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 #endif
 196
 197
 198 /* ISO C99 defines some generic macros which work on any data type.  */
 199 #if defined(__USE_ISOC99) || defined(__USE_BSD)
 200
 201 /* Get the architecture specific values describing the floating-point
 202    evaluation.  The following symbols will get defined:
 203
 204     float_t     floating-point type at least as wide as `float' used
 205                 to evaluate `float' expressions
 206     double_t    floating-point type at least as wide as `double' used
 207                 to evaluate `double' expressions
 208
 209     FLT_EVAL_METHOD
 210                 Defined to
 211                   0     if `float_t' is `float' and `double_t' is `double'
 212                   1     if `float_t' and `double_t' are `double'
 213                   2     if `float_t' and `double_t' are `long double'
 214                   else  `float_t' and `double_t' are unspecified
 215
 216     INFINITY    representation of the infinity value of type `float'
 217
 218     FP_FAST_FMA
 219     FP_FAST_FMAF
 220     FP_FAST_FMAL
 221                 If defined it indicates that the `fma' function
 222                 generally executes about as fast as a multiply and an add.
 223                 This macro is defined only iff the `fma' function is
 224                 implemented directly with a hardware multiply-add instructions.
 225
 226     FP_ILOGB0   Expands to a value returned by `ilogb (0.0)'.
 227     FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
 228
 229     DECIMAL_DIG Number of decimal digits supported by conversion between
 230                 decimal and all internal floating-point formats.
 231
 232 */
 233
 234 /* All floating-point numbers can be put in one of these categories.  */
 235 enum
 236   {
 237     FP_NAN,
 238 # define FP_NAN FP_NAN
 239     FP_INFINITE,
 240 # define FP_INFINITE FP_INFINITE
 241     FP_ZERO,
 242 # define FP_ZERO FP_ZERO
 243     FP_SUBNORMAL,
 244 # define FP_SUBNORMAL FP_SUBNORMAL
 245     FP_NORMAL
 246 # define FP_NORMAL FP_NORMAL
 247   };
 248
 249 /* Return number of classification appropriate for X.  */
 250 # ifdef __NO_LONG_DOUBLE_MATH
 251 #  define fpclassify(x) \
 252      (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
 253 # else
 254 #  define fpclassify(x) \
 255      (sizeof (x) == sizeof (float)                                            \
 256       ? __fpclassifyf (x)                                                     \
 257       : sizeof (x) == sizeof (double)                                         \
 258       ? __fpclassify (x) : __fpclassifyl (x))
 259 # endif
 260
 261 /* Return nonzero value if sign of X is negative.  */
 262 # ifdef __NO_LONG_DOUBLE_MATH
 263 #  define signbit(x) \
 264      (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
 265 # else
 266 #  define signbit(x) \
 267      (sizeof (x) == sizeof (float)                                            \
 268       ? __signbitf (x)                                                        \
 269       : sizeof (x) == sizeof (double)                                         \
 270       ? __signbit (x) : __signbitl (x))
 271 # endif
 272
 273 /* Return nonzero value if X is not +-Inf or NaN.  */
 274 # ifdef __NO_LONG_DOUBLE_MATH
 275 #  define isfinite(x) \
 276      (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
 277 # else
 278 #  define isfinite(x) \
 279      (sizeof (x) == sizeof (float)                                            \
 280       ? __finitef (x)                                                         \
 281       : sizeof (x) == sizeof (double)                                         \
 282       ? __finite (x) : __finitel (x))
 283 # endif
 284
 285 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
 286 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
 287
 288 /* Return nonzero value if X is a NaN.  We could use `fpclassify' but
 289    we already have this functions `__isnan' and it is faster.  */
 290 # ifdef __NO_LONG_DOUBLE_MATH
 291 #  define isnan(x) \
 292      (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
 293 # else
 294 #  define isnan(x) \
 295      (sizeof (x) == sizeof (float)                                            \
 296       ? __isnanf (x)                                                          \
 297       : sizeof (x) == sizeof (double)                                         \
 298       ? __isnan (x) : __isnanl (x))
 299 # endif
 300
 301 /* Return nonzero value is X is positive or negative infinity.  */
 302 # ifdef __NO_LONG_DOUBLE_MATH
 303 #  define isinf(x) \
 304      (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
 305 # else
 306 #  define isinf(x) \
 307      (sizeof (x) == sizeof (float)                                            \
 308       ? __isinff (x)                                                          \
 309       : sizeof (x) == sizeof (double)                                         \
 310       ? __isinf (x) : __isinfl (x))
 311 # endif
 312
 313 /* Bitmasks for the math_errhandling macro.  */
 314 # define MATH_ERRNO     1       /* errno set by math functions.  */
 315 # define MATH_ERREXCEPT 2       /* Exceptions raised by math functions.  */
 316
 317 #endif /* Use ISO C99.  */
 318
 319 /* BSD compat */
 320 #define finite(x) __finite(x)
 321 #define finitef(x) __finitef(x)
 322 #define finitel(x) __finitel(x)
 323
 324 #ifdef  __USE_MISC
 325 /* Support for various different standard error handling behaviors.  */
 326 typedef enum
 327 {
 328   _IEEE_ = -1,  /* According to IEEE 754/IEEE 854.  */
 329   _SVID_,       /* According to System V, release 4.  */
 330   _XOPEN_,      /* Nowadays also Unix98.  */
 331   _POSIX_,
 332   _ISOC_        /* Actually this is ISO C99.  */
 333 } _LIB_VERSION_TYPE;
 334
 335 /* This variable can be changed at run-time to any of the values above to
 336    affect floating point error handling behavior (it may also be necessary
 337    to change the hardware FPU exception settings).  */
 338 extern _LIB_VERSION_TYPE _LIB_VERSION;
 339 #endif
 340
 341
 342 #ifdef __USE_SVID
 343 /* In SVID error handling, `matherr' is called with this description
 344    of the exceptional condition.
 345
 346    We have a problem when using C++ since `exception' is a reserved
 347    name in C++.  */
 348 # ifdef __cplusplus
 349 struct __exception
 350 # else
 351 struct exception
 352 # endif
 353   {
 354     int type;
 355     char *name;
 356     double arg1;
 357     double arg2;
 358     double retval;
 359   };
 360
 361 # ifdef __cplusplus
 362 extern int matherr (struct __exception *__exc) throw ();
 363 # else
 364 extern int matherr (struct exception *__exc);
 365 # endif
 366
 367 # define X_TLOSS        1.41484755040568800000e+16
 368
 369 /* Types of exceptions in the `type' field.  */
 370 # define DOMAIN         1
 371 # define SING           2
 372 # define OVERFLOW       3
 373 # define UNDERFLOW      4
 374 # define TLOSS          5
 375 # define PLOSS          6
 376
 377 /* SVID mode specifies returning this large value instead of infinity.  */
 378 # define HUGE           3.40282347e+38F
 379
 380 #else   /* !SVID */
 381
 382 # ifdef __USE_XOPEN
 383 #  ifdef __UCLIBC_SUSV4_LEGACY__
 384 /* X/Open wants another strange constant.  */
 385 #  define MAXFLOAT      3.40282347e+38F
 386 #  endif
 387 # endif
 388
 389 #endif  /* SVID */
 390
 391
 392 /* Some useful constants.  */
 393 #if defined __USE_BSD || defined __USE_XOPEN
 394 # define M_E            2.7182818284590452354   /* e */
 395 # define M_LOG2E        1.4426950408889634074   /* log_2 e */
 396 # define M_LOG10E       0.43429448190325182765  /* log_10 e */
 397 # define M_LN2          0.69314718055994530942  /* log_e 2 */
 398 # define M_LN10         2.30258509299404568402  /* log_e 10 */
 399 # define M_PI           3.14159265358979323846  /* pi */
 400 # define M_PI_2         1.57079632679489661923  /* pi/2 */
 401 # define M_PI_4         0.78539816339744830962  /* pi/4 */
 402 # define M_1_PI         0.31830988618379067154  /* 1/pi */
 403 # define M_2_PI         0.63661977236758134308  /* 2/pi */
 404 # define M_2_SQRTPI     1.12837916709551257390  /* 2/sqrt(pi) */
 405 # define M_SQRT2        1.41421356237309504880  /* sqrt(2) */
 406 # define M_SQRT1_2      0.70710678118654752440  /* 1/sqrt(2) */
 407 #endif
 408
 409 /* The above constants are not adequate for computation using `long double's.
