  Floating point error is an inevitable drawback of embedded systems
implementation. Computing rigorous upper bounds of roundoff errors is
absolutely necessary to the validation of critical software. This problem 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 FPKiSten, 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.
