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, see
  18    <http://www.gnu.org/licenses/>.  */
  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 #ifdef __USE_ISOC99
  35 # include <bits/huge_valf.h>
  36 # include <bits/huge_vall.h>
  37
  38 /* Get machine-dependent INFINITY value.  */
  39 # include <bits/inf.h>
  40
  41 /* Get machine-dependent NAN value (returned for some domain errors).  */
  42 # include <bits/nan.h>
  43 #endif /* __USE_ISOC99 */
  44
  45 /* Get general and ISO C99 specific information.  */
  46 #include <bits/mathdef.h>
  47
  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 __MATHDECL_1(type,function,suffix,args) \
  55         extern type __MATH_PRECNAME(function,suffix) args __THROW
  56
  57 #define __MATHDECL(type,function,suffix,args) \
  58         __MATHDECL_1(type,function,suffix,args);
  59
  60 #define __MATHCALL(function,suffix,args) \
  61         __MATHDECL(_Mdouble_,function,suffix,args)
  62
  63 #define __MATHDECLX(type,function,suffix,args,attrib) \
  64         __MATHDECL_1(type,function,suffix,args) __attribute__ (attrib); \
  65         __MATH_maybe_libm_hidden_proto(function)
  66
  67 #define __MATHCALLX(function,suffix,args,attrib) \
  68         __MATHDECLX(_Mdouble_,function,suffix,args,attrib)
  69
  70 /* Decls which are also used internally in libm.
  71    Only the main variant is used internally, no need to try to avoid relocs
  72    for the {l,f} variants.  */
  73 #define __MATHDECLI(type,function,suffix,args) \
  74         __MATHDECL_1(type,function,suffix,args); \
  75         __MATH_maybe_libm_hidden_proto(function)
  76
  77 #define __MATHCALLI(function,suffix,args) \
  78         __MATHDECLI(_Mdouble_,function,suffix,args)
  79
  80 /* Private helpers for purely macro impls below.
  81    Only make __foo{,f,l} visible but not (the macro-only) foo.  */
  82 #if defined _LIBC
  83 # define __MATHDECL_PRIV(type,function,suffix,args,attrib) \
  84         __MATHDECL_1(type,__CONCAT(__,function),suffix,args) __attribute__ (attrib); \
  85         libm_hidden_proto(__MATH_PRECNAME(__##function,suffix))
  86 #else
  87 # define __MATHDECL_PRIV(type,function,suffix,args,attrib) \
  88         __MATHDECL_1(type,__CONCAT(__,function),suffix,args) __attribute__ (attrib);
  89 #endif
  90
  91
  92 /* Include the file of declarations, declaring double versions */
  93
  94 #if defined _LIBC
  95 # define __MATH_maybe_libm_hidden_proto(x) libm_hidden_proto(x)
  96 #else
  97 # define __MATH_maybe_libm_hidden_proto(x)
  98 #endif
  99 #define _Mdouble_                double
 100 #define __MATH_PRECNAME(name,r)  __CONCAT(name,r)
 101 #define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
 102 #define _Mdouble_END_NAMESPACE   __END_NAMESPACE_STD
 103 #include <bits/mathcalls.h>
 104 #undef  _Mdouble_
 105 #undef _Mdouble_BEGIN_NAMESPACE
 106 #undef _Mdouble_END_NAMESPACE
 107 #undef __MATH_PRECNAME
 108 #undef __MATH_maybe_libm_hidden_proto
 109
 110
 111 #if defined __USE_MISC || defined __USE_ISOC99
 112
 113 /* Include the file of declarations again, this time using `float'
 114    instead of `double' and appending f to each function name.  */
 115
 116 # define __MATH_maybe_libm_hidden_proto(x)
 117 # ifndef _Mfloat_
 118 #  define _Mfloat_              float
 119 # endif
 120 # define _Mdouble_              _Mfloat_
 121 # ifdef __STDC__
 122 #  define __MATH_PRECNAME(name,r) name##f##r
 123 # else
 124 #  define __MATH_PRECNAME(name,r) name/**/f/**/r
 125 # endif
 126 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
 127 # define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
 128 # include <bits/mathcalls.h>
 129 # undef _Mdouble_
 130 # undef _Mdouble_BEGIN_NAMESPACE
 131 # undef _Mdouble_END_NAMESPACE
 132 # undef _Mfloat_
 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 _Mlong_double_
 181 #  undef __MATH_PRECNAME
 182 #  undef __MATH_maybe_libm_hidden_proto
 183
 184 # endif /* __STDC__ || __GNUC__ */
 185
 186 #endif  /* Use misc or ISO C99.  */
 187 #undef  __MATHDECL_1
 188 #undef  __MATHDECL
 189 #undef  __MATHCALL
 190
 191
 192 #if defined __USE_MISC || defined __USE_XOPEN
 193 /* This variable is used by `gamma' and `lgamma'.  */
 194 extern int signgam;
 195 #else
 196 /* This is used when standart of libm
 197  * should prevent lgamma(x) of modifying signgam variable.
