/*
 * 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.
 */
package csci3366.sample.numint;
import csci3366.sample.utility.Utility;

public class NumIntSeq {

    /* 
     * global variables:
     * global so in the parallel version all threads will have easy access 
     */ 
    private static long numSteps;
    private static double step;
    private static double sum = 0.0;

    /* main method */

    public static void main(String[] args) {

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

        /* process command-line arguments */

        String usageMessage = "arguments:  number_of_steps";

        numSteps = Utility.getLongArg(args, 0, 1, 
                "number_of_steps", usageMessage);

        /* do computation */

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

        /* end timing and print result */
        long endTime = System.currentTimeMillis();
        System.out.printf( "sequential program results with %d steps\n",
                numSteps);
        System.out.printf("computed pi = %17.15f\n" , pi);
        System.out.printf(
                "difference between estimated pi and Math.PI = %17.15f\n",
                Math.abs(pi - Math.PI));
        System.out.printf("time to compute = %g seconds\n",
                (double) (endTime - startTime) / 1000);
    }
}