/*
 * numerical integration example, as discussed in textbook:  
 *
 * compute pi by approximating the area under the curve f(x) = 4 / (1 + x*x)
 * between 0 and 1.
 *
 * sequential version using Java.
 */
public class NumIntSeq {

    /* constants */

    private static final int NUM_STEPS = 1000000000;
    private static final double step = 1.0/(double) NUM_STEPS; 

    /* main method */

    public static void main(String[] args) {

        /* start timing */
        long startTime = System.currentTimeMillis();

        /* do computation */

        double sum = 0.0;
        for (int i=0; i < NUM_STEPS; ++i) {
            double x = (i+0.5)*step;
            sum = sum + 4.0/(1.0+x*x);
        }
        double pi = sum * step;

        /* end timing and print result */
        long endTime = System.currentTimeMillis();
        System.out.println("sequential program results");
        System.out.println("pi = " + pi);
        System.out.println("time to compute = " + 
                (double) (endTime - startTime) / 1000);
    }
}