1// -*- C++ -*- C forwarding header.
2
3// Copyright (C) 1997-2025 Free Software Foundation, Inc.
4//
5// This file is part of the GNU ISO C++ Library. This library is free
6// software; you can redistribute it and/or modify it under the
7// terms of the GNU General Public License as published by the
8// Free Software Foundation; either version 3, or (at your option)
9// any later version.
10
11// This library is distributed in the hope that it will be useful,
12// but WITHOUT ANY WARRANTY; without even the implied warranty of
13// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14// GNU General Public License for more details.
15
16// Under Section 7 of GPL version 3, you are granted additional
17// permissions described in the GCC Runtime Library Exception, version
18// 3.1, as published by the Free Software Foundation.
19
20// You should have received a copy of the GNU General Public License and
21// a copy of the GCC Runtime Library Exception along with this program;
22// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
23// <http://www.gnu.org/licenses/>.
24
25/** @file include/cmath
26 * This is a Standard C++ Library file. You should @c \#include this file
27 * in your programs, rather than any of the @a *.h implementation files.
28 *
29 * This is the C++ version of the Standard C Library header @c math.h,
30 * and its contents are (mostly) the same as that header, but are all
31 * contained in the namespace @c std (except for names which are defined
32 * as macros in C).
33 */
34
35//
36// ISO C++ 14882: 26.5 C library
37//
38
39#ifndef _GLIBCXX_CMATH
40#define _GLIBCXX_CMATH 1
41
42#ifdef _GLIBCXX_SYSHDR
43#pragma GCC system_header
44#endif
45
46#include <bits/requires_hosted.h>
47
48#include <bits/c++config.h>
49#include <bits/cpp_type_traits.h>
50#include <ext/type_traits.h>
51
52#pragma GCC diagnostic push
53#pragma GCC diagnostic ignored "-Wpedantic" // include_next
54#define _GLIBCXX_INCLUDE_NEXT_C_HEADERS
55#include_next <math.h>
56#undef _GLIBCXX_INCLUDE_NEXT_C_HEADERS
57#pragma GCC diagnostic pop
58
59#include <bits/std_abs.h>
60
61#define __glibcxx_want_hypot
62#define __glibcxx_want_interpolate
63#include <bits/version.h>
64
65// Get rid of those macros defined in <math.h> in lieu of real functions.
66#undef div
67#undef acos
68#undef asin
69#undef atan
70#undef atan2
71#undef ceil
72#undef cos
73#undef cosh
74#undef exp
75#undef fabs
76#undef floor
77#undef fmod
78#undef frexp
79#undef ldexp
80#undef log
81#undef log10
82#undef modf
83#undef pow
84#undef sin
85#undef sinh
86#undef sqrt
87#undef tan
88#undef tanh
89
90extern "C++"
91{
92namespace std _GLIBCXX_VISIBILITY(default)
93{
94_GLIBCXX_BEGIN_NAMESPACE_VERSION
95
96 using ::acos;
97
98#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
99 inline _GLIBCXX_CONSTEXPR float
100 acos(float __x)
101 { return __builtin_acosf(__x); }
102
103 inline _GLIBCXX_CONSTEXPR long double
104 acos(long double __x)
105 { return __builtin_acosl(__x); }
106#endif
107
108 template<typename _Tp>
109 inline _GLIBCXX_CONSTEXPR
110 typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
111 double>::__type
112 acos(_Tp __x)
113 { return __builtin_acos(__x); }
114
115 using ::asin;
116
117#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
118 inline _GLIBCXX_CONSTEXPR float
119 asin(float __x)
120 { return __builtin_asinf(__x); }
121
122 inline _GLIBCXX_CONSTEXPR long double
123 asin(long double __x)
124 { return __builtin_asinl(__x); }
125#endif
126
127 template<typename _Tp>
128 inline _GLIBCXX_CONSTEXPR
129 typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
130 double>::__type
131 asin(_Tp __x)
132 { return __builtin_asin(__x); }
133
134 using ::atan;
135
136#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
137 inline _GLIBCXX_CONSTEXPR float
138 atan(float __x)
139 { return __builtin_atanf(__x); }
140
141 inline _GLIBCXX_CONSTEXPR long double
142 atan(long double __x)
143 { return __builtin_atanl(__x); }
144#endif
145
146 template<typename _Tp>
147 inline _GLIBCXX_CONSTEXPR
148 typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
149 double>::__type
150 atan(_Tp __x)
151 { return __builtin_atan(__x); }
152
153 using ::atan2;
154
155#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
156 inline _GLIBCXX_CONSTEXPR float
157 atan2(float __y, float __x)
158 { return __builtin_atan2f(__y, __x); }
159
160 inline _GLIBCXX_CONSTEXPR long double
161 atan2(long double __y, long double __x)
162 { return __builtin_atan2l(__y, __x); }
163#endif
164
165 using ::ceil;
166
167#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
168 inline _GLIBCXX_CONSTEXPR float
169 ceil(float __x)
170 { return __builtin_ceilf(__x); }
171
172 inline _GLIBCXX_CONSTEXPR long double
173 ceil(long double __x)
174 { return __builtin_ceill(__x); }
175#endif
176
177 template<typename _Tp>
178 inline _GLIBCXX_CONSTEXPR
179 typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
180 double>::__type
181 ceil(_Tp __x)
182 { return __builtin_ceil(__x); }
183
184 using ::cos;
185
186#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
187 inline _GLIBCXX_CONSTEXPR float
188 cos(float __x)
189 { return __builtin_cosf(__x); }
190
191 inline _GLIBCXX_CONSTEXPR long double
192 cos(long double __x)
193 { return __builtin_cosl(__x); }
194#endif
195
196 template<typename _Tp>
197 inline _GLIBCXX_CONSTEXPR
198 typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
199 double>::__type
200 cos(_Tp __x)
201 { return __builtin_cos(__x); }
202
203 using ::cosh;
204
205#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
206 inline _GLIBCXX_CONSTEXPR float
207 cosh(float __x)
208 { return __builtin_coshf(__x); }
209
210 inline _GLIBCXX_CONSTEXPR long double
211 cosh(long double __x)
212 { return __builtin_coshl(__x); }
213#endif
214
215 template<typename _Tp>
216 inline _GLIBCXX_CONSTEXPR
217 typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
218 double>::__type
219 cosh(_Tp __x)
220 { return __builtin_cosh(__x); }
221
222 using ::exp;
223
224#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
225 inline _GLIBCXX_CONSTEXPR float
226 exp(float __x)
227 { return __builtin_expf(__x); }
228
229 inline _GLIBCXX_CONSTEXPR long double
230 exp(long double __x)
231 { return __builtin_expl(__x); }
232#endif
233
234 template<typename _Tp>
235 inline _GLIBCXX_CONSTEXPR
236 typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
237 double>::__type
238 exp(_Tp __x)
239 { return __builtin_exp(__x); }
240
241 using ::fabs;
242
243#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
244 inline _GLIBCXX_CONSTEXPR float
245 fabs(float __x)
246 { return __builtin_fabsf(__x); }
247
248 inline _GLIBCXX_CONSTEXPR long double
249 fabs(long double __x)
250 { return __builtin_fabsl(__x); }
251#endif
252
253 template<typename _Tp>
254 inline _GLIBCXX_CONSTEXPR
255 typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
256 double>::__type
257 fabs(_Tp __x)
258 { return __builtin_fabs(__x); }
259
260 using ::floor;
261
262#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
263 inline _GLIBCXX_CONSTEXPR float
264 floor(float __x)
265 { return __builtin_floorf(__x); }
266
267 inline _GLIBCXX_CONSTEXPR long double
268 floor(long double __x)
269 { return __builtin_floorl(__x); }
270#endif
271
272 template<typename _Tp>
273 inline _GLIBCXX_CONSTEXPR
274 typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
275 double>::__type
276 floor(_Tp __x)
277 { return __builtin_floor(__x); }
278
279 using ::fmod;
280
281#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
282 inline _GLIBCXX_CONSTEXPR float
283 fmod(float __x, float __y)
284 { return __builtin_fmodf(__x, __y); }
285
286 inline _GLIBCXX_CONSTEXPR long double
287 fmod(long double __x, long double __y)
288 { return __builtin_fmodl(__x, __y); }
289#endif
290
291 using ::frexp;
292
293#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
294 inline float
295 frexp(float __x, int* __exp)
296 { return __builtin_frexpf(__x, __exp); }
297
298 inline long double
299 frexp(long double __x, int* __exp)
300 { return __builtin_frexpl(__x, __exp); }
301#endif
302
303 template<typename _Tp>
304 inline _GLIBCXX_CONSTEXPR
305 typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
306 double>::__type
307 frexp(_Tp __x, int* __exp)
308 { return __builtin_frexp(__x, __exp); }
309
310 using ::ldexp;
311
312#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
313 inline _GLIBCXX_CONSTEXPR float
314 ldexp(float __x, int __exp)
315 { return __builtin_ldexpf(__x, __exp); }
316
317 inline _GLIBCXX_CONSTEXPR long double
318 ldexp(long double __x, int __exp)
319 { return __builtin_ldexpl(__x, __exp); }
320#endif
321
322 template<typename _Tp>
323 inline _GLIBCXX_CONSTEXPR
324 typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
325 double>::__type
326 ldexp(_Tp __x, int __exp)
327 { return __builtin_ldexp(__x, __exp); }
328
329 using ::log;
330
331#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
332 inline _GLIBCXX_CONSTEXPR float
333 log(float __x)
334 { return __builtin_logf(__x); }
335
336 inline _GLIBCXX_CONSTEXPR long double
337 log(long double __x)
338 { return __builtin_logl(__x); }
339#endif
340
341 template<typename _Tp>
342 inline _GLIBCXX_CONSTEXPR
343 typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
344 double>::__type
345 log(_Tp __x)
346 { return __builtin_log(__x); }
347
348 using ::log10;
349
350#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
351 inline _GLIBCXX_CONSTEXPR float
352 log10(float __x)
353 { return __builtin_log10f(__x); }
354
355 inline _GLIBCXX_CONSTEXPR long double
356 log10(long double __x)
357 { return __builtin_log10l(__x); }
358#endif
359
360 template<typename _Tp>
361 inline _GLIBCXX_CONSTEXPR
362 typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
363 double>::__type
364 log10(_Tp __x)
365 { return __builtin_log10(__x); }
366
367 using ::modf;
368
369#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
370 inline float
371 modf(float __x, float* __iptr)
372 { return __builtin_modff(__x, __iptr); }
373
374 inline long double
375 modf(long double __x, long double* __iptr)
376 { return __builtin_modfl(__x, __iptr); }
377#endif
378
379 using ::pow;
380
381#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
382 inline _GLIBCXX_CONSTEXPR float
383 pow(float __x, float __y)
384 { return __builtin_powf(__x, __y); }
385
386 inline _GLIBCXX_CONSTEXPR long double
387 pow(long double __x, long double __y)
388 { return __builtin_powl(__x, __y); }
389
390#if __cplusplus < 201103L
391 // _GLIBCXX_RESOLVE_LIB_DEFECTS
392 // DR 550. What should the return type of pow(float,int) be?
