xref: /freebsd/contrib/llvm-project/libcxx/include/__cxx03/complex (revision 700637cbb5e582861067a11aaca4d053546871d2) 
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___CXX03_COMPLEX
11#define _LIBCPP___CXX03_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  // [complex.tuple], tuple interface
231  template<class T> struct tuple_size;                               // Since C++26
232  template<size_t I, class T> struct tuple_element;                  // Since C++26
233  template<class T> struct tuple_size<complex<T>>;                   // Since C++26
234  template<size_t I, class T> struct tuple_element<I, complex<T>>;   // Since C++26
235  template<size_t I, class T>
236    constexpr T& get(complex<T>&) noexcept;                          // Since C++26
237  template<size_t I, class T>
238    constexpr T&& get(complex<T>&&) noexcept;                        // Since C++26
239  template<size_t I, class T>
240    constexpr const T& get(const complex<T>&) noexcept;              // Since C++26
241  template<size_t I, class T>
242    constexpr const T&& get(const complex<T>&&) noexcept;            // Since C++26
243
244  // [complex.literals], complex literals
245  inline namespace literals {
246  inline namespace complex_literals {
247    constexpr complex<long double> operator""il(long double);        // Since C++14
248    constexpr complex<long double> operator""il(unsigned long long); // Since C++14
249    constexpr complex<double> operator""i(long double);              // Since C++14
250    constexpr complex<double> operator""i(unsigned long long);       // Since C++14
251    constexpr complex<float> operator""if(long double);              // Since C++14
252    constexpr complex<float> operator""if(unsigned long long);       // Since C++14
253  }
254  }
255}  // std
256
257*/
258
259#include <__cxx03/__config>
260#include <__cxx03/__fwd/complex.h>
261#include <__cxx03/__fwd/tuple.h>
262#include <__cxx03/__tuple/tuple_element.h>
263#include <__cxx03/__tuple/tuple_size.h>
264#include <__cxx03/__type_traits/conditional.h>
265#include <__cxx03/__utility/move.h>
266#include <__cxx03/cmath>
267#include <__cxx03/version>
268
269#if !defined(_LIBCPP_HAS_NO_LOCALIZATION)
270#  include <__cxx03/sstream> // for std::basic_ostringstream
271#endif
272
273#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
274#  pragma GCC system_header
275#endif
276
277_LIBCPP_PUSH_MACROS
278#include <__cxx03/__undef_macros>
279
280_LIBCPP_BEGIN_NAMESPACE_STD
281
282template <class _Tp>
283class _LIBCPP_TEMPLATE_VIS complex;
284
285template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> = 0>
286_LIBCPP_HIDE_FROM_ABI complex<_Tp> operator*(const complex<_Tp>& __z, const complex<_Tp>& __w);
287
288template <class _Tp, __enable_if_t<!is_floating_point<_Tp>::value, int> = 0>
289_LIBCPP_HIDE_FROM_ABI complex<_Tp> operator*(const complex<_Tp>& __z, const complex<_Tp>& __w);
290
291template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> = 0>
292_LIBCPP_HIDE_FROM_ABI complex<_Tp> operator/(const complex<_Tp>& __x, const complex<_Tp>& __y);
293
294template <class _Tp, __enable_if_t<!is_floating_point<_Tp>::value, int> = 0>
295_LIBCPP_HIDE_FROM_ABI complex<_Tp> operator/(const complex<_Tp>& __x, const complex<_Tp>& __y);
296
297template <class _Tp>
298class _LIBCPP_TEMPLATE_VIS complex {
299public:
300  typedef _Tp value_type;
301
302private:
303  value_type __re_;
304  value_type __im_;
305
306public:
307  _LIBCPP_HIDE_FROM_ABI complex(const value_type& __re = value_type(), const value_type& __im = value_type())
308      : __re_(__re), __im_(__im) {}
309  template <class _Xp>
310  _LIBCPP_HIDE_FROM_ABI complex(const complex<_Xp>& __c) : __re_(__c.real()), __im_(__c.imag()) {}
311
312  _LIBCPP_HIDE_FROM_ABI value_type real() const { return __re_; }
313  _LIBCPP_HIDE_FROM_ABI value_type imag() const { return __im_; }
314
315  _LIBCPP_HIDE_FROM_ABI void real(value_type __re) { __re_ = __re; }
316  _LIBCPP_HIDE_FROM_ABI void imag(value_type __im) { __im_ = __im; }
317
318  _LIBCPP_HIDE_FROM_ABI complex& operator=(const value_type& __re) {
319    __re_ = __re;
320    __im_ = value_type();
321    return *this;
322  }
323  _LIBCPP_HIDE_FROM_ABI complex& operator+=(const value_type& __re) {
324    __re_ += __re;
325    return *this;
326  }
327  _LIBCPP_HIDE_FROM_ABI complex& operator-=(const value_type& __re) {
328    __re_ -= __re;
329    return *this;
330  }
331  _LIBCPP_HIDE_FROM_ABI complex& operator*=(const value_type& __re) {
332    __re_ *= __re;
333    __im_ *= __re;
334    return *this;
335  }
336  _LIBCPP_HIDE_FROM_ABI complex& operator/=(const value_type& __re) {
337    __re_ /= __re;
338    __im_ /= __re;
339    return *this;
340  }
341
342  template <class _Xp>
343  _LIBCPP_HIDE_FROM_ABI complex& operator=(const complex<_Xp>& __c) {
344    __re_ = __c.real();
345    __im_ = __c.imag();
