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.

The AMD APU (Accelerated Processing Unit) architecture, which combines CPU and GPU cores on the same die, is promising for GPU applications which performance is bottlenecked by the low PCI Express communication rate. However the first APU generations still have different CPU and GPU memory partitions. Currently, the APU integrated GPUs are also less powerful than discrete GPUs. In this paper we therefore investigate the interest of APUs for scientific computing by evaluating and comparing the performance of two successive AMD APUs (family codename Llano and Trinity), two successive discrete GPUs (chip codename Cayman and Tahiti) and one hexa-core AMD CPU. For this purpose, we rely on a 3D finite difference stencil, that is optimized and tuned in OpenCL. We detail the most interesting optimizations for each architecture and show very good performance in OpenCL: up to 500 Gflops on Tahiti. Finally, our results show that APU integrated GPUs outperform CPUs, and that integrated GPUs of upcoming APUs may match discrete GPUs for problems with high communication requirements.