math/math.h

   1 /* Declarations for math functions.
   2    Copyright (C) 1991-2016 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 machine-dependent vector math functions declarations.  */
  32 #include <bits/math-vector.h>
  33
  34 /* Get machine-dependent HUGE_VAL value (returned on overflow).
  35    On all IEEE754 machines, this is +Infinity.  */
  36 #include <bits/huge_val.h>
  37 #ifdef __USE_ISOC99
  38 # include <bits/huge_valf.h>
  39 # include <bits/huge_vall.h>
  40
  41 /* Get machine-dependent INFINITY value.  */
  42 # include <bits/inf.h>
  43
  44 /* Get machine-dependent NAN value (returned for some domain errors).  */
  45 # include <bits/nan.h>
  46 #endif /* __USE_ISOC99 */
  47
  48 #if __GLIBC_USE (IEC_60559_BFP_EXT)
  49 /* Signaling NaN macros, if supported.  */
  50 # if __GNUC_PREREQ (3, 3)
  51 #  define SNANF (__builtin_nansf (""))
  52 #  define SNAN (__builtin_nans (""))
  53 #  define SNANL (__builtin_nansl (""))
  54 # endif
  55 #endif
  56
  57 /* Get __GLIBC_FLT_EVAL_METHOD.  */
  58 #include <bits/flt-eval-method.h>
  59
  60 #ifdef __USE_ISOC99
  61 /* Define the following typedefs.
  62
  63     float_t     floating-point type at least as wide as `float' used
  64                 to evaluate `float' expressions
  65     double_t    floating-point type at least as wide as `double' used
  66                 to evaluate `double' expressions
  67 */
  68 # if __GLIBC_FLT_EVAL_METHOD == 0 || __GLIBC_FLT_EVAL_METHOD == 16
  69 typedef float float_t;
  70 typedef double double_t;
  71 # elif __GLIBC_FLT_EVAL_METHOD == 1
  72 typedef double float_t;
  73 typedef double double_t;
  74 # elif __GLIBC_FLT_EVAL_METHOD == 2
  75 typedef long double float_t;
  76 typedef long double double_t;
  77 # elif __GLIBC_FLT_EVAL_METHOD == 32
  78 typedef _Float32 float_t;
  79 typedef double double_t;
  80 # elif __GLIBC_FLT_EVAL_METHOD == 33
  81 typedef _Float32x float_t;
  82 typedef _Float32x double_t;
  83 # elif __GLIBC_FLT_EVAL_METHOD == 64
  84 typedef _Float64 float_t;
  85 typedef _Float64 double_t;
  86 # elif __GLIBC_FLT_EVAL_METHOD == 65
  87 typedef _Float64x float_t;
  88 typedef _Float64x double_t;
  89 # elif __GLIBC_FLT_EVAL_METHOD == 128
  90 typedef _Float128 float_t;
  91 typedef _Float128 double_t;
  92 # elif __GLIBC_FLT_EVAL_METHOD == 129
  93 typedef _Float128x float_t;
  94 typedef _Float128x double_t;
  95 # else
  96 #  error "Unknown __GLIBC_FLT_EVAL_METHOD"
  97 # endif
  98 #endif
  99
 100 /* Define macros for the return value of ilogb.
 101
 102     FP_ILOGB0   Expands to a value returned by `ilogb (0.0)'.
 103     FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
 104
 105 */
 106
 107 #include <bits/mathdef.h>
 108
 109 /* Get the architecture specific values describing the floating-point
 110    evaluation.  The following symbols will get defined:
 111
 112     FP_FAST_FMA
 113     FP_FAST_FMAF
 114     FP_FAST_FMAL
 115                 If defined it indicates that the `fma' function
 116                 generally executes about as fast as a multiply and an add.
 117                 This macro is defined only iff the `fma' function is
 118                 implemented directly with a hardware multiply-add instructions.
