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
72typedef float float_t;
73typedef double double_t;
74# elif __GLIBC_FLT_EVAL_METHOD == 1
75typedef double float_t;
76typedef double double_t;
77# elif __GLIBC_FLT_EVAL_METHOD == 2
78typedef long double float_t;
79typedef long double double_t;
80# elif __GLIBC_FLT_EVAL_METHOD == 32
81typedef _Float32 float_t;
82typedef double double_t;
83# elif __GLIBC_FLT_EVAL_METHOD == 33
84typedef _Float32x float_t;
85typedef _Float32x double_t;
86# elif __GLIBC_FLT_EVAL_METHOD == 64
87typedef _Float64 float_t;
88typedef _Float64 double_t;
89# elif __GLIBC_FLT_EVAL_METHOD == 65
90typedef _Float64x float_t;
91typedef _Float64x double_t;
92# elif __GLIBC_FLT_EVAL_METHOD == 128
93typedef _Float128 float_t;
94typedef _Float128 double_t;
95# elif __GLIBC_FLT_EVAL_METHOD == 129
96typedef _Float128x float_t;
97typedef _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. */
160enum
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.h>
214#undef _Mdouble_
215#undef _Mdouble_BEGIN_NAMESPACE
216#undef _Mdouble_END_NAMESPACE
217#undef __MATH_PRECNAME
218#undef __MATH_DECLARING_DOUBLE
219
220#ifdef __USE_ISOC99
221
222
223/* Include the file of declarations again, this time using `float'
224 instead of `double' and appending f to each function name. */
225
226# ifndef _Mfloat_
227# define _Mfloat_ float
228# endif
229# define _Mdouble_ _Mfloat_
230# define __MATH_PRECNAME(name,r) name##f##r
231# define __MATH_DECLARING_DOUBLE 0
232# define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
233# define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99
234# include <bits/mathcalls.h>
235# undef _Mdouble_
236# undef _Mdouble_BEGIN_NAMESPACE
237# undef _Mdouble_END_NAMESPACE
238# undef __MATH_PRECNAME
239# undef __MATH_DECLARING_DOUBLE
240
241# if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
242 || defined __LDBL_COMPAT \
243 || defined _LIBC_TEST
244# ifdef __LDBL_COMPAT
245
246# ifdef __USE_ISOC99
247extern float __nldbl_nexttowardf (float __x, long double __y)
248 __THROW __attribute__ ((__const__));
249# ifdef __REDIRECT_NTH
250extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
251 __nldbl_nexttowardf)
252 __attribute__ ((__const__));
253extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
254 nextafter) __attribute__ ((__const__));
255extern long double __REDIRECT_NTH (nexttowardl,
256 (long double __x, long double __y),
257 nextafter) __attribute__ ((__const__));
258# endif
259# endif
260
261# undef __MATHDECL_1
262# define __MATHDECL_2(type, function,suffix, args, alias) \
263 extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
264 args, alias)
265# define __MATHDECL_1(type, function,suffix, args) \
266 __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
267# endif
268
269/* Include the file of declarations again, this time using `long double'
270 instead of `double' and appending l to each function name. */
271
272# ifndef _Mlong_double_
273# define _Mlong_double_ long double
274# endif
275# define _Mdouble_ _Mlong_double_
276# define __MATH_PRECNAME(name,r) name##l##r
277# define __MATH_DECLARING_DOUBLE 0
278# define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
279# define _Mdouble_END_NAMESPACE __END_NAMESPACE_C99
280# define __MATH_DECLARE_LDOUBLE 1
281# include <bits/mathcalls.h>
282# undef _Mdouble_
283# undef _Mdouble_BEGIN_NAMESPACE
284# undef _Mdouble_END_NAMESPACE
285# undef __MATH_PRECNAME
286# undef __MATH_DECLARING_DOUBLE
287
288# endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */
289
290#endif /* Use ISO C99. */
291#undef __MATHDECL_1
292#undef __MATHDECL
293#undef __MATHCALL
294
295
296#if defined __USE_MISC || defined __USE_XOPEN
297/* This variable is used by `gamma' and `lgamma'. */
298extern int signgam;
299#endif
300
301
302/* Depending on the type of TG_ARG, call an appropriately suffixed
303 version of FUNC with arguments (including parentheses) ARGS.
