Determine whether the high-limb dp4a reuse optimization is attainable

Determine whether an explicit common-subexpression schedule can reduce the published-modulus pure-SIMT dp4a deconstruction cost from approximately 10.3 to approximately 7.5 instructions per modulus and validate the resulting SASS implementation.

Background

The L1 route performs both limbs of the exact modular reduction with packed dp4a instructions. The paper identifies shared high-limb coefficient vectors among some moduli and estimates that common-subexpression reuse might lower the cost substantially.

This lower count is excluded from all performance envelopes because no reuse schedule or compiled instruction count has yet been demonstrated. The authors explicitly classify it as an unverified optimization target.

References

The high-limb vectors are narrow (entries $\le 4$) and partially shared---$509$ and $487$ have identical ones---so an explicit common-subexpression schedule could plausibly reach $c_q \approx 7.5$; we carry that figure only as an \emph{unverified optimisation target}, excluded from the dispatch envelope until a reuse schedule and SASS count exist.

— Ozaki 2.5: Engineering the Deconstruction Path of fp64-Emulated Dense Matrix Multiplication on FP8 Tensor Cores  (2609.09095 - Matsuoka, 8 Sep 2026) in Section 5, paragraph “The same dot product on SIMT: the dp4a instruction and route L1”