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 libm_hidden_proto(signgam)
 197 #endif
 198
 199
 200 /* ISO C99 defines some generic macros which work on any data type.  */
 201 #ifdef __USE_ISOC99
 202
 203 /* Get the architecture specific values describing the floating-point
 204    evaluation.  The following symbols will get defined:
 205
 206     float_t     floating-point type at least as wide as `float' used
 207                 to evaluate `float' expressions
 208     double_t    floating-point type at least as wide as `double' used
 209                 to evaluate `double' expressions
 210
 211     FLT_EVAL_METHOD
 212                 Defined to
 213                   0     if `float_t' is `float' and `double_t' is `double'
 214                   1     if `float_t' and `double_t' are `double'
 215                   2     if `float_t' and `double_t' are `long double'
 216                   else  `float_t' and `double_t' are unspecified
 217
 218     INFINITY    representation of the infinity value of type `float'
 219
 220     FP_FAST_FMA
 221     FP_FAST_FMAF
 222     FP_FAST_FMAL
 223                 If defined it indicates that the `fma' function
 224                 generally executes about as fast as a multiply and an add.
 225                 This macro is defined only iff the `fma' function is
 226                 implemented directly with a hardware multiply-add instructions.
 227
 228     FP_ILOGB0   Expands to a value returned by `ilogb (0.0)'.
 229     FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
 230
 231     DECIMAL_DIG Number of decimal digits supported by conversion between
 232                 decimal and all internal floating-point formats.
 233
 234 */
 235
 236 /* All floating-point numbers can be put in one of these categories.  */
 237 enum
 238   {
 239     FP_NAN,
 240 # define FP_NAN FP_NAN
 241     FP_INFINITE,
 242 # define FP_INFINITE FP_INFINITE
 243     FP_ZERO,
 244 # define FP_ZERO FP_ZERO
 245     FP_SUBNORMAL,
 246 # define FP_SUBNORMAL FP_SUBNORMAL
 247     FP_NORMAL
 248 # define FP_NORMAL FP_NORMAL
 249   };
 250
 251 /* Return number of classification appropriate for X.  */
 252 # ifdef __NO_LONG_DOUBLE_MATH
 253 #  define fpclassify(x) \
 254      (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
 255 # else
 256 #  define fpclassify(x) \
 257      (sizeof (x) == sizeof (float)                                            \
 258       ? __fpclassifyf (x)                                                     \
 259       : sizeof (x) == sizeof (double)                                         \
 260       ? __fpclassify (x) : __fpclassifyl (x))
 261 # endif
 262
 263 /* Return nonzero value if sign of X is negative.  */
 264 # ifdef __NO_LONG_DOUBLE_MATH
 265 #  define signbit(x) \
 266      (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
 267 # else
 268 #  define signbit(x) \
 269      (sizeof (x) == sizeof (float)                                            \
 270       ? __signbitf (x)                                                        \
 271       : sizeof (x) == sizeof (double)                                         \
 272       ? __signbit (x) : __signbitl (x))
 273 # endif
 274
 275 /* Return nonzero value if X is not +-Inf or NaN.  */
 276 # ifdef __NO_LONG_DOUBLE_MATH
 277 #  define isfinite(x) \
 278      (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
 279 # else
 280 #  define isfinite(x) \
 281      (sizeof (x) == sizeof (float)                                            \
 282       ? __finitef (x)                                                         \
 283       : sizeof (x) == sizeof (double)                                         \
 284       ? __finite (x) : __finitel (x))
 285 # endif
 286
 287 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
 288 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
 289
 290 /* Return nonzero value if X is a NaN.  We could use `fpclassify' but
 291    we already have this functions `__isnan' and it is faster.  */
 292 # ifdef __NO_LONG_DOUBLE_MATH
 293 #  define isnan(x) \
 294      (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
 295 # else
