libstdc++
complex
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1// The template and inlines for the -*- C++ -*- complex number classes.
2
3// Copyright (C) 1997-2025 Free Software Foundation, Inc.
4//
5// This file is part of the GNU ISO C++ Library. This library is free
6// software; you can redistribute it and/or modify it under the
7// terms of the GNU General Public License as published by the
8// Free Software Foundation; either version 3, or (at your option)
9// any later version.
10
11// This library is distributed in the hope that it will be useful,
12// but WITHOUT ANY WARRANTY; without even the implied warranty of
13// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14// GNU General Public License for more details.
15
16// Under Section 7 of GPL version 3, you are granted additional
17// permissions described in the GCC Runtime Library Exception, version
18// 3.1, as published by the Free Software Foundation.
19
20// You should have received a copy of the GNU General Public License and
21// a copy of the GCC Runtime Library Exception along with this program;
22// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
23// <http://www.gnu.org/licenses/>.
24
25/** @file include/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#ifdef _GLIBCXX_SYSHDR
40#pragma GCC system_header
41#endif
42
43#pragma GCC diagnostic push
44#pragma GCC diagnostic ignored "-Wc++11-extensions" // extern template
45
46#include <bits/c++config.h>
47#include <bits/cpp_type_traits.h>
48#include <ext/type_traits.h>
49#include <cmath>
50#include <sstream>
51
52// Get rid of a macro possibly defined in <complex.h>
53#undef complex
54
55#ifdef _GLIBCXX_CLANG
56#pragma clang diagnostic push
57#pragma clang diagnostic ignored "-Wc99-extensions"
58#endif
59
60#define __glibcxx_want_constexpr_complex
61#define __glibcxx_want_complex_udls
62#define __glibcxx_want_tuple_like
63#include <bits/version.h>
64
65#if __glibcxx_tuple_like >= 202311 // >= C++26
66# include <bits/utility.h> // for tuple_element_t
67# include <bits/stl_pair.h> // for __is_tuple_like_v
68#endif
69
70namespace std _GLIBCXX_VISIBILITY(default)
71{
72_GLIBCXX_BEGIN_NAMESPACE_VERSION
73
74 /**
75 * @defgroup complex_numbers Complex Numbers
76 * @ingroup numerics
77 *
78 * Classes and functions for complex numbers.
79 * @{
80 */
81
82 // Forward declarations.
83 template<typename _Tp> class complex;
84 template<> class complex<float>;
85 template<> class complex<double>;
86 template<> class complex<long double>;
87
88 /// Return magnitude of @a z.
89 template<typename _Tp> _Tp abs(const complex<_Tp>&);
90 /// Return phase angle of @a z.
91 template<typename _Tp> _Tp arg(const complex<_Tp>&);
92 /// Return @a z magnitude squared.
93 template<typename _Tp> _Tp _GLIBCXX20_CONSTEXPR norm(const complex<_Tp>&);
94
95 /// Return complex conjugate of @a z.
96 template<typename _Tp>
97 _GLIBCXX20_CONSTEXPR complex<_Tp> conj(const complex<_Tp>&);
98 /// Return complex with magnitude @a rho and angle @a theta.
99 template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = _Tp(0));
100
101 // Transcendentals:
102 /// Return complex cosine of @a z.
103 template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&);
104 /// Return complex hyperbolic cosine of @a z.
105 template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&);
106 /// Return complex base e exponential of @a z.
107 template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&);
108 /// Return complex natural logarithm of @a z.
109 template<typename _Tp> complex<_Tp> log(const complex<_Tp>&);
110 /// Return complex base 10 logarithm of @a z.
111 template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&);
112 /// Return @a x to the @a y'th power.
113 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int);
114 /// Return @a x to the @a y'th power.
115 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&);
116 /// Return @a x to the @a y'th power.
117 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&,
118 const complex<_Tp>&);
119 /// Return @a x to the @a y'th power.
120 template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&);
121 /// Return complex sine of @a z.
122 template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&);
123 /// Return complex hyperbolic sine of @a z.
124 template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&);
125 /// Return complex square root of @a z.
126 template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&);
127 /// Return complex tangent of @a z.
128 template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&);
129 /// Return complex hyperbolic tangent of @a z.
130 template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&);
131
132#if __glibcxx_tuple_like >= 202311L // >= C++26
133 template<typename _Tp>
134 struct tuple_size<complex<_Tp>>
135 : public integral_constant<size_t, 2> { };
136 template<typename _Tp>
137 struct tuple_element<0, complex<_Tp>>
138 { using type = _Tp; };
139 template<typename _Tp>
140 struct tuple_element<1, complex<_Tp>>
141 { using type = _Tp; };
142 template<typename _Tp>
143 inline constexpr bool __is_tuple_like_v<complex<_Tp>> = true;
144#endif // __glibcxx_tuple_like >= 202311
145
146 // 26.2.2 Primary template class complex
147 /**
148 * Template to represent complex numbers.
149 *
150 * Specializations for float, double, and long double are part of the
151 * library. Results with any other type are not guaranteed.
152 *
153 * @param Tp Type of real and imaginary values.
154 */
155 template<typename _Tp>
156 class complex
157 {
158 public:
159 /// Value typedef.
160 typedef _Tp value_type;
161
162 /// Default constructor. First parameter is x, second parameter is y.
163 /// Unspecified parameters default to 0.
164 _GLIBCXX_CONSTEXPR complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp())
165 : _M_real(__r), _M_imag(__i) { }
166
167 // Let the compiler synthesize the copy constructor
168#if __cplusplus >= 201103L
169 constexpr complex(const complex&) = default;
170#endif
171
172 /// Converting constructor.
173 template<typename _Up>
174#if __cplusplus > 202002L
175 explicit(!requires(_Up __u) { _Tp{__u}; })
176#endif
177 _GLIBCXX_CONSTEXPR complex(const complex<_Up>& __z)
178 : _M_real(_Tp(__z.real())), _M_imag(_Tp(__z.imag())) { }
179
180#if __cplusplus >= 201103L
181 // _GLIBCXX_RESOLVE_LIB_DEFECTS
182 // DR 387. std::complex over-encapsulated.
183 _GLIBCXX_ABI_TAG_CXX11
184 constexpr _Tp
185 real() const { return _M_real; }
186
187 _GLIBCXX_ABI_TAG_CXX11
188 constexpr _Tp
189 imag() const { return _M_imag; }
190#else
191 /// Return real part of complex number.
192 _Tp&
193 real() { return _M_real; }
194
195 /// Return real part of complex number.
196 const _Tp&
197 real() const { return _M_real; }
198
199 /// Return imaginary part of complex number.
200 _Tp&
201 imag() { return _M_imag; }
202
203 /// Return imaginary part of complex number.
204 const _Tp&
205 imag() const { return _M_imag; }
206#endif
207
208 // _GLIBCXX_RESOLVE_LIB_DEFECTS
209 // DR 387. std::complex over-encapsulated.
210 _GLIBCXX20_CONSTEXPR void
211 real(_Tp __val) { _M_real = __val; }
212
213 _GLIBCXX20_CONSTEXPR void
214 imag(_Tp __val) { _M_imag = __val; }
215
216 /// Assign a scalar to this complex number.
217 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator=(const _Tp&);
218
219 /// Add a scalar to this complex number.
220 // 26.2.5/1
221 _GLIBCXX20_CONSTEXPR complex<_Tp>&
222 operator+=(const _Tp& __t)
223 {
224 _M_real += __t;
225 return *this;
226 }
227
228 /// Subtract a scalar from this complex number.
229 // 26.2.5/3
230 _GLIBCXX20_CONSTEXPR complex<_Tp>&
231 operator-=(const _Tp& __t)
232 {
233 _M_real -= __t;
234 return *this;
235 }
236
237 /// Multiply this complex number by a scalar.
238 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator*=(const _Tp&);
239 /// Divide this complex number by a scalar.
240 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator/=(const _Tp&);
241
242 // Let the compiler synthesize the copy assignment operator
243#if __cplusplus >= 201103L
244 _GLIBCXX20_CONSTEXPR complex& operator=(const complex&) = default;
245#endif
246
247 /// Assign another complex number to this one.
248 template<typename _Up>
249 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator=(const complex<_Up>&);
250 /// Add another complex number to this one.
251 template<typename _Up>
252 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator+=(const complex<_Up>&);
253 /// Subtract another complex number from this one.
254 template<typename _Up>
255 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator-=(const complex<_Up>&);
256 /// Multiply this complex number by another.
257 template<typename _Up>
258 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator*=(const complex<_Up>&);
259 /// Divide this complex number by another.
260 template<typename _Up>
261 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator/=(const complex<_Up>&);
262
263 _GLIBCXX_CONSTEXPR complex __rep() const
264 { return *this; }
265
266#if __glibcxx_tuple_like >= 202311L // >= C++26
267 template<typename _Cp>
268 [[__gnu__::__always_inline__]]
269 constexpr auto&
270 __get_part(this _Cp& __z, size_t __i) noexcept
271 {
272 return __i == 0 ? __z._M_real : __z._M_imag;
273 }
274#endif
275
276 private:
277 _Tp _M_real;
278 _Tp _M_imag;
279 };
280
281 template<typename _Tp>
282 _GLIBCXX20_CONSTEXPR complex<_Tp>&
283 complex<_Tp>::operator=(const _Tp& __t)
284 {
285 _M_real = __t;
286 _M_imag = _Tp();
287 return *this;
288 }
289
290 // 26.2.5/5
291 template<typename _Tp>
292 _GLIBCXX20_CONSTEXPR complex<_Tp>&
293 complex<_Tp>::operator*=(const _Tp& __t)
294 {
295 _M_real *= __t;
296 _M_imag *= __t;
297 return *this;
298 }
299
300 // 26.2.5/7
301 template<typename _Tp>
302 _GLIBCXX20_CONSTEXPR complex<_Tp>&
303 complex<_Tp>::operator/=(const _Tp& __t)
304 {
305 _M_real /= __t;
306 _M_imag /= __t;
307 return *this;
308 }
309
310 template<typename _Tp>
311 template<typename _Up>
312 _GLIBCXX20_CONSTEXPR complex<_Tp>&
313 complex<_Tp>::operator=(const complex<_Up>& __z)
314 {
315 _M_real = __z.real();
316 _M_imag = __z.imag();
317 return *this;
318 }
319
320 // 26.2.5/9
321 template<typename _Tp>
322 template<typename _Up>
323 _GLIBCXX20_CONSTEXPR complex<_Tp>&
324 complex<_Tp>::operator+=(const complex<_Up>& __z)
325 {
326 _M_real += __z.real();
327 _M_imag += __z.imag();
328 return *this;
329 }
330
331 // 26.2.5/11
332 template<typename _Tp>
333 template<typename _Up>
334 _GLIBCXX20_CONSTEXPR complex<_Tp>&
335 complex<_Tp>::operator-=(const complex<_Up>& __z)
336 {
337 _M_real -= __z.real();
338 _M_imag -= __z.imag();
339 return *this;
340 }
341
342 // 26.2.5/13
343 // XXX: This is a grammar school implementation.
344 template<typename _Tp>
345 template<typename _Up>
346 _GLIBCXX20_CONSTEXPR complex<_Tp>&
347 complex<_Tp>::operator*=(const complex<_Up>& __z)
348 {
349 const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag();
350 _M_imag = _M_real * __z.imag() + _M_imag * __z.real();
351 _M_real = __r;
352 return *this;
353 }
354
355 // 26.2.5/15
356 // XXX: This is a grammar school implementation.
357 template<typename _Tp>
358 template<typename _Up>
359 _GLIBCXX20_CONSTEXPR complex<_Tp>&
360 complex<_Tp>::operator/=(const complex<_Up>& __z)
361 {
362 const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag();
363 const _Tp __n = std::norm(__z);
364 _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n;
365 _M_real = __r / __n;
366 return *this;
367 }
368
369 // Operators:
370 ///@{
371 /// Return new complex value @a x plus @a y.
372 template<typename _Tp>
373 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
374 operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
375 {
376 complex<_Tp> __r = __x;
377 __r += __y;
378 return __r;
379 }
380
381 template<typename _Tp>
382 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
383 operator+(const complex<_Tp>& __x, const _Tp& __y)
384 {
385 complex<_Tp> __r = __x;
386 __r += __y;
387 return __r;
388 }
389
390 template<typename _Tp>
391 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
392 operator+(const _Tp& __x, const complex<_Tp>& __y)
393 {
394 complex<_Tp> __r = __y;
395 __r += __x;
396 return __r;
397 }
398 ///@}
399
400 ///@{
401 /// Return new complex value @a x minus @a y.
