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1// The template and inlines for the -*- C++ -*- complex number classes.
2
3// Copyright (C) 1997-2018 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/complex
26 * This is a Standard C++ Library header.
27 */
28
29//
30// ISO C++ 14882: 26.2 Complex Numbers
31// Note: this is not a conforming implementation.
32// Initially implemented by Ulrich Drepper <drepper@cygnus.com>
33// Improved by Gabriel Dos Reis <dosreis@cmla.ens-cachan.fr>
34//
35
36#ifndef _GLIBCXX_COMPLEX
37#define _GLIBCXX_COMPLEX 1
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#include <cmath>
45#include <sstream>
46
47// Get rid of a macro possibly defined in <complex.h>
48#undef complex
49
50namespace std _GLIBCXX_VISIBILITY(default)
51{
52_GLIBCXX_BEGIN_NAMESPACE_VERSION
53
54 /**
55 * @defgroup complex_numbers Complex Numbers
56 * @ingroup numerics
57 *
58 * Classes and functions for complex numbers.
59 * @{
60 */
61
62 // Forward declarations.
63 template<typename _Tp> class complex;
64 template<> class complex<float>;
65 template<> class complex<double>;
66 template<> class complex<long double>;
67
68 /// Return magnitude of @a z.
69 template<typename _Tp> _Tp abs(const complex<_Tp>&);
70 /// Return phase angle of @a z.
71 template<typename _Tp> _Tp arg(const complex<_Tp>&);
72 /// Return @a z magnitude squared.
73 template<typename _Tp> _Tp norm(const complex<_Tp>&);
74
75 /// Return complex conjugate of @a z.
76 template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&);
77 /// Return complex with magnitude @a rho and angle @a theta.
78 template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0);
79
80 // Transcendentals:
81 /// Return complex cosine of @a z.
82 template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&);
83 /// Return complex hyperbolic cosine of @a z.
84 template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&);
85 /// Return complex base e exponential of @a z.
86 template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&);
87 /// Return complex natural logarithm of @a z.
88 template<typename _Tp> complex<_Tp> log(const complex<_Tp>&);
89 /// Return complex base 10 logarithm of @a z.
90 template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&);
91 /// Return @a x to the @a y'th power.
92 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int);
93 /// Return @a x to the @a y'th power.
94 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&);
95 /// Return @a x to the @a y'th power.
96 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&,
97 const complex<_Tp>&);
98 /// Return @a x to the @a y'th power.
99 template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&);
100 /// Return complex sine of @a z.
101 template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&);
102 /// Return complex hyperbolic sine of @a z.
103 template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&);
104 /// Return complex square root of @a z.
105 template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&);
106 /// Return complex tangent of @a z.
107 template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&);
108 /// Return complex hyperbolic tangent of @a z.
109 template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&);
110
111
112 // 26.2.2 Primary template class complex
113 /**
114 * Template to represent complex numbers.
115 *
116 * Specializations for float, double, and long double are part of the
117 * library. Results with any other type are not guaranteed.
118 *
119 * @param Tp Type of real and imaginary values.
120 */
121 template<typename _Tp>
122 struct complex
123 {
124 /// Value typedef.
125 typedef _Tp value_type;
126
127 /// Default constructor. First parameter is x, second parameter is y.
128 /// Unspecified parameters default to 0.
129 _GLIBCXX_CONSTEXPR complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp())
130 : _M_real(__r), _M_imag(__i) { }
131
132 // Let the compiler synthesize the copy constructor
133#if __cplusplus >= 201103L
134 constexpr complex(const complex&) = default;
135#endif
136
137 /// Converting constructor.
138 template<typename _Up>
139 _GLIBCXX_CONSTEXPR complex(const complex<_Up>& __z)
140 : _M_real(__z.real()), _M_imag(__z.imag()) { }
141
142#if __cplusplus >= 201103L
143 // _GLIBCXX_RESOLVE_LIB_DEFECTS
144 // DR 387. std::complex over-encapsulated.
145 _GLIBCXX_ABI_TAG_CXX11
146 constexpr _Tp
147 real() const { return _M_real; }
148
149 _GLIBCXX_ABI_TAG_CXX11
150 constexpr _Tp
151 imag() const { return _M_imag; }
152#else
153 /// Return real part of complex number.
154 _Tp&
155 real() { return _M_real; }
156
157 /// Return real part of complex number.
158 const _Tp&
159 real() const { return _M_real; }
160
161 /// Return imaginary part of complex number.
162 _Tp&
163 imag() { return _M_imag; }
164
165 /// Return imaginary part of complex number.
166 const _Tp&
167 imag() const { return _M_imag; }
168#endif
169
170 // _GLIBCXX_RESOLVE_LIB_DEFECTS
171 // DR 387. std::complex over-encapsulated.
172 void
173 real(_Tp __val) { _M_real = __val; }
174
175 void
176 imag(_Tp __val) { _M_imag = __val; }
177
178 /// Assign a scalar to this complex number.
179 complex<_Tp>& operator=(const _Tp&);
180
181 /// Add a scalar to this complex number.
182 // 26.2.5/1
183 complex<_Tp>&
184 operator+=(const _Tp& __t)
185 {
186 _M_real += __t;
187 return *this;
188 }
189
190 /// Subtract a scalar from this complex number.
191 // 26.2.5/3
192 complex<_Tp>&
193 operator-=(const _Tp& __t)
194 {
195 _M_real -= __t;
196 return *this;
197 }
198
199 /// Multiply this complex number by a scalar.
200 complex<_Tp>& operator*=(const _Tp&);
201 /// Divide this complex number by a scalar.
202 complex<_Tp>& operator/=(const _Tp&);
203
204 // Let the compiler synthesize the copy assignment operator
205#if __cplusplus >= 201103L
206 complex& operator=(const complex&) = default;
207#endif
208
209 /// Assign another complex number to this one.
210 template<typename _Up>
211 complex<_Tp>& operator=(const complex<_Up>&);
212 /// Add another complex number to this one.
213 template<typename _Up>
214 complex<_Tp>& operator+=(const complex<_Up>&);
215 /// Subtract another complex number from this one.
216 template<typename _Up>
217 complex<_Tp>& operator-=(const complex<_Up>&);
218 /// Multiply this complex number by another.
219 template<typename _Up>
220 complex<_Tp>& operator*=(const complex<_Up>&);
221 /// Divide this complex number by another.
222 template<typename _Up>
223 complex<_Tp>& operator/=(const complex<_Up>&);
224
225 _GLIBCXX_CONSTEXPR complex __rep() const
226 { return *this; }
227
228 private:
229 _Tp _M_real;
230 _Tp _M_imag;
231 };
232
233 template<typename _Tp>
234 complex<_Tp>&
235 complex<_Tp>::operator=(const _Tp& __t)
236 {
237 _M_real = __t;
238 _M_imag = _Tp();
239 return *this;
240 }
241
242 // 26.2.5/5
243 template<typename _Tp>
244 complex<_Tp>&
245 complex<_Tp>::operator*=(const _Tp& __t)
246 {
247 _M_real *= __t;
248 _M_imag *= __t;
249 return *this;
250 }
251
252 // 26.2.5/7
253 template<typename _Tp>
254 complex<_Tp>&
255 complex<_Tp>::operator/=(const _Tp& __t)
256 {
257 _M_real /= __t;
258 _M_imag /= __t;
259 return *this;
260 }
261
262 template<typename _Tp>
263 template<typename _Up>
264 complex<_Tp>&
265 complex<_Tp>::operator=(const complex<_Up>& __z)
266 {
267 _M_real = __z.real();
268 _M_imag = __z.imag();
269 return *this;
270 }
271
272 // 26.2.5/9
273 template<typename _Tp>
274 template<typename _Up>
275 complex<_Tp>&
276 complex<_Tp>::operator+=(const complex<_Up>& __z)
277 {
278 _M_real += __z.real();
279 _M_imag += __z.imag();
280 return *this;
281 }
282
283 // 26.2.5/11
284 template<typename _Tp>
285 template<typename _Up>
286 complex<_Tp>&
287 complex<_Tp>::operator-=(const complex<_Up>& __z)
288 {
289 _M_real -= __z.real();
290 _M_imag -= __z.imag();
291 return *this;
292 }
293
294 // 26.2.5/13
295 // XXX: This is a grammar school implementation.
