1// -*- C++ -*-
2//===--------------------------- complex ----------------------------------===//
3//
4// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
5// See https://llvm.org/LICENSE.txt for license information.
6// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
7//
8//===----------------------------------------------------------------------===//
9
10#ifndef _LIBCPP_COMPLEX
11#define _LIBCPP_COMPLEX
12
13/*
14 complex synopsis
15
16namespace std
17{
18
19template<class T>
20class complex
21{
22public:
23 typedef T value_type;
24
25 complex(const T& re = T(), const T& im = T()); // constexpr in C++14
26 complex(const complex&); // constexpr in C++14
27 template<class X> complex(const complex<X>&); // constexpr in C++14
28
29 T real() const; // constexpr in C++14
30 T imag() const; // constexpr in C++14
31
32 void real(T);
33 void imag(T);
34
35 complex<T>& operator= (const T&);
36 complex<T>& operator+=(const T&);
37 complex<T>& operator-=(const T&);
38 complex<T>& operator*=(const T&);
39 complex<T>& operator/=(const T&);
40
41 complex& operator=(const complex&);
42 template<class X> complex<T>& operator= (const complex<X>&);
43 template<class X> complex<T>& operator+=(const complex<X>&);
44 template<class X> complex<T>& operator-=(const complex<X>&);
45 template<class X> complex<T>& operator*=(const complex<X>&);
46 template<class X> complex<T>& operator/=(const complex<X>&);
47};
48
49template<>
50class complex<float>
51{
52public:
53 typedef float value_type;
54
55 constexpr complex(float re = 0.0f, float im = 0.0f);
56 explicit constexpr complex(const complex<double>&);
57 explicit constexpr complex(const complex<long double>&);
58
59 constexpr float real() const;
60 void real(float);
61 constexpr float imag() const;
62 void imag(float);
63
64 complex<float>& operator= (float);
65 complex<float>& operator+=(float);
66 complex<float>& operator-=(float);
67 complex<float>& operator*=(float);
68 complex<float>& operator/=(float);
69
70 complex<float>& operator=(const complex<float>&);
71 template<class X> complex<float>& operator= (const complex<X>&);
72 template<class X> complex<float>& operator+=(const complex<X>&);
73 template<class X> complex<float>& operator-=(const complex<X>&);
74 template<class X> complex<float>& operator*=(const complex<X>&);
75 template<class X> complex<float>& operator/=(const complex<X>&);
76};
77
78template<>
79class complex<double>
80{
81public:
82 typedef double value_type;
83
84 constexpr complex(double re = 0.0, double im = 0.0);
85 constexpr complex(const complex<float>&);
86 explicit constexpr complex(const complex<long double>&);
87
88 constexpr double real() const;
89 void real(double);
90 constexpr double imag() const;
91 void imag(double);
92
93 complex<double>& operator= (double);
94 complex<double>& operator+=(double);
95 complex<double>& operator-=(double);
96 complex<double>& operator*=(double);
97 complex<double>& operator/=(double);
98 complex<double>& operator=(const complex<double>&);
99
100 template<class X> complex<double>& operator= (const complex<X>&);
101 template<class X> complex<double>& operator+=(const complex<X>&);
102 template<class X> complex<double>& operator-=(const complex<X>&);
103 template<class X> complex<double>& operator*=(const complex<X>&);
104 template<class X> complex<double>& operator/=(const complex<X>&);
105};
106
107template<>
108class complex<long double>
109{
110public:
111 typedef long double value_type;
112
113 constexpr complex(long double re = 0.0L, long double im = 0.0L);
114 constexpr complex(const complex<float>&);
115 constexpr complex(const complex<double>&);
116
117 constexpr long double real() const;
118 void real(long double);
119 constexpr long double imag() const;
120 void imag(long double);
121
122 complex<long double>& operator=(const complex<long double>&);
123 complex<long double>& operator= (long double);
124 complex<long double>& operator+=(long double);
125 complex<long double>& operator-=(long double);
126 complex<long double>& operator*=(long double);
127 complex<long double>& operator/=(long double);
128
129 template<class X> complex<long double>& operator= (const complex<X>&);
130 template<class X> complex<long double>& operator+=(const complex<X>&);
131 template<class X> complex<long double>& operator-=(const complex<X>&);
132 template<class X> complex<long double>& operator*=(const complex<X>&);
133 template<class X> complex<long double>& operator/=(const complex<X>&);
134};
135
136// 26.3.6 operators:
137template<class T> complex<T> operator+(const complex<T>&, const complex<T>&);
138template<class T> complex<T> operator+(const complex<T>&, const T&);
139template<class T> complex<T> operator+(const T&, const complex<T>&);
140template<class T> complex<T> operator-(const complex<T>&, const complex<T>&);
141template<class T> complex<T> operator-(const complex<T>&, const T&);
142template<class T> complex<T> operator-(const T&, const complex<T>&);
143template<class T> complex<T> operator*(const complex<T>&, const complex<T>&);
144template<class T> complex<T> operator*(const complex<T>&, const T&);
145template<class T> complex<T> operator*(const T&, const complex<T>&);
146template<class T> complex<T> operator/(const complex<T>&, const complex<T>&);
147template<class T> complex<T> operator/(const complex<T>&, const T&);
148template<class T> complex<T> operator/(const T&, const complex<T>&);
149template<class T> complex<T> operator+(const complex<T>&);
150template<class T> complex<T> operator-(const complex<T>&);
151template<class T> bool operator==(const complex<T>&, const complex<T>&); // constexpr in C++14
152template<class T> bool operator==(const complex<T>&, const T&); // constexpr in C++14
