1// -*- C++ -*- C forwarding header.
2
3// Copyright (C) 1997-2020 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#pragma GCC system_header
40
41#include <bits/c++config.h>
42#include <bits/cpp_type_traits.h>
43#include <ext/type_traits.h>
44#define _GLIBCXX_INCLUDE_NEXT_C_HEADERS
45#include_next <math.h>
46#undef _GLIBCXX_INCLUDE_NEXT_C_HEADERS
47#include <bits/std_abs.h>
48
49#ifndef _GLIBCXX_CMATH
50#define _GLIBCXX_CMATH 1
51
52// Get rid of those macros defined in <math.h> in lieu of real functions.
53#undef div
54#undef acos
55#undef asin
56#undef atan
57#undef atan2
58#undef ceil
59#undef cos
60#undef cosh
61#undef exp
62#undef fabs
63#undef floor
64#undef fmod
65#undef frexp
66#undef ldexp
67#undef log
68#undef log10
69#undef modf
70#undef pow
71#undef sin
72#undef sinh
73#undef sqrt
74#undef tan
75#undef tanh
76
77extern "C++"
78{
79namespace std _GLIBCXX_VISIBILITY(default)
80{
81_GLIBCXX_BEGIN_NAMESPACE_VERSION
82
83  using ::acos;
84
85#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
86  inline _GLIBCXX_CONSTEXPR float
87  acos(float __x)
88  { return __builtin_acosf(__x); }
89
90  inline _GLIBCXX_CONSTEXPR long double
91  acos(long double __x)
92  { return __builtin_acosl(__x); }
93#endif
94
95  template<typename _Tp>
96    inline _GLIBCXX_CONSTEXPR
97    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
98                                    double>::__type
99    acos(_Tp __x)
100    { return __builtin_acos(__x); }
101
102  using ::asin;
103
104#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
105  inline _GLIBCXX_CONSTEXPR float
106  asin(float __x)
107  { return __builtin_asinf(__x); }
108
109  inline _GLIBCXX_CONSTEXPR long double
110  asin(long double __x)
111  { return __builtin_asinl(__x); }
112#endif
113
114  template<typename _Tp>
115    inline _GLIBCXX_CONSTEXPR
116    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
117                                    double>::__type
118    asin(_Tp __x)
119    { return __builtin_asin(__x); }
120
121  using ::atan;
122
123#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
124  inline _GLIBCXX_CONSTEXPR float
125  atan(float __x)
126  { return __builtin_atanf(__x); }
127
128  inline _GLIBCXX_CONSTEXPR long double
129  atan(long double __x)
130  { return __builtin_atanl(__x); }
131#endif
132
133  template<typename _Tp>
134    inline _GLIBCXX_CONSTEXPR
135    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
136                                    double>::__type
137    atan(_Tp __x)
138    { return __builtin_atan(__x); }
139
140  using ::atan2;
141
142#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
143  inline _GLIBCXX_CONSTEXPR float
144  atan2(float __y, float __x)
145  { return __builtin_atan2f(__y, __x); }
146
147  inline _GLIBCXX_CONSTEXPR long double
148  atan2(long double __y, long double __x)
149  { return __builtin_atan2l(__y, __x); }
150#endif
151
152  template<typename _Tp, typename _Up>
153    inline _GLIBCXX_CONSTEXPR
154    typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
155    atan2(_Tp __y, _Up __x)
156    {
157      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
158      return atan2(__type(__y), __type(__x));
159    }
160
161  using ::ceil;
162
163#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
164  inline _GLIBCXX_CONSTEXPR float
165  ceil(float __x)
166  { return __builtin_ceilf(__x); }
167
168  inline _GLIBCXX_CONSTEXPR long double
169  ceil(long double __x)
170  { return __builtin_ceill(__x); }
171#endif
172
173  template<typename _Tp>
174    inline _GLIBCXX_CONSTEXPR
175    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
176                                    double>::__type
177    ceil(_Tp __x)
178    { return __builtin_ceil(__x); }
179
180  using ::cos;
181
182#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
183  inline _GLIBCXX_CONSTEXPR float
184  cos(float __x)
185  { return __builtin_cosf(__x); }
186
187  inline _GLIBCXX_CONSTEXPR long double
188  cos(long double __x)
189  { return __builtin_cosl(__x); }
190#endif
191
192  template<typename _Tp>
193    inline _GLIBCXX_CONSTEXPR
194    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
195                                    double>::__type
196    cos(_Tp __x)
197    { return __builtin_cos(__x); }
198
199  using ::cosh;
200
201#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
202  inline _GLIBCXX_CONSTEXPR float
203  cosh(float __x)
204  { return __builtin_coshf(__x); }
205
206  inline _GLIBCXX_CONSTEXPR long double
207  cosh(long double __x)
208  { return __builtin_coshl(__x); }
209#endif
210
211  template<typename _Tp>
212    inline _GLIBCXX_CONSTEXPR
213    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
214                                    double>::__type
215    cosh(_Tp __x)
216    { return __builtin_cosh(__x); }
217
218  using ::exp;
219
220#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
221  inline _GLIBCXX_CONSTEXPR float
222  exp(float __x)
223  { return __builtin_expf(__x); }
224
225  inline _GLIBCXX_CONSTEXPR long double
226  exp(long double __x)
227  { return __builtin_expl(__x); }
228#endif
229
230  template<typename _Tp>
231    inline _GLIBCXX_CONSTEXPR
232    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
233                                    double>::__type
234    exp(_Tp __x)
235    { return __builtin_exp(__x); }
236
237  using ::fabs;
238
239#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
240  inline _GLIBCXX_CONSTEXPR float
241  fabs(float __x)
242  { return __builtin_fabsf(__x); }
243
244  inline _GLIBCXX_CONSTEXPR long double
245  fabs(long double __x)
246  { return __builtin_fabsl(__x); }
247#endif
248
249  template<typename _Tp>
250    inline _GLIBCXX_CONSTEXPR
251    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
252                                    double>::__type
253    fabs(_Tp __x)
254    { return __builtin_fabs(__x); }
255
256  using ::floor;
257
258#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
259  inline _GLIBCXX_CONSTEXPR float
260  floor(float __x)
261  { return __builtin_floorf(__x); }
262
263  inline _GLIBCXX_CONSTEXPR long double
264  floor(long double __x)
265  { return __builtin_floorl(__x); }
266#endif
267
268  template<typename _Tp>
269    inline _GLIBCXX_CONSTEXPR
270    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
271                                    double>::__type
272    floor(_Tp __x)
273    { return __builtin_floor(__x); }
274
275  using ::fmod;
276
277#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
278  inline _GLIBCXX_CONSTEXPR float
279  fmod(float __x, float __y)
280  { return __builtin_fmodf(__x, __y); }
281
282  inline _GLIBCXX_CONSTEXPR long double
283  fmod(long double __x, long double __y)
284  { return __builtin_fmodl(__x, __y); }
285#endif
