xref: /freebsd/contrib/llvm-project/libcxx/include/complex (revision e9e8876a4d6afc1ad5315faaa191b25121a813d7) 
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
230}  // std
231
232*/
233
234#include <__config>
235#include <cmath>
236#include <iosfwd>
237#include <stdexcept>
238#include <type_traits>
239#include <version>
240
241#if !defined(_LIBCPP_HAS_NO_LOCALIZATION)
242#   include <sstream> // for std::basic_ostringstream
243#endif
244
245#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
246#pragma GCC system_header
247#endif
248
249_LIBCPP_BEGIN_NAMESPACE_STD
250
251template<class _Tp> class _LIBCPP_TEMPLATE_VIS complex;
252
253template<class _Tp> complex<_Tp> operator*(const complex<_Tp>& __z, const complex<_Tp>& __w);
254template<class _Tp> complex<_Tp> operator/(const complex<_Tp>& __x, const complex<_Tp>& __y);
255
256template<class _Tp>
257class _LIBCPP_TEMPLATE_VIS complex
258{
259public:
260    typedef _Tp value_type;
261private:
262    value_type __re_;
263    value_type __im_;
264public:
265    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
266    complex(const value_type& __re = value_type(), const value_type& __im = value_type())
267        : __re_(__re), __im_(__im) {}
268    template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
269    complex(const complex<_Xp>& __c)
270        : __re_(__c.real()), __im_(__c.imag()) {}
271
272    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 value_type real() const {return __re_;}
273    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 value_type imag() const {return __im_;}
274
275    _LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
276    _LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
277
278    _LIBCPP_INLINE_VISIBILITY complex& operator= (const value_type& __re)
279        {__re_ = __re; __im_ = value_type(); return *this;}
280    _LIBCPP_INLINE_VISIBILITY complex& operator+=(const value_type& __re) {__re_ += __re; return *this;}
281    _LIBCPP_INLINE_VISIBILITY complex& operator-=(const value_type& __re) {__re_ -= __re; return *this;}
282    _LIBCPP_INLINE_VISIBILITY complex& operator*=(const value_type& __re) {__re_ *= __re; __im_ *= __re; return *this;}
283    _LIBCPP_INLINE_VISIBILITY complex& operator/=(const value_type& __re) {__re_ /= __re; __im_ /= __re; return *this;}
284
285    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
286        {
287            __re_ = __c.real();
288            __im_ = __c.imag();
289            return *this;
290        }
291    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
292        {
293            __re_ += __c.real();
294            __im_ += __c.imag();
295            return *this;
296        }
297    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
298        {
299            __re_ -= __c.real();
300            __im_ -= __c.imag();
301            return *this;
302        }
303    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
304        {
305            *this = *this * complex(__c.real(), __c.imag());
306            return *this;
307        }
308    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
309        {
310            *this = *this / complex(__c.real(), __c.imag());
311            return *this;
312        }
313};
314
315template<> class _LIBCPP_TEMPLATE_VIS complex<double>;
316template<> class _LIBCPP_TEMPLATE_VIS complex<long double>;
317
318template<>
319class _LIBCPP_TEMPLATE_VIS complex<float>
320{
321    float __re_;
322    float __im_;
323public:
324    typedef float value_type;
325
326    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(float __re = 0.0f, float __im = 0.0f)
327        : __re_(__re), __im_(__im) {}
328    _LIBCPP_INLINE_VISIBILITY
329    explicit _LIBCPP_CONSTEXPR complex(const complex<double>& __c);
330    _LIBCPP_INLINE_VISIBILITY
331    explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c);
332
333    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR float real() const {return __re_;}
334    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR float imag() const {return __im_;}
335
336    _LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
337    _LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
338
339    _LIBCPP_INLINE_VISIBILITY complex& operator= (float __re)
340        {__re_ = __re; __im_ = value_type(); return *this;}
341    _LIBCPP_INLINE_VISIBILITY complex& operator+=(float __re) {__re_ += __re; return *this;}
342    _LIBCPP_INLINE_VISIBILITY complex& operator-=(float __re) {__re_ -= __re; return *this;}
343    _LIBCPP_INLINE_VISIBILITY complex& operator*=(float __re) {__re_ *= __re; __im_ *= __re; return *this;}
344    _LIBCPP_INLINE_VISIBILITY complex& operator/=(float __re) {__re_ /= __re; __im_ /= __re; return *this;}
345
346    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
347        {
348            __re_ = __c.real();
349            __im_ = __c.imag();
350            return *this;
351        }
352    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
353        {
354            __re_ += __c.real();