153template<class T> bool operator==(const T&, const complex<T>&); // constexpr in C++14
154template<class T> bool operator!=(const complex<T>&, const complex<T>&); // constexpr in C++14
155template<class T> bool operator!=(const complex<T>&, const T&); // constexpr in C++14
156template<class T> bool operator!=(const T&, const complex<T>&); // constexpr in C++14
157
158template<class T, class charT, class traits>
159 basic_istream<charT, traits>&
160 operator>>(basic_istream<charT, traits>&, complex<T>&);
161template<class T, class charT, class traits>
162 basic_ostream<charT, traits>&
163 operator<<(basic_ostream<charT, traits>&, const complex<T>&);
164
165// 26.3.7 values:
166
167template<class T> T real(const complex<T>&); // constexpr in C++14
168 long double real(long double); // constexpr in C++14
169 double real(double); // constexpr in C++14
170template<Integral T> double real(T); // constexpr in C++14
171 float real(float); // constexpr in C++14
172
173template<class T> T imag(const complex<T>&); // constexpr in C++14
174 long double imag(long double); // constexpr in C++14
175 double imag(double); // constexpr in C++14
176template<Integral T> double imag(T); // constexpr in C++14
177 float imag(float); // constexpr in C++14
178
179template<class T> T abs(const complex<T>&);
180
181template<class T> T arg(const complex<T>&);
182 long double arg(long double);
183 double arg(double);
184template<Integral T> double arg(T);
185 float arg(float);
186
187template<class T> T norm(const complex<T>&);
188 long double norm(long double);
189 double norm(double);
190template<Integral T> double norm(T);
191 float norm(float);
192
193template<class T> complex<T> conj(const complex<T>&);
194 complex<long double> conj(long double);
195 complex<double> conj(double);
196template<Integral T> complex<double> conj(T);
197 complex<float> conj(float);
198
199template<class T> complex<T> proj(const complex<T>&);
200 complex<long double> proj(long double);
201 complex<double> proj(double);
202template<Integral T> complex<double> proj(T);
203 complex<float> proj(float);
204
205template<class T> complex<T> polar(const T&, const T& = T());
206
207// 26.3.8 transcendentals:
208template<class T> complex<T> acos(const complex<T>&);
209template<class T> complex<T> asin(const complex<T>&);
210template<class T> complex<T> atan(const complex<T>&);
211template<class T> complex<T> acosh(const complex<T>&);
212template<class T> complex<T> asinh(const complex<T>&);
213template<class T> complex<T> atanh(const complex<T>&);
214template<class T> complex<T> cos (const complex<T>&);
215template<class T> complex<T> cosh (const complex<T>&);
216template<class T> complex<T> exp (const complex<T>&);
217template<class T> complex<T> log (const complex<T>&);
218template<class T> complex<T> log10(const complex<T>&);
219
220template<class T> complex<T> pow(const complex<T>&, const T&);
221template<class T> complex<T> pow(const complex<T>&, const complex<T>&);
222template<class T> complex<T> pow(const T&, const complex<T>&);
223
224template<class T> complex<T> sin (const complex<T>&);
225template<class T> complex<T> sinh (const complex<T>&);
226template<class T> complex<T> sqrt (const complex<T>&);
227template<class T> complex<T> tan (const complex<T>&);
228template<class T> complex<T> tanh (const complex<T>&);
229
230template<class T, class charT, class traits>
231 basic_istream<charT, traits>&
232 operator>>(basic_istream<charT, traits>& is, complex<T>& x);
233
234template<class T, class charT, class traits>
235 basic_ostream<charT, traits>&
236 operator<<(basic_ostream<charT, traits>& o, const complex<T>& x);
237
238} // std
239
240*/
241
242#include <__config>
243#include <type_traits>
244#include <stdexcept>
245#include <cmath>
246#include <sstream>
247#include <version>
248
249#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
250#pragma GCC system_header
251#endif
252
253_LIBCPP_BEGIN_NAMESPACE_STD
254
255template<class _Tp> class _LIBCPP_TEMPLATE_VIS complex;
256
257template<class _Tp> complex<_Tp> operator*(const complex<_Tp>& __z, const complex<_Tp>& __w);
258template<class _Tp> complex<_Tp> operator/(const complex<_Tp>& __x, const complex<_Tp>& __y);
259
260template<class _Tp>
261class _LIBCPP_TEMPLATE_VIS complex
262{
263public:
264 typedef _Tp value_type;
265private:
266 value_type __re_;
267 value_type __im_;
268public:
269 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
270 complex(const value_type& __re = value_type(), const value_type& __im = value_type())
271 : __re_(__re), __im_(__im) {}
272 template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
273 complex(const complex<_Xp>& __c)
274 : __re_(__c.real()), __im_(__c.imag()) {}
275
276 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 value_type real() const {return __re_;}
277 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 value_type imag() const {return __im_;}
278
279 _LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
280 _LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
281
282 _LIBCPP_INLINE_VISIBILITY complex& operator= (const value_type& __re)
283 {__re_ = __re; __im_ = value_type(); return *this;}
284 _LIBCPP_INLINE_VISIBILITY complex& operator+=(const value_type& __re) {__re_ += __re; return *this;}
285 _LIBCPP_INLINE_VISIBILITY complex& operator-=(const value_type& __re) {__re_ -= __re; return *this;}
286 _LIBCPP_INLINE_VISIBILITY complex& operator*=(const value_type& __re) {__re_ *= __re; __im_ *= __re; return *this;}
287 _LIBCPP_INLINE_VISIBILITY complex& operator/=(const value_type& __re) {__re_ /= __re; __im_ /= __re; return *this;}
288