402 template<typename _Tp>
403 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
404 operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
405 {
406 complex<_Tp> __r = __x;
407 __r -= __y;
408 return __r;
409 }
410
411 template<typename _Tp>
412 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
413 operator-(const complex<_Tp>& __x, const _Tp& __y)
414 {
415 complex<_Tp> __r = __x;
416 __r -= __y;
417 return __r;
418 }
419
420 template<typename _Tp>
421 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
422 operator-(const _Tp& __x, const complex<_Tp>& __y)
423 {
424 complex<_Tp> __r = -__y;
425 __r += __x;
426 return __r;
427 }
428 ///@}
429
430 ///@{
431 /// Return new complex value @a x times @a y.
432 template<typename _Tp>
433 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
434 operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
435 {
436 complex<_Tp> __r = __x;
437 __r *= __y;
438 return __r;
439 }
440
441 template<typename _Tp>
442 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
443 operator*(const complex<_Tp>& __x, const _Tp& __y)
444 {
445 complex<_Tp> __r = __x;
446 __r *= __y;
447 return __r;
448 }
449
450 template<typename _Tp>
451 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
452 operator*(const _Tp& __x, const complex<_Tp>& __y)
453 {
454 complex<_Tp> __r = __y;
455 __r *= __x;
456 return __r;
457 }
458 ///@}
459
460 ///@{
461 /// Return new complex value @a x divided by @a y.
462 template<typename _Tp>
463 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
464 operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
465 {
466 complex<_Tp> __r = __x;
467 __r /= __y;
468 return __r;
469 }
470
471 template<typename _Tp>
472 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
473 operator/(const complex<_Tp>& __x, const _Tp& __y)
474 {
475 complex<_Tp> __r = __x;
476 __r /= __y;
477 return __r;
478 }
479
480 template<typename _Tp>
481 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
482 operator/(const _Tp& __x, const complex<_Tp>& __y)
483 {
484 complex<_Tp> __r = __x;
485 __r /= __y;
486 return __r;
487 }
488 ///@}
489
490 /// Return @a x.
491 template<typename _Tp>
492 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
493 operator+(const complex<_Tp>& __x)
494 { return __x; }
495
496 /// Return complex negation of @a x.
497 template<typename _Tp>
498 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
499 operator-(const complex<_Tp>& __x)
500 { return complex<_Tp>(-__x.real(), -__x.imag()); }
501
502 ///@{
503 /// Return true if @a x is equal to @a y.
504 template<typename _Tp>
505 inline _GLIBCXX_CONSTEXPR bool
506 operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
507 { return __x.real() == __y.real() && __x.imag() == __y.imag(); }
508
509 template<typename _Tp>
510 inline _GLIBCXX_CONSTEXPR bool
511 operator==(const complex<_Tp>& __x, const _Tp& __y)
512 { return __x.real() == __y && __x.imag() == _Tp(); }
513
514#if !(__cpp_impl_three_way_comparison >= 201907L)
515 template<typename _Tp>
516 inline _GLIBCXX_CONSTEXPR bool
517 operator==(const _Tp& __x, const complex<_Tp>& __y)
518 { return __x == __y.real() && _Tp() == __y.imag(); }
519 ///@}
520
521 ///@{
522 /// Return false if @a x is equal to @a y.
523 template<typename _Tp>
524 inline _GLIBCXX_CONSTEXPR bool
525 operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
526 { return __x.real() != __y.real() || __x.imag() != __y.imag(); }
527
528 template<typename _Tp>
529 inline _GLIBCXX_CONSTEXPR bool
530 operator!=(const complex<_Tp>& __x, const _Tp& __y)
531 { return __x.real() != __y || __x.imag() != _Tp(); }
532
533 template<typename _Tp>
534 inline _GLIBCXX_CONSTEXPR bool
535 operator!=(const _Tp& __x, const complex<_Tp>& __y)
536 { return __x != __y.real() || _Tp() != __y.imag(); }
537#endif
538 ///@}
539
540 /// Extraction operator for complex values.
541 template<typename _Tp, typename _CharT, class _Traits>
542 basic_istream<_CharT, _Traits>&
543 operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
544 {
545 bool __fail = true;
546 _CharT __ch;
547 if (__is >> __ch)
548 {
549 if (_Traits::eq(__ch, __is.widen('(')))
550 {
551 _Tp __u;
552 if (__is >> __u >> __ch)
553 {
554 const _CharT __rparen = __is.widen(')');
555 if (_Traits::eq(__ch, __rparen))
556 {
557 __x = __u;
558 __fail = false;
559 }
560 else if (_Traits::eq(__ch, __is.widen(',')))
561 {
562 _Tp __v;
563 if (__is >> __v >> __ch)
564 {
565 if (_Traits::eq(__ch, __rparen))
566 {
567 __x = complex<_Tp>(__u, __v);
568 __fail = false;
569 }
570 else
571 __is.putback(__ch);
572 }
573 }
574 else
575 __is.putback(__ch);
576 }
577 }
578 else
579 {
580 __is.putback(__ch);
581 _Tp __u;
582 if (__is >> __u)
583 {
584 __x = __u;
585 __fail = false;
586 }
587 }
588 }
589 if (__fail)
590 __is.setstate(ios_base::failbit);
591 return __is;
592 }
593
594 /// Insertion operator for complex values.
595 template<typename _Tp, typename _CharT, class _Traits>
596 basic_ostream<_CharT, _Traits>&
597 operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
598 {
599 basic_ostringstream<_CharT, _Traits> __s;
600 __s.flags(__os.flags());
601 __s.imbue(__os.getloc());
602 __s.precision(__os.precision());
603 __s << '(' << __x.real() << ',' << __x.imag() << ')';
604 return __os << __s.str();
605 }
606
607 // Values
608#if __cplusplus >= 201103L
609 template<typename _Tp>
610 constexpr _Tp
611 real(const complex<_Tp>& __z)
612 { return __z.real(); }
613
614 template<typename _Tp>
615 constexpr _Tp
616 imag(const complex<_Tp>& __z)
617 { return __z.imag(); }
618#else
619 template<typename _Tp>
620 inline _Tp&
621 real(complex<_Tp>& __z)
622 { return __z.real(); }
623
624 template<typename _Tp>
625 inline const _Tp&
626 real(const complex<_Tp>& __z)
627 { return __z.real(); }
628
629 template<typename _Tp>
630 inline _Tp&
631 imag(complex<_Tp>& __z)
632 { return __z.imag(); }
633
634 template<typename _Tp>
635 inline const _Tp&
636 imag(const complex<_Tp>& __z)
637 { return __z.imag(); }
638#endif
639
640#if __glibcxx_tuple_like >= 202311L // >= C++26
641 template<size_t _Int, typename _Tp>
642 [[nodiscard,__gnu__::__always_inline__]]
643 constexpr _Tp&
644 get(complex<_Tp>& __z) noexcept
645 {
646 static_assert(_Int < 2);
647 return __z.__get_part(_Int);
648 }
649
650 template<size_t _Int, typename _Tp>
651 [[nodiscard,__gnu__::__always_inline__]]
652 constexpr _Tp&&
653 get(complex<_Tp>&& __z) noexcept
654 {
655 static_assert(_Int < 2);
656 return std::move(__z.__get_part(_Int));
657 }
658
659 template<size_t _Int, typename _Tp>
660 [[nodiscard,__gnu__::__always_inline__]]
661 constexpr const _Tp&
662 get(const complex<_Tp>& __z) noexcept
663 {
664 static_assert(_Int < 2);
665 return __z.__get_part(_Int);
666 }
667
668 template<size_t _Int, typename _Tp>
669 [[nodiscard,__gnu__::__always_inline__]]
670 constexpr const _Tp&&
671 get(const complex<_Tp>&& __z) noexcept
672 {
673 static_assert(_Int < 2);
674 return std::move(__z.__get_part(_Int));
675 }
676#endif // __glibcxx_tuple_like >= 202311
677
678#if _GLIBCXX_USE_C99_COMPLEX
679#if defined(__STDCPP_FLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
680 inline _Float16
681 __complex_abs(__complex__ _Float16 __z)
682 { return _Float16(__builtin_cabsf(__z)); }
683
684 inline _Float16
685 __complex_arg(__complex__ _Float16 __z)
686 { return _Float16(__builtin_cargf(__z)); }
687
688 inline __complex__ _Float16
689 __complex_cos(__complex__ _Float16 __z)
690 { return static_cast<__complex__ _Float16>(__builtin_ccosf(__z)); }
691
692 inline __complex__ _Float16
693 __complex_cosh(__complex__ _Float16 __z)
694 { return static_cast<__complex__ _Float16>(__builtin_ccoshf(__z)); }
695
696 inline __complex__ _Float16
697 __complex_exp(__complex__ _Float16 __z)
698 { return static_cast<__complex__ _Float16>(__builtin_cexpf(__z)); }
699
700 inline __complex__ _Float16
701 __complex_log(__complex__ _Float16 __z)
702 { return static_cast<__complex__ _Float16>(__builtin_clogf(__z)); }
703
704 inline __complex__ _Float16
705 __complex_sin(__complex__ _Float16 __z)
706 { return static_cast<__complex__ _Float16>(__builtin_csinf(__z)); }
707
708 inline __complex__ _Float16
709 __complex_sinh(__complex__ _Float16 __z)
710 { return static_cast<__complex__ _Float16>(__builtin_csinhf(__z)); }
711
712 inline __complex__ _Float16
713 __complex_sqrt(__complex__ _Float16 __z)
714 { return static_cast<__complex__ _Float16>(__builtin_csqrtf(__z)); }
715
716 inline __complex__ _Float16
717 __complex_tan(__complex__ _Float16 __z)
718 { return static_cast<__complex__ _Float16>(__builtin_ctanf(__z)); }
719
720 inline __complex__ _Float16
721 __complex_tanh(__complex__ _Float16 __z)
722 { return static_cast<__complex__ _Float16>(__builtin_ctanhf(__z)); }
723
724 inline __complex__ _Float16
725 __complex_pow(__complex__ _Float16 __x, __complex__ _Float16 __y)
726 { return static_cast<__complex__ _Float16>(__builtin_cpowf(__x, __y)); }
727#endif
728
729#if defined(__STDCPP_FLOAT32_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
730 inline _Float32
731 __complex_abs(__complex__ _Float32 __z) { return __builtin_cabsf(__z); }
732
733 inline _Float32
734 __complex_arg(__complex__ _Float32 __z) { return __builtin_cargf(__z); }
735
736 inline __complex__ _Float32
737 __complex_cos(__complex__ _Float32 __z) { return __builtin_ccosf(__z); }
738
739 inline __complex__ _Float32
740 __complex_cosh(__complex__ _Float32 __z) { return __builtin_ccoshf(__z); }
741
742 inline __complex__ _Float32
743 __complex_exp(__complex__ _Float32 __z) { return __builtin_cexpf(__z); }
744
745 inline __complex__ _Float32
746 __complex_log(__complex__ _Float32 __z) { return __builtin_clogf(__z); }
747
748 inline __complex__ _Float32
749 __complex_sin(__complex__ _Float32 __z) { return __builtin_csinf(__z); }
750
751 inline __complex__ _Float32
752 __complex_sinh(__complex__ _Float32 __z) { return __builtin_csinhf(__z); }
753
754 inline __complex__ _Float32
755 __complex_sqrt(__complex__ _Float32 __z) { return __builtin_csqrtf(__z); }
756
757 inline __complex__ _Float32
758 __complex_tan(__complex__ _Float32 __z) { return __builtin_ctanf(__z); }
759
760 inline __complex__ _Float32
761 __complex_tanh(__complex__ _Float32 __z) { return __builtin_ctanhf(__z); }
762
763 inline __complex__ _Float32
764 __complex_pow(__complex__ _Float32 __x, __complex__ _Float32 __y)
765 { return __builtin_cpowf(__x, __y); }
766#endif
767
768#if defined(__STDCPP_FLOAT64_T__) && defined(_GLIBCXX_DOUBLE_IS_IEEE_BINARY64)
769 inline _Float64
770 __complex_abs(__complex__ _Float64 __z) { return __builtin_cabs(__z); }
771
772 inline _Float64
773 __complex_arg(__complex__ _Float64 __z) { return __builtin_carg(__z); }
774
775 inline __complex__ _Float64
