Estimation of Round-off Errors on Several Computers Architectures

Jalil Asserrhine (Laboratoire MASI-IBP, URA-818 du CNRS, Université Pierre et Marie Curie, 4 place Jussieu, France)

Jean-Marie Chesneaux (Laboratoire MASI-IBP, URA-818 du CNRS, Université Pierre et Marie Curie, 4 place Jussieu, France)

Jean-Luc Lamotte (Laboratoire MASI-IBP, URA-818 du CNRS, Université Pierre et Marie Curie, 4 place Jussieu, France)

Abstract: Numerical validation of computed results in scientific computation is always an essential problem as well on sequential architecture as on parallel architecture. The probabilistic approach is the only one that allows to estimate the round-off error propagation of the floating point arithmetic on computers. We begin by recalling the basics of the CESTAC method (Controle et Estimation Stochastique des Arrondis de Calculs). Then, the use of the CADNA software (Control of Accuracy and Debugging For Numerical Applications) is presented for numerical validation on sequential architecture. On parallel architecture, we present two solutions for the control of round-off errors. The first one is the combination of CADNA and the PVM library. This solution allows to control round-off errors of parallel codes with the same architecture. It does not need more processors than the classical parallel code. The second solution is represented by the RAPP prototype. In this approach, the CESTAC method is directly parallelized. It works both on sequential and parallel programs. The essential difference is that this solution requires more processors than the classical codes. These different approaches are tested on sequential and parallel programs of multiplication of matrices.

Categories: B.2