Initial data commit

Task/Average-loop-length/F-Sharp/average-loop-length.fs

@@ -0,0 +1,49 @@
+open System
+
+let gamma z =
+    let lanczosCoefficients = [76.18009172947146;-86.50532032941677;24.01409824083091;-1.231739572450155;0.1208650973866179e-2;-0.5395239384953e-5]
+    let rec sumCoefficients acc i coefficients =
+        match coefficients with
+        | []   -> acc
+        | h::t -> sumCoefficients (acc + (h/i)) (i+1.0) t
+    let gamma = 5.0
+    let x = z - 1.0
+    Math.Pow(x + gamma + 0.5, x + 0.5) * Math.Exp( -(x + gamma + 0.5) ) * Math.Sqrt( 2.0 * Math.PI ) * sumCoefficients 1.000000000190015 (x + 1.0) lanczosCoefficients
+
+let factorial n = gamma ((float n) + 1.)
+
+let expected n =
+    seq {for i in 1 .. n do yield (factorial n) / System.Math.Pow((float n), (float i)) / (factorial (n - i)) }
+    |> Seq.sum
+
+let r = System.Random()
+
+let trial n =
+    let count = ref 0
+    let x = ref 1
+    let bits = ref 0
+    while (!bits &&& !x) = 0 do
+        count := !count + 1
+        bits := !bits ||| !x
+        x := 1 <<< r.Next(n)
+    !count
+
+
+let tested n times = (float (Seq.sum (seq { for i in 1 .. times do yield (trial n) }))) / (float times)
+
+let results = seq {
+    for n in 1 .. 20 do
+        let avg = tested n 1000000
+        let theory = expected n
+        yield n, avg, theory
+    }
+
+
+[<EntryPoint>]
+let main argv =
+    printfn " N     average   analytical   (error)"
+    printfn "------------------------------------"
+    results
+    |> Seq.iter (fun (n, avg, theory) ->
+        printfn "%2i    %2.6f    %2.6f    %+2.3f%%" n avg theory ((avg / theory - 1.) * 100.))
+    0