Gah, I did misunderstand some things. The picture is now worse than I realized! EDIT: and yet also better; see https://news.ycombinator.com/item?id=27951017 . It's hard to get it working right but this is a really fast algorithm.
fluxsort takes a function pointer and has no way to inline it. The fluxsort.c is included from fluxsort.h (this is not standard style by the way; template files should have a .h suffix), so the compiler might choose to inline it, and the benchmarks use noinline on the comparison functions to avoid this.
BlockQuicksort makes no sense without inlined comparisons. Yes, pdqsort allows a comparison function in order to be a general-purpose sort, but this isn't the case that it targets.
Are these benchmarks run with inline comparisons? Seems pretty hard to get bench.c to inline anything since test_sort takes a comparison function as input (though I'm working on it).