Shadow computation with BFloat16 to estimate thenumerical accuracy of summations

David Defour (1) , Pablo de Oliveira Castro , Matei Istoan , Eric Petit

1 LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations

In this article, we propose to exploit the new computational capability offered by the Bfloat16 representation format to perform shadow computations and compute estimations of the relative error. We demonstrate and evaluate the assumptions under which shadow computation is valid for the summation problem.

Domaines: Architectures Matérielles [cs.AR]; Arithmétique des ordinateurs

David Defour, Pablo de Oliveira Castro, Matei Istoan, Eric Petit. Shadow computation with BFloat16 to estimate thenumerical accuracy of summations. IEEE 28th Symposium on Computer Arithmetic (ARITH), Jun 2021, Virtual Conference, France. ⟨hal-03159965v2⟩