296 template<typename _Tp>
297 template<typename _Up>
298 complex<_Tp>&
299 complex<_Tp>::operator*=(const complex<_Up>& __z)
300 {
301 const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag();
302 _M_imag = _M_real * __z.imag() + _M_imag * __z.real();
303 _M_real = __r;
304 return *this;
305 }
306
307 // 26.2.5/15
308 // XXX: This is a grammar school implementation.
309 template<typename _Tp>
310 template<typename _Up>
311 complex<_Tp>&
312 complex<_Tp>::operator/=(const complex<_Up>& __z)
313 {
314 const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag();
315 const _Tp __n = std::norm(__z);
316 _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n;
317 _M_real = __r / __n;
318 return *this;
319 }
320
321 // Operators:
322 //@{
323 /// Return new complex value @a x plus @a y.
324 template<typename _Tp>
325 inline complex<_Tp>
326 operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
327 {
328 complex<_Tp> __r = __x;
329 __r += __y;
330 return __r;
331 }
332
333 template<typename _Tp>
334 inline complex<_Tp>
335 operator+(const complex<_Tp>& __x, const _Tp& __y)
336 {
337 complex<_Tp> __r = __x;
338 __r += __y;
339 return __r;
340 }
341
342 template<typename _Tp>
343 inline complex<_Tp>
344 operator+(const _Tp& __x, const complex<_Tp>& __y)
345 {
346 complex<_Tp> __r = __y;
347 __r += __x;
348 return __r;
349 }
350 //@}
351
352 //@{
353 /// Return new complex value @a x minus @a y.
354 template<typename _Tp>
355 inline complex<_Tp>
356 operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
357 {
358 complex<_Tp> __r = __x;
359 __r -= __y;
360 return __r;
361 }
362
363 template<typename _Tp>
364 inline complex<_Tp>
365 operator-(const complex<_Tp>& __x, const _Tp& __y)
366 {
367 complex<_Tp> __r = __x;
368 __r -= __y;
369 return __r;
370 }
371
372 template<typename _Tp>
373 inline complex<_Tp>
374 operator-(const _Tp& __x, const complex<_Tp>& __y)
375 {
376 complex<_Tp> __r(__x, -__y.imag());
377 __r -= __y.real();
378 return __r;
379 }
380 //@}
381
382 //@{
383 /// Return new complex value @a x times @a y.
384 template<typename _Tp>
385 inline complex<_Tp>
386 operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
387 {
388 complex<_Tp> __r = __x;
389 __r *= __y;
390 return __r;
391 }
392
393 template<typename _Tp>
394 inline complex<_Tp>
395 operator*(const complex<_Tp>& __x, const _Tp& __y)
396 {
397 complex<_Tp> __r = __x;
398 __r *= __y;
399 return __r;
400 }
401
402 template<typename _Tp>
403 inline complex<_Tp>
404 operator*(const _Tp& __x, const complex<_Tp>& __y)
405 {
406 complex<_Tp> __r = __y;
407 __r *= __x;
408 return __r;
409 }
410 //@}
411
412 //@{
413 /// Return new complex value @a x divided by @a y.
414 template<typename _Tp>
415 inline complex<_Tp>
416 operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
417 {
418 complex<_Tp> __r = __x;
419 __r /= __y;
420 return __r;
421 }
422
423 template<typename _Tp>
424 inline complex<_Tp>
425 operator/(const complex<_Tp>& __x, const _Tp& __y)
426 {
427 complex<_Tp> __r = __x;
428 __r /= __y;
429 return __r;
430 }
431
432 template<typename _Tp>
433 inline complex<_Tp>
434 operator/(const _Tp& __x, const complex<_Tp>& __y)
435 {
436 complex<_Tp> __r = __x;
437 __r /= __y;
438 return __r;
439 }
440 //@}
441
442 /// Return @a x.
443 template<typename _Tp>
444 inline complex<_Tp>
445 operator+(const complex<_Tp>& __x)
446 { return __x; }
447
448 /// Return complex negation of @a x.
449 template<typename _Tp>
450 inline complex<_Tp>
451 operator-(const complex<_Tp>& __x)
452 { return complex<_Tp>(-__x.real(), -__x.imag()); }
453
454 //@{
455 /// Return true if @a x is equal to @a y.
456 template<typename _Tp>
457 inline _GLIBCXX_CONSTEXPR bool
458 operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
459 { return __x.real() == __y.real() && __x.imag() == __y.imag(); }
460
461 template<typename _Tp>
462 inline _GLIBCXX_CONSTEXPR bool
463 operator==(const complex<_Tp>& __x, const _Tp& __y)
464 { return __x.real() == __y && __x.imag() == _Tp(); }
465
466 template<typename _Tp>
467 inline _GLIBCXX_CONSTEXPR bool
468 operator==(const _Tp& __x, const complex<_Tp>& __y)
469 { return __x == __y.real() && _Tp() == __y.imag(); }
470 //@}
471
472 //@{
473 /// Return false if @a x is equal to @a y.
474 template<typename _Tp>
475 inline _GLIBCXX_CONSTEXPR bool
476 operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
477 { return __x.real() != __y.real() || __x.imag() != __y.imag(); }
478
479 template<typename _Tp>
480 inline _GLIBCXX_CONSTEXPR bool
481 operator!=(const complex<_Tp>& __x, const _Tp& __y)
482 { return __x.real() != __y || __x.imag() != _Tp(); }
483
484 template<typename _Tp>
485 inline _GLIBCXX_CONSTEXPR bool
486 operator!=(const _Tp& __x, const complex<_Tp>& __y)
487 { return __x != __y.real() || _Tp() != __y.imag(); }
488 //@}
489
490 /// Extraction operator for complex values.
491 template<typename _Tp, typename _CharT, class _Traits>
492 basic_istream<_CharT, _Traits>&
493 operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
494 {
495 bool __fail = true;
496 _CharT __ch;
497 if (__is >> __ch)
498 {
499 if (_Traits::eq(__ch, __is.widen('(')))
500 {
501 _Tp __u;
502 if (__is >> __u >> __ch)
503 {
504 const _CharT __rparen = __is.widen(')');
505 if (_Traits::eq(__ch, __rparen))
506 {
507 __x = __u;
508 __fail = false;
509 }
510 else if (_Traits::eq(__ch, __is.widen(',')))
511 {
512 _Tp __v;
513 if (__is >> __v >> __ch)
514 {
515 if (_Traits::eq(__ch, __rparen))
516 {
517 __x = complex<_Tp>(__u, __v);
518 __fail = false;
519 }
520 else
521 __is.putback(__ch);
522 }
523 }
524 else
525 __is.putback(__ch);
526 }
527 }
528 else
529 {
530 __is.putback(__ch);
531 _Tp __u;
532 if (__is >> __u)
533 {
534 __x = __u;
535 __fail = false;
536 }
537 }
538 }
539 if (__fail)
540 __is.setstate(ios_base::failbit);
541 return __is;
542 }
543
544 /// Insertion operator for complex values.
