math/math.h

   1 /* Declarations for math functions.
   2    Copyright (C) 1991-1993, 1995-1999, 2001, 2002, 2004, 2006, 2009, 2011
   3    Free Software Foundation, Inc.
   4    This file is part of the GNU C Library.
   5
   6    The GNU C Library is free software; you can redistribute it and/or
   7    modify it under the terms of the GNU Lesser General Public
   8    License as published by the Free Software Foundation; either
   9    version 2.1 of the License, or (at your option) any later version.
  10
  11    The GNU C Library is distributed in the hope that it will be useful,
  12    but WITHOUT ANY WARRANTY; without even the implied warranty of
  13    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  14    Lesser General Public License for more details.
  15
  16    You should have received a copy of the GNU Lesser General Public
  17    License along with the GNU C Library; if not, write to the Free
  18    Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
  19    02111-1307 USA.  */
  20
  21 /*
  22  *      ISO C99 Standard: 7.12 Mathematics      <math.h>
  23  */
  24
  25 #ifndef _MATH_H
  26 #define _MATH_H 1
  27
  28 #include <features.h>
  29
  30 __BEGIN_DECLS
  31
  32 /* Get machine-dependent HUGE_VAL value (returned on overflow).
  33    On all IEEE754 machines, this is +Infinity.  */
  34 #include <bits/huge_val.h>
  35 #ifdef __USE_ISOC99
  36 # include <bits/huge_valf.h>
  37 # include <bits/huge_vall.h>
  38
  39 /* Get machine-dependent INFINITY value.  */
  40 # include <bits/inf.h>
  41
  42 /* Get machine-dependent NAN value (returned for some domain errors).  */
  43 # include <bits/nan.h>
  44 #endif /* __USE_ISOC99 */
  45
  46 /* Get general and ISO C99 specific information.  */
  47 #include <bits/mathdef.h>
  48
  49 /* The file <bits/mathcalls.h> contains the prototypes for all the
  50    actual math functions.  These macros are used for those prototypes,
  51    so we can easily declare each function as both `name' and `__name',
  52    and can declare the float versions `namef' and `__namef'.  */
  53
  54 #define __MATHCALL(function,suffix, args)       \
  55   __MATHDECL (_Mdouble_,function,suffix, args)
  56 #define __MATHDECL(type, function,suffix, args) \
  57   __MATHDECL_1(type, function,suffix, args); \
  58   __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
  59 #define __MATHCALLX(function,suffix, args, attrib)      \
  60   __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
  61 #define __MATHDECLX(type, function,suffix, args, attrib) \
  62   __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
  63   __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
  64 #define __MATHDECL_1(type, function,suffix, args) \
  65   extern type __MATH_PRECNAME(function,suffix) args __THROW
  66
  67 #define _Mdouble_               double
  68 #define __MATH_PRECNAME(name,r) __CONCAT(name,r)
  69 #define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
  70 #define _Mdouble_END_NAMESPACE   __END_NAMESPACE_STD
  71 #include <bits/mathcalls.h>
  72 #undef  _Mdouble_
  73 #undef _Mdouble_BEGIN_NAMESPACE
  74 #undef _Mdouble_END_NAMESPACE
  75 #undef  __MATH_PRECNAME
  76
  77 #if defined __USE_MISC || defined __USE_ISOC99
  78
  79
  80 /* Include the file of declarations again, this time using `float'
  81    instead of `double' and appending f to each function name.  */
  82
  83 # ifndef _Mfloat_
  84 #  define _Mfloat_              float
  85 # endif
  86 # define _Mdouble_              _Mfloat_
  87 # ifdef __STDC__
  88 #  define __MATH_PRECNAME(name,r) name##f##r
  89 # else
  90 #  define __MATH_PRECNAME(name,r) name/**/f/**/r
  91 # endif
  92 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
  93 # define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
  94 # include <bits/mathcalls.h>
  95 # undef _Mdouble_
  96 # undef _Mdouble_BEGIN_NAMESPACE
  97 # undef _Mdouble_END_NAMESPACE
  98 # undef __MATH_PRECNAME
  99
