Efficient computation of positional population counts using SIMD instructions. (3rd May 2021) - Klarqvist, Marcus D. R.; Muła, Wojciech; Lemire, Daniel
Summary: In several fields such as statistics, machine learning, and bioinformatics, categorical variables are frequently represented as one‐hot encoded vectors. For example, given eight distinct values, we map each value to a byte where only a single bit has been set. We are motivated to quickly compute statistics over such encodings. Given a stream of k ‐bit words, we seek to compute k  distinct sums corresponding to bit values at indexes 0, 1, 2, …, k  − 1. If the k ‐bit words are one‐hot encoded then the sums correspond to a frequency histogram. This multiple‐sum problem is a generalization of the population‐count problem where we seek the sum of all bit values. Accordingly, we refer to the multiple‐sum problem as a positional population‐count . Using SIMD (Single Instruction, Multiple Data) instructions from recent Intel processors, we describe algorithms for computing the 16‐bit position population count using less than half of a CPU cycle per 16‐bit word. Our best approach uses up to 400 times fewer instructions and is up to 50 times faster than baseline code using only regular (non‐SIMD) instructions, for sufficiently large inputs.