545 template<typename _Tp, typename _CharT, class _Traits>
546 basic_ostream<_CharT, _Traits>&
547 operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
548 {
549 basic_ostringstream<_CharT, _Traits> __s;
550 __s.flags(__os.flags());
551 __s.imbue(__os.getloc());
552 __s.precision(__os.precision());
553 __s << '(' << __x.real() << ',' << __x.imag() << ')';
554 return __os << __s.str();
555 }
556
557 // Values
558#if __cplusplus >= 201103L
559 template<typename _Tp>
560 constexpr _Tp
561 real(const complex<_Tp>& __z)
562 { return __z.real(); }
563
564 template<typename _Tp>
565 constexpr _Tp
566 imag(const complex<_Tp>& __z)
567 { return __z.imag(); }
568#else
569 template<typename _Tp>
570 inline _Tp&
571 real(complex<_Tp>& __z)
572 { return __z.real(); }
573
574 template<typename _Tp>
575 inline const _Tp&
576 real(const complex<_Tp>& __z)
577 { return __z.real(); }
578
579 template<typename _Tp>
580 inline _Tp&
581 imag(complex<_Tp>& __z)
582 { return __z.imag(); }
583
584 template<typename _Tp>
585 inline const _Tp&
586 imag(const complex<_Tp>& __z)
587 { return __z.imag(); }
588#endif
589
590 // 26.2.7/3 abs(__z): Returns the magnitude of __z.
591 template<typename _Tp>
592 inline _Tp
593 __complex_abs(const complex<_Tp>& __z)
594 {
595 _Tp __x = __z.real();
596 _Tp __y = __z.imag();
597 const _Tp __s = std::max(abs(__x), abs(__y));
598 if (__s == _Tp()) // well ...
599 return __s;
600 __x /= __s;
601 __y /= __s;
602 return __s * sqrt(__x * __x + __y * __y);
603 }
604
605#if _GLIBCXX_USE_C99_COMPLEX
606 inline float
607 __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); }
608
609 inline double
610 __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); }
611
612 inline long double
613 __complex_abs(const __complex__ long double& __z)
614 { return __builtin_cabsl(__z); }
615
616 template<typename _Tp>
617 inline _Tp
618 abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); }
619#else
620 template<typename _Tp>
621 inline _Tp
622 abs(const complex<_Tp>& __z) { return __complex_abs(__z); }
623#endif
624
625
626 // 26.2.7/4: arg(__z): Returns the phase angle of __z.
627 template<typename _Tp>
628 inline _Tp
629 __complex_arg(const complex<_Tp>& __z)
630 { return atan2(__z.imag(), __z.real()); }
631
632#if _GLIBCXX_USE_C99_COMPLEX
633 inline float
634 __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); }
635
636 inline double
637 __complex_arg(__complex__ double __z) { return __builtin_carg(__z); }
638
639 inline long double
640 __complex_arg(const __complex__ long double& __z)
641 { return __builtin_cargl(__z); }
642
643 template<typename _Tp>
644 inline _Tp
645 arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); }
646#else
647 template<typename _Tp>
648 inline _Tp
649 arg(const complex<_Tp>& __z) { return __complex_arg(__z); }
650#endif
651
652 // 26.2.7/5: norm(__z) returns the squared magnitude of __z.
653 // As defined, norm() is -not- a norm is the common mathematical
654 // sense used in numerics. The helper class _Norm_helper<> tries to
655 // distinguish between builtin floating point and the rest, so as
656 // to deliver an answer as close as possible to the real value.
657 template<bool>
658 struct _Norm_helper
659 {
660 template<typename _Tp>
661 static inline _Tp _S_do_it(const complex<_Tp>& __z)
662 {
663 const _Tp __x = __z.real();
664 const _Tp __y = __z.imag();
665 return __x * __x + __y * __y;
666 }
667 };
668
669 template<>
670 struct _Norm_helper<true>
671 {
672 template<typename _Tp>
673 static inline _Tp _S_do_it(const complex<_Tp>& __z)
674 {
675 _Tp __res = std::abs(__z);
676 return __res * __res;
677 }
678 };
679
680 template<typename _Tp>
681 inline _Tp
682 norm(const complex<_Tp>& __z)
683 {
684 return _Norm_helper<__is_floating<_Tp>::__value
685 && !_GLIBCXX_FAST_MATH>::_S_do_it(__z);
686 }
687
688 template<typename _Tp>
689 inline complex<_Tp>
690 polar(const _Tp& __rho, const _Tp& __theta)
691 {
692 __glibcxx_assert( __rho >= 0 );
693 return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta));
694 }
695
696 template<typename _Tp>
697 inline complex<_Tp>
698 conj(const complex<_Tp>& __z)
699 { return complex<_Tp>(__z.real(), -__z.imag()); }
700
701 // Transcendentals
702
703 // 26.2.8/1 cos(__z): Returns the cosine of __z.
704 template<typename _Tp>
705 inline complex<_Tp>
706 __complex_cos(const complex<_Tp>& __z)
707 {
708 const _Tp __x = __z.real();
709 const _Tp __y = __z.imag();
710 return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y));
711 }
712
713#if _GLIBCXX_USE_C99_COMPLEX
714 inline __complex__ float
715 __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); }
716
717 inline __complex__ double
718 __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); }
719
720 inline __complex__ long double
721 __complex_cos(const __complex__ long double& __z)
722 { return __builtin_ccosl(__z); }
723
724 template<typename _Tp>
725 inline complex<_Tp>
726 cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); }
727#else
728 template<typename _Tp>
729 inline complex<_Tp>
730 cos(const complex<_Tp>& __z) { return __complex_cos(__z); }
731#endif
732
733 // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z.
734 template<typename _Tp>
735 inline complex<_Tp>
736 __complex_cosh(const complex<_Tp>& __z)
737 {
738 const _Tp __x = __z.real();
739 const _Tp __y = __z.imag();
740 return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y));
741 }
742
743#if _GLIBCXX_USE_C99_COMPLEX
744 inline __complex__ float
745 __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); }
746
747 inline __complex__ double
748 __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); }
749
750 inline __complex__ long double
751 __complex_cosh(const __complex__ long double& __z)
752 { return __builtin_ccoshl(__z); }
753
754 template<typename _Tp>
755 inline complex<_Tp>
756 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); }
757#else
758 template<typename _Tp>
759 inline complex<_Tp>
760 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); }
761#endif
762
763 // 26.2.8/3 exp(__z): Returns the complex base e exponential of x
764 template<typename _Tp>
765 inline complex<_Tp>
766 __complex_exp(const complex<_Tp>& __z)
767 { return std::polar<_Tp>(exp(__z.real()), __z.imag()); }
768
769#if _GLIBCXX_USE_C99_COMPLEX
770 inline __complex__ float
771 __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); }
772
773 inline __complex__ double
774 __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); }
775
776 inline __complex__ long double
777 __complex_exp(const __complex__ long double& __z)
778 { return __builtin_cexpl(__z); }
779
780 template<typename _Tp>
781 inline complex<_Tp>
782 exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); }
783#else
784 template<typename _Tp>
785 inline complex<_Tp>
786 exp(const complex<_Tp>& __z) { return __complex_exp(__z); }
787#endif
788
789 // 26.2.8/5 log(__z): Returns the natural complex logarithm of __z.
