#include <stdio.h>
#include "mpi.h"

/* If you'd like to use this external function to calculate each trapezoid...  */

double Trap( double local_a, double local_b, int local_n, double h)
{
  double integral;  /* Store result in 'integral' */
  double x;
  int i;

  double f(double x);  /* function being integrated */

   /*  code goes here */

  return integral;
}

int main(int argc, char **argv)
{
  double a = 0.0;
  double b = 1.0;
  int n = 1024;
  double h;
  double local_a; /* Left endpoint of the process */
  double local_b; /* Right endpoint of the process */
  int local_n;   /*  Number of trapezoids for one process's calculation */
  double integral;  /* Integral over one process's interval */
  double total;     /* Total integral */
  int source;       /* one process sending an integral */
  int dest = 0;     /* all processes send to 0 */
  int tag  = 0;
  int rank, size;

  MPI_Status status;

  MPI_Init(&argc, &argv);
  MPI_Comm_rank(MPI_COMM_WORLD, &rank);
  MPI_Comm_size(MPI_COMM_WORLD, &size);

  h = (b - a)/n;
  local_n = n/size;

/* Length of each process's interval of integration = local_n * h.  
   So each process's interval starts at: */

  local_a = a + ???;
  local_b = local_a + ???;
  integral = Trap(local_a, local_b, local_n, h);

  if (rank == 0) {
    total = integral;
    for(source = 1; source < size; source++) {
               
	       ???

    }
  } else {
            ???
  }

  if (rank == 0) {
    printf("With n = %d trapezoids, the estimate ",n);
    printf("of the integral from %lf to %lf = %lf\n", a, b, total);
  }

  MPI_Finalize();

  return 0;
}

double f(double x) {
  return x * x;
}

/*
CRAY SV1:

cc integralMPI.c

mpirun -np 4 a.out

*/