-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathcomplex
1489 lines (1266 loc) · 39.9 KB
/
complex
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
// The template and inlines for the -*- C++ -*- complex number classes.
// Copyright (C) 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005
// Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library. This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 2, or (at your option)
// any later version.
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// You should have received a copy of the GNU General Public License along
// with this library; see the file COPYING. If not, write to the Free
// Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
// USA.
// As a special exception, you may use this file as part of a free software
// library without restriction. Specifically, if other files instantiate
// templates or use macros or inline functions from this file, or you compile
// this file and link it with other files to produce an executable, this
// file does not by itself cause the resulting executable to be covered by
// the GNU General Public License. This exception does not however
// invalidate any other reasons why the executable file might be covered by
// the GNU General Public License.
/** @file complex
* This is a Standard C++ Library header.
*/
//
// ISO C++ 14882: 26.2 Complex Numbers
// Note: this is not a conforming implementation.
// Initially implemented by Ulrich Drepper <[email protected]>
// Improved by Gabriel Dos Reis <[email protected]>
//
#ifndef _GLIBCXX_COMPLEX
#define _GLIBCXX_COMPLEX 1
#pragma GCC system_header
#include <bits/c++config.h>
#include <bits/cpp_type_traits.h>
#include <cmath>
#include <sstream>
namespace std {
// Forward declarations.
template<typename _Tp> class complex;
template<> class complex<float>;
template<> class complex<double>;
template<> class complex<long double>;
/// Return magnitude of @a z.
template<typename _Tp> _Tp abs(const complex<_Tp>&);
/// Return phase angle of @a z.
template<typename _Tp> _Tp arg(const complex<_Tp>&);
/// Return @a z magnitude squared.
template<typename _Tp> _Tp norm(const complex<_Tp>&);
/// Return complex conjugate of @a z.
template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&);
/// Return complex with magnitude @a rho and angle @a theta.
template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0);
// Transcendentals:
/// Return complex cosine of @a z.
template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&);
/// Return complex hyperbolic cosine of @a z.
template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&);
/// Return complex base e exponential of @a z.
template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&);
/// Return complex natural logarithm of @a z.
template<typename _Tp> complex<_Tp> log(const complex<_Tp>&);
/// Return complex base 10 logarithm of @a z.
template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&);
/// Return complex cosine of @a z.
template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int);
/// Return @a x to the @a y'th power.
template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&);
/// Return @a x to the @a y'th power.
template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&,
const complex<_Tp>&);
/// Return @a x to the @a y'th power.
template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&);
/// Return complex sine of @a z.
template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&);
/// Return complex hyperbolic sine of @a z.
template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&);
/// Return complex square root of @a z.
template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&);
/// Return complex tangent of @a z.
template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&);
/// Return complex hyperbolic tangent of @a z.
template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&);
//@}
// 26.2.2 Primary template class complex
/**
* Template to represent complex numbers.
*
* Specializations for float, double, and long double are part of the
* library. Results with any other type are not guaranteed.
*
* @param Tp Type of real and imaginary values.
*/
template<typename _Tp>
struct complex
{
/// Value typedef.
typedef _Tp value_type;
/// Default constructor. First parameter is x, second parameter is y.
/// Unspecified parameters default to 0.
complex(const _Tp& = _Tp(), const _Tp & = _Tp());
// Lets the compiler synthesize the copy constructor
// complex (const complex<_Tp>&);
/// Copy constructor.
template<typename _Up>
complex(const complex<_Up>&);
/// Return real part of complex number.
_Tp& real();
/// Return real part of complex number.
const _Tp& real() const;
/// Return imaginary part of complex number.
