include/math.h

   1 /* Declarations for math functions.
   2    Copyright (C) 1991-1993, 1995-1999, 2001, 2002, 2004, 2006
   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
  50 /* The file <bits/mathcalls.h> contains the prototypes for all the
  51    actual math functions.  These macros are used for those prototypes,
  52    so we can easily declare each function as both `name' and `__name',
  53    and can declare the float versions `namef' and `__namef'.  */
  54
  55 #define __MATHDECL_1(type,function,suffix,args) \
  56   extern type __MATH_PRECNAME(function,suffix) args __THROW
  57
  58 #define __MATHDECL(type,function,suffix,args) \
  59   __MATHDECL_1(type,function,suffix,args);
  60
  61 #define __MATHCALL(function,suffix,args)        \
  62   __MATHDECL(_Mdouble_,function,suffix,args)
  63
  64 #define __MATHDECLX(type,function,suffix,args,attrib) \
  65   __MATHDECL_1(type,function,suffix,args) __attribute__ (attrib); \
  66   __MATH_maybe_libm_hidden_proto(function)
  67
  68 #define __MATHCALLX(function,suffix,args,attrib)        \
  69   __MATHDECLX(_Mdouble_,function,suffix,args,attrib)
  70
  71 /* Decls which are also used internally in libm.
  72    Only the main variant is used internally, no need to try to avoid relocs
  73    for the {l,f} variants.  */
  74 #define __MATHDECLI(type,function,suffix,args) \
  75   __MATHDECL_1(type,function,suffix,args); \
  76   __MATH_maybe_libm_hidden_proto(function)
  77
  78 #define __MATHCALLI(function,suffix,args)       \
  79   __MATHDECLI(_Mdouble_,function,suffix,args)
  80
  81 /* Private helpers for purely macro impls below.
  82    Only make __foo{,f,l} visible but not (the macro-only) foo.  */
  83 #if defined _LIBC
  84 # define __MATHDECL_PRIV(type,function,suffix,args,attrib) \
  85   __MATHDECL_1(type,__CONCAT(__,function),suffix,args) __attribute__ (attrib); \
  86   libm_hidden_proto(__MATH_PRECNAME(__##function,suffix))
  87 #else
  88 # define __MATHDECL_PRIV(type,function,suffix,args,attrib) \
  89   __MATHDECL_1(type,__CONCAT(__,function),suffix,args) __attribute__ (attrib);
  90 #endif
  91
  92
  93 /* Include the file of declarations, declaring double versions */
  94
  95 #if defined _LIBC
  96 # define __MATH_maybe_libm_hidden_proto(x) libm_hidden_proto(x)
  97 #else
  98 # define __MATH_maybe_libm_hidden_proto(x)
  99 #endif
 100 #define _Mdouble_                double
 101 #define __MATH_PRECNAME(name,r)  __CONCAT(name,r)
 102 #define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
 103 #define _Mdouble_END_NAMESPACE   __END_NAMESPACE_STD
 104 #include <bits/mathcalls.h>
 105 #undef  _Mdouble_
 106 #undef _Mdouble_BEGIN_NAMESPACE
 107 #undef _Mdouble_END_NAMESPACE
 108 #undef __MATH_PRECNAME
 109 #undef __MATH_maybe_libm_hidden_proto
 110
 111
 112 #if defined __USE_MISC || defined __USE_ISOC99
 113
 114 /* Include the file of declarations again, this time using `float'
 115    instead of `double' and appending f to each function name.  */
 116
 117 # define __MATH_maybe_libm_hidden_proto(x)
 118 # ifndef _Mfloat_
 119 #  define _Mfloat_              float
 120 # endif
 121 # define _Mdouble_              _Mfloat_
 122 # ifdef __STDC__
 123 #  define __MATH_PRECNAME(name,r) name##f##r
 124 # else
 125 #  define __MATH_PRECNAME(name,r) name/**/f/**/r
 126 # endif
 127 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
 128 # define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
 129 # include <bits/mathcalls.h>
 130 # undef _Mdouble_
 131 # undef _Mdouble_BEGIN_NAMESPACE
 132 # undef _Mdouble_END_NAMESPACE
 133 # undef __MATH_PRECNAME
