Search in sorted matrix NxM
With regards to your code, the only comments I have are that lo and hi may be better names than up and down, and that you probably should have a more specific name than search. As to why you don't see this in the wild, the biggest reason is that Step-wise Linear Search is almost always faster, and simpler to implement. step-wise linear search takes 2n steps to complete, has no recursion, and uses no memory. quad-partitioning, on the other hand, is more complicated, has worse complexity (n^ln(3) vs 2n), and has worse constant factors (due to more branching, and recursion).