A Hybrid Implementation of Hamming Weight

The hamming weight (also known as population count) of a bitstring is the number of 1's in the bitstring. It has applications in scopes like cryptography, chemical informatics and information theory. Typical bitstring lengths range from the processor's word length to several thousands of bits. A plethora of hamming weight algorithms have been proposed. While some implementations expose just scalar parallelism, others expose vector parallelism. Moreover, some implementations use special machine instructions that compute the hamming weight of a processor's word. This paper presents a new hybrid scalar-vector hamming weight implementation that exposes both scalar and vector parallelism. This implementation will be useful on platforms that can exploit both kinds of parallelism simultaneously. On a Sandy Bridge platform, our hybrid implementation outperforms by up to 1.23X and 1.6X the, to the best of our knowledge, best scalar and vector implementations respectively.