Simd (#13262)

* mera added

* basic

* vector and matrix

* remarks

* fixing headers problem

* Update simd.md

- Updated the date
- Changed terms from **SIMD-enabled** to **SIMD-accelerated**
- Fixed any spelling errors
- Fixed code spacing
- Adjusted markdown structure
- Brought acro score from 77 to 92

* Update docs/standard/simd.md

Co-Authored-By: Tanner Gooding <[email protected]>

* Update docs/standard/simd.md

Co-Authored-By: Tanner Gooding <[email protected]>

* Apply suggestions from code review

Co-Authored-By: Tanner Gooding <[email protected]>

Co-authored-by: Andy De George <[email protected]>
Co-authored-by: Tanner Gooding <[email protected]>

docs/standard/simd.md

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+---
+title: SIMD in .NET
+description: This tutorial demonstrates how to use hardware SIMD operations in C# and .NET Core.
+author: FIVIL
+ms.author: tagoo
+ms.date: 03/31/2020
+ms.technology: dotnet-standard
+---
+
+# Overview
+
+SIMD (Single instruction, multiple data) provides hardware support for performing an operation on multiple pieces of data, in parallel, using a single instruction. In .NET, there's set of SIMD-accelerated types under the <xref:System.Numerics> namespace. SIMD operations can be parallelized at the hardware level. That increases the throughput of the vectorized computations, which are common in mathematical, scientific, and graphics apps.
+
+## .NET SIMD-accelerated types
+
+The .NET SIMD-accelerated types include the following types:
+
+- The <xref:System.Numerics.Vector2>, <xref:System.Numerics.Vector3>, and <xref:System.Numerics.Vector4> types, which represent vectors with 2, 3, and 4 <xref:System.Single> values.
+
+- Two matrix types, <xref:System.Numerics.Matrix3x2>, which represents a 3x2 matrix, and <xref:System.Numerics.Matrix4x4>, which represents a 4x4 matrix of <xref:System.Single> values.
+
+- The <xref:System.Numerics.Plane> type, which represents a plane in three-dimensional space using <xref:System.Single> values.
+
+- The <xref:System.Numerics.Quaternion> type, which represents a vector that is used to encode three-dimensional physical rotations using <xref:System.Single> values.
+
+- The <xref:System.Numerics.Vector%601> type, which represents a vector of a specified numeric type and provides a broad set of operators that benefit from SIMD support. The count of a <xref:System.Numerics.Vector%601> instance is fixed for the lifetime of an application, but its value <xref:System.Numerics.Vector%601.Count%2A?displayProperty=nameWithType> depends on the CPU of the machine running the code.
+
+  > [!NOTE]
+  > The <xref:System.Numerics.Vector%601> type is not included in the .NET Framework. You must install the [System.Numerics.Vectors](https://www.nuget.org/packages/System.Numerics.Vectors) NuGet package to get access to this type.
+  
+The SIMD-accelerated types are implemented in such a way that they can be used with non-SIMD-accelerated hardware or JIT compilers. To take advantage of SIMD instructions, your 64-bit apps must be run by the runtime that uses the **RyuJIT** compiler. A **RyuJIT** compiler is included in .NET Core and in .NET Framework 4.6 and later. SIMD support is only provided when targeting 64-bit processors.
+
+## How to use SIMD?
+
+Before executing custom SIMD algorithms, it's possible to check if the host machine supports SIMD by using <xref:System.Numerics.Vector.IsHardwareAccelerated?displayProperty=nameWithType>, which returns a <xref:System.Boolean>. This doesn't guarantee that SIMD-acceleration is enabled for a specific type, but is an indicator that it's supported by some types.
+
+## Simple Vectors
+
+The most primitive SIMD-accelerated types in .NET are <xref:System.Numerics.Vector2>, <xref:System.Numerics.Vector3>, and <xref:System.Numerics.Vector4> types, which represent vectors with 2, 3, and 4 <xref:System.Single> values. The example below uses <xref:System.Numerics.Vector2> to add two vectors.
+
+```csharp
+var v1 = new Vector2(0.1f, 0.2f);
+var v2 = new Vector2(1.1f, 2.2f);
+var vResutl = v1 + v2;
+```
+
+It's also possible to use .NET vectors to calculate other mathematical properties of vectors such as `Dot product`, `Transform`, `Clamp` and so on.
+
+```csharp
+var v1 = new Vector2(0.1f, 0.2f);
+var v2 = new Vector2(1.1f, 2.2f);
+var vResutl1 = Vector2.Dot(v1, v2);
+var vResutl2 = Vector2.Distance(v1, v2);
+var vResutl3 = Vector2.Clamp(v1, Vector2.Zero, Vector2.One);
+```
+
+## Matrix
+
+<xref:System.Numerics.Matrix3x2>, which represents a 3x2 matrix, and <xref:System.Numerics.Matrix4x4>, which represents a 4x4 matrix. Can be used for matrix-related calculations. The example below demonstrates multiplication of a matrix to its correspondent transpose matrix using SIMD.
+
+```csharp
+var m1 = new Matrix4x4(
+            1.1f, 1.2f, 1.3f, 1.4f,
+            2.1f, 2.2f, 3.3f, 4.4f,
+            3.1f, 3.2f, 3.3f, 3.4f,
+            4.1f, 4.2f, 4.3f, 4.4f);
+
+var m2 = Matrix4x4.Transpose(m1);
+var mResult = Matrix4x4.Multiply(m1, m2);
+```
+
+## Vector\<T>
+
+The <xref:System.Numerics.Vector%601> gives the ability to use longer vectors. The count of a <xref:System.Numerics.Vector%601> instance is fixed, but its value <xref:System.Numerics.Vector%601.Count%2A?displayProperty=nameWithType> depends on the CPU of the machine running the code.
+
+The example below demonstrates adding long arrays elements using <xref:System.Numerics.Vector%601>.
+
+```csharp
+double[] SimdVectorProd(double[] left, double[] right)
+{
+    var offset = Vector<double>.Count;
+    double[] result = new double[left.Length];
+    int i = 0;
+    for (i = 0; i < left.Length; i += offset)
+    {
+        var v1 = new Vector<double>(left, i);
+        var v2 = new Vector<double>(right, i);
+        (v1 * v2).CopyTo(result, i);
+    }
+
+    //remaining items
+    for (; i < left.Length; ++i)
+    {
+        result[i] = left[i] * right[i];
+    }
+
+    return result;
+}
+```
+
+## Remarks
+
+SIMD is more likely to remove one bottleneck and expose the next, for example memory throughput. In general the performance benefit of using SIMD varies depending on the specific scenario, and in some cases it can even perform worse than simpler non-SIMD equivalent code.