82 # include <bits/mathcalls.h>
  83 # undef _Mdouble_
  84 # undef __MATH_PRECNAME
  85
  86 # if (__STDC__ - 0 || __GNUC__ - 0) && !defined __NO_LONG_DOUBLE_MATH
  87 /* Include the file of declarations again, this time using `long double'
  88    instead of `double' and appending l to each function name.  */
  89
  90 #  ifndef _Mlong_double_
  91 #   define _Mlong_double_       long double
  92 #  endif
  93 #  define _Mdouble_             _Mlong_double_
  94 #  ifdef __STDC__
  95 #   define __MATH_PRECNAME(name,r) name##l##r
  96 #  else
  97 #   define __MATH_PRECNAME(name,r) name/**/l/**/r
  98 #  endif
  99 #  include <bits/mathcalls.h>
 100 #  undef _Mdouble_
 101 #  undef __MATH_PRECNAME
 102
 103 # endif /* __STDC__ || __GNUC__ */
 104
 105 #endif  /* Use misc or ISO C99.  */
 106 #undef  __MATHDECL_1
 107 #undef  __MATHDECL
 108 #undef  __MATHCALL
 109
 110
 111 #if defined __USE_MISC || defined __USE_XOPEN
 112 /* This variable is used by `gamma' and `lgamma'.  */
 113 extern int signgam;
 114 #endif
 115
 116
 117 /* ISO C99 defines some generic macros which work on any data type.  */
 118 #if __USE_ISOC99
 119
 120 /* Get the architecture specific values describing the floating-point
 121    evaluation.  The following symbols will get defined:
 122
 123     float_t     floating-point type at least as wide as `float' used
 124                 to evaluate `float' expressions
 125     double_t    floating-point type at least as wide as `double' used
 126                 to evaluate `double' expressions
 127
 128     FLT_EVAL_METHOD
 129                 Defined to
 130                   0     if `float_t' is `float' and `double_t' is `double'
 131                   1     if `float_t' and `double_t' are `double'
 132                   2     if `float_t' and `double_t' are `long double'
 133                   else  `float_t' and `double_t' are unspecified
 134
 135     INFINITY    representation of the infinity value of type `float'
 136
 137     FP_FAST_FMA
 138     FP_FAST_FMAF
 139     FP_FAST_FMAL
 140                 If defined it indicates that the `fma' function
 141                 generally executes about as fast as a multiply and an add.
 142                 This macro is defined only iff the `fma' function is
 143                 implemented directly with a hardware multiply-add instructions.
 144
 145     FP_ILOGB0   Expands to a value returned by `ilogb (0.0)'.
 146     FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
 147
 148     DECIMAL_DIG Number of decimal digits supported by conversion between
 149                 decimal and all internal floating-point formats.
 150
 151 */
 152
 153 /* All floating-point numbers can be put in one of these categories.  */
 154 enum
 155   {
 156     FP_NAN,
 157 # define FP_NAN FP_NAN
 158     FP_INFINITE,
 159 # define FP_INFINITE FP_INFINITE
 160     FP_ZERO,
 161 # define FP_ZERO FP_ZERO
 162     FP_SUBNORMAL,
 163 # define FP_SUBNORMAL FP_SUBNORMAL
 164     FP_NORMAL
 165 # define FP_NORMAL FP_NORMAL
 166   };
 167
 168 /* Return number of classification appropriate for X.  */
 169 # ifdef __NO_LONG_DOUBLE_MATH
 170 #  define fpclassify(x) \
 171      (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
 172 # else
 173 #  define fpclassify(x) \
 174      (sizeof (x) == sizeof (float)                                            \
 175       ? __fpclassifyf (x)                                                     \
 176       : sizeof (x) == sizeof (double)                                         \
 177       ? __fpclassify (x) : __fpclassifyl (x))
 178 # endif
 179
 180 /* Return nonzero value if sign of X is negative.  */
 181 # ifdef __NO_LONG_DOUBLE_MATH
 182 #  define signbit(x) \
 183      (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
 184 # else
 185 #  define signbit(x) \
 186      (sizeof (x) == sizeof (float)                                            \
 187       ? __signbitf (x)                                                        \
 188       : sizeof (x) == sizeof (double)                                         \
 189       ? __signbit (x) : __signbitl (x))
 190 # endif
 191
 192 /* Return nonzero value if X is not +-Inf or NaN.  */
 193 # ifdef __NO_LONG_DOUBLE_MATH
 194 #  define isfinite(x) \
 195      (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
 196 # else
 197 #  define isfinite(x) \
 198      (sizeof (x) == sizeof (float)                                            \
 199       ? __finitef (x)                                                         \
 200       : sizeof (x) == sizeof (double)                                         \
