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complex
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// -*- C++ -*-
//===--------------------------- complex ----------------------------------===//
//
// 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);
void imag(T);
complex<T>& operator= (const T&);
complex<T>& operator+=(const T&);
complex<T>& operator-=(const T&);
complex<T>& operator*=(const T&);
complex<T>& operator/=(const T&);
complex& operator=(const complex&);
template<class X> complex<T>& operator= (const complex<X>&);
template<class X> complex<T>& operator+=(const complex<X>&);
template<class X> complex<T>& operator-=(const complex<X>&);
template<class X> complex<T>& operator*=(const complex<X>&);
template<class X> complex<T>& operator/=(const complex<X>&);
};
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 float imag() const;
void imag(float);
complex<float>& operator= (float);
complex<float>& operator+=(float);
complex<float>& operator-=(float);
complex<float>& operator*=(float);
complex<float>& operator/=(float);
complex<float>& operator=(const complex<float>&);
template<class X> complex<float>& operator= (const complex<X>&);
template<class X> complex<float>& operator+=(const complex<X>&);
template<class X> complex<float>& operator-=(const complex<X>&);
template<class X> complex<float>& operator*=(const complex<X>&);
template<class X> complex<float>& operator/=(const complex<X>&);
};
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 double imag() const;
void imag(double);
complex<double>& operator= (double);
complex<double>& operator+=(double);
complex<double>& operator-=(double);
complex<double>& operator*=(double);
complex<double>& operator/=(double);
complex<double>& operator=(const complex<double>&);
template<class X> complex<double>& operator= (const complex<X>&);
template<class X> complex<double>& operator+=(const complex<X>&);
template<class X> complex<double>& operator-=(const complex<X>&);
template<class X> complex<double>& operator*=(const complex<X>&);
template<class X> complex<double>& operator/=(const complex<X>&);
};
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 long double imag() const;
void imag(long double);
complex<long double>& operator=(const complex<long double>&);
complex<long double>& operator= (long double);
complex<long double>& operator+=(long double);
complex<long double>& operator-=(long double);
complex<long double>& operator*=(long double);
complex<long double>& operator/=(long double);
template<class X> complex<long double>& operator= (const complex<X>&);
template<class X> complex<long double>& operator+=(const complex<X>&);
template<class X> complex<long double>& operator-=(const complex<X>&);
template<class X> complex<long double>& operator*=(const complex<X>&);
template<class X> complex<long double>& operator/=(const complex<X>&);
};
// 26.3.6 operators:
template<class T> complex<T> operator+(const complex<T>&, const complex<T>&);
template<class T> complex<T> operator+(const complex<T>&, const T&);
template<class T> complex<T> operator+(const T&, const complex<T>&);
template<class T> complex<T> operator-(const complex<T>&, const complex<T>&);
template<class T> complex<T> operator-(const complex<T>&, const T&);
template<class T> complex<T> operator-(const T&, const complex<T>&);
template<class T> complex<T> operator*(const complex<T>&, const complex<T>&);
template<class T> complex<T> operator*(const complex<T>&, const T&);
template<class T> complex<T> operator*(const T&, const complex<T>&);
template<class T> complex<T> operator/(const complex<T>&, const complex<T>&);
template<class T> complex<T> operator/(const complex<T>&, const T&);
template<class T> complex<T> operator/(const T&, const complex<T>&);
template<class T> complex<T> operator+(const complex<T>&);
template<class T> complex<T> operator-(const complex<T>&);
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
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
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>&);
long double norm(long double);
double norm(double);
template<Integral T> double norm(T);
float norm(float);
template<class T> complex<T> conj(const complex<T>&);
complex<long double> conj(long double);
