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