1// -*- C++ -*-
2//===--------------------------- complex ----------------------------------===//
3//
4//                     The LLVM Compiler Infrastructure
5//
6// This file is dual licensed under the MIT and the University of Illinois Open
7// Source Licenses. See LICENSE.TXT for details.
8//
9//===----------------------------------------------------------------------===//
10
11#ifndef _LIBCPP_COMPLEX
12#define _LIBCPP_COMPLEX
13
14/*
15    complex synopsis
16
17namespace std
18{
19
20template<class T>
21class complex
22{
23public:
24    typedef T value_type;
25
26    complex(const T& re = T(), const T& im = T()); // constexpr in C++14
27    complex(const complex&);  // constexpr in C++14
28    template<class X> complex(const complex<X>&);  // constexpr in C++14
29
30    T real() const; // constexpr in C++14
31    T imag() const; // constexpr in C++14
32
33    void real(T);
34    void imag(T);
35
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    complex<T>& operator/=(const T&);
41
42    complex& operator=(const complex&);
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    template<class X> complex<T>& operator/=(const complex<X>&);
48};
49
50template<>
51class complex<float>
52{
53public:
54    typedef float value_type;
55
56    constexpr complex(float re = 0.0f, float im = 0.0f);
57    explicit constexpr complex(const complex<double>&);
58    explicit constexpr complex(const complex<long double>&);
59
60    constexpr float real() const;
61    void real(float);
62    constexpr float imag() const;
63    void imag(float);
64
65    complex<float>& operator= (float);
66    complex<float>& operator+=(float);
67    complex<float>& operator-=(float);
68    complex<float>& operator*=(float);
69    complex<float>& operator/=(float);
70
71    complex<float>& operator=(const complex<float>&);
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    template<class X> complex<float>& operator/=(const complex<X>&);
77};
78
79template<>
80class complex<double>
81{
82public:
83    typedef double value_type;
84
85    constexpr complex(double re = 0.0, double im = 0.0);
86    constexpr complex(const complex<float>&);
87    explicit constexpr complex(const complex<long double>&);
88
89    constexpr double real() const;
90    void real(double);
91    constexpr double imag() const;
92    void imag(double);
93
94    complex<double>& operator= (double);
95    complex<double>& operator+=(double);
96    complex<double>& operator-=(double);
97    complex<double>& operator*=(double);
98    complex<double>& operator/=(double);
99    complex<double>& operator=(const complex<double>&);
100
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    template<class X> complex<double>& operator/=(const complex<X>&);
106};
107
108template<>
109class complex<long double>
110{
111public:
112    typedef long double value_type;
113
114    constexpr complex(long double re = 0.0L, long double im = 0.0L);
115    constexpr complex(const complex<float>&);
116    constexpr complex(const complex<double>&);
117
118    constexpr long double real() const;
119    void real(long double);
120    constexpr long double imag() const;
121    void imag(long double);
122
123    complex<long double>& operator=(const complex<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    complex<long double>& operator/=(long double);
129
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    template<class X> complex<long double>& operator/=(const complex<X>&);
135};
136
137// 26.3.6 operators:
138template<class T> complex<T> operator+(const complex<T>&, const complex<T>&);
139template<class T> complex<T> operator+(const complex<T>&, const T&);
140template<class T> complex<T> operator+(const T&, const complex<T>&);
141template<class T> complex<T> operator-(const complex<T>&, const complex<T>&);
142template<class T> complex<T> operator-(const complex<T>&, const T&);
