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Closing the Performance Gap between Doubles and Rationals for Octagons

Chawdhary, Aziem and King, Andy (2018) Closing the Performance Gap between Doubles and Rationals for Octagons. In: Podelski, Andreas, ed. Static Analysis. Lecture Notes in Computer Science, 11002 . Springer, pp. 187-204. ISBN 978-3-319-99724-7. E-ISBN 978-3-319-99725-4. (doi:10.1007/978-3-319-99725-4_13) (KAR id:67227)

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Official URL:
https://doi.org/10.1007/978-3-319-99725-4_13

Abstract

Octagons have enduring appeal because their domain operations are simple, readily mapping to for-loops which apply max, min and sum to the entries of a Difference Bound Matrix (DBM). In the quest for efficiency, arithmetic is often realised with double-precision floating-point, albeit at the cost of the certainty provided by arbitrary-precision rationals. In this paper we show how Compact DBMs (CoDBMs), which has recently been proposed as a memory refinement for DBMs, enable arithmetic calculation to be short-circuited in various domain operations. We also show how comparisons can be avoided by changing the tables which underpin CoDBMs. From the perspective of implementation, the optimisations are attractive because they too are conceptually simple, following the ethos of Octagons. Yet they halve the running time on rationals, putting CoDBMs on rationals on a par with DBMs on doubles.

Item Type: Book section
DOI/Identification number: 10.1007/978-3-319-99725-4_13
Subjects: Q Science
T Technology > T Technology (General)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Computing
Depositing User: Andy King
Date Deposited: 07 Jun 2018 08:58 UTC
Last Modified: 06 Nov 2023 12:32 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/67227 (The current URI for this page, for reference purposes)

University of Kent Author Information

Chawdhary, Aziem.

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CReDIT Contributor Roles:

King, Andy.

Creator's ORCID: https://orcid.org/0000-0001-5806-4822
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