286
287  template<typename _Tp, typename _Up>
288    inline _GLIBCXX_CONSTEXPR
289    typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
290    fmod(_Tp __x, _Up __y)
291    {
292      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
293      return fmod(__type(__x), __type(__y));
294    }
295
296  using ::frexp;
297
298#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
299  inline float
300  frexp(float __x, int* __exp)
301  { return __builtin_frexpf(__x, __exp); }
302
303  inline long double
304  frexp(long double __x, int* __exp)
305  { return __builtin_frexpl(__x, __exp); }
306#endif
307
308  template<typename _Tp>
309    inline _GLIBCXX_CONSTEXPR
310    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
311                                    double>::__type
312    frexp(_Tp __x, int* __exp)
313    { return __builtin_frexp(__x, __exp); }
314
315  using ::ldexp;
316
317#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
318  inline _GLIBCXX_CONSTEXPR float
319  ldexp(float __x, int __exp)
320  { return __builtin_ldexpf(__x, __exp); }
321
322  inline _GLIBCXX_CONSTEXPR long double
323  ldexp(long double __x, int __exp)
324  { return __builtin_ldexpl(__x, __exp); }
325#endif
326
327  template<typename _Tp>
328    inline _GLIBCXX_CONSTEXPR
329    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
330                                    double>::__type
331    ldexp(_Tp __x, int __exp)
332    { return __builtin_ldexp(__x, __exp); }
333
334  using ::log;
335
336#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
337  inline _GLIBCXX_CONSTEXPR float
338  log(float __x)
339  { return __builtin_logf(__x); }
340
341  inline _GLIBCXX_CONSTEXPR long double
342  log(long double __x)
343  { return __builtin_logl(__x); }
344#endif
345
346  template<typename _Tp>
347    inline _GLIBCXX_CONSTEXPR
348    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
349                                    double>::__type
350    log(_Tp __x)
351    { return __builtin_log(__x); }
352
353  using ::log10;
354
355#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
356  inline _GLIBCXX_CONSTEXPR float
357  log10(float __x)
358  { return __builtin_log10f(__x); }
359
360  inline _GLIBCXX_CONSTEXPR long double
361  log10(long double __x)
362  { return __builtin_log10l(__x); }
363#endif
364
365  template<typename _Tp>
366    inline _GLIBCXX_CONSTEXPR
367    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
368                                    double>::__type
369    log10(_Tp __x)
370    { return __builtin_log10(__x); }
371
372  using ::modf;
373
374#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
375  inline float
376  modf(float __x, float* __iptr)
377  { return __builtin_modff(__x, __iptr); }
378
379  inline long double
380  modf(long double __x, long double* __iptr)
381  { return __builtin_modfl(__x, __iptr); }
382#endif
383
384  using ::pow;
385
386#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
387  inline _GLIBCXX_CONSTEXPR float
388  pow(float __x, float __y)
389  { return __builtin_powf(__x, __y); }
390
391  inline _GLIBCXX_CONSTEXPR long double
392  pow(long double __x, long double __y)
393  { return __builtin_powl(__x, __y); }
394
395#if __cplusplus < 201103L
396  // _GLIBCXX_RESOLVE_LIB_DEFECTS
397  // DR 550. What should the return type of pow(float,int) be?
398  inline double
399  pow(double __x, int __i)
400  { return __builtin_powi(__x, __i); }
401
402  inline float
403  pow(float __x, int __n)
404  { return __builtin_powif(__x, __n); }
405
406  inline long double
407  pow(long double __x, int __n)
408  { return __builtin_powil(__x, __n); }
409#endif
410#endif
411
412  template<typename _Tp, typename _Up>
413    inline _GLIBCXX_CONSTEXPR
414    typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
415    pow(_Tp __x, _Up __y)
416    {
417      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
418      return pow(__type(__x), __type(__y));
419    }
420
421  using ::sin;
422
423#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
424  inline _GLIBCXX_CONSTEXPR float
425  sin(float __x)
426  { return __builtin_sinf(__x); }
427
428  inline _GLIBCXX_CONSTEXPR long double
429  sin(long double __x)
430  { return __builtin_sinl(__x); }
431#endif
432
433  template<typename _Tp>
434    inline _GLIBCXX_CONSTEXPR
435    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
436                                    double>::__type
437    sin(_Tp __x)
438    { return __builtin_sin(__x); }
439
440  using ::sinh;
441
442#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
443  inline _GLIBCXX_CONSTEXPR float
444  sinh(float __x)
445  { return __builtin_sinhf(__x); }
446
447  inline _GLIBCXX_CONSTEXPR long double
448  sinh(long double __x)
449  { return __builtin_sinhl(__x); }
450#endif
451
452  template<typename _Tp>
453    inline _GLIBCXX_CONSTEXPR
454    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
455                                    double>::__type
456    sinh(_Tp __x)
457    { return __builtin_sinh(__x); }
458
459  using ::sqrt;
460
461#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
462  inline _GLIBCXX_CONSTEXPR float
463  sqrt(float __x)
464  { return __builtin_sqrtf(__x); }
465
466  inline _GLIBCXX_CONSTEXPR long double
467  sqrt(long double __x)
468  { return __builtin_sqrtl(__x); }
469#endif
470
471  template<typename _Tp>
472    inline _GLIBCXX_CONSTEXPR
473    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
474                                    double>::__type
475    sqrt(_Tp __x)
476    { return __builtin_sqrt(__x); }
477
478  using ::tan;
479
480#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
481  inline _GLIBCXX_CONSTEXPR float
482  tan(float __x)
483  { return __builtin_tanf(__x); }
484
485  inline _GLIBCXX_CONSTEXPR long double
486  tan(long double __x)
487  { return __builtin_tanl(__x); }
488#endif
489
490  template<typename _Tp>
491    inline _GLIBCXX_CONSTEXPR
492    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
493                                    double>::__type
494    tan(_Tp __x)
495    { return __builtin_tan(__x); }
496
497  using ::tanh;
498
499#ifndef __CORRECT_ISO_CPP_MATH_H_PROTO
500  inline _GLIBCXX_CONSTEXPR float
501  tanh(float __x)
502  { return __builtin_tanhf(__x); }
503
504  inline _GLIBCXX_CONSTEXPR long double
505  tanh(long double __x)
506  { return __builtin_tanhl(__x); }
507#endif
508
509  template<typename _Tp>
510    inline _GLIBCXX_CONSTEXPR
511    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
512                                    double>::__type
513    tanh(_Tp __x)
514    { return __builtin_tanh(__x); }
515
516#if _GLIBCXX_USE_C99_MATH
517#if !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC
518
519// These are possible macros imported from C99-land.