393 inline double
394 pow(double __x, int __i)
395 { return __builtin_powi(__x, __i); }
396
397 inline float
398 pow(float __x, int __n)
399 { return __builtin_powif(__x, __n); }
400
401 inline long double
402 pow(long double __x, int __n)
403 { return __builtin_powil(__x, __n); }
404#endif
405#endif
406
407 using ::sin;
408
409#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
410 inline _GLIBCXX_CONSTEXPR float
411 sin(float __x)
412 { return __builtin_sinf(__x); }
413
414 inline _GLIBCXX_CONSTEXPR long double
415 sin(long double __x)
416 { return __builtin_sinl(__x); }
417#endif
418
419 template<typename _Tp>
420 inline _GLIBCXX_CONSTEXPR
421 typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
422 double>::__type
423 sin(_Tp __x)
424 { return __builtin_sin(__x); }
425
426 using ::sinh;
427
428#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
429 inline _GLIBCXX_CONSTEXPR float
430 sinh(float __x)
431 { return __builtin_sinhf(__x); }
432
433 inline _GLIBCXX_CONSTEXPR long double
434 sinh(long double __x)
435 { return __builtin_sinhl(__x); }
436#endif
437
438 template<typename _Tp>
439 inline _GLIBCXX_CONSTEXPR
440 typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
441 double>::__type
442 sinh(_Tp __x)
443 { return __builtin_sinh(__x); }
444
445 using ::sqrt;
446
447#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
448 inline _GLIBCXX_CONSTEXPR float
449 sqrt(float __x)
450 { return __builtin_sqrtf(__x); }
451
452 inline _GLIBCXX_CONSTEXPR long double
453 sqrt(long double __x)
454 { return __builtin_sqrtl(__x); }
455#endif
456
457 template<typename _Tp>
458 inline _GLIBCXX_CONSTEXPR
459 typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
460 double>::__type
461 sqrt(_Tp __x)
462 { return __builtin_sqrt(__x); }
463
464 using ::tan;
465
466#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
467 inline _GLIBCXX_CONSTEXPR float
468 tan(float __x)
469 { return __builtin_tanf(__x); }
470
471 inline _GLIBCXX_CONSTEXPR long double
472 tan(long double __x)
473 { return __builtin_tanl(__x); }
474#endif
475
476 template<typename _Tp>
477 inline _GLIBCXX_CONSTEXPR
478 typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
479 double>::__type
480 tan(_Tp __x)
481 { return __builtin_tan(__x); }
482
483 using ::tanh;
484
485#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
486 inline _GLIBCXX_CONSTEXPR float
487 tanh(float __x)
488 { return __builtin_tanhf(__x); }
489
490 inline _GLIBCXX_CONSTEXPR long double
491 tanh(long double __x)
492 { return __builtin_tanhl(__x); }
493#endif
494
495 template<typename _Tp>
496 inline _GLIBCXX_CONSTEXPR
497 typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
498 double>::__type
499 tanh(_Tp __x)
500 { return __builtin_tanh(__x); }
501
502#if defined(__STDCPP_FLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
503 constexpr _Float16
504 acos(_Float16 __x)
505 { return _Float16(__builtin_acosf(__x)); }
506
507 constexpr _Float16
508 asin(_Float16 __x)
509 { return _Float16(__builtin_asinf(__x)); }
510
511 constexpr _Float16
512 atan(_Float16 __x)
513 { return _Float16(__builtin_atanf(__x)); }
514
515 constexpr _Float16
516 atan2(_Float16 __y, _Float16 __x)
517 { return _Float16(__builtin_atan2f(__y, __x)); }
518
519 constexpr _Float16
520 ceil(_Float16 __x)
521 { return _Float16(__builtin_ceilf(__x)); }
522
523 constexpr _Float16
524 cos(_Float16 __x)
525 { return _Float16(__builtin_cosf(__x)); }
526
527 constexpr _Float16
528 cosh(_Float16 __x)
529 { return _Float16(__builtin_coshf(__x)); }
530
531 constexpr _Float16
532 exp(_Float16 __x)
533 { return _Float16(__builtin_expf(__x)); }
534
535 constexpr _Float16
536 fabs(_Float16 __x)
537 { return _Float16(__builtin_fabsf(__x)); }
538
539 constexpr _Float16
540 floor(_Float16 __x)
541 { return _Float16(__builtin_floorf(__x)); }
542
543 constexpr _Float16
544 fmod(_Float16 __x, _Float16 __y)
545 { return _Float16(__builtin_fmodf(__x, __y)); }
546
547 inline _Float16
548 frexp(_Float16 __x, int* __exp)
549 { return _Float16(__builtin_frexpf(__x, __exp)); }
550
551 constexpr _Float16
552 ldexp(_Float16 __x, int __exp)
553 { return _Float16(__builtin_ldexpf(__x, __exp)); }
554
555 constexpr _Float16
556 log(_Float16 __x)
557 { return _Float16(__builtin_logf(__x)); }
558
559 constexpr _Float16
560 log10(_Float16 __x)
561 { return _Float16(__builtin_log10f(__x)); }
562
563 inline _Float16
564 modf(_Float16 __x, _Float16* __iptr)
565 {
566 float __i, __ret = __builtin_modff(__x, &__i);
567 *__iptr = _Float16(__i);
568 return _Float16(__ret);
569 }
570
571 constexpr _Float16
572 pow(_Float16 __x, _Float16 __y)
573 { return _Float16(__builtin_powf(__x, __y)); }
574
575 constexpr _Float16
576 sin(_Float16 __x)
577 { return _Float16(__builtin_sinf(__x)); }
578
579 constexpr _Float16
580 sinh(_Float16 __x)
581 { return _Float16(__builtin_sinhf(__x)); }
582
583 constexpr _Float16
584 sqrt(_Float16 __x)
585 { return _Float16(__builtin_sqrtf(__x)); }
586
587 constexpr _Float16
588 tan(_Float16 __x)
589 { return _Float16(__builtin_tanf(__x)); }
590
591 constexpr _Float16
592 tanh(_Float16 __x)
593 { return _Float16(__builtin_tanhf(__x)); }
594#endif
595
596#if defined(__STDCPP_FLOAT32_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
597 constexpr _Float32
598 acos(_Float32 __x)
599 { return __builtin_acosf(__x); }
600
601 constexpr _Float32
602 asin(_Float32 __x)
603 { return __builtin_asinf(__x); }
604
605 constexpr _Float32
606 atan(_Float32 __x)
607 { return __builtin_atanf(__x); }
608
609 constexpr _Float32
610 atan2(_Float32 __y, _Float32 __x)
611 { return __builtin_atan2f(__y, __x); }
612
613 constexpr _Float32
614 ceil(_Float32 __x)
615 { return __builtin_ceilf(__x); }
616
617 constexpr _Float32
618 cos(_Float32 __x)
619 { return __builtin_cosf(__x); }
620
621 constexpr _Float32
622 cosh(_Float32 __x)
623 { return __builtin_coshf(__x); }
624
625 constexpr _Float32
626 exp(_Float32 __x)
627 { return __builtin_expf(__x); }
628
629 constexpr _Float32
630 fabs(_Float32 __x)
631 { return __builtin_fabsf(__x); }
632
633 constexpr _Float32
634 floor(_Float32 __x)
635 { return __builtin_floorf(__x); }
636
637 constexpr _Float32
638 fmod(_Float32 __x, _Float32 __y)
639 { return __builtin_fmodf(__x, __y); }
640
641 inline _Float32
642 frexp(_Float32 __x, int* __exp)
643 { return __builtin_frexpf(__x, __exp); }
644
645 constexpr _Float32
646 ldexp(_Float32 __x, int __exp)
647 { return __builtin_ldexpf(__x, __exp); }
648
649 constexpr _Float32
650 log(_Float32 __x)
651 { return __builtin_logf(__x); }
652
653 constexpr _Float32
654 log10(_Float32 __x)
655 { return __builtin_log10f(__x); }
656
657 inline _Float32
658 modf(_Float32 __x, _Float32* __iptr)
659 {
660 float __i, __ret = __builtin_modff(__x, &__i);
661 *__iptr = __i;
662 return __ret;
663 }
664
665 constexpr _Float32
666 pow(_Float32 __x, _Float32 __y)
667 { return __builtin_powf(__x, __y); }
668
669 constexpr _Float32
670 sin(_Float32 __x)
671 { return __builtin_sinf(__x); }
672
673 constexpr _Float32
674 sinh(_Float32 __x)
675 { return __builtin_sinhf(__x); }
676
677 constexpr _Float32
678 sqrt(_Float32 __x)
679 { return __builtin_sqrtf(__x); }
680
681 constexpr _Float32
682 tan(_Float32 __x)
683 { return __builtin_tanf(__x); }
684
685 constexpr _Float32
686 tanh(_Float32 __x)
687 { return __builtin_tanhf(__x); }
688#endif
689
690#if defined(__STDCPP_FLOAT64_T__) && defined(_GLIBCXX_DOUBLE_IS_IEEE_BINARY64)
691 constexpr _Float64
692 acos(_Float64 __x)
693 { return __builtin_acos(__x); }
694
695 constexpr _Float64
696 asin(_Float64 __x)
697 { return __builtin_asin(__x); }
698
699 constexpr _Float64
700 atan(_Float64 __x)
701 { return __builtin_atan(__x); }
702
703 constexpr _Float64
704 atan2(_Float64 __y, _Float64 __x)
705 { return __builtin_atan2(__y, __x); }
706
707 constexpr _Float64
708 ceil(_Float64 __x)
709 { return __builtin_ceil(__x); }
710
711 constexpr _Float64
712 cos(_Float64 __x)
713 { return __builtin_cos(__x); }
714
715 constexpr _Float64
716 cosh(_Float64 __x)
717 { return __builtin_cosh(__x); }
718
719 constexpr _Float64
720 exp(_Float64 __x)
721 { return __builtin_exp(__x); }
722
723 constexpr _Float64
724 fabs(_Float64 __x)
725 { return __builtin_fabs(__x); }
726
727 constexpr _Float64
728 floor(_Float64 __x)
729 { return __builtin_floor(__x); }
730
731 constexpr _Float64
732 fmod(_Float64 __x, _Float64 __y)
733 { return __builtin_fmod(__x, __y); }
734
735 inline _Float64
736 frexp(_Float64 __x, int* __exp)
737 { return __builtin_frexp(__x, __exp); }
738
739 constexpr _Float64
740 ldexp(_Float64 __x, int __exp)
741 { return __builtin_ldexp(__x, __exp); }
742
743 constexpr _Float64
744 log(_Float64 __x)
745 { return __builtin_log(__x); }
746
747 constexpr _Float64
748 log10(_Float64 __x)
749 { return __builtin_log10(__x); }
750
751 inline _Float64
752 modf(_Float64 __x, _Float64* __iptr)
753 {
754 double __i, __ret = __builtin_modf(__x, &__i);
755 *__iptr = __i;
756 return __ret;
757 }
758
759 constexpr _Float64
760 pow(_Float64 __x, _Float64 __y)
761 { return __builtin_pow(__x, __y); }
762
763 constexpr _Float64
764 sin(_Float64 __x)
765 { return __builtin_sin(__x); }
766
767 constexpr _Float64
768 sinh(_Float64 __x)
769 { return __builtin_sinh(__x); }
770
771 constexpr _Float64
772 sqrt(_Float64 __x)
773 { return __builtin_sqrt(__x); }
774
775 constexpr _Float64
776 tan(_Float64 __x)
777 { return __builtin_tan(__x); }
778
779 constexpr _Float64
780 tanh(_Float64 __x)
781 { return __builtin_tanh(__x); }
782#endif
783
784#if defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_LDOUBLE_IS_IEEE_BINARY128)
785 constexpr _Float128
786 acos(_Float128 __x)
787 { return __builtin_acosl(__x); }
788
789 constexpr _Float128
790 asin(_Float128 __x)
791 { return __builtin_asinl(__x); }
792
793 constexpr _Float128
794 atan(_Float128 __x)
795 { return __builtin_atanl(__x); }
796
797 constexpr _Float128
798 atan2(_Float128 __y, _Float128 __x)
799 { return __builtin_atan2l(__y, __x); }
800
801 constexpr _Float128
802 ceil(_Float128 __x)
803 { return __builtin_ceill(__x); }
804
805 constexpr _Float128
806 cos(_Float128 __x)
807 { return __builtin_cosl(__x); }
808
809 constexpr _Float128
810 cosh(_Float128 __x)
811 { return __builtin_coshl(__x); }
812
813 constexpr _Float128
814 exp(_Float128 __x)
815 { return __builtin_expl(__x); }
816
817 constexpr _Float128
818 fabs(_Float128 __x)
819 { return __builtin_fabsl(__x); }
820
821 constexpr _Float128
822 floor(_Float128 __x)
823 { return __builtin_floorl(__x); }
824
825 constexpr _Float128
826 fmod(_Float128 __x, _Float128 __y)
827 { return __builtin_fmodl(__x, __y); }
828
829 inline _Float128
830 frexp(_Float128 __x, int* __exp)
831 { return __builtin_frexpl(__x, __exp); }
832
833 constexpr _Float128
834 ldexp(_Float128 __x, int __exp)
835 { return __builtin_ldexpl(__x, __exp); }
836
837 constexpr _Float128
838 log(_Float128 __x)
839 { return __builtin_logl(__x); }
840
841 constexpr _Float128
842 log10(_Float128 __x)
843 { return __builtin_log10l(__x); }
844
845 inline _Float128
846 modf(_Float128 __x, _Float128* __iptr)
847 {
848 long double __i, __ret = __builtin_modfl(__x, &__i);
849 *__iptr = __i;
850 return __ret;
851 }
852
853 constexpr _Float128
854 pow(_Float128 __x, _Float128 __y)
855 { return __builtin_powl(__x, __y); }
856
857 constexpr _Float128
858 sin(_Float128 __x)
859 { return __builtin_sinl(__x); }
860
861 constexpr _Float128
862 sinh(_Float128 __x)
863 { return __builtin_sinhl(__x); }
864
865 constexpr _Float128
866 sqrt(_Float128 __x)
867 { return __builtin_sqrtl(__x); }
868
869 constexpr _Float128
870 tan(_Float128 __x)
871 { return __builtin_tanl(__x); }
872
873 constexpr _Float128
874 tanh(_Float128 __x)
875 { return __builtin_tanhl(__x); }
876#elif defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_HAVE_FLOAT128_MATH)
877 constexpr _Float128
878 acos(_Float128 __x)
879 { return __builtin_acosf128(__x); }
880
881 constexpr _Float128
882 asin(_Float128 __x)
883 { return __builtin_asinf128(__x); }
884
885 constexpr _Float128
886 atan(_Float128 __x)
887 { return __builtin_atanf128(__x); }
888
889 constexpr _Float128
890 atan2(_Float128 __y, _Float128 __x)
891 { return __builtin_atan2f128(__y, __x); }
892
893 constexpr _Float128
894 ceil(_Float128 __x)
895 { return __builtin_ceilf128(__x); }
896
897 constexpr _Float128
898 cos(_Float128 __x)
899 { return __builtin_cosf128(__x); }
900
901 constexpr _Float128
902 cosh(_Float128 __x)
903 { return __builtin_coshf128(__x); }
904
905 constexpr _Float128
906 exp(_Float128 __x)
907 { return __builtin_expf128(__x); }
908
909 constexpr _Float128
910 fabs(_Float128 __x)
911 { return __builtin_fabsf128(__x); }
912
913 constexpr _Float128
914 floor(_Float128 __x)
915 { return __builtin_floorf128(__x); }
916
917 constexpr _Float128
918 fmod(_Float128 __x, _Float128 __y)
919 { return __builtin_fmodf128(__x, __y); }
920
921 inline _Float128
922 frexp(_Float128 __x, int* __exp)
923 { return __builtin_frexpf128(__x, __exp); }
924
925 constexpr _Float128
926 ldexp(_Float128 __x, int __exp)
927 { return __builtin_ldexpf128(__x, __exp); }
928
929 constexpr _Float128
930 log(_Float128 __x)
931 { return __builtin_logf128(__x); }
932
933 constexpr _Float128
934 log10(_Float128 __x)
935 { return __builtin_log10f128(__x); }
936
937 inline _Float128
938 modf(_Float128 __x, _Float128* __iptr)
939 { return __builtin_modff128(__x, __iptr); }
940
941 constexpr _Float128
942 pow(_Float128 __x, _Float128 __y)
943 { return __builtin_powf128(__x, __y); }
944
945 constexpr _Float128
946 sin(_Float128 __x)
947 { return __builtin_sinf128(__x); }
948
949 constexpr _Float128
950 sinh(_Float128 __x)
951 { return __builtin_sinhf128(__x); }
952
953 constexpr _Float128
954 sqrt(_Float128 __x)
955 { return __builtin_sqrtf128(__x); }
956
957 constexpr _Float128
958 tan(_Float128 __x)
959 { return __builtin_tanf128(__x); }
960
961 constexpr _Float128
962 tanh(_Float128 __x)
963 { return __builtin_tanhf128(__x); }
964#endif
965
966#if defined(__STDCPP_BFLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
967 constexpr __gnu_cxx::__bfloat16_t
968 acos(__gnu_cxx::__bfloat16_t __x)
969 { return __gnu_cxx::__bfloat16_t(__builtin_acosf(__x)); }
970
971 constexpr __gnu_cxx::__bfloat16_t
972 asin(__gnu_cxx::__bfloat16_t __x)
973 { return __gnu_cxx::__bfloat16_t(__builtin_asinf(__x)); }
974
975 constexpr __gnu_cxx::__bfloat16_t
976 atan(__gnu_cxx::__bfloat16_t __x)
977 { return __gnu_cxx::__bfloat16_t(__builtin_atanf(__x)); }
978
979 constexpr __gnu_cxx::__bfloat16_t
980 atan2(__gnu_cxx::__bfloat16_t __y, __gnu_cxx::__bfloat16_t __x)
981 { return __gnu_cxx::__bfloat16_t(__builtin_atan2f(__y, __x)); }
982
983 constexpr __gnu_cxx::__bfloat16_t
984 ceil(__gnu_cxx::__bfloat16_t __x)
985 { return __gnu_cxx::__bfloat16_t(__builtin_ceilf(__x)); }
986
987 constexpr __gnu_cxx::__bfloat16_t
988 cos(__gnu_cxx::__bfloat16_t __x)
989 { return __gnu_cxx::__bfloat16_t(__builtin_cosf(__x)); }
990
991 constexpr __gnu_cxx::__bfloat16_t
992 cosh(__gnu_cxx::__bfloat16_t __x)
993 { return __gnu_cxx::__bfloat16_t(__builtin_coshf(__x)); }
994
995 constexpr __gnu_cxx::__bfloat16_t
996 exp(__gnu_cxx::__bfloat16_t __x)
997 { return __gnu_cxx::__bfloat16_t(__builtin_expf(__x)); }
998
999 constexpr __gnu_cxx::__bfloat16_t
1000 fabs(__gnu_cxx::__bfloat16_t __x)
1001 { return __gnu_cxx::__bfloat16_t(__builtin_fabsf(__x)); }
1002
1003 constexpr __gnu_cxx::__bfloat16_t
1004 floor(__gnu_cxx::__bfloat16_t __x)
1005 { return __gnu_cxx::__bfloat16_t(__builtin_floorf(__x)); }
1006
1007 constexpr __gnu_cxx::__bfloat16_t
1008 fmod(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
1009 { return __gnu_cxx::__bfloat16_t(__builtin_fmodf(__x, __y)); }
1010
1011 inline __gnu_cxx::__bfloat16_t
1012 frexp(__gnu_cxx::__bfloat16_t __x, int* __exp)
1013 { return __gnu_cxx::__bfloat16_t(__builtin_frexpf(__x, __exp)); }
1014
1015 constexpr __gnu_cxx::__bfloat16_t
1016 ldexp(__gnu_cxx::__bfloat16_t __x, int __exp)
1017 { return __gnu_cxx::__bfloat16_t(__builtin_ldexpf(__x, __exp)); }
1018
1019 constexpr __gnu_cxx::__bfloat16_t
1020 log(__gnu_cxx::__bfloat16_t __x)
1021 { return __gnu_cxx::__bfloat16_t(__builtin_logf(__x)); }
1022
1023 constexpr __gnu_cxx::__bfloat16_t
1024 log10(__gnu_cxx::__bfloat16_t __x)
1025 { return __gnu_cxx::__bfloat16_t(__builtin_log10f(__x)); }
1026
1027 inline __gnu_cxx::__bfloat16_t
1028 modf(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t* __iptr)
1029 {
1030 float __i, __ret = __builtin_modff(__x, &__i);
1031 *__iptr = __gnu_cxx::__bfloat16_t(__i);
1032 return __gnu_cxx::__bfloat16_t(__ret);
1033 }
1034
1035 constexpr __gnu_cxx::__bfloat16_t
1036 pow(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
1037 { return __gnu_cxx::__bfloat16_t(__builtin_powf(__x, __y)); }
1038
1039 constexpr __gnu_cxx::__bfloat16_t
1040 sin(__gnu_cxx::__bfloat16_t __x)
1041 { return __gnu_cxx::__bfloat16_t(__builtin_sinf(__x)); }
1042
1043 constexpr __gnu_cxx::__bfloat16_t
1044 sinh(__gnu_cxx::__bfloat16_t __x)
1045 { return __gnu_cxx::__bfloat16_t(__builtin_sinhf(__x)); }
1046
1047 constexpr __gnu_cxx::__bfloat16_t
1048 sqrt(__gnu_cxx::__bfloat16_t __x)
1049 { return __gnu_cxx::__bfloat16_t(__builtin_sqrtf(__x)); }
1050
1051 constexpr __gnu_cxx::__bfloat16_t
1052 tan(__gnu_cxx::__bfloat16_t __x)
1053 { return __gnu_cxx::__bfloat16_t(__builtin_tanf(__x)); }
1054
1055 constexpr __gnu_cxx::__bfloat16_t
1056 tanh(__gnu_cxx::__bfloat16_t __x)
1057 { return __gnu_cxx::__bfloat16_t(__builtin_tanhf(__x)); }
1058#endif
1059
1060 template<typename _Tp, typename _Up>
1061 inline _GLIBCXX_CONSTEXPR
1062 typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
1063 atan2(_Tp __y, _Up __x)
1064 {
1065 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1066 return atan2(__type(__y), __type(__x));
1067 }
1068
1069 template<typename _Tp, typename _Up>
1070 inline _GLIBCXX_CONSTEXPR
1071 typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
1072 fmod(_Tp __x, _Up __y)
1073 {
1074 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1075 return fmod(__type(__x), __type(__y));
1076 }
1077
1078 template<typename _Tp, typename _Up>
1079 inline _GLIBCXX_CONSTEXPR
1080 typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
1081 pow(_Tp __x, _Up __y)
1082 {
1083 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1084 return pow(__type(__x), __type(__y));
1085 }
1086
1087#if _GLIBCXX_USE_C99_MATH
1088#if !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC
1089
1090// These are possible macros imported from C99-land.
