libstdc++
complex
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1// The template and inlines for the -*- C++ -*- complex number classes.
2
3// Copyright (C) 1997-2021 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 <[email protected]>
33// Improved by Gabriel Dos Reis <[email protected]>
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
50#if __cplusplus > 201703L
51# define __cpp_lib_constexpr_complex 201711L
52#endif
53
54namespace std _GLIBCXX_VISIBILITY(default)
55{
56_GLIBCXX_BEGIN_NAMESPACE_VERSION
57
58 /**
59 * @defgroup complex_numbers Complex Numbers
60 * @ingroup numerics
61 *
62 * Classes and functions for complex numbers.
63 * @{
64 */
65
66 // Forward declarations.
67 template<typename _Tp> class complex;
68 template<> class complex<float>;
69 template<> class complex<double>;
70 template<> class complex<long double>;
71
72 /// Return magnitude of @a z.
73 template<typename _Tp> _Tp abs(const complex<_Tp>&);
74 /// Return phase angle of @a z.
75 template<typename _Tp> _Tp arg(const complex<_Tp>&);
76 /// Return @a z magnitude squared.
77 template<typename _Tp> _Tp _GLIBCXX20_CONSTEXPR norm(const complex<_Tp>&);
78
79 /// Return complex conjugate of @a z.
80 template<typename _Tp>
81 _GLIBCXX20_CONSTEXPR complex<_Tp> conj(const complex<_Tp>&);
82 /// Return complex with magnitude @a rho and angle @a theta.
83 template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0);
84
85 // Transcendentals:
86 /// Return complex cosine of @a z.
87 template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&);
88 /// Return complex hyperbolic cosine of @a z.
89 template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&);
90 /// Return complex base e exponential of @a z.
91 template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&);
92 /// Return complex natural logarithm of @a z.
93 template<typename _Tp> complex<_Tp> log(const complex<_Tp>&);
94 /// Return complex base 10 logarithm of @a z.
95 template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&);
96 /// Return @a x to the @a y'th power.
97 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int);
98 /// Return @a x to the @a y'th power.
99 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&);
100 /// Return @a x to the @a y'th power.
101 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&,
102 const complex<_Tp>&);
103 /// Return @a x to the @a y'th power.
104 template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&);
105 /// Return complex sine of @a z.
106 template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&);
107 /// Return complex hyperbolic sine of @a z.
108 template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&);
109 /// Return complex square root of @a z.
110 template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&);
111 /// Return complex tangent of @a z.
112 template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&);
113 /// Return complex hyperbolic tangent of @a z.
114 template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&);
115
116
117 // 26.2.2 Primary template class complex
118 /**
119 * Template to represent complex numbers.
120 *
121 * Specializations for float, double, and long double are part of the
122 * library. Results with any other type are not guaranteed.
123 *
124 * @param Tp Type of real and imaginary values.
125 */
126 template<typename _Tp>
127 class complex
128 {
129 public:
130 /// Value typedef.
131 typedef _Tp value_type;
132
133 /// Default constructor. First parameter is x, second parameter is y.
134 /// Unspecified parameters default to 0.
135 _GLIBCXX_CONSTEXPR complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp())
136 : _M_real(__r), _M_imag(__i) { }
137
138 // Let the compiler synthesize the copy constructor
139#if __cplusplus >= 201103L
140 constexpr complex(const complex&) = default;
141#endif
142
143 /// Converting constructor.
144 template<typename _Up>
145 _GLIBCXX_CONSTEXPR complex(const complex<_Up>& __z)
146 : _M_real(__z.real()), _M_imag(__z.imag()) { }
147
148#if __cplusplus >= 201103L
149 // _GLIBCXX_RESOLVE_LIB_DEFECTS
150 // DR 387. std::complex over-encapsulated.
151 _GLIBCXX_ABI_TAG_CXX11
152 constexpr _Tp
153 real() const { return _M_real; }
154
155 _GLIBCXX_ABI_TAG_CXX11
156 constexpr _Tp
157 imag() const { return _M_imag; }
158#else
159 /// Return real part of complex number.
160 _Tp&
161 real() { return _M_real; }
162
163 /// Return real part of complex number.
164 const _Tp&
165 real() const { return _M_real; }
166
167 /// Return imaginary part of complex number.
168 _Tp&
169 imag() { return _M_imag; }
170
171 /// Return imaginary part of complex number.
172 const _Tp&
173 imag() const { return _M_imag; }
174#endif
175
176 // _GLIBCXX_RESOLVE_LIB_DEFECTS
177 // DR 387. std::complex over-encapsulated.
178 _GLIBCXX20_CONSTEXPR void
179 real(_Tp __val) { _M_real = __val; }
180
181 _GLIBCXX20_CONSTEXPR void
182 imag(_Tp __val) { _M_imag = __val; }
183
184 /// Assign a scalar to this complex number.
185 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator=(const _Tp&);
186
187 /// Add a scalar to this complex number.
188 // 26.2.5/1
189 _GLIBCXX20_CONSTEXPR complex<_Tp>&
190 operator+=(const _Tp& __t)
191 {
192 _M_real += __t;
193 return *this;
194 }
195
196 /// Subtract a scalar from this complex number.
197 // 26.2.5/3
198 _GLIBCXX20_CONSTEXPR complex<_Tp>&
199 operator-=(const _Tp& __t)
200 {
201 _M_real -= __t;
202 return *this;
203 }
204
205 /// Multiply this complex number by a scalar.
206 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator*=(const _Tp&);
207 /// Divide this complex number by a scalar.
208 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator/=(const _Tp&);
209
210 // Let the compiler synthesize the copy assignment operator
211#if __cplusplus >= 201103L
212 _GLIBCXX20_CONSTEXPR complex& operator=(const complex&) = default;
213#endif
214
215 /// Assign another complex number to this one.
216 template<typename _Up>
217 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator=(const complex<_Up>&);
218 /// Add another complex number to this one.
