SIMD Vectorization

Decision Gate

1. Check Span<T> and MemoryExtensions first. If the operation can be expressed using built-in Span<T> methods (e.g., Contains, IndexOf, CopyTo, SequenceEqual) or MemoryExtensions, use them — no additional dependency is needed and the runtime already vectorizes many of these internally.
2. Check for TensorPrimitives next. If one or more TensorPrimitives methods cover the operation → use them. If the .csproj does NOT already reference System.Numerics.Tensors, add the package, for example: <PackageReference Include="System.Numerics.Tensors" /> (or use the versioning approach already used by your solution). Then replace the scalar loop with TP calls and stop. See the full API table below. Compose multiple TP calls when needed (e.g., finding both min and max → TensorPrimitives.Min(span) + TensorPrimitives.Max(span) as two calls). Do NOT write manual Vector128 code for operations TP already handles.
3. Scalar loop over contiguous array/span of byte, sbyte, short, ushort, int, uint, long, ulong, nint, nuint, float, double (and char via reinterpretation as ushort)? → Implement with explicit Vector128<T> / Vector256<T> / Vector512<T> intrinsics using the patterns below.
4. No contiguous numeric arrays to process (dictionary lookups, tree traversals, linked lists, state machines, string formatting, small collections, enum comparisons, recursive algorithms, decimal arithmetic)? → Report [NO SIMD OPPORTUNITY] and write a full paragraph explaining WHY, referencing the specific code characteristics that prevent vectorization (e.g., "State machines require sequential branching on enum values — there are no contiguous numeric arrays to process in parallel, and each transition depends on the previous state"). This explanation is graded.

TensorPrimitives API Reference

TensorPrimitives APIs are generic and work for any primitive type that satisfies the method's generic constraints — not just float/double. For example, Sum requires IAdditionOperators<T,T,T> + IAdditiveIdentity<T,T> and works for all primitive numeric types, while CosineSimilarity requires IRootFunctions<T> and only works for float/double. If the project doesn't already reference System.Numerics.Tensors, add it to the .csproj. Replace the entire manual loop with one or more TensorPrimitives calls as needed (prefer a single call when possible):

Reductions (span → scalar)

Operation	API
Sum	TensorPrimitives.Sum(span)
Sum of squares	TensorPrimitives.SumOfSquares(span)
Sum of magnitudes (L1 norm)	TensorPrimitives.SumOfMagnitudes(span)
L2 norm	TensorPrimitives.Norm(span)
Product of all elements	TensorPrimitives.Product(span)
Min value	TensorPrimitives.Min(span)
Max value	TensorPrimitives.Max(span)
Index of max	TensorPrimitives.IndexOfMax(span)
Index of min	TensorPrimitives.IndexOfMin(span)
Dot product	TensorPrimitives.Dot(a, b)
Cosine similarity	TensorPrimitives.CosineSimilarity(a, b)
Euclidean distance	TensorPrimitives.Distance(a, b)

Element-wise transforms (span → span)

Operation	API
Negate	TensorPrimitives.Negate(src, dst)
Abs	TensorPrimitives.Abs(src, dst)
Sqrt	TensorPrimitives.Sqrt(src, dst)
Exp	TensorPrimitives.Exp(src, dst)
Log	TensorPrimitives.Log(src, dst)
Log2	TensorPrimitives.Log2(src, dst)
Tanh	TensorPrimitives.Tanh(src, dst)
Sigmoid	TensorPrimitives.Sigmoid(src, dst)
SoftMax	TensorPrimitives.SoftMax(src, dst)
Sinh	TensorPrimitives.Sinh(src, dst)
Cosh	TensorPrimitives.Cosh(src, dst)
Round	TensorPrimitives.Round(src, dst)
Floor	TensorPrimitives.Floor(src, dst)
Ceiling	TensorPrimitives.Ceiling(src, dst)
CopySign	TensorPrimitives.CopySign(src, sign, dst)
Pow	TensorPrimitives.Pow(bases, exponents, dst)

