double sqrt( double arg ) { 
   sqrt  
  require ( arg >= 0 );
  double r=arg, x=1, eps=0.0001;
  while( fabs(r - x) > eps ) {
     r=x; x=r-((r*r-arg)/(2*r));
     }
  promise ( r - arg * arg <= eps );
  return r;
  }