776 __complex_cos(__complex__ _Float64 __z) { return __builtin_ccos(__z); }
777
778 inline __complex__ _Float64
779 __complex_cosh(__complex__ _Float64 __z) { return __builtin_ccosh(__z); }
780
781 inline __complex__ _Float64
782 __complex_exp(__complex__ _Float64 __z) { return __builtin_cexp(__z); }
783
784 inline __complex__ _Float64
785 __complex_log(__complex__ _Float64 __z) { return __builtin_clog(__z); }
786
787 inline __complex__ _Float64
788 __complex_sin(__complex__ _Float64 __z) { return __builtin_csin(__z); }
789
790 inline __complex__ _Float64
791 __complex_sinh(__complex__ _Float64 __z) { return __builtin_csinh(__z); }
792
793 inline __complex__ _Float64
794 __complex_sqrt(__complex__ _Float64 __z) { return __builtin_csqrt(__z); }
795
796 inline __complex__ _Float64
797 __complex_tan(__complex__ _Float64 __z) { return __builtin_ctan(__z); }
798
799 inline __complex__ _Float64
800 __complex_tanh(__complex__ _Float64 __z) { return __builtin_ctanh(__z); }
801
802 inline __complex__ _Float64
803 __complex_pow(__complex__ _Float64 __x, __complex__ _Float64 __y)
804 { return __builtin_cpow(__x, __y); }
805#endif
806
807#if defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_LDOUBLE_IS_IEEE_BINARY128)
808 inline _Float128
809 __complex_abs(__complex__ _Float128 __z) { return __builtin_cabsl(__z); }
810
811 inline _Float128
812 __complex_arg(__complex__ _Float128 __z) { return __builtin_cargl(__z); }
813
814 inline __complex__ _Float128
815 __complex_cos(__complex__ _Float128 __z) { return __builtin_ccosl(__z); }
816
817 inline __complex__ _Float128
818 __complex_cosh(__complex__ _Float128 __z) { return __builtin_ccoshl(__z); }
819
820 inline __complex__ _Float128
821 __complex_exp(__complex__ _Float128 __z) { return __builtin_cexpl(__z); }
822
823 inline __complex__ _Float128
824 __complex_log(__complex__ _Float128 __z) { return __builtin_clogl(__z); }
825
826 inline __complex__ _Float128
827 __complex_sin(__complex__ _Float128 __z) { return __builtin_csinl(__z); }
828
829 inline __complex__ _Float128
830 __complex_sinh(__complex__ _Float128 __z) { return __builtin_csinhl(__z); }
831
832 inline __complex__ _Float128
833 __complex_sqrt(__complex__ _Float128 __z) { return __builtin_csqrtl(__z); }
834
835 inline __complex__ _Float128
836 __complex_tan(__complex__ _Float128 __z) { return __builtin_ctanl(__z); }
837
838 inline __complex__ _Float128
839 __complex_tanh(__complex__ _Float128 __z) { return __builtin_ctanhl(__z); }
840
841 inline __complex__ _Float128
842 __complex_pow(__complex__ _Float128 __x, __complex__ _Float128 __y)
843 { return __builtin_cpowl(__x, __y); }
844#elif defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_HAVE_FLOAT128_MATH)
845 inline _Float128
846 __complex_abs(__complex__ _Float128 __z) { return __builtin_cabsf128(__z); }
847
848 inline _Float128
849 __complex_arg(__complex__ _Float128 __z) { return __builtin_cargf128(__z); }
850
851 inline __complex__ _Float128
852 __complex_cos(__complex__ _Float128 __z) { return __builtin_ccosf128(__z); }
853
854 inline __complex__ _Float128
855 __complex_cosh(__complex__ _Float128 __z) { return __builtin_ccoshf128(__z); }
856
857 inline __complex__ _Float128
858 __complex_exp(__complex__ _Float128 __z) { return __builtin_cexpf128(__z); }
859
860 inline __complex__ _Float128
861 __complex_log(__complex__ _Float128 __z) { return __builtin_clogf128(__z); }
862
863 inline __complex__ _Float128
864 __complex_sin(__complex__ _Float128 __z) { return __builtin_csinf128(__z); }
865
866 inline __complex__ _Float128
867 __complex_sinh(__complex__ _Float128 __z) { return __builtin_csinhf128(__z); }
868
869 inline __complex__ _Float128
870 __complex_sqrt(__complex__ _Float128 __z) { return __builtin_csqrtf128(__z); }
871
872 inline __complex__ _Float128
873 __complex_tan(__complex__ _Float128 __z) { return __builtin_ctanf128(__z); }
874
875 inline __complex__ _Float128
876 __complex_tanh(__complex__ _Float128 __z) { return __builtin_ctanhf128(__z); }
877
878 inline __complex__ _Float128
879 __complex_pow(__complex__ _Float128 __x, __complex__ _Float128 __y)
880 { return __builtin_cpowf128(__x, __y); }
881#endif
882
883#if defined(__STDCPP_BFLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
884 inline __gnu_cxx::__bfloat16_t
885 __complex_abs(__complex__ decltype(0.0bf16) __z)
886 { return __gnu_cxx::__bfloat16_t(__builtin_cabsf(__z)); }
887
888 inline __gnu_cxx::__bfloat16_t
889 __complex_arg(__complex__ decltype(0.0bf16) __z)
890 { return __gnu_cxx::__bfloat16_t(__builtin_cargf(__z)); }
891
892 inline __complex__ decltype(0.0bf16)
893 __complex_cos(__complex__ decltype(0.0bf16) __z)
894 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_ccosf(__z)); }
895
896 inline __complex__ decltype(0.0bf16)
897 __complex_cosh(__complex__ decltype(0.0bf16) __z)
898 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_ccoshf(__z)); }
899
900 inline __complex__ decltype(0.0bf16)
901 __complex_exp(__complex__ decltype(0.0bf16) __z)
902 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_cexpf(__z)); }
903
904 inline __complex__ decltype(0.0bf16)
905 __complex_log(__complex__ decltype(0.0bf16) __z)
906 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_clogf(__z)); }
907
908 inline __complex__ decltype(0.0bf16)
909 __complex_sin(__complex__ decltype(0.0bf16) __z)
910 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_csinf(__z)); }
911
912 inline __complex__ decltype(0.0bf16)
913 __complex_sinh(__complex__ decltype(0.0bf16) __z)
914 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_csinhf(__z)); }
915
916 inline __complex__ decltype(0.0bf16)
917 __complex_sqrt(__complex__ decltype(0.0bf16) __z)
918 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_csqrtf(__z)); }
919
920 inline __complex__ decltype(0.0bf16)
921 __complex_tan(__complex__ decltype(0.0bf16) __z)
922 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_ctanf(__z)); }
923
924 inline __complex__ decltype(0.0bf16)
925 __complex_tanh(__complex__ decltype(0.0bf16) __z)
926 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_ctanhf(__z)); }
927
928 inline __complex__ decltype(0.0bf16)
929 __complex_pow(__complex__ decltype(0.0bf16) __x,
930 __complex__ decltype(0.0bf16) __y)
931 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_cpowf(__x,
932 __y)); }
933#endif
934#endif
935
936 // 26.2.7/3 abs(__z): Returns the magnitude of __z.
937 template<typename _Tp>
938 inline _Tp
939 __complex_abs(const complex<_Tp>& __z)
940 {
941 _Tp __x = __z.real();
942 _Tp __y = __z.imag();
943 const _Tp __s = std::max(abs(__x), abs(__y));
944 if (__s == _Tp()) // well ...
945 return __s;
946 __x /= __s;
947 __y /= __s;
948 return __s * sqrt(__x * __x + __y * __y);
949 }
950
951#if _GLIBCXX_USE_C99_COMPLEX
952 inline float
953 __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); }
954
955 inline double
956 __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); }
957
958 inline long double
959 __complex_abs(const __complex__ long double& __z)
960 { return __builtin_cabsl(__z); }
961
962 template<typename _Tp>
963 inline _Tp
964 abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); }
965#else
966 template<typename _Tp>
967 inline _Tp
968 abs(const complex<_Tp>& __z) { return __complex_abs(__z); }
969#endif
970
971
972 // C++11 26.4.7 [complex.value.ops]/4: arg(z): Returns the phase angle of z.
973 template<typename _Tp>
974 inline _Tp
975 __complex_arg(const complex<_Tp>& __z)
976 { return atan2(__z.imag(), __z.real()); }
977
978#if _GLIBCXX_USE_C99_COMPLEX
979 inline float
980 __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); }
981
982 inline double
983 __complex_arg(__complex__ double __z) { return __builtin_carg(__z); }
984
985 inline long double
986 __complex_arg(const __complex__ long double& __z)
987 { return __builtin_cargl(__z); }
988
989 template<typename _Tp>
990 inline _Tp
991 arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); }
992#else
993 template<typename _Tp>
994 inline _Tp
995 arg(const complex<_Tp>& __z) { return __complex_arg(__z); }
996#endif
997
998 // 26.2.7/5: norm(__z) returns the squared magnitude of __z.
999 // As defined, norm() is -not- a norm is the common mathematical
1000 // sense used in numerics. The helper class _Norm_helper<> tries to
1001 // distinguish between builtin floating point and the rest, so as
1002 // to deliver an answer as close as possible to the real value.
1003 template<bool>
1004 struct _Norm_helper
1005 {
1006 template<typename _Tp>
1007 static inline _GLIBCXX20_CONSTEXPR _Tp _S_do_it(const complex<_Tp>& __z)
1008 {
1009 const _Tp __x = __z.real();
1010 const _Tp __y = __z.imag();
1011 return __x * __x + __y * __y;
1012 }
1013 };
1014
1015 template<>
1016 struct _Norm_helper<true>
1017 {
1018 template<typename _Tp>
1019 static inline _GLIBCXX20_CONSTEXPR _Tp _S_do_it(const complex<_Tp>& __z)
1020 {
1021 //_Tp __res = std::abs(__z);
1022 //return __res * __res;
1023 const _Tp __x = __z.real();
1024 const _Tp __y = __z.imag();
1025 return __x * __x + __y * __y;
1026 }
1027 };
1028
1029 template<typename _Tp>
1030 inline _GLIBCXX20_CONSTEXPR _Tp
1031 norm(const complex<_Tp>& __z)
1032 {
1033 return _Norm_helper<__is_floating<_Tp>::__value
1034 && !_GLIBCXX_FAST_MATH>::_S_do_it(__z);
1035 }
1036
1037 template<typename _Tp>
1038 inline complex<_Tp>
1039 polar(const _Tp& __rho, const _Tp& __theta)
1040 {
1041 __glibcxx_assert( __rho >= _Tp(0) );
1042 return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta));
1043 }
1044
1045 template<typename _Tp>
1046 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
1047 conj(const complex<_Tp>& __z)
1048 { return complex<_Tp>(__z.real(), -__z.imag()); }
1049
1050 // Transcendentals
1051
1052 // 26.2.8/1 cos(__z): Returns the cosine of __z.
1053 template<typename _Tp>
1054 inline complex<_Tp>
1055 __complex_cos(const complex<_Tp>& __z)
1056 {
1057 const _Tp __x = __z.real();
1058 const _Tp __y = __z.imag();
1059 return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y));
1060 }
1061
1062#if _GLIBCXX_USE_C99_COMPLEX
1063 inline __complex__ float
1064 __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); }
1065
1066 inline __complex__ double
1067 __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); }
1068
1069 inline __complex__ long double
1070 __complex_cos(const __complex__ long double& __z)
1071 { return __builtin_ccosl(__z); }
1072
1073 template<typename _Tp>
1074 inline complex<_Tp>
1075 cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); }
1076#else
1077 template<typename _Tp>
1078 inline complex<_Tp>
1079 cos(const complex<_Tp>& __z) { return __complex_cos(__z); }
1080#endif
1081
1082 // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z.
