/* Second mystery function
 * Challenge: debug if necessary and find contract and invariant
 *
 * 15-122 Principles of Imperative Computation, Spring 2011
 * Frank Pfenning
 * Solution due to Prasanth Samasundar
 *
 * Warning: this still has a bug!  Find it first for extra credit!
 */

#use <conio>

/* pow(x,y) = x to the yth power */
int pow (int x, int y)
//@requires y >= 0;
{
  if (y == 0)
    return 1;
  else
    return x * pow(x, y-1);
}

/* integer cubic root */
int icbrt (int x)
//@requires 0 <= x;
//@ensures pow(\result-1, 3) < x && x <= pow(\result, 3);
{
  int i = 0;
  int j = 0;
  int k = 0;
  while (j < x)
    //@loop_invariant 0 <= i;
    //@loop_invariant k == 3*i*i;
    //@loop_invariant j == i*i*i;
    {
      j = j+k+3*i+1;
      k = k+6*i+3;
      i = i+1;
    }
  return i;
}