289 template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
290 {
291 __re_ = __c.real();
292 __im_ = __c.imag();
293 return *this;
294 }
295 template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
296 {
297 __re_ += __c.real();
298 __im_ += __c.imag();
299 return *this;
300 }
301 template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
302 {
303 __re_ -= __c.real();
304 __im_ -= __c.imag();
305 return *this;
306 }
307 template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
308 {
309 *this = *this * complex(__c.real(), __c.imag());
310 return *this;
311 }
312 template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
313 {
314 *this = *this / complex(__c.real(), __c.imag());
315 return *this;
316 }
317};
318
319template<> class _LIBCPP_TEMPLATE_VIS complex<double>;
320template<> class _LIBCPP_TEMPLATE_VIS complex<long double>;
321
322template<>
323class _LIBCPP_TEMPLATE_VIS complex<float>
324{
325 float __re_;
326 float __im_;
327public:
328 typedef float value_type;
329
330 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(float __re = 0.0f, float __im = 0.0f)
331 : __re_(__re), __im_(__im) {}
332 _LIBCPP_INLINE_VISIBILITY
333 explicit _LIBCPP_CONSTEXPR complex(const complex<double>& __c);
334 _LIBCPP_INLINE_VISIBILITY
335 explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c);
336
337 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR float real() const {return __re_;}
338 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR float imag() const {return __im_;}
339
340 _LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
341 _LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
342
343 _LIBCPP_INLINE_VISIBILITY complex& operator= (float __re)
344 {__re_ = __re; __im_ = value_type(); return *this;}
345 _LIBCPP_INLINE_VISIBILITY complex& operator+=(float __re) {__re_ += __re; return *this;}
346 _LIBCPP_INLINE_VISIBILITY complex& operator-=(float __re) {__re_ -= __re; return *this;}
347 _LIBCPP_INLINE_VISIBILITY complex& operator*=(float __re) {__re_ *= __re; __im_ *= __re; return *this;}
348 _LIBCPP_INLINE_VISIBILITY complex& operator/=(float __re) {__re_ /= __re; __im_ /= __re; return *this;}
349
350 template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
351 {
352 __re_ = __c.real();
353 __im_ = __c.imag();
354 return *this;
355 }
356 template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
357 {
358 __re_ += __c.real();
359 __im_ += __c.imag();
360 return *this;
361 }
362 template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
363 {
364 __re_ -= __c.real();
365 __im_ -= __c.imag();
366 return *this;
367 }
368 template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
369 {
370 *this = *this * complex(__c.real(), __c.imag());
371 return *this;
372 }
373 template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
374 {
375 *this = *this / complex(__c.real(), __c.imag());
376 return *this;
377 }
378};
379
380template<>
381class _LIBCPP_TEMPLATE_VIS complex<double>
382{
383 double __re_;
384 double __im_;
385public:
386 typedef double value_type;
387
388 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(double __re = 0.0, double __im = 0.0)
389 : __re_(__re), __im_(__im) {}
390 _LIBCPP_INLINE_VISIBILITY
391 _LIBCPP_CONSTEXPR complex(const complex<float>& __c);
392 _LIBCPP_INLINE_VISIBILITY
393 explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c);
394
395 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR double real() const {return __re_;}
396 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR double imag() const {return __im_;}
397
398 _LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
399 _LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
400
401 _LIBCPP_INLINE_VISIBILITY complex& operator= (double __re)
402 {__re_ = __re; __im_ = value_type(); return *this;}
403 _LIBCPP_INLINE_VISIBILITY complex& operator+=(double __re) {__re_ += __re; return *this;}
404 _LIBCPP_INLINE_VISIBILITY complex& operator-=(double __re) {__re_ -= __re; return *this;}
405 _LIBCPP_INLINE_VISIBILITY complex& operator*=(double __re) {__re_ *= __re; __im_ *= __re; return *this;}
406 _LIBCPP_INLINE_VISIBILITY complex& operator/=(double __re) {__re_ /= __re; __im_ /= __re; return *this;}
407
408 template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
409 {
410 __re_ = __c.real();
411 __im_ = __c.imag();
412 return *this;
413 }
414 template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
415 {
416 __re_ += __c.real();
417 __im_ += __c.imag();
418 return *this;
419 }
420 template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
421 {
422 __re_ -= __c.real();
423 __im_ -= __c.imag();
424 return *this;
425 }
426 template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
427 {
428 *this = *this * complex(__c.real(), __c.imag());
429 return *this;
430 }
431 template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
432 {
433 *this = *this / complex(__c.real(), __c.imag());
434 return *this;
435 }
436};
437
438template<>
439class _LIBCPP_TEMPLATE_VIS complex<long double>
440{
441 long double __re_;
442 long double __im_;
443public:
444 typedef long double value_type;
445
446 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(long double __re = 0.0L, long double __im = 0.0L)
447 : __re_(__re), __im_(__im) {}
448 _LIBCPP_INLINE_VISIBILITY
449 _LIBCPP_CONSTEXPR complex(const complex<float>& __c);
450 _LIBCPP_INLINE_VISIBILITY
451 _LIBCPP_CONSTEXPR complex(const complex<double>& __c);
452
453 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR long double real() const {return __re_;}
454 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR long double imag() const {return __im_;}
455
456 _LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
