1 /* Declarations for math functions.
2 Copyright (C) 1991-2018 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
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.
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.
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/>. */
20 * ISO C99 Standard: 7.12 Mathematics <math.h>
26 #define __GLIBC_INTERNAL_STARTING_HEADER_IMPLEMENTATION
27 #include <bits/libc-header-start.h>
29 #if defined log && defined __GNUC__
30 # warning A macro called log was already defined when <math.h> was included.
31 # warning This will cause compilation problems.
36 /* Get definitions of __intmax_t and __uintmax_t. */
37 #include <bits/types.h>
39 /* Get machine-dependent vector math functions declarations. */
40 #include <bits/math-vector.h>
42 /* Gather machine dependent type support. */
43 #include <bits/floatn.h>
45 /* Value returned on overflow. With IEEE 754 floating point, this is
46 +Infinity, otherwise the largest representable positive value. */
47 #if __GNUC_PREREQ (3, 3)
48 # define HUGE_VAL (__builtin_huge_val ())
50 /* This may provoke compiler warnings, and may not be rounded to
51 +Infinity in all IEEE 754 rounding modes, but is the best that can
52 be done in ISO C while remaining a constant expression. 10,000 is
53 greater than the maximum (decimal) exponent for all supported
54 floating-point formats and widths. */
55 # define HUGE_VAL 1e10000
58 # if __GNUC_PREREQ (3, 3)
59 # define HUGE_VALF (__builtin_huge_valf ())
60 # define HUGE_VALL (__builtin_huge_vall ())
62 # define HUGE_VALF 1e10000f
63 # define HUGE_VALL 1e10000L
66 #if __HAVE_FLOAT16 && __GLIBC_USE (IEC_60559_TYPES_EXT)
67 # define HUGE_VAL_F16 (__builtin_huge_valf16 ())
69 #if __HAVE_FLOAT32 && __GLIBC_USE (IEC_60559_TYPES_EXT)
70 # define HUGE_VAL_F32 (__builtin_huge_valf32 ())
72 #if __HAVE_FLOAT64 && __GLIBC_USE (IEC_60559_TYPES_EXT)
73 # define HUGE_VAL_F64 (__builtin_huge_valf64 ())
75 #if __HAVE_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
76 # define HUGE_VAL_F128 (__builtin_huge_valf128 ())
78 #if __HAVE_FLOAT32X && __GLIBC_USE (IEC_60559_TYPES_EXT)
79 # define HUGE_VAL_F32X (__builtin_huge_valf32x ())
81 #if __HAVE_FLOAT64X && __GLIBC_USE (IEC_60559_TYPES_EXT)
82 # define HUGE_VAL_F64X (__builtin_huge_valf64x ())
84 #if __HAVE_FLOAT128X && __GLIBC_USE (IEC_60559_TYPES_EXT)
85 # define HUGE_VAL_F128X (__builtin_huge_valf128x ())
89 /* IEEE positive infinity. */
90 # if __GNUC_PREREQ (3, 3)
91 # define INFINITY (__builtin_inff ())
93 # define INFINITY HUGE_VALF
96 /* IEEE Not A Number. */
97 # if __GNUC_PREREQ (3, 3)
98 # define NAN (__builtin_nanf (""))
100 /* This will raise an "invalid" exception outside static initializers,
101 but is the best that can be done in ISO C while remaining a
102 constant expression. */
103 # define NAN (0.0f / 0.0f)
105 #endif /* __USE_ISOC99 */
107 #if __GLIBC_USE (IEC_60559_BFP_EXT)
108 /* Signaling NaN macros, if supported. */
109 # if __GNUC_PREREQ (3, 3)
110 # define SNANF (__builtin_nansf (""))
111 # define SNAN (__builtin_nans (""))
112 # define SNANL (__builtin_nansl (""))
115 #if __HAVE_FLOAT16 && __GLIBC_USE (IEC_60559_TYPES_EXT)
116 # define SNANF16 (__builtin_nansf16 (""))
118 #if __HAVE_FLOAT32 && __GLIBC_USE (IEC_60559_TYPES_EXT)
119 # define SNANF32 (__builtin_nansf32 (""))
121 #if __HAVE_FLOAT64 && __GLIBC_USE (IEC_60559_TYPES_EXT)
122 # define SNANF64 (__builtin_nansf64 (""))
124 #if __HAVE_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
125 # define SNANF128 (__builtin_nansf128 (""))
127 #if __HAVE_FLOAT32X && __GLIBC_USE (IEC_60559_TYPES_EXT)
128 # define SNANF32X (__builtin_nansf32x (""))
130 #if __HAVE_FLOAT64X && __GLIBC_USE (IEC_60559_TYPES_EXT)
131 # define SNANF64X (__builtin_nansf64x (""))
133 #if __HAVE_FLOAT128X && __GLIBC_USE (IEC_60559_TYPES_EXT)
134 # define SNANF128X (__builtin_nansf128x (""))
137 /* Get __GLIBC_FLT_EVAL_METHOD. */
138 #include <bits/flt-eval-method.h>
141 /* Define the following typedefs.
143 float_t floating-point type at least as wide as `float' used
144 to evaluate `float' expressions
145 double_t floating-point type at least as wide as `double' used
146 to evaluate `double' expressions
148 # if __GLIBC_FLT_EVAL_METHOD == 0 || __GLIBC_FLT_EVAL_METHOD == 16
149 typedef float float_t
;
150 typedef double double_t
;
151 # elif __GLIBC_FLT_EVAL_METHOD == 1
152 typedef double float_t
;
153 typedef double double_t
;
154 # elif __GLIBC_FLT_EVAL_METHOD == 2
155 typedef long double float_t
;
156 typedef long double double_t
;
157 # elif __GLIBC_FLT_EVAL_METHOD == 32
158 typedef _Float32 float_t
;
159 typedef double double_t
;
160 # elif __GLIBC_FLT_EVAL_METHOD == 33
161 typedef _Float32x float_t
;
162 typedef _Float32x double_t
;
163 # elif __GLIBC_FLT_EVAL_METHOD == 64
164 typedef _Float64 float_t
;
165 typedef _Float64 double_t
;
166 # elif __GLIBC_FLT_EVAL_METHOD == 65
167 typedef _Float64x float_t
;
168 typedef _Float64x double_t
;
169 # elif __GLIBC_FLT_EVAL_METHOD == 128
170 typedef _Float128 float_t
;
171 typedef _Float128 double_t
;
172 # elif __GLIBC_FLT_EVAL_METHOD == 129
173 typedef _Float128x float_t
;
174 typedef _Float128x double_t
;
176 # error "Unknown __GLIBC_FLT_EVAL_METHOD"
180 /* Define macros for the return values of ilogb and llogb, based on
181 __FP_LOGB0_IS_MIN and __FP_LOGBNAN_IS_MIN.
