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 __MATH_DECLARING_DOUBLE  1
  81 #define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
  82 #define _Mdouble_END_NAMESPACE   __END_NAMESPACE_STD
  83 #include <bits/mathcalls.h>
  84 #undef  _Mdouble_
  85 #undef _Mdouble_BEGIN_NAMESPACE
  86 #undef _Mdouble_END_NAMESPACE
  87 #undef  __MATH_PRECNAME
  88 #undef __MATH_DECLARING_DOUBLE
  89
  90 #ifdef __USE_ISOC99
  91
  92
  93 /* Include the file of declarations again, this time using `float'
  94    instead of `double' and appending f to each function name.  */
  95
  96 # ifndef _Mfloat_
  97 #  define _Mfloat_              float
  98 # endif
  99 # define _Mdouble_              _Mfloat_
 100 # define __MATH_PRECNAME(name,r) name##f##r
 101 # define __MATH_DECLARING_DOUBLE  0
 102 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
 103 # define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
 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_DECLARING_DOUBLE
 110
 111 # if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
 112      || defined __LDBL_COMPAT \
 113      || defined _LIBC_TEST
 114 #  ifdef __LDBL_COMPAT
 115
 116 #   ifdef __USE_ISOC99
 117 extern float __nldbl_nexttowardf (float __x, long double __y)
 118                                   __THROW __attribute__ ((__const__));
 119 #    ifdef __REDIRECT_NTH
 120 extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
 121                              __nldbl_nexttowardf)
 122      __attribute__ ((__const__));
 123 extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
 124                               nextafter) __attribute__ ((__const__));
 125 extern long double __REDIRECT_NTH (nexttowardl,
 126                                    (long double __x, long double __y),
 127                                    nextafter) __attribute__ ((__const__));
 128 #    endif
 129 #   endif
 130
 131 #   undef __MATHDECL_1
 132 #   define __MATHDECL_2(type, function,suffix, args, alias) \
 133   extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
 134                              args, alias)
 135 #   define __MATHDECL_1(type, function,suffix, args) \
 136   __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
 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 #  ifndef _Mlong_double_
 143 #   define _Mlong_double_       long double
 144 #  endif
 145 #  define _Mdouble_             _Mlong_double_
 146 #  define __MATH_PRECNAME(name,r) name##l##r
 147 #  define __MATH_DECLARING_DOUBLE  0
 148 #  define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
 149 #  define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
 150 #  define __MATH_DECLARE_LDOUBLE   1
 151 #  include <bits/mathcalls.h>
 152 #  undef _Mdouble_
 153 #  undef _Mdouble_BEGIN_NAMESPACE
 154 #  undef _Mdouble_END_NAMESPACE
 155 #  undef __MATH_PRECNAME
 156 #  undef __MATH_DECLARING_DOUBLE
 157
 158 # endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */
 159
 160 #endif  /* Use ISO C99.  */
 161 #undef  __MATHDECL_1
 162 #undef  __MATHDECL
 163 #undef  __MATHCALL
 164
 165
 166 #if defined __USE_MISC || defined __USE_XOPEN
 167 /* This variable is used by `gamma' and `lgamma'.  */
 168 extern int signgam;
 169 #endif
 170
 171
 172 /* ISO C99 defines some generic macros which work on any data type.  */
 173 #ifdef __USE_ISOC99
 174
 175 /* Get the architecture specific values describing the floating-point
 176    evaluation.  The following symbols will get defined:
 177
 178     float_t     floating-point type at least as wide as `float' used
 179                 to evaluate `float' expressions
 180     double_t    floating-point type at least as wide as `double' used
 181                 to evaluate `double' expressions
 182
 183     FLT_EVAL_METHOD
 184                 Defined to
 185                   0     if `float_t' is `float' and `double_t' is `double'
 186                   1     if `float_t' and `double_t' are `double'
 187                   2     if `float_t' and `double_t' are `long double'
 188                   else  `float_t' and `double_t' are unspecified
 189
 190     INFINITY    representation of the infinity value of type `float'
 191
 192     FP_FAST_FMA
 193     FP_FAST_FMAF
 194     FP_FAST_FMAL
 195                 If defined it indicates that the `fma' function
 196                 generally executes about as fast as a multiply and an add.
 197                 This macro is defined only iff the `fma' function is
 198                 implemented directly with a hardware multiply-add instructions.
