Improving the Numerical Accuracy of High Performance Computing Programs by Process Specialization

13 pages•Published: October 11, 2018

Abstract

In high performance computing, nearly all the implementations and published experiments use floating-point arithmetic. However, since floating-point numbers are finite approximations of real numbers, it may result in hazards because of the accumulated errors. These round-off errors may cause damages whose gravity varies depending on the critical level of the application. To deal with this issue, we have developed a tool which im- proves the numerical accuracy of computations by automatically transforming programs in a source-to-source manner. Our transformation, relies on static analysis by abstract interpretation and operates on pieces of code with assignments, conditionals, loops, functions and arrays. In this article, we apply our techniques to optimize a parallel program representative of the high performance computing domain. Parallelism introduces new numerical accuracy problems due to the order of operations in this kind of systems. We are also interested in studying the compromise between execution time and numerical accuracy.

Keyphrases: Convergence Acceleration, floating-point arithmetic, High Performance Computing, Numerical accuracy, parallel programs, Transformation of program

In: Matthieu Martel, Nasrine Damouche and Julien Alexandre Dit Sandretto (editors). TNC'18. Trusted Numerical Computations, vol 8, pages 11--23

Links:	https://easychair.org/publications/paper/ctp1
	https://doi.org/10.29007/tfls