183 FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'.
184 FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
185 FP_LLOGB0 Expands to a value returned by `llogb (0.0)'.
186 FP_LLOGBNAN Expands to a value returned by `llogb (NAN)'.
190 #include <bits/fp-logb.h>
192 # if __FP_LOGB0_IS_MIN
193 # define FP_ILOGB0 (-2147483647 - 1)
195 # define FP_ILOGB0 (-2147483647)
197 # if __FP_LOGBNAN_IS_MIN
198 # define FP_ILOGBNAN (-2147483647 - 1)
200 # define FP_ILOGBNAN 2147483647
203 #if __GLIBC_USE (IEC_60559_BFP_EXT)
204 # if __WORDSIZE == 32
205 # define __FP_LONG_MAX 0x7fffffffL
207 # define __FP_LONG_MAX 0x7fffffffffffffffL
209 # if __FP_LOGB0_IS_MIN
210 # define FP_LLOGB0 (-__FP_LONG_MAX - 1)
212 # define FP_LLOGB0 (-__FP_LONG_MAX)
214 # if __FP_LOGBNAN_IS_MIN
215 # define FP_LLOGBNAN (-__FP_LONG_MAX - 1)
217 # define FP_LLOGBNAN __FP_LONG_MAX
221 /* Get the architecture specific values describing the floating-point
222 evaluation. The following symbols will get defined:
227 If defined it indicates that the `fma' function
228 generally executes about as fast as a multiply and an add.
229 This macro is defined only iff the `fma' function is
230 implemented directly with a hardware multiply-add instructions.
233 #include <bits/fp-fast.h>
235 #if __GLIBC_USE (IEC_60559_BFP_EXT)
236 /* Rounding direction macros for fromfp functions. */
240 # define FP_INT_UPWARD 0
243 # define FP_INT_DOWNWARD 1
246 # define FP_INT_TOWARDZERO 2
248 FP_INT_TONEARESTFROMZERO
=
249 # define FP_INT_TONEARESTFROMZERO 3
250 FP_INT_TONEARESTFROMZERO
,
252 # define FP_INT_TONEAREST 4
257 /* The file <bits/mathcalls.h> contains the prototypes for all the
258 actual math functions. These macros are used for those prototypes,
259 so we can easily declare each function as both `name' and `__name',
260 and can declare the float versions `namef' and `__namef'. */
262 #define __SIMD_DECL(function) __CONCAT (__DECL_SIMD_, function)
264 #define __MATHCALL_VEC(function, suffix, args) \
265 __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
266 __MATHCALL (function, suffix, args)
268 #define __MATHDECL_VEC(type, function,suffix, args) \
269 __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
270 __MATHDECL(type, function,suffix, args)
272 #define __MATHCALL(function,suffix, args) \
273 __MATHDECL (_Mdouble_,function,suffix, args)
274 #define __MATHDECL(type, function,suffix, args) \
275 __MATHDECL_1(type, function,suffix, args); \
276 __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
277 #define __MATHCALLX(function,suffix, args, attrib) \
278 __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
279 #define __MATHDECLX(type, function,suffix, args, attrib) \
280 __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
281 __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
282 #define __MATHDECL_1(type, function,suffix, args) \
283 extern type __MATH_PRECNAME(function,suffix) args __THROW
285 #define _Mdouble_ double
286 #define __MATH_PRECNAME(name,r) __CONCAT(name,r)
287 #define __MATH_DECLARING_DOUBLE 1
288 #define __MATH_DECLARING_FLOATN 0
289 #include <bits/mathcalls-helper-functions.h>
290 #include <bits/mathcalls.h>
292 #undef __MATH_PRECNAME
293 #undef __MATH_DECLARING_DOUBLE
294 #undef __MATH_DECLARING_FLOATN
299 /* Include the file of declarations again, this time using `float'
300 instead of `double' and appending f to each function name. */
302 # define _Mdouble_ float
303 # define __MATH_PRECNAME(name,r) name##f##r
304 # define __MATH_DECLARING_DOUBLE 0
305 # define __MATH_DECLARING_FLOATN 0
306 # include <bits/mathcalls-helper-functions.h>
307 # include <bits/mathcalls.h>
309 # undef __MATH_PRECNAME
310 # undef __MATH_DECLARING_DOUBLE
311 # undef __MATH_DECLARING_FLOATN
313 # if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
314 || defined __LDBL_COMPAT \
315 || defined _LIBC_TEST
316 # ifdef __LDBL_COMPAT
319 extern float __nldbl_nexttowardf (float __x
, long double __y
)
320 __THROW
__attribute__ ((__const__
));
321 # ifdef __REDIRECT_NTH
322 extern float __REDIRECT_NTH (nexttowardf
, (float __x
, long double __y
),
324 __attribute__ ((__const__
));
325 extern double __REDIRECT_NTH (nexttoward
, (double __x
, long double __y
),
326 nextafter
) __attribute__ ((__const__
));
327 extern long double __REDIRECT_NTH (nexttowardl
,
328 (long double __x
, long double __y
),
329 nextafter
) __attribute__ ((__const__
));
334 # define __MATHDECL_2(type, function,suffix, args, alias) \
335 extern type __REDIRECT_NTH(__MATH_PRECNAME(function,suffix), \
337 # define __MATHDECL_1(type, function,suffix, args) \
338 __MATHDECL_2(type, function,suffix, args, __CONCAT(function,suffix))
341 /* Include the file of declarations again, this time using `long double'
342 instead of `double' and appending l to each function name. */
344 # define _Mdouble_ long double
345 # define __MATH_PRECNAME(name,r) name##l##r
346 # define __MATH_DECLARING_DOUBLE 0
347 # define __MATH_DECLARING_FLOATN 0
348 # define __MATH_DECLARE_LDOUBLE 1
349 # include <bits/mathcalls-helper-functions.h>
350 # include <bits/mathcalls.h>
352 # undef __MATH_PRECNAME
353 # undef __MATH_DECLARING_DOUBLE
354 # undef __MATH_DECLARING_FLOATN
