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Lua (Ierusalimschy et al., 1996) is a well-known scripting language, popularamong many programmers, most notably in the gaming industry. Remarkably, theonly data-structuring mechanism in Lua are associative arrays, called tables.With Lua 5.0, the reference implementation of Lua introduced hybrid tables toimplement tables using both a hashmap and a dynamically growing array combinedtogether: the values associated with integer keys are stored in the array part,when suitable, everything else is stored in the hashmap. All this istransparent 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'stables, by considering various worst-case and probabilistic scenarios. Inparticular, we uncover some problematic situations for the simple probabilisticmodel where we add a new key with some fixed probability $p>\frac12$ and deletea key with probability $1-p$: the cost of performing T such operations isproved to be $\Omega(T\log T)$ with high probability, where linear complexityis expected instead.

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