let curry f = function a-> (function b -> f (a,b));;
let decurry f = function (a,b) -> f a b;;

let u n = 
  let u0 = ref 1.0 in
  for i = 0 to n do
    u0 := sin !u0
  done;
  !u0
;;

let u = ref 1. and n = ref 0 in
  while !u > 0.0001 do
    u := sin !u;
    n := !n + 1
  done;
  !n;;

let factoriter n =
  let k = ref 1 in
  for i = 2 to n do
    k := !k * i
  done;
  !k;;

let puissance x n = let p = ref 1 in 
  for i = 1 to n do
    p := !p * x
  done;
  !p;;

let sum m n = let s = ref 0. and c = ref 0. in
  for i = m to n do
    c := !c +. 1.;
    if i >= m then
      s := !s +. 1. /. !c
    done;
  !s
;;

let pgcd a b = let c = ref a and d = ref b and e = ref 0 in
  while !c mod !d <> 0 do
    e := !c;
    c := !d;
    d := !e mod !d
  done;
  !d;;

let valuation p n = let v = ref 0 and aux = ref n in 
  while !aux mod p = 0 do 
    v := !v +1;
    aux := !aux / p
  done;
  !v;;

let maximum a = let max = ref a.(0) in 
  for i = 0 to Array.length(a)-1 do 
    if a.(i) > !max then
      max := a.(i)
  done;
  !max;;

let mirroir t = 
  let n = Array.length t in 
    let u = Array.make n t.(0) in
      for i = 0 to n-1 do
        u.(i) <- t.(n-1-i)
      done;
    u;;

let appartenance t x= let a = ref 0 and b = ref false in
    while t.(!a) <> x && !a< Array.length t do 
      a := !a +1;
    done;
    if !a > 0 then
      b := true;
    !b
    ;;

let appartprof t x = let n = Array.length t and i = ref 0 in
    while !i<n && x <> t.(!i) do
      i := !i+1
    done;
    !i<n;;

let appartsenti t x = let n = Array.length t and i = ref 0 in 
    let aux = t.(n-1) in 
      t.(n-1) <- x;
      while x<> t.(!i) do 
        i := !i+1
      done;
      (!i<(n-1) )||(x=aux );;

let permut t = let n = Array.length t in 
  let b = ref true in
    for i = 0 to n-1 do 
      if t.(i)>=n || t.(0)<0 then
        b := false;
      for j=i+1 to n-1 do 
        if t.(i)=t.(j) then
          b := false
        done;
      done;
      !b;;

let f x = x*x;;
let u u0 n = let un = ref u0 in 
  for k= 0 to n do 
    un := f !un
  done;
  !un;;

let rec suite_rec u0 n = 
  if n= 0 then
    u0
  else f (suite_rec u0 (n-1));;

let factoiter n = let u = ref 1 in
  for k=1 to n do 
    u := !u * k
  done;
  !u;;

let rec factorecu n = match n with
| 0 -> 1
| _ -> n*factorecu (n-1);;

let rec puissancerecu a n = match n with
| 0 -> 1
| _ -> a* puissancerecu a (n-1);;

let puissanceiter a n = let b = ref 1 in 
for k=1 to n do 
  b := !b * a
done;
!b;;


let rec carrerecu b = match b with
| 0 -> 0
| _ -> carrerecu (b-1) + 2*b -1

let rec sumpq p q = match q with
| 0 -> p
| _ -> sumpq (p+1) (q-1);;

let rec productpq p q = match q with
| 0 -> 0
| _-> (productpq p (q-1))+q;;

let rec minimumtab t =
  let n = Array.length t in
    if n=1 then
      t.(0)
    else
      let m = minimumtab (Array.sub t 1 (n-1)) in 
        if t.(0)<m then
          t.(0)
        else
          m;;

let rec minimumtabindice t =
  let n = Array.length t in
    if n=1 then
      0
    else
      let m = 1+minimumtabindice (Array.sub t 1 (n-1)) in 
        if t.(0)<t.(m) then
          0
        else
          m;;

let rec min2_aux t i = 
  let n = Array.length t in 
    if i =n-1 then
      i
    else
      let m = min2_aux t (i+1) in 
        if t.(i)<t.(m) then
          i
        else
          m;;
let min2 t = min2_aux t 0;;

let rec minmax_aux t i = 
  let n = Array.length t in 
    if i =n-1 then
      (i,i)
    else
      let (m,o) = minmax_aux t (i+1) in 
        match i with
        | i when t.(i)<t.(m) -> (i,o)
        | i when t.(i)>t.(o) -> (m,i)
        | _ -> (m,o);;

let minmax t = minmax_aux t 0;;

let rec productegypt p q = match q with
| 0 -> 0
| q when q mod 2 = 0 -> productegypt (2*p) (q/2)
| _ ->p+ productegypt p (q-1);;

let rec divisioneucli1 a b =
  if a<b then(0,a)
  else
    let q,r= divisioneucli1(a-b) b in 
    (q+1,r);;

let rec pgcd a b =
  if b = 0 then a
  else pgcd b (a mod b);;

let rec pgcdprof a b = 
  if a = b then a
  else let r = snd (divisioneucli1 a b) in 
    pgcdprof b r;;

let rec pgcd2prof a b = match (a,b) with
| (a,0) -> a
| (a,b) when a<b -> pgcd2prof b a
| _ -> pgcd2prof (a-b) b;;

let rec fib n =
  if n <= 0 then 0.
  else if n = 1 then 1.
  else fib (n-1) +. fib (n-2);;

let rec coeffbinom n p = match (p,n) with
| (0,n) -> 1
| (p,n) when p = n-> 1
| _ -> (coeffbinom (n-1) p) + (coeffbinom (n-1) (p-1));;

let rec coeffbinom2duprof p n = match (p,n) with
| (0,n) -> 1
| _ -> (n* coeffbinom2duprof (p-1) (n-1))/(p);;