#include <stdio.h>
  #include <stdlib.h>
  #include <mpi.h>
  
  double f(double x){
    return sin(x);
  }


int main(int argc, char** argv) {
  
  double a, b, delx, x, y, tot;
  int n, i;

//   MPI
  MPI_Init(&argc, &argv);
  int myid;
  MPI_Comm_rank(MPI_COMM_WORLD, &myid);
  int world_size;
  MPI_Comm_size(MPI_COMM_WORLD, &world_size);  
//   MPI

  a = 0.0;
  b=3.141592653589793;
  n = atoi(argv[1]);
  delx = (b-a)/n;

// MPI  
  int rest = n%world_size;  
  int nloc = n/world_size;

  if(myid < rest) {
    nloc++;
  }
  
  int start_index = nloc*myid;
  if(myid >= rest) {
    start_index += rest;
  }
  int end_index = start_index + nloc;
// MPI

  x = a;
  tot = 0.0;

//   for(i=1;i<n;++i){
  for(i=start_index;i<end_index;++i){
    x = a + i*delx;
    y=f(x);
    tot = tot + y;
  }
  
  MPI_Allreduce(MPI_IN_PLACE, &tot, 1, MPI_DOUBLE,MPI_SUM, MPI_COMM_WORLD);
  tot = delx * ((f(a)+f(b))/2.0 + tot);

  printf("approximate integral using %d intervals = %lf\n", n,tot);
  
  MPI_Finalize();
  return 0;
}