Since pdqsort (an older project of mine) was mentioned, I felt it wouldn't be entirely inappropriate to mention that I've since then collaborated with Lukas Bergdoll to provide two high-quality sort implementations for the Rust standard library, ipnsort (unstable) and driftsort (stable).

So if you use Rust, you get these by simply calling [T]::sort(_unstable). Great performance out of the box :)

On my machine (Apple M2), using the benchmarks from the repository on Apple clang 17 and Rust 1.98 nightly:

    Sorting 50 million doubles:
    ipnsort             0.79s
    blqs                0.90s
    driftsort           1.13s   (stable)
    std::sort           1.22s
    std::stable_sort    4.64s   (stable)

    Sorting 50 million (i32, i32) structs:
    ipnsort             0.82s
    blqs                0.89s
    driftsort           1.07s   (stable)
    std::sort           3.09s
    std::stable_sort    3.15s   (stable)

And now for a cool party trick, let's repeat the 50 million doubles experiment again, but have the first 90% already sorted, last 10% random:

    driftsort           0.29s   (stable)
    ipnsort             0.81s
    std::sort           1.15s
    std::stable_sort    1.63s   (stable)
    blqs                1.89s

Aren't there several bitonic sort network implementations that are vectorized, Intel's in particular?

Why not compare against that?

It is so simple that I had to look very slowly to understand. Nicely done.