/*******************************************************************************
 * This is a simple program that shows the numerical integration example.
 * It computes pi by approximating the area under the curve:
 *      f(x) = 4 / (1+x*x) between 0 and 1.
 * To do this intergration numerically, the interval from 0 to 1 is divided into
 * some number (num_sub_intervals) subintervals and added up the area of
 * rectangles
 * The larger the value of the num_sub_interval the more accurate your result
 * will be.
 *
 * The program first asks the user to input a value for subintervals, it
 * computes
 * the approximation for pi, and then compares it to a more accurate aproximate 
 * value of pi in the math.h library.
 *
 * This program is just a serial version. 
 *
 * Author: Mobeen Ludin
 *
 * How to Compile:
 *	$  
 *
 * 
 *
 ******************************************************************************/

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

int main(int argc, char *argv[]) {
	int num_sub_intervals = 0;
	double start_time, end_time, time_diff;
	double x, pi, pi_tot;
	double sum = 0.0;
	double step;
	int i;
	int r;
	int work;
	int low;
	int high;

	// MPI Initialization part
	int pRank, pNum;
	MPI_Init(&argc, &argv);
	MPI_Comm_size(MPI_COMM_WORLD, &pNum);
	MPI_Comm_rank(MPI_COMM_WORLD, &pRank);

	if(pRank == 0){
		printf("Please enter the number of iterations used to compute pi: \n");
		scanf("%d", &num_sub_intervals);
	}
	//Sending the number of sub intervals to all process in the communicator
	MPI_Bcast(&num_sub_intervals, 1, MPI_INT, 0, MPI_COMM_WORLD);

	step = 1.0/(double) num_sub_intervals;

	// Record the start time from here on:
	start_time = MPI_Wtime();

	for(i=pRank+1; i<=num_sub_intervals; i+=pNum){
		x = step*((double)i-0.5);
		sum += 4.0/(1.0+x*x);
	}
	pi = step * sum;

	MPI_Reduce(&pi, &pi_tot, 1, MPI_DOUBLE, MPI_SUM, 0, MPI_COMM_WORLD);
	//End recording the time here.
	end_time = MPI_Wtime();
	time_diff = end_time - start_time;

	if(pRank == 0){
		// print the result here:
		printf("computed pi value is = %g (%17.15f)\n\n", pi_tot,pi_tot);
		printf("M_PI accurate value from math.h is: %17.15f \n\n", M_PI);
		printf("Difference between computed pi and math.h M_PI = %17.15f\n\n",
				fabs(pi_tot - M_PI));
		printf("Time to compute = %g seconds\n\n", time_diff);
	}
	MPI_Finalize();
	return EXIT_SUCCESS;
}