let log2 x =
    (log x) /. (log 2.0);;

let ceil y =
    let rec iceil x y =
        if y <= 0.0 then
            x
        else
            iceil (x+1) (y -. 1.0) in
        iceil 0 y;;

let pow y =
    let rec ipow x y =
     match y with
        0 -> x |
        y -> ipow (x*2) (y-1) in
            ipow 1 y;;

let biject x y =
    let width = ceil (log2 (float_of_int x)) in
    let raised = pow y in
    raised + x;;