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The signature of every document in a resident batch.

public IReadOnlyList<uint[]> Signatures(DeviceTokenHashes documents, ReadOnlySpan<ulong> multipliers, ReadOnlySpan<ulong> addends)
public IReadOnlyList<uint[]> Signatures(DeviceTokenHashes documents, ReadOnlySpan<ulong> multipliers, ReadOnlySpan<ulong> addends, MinHashScheme scheme)

Parameters — documents is the resident token hashes. multipliers holds the a coefficient of each permutation and addends the b, one per multiplier. scheme is which arithmetic the coefficients belong to; naming none means MinHashScheme.Legacy.

Returns — one signature per document, each as long as there are permutations.

Exceptions — ArgumentNullException when documents is null; ArgumentException when the two coefficient spans are not the same non-zero length, when scheme is not a declared member, or when a coefficient does not fit the scheme it is given.

Example — an empty document gives every slot its maximum.

using Lodestar.Gpu.Compute;

using var context = GpuContext.Create(preferCpu: true);
using var resident = DeviceTokenHashes.Upload(context, [[]]);

IReadOnlyList<uint[]> signatures =
    new TiledMinHashSignatures(context).Signatures(resident, [3UL], [13UL]);

bool atMaximum = signatures[0][0] == uint.MaxValue;  // => True

Example — the same residency, read through the reference's current default.

using Lodestar.Gpu.Compute;

using var context = GpuContext.Create(preferCpu: true);
using var resident = DeviceTokenHashes.Upload(context, [[11u, 22u, 33u]]);
var kernel = new TiledMinHashSignatures(context);

IReadOnlyList<uint[]> legacy = kernel.Signatures(resident, [3UL], [13UL]);
IReadOnlyList<uint[]> affine =
    kernel.Signatures(resident, [3UL], [13UL], MinHashScheme.Affine32);

bool agree = legacy[0][0] == affine[0][0];  // => False

Remarks — that maximum is the identity a minimum starts from, not a sentinel, so two empty documents estimate a similarity of 1 — exactly as they do on the CPU path. A caller who wants an empty document to match nothing has to check for it before comparing.

The coefficients are uploaded per call and the batch is not, which is the same division every kernel here makes: the small operand travels, the corpus stays. With 128 permutations that upload is two kilobytes against a corpus of any size.

Signatures come back as one array per document rather than one flat block, because what a caller does next is compare two of them — and MinHash.Jaccard takes two spans.

One residency serves both families. Affine32 needs the MurmurHash3 finalizer applied to each hash, and that runs inside the kernel, as the shared tile fills — once per token per group rather than once per token per thread. Mixing before upload would have been cheaper still and would have made a resident batch belong to one scheme, which is what residency exists not to do.

Applies to — net10.0, netstandard2.1.

See also — TiledMinHashSignatures, MinHashScheme.