1// -*- C++ -*-
2//===----------------------------------------------------------------------===//
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); // constexpr in C++20
33    void imag(T); // constexpr in C++20
34
35    complex<T>& operator= (const T&); // constexpr in C++20
36    complex<T>& operator+=(const T&); // constexpr in C++20
37    complex<T>& operator-=(const T&); // constexpr in C++20
38    complex<T>& operator*=(const T&); // constexpr in C++20
39    complex<T>& operator/=(const T&); // constexpr in C++20
40
41    complex& operator=(const complex&); // constexpr in C++20
42    template<class X> complex<T>& operator= (const complex<X>&); // constexpr in C++20
43    template<class X> complex<T>& operator+=(const complex<X>&); // constexpr in C++20
44    template<class X> complex<T>& operator-=(const complex<X>&); // constexpr in C++20
45    template<class X> complex<T>& operator*=(const complex<X>&); // constexpr in C++20
46    template<class X> complex<T>& operator/=(const complex<X>&); // constexpr in C++20
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); // constexpr in C++20
61    constexpr float imag() const;
62    void imag(float); // constexpr in C++20
63
64    complex<float>& operator= (float); // constexpr in C++20
65    complex<float>& operator+=(float); // constexpr in C++20
66    complex<float>& operator-=(float); // constexpr in C++20
67    complex<float>& operator*=(float); // constexpr in C++20
68    complex<float>& operator/=(float); // constexpr in C++20
69
70    complex<float>& operator=(const complex<float>&); // constexpr in C++20
71    template<class X> complex<float>& operator= (const complex<X>&); // constexpr in C++20
72    template<class X> complex<float>& operator+=(const complex<X>&); // constexpr in C++20
73    template<class X> complex<float>& operator-=(const complex<X>&); // constexpr in C++20
74    template<class X> complex<float>& operator*=(const complex<X>&); // constexpr in C++20
75    template<class X> complex<float>& operator/=(const complex<X>&); // constexpr in C++20
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); // constexpr in C++20
90    constexpr double imag() const;
91    void imag(double); // constexpr in C++20
92
93    complex<double>& operator= (double); // constexpr in C++20
94    complex<double>& operator+=(double); // constexpr in C++20
95    complex<double>& operator-=(double); // constexpr in C++20
96    complex<double>& operator*=(double); // constexpr in C++20
97    complex<double>& operator/=(double); // constexpr in C++20
98    complex<double>& operator=(const complex<double>&); // constexpr in C++20
99
100    template<class X> complex<double>& operator= (const complex<X>&); // constexpr in C++20
101    template<class X> complex<double>& operator+=(const complex<X>&); // constexpr in C++20
102    template<class X> complex<double>& operator-=(const complex<X>&); // constexpr in C++20
103    template<class X> complex<double>& operator*=(const complex<X>&); // constexpr in C++20
104    template<class X> complex<double>& operator/=(const complex<X>&); // constexpr in C++20
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); // constexpr in C++20
119    constexpr long double imag() const;
120    void imag(long double); // constexpr in C++20
121
122    complex<long double>& operator=(const complex<long double>&); // constexpr in C++20
123    complex<long double>& operator= (long double); // constexpr in C++20
124    complex<long double>& operator+=(long double); // constexpr in C++20
125    complex<long double>& operator-=(long double); // constexpr in C++20
126    complex<long double>& operator*=(long double); // constexpr in C++20
127    complex<long double>& operator/=(long double); // constexpr in C++20
128
129    template<class X> complex<long double>& operator= (const complex<X>&); // constexpr in C++20
130    template<class X> complex<long double>& operator+=(const complex<X>&); // constexpr in C++20
131    template<class X> complex<long double>& operator-=(const complex<X>&); // constexpr in C++20
132    template<class X> complex<long double>& operator*=(const complex<X>&); // constexpr in C++20
133    template<class X> complex<long double>& operator/=(const complex<X>&); // constexpr in C++20
134};
135
136// 26.3.6 operators:
137template<class T> complex<T> operator+(const complex<T>&, const complex<T>&); // constexpr in C++20
138template<class T> complex<T> operator+(const complex<T>&, const T&);          // constexpr in C++20
139template<class T> complex<T> operator+(const T&, const complex<T>&);          // constexpr in C++20
140template<class T> complex<T> operator-(const complex<T>&, const complex<T>&); // constexpr in C++20
141template<class T> complex<T> operator-(const complex<T>&, const T&);          // constexpr in C++20
142template<class T> complex<T> operator-(const T&, const complex<T>&);          // constexpr in C++20
143template<class T> complex<T> operator*(const complex<T>&, const complex<T>&); // constexpr in C++20
144template<class T> complex<T> operator*(const complex<T>&, const T&);          // constexpr in C++20
145template<class T> complex<T> operator*(const T&, const complex<T>&);          // constexpr in C++20
146template<class T> complex<T> operator/(const complex<T>&, const complex<T>&); // constexpr in C++20
147template<class T> complex<T> operator/(const complex<T>&, const T&);          // constexpr in C++20
148template<class T> complex<T> operator/(const T&, const complex<T>&);          // constexpr in C++20
149template<class T> complex<T> operator+(const complex<T>&);                    // constexpr in C++20
150template<class T> complex<T> operator-(const complex<T>&);                    // constexpr in C++20
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, removed in C++20
154template<class T> bool operator!=(const complex<T>&, const complex<T>&);      // constexpr in C++14, removed in C++20
155template<class T> bool operator!=(const complex<T>&, const T&);               // constexpr in C++14, removed in C++20
156template<class T> bool operator!=(const T&, const complex<T>&);               // constexpr in C++14, removed in C++20
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>&); // constexpr in C++20
188                     long double norm(long double);       // constexpr in C++20
189                          double norm(double);            // constexpr in C++20
190template<Integral T>      double norm(T);                 // constexpr in C++20
191                          float  norm(float);             // constexpr in C++20
192
193template<class T>      complex<T>           conj(const complex<T>&); // constexpr in C++20
194                       complex<long double> conj(long double);       // constexpr in C++20
