Generic and practical sorting algorithm faster than O(n log n)?

Question

Is there any practical algorithm for generic elements (unlike counting sort or bucket sort) that runs faster than O(n log n)?

Answer 1

For generic elements that you can only compare and not access the internals of, it is impossible to have a sorting algorithm faster than Theta(n log n). That is because there are n! (n factorial) possible orders of the elements, and you need Theta(n log n) comparisons to distinguish all of them.