/*** Thermodynamik und Statistik, SoSe 2002 ***/
/*** Blatt 2, Aufgabe 4                     ***/
/*** sphere.c                               ***/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>


int main(int argc, char *argv[])
{
  double x;                                        /* random coordinate x */
  double sum;                                         /* hits below curve */
  int d, t;                                              /* loop counters */
  int num_runs;                     /* number of generated random numbers */
  int dim, dim_max;                    /* dimension and maximal dimension */
  double length2;           /* length of dim-domensional vector (squared) */
  double volume, last_volume, second_last_volume;  

  num_runs = atoi(argv[1]);                            /* read parameters */
  dim_max = atoi(argv[2]);                             /* read parameters */
  dim = 2;
  second_last_volume = 1.0;                /* volume of unit-sphere in 1d */
  last_volume = 2.0;                

  for(dim=2; dim<=dim_max; dim++)
  {
    sum = 0.0;
    for(t=0; t<num_runs; t++)
    {
      length2 = 0.0;
      for(d=0; d<dim; d++)        /* generate random vector in [-1,1]^dim */
      {
        x = 2*drand48()-1;            /* generate random number in [-1,1] */ 
	length2 += x*x;                               /* calculate length */
      }
      if(length2 < 1)                         /* is point within sphere ? */
	sum += 1;          
    }
    volume = pow(2, dim)*sum/num_runs;                /* calculate volume */
    if(dim > 2)
      printf("%d %f\n", dim, second_last_volume/volume);  /* print result */
    second_last_volume = last_volume;
    last_volume = volume;
  }

  return(0);
}