 119 */
 120
 121 #include <bits/fp-fast.h>
 122
 123 /* The file <bits/mathcalls.h> contains the prototypes for all the
 124    actual math functions.  These macros are used for those prototypes,
 125    so we can easily declare each function as both `name' and `__name',
 126    and can declare the float versions `namef' and `__namef'.  */
 127
 128 #define __SIMD_DECL(function) __CONCAT (__DECL_SIMD_, function)
 129
 130 #define __MATHCALL_VEC(function, suffix, args)  \
 131   __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
 132   __MATHCALL (function, suffix, args)
 133
 134 #define __MATHDECL_VEC(type, function,suffix, args) \
 135   __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
 136   __MATHDECL(type, function,suffix, args)
 137
 138 #define __MATHCALL(function,suffix, args)       \
 139   __MATHDECL (_Mdouble_,function,suffix, args)
 140 #define __MATHDECL(type, function,suffix, args) \
 141   __MATHDECL_1(type, function,suffix, args); \
 142   __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
 143 #define __MATHCALLX(function,suffix, args, attrib)      \
 144   __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
 145 #define __MATHDECLX(type, function,suffix, args, attrib) \
 146   __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
 147   __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
 148 #define __MATHDECL_1(type, function,suffix, args) \
 149   extern type __MATH_PRECNAME(function,suffix) args __THROW
 150
 151 #define _Mdouble_               double
 152 #define __MATH_PRECNAME(name,r) __CONCAT(name,r)
 153 #define __MATH_DECLARING_DOUBLE  1
 154 #define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
 155 #define _Mdouble_END_NAMESPACE   __END_NAMESPACE_STD
 156 #include <bits/mathcalls.h>
 157 #undef  _Mdouble_
 158 #undef _Mdouble_BEGIN_NAMESPACE
 159 #undef _Mdouble_END_NAMESPACE
 160 #undef  __MATH_PRECNAME
 161 #undef __MATH_DECLARING_DOUBLE
 162
 163 #ifdef __USE_ISOC99
 164
 165
 166 /* Include the file of declarations again, this time using `float'
 167    instead of `double' and appending f to each function name.  */
 168
 169 # ifndef _Mfloat_
 170 #  define _Mfloat_              float
 171 # endif
 172 # define _Mdouble_              _Mfloat_
 173 # define __MATH_PRECNAME(name,r) name##f##r
 174 # define __MATH_DECLARING_DOUBLE  0
 175 # define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
 176 # define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
 177 # include <bits/mathcalls.h>
 178 # undef _Mdouble_
 179 # undef _Mdouble_BEGIN_NAMESPACE
 180 # undef _Mdouble_END_NAMESPACE
 181 # undef __MATH_PRECNAME
 182 # undef __MATH_DECLARING_DOUBLE
 183
 184 # if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
 185      || defined __LDBL_COMPAT \
 186      || defined _LIBC_TEST
 187 #  ifdef __LDBL_COMPAT
 188
 189 #   ifdef __USE_ISOC99
 190 extern float __nldbl_nexttowardf (float __x, long double __y)
 191                                   __THROW __attribute__ ((__const__));
 192 #    ifdef __REDIRECT_NTH
 193 extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
 194                              __nldbl_nexttowardf)
 195      __attribute__ ((__const__));
 196 extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
 197                               nextafter) __attribute__ ((__const__));
 198 extern long double __REDIRECT_NTH (nexttowardl,
 199                                    (long double __x, long double __y),
 200                                    nextafter) __attribute__ ((__const__));
 201 #    endif
 202 #   endif
 203
 204 #   undef __MATHDECL_1
 205 #   define __MATHDECL_2(type, function,suffix, args, alias) \
 206   extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
 207                              args, alias)
 208 #   define __MATHDECL_1(type, function,suffix, args) \
 209   __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
 210 #  endif
 211
 212 /* Include the file of declarations again, this time using `long double'
 213    instead of `double' and appending l to each function name.  */
 214
 215 #  ifndef _Mlong_double_
 216 #   define _Mlong_double_       long double
 217 #  endif
 218 #  define _Mdouble_             _Mlong_double_
 219 #  define __MATH_PRECNAME(name,r) name##l##r
 220 #  define __MATH_DECLARING_DOUBLE  0
 221 #  define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
 222 #  define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
 223 #  define __MATH_DECLARE_LDOUBLE   1
 224 #  include <bits/mathcalls.h>
 225 #  undef _Mdouble_
 226 #  undef _Mdouble_BEGIN_NAMESPACE
 227 #  undef _Mdouble_END_NAMESPACE
 228 #  undef __MATH_PRECNAME
 229 #  undef __MATH_DECLARING_DOUBLE
 230
 231 # endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */
 232
 233 #endif  /* Use ISO C99.  */
 234 #undef  __MATHDECL_1
 235 #undef  __MATHDECL
 236 #undef  __MATHCALL
 237
 238
 239 #if defined __USE_MISC || defined __USE_XOPEN
 240 /* This variable is used by `gamma' and `lgamma'.  */
 241 extern int signgam;
 242 #endif
 243
 244
 245 /* Depending on the type of TG_ARG, call an appropriately suffixed
 246    version of FUNC with arguments (including parentheses) ARGS.
