algebra: derive the free-module opgen table instead of storing it - #291
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ChangesFree module lookup
Estimated code review effort: 4 (Complex) | ~45 minutes Merge Risk: ⚪ Minimal · up to The lookup refactor reduces memory use while preserving homomorphism behavior and throughput, with no remaining concrete merge-blocking risk. Sequence Diagram(s)sequenceDiagram
participant Homomorphism
participant OpGenCursor
participant MuFreeModule
participant TargetModule
Homomorphism->>MuFreeModule: opgen_cursor(input_degree)
Homomorphism->>OpGenCursor: get(input_index)
OpGenCursor->>MuFreeModule: block lookup on cache miss
MuFreeModule-->>OpGenCursor: OperationGeneratorPair
Homomorphism->>TargetModule: act(operation, generator, coefficient)
TargetModule-->>Homomorphism: updated result
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✅ Passed checks (4 passed)
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In `@ext/crates/algebra/src/module/free_module.rs`:
- Line 361: Update the dimension publication in MuFreeModule::add_generators to
use Release ordering, and change the corresponding dimension loads in dimension
and index_to_op_gen to Acquire ordering so appended generator_to_index offsets
are visible before readers observe the new dimension. Add a concurrent
regression test covering readers accessing the newly published range while
generators are appended.
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The dimension counter was written and read with `Relaxed`, which is not enough. `add_generators` pushes into `generator_to_index` and then stores the new dimension; with a relaxed pair there is no happens-before edge between the two, so a reader could observe the larger dimension while the offsets backing it were still invisible, and then index a stale array. The mutex `add_generators` holds does not help: it excludes other writers, and readers never take it. The race is writer-to-reader. The version this replaced was accidentally safe -- `dimension` returned `basis_element_to_opgen`'s length, whose `OnceVec` push and read carry the ordering, and those pushes were sequenced after the offset pushes. Deriving the records dropped that pairing along with the table. * the publishing store is now `Release`, and every reader load `Acquire` * the memo no longer bounds a block with the dimension counter. Only the final block of a degree lacks a following offset, and its extent can grow under a concurrent `add_generators`; caching that range would let an index from a newly pushed block hit the entry and be attributed to the wrong generator. That block is simply not memoised. * `NEXT_MODULE_ID` stays `Relaxed`, with a note: nothing is published through the id, and fetch-and-add is atomic, so uniqueness holds under any ordering. Reported by CodeRabbit on SpectralSequences#291. Note for anyone trying to reproduce it: x86 is unlikely to exhibit this, since its store ordering makes the relaxed pair behave like release/acquire in practice. It is a real defect under the memory model and on weaker architectures, not a hypothetical one, but a test on this hardware would not have caught it. Verified unchanged: `EXT_OPGEN_VERIFY=1` reports no disagreements over full resolutions at two stems, and `just lint` (feature powerset), `just docs` and `just test` all pass. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01RuauwDGczEvcusxMZB8Vvs
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In `@ext/crates/algebra/src/module/free_module.rs`:
- Line 433: In the relevant free-module index-resolution logic, make the
dimensions load with Ordering::Acquire unconditionally rather than only inside
debug_assert!, and use the loaded value for any release-visible bounds check.
Preserve synchronization with the Release publication in the generator append
path for callers such as basis_element_to_string and index_to_op_gen.
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A `OnceVec` stores its elements in a chunked `Grove` rather than one allocation, so it cannot be viewed as a slice and handed to `slice::partition_point`. Callers wanting to binary search one have had to write the loop themselves. Same contract as the standard library's: the number of leading elements satisfying a predicate that is true on a prefix and false thereafter. `OnceBiVec` returns a degree rather than an index, so `partition_point` there answers "the first degree at which the predicate fails". Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01VoekBuKuFDw25e5pgmJ3ze
Rayon's `ParallelIterator::for_each_init` builds a value per worker and threads it through that worker's items. It is the combinator for per-worker scratch state, and a caller that wants it has had no way to write one call site that compiles both with and without the `concurrent` feature. The concurrent build already has it through `ParallelIterator`. The sequential build now offers the same signature, calling `init` once, since there is one worker. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01VoekBuKuFDw25e5pgmJ3ze
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Inline comments:
In `@ext/crates/algebra/src/module/homomorphism/free_module_homomorphism.rs`:
- Line 141: Update the matrix allocation in the homomorphism application flow to
use the target dimension at degree minus self.degree_shift, matching the row
size required by apply_to_basis_element_with. Preserve the existing prime and
input-row dimensions.
