You are obviously already on top of the concept, but in the paper "Faster Population Counts Using AVX2 Instructions" we tried to give a clear explanation (with

You are obviously already on top of the concept, but in the paper "Faster Population Counts Using AVX2 Instructions" we tried to give a clear explanation (with diagrams) of how it can be faster to roll your own popcnt using Carry-Save-Adders: https://arxiv.org/abs/1611.07612 https://arxiv.org/abs/1611.07612