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