 134 # undef __MATH_maybe_libm_hidden_proto
 135
 136
 137 # if (defined __STDC__ || defined __GNUC__) \
 138      && (!defined __NO_LONG_DOUBLE_MATH || defined __LDBL_COMPAT)
 139 #  ifdef __LDBL_COMPAT
 140
 141 #   ifdef __USE_ISOC99
 142 extern float __nldbl_nexttowardf (float __x, long double __y)
 143                                   __THROW __attribute__ ((__const__));
 144 #    ifdef __REDIRECT_NTH
 145 extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
 146                              __nldbl_nexttowardf)
 147      __attribute__ ((__const__));
 148 extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
 149                               nextafter) __attribute__ ((__const__));
 150 extern long double __REDIRECT_NTH (nexttowardl,
 151                                    (long double __x, long double __y),
 152                                    nextafter) __attribute__ ((__const__));
 153 #    endif
 154 #   endif
 155
 156 /* Include the file of declarations again, this time using `long double'
 157    instead of `double' and appending l to each function name.  */
 158
 159 #   undef __MATHDECL_1
 160 #   define __MATHDECL_2(type,function,suffix,args,alias) \
 161   extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix),args,alias)
 162 #   define __MATHDECL_1(type,function,suffix,args) \
 163   __MATHDECL_2(type,function,suffix,args,__CONCAT(function,suffix))
 164 #  endif
 165
 166 #  define __MATH_maybe_libm_hidden_proto(x)
 167 #  ifndef _Mlong_double_
 168 #   define _Mlong_double_       long double
 169 #  endif
 170 #  define _Mdouble_             _Mlong_double_
 171 #  ifdef __STDC__
 172 #   define __MATH_PRECNAME(name,r) name##l##r
 173 #  else
 174 #   define __MATH_PRECNAME(name,r) name/**/l/**/r
 175 #  endif
 176 #  define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
 177 #  define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
 178 #  include <bits/mathcalls.h>
 179 #  undef _Mdouble_
 180 #  undef _Mdouble_BEGIN_NAMESPACE
 181 #  undef _Mdouble_END_NAMESPACE
 182 #  undef __MATH_PRECNAME
 183 #  undef __MATH_maybe_libm_hidden_proto
 184
 185 # endif /* __STDC__ || __GNUC__ */
 186
 187 #endif  /* Use misc or ISO C99.  */
 188 #undef  __MATHDECL_1
 189 #undef  __MATHDECL
 190 #undef  __MATHCALL
 191
 192
 193 #if defined __USE_MISC || defined __USE_XOPEN
 194 /* This variable is used by `gamma' and `lgamma'.  */
 195 extern int signgam;
 196 #endif
 197
 198
 199 /* ISO C99 defines some generic macros which work on any data type.  */
 200 #ifdef __USE_ISOC99
 201
 202 /* Get the architecture specific values describing the floating-point
 203    evaluation.  The following symbols will get defined:
 204
 205     float_t     floating-point type at least as wide as `float' used
 206                 to evaluate `float' expressions
 207     double_t    floating-point type at least as wide as `double' used
 208                 to evaluate `double' expressions
 209
 210     FLT_EVAL_METHOD
 211                 Defined to
 212                   0     if `float_t' is `float' and `double_t' is `double'
 213                   1     if `float_t' and `double_t' are `double'
 214                   2     if `float_t' and `double_t' are `long double'
 215                   else  `float_t' and `double_t' are unspecified
 216
 217     INFINITY    representation of the infinity value of type `float'
 218
 219     FP_FAST_FMA
 220     FP_FAST_FMAF
 221     FP_FAST_FMAL
 222                 If defined it indicates that the `fma' function
 223                 generally executes about as fast as a multiply and an add.
