Improving the numerical accuracy of programs by automatic transformation

The dangers of programs performing floating-point 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 numer...

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Bibliographic Details
Published in:International journal on software tools for technology transfer Vol. 19; no. 4; pp. 427 - 448
Main Authors: Damouche, Nasrine, Martel, Matthieu, Chapoutot, Alexandre
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2017
Springer Nature B.V
Springer Verlag
Subjects:
Accuracy
Algorithms
Arithmetic
Computer Arithmetic
Computer programs
Computer Science
Data Structures and Algorithms
Embedded systems
Engineering Sciences
Floating point arithmetic
Floating structures
Fmics 2015/2016
Formulas (mathematics)
Other
Software Engineering
Software Engineering/Programming and Operating Systems
Software quality
Static code analysis
Theory of Computation
Transformations
Floating-point numbers
Numerical accuracy
IEEE754 standard
Program transformation
Static analysis
ISSN:1433-2779, 1433-2787
Online Access:Get full text
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Summary:The dangers of programs performing floating-point 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.
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ISSN:1433-2779
1433-2787
DOI:10.1007/s10009-016-0435-0