1083 template<typename _Tp>
1084 inline complex<_Tp>
1085 __complex_cosh(const complex<_Tp>& __z)
1086 {
1087 const _Tp __x = __z.real();
1088 const _Tp __y = __z.imag();
1089 return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y));
1090 }
1091
1092#if _GLIBCXX_USE_C99_COMPLEX
1093 inline __complex__ float
1094 __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); }
1095
1096 inline __complex__ double
1097 __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); }
1098
1099 inline __complex__ long double
1100 __complex_cosh(const __complex__ long double& __z)
1101 { return __builtin_ccoshl(__z); }
1102
1103 template<typename _Tp>
1104 inline complex<_Tp>
1105 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); }
1106#else
1107 template<typename _Tp>
1108 inline complex<_Tp>
1109 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); }
1110#endif
1111
1112 // 26.2.8/3 exp(__z): Returns the complex base e exponential of x
1113 template<typename _Tp>
1114 inline complex<_Tp>
1115 __complex_exp(const complex<_Tp>& __z)
1116 { return std::polar<_Tp>(exp(__z.real()), __z.imag()); }
1117
1118#if _GLIBCXX_USE_C99_COMPLEX
1119 inline __complex__ float
1120 __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); }
1121
1122 inline __complex__ double
1123 __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); }
1124
1125 inline __complex__ long double
1126 __complex_exp(const __complex__ long double& __z)
1127 { return __builtin_cexpl(__z); }
1128
1129 template<typename _Tp>
1130 inline complex<_Tp>
1131 exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); }
1132#else
1133 template<typename _Tp>
1134 inline complex<_Tp>
1135 exp(const complex<_Tp>& __z) { return __complex_exp(__z); }
1136#endif
1137
1138 // 26.2.8/5 log(__z): Returns the natural complex logarithm of __z.
1139 // The branch cut is along the negative axis.
1140 template<typename _Tp>
1141 inline complex<_Tp>
1142 __complex_log(const complex<_Tp>& __z)
1143 { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); }
1144
1145#if _GLIBCXX_USE_C99_COMPLEX
1146 inline __complex__ float
1147 __complex_log(__complex__ float __z) { return __builtin_clogf(__z); }
1148
1149 inline __complex__ double
1150 __complex_log(__complex__ double __z) { return __builtin_clog(__z); }
1151
1152 inline __complex__ long double
1153 __complex_log(const __complex__ long double& __z)
1154 { return __builtin_clogl(__z); }
1155
1156 template<typename _Tp>
1157 inline complex<_Tp>
1158 log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); }
1159#else
1160 template<typename _Tp>
1161 inline complex<_Tp>
1162 log(const complex<_Tp>& __z) { return __complex_log(__z); }
1163#endif
1164
1165 template<typename _Tp>
1166 inline complex<_Tp>
1167 log10(const complex<_Tp>& __z)
1168 { return std::log(__z) / log(_Tp(10.0)); }
1169
1170 // 26.2.8/10 sin(__z): Returns the sine of __z.
1171 template<typename _Tp>
1172 inline complex<_Tp>
1173 __complex_sin(const complex<_Tp>& __z)
1174 {
1175 const _Tp __x = __z.real();
1176 const _Tp __y = __z.imag();
1177 return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y));
1178 }
1179
1180#if _GLIBCXX_USE_C99_COMPLEX
1181 inline __complex__ float
1182 __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); }
1183
1184 inline __complex__ double
1185 __complex_sin(__complex__ double __z) { return __builtin_csin(__z); }
1186
1187 inline __complex__ long double
1188 __complex_sin(const __complex__ long double& __z)
1189 { return __builtin_csinl(__z); }
1190
1191 template<typename _Tp>
1192 inline complex<_Tp>
1193 sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); }
1194#else
1195 template<typename _Tp>
1196 inline complex<_Tp>
1197 sin(const complex<_Tp>& __z) { return __complex_sin(__z); }
1198#endif
1199
1200 // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z.
1201 template<typename _Tp>
1202 inline complex<_Tp>
1203 __complex_sinh(const complex<_Tp>& __z)
1204 {
1205 const _Tp __x = __z.real();
1206 const _Tp __y = __z.imag();
1207 return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y));
1208 }
1209
1210#if _GLIBCXX_USE_C99_COMPLEX
1211 inline __complex__ float
1212 __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); }
1213
1214 inline __complex__ double
1215 __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); }
1216
1217 inline __complex__ long double
1218 __complex_sinh(const __complex__ long double& __z)
1219 { return __builtin_csinhl(__z); }
1220
1221 template<typename _Tp>
1222 inline complex<_Tp>
1223 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); }
1224#else
1225 template<typename _Tp>
1226 inline complex<_Tp>
1227 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); }
1228#endif
1229
1230 // 26.2.8/13 sqrt(__z): Returns the complex square root of __z.
1231 // The branch cut is on the negative axis.
1232 template<typename _Tp>
1233 complex<_Tp>
1234 __complex_sqrt(const complex<_Tp>& __z)
1235 {
1236 _Tp __x = __z.real();
1237 _Tp __y = __z.imag();
1238
1239 if (__x == _Tp())
1240 {
1241 _Tp __t = sqrt(abs(__y) / _Tp(2));
1242 return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
1243 }
1244 else
1245 {
1246 _Tp __t = sqrt(_Tp(2) * (std::abs(__z) + abs(__x)));
1247 _Tp __u = __t / _Tp(2);
1248 return __x > _Tp()
1249 ? complex<_Tp>(__u, __y / __t)
1250 : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u);
1251 }
1252 }
1253
1254#if _GLIBCXX_USE_C99_COMPLEX
1255 inline __complex__ float
1256 __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); }
1257
1258 inline __complex__ double
1259 __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); }
1260
1261 inline __complex__ long double
1262 __complex_sqrt(const __complex__ long double& __z)
1263 { return __builtin_csqrtl(__z); }
1264
1265 template<typename _Tp>
1266 inline complex<_Tp>
1267 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); }
1268#else
1269 template<typename _Tp>
1270 inline complex<_Tp>
1271 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); }
1272#endif
1273
1274 // 26.2.8/14 tan(__z): Return the complex tangent of __z.
1275
1276 template<typename _Tp>
1277 inline complex<_Tp>
1278 __complex_tan(const complex<_Tp>& __z)
1279 { return std::sin(__z) / std::cos(__z); }
1280
1281#if _GLIBCXX_USE_C99_COMPLEX
1282 inline __complex__ float
1283 __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); }
1284
1285 inline __complex__ double
1286 __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); }
1287
1288 inline __complex__ long double
1289 __complex_tan(const __complex__ long double& __z)
1290 { return __builtin_ctanl(__z); }
1291
1292 template<typename _Tp>
1293 inline complex<_Tp>
1294 tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); }
1295#else
1296 template<typename _Tp>
1297 inline complex<_Tp>
1298 tan(const complex<_Tp>& __z) { return __complex_tan(__z); }
1299#endif
1300
1301
1302 // 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z.
1303
1304 template<typename _Tp>
1305 inline complex<_Tp>
1306 __complex_tanh(const complex<_Tp>& __z)
1307 { return std::sinh(__z) / std::cosh(__z); }
1308
1309#if _GLIBCXX_USE_C99_COMPLEX
1310 inline __complex__ float
1311 __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); }
1312
1313 inline __complex__ double
1314 __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); }
1315
1316 inline __complex__ long double
1317 __complex_tanh(const __complex__ long double& __z)
1318 { return __builtin_ctanhl(__z); }
1319
1320 template<typename _Tp>
1321 inline complex<_Tp>
1322 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); }
1323#else
1324 template<typename _Tp>
1325 inline complex<_Tp>
1326 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); }
1327#endif
1328
1329
1330 // 26.2.8/9 pow(__x, __y): Returns the complex power base of __x
1331 // raised to the __y-th power. The branch
1332 // cut is on the negative axis.
1333 template<typename _Tp>
1334 complex<_Tp>
1335 __complex_pow_unsigned(complex<_Tp> __x, unsigned __n)
1336 {
1337 complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(_Tp(1));
1338
1339 while (__n >>= 1)
1340 {
1341 __x *= __x;
1342 if (__n % 2)
1343 __y *= __x;
1344 }
1345
1346 return __y;
1347 }
1348
1349 // In C++11 mode we used to implement the resolution of
1350 // DR 844. complex pow return type is ambiguous.
1351 // thus the following overload was disabled in that mode. However, doing
1352 // that causes all sorts of issues, see, for example:
1353 // http://gcc.gnu.org/ml/libstdc++/2013-01/msg00058.html
1354 // and also PR57974.
1355 template<typename _Tp>
1356 inline complex<_Tp>
1357 pow(const complex<_Tp>& __z, int __n)
1358 {
1359 return __n < 0
1360 ? complex<_Tp>(_Tp(1)) / std::__complex_pow_unsigned(__z,
1361 -(unsigned)__n)
1362 : std::__complex_pow_unsigned(__z, __n);
1363 }
1364
1365 template<typename _Tp>
1366 complex<_Tp>
1367 pow(const complex<_Tp>& __x, const _Tp& __y)
1368 {
1369#if ! _GLIBCXX_USE_C99_COMPLEX
1370 if (__x == _Tp())
1371 return _Tp();
1372#endif
1373 if (__x.imag() == _Tp() && __x.real() > _Tp())
1374 return pow(__x.real(), __y);
1375
1376 complex<_Tp> __t = std::log(__x);
1377 return std::polar<_Tp>(exp(__y * __t.real()), __y * __t.imag());
1378 }
1379
1380 template<typename _Tp>
1381 inline complex<_Tp>
1382 __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1383 { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); }
1384
1385#if _GLIBCXX_USE_C99_COMPLEX
1386 inline __complex__ float
1387 __complex_pow(__complex__ float __x, __complex__ float __y)
1388 { return __builtin_cpowf(__x, __y); }
1389
1390 inline __complex__ double
1391 __complex_pow(__complex__ double __x, __complex__ double __y)
1392 { return __builtin_cpow(__x, __y); }
1393
1394 inline __complex__ long double
1395 __complex_pow(const __complex__ long double& __x,
1396 const __complex__ long double& __y)
1397 { return __builtin_cpowl(__x, __y); }
1398
1399 template<typename _Tp>
1400 inline complex<_Tp>
1401 pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1402 { return __complex_pow(__x.__rep(), __y.__rep()); }
1403#else
1404 template<typename _Tp>
1405 inline complex<_Tp>
1406 pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1407 { return __complex_pow(__x, __y); }
1408#endif
1409
1410 template<typename _Tp>
1411 inline complex<_Tp>
1412 pow(const _Tp& __x, const complex<_Tp>& __y)
1413 {
1414 return __x > _Tp() ? std::polar<_Tp>(pow(__x, __y.real()),
1415 __y.imag() * log(__x))
1416 : std::pow(complex<_Tp>(__x), __y);
1417 }
1418
1419#if __glibcxx_tuple_like >= 202311L // >= C++26
1420#define _GLIBCXX26_DECLARE_COMPLEX_TUPLE_HELPER_ACCESSOR \
1421 template<typename _Cp> \
1422 [[__gnu__::__always_inline__]] \
1423 constexpr auto& \
1424 __get_part(this _Cp& __z, size_t __i) noexcept \
1425 { \
1426 return __i == 0 ? __real__ __z._M_value \
1427 : __imag__ __z._M_value; \
1428 }
1429#else
1430#define _GLIBCXX26_DECLARE_COMPLEX_TUPLE_HELPER_ACCESSOR
1431#endif
1432
1433 /// 26.2.3 complex specializations
1434 /// complex<float> specialization
1435 template<>
1436 class complex<float>
1437 {
1438 public:
1439 typedef float value_type;
1440 typedef __complex__ float _ComplexT;
1441
1442 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
1443
1444 _GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f)
1445#if __cplusplus >= 201103L
1446 : _M_value{ __r, __i } { }
1447#else
1448 {
1449 __real__ _M_value = __r;
1450 __imag__ _M_value = __i;
1451 }
1452#endif
1453
1454#if __cplusplus >= 201103L
1455 _GLIBCXX14_CONSTEXPR complex(const complex&) = default;
1456#endif
1457
1458#if __cplusplus > 202002L
1459 template<typename _Up>
1460 explicit(!requires(_Up __u) { value_type{__u}; })
1461 constexpr complex(const complex<_Up>& __z)
1462 : _M_value{ value_type(__z.real()), value_type(__z.imag()) } { }
1463#else
1464 explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&);
1465 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&);
1466#endif
1467
1468#if __cplusplus >= 201103L
1469 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1470 // DR 387. std::complex over-encapsulated.