 100 # if (__STDC__ - 0 || __GNUC__ - 0) \
 101      && (!(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
 102          || defined __LDBL_COMPAT)
 103 #  ifdef __LDBL_COMPAT
 104
 105 #   ifdef __USE_ISOC99
 106 extern float __nldbl_nexttowardf (float __x, long double __y)
 107                                   __THROW __attribute__ ((__const__));
 108 #    ifdef __REDIRECT_NTH
 109 extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
 110                              __nldbl_nexttowardf)
 111      __attribute__ ((__const__));
 112 extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
 113                               nextafter) __attribute__ ((__const__));
 114 extern long double __REDIRECT_NTH (nexttowardl,
 115                                    (long double __x, long double __y),
 116                                    nextafter) __attribute__ ((__const__));
 117 #    endif
 118 #   endif
 119
 120 #   undef __MATHDECL_1
 121 #   define __MATHDECL_2(type, function,suffix, args, alias) \
 122   extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
 123                              args, alias)
 124 #   define __MATHDECL_1(type, function,suffix, args) \
 125   __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
 126 #  endif
 127
 128 /* Include the file of declarations again, this time using `long double'
 129    instead of `double' and appending l to each function name.  */
 130
 131 #  ifndef _Mlong_double_
 132 #   define _Mlong_double_       long double
 133 #  endif
 134 #  define _Mdouble_             _Mlong_double_
 135 #  ifdef __STDC__
 136 #   define __MATH_PRECNAME(name,r) name##l##r
 137 #  else
 138 #   define __MATH_PRECNAME(name,r) name/**/l/**/r
 139 #  endif
 140 #  define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
 141 #  define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
 142 #  define __MATH_DECLARE_LDOUBLE   1
 143 #  include <bits/mathcalls.h>
 144 #  undef _Mdouble_
 145 #  undef _Mdouble_BEGIN_NAMESPACE
 146 #  undef _Mdouble_END_NAMESPACE
 147 #  undef __MATH_PRECNAME
 148
 149 # endif /* __STDC__ || __GNUC__ */
 150
 151 #endif  /* Use misc or ISO C99.  */
 152 #undef  __MATHDECL_1
 153 #undef  __MATHDECL
 154 #undef  __MATHCALL
 155
 156
 157 #if defined __USE_MISC || defined __USE_XOPEN
 158 /* This variable is used by `gamma' and `lgamma'.  */
 159 extern int signgam;
 160 #endif
 161
 162
 163 /* ISO C99 defines some generic macros which work on any data type.  */
 164 #ifdef __USE_ISOC99
 165
 166 /* Get the architecture specific values describing the floating-point
 167    evaluation.  The following symbols will get defined:
 168
 169     float_t     floating-point type at least as wide as `float' used
 170                 to evaluate `float' expressions
 171     double_t    floating-point type at least as wide as `double' used
 172                 to evaluate `double' expressions
 173
 174     FLT_EVAL_METHOD
 175                 Defined to
 176                   0     if `float_t' is `float' and `double_t' is `double'
 177                   1     if `float_t' and `double_t' are `double'
 178                   2     if `float_t' and `double_t' are `long double'
 179                   else  `float_t' and `double_t' are unspecified
 180
 181     INFINITY    representation of the infinity value of type `float'
 182
 183     FP_FAST_FMA
 184     FP_FAST_FMAF
 185     FP_FAST_FMAL
 186                 If defined it indicates that the `fma' function
 187                 generally executes about as fast as a multiply and an add.
 188                 This macro is defined only iff the `fma' function is
 189                 implemented directly with a hardware multiply-add instructions.
 190
 191     FP_ILOGB0   Expands to a value returned by `ilogb (0.0)'.
 192     FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
 193
 194     DECIMAL_DIG Number of decimal digits supported by conversion between
 195                 decimal and all internal floating-point formats.
