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Improving the numerical accuracy of programs by automatic transformation

Damouche, Nasrine and Martel, Matthieu and Chapoutot, Alexandre Improving the numerical accuracy of programs by automatic transformation. (2017) International Journal on Software Tools for Technology Transfer, 19. 427-448. ISSN 1433-2779

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Official URL: https://doi.org/10.1007/s10009-016-0435-0


The dangers of programs performing floatingpoint computations are well known. This is due to the sensitivity of the results to the way formulæ are written. These last years, several techniques have been proposed concerning the transformation of arithmetic expressions in order to improve their numerical accuracy and, in this article, we go one step further by automatically transforming larger pieces of code containing assignments and control structures. We define a set of transformation rules allowing the generation, under certain conditions and in polynomial time, of larger expressions by performing limited formal computations, possibly among several iterations of a loop. These larger expressions are better suited to improve, by reparsing, the numerical accuracy of the program results. We use abstract interpretation-based static analysis techniques to over-approximate the round-off errors in programs and during the transformation of expressions. A tool has been implemented and experimental results are presented concerning classical numerical algorithms and algorithms for embedded systems.

Item Type:Article
Audience (journal):International peer-reviewed journal
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:Other partners > Ecole Nationale Supérieure de Techniques Avancées - ENSTA (FRANCE)
Other partners > Université Paris-Saclay (FRANCE)
Other partners > Université de Perpignan Via Domitia - UPVD (FRANCE)
Laboratory name:
Deposited On:03 Feb 2023 15:36

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