304 Suffixed functions may not exist for long double if it has the same
305 format as double, or for other types with the same format as float,
306 double or long double. The behavior is undefined if the argument
307 does not have a real floating type. The definition may use a
308 conditional expression, so all suffixed versions of FUNC must
309 return the same type (FUNC may include a cast if necessary rather
310 than being a single identifier). */
311#ifdef __NO_LONG_DOUBLE_MATH
312# define __MATH_TG(TG_ARG, FUNC, ARGS) \
313 (sizeof (TG_ARG) == sizeof (float) ? FUNC ## f ARGS : FUNC ARGS)
314#else
315# define __MATH_TG(TG_ARG, FUNC, ARGS) \
316 (sizeof (TG_ARG) == sizeof (float) \
317 ? FUNC ## f ARGS \
318 : sizeof (TG_ARG) == sizeof (double) \
319 ? FUNC ARGS \
320 : FUNC ## l ARGS)
321#endif
322
323/* ISO C99 defines some generic macros which work on any data type. */
324#ifdef __USE_ISOC99
325
326/* All floating-point numbers can be put in one of these categories. */
327enum
328 {
329 FP_NAN =
330# define FP_NAN 0
331 FP_NAN,
332 FP_INFINITE =
333# define FP_INFINITE 1
334 FP_INFINITE,
335 FP_ZERO =
336# define FP_ZERO 2
337 FP_ZERO,
338 FP_SUBNORMAL =
339# define FP_SUBNORMAL 3
340 FP_SUBNORMAL,
341 FP_NORMAL =
342# define FP_NORMAL 4
343 FP_NORMAL
344 };
345
346/* GCC bug 66462 means we cannot use the math builtins with -fsignaling-nan,
347 so disable builtins if this is enabled. When fixed in a newer GCC,
348 the __SUPPORT_SNAN__ check may be skipped for those versions. */
349
350/* Return number of classification appropriate for X. */
351# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__ \
352 && !defined __OPTIMIZE_SIZE__
353# define fpclassify(x) __builtin_fpclassify (FP_NAN, FP_INFINITE, \
354 FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x)
355# else
356# define fpclassify(x) __MATH_TG ((x), __fpclassify, (x))
357# endif
358
359/* Return nonzero value if sign of X is negative. */
360# if __GNUC_PREREQ (4,0)
361# define signbit(x) __MATH_TG ((x), __builtin_signbit, (x))
362# else
363# define signbit(x) __MATH_TG ((x), __signbit, (x))
364# endif
365
366/* Return nonzero value if X is not +-Inf or NaN. */
367# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
368# define isfinite(x) __builtin_isfinite (x)
369# else
370# define isfinite(x) __MATH_TG ((x), __finite, (x))
371# endif
372
373/* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */
374# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
375# define isnormal(x) __builtin_isnormal (x)
376# else
377# define isnormal(x) (fpclassify (x) == FP_NORMAL)
378# endif
379
380/* Return nonzero value if X is a NaN. We could use `fpclassify' but
381 we already have this functions `__isnan' and it is faster. */
382# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
383# define isnan(x) __builtin_isnan (x)
384# else
385# define isnan(x) __MATH_TG ((x), __isnan, (x))
386# endif
387
388/* Return nonzero value if X is positive or negative infinity. */
389# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
390# define isinf(x) __builtin_isinf_sign (x)
391# else
392# define isinf(x) __MATH_TG ((x), __isinf, (x))
393# endif
394
395/* Bitmasks for the math_errhandling macro. */
396# define MATH_ERRNO 1 /* errno set by math functions. */
397# define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */
398
399/* By default all functions support both errno and exception handling.