 196
 197 */
 198
 199 /* All floating-point numbers can be put in one of these categories.  */
 200 enum
 201   {
 202     FP_NAN,
 203 # define FP_NAN FP_NAN
 204     FP_INFINITE,
 205 # define FP_INFINITE FP_INFINITE
 206     FP_ZERO,
 207 # define FP_ZERO FP_ZERO
 208     FP_SUBNORMAL,
 209 # define FP_SUBNORMAL FP_SUBNORMAL
 210     FP_NORMAL
 211 # define FP_NORMAL FP_NORMAL
 212   };
 213
 214 /* Return number of classification appropriate for X.  */
 215 # ifdef __NO_LONG_DOUBLE_MATH
 216 #  define fpclassify(x) \
 217      (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
 218 # else
 219 #  define fpclassify(x) \
 220      (sizeof (x) == sizeof (float)                                            \
 221       ? __fpclassifyf (x)                                                     \
 222       : sizeof (x) == sizeof (double)                                         \
 223       ? __fpclassify (x) : __fpclassifyl (x))
 224 # endif
 225
 226 /* Return nonzero value if sign of X is negative.  */
 227 # ifdef __NO_LONG_DOUBLE_MATH
 228 #  define signbit(x) \
 229      (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
 230 # else
 231 #  define signbit(x) \
 232      (sizeof (x) == sizeof (float)                                            \
 233       ? __signbitf (x)                                                        \
 234       : sizeof (x) == sizeof (double)                                         \
 235       ? __signbit (x) : __signbitl (x))
 236 # endif
 237
 238 /* Return nonzero value if X is not +-Inf or NaN.  */
 239 # ifdef __NO_LONG_DOUBLE_MATH
 240 #  define isfinite(x) \
 241      (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
 242 # else
 243 #  define isfinite(x) \
 244      (sizeof (x) == sizeof (float)                                            \
 245       ? __finitef (x)                                                         \
 246       : sizeof (x) == sizeof (double)                                         \
 247       ? __finite (x) : __finitel (x))
 248 # endif
 249
 250 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
 251 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
 252
 253 /* Return nonzero value if X is a NaN.  We could use `fpclassify' but
 254    we already have this functions `__isnan' and it is faster.  */
 255 # ifdef __NO_LONG_DOUBLE_MATH
 256 #  define isnan(x) \
 257      (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
 258 # else
 259 #  define isnan(x) \
 260      (sizeof (x) == sizeof (float)                                            \
 261       ? __isnanf (x)                                                          \
 262       : sizeof (x) == sizeof (double)                                         \
 263       ? __isnan (x) : __isnanl (x))
 264 # endif
 265
 266 /* Return nonzero value if X is positive or negative infinity.  */
 267 # ifdef __NO_LONG_DOUBLE_MATH
 268 #  define isinf(x) \
 269      (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
 270 # else
 271 #  define isinf(x) \
 272      (sizeof (x) == sizeof (float)                                            \
 273       ? __isinff (x)                                                          \
 274       : sizeof (x) == sizeof (double)                                         \
 275       ? __isinf (x) : __isinfl (x))
 276 # endif
 277
 278 /* Bitmasks for the math_errhandling macro.  */
 279 # define MATH_ERRNO     1       /* errno set by math functions.  */
 280 # define MATH_ERREXCEPT 2       /* Exceptions raised by math functions.  */
 281
 282 /* By default all functions support both errno and exception handling.
 283    In gcc's fast math mode and if inline functions are defined this
 284    might not be true.  */
 285 # ifndef __FAST_MATH__
 286 #  define math_errhandling      (MATH_ERRNO | MATH_ERREXCEPT)
 287 # endif
 288
 289 #endif /* Use ISO C99.  */
 290
 291 #ifdef  __USE_MISC
 292 /* Support for various different standard error handling behaviors.  */
 293 typedef enum
 294 {
 295   _IEEE_ = -1,  /* According to IEEE 754/IEEE 854.  */
 296   _SVID_,       /* According to System V, release 4.  */
 297   _XOPEN_,      /* Nowadays also Unix98.  */
 298   _POSIX_,
 299   _ISOC_        /* Actually this is ISO C99.  */
 300 } _LIB_VERSION_TYPE;
 301
 302 /* This variable can be changed at run-time to any of the values above to
 303    affect floating point error handling behavior (it may also be necessary
 304    to change the hardware FPU exception settings).  */
 305 extern _LIB_VERSION_TYPE _LIB_VERSION;
 306 #endif
 307
 308
 309 #ifdef __USE_SVID
 310 /* In SVID error handling, `matherr' is called with this description
 311    of the exceptional condition.
