import java.awt.Graphics;

public class TaylorSeries extends java.applet.Applet {
    double sq(double x) {
        double y;

        y = x*x;
        return y;
    }

    double cu(double x) {
        double y;

        y = x*x*x;
        return y;
    }

    double my_power(double x, int exponent) {
        double y;
        int n;

        y = 1.0;
 
        if (exponent < 0) y = 0.0; // wrong
        if (exponent > 0 ) {

            for (n = 0; n < exponent; n++) {
                y = y*x;
            }
        }

        return y;
  
    }

    int my_factorial(int n)
    {
        int i;
        int f;

        f = 1;
        if (n <= 0) return 1; // wrong
        if (n == 1) return 1;
        if (n >  1)
        {

            for (i = 2; i <= n; i++)
            {
                f = f*i;
            }
        }
        return f;
    }

    double deriv_sin(int n) {
        if (n%4 == 0) return  0.0;
        if (n%4 == 1) return  1.0;
        if (n%4 == 2) return  0.0;
        if (n%4 == 3) return -1.0;
        return 0.0; // never happens
    }

    double taylor_sin(double x, int terms)
    {
        int n;
        double y;

        y = 0.0;

        if (terms <= 0) {
            // wrong
            return y;
        }
        if (terms == 1) {
            return y;
        }
        if (terms >  1)
        {
            for (n = 1; n <= terms; n++)
            {
                y = y + deriv_sin(n)*my_power(x, n)/(double)my_factorial(n);
            }
        }
        return y;
    }

    public void paint(Graphics g) {
        int x, x1, y, y1;
	double ax, ay, ax1, ay1;

        // draw axes

        g.drawLine(0, size().height/2, size().width - 1, size().height/2);
        g.drawLine(size().width/2, 0, size().width/2, size().height - 1);
       
        // draw functions
 
        for (x = 0 ; x < size().width ; x++) {

//      ax = actual x, ay = actual y (not in pixels)
//           I want ax to range from -2 to 2

            ax = ((double)x - size().width/2)/(size().width/4);
//          ay = sq(ax);
            ay = taylor_sin(ax, 2);
            y = (int)(-ay*size().height/4 + size().height/2);
 
            ax1 = ((double)x + 1 - size().width/2)/(size().width/4);
//          ay1 = sq(ax1);
            ay1 = taylor_sin(ax1, 2);
            y1 = (int)(-ay1*size().height/4 + size().height/2);

            if (x >= 0 && y >= 0 && x < size().width && y < size().height) {
                g.drawLine(x, (int)y, x + 1, (int)y1);
                }

//          ay = cu(ax);
            ay = taylor_sin(ax, 4);
            y = (int)(-ay*size().height/4 + size().height/2);

//          ay1 = cu(ax1);
            ay1 = taylor_sin(ax1, 4);
            y1 = (int)(-ay1*size().height/4 + size().height/2);

            if (x >= 0 && y >= 0 && x < size().width && y < size().height) {
                g.drawLine(x, (int)y, x + 1, (int)y1);
                }
        }
    }
  public String getAppletInfo() {
    return "Draws Taylor approximations of sine.";
  }
}