/*
 * complex.h - complex number class definitions
 *
 * Copyright (C) lartely <luda@hitwh.edu.cn>
 *	
 */
#include <math.h>
#include <iostream.h>
#ifndef _COMPLEX_DOT_H_
#define _COMPLEX_DOT_H_
#ifndef M_PI
#define M_PI      3.1415926535897932384626433832795029
#endif

class complex;
// create a complex object given polar coordinates
complex polar (const double mag, const double ang = 0.0);
			
// complex manipulations
double  re (const double);
double  im (const double);
double  norm (const double);
double  conj (const double);

// overloaded math functions
double xhypot (const double, const double);
double    abs (const double);
class complex 
{
public:
	double real,imag;

public:
	complex (double real,double imag=0.0);
	complex ();
	complex (const complex&);

	friend double arg (const complex);
	friend double re(const complex);
	friend double im(const complex);
	friend double norm (const complex);
	friend complex conj(const complex);
  double re (void);  // the real part
  double im (void);  // the imaginary part
  complex conj (void);  // the complex conjugate
  double abs  (void);  // the magnitude
  //overroad basic math function
  friend complex exp (const complex);
  friend complex sin (const complex);
  friend complex cos (const complex);
  friend complex pow (const complex, const double);
  // operator functions
  friend complex operator + (const complex, const complex);
  friend complex operator + (const complex, const double);
  friend complex operator + (const double, const complex);

  friend complex operator - (const complex, const complex);
  friend complex operator - (const complex, const double);
  friend complex operator - (const double, const complex);

  friend complex operator * (const complex, const complex);
  friend complex operator * (const complex, const double);
  friend complex operator * (const double, const complex);

  friend complex operator / (const complex, const complex);
  friend complex operator / (const complex, const double);
  friend complex operator / (const double, const complex);
  friend complex operator ^ (const complex, const double); 
  // comparisons
  friend bool    operator == (const complex, const complex);
  friend bool    operator != (const complex, const complex);
		
  // assignment operations
  complex&       operator  = (const complex);
  complex&       operator  = (const double);

  complex&       operator += (const complex);
  complex&       operator += (const double);

  complex&       operator -= (const complex);
  complex&       operator -= (const double);

  complex&       operator *= (const complex);
  complex&       operator *= (const double);

  complex        operator +  ();
  complex        operator -  ();

  // debugging
  void print (void);
};

#endif /* _COMPLEX_DOT_H_ */