open Printf

let a = float_of_string Sys.argv.(1)

let pi = 4.0 *. atan 1.0

let f x = sin((a*.x)/.(1.+.x))-.x**2.
let df x = sin((a*.x)/.(1.+.x))+. x*. cos((a*.x)/.(1.+.x))*.(a/.(x+.1.)**2.)-.2.*.x

let get_bound_plus k = (2.*.pi*.k)/.(a-.2.*.k*.pi)
let get_bound_moins k = (pi+.2.*.k*.pi)/.(a-.pi-.2.*.k*.pi)

let good_enough a b err =
  abs_float(a -. b) < err *. ((abs_float(a) +. abs_float(b))/. 2.)

let rec bissec g borneA borneB accuracy =
      if g borneA =0. then
          borneA
      else if g borneB =0. then
          borneB
      else if g borneA *. g borneB > 0. then
          -.1.
      else
          let mid = ((borneA +. borneB)/. 2.)in
          if good_enough borneA borneB accuracy then
              mid
          else if g borneA *. g mid <= 0. then
              bissec g borneA mid accuracy
          else
              bissec g mid borneB accuracy


let find_max accuracy step =
    let borne_pos =
        let x = get_bound_plus (ceil (step/.2.)) in
        if x = 0. then accuracy else x in
    let borne_neg = get_bound_moins (floor (step/.2.)) in
    bissec df borne_pos borne_neg accuracy

let main g b accuracy=
    if a<= pi then
        let tmp = bissec g (0.+.accuracy) 1. accuracy in
        printf "%.13g %.13g\n" tmp (sqrt(tmp))
    else
        let step = ref (0.) in
        let der_rac_one = ref (0.) in
        let der_rac_two = ref (find_max accuracy 0.) in
        while (!current_bound_neg < 1. && !current_bound_pos < 1.) do
            let tmp = bissec f !der_rac_one !der_rac_two accuracy in
            if tmp = -.1. then (
                step := !step+.1.;
                if ((int_of_float !step) mod 2 = 1) then
                    der_rac_one := (find_max accuracy !step)
                else
                    der_rac_two := (find_max accuracy !step)
            )
            else (
                printf "%.13g %.13g\n" tmp (sqrt(tmp));
                step := !step+.1.;
                if (int_of_float !step) mod 2 = 1 then
                    der_rac_one := (find_max accuracy !step)
                else
                    der_rac_two := (find_max accuracy !step)
            )
        done;
        let borne = min der_rac_one der_rac_two in
        (*min car si on sort de la boucle c'est qu'une borne depasse 1 *)
        let x = bissec g borne 1. accuracy in
        if x <> -1. then
            printf "%.13g %.13g\n" x (sqrt(x))

let ()=
    printf "%g\n" a;
    let tmp = bissec df (1e-14) (get_bound_moins (floor (1./.2.))) (1e-14) in
    printf "%g\n" tmp