355            __im_ += __c.imag();
356            return *this;
357        }
358    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
359        {
360            __re_ -= __c.real();
361            __im_ -= __c.imag();
362            return *this;
363        }
364    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
365        {
366            *this = *this * complex(__c.real(), __c.imag());
367            return *this;
368        }
369    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
370        {
371            *this = *this / complex(__c.real(), __c.imag());
372            return *this;
373        }
374};
375
376template<>
377class _LIBCPP_TEMPLATE_VIS complex<double>
378{
379    double __re_;
380    double __im_;
381public:
382    typedef double value_type;
383
384    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(double __re = 0.0, double __im = 0.0)
385        : __re_(__re), __im_(__im) {}
386    _LIBCPP_INLINE_VISIBILITY
387    _LIBCPP_CONSTEXPR complex(const complex<float>& __c);
388    _LIBCPP_INLINE_VISIBILITY
389    explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c);
390
391    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR double real() const {return __re_;}
392    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR double imag() const {return __im_;}
393
394    _LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
395    _LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
396
397    _LIBCPP_INLINE_VISIBILITY complex& operator= (double __re)
398        {__re_ = __re; __im_ = value_type(); return *this;}
399    _LIBCPP_INLINE_VISIBILITY complex& operator+=(double __re) {__re_ += __re; return *this;}
400    _LIBCPP_INLINE_VISIBILITY complex& operator-=(double __re) {__re_ -= __re; return *this;}
401    _LIBCPP_INLINE_VISIBILITY complex& operator*=(double __re) {__re_ *= __re; __im_ *= __re; return *this;}
402    _LIBCPP_INLINE_VISIBILITY complex& operator/=(double __re) {__re_ /= __re; __im_ /= __re; return *this;}
403
404    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
405        {
406            __re_ = __c.real();
407            __im_ = __c.imag();
408            return *this;
409        }
410    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
411        {
412            __re_ += __c.real();
413            __im_ += __c.imag();
414            return *this;
415        }
416    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
417        {
418            __re_ -= __c.real();
419            __im_ -= __c.imag();
420            return *this;
421        }
422    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
423        {
424            *this = *this * complex(__c.real(), __c.imag());
425            return *this;
426        }
427    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
428        {
429            *this = *this / complex(__c.real(), __c.imag());
430            return *this;
431        }
432};
433
434template<>
435class _LIBCPP_TEMPLATE_VIS complex<long double>
436{
437    long double __re_;
438    long double __im_;
439public:
440    typedef long double value_type;
441
442    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(long double __re = 0.0L, long double __im = 0.0L)
443        : __re_(__re), __im_(__im) {}
444    _LIBCPP_INLINE_VISIBILITY
445    _LIBCPP_CONSTEXPR complex(const complex<float>& __c);
446    _LIBCPP_INLINE_VISIBILITY
447    _LIBCPP_CONSTEXPR complex(const complex<double>& __c);
448
449    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR long double real() const {return __re_;}
450    _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR long double imag() const {return __im_;}
451
452    _LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
453    _LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
454
455    _LIBCPP_INLINE_VISIBILITY complex& operator= (long double __re)
456        {__re_ = __re; __im_ = value_type(); return *this;}
457    _LIBCPP_INLINE_VISIBILITY complex& operator+=(long double __re) {__re_ += __re; return *this;}
458    _LIBCPP_INLINE_VISIBILITY complex& operator-=(long double __re) {__re_ -= __re; return *this;}
459    _LIBCPP_INLINE_VISIBILITY complex& operator*=(long double __re) {__re_ *= __re; __im_ *= __re; return *this;}
460    _LIBCPP_INLINE_VISIBILITY complex& operator/=(long double __re) {__re_ /= __re; __im_ /= __re; return *this;}
461
462    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
463        {
464            __re_ = __c.real();
465            __im_ = __c.imag();
466            return *this;
467        }
468    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
469        {
470            __re_ += __c.real();
471            __im_ += __c.imag();
472            return *this;
473        }
474    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
475        {
476            __re_ -= __c.real();
477            __im_ -= __c.imag();
478            return *this;
479        }
480    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
481        {
482            *this = *this * complex(__c.real(), __c.imag());