219 template<typename _Up>
220 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator+=(const complex<_Up>&);
221 /// Subtract another complex number from this one.
222 template<typename _Up>
223 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator-=(const complex<_Up>&);
224 /// Multiply this complex number by another.
225 template<typename _Up>
226 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator*=(const complex<_Up>&);
227 /// Divide this complex number by another.
228 template<typename _Up>
229 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator/=(const complex<_Up>&);
230
231 _GLIBCXX_CONSTEXPR complex __rep() const
232 { return *this; }
233
234 private:
235 _Tp _M_real;
236 _Tp _M_imag;
237 };
238
239 template<typename _Tp>
240 _GLIBCXX20_CONSTEXPR complex<_Tp>&
241 complex<_Tp>::operator=(const _Tp& __t)
242 {
243 _M_real = __t;
244 _M_imag = _Tp();
245 return *this;
246 }
247
248 // 26.2.5/5
249 template<typename _Tp>
250 _GLIBCXX20_CONSTEXPR complex<_Tp>&
251 complex<_Tp>::operator*=(const _Tp& __t)
252 {
253 _M_real *= __t;
254 _M_imag *= __t;
255 return *this;
256 }
257
258 // 26.2.5/7
259 template<typename _Tp>
260 _GLIBCXX20_CONSTEXPR complex<_Tp>&
261 complex<_Tp>::operator/=(const _Tp& __t)
262 {
263 _M_real /= __t;
264 _M_imag /= __t;
265 return *this;
266 }
267
268 template<typename _Tp>
269 template<typename _Up>
270 _GLIBCXX20_CONSTEXPR complex<_Tp>&
271 complex<_Tp>::operator=(const complex<_Up>& __z)
272 {
273 _M_real = __z.real();
274 _M_imag = __z.imag();
275 return *this;
276 }
277
278 // 26.2.5/9
279 template<typename _Tp>
280 template<typename _Up>
281 _GLIBCXX20_CONSTEXPR complex<_Tp>&
282 complex<_Tp>::operator+=(const complex<_Up>& __z)
283 {
284 _M_real += __z.real();
285 _M_imag += __z.imag();
286 return *this;
287 }
288
289 // 26.2.5/11
290 template<typename _Tp>
291 template<typename _Up>
292 _GLIBCXX20_CONSTEXPR complex<_Tp>&
293 complex<_Tp>::operator-=(const complex<_Up>& __z)
294 {
295 _M_real -= __z.real();
296 _M_imag -= __z.imag();
297 return *this;
298 }
299
300 // 26.2.5/13
301 // XXX: This is a grammar school implementation.
302 template<typename _Tp>
303 template<typename _Up>
304 _GLIBCXX20_CONSTEXPR complex<_Tp>&
305 complex<_Tp>::operator*=(const complex<_Up>& __z)
306 {
307 const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag();
308 _M_imag = _M_real * __z.imag() + _M_imag * __z.real();
309 _M_real = __r;
310 return *this;
311 }
312
313 // 26.2.5/15
314 // XXX: This is a grammar school implementation.
315 template<typename _Tp>
316 template<typename _Up>
317 _GLIBCXX20_CONSTEXPR complex<_Tp>&
318 complex<_Tp>::operator/=(const complex<_Up>& __z)
319 {
320 const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag();
321 const _Tp __n = std::norm(__z);
322 _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n;
323 _M_real = __r / __n;
324 return *this;
325 }
326
327 // Operators:
328 ///@{
329 /// Return new complex value @a x plus @a y.
330 template<typename _Tp>
331 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
332 operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
333 {
334 complex<_Tp> __r = __x;
335 __r += __y;
336 return __r;
337 }
338
339 template<typename _Tp>
340 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
341 operator+(const complex<_Tp>& __x, const _Tp& __y)
342 {
343 complex<_Tp> __r = __x;
344 __r += __y;
345 return __r;
346 }
347
348 template<typename _Tp>
349 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
350 operator+(const _Tp& __x, const complex<_Tp>& __y)
351 {
352 complex<_Tp> __r = __y;
353 __r += __x;
354 return __r;
355 }
356 ///@}
357
358 ///@{
359 /// Return new complex value @a x minus @a y.
360 template<typename _Tp>
361 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
362 operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
363 {
364 complex<_Tp> __r = __x;
365 __r -= __y;
366 return __r;
367 }
368
369 template<typename _Tp>
370 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
371 operator-(const complex<_Tp>& __x, const _Tp& __y)
372 {
373 complex<_Tp> __r = __x;
374 __r -= __y;
375 return __r;
376 }
377
378 template<typename _Tp>
379 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
380 operator-(const _Tp& __x, const complex<_Tp>& __y)
381 {
382 complex<_Tp> __r = -__y;
383 __r += __x;
384 return __r;
385 }
386 ///@}
387
388 ///@{
389 /// Return new complex value @a x times @a y.
390 template<typename _Tp>
391 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
392 operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
393 {
394 complex<_Tp> __r = __x;
395 __r *= __y;
396 return __r;
397 }
398
399 template<typename _Tp>
400 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
401 operator*(const complex<_Tp>& __x, const _Tp& __y)
402 {
403 complex<_Tp> __r = __x;
404 __r *= __y;
405 return __r;
406 }
407
408 template<typename _Tp>
409 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
410 operator*(const _Tp& __x, const complex<_Tp>& __y)
411 {
412 complex<_Tp> __r = __y;
413 __r *= __x;
414 return __r;
415 }
416 ///@}
417
418 ///@{
419 /// Return new complex value @a x divided by @a y.
420 template<typename _Tp>
421 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
422 operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
423 {
424 complex<_Tp> __r = __x;
425 __r /= __y;
426 return __r;
427 }
428
429 template<typename _Tp>
430 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
431 operator/(const complex<_Tp>& __x, const _Tp& __y)
432 {
433 complex<_Tp> __r = __x;
434 __r /= __y;
435 return __r;
436 }
437
438 template<typename _Tp>
439 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
440 operator/(const _Tp& __x, const complex<_Tp>& __y)
441 {
442 complex<_Tp> __r = __x;
443 __r /= __y;
444 return __r;
445 }
446 ///@}
447
448 /// Return @a x.
