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 __MATHCALL(function,suffix, args)       \
  62   __MATHDECL (_Mdouble_,function,suffix, args)
  63 #define __MATHDECL(type, function,suffix, args) \
  64   __MATHDECL_1(type, function,suffix, args); \
  65   __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
  66 #define __MATHCALLX(function,suffix, args, attrib)      \
  67   __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
  68 #define __MATHDECLX(type, function,suffix, args, attrib) \
  69   __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
  70   __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
  71 #define __MATHDECL_1(type, function,suffix, args) \
  72   extern type __MATH_PRECNAME(function,suffix) args __THROW
  73
  74 #define _Mdouble_               double
  75 #define __MATH_PRECNAME(name,r) __CONCAT(name,r)
  76 #define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
  77 #define _Mdouble_END_NAMESPACE   __END_NAMESPACE_STD
  78 #include <bits/mathcalls.h>
  79 #undef  _Mdouble_
  80 #undef _Mdouble_BEGIN_NAMESPACE
  81 #undef _Mdouble_END_NAMESPACE
  82 #undef  __MATH_PRECNAME
  83
  84 #ifdef __USE_ISOC99
  85
  86
  87 /* Include the file of declarations again, this time using `float'
  88    instead of `double' and appending f to each function name.  */
  89
  90 # ifndef _Mfloat_
  91 #  define _Mfloat_              float
  92 # endif
  93 # define _Mdouble_              _Mfloat_
  94 # define __MATH_PRECNAME(name,r) name##f##r
  95 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
  96 # define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
  97 # include <bits/mathcalls.h>
  98 # undef _Mdouble_
  99 # undef _Mdouble_BEGIN_NAMESPACE
 100 # undef _Mdouble_END_NAMESPACE
 101 # undef __MATH_PRECNAME
 102
 103 # if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
 104      || defined __LDBL_COMPAT \
 105      || defined _LIBC_TEST
 106 #  ifdef __LDBL_COMPAT
 107
 108 #   ifdef __USE_ISOC99
 109 extern float __nldbl_nexttowardf (float __x, long double __y)
 110                                   __THROW __attribute__ ((__const__));
 111 #    ifdef __REDIRECT_NTH
 112 extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
 113                              __nldbl_nexttowardf)
 114      __attribute__ ((__const__));
 115 extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
 116                               nextafter) __attribute__ ((__const__));
 117 extern long double __REDIRECT_NTH (nexttowardl,
 118                                    (long double __x, long double __y),
 119                                    nextafter) __attribute__ ((__const__));
 120 #    endif
 121 #   endif
 122
 123 #   undef __MATHDECL_1
 124 #   define __MATHDECL_2(type, function,suffix, args, alias) \
 125   extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
 126                              args, alias)
 127 #   define __MATHDECL_1(type, function,suffix, args) \
 128   __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
 129 #  endif
 130
 131 /* Include the file of declarations again, this time using `long double'
 132    instead of `double' and appending l to each function name.  */
 133
 134 #  ifndef _Mlong_double_
 135 #   define _Mlong_double_       long double
 136 #  endif
 137 #  define _Mdouble_             _Mlong_double_
 138 #  define __MATH_PRECNAME(name,r) name##l##r
 139 #  define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
 140 #  define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
 141 #  define __MATH_DECLARE_LDOUBLE   1
 142 #  include <bits/mathcalls.h>
 143 #  undef _Mdouble_
 144 #  undef _Mdouble_BEGIN_NAMESPACE
 145 #  undef _Mdouble_END_NAMESPACE
 146 #  undef __MATH_PRECNAME
 147
 148 # endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */
 149
 150 #endif  /* Use ISO C99.  */
 151 #undef  __MATHDECL_1
 152 #undef  __MATHDECL
 153 #undef  __MATHCALL
 154
 155
 156 #if defined __USE_MISC || defined __USE_XOPEN
 157 /* This variable is used by `gamma' and `lgamma'.  */
 158 extern int signgam;
 159 #endif
 160
 161
 162 /* ISO C99 defines some generic macros which work on any data type.  */
 163 #ifdef __USE_ISOC99
 164
 165 /* Get the architecture specific values describing the floating-point
 166    evaluation.  The following symbols will get defined:
 167
 168     float_t     floating-point type at least as wide as `float' used
 169                 to evaluate `float' expressions
 170     double_t    floating-point type at least as wide as `double' used
 171                 to evaluate `double' expressions
 172
 173     FLT_EVAL_METHOD
 174                 Defined to
 175                   0     if `float_t' is `float' and `double_t' is `double'
 176                   1     if `float_t' and `double_t' are `double'
 177                   2     if `float_t' and `double_t' are `long double'
 178                   else  `float_t' and `double_t' are unspecified
 179
 180     INFINITY    representation of the infinity value of type `float'
 181
 182     FP_FAST_FMA
 183     FP_FAST_FMAF
 184     FP_FAST_FMAL
 185                 If defined it indicates that the `fma' function
 186                 generally executes about as fast as a multiply and an add.
