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

#define f(x) ((float)(4.0/(1.0+x*x)))
#define pi ((float)(4.0*atan(1.0)))

main(int argc, char * argv[])
{

  /* This simple program approximates pi by computing pi = integral
   * from 0 to 1 of 4/(1+x*x)dx which is approximated by sum 
   * from k=1 to N of 4 / ((1 + (k-1/2)**2 ).  The only input data 
   * required is N.                                       
   */

  /* Each process is given a chunk of the interval to do. */

  float err, sum, w;
  int i, N;


  printf ("Enter number of approximation intervals:(0 to exit)\n");
  scanf("%d",&N);
  
  while (N > 0) 
  {
      /* calcualte step width, initialize sum */
      w = 1.0/(float)N;
      sum = 0.0;

      for (i = 0; i < N; i++)
	  sum = sum + f(((float)i-0.5)*w);

      sum = sum * w;
      err = sum - pi;
      printf("sum = %7.5f, err = %10e\n",sum, err);

      printf ("Enter number of approximation intervals:(0 to exit)\n");
      scanf("%d",&N);
  
  }   /* while (N > 0) */
}