Improving the Numerical Accuracy of Floating-Point Programs with Automatic Code Transformation Methods

Abstract : Critical software based on floating-point arithmetic requires rigorous verification and validation process to improve our confidence in their reliability and their safety. Unfortunately available techniques for this task often provide overestimates of the round-off errors. We can cite Arian 5, Patriot rocket as well-known examples of disasters. These last years, several techniques have been proposed concerning the transformation of arithmetic expressions in order to improve their numerical accuracy and, in this work, we go one step further by automatically transforming larger pieces of code containing assignments, control structures and functions. 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 re-parsing, 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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Nasrine Damouche. Improving the Numerical Accuracy of Floating-Point Programs with Automatic Code Transformation Methods. Computer Arithmetic. Université de Perpignan, 2016. English. ⟨NNT : 2016PERP0032⟩. ⟨tel-01455727⟩

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