Efficient Generation of Error-Inducing Floating-Point Inputs via Symbolic Execution

Floating point is widely used in software to emulate arithmetic over reals. Unfortunately, floating point leads to rounding errors that propagate and accumulate during execution. Generating inputs to maximize the numerical error is critical when evaluating the accuracy of floating-point code. In thi...

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Veröffentlicht in:2020 IEEE/ACM 42nd International Conference on Software Engineering (ICSE) S. 1261 - 1272
Hauptverfasser: Guo, Hui, Rubio-Gonzalez, Cindy
Format: Tagungsbericht
Sprache:Englisch
Veröffentlicht: ACM 01.10.2020
Schlagworte:
catastrophic cancellation
floating-point
roundoff errors
symbolic execution
testing
ISSN:1558-1225
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Zusammenfassung:Floating point is widely used in software to emulate arithmetic over reals. Unfortunately, floating point leads to rounding errors that propagate and accumulate during execution. Generating inputs to maximize the numerical error is critical when evaluating the accuracy of floating-point code. In this paper, we formulate the problem of generating high error-inducing floating-point inputs as a code coverage maximization problem solved using symbolic execution. Specifically, we define inaccuracy checks to detect large precision loss and cancellation. We inject these checks at strategic program locations to construct specialized branches that, when covered by a given input, are likely to lead to large errors in the result. We apply symbolic execution to generate inputs that exercise these specialized branches, and describe optimizations that make our approach practical. We implement a tool named FPGen and present an evaluation on 21 numerical programs including matrix computation and statistics libraries. We show that FPGen exposes errors for 20 of these programs and triggers errors that are, on average, over 2 orders of magnitude larger than the state of the art.
ISSN:1558-1225
DOI:10.1145/3377811.3380359