I'd like to implement a numerical approximation to the log Gamma function, and I found Gergő Nemes' approximation described here: https://en.wikipedia.org/wiki/Stirling%27s_approximation.
This seems to work great when $z$ is big, but not so well for small $z$.
The docs for Boost's lgamma function suggest a funny trick though: just do LogGammaApprox(z + 1) - Log(z). And indeed, that does seem to work well for small $z$ with the Nemes approximation.
I have a naive question then: what are the downsides to just always using that trick? It'll obviously be less efficient for larger $z$ where the original approximation was already good, but is it expected to be less accurate as well?