(* ---------------------------------------------------------------

   This program determines if its command-line argument, a number,
   is "excellent": when split on half n=ab, b*b - a*a = n.  For
   example, 48 is excellent, because 8**2 - 4**2 == 48.

   http://programmingpraxis.com/2015/03/24/excellent-numbers/

   --------------------------------------------------------------- *)

(* ----------------------------------------------
   functions from the Klein library
   ---------------------------------------------- *)

function MOD(m : integer, n : integer) : integer
  m - n*(m/n)

function EXP(m : integer, n : integer) : integer
  if n = 0
    then 1
    else m * EXP(m, n-1)

function ODD( n : integer ) : boolean
  if 0 < n 
    then (2 * (n/2)) < n
    else ODD(-n)

(* ----------------------------------------------
   helper functions
   ---------------------------------------------- *)

function length(n : integer) : integer
  if n < 10
    then 1
    else 1 + length(n / 10)

function a(n : integer) : integer     (* we could implement this with take *)
  n / EXP(10, length(n)/2)

function b(n : integer) : integer     (* we could implement this with drop *)
  MOD(n, EXP(10, length(n)/2))

function excellentDiff(a : integer, b : integer) : integer
  b*b - a*a

(* ----------------------------------------------
   primary functions
   ---------------------------------------------- *)

function isExcellentSwitch(n : integer, length : integer) : boolean
  if ODD(length)
    then false
    else n = excellentDiff(a(n), b(n))

function isExcellent(n : integer) : boolean
  isExcellentSwitch(n, length(n))

function main(n : integer) : boolean
  isExcellent(n)