complex<double> conj(double);
template<Integral T> complex<double> conj(T);
complex<float> conj(float);
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>&);
template<class T, class charT, class traits>
basic_istream<charT, traits>&
operator>>(basic_istream<charT, traits>& is, complex<T>& x);
template<class T, class charT, class traits>
basic_ostream<charT, traits>&
operator<<(basic_ostream<charT, traits>& o, const complex<T>& x);
} // std
*/
#include <__config>
#include <type_traits>
#include <stdexcept>
#include <cmath>
#include <sstream>
#include <version>
#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
#pragma GCC system_header
#endif
_LIBCPP_BEGIN_NAMESPACE_STD
template<class _Tp> class _LIBCPP_TEMPLATE_VIS complex;
template<class _Tp> complex<_Tp> operator*(const complex<_Tp>& __z, const complex<_Tp>& __w);
template<class _Tp> complex<_Tp> operator/(const complex<_Tp>& __x, const complex<_Tp>& __y);
template<class _Tp>
class _LIBCPP_TEMPLATE_VIS complex
{
public:
typedef _Tp value_type;
private:
value_type __re_;
value_type __im_;
public:
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
complex(const value_type& __re = value_type(), const value_type& __im = value_type())
: __re_(__re), __im_(__im) {}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
complex(const complex<_Xp>& __c)
: __re_(__c.real()), __im_(__c.imag()) {}
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 value_type real() const {return __re_;}
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 value_type imag() const {return __im_;}
_LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
_LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
_LIBCPP_INLINE_VISIBILITY complex& operator= (const value_type& __re)
{__re_ = __re; __im_ = value_type(); return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator+=(const value_type& __re) {__re_ += __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator-=(const value_type& __re) {__re_ -= __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator*=(const value_type& __re) {__re_ *= __re; __im_ *= __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator/=(const value_type& __re) {__re_ /= __re; __im_ /= __re; return *this;}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
{
__re_ = __c.real();
__im_ = __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
{
__re_ += __c.real();
__im_ += __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
{
__re_ -= __c.real();
__im_ -= __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
{
*this = *this * complex(__c.real(), __c.imag());
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
{
*this = *this / complex(__c.real(), __c.imag());
return *this;
}
};
template<> class _LIBCPP_TEMPLATE_VIS complex<double>;
template<> class _LIBCPP_TEMPLATE_VIS complex<long double>;
template<>
class _LIBCPP_TEMPLATE_VIS complex<float>
{
float __re_;
float __im_;
public:
typedef float value_type;
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(float __re = 0.0f, float __im = 0.0f)
: __re_(__re), __im_(__im) {}
_LIBCPP_INLINE_VISIBILITY
explicit _LIBCPP_CONSTEXPR complex(const complex<double>& __c);
_LIBCPP_INLINE_VISIBILITY
explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c);
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR float real() const {return __re_;}
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR float imag() const {return __im_;}
_LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
_LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
_LIBCPP_INLINE_VISIBILITY complex& operator= (float __re)
{__re_ = __re; __im_ = value_type(); return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator+=(float __re) {__re_ += __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator-=(float __re) {__re_ -= __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator*=(float __re) {__re_ *= __re; __im_ *= __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator/=(float __re) {__re_ /= __re; __im_ /= __re; return *this;}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
{
__re_ = __c.real();
__im_ = __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
{
__re_ += __c.real();
__im_ += __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
{
