Certified Roundoff Error Bounds using Bernstein Expansions and Sparse Krivine-Stengle Representations

Victor Magron 1, 2 Alexandre Rocca 3 Thao Dang 1
2 PolSys - Polynomial Systems
Inria de Paris, LIP6 - Laboratoire d'Informatique de Paris 6
3 TIMC-IMAG-BCM - Biologie Computationnelle et Mathématique
TIMC-IMAG - Techniques de l'Ingénierie Médicale et de la Complexité - Informatique, Mathématiques et Applications, Grenoble - UMR 5525
Abstract : Floating point error is a drawback of embedded systems implementation that is difficult to avoid. Computing rigorous upper bounds of roundoff errors is absolutely necessary for the validation of critical software. This problem of computing rigorous upper bounds is even more challenging when addressing non-linear programs. In this paper, we propose and compare two new algorithms based on Bernstein expansions and sparse Krivine-Stengle representations, adapted from the field of the global optimization, to compute upper bounds of roundoff errors for programs implementing polynomial and rational functions. We also provide the convergence rate of these two algorithms. We release two related software package FPBern and FPKriSten, and compare them with the state-of-the-art tools. We show that these two methods achieve competitive performance, while providing accurate upper bounds by comparison with the other tools.
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Submitted on : Sunday, December 16, 2018 - 6:03:15 PM
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Victor Magron, Alexandre Rocca, Thao Dang. Certified Roundoff Error Bounds using Bernstein Expansions and Sparse Krivine-Stengle Representations. IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, In press, ⟨10.1109/TC.2018.2851235⟩. ⟨hal-01956817⟩



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