/************************************************************
 * File: cpi_parallel.c
 * Purpose: Parallel computation of pi in C with measurement 
 *          of the time taken to complete the computation.
 ************************************************************/
#include <mpi.h>
#include <stdio.h> 
#include <time.h> 

int main(int argc, char *argv[]) {
  int n = 4800000, myid, numprocs, i;
  int average, extra, n2, sp, ep; 
  double mypi, pi, h, sum = 0.0, x;
  clock_t st, et;
 
  MPI_Init(&argc, &argv);
  MPI_Comm_size(MPI_COMM_WORLD, &numprocs);
  MPI_Comm_rank(MPI_COMM_WORLD, &myid);

  // determine the start and end interval numbers (sp and ep) 
  // for the pi computation 
  average = n / numprocs;
  extra = n % numprocs;
  n2 = (myid+1 <= extra) ? average+1 : average;
  sp = (myid <= extra) ? myid*(average+1)+1 : myid*average+1;
  ep = sp + n2 - 1;

  MPI_Barrier(MPI_COMM_WORLD);
 
  st = clock();  // get the start time for the pi computation
  h = 1.0 / n;
  for(i=sp; i<=ep; i++) {
    x = h * (i-0.5);
    sum = sum + 4.0/(1.0+x*x);
  }
  mypi = h * sum;

  MPI_Reduce(&mypi, &pi, 1, MPI_DOUBLE, MPI_SUM, 0, MPI_COMM_WORLD);

  if(myid == 0) {
    et = clock();  // get the end time for the pi computation
    printf("pi: %.16f\n", pi);
    printf("execution time: %.6f\n", (double)(et-st)/(double)CLOCKS_PER_SEC);
  }

  MPI_Finalize();

  return 0;
}