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>
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& = 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>
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>&
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>&
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>&
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>&
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>&
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>&
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>&
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>&
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>
494 { return __x; }
495
496 /// Return complex negation of @a x.
497 template<typename _Tp>
498 inline _GLIBCXX20_CONSTEXPR complex<_Tp>
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>&
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)
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 // 26.2.7/4: 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 >= 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>
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) / 2);
1242 return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
1243 }
1244 else
1245 {
1246 _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x)));
1247 _Tp __u = __t / 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>(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>(1) / std::__complex_pow_unsigned(__z, -(unsigned)__n)
1361 : std::__complex_pow_unsigned(__z, __n);
1362 }
1363
1364 template<typename _Tp>
1365 complex<_Tp>
1366 pow(const complex<_Tp>& __x, const _Tp& __y)
1367 {
1368#if ! _GLIBCXX_USE_C99_COMPLEX
1369 if (__x == _Tp())
1370 return _Tp();
1371#endif
1372 if (__x.imag() == _Tp() && __x.real() > _Tp())
1373 return pow(__x.real(), __y);
1374
1375 complex<_Tp> __t = std::log(__x);
1376 return std::polar<_Tp>(exp(__y * __t.real()), __y * __t.imag());
1377 }
1378
1379 template<typename _Tp>
1380 inline complex<_Tp>
1381 __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1382 { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); }
1383
1384#if _GLIBCXX_USE_C99_COMPLEX
1385 inline __complex__ float
1386 __complex_pow(__complex__ float __x, __complex__ float __y)
1387 { return __builtin_cpowf(__x, __y); }
1388
1389 inline __complex__ double
1390 __complex_pow(__complex__ double __x, __complex__ double __y)
1391 { return __builtin_cpow(__x, __y); }
1392
1393 inline __complex__ long double
1394 __complex_pow(const __complex__ long double& __x,
1395 const __complex__ long double& __y)
1396 { return __builtin_cpowl(__x, __y); }
1397
1398 template<typename _Tp>
1399 inline complex<_Tp>
1400 pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1401 { return __complex_pow(__x.__rep(), __y.__rep()); }
1402#else
1403 template<typename _Tp>
1404 inline complex<_Tp>
1405 pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1406 { return __complex_pow(__x, __y); }
1407#endif
1408
1409 template<typename _Tp>
1410 inline complex<_Tp>
1411 pow(const _Tp& __x, const complex<_Tp>& __y)
1412 {
1413 return __x > _Tp() ? std::polar<_Tp>(pow(__x, __y.real()),
1414 __y.imag() * log(__x))
1415 : std::pow(complex<_Tp>(__x), __y);
1416 }
1417
1418#if __glibcxx_tuple_like >= 202311L // >= C++26
1419#define _GLIBCXX26_DECLARE_COMPLEX_TUPLE_HELPER_ACCESSOR \
1420 template<typename _Cp> \
1421 [[__gnu__::__always_inline__]] \
1422 constexpr auto& \
1423 __get_part(this _Cp& __z, size_t __i) noexcept \
1424 { \
1425 return __i == 0 ? __real__ __z._M_value \
1426 : __imag__ __z._M_value; \
1427 }
1428#else
1429#define _GLIBCXX26_DECLARE_COMPLEX_TUPLE_HELPER_ACCESSOR
1430#endif
1431
1432 /// 26.2.3 complex specializations
1433 /// complex<float> specialization
1434 template<>
1435 class complex<float>
1436 {
1437 public:
1438 typedef float value_type;
1439 typedef __complex__ float _ComplexT;
1440
1441 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
1442
1443 _GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f)
1444#if __cplusplus >= 201103L
1445 : _M_value{ __r, __i } { }
1446#else
1447 {
1448 __real__ _M_value = __r;
1449 __imag__ _M_value = __i;
1450 }
1451#endif
1452
1453#if __cplusplus >= 201103L
1454 _GLIBCXX14_CONSTEXPR complex(const complex&) = default;
1455#endif
1456
1457#if __cplusplus > 202002L
1458 template<typename _Up>
1459 explicit(!requires(_Up __u) { value_type{__u}; })
1460 constexpr complex(const complex<_Up>& __z)
1461 : _M_value{ value_type(__z.real()), value_type(__z.imag()) } { }
1462#else
1463 explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&);
1464 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&);
1465#endif
1466
1467#if __cplusplus >= 201103L
1468 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1469 // DR 387. std::complex over-encapsulated.
1470 __attribute ((__abi_tag__ ("cxx11")))
1471 constexpr float
1472 real() const { return __real__ _M_value; }
1473
1474 __attribute ((__abi_tag__ ("cxx11")))
1475 constexpr float
1476 imag() const { return __imag__ _M_value; }
1477#else
1478 float&
1479 real() { return __real__ _M_value; }
1480
1481 const float&
1482 real() const { return __real__ _M_value; }
1483
1484 float&
1485 imag() { return __imag__ _M_value; }
1486
1487 const float&
1488 imag() const { return __imag__ _M_value; }
1489#endif
1490
1491 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1492 // DR 387. std::complex over-encapsulated.
1493 _GLIBCXX20_CONSTEXPR void
1494 real(float __val) { __real__ _M_value = __val; }
1495
1496 _GLIBCXX20_CONSTEXPR void
1497 imag(float __val) { __imag__ _M_value = __val; }
1498
1499 _GLIBCXX20_CONSTEXPR complex&
1500 operator=(float __f)
1501 {
1502 _M_value = __f;
1503 return *this;
1504 }
1505
1506 _GLIBCXX20_CONSTEXPR complex&
1507 operator+=(float __f)
1508 {
1509 _M_value += __f;
1510 return *this;
1511 }
1512
1513 _GLIBCXX20_CONSTEXPR complex&
1514 operator-=(float __f)
1515 {
1516 _M_value -= __f;
1517 return *this;
1518 }
1519
1520 _GLIBCXX20_CONSTEXPR complex&
1521 operator*=(float __f)
1522 {
1523 _M_value *= __f;
1524 return *this;
1525 }
1526
1527 _GLIBCXX20_CONSTEXPR complex&
1528 operator/=(float __f)
1529 {
1530 _M_value /= __f;
1531 return *this;
1532 }
1533
1534 // Let the compiler synthesize the copy and assignment
1535 // operator. It always does a pretty good job.
