Numerical validation of half precision simulations

Fabienne Jézéquel (1, 2) , Sara Sadat Hoseininasab (2) , Thibault Hilaire (2)

1 UP2 - Université Panthéon-Assas
2 PEQUAN - Performance et Qualité des Algorithmes Numériques

In this article, we show how to control the numerical quality of half precision computations using stochastic arithmetic. The CADNA library that is used to estimate rounding errors and detect numerical instabilities in floating-point codes has been improved and extended to support half precision. A performance gain up to a factor 20 has been observed w.r.t. accuracy estimation in arbitrary precision. Furthermore we present how to generate codes mixing half, single, and double precision with a requested accuracy on results providing a user-defined numerical quality of the code. Control of robustness and floating-point auto-tuning taking into account half precision have been successfully performed on various numerical simulations, in particular a control application.

Mots clés: numerical quality; numerical validation; rounding errors; auto-tuning; discrete stochastic arithmetic; floating-point arithmetic; half precision; mixed precision

Domaines: Informatique [cs]

Fabienne Jézéquel, Sara Sadat Hoseininasab, Thibault Hilaire. Numerical validation of half precision simulations. 1st Workshop on Code Quality and Security (CQS 2021) in conjunction with WorldCIST'21 (9th World Conference on Information Systems and Technologies), Mar 2021, Terceira Island, Azores, Portugal. ⟨hal-03138494⟩