windows-xp/Source/XPSP1/NT/base/crts/crtw32/stdhpp/xcomplex

// xcomplex internal header
#pragma once
#ifndef _XCOMPLEX_
#define _XCOMPLEX_

		// TEMPLATE FUNCTION imag
_TMPLT(_Ty) inline
	_Ty __cdecl imag(const _CMPLX(_Ty)& _Left)
	{	// return imaginary component
	return (_Left.imag());
	}

		// TEMPLATE FUNCTION real
_TMPLT(_Ty) inline
	_Ty __cdecl real(const _CMPLX(_Ty)& _Left)
	{	// return real component
	return (_Left.real());
	}

		// TEMPLATE FUNCTION _Fabs
_TMPLT(_Ty) inline
	_Ty __cdecl _Fabs(const _CMPLX(_Ty)& _Left, int *_Pexp)
	{	// return magnitude and scale factor
	*_Pexp = 0;
	_Ty _Av = real(_Left);
	_Ty _Bv = imag(_Left);

	if (_CTR(_Ty)::_Isinf(_Av) || _CTR(_Ty)::_Isinf(_Bv))
		return (_CTR(_Ty)::_Infv(_Bv));	// at least one component is INF
	else if (_CTR(_Ty)::_Isnan(_Av))
		return (_Av);	//	real component is NaN
	else if (_CTR(_Ty)::_Isnan(_Bv))
		return (_Bv);	// imaginary component is NaN
	else
		{	// neither component is NaN or INF
		if (_Av < 0)
			_Av = -_Av;
		if (_Bv < 0)
			_Bv = -_Bv;
		if (_Av < _Bv)
			{	// ensure that |_Bv| <= |_Av|
			_Ty _Tmp = _Av;
			_Av = _Bv;
			_Bv = _Tmp;
			}

		if (_Av == 0)
			return (_Av);	// |0| == 0
		if (1 <= _Av)
			*_Pexp = 2, _Av = _Av * (_Ty)0.25, _Bv = _Bv * (_Ty)0.25;
		else
			*_Pexp = -2, _Av = _Av * 4, _Bv = _Bv * 4;

		_Ty _Tmp = _Av - _Bv;
		if (_Tmp == _Av)
			return (_Av);	// _Bv unimportant
		else if (_Bv < _Tmp)
			{	// use simple approximation
			const _Ty _Qv = _Av / _Bv;
			return (_Av + _Bv / (_Qv + _CTR(_Ty)::sqrt(_Qv * _Qv + 1)));
			}
		else
			{	// use 1 1/2 precision to preserve bits
			static const _Ty _Root2 =
				(_Ty)1.4142135623730950488016887242096981L;
			static const _Ty _Oneplusroot2high = (_Ty)2.4142L;
			static const _Ty _Oneplusroot2low =
				(_Ty)0.0000135623730950488016887242096980785697L;

			const _Ty _Qv = _Tmp / _Bv;
			const _Ty _Rv = (_Qv + 2) * _Qv;
			const _Ty _Sv = _Rv / (_Root2 + _CTR(_Ty)::sqrt(_Rv + 2))
				+ _Oneplusroot2low + _Qv + _Oneplusroot2high;
			return (_Av + _Bv / _Sv);
			}
		}
	}

		// TEMPLATE FUNCTION operator+
_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl operator+(const _CMPLX(_Ty)& _Left,
		const _CMPLX(_Ty)& _Right)
	{	// add complex to complex
	_CMPLX(_Ty) _Tmp(_Left);
	return (_Tmp += _Right);
	}

_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl operator+(const _CMPLX(_Ty)& _Left,
		const _Ty& _Right)
	{	// add real to complex
	_CMPLX(_Ty) _Tmp(_Left);
	_Tmp.real(_Tmp.real() + _Right);
	return (_Tmp);
	}

