A Probabilistic Model for Rounding Errors: A New Look at the Table-Maker’s Dilemma

Jonathan Devor; Daniel Khankin; Oded Margalit

doi:10.1007/978-3-031-76934-4_17

A Probabilistic Model for Rounding Errors: A New Look at the Table-Maker’s Dilemma

Jonathan Devor
, Daniel Khankin
, Oded Margalit

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

When computing transcendental functions (e.g., sin, exp, tanh), there is a risk for rounding errors even if the function is computed to a very high precision. This well-known phenomenon is called “The Table-Maker’s Dilemma”. In this paper we describe a probabilistic model for estimating the expected number of rounding errors for a given function implementation. We show that this model is robust, even when using crude assumptions about the function. Furthermore, one can use this model to optimize the function implementations, without the need for exhaustive testing, which are often very expensive or entirely impractical.

Original language	English
Title of host publication	Cyber Security, Cryptology, and Machine Learning - 8th International Symposium, CSCML 2024, Proceedings
Editors	Shlomi Dolev, Michael Elhadad, Mirosław Kutyłowski, Giuseppe Persiano
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	190-200
Number of pages	11
ISBN (Print)	9783031769337
DOIs	https://doi.org/10.1007/978-3-031-76934-4_17
State	Published - 1 Jan 2025
Event	8th International Symposium on Cyber Security, Cryptology, and Machine Learning, CSCML 2024 - Be'er Sheva, Israel Duration: 19 Dec 2024 → 20 Dec 2024

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	15349 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	8th International Symposium on Cyber Security, Cryptology, and Machine Learning, CSCML 2024
Country/Territory	Israel
City	Be'er Sheva
Period	19/12/24 → 20/12/24

Keywords

Approximation
computer arithmetic
numerical analysis

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-031-76934-4_17

Cite this

Devor, J., Khankin, D., & Margalit, O. (2025). A Probabilistic Model for Rounding Errors: A New Look at the Table-Maker’s Dilemma. In S. Dolev, M. Elhadad, M. Kutyłowski, & G. Persiano (Eds.), Cyber Security, Cryptology, and Machine Learning - 8th International Symposium, CSCML 2024, Proceedings (pp. 190-200). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 15349 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-76934-4_17

Devor, Jonathan ; Khankin, Daniel ; Margalit, Oded. / A Probabilistic Model for Rounding Errors : A New Look at the Table-Maker’s Dilemma. Cyber Security, Cryptology, and Machine Learning - 8th International Symposium, CSCML 2024, Proceedings. editor / Shlomi Dolev ; Michael Elhadad ; Mirosław Kutyłowski ; Giuseppe Persiano. Springer Science and Business Media Deutschland GmbH, 2025. pp. 190-200 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "When computing transcendental functions (e.g., sin, exp, tanh), there is a risk for rounding errors even if the function is computed to a very high precision. This well-known phenomenon is called “The Table-Maker{\textquoteright}s Dilemma”. In this paper we describe a probabilistic model for estimating the expected number of rounding errors for a given function implementation. We show that this model is robust, even when using crude assumptions about the function. Furthermore, one can use this model to optimize the function implementations, without the need for exhaustive testing, which are often very expensive or entirely impractical.",

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Devor, J, Khankin, D & Margalit, O 2025, A Probabilistic Model for Rounding Errors: A New Look at the Table-Maker’s Dilemma. in S Dolev, M Elhadad, M Kutyłowski & G Persiano (eds), Cyber Security, Cryptology, and Machine Learning - 8th International Symposium, CSCML 2024, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 15349 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 190-200, 8th International Symposium on Cyber Security, Cryptology, and Machine Learning, CSCML 2024, Be'er Sheva, Israel, 19/12/24. https://doi.org/10.1007/978-3-031-76934-4_17

A Probabilistic Model for Rounding Errors: A New Look at the Table-Maker’s Dilemma. / Devor, Jonathan; Khankin, Daniel; Margalit, Oded.
Cyber Security, Cryptology, and Machine Learning - 8th International Symposium, CSCML 2024, Proceedings. ed. / Shlomi Dolev; Michael Elhadad; Mirosław Kutyłowski; Giuseppe Persiano. Springer Science and Business Media Deutschland GmbH, 2025. p. 190-200 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 15349 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Devor J, Khankin D, Margalit O. A Probabilistic Model for Rounding Errors: A New Look at the Table-Maker’s Dilemma. In Dolev S, Elhadad M, Kutyłowski M, Persiano G, editors, Cyber Security, Cryptology, and Machine Learning - 8th International Symposium, CSCML 2024, Proceedings. Springer Science and Business Media Deutschland GmbH. 2025. p. 190-200. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-76934-4_17