I'm going to present a work on numerical stability of the acoustic terms in #SPH, and as I'm finalizing the conference paper with some benchmarks, I've come across an interesting situation. The cornerstone of the work involves replacing a powf() function with a combination of exp1mf() and logp1f() for higher accuracy.
How much of a performance loss does this higher accuracy involve?
And here's where things get weird.
When benchmarking just the acoustic terms, the explog form is not only more accurate, but also faster for values of the argument up to FLT_MIN (between 10% and 30% faster), dropping to marginally slower (around 10%) in the remaining range.
HOWEVER, performance on #GPU (both #NVIDIA and #AMD) for an entire simulation when using explog is consistently better (around 4%), whereas on #CPU the same simulation runs 25% slower compared to using the power form.
I found this drop in performance to be rather surprising. I've only tested this on a low-end AMD Ryzen, so I'm going to run some additional tests on other archs, but I really wonder what could be causing such a drop. (Increased register pressure would be my first guess.)
The problem is, I don't even want to spend that much time on the CPU backend, but at the same time, it's the more general on, we wouldn't want it to be unfairly penalized …
The plot thickens! I'm now running on an Android cellphone in Termux, and performance —as pathetic as it might be— is essentially the same for the pow and explog forms.
I think I need at least one more datapoint with an Intel CPU now.
OK interesting, on an oldish dual-socket Intel(R) Xeon(R) Silver 4110 CPU @ 2.10GHz (32 threads total), the explog form performance is again on the lowsh side (around 77.5% of the pow form, not as low as the 75% on the AMD Ryzen, but still measurably worse than the 90%, maybe 80% one would expect based on microbenchmarks.
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