356 # endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */
358 #endif /* Use ISO C99. */
360 /* Include the file of declarations for _FloatN and _FloatNx
363 #if __HAVE_DISTINCT_FLOAT16 || (__HAVE_FLOAT16 && !defined _LIBC)
364 # define _Mdouble_ _Float16
365 # define __MATH_PRECNAME(name,r) name##f16##r
366 # define __MATH_DECLARING_DOUBLE 0
367 # define __MATH_DECLARING_FLOATN 1
368 # if __HAVE_DISTINCT_FLOAT16
369 # include <bits/mathcalls-helper-functions.h>
371 # if __GLIBC_USE (IEC_60559_TYPES_EXT)
372 # include <bits/mathcalls.h>
375 # undef __MATH_PRECNAME
376 # undef __MATH_DECLARING_DOUBLE
377 # undef __MATH_DECLARING_FLOATN
378 #endif /* __HAVE_DISTINCT_FLOAT16 || (__HAVE_FLOAT16 && !_LIBC). */
380 #if __HAVE_DISTINCT_FLOAT32 || (__HAVE_FLOAT32 && !defined _LIBC)
381 # define _Mdouble_ _Float32
382 # define __MATH_PRECNAME(name,r) name##f32##r
383 # define __MATH_DECLARING_DOUBLE 0
384 # define __MATH_DECLARING_FLOATN 1
385 # if __HAVE_DISTINCT_FLOAT32
386 # include <bits/mathcalls-helper-functions.h>
388 # if __GLIBC_USE (IEC_60559_TYPES_EXT)
389 # include <bits/mathcalls.h>
392 # undef __MATH_PRECNAME
393 # undef __MATH_DECLARING_DOUBLE
394 # undef __MATH_DECLARING_FLOATN
395 #endif /* __HAVE_DISTINCT_FLOAT32 || (__HAVE_FLOAT32 && !_LIBC). */
397 #if __HAVE_DISTINCT_FLOAT64 || (__HAVE_FLOAT64 && !defined _LIBC)
398 # define _Mdouble_ _Float64
399 # define __MATH_PRECNAME(name,r) name##f64##r
400 # define __MATH_DECLARING_DOUBLE 0
401 # define __MATH_DECLARING_FLOATN 1
402 # if __HAVE_DISTINCT_FLOAT64
403 # include <bits/mathcalls-helper-functions.h>
405 # if __GLIBC_USE (IEC_60559_TYPES_EXT)
406 # include <bits/mathcalls.h>
409 # undef __MATH_PRECNAME
410 # undef __MATH_DECLARING_DOUBLE
411 # undef __MATH_DECLARING_FLOATN
412 #endif /* __HAVE_DISTINCT_FLOAT64 || (__HAVE_FLOAT64 && !_LIBC). */
414 #if __HAVE_DISTINCT_FLOAT128 || (__HAVE_FLOAT128 && !defined _LIBC)
415 # define _Mdouble_ _Float128
416 # define __MATH_PRECNAME(name,r) name##f128##r
417 # define __MATH_DECLARING_DOUBLE 0
418 # define __MATH_DECLARING_FLOATN 1
419 # if __HAVE_DISTINCT_FLOAT128
420 # include <bits/mathcalls-helper-functions.h>
422 # if __GLIBC_USE (IEC_60559_TYPES_EXT)
423 # include <bits/mathcalls.h>
426 # undef __MATH_PRECNAME
427 # undef __MATH_DECLARING_DOUBLE
428 # undef __MATH_DECLARING_FLOATN
429 #endif /* __HAVE_DISTINCT_FLOAT128 || (__HAVE_FLOAT128 && !_LIBC). */
431 #if __HAVE_DISTINCT_FLOAT32X || (__HAVE_FLOAT32X && !defined _LIBC)
432 # define _Mdouble_ _Float32x
433 # define __MATH_PRECNAME(name,r) name##f32x##r
434 # define __MATH_DECLARING_DOUBLE 0
435 # define __MATH_DECLARING_FLOATN 1
436 # if __HAVE_DISTINCT_FLOAT32X
437 # include <bits/mathcalls-helper-functions.h>
439 # if __GLIBC_USE (IEC_60559_TYPES_EXT)
440 # include <bits/mathcalls.h>
443 # undef __MATH_PRECNAME
444 # undef __MATH_DECLARING_DOUBLE
445 # undef __MATH_DECLARING_FLOATN
446 #endif /* __HAVE_DISTINCT_FLOAT32X || (__HAVE_FLOAT32X && !_LIBC). */
448 #if __HAVE_DISTINCT_FLOAT64X || (__HAVE_FLOAT64X && !defined _LIBC)
449 # define _Mdouble_ _Float64x
450 # define __MATH_PRECNAME(name,r) name##f64x##r
451 # define __MATH_DECLARING_DOUBLE 0
452 # define __MATH_DECLARING_FLOATN 1
453 # if __HAVE_DISTINCT_FLOAT64X
454 # include <bits/mathcalls-helper-functions.h>
456 # if __GLIBC_USE (IEC_60559_TYPES_EXT)
457 # include <bits/mathcalls.h>
460 # undef __MATH_PRECNAME
461 # undef __MATH_DECLARING_DOUBLE
462 # undef __MATH_DECLARING_FLOATN
463 #endif /* __HAVE_DISTINCT_FLOAT64X || (__HAVE_FLOAT64X && !_LIBC). */
465 #if __HAVE_DISTINCT_FLOAT128X || (__HAVE_FLOAT128X && !defined _LIBC)
466 # define _Mdouble_ _Float128x
467 # define __MATH_PRECNAME(name,r) name##f128x##r
468 # define __MATH_DECLARING_DOUBLE 0
469 # define __MATH_DECLARING_FLOATN 1
470 # if __HAVE_DISTINCT_FLOAT128X
471 # include <bits/mathcalls-helper-functions.h>
473 # if __GLIBC_USE (IEC_60559_TYPES_EXT)
474 # include <bits/mathcalls.h>
477 # undef __MATH_PRECNAME
478 # undef __MATH_DECLARING_DOUBLE
479 # undef __MATH_DECLARING_FLOATN
480 #endif /* __HAVE_DISTINCT_FLOAT128X || (__HAVE_FLOAT128X && !_LIBC). */
487 #if defined __USE_MISC || defined __USE_XOPEN
488 /* This variable is used by `gamma' and `lgamma'. */
492 #if (__HAVE_DISTINCT_FLOAT16 \
493 || __HAVE_DISTINCT_FLOAT32 \
494 || __HAVE_DISTINCT_FLOAT64 \
495 || __HAVE_DISTINCT_FLOAT32X \
496 || __HAVE_DISTINCT_FLOAT64X \
497 || __HAVE_DISTINCT_FLOAT128X)
498 # error "Unsupported _FloatN or _FloatNx types for <math.h>."
501 /* Depending on the type of TG_ARG, call an appropriately suffixed
502 version of FUNC with arguments (including parentheses) ARGS.
503 Suffixed functions may not exist for long double if it has the same
504 format as double, or for other types with the same format as float,
505 double or long double. The behavior is undefined if the argument
506 does not have a real floating type. The definition may use a
507 conditional expression, so all suffixed versions of FUNC must
508 return the same type (FUNC may include a cast if necessary rather
509 than being a single identifier). */
510 #ifdef __NO_LONG_DOUBLE_MATH
511 # if __HAVE_DISTINCT_FLOAT128
512 # error "Distinct _Float128 without distinct long double not supported."
