Error Estimation and Correction Using the Forward CENA Method

The increasing use of heterogeneous and more energy-efficient computing systems has led to a renewed demand for reduced- or mixed-precision floating-point arithmetic. In light of this, we present the forward CENA method as an efficient roundoff error estimator and corrector. Unlike the previously published CENA method, our forward variant can be easily used in parallel high-performance computing applications. Just like the original variant, its error estimation capabilities can point out code regions where reduced or mixed precision still achieves sufficient accuracy, while the error correction capabilities can increase precision over what is natively supported on a given hardware platform, whenever higher accuracy is needed. CENA methods can also be used to increase the reproducibility of parallel sum reductions.