# Reproducible floating-point atomic addition in data-parallel environment

## David Defour, Sylvain Collange

DOI: http://dx.doi.org/10.15439/2015F86

Citation: Proceedings of the 2015 Federated Conference on Computer Science and Information Systems, M. Ganzha, L. Maciaszek, M. Paprzycki (eds). ACSIS, Vol. 5, pages 721–728 (2015)

Abstract. Floating-point additions in concurrent execution environment are known to be hazardous, as the result depends on the order in which operations are performed. This problem is encountered in data parallel execution environments such as GPUs, where reproducibility involving floating-point atomic addition is challenging. This problem is due to the rounding error or cancellation that appears for each operation, combined with the lack of control over execution order. In this article we propose two solutions to address this problem: work reassignment and fixed-point accumulation. Work reassignment consists in enforcing an execution order that leads to weak reproducibility. Fixed-point accumulation consists in avoiding rounding error performed at each operation thanks to a long accumulator that leads to strong reproducibility.