449 template<typename _Tp>
450 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
451 operator+(const complex<_Tp>& __x)
452 { return __x; }
453
454 /// Return complex negation of @a x.
455 template<typename _Tp>
456 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
457 operator-(const complex<_Tp>& __x)
458 { return complex<_Tp>(-__x.real(), -__x.imag()); }
459
460 ///@{
461 /// Return true if @a x is equal to @a y.
462 template<typename _Tp>
463 inline _GLIBCXX_CONSTEXPR bool
464 operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
465 { return __x.real() == __y.real() && __x.imag() == __y.imag(); }
466
467 template<typename _Tp>
468 inline _GLIBCXX_CONSTEXPR bool
469 operator==(const complex<_Tp>& __x, const _Tp& __y)
470 { return __x.real() == __y && __x.imag() == _Tp(); }
471
472#if !(__cpp_impl_three_way_comparison >= 201907L)
473 template<typename _Tp>
474 inline _GLIBCXX_CONSTEXPR bool
475 operator==(const _Tp& __x, const complex<_Tp>& __y)
476 { return __x == __y.real() && _Tp() == __y.imag(); }
477 ///@}
478
479 ///@{
480 /// Return false if @a x is equal to @a y.
481 template<typename _Tp>
482 inline _GLIBCXX_CONSTEXPR bool
483 operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
484 { return __x.real() != __y.real() || __x.imag() != __y.imag(); }
485
486 template<typename _Tp>
487 inline _GLIBCXX_CONSTEXPR bool
488 operator!=(const complex<_Tp>& __x, const _Tp& __y)
489 { return __x.real() != __y || __x.imag() != _Tp(); }
490
491 template<typename _Tp>
492 inline _GLIBCXX_CONSTEXPR bool
493 operator!=(const _Tp& __x, const complex<_Tp>& __y)
494 { return __x != __y.real() || _Tp() != __y.imag(); }
495#endif
496 ///@}
497
498 /// Extraction operator for complex values.
499 template<typename _Tp, typename _CharT, class _Traits>
500 basic_istream<_CharT, _Traits>&
501 operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
502 {
503 bool __fail = true;
504 _CharT __ch;
505 if (__is >> __ch)
506 {
507 if (_Traits::eq(__ch, __is.widen('(')))
508 {
509 _Tp __u;
510 if (__is >> __u >> __ch)
511 {
512 const _CharT __rparen = __is.widen(')');
513 if (_Traits::eq(__ch, __rparen))
514 {
515 __x = __u;
516 __fail = false;
517 }
518 else if (_Traits::eq(__ch, __is.widen(',')))
519 {
520 _Tp __v;
521 if (__is >> __v >> __ch)
522 {
523 if (_Traits::eq(__ch, __rparen))
524 {
525 __x = complex<_Tp>(__u, __v);
526 __fail = false;
527 }
528 else
529 __is.putback(__ch);
530 }
531 }
532 else
533 __is.putback(__ch);
534 }
535 }
536 else
537 {
538 __is.putback(__ch);
539 _Tp __u;
540 if (__is >> __u)
541 {
542 __x = __u;
543 __fail = false;
544 }
545 }
546 }
547 if (__fail)
548 __is.setstate(ios_base::failbit);
549 return __is;
550 }
551
552 /// Insertion operator for complex values.
553 template<typename _Tp, typename _CharT, class _Traits>
554 basic_ostream<_CharT, _Traits>&
555 operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
556 {
557 basic_ostringstream<_CharT, _Traits> __s;
558 __s.flags(__os.flags());
559 __s.imbue(__os.getloc());
560 __s.precision(__os.precision());
561 __s << '(' << __x.real() << ',' << __x.imag() << ')';
562 return __os << __s.str();
563 }
564
565 // Values
566#if __cplusplus >= 201103L
567 template<typename _Tp>
568 constexpr _Tp
569 real(const complex<_Tp>& __z)
570 { return __z.real(); }
571
572 template<typename _Tp>
573 constexpr _Tp
574 imag(const complex<_Tp>& __z)
575 { return __z.imag(); }
576#else
577 template<typename _Tp>
578 inline _Tp&
579 real(complex<_Tp>& __z)
580 { return __z.real(); }
581
582 template<typename _Tp>
583 inline const _Tp&
584 real(const complex<_Tp>& __z)
585 { return __z.real(); }
586
587 template<typename _Tp>
588 inline _Tp&
589 imag(complex<_Tp>& __z)
590 { return __z.imag(); }
591
592 template<typename _Tp>
593 inline const _Tp&
594 imag(const complex<_Tp>& __z)
595 { return __z.imag(); }
596#endif
597
598 // 26.2.7/3 abs(__z): Returns the magnitude of __z.
599 template<typename _Tp>
600 inline _Tp
601 __complex_abs(const complex<_Tp>& __z)
602 {
603 _Tp __x = __z.real();
604 _Tp __y = __z.imag();
605 const _Tp __s = std::max(abs(__x), abs(__y));
606 if (__s == _Tp()) // well ...
607 return __s;
608 __x /= __s;
609 __y /= __s;
610 return __s * sqrt(__x * __x + __y * __y);
611 }
612
613#if _GLIBCXX_USE_C99_COMPLEX
614 inline float
615 __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); }
616
617 inline double
618 __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); }
619
620 inline long double
621 __complex_abs(const __complex__ long double& __z)
622 { return __builtin_cabsl(__z); }
623
624 template<typename _Tp>
625 inline _Tp
626 abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); }
627#else
628 template<typename _Tp>
629 inline _Tp
630 abs(const complex<_Tp>& __z) { return __complex_abs(__z); }
631#endif
632
633
634 // 26.2.7/4: arg(__z): Returns the phase angle of __z.