_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl operator+(const _Ty& _Left,
		const _CMPLX(_Ty)& _Right)
	{	// add complex to real
	_CMPLX(_Ty) _Tmp(_Left);
	return (_Tmp += _Right);
	}

		// TEMPLATE FUNCTION operator-
_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl operator-(const _CMPLX(_Ty)& _Left,
		const _CMPLX(_Ty)& _Right)
	{	// subtract complex from complex
	_CMPLX(_Ty) _Tmp(_Left);
	return (_Tmp -= _Right);
	}

_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl operator-(const _CMPLX(_Ty)& _Left,
		const _Ty& _Right)
	{	// subtract real from complex
	_CMPLX(_Ty) _Tmp(_Left);
	_Tmp.real(_Tmp.real() - _Right);
	return (_Tmp);
	}

_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl operator-(const _Ty& _Left,
		const _CMPLX(_Ty)& _Right)
	{	// subtract complex from real
	_CMPLX(_Ty) _Tmp(_Left);
	return (_Tmp -= _Right);
	}

		// TEMPLATE FUNCTION operator*
_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl operator*(const _CMPLX(_Ty)& _Left,
		const _CMPLX(_Ty)& _Right)
	{	// multiply complex by complex
	_CMPLX(_Ty) _Tmp(_Left);
	return (_Tmp *= _Right);
	}

_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl operator*(const _CMPLX(_Ty)& _Left,
		const _Ty& _Right)
	{	// multiply complex by real
	_CMPLX(_Ty) _Tmp(_Left);
	_Tmp.real(_Tmp.real() * _Right);
	_Tmp.imag(_Tmp.imag() * _Right);
	return (_Tmp);
	}

_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl operator*(const _Ty& _Left,
		const _CMPLX(_Ty)& _Right)
	{	// multiply real by complex
	_CMPLX(_Ty) _Tmp(_Left);
	return (_Tmp *= _Right);
	}

		// TEMPLATE FUNCTION operator/
_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl operator/(const _CMPLX(_Ty)& _Left,
		const _CMPLX(_Ty)& _Right)
	{	// divide complex by complex
	_CMPLX(_Ty) _Tmp(_Left);
	return (_Tmp /= _Right);
	}

_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl operator/(const _CMPLX(_Ty)& _Left,
		const _Ty& _Right)
	{	// divide complex by real
	_CMPLX(_Ty) _Tmp(_Left);
	_Tmp.real(_Tmp.real() / _Right);
	_Tmp.imag(_Tmp.imag() / _Right);
	return (_Tmp);
	}

_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl operator/(const _Ty& _Left,
		const _CMPLX(_Ty)& _Right)
	{	// divide real by complex
	_CMPLX(_Ty) _Tmp(_Left);
	return (_Tmp /= _Right);
	}

		// TEMPLATE FUNCTION UNARY operator+
_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl operator+(const _CMPLX(_Ty)& _Left)
	{	// return +complex
	return (_CMPLX(_Ty)(_Left));
	}

		// TEMPLATE FUNCTION UNARY operator-
_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl operator-(const _CMPLX(_Ty)& _Left)
	{	// return -complex
	return (_CMPLX(_Ty)(-real(_Left), -imag(_Left)));
	}

		// TEMPLATE FUNCTION operator==
_TMPLT(_Ty) inline
	bool __cdecl operator==(const _CMPLX(_Ty)& _Left,
		const _CMPLX(_Ty)& _Right)
	{	// test complex equal to complex
	return (real(_Left) == real(_Right) && imag(_Left) == imag(_Right));
	}

_TMPLT(_Ty) inline
	bool __cdecl operator==(const _CMPLX(_Ty)& _Left,
		const _Ty& _Right)
	{	// test real equal to complex
	return (real(_Left) == _Right && imag(_Left) == 0);
	}

_TMPLT(_Ty) inline
	bool __cdecl operator==(const _Ty& _Left,
		const _CMPLX(_Ty)& _Right)
	{	// test complex equal to real
	return (_Left == real(_Right) && 0 == imag(_Right));
	}

