math/math.h

   1 /* Declarations for math functions.
   2    Copyright (C) 1991-2015 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 vector math functions declarations.  */
  31 #include <bits/math-vector.h>
  32
  33 /* Get machine-dependent HUGE_VAL value (returned on overflow).
  34    On all IEEE754 machines, this is +Infinity.  */
  35 #include <bits/huge_val.h>
  36 #ifdef __USE_ISOC99
  37 # include <bits/huge_valf.h>
  38 # include <bits/huge_vall.h>
  39
  40 /* Get machine-dependent INFINITY value.  */
  41 # include <bits/inf.h>
  42
  43 /* Get machine-dependent NAN value (returned for some domain errors).  */
  44 # include <bits/nan.h>
  45 #endif /* __USE_ISOC99 */
  46
  47 /* Get general and ISO C99 specific information.  */
  48 #include <bits/mathdef.h>
  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 __SIMD_DECL(function) __CONCAT (__DECL_SIMD_, function)
  56
  57 #define __MATHCALL_VEC(function, suffix, args)  \
  58   __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
  59   __MATHCALL (function, suffix, args)
  60
  61 #define __MATHDECL_VEC(type, function,suffix, args) \
  62   __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
  63   __MATHDECL(type, function,suffix, args)
  64
  65 #define __MATHCALL(function,suffix, args)       \
  66   __MATHDECL (_Mdouble_,function,suffix, args)
  67 #define __MATHDECL(type, function,suffix, args) \
  68   __MATHDECL_1(type, function,suffix, args); \
  69   __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
  70 #define __MATHCALLX(function,suffix, args, attrib)      \
  71   __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
  72 #define __MATHDECLX(type, function,suffix, args, attrib) \
  73   __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
  74   __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
  75 #define __MATHDECL_1(type, function,suffix, args) \
  76   extern type __MATH_PRECNAME(function,suffix) args __THROW
  77
  78 #define _Mdouble_               double
  79 #define __MATH_PRECNAME(name,r) __CONCAT(name,r)
  80 #define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
  81 #define _Mdouble_END_NAMESPACE   __END_NAMESPACE_STD
  82 #include <bits/mathcalls.h>
  83 #undef  _Mdouble_
  84 #undef _Mdouble_BEGIN_NAMESPACE
  85 #undef _Mdouble_END_NAMESPACE
  86 #undef  __MATH_PRECNAME
  87
  88 #ifdef __USE_ISOC99
  89
  90
  91 /* Include the file of declarations again, this time using `float'
  92    instead of `double' and appending f to each function name.  */
  93
  94 # ifndef _Mfloat_
  95 #  define _Mfloat_              float
  96 # endif
  97 # define _Mdouble_              _Mfloat_
  98 # define __MATH_PRECNAME(name,r) name##f##r
  99 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
 100 # define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
 101 # include <bits/mathcalls.h>
 102 # undef _Mdouble_
 103 # undef _Mdouble_BEGIN_NAMESPACE
 104 # undef _Mdouble_END_NAMESPACE
 105 # undef __MATH_PRECNAME
 106
 107 # if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
 108      || defined __LDBL_COMPAT \
 109      || defined _LIBC_TEST
 110 #  ifdef __LDBL_COMPAT
 111
 112 #   ifdef __USE_ISOC99
 113 extern float __nldbl_nexttowardf (float __x, long double __y)
 114                                   __THROW __attribute__ ((__const__));
 115 #    ifdef __REDIRECT_NTH
 116 extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
 117                              __nldbl_nexttowardf)
 118      __attribute__ ((__const__));
 119 extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
 120                               nextafter) __attribute__ ((__const__));
 121 extern long double __REDIRECT_NTH (nexttowardl,
 122                                    (long double __x, long double __y),
 123                                    nextafter) __attribute__ ((__const__));
 124 #    endif
 125 #   endif
 126
 127 #   undef __MATHDECL_1
 128 #   define __MATHDECL_2(type, function,suffix, args, alias) \
 129   extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
 130                              args, alias)
 131 #   define __MATHDECL_1(type, function,suffix, args) \
 132   __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
 133 #  endif
 134
 135 /* Include the file of declarations again, this time using `long double'
 136    instead of `double' and appending l to each function name.  */
 137
 138 #  ifndef _Mlong_double_
 139 #   define _Mlong_double_       long double
 140 #  endif
 141 #  define _Mdouble_             _Mlong_double_
 142 #  define __MATH_PRECNAME(name,r) name##l##r
 143 #  define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
 144 #  define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
 145 #  define __MATH_DECLARE_LDOUBLE   1
 146 #  include <bits/mathcalls.h>
 147 #  undef _Mdouble_
 148 #  undef _Mdouble_BEGIN_NAMESPACE
 149 #  undef _Mdouble_END_NAMESPACE
 150 #  undef __MATH_PRECNAME
 151
 152 # endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */
 153
 154 #endif  /* Use ISO C99.  */
 155 #undef  __MATHDECL_1
 156 #undef  __MATHDECL
 157 #undef  __MATHCALL
 158
 159
 160 #if defined __USE_MISC || defined __USE_XOPEN
 161 /* This variable is used by `gamma' and `lgamma'.  */
 162 extern int signgam;
 163 #endif
 164
 165