 224                 This macro is defined only iff the `fma' function is
 225                 implemented directly with a hardware multiply-add instructions.
 226
 227     FP_ILOGB0   Expands to a value returned by `ilogb (0.0)'.
 228     FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
 229
 230     DECIMAL_DIG Number of decimal digits supported by conversion between
 231                 decimal and all internal floating-point formats.
 232
 233 */
 234
 235 /* All floating-point numbers can be put in one of these categories.  */
 236 enum
 237   {
 238     FP_NAN,
 239 # define FP_NAN FP_NAN
 240     FP_INFINITE,
 241 # define FP_INFINITE FP_INFINITE
 242     FP_ZERO,
 243 # define FP_ZERO FP_ZERO
 244     FP_SUBNORMAL,
 245 # define FP_SUBNORMAL FP_SUBNORMAL
 246     FP_NORMAL
 247 # define FP_NORMAL FP_NORMAL
 248   };
 249
 250 /* Return number of classification appropriate for X.  */
 251 # ifdef __NO_LONG_DOUBLE_MATH
 252 #  define fpclassify(x) \
 253      (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
 254 # else
 255 #  define fpclassify(x) \
 256      (sizeof (x) == sizeof (float)                                            \
 257       ? __fpclassifyf (x)                                                     \
 258       : sizeof (x) == sizeof (double)                                         \
 259       ? __fpclassify (x) : __fpclassifyl (x))
 260 # endif
 261
 262 /* Return nonzero value if sign of X is negative.  */
 263 # ifdef __NO_LONG_DOUBLE_MATH
 264 #  define signbit(x) \
 265      (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
 266 # else
 267 #  define signbit(x) \
 268      (sizeof (x) == sizeof (float)                                            \
 269       ? __signbitf (x)                                                        \
 270       : sizeof (x) == sizeof (double)                                         \
 271       ? __signbit (x) : __signbitl (x))
 272 # endif
 273
 274 /* Return nonzero value if X is not +-Inf or NaN.  */
 275 # ifdef __NO_LONG_DOUBLE_MATH
 276 #  define isfinite(x) \
 277      (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
 278 # else
 279 #  define isfinite(x) \
 280      (sizeof (x) == sizeof (float)                                            \
 281       ? __finitef (x)                                                         \
 282       : sizeof (x) == sizeof (double)                                         \
 283       ? __finite (x) : __finitel (x))
 284 # endif
 285
 286 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
 287 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
 288
 289 /* Return nonzero value if X is a NaN.  We could use `fpclassify' but
 290    we already have this functions `__isnan' and it is faster.  */
 291 # ifdef __NO_LONG_DOUBLE_MATH
 292 #  define isnan(x) \
 293      (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
 294 # else
 295 #  define isnan(x) \
 296      (sizeof (x) == sizeof (float)                                            \
 297       ? __isnanf (x)                                                          \
 298       : sizeof (x) == sizeof (double)                                         \
 299       ? __isnan (x) : __isnanl (x))
 300 # endif
 301
 302 /* Return nonzero value is X is positive or negative infinity.  */
 303 # ifdef __NO_LONG_DOUBLE_MATH
 304 #  define isinf(x) \
 305      (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
 306 # else
 307 #  define isinf(x) \
 308      (sizeof (x) == sizeof (float)                                            \
 309       ? __isinff (x)                                                          \
 310       : sizeof (x) == sizeof (double)                                         \
 311       ? __isinf (x) : __isinfl (x))
 312 # endif
 313
 314 /* Bitmasks for the math_errhandling macro.  */
 315 # define MATH_ERRNO     1       /* errno set by math functions.  */
 316 # define MATH_ERREXCEPT 2       /* Exceptions raised by math functions.  */
 317
 318 #endif /* Use ISO C99.  */
 319
 320 #ifdef  __USE_MISC
 321 /* Support for various different standard error handling behaviors.  */
 322 typedef enum
 323 {
 324   _IEEE_ = -1,  /* According to IEEE 754/IEEE 854.  */
 325   _SVID_,       /* According to System V, release 4.  */
 326   _XOPEN_,      /* Nowadays also Unix98.  */
 327   _POSIX_,
 328   _ISOC_        /* Actually this is ISO C99.  */
 329 } _LIB_VERSION_TYPE;
 330
 331 /* This variable can be changed at run-time to any of the values above to
 332    affect floating point error handling behavior (it may also be necessary
 333    to change the hardware FPU exception settings).  */
 334 extern _LIB_VERSION_TYPE _LIB_VERSION;
 335 #endif
 336
 337
 338 #ifdef __USE_SVID
 339 /* In SVID error handling, `matherr' is called with this description
 340    of the exceptional condition.