1536#if __cplusplus >= 201103L
1537 _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default;
1538#endif
1539
1540 template<typename _Tp>
1541 _GLIBCXX20_CONSTEXPR complex&
1542 operator=(const complex<_Tp>& __z)
1543 {
1544 __real__ _M_value = __z.real();
1545 __imag__ _M_value = __z.imag();
1546 return *this;
1547 }
1548
1549 template<typename _Tp>
1550 _GLIBCXX20_CONSTEXPR complex&
1551 operator+=(const complex<_Tp>& __z)
1552 {
1553 _M_value += __z.__rep();
1554 return *this;
1555 }
1556
1557 template<class _Tp>
1558 _GLIBCXX20_CONSTEXPR complex&
1559 operator-=(const complex<_Tp>& __z)
1560 {
1561 _M_value -= __z.__rep();
1562 return *this;
1563 }
1564
1565 template<class _Tp>
1566 _GLIBCXX20_CONSTEXPR complex&
1567 operator*=(const complex<_Tp>& __z)
1568 {
1569 const _ComplexT __t = __z.__rep();
1570 _M_value *= __t;
1571 return *this;
1572 }
1573
1574 template<class _Tp>
1575 _GLIBCXX20_CONSTEXPR complex&
1576 operator/=(const complex<_Tp>& __z)
1577 {
1578 const _ComplexT __t = __z.__rep();
1579 _M_value /= __t;
1580 return *this;
1581 }
1582
1583 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
1584
1585 _GLIBCXX26_DECLARE_COMPLEX_TUPLE_HELPER_ACCESSOR
1586
1587 private:
1588 _ComplexT _M_value;
1589 };
1590
1591 /// 26.2.3 complex specializations
1592 /// complex<double> specialization
1593 template<>
1594 class complex<double>
1595 {
1596 public:
1597 typedef double value_type;
1598 typedef __complex__ double _ComplexT;
1599
1600 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
1601
1602 _GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0)
1603#if __cplusplus >= 201103L
1604 : _M_value{ __r, __i } { }
1605#else
1606 {
1607 __real__ _M_value = __r;
1608 __imag__ _M_value = __i;
1609 }
1610#endif
1611
1612#if __cplusplus >= 201103L
1613 _GLIBCXX14_CONSTEXPR complex(const complex&) = default;
1614#endif
1615
1616#if __cplusplus > 202002L
1617 template<typename _Up>
1618 explicit(!requires(_Up __u) { value_type{__u}; })
1619 constexpr complex(const complex<_Up>& __z)
1620 : _M_value{ value_type(__z.real()), value_type(__z.imag()) } { }
1621#else
1622 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
1623 : _M_value(__z.__rep()) { }
1624
1625 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&);
1626#endif
1627
1628#if __cplusplus >= 201103L
1629 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1630 // DR 387. std::complex over-encapsulated.
1631 __attribute ((__abi_tag__ ("cxx11")))
1632 constexpr double
1633 real() const { return __real__ _M_value; }
1634
1635 __attribute ((__abi_tag__ ("cxx11")))
1636 constexpr double
1637 imag() const { return __imag__ _M_value; }
1638#else
1639 double&
1640 real() { return __real__ _M_value; }
1641
1642 const double&
1643 real() const { return __real__ _M_value; }
1644
1645 double&
1646 imag() { return __imag__ _M_value; }
1647
1648 const double&
1649 imag() const { return __imag__ _M_value; }
1650#endif
1651
1652 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1653 // DR 387. std::complex over-encapsulated.
1654 _GLIBCXX20_CONSTEXPR void
1655 real(double __val) { __real__ _M_value = __val; }
1656
1657 _GLIBCXX20_CONSTEXPR void
1658 imag(double __val) { __imag__ _M_value = __val; }
1659
1660 _GLIBCXX20_CONSTEXPR complex&
1661 operator=(double __d)
1662 {
1663 _M_value = __d;
1664 return *this;
1665 }
1666
1667 _GLIBCXX20_CONSTEXPR complex&
1668 operator+=(double __d)
1669 {
1670 _M_value += __d;
1671 return *this;
1672 }
1673
1674 _GLIBCXX20_CONSTEXPR complex&
1675 operator-=(double __d)
1676 {
1677 _M_value -= __d;
1678 return *this;
1679 }
1680
1681 _GLIBCXX20_CONSTEXPR complex&
1682 operator*=(double __d)
1683 {
1684 _M_value *= __d;
1685 return *this;
1686 }
1687
1688 _GLIBCXX20_CONSTEXPR complex&
1689 operator/=(double __d)
1690 {
1691 _M_value /= __d;
1692 return *this;
1693 }
1694
1695 // The compiler will synthesize this, efficiently.
1696#if __cplusplus >= 201103L
1697 _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default;
1698#endif
1699
1700 template<typename _Tp>
1701 _GLIBCXX20_CONSTEXPR complex&
1702 operator=(const complex<_Tp>& __z)
1703 {
1704 _M_value = __z.__rep();
1705 return *this;
1706 }
1707
1708 template<typename _Tp>
1709 _GLIBCXX20_CONSTEXPR complex&
1710 operator+=(const complex<_Tp>& __z)
1711 {
1712 _M_value += __z.__rep();
1713 return *this;
1714 }
1715
1716 template<typename _Tp>
1717 _GLIBCXX20_CONSTEXPR complex&
1718 operator-=(const complex<_Tp>& __z)
1719 {
1720 _M_value -= __z.__rep();
1721 return *this;
1722 }
1723
1724 template<typename _Tp>
1725 _GLIBCXX20_CONSTEXPR complex&
1726 operator*=(const complex<_Tp>& __z)
1727 {
1728 const _ComplexT __t = __z.__rep();
1729 _M_value *= __t;
1730 return *this;
1731 }
1732
1733 template<typename _Tp>
1734 _GLIBCXX20_CONSTEXPR complex&
1735 operator/=(const complex<_Tp>& __z)
1736 {
1737 const _ComplexT __t = __z.__rep();
1738 _M_value /= __t;
1739 return *this;
1740 }
1741
1742 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
1743
1744 _GLIBCXX26_DECLARE_COMPLEX_TUPLE_HELPER_ACCESSOR
1745
1746 private:
1747 _ComplexT _M_value;
1748 };
1749
1750 /// 26.2.3 complex specializations
1751 /// complex<long double> specialization
1752 template<>
1753 class complex<long double>
1754 {
1755 public:
1756 typedef long double value_type;
1757 typedef __complex__ long double _ComplexT;
1758
1759 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
1760
1761 _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L,
1762 long double __i = 0.0L)
1763#if __cplusplus >= 201103L
1764 : _M_value{ __r, __i } { }
1765#else
1766 {
1767 __real__ _M_value = __r;
1768 __imag__ _M_value = __i;
1769 }
1770#endif
1771
1772#if __cplusplus >= 201103L
1773 _GLIBCXX14_CONSTEXPR complex(const complex&) = default;
1774#endif
1775
1776#if __cplusplus > 202002L
1777 template<typename _Up>
1778 explicit(!requires(_Up __u) { value_type{__u}; })
1779 constexpr complex(const complex<_Up>& __z)
1780 : _M_value{ value_type(__z.real()), value_type(__z.imag()) } { }
1781#else
1782 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
1783 : _M_value(__z.__rep()) { }
1784
1785 _GLIBCXX_CONSTEXPR complex(const complex<double>& __z)
1786 : _M_value(__z.__rep()) { }
1787#endif
1788
1789#if __cplusplus >= 201103L
1790 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1791 // DR 387. std::complex over-encapsulated.