 199
 200     FP_ILOGB0   Expands to a value returned by `ilogb (0.0)'.
 201     FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
 202
 203     DECIMAL_DIG Number of decimal digits supported by conversion between
 204                 decimal and all internal floating-point formats.
 205
 206 */
 207
 208 /* All floating-point numbers can be put in one of these categories.  */
 209 enum
 210   {
 211     FP_NAN =
 212 # define FP_NAN 0
 213       FP_NAN,
 214     FP_INFINITE =
 215 # define FP_INFINITE 1
 216       FP_INFINITE,
 217     FP_ZERO =
 218 # define FP_ZERO 2
 219       FP_ZERO,
 220     FP_SUBNORMAL =
 221 # define FP_SUBNORMAL 3
 222       FP_SUBNORMAL,
 223     FP_NORMAL =
 224 # define FP_NORMAL 4
 225       FP_NORMAL
 226   };
 227
 228 /* Return number of classification appropriate for X.  */
 229 # ifdef __NO_LONG_DOUBLE_MATH
 230 #  define fpclassify(x) \
 231      (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
 232 # else
 233 #  define fpclassify(x) \
 234      (sizeof (x) == sizeof (float)                                            \
 235       ? __fpclassifyf (x)                                                     \
 236       : sizeof (x) == sizeof (double)                                         \
 237       ? __fpclassify (x) : __fpclassifyl (x))
 238 # endif
 239
 240 /* Return nonzero value if sign of X is negative.  */
 241 # ifdef __NO_LONG_DOUBLE_MATH
 242 #  define signbit(x) \
 243      (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
 244 # else
 245 #  define signbit(x) \
 246      (sizeof (x) == sizeof (float)                                            \
 247       ? __signbitf (x)                                                        \
 248       : sizeof (x) == sizeof (double)                                         \
 249       ? __signbit (x) : __signbitl (x))
 250 # endif
 251
 252 /* Return nonzero value if X is not +-Inf or NaN.  */
 253 # ifdef __NO_LONG_DOUBLE_MATH
 254 #  define isfinite(x) \
 255      (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
 256 # else
 257 #  define isfinite(x) \
 258      (sizeof (x) == sizeof (float)                                            \
 259       ? __finitef (x)                                                         \
 260       : sizeof (x) == sizeof (double)                                         \
 261       ? __finite (x) : __finitel (x))
 262 # endif
 263
 264 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
 265 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
 266
 267 /* Return nonzero value if X is a NaN.  We could use `fpclassify' but
 268    we already have this functions `__isnan' and it is faster.  */
 269 # ifdef __NO_LONG_DOUBLE_MATH
 270 #  define isnan(x) \
 271      (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
 272 # else
 273 #  define isnan(x) \
 274      (sizeof (x) == sizeof (float)                                            \
 275       ? __isnanf (x)                                                          \
 276       : sizeof (x) == sizeof (double)                                         \
 277       ? __isnan (x) : __isnanl (x))
 278 # endif
 279
 280 /* Return nonzero value if X is positive or negative infinity.  */
 281 # ifdef __NO_LONG_DOUBLE_MATH
 282 #  define isinf(x) \
 283      (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
 284 # else
 285 #  define isinf(x) \
 286      (sizeof (x) == sizeof (float)                                            \
 287       ? __isinff (x)                                                          \
 288       : sizeof (x) == sizeof (double)                                         \
 289       ? __isinf (x) : __isinfl (x))
 290 # endif
 291
 292 /* Bitmasks for the math_errhandling macro.  */
 293 # define MATH_ERRNO     1       /* errno set by math functions.  */
 294 # define MATH_ERREXCEPT 2       /* Exceptions raised by math functions.  */
 295
 296 /* By default all functions support both errno and exception handling.
