[purplesyringa]

Thank you! This point has been driving me mad for the last couple of years.

While answering a sibling comment, I found a paper analyzing various libms for their precision: https://homepages.loria.fr/pzimmermann/papers/glibc238-20230... (2023). I only skimmed it, but it looks like only LLVM's libm guarantees 0.5 ulp for every supported single-precision operation, and everyone else is wildly off. That's a pretty good result, though -- it means there's at least one reasonably compliant libm :)

Another sibling comments says that guaranteeing 0.5 ulp for double-precision operations is nigh impossible (and then another says it is after all). I don't have the knowledge to confirm which is true, but it's possible that this is the best we can get.

[kaathewise]

Table--Maker's dilemma [0] says that we probably can't get correct rounding for some functions. That said, you can still calculate every function within 1 ULP by using extended precision (for example the double-double arithmetic, which uses two doubles to represent a single fp number) and rounding.

But I don't think anyone does this in practice. Simulations don't need perfect precision, anything involving real data has to deal with measurement errors which are usually much larger than f64 ULP scales, and then there's configurable arbitrary-precision for when it's really needed.

[0]: https://people.eecs.berkeley.edu/~wkahan/LOG10HAF.TXT, which coincidentally is also about the log function