 312
 313    We have a problem when using C++ since `exception' is a reserved
 314    name in C++.  */
 315 # ifdef __cplusplus
 316 struct __exception
 317 # else
 318 struct exception
 319 # endif
 320   {
 321     int type;
 322     char *name;
 323     double arg1;
 324     double arg2;
 325     double retval;
 326   };
 327
 328 # ifdef __cplusplus
 329 extern int matherr (struct __exception *__exc) throw ();
 330 # else
 331 extern int matherr (struct exception *__exc);
 332 # endif
 333
 334 # define X_TLOSS        1.41484755040568800000e+16
 335
 336 /* Types of exceptions in the `type' field.  */
 337 # define DOMAIN         1
 338 # define SING           2
 339 # define OVERFLOW       3
 340 # define UNDERFLOW      4
 341 # define TLOSS          5
 342 # define PLOSS          6
 343
 344 /* SVID mode specifies returning this large value instead of infinity.  */
 345 # define HUGE           3.40282347e+38F
 346
 347 #else   /* !SVID */
 348
 349 # ifdef __USE_XOPEN
 350 /* X/Open wants another strange constant.  */
 351 #  define MAXFLOAT      3.40282347e+38F
 352 # endif
 353
 354 #endif  /* SVID */
 355
 356
 357 /* Some useful constants.  */
 358 #if defined __USE_BSD || defined __USE_XOPEN
 359 # define M_E            2.7182818284590452354   /* e */
 360 # define M_LOG2E        1.4426950408889634074   /* log_2 e */
 361 # define M_LOG10E       0.43429448190325182765  /* log_10 e */
 362 # define M_LN2          0.69314718055994530942  /* log_e 2 */
 363 # define M_LN10         2.30258509299404568402  /* log_e 10 */
 364 # define M_PI           3.14159265358979323846  /* pi */
 365 # define M_PI_2         1.57079632679489661923  /* pi/2 */
 366 # define M_PI_4         0.78539816339744830962  /* pi/4 */
 367 # define M_1_PI         0.31830988618379067154  /* 1/pi */
 368 # define M_2_PI         0.63661977236758134308  /* 2/pi */
 369 # define M_2_SQRTPI     1.12837916709551257390  /* 2/sqrt(pi) */
 370 # define M_SQRT2        1.41421356237309504880  /* sqrt(2) */
 371 # define M_SQRT1_2      0.70710678118654752440  /* 1/sqrt(2) */
 372 #endif
 373
 374 /* The above constants are not adequate for computation using `long double's.
