///////Program.fs
open System
open System.Threading
open System.Diagnostics
type BarrierHandle(threads:int) = 
    let mutable current = threads
    let mutable handle = new ManualResetEvent(false)

    member x.WaitOne() =
        let h = handle
        if Interlocked.Decrement(&current) > 0 then 
            h.WaitOne() |> ignore;
        else
            handle <- new ManualResetEvent(false);
            Interlocked.Exchange(&current, threads) |> ignore;
            h.Set() |> ignore;
            h.Close();

let Approximate(u:double[], v:double[], tmp:double[], rbegin, rend, barrier: BarrierHandle) =

    let mutable vBv = 0.0
    let mutable vv = 0.0

    // return element i,j of infinite matrix A 
    let A i j = 1.0 / float((i + j) * (i + j + 1) / 2 + i + 1)

    // multiply vector v by matrix A 
    let multiplyAv(v:double[], Av:double[]) =
        for i = rbegin to rend - 1 do 
            let mutable sum = 0.0;
            for j = 0 to v.Length - 1 do 
                sum <- sum + A i j * v.[j];
            Av.[i] <- sum

    // multiply vector v by matrix A transposed 
    let multiplyAtv(v:double[], atv:double[]) =
        for i = rbegin to rend - 1 do
            let mutable sum = 0.0
            for j = 0 to v.Length - 1 do 
                sum <- sum + A j i * v.[j];
            atv.[i] <- sum;

    // multiply vector v by matrix A and then by matrix A transposed 
    let multiplyatAv(v:double[], tmp:double[], atAv:double[]) =
        multiplyAv(v, tmp);
        barrier.WaitOne();

        multiplyAtv(tmp, atAv);
        barrier.WaitOne();

    for i = 0 to 9 do 
        multiplyatAv(u, tmp, v);
        multiplyatAv(v, tmp, u);

    for i = rbegin to rend - 1 do
        vBv <- vBv + u.[i] * v.[i];
        vv <- vv + v.[i] * v.[i];

    (vBv, vv)


let RunGame n = 
    // create unit vector
    let u = Array.create n 1.0
    let tmp = Array.zeroCreate n 
    let v = Array.zeroCreate n 

    let nthread = Environment.ProcessorCount;

    let barrier = new BarrierHandle(nthread);
        // create thread and hand out tasks
    let chunk = n / nthread;
        // objects contain result of each thread
    let aps = 
        Async.Parallel 
          [ for i in 0 .. nthread - 1 do
                let r1 = i * chunk;
                let r2 = if (i < (nthread - 1)) then r1 + chunk else n
                yield async { return Approximate(u, v, tmp, r1, r2, barrier) } ]
         |> Async.RunSynchronously

    let vBv = aps |> Array.sumBy fst
    let vv = aps |> Array.sumBy snd

    Math.Sqrt(vBv / vv);

[<EntryPoint>]
let main args =
    let sw = new Stopwatch ()
    sw.Start ()
    let n = try int <| args.[0] with _ -> 2500
    System.Console.WriteLine("{0:f9}", RunGame n);
    sw.Stop()
    printfn "Took %d Ticks." sw.ElapsedTicks
    Console.ReadKey(true) |> ignore
    0


///////When run by Mono 2.10.2, this error comes up. 
(*
Unhandled Exception: System.TypeInitializationException: An exception was thrown
 by the type initializer for System.Diagnostics.Stopwatch ---> System.InvalidPro
gramException: Invalid IL code in System.Diagnostics.Stopwatch:.cctor (): method
 body is empty.

  --- End of inner exception stack trace ---
  at Program.main (System.String[] args) [0x00000] in <filename unknown>:0

*)
//////////The program was compiled in Visual Studio for .NET 4.0 (not Client Profile).
//////////All .NET assemblies the project uses have been copied next to the executable.