Use linear scans instead of hashing for contraction labels#190
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## main #190 +/- ##
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## Summary Does the dimname/label bookkeeping in the out-of-place contraction path with linear scans instead of the `Set`- and `Dict`-based `Base.setdiff`/`intersect`/`indexin`. For the handful of labels a tensor carries the hashing those build dominates, and on a small contraction it costs more than the matrix multiply itself. `biperms` and `contract_labels` use order-preserving `Vector` comprehensions for the output and contracted labels, and `tuple_indexin` finds label positions with `findfirst` rather than `Base.indexin`. The old check that every label appears exactly twice is replaced by a check that the destination carries exactly the uncontracted labels: the contracted and output groups partition the operands by construction, so that is the only consistency left to verify. These all assume the labels within each group are unique, which holds for a contraction. On a 4x4 contraction sharing one index, `a1 * a2` drops from 4.6 μs / 124 allocations to 1.9 μs / 60.
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## Summary Derives the bipartitioned permutations for `contract` as concretely-typed tuples behind a single `Val` function-barrier on the contracted count, rather than building them by converting runtime-length `Vector`s into abstract-typed tuples. The abstract tuples defeated the type stability of the downstream `matricize` pipeline, which is built around statically-sized tuples and `Val` barriers, so the per-call bookkeeping for a small contraction boxed heavily. This is a second pass on the label-derivation layer, after #190 removed the `Set` and `Dict` hashing from the same path. For a 4x4 matrix multiply the per-call cost drops from 51 allocations to 17 and is several times faster, landing just above the floor set by the lower-level entry point that takes the permutations directly. The remaining allocations are the output array temporaries and the destination-label `Vector`. The public `biperms` and `biperm` signatures are unchanged. The type-stable core is a new `Val`-parameterized method of `biperms`, and the two label entry points cross into `Val`-specialized helpers so the contraction itself runs type-stably.
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Summary
Does the dimname/label bookkeeping in the out-of-place contraction path with linear scans instead of the
Set- andDict-basedBase.setdiff/intersect/indexin. For the handful of labels a tensor carries the hashing those build dominates, and on a small contraction it costs more than the matrix multiply itself.bipermsandcontract_labelsuse order-preservingVectorcomprehensions for the output and contracted labels, andtuple_indexinfinds label positions withfindfirstrather thanBase.indexin. The old check that every label appears exactly twice is replaced by a check that the destination carries exactly the uncontracted labels: the contracted and output groups partition the operands by construction, so that is the only consistency left to verify. These all assume the labels within each group are unique, which holds for a contraction.On a 4x4 contraction sharing one index,
a1 * a2drops from 4.6 μs / 124 allocations to 1.9 μs / 60.