derivative(xlogx, 0.) gives 0 (should be -Inf)

[cossio]

Consider the definition of xlogx:

https://github.com/JuliaStats/StatsFuns.jl/blob/7473d0d8f7c5b2f4a53f0625ada5f2323c84ffe4/src/basicfuns.jl#L14

xlogx(x::Real) = x > zero(x) ? x * log(x) : zero(log(x))

Then derivative(xlogx, 0.) returns 0.. The correct answer is -Inf.

I understand this is due to the singular branch at x=0, and I'm not even sure if there is any way that ForwardDiff can handle this.

[andreasnoack]

You can add it as a rule for xlogx in https://github.com/JuliaDiff/DiffRules.jl. See e.g. https://github.com/JuliaDiff/DiffRules.jl/blob/master/src/rules.jl#L14

[devmotion]

The rules for xlogx and other functions from LogExpFunctions were added to DiffRules a while ago.