Inverse factorial improved

A couple years ago I wrote about how to compute the inverse of factorial. I used that code in writing the previous post because the post required solving the equation ⌊log2(n!)⌋ = b given b. That is, given a number of bits b, find the smallest value of n such that n! > 2b. What the code got right Looking back on the code in that post, there are a few changes I’d like to make. But first of all, I’d like to point out something the post does right: instead of trying to solve Γ(y) = x it solves log Γ(y) = log x. That’s why the argument to inverse_log_gamma is logarg. That makes the code useful for values of x that would far exceed the maximum floating point value, such as in the calculations for the previous post. What I’d change Rounding The function inverse_factorial from the old post solves finds the closest integer solution. It would be better for it to return the solution without rounding and then let the user round result if they want to. In my calculations in the previous post, I…