Séminaires 2023-2024

Abstract: Stochastic Rounding (SR) mode is a probabilistic rounding mode: an inexact computation is rounded to the next smaller or larger floating-point number with probability depending on the distances to those numbers. We investigate non-linear errors using SR in variance computation algorithms. We estimate the forward error of computations under SR through two methods: 1 a bound of the variance and Bienaymé–Chebyshev inequality, 2 martingales and Azuma–Hoeffding inequality. We examine two algorithms, "textbook" and "two-pass", both with non-linear errors. We show that they have probabilistic bounds under SR in $O(\sqrt{n}u)$ instead of $nu$ for the deterministic bounds.