Abstract. Numerical reproducibility failures appear in massively parallel floating-point computations. One way to guarantee the numerical reproducibility is to extend the IEEE-754 correct rounding to larger computing sequences, as for instance for the BLAS libraries. Is the overcost for numerical reproducibility acceptable in practice? We present solutions and experiments for the level 1 BLAS and we conclude about the efficiency of these reproducible routines.
Abstract. Numerical reproducibility failures rise in parallel computation because floating-point summation is non-associative. Massively parallel and optimized executions dynamically modify the floating-point operation order. Hence, numerical results may change from one run to another. We propose to ensure reproducibility by extending as far as possible the IEEE-754 correct rounding property to larger operation sequences. We introduce our RARE-BLAS (Reproducible, Accurately Rounded and Efficient BLAS) that benefits from recent accurate and efficient summation algorithms. Solutions for level 1 (asum, dot and nrm2) and level 2 (gemv) routines are presented. Their performance is studied compared to the Intel MKL library and other existing reproducible algorithms. For both shared and distributed memory parallel systems, we exhibit an extra-cost of 2× in the worst case scenario, which is satisfying for a wide range of applications. For Intel Xeon Phi accelerator a larger extra-cost (4× to 6×) is observed, which is still helpful at least for debugging and validation steps.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.