#include <mpi.h>
#include <math.h>
#include <stdio.h>
/* Prototype */
float integral(float ai, float h, int n);
int main(int argc, char* argv[])
/*###############################################################################
 #                                                                              #
 # This is an MPI example on parallel integration to demonstrate the use of:    #
 #                                                                              #
 # * MPI_Init, MPI_Comm_rank, MPI_Comm_size, MPI_Finalize                       #
 # * MPI_Gather                                                                 #
 #                                                                              #
 # Dr. Kadin Tseng                                                              #
 # Scientific Computing and Visualization                                       #
 # Boston University                                                            #
 # 1998                                                                         #
 #                                                                              #
 ###############################################################################*/
{
      int n, p, myid, tag, proc, ierr, i;
      float h, integral_sum, a, b, ai, pi, my_int, buf[50];
      int master = 0;  /* processor performing total sum */
      MPI_Comm comm;

      comm = MPI_COMM_WORLD;      
      ierr = MPI_Init(&argc, &argv);         /* starts MPI */
      MPI_Comm_rank(comm, &myid);            /* get current process id */
      MPI_Comm_size(comm, &p);               /* get number of processes */

      pi = acos(-1.0);  /* = 3.14159... */
      a = 0.;           /* lower limit of integration */
      b = pi*1./2.;     /* upper limit of integration */
      n = 500;          /* number of increment within each process */
      h = (b-a)/n/p;    /* length of increment */

      ai = a + myid*n*h;  /* lower limit of integration for partition myid */
      my_int = integral(ai, h, n); 

      printf("Process %d has the partial sum of %f\n", myid,my_int);

      MPI_Gather( 
            &my_int, 1, MPI_FLOAT, 
            buf, 1, MPI_FLOAT, 
            master, comm); 

      if(myid == master) {
        integral_sum = 0.0;
        for (i=0; i<p; i++) {
          integral_sum += buf[i];
        }
        printf("The Integral =%f\n",integral_sum);
      }

      MPI_Finalize();                       /* let MPI finish up ... */
}

float integral(float ai, float h, int n)
{
      int j;
      float aij, integ;

      integ = 0.0;                 /* initialize */
      for (j=0;j<n;j++) {          /* sum integrals */
        aij = ai + (j+0.5)*h;      /* mid-point */
        integ += cos(aij)*h;
      }
      return integ;
}