635 template<typename _Tp>
636 inline _Tp
637 __complex_arg(const complex<_Tp>& __z)
638 { return atan2(__z.imag(), __z.real()); }
639
640#if _GLIBCXX_USE_C99_COMPLEX
641 inline float
642 __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); }
643
644 inline double
645 __complex_arg(__complex__ double __z) { return __builtin_carg(__z); }
646
647 inline long double
648 __complex_arg(const __complex__ long double& __z)
649 { return __builtin_cargl(__z); }
650
651 template<typename _Tp>
652 inline _Tp
653 arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); }
654#else
655 template<typename _Tp>
656 inline _Tp
657 arg(const complex<_Tp>& __z) { return __complex_arg(__z); }
658#endif
659
660 // 26.2.7/5: norm(__z) returns the squared magnitude of __z.
661 // As defined, norm() is -not- a norm is the common mathematical
662 // sense used in numerics. The helper class _Norm_helper<> tries to
663 // distinguish between builtin floating point and the rest, so as
664 // to deliver an answer as close as possible to the real value.
665 template<bool>
666 struct _Norm_helper
667 {
668 template<typename _Tp>
669 static inline _GLIBCXX20_CONSTEXPR _Tp _S_do_it(const complex<_Tp>& __z)
670 {
671 const _Tp __x = __z.real();
672 const _Tp __y = __z.imag();
673 return __x * __x + __y * __y;
674 }
675 };
676
677 template<>
678 struct _Norm_helper<true>
679 {
680 template<typename _Tp>
681 static inline _GLIBCXX20_CONSTEXPR _Tp _S_do_it(const complex<_Tp>& __z)
682 {
683 //_Tp __res = std::abs(__z);
684 //return __res * __res;
685 const _Tp __x = __z.real();
686 const _Tp __y = __z.imag();
687 return __x * __x + __y * __y;
688 }
689 };
690
691 template<typename _Tp>
692 inline _GLIBCXX20_CONSTEXPR _Tp
693 norm(const complex<_Tp>& __z)
694 {
695 return _Norm_helper<__is_floating<_Tp>::__value
696 && !_GLIBCXX_FAST_MATH>::_S_do_it(__z);
697 }
698
699 template<typename _Tp>
700 inline complex<_Tp>
701 polar(const _Tp& __rho, const _Tp& __theta)
702 {
703 __glibcxx_assert( __rho >= 0 );
704 return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta));
705 }
706
707 template<typename _Tp>
708 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
709 conj(const complex<_Tp>& __z)
710 { return complex<_Tp>(__z.real(), -__z.imag()); }
711
712 // Transcendentals
713
714 // 26.2.8/1 cos(__z): Returns the cosine of __z.
715 template<typename _Tp>
716 inline complex<_Tp>
717 __complex_cos(const complex<_Tp>& __z)
718 {
719 const _Tp __x = __z.real();
720 const _Tp __y = __z.imag();
721 return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y));
722 }
723
724#if _GLIBCXX_USE_C99_COMPLEX
725 inline __complex__ float
726 __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); }
727
728 inline __complex__ double
729 __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); }
730
731 inline __complex__ long double
732 __complex_cos(const __complex__ long double& __z)
733 { return __builtin_ccosl(__z); }
734
735 template<typename _Tp>
736 inline complex<_Tp>
737 cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); }
738#else
739 template<typename _Tp>
740 inline complex<_Tp>
741 cos(const complex<_Tp>& __z) { return __complex_cos(__z); }
742#endif
743
744 // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z.
745 template<typename _Tp>
746 inline complex<_Tp>
747 __complex_cosh(const complex<_Tp>& __z)
748 {
749 const _Tp __x = __z.real();
750 const _Tp __y = __z.imag();
751 return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y));
752 }
753
754#if _GLIBCXX_USE_C99_COMPLEX
755 inline __complex__ float
756 __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); }
757
758 inline __complex__ double
759 __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); }
760
761 inline __complex__ long double
762 __complex_cosh(const __complex__ long double& __z)
763 { return __builtin_ccoshl(__z); }
764
765 template<typename _Tp>
766 inline complex<_Tp>
767 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); }
768#else
769 template<typename _Tp>
770 inline complex<_Tp>
771 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); }
772#endif
773
774 // 26.2.8/3 exp(__z): Returns the complex base e exponential of x
775 template<typename _Tp>
776 inline complex<_Tp>
777 __complex_exp(const complex<_Tp>& __z)
778 { return std::polar<_Tp>(exp(__z.real()), __z.imag()); }
779
780#if _GLIBCXX_USE_C99_COMPLEX
781 inline __complex__ float
782 __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); }
783
784 inline __complex__ double
785 __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); }
786
787 inline __complex__ long double
788 __complex_exp(const __complex__ long double& __z)
789 { return __builtin_cexpl(__z); }
790
791 template<typename _Tp>
792 inline complex<_Tp>
793 exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); }
794#else
795 template<typename _Tp>
796 inline complex<_Tp>
797 exp(const complex<_Tp>& __z) { return __complex_exp(__z); }
798#endif
799
800 // 26.2.8/5 log(__z): Returns the natural complex logarithm of __z.
801 // The branch cut is along the negative axis.
802 template<typename _Tp>
803 inline complex<_Tp>
804 __complex_log(const complex<_Tp>& __z)
805 { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); }
806
807#if _GLIBCXX_USE_C99_COMPLEX
808 inline __complex__ float
809 __complex_log(__complex__ float __z) { return __builtin_clogf(__z); }
810
811 inline __complex__ double
812 __complex_log(__complex__ double __z) { return __builtin_clog(__z); }
813
814 inline __complex__ long double
815 __complex_log(const __complex__ long double& __z)
816 { return __builtin_clogl(__z); }
817
818 template<typename _Tp>
819 inline complex<_Tp>
820 log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); }
821#else
822 template<typename _Tp>
823 inline complex<_Tp>
824 log(const complex<_Tp>& __z) { return __complex_log(__z); }
825#endif
826
827 template<typename _Tp>
828 inline complex<_Tp>
829 log10(const complex<_Tp>& __z)
830 { return std::log(__z) / log(_Tp(10.0)); }
831
832 // 26.2.8/10 sin(__z): Returns the sine of __z.
