I can. About 10 years ago I put together a series of blog posts on the topic. It's even referenced from the linked-to article. Most of the algorithms are descr

I can. About 10 years ago I put together a series of blog posts on the topic. It's even referenced from the linked-to article. Most of the algorithms are described at http://www.dalkescientific.com/writings/diary/archive/2008/07/03/hakmem_and_other_popcounts.html http://www.dalkescientific.com/writings/diary/archive/2008/0... . http://dalkescientific.com/writings/diary/archive/2011/11/02/faster_popcount_update.html http://dalkescientific.com/writings/diary/archive/2011/11/02... has a link to http://dalkescientific.com/writings/diary/popcnt.cpp http://dalkescientific.com/writings/diary/popcnt.cpp containing implementations in a benchmark. That code only goes up to the POPCNT instruction. Faster implementations use AVX2 instruction set to implement the Harley-Seal algorithm, and there's VPOPCNTDQ in AVX 512 which does 512 bits at a time. Table of my preprint at https://chemrxiv.org/articles/The_Chemfp_Project/7877846 https://chemrxiv.org/articles/The_Chemfp_Project/7877846 shows the comparison of the most reasonable algorithms (for my definition of 'reasonable') on relatively modern hardware. For my case, the AVX2 implementation, fully optimized, is 11x faster than a lookup table and 30% faster than AVX2. Note that my case handles (typically) multiword popcounts containing 512-2048 bits. Some of the implementations sum the popcount of each word, a few of them use techniques to work on multiple words at a time. (For example, the Gillies-Miller method for "sideways addition" - an old term for popcount - dates from the 1950s. https://archive.org/details/programsforelect00wilk/page/190 https://archive.org/details/programsforelect00wilk/page/190 . )