/*
 * 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.
 *
 * parallel version using MPI, as discussed in Appendix B.
 */
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
/* copied from not-strictly-standard part of math.h */
#define M_PI		3.14159265358979323846
#include <mpi.h>		/* MPI header file */

#include "timer.h"
#include "utility.h"    /* has error_exit() */

#define NUM_STEPS 400000000

/* main program */
int main(int argc, char *argv[]) {

    int nprocs;
    int myid;
    double start_time, end_time;
    double x, pi;
    double sum = 0.0;
    double step = 1.0/(double) NUM_STEPS; 

    /* initialize for MPI */
    MPI_Init(&argc, &argv);

    /* get number of processes */
    MPI_Comm_size(MPI_COMM_WORLD, &nprocs);

    /* get this process's number (ranges from 0 to nprocs - 1) */
    MPI_Comm_rank(MPI_COMM_WORLD, &myid);

    /* record start time */
    /* could use MPI_Wtime but get_time is what sequential code uses */
    start_time = get_time();

    /* do computation */
    for (int i=myid; i < NUM_STEPS; i += nprocs) {      /* changed */
        x = (i+0.5)*step;
        sum += 4.0/(1.0+x*x);
    }
    sum *= step;
    MPI_Reduce(&sum, &pi, 1, MPI_DOUBLE, MPI_SUM, 0, MPI_COMM_WORLD);/* added */

    /* record end time */
    end_time = get_time();

    /* print results */
    if (myid == 0) {
        printf("parallel program results with %d processes and %d steps:\n", 
                nprocs, NUM_STEPS);
        printf("computed pi = %g  (%17.15f)\n",pi, pi);
        printf("difference between computed pi and math.h M_PI = %17.15f\n", 
                fabs(pi - M_PI));
        printf("time to compute = %g seconds\n", end_time - start_time);
    }

    /* clean up for MPI */
    MPI_Finalize();

    return EXIT_SUCCESS;
}