__re_ -= __c.real();
__im_ -= __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
{
*this = *this * complex(__c.real(), __c.imag());
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
{
*this = *this / complex(__c.real(), __c.imag());
return *this;
}
};
template<>
class _LIBCPP_TEMPLATE_VIS complex<double>
{
double __re_;
double __im_;
public:
typedef double value_type;
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(double __re = 0.0, double __im = 0.0)
: __re_(__re), __im_(__im) {}
_LIBCPP_INLINE_VISIBILITY
_LIBCPP_CONSTEXPR complex(const complex<float>& __c);
_LIBCPP_INLINE_VISIBILITY
explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c);
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR double real() const {return __re_;}
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR double imag() const {return __im_;}
_LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
_LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
_LIBCPP_INLINE_VISIBILITY complex& operator= (double __re)
{__re_ = __re; __im_ = value_type(); return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator+=(double __re) {__re_ += __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator-=(double __re) {__re_ -= __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator*=(double __re) {__re_ *= __re; __im_ *= __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator/=(double __re) {__re_ /= __re; __im_ /= __re; return *this;}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
{
__re_ = __c.real();
__im_ = __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
{
__re_ += __c.real();
__im_ += __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
{
__re_ -= __c.real();
__im_ -= __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
{
*this = *this * complex(__c.real(), __c.imag());
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
{
*this = *this / complex(__c.real(), __c.imag());
return *this;
}
};
template<>
class _LIBCPP_TEMPLATE_VIS complex<long double>
{
long double __re_;
long double __im_;
public:
typedef long double value_type;
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(long double __re = 0.0L, long double __im = 0.0L)
: __re_(__re), __im_(__im) {}
_LIBCPP_INLINE_VISIBILITY
_LIBCPP_CONSTEXPR complex(const complex<float>& __c);
_LIBCPP_INLINE_VISIBILITY
_LIBCPP_CONSTEXPR complex(const complex<double>& __c);
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR long double real() const {return __re_;}
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR long double imag() const {return __im_;}
_LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
_LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
_LIBCPP_INLINE_VISIBILITY complex& operator= (long double __re)
{__re_ = __re; __im_ = value_type(); return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator+=(long double __re) {__re_ += __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator-=(long double __re) {__re_ -= __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator*=(long double __re) {__re_ *= __re; __im_ *= __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator/=(long double __re) {__re_ /= __re; __im_ /= __re; return *this;}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
{
__re_ = __c.real();
__im_ = __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
{
__re_ += __c.real();
__im_ += __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
{
__re_ -= __c.real();
__im_ -= __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
{
*this = *this * complex(__c.real(), __c.imag());
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
{
*this = *this / complex(__c.real(), __c.imag());
return *this;
}
};
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_INLINE_VISIBILITY
complex<_Tp>
operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
complex<_Tp> __t(__x);
__t += __y;
return __t;
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator+(const complex<_Tp>& __x, const _Tp& __y)
{
complex<_Tp> __t(__x);
__t += __y;
return __t;
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator+(const _Tp& __x, const complex<_Tp>& __y)
{
complex<_Tp> __t(__y);
__t += __x;
return __t;
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