143template<class T> complex<T> operator-(const T&, const complex<T>&);
144template<class T> complex<T> operator*(const complex<T>&, const complex<T>&);
145template<class T> complex<T> operator*(const complex<T>&, const T&);
146template<class T> complex<T> operator*(const T&, const complex<T>&);
147template<class T> complex<T> operator/(const complex<T>&, const complex<T>&);
148template<class T> complex<T> operator/(const complex<T>&, const T&);
149template<class T> complex<T> operator/(const T&, const complex<T>&);
150template<class T> complex<T> operator+(const complex<T>&);
151template<class T> complex<T> operator-(const complex<T>&);
152template<class T> bool operator==(const complex<T>&, const complex<T>&); // constexpr in C++14
153template<class T> bool operator==(const complex<T>&, const T&); // constexpr in C++14
154template<class T> bool operator==(const T&, const complex<T>&); // constexpr in C++14
155template<class T> bool operator!=(const complex<T>&, const complex<T>&); // constexpr in C++14
156template<class T> bool operator!=(const complex<T>&, const T&); // constexpr in C++14
157template<class T> bool operator!=(const T&, const complex<T>&); // constexpr in C++14
158
159template<class T, class charT, class traits>
160  basic_istream<charT, traits>&
161  operator>>(basic_istream<charT, traits>&, complex<T>&);
162template<class T, class charT, class traits>
163  basic_ostream<charT, traits>&
164  operator<<(basic_ostream<charT, traits>&, const complex<T>&);
165
166// 26.3.7 values:
167
168template<class T>              T real(const complex<T>&); // constexpr in C++14
169                     long double real(long double);       // constexpr in C++14
170                          double real(double);            // constexpr in C++14
171template<Integral T>      double real(T);                 // constexpr in C++14
172                          float  real(float);             // constexpr in C++14
173
174template<class T>              T imag(const complex<T>&); // constexpr in C++14
175                     long double imag(long double);       // constexpr in C++14
176                          double imag(double);            // constexpr in C++14
177template<Integral T>      double imag(T);                 // constexpr in C++14
178                          float  imag(float);             // constexpr in C++14
179
180template<class T> T abs(const complex<T>&);
181
182template<class T>              T arg(const complex<T>&);
183                     long double arg(long double);
184                          double arg(double);
185template<Integral T>      double arg(T);
186                          float  arg(float);
187
188template<class T>              T norm(const complex<T>&);
189                     long double norm(long double);
190                          double norm(double);
191template<Integral T>      double norm(T);
192                          float  norm(float);
193
194template<class T>      complex<T>           conj(const complex<T>&);
195                       complex<long double> conj(long double);
196                       complex<double>      conj(double);
197template<Integral T>   complex<double>      conj(T);
198                       complex<float>       conj(float);
199
200template<class T>    complex<T>           proj(const complex<T>&);
201                     complex<long double> proj(long double);
202                     complex<double>      proj(double);
203template<Integral T> complex<double>      proj(T);
204                     complex<float>       proj(float);
205
206template<class T> complex<T> polar(const T&, const T& = 0);
207
208// 26.3.8 transcendentals:
209template<class T> complex<T> acos(const complex<T>&);
210template<class T> complex<T> asin(const complex<T>&);
211template<class T> complex<T> atan(const complex<T>&);
212template<class T> complex<T> acosh(const complex<T>&);
213template<class T> complex<T> asinh(const complex<T>&);