457 _LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
458
459 _LIBCPP_INLINE_VISIBILITY complex& operator= (long double __re)
460 {__re_ = __re; __im_ = value_type(); return *this;}
461 _LIBCPP_INLINE_VISIBILITY complex& operator+=(long double __re) {__re_ += __re; return *this;}
462 _LIBCPP_INLINE_VISIBILITY complex& operator-=(long double __re) {__re_ -= __re; return *this;}
463 _LIBCPP_INLINE_VISIBILITY complex& operator*=(long double __re) {__re_ *= __re; __im_ *= __re; return *this;}
464 _LIBCPP_INLINE_VISIBILITY complex& operator/=(long double __re) {__re_ /= __re; __im_ /= __re; return *this;}
465
466 template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
467 {
468 __re_ = __c.real();
469 __im_ = __c.imag();
470 return *this;
471 }
472 template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
473 {
474 __re_ += __c.real();
475 __im_ += __c.imag();
476 return *this;
477 }
478 template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
479 {
480 __re_ -= __c.real();
481 __im_ -= __c.imag();
482 return *this;
483 }
484 template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
485 {
486 *this = *this * complex(__c.real(), __c.imag());
487 return *this;
488 }
489 template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
490 {
491 *this = *this / complex(__c.real(), __c.imag());
492 return *this;
493 }
494};
495
496inline
497_LIBCPP_CONSTEXPR
498complex<float>::complex(const complex<double>& __c)
499 : __re_(__c.real()), __im_(__c.imag()) {}
500
501inline
502_LIBCPP_CONSTEXPR
503complex<float>::complex(const complex<long double>& __c)
504 : __re_(__c.real()), __im_(__c.imag()) {}
505
506inline
507_LIBCPP_CONSTEXPR
508complex<double>::complex(const complex<float>& __c)
509 : __re_(__c.real()), __im_(__c.imag()) {}
510
511inline
512_LIBCPP_CONSTEXPR
513complex<double>::complex(const complex<long double>& __c)
514 : __re_(__c.real()), __im_(__c.imag()) {}
515
516inline
517_LIBCPP_CONSTEXPR
518complex<long double>::complex(const complex<float>& __c)
519 : __re_(__c.real()), __im_(__c.imag()) {}
520
521inline
522_LIBCPP_CONSTEXPR
523complex<long double>::complex(const complex<double>& __c)
524 : __re_(__c.real()), __im_(__c.imag()) {}
525
526// 26.3.6 operators:
527
528template<class _Tp>
529inline _LIBCPP_INLINE_VISIBILITY
530complex<_Tp>
531operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
532{
533 complex<_Tp> __t(__x);
534 __t += __y;
535 return __t;
536}
537
538template<class _Tp>
539inline _LIBCPP_INLINE_VISIBILITY
540complex<_Tp>
541operator+(const complex<_Tp>& __x, const _Tp& __y)
542{
543 complex<_Tp> __t(__x);
544 __t += __y;
545 return __t;
546}
547
548template<class _Tp>
549inline _LIBCPP_INLINE_VISIBILITY
550complex<_Tp>
551operator+(const _Tp& __x, const complex<_Tp>& __y)
552{
553 complex<_Tp> __t(__y);
554 __t += __x;
555 return __t;
556}
557
558template<class _Tp>
559inline _LIBCPP_INLINE_VISIBILITY
560complex<_Tp>
561operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
562{
563 complex<_Tp> __t(__x);
564 __t -= __y;
565 return __t;
566}
567
568template<class _Tp>
569inline _LIBCPP_INLINE_VISIBILITY
570complex<_Tp>
571operator-(const complex<_Tp>& __x, const _Tp& __y)
572{
573 complex<_Tp> __t(__x);
574 __t -= __y;
575 return __t;
576}
577
578template<class _Tp>
579inline _LIBCPP_INLINE_VISIBILITY
580complex<_Tp>
581operator-(const _Tp& __x, const complex<_Tp>& __y)
582{
583 complex<_Tp> __t(-__y);
584 __t += __x;
585 return __t;
586}
587
588template<class _Tp>
589complex<_Tp>
590operator*(const complex<_Tp>& __z, const complex<_Tp>& __w)
591{
592 _Tp __a = __z.real();
593 _Tp __b = __z.imag();
594 _Tp __c = __w.real();
595 _Tp __d = __w.imag();
596 _Tp __ac = __a * __c;
597 _Tp __bd = __b * __d;
598 _Tp __ad = __a * __d;
599 _Tp __bc = __b * __c;
600 _Tp __x = __ac - __bd;
601 _Tp __y = __ad + __bc;
602 if (__libcpp_isnan_or_builtin(__x) && __libcpp_isnan_or_builtin(__y))
603 {
604 bool __recalc = false;
605 if (__libcpp_isinf_or_builtin(__a) || __libcpp_isinf_or_builtin(__b))
606 {
607 __a = copysign(__libcpp_isinf_or_builtin(__a) ? _Tp(1) : _Tp(0), __a);
608 __b = copysign(__libcpp_isinf_or_builtin(__b) ? _Tp(1) : _Tp(0), __b);
609 if (__libcpp_isnan_or_builtin(__c))
610 __c = copysign(_Tp(0), __c);
611 if (__libcpp_isnan_or_builtin(__d))
612 __d = copysign(_Tp(0), __d);
613 __recalc = true;
614 }
615 if (__libcpp_isinf_or_builtin(__c) || __libcpp_isinf_or_builtin(__d))
616 {
617 __c = copysign(__libcpp_isinf_or_builtin(__c) ? _Tp(1) : _Tp(0), __c);
618 __d = copysign(__libcpp_isinf_or_builtin(__d) ? _Tp(1) : _Tp(0), __d);
619 if (__libcpp_isnan_or_builtin(__a))
620 __a = copysign(_Tp(0), __a);
621 if (__libcpp_isnan_or_builtin(__b))
622 __b = copysign(_Tp(0), __b);
623 __recalc = true;
624 }
625 if (!__recalc && (__libcpp_isinf_or_builtin(__ac) || __libcpp_isinf_or_builtin(__bd) ||
626 __libcpp_isinf_or_builtin(__ad) || __libcpp_isinf_or_builtin(__bc)))
627 {
628 if (__libcpp_isnan_or_builtin(__a))
629 __a = copysign(_Tp(0), __a);
630 if (__libcpp_isnan_or_builtin(__b))
631 __b = copysign(_Tp(0), __b);
632 if (__libcpp_isnan_or_builtin(__c))
633 __c = copysign(_Tp(0), __c);
634 if (__libcpp_isnan_or_builtin(__d))
635 __d = copysign(_Tp(0), __d);
636 __recalc = true;
637 }
638 if (__recalc)
639 {
640 __x = _Tp(INFINITY) * (__a * __c - __b * __d);
641 __y = _Tp(INFINITY) * (__a * __d + __b * __c);
642 }
643 }
644 return complex<_Tp>(__x, __y);
645}
646
647template<class _Tp>
648inline _LIBCPP_INLINE_VISIBILITY
649complex<_Tp>
650operator*(const complex<_Tp>& __x, const _Tp& __y)
651{
652 complex<_Tp> __t(__x);
653 __t *= __y;
654 return __t;
655}
656
657template<class _Tp>
