Precise analysis of simd hash tables reveals performance dynamics
Fine-Grained Analysis of SIMD-Based Hash Table Implementations
Data Structures and Algorithms
Summary
Hash tables are a common way to quickly find information, and SIMD instructions let computers handle many pieces of data at once to speed things up. The authors examined how these SIMD-based hash tables behave over time using a mathematical method originally designed for studying complex networks. Their detailed work provides accurate predictions that closely match actual experiments, even for moderately sized hash tables. This helps explain why these faster hash tables work well and guides engineers in designing them.
What this means in practice
- •For software engineers: Optimize hash table implementations that use SIMD for faster data processing by understanding their internal dynamics.
- •For database developers: Improve query performance by selecting and tuning SIMD-accelerated hash tables with predictable high-probability behavior.
Authors
Cyril Nicaud, Pablo Rotondo
Abstract
In recent years, several variants of classical hash table schemes have been developed by engineers in order to take advantage of the processor's internal parallelism using SIMD instructions, which make it possible to operate on multiple bytes simultaneously. At a small additional memory cost, this enables a significant speedup, making it a data structure that is increasingly popular in practice, when very high performance is required. In this article, we provide a detailed theoretical analysis of the dynamics of such hash tables. From a methodological standpoint, we use and adapt a technique developed by Wormald in the 1990s to study dynamic graphs. This approach, which can be adapted to many variants, enables us to accurately estimate the quantities of interest by capturing the dynamics of the data structure through systems of differential equations. Although complex, we provide an explicit description of the solutions of these systems, which can furthermore be efficiently approximated numerically. Our main results are stated with high probability, which is significantly more precise than average-case analyses, and they match experimental results remarkably well, even for hash tables of moderate size.