 247    Suffixed functions may not exist for long double if it has the same
 248    format as double, or for other types with the same format as float,
 249    double or long double.  The behavior is undefined if the argument
 250    does not have a real floating type.  The definition may use a
 251    conditional expression, so all suffixed versions of FUNC must
 252    return the same type (FUNC may include a cast if necessary rather
 253    than being a single identifier).  */
 254 #ifdef __NO_LONG_DOUBLE_MATH
 255 # define __MATH_TG(TG_ARG, FUNC, ARGS)                                  \
 256   (sizeof (TG_ARG) == sizeof (float) ? FUNC ## f ARGS : FUNC ARGS)
 257 #else
 258 # define __MATH_TG(TG_ARG, FUNC, ARGS)          \
 259   (sizeof (TG_ARG) == sizeof (float)            \
 260    ? FUNC ## f ARGS                             \
 261    : sizeof (TG_ARG) == sizeof (double)         \
 262    ? FUNC ARGS                                  \
 263    : FUNC ## l ARGS)
 264 #endif
 265
 266 /* ISO C99 defines some generic macros which work on any data type.  */
 267 #ifdef __USE_ISOC99
 268
 269 /* All floating-point numbers can be put in one of these categories.  */
 270 enum
 271   {
 272     FP_NAN =
 273 # define FP_NAN 0
 274       FP_NAN,
 275     FP_INFINITE =
 276 # define FP_INFINITE 1
 277       FP_INFINITE,
 278     FP_ZERO =
 279 # define FP_ZERO 2
 280       FP_ZERO,
 281     FP_SUBNORMAL =
 282 # define FP_SUBNORMAL 3
 283       FP_SUBNORMAL,
 284     FP_NORMAL =
 285 # define FP_NORMAL 4
 286       FP_NORMAL
 287   };
 288
 289 /* GCC bug 66462 means we cannot use the math builtins with -fsignaling-nan,
 290    so disable builtins if this is enabled.  When fixed in a newer GCC,
 291    the __SUPPORT_SNAN__ check may be skipped for those versions.  */
 292
 293 /* Return number of classification appropriate for X.  */
 294 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__                         \
 295      && !defined __OPTIMIZE_SIZE__
 296 #  define fpclassify(x) __builtin_fpclassify (FP_NAN, FP_INFINITE,            \
 297      FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x)
 298 # else
 299 #  define fpclassify(x) __MATH_TG ((x), __fpclassify, (x))
 300 # endif
 301
 302 /* Return nonzero value if sign of X is negative.  */
 303 # if __GNUC_PREREQ (4,0)
 304 #  define signbit(x) __MATH_TG ((x), __builtin_signbit, (x))
 305 # else
 306 #  define signbit(x) __MATH_TG ((x), __signbit, (x))
 307 # endif
 308
 309 /* Return nonzero value if X is not +-Inf or NaN.  */
 310 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
 311 #  define isfinite(x) __builtin_isfinite (x)
 312 # else
 313 #  define isfinite(x) __MATH_TG ((x), __finite, (x))
 314 # endif
 315
 316 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
 317 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
 318 #  define isnormal(x) __builtin_isnormal (x)
 319 # else
