Certified Roundoff Error Bounds using Bernstein Expansions and Sparse Krivine-Stengle Representations - Archive ouverte HAL Access content directly
Journal Articles IEEE Transactions on Computers Year : 2019

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

Victor Magron
Thao Dang

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.

Dates and versions

hal-01956817 , version 1 (16-12-2018)

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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, 2019, 68 (7), pp.953-966. ⟨10.1109/TC.2018.2851235⟩. ⟨hal-01956817⟩
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