let iters1 max_iter xc yc =
  let rec aux count x y =
    if count = max_iter then max_iter else begin
      if x *. x  +. y *. y >= 4.0 then count else
      aux (count+1) (x *. x -. y *. y +. xc) (2.0 *. x *. y +. yc)
    end in
  aux 0 xc yc

type point = { x : float; y : float }
let iters2 max_iter pc =
  let {x=xc;y=yc} = pc in
  let rec aux count p =
    if count = max_iter then max_iter else begin
      let {x;y} = p in
      if x *. x  +. y *. y >= 4.0 then count else
        aux (count+1) {p with x = x *. x -. y *. y +. xc; y = 2.0 *. x *. y +. yc}
    end in
  aux 0 {x=0.;y=0.}

* use with "-pp camlp4of" *)
DEFINE UNBOX(e) = (e +. 0.)

let iters6 max_iter xc_boxed yc_boxed =
  let xc = UNBOX xc_boxed in
  let yc = UNBOX yc_boxed in
  let x = ref (UNBOX xc) in
  let y = ref (UNBOX yc) in
  let count = ref 0 in
  for i = 1 to max_iter do
    if !x *. !x  +. !y *. !y >= 4.0 then raise Exit;
    x := (!x *. !x -. !y *. !y +. xc);
    y := (2.0 *. !x *. !y +. yc);
  done; !count