346    return *this;
347  }
348  template <class _Xp>
349  _LIBCPP_HIDE_FROM_ABI complex& operator+=(const complex<_Xp>& __c) {
350    __re_ += __c.real();
351    __im_ += __c.imag();
352    return *this;
353  }
354  template <class _Xp>
355  _LIBCPP_HIDE_FROM_ABI complex& operator-=(const complex<_Xp>& __c) {
356    __re_ -= __c.real();
357    __im_ -= __c.imag();
358    return *this;
359  }
360  template <class _Xp>
361  _LIBCPP_HIDE_FROM_ABI complex& operator*=(const complex<_Xp>& __c) {
362    *this = *this * complex(__c.real(), __c.imag());
363    return *this;
364  }
365  template <class _Xp>
366  _LIBCPP_HIDE_FROM_ABI complex& operator/=(const complex<_Xp>& __c) {
367    *this = *this / complex(__c.real(), __c.imag());
368    return *this;
369  }
370};
371
372template <>
373class _LIBCPP_TEMPLATE_VIS complex<double>;
374template <>
375class _LIBCPP_TEMPLATE_VIS complex<long double>;
376
377struct __from_builtin_tag {};
378
379template <class _Tp>
380using __complex_t =
381    __conditional_t<is_same<_Tp, float>::value,
382                    _Complex float,
383                    __conditional_t<is_same<_Tp, double>::value, _Complex double, _Complex long double> >;
384
385template <class _Tp>
386_LIBCPP_HIDE_FROM_ABI __complex_t<_Tp> __make_complex(_Tp __re, _Tp __im) {
387#if __has_builtin(__builtin_complex)
388  return __builtin_complex(__re, __im);
389#else
390  return __complex_t<_Tp>{__re, __im};
391#endif
392}
393
394template <>
395class _LIBCPP_TEMPLATE_VIS complex<float> {
396  float __re_;
397  float __im_;
398
399public:
400  typedef float value_type;
401
402  _LIBCPP_HIDE_FROM_ABI complex(float __re = 0.0f, float __im = 0.0f) : __re_(__re), __im_(__im) {}
403
404  template <class _Tag, __enable_if_t<_IsSame<_Tag, __from_builtin_tag>::value, int> = 0>
405  _LIBCPP_HIDE_FROM_ABI explicit complex(_Tag, _Complex float __v) : __re_(__real__ __v), __im_(__imag__ __v) {}
406
407  _LIBCPP_HIDE_FROM_ABI explicit complex(const complex<double>& __c);
408  _LIBCPP_HIDE_FROM_ABI explicit complex(const complex<long double>& __c);
409
410  _LIBCPP_HIDE_FROM_ABI float real() const { return __re_; }
411  _LIBCPP_HIDE_FROM_ABI float imag() const { return __im_; }
412
413  _LIBCPP_HIDE_FROM_ABI void real(value_type __re) { __re_ = __re; }
414  _LIBCPP_HIDE_FROM_ABI void imag(value_type __im) { __im_ = __im; }
415
416  _LIBCPP_HIDE_FROM_ABI _Complex float __builtin() const { return std::__make_complex(__re_, __im_); }
417  _LIBCPP_HIDE_FROM_ABI void __builtin(_Complex float __f) {
418    __re_ = __real__ __f;
419    __im_ = __imag__ __f;
420  }
421
422  _LIBCPP_HIDE_FROM_ABI complex& operator=(float __re) {
423    __re_ = __re;
424    __im_ = value_type();
425    return *this;
426  }
427  _LIBCPP_HIDE_FROM_ABI complex& operator+=(float __re) {
428    __re_ += __re;
429    return *this;
430  }
431  _LIBCPP_HIDE_FROM_ABI complex& operator-=(float __re) {
432    __re_ -= __re;
433    return *this;
434  }
435  _LIBCPP_HIDE_FROM_ABI complex& operator*=(float __re) {
436    __re_ *= __re;
437    __im_ *= __re;
438    return *this;
439  }
440  _LIBCPP_HIDE_FROM_ABI complex& operator/=(float __re) {
441    __re_ /= __re;
442    __im_ /= __re;
443    return *this;
444  }
445
446  template <class _Xp>
447  _LIBCPP_HIDE_FROM_ABI complex& operator=(const complex<_Xp>& __c) {
448    __re_ = __c.real();
449    __im_ = __c.imag();
450    return *this;
451  }
452  template <class _Xp>
453  _LIBCPP_HIDE_FROM_ABI complex& operator+=(const complex<_Xp>& __c) {
454    __re_ += __c.real();
455    __im_ += __c.imag();
456    return *this;
457  }
458  template <class _Xp>
459  _LIBCPP_HIDE_FROM_ABI complex& operator-=(const complex<_Xp>& __c) {
460    __re_ -= __c.real();
461    __im_ -= __c.imag();
462    return *this;
463  }
464  template <class _Xp>
465  _LIBCPP_HIDE_FROM_ABI complex& operator*=(const complex<_Xp>& __c) {
466    *this = *this * complex(__c.real(), __c.imag());
467    return *this;
468  }
469  template <class _Xp>
470  _LIBCPP_HIDE_FROM_ABI complex& operator/=(const complex<_Xp>& __c) {
471    *this = *this / complex(__c.real(), __c.imag());
472    return *this;
473  }
474};
475
476template <>
477class _LIBCPP_TEMPLATE_VIS complex<double> {
478  double __re_;
479  double __im_;
480
481public:
482  typedef double value_type;
483
484  _LIBCPP_HIDE_FROM_ABI complex(double __re = 0.0, double __im = 0.0) : __re_(__re), __im_(__im) {}
485
486  template <class _Tag, __enable_if_t<_IsSame<_Tag, __from_builtin_tag>::value, int> = 0>
487  _LIBCPP_HIDE_FROM_ABI explicit complex(_Tag, _Complex double __v) : __re_(__real__ __v), __im_(__imag__ __v) {}
488
489  _LIBCPP_HIDE_FROM_ABI complex(const complex<float>& __c);
490  _LIBCPP_HIDE_FROM_ABI explicit complex(const complex<long double>& __c);
491
492  _LIBCPP_HIDE_FROM_ABI double real() const { return __re_; }