195                       complex<double>      conj(double);            // constexpr in C++20
196template<Integral T>   complex<double>      conj(T);                 // constexpr in C++20
197                       complex<float>       conj(float);             // constexpr in C++20
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 <__assert> // all public C++ headers provide the assertion handler
235#include <__config>
236#include <cmath>
237#include <version>
238
239#if !defined(_LIBCPP_HAS_NO_LOCALIZATION)
240#   include <sstream> // for std::basic_ostringstream
241#endif
242
243#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
244#  pragma GCC system_header
245#endif
246
247_LIBCPP_BEGIN_NAMESPACE_STD
248
249template<class _Tp> class _LIBCPP_TEMPLATE_VIS complex;
250
251template<class _Tp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator*(const complex<_Tp>& __z, const complex<_Tp>& __w);
252template<class _Tp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator/(const complex<_Tp>& __x, const complex<_Tp>& __y);
253
254template<class _Tp>
255class _LIBCPP_TEMPLATE_VIS complex
256{
257public:
258    typedef _Tp value_type;
259private:
260    value_type __re_;
261    value_type __im_;
262public:
263    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14
264    complex(const value_type& __re = value_type(), const value_type& __im = value_type())
265        : __re_(__re), __im_(__im) {}
266    template<class _Xp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14
267    complex(const complex<_Xp>& __c)
268        : __re_(__c.real()), __im_(__c.imag()) {}
269
270    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 value_type real() const {return __re_;}
271    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 value_type imag() const {return __im_;}
272
273    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) {__re_ = __re;}
274    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) {__im_ = __im;}
275
276    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (const value_type& __re)
277        {__re_ = __re; __im_ = value_type(); return *this;}
278    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const value_type& __re) {__re_ += __re; return *this;}
279    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const value_type& __re) {__re_ -= __re; return *this;}
280    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const value_type& __re) {__re_ *= __re; __im_ *= __re; return *this;}
281    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const value_type& __re) {__re_ /= __re; __im_ /= __re; return *this;}
282
283    template<class _Xp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (const complex<_Xp>& __c)
284        {
285            __re_ = __c.real();
286            __im_ = __c.imag();
287            return *this;
288        }
289    template<class _Xp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c)
290        {
291            __re_ += __c.real();
292            __im_ += __c.imag();
293            return *this;
294        }
295    template<class _Xp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c)
296        {
297            __re_ -= __c.real();
298            __im_ -= __c.imag();
299            return *this;
300        }
301    template<class _Xp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c)
302        {
303            *this = *this * complex(__c.real(), __c.imag());
304            return *this;
305        }
306    template<class _Xp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const complex<_Xp>& __c)
307        {
308            *this = *this / complex(__c.real(), __c.imag());
309            return *this;
310        }
311};
312
313template<> class _LIBCPP_TEMPLATE_VIS complex<double>;
314template<> class _LIBCPP_TEMPLATE_VIS complex<long double>;
315
316template<>
317class _LIBCPP_TEMPLATE_VIS complex<float>
318{
319    float __re_;
320    float __im_;
321public:
322    typedef float value_type;
323
324    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(float __re = 0.0f, float __im = 0.0f)
325        : __re_(__re), __im_(__im) {}
326    _LIBCPP_HIDE_FROM_ABI
327    explicit _LIBCPP_CONSTEXPR complex(const complex<double>& __c);
328    _LIBCPP_HIDE_FROM_ABI
329    explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c);
330
331    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR float real() const {return __re_;}
332    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR float imag() const {return __im_;}
333
334    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) {__re_ = __re;}
335    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) {__im_ = __im;}
336
337    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (float __re)
338        {__re_ = __re; __im_ = value_type(); return *this;}
339    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(float __re) {__re_ += __re; return *this;}
340    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(float __re) {__re_ -= __re; return *this;}
341    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(float __re) {__re_ *= __re; __im_ *= __re; return *this;}
342    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(float __re) {__re_ /= __re; __im_ /= __re; return *this;}
343
344    template<class _Xp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (const complex<_Xp>& __c)
345        {
346            __re_ = __c.real();
347            __im_ = __c.imag();
348            return *this;
349        }
350    template<class _Xp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c)
351        {
352            __re_ += __c.real();
353            __im_ += __c.imag();
354            return *this;
355        }
356    template<class _Xp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c)
357        {
358            __re_ -= __c.real();
359            __im_ -= __c.imag();
360            return *this;
361        }
362    template<class _Xp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c)
363        {
364            *this = *this * complex(__c.real(), __c.imag());
365            return *this;
366        }
367    template<class _Xp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const complex<_Xp>& __c)
368        {
369            *this = *this / complex(__c.real(), __c.imag());
370            return *this;
371        }
372};
373
374template<>
375class _LIBCPP_TEMPLATE_VIS complex<double>
376{
377    double __re_;
378    double __im_;
379public:
380    typedef double value_type;
381
382    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(double __re = 0.0, double __im = 0.0)
383        : __re_(__re), __im_(__im) {}
384    _LIBCPP_HIDE_FROM_ABI
385    _LIBCPP_CONSTEXPR complex(const complex<float>& __c);
386    _LIBCPP_HIDE_FROM_ABI
387    explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c);