complex<_Tp> __t(__x);
__t -= __y;
return __t;
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator-(const complex<_Tp>& __x, const _Tp& __y)
{
complex<_Tp> __t(__x);
__t -= __y;
return __t;
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator-(const _Tp& __x, const complex<_Tp>& __y)
{
complex<_Tp> __t(-__y);
__t += __x;
return __t;
}
template<class _Tp>
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 __ac = __a * __c;
_Tp __bd = __b * __d;
_Tp __ad = __a * __d;
_Tp __bc = __b * __c;
_Tp __x = __ac - __bd;
_Tp __y = __ad + __bc;
if (__libcpp_isnan_or_builtin(__x) && __libcpp_isnan_or_builtin(__y))
{
bool __recalc = false;
if (__libcpp_isinf_or_builtin(__a) || __libcpp_isinf_or_builtin(__b))
{
__a = copysign(__libcpp_isinf_or_builtin(__a) ? _Tp(1) : _Tp(0), __a);
__b = copysign(__libcpp_isinf_or_builtin(__b) ? _Tp(1) : _Tp(0), __b);
if (__libcpp_isnan_or_builtin(__c))
__c = copysign(_Tp(0), __c);
if (__libcpp_isnan_or_builtin(__d))
__d = copysign(_Tp(0), __d);
__recalc = true;
}
if (__libcpp_isinf_or_builtin(__c) || __libcpp_isinf_or_builtin(__d))
{
__c = copysign(__libcpp_isinf_or_builtin(__c) ? _Tp(1) : _Tp(0), __c);
__d = copysign(__libcpp_isinf_or_builtin(__d) ? _Tp(1) : _Tp(0), __d);
if (__libcpp_isnan_or_builtin(__a))
__a = copysign(_Tp(0), __a);
if (__libcpp_isnan_or_builtin(__b))
__b = copysign(_Tp(0), __b);
__recalc = true;
}
if (!__recalc && (__libcpp_isinf_or_builtin(__ac) || __libcpp_isinf_or_builtin(__bd) ||
__libcpp_isinf_or_builtin(__ad) || __libcpp_isinf_or_builtin(__bc)))
{
if (__libcpp_isnan_or_builtin(__a))
__a = copysign(_Tp(0), __a);
if (__libcpp_isnan_or_builtin(__b))
__b = copysign(_Tp(0), __b);
if (__libcpp_isnan_or_builtin(__c))
__c = copysign(_Tp(0), __c);
if (__libcpp_isnan_or_builtin(__d))
__d = copysign(_Tp(0), __d);
__recalc = true;
}
if (__recalc)
{
__x = _Tp(INFINITY) * (__a * __c - __b * __d);
__y = _Tp(INFINITY) * (__a * __d + __b * __c);
}
}
return complex<_Tp>(__x, __y);
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator*(const complex<_Tp>& __x, const _Tp& __y)
{
complex<_Tp> __t(__x);
__t *= __y;
return __t;
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator*(const _Tp& __x, const complex<_Tp>& __y)
{
complex<_Tp> __t(__y);
__t *= __x;
return __t;
}
template<class _Tp>
complex<_Tp>
operator/(const complex<_Tp>& __z, const complex<_Tp>& __w)
{
int __ilogbw = 0;
_Tp __a = __z.real();
_Tp __b = __z.imag();
_Tp __c = __w.real();
_Tp __d = __w.imag();
_Tp __logbw = logb(fmax(fabs(__c), fabs(__d)));
if (__libcpp_isfinite_or_builtin(__logbw))
{
__ilogbw = static_cast<int>(__logbw);
__c = scalbn(__c, -__ilogbw);
__d = scalbn(__d, -__ilogbw);
}
_Tp __denom = __c * __c + __d * __d;
_Tp __x = scalbn((__a * __c + __b * __d) / __denom, -__ilogbw);
_Tp __y = scalbn((__b * __c - __a * __d) / __denom, -__ilogbw);
if (__libcpp_isnan_or_builtin(__x) && __libcpp_isnan_or_builtin(__y))
{
if ((__denom == _Tp(0)) && (!__libcpp_isnan_or_builtin(__a) || !__libcpp_isnan_or_builtin(__b)))
{
__x = copysign(_Tp(INFINITY), __c) * __a;
__y = copysign(_Tp(INFINITY), __c) * __b;
}
else if ((__libcpp_isinf_or_builtin(__a) || __libcpp_isinf_or_builtin(__b)) && __libcpp_isfinite_or_builtin(__c) && __libcpp_isfinite_or_builtin(__d))
{
__a = copysign(__libcpp_isinf_or_builtin(__a) ? _Tp(1) : _Tp(0), __a);
__b = copysign(__libcpp_isinf_or_builtin(__b) ? _Tp(1) : _Tp(0), __b);
__x = _Tp(INFINITY) * (__a * __c + __b * __d);
__y = _Tp(INFINITY) * (__b * __c - __a * __d);
}
else if (__libcpp_isinf_or_builtin(__logbw) && __logbw > _Tp(0) && __libcpp_isfinite_or_builtin(__a) && __libcpp_isfinite_or_builtin(__b))
{
__c = copysign(__libcpp_isinf_or_builtin(__c) ? _Tp(1) : _Tp(0), __c);
__d = copysign(__libcpp_isinf_or_builtin(__d) ? _Tp(1) : _Tp(0), __d);
__x = _Tp(0) * (__a * __c + __b * __d);
__y = _Tp(0) * (__b * __c - __a * __d);
}
}
return complex<_Tp>(__x, __y);
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator/(const complex<_Tp>& __x, const _Tp& __y)
{
return complex<_Tp>(__x.real() / __y, __x.imag() / __y);
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator/(const _Tp& __x, const complex<_Tp>& __y)
{
complex<_Tp> __t(__x);
__t /= __y;
return __t;
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator+(const complex<_Tp>& __x)