214template<class T> complex<T> atanh(const complex<T>&);
215template<class T> complex<T> cos (const complex<T>&);
216template<class T> complex<T> cosh (const complex<T>&);
217template<class T> complex<T> exp (const complex<T>&);
218template<class T> complex<T> log (const complex<T>&);
219template<class T> complex<T> log10(const complex<T>&);
220
221template<class T> complex<T> pow(const complex<T>&, const T&);
222template<class T> complex<T> pow(const complex<T>&, const complex<T>&);
223template<class T> complex<T> pow(const T&, const complex<T>&);
224
225template<class T> complex<T> sin (const complex<T>&);
226template<class T> complex<T> sinh (const complex<T>&);
227template<class T> complex<T> sqrt (const complex<T>&);
228template<class T> complex<T> tan (const complex<T>&);
229template<class T> complex<T> tanh (const complex<T>&);
230
231template<class T, class charT, class traits>
232  basic_istream<charT, traits>&
233  operator>>(basic_istream<charT, traits>& is, complex<T>& x);
234
235template<class T, class charT, class traits>
236  basic_ostream<charT, traits>&
237  operator<<(basic_ostream<charT, traits>& o, const complex<T>& x);
238
239}  // std
240
241*/
242
243#include <__config>
244#include <type_traits>
245#include <stdexcept>
246#include <cmath>
247#include <sstream>
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_TYPE_VIS_ONLY 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_TYPE_VIS_ONLY 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_TYPE_VIS_ONLY complex<double>;
320template<> class _LIBCPP_TYPE_VIS_ONLY complex<long double>;
321
322template<>
323class _LIBCPP_TYPE_VIS_ONLY 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_TYPE_VIS_ONLY 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_TYPE_VIS_ONLY 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 (isnan(__x) && isnan(__y))
603    {
604        bool __recalc = false;
605        if (isinf(__a) || isinf(__b))
606        {
607            __a = copysign(isinf(__a) ? _Tp(1) : _Tp(0), __a);
608            __b = copysign(isinf(__b) ? _Tp(1) : _Tp(0), __b);
609            if (isnan(__c))
610                __c = copysign(_Tp(0), __c);
611            if (isnan(__d))
612                __d = copysign(_Tp(0), __d);
613            __recalc = true;
614        }
615        if (isinf(__c) || isinf(__d))
616        {
617            __c = copysign(isinf(__c) ? _Tp(1) : _Tp(0), __c);
618            __d = copysign(isinf(__d) ? _Tp(1) : _Tp(0), __d);
619            if (isnan(__a))
620                __a = copysign(_Tp(0), __a);
621            if (isnan(__b))
622                __b = copysign(_Tp(0), __b);
623            __recalc = true;
624        }
625        if (!__recalc && (isinf(__ac) || isinf(__bd) ||
626                          isinf(__ad) || isinf(__bc)))
627        {
628            if (isnan(__a))
629                __a = copysign(_Tp(0), __a);
630            if (isnan(__b))
631                __b = copysign(_Tp(0), __b);
632            if (isnan(__c))
633                __c = copysign(_Tp(0), __c);
634            if (isnan(__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 (isfinite(__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 (isnan(__x) && isnan(__y))
687    {
688        if ((__denom == _Tp(0)) && (!isnan(__a) || !isnan(__b)))
689        {
690            __x = copysign(_Tp(INFINITY), __c) * __a;
691            __y = copysign(_Tp(INFINITY), __c) * __b;
692        }
693        else if ((isinf(__a) || isinf(__b)) && isfinite(__c) && isfinite(__d))
694        {
695            __a = copysign(isinf(__a) ? _Tp(1) : _Tp(0), __a);
696            __b = copysign(isinf(__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 (isinf(__logbw) && __logbw > _Tp(0) && isfinite(__a) && isfinite(__b))
701        {
702            __c = copysign(isinf(__c) ? _Tp(1) : _Tp(0), __c);
703            __d = copysign(isinf(__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 __re)