 198  */
 199 # define lgammaf(arg) \
 200 ({ \
 201 int local_signgam = 0; \
 202 float result = lgammaf_r((float)arg, &local_signgam); \
 203 result; \
 204 })
 205
 206 # define lgamma(arg) \
 207 ({ \
 208 int local_signgam = 0; \
 209 double result = lgamma_r(arg, &local_signgam); \
 210 result; \
 211 })
 212
 213 # define lgammal(arg) \
 214 ({ \
 215 int local_signgam = 0; \
 216 long double result = lgammal_r(arg, &local_signgam); \
 217 result; \
 218 })
 219 #endif
 220
 221
 222 /* ISO C99 defines some generic macros which work on any data type.  */
 223 #if defined(__USE_ISOC99) || defined(__USE_BSD)
 224
 225 /* Get the architecture specific values describing the floating-point
 226    evaluation.  The following symbols will get defined:
 227
 228     float_t     floating-point type at least as wide as `float' used
 229                 to evaluate `float' expressions
 230     double_t    floating-point type at least as wide as `double' used
 231                 to evaluate `double' expressions
 232
 233     FLT_EVAL_METHOD
 234                 Defined to
 235                   0     if `float_t' is `float' and `double_t' is `double'
 236                   1     if `float_t' and `double_t' are `double'
 237                   2     if `float_t' and `double_t' are `long double'
 238                   else  `float_t' and `double_t' are unspecified
 239
 240     INFINITY    representation of the infinity value of type `float'
 241
 242     FP_FAST_FMA
 243     FP_FAST_FMAF
 244     FP_FAST_FMAL
 245                 If defined it indicates that the `fma' function
 246                 generally executes about as fast as a multiply and an add.
 247                 This macro is defined only iff the `fma' function is
 248                 implemented directly with a hardware multiply-add instructions.
 249
 250     FP_ILOGB0   Expands to a value returned by `ilogb (0.0)'.
 251     FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
 252
 253     DECIMAL_DIG Number of decimal digits supported by conversion between
 254                 decimal and all internal floating-point formats.
 255
 256 */
 257
 258 /* All floating-point numbers can be put in one of these categories.  */
 259 enum
 260   {
 261     FP_NAN,
 262 # define FP_NAN FP_NAN
 263     FP_INFINITE,
 264 # define FP_INFINITE FP_INFINITE
 265     FP_ZERO,
 266 # define FP_ZERO FP_ZERO
 267     FP_SUBNORMAL,
 268 # define FP_SUBNORMAL FP_SUBNORMAL
 269     FP_NORMAL
 270 # define FP_NORMAL FP_NORMAL
 271   };
 272
 273 /* Return number of classification appropriate for X.  */
 274 # ifdef __NO_LONG_DOUBLE_MATH
 275 #  define fpclassify(x) \
 276      (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
 277 # else
 278 #  define fpclassify(x) \
 279      (sizeof (x) == sizeof (float)                                            \
 280       ? __fpclassifyf (x)                                                     \
 281       : sizeof (x) == sizeof (double)                                         \
 282       ? __fpclassify (x) : __fpclassifyl (x))
 283 # endif
 284
 285 /* Return nonzero value if sign of X is negative.  */
 286 # ifdef __NO_LONG_DOUBLE_MATH
 287 #  define signbit(x) \
 288      (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
 289 # else
 290 #  define signbit(x) \
 291      (sizeof (x) == sizeof (float)                                            \
 292       ? __signbitf (x)                                                        \
 293       : sizeof (x) == sizeof (double)                                         \
 294       ? __signbit (x) : __signbitl (x))
 295 # endif
 296
 297 /* Return nonzero value if X is not +-Inf or NaN.  */
 298 # ifdef __NO_LONG_DOUBLE_MATH
 299 #  define isfinite(x) \
 300      (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
 301 # else
 302 #  define isfinite(x) \
 303      (sizeof (x) == sizeof (float)                                            \
 304       ? __finitef (x)                                                         \
 305       : sizeof (x) == sizeof (double)                                         \
 306       ? __finite (x) : __finitel (x))
 307 # endif
 308
 309 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
 310 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
 311
 312 /* Return nonzero value if X is a NaN.  We could use `fpclassify' but
 313    we already have this functions `__isnan' and it is faster.  */
 314 # ifdef __NO_LONG_DOUBLE_MATH