514 # define __MATH_TG(TG_ARG, FUNC, ARGS) \
515 (sizeof (TG_ARG) == sizeof (float) ? FUNC ## f ARGS : FUNC ARGS)
516 #elif __HAVE_DISTINCT_FLOAT128
517 # if __HAVE_GENERIC_SELECTION
518 # if __HAVE_FLOATN_NOT_TYPEDEF && __HAVE_FLOAT32
519 # define __MATH_TG_F32(FUNC, ARGS) _Float32: FUNC ## f ARGS,
521 # define __MATH_TG_F32(FUNC, ARGS)
523 # if __HAVE_FLOATN_NOT_TYPEDEF && __HAVE_FLOAT64X
524 # if __HAVE_FLOAT64X_LONG_DOUBLE
525 # define __MATH_TG_F64X(FUNC, ARGS) _Float64x: FUNC ## l ARGS,
527 # define __MATH_TG_F64X(FUNC, ARGS) _Float64x: FUNC ## f128 ARGS,
530 # define __MATH_TG_F64X(FUNC, ARGS)
532 # define __MATH_TG(TG_ARG, FUNC, ARGS) \
533 _Generic ((TG_ARG), \
534 float: FUNC ## f ARGS, \
535 __MATH_TG_F32 (FUNC, ARGS) \
536 default: FUNC ARGS, \
537 long double: FUNC ## l ARGS, \
538 __MATH_TG_F64X (FUNC, ARGS) \
539 _Float128: FUNC ## f128 ARGS)
541 # if __HAVE_FLOATN_NOT_TYPEDEF
542 # error "Non-typedef _FloatN but no _Generic."
544 # define __MATH_TG(TG_ARG, FUNC, ARGS) \
545 __builtin_choose_expr \
546 (__builtin_types_compatible_p (__typeof (TG_ARG), float), \
548 __builtin_choose_expr \
549 (__builtin_types_compatible_p (__typeof (TG_ARG), double), \
551 __builtin_choose_expr \
552 (__builtin_types_compatible_p (__typeof (TG_ARG), long double), \
557 # define __MATH_TG(TG_ARG, FUNC, ARGS) \
558 (sizeof (TG_ARG) == sizeof (float) \
560 : sizeof (TG_ARG) == sizeof (double) \
565 /* ISO C99 defines some generic macros which work on any data type. */
568 /* All floating-point numbers can be put in one of these categories. */
575 # define FP_INFINITE 1
581 # define FP_SUBNORMAL 3
588 /* GCC bug 66462 means we cannot use the math builtins with -fsignaling-nan,
589 so disable builtins if this is enabled. When fixed in a newer GCC,
590 the __SUPPORT_SNAN__ check may be skipped for those versions. */
592 /* Return number of classification appropriate for X. */
593 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__ \
594 && (!defined __OPTIMIZE_SIZE__ || defined __cplusplus)
595 /* The check for __cplusplus allows the use of the builtin, even
596 when optimization for size is on. This is provided for
597 libstdc++, only to let its configure test work when it is built
598 with -Os. No further use of this definition of fpclassify is
599 expected in C++ mode, since libstdc++ provides its own version
600 of fpclassify in cmath (which undefines fpclassify). */
601 # define fpclassify(x) __builtin_fpclassify (FP_NAN, FP_INFINITE, \
602 FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x)
604 # define fpclassify(x) __MATH_TG ((x), __fpclassify, (x))
607 /* Return nonzero value if sign of X is negative. */
608 # if __GNUC_PREREQ (6,0)
609 # define signbit(x) __builtin_signbit (x)
610 # elif defined __cplusplus
611 /* In C++ mode, __MATH_TG cannot be used, because it relies on
612 __builtin_types_compatible_p, which is a C-only builtin.
613 The check for __cplusplus allows the use of the builtin instead of
614 __MATH_TG. This is provided for libstdc++, only to let its configure
615 test work. No further use of this definition of signbit is expected
616 in C++ mode, since libstdc++ provides its own version of signbit
617 in cmath (which undefines signbit). */
618 # define signbit(x) __builtin_signbitl (x)
619 # elif __GNUC_PREREQ (4,0)
620 # define signbit(x) __MATH_TG ((x), __builtin_signbit, (x))
622 # define signbit(x) __MATH_TG ((x), __signbit, (x))
625 /* Return nonzero value if X is not +-Inf or NaN. */
626 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
627 # define isfinite(x) __builtin_isfinite (x)
629 # define isfinite(x) __MATH_TG ((x), __finite, (x))
632 /* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */
633 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
634 # define isnormal(x) __builtin_isnormal (x)
636 # define isnormal(x) (fpclassify (x) == FP_NORMAL)
639 /* Return nonzero value if X is a NaN. We could use `fpclassify' but
640 we already have this functions `__isnan' and it is faster. */
641 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
642 # define isnan(x) __builtin_isnan (x)
644 # define isnan(x) __MATH_TG ((x), __isnan, (x))
647 /* Return nonzero value if X is positive or negative infinity. */
648 # if __HAVE_DISTINCT_FLOAT128 && !__GNUC_PREREQ (7,0) \
649 && !defined __SUPPORT_SNAN__ && !defined __cplusplus
650 /* Since __builtin_isinf_sign is broken for float128 before GCC 7.0,
651 use the helper function, __isinff128, with older compilers. This is
652 only provided for C mode, because in C++ mode, GCC has no support
653 for __builtin_types_compatible_p (and when in C++ mode, this macro is
654 not used anyway, because libstdc++ headers undefine it). */
656 (__builtin_types_compatible_p (__typeof (x), _Float128) \
657 ? __isinff128 (x) : __builtin_isinf_sign (x))
658 # elif __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
659 # define isinf(x) __builtin_isinf_sign (x)
661 # define isinf(x) __MATH_TG ((x), __isinf, (x))
664 /* Bitmasks for the math_errhandling macro. */
665 # define MATH_ERRNO 1 /* errno set by math functions. */
666 # define MATH_ERREXCEPT 2 /* Exceptions raised by math functions. */
668 /* By default all math functions support both errno and exception handling
669 (except for soft floating point implementations which may only support
670 errno handling). If errno handling is disabled, exceptions are still
671 supported by GLIBC. Set math_errhandling to 0 with -ffast-math (this is
672 nonconforming but it is more useful than leaving it undefined). */
673 # ifdef __FAST_MATH__
674 # define math_errhandling 0
675 # elif defined __NO_MATH_ERRNO__