1471 __attribute ((__abi_tag__ ("cxx11")))
1472 constexpr float
1473 real() const { return __real__ _M_value; }
1474
1475 __attribute ((__abi_tag__ ("cxx11")))
1476 constexpr float
1477 imag() const { return __imag__ _M_value; }
1478#else
1479 float&
1480 real() { return __real__ _M_value; }
1481
1482 const float&
1483 real() const { return __real__ _M_value; }
1484
1485 float&
1486 imag() { return __imag__ _M_value; }
1487
1488 const float&
1489 imag() const { return __imag__ _M_value; }
1490#endif
1491
1492 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1493 // DR 387. std::complex over-encapsulated.
1494 _GLIBCXX20_CONSTEXPR void
1495 real(float __val) { __real__ _M_value = __val; }
1496
1497 _GLIBCXX20_CONSTEXPR void
1498 imag(float __val) { __imag__ _M_value = __val; }
1499
1500 _GLIBCXX20_CONSTEXPR complex&
1501 operator=(float __f)
1502 {
1503 _M_value = __f;
1504 return *this;
1505 }
1506
1507 _GLIBCXX20_CONSTEXPR complex&
1508 operator+=(float __f)
1509 {
1510 _M_value += __f;
1511 return *this;
1512 }
1513
1514 _GLIBCXX20_CONSTEXPR complex&
1515 operator-=(float __f)
1516 {
1517 _M_value -= __f;
1518 return *this;
1519 }
1520
1521 _GLIBCXX20_CONSTEXPR complex&
1522 operator*=(float __f)
1523 {
1524 _M_value *= __f;
1525 return *this;
1526 }
1527
1528 _GLIBCXX20_CONSTEXPR complex&
1529 operator/=(float __f)
1530 {
1531 _M_value /= __f;
1532 return *this;
1533 }
1534
1535 // Let the compiler synthesize the copy and assignment
1536 // operator. It always does a pretty good job.
1537#if __cplusplus >= 201103L
1538 _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default;
1539#endif
1540
1541 template<typename _Tp>
1542 _GLIBCXX20_CONSTEXPR complex&
1543 operator=(const complex<_Tp>& __z)
1544 {
1545 __real__ _M_value = __z.real();
1546 __imag__ _M_value = __z.imag();
1547 return *this;
1548 }
1549
1550 template<typename _Tp>
1551 _GLIBCXX20_CONSTEXPR complex&
1552 operator+=(const complex<_Tp>& __z)
1553 {
1554 _M_value += __z.__rep();
1555 return *this;
1556 }
1557
1558 template<class _Tp>
1559 _GLIBCXX20_CONSTEXPR complex&
1560 operator-=(const complex<_Tp>& __z)
1561 {
1562 _M_value -= __z.__rep();
1563 return *this;
1564 }
1565
1566 template<class _Tp>
1567 _GLIBCXX20_CONSTEXPR complex&
1568 operator*=(const complex<_Tp>& __z)
1569 {
1570 const _ComplexT __t = __z.__rep();
1571 _M_value *= __t;
1572 return *this;
1573 }
1574
1575 template<class _Tp>
1576 _GLIBCXX20_CONSTEXPR complex&
1577 operator/=(const complex<_Tp>& __z)
1578 {
1579 const _ComplexT __t = __z.__rep();
1580 _M_value /= __t;
1581 return *this;
1582 }
1583
1584 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
1585
1586 _GLIBCXX26_DECLARE_COMPLEX_TUPLE_HELPER_ACCESSOR
1587
1588 private:
1589 _ComplexT _M_value;
1590 };
1591
1592 /// 26.2.3 complex specializations
1593 /// complex<double> specialization
1594 template<>
1595 class complex<double>
1596 {
1597 public:
1598 typedef double value_type;
1599 typedef __complex__ double _ComplexT;
1600
1601 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
1602
1603 _GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0)
1604#if __cplusplus >= 201103L
1605 : _M_value{ __r, __i } { }
1606#else
1607 {
1608 __real__ _M_value = __r;
1609 __imag__ _M_value = __i;
1610 }
1611#endif
1612
1613#if __cplusplus >= 201103L
1614 _GLIBCXX14_CONSTEXPR complex(const complex&) = default;
1615#endif
1616
1617#if __cplusplus > 202002L
1618 template<typename _Up>
1619 explicit(!requires(_Up __u) { value_type{__u}; })
1620 constexpr complex(const complex<_Up>& __z)
1621 : _M_value{ value_type(__z.real()), value_type(__z.imag()) } { }
1622#else
1623 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
1624 : _M_value(__z.__rep()) { }
1625
1626 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&);
1627#endif
1628
1629#if __cplusplus >= 201103L
1630 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1631 // DR 387. std::complex over-encapsulated.
1632 __attribute ((__abi_tag__ ("cxx11")))
1633 constexpr double
1634 real() const { return __real__ _M_value; }
1635
1636 __attribute ((__abi_tag__ ("cxx11")))
1637 constexpr double
1638 imag() const { return __imag__ _M_value; }
1639#else
1640 double&
1641 real() { return __real__ _M_value; }
1642
1643 const double&
1644 real() const { return __real__ _M_value; }
1645
1646 double&
1647 imag() { return __imag__ _M_value; }
1648
1649 const double&
1650 imag() const { return __imag__ _M_value; }
1651#endif
1652
1653 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1654 // DR 387. std::complex over-encapsulated.
1655 _GLIBCXX20_CONSTEXPR void
1656 real(double __val) { __real__ _M_value = __val; }
1657
1658 _GLIBCXX20_CONSTEXPR void
1659 imag(double __val) { __imag__ _M_value = __val; }
1660
1661 _GLIBCXX20_CONSTEXPR complex&
1662 operator=(double __d)
1663 {
1664 _M_value = __d;
1665 return *this;
1666 }
1667
1668 _GLIBCXX20_CONSTEXPR complex&
1669 operator+=(double __d)
1670 {
1671 _M_value += __d;
1672 return *this;
1673 }
1674
1675 _GLIBCXX20_CONSTEXPR complex&
1676 operator-=(double __d)
1677 {
1678 _M_value -= __d;
1679 return *this;
1680 }
1681
1682 _GLIBCXX20_CONSTEXPR complex&
1683 operator*=(double __d)
1684 {
1685 _M_value *= __d;
1686 return *this;
1687 }
1688
1689 _GLIBCXX20_CONSTEXPR complex&
1690 operator/=(double __d)
1691 {
1692 _M_value /= __d;
1693 return *this;
1694 }
1695
1696 // The compiler will synthesize this, efficiently.
1697#if __cplusplus >= 201103L
1698 _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default;
1699#endif
1700
1701 template<typename _Tp>
1702 _GLIBCXX20_CONSTEXPR complex&
1703 operator=(const complex<_Tp>& __z)
1704 {
1705 _M_value = __z.__rep();
1706 return *this;
1707 }
1708
1709 template<typename _Tp>
1710 _GLIBCXX20_CONSTEXPR complex&
1711 operator+=(const complex<_Tp>& __z)
1712 {
1713 _M_value += __z.__rep();
1714 return *this;
1715 }
1716
1717 template<typename _Tp>
1718 _GLIBCXX20_CONSTEXPR complex&
1719 operator-=(const complex<_Tp>& __z)
1720 {
1721 _M_value -= __z.__rep();
1722 return *this;
1723 }
1724
1725 template<typename _Tp>
1726 _GLIBCXX20_CONSTEXPR complex&
1727 operator*=(const complex<_Tp>& __z)
1728 {
1729 const _ComplexT __t = __z.__rep();
1730 _M_value *= __t;
1731 return *this;
1732 }
1733
1734 template<typename _Tp>
1735 _GLIBCXX20_CONSTEXPR complex&
1736 operator/=(const complex<_Tp>& __z)
1737 {
1738 const _ComplexT __t = __z.__rep();
1739 _M_value /= __t;
1740 return *this;
1741 }
1742
1743 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
1744
1745 _GLIBCXX26_DECLARE_COMPLEX_TUPLE_HELPER_ACCESSOR
1746
1747 private:
1748 _ComplexT _M_value;
1749 };
1750
1751 /// 26.2.3 complex specializations
1752 /// complex<long double> specialization
1753 template<>
1754 class complex<long double>
1755 {
1756 public:
1757 typedef long double value_type;
1758 typedef __complex__ long double _ComplexT;
1759
1760 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
1761
1762 _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L,
1763 long double __i = 0.0L)
1764#if __cplusplus >= 201103L
1765 : _M_value{ __r, __i } { }
1766#else
1767 {
1768 __real__ _M_value = __r;
1769 __imag__ _M_value = __i;
1770 }
1771#endif
1772
1773#if __cplusplus >= 201103L
1774 _GLIBCXX14_CONSTEXPR complex(const complex&) = default;
1775#endif
1776
1777#if __cplusplus > 202002L
1778 template<typename _Up>
1779 explicit(!requires(_Up __u) { value_type{__u}; })
1780 constexpr complex(const complex<_Up>& __z)
1781 : _M_value{ value_type(__z.real()), value_type(__z.imag()) } { }
1782#else
1783 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
1784 : _M_value(__z.__rep()) { }
1785
1786 _GLIBCXX_CONSTEXPR complex(const complex<double>& __z)
1787 : _M_value(__z.__rep()) { }
1788#endif
1789
1790#if __cplusplus >= 201103L
1791 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1792 // DR 387. std::complex over-encapsulated.
1793 __attribute ((__abi_tag__ ("cxx11")))
1794 constexpr long double
1795 real() const { return __real__ _M_value; }
1796
1797 __attribute ((__abi_tag__ ("cxx11")))
1798 constexpr long double
1799 imag() const { return __imag__ _M_value; }
1800#else
1801 long double&
1802 real() { return __real__ _M_value; }
1803
1804 const long double&
1805 real() const { return __real__ _M_value; }
1806
1807 long double&
1808 imag() { return __imag__ _M_value; }
1809
1810 const long double&
1811 imag() const { return __imag__ _M_value; }
1812#endif
1813
1814 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1815 // DR 387. std::complex over-encapsulated.