 166 /* ISO C99 defines some generic macros which work on any data type.  */
 167 #ifdef __USE_ISOC99
 168
 169 /* Get the architecture specific values describing the floating-point
 170    evaluation.  The following symbols will get defined:
 171
 172     float_t     floating-point type at least as wide as `float' used
 173                 to evaluate `float' expressions
 174     double_t    floating-point type at least as wide as `double' used
 175                 to evaluate `double' expressions
 176
 177     FLT_EVAL_METHOD
 178                 Defined to
 179                   0     if `float_t' is `float' and `double_t' is `double'
 180                   1     if `float_t' and `double_t' are `double'
 181                   2     if `float_t' and `double_t' are `long double'
 182                   else  `float_t' and `double_t' are unspecified
 183
 184     INFINITY    representation of the infinity value of type `float'
 185
 186     FP_FAST_FMA
 187     FP_FAST_FMAF
 188     FP_FAST_FMAL
 189                 If defined it indicates that the `fma' function
 190                 generally executes about as fast as a multiply and an add.
 191                 This macro is defined only iff the `fma' function is
 192                 implemented directly with a hardware multiply-add instructions.
 193
 194     FP_ILOGB0   Expands to a value returned by `ilogb (0.0)'.
 195     FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
 196
 197     DECIMAL_DIG Number of decimal digits supported by conversion between
 198                 decimal and all internal floating-point formats.
 199
 200 */
 201
 202 /* All floating-point numbers can be put in one of these categories.  */
 203 enum
 204   {
 205     FP_NAN =
 206 # define FP_NAN 0
 207       FP_NAN,
 208     FP_INFINITE =
 209 # define FP_INFINITE 1
 210       FP_INFINITE,
 211     FP_ZERO =
 212 # define FP_ZERO 2
 213       FP_ZERO,
 214     FP_SUBNORMAL =
 215 # define FP_SUBNORMAL 3
 216       FP_SUBNORMAL,
 217     FP_NORMAL =
 218 # define FP_NORMAL 4
 219       FP_NORMAL
 220   };
 221
 222 /* Return number of classification appropriate for X.  */
 223 # ifdef __NO_LONG_DOUBLE_MATH
 224 #  define fpclassify(x) \
 225      (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
 226 # else
 227 #  define fpclassify(x) \
 228      (sizeof (x) == sizeof (float)                                            \
 229       ? __fpclassifyf (x)                                                     \
 230       : sizeof (x) == sizeof (double)                                         \
 231       ? __fpclassify (x) : __fpclassifyl (x))
 232 # endif
 233
 234 /* Return nonzero value if sign of X is negative.  */
 235 # ifdef __NO_LONG_DOUBLE_MATH
 236 #  define signbit(x) \
 237      (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
 238 # else
 239 #  define signbit(x) \
 240      (sizeof (x) == sizeof (float)                                            \
 241       ? __signbitf (x)                                                        \
 242       : sizeof (x) == sizeof (double)                                         \
 243       ? __signbit (x) : __signbitl (x))
 244 # endif
 245
 246 /* Return nonzero value if X is not +-Inf or NaN.  */
 247 # ifdef __NO_LONG_DOUBLE_MATH
 248 #  define isfinite(x) \
 249      (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
 250 # else
 251 #  define isfinite(x) \
 252      (sizeof (x) == sizeof (float)                                            \
 253       ? __finitef (x)                                                         \
 254       : sizeof (x) == sizeof (double)                                         \
 255       ? __finite (x) : __finitel (x))
 256 # endif
 257
 258 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
 259 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
 260
 261 /* Return nonzero value if X is a NaN.  We could use `fpclassify' but
 262    we already have this functions `__isnan' and it is faster.  */
 263 # ifdef __NO_LONG_DOUBLE_MATH
 264 #  define isnan(x) \
 265      (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
 266 # else
 267 #  define isnan(x) \
 268      (sizeof (x) == sizeof (float)                                            \
 269       ? __isnanf (x)                                                          \
 270       : sizeof (x) == sizeof (double)                                         \
 271       ? __isnan (x) : __isnanl (x))
 272 # endif
 273
 274 /* Return nonzero value if X is positive or negative infinity.  */
 275 # ifdef __NO_LONG_DOUBLE_MATH
 276 #  define isinf(x) \
 277      (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
 278 # else
 279 #  define isinf(x) \
 280      (sizeof (x) == sizeof (float)                                            \
 281       ? __isinff (x)                                                          \
 282       : sizeof (x) == sizeof (double)                                         \
 283       ? __isinf (x) : __isinfl (x))
 284 # endif
 285
 286 /* Bitmasks for the math_errhandling macro.  */
 287 # define MATH_ERRNO     1       /* errno set by math functions.  */
 288 # define MATH_ERREXCEPT 2       /* Exceptions raised by math functions.  */
 289
 290 /* By default all functions support both errno and exception handling.
