A (quite) accurate ln1+x function, or "how close can you get" part II

[htom trites]

I'm curious about monotonic and inverse behaviors.

For a and a+ULP, is (f(a+ULP) - f(a)) positive, zero, or negative. Hopefully they'd all be positive, but it can happen that there's a place where you get a string of zeros where f(a) is changing much slower than a. You shouldn't ever find a negative.

The value of the error of a-inverse(function(a)) and a-function(inverse(a)) would ideally be always zero, of course, but unless both the function and the inverse are absolutely monotonic that won't happen.