Data commit

Task/Fibonacci-sequence/F-Sharp/fibonacci-sequence-1.fs

@@ -0,0 +1,9 @@
+let fibonacci n : bigint =
+  let rec f a b n =
+    match n with
+    | 0 -> a
+    | 1 -> b
+    | n -> (f b (a + b) (n - 1))
+  f (bigint 0) (bigint 1) n
+> fibonacci 100;;
+val it : bigint = 354224848179261915075I

Task/Fibonacci-sequence/F-Sharp/fibonacci-sequence-2.fs

@@ -0,0 +1,2 @@
+let rec fib = seq { yield! [0;1];
+                    for (a,b) in Seq.zip fib (Seq.skip 1 fib) -> a+b}

Task/Fibonacci-sequence/F-Sharp/fibonacci-sequence-3.fs

@@ -0,0 +1,2 @@
+let fibonacci = Seq.unfold (fun (x, y) -> Some(x, (y, x + y))) (0I,1I)
+fibonacci |> Seq.nth 10000

Task/Fibonacci-sequence/F-Sharp/fibonacci-sequence-4.fs

@@ -0,0 +1,43 @@
+open System
+open System.Diagnostics
+open System.Numerics
+
+/// Finds the highest power of two which is less than or equal to a given input.
+let inline prevPowTwo (x : int) =
+    let mutable n = x
+    n <- n - 1
+    n <- n ||| (n >>> 1)
+    n <- n ||| (n >>> 2)
+    n <- n ||| (n >>> 4)
+    n <- n ||| (n >>> 8)
+    n <- n ||| (n >>> 16)
+    n <- n + 1
+    match x with
+    | x when x = n -> x
+    | _ -> n/2
+
+/// Evaluates the nth Fibonacci number using matrix arithmetic and
+/// exponentiation by squaring.
+let crazyFib (n : int) =
+    let powTwo = prevPowTwo n
+
+    /// Applies 2n rule repeatedly until another application of the rule would
+    /// go over the target value (or the target value has been reached).
+    let rec iter1 i q r s =
+        match i with
+        | i when i < powTwo ->
+            iter1 (i*2) (q*q + r*r) (r * (q+s)) (r*r + s*s)
+        | _ -> i, q, r, s
+
+    /// Applies n+1 rule until the target value is reached.
+    let rec iter2 (i, q, r, s) =
+        match i with
+        | i when i < n ->
+            iter2 ((i+1), (q+r), q, r)
+        | _ -> q
+
+    match n with
+    | 0 -> 1I
+    | _ ->
+        iter1 1 1I 1I 0I
+        |> iter2