/*
 * Monte Carlo calculations of the area of intersection of
 * a circle and an ellips
 * 
 * x = sin(t), y = cos(t);  x = sin(t + pi/4), y = cos(t)
 */

#include <math.h>

#include <gsl/gsl_rng.h>

double area(long m, gsl_rng *r)
{
   double x, y;       /* x,y coordinate, both between 0 and 1  */
   long count = 0L, n;

   for (n = 0; n < m; n++) 
   {
      /* generate random coordinates */
      x = 2*gsl_rng_uniform(r) - 1;
      y = 2*gsl_rng_uniform(r) - 1;

      /* count when a point lands in the area of interest */
      if ( (x*x + y*y < 1) && (x*x + y*y + sqrt(2.)*x*y < 0.5) )
      {
         count += 1;
      }
   }

   return(((double)count)/((double)m));

}