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 (isinf(__c.real()))
914        return abs(__c.real());
915    if (isinf(__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 (isinf(__c.real()) || isinf(__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 (isinf(__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
991// polar
992
993template<class _Tp>
994complex<_Tp>
995polar(const _Tp& __rho, const _Tp& __theta = _Tp(0))
996{
997    if (isnan(__rho) || signbit(__rho))
998        return complex<_Tp>(_Tp(NAN), _Tp(NAN));
999    if (isnan(__theta))
1000    {
1001        if (isinf(__rho))
1002            return complex<_Tp>(__rho, __theta);
1003        return complex<_Tp>(__theta, __theta);
1004    }
1005    if (isinf(__theta))
1006    {
1007        if (isinf(__rho))
1008            return complex<_Tp>(__rho, _Tp(NAN));
1009        return complex<_Tp>(_Tp(NAN), _Tp(NAN));
1010    }
1011    _Tp __x = __rho * cos(__theta);
1012    if (isnan(__x))
1013        __x = 0;
1014    _Tp __y = __rho * sin(__theta);
1015    if (isnan(__y))
1016        __y = 0;
1017    return complex<_Tp>(__x, __y);
1018}
1019
1020// log
1021
1022template<class _Tp>
1023inline _LIBCPP_INLINE_VISIBILITY
1024complex<_Tp>
1025log(const complex<_Tp>& __x)
1026{
1027    return complex<_Tp>(log(abs(__x)), arg(__x));
1028}
1029
1030// log10
1031
1032template<class _Tp>
1033inline _LIBCPP_INLINE_VISIBILITY
1034complex<_Tp>
1035log10(const complex<_Tp>& __x)
1036{
1037    return log(__x) / log(_Tp(10));
1038}
1039
1040// sqrt
1041
1042template<class _Tp>
1043complex<_Tp>
1044sqrt(const complex<_Tp>& __x)
1045{
1046    if (isinf(__x.imag()))
1047        return complex<_Tp>(_Tp(INFINITY), __x.imag());
1048    if (isinf(__x.real()))
1049    {
1050        if (__x.real() > _Tp(0))
1051            return complex<_Tp>(__x.real(), isnan(__x.imag()) ? __x.imag() : copysign(_Tp(0), __x.imag()));
1052        return complex<_Tp>(isnan(__x.imag()) ? __x.imag() : _Tp(0), copysign(__x.real(), __x.imag()));
1053    }
1054    return polar(sqrt(abs(__x)), arg(__x) / _Tp(2));
1055}
1056
1057// exp
1058
1059template<class _Tp>
1060complex<_Tp>
1061exp(const complex<_Tp>& __x)
1062{
1063    _Tp __i = __x.imag();
1064    if (isinf(__x.real()))
1065    {
1066        if (__x.real() < _Tp(0))
1067        {
1068            if (!isfinite(__i))
1069                __i = _Tp(1);
1070        }
1071        else if (__i == 0 || !isfinite(__i))
1072        {
1073            if (isinf(__i))
1074                __i = _Tp(NAN);
1075            return complex<_Tp>(__x.real(), __i);
1076        }
1077    }
1078    else if (isnan(__x.real()) && __x.imag() == 0)
1079        return __x;
1080    _Tp __e = exp(__x.real());
1081    return complex<_Tp>(__e * cos(__i), __e * sin(__i));
1082}
1083
1084// pow
1085
1086template<class _Tp>
1087inline _LIBCPP_INLINE_VISIBILITY
1088complex<_Tp>
1089pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1090{
1091    return exp(__y * log(__x));
1092}
1093
1094template<class _Tp, class _Up>
1095inline _LIBCPP_INLINE_VISIBILITY
1096complex<typename __promote<_Tp, _Up>::type>
1097pow(const complex<_Tp>& __x, const complex<_Up>& __y)
1098{
1099    typedef complex<typename __promote<_Tp, _Up>::type> result_type;
1100    return _VSTD::pow(result_type(__x), result_type(__y));
1101}
1102
1103template<class _Tp, class _Up>
1104inline _LIBCPP_INLINE_VISIBILITY
1105typename enable_if
1106<
1107    is_arithmetic<_Up>::value,
1108    complex<typename __promote<_Tp, _Up>::type>
1109>::type
1110pow(const complex<_Tp>& __x, const _Up& __y)
1111{
1112    typedef complex<typename __promote<_Tp, _Up>::type> result_type;
1113    return _VSTD::pow(result_type(__x), result_type(__y));
1114}
1115
1116template<class _Tp, class _Up>
1117inline _LIBCPP_INLINE_VISIBILITY
1118typename enable_if
1119<
1120    is_arithmetic<_Tp>::value,
