math/math.h

   1 /* Declarations for math functions.
   2    Copyright (C) 1991-2013 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4
   5    The GNU C Library is free software; you can redistribute it and/or
   6    modify it under the terms of the GNU Lesser General Public
   7    License as published by the Free Software Foundation; either
   8    version 2.1 of the License, or (at your option) any later version.
   9
  10    The GNU C Library is distributed in the hope that it will be useful,
  11    but WITHOUT ANY WARRANTY; without even the implied warranty of
  12    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13    Lesser General Public License for more details.
  14
  15    You should have received a copy of the GNU Lesser General Public
  16    License along with the GNU C Library; if not, see
  17    <http://www.gnu.org/licenses/>.  */
  18
  19 /*
  20  *      ISO C99 Standard: 7.12 Mathematics      <math.h>
  21  */
  22
  23 #ifndef _MATH_H
  24 #define _MATH_H 1
  25
  26 #include <features.h>
  27
  28 __BEGIN_DECLS
  29
  30 /* Get machine-dependent HUGE_VAL value (returned on overflow).
  31    On all IEEE754 machines, this is +Infinity.  */
  32 #include <bits/huge_val.h>
  33 #ifdef __USE_ISOC99
  34 # include <bits/huge_valf.h>
  35 # include <bits/huge_vall.h>
  36
  37 /* Get machine-dependent INFINITY value.  */
  38 # include <bits/inf.h>
  39
  40 /* Get machine-dependent NAN value (returned for some domain errors).  */
  41 # include <bits/nan.h>
  42 #endif /* __USE_ISOC99 */
  43
  44 /* Get general and ISO C99 specific information.  */
  45 #include <bits/mathdef.h>
  46
  47 /* The file <bits/mathcalls.h> contains the prototypes for all the
  48    actual math functions.  These macros are used for those prototypes,
  49    so we can easily declare each function as both `name' and `__name',
  50    and can declare the float versions `namef' and `__namef'.  */
  51
  52 #define __MATHCALL(function,suffix, args)       \
  53   __MATHDECL (_Mdouble_,function,suffix, args)
  54 #define __MATHDECL(type, function,suffix, args) \
  55   __MATHDECL_1(type, function,suffix, args); \
  56   __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
  57 #define __MATHCALLX(function,suffix, args, attrib)      \
  58   __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
  59 #define __MATHDECLX(type, function,suffix, args, attrib) \
  60   __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
  61   __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
  62 #define __MATHDECL_1(type, function,suffix, args) \
  63   extern type __MATH_PRECNAME(function,suffix) args __THROW
  64
  65 #define _Mdouble_               double
  66 #define __MATH_PRECNAME(name,r) __CONCAT(name,r)
  67 #define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
  68 #define _Mdouble_END_NAMESPACE   __END_NAMESPACE_STD
  69 #include <bits/mathcalls.h>
  70 #undef  _Mdouble_
  71 #undef _Mdouble_BEGIN_NAMESPACE
  72 #undef _Mdouble_END_NAMESPACE
  73 #undef  __MATH_PRECNAME
  74
  75 #if defined __USE_MISC || defined __USE_ISOC99
  76
  77
  78 /* Include the file of declarations again, this time using `float'
  79    instead of `double' and appending f to each function name.  */
  80
  81 # ifndef _Mfloat_
  82 #  define _Mfloat_              float
  83 # endif
  84 # define _Mdouble_              _Mfloat_
  85 # define __MATH_PRECNAME(name,r) name##f##r
  86 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
  87 # define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
  88 # include <bits/mathcalls.h>
  89 # undef _Mdouble_
  90 # undef _Mdouble_BEGIN_NAMESPACE
  91 # undef _Mdouble_END_NAMESPACE
  92 # undef __MATH_PRECNAME
  93
  94 # if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