520#undef fpclassify
521#undef isfinite
522#undef isinf
523#undef isnan
524#undef isnormal
525#undef signbit
526#undef isgreater
527#undef isgreaterequal
528#undef isless
529#undef islessequal
530#undef islessgreater
531#undef isunordered
532
533#if __cplusplus >= 201103L
534
535#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
536  constexpr int
537  fpclassify(float __x)
538  { return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
539				FP_SUBNORMAL, FP_ZERO, __x); }
540
541  constexpr int
542  fpclassify(double __x)
543  { return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
544				FP_SUBNORMAL, FP_ZERO, __x); }
545
546  constexpr int
547  fpclassify(long double __x)
548  { return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
549				FP_SUBNORMAL, FP_ZERO, __x); }
550#endif
551
552#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
553  template<typename _Tp>
554    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
555                                              int>::__type
556    fpclassify(_Tp __x)
557    { return __x != 0 ? FP_NORMAL : FP_ZERO; }
558#endif
559
560#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
561  constexpr bool
562  isfinite(float __x)
563  { return __builtin_isfinite(__x); }
564
565  constexpr bool
566  isfinite(double __x)
567  { return __builtin_isfinite(__x); }
568
569  constexpr bool
570  isfinite(long double __x)
571  { return __builtin_isfinite(__x); }
572#endif
573
574#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
575  template<typename _Tp>
576    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
577                                              bool>::__type
578    isfinite(_Tp __x)
579    { return true; }
580#endif
581
582#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
583  constexpr bool
584  isinf(float __x)
585  { return __builtin_isinf(__x); }
586
587#if _GLIBCXX_HAVE_OBSOLETE_ISINF \
588  && !_GLIBCXX_NO_OBSOLETE_ISINF_ISNAN_DYNAMIC
589  using ::isinf;
590#else
591  constexpr bool
592  isinf(double __x)
593  { return __builtin_isinf(__x); }
594#endif
595
596  constexpr bool
597  isinf(long double __x)
598  { return __builtin_isinf(__x); }
599#endif
600
601#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
602  template<typename _Tp>
603    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
604                                              bool>::__type
605    isinf(_Tp __x)
606    { return false; }
607#endif
608
609#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
610  constexpr bool
611  isnan(float __x)
612  { return __builtin_isnan(__x); }
613
614#if _GLIBCXX_HAVE_OBSOLETE_ISNAN \
615  && !_GLIBCXX_NO_OBSOLETE_ISINF_ISNAN_DYNAMIC
616  using ::isnan;
617#else
618  constexpr bool
619  isnan(double __x)
620  { return __builtin_isnan(__x); }
621#endif
622
623  constexpr bool
624  isnan(long double __x)
625  { return __builtin_isnan(__x); }
626#endif
627
628#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
629  template<typename _Tp>
630    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
631                                              bool>::__type
632    isnan(_Tp __x)
633    { return false; }
634#endif
635
636#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
637  constexpr bool
638  isnormal(float __x)
639  { return __builtin_isnormal(__x); }
640
641  constexpr bool
642  isnormal(double __x)
643  { return __builtin_isnormal(__x); }
644
645  constexpr bool
646  isnormal(long double __x)
647  { return __builtin_isnormal(__x); }
648#endif
649
650#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
651  template<typename _Tp>
652    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
653                                              bool>::__type
654    isnormal(_Tp __x)
655    { return __x != 0 ? true : false; }
656#endif
657
658#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
659  // Note: middle-end/36757 is fixed, __builtin_signbit is type-generic.