833 template<typename _Tp>
834 inline complex<_Tp>
835 __complex_sin(const complex<_Tp>& __z)
836 {
837 const _Tp __x = __z.real();
838 const _Tp __y = __z.imag();
839 return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y));
840 }
841
842#if _GLIBCXX_USE_C99_COMPLEX
843 inline __complex__ float
844 __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); }
845
846 inline __complex__ double
847 __complex_sin(__complex__ double __z) { return __builtin_csin(__z); }
848
849 inline __complex__ long double
850 __complex_sin(const __complex__ long double& __z)
851 { return __builtin_csinl(__z); }
852
853 template<typename _Tp>
854 inline complex<_Tp>
855 sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); }
856#else
857 template<typename _Tp>
858 inline complex<_Tp>
859 sin(const complex<_Tp>& __z) { return __complex_sin(__z); }
860#endif
861
862 // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z.
863 template<typename _Tp>
864 inline complex<_Tp>
865 __complex_sinh(const complex<_Tp>& __z)
866 {
867 const _Tp __x = __z.real();
868 const _Tp __y = __z.imag();
869 return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y));
870 }
871
872#if _GLIBCXX_USE_C99_COMPLEX
873 inline __complex__ float
874 __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); }
875
876 inline __complex__ double
877 __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); }
878
879 inline __complex__ long double
880 __complex_sinh(const __complex__ long double& __z)
881 { return __builtin_csinhl(__z); }
882
883 template<typename _Tp>
884 inline complex<_Tp>
885 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); }
886#else
887 template<typename _Tp>
888 inline complex<_Tp>
889 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); }
890#endif
891
892 // 26.2.8/13 sqrt(__z): Returns the complex square root of __z.
893 // The branch cut is on the negative axis.
894 template<typename _Tp>
895 complex<_Tp>
896 __complex_sqrt(const complex<_Tp>& __z)
897 {
898 _Tp __x = __z.real();
899 _Tp __y = __z.imag();
900
901 if (__x == _Tp())
902 {
903 _Tp __t = sqrt(abs(__y) / 2);
904 return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
905 }
906 else
907 {
908 _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x)));
909 _Tp __u = __t / 2;
910 return __x > _Tp()
911 ? complex<_Tp>(__u, __y / __t)
912 : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u);
913 }
914 }
915
916#if _GLIBCXX_USE_C99_COMPLEX
917 inline __complex__ float
918 __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); }
919
920 inline __complex__ double
921 __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); }
922
923 inline __complex__ long double
924 __complex_sqrt(const __complex__ long double& __z)
925 { return __builtin_csqrtl(__z); }
926
927 template<typename _Tp>
928 inline complex<_Tp>
929 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); }
930#else
931 template<typename _Tp>
932 inline complex<_Tp>
933 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); }
934#endif
935
936 // 26.2.8/14 tan(__z): Return the complex tangent of __z.
937
938 template<typename _Tp>
939 inline complex<_Tp>
940 __complex_tan(const complex<_Tp>& __z)
941 { return std::sin(__z) / std::cos(__z); }
942
943#if _GLIBCXX_USE_C99_COMPLEX
944 inline __complex__ float
945 __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); }
946
947 inline __complex__ double
948 __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); }
949
950 inline __complex__ long double
951 __complex_tan(const __complex__ long double& __z)
952 { return __builtin_ctanl(__z); }
953
954 template<typename _Tp>
955 inline complex<_Tp>
956 tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); }
957#else
958 template<typename _Tp>
959 inline complex<_Tp>
960 tan(const complex<_Tp>& __z) { return __complex_tan(__z); }
961#endif
962
963
964 // 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z.
965
966 template<typename _Tp>
967 inline complex<_Tp>
968 __complex_tanh(const complex<_Tp>& __z)
969 { return std::sinh(__z) / std::cosh(__z); }
970
971#if _GLIBCXX_USE_C99_COMPLEX
972 inline __complex__ float
973 __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); }
974
975 inline __complex__ double
976 __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); }
977
978 inline __complex__ long double
979 __complex_tanh(const __complex__ long double& __z)
980 { return __builtin_ctanhl(__z); }
981
982 template<typename _Tp>
983 inline complex<_Tp>
984 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); }
985#else
986 template<typename _Tp>
987 inline complex<_Tp>
988 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); }
989#endif
990
991
992 // 26.2.8/9 pow(__x, __y): Returns the complex power base of __x
993 // raised to the __y-th power. The branch
994 // cut is on the negative axis.
995 template<typename _Tp>
996 complex<_Tp>
997 __complex_pow_unsigned(complex<_Tp> __x, unsigned __n)
998 {
999 complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1);
1000
1001 while (__n >>= 1)
1002 {
1003 __x *= __x;
1004 if (__n % 2)
1005 __y *= __x;
1006 }
1007
1008 return __y;
1009 }
1010
1011 // In C++11 mode we used to implement the resolution of
1012 // DR 844. complex pow return type is ambiguous.
1013 // thus the following overload was disabled in that mode. However, doing
1014 // that causes all sorts of issues, see, for example:
1015 // http://gcc.gnu.org/ml/libstdc++/2013-01/msg00058.html
1016 // and also PR57974.