483            return *this;
484        }
485    template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
486        {
487            *this = *this / complex(__c.real(), __c.imag());
488            return *this;
489        }
490};
491
492inline
493_LIBCPP_CONSTEXPR
494complex<float>::complex(const complex<double>& __c)
495    : __re_(__c.real()), __im_(__c.imag()) {}
496
497inline
498_LIBCPP_CONSTEXPR
499complex<float>::complex(const complex<long double>& __c)
500    : __re_(__c.real()), __im_(__c.imag()) {}
501
502inline
503_LIBCPP_CONSTEXPR
504complex<double>::complex(const complex<float>& __c)
505    : __re_(__c.real()), __im_(__c.imag()) {}
506
507inline
508_LIBCPP_CONSTEXPR
509complex<double>::complex(const complex<long double>& __c)
510    : __re_(__c.real()), __im_(__c.imag()) {}
511
512inline
513_LIBCPP_CONSTEXPR
514complex<long double>::complex(const complex<float>& __c)
515    : __re_(__c.real()), __im_(__c.imag()) {}
516
517inline
518_LIBCPP_CONSTEXPR
519complex<long double>::complex(const complex<double>& __c)
520    : __re_(__c.real()), __im_(__c.imag()) {}
521
522// 26.3.6 operators:
523
524template<class _Tp>
525inline _LIBCPP_INLINE_VISIBILITY
526complex<_Tp>
527operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
528{
529    complex<_Tp> __t(__x);
530    __t += __y;
531    return __t;
532}
533
534template<class _Tp>
535inline _LIBCPP_INLINE_VISIBILITY
536complex<_Tp>
537operator+(const complex<_Tp>& __x, const _Tp& __y)
538{
539    complex<_Tp> __t(__x);
540    __t += __y;
541    return __t;
542}
543
544template<class _Tp>
545inline _LIBCPP_INLINE_VISIBILITY
546complex<_Tp>
547operator+(const _Tp& __x, const complex<_Tp>& __y)
548{
549    complex<_Tp> __t(__y);
550    __t += __x;
551    return __t;
552}
553
554template<class _Tp>
555inline _LIBCPP_INLINE_VISIBILITY
556complex<_Tp>
557operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
558{
559    complex<_Tp> __t(__x);
560    __t -= __y;
561    return __t;
562}
563
564template<class _Tp>
565inline _LIBCPP_INLINE_VISIBILITY
566complex<_Tp>
567operator-(const complex<_Tp>& __x, const _Tp& __y)
568{
569    complex<_Tp> __t(__x);
570    __t -= __y;
571    return __t;
572}
573
574template<class _Tp>
575inline _LIBCPP_INLINE_VISIBILITY
576complex<_Tp>
577operator-(const _Tp& __x, const complex<_Tp>& __y)
578{
579    complex<_Tp> __t(-__y);
580    __t += __x;
581    return __t;
582}
583
584template<class _Tp>
585complex<_Tp>
586operator*(const complex<_Tp>& __z, const complex<_Tp>& __w)
587{
588    _Tp __a = __z.real();
589    _Tp __b = __z.imag();
590    _Tp __c = __w.real();
591    _Tp __d = __w.imag();
592    _Tp __ac = __a * __c;
593    _Tp __bd = __b * __d;
594    _Tp __ad = __a * __d;
595    _Tp __bc = __b * __c;
596    _Tp __x = __ac - __bd;
597    _Tp __y = __ad + __bc;
598    if (__libcpp_isnan_or_builtin(__x) && __libcpp_isnan_or_builtin(__y))
599    {
600        bool __recalc = false;
601        if (__libcpp_isinf_or_builtin(__a) || __libcpp_isinf_or_builtin(__b))
602        {
603            __a = copysign(__libcpp_isinf_or_builtin(__a) ? _Tp(1) : _Tp(0), __a);
604            __b = copysign(__libcpp_isinf_or_builtin(__b) ? _Tp(1) : _Tp(0), __b);
605            if (__libcpp_isnan_or_builtin(__c))
606                __c = copysign(_Tp(0), __c);
607            if (__libcpp_isnan_or_builtin(__d))
608                __d = copysign(_Tp(0), __d);
609            __recalc = true;
610        }
611        if (__libcpp_isinf_or_builtin(__c) || __libcpp_isinf_or_builtin(__d))
612        {
613            __c = copysign(__libcpp_isinf_or_builtin(__c) ? _Tp(1) : _Tp(0), __c);
614            __d = copysign(__libcpp_isinf_or_builtin(__d) ? _Tp(1) : _Tp(0), __d);
615            if (__libcpp_isnan_or_builtin(__a))
616                __a = copysign(_Tp(0), __a);
617            if (__libcpp_isnan_or_builtin(__b))
618                __b = copysign(_Tp(0), __b);
619            __recalc = true;
620        }
621        if (!__recalc && (__libcpp_isinf_or_builtin(__ac) || __libcpp_isinf_or_builtin(__bd) ||
622                          __libcpp_isinf_or_builtin(__ad) || __libcpp_isinf_or_builtin(__bc)))
623        {
624            if (__libcpp_isnan_or_builtin(__a))
625                __a = copysign(_Tp(0), __a);
626            if (__libcpp_isnan_or_builtin(__b))
627                __b = copysign(_Tp(0), __b);
628            if (__libcpp_isnan_or_builtin(__c))
629                __c = copysign(_Tp(0), __c);
630            if (__libcpp_isnan_or_builtin(__d))
631                __d = copysign(_Tp(0), __d);
632            __recalc = true;
633        }
634        if (__recalc)
635        {
636            __x = _Tp(INFINITY) * (__a * __c - __b * __d);
637            __y = _Tp(INFINITY) * (__a * __d + __b * __c);
638        }
639    }
640    return complex<_Tp>(__x, __y);
641}
642
643template<class _Tp>
644inline _LIBCPP_INLINE_VISIBILITY
645complex<_Tp>
646operator*(const complex<_Tp>& __x, const _Tp& __y)
647{
648    complex<_Tp> __t(__x);
649    __t *= __y;
650    return __t;
651}
652
653template<class _Tp>
