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// -*- C++ -*-
//===--------------------------- complex ----------------------------------===//
//
// The LLVM Compiler Infrastructure
//
// This file is dual licensed under the MIT and the University of Illinois Open
// Source Licenses. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
#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());
complex(const complex&);
template<class X> complex(const complex<X>&);
T real() const;
T imag() const;
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>&);
template<class T> bool operator==(const complex<T>&, const T&);
template<class T> bool operator==(const T&, const complex<T>&);
template<class T> bool operator!=(const complex<T>&, const complex<T>&);
template<class T> bool operator!=(const complex<T>&, const T&);
template<class T> bool operator!=(const T&, const complex<T>&);
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>&);
long double real(long double);
double real(double);
template<Integral T> double real(T);
float real(float);
template<class T> T imag(const complex<T>&);
long double imag(long double);
double imag(double);
template<Integral T> double imag(T);
float imag(float);
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& = 0);
// 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>
#if defined(_LIBCPP_NO_EXCEPTIONS)
#include <cassert>
#endif
#pragma GCC system_header
_LIBCPP_BEGIN_NAMESPACE_STD
template<class _Tp> class _LIBCPP_VISIBLE 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_VISIBLE complex
{
public:
typedef _Tp value_type;
private:
value_type __re_;
value_type __im_;
public:
_LIBCPP_INLINE_VISIBILITY
complex(const value_type& __re = value_type(), const value_type& __im = value_type())
: __re_(__re), __im_(__im) {}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY
complex(const complex<_Xp>& __c)
: __re_(__c.real()), __im_(__c.imag()) {}
_LIBCPP_INLINE_VISIBILITY value_type real() const {return __re_;}
_LIBCPP_INLINE_VISIBILITY 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; 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 * __c;
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
{
*this = *this / __c;
return *this;
}
};
template<> class _LIBCPP_VISIBLE complex<double>;
template<> class _LIBCPP_VISIBLE complex<long double>;
template<>
class _LIBCPP_VISIBLE complex<float>
{
float __re_;
float __im_;
public:
typedef float value_type;
/*constexpr*/ _LIBCPP_INLINE_VISIBILITY complex(float __re = 0.0f, float __im = 0.0f)
: __re_(__re), __im_(__im) {}
explicit /*constexpr*/ complex(const complex<double>& __c);
explicit /*constexpr*/ complex(const complex<long double>& __c);
/*constexpr*/ _LIBCPP_INLINE_VISIBILITY float real() const {return __re_;}
/*constexpr*/ _LIBCPP_INLINE_VISIBILITY 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; 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 * __c;
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
{
*this = *this / __c;
return *this;
}
};
template<>
class _LIBCPP_VISIBLE complex<double>
{
double __re_;
double __im_;
public:
typedef double value_type;
/*constexpr*/ _LIBCPP_INLINE_VISIBILITY complex(double __re = 0.0, double __im = 0.0)
: __re_(__re), __im_(__im) {}
/*constexpr*/ complex(const complex<float>& __c);
explicit /*constexpr*/ complex(const complex<long double>& __c);
/*constexpr*/ _LIBCPP_INLINE_VISIBILITY double real() const {return __re_;}