1121    complex<typename __promote<_Tp, _Up>::type>
1122>::type
1123pow(const _Tp& __x, const complex<_Up>& __y)
1124{
1125    typedef complex<typename __promote<_Tp, _Up>::type> result_type;
1126    return _VSTD::pow(result_type(__x), result_type(__y));
1127}
1128
1129// asinh
1130
1131template<class _Tp>
1132complex<_Tp>
1133asinh(const complex<_Tp>& __x)
1134{
1135    const _Tp __pi(atan2(+0., -0.));
1136    if (isinf(__x.real()))
1137    {
1138        if (isnan(__x.imag()))
1139            return __x;
1140        if (isinf(__x.imag()))
1141            return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag()));
1142        return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
1143    }
1144    if (isnan(__x.real()))
1145    {
1146        if (isinf(__x.imag()))
1147            return complex<_Tp>(__x.imag(), __x.real());
1148        if (__x.imag() == 0)
1149            return __x;
1150        return complex<_Tp>(__x.real(), __x.real());
1151    }
1152    if (isinf(__x.imag()))
1153        return complex<_Tp>(copysign(__x.imag(), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
1154    complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) + _Tp(1)));
1155    return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag()));
1156}
1157
1158// acosh
1159
1160template<class _Tp>
1161complex<_Tp>
1162acosh(const complex<_Tp>& __x)
1163{
1164    const _Tp __pi(atan2(+0., -0.));
1165    if (isinf(__x.real()))
1166    {
1167        if (isnan(__x.imag()))
1168            return complex<_Tp>(abs(__x.real()), __x.imag());
1169        if (isinf(__x.imag()))
1170        {
1171            if (__x.real() > 0)
1172                return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag()));
1173            else
1174                return complex<_Tp>(-__x.real(), copysign(__pi * _Tp(0.75), __x.imag()));
1175        }
1176        if (__x.real() < 0)
1177            return complex<_Tp>(-__x.real(), copysign(__pi, __x.imag()));
1178        return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
1179    }
1180    if (isnan(__x.real()))
1181    {
1182        if (isinf(__x.imag()))
1183            return complex<_Tp>(abs(__x.imag()), __x.real());
1184        return complex<_Tp>(__x.real(), __x.real());
1185    }
1186    if (isinf(__x.imag()))
1187        return complex<_Tp>(abs(__x.imag()), copysign(__pi/_Tp(2), __x.imag()));
1188    complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1)));
1189    return complex<_Tp>(copysign(__z.real(), _Tp(0)), copysign(__z.imag(), __x.imag()));
1190}
1191
1192// atanh
1193
1194template<class _Tp>
1195complex<_Tp>
1196atanh(const complex<_Tp>& __x)
1197{
1198    const _Tp __pi(atan2(+0., -0.));
1199    if (isinf(__x.imag()))
1200    {
1201        return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
1202    }
1203    if (isnan(__x.imag()))
1204    {
1205        if (isinf(__x.real()) || __x.real() == 0)
1206            return complex<_Tp>(copysign(_Tp(0), __x.real()), __x.imag());
1207        return complex<_Tp>(__x.imag(), __x.imag());
1208    }
1209    if (isnan(__x.real()))
1210    {
1211        return complex<_Tp>(__x.real(), __x.real());
1212    }
1213    if (isinf(__x.real()))
1214    {
1215        return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
1216    }
1217    if (abs(__x.real()) == _Tp(1) && __x.imag() == _Tp(0))
1218    {
1219        return complex<_Tp>(copysign(_Tp(INFINITY), __x.real()), copysign(_Tp(0), __x.imag()));
1220    }
1221    complex<_Tp> __z = log((_Tp(1) + __x) / (_Tp(1) - __x)) / _Tp(2);
1222    return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag()));
1223}
1224
1225// sinh
1226
1227template<class _Tp>
1228complex<_Tp>
1229sinh(const complex<_Tp>& __x)
1230{
1231    if (isinf(__x.real()) && !isfinite(__x.imag()))
1232        return complex<_Tp>(__x.real(), _Tp(NAN));
1233    if (__x.real() == 0 && !isfinite(__x.imag()))
1234        return complex<_Tp>(__x.real(), _Tp(NAN));
