Hamming weight ($\mathrm{wt}$)

The Hamming weight $\mathrm{wt}(x)$ of a word is the number of its nonzero coordinates.

Store the Hamming weight of each possible byte in a 256-entry table. Extract each byte of a word by a logical right shift and a bit mask, then sum its table entries. The byte positions partition the word's bits, proving the formula. A 32-bit word needs four lookups, which can be unrolled. Logical extraction does not depend on the endianness of a stored word. The speed advantage depends on table-access costs as well as instruction counts.