 320 #  define isnormal(x) (fpclassify (x) == FP_NORMAL)
 321 # endif
 322
 323 /* Return nonzero value if X is a NaN.  We could use `fpclassify' but
 324    we already have this functions `__isnan' and it is faster.  */
 325 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
 326 #  define isnan(x) __builtin_isnan (x)
 327 # else
 328 #  define isnan(x) __MATH_TG ((x), __isnan, (x))
 329 # endif
 330
 331 /* Return nonzero value if X is positive or negative infinity.  */
 332 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
 333 #  define isinf(x) __builtin_isinf_sign (x)
 334 # else
 335 #  define isinf(x) __MATH_TG ((x), __isinf, (x))
 336 # endif
 337
 338 /* Bitmasks for the math_errhandling macro.  */
 339 # define MATH_ERRNO     1       /* errno set by math functions.  */
 340 # define MATH_ERREXCEPT 2       /* Exceptions raised by math functions.  */
 341
 342 /* By default all functions support both errno and exception handling.
 343    In gcc's fast math mode and if inline functions are defined this
 344    might not be true.  */
 345 # ifndef __FAST_MATH__
 346 #  define math_errhandling      (MATH_ERRNO | MATH_ERREXCEPT)
 347 # endif
 348
 349 #endif /* Use ISO C99.  */
 350
 351 #if __GLIBC_USE (IEC_60559_BFP_EXT)
 352 # include <bits/iscanonical.h>
 353
 354 /* Return nonzero value if X is a signaling NaN.  */
 355 # define issignaling(x) __MATH_TG ((x), __issignaling, (x))
 356
 357 /* Return nonzero value if X is subnormal.  */
 358 # define issubnormal(x) (fpclassify (x) == FP_SUBNORMAL)
 359
 360 /* Return nonzero value if X is zero.  */
 361 # ifndef __cplusplus
 362 #  ifdef __SUPPORT_SNAN__
 363 #   define iszero(x) (fpclassify (x) == FP_ZERO)
 364 #  else
 365 #   define iszero(x) (((__typeof (x)) (x)) == 0)
 366 #  endif
 367 # else  /* __cplusplus */
 368 extern "C++" {
 369 template <class __T> inline bool
 370 iszero (__T __val)
 371 {
 372 #  ifdef __SUPPORT_SNAN__
 373   return fpclassify (__val) == FP_ZERO;
 374 #  else
 375   return __val == 0;
 376 #  endif
 377 }
 378 } /* extern C++ */
 379 # endif /* __cplusplus */
 380 #endif /* Use IEC_60559_BFP_EXT.  */
 381
 382 #ifdef  __USE_MISC
 383 /* Support for various different standard error handling behaviors.  */
 384 typedef enum
 385 {
 386   _IEEE_ = -1,  /* According to IEEE 754/IEEE 854.  */
 387   _SVID_,       /* According to System V, release 4.  */
 388   _XOPEN_,      /* Nowadays also Unix98.  */
 389   _POSIX_,
 390   _ISOC_        /* Actually this is ISO C99.  */
 391 } _LIB_VERSION_TYPE;
 392
 393 /* This variable can be changed at run-time to any of the values above to
 394    affect floating point error handling behavior (it may also be necessary
 395    to change the hardware FPU exception settings).  */
 396 extern _LIB_VERSION_TYPE _LIB_VERSION;
 397 #endif
 398
 399
 400 #ifdef __USE_MISC
 401 /* In SVID error handling, `matherr' is called with this description
 402    of the exceptional condition.