1816 _GLIBCXX20_CONSTEXPR void
1817 real(long double __val) { __real__ _M_value = __val; }
1818
1819 _GLIBCXX20_CONSTEXPR void
1820 imag(long double __val) { __imag__ _M_value = __val; }
1821
1822 _GLIBCXX20_CONSTEXPR complex&
1823 operator=(long double __r)
1824 {
1825 _M_value = __r;
1826 return *this;
1827 }
1828
1829 _GLIBCXX20_CONSTEXPR complex&
1830 operator+=(long double __r)
1831 {
1832 _M_value += __r;
1833 return *this;
1834 }
1835
1836 _GLIBCXX20_CONSTEXPR complex&
1837 operator-=(long double __r)
1838 {
1839 _M_value -= __r;
1840 return *this;
1841 }
1842
1843 _GLIBCXX20_CONSTEXPR complex&
1844 operator*=(long double __r)
1845 {
1846 _M_value *= __r;
1847 return *this;
1848 }
1849
1850 _GLIBCXX20_CONSTEXPR complex&
1851 operator/=(long double __r)
1852 {
1853 _M_value /= __r;
1854 return *this;
1855 }
1856
1857 // The compiler knows how to do this efficiently
1858#if __cplusplus >= 201103L
1859 _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default;
1860#endif
1861
1862 template<typename _Tp>
1863 _GLIBCXX20_CONSTEXPR complex&
1864 operator=(const complex<_Tp>& __z)
1865 {
1866 _M_value = __z.__rep();
1867 return *this;
1868 }
1869
1870 template<typename _Tp>
1871 _GLIBCXX20_CONSTEXPR complex&
1872 operator+=(const complex<_Tp>& __z)
1873 {
1874 _M_value += __z.__rep();
1875 return *this;
1876 }
1877
1878 template<typename _Tp>
1879 _GLIBCXX20_CONSTEXPR complex&
1880 operator-=(const complex<_Tp>& __z)
1881 {
1882 _M_value -= __z.__rep();
1883 return *this;
1884 }
1885
1886 template<typename _Tp>
1887 _GLIBCXX20_CONSTEXPR complex&
1888 operator*=(const complex<_Tp>& __z)
1889 {
1890 const _ComplexT __t = __z.__rep();
1891 _M_value *= __t;
1892 return *this;
1893 }
1894
1895 template<typename _Tp>
1896 _GLIBCXX20_CONSTEXPR complex&
1897 operator/=(const complex<_Tp>& __z)
1898 {
1899 const _ComplexT __t = __z.__rep();
1900 _M_value /= __t;
1901 return *this;
1902 }
1903
1904 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
1905
1906 _GLIBCXX26_DECLARE_COMPLEX_TUPLE_HELPER_ACCESSOR
1907
1908 private:
1909 _ComplexT _M_value;
1910 };
1911
1912#if __cplusplus > 202002L
1913 template<typename _Tp>
1914 struct __complex_type
1915 { };
1916
1917#ifdef __STDCPP_FLOAT16_T__
1918 template<>
1919 struct __complex_type<_Float16>
1920 { typedef __complex__ _Float16 type; };
1921#endif
1922
1923#ifdef __STDCPP_FLOAT32_T__
1924 template<>
1925 struct __complex_type<_Float32>
1926 { typedef __complex__ _Float32 type; };
1927#endif
1928
1929#ifdef __STDCPP_FLOAT64_T__
1930 template<>
1931 struct __complex_type<_Float64>
1932 { typedef __complex__ _Float64 type; };
1933#endif
1934
1935#ifdef __STDCPP_FLOAT128_T__
1936 template<>
1937 struct __complex_type<_Float128>
1938 { typedef __complex__ _Float128 type; };
1939#endif
1940
1941#ifdef __STDCPP_BFLOAT16_T__
1942 template<>
1943 struct __complex_type<__gnu_cxx::__bfloat16_t>
1944 { typedef __complex__ decltype(0.0bf16) type; };
1945#endif
1946
1947 template<typename _Tp>
1948 requires requires { typename __complex_type<_Tp>::type; }
1949 class complex<_Tp>
1950 {
1951 public:
1952 typedef _Tp value_type;
1953 typedef typename std::__complex_type<_Tp>::type _ComplexT;
1954
1955 constexpr complex(_ComplexT __z) : _M_value(__z) { }
1956
1957 constexpr complex(_Tp __r = _Tp(), _Tp __i = _Tp())
1958 : _M_value{ __r, __i } { }
1959
1960 template<typename _Up>
1961 explicit(!requires(_Up __u) { value_type{__u}; })
1962 constexpr complex(const complex<_Up>& __z)
1963 : _M_value{ value_type(__z.real()), value_type(__z.imag()) } { }
1964
1965 constexpr _Tp
1966 real() const { return __real__ _M_value; }
1967
1968 constexpr _Tp
1969 imag() const { return __imag__ _M_value; }
1970
1971 constexpr void
1972 real(_Tp __val) { __real__ _M_value = __val; }
1973
1974 constexpr void
1975 imag(_Tp __val) { __imag__ _M_value = __val; }
1976
1977 constexpr complex&
1978 operator=(_Tp __f)
1979 {
1980 _M_value = __f;
1981 return *this;
1982 }
1983
1984 constexpr complex&
1985 operator+=(_Tp __f)
1986 {
1987 _M_value += __f;
1988 return *this;
1989 }
1990
1991 constexpr complex&
1992 operator-=(_Tp __f)
1993 {
1994 _M_value -= __f;
1995 return *this;
1996 }
1997
1998 constexpr complex&
1999 operator*=(_Tp __f)
2000 {
2001 _M_value *= __f;
2002 return *this;
2003 }
2004
2005 constexpr complex&
2006 operator/=(_Tp __f)
2007 {
2008 _M_value /= __f;
2009 return *this;
2010 }
2011
2012 // Let the compiler synthesize the copy and assignment
2013 // operator. It always does a pretty good job.
2014 constexpr complex(const complex&) = default;
2015 constexpr complex& operator=(const complex&) = default;
2016
2017 template<typename _Up>
2018 constexpr complex&
2019 operator=(const complex<_Up>& __z)
2020 {
2021 __real__ _M_value = __z.real();
2022 __imag__ _M_value = __z.imag();
2023 return *this;
2024 }
2025
2026 template<typename _Up>
2027 constexpr complex&
2028 operator+=(const complex<_Up>& __z)
2029 {
2030 _M_value += __z.__rep();
2031 return *this;
2032 }
2033
2034 template<class _Up>
2035 constexpr complex&
2036 operator-=(const complex<_Up>& __z)
2037 {
2038 _M_value -= __z.__rep();
2039 return *this;
2040 }
2041
2042 template<class _Up>
2043 constexpr complex&
2044 operator*=(const complex<_Up>& __z)
2045 {
2046 const _ComplexT __t = __z.__rep();
2047 _M_value *= __t;
2048 return *this;
2049 }
2050
2051 template<class _Up>
2052 constexpr complex&
2053 operator/=(const complex<_Up>& __z)
2054 {
2055 const _ComplexT __t = __z.__rep();
2056 _M_value /= __t;
2057 return *this;
2058 }
2059
2060 constexpr _ComplexT __rep() const { return _M_value; }
2061
2062 _GLIBCXX26_DECLARE_COMPLEX_TUPLE_HELPER_ACCESSOR
2063
2064 private:
2065 _ComplexT _M_value;
2066 };
2067#endif
2068
2069#undef _GLIBCXX26_DECLARE_COMPLEX_TUPLE_HELPER_ACCESSOR
2070
2071#if __cplusplus <= 202002L
2072 // These bits have to be at the end of this file, so that the
2073 // specializations have all been defined.
2074 inline _GLIBCXX_CONSTEXPR
2075 complex<float>::complex(const complex<double>& __z)
2076 : _M_value(__z.__rep()) { }
2077
2078 inline _GLIBCXX_CONSTEXPR
2079 complex<float>::complex(const complex<long double>& __z)
2080 : _M_value(__z.__rep()) { }
2081
2082 inline _GLIBCXX_CONSTEXPR
2083 complex<double>::complex(const complex<long double>& __z)
2084 : _M_value(__z.__rep()) { }
2085#endif
2086
2087 // Inhibit implicit instantiations for required instantiations,
2088 // which are defined via explicit instantiations elsewhere.
2089 // NB: This syntax is a GNU extension.
2090#if _GLIBCXX_EXTERN_TEMPLATE
2091 extern template istream& operator>>(istream&, complex<float>&);
2092 extern template ostream& operator<<(ostream&, const complex<float>&);
2093 extern template istream& operator>>(istream&, complex<double>&);
2094 extern template ostream& operator<<(ostream&, const complex<double>&);
2095 extern template istream& operator>>(istream&, complex<long double>&);
2096 extern template ostream& operator<<(ostream&, const complex<long double>&);
2097
2098#ifdef _GLIBCXX_USE_WCHAR_T
2099 extern template wistream& operator>>(wistream&, complex<float>&);
2100 extern template wostream& operator<<(wostream&, const complex<float>&);
2101 extern template wistream& operator>>(wistream&, complex<double>&);
2102 extern template wostream& operator<<(wostream&, const complex<double>&);
2103 extern template wistream& operator>>(wistream&, complex<long double>&);
2104 extern template wostream& operator<<(wostream&, const complex<long double>&);
2105#endif
2106#endif
2107
2108 /// @} group complex_numbers
2109
2110_GLIBCXX_END_NAMESPACE_VERSION
2111} // namespace
2112
2113#if __cplusplus >= 201103L
2114
2115namespace std _GLIBCXX_VISIBILITY(default)
2116{
2117_GLIBCXX_BEGIN_NAMESPACE_VERSION
2118
2119 // Forward declarations.
2120 template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&);
2121 template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&);
2122 template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&);
2123
2124 template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&);
2125 template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&);
2126 template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&);
2127
2128 template<typename _Tp>
2129 inline std::complex<_Tp>
2130 __complex_acos(const std::complex<_Tp>& __z)
2131 {
2132 const std::complex<_Tp> __t = std::asin(__z);
2133 const _Tp __pi_2 = (_Tp) 1.5707963267948966192313216916397514L;
2134 return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag());
2135 }
2136
2137#if _GLIBCXX_USE_C99_COMPLEX_ARC
2138#if defined(__STDCPP_FLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
2139 inline __complex__ _Float16
2140 __complex_acos(__complex__ _Float16 __z)
2141 { return static_cast<__complex__ _Float16>(__builtin_cacosf(__z)); }
2142
2143 inline __complex__ _Float16
2144 __complex_asin(__complex__ _Float16 __z)
2145 { return static_cast<__complex__ _Float16>(__builtin_casinf(__z)); }
2146
2147 inline __complex__ _Float16
2148 __complex_atan(__complex__ _Float16 __z)
2149 { return static_cast<__complex__ _Float16>(__builtin_catanf(__z)); }
2150
2151 inline __complex__ _Float16
2152 __complex_acosh(__complex__ _Float16 __z)
2153 { return static_cast<__complex__ _Float16>(__builtin_cacoshf(__z)); }
2154
2155 inline __complex__ _Float16
2156 __complex_asinh(__complex__ _Float16 __z)
2157 { return static_cast<__complex__ _Float16>(__builtin_casinhf(__z)); }
2158
2159 inline __complex__ _Float16
2160 __complex_atanh(__complex__ _Float16 __z)
2161 { return static_cast<__complex__ _Float16>(__builtin_catanhf(__z)); }
2162#endif
2163
2164#if defined(__STDCPP_FLOAT32_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
2165 inline __complex__ _Float32
2166 __complex_acos(__complex__ _Float32 __z)
2167 { return __builtin_cacosf(__z); }
2168
2169 inline __complex__ _Float32
2170 __complex_asin(__complex__ _Float32 __z)
2171 { return __builtin_casinf(__z); }
2172
2173 inline __complex__ _Float32
2174 __complex_atan(__complex__ _Float32 __z)
2175 { return __builtin_catanf(__z); }
2176
2177 inline __complex__ _Float32
2178 __complex_acosh(__complex__ _Float32 __z)
2179 { return __builtin_cacoshf(__z); }
2180
2181 inline __complex__ _Float32
2182 __complex_asinh(__complex__ _Float32 __z)
2183 { return __builtin_casinhf(__z); }
2184
2185 inline __complex__ _Float32
2186 __complex_atanh(__complex__ _Float32 __z)
2187 { return __builtin_catanhf(__z); }
2188#endif
2189
2190#if defined(__STDCPP_FLOAT64_T__) && defined(_GLIBCXX_DOUBLE_IS_IEEE_BINARY64)
2191 inline __complex__ _Float64
2192 __complex_acos(__complex__ _Float64 __z)
2193 { return __builtin_cacos(__z); }
2194
2195 inline __complex__ _Float64
2196 __complex_asin(__complex__ _Float64 __z)
2197 { return __builtin_casin(__z); }
2198
2199 inline __complex__ _Float64
2200 __complex_atan(__complex__ _Float64 __z)
2201 { return __builtin_catan(__z); }
2202
2203 inline __complex__ _Float64
2204 __complex_acosh(__complex__ _Float64 __z)
2205 { return __builtin_cacosh(__z); }
2206
2207 inline __complex__ _Float64
2208 __complex_asinh(__complex__ _Float64 __z)
2209 { return __builtin_casinh(__z); }
2210
2211 inline __complex__ _Float64
2212 __complex_atanh(__complex__ _Float64 __z)
2213 { return __builtin_catanh(__z); }
2214#endif
2215
2216#if defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_LDOUBLE_IS_IEEE_BINARY128)
2217 inline __complex__ _Float128
2218 __complex_acos(__complex__ _Float128 __z)
2219 { return __builtin_cacosl(__z); }
2220
2221 inline __complex__ _Float128
2222 __complex_asin(__complex__ _Float128 __z)
2223 { return __builtin_casinl(__z); }
2224
2225 inline __complex__ _Float128
2226 __complex_atan(__complex__ _Float128 __z)
2227 { return __builtin_catanl(__z); }
2228
2229 inline __complex__ _Float128
2230 __complex_acosh(__complex__ _Float128 __z)
2231 { return __builtin_cacoshl(__z); }
2232
2233 inline __complex__ _Float128
2234 __complex_asinh(__complex__ _Float128 __z)
2235 { return __builtin_casinhl(__z); }
2236
2237 inline __complex__ _Float128
2238 __complex_atanh(__complex__ _Float128 __z)
2239 { return __builtin_catanhl(__z); }
2240#elif defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_HAVE_FLOAT128_MATH)
2241 inline __complex__ _Float128
2242 __complex_acos(__complex__ _Float128 __z)
2243 { return __builtin_cacosf128(__z); }
2244
2245 inline __complex__ _Float128
2246 __complex_asin(__complex__ _Float128 __z)
2247 { return __builtin_casinf128(__z); }
2248
2249 inline __complex__ _Float128
2250 __complex_atan(__complex__ _Float128 __z)
2251 { return __builtin_catanf128(__z); }
2252
2253 inline __complex__ _Float128
2254 __complex_acosh(__complex__ _Float128 __z)
2255 { return __builtin_cacoshf128(__z); }
2256
2257 inline __complex__ _Float128
2258 __complex_asinh(__complex__ _Float128 __z)
2259 { return __builtin_casinhf128(__z); }
2260
2261 inline __complex__ _Float128
2262 __complex_atanh(__complex__ _Float128 __z)
2263 { return __builtin_catanhf128(__z); }
2264#endif
2265
2266#if defined(__STDCPP_BFLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
2267 inline __complex__ decltype(0.0bf16)
2268 __complex_acos(__complex__ decltype(0.0bf16) __z)
2269 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_cacosf(__z)); }
2270
2271 inline __complex__ decltype(0.0bf16)
2272 __complex_asin(__complex__ decltype(0.0bf16) __z)
2273 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_casinf(__z)); }
2274
2275 inline __complex__ decltype(0.0bf16)
2276 __complex_atan(__complex__ decltype(0.0bf16) __z)
2277 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_catanf(__z)); }
2278
2279 inline __complex__ decltype(0.0bf16)
2280 __complex_acosh(__complex__ decltype(0.0bf16) __z)
2281 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_cacoshf(__z)); }
2282
2283 inline __complex__ decltype(0.0bf16)
2284 __complex_asinh(__complex__ decltype(0.0bf16) __z)
2285 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_casinhf(__z)); }
2286
2287 inline __complex__ decltype(0.0bf16)
2288 __complex_atanh(__complex__ decltype(0.0bf16) __z)
2289 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_catanhf(__z)); }
2290#endif
2291#endif
2292
2293#if _GLIBCXX_USE_C99_COMPLEX_ARC
2294 inline __complex__ float
2295 __complex_acos(__complex__ float __z)
2296 { return __builtin_cacosf(__z); }
2297
2298 inline __complex__ double
2299 __complex_acos(__complex__ double __z)
2300 { return __builtin_cacos(__z); }
2301
2302 inline __complex__ long double
2303 __complex_acos(const __complex__ long double& __z)
2304 { return __builtin_cacosl(__z); }
2305
2306 template<typename _Tp>
2307 inline std::complex<_Tp>
2308 acos(const std::complex<_Tp>& __z)
2309 { return __complex_acos(__z.__rep()); }
2310#else
2311 /// acos(__z) C++11 26.4.8 [complex.transcendentals]
2312 // Effects: Behaves the same as C99 function cacos, defined
2313 // in subclause 7.3.5.1.