658inline _LIBCPP_INLINE_VISIBILITY
659complex<_Tp>
660operator*(const _Tp& __x, const complex<_Tp>& __y)
661{
662 complex<_Tp> __t(__y);
663 __t *= __x;
664 return __t;
665}
666
667template<class _Tp>
668complex<_Tp>
669operator/(const complex<_Tp>& __z, const complex<_Tp>& __w)
670{
671 int __ilogbw = 0;
672 _Tp __a = __z.real();
673 _Tp __b = __z.imag();
674 _Tp __c = __w.real();
675 _Tp __d = __w.imag();
676 _Tp __logbw = logb(fmax(fabs(__c), fabs(__d)));
677 if (__libcpp_isfinite_or_builtin(__logbw))
678 {
679 __ilogbw = static_cast<int>(__logbw);
680 __c = scalbn(__c, -__ilogbw);
681 __d = scalbn(__d, -__ilogbw);
682 }
683 _Tp __denom = __c * __c + __d * __d;
684 _Tp __x = scalbn((__a * __c + __b * __d) / __denom, -__ilogbw);
685 _Tp __y = scalbn((__b * __c - __a * __d) / __denom, -__ilogbw);
686 if (__libcpp_isnan_or_builtin(__x) && __libcpp_isnan_or_builtin(__y))
687 {
688 if ((__denom == _Tp(0)) && (!__libcpp_isnan_or_builtin(__a) || !__libcpp_isnan_or_builtin(__b)))
689 {
690 __x = copysign(_Tp(INFINITY), __c) * __a;
691 __y = copysign(_Tp(INFINITY), __c) * __b;
692 }
693 else if ((__libcpp_isinf_or_builtin(__a) || __libcpp_isinf_or_builtin(__b)) && __libcpp_isfinite_or_builtin(__c) && __libcpp_isfinite_or_builtin(__d))
694 {
695 __a = copysign(__libcpp_isinf_or_builtin(__a) ? _Tp(1) : _Tp(0), __a);
696 __b = copysign(__libcpp_isinf_or_builtin(__b) ? _Tp(1) : _Tp(0), __b);
697 __x = _Tp(INFINITY) * (__a * __c + __b * __d);
698 __y = _Tp(INFINITY) * (__b * __c - __a * __d);
699 }
700 else if (__libcpp_isinf_or_builtin(__logbw) && __logbw > _Tp(0) && __libcpp_isfinite_or_builtin(__a) && __libcpp_isfinite_or_builtin(__b))
701 {
702 __c = copysign(__libcpp_isinf_or_builtin(__c) ? _Tp(1) : _Tp(0), __c);
703 __d = copysign(__libcpp_isinf_or_builtin(__d) ? _Tp(1) : _Tp(0), __d);
704 __x = _Tp(0) * (__a * __c + __b * __d);
705 __y = _Tp(0) * (__b * __c - __a * __d);
706 }
707 }
708 return complex<_Tp>(__x, __y);
709}
710
711template<class _Tp>
712inline _LIBCPP_INLINE_VISIBILITY
713complex<_Tp>
714operator/(const complex<_Tp>& __x, const _Tp& __y)
715{
716 return complex<_Tp>(__x.real() / __y, __x.imag() / __y);
717}
718
719template<class _Tp>
720inline _LIBCPP_INLINE_VISIBILITY
721complex<_Tp>
722operator/(const _Tp& __x, const complex<_Tp>& __y)
723{
724 complex<_Tp> __t(__x);
725 __t /= __y;
726 return __t;
727}
728
729template<class _Tp>
730inline _LIBCPP_INLINE_VISIBILITY
731complex<_Tp>
732operator+(const complex<_Tp>& __x)
733{
734 return __x;
735}
736
737template<class _Tp>
738inline _LIBCPP_INLINE_VISIBILITY
739complex<_Tp>
740operator-(const complex<_Tp>& __x)
741{
742 return complex<_Tp>(-__x.real(), -__x.imag());
743}
744
745template<class _Tp>
746inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
747bool
748operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
749{
750 return __x.real() == __y.real() && __x.imag() == __y.imag();
751}
752
753template<class _Tp>
754inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
755bool
756operator==(const complex<_Tp>& __x, const _Tp& __y)
757{
758 return __x.real() == __y && __x.imag() == 0;
759}
760
761template<class _Tp>
762inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
763bool
764operator==(const _Tp& __x, const complex<_Tp>& __y)
765{
766 return __x == __y.real() && 0 == __y.imag();
767}
768
769template<class _Tp>
770inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
771bool
772operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
773{
774 return !(__x == __y);
775}
776
777template<class _Tp>
778inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
779bool
780operator!=(const complex<_Tp>& __x, const _Tp& __y)
781{
782 return !(__x == __y);
783}
784
785template<class _Tp>
786inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
787bool
788operator!=(const _Tp& __x, const complex<_Tp>& __y)
789{
790 return !(__x == __y);
791}
792
793// 26.3.7 values:
794
795template <class _Tp, bool = is_integral<_Tp>::value,
796 bool = is_floating_point<_Tp>::value
797 >
798struct __libcpp_complex_overload_traits {};
799
800// Integral Types
801template <class _Tp>
802struct __libcpp_complex_overload_traits<_Tp, true, false>
803{
804 typedef double _ValueType;
805 typedef complex<double> _ComplexType;
806};
807
808// Floating point types
809template <class _Tp>
810struct __libcpp_complex_overload_traits<_Tp, false, true>
811{
812 typedef _Tp _ValueType;
813 typedef complex<_Tp> _ComplexType;
814};
815
816// real
817
818template<class _Tp>
819inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
820_Tp
821real(const complex<_Tp>& __c)
822{
823 return __c.real();
824}
825
826template <class _Tp>
827inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
828typename __libcpp_complex_overload_traits<_Tp>::_ValueType
829real(_Tp __re)
830{
831 return __re;
832}
833
834// imag
835
836template<class _Tp>
837inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
838_Tp
839imag(const complex<_Tp>& __c)
840{
841 return __c.imag();
842}
843
844template <class _Tp>
845inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
846typename __libcpp_complex_overload_traits<_Tp>::_ValueType
847imag(_Tp)
848{
849 return 0;
850}
851
852// abs
853
854template<class _Tp>
855inline _LIBCPP_INLINE_VISIBILITY
856_Tp
857abs(const complex<_Tp>& __c)
858{
859 return hypot(__c.real(), __c.imag());
860}
861
862// arg
863
864template<class _Tp>
865inline _LIBCPP_INLINE_VISIBILITY
866_Tp
867arg(const complex<_Tp>& __c)
868{
869 return atan2(__c.imag(), __c.real());
870}
871
872template <class _Tp>
873inline _LIBCPP_INLINE_VISIBILITY
874typename enable_if<
875 is_same<_Tp, long double>::value,
876 long double
877>::type
878arg(_Tp __re)
879{
