math/math.h

   1 /* Declarations for math functions.
   2    Copyright (C) 1991-2017 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 #define __GLIBC_INTERNAL_STARTING_HEADER_IMPLEMENTATION
  27 #include <bits/libc-header-start.h>
  28
  29 __BEGIN_DECLS
  30
  31 /* Get definitions of __intmax_t and __uintmax_t.  */
  32 #include <bits/types.h>
  33
  34 /* Get machine-dependent vector math functions declarations.  */
  35 #include <bits/math-vector.h>
  36
  37 /* Get machine-dependent HUGE_VAL value (returned on overflow).
  38    On all IEEE754 machines, this is +Infinity.  */
  39 #include <bits/huge_val.h>
  40 #ifdef __USE_ISOC99
  41 # include <bits/huge_valf.h>
  42 # include <bits/huge_vall.h>
  43
  44 /* Get machine-dependent INFINITY value.  */
  45 # include <bits/inf.h>
  46
  47 /* Get machine-dependent NAN value (returned for some domain errors).  */
  48 # include <bits/nan.h>
  49 #endif /* __USE_ISOC99 */
  50
  51 #if __GLIBC_USE (IEC_60559_BFP_EXT)
  52 /* Signaling NaN macros, if supported.  */
  53 # if __GNUC_PREREQ (3, 3)
  54 #  define SNANF (__builtin_nansf (""))
  55 #  define SNAN (__builtin_nans (""))
  56 #  define SNANL (__builtin_nansl (""))
  57 # endif
  58 #endif
  59
  60 /* Get __GLIBC_FLT_EVAL_METHOD.  */
  61 #include <bits/flt-eval-method.h>
  62
  63 #ifdef __USE_ISOC99
  64 /* Define the following typedefs.
  65
  66     float_t     floating-point type at least as wide as `float' used
  67                 to evaluate `float' expressions
  68     double_t    floating-point type at least as wide as `double' used
  69                 to evaluate `double' expressions
  70 */
  71 # if __GLIBC_FLT_EVAL_METHOD == 0 || __GLIBC_FLT_EVAL_METHOD == 16
  72 typedef float float_t;
  73 typedef double double_t;
  74 # elif __GLIBC_FLT_EVAL_METHOD == 1
  75 typedef double float_t;
  76 typedef double double_t;
  77 # elif __GLIBC_FLT_EVAL_METHOD == 2
  78 typedef long double float_t;
  79 typedef long double double_t;
  80 # elif __GLIBC_FLT_EVAL_METHOD == 32
  81 typedef _Float32 float_t;
  82 typedef double double_t;
  83 # elif __GLIBC_FLT_EVAL_METHOD == 33
  84 typedef _Float32x float_t;
  85 typedef _Float32x double_t;
  86 # elif __GLIBC_FLT_EVAL_METHOD == 64
  87 typedef _Float64 float_t;
  88 typedef _Float64 double_t;
  89 # elif __GLIBC_FLT_EVAL_METHOD == 65
  90 typedef _Float64x float_t;
  91 typedef _Float64x double_t;
  92 # elif __GLIBC_FLT_EVAL_METHOD == 128
  93 typedef _Float128 float_t;
  94 typedef _Float128 double_t;
  95 # elif __GLIBC_FLT_EVAL_METHOD == 129
  96 typedef _Float128x float_t;
  97 typedef _Float128x double_t;
  98 # else
  99 #  error "Unknown __GLIBC_FLT_EVAL_METHOD"
 100 # endif
 101 #endif
 102
 103 /* Define macros for the return values of ilogb and llogb, based on
 104    __FP_LOGB0_IS_MIN and __FP_LOGBNAN_IS_MIN.
