# spectral-norm F# .NET Core #2 program

## source code

```﻿// The Computer Language Benchmarks Game
// https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
//
// Based on C# version by Isaac Gouy, The Anh Tran, Alan McGovern
// Contributed by Don Syme

open System

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);
h.Set() |> ignore;
h.Dispose();

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 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 n = try int <| args.[0] with _ -> 2500

System.Console.WriteLine("{0:f9}", RunGame n);
0

```

## notes, command-line, and program output

```NOTES:
.NET Core SDK   2.2.100
Commit:    1249f08fed
Host 2.2.0
<ServerGarbageCollection>true
<ConcurrentGarbageCollection>true

Thu, 06 Dec 2018 02:25:55 GMT

MAKE:
cp spectralnorm.fsharpcore-2.fsharpcore Program.fs
cp Include/fsharpcore/tmp.fsproj .
cp Include/fsharpcore/runtimeconfig.template.json .
mkdir obj
cp Include/fsharpcore/project.assets.json ./obj
cp Include/fsharpcore/tmp.fsproj.nuget.g.props ./obj
cp Include/fsharpcore/tmp.fsproj.nuget.g.targets ./obj
/usr/bin/dotnet build -c Release --no-restore
Microsoft (R) Build Engine version 15.9.20+g88f5fadfbe for .NET Core

Build succeeded.
0 Warning(s)
0 Error(s)

Time Elapsed 00:00:09.98

13.29s to complete and log all make actions

COMMAND LINE:
/usr/bin/dotnet ./bin/Release/netcoreapp2.2/tmp.dll 5500

PROGRAM OUTPUT:
1.274224153
```