Faster Positional-Population Counts for AVX2, AVX-512, and ASIMD

TL;DR

This paper presents optimized SIMD algorithms for positional population counts, significantly improving speed and efficiency across multiple instruction sets like AVX2, AVX-512, and ASIMD, especially for small input arrays.

Contribution

The paper introduces a new SIMD-based algorithm for positional population counts with enhanced handling of unaligned and short arrays, achieving near memory-bound performance.

Findings

Approaches achieve near memory-bound speeds for small arrays.

Enhanced handling of unaligned and very short arrays.

Implementations for AVX2, AVX-512, and ASIMD are provided.

Abstract

The positional population count operation pospopcnt() counts for an array of w-bit words how often each of the w bits was set. Various applications in bioinformatics, database engineering, and digital processing exist. Building on earlier work by Klarqvist et al., we show how positional population counts can be rapidly computed using SIMD techniques with good performance from the first byte, approaching memory-bound speeds for input arrays of as little as 4 KiB. Improvements include an improved algorithm structure, better handling of unaligned and very short arrays, as well as faster bit-parallel accumulation of intermediate results. We provide a generic algorithm description as well as implementations for various SIMD instruction set extensions, including Intel AVX2, AVX-512, and ARM ASIMD, and discuss the adaption of our algorithm to other platforms.