 291    In gcc's fast math mode and if inline functions are defined this
 292    might not be true.  */
 293 # ifndef __FAST_MATH__
 294 #  define math_errhandling      (MATH_ERRNO | MATH_ERREXCEPT)
 295 # endif
 296
 297 #endif /* Use ISO C99.  */
 298
 299 #ifdef __USE_GNU
 300 /* Return nonzero value if X is a signaling NaN.  */
 301 # ifdef __NO_LONG_DOUBLE_MATH
 302 #  define issignaling(x) \
 303      (sizeof (x) == sizeof (float) ? __issignalingf (x) : __issignaling (x))
 304 # else
 305 #  define issignaling(x) \
 306      (sizeof (x) == sizeof (float)                                            \
 307       ? __issignalingf (x)                                                    \
 308       : sizeof (x) == sizeof (double)                                         \
 309       ? __issignaling (x) : __issignalingl (x))
 310 # endif
 311 #endif /* Use GNU.  */
 312
 313 #ifdef  __USE_MISC
 314 /* Support for various different standard error handling behaviors.  */
 315 typedef enum
 316 {
 317   _IEEE_ = -1,  /* According to IEEE 754/IEEE 854.  */
 318   _SVID_,       /* According to System V, release 4.  */
 319   _XOPEN_,      /* Nowadays also Unix98.  */
 320   _POSIX_,
 321   _ISOC_        /* Actually this is ISO C99.  */
 322 } _LIB_VERSION_TYPE;
 323
 324 /* This variable can be changed at run-time to any of the values above to
 325    affect floating point error handling behavior (it may also be necessary
 326    to change the hardware FPU exception settings).  */
 327 extern _LIB_VERSION_TYPE _LIB_VERSION;
 328 #endif
 329
 330
 331 #ifdef __USE_MISC
 332 /* In SVID error handling, `matherr' is called with this description
 333    of the exceptional condition.
 334
 335    We have a problem when using C++ since `exception' is a reserved
 336    name in C++.  */
 337 # ifdef __cplusplus
 338 struct __exception
 339 # else
 340 struct exception
 341 # endif
 342   {
 343     int type;
 344     char *name;
 345     double arg1;
 346     double arg2;
 347     double retval;
 348   };
 349
 350 # ifdef __cplusplus
 351 extern int matherr (struct __exception *__exc) throw ();
 352 # else
 353 extern int matherr (struct exception *__exc);
 354 # endif
 355
 356 # define X_TLOSS        1.41484755040568800000e+16
 357
 358 /* Types of exceptions in the `type' field.  */
 359 # define DOMAIN         1
 360 # define SING           2
 361 # define OVERFLOW       3
 362 # define UNDERFLOW      4
 363 # define TLOSS          5
 364 # define PLOSS          6
 365
 366 /* SVID mode specifies returning this large value instead of infinity.  */
 367 # define HUGE           3.40282347e+38F
 368
 369 #else   /* !Misc.  */
 370
 371 # ifdef __USE_XOPEN
 372 /* X/Open wants another strange constant.  */
 373 #  define MAXFLOAT      3.40282347e+38F
 374 # endif
 375
 376 #endif  /* Misc.  */
 377
 378
 379 /* Some useful constants.  */
 380 #if defined __USE_MISC || defined __USE_XOPEN
 381 # define M_E            2.7182818284590452354   /* e */
 382 # define M_LOG2E        1.4426950408889634074   /* log_2 e */
 383 # define M_LOG10E       0.43429448190325182765  /* log_10 e */
 384 # define M_LN2          0.69314718055994530942  /* log_e 2 */
 385 # define M_LN10         2.30258509299404568402  /* log_e 10 */
 386 # define M_PI           3.14159265358979323846  /* pi */
 387 # define M_PI_2         1.57079632679489661923  /* pi/2 */
 388 # define M_PI_4         0.78539816339744830962  /* pi/4 */
 389 # define M_1_PI         0.31830988618379067154  /* 1/pi */
 390 # define M_2_PI         0.63661977236758134308  /* 2/pi */
 391 # define M_2_SQRTPI     1.12837916709551257390  /* 2/sqrt(pi) */
 392 # define M_SQRT2        1.41421356237309504880  /* sqrt(2) */
 393 # define M_SQRT1_2      0.70710678118654752440  /* 1/sqrt(2) */
 394 #endif
 395
 396 /* The above constants are not adequate for computation using `long double's.