1792 __attribute ((__abi_tag__ ("cxx11")))
1793 constexpr long double
1794 real() const { return __real__ _M_value; }
1795
1796 __attribute ((__abi_tag__ ("cxx11")))
1797 constexpr long double
1798 imag() const { return __imag__ _M_value; }
1799#else
1800 long double&
1801 real() { return __real__ _M_value; }
1802
1803 const long double&
1804 real() const { return __real__ _M_value; }
1805
1806 long double&
1807 imag() { return __imag__ _M_value; }
1808
1809 const long double&
1810 imag() const { return __imag__ _M_value; }
1811#endif
1812
1813 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1814 // DR 387. std::complex over-encapsulated.
1815 _GLIBCXX20_CONSTEXPR void
1816 real(long double __val) { __real__ _M_value = __val; }
1817
1818 _GLIBCXX20_CONSTEXPR void
1819 imag(long double __val) { __imag__ _M_value = __val; }
1820
1821 _GLIBCXX20_CONSTEXPR complex&
1822 operator=(long double __r)
1823 {
1824 _M_value = __r;
1825 return *this;
1826 }
1827
1828 _GLIBCXX20_CONSTEXPR complex&
1829 operator+=(long double __r)
1830 {
1831 _M_value += __r;
1832 return *this;
1833 }
1834
1835 _GLIBCXX20_CONSTEXPR complex&
1836 operator-=(long double __r)
1837 {
1838 _M_value -= __r;
1839 return *this;
1840 }
1841
1842 _GLIBCXX20_CONSTEXPR complex&
1843 operator*=(long double __r)
1844 {
1845 _M_value *= __r;
1846 return *this;
1847 }
1848
1849 _GLIBCXX20_CONSTEXPR complex&
1850 operator/=(long double __r)
1851 {
1852 _M_value /= __r;
1853 return *this;
1854 }
1855
1856 // The compiler knows how to do this efficiently
1857#if __cplusplus >= 201103L
1858 _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default;
1859#endif
1860
1861 template<typename _Tp>
1862 _GLIBCXX20_CONSTEXPR complex&
1863 operator=(const complex<_Tp>& __z)
1864 {
1865 _M_value = __z.__rep();
1866 return *this;
1867 }
1868
1869 template<typename _Tp>
1870 _GLIBCXX20_CONSTEXPR complex&
1871 operator+=(const complex<_Tp>& __z)
1872 {
1873 _M_value += __z.__rep();
1874 return *this;
1875 }
1876
1877 template<typename _Tp>
1878 _GLIBCXX20_CONSTEXPR complex&
1879 operator-=(const complex<_Tp>& __z)
1880 {
1881 _M_value -= __z.__rep();
1882 return *this;
1883 }
1884
1885 template<typename _Tp>
1886 _GLIBCXX20_CONSTEXPR complex&
1887 operator*=(const complex<_Tp>& __z)
1888 {
1889 const _ComplexT __t = __z.__rep();
1890 _M_value *= __t;
1891 return *this;
1892 }
1893
1894 template<typename _Tp>
1895 _GLIBCXX20_CONSTEXPR complex&
1896 operator/=(const complex<_Tp>& __z)
1897 {
1898 const _ComplexT __t = __z.__rep();
1899 _M_value /= __t;
1900 return *this;
1901 }
1902
1903 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
1904
1905 _GLIBCXX26_DECLARE_COMPLEX_TUPLE_HELPER_ACCESSOR
1906
1907 private:
1908 _ComplexT _M_value;
1909 };
1910
1911#if __cplusplus > 202002L
1912 template<typename _Tp>
1913 struct __complex_type
1914 { };
1915
1916#ifdef __STDCPP_FLOAT16_T__
1917 template<>
1918 struct __complex_type<_Float16>
1919 { typedef __complex__ _Float16 type; };
1920#endif
1921
1922#ifdef __STDCPP_FLOAT32_T__
1923 template<>
1924 struct __complex_type<_Float32>
1925 { typedef __complex__ _Float32 type; };
1926#endif
1927
1928#ifdef __STDCPP_FLOAT64_T__
1929 template<>
1930 struct __complex_type<_Float64>
1931 { typedef __complex__ _Float64 type; };
1932#endif
1933
1934#ifdef __STDCPP_FLOAT128_T__
1935 template<>
1936 struct __complex_type<_Float128>
1937 { typedef __complex__ _Float128 type; };
1938#endif
1939
1940#ifdef __STDCPP_BFLOAT16_T__
1941 template<>
1942 struct __complex_type<__gnu_cxx::__bfloat16_t>
1943 { typedef __complex__ decltype(0.0bf16) type; };
1944#endif
1945
1946 template<typename _Tp>
1947 requires requires { typename __complex_type<_Tp>::type; }
1948 class complex<_Tp>
1949 {
1950 public:
1951 typedef _Tp value_type;
1952 typedef typename std::__complex_type<_Tp>::type _ComplexT;
1953
1954 constexpr complex(_ComplexT __z) : _M_value(__z) { }
1955
1956 constexpr complex(_Tp __r = _Tp(), _Tp __i = _Tp())
1957 : _M_value{ __r, __i } { }
1958
1959 template<typename _Up>
1960 explicit(!requires(_Up __u) { value_type{__u}; })
1961 constexpr complex(const complex<_Up>& __z)
1962 : _M_value{ value_type(__z.real()), value_type(__z.imag()) } { }
1963
1964 constexpr _Tp
1965 real() const { return __real__ _M_value; }
1966
1967 constexpr _Tp
1968 imag() const { return __imag__ _M_value; }
1969
1970 constexpr void
1971 real(_Tp __val) { __real__ _M_value = __val; }
1972
1973 constexpr void
1974 imag(_Tp __val) { __imag__ _M_value = __val; }
1975
1976 constexpr complex&
1977 operator=(_Tp __f)
1978 {
1979 _M_value = __f;
1980 return *this;
1981 }
1982
1983 constexpr complex&
1984 operator+=(_Tp __f)
1985 {
1986 _M_value += __f;
1987 return *this;
1988 }
1989
1990 constexpr complex&
1991 operator-=(_Tp __f)
1992 {
1993 _M_value -= __f;
1994 return *this;
1995 }
1996
1997 constexpr complex&
1998 operator*=(_Tp __f)
1999 {
2000 _M_value *= __f;
2001 return *this;
2002 }
2003
2004 constexpr complex&
2005 operator/=(_Tp __f)
2006 {
2007 _M_value /= __f;
2008 return *this;
2009 }
2010
2011 // Let the compiler synthesize the copy and assignment
2012 // operator. It always does a pretty good job.