400 In gcc's fast math mode and if inline functions are defined this
401 might not be true. */
402# ifndef __FAST_MATH__
403# define math_errhandling (MATH_ERRNO | MATH_ERREXCEPT)
404# endif
405
406#endif /* Use ISO C99. */
407
408#if __GLIBC_USE (IEC_60559_BFP_EXT)
409# include <bits/iscanonical.h>
410
411/* Return nonzero value if X is a signaling NaN. */
412# define issignaling(x) __MATH_TG ((x), __issignaling, (x))
413
414/* Return nonzero value if X is subnormal. */
415# define issubnormal(x) (fpclassify (x) == FP_SUBNORMAL)
416
417/* Return nonzero value if X is zero. */
418# ifndef __cplusplus
419# ifdef __SUPPORT_SNAN__
420# define iszero(x) (fpclassify (x) == FP_ZERO)
421# else
422# define iszero(x) (((__typeof (x)) (x)) == 0)
423# endif
424# else /* __cplusplus */
425extern "C++" {
426template <class __T> inline bool
427iszero (__T __val)
428{
429# ifdef __SUPPORT_SNAN__
430 return fpclassify (__val) == FP_ZERO;
431# else
432 return __val == 0;
433# endif
434}
435} /* extern C++ */
436# endif /* __cplusplus */
437#endif /* Use IEC_60559_BFP_EXT. */
438
439#ifdef __USE_MISC
440/* Support for various different standard error handling behaviors. */
441typedef enum
442{
443 _IEEE_ = -1, /* According to IEEE 754/IEEE 854. */
444 _SVID_, /* According to System V, release 4. */
445 _XOPEN_, /* Nowadays also Unix98. */
446 _POSIX_,
447 _ISOC_ /* Actually this is ISO C99. */
448} _LIB_VERSION_TYPE;
449
450/* This variable can be changed at run-time to any of the values above to
451 affect floating point error handling behavior (it may also be necessary
452 to change the hardware FPU exception settings). */
453extern _LIB_VERSION_TYPE _LIB_VERSION;
454#endif
455
456
457#ifdef __USE_MISC
458/* In SVID error handling, `matherr' is called with this description
459 of the exceptional condition.
460
461 We have a problem when using C++ since `exception' is a reserved
462 name in C++. */
463# ifdef __cplusplus
464struct __exception
465# else
466struct exception
467# endif
468 {
469 int type;
470 char *name;
471 double arg1;
472 double arg2;
473 double retval;
474 };
475
476# ifdef __cplusplus
477extern int matherr (struct __exception *__exc) throw ();
478# else
479extern int matherr (struct exception *__exc);
480# endif
481
482# define X_TLOSS 1.41484755040568800000e+16
483
484/* Types of exceptions in the `type' field. */
485# define DOMAIN 1
486# define SING 2
487# define OVERFLOW 3
488# define UNDERFLOW 4
489# define TLOSS 5
490# define PLOSS 6
491
492/* SVID mode specifies returning this large value instead of infinity. */
493# define HUGE 3.40282347e+38F
494
495#else /* !Misc. */
496
497# ifdef __USE_XOPEN
498/* X/Open wants another strange constant. */
499# define MAXFLOAT 3.40282347e+38F
500# endif
501
502#endif /* Misc. */
503
504
505/* Some useful constants. */
506#if defined __USE_MISC || defined __USE_XOPEN
507# define M_E 2.7182818284590452354 /* e */
508# define M_LOG2E 1.4426950408889634074 /* log_2 e */
509# define M_LOG10E 0.43429448190325182765 /* log_10 e */
510# define M_LN2 0.69314718055994530942 /* log_e 2 */
511# define M_LN10 2.30258509299404568402 /* log_e 10 */
512# define M_PI 3.14159265358979323846 /* pi */
513# define M_PI_2 1.57079632679489661923 /* pi/2 */
514# define M_PI_4 0.78539816339744830962 /* pi/4 */
515# define M_1_PI 0.31830988618379067154 /* 1/pi */
516# define M_2_PI 0.63661977236758134308 /* 2/pi */
517# define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
518# define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
519# define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
520#endif
521
522/* The above constants are not adequate for computation using `long double's.