_Tp& imag();
/// Return imaginary part of complex number.
const _Tp& imag() const;
/// Assign this complex number to scalar @a t.
complex<_Tp>& operator=(const _Tp&);
/// Add @a t to this complex number.
complex<_Tp>& operator+=(const _Tp&);
/// Subtract @a t from this complex number.
complex<_Tp>& operator-=(const _Tp&);
/// Multiply this complex number by @a t.
complex<_Tp>& operator*=(const _Tp&);
/// Divide this complex number by @a t.
complex<_Tp>& operator/=(const _Tp&);
// Lets the compiler synthesize the
// copy and assignment operator
// complex<_Tp>& operator= (const complex<_Tp>&);
/// Assign this complex number to complex @a z.
template<typename _Up>
complex<_Tp>& operator=(const complex<_Up>&);
/// Add @a z to this complex number.
template<typename _Up>
complex<_Tp>& operator+=(const complex<_Up>&);
/// Subtract @a z from this complex number.
template<typename _Up>
complex<_Tp>& operator-=(const complex<_Up>&);
/// Multiply this complex number by @a z.
template<typename _Up>
complex<_Tp>& operator*=(const complex<_Up>&);
/// Divide this complex number by @a z.
template<typename _Up>
complex<_Tp>& operator/=(const complex<_Up>&);
const complex& __rep() const;
private:
_Tp _M_real;
_Tp _M_imag;
};
template<typename _Tp>
inline _Tp&
complex<_Tp>::real() { return _M_real; }
template<typename _Tp>
inline const _Tp&
complex<_Tp>::real() const { return _M_real; }
template<typename _Tp>
inline _Tp&
complex<_Tp>::imag() { return _M_imag; }
template<typename _Tp>
inline const _Tp&
complex<_Tp>::imag() const { return _M_imag; }
template<typename _Tp>
inline
complex<_Tp>::complex(const _Tp& __r, const _Tp& __i)
: _M_real(__r), _M_imag(__i) { }
template<typename _Tp>
template<typename _Up>
inline
complex<_Tp>::complex(const complex<_Up>& __z)
: _M_real(__z.real()), _M_imag(__z.imag()) { }
template<typename _Tp>
complex<_Tp>&
complex<_Tp>::operator=(const _Tp& __t)
{
_M_real = __t;
_M_imag = _Tp();
return *this;
}
// 26.2.5/1
template<typename _Tp>
inline complex<_Tp>&
complex<_Tp>::operator+=(const _Tp& __t)
{
_M_real += __t;
return *this;
}
// 26.2.5/3
template<typename _Tp>
inline complex<_Tp>&
complex<_Tp>::operator-=(const _Tp& __t)
{
_M_real -= __t;
return *this;
}
// 26.2.5/5
template<typename _Tp>
complex<_Tp>&
complex<_Tp>::operator*=(const _Tp& __t)
{
_M_real *= __t;
_M_imag *= __t;
return *this;
}
// 26.2.5/7
template<typename _Tp>
complex<_Tp>&
complex<_Tp>::operator/=(const _Tp& __t)
{
_M_real /= __t;
_M_imag /= __t;
return *this;
}
template<typename _Tp>
template<typename _Up>
complex<_Tp>&
complex<_Tp>::operator=(const complex<_Up>& __z)
{
_M_real = __z.real();
_M_imag = __z.imag();
return *this;
}
// 26.2.5/9
template<typename _Tp>
template<typename _Up>
complex<_Tp>&
complex<_Tp>::operator+=(const complex<_Up>& __z)
{
_M_real += __z.real();
_M_imag += __z.imag();
return *this;
}
// 26.2.5/11
template<typename _Tp>
template<typename _Up>
complex<_Tp>&
complex<_Tp>::operator-=(const complex<_Up>& __z)
{
_M_real -= __z.real();
_M_imag -= __z.imag();
return *this;
}
// 26.2.5/13
// XXX: This is a grammar school implementation.
template<typename _Tp>
template<typename _Up>
complex<_Tp>&
complex<_Tp>::operator*=(const complex<_Up>& __z)
{
const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag();
_M_imag = _M_real * __z.imag() + _M_imag * __z.real();
_M_real = __r;
return *this;
}
// 26.2.5/15
// XXX: This is a grammar school implementation.
template<typename _Tp>
template<typename _Up>
complex<_Tp>&
complex<_Tp>::operator/=(const complex<_Up>& __z)
{
const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag();
const _Tp __n = std::norm(__z);
_M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n;
_M_real = __r / __n;
return *this;
}
template<typename _Tp>
inline const complex<_Tp>&
complex<_Tp>::__rep() const { return *this; }
// Operators:
//@{
/// Return new complex value @a x plus @a y.