/*constexpr*/ _LIBCPP_INLINE_VISIBILITY 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; 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 * __c;
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
{
*this = *this / __c;
return *this;
}
};
template<>
class _LIBCPP_VISIBLE complex<long double>
{
long double __re_;
long double __im_;
public:
typedef long double value_type;
/*constexpr*/ _LIBCPP_INLINE_VISIBILITY complex(long double __re = 0.0L, long double __im = 0.0L)
: __re_(__re), __im_(__im) {}
/*constexpr*/ complex(const complex<float>& __c);
/*constexpr*/ complex(const complex<double>& __c);
/*constexpr*/ _LIBCPP_INLINE_VISIBILITY long double real() const {return __re_;}
/*constexpr*/ _LIBCPP_INLINE_VISIBILITY 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; 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 * __c;
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
{
*this = *this / __c;
return *this;
}
};
//constexpr
inline _LIBCPP_INLINE_VISIBILITY
complex<float>::complex(const complex<double>& __c)
: __re_(__c.real()), __im_(__c.imag()) {}
//constexpr
inline _LIBCPP_INLINE_VISIBILITY
complex<float>::complex(const complex<long double>& __c)
: __re_(__c.real()), __im_(__c.imag()) {}
//constexpr
inline _LIBCPP_INLINE_VISIBILITY
complex<double>::complex(const complex<float>& __c)
: __re_(__c.real()), __im_(__c.imag()) {}
//constexpr
inline _LIBCPP_INLINE_VISIBILITY
complex<double>::complex(const complex<long double>& __c)
: __re_(__c.real()), __im_(__c.imag()) {}
//constexpr
inline _LIBCPP_INLINE_VISIBILITY
complex<long double>::complex(const complex<float>& __c)
: __re_(__c.real()), __im_(__c.imag()) {}
//constexpr
inline _LIBCPP_INLINE_VISIBILITY
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 (isnan(__x) && isnan(__y))
{
bool __recalc = false;
if (isinf(__a) || isinf(__b))
{
__a = copysign(isinf(__a) ? _Tp(1) : _Tp(0), __a);
__b = copysign(isinf(__b) ? _Tp(1) : _Tp(0), __b);
if (isnan(__c))
__c = copysign(_Tp(0), __c);
if (isnan(__d))
__d = copysign(_Tp(0), __d);
__recalc = true;
}
if (isinf(__c) || isinf(__d))
{
__c = copysign(isinf(__c) ? _Tp(1) : _Tp(0), __c);
__d = copysign(isinf(__d) ? _Tp(1) : _Tp(0), __d);
if (isnan(__a))
__a = copysign(_Tp(0), __a);
if (isnan(__b))
__b = copysign(_Tp(0), __b);
__recalc = true;
}
if (!__recalc && (isinf(__ac) || isinf(__bd) ||
isinf(__ad) || isinf(__bc)))
{
if (isnan(__a))
__a = copysign(_Tp(0), __a);
if (isnan(__b))
__b = copysign(_Tp(0), __b);
if (isnan(__c))
__c = copysign(_Tp(0), __c);
if (isnan(__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 (isfinite(__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 (isnan(__x) && isnan(__y))
{
if ((__denom == _Tp(0)) && (!isnan(__a) || !isnan(__b)))
{
__x = copysign(_Tp(INFINITY), __c) * __a;
__y = copysign(_Tp(INFINITY), __c) * __b;
}
else if ((isinf(__a) || isinf(__b)) && isfinite(__c) && isfinite(__d))
{
__a = copysign(isinf(__a) ? _Tp(1) : _Tp(0), __a);
__b = copysign(isinf(__b) ? _Tp(1) : _Tp(0), __b);
__x = _Tp(INFINITY) * (__a * __c + __b * __d);
__y = _Tp(INFINITY) * (__b * __c - __a * __d);
}
else if (isinf(__logbw) && __logbw > _Tp(0) && isfinite(__a) && isfinite(__b))
{
__c = copysign(isinf(__c) ? _Tp(1) : _Tp(0), __c);
__d = copysign(isinf(__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
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
bool
operator==(const complex<_Tp>& __x, const _Tp& __y)
{
return __x.real() == __y && __x.imag() == 0;
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
