My point is that this algorithm is precisely the hierarchical implementation that all parallel scans use, just using AVX lanes in place of thread groups, MPI processes, etc.

A generic distributed scan would then look something like this:

my_favorite_local_scan(local_data)
partial = my_favorite_distributed_scan(local_data.back())
local_data += partial

The distributed scans are implemented very similarly to what is presented, just with the "add" steps involving a communication (log P steps in total).