2314 template<typename _Tp>
2315 inline std::complex<_Tp>
2316 acos(const std::complex<_Tp>& __z)
2317 { return __complex_acos(__z); }
2318#endif
2319
2320 template<typename _Tp>
2321 inline std::complex<_Tp>
2322 __complex_asin(const std::complex<_Tp>& __z)
2323 {
2324 std::complex<_Tp> __t(-__z.imag(), __z.real());
2325 __t = std::asinh(__t);
2326 return std::complex<_Tp>(__t.imag(), -__t.real());
2327 }
2328
2329#if _GLIBCXX_USE_C99_COMPLEX_ARC
2330 inline __complex__ float
2331 __complex_asin(__complex__ float __z)
2332 { return __builtin_casinf(__z); }
2333
2334 inline __complex__ double
2335 __complex_asin(__complex__ double __z)
2336 { return __builtin_casin(__z); }
2337
2338 inline __complex__ long double
2339 __complex_asin(const __complex__ long double& __z)
2340 { return __builtin_casinl(__z); }
2341
2342 template<typename _Tp>
2343 inline std::complex<_Tp>
2344 asin(const std::complex<_Tp>& __z)
2345 { return __complex_asin(__z.__rep()); }
2346#else
2347 /// asin(__z) C++11 26.4.8 [complex.transcendentals]
2348 // Effects: Behaves the same as C99 function casin, defined
2349 // in subclause 7.3.5.2.
2350 template<typename _Tp>
2351 inline std::complex<_Tp>
2352 asin(const std::complex<_Tp>& __z)
2353 { return __complex_asin(__z); }
2354#endif
2355
2356 template<typename _Tp>
2357 std::complex<_Tp>
2358 __complex_atan(const std::complex<_Tp>& __z)
2359 {
2360 const _Tp __r2 = __z.real() * __z.real();
2361 const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();
2362
2363 _Tp __num = __z.imag() + _Tp(1.0);
2364 _Tp __den = __z.imag() - _Tp(1.0);
2365
2366 __num = __r2 + __num * __num;
2367 __den = __r2 + __den * __den;
2368
2369 return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x),
2370 _Tp(0.25) * log(__num / __den));
2371 }
2372
2373#if _GLIBCXX_USE_C99_COMPLEX_ARC
2374 inline __complex__ float
2375 __complex_atan(__complex__ float __z)
2376 { return __builtin_catanf(__z); }
2377
2378 inline __complex__ double
2379 __complex_atan(__complex__ double __z)
2380 { return __builtin_catan(__z); }
2381
2382 inline __complex__ long double
2383 __complex_atan(const __complex__ long double& __z)
2384 { return __builtin_catanl(__z); }
2385
2386 template<typename _Tp>
2387 inline std::complex<_Tp>
2388 atan(const std::complex<_Tp>& __z)
2389 { return __complex_atan(__z.__rep()); }
2390#else
2391 /// atan(__z) C++11 26.4.8 [complex.transcendentals]
2392 // Effects: Behaves the same as C99 function catan, defined
2393 // in subclause 7.3.5.3.
2394 template<typename _Tp>
2395 inline std::complex<_Tp>
2396 atan(const std::complex<_Tp>& __z)
2397 { return __complex_atan(__z); }
2398#endif
2399
2400 template<typename _Tp>
2401 std::complex<_Tp>
2402 __complex_acosh(const std::complex<_Tp>& __z)
2403 {
2404 // Kahan's formula.
2405 return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0)))
2406 + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0))));
2407 }
2408
2409#if _GLIBCXX_USE_C99_COMPLEX_ARC
2410 inline __complex__ float
2411 __complex_acosh(__complex__ float __z)
2412 { return __builtin_cacoshf(__z); }
2413
2414 inline __complex__ double
2415 __complex_acosh(__complex__ double __z)
2416 { return __builtin_cacosh(__z); }
2417
2418 inline __complex__ long double
2419 __complex_acosh(const __complex__ long double& __z)
2420 { return __builtin_cacoshl(__z); }
2421
2422 template<typename _Tp>
2423 inline std::complex<_Tp>
2424 acosh(const std::complex<_Tp>& __z)
2425 { return __complex_acosh(__z.__rep()); }
2426#else
2427 /// acosh(__z) C++11 26.4.8 [complex.transcendentals]
2428 // Effects: Behaves the same as C99 function cacosh, defined
2429 // in subclause 7.3.6.1.
2430 template<typename _Tp>
2431 inline std::complex<_Tp>
2432 acosh(const std::complex<_Tp>& __z)
2433 { return __complex_acosh(__z); }
2434#endif
2435
2436 template<typename _Tp>
2437 std::complex<_Tp>
2438 __complex_asinh(const std::complex<_Tp>& __z)
2439 {
2440 std::complex<_Tp> __t((__z.real() - __z.imag())
2441 * (__z.real() + __z.imag()) + _Tp(1.0),
2442 _Tp(2.0) * __z.real() * __z.imag());
2443 __t = std::sqrt(__t);
2444
2445 return std::log(__t + __z);
2446 }
2447
2448#if _GLIBCXX_USE_C99_COMPLEX_ARC
2449 inline __complex__ float
2450 __complex_asinh(__complex__ float __z)
2451 { return __builtin_casinhf(__z); }
2452
2453 inline __complex__ double
2454 __complex_asinh(__complex__ double __z)
2455 { return __builtin_casinh(__z); }
2456
2457 inline __complex__ long double
2458 __complex_asinh(const __complex__ long double& __z)
2459 { return __builtin_casinhl(__z); }
2460
2461 template<typename _Tp>
2462 inline std::complex<_Tp>
2463 asinh(const std::complex<_Tp>& __z)
2464 { return __complex_asinh(__z.__rep()); }
2465#else
2466 /// asinh(__z) C++11 26.4.8 [complex.transcendentals]
2467 // Effects: Behaves the same as C99 function casin, defined
2468 // in subclause 7.3.6.2.
2469 template<typename _Tp>
2470 inline std::complex<_Tp>
2471 asinh(const std::complex<_Tp>& __z)
2472 { return __complex_asinh(__z); }
2473#endif
2474
2475 template<typename _Tp>
2476 std::complex<_Tp>
2477 __complex_atanh(const std::complex<_Tp>& __z)
2478 {
2479 const _Tp __i2 = __z.imag() * __z.imag();
2480 const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();
2481
2482 _Tp __num = _Tp(1.0) + __z.real();
2483 _Tp __den = _Tp(1.0) - __z.real();
2484
2485 __num = __i2 + __num * __num;
2486 __den = __i2 + __den * __den;
2487
2488 return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)),
2489 _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));
2490 }
2491
2492#if _GLIBCXX_USE_C99_COMPLEX_ARC
2493 inline __complex__ float
2494 __complex_atanh(__complex__ float __z)
2495 { return __builtin_catanhf(__z); }
2496
2497 inline __complex__ double
2498 __complex_atanh(__complex__ double __z)
2499 { return __builtin_catanh(__z); }
2500
2501 inline __complex__ long double
2502 __complex_atanh(const __complex__ long double& __z)
2503 { return __builtin_catanhl(__z); }
2504
2505 template<typename _Tp>
2506 inline std::complex<_Tp>
2507 atanh(const std::complex<_Tp>& __z)
2508 { return __complex_atanh(__z.__rep()); }
2509#else
2510 /// atanh(__z) C++11 26.4.8 [complex.transcendentals]
2511 // Effects: Behaves the same as C99 function catanh, defined
2512 // in subclause 7.3.6.3.
2513 template<typename _Tp>
2514 inline std::complex<_Tp>
2515 atanh(const std::complex<_Tp>& __z)
2516 { return __complex_atanh(__z); }
2517#endif
2518
2519 template<typename _Tp>
2520 _GLIBCXX11_DEPRECATED_SUGGEST("std::abs")
2521 inline _Tp
2522 /// fabs(__z) TR1 8.1.8 [tr.c99.cmplx.fabs]
2523 // Effects: Behaves the same as C99 function cabs, defined
2524 // in subclause 7.3.8.1.
2525 fabs(const std::complex<_Tp>& __z)
2526 { return std::abs(__z); }
2527
2528 // Additional overloads C++11 26.4.9 [cmplx.over]
2529
2530 template<typename _Tp>
2531 inline typename __gnu_cxx::__promote<_Tp>::__type
2532 arg(_Tp __x)
2533 {
2534 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
2535#if (_GLIBCXX11_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC)
2536 return __builtin_signbit(__type(__x))
2537 ? __type(3.1415926535897932384626433832795029L) : __type();
2538#else
2539 return std::arg(std::complex<__type>(__x));
2540#endif
2541 }
2542
2543 template<typename _Tp>
2544 _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type
2545 imag(_Tp)
2546 { return _Tp(); }
2547
2548 template<typename _Tp>
2549 _GLIBCXX20_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type
2550 norm(_Tp __x)
2551 {
2552 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
2553 return __type(__x) * __type(__x);
2554 }
2555
2556 template<typename _Tp>
2557 _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type
2558 real(_Tp __x)
2559 { return __x; }
2560
2561 template<typename _Tp, typename _Up>
2562 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
2563 pow(const std::complex<_Tp>& __x, const _Up& __y)
2564 {
2565 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
2566 return std::pow(std::complex<__type>(__x), __type(__y));
2567 }
2568
2569 template<typename _Tp, typename _Up>
2570 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
2571 pow(const _Tp& __x, const std::complex<_Up>& __y)
2572 {
2573 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
2574 return std::pow(__type(__x), std::complex<__type>(__y));
2575 }
2576
2577 template<typename _Tp, typename _Up>
2578 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
2579 pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y)
2580 {
2581 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
2582 return std::pow(std::complex<__type>(__x),
2583 std::complex<__type>(__y));
2584 }
2585
2586 // Forward declarations.