660  constexpr bool
661  signbit(float __x)
662  { return __builtin_signbit(__x); }
663
664  constexpr bool
665  signbit(double __x)
666  { return __builtin_signbit(__x); }
667
668  constexpr bool
669  signbit(long double __x)
670  { return __builtin_signbit(__x); }
671#endif
672
673#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
674  template<typename _Tp>
675    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
676                                              bool>::__type
677    signbit(_Tp __x)
678    { return __x < 0 ? true : false; }
679#endif
680
681#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
682  constexpr bool
683  isgreater(float __x, float __y)
684  { return __builtin_isgreater(__x, __y); }
685
686  constexpr bool
687  isgreater(double __x, double __y)
688  { return __builtin_isgreater(__x, __y); }
689
690  constexpr bool
691  isgreater(long double __x, long double __y)
692  { return __builtin_isgreater(__x, __y); }
693#endif
694
695#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
696  template<typename _Tp, typename _Up>
697    constexpr typename
698    __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
699			    && __is_arithmetic<_Up>::__value), bool>::__type
700    isgreater(_Tp __x, _Up __y)
701    {
702      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
703      return __builtin_isgreater(__type(__x), __type(__y));
704    }
705#endif
706
707#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
708  constexpr bool
709  isgreaterequal(float __x, float __y)
710  { return __builtin_isgreaterequal(__x, __y); }
711
712  constexpr bool
713  isgreaterequal(double __x, double __y)
714  { return __builtin_isgreaterequal(__x, __y); }
715
716  constexpr bool
717  isgreaterequal(long double __x, long double __y)
718  { return __builtin_isgreaterequal(__x, __y); }
719#endif
720
721#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
722  template<typename _Tp, typename _Up>
723    constexpr typename
724    __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
725			    && __is_arithmetic<_Up>::__value), bool>::__type
726    isgreaterequal(_Tp __x, _Up __y)
727    {
728      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
729      return __builtin_isgreaterequal(__type(__x), __type(__y));
730    }
731#endif
732
733#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
734  constexpr bool
735  isless(float __x, float __y)
736  { return __builtin_isless(__x, __y); }
737
738  constexpr bool
739  isless(double __x, double __y)
740  { return __builtin_isless(__x, __y); }
741
742  constexpr bool
743  isless(long double __x, long double __y)
744  { return __builtin_isless(__x, __y); }
745#endif
746
747#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
748  template<typename _Tp, typename _Up>
749    constexpr typename
750    __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
751			    && __is_arithmetic<_Up>::__value), bool>::__type
752    isless(_Tp __x, _Up __y)
753    {
754      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
755      return __builtin_isless(__type(__x), __type(__y));
756    }
757#endif
758
759#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
760  constexpr bool
761  islessequal(float __x, float __y)
762  { return __builtin_islessequal(__x, __y); }
763
764  constexpr bool
765  islessequal(double __x, double __y)
766  { return __builtin_islessequal(__x, __y); }
767
768  constexpr bool
769  islessequal(long double __x, long double __y)
770  { return __builtin_islessequal(__x, __y); }
771#endif
772
773#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
774  template<typename _Tp, typename _Up>
775    constexpr typename
776    __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
777			    && __is_arithmetic<_Up>::__value), bool>::__type
778    islessequal(_Tp __x, _Up __y)
779    {
780      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
781      return __builtin_islessequal(__type(__x), __type(__y));
782    }
783#endif
784
785#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
786  constexpr bool
787  islessgreater(float __x, float __y)
788  { return __builtin_islessgreater(__x, __y); }
789
790  constexpr bool
791  islessgreater(double __x, double __y)
792  { return __builtin_islessgreater(__x, __y); }
793
794  constexpr bool
795  islessgreater(long double __x, long double __y)
796  { return __builtin_islessgreater(__x, __y); }
797#endif
798
799#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
800  template<typename _Tp, typename _Up>
801    constexpr typename
802    __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
803			    && __is_arithmetic<_Up>::__value), bool>::__type
804    islessgreater(_Tp __x, _Up __y)
805    {
806      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
807      return __builtin_islessgreater(__type(__x), __type(__y));
808    }
809#endif
810
811#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
812  constexpr bool
813  isunordered(float __x, float __y)
814  { return __builtin_isunordered(__x, __y); }
815
816  constexpr bool
817  isunordered(double __x, double __y)
818  { return __builtin_isunordered(__x, __y); }
819
820  constexpr bool
821  isunordered(long double __x, long double __y)
822  { return __builtin_isunordered(__x, __y); }
823#endif
824
825#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
826  template<typename _Tp, typename _Up>
827    constexpr typename
828    __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
829			    && __is_arithmetic<_Up>::__value), bool>::__type
830    isunordered(_Tp __x, _Up __y)
831    {
832      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
833      return __builtin_isunordered(__type(__x), __type(__y));
834    }
835#endif
836
837#else
838
839  template<typename _Tp>
840    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
841					   int>::__type
842    fpclassify(_Tp __f)
843    {
844      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
845      return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
846				  FP_SUBNORMAL, FP_ZERO, __type(__f));
847    }
848
849  template<typename _Tp>
850    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
851					   int>::__type
852    isfinite(_Tp __f)
853    {
854      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
855      return __builtin_isfinite(__type(__f));
856    }
857
858  template<typename _Tp>
859    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
860					   int>::__type
861    isinf(_Tp __f)
862    {
863      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
864      return __builtin_isinf(__type(__f));
865    }
866
867  template<typename _Tp>
868    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
869					   int>::__type
870    isnan(_Tp __f)
871    {
872      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
873      return __builtin_isnan(__type(__f));
874    }
875
876  template<typename _Tp>
877    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
878					   int>::__type