388
389    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR double real() const {return __re_;}
390    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR double imag() const {return __im_;}
391
392    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) {__re_ = __re;}
393    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) {__im_ = __im;}
394
395    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (double __re)
396        {__re_ = __re; __im_ = value_type(); return *this;}
397    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(double __re) {__re_ += __re; return *this;}
398    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(double __re) {__re_ -= __re; return *this;}
399    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(double __re) {__re_ *= __re; __im_ *= __re; return *this;}
400    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(double __re) {__re_ /= __re; __im_ /= __re; return *this;}
401
402    template<class _Xp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (const complex<_Xp>& __c)
403        {
404            __re_ = __c.real();
405            __im_ = __c.imag();
406            return *this;
407        }
408    template<class _Xp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c)
409        {
410            __re_ += __c.real();
411            __im_ += __c.imag();
412            return *this;
413        }
414    template<class _Xp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c)
415        {
416            __re_ -= __c.real();
417            __im_ -= __c.imag();
418            return *this;
419        }
420    template<class _Xp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c)
421        {
422            *this = *this * complex(__c.real(), __c.imag());
423            return *this;
424        }
425    template<class _Xp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const complex<_Xp>& __c)
426        {
427            *this = *this / complex(__c.real(), __c.imag());
428            return *this;
429        }
430};
431
432template<>
433class _LIBCPP_TEMPLATE_VIS complex<long double>
434{
435    long double __re_;
436    long double __im_;
437public:
438    typedef long double value_type;
439
440    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(long double __re = 0.0L, long double __im = 0.0L)
441        : __re_(__re), __im_(__im) {}
442    _LIBCPP_HIDE_FROM_ABI
443    _LIBCPP_CONSTEXPR complex(const complex<float>& __c);
444    _LIBCPP_HIDE_FROM_ABI
445    _LIBCPP_CONSTEXPR complex(const complex<double>& __c);
446
447    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR long double real() const {return __re_;}
448    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR long double imag() const {return __im_;}
449
450    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) {__re_ = __re;}
451    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) {__im_ = __im;}
452
453    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (long double __re)
454        {__re_ = __re; __im_ = value_type(); return *this;}
455    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(long double __re) {__re_ += __re; return *this;}
456    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(long double __re) {__re_ -= __re; return *this;}
457    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(long double __re) {__re_ *= __re; __im_ *= __re; return *this;}
458    _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(long double __re) {__re_ /= __re; __im_ /= __re; return *this;}
459
460    template<class _Xp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator= (const complex<_Xp>& __c)
461        {
462            __re_ = __c.real();
463            __im_ = __c.imag();
464            return *this;
465        }
466    template<class _Xp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c)
467        {
468            __re_ += __c.real();
469            __im_ += __c.imag();
470            return *this;
471        }
472    template<class _Xp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c)
473        {
474            __re_ -= __c.real();
475            __im_ -= __c.imag();
476            return *this;
477        }
478    template<class _Xp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c)
479        {
480            *this = *this * complex(__c.real(), __c.imag());
481            return *this;
482        }
483    template<class _Xp> _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const complex<_Xp>& __c)
484        {
485            *this = *this / complex(__c.real(), __c.imag());
486            return *this;
487        }
488};
489
490inline
491_LIBCPP_CONSTEXPR
492complex<float>::complex(const complex<double>& __c)
493    : __re_(__c.real()), __im_(__c.imag()) {}
494
495inline
496_LIBCPP_CONSTEXPR
497complex<float>::complex(const complex<long double>& __c)
498    : __re_(__c.real()), __im_(__c.imag()) {}
499
500inline
501_LIBCPP_CONSTEXPR
502complex<double>::complex(const complex<float>& __c)
503    : __re_(__c.real()), __im_(__c.imag()) {}
504
505inline
506_LIBCPP_CONSTEXPR
507complex<double>::complex(const complex<long double>& __c)
508    : __re_(__c.real()), __im_(__c.imag()) {}
509
510inline
511_LIBCPP_CONSTEXPR
512complex<long double>::complex(const complex<float>& __c)
513    : __re_(__c.real()), __im_(__c.imag()) {}
514
515inline
516_LIBCPP_CONSTEXPR
517complex<long double>::complex(const complex<double>& __c)
518    : __re_(__c.real()), __im_(__c.imag()) {}
519
520// 26.3.6 operators:
521
522template<class _Tp>
523inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20
524complex<_Tp>
525operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
526{
527    complex<_Tp> __t(__x);
528    __t += __y;
529    return __t;
530}
531
532template<class _Tp>
533inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20
534complex<_Tp>
535operator+(const complex<_Tp>& __x, const _Tp& __y)
536{
537    complex<_Tp> __t(__x);
538    __t += __y;
539    return __t;
540}
541
542template<class _Tp>
543inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20
544complex<_Tp>
545operator+(const _Tp& __x, const complex<_Tp>& __y)
546{
547    complex<_Tp> __t(__y);
548    __t += __x;
549    return __t;
550}
551
552template<class _Tp>
553inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20
554complex<_Tp>
555operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
556{
557    complex<_Tp> __t(__x);
558    __t -= __y;
559    return __t;
560}
561
562template<class _Tp>
563inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20
564complex<_Tp>
565operator-(const complex<_Tp>& __x, const _Tp& __y)
566{
567    complex<_Tp> __t(__x);
568    __t -= __y;
569    return __t;
570}
571
572template<class _Tp>
573inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20
