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

Floating point error is a notable drawback of embedded systems implementation. 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 methods 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 functions. We release two related software package FPBern and FPKriSten, and compare them with state of the art tools. We show that these two methods achieve competitive performance, while computing accurate upper bounds by comparison with other tools.