{
return __x;
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator-(const complex<_Tp>& __x)
{
return complex<_Tp>(-__x.real(), -__x.imag());
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
bool
operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
return __x.real() == __y.real() && __x.imag() == __y.imag();
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
bool
operator==(const complex<_Tp>& __x, const _Tp& __y)
{
return __x.real() == __y && __x.imag() == 0;
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
bool
operator==(const _Tp& __x, const complex<_Tp>& __y)
{
return __x == __y.real() && 0 == __y.imag();
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
bool
operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
return !(__x == __y);
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
bool
operator!=(const complex<_Tp>& __x, const _Tp& __y)
{
return !(__x == __y);
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
bool
operator!=(const _Tp& __x, const complex<_Tp>& __y)
{
return !(__x == __y);
}
// 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_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
_Tp
real(const complex<_Tp>& __c)
{
return __c.real();
}
template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
typename __libcpp_complex_overload_traits<_Tp>::_ValueType
real(_Tp __re)
{
return __re;
}
// imag
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
_Tp
imag(const complex<_Tp>& __c)
{
return __c.imag();
}
template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
typename __libcpp_complex_overload_traits<_Tp>::_ValueType
imag(_Tp)
{
return 0;
}
// abs
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
_Tp
abs(const complex<_Tp>& __c)
{
return hypot(__c.real(), __c.imag());
}
// arg
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
_Tp
arg(const complex<_Tp>& __c)
{
return atan2(__c.imag(), __c.real());
}
template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
typename enable_if<
is_same<_Tp, long double>::value,
long double
>::type
arg(_Tp __re)
{
return atan2l(0.L, __re);
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
typename enable_if
<
is_integral<_Tp>::value || is_same<_Tp, double>::value,
double
>::type
arg(_Tp __re)
{
return atan2(0., __re);
}
template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
typename enable_if<
is_same<_Tp, float>::value,
float
>::type
arg(_Tp __re)
{
return atan2f(0.F, __re);
}
// norm
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
_Tp
norm(const complex<_Tp>& __c)
{
if (__libcpp_isinf_or_builtin(__c.real()))
return abs(__c.real());
if (__libcpp_isinf_or_builtin(__c.imag()))
return abs(__c.imag());
return __c.real() * __c.real() + __c.imag() * __c.imag();
}
template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
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_INLINE_VISIBILITY
complex<_Tp>
conj(const complex<_Tp>& __c)
{
return complex<_Tp>(__c.real(), -__c.imag());
}
template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
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>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
proj(const complex<_Tp>& __c)
{
std::complex<_Tp> __r = __c;
if (__libcpp_isinf_or_builtin(__c.real()) || __libcpp_isinf_or_builtin(__c.imag()))
__r = complex<_Tp>(INFINITY, copysign(_Tp(0), __c.imag()));
return __r;
}
template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
typename enable_if
<
is_floating_point<_Tp>::value,
typename __libcpp_complex_overload_traits<_Tp>::_ComplexType
>::type
proj(_Tp __re)
{
if (__libcpp_isinf_or_builtin(__re))
__re = abs(__re);
return complex<_Tp>(__re);
}
template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
typename enable_if
<
is_integral<_Tp>::value,
typename __libcpp_complex_overload_traits<_Tp>::_ComplexType
>::type
proj(_Tp __re)
{
typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType;
return _ComplexType(__re);
}
// polar
template<class _Tp>
complex<_Tp>
polar(const _Tp& __rho, const _Tp& __theta = _Tp())
{
if (__libcpp_isnan_or_builtin(__rho) || signbit(__rho))
return complex<_Tp>(_Tp(NAN), _Tp(NAN));
if (__libcpp_isnan_or_builtin(__theta))
{
if (__libcpp_isinf_or_builtin(__rho))