790 // The branch cut is along the negative axis.
791 template<typename _Tp>
792 inline complex<_Tp>
793 __complex_log(const complex<_Tp>& __z)
794 { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); }
795
796#if _GLIBCXX_USE_C99_COMPLEX
797 inline __complex__ float
798 __complex_log(__complex__ float __z) { return __builtin_clogf(__z); }
799
800 inline __complex__ double
801 __complex_log(__complex__ double __z) { return __builtin_clog(__z); }
802
803 inline __complex__ long double
804 __complex_log(const __complex__ long double& __z)
805 { return __builtin_clogl(__z); }
806
807 template<typename _Tp>
808 inline complex<_Tp>
809 log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); }
810#else
811 template<typename _Tp>
812 inline complex<_Tp>
813 log(const complex<_Tp>& __z) { return __complex_log(__z); }
814#endif
815
816 template<typename _Tp>
817 inline complex<_Tp>
818 log10(const complex<_Tp>& __z)
819 { return std::log(__z) / log(_Tp(10.0)); }
820
821 // 26.2.8/10 sin(__z): Returns the sine of __z.
822 template<typename _Tp>
823 inline complex<_Tp>
824 __complex_sin(const complex<_Tp>& __z)
825 {
826 const _Tp __x = __z.real();
827 const _Tp __y = __z.imag();
828 return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y));
829 }
830
831#if _GLIBCXX_USE_C99_COMPLEX
832 inline __complex__ float
833 __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); }
834
835 inline __complex__ double
836 __complex_sin(__complex__ double __z) { return __builtin_csin(__z); }
837
838 inline __complex__ long double
839 __complex_sin(const __complex__ long double& __z)
840 { return __builtin_csinl(__z); }
841
842 template<typename _Tp>
843 inline complex<_Tp>
844 sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); }
845#else
846 template<typename _Tp>
847 inline complex<_Tp>
848 sin(const complex<_Tp>& __z) { return __complex_sin(__z); }
849#endif
850
851 // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z.
852 template<typename _Tp>
853 inline complex<_Tp>
854 __complex_sinh(const complex<_Tp>& __z)
855 {
856 const _Tp __x = __z.real();
857 const _Tp __y = __z.imag();
858 return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y));
859 }
860
861#if _GLIBCXX_USE_C99_COMPLEX
862 inline __complex__ float
863 __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); }
864
865 inline __complex__ double
866 __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); }
867
868 inline __complex__ long double
869 __complex_sinh(const __complex__ long double& __z)
870 { return __builtin_csinhl(__z); }
871
872 template<typename _Tp>
873 inline complex<_Tp>
874 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); }
875#else
876 template<typename _Tp>
877 inline complex<_Tp>
878 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); }
879#endif
880
881 // 26.2.8/13 sqrt(__z): Returns the complex square root of __z.
882 // The branch cut is on the negative axis.
883 template<typename _Tp>
884 complex<_Tp>
885 __complex_sqrt(const complex<_Tp>& __z)
886 {
887 _Tp __x = __z.real();
888 _Tp __y = __z.imag();
889
890 if (__x == _Tp())
891 {
892 _Tp __t = sqrt(abs(__y) / 2);
893 return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
894 }
895 else
896 {
897 _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x)));
898 _Tp __u = __t / 2;
899 return __x > _Tp()
900 ? complex<_Tp>(__u, __y / __t)
901 : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u);
902 }
903 }
904
905#if _GLIBCXX_USE_C99_COMPLEX
906 inline __complex__ float
907 __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); }
908
909 inline __complex__ double
910 __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); }
911
912 inline __complex__ long double
913 __complex_sqrt(const __complex__ long double& __z)
914 { return __builtin_csqrtl(__z); }
915
916 template<typename _Tp>
917 inline complex<_Tp>
918 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); }
919#else
920 template<typename _Tp>
921 inline complex<_Tp>
922 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); }
923#endif
924
925 // 26.2.8/14 tan(__z): Return the complex tangent of __z.
926
927 template<typename _Tp>
928 inline complex<_Tp>
929 __complex_tan(const complex<_Tp>& __z)
930 { return std::sin(__z) / std::cos(__z); }
931
932#if _GLIBCXX_USE_C99_COMPLEX
933 inline __complex__ float
934 __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); }
935
936 inline __complex__ double
937 __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); }
938
939 inline __complex__ long double
940 __complex_tan(const __complex__ long double& __z)
941 { return __builtin_ctanl(__z); }
942
943 template<typename _Tp>
944 inline complex<_Tp>
945 tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); }
946#else
947 template<typename _Tp>
948 inline complex<_Tp>
949 tan(const complex<_Tp>& __z) { return __complex_tan(__z); }
950#endif
951
952
953 // 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z.
954
955 template<typename _Tp>
956 inline complex<_Tp>
957 __complex_tanh(const complex<_Tp>& __z)
958 { return std::sinh(__z) / std::cosh(__z); }
959
960#if _GLIBCXX_USE_C99_COMPLEX
961 inline __complex__ float
962 __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); }
963
964 inline __complex__ double
965 __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); }
966
967 inline __complex__ long double
968 __complex_tanh(const __complex__ long double& __z)
969 { return __builtin_ctanhl(__z); }
970
971 template<typename _Tp>
972 inline complex<_Tp>
973 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); }
974#else
975 template<typename _Tp>
976 inline complex<_Tp>
977 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); }
978#endif
979
980
981 // 26.2.8/9 pow(__x, __y): Returns the complex power base of __x
982 // raised to the __y-th power. The branch
983 // cut is on the negative axis.
984 template<typename _Tp>
985 complex<_Tp>
986 __complex_pow_unsigned(complex<_Tp> __x, unsigned __n)
987 {
988 complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1);
989
990 while (__n >>= 1)
991 {
992 __x *= __x;
993 if (__n % 2)
994 __y *= __x;
995 }
996
997 return __y;
998 }
999
1000 // In C++11 mode we used to implement the resolution of
1001 // DR 844. complex pow return type is ambiguous.
1002 // thus the following overload was disabled in that mode. However, doing
1003 // that causes all sorts of issues, see, for example:
1004 // http://gcc.gnu.org/ml/libstdc++/2013-01/msg00058.html
1005 // and also PR57974.