Two-span operations (a, b → dst)

Operation	API
Add	TensorPrimitives.Add(a, b, dst)
Subtract	TensorPrimitives.Subtract(a, b, dst)
Multiply	TensorPrimitives.Multiply(a, b, dst)
Divide	TensorPrimitives.Divide(a, b, dst)
Element-wise Min	TensorPrimitives.Min(a, b, dst)
Element-wise Max	TensorPrimitives.Max(a, b, dst)

Three-span fused operations

Operation	API
(x+y)*z	TensorPrimitives.AddMultiply(x, y, z, dst)
x*y+z	TensorPrimitives.MultiplyAdd(x, y, z, dst)
fma(x,y,z)	TensorPrimitives.FusedMultiplyAdd(x, y, z, dst)

AddMultiply and MultiplyAdd are distinct — they optimize differently depending on whether the dependency chain flows from the addend or the multiplier. FusedMultiplyAdd is the IEEE 754 fused form of (x*y)+z with a single rounding step.

Manual SIMD with Vector128/Vector256/Vector512

Use this when TensorPrimitives doesn't have a single API for the operation. This is required for byte-level operations, character class counting, range validation, bitwise bulk ops, cross-type conversions, and custom patterns.

Required imports

using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using System.Runtime.Intrinsics;

Prefer cross-platform APIs (System.Runtime.Intrinsics). Only use platform-specific intrinsics (System.Runtime.Intrinsics.X86, .Arm) when there is a significant performance advantage that justifies the increased code complexity of maintaining separate code paths.

Three-tier dispatch pattern

Always include all three tiers. Use if/else if so that small inputs hit only one branch before reaching the scalar fallback — a fallthrough pattern (sequential ifs) pessimizes the scalar case by requiring up to three not-taken branches that may mispredict. The IsHardwareAccelerated checks are JIT-time constants, so dead paths are eliminated at compile time:

ref var src = ref MemoryMarshal.GetReference(span);
uint i = 0;
uint length = (uint)span.Length;

if (Vector512.IsHardwareAccelerated && Vector512<T>.IsSupported)
{
    uint vec512Count = (uint)Vector512<T>.Count;
    while (i + vec512Count <= length)
    {
        var vec = Vector512.LoadUnsafe(ref src, i);
        // ... process vec ...
        i += vec512Count;
    }
}
else if (Vector256.IsHardwareAccelerated && Vector256<T>.IsSupported)
{
    uint vec256Count = (uint)Vector256<T>.Count;
    while (i + vec256Count <= length)
    {
        var vec = Vector256.LoadUnsafe(ref src, i);
        // ... process vec ...
        i += vec256Count;
    }
}
else if (Vector128.IsHardwareAccelerated && Vector128<T>.IsSupported)
{
    uint vec128Count = (uint)Vector128<T>.Count;
    while (i + vec128Count <= length)
    {
        var vec = Vector128.LoadUnsafe(ref src, i);
        // ... process vec ...
        i += vec128Count;
    }
}
// Scalar fallback for remaining elements (and the only loop hit for small inputs)
for (; i < length; i++)
{
    // ... scalar processing ...
}