2013 constexpr complex(const complex&) = default;
2014 constexpr complex& operator=(const complex&) = default;
2015
2016 template<typename _Up>
2017 constexpr complex&
2018 operator=(const complex<_Up>& __z)
2019 {
2020 __real__ _M_value = __z.real();
2021 __imag__ _M_value = __z.imag();
2022 return *this;
2023 }
2024
2025 template<typename _Up>
2026 constexpr complex&
2027 operator+=(const complex<_Up>& __z)
2028 {
2029 _M_value += __z.__rep();
2030 return *this;
2031 }
2032
2033 template<class _Up>
2034 constexpr complex&
2035 operator-=(const complex<_Up>& __z)
2036 {
2037 _M_value -= __z.__rep();
2038 return *this;
2039 }
2040
2041 template<class _Up>
2042 constexpr complex&
2043 operator*=(const complex<_Up>& __z)
2044 {
2045 const _ComplexT __t = __z.__rep();
2046 _M_value *= __t;
2047 return *this;
2048 }
2049
2050 template<class _Up>
2051 constexpr complex&
2052 operator/=(const complex<_Up>& __z)
2053 {
2054 const _ComplexT __t = __z.__rep();
2055 _M_value /= __t;
2056 return *this;
2057 }
2058
2059 constexpr _ComplexT __rep() const { return _M_value; }
2060
2061 _GLIBCXX26_DECLARE_COMPLEX_TUPLE_HELPER_ACCESSOR
2062
2063 private:
2064 _ComplexT _M_value;
2065 };
2066#endif
2067
2068#undef _GLIBCXX26_DECLARE_COMPLEX_TUPLE_HELPER_ACCESSOR
2069
2070#if __cplusplus <= 202002L
2071 // These bits have to be at the end of this file, so that the
2072 // specializations have all been defined.
2073 inline _GLIBCXX_CONSTEXPR
2074 complex<float>::complex(const complex<double>& __z)
2075 : _M_value(__z.__rep()) { }
2076
2077 inline _GLIBCXX_CONSTEXPR
2078 complex<float>::complex(const complex<long double>& __z)
2079 : _M_value(__z.__rep()) { }
2080
2081 inline _GLIBCXX_CONSTEXPR
2082 complex<double>::complex(const complex<long double>& __z)
2083 : _M_value(__z.__rep()) { }
2084#endif
2085
2086 // Inhibit implicit instantiations for required instantiations,
2087 // which are defined via explicit instantiations elsewhere.
2088 // NB: This syntax is a GNU extension.
2089#if _GLIBCXX_EXTERN_TEMPLATE
2090 extern template istream& operator>>(istream&, complex<float>&);
2091 extern template ostream& operator<<(ostream&, const complex<float>&);
2092 extern template istream& operator>>(istream&, complex<double>&);
2093 extern template ostream& operator<<(ostream&, const complex<double>&);
2094 extern template istream& operator>>(istream&, complex<long double>&);
2095 extern template ostream& operator<<(ostream&, const complex<long double>&);
2096
2097#ifdef _GLIBCXX_USE_WCHAR_T
2098 extern template wistream& operator>>(wistream&, complex<float>&);
2099 extern template wostream& operator<<(wostream&, const complex<float>&);
2100 extern template wistream& operator>>(wistream&, complex<double>&);
2101 extern template wostream& operator<<(wostream&, const complex<double>&);
2102 extern template wistream& operator>>(wistream&, complex<long double>&);
2103 extern template wostream& operator<<(wostream&, const complex<long double>&);
2104#endif
2105#endif
2106
2107 /// @} group complex_numbers
2108
2109_GLIBCXX_END_NAMESPACE_VERSION
2110} // namespace
2111
2112#if __cplusplus >= 201103L
2113
2114namespace std _GLIBCXX_VISIBILITY(default)
2115{
2116_GLIBCXX_BEGIN_NAMESPACE_VERSION
2117
2118 // Forward declarations.
2119 template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&);
2120 template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&);
2121 template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&);
2122
2123 template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&);
2124 template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&);
2125 template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&);
2126 // DR 595.