1091#undef fpclassify
1092#undef isfinite
1093#undef isinf
1094#undef isnan
1095#undef isnormal
1096#undef signbit
1097#undef isgreater
1098#undef isgreaterequal
1099#undef isless
1100#undef islessequal
1101#undef islessgreater
1102#undef isunordered
1103
1104#if __cplusplus >= 201103L
1105
1106#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1107 constexpr int
1108 fpclassify(float __x)
1109 { return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
1110 FP_SUBNORMAL, FP_ZERO, __x); }
1111
1112 constexpr int
1113 fpclassify(double __x)
1114 { return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
1115 FP_SUBNORMAL, FP_ZERO, __x); }
1116
1117 constexpr int
1118 fpclassify(long double __x)
1119 { return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
1120 FP_SUBNORMAL, FP_ZERO, __x); }
1121#endif
1122
1123#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1124 template<typename _Tp>
1125 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1126 int>::__type
1127 fpclassify(_Tp __x)
1128 { return __x != 0 ? FP_NORMAL : FP_ZERO; }
1129#endif
1130
1131#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1132 constexpr bool
1133 isfinite(float __x)
1134 { return __builtin_isfinite(__x); }
1135
1136 constexpr bool
1137 isfinite(double __x)
1138 { return __builtin_isfinite(__x); }
1139
1140 constexpr bool
1141 isfinite(long double __x)
1142 { return __builtin_isfinite(__x); }
1143#endif
1144
1145#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1146 template<typename _Tp>
1147 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1148 bool>::__type
1149 isfinite(_Tp)
1150 { return true; }
1151#endif
1152
1153#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1154 constexpr bool
1155 isinf(float __x)
1156 { return __builtin_isinf(__x); }
1157
1158#if _GLIBCXX_HAVE_OBSOLETE_ISINF \
1159 && !_GLIBCXX_NO_OBSOLETE_ISINF_ISNAN_DYNAMIC
1160 using ::isinf;
1161#else
1162 constexpr bool
1163 isinf(double __x)
1164 { return __builtin_isinf(__x); }
1165#endif
1166
1167 constexpr bool
1168 isinf(long double __x)
1169 { return __builtin_isinf(__x); }
1170#endif
1171
1172#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1173 template<typename _Tp>
1174 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1175 bool>::__type
1176 isinf(_Tp)
1177 { return false; }
1178#endif
1179
1180#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1181 constexpr bool
1182 isnan(float __x)
1183 { return __builtin_isnan(__x); }
1184
1185#if _GLIBCXX_HAVE_OBSOLETE_ISNAN \
1186 && !_GLIBCXX_NO_OBSOLETE_ISINF_ISNAN_DYNAMIC
1187 using ::isnan;
1188#else
1189 constexpr bool
1190 isnan(double __x)
1191 { return __builtin_isnan(__x); }
1192#endif
1193
1194 constexpr bool
1195 isnan(long double __x)
1196 { return __builtin_isnan(__x); }
1197#endif
1198
1199#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1200 template<typename _Tp>
1201 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1202 bool>::__type
1203 isnan(_Tp)
1204 { return false; }
1205#endif
1206
1207#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1208 constexpr bool
1209 isnormal(float __x)
1210 { return __builtin_isnormal(__x); }
1211
1212 constexpr bool
1213 isnormal(double __x)
1214 { return __builtin_isnormal(__x); }
1215
1216 constexpr bool
1217 isnormal(long double __x)
1218 { return __builtin_isnormal(__x); }
1219#endif
1220
1221#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1222 template<typename _Tp>
1223 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1224 bool>::__type
1225 isnormal(_Tp __x)
1226 { return __x != 0 ? true : false; }
1227#endif
1228
1229#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1230 // Note: middle-end/36757 is fixed, __builtin_signbit is type-generic.
1231 constexpr bool
1232 signbit(float __x)
1233 { return __builtin_signbit(__x); }
1234
1235 constexpr bool
1236 signbit(double __x)
1237 { return __builtin_signbit(__x); }
1238
1239 constexpr bool
1240 signbit(long double __x)
1241 { return __builtin_signbit(__x); }
1242#endif
1243
1244#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1245 template<typename _Tp>
1246 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1247 bool>::__type
1248 signbit(_Tp __x)
1249 { return __x < 0 ? true : false; }
1250#endif
1251
1252#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1253 constexpr bool
1254 isgreater(float __x, float __y)
1255 { return __builtin_isgreater(__x, __y); }
1256
1257 constexpr bool
1258 isgreater(double __x, double __y)
1259 { return __builtin_isgreater(__x, __y); }
1260
1261 constexpr bool
1262 isgreater(long double __x, long double __y)
1263 { return __builtin_isgreater(__x, __y); }
1264#endif
1265
1266#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1267 template<typename _Tp, typename _Up>
1268 constexpr typename
1269 __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
1270 && __is_arithmetic<_Up>::__value), bool>::__type
1271 isgreater(_Tp __x, _Up __y)
1272 {
1273 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1274 return __builtin_isgreater(__type(__x), __type(__y));
1275 }
1276#endif
1277
1278#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1279 constexpr bool
1280 isgreaterequal(float __x, float __y)
1281 { return __builtin_isgreaterequal(__x, __y); }
1282
1283 constexpr bool
1284 isgreaterequal(double __x, double __y)
1285 { return __builtin_isgreaterequal(__x, __y); }
1286
1287 constexpr bool
1288 isgreaterequal(long double __x, long double __y)
1289 { return __builtin_isgreaterequal(__x, __y); }
1290#endif
1291
1292#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1293 template<typename _Tp, typename _Up>
1294 constexpr typename
1295 __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
1296 && __is_arithmetic<_Up>::__value), bool>::__type
1297 isgreaterequal(_Tp __x, _Up __y)
1298 {
1299 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1300 return __builtin_isgreaterequal(__type(__x), __type(__y));
1301 }
1302#endif
1303
1304#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1305 constexpr bool
1306 isless(float __x, float __y)
1307 { return __builtin_isless(__x, __y); }
1308
1309 constexpr bool
1310 isless(double __x, double __y)
1311 { return __builtin_isless(__x, __y); }
1312
1313 constexpr bool
1314 isless(long double __x, long double __y)
1315 { return __builtin_isless(__x, __y); }
1316#endif
1317
1318#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1319 template<typename _Tp, typename _Up>
1320 constexpr typename
1321 __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
1322 && __is_arithmetic<_Up>::__value), bool>::__type
1323 isless(_Tp __x, _Up __y)
1324 {
1325 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1326 return __builtin_isless(__type(__x), __type(__y));
1327 }
1328#endif
1329
1330#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1331 constexpr bool
1332 islessequal(float __x, float __y)
1333 { return __builtin_islessequal(__x, __y); }
1334
1335 constexpr bool
1336 islessequal(double __x, double __y)
1337 { return __builtin_islessequal(__x, __y); }
1338
1339 constexpr bool
1340 islessequal(long double __x, long double __y)
1341 { return __builtin_islessequal(__x, __y); }
1342#endif
1343
1344#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1345 template<typename _Tp, typename _Up>
1346 constexpr typename
1347 __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
1348 && __is_arithmetic<_Up>::__value), bool>::__type
1349 islessequal(_Tp __x, _Up __y)
1350 {
1351 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1352 return __builtin_islessequal(__type(__x), __type(__y));
1353 }
1354#endif
1355
1356#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1357 constexpr bool
1358 islessgreater(float __x, float __y)
1359 { return __builtin_islessgreater(__x, __y); }
1360
1361 constexpr bool
1362 islessgreater(double __x, double __y)
1363 { return __builtin_islessgreater(__x, __y); }
1364
1365 constexpr bool
1366 islessgreater(long double __x, long double __y)
1367 { return __builtin_islessgreater(__x, __y); }
1368#endif
1369
1370#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1371 template<typename _Tp, typename _Up>
1372 constexpr typename
1373 __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
1374 && __is_arithmetic<_Up>::__value), bool>::__type
1375 islessgreater(_Tp __x, _Up __y)
1376 {
1377 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1378 return __builtin_islessgreater(__type(__x), __type(__y));
1379 }
1380#endif
1381
1382#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1383 constexpr bool
1384 isunordered(float __x, float __y)
1385 { return __builtin_isunordered(__x, __y); }
1386
1387 constexpr bool
1388 isunordered(double __x, double __y)
1389 { return __builtin_isunordered(__x, __y); }
1390
1391 constexpr bool
1392 isunordered(long double __x, long double __y)
1393 { return __builtin_isunordered(__x, __y); }
1394#endif
1395
1396#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1397 template<typename _Tp, typename _Up>
1398 constexpr typename
1399 __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
1400 && __is_arithmetic<_Up>::__value), bool>::__type
1401 isunordered(_Tp __x, _Up __y)
1402 {
1403 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1404 return __builtin_isunordered(__type(__x), __type(__y));
1405 }
1406#endif
1407
1408#else
1409
1410 template<typename _Tp>
1411 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
1412 int>::__type
1413 fpclassify(_Tp __f)
1414 {
1415 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1416 return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
1417 FP_SUBNORMAL, FP_ZERO, __type(__f));
1418 }
1419
1420 template<typename _Tp>
1421 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
1422 int>::__type
1423 isfinite(_Tp __f)
1424 {
1425 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1426 return __builtin_isfinite(__type(__f));
1427 }
1428
1429 template<typename _Tp>
1430 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
1431 int>::__type
1432 isinf(_Tp __f)
1433 {
1434 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1435 return __builtin_isinf(__type(__f));
1436 }
1437
1438 template<typename _Tp>
1439 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
1440 int>::__type
1441 isnan(_Tp __f)
1442 {
1443 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1444 return __builtin_isnan(__type(__f));
1445 }
1446
1447 template<typename _Tp>
1448 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
1449 int>::__type
1450 isnormal(_Tp __f)
1451 {
1452 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1453 return __builtin_isnormal(__type(__f));
1454 }
1455
1456 template<typename _Tp>
1457 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
1458 int>::__type
1459 signbit(_Tp __f)
1460 {
1461 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1462 return __builtin_signbit(__type(__f));
1463 }
1464
1465 template<typename _Tp>
1466 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
1467 int>::__type
1468 isgreater(_Tp __f1, _Tp __f2)
1469 {
1470 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1471 return __builtin_isgreater(__type(__f1), __type(__f2));
1472 }
1473
1474 template<typename _Tp>
1475 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
1476 int>::__type
1477 isgreaterequal(_Tp __f1, _Tp __f2)
1478 {
1479 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1480 return __builtin_isgreaterequal(__type(__f1), __type(__f2));
1481 }
1482
1483 template<typename _Tp>
1484 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
1485 int>::__type
1486 isless(_Tp __f1, _Tp __f2)
1487 {
1488 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1489 return __builtin_isless(__type(__f1), __type(__f2));
1490 }
1491
1492 template<typename _Tp>
1493 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
1494 int>::__type
1495 islessequal(_Tp __f1, _Tp __f2)
1496 {
1497 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1498 return __builtin_islessequal(__type(__f1), __type(__f2));
1499 }
1500
1501 template<typename _Tp>
1502 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
1503 int>::__type