template<typename _Tp>
inline complex<_Tp>
operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
complex<_Tp> __r = __x;
__r += __y;
return __r;
}
template<typename _Tp>
inline complex<_Tp>
operator+(const complex<_Tp>& __x, const _Tp& __y)
{
complex<_Tp> __r = __x;
__r.real() += __y;
return __r;
}
template<typename _Tp>
inline complex<_Tp>
operator+(const _Tp& __x, const complex<_Tp>& __y)
{
complex<_Tp> __r = __y;
__r.real() += __x;
return __r;
}
//@}
//@{
/// Return new complex value @a x minus @a y.
template<typename _Tp>
inline complex<_Tp>
operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
complex<_Tp> __r = __x;
__r -= __y;
return __r;
}
template<typename _Tp>
inline complex<_Tp>
operator-(const complex<_Tp>& __x, const _Tp& __y)
{
complex<_Tp> __r = __x;
__r.real() -= __y;
return __r;
}
template<typename _Tp>
inline complex<_Tp>
operator-(const _Tp& __x, const complex<_Tp>& __y)
{
complex<_Tp> __r(__x, -__y.imag());
__r.real() -= __y.real();
return __r;
}
//@}
//@{
/// Return new complex value @a x times @a y.
template<typename _Tp>
inline complex<_Tp>
operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
complex<_Tp> __r = __x;
__r *= __y;
return __r;
}
template<typename _Tp>
inline complex<_Tp>
operator*(const complex<_Tp>& __x, const _Tp& __y)
{
complex<_Tp> __r = __x;
__r *= __y;
return __r;
}
template<typename _Tp>
inline complex<_Tp>
operator*(const _Tp& __x, const complex<_Tp>& __y)
{
complex<_Tp> __r = __y;
__r *= __x;
return __r;
}
//@}
//@{
/// Return new complex value @a x divided by @a y.
template<typename _Tp>
inline complex<_Tp>
operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
complex<_Tp> __r = __x;
__r /= __y;
return __r;
}
template<typename _Tp>
inline complex<_Tp>
operator/(const complex<_Tp>& __x, const _Tp& __y)
{
complex<_Tp> __r = __x;
__r /= __y;
return __r;
}
template<typename _Tp>
inline complex<_Tp>
operator/(const _Tp& __x, const complex<_Tp>& __y)
{
complex<_Tp> __r = __x;
__r /= __y;
return __r;
}
//@}
/// Return @a x.
template<typename _Tp>
inline complex<_Tp>
operator+(const complex<_Tp>& __x)
{ return __x; }
/// Return complex negation of @a x.
template<typename _Tp>
inline complex<_Tp>
operator-(const complex<_Tp>& __x)
{ return complex<_Tp>(-__x.real(), -__x.imag()); }
//@{
/// Return true if @a x is equal to @a y.
template<typename _Tp>
inline bool
operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
{ return __x.real() == __y.real() && __x.imag() == __y.imag(); }
template<typename _Tp>
inline bool
operator==(const complex<_Tp>& __x, const _Tp& __y)
{ return __x.real() == __y && __x.imag() == _Tp(); }
template<typename _Tp>
inline bool
operator==(const _Tp& __x, const complex<_Tp>& __y)
{ return __x == __y.real() && _Tp() == __y.imag(); }
//@}
//@{
/// Return false if @a x is equal to @a y.
template<typename _Tp>
inline bool
operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
{ return __x.real() != __y.real() || __x.imag() != __y.imag(); }
template<typename _Tp>
inline bool
operator!=(const complex<_Tp>& __x, const _Tp& __y)
{ return __x.real() != __y || __x.imag() != _Tp(); }
template<typename _Tp>
inline bool
operator!=(const _Tp& __x, const complex<_Tp>& __y)
{ return __x != __y.real() || _Tp() != __y.imag(); }
//@}
/// Extraction operator for complex values.
