Open Kolaru opened 2 years ago
There is IntervalSpecialFunctions.jl, but the repo hasn't been updated in a while (I don't . It also has this PR which despite the name adds support for several special functions using Arb. Not sure how mature it is etc, but I can try to resurrect the repo and have a look at the PR.
That being said, computing special functions of intervals is a nice beast of itself. This paper from Fredrik Johansson describes some techniques for hypergeometric functions (which cover a good piece of special functions)
Supporting special functions would be nice (see e.g. https://github.com/JuliaIntervals/IntervalRootFinding.jl/issues/175).
I thought already was an issue here about this, but I can't find it.
This is only easy to do for monotonous functions for which we can guarantee rounding correctness (e.g. by going through BigFloat or if a rounding mode is directly available). I don't think there is a general way to treat the other special functions.
The "good" think is that special functions seem to error (more or less gracefully) right now, rather that returning incorrect results: