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complex
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// -*- C++ -*-
//===----------------------------------------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#ifndef _LIBCPP_COMPLEX
#define _LIBCPP_COMPLEX
/*
complex synopsis
namespace std
{
template<class T>
class complex
{
public:
typedef T value_type;
complex(const T& re = T(), const T& im = T()); // constexpr in C++14
complex(const complex&); // constexpr in C++14
template<class X> complex(const complex<X>&); // constexpr in C++14
T real() const; // constexpr in C++14
T imag() const; // constexpr in C++14
void real(T); // constexpr in C++20
void imag(T); // constexpr in C++20
complex<T>& operator= (const T&); // constexpr in C++20
complex<T>& operator+=(const T&); // constexpr in C++20
complex<T>& operator-=(const T&); // constexpr in C++20
complex<T>& operator*=(const T&); // constexpr in C++20
complex<T>& operator/=(const T&); // constexpr in C++20
complex& operator=(const complex&); // constexpr in C++20
template<class X> complex<T>& operator= (const complex<X>&); // constexpr in C++20
template<class X> complex<T>& operator+=(const complex<X>&); // constexpr in C++20
template<class X> complex<T>& operator-=(const complex<X>&); // constexpr in C++20
template<class X> complex<T>& operator*=(const complex<X>&); // constexpr in C++20
template<class X> complex<T>& operator/=(const complex<X>&); // constexpr in C++20
};
template<>
class complex<float>
{
public:
typedef float value_type;
constexpr complex(float re = 0.0f, float im = 0.0f);
explicit constexpr complex(const complex<double>&);
explicit constexpr complex(const complex<long double>&);
constexpr float real() const;
void real(float); // constexpr in C++20
constexpr float imag() const;
void imag(float); // constexpr in C++20
complex<float>& operator= (float); // constexpr in C++20
complex<float>& operator+=(float); // constexpr in C++20
complex<float>& operator-=(float); // constexpr in C++20
complex<float>& operator*=(float); // constexpr in C++20
complex<float>& operator/=(float); // constexpr in C++20
complex<float>& operator=(const complex<float>&); // constexpr in C++20
template<class X> complex<float>& operator= (const complex<X>&); // constexpr in C++20
template<class X> complex<float>& operator+=(const complex<X>&); // constexpr in C++20
template<class X> complex<float>& operator-=(const complex<X>&); // constexpr in C++20
template<class X> complex<float>& operator*=(const complex<X>&); // constexpr in C++20
template<class X> complex<float>& operator/=(const complex<X>&); // constexpr in C++20
};
template<>
class complex<double>
{
public:
typedef double value_type;
constexpr complex(double re = 0.0, double im = 0.0);
constexpr complex(const complex<float>&);
explicit constexpr complex(const complex<long double>&);
constexpr double real() const;
void real(double); // constexpr in C++20
constexpr double imag() const;
void imag(double); // constexpr in C++20
complex<double>& operator= (double); // constexpr in C++20
complex<double>& operator+=(double); // constexpr in C++20
complex<double>& operator-=(double); // constexpr in C++20
complex<double>& operator*=(double); // constexpr in C++20
complex<double>& operator/=(double); // constexpr in C++20
complex<double>& operator=(const complex<double>&); // constexpr in C++20
template<class X> complex<double>& operator= (const complex<X>&); // constexpr in C++20
template<class X> complex<double>& operator+=(const complex<X>&); // constexpr in C++20
template<class X> complex<double>& operator-=(const complex<X>&); // constexpr in C++20
template<class X> complex<double>& operator*=(const complex<X>&); // constexpr in C++20
template<class X> complex<double>& operator/=(const complex<X>&); // constexpr in C++20
};
template<>
class complex<long double>
{
public:
typedef long double value_type;
constexpr complex(long double re = 0.0L, long double im = 0.0L);
constexpr complex(const complex<float>&);
constexpr complex(const complex<double>&);
constexpr long double real() const;
void real(long double); // constexpr in C++20
constexpr long double imag() const;
void imag(long double); // constexpr in C++20
complex<long double>& operator=(const complex<long double>&); // constexpr in C++20
complex<long double>& operator= (long double); // constexpr in C++20
complex<long double>& operator+=(long double); // constexpr in C++20
complex<long double>& operator-=(long double); // constexpr in C++20
complex<long double>& operator*=(long double); // constexpr in C++20
complex<long double>& operator/=(long double); // constexpr in C++20
template<class X> complex<long double>& operator= (const complex<X>&); // constexpr in C++20