template<typename _Tp, typename _CharT, class _Traits>
basic_istream<_CharT, _Traits>&
operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
{
_Tp __re_x, __im_x;
_CharT __ch;
__is >> __ch;
if (__ch == '(')
{
__is >> __re_x >> __ch;
if (__ch == ',')
{
__is >> __im_x >> __ch;
if (__ch == ')')
__x = complex<_Tp>(__re_x, __im_x);
else
__is.setstate(ios_base::failbit);
}
else if (__ch == ')')
__x = __re_x;
else
__is.setstate(ios_base::failbit);
}
else
{
__is.putback(__ch);
__is >> __re_x;
__x = __re_x;
}
return __is;
}
/// Insertion operator for complex values.
template<typename _Tp, typename _CharT, class _Traits>
basic_ostream<_CharT, _Traits>&
operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
{
basic_ostringstream<_CharT, _Traits> __s;
__s.flags(__os.flags());
__s.imbue(__os.getloc());
__s.precision(__os.precision());
__s << '(' << __x.real() << ',' << __x.imag() << ')';
return __os << __s.str();
}
// Values
template<typename _Tp>
inline _Tp&
real(complex<_Tp>& __z)
{ return __z.real(); }
template<typename _Tp>
inline const _Tp&
real(const complex<_Tp>& __z)
{ return __z.real(); }
template<typename _Tp>
inline _Tp&
imag(complex<_Tp>& __z)
{ return __z.imag(); }
template<typename _Tp>
inline const _Tp&
imag(const complex<_Tp>& __z)
{ return __z.imag(); }
// 26.2.7/3 abs(__z): Returns the magnitude of __z.
template<typename _Tp>
inline _Tp
__complex_abs(const complex<_Tp>& __z)
{
_Tp __x = __z.real();
_Tp __y = __z.imag();
const _Tp __s = std::max(abs(__x), abs(__y));
if (__s == _Tp()) // well ...
return __s;
__x /= __s;
__y /= __s;
return __s * sqrt(__x * __x + __y * __y);
}
#if _GLIBCXX_USE_C99_COMPLEX
inline float
__complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); }
inline double
__complex_abs(__complex__ double __z) { return __builtin_cabs(__z); }
inline long double
__complex_abs(const __complex__ long double& __z)
{ return __builtin_cabsl(__z); }
template<typename _Tp>
inline _Tp
abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); }
#else
template<typename _Tp>
inline _Tp
abs(const complex<_Tp>& __z) { return __complex_abs(__z); }
#endif
// 26.2.7/4: arg(__z): Returns the phase angle of __z.
template<typename _Tp>
inline _Tp
__complex_arg(const complex<_Tp>& __z)
{ return atan2(__z.imag(), __z.real()); }
#if _GLIBCXX_USE_C99_COMPLEX
inline float
__complex_arg(__complex__ float __z) { return __builtin_cargf(__z); }
inline double
__complex_arg(__complex__ double __z) { return __builtin_carg(__z); }
inline long double
__complex_arg(const __complex__ long double& __z)
{ return __builtin_cargl(__z); }
template<typename _Tp>
inline _Tp
arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); }
#else
template<typename _Tp>
inline _Tp
arg(const complex<_Tp>& __z) { return __complex_arg(__z); }
#endif
// 26.2.7/5: norm(__z) returns the squared magintude of __z.
// As defined, norm() is -not- a norm is the common mathematical
// sens used in numerics. The helper class _Norm_helper<> tries to
// distinguish between builtin floating point and the rest, so as
// to deliver an answer as close as possible to the real value.
template<bool>
struct _Norm_helper
{
template<typename _Tp>
static inline _Tp _S_do_it(const complex<_Tp>& __z)
{
const _Tp __x = __z.real();
const _Tp __y = __z.imag();
return __x * __x + __y * __y;
}
};
template<>
struct _Norm_helper<true>
{
template<typename _Tp>
static inline _Tp _S_do_it(const complex<_Tp>& __z)
{
_Tp __res = std::abs(__z);
return __res * __res;
}
};
template<typename _Tp>
inline _Tp
norm(const complex<_Tp>& __z)
{
return _Norm_helper<__is_floating<_Tp>::__value
&& !_GLIBCXX_FAST_MATH>::_S_do_it(__z);
}
template<typename _Tp>
inline complex<_Tp>
polar(const _Tp& __rho, const _Tp& __theta)
{ return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); }
template<typename _Tp>
inline complex<_Tp>
conj(const complex<_Tp>& __z)
{ return complex<_Tp>(__z.real(), -__z.imag()); }
// Transcendentals
// 26.2.8/1 cos(__z): Returns the cosine of __z.