1006 template<typename _Tp>
1007 inline complex<_Tp>
1008 pow(const complex<_Tp>& __z, int __n)
1009 {
1010 return __n < 0
1011 ? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -(unsigned)__n)
1012 : std::__complex_pow_unsigned(__z, __n);
1013 }
1014
1015 template<typename _Tp>
1016 complex<_Tp>
1017 pow(const complex<_Tp>& __x, const _Tp& __y)
1018 {
1019#if ! _GLIBCXX_USE_C99_COMPLEX
1020 if (__x == _Tp())
1021 return _Tp();
1022#endif
1023 if (__x.imag() == _Tp() && __x.real() > _Tp())
1024 return pow(__x.real(), __y);
1025
1026 complex<_Tp> __t = std::log(__x);
1027 return std::polar<_Tp>(exp(__y * __t.real()), __y * __t.imag());
1028 }
1029
1030 template<typename _Tp>
1031 inline complex<_Tp>
1032 __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1033 { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); }
1034
1035#if _GLIBCXX_USE_C99_COMPLEX
1036 inline __complex__ float
1037 __complex_pow(__complex__ float __x, __complex__ float __y)
1038 { return __builtin_cpowf(__x, __y); }
1039
1040 inline __complex__ double
1041 __complex_pow(__complex__ double __x, __complex__ double __y)
1042 { return __builtin_cpow(__x, __y); }
1043
1044 inline __complex__ long double
1045 __complex_pow(const __complex__ long double& __x,
1046 const __complex__ long double& __y)
1047 { return __builtin_cpowl(__x, __y); }
1048
1049 template<typename _Tp>
1050 inline complex<_Tp>
1051 pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1052 { return __complex_pow(__x.__rep(), __y.__rep()); }
1053#else
1054 template<typename _Tp>
1055 inline complex<_Tp>
1056 pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1057 { return __complex_pow(__x, __y); }
1058#endif
1059
1060 template<typename _Tp>
1061 inline complex<_Tp>
1062 pow(const _Tp& __x, const complex<_Tp>& __y)
1063 {
1064 return __x > _Tp() ? std::polar<_Tp>(pow(__x, __y.real()),
1065 __y.imag() * log(__x))
1066 : std::pow(complex<_Tp>(__x), __y);
1067 }
1068
1069 /// 26.2.3 complex specializations
1070 /// complex<float> specialization
1071 template<>
1072 struct complex<float>
1073 {
1074 typedef float value_type;
1075 typedef __complex__ float _ComplexT;
1076
1077 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
1078
1079 _GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f)
1080#if __cplusplus >= 201103L
1081 : _M_value{ __r, __i } { }
1082#else
1083 {
1084 __real__ _M_value = __r;
1085 __imag__ _M_value = __i;
1086 }
1087#endif
1088
1089 explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&);
1090 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&);
1091
1092#if __cplusplus >= 201103L
1093 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1094 // DR 387. std::complex over-encapsulated.
1095 __attribute ((__abi_tag__ ("cxx11")))
1096 constexpr float
1097 real() const { return __real__ _M_value; }
1098
1099 __attribute ((__abi_tag__ ("cxx11")))
1100 constexpr float
1101 imag() const { return __imag__ _M_value; }
1102#else
1103 float&
1104 real() { return __real__ _M_value; }
1105
1106 const float&
1107 real() const { return __real__ _M_value; }
1108
1109 float&
1110 imag() { return __imag__ _M_value; }
1111
1112 const float&
1113 imag() const { return __imag__ _M_value; }
1114#endif
1115
1116 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1117 // DR 387. std::complex over-encapsulated.
1118 void
1119 real(float __val) { __real__ _M_value = __val; }
1120
1121 void
1122 imag(float __val) { __imag__ _M_value = __val; }
1123
1124 complex&
1125 operator=(float __f)
1126 {
1127 _M_value = __f;
1128 return *this;
1129 }
1130
1131 complex&
1132 operator+=(float __f)
1133 {
1134 _M_value += __f;
1135 return *this;
1136 }
1137
1138 complex&
1139 operator-=(float __f)
1140 {
1141 _M_value -= __f;
1142 return *this;
1143 }
1144
1145 complex&
1146 operator*=(float __f)
1147 {
1148 _M_value *= __f;
1149 return *this;
1150 }
1151
1152 complex&
1153 operator/=(float __f)
1154 {
1155 _M_value /= __f;
1156 return *this;
1157 }
1158
1159 // Let the compiler synthesize the copy and assignment
1160 // operator. It always does a pretty good job.
1161 // complex& operator=(const complex&);
1162
1163 template<typename _Tp>
1164 complex&
1165 operator=(const complex<_Tp>& __z)
1166 {
1167 __real__ _M_value = __z.real();
1168 __imag__ _M_value = __z.imag();
1169 return *this;
1170 }
1171
1172 template<typename _Tp>
1173 complex&
1174 operator+=(const complex<_Tp>& __z)
1175 {
1176 __real__ _M_value += __z.real();
1177 __imag__ _M_value += __z.imag();
1178 return *this;
1179 }
1180
1181 template<class _Tp>
1182 complex&
1183 operator-=(const complex<_Tp>& __z)
1184 {
1185 __real__ _M_value -= __z.real();
1186 __imag__ _M_value -= __z.imag();
1187 return *this;
1188 }
1189
1190 template<class _Tp>
1191 complex&
1192 operator*=(const complex<_Tp>& __z)
1193 {
1194 _ComplexT __t;
1195 __real__ __t = __z.real();
1196 __imag__ __t = __z.imag();
1197 _M_value *= __t;
1198 return *this;
1199 }
1200
1201 template<class _Tp>
1202 complex&
1203 operator/=(const complex<_Tp>& __z)
1204 {
1205 _ComplexT __t;
1206 __real__ __t = __z.real();
1207 __imag__ __t = __z.imag();
1208 _M_value /= __t;
1209 return *this;
1210 }
1211
1212 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
1213
1214 private:
1215 _ComplexT _M_value;
1216 };
1217
1218 /// 26.2.3 complex specializations
1219 /// complex<double> specialization
1220 template<>
1221 struct complex<double>
1222 {
1223 typedef double value_type;
1224 typedef __complex__ double _ComplexT;
1225
1226 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
1227
1228 _GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0)
1229#if __cplusplus >= 201103L
1230 : _M_value{ __r, __i } { }
1231#else
1232 {
1233 __real__ _M_value = __r;
1234 __imag__ _M_value = __i;
1235 }
1236#endif
1237
1238 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
1239 : _M_value(__z.__rep()) { }
1240
1241 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&);
1242
1243#if __cplusplus >= 201103L
1244 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1245 // DR 387. std::complex over-encapsulated.
1246 __attribute ((__abi_tag__ ("cxx11")))
1247 constexpr double
1248 real() const { return __real__ _M_value; }
1249
1250 __attribute ((__abi_tag__ ("cxx11")))
1251 constexpr double
1252 imag() const { return __imag__ _M_value; }
1253#else
1254 double&
1255 real() { return __real__ _M_value; }
1256
1257 const double&
1258 real() const { return __real__ _M_value; }
1259
1260 double&
1261 imag() { return __imag__ _M_value; }
1262
1263 const double&
1264 imag() const { return __imag__ _M_value; }
1265#endif
1266
1267 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1268 // DR 387. std::complex over-encapsulated.
1269 void
1270 real(double __val) { __real__ _M_value = __val; }
1271
1272 void
1273 imag(double __val) { __imag__ _M_value = __val; }
1274
1275 complex&
1276 operator=(double __d)
1277 {
1278 _M_value = __d;
1279 return *this;
1280 }
1281
1282 complex&
1283 operator+=(double __d)
1284 {
1285 _M_value += __d;
1286 return *this;
1287 }
1288
1289 complex&
1290 operator-=(double __d)
1291 {
1292 _M_value -= __d;
1293 return *this;
1294 }
1295
1296 complex&
1297 operator*=(double __d)
1298 {
1299 _M_value *= __d;
1300 return *this;
1301 }
1302
1303 complex&
1304 operator/=(double __d)
1305 {
1306 _M_value /= __d;
1307 return *this;
1308 }
1309
1310 // The compiler will synthesize this, efficiently.