879    isnormal(_Tp __f)
880    {
881      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
882      return __builtin_isnormal(__type(__f));
883    }
884
885  template<typename _Tp>
886    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
887					   int>::__type
888    signbit(_Tp __f)
889    {
890      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
891      return __builtin_signbit(__type(__f));
892    }
893
894  template<typename _Tp>
895    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
896					   int>::__type
897    isgreater(_Tp __f1, _Tp __f2)
898    {
899      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
900      return __builtin_isgreater(__type(__f1), __type(__f2));
901    }
902
903  template<typename _Tp>
904    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
905					   int>::__type
906    isgreaterequal(_Tp __f1, _Tp __f2)
907    {
908      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
909      return __builtin_isgreaterequal(__type(__f1), __type(__f2));
910    }
911
912  template<typename _Tp>
913    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
914					   int>::__type
915    isless(_Tp __f1, _Tp __f2)
916    {
917      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
918      return __builtin_isless(__type(__f1), __type(__f2));
919    }
920
921  template<typename _Tp>
922    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
923					   int>::__type
924    islessequal(_Tp __f1, _Tp __f2)
925    {
926      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
927      return __builtin_islessequal(__type(__f1), __type(__f2));
928    }
929
930  template<typename _Tp>
931    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
932					   int>::__type
933    islessgreater(_Tp __f1, _Tp __f2)
934    {
935      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
936      return __builtin_islessgreater(__type(__f1), __type(__f2));
937    }
938
939  template<typename _Tp>
940    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
941					   int>::__type
942    isunordered(_Tp __f1, _Tp __f2)
943    {
944      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
945      return __builtin_isunordered(__type(__f1), __type(__f2));
946    }
947
948#endif // C++11
949#endif /* _GLIBCXX_USE_C99_FP_MACROS_DYNAMIC */
950#endif /* _GLIBCXX_USE_C99_MATH */
951
952#if __cplusplus >= 201103L
953
954#ifdef _GLIBCXX_USE_C99_MATH_TR1
955
956#undef acosh
957#undef acoshf
958#undef acoshl
959#undef asinh
960#undef asinhf
961#undef asinhl
962#undef atanh
963#undef atanhf
964#undef atanhl
965#undef cbrt
966#undef cbrtf
967#undef cbrtl
968#undef copysign
969#undef copysignf
970#undef copysignl
971#undef erf
972#undef erff
973#undef erfl
974#undef erfc
975#undef erfcf
976#undef erfcl
977#undef exp2
978#undef exp2f
979#undef exp2l
980#undef expm1
981#undef expm1f
982#undef expm1l
983#undef fdim
984#undef fdimf
985#undef fdiml
986#undef fma
987#undef fmaf
988#undef fmal
989#undef fmax
990#undef fmaxf
991#undef fmaxl
992#undef fmin
993#undef fminf
994#undef fminl
995#undef hypot
996#undef hypotf
997#undef hypotl
998#undef ilogb
999#undef ilogbf
1000#undef ilogbl
1001#undef lgamma
1002#undef lgammaf
1003#undef lgammal
1004#ifndef _GLIBCXX_NO_C99_ROUNDING_FUNCS
1005#undef llrint
1006#undef llrintf
1007#undef llrintl
1008#undef llround
1009#undef llroundf
1010#undef llroundl
1011#endif
1012#undef log1p
1013#undef log1pf
1014#undef log1pl
1015#undef log2
1016#undef log2f
1017#undef log2l
1018#undef logb
1019#undef logbf
1020#undef logbl
1021#undef lrint
1022#undef lrintf
1023#undef lrintl
1024#undef lround
1025#undef lroundf
1026#undef lroundl
1027#undef nan
1028#undef nanf
1029#undef nanl
1030#undef nearbyint
1031#undef nearbyintf
1032#undef nearbyintl
1033#undef nextafter
1034#undef nextafterf
1035#undef nextafterl
1036#undef nexttoward
1037#undef nexttowardf
1038#undef nexttowardl
1039#undef remainder
1040#undef remainderf
1041#undef remainderl
1042#undef remquo
1043#undef remquof
1044#undef remquol
1045#undef rint
1046#undef rintf
1047#undef rintl
1048#undef round
1049#undef roundf
1050#undef roundl
1051#undef scalbln
1052#undef scalblnf
1053#undef scalblnl
1054#undef scalbn
1055#undef scalbnf
1056#undef scalbnl
1057#undef tgamma
1058#undef tgammaf
1059#undef tgammal
1060#undef trunc
1061#undef truncf
1062#undef truncl
1063
1064  // types
1065  using ::double_t;
1066  using ::float_t;
1067
1068  // functions
1069  using ::acosh;
1070  using ::acoshf;
1071  using ::acoshl;
1072
1073  using ::asinh;
1074  using ::asinhf;
1075  using ::asinhl;
1076
1077  using ::atanh;
1078  using ::atanhf;
1079  using ::atanhl;
1080
1081  using ::cbrt;
1082  using ::cbrtf;
1083  using ::cbrtl;
1084
1085  using ::copysign;
1086  using ::copysignf;
1087  using ::copysignl;
1088
1089  using ::erf;
1090  using ::erff;
1091  using ::erfl;
1092
1093  using ::erfc;
1094  using ::erfcf;
1095  using ::erfcl;
1096
1097  using ::exp2;
1098  using ::exp2f;
1099  using ::exp2l;
1100
1101  using ::expm1;
1102  using ::expm1f;
1103  using ::expm1l;
1104
1105  using ::fdim;
1106  using ::fdimf;
1107  using ::fdiml;
1108
1109  using ::fma;
1110  using ::fmaf;
1111  using ::fmal;
1112
1113  using ::fmax;
1114  using ::fmaxf;
1115  using ::fmaxl;
1116
1117  using ::fmin;
1118  using ::fminf;
1119  using ::fminl;
1120
1121  using ::hypot;
1122  using ::hypotf;
1123  using ::hypotl;
1124
1125  using ::ilogb;
1126  using ::ilogbf;
1127  using ::ilogbl;
1128
1129  using ::lgamma;
1130  using ::lgammaf;
1131  using ::lgammal;
1132
1133#ifndef _GLIBCXX_NO_C99_ROUNDING_FUNCS
1134  using ::llrint;
1135  using ::llrintf;
1136  using ::llrintl;
1137
1138  using ::llround;
1139  using ::llroundf;
1140  using ::llroundl;
1141#endif
1142
1143  using ::log1p;
1144  using ::log1pf;
1145  using ::log1pl;
1146
1147  using ::log2;
1148  using ::log2f;
1149  using ::log2l;
1150
1151  using ::logb;
1152  using ::logbf;
1153  using ::logbl;
1154
1155  using ::lrint;
1156  using ::lrintf;
1157  using ::lrintl;
1158
1159  using ::lround;
1160  using ::lroundf;
1161  using ::lroundl;
1162
1163  using ::nan;
1164  using ::nanf;
1165  using ::nanl;
1166
1167  using ::nearbyint;
1168  using ::nearbyintf;
1169  using ::nearbyintl;
1170
1171  using ::nextafter;
1172  using ::nextafterf;
1173  using ::nextafterl;
1174
1175  using ::nexttoward;
1176  using ::nexttowardf;
1177  using ::nexttowardl;
1178
1179  using ::remainder;
1180  using ::remainderf;
1181  using ::remainderl;
1182
1183  using ::remquo;
1184  using ::remquof;
1185  using ::remquol;
1186
1187  using ::rint;
1188  using ::rintf;
1189  using ::rintl;
1190
1191  using ::round;
1192  using ::roundf;
1193  using ::roundl;
1194
1195  using ::scalbln;
1196  using ::scalblnf;
1197  using ::scalblnl;
1198
1199  using ::scalbn;
1200  using ::scalbnf;
1201  using ::scalbnl;
1202
1203  using ::tgamma;
1204  using ::tgammaf;
1205  using ::tgammal;
1206
1207  using ::trunc;
1208  using ::truncf;
1209  using ::truncl;
1210
1211  /// Additional overloads.