 375    Therefore we provide as an extension constants with similar names as a
 376    GNU extension.  Provide enough digits for the 128-bit IEEE quad.  */
 377 #ifdef __USE_GNU
 378 # define M_El           2.7182818284590452353602874713526625L  /* e */
 379 # define M_LOG2El       1.4426950408889634073599246810018921L  /* log_2 e */
 380 # define M_LOG10El      0.4342944819032518276511289189166051L  /* log_10 e */
 381 # define M_LN2l         0.6931471805599453094172321214581766L  /* log_e 2 */
 382 # define M_LN10l        2.3025850929940456840179914546843642L  /* log_e 10 */
 383 # define M_PIl          3.1415926535897932384626433832795029L  /* pi */
 384 # define M_PI_2l        1.5707963267948966192313216916397514L  /* pi/2 */
 385 # define M_PI_4l        0.7853981633974483096156608458198757L  /* pi/4 */
 386 # define M_1_PIl        0.3183098861837906715377675267450287L  /* 1/pi */
 387 # define M_2_PIl        0.6366197723675813430755350534900574L  /* 2/pi */
 388 # define M_2_SQRTPIl    1.1283791670955125738961589031215452L  /* 2/sqrt(pi) */
 389 # define M_SQRT2l       1.4142135623730950488016887242096981L  /* sqrt(2) */
 390 # define M_SQRT1_2l     0.7071067811865475244008443621048490L  /* 1/sqrt(2) */
 391 #endif
 392
 393
 394 /* When compiling in strict ISO C compatible mode we must not use the
 395    inline functions since they, among other things, do not set the
 396    `errno' variable correctly.  */
 397 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
 398 # define __NO_MATH_INLINES      1
 399 #endif
 400
 401 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
 402 /* ISO C99 defines some macros to compare number while taking care for
 403    unordered numbers.  Many FPUs provide special instructions to support
 404    these operations.  Generic support in GCC for these as builtins went
 405    in before 3.0.0, but not all cpus added their patterns.  We define
 406    versions that use the builtins here, and <bits/mathinline.h> will
 407    undef/redefine as appropriate for the specific GCC version in use.  */
 408 # define isgreater(x, y)        __builtin_isgreater(x, y)
 409 # define isgreaterequal(x, y)   __builtin_isgreaterequal(x, y)
 410 # define isless(x, y)           __builtin_isless(x, y)
 411 # define islessequal(x, y)      __builtin_islessequal(x, y)
 412 # define islessgreater(x, y)    __builtin_islessgreater(x, y)
 413 # define isunordered(u, v)      __builtin_isunordered(u, v)
 414 #endif
 415
 416 /* Get machine-dependent inline versions (if there are any).  */
 417 #ifdef __USE_EXTERN_INLINES
 418 # include <bits/mathinline.h>
 419 #endif
 420
 421 /* Define special entry points to use when the compiler got told to
 422    only expect finite results.  */
 423 #if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0
 424 # include <bits/math-finite.h>
 425 #endif
 426
 427 #ifdef __USE_ISOC99
 428 /* If we've still got undefined comparison macros, provide defaults.  */
 429
 430 /* Return nonzero value if X is greater than Y.  */
 431 # ifndef isgreater
 432 #  define isgreater(x, y) \
 433   (__extension__                                                              \
 434    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 435       !isunordered (__x, __y) && __x > __y; }))
 436 # endif
 437
 438 /* Return nonzero value if X is greater than or equal to Y.  */
 439 # ifndef isgreaterequal
 440 #  define isgreaterequal(x, y) \
 441   (__extension__                                                              \
 442    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 443       !isunordered (__x, __y) && __x >= __y; }))
 444 # endif
 445
 446 /* Return nonzero value if X is less than Y.  */
 447 # ifndef isless
 448 #  define isless(x, y) \
 449   (__extension__                                                              \
 450    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 451       !isunordered (__x, __y) && __x < __y; }))
 452 # endif
 453
 454 /* Return nonzero value if X is less than or equal to Y.  */
 455 # ifndef islessequal
 456 #  define islessequal(x, y) \
 457   (__extension__                                                              \
 458    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 459       !isunordered (__x, __y) && __x <= __y; }))
 460 # endif
 461
 462 /* Return nonzero value if either X is less than Y or Y is less than X.  */
 463 # ifndef islessgreater
 464 #  define islessgreater(x, y) \
 465   (__extension__                                                              \
 466    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 467       !isunordered (__x, __y) && (__x < __y || __y < __x); }))
 468 # endif
 469
 470 /* Return nonzero value if arguments are unordered.  */
 471 # ifndef isunordered
 472 #  define isunordered(u, v) \
 473   (__extension__                                                              \
 474    ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v);                       \
 475       fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
 476 # endif
 477
 478 #endif
 479
 480 __END_DECLS
 481
 482
 483 #endif /* math.h  */