 105
 106     FP_ILOGB0   Expands to a value returned by `ilogb (0.0)'.
 107     FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
 108     FP_LLOGB0   Expands to a value returned by `llogb (0.0)'.
 109     FP_LLOGBNAN Expands to a value returned by `llogb (NAN)'.
 110
 111 */
 112
 113 #include <bits/fp-logb.h>
 114 #ifdef __USE_ISOC99
 115 # if __FP_LOGB0_IS_MIN
 116 #  define FP_ILOGB0     (-2147483647 - 1)
 117 # else
 118 #  define FP_ILOGB0     (-2147483647)
 119 # endif
 120 # if __FP_LOGBNAN_IS_MIN
 121 #  define FP_ILOGBNAN   (-2147483647 - 1)
 122 # else
 123 #  define FP_ILOGBNAN   2147483647
 124 # endif
 125 #endif
 126 #if __GLIBC_USE (IEC_60559_BFP_EXT)
 127 # if __WORDSIZE == 32
 128 #  define __FP_LONG_MAX 0x7fffffffL
 129 # else
 130 #  define __FP_LONG_MAX 0x7fffffffffffffffL
 131 # endif
 132 # if __FP_LOGB0_IS_MIN
 133 #  define FP_LLOGB0     (-__FP_LONG_MAX - 1)
 134 # else
 135 #  define FP_LLOGB0     (-__FP_LONG_MAX)
 136 # endif
 137 # if __FP_LOGBNAN_IS_MIN
 138 #  define FP_LLOGBNAN   (-__FP_LONG_MAX - 1)
 139 # else
 140 #  define FP_LLOGBNAN   __FP_LONG_MAX
 141 # endif
 142 #endif
 143
 144 /* Get the architecture specific values describing the floating-point
 145    evaluation.  The following symbols will get defined:
 146
 147     FP_FAST_FMA
 148     FP_FAST_FMAF
 149     FP_FAST_FMAL
 150                 If defined it indicates that the `fma' function
 151                 generally executes about as fast as a multiply and an add.
 152                 This macro is defined only iff the `fma' function is
 153                 implemented directly with a hardware multiply-add instructions.
 154 */
 155
 156 #include <bits/fp-fast.h>
 157
 158 #if __GLIBC_USE (IEC_60559_BFP_EXT)
 159 /* Rounding direction macros for fromfp functions.  */
 160 enum
 161   {
 162     FP_INT_UPWARD =
 163 # define FP_INT_UPWARD 0
 164       FP_INT_UPWARD,
 165     FP_INT_DOWNWARD =
 166 # define FP_INT_DOWNWARD 1
 167       FP_INT_DOWNWARD,
 168     FP_INT_TOWARDZERO =
 169 # define FP_INT_TOWARDZERO 2
 170       FP_INT_TOWARDZERO,
 171     FP_INT_TONEARESTFROMZERO =
 172 # define FP_INT_TONEARESTFROMZERO 3
 173       FP_INT_TONEARESTFROMZERO,
 174     FP_INT_TONEAREST =
 175 # define FP_INT_TONEAREST 4
 176       FP_INT_TONEAREST,
 177   };
 178 #endif
 179
 180 /* The file <bits/mathcalls.h> contains the prototypes for all the
 181    actual math functions.  These macros are used for those prototypes,
 182    so we can easily declare each function as both `name' and `__name',
 183    and can declare the float versions `namef' and `__namef'.  */
 184
 185 #define __SIMD_DECL(function) __CONCAT (__DECL_SIMD_, function)
 186
 187 #define __MATHCALL_VEC(function, suffix, args)  \
 188   __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
 189   __MATHCALL (function, suffix, args)
 190
 191 #define __MATHDECL_VEC(type, function,suffix, args) \
 192   __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
 193   __MATHDECL(type, function,suffix, args)
 194
 195 #define __MATHCALL(function,suffix, args)       \
 196   __MATHDECL (_Mdouble_,function,suffix, args)
 197 #define __MATHDECL(type, function,suffix, args) \
 198   __MATHDECL_1(type, function,suffix, args); \
 199   __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
 200 #define __MATHCALLX(function,suffix, args, attrib)      \
 201   __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
 202 #define __MATHDECLX(type, function,suffix, args, attrib) \
 203   __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
 204   __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
 205 #define __MATHDECL_1(type, function,suffix, args) \
 206   extern type __MATH_PRECNAME(function,suffix) args __THROW
 207
 208 #define _Mdouble_               double
