Mathematical Models to Analyze Lua Hybrid Tables and Why They Need a Fix

TL;DR

This paper analyzes the performance of Lua's hybrid tables, revealing problematic scenarios where their complexity can degrade from linear to logarithmic, highlighting the need for improvements.

Contribution

It provides a theoretical analysis of Lua's hybrid tables, identifying worst-case scenarios that cause performance degradation and suggesting the need for fixes.

Findings

Performance degrades to (T \u2212  T  T) in worst-case probabilistic scenarios

Hybrid tables can exhibit (T   T  T) complexity under certain operations

The analysis highlights the necessity for improvements in Lua's table implementation.

Abstract

Lua (Ierusalimschy et al., 1996) is a well-known scripting language, popular among many programmers, most notably in the gaming industry. Remarkably, the only data-structuring mechanism in Lua are associative arrays, called tables. With Lua 5.0, the reference implementation of Lua introduced hybrid tables to implement tables using both a hashmap and a dynamically growing array combined together: the values associated with integer keys are stored in the array part, when suitable, everything else is stored in the hashmap. All this is transparent to the user, who gets a unique simple interface to handle tables. In this paper we carry out a theoretical analysis of the performance of Lua's tables, by considering various worst-case and probabilistic scenarios. In particular, we uncover some problematic situations for the simple probabilistic model where we add a new key with some fixed probability $p>\frac12$ and delete a key with probability $1-p$: the cost of performing T such operations is proved to be $\Omega(T\log T)$ with high probability, where linear complexity is expected instead.