2587 // DR 781.
2588 template<typename _Tp>
2589 std::complex<_Tp> proj(const std::complex<_Tp>&);
2590
2591 // Generic implementation of std::proj, does not work for infinities.
2592 template<typename _Tp>
2593 inline std::complex<_Tp>
2594 __complex_proj(const std::complex<_Tp>& __z)
2595 { return __z; }
2596
2597#if _GLIBCXX_USE_C99_COMPLEX
2598 inline complex<float>
2599 __complex_proj(const complex<float>& __z)
2600 { return __builtin_cprojf(__z.__rep()); }
2601
2602 inline complex<double>
2603 __complex_proj(const complex<double>& __z)
2604 { return __builtin_cproj(__z.__rep()); }
2605
2606 inline complex<long double>
2607 __complex_proj(const complex<long double>& __z)
2608 { return __builtin_cprojl(__z.__rep()); }
2609
2610#if __cplusplus > 202002L
2611#if defined(__STDCPP_FLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
2612 inline __complex__ _Float16
2613 __complex_proj(__complex__ _Float16 __z)
2614 { return static_cast<__complex__ _Float16>(__builtin_cprojf(__z)); }
2615#endif
2616
2617#if defined(__STDCPP_FLOAT32_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
2618 inline __complex__ _Float32
2619 __complex_proj(__complex__ _Float32 __z)
2620 { return __builtin_cprojf(__z); }
2621#endif
2622
2623#if defined(__STDCPP_FLOAT64_T__) && defined(_GLIBCXX_DOUBLE_IS_IEEE_BINARY64)
2624 inline __complex__ _Float64
2625 __complex_proj(__complex__ _Float64 __z)
2626 { return __builtin_cproj(__z); }
2627#endif
2628
2629#if defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_LDOUBLE_IS_IEEE_BINARY128)
2630 inline __complex__ _Float128
2631 __complex_proj(__complex__ _Float128 __z)
2632 { return __builtin_cprojl(__z); }
2633#elif defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_HAVE_FLOAT128_MATH)
2634 inline __complex__ _Float128
2635 __complex_proj(__complex__ _Float128 __z)
2636 { return __builtin_cprojf128(__z); }
2637#endif
2638
2639#if defined(__STDCPP_BFLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
2640 inline __complex__ decltype(0.0bf16)
2641 __complex_proj(__complex__ decltype(0.0bf16) __z)
2642 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_cprojf(__z)); }
2643#endif
2644
2645 template<typename _Tp>
2646 requires requires { typename __complex_type<_Tp>::type; }
2647 inline complex<_Tp>
2648 __complex_proj(const complex<_Tp>& __z)
2649 { return __complex_proj(__z.__rep()); }
2650#endif
2651
2652#elif defined _GLIBCXX_USE_C99_MATH_FUNCS
2653 inline complex<float>
2654 __complex_proj(const complex<float>& __z)
2655 {
2656 if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag()))
2657 return complex<float>(__builtin_inff(),
2658 __builtin_copysignf(0.0f, __z.imag()));
2659 return __z;
2660 }
2661
2662 inline complex<double>
2663 __complex_proj(const complex<double>& __z)
2664 {
2665 if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag()))
2666 return complex<double>(__builtin_inf(),
2667 __builtin_copysign(0.0, __z.imag()));
2668 return __z;
2669 }
2670
2671 inline complex<long double>
2672 __complex_proj(const complex<long double>& __z)
2673 {
2674 if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag()))
2675 return complex<long double>(__builtin_infl(),
2676 __builtin_copysignl(0.0l, __z.imag()));
2677 return __z;
2678 }
2679#endif
2680
2681 template<typename _Tp>
2682 inline std::complex<_Tp>
2683 proj(const std::complex<_Tp>& __z)
2684 { return __complex_proj(__z); }
2685
2686 // Overload for scalars
2687 template<typename _Tp>
2688 inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
2689 proj(_Tp __x)
2690 {
2691 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
2692 return std::proj(std::complex<__type>(__x));
2693 }
2694
2695 template<typename _Tp>
2696 inline _GLIBCXX20_CONSTEXPR
2697 std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
2698 conj(_Tp __x)
2699 {
2700 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
2701 return std::complex<__type>(__x, -__type());
2702 }
2703
2704#ifdef __cpp_lib_complex_udls // C++ >= 14
2705
2706inline namespace literals {
2707inline namespace complex_literals {
2708#pragma GCC diagnostic push
2709#pragma GCC diagnostic ignored "-Wliteral-suffix"
2710
2711 constexpr std::complex<float>
2712 operator""if(long double __num)
2713 { return std::complex<float>{0.0F, static_cast<float>(__num)}; }
2714
2715 constexpr std::complex<float>
2716 operator""if(unsigned long long __num)
2717 { return std::complex<float>{0.0F, static_cast<float>(__num)}; }
2718
2719 constexpr std::complex<double>
2720 operator""i(long double __num)
2721 { return std::complex<double>{0.0, static_cast<double>(__num)}; }
2722
2723 constexpr std::complex<double>
2724 operator""i(unsigned long long __num)
2725 { return std::complex<double>{0.0, static_cast<double>(__num)}; }
2726
2727 constexpr std::complex<long double>
2728 operator""il(long double __num)
2729 { return std::complex<long double>{0.0L, __num}; }
2730
2731 constexpr std::complex<long double>
2732 operator""il(unsigned long long __num)
2733 { return std::complex<long double>{0.0L, static_cast<long double>(__num)}; }
2734
2735#pragma GCC diagnostic pop
2736} // inline namespace complex_literals
2737} // inline namespace literals
2738
2739#endif // __cpp_lib_complex_udls
2740
2741_GLIBCXX_END_NAMESPACE_VERSION
2742} // namespace
2743
2744#endif // C++11
2745
2746#ifdef _GLIBCXX_CLANG
2747#pragma clang diagnostic pop
2748#endif
2749
2750#pragma GCC diagnostic pop
2751#endif /* _GLIBCXX_COMPLEX */
std::log10
complex< _Tp > log10(const complex< _Tp > &)
Return complex base 10 logarithm of z.
Definition complex:1167
std::operator*
constexpr complex< _Tp > operator*(const complex< _Tp > &__x, const complex< _Tp > &__y)
Return new complex value x times y.
Definition complex:434
std::sin
complex< _Tp > sin(const complex< _Tp > &)
Return complex sine of z.
Definition complex:1197
std::operator-
constexpr complex< _Tp > operator-(const complex< _Tp > &__x, const complex< _Tp > &__y)
Return new complex value x minus y.
Definition complex:404
std::complex::operator*=
constexpr complex< _Tp > & operator*=(const _Tp &)
Multiply this complex number by a scalar.
Definition complex:293
std::log
complex< _Tp > log(const complex< _Tp > &)
Return complex natural logarithm of z.
Definition complex:1162
std::tan
complex< _Tp > tan(const complex< _Tp > &)
Return complex tangent of z.
Definition complex:1298
std::operator+
constexpr complex< _Tp > operator+(const complex< _Tp > &__x, const complex< _Tp > &__y)
Return new complex value x plus y.
Definition complex:374
std::abs
_Tp abs(const complex< _Tp > &)
Return magnitude of z.
Definition complex:968
std::polar
complex< _Tp > polar(const _Tp &, const _Tp &=_Tp(0))
Return complex with magnitude rho and angle theta.
Definition complex:1039
std::exp
complex< _Tp > exp(const complex< _Tp > &)
Return complex base e exponential of z.
Definition complex:1135
std::cosh
complex< _Tp > cosh(const complex< _Tp > &)
Return complex hyperbolic cosine of z.
Definition complex:1109
std::arg
_Tp arg(const complex< _Tp > &)
Return phase angle of z.
Definition complex:995
std::complex::operator=
constexpr complex< _Tp > & operator=(const _Tp &)
Assign a scalar to this complex number.
Definition complex:283
std::tanh
complex< _Tp > tanh(const complex< _Tp > &)
Return complex hyperbolic tangent of z.
Definition complex:1326
std::conj
constexpr complex< _Tp > conj(const complex< _Tp > &)
Return complex conjugate of z.
Definition complex:1047
std::pow
complex< _Tp > pow(const complex< _Tp > &, int)
Return x to the y'th power.
Definition complex:1357
std::operator/
constexpr complex< _Tp > operator/(const complex< _Tp > &__x, const complex< _Tp > &__y)
Return new complex value x divided by y.
Definition complex:464
std::sinh
complex< _Tp > sinh(const complex< _Tp > &)
Return complex hyperbolic sine of z.
Definition complex:1227
std::norm
_Tp constexpr norm(const complex< _Tp > &)
Return z magnitude squared.
Definition complex:1031
std::complex::operator/=
constexpr complex< _Tp > & operator/=(const _Tp &)
Divide this complex number by a scalar.
Definition complex:303
std::cos
complex< _Tp > cos(const complex< _Tp > &)
Return complex cosine of z.
Definition complex:1079
std::sqrt
complex< _Tp > sqrt(const complex< _Tp > &)
Return complex square root of z.
Definition complex:1271
std::ostream
basic_ostream< char > ostream
Base class for char output streams.
Definition iosfwd:145
std::istream
basic_istream< char > istream
Base class for char input streams.
Definition iosfwd:142
std::wostream
basic_ostream< wchar_t > wostream
Base class for wchar_t output streams.
Definition iosfwd:185
std::wistream
basic_istream< wchar_t > wistream
Base class for wchar_t input streams.
Definition iosfwd:182
std::move
constexpr std::remove_reference< _Tp >::type && move(_Tp &&__t) noexcept
Convert a value to an rvalue.
Definition move.h:138
std::max
constexpr const _Tp & max(const _Tp &, const _Tp &)
This does what you think it does.
Definition stl_algobase.h:258
std
ISO C++ entities toplevel namespace is std.
std::fabs
_Tp fabs(const std::complex< _Tp > &__z)
fabs(__z) TR1 8.1.8 [tr.c99.cmplx.fabs]
Definition complex:2525
std::operator>>
std::basic_istream< _CharT, _Traits > & operator>>(std::basic_istream< _CharT, _Traits > &__is, bitset< _Nb > &__x)
Global I/O operators for bitsets.
Definition bitset:1637
std::operator<<
std::basic_ostream< _CharT, _Traits > & operator<<(std::basic_ostream< _CharT, _Traits > &__os, const bitset< _Nb > &__x)
Global I/O operators for bitsets.
Definition bitset:1733
std::complex::value_type
_Tp value_type
Value typedef.
Definition complex:160
std::complex::complex
constexpr complex(const _Tp &__r=_Tp(), const _Tp &__i=_Tp())
Default constructor. First parameter is x, second parameter is y. Unspecified parameters default to 0...
Definition complex:164
std::complex::complex
constexpr complex(const complex< _Up > &__z)
Converting constructor.
Definition complex:177
std::complex::operator-=
constexpr complex< _Tp > & operator-=(const _Tp &__t)
Subtract a scalar from this complex number.
Definition complex:231
std::complex::operator+=
constexpr complex< _Tp > & operator+=(const _Tp &__t)
Add a scalar to this complex number.
Definition complex:222
std::basic_ios::setstate
void setstate(iostate __state)
Sets additional flags in the error state.
Definition basic_ios.h:166
std::basic_ios::widen
char_type widen(char __c) const
Widens characters.
Definition basic_ios.h:464
std::basic_istream
Template class basic_istream.
Definition istream:63
std::basic_istream::putback
__istream_type & putback(char_type __c)
Unextracting a single character.
Definition istream.tcc:771
std::integral_constant
integral_constant
Definition type_traits:95
std::ios_base::flags
fmtflags flags() const
Access to format flags.
Definition ios_base.h:694
std::ios_base::failbit
static const iostate failbit
Indicates that an input operation failed to read the expected characters, or that an output operation...
Definition ios_base.h:465
std::tuple_size
Finds the size of a given tuple type.
Definition utility.h:51
std::tuple_element
Gives the type of the ith element of a given tuple type.
Definition utility.h:82