 209 #define __MATH_PRECNAME(name,r) __CONCAT(name,r)
 210 #define __MATH_DECLARING_DOUBLE  1
 211 #define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
 212 #define _Mdouble_END_NAMESPACE   __END_NAMESPACE_STD
 213 #include <bits/mathcalls-helper-functions.h>
 214 #include <bits/mathcalls.h>
 215 #undef  _Mdouble_
 216 #undef _Mdouble_BEGIN_NAMESPACE
 217 #undef _Mdouble_END_NAMESPACE
 218 #undef  __MATH_PRECNAME
 219 #undef __MATH_DECLARING_DOUBLE
 220
 221 #ifdef __USE_ISOC99
 222
 223
 224 /* Include the file of declarations again, this time using `float'
 225    instead of `double' and appending f to each function name.  */
 226
 227 # ifndef _Mfloat_
 228 #  define _Mfloat_              float
 229 # endif
 230 # define _Mdouble_              _Mfloat_
 231 # define __MATH_PRECNAME(name,r) name##f##r
 232 # define __MATH_DECLARING_DOUBLE  0
 233 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
 234 # define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
 235 # include <bits/mathcalls-helper-functions.h>
 236 # include <bits/mathcalls.h>
 237 # undef _Mdouble_
 238 # undef _Mdouble_BEGIN_NAMESPACE
 239 # undef _Mdouble_END_NAMESPACE
 240 # undef __MATH_PRECNAME
 241 # undef __MATH_DECLARING_DOUBLE
 242
 243 # if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
 244      || defined __LDBL_COMPAT \
 245      || defined _LIBC_TEST
 246 #  ifdef __LDBL_COMPAT
 247
 248 #   ifdef __USE_ISOC99
 249 extern float __nldbl_nexttowardf (float __x, long double __y)
 250                                   __THROW __attribute__ ((__const__));
 251 #    ifdef __REDIRECT_NTH
 252 extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
 253                              __nldbl_nexttowardf)
 254      __attribute__ ((__const__));
 255 extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
 256                               nextafter) __attribute__ ((__const__));
 257 extern long double __REDIRECT_NTH (nexttowardl,
 258                                    (long double __x, long double __y),
 259                                    nextafter) __attribute__ ((__const__));
 260 #    endif
 261 #   endif
 262
 263 #   undef __MATHDECL_1
 264 #   define __MATHDECL_2(type, function,suffix, args, alias) \
 265   extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
 266                              args, alias)
 267 #   define __MATHDECL_1(type, function,suffix, args) \
 268   __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
 269 #  endif
 270
 271 /* Include the file of declarations again, this time using `long double'
 272    instead of `double' and appending l to each function name.  */
 273
 274 #  ifndef _Mlong_double_
 275 #   define _Mlong_double_       long double
 276 #  endif
 277 #  define _Mdouble_             _Mlong_double_
 278 #  define __MATH_PRECNAME(name,r) name##l##r
 279 #  define __MATH_DECLARING_DOUBLE  0
 280 #  define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
 281 #  define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
 282 #  define __MATH_DECLARE_LDOUBLE   1
 283 #  include <bits/mathcalls-helper-functions.h>
 284 #  include <bits/mathcalls.h>
 285 #  undef _Mdouble_
 286 #  undef _Mdouble_BEGIN_NAMESPACE
 287 #  undef _Mdouble_END_NAMESPACE
 288 #  undef __MATH_PRECNAME
 289 #  undef __MATH_DECLARING_DOUBLE
 290
 291 # endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */
 292
 293 #endif  /* Use ISO C99.  */
 294 #undef  __MATHDECL_1
 295 #undef  __MATHDECL
 296 #undef  __MATHCALL
 297
 298
 299 #if defined __USE_MISC || defined __USE_XOPEN
 300 /* This variable is used by `gamma' and `lgamma'.  */
 301 extern int signgam;
 302 #endif
 303
 304
 305 /* Depending on the type of TG_ARG, call an appropriately suffixed
 306    version of FUNC with arguments (including parentheses) ARGS.
