On 10/17/18 3:25 PM, Giuliano Augusto Faulin Belinassi wrote: >> Hmm, do we have problems as we get close to -1 or 1 where the outputs of >> the two forms might diverge? > > Well, I did some minor testing with that with input x around nextafter(1, -1); > There are a minor imprecision when comparing directly with > sinh(atanh(x)) and cosh(atanh(x)). > * On 32-bits floats, for such x the error is about 10^-4 > * On 64-bits floats, for such x the error is about 10^-7 > * On 80-bits floats, for such x the error is about 10^-9 > > here are the code that I used for the test: https://pastebin.com/JzYZyigQ > > I can create a testcase based on this if needed :-) My gut instinct is those errors are too significant in practice.
It also just occurred to me that we may have problems as X approaches X from either direction. Clearly when x^2 is indistinguishable from 0 or 1, then the result has to be +-0 or +-1. But I'm not sure if figuring out where those points are is sufficient to avoid the imprecisions noted above. This is *well* outside my areas of expertise. jeff
