Year: 2018
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Institutions: National Institute of Aerospace, Langley Research Center
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950372182