 187                 This macro is defined only iff the `fma' function is
 188                 implemented directly with a hardware multiply-add instructions.
 189
 190     FP_ILOGB0   Expands to a value returned by `ilogb (0.0)'.
 191     FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
 192
 193     DECIMAL_DIG Number of decimal digits supported by conversion between
 194                 decimal and all internal floating-point formats.
 195
 196 */
 197
 198 /* All floating-point numbers can be put in one of these categories.  */
 199 enum
 200   {
 201     FP_NAN =
 202 # define FP_NAN 0
 203       FP_NAN,
 204     FP_INFINITE =
 205 # define FP_INFINITE 1
 206       FP_INFINITE,
 207     FP_ZERO =
 208 # define FP_ZERO 2
 209       FP_ZERO,
 210     FP_SUBNORMAL =
 211 # define FP_SUBNORMAL 3
 212       FP_SUBNORMAL,
 213     FP_NORMAL =
 214 # define FP_NORMAL 4
 215       FP_NORMAL
 216   };
 217
 218 /* Return number of classification appropriate for X.  */
 219 # ifdef __NO_LONG_DOUBLE_MATH
 220 #  define fpclassify(x) \
 221      (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
 222 # else
 223 #  define fpclassify(x) \
 224      (sizeof (x) == sizeof (float)                                            \
 225       ? __fpclassifyf (x)                                                     \
 226       : sizeof (x) == sizeof (double)                                         \
 227       ? __fpclassify (x) : __fpclassifyl (x))
 228 # endif
 229
 230 /* Return nonzero value if sign of X is negative.  */
 231 # ifdef __NO_LONG_DOUBLE_MATH
 232 #  define signbit(x) \
 233      (sizeof (x) == sizeof (float) ? __signbitf (x) : __signbit (x))
 234 # else
 235 #  define signbit(x) \
 236      (sizeof (x) == sizeof (float)                                            \
 237       ? __signbitf (x)                                                        \
 238       : sizeof (x) == sizeof (double)                                         \
 239       ? __signbit (x) : __signbitl (x))
 240 # endif
 241
 242 /* Return nonzero value if X is not +-Inf or NaN.  */
 243 # ifdef __NO_LONG_DOUBLE_MATH
 244 #  define isfinite(x) \
 245      (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
 246 # else
 247 #  define isfinite(x) \
 248      (sizeof (x) == sizeof (float)                                            \
 249       ? __finitef (x)                                                         \
 250       : sizeof (x) == sizeof (double)                                         \
 251       ? __finite (x) : __finitel (x))
 252 # endif
 253
 254 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
 255 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
 256
 257 /* Return nonzero value if X is a NaN.  We could use `fpclassify' but
 258    we already have this functions `__isnan' and it is faster.  */
 259 # ifdef __NO_LONG_DOUBLE_MATH
 260 #  define isnan(x) \
 261      (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
 262 # else
 263 #  define isnan(x) \
 264      (sizeof (x) == sizeof (float)                                            \
 265       ? __isnanf (x)                                                          \
 266       : sizeof (x) == sizeof (double)                                         \
 267       ? __isnan (x) : __isnanl (x))
 268 # endif
 269
 270 /* Return nonzero value if X is positive or negative infinity.  */
 271 # ifdef __NO_LONG_DOUBLE_MATH
 272 #  define isinf(x) \
 273      (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
 274 # else
 275 #  define isinf(x) \
 276      (sizeof (x) == sizeof (float)                                            \
 277       ? __isinff (x)                                                          \
 278       : sizeof (x) == sizeof (double)                                         \
 279       ? __isinf (x) : __isinfl (x))
 280 # endif
 281
 282 /* Bitmasks for the math_errhandling macro.  */
 283 # define MATH_ERRNO     1       /* errno set by math functions.  */
 284 # define MATH_ERREXCEPT 2       /* Exceptions raised by math functions.  */
 285
 286 /* By default all functions support both errno and exception handling.