523 Therefore we provide as an extension constants with similar names as a
524 GNU extension. Provide enough digits for the 128-bit IEEE quad. */
525#ifdef __USE_GNU
526# define M_El 2.718281828459045235360287471352662498L /* e */
527# define M_LOG2El 1.442695040888963407359924681001892137L /* log_2 e */
528# define M_LOG10El 0.434294481903251827651128918916605082L /* log_10 e */
529# define M_LN2l 0.693147180559945309417232121458176568L /* log_e 2 */
530# define M_LN10l 2.302585092994045684017991454684364208L /* log_e 10 */
531# define M_PIl 3.141592653589793238462643383279502884L /* pi */
532# define M_PI_2l 1.570796326794896619231321691639751442L /* pi/2 */
533# define M_PI_4l 0.785398163397448309615660845819875721L /* pi/4 */
534# define M_1_PIl 0.318309886183790671537767526745028724L /* 1/pi */
535# define M_2_PIl 0.636619772367581343075535053490057448L /* 2/pi */
536# define M_2_SQRTPIl 1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
537# define M_SQRT2l 1.414213562373095048801688724209698079L /* sqrt(2) */
538# define M_SQRT1_2l 0.707106781186547524400844362104849039L /* 1/sqrt(2) */
539#endif
540
541
542/* When compiling in strict ISO C compatible mode we must not use the
543 inline functions since they, among other things, do not set the
544 `errno' variable correctly. */
545#if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
546# define __NO_MATH_INLINES 1
547#endif
548
549#if defined __USE_ISOC99 && __GNUC_PREREQ(2,97)
550/* ISO C99 defines some macros to compare number while taking care for
551 unordered numbers. Many FPUs provide special instructions to support
552 these operations. Generic support in GCC for these as builtins went
553 in before 3.0.0, but not all cpus added their patterns. We define
554 versions that use the builtins here, and <bits/mathinline.h> will
555 undef/redefine as appropriate for the specific GCC version in use. */
556# define isgreater(x, y) __builtin_isgreater(x, y)
557# define isgreaterequal(x, y) __builtin_isgreaterequal(x, y)
558# define isless(x, y) __builtin_isless(x, y)
559# define islessequal(x, y) __builtin_islessequal(x, y)
560# define islessgreater(x, y) __builtin_islessgreater(x, y)
561# define isunordered(u, v) __builtin_isunordered(u, v)
562#endif
563
564/* Get machine-dependent inline versions (if there are any). */
565#ifdef __USE_EXTERN_INLINES
566# include <bits/mathinline.h>
567#endif
568
569/* Define special entry points to use when the compiler got told to
570 only expect finite results. */
571#if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0
572# include <bits/math-finite.h>
573#endif
574
575#ifdef __USE_ISOC99
576/* If we've still got undefined comparison macros, provide defaults. */
577
578/* Return nonzero value if X is greater than Y. */
579# ifndef isgreater
580# define isgreater(x, y) \
581 (__extension__ \
582 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
583 !isunordered (__x, __y) && __x > __y; }))
584# endif
585
586/* Return nonzero value if X is greater than or equal to Y. */
587# ifndef isgreaterequal
588# define isgreaterequal(x, y) \
589 (__extension__ \
590 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
591 !isunordered (__x, __y) && __x >= __y; }))
592# endif
593
594/* Return nonzero value if X is less than Y. */
595# ifndef isless
596# define isless(x, y) \
597 (__extension__ \
598 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
599 !isunordered (__x, __y) && __x < __y; }))
600# endif
601
602/* Return nonzero value if X is less than or equal to Y. */
603# ifndef islessequal
604# define islessequal(x, y) \
605 (__extension__ \
606 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
607 !isunordered (__x, __y) && __x <= __y; }))
608# endif
609
610/* Return nonzero value if either X is less than Y or Y is less than X. */
611# ifndef islessgreater
612# define islessgreater(x, y) \
613 (__extension__ \
614 ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
615 !isunordered (__x, __y) && (__x < __y || __y < __x); }))
616# endif
617
618/* Return nonzero value if arguments are unordered. */
619# ifndef isunordered
620# define isunordered(u, v) \
621 (__extension__ \
622 ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \
623 fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
624# endif
625
626#endif
627
628#if __GLIBC_USE (IEC_60559_BFP_EXT)
629/* An expression whose type has the widest of the evaluation formats
630 of X and Y (which are of floating-point types). */
631# if __FLT_EVAL_METHOD__ == 2 || __FLT_EVAL_METHOD__ > 64
632# define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0L)
633# elif __FLT_EVAL_METHOD__ == 1 || __FLT_EVAL_METHOD__ > 32
634# define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0)
635# else
636# define __MATH_EVAL_FMT2(x, y) ((x) + (y))
637# endif
638
639/* Return X == Y but raising "invalid" and setting errno if X or Y is
640 a NaN. */
641# define iseqsig(x, y) \
642 __MATH_TG (__MATH_EVAL_FMT2 (x, y), __iseqsig, ((x), (y)))
643#endif
644
645__END_DECLS
646
647
648#endif /* math.h */
649