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

/* Numerical integration of the integral from 1 to 2 */
/* of the function 1/x: the exact value is ln 2      */
/* Integration ??? */
/* with various choices of the discretization step h */

int main()
  {
  float xnp1, xn, tn, h, ln2;
  int nb_steps, i;

  ln2 = log(2.0); /* exact value */

  nb_steps = 1;
  while (nb_steps <= 1073741824)
  {
    h = 1.0 / (double)(nb_steps);

    tn=1.0; xn=0.0;
    for (i=0; i<nb_steps; i++)
    {
      xnp1 = xn + h/tn;
      tn += h; xn = xnp1;
    }

    printf("Nb steps = %d, step size = %2.15f, error = %2.15f\n", nb_steps, h, ln2 - xn);
    if (nb_steps< 1073741824) nb_steps *=2; else nb_steps+=1;
  }

  return 0;
  }