		// TEMPLATE FUNCTION operator!=
_TMPLT(_Ty) inline
	bool __cdecl operator!=(const _CMPLX(_Ty)& _Left,
		const _CMPLX(_Ty)& _Right)
	{	// test complex not equal to complex
	return (!(_Left == _Right));
	}

_TMPLT(_Ty) inline
	bool __cdecl operator!=(const _CMPLX(_Ty)& _Left,
		const _Ty& _Right)
	{	// test real not equal to complex
	return (!(_Left == _Right));
	}

_TMPLT(_Ty) inline
	bool __cdecl operator!=(const _Ty& _Left,
		const _CMPLX(_Ty)& _Right)
	{	// test complex not equal to real
	return (!(_Left == _Right));
	}

		// TEMPLATE FUNCTION abs
_TMPLT(_Ty) inline
	_Ty __cdecl abs(const _CMPLX(_Ty)& _Left)
	{	// return |complex| as real
	int _Leftexp;
	_Ty _Rho = _Fabs(_Left, &_Leftexp);	// get magnitude and scale factor

	if (_Leftexp == 0)
		return (_Rho);	// no scale factor
	else
		return (_CTR(_Ty)::ldexp(_Rho, _Leftexp));	// scale result
	}

		// TEMPLATE FUNCTION arg
_TMPLT(_Ty) inline
	_Ty __cdecl arg(const _CMPLX(_Ty)& _Left)
	{	// return phase angle of complex as real
	return (_CTR(_Ty)::atan2(imag(_Left), real(_Left)));
	}

		// TEMPLATE FUNCTION conj
_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl conj(const _CMPLX(_Ty)& _Left)
	{	// return complex conjugate
	return (_CMPLX(_Ty)(real(_Left), -imag(_Left)));
	}

		// TEMPLATE FUNCTION cos
_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl cos(const _CMPLX(_Ty)& _Left)
	{	// return cos(complex)
	return (_CMPLX(_Ty)(
		_CTR(_Ty)::_Cosh(imag(_Left), _CTR(_Ty)::cos(real(_Left))),
		-_CTR(_Ty)::_Sinh(imag(_Left),
			_CTR(_Ty)::sin(real(_Left)))));
	}

		// TEMPLATE FUNCTION cosh
_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl cosh(const _CMPLX(_Ty)& _Left)
	{	// return cosh(complex)
	return (_CMPLX(_Ty)(
		_CTR(_Ty)::_Cosh(real(_Left), _CTR(_Ty)::cos(imag(_Left))),
		_CTR(_Ty)::_Sinh(real(_Left), _CTR(_Ty)::sin(imag(_Left)))));
	}

		// TEMPLATE FUNCTION exp
_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl exp(const _CMPLX(_Ty)& _Left)
	{	// return exp(complex)
	_Ty _Real(real(_Left)), _Imag(real(_Left));
	_CTR(_Ty)::_Exp(&_Real, _CTR(_Ty)::cos(imag(_Left)), 0);
	_CTR(_Ty)::_Exp(&_Imag, _CTR(_Ty)::sin(imag(_Left)), 0);
	return (_CMPLX(_Ty)(_Real, _Imag));
	}

		// TEMPLATE FUNCTION log
_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl log(const _CMPLX(_Ty)& _Left)
	{	// return log(complex)
	_Ty _Theta = _CTR(_Ty)::atan2(imag(_Left), real(_Left));	// get phase

	if (_CTR(_Ty)::_Isnan(_Theta))
		return (_CMPLX(_Ty)(_Theta, _Theta));	// real or imag is NaN
	else
		{	// use 1 1/2 precision to preserve bits
		static const _Ty _Cm = (_Ty)(22713.0L / 32768.0L);
		static const _Ty _Cl = (_Ty)1.4286068203094172321214581765680755e-6L;
		int _Leftexp;
		_Ty _Rho = _Fabs(_Left, &_Leftexp);	// get magnitude and scale factor