 410    Therefore we provide as an extension constants with similar names as a
 411    GNU extension.  Provide enough digits for the 128-bit IEEE quad.  */
 412 #ifdef __USE_GNU
 413 # define M_El           2.7182818284590452353602874713526625L  /* e */
 414 # define M_LOG2El       1.4426950408889634073599246810018921L  /* log_2 e */
 415 # define M_LOG10El      0.4342944819032518276511289189166051L  /* log_10 e */
 416 # define M_LN2l         0.6931471805599453094172321214581766L  /* log_e 2 */
 417 # define M_LN10l        2.3025850929940456840179914546843642L  /* log_e 10 */
 418 # define M_PIl          3.1415926535897932384626433832795029L  /* pi */
 419 # define M_PI_2l        1.5707963267948966192313216916397514L  /* pi/2 */
 420 # define M_PI_4l        0.7853981633974483096156608458198757L  /* pi/4 */
 421 # define M_1_PIl        0.3183098861837906715377675267450287L  /* 1/pi */
 422 # define M_2_PIl        0.6366197723675813430755350534900574L  /* 2/pi */
 423 # define M_2_SQRTPIl    1.1283791670955125738961589031215452L  /* 2/sqrt(pi) */
 424 # define M_SQRT2l       1.4142135623730950488016887242096981L  /* sqrt(2) */
 425 # define M_SQRT1_2l     0.7071067811865475244008443621048490L  /* 1/sqrt(2) */
 426 #endif
 427
 428
 429 /* When compiling in strict ISO C compatible mode we must not use the
 430    inline functions since they, among other things, do not set the
 431    `errno' variable correctly.  */
 432 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
 433 # define __NO_MATH_INLINES      1
 434 #endif
 435
 436 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
 437 /* ISO C99 defines some macros to compare number while taking care for
 438    unordered numbers.  Many FPUs provide special instructions to support
 439    these operations.  Generic support in GCC for these as builtins went
 440    in before 3.0.0, but not all cpus added their patterns.  We define
 441    versions that use the builtins here, and <bits/mathinline.h> will
 442    undef/redefine as appropriate for the specific GCC version in use.  */
 443 # define isgreater(x, y)        __builtin_isgreater(x, y)
 444 # define isgreaterequal(x, y)   __builtin_isgreaterequal(x, y)
 445 # define isless(x, y)           __builtin_isless(x, y)
 446 # define islessequal(x, y)      __builtin_islessequal(x, y)
 447 # define islessgreater(x, y)    __builtin_islessgreater(x, y)
 448 # define isunordered(u, v)      __builtin_isunordered(u, v)
 449 #endif
 450
 451 /* Get machine-dependent inline versions (if there are any).  */
 452 #ifdef __USE_EXTERN_INLINES
 453 # include <bits/mathinline.h>
 454 #endif
 455
 456 #ifdef __USE_ISOC99
 457 /* If we've still got undefined comparison macros, provide defaults.  */
 458
 459 /* Return nonzero value if X is greater than Y.  */
 460 # ifndef isgreater
 461 #  define isgreater(x, y) \
 462   (__extension__                                                              \
 463    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 464       !isunordered (__x, __y) && __x > __y; }))
 465 # endif
 466
 467 /* Return nonzero value if X is greater than or equal to Y.  */
 468 # ifndef isgreaterequal
 469 #  define isgreaterequal(x, y) \
 470   (__extension__                                                              \
 471    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 472       !isunordered (__x, __y) && __x >= __y; }))
 473 # endif
 474
 475 /* Return nonzero value if X is less than Y.  */
 476 # ifndef isless
 477 #  define isless(x, y) \
 478   (__extension__                                                              \
 479    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 480       !isunordered (__x, __y) && __x < __y; }))
 481 # endif
 482
 483 /* Return nonzero value if X is less than or equal to Y.  */
 484 # ifndef islessequal
 485 #  define islessequal(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 either X is less than Y or Y is less than X.  */
 492 # ifndef islessgreater
 493 #  define islessgreater(x, y) \
 494   (__extension__                                                              \
 495    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 496       !isunordered (__x, __y) && (__x < __y || __y < __x); }))
 497 # endif
 498
 499 /* Return nonzero value if arguments are unordered.  */
 500 # ifndef isunordered
 501 #  define isunordered(u, v) \
 502   (__extension__                                                              \
 503    ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v);                       \
 504       fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
 505 # endif
 506
 507 #endif
 508
 509 __END_DECLS
 510
 511
 512 #endif /* math.h  */