1504 islessgreater(_Tp __f1, _Tp __f2)
1505 {
1506 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1507 return __builtin_islessgreater(__type(__f1), __type(__f2));
1508 }
1509
1510 template<typename _Tp>
1511 inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
1512 int>::__type
1513 isunordered(_Tp __f1, _Tp __f2)
1514 {
1515 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1516 return __builtin_isunordered(__type(__f1), __type(__f2));
1517 }
1518
1519#endif // C++11
1520
1521#ifdef __STDCPP_FLOAT16_T__
1522 constexpr int
1523 fpclassify(_Float16 __x)
1524 { return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
1525 FP_SUBNORMAL, FP_ZERO, __x); }
1526
1527 constexpr bool
1528 isfinite(_Float16 __x)
1529 { return __builtin_isfinite(__x); }
1530
1531 constexpr bool
1532 isinf(_Float16 __x)
1533 { return __builtin_isinf(__x); }
1534
1535 constexpr bool
1536 isnan(_Float16 __x)
1537 { return __builtin_isnan(__x); }
1538
1539 constexpr bool
1540 isnormal(_Float16 __x)
1541 { return __builtin_isnormal(__x); }
1542
1543 constexpr bool
1544 signbit(_Float16 __x)
1545 { return __builtin_signbit(__x); }
1546
1547 constexpr bool
1548 isgreater(_Float16 __x, _Float16 __y)
1549 { return __builtin_isgreater(__x, __y); }
1550
1551 constexpr bool
1552 isgreaterequal(_Float16 __x, _Float16 __y)
1553 { return __builtin_isgreaterequal(__x, __y); }
1554
1555 constexpr bool
1556 isless(_Float16 __x, _Float16 __y)
1557 { return __builtin_isless(__x, __y); }
1558
1559 constexpr bool
1560 islessequal(_Float16 __x, _Float16 __y)
1561 { return __builtin_islessequal(__x, __y); }
1562
1563 constexpr bool
1564 islessgreater(_Float16 __x, _Float16 __y)
1565 { return __builtin_islessgreater(__x, __y); }
1566
1567 constexpr bool
1568 isunordered(_Float16 __x, _Float16 __y)
1569 { return __builtin_isunordered(__x, __y); }
1570#endif
1571
1572#ifdef __STDCPP_FLOAT32_T__
1573 constexpr int
1574 fpclassify(_Float32 __x)
1575 { return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
1576 FP_SUBNORMAL, FP_ZERO, __x); }
1577
1578 constexpr bool
1579 isfinite(_Float32 __x)
1580 { return __builtin_isfinite(__x); }
1581
1582 constexpr bool
1583 isinf(_Float32 __x)
1584 { return __builtin_isinf(__x); }
1585
1586 constexpr bool
1587 isnan(_Float32 __x)
1588 { return __builtin_isnan(__x); }
1589
1590 constexpr bool
1591 isnormal(_Float32 __x)
1592 { return __builtin_isnormal(__x); }
1593
1594 constexpr bool
1595 signbit(_Float32 __x)
1596 { return __builtin_signbit(__x); }
1597
1598 constexpr bool
1599 isgreater(_Float32 __x, _Float32 __y)
1600 { return __builtin_isgreater(__x, __y); }
1601
1602 constexpr bool
1603 isgreaterequal(_Float32 __x, _Float32 __y)
1604 { return __builtin_isgreaterequal(__x, __y); }
1605
1606 constexpr bool
1607 isless(_Float32 __x, _Float32 __y)
1608 { return __builtin_isless(__x, __y); }
1609
1610 constexpr bool
1611 islessequal(_Float32 __x, _Float32 __y)
1612 { return __builtin_islessequal(__x, __y); }
1613
1614 constexpr bool
1615 islessgreater(_Float32 __x, _Float32 __y)
1616 { return __builtin_islessgreater(__x, __y); }
1617
1618 constexpr bool
1619 isunordered(_Float32 __x, _Float32 __y)
1620 { return __builtin_isunordered(__x, __y); }
1621#endif
1622
1623#ifdef __STDCPP_FLOAT64_T__
1624 constexpr int
1625 fpclassify(_Float64 __x)
1626 { return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
1627 FP_SUBNORMAL, FP_ZERO, __x); }
1628
1629 constexpr bool
1630 isfinite(_Float64 __x)
1631 { return __builtin_isfinite(__x); }
1632
1633 constexpr bool
1634 isinf(_Float64 __x)
1635 { return __builtin_isinf(__x); }
1636
1637 constexpr bool
1638 isnan(_Float64 __x)
1639 { return __builtin_isnan(__x); }
1640
1641 constexpr bool
1642 isnormal(_Float64 __x)
1643 { return __builtin_isnormal(__x); }
1644
1645 constexpr bool
1646 signbit(_Float64 __x)
1647 { return __builtin_signbit(__x); }
1648
1649 constexpr bool
1650 isgreater(_Float64 __x, _Float64 __y)
1651 { return __builtin_isgreater(__x, __y); }
1652
1653 constexpr bool
1654 isgreaterequal(_Float64 __x, _Float64 __y)
1655 { return __builtin_isgreaterequal(__x, __y); }
1656
1657 constexpr bool
1658 isless(_Float64 __x, _Float64 __y)
1659 { return __builtin_isless(__x, __y); }
1660
1661 constexpr bool
1662 islessequal(_Float64 __x, _Float64 __y)
1663 { return __builtin_islessequal(__x, __y); }
1664
1665 constexpr bool
1666 islessgreater(_Float64 __x, _Float64 __y)
1667 { return __builtin_islessgreater(__x, __y); }
1668
1669 constexpr bool
1670 isunordered(_Float64 __x, _Float64 __y)
1671 { return __builtin_isunordered(__x, __y); }
1672#endif
1673
1674#ifdef __STDCPP_FLOAT128_T__
1675 constexpr int
1676 fpclassify(_Float128 __x)
1677 { return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
1678 FP_SUBNORMAL, FP_ZERO, __x); }
1679
1680 constexpr bool
1681 isfinite(_Float128 __x)
1682 { return __builtin_isfinite(__x); }
1683
1684 constexpr bool
1685 isinf(_Float128 __x)
1686 { return __builtin_isinf(__x); }
1687
1688 constexpr bool
1689 isnan(_Float128 __x)
1690 { return __builtin_isnan(__x); }
1691
1692 constexpr bool
1693 isnormal(_Float128 __x)
1694 { return __builtin_isnormal(__x); }
1695
1696 constexpr bool
1697 signbit(_Float128 __x)
1698 { return __builtin_signbit(__x); }
1699
1700 constexpr bool
1701 isgreater(_Float128 __x, _Float128 __y)
1702 { return __builtin_isgreater(__x, __y); }
1703
1704 constexpr bool
1705 isgreaterequal(_Float128 __x, _Float128 __y)
1706 { return __builtin_isgreaterequal(__x, __y); }
1707
1708 constexpr bool
1709 isless(_Float128 __x, _Float128 __y)
1710 { return __builtin_isless(__x, __y); }
1711
1712 constexpr bool
1713 islessequal(_Float128 __x, _Float128 __y)
1714 { return __builtin_islessequal(__x, __y); }
1715
1716 constexpr bool
1717 islessgreater(_Float128 __x, _Float128 __y)
1718 { return __builtin_islessgreater(__x, __y); }
1719
1720 constexpr bool
1721 isunordered(_Float128 __x, _Float128 __y)
1722 { return __builtin_isunordered(__x, __y); }
1723#endif
1724
1725#ifdef __STDCPP_BFLOAT16_T__
1726 constexpr int
1727 fpclassify(__gnu_cxx::__bfloat16_t __x)
1728 { return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
1729 FP_SUBNORMAL, FP_ZERO, __x); }
1730
1731 constexpr bool
1732 isfinite(__gnu_cxx::__bfloat16_t __x)
1733 { return __builtin_isfinite(__x); }
1734
1735 constexpr bool
1736 isinf(__gnu_cxx::__bfloat16_t __x)
1737 { return __builtin_isinf(__x); }
1738
1739 constexpr bool
1740 isnan(__gnu_cxx::__bfloat16_t __x)
1741 { return __builtin_isnan(__x); }
1742
1743 constexpr bool
1744 isnormal(__gnu_cxx::__bfloat16_t __x)
1745 { return __builtin_isnormal(__x); }
1746
1747 constexpr bool
1748 signbit(__gnu_cxx::__bfloat16_t __x)
1749 { return __builtin_signbit(__x); }
1750
1751 constexpr bool
1752 isgreater(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
1753 { return __builtin_isgreater(__x, __y); }
1754
1755 constexpr bool
1756 isgreaterequal(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
1757 { return __builtin_isgreaterequal(__x, __y); }
1758
1759 constexpr bool
1760 isless(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
1761 { return __builtin_isless(__x, __y); }
1762
1763 constexpr bool
1764 islessequal(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
1765 { return __builtin_islessequal(__x, __y); }
1766
1767 constexpr bool
1768 islessgreater(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
1769 { return __builtin_islessgreater(__x, __y); }
1770
1771 constexpr bool
1772 isunordered(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
1773 { return __builtin_isunordered(__x, __y); }
1774#endif
1775
1776#endif /* _GLIBCXX_USE_C99_FP_MACROS_DYNAMIC */
1777#endif /* _GLIBCXX_USE_C99_MATH */
1778
1779#if __cplusplus >= 201103L
1780
1781#undef acosf
1782#undef acosl
1783#undef asinf
1784#undef asinl
1785#undef atanf
1786#undef atanl
1787#undef atan2f
1788#undef atan2l
1789#undef ceilf
1790#undef ceill
1791#undef cosf
1792#undef cosl
1793#undef coshf
1794#undef coshl
1795#undef expf
1796#undef expl
1797#undef fabsf
1798#undef fabsl
1799#undef floorf
1800#undef floorl
1801#undef fmodf
1802#undef fmodl
1803#undef frexpf
1804#undef frexpl
1805#undef ldexpf
1806#undef ldexpl
1807#undef logf
1808#undef logl
1809#undef log10f
1810#undef log10l
1811#undef modff
1812#undef modfl
1813#undef powf
1814#undef powl
1815#undef sinf
1816#undef sinl
1817#undef sinhf
1818#undef sinhl
1819#undef sqrtf
1820#undef sqrtl
1821#undef tanf
1822#undef tanl
1823#undef tanhf
1824#undef tanhl
1825
1826#ifdef _GLIBCXX_HAVE_ACOSF
1827 using ::acosf;
1828#endif
1829#ifdef _GLIBCXX_HAVE_ACOSL
1830 using ::acosl;
1831#endif
1832
1833#ifdef _GLIBCXX_HAVE_ASINF
1834 using ::asinf;
1835#endif
1836#ifdef _GLIBCXX_HAVE_ASINL
1837 using ::asinl;
1838#endif
1839
1840#ifdef _GLIBCXX_HAVE_ATANF
1841 using ::atanf;
1842#endif
1843#ifdef _GLIBCXX_HAVE_ATANL
1844 using ::atanl;
1845#endif
1846
1847#ifdef _GLIBCXX_HAVE_ATAN2F
1848 using ::atan2f;
1849#endif
1850#ifdef _GLIBCXX_HAVE_ATAN2L
1851 using ::atan2l;
1852#endif
1853
1854#ifdef _GLIBCXX_HAVE_CEILF
1855 using ::ceilf;
1856#endif
1857#ifdef _GLIBCXX_HAVE_CEILL
1858 using ::ceill;
1859#endif
1860
1861#ifdef _GLIBCXX_HAVE_COSF
1862 using ::cosf;
1863#endif
1864#ifdef _GLIBCXX_HAVE_COSL
1865 using ::cosl;
1866#endif
1867
1868#ifdef _GLIBCXX_HAVE_COSHF
1869 using ::coshf;
1870#endif
1871#ifdef _GLIBCXX_HAVE_COSHL
1872 using ::coshl;
1873#endif
1874
1875#ifdef _GLIBCXX_HAVE_EXPF
1876 using ::expf;
1877#endif
1878#ifdef _GLIBCXX_HAVE_EXPL
1879 using ::expl;
1880#endif
1881
1882#ifdef _GLIBCXX_HAVE_FABSF
1883 using ::fabsf;
1884#endif
1885#ifdef _GLIBCXX_HAVE_FABSL
1886 using ::fabsl;
1887#endif
1888
1889#ifdef _GLIBCXX_HAVE_FLOORF
1890 using ::floorf;
1891#endif
1892#ifdef _GLIBCXX_HAVE_FLOORL
1893 using ::floorl;
1894#endif
1895
1896#ifdef _GLIBCXX_HAVE_FMODF
1897 using ::fmodf;
1898#endif
1899#ifdef _GLIBCXX_HAVE_FMODL
1900 using ::fmodl;
1901#endif
1902
1903#ifdef _GLIBCXX_HAVE_FREXPF
1904 using ::frexpf;
1905#endif
1906#ifdef _GLIBCXX_HAVE_FREXPL
1907 using ::frexpl;
1908#endif
1909
1910#ifdef _GLIBCXX_HAVE_LDEXPF
1911 using ::ldexpf;
1912#endif
1913#ifdef _GLIBCXX_HAVE_LDEXPL
1914 using ::ldexpl;
1915#endif
1916
1917#ifdef _GLIBCXX_HAVE_LOGF
1918 using ::logf;
1919#endif
1920#ifdef _GLIBCXX_HAVE_LOGL
1921 using ::logl;
1922#endif
1923
1924#ifdef _GLIBCXX_HAVE_LOG10F
1925 using ::log10f;
1926#endif
1927#ifdef _GLIBCXX_HAVE_LOG10L
1928 using ::log10l;
1929#endif
1930
1931#ifdef _GLIBCXX_HAVE_MODFF
1932 using ::modff;
1933#endif
1934#ifdef _GLIBCXX_HAVE_MODFL
1935 using ::modfl;
1936#endif
1937
1938#ifdef _GLIBCXX_HAVE_POWF
1939 using ::powf;
1940#endif
1941#ifdef _GLIBCXX_HAVE_POWL
1942 using ::powl;
1943#endif
1944
1945#ifdef _GLIBCXX_HAVE_SINF
1946 using ::sinf;
1947#endif
1948#ifdef _GLIBCXX_HAVE_SINL
1949 using ::sinl;
1950#endif
1951
1952#ifdef _GLIBCXX_HAVE_SINHF
1953 using ::sinhf;
1954#endif
1955#ifdef _GLIBCXX_HAVE_SINHL
1956 using ::sinhl;
1957#endif
1958
1959#ifdef _GLIBCXX_HAVE_SQRTF
1960 using ::sqrtf;
1961#endif
1962#ifdef _GLIBCXX_HAVE_SQRTL
1963 using ::sqrtl;
1964#endif
1965
1966#ifdef _GLIBCXX_HAVE_TANF
1967 using ::tanf;
1968#endif
1969#ifdef _GLIBCXX_HAVE_TANL
1970 using ::tanl;
1971#endif
1972
1973#ifdef _GLIBCXX_HAVE_TANHF
1974 using ::tanhf;
1975#endif
1976#ifdef _GLIBCXX_HAVE_TANHL
1977 using ::tanhl;
1978#endif
1979
1980#ifdef _GLIBCXX_USE_C99_MATH_FUNCS
1981
1982#undef acosh
1983#undef acoshf
1984#undef acoshl
1985#undef asinh
1986#undef asinhf
1987#undef asinhl
1988#undef atanh
1989#undef atanhf
1990#undef atanhl
1991#undef cbrt
1992#undef cbrtf
1993#undef cbrtl
1994#undef copysign
1995#undef copysignf
1996#undef copysignl
1997#undef erf
1998#undef erff
1999#undef erfl
2000#undef erfc
2001#undef erfcf
2002#undef erfcl
2003#undef exp2
2004#undef exp2f
2005#undef exp2l
2006#undef expm1
2007#undef expm1f
2008#undef expm1l
2009#undef fdim
2010#undef fdimf
2011#undef fdiml
2012#undef fma
2013#undef fmaf
2014#undef fmal
2015#undef fmax
2016#undef fmaxf
2017#undef fmaxl
2018#undef fmin
2019#undef fminf
2020#undef fminl
2021#undef hypot
2022#undef hypotf
2023#undef hypotl
2024#undef ilogb
2025#undef ilogbf
