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, is an associative array called a table. With Lua 5.0, the reference implementation of Lua introduced hybrid tables to implement tables using both a hash table and a dynamically growing array combined together: the values associated with integer keys are stored in the array part, when suitable. All this is transparent to the user, which has 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 \(p>\frac{1}{2}\) and delete a key with probability \(1-p\): the cost of performing T such operations is proved to be \(\varOmega (T\log T)\) with high probability, instead of linear in T.
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.
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Notes
- 1.
- 2.
- 3.
From the Portuguese “lua”, meaning moon.
- 4.
We will sometimes also refer to the hashmap as the hash table.
- 5.
All detailed descriptions in the remaining of the paper and our analysis refer to version 5.4.4 of Lua (the most recent).
- 6.
We use the Greek letter \(\nu \) for consistency with the other notation in this section, \(\nu _t\) corresponds to \(N \) when no deletions occur.
- 7.
This is done in linear time by counting the number of integer keys between \(2^{\ell -1}\) and \(2^{\ell }\) for each \(\ell \), for \(1\le 2^\ell \le M\).
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Martínez, C., Nicaud, C., Rotondo, P. (2022). A Probabilistic Model Revealing Shortcomings in Lua’s Hybrid Tables. In: Zhang, Y., Miao, D., Möhring, R. (eds) Computing and Combinatorics. COCOON 2022. Lecture Notes in Computer Science, vol 13595. Springer, Cham. https://doi.org/10.1007/978-3-031-22105-7_34
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