NDLI: Perturbing numerical calculations for statistical analysis of floating-point program (in)stability

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Perturbing numerical calculations for statistical analysis of floating-point program (in)stability

Content Provider	ACM Digital Library
Author	Barr, Earl Su, Zhendong Tang, Enyi Li, Xuandong
Abstract	Writing reliable software is difficult. It becomes even more difficult when writing scientific software involving floating-point numbers. Computers provide numbers with limited precision; when confronted with a real whose precision exceeds that limit, they introduce approximation and error. Numerical analysts have developed sophisticated mathematical techniques for performing error and stability analysis of numerical algorithms. However, these are generally not accessible to application programmers or scientists who often do not have in-depth training in numerical analysis and who thus need more automated techniques to analyze their code. In this paper, we develop a novel, practical technique to help application programmers (or even numerical experts) obtain high-level information regarding the numerical stability and accuracy of their code. Our main insight is that by systematically altering (or perturbing) the underlying numerical calculation, we can uncover potential pitfalls in the numerical code. We propose two complementary perturbations to statistically measure numerical stability: value perturbation and expression perturbation. Value perturbation dynamically replaces the least significant bits of each floating-point value, including intermediate values, with random bits to statistically induce numerical error in the code. Expression perturbation statically changes the numerical expressions in the user program to mathematically equivalent (in the reals, likely not in floating-point numbers), but syntactically different forms. We then compare the executions of these "equivalent" forms to help discover and remedy potential instabilities. Value perturbation can overstate error, while expression perturbation is relatively conservative, so we use value perturbation to generate candidates for expression perturbation. We have implemented our technique, and evaluation results on various programs from the literature and the GNU Scientific Library (GSL) show that our technique is effective and offers a practical alternative for understanding numerical stability in scientific software.
Starting Page	131
Ending Page	142
Page Count	12
File Format	PDF
ISBN	9781605588230
DOI	10.1145/1831708.1831724
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2010-07-12
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Numerical code Stability Floating-point Perturbation Testing
Content Type	Text
Resource Type	Article

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