676 # define math_errhandling (MATH_ERREXCEPT)
678 # define math_errhandling (MATH_ERRNO | MATH_ERREXCEPT)
681 #endif /* Use ISO C99. */
683 #if __GLIBC_USE (IEC_60559_BFP_EXT)
684 # include <bits/iscanonical.h>
686 /* Return nonzero value if X is a signaling NaN. */
688 # define issignaling(x) __MATH_TG ((x), __issignaling, (x))
690 /* In C++ mode, __MATH_TG cannot be used, because it relies on
691 __builtin_types_compatible_p, which is a C-only builtin. On the
692 other hand, overloading provides the means to distinguish between
693 the floating-point types. The overloading resolution will match
694 the correct parameter (regardless of type qualifiers (i.e.: const
697 inline int issignaling (float __val
) { return __issignalingf (__val
); }
698 inline int issignaling (double __val
) { return __issignaling (__val
); }
700 issignaling (long double __val
)
702 # ifdef __NO_LONG_DOUBLE_MATH
703 return __issignaling (__val
);
705 return __issignalingl (__val
);
708 # if __HAVE_DISTINCT_FLOAT128
709 inline int issignaling (_Float128 __val
) { return __issignalingf128 (__val
); }
714 /* Return nonzero value if X is subnormal. */
715 # define issubnormal(x) (fpclassify (x) == FP_SUBNORMAL)
717 /* Return nonzero value if X is zero. */
719 # ifdef __SUPPORT_SNAN__
720 # define iszero(x) (fpclassify (x) == FP_ZERO)
722 # define iszero(x) (((__typeof (x)) (x)) == 0)
724 # else /* __cplusplus */
726 # ifdef __SUPPORT_SNAN__
730 return __fpclassifyf (__val
) == FP_ZERO
;
733 iszero (double __val
)
735 return __fpclassify (__val
) == FP_ZERO
;
738 iszero (long double __val
)
740 # ifdef __NO_LONG_DOUBLE_MATH
741 return __fpclassify (__val
) == FP_ZERO
;
743 return __fpclassifyl (__val
) == FP_ZERO
;
746 # if __HAVE_DISTINCT_FLOAT128
748 iszero (_Float128 __val
)
750 return __fpclassifyf128 (__val
) == FP_ZERO
;
754 template <class __T
> inline bool
761 # endif /* __cplusplus */
762 #endif /* Use IEC_60559_BFP_EXT. */
765 /* X/Open wants another strange constant. */
766 # define MAXFLOAT 3.40282347e+38F
770 /* Some useful constants. */
771 #if defined __USE_MISC || defined __USE_XOPEN
772 # define M_E 2.7182818284590452354 /* e */
773 # define M_LOG2E 1.4426950408889634074 /* log_2 e */
774 # define M_LOG10E 0.43429448190325182765 /* log_10 e */
775 # define M_LN2 0.69314718055994530942 /* log_e 2 */
776 # define M_LN10 2.30258509299404568402 /* log_e 10 */
777 # define M_PI 3.14159265358979323846 /* pi */
778 # define M_PI_2 1.57079632679489661923 /* pi/2 */
779 # define M_PI_4 0.78539816339744830962 /* pi/4 */
780 # define M_1_PI 0.31830988618379067154 /* 1/pi */
781 # define M_2_PI 0.63661977236758134308 /* 2/pi */
782 # define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
783 # define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
784 # define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
787 /* The above constants are not adequate for computation using `long double's.
788 Therefore we provide as an extension constants with similar names as a
789 GNU extension. Provide enough digits for the 128-bit IEEE quad. */
791 # define M_El 2.718281828459045235360287471352662498L /* e */
792 # define M_LOG2El 1.442695040888963407359924681001892137L /* log_2 e */
793 # define M_LOG10El 0.434294481903251827651128918916605082L /* log_10 e */
794 # define M_LN2l 0.693147180559945309417232121458176568L /* log_e 2 */
795 # define M_LN10l 2.302585092994045684017991454684364208L /* log_e 10 */
796 # define M_PIl 3.141592653589793238462643383279502884L /* pi */
797 # define M_PI_2l 1.570796326794896619231321691639751442L /* pi/2 */
798 # define M_PI_4l 0.785398163397448309615660845819875721L /* pi/4 */
799 # define M_1_PIl 0.318309886183790671537767526745028724L /* 1/pi */
800 # define M_2_PIl 0.636619772367581343075535053490057448L /* 2/pi */
801 # define M_2_SQRTPIl 1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
802 # define M_SQRT2l 1.414213562373095048801688724209698079L /* sqrt(2) */
803 # define M_SQRT1_2l 0.707106781186547524400844362104849039L /* 1/sqrt(2) */
806 #if __HAVE_FLOAT16 && defined __USE_GNU
807 # define M_Ef16 __f16 (2.718281828459045235360287471352662498) /* e */
808 # define M_LOG2Ef16 __f16 (1.442695040888963407359924681001892137) /* log_2 e */
809 # define M_LOG10Ef16 __f16 (0.434294481903251827651128918916605082) /* log_10 e */
810 # define M_LN2f16 __f16 (0.693147180559945309417232121458176568) /* log_e 2 */
811 # define M_LN10f16 __f16 (2.302585092994045684017991454684364208) /* log_e 10 */
812 # define M_PIf16 __f16 (3.141592653589793238462643383279502884) /* pi */
813 # define M_PI_2f16 __f16 (1.570796326794896619231321691639751442) /* pi/2 */
814 # define M_PI_4f16 __f16 (0.785398163397448309615660845819875721) /* pi/4 */
815 # define M_1_PIf16 __f16 (0.318309886183790671537767526745028724) /* 1/pi */
816 # define M_2_PIf16 __f16 (0.636619772367581343075535053490057448) /* 2/pi */
817 # define M_2_SQRTPIf16 __f16 (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
818 # define M_SQRT2f16 __f16 (1.414213562373095048801688724209698079) /* sqrt(2) */
819 # define M_SQRT1_2f16 __f16 (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
822 #if __HAVE_FLOAT32 && defined __USE_GNU
823 # define M_Ef32 __f32 (2.718281828459045235360287471352662498) /* e */
824 # define M_LOG2Ef32 __f32 (1.442695040888963407359924681001892137) /* log_2 e */
825 # define M_LOG10Ef32 __f32 (0.434294481903251827651128918916605082) /* log_10 e */
826 # define M_LN2f32 __f32 (0.693147180559945309417232121458176568) /* log_e 2 */
827 # define M_LN10f32 __f32 (2.302585092994045684017991454684364208) /* log_e 10 */