bool
operator==(const _Tp& __x, const complex<_Tp>& __y)
{
return __x == __y.real() && 0 == __y.imag();
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
bool
operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
return !(__x == __y);
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
bool
operator!=(const complex<_Tp>& __x, const _Tp& __y)
{
return !(__x == __y);
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
bool
operator!=(const _Tp& __x, const complex<_Tp>& __y)
{
return !(__x == __y);
}
// 26.3.7 values:
// real
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
_Tp
real(const complex<_Tp>& __c)
{
return __c.real();
}
inline _LIBCPP_INLINE_VISIBILITY
long double
real(long double __re)
{
return __re;
}
inline _LIBCPP_INLINE_VISIBILITY
double
real(double __re)
{
return __re;
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
typename enable_if
<
is_integral<_Tp>::value,
double
>::type
real(_Tp __re)
{
return __re;
}
inline _LIBCPP_INLINE_VISIBILITY
float
real(float __re)
{
return __re;
}
// imag
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
_Tp
imag(const complex<_Tp>& __c)
{
return __c.imag();
}
inline _LIBCPP_INLINE_VISIBILITY
long double
imag(long double __re)
{
return 0;
}
inline _LIBCPP_INLINE_VISIBILITY
double
imag(double __re)
{
return 0;
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
typename enable_if
<
is_integral<_Tp>::value,
double
>::type
imag(_Tp __re)
{
return 0;
}
inline _LIBCPP_INLINE_VISIBILITY
float
imag(float __re)
{
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());
}
inline _LIBCPP_INLINE_VISIBILITY
long double
arg(long double __re)
{
return atan2l(0.L, __re);
}
inline _LIBCPP_INLINE_VISIBILITY
double
arg(double __re)
{
return atan2(0., __re);
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
typename enable_if
<
is_integral<_Tp>::value,
double
>::type
arg(_Tp __re)
{
return atan2(0., __re);
}
inline _LIBCPP_INLINE_VISIBILITY
float
arg(float __re)
{
return atan2f(0.F, __re);
}
// norm
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
_Tp
norm(const complex<_Tp>& __c)
{
if (isinf(__c.real()))
return abs(__c.real());
if (isinf(__c.imag()))
return abs(__c.imag());
return __c.real() * __c.real() + __c.imag() * __c.imag();
}
inline _LIBCPP_INLINE_VISIBILITY
long double
norm(long double __re)
{
return __re * __re;
}
inline _LIBCPP_INLINE_VISIBILITY
double
norm(double __re)
{
return __re * __re;
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
typename enable_if
<
is_integral<_Tp>::value,
double
>::type
norm(_Tp __re)
{
return (double)__re * __re;
}
inline _LIBCPP_INLINE_VISIBILITY
float
norm(float __re)
{
return __re * __re;
}
// conj
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
conj(const complex<_Tp>& __c)
{
return complex<_Tp>(__c.real(), -__c.imag());
}
inline _LIBCPP_INLINE_VISIBILITY
complex<long double>
conj(long double __re)
{
return complex<long double>(__re);
}
inline _LIBCPP_INLINE_VISIBILITY
complex<double>
conj(double __re)
{
return complex<double>(__re);
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
typename enable_if
<
is_integral<_Tp>::value,
complex<double>
>::type
conj(_Tp __re)
{
return complex<double>(__re);
}
inline _LIBCPP_INLINE_VISIBILITY
complex<float>
conj(float __re)
{
return complex<float>(__re);
}
// proj
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
proj(const complex<_Tp>& __c)
{
std::complex<_Tp> __r = __c;
if (isinf(__c.real()) || isinf(__c.imag()))