1212#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1213  constexpr float
1214  acosh(float __x)
1215  { return __builtin_acoshf(__x); }
1216
1217  constexpr long double
1218  acosh(long double __x)
1219  { return __builtin_acoshl(__x); }
1220#endif
1221
1222#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1223  template<typename _Tp>
1224    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1225                                              double>::__type
1226    acosh(_Tp __x)
1227    { return __builtin_acosh(__x); }
1228#endif
1229
1230#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1231  constexpr float
1232  asinh(float __x)
1233  { return __builtin_asinhf(__x); }
1234
1235  constexpr long double
1236  asinh(long double __x)
1237  { return __builtin_asinhl(__x); }
1238#endif
1239
1240#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1241  template<typename _Tp>
1242    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1243                                              double>::__type
1244    asinh(_Tp __x)
1245    { return __builtin_asinh(__x); }
1246#endif
1247
1248#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1249  constexpr float
1250  atanh(float __x)
1251  { return __builtin_atanhf(__x); }
1252
1253  constexpr long double
1254  atanh(long double __x)
1255  { return __builtin_atanhl(__x); }
1256#endif
1257
1258#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1259  template<typename _Tp>
1260    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1261                                              double>::__type
1262    atanh(_Tp __x)
1263    { return __builtin_atanh(__x); }
1264#endif
1265
1266#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1267  constexpr float
1268  cbrt(float __x)
1269  { return __builtin_cbrtf(__x); }
1270
1271  constexpr long double
1272  cbrt(long double __x)
1273  { return __builtin_cbrtl(__x); }
1274#endif
1275
1276#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1277  template<typename _Tp>
1278    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1279                                              double>::__type
1280    cbrt(_Tp __x)
1281    { return __builtin_cbrt(__x); }
1282#endif
1283
1284#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1285  constexpr float
1286  copysign(float __x, float __y)
1287  { return __builtin_copysignf(__x, __y); }
1288
1289  constexpr long double
1290  copysign(long double __x, long double __y)
1291  { return __builtin_copysignl(__x, __y); }
1292#endif
1293
1294#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1295  template<typename _Tp, typename _Up>
1296    constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
1297    copysign(_Tp __x, _Up __y)
1298    {
1299      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1300      return copysign(__type(__x), __type(__y));
1301    }
1302#endif
1303
1304#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1305  constexpr float
1306  erf(float __x)
1307  { return __builtin_erff(__x); }
1308
1309  constexpr long double
1310  erf(long double __x)
1311  { return __builtin_erfl(__x); }
1312#endif
1313
1314#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1315  template<typename _Tp>
1316    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1317                                              double>::__type
1318    erf(_Tp __x)
1319    { return __builtin_erf(__x); }
1320#endif
1321
1322#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1323  constexpr float
1324  erfc(float __x)
1325  { return __builtin_erfcf(__x); }
1326
1327  constexpr long double
1328  erfc(long double __x)
1329  { return __builtin_erfcl(__x); }
1330#endif
1331
1332#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1333  template<typename _Tp>
1334    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1335                                              double>::__type
1336    erfc(_Tp __x)
1337    { return __builtin_erfc(__x); }
1338#endif
1339
1340#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1341  constexpr float
1342  exp2(float __x)
1343  { return __builtin_exp2f(__x); }
1344
1345  constexpr long double
1346  exp2(long double __x)
1347  { return __builtin_exp2l(__x); }
1348#endif
1349
1350#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1351  template<typename _Tp>
1352    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1353                                              double>::__type
1354    exp2(_Tp __x)
1355    { return __builtin_exp2(__x); }
1356#endif
1357
1358#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1359  constexpr float
1360  expm1(float __x)
1361  { return __builtin_expm1f(__x); }
1362
1363  constexpr long double
1364  expm1(long double __x)
1365  { return __builtin_expm1l(__x); }
1366#endif
1367
1368#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1369  template<typename _Tp>
1370    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1371                                              double>::__type
1372    expm1(_Tp __x)
1373    { return __builtin_expm1(__x); }
1374#endif
1375
1376#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1377  constexpr float
1378  fdim(float __x, float __y)
1379  { return __builtin_fdimf(__x, __y); }
1380
1381  constexpr long double
1382  fdim(long double __x, long double __y)
1383  { return __builtin_fdiml(__x, __y); }
1384#endif
1385
1386#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1387  template<typename _Tp, typename _Up>
1388    constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
1389    fdim(_Tp __x, _Up __y)
1390    {
1391      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1392      return fdim(__type(__x), __type(__y));
1393    }
1394#endif
1395
1396#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1397  constexpr float
1398  fma(float __x, float __y, float __z)
1399  { return __builtin_fmaf(__x, __y, __z); }
1400
1401  constexpr long double
1402  fma(long double __x, long double __y, long double __z)
1403  { return __builtin_fmal(__x, __y, __z); }
1404#endif
1405
1406#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1407  template<typename _Tp, typename _Up, typename _Vp>
1408    constexpr typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type
1409    fma(_Tp __x, _Up __y, _Vp __z)
1410    {
1411      typedef typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type __type;
1412      return fma(__type(__x), __type(__y), __type(__z));
1413    }
1414#endif
1415
1416#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1417  constexpr float
1418  fmax(float __x, float __y)
1419  { return __builtin_fmaxf(__x, __y); }
1420
1421  constexpr long double
1422  fmax(long double __x, long double __y)
1423  { return __builtin_fmaxl(__x, __y); }
1424#endif
1425
1426#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1427  template<typename _Tp, typename _Up>
1428    constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
1429    fmax(_Tp __x, _Up __y)
1430    {
1431      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1432      return fmax(__type(__x), __type(__y));
1433    }
1434#endif
1435
1436#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1437  constexpr float
1438  fmin(float __x, float __y)
1439  { return __builtin_fminf(__x, __y); }
1440
1441  constexpr long double
1442  fmin(long double __x, long double __y)
1443  { return __builtin_fminl(__x, __y); }
1444#endif
1445
1446#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1447  template<typename _Tp, typename _Up>
1448    constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
1449    fmin(_Tp __x, _Up __y)
1450    {