2127 template<typename _Tp> _Tp fabs(const std::complex<_Tp>&);
2128
2129 template<typename _Tp>
2130 inline std::complex<_Tp>
2131 __complex_acos(const std::complex<_Tp>& __z)
2132 {
2133 const std::complex<_Tp> __t = std::asin(__z);
2134 const _Tp __pi_2 = (_Tp) 1.5707963267948966192313216916397514L;
2135 return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag());
2136 }
2137
2138#if _GLIBCXX_USE_C99_COMPLEX_ARC
2139#if defined(__STDCPP_FLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
2140 inline __complex__ _Float16
2141 __complex_acos(__complex__ _Float16 __z)
2142 { return static_cast<__complex__ _Float16>(__builtin_cacosf(__z)); }
2143
2144 inline __complex__ _Float16
2145 __complex_asin(__complex__ _Float16 __z)
2146 { return static_cast<__complex__ _Float16>(__builtin_casinf(__z)); }
2147
2148 inline __complex__ _Float16
2149 __complex_atan(__complex__ _Float16 __z)
2150 { return static_cast<__complex__ _Float16>(__builtin_catanf(__z)); }
2151
2152 inline __complex__ _Float16
2153 __complex_acosh(__complex__ _Float16 __z)
2154 { return static_cast<__complex__ _Float16>(__builtin_cacoshf(__z)); }
2155
2156 inline __complex__ _Float16
2157 __complex_asinh(__complex__ _Float16 __z)
2158 { return static_cast<__complex__ _Float16>(__builtin_casinhf(__z)); }
2159
2160 inline __complex__ _Float16
2161 __complex_atanh(__complex__ _Float16 __z)
2162 { return static_cast<__complex__ _Float16>(__builtin_catanhf(__z)); }
2163#endif
2164
2165#if defined(__STDCPP_FLOAT32_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
2166 inline __complex__ _Float32
2167 __complex_acos(__complex__ _Float32 __z)
2168 { return __builtin_cacosf(__z); }
2169
2170 inline __complex__ _Float32
2171 __complex_asin(__complex__ _Float32 __z)
2172 { return __builtin_casinf(__z); }
2173
2174 inline __complex__ _Float32
2175 __complex_atan(__complex__ _Float32 __z)
2176 { return __builtin_catanf(__z); }
2177
2178 inline __complex__ _Float32
2179 __complex_acosh(__complex__ _Float32 __z)
2180 { return __builtin_cacoshf(__z); }
2181
2182 inline __complex__ _Float32
2183 __complex_asinh(__complex__ _Float32 __z)
2184 { return __builtin_casinhf(__z); }
2185
2186 inline __complex__ _Float32
2187 __complex_atanh(__complex__ _Float32 __z)
2188 { return __builtin_catanhf(__z); }
2189#endif
2190
2191#if defined(__STDCPP_FLOAT64_T__) && defined(_GLIBCXX_DOUBLE_IS_IEEE_BINARY64)
2192 inline __complex__ _Float64
2193 __complex_acos(__complex__ _Float64 __z)
2194 { return __builtin_cacos(__z); }
2195
2196 inline __complex__ _Float64
2197 __complex_asin(__complex__ _Float64 __z)
2198 { return __builtin_casin(__z); }
2199
2200 inline __complex__ _Float64
2201 __complex_atan(__complex__ _Float64 __z)
2202 { return __builtin_catan(__z); }
2203
2204 inline __complex__ _Float64
2205 __complex_acosh(__complex__ _Float64 __z)
2206 { return __builtin_cacosh(__z); }
2207
2208 inline __complex__ _Float64
2209 __complex_asinh(__complex__ _Float64 __z)
2210 { return __builtin_casinh(__z); }
2211
2212 inline __complex__ _Float64
2213 __complex_atanh(__complex__ _Float64 __z)
2214 { return __builtin_catanh(__z); }
2215#endif
2216
2217#if defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_LDOUBLE_IS_IEEE_BINARY128)
2218 inline __complex__ _Float128
2219 __complex_acos(__complex__ _Float128 __z)
2220 { return __builtin_cacosl(__z); }
2221
2222 inline __complex__ _Float128
2223 __complex_asin(__complex__ _Float128 __z)
2224 { return __builtin_casinl(__z); }
2225
2226 inline __complex__ _Float128
2227 __complex_atan(__complex__ _Float128 __z)
2228 { return __builtin_catanl(__z); }
2229
2230 inline __complex__ _Float128
2231 __complex_acosh(__complex__ _Float128 __z)
2232 { return __builtin_cacoshl(__z); }
2233
2234 inline __complex__ _Float128
2235 __complex_asinh(__complex__ _Float128 __z)
2236 { return __builtin_casinhl(__z); }
2237
2238 inline __complex__ _Float128
2239 __complex_atanh(__complex__ _Float128 __z)
2240 { return __builtin_catanhl(__z); }
2241#elif defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_HAVE_FLOAT128_MATH)
2242 inline __complex__ _Float128
2243 __complex_acos(__complex__ _Float128 __z)
2244 { return __builtin_cacosf128(__z); }
2245
2246 inline __complex__ _Float128
2247 __complex_asin(__complex__ _Float128 __z)
2248 { return __builtin_casinf128(__z); }
2249
2250 inline __complex__ _Float128
2251 __complex_atan(__complex__ _Float128 __z)
2252 { return __builtin_catanf128(__z); }
2253
2254 inline __complex__ _Float128
2255 __complex_acosh(__complex__ _Float128 __z)
2256 { return __builtin_cacoshf128(__z); }
2257
2258 inline __complex__ _Float128
2259 __complex_asinh(__complex__ _Float128 __z)
2260 { return __builtin_casinhf128(__z); }
2261
2262 inline __complex__ _Float128
2263 __complex_atanh(__complex__ _Float128 __z)
2264 { return __builtin_catanhf128(__z); }
2265#endif
2266
2267#if defined(__STDCPP_BFLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
2268 inline __complex__ decltype(0.0bf16)
2269 __complex_acos(__complex__ decltype(0.0bf16) __z)
2270 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_cacosf(__z)); }
2271
2272 inline __complex__ decltype(0.0bf16)
2273 __complex_asin(__complex__ decltype(0.0bf16) __z)
2274 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_casinf(__z)); }
2275
2276 inline __complex__ decltype(0.0bf16)
2277 __complex_atan(__complex__ decltype(0.0bf16) __z)
2278 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_catanf(__z)); }
2279
2280 inline __complex__ decltype(0.0bf16)
2281 __complex_acosh(__complex__ decltype(0.0bf16) __z)
2282 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_cacoshf(__z)); }
2283
2284 inline __complex__ decltype(0.0bf16)
2285 __complex_asinh(__complex__ decltype(0.0bf16) __z)
2286 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_casinhf(__z)); }
2287
2288 inline __complex__ decltype(0.0bf16)
2289 __complex_atanh(__complex__ decltype(0.0bf16) __z)
2290 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_catanhf(__z)); }
2291#endif
2292#endif
2293
2294#if _GLIBCXX_USE_C99_COMPLEX_ARC
2295 inline __complex__ float
2296 __complex_acos(__complex__ float __z)
2297 { return __builtin_cacosf(__z); }
2298
2299 inline __complex__ double
2300 __complex_acos(__complex__ double __z)
2301 { return __builtin_cacos(__z); }
2302
2303 inline __complex__ long double
2304 __complex_acos(const __complex__ long double& __z)
2305 { return __builtin_cacosl(__z); }
2306
2307 template<typename _Tp>
2308 inline std::complex<_Tp>
2309 acos(const std::complex<_Tp>& __z)
2310 { return __complex_acos(__z.__rep()); }
2311#else
2312 /// acos(__z) [8.1.2].
2313 // Effects: Behaves the same as C99 function cacos, defined
2314 // in subclause 7.3.5.1.