template<class X> complex<long double>& operator+=(const complex<X>&); // constexpr in C++20
template<class X> complex<long double>& operator-=(const complex<X>&); // constexpr in C++20
template<class X> complex<long double>& operator*=(const complex<X>&); // constexpr in C++20
template<class X> complex<long double>& operator/=(const complex<X>&); // constexpr in C++20
};
// 26.3.6 operators:
template<class T> complex<T> operator+(const complex<T>&, const complex<T>&); // constexpr in C++20
template<class T> complex<T> operator+(const complex<T>&, const T&); // constexpr in C++20
template<class T> complex<T> operator+(const T&, const complex<T>&); // constexpr in C++20
template<class T> complex<T> operator-(const complex<T>&, const complex<T>&); // constexpr in C++20
template<class T> complex<T> operator-(const complex<T>&, const T&); // constexpr in C++20
template<class T> complex<T> operator-(const T&, const complex<T>&); // constexpr in C++20
template<class T> complex<T> operator*(const complex<T>&, const complex<T>&); // constexpr in C++20
template<class T> complex<T> operator*(const complex<T>&, const T&); // constexpr in C++20
template<class T> complex<T> operator*(const T&, const complex<T>&); // constexpr in C++20
template<class T> complex<T> operator/(const complex<T>&, const complex<T>&); // constexpr in C++20
template<class T> complex<T> operator/(const complex<T>&, const T&); // constexpr in C++20
template<class T> complex<T> operator/(const T&, const complex<T>&); // constexpr in C++20
template<class T> complex<T> operator+(const complex<T>&); // constexpr in C++20
template<class T> complex<T> operator-(const complex<T>&); // constexpr in C++20
template<class T> bool operator==(const complex<T>&, const complex<T>&); // constexpr in C++14
template<class T> bool operator==(const complex<T>&, const T&); // constexpr in C++14
template<class T> bool operator==(const T&, const complex<T>&); // constexpr in C++14, removed in C++20
template<class T> bool operator!=(const complex<T>&, const complex<T>&); // constexpr in C++14, removed in C++20
template<class T> bool operator!=(const complex<T>&, const T&); // constexpr in C++14, removed in C++20
template<class T> bool operator!=(const T&, const complex<T>&); // constexpr in C++14, removed in C++20
template<class T, class charT, class traits>
basic_istream<charT, traits>&
operator>>(basic_istream<charT, traits>&, complex<T>&);
template<class T, class charT, class traits>
basic_ostream<charT, traits>&
operator<<(basic_ostream<charT, traits>&, const complex<T>&);
// 26.3.7 values:
template<class T> T real(const complex<T>&); // constexpr in C++14
long double real(long double); // constexpr in C++14
double real(double); // constexpr in C++14
template<Integral T> double real(T); // constexpr in C++14
float real(float); // constexpr in C++14
template<class T> T imag(const complex<T>&); // constexpr in C++14
long double imag(long double); // constexpr in C++14
double imag(double); // constexpr in C++14
template<Integral T> double imag(T); // constexpr in C++14
float imag(float); // constexpr in C++14
template<class T> T abs(const complex<T>&);
template<class T> T arg(const complex<T>&);
long double arg(long double);
double arg(double);
template<Integral T> double arg(T);
float arg(float);
template<class T> T norm(const complex<T>&); // constexpr in C++20
long double norm(long double); // constexpr in C++20
double norm(double); // constexpr in C++20
template<Integral T> double norm(T); // constexpr in C++20
float norm(float); // constexpr in C++20
template<class T> complex<T> conj(const complex<T>&); // constexpr in C++20
complex<long double> conj(long double); // constexpr in C++20
complex<double> conj(double); // constexpr in C++20
template<Integral T> complex<double> conj(T); // constexpr in C++20
complex<float> conj(float); // constexpr in C++20
template<class T> complex<T> proj(const complex<T>&);
complex<long double> proj(long double);
complex<double> proj(double);
template<Integral T> complex<double> proj(T);
complex<float> proj(float);
template<class T> complex<T> polar(const T&, const T& = T());
// 26.3.8 transcendentals:
template<class T> complex<T> acos(const complex<T>&);
template<class T> complex<T> asin(const complex<T>&);
template<class T> complex<T> atan(const complex<T>&);
template<class T> complex<T> acosh(const complex<T>&);
template<class T> complex<T> asinh(const complex<T>&);
template<class T> complex<T> atanh(const complex<T>&);
template<class T> complex<T> cos (const complex<T>&);
template<class T> complex<T> cosh (const complex<T>&);
template<class T> complex<T> exp (const complex<T>&);