1451      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1452      return fmin(__type(__x), __type(__y));
1453    }
1454#endif
1455
1456#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1457  constexpr float
1458  hypot(float __x, float __y)
1459  { return __builtin_hypotf(__x, __y); }
1460
1461  constexpr long double
1462  hypot(long double __x, long double __y)
1463  { return __builtin_hypotl(__x, __y); }
1464#endif
1465
1466#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1467  template<typename _Tp, typename _Up>
1468    constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
1469    hypot(_Tp __x, _Up __y)
1470    {
1471      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1472      return hypot(__type(__x), __type(__y));
1473    }
1474#endif
1475
1476#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1477  constexpr int
1478  ilogb(float __x)
1479  { return __builtin_ilogbf(__x); }
1480
1481  constexpr int
1482  ilogb(long double __x)
1483  { return __builtin_ilogbl(__x); }
1484#endif
1485
1486#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1487  template<typename _Tp>
1488    constexpr
1489    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1490                                    int>::__type
1491    ilogb(_Tp __x)
1492    { return __builtin_ilogb(__x); }
1493#endif
1494
1495#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1496  constexpr float
1497  lgamma(float __x)
1498  { return __builtin_lgammaf(__x); }
1499
1500  constexpr long double
1501  lgamma(long double __x)
1502  { return __builtin_lgammal(__x); }
1503#endif
1504
1505#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1506  template<typename _Tp>
1507    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1508                                              double>::__type
1509    lgamma(_Tp __x)
1510    { return __builtin_lgamma(__x); }
1511#endif
1512
1513#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1514  constexpr long long
1515  llrint(float __x)
1516  { return __builtin_llrintf(__x); }
1517
1518  constexpr long long
1519  llrint(long double __x)
1520  { return __builtin_llrintl(__x); }
1521#endif
1522
1523#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1524  template<typename _Tp>
1525    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1526                                              long long>::__type
1527    llrint(_Tp __x)
1528    { return __builtin_llrint(__x); }
1529#endif
1530
1531#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1532  constexpr long long
1533  llround(float __x)
1534  { return __builtin_llroundf(__x); }
1535
1536  constexpr long long
1537  llround(long double __x)
1538  { return __builtin_llroundl(__x); }
1539#endif
1540
1541#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1542  template<typename _Tp>
1543    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1544                                              long long>::__type
1545    llround(_Tp __x)
1546    { return __builtin_llround(__x); }
1547#endif
1548
1549#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1550  constexpr float
1551  log1p(float __x)
1552  { return __builtin_log1pf(__x); }
1553
1554  constexpr long double
1555  log1p(long double __x)
1556  { return __builtin_log1pl(__x); }
1557#endif
1558
1559#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1560  template<typename _Tp>
1561    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1562                                              double>::__type
1563    log1p(_Tp __x)
1564    { return __builtin_log1p(__x); }
1565#endif
1566
1567#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1568  // DR 568.
1569  constexpr float
1570  log2(float __x)
1571  { return __builtin_log2f(__x); }
1572
1573  constexpr long double
1574  log2(long double __x)
1575  { return __builtin_log2l(__x); }
1576#endif
1577
1578#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1579  template<typename _Tp>
1580    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1581                                              double>::__type
1582    log2(_Tp __x)
1583    { return __builtin_log2(__x); }
1584#endif
1585
1586#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1587  constexpr float
1588  logb(float __x)
1589  { return __builtin_logbf(__x); }
1590
1591  constexpr long double
1592  logb(long double __x)
1593  { return __builtin_logbl(__x); }
1594#endif
1595
1596#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1597  template<typename _Tp>
1598    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1599                                              double>::__type
1600    logb(_Tp __x)
1601    { return __builtin_logb(__x); }
1602#endif
1603
1604#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1605  constexpr long
1606  lrint(float __x)
1607  { return __builtin_lrintf(__x); }
1608
1609  constexpr long
1610  lrint(long double __x)
1611  { return __builtin_lrintl(__x); }
1612#endif
1613
1614#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1615  template<typename _Tp>
1616    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1617                                              long>::__type
1618    lrint(_Tp __x)
1619    { return __builtin_lrint(__x); }
1620#endif
1621
1622#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1623  constexpr long
1624  lround(float __x)
1625  { return __builtin_lroundf(__x); }
1626
1627  constexpr long
1628  lround(long double __x)
1629  { return __builtin_lroundl(__x); }
1630#endif
1631
1632#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1633  template<typename _Tp>
1634    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1635                                              long>::__type
1636    lround(_Tp __x)
1637    { return __builtin_lround(__x); }
1638#endif
1639
1640#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1641  constexpr float
1642  nearbyint(float __x)
1643  { return __builtin_nearbyintf(__x); }
1644
1645  constexpr long double
1646  nearbyint(long double __x)
1647  { return __builtin_nearbyintl(__x); }
1648#endif
1649
1650#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1651  template<typename _Tp>
1652    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1653                                              double>::__type
1654    nearbyint(_Tp __x)
1655    { return __builtin_nearbyint(__x); }
1656#endif
1657
1658#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1659  constexpr float
1660  nextafter(float __x, float __y)
1661  { return __builtin_nextafterf(__x, __y); }
1662
1663  constexpr long double
1664  nextafter(long double __x, long double __y)
1665  { return __builtin_nextafterl(__x, __y); }
1666#endif
1667
1668#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1669  template<typename _Tp, typename _Up>
1670    constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
1671    nextafter(_Tp __x, _Up __y)
1672    {
1673      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1674      return nextafter(__type(__x), __type(__y));
1675    }
1676#endif
1677
1678#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1679  constexpr float
1680  nexttoward(float __x, long double __y)
1681  { return __builtin_nexttowardf(__x, __y); }
1682
1683  constexpr long double
1684  nexttoward(long double __x, long double __y)
1685  { return __builtin_nexttowardl(__x, __y); }
1686#endif
1687
1688#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1689  template<typename _Tp>
1690    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1691                                              double>::__type
1692    nexttoward(_Tp __x, long double __y)