Core SIMD operations

• Load/Store: Vector128.LoadUnsafe(ref src, offset) / .StoreUnsafe(ref dst, offset)
• Arithmetic: +, -, *, / operators on vector types
• Multiply-add (approximate): Vector128.MultiplyAddEstimate(a, b, c) — performs a multiply-add with implementation-defined approximation; not guaranteed to be a strict IEEE fused multiply-add. For precise fused semantics, use Vector128.FusedMultiplyAdd(a, b, c).
• Comparison: Vector128.Equals, .LessThan, .GreaterThan — returns mask vector
• Mask ops: Vector128.All(mask), .Any(mask), .None(mask), .Count(mask), .CountWhereAllBitsSet(mask)
• Horizontal: Vector128.Sum(vec) for reduction; .Min(a,b), .Max(a,b) element-wise
• Broadcast: Vector128.Create(scalarValue) — fill all lanes with one value
• Bitwise: &, |, ^, ~ operators; Vector128.ShiftLeft, .ShiftRightLogical
• Widening: Vector128.WidenLower(v) / .WidenUpper(v) for byte→short, short→int
• Narrowing: Vector128.Narrow(lower, upper) for int→short, short→byte
• Type convert: Vector128.ConvertToSingle(intVec), .ConvertToInt32(floatVec)
• Shuffle: Vector128.Shuffle(vec, indices) — lookup table / permutation
• Conditional: Vector128.ConditionalSelect(mask, trueVec, falseVec)

Pattern: Unsigned range check (byte-range validation)

For checking if all bytes are in range [lo, hi]:

var vLo = Vector128.Create((byte)lo);
var vRange = Vector128.Create((byte)(hi - lo));
// (b - lo) > range means out-of-range (unsigned wraparound catches b < lo)
var shifted = Vector128.Subtract(vec, vLo);
var inRange = Vector128.LessThanOrEqual(shifted, vRange);
if (!Vector128.All(inRange.AsByte())) return false; // for validation
// or: count += Vector128.CountWhereAllBitsSet(inRange); // for counting

Pattern: Nibble-lookup counting (character classes, popcount, etc.)

For counting bytes matching a sparse set of values (vowels, digits, punctuation, bit counts) — build two 16-byte lookup tables indexed by low/high nibble:

var lo_lut = Vector128.Create(/* 16 bytes: bit pattern for low nibble match */);
var hi_lut = Vector128.Create(/* 16 bytes: bit pattern for high nibble match */);
var nibbleMask = Vector128.Create((byte)0x0F);

var lo_nibble = vec & nibbleMask;
var hi_nibble = Vector128.ShiftRightLogical(vec.AsUInt16(), 4).AsByte() & nibbleMask;
var lo_match = Vector128.Shuffle(lo_lut, lo_nibble);
var hi_match = Vector128.Shuffle(hi_lut, hi_nibble);
var match = lo_match & hi_match;
count += Vector128.CountWhereAllBitsSet(~Vector128.Equals(match, Vector128<byte>.Zero));

This same technique works for popcount (LUT = {0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4}). For simpler cases (single byte value, adjacent range), use Equals + Count or range check instead.

Pattern: Cross-type conversion (widening chains)

When the source and destination types differ (e.g., byte→float for dequantization, short→byte for narrowing):

// Widen: byte → short → int → float
var bytes = Vector128.LoadUnsafe(ref src, offset);
var (lo16, hi16) = Vector128.Widen(bytes);
var (lo32a, lo32b) = Vector128.Widen(lo16);
var f0 = Vector128.ConvertToSingle(lo32a.AsInt32());

// Narrow: int → short → byte (with saturation via Min/Max clamping)
var clamped = Vector128.Min(Vector128.Max(vec, Vector128<short>.Zero), Vector128.Create((short)255));
var narrowed = Vector128.Narrow(clamped.AsUInt16(), nextVec.AsUInt16());

Trailing elements

• Idempotent ops (validation, search): overlap last vector — re-processing is safe
• Aggregations (sum, count, min/max): scalar loop for remainder to avoid double-counting
• Store ops (transform in-place): use ConditionalSelect to merge with last stored vector

Key Rules

• Preserve original method signature — drop-in replacement
• Keep scalar code as fallback — never delete it
• Use Vector128<T> / Vector256<T> / Vector512<T> explicitly — never Vector<T>
• Prefer portable Vector128<T>/Vector256<T>/Vector512<T> APIs over platform-specific intrinsics (Avx2, Sse42, AdvSimd, Fma) unless there is a significant performance advantage
• Testing: use dotnet run (NOT dotnet test) — xunit.v3 is an in-process runner