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`basis_element_to_opgen` stored one `OperationGeneratorPair` per basis element per degree. At high stems that table was roughly three quarters of the resolution's live heap, by a wide margin its largest single consumer. All four of its fields are derivable, so it is now derived. The basis of degree `t` is consecutive per-generator blocks in `(gen_deg, gen_idx)` order, and the block offsets are ALREADY stored in `generator_to_index`, which is indexed per generator and so is smaller than the per-basis-element table by a factor of the algebra's dimension. `index_to_op_gen` finds the block containing an index and computes `operation_index = index - offset` and `operation_degree = degree - generator_degree`. What remains of the old table is a per-degree dimension counter, which also takes over the mutex `add_generators` held on it. How much this saves: a free module over the Milnor algebra with two generators per degree through t=300 has 500,963,726 basis elements, so the old table would want 11.5 GiB. The offsets it is derived from are 90,902 entries, well under a megabyte. There is essentially nothing left to reclaim here, so nothing further is attempted. Finding the block is `partition_point` over the offsets, and the generator's degree is read out of `internal_idx_to_gen_deg`, one `i32` per generator, rather than found by a second search inverting `gen_deg_idx_to_internal_idx`. Two subtleties are worth keeping in mind when reading it: * A generator with `num_ops == 0` yields an EMPTY block sharing its offset with the next one, so the search must take the LAST block whose offset is `<= index`. Taking the first returns a zero-width block, and would be wrong exactly on the degrees where the algebra runs out of operations. * `index_to_op_gen` returns `OperationGeneratorPair` by value rather than by reference, since there is no longer a stored record to borrow. The type is `Copy`. Ordering. The dimension counter is stored with release and loaded with acquire, and that pairing is what orders a lookup against a concurrent `add_generators`: the offsets for a degree are pushed before the dimension counting them is published, so a caller that acquired the dimension also sees the offsets. The edge comes from the CALLER; nothing inside `index_to_op_gen` establishes it. Its bounds check is exactly that, a bounds check, and it is a real one rather than a `debug_assert`: without it an out-of-range index underflows a subtraction and fails somewhere further in, which is a worse way to learn the same thing. It costs about 4 ns of the per-call form's 21 ns and nothing at all on the cursor path, which is what the dense callers use. Callers that look up many indices in one degree take an `OpGenCursor`, which remembers the block it is in and answers from a range check. On a walk of every basis element through t=200, 46.6M lookups, that is 0.6 ns per lookup against 17.0 ns for the per-call form. Its identity comes from the borrow: it cannot outlive the module whose layout it caches, and it pins the dimension it was built with, which is what bounds the final block while `add_generators` may still be extending it. Lookups need not ascend -- a scattered walk just misses more often -- and the tests check ascending, descending and strided orders against `index_to_op_gen`. The dense callers are the free module homomorphism's: `apply`, over the ascending nonzero terms of its input, and `get_matrix` and `get_partial_matrix`, one cursor per worker via `for_each_init`. The cursor holds its extent as a `core::range::Range` rather than a `start`/`end` pair. `std::ops::Range` will not do: it is an iterator, so it is deliberately not `Copy`, and reading it out of the field to test it would mean cloning. The range type is stable since 1.96 and its module since 1.95. Verification. Every basis element round-trips through `index_to_op_gen` and back through `operation_generator_to_index`, over modules with empty generator degrees, empty blocks, `extend_by_zero`, generators added to already-computed degrees, and an odd prime. Flipping the search to take the first matching block rather than the last fails all of them. Measured against the stored-table version on a full-size resolution, comparing the two runs on the bidegrees they both computed -- pairing on `(s, t)` and summing per-bidegree wall time, so the comparison controls for which bidegrees each run happened to reach: * total work: unchanged, within 0.1% * per-bidegree wall time: median ratio 0.95 * peak RSS: a little over half the stored-table version's Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01VoekBuKuFDw25e5pgmJ3ze
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basis_element_to_opgenstored oneOperationGeneratorPairper basis element per degree. At high stems that table was roughly three quarters of the resolution's live heap, by a wide margin its largest single consumer.All four of its fields are derivable. The basis of degree
tis consecutive per-generator blocks in(gen_deg, gen_idx)order, and the block offsets are already stored ingenerator_to_index, which is indexed per generator and so is smaller than the per-basis-element table by a factor of the algebra's dimension.index_to_op_gennow does two binary searches — offsets to find the generator ordinal,gen_deg_idx_to_internal_idxto find that ordinal's degree — and computesoperation_index = index - offsetandoperation_degree = degree - generator_degree.What remains of the table is a per-degree dimension counter, which also takes over the mutex
add_generatorspreviously held on it.Two subtleties worth knowing when reading the search:
num_ops == 0yields an empty block that shares its offset with the next one, so the search must take the last block whose offset is<= index. Taking the first returns a zero-width block, and would be wrong exactly on the degrees where the algebra runs out of operations.index_to_op_gennow returnsOperationGeneratorPairby value rather than by reference, since there is no longer a stored record to borrow. The type isCopy.Callers walk their input indices in ascending order — the restricted-matrix builds do this per row — so consecutive lookups land in the same generator block nearly every time. A one-entry per-thread memo turns that common case into a range check rather than two searches. Its soundness rests on two things:
generator_to_indexis append-only and existing offsets are never mutated, so a cached[start, end)stays valid for the module's life. For the last block,endis the dimension at cache time; if generators are added later the dimension grows and indices past the cachedendsimply miss and take the slow path. A hit therefore always describes the block it claims.Measurements
Against the stored-table version on a full-size resolution, comparing the two runs on the bidegrees they both computed — pairing on
(s, t)and summing per-bidegree wall time, so the comparison controls for which bidegrees each run happened to reach:So the table can be dropped for roughly half the peak memory at no throughput cost.
These were measured on a downstream branch carrying the GPU resolution path, which is what makes resolutions of that size reachable; the algebra change itself is identical to the one here.
Verification
EXT_OPGEN_VERIFY=1materialises the old table alongside and asserts every derived lookup, memo fast path included, against it. No disagreements over full resolutions at two different stems, and the resulting Ext charts are identical to those from the unmodified code. The flag should stay off outside validation — it restores the memory this removes.just lint(including thecargo hackfeature powerset),just docs, andjust testall pass.Summary by CodeRabbit
Performance
Compatibility
Reliability