654inline _LIBCPP_INLINE_VISIBILITY
655complex<_Tp>
656operator*(const _Tp& __x, const complex<_Tp>& __y)
657{
658    complex<_Tp> __t(__y);
659    __t *= __x;
660    return __t;
661}
662
663template<class _Tp>
664complex<_Tp>
665operator/(const complex<_Tp>& __z, const complex<_Tp>& __w)
666{
667    int __ilogbw = 0;
668    _Tp __a = __z.real();
669    _Tp __b = __z.imag();
670    _Tp __c = __w.real();
671    _Tp __d = __w.imag();
672    _Tp __logbw = logb(fmax(fabs(__c), fabs(__d)));
673    if (__libcpp_isfinite_or_builtin(__logbw))
674    {
675        __ilogbw = static_cast<int>(__logbw);
676        __c = scalbn(__c, -__ilogbw);
677        __d = scalbn(__d, -__ilogbw);
678    }
679    _Tp __denom = __c * __c + __d * __d;
680    _Tp __x = scalbn((__a * __c + __b * __d) / __denom, -__ilogbw);
681    _Tp __y = scalbn((__b * __c - __a * __d) / __denom, -__ilogbw);
682    if (__libcpp_isnan_or_builtin(__x) && __libcpp_isnan_or_builtin(__y))
683    {
684        if ((__denom == _Tp(0)) && (!__libcpp_isnan_or_builtin(__a) || !__libcpp_isnan_or_builtin(__b)))
685        {
686            __x = copysign(_Tp(INFINITY), __c) * __a;
687            __y = copysign(_Tp(INFINITY), __c) * __b;
688        }
689        else if ((__libcpp_isinf_or_builtin(__a) || __libcpp_isinf_or_builtin(__b)) && __libcpp_isfinite_or_builtin(__c) && __libcpp_isfinite_or_builtin(__d))
690        {
691            __a = copysign(__libcpp_isinf_or_builtin(__a) ? _Tp(1) : _Tp(0), __a);
692            __b = copysign(__libcpp_isinf_or_builtin(__b) ? _Tp(1) : _Tp(0), __b);
693            __x = _Tp(INFINITY) * (__a * __c + __b * __d);
694            __y = _Tp(INFINITY) * (__b * __c - __a * __d);
695        }
696        else if (__libcpp_isinf_or_builtin(__logbw) && __logbw > _Tp(0) && __libcpp_isfinite_or_builtin(__a) && __libcpp_isfinite_or_builtin(__b))
697        {
698            __c = copysign(__libcpp_isinf_or_builtin(__c) ? _Tp(1) : _Tp(0), __c);
699            __d = copysign(__libcpp_isinf_or_builtin(__d) ? _Tp(1) : _Tp(0), __d);
700            __x = _Tp(0) * (__a * __c + __b * __d);
701            __y = _Tp(0) * (__b * __c - __a * __d);
702        }
703    }
704    return complex<_Tp>(__x, __y);
705}
706
707template<class _Tp>
708inline _LIBCPP_INLINE_VISIBILITY
709complex<_Tp>
710operator/(const complex<_Tp>& __x, const _Tp& __y)
711{
712    return complex<_Tp>(__x.real() / __y, __x.imag() / __y);
713}
714
715template<class _Tp>
716inline _LIBCPP_INLINE_VISIBILITY
717complex<_Tp>
718operator/(const _Tp& __x, const complex<_Tp>& __y)
719{
720    complex<_Tp> __t(__x);
721    __t /= __y;
722    return __t;
723}
724
725template<class _Tp>
726inline _LIBCPP_INLINE_VISIBILITY
727complex<_Tp>
728operator+(const complex<_Tp>& __x)
729{
730    return __x;
731}
732
733template<class _Tp>
734inline _LIBCPP_INLINE_VISIBILITY
735complex<_Tp>
736operator-(const complex<_Tp>& __x)
737{
738    return complex<_Tp>(-__x.real(), -__x.imag());
739}
740
741template<class _Tp>
742inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
743bool
744operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
745{
746    return __x.real() == __y.real() && __x.imag() == __y.imag();
747}
748
749template<class _Tp>
750inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
751bool
752operator==(const complex<_Tp>& __x, const _Tp& __y)
753{
754    return __x.real() == __y && __x.imag() == 0;
755}
756
757template<class _Tp>
758inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
759bool
760operator==(const _Tp& __x, const complex<_Tp>& __y)
761{
762    return __x == __y.real() && 0 == __y.imag();
763}
764
765template<class _Tp>
766inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
767bool
768operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
769{
770    return !(__x == __y);
771}
772
773template<class _Tp>
774inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
775bool
776operator!=(const complex<_Tp>& __x, const _Tp& __y)
777{
778    return !(__x == __y);
779}
780
781template<class _Tp>
782inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
783bool
784operator!=(const _Tp& __x, const complex<_Tp>& __y)
785{
786    return !(__x == __y);
787}
788
789// 26.3.7 values:
790
791template <class _Tp, bool = is_integral<_Tp>::value,
792                     bool = is_floating_point<_Tp>::value
793                     >
794struct __libcpp_complex_overload_traits {};
795
796// Integral Types
797template <class _Tp>
798struct __libcpp_complex_overload_traits<_Tp, true, false>
799{
800    typedef double _ValueType;
801    typedef complex<double> _ComplexType;
802};
803
804// Floating point types
805template <class _Tp>
806struct __libcpp_complex_overload_traits<_Tp, false, true>
807{
808    typedef _Tp _ValueType;
809    typedef complex<_Tp> _ComplexType;
810};
811
812// real
813
814template<class _Tp>
815inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
816_Tp
817real(const complex<_Tp>& __c)
818{
819    return __c.real();
820}
821
822template <class _Tp>
823inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
