Predecessor problem on smooth distributions

We follow a research thread studying the predecessor problem on “smooth” distribution families. We propose a conceptually simpler solution utilizing well-known results from much better studied variant of the problem that assumes nothing about the input. As a side effect, we are able to extend the range of handled input distributions for the most studied case needing expected $\mathcal{O}(\log \log n)$ time, and we provide better insight into why the related methods are faster on smooth inputs.