 403
 404    We have a problem when using C++ since `exception' is a reserved
 405    name in C++.  */
 406 # ifdef __cplusplus
 407 struct __exception
 408 # else
 409 struct exception
 410 # endif
 411   {
 412     int type;
 413     char *name;
 414     double arg1;
 415     double arg2;
 416     double retval;
 417   };
 418
 419 # ifdef __cplusplus
 420 extern int matherr (struct __exception *__exc) throw ();
 421 # else
 422 extern int matherr (struct exception *__exc);
 423 # endif
 424
 425 # define X_TLOSS        1.41484755040568800000e+16
 426
 427 /* Types of exceptions in the `type' field.  */
 428 # define DOMAIN         1
 429 # define SING           2
 430 # define OVERFLOW       3
 431 # define UNDERFLOW      4
 432 # define TLOSS          5
 433 # define PLOSS          6
 434
 435 /* SVID mode specifies returning this large value instead of infinity.  */
 436 # define HUGE           3.40282347e+38F
 437
 438 #else   /* !Misc.  */
 439
 440 # ifdef __USE_XOPEN
 441 /* X/Open wants another strange constant.  */
 442 #  define MAXFLOAT      3.40282347e+38F
 443 # endif
 444
 445 #endif  /* Misc.  */
 446
 447
 448 /* Some useful constants.  */
 449 #if defined __USE_MISC || defined __USE_XOPEN
 450 # define M_E            2.7182818284590452354   /* e */
 451 # define M_LOG2E        1.4426950408889634074   /* log_2 e */
 452 # define M_LOG10E       0.43429448190325182765  /* log_10 e */
 453 # define M_LN2          0.69314718055994530942  /* log_e 2 */
 454 # define M_LN10         2.30258509299404568402  /* log_e 10 */
 455 # define M_PI           3.14159265358979323846  /* pi */
 456 # define M_PI_2         1.57079632679489661923  /* pi/2 */
 457 # define M_PI_4         0.78539816339744830962  /* pi/4 */
 458 # define M_1_PI         0.31830988618379067154  /* 1/pi */
 459 # define M_2_PI         0.63661977236758134308  /* 2/pi */
 460 # define M_2_SQRTPI     1.12837916709551257390  /* 2/sqrt(pi) */
 461 # define M_SQRT2        1.41421356237309504880  /* sqrt(2) */
 462 # define M_SQRT1_2      0.70710678118654752440  /* 1/sqrt(2) */
 463 #endif
 464
 465 /* The above constants are not adequate for computation using `long double's.
 466    Therefore we provide as an extension constants with similar names as a
 467    GNU extension.  Provide enough digits for the 128-bit IEEE quad.  */
 468 #ifdef __USE_GNU
 469 # define M_El           2.718281828459045235360287471352662498L /* e */
 470 # define M_LOG2El       1.442695040888963407359924681001892137L /* log_2 e */
 471 # define M_LOG10El      0.434294481903251827651128918916605082L /* log_10 e */
 472 # define M_LN2l         0.693147180559945309417232121458176568L /* log_e 2 */
 473 # define M_LN10l        2.302585092994045684017991454684364208L /* log_e 10 */
 474 # define M_PIl          3.141592653589793238462643383279502884L /* pi */
 475 # define M_PI_2l        1.570796326794896619231321691639751442L /* pi/2 */
 476 # define M_PI_4l        0.785398163397448309615660845819875721L /* pi/4 */
 477 # define M_1_PIl        0.318309886183790671537767526745028724L /* 1/pi */
 478 # define M_2_PIl        0.636619772367581343075535053490057448L /* 2/pi */
 479 # define M_2_SQRTPIl    1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
 480 # define M_SQRT2l       1.414213562373095048801688724209698079L /* sqrt(2) */
 481 # define M_SQRT1_2l     0.707106781186547524400844362104849039L /* 1/sqrt(2) */
 482 #endif
 483
 484
 485 /* When compiling in strict ISO C compatible mode we must not use the
 486    inline functions since they, among other things, do not set the
 487    `errno' variable correctly.  */
 488 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
 489 # define __NO_MATH_INLINES      1
 490 #endif
 491
 492 #if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
 493 /* ISO C99 defines some macros to compare number while taking care for
 494    unordered numbers.  Many FPUs provide special instructions to support
 495    these operations.  Generic support in GCC for these as builtins went