 315 #  define isnan(x) \
 316      (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
 317 # else
 318 #  define isnan(x) \
 319      (sizeof (x) == sizeof (float)                                            \
 320       ? __isnanf (x)                                                          \
 321       : sizeof (x) == sizeof (double)                                         \
 322       ? __isnan (x) : __isnanl (x))
 323 # endif
 324
 325 /* Return nonzero value is X is positive or negative infinity.  */
 326 # ifdef __NO_LONG_DOUBLE_MATH
 327 #  define isinf(x) \
 328      (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
 329 # else
 330 #  define isinf(x) \
 331      (sizeof (x) == sizeof (float)                                            \
 332       ? __isinff (x)                                                          \
 333       : sizeof (x) == sizeof (double)                                         \
 334       ? __isinf (x) : __isinfl (x))
 335 # endif
 336
 337 /* Bitmasks for the math_errhandling macro.  */
 338 # define MATH_ERRNO     1       /* errno set by math functions.  */
 339 # define MATH_ERREXCEPT 2       /* Exceptions raised by math functions.  */
 340
 341 #endif /* Use ISO C99.  */
 342
 343 /* BSD compat */
 344 #define finite(x) __finite(x)
 345 #define finitef(x) __finitef(x)
 346 #define finitel(x) __finitel(x)
 347
 348 #ifdef  __USE_MISC
 349 /* Support for various different standard error handling behaviors.  */
 350 typedef enum
 351 {
 352   _IEEE_ = -1,  /* According to IEEE 754/IEEE 854.  */
 353   _SVID_,       /* According to System V, release 4.  */
 354   _XOPEN_,      /* Nowadays also Unix98.  */
 355   _POSIX_,
 356   _ISOC_        /* Actually this is ISO C99.  */
 357 } _LIB_VERSION_TYPE;
 358
 359 /* This variable can be changed at run-time to any of the values above to
 360    affect floating point error handling behavior (it may also be necessary
 361    to change the hardware FPU exception settings).  */
 362 extern _LIB_VERSION_TYPE _LIB_VERSION;
 363 #endif
 364
 365
 366 #ifdef __USE_SVID
 367 /* In SVID error handling, `matherr' is called with this description
 368    of the exceptional condition.
 369
 370    We have a problem when using C++ since `exception' is a reserved
 371    name in C++.  */
 372 # ifdef __cplusplus
 373 struct __exception
 374 # else
 375 struct exception
 376 # endif
 377   {
 378     int type;
 379     char *name;
 380     double arg1;
 381     double arg2;
 382     double retval;
 383   };
 384
 385 # ifdef __cplusplus
 386 extern int matherr (struct __exception *__exc) throw ();
 387 # else
 388 extern int __attribute__ ((weak)) matherr (struct exception *__exc);
 389 # endif
 390
 391 # define X_TLOSS        1.41484755040568800000e+16
 392
 393 /* Types of exceptions in the `type' field.  */
 394 # define DOMAIN         1
 395 # define SING           2
 396 # define OVERFLOW       3
 397 # define UNDERFLOW      4
 398 # define TLOSS          5
 399 # define PLOSS          6
 400
 401 /* SVID mode specifies returning this large value instead of infinity.  */
 402 # define HUGE           3.40282347e+38F
 403
 404 #else   /* !SVID */
 405
 406 # ifdef __USE_XOPEN
 407 #  ifdef __UCLIBC_SUSV4_LEGACY__
 408 /* X/Open wants another strange constant.  */
 409 #  define MAXFLOAT      3.40282347e+38F
 410 #  endif
 411 # endif
 412
 413 #endif  /* SVID */
 414
 415
 416 /* Some useful constants.  */
 417 #if defined __USE_BSD || defined __USE_XOPEN
 418 # define M_E            2.7182818284590452354   /* e */
 419 # define M_LOG2E        1.4426950408889634074   /* log_2 e */
 420 # define M_LOG10E       0.43429448190325182765  /* log_10 e */
 421 # define M_LN2          0.69314718055994530942  /* log_e 2 */
 422 # define M_LN10         2.30258509299404568402  /* log_e 10 */
 423 # define M_PI           3.14159265358979323846  /* pi */
 424 # define M_PI_2         1.57079632679489661923  /* pi/2 */
 425 # define M_PI_4         0.78539816339744830962  /* pi/4 */
 426 # define M_1_PI         0.31830988618379067154  /* 1/pi */
 427 # define M_2_PI         0.63661977236758134308  /* 2/pi */
 428 # define M_2_SQRTPI     1.12837916709551257390  /* 2/sqrt(pi) */
 429 # define M_SQRT2        1.41421356237309504880  /* sqrt(2) */
 430 # define M_SQRT1_2      0.70710678118654752440  /* 1/sqrt(2) */
 431 #endif
 432
 433 /* The above constants are not adequate for computation using `long double's.
