# Loop parallelization

Estimate π using integral. Parallelization performed by work distribution (loop parallelization).

The value of πis calculated using rectangles method that approximates following integral:

π = ∫ 4.0 / (1 + x2 ) dx

In our code, the interval is divided into equal subintervals and we take top middle point of each subinterval to calculate area of the rectangle.

The calculations will start by executing the main method from PcjExamplePiI class. Four tasks will be involved in calculations: on local machine. The listing contains comments that should clarify what program is doing. The user can easily change number of tasks by providing more host names to the deploy method. The PCJ will launch calculations on specified nodes.

`import org.pcj.NodesDescription;import org.pcj.PCJ;import org.pcj.StartPoint;import org.pcj.Storage;import org.pcj.PcjFuture;import org.pcj.RegisterStorage;​@RegisterStorage(PcjExamplePiI.Shared.class)public class PcjExamplePiI implements StartPoint {​    private double f(final double x) {        return (4.0 / (1.0 + x * x));    }​    @Storage(PcjExamplePiI.class)    enum Shared {        sum    }    double sum;​    @Override    public void main() {​        PCJ.barrier();        double time = System.nanoTime();​        long nAll = 1_280_000_000;        double w = 1.0 / (double) nAll;        sum = 0.0;// Calculate partial results with the cyclic distribution        for (int i = PCJ.myId(); i < nAll; i += PCJ.threadCount()) {            sum = sum + f(((double) i + 0.5) * w);        }        sum = sum * w;​// Wait for all tasksk to finish        PCJ.barrier();​// Gather results        PcjFuture cL[] = new PcjFuture[PCJ.threadCount()];        double pi = sum;        if (PCJ.myId() == 0) {            for (int p = 1; p < PCJ.threadCount(); p++) {                cL[p] = PCJ.asyncGet(p, Shared.sum);            }            for (int p = 1; p < PCJ.threadCount(); p++) {                pi = pi + cL[p].get();            }        }​        PCJ.barrier();// Print results        time = System.nanoTime() - time;​        if (PCJ.myId() == 0) {            System.out.format(" %.7f  %.7f time %.5f \n", pi, time * 1.0E-9, time);        }    }​    public static void main(String[] args) throws IOException {    String nodesFile  = "nodes.txt";    PCJ.executionBuilder (PcjExample.class)                .addNodes(new File("nodes.txt"))                .start();    }}​​`