First steps towards more numerical reproducibility

Questions whether numerical simulation is reproducible or not have been reported in several sensitive applications. Numerical reproducibility failure mainly comes from the finite precision of computer arithmetic. Results of floating-point computation depends on the computer arithmetic precision and on the order of arithmetic operations. Massive parallel HPC which merges, for instance, many-core CPU and GPU, clearly modifies these two parameters even from run to run on a given computing platform. How to trust such computed results? This paper presents how three classic approaches in computer arithmetic may provide some first steps towards more numerical reproducibility