Estimation of numerical reproducibility on CPU and GPU

Differences in simulation results may be observed from one architecture to another or even inside the same architecture. Such reproducibility failures are often due to different rounding errors generated by different orders in the sequence of arithmetic operations. Reproducibility problems are particularly noticeable on new computing architectures such as multicore processors or GPUs (Graphics Processing Units). DSA (Discrete Stochastic Arithmetic) enables one to estimate rounding error propagation in simulation programs. In this paper, it is shown that DSA can be used to estimate which digits in simulation results may be different from one environment to another because of rounding errors. A particular implementation of DSA, which enables numerical validation in hybrid CPU-GPU environments, is described. The estimation of numerical reproducibility using DSA is illustrated by a wave propagation code which can be affected by reproducibility problems when executed on different architectures.