		_Ty _Leftn = (_Ty)_Leftexp;
		_CMPLX(_Ty) _Tmp(
			_Rho == 0 ? -_CTR(_Ty)::_Infv(_Rho)	// log(0) == -INF
			: _CTR(_Ty)::_Isinf(_Rho) ? _Rho	// log(INF) == INF
			: _CTR(_Ty)::log(_Rho) + _Leftn * _Cl + _Leftn * _Cm,
				_Theta);
		return (_Tmp);
		}
	}

		// TEMPLATE FUNCTION log10
_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl log10(const _CMPLX(_Ty)& _Left)
	{	// return log10(complex)
	return (log(_Left) * (_Ty)0.43429448190325182765112891891660508L);
	}

		// TEMPLATE FUNCTION norm
_TMPLT(_Ty) inline
	_Ty __cdecl norm(const _CMPLX(_Ty)& _Left)
	{	// return squared magnitude
	return (real(_Left) * real(_Left) + imag(_Left) * imag(_Left));
	}

		// TEMPLATE FUNCTION polar
_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl polar(const _Ty& _Rho, const _Ty& _Theta)
	{	// return _Rho * exp(i * _Theta) as complex
	return (_CMPLX(_Ty)(_Rho * _CTR(_Ty)::cos(_Theta),
		_Rho * _CTR(_Ty)::sin(_Theta)));
	}

_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl polar(const _Ty& _Rho)
	{	// return _Rho * exp(i * 0) as complex
	return (_CMPLX(_Ty)(_Rho, (_Ty)0));
	}

		// TEMPLATE FUNCTION pow
_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl pow(const _CMPLX(_Ty)& _Left, const _Ty& _Right)
	{	// return complex ^ real
	if (imag(_Left) == 0 && 0 <= real(_Left))
		return (_CMPLX(_Ty)(_CTR(_Ty)::pow(real(_Left), _Right)));
	else
		return (exp(_Right * log(_Left)));
	}

_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl pow(const _CMPLX(_Ty)& _Left, int _Right)
	{	// return complex ^ integer
	_CMPLX(_Ty) _Tmp = _Left;
	unsigned int _Count = _Right;

	if (_Right < 0)
		_Count = 0 - _Count;	// safe negation as unsigned

	for (_CMPLX(_Ty) _Zv = _CMPLX(_Ty)(1); ; _Tmp *= _Tmp)
		{	// fold in _Left ^ (2 ^ _Count) as needed
		if ((_Count & 1) != 0)
			_Zv *= _Tmp;
		if ((_Count >>= 1) == 0)
			return (_Right < 0 ? _CMPLX(_Ty)(1) / _Zv : _Zv);
		}
	}

_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl pow(const _Ty& _Left, const _CMPLX(_Ty)& _Right)
	{	// return real ^ complex
	if (imag(_Right) == 0)
		return (_CMPLX(_Ty)(_CTR(_Ty)::pow(_Left, real(_Right))));
	else
		return (exp(_Right * _CTR(_Ty)::log(_Left)));
	}

_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl pow(const _CMPLX(_Ty)& _Left,
		const _CMPLX(_Ty)& _Right)
	{	// return complex ^ complex
	if (imag(_Right) == 0)
		return (pow(_Left, real(_Right)));
	else if (imag(_Left) == 0)
		return (_CMPLX(_Ty)(pow(real(_Left), _Right)));
	else
		return (exp(_Right * log(_Left)));
	}

		// TEMPLATE FUNCTION sin
_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl sin(const _CMPLX(_Ty)& _Left)
	{	// return sin(complex)
	return (_CMPLX(_Ty)(
		_CTR(_Ty)::_Cosh(imag(_Left), _CTR(_Ty)::sin(real(_Left))),
		_CTR(_Ty)::_Sinh(imag(_Left), _CTR(_Ty)::cos(real(_Left)))));
	}