880 return atan2l(0.L, __re);
881}
882
883template<class _Tp>
884inline _LIBCPP_INLINE_VISIBILITY
885typename enable_if
886<
887 is_integral<_Tp>::value || is_same<_Tp, double>::value,
888 double
889>::type
890arg(_Tp __re)
891{
892 return atan2(0., __re);
893}
894
895template <class _Tp>
896inline _LIBCPP_INLINE_VISIBILITY
897typename enable_if<
898 is_same<_Tp, float>::value,
899 float
900>::type
901arg(_Tp __re)
902{
903 return atan2f(0.F, __re);
904}
905
906// norm
907
908template<class _Tp>
909inline _LIBCPP_INLINE_VISIBILITY
910_Tp
911norm(const complex<_Tp>& __c)
912{
913 if (__libcpp_isinf_or_builtin(__c.real()))
914 return abs(__c.real());
915 if (__libcpp_isinf_or_builtin(__c.imag()))
916 return abs(__c.imag());
917 return __c.real() * __c.real() + __c.imag() * __c.imag();
918}
919
920template <class _Tp>
921inline _LIBCPP_INLINE_VISIBILITY
922typename __libcpp_complex_overload_traits<_Tp>::_ValueType
923norm(_Tp __re)
924{
925 typedef typename __libcpp_complex_overload_traits<_Tp>::_ValueType _ValueType;
926 return static_cast<_ValueType>(__re) * __re;
927}
928
929// conj
930
931template<class _Tp>
932inline _LIBCPP_INLINE_VISIBILITY
933complex<_Tp>
934conj(const complex<_Tp>& __c)
935{
936 return complex<_Tp>(__c.real(), -__c.imag());
937}
938
939template <class _Tp>
940inline _LIBCPP_INLINE_VISIBILITY
941typename __libcpp_complex_overload_traits<_Tp>::_ComplexType
942conj(_Tp __re)
943{
944 typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType;
945 return _ComplexType(__re);
946}
947
948
949
950// proj
951
952template<class _Tp>
953inline _LIBCPP_INLINE_VISIBILITY
954complex<_Tp>
955proj(const complex<_Tp>& __c)
956{
957 std::complex<_Tp> __r = __c;
958 if (__libcpp_isinf_or_builtin(__c.real()) || __libcpp_isinf_or_builtin(__c.imag()))
959 __r = complex<_Tp>(INFINITY, copysign(_Tp(0), __c.imag()));
960 return __r;
961}
962
963template <class _Tp>
964inline _LIBCPP_INLINE_VISIBILITY
965typename enable_if
966<
967 is_floating_point<_Tp>::value,
968 typename __libcpp_complex_overload_traits<_Tp>::_ComplexType
969>::type
970proj(_Tp __re)
971{
972 if (__libcpp_isinf_or_builtin(__re))
973 __re = abs(__re);
974 return complex<_Tp>(__re);
975}
976
977template <class _Tp>
978inline _LIBCPP_INLINE_VISIBILITY
979typename enable_if
980<
981 is_integral<_Tp>::value,
982 typename __libcpp_complex_overload_traits<_Tp>::_ComplexType
983>::type
984proj(_Tp __re)
985{
986 typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType;
987 return _ComplexType(__re);
988}
989
990// polar
991
992template<class _Tp>
993complex<_Tp>
994polar(const _Tp& __rho, const _Tp& __theta = _Tp())
995{
996 if (__libcpp_isnan_or_builtin(__rho) || signbit(__rho))
997 return complex<_Tp>(_Tp(NAN), _Tp(NAN));
998 if (__libcpp_isnan_or_builtin(__theta))
999 {
1000 if (__libcpp_isinf_or_builtin(__rho))
1001 return complex<_Tp>(__rho, __theta);
1002 return complex<_Tp>(__theta, __theta);
1003 }
1004 if (__libcpp_isinf_or_builtin(__theta))
1005 {
1006 if (__libcpp_isinf_or_builtin(__rho))
1007 return complex<_Tp>(__rho, _Tp(NAN));
1008 return complex<_Tp>(_Tp(NAN), _Tp(NAN));
1009 }
1010 _Tp __x = __rho * cos(__theta);
1011 if (__libcpp_isnan_or_builtin(__x))
1012 __x = 0;
1013 _Tp __y = __rho * sin(__theta);
1014 if (__libcpp_isnan_or_builtin(__y))
1015 __y = 0;
1016 return complex<_Tp>(__x, __y);
1017}
1018
1019// log
1020
1021template<class _Tp>
1022inline _LIBCPP_INLINE_VISIBILITY
1023complex<_Tp>
1024log(const complex<_Tp>& __x)
1025{
1026 return complex<_Tp>(log(abs(__x)), arg(__x));
1027}
1028
1029// log10
1030
1031template<class _Tp>
1032inline _LIBCPP_INLINE_VISIBILITY
1033complex<_Tp>
1034log10(const complex<_Tp>& __x)
1035{
1036 return log(__x) / log(_Tp(10));
1037}
1038
1039// sqrt
1040
1041template<class _Tp>
1042complex<_Tp>
1043sqrt(const complex<_Tp>& __x)
1044{
1045 if (__libcpp_isinf_or_builtin(__x.imag()))
1046 return complex<_Tp>(_Tp(INFINITY), __x.imag());
1047 if (__libcpp_isinf_or_builtin(__x.real()))
1048 {
1049 if (__x.real() > _Tp(0))
1050 return complex<_Tp>(__x.real(), __libcpp_isnan_or_builtin(__x.imag()) ? __x.imag() : copysign(_Tp(0), __x.imag()));
1051 return complex<_Tp>(__libcpp_isnan_or_builtin(__x.imag()) ? __x.imag() : _Tp(0), copysign(__x.real(), __x.imag()));
1052 }
1053 return polar(sqrt(abs(__x)), arg(__x) / _Tp(2));
1054}
1055
1056// exp
1057
1058template<class _Tp>
1059complex<_Tp>
1060exp(const complex<_Tp>& __x)
1061{
1062 _Tp __i = __x.imag();
1063 if (__libcpp_isinf_or_builtin(__x.real()))
1064 {
1065 if (__x.real() < _Tp(0))
1066 {
1067 if (!__libcpp_isfinite_or_builtin(__i))
1068 __i = _Tp(1);
1069 }
1070 else if (__i == 0 || !__libcpp_isfinite_or_builtin(__i))
1071 {
1072 if (__libcpp_isinf_or_builtin(__i))
1073 __i = _Tp(NAN);
1074 return complex<_Tp>(__x.real(), __i);
1075 }
1076 }
1077 else if (__libcpp_isnan_or_builtin(__x.real()) && __x.imag() == 0)
1078 return __x;
1079 _Tp __e = exp(__x.real());
1080 return complex<_Tp>(__e * cos(__i), __e * sin(__i));
1081}
1082
1083// pow
1084
1085template<class _Tp>
1086inline _LIBCPP_INLINE_VISIBILITY
1087complex<_Tp>
1088pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1089{
1090 return exp(__y * log(__x));
1091}
1092
1093template<class _Tp, class _Up>
1094inline _LIBCPP_INLINE_VISIBILITY
1095complex<typename __promote<_Tp, _Up>::type>
1096pow(const complex<_Tp>& __x, const complex<_Up>& __y)
1097{
1098 typedef complex<typename __promote<_Tp, _Up>::type> result_type;
1099 return _VSTD::pow(result_type(__x), result_type(__y));
1100}
1101
1102template<class _Tp, class _Up>
1103inline _LIBCPP_INLINE_VISIBILITY
1104typename enable_if
1105<
1106 is_arithmetic<_Up>::value,
1107 complex<typename __promote<_Tp, _Up>::type>