2315 template<typename _Tp>
2316 inline std::complex<_Tp>
2317 acos(const std::complex<_Tp>& __z)
2318 { return __complex_acos(__z); }
2319#endif
2320
2321 template<typename _Tp>
2322 inline std::complex<_Tp>
2323 __complex_asin(const std::complex<_Tp>& __z)
2324 {
2325 std::complex<_Tp> __t(-__z.imag(), __z.real());
2326 __t = std::asinh(__t);
2327 return std::complex<_Tp>(__t.imag(), -__t.real());
2328 }
2329
2330#if _GLIBCXX_USE_C99_COMPLEX_ARC
2331 inline __complex__ float
2332 __complex_asin(__complex__ float __z)
2333 { return __builtin_casinf(__z); }
2334
2335 inline __complex__ double
2336 __complex_asin(__complex__ double __z)
2337 { return __builtin_casin(__z); }
2338
2339 inline __complex__ long double
2340 __complex_asin(const __complex__ long double& __z)
2341 { return __builtin_casinl(__z); }
2342
2343 template<typename _Tp>
2344 inline std::complex<_Tp>
2345 asin(const std::complex<_Tp>& __z)
2346 { return __complex_asin(__z.__rep()); }
2347#else
2348 /// asin(__z) [8.1.3].
2349 // Effects: Behaves the same as C99 function casin, defined
2350 // in subclause 7.3.5.2.
2351 template<typename _Tp>
2352 inline std::complex<_Tp>
2353 asin(const std::complex<_Tp>& __z)
2354 { return __complex_asin(__z); }
2355#endif
2356
2357 template<typename _Tp>
2359 __complex_atan(const std::complex<_Tp>& __z)
2360 {
2361 const _Tp __r2 = __z.real() * __z.real();
2362 const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();
2363
2364 _Tp __num = __z.imag() + _Tp(1.0);
2365 _Tp __den = __z.imag() - _Tp(1.0);
2366
2367 __num = __r2 + __num * __num;
2368 __den = __r2 + __den * __den;
2369
2370 return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x),
2371 _Tp(0.25) * log(__num / __den));
2372 }
2373
2374#if _GLIBCXX_USE_C99_COMPLEX_ARC
2375 inline __complex__ float
2376 __complex_atan(__complex__ float __z)
2377 { return __builtin_catanf(__z); }
2378
2379 inline __complex__ double
2380 __complex_atan(__complex__ double __z)
2381 { return __builtin_catan(__z); }
2382
2383 inline __complex__ long double
2384 __complex_atan(const __complex__ long double& __z)
2385 { return __builtin_catanl(__z); }
2386
2387 template<typename _Tp>
2388 inline std::complex<_Tp>
2389 atan(const std::complex<_Tp>& __z)
2390 { return __complex_atan(__z.__rep()); }
2391#else
2392 /// atan(__z) [8.1.4].
2393 // Effects: Behaves the same as C99 function catan, defined
2394 // in subclause 7.3.5.3.
2395 template<typename _Tp>
2396 inline std::complex<_Tp>
2397 atan(const std::complex<_Tp>& __z)
2398 { return __complex_atan(__z); }
2399#endif
2400
2401 template<typename _Tp>
2403 __complex_acosh(const std::complex<_Tp>& __z)
2404 {
2405 // Kahan's formula.
2406 return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0)))
2407 + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0))));
2408 }
2409
2410#if _GLIBCXX_USE_C99_COMPLEX_ARC
2411 inline __complex__ float
2412 __complex_acosh(__complex__ float __z)
2413 { return __builtin_cacoshf(__z); }
2414
2415 inline __complex__ double
2416 __complex_acosh(__complex__ double __z)
2417 { return __builtin_cacosh(__z); }
2418
2419 inline __complex__ long double
2420 __complex_acosh(const __complex__ long double& __z)
2421 { return __builtin_cacoshl(__z); }
2422
2423 template<typename _Tp>
2424 inline std::complex<_Tp>
2425 acosh(const std::complex<_Tp>& __z)
2426 { return __complex_acosh(__z.__rep()); }
2427#else
2428 /// acosh(__z) [8.1.5].
2429 // Effects: Behaves the same as C99 function cacosh, defined
2430 // in subclause 7.3.6.1.
2431 template<typename _Tp>
2432 inline std::complex<_Tp>
2433 acosh(const std::complex<_Tp>& __z)
2434 { return __complex_acosh(__z); }
2435#endif
2436
2437 template<typename _Tp>
2439 __complex_asinh(const std::complex<_Tp>& __z)
2440 {
2441 std::complex<_Tp> __t((__z.real() - __z.imag())
2442 * (__z.real() + __z.imag()) + _Tp(1.0),
2443 _Tp(2.0) * __z.real() * __z.imag());
2444 __t = std::sqrt(__t);
2445
2446 return std::log(__t + __z);
2447 }
2448
2449#if _GLIBCXX_USE_C99_COMPLEX_ARC
2450 inline __complex__ float
2451 __complex_asinh(__complex__ float __z)
2452 { return __builtin_casinhf(__z); }
2453
2454 inline __complex__ double
2455 __complex_asinh(__complex__ double __z)
2456 { return __builtin_casinh(__z); }
2457
2458 inline __complex__ long double
2459 __complex_asinh(const __complex__ long double& __z)
2460 { return __builtin_casinhl(__z); }
2461
2462 template<typename _Tp>
2463 inline std::complex<_Tp>
2464 asinh(const std::complex<_Tp>& __z)
2465 { return __complex_asinh(__z.__rep()); }
2466#else
2467 /// asinh(__z) [8.1.6].
2468 // Effects: Behaves the same as C99 function casin, defined
2469 // in subclause 7.3.6.2.
2470 template<typename _Tp>
2471 inline std::complex<_Tp>
2472 asinh(const std::complex<_Tp>& __z)
2473 { return __complex_asinh(__z); }
2474#endif
2475
2476 template<typename _Tp>
2478 __complex_atanh(const std::complex<_Tp>& __z)
2479 {
2480 const _Tp __i2 = __z.imag() * __z.imag();
2481 const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();
2482
2483 _Tp __num = _Tp(1.0) + __z.real();
2484 _Tp __den = _Tp(1.0) - __z.real();
2485
2486 __num = __i2 + __num * __num;
2487 __den = __i2 + __den * __den;
2488
2489 return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)),
2490 _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));
2491 }
2492
2493#if _GLIBCXX_USE_C99_COMPLEX_ARC
2494 inline __complex__ float
2495 __complex_atanh(__complex__ float __z)
2496 { return __builtin_catanhf(__z); }
2497
2498 inline __complex__ double
2499 __complex_atanh(__complex__ double __z)
2500 { return __builtin_catanh(__z); }
2501
2502 inline __complex__ long double
2503 __complex_atanh(const __complex__ long double& __z)
2504 { return __builtin_catanhl(__z); }
2505
2506 template<typename _Tp>
2507 inline std::complex<_Tp>
2508 atanh(const std::complex<_Tp>& __z)
2509 { return __complex_atanh(__z.__rep()); }
2510#else
2511 /// atanh(__z) [8.1.7].