template<class T> complex<T> log (const complex<T>&);
template<class T> complex<T> log10(const complex<T>&);
template<class T> complex<T> pow(const complex<T>&, const T&);
template<class T> complex<T> pow(const complex<T>&, const complex<T>&);
template<class T> complex<T> pow(const T&, const complex<T>&);
template<class T> complex<T> sin (const complex<T>&);
template<class T> complex<T> sinh (const complex<T>&);
template<class T> complex<T> sqrt (const complex<T>&);
template<class T> complex<T> tan (const complex<T>&);
template<class T> complex<T> tanh (const complex<T>&);
// [complex.tuple], tuple interface
template<class T> struct tuple_size; // Since C++26
template<size_t I, class T> struct tuple_element; // Since C++26
template<class T> struct tuple_size<complex<T>>; // Since C++26
template<size_t I, class T> struct tuple_element<I, complex<T>>; // Since C++26
template<size_t I, class T>
constexpr T& get(complex<T>&) noexcept; // Since C++26
template<size_t I, class T>
constexpr T&& get(complex<T>&&) noexcept; // Since C++26
template<size_t I, class T>
constexpr const T& get(const complex<T>&) noexcept; // Since C++26
template<size_t I, class T>
constexpr const T&& get(const complex<T>&&) noexcept; // Since C++26
// [complex.literals], complex literals
inline namespace literals {
inline namespace complex_literals {
constexpr complex<long double> operator""il(long double); // Since C++14
constexpr complex<long double> operator""il(unsigned long long); // Since C++14
constexpr complex<double> operator""i(long double); // Since C++14
constexpr complex<double> operator""i(unsigned long long); // Since C++14
constexpr complex<float> operator""if(long double); // Since C++14
constexpr complex<float> operator""if(unsigned long long); // Since C++14
}
}
} // std
*/
#if __cplusplus < 201103L && defined(_LIBCPP_USE_FROZEN_CXX03_HEADERS)
# include <__cxx03/complex>
#else
# include <__config>
# include <__fwd/complex.h>
# include <__fwd/tuple.h>
# include <__tuple/tuple_element.h>
# include <__tuple/tuple_size.h>
# include <__type_traits/conditional.h>
# include <__utility/move.h>
# include <cmath>
# include <version>
# if _LIBCPP_HAS_LOCALIZATION
# include <sstream> // for std::basic_ostringstream
# endif
# if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
# pragma GCC system_header
# endif
_LIBCPP_PUSH_MACROS
# include <__undef_macros>
_LIBCPP_BEGIN_NAMESPACE_STD
template <class _Tp>
class complex;
template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> = 0>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
operator*(const complex<_Tp>& __z, const complex<_Tp>& __w);
template <class _Tp, __enable_if_t<!is_floating_point<_Tp>::value, int> = 0>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
operator*(const complex<_Tp>& __z, const complex<_Tp>& __w);
template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> = 0>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
operator/(const complex<_Tp>& __x, const complex<_Tp>& __y);
template <class _Tp, __enable_if_t<!is_floating_point<_Tp>::value, int> = 0>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
operator/(const complex<_Tp>& __x, const complex<_Tp>& __y);
template <class _Tp>
class complex {
public:
typedef _Tp value_type;
private:
value_type __re_;
value_type __im_;
public:
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14
complex(const value_type& __re = value_type(), const value_type& __im = value_type())
: __re_(__re), __im_(__im) {}
template <class _Xp>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 complex(const complex<_Xp>& __c)
: __re_(__c.real()), __im_(__c.imag()) {}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 value_type real() const { return __re_; }
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 value_type imag() const { return __im_; }
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) { __re_ = __re; }
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) { __im_ = __im; }
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(const value_type& __re) {
__re_ = __re;
__im_ = value_type();
return *this;
}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const value_type& __re) {
__re_ += __re;
return *this;
}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const value_type& __re) {
__re_ -= __re;
return *this;
}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const value_type& __re) {
__re_ *= __re;
__im_ *= __re;
return *this;
}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const value_type& __re) {
__re_ /= __re;
__im_ /= __re;
return *this;
}
template <class _Xp>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(const complex<_Xp>& __c) {