 287    In gcc's fast math mode and if inline functions are defined this
 288    might not be true.  */
 289 # ifndef __FAST_MATH__
 290 #  define math_errhandling      (MATH_ERRNO | MATH_ERREXCEPT)
 291 # endif
 292
 293 #endif /* Use ISO C99.  */
 294
 295 #ifdef __USE_GNU
 296 /* Return nonzero value if X is a signaling NaN.  */
 297 # ifdef __NO_LONG_DOUBLE_MATH
 298 #  define issignaling(x) \
 299      (sizeof (x) == sizeof (float) ? __issignalingf (x) : __issignaling (x))
 300 # else
 301 #  define issignaling(x) \
 302      (sizeof (x) == sizeof (float)                                            \
 303       ? __issignalingf (x)                                                    \
 304       : sizeof (x) == sizeof (double)                                         \
 305       ? __issignaling (x) : __issignalingl (x))
 306 # endif
 307 #endif /* Use GNU.  */
 308
 309 #ifdef  __USE_MISC
 310 /* Support for various different standard error handling behaviors.  */
 311 typedef enum
 312 {
 313   _IEEE_ = -1,  /* According to IEEE 754/IEEE 854.  */
 314   _SVID_,       /* According to System V, release 4.  */
 315   _XOPEN_,      /* Nowadays also Unix98.  */
 316   _POSIX_,
 317   _ISOC_        /* Actually this is ISO C99.  */
 318 } _LIB_VERSION_TYPE;
 319
 320 /* This variable can be changed at run-time to any of the values above to
 321    affect floating point error handling behavior (it may also be necessary
 322    to change the hardware FPU exception settings).  */
 323 extern _LIB_VERSION_TYPE _LIB_VERSION;
 324 #endif
 325
 326
 327 #ifdef __USE_MISC
 328 /* In SVID error handling, `matherr' is called with this description
 329    of the exceptional condition.
 330
 331    We have a problem when using C++ since `exception' is a reserved
 332    name in C++.  */
 333 # ifdef __cplusplus
 334 struct __exception
 335 # else
 336 struct exception
 337 # endif
 338   {
 339     int type;
 340     char *name;
 341     double arg1;
 342     double arg2;
 343     double retval;
 344   };
 345
 346 # ifdef __cplusplus
 347 extern int matherr (struct __exception *__exc) throw ();
 348 # else
 349 extern int matherr (struct exception *__exc);
 350 # endif
 351
 352 # define X_TLOSS        1.41484755040568800000e+16
 353
 354 /* Types of exceptions in the `type' field.  */
 355 # define DOMAIN         1
 356 # define SING           2
 357 # define OVERFLOW       3
 358 # define UNDERFLOW      4
 359 # define TLOSS          5
 360 # define PLOSS          6
 361
 362 /* SVID mode specifies returning this large value instead of infinity.  */
 363 # define HUGE           3.40282347e+38F
 364
 365 #else   /* !Misc.  */
 366
 367 # ifdef __USE_XOPEN
 368 /* X/Open wants another strange constant.  */
 369 #  define MAXFLOAT      3.40282347e+38F
 370 # endif
 371
 372 #endif  /* Misc.  */
 373
 374
 375 /* Some useful constants.  */
 376 #if defined __USE_MISC || defined __USE_XOPEN
 377 # define M_E            2.7182818284590452354   /* e */
 378 # define M_LOG2E        1.4426950408889634074   /* log_2 e */
 379 # define M_LOG10E       0.43429448190325182765  /* log_10 e */
 380 # define M_LN2          0.69314718055994530942  /* log_e 2 */
 381 # define M_LN10         2.30258509299404568402  /* log_e 10 */
 382 # define M_PI           3.14159265358979323846  /* pi */
 383 # define M_PI_2         1.57079632679489661923  /* pi/2 */
 384 # define M_PI_4         0.78539816339744830962  /* pi/4 */
 385 # define M_1_PI         0.31830988618379067154  /* 1/pi */
 386 # define M_2_PI         0.63661977236758134308  /* 2/pi */
 387 # define M_2_SQRTPI     1.12837916709551257390  /* 2/sqrt(pi) */
 388 # define M_SQRT2        1.41421356237309504880  /* sqrt(2) */
 389 # define M_SQRT1_2      0.70710678118654752440  /* 1/sqrt(2) */
 390 #endif
 391
 392 /* The above constants are not adequate for computation using `long double's.