		// TEMPLATE FUNCTION sinh
_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl sinh(const _CMPLX(_Ty)& _Left)
	{	// return sinh(complex)
	return (_CMPLX(_Ty)(
		_CTR(_Ty)::_Sinh(real(_Left), _CTR(_Ty)::cos(imag(_Left))),
		_CTR(_Ty)::_Cosh(real(_Left), _CTR(_Ty)::sin(imag(_Left)))));
	}

		// TEMPLATE FUNCTION sqrt
_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl sqrt(const _CMPLX(_Ty)& _Left)
	{	// return sqrt(complex)
	int _Leftexp;
	_Ty _Rho = _Fabs(_Left, &_Leftexp);	// get magnitude and scale factor

	if (_Leftexp == 0)
		return (_CMPLX(_Ty)(_Rho, _Rho));	// argument is zero, INF, or NaN
	else
		{	// compute in safest quadrant
		_Ty _Realmag = _CTR(_Ty)::ldexp(real(_Left) < 0
			? - real(_Left) : real(_Left), -_Leftexp);
		_Rho = _CTR(_Ty)::ldexp(_CTR(_Ty)::sqrt(
			2 * (_Realmag + _Rho)), _Leftexp / 2 - 1);

		if (0 <= real(_Left))
			return (_CMPLX(_Ty)(_Rho, imag(_Left) / (2 * _Rho)));
		else if (imag(_Left) < 0)
			return (_CMPLX(_Ty)(-imag(_Left) / (2 * _Rho), -_Rho));
		else
			return (_CMPLX(_Ty)(imag(_Left) / (2 * _Rho), _Rho));
		}
	}

		// TEMPLATE FUNCTION tanh
_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl tanh(const _CMPLX(_Ty)& _Left)
	{	// return tanh(complex)
	_Ty _Tv = _CTR(_Ty)::tan(imag(_Left));
	_Ty _Sv = _CTR(_Ty)::_Sinh(real(_Left), (_Ty)(1));
	_Ty _Bv = _Sv *((_Ty)(1) + _Tv * _Tv);
	_Ty _Dv = (_Ty)(1) + _Bv * _Sv;
	return (_CMPLX(_Ty)((_CTR(_Ty)::sqrt((_Ty)(1) + _Sv * _Sv))
		* _Bv / _Dv, _Tv / _Dv));
	}

		// TEMPLATE FUNCTION tan
_TMPLT(_Ty) inline
	_CMPLX(_Ty) __cdecl tan(const _CMPLX(_Ty)& _Left)
	{	// return tan(complex)
	_CMPLX(_Ty) _Zv(tanh(_CMPLX(_Ty)(-imag(_Left), real(_Left))));
	return (_CMPLX(_Ty)(imag(_Zv), -real(_Zv)));
	}