 297    In gcc's fast math mode and if inline functions are defined this
 298    might not be true.  */
 299 # ifndef __FAST_MATH__
 300 #  define math_errhandling      (MATH_ERRNO | MATH_ERREXCEPT)
 301 # endif
 302
 303 #endif /* Use ISO C99.  */
 304
 305 #ifdef __USE_GNU
 306 /* Return nonzero value if X is a signaling NaN.  */
 307 # ifdef __NO_LONG_DOUBLE_MATH
 308 #  define issignaling(x) \
 309      (sizeof (x) == sizeof (float) ? __issignalingf (x) : __issignaling (x))
 310 # else
 311 #  define issignaling(x) \
 312      (sizeof (x) == sizeof (float)                                            \
 313       ? __issignalingf (x)                                                    \
 314       : sizeof (x) == sizeof (double)                                         \
 315       ? __issignaling (x) : __issignalingl (x))
 316 # endif
 317 #endif /* Use GNU.  */
 318
 319 #ifdef  __USE_MISC
 320 /* Support for various different standard error handling behaviors.  */
 321 typedef enum
 322 {
 323   _IEEE_ = -1,  /* According to IEEE 754/IEEE 854.  */
 324   _SVID_,       /* According to System V, release 4.  */
 325   _XOPEN_,      /* Nowadays also Unix98.  */
 326   _POSIX_,
 327   _ISOC_        /* Actually this is ISO C99.  */
 328 } _LIB_VERSION_TYPE;
 329
 330 /* This variable can be changed at run-time to any of the values above to
 331    affect floating point error handling behavior (it may also be necessary
 332    to change the hardware FPU exception settings).  */
 333 extern _LIB_VERSION_TYPE _LIB_VERSION;
 334 #endif
 335
 336
 337 #ifdef __USE_MISC
 338 /* In SVID error handling, `matherr' is called with this description
 339    of the exceptional condition.
 340
 341    We have a problem when using C++ since `exception' is a reserved
 342    name in C++.  */
 343 # ifdef __cplusplus
 344 struct __exception
 345 # else
 346 struct exception
 347 # endif
 348   {
 349     int type;
 350     char *name;
 351     double arg1;
 352     double arg2;
 353     double retval;
 354   };
 355
 356 # ifdef __cplusplus
 357 extern int matherr (struct __exception *__exc) throw ();
 358 # else
 359 extern int matherr (struct exception *__exc);
 360 # endif
 361
 362 # define X_TLOSS        1.41484755040568800000e+16
 363
 364 /* Types of exceptions in the `type' field.  */
 365 # define DOMAIN         1
 366 # define SING           2
 367 # define OVERFLOW       3
 368 # define UNDERFLOW      4
 369 # define TLOSS          5
 370 # define PLOSS          6
 371
 372 /* SVID mode specifies returning this large value instead of infinity.  */
 373 # define HUGE           3.40282347e+38F
 374
 375 #else   /* !Misc.  */
 376
 377 # ifdef __USE_XOPEN
 378 /* X/Open wants another strange constant.  */
 379 #  define MAXFLOAT      3.40282347e+38F
 380 # endif
 381
 382 #endif  /* Misc.  */
 383
 384
 385 /* Some useful constants.  */
 386 #if defined __USE_MISC || defined __USE_XOPEN
 387 # define M_E            2.7182818284590452354   /* e */
 388 # define M_LOG2E        1.4426950408889634074   /* log_2 e */
 389 # define M_LOG10E       0.43429448190325182765  /* log_10 e */
 390 # define M_LN2          0.69314718055994530942  /* log_e 2 */
 391 # define M_LN10         2.30258509299404568402  /* log_e 10 */
 392 # define M_PI           3.14159265358979323846  /* pi */
 393 # define M_PI_2         1.57079632679489661923  /* pi/2 */
 394 # define M_PI_4         0.78539816339744830962  /* pi/4 */
 395 # define M_1_PI         0.31830988618379067154  /* 1/pi */
 396 # define M_2_PI         0.63661977236758134308  /* 2/pi */
 397 # define M_2_SQRTPI     1.12837916709551257390  /* 2/sqrt(pi) */
 398 # define M_SQRT2        1.41421356237309504880  /* sqrt(2) */
 399 # define M_SQRT1_2      0.70710678118654752440  /* 1/sqrt(2) */
 400 #endif
 401
 402 /* The above constants are not adequate for computation using `long double's.
