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perf(amr): source-centric transposed CSR for the coarse–fine fill adjoint

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5/5
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Hơn một tuần
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45/100
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Khá rõ ràng
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Sôi nổi
Công nghệ
julia
Lĩnh vực
distributed-systems, performance

Hướng nghiên cứu

Start with halo_update_adjoint! and the existing (fills, terms) CSR, then review the forward fusion in #84 and descriptor context from #42. Measure schedule rebuild cost and transposed-CSR footprint for both layouts, and run test/exchange_schedule.jl, including its bit-parity and zero-allocation assertions. Done means the adjoint remains the exact transpose, preserves bit parity, and passes both layout checks.

Do mô hình lập chỉ mục viết ra từ nội dung của issue.

Mô tả

performance

What

halo_update_adjoint! still runs one scatter-add broadcast per CSR term, and after the forward gather was fused (#84) it is by far the slower half of the exchange. Fusing it bit-identically needs a source-centric transposed CSR built at schedule time; this issue is that work.

Why it was not done in #84

The forward gather is dst-centric and each dst cell is written by exactly one fill, so one broadcast per fill reproduces the per-term loop's arithmetic exactly. The transpose is a scatter, and a fill's term windows collide on shared source cells, so a dst-centric single pass would accumulate into a colliding cell in dst-cell order instead of term order and change the roundoff. Measured on refined forests (x < 0.5, maxlevel 2), counting the scatter-adds a phase issues and how many land on a cell some earlier term of the same fill already wrote:

forest phase fills scatter-adds colliding
3D 32³, 8³ blocks interpolation 1024 77 824 40 960
3D 32³, 8³ blocks restriction 64 9 216 0
3D 32³, 4³ blocks interpolation 4096 77 824 0
2D 256², 32² blocks interpolation 64 3 584 1 792
2D 256², 32² blocks restriction 16 1 280 0

Restriction rows never collide, and interpolation rows only collide once the tangential windows are wider than one cell (blocksize ≥ 6). Fusing "only collision-free rows" was considered and rejected: it makes the exchange's cost depend on the blocksize in a way nothing in the API hints at.

The measured lopsidedness

Min-of-N, alternating processes, three rounds, on this machine (macOS/aarch64, Julia 1.12), µs:

leg forward (fused) adjoint (per-term)
3D 32³ / 4³ blocks, BlockField 677 3322
3D 32³ / 4³ blocks, packed 672 3448
3D 32³ / 8³ blocks, packed 205 983
2D 256² / 32² blocks, packed 14.5 46.2

So the adjoint is 3–5× the forward on exactly the geometry #84 was aimed at, and #84's acceptance is met on the forward half only.

Shape of the fix

Emit, alongside each phase's (fills, terms) CSR, a transposed CSR keyed by source cell: for every source cell touched by the phase, the list of (dst cell, weight) contributions in the order the current loop applies them — fills in reverse order, terms within a fill in forward order. The adjoint sweep then walks source cells once, accumulating left to right, which is the same accumulation sequence per cell and therefore bit-identical, followed by the dst zeroing pass.

Things to settle before building it:

  • Storage. This is cell-granular, not slab-granular: ~78 k contributions for the 3D interpolation phase above, each needing a block index plus a Cartesian index on both ends. That is the descriptor bloat #42/#84's CSR shape was chosen to avoid, and it is rebuilt on every regrid — measure the build cost and the footprint before committing to it.
  • Layout independence. Contributions cannot be precomputed as linear indices: BlockField and PackedBlockField index the same cell differently, so the record has to stay (block, CartesianIndex) and the sweep pays the decode.
  • Acceptance. The exchange must stay the exact transpose of the forward (dot-product identity to roundoff), the existing bit-parity testsets in test/exchange_schedule.jl must keep comparing against something that is not a re-written copy of the new loop, and the zero-allocation assertions must hold for both layouts.

Related: #84 (forward fusion), #42 (isbits descriptors).

🤖 Filed by Claude — Kyle's ghost cells, my scatter-adds.

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