574complex<_Tp>
575operator-(const _Tp& __x, const complex<_Tp>& __y)
576{
577    complex<_Tp> __t(-__y);
578    __t += __x;
579    return __t;
580}
581
582template<class _Tp>
583_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
584operator*(const complex<_Tp>& __z, const complex<_Tp>& __w)
585{
586    _Tp __a = __z.real();
587    _Tp __b = __z.imag();
588    _Tp __c = __w.real();
589    _Tp __d = __w.imag();
590
591    // Avoid floating point operations that are invalid during constant evaluation
592    if (__libcpp_is_constant_evaluated()) {
593        bool __z_zero = __a == _Tp(0) && __b == _Tp(0);
594        bool __w_zero = __c == _Tp(0) && __d == _Tp(0);
595        bool __z_inf = std::__constexpr_isinf(__a) || std::__constexpr_isinf(__b);
596        bool __w_inf = std::__constexpr_isinf(__c) || std::__constexpr_isinf(__d);
597        bool __z_nan = !__z_inf && (
598            (std::__constexpr_isnan(__a) && std::__constexpr_isnan(__b))
599            || (std::__constexpr_isnan(__a) && __b == _Tp(0))
600            || (__a == _Tp(0) && std::__constexpr_isnan(__b))
601        );
602        bool __w_nan = !__w_inf && (
603            (std::__constexpr_isnan(__c) && std::__constexpr_isnan(__d))
604            || (std::__constexpr_isnan(__c) && __d == _Tp(0))
605            || (__c == _Tp(0) && std::__constexpr_isnan(__d))
606        );
607        if (__z_nan || __w_nan) {
608            return complex<_Tp>(_Tp(numeric_limits<_Tp>::quiet_NaN()), _Tp(0));
609        }
610        if (__z_inf || __w_inf) {
611            if (__z_zero || __w_zero) {
612                return complex<_Tp>(_Tp(numeric_limits<_Tp>::quiet_NaN()), _Tp(0));
613            }
614            return complex<_Tp>(_Tp(numeric_limits<_Tp>::infinity()), _Tp(numeric_limits<_Tp>::infinity()));
615        }
616        bool __z_nonzero_nan = !__z_inf && !__z_nan && (std::__constexpr_isnan(__a) || std::__constexpr_isnan(__b));
617        bool __w_nonzero_nan = !__w_inf && !__w_nan && (std::__constexpr_isnan(__c) || std::__constexpr_isnan(__d));
618        if (__z_nonzero_nan || __w_nonzero_nan) {
619            return complex<_Tp>(_Tp(numeric_limits<_Tp>::quiet_NaN()), _Tp(0));
620        }
621    }
622
623    _Tp __ac = __a * __c;
624    _Tp __bd = __b * __d;
625    _Tp __ad = __a * __d;
626    _Tp __bc = __b * __c;
627    _Tp __x = __ac - __bd;
628    _Tp __y = __ad + __bc;
629    if (std::__constexpr_isnan(__x) && std::__constexpr_isnan(__y))
630    {
631        bool __recalc = false;
632        if (std::__constexpr_isinf(__a) || std::__constexpr_isinf(__b))
633        {
634            __a = std::__constexpr_copysign(std::__constexpr_isinf(__a) ? _Tp(1) : _Tp(0), __a);
635            __b = std::__constexpr_copysign(std::__constexpr_isinf(__b) ? _Tp(1) : _Tp(0), __b);
636            if (std::__constexpr_isnan(__c))
637                __c = std::__constexpr_copysign(_Tp(0), __c);
638            if (std::__constexpr_isnan(__d))
639                __d = std::__constexpr_copysign(_Tp(0), __d);
640            __recalc = true;
641        }
642        if (std::__constexpr_isinf(__c) || std::__constexpr_isinf(__d))
643        {
644            __c = std::__constexpr_copysign(std::__constexpr_isinf(__c) ? _Tp(1) : _Tp(0), __c);
645            __d = std::__constexpr_copysign(std::__constexpr_isinf(__d) ? _Tp(1) : _Tp(0), __d);
646            if (std::__constexpr_isnan(__a))
647                __a = std::__constexpr_copysign(_Tp(0), __a);
648            if (std::__constexpr_isnan(__b))
649                __b = std::__constexpr_copysign(_Tp(0), __b);
650            __recalc = true;
651        }
652        if (!__recalc && (std::__constexpr_isinf(__ac) || std::__constexpr_isinf(__bd) ||
653                          std::__constexpr_isinf(__ad) || std::__constexpr_isinf(__bc)))
654        {
655            if (std::__constexpr_isnan(__a))
656                __a = std::__constexpr_copysign(_Tp(0), __a);
657            if (std::__constexpr_isnan(__b))
658                __b = std::__constexpr_copysign(_Tp(0), __b);
659            if (std::__constexpr_isnan(__c))
660                __c = std::__constexpr_copysign(_Tp(0), __c);
661            if (std::__constexpr_isnan(__d))
662                __d = std::__constexpr_copysign(_Tp(0), __d);
663            __recalc = true;
664        }
665        if (__recalc)
666        {
667            __x = _Tp(INFINITY) * (__a * __c - __b * __d);
668            __y = _Tp(INFINITY) * (__a * __d + __b * __c);
669        }
670    }
671    return complex<_Tp>(__x, __y);
672}
673
674template<class _Tp>
675inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20
676complex<_Tp>
677operator*(const complex<_Tp>& __x, const _Tp& __y)
678{
679    complex<_Tp> __t(__x);
680    __t *= __y;
681    return __t;
682}
683
684template<class _Tp>
685inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20
686complex<_Tp>
687operator*(const _Tp& __x, const complex<_Tp>& __y)
688{
689    complex<_Tp> __t(__y);
690    __t *= __x;
691    return __t;
692}
693
694template<class _Tp>
695_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
696operator/(const complex<_Tp>& __z, const complex<_Tp>& __w)
697{
698    int __ilogbw = 0;
699    _Tp __a = __z.real();
700    _Tp __b = __z.imag();
701    _Tp __c = __w.real();
702    _Tp __d = __w.imag();
703    _Tp __logbw = std::__constexpr_logb(std::__constexpr_fmax(std::__constexpr_fabs(__c), std::__constexpr_fabs(__d)));
704    if (std::__constexpr_isfinite(__logbw))
705    {
706        __ilogbw = static_cast<int>(__logbw);
707        __c = std::__constexpr_scalbn(__c, -__ilogbw);
708        __d = std::__constexpr_scalbn(__d, -__ilogbw);
709    }
710
711    // Avoid floating point operations that are invalid during constant evaluation
712    if (__libcpp_is_constant_evaluated()) {
713        bool __z_zero = __a == _Tp(0) && __b == _Tp(0);
714        bool __w_zero = __c == _Tp(0) && __d == _Tp(0);
715        bool __z_inf = std::__constexpr_isinf(__a) || std::__constexpr_isinf(__b);
716        bool __w_inf = std::__constexpr_isinf(__c) || std::__constexpr_isinf(__d);
717        bool __z_nan = !__z_inf && (
718            (std::__constexpr_isnan(__a) && std::__constexpr_isnan(__b))
719            || (std::__constexpr_isnan(__a) && __b == _Tp(0))
720            || (__a == _Tp(0) && std::__constexpr_isnan(__b))
721        );
722        bool __w_nan = !__w_inf && (
723            (std::__constexpr_isnan(__c) && std::__constexpr_isnan(__d))
724            || (std::__constexpr_isnan(__c) && __d == _Tp(0))
725            || (__c == _Tp(0) && std::__constexpr_isnan(__d))
726        );
727        if ((__z_nan || __w_nan) || (__z_inf && __w_inf)) {
728            return complex<_Tp>(_Tp(numeric_limits<_Tp>::quiet_NaN()), _Tp(0));
729        }