493  _LIBCPP_HIDE_FROM_ABI double imag() const { return __im_; }
494
495  _LIBCPP_HIDE_FROM_ABI void real(value_type __re) { __re_ = __re; }
496  _LIBCPP_HIDE_FROM_ABI void imag(value_type __im) { __im_ = __im; }
497
498  _LIBCPP_HIDE_FROM_ABI _Complex double __builtin() const { return std::__make_complex(__re_, __im_); }
499
500  _LIBCPP_HIDE_FROM_ABI void __builtin(_Complex double __f) {
501    __re_ = __real__ __f;
502    __im_ = __imag__ __f;
503  }
504
505  _LIBCPP_HIDE_FROM_ABI complex& operator=(double __re) {
506    __re_ = __re;
507    __im_ = value_type();
508    return *this;
509  }
510  _LIBCPP_HIDE_FROM_ABI complex& operator+=(double __re) {
511    __re_ += __re;
512    return *this;
513  }
514  _LIBCPP_HIDE_FROM_ABI complex& operator-=(double __re) {
515    __re_ -= __re;
516    return *this;
517  }
518  _LIBCPP_HIDE_FROM_ABI complex& operator*=(double __re) {
519    __re_ *= __re;
520    __im_ *= __re;
521    return *this;
522  }
523  _LIBCPP_HIDE_FROM_ABI complex& operator/=(double __re) {
524    __re_ /= __re;
525    __im_ /= __re;
526    return *this;
527  }
528
529  template <class _Xp>
530  _LIBCPP_HIDE_FROM_ABI complex& operator=(const complex<_Xp>& __c) {
531    __re_ = __c.real();
532    __im_ = __c.imag();
533    return *this;
534  }
535  template <class _Xp>
536  _LIBCPP_HIDE_FROM_ABI complex& operator+=(const complex<_Xp>& __c) {
537    __re_ += __c.real();
538    __im_ += __c.imag();
539    return *this;
540  }
541  template <class _Xp>
542  _LIBCPP_HIDE_FROM_ABI complex& operator-=(const complex<_Xp>& __c) {
543    __re_ -= __c.real();
544    __im_ -= __c.imag();
545    return *this;
546  }
547  template <class _Xp>
548  _LIBCPP_HIDE_FROM_ABI complex& operator*=(const complex<_Xp>& __c) {
549    *this = *this * complex(__c.real(), __c.imag());
550    return *this;
551  }
552  template <class _Xp>
553  _LIBCPP_HIDE_FROM_ABI complex& operator/=(const complex<_Xp>& __c) {
554    *this = *this / complex(__c.real(), __c.imag());
555    return *this;
556  }
557};
558
559template <>
560class _LIBCPP_TEMPLATE_VIS complex<long double> {
561  long double __re_;
562  long double __im_;
563
564public:
565  typedef long double value_type;
566
567  _LIBCPP_HIDE_FROM_ABI complex(long double __re = 0.0L, long double __im = 0.0L) : __re_(__re), __im_(__im) {}
568
569  template <class _Tag, __enable_if_t<_IsSame<_Tag, __from_builtin_tag>::value, int> = 0>
570  _LIBCPP_HIDE_FROM_ABI explicit complex(_Tag, _Complex long double __v) : __re_(__real__ __v), __im_(__imag__ __v) {}
571
572  _LIBCPP_HIDE_FROM_ABI complex(const complex<float>& __c);
573  _LIBCPP_HIDE_FROM_ABI complex(const complex<double>& __c);
574
575  _LIBCPP_HIDE_FROM_ABI long double real() const { return __re_; }
576  _LIBCPP_HIDE_FROM_ABI long double imag() const { return __im_; }
577
578  _LIBCPP_HIDE_FROM_ABI void real(value_type __re) { __re_ = __re; }
579  _LIBCPP_HIDE_FROM_ABI void imag(value_type __im) { __im_ = __im; }
580
581  _LIBCPP_HIDE_FROM_ABI _Complex long double __builtin() const { return std::__make_complex(__re_, __im_); }
582
583  _LIBCPP_HIDE_FROM_ABI void __builtin(_Complex long double __f) {
584    __re_ = __real__ __f;
585    __im_ = __imag__ __f;
586  }
587
588  _LIBCPP_HIDE_FROM_ABI complex& operator=(long double __re) {
589    __re_ = __re;
590    __im_ = value_type();
591    return *this;
592  }
593  _LIBCPP_HIDE_FROM_ABI complex& operator+=(long double __re) {
594    __re_ += __re;
595    return *this;
596  }
597  _LIBCPP_HIDE_FROM_ABI complex& operator-=(long double __re) {
598    __re_ -= __re;
599    return *this;
600  }
601  _LIBCPP_HIDE_FROM_ABI complex& operator*=(long double __re) {
602    __re_ *= __re;
603    __im_ *= __re;
604    return *this;
605  }
606  _LIBCPP_HIDE_FROM_ABI complex& operator/=(long double __re) {
607    __re_ /= __re;
608    __im_ /= __re;
609    return *this;
610  }
611
612  template <class _Xp>
613  _LIBCPP_HIDE_FROM_ABI complex& operator=(const complex<_Xp>& __c) {
614    __re_ = __c.real();
615    __im_ = __c.imag();
616    return *this;
617  }
618  template <class _Xp>
619  _LIBCPP_HIDE_FROM_ABI complex& operator+=(const complex<_Xp>& __c) {
620    __re_ += __c.real();
621    __im_ += __c.imag();
622    return *this;
623  }
624  template <class _Xp>
625  _LIBCPP_HIDE_FROM_ABI complex& operator-=(const complex<_Xp>& __c) {
626    __re_ -= __c.real();
627    __im_ -= __c.imag();
628    return *this;
629  }
630  template <class _Xp>
631  _LIBCPP_HIDE_FROM_ABI complex& operator*=(const complex<_Xp>& __c) {
632    *this = *this * complex(__c.real(), __c.imag());
633    return *this;
634  }
635  template <class _Xp>
636  _LIBCPP_HIDE_FROM_ABI complex& operator/=(const complex<_Xp>& __c) {
637    *this = *this / complex(__c.real(), __c.imag());
638    return *this;
639  }
640};
641
642inline complex<float>::complex(const complex<double>& __c) : __re_(__c.real()), __im_(__c.imag()) {}