824typename __libcpp_complex_overload_traits<_Tp>::_ValueType
825real(_Tp __re)
826{
827    return __re;
828}
829
830// imag
831
832template<class _Tp>
833inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
834_Tp
835imag(const complex<_Tp>& __c)
836{
837    return __c.imag();
838}
839
840template <class _Tp>
841inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
842typename __libcpp_complex_overload_traits<_Tp>::_ValueType
843imag(_Tp)
844{
845    return 0;
846}
847
848// abs
849
850template<class _Tp>
851inline _LIBCPP_INLINE_VISIBILITY
852_Tp
853abs(const complex<_Tp>& __c)
854{
855    return hypot(__c.real(), __c.imag());
856}
857
858// arg
859
860template<class _Tp>
861inline _LIBCPP_INLINE_VISIBILITY
862_Tp
863arg(const complex<_Tp>& __c)
864{
865    return atan2(__c.imag(), __c.real());
866}
867
868template <class _Tp>
869inline _LIBCPP_INLINE_VISIBILITY
870typename enable_if<
871    is_same<_Tp, long double>::value,
872    long double
873>::type
874arg(_Tp __re)
875{
876    return atan2l(0.L, __re);
877}
878
879template<class _Tp>
880inline _LIBCPP_INLINE_VISIBILITY
881typename enable_if
882<
883    is_integral<_Tp>::value || is_same<_Tp, double>::value,
884    double
885>::type
886arg(_Tp __re)
887{
888    return atan2(0., __re);
889}
890
891template <class _Tp>
892inline _LIBCPP_INLINE_VISIBILITY
893typename enable_if<
894    is_same<_Tp, float>::value,
895    float
896>::type
897arg(_Tp __re)
898{
899    return atan2f(0.F, __re);
900}
901
902// norm
903
904template<class _Tp>
905inline _LIBCPP_INLINE_VISIBILITY
906_Tp
907norm(const complex<_Tp>& __c)
908{
909    if (__libcpp_isinf_or_builtin(__c.real()))
910        return abs(__c.real());
911    if (__libcpp_isinf_or_builtin(__c.imag()))
912        return abs(__c.imag());
913    return __c.real() * __c.real() + __c.imag() * __c.imag();
914}
915
916template <class _Tp>
917inline _LIBCPP_INLINE_VISIBILITY
918typename __libcpp_complex_overload_traits<_Tp>::_ValueType
919norm(_Tp __re)
920{
921    typedef typename __libcpp_complex_overload_traits<_Tp>::_ValueType _ValueType;
922    return static_cast<_ValueType>(__re) * __re;
923}
924
925// conj
926
927template<class _Tp>
928inline _LIBCPP_INLINE_VISIBILITY
929complex<_Tp>
930conj(const complex<_Tp>& __c)
931{
932    return complex<_Tp>(__c.real(), -__c.imag());
933}
934
935template <class _Tp>
936inline _LIBCPP_INLINE_VISIBILITY
937typename __libcpp_complex_overload_traits<_Tp>::_ComplexType
938conj(_Tp __re)
939{
940    typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType;
941    return _ComplexType(__re);
942}
943
944
945
946// proj
947
948template<class _Tp>
949inline _LIBCPP_INLINE_VISIBILITY
950complex<_Tp>
951proj(const complex<_Tp>& __c)
952{
953    complex<_Tp> __r = __c;
954    if (__libcpp_isinf_or_builtin(__c.real()) || __libcpp_isinf_or_builtin(__c.imag()))
955        __r = complex<_Tp>(INFINITY, copysign(_Tp(0), __c.imag()));
956    return __r;
957}
958
959template <class _Tp>
960inline _LIBCPP_INLINE_VISIBILITY
961typename enable_if
962<
963    is_floating_point<_Tp>::value,
964    typename __libcpp_complex_overload_traits<_Tp>::_ComplexType
965>::type
966proj(_Tp __re)
967{
968    if (__libcpp_isinf_or_builtin(__re))
969        __re = abs(__re);
970    return complex<_Tp>(__re);
971}
972
973template <class _Tp>
974inline _LIBCPP_INLINE_VISIBILITY
975typename enable_if
976<
977    is_integral<_Tp>::value,
978    typename __libcpp_complex_overload_traits<_Tp>::_ComplexType
979>::type
980proj(_Tp __re)
981{
982    typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType;
983    return _ComplexType(__re);
984}
985
986// polar
987
988template<class _Tp>
989complex<_Tp>
990polar(const _Tp& __rho, const _Tp& __theta = _Tp())
991{
992    if (__libcpp_isnan_or_builtin(__rho) || signbit(__rho))
993        return complex<_Tp>(_Tp(NAN), _Tp(NAN));
994    if (__libcpp_isnan_or_builtin(__theta))
995    {
996        if (__libcpp_isinf_or_builtin(__rho))
997            return complex<_Tp>(__rho, __theta);
998        return complex<_Tp>(__theta, __theta);
999    }
1000    if (__libcpp_isinf_or_builtin(__theta))
1001    {
1002        if (__libcpp_isinf_or_builtin(__rho))
1003            return complex<_Tp>(__rho, _Tp(NAN));
1004        return complex<_Tp>(_Tp(NAN), _Tp(NAN));
1005    }
1006    _Tp __x = __rho * cos(__theta);
1007    if (__libcpp_isnan_or_builtin(__x))
1008        __x = 0;
1009    _Tp __y = __rho * sin(__theta);
1010    if (__libcpp_isnan_or_builtin(__y))
1011        __y = 0;
1012    return complex<_Tp>(__x, __y);
1013}
1014
1015// log
1016
1017template<class _Tp>
1018inline _LIBCPP_INLINE_VISIBILITY
1019complex<_Tp>
1020log(const complex<_Tp>& __x)
1021{
1022    return complex<_Tp>(log(abs(__x)), arg(__x));
1023}
1024
1025// log10
1026
1027template<class _Tp>
1028inline _LIBCPP_INLINE_VISIBILITY
1029complex<_Tp>
1030log10(const complex<_Tp>& __x)
1031{
1032    return log(__x) / log(_Tp(10));
1033}
1034
1035// sqrt
1036
1037template<class _Tp>
1038complex<_Tp>
1039sqrt(const complex<_Tp>& __x)
1040{
1041    if (__libcpp_isinf_or_builtin(__x.imag()))