__re_ = __c.real();
__im_ = __c.imag();
return *this;
}
template <class _Xp>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c) {
__re_ += __c.real();
__im_ += __c.imag();
return *this;
}
template <class _Xp>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c) {
__re_ -= __c.real();
__im_ -= __c.imag();
return *this;
}
template <class _Xp>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c) {
*this = *this * complex(__c.real(), __c.imag());
return *this;
}
template <class _Xp>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const complex<_Xp>& __c) {
*this = *this / complex(__c.real(), __c.imag());
return *this;
}
# if _LIBCPP_STD_VER >= 26
template <size_t _Ip, class _Xp>
friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp& get(complex<_Xp>&) noexcept;
template <size_t _Ip, class _Xp>
friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp&& get(complex<_Xp>&&) noexcept;
template <size_t _Ip, class _Xp>
friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp& get(const complex<_Xp>&) noexcept;
template <size_t _Ip, class _Xp>
friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp&& get(const complex<_Xp>&&) noexcept;
# endif
};
template <>
class complex<double>;
template <>
class complex<long double>;
struct __from_builtin_tag {};
template <class _Tp>
using __complex_t _LIBCPP_NODEBUG =
__conditional_t<is_same<_Tp, float>::value,
_Complex float,
__conditional_t<is_same<_Tp, double>::value, _Complex double, _Complex long double> >;
template <class _Tp>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR __complex_t<_Tp> __make_complex(_Tp __re, _Tp __im) {
# if __has_builtin(__builtin_complex)
return __builtin_complex(__re, __im);
# else
return __complex_t<_Tp>{__re, __im};
# endif
}
template <>
class complex<float> {
float __re_;
float __im_;
public:
typedef float value_type;
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(float __re = 0.0f, float __im = 0.0f) : __re_(__re), __im_(__im) {}
template <class _Tag, __enable_if_t<_IsSame<_Tag, __from_builtin_tag>::value, int> = 0>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR explicit complex(_Tag, _Complex float __v)
: __re_(__real__ __v), __im_(__imag__ __v) {}
_LIBCPP_HIDE_FROM_ABI explicit _LIBCPP_CONSTEXPR complex(const complex<double>& __c);
_LIBCPP_HIDE_FROM_ABI explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c);
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR float real() const { return __re_; }
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR float imag() const { return __im_; }
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) { __re_ = __re; }
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) { __im_ = __im; }
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR _Complex float __builtin() const { return std::__make_complex(__re_, __im_); }
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 void __builtin(_Complex float __f) {
__re_ = __real__ __f;
__im_ = __imag__ __f;
}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(float __re) {
__re_ = __re;
__im_ = value_type();
return *this;
}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(float __re) {
__re_ += __re;
return *this;
}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(float __re) {
__re_ -= __re;
return *this;
}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(float __re) {
__re_ *= __re;
__im_ *= __re;
return *this;
}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(float __re) {
__re_ /= __re;
__im_ /= __re;
return *this;
}
template <class _Xp>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(const complex<_Xp>& __c) {
__re_ = __c.real();
__im_ = __c.imag();
return *this;
}
template <class _Xp>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c) {
__re_ += __c.real();
__im_ += __c.imag();
return *this;
}
template <class _Xp>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c) {
__re_ -= __c.real();
__im_ -= __c.imag();
return *this;
}
template <class _Xp>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c) {
*this = *this * complex(__c.real(), __c.imag());
return *this;
}
template <class _Xp>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const complex<_Xp>& __c) {
*this = *this / complex(__c.real(), __c.imag());
return *this;
}
# if _LIBCPP_STD_VER >= 26
template <size_t _Ip, class _Xp>
friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp& get(complex<_Xp>&) noexcept;
template <size_t _Ip, class _Xp>
friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp&& get(complex<_Xp>&&) noexcept;
template <size_t _Ip, class _Xp>
friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp& get(const complex<_Xp>&) noexcept;
template <size_t _Ip, class _Xp>
friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp&& get(const complex<_Xp>&&) noexcept;
# endif
};
template <>
class complex<double> {
double __re_;
double __im_;
public:
typedef double value_type;
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(double __re = 0.0, double __im = 0.0) : __re_(__re), __im_(__im) {}
template <class _Tag, __enable_if_t<_IsSame<_Tag, __from_builtin_tag>::value, int> = 0>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR explicit complex(_Tag, _Complex double __v)
: __re_(__real__ __v), __im_(__imag__ __v) {}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(const complex<float>& __c);
_LIBCPP_HIDE_FROM_ABI explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c);
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR double real() const { return __re_; }
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR double imag() const { return __im_; }
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) { __re_ = __re; }
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) { __im_ = __im; }
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR _Complex double __builtin() const {
return std::__make_complex(__re_, __im_);
}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 void __builtin(_Complex double __f) {
__re_ = __real__ __f;
__im_ = __imag__ __f;
}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(double __re) {
__re_ = __re;
__im_ = value_type();
return *this;
}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(double __re) {
__re_ += __re;
return *this;
}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(double __re) {
__re_ -= __re;
return *this;
}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(double __re) {
__re_ *= __re;
__im_ *= __re;
return *this;
}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(double __re) {
__re_ /= __re;
__im_ /= __re;
return *this;
}
template <class _Xp>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(const complex<_Xp>& __c) {
__re_ = __c.real();
__im_ = __c.imag();
return *this;
}
template <class _Xp>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c) {
__re_ += __c.real();
__im_ += __c.imag();
return *this;
}
template <class _Xp>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c) {
__re_ -= __c.real();
__im_ -= __c.imag();
return *this;
}
template <class _Xp>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c) {
*this = *this * complex(__c.real(), __c.imag());
return *this;
}
template <class _Xp>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const complex<_Xp>& __c) {
*this = *this / complex(__c.real(), __c.imag());
return *this;
}
# if _LIBCPP_STD_VER >= 26
template <size_t _Ip, class _Xp>
friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp& get(complex<_Xp>&) noexcept;
template <size_t _Ip, class _Xp>
friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp&& get(complex<_Xp>&&) noexcept;
template <size_t _Ip, class _Xp>
friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp& get(const complex<_Xp>&) noexcept;
template <size_t _Ip, class _Xp>
friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp&& get(const complex<_Xp>&&) noexcept;
# endif
};
template <>
class complex<long double> {
long double __re_;
long double __im_;
public:
typedef long double value_type;
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(long double __re = 0.0L, long double __im = 0.0L)
: __re_(__re), __im_(__im) {}
template <class _Tag, __enable_if_t<_IsSame<_Tag, __from_builtin_tag>::value, int> = 0>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR explicit complex(_Tag, _Complex long double __v)
: __re_(__real__ __v), __im_(__imag__ __v) {}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(const complex<float>& __c);
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR complex(const complex<double>& __c);
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR long double real() const { return __re_; }
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR long double imag() const { return __im_; }
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void real(value_type __re) { __re_ = __re; }
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void imag(value_type __im) { __im_ = __im; }
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR _Complex long double __builtin() const {
return std::__make_complex(__re_, __im_);
}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 void __builtin(_Complex long double __f) {
__re_ = __real__ __f;
__im_ = __imag__ __f;
}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(long double __re) {
__re_ = __re;
__im_ = value_type();
return *this;
}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(long double __re) {