1311 // complex& operator=(const complex&);
1312
1313 template<typename _Tp>
1314 complex&
1315 operator=(const complex<_Tp>& __z)
1316 {
1317 __real__ _M_value = __z.real();
1318 __imag__ _M_value = __z.imag();
1319 return *this;
1320 }
1321
1322 template<typename _Tp>
1323 complex&
1324 operator+=(const complex<_Tp>& __z)
1325 {
1326 __real__ _M_value += __z.real();
1327 __imag__ _M_value += __z.imag();
1328 return *this;
1329 }
1330
1331 template<typename _Tp>
1332 complex&
1333 operator-=(const complex<_Tp>& __z)
1334 {
1335 __real__ _M_value -= __z.real();
1336 __imag__ _M_value -= __z.imag();
1337 return *this;
1338 }
1339
1340 template<typename _Tp>
1341 complex&
1342 operator*=(const complex<_Tp>& __z)
1343 {
1344 _ComplexT __t;
1345 __real__ __t = __z.real();
1346 __imag__ __t = __z.imag();
1347 _M_value *= __t;
1348 return *this;
1349 }
1350
1351 template<typename _Tp>
1352 complex&
1353 operator/=(const complex<_Tp>& __z)
1354 {
1355 _ComplexT __t;
1356 __real__ __t = __z.real();
1357 __imag__ __t = __z.imag();
1358 _M_value /= __t;
1359 return *this;
1360 }
1361
1362 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
1363
1364 private:
1365 _ComplexT _M_value;
1366 };
1367
1368 /// 26.2.3 complex specializations
1369 /// complex<long double> specialization
1370 template<>
1371 struct complex<long double>
1372 {
1373 typedef long double value_type;
1374 typedef __complex__ long double _ComplexT;
1375
1376 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
1377
1378 _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L,
1379 long double __i = 0.0L)
1380#if __cplusplus >= 201103L
1381 : _M_value{ __r, __i } { }
1382#else
1383 {
1384 __real__ _M_value = __r;
1385 __imag__ _M_value = __i;
1386 }
1387#endif
1388
1389 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
1390 : _M_value(__z.__rep()) { }
1391
1392 _GLIBCXX_CONSTEXPR complex(const complex<double>& __z)
1393 : _M_value(__z.__rep()) { }
1394
1395#if __cplusplus >= 201103L
1396 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1397 // DR 387. std::complex over-encapsulated.
1398 __attribute ((__abi_tag__ ("cxx11")))
1399 constexpr long double
1400 real() const { return __real__ _M_value; }
1401
1402 __attribute ((__abi_tag__ ("cxx11")))
1403 constexpr long double
1404 imag() const { return __imag__ _M_value; }
1405#else
1406 long double&
1407 real() { return __real__ _M_value; }
1408
1409 const long double&
1410 real() const { return __real__ _M_value; }
1411
1412 long double&
1413 imag() { return __imag__ _M_value; }
1414
1415 const long double&
1416 imag() const { return __imag__ _M_value; }
1417#endif
1418
1419 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1420 // DR 387. std::complex over-encapsulated.
1421 void
1422 real(long double __val) { __real__ _M_value = __val; }
1423
1424 void
1425 imag(long double __val) { __imag__ _M_value = __val; }
1426
1427 complex&
1428 operator=(long double __r)
1429 {
1430 _M_value = __r;
1431 return *this;
1432 }
1433
1434 complex&
1435 operator+=(long double __r)
1436 {
1437 _M_value += __r;
1438 return *this;
1439 }
1440
1441 complex&
1442 operator-=(long double __r)
1443 {
1444 _M_value -= __r;
1445 return *this;
1446 }
1447
1448 complex&
1449 operator*=(long double __r)
1450 {
1451 _M_value *= __r;
1452 return *this;
1453 }
1454
1455 complex&
1456 operator/=(long double __r)
1457 {
1458 _M_value /= __r;
1459 return *this;
1460 }
1461
1462 // The compiler knows how to do this efficiently
1463 // complex& operator=(const complex&);
1464
1465 template<typename _Tp>
1466 complex&
1467 operator=(const complex<_Tp>& __z)
1468 {
1469 __real__ _M_value = __z.real();
1470 __imag__ _M_value = __z.imag();
1471 return *this;
1472 }
1473
1474 template<typename _Tp>
1475 complex&
1476 operator+=(const complex<_Tp>& __z)
1477 {
1478 __real__ _M_value += __z.real();
1479 __imag__ _M_value += __z.imag();
1480 return *this;
1481 }
1482
1483 template<typename _Tp>
1484 complex&
1485 operator-=(const complex<_Tp>& __z)
1486 {
1487 __real__ _M_value -= __z.real();
1488 __imag__ _M_value -= __z.imag();
1489 return *this;
1490 }
1491
1492 template<typename _Tp>
1493 complex&
1494 operator*=(const complex<_Tp>& __z)
1495 {
1496 _ComplexT __t;
1497 __real__ __t = __z.real();
1498 __imag__ __t = __z.imag();
1499 _M_value *= __t;
1500 return *this;
1501 }
1502
1503 template<typename _Tp>
1504 complex&
1505 operator/=(const complex<_Tp>& __z)
1506 {
1507 _ComplexT __t;
1508 __real__ __t = __z.real();
1509 __imag__ __t = __z.imag();
1510 _M_value /= __t;
1511 return *this;
1512 }
1513
1514 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
1515
1516 private:
1517 _ComplexT _M_value;
1518 };
1519
1520 // These bits have to be at the end of this file, so that the
1521 // specializations have all been defined.
1522 inline _GLIBCXX_CONSTEXPR
1523 complex<float>::complex(const complex<double>& __z)
1524 : _M_value(__z.__rep()) { }
1525
1526 inline _GLIBCXX_CONSTEXPR
1527 complex<float>::complex(const complex<long double>& __z)
1528 : _M_value(__z.__rep()) { }
1529
1530 inline _GLIBCXX_CONSTEXPR
1531 complex<double>::complex(const complex<long double>& __z)
1532 : _M_value(__z.__rep()) { }
1533
1534 // Inhibit implicit instantiations for required instantiations,
1535 // which are defined via explicit instantiations elsewhere.
1536 // NB: This syntax is a GNU extension.
1537#if _GLIBCXX_EXTERN_TEMPLATE
1538 extern template istream& operator>>(istream&, complex<float>&);
1539 extern template ostream& operator<<(ostream&, const complex<float>&);
1540 extern template istream& operator>>(istream&, complex<double>&);
1541 extern template ostream& operator<<(ostream&, const complex<double>&);
1542 extern template istream& operator>>(istream&, complex<long double>&);
1543 extern template ostream& operator<<(ostream&, const complex<long double>&);
1544
1545#ifdef _GLIBCXX_USE_WCHAR_T
1546 extern template wistream& operator>>(wistream&, complex<float>&);
1547 extern template wostream& operator<<(wostream&, const complex<float>&);
1548 extern template wistream& operator>>(wistream&, complex<double>&);
1549 extern template wostream& operator<<(wostream&, const complex<double>&);
1550 extern template wistream& operator>>(wistream&, complex<long double>&);
1551 extern template wostream& operator<<(wostream&, const complex<long double>&);
1552#endif
1553#endif
1554
1555 // @} group complex_numbers
1556
1557_GLIBCXX_END_NAMESPACE_VERSION
1558} // namespace
1559
1560namespace __gnu_cxx _GLIBCXX_VISIBILITY(default)
1561{
1562_GLIBCXX_BEGIN_NAMESPACE_VERSION
1563
1564 // See ext/type_traits.h for the primary template.
