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