///////////////////////////////////////////////////////////
// cmplx.h, 2D complex basic math by stephen c. ferguson
///////////////////////////////////////////////////////////

#include "math.h"

#define zerotol 1e-24

class cmplx
{
public:
  double x,y;

  cmplx( double xx , double yy); //create
  cmplx(); //create
  
	inline cmplx& operator+(cmplx& v) {return cmplx(x+v.x, y+v.y);} // add
  inline cmplx& operator-(cmplx& v) {return cmplx(x-v.x, y-v.y);} // subtract
  inline cmplx& operator*(cmplx& v) {return cmplx(v.x*x-v.y*y, v.x*y+v.y*x);} // multiply
  inline cmplx& operator/(cmplx& v)
	{ 
		return cmplx((v.x*x+v.y*y)/(v.x*v.x+v.y*v.y),
               (v.x*y-v.y*x)/(v.x*v.x+v.y*v.y));  // divide
  }
	inline cmplx& operator-() { return cmplx( -x, -y); }
	inline double sqrs() { return x*x+y*y; }
	inline double magnitude() { return sqrt (x*x+y*y) ; }

	inline friend cmplx &operator*(cmplx &num,double real)
         {return cmplx(num.x*real,num.y*real);}
  
	inline friend cmplx &operator*(double real,cmplx &num)
         {return cmplx(num.x*real,num.y*real);}
  
	inline friend cmplx &operator+(cmplx &num,double real)
         {return cmplx(num.x+real,num.y);}
  
	inline friend cmplx &operator+(double real, cmplx &num)
         {return cmplx(num.x+real,num.y);} 	
	
	inline friend cmplx &operator/(cmplx &num, double real)
         {return cmplx(num.x/real,num.y/real);}
  
	inline friend cmplx &operator-(cmplx &num,double real)
         {return cmplx(num.x-real,num.y);}
  
	inline friend cmplx &operator-(double real,cmplx &num)
         {return cmplx(real-num.x,-num.y);}
			
  inline cmplx &operator^(double expon)
	{
		return ((*this).clog( ) * expon).cexp();			
	}
			
  inline cmplx &operator^(cmplx &expon)
	{
		return ((*this).clog( ) * expon).cexp();
	}

  inline friend cmplx &operator^(double base, cmplx &expon);      

	inline cmplx &cexp() 
	{
		return cmplx(exp(x)*cos(y),exp(x)*sin(y));
	}

	inline cmplx &clog() 
	{
		return cmplx(log(fabs((*this).magnitude())),atan2(y,x));
	}

	cmplx csin();
	cmplx ccos();

	/*
	inline cmplx &csin()
	{
		return cmplx(.5*(exp(y)+1./exp(y))*sin(x),cos(x)*.5*(exp(y)-1./exp(y)));
	}

	inline cmplx &ccos()
	{
		return cmplx(.5*(exp(y)+1./exp(y))*cos(x),-sin(x)*.5*(exp(y)-1./exp(y)));
	}
	*/

};




cmplx tangent (cmplx x);
cmplx sinh		(cmplx& x);
cmplx asin		(cmplx&	x);
cmplx acos		(cmplx&	x);
cmplx arctan	(cmplx& x);