xref: /freebsd/contrib/llvm-project/libcxx/include/complex (revision d13def78ccef6dbc25c2e197089ee5fc4d7b82c3) 
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