(* Works in SML/NJ on omega:  /opt/sml/bin/sml or at 
http://www.smlserver.org/smltojs_prompt/ *)

fun gcd2(a,b)=
  if a=b then a
         else if a>b then gcd2(a-b,b)
                     else gcd2(b-a,a);;

(* This version incorrectly uses /.  Caught by type inferencing

fun gcdExtHelp((u1,u2,u3),(v1,v2,v3))=
  if v3=0 then (u1,u2,u3)
           else
             let val q=u3/v3
             in gcdExtHelp((v1,v2,v3),(u1-v1*q,u2-v2*q,u3-v3*q))
             end;;

*)

(* This version correctly uses div.  Type inferencing makes everything an int.*)

fun gcdExtHelp((u1,u2,u3),(v1,v2,v3))=
  if v3=0 then (u1,u2,u3)
           else
             let val q=u3 div v3
             in gcdExtHelp((v1,v2,v3),(u1-v1*q,u2-v2*q,u3-v3*q))
             end;;

fun gcdExt(u,v)=gcdExtHelp((1,0,u),(0,1,v));;

fun both(a,b)=
  let val (u1,u2,u3)=gcdExt(a,b) in
    "gcd of " ^ Int.toString(a) ^ " and " ^
    Int.toString(b) ^ " is " ^ Int.toString(gcd2(a,b)) ^ "   " ^
    Int.toString(a) ^ "*" ^ Int.toString(u1) ^ " + " ^
    Int.toString(b) ^ "*" ^ Int.toString(u2) ^ " = " ^
    Int.toString(u3) ^ " = " ^ "gcd(" ^ Int.toString(a) ^ "," ^
    Int.toString(b) ^ ")" ^ "\n"
  end;;

print(both(1870,1045));;

print(both(210,231));;