  95      || defined __LDBL_COMPAT
  96 #  ifdef __LDBL_COMPAT
  97
  98 #   ifdef __USE_ISOC99
  99 extern float __nldbl_nexttowardf (float __x, long double __y)
 100                                   __THROW __attribute__ ((__const__));
 101 #    ifdef __REDIRECT_NTH
 102 extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
 103                              __nldbl_nexttowardf)
 104      __attribute__ ((__const__));
 105 extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
 106                               nextafter) __attribute__ ((__const__));
 107 extern long double __REDIRECT_NTH (nexttowardl,
 108                                    (long double __x, long double __y),
 109                                    nextafter) __attribute__ ((__const__));
 110 #    endif
 111 #   endif
 112
 113 #   undef __MATHDECL_1
 114 #   define __MATHDECL_2(type, function,suffix, args, alias) \
 115   extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
 116                              args, alias)
 117 #   define __MATHDECL_1(type, function,suffix, args) \
 118   __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
 119 #  endif
 120
 121 /* Include the file of declarations again, this time using `long double'
 122    instead of `double' and appending l to each function name.  */
 123
 124 #  ifndef _Mlong_double_
 125 #   define _Mlong_double_       long double
 126 #  endif
 127 #  define _Mdouble_             _Mlong_double_
 128 #  define __MATH_PRECNAME(name,r) name##l##r
 129 #  define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
 130 #  define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
 131 #  define __MATH_DECLARE_LDOUBLE   1
 132 #  include <bits/mathcalls.h>
 133 #  undef _Mdouble_
 134 #  undef _Mdouble_BEGIN_NAMESPACE
 135 #  undef _Mdouble_END_NAMESPACE
 136 #  undef __MATH_PRECNAME
 137
 138 # endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */
 139
 140 #endif  /* Use misc or ISO C99.  */
 141 #undef  __MATHDECL_1
 142 #undef  __MATHDECL
 143 #undef  __MATHCALL
 144
 145
 146 #if defined __USE_MISC || defined __USE_XOPEN
 147 /* This variable is used by `gamma' and `lgamma'.  */
 148 extern int signgam;
 149 #endif
 150
 151
 152 /* ISO C99 defines some generic macros which work on any data type.  */
 153 #ifdef __USE_ISOC99
 154
 155 /* Get the architecture specific values describing the floating-point
 156    evaluation.  The following symbols will get defined:
 157
 158     float_t     floating-point type at least as wide as `float' used
 159                 to evaluate `float' expressions
 160     double_t    floating-point type at least as wide as `double' used
 161                 to evaluate `double' expressions
 162
 163     FLT_EVAL_METHOD
 164                 Defined to
 165                   0     if `float_t' is `float' and `double_t' is `double'
 166                   1     if `float_t' and `double_t' are `double'
 167                   2     if `float_t' and `double_t' are `long double'
 168                   else  `float_t' and `double_t' are unspecified
 169
 170     INFINITY    representation of the infinity value of type `float'
 171
 172     FP_FAST_FMA
 173     FP_FAST_FMAF
 174     FP_FAST_FMAL
 175                 If defined it indicates that the `fma' function
 176                 generally executes about as fast as a multiply and an add.
 177                 This macro is defined only iff the `fma' function is
 178                 implemented directly with a hardware multiply-add instructions.
 179
 180     FP_ILOGB0   Expands to a value returned by `ilogb (0.0)'.
 181     FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
 182
 183     DECIMAL_DIG Number of decimal digits supported by conversion between
 184                 decimal and all internal floating-point formats.
