A Practical Approach to Verification of Floating-Point C/C++ Programs with math.h/cmath Functions
| Autor: | Abramo Bagnara, Roberto Bagnara, Michele Chiari, Roberta Gori |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Model checking
Programming language Computer science Test data generation constraint propagation 020207 software engineering 010103 numerical & computational mathematics 02 engineering and technology Interval (mathematics) Symbolic execution computer.software_genre Abstract interpretation 01 natural sciences model checking program verification 0202 electrical engineering electronic engineering information engineering Piecewise abstract interpretation 0101 mathematics Dichotomic search Formal verification computer Floating-point numbers Software symbolic execution |
| Popis: | Verification of C/C++ programs has seen considerable progress in several areas, but not for programs that use these languages’ mathematical libraries. The reason is that all libraries in widespread use come with no guarantees about the computed results. This would seem to prevent any attempt at formal verification of programs that use them: without a specification for the functions, no conclusion can be drawn statically about the behavior of the program. We propose an alternative to surrender. We introduce a pragmatic approach that leverages the fact that most math.h/cmath functions are almost piecewise monotonic: as we discovered through exhaustive testing, they may have glitches , often of very small size and in small numbers. We develop interval refinement techniques for such functions based on a modified dichotomic search, which enable verification via symbolic execution based model checking, abstract interpretation, and test data generation. To the best of our knowledge, our refinement algorithms are the first in the literature to be able to handle non-correctly rounded function implementations, enabling verification in the presence of the most common implementations. We experimentally evaluate our approach on real-world code, showing its ability to detect or rule out anomalous behaviors. |
| Databáze: | OpenAIRE |
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