730        bool __z_nonzero_nan = !__z_inf && !__z_nan && (std::__constexpr_isnan(__a) || std::__constexpr_isnan(__b));
731        bool __w_nonzero_nan = !__w_inf && !__w_nan && (std::__constexpr_isnan(__c) || std::__constexpr_isnan(__d));
732        if (__z_nonzero_nan || __w_nonzero_nan) {
733            if (__w_zero) {
734                return complex<_Tp>(_Tp(numeric_limits<_Tp>::infinity()), _Tp(numeric_limits<_Tp>::infinity()));
735            }
736            return complex<_Tp>(_Tp(numeric_limits<_Tp>::quiet_NaN()), _Tp(0));
737        }
738        if (__w_inf) {
739            return complex<_Tp>(_Tp(0), _Tp(0));
740        }
741        if (__z_inf) {
742            return complex<_Tp>(_Tp(numeric_limits<_Tp>::infinity()), _Tp(numeric_limits<_Tp>::infinity()));
743        }
744        if (__w_zero) {
745            if (__z_zero) {
746                return complex<_Tp>(_Tp(numeric_limits<_Tp>::quiet_NaN()), _Tp(0));
747            }
748            return complex<_Tp>(_Tp(numeric_limits<_Tp>::infinity()), _Tp(numeric_limits<_Tp>::infinity()));
749        }
750    }
751
752    _Tp __denom = __c * __c + __d * __d;
753    _Tp __x = std::__constexpr_scalbn((__a * __c + __b * __d) / __denom, -__ilogbw);
754    _Tp __y = std::__constexpr_scalbn((__b * __c - __a * __d) / __denom, -__ilogbw);
755    if (std::__constexpr_isnan(__x) && std::__constexpr_isnan(__y))
756    {
757        if ((__denom == _Tp(0)) && (!std::__constexpr_isnan(__a) || !std::__constexpr_isnan(__b)))
758        {
759            __x = std::__constexpr_copysign(_Tp(INFINITY), __c) * __a;
760            __y = std::__constexpr_copysign(_Tp(INFINITY), __c) * __b;
761        } else if ((std::__constexpr_isinf(__a) || std::__constexpr_isinf(__b)) && std::__constexpr_isfinite(__c) &&
762                   std::__constexpr_isfinite(__d)) {
763            __a = std::__constexpr_copysign(std::__constexpr_isinf(__a) ? _Tp(1) : _Tp(0), __a);
764            __b = std::__constexpr_copysign(std::__constexpr_isinf(__b) ? _Tp(1) : _Tp(0), __b);
765            __x = _Tp(INFINITY) * (__a * __c + __b * __d);
766            __y = _Tp(INFINITY) * (__b * __c - __a * __d);
767        } else if (std::__constexpr_isinf(__logbw) && __logbw > _Tp(0) && std::__constexpr_isfinite(__a) &&
768                   std::__constexpr_isfinite(__b)) {
769            __c = std::__constexpr_copysign(std::__constexpr_isinf(__c) ? _Tp(1) : _Tp(0), __c);
770            __d = std::__constexpr_copysign(std::__constexpr_isinf(__d) ? _Tp(1) : _Tp(0), __d);
771            __x = _Tp(0) * (__a * __c + __b * __d);
772            __y = _Tp(0) * (__b * __c - __a * __d);
773        }
774    }
775    return complex<_Tp>(__x, __y);
776}
777
778template<class _Tp>
779inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20
780complex<_Tp>
781operator/(const complex<_Tp>& __x, const _Tp& __y)
782{
783    return complex<_Tp>(__x.real() / __y, __x.imag() / __y);
784}
785
786template<class _Tp>
787inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20
788complex<_Tp>
789operator/(const _Tp& __x, const complex<_Tp>& __y)
790{
791    complex<_Tp> __t(__x);
792    __t /= __y;
793    return __t;
794}
795
796template<class _Tp>
797inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20
798complex<_Tp>
799operator+(const complex<_Tp>& __x)
800{
801    return __x;
802}
803
804template<class _Tp>
805inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20
806complex<_Tp>
807operator-(const complex<_Tp>& __x)
808{
809    return complex<_Tp>(-__x.real(), -__x.imag());
810}
811
812template<class _Tp>
813inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14
814bool
815operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
816{
817    return __x.real() == __y.real() && __x.imag() == __y.imag();
818}
819
820template<class _Tp>
821inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14
822bool
823operator==(const complex<_Tp>& __x, const _Tp& __y)
824{
825    return __x.real() == __y && __x.imag() == 0;
826}
827
828#if _LIBCPP_STD_VER <= 17
829
830template<class _Tp>
831inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14
832bool
833operator==(const _Tp& __x, const complex<_Tp>& __y)
834{
835    return __x == __y.real() && 0 == __y.imag();
836}
837
838template<class _Tp>
839inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14
840bool
841operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
842{
843    return !(__x == __y);
844}
845
846template<class _Tp>
847inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14
848bool
849operator!=(const complex<_Tp>& __x, const _Tp& __y)
850{
851    return !(__x == __y);
852}
853
854template<class _Tp>
855inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14
856bool
857operator!=(const _Tp& __x, const complex<_Tp>& __y)
858{
859    return !(__x == __y);
860}
861
862#endif
863
864// 26.3.7 values:
865
866template <class _Tp, bool = is_integral<_Tp>::value,
867                     bool = is_floating_point<_Tp>::value
868                     >
869struct __libcpp_complex_overload_traits {};
870
871// Integral Types
872template <class _Tp>
873struct __libcpp_complex_overload_traits<_Tp, true, false>
874{
875    typedef double _ValueType;
876    typedef complex<double> _ComplexType;
877};
878
879// Floating point types
880template <class _Tp>
881struct __libcpp_complex_overload_traits<_Tp, false, true>
882{
883    typedef _Tp _ValueType;
884    typedef complex<_Tp> _ComplexType;
885};
886
887// real
888
889template<class _Tp>
890inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14
891_Tp
892real(const complex<_Tp>& __c)
893{
894    return __c.real();
895}
896
897template <class _Tp>
898inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14
899typename __libcpp_complex_overload_traits<_Tp>::_ValueType
900real(_Tp __re)
901{
902    return __re;
903}
904
905// imag
906
907template<class _Tp>
908inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14
909_Tp
910imag(const complex<_Tp>& __c)
911{
912    return __c.imag();
913}
914
915template <class _Tp>
916inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14
917typename __libcpp_complex_overload_traits<_Tp>::_ValueType
918imag(_Tp)
919{
920    return 0;
921}
922
923// abs
924
925template<class _Tp>
926inline _LIBCPP_HIDE_FROM_ABI
927_Tp
928abs(const complex<_Tp>& __c)
929{
930    return std::hypot(__c.real(), __c.imag());
931}
932
933// arg
934
935template<class _Tp>
936inline _LIBCPP_HIDE_FROM_ABI
937_Tp
938arg(const complex<_Tp>& __c)
939{
940    return std::atan2(__c.imag(), __c.real());
941}
942
943template <class _Tp, __enable_if_t<is_same<_Tp, long double>::value, int> = 0>
944inline _LIBCPP_HIDE_FROM_ABI
945long double
946arg(_Tp __re)
947{
948    return std::atan2l(0.L, __re);
949}
950