__r = complex<_Tp>(INFINITY, copysign(_Tp(0), __c.imag()));
return __r;
}
inline _LIBCPP_INLINE_VISIBILITY
complex<long double>
proj(long double __re)
{
if (isinf(__re))
__re = abs(__re);
return complex<long double>(__re);
}
inline _LIBCPP_INLINE_VISIBILITY
complex<double>
proj(double __re)
{
if (isinf(__re))
__re = abs(__re);
return complex<double>(__re);
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
typename enable_if
<
is_integral<_Tp>::value,
complex<double>
>::type
proj(_Tp __re)
{
return complex<double>(__re);
}
inline _LIBCPP_INLINE_VISIBILITY
complex<float>
proj(float __re)
{
if (isinf(__re))
__re = abs(__re);
return complex<float>(__re);
}
// polar
template<class _Tp>
complex<_Tp>
polar(const _Tp& __rho, const _Tp& __theta = _Tp(0))
{
if (isnan(__rho) || signbit(__rho))
return complex<_Tp>(_Tp(NAN), _Tp(NAN));
if (isnan(__theta))
{
if (isinf(__rho))
return complex<_Tp>(__rho, __theta);
return complex<_Tp>(__theta, __theta);
}
if (isinf(__theta))
{
if (isinf(__rho))
return complex<_Tp>(__rho, _Tp(NAN));
return complex<_Tp>(_Tp(NAN), _Tp(NAN));
}
_Tp __x = __rho * cos(__theta);
if (isnan(__x))
__x = 0;
_Tp __y = __rho * sin(__theta);
if (isnan(__y))
__y = 0;
return complex<_Tp>(__x, __y);
}
// log
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
log(const complex<_Tp>& __x)
{
return complex<_Tp>(log(abs(__x)), arg(__x));
}
// log10
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
log10(const complex<_Tp>& __x)
{
return log(__x) / log(_Tp(10));
}
// sqrt
template<class _Tp>
complex<_Tp>
sqrt(const complex<_Tp>& __x)
{
if (isinf(__x.imag()))
return complex<_Tp>(_Tp(INFINITY), __x.imag());
if (isinf(__x.real()))
{
if (__x.real() > _Tp(0))
return complex<_Tp>(__x.real(), isnan(__x.imag()) ? __x.imag() : copysign(_Tp(0), __x.imag()));
return complex<_Tp>(isnan(__x.imag()) ? __x.imag() : _Tp(0), copysign(__x.real(), __x.imag()));
}
return polar(sqrt(abs(__x)), arg(__x) / _Tp(2));
}
// exp
template<class _Tp>
complex<_Tp>
exp(const complex<_Tp>& __x)
{
_Tp __i = __x.imag();
if (isinf(__x.real()))
{
if (__x.real() < _Tp(0))
{
if (!isfinite(__i))
__i = _Tp(1);
}
else if (__i == 0 || !isfinite(__i))
{
if (isinf(__i))
__i = _Tp(NAN);
return complex<_Tp>(__x.real(), __i);
}
}
else if (isnan(__x.real()) && __x.imag() == 0)
return __x;
_Tp __e = exp(__x.real());
return complex<_Tp>(__e * cos(__i), __e * sin(__i));
}
// pow
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
return exp(__y * log(__x));
}
template<class _Tp, class _Up>
inline _LIBCPP_INLINE_VISIBILITY
complex<typename __promote<_Tp, _Up>::type>
pow(const complex<_Tp>& __x, const complex<_Up>& __y)
{
typedef complex<typename __promote<_Tp, _Up>::type> result_type;
return _VSTD::pow(result_type(__x), result_type(__y));
}
template<class _Tp, class _Up>
inline _LIBCPP_INLINE_VISIBILITY
typename enable_if
<
is_arithmetic<_Up>::value,
complex<typename __promote<_Tp, _Up>::type>
>::type
pow(const complex<_Tp>& __x, const _Up& __y)
{
typedef complex<typename __promote<_Tp, _Up>::type> result_type;
return _VSTD::pow(result_type(__x), result_type(__y));
}
template<class _Tp, class _Up>
inline _LIBCPP_INLINE_VISIBILITY
typename enable_if
<
is_arithmetic<_Tp>::value,
complex<typename __promote<_Tp, _Up>::type>
>::type
pow(const _Tp& __x, const complex<_Up>& __y)
{
typedef complex<typename __promote<_Tp, _Up>::type> result_type;
return _VSTD::pow(result_type(__x), result_type(__y));
}
// asinh
template<class _Tp>
complex<_Tp>
asinh(const complex<_Tp>& __x)
