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 is given by 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 > 1/2 and delete a key with probability 1-p: the cost of performing T such operations is proved to be O(TlogT) with high probability, where linear complexity would be assumed for such data structure. If there is no deletion, we prove that the tables behave better overall. In particular, we establish that inserting the T integers from 1 to T in a random order is done in an essentially linear time.

The work of the first author has been supported by funds from project MOTION (Project PID2020-112581GB-C21) of the Spanish Ministry of Science & Innovation MCIN/AEI/10.13039/501100011033.

Peer Reviewed