Initial data commit

Task/Fibonacci-sequence/OCaml/fibonacci-sequence-1.ocaml

@@ -0,0 +1,5 @@
+let fib n =
+  let rec aux i a b =
+    if i = 0 then a else aux (pred i) b (a + b)
+  in
+  aux n 0 1

Task/Fibonacci-sequence/OCaml/fibonacci-sequence-2.ocaml

@@ -0,0 +1,11 @@
+let fib_iter n =
+  if n < 2 then
+    n
+  else let fib_prev = ref 1
+  and fib = ref 1 in
+    for num = 2 to n - 1 do
+      let temp = !fib in
+        fib := !fib + !fib_prev;
+        fib_prev := temp
+    done;
+    !fib

Task/Fibonacci-sequence/OCaml/fibonacci-sequence-3.ocaml

@@ -0,0 +1,11 @@
+let rec fib_rec n =
+  if n < 2 then
+    n
+  else
+    fib_rec (n - 1) + fib_rec (n - 2)
+
+let rec fib = function
+    0 -> 0
+  | 1 -> 1
+  | n -> if n > 0 then fib (n-1) + fib (n-2)
+         else fib (n+2) - fib (n+1)

Task/Fibonacci-sequence/OCaml/fibonacci-sequence-4.ocaml

@@ -0,0 +1,19 @@
+open Num
+
+let fib =
+  let rec fib_aux f0 f1 = function
+    | 0 -> f0
+    | 1 -> f1
+    | n -> fib_aux f1 (f1 +/ f0) (n - 1)
+  in
+  fib_aux (num_of_int 0) (num_of_int 1)
+
+(* support for negatives *)
+let fib n =
+      if n < 0 && n mod 2 = 0 then minus_num (fib (abs n))
+      else fib (abs n)
+;;
+(* It can be called from the command line with an argument *)
+(* Result is send to standart output *)
+let n = int_of_string Sys.argv.(1) in
+print_endline (string_of_num (fib n))

Task/Fibonacci-sequence/OCaml/fibonacci-sequence-5.ocaml

@@ -0,0 +1,16 @@
+open Num
+
+let mul (a,b,c) (d,e,f) = let bxe = b*/e in
+  (a*/d +/ bxe, a*/e +/ b*/f, bxe +/ c*/f)
+
+let id = (Int 1, Int 0, Int 1)
+let rec pow a n =
+  if n=0 then id else
+    let b = pow a (n/2) in
+    if (n mod 2) = 0 then mul b b else mul a (mul b b)
+
+let fib n =
+  let (_,y,_) = (pow (Int 1, Int 1, Int 0) n) in
+  string_of_num y
+;;
+Printf.printf "fib %d = %s\n" 300 (fib 300)

Task/Fibonacci-sequence/OCaml/fibonacci-sequence-6.ocaml

@@ -0,0 +1,27 @@
+open List
+;;
+let rec bin n =
+  if n < 2 then [n mod 2 = 1]
+  else bin (n/2) @ [n mod 2 = 1]
+;;
+let cut = function
+  | [] -> []
+  | _ :: x -> x
+;;
+let multiply a b =
+  let ((p, q), (r, s)) = a in
+  let ((t, u), (v, w)) = b in
+  ((p*t+q*v, p*u+q*w), (r*t+s*v, r*u+s*w))
+;;
+let fib n =
+  let rec f p q r =
+    if length r = 1 then
+      if nth r 0 then (multiply p q, q)
+      else (p, q)
+    else
+      let (pp, qq) = f p q (cut r) in
+      let qqq = multiply qq qq in
+      if nth r 0 then (multiply pp qqq, qqq)
+      else (pp, qqq) in
+  f ((1L, 0L), (0L, 1L)) ((1L, 1L), (1L, 0L)) (bin n) |> fst |> fst |> snd
+;;