You're right, with that setting fluxsort beats pdqsort slightly for either 1e5 or 1e6 random 4-byte ints. I'm really sorry; I shouldn't have assumed I knew what your benchmark looked like. Although I guess now I'm even more confused about why there are no pdqsort benchmarks in the repository? Beating it is really impressive!

I'll be running my own timings, but do you know where the improvement comes from? Is the base case faster than insertion sort, is the partition faster, or both? I wasn't expecting a stable partition to beat an unstable one because it does twice as much data movement, but it wouldn't be the first time an algorithm using more memory beats one using less.