1108>::type
1109pow(const complex<_Tp>& __x, const _Up& __y)
1110{
1111 typedef complex<typename __promote<_Tp, _Up>::type> result_type;
1112 return _VSTD::pow(result_type(__x), result_type(__y));
1113}
1114
1115template<class _Tp, class _Up>
1116inline _LIBCPP_INLINE_VISIBILITY
1117typename enable_if
1118<
1119 is_arithmetic<_Tp>::value,
1120 complex<typename __promote<_Tp, _Up>::type>
1121>::type
1122pow(const _Tp& __x, const complex<_Up>& __y)
1123{
1124 typedef complex<typename __promote<_Tp, _Up>::type> result_type;
1125 return _VSTD::pow(result_type(__x), result_type(__y));
1126}
1127
1128// __sqr, computes pow(x, 2)
1129
1130template<class _Tp>
1131inline _LIBCPP_INLINE_VISIBILITY
1132complex<_Tp>
1133__sqr(const complex<_Tp>& __x)
1134{
1135 return complex<_Tp>((__x.real() - __x.imag()) * (__x.real() + __x.imag()),
1136 _Tp(2) * __x.real() * __x.imag());
1137}
1138
1139// asinh
1140
1141template<class _Tp>
1142complex<_Tp>
1143asinh(const complex<_Tp>& __x)
1144{
1145 const _Tp __pi(atan2(+0., -0.));
1146 if (__libcpp_isinf_or_builtin(__x.real()))
1147 {
1148 if (__libcpp_isnan_or_builtin(__x.imag()))
1149 return __x;
1150 if (__libcpp_isinf_or_builtin(__x.imag()))
1151 return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag()));
1152 return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
1153 }
1154 if (__libcpp_isnan_or_builtin(__x.real()))
1155 {
1156 if (__libcpp_isinf_or_builtin(__x.imag()))
1157 return complex<_Tp>(__x.imag(), __x.real());
1158 if (__x.imag() == 0)
1159 return __x;
1160 return complex<_Tp>(__x.real(), __x.real());
1161 }
1162 if (__libcpp_isinf_or_builtin(__x.imag()))
1163 return complex<_Tp>(copysign(__x.imag(), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
1164 complex<_Tp> __z = log(__x + sqrt(__sqr(__x) + _Tp(1)));
1165 return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag()));
1166}
1167
1168// acosh
1169
1170template<class _Tp>
1171complex<_Tp>
1172acosh(const complex<_Tp>& __x)
1173{
1174 const _Tp __pi(atan2(+0., -0.));
1175 if (__libcpp_isinf_or_builtin(__x.real()))
1176 {
1177 if (__libcpp_isnan_or_builtin(__x.imag()))
1178 return complex<_Tp>(abs(__x.real()), __x.imag());
1179 if (__libcpp_isinf_or_builtin(__x.imag()))
1180 {
1181 if (__x.real() > 0)
1182 return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag()));
1183 else
1184 return complex<_Tp>(-__x.real(), copysign(__pi * _Tp(0.75), __x.imag()));
1185 }
1186 if (__x.real() < 0)
1187 return complex<_Tp>(-__x.real(), copysign(__pi, __x.imag()));
1188 return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
1189 }
1190 if (__libcpp_isnan_or_builtin(__x.real()))
1191 {
1192 if (__libcpp_isinf_or_builtin(__x.imag()))
1193 return complex<_Tp>(abs(__x.imag()), __x.real());
1194 return complex<_Tp>(__x.real(), __x.real());
1195 }
1196 if (__libcpp_isinf_or_builtin(__x.imag()))
1197 return complex<_Tp>(abs(__x.imag()), copysign(__pi/_Tp(2), __x.imag()));
1198 complex<_Tp> __z = log(__x + sqrt(__sqr(__x) - _Tp(1)));
1199 return complex<_Tp>(copysign(__z.real(), _Tp(0)), copysign(__z.imag(), __x.imag()));
1200}
1201
1202// atanh
1203
1204template<class _Tp>
1205complex<_Tp>
1206atanh(const complex<_Tp>& __x)
1207{
1208 const _Tp __pi(atan2(+0., -0.));
1209 if (__libcpp_isinf_or_builtin(__x.imag()))
1210 {
1211 return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
1212 }
1213 if (__libcpp_isnan_or_builtin(__x.imag()))
1214 {
1215 if (__libcpp_isinf_or_builtin(__x.real()) || __x.real() == 0)
1216 return complex<_Tp>(copysign(_Tp(0), __x.real()), __x.imag());
1217 return complex<_Tp>(__x.imag(), __x.imag());
1218 }
1219 if (__libcpp_isnan_or_builtin(__x.real()))
1220 {
1221 return complex<_Tp>(__x.real(), __x.real());
1222 }
1223 if (__libcpp_isinf_or_builtin(__x.real()))
1224 {
1225 return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
1226 }
1227 if (abs(__x.real()) == _Tp(1) && __x.imag() == _Tp(0))
1228 {
1229 return complex<_Tp>(copysign(_Tp(INFINITY), __x.real()), copysign(_Tp(0), __x.imag()));
1230 }
1231 complex<_Tp> __z = log((_Tp(1) + __x) / (_Tp(1) - __x)) / _Tp(2);
1232 return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag()));
1233}
1234
1235// sinh
1236
1237template<class _Tp>
1238complex<_Tp>
1239sinh(const complex<_Tp>& __x)
1240{
1241 if (__libcpp_isinf_or_builtin(__x.real()) && !__libcpp_isfinite_or_builtin(__x.imag()))
1242 return complex<_Tp>(__x.real(), _Tp(NAN));
1243 if (__x.real() == 0 && !__libcpp_isfinite_or_builtin(__x.imag()))
1244 return complex<_Tp>(__x.real(), _Tp(NAN));
1245 if (__x.imag() == 0 && !__libcpp_isfinite_or_builtin(__x.real()))
1246 return __x;
1247 return complex<_Tp>(sinh(__x.real()) * cos(__x.imag()), cosh(__x.real()) * sin(__x.imag()));
1248}
1249
1250// cosh
1251
1252template<class _Tp>
1253complex<_Tp>
1254cosh(const complex<_Tp>& __x)
1255{
1256 if (__libcpp_isinf_or_builtin(__x.real()) && !__libcpp_isfinite_or_builtin(__x.imag()))
1257 return complex<_Tp>(abs(__x.real()), _Tp(NAN));
1258 if (__x.real() == 0 && !__libcpp_isfinite_or_builtin(__x.imag()))
1259 return complex<_Tp>(_Tp(NAN), __x.real());
1260 if (__x.real() == 0 && __x.imag() == 0)
1261 return complex<_Tp>(_Tp(1), __x.imag());
1262 if (__x.imag() == 0 && !__libcpp_isfinite_or_builtin(__x.real()))
1263 return complex<_Tp>(abs(__x.real()), __x.imag());
1264 return complex<_Tp>(cosh(__x.real()) * cos(__x.imag()), sinh(__x.real()) * sin(__x.imag()));
1265}
1266
1267// tanh
1268
1269template<class _Tp>
1270complex<_Tp>
1271tanh(const complex<_Tp>& __x)
1272{
1273 if (__libcpp_isinf_or_builtin(__x.real()))
1274 {
1275 if (!__libcpp_isfinite_or_builtin(__x.imag()))
1276 return complex<_Tp>(_Tp(1), _Tp(0));
