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Intra-procedural Optimization of the Numerical Accuracy of Programs

Damouche, Nasrine and Martel, Matthieu and Chapoutot, Alexandre Intra-procedural Optimization of the Numerical Accuracy of Programs. (2015) In: Formal Methods for Industrial Critical Systems - 20th International Workshop (FMICS 2015), 22 June 2015 - 23 June 2015 (Oslo, Norway).

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Official URL: https://doi.org/10.1007/978-3-319-19458-5_3

Abstract

Numerical programs performing oating-point computations are very sensitive to the way formulas are written. These last years, several techniques have been proposed concerning the transformation of arithmetic expressions in order to improve their 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 the numerical accuracy of the target variable. We use abstract interpretation-based static analysis techniques to over-approximate the roundoff errors in programs and during the transformation of expressions. A prototype has been implemented and experimental results are presented concerning classical numerical algorithm analysis and algorithm for embedded systems.

Item Type:Conference or Workshop Item (Paper)
Additional Information:vol 9128
HAL Id:hal-03972635
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Ecole Nationale Supérieure de Techniques Avancées - ENSTA (FRANCE)
Other partners > Université de Montpellier (FRANCE)
Other partners > Université de Perpignan Via Domitia - UPVD (FRANCE)
Laboratory name:
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Deposited On:03 Feb 2023 15:12

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