Regular and almost universal hashing: an efficient implementation

TL;DR

This paper introduces an efficient implementation of a non-cryptographic hash family, PM+, which offers almost universal and regular hashing guarantees with high performance on modern processors.

Contribution

The paper presents a new hash family, PM+, with theoretical guarantees and optimized implementation achieving high speed on contemporary hardware.

Findings

PM+ achieves 4.7 bytes/cycle for 32-bit outputs on Intel processors.

PM+ offers almost universality and component-wise regularity.

Implementation is comparable to state-of-the-art performance.

Abstract

Random hashing can provide guarantees regarding the performance of data structures such as hash tables---even in an adversarial setting. Many existing families of hash functions are universal: given two data objects, the probability that they have the same hash value is low given that we pick hash functions at random. However, universality fails to ensure that all hash functions are well behaved. We further require regularity: when picking data objects at random they should have a low probability of having the same hash value, for any fixed hash function. We present the efficient implementation of a family of non-cryptographic hash functions (PM+) offering good running times, good memory usage as well as distinguishing theoretical guarantees: almost universality and component-wise regularity. On a variety of platforms, our implementations are comparable to the state of the art in performance. On recent Intel processors, PM+ achieves a speed of 4.7 bytes per cycle for 32-bit outputs and 3.3 bytes per cycle for 64-bit outputs. We review vectorization through SIMD instructions (e.g., AVX2) and optimizations for superscalar execution.