Automated backward error analysis for numerical code

FuZhoulai,; BaiZhaojun,; Su, Zhendong

doi:10.1145/2858965.2814317

Cited by 7 publications

(10 citation statements)

References 33 publications

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“…5.5.1 Challenges for Using High-Precision Floating-Point Implementations. In numerical analysis, it is common to use a high-precision programf high to simulate the conceptional mathematical function f [Bao and Zhang 2013;Benz et al 2012;Fu et al 2015]. However, as discussed in Section 1, it is costly to usef high in terms of both runtime and development cost, which we further elaborate on.…”

Section: Discussionmentioning

confidence: 99%

“…Several techniques [Fu et al 2015;Yi et al 2017] propose the use of global conditions to analyze the (in)accuracy of floating-point programs. They treat the given program as a black-box and compute its global conditions to measure the program's (in)stability [Fu et al 2015]. Compared with global conditions, atomic conditions bring several important benefits which are summarized in Table 6 and further discussed below:…”

Section: Discussionmentioning

confidence: 99%

“…Computing global conditions, on the other hand, involves high-precisionf high [Fu et al 2015], which introduces both high runtime overhead and expensive development cost. • Soundness: By using the pre-calculated formulae, atomic conditions are guaranteed to be unbiased.…”

Section: Discussionmentioning

confidence: 99%

“…The condition number measures the relative change in the output for a given relative change in the input, i.e., how much the relative error |∆x/x | carried by the input will be amplified in the output by the mathematical function f . Note that computing the condition number Γ f (x) is commonly regarded as more difficult than computing the original mathematical function f (x) [Higham 2002], since f ′ (x) cannot be easily obtained unless some quantities are already pre-calculated [Fu et al 2015].…”

Section: Condition Numbersmentioning

confidence: 99%

“…As we discussed in Section 2.4, computing the condition number Γ f (x) is commonly regarded as more difficult than computing the original function f (x) [Higham 2002], since f ′ (x) cannot be easily obtained unless certain quantities have already been pre-calculated [Fu et al 2015].…”

Section: Error Propagation Atomic Conditions and Danger Zonesmentioning

confidence: 99%

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Detecting floating-point errors via atomic conditions

Zou

Zeng

Xiong

et al. 2019

Proc. ACM Program. Lang.

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This paper tackles the important, difficult problem of detecting program inputs that trigger large floating-point errors in numerical code. It introduces a novel, principled dynamic analysis that leverages the mathematically rigorously analyzed condition numbers for atomic numerical operations, which we call atomic conditions, to effectively guide the search for large floating-point errors. Compared with existing approaches, our work based on atomic conditions has several distinctive benefits: (1) it does not rely on high-precision implementations to act as approximate oracles, which are difficult to obtain in general and computationally costly; and (2) atomic conditions provide accurate, modular search guidance. These benefits in combination lead to a highly effective approach that detects more significant errors in real-world code (e.g., widely-used numerical library functions) and achieves several orders of speedups over the state-of-the-art, thus making error analysis significantly more practical. We expect the methodology and principles behind our approach to benefit other floating-point program analysis tasks such as debugging, repair and synthesis. To facilitate the reproduction of our work, we have made our implementation, evaluation data and results publicly available on GitHub at https://github.com/FP-Analysis/atomic-condition. CCS Concepts: • Software and its engineering → General programming languages; Software testing and debugging.

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Section: Discussionmentioning

confidence: 99%