li(n, z) returns incorrect values for Complex{ForwardDiff.Dual} inputs

[NAThompson]

PolyLog.li(2, z) returns incorrect values when z is Complex{ForwardDiff.Dual}. The value components of the returned Duals differ from the values computed for plain Complex{Float64} at the same point.

Reproducer

using ForwardDiff
using PolyLog
z = 0.5 + 0.8im
li2_plain = li(2, z)
z_dual = complex(ForwardDiff.Dual(real(z)), ForwardDiff.Dual(imag(z)))
li2_dual  = li(2, z_dual)

@assert li2_plain.re ≈ li2_dual.re.value # will fail
@assert li2_plain.im ≈ li2_dual.im.value # will fail

Impact

This bug propagates to downstream packages-I found this one in ClausenFunctions.jl.

[Expander]

Thanks for reporting this issue! I can reproduce the problem. I'll look deeper into this and prepare a fix.

[NAThompson]

@Expander : I hope this isn't rude (because I don't understand this code at all) but I asked claude for a patchfile to fix it which is attached.

I don't want to indicate this is the right fix, but indeed the reproducer is fixed with this, and perhaps this can help you get started with a good fix.

polylog_li2_fix.patch

[Expander]

Thanks for the patch! No worries about asking claude. As you said, it can be a good start to fix the issue (and the patch is actually not bad).