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