1017 template<typename _Tp>
1018 inline complex<_Tp>
1019 pow(const complex<_Tp>& __z, int __n)
1020 {
1021 return __n < 0
1022 ? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -(unsigned)__n)
1023 : std::__complex_pow_unsigned(__z, __n);
1024 }
1025
1026 template<typename _Tp>
1027 complex<_Tp>
1028 pow(const complex<_Tp>& __x, const _Tp& __y)
1029 {
1030#if ! _GLIBCXX_USE_C99_COMPLEX
1031 if (__x == _Tp())
1032 return _Tp();
1033#endif
1034 if (__x.imag() == _Tp() && __x.real() > _Tp())
1035 return pow(__x.real(), __y);
1036
1037 complex<_Tp> __t = std::log(__x);
1038 return std::polar<_Tp>(exp(__y * __t.real()), __y * __t.imag());
1039 }
1040
1041 template<typename _Tp>
1042 inline complex<_Tp>
1043 __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1044 { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); }
1045
1046#if _GLIBCXX_USE_C99_COMPLEX
1047 inline __complex__ float
1048 __complex_pow(__complex__ float __x, __complex__ float __y)
1049 { return __builtin_cpowf(__x, __y); }
1050
1051 inline __complex__ double
1052 __complex_pow(__complex__ double __x, __complex__ double __y)
1053 { return __builtin_cpow(__x, __y); }
1054
1055 inline __complex__ long double
1056 __complex_pow(const __complex__ long double& __x,
1057 const __complex__ long double& __y)
1058 { return __builtin_cpowl(__x, __y); }
1059
1060 template<typename _Tp>
1061 inline complex<_Tp>
1062 pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1063 { return __complex_pow(__x.__rep(), __y.__rep()); }
1064#else
1065 template<typename _Tp>
1066 inline complex<_Tp>
1067 pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1068 { return __complex_pow(__x, __y); }
1069#endif
1070
1071 template<typename _Tp>
1072 inline complex<_Tp>
1073 pow(const _Tp& __x, const complex<_Tp>& __y)
1074 {
1075 return __x > _Tp() ? std::polar<_Tp>(pow(__x, __y.real()),
1076 __y.imag() * log(__x))
1077 : std::pow(complex<_Tp>(__x), __y);
1078 }
1079
1080 /// 26.2.3 complex specializations
1081 /// complex<float> specialization
1082 template<>
1083 class complex<float>
1084 {
1085 public:
1086 typedef float value_type;
1087 typedef __complex__ float _ComplexT;
1088
1089 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
1090
1091 _GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f)
1092#if __cplusplus >= 201103L
1093 : _M_value{ __r, __i } { }
1094#else
1095 {
1096 __real__ _M_value = __r;
1097 __imag__ _M_value = __i;
1098 }
1099#endif
1100
1101 explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&);
1102 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&);
1103
1104#if __cplusplus >= 201103L
1105 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1106 // DR 387. std::complex over-encapsulated.
1107 __attribute ((__abi_tag__ ("cxx11")))
1108 constexpr float
1109 real() const { return __real__ _M_value; }
1110
1111 __attribute ((__abi_tag__ ("cxx11")))
1112 constexpr float
1113 imag() const { return __imag__ _M_value; }
1114#else
1115 float&
1116 real() { return __real__ _M_value; }
1117
1118 const float&
1119 real() const { return __real__ _M_value; }
1120
1121 float&
1122 imag() { return __imag__ _M_value; }
1123
1124 const float&
1125 imag() const { return __imag__ _M_value; }
1126#endif
1127
1128 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1129 // DR 387. std::complex over-encapsulated.
1130 _GLIBCXX20_CONSTEXPR void
1131 real(float __val) { __real__ _M_value = __val; }
1132
1133 _GLIBCXX20_CONSTEXPR void
1134 imag(float __val) { __imag__ _M_value = __val; }
1135
1136 _GLIBCXX20_CONSTEXPR complex&
1137 operator=(float __f)
1138 {
1139 _M_value = __f;
1140 return *this;
1141 }
1142
1143 _GLIBCXX20_CONSTEXPR complex&
1144 operator+=(float __f)
1145 {
1146 _M_value += __f;
1147 return *this;
1148 }
1149
1150 _GLIBCXX20_CONSTEXPR complex&
1151 operator-=(float __f)
1152 {
1153 _M_value -= __f;
1154 return *this;
1155 }
1156
1157 _GLIBCXX20_CONSTEXPR complex&
1158 operator*=(float __f)
1159 {
1160 _M_value *= __f;
1161 return *this;
1162 }
1163
1164 _GLIBCXX20_CONSTEXPR complex&
1165 operator/=(float __f)
1166 {
1167 _M_value /= __f;
1168 return *this;
1169 }
1170
1171 // Let the compiler synthesize the copy and assignment
1172 // operator. It always does a pretty good job.
1173#if __cplusplus >= 201103L
1174 _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default;
1175#endif
1176
1177 template<typename _Tp>
1178 _GLIBCXX20_CONSTEXPR complex&
1179 operator=(const complex<_Tp>& __z)
1180 {
1181 __real__ _M_value = __z.real();
1182 __imag__ _M_value = __z.imag();
1183 return *this;
1184 }
1185
1186 template<typename _Tp>
1187 _GLIBCXX20_CONSTEXPR complex&
1188 operator+=(const complex<_Tp>& __z)
1189 {
1190 _M_value += __z.__rep();
1191 return *this;
1192 }
1193
1194 template<class _Tp>
1195 _GLIBCXX20_CONSTEXPR complex&
1196 operator-=(const complex<_Tp>& __z)
1197 {
1198 _M_value -= __z.__rep();
1199 return *this;
1200 }
1201
1202 template<class _Tp>
1203 _GLIBCXX20_CONSTEXPR complex&
1204 operator*=(const complex<_Tp>& __z)
1205 {
1206 const _ComplexT __t = __z.__rep();
1207 _M_value *= __t;
1208 return *this;
1209 }
1210
1211 template<class _Tp>
1212 _GLIBCXX20_CONSTEXPR complex&
1213 operator/=(const complex<_Tp>& __z)
1214 {
1215 const _ComplexT __t = __z.__rep();
1216 _M_value /= __t;
1217 return *this;
1218 }
1219
1220 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
1221
1222 private:
1223 _ComplexT _M_value;
1224 };
1225
1226 /// 26.2.3 complex specializations
1227 /// complex<double> specialization
1228 template<>
1229 class complex<double>
1230 {
1231 public:
1232 typedef double value_type;
1233 typedef __complex__ double _ComplexT;
1234
1235 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
1236
1237 _GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0)
1238#if __cplusplus >= 201103L
1239 : _M_value{ __r, __i } { }
1240#else
1241 {
1242 __real__ _M_value = __r;
1243 __imag__ _M_value = __i;
1244 }
1245#endif
1246
1247 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
1248 : _M_value(__z.__rep()) { }
1249
1250 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&);
1251
1252#if __cplusplus >= 201103L
1253 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1254 // DR 387. std::complex over-encapsulated.
