(*
   This uses Newton's general method to approximate a square root
   in Klein's wonderful world of integers.  The generalized method
   can be used to compute the roots of any (real-valued) function.
   If we know that we are computing a square root, an even simpler
   form of Newton's method works: guess = (n/guess + guess) / 2.
*)

function ABS( n : integer ) : integer     (* from the Klein library *)
  if n < 0 then
    -n
  else
    n

function f( x : integer, n : integer ) : integer
  x * x - n

function df( x : integer ) : integer
  2 * x

function newtonAux( guess   : integer, previous : integer,
           epsilon : integer, n        : integer ) : integer
  if epsilon < ABS(previous-guess) then
    newtonAux( guess - f(guess,n)/df(guess), guess, epsilon, n )
  else
    guess

function newton( guess : integer, epsilon : integer, n : integer ) : integer
  newtonAux( guess - f(guess,n)/df(guess), guess, epsilon, n )

function main(n : integer, epsilon : integer) : integer
  newton(n/2, epsilon, n)