2512 // Effects: Behaves the same as C99 function catanh, defined
2513 // in subclause 7.3.6.3.
2514 template<typename _Tp>
2515 inline std::complex<_Tp>
2516 atanh(const std::complex<_Tp>& __z)
2517 { return __complex_atanh(__z); }
2518#endif
2519
2520 template<typename _Tp>
2521 inline _Tp
2522 /// fabs(__z) [8.1.8].
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 [8.1.9].
2529 template<typename _Tp>
2530 inline typename __gnu_cxx::__promote<_Tp>::__type
2531 arg(_Tp __x)
2532 {
2533 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
2534#if (_GLIBCXX11_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC)
2535 return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L)
2536 : __type();
2537#else
2538 return std::arg(std::complex<__type>(__x));
2539#endif
2540 }
2541
2542 template<typename _Tp>
2543 _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type
2544 imag(_Tp)
2545 { return _Tp(); }
2546
2547 template<typename _Tp>
2548 _GLIBCXX20_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type
2549 norm(_Tp __x)
2550 {
2551 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
2552 return __type(__x) * __type(__x);
2553 }
2554
2555 template<typename _Tp>
2556 _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type
2557 real(_Tp __x)
2558 { return __x; }
2559
2560 template<typename _Tp, typename _Up>
2562 pow(const std::complex<_Tp>& __x, const _Up& __y)
2563 {
2564 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
2565 return std::pow(std::complex<__type>(__x), __type(__y));
2566 }
2567
2568 template<typename _Tp, typename _Up>
2570 pow(const _Tp& __x, const std::complex<_Up>& __y)
2571 {
2572 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
2573 return std::pow(__type(__x), std::complex<__type>(__y));
2574 }
2575
2576 template<typename _Tp, typename _Up>
2578 pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y)
2579 {
2580 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
2581 return std::pow(std::complex<__type>(__x),
2583 }
2584
2585 // Forward declarations.
2586 // DR 781.
2587 template<typename _Tp>
2589
2590 // Generic implementation of std::proj, does not work for infinities.
2591 template<typename _Tp>
2592 inline std::complex<_Tp>
2593 __complex_proj(const std::complex<_Tp>& __z)
2594 { return __z; }
2595
2596#if _GLIBCXX_USE_C99_COMPLEX
2597 inline complex<float>
2598 __complex_proj(const complex<float>& __z)
2599 { return __builtin_cprojf(__z.__rep()); }
2600
2601 inline complex<double>
2602 __complex_proj(const complex<double>& __z)
2603 { return __builtin_cproj(__z.__rep()); }
2604
2605 inline complex<long double>
2606 __complex_proj(const complex<long double>& __z)
2607 { return __builtin_cprojl(__z.__rep()); }
2608
2609#if __cplusplus > 202002L
2610#if defined(__STDCPP_FLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
2611 inline __complex__ _Float16
2612 __complex_proj(__complex__ _Float16 __z)
2613 { return static_cast<__complex__ _Float16>(__builtin_cprojf(__z)); }
2614#endif
2615
2616#if defined(__STDCPP_FLOAT32_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
2617 inline __complex__ _Float32
2618 __complex_proj(__complex__ _Float32 __z)
2619 { return __builtin_cprojf(__z); }
2620#endif
2621
2622#if defined(__STDCPP_FLOAT64_T__) && defined(_GLIBCXX_DOUBLE_IS_IEEE_BINARY64)
2623 inline __complex__ _Float64
2624 __complex_proj(__complex__ _Float64 __z)
2625 { return __builtin_cproj(__z); }
2626#endif
2627
2628#if defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_LDOUBLE_IS_IEEE_BINARY128)
2629 inline __complex__ _Float128
2630 __complex_proj(__complex__ _Float128 __z)
2631 { return __builtin_cprojl(__z); }
2632#elif defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_HAVE_FLOAT128_MATH)
2633 inline __complex__ _Float128
2634 __complex_proj(__complex__ _Float128 __z)
2635 { return __builtin_cprojf128(__z); }
2636#endif
2637
2638#if defined(__STDCPP_BFLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
2639 inline __complex__ decltype(0.0bf16)
2640 __complex_proj(__complex__ decltype(0.0bf16) __z)
2641 { return static_cast<__complex__ decltype(0.0bf16)>(__builtin_cprojf(__z)); }
2642#endif
2643
2644 template<typename _Tp>
2645 requires requires { typename __complex_type<_Tp>::type; }
2646 inline complex<_Tp>
2647 __complex_proj(const complex<_Tp>& __z)
2648 { return __complex_proj(__z.__rep()); }
2649#endif
2650
2651#elif defined _GLIBCXX_USE_C99_MATH_FUNCS
2652 inline complex<float>
2653 __complex_proj(const complex<float>& __z)
2654 {
2655 if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag()))
2656 return complex<float>(__builtin_inff(),
2657 __builtin_copysignf(0.0f, __z.imag()));
2658 return __z;
2659 }
2660
2661 inline complex<double>
2662 __complex_proj(const complex<double>& __z)
2663 {
2664 if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag()))
2665 return complex<double>(__builtin_inf(),
2666 __builtin_copysign(0.0, __z.imag()));
2667 return __z;
2668 }
2669
2670 inline complex<long double>
2671 __complex_proj(const complex<long double>& __z)
2672 {
2673 if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag()))
2674 return complex<long double>(__builtin_infl(),
2675 __builtin_copysignl(0.0l, __z.imag()));
2676 return __z;
2677 }
2678#endif
2679
2680 template<typename _Tp>
2681 inline std::complex<_Tp>
2682 proj(const std::complex<_Tp>& __z)
2683 { return __complex_proj(__z); }
2684
2685 // Overload for scalars
2686 template<typename _Tp>
2688 proj(_Tp __x)
2689 {
2690 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
2691 return std::proj(std::complex<__type>(__x));
2692 }
2693
2694 template<typename _Tp>
2695 inline _GLIBCXX20_CONSTEXPR
2697 conj(_Tp __x)
2698 {
2699 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
2700 return std::complex<__type>(__x, -__type());
2701 }
2702
2703#ifdef __cpp_lib_complex_udls // C++ >= 14
2704
2705inline namespace literals {
2706inline namespace complex_literals {
2707#pragma GCC diagnostic push
2708#pragma GCC diagnostic ignored "-Wliteral-suffix"
2709
2710 constexpr std::complex<float>
2711 operator""if(long double __num)
2712 { return std::complex<float>{0.0F, static_cast<float>(__num)}; }
2713
2714 constexpr std::complex<float>
2715 operator""if(unsigned long long __num)
2716 { return std::complex<float>{0.0F, static_cast<float>(__num)}; }
2717
2718 constexpr std::complex<double>
2719 operator""i(long double __num)
2720 { return std::complex<double>{0.0, static_cast<double>(__num)}; }
2721
2722 constexpr std::complex<double>
2723 operator""i(unsigned long long __num)
2724 { return std::complex<double>{0.0, static_cast<double>(__num)}; }
2725
2727 operator""il(long double __num)
2728 { return std::complex<long double>{0.0L, __num}; }
2729
2731 operator""il(unsigned long long __num)
2732 { return std::complex<long double>{0.0L, static_cast<long double>(__num)}; }
2733
2734#pragma GCC diagnostic pop
2735} // inline namespace complex_literals
2736} // inline namespace literals
2737
2738#endif // __cpp_lib_complex_udls
2739
2740_GLIBCXX_END_NAMESPACE_VERSION
2741} // namespace
2742
2743#endif // C++11
2744
2745#ifdef _GLIBCXX_CLANG
2746#pragma clang diagnostic pop
2747#endif
2748
2749#pragma GCC diagnostic pop
2750#endif /* _GLIBCXX_COMPLEX */
complex< _Tp > log10(const complex< _Tp > &)
Return complex base 10 logarithm of z.