643
644inline complex<float>::complex(const complex<long double>& __c) : __re_(__c.real()), __im_(__c.imag()) {}
645
646inline complex<double>::complex(const complex<float>& __c) : __re_(__c.real()), __im_(__c.imag()) {}
647
648inline complex<double>::complex(const complex<long double>& __c) : __re_(__c.real()), __im_(__c.imag()) {}
649
650inline complex<long double>::complex(const complex<float>& __c) : __re_(__c.real()), __im_(__c.imag()) {}
651
652inline complex<long double>::complex(const complex<double>& __c) : __re_(__c.real()), __im_(__c.imag()) {}
653
654// 26.3.6 operators:
655
656template <class _Tp>
657inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> operator+(const complex<_Tp>& __x, const complex<_Tp>& __y) {
658  complex<_Tp> __t(__x);
659  __t += __y;
660  return __t;
661}
662
663template <class _Tp>
664inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> operator+(const complex<_Tp>& __x, const _Tp& __y) {
665  complex<_Tp> __t(__x);
666  __t += __y;
667  return __t;
668}
669
670template <class _Tp>
671inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> operator+(const _Tp& __x, const complex<_Tp>& __y) {
672  complex<_Tp> __t(__y);
673  __t += __x;
674  return __t;
675}
676
677template <class _Tp>
678inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> operator-(const complex<_Tp>& __x, const complex<_Tp>& __y) {
679  complex<_Tp> __t(__x);
680  __t -= __y;
681  return __t;
682}
683
684template <class _Tp>
685inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> operator-(const complex<_Tp>& __x, const _Tp& __y) {
686  complex<_Tp> __t(__x);
687  __t -= __y;
688  return __t;
689}
690
691template <class _Tp>
692inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> operator-(const _Tp& __x, const complex<_Tp>& __y) {
693  complex<_Tp> __t(-__y);
694  __t += __x;
695  return __t;
696}
697
698template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> >
699_LIBCPP_HIDE_FROM_ABI complex<_Tp> operator*(const complex<_Tp>& __lhs, const complex<_Tp>& __rhs) {
700  return complex<_Tp>(__from_builtin_tag(), __lhs.__builtin() * __rhs.__builtin());
701}
702
703template <class _Tp, __enable_if_t<!is_floating_point<_Tp>::value, int> >
704_LIBCPP_HIDE_FROM_ABI complex<_Tp> operator*(const complex<_Tp>& __z, const complex<_Tp>& __w) {
705  _Tp __a = __z.real();
706  _Tp __b = __z.imag();
707  _Tp __c = __w.real();
708  _Tp __d = __w.imag();
709
710  return complex<_Tp>((__a * __c) - (__b * __d), (__a * __d) + (__b * __c));
711}
712
713template <class _Tp>
714inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> operator*(const complex<_Tp>& __x, const _Tp& __y) {
715  complex<_Tp> __t(__x);
716  __t *= __y;
717  return __t;
718}
719
720template <class _Tp>
721inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> operator*(const _Tp& __x, const complex<_Tp>& __y) {
722  complex<_Tp> __t(__y);
723  __t *= __x;
724  return __t;
725}
726
727template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> >
728_LIBCPP_HIDE_FROM_ABI complex<_Tp> operator/(const complex<_Tp>& __lhs, const complex<_Tp>& __rhs) {
729  return complex<_Tp>(__from_builtin_tag(), __lhs.__builtin() / __rhs.__builtin());
730}
731
732template <class _Tp, __enable_if_t<!is_floating_point<_Tp>::value, int> >
733_LIBCPP_HIDE_FROM_ABI complex<_Tp> operator/(const complex<_Tp>& __z, const complex<_Tp>& __w) {
734  _Tp __a = __z.real();
735  _Tp __b = __z.imag();
736  _Tp __c = __w.real();
737  _Tp __d = __w.imag();
738
739  _Tp __denom = __c * __c + __d * __d;
740  return complex<_Tp>((__a * __c + __b * __d) / __denom, (__b * __c - __a * __d) / __denom);
741}
742
743template <class _Tp>
744inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> operator/(const complex<_Tp>& __x, const _Tp& __y) {
745  return complex<_Tp>(__x.real() / __y, __x.imag() / __y);
746}
747
748template <class _Tp>
749inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> operator/(const _Tp& __x, const complex<_Tp>& __y) {
750  complex<_Tp> __t(__x);
751  __t /= __y;
752  return __t;
753}
754
755template <class _Tp>
756inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> operator+(const complex<_Tp>& __x) {
757  return __x;
758}
759
760template <class _Tp>
761inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> operator-(const complex<_Tp>& __x) {
762  return complex<_Tp>(-__x.real(), -__x.imag());
763}
764
765template <class _Tp>
766inline _LIBCPP_HIDE_FROM_ABI bool operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) {
767  return __x.real() == __y.real() && __x.imag() == __y.imag();
768}
769
770template <class _Tp>
771inline _LIBCPP_HIDE_FROM_ABI bool operator==(const complex<_Tp>& __x, const _Tp& __y) {
772  return __x.real() == __y && __x.imag() == 0;
773}
774
775template <class _Tp>
776inline _LIBCPP_HIDE_FROM_ABI bool operator==(const _Tp& __x, const complex<_Tp>& __y) {