 341
 342    We have a problem when using C++ since `exception' is a reserved
 343    name in C++.  */
 344 # ifdef __cplusplus
 345 struct __exception
 346 # else
 347 struct exception
 348 # endif
 349   {
 350     int type;
 351     char *name;
 352     double arg1;
 353     double arg2;
 354     double retval;
 355   };
 356
 357 # ifdef __cplusplus
 358 extern int matherr (struct __exception *__exc) throw ();
 359 # else
 360 extern int matherr (struct exception *__exc);
 361 # endif
 362
 363 # define X_TLOSS        1.41484755040568800000e+16
 364
 365 /* Types of exceptions in the `type' field.  */
 366 # define DOMAIN         1
 367 # define SING           2
 368 # define OVERFLOW       3
 369 # define UNDERFLOW      4
 370 # define TLOSS          5
 371 # define PLOSS          6
 372
 373 /* SVID mode specifies returning this large value instead of infinity.  */
 374 # define HUGE           3.40282347e+38F
 375
 376 #else   /* !SVID */
 377
 378 # ifdef __USE_XOPEN
 379 #  ifdef __UCLIBC_SUSV4_LEGACY__
 380 /* X/Open wants another strange constant.  */
 381 #  define MAXFLOAT      3.40282347e+38F
 382 #  endif
 383 # endif
 384
 385 #endif  /* SVID */
 386
 387
 388 /* Some useful constants.  */
 389 #if defined __USE_BSD || defined __USE_XOPEN
 390 # define M_E            2.7182818284590452354   /* e */
 391 # define M_LOG2E        1.4426950408889634074   /* log_2 e */
 392 # define M_LOG10E       0.43429448190325182765  /* log_10 e */
 393 # define M_LN2          0.69314718055994530942  /* log_e 2 */
 394 # define M_LN10         2.30258509299404568402  /* log_e 10 */
 395 # define M_PI           3.14159265358979323846  /* pi */
 396 # define M_PI_2         1.57079632679489661923  /* pi/2 */
 397 # define M_PI_4         0.78539816339744830962  /* pi/4 */
 398 # define M_1_PI         0.31830988618379067154  /* 1/pi */
 399 # define M_2_PI         0.63661977236758134308  /* 2/pi */
 400 # define M_2_SQRTPI     1.12837916709551257390  /* 2/sqrt(pi) */
 401 # define M_SQRT2        1.41421356237309504880  /* sqrt(2) */
 402 # define M_SQRT1_2      0.70710678118654752440  /* 1/sqrt(2) */
 403 #endif
 404
 405 /* The above constants are not adequate for computation using `long double's.