 393    Therefore we provide as an extension constants with similar names as a
 394    GNU extension.  Provide enough digits for the 128-bit IEEE quad.  */
 395 #ifdef __USE_GNU
 396 # define M_El           2.718281828459045235360287471352662498L /* e */
 397 # define M_LOG2El       1.442695040888963407359924681001892137L /* log_2 e */
 398 # define M_LOG10El      0.434294481903251827651128918916605082L /* log_10 e */
 399 # define M_LN2l         0.693147180559945309417232121458176568L /* log_e 2 */
 400 # define M_LN10l        2.302585092994045684017991454684364208L /* log_e 10 */
 401 # define M_PIl          3.141592653589793238462643383279502884L /* pi */
 402 # define M_PI_2l        1.570796326794896619231321691639751442L /* pi/2 */
 403 # define M_PI_4l        0.785398163397448309615660845819875721L /* pi/4 */
 404 # define M_1_PIl        0.318309886183790671537767526745028724L /* 1/pi */
 405 # define M_2_PIl        0.636619772367581343075535053490057448L /* 2/pi */
 406 # define M_2_SQRTPIl    1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
 407 # define M_SQRT2l       1.414213562373095048801688724209698079L /* sqrt(2) */
 408 # define M_SQRT1_2l     0.707106781186547524400844362104849039L /* 1/sqrt(2) */
 409 #endif
 410
 411
 412 /* When compiling in strict ISO C compatible mode we must not use the
 413    inline functions since they, among other things, do not set the
 414    `errno' variable correctly.  */
 415 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
 416 # define __NO_MATH_INLINES      1
 417 #endif
 418
 419 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
 420 /* ISO C99 defines some macros to compare number while taking care for
 421    unordered numbers.  Many FPUs provide special instructions to support
 422    these operations.  Generic support in GCC for these as builtins went
 423    in before 3.0.0, but not all cpus added their patterns.  We define
 424    versions that use the builtins here, and <bits/mathinline.h> will
 425    undef/redefine as appropriate for the specific GCC version in use.  */
 426 # define isgreater(x, y)        __builtin_isgreater(x, y)
 427 # define isgreaterequal(x, y)   __builtin_isgreaterequal(x, y)
 428 # define isless(x, y)           __builtin_isless(x, y)
 429 # define islessequal(x, y)      __builtin_islessequal(x, y)
 430 # define islessgreater(x, y)    __builtin_islessgreater(x, y)
 431 # define isunordered(u, v)      __builtin_isunordered(u, v)
 432 #endif
 433
 434 /* Get machine-dependent inline versions (if there are any).  */
 435 #ifdef __USE_EXTERN_INLINES
 436 # include <bits/mathinline.h>
 437 #endif
 438
 439 /* Define special entry points to use when the compiler got told to
 440    only expect finite results.  */
 441 #if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0
 442 # include <bits/math-finite.h>
 443 #endif
 444
 445 #ifdef __USE_ISOC99
 446 /* If we've still got undefined comparison macros, provide defaults.  */
 447
 448 /* Return nonzero value if X is greater than Y.  */
 449 # ifndef isgreater
 450 #  define isgreater(x, y) \
 451   (__extension__                                                              \
 452    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 453       !isunordered (__x, __y) && __x > __y; }))
 454 # endif
 455
 456 /* Return nonzero value if X is greater than or equal to Y.  */
 457 # ifndef isgreaterequal
 458 #  define isgreaterequal(x, y) \
 459   (__extension__                                                              \
 460    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 461       !isunordered (__x, __y) && __x >= __y; }))
 462 # endif
 463
 464 /* Return nonzero value if X is less than Y.  */
 465 # ifndef isless
 466 #  define isless(x, y) \
 467   (__extension__                                                              \
 468    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 469       !isunordered (__x, __y) && __x < __y; }))
 470 # endif
 471
 472 /* Return nonzero value if X is less than or equal to Y.  */
 473 # ifndef islessequal
 474 #  define islessequal(x, y) \
 475   (__extension__                                                              \
 476    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 477       !isunordered (__x, __y) && __x <= __y; }))
 478 # endif
 479
 480 /* Return nonzero value if either X is less than Y or Y is less than X.  */
 481 # ifndef islessgreater
 482 #  define islessgreater(x, y) \
 483   (__extension__                                                              \
 484    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 485       !isunordered (__x, __y) && (__x < __y || __y < __x); }))
 486 # endif
 487
 488 /* Return nonzero value if arguments are unordered.  */
 489 # ifndef isunordered
 490 #  define isunordered(u, v) \
 491   (__extension__                                                              \
 492    ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v);                       \
 493       fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
 494 # endif
 495
 496 #endif
 497
 498 __END_DECLS
 499
 500
 501 #endif /* math.h  */