 434    Therefore we provide as an extension constants with similar names as a
 435    GNU extension.  Provide enough digits for the 128-bit IEEE quad.  */
 436 #ifdef __USE_GNU
 437 # define M_El           2.7182818284590452353602874713526625L  /* e */
 438 # define M_LOG2El       1.4426950408889634073599246810018921L  /* log_2 e */
 439 # define M_LOG10El      0.4342944819032518276511289189166051L  /* log_10 e */
 440 # define M_LN2l         0.6931471805599453094172321214581766L  /* log_e 2 */
 441 # define M_LN10l        2.3025850929940456840179914546843642L  /* log_e 10 */
 442 # define M_PIl          3.1415926535897932384626433832795029L  /* pi */
 443 # define M_PI_2l        1.5707963267948966192313216916397514L  /* pi/2 */
 444 # define M_PI_4l        0.7853981633974483096156608458198757L  /* pi/4 */
 445 # define M_1_PIl        0.3183098861837906715377675267450287L  /* 1/pi */
 446 # define M_2_PIl        0.6366197723675813430755350534900574L  /* 2/pi */
 447 # define M_2_SQRTPIl    1.1283791670955125738961589031215452L  /* 2/sqrt(pi) */
 448 # define M_SQRT2l       1.4142135623730950488016887242096981L  /* sqrt(2) */
 449 # define M_SQRT1_2l     0.7071067811865475244008443621048490L  /* 1/sqrt(2) */
 450 #endif
 451
 452
 453 /* When compiling in strict ISO C compatible mode we must not use the
 454    inline functions since they, among other things, do not set the
 455    `errno' variable correctly.  */
 456 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
 457 # define __NO_MATH_INLINES      1
 458 #endif
 459
 460 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
 461 /* ISO C99 defines some macros to compare number while taking care for
 462    unordered numbers.  Many FPUs provide special instructions to support
 463    these operations.  Generic support in GCC for these as builtins went
 464    in before 3.0.0, but not all cpus added their patterns.  We define
 465    versions that use the builtins here, and <bits/mathinline.h> will
 466    undef/redefine as appropriate for the specific GCC version in use.  */
 467 # define isgreater(x, y)        __builtin_isgreater(x, y)
 468 # define isgreaterequal(x, y)   __builtin_isgreaterequal(x, y)
 469 # define isless(x, y)           __builtin_isless(x, y)
 470 # define islessequal(x, y)      __builtin_islessequal(x, y)
 471 # define islessgreater(x, y)    __builtin_islessgreater(x, y)
 472 # define isunordered(u, v)      __builtin_isunordered(u, v)
 473 #endif
 474
 475 /* Get machine-dependent inline versions (if there are any).  */
 476 #ifdef __USE_EXTERN_INLINES
 477 # include <bits/mathinline.h>
 478 #endif
 479
 480 #ifdef __USE_ISOC99
 481 /* If we've still got undefined comparison macros, provide defaults.  */
 482
 483 /* Return nonzero value if X is greater than Y.  */
 484 # ifndef isgreater
 485 #  define isgreater(x, y) \
 486   (__extension__                                                              \
 487    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 488       !isunordered (__x, __y) && __x > __y; }))
 489 # endif
 490
 491 /* Return nonzero value if X is greater than or equal to Y.  */
 492 # ifndef isgreaterequal
 493 #  define isgreaterequal(x, y) \
 494   (__extension__                                                              \
 495    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 496       !isunordered (__x, __y) && __x >= __y; }))
 497 # endif
 498
 499 /* Return nonzero value if X is less than Y.  */
 500 # ifndef isless
 501 #  define isless(x, y) \
 502   (__extension__                                                              \
 503    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 504       !isunordered (__x, __y) && __x < __y; }))
 505 # endif
 506
 507 /* Return nonzero value if X is less than or equal to Y.  */
 508 # ifndef islessequal
 509 #  define islessequal(x, y) \
 510   (__extension__                                                              \
 511    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 512       !isunordered (__x, __y) && __x <= __y; }))
 513 # endif
 514
 515 /* Return nonzero value if either X is less than Y or Y is less than X.  */
 516 # ifndef islessgreater
 517 #  define islessgreater(x, y) \
 518   (__extension__                                                              \
 519    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 520       !isunordered (__x, __y) && (__x < __y || __y < __x); }))
 521 # endif
 522
 523 /* Return nonzero value if arguments are unordered.  */
 524 # ifndef isunordered
 525 #  define isunordered(u, v) \
 526   (__extension__                                                              \
 527    ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v);                       \
 528       fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
 529 # endif
 530
 531 #endif
 532
 533 __END_DECLS
 534
 535
 536 #endif /* math.h  */