Verificarlo: checking floating point accuracy through Monte Carlo Arithmetic

Christophe Denis (1, 2) , Pablo de Oliveira Castro (3, 2, 4) , Eric Petit (4, 2)

1 CMLA - Centre de Mathématiques et de Leurs Applications
2 Université Paris-Saclay
3 LI-PaRAD - Laboratoire d'Informatique Parallélisme Réseaux Algorithmes Distribués
4 UVSQ - Université de Versailles Saint-Quentin-en-Yvelines

Numerical accuracy of floating point computation is a well studied topic which has not made its way to the end-user in scientific computing. Yet, it has become a critical issue with the recent requirements for code modernization to harness new highly parallel hardware and perform higher resolution computation. To democratize numerical accuracy analysis, it is important to propose tools and methodologies to study large use cases in a reliable and automatic way. In this paper, we propose verificarlo, an extension to the LLVM compiler to automatically use Monte Carlo Arithmetic in a transparent way for the end-user. It supports all the major languages including C, C++, and Fortran. Unlike source-to-source approaches, our implementation captures the influence of compiler optimizations on the numerical accuracy. We illustrate how Monte Carlo Arithmetic using the verificarlo tool outperforms the existing approaches on various use cases and is a step toward automatic numerical analysis.

Mots clés: floating point arithmetic; compilers; numerical analysis; Monte Carlo arithmetic

Domaines: Analyse numérique [cs.NA]; Arithmétique des ordinateurs; Performance et fiabilité [cs.PF]

Christophe Denis, Pablo de Oliveira Castro, Eric Petit. Verificarlo: checking floating point accuracy through Monte Carlo Arithmetic. 2016 IEEE 23nd Symposium on Computer Arithmetic (ARITH), Jul 2016, Santa Clara, United States. ⟨10.1109/ARITH.2016.31⟩. ⟨hal-01192668v4⟩