import java.applet.Applet;
import java.awt.event.*;
import java.awt.*;

/**This class does the basic arithmetic of complex numbers */

public class GaussianInteger {
    int x,y;


    public GaussianInteger() {
        this.x=0;
        this.y=0;
    } 

    public GaussianInteger(int x,int y) {
        this.x=x;
        this.y=y;
    }

    public GaussianInteger(GaussianInteger g) {
        this.x=g.x;
        this.y=g.y;
    }

    /**This operation only makes sense when we are averaging even numbers.**/

    /**printout**/
     public void print() {
 	System.out.println("Gaussian: "+this.x+" "+this.y);
    } 


    public static GaussianInteger average(GaussianInteger g1,GaussianInteger g2) throws ProofException {

	int test=0;
	if(g1.x%2==1) test=1;
	if(g1.y%2==1) test=1;
	if(g2.x%2==1) test=1;
	if(g2.y%2==1) test=1;
	if(test==1) throw new ProofException("Gaussian: odd integers now allowed.");

	int x=(g1.x+g2.x)/2;
	int y=(g1.y+g2.y)/2;
	GaussianInteger g=new GaussianInteger(x,y);
	return(g);
    }

    public static GaussianInteger convert(Complex z,int n) {
	double xx=z.x*Math.pow(2,n);
	double yy=z.y*Math.pow(2,n);
	int x=(int)(xx);
	int y=(int)(yy);
	if(Math.abs(x-xx)>.000000001) System.out.println("warning: Gaussian Integer ill defined");
	if(Math.abs(y-yy)>.000000001) System.out.println("warning: Gaussian Integer illdefined");
	GaussianInteger g=new GaussianInteger(x,y);
	return(g);
    }


}