 185
 186 */
 187
 188 /* All floating-point numbers can be put in one of these categories.  */
 189 enum
 190   {
 191     FP_NAN =
 192 # define FP_NAN 0
 193       FP_NAN,
 194     FP_INFINITE =
 195 # define FP_INFINITE 1
 196       FP_INFINITE,
 197     FP_ZERO =
 198 # define FP_ZERO 2
 199       FP_ZERO,
 200     FP_SUBNORMAL =
 201 # define FP_SUBNORMAL 3
 202       FP_SUBNORMAL,
 203     FP_NORMAL =
 204 # define FP_NORMAL 4
 205       FP_NORMAL
 206   };
 207
 208 /* Return number of classification appropriate for X.  */
 209 # ifdef __NO_LONG_DOUBLE_MATH
 210 #  define fpclassify(x) \
 211      (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
 212 # else
 213 #  define fpclassify(x) \
 214      (sizeof (x) == sizeof (float)                                            \
 215       ? __fpclassifyf (x)                                                     \
 216       : sizeof (x) == sizeof (double)                                         \
 217       ? __fpclassify (x) : __fpclassifyl (x))
 218 # endif
 219
 220 /* Return nonzero value if sign of X is negative.  */
 221 # ifdef __NO_LONG_DOUBLE_MATH
 222 #  define signbit(x) \
 223      (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
 224 # else
 225 #  define signbit(x) \
 226      (sizeof (x) == sizeof (float)                                            \
 227       ? __signbitf (x)                                                        \
 228       : sizeof (x) == sizeof (double)                                         \
 229       ? __signbit (x) : __signbitl (x))
 230 # endif
 231
 232 /* Return nonzero value if X is not +-Inf or NaN.  */
 233 # ifdef __NO_LONG_DOUBLE_MATH
 234 #  define isfinite(x) \
 235      (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
 236 # else
 237 #  define isfinite(x) \
 238      (sizeof (x) == sizeof (float)                                            \
 239       ? __finitef (x)                                                         \
 240       : sizeof (x) == sizeof (double)                                         \
 241       ? __finite (x) : __finitel (x))
 242 # endif
 243
 244 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
 245 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
 246
 247 /* Return nonzero value if X is a NaN.  We could use `fpclassify' but
 248    we already have this functions `__isnan' and it is faster.  */
 249 # ifdef __NO_LONG_DOUBLE_MATH
 250 #  define isnan(x) \
 251      (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
 252 # else
 253 #  define isnan(x) \
 254      (sizeof (x) == sizeof (float)                                            \
 255       ? __isnanf (x)                                                          \
 256       : sizeof (x) == sizeof (double)                                         \
 257       ? __isnan (x) : __isnanl (x))
 258 # endif
 259
 260 /* Return nonzero value if X is positive or negative infinity.  */
 261 # ifdef __NO_LONG_DOUBLE_MATH
 262 #  define isinf(x) \
 263      (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
 264 # else
 265 #  define isinf(x) \
 266      (sizeof (x) == sizeof (float)                                            \
 267       ? __isinff (x)                                                          \
 268       : sizeof (x) == sizeof (double)                                         \
 269       ? __isinf (x) : __isinfl (x))
 270 # endif
 271
 272 /* Bitmasks for the math_errhandling macro.  */
 273 # define MATH_ERRNO     1       /* errno set by math functions.  */
 274 # define MATH_ERREXCEPT 2       /* Exceptions raised by math functions.  */
 275
 276 /* By default all functions support both errno and exception handling.
 277    In gcc's fast math mode and if inline functions are defined this
 278    might not be true.  */
 279 # ifndef __FAST_MATH__
 280 #  define math_errhandling      (MATH_ERRNO | MATH_ERREXCEPT)
 281 # endif
 282
 283 #endif /* Use ISO C99.  */
 284
 285 #ifdef __USE_GNU
 286 /* Return nonzero value if X is a signaling NaN.  */
 287 # ifdef __NO_LONG_DOUBLE_MATH
 288 #  define issignaling(x) \
 289      (sizeof (x) == sizeof (float) ? __issignalingf (x) : __issignaling (x))
 290 # else
 291 #  define issignaling(x) \
 292      (sizeof (x) == sizeof (float)                                            \
 293       ? __issignalingf (x)                                                    \
 294       : sizeof (x) == sizeof (double)                                         \
 295       ? __issignaling (x) : __issignalingl (x))
 296 # endif
 297 #endif /* Use GNU.  */
 298
 299 #ifdef  __USE_MISC
 300 /* Support for various different standard error handling behaviors.  */
 301 typedef enum
 302 {
 303   _IEEE_ = -1,  /* According to IEEE 754/IEEE 854.  */
 304   _SVID_,       /* According to System V, release 4.  */
 305   _XOPEN_,      /* Nowadays also Unix98.  */
 306   _POSIX_,
 307   _ISOC_        /* Actually this is ISO C99.  */
 308 } _LIB_VERSION_TYPE;
 309
 310 /* This variable can be changed at run-time to any of the values above to
 311    affect floating point error handling behavior (it may also be necessary
 312    to change the hardware FPU exception settings).  */
 313 extern _LIB_VERSION_TYPE _LIB_VERSION;
 314 #endif
 315
 316
 317 #ifdef __USE_SVID
 318 /* In SVID error handling, `matherr' is called with this description
 319    of the exceptional condition.