 296 #  define isnan(x) \
 297      (sizeof (x) == sizeof (float)                                            \
 298       ? __isnanf (x)                                                          \
 299       : sizeof (x) == sizeof (double)                                         \
 300       ? __isnan (x) : __isnanl (x))
 301 # endif
 302
 303 /* Return nonzero value is X is positive or negative infinity.  */
 304 # ifdef __NO_LONG_DOUBLE_MATH
 305 #  define isinf(x) \
 306      (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
 307 # else
 308 #  define isinf(x) \
 309      (sizeof (x) == sizeof (float)                                            \
 310       ? __isinff (x)                                                          \
 311       : sizeof (x) == sizeof (double)                                         \
 312       ? __isinf (x) : __isinfl (x))
 313 # endif
 314
 315 /* Bitmasks for the math_errhandling macro.  */
 316 # define MATH_ERRNO     1       /* errno set by math functions.  */
 317 # define MATH_ERREXCEPT 2       /* Exceptions raised by math functions.  */
 318
 319 #endif /* Use ISO C99.  */
 320
 321 #ifdef  __USE_MISC
 322 /* Support for various different standard error handling behaviors.  */
 323 typedef enum
 324 {
 325   _IEEE_ = -1,  /* According to IEEE 754/IEEE 854.  */
 326   _SVID_,       /* According to System V, release 4.  */
 327   _XOPEN_,      /* Nowadays also Unix98.  */
 328   _POSIX_,
 329   _ISOC_        /* Actually this is ISO C99.  */
 330 } _LIB_VERSION_TYPE;
 331
 332 /* This variable can be changed at run-time to any of the values above to
 333    affect floating point error handling behavior (it may also be necessary
 334    to change the hardware FPU exception settings).  */
 335 extern _LIB_VERSION_TYPE _LIB_VERSION;
 336 #endif
 337
 338
 339 #ifdef __USE_SVID
 340 /* In SVID error handling, `matherr' is called with this description
 341    of the exceptional condition.
 342
 343    We have a problem when using C++ since `exception' is a reserved
 344    name in C++.  */
 345 # ifdef __cplusplus
 346 struct __exception
 347 # else
 348 struct exception
 349 # endif
 350   {
 351     int type;
 352     char *name;
 353     double arg1;
 354     double arg2;
 355     double retval;
 356   };
 357
 358 # ifdef __cplusplus
 359 extern int matherr (struct __exception *__exc) throw ();
 360 # else
 361 extern int matherr (struct exception *__exc);
 362 # endif
 363
 364 # define X_TLOSS        1.41484755040568800000e+16
 365
 366 /* Types of exceptions in the `type' field.  */
 367 # define DOMAIN         1
 368 # define SING           2
 369 # define OVERFLOW       3
 370 # define UNDERFLOW      4
 371 # define TLOSS          5
 372 # define PLOSS          6
 373
 374 /* SVID mode specifies returning this large value instead of infinity.  */
 375 # define HUGE           3.40282347e+38F
 376
 377 #else   /* !SVID */
 378
 379 # ifdef __USE_XOPEN
 380 #  ifdef __UCLIBC_SUSV4_LEGACY__
 381 /* X/Open wants another strange constant.  */
 382 #  define MAXFLOAT      3.40282347e+38F
 383 #  endif
 384 # endif
 385
 386 #endif  /* SVID */
 387
 388
 389 /* Some useful constants.  */
 390 #if defined __USE_BSD || defined __USE_XOPEN
 391 # define M_E            2.7182818284590452354   /* e */
 392 # define M_LOG2E        1.4426950408889634074   /* log_2 e */
 393 # define M_LOG10E       0.43429448190325182765  /* log_10 e */
 394 # define M_LN2          0.69314718055994530942  /* log_e 2 */
 395 # define M_LN10         2.30258509299404568402  /* log_e 10 */
 396 # define M_PI           3.14159265358979323846  /* pi */
 397 # define M_PI_2         1.57079632679489661923  /* pi/2 */
 398 # define M_PI_4         0.78539816339744830962  /* pi/4 */
 399 # define M_1_PI         0.31830988618379067154  /* 1/pi */
 400 # define M_2_PI         0.63661977236758134308  /* 2/pi */
 401 # define M_2_SQRTPI     1.12837916709551257390  /* 2/sqrt(pi) */
 402 # define M_SQRT2        1.41421356237309504880  /* sqrt(2) */
 403 # define M_SQRT1_2      0.70710678118654752440  /* 1/sqrt(2) */
 404 #endif
 405
 406 /* The above constants are not adequate for computation using `long double's.