1235    if (__x.imag() == 0 && !isfinite(__x.real()))
1236        return __x;
1237    return complex<_Tp>(sinh(__x.real()) * cos(__x.imag()), cosh(__x.real()) * sin(__x.imag()));
1238}
1239
1240// cosh
1241
1242template<class _Tp>
1243complex<_Tp>
1244cosh(const complex<_Tp>& __x)
1245{
1246    if (isinf(__x.real()) && !isfinite(__x.imag()))
1247        return complex<_Tp>(abs(__x.real()), _Tp(NAN));
1248    if (__x.real() == 0 && !isfinite(__x.imag()))
1249        return complex<_Tp>(_Tp(NAN), __x.real());
1250    if (__x.real() == 0 && __x.imag() == 0)
1251        return complex<_Tp>(_Tp(1), __x.imag());
1252    if (__x.imag() == 0 && !isfinite(__x.real()))
1253        return complex<_Tp>(abs(__x.real()), __x.imag());
1254    return complex<_Tp>(cosh(__x.real()) * cos(__x.imag()), sinh(__x.real()) * sin(__x.imag()));
1255}
1256
1257// tanh
1258
1259template<class _Tp>
1260complex<_Tp>
1261tanh(const complex<_Tp>& __x)
1262{
1263    if (isinf(__x.real()))
1264    {
1265        if (!isfinite(__x.imag()))
1266            return complex<_Tp>(_Tp(1), _Tp(0));
1267        return complex<_Tp>(_Tp(1), copysign(_Tp(0), sin(_Tp(2) * __x.imag())));
1268    }
1269    if (isnan(__x.real()) && __x.imag() == 0)
1270        return __x;
1271    _Tp __2r(_Tp(2) * __x.real());
1272    _Tp __2i(_Tp(2) * __x.imag());
1273    _Tp __d(cosh(__2r) + cos(__2i));
1274    _Tp __2rsh(sinh(__2r));
1275    if (isinf(__2rsh) && isinf(__d))
1276        return complex<_Tp>(__2rsh > _Tp(0) ? _Tp(1) : _Tp(-1),
1277                            __2i > _Tp(0) ? _Tp(0) : _Tp(-0.));
1278    return  complex<_Tp>(__2rsh/__d, sin(__2i)/__d);
1279}
1280
1281// asin
1282
1283template<class _Tp>
1284complex<_Tp>
1285asin(const complex<_Tp>& __x)
1286{
1287    complex<_Tp> __z = asinh(complex<_Tp>(-__x.imag(), __x.real()));
1288    return complex<_Tp>(__z.imag(), -__z.real());
1289}
1290
1291// acos
1292
1293template<class _Tp>
1294complex<_Tp>
1295acos(const complex<_Tp>& __x)
1296{
1297    const _Tp __pi(atan2(+0., -0.));
1298    if (isinf(__x.real()))
1299    {
1300        if (isnan(__x.imag()))
1301            return complex<_Tp>(__x.imag(), __x.real());
1302        if (isinf(__x.imag()))
1303        {
1304            if (__x.real() < _Tp(0))
1305                return complex<_Tp>(_Tp(0.75) * __pi, -__x.imag());
1306            return complex<_Tp>(_Tp(0.25) * __pi, -__x.imag());
1307        }
1308        if (__x.real() < _Tp(0))
1309            return complex<_Tp>(__pi, signbit(__x.imag()) ? -__x.real() : __x.real());
1310        return complex<_Tp>(_Tp(0), signbit(__x.imag()) ? __x.real() : -__x.real());
1311    }
1312    if (isnan(__x.real()))
1313    {
1314        if (isinf(__x.imag()))
1315            return complex<_Tp>(__x.real(), -__x.imag());
1316        return complex<_Tp>(__x.real(), __x.real());
1317    }
1318    if (isinf(__x.imag()))
1319        return complex<_Tp>(__pi/_Tp(2), -__x.imag());
1320    if (__x.real() == 0 && (__x.imag() == 0 || isnan(__x.imag())))
1321        return complex<_Tp>(__pi/_Tp(2), -__x.imag());
1322    complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1)));
1323    if (signbit(__x.imag()))
1324        return complex<_Tp>(abs(__z.imag()), abs(__z.real()));
1325    return complex<_Tp>(abs(__z.imag()), -abs(__z.real()));
1326}
1327
1328// atan
1329
1330template<class _Tp>
1331complex<_Tp>
1332atan(const complex<_Tp>& __x)
1333{
1334    complex<_Tp> __z = atanh(complex<_Tp>(-__x.imag(), __x.real()));
1335    return complex<_Tp>(__z.imag(), -__z.real());
1336}
1337
1338// sin
1339
1340template<class _Tp>
1341complex<_Tp>
1342sin(const complex<_Tp>& __x)
1343{
1344    complex<_Tp> __z = sinh(complex<_Tp>(-__x.imag(), __x.real()));
1345    return complex<_Tp>(__z.imag(), -__z.real());
1346}
1347
1348// cos
1349
1350template<class _Tp>
1351inline _LIBCPP_INLINE_VISIBILITY
1352complex<_Tp>
1353cos(const complex<_Tp>& __x)
