/**********************************************************************
 * FILE: mpi_pi_reduce.c
 * OTHER FILES: dboard.c
 * DESCRIPTION:  
 *   MPI pi Calculation Example - C Version 
 *   Collective Communication example:  
 *   This program calculates pi using a "dartboard" algorithm.  See
 *   Fox et al.(1988) Solving Problems on Concurrent Processors, vol.1
 *   page 207.  All processes contribute to the calculation, with the
 *   master averaging the values for pi. This version uses mpc_reduce to 
 *   collect results
 * AUTHOR: Blaise Barney. Adapted from Ros Leibensperger, Cornell Theory
 *   Center. Converted to MPI: George L. Gusciora, MHPCC (1/95) 
 * LAST REVISED: 06/13/13 Blaise Barney
**********************************************************************/
#include "mpi.h"
#include <stdio.h>
#include <stdlib.h>

void srandom (unsigned seed);
double dboard (int darts);
#define DARTS 50000     /* number of throws at dartboard */
#define ROUNDS 100      /* number of times "darts" is iterated */
#define MASTER 0        /* task ID of master task */

int main (int argc, char *argv[])
{
double	homepi,         /* value of pi calculated by current task */
	pisum,	        /* sum of tasks' pi values */
	pi,	        /* average of pi after "darts" is thrown */
	avepi;	        /* average pi value for all iterations */
int	taskid,	        /* task ID - also used as seed number */
	numtasks,       /* number of tasks */
	rc,             /* return code */
	i;
MPI_Status status;

/* Obtain number of tasks and task ID */
MPI_Init(&argc,&argv);
MPI_Comm_size(MPI_COMM_WORLD,&numtasks);
MPI_Comm_rank(MPI_COMM_WORLD,&taskid);
printf ("MPI task %d has started...\n", taskid);

/* Set seed for random number generator equal to task ID */
srandom (taskid);

avepi = 0;
for (i = 0; i < ROUNDS; i++) {
   /* All tasks calculate pi using dartboard algorithm */
   homepi = dboard(DARTS);

   /* Use MPI_Reduce to sum values of homepi across all tasks 
    * Master will store the accumulated value in pisum 
    * - homepi is the send buffer
    * - pisum is the receive buffer (used by the receiving task only)
    * - the size of the message is sizeof(double)
    * - MASTER is the task that will receive the result of the reduction
    *   operation
    * - MPI_SUM is a pre-defined reduction function (double-precision
    *   floating-point vector addition).  Must be declared extern.
    * - MPI_COMM_WORLD is the group of tasks that will participate.
    */

   rc = MPI_Reduce(&homepi, &pisum, 1, MPI_DOUBLE, MPI_SUM,
                   MASTER, MPI_COMM_WORLD);
   if (rc != MPI_SUCCESS)
      printf("%d: failure on mpc_reduce\n", taskid);

   /* Master computes average for this iteration and all iterations */
   if (taskid == MASTER) {
      pi = pisum/numtasks;
      avepi = ((avepi * i) + pi)/(i + 1); 
      printf("   After %8d throws, average value of pi = %10.8f\n",
              (DARTS * (i + 1)),avepi);
   }    
} 
if (taskid == MASTER) 
   printf ("\nReal value of PI: 3.1415926535897 \n");

MPI_Finalize();
return 0;
}



/**************************************************************************
* subroutine dboard
* DESCRIPTION:
*   Used in pi calculation example codes. 
*   See mpi_pi_send.c and mpi_pi_reduce.c  
*   Throw darts at board.  Done by generating random numbers 
*   between 0 and 1 and converting them to values for x and y 
*   coordinates and then testing to see if they "land" in 
*   the circle."  If so, score is incremented.  After throwing the 
*   specified number of darts, pi is calculated.  The computed value 
*   of pi is returned as the value of this function, dboard. 
*
*   Explanation of constants and variables used in this function:
*   darts       = number of throws at dartboard
*   score       = number of darts that hit circle
*   n           = index variable
*   r           = random number scaled between 0 and 1
*   x_coord     = x coordinate, between -1 and 1
*   x_sqr       = square of x coordinate
*   y_coord     = y coordinate, between -1 and 1
*   y_sqr       = square of y coordinate
*   pi          = computed value of pi
****************************************************************************/

double dboard(int darts)
{
#define sqr(x)	((x)*(x))
long random(void);
double x_coord, y_coord, pi, r; 
int score, n;
unsigned int cconst;  /* must be 4-bytes in size */
/*************************************************************************
 * The cconst variable must be 4 bytes. We check this and bail if it is
 * not the right size
 ************************************************************************/
if (sizeof(cconst) != 4) {
   printf("Wrong data size for cconst variable in dboard routine!\n");
   printf("See comments in source file. Quitting.\n");
   exit(1);
   }
   /* 2 bit shifted to MAX_RAND later used to scale random number between 0 and 1 */
   cconst = 2 << (31 - 1);
   score = 0;

   /* "throw darts at board" */
   for (n = 1; n <= darts; n++)  {
      /* generate random numbers for x and y coordinates */
      r = (double)random()/cconst;
      x_coord = (2.0 * r) - 1.0;
      r = (double)random()/cconst;
      y_coord = (2.0 * r) - 1.0;

      /* if dart lands in circle, increment score */
      if ((sqr(x_coord) + sqr(y_coord)) <= 1.0)
           score++;
      }

/* calculate pi */
pi = 4.0 * (double)score/(double)darts;
return(pi);
}