 397    Therefore we provide as an extension constants with similar names as a
 398    GNU extension.  Provide enough digits for the 128-bit IEEE quad.  */
 399 #ifdef __USE_GNU
 400 # define M_El           2.718281828459045235360287471352662498L /* e */
 401 # define M_LOG2El       1.442695040888963407359924681001892137L /* log_2 e */
 402 # define M_LOG10El      0.434294481903251827651128918916605082L /* log_10 e */
 403 # define M_LN2l         0.693147180559945309417232121458176568L /* log_e 2 */
 404 # define M_LN10l        2.302585092994045684017991454684364208L /* log_e 10 */
 405 # define M_PIl          3.141592653589793238462643383279502884L /* pi */
 406 # define M_PI_2l        1.570796326794896619231321691639751442L /* pi/2 */
 407 # define M_PI_4l        0.785398163397448309615660845819875721L /* pi/4 */
 408 # define M_1_PIl        0.318309886183790671537767526745028724L /* 1/pi */
 409 # define M_2_PIl        0.636619772367581343075535053490057448L /* 2/pi */
 410 # define M_2_SQRTPIl    1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
 411 # define M_SQRT2l       1.414213562373095048801688724209698079L /* sqrt(2) */
 412 # define M_SQRT1_2l     0.707106781186547524400844362104849039L /* 1/sqrt(2) */
 413 #endif
 414
 415
 416 /* When compiling in strict ISO C compatible mode we must not use the
 417    inline functions since they, among other things, do not set the
 418    `errno' variable correctly.  */
 419 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
 420 # define __NO_MATH_INLINES      1
 421 #endif
 422
 423 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
 424 /* ISO C99 defines some macros to compare number while taking care for
 425    unordered numbers.  Many FPUs provide special instructions to support
 426    these operations.  Generic support in GCC for these as builtins went
 427    in before 3.0.0, but not all cpus added their patterns.  We define
 428    versions that use the builtins here, and <bits/mathinline.h> will
 429    undef/redefine as appropriate for the specific GCC version in use.  */
 430 # define isgreater(x, y)        __builtin_isgreater(x, y)
 431 # define isgreaterequal(x, y)   __builtin_isgreaterequal(x, y)
 432 # define isless(x, y)           __builtin_isless(x, y)
 433 # define islessequal(x, y)      __builtin_islessequal(x, y)
 434 # define islessgreater(x, y)    __builtin_islessgreater(x, y)
 435 # define isunordered(u, v)      __builtin_isunordered(u, v)
 436 #endif
 437
 438 /* Get machine-dependent inline versions (if there are any).  */
 439 #ifdef __USE_EXTERN_INLINES
 440 # include <bits/mathinline.h>
 441 #endif
 442
 443 /* Define special entry points to use when the compiler got told to
 444    only expect finite results.  */
 445 #if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0
 446 # include <bits/math-finite.h>
 447 #endif
 448
 449 #ifdef __USE_ISOC99
 450 /* If we've still got undefined comparison macros, provide defaults.  */
 451
 452 /* Return nonzero value if X is greater than Y.  */
 453 # ifndef isgreater
 454 #  define isgreater(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 greater than or equal to Y.  */
 461 # ifndef isgreaterequal
 462 #  define isgreaterequal(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 X is less than Y.  */
 469 # ifndef isless
 470 #  define isless(x, y) \
 471   (__extension__                                                              \
 472    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 473       !isunordered (__x, __y) && __x < __y; }))
 474 # endif
 475
 476 /* Return nonzero value if X is less than or equal to Y.  */
 477 # ifndef islessequal
 478 #  define islessequal(x, y) \
 479   (__extension__                                                              \
 480    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 481       !isunordered (__x, __y) && __x <= __y; }))
 482 # endif
 483
 484 /* Return nonzero value if either X is less than Y or Y is less than X.  */
 485 # ifndef islessgreater
 486 #  define islessgreater(x, y) \
 487   (__extension__                                                              \
 488    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 489       !isunordered (__x, __y) && (__x < __y || __y < __x); }))
 490 # endif
 491
 492 /* Return nonzero value if arguments are unordered.  */
 493 # ifndef isunordered
 494 #  define isunordered(u, v) \
 495   (__extension__                                                              \
 496    ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v);                       \
 497       fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
 498 # endif
 499
 500 #endif
 501
 502 __END_DECLS
 503
 504
 505 #endif /* math.h  */