1693    { return __builtin_nexttoward(__x, __y); }
1694#endif
1695
1696#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1697  constexpr float
1698  remainder(float __x, float __y)
1699  { return __builtin_remainderf(__x, __y); }
1700
1701  constexpr long double
1702  remainder(long double __x, long double __y)
1703  { return __builtin_remainderl(__x, __y); }
1704#endif
1705
1706#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1707  template<typename _Tp, typename _Up>
1708    constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
1709    remainder(_Tp __x, _Up __y)
1710    {
1711      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1712      return remainder(__type(__x), __type(__y));
1713    }
1714#endif
1715
1716#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1717  inline float
1718  remquo(float __x, float __y, int* __pquo)
1719  { return __builtin_remquof(__x, __y, __pquo); }
1720
1721  inline long double
1722  remquo(long double __x, long double __y, int* __pquo)
1723  { return __builtin_remquol(__x, __y, __pquo); }
1724#endif
1725
1726#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1727  template<typename _Tp, typename _Up>
1728    inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
1729    remquo(_Tp __x, _Up __y, int* __pquo)
1730    {
1731      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1732      return remquo(__type(__x), __type(__y), __pquo);
1733    }
1734#endif
1735
1736#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1737  constexpr float
1738  rint(float __x)
1739  { return __builtin_rintf(__x); }
1740
1741  constexpr long double
1742  rint(long double __x)
1743  { return __builtin_rintl(__x); }
1744#endif
1745
1746#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1747  template<typename _Tp>
1748    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1749                                              double>::__type
1750    rint(_Tp __x)
1751    { return __builtin_rint(__x); }
1752#endif
1753
1754#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1755  constexpr float
1756  round(float __x)
1757  { return __builtin_roundf(__x); }
1758
1759  constexpr long double
1760  round(long double __x)
1761  { return __builtin_roundl(__x); }
1762#endif
1763
1764#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1765  template<typename _Tp>
1766    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1767                                              double>::__type
1768    round(_Tp __x)
1769    { return __builtin_round(__x); }
1770#endif
1771
1772#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1773  constexpr float
1774  scalbln(float __x, long __ex)
1775  { return __builtin_scalblnf(__x, __ex); }
1776
1777  constexpr long double
1778  scalbln(long double __x, long __ex)
1779  { return __builtin_scalblnl(__x, __ex); }
1780#endif
1781
1782#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1783  template<typename _Tp>
1784    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1785                                              double>::__type
1786    scalbln(_Tp __x, long __ex)
1787    { return __builtin_scalbln(__x, __ex); }
1788#endif
1789
1790#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1791  constexpr float
1792  scalbn(float __x, int __ex)
1793  { return __builtin_scalbnf(__x, __ex); }
1794
1795  constexpr long double
1796  scalbn(long double __x, int __ex)
1797  { return __builtin_scalbnl(__x, __ex); }
1798#endif
1799
1800#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1801  template<typename _Tp>
1802    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1803                                              double>::__type
1804    scalbn(_Tp __x, int __ex)
1805    { return __builtin_scalbn(__x, __ex); }
1806#endif
1807
1808#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1809  constexpr float
1810  tgamma(float __x)
1811  { return __builtin_tgammaf(__x); }
1812
1813  constexpr long double
1814  tgamma(long double __x)
1815  { return __builtin_tgammal(__x); }
1816#endif
1817
1818#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1819  template<typename _Tp>
1820    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1821                                              double>::__type
1822    tgamma(_Tp __x)
1823    { return __builtin_tgamma(__x); }
1824#endif
1825
1826#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_FP
1827  constexpr float
1828  trunc(float __x)
1829  { return __builtin_truncf(__x); }
1830
1831  constexpr long double
1832  trunc(long double __x)
1833  { return __builtin_truncl(__x); }
1834#endif
1835
1836#ifndef __CORRECT_ISO_CPP11_MATH_H_PROTO_INT
1837  template<typename _Tp>
1838    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
1839                                              double>::__type
1840    trunc(_Tp __x)
1841    { return __builtin_trunc(__x); }
1842#endif
1843
1844#endif // _GLIBCXX_USE_C99_MATH_TR1
1845#endif // C++11
1846
1847#if __cplusplus > 201402L
1848
1849  // [c.math.hypot3], three-dimensional hypotenuse
1850#define __cpp_lib_hypot 201603
1851
1852  template<typename _Tp>
1853    inline _Tp
1854    __hypot3(_Tp __x, _Tp __y, _Tp __z)
1855    {
1856      __x = std::abs(__x);
1857      __y = std::abs(__y);
1858      __z = std::abs(__z);
1859      if (_Tp __a = __x < __y ? __y < __z ? __z : __y : __x < __z ? __z : __x)
1860	return __a * std::sqrt((__x / __a) * (__x / __a)
1861			       + (__y / __a) * (__y / __a)
1862			       + (__z / __a) * (__z / __a));
1863      else
1864	return {};
1865    }
1866
1867  inline float
1868  hypot(float __x, float __y, float __z)
1869  { return std::__hypot3<float>(__x, __y, __z); }
1870
1871  inline double
1872  hypot(double __x, double __y, double __z)
1873  { return std::__hypot3<double>(__x, __y, __z); }
1874
1875  inline long double
1876  hypot(long double __x, long double __y, long double __z)
1877  { return std::__hypot3<long double>(__x, __y, __z); }
1878
1879  template<typename _Tp, typename _Up, typename _Vp>
1880    typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type
1881    hypot(_Tp __x, _Up __y, _Vp __z)
1882    {
1883      using __type = typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type;
1884      return std::__hypot3<__type>(__x, __y, __z);
1885    }
1886#endif // C++17
1887
1888#if __cplusplus > 201703L
1889  // linear interpolation
1890# define __cpp_lib_interpolate 201902L
1891
1892  template<typename _Fp>
1893    constexpr _Fp
1894    __lerp(_Fp __a, _Fp __b, _Fp __t) noexcept
1895    {
1896      if (__a <= 0 && __b >= 0 || __a >= 0 && __b <= 0)
1897	return __t * __b + (1 - __t) * __a;
1898
1899      if (__t == 1)
1900	return __b;                        // exact
1901
1902      // Exact at __t=0, monotonic except near __t=1,
1903      // bounded, determinate, and consistent:
1904      const _Fp __x = __a + __t * (__b - __a);
1905      return __t > 1 == __b > __a
1906	? (__b < __x ? __x : __b)
1907	: (__b > __x ? __x : __b);  // monotonic near __t=1
1908    }
1909
1910  constexpr float
1911  lerp(float __a, float __b, float __t) noexcept
1912  { return std::__lerp(__a, __b, __t); }
1913
1914  constexpr double
1915  lerp(double __a, double __b, double __t) noexcept
1916  { return std::__lerp(__a, __b, __t); }
1917
1918  constexpr long double
1919  lerp(long double __a, long double __b, long double __t) noexcept
1920  { return std::__lerp(__a, __b, __t); }
1921#endif // C++20
1922
1923_GLIBCXX_END_NAMESPACE_VERSION
1924} // namespace
1925
1926#if _GLIBCXX_USE_STD_SPEC_FUNCS
1927#  include <bits/specfun.h>
1928#endif
1929
1930} // extern "C++"
1931
1932#endif
1933