828 # define M_PIf32 __f32 (3.141592653589793238462643383279502884) /* pi */
829 # define M_PI_2f32 __f32 (1.570796326794896619231321691639751442) /* pi/2 */
830 # define M_PI_4f32 __f32 (0.785398163397448309615660845819875721) /* pi/4 */
831 # define M_1_PIf32 __f32 (0.318309886183790671537767526745028724) /* 1/pi */
832 # define M_2_PIf32 __f32 (0.636619772367581343075535053490057448) /* 2/pi */
833 # define M_2_SQRTPIf32 __f32 (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
834 # define M_SQRT2f32 __f32 (1.414213562373095048801688724209698079) /* sqrt(2) */
835 # define M_SQRT1_2f32 __f32 (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
838 #if __HAVE_FLOAT64 && defined __USE_GNU
839 # define M_Ef64 __f64 (2.718281828459045235360287471352662498) /* e */
840 # define M_LOG2Ef64 __f64 (1.442695040888963407359924681001892137) /* log_2 e */
841 # define M_LOG10Ef64 __f64 (0.434294481903251827651128918916605082) /* log_10 e */
842 # define M_LN2f64 __f64 (0.693147180559945309417232121458176568) /* log_e 2 */
843 # define M_LN10f64 __f64 (2.302585092994045684017991454684364208) /* log_e 10 */
844 # define M_PIf64 __f64 (3.141592653589793238462643383279502884) /* pi */
845 # define M_PI_2f64 __f64 (1.570796326794896619231321691639751442) /* pi/2 */
846 # define M_PI_4f64 __f64 (0.785398163397448309615660845819875721) /* pi/4 */
847 # define M_1_PIf64 __f64 (0.318309886183790671537767526745028724) /* 1/pi */
848 # define M_2_PIf64 __f64 (0.636619772367581343075535053490057448) /* 2/pi */
849 # define M_2_SQRTPIf64 __f64 (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
850 # define M_SQRT2f64 __f64 (1.414213562373095048801688724209698079) /* sqrt(2) */
851 # define M_SQRT1_2f64 __f64 (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
854 #if __HAVE_FLOAT128 && defined __USE_GNU
855 # define M_Ef128 __f128 (2.718281828459045235360287471352662498) /* e */
856 # define M_LOG2Ef128 __f128 (1.442695040888963407359924681001892137) /* log_2 e */
857 # define M_LOG10Ef128 __f128 (0.434294481903251827651128918916605082) /* log_10 e */
858 # define M_LN2f128 __f128 (0.693147180559945309417232121458176568) /* log_e 2 */
859 # define M_LN10f128 __f128 (2.302585092994045684017991454684364208) /* log_e 10 */
860 # define M_PIf128 __f128 (3.141592653589793238462643383279502884) /* pi */
861 # define M_PI_2f128 __f128 (1.570796326794896619231321691639751442) /* pi/2 */
862 # define M_PI_4f128 __f128 (0.785398163397448309615660845819875721) /* pi/4 */
863 # define M_1_PIf128 __f128 (0.318309886183790671537767526745028724) /* 1/pi */
864 # define M_2_PIf128 __f128 (0.636619772367581343075535053490057448) /* 2/pi */
865 # define M_2_SQRTPIf128 __f128 (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
866 # define M_SQRT2f128 __f128 (1.414213562373095048801688724209698079) /* sqrt(2) */
867 # define M_SQRT1_2f128 __f128 (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
870 #if __HAVE_FLOAT32X && defined __USE_GNU
871 # define M_Ef32x __f32x (2.718281828459045235360287471352662498) /* e */
872 # define M_LOG2Ef32x __f32x (1.442695040888963407359924681001892137) /* log_2 e */
873 # define M_LOG10Ef32x __f32x (0.434294481903251827651128918916605082) /* log_10 e */
874 # define M_LN2f32x __f32x (0.693147180559945309417232121458176568) /* log_e 2 */
875 # define M_LN10f32x __f32x (2.302585092994045684017991454684364208) /* log_e 10 */
876 # define M_PIf32x __f32x (3.141592653589793238462643383279502884) /* pi */
877 # define M_PI_2f32x __f32x (1.570796326794896619231321691639751442) /* pi/2 */
878 # define M_PI_4f32x __f32x (0.785398163397448309615660845819875721) /* pi/4 */
879 # define M_1_PIf32x __f32x (0.318309886183790671537767526745028724) /* 1/pi */
880 # define M_2_PIf32x __f32x (0.636619772367581343075535053490057448) /* 2/pi */
881 # define M_2_SQRTPIf32x __f32x (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
882 # define M_SQRT2f32x __f32x (1.414213562373095048801688724209698079) /* sqrt(2) */
883 # define M_SQRT1_2f32x __f32x (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
886 #if __HAVE_FLOAT64X && defined __USE_GNU
887 # define M_Ef64x __f64x (2.718281828459045235360287471352662498) /* e */
888 # define M_LOG2Ef64x __f64x (1.442695040888963407359924681001892137) /* log_2 e */
889 # define M_LOG10Ef64x __f64x (0.434294481903251827651128918916605082) /* log_10 e */
890 # define M_LN2f64x __f64x (0.693147180559945309417232121458176568) /* log_e 2 */
891 # define M_LN10f64x __f64x (2.302585092994045684017991454684364208) /* log_e 10 */
892 # define M_PIf64x __f64x (3.141592653589793238462643383279502884) /* pi */
893 # define M_PI_2f64x __f64x (1.570796326794896619231321691639751442) /* pi/2 */
894 # define M_PI_4f64x __f64x (0.785398163397448309615660845819875721) /* pi/4 */
895 # define M_1_PIf64x __f64x (0.318309886183790671537767526745028724) /* 1/pi */
896 # define M_2_PIf64x __f64x (0.636619772367581343075535053490057448) /* 2/pi */
897 # define M_2_SQRTPIf64x __f64x (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
898 # define M_SQRT2f64x __f64x (1.414213562373095048801688724209698079) /* sqrt(2) */
899 # define M_SQRT1_2f64x __f64x (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
902 #if __HAVE_FLOAT128X && defined __USE_GNU
903 # error "M_* values needed for _Float128x"
906 /* When compiling in strict ISO C compatible mode we must not use the
907 inline functions since they, among other things, do not set the
908 `errno' variable correctly. */
909 #if defined __STRICT_ANSI__ && !defined __NO_MATH_INLINES
910 # define __NO_MATH_INLINES 1
914 # if __GNUC_PREREQ (3, 1)
