vault backup: 2023-09-25 13:42:45

Algo/Séminaire/Exercices seminaire.md

@@ -408,6 +408,23 @@ let power x n = match n with
 		| -1. -> if n mod 2 = 0 then 1. else -1.)
 		| _ -> (let rec p = function
 			| 0 -> 1.
-			| n -> x*.p(n-1) in p n)
+			| n -> (let res. = p x (n/2) in 
+					res *. res *. (if n mod 2 = 1 then x else 1.)
+			in p x n)
+;;
+
+(*Correction v3*)
+let power x n = match n with
+	| 0 -> (match x with
+		| 0. -> failwith "power 0^0 impossible"
+		| _ -> 1.)
+	| _ -> (match x with 
+		| 1. -> 1.
+		| 0. -> 0.
+		| -1. -> if n mod 2 = 0 then 1. else -1.)
+		| _ -> (let rec p x = function
+			| 0 -> 1.
+			| n -> p (x*x) (n/2) *. (if n mod 2 = 1 then x else 1.)
+			in p x n)
 ;;
 ```