Code

The code is straight forward and self-explainitory.

#include	<stdio.h>
#include	<mpi.h>
#include        <math.h>
#include        <stddef.h>
#include        <stdlib.h>

#define d_sphere 5    /** the number of dimensions of the sphere ***/
#define num_trials 1000000  /** the number of trials for each processor ***/

void srand48();
double drand48();

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

   int numprocs;  /* Number of processors */
   int procnum;   /* Processor number */
   int j,i,*int_arr;
   double volume,pi,r2,avg,sigma,volume_arr[4],sigma_arr[4];
   MPI_Status status;

   MPI_Init(&argc, &argv);
   MPI_Comm_rank(MPI_COMM_WORLD, &procnum);
   MPI_Comm_size(MPI_COMM_WORLD, &numprocs);
   srand48 ( (long) procnum);
   int_arr = (int *) malloc((num_trials + 1) * sizeof(int));

   for(i=1;i<=num_trials;i++)
   {
      /*** calculate one point ***/
      r2 = 0.0;
      for(j=1;j<=d_sphere;j++)
         r2 += pow(drand48(),2.0);
      if(r2 <= 1.0)
      {
         int_arr[i] = 1;
      }
      else
      {
         int_arr[i] = 0;
      }
   }
   /*** now get average and standard deviation ***/
   avg = 0.0;
   for(i=1;i<=num_trials;i++)
      avg += ((double) int_arr[i]);
   avg /= ((double) num_trials);
   volume = avg * pow(2.0,d_sphere);
   sigma = 0.0;
   for(i=1;i<=num_trials;i++)
      sigma += pow(((double) int_arr[i]) - avg,2.0);
   sigma = sigma / ((double) num_trials);
   sigma = sqrt(sigma);


   /*** send and receive global data ***/
   if(procnum == 0)
   {
      volume_arr[0] = volume;
      sigma_arr[0] = sigma;
      for(i=1;i<numprocs;i++)
      {
         MPI_Recv(&(volume_arr[i]),1,MPI_DOUBLE,i,0,MPI_COMM_WORLD,&status);
         MPI_Recv(&(sigma_arr[i]),1,MPI_DOUBLE,i,0,MPI_COMM_WORLD,&status);
printf("%d vol is %25.16e \n",i,volume_arr[i]);
      }
   }
   else
   {
      MPI_Send(&volume,1,MPI_DOUBLE,0,0,MPI_COMM_WORLD);
      MPI_Send(&sigma,1,MPI_DOUBLE,0,0,MPI_COMM_WORLD);
   }

   /*** compute and print out global information ***/

   if(procnum == 0)
   {
      /*** compute global averages ***/
      sigma = 0.0;
      volume = 0.0;
      for(i=0;i<numprocs;i++)
      {
         volume += volume_arr[i];
         sigma += sigma_arr[i];
      }
      volume /= ((double) numprocs);
      sigma /= ((double) numprocs);
      printf("--------------------------------------------- \n");
      printf("VALUES AVERAGED OVER ALL PROCESSORS: \n");
      printf(" volume of %d sphere is %25.16e \n",d_sphere,volume);
      if(d_sphere == 2)
         printf("in  2 dim, volume = pi = %25.16e \n",volume);
      printf(" st. dev. is %25.16e \n",sigma);
      printf(" total number of points: %d \n",4*num_trials);
      printf("--------------------------------------------- \n");
   }


   MPI_Finalize();

}