 #ifdef _DLL_CPPLIB
  #ifndef CRTDLL2
template _CRTIMP2 float
	__cdecl imag(const complex<float>&);
template _CRTIMP2 float
	__cdecl real(const complex<float>&);
template _CRTIMP2 float
	__cdecl _Fabs(const complex<float>&, int *);
template _CRTIMP2 complex<float>
	__cdecl operator+(const complex<float>&, const complex<float>&);
template _CRTIMP2 complex<float>
	__cdecl operator+(const complex<float>&, const float&);
template _CRTIMP2 complex<float>
	__cdecl operator+(const float&, const complex<float>&);
template _CRTIMP2 complex<float>
	__cdecl operator-(const complex<float>&, const complex<float>&);
template _CRTIMP2 complex<float>
	__cdecl operator-(const complex<float>&, const float&);
template _CRTIMP2 complex<float>
	__cdecl operator-(const float&, const complex<float>&);
template _CRTIMP2 complex<float>
	__cdecl operator*(const complex<float>&, const complex<float>&);
template _CRTIMP2 complex<float>
	__cdecl operator*(const complex<float>&, const float&);
template _CRTIMP2 complex<float>
	__cdecl operator*(const float&, const complex<float>&);
template _CRTIMP2 complex<float>
	__cdecl operator/(const complex<float>&, const complex<float>&);
template _CRTIMP2 complex<float>
	__cdecl operator/(const complex<float>&, const float&);
template _CRTIMP2 complex<float>
	__cdecl operator/(const float&, const complex<float>&);
template _CRTIMP2 complex<float>
	__cdecl operator+(const complex<float>&);
template _CRTIMP2 complex<float>
	__cdecl operator-(const complex<float>&);
template _CRTIMP2 bool
	__cdecl operator==(const complex<float>&, const complex<float>&);
template _CRTIMP2 bool
	__cdecl operator==(const complex<float>&, const float&);
template _CRTIMP2 bool
	__cdecl operator==(const float&, const complex<float>&);
template _CRTIMP2 bool
	__cdecl operator!=(const complex<float>&, const complex<float>&);
template _CRTIMP2 bool
	__cdecl operator!=(const complex<float>&, const float&);
template _CRTIMP2 bool
	__cdecl operator!=(const float&, const complex<float>&);
template _CRTIMP2 float
	__cdecl abs(const complex<float>&);
template _CRTIMP2 float
	__cdecl arg(const complex<float>&);
template _CRTIMP2 complex<float>
	__cdecl conj(const complex<float>&);
template _CRTIMP2 complex<float>
	__cdecl cos(const complex<float>&);
template _CRTIMP2 complex<float>
	__cdecl cosh(const complex<float>&);
template _CRTIMP2 complex<float>
	__cdecl exp(const complex<float>&);
template _CRTIMP2 complex<float>
	__cdecl log(const complex<float>&);
template _CRTIMP2 complex<float>
	__cdecl log10(const complex<float>&);
template _CRTIMP2 float
	__cdecl norm(const complex<float>&);
template _CRTIMP2 complex<float>
	__cdecl polar(const float&, const float&);
template _CRTIMP2 complex<float>
	__cdecl polar(const float&);
template _CRTIMP2 complex<float>
	__cdecl pow(const complex<float>&, const float&);
template _CRTIMP2 complex<float>
	__cdecl pow(const complex<float>&, int);
template _CRTIMP2 complex<float>
	__cdecl pow(const float&, const complex<float>&);
template _CRTIMP2 complex<float>
	__cdecl pow(const complex<float>&, const complex<float>&);
template _CRTIMP2 complex<float>
	__cdecl sin(const complex<float>&);
template _CRTIMP2 complex<float>
	__cdecl sinh(const complex<float>&);
template _CRTIMP2 complex<float>
	__cdecl sqrt(const complex<float>&);
template _CRTIMP2 complex<float>
	__cdecl tanh(const complex<float>&);
template _CRTIMP2 complex<float>
	__cdecl tan(const complex<float>&);