2026#undef ilogbl
2027#undef lgamma
2028#undef lgammaf
2029#undef lgammal
2030#ifndef _GLIBCXX_NO_C99_ROUNDING_FUNCS
2031#undef llrint
2032#undef llrintf
2033#undef llrintl
2034#undef llround
2035#undef llroundf
2036#undef llroundl
2037#endif
2038#undef log1p
2039#undef log1pf
2040#undef log1pl
2041#undef log2
2042#undef log2f
2043#undef log2l
2044#undef logb
2045#undef logbf
2046#undef logbl
2047#undef lrint
2048#undef lrintf
2049#undef lrintl
2050#undef lround
2051#undef lroundf
2052#undef lroundl
2053#undef nan
2054#undef nanf
2055#undef nanl
2056#undef nearbyint
2057#undef nearbyintf
2058#undef nearbyintl
2059#undef nextafter
2060#undef nextafterf
2061#undef nextafterl
2062#undef nexttoward
2063#undef nexttowardf
2064#undef nexttowardl
2065#undef remainder
2066#undef remainderf
2067#undef remainderl
2068#undef remquo
2069#undef remquof
2070#undef remquol
2071#undef rint
2072#undef rintf
2073#undef rintl
2074#undef round
2075#undef roundf
2076#undef roundl
2077#undef scalbln
2078#undef scalblnf
2079#undef scalblnl
2080#undef scalbn
2081#undef scalbnf
2082#undef scalbnl
2083#undef tgamma
2084#undef tgammaf
2085#undef tgammal
2086#undef trunc
2087#undef truncf
2088#undef truncl
2089
2090#ifdef _GLIBCXX_HAVE_C99_FLT_EVAL_TYPES
2091 // types
2092 using ::double_t;
2093 using ::float_t;
2094#endif
2095
2096 // functions
2097 using ::acosh;
2098 using ::acoshf;
2099 using ::acoshl;
2100
2101 using ::asinh;
2102 using ::asinhf;
2103 using ::asinhl;
2104
2105 using ::atanh;
2106 using ::atanhf;
2107 using ::atanhl;
2108
2109 using ::cbrt;
2110 using ::cbrtf;
2111 using ::cbrtl;
2112
2113 using ::copysign;
2114 using ::copysignf;
2115 using ::copysignl;
2116
2117 using ::erf;
2118 using ::erff;
2119 using ::erfl;
2120
2121 using ::erfc;
2122 using ::erfcf;
2123 using ::erfcl;
2124
2125 using ::exp2;
2126 using ::exp2f;
2127 using ::exp2l;
2128
2129 using ::expm1;
2130 using ::expm1f;
2131 using ::expm1l;
2132
2133 using ::fdim;
2134 using ::fdimf;
2135 using ::fdiml;
2136
2137 using ::fma;
2138 using ::fmaf;
2139 using ::fmal;
2140
2141 using ::fmax;
2142 using ::fmaxf;
2143 using ::fmaxl;
2144
2145 using ::fmin;
2146 using ::fminf;
2147 using ::fminl;
2148
2149 using ::hypot;
2150 using ::hypotf;
2151 using ::hypotl;
2152
2153 using ::ilogb;
2154 using ::ilogbf;
2155 using ::ilogbl;
2156
2157 using ::lgamma;
2158 using ::lgammaf;
2159 using ::lgammal;
2160
2161#ifndef _GLIBCXX_NO_C99_ROUNDING_FUNCS
2162 using ::llrint;
2163 using ::llrintf;
2164 using ::llrintl;
2165
2166 using ::llround;
2167 using ::llroundf;
2168 using ::llroundl;
2169#endif
2170
2171 using ::log1p;
2172 using ::log1pf;
2173 using ::log1pl;
2174
2175 using ::log2;
2176 using ::log2f;
2177 using ::log2l;
2178
2179 using ::logb;
2180 using ::logbf;
2181 using ::logbl;
2182
2183 using ::lrint;
2184 using ::lrintf;
2185 using ::lrintl;
2186
2187 using ::lround;
2188 using ::lroundf;
2189 using ::lroundl;
2190
2191 using ::nan;
2192 using ::nanf;
2193 using ::nanl;
2194
2195 using ::nearbyint;
2196 using ::nearbyintf;
2197 using ::nearbyintl;
2198
2199 using ::nextafter;
2200 using ::nextafterf;
2201 using ::nextafterl;
2202
2203 using ::nexttoward;
2204 using ::nexttowardf;
2205 using ::nexttowardl;
2206
2207 using ::remainder;
2208 using ::remainderf;
2209 using ::remainderl;
2210
2211 using ::remquo;
2212 using ::remquof;
2213 using ::remquol;
2214
2215 using ::rint;
2216 using ::rintf;
2217 using ::rintl;
2218
2219 using ::round;
2220 using ::roundf;
2221 using ::roundl;
2222
2223 using ::scalbln;
2224 using ::scalblnf;
2225 using ::scalblnl;
2226
2227 using ::scalbn;
2228 using ::scalbnf;
2229 using ::scalbnl;
2230
2231 using ::tgamma;
2232 using ::tgammaf;
2233 using ::tgammal;
2234
2235 using ::trunc;
2236 using ::truncf;
2237 using ::truncl;
2238
2239 /// Additional overloads.
2240#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2241 constexpr float
2242 acosh(float __x)
2243 { return __builtin_acoshf(__x); }
2244
2245 constexpr long double
2246 acosh(long double __x)
2247 { return __builtin_acoshl(__x); }
2248#endif
2249
2250#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2251 template<typename _Tp>
2252 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2253 double>::__type
2254 acosh(_Tp __x)
2255 { return __builtin_acosh(__x); }
2256#endif
2257
2258#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2259 constexpr float
2260 asinh(float __x)
2261 { return __builtin_asinhf(__x); }
2262
2263 constexpr long double
2264 asinh(long double __x)
2265 { return __builtin_asinhl(__x); }
2266#endif
2267
2268#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2269 template<typename _Tp>
2270 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2271 double>::__type
2272 asinh(_Tp __x)
2273 { return __builtin_asinh(__x); }
2274#endif
2275
2276#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2277 constexpr float
2278 atanh(float __x)
2279 { return __builtin_atanhf(__x); }
2280
2281 constexpr long double
2282 atanh(long double __x)
2283 { return __builtin_atanhl(__x); }
2284#endif
2285
2286#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2287 template<typename _Tp>
2288 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2289 double>::__type
2290 atanh(_Tp __x)
2291 { return __builtin_atanh(__x); }
2292#endif
2293
2294#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2295 constexpr float
2296 cbrt(float __x)
2297 { return __builtin_cbrtf(__x); }
2298
2299 constexpr long double
2300 cbrt(long double __x)
2301 { return __builtin_cbrtl(__x); }
2302#endif
2303
2304#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2305 template<typename _Tp>
2306 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2307 double>::__type
2308 cbrt(_Tp __x)
2309 { return __builtin_cbrt(__x); }
2310#endif
2311
2312#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2313 constexpr float
2314 copysign(float __x, float __y)
2315 { return __builtin_copysignf(__x, __y); }
2316
2317 constexpr long double
2318 copysign(long double __x, long double __y)
2319 { return __builtin_copysignl(__x, __y); }
2320#endif
2321
2322#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2323 constexpr float
2324 erf(float __x)
2325 { return __builtin_erff(__x); }
2326
2327 constexpr long double
2328 erf(long double __x)
2329 { return __builtin_erfl(__x); }
2330#endif
2331
2332#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2333 template<typename _Tp>
2334 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2335 double>::__type
2336 erf(_Tp __x)
2337 { return __builtin_erf(__x); }
2338#endif
2339
2340#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2341 constexpr float
2342 erfc(float __x)
2343 { return __builtin_erfcf(__x); }
2344
2345 constexpr long double
2346 erfc(long double __x)
2347 { return __builtin_erfcl(__x); }
2348#endif
2349
2350#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2351 template<typename _Tp>
2352 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2353 double>::__type
2354 erfc(_Tp __x)
2355 { return __builtin_erfc(__x); }
2356#endif
2357
2358#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2359 constexpr float
2360 exp2(float __x)
2361 { return __builtin_exp2f(__x); }
2362
2363 constexpr long double
2364 exp2(long double __x)
2365 { return __builtin_exp2l(__x); }
2366#endif
2367
2368#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2369 template<typename _Tp>
2370 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2371 double>::__type
2372 exp2(_Tp __x)
2373 { return __builtin_exp2(__x); }
2374#endif
2375
2376#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2377 constexpr float
2378 expm1(float __x)
2379 { return __builtin_expm1f(__x); }
2380
2381 constexpr long double
2382 expm1(long double __x)
2383 { return __builtin_expm1l(__x); }
2384#endif
2385
2386#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2387 template<typename _Tp>
2388 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2389 double>::__type
2390 expm1(_Tp __x)
2391 { return __builtin_expm1(__x); }
2392#endif
2393
2394#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2395 constexpr float
2396 fdim(float __x, float __y)
2397 { return __builtin_fdimf(__x, __y); }
2398
2399 constexpr long double
2400 fdim(long double __x, long double __y)
2401 { return __builtin_fdiml(__x, __y); }
2402#endif
2403
2404#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2405 constexpr float
2406 fma(float __x, float __y, float __z)
2407 { return __builtin_fmaf(__x, __y, __z); }
2408
2409 constexpr long double
2410 fma(long double __x, long double __y, long double __z)
2411 { return __builtin_fmal(__x, __y, __z); }
2412#endif
2413
2414#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2415 constexpr float
2416 fmax(float __x, float __y)
2417 { return __builtin_fmaxf(__x, __y); }
2418
2419 constexpr long double
2420 fmax(long double __x, long double __y)
2421 { return __builtin_fmaxl(__x, __y); }
2422#endif
2423
2424#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2425 constexpr float
2426 fmin(float __x, float __y)
2427 { return __builtin_fminf(__x, __y); }
2428
2429 constexpr long double
2430 fmin(long double __x, long double __y)
2431 { return __builtin_fminl(__x, __y); }
2432#endif
2433
2434#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2435 constexpr float
2436 hypot(float __x, float __y)
2437 { return __builtin_hypotf(__x, __y); }
2438
2439 constexpr long double
2440 hypot(long double __x, long double __y)
2441 { return __builtin_hypotl(__x, __y); }
2442#endif
2443
2444#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2445 constexpr int
2446 ilogb(float __x)
2447 { return __builtin_ilogbf(__x); }
2448
2449 constexpr int
2450 ilogb(long double __x)
2451 { return __builtin_ilogbl(__x); }
2452#endif
2453
2454#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2455 template<typename _Tp>
2456 constexpr
2457 typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2458 int>::__type
2459 ilogb(_Tp __x)
2460 { return __builtin_ilogb(__x); }
2461#endif
2462
2463#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2464 constexpr float
2465 lgamma(float __x)
2466 { return __builtin_lgammaf(__x); }
2467
2468 constexpr long double
2469 lgamma(long double __x)
2470 { return __builtin_lgammal(__x); }
2471#endif
2472
2473#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2474 template<typename _Tp>
2475 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2476 double>::__type
2477 lgamma(_Tp __x)
2478 { return __builtin_lgamma(__x); }
2479#endif
2480
2481#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2482 constexpr long long
2483 llrint(float __x)
2484 { return __builtin_llrintf(__x); }
2485
2486 constexpr long long
2487 llrint(long double __x)
2488 { return __builtin_llrintl(__x); }
2489#endif
2490
2491#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2492 template<typename _Tp>
2493 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2494 long long>::__type
2495 llrint(_Tp __x)
2496 { return __builtin_llrint(__x); }
2497#endif
2498
2499#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2500 constexpr long long
2501 llround(float __x)
2502 { return __builtin_llroundf(__x); }
2503
2504 constexpr long long
2505 llround(long double __x)
2506 { return __builtin_llroundl(__x); }
2507#endif
2508
2509#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2510 template<typename _Tp>
2511 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2512 long long>::__type
2513 llround(_Tp __x)
2514 { return __builtin_llround(__x); }
2515#endif
2516
2517#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2518 constexpr float
2519 log1p(float __x)
2520 { return __builtin_log1pf(__x); }
2521
2522 constexpr long double
2523 log1p(long double __x)
2524 { return __builtin_log1pl(__x); }
2525#endif
2526
2527#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2528 template<typename _Tp>
2529 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2530 double>::__type
2531 log1p(_Tp __x)
2532 { return __builtin_log1p(__x); }
2533#endif
2534
2535#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2536 // DR 568.