1255 __attribute ((__abi_tag__ ("cxx11")))
1256 constexpr double
1257 real() const { return __real__ _M_value; }
1258
1259 __attribute ((__abi_tag__ ("cxx11")))
1260 constexpr double
1261 imag() const { return __imag__ _M_value; }
1262#else
1263 double&
1264 real() { return __real__ _M_value; }
1265
1266 const double&
1267 real() const { return __real__ _M_value; }
1268
1269 double&
1270 imag() { return __imag__ _M_value; }
1271
1272 const double&
1273 imag() const { return __imag__ _M_value; }
1274#endif
1275
1276 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1277 // DR 387. std::complex over-encapsulated.
1278 _GLIBCXX20_CONSTEXPR void
1279 real(double __val) { __real__ _M_value = __val; }
1280
1281 _GLIBCXX20_CONSTEXPR void
1282 imag(double __val) { __imag__ _M_value = __val; }
1283
1284 _GLIBCXX20_CONSTEXPR complex&
1285 operator=(double __d)
1286 {
1287 _M_value = __d;
1288 return *this;
1289 }
1290
1291 _GLIBCXX20_CONSTEXPR complex&
1292 operator+=(double __d)
1293 {
1294 _M_value += __d;
1295 return *this;
1296 }
1297
1298 _GLIBCXX20_CONSTEXPR complex&
1299 operator-=(double __d)
1300 {
1301 _M_value -= __d;
1302 return *this;
1303 }
1304
1305 _GLIBCXX20_CONSTEXPR complex&
1306 operator*=(double __d)
1307 {
1308 _M_value *= __d;
1309 return *this;
1310 }
1311
1312 _GLIBCXX20_CONSTEXPR complex&
1313 operator/=(double __d)
1314 {
1315 _M_value /= __d;
1316 return *this;
1317 }
1318
1319 // The compiler will synthesize this, efficiently.
1320#if __cplusplus >= 201103L
1321 _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default;
1322#endif
1323
1324 template<typename _Tp>
1325 _GLIBCXX20_CONSTEXPR complex&
1326 operator=(const complex<_Tp>& __z)
1327 {
1328 _M_value = __z.__rep();
1329 return *this;
1330 }
1331
1332 template<typename _Tp>
1333 _GLIBCXX20_CONSTEXPR complex&
1334 operator+=(const complex<_Tp>& __z)
1335 {
1336 _M_value += __z.__rep();
1337 return *this;
1338 }
1339
1340 template<typename _Tp>
1341 _GLIBCXX20_CONSTEXPR complex&
1342 operator-=(const complex<_Tp>& __z)
1343 {
1344 _M_value -= __z.__rep();
1345 return *this;
1346 }
1347
1348 template<typename _Tp>
1349 _GLIBCXX20_CONSTEXPR complex&
1350 operator*=(const complex<_Tp>& __z)
1351 {
1352 const _ComplexT __t = __z.__rep();
1353 _M_value *= __t;
1354 return *this;
1355 }
1356
1357 template<typename _Tp>
1358 _GLIBCXX20_CONSTEXPR complex&
1359 operator/=(const complex<_Tp>& __z)
1360 {
1361 const _ComplexT __t = __z.__rep();
1362 _M_value /= __t;
1363 return *this;
1364 }
1365
1366 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
1367
1368 private:
1369 _ComplexT _M_value;
1370 };
1371
1372 /// 26.2.3 complex specializations
1373 /// complex<long double> specialization
1374 template<>
1375 class complex<long double>
1376 {
1377 public:
1378 typedef long double value_type;
1379 typedef __complex__ long double _ComplexT;
1380
1381 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
1382
1383 _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L,
1384 long double __i = 0.0L)
1385#if __cplusplus >= 201103L
1386 : _M_value{ __r, __i } { }
1387#else
1388 {
1389 __real__ _M_value = __r;
1390 __imag__ _M_value = __i;
1391 }
1392#endif
1393
1394 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
1395 : _M_value(__z.__rep()) { }
1396
1397 _GLIBCXX_CONSTEXPR complex(const complex<double>& __z)
1398 : _M_value(__z.__rep()) { }
1399
1400#if __cplusplus >= 201103L
1401 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1402 // DR 387. std::complex over-encapsulated.
1403 __attribute ((__abi_tag__ ("cxx11")))
1404 constexpr long double
1405 real() const { return __real__ _M_value; }
1406
1407 __attribute ((__abi_tag__ ("cxx11")))
1408 constexpr long double
1409 imag() const { return __imag__ _M_value; }
1410#else
1411 long double&
1412 real() { return __real__ _M_value; }
1413
1414 const long double&
1415 real() const { return __real__ _M_value; }
1416
1417 long double&
1418 imag() { return __imag__ _M_value; }
1419
1420 const long double&
1421 imag() const { return __imag__ _M_value; }
1422#endif
1423
1424 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1425 // DR 387. std::complex over-encapsulated.
