> This is an extremely well-known technique. You can see a similar version
> that uses a multiply for the last few steps at
> http://graphics.stanford.edu/~seander/bithacks.html#CountBitsSetParallel
> whch refers to
> "Software Optimization Guide for AMD Athlon 64 and Opteron Processors"
> http://www.amd.com/us-en/assets/content_type/white_papers_and_tech_docs/25112.PDF
>
> It's section 8.6, "Efficient Implementation of Population-Count Function
> in 32-bit Mode", pages 179-180.
Thanks for doing this. The proof looks good except for what has been
already pointed out by Grant Grundler.
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