__re_ += __re;
return *this;
}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(long double __re) {
__re_ -= __re;
return *this;
}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(long double __re) {
__re_ *= __re;
__im_ *= __re;
return *this;
}
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(long double __re) {
__re_ /= __re;
__im_ /= __re;
return *this;
}
template <class _Xp>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator=(const complex<_Xp>& __c) {
__re_ = __c.real();
__im_ = __c.imag();
return *this;
}
template <class _Xp>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator+=(const complex<_Xp>& __c) {
__re_ += __c.real();
__im_ += __c.imag();
return *this;
}
template <class _Xp>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator-=(const complex<_Xp>& __c) {
__re_ -= __c.real();
__im_ -= __c.imag();
return *this;
}
template <class _Xp>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator*=(const complex<_Xp>& __c) {
*this = *this * complex(__c.real(), __c.imag());
return *this;
}
template <class _Xp>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex& operator/=(const complex<_Xp>& __c) {
*this = *this / complex(__c.real(), __c.imag());
return *this;
}
# if _LIBCPP_STD_VER >= 26
template <size_t _Ip, class _Xp>
friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp& get(complex<_Xp>&) noexcept;
template <size_t _Ip, class _Xp>
friend _LIBCPP_HIDE_FROM_ABI constexpr _Xp&& get(complex<_Xp>&&) noexcept;
template <size_t _Ip, class _Xp>
friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp& get(const complex<_Xp>&) noexcept;
template <size_t _Ip, class _Xp>
friend _LIBCPP_HIDE_FROM_ABI constexpr const _Xp&& get(const complex<_Xp>&&) noexcept;
# endif
};
inline _LIBCPP_CONSTEXPR complex<float>::complex(const complex<double>& __c) : __re_(__c.real()), __im_(__c.imag()) {}
inline _LIBCPP_CONSTEXPR complex<float>::complex(const complex<long double>& __c)
: __re_(__c.real()), __im_(__c.imag()) {}
inline _LIBCPP_CONSTEXPR complex<double>::complex(const complex<float>& __c) : __re_(__c.real()), __im_(__c.imag()) {}
inline _LIBCPP_CONSTEXPR complex<double>::complex(const complex<long double>& __c)
: __re_(__c.real()), __im_(__c.imag()) {}
inline _LIBCPP_CONSTEXPR complex<long double>::complex(const complex<float>& __c)
: __re_(__c.real()), __im_(__c.imag()) {}
inline _LIBCPP_CONSTEXPR complex<long double>::complex(const complex<double>& __c)
: __re_(__c.real()), __im_(__c.imag()) {}
// 26.3.6 operators:
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
operator+(const complex<_Tp>& __x, const complex<_Tp>& __y) {
complex<_Tp> __t(__x);
__t += __y;
return __t;
}
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
operator+(const complex<_Tp>& __x, const _Tp& __y) {
complex<_Tp> __t(__x);
__t += __y;
return __t;
}
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
operator+(const _Tp& __x, const complex<_Tp>& __y) {
complex<_Tp> __t(__y);
__t += __x;
return __t;
}
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
operator-(const complex<_Tp>& __x, const complex<_Tp>& __y) {
complex<_Tp> __t(__x);
__t -= __y;
return __t;
}
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
operator-(const complex<_Tp>& __x, const _Tp& __y) {
complex<_Tp> __t(__x);
__t -= __y;
return __t;
}
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
operator-(const _Tp& __x, const complex<_Tp>& __y) {
complex<_Tp> __t(-__y);
__t += __x;
return __t;
}
template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> >
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
operator*(const complex<_Tp>& __lhs, const complex<_Tp>& __rhs) {
return complex<_Tp>(__from_builtin_tag(), __lhs.__builtin() * __rhs.__builtin());
}
template <class _Tp, __enable_if_t<!is_floating_point<_Tp>::value, int> >
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
operator*(const complex<_Tp>& __z, const complex<_Tp>& __w) {
_Tp __a = __z.real();
_Tp __b = __z.imag();
_Tp __c = __w.real();
_Tp __d = __w.imag();
return complex<_Tp>((__a * __c) - (__b * __d), (__a * __d) + (__b * __c));
}
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
operator*(const complex<_Tp>& __x, const _Tp& __y) {
complex<_Tp> __t(__x);
__t *= __y;
return __t;
}
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
operator*(const _Tp& __x, const complex<_Tp>& __y) {
complex<_Tp> __t(__y);
__t *= __x;
return __t;
}
template <class _Tp, __enable_if_t<is_floating_point<_Tp>::value, int> >
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
operator/(const complex<_Tp>& __lhs, const complex<_Tp>& __rhs) {
return complex<_Tp>(__from_builtin_tag(), __lhs.__builtin() / __rhs.__builtin());
}