 320
 321    We have a problem when using C++ since `exception' is a reserved
 322    name in C++.  */
 323 # ifdef __cplusplus
 324 struct __exception
 325 # else
 326 struct exception
 327 # endif
 328   {
 329     int type;
 330     char *name;
 331     double arg1;
 332     double arg2;
 333     double retval;
 334   };
 335
 336 # ifdef __cplusplus
 337 extern int matherr (struct __exception *__exc) throw ();
 338 # else
 339 extern int matherr (struct exception *__exc);
 340 # endif
 341
 342 # define X_TLOSS        1.41484755040568800000e+16
 343
 344 /* Types of exceptions in the `type' field.  */
 345 # define DOMAIN         1
 346 # define SING           2
 347 # define OVERFLOW       3
 348 # define UNDERFLOW      4
 349 # define TLOSS          5
 350 # define PLOSS          6
 351
 352 /* SVID mode specifies returning this large value instead of infinity.  */
 353 # define HUGE           3.40282347e+38F
 354
 355 #else   /* !SVID */
 356
 357 # ifdef __USE_XOPEN
 358 /* X/Open wants another strange constant.  */
 359 #  define MAXFLOAT      3.40282347e+38F
 360 # endif
 361
 362 #endif  /* SVID */
 363
 364
 365 /* Some useful constants.  */
 366 #if defined __USE_BSD || defined __USE_XOPEN
 367 # define M_E            2.7182818284590452354   /* e */
 368 # define M_LOG2E        1.4426950408889634074   /* log_2 e */
 369 # define M_LOG10E       0.43429448190325182765  /* log_10 e */
 370 # define M_LN2          0.69314718055994530942  /* log_e 2 */
 371 # define M_LN10         2.30258509299404568402  /* log_e 10 */
 372 # define M_PI           3.14159265358979323846  /* pi */
 373 # define M_PI_2         1.57079632679489661923  /* pi/2 */
 374 # define M_PI_4         0.78539816339744830962  /* pi/4 */
 375 # define M_1_PI         0.31830988618379067154  /* 1/pi */
 376 # define M_2_PI         0.63661977236758134308  /* 2/pi */
 377 # define M_2_SQRTPI     1.12837916709551257390  /* 2/sqrt(pi) */
 378 # define M_SQRT2        1.41421356237309504880  /* sqrt(2) */
 379 # define M_SQRT1_2      0.70710678118654752440  /* 1/sqrt(2) */
 380 #endif
 381
 382 /* The above constants are not adequate for computation using `long double's.
