Sys.command "ocaml -version";;
print_endline Sys.ocaml_version;;

let print f =
    let r = Printf.printf f in
    flush_all();
    r
;;

let premiercalcul (rho : float) (n : int) =
    let somme = ref 0. in
    let unmoinsunsurrho = 1. -. (1. /. rho) in
    let terme = ref 1. in
    for _ = 0 to n do  (* terme = (1-1/rho)^j pour j = _ *)
        somme := !somme +. !terme; (* somme = sum_k=0^j terme_k *)
        terme := !terme *. unmoinsunsurrho; (* conserve l'invariant de boucle *)
    done;
    !somme
;;

let rho = 2. ** 20.;;

1. -. 1. /. rho;;

for n = 0 to 10 do
    print "\nS_%i \t= %g" n (premiercalcul rho n);
done;

for n = 1000 to 1010 do
    print "\nS_%i \t= %g" n (premiercalcul rho n);
done;

let deuxiemecalcul (rho : float) (k : int) (n : int) =
    let somme = ref 0. in
    let unmoinsunsurrho = 1. -. (1. /. rho) in
    let terme = ref 1. in
    for _ = 0 to n do
        for _ = 0 to k-1 do
            somme := !somme +. !terme;
            terme := !terme *. unmoinsunsurrho;
        done;
        terme := !terme *. unmoinsunsurrho;
    done;
    !somme
;;

let valeurs_k = [|1; 10; 100; 1000; 10000|] in

for i = 0 to (Array.length valeurs_k) - 1 do
    let k = valeurs_k.(i) in
    print "\n\nFor K = %i ..." k;
    for n = 0 to 10 do
        print "\nS_%i \t= %g" n (deuxiemecalcul rho k n);
    done;
done;

let valeurs_n = [|100; 1000; 10000; 100000|] in
let valeurs_k = [|1; 10; 100; 1000; 10000|] in

for i = 0 to (Array.length valeurs_k) - 1 do
    let k = valeurs_k.(i) in
    print "\n\nFor K = %i ..." k;
    for j = 0 to (Array.length valeurs_n) - 1 do
        let n = valeurs_n.(j) in
        print "\nS_%i \t= %g" n (deuxiemecalcul rho k n);
    done;
done;