Numerical program optimisation by automatic improvement of the accuracy of computations. (2018)

• Record Type: Journal Article
• Authors: Damouche, Nasrine; Martel, Matthieu; Chapoutot, Alexandre
• Is Part Of: International journal of intelligent engineering informatics. Volume 6:Number 1/2(2018)
• Page Start: 115
• Page End: 145
• Publication Date: 2018
• Subjects: program transformation -- floating-point numbers -- IEEE754 standard -- data-types format optimisation -- convergence acceleration; Artificial intelligence -- Engineering applications -- Periodicals; Engineering -- Computer programs -- Periodicals; Knowledge management -- Periodicals; 620.0028563
• Languages: English
• ISSNs: 1758-8715

Abstract

Over the last decade, guaranteeing the accuracy of computations relying on the IEEE754 floating-point arithmetic has become increasingly complex. Failures, caused by small or large perturbations due to round-off errors, have been registered. To cope with this issue, we have developed a tool which corrects these errors by automatically transforming programs in a source to source manner. Our transformation, relying on static analysis by abstract abstraction, operates on pieces of code with assignments, conditionals and loops. By transforming programs, we can significantly optimise the numerical accuracy of computations by minimising the error relatively to the exact result. In this article, we present two important desirable side-effects of our transformation. Firstly, we show that our transformed programs, executed in single precision, may compete with not transformed codes executed in double precision. Secondly, we show that optimising the numerical accuracy of programs accelerates the convergence of numerical iterative methods. Both of these properties of our transformation are of great interest for numerical software.