The algorithm was esoteric, confined to compilers. But there was no technical reason why it could not be implemented in a library: just nobody had done it yet. It was a hole waiting to be filled. It's also really fun to embarrass the compiler!

A deep understanding of the algorithm took me a long time, I think a few months. That was mainly due a lack of information describing the technique. The paper that Andrei linked to (Granlund-Montgomery) is dense and contains a significant error, which I was never able to get resolved. Henry Warren's celebrated Hacker's Delight is more accessible, but is also more of a proof-of-correctness than a learning resource. So my intuitive understanding came from my own investigating and playing around, which is what lead me to find an improvement on the algorithm.

Implementing libdivide took me maybe six months of my hobby time. It's not just the core algorithm - there's a lot of auxiliary functions, for example to compute the high half of a 64 bit multiply in SSE. But working at that level is tons of fun.

Incidentally, I wrote up what I hope to be the most accessible (yet still rigorous) description of the algorithm at http://ridiculousfish.com/blog/posts/labor-of-division-episo... . I advise anyone interested in learning more to start there, instead of the Granlund paper.