Editors: Will be set by the publisher FIRST STEPS TOWARDS MORE NUMERICAL REPRODUCIBILITY ∗

Abstract. 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. 1. Numerical reproducibility: context and motivations As computing power increases towards exascale, more complex and larger scale numerical simulations are performed in various domains. Questions whether such simulated results are reproducible or not have been reported more or less recently, e.g. in energy science [1], dynamic weather forecasting [2], atomic or molecular dynamic [3,4], fluid dynamic [5]. This paper focuses on numerical non-reproducibility due to the finite precision of computer arithmetic – see [6] for other issues about “reproducible research ” in computational mathematics. The following example illustrates a typical failure of numerical reproducibility. In the energetic field, power system state simulation aims to compute at “real time ” a reliable estimate of the bus voltages for a give