777  return __x == __y.real() && 0 == __y.imag();
778}
779
780template <class _Tp>
781inline _LIBCPP_HIDE_FROM_ABI bool operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) {
782  return !(__x == __y);
783}
784
785template <class _Tp>
786inline _LIBCPP_HIDE_FROM_ABI bool operator!=(const complex<_Tp>& __x, const _Tp& __y) {
787  return !(__x == __y);
788}
789
790template <class _Tp>
791inline _LIBCPP_HIDE_FROM_ABI bool operator!=(const _Tp& __x, const complex<_Tp>& __y) {
792  return !(__x == __y);
793}
794
795// 26.3.7 values:
796
797template <class _Tp, bool = is_integral<_Tp>::value, bool = is_floating_point<_Tp>::value >
798struct __libcpp_complex_overload_traits {};
799
800// Integral Types
801template <class _Tp>
802struct __libcpp_complex_overload_traits<_Tp, true, false> {
803  typedef double _ValueType;
804  typedef complex<double> _ComplexType;
805};
806
807// Floating point types
808template <class _Tp>
809struct __libcpp_complex_overload_traits<_Tp, false, true> {
810  typedef _Tp _ValueType;
811  typedef complex<_Tp> _ComplexType;
812};
813
814// real
815
816template <class _Tp>
817inline _LIBCPP_HIDE_FROM_ABI _Tp real(const complex<_Tp>& __c) {
818  return __c.real();
819}
820
821template <class _Tp>
822inline _LIBCPP_HIDE_FROM_ABI typename __libcpp_complex_overload_traits<_Tp>::_ValueType real(_Tp __re) {
823  return __re;
824}
825
826// imag
827
828template <class _Tp>
829inline _LIBCPP_HIDE_FROM_ABI _Tp imag(const complex<_Tp>& __c) {
830  return __c.imag();
831}
832
833template <class _Tp>
834inline _LIBCPP_HIDE_FROM_ABI typename __libcpp_complex_overload_traits<_Tp>::_ValueType imag(_Tp) {
835  return 0;
836}
837
838// abs
839
840template <class _Tp>
841inline _LIBCPP_HIDE_FROM_ABI _Tp abs(const complex<_Tp>& __c) {
842  return std::hypot(__c.real(), __c.imag());
843}
844
845// arg
846
847template <class _Tp>
848inline _LIBCPP_HIDE_FROM_ABI _Tp arg(const complex<_Tp>& __c) {
849  return std::atan2(__c.imag(), __c.real());
850}
851
852template <class _Tp, __enable_if_t<is_same<_Tp, long double>::value, int> = 0>
853inline _LIBCPP_HIDE_FROM_ABI long double arg(_Tp __re) {
854  return std::atan2l(0.L, __re);
855}
856
857template <class _Tp, __enable_if_t<is_integral<_Tp>::value || is_same<_Tp, double>::value, int> = 0>
858inline _LIBCPP_HIDE_FROM_ABI double arg(_Tp __re) {
859  return std::atan2(0., __re);
860}
861
862template <class _Tp, __enable_if_t<is_same<_Tp, float>::value, int> = 0>
863inline _LIBCPP_HIDE_FROM_ABI float arg(_Tp __re) {
864  return std::atan2f(0.F, __re);
865}
866
867// norm
868
869template <class _Tp>
870inline _LIBCPP_HIDE_FROM_ABI _Tp norm(const complex<_Tp>& __c) {
871  if (std::__constexpr_isinf(__c.real()))
872    return std::abs(__c.real());
873  if (std::__constexpr_isinf(__c.imag()))
874    return std::abs(__c.imag());
875  return __c.real() * __c.real() + __c.imag() * __c.imag();
876}
877
878template <class _Tp>
879inline _LIBCPP_HIDE_FROM_ABI typename __libcpp_complex_overload_traits<_Tp>::_ValueType norm(_Tp __re) {
880  typedef typename __libcpp_complex_overload_traits<_Tp>::_ValueType _ValueType;
881  return static_cast<_ValueType>(__re) * __re;
882}
883
884// conj
885
886template <class _Tp>
887inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> conj(const complex<_Tp>& __c) {
888  return complex<_Tp>(__c.real(), -__c.imag());
889}
890
891template <class _Tp>
892inline _LIBCPP_HIDE_FROM_ABI typename __libcpp_complex_overload_traits<_Tp>::_ComplexType conj(_Tp __re) {
893  typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType;
894  return _ComplexType(__re);
895}
896
897// proj
898
899template <class _Tp>
900inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> proj(const complex<_Tp>& __c) {
901  complex<_Tp> __r = __c;
902  if (std::__constexpr_isinf(__c.real()) || std::__constexpr_isinf(__c.imag()))
903    __r = complex<_Tp>(INFINITY, std::copysign(_Tp(0), __c.imag()));
904  return __r;
905}
906
907template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> = 0>
908inline _LIBCPP_HIDE_FROM_ABI typename __libcpp_complex_overload_traits<_Tp>::_ComplexType proj(_Tp __re) {
909  if (std::__constexpr_isinf(__re))
910    __re = std::abs(__re);
911  return complex<_Tp>(__re);
912}
913
914template <class _Tp, __enable_if_t<is_integral<_Tp>::value, int> = 0>
915inline _LIBCPP_HIDE_FROM_ABI typename __libcpp_complex_overload_traits<_Tp>::_ComplexType proj(_Tp __re) {
916  typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType;
917  return _ComplexType(__re);
918}
919
920// polar
921
922template <class _Tp>
923_LIBCPP_HIDE_FROM_ABI complex<_Tp> polar(const _Tp& __rho, const _Tp& __theta = _Tp()) {
924  if (std::__constexpr_isnan(__rho) || std::signbit(__rho))
925    return complex<_Tp>(_Tp(NAN), _Tp(NAN));
926  if (std::__constexpr_isnan(__theta)) {