915 /* ISO C99 defines some macros to compare number while taking care for
916 unordered numbers. Many FPUs provide special instructions to support
917 these operations. Generic support in GCC for these as builtins went
918 in 2.97, but not all cpus added their patterns until 3.1. Therefore
919 we enable the builtins from 3.1 onwards and use a generic implementation
921 # define isgreater(x, y) __builtin_isgreater(x, y)
922 # define isgreaterequal(x, y) __builtin_isgreaterequal(x, y)
923 # define isless(x, y) __builtin_isless(x, y)
924 # define islessequal(x, y) __builtin_islessequal(x, y)
925 # define islessgreater(x, y) __builtin_islessgreater(x, y)
926 # define isunordered(x, y) __builtin_isunordered(x, y)
928 # define isgreater(x, y) \
929 (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
930 !isunordered (__x, __y) && __x > __y; }))
931 # define isgreaterequal(x, y) \
932 (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
933 !isunordered (__x, __y) && __x >= __y; }))
934 # define isless(x, y) \
935 (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
936 !isunordered (__x, __y) && __x < __y; }))
937 # define islessequal(x, y) \
938 (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
939 !isunordered (__x, __y) && __x <= __y; }))
940 # define islessgreater(x, y) \
941 (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
942 !isunordered (__x, __y) && __x != __y; }))
943 /* isunordered must always check both operands first for signaling NaNs. */
944 # define isunordered(x, y) \
945 (__extension__ ({ __typeof__ (x) __u = (x); __typeof__ (y) __v = (y); \
946 __u != __v && (__u != __u || __v != __v); }))
950 /* Get machine-dependent inline versions (if there are any). */
951 #ifdef __USE_EXTERN_INLINES
952 # include <bits/mathinline.h>
955 /* Define special entry points to use when the compiler got told to
956 only expect finite results. */
957 #if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0
959 /* Include bits/math-finite.h for double. */
960 # define _Mdouble_ double
961 # define __MATH_DECLARING_DOUBLE 1
962 # define __MATH_DECLARING_FLOATN 0
963 # define __REDIRFROM_X(function, reentrant) \
964 function ## reentrant
965 # define __REDIRTO_X(function, reentrant) \
966 __ ## function ## reentrant ## _finite
967 # include <bits/math-finite.h>
969 # undef __MATH_DECLARING_DOUBLE
970 # undef __MATH_DECLARING_FLOATN
971 # undef __REDIRFROM_X
974 /* When __USE_ISOC99 is defined, include math-finite for float and
975 long double, as well. */
978 /* Include bits/math-finite.h for float. */
979 # define _Mdouble_ float
980 # define __MATH_DECLARING_DOUBLE 0
981 # define __MATH_DECLARING_FLOATN 0
982 # define __REDIRFROM_X(function, reentrant) \
983 function ## f ## reentrant
984 # define __REDIRTO_X(function, reentrant) \
985 __ ## function ## f ## reentrant ## _finite
986 # include <bits/math-finite.h>
988 # undef __MATH_DECLARING_DOUBLE
989 # undef __MATH_DECLARING_FLOATN
990 # undef __REDIRFROM_X
993 /* Include bits/math-finite.h for long double. */
994 # ifdef __MATH_DECLARE_LDOUBLE
995 # define _Mdouble_ long double
996 # define __MATH_DECLARING_DOUBLE 0
997 # define __MATH_DECLARING_FLOATN 0
998 # define __REDIRFROM_X(function, reentrant) \
999 function ## l ## reentrant
1000 # ifdef __NO_LONG_DOUBLE_MATH
1001 # define __REDIRTO_X(function, reentrant) \
1002 __ ## function ## reentrant ## _finite
1004 # define __REDIRTO_X(function, reentrant) \
1005 __ ## function ## l ## reentrant ## _finite
1007 # include <bits/math-finite.h>
1009 # undef __MATH_DECLARING_DOUBLE
1010 # undef __MATH_DECLARING_FLOATN
1011 # undef __REDIRFROM_X
1015 # endif /* __USE_ISOC99. */
1017 /* Include bits/math-finite.h for _FloatN and _FloatNx. */
1019 # if (__HAVE_DISTINCT_FLOAT16 || (__HAVE_FLOAT16 && !defined _LIBC)) \
1020 && __GLIBC_USE (IEC_60559_TYPES_EXT)
1021 # define _Mdouble_ _Float16
1022 # define __MATH_DECLARING_DOUBLE 0
1023 # define __MATH_DECLARING_FLOATN 1
1024 # define __REDIRFROM_X(function, reentrant) \
1025 function ## f16 ## reentrant
1026 # if __HAVE_DISTINCT_FLOAT16
1027 # define __REDIRTO_X(function, reentrant) \
1028 __ ## function ## f16 ## reentrant ## _finite
1030 # error "non-disinct _Float16"
1032 # include <bits/math-finite.h>
1034 # undef __MATH_DECLARING_DOUBLE
1035 # undef __MATH_DECLARING_FLOATN
1036 # undef __REDIRFROM_X
1040 # if (__HAVE_DISTINCT_FLOAT32 || (__HAVE_FLOAT32 && !defined _LIBC)) \
1041 && __GLIBC_USE (IEC_60559_TYPES_EXT)
1042 # define _Mdouble_ _Float32
1043 # define __MATH_DECLARING_DOUBLE 0
1044 # define __MATH_DECLARING_FLOATN 1
1045 # define __REDIRFROM_X(function, reentrant) \
1046 function ## f32 ## reentrant
1047 # if __HAVE_DISTINCT_FLOAT32
1048 # define __REDIRTO_X(function, reentrant) \
1049 __ ## function ## f32 ## reentrant ## _finite
1051 # define __REDIRTO_X(function, reentrant) \
1052 __ ## function ## f ## reentrant ## _finite
1054 # include <bits/math-finite.h>
1056 # undef __MATH_DECLARING_DOUBLE
1057 # undef __MATH_DECLARING_FLOATN
1058 # undef __REDIRFROM_X
1062 # if (__HAVE_DISTINCT_FLOAT64 || (__HAVE_FLOAT64 && !defined _LIBC)) \
1063 && __GLIBC_USE (IEC_60559_TYPES_EXT)
1064 # define _Mdouble_ _Float64
1065 # define __MATH_DECLARING_DOUBLE 0
1066 # define __MATH_DECLARING_FLOATN 1
1067 # define __REDIRFROM_X(function, reentrant) \
1068 function ## f64 ## reentrant
1069 # if __HAVE_DISTINCT_FLOAT64
1070 # define __REDIRTO_X(function, reentrant) \
1071 __ ## function ## f64 ## reentrant ## _finite
1073 # define __REDIRTO_X(function, reentrant) \
1074 __ ## function ## reentrant ## _finite
1076 # include <bits/math-finite.h>
1078 # undef __MATH_DECLARING_DOUBLE