951template<class _Tp, __enable_if_t<is_integral<_Tp>::value || is_same<_Tp, double>::value, int> = 0>
952inline _LIBCPP_HIDE_FROM_ABI
953double
954arg(_Tp __re)
955{
956    return std::atan2(0., __re);
957}
958
959template <class _Tp, __enable_if_t<is_same<_Tp, float>::value, int> = 0>
960inline _LIBCPP_HIDE_FROM_ABI
961float
962arg(_Tp __re)
963{
964    return std::atan2f(0.F, __re);
965}
966
967// norm
968
969template<class _Tp>
970inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20
971_Tp
972norm(const complex<_Tp>& __c)
973{
974    if (std::__constexpr_isinf(__c.real()))
975        return std::abs(__c.real());
976    if (std::__constexpr_isinf(__c.imag()))
977        return std::abs(__c.imag());
978    return __c.real() * __c.real() + __c.imag() * __c.imag();
979}
980
981template <class _Tp>
982inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20
983typename __libcpp_complex_overload_traits<_Tp>::_ValueType
984norm(_Tp __re)
985{
986    typedef typename __libcpp_complex_overload_traits<_Tp>::_ValueType _ValueType;
987    return static_cast<_ValueType>(__re) * __re;
988}
989
990// conj
991
992template<class _Tp>
993inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20
994complex<_Tp>
995conj(const complex<_Tp>& __c)
996{
997    return complex<_Tp>(__c.real(), -__c.imag());
998}
999
1000template <class _Tp>
1001inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20
1002typename __libcpp_complex_overload_traits<_Tp>::_ComplexType
1003conj(_Tp __re)
1004{
1005    typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType;
1006    return _ComplexType(__re);
1007}
1008
1009
1010
1011// proj
1012
1013template<class _Tp>
1014inline _LIBCPP_HIDE_FROM_ABI
1015complex<_Tp>
1016proj(const complex<_Tp>& __c)
1017{
1018    complex<_Tp> __r = __c;
1019    if (std::__constexpr_isinf(__c.real()) || std::__constexpr_isinf(__c.imag()))
1020        __r = complex<_Tp>(INFINITY, std::copysign(_Tp(0), __c.imag()));
1021    return __r;
1022}
1023
1024template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> = 0>
1025inline _LIBCPP_HIDE_FROM_ABI
1026typename __libcpp_complex_overload_traits<_Tp>::_ComplexType
1027proj(_Tp __re)
1028{
1029    if (std::__constexpr_isinf(__re))
1030        __re = std::abs(__re);
1031    return complex<_Tp>(__re);
1032}
1033
1034template <class _Tp, __enable_if_t<is_integral<_Tp>::value, int> = 0>
1035inline _LIBCPP_HIDE_FROM_ABI
1036typename __libcpp_complex_overload_traits<_Tp>::_ComplexType
1037proj(_Tp __re)
1038{
1039    typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType;
1040    return _ComplexType(__re);
1041}
1042
1043// polar
1044
1045template<class _Tp>
1046_LIBCPP_HIDE_FROM_ABI complex<_Tp>
1047polar(const _Tp& __rho, const _Tp& __theta = _Tp())
1048{
1049    if (std::__constexpr_isnan(__rho) || std::signbit(__rho))
1050        return complex<_Tp>(_Tp(NAN), _Tp(NAN));
1051    if (std::__constexpr_isnan(__theta))
1052    {
1053        if (std::__constexpr_isinf(__rho))
1054            return complex<_Tp>(__rho, __theta);
1055        return complex<_Tp>(__theta, __theta);
1056    }
1057    if (std::__constexpr_isinf(__theta))
1058    {
1059        if (std::__constexpr_isinf(__rho))
1060            return complex<_Tp>(__rho, _Tp(NAN));
1061        return complex<_Tp>(_Tp(NAN), _Tp(NAN));
1062    }
1063    _Tp __x = __rho * std::cos(__theta);
1064    if (std::__constexpr_isnan(__x))
1065        __x = 0;
1066    _Tp __y = __rho * std::sin(__theta);
1067    if (std::__constexpr_isnan(__y))
1068        __y = 0;
1069    return complex<_Tp>(__x, __y);
1070}
1071
1072// log
1073
1074template<class _Tp>
1075inline _LIBCPP_HIDE_FROM_ABI
1076complex<_Tp>
1077log(const complex<_Tp>& __x)
1078{
1079    return complex<_Tp>(std::log(std::abs(__x)), std::arg(__x));
1080}
1081
1082// log10
1083
1084template<class _Tp>
1085inline _LIBCPP_HIDE_FROM_ABI
1086complex<_Tp>
1087log10(const complex<_Tp>& __x)
1088{
1089    return std::log(__x) / std::log(_Tp(10));
1090}
1091
1092// sqrt
1093
1094template<class _Tp>
1095_LIBCPP_HIDE_FROM_ABI complex<_Tp>
1096sqrt(const complex<_Tp>& __x)
1097{
1098    if (std::__constexpr_isinf(__x.imag()))
1099        return complex<_Tp>(_Tp(INFINITY), __x.imag());
1100    if (std::__constexpr_isinf(__x.real()))
1101    {
1102        if (__x.real() > _Tp(0))
1103            return complex<_Tp>(__x.real(), std::__constexpr_isnan(__x.imag()) ? __x.imag() : std::copysign(_Tp(0), __x.imag()));
1104        return complex<_Tp>(std::__constexpr_isnan(__x.imag()) ? __x.imag() : _Tp(0), std::copysign(__x.real(), __x.imag()));
1105    }
1106    return std::polar(std::sqrt(std::abs(__x)), std::arg(__x) / _Tp(2));
1107}
1108
1109// exp
1110
1111template<class _Tp>
1112_LIBCPP_HIDE_FROM_ABI complex<_Tp>
1113exp(const complex<_Tp>& __x)
1114{
1115    _Tp __i = __x.imag();
1116    if (__i == 0) {
1117        return complex<_Tp>(std::exp(__x.real()), std::copysign(_Tp(0), __x.imag()));
1118    }
1119    if (std::__constexpr_isinf(__x.real()))
1120    {
1121        if (__x.real() < _Tp(0))
1122        {
1123            if (!std::__constexpr_isfinite(__i))
1124                __i = _Tp(1);
1125        }
1126        else if (__i == 0 || !std::__constexpr_isfinite(__i))
1127        {
1128            if (std::__constexpr_isinf(__i))
1129                __i = _Tp(NAN);
1130            return complex<_Tp>(__x.real(), __i);
1131        }
1132    }
1133    _Tp __e = std::exp(__x.real());
1134    return complex<_Tp>(__e * std::cos(__i), __e * std::sin(__i));
1135}
1136
1137// pow
1138
1139template<class _Tp>
1140inline _LIBCPP_HIDE_FROM_ABI
1141complex<_Tp>
1142pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1143{
1144    return std::exp(__y * std::log(__x));
1145}
1146
1147template<class _Tp, class _Up>
1148inline _LIBCPP_HIDE_FROM_ABI
1149complex<typename __promote<_Tp, _Up>::type>
1150pow(const complex<_Tp>& __x, const complex<_Up>& __y)
1151{
1152    typedef complex<typename __promote<_Tp, _Up>::type> result_type;
1153    return std::pow(result_type(__x), result_type(__y));
1154}
1155
1156template<class _Tp, class _Up, __enable_if_t<is_arithmetic<_Up>::value, int> = 0>
1157inline _LIBCPP_HIDE_FROM_ABI
1158complex<typename __promote<_Tp, _Up>::type>
1159pow(const complex<_Tp>& __x, const _Up& __y)
1160{
1161    typedef complex<typename __promote<_Tp, _Up>::type> result_type;
1162    return std::pow(result_type(__x), result_type(__y));
1163}
1164
1165template<class _Tp, class _Up, __enable_if_t<is_arithmetic<_Tp>::value, int> = 0>
1166inline _LIBCPP_HIDE_FROM_ABI
1167complex<typename __promote<_Tp, _Up>::type>
1168pow(const _Tp& __x, const complex<_Up>& __y)
1169{
1170    typedef complex<typename __promote<_Tp, _Up>::type> result_type;
1171    return std::pow(result_type(__x), result_type(__y));
1172}
1173
1174// __sqr, computes pow(x, 2)
1175