{
const _Tp __pi(atan2(+0., -0.));
if (isinf(__x.real()))
{
if (isnan(__x.imag()))
return __x;
if (isinf(__x.imag()))
return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag()));
return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
}
if (isnan(__x.real()))
{
if (isinf(__x.imag()))
return complex<_Tp>(__x.imag(), __x.real());
if (__x.imag() == 0)
return __x;
return complex<_Tp>(__x.real(), __x.real());
}
if (isinf(__x.imag()))
return complex<_Tp>(copysign(__x.imag(), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) + _Tp(1)));
return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag()));
}
// acosh
template<class _Tp>
complex<_Tp>
acosh(const complex<_Tp>& __x)
{
const _Tp __pi(atan2(+0., -0.));
if (isinf(__x.real()))
{
if (isnan(__x.imag()))
return complex<_Tp>(abs(__x.real()), __x.imag());
if (isinf(__x.imag()))
if (__x.real() > 0)
return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag()));
else
return complex<_Tp>(-__x.real(), copysign(__pi * _Tp(0.75), __x.imag()));
if (__x.real() < 0)
return complex<_Tp>(-__x.real(), copysign(__pi, __x.imag()));
return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
}
if (isnan(__x.real()))
{
if (isinf(__x.imag()))
return complex<_Tp>(abs(__x.imag()), __x.real());
return complex<_Tp>(__x.real(), __x.real());
}
if (isinf(__x.imag()))
return complex<_Tp>(abs(__x.imag()), copysign(__pi/_Tp(2), __x.imag()));
complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1)));
return complex<_Tp>(copysign(__z.real(), _Tp(0)), copysign(__z.imag(), __x.imag()));
}
// atanh
template<class _Tp>
complex<_Tp>
atanh(const complex<_Tp>& __x)
{
const _Tp __pi(atan2(+0., -0.));
if (isinf(__x.imag()))
{
return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
}
if (isnan(__x.imag()))
{
if (isinf(__x.real()) || __x.real() == 0)
return complex<_Tp>(copysign(_Tp(0), __x.real()), __x.imag());
return complex<_Tp>(__x.imag(), __x.imag());
}
if (isnan(__x.real()))
{
return complex<_Tp>(__x.real(), __x.real());
}
if (isinf(__x.real()))
{
return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
}
if (abs(__x.real()) == _Tp(1) && __x.imag() == _Tp(0))
{
return complex<_Tp>(copysign(_Tp(INFINITY), __x.real()), copysign(_Tp(0), __x.imag()));
}
complex<_Tp> __z = log((_Tp(1) + __x) / (_Tp(1) - __x)) / _Tp(2);
return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag()));
}
// sinh
template<class _Tp>
complex<_Tp>
sinh(const complex<_Tp>& __x)
{
if (isinf(__x.real()) && !isfinite(__x.imag()))
return complex<_Tp>(__x.real(), _Tp(NAN));
if (__x.real() == 0 && !isfinite(__x.imag()))
return complex<_Tp>(__x.real(), _Tp(NAN));
if (__x.imag() == 0 && !isfinite(__x.real()))
return __x;
return complex<_Tp>(sinh(__x.real()) * cos(__x.imag()), cosh(__x.real()) * sin(__x.imag()));
}
// cosh
template<class _Tp>
complex<_Tp>
cosh(const complex<_Tp>& __x)
{
if (isinf(__x.real()) && !isfinite(__x.imag()))
return complex<_Tp>(abs(__x.real()), _Tp(NAN));
if (__x.real() == 0 && !isfinite(__x.imag()))
return complex<_Tp>(_Tp(NAN), __x.real());
if (__x.real() == 0 && __x.imag() == 0)
return complex<_Tp>(_Tp(1), __x.imag());
if (__x.imag() == 0 && !isfinite(__x.real()))
return complex<_Tp>(abs(__x.real()), __x.imag());
return complex<_Tp>(cosh(__x.real()) * cos(__x.imag()), sinh(__x.real()) * sin(__x.imag()));
}
// tanh
template<class _Tp>
complex<_Tp>
tanh(const complex<_Tp>& __x)
{
if (isinf(__x.real()))
{
if (!isfinite(__x.imag()))
return complex<_Tp>(_Tp(1), _Tp(0));
