Background and motivation

Given two vectors/lists/strings, Hamming distance is the number of positions at which the two vectors differ. This has a variety of uses (https://en.wikipedia.org/wiki/Hamming_distance), but when focusing on sequences of bits, it's commonly used with embedding vectors that have been quantized down to a single bit per element, with the Hamming distance between two embeddings then used as the similarity/distance metric. When used as such, Hamming distance is computable as the popcount of the xor of the bits.

API Proposal

namespace System.Numerics.Tensors;

public static class TensorPrimitives
{
    // Existing
    public static void PopCount<T>(ReadOnlySpan<T> x, Span<T> destination);
    
    // New
+   public static long PopCount<T>(ReadOnlySpan<T> x) where T : IBinaryInteger<T>;
+   public static int HammingDistance<T>(ReadOnlySpan<T> x, ReadOnlySpan<T> y); // computes number of differing elements
+   public static long HammingBitDistance<T>(ReadOnlySpan<T> x, ReadOnlySpan<T> y) where T : IBinaryInteger<T>; // computes number of differing bits
}

(I've included the new PopCount overload as it felt strange to have a method that effectively did the same thing for the xor of two inputs but not for a single input. It's also useful in its own right.)

API Usage

ReadOnlySpan<byte> singleBitEmbedding1 = ...;
ReadOnlySpan<byte> singleBitEmbedding2 = ...;
long distance = TensorPrimitives.HammingBitDistance(singleBitEmbedding1, singleBitEmbedding2);

Alternative Designs

• Different names to distinguish bits from elements?
• OperationStatus / Try-based PopCount that could accomodate continugous memory with more than 2^63 bits.
• Another HammingDistance overload accepting an IEqualityComparer (or a generic constrained to one).

Risks

n/a