1426 _GLIBCXX20_CONSTEXPR void
1427 real(long double __val) { __real__ _M_value = __val; }
1428
1429 _GLIBCXX20_CONSTEXPR void
1430 imag(long double __val) { __imag__ _M_value = __val; }
1431
1432 _GLIBCXX20_CONSTEXPR complex&
1433 operator=(long double __r)
1434 {
1435 _M_value = __r;
1436 return *this;
1437 }
1438
1439 _GLIBCXX20_CONSTEXPR complex&
1440 operator+=(long double __r)
1441 {
1442 _M_value += __r;
1443 return *this;
1444 }
1445
1446 _GLIBCXX20_CONSTEXPR complex&
1447 operator-=(long double __r)
1448 {
1449 _M_value -= __r;
1450 return *this;
1451 }
1452
1453 _GLIBCXX20_CONSTEXPR complex&
1454 operator*=(long double __r)
1455 {
1456 _M_value *= __r;
1457 return *this;
1458 }
1459
1460 _GLIBCXX20_CONSTEXPR complex&
1461 operator/=(long double __r)
1462 {
1463 _M_value /= __r;
1464 return *this;
1465 }
1466
1467 // The compiler knows how to do this efficiently
1468#if __cplusplus >= 201103L
1469 _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default;
1470#endif
1471
1472 template<typename _Tp>
1473 _GLIBCXX20_CONSTEXPR complex&
1474 operator=(const complex<_Tp>& __z)
1475 {
1476 _M_value = __z.__rep();
1477 return *this;
1478 }
1479
1480 template<typename _Tp>
1481 _GLIBCXX20_CONSTEXPR complex&
1482 operator+=(const complex<_Tp>& __z)
1483 {
1484 _M_value += __z.__rep();
1485 return *this;
1486 }
1487
1488 template<typename _Tp>
1489 _GLIBCXX20_CONSTEXPR complex&
1490 operator-=(const complex<_Tp>& __z)
1491 {
1492 _M_value -= __z.__rep();
1493 return *this;
1494 }
1495
1496 template<typename _Tp>
1497 _GLIBCXX20_CONSTEXPR complex&
1498 operator*=(const complex<_Tp>& __z)
1499 {
1500 const _ComplexT __t = __z.__rep();
1501 _M_value *= __t;
1502 return *this;
1503 }
1504
1505 template<typename _Tp>
1506 _GLIBCXX20_CONSTEXPR complex&
1507 operator/=(const complex<_Tp>& __z)
1508 {
1509 const _ComplexT __t = __z.__rep();
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 _GLIBCXX20_CONSTEXPR 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>
1909 std::complex<_Tp> proj(const std::complex<_Tp>&);
1910
1911 // Generic implementation of std::proj, does not work for infinities.
1912 template<typename _Tp>
1913 inline std::complex<_Tp>
1914 __complex_proj(const std::complex<_Tp>& __z)
1915 { return __z; }
1916
1917#if _GLIBCXX_USE_C99_COMPLEX
1918 inline complex<float>
1919 __complex_proj(const complex<float>& __z)
1920 { return __builtin_cprojf(__z.__rep()); }
1921
1922 inline complex<double>
1923 __complex_proj(const complex<double>& __z)
1924 { return __builtin_cproj(__z.__rep()); }
1925
1926 inline complex<long double>
1927 __complex_proj(const complex<long double>& __z)
1928 { return __builtin_cprojl(__z.__rep()); }
1929#elif defined _GLIBCXX_USE_C99_MATH_TR1
1930 inline complex<float>
1931 __complex_proj(const complex<float>& __z)
1932 {
1933 if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag()))
1934 return complex<float>(__builtin_inff(),
1935 __builtin_copysignf(0.0f, __z.imag()));
1936 return __z;
1937 }
1938
1939 inline complex<double>
1940 __complex_proj(const complex<double>& __z)
1941 {
1942 if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag()))
1943 return complex<double>(__builtin_inf(),
1944 __builtin_copysign(0.0, __z.imag()));
1945 return __z;
1946 }
1947
1948 inline complex<long double>
1949 __complex_proj(const complex<long double>& __z)
1950 {
1951 if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag()))
1952 return complex<long double>(__builtin_infl(),
1953 __builtin_copysignl(0.0l, __z.imag()));
1954 return __z;
1955 }
1956#endif
1957
1958 template<typename _Tp>
1959 inline std::complex<_Tp>
1960 proj(const std::complex<_Tp>& __z)
1961 { return __complex_proj(__z); }
1962
1963 // Overload for scalars
1964 template<typename _Tp>
1965 inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
1966 proj(_Tp __x)
1967 {
1968 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1969 return std::proj(std::complex<__type>(__x));
1970 }
1971
1972 template<typename _Tp>
1973 inline _GLIBCXX20_CONSTEXPR
1974 std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
1975 conj(_Tp __x)
1976 {
1977 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1978 return std::complex<__type>(__x, -__type());
1979 }
1980
1981#if __cplusplus > 201103L
1982
1983inline namespace literals {
1984inline namespace complex_literals {
1985#pragma GCC diagnostic push
1986#pragma GCC diagnostic ignored "-Wliteral-suffix"
1987#define __cpp_lib_complex_udls 201309
1988
1989 constexpr std::complex<float>
1990 operator""if(long double __num)
1991 { return std::complex<float>{0.0F, static_cast<float>(__num)}; }
1992
1993 constexpr std::complex<float>
1994 operator""if(unsigned long long __num)
1995 { return std::complex<float>{0.0F, static_cast<float>(__num)}; }
1996
1997 constexpr std::complex<double>
1998 operator""i(long double __num)
1999 { return std::complex<double>{0.0, static_cast<double>(__num)}; }
2000
2001 constexpr std::complex<double>
2002 operator""i(unsigned long long __num)
2003 { return std::complex<double>{0.0, static_cast<double>(__num)}; }
2004
2005 constexpr std::complex<long double>
2006 operator""il(long double __num)
2007 { return std::complex<long double>{0.0L, __num}; }
2008
2009 constexpr std::complex<long double>
2010 operator""il(unsigned long long __num)
2011 { return std::complex<long double>{0.0L, static_cast<long double>(__num)}; }
2012
2013#pragma GCC diagnostic pop
2014} // inline namespace complex_literals
2015} // inline namespace literals
2016
2017#endif // C++14
2018
2019_GLIBCXX_END_NAMESPACE_VERSION
2020} // namespace
2021
2022#endif // C++11
2023
2024#endif /* _GLIBCXX_COMPLEX */