1354{
1355    return cosh(complex<_Tp>(-__x.imag(), __x.real()));
1356}
1357
1358// tan
1359
1360template<class _Tp>
1361complex<_Tp>
1362tan(const complex<_Tp>& __x)
1363{
1364    complex<_Tp> __z = tanh(complex<_Tp>(-__x.imag(), __x.real()));
1365    return complex<_Tp>(__z.imag(), -__z.real());
1366}
1367
1368template<class _Tp, class _CharT, class _Traits>
1369basic_istream<_CharT, _Traits>&
1370operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
1371{
1372    if (__is.good())
1373    {
1374        ws(__is);
1375        if (__is.peek() == _CharT('('))
1376        {
1377            __is.get();
1378            _Tp __r;
1379            __is >> __r;
1380            if (!__is.fail())
1381            {
1382                ws(__is);
1383                _CharT __c = __is.peek();
1384                if (__c == _CharT(','))
1385                {
1386                    __is.get();
1387                    _Tp __i;
1388                    __is >> __i;
1389                    if (!__is.fail())
1390                    {
1391                        ws(__is);
1392                        __c = __is.peek();
1393                        if (__c == _CharT(')'))
1394                        {
1395                            __is.get();
1396                            __x = complex<_Tp>(__r, __i);
1397                        }
1398                        else
1399                            __is.setstate(ios_base::failbit);
1400                    }
1401                    else
1402                        __is.setstate(ios_base::failbit);
1403                }
1404                else if (__c == _CharT(')'))
1405                {
1406                    __is.get();
1407                    __x = complex<_Tp>(__r, _Tp(0));
1408                }
1409                else
1410                    __is.setstate(ios_base::failbit);
1411            }
1412            else
1413                __is.setstate(ios_base::failbit);
1414        }
1415        else
1416        {
1417            _Tp __r;
1418            __is >> __r;
1419            if (!__is.fail())
1420                __x = complex<_Tp>(__r, _Tp(0));
1421            else
1422                __is.setstate(ios_base::failbit);
1423        }
1424    }
1425    else
1426        __is.setstate(ios_base::failbit);
1427    return __is;
1428}
1429
1430template<class _Tp, class _CharT, class _Traits>
1431basic_ostream<_CharT, _Traits>&
1432operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
1433{
1434    basic_ostringstream<_CharT, _Traits> __s;
1435    __s.flags(__os.flags());
1436    __s.imbue(__os.getloc());
1437    __s.precision(__os.precision());
1438    __s << '(' << __x.real() << ',' << __x.imag() << ')';
1439    return __os << __s.str();
1440}
1441
1442#if _LIBCPP_STD_VER > 11
1443// Literal suffix for complex number literals [complex.literals]
1444inline namespace literals
1445{
1446  inline namespace complex_literals
1447  {
1448    constexpr complex<long double> operator""il(long double __im)
1449    {
1450        return { 0.0l, __im };
1451    }
1452
1453    constexpr complex<long double> operator""il(unsigned long long __im)
1454    {
1455        return { 0.0l, static_cast<long double>(__im) };
1456    }
1457
1458
1459    constexpr complex<double> operator""i(long double __im)
1460    {
1461        return { 0.0, static_cast<double>(__im) };
1462    }
1463
1464    constexpr complex<double> operator""i(unsigned long long __im)
1465    {
1466        return { 0.0, static_cast<double>(__im) };
1467    }
1468
1469
1470    constexpr complex<float> operator""if(long double __im)
1471    {
1472        return { 0.0f, static_cast<float>(__im) };
1473    }
1474
1475    constexpr complex<float> operator""if(unsigned long long __im)
1476    {
1477        return { 0.0f, static_cast<float>(__im) };
1478    }
1479  }
1480}
1481#endif
1482
1483_LIBCPP_END_NAMESPACE_STD
1484
1485#endif  // _LIBCPP_COMPLEX
1486