Sys.command "ocaml -version";;

type entier = {
    base : int;
    t : int array
}
;;

let quatre = {
    base = 10;
    t = [| 4 |]
}

let quarantedeux = {
    base = 10;
    t = [| 2; 4 |]
}

let n2006 = {
    base = 10;
    t = [| 6; 0; 0; 2 |]
}

let n2006 = {
    base = 10;
    t = [| 6; 0; 0; 2 |]
}

let n2006_2 = {
    base = 10;
    t = [| -4; 1; 0; 2 |]
}

let n2006_3 = {
    base = 10;
    t = [| 6; 0; 0; -8; 1 |]
}

let n2006_4 = {
    base = 10;
    t = [| -4; 1; 0; -8; 1 |]
}

let rec puissance x k = 
    match k with
    | 0 -> 1
    | 1 -> x
    | k when k mod 2 = 0 ->
        (* x^k = x^(k/2 * 2) = (x^2)^(k/2) *)
        puissance (x * x) (k / 2)
    | k ->
        (* x^k = x^((k-1)/2 * 2 + 1) = x * (x^2)^((k-1)/2) *)
        x * (puissance (x * x) ((k - 1) / 2))
;;

puissance 10 0;;
puissance 10 1;;
puissance 10 2;;
puissance 10 3;;
puissance 10 4;;

let valeur {base=b; t=t} =
    let v = ref 0 in
    let n = Array.length t in
    for k = 0 to n - 1 do
        v := !v + (t.(k) * (puissance b k))
    done;
    !v
;;

valeur quatre;;

valeur quarantedeux;;

valeur n2006;;
valeur n2006_2;;
valeur n2006_3;;
valeur n2006_4;;

let compare_entiers (a : entier) (b : entier) : int =
    let va = valeur a in
    let vb = valeur b in
    compare va vb
;;

compare_entiers quatre quarantedeux;;
compare_entiers quarantedeux quatre;;
compare_entiers quatre quatre;;
compare_entiers quarantedeux quarantedeux;;

compare_entiers n2006 quarantedeux;;