template<typename _Tp>
inline complex<_Tp>
__complex_cos(const complex<_Tp>& __z)
{
const _Tp __x = __z.real();
const _Tp __y = __z.imag();
return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y));
}
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
__complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); }
inline __complex__ double
__complex_cos(__complex__ double __z) { return __builtin_ccos(__z); }
inline __complex__ long double
__complex_cos(const __complex__ long double& __z)
{ return __builtin_ccosl(__z); }
template<typename _Tp>
inline complex<_Tp>
cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); }
#else
template<typename _Tp>
inline complex<_Tp>
cos(const complex<_Tp>& __z) { return __complex_cos(__z); }
#endif
// 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z.
template<typename _Tp>
inline complex<_Tp>
__complex_cosh(const complex<_Tp>& __z)
{
const _Tp __x = __z.real();
const _Tp __y = __z.imag();
return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y));
}
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
__complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); }
inline __complex__ double
__complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); }
inline __complex__ long double
__complex_cosh(const __complex__ long double& __z)
{ return __builtin_ccoshl(__z); }
template<typename _Tp>
inline complex<_Tp>
cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); }
#else
template<typename _Tp>
inline complex<_Tp>
cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); }
#endif
// 26.2.8/3 exp(__z): Returns the complex base e exponential of x
template<typename _Tp>
inline complex<_Tp>
__complex_exp(const complex<_Tp>& __z)
{ return std::polar(exp(__z.real()), __z.imag()); }
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
__complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); }
inline __complex__ double
__complex_exp(__complex__ double __z) { return __builtin_cexp(__z); }
inline __complex__ long double
__complex_exp(const __complex__ long double& __z)
{ return __builtin_cexpl(__z); }
template<typename _Tp>
inline complex<_Tp>
exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); }
#else
template<typename _Tp>
inline complex<_Tp>
exp(const complex<_Tp>& __z) { return __complex_exp(__z); }
#endif
// 26.2.8/5 log(__z): Reurns the natural complex logaritm of __z.
// The branch cut is along the negative axis.
template<typename _Tp>
inline complex<_Tp>
__complex_log(const complex<_Tp>& __z)
{ return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); }
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
__complex_log(__complex__ float __z) { return __builtin_clogf(__z); }
inline __complex__ double
__complex_log(__complex__ double __z) { return __builtin_clog(__z); }
inline __complex__ long double
__complex_log(const __complex__ long double& __z)
{ return __builtin_clogl(__z); }
template<typename _Tp>
inline complex<_Tp>
log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); }
#else
template<typename _Tp>
inline complex<_Tp>
log(const complex<_Tp>& __z) { return __complex_log(__z); }
#endif
template<typename _Tp>
inline complex<_Tp>
log10(const complex<_Tp>& __z)
{ return std::log(__z) / log(_Tp(10.0)); }
// 26.2.8/10 sin(__z): Returns the sine of __z.
template<typename _Tp>
inline complex<_Tp>
__complex_sin(const complex<_Tp>& __z)
{
const _Tp __x = __z.real();
const _Tp __y = __z.imag();
return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y));
}
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
__complex_sin(__complex__ float __z) { return __builtin_csinf(__z); }
inline __complex__ double
__complex_sin(__complex__ double __z) { return __builtin_csin(__z); }
inline __complex__ long double
__complex_sin(const __complex__ long double& __z)
{ return __builtin_csinl(__z); }
template<typename _Tp>
inline complex<_Tp>
sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); }
#else
template<typename _Tp>
inline complex<_Tp>
sin(const complex<_Tp>& __z) { return __complex_sin(__z); }
#endif
// 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z.
template<typename _Tp>
inline complex<_Tp>
__complex_sinh(const complex<_Tp>& __z)
{
const _Tp __x = __z.real();
const _Tp __y = __z.imag();
return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y));
}
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
__complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); }
inline __complex__ double
__complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); }
inline __complex__ long double
__complex_sinh(const __complex__ long double& __z)
{ return __builtin_csinhl(__z); }
template<typename _Tp>
inline complex<_Tp>
sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); }
#else
template<typename _Tp>
inline complex<_Tp>
sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); }
#endif
// 26.2.8/13 sqrt(__z): Returns the complex square root of __z.