 201       ? __finite (x) : __finitel (x))
 202 # endif
 203
 204 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
 205 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
 206
 207 /* Return nonzero value if X is a NaN.  We could use `fpclassify' but
 208    we already have this functions `__isnan' and it is faster.  */
 209 # ifdef __NO_LONG_DOUBLE_MATH
 210 #  define isnan(x) \
 211      (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
 212 # else
 213 #  define isnan(x) \
 214      (sizeof (x) == sizeof (float)                                            \
 215       ? __isnanf (x)                                                          \
 216       : sizeof (x) == sizeof (double)                                         \
 217       ? __isnan (x) : __isnanl (x))
 218 # endif
 219
 220 /* Return nonzero value is X is positive or negative infinity.  */
 221 # ifdef __NO_LONG_DOUBLE_MATH
 222 #  define isinf(x) \
 223      (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
 224 # else
 225 #  define isinf(x) \
 226      (sizeof (x) == sizeof (float)                                            \
 227       ? __isinff (x)                                                          \
 228       : sizeof (x) == sizeof (double)                                         \
 229       ? __isinf (x) : __isinfl (x))
 230 # endif
 231
 232 /* Bitmasks for the math_errhandling macro.  */
 233 # define MATH_ERRNO     1       /* errno set by math functions.  */
 234 # define MATH_ERREXCEPT 2       /* Exceptions raised by math functions.  */
 235
 236 #endif /* Use ISO C99.  */
 237
 238 #ifdef  __USE_MISC
 239 /* Support for various different standard error handling behaviors.  */
 240 typedef enum
 241 {
 242   _IEEE_ = -1,  /* According to IEEE 754/IEEE 854.  */
 243   _SVID_,       /* According to System V, release 4.  */
 244   _XOPEN_,      /* Nowadays also Unix98.  */
 245   _POSIX_,
 246   _ISOC_        /* Actually this is ISO C99.  */
 247 } _LIB_VERSION_TYPE;
 248
 249 /* This variable can be changed at run-time to any of the values above to
 250    affect floating point error handling behavior (it may also be necessary
 251    to change the hardware FPU exception settings).  */
 252 extern _LIB_VERSION_TYPE _LIB_VERSION;
 253 #endif
 254
 255
 256 #ifdef __USE_SVID
 257 /* In SVID error handling, `matherr' is called with this description
 258    of the exceptional condition.
 259
 260    We have a problem when using C++ since `exception' is a reserved
 261    name in C++.  */
 262 # ifdef __cplusplus
 263 struct __exception
 264 # else
 265 struct exception
 266 # endif
 267   {
 268     int type;
 269     char *name;
 270     double arg1;
 271     double arg2;
 272     double retval;
 273   };
 274
 275 # ifdef __cplusplus
 276 extern int matherr (struct __exception *__exc) throw ();
 277 # else
 278 extern int matherr (struct exception *__exc);
 279 # endif
 280
 281 # define X_TLOSS        1.41484755040568800000e+16
 282
 283 /* Types of exceptions in the `type' field.  */
 284 # define DOMAIN         1
 285 # define SING           2
 286 # define OVERFLOW       3
 287 # define UNDERFLOW      4
 288 # define TLOSS          5
 289 # define PLOSS          6
 290
 291 /* SVID mode specifies returning this large value instead of infinity.  */
 292 # define HUGE           3.40282347e+38F
 293
 294 #else   /* !SVID */
 295
 296 # ifdef __USE_XOPEN
 297 /* X/Open wants another strange constant.  */
 298 #  define MAXFLOAT      3.40282347e+38F
 299 # endif
 300
 301 #endif  /* SVID */
 302
 303
 304 /* Some useful constants.  */
 305 #if defined __USE_BSD || defined __USE_XOPEN
 306 # define M_E            2.7182818284590452354   /* e */
 307 # define M_LOG2E        1.4426950408889634074   /* log_2 e */
 308 # define M_LOG10E       0.43429448190325182765  /* log_10 e */
 309 # define M_LN2          0.69314718055994530942  /* log_e 2 */
 310 # define M_LN10         2.30258509299404568402  /* log_e 10 */
 311 # define M_PI           3.14159265358979323846  /* pi */
 312 # define M_PI_2         1.57079632679489661923  /* pi/2 */
 313 # define M_PI_4         0.78539816339744830962  /* pi/4 */
 314 # define M_1_PI         0.31830988618379067154  /* 1/pi */
 315 # define M_2_PI         0.63661977236758134308  /* 2/pi */
 316 # define M_2_SQRTPI     1.12837916709551257390  /* 2/sqrt(pi) */
 317 # define M_SQRT2        1.41421356237309504880  /* sqrt(2) */
 318 # define M_SQRT1_2      0.70710678118654752440  /* 1/sqrt(2) */
 319 #endif
 320
 321 /* The above constants are not adequate for computation using `long double's.
