I Wrote a Faster Sorting Algorithm
It took me more than a day of staring at profiling numbers before I realized why this was faster: It has better instruction level parallelism. You couldn’t have invented this algorithm on old computers because it would have been slower on old computers. The big problem with American Flag Sort is that it has to wait for the current swap to finish before it can start on the next swap. It doesn’t matter that there is no cache-miss: Modern CPUs could execute several swaps at once if only they didn’t have to wait for the previous one to finish. Unrolling the inner loop also helps to ensure this. Modern CPUs are amazing, so they could actually run several loops in parallel even without loop unrolling, but the loop unrolling helps.
.. In American Flag Sort my CPU achieves 1.61 instructions per cycle. In this new sorting algorithm it achieves 2.24 instructions per cycle. It doesn’t matter if you have to do a few instructions more, if you can do 40% more at a time.