/*  This program approximates Pi by picking a points in a sqaure and   *
 *  and determining how often they are also in an appropriate circle.  */

#include <stdio.h>

/* libraries for the pseudo-random number generator */
#include <stdlib.h>
#include <time.h>

/* function prototypes */

/* generate a point in the square and determine if it is in the circle
 * parameter max_rand:  the maximum size of a random number, as a double
 * return:  1 if the generated point is in the circle
            0 if not
*/
int gen_and_check_point (double max_rane);

/* perform simulation for many trials
 * parameter numTrials:  number of points to be considered
 * return:  number of generated points in circle
 */
int conduct_trials (int numTrials, double maxRandReal);

/* global variables */
int MaxRandDouble = (double) RAND_MAX;
int NumberOfTrials = 10000;

int main ()
{
   /* initialize pseudo-random number generator */
      printf ("This program approximates Pi by picking %d points in a square\n", 
            NumberOfTrials);
   printf ("and counting the number in an appropriate circle.\n\n");

   // initialize random number generator, based on the time of day
   srand (time ((time_t *) 0) );
   printf ("RAND_MAX:  %d\n", RAND_MAX);
   /* conduct simulation */
   double number_in = conduct_trials (NumberOfTrials, MaxRandDouble);
   double pi_approx = 4.0 * number_in / NumberOfTrials ;

   /* report results */
   printf ("The approximate value of Pi is %.5lf .\n", pi_approx);
   return 0;
}

/* full function bodies */
/* generate a point in the square and determine if it is in the circle
 * parameter maxReal:  the maximum size of a random number, as a double
 * return:  1 if the generated point is in the circle
            0 if not
*/
int gen_and_check_point (double max_rand)
{
  double x, y;
  x = 2.0 * rand() / max_rand;
  y = 2.0 * rand() / max_rand;
  return (x*x + y*y <= 2.0*2.0);
}

/* perform simulation for many trials
 * parameter numTrials:  number of points to be considered
 * return:  number of generated points in circle
 */
int conduct_trials (int numTrials, double maxRandReal)
{
  int i;
  int counter = 0;
   // pick points in first quadrant with coordinates between 0 and 1
   // determine how many are in the circle of radius 1
   for (i = 1; i <= NumberOfTrials; i++) 
     {
       if (gen_and_check_point (maxRandReal)) counter++;
     }

   return counter;
}