2537 constexpr float
2538 log2(float __x)
2539 { return __builtin_log2f(__x); }
2540
2541 constexpr long double
2542 log2(long double __x)
2543 { return __builtin_log2l(__x); }
2544#endif
2545
2546#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2547 template<typename _Tp>
2548 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2549 double>::__type
2550 log2(_Tp __x)
2551 { return __builtin_log2(__x); }
2552#endif
2553
2554#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2555 constexpr float
2556 logb(float __x)
2557 { return __builtin_logbf(__x); }
2558
2559 constexpr long double
2560 logb(long double __x)
2561 { return __builtin_logbl(__x); }
2562#endif
2563
2564#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2565 template<typename _Tp>
2566 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2567 double>::__type
2568 logb(_Tp __x)
2569 { return __builtin_logb(__x); }
2570#endif
2571
2572#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2573 constexpr long
2574 lrint(float __x)
2575 { return __builtin_lrintf(__x); }
2576
2577 constexpr long
2578 lrint(long double __x)
2579 { return __builtin_lrintl(__x); }
2580#endif
2581
2582#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2583 template<typename _Tp>
2584 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2585 long>::__type
2586 lrint(_Tp __x)
2587 { return __builtin_lrint(__x); }
2588#endif
2589
2590#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2591 constexpr long
2592 lround(float __x)
2593 { return __builtin_lroundf(__x); }
2594
2595 constexpr long
2596 lround(long double __x)
2597 { return __builtin_lroundl(__x); }
2598#endif
2599
2600#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2601 template<typename _Tp>
2602 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2603 long>::__type
2604 lround(_Tp __x)
2605 { return __builtin_lround(__x); }
2606#endif
2607
2608#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2609 constexpr float
2610 nearbyint(float __x)
2611 { return __builtin_nearbyintf(__x); }
2612
2613 constexpr long double
2614 nearbyint(long double __x)
2615 { return __builtin_nearbyintl(__x); }
2616#endif
2617
2618#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2619 template<typename _Tp>
2620 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2621 double>::__type
2622 nearbyint(_Tp __x)
2623 { return __builtin_nearbyint(__x); }
2624#endif
2625
2626#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2627 constexpr float
2628 nextafter(float __x, float __y)
2629 { return __builtin_nextafterf(__x, __y); }
2630
2631 constexpr long double
2632 nextafter(long double __x, long double __y)
2633 { return __builtin_nextafterl(__x, __y); }
2634#endif
2635
2636#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2637 constexpr float
2638 nexttoward(float __x, long double __y)
2639 { return __builtin_nexttowardf(__x, __y); }
2640
2641 constexpr long double
2642 nexttoward(long double __x, long double __y)
2643 { return __builtin_nexttowardl(__x, __y); }
2644#endif
2645
2646#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2647 template<typename _Tp>
2648 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2649 double>::__type
2650 nexttoward(_Tp __x, long double __y)
2651 { return __builtin_nexttoward(__x, __y); }
2652#endif
2653
2654#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2655 constexpr float
2656 remainder(float __x, float __y)
2657 { return __builtin_remainderf(__x, __y); }
2658
2659 constexpr long double
2660 remainder(long double __x, long double __y)
2661 { return __builtin_remainderl(__x, __y); }
2662#endif
2663
2664#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2665 inline float
2666 remquo(float __x, float __y, int* __pquo)
2667 { return __builtin_remquof(__x, __y, __pquo); }
2668
2669 inline long double
2670 remquo(long double __x, long double __y, int* __pquo)
2671 { return __builtin_remquol(__x, __y, __pquo); }
2672#endif
2673
2674#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2675 constexpr float
2676 rint(float __x)
2677 { return __builtin_rintf(__x); }
2678
2679 constexpr long double
2680 rint(long double __x)
2681 { return __builtin_rintl(__x); }
2682#endif
2683
2684#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2685 template<typename _Tp>
2686 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2687 double>::__type
2688 rint(_Tp __x)
2689 { return __builtin_rint(__x); }
2690#endif
2691
2692#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2693 constexpr float
2694 round(float __x)
2695 { return __builtin_roundf(__x); }
2696
2697 constexpr long double
2698 round(long double __x)
2699 { return __builtin_roundl(__x); }
2700#endif
2701
2702#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2703 template<typename _Tp>
2704 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2705 double>::__type
2706 round(_Tp __x)
2707 { return __builtin_round(__x); }
2708#endif
2709
2710#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2711 constexpr float
2712 scalbln(float __x, long __ex)
2713 { return __builtin_scalblnf(__x, __ex); }
2714
2715 constexpr long double
2716 scalbln(long double __x, long __ex)
2717 { return __builtin_scalblnl(__x, __ex); }
2718#endif
2719
2720#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2721 template<typename _Tp>
2722 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2723 double>::__type
2724 scalbln(_Tp __x, long __ex)
2725 { return __builtin_scalbln(__x, __ex); }
2726#endif
2727
2728#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2729 constexpr float
2730 scalbn(float __x, int __ex)
2731 { return __builtin_scalbnf(__x, __ex); }
2732
2733 constexpr long double
2734 scalbn(long double __x, int __ex)
2735 { return __builtin_scalbnl(__x, __ex); }
2736#endif
2737
2738#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2739 template<typename _Tp>
2740 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2741 double>::__type
2742 scalbn(_Tp __x, int __ex)
2743 { return __builtin_scalbn(__x, __ex); }
2744#endif
2745
2746#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2747 constexpr float
2748 tgamma(float __x)
2749 { return __builtin_tgammaf(__x); }
2750
2751 constexpr long double
2752 tgamma(long double __x)
2753 { return __builtin_tgammal(__x); }
2754#endif
2755
2756#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2757 template<typename _Tp>
2758 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2759 double>::__type
2760 tgamma(_Tp __x)
2761 { return __builtin_tgamma(__x); }
2762#endif
2763
2764#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
2765 constexpr float
2766 trunc(float __x)
2767 { return __builtin_truncf(__x); }
2768
2769 constexpr long double
2770 trunc(long double __x)
2771 { return __builtin_truncl(__x); }
2772#endif
2773
2774#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
2775 template<typename _Tp>
2776 constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
2777 double>::__type
2778 trunc(_Tp __x)
2779 { return __builtin_trunc(__x); }
2780#endif
2781
2782#if defined(__STDCPP_FLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
2783 constexpr _Float16
2784 acosh(_Float16 __x)
2785 { return _Float16(__builtin_acoshf(__x)); }
2786
2787 constexpr _Float16
2788 asinh(_Float16 __x)
2789 { return _Float16(__builtin_asinhf(__x)); }
2790
2791 constexpr _Float16
2792 atanh(_Float16 __x)
2793 { return _Float16(__builtin_atanhf(__x)); }
2794
2795 constexpr _Float16
2796 cbrt(_Float16 __x)
2797 { return _Float16(__builtin_cbrtf(__x)); }
2798
2799 constexpr _Float16
2800 copysign(_Float16 __x, _Float16 __y)
2801 { return __builtin_copysignf16(__x, __y); }
2802
2803 constexpr _Float16
2804 erf(_Float16 __x)
2805 { return _Float16(__builtin_erff(__x)); }
2806
2807 constexpr _Float16
2808 erfc(_Float16 __x)
2809 { return _Float16(__builtin_erfcf(__x)); }
2810
2811 constexpr _Float16
2812 exp2(_Float16 __x)
2813 { return _Float16(__builtin_exp2f(__x)); }
2814
2815 constexpr _Float16
2816 expm1(_Float16 __x)
2817 { return _Float16(__builtin_expm1f(__x)); }
2818
2819 constexpr _Float16
2820 fdim(_Float16 __x, _Float16 __y)
2821 { return _Float16(__builtin_fdimf(__x, __y)); }
2822
2823 constexpr _Float16
2824 fma(_Float16 __x, _Float16 __y, _Float16 __z)
2825 { return _Float16(__builtin_fmaf(__x, __y, __z)); }
2826
2827 constexpr _Float16
2828 fmax(_Float16 __x, _Float16 __y)
2829 { return _Float16(__builtin_fmaxf(__x, __y)); }
2830
2831 constexpr _Float16
2832 fmin(_Float16 __x, _Float16 __y)
2833 { return _Float16(__builtin_fminf(__x, __y)); }
2834
2835 constexpr _Float16
2836 hypot(_Float16 __x, _Float16 __y)
2837 { return _Float16(__builtin_hypotf(__x, __y)); }
2838
2839 constexpr int
2840 ilogb(_Float16 __x)
2841 { return __builtin_ilogbf(__x); }
2842
2843 constexpr _Float16
2844 lgamma(_Float16 __x)
2845 { return _Float16(__builtin_lgammaf(__x)); }
2846
2847 constexpr long long
2848 llrint(_Float16 __x)
2849 { return __builtin_llrintf(__x); }
2850
2851 constexpr long long
2852 llround(_Float16 __x)
2853 { return __builtin_llroundf(__x); }
2854
2855 constexpr _Float16
2856 log1p(_Float16 __x)
2857 { return _Float16(__builtin_log1pf(__x)); }
2858
2859 // DR 568.
2860 constexpr _Float16
2861 log2(_Float16 __x)
2862 { return _Float16(__builtin_log2f(__x)); }
2863
2864 constexpr _Float16
2865 logb(_Float16 __x)
2866 { return _Float16(__builtin_logbf(__x)); }
2867
2868 constexpr long
2869 lrint(_Float16 __x)
2870 { return __builtin_lrintf(__x); }
2871
2872 constexpr long
2873 lround(_Float16 __x)
2874 { return __builtin_lroundf(__x); }
2875
2876 constexpr _Float16
2877 nearbyint(_Float16 __x)
2878 { return _Float16(__builtin_nearbyintf(__x)); }
2879
2880 constexpr _Float16
2881 nextafter(_Float16 __x, _Float16 __y)
2882 {
2883#if __cpp_if_consteval >= 202106L
2884 // Can't use if (std::__is_constant_evaluated()) here, as it
2885 // doesn't guarantee optimizing the body away at -O0 and
2886 // nothing defines nextafterf16.
2887 if consteval { return __builtin_nextafterf16(__x, __y); }
2888#endif
2889#ifdef __INT16_TYPE__
2890 using __float16_int_type = __INT16_TYPE__;
2891#else
2892 using __float16_int_type = short int;
2893#endif
2894 __float16_int_type __hx, __hy, __ix, __iy;
2895 __builtin_memcpy(&__hx, &__x, sizeof(__x));
2896 __builtin_memcpy(&__hy, &__y, sizeof(__x));
2897 __ix = __hx & 0x7fff; // |x|
2898 __iy = __hy & 0x7fff; // |y|
2899 if (__ix > 0x7c00 || __iy > 0x7c00) // x or y is NaN
2900 return __x + __y;
2901 if (__x == __y)
2902 return __y; // x == y, return y
2903 if (__ix == 0) // x == 0
2904 {
2905 __hy = (__hy & 0x8000) | 1; // return +-__FLT16_DENORM_MIN__
2906 __builtin_memcpy(&__x, &__hy, sizeof(__x));
2907 __builtin_nextafterf(0.0f, 1.0f); // raise underflow
2908 return __x;
2909 }
2910 if (__hx >= 0) // x > 0
2911 {
2912 if (__hx > __hy) // x > y, x -= ulp
2913 --__hx;
2914 else // x < y, x += ulp
2915 ++__hx;
2916 }
2917 else // x < 0
2918 {
2919 if (__hy >= 0 || __hx > __hy) // x < y, x -= ulp
2920 --__hx;
2921 else // x > y, x += ulp
2922 ++__hx;
2923 }
2924 __hy = __hx & 0x7c00;
2925 if (__hy >= 0x7c00)
2926 __builtin_nextafterf(__FLT_MAX__, __builtin_inff()); // overflow
2927 else if (__hy < 0x0400)
2928 __builtin_nextafterf(__FLT_MIN__, 0.0f); // underflow
2929 __builtin_memcpy(&__x, &__hx, sizeof(__x));
2930 return __x;
2931 }
2932
2933 constexpr _Float16
2934 remainder(_Float16 __x, _Float16 __y)
2935 { return _Float16(__builtin_remainderf(__x, __y)); }
2936
2937 inline _Float16
2938 remquo(_Float16 __x, _Float16 __y, int* __pquo)
2939 { return _Float16(__builtin_remquof(__x, __y, __pquo)); }
2940
2941 constexpr _Float16
2942 rint(_Float16 __x)
2943 { return _Float16(__builtin_rintf(__x)); }
2944
2945 constexpr _Float16
2946 round(_Float16 __x)
2947 { return _Float16(__builtin_roundf(__x)); }
2948
2949 constexpr _Float16
2950 scalbln(_Float16 __x, long __ex)
2951 { return _Float16(__builtin_scalblnf(__x, __ex)); }
2952
2953 constexpr _Float16
2954 scalbn(_Float16 __x, int __ex)
2955 { return _Float16(__builtin_scalbnf(__x, __ex)); }
2956
2957 constexpr _Float16
2958 tgamma(_Float16 __x)
2959 { return _Float16(__builtin_tgammaf(__x)); }
2960
2961 constexpr _Float16
2962 trunc(_Float16 __x)
2963 { return _Float16(__builtin_truncf(__x)); }
2964#endif
2965
2966#if defined(__STDCPP_FLOAT32_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
2967 constexpr _Float32
2968 acosh(_Float32 __x)
2969 { return __builtin_acoshf(__x); }
2970
2971 constexpr _Float32
2972 asinh(_Float32 __x)
2973 { return __builtin_asinhf(__x); }
2974
2975 constexpr _Float32
2976 atanh(_Float32 __x)
2977 { return __builtin_atanhf(__x); }
2978
2979 constexpr _Float32
2980 cbrt(_Float32 __x)
2981 { return __builtin_cbrtf(__x); }
2982
2983 constexpr _Float32
2984 copysign(_Float32 __x, _Float32 __y)
2985 { return __builtin_copysignf(__x, __y); }
2986
2987 constexpr _Float32
2988 erf(_Float32 __x)
2989 { return __builtin_erff(__x); }
2990
2991 constexpr _Float32
2992 erfc(_Float32 __x)
2993 { return __builtin_erfcf(__x); }
2994
2995 constexpr _Float32
2996 exp2(_Float32 __x)
2997 { return __builtin_exp2f(__x); }
2998
2999 constexpr _Float32
3000 expm1(_Float32 __x)
3001 { return __builtin_expm1f(__x); }
3002
3003 constexpr _Float32
3004 fdim(_Float32 __x, _Float32 __y)
3005 { return __builtin_fdimf(__x, __y); }
3006
3007 constexpr _Float32
3008 fma(_Float32 __x, _Float32 __y, _Float32 __z)
3009 { return __builtin_fmaf(__x, __y, __z); }
3010
3011 constexpr _Float32
3012 fmax(_Float32 __x, _Float32 __y)
3013 { return __builtin_fmaxf(__x, __y); }
3014
3015 constexpr _Float32
3016 fmin(_Float32 __x, _Float32 __y)
3017 { return __builtin_fminf(__x, __y); }
3018
3019 constexpr _Float32
3020 hypot(_Float32 __x, _Float32 __y)
3021 { return __builtin_hypotf(__x, __y); }
3022
3023 constexpr int
3024 ilogb(_Float32 __x)
3025 { return __builtin_ilogbf(__x); }
3026
3027 constexpr _Float32
3028 lgamma(_Float32 __x)
3029 { return __builtin_lgammaf(__x); }
3030
3031 constexpr long long
3032 llrint(_Float32 __x)
3033 { return __builtin_llrintf(__x); }
3034
3035 constexpr long long
3036 llround(_Float32 __x)
3037 { return __builtin_llroundf(__x); }
3038
3039 constexpr _Float32
3040 log1p(_Float32 __x)
3041 { return __builtin_log1pf(__x); }
3042
3043 // DR 568.
3044 constexpr _Float32
3045 log2(_Float32 __x)
3046 { return __builtin_log2f(__x); }
3047
3048 constexpr _Float32
3049 logb(_Float32 __x)
3050 { return __builtin_logbf(__x); }
3051
3052 constexpr long
3053 lrint(_Float32 __x)
3054 { return __builtin_lrintf(__x); }
3055
3056 constexpr long
3057 lround(_Float32 __x)
3058 { return __builtin_lroundf(__x); }
3059
3060 constexpr _Float32
3061 nearbyint(_Float32 __x)
3062 { return __builtin_nearbyintf(__x); }
3063
3064 constexpr _Float32
3065 nextafter(_Float32 __x, _Float32 __y)
3066 { return __builtin_nextafterf(__x, __y); }
3067
3068 constexpr _Float32
3069 remainder(_Float32 __x, _Float32 __y)
3070 { return __builtin_remainderf(__x, __y); }
3071
3072 inline _Float32
3073 remquo(_Float32 __x, _Float32 __y, int* __pquo)
3074 { return __builtin_remquof(__x, __y, __pquo); }
3075
3076 constexpr _Float32
3077 rint(_Float32 __x)
3078 { return __builtin_rintf(__x); }
3079
3080 constexpr _Float32
3081 round(_Float32 __x)
3082 { return __builtin_roundf(__x); }
3083
3084 constexpr _Float32
3085 scalbln(_Float32 __x, long __ex)
3086 { return __builtin_scalblnf(__x, __ex); }
3087
3088 constexpr _Float32
3089 scalbn(_Float32 __x, int __ex)
3090 { return __builtin_scalbnf(__x, __ex); }
3091
3092 constexpr _Float32
3093 tgamma(_Float32 __x)
3094 { return __builtin_tgammaf(__x); }
3095
3096 constexpr _Float32
3097 trunc(_Float32 __x)
3098 { return __builtin_truncf(__x); }
3099#endif
3100
3101#if defined(__STDCPP_FLOAT64_T__) && defined(_GLIBCXX_DOUBLE_IS_IEEE_BINARY64)
3102 constexpr _Float64
3103 acosh(_Float64 __x)
3104 { return __builtin_acosh(__x); }
3105
3106 constexpr _Float64
3107 asinh(_Float64 __x)
3108 { return __builtin_asinh(__x); }
3109
3110 constexpr _Float64
3111 atanh(_Float64 __x)
3112 { return __builtin_atanh(__x); }
3113
3114 constexpr _Float64
3115 cbrt(_Float64 __x)
3116 { return __builtin_cbrt(__x); }
3117
3118 constexpr _Float64
3119 copysign(_Float64 __x, _Float64 __y)
3120 { return __builtin_copysign(__x, __y); }
3121
3122 constexpr _Float64
3123 erf(_Float64 __x)
3124 { return __builtin_erf(__x); }
3125
3126 constexpr _Float64
3127 erfc(_Float64 __x)
3128 { return __builtin_erfc(__x); }
3129
3130 constexpr _Float64
3131 exp2(_Float64 __x)
3132 { return __builtin_exp2(__x); }
3133
3134 constexpr _Float64
3135 expm1(_Float64 __x)
3136 { return __builtin_expm1(__x); }
3137
3138 constexpr _Float64
3139 fdim(_Float64 __x, _Float64 __y)
3140 { return __builtin_fdim(__x, __y); }
3141
3142 constexpr _Float64
3143 fma(_Float64 __x, _Float64 __y, _Float64 __z)
3144 { return __builtin_fma(__x, __y, __z); }
3145
3146 constexpr _Float64
3147 fmax(_Float64 __x, _Float64 __y)
3148 { return __builtin_fmax(__x, __y); }
3149
3150 constexpr _Float64
3151 fmin(_Float64 __x, _Float64 __y)
3152 { return __builtin_fmin(__x, __y); }
3153
3154 constexpr _Float64
3155 hypot(_Float64 __x, _Float64 __y)
3156 { return __builtin_hypot(__x, __y); }
3157
3158 constexpr int
3159 ilogb(_Float64 __x)
3160 { return __builtin_ilogb(__x); }
3161
3162 constexpr _Float64
3163 lgamma(_Float64 __x)
3164 { return __builtin_lgamma(__x); }
3165
3166 constexpr long long
3167 llrint(_Float64 __x)
3168 { return __builtin_llrint(__x); }
3169
3170 constexpr long long
3171 llround(_Float64 __x)
3172 { return __builtin_llround(__x); }
3173
3174 constexpr _Float64
3175 log1p(_Float64 __x)
3176 { return __builtin_log1p(__x); }
3177
3178 // DR 568.