template _CRTIMP2 double
	__cdecl imag(const complex<double>&);
template _CRTIMP2 double
	__cdecl real(const complex<double>&);
template _CRTIMP2 double
	__cdecl _Fabs(const complex<double>&, int *);
template _CRTIMP2 complex<double>
	__cdecl operator+(const complex<double>&, const complex<double>&);
template _CRTIMP2 complex<double>
	__cdecl operator+(const complex<double>&, const double&);
template _CRTIMP2 complex<double>
	__cdecl operator+(const double&, const complex<double>&);
template _CRTIMP2 complex<double>
	__cdecl operator-(const complex<double>&, const complex<double>&);
template _CRTIMP2 complex<double>
	__cdecl operator-(const complex<double>&, const double&);
template _CRTIMP2 complex<double>
	__cdecl operator-(const double&, const complex<double>&);
template _CRTIMP2 complex<double>
	__cdecl operator*(const complex<double>&, const complex<double>&);
template _CRTIMP2 complex<double>
	__cdecl operator*(const complex<double>&, const double&);
template _CRTIMP2 complex<double>
	__cdecl operator*(const double&, const complex<double>&);
template _CRTIMP2 complex<double>
	__cdecl operator/(const complex<double>&, const complex<double>&);
template _CRTIMP2 complex<double>
	__cdecl operator/(const complex<double>&, const double&);
template _CRTIMP2 complex<double>
	__cdecl operator/(const double&, const complex<double>&);
template _CRTIMP2 complex<double>
	__cdecl operator+(const complex<double>&);
template _CRTIMP2 complex<double>
	__cdecl operator-(const complex<double>&);
template _CRTIMP2 bool
	__cdecl operator==(const complex<double>&, const complex<double>&);
template _CRTIMP2 bool
	__cdecl operator==(const complex<double>&, const double&);
template _CRTIMP2 bool
	__cdecl operator==(const double&, const complex<double>&);
template _CRTIMP2 bool
	__cdecl operator!=(const complex<double>&, const complex<double>&);
template _CRTIMP2 bool
	__cdecl operator!=(const complex<double>&, const double&);
template _CRTIMP2 bool
	__cdecl operator!=(const double&, const complex<double>&);
template _CRTIMP2 double
	__cdecl abs(const complex<double>&);
template _CRTIMP2 double
	__cdecl arg(const complex<double>&);
template _CRTIMP2 complex<double>
	__cdecl conj(const complex<double>&);
template _CRTIMP2 complex<double>
	__cdecl cos(const complex<double>&);
template _CRTIMP2 complex<double>
	__cdecl cosh(const complex<double>&);
template _CRTIMP2 complex<double>
	__cdecl exp(const complex<double>&);
template _CRTIMP2 complex<double>
	__cdecl log(const complex<double>&);
template _CRTIMP2 complex<double>
	__cdecl log10(const complex<double>&);
template _CRTIMP2 double
	__cdecl norm(const complex<double>&);
template _CRTIMP2 complex<double>
	__cdecl polar(const double&, const double&);
template _CRTIMP2 complex<double>
	__cdecl polar(const double&);
template _CRTIMP2 complex<double>
	__cdecl pow(const complex<double>&, const double&);
template _CRTIMP2 complex<double>
	__cdecl pow(const complex<double>&, int);
template _CRTIMP2 complex<double>
	__cdecl pow(const double&,	const complex<double>&);
template _CRTIMP2 complex<double>
	__cdecl pow(const complex<double>&, const complex<double>&);
template _CRTIMP2 complex<double>
	__cdecl sin(const complex<double>&);
template _CRTIMP2 complex<double>
	__cdecl sinh(const complex<double>&);
template _CRTIMP2 complex<double>
	__cdecl sqrt(const complex<double>&);
template _CRTIMP2 complex<double>
	__cdecl tanh(const complex<double>&);
template _CRTIMP2 complex<double>
	__cdecl tan(const complex<double>&);