 322    Therefore we provide as an extension constants with similar names as a
 323    GNU extension.  Provide enough digits for the 128-bit IEEE quad.  */
 324 #ifdef __USE_GNU
 325 # define M_El           2.7182818284590452353602874713526625L  /* e */
 326 # define M_LOG2El       1.4426950408889634073599246810018922L  /* log_2 e */
 327 # define M_LOG10El      0.4342944819032518276511289189166051L  /* log_10 e */
 328 # define M_LN2l         0.6931471805599453094172321214581766L  /* log_e 2 */
 329 # define M_LN10l        2.3025850929940456840179914546843642L  /* log_e 10 */
 330 # define M_PIl          3.1415926535897932384626433832795029L  /* pi */
 331 # define M_PI_2l        1.5707963267948966192313216916397514L  /* pi/2 */
 332 # define M_PI_4l        0.7853981633974483096156608458198757L  /* pi/4 */
 333 # define M_1_PIl        0.3183098861837906715377675267450287L  /* 1/pi */
 334 # define M_2_PIl        0.6366197723675813430755350534900574L  /* 2/pi */
 335 # define M_2_SQRTPIl    1.1283791670955125738961589031215452L  /* 2/sqrt(pi) */
 336 # define M_SQRT2l       1.4142135623730950488016887242096981L  /* sqrt(2) */
 337 # define M_SQRT1_2l     0.7071067811865475244008443621048490L  /* 1/sqrt(2) */
 338 #endif
 339
 340
 341 /* When compiling in strict ISO C compatible mode we must not use the
 342    inline functions since they, among other things, do not set the
 343    `errno' variable correctly.  */
 344 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
 345 # define __NO_MATH_INLINES      1
 346 #endif
 347
 348 /* Get machine-dependent inline versions (if there are any).  */
 349 #ifdef __USE_EXTERN_INLINES
 350 # include <bits/mathinline.h>
 351 #endif
 352
 353
 354 #if __USE_ISOC99
 355 /* ISO C99 defines some macros to compare number while taking care
 356    for unordered numbers.  Since many FPUs provide special
 357    instructions to support these operations and these tests are
 358    defined in <bits/mathinline.h>, we define the generic macros at
 359    this late point and only if they are not defined yet.  */
 360
 361 /* Return nonzero value if X is greater than Y.  */
 362 # ifndef isgreater
 363 #  define isgreater(x, y) \
 364   (__extension__                                                              \
 365    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 366       !isunordered (__x, __y) && __x > __y; }))
 367 # endif
 368
 369 /* Return nonzero value if X is greater than or equal to Y.  */
 370 # ifndef isgreaterequal
 371 #  define isgreaterequal(x, y) \
 372   (__extension__                                                              \
 373    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 374       !isunordered (__x, __y) && __x >= __y; }))
 375 # endif
 376
 377 /* Return nonzero value if X is less than Y.  */
 378 # ifndef isless
 379 #  define isless(x, y) \
 380   (__extension__                                                              \
 381    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 382       !isunordered (__x, __y) && __x < __y; }))
 383 # endif
 384
 385 /* Return nonzero value if X is less than or equal to Y.  */
 386 # ifndef islessequal
 387 #  define islessequal(x, y) \
 388   (__extension__                                                              \
 389    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 390       !isunordered (__x, __y) && __x <= __y; }))
 391 # endif
 392
 393 /* Return nonzero value if either X is less than Y or Y is less than X.  */
 394 # ifndef islessgreater
 395 #  define islessgreater(x, y) \
 396   (__extension__                                                              \
 397    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 398       !isunordered (__x, __y) && (__x < __y || __y < __x); }))
 399 # endif
 400
 401 /* Return nonzero value if arguments are unordered.  */
 402 # ifndef isunordered
 403 #  define isunordered(u, v) \
 404   (__extension__                                                              \
 405    ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v);                       \
 406       fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
 407 # endif
 408
 409 #endif
 410
 411 __END_DECLS
 412
 413
 414 #endif /* math.h  */