Automatic source-to-source error compensation of floating-point programs: code synthesis to optimize accuracy and time

Laurent Thévenoux 1, 2 Philippe Langlois 3 Matthieu Martel 3
1 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
2 LIP - Laboratoire de l'Informatique du Parallélisme
3 DALI - Digits, Architectures et Logiciels Informatiques
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier, UPVD - Université de Perpignan Via Domitia
Abstract : Numerical programs with IEEE 754 floating-point computations may suffer from inaccuracies, since finite precision arithmetic is an approximation of real arithmetic. Solutions that reduce the loss of accuracy are available, such as, compensated algorithms or double-double precision floating-point arithmetic. Our goal is to automatically improve the numerical quality of a numerical program with the smallest impact on its performance. We define and implement source code transformations in order to derive automatically compensated programs. We present several experimental results to compare the transformed programs and existing solutions. The transformed programs are as accurate and efficient as the implementations of compensated algorithms when the latter exist. Furthermore, we propose some transformation strategies allowing us to improve partially the accuracy of programs and to tune the impact on execution time. Trade-offs between accuracy and performance are assured by code synthesis. Experimental results show that user-defined trade-offs are achievable in a reasonable amount of time, with the help of the tools we present in the paper.
Keywords : execution-time performance multi-criteria optimization floating-point arithmetic code synthesis numerical accuracy compensation
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Concurrency and Computation: Practice and Experience, Wiley, 2017, Concurrency and Computation: Practice and Experience, 29 (7), pp.e3953. 〈10.1002/cpe.3953〉
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Laurent Thévenoux, Philippe Langlois, Matthieu Martel. Automatic source-to-source error compensation of floating-point programs: code synthesis to optimize accuracy and time. Concurrency and Computation: Practice and Experience, Wiley, 2017, Concurrency and Computation: Practice and Experience, 29 (7), pp.e3953. 〈10.1002/cpe.3953〉. 〈hal-01236919v2〉

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