1277 return complex<_Tp>(_Tp(1), copysign(_Tp(0), sin(_Tp(2) * __x.imag())));
1278 }
1279 if (__libcpp_isnan_or_builtin(__x.real()) && __x.imag() == 0)
1280 return __x;
1281 _Tp __2r(_Tp(2) * __x.real());
1282 _Tp __2i(_Tp(2) * __x.imag());
1283 _Tp __d(cosh(__2r) + cos(__2i));
1284 _Tp __2rsh(sinh(__2r));
1285 if (__libcpp_isinf_or_builtin(__2rsh) && __libcpp_isinf_or_builtin(__d))
1286 return complex<_Tp>(__2rsh > _Tp(0) ? _Tp(1) : _Tp(-1),
1287 __2i > _Tp(0) ? _Tp(0) : _Tp(-0.));
1288 return complex<_Tp>(__2rsh/__d, sin(__2i)/__d);
1289}
1290
1291// asin
1292
1293template<class _Tp>
1294complex<_Tp>
1295asin(const complex<_Tp>& __x)
1296{
1297 complex<_Tp> __z = asinh(complex<_Tp>(-__x.imag(), __x.real()));
1298 return complex<_Tp>(__z.imag(), -__z.real());
1299}
1300
1301// acos
1302
1303template<class _Tp>
1304complex<_Tp>
1305acos(const complex<_Tp>& __x)
1306{
1307 const _Tp __pi(atan2(+0., -0.));
1308 if (__libcpp_isinf_or_builtin(__x.real()))
1309 {
1310 if (__libcpp_isnan_or_builtin(__x.imag()))
1311 return complex<_Tp>(__x.imag(), __x.real());
1312 if (__libcpp_isinf_or_builtin(__x.imag()))
1313 {
1314 if (__x.real() < _Tp(0))
1315 return complex<_Tp>(_Tp(0.75) * __pi, -__x.imag());
1316 return complex<_Tp>(_Tp(0.25) * __pi, -__x.imag());
1317 }
1318 if (__x.real() < _Tp(0))
1319 return complex<_Tp>(__pi, signbit(__x.imag()) ? -__x.real() : __x.real());
1320 return complex<_Tp>(_Tp(0), signbit(__x.imag()) ? __x.real() : -__x.real());
1321 }
1322 if (__libcpp_isnan_or_builtin(__x.real()))
1323 {
1324 if (__libcpp_isinf_or_builtin(__x.imag()))
1325 return complex<_Tp>(__x.real(), -__x.imag());
1326 return complex<_Tp>(__x.real(), __x.real());
1327 }
1328 if (__libcpp_isinf_or_builtin(__x.imag()))
1329 return complex<_Tp>(__pi/_Tp(2), -__x.imag());
1330 if (__x.real() == 0 && (__x.imag() == 0 || isnan(__x.imag())))
1331 return complex<_Tp>(__pi/_Tp(2), -__x.imag());
1332 complex<_Tp> __z = log(__x + sqrt(__sqr(__x) - _Tp(1)));
1333 if (signbit(__x.imag()))
1334 return complex<_Tp>(abs(__z.imag()), abs(__z.real()));
1335 return complex<_Tp>(abs(__z.imag()), -abs(__z.real()));
1336}
1337
1338// atan
1339
1340template<class _Tp>
1341complex<_Tp>
1342atan(const complex<_Tp>& __x)
1343{
1344 complex<_Tp> __z = atanh(complex<_Tp>(-__x.imag(), __x.real()));
1345 return complex<_Tp>(__z.imag(), -__z.real());
1346}
1347
1348// sin
1349
1350template<class _Tp>
1351complex<_Tp>
1352sin(const complex<_Tp>& __x)
1353{
1354 complex<_Tp> __z = sinh(complex<_Tp>(-__x.imag(), __x.real()));
1355 return complex<_Tp>(__z.imag(), -__z.real());
1356}
1357
1358// cos
1359
1360template<class _Tp>
1361inline _LIBCPP_INLINE_VISIBILITY
1362complex<_Tp>
1363cos(const complex<_Tp>& __x)
1364{
1365 return cosh(complex<_Tp>(-__x.imag(), __x.real()));
1366}
1367
1368// tan
1369
1370template<class _Tp>
1371complex<_Tp>
1372tan(const complex<_Tp>& __x)
1373{
1374 complex<_Tp> __z = tanh(complex<_Tp>(-__x.imag(), __x.real()));
1375 return complex<_Tp>(__z.imag(), -__z.real());
1376}
1377
1378template<class _Tp, class _CharT, class _Traits>
1379basic_istream<_CharT, _Traits>&
1380operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
1381{
1382 if (__is.good())
1383 {
1384 ws(__is);
1385 if (__is.peek() == _CharT('('))
1386 {
1387 __is.get();
1388 _Tp __r;
1389 __is >> __r;
1390 if (!__is.fail())
1391 {
1392 ws(__is);
1393 _CharT __c = __is.peek();
1394 if (__c == _CharT(','))
1395 {
1396 __is.get();
1397 _Tp __i;
1398 __is >> __i;
1399 if (!__is.fail())
1400 {
1401 ws(__is);
1402 __c = __is.peek();
1403 if (__c == _CharT(')'))
1404 {
1405 __is.get();
1406 __x = complex<_Tp>(__r, __i);
1407 }
1408 else
1409 __is.setstate(ios_base::failbit);
1410 }
1411 else
1412 __is.setstate(ios_base::failbit);
1413 }
1414 else if (__c == _CharT(')'))
1415 {
1416 __is.get();
1417 __x = complex<_Tp>(__r, _Tp(0));
1418 }
1419 else
1420 __is.setstate(ios_base::failbit);
1421 }
1422 else
1423 __is.setstate(ios_base::failbit);
1424 }
1425 else
1426 {
1427 _Tp __r;
1428 __is >> __r;
1429 if (!__is.fail())
1430 __x = complex<_Tp>(__r, _Tp(0));
1431 else
1432 __is.setstate(ios_base::failbit);
1433 }
1434 }
1435 else
1436 __is.setstate(ios_base::failbit);
1437 return __is;
1438}
1439
1440template<class _Tp, class _CharT, class _Traits>
1441basic_ostream<_CharT, _Traits>&
1442operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
1443{
1444 basic_ostringstream<_CharT, _Traits> __s;
1445 __s.flags(__os.flags());
1446 __s.imbue(__os.getloc());
1447 __s.precision(__os.precision());
1448 __s << '(' << __x.real() << ',' << __x.imag() << ')';
1449 return __os << __s.str();
1450}
1451
1452#if _LIBCPP_STD_VER > 11
1453// Literal suffix for complex number literals [complex.literals]
1454inline namespace literals
1455{
1456 inline namespace complex_literals
1457 {
1458 constexpr complex<long double> operator""il(long double __im)
1459 {
1460 return { 0.0l, __im };
1461 }
1462
1463 constexpr complex<long double> operator""il(unsigned long long __im)
1464 {
1465 return { 0.0l, static_cast<long double>(__im) };
1466 }
1467
1468
1469 constexpr complex<double> operator""i(long double __im)
1470 {
1471 return { 0.0, static_cast<double>(__im) };
1472 }
1473
1474 constexpr complex<double> operator""i(unsigned long long __im)
1475 {
1476 return { 0.0, static_cast<double>(__im) };
1477 }
1478
1479
1480 constexpr complex<float> operator""if(long double __im)
1481 {
1482 return { 0.0f, static_cast<float>(__im) };
1483 }
1484
1485 constexpr complex<float> operator""if(unsigned long long __im)
1486 {
1487 return { 0.0f, static_cast<float>(__im) };
1488 }
1489 }
1490}
1491#endif
1492
1493_LIBCPP_END_NAMESPACE_STD
1494
1495#endif // _LIBCPP_COMPLEX
1496