1176template<class _Tp>
1177inline _LIBCPP_HIDE_FROM_ABI
1178complex<_Tp>
1179__sqr(const complex<_Tp>& __x)
1180{
1181    return complex<_Tp>((__x.real() - __x.imag()) * (__x.real() + __x.imag()),
1182                        _Tp(2) * __x.real() * __x.imag());
1183}
1184
1185// asinh
1186
1187template<class _Tp>
1188_LIBCPP_HIDE_FROM_ABI complex<_Tp>
1189asinh(const complex<_Tp>& __x)
1190{
1191    const _Tp __pi(atan2(+0., -0.));
1192    if (std::__constexpr_isinf(__x.real()))
1193    {
1194        if (std::__constexpr_isnan(__x.imag()))
1195            return __x;
1196        if (std::__constexpr_isinf(__x.imag()))
1197            return complex<_Tp>(__x.real(), std::copysign(__pi * _Tp(0.25), __x.imag()));
1198        return complex<_Tp>(__x.real(), std::copysign(_Tp(0), __x.imag()));
1199    }
1200    if (std::__constexpr_isnan(__x.real()))
1201    {
1202        if (std::__constexpr_isinf(__x.imag()))
1203            return complex<_Tp>(__x.imag(), __x.real());
1204        if (__x.imag() == 0)
1205            return __x;
1206        return complex<_Tp>(__x.real(), __x.real());
1207    }
1208    if (std::__constexpr_isinf(__x.imag()))
1209        return complex<_Tp>(std::copysign(__x.imag(), __x.real()), std::copysign(__pi/_Tp(2), __x.imag()));
1210    complex<_Tp> __z = std::log(__x + std::sqrt(std::__sqr(__x) + _Tp(1)));
1211    return complex<_Tp>(std::copysign(__z.real(), __x.real()), std::copysign(__z.imag(), __x.imag()));
1212}
1213
1214// acosh
1215
1216template<class _Tp>
1217_LIBCPP_HIDE_FROM_ABI complex<_Tp>
1218acosh(const complex<_Tp>& __x)
1219{
1220    const _Tp __pi(atan2(+0., -0.));
1221    if (std::__constexpr_isinf(__x.real()))
1222    {
1223        if (std::__constexpr_isnan(__x.imag()))
1224            return complex<_Tp>(std::abs(__x.real()), __x.imag());
1225        if (std::__constexpr_isinf(__x.imag()))
1226        {
1227            if (__x.real() > 0)
1228                return complex<_Tp>(__x.real(), std::copysign(__pi * _Tp(0.25), __x.imag()));
1229            else
1230                return complex<_Tp>(-__x.real(), std::copysign(__pi * _Tp(0.75), __x.imag()));
1231        }
1232        if (__x.real() < 0)
1233            return complex<_Tp>(-__x.real(), std::copysign(__pi, __x.imag()));
1234        return complex<_Tp>(__x.real(), std::copysign(_Tp(0), __x.imag()));
1235    }
1236    if (std::__constexpr_isnan(__x.real()))
1237    {
1238        if (std::__constexpr_isinf(__x.imag()))
1239            return complex<_Tp>(std::abs(__x.imag()), __x.real());
1240        return complex<_Tp>(__x.real(), __x.real());
1241    }
1242    if (std::__constexpr_isinf(__x.imag()))
1243        return complex<_Tp>(std::abs(__x.imag()), std::copysign(__pi/_Tp(2), __x.imag()));
1244    complex<_Tp> __z = std::log(__x + std::sqrt(std::__sqr(__x) - _Tp(1)));
1245    return complex<_Tp>(std::copysign(__z.real(), _Tp(0)), std::copysign(__z.imag(), __x.imag()));
1246}
1247
1248// atanh
1249
1250template<class _Tp>
1251_LIBCPP_HIDE_FROM_ABI complex<_Tp>
1252atanh(const complex<_Tp>& __x)
1253{
1254    const _Tp __pi(atan2(+0., -0.));
1255    if (std::__constexpr_isinf(__x.imag()))
1256    {
1257        return complex<_Tp>(std::copysign(_Tp(0), __x.real()), std::copysign(__pi/_Tp(2), __x.imag()));
1258    }
1259    if (std::__constexpr_isnan(__x.imag()))
1260    {
1261        if (std::__constexpr_isinf(__x.real()) || __x.real() == 0)
1262            return complex<_Tp>(std::copysign(_Tp(0), __x.real()), __x.imag());
1263        return complex<_Tp>(__x.imag(), __x.imag());
1264    }
1265    if (std::__constexpr_isnan(__x.real()))
1266    {
1267        return complex<_Tp>(__x.real(), __x.real());
1268    }
1269    if (std::__constexpr_isinf(__x.real()))
1270    {
1271        return complex<_Tp>(std::copysign(_Tp(0), __x.real()), std::copysign(__pi/_Tp(2), __x.imag()));
1272    }
1273    if (std::abs(__x.real()) == _Tp(1) && __x.imag() == _Tp(0))
1274    {
1275        return complex<_Tp>(std::copysign(_Tp(INFINITY), __x.real()), std::copysign(_Tp(0), __x.imag()));
1276    }
1277    complex<_Tp> __z = std::log((_Tp(1) + __x) / (_Tp(1) - __x)) / _Tp(2);
1278    return complex<_Tp>(std::copysign(__z.real(), __x.real()), std::copysign(__z.imag(), __x.imag()));
1279}
1280
1281// sinh
1282
1283template<class _Tp>
1284_LIBCPP_HIDE_FROM_ABI complex<_Tp>
1285sinh(const complex<_Tp>& __x)
1286{
1287    if (std::__constexpr_isinf(__x.real()) && !std::__constexpr_isfinite(__x.imag()))
1288        return complex<_Tp>(__x.real(), _Tp(NAN));
1289    if (__x.real() == 0 && !std::__constexpr_isfinite(__x.imag()))
1290        return complex<_Tp>(__x.real(), _Tp(NAN));
1291    if (__x.imag() == 0 && !std::__constexpr_isfinite(__x.real()))
1292        return __x;
1293    return complex<_Tp>(std::sinh(__x.real()) * std::cos(__x.imag()), std::cosh(__x.real()) * std::sin(__x.imag()));
1294}
1295
1296// cosh
1297
1298template<class _Tp>
1299_LIBCPP_HIDE_FROM_ABI complex<_Tp>
1300cosh(const complex<_Tp>& __x)
1301{
1302    if (std::__constexpr_isinf(__x.real()) && !std::__constexpr_isfinite(__x.imag()))
1303        return complex<_Tp>(std::abs(__x.real()), _Tp(NAN));
1304    if (__x.real() == 0 && !std::__constexpr_isfinite(__x.imag()))
1305        return complex<_Tp>(_Tp(NAN), __x.real());
1306    if (__x.real() == 0 && __x.imag() == 0)
1307        return complex<_Tp>(_Tp(1), __x.imag());
1308    if (__x.imag() == 0 && !std::__constexpr_isfinite(__x.real()))
1309        return complex<_Tp>(std::abs(__x.real()), __x.imag());
1310    return complex<_Tp>(std::cosh(__x.real()) * std::cos(__x.imag()), std::sinh(__x.real()) * std::sin(__x.imag()));
1311}
1312
1313// tanh
1314
1315template<class _Tp>
1316_LIBCPP_HIDE_FROM_ABI complex<_Tp>
1317tanh(const complex<_Tp>& __x)
1318{
1319    if (std::__constexpr_isinf(__x.real()))
1320    {
1321        if (!std::__constexpr_isfinite(__x.imag()))
1322            return complex<_Tp>(std::copysign(_Tp(1), __x.real()), _Tp(0));
1323        return complex<_Tp>(std::copysign(_Tp(1), __x.real()), std::copysign(_Tp(0), std::sin(_Tp(2) * __x.imag())));
1324    }
1325    if (std::__constexpr_isnan(__x.real()) && __x.imag() == 0)
1326        return __x;
1327    _Tp __2r(_Tp(2) * __x.real());
1328    _Tp __2i(_Tp(2) * __x.imag());
1329    _Tp __d(std::cosh(__2r) + std::cos(__2i));
1330    _Tp __2rsh(std::sinh(__2r));
1331    if (std::__constexpr_isinf(__2rsh) && std::__constexpr_isinf(__d))
1332        return complex<_Tp>(__2rsh > _Tp(0) ? _Tp(1) : _Tp(-1),
1333                            __2i > _Tp(0) ? _Tp(0) : _Tp(-0.));
1334    return  complex<_Tp>(__2rsh/__d, std::sin(__2i)/__d);
1335}
1336
1337// asin
1338
1339template<class _Tp>
1340_LIBCPP_HIDE_FROM_ABI complex<_Tp>
1341asin(const complex<_Tp>& __x)
1342{
1343    complex<_Tp> __z = std::asinh(complex<_Tp>(-__x.imag(), __x.real()));
