spectral-norm C# .NET #5 program

/* The Computer Language Benchmarks Game
   https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
 
   contributed by Jesper Meyer
*/

using System;
using System.Runtime.CompilerServices;
using System.Runtime.Intrinsics;
using System.Runtime.Intrinsics.X86;
using System.Threading.Tasks;

namespace SpectralNorm
{
    unsafe class Program
    {
        public static void Main(string[] args)
        {
            int n = 100;
            if (args.Length > 0) n = int.Parse(args[0]);

            fixed (double* u = new double[n])
            fixed (double* v = new double[n])
            {
                new Span<double>(u, n).Fill(1);
                for (var i = 0; i < 10; i++)
                {
                    mult_AtAv(u, v, n);
                    mult_AtAv(v, u, n);
                }

                var result = Math.Sqrt(dot(u, v, n) / dot(v, v, n));
                Console.WriteLine("{0:f9}", result);
            }
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        private static double A(int i, int j)
        {
            return (i + j) * (i + j + 1) / 2 + i + 1;
        }

        private static double dot(double* v, double* u, int n)
        {
            double sum = 0;
            for (var i = 0; i < n; i++)
                sum += v[i] * u[i];
            return sum;
        }

        [MethodImpl(MethodImplOptions.AggressiveOptimization)]
        private static void mult_Av(double* v, double* outv, int n)
        {
            Parallel.For(0, n, i =>
            {
                var sum = Vector128<double>.Zero;
                for (var j = 0; j < n; j += 2)
                {
                    var b = Sse2.LoadVector128(v + j);
                    var a = Vector128.Create(A(i, j), A(i, j + 1));
                    sum = Sse2.Add(sum, Sse2.Divide(b, a));
                }

                var add = Sse3.HorizontalAdd(sum, sum);
                var value = Unsafe.As<Vector128<double>, double>(ref add);
                Unsafe.WriteUnaligned(outv + i, value);
            });
        }

        [MethodImpl(MethodImplOptions.AggressiveOptimization)]
        private static void mult_Atv(double* v, double* outv, int n)
        {
            Parallel.For(0, n, i =>
            {
                var sum = Vector128<double>.Zero;
                for (var j = 0; j < n; j += 2)
                {
                    var b = Sse2.LoadVector128(v + j);
                    var a = Vector128.Create(A(j, i), A(j + 1, i));
                    sum = Sse2.Add(sum, Sse2.Divide(b, a));
                }

                var add = Sse3.HorizontalAdd(sum, sum);
                var value = Unsafe.As<Vector128<double>, double>(ref add);
                Unsafe.WriteUnaligned(outv + i, value);
            });
        }

        private static void mult_AtAv(double* v, double* outv, int n)
        {
            fixed (double* tmp = new double[n])
            {
                mult_Av(v, tmp, n);
                mult_Atv(tmp, outv, n);
            }
        }
    }
}
    

NOTES:
64-bit Ubuntu quad core
.NET SDK 9.0.100
Host Version: 9.0.0
Commit: 9d5a6a9aa4

<OutputType>Exe
<TargetFramework>net9.0
<ImplicitUsings>enable
<Nullable>enable
<AllowUnsafeBlocks>true
<ServerGarbageCollection>true
<ConcurrentGarbageCollection>true
<PublishAot>false



 Wed, 13 Nov 2024 23:14:51 GMT

MAKE:
cp spectralnorm.csharpcore-5.csharpcore Program.cs
cp Include/csharpcore/program.csproj .
mkdir obj
cp Include/csharpcore/project.assets.json ./obj
/opt/src/dotnet-sdk-9.0.100/dotnet build -c Release --use-current-runtime  	
  Determining projects to restore...
/home/dunham/all-benchmarksgame/benchmarksgame_i53330/spectralnorm/tmp/program.csproj : warning NU1900: Error occurred while getting package vulnerability data: Unable to load the service index for source https://api.nuget.org/v3/index.json.
  Restored /home/dunham/all-benchmarksgame/benchmarksgame_i53330/spectralnorm/tmp/program.csproj (in 6.05 sec).
/home/dunham/all-benchmarksgame/benchmarksgame_i53330/spectralnorm/tmp/program.csproj : warning NU1900: Error occurred while getting package vulnerability data: Unable to load the service index for source https://api.nuget.org/v3/index.json.
  program -> /home/dunham/all-benchmarksgame/benchmarksgame_i53330/spectralnorm/tmp/bin/Release/net9.0/linux-x64/program.dll

Build succeeded.

/home/dunham/all-benchmarksgame/benchmarksgame_i53330/spectralnorm/tmp/program.csproj : warning NU1900: Error occurred while getting package vulnerability data: Unable to load the service index for source https://api.nuget.org/v3/index.json.
/home/dunham/all-benchmarksgame/benchmarksgame_i53330/spectralnorm/tmp/program.csproj : warning NU1900: Error occurred while getting package vulnerability data: Unable to load the service index for source https://api.nuget.org/v3/index.json.
    2 Warning(s)
    0 Error(s)

Time Elapsed 00:00:11.08

13.01s to complete and log all make actions

COMMAND LINE:
 ./bin/Release/net9.0/linux-x64/program 5500

PROGRAM OUTPUT:
1.274224153