TL;DR: A high-performance nearly in-place general-case sorting algorithm named SpreadSort is demonstrated, which can operate recursively, but is O(n) for continuous integrable functions, and has better than O( nlog(n)) worst-case performance when used with distributions where the keys have finite length.
Abstract: A high-performance nearly in-place general-case sorting algorithm named SpreadSort is demonstrated. It is approximately 4X as fast as Quicksort in normal cases, and up to 18X as fast with distributions of limited variation (much like Bucketsort). The technique is mixed distributional and comparison-based, merging many of the advantages of both techniques. Spreadsort can operate recursively, but is O(n) for continuous integrable functions, and has better than O(nlog(n)) worst-case performance when used with distributions where the keys have finite length, so recursion past the second iteration is rare. This algorithm can be modified to be in-place with a modest speed loss.