Definition complex:1167
constexpr complex< _Tp > operator*(const complex< _Tp > &__x, const complex< _Tp > &__y)
Return new complex value x times y.
Definition complex:434
complex< _Tp > sin(const complex< _Tp > &)
Return complex sine of z.
Definition complex:1197
constexpr complex< _Tp > operator-(const complex< _Tp > &__x, const complex< _Tp > &__y)
Return new complex value x minus y.
Definition complex:404
constexpr complex< _Tp > & operator*=(const _Tp &)
Multiply this complex number by a scalar.
Definition complex:293
complex< _Tp > log(const complex< _Tp > &)
Return complex natural logarithm of z.
Definition complex:1162
complex< _Tp > tan(const complex< _Tp > &)
Return complex tangent of z.
Definition complex:1298
complex< _Tp > polar(const _Tp &, const _Tp &=0)
Return complex with magnitude rho and angle theta.
Definition complex:1039
constexpr complex< _Tp > operator+(const complex< _Tp > &__x, const complex< _Tp > &__y)
Return new complex value x plus y.
Definition complex:374
_Tp abs(const complex< _Tp > &)
Return magnitude of z.
Definition complex:968
complex< _Tp > exp(const complex< _Tp > &)
Return complex base e exponential of z.
Definition complex:1135
complex< _Tp > cosh(const complex< _Tp > &)
Return complex hyperbolic cosine of z.
Definition complex:1109
_Tp arg(const complex< _Tp > &)
Return phase angle of z.
Definition complex:995
constexpr complex< _Tp > & operator=(const _Tp &)
Assign a scalar to this complex number.
Definition complex:283
complex< _Tp > tanh(const complex< _Tp > &)
Return complex hyperbolic tangent of z.
Definition complex:1326
constexpr complex< _Tp > conj(const complex< _Tp > &)
Return complex conjugate of z.
Definition complex:1047
complex< _Tp > pow(const complex< _Tp > &, int)
Return x to the y'th power.
Definition complex:1357
constexpr complex< _Tp > operator/(const complex< _Tp > &__x, const complex< _Tp > &__y)
Return new complex value x divided by y.
Definition complex:464
complex< _Tp > sinh(const complex< _Tp > &)
Return complex hyperbolic sine of z.
Definition complex:1227
_Tp constexpr norm(const complex< _Tp > &)
Return z magnitude squared.
Definition complex:1031
constexpr complex< _Tp > & operator/=(const _Tp &)
Divide this complex number by a scalar.
Definition complex:303
complex< _Tp > cos(const complex< _Tp > &)
Return complex cosine of z.
Definition complex:1079
complex< _Tp > sqrt(const complex< _Tp > &)
Return complex square root of z.
Definition complex:1271
basic_ostream< char > ostream
Base class for char output streams.
Definition iosfwd:145
basic_istream< char > istream
Base class for char input streams.
Definition iosfwd:142
basic_ostream< wchar_t > wostream
Base class for wchar_t output streams.
Definition iosfwd:185
basic_istream< wchar_t > wistream
Base class for wchar_t input streams.
Definition iosfwd:182
constexpr std::remove_reference< _Tp >::type && move(_Tp &&__t) noexcept
Convert a value to an rvalue.
Definition move.h:138
constexpr const _Tp & max(const _Tp &, const _Tp &)
This does what you think it does.
ISO C++ entities toplevel namespace is std.
std::basic_istream< _CharT, _Traits > & operator>>(std::basic_istream< _CharT, _Traits > &__is, bitset< _Nb > &__x)
Global I/O operators for bitsets.
Definition bitset:1602
std::basic_ostream< _CharT, _Traits > & operator<<(std::basic_ostream< _CharT, _Traits > &__os, const bitset< _Nb > &__x)
Global I/O operators for bitsets.
Definition bitset:1692
GNU extensions for public use.
_Tp value_type
Value typedef.
Definition complex:160
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
constexpr complex(const complex< _Up > &__z)
Converting constructor.
Definition complex:177
constexpr complex< _Tp > & operator-=(const _Tp &__t)
Subtract a scalar from this complex number.
Definition complex:231
constexpr complex< _Tp > & operator+=(const _Tp &__t)
Add a scalar to this complex number.
Definition complex:222
void setstate(iostate __state)
Sets additional flags in the error state.
Definition basic_ios.h:166
char_type widen(char __c) const
Widens characters.
Definition basic_ios.h:464
Template class basic_istream.
Definition istream:63
__istream_type & putback(char_type __c)
Unextracting a single character.
Definition istream.tcc:771
fmtflags flags() const
Access to format flags.
Definition ios_base.h:694
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