[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