return complex<_Tp>(_Tp(1), copysign(_Tp(0), sin(_Tp(2) * __x.imag())));
}
if (isnan(__x.real()) && __x.imag() == 0)
return __x;
_Tp __2r(_Tp(2) * __x.real());
_Tp __2i(_Tp(2) * __x.imag());
_Tp __d(cosh(__2r) + cos(__2i));
return complex<_Tp>(sinh(__2r)/__d, sin(__2i)/__d);
}
// asin
template<class _Tp>
complex<_Tp>
asin(const complex<_Tp>& __x)
{
complex<_Tp> __z = asinh(complex<_Tp>(-__x.imag(), __x.real()));
return complex<_Tp>(__z.imag(), -__z.real());
}
// acos
template<class _Tp>
complex<_Tp>
acos(const complex<_Tp>& __x)
{
const _Tp __pi(atan2(+0., -0.));
if (isinf(__x.real()))
{
if (isnan(__x.imag()))
return complex<_Tp>(__x.imag(), __x.real());
if (isinf(__x.imag()))
{
if (__x.real() < _Tp(0))
return complex<_Tp>(_Tp(0.75) * __pi, -__x.imag());
return complex<_Tp>(_Tp(0.25) * __pi, -__x.imag());
}
if (__x.real() < _Tp(0))
return complex<_Tp>(__pi, signbit(__x.imag()) ? -__x.real() : __x.real());
return complex<_Tp>(_Tp(0), signbit(__x.imag()) ? __x.real() : -__x.real());
}
if (isnan(__x.real()))
{
if (isinf(__x.imag()))
return complex<_Tp>(__x.real(), -__x.imag());
return complex<_Tp>(__x.real(), __x.real());
}
if (isinf(__x.imag()))
return complex<_Tp>(__pi/_Tp(2), -__x.imag());
if (__x.real() == 0)
return complex<_Tp>(__pi/_Tp(2), -__x.imag());
complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1)));
if (signbit(__x.imag()))
return complex<_Tp>(abs(__z.imag()), abs(__z.real()));
return complex<_Tp>(abs(__z.imag()), -abs(__z.real()));
}
// atan
template<class _Tp>
complex<_Tp>
atan(const complex<_Tp>& __x)
{
complex<_Tp> __z = atanh(complex<_Tp>(-__x.imag(), __x.real()));
return complex<_Tp>(__z.imag(), -__z.real());
}
// sin
template<class _Tp>
complex<_Tp>
sin(const complex<_Tp>& __x)
{
complex<_Tp> __z = sinh(complex<_Tp>(-__x.imag(), __x.real()));
return complex<_Tp>(__z.imag(), -__z.real());
}
// cos
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
cos(const complex<_Tp>& __x)
{
return cosh(complex<_Tp>(-__x.imag(), __x.real()));
}
// tan
template<class _Tp>
complex<_Tp>
tan(const complex<_Tp>& __x)
{
complex<_Tp> __z = tanh(complex<_Tp>(-__x.imag(), __x.real()));
return complex<_Tp>(__z.imag(), -__z.real());
}
template<class _Tp, class _CharT, class _Traits>
basic_istream<_CharT, _Traits>&
operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
{
if (__is.good())
{
ws(__is);
if (__is.peek() == _CharT('('))
{
__is.get();
_Tp __r;
__is >> __r;
if (!__is.fail())
{
ws(__is);
_CharT __c = __is.peek();
if (__c == _CharT(','))
{
__is.get();
_Tp __i;
__is >> __i;
if (!__is.fail())
{
ws(__is);
__c = __is.peek();
if (__c == _CharT(')'))
{
__is.get();
__x = complex<_Tp>(__r, __i);
}
else
__is.setstate(ios_base::failbit);
}
else
__is.setstate(ios_base::failbit);
}
else if (__c == _CharT(')'))
{
__is.get();
__x = complex<_Tp>(__r, _Tp(0));
}
else
__is.setstate(ios_base::failbit);
}
else
__is.setstate(ios_base::failbit);
}
else
{
_Tp __r;
__is >> __r;
if (!__is.fail())
__x = complex<_Tp>(__r, _Tp(0));
else
__is.setstate(ios_base::failbit);
}
}
else
__is.setstate(ios_base::failbit);
return __is;
}
template<class _Tp, class _CharT, class _Traits>
basic_ostream<_CharT, _Traits>&
operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
{
basic_ostringstream<_CharT, _Traits> __s;
__s.flags(__os.flags());
__s.imbue(__os.getloc());
__s.precision(__os.precision());
__s << '(' << __x.real() << ',' << __x.imag() << ')';
return __os << __s.str();
}
_LIBCPP_END_NAMESPACE_STD
#endif // _LIBCPP_COMPLEX