// The branch cut is on the negative axis.
template<typename _Tp>
complex<_Tp>
__complex_sqrt(const complex<_Tp>& __z)
{
_Tp __x = __z.real();
_Tp __y = __z.imag();
if (__x == _Tp())
{
_Tp __t = sqrt(abs(__y) / 2);
return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
}
else
{
_Tp __t = sqrt(2 * (std::abs(__z) + abs(__x)));
_Tp __u = __t / 2;
return __x > _Tp()
? complex<_Tp>(__u, __y / __t)
: complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u);
}
}
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
__complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); }
inline __complex__ double
__complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); }
inline __complex__ long double
__complex_sqrt(const __complex__ long double& __z)
{ return __builtin_csqrtl(__z); }
template<typename _Tp>
inline complex<_Tp>
sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); }
#else
template<typename _Tp>
inline complex<_Tp>
sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); }
#endif
// 26.2.8/14 tan(__z): Return the complex tangent of __z.
template<typename _Tp>
inline complex<_Tp>
__complex_tan(const complex<_Tp>& __z)
{ return std::sin(__z) / std::cos(__z); }
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
__complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); }
inline __complex__ double
__complex_tan(__complex__ double __z) { return __builtin_ctan(__z); }
inline __complex__ long double
__complex_tan(const __complex__ long double& __z)
{ return __builtin_ctanl(__z); }
template<typename _Tp>
inline complex<_Tp>
tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); }
#else
template<typename _Tp>
inline complex<_Tp>
tan(const complex<_Tp>& __z) { return __complex_tan(__z); }
#endif
// 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z.
template<typename _Tp>
inline complex<_Tp>
__complex_tanh(const complex<_Tp>& __z)
{ return std::sinh(__z) / std::cosh(__z); }
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
__complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); }
inline __complex__ double
__complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); }
inline __complex__ long double
__complex_tanh(const __complex__ long double& __z)
{ return __builtin_ctanhl(__z); }
template<typename _Tp>
inline complex<_Tp>
tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); }
#else
template<typename _Tp>
inline complex<_Tp>
tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); }
#endif
// 26.2.8/9 pow(__x, __y): Returns the complex power base of __x
// raised to the __y-th power. The branch
// cut is on the negative axis.
template<typename _Tp>
inline complex<_Tp>
pow(const complex<_Tp>& __z, int __n)
{ return std::__pow_helper(__z, __n); }
template<typename _Tp>
complex<_Tp>
pow(const complex<_Tp>& __x, const _Tp& __y)
{
#ifndef _GLIBCXX_USE_C99_COMPLEX
if (__x == _Tp())
return _Tp();
#endif
if (__x.imag() == _Tp() && __x.real() > _Tp())
return pow(__x.real(), __y);
complex<_Tp> __t = std::log(__x);
return std::polar(exp(__y * __t.real()), __y * __t.imag());
}
template<typename _Tp>
inline complex<_Tp>
__complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
{ return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); }
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
__complex_pow(__complex__ float __x, __complex__ float __y)
{ return __builtin_cpowf(__x, __y); }
inline __complex__ double
__complex_pow(__complex__ double __x, __complex__ double __y)
{ return __builtin_cpow(__x, __y); }
inline __complex__ long double
__complex_pow(const __complex__ long double& __x,
const __complex__ long double& __y)
{ return __builtin_cpowl(__x, __y); }
template<typename _Tp>
inline complex<_Tp>
pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
{ return __complex_pow(__x.__rep(), __y.__rep()); }
#else
template<typename _Tp>
inline complex<_Tp>
pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
{ return __complex_pow(__x, __y); }
#endif
template<typename _Tp>
inline complex<_Tp>
pow(const _Tp& __x, const complex<_Tp>& __y)
{
return __x > _Tp() ? std::polar(pow(__x, __y.real()),
__y.imag() * log(__x))
: std::pow(complex<_Tp>(__x, _Tp()), __y);
}
// 26.2.3 complex specializations
// complex<float> specialization