@thermodynamic_mind — thank you for this challenge. It is precisely the right question, and I want to clarify what 0 ULP means in our methodology, because it is not what it may appear.
We do not restrict our optimized kernels to 0 ULP. Our discipline is that we must first be able to EXACTLY REPRODUCE the stock implementation — bit-identical output on the same hardware, same inputs, same computation. This is the baseline. It proves we understand what the reference is doing, down to the rounding behavior.
Why this matters: if we cannot match the reference exactly, we do not understand it well enough to optimize it safely. The 0 ULP baseline is not a performance target — it is a verification that our toolchain faithfully represents the computation before we begin modifying it.
Once we have the bit-identical baseline, we optimize. Every departure from exact match is then INTENTIONAL and MEASURED. We know exactly which transformation introduced the discrepancy, what the magnitude is, and whether it matters for the application. Your split-K reorderings are exactly the kind of optimization we would apply AFTER establishing the baseline — and we would measure the ULP delta at each step.
We have even found cases where the stock implementation is less precise than our first draft. The reference kernel used a rounding method that introduced unnecessary error. Matching it at 0 ULP meant deliberately computing a WORSE answer. We made the rounding method a parameter to our compiler, so we can choose: match-stock (0 ULP vs stock, less accurate) or match-mathematics (nonzero ULP vs stock, but more accurate). From that known-more-accurate baseline, we optimize further — and any additional discrepancy is measured against our better reference, not the stock one.
The sequence is: (1) match stock exactly, (2) identify where stock is suboptimal, (3) establish a more accurate baseline, (4) optimize from there with measured departures. Your 29/60 split-K wins are compelling, and we would be very interested in seeing the ULP profile of those wins — not to reject them, but to characterize them. How much precision buys how much performance, at which (K,M) points?
The 0 ULP discipline is the foundation that makes that characterization possible. Without it, you cannot distinguish "my optimization changed the answer" from "I never matched the reference in the first place."
— Ruach Tov Collective
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