1079 # undef __MATH_DECLARING_FLOATN
1080 # undef __REDIRFROM_X
1084 # if (__HAVE_DISTINCT_FLOAT128 || (__HAVE_FLOAT128 && !defined _LIBC)) \
1085 && __GLIBC_USE (IEC_60559_TYPES_EXT)
1086 # define _Mdouble_ _Float128
1087 # define __MATH_DECLARING_DOUBLE 0
1088 # define __MATH_DECLARING_FLOATN 1
1089 # define __REDIRFROM_X(function, reentrant) \
1090 function ## f128 ## reentrant
1091 # if __HAVE_DISTINCT_FLOAT128
1092 # define __REDIRTO_X(function, reentrant) \
1093 __ ## function ## f128 ## reentrant ## _finite
1095 # define __REDIRTO_X(function, reentrant) \
1096 __ ## function ## l ## reentrant ## _finite
1098 # include <bits/math-finite.h>
1100 # undef __MATH_DECLARING_DOUBLE
1101 # undef __MATH_DECLARING_FLOATN
1102 # undef __REDIRFROM_X
1106 # if (__HAVE_DISTINCT_FLOAT32X || (__HAVE_FLOAT32X && !defined _LIBC)) \
1107 && __GLIBC_USE (IEC_60559_TYPES_EXT)
1108 # define _Mdouble_ _Float32x
1109 # define __MATH_DECLARING_DOUBLE 0
1110 # define __MATH_DECLARING_FLOATN 1
1111 # define __REDIRFROM_X(function, reentrant) \
1112 function ## f32x ## reentrant
1113 # if __HAVE_DISTINCT_FLOAT32X
1114 # define __REDIRTO_X(function, reentrant) \
1115 __ ## function ## f32x ## reentrant ## _finite
1117 # define __REDIRTO_X(function, reentrant) \
1118 __ ## function ## reentrant ## _finite
1120 # include <bits/math-finite.h>
1122 # undef __MATH_DECLARING_DOUBLE
1123 # undef __MATH_DECLARING_FLOATN
1124 # undef __REDIRFROM_X
1128 # if (__HAVE_DISTINCT_FLOAT64X || (__HAVE_FLOAT64X && !defined _LIBC)) \
1129 && __GLIBC_USE (IEC_60559_TYPES_EXT)
1130 # define _Mdouble_ _Float64x
1131 # define __MATH_DECLARING_DOUBLE 0
1132 # define __MATH_DECLARING_FLOATN 1
1133 # define __REDIRFROM_X(function, reentrant) \
1134 function ## f64x ## reentrant
1135 # if __HAVE_DISTINCT_FLOAT64X
1136 # define __REDIRTO_X(function, reentrant) \
1137 __ ## function ## f64x ## reentrant ## _finite
1138 # elif __HAVE_FLOAT64X_LONG_DOUBLE
1139 # define __REDIRTO_X(function, reentrant) \
1140 __ ## function ## l ## reentrant ## _finite
1142 # define __REDIRTO_X(function, reentrant) \
1143 __ ## function ## f128 ## reentrant ## _finite
1145 # include <bits/math-finite.h>
1147 # undef __MATH_DECLARING_DOUBLE
1148 # undef __MATH_DECLARING_FLOATN
1149 # undef __REDIRFROM_X
1153 # if (__HAVE_DISTINCT_FLOAT128X || (__HAVE_FLOAT128X && !defined _LIBC)) \
1154 && __GLIBC_USE (IEC_60559_TYPES_EXT)
1155 # define _Mdouble_ _Float128x
1156 # define __MATH_DECLARING_DOUBLE 0
1157 # define __MATH_DECLARING_FLOATN 1
1158 # define __REDIRFROM_X(function, reentrant) \
1159 function ## f128x ## reentrant
1160 # if __HAVE_DISTINCT_FLOAT128X
1161 # define __REDIRTO_X(function, reentrant) \
1162 __ ## function ## f128x ## reentrant ## _finite
1164 # error "non-disinct _Float128x"
1166 # include <bits/math-finite.h>
1168 # undef __MATH_DECLARING_DOUBLE
1169 # undef __MATH_DECLARING_FLOATN
1170 # undef __REDIRFROM_X
1174 #endif /* __FINITE_MATH_ONLY__ > 0. */
1176 #if __GLIBC_USE (IEC_60559_BFP_EXT)
1177 /* An expression whose type has the widest of the evaluation formats
1178 of X and Y (which are of floating-point types). */
1179 # if __FLT_EVAL_METHOD__ == 2 || __FLT_EVAL_METHOD__ > 64
1180 # define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0L)
1181 # elif __FLT_EVAL_METHOD__ == 1 || __FLT_EVAL_METHOD__ > 32
1182 # define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0)
1183 # elif __FLT_EVAL_METHOD__ == 0 || __FLT_EVAL_METHOD__ == 32
1184 # define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0f)
1186 # define __MATH_EVAL_FMT2(x, y) ((x) + (y))
1189 /* Return X == Y but raising "invalid" and setting errno if X or Y is
1191 # if !defined __cplusplus || (__cplusplus < 201103L && !defined __GNUC__)
1192 # define iseqsig(x, y) \
1193 __MATH_TG (__MATH_EVAL_FMT2 (x, y), __iseqsig, ((x), (y)))
1195 /* In C++ mode, __MATH_TG cannot be used, because it relies on
1196 __builtin_types_compatible_p, which is a C-only builtin. Moreover,
1197 the comparison macros from ISO C take two floating-point arguments,
1198 which need not have the same type. Choosing what underlying function
1199 to call requires evaluating the formats of the arguments, then
1200 selecting which is wider. The macro __MATH_EVAL_FMT2 provides this
1201 information, however, only the type of the macro expansion is
1202 relevant (actually evaluating the expression would be incorrect).
1203 Thus, the type is used as a template parameter for __iseqsig_type,
1204 which calls the appropriate underlying function. */
1206 template<typename
> struct __iseqsig_type
;
1208 template<> struct __iseqsig_type
<float>
1210 static int __call (float __x
, float __y
) throw ()
1212 return __iseqsigf (__x
, __y
);
1216 template<> struct __iseqsig_type
<double>
1218 static int __call (double __x
, double __y
) throw ()
1220 return __iseqsig (__x
, __y
);
1224 template<> struct __iseqsig_type
<long double>
1226 static int __call (double __x
, double __y
) throw ()
1228 # ifndef __NO_LONG_DOUBLE_MATH
1229 return __iseqsigl (__x
, __y
);
1231 return __iseqsig (__x
, __y
);
1236 # if __HAVE_DISTINCT_FLOAT128
1237 template<> struct __iseqsig_type
<_Float128
>
1239 static int __call (_Float128 __x
, _Float128 __y
) throw ()
1241 return __iseqsigf128 (__x
, __y
);
1246 template<typename _T1
, typename _T2
>
1248 iseqsig (_T1 __x
, _T2 __y
) throw ()
1250 # if __cplusplus >= 201103L
1251 typedef decltype (__MATH_EVAL_FMT2 (__x
, __y
)) _T3
;
1253 typedef __typeof (__MATH_EVAL_FMT2 (__x
, __y
)) _T3
;
1255 return __iseqsig_type
<_T3
>::__call (__x
, __y
);
1258 } /* extern "C++" */
1259 # endif /* __cplusplus */