1565 template<typename _Tp, typename _Up>
1566 struct __promote_2<std::complex<_Tp>, _Up>
1567 {
1568 public:
1569 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
1570 };
1571
1572 template<typename _Tp, typename _Up>
1573 struct __promote_2<_Tp, std::complex<_Up> >
1574 {
1575 public:
1576 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
1577 };
1578
1579 template<typename _Tp, typename _Up>
1580 struct __promote_2<std::complex<_Tp>, std::complex<_Up> >
1581 {
1582 public:
1583 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
1584 };
1585
1586_GLIBCXX_END_NAMESPACE_VERSION
1587} // namespace
1588
1589#if __cplusplus >= 201103L
1590
1591namespace std _GLIBCXX_VISIBILITY(default)
1592{
1593_GLIBCXX_BEGIN_NAMESPACE_VERSION
1594
1595 // Forward declarations.
1596 template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&);
1597 template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&);
1598 template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&);
1599
1600 template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&);
1601 template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&);
1602 template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&);
1603 // DR 595.
1604 template<typename _Tp> _Tp fabs(const std::complex<_Tp>&);
1605
1606 template<typename _Tp>
1607 inline std::complex<_Tp>
1608 __complex_acos(const std::complex<_Tp>& __z)
1609 {
1610 const std::complex<_Tp> __t = std::asin(__z);
1611 const _Tp __pi_2 = 1.5707963267948966192313216916397514L;
1612 return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag());
1613 }
1614
1615#if _GLIBCXX_USE_C99_COMPLEX_TR1
1616 inline __complex__ float
1617 __complex_acos(__complex__ float __z)
1618 { return __builtin_cacosf(__z); }
1619
1620 inline __complex__ double
1621 __complex_acos(__complex__ double __z)
1622 { return __builtin_cacos(__z); }
1623
1624 inline __complex__ long double
1625 __complex_acos(const __complex__ long double& __z)
1626 { return __builtin_cacosl(__z); }
1627
1628 template<typename _Tp>
1629 inline std::complex<_Tp>
1630 acos(const std::complex<_Tp>& __z)
1631 { return __complex_acos(__z.__rep()); }
1632#else
1633 /// acos(__z) [8.1.2].
1634 // Effects: Behaves the same as C99 function cacos, defined
1635 // in subclause 7.3.5.1.
1636 template<typename _Tp>
1637 inline std::complex<_Tp>
1638 acos(const std::complex<_Tp>& __z)
1639 { return __complex_acos(__z); }
1640#endif
1641
1642 template<typename _Tp>
1643 inline std::complex<_Tp>
1644 __complex_asin(const std::complex<_Tp>& __z)
1645 {
1646 std::complex<_Tp> __t(-__z.imag(), __z.real());
1647 __t = std::asinh(__t);
1648 return std::complex<_Tp>(__t.imag(), -__t.real());
1649 }
1650
1651#if _GLIBCXX_USE_C99_COMPLEX_TR1
1652 inline __complex__ float
1653 __complex_asin(__complex__ float __z)
1654 { return __builtin_casinf(__z); }
1655
1656 inline __complex__ double
1657 __complex_asin(__complex__ double __z)
1658 { return __builtin_casin(__z); }
1659
1660 inline __complex__ long double
1661 __complex_asin(const __complex__ long double& __z)
1662 { return __builtin_casinl(__z); }
1663
1664 template<typename _Tp>
1665 inline std::complex<_Tp>
1666 asin(const std::complex<_Tp>& __z)
1667 { return __complex_asin(__z.__rep()); }
1668#else
1669 /// asin(__z) [8.1.3].
1670 // Effects: Behaves the same as C99 function casin, defined
1671 // in subclause 7.3.5.2.
1672 template<typename _Tp>
1673 inline std::complex<_Tp>
1674 asin(const std::complex<_Tp>& __z)
1675 { return __complex_asin(__z); }
1676#endif
1677
1678 template<typename _Tp>
1679 std::complex<_Tp>
1680 __complex_atan(const std::complex<_Tp>& __z)
1681 {
1682 const _Tp __r2 = __z.real() * __z.real();
1683 const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();
1684
1685 _Tp __num = __z.imag() + _Tp(1.0);
1686 _Tp __den = __z.imag() - _Tp(1.0);
1687
1688 __num = __r2 + __num * __num;
1689 __den = __r2 + __den * __den;
1690
1691 return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x),
1692 _Tp(0.25) * log(__num / __den));
1693 }
1694
1695#if _GLIBCXX_USE_C99_COMPLEX_TR1
1696 inline __complex__ float
1697 __complex_atan(__complex__ float __z)
1698 { return __builtin_catanf(__z); }
1699
1700 inline __complex__ double
1701 __complex_atan(__complex__ double __z)
1702 { return __builtin_catan(__z); }
1703
1704 inline __complex__ long double
1705 __complex_atan(const __complex__ long double& __z)
1706 { return __builtin_catanl(__z); }
1707
1708 template<typename _Tp>
1709 inline std::complex<_Tp>
1710 atan(const std::complex<_Tp>& __z)
1711 { return __complex_atan(__z.__rep()); }
1712#else
1713 /// atan(__z) [8.1.4].
1714 // Effects: Behaves the same as C99 function catan, defined
1715 // in subclause 7.3.5.3.
1716 template<typename _Tp>
1717 inline std::complex<_Tp>
1718 atan(const std::complex<_Tp>& __z)
1719 { return __complex_atan(__z); }
1720#endif
1721
1722 template<typename _Tp>
1723 std::complex<_Tp>
1724 __complex_acosh(const std::complex<_Tp>& __z)
1725 {
1726 // Kahan's formula.
1727 return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0)))
1728 + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0))));
1729 }
1730
1731#if _GLIBCXX_USE_C99_COMPLEX_TR1
1732 inline __complex__ float
1733 __complex_acosh(__complex__ float __z)
1734 { return __builtin_cacoshf(__z); }
1735
1736 inline __complex__ double
1737 __complex_acosh(__complex__ double __z)
1738 { return __builtin_cacosh(__z); }
1739
1740 inline __complex__ long double
1741 __complex_acosh(const __complex__ long double& __z)
1742 { return __builtin_cacoshl(__z); }
1743
1744 template<typename _Tp>
1745 inline std::complex<_Tp>
1746 acosh(const std::complex<_Tp>& __z)
1747 { return __complex_acosh(__z.__rep()); }
1748#else
1749 /// acosh(__z) [8.1.5].
1750 // Effects: Behaves the same as C99 function cacosh, defined
1751 // in subclause 7.3.6.1.
1752 template<typename _Tp>
1753 inline std::complex<_Tp>
1754 acosh(const std::complex<_Tp>& __z)
1755 { return __complex_acosh(__z); }
1756#endif
1757
1758 template<typename _Tp>
1759 std::complex<_Tp>
1760 __complex_asinh(const std::complex<_Tp>& __z)
1761 {
1762 std::complex<_Tp> __t((__z.real() - __z.imag())
1763 * (__z.real() + __z.imag()) + _Tp(1.0),
1764 _Tp(2.0) * __z.real() * __z.imag());
1765 __t = std::sqrt(__t);
1766
1767 return std::log(__t + __z);
1768 }
1769
1770#if _GLIBCXX_USE_C99_COMPLEX_TR1
1771 inline __complex__ float
1772 __complex_asinh(__complex__ float __z)
1773 { return __builtin_casinhf(__z); }
1774
1775 inline __complex__ double
1776 __complex_asinh(__complex__ double __z)
1777 { return __builtin_casinh(__z); }
1778
1779 inline __complex__ long double
1780 __complex_asinh(const __complex__ long double& __z)
1781 { return __builtin_casinhl(__z); }
1782
1783 template<typename _Tp>
1784 inline std::complex<_Tp>
1785 asinh(const std::complex<_Tp>& __z)
1786 { return __complex_asinh(__z.__rep()); }
1787#else
1788 /// asinh(__z) [8.1.6].
