(* Exercice 1 *)

(* Question 1 : on doit trouver 1.02530490368186422 *)


let th x =
  failwith "à coder"
;;

th 1. ;; (* 0.761594155955764851 *)

(* Exercice 2 *)

failwith "à coder"

(* Exercice 3 *)

let rec s n = 
  if n = 0 then 0
  else n + s (n-1)
;;

let s n =
  failwith "à coder"
;;

(* Exercice 4 *)

let rec puiss x n =
  failwith "à coder"
;;

let puiss_term x n =
  failwith "à coder"
;;

puiss_term 2 10 ;; (* 1024 *)

let rec expo_rapide x n =
  failwith "à coder"
;;

expo_rapide 2 10 ;; (* 1024 *)

(* Exercice 5 *)

let rec pgcd u v =
  failwith "à coder"
;;

pgcd 189 231 ;; (* 21 *)

(* Exercice 6 *)

let rec nb_chiffres b n =
  failwith "à coder"
;;

nb_chiffres 10 999 ;; (* 3 *)

nb_chiffres 10 1000 ;; (* 4 *)

let rec mystere f n m =
  if n > m then 1.
  else f (float_of_int n) *. mystere f (n+1) m
;;

let rec fibo n =
  failwith "à coder"
;;

fibo 5 ;; (* 8 *)

(* #trace fibo ;; *)

fibo 5 ;;

(* #untrace fibo ;; *)

(* Exercice 9 : Algorithme de Floyd *)

let f x = (x*x + 92) mod 32069 ;;

(* Q1 *)
let rec itere f x0 n =
  failwith "à coder"
;;

(* Q2 *)
let rec itereBis f x0 n =
  failwith "à coder"
;;

(* Q3 *)
let floyd1 f x0 =
  failwith "à coder"
;;

floyd1 f 33 ;; (* 11326 *)

(* Q4 *)
let floyd2 f x0 =
  failwith "à coder"
;;

floyd2 f 33 ;; (* 320 *)

(* Q6 *)
let periode f x0 =
  failwith "à coder"
;;

periode f 33 ;; (* 8 *)

(* Q7 *)
let prePeriode f x0 =
  failwith "à coder"
;;

prePeriode f 33 ;; (* 313 *)

(* Q8 *)
let brent f x0 =
  failwith "à coder"
;;

brent f 33 ;; (* 511, 519 *)