template _CRTIMP2 long double
	__cdecl imag(const complex<long double>&);
template _CRTIMP2 long double
	__cdecl real(const complex<long double>&);
template _CRTIMP2 long double
	__cdecl _Fabs(const complex<long double>&, int *);
template _CRTIMP2 complex<long double>
	__cdecl operator+(const complex<long double>&,
		const complex<long double>&);
template _CRTIMP2 complex<long double>
	__cdecl operator+(const complex<long double>&, const long double&);
template _CRTIMP2 complex<long double>
	__cdecl operator+(const long double&, const complex<long double>&);
template _CRTIMP2 complex<long double>
	__cdecl operator-(const complex<long double>&,
		const complex<long double>&);
template _CRTIMP2 complex<long double>
	__cdecl operator-(const complex<long double>&, const long double&);
template _CRTIMP2 complex<long double>
	__cdecl operator-(const long double&, const complex<long double>&);
template _CRTIMP2 complex<long double>
	__cdecl operator*(const complex<long double>&,
		const complex<long double>&);
template _CRTIMP2 complex<long double>
	__cdecl operator*(const complex<long double>&, const long double&);
template _CRTIMP2 complex<long double>
	__cdecl operator*(const long double&, const complex<long double>&);
template _CRTIMP2 complex<long double>
	__cdecl operator/(const complex<long double>&,
		const complex<long double>&);
template _CRTIMP2 complex<long double>
	__cdecl operator/(const complex<long double>&, const long double&);
template _CRTIMP2 complex<long double>
	__cdecl operator/(const long double&, const complex<long double>&);
template _CRTIMP2 complex<long double>
	__cdecl operator+(const complex<long double>&);
template _CRTIMP2 complex<long double>
	__cdecl operator-(const complex<long double>&);
template _CRTIMP2 bool
	__cdecl operator==(const complex<long double>&,
		const complex<long double>&);
template _CRTIMP2 bool
	__cdecl operator==(const complex<long double>&, const long double&);
template _CRTIMP2 bool
	__cdecl operator==(const long double&, const complex<long double>&);
template _CRTIMP2 bool
	__cdecl operator!=(const complex<long double>&,
		const complex<long double>&);
template _CRTIMP2 bool
	__cdecl operator!=(const complex<long double>&, const long double&);
template _CRTIMP2 bool
	__cdecl operator!=(const long double&, const complex<long double>&);
template _CRTIMP2 long double
	__cdecl abs(const complex<long double>&);
template _CRTIMP2 long double
	__cdecl arg(const complex<long double>&);
template _CRTIMP2 complex<long double>
	__cdecl conj(const complex<long double>&);
template _CRTIMP2 complex<long double>
	__cdecl cos(const complex<long double>&);
template _CRTIMP2 complex<long double>
	__cdecl cosh(const complex<long double>&);
template _CRTIMP2 complex<long double>
	__cdecl exp(const complex<long double>&);
template _CRTIMP2 complex<long double>
	__cdecl log(const complex<long double>&);
template _CRTIMP2 complex<long double>
	__cdecl log10(const complex<long double>&);
template _CRTIMP2 long double
	__cdecl norm(const complex<long double>&);
template _CRTIMP2 complex<long double>
	__cdecl polar(const long double&, const long double&);
template _CRTIMP2 complex<long double>
	__cdecl polar(const long double&);
template _CRTIMP2 complex<long double>
	__cdecl pow(const complex<long double>&, const long double&);
template _CRTIMP2 complex<long double>
	__cdecl pow(const complex<long double>&, int);
template _CRTIMP2 complex<long double>
	__cdecl pow(const long double&, const complex<long double>&);
template _CRTIMP2 complex<long double>
	__cdecl pow(const complex<long double>&, const complex<long double>&);
template _CRTIMP2 complex<long double>
	__cdecl sin(const complex<long double>&);
template _CRTIMP2 complex<long double>
	__cdecl sinh(const complex<long double>&);
template _CRTIMP2 complex<long double>
	__cdecl sqrt(const complex<long double>&);
template _CRTIMP2 complex<long double>
	__cdecl tanh(const complex<long double>&);
template _CRTIMP2 complex<long double>
	__cdecl tan(const complex<long double>&);
  #endif	// CRTDLL2
 #endif	// _DLL_CPPLIB

#undef _XCOMPLEX_	/* SIC: may be included multiple times */
#endif /* _XCOMPLEX_ */

/*
* Copyright (c) 1992-2001 by P.J. Plauger.  ALL RIGHTS RESERVED.
 * Consult your license regarding permissions and restrictions.
 V3.10:0009 */