 307    Suffixed functions may not exist for long double if it has the same
 308    format as double, or for other types with the same format as float,
 309    double or long double.  The behavior is undefined if the argument
 310    does not have a real floating type.  The definition may use a
 311    conditional expression, so all suffixed versions of FUNC must
 312    return the same type (FUNC may include a cast if necessary rather
 313    than being a single identifier).  */
 314 #ifdef __NO_LONG_DOUBLE_MATH
 315 # define __MATH_TG(TG_ARG, FUNC, ARGS)                                  \
 316   (sizeof (TG_ARG) == sizeof (float) ? FUNC ## f ARGS : FUNC ARGS)
 317 #else
 318 # define __MATH_TG(TG_ARG, FUNC, ARGS)          \
 319   (sizeof (TG_ARG) == sizeof (float)            \
 320    ? FUNC ## f ARGS                             \
 321    : sizeof (TG_ARG) == sizeof (double)         \
 322    ? FUNC ARGS                                  \
 323    : FUNC ## l ARGS)
 324 #endif
 325
 326 /* ISO C99 defines some generic macros which work on any data type.  */
 327 #ifdef __USE_ISOC99
 328
 329 /* All floating-point numbers can be put in one of these categories.  */
 330 enum
 331   {
 332     FP_NAN =
 333 # define FP_NAN 0
 334       FP_NAN,
 335     FP_INFINITE =
 336 # define FP_INFINITE 1
 337       FP_INFINITE,
 338     FP_ZERO =
 339 # define FP_ZERO 2
 340       FP_ZERO,
 341     FP_SUBNORMAL =
 342 # define FP_SUBNORMAL 3
 343       FP_SUBNORMAL,
 344     FP_NORMAL =
 345 # define FP_NORMAL 4
 346       FP_NORMAL
 347   };
 348
 349 /* GCC bug 66462 means we cannot use the math builtins with -fsignaling-nan,
 350    so disable builtins if this is enabled.  When fixed in a newer GCC,
 351    the __SUPPORT_SNAN__ check may be skipped for those versions.  */
 352
 353 /* Return number of classification appropriate for X.  */
 354 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__                         \
 355      && !defined __OPTIMIZE_SIZE__
 356 #  define fpclassify(x) __builtin_fpclassify (FP_NAN, FP_INFINITE,            \
 357      FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x)
 358 # else
 359 #  define fpclassify(x) __MATH_TG ((x), __fpclassify, (x))
 360 # endif
 361
 362 /* Return nonzero value if sign of X is negative.  */
 363 # if __GNUC_PREREQ (4,0)
 364 #  define signbit(x) __MATH_TG ((x), __builtin_signbit, (x))
 365 # else
 366 #  define signbit(x) __MATH_TG ((x), __signbit, (x))
 367 # endif
 368
 369 /* Return nonzero value if X is not +-Inf or NaN.  */
 370 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
 371 #  define isfinite(x) __builtin_isfinite (x)
 372 # else
 373 #  define isfinite(x) __MATH_TG ((x), __finite, (x))
 374 # endif
 375
 376 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
 377 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
 378 #  define isnormal(x) __builtin_isnormal (x)
 379 # else
 380 #  define isnormal(x) (fpclassify (x) == FP_NORMAL)
 381 # endif
 382
 383 /* Return nonzero value if X is a NaN.  We could use `fpclassify' but
 384    we already have this functions `__isnan' and it is faster.  */
 385 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
 386 #  define isnan(x) __builtin_isnan (x)
 387 # else
 388 #  define isnan(x) __MATH_TG ((x), __isnan, (x))
 389 # endif
 390
 391 /* Return nonzero value if X is positive or negative infinity.  */
 392 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
 393 #  define isinf(x) __builtin_isinf_sign (x)
 394 # else
 395 #  define isinf(x) __MATH_TG ((x), __isinf, (x))
 396 # endif
 397
 398 /* Bitmasks for the math_errhandling macro.  */
 399 # define MATH_ERRNO     1       /* errno set by math functions.  */
 400 # define MATH_ERREXCEPT 2       /* Exceptions raised by math functions.  */
 401
 402 /* By default all functions support both errno and exception handling.
 403    In gcc's fast math mode and if inline functions are defined this
 404    might not be true.  */
 405 # ifndef __FAST_MATH__
 406 #  define math_errhandling      (MATH_ERRNO | MATH_ERREXCEPT)
 407 # endif
 408
 409 #endif /* Use ISO C99.  */
 410
 411 #if __GLIBC_USE (IEC_60559_BFP_EXT)
 412 # include <bits/iscanonical.h>
 413
 414 /* Return nonzero value if X is a signaling NaN.  */
 415 # define issignaling(x) __MATH_TG ((x), __issignaling, (x))
 416
 417 /* Return nonzero value if X is subnormal.  */
 418 # define issubnormal(x) (fpclassify (x) == FP_SUBNORMAL)
 419
 420 /* Return nonzero value if X is zero.  */
 421 # ifndef __cplusplus
 422 #  ifdef __SUPPORT_SNAN__
 423 #   define iszero(x) (fpclassify (x) == FP_ZERO)
 424 #  else
 425 #   define iszero(x) (((__typeof (x)) (x)) == 0)
 426 #  endif
 427 # else  /* __cplusplus */
 428 extern "C++" {
 429 template <class __T> inline bool
 430 iszero (__T __val)
 431 {
 432 #  ifdef __SUPPORT_SNAN__
 433   return fpclassify (__val) == FP_ZERO;
 434 #  else
 435   return __val == 0;
 436 #  endif
 437 }
 438 } /* extern C++ */
 439 # endif /* __cplusplus */
 440 #endif /* Use IEC_60559_BFP_EXT.  */
 441
 442 #ifdef  __USE_MISC
 443 /* Support for various different standard error handling behaviors.  */
 444 typedef enum
 445 {
 446   _IEEE_ = -1,  /* According to IEEE 754/IEEE 854.  */
 447   _SVID_,       /* According to System V, release 4.  */
 448   _XOPEN_,      /* Nowadays also Unix98.  */
 449   _POSIX_,
 450   _ISOC_        /* Actually this is ISO C99.  */
 451 } _LIB_VERSION_TYPE;
 452
 453 /* This variable can be changed at run-time to any of the values above to
 454    affect floating point error handling behavior (it may also be necessary
 455    to change the hardware FPU exception settings).  */
 456 extern _LIB_VERSION_TYPE _LIB_VERSION;
 457 #endif
 458
 459
 460 #ifdef __USE_MISC
 461 /* In SVID error handling, `matherr' is called with this description
 462    of the exceptional condition.