1789 // Effects: Behaves the same as C99 function casin, defined
1790 // in subclause 7.3.6.2.
1791 template<typename _Tp>
1792 inline std::complex<_Tp>
1793 asinh(const std::complex<_Tp>& __z)
1794 { return __complex_asinh(__z); }
1795#endif
1796
1797 template<typename _Tp>
1798 std::complex<_Tp>
1799 __complex_atanh(const std::complex<_Tp>& __z)
1800 {
1801 const _Tp __i2 = __z.imag() * __z.imag();
1802 const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();
1803
1804 _Tp __num = _Tp(1.0) + __z.real();
1805 _Tp __den = _Tp(1.0) - __z.real();
1806
1807 __num = __i2 + __num * __num;
1808 __den = __i2 + __den * __den;
1809
1810 return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)),
1811 _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));
1812 }
1813
1814#if _GLIBCXX_USE_C99_COMPLEX_TR1
1815 inline __complex__ float
1816 __complex_atanh(__complex__ float __z)
1817 { return __builtin_catanhf(__z); }
1818
1819 inline __complex__ double
1820 __complex_atanh(__complex__ double __z)
1821 { return __builtin_catanh(__z); }
1822
1823 inline __complex__ long double
1824 __complex_atanh(const __complex__ long double& __z)
1825 { return __builtin_catanhl(__z); }
1826
1827 template<typename _Tp>
1828 inline std::complex<_Tp>
1829 atanh(const std::complex<_Tp>& __z)
1830 { return __complex_atanh(__z.__rep()); }
1831#else
1832 /// atanh(__z) [8.1.7].
1833 // Effects: Behaves the same as C99 function catanh, defined
1834 // in subclause 7.3.6.3.
1835 template<typename _Tp>
1836 inline std::complex<_Tp>
1837 atanh(const std::complex<_Tp>& __z)
1838 { return __complex_atanh(__z); }
1839#endif
1840
1841 template<typename _Tp>
1842 inline _Tp
1843 /// fabs(__z) [8.1.8].
1844 // Effects: Behaves the same as C99 function cabs, defined
1845 // in subclause 7.3.8.1.
1846 fabs(const std::complex<_Tp>& __z)
1847 { return std::abs(__z); }
1848
1849 /// Additional overloads [8.1.9].
1850 template<typename _Tp>
1851 inline typename __gnu_cxx::__promote<_Tp>::__type
1852 arg(_Tp __x)
1853 {
1854 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1855#if (_GLIBCXX11_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC)
1856 return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L)
1857 : __type();
1858#else
1859 return std::arg(std::complex<__type>(__x));
1860#endif
1861 }
1862
1863 template<typename _Tp>
1864 _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type
1865 imag(_Tp)
1866 { return _Tp(); }
1867
1868 template<typename _Tp>
1869 inline typename __gnu_cxx::__promote<_Tp>::__type
1870 norm(_Tp __x)
1871 {
1872 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1873 return __type(__x) * __type(__x);
1874 }
1875
1876 template<typename _Tp>
1877 _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type
1878 real(_Tp __x)
1879 { return __x; }
1880
1881 template<typename _Tp, typename _Up>
1882 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
1883 pow(const std::complex<_Tp>& __x, const _Up& __y)
1884 {
1885 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1886 return std::pow(std::complex<__type>(__x), __type(__y));
1887 }
1888
1889 template<typename _Tp, typename _Up>
1890 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
1891 pow(const _Tp& __x, const std::complex<_Up>& __y)
1892 {
1893 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1894 return std::pow(__type(__x), std::complex<__type>(__y));
1895 }
1896
1897 template<typename _Tp, typename _Up>
1898 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
1899 pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y)
1900 {
1901 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1902 return std::pow(std::complex<__type>(__x),
1903 std::complex<__type>(__y));
1904 }
1905
1906 // Forward declarations.
1907 // DR 781.
1908 template<typename _Tp> std::complex<_Tp> proj(const std::complex<_Tp>&);
1909
1910 template<typename _Tp>
1911 std::complex<_Tp>
1912 __complex_proj(const std::complex<_Tp>& __z)
1913 {
1914 const _Tp __den = (__z.real() * __z.real()
1915 + __z.imag() * __z.imag() + _Tp(1.0));
1916
1917 return std::complex<_Tp>((_Tp(2.0) * __z.real()) / __den,
1918 (_Tp(2.0) * __z.imag()) / __den);
1919 }
1920
1921#if _GLIBCXX_USE_C99_COMPLEX
1922 inline __complex__ float
1923 __complex_proj(__complex__ float __z)
1924 { return __builtin_cprojf(__z); }
1925
1926 inline __complex__ double
1927 __complex_proj(__complex__ double __z)
1928 { return __builtin_cproj(__z); }
1929
1930 inline __complex__ long double
1931 __complex_proj(const __complex__ long double& __z)
1932 { return __builtin_cprojl(__z); }
1933
1934 template<typename _Tp>
1935 inline std::complex<_Tp>
1936 proj(const std::complex<_Tp>& __z)
1937 { return __complex_proj(__z.__rep()); }
1938#else
1939 template<typename _Tp>
1940 inline std::complex<_Tp>
1941 proj(const std::complex<_Tp>& __z)
1942 { return __complex_proj(__z); }
1943#endif
1944
1945 template<typename _Tp>
1946 inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
1947 proj(_Tp __x)
1948 {
1949 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1950 return std::proj(std::complex<__type>(__x));
1951 }
1952
1953 template<typename _Tp>
1954 inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
1955 conj(_Tp __x)
1956 {
1957 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1958 return std::complex<__type>(__x, -__type());
1959 }
1960
1961#if __cplusplus > 201103L
1962
1963inline namespace literals {
1964inline namespace complex_literals {
1965#pragma GCC diagnostic push
1966#pragma GCC diagnostic ignored "-Wliteral-suffix"
1967#define __cpp_lib_complex_udls 201309
1968
1969 constexpr std::complex<float>
1970 operator""if(long double __num)
1971 { return std::complex<float>{0.0F, static_cast<float>(__num)}; }
1972
1973 constexpr std::complex<float>
1974 operator""if(unsigned long long __num)
1975 { return std::complex<float>{0.0F, static_cast<float>(__num)}; }
1976
1977 constexpr std::complex<double>
1978 operator""i(long double __num)
1979 { return std::complex<double>{0.0, static_cast<double>(__num)}; }
1980
1981 constexpr std::complex<double>
1982 operator""i(unsigned long long __num)
1983 { return std::complex<double>{0.0, static_cast<double>(__num)}; }
1984
1985 constexpr std::complex<long double>
1986 operator""il(long double __num)
1987 { return std::complex<long double>{0.0L, __num}; }
1988
1989 constexpr std::complex<long double>
1990 operator""il(unsigned long long __num)
1991 { return std::complex<long double>{0.0L, static_cast<long double>(__num)}; }
1992
1993#pragma GCC diagnostic pop
1994} // inline namespace complex_literals
1995} // inline namespace literals
1996
1997#endif // C++14
1998
1999_GLIBCXX_END_NAMESPACE_VERSION
2000} // namespace
2001
2002#endif // C++11
2003
2004#endif /* _GLIBCXX_COMPLEX */
2005

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