1042        return complex<_Tp>(_Tp(INFINITY), __x.imag());
1043    if (__libcpp_isinf_or_builtin(__x.real()))
1044    {
1045        if (__x.real() > _Tp(0))
1046            return complex<_Tp>(__x.real(), __libcpp_isnan_or_builtin(__x.imag()) ? __x.imag() : copysign(_Tp(0), __x.imag()));
1047        return complex<_Tp>(__libcpp_isnan_or_builtin(__x.imag()) ? __x.imag() : _Tp(0), copysign(__x.real(), __x.imag()));
1048    }
1049    return polar(sqrt(abs(__x)), arg(__x) / _Tp(2));
1050}
1051
1052// exp
1053
1054template<class _Tp>
1055complex<_Tp>
1056exp(const complex<_Tp>& __x)
1057{
1058    _Tp __i = __x.imag();
1059    if (__libcpp_isinf_or_builtin(__x.real()))
1060    {
1061        if (__x.real() < _Tp(0))
1062        {
1063            if (!__libcpp_isfinite_or_builtin(__i))
1064                __i = _Tp(1);
1065        }
1066        else if (__i == 0 || !__libcpp_isfinite_or_builtin(__i))
1067        {
1068            if (__libcpp_isinf_or_builtin(__i))
1069                __i = _Tp(NAN);
1070            return complex<_Tp>(__x.real(), __i);
1071        }
1072    }
1073    else if (__libcpp_isnan_or_builtin(__x.real()) && __x.imag() == 0)
1074        return __x;
1075    _Tp __e = exp(__x.real());
1076    return complex<_Tp>(__e * cos(__i), __e * sin(__i));
1077}
1078
1079// pow
1080
1081template<class _Tp>
1082inline _LIBCPP_INLINE_VISIBILITY
1083complex<_Tp>
1084pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1085{
1086    return exp(__y * log(__x));
1087}
1088
1089template<class _Tp, class _Up>
1090inline _LIBCPP_INLINE_VISIBILITY
1091complex<typename __promote<_Tp, _Up>::type>
1092pow(const complex<_Tp>& __x, const complex<_Up>& __y)
1093{
1094    typedef complex<typename __promote<_Tp, _Up>::type> result_type;
1095    return _VSTD::pow(result_type(__x), result_type(__y));
1096}
1097
1098template<class _Tp, class _Up>
1099inline _LIBCPP_INLINE_VISIBILITY
1100typename enable_if
1101<
1102    is_arithmetic<_Up>::value,
1103    complex<typename __promote<_Tp, _Up>::type>
1104>::type
1105pow(const complex<_Tp>& __x, const _Up& __y)
1106{
1107    typedef complex<typename __promote<_Tp, _Up>::type> result_type;
1108    return _VSTD::pow(result_type(__x), result_type(__y));
1109}
1110
1111template<class _Tp, class _Up>
1112inline _LIBCPP_INLINE_VISIBILITY
1113typename enable_if
1114<
1115    is_arithmetic<_Tp>::value,
1116    complex<typename __promote<_Tp, _Up>::type>
1117>::type
1118pow(const _Tp& __x, const complex<_Up>& __y)
1119{
1120    typedef complex<typename __promote<_Tp, _Up>::type> result_type;
1121    return _VSTD::pow(result_type(__x), result_type(__y));
1122}
1123
1124// __sqr, computes pow(x, 2)
1125
1126template<class _Tp>
1127inline _LIBCPP_INLINE_VISIBILITY
1128complex<_Tp>
1129__sqr(const complex<_Tp>& __x)
1130{
1131    return complex<_Tp>((__x.real() - __x.imag()) * (__x.real() + __x.imag()),
1132                        _Tp(2) * __x.real() * __x.imag());
1133}
1134
1135// asinh
1136
1137template<class _Tp>
1138complex<_Tp>
1139asinh(const complex<_Tp>& __x)
1140{
1141    const _Tp __pi(atan2(+0., -0.));
1142    if (__libcpp_isinf_or_builtin(__x.real()))
1143    {
1144        if (__libcpp_isnan_or_builtin(__x.imag()))
1145            return __x;
1146        if (__libcpp_isinf_or_builtin(__x.imag()))
1147            return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag()));
1148        return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
1149    }
1150    if (__libcpp_isnan_or_builtin(__x.real()))
1151    {
1152        if (__libcpp_isinf_or_builtin(__x.imag()))
1153            return complex<_Tp>(__x.imag(), __x.real());
1154        if (__x.imag() == 0)
1155            return __x;
1156        return complex<_Tp>(__x.real(), __x.real());
1157    }
1158    if (__libcpp_isinf_or_builtin(__x.imag()))
1159        return complex<_Tp>(copysign(__x.imag(), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
1160    complex<_Tp> __z = log(__x + sqrt(__sqr(__x) + _Tp(1)));
1161    return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag()));
1162}
1163
1164// acosh
1165
1166template<class _Tp>
1167complex<_Tp>
1168acosh(const complex<_Tp>& __x)
1169{
1170    const _Tp __pi(atan2(+0., -0.));
1171    if (__libcpp_isinf_or_builtin(__x.real()))
1172    {
1173        if (__libcpp_isnan_or_builtin(__x.imag()))
1174            return complex<_Tp>(abs(__x.real()), __x.imag());
1175        if (__libcpp_isinf_or_builtin(__x.imag()))
1176        {
1177            if (__x.real() > 0)
1178                return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag()));
1179            else
1180                return complex<_Tp>(-__x.real(), copysign(__pi * _Tp(0.75), __x.imag()));
1181        }
1182        if (__x.real() < 0)
1183            return complex<_Tp>(-__x.real(), copysign(__pi, __x.imag()));
1184        return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
1185    }
1186    if (__libcpp_isnan_or_builtin(__x.real()))
1187    {
1188        if (__libcpp_isinf_or_builtin(__x.imag()))