 463
 464    We have a problem when using C++ since `exception' is a reserved
 465    name in C++.  */
 466 # ifdef __cplusplus
 467 struct __exception
 468 # else
 469 struct exception
 470 # endif
 471   {
 472     int type;
 473     char *name;
 474     double arg1;
 475     double arg2;
 476     double retval;
 477   };
 478
 479 # ifdef __cplusplus
 480 extern int matherr (struct __exception *__exc) throw ();
 481 # else
 482 extern int matherr (struct exception *__exc);
 483 # endif
 484
 485 # define X_TLOSS        1.41484755040568800000e+16
 486
 487 /* Types of exceptions in the `type' field.  */
 488 # define DOMAIN         1
 489 # define SING           2
 490 # define OVERFLOW       3
 491 # define UNDERFLOW      4
 492 # define TLOSS          5
 493 # define PLOSS          6
 494
 495 /* SVID mode specifies returning this large value instead of infinity.  */
 496 # define HUGE           3.40282347e+38F
 497
 498 #else   /* !Misc.  */
 499
 500 # ifdef __USE_XOPEN
 501 /* X/Open wants another strange constant.  */
 502 #  define MAXFLOAT      3.40282347e+38F
 503 # endif
 504
 505 #endif  /* Misc.  */
 506
 507
 508 /* Some useful constants.  */
 509 #if defined __USE_MISC || defined __USE_XOPEN
 510 # define M_E            2.7182818284590452354   /* e */
 511 # define M_LOG2E        1.4426950408889634074   /* log_2 e */
 512 # define M_LOG10E       0.43429448190325182765  /* log_10 e */
 513 # define M_LN2          0.69314718055994530942  /* log_e 2 */
 514 # define M_LN10         2.30258509299404568402  /* log_e 10 */
 515 # define M_PI           3.14159265358979323846  /* pi */
 516 # define M_PI_2         1.57079632679489661923  /* pi/2 */
 517 # define M_PI_4         0.78539816339744830962  /* pi/4 */
 518 # define M_1_PI         0.31830988618379067154  /* 1/pi */
 519 # define M_2_PI         0.63661977236758134308  /* 2/pi */
 520 # define M_2_SQRTPI     1.12837916709551257390  /* 2/sqrt(pi) */
 521 # define M_SQRT2        1.41421356237309504880  /* sqrt(2) */
 522 # define M_SQRT1_2      0.70710678118654752440  /* 1/sqrt(2) */
 523 #endif
 524
 525 /* The above constants are not adequate for computation using `long double's.