927    if (std::__constexpr_isinf(__rho))
928      return complex<_Tp>(__rho, __theta);
929    return complex<_Tp>(__theta, __theta);
930  }
931  if (std::__constexpr_isinf(__theta)) {
932    if (std::__constexpr_isinf(__rho))
933      return complex<_Tp>(__rho, _Tp(NAN));
934    return complex<_Tp>(_Tp(NAN), _Tp(NAN));
935  }
936  _Tp __x = __rho * std::cos(__theta);
937  if (std::__constexpr_isnan(__x))
938    __x = 0;
939  _Tp __y = __rho * std::sin(__theta);
940  if (std::__constexpr_isnan(__y))
941    __y = 0;
942  return complex<_Tp>(__x, __y);
943}
944
945// log
946
947template <class _Tp>
948inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> log(const complex<_Tp>& __x) {
949  return complex<_Tp>(std::log(std::abs(__x)), std::arg(__x));
950}
951
952// log10
953
954template <class _Tp>
955inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> log10(const complex<_Tp>& __x) {
956  return std::log(__x) / std::log(_Tp(10));
957}
958
959// sqrt
960
961template <class _Tp>
962_LIBCPP_HIDE_FROM_ABI complex<_Tp> sqrt(const complex<_Tp>& __x) {
963  if (std::__constexpr_isinf(__x.imag()))
964    return complex<_Tp>(_Tp(INFINITY), __x.imag());
965  if (std::__constexpr_isinf(__x.real())) {
966    if (__x.real() > _Tp(0))
967      return complex<_Tp>(
968          __x.real(), std::__constexpr_isnan(__x.imag()) ? __x.imag() : std::copysign(_Tp(0), __x.imag()));
969    return complex<_Tp>(
970        std::__constexpr_isnan(__x.imag()) ? __x.imag() : _Tp(0), std::copysign(__x.real(), __x.imag()));
971  }
972  return std::polar(std::sqrt(std::abs(__x)), std::arg(__x) / _Tp(2));
973}
974
975// exp
976
977template <class _Tp>
978_LIBCPP_HIDE_FROM_ABI complex<_Tp> exp(const complex<_Tp>& __x) {
979  _Tp __i = __x.imag();
980  if (__i == 0) {
981    return complex<_Tp>(std::exp(__x.real()), std::copysign(_Tp(0), __x.imag()));
982  }
983  if (std::__constexpr_isinf(__x.real())) {
984    if (__x.real() < _Tp(0)) {
985      if (!std::__constexpr_isfinite(__i))
986        __i = _Tp(1);
987    } else if (__i == 0 || !std::__constexpr_isfinite(__i)) {
988      if (std::__constexpr_isinf(__i))
989        __i = _Tp(NAN);
990      return complex<_Tp>(__x.real(), __i);
991    }
992  }
993  _Tp __e = std::exp(__x.real());
994  return complex<_Tp>(__e * std::cos(__i), __e * std::sin(__i));
995}
996
997// pow
998
999template <class _Tp>
1000inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> pow(const complex<_Tp>& __x, const complex<_Tp>& __y) {
1001  return std::exp(__y * std::log(__x));
1002}
1003
1004template <class _Tp, class _Up>
1005inline _LIBCPP_HIDE_FROM_ABI complex<typename __promote<_Tp, _Up>::type>
1006pow(const complex<_Tp>& __x, const complex<_Up>& __y) {
1007  typedef complex<typename __promote<_Tp, _Up>::type> result_type;
1008  return std::pow(result_type(__x), result_type(__y));
1009}
1010
1011template <class _Tp, class _Up, __enable_if_t<is_arithmetic<_Up>::value, int> = 0>
1012inline _LIBCPP_HIDE_FROM_ABI complex<typename __promote<_Tp, _Up>::type> pow(const complex<_Tp>& __x, const _Up& __y) {
1013  typedef complex<typename __promote<_Tp, _Up>::type> result_type;
1014  return std::pow(result_type(__x), result_type(__y));
1015}
1016
1017template <class _Tp, class _Up, __enable_if_t<is_arithmetic<_Tp>::value, int> = 0>
1018inline _LIBCPP_HIDE_FROM_ABI complex<typename __promote<_Tp, _Up>::type> pow(const _Tp& __x, const complex<_Up>& __y) {
1019  typedef complex<typename __promote<_Tp, _Up>::type> result_type;
1020  return std::pow(result_type(__x), result_type(__y));
1021}
1022
1023// __sqr, computes pow(x, 2)
1024
1025template <class _Tp>
1026inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> __sqr(const complex<_Tp>& __x) {
1027  return complex<_Tp>((__x.real() - __x.imag()) * (__x.real() + __x.imag()), _Tp(2) * __x.real() * __x.imag());
1028}
1029
1030// asinh
1031
1032template <class _Tp>
1033_LIBCPP_HIDE_FROM_ABI complex<_Tp> asinh(const complex<_Tp>& __x) {
1034  const _Tp __pi(atan2(+0., -0.));
1035  if (std::__constexpr_isinf(__x.real())) {
1036    if (std::__constexpr_isnan(__x.imag()))
1037      return __x;
1038    if (std::__constexpr_isinf(__x.imag()))
1039      return complex<_Tp>(__x.real(), std::copysign(__pi * _Tp(0.25), __x.imag()));
1040    return complex<_Tp>(__x.real(), std::copysign(_Tp(0), __x.imag()));
1041  }
1042  if (std::__constexpr_isnan(__x.real())) {
1043    if (std::__constexpr_isinf(__x.imag()))
1044      return complex<_Tp>(__x.imag(), __x.real());
1045    if (__x.imag() == 0)
1046      return __x;
1047    return complex<_Tp>(__x.real(), __x.real());
1048  }
1049  if (std::__constexpr_isinf(__x.imag()))
1050    return complex<_Tp>(std::copysign(__x.imag(), __x.real()), std::copysign(__pi / _Tp(2), __x.imag()));
1051  complex<_Tp> __z = std::log(__x + std::sqrt(std::__sqr(__x) + _Tp(1)));
1052  return complex<_Tp>(std::copysign(__z.real(), __x.real()), std::copysign(__z.imag(), __x.imag()));