1189            return complex<_Tp>(abs(__x.imag()), __x.real());
1190        return complex<_Tp>(__x.real(), __x.real());
1191    }
1192    if (__libcpp_isinf_or_builtin(__x.imag()))
1193        return complex<_Tp>(abs(__x.imag()), copysign(__pi/_Tp(2), __x.imag()));
1194    complex<_Tp> __z = log(__x + sqrt(__sqr(__x) - _Tp(1)));
1195    return complex<_Tp>(copysign(__z.real(), _Tp(0)), copysign(__z.imag(), __x.imag()));
1196}
1197
1198// atanh
1199
1200template<class _Tp>
1201complex<_Tp>
1202atanh(const complex<_Tp>& __x)
1203{
1204    const _Tp __pi(atan2(+0., -0.));
1205    if (__libcpp_isinf_or_builtin(__x.imag()))
1206    {
1207        return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
1208    }
1209    if (__libcpp_isnan_or_builtin(__x.imag()))
1210    {
1211        if (__libcpp_isinf_or_builtin(__x.real()) || __x.real() == 0)
1212            return complex<_Tp>(copysign(_Tp(0), __x.real()), __x.imag());
1213        return complex<_Tp>(__x.imag(), __x.imag());
1214    }
1215    if (__libcpp_isnan_or_builtin(__x.real()))
1216    {
1217        return complex<_Tp>(__x.real(), __x.real());
1218    }
1219    if (__libcpp_isinf_or_builtin(__x.real()))
1220    {
1221        return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
1222    }
1223    if (abs(__x.real()) == _Tp(1) && __x.imag() == _Tp(0))
1224    {
1225        return complex<_Tp>(copysign(_Tp(INFINITY), __x.real()), copysign(_Tp(0), __x.imag()));
1226    }
1227    complex<_Tp> __z = log((_Tp(1) + __x) / (_Tp(1) - __x)) / _Tp(2);
1228    return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag()));
1229}
1230
1231// sinh
1232
1233template<class _Tp>
1234complex<_Tp>
1235sinh(const complex<_Tp>& __x)
1236{
1237    if (__libcpp_isinf_or_builtin(__x.real()) && !__libcpp_isfinite_or_builtin(__x.imag()))
1238        return complex<_Tp>(__x.real(), _Tp(NAN));
1239    if (__x.real() == 0 && !__libcpp_isfinite_or_builtin(__x.imag()))
1240        return complex<_Tp>(__x.real(), _Tp(NAN));
1241    if (__x.imag() == 0 && !__libcpp_isfinite_or_builtin(__x.real()))
1242        return __x;
1243    return complex<_Tp>(sinh(__x.real()) * cos(__x.imag()), cosh(__x.real()) * sin(__x.imag()));
1244}
1245
1246// cosh
1247
1248template<class _Tp>
1249complex<_Tp>
1250cosh(const complex<_Tp>& __x)
1251{
1252    if (__libcpp_isinf_or_builtin(__x.real()) && !__libcpp_isfinite_or_builtin(__x.imag()))
1253        return complex<_Tp>(abs(__x.real()), _Tp(NAN));
1254    if (__x.real() == 0 && !__libcpp_isfinite_or_builtin(__x.imag()))
1255        return complex<_Tp>(_Tp(NAN), __x.real());
1256    if (__x.real() == 0 && __x.imag() == 0)
1257        return complex<_Tp>(_Tp(1), __x.imag());
1258    if (__x.imag() == 0 && !__libcpp_isfinite_or_builtin(__x.real()))
1259        return complex<_Tp>(abs(__x.real()), __x.imag());
1260    return complex<_Tp>(cosh(__x.real()) * cos(__x.imag()), sinh(__x.real()) * sin(__x.imag()));
1261}
1262
1263// tanh
1264
1265template<class _Tp>
1266complex<_Tp>
1267tanh(const complex<_Tp>& __x)
1268{
1269    if (__libcpp_isinf_or_builtin(__x.real()))
1270    {
1271        if (!__libcpp_isfinite_or_builtin(__x.imag()))
1272            return complex<_Tp>(_Tp(1), _Tp(0));
1273        return complex<_Tp>(_Tp(1), copysign(_Tp(0), sin(_Tp(2) * __x.imag())));
1274    }
1275    if (__libcpp_isnan_or_builtin(__x.real()) && __x.imag() == 0)
1276        return __x;
1277    _Tp __2r(_Tp(2) * __x.real());
1278    _Tp __2i(_Tp(2) * __x.imag());
1279    _Tp __d(cosh(__2r) + cos(__2i));
1280    _Tp __2rsh(sinh(__2r));
1281    if (__libcpp_isinf_or_builtin(__2rsh) && __libcpp_isinf_or_builtin(__d))
1282        return complex<_Tp>(__2rsh > _Tp(0) ? _Tp(1) : _Tp(-1),
1283                            __2i > _Tp(0) ? _Tp(0) : _Tp(-0.));
1284    return  complex<_Tp>(__2rsh/__d, sin(__2i)/__d);
1285}
1286
1287// asin
1288
1289template<class _Tp>
1290complex<_Tp>
1291asin(const complex<_Tp>& __x)
1292{
1293    complex<_Tp> __z = asinh(complex<_Tp>(-__x.imag(), __x.real()));
1294    return complex<_Tp>(__z.imag(), -__z.real());
1295}
1296
1297// acos
1298
1299template<class _Tp>
1300complex<_Tp>
1301acos(const complex<_Tp>& __x)
1302{
1303    const _Tp __pi(atan2(+0., -0.));
1304    if (__libcpp_isinf_or_builtin(__x.real()))
1305    {
1306        if (__libcpp_isnan_or_builtin(__x.imag()))
1307            return complex<_Tp>(__x.imag(), __x.real());
1308        if (__libcpp_isinf_or_builtin(__x.imag()))
1309        {
1310            if (__x.real() < _Tp(0))
1311                return complex<_Tp>(_Tp(0.75) * __pi, -__x.imag());
1312            return complex<_Tp>(_Tp(0.25) * __pi, -__x.imag());
1313        }
1314        if (__x.real() < _Tp(0))
1315            return complex<_Tp>(__pi, signbit(__x.imag()) ? -__x.real() : __x.real());
1316        return complex<_Tp>(_Tp(0), signbit(__x.imag()) ? __x.real() : -__x.real());
1317    }
1318    if (__libcpp_isnan_or_builtin(__x.real()))
1319    {
1320        if (__libcpp_isinf_or_builtin(__x.imag()))
1321            return complex<_Tp>(__x.real(), -__x.imag());
1322        return complex<_Tp>(__x.real(), __x.real());
