Eliminating Unstable Tests in Floating-Point Programs

Round-off errors arising from the difference between real numbers and their floating-point representation cause the control flow of conditional floating-point statements to deviate from the ideal flow of the real-number computation. This problem, which is called test instability, may result in a sig...

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Bibliographic Details
Published in:arXiv.org 2018-12
Main Authors: Titolo, Laura, Muñoz, Cesar A, Feliu, Marco A, Moscato, Mariano M
Format: Article
Language:English
Subjects:
Computation
Containment
Floating point arithmetic
Flow stability
Geofences
Microprocessors
Real numbers
Roundoff error
Transformations
Unmanned aircraft
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Summary:Round-off errors arising from the difference between real numbers and their floating-point representation cause the control flow of conditional floating-point statements to deviate from the ideal flow of the real-number computation. This problem, which is called test instability, may result in a significant difference between the computation of a floating-point program and the expected output in real arithmetic. In this paper, a formally proven program transformation is proposed to detect and correct the effects of unstable tests. The output of this transformation is a floating-point program that is guaranteed to return either the result of the original floating-point program when it can be assured that both its real and its floating-point flows agree or a warning when these flows may diverge. The proposed approach is illustrated with the transformation of the core computation of a polygon containment algorithm developed at NASA that is used in a geofencing system for unmanned aircraft systems.
ISSN:2331-8422