City Research Online

Abstract

Automated reasoning procedures are essential for a number of applications that involve bit-exact floating-point computations. This paper presents conditions that characterize when a variable in a floating-point constraint has a solution, which we call invertibility conditions. We describe a novel workflow that combines human interaction and a syntax-guided synthesis (SyGuS) solver that was used for discovering these conditions. We verify our conditions for several floating-point formats. One implication of this result is that a fragment of floating-point arithmetic admits compact quantifier elimination. We implement our invertibility conditions in a prototype extension of our solver CVC4, showing their usefulness for solving quantified constraints over floating-points.

Publication Type:	Conference or Workshop Item (Paper)
Additional Information:	© The Author(s) 2019. This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments:	School of Science & Technology > Computer Science School of Science & Technology > Computer Science > Software Reliability

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