Efficient Computation of Positional Population Counts Using SIMD Instructions

TL;DR

This paper introduces SIMD-based algorithms for efficiently computing positional population counts, significantly outperforming traditional methods in speed and instruction count for large datasets.

Contribution

It presents novel SIMD algorithms for fast positional population counts, reducing instruction count and increasing speed compared to baseline methods.

Findings

Up to 400 times fewer instructions needed.

Up to 50 times faster execution for large inputs.

Efficient computation of positional population counts using SIMD.

Abstract

In several fields such as statistics, machine learning, and bioinformatics, categorical variables are frequently represented as one-hot encoded vectors. For example, given 8 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.