1053}
1054
1055// acosh
1056
1057template <class _Tp>
1058_LIBCPP_HIDE_FROM_ABI complex<_Tp> acosh(const complex<_Tp>& __x) {
1059  const _Tp __pi(atan2(+0., -0.));
1060  if (std::__constexpr_isinf(__x.real())) {
1061    if (std::__constexpr_isnan(__x.imag()))
1062      return complex<_Tp>(std::abs(__x.real()), __x.imag());
1063    if (std::__constexpr_isinf(__x.imag())) {
1064      if (__x.real() > 0)
1065        return complex<_Tp>(__x.real(), std::copysign(__pi * _Tp(0.25), __x.imag()));
1066      else
1067        return complex<_Tp>(-__x.real(), std::copysign(__pi * _Tp(0.75), __x.imag()));
1068    }
1069    if (__x.real() < 0)
1070      return complex<_Tp>(-__x.real(), std::copysign(__pi, __x.imag()));
1071    return complex<_Tp>(__x.real(), std::copysign(_Tp(0), __x.imag()));
1072  }
1073  if (std::__constexpr_isnan(__x.real())) {
1074    if (std::__constexpr_isinf(__x.imag()))
1075      return complex<_Tp>(std::abs(__x.imag()), __x.real());
1076    return complex<_Tp>(__x.real(), __x.real());
1077  }
1078  if (std::__constexpr_isinf(__x.imag()))
1079    return complex<_Tp>(std::abs(__x.imag()), std::copysign(__pi / _Tp(2), __x.imag()));
1080  complex<_Tp> __z = std::log(__x + std::sqrt(std::__sqr(__x) - _Tp(1)));
1081  return complex<_Tp>(std::copysign(__z.real(), _Tp(0)), std::copysign(__z.imag(), __x.imag()));
1082}
1083
1084// atanh
1085
1086template <class _Tp>
1087_LIBCPP_HIDE_FROM_ABI complex<_Tp> atanh(const complex<_Tp>& __x) {
1088  const _Tp __pi(atan2(+0., -0.));
1089  if (std::__constexpr_isinf(__x.imag())) {
1090    return complex<_Tp>(std::copysign(_Tp(0), __x.real()), std::copysign(__pi / _Tp(2), __x.imag()));
1091  }
1092  if (std::__constexpr_isnan(__x.imag())) {
1093    if (std::__constexpr_isinf(__x.real()) || __x.real() == 0)
1094      return complex<_Tp>(std::copysign(_Tp(0), __x.real()), __x.imag());
1095    return complex<_Tp>(__x.imag(), __x.imag());
1096  }
1097  if (std::__constexpr_isnan(__x.real())) {
1098    return complex<_Tp>(__x.real(), __x.real());
1099  }
1100  if (std::__constexpr_isinf(__x.real())) {
1101    return complex<_Tp>(std::copysign(_Tp(0), __x.real()), std::copysign(__pi / _Tp(2), __x.imag()));
1102  }
1103  if (std::abs(__x.real()) == _Tp(1) && __x.imag() == _Tp(0)) {
1104    return complex<_Tp>(std::copysign(_Tp(INFINITY), __x.real()), std::copysign(_Tp(0), __x.imag()));
1105  }
1106  complex<_Tp> __z = std::log((_Tp(1) + __x) / (_Tp(1) - __x)) / _Tp(2);
1107  return complex<_Tp>(std::copysign(__z.real(), __x.real()), std::copysign(__z.imag(), __x.imag()));
1108}
1109
1110// sinh
1111
1112template <class _Tp>
1113_LIBCPP_HIDE_FROM_ABI complex<_Tp> sinh(const complex<_Tp>& __x) {
1114  if (std::__constexpr_isinf(__x.real()) && !std::__constexpr_isfinite(__x.imag()))
1115    return complex<_Tp>(__x.real(), _Tp(NAN));
1116  if (__x.real() == 0 && !std::__constexpr_isfinite(__x.imag()))
1117    return complex<_Tp>(__x.real(), _Tp(NAN));
1118  if (__x.imag() == 0 && !std::__constexpr_isfinite(__x.real()))
1119    return __x;
1120  return complex<_Tp>(std::sinh(__x.real()) * std::cos(__x.imag()), std::cosh(__x.real()) * std::sin(__x.imag()));
1121}
1122
1123// cosh
1124
1125template <class _Tp>
1126_LIBCPP_HIDE_FROM_ABI complex<_Tp> cosh(const complex<_Tp>& __x) {
1127  if (std::__constexpr_isinf(__x.real()) && !std::__constexpr_isfinite(__x.imag()))
1128    return complex<_Tp>(std::abs(__x.real()), _Tp(NAN));
1129  if (__x.real() == 0 && !std::__constexpr_isfinite(__x.imag()))
1130    return complex<_Tp>(_Tp(NAN), __x.real());
1131  if (__x.real() == 0 && __x.imag() == 0)
1132    return complex<_Tp>(_Tp(1), __x.imag());
1133  if (__x.imag() == 0 && !std::__constexpr_isfinite(__x.real()))
1134    return complex<_Tp>(std::abs(__x.real()), __x.imag());
1135  return complex<_Tp>(std::cosh(__x.real()) * std::cos(__x.imag()), std::sinh(__x.real()) * std::sin(__x.imag()));
1136}
1137
1138// tanh
1139
1140template <class _Tp>
1141_LIBCPP_HIDE_FROM_ABI complex<_Tp> tanh(const complex<_Tp>& __x) {
1142  if (std::__constexpr_isinf(__x.real())) {
1143    if (!std::__constexpr_isfinite(__x.imag()))
1144      return complex<_Tp>(std::copysign(_Tp(1), __x.real()), _Tp(0));
1145    return complex<_Tp>(std::copysign(_Tp(1), __x.real()), std::copysign(_Tp(0), std::sin(_Tp(2) * __x.imag())));
1146  }
1147  if (std::__constexpr_isnan(__x.real()) && __x.imag() == 0)
1148    return __x;
1149  _Tp __2r(_Tp(2) * __x.real());
1150  _Tp __2i(_Tp(2) * __x.imag());
1151  _Tp __d(std::cosh(__2r) + std::cos(__2i));
1152  _Tp __2rsh(std::sinh(__2r));
1153  if (std::__constexpr_isinf(__2rsh) && std::__constexpr_isinf(__d))
1154    return complex<_Tp>(__2rsh > _Tp(0) ? _Tp(1) : _Tp(-1), __2i > _Tp(0) ? _Tp(0) : _Tp(-0.));
1155  return complex<_Tp>(__2rsh / __d, std::sin(__2i) / __d);
1156}
1157
1158// asin
