Verification of C/C<bold>++</bold> 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 <monospace>math.h/cmath</monospace> 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.
Verification of programs using floating-point arithmetic is challenging on several accounts. One of the difficulties of reasoning about such programs is due to the peculiarities of floating-point arithmetic: rounding errors, infinities, non-numeric objects (NaNs), signed zeroes, denormal numbers, different rounding modes, etc. One possibility to reason about floating-point arithmetic is to model a program computation path by means of a set of ternary constraints of the form "Image missing"and use constraint propagation techniques to infer new information on the variables’ possible values. In this setting, we define and prove the correctness of algorithms to precisely bound the value of one of the variables x, y or z, starting from the bounds known for the other two. We do this for each of the operations and for each rounding mode defined by the IEEE 754 binary floating-point standard, even in the case the rounding mode in effect is only partially known. This is the first time that such so-called filtering algorithms are defined and their correctness is formally proved. This is an important slab for paving the way to formal verification of programs that use floating-point arithmetics.
MISRA C is the most authoritative language subset for the C programming language that is a de facto standard in several industry sectors where safety and security are of paramount importance. While MISRA C is currently encoded in 175 guidelines (coding rules and directives), it does not coincide with them: proper adoption of MISRA C requires embracing its preventive approach (as opposed to the "bug finding" approach) and a documented development process where justifiable noncompliances are authorized and recorded as deviations. MISRA C guidelines are classified along several axes in the official MISRA documents. In this paper, we add to these an orthogonal classification that associates guidelines with their main rationale. The advantages of this new classification are illustrated for different kinds of projects, including those not (yet) having MISRA compliance among their objectives.
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