3179 constexpr _Float64
3180 log2(_Float64 __x)
3181 { return __builtin_log2(__x); }
3182
3183 constexpr _Float64
3184 logb(_Float64 __x)
3185 { return __builtin_logb(__x); }
3186
3187 constexpr long
3188 lrint(_Float64 __x)
3189 { return __builtin_lrint(__x); }
3190
3191 constexpr long
3192 lround(_Float64 __x)
3193 { return __builtin_lround(__x); }
3194
3195 constexpr _Float64
3196 nearbyint(_Float64 __x)
3197 { return __builtin_nearbyint(__x); }
3198
3199 constexpr _Float64
3200 nextafter(_Float64 __x, _Float64 __y)
3201 { return __builtin_nextafter(__x, __y); }
3202
3203 constexpr _Float64
3204 remainder(_Float64 __x, _Float64 __y)
3205 { return __builtin_remainder(__x, __y); }
3206
3207 inline _Float64
3208 remquo(_Float64 __x, _Float64 __y, int* __pquo)
3209 { return __builtin_remquo(__x, __y, __pquo); }
3210
3211 constexpr _Float64
3212 rint(_Float64 __x)
3213 { return __builtin_rint(__x); }
3214
3215 constexpr _Float64
3216 round(_Float64 __x)
3217 { return __builtin_round(__x); }
3218
3219 constexpr _Float64
3220 scalbln(_Float64 __x, long __ex)
3221 { return __builtin_scalbln(__x, __ex); }
3222
3223 constexpr _Float64
3224 scalbn(_Float64 __x, int __ex)
3225 { return __builtin_scalbn(__x, __ex); }
3226
3227 constexpr _Float64
3228 tgamma(_Float64 __x)
3229 { return __builtin_tgamma(__x); }
3230
3231 constexpr _Float64
3232 trunc(_Float64 __x)
3233 { return __builtin_trunc(__x); }
3234#endif
3235
3236#if defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_LDOUBLE_IS_IEEE_BINARY128)
3237 constexpr _Float128
3238 acosh(_Float128 __x)
3239 { return __builtin_acoshl(__x); }
3240
3241 constexpr _Float128
3242 asinh(_Float128 __x)
3243 { return __builtin_asinhl(__x); }
3244
3245 constexpr _Float128
3246 atanh(_Float128 __x)
3247 { return __builtin_atanhl(__x); }
3248
3249 constexpr _Float128
3250 cbrt(_Float128 __x)
3251 { return __builtin_cbrtl(__x); }
3252
3253 constexpr _Float128
3254 copysign(_Float128 __x, _Float128 __y)
3255 { return __builtin_copysignl(__x, __y); }
3256
3257 constexpr _Float128
3258 erf(_Float128 __x)
3259 { return __builtin_erfl(__x); }
3260
3261 constexpr _Float128
3262 erfc(_Float128 __x)
3263 { return __builtin_erfcl(__x); }
3264
3265 constexpr _Float128
3266 exp2(_Float128 __x)
3267 { return __builtin_exp2l(__x); }
3268
3269 constexpr _Float128
3270 expm1(_Float128 __x)
3271 { return __builtin_expm1l(__x); }
3272
3273 constexpr _Float128
3274 fdim(_Float128 __x, _Float128 __y)
3275 { return __builtin_fdiml(__x, __y); }
3276
3277 constexpr _Float128
3278 fma(_Float128 __x, _Float128 __y, _Float128 __z)
3279 { return __builtin_fmal(__x, __y, __z); }
3280
3281 constexpr _Float128
3282 fmax(_Float128 __x, _Float128 __y)
3283 { return __builtin_fmaxl(__x, __y); }
3284
3285 constexpr _Float128
3286 fmin(_Float128 __x, _Float128 __y)
3287 { return __builtin_fminl(__x, __y); }
3288
3289 constexpr _Float128
3290 hypot(_Float128 __x, _Float128 __y)
3291 { return __builtin_hypotl(__x, __y); }
3292
3293 constexpr int
3294 ilogb(_Float128 __x)
3295 { return __builtin_ilogbl(__x); }
3296
3297 constexpr _Float128
3298 lgamma(_Float128 __x)
3299 { return __builtin_lgammal(__x); }
3300
3301 constexpr long long
3302 llrint(_Float128 __x)
3303 { return __builtin_llrintl(__x); }
3304
3305 constexpr long long
3306 llround(_Float128 __x)
3307 { return __builtin_llroundl(__x); }
3308
3309 constexpr _Float128
3310 log1p(_Float128 __x)
3311 { return __builtin_log1pl(__x); }
3312
3313 // DR 568.
3314 constexpr _Float128
3315 log2(_Float128 __x)
3316 { return __builtin_log2l(__x); }
3317
3318 constexpr _Float128
3319 logb(_Float128 __x)
3320 { return __builtin_logbl(__x); }
3321
3322 constexpr long
3323 lrint(_Float128 __x)
3324 { return __builtin_lrintl(__x); }
3325
3326 constexpr long
3327 lround(_Float128 __x)
3328 { return __builtin_lroundl(__x); }
3329
3330 constexpr _Float128
3331 nearbyint(_Float128 __x)
3332 { return __builtin_nearbyintl(__x); }
3333
3334 constexpr _Float128
3335 nextafter(_Float128 __x, _Float128 __y)
3336 { return __builtin_nextafterl(__x, __y); }
3337
3338 constexpr _Float128
3339 remainder(_Float128 __x, _Float128 __y)
3340 { return __builtin_remainderl(__x, __y); }
3341
3342 inline _Float128
3343 remquo(_Float128 __x, _Float128 __y, int* __pquo)
3344 { return __builtin_remquol(__x, __y, __pquo); }
3345
3346 constexpr _Float128
3347 rint(_Float128 __x)
3348 { return __builtin_rintl(__x); }
3349
3350 constexpr _Float128
3351 round(_Float128 __x)
3352 { return __builtin_roundl(__x); }
3353
3354 constexpr _Float128
3355 scalbln(_Float128 __x, long __ex)
3356 { return __builtin_scalblnl(__x, __ex); }
3357
3358 constexpr _Float128
3359 scalbn(_Float128 __x, int __ex)
3360 { return __builtin_scalbnl(__x, __ex); }
3361
3362 constexpr _Float128
3363 tgamma(_Float128 __x)
3364 { return __builtin_tgammal(__x); }
3365
3366 constexpr _Float128
3367 trunc(_Float128 __x)
3368 { return __builtin_truncl(__x); }
3369#elif defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_HAVE_FLOAT128_MATH)
3370 constexpr _Float128
3371 acosh(_Float128 __x)
3372 { return __builtin_acoshf128(__x); }
3373
3374 constexpr _Float128
3375 asinh(_Float128 __x)
3376 { return __builtin_asinhf128(__x); }
3377
3378 constexpr _Float128
3379 atanh(_Float128 __x)
3380 { return __builtin_atanhf128(__x); }
3381
3382 constexpr _Float128
3383 cbrt(_Float128 __x)
3384 { return __builtin_cbrtf128(__x); }
3385
3386 constexpr _Float128
3387 copysign(_Float128 __x, _Float128 __y)
3388 { return __builtin_copysignf128(__x, __y); }
3389
3390 constexpr _Float128
3391 erf(_Float128 __x)
3392 { return __builtin_erff128(__x); }
3393
3394 constexpr _Float128
3395 erfc(_Float128 __x)
3396 { return __builtin_erfcf128(__x); }
3397
3398 constexpr _Float128
3399 exp2(_Float128 __x)
3400 { return __builtin_exp2f128(__x); }
3401
3402 constexpr _Float128
3403 expm1(_Float128 __x)
3404 { return __builtin_expm1f128(__x); }
3405
3406 constexpr _Float128
3407 fdim(_Float128 __x, _Float128 __y)
3408 { return __builtin_fdimf128(__x, __y); }
3409
3410 constexpr _Float128
3411 fma(_Float128 __x, _Float128 __y, _Float128 __z)
3412 { return __builtin_fmaf128(__x, __y, __z); }
3413
3414 constexpr _Float128
3415 fmax(_Float128 __x, _Float128 __y)
3416 { return __builtin_fmaxf128(__x, __y); }
3417
3418 constexpr _Float128
3419 fmin(_Float128 __x, _Float128 __y)
3420 { return __builtin_fminf128(__x, __y); }
3421
3422 constexpr _Float128
3423 hypot(_Float128 __x, _Float128 __y)
3424 { return __builtin_hypotf128(__x, __y); }
3425
3426 constexpr int
3427 ilogb(_Float128 __x)
3428 { return __builtin_ilogbf128(__x); }
3429
3430 constexpr _Float128
3431 lgamma(_Float128 __x)
3432 { return __builtin_lgammaf128(__x); }
3433
3434 constexpr long long
3435 llrint(_Float128 __x)
3436 { return __builtin_llrintf128(__x); }
3437
3438 constexpr long long
3439 llround(_Float128 __x)
3440 { return __builtin_llroundf128(__x); }
3441
3442 constexpr _Float128
3443 log1p(_Float128 __x)
3444 { return __builtin_log1pf128(__x); }
3445
3446 // DR 568.
3447 constexpr _Float128
3448 log2(_Float128 __x)
3449 { return __builtin_log2f128(__x); }
3450
3451 constexpr _Float128
3452 logb(_Float128 __x)
3453 { return __builtin_logbf128(__x); }
3454
3455 constexpr long
3456 lrint(_Float128 __x)
3457 { return __builtin_lrintf128(__x); }
3458
3459 constexpr long
3460 lround(_Float128 __x)
3461 { return __builtin_lroundf128(__x); }
3462
3463 constexpr _Float128
3464 nearbyint(_Float128 __x)
3465 { return __builtin_nearbyintf128(__x); }
3466
3467 constexpr _Float128
3468 nextafter(_Float128 __x, _Float128 __y)
3469 { return __builtin_nextafterf128(__x, __y); }
3470
3471 constexpr _Float128
3472 remainder(_Float128 __x, _Float128 __y)
3473 { return __builtin_remainderf128(__x, __y); }
3474
3475 inline _Float128
3476 remquo(_Float128 __x, _Float128 __y, int* __pquo)
3477 { return __builtin_remquof128(__x, __y, __pquo); }
3478
3479 constexpr _Float128
3480 rint(_Float128 __x)
3481 { return __builtin_rintf128(__x); }
3482
3483 constexpr _Float128
3484 round(_Float128 __x)
3485 { return __builtin_roundf128(__x); }
3486
3487 constexpr _Float128
3488 scalbln(_Float128 __x, long __ex)
3489 { return __builtin_scalblnf128(__x, __ex); }
3490
3491 constexpr _Float128
3492 scalbn(_Float128 __x, int __ex)
3493 { return __builtin_scalbnf128(__x, __ex); }
3494
3495 constexpr _Float128
3496 tgamma(_Float128 __x)
3497 { return __builtin_tgammaf128(__x); }
3498
3499 constexpr _Float128
3500 trunc(_Float128 __x)
3501 { return __builtin_truncf128(__x); }
3502#endif
3503
3504#if defined(__STDCPP_BFLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
3505 constexpr __gnu_cxx::__bfloat16_t
3506 acosh(__gnu_cxx::__bfloat16_t __x)
3507 { return __gnu_cxx::__bfloat16_t(__builtin_acoshf(__x)); }
3508
3509 constexpr __gnu_cxx::__bfloat16_t
3510 asinh(__gnu_cxx::__bfloat16_t __x)
3511 { return __gnu_cxx::__bfloat16_t(__builtin_asinhf(__x)); }
3512
3513 constexpr __gnu_cxx::__bfloat16_t
3514 atanh(__gnu_cxx::__bfloat16_t __x)
3515 { return __gnu_cxx::__bfloat16_t(__builtin_atanhf(__x)); }
3516
3517 constexpr __gnu_cxx::__bfloat16_t
3518 cbrt(__gnu_cxx::__bfloat16_t __x)
3519 { return __gnu_cxx::__bfloat16_t(__builtin_cbrtf(__x)); }
3520
3521 constexpr __gnu_cxx::__bfloat16_t
3522 copysign(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
3523 { return __gnu_cxx::__bfloat16_t(__builtin_copysignf(__x, __y)); }
3524
3525 constexpr __gnu_cxx::__bfloat16_t
3526 erf(__gnu_cxx::__bfloat16_t __x)
3527 { return __gnu_cxx::__bfloat16_t(__builtin_erff(__x)); }
3528
3529 constexpr __gnu_cxx::__bfloat16_t
3530 erfc(__gnu_cxx::__bfloat16_t __x)
3531 { return __gnu_cxx::__bfloat16_t(__builtin_erfcf(__x)); }
3532
3533 constexpr __gnu_cxx::__bfloat16_t
3534 exp2(__gnu_cxx::__bfloat16_t __x)
3535 { return __gnu_cxx::__bfloat16_t(__builtin_exp2f(__x)); }
3536
3537 constexpr __gnu_cxx::__bfloat16_t
3538 expm1(__gnu_cxx::__bfloat16_t __x)
3539 { return __gnu_cxx::__bfloat16_t(__builtin_expm1f(__x)); }
3540
3541 constexpr __gnu_cxx::__bfloat16_t
3542 fdim(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
3543 { return __gnu_cxx::__bfloat16_t(__builtin_fdimf(__x, __y)); }
3544
3545 constexpr __gnu_cxx::__bfloat16_t
3546 fma(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y, __gnu_cxx::__bfloat16_t __z)
3547 { return __gnu_cxx::__bfloat16_t(__builtin_fmaf(__x, __y, __z)); }
3548
3549 constexpr __gnu_cxx::__bfloat16_t
3550 fmax(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
3551 { return __gnu_cxx::__bfloat16_t(__builtin_fmaxf(__x, __y)); }
3552
3553 constexpr __gnu_cxx::__bfloat16_t
3554 fmin(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
3555 { return __gnu_cxx::__bfloat16_t(__builtin_fminf(__x, __y)); }
3556
3557 constexpr __gnu_cxx::__bfloat16_t
3558 hypot(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
3559 { return __gnu_cxx::__bfloat16_t(__builtin_hypotf(__x, __y)); }
3560
3561 constexpr int
3562 ilogb(__gnu_cxx::__bfloat16_t __x)
3563 { return __builtin_ilogbf(__x); }
3564
3565 constexpr __gnu_cxx::__bfloat16_t
3566 lgamma(__gnu_cxx::__bfloat16_t __x)
3567 { return __gnu_cxx::__bfloat16_t(__builtin_lgammaf(__x)); }
3568
3569 constexpr long long
3570 llrint(__gnu_cxx::__bfloat16_t __x)
3571 { return __builtin_llrintf(__x); }
3572
3573 constexpr long long
3574 llround(__gnu_cxx::__bfloat16_t __x)
3575 { return __builtin_llroundf(__x); }
3576
3577 constexpr __gnu_cxx::__bfloat16_t
3578 log1p(__gnu_cxx::__bfloat16_t __x)
3579 { return __gnu_cxx::__bfloat16_t(__builtin_log1pf(__x)); }
3580
3581 // DR 568.