1323    }
1324    if (__libcpp_isinf_or_builtin(__x.imag()))
1325        return complex<_Tp>(__pi/_Tp(2), -__x.imag());
1326    if (__x.real() == 0 && (__x.imag() == 0 || isnan(__x.imag())))
1327        return complex<_Tp>(__pi/_Tp(2), -__x.imag());
1328    complex<_Tp> __z = log(__x + sqrt(__sqr(__x) - _Tp(1)));
1329    if (signbit(__x.imag()))
1330        return complex<_Tp>(abs(__z.imag()), abs(__z.real()));
1331    return complex<_Tp>(abs(__z.imag()), -abs(__z.real()));
1332}
1333
1334// atan
1335
1336template<class _Tp>
1337complex<_Tp>
1338atan(const complex<_Tp>& __x)
1339{
1340    complex<_Tp> __z = atanh(complex<_Tp>(-__x.imag(), __x.real()));
1341    return complex<_Tp>(__z.imag(), -__z.real());
1342}
1343
1344// sin
1345
1346template<class _Tp>
1347complex<_Tp>
1348sin(const complex<_Tp>& __x)
1349{
1350    complex<_Tp> __z = sinh(complex<_Tp>(-__x.imag(), __x.real()));
1351    return complex<_Tp>(__z.imag(), -__z.real());
1352}
1353
1354// cos
1355
1356template<class _Tp>
1357inline _LIBCPP_INLINE_VISIBILITY
1358complex<_Tp>
1359cos(const complex<_Tp>& __x)
1360{
1361    return cosh(complex<_Tp>(-__x.imag(), __x.real()));
1362}
1363
1364// tan
1365
1366template<class _Tp>
1367complex<_Tp>
1368tan(const complex<_Tp>& __x)
1369{
1370    complex<_Tp> __z = tanh(complex<_Tp>(-__x.imag(), __x.real()));
1371    return complex<_Tp>(__z.imag(), -__z.real());
1372}
1373
1374template<class _Tp, class _CharT, class _Traits>
1375basic_istream<_CharT, _Traits>&
1376operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
1377{
1378    if (__is.good())
1379    {
1380        ws(__is);
1381        if (__is.peek() == _CharT('('))
1382        {
1383            __is.get();
1384            _Tp __r;
1385            __is >> __r;
1386            if (!__is.fail())
1387            {
1388                ws(__is);
1389                _CharT __c = __is.peek();
1390                if (__c == _CharT(','))
1391                {
1392                    __is.get();
1393                    _Tp __i;
1394                    __is >> __i;
1395                    if (!__is.fail())
1396                    {
1397                        ws(__is);
1398                        __c = __is.peek();
1399                        if (__c == _CharT(')'))
1400                        {
1401                            __is.get();
1402                            __x = complex<_Tp>(__r, __i);
1403                        }
1404                        else
1405                            __is.setstate(__is.failbit);
1406                    }
1407                    else
1408                        __is.setstate(__is.failbit);
1409                }
1410                else if (__c == _CharT(')'))
1411                {
1412                    __is.get();
1413                    __x = complex<_Tp>(__r, _Tp(0));
1414                }
1415                else
1416                    __is.setstate(__is.failbit);
1417            }
1418            else
1419                __is.setstate(__is.failbit);
1420        }
1421        else
1422        {
1423            _Tp __r;
1424            __is >> __r;
1425            if (!__is.fail())
1426                __x = complex<_Tp>(__r, _Tp(0));
1427            else
1428                __is.setstate(__is.failbit);
1429        }
1430    }
1431    else
1432        __is.setstate(__is.failbit);
1433    return __is;
1434}
1435
1436#if !defined(_LIBCPP_HAS_NO_LOCALIZATION)
1437template<class _Tp, class _CharT, class _Traits>
1438basic_ostream<_CharT, _Traits>&
1439operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
1440{
1441    basic_ostringstream<_CharT, _Traits> __s;
1442    __s.flags(__os.flags());
1443    __s.imbue(__os.getloc());
1444    __s.precision(__os.precision());
1445    __s << '(' << __x.real() << ',' << __x.imag() << ')';
1446    return __os << __s.str();
1447}
1448#endif // !_LIBCPP_HAS_NO_LOCALIZATION
1449
1450#if _LIBCPP_STD_VER > 11
1451// Literal suffix for complex number literals [complex.literals]
1452inline namespace literals
1453{
1454  inline namespace complex_literals
1455  {
1456    constexpr complex<long double> operator""il(long double __im)
1457    {
1458        return { 0.0l, __im };
1459    }
1460
1461    constexpr complex<long double> operator""il(unsigned long long __im)
1462    {
1463        return { 0.0l, static_cast<long double>(__im) };
1464    }
1465
1466
1467    constexpr complex<double> operator""i(long double __im)
1468    {
1469        return { 0.0, static_cast<double>(__im) };
1470    }
1471
1472    constexpr complex<double> operator""i(unsigned long long __im)
1473    {
1474        return { 0.0, static_cast<double>(__im) };
1475    }
1476
1477
1478    constexpr complex<float> operator""if(long double __im)
1479    {
1480        return { 0.0f, static_cast<float>(__im) };
1481    }
1482
1483    constexpr complex<float> operator""if(unsigned long long __im)
1484    {
1485        return { 0.0f, static_cast<float>(__im) };
1486    }
1487  }
1488}
1489#endif
1490
1491_LIBCPP_END_NAMESPACE_STD
1492
1493#endif // _LIBCPP_COMPLEX
1494