 407    Therefore we provide as an extension constants with similar names as a
 408    GNU extension.  Provide enough digits for the 128-bit IEEE quad.  */
 409 #ifdef __USE_GNU
 410 # define M_El           2.7182818284590452353602874713526625L  /* e */
 411 # define M_LOG2El       1.4426950408889634073599246810018921L  /* log_2 e */
 412 # define M_LOG10El      0.4342944819032518276511289189166051L  /* log_10 e */
 413 # define M_LN2l         0.6931471805599453094172321214581766L  /* log_e 2 */
 414 # define M_LN10l        2.3025850929940456840179914546843642L  /* log_e 10 */
 415 # define M_PIl          3.1415926535897932384626433832795029L  /* pi */
 416 # define M_PI_2l        1.5707963267948966192313216916397514L  /* pi/2 */
 417 # define M_PI_4l        0.7853981633974483096156608458198757L  /* pi/4 */
 418 # define M_1_PIl        0.3183098861837906715377675267450287L  /* 1/pi */
 419 # define M_2_PIl        0.6366197723675813430755350534900574L  /* 2/pi */
 420 # define M_2_SQRTPIl    1.1283791670955125738961589031215452L  /* 2/sqrt(pi) */
 421 # define M_SQRT2l       1.4142135623730950488016887242096981L  /* sqrt(2) */
 422 # define M_SQRT1_2l     0.7071067811865475244008443621048490L  /* 1/sqrt(2) */
 423 #endif
 424
 425
 426 /* When compiling in strict ISO C compatible mode we must not use the
 427    inline functions since they, among other things, do not set the
 428    `errno' variable correctly.  */
 429 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
 430 # define __NO_MATH_INLINES      1
 431 #endif
 432
 433 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
 434 /* ISO C99 defines some macros to compare number while taking care for
 435    unordered numbers.  Many FPUs provide special instructions to support
 436    these operations.  Generic support in GCC for these as builtins went
 437    in before 3.0.0, but not all cpus added their patterns.  We define
 438    versions that use the builtins here, and <bits/mathinline.h> will
 439    undef/redefine as appropriate for the specific GCC version in use.  */
 440 # define isgreater(x, y)        __builtin_isgreater(x, y)
 441 # define isgreaterequal(x, y)   __builtin_isgreaterequal(x, y)
 442 # define isless(x, y)           __builtin_isless(x, y)
 443 # define islessequal(x, y)      __builtin_islessequal(x, y)
 444 # define islessgreater(x, y)    __builtin_islessgreater(x, y)
 445 # define isunordered(u, v)      __builtin_isunordered(u, v)
 446 #endif
 447
 448 /* Get machine-dependent inline versions (if there are any).  */
 449 #ifdef __USE_EXTERN_INLINES
 450 # include <bits/mathinline.h>
 451 #endif
 452
 453 #ifdef __USE_ISOC99
 454 /* If we've still got undefined comparison macros, provide defaults.  */
 455
 456 /* Return nonzero value if X is greater than Y.  */
 457 # ifndef isgreater
 458 #  define isgreater(x, y) \
 459   (__extension__                                                              \
 460    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 461       !isunordered (__x, __y) && __x > __y; }))
 462 # endif
 463
 464 /* Return nonzero value if X is greater than or equal to Y.  */
 465 # ifndef isgreaterequal
 466 #  define isgreaterequal(x, y) \
 467   (__extension__                                                              \
 468    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 469       !isunordered (__x, __y) && __x >= __y; }))
 470 # endif
 471
 472 /* Return nonzero value if X is less than Y.  */
 473 # ifndef isless
 474 #  define isless(x, y) \
 475   (__extension__                                                              \
 476    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 477       !isunordered (__x, __y) && __x < __y; }))
 478 # endif
 479
 480 /* Return nonzero value if X is less than or equal to Y.  */
 481 # ifndef islessequal
 482 #  define islessequal(x, y) \
 483   (__extension__                                                              \
 484    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 485       !isunordered (__x, __y) && __x <= __y; }))
 486 # endif
 487
 488 /* Return nonzero value if either X is less than Y or Y is less than X.  */
 489 # ifndef islessgreater
 490 #  define islessgreater(x, y) \
 491   (__extension__                                                              \
 492    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 493       !isunordered (__x, __y) && (__x < __y || __y < __x); }))
 494 # endif
 495
 496 /* Return nonzero value if arguments are unordered.  */
 497 # ifndef isunordered
 498 #  define isunordered(u, v) \
 499   (__extension__                                                              \
 500    ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v);                       \
 501       fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
 502 # endif
 503
 504 #endif
 505
 506 __END_DECLS
 507
 508
 509 #endif /* math.h  */