 403    Therefore we provide as an extension constants with similar names as a
 404    GNU extension.  Provide enough digits for the 128-bit IEEE quad.  */
 405 #ifdef __USE_GNU
 406 # define M_El           2.718281828459045235360287471352662498L /* e */
 407 # define M_LOG2El       1.442695040888963407359924681001892137L /* log_2 e */
 408 # define M_LOG10El      0.434294481903251827651128918916605082L /* log_10 e */
 409 # define M_LN2l         0.693147180559945309417232121458176568L /* log_e 2 */
 410 # define M_LN10l        2.302585092994045684017991454684364208L /* log_e 10 */
 411 # define M_PIl          3.141592653589793238462643383279502884L /* pi */
 412 # define M_PI_2l        1.570796326794896619231321691639751442L /* pi/2 */
 413 # define M_PI_4l        0.785398163397448309615660845819875721L /* pi/4 */
 414 # define M_1_PIl        0.318309886183790671537767526745028724L /* 1/pi */
 415 # define M_2_PIl        0.636619772367581343075535053490057448L /* 2/pi */
 416 # define M_2_SQRTPIl    1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
 417 # define M_SQRT2l       1.414213562373095048801688724209698079L /* sqrt(2) */
 418 # define M_SQRT1_2l     0.707106781186547524400844362104849039L /* 1/sqrt(2) */
 419 #endif
 420
 421
 422 /* When compiling in strict ISO C compatible mode we must not use the
 423    inline functions since they, among other things, do not set the
 424    `errno' variable correctly.  */
 425 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
 426 # define __NO_MATH_INLINES      1
 427 #endif
 428
 429 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
 430 /* ISO C99 defines some macros to compare number while taking care for
 431    unordered numbers.  Many FPUs provide special instructions to support
 432    these operations.  Generic support in GCC for these as builtins went
 433    in before 3.0.0, but not all cpus added their patterns.  We define
 434    versions that use the builtins here, and <bits/mathinline.h> will
 435    undef/redefine as appropriate for the specific GCC version in use.  */
 436 # define isgreater(x, y)        __builtin_isgreater(x, y)
 437 # define isgreaterequal(x, y)   __builtin_isgreaterequal(x, y)
 438 # define isless(x, y)           __builtin_isless(x, y)
 439 # define islessequal(x, y)      __builtin_islessequal(x, y)
 440 # define islessgreater(x, y)    __builtin_islessgreater(x, y)
 441 # define isunordered(u, v)      __builtin_isunordered(u, v)
 442 #endif
 443
 444 /* Get machine-dependent inline versions (if there are any).  */
 445 #ifdef __USE_EXTERN_INLINES
 446 # include <bits/mathinline.h>
 447 #endif
 448
 449 /* Define special entry points to use when the compiler got told to
 450    only expect finite results.  */
 451 #if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0
 452 # include <bits/math-finite.h>
 453 #endif
 454
 455 #ifdef __USE_ISOC99
 456 /* If we've still got undefined comparison macros, provide defaults.  */
 457
 458 /* Return nonzero value if X is greater than Y.  */
 459 # ifndef isgreater
 460 #  define isgreater(x, y) \
 461   (__extension__                                                              \
 462    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 463       !isunordered (__x, __y) && __x > __y; }))
 464 # endif
 465
 466 /* Return nonzero value if X is greater than or equal to Y.  */
 467 # ifndef isgreaterequal
 468 #  define isgreaterequal(x, y) \
 469   (__extension__                                                              \
 470    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 471       !isunordered (__x, __y) && __x >= __y; }))
 472 # endif
 473
 474 /* Return nonzero value if X is less than Y.  */
 475 # ifndef isless
 476 #  define isless(x, y) \
 477   (__extension__                                                              \
 478    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 479       !isunordered (__x, __y) && __x < __y; }))
 480 # endif
 481
 482 /* Return nonzero value if X is less than or equal to Y.  */
 483 # ifndef islessequal
 484 #  define islessequal(x, y) \
 485   (__extension__                                                              \
 486    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 487       !isunordered (__x, __y) && __x <= __y; }))
 488 # endif
 489
 490 /* Return nonzero value if either X is less than Y or Y is less than X.  */
 491 # ifndef islessgreater
 492 #  define islessgreater(x, y) \
 493   (__extension__                                                              \
 494    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 495       !isunordered (__x, __y) && (__x < __y || __y < __x); }))
 496 # endif
 497
 498 /* Return nonzero value if arguments are unordered.  */
 499 # ifndef isunordered
 500 #  define isunordered(u, v) \
 501   (__extension__                                                              \
 502    ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v);                       \
 503       fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
 504 # endif
 505
 506 #endif
 507
 508 __END_DECLS
 509
 510
 511 #endif /* math.h  */