#641 - Use SIMD instructions for Vector/Matrix calculations.

xFunc.Benchmark/Benchmarks/ProcessorBenchmark.cs

@@ -15,7 +15,7 @@ public void Setup()
 
     [Benchmark]
     public IExpression Parse()
-        => processor.Parse("(100.1 + 2(3sin(4cos(5tan(6ctg(10x)))) * 3) / (func(a, b, c) ^ 2)) - (cos(y) - 111.3) & (true | false impl true eq false) + (det({{1, 2}, {3, 4}}) * 10log(2, 3)) + re(3 + 2i) - im(2 - 9i) + (9 + 2i)");
+        => processor.Parse("(100.1 + 2 * (3 * sin(4 * cos(5 * tan(6 * ctg(10 * x)))) * 3) / (func(a, b, c) ^ 2)) - (cos(y) - 111.3) & (true | false impl true eq false) + (det({{1, 2}, {3, 4}}) * 10 * log(2, 3)) + re(3 + 2 * i) - im(2 - 9 * i) + (9 + 2 * i)");
 
     [Benchmark]
     public NumberResult Solve()

xFunc.Benchmark/Benchmarks/VectorBenchmark.cs

@@ -29,6 +29,10 @@ private Vector CreateVector()
         return new Vector(vector.ToImmutableArray());
     }
 
+    [Benchmark]
+    public object AbsVector()
+        => new Abs(vector1).Execute();
+
     [Benchmark]
     public object AddVectors()
         => new Add(vector1, vector2).Execute();

xFunc.Maths/Expressions/Matrices/VectorValue.cs

@@ -5,6 +5,7 @@
 using System.Diagnostics.CodeAnalysis;
 using System.Runtime.CompilerServices;
 using System.Text;
+using Simd = System.Numerics;
 
 namespace xFunc.Maths.Expressions.Matrices;
 
@@ -160,6 +161,27 @@ public NumberValue[] ToArray()
         return copy;
     }
 
+    /// <summary>
+    /// Computes the average of a sequence of numeric values.
+    /// </summary>
+    /// <returns>The average value.</returns>
+    public NumberValue Average()
+        => Sum() / Size;
+
+    /// <summary>
+    /// Computes the sum of a sequence of numeric values.
+    /// </summary>
+    /// <returns>The sum of the values in the vector.</returns>
+    public NumberValue Sum()
+    {
+        var sum = NumberValue.Zero;
+
+        for (var i = 0; i < Size; i++)
+            sum += array[i];
+
+        return sum;
+    }
+
     /// <summary>
     /// Gets the size of the current vector.
     /// </summary>
@@ -173,9 +195,36 @@ public int Size
     /// <returns>Return the absolute value of vector.</returns>
     public static object Abs(VectorValue vector)
     {
-        var sum = vector.array.Aggregate(NumberValue.Zero, (acc, value) => acc + value * value);
+        var size = Simd.Vector<double>.Count;
+
+        if (Simd.Vector.IsHardwareAccelerated && vector.Size >= size)
+        {
+            var span = Unsafe.As<double[]>(vector.array).AsSpan();
+
+            var v = Simd.Vector<double>.Zero;
+            var i = 0;
+
+            for (; i <= span.Length - size; i += size)
+            {
+                var chunkVector = new Simd.Vector<double>(span[i..]);
+                v += chunkVector * chunkVector;
+            }
+
+            var sum = Simd.Vector.Sum(v);
+
+            for (; i < span.Length; i++)
+                sum += span[i] * span[i];
+
+            return NumberValue.Sqrt(new NumberValue(sum));
+        }
+        else
+        {
+            var sum = NumberValue.Zero;
+            for (var i = 0; i < vector.Size; i++)
+                sum += vector[i] * vector[i];
 
-        return NumberValue.Sqrt(sum);
+            return NumberValue.Sqrt(sum);
+        }
     }
 
     /// <summary>

xFunc.Maths/Processor.cs

@@ -148,6 +148,12 @@ IExpression expression
             Lambda lambda
                 => new LambdaResult(lambda),
 
+            VectorValue vectorValue
+                => new VectorValueResult(vectorValue),
+
+            MatrixValue matrixValue
+                => new MatrixValueResult(matrixValue),
+
             _ => throw new InvalidResultException(),
         };
     }

xFunc.Maths/Results/MatrixValueResult.cs

@@ -0,0 +1,25 @@
+// Copyright (c) Dmytro Kyshchenko. All rights reserved.
+// Licensed under the MIT license. See LICENSE file in the project root for full license information.
+
+namespace xFunc.Maths.Results;
+
+/// <summary>
+/// Represents the matrix result.
+/// </summary>
+public class MatrixValueResult : IResult
+{
+    /// <summary>
+    /// Initializes a new instance of the <see cref="MatrixValueResult"/> class.
+    /// </summary>
+    /// <param name="value">The representation of result.</param>
+    public MatrixValueResult(MatrixValue value) => Result = value;
+
+    /// <inheritdoc />
+    public override string ToString() => Result.ToString();
+
+    /// <inheritdoc cref="IResult.Result" />
+    public MatrixValue Result { get; }
+
+    /// <inheritdoc />
+    object IResult.Result => Result;
+}

xFunc.Maths/Results/VectorValueResult.cs

@@ -0,0 +1,25 @@
+// Copyright (c) Dmytro Kyshchenko. All rights reserved.
+// Licensed under the MIT license. See LICENSE file in the project root for full license information.
+
+namespace xFunc.Maths.Results;
+
+/// <summary>
+/// Represents the vector result.
+/// </summary>
+public class VectorValueResult : IResult
+{
+    /// <summary>
+    /// Initializes a new instance of the <see cref="VectorValueResult"/> class.
+    /// </summary>
+    /// <param name="value">The representation of result.</param>
+    public VectorValueResult(VectorValue value) => Result = value;
+
+    /// <inheritdoc />
+    public override string ToString() => Result.ToString();
+
+    /// <inheritdoc cref="IResult.Result" />
+    public VectorValue Result { get; }
+
+    /// <inheritdoc />
+    object IResult.Result => Result;
+}