 496    in before 3.0.0, but not all cpus added their patterns.  We define
 497    versions that use the builtins here, and <bits/mathinline.h> will
 498    undef/redefine as appropriate for the specific GCC version in use.  */
 499 # define isgreater(x, y)        __builtin_isgreater(x, y)
 500 # define isgreaterequal(x, y)   __builtin_isgreaterequal(x, y)
 501 # define isless(x, y)           __builtin_isless(x, y)
 502 # define islessequal(x, y)      __builtin_islessequal(x, y)
 503 # define islessgreater(x, y)    __builtin_islessgreater(x, y)
 504 # define isunordered(u, v)      __builtin_isunordered(u, v)
 505 #endif
 506
 507 /* Get machine-dependent inline versions (if there are any).  */
 508 #ifdef __USE_EXTERN_INLINES
 509 # include <bits/mathinline.h>
 510 #endif
 511
 512 /* Define special entry points to use when the compiler got told to
 513    only expect finite results.  */
 514 #if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0
 515 # include <bits/math-finite.h>
 516 #endif
 517
 518 #ifdef __USE_ISOC99
 519 /* If we've still got undefined comparison macros, provide defaults.  */
 520
 521 /* Return nonzero value if X is greater than Y.  */
 522 # ifndef isgreater
 523 #  define isgreater(x, y) \
 524   (__extension__                                                              \
 525    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 526       !isunordered (__x, __y) && __x > __y; }))
 527 # endif
 528
 529 /* Return nonzero value if X is greater than or equal to Y.  */
 530 # ifndef isgreaterequal
 531 #  define isgreaterequal(x, y) \
 532   (__extension__                                                              \
 533    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 534       !isunordered (__x, __y) && __x >= __y; }))
 535 # endif
 536
 537 /* Return nonzero value if X is less than Y.  */
 538 # ifndef isless
 539 #  define isless(x, y) \
 540   (__extension__                                                              \
 541    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 542       !isunordered (__x, __y) && __x < __y; }))
 543 # endif
 544
 545 /* Return nonzero value if X is less than or equal to Y.  */
 546 # ifndef islessequal
 547 #  define islessequal(x, y) \
 548   (__extension__                                                              \
 549    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 550       !isunordered (__x, __y) && __x <= __y; }))
 551 # endif
 552
 553 /* Return nonzero value if either X is less than Y or Y is less than X.  */
 554 # ifndef islessgreater
 555 #  define islessgreater(x, y) \
 556   (__extension__                                                              \
 557    ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y);                       \
 558       !isunordered (__x, __y) && (__x < __y || __y < __x); }))
 559 # endif
 560
 561 /* Return nonzero value if arguments are unordered.  */
 562 # ifndef isunordered
 563 #  define isunordered(u, v) \
 564   (__extension__                                                              \
 565    ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v);                       \
 566       fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
 567 # endif
 568
 569 #endif
 570
 571 #if __GLIBC_USE (IEC_60559_BFP_EXT)
 572 /* An expression whose type has the widest of the evaluation formats
 573    of X and Y (which are of floating-point types).  */
 574 # if __FLT_EVAL_METHOD__ == 2 || __FLT_EVAL_METHOD__ > 64
 575 #  define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0L)
 576 # elif __FLT_EVAL_METHOD__ == 1 || __FLT_EVAL_METHOD__ > 32
 577 #  define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0)
 578 # else
 579 #  define __MATH_EVAL_FMT2(x, y) ((x) + (y))
 580 # endif
 581
 582 /* Return X == Y but raising "invalid" and setting errno if X or Y is
 583    a NaN.  */
 584 # define iseqsig(x, y) \
 585   __MATH_TG (__MATH_EVAL_FMT2 (x, y), __iseqsig, ((x), (y)))
 586 #endif
 587
 588 __END_DECLS
 589
 590
 591 #endif /* math.h  */