1344    return complex<_Tp>(__z.imag(), -__z.real());
1345}
1346
1347// acos
1348
1349template<class _Tp>
1350_LIBCPP_HIDE_FROM_ABI complex<_Tp>
1351acos(const complex<_Tp>& __x)
1352{
1353    const _Tp __pi(atan2(+0., -0.));
1354    if (std::__constexpr_isinf(__x.real()))
1355    {
1356        if (std::__constexpr_isnan(__x.imag()))
1357            return complex<_Tp>(__x.imag(), __x.real());
1358        if (std::__constexpr_isinf(__x.imag()))
1359        {
1360            if (__x.real() < _Tp(0))
1361                return complex<_Tp>(_Tp(0.75) * __pi, -__x.imag());
1362            return complex<_Tp>(_Tp(0.25) * __pi, -__x.imag());
1363        }
1364        if (__x.real() < _Tp(0))
1365            return complex<_Tp>(__pi, std::signbit(__x.imag()) ? -__x.real() : __x.real());
1366        return complex<_Tp>(_Tp(0), std::signbit(__x.imag()) ? __x.real() : -__x.real());
1367    }
1368    if (std::__constexpr_isnan(__x.real()))
1369    {
1370        if (std::__constexpr_isinf(__x.imag()))
1371            return complex<_Tp>(__x.real(), -__x.imag());
1372        return complex<_Tp>(__x.real(), __x.real());
1373    }
1374    if (std::__constexpr_isinf(__x.imag()))
1375        return complex<_Tp>(__pi/_Tp(2), -__x.imag());
1376    if (__x.real() == 0 && (__x.imag() == 0 || std::isnan(__x.imag())))
1377        return complex<_Tp>(__pi/_Tp(2), -__x.imag());
1378    complex<_Tp> __z = std::log(__x + std::sqrt(std::__sqr(__x) - _Tp(1)));
1379    if (std::signbit(__x.imag()))
1380        return complex<_Tp>(std::abs(__z.imag()), std::abs(__z.real()));
1381    return complex<_Tp>(std::abs(__z.imag()), -std::abs(__z.real()));
1382}
1383
1384// atan
1385
1386template<class _Tp>
1387_LIBCPP_HIDE_FROM_ABI complex<_Tp>
1388atan(const complex<_Tp>& __x)
1389{
1390    complex<_Tp> __z = std::atanh(complex<_Tp>(-__x.imag(), __x.real()));
1391    return complex<_Tp>(__z.imag(), -__z.real());
1392}
1393
1394// sin
1395
1396template<class _Tp>
1397_LIBCPP_HIDE_FROM_ABI complex<_Tp>
1398sin(const complex<_Tp>& __x)
1399{
1400    complex<_Tp> __z = std::sinh(complex<_Tp>(-__x.imag(), __x.real()));
1401    return complex<_Tp>(__z.imag(), -__z.real());
1402}
1403
1404// cos
1405
1406template<class _Tp>
1407inline _LIBCPP_HIDE_FROM_ABI
1408complex<_Tp>
1409cos(const complex<_Tp>& __x)
1410{
1411    return std::cosh(complex<_Tp>(-__x.imag(), __x.real()));
1412}
1413
1414// tan
1415
1416template<class _Tp>
1417_LIBCPP_HIDE_FROM_ABI complex<_Tp>
1418tan(const complex<_Tp>& __x)
1419{
1420    complex<_Tp> __z = std::tanh(complex<_Tp>(-__x.imag(), __x.real()));
1421    return complex<_Tp>(__z.imag(), -__z.real());
1422}
1423
1424#if !defined(_LIBCPP_HAS_NO_LOCALIZATION)
1425template<class _Tp, class _CharT, class _Traits>
1426_LIBCPP_HIDE_FROM_ABI basic_istream<_CharT, _Traits>&
1427operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
1428{
1429    if (__is.good())
1430    {
1431        std::ws(__is);
1432        if (__is.peek() == _CharT('('))
1433        {
1434            __is.get();
1435            _Tp __r;
1436            __is >> __r;
1437            if (!__is.fail())
1438            {
1439                std::ws(__is);
1440                _CharT __c = __is.peek();
1441                if (__c == _CharT(','))
1442                {
1443                    __is.get();
1444                    _Tp __i;
1445                    __is >> __i;
1446                    if (!__is.fail())
1447                    {
1448                        std::ws(__is);
1449                        __c = __is.peek();
1450                        if (__c == _CharT(')'))
1451                        {
1452                            __is.get();
1453                            __x = complex<_Tp>(__r, __i);
1454                        }
1455                        else
1456                            __is.setstate(__is.failbit);
1457                    }
1458                    else
1459                        __is.setstate(__is.failbit);
1460                }
1461                else if (__c == _CharT(')'))
1462                {
1463                    __is.get();
1464                    __x = complex<_Tp>(__r, _Tp(0));
1465                }
1466                else
1467                    __is.setstate(__is.failbit);
1468            }
1469            else
1470                __is.setstate(__is.failbit);
1471        }
1472        else
1473        {
1474            _Tp __r;
1475            __is >> __r;
1476            if (!__is.fail())
1477                __x = complex<_Tp>(__r, _Tp(0));
1478            else
1479                __is.setstate(__is.failbit);
1480        }
1481    }
1482    else
1483        __is.setstate(__is.failbit);
1484    return __is;
1485}
1486
1487template<class _Tp, class _CharT, class _Traits>
1488_LIBCPP_HIDE_FROM_ABI basic_ostream<_CharT, _Traits>&
1489operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
1490{
1491    basic_ostringstream<_CharT, _Traits> __s;
1492    __s.flags(__os.flags());
1493    __s.imbue(__os.getloc());
1494    __s.precision(__os.precision());
1495    __s << '(' << __x.real() << ',' << __x.imag() << ')';
1496    return __os << __s.str();
1497}
1498#endif // !_LIBCPP_HAS_NO_LOCALIZATION
1499
1500#if _LIBCPP_STD_VER >= 14
1501// Literal suffix for complex number literals [complex.literals]
1502inline namespace literals
1503{
1504  inline namespace complex_literals
1505  {
1506    _LIBCPP_HIDE_FROM_ABI inline constexpr complex<long double> operator""il(long double __im)
1507    {
1508        return { 0.0l, __im };
1509    }
1510
1511    _LIBCPP_HIDE_FROM_ABI inline constexpr complex<long double> operator""il(unsigned long long __im)
1512    {
1513        return { 0.0l, static_cast<long double>(__im) };
1514    }
1515
1516
1517    _LIBCPP_HIDE_FROM_ABI inline constexpr complex<double> operator""i(long double __im)
1518    {
1519        return { 0.0, static_cast<double>(__im) };
1520    }
1521
1522    _LIBCPP_HIDE_FROM_ABI inline constexpr complex<double> operator""i(unsigned long long __im)
1523    {
1524        return { 0.0, static_cast<double>(__im) };
1525    }
1526
1527
1528    _LIBCPP_HIDE_FROM_ABI inline constexpr complex<float> operator""if(long double __im)
1529    {
1530        return { 0.0f, static_cast<float>(__im) };
1531    }
1532
1533    _LIBCPP_HIDE_FROM_ABI inline constexpr complex<float> operator""if(unsigned long long __im)
1534    {
1535        return { 0.0f, static_cast<float>(__im) };
1536    }
1537  } // namespace complex_literals
1538} // namespace literals
1539#endif
1540
1541_LIBCPP_END_NAMESPACE_STD
1542
1543#if !defined(_LIBCPP_REMOVE_TRANSITIVE_INCLUDES) && _LIBCPP_STD_VER <= 20
1544#  include <iosfwd>
1545#  include <stdexcept>
1546#  include <type_traits>
1547#endif
1548
1549#endif // _LIBCPP_COMPLEX
1550