 383    Therefore we provide as an extension constants with similar names as a
 384    GNU extension.  Provide enough digits for the 128-bit IEEE quad.  */
 385 #ifdef __USE_GNU
 386 # define M_El           2.718281828459045235360287471352662498L /* e */
 387 # define M_LOG2El       1.442695040888963407359924681001892137L /* log_2 e */
 388 # define M_LOG10El      0.434294481903251827651128918916605082L /* log_10 e */
 389 # define M_LN2l         0.693147180559945309417232121458176568L /* log_e 2 */
 390 # define M_LN10l        2.302585092994045684017991454684364208L /* log_e 10 */
 391 # define M_PIl          3.141592653589793238462643383279502884L /* pi */
 392 # define M_PI_2l        1.570796326794896619231321691639751442L /* pi/2 */
 393 # define M_PI_4l        0.785398163397448309615660845819875721L /* pi/4 */
 394 # define M_1_PIl        0.318309886183790671537767526745028724L /* 1/pi */
 395 # define M_2_PIl        0.636619772367581343075535053490057448L /* 2/pi */
 396 # define M_2_SQRTPIl    1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
 397 # define M_SQRT2l       1.414213562373095048801688724209698079L /* sqrt(2) */
 398 # define M_SQRT1_2l     0.707106781186547524400844362104849039L /* 1/sqrt(2) */
 399 #endif
 400
 401
 402 /* When compiling in strict ISO C compatible mode we must not use the
 403    inline functions since they, among other things, do not set the
 404    `errno' variable correctly.  */
 405 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
 406 # define __NO_MATH_INLINES      1
 407 #endif
 408
 409 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
 410 /* ISO C99 defines some macros to compare number while taking care for
 411    unordered numbers.  Many FPUs provide special instructions to support
 412    these operations.  Generic support in GCC for these as builtins went
 413    in before 3.0.0, but not all cpus added their patterns.  We define
 414    versions that use the builtins here, and <bits/mathinline.h> will
 415    undef/redefine as appropriate for the specific GCC version in use.  */
 416 # define isgreater(x, y)        __builtin_isgreater(x, y)
 417 # define isgreaterequal(x, y)   __builtin_isgreaterequal(x, y)
 418 # define isless(x, y)           __builtin_isless(x, y)
 419 # define islessequal(x, y)      __builtin_islessequal(x, y)
 420 # define islessgreater(x, y)    __builtin_islessgreater(x, y)
 421 # define isunordered(u, v)      __builtin_isunordered(u, v)
 422 #endif
 423
 424 /* Get machine-dependent inline versions (if there are any).  */
 425 #ifdef __USE_EXTERN_INLINES
 426 # include <bits/mathinline.h>
 427 #endif
 428
 429 /* Define special entry points to use when the compiler got told to
 430    only expect finite results.  */
 431 #if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0
 432 # include <bits/math-finite.h>
 433 #endif
 434
 435 #ifdef __USE_ISOC99
 436 /* If we've still got undefined comparison macros, provide defaults.  */
 437
 438 /* Return nonzero value if X is greater than Y.  */
 439 # ifndef isgreater
 440 #  define isgreater(x, y) \
 441   (__extension__                                                              \
 442    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 443       !isunordered (__x, __y) && __x > __y; }))
 444 # endif
 445
 446 /* Return nonzero value if X is greater than or equal to Y.  */
 447 # ifndef isgreaterequal
 448 #  define isgreaterequal(x, y) \
 449   (__extension__                                                              \
 450    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 451       !isunordered (__x, __y) && __x >= __y; }))
 452 # endif
 453
 454 /* Return nonzero value if X is less than Y.  */
 455 # ifndef isless
 456 #  define isless(x, y) \
 457   (__extension__                                                              \
 458    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 459       !isunordered (__x, __y) && __x < __y; }))
 460 # endif
 461
 462 /* Return nonzero value if X is less than or equal to Y.  */
 463 # ifndef islessequal
 464 #  define islessequal(x, y) \
 465   (__extension__                                                              \
 466    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 467       !isunordered (__x, __y) && __x <= __y; }))
 468 # endif
 469
 470 /* Return nonzero value if either X is less than Y or Y is less than X.  */
 471 # ifndef islessgreater
 472 #  define islessgreater(x, y) \
 473   (__extension__                                                              \
 474    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 475       !isunordered (__x, __y) && (__x < __y || __y < __x); }))
 476 # endif
 477
 478 /* Return nonzero value if arguments are unordered.  */
 479 # ifndef isunordered
 480 #  define isunordered(u, v) \
 481   (__extension__                                                              \
 482    ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v);                       \
 483       fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
 484 # endif
 485
 486 #endif
 487
 488 __END_DECLS
 489
 490
 491 #endif /* math.h  */