1159
1160template <class _Tp>
1161_LIBCPP_HIDE_FROM_ABI complex<_Tp> asin(const complex<_Tp>& __x) {
1162  complex<_Tp> __z = std::asinh(complex<_Tp>(-__x.imag(), __x.real()));
1163  return complex<_Tp>(__z.imag(), -__z.real());
1164}
1165
1166// acos
1167
1168template <class _Tp>
1169_LIBCPP_HIDE_FROM_ABI complex<_Tp> acos(const complex<_Tp>& __x) {
1170  const _Tp __pi(atan2(+0., -0.));
1171  if (std::__constexpr_isinf(__x.real())) {
1172    if (std::__constexpr_isnan(__x.imag()))
1173      return complex<_Tp>(__x.imag(), __x.real());
1174    if (std::__constexpr_isinf(__x.imag())) {
1175      if (__x.real() < _Tp(0))
1176        return complex<_Tp>(_Tp(0.75) * __pi, -__x.imag());
1177      return complex<_Tp>(_Tp(0.25) * __pi, -__x.imag());
1178    }
1179    if (__x.real() < _Tp(0))
1180      return complex<_Tp>(__pi, std::signbit(__x.imag()) ? -__x.real() : __x.real());
1181    return complex<_Tp>(_Tp(0), std::signbit(__x.imag()) ? __x.real() : -__x.real());
1182  }
1183  if (std::__constexpr_isnan(__x.real())) {
1184    if (std::__constexpr_isinf(__x.imag()))
1185      return complex<_Tp>(__x.real(), -__x.imag());
1186    return complex<_Tp>(__x.real(), __x.real());
1187  }
1188  if (std::__constexpr_isinf(__x.imag()))
1189    return complex<_Tp>(__pi / _Tp(2), -__x.imag());
1190  if (__x.real() == 0 && (__x.imag() == 0 || std::isnan(__x.imag())))
1191    return complex<_Tp>(__pi / _Tp(2), -__x.imag());
1192  complex<_Tp> __z = std::log(__x + std::sqrt(std::__sqr(__x) - _Tp(1)));
1193  if (std::signbit(__x.imag()))
1194    return complex<_Tp>(std::abs(__z.imag()), std::abs(__z.real()));
1195  return complex<_Tp>(std::abs(__z.imag()), -std::abs(__z.real()));
1196}
1197
1198// atan
1199
1200template <class _Tp>
1201_LIBCPP_HIDE_FROM_ABI complex<_Tp> atan(const complex<_Tp>& __x) {
1202  complex<_Tp> __z = std::atanh(complex<_Tp>(-__x.imag(), __x.real()));
1203  return complex<_Tp>(__z.imag(), -__z.real());
1204}
1205
1206// sin
1207
1208template <class _Tp>
1209_LIBCPP_HIDE_FROM_ABI complex<_Tp> sin(const complex<_Tp>& __x) {
1210  complex<_Tp> __z = std::sinh(complex<_Tp>(-__x.imag(), __x.real()));
1211  return complex<_Tp>(__z.imag(), -__z.real());
1212}
1213
1214// cos
1215
1216template <class _Tp>
1217inline _LIBCPP_HIDE_FROM_ABI complex<_Tp> cos(const complex<_Tp>& __x) {
1218  return std::cosh(complex<_Tp>(-__x.imag(), __x.real()));
1219}
1220
1221// tan
1222
1223template <class _Tp>
1224_LIBCPP_HIDE_FROM_ABI complex<_Tp> tan(const complex<_Tp>& __x) {
1225  complex<_Tp> __z = std::tanh(complex<_Tp>(-__x.imag(), __x.real()));
1226  return complex<_Tp>(__z.imag(), -__z.real());
1227}
1228
1229#if !defined(_LIBCPP_HAS_NO_LOCALIZATION)
1230template <class _Tp, class _CharT, class _Traits>
1231_LIBCPP_HIDE_FROM_ABI basic_istream<_CharT, _Traits>&
1232operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x) {
1233  if (__is.good()) {
1234    std::ws(__is);
1235    if (__is.peek() == _CharT('(')) {
1236      __is.get();
1237      _Tp __r;
1238      __is >> __r;
1239      if (!__is.fail()) {
1240        std::ws(__is);
1241        _CharT __c = __is.peek();
1242        if (__c == _CharT(',')) {
1243          __is.get();
1244          _Tp __i;
1245          __is >> __i;
1246          if (!__is.fail()) {
1247            std::ws(__is);
1248            __c = __is.peek();
1249            if (__c == _CharT(')')) {
1250              __is.get();
1251              __x = complex<_Tp>(__r, __i);
1252            } else
1253              __is.setstate(__is.failbit);
1254          } else
1255            __is.setstate(__is.failbit);
1256        } else if (__c == _CharT(')')) {
1257          __is.get();
1258          __x = complex<_Tp>(__r, _Tp(0));
1259        } else
1260          __is.setstate(__is.failbit);
1261      } else
1262        __is.setstate(__is.failbit);
1263    } else {
1264      _Tp __r;
1265      __is >> __r;
1266      if (!__is.fail())
1267        __x = complex<_Tp>(__r, _Tp(0));
1268      else
1269        __is.setstate(__is.failbit);
1270    }
1271  } else
1272    __is.setstate(__is.failbit);
1273  return __is;
1274}
1275
1276template <class _Tp, class _CharT, class _Traits>
1277_LIBCPP_HIDE_FROM_ABI basic_ostream<_CharT, _Traits>&
1278operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x) {
1279  basic_ostringstream<_CharT, _Traits> __s;
1280  __s.flags(__os.flags());
1281  __s.imbue(__os.getloc());
1282  __s.precision(__os.precision());
1283  __s << '(' << __x.real() << ',' << __x.imag() << ')';
1284  return __os << __s.str();
1285}
1286#endif // !_LIBCPP_HAS_NO_LOCALIZATION
1287
1288_LIBCPP_END_NAMESPACE_STD
1289
1290_LIBCPP_POP_MACROS
1291
1292#if !defined(_LIBCPP_REMOVE_TRANSITIVE_INCLUDES)
1293#  include <__cxx03/iosfwd>
1294#  include <__cxx03/stdexcept>
1295#  include <__cxx03/type_traits>
1296#endif
1297
1298#endif // _LIBCPP___CXX03_COMPLEX
1299