Abstract
We introduce a relational static analysis to determine the stability of the numerical errors arising inside a loop in which floating-point computations are carried out. This analysis is based on a stability test for non-linear functions and on a precise semantics for floating-point numbers that computes the propagation of the errors made at each operation. A major advantage of this approach is that higher-order error terms are not neglected. We introduce two algorithms for the analysis. The first one, less complex, only determines the global stability of the loop. The second algorithm determines which particular operation makes a loop unstable. Both algorithms have been implemented and we present some experimental results.
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Martel, M. (2002). Static Analysis of the Numerical Stability of Loops. In: Hermenegildo, M.V., Puebla, G. (eds) Static Analysis. SAS 2002. Lecture Notes in Computer Science, vol 2477. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45789-5_12
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DOI: https://doi.org/10.1007/3-540-45789-5_12
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