 406    Therefore we provide as an extension constants with similar names as a
 407    GNU extension.  Provide enough digits for the 128-bit IEEE quad.  */
 408 #ifdef __USE_GNU
 409 # define M_El           2.7182818284590452353602874713526625L  /* e */
 410 # define M_LOG2El       1.4426950408889634073599246810018921L  /* log_2 e */
 411 # define M_LOG10El      0.4342944819032518276511289189166051L  /* log_10 e */
 412 # define M_LN2l         0.6931471805599453094172321214581766L  /* log_e 2 */
 413 # define M_LN10l        2.3025850929940456840179914546843642L  /* log_e 10 */
 414 # define M_PIl          3.1415926535897932384626433832795029L  /* pi */
 415 # define M_PI_2l        1.5707963267948966192313216916397514L  /* pi/2 */
 416 # define M_PI_4l        0.7853981633974483096156608458198757L  /* pi/4 */
 417 # define M_1_PIl        0.3183098861837906715377675267450287L  /* 1/pi */
 418 # define M_2_PIl        0.6366197723675813430755350534900574L  /* 2/pi */
 419 # define M_2_SQRTPIl    1.1283791670955125738961589031215452L  /* 2/sqrt(pi) */
 420 # define M_SQRT2l       1.4142135623730950488016887242096981L  /* sqrt(2) */
 421 # define M_SQRT1_2l     0.7071067811865475244008443621048490L  /* 1/sqrt(2) */
 422 #endif
 423
 424
 425 /* When compiling in strict ISO C compatible mode we must not use the
 426    inline functions since they, among other things, do not set the
 427    `errno' variable correctly.  */
 428 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
 429 # define __NO_MATH_INLINES      1
 430 #endif
 431
 432 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
 433 /* ISO C99 defines some macros to compare number while taking care for
 434    unordered numbers.  Many FPUs provide special instructions to support
 435    these operations.  Generic support in GCC for these as builtins went
 436    in before 3.0.0, but not all cpus added their patterns.  We define
 437    versions that use the builtins here, and <bits/mathinline.h> will
 438    undef/redefine as appropriate for the specific GCC version in use.  */
 439 # define isgreater(x, y)        __builtin_isgreater(x, y)
 440 # define isgreaterequal(x, y)   __builtin_isgreaterequal(x, y)
 441 # define isless(x, y)           __builtin_isless(x, y)
 442 # define islessequal(x, y)      __builtin_islessequal(x, y)
 443 # define islessgreater(x, y)    __builtin_islessgreater(x, y)
 444 # define isunordered(u, v)      __builtin_isunordered(u, v)
 445 #endif
 446
 447 /* Get machine-dependent inline versions (if there are any).  */
 448 #ifdef __USE_EXTERN_INLINES
 449 # include <bits/mathinline.h>
 450 #endif
 451
 452 #ifdef __USE_ISOC99
 453 /* If we've still got undefined comparison macros, provide defaults.  */
 454
 455 /* Return nonzero value if X is greater than Y.  */
 456 # ifndef isgreater
 457 #  define isgreater(x, y) \
 458   (__extension__                                                              \
 459    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 460       !isunordered (__x, __y) && __x > __y; }))
 461 # endif
 462
 463 /* Return nonzero value if X is greater than or equal to Y.  */
 464 # ifndef isgreaterequal
 465 #  define isgreaterequal(x, y) \
 466   (__extension__                                                              \
 467    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 468       !isunordered (__x, __y) && __x >= __y; }))
 469 # endif
 470
 471 /* Return nonzero value if X is less than Y.  */
 472 # ifndef isless
 473 #  define isless(x, y) \
 474   (__extension__                                                              \
 475    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 476       !isunordered (__x, __y) && __x < __y; }))
 477 # endif
 478
 479 /* Return nonzero value if X is less than or equal to Y.  */
 480 # ifndef islessequal
 481 #  define islessequal(x, y) \
 482   (__extension__                                                              \
 483    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 484       !isunordered (__x, __y) && __x <= __y; }))
 485 # endif
 486
 487 /* Return nonzero value if either X is less than Y or Y is less than X.  */
 488 # ifndef islessgreater
 489 #  define islessgreater(x, y) \
 490   (__extension__                                                              \
 491    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 492       !isunordered (__x, __y) && (__x < __y || __y < __x); }))
 493 # endif
 494
 495 /* Return nonzero value if arguments are unordered.  */
 496 # ifndef isunordered
 497 #  define isunordered(u, v) \
 498   (__extension__                                                              \
 499    ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v);                       \
 500       fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
 501 # endif
 502
 503 #endif
 504
 505 __END_DECLS
 506
 507
 508 #endif /* math.h  */