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…ime-B front kernels The fused subtree kernel and the regime-B panel helper performed the rank-1 trailing update with the UNSCALED column, dividing both factors by the pivot inside the inner loop: two f64 divisions per updated element, which on the 78k-bus ACOPF condensed KKT (pglib_opf_case78484_epigrids, n = 674562) is ~1.2e9 divisions per refactorization, each an order of magnitude costlier than the fused multiply-add. Restructured both column steps as scale-first: the first half checks the pivot and scales the column below the diagonal by one reciprocal (recomputed per work item from local memory, so no extra barrier and no shared pivot cell), the second half does the trailing rank-1 update with multiply-adds only and writes the diagonal (the diagonal is untouched in the first half so no work item reads a value another one is overwriting). Same barrier count, same pivot sequence, same failure semantics (info = first non-positive column, NaN included). Measured on a GV100 (fused refactorization of the 78k KKT, correctness-gated against the reference solve): regime-A subtree phase 10.3 -> 6.2 ms, fused panel/mega phase 16.4 -> 11.6 ms, end-to-end refactorization 29.3 -> 25.7 ms (cuDSS with its own reordering: 24.3 ms). Tests: full CPU suite 9813 pass (all four element types); CUDA suite pending CI.
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Local CUDA validation (GV100, |
The rank-1 trailing-update loops of the regime-A and regime-B column steps iterated the full r x r square and discarded the upper half with a guard, wasting half the work items (divergent lanes idle through the local-memory traffic of their warp). _tri_decode inverts the packed lower-triangle enumeration (one float sqrt plus two exact fixups, verified exhaustively for r = 1..700), so the loops now launch r(r+1)/2 work items with no guard. GV100, 78k ACOPF condensed KKT: fused refactorization 25.3 -> 24.4 ms (regime-A subtree phase 6.2 -> 5.1 ms); cuDSS with its own reordering on the same device: 24.3 ms. CPU suite green (cholesky + refactorization selections); CUDA suite pending.
One command on a clean NVIDIA box: installs Julia 1.13 via juliaup, clones the branch, runs the CPU and CUDA test suites, then the end-to-end MadNLP ACOPF solve (78k-bus pglib case) with cuDSS and with the SDS prototype wrapper on the same device. SDS_BRANCH/SDS_DIR/SKIP_TESTS/CPU_ONLY_TESTS knobs documented in the header.
…GPU suite, run_amd.jl)
…d, nohup/sbatch usage in the header)
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Second commit (packed-triangle enumeration, |
A readable alternative to fresh_machine.sh for the workflow itself: a single julia file that bootstraps its own environment (registered packages plus this repository at the tested rev), then reads as the workflow does — using SparseDirectSolver, MadNLP, MadNLPGPU, ExaModels, ExaModelsPower; build the 78k-bus ACOPF; solve with cuDSS and with SDS on the same device. The shell script remains for the full test-suite pass.
…-split environment)
…/.julia/dev) instead of a frozen add
…der SparseCondensedKKTSystem)
…ng T23 The previous commits copied subtree.jl/front.jl wholesale from a pre-T23 checkout, silently reverting the per-backend local-memory machinery (the 5-entry SUBTREE_LOCAL_SIZES and the matching _with_local_bytes), which made every analysis fail with 'update _with_local_bytes' on a clean clone. Both files are rebuilt from origin/main with only the two optimization hunks applied (division-free scale-first column step; packed-triangle enumeration of the trailing update).
…sion requires it to activate the GPU condensed-KKT path)
…hout a driver chose cuda on AMD nodes); document --startup-file=no everywhere
… clean nvidia-smi exit
This was referenced Oct 10, 2026
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Oct 13, 2026
…ering knobs, division-free Cholesky, GV100 record (#126) Device-built symbolic maps, the nd_nseps/nd_seed ordering parameters, the division-free Cholesky column step, the fused factorization/solve pipeline (src/fused.jl) with its no-pivot LDL mode and per-architecture tuning, the MadNLP package extension (exported SDSSolver with sds_factorization = :ldl and true inertia; no-pivot LDL disables 2x2 pivot-pair detection), the CPU fast path and HSL reference benches, the fresh-machine @sds workflow, and the campaign write-ups. Full validation record in the PR body. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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What
The regime-A subtree kernel and the regime-B panel helper did the rank-1 trailing update with the unscaled column, dividing both factors by the pivot inside the inner loop — two f64 divisions per updated element (~1.2e9 per refactorization on the 78k-bus ACOPF condensed KKT), each ~10-20x the cost of the fused multiply-add that does the real work.
Both column steps are now scale-first: half one checks the pivot and scales the column by one reciprocal per work item (recomputed locally, so no extra barrier and no shared pivot cell); half two is a pure multiply-add trailing update and writes the diagonal. Same barrier count, same pivot sequence, same failure semantics.
Measured (GV100, 78k ACOPF condensed KKT, correctness-gated)
(cuDSS with its own reordering on the same device: 24.3 ms.)
Residuals unchanged; the arithmetic differs only in rounding ((a/d)(b/d) vs (a·rd)(b·rd)).
Tests
🤖 Generated with Claude Code