 526    Therefore we provide as an extension constants with similar names as a
 527    GNU extension.  Provide enough digits for the 128-bit IEEE quad.  */
 528 #ifdef __USE_GNU
 529 # define M_El           2.718281828459045235360287471352662498L /* e */
 530 # define M_LOG2El       1.442695040888963407359924681001892137L /* log_2 e */
 531 # define M_LOG10El      0.434294481903251827651128918916605082L /* log_10 e */
 532 # define M_LN2l         0.693147180559945309417232121458176568L /* log_e 2 */
 533 # define M_LN10l        2.302585092994045684017991454684364208L /* log_e 10 */
 534 # define M_PIl          3.141592653589793238462643383279502884L /* pi */
 535 # define M_PI_2l        1.570796326794896619231321691639751442L /* pi/2 */
 536 # define M_PI_4l        0.785398163397448309615660845819875721L /* pi/4 */
 537 # define M_1_PIl        0.318309886183790671537767526745028724L /* 1/pi */
 538 # define M_2_PIl        0.636619772367581343075535053490057448L /* 2/pi */
 539 # define M_2_SQRTPIl    1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
 540 # define M_SQRT2l       1.414213562373095048801688724209698079L /* sqrt(2) */
 541 # define M_SQRT1_2l     0.707106781186547524400844362104849039L /* 1/sqrt(2) */
 542 #endif
 543
 544
 545 /* When compiling in strict ISO C compatible mode we must not use the
 546    inline functions since they, among other things, do not set the
 547    `errno' variable correctly.  */
 548 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
 549 # define __NO_MATH_INLINES      1
 550 #endif
 551
 552 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
 553 /* ISO C99 defines some macros to compare number while taking care for
 554    unordered numbers.  Many FPUs provide special instructions to support
 555    these operations.  Generic support in GCC for these as builtins went
 556    in before 3.0.0, but not all cpus added their patterns.  We define
 557    versions that use the builtins here, and <bits/mathinline.h> will
 558    undef/redefine as appropriate for the specific GCC version in use.  */
 559 # define isgreater(x, y)        __builtin_isgreater(x, y)
 560 # define isgreaterequal(x, y)   __builtin_isgreaterequal(x, y)
 561 # define isless(x, y)           __builtin_isless(x, y)
 562 # define islessequal(x, y)      __builtin_islessequal(x, y)
 563 # define islessgreater(x, y)    __builtin_islessgreater(x, y)
 564 # define isunordered(u, v)      __builtin_isunordered(u, v)
 565 #endif
 566
 567 /* Get machine-dependent inline versions (if there are any).  */
 568 #ifdef __USE_EXTERN_INLINES
 569 # include <bits/mathinline.h>
 570 #endif
 571
 572 /* Define special entry points to use when the compiler got told to
 573    only expect finite results.  */
 574 #if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0
 575 # include <bits/math-finite.h>
 576 #endif
 577
 578 #ifdef __USE_ISOC99
 579 /* If we've still got undefined comparison macros, provide defaults.  */
 580
 581 /* Return nonzero value if X is greater than Y.  */
 582 # ifndef isgreater
 583 #  define isgreater(x, y) \
 584   (__extension__                                                              \
 585    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 586       !isunordered (__x, __y) && __x > __y; }))
 587 # endif
 588
 589 /* Return nonzero value if X is greater than or equal to Y.  */
 590 # ifndef isgreaterequal
 591 #  define isgreaterequal(x, y) \
 592   (__extension__                                                              \
 593    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 594       !isunordered (__x, __y) && __x >= __y; }))
 595 # endif
 596
 597 /* Return nonzero value if X is less than Y.  */
 598 # ifndef isless
 599 #  define isless(x, y) \
 600   (__extension__                                                              \
 601    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 602       !isunordered (__x, __y) && __x < __y; }))
 603 # endif
 604
 605 /* Return nonzero value if X is less than or equal to Y.  */
 606 # ifndef islessequal
 607 #  define islessequal(x, y) \
 608   (__extension__                                                              \
 609    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 610       !isunordered (__x, __y) && __x <= __y; }))
 611 # endif
 612
 613 /* Return nonzero value if either X is less than Y or Y is less than X.  */
 614 # ifndef islessgreater
 615 #  define islessgreater(x, y) \
 616   (__extension__                                                              \
 617    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 618       !isunordered (__x, __y) && (__x < __y || __y < __x); }))
 619 # endif
 620
 621 /* Return nonzero value if arguments are unordered.  */
 622 # ifndef isunordered
 623 #  define isunordered(u, v) \
 624   (__extension__                                                              \
 625    ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v);                       \
 626       fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
 627 # endif
 628
 629 #endif
 630
 631 #if __GLIBC_USE (IEC_60559_BFP_EXT)
 632 /* An expression whose type has the widest of the evaluation formats
 633    of X and Y (which are of floating-point types).  */
 634 # if __FLT_EVAL_METHOD__ == 2 || __FLT_EVAL_METHOD__ > 64
 635 #  define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0L)
 636 # elif __FLT_EVAL_METHOD__ == 1 || __FLT_EVAL_METHOD__ > 32
 637 #  define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0)
 638 # else
 639 #  define __MATH_EVAL_FMT2(x, y) ((x) + (y))
 640 # endif
 641
 642 /* Return X == Y but raising "invalid" and setting errno if X or Y is
 643    a NaN.  */
 644 # define iseqsig(x, y) \
 645   __MATH_TG (__MATH_EVAL_FMT2 (x, y), __iseqsig, ((x), (y)))
 646 #endif
 647
 648 __END_DECLS
 649
 650
 651 #endif /* math.h  */