3582 constexpr __gnu_cxx::__bfloat16_t
3583 log2(__gnu_cxx::__bfloat16_t __x)
3584 { return __gnu_cxx::__bfloat16_t(__builtin_log2f(__x)); }
3585
3586 constexpr __gnu_cxx::__bfloat16_t
3587 logb(__gnu_cxx::__bfloat16_t __x)
3588 { return __gnu_cxx::__bfloat16_t(__builtin_logbf(__x)); }
3589
3590 constexpr long
3591 lrint(__gnu_cxx::__bfloat16_t __x)
3592 { return __builtin_lrintf(__x); }
3593
3594 constexpr long
3595 lround(__gnu_cxx::__bfloat16_t __x)
3596 { return __builtin_lroundf(__x); }
3597
3598 constexpr __gnu_cxx::__bfloat16_t
3599 nearbyint(__gnu_cxx::__bfloat16_t __x)
3600 { return __gnu_cxx::__bfloat16_t(__builtin_nearbyintf(__x)); }
3601
3602 constexpr __gnu_cxx::__bfloat16_t
3603 nextafter(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
3604 {
3605#if __cpp_if_consteval >= 202106L
3606 // Can't use if (std::__is_constant_evaluated()) here, as it
3607 // doesn't guarantee optimizing the body away at -O0 and
3608 // nothing defines nextafterf16b.
3609 if consteval { return __builtin_nextafterf16b(__x, __y); }
3610#endif
3611#ifdef __INT16_TYPE__
3612 using __bfloat16_int_type = __INT16_TYPE__;
3613#else
3614 using __bfloat16_int_type = short int;
3615#endif
3616 __bfloat16_int_type __hx, __hy, __ix, __iy;
3617 __builtin_memcpy(&__hx, &__x, sizeof(__x));
3618 __builtin_memcpy(&__hy, &__y, sizeof(__x));
3619 __ix = __hx & 0x7fff; // |x|
3620 __iy = __hy & 0x7fff; // |y|
3621 if (__ix > 0x7f80 || __iy > 0x7f80) // x or y is NaN
3622 return __x + __y;
3623 if (__x == __y)
3624 return __y; // x == y, return y
3625 if (__ix == 0) // x == 0
3626 {
3627 __hy = (__hy & 0x8000) | 1; // return +-__BFLT16_DENORM_MIN__
3628 __builtin_memcpy(&__x, &__hy, sizeof(__x));
3629 __builtin_nextafterf(0.0f, 1.0f); // raise underflow
3630 return __x;
3631 }
3632 if (__hx >= 0) // x > 0
3633 {
3634 if (__hx > __hy) // x > y, x -= ulp
3635 --__hx;
3636 else // x < y, x += ulp
3637 ++__hx;
3638 }
3639 else // x < 0
3640 {
3641 if (__hy >= 0 || __hx > __hy) // x < y, x -= ulp
3642 --__hx;
3643 else // x > y, x += ulp
3644 ++__hx;
3645 }
3646 __hy = __hx & 0x7f80;
3647 if (__hy >= 0x7f80)
3648 __builtin_nextafterf(__FLT_MAX__, __builtin_inff()); // overflow
3649 else if (__hy < 0x0080)
3650 __builtin_nextafterf(__FLT_MIN__, 0.0f); // underflow
3651 __builtin_memcpy(&__x, &__hx, sizeof(__x));
3652 return __x;
3653 }
3654
3655 constexpr __gnu_cxx::__bfloat16_t
3656 remainder(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y)
3657 { return __gnu_cxx::__bfloat16_t(__builtin_remainderf(__x, __y)); }
3658
3659 inline __gnu_cxx::__bfloat16_t
3660 remquo(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y, int* __pquo)
3661 { return __gnu_cxx::__bfloat16_t(__builtin_remquof(__x, __y, __pquo)); }
3662
3663 constexpr __gnu_cxx::__bfloat16_t
3664 rint(__gnu_cxx::__bfloat16_t __x)
3665 { return __gnu_cxx::__bfloat16_t(__builtin_rintf(__x)); }
3666
3667 constexpr __gnu_cxx::__bfloat16_t
3668 round(__gnu_cxx::__bfloat16_t __x)
3669 { return __gnu_cxx::__bfloat16_t(__builtin_roundf(__x)); }
3670
3671 constexpr __gnu_cxx::__bfloat16_t
3672 scalbln(__gnu_cxx::__bfloat16_t __x, long __ex)
3673 { return __gnu_cxx::__bfloat16_t(__builtin_scalblnf(__x, __ex)); }
3674
3675 constexpr __gnu_cxx::__bfloat16_t
3676 scalbn(__gnu_cxx::__bfloat16_t __x, int __ex)
3677 { return __gnu_cxx::__bfloat16_t(__builtin_scalbnf(__x, __ex)); }
3678
3679 constexpr __gnu_cxx::__bfloat16_t
3680 tgamma(__gnu_cxx::__bfloat16_t __x)
3681 { return __gnu_cxx::__bfloat16_t(__builtin_tgammaf(__x)); }
3682
3683 constexpr __gnu_cxx::__bfloat16_t
3684 trunc(__gnu_cxx::__bfloat16_t __x)
3685 { return __gnu_cxx::__bfloat16_t(__builtin_truncf(__x)); }
3686#endif
3687
3688#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
3689 template<typename _Tp, typename _Up>
3690 constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
3691 copysign(_Tp __x, _Up __y)
3692 {
3693 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
3694 return copysign(__type(__x), __type(__y));
3695 }
3696
3697 template<typename _Tp, typename _Up>
3698 constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
3699 fdim(_Tp __x, _Up __y)
3700 {
3701 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
3702 return fdim(__type(__x), __type(__y));
3703 }
3704
3705 template<typename _Tp, typename _Up>
3706 constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
3707 fmax(_Tp __x, _Up __y)
3708 {
3709 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
3710 return fmax(__type(__x), __type(__y));
3711 }
3712
3713 template<typename _Tp, typename _Up>
3714 constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
3715 fmin(_Tp __x, _Up __y)
3716 {
3717 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
3718 return fmin(__type(__x), __type(__y));
3719 }
3720
3721 template<typename _Tp, typename _Up>
3722 constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
3723 hypot(_Tp __x, _Up __y)
3724 {
3725 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
3726 return hypot(__type(__x), __type(__y));
3727 }
3728
3729 template<typename _Tp, typename _Up>
3730 constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
3731 nextafter(_Tp __x, _Up __y)
3732 {
3733 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
3734 return nextafter(__type(__x), __type(__y));
3735 }
3736
3737 template<typename _Tp, typename _Up>
3738 constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
3739 remainder(_Tp __x, _Up __y)
3740 {
3741 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
3742 return remainder(__type(__x), __type(__y));
3743 }
3744
3745 template<typename _Tp, typename _Up>
3746 inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
3747 remquo(_Tp __x, _Up __y, int* __pquo)
3748 {
3749 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
3750 return remquo(__type(__x), __type(__y), __pquo);
3751 }
3752
3753 template<typename _Tp, typename _Up, typename _Vp>
3754 constexpr typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type
3755 fma(_Tp __x, _Up __y, _Vp __z)
3756 {
3757 typedef typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type __type;
3758 return fma(__type(__x), __type(__y), __type(__z));
3759 }
3760#endif
3761
3762#endif // _GLIBCXX_USE_C99_MATH_FUNCS
3763#endif // C++11
3764
3765#ifdef __cpp_lib_hypot // C++ >= 17 && HOSTED
3766 // [c.math.hypot3], three-dimensional hypotenuse
3767 template<typename _Tp>
3768 inline _Tp
3769 __hypot3(_Tp __x, _Tp __y, _Tp __z)
3770 {
3771 __x = std::abs(__x);
3772 __y = std::abs(__y);
3773 __z = std::abs(__z);
3774 if (_Tp __a = __x < __y ? __y < __z ? __z : __y : __x < __z ? __z : __x)
3775 return __a * std::sqrt((__x / __a) * (__x / __a)
3776 + (__y / __a) * (__y / __a)
3777 + (__z / __a) * (__z / __a));
3778 else
3779 return {};
3780 }
3781
3782 inline float
3783 hypot(float __x, float __y, float __z)
3784 { return std::__hypot3<float>(__x, __y, __z); }
3785
3786 inline double
3787 hypot(double __x, double __y, double __z)
3788 { return std::__hypot3<double>(__x, __y, __z); }
3789
3790 inline long double
3791 hypot(long double __x, long double __y, long double __z)
3792 { return std::__hypot3<long double>(__x, __y, __z); }
3793
3794 template<typename _Tp, typename _Up, typename _Vp>
3795 typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type
3796 hypot(_Tp __x, _Up __y, _Vp __z)
3797 {
3798 using __type = typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type;
3799 return std::__hypot3<__type>(__x, __y, __z);
3800 }
3801
3802#if defined(__STDCPP_FLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
3803 inline _Float16
3804 hypot(_Float16 __x, _Float16 __y, _Float16 __z)
3805 { return std::__hypot3<_Float16>(__x, __y, __z); }
3806#endif
3807
3808#if defined(__STDCPP_FLOAT32_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
3809 inline _Float32
3810 hypot(_Float32 __x, _Float32 __y, _Float32 __z)
3811 { return std::__hypot3<_Float32>(__x, __y, __z); }
3812#endif
3813
3814#if defined(__STDCPP_FLOAT64_T__) && defined(_GLIBCXX_DOUBLE_IS_IEEE_BINARY64)
3815 inline _Float64
3816 hypot(_Float64 __x, _Float64 __y, _Float64 __z)
3817 { return std::__hypot3<_Float64>(__x, __y, __z); }
3818#endif
3819
3820#if defined(__STDCPP_FLOAT128_T__) \
3821 && (defined(_GLIBCXX_LDOUBLE_IS_IEEE_BINARY128) \
3822 || defined(_GLIBCXX_HAVE_FLOAT128_MATH))
3823 inline _Float128
3824 hypot(_Float128 __x, _Float128 __y, _Float128 __z)
3825 { return std::__hypot3<_Float128>(__x, __y, __z); }
3826#endif
3827
3828#if defined(__STDCPP_BFLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
3829 inline __gnu_cxx::__bfloat16_t
3830 hypot(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y, __gnu_cxx::__bfloat16_t __z)
3831 { return std::__hypot3<__gnu_cxx::__bfloat16_t>(__x, __y, __z); }
3832#endif
3833
3834#endif // __cpp_lib_hypot
3835
3836#ifdef __cpp_lib_interpolate // C++ >= 20
3837 // linear interpolation
3838 template<typename _Fp>
3839 constexpr _Fp
3840 __lerp(_Fp __a, _Fp __b, _Fp __t) noexcept
3841 {
3842 if ((__a <= 0 && __b >= 0) || (__a >= 0 && __b <= 0))
3843 return __t * __b + (1 - __t) * __a;
3844
3845 if (__t == 1)
3846 return __b; // exact
3847
3848 // Exact at __t=0, monotonic except near __t=1,
3849 // bounded, determinate, and consistent:
3850 const _Fp __x = __a + __t * (__b - __a);
3851 return (__t > 1) == (__b > __a)
3852 ? (__b < __x ? __x : __b)
3853 : (__b > __x ? __x : __b); // monotonic near __t=1
3854 }
3855
3856 constexpr float
3857 lerp(float __a, float __b, float __t) noexcept
3858 { return std::__lerp(__a, __b, __t); }
3859
3860 constexpr double
3861 lerp(double __a, double __b, double __t) noexcept
3862 { return std::__lerp(__a, __b, __t); }
3863
3864 constexpr long double
3865 lerp(long double __a, long double __b, long double __t) noexcept
3866 { return std::__lerp(__a, __b, __t); }
3867
3868 template<typename _Tp, typename _Up, typename _Vp>
3869 constexpr __gnu_cxx::__promoted_t<_Tp, _Up, _Vp>
3870 lerp(_Tp __x, _Up __y, _Vp __z) noexcept
3871 {
3872 using __type = __gnu_cxx::__promoted_t<_Tp, _Up, _Vp>;
3873 return std::__lerp<__type>(__x, __y, __z);
3874 }
3875
3876#if defined(__STDCPP_FLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
3877 inline _Float16
3878 lerp(_Float16 __x, _Float16 __y, _Float16 __z) noexcept
3879 { return std::__lerp<_Float16>(__x, __y, __z); }
3880#endif
3881
3882#if defined(__STDCPP_FLOAT32_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
3883 inline _Float32
3884 lerp(_Float32 __x, _Float32 __y, _Float32 __z) noexcept
3885 { return std::__lerp<_Float32>(__x, __y, __z); }
3886#endif
3887
3888#if defined(__STDCPP_FLOAT64_T__) && defined(_GLIBCXX_DOUBLE_IS_IEEE_BINARY64)
3889 inline _Float64
3890 lerp(_Float64 __x, _Float64 __y, _Float64 __z) noexcept
3891 { return std::__lerp<_Float64>(__x, __y, __z); }
3892#endif
3893
3894#if defined(__STDCPP_FLOAT128_T__) \
3895 && (defined(_GLIBCXX_LDOUBLE_IS_IEEE_BINARY128) \
3896 || defined(_GLIBCXX_HAVE_FLOAT128_MATH))
3897 inline _Float128
3898 lerp(_Float128 __x, _Float128 __y, _Float128 __z) noexcept
3899 { return std::__lerp<_Float128>(__x, __y, __z); }
3900#endif
3901
3902#if defined(__STDCPP_BFLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
3903 inline __gnu_cxx::__bfloat16_t
3904 lerp(__gnu_cxx::__bfloat16_t __x, __gnu_cxx::__bfloat16_t __y, __gnu_cxx::__bfloat16_t __z) noexcept
3905 { return std::__lerp<__gnu_cxx::__bfloat16_t>(__x, __y, __z); }
3906#endif
3907#endif // __cpp_lib_interpolate
3908
3909_GLIBCXX_END_NAMESPACE_VERSION
3910} // namespace
3911
3912#if _GLIBCXX_USE_STD_SPEC_FUNCS
3913# include <bits/specfun.h>
3914#endif
3915
3916} // extern "C++"
3917
3918#endif
3919