template <class _Tp, __enable_if_t<!is_floating_point<_Tp>::value, int> >
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
operator/(const complex<_Tp>& __z, const complex<_Tp>& __w) {
_Tp __a = __z.real();
_Tp __b = __z.imag();
_Tp __c = __w.real();
_Tp __d = __w.imag();
_Tp __denom = __c * __c + __d * __d;
return complex<_Tp>((__a * __c + __b * __d) / __denom, (__b * __c - __a * __d) / __denom);
}
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
operator/(const complex<_Tp>& __x, const _Tp& __y) {
return complex<_Tp>(__x.real() / __y, __x.imag() / __y);
}
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp>
operator/(const _Tp& __x, const complex<_Tp>& __y) {
complex<_Tp> __t(__x);
__t /= __y;
return __t;
}
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator+(const complex<_Tp>& __x) {
return __x;
}
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> operator-(const complex<_Tp>& __x) {
return complex<_Tp>(-__x.real(), -__x.imag());
}
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 bool
operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) {
return __x.real() == __y.real() && __x.imag() == __y.imag();
}
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 bool operator==(const complex<_Tp>& __x, const _Tp& __y) {
return __x.real() == __y && __x.imag() == 0;
}
# if _LIBCPP_STD_VER <= 17
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 bool operator==(const _Tp& __x, const complex<_Tp>& __y) {
return __x == __y.real() && 0 == __y.imag();
}
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 bool
operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) {
return !(__x == __y);
}
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 bool operator!=(const complex<_Tp>& __x, const _Tp& __y) {
return !(__x == __y);
}
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 bool operator!=(const _Tp& __x, const complex<_Tp>& __y) {
return !(__x == __y);
}
# endif
// 26.3.7 values:
template <class _Tp, bool = is_integral<_Tp>::value, bool = is_floating_point<_Tp>::value >
struct __libcpp_complex_overload_traits {};
// Integral Types
template <class _Tp>
struct __libcpp_complex_overload_traits<_Tp, true, false> {
typedef double _ValueType;
typedef complex<double> _ComplexType;
};
// Floating point types
template <class _Tp>
struct __libcpp_complex_overload_traits<_Tp, false, true> {
typedef _Tp _ValueType;
typedef complex<_Tp> _ComplexType;
};
// real
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 _Tp real(const complex<_Tp>& __c) {
return __c.real();
}
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 typename __libcpp_complex_overload_traits<_Tp>::_ValueType
real(_Tp __re) {
return __re;
}
// imag
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 _Tp imag(const complex<_Tp>& __c) {
return __c.imag();
}
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 typename __libcpp_complex_overload_traits<_Tp>::_ValueType
imag(_Tp) {
return 0;
}
// abs
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _Tp abs(const complex<_Tp>& __c) {
return std::hypot(__c.real(), __c.imag());
}
// arg
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _Tp arg(const complex<_Tp>& __c) {
return std::atan2(__c.imag(), __c.real());
}
template <class _Tp, __enable_if_t<is_same<_Tp, long double>::value, int> = 0>
inline _LIBCPP_HIDE_FROM_ABI long double arg(_Tp __re) {
return std::atan2l(0.L, __re);
}
template <class _Tp, __enable_if_t<is_integral<_Tp>::value || is_same<_Tp, double>::value, int> = 0>
inline _LIBCPP_HIDE_FROM_ABI double arg(_Tp __re) {
return std::atan2(0., __re);
}
template <class _Tp, __enable_if_t<is_same<_Tp, float>::value, int> = 0>
inline _LIBCPP_HIDE_FROM_ABI float arg(_Tp __re) {
return std::atan2f(0.F, __re);
}
// norm
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 _Tp norm(const complex<_Tp>& __c) {
if (std::__constexpr_isinf(__c.real()))
return std::abs(__c.real());
if (std::__constexpr_isinf(__c.imag()))
return std::abs(__c.imag());
return __c.real() * __c.real() + __c.imag() * __c.imag();
}
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 typename __libcpp_complex_overload_traits<_Tp>::_ValueType
norm(_Tp __re) {
typedef typename __libcpp_complex_overload_traits<_Tp>::_ValueType _ValueType;
return static_cast<_ValueType>(__re) * __re;
}
// conj
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 complex<_Tp> conj(const complex<_Tp>& __c) {
return complex<_Tp>(__c.real(), -__c.imag());
}
template <class _Tp>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 typename __libcpp_complex_overload_traits<_Tp>::_ComplexType
conj(_Tp __re) {
typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType;
return _ComplexType(__re);
}
// proj
template <class _Tp>