Symbolic execution of floating‐point computations

Botella, Bernard; Gotlieb, Arnaud; Michel, Claude

doi:10.1002/stvr.333

Cited by 66 publications

(41 citation statements)

References 27 publications

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“…We implement deduction using standard Interval Constraint Propagation (ICP) techniques for floating-point numbers, defined e.g., in [8,54]. The implementation operates on CNF formulae over floating-point predicates.…”

Section: Deductionsmentioning

confidence: 99%

“…Work in constraint programming [55] shows how approximation with real numbers can be used to soundly restrict the scope of floating-point values. In [8], a symbolic execution approach for floating-point problems is presented, which combines interval propagation with explicit search for satisfiable floating-point assignments. An SMTLIB theory of FPA was presented in [63].…”

Section: Decision Proceduresmentioning

confidence: 99%

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Deciding floating-point logic with abstract conflict driven clause learning

Brain

D’Silva

Griggio

et al. 2013

Form Methods Syst Des

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We present a bit-precise decision procedure for the theory of floating-point arithmetic. The core of our approach is a non-trivial, lattice-theoretic generalisation of the conflict-driven clause learning algorithm in modern SAT solvers to lattice-based abstractions. We use floating-point intervals to reason about the ranges of variables, which allows us to directly handle arithmetic and is more efficient than encoding a formula as a bit-vector as in current floating-point solvers. Interval reasoning alone is incomplete, and we obtain completeness by developing a conflict analysis algorithm that reasons natively about intervals. We have implemented this method in the MATHSAT5 SMT solver and evaluated it on assertion checking problems that bound the values of program variables. Our new technique is faster than a bit-vector encoding approach on 80 % of the benchmarks, and is faster by one order of magnitude or more on 60 % of the benchmarks. The generalisation of CDCL we propose is widely applicable and can be used to derive abstraction-based SMT solvers for other theories.

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Section: Deductionsmentioning

confidence: 99%

Section: Decision Proceduresmentioning

confidence: 99%

Deciding floating-point logic with abstract conflict driven clause learning

Brain

D’Silva

Griggio

et al. 2013

Form Methods Syst Des

View full text Add to dashboard Cite

show abstract

“…Sine iter computes the function sine with an iterative method and comes from the SNU real time library 5 . Qurt computes the real and imaginary roots of a quadratic equation and also comes from the SNU library.…”

Section: Methodsmentioning

confidence: 99%

“…box-consistency and 2B-consistency) over R [21], [20,5]. However FP solvers based on these techniques do not really scale up to large constraint systems.…”

mentioning

confidence: 99%

Boosting Local Consistency Algorithms over Floating-Point Numbers

Belaid¹,

Michel²,

Rueher³

2012

Lecture Notes in Computer Science

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Abstract. Solving constraints over oating-point numbers is a critical issue in numerous applications notably in program veri cation. Capabilities of ltering algorithms over the oating-point numbers (F) have been so far limited to 2b-consistency and its derivatives. Though safe, such ltering techniques su er from the well known pathological problems of local consistencies, e.g., inability to e ciently handle multiple occurrences of the variables. These limitations also have their origins in the strongly restricted oating-point arithmetic. To circumvent the poor properties of oating-point arithmetic, we propose in this paper a new ltering algorithm, called FPLP, which relies on various relaxations over the real numbers of the problem over F. Safe bounds of the domains are computed with a mixed integer linear programming solver (MILP) on safe linearizations of these relaxations. Preliminary experiments on a relevant set of benchmarks are promising and show that this approach can be e ective for boosting local consistency algorithms over F. IntroductionCritical systems are more and more relying on oating-point (FP) computations. For instance, embedded systems are typically controlled by software that store measurements and environment data as oating-point number (F). The initial values and the results of all operations must therefore be rounded to some nearby oat. This rounding process can lead to signi cant changes, and, for example, can modify the control ow of the program. Thus, the veri cation of programs performing FP computations is a key issue in the development of critical systems.Methods for verifying programs performing FP computations are mainly derived from standard program veri cation methods. Bounded model checking (BMC) techniques have been widely used for nding bugs in hardware design [3] and software [11]. SMT solvers are now used in most of the state-of-the-art BMC tools to directly work on high level formula (see [2,9,11]). The bounded model checker CBMC encodes each FP operation of the program with a set of logic This work was partially supported by ANR VACSIM (ANR-11-INSE-0004), ANR AEOLUS (ANR-10-SEGI-0013) and OSEO ISI PAJERO projects.

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“…In [32] the authors addressed the peculiarities of the symbolic execution of programs with floating-point numbers, while [23] proposes to use Mixed Integer Linear programming for boosting local consistency algorithms over floating-point numbers.…”

Section: Other Variablesmentioning

confidence: 99%

Portfolio approaches in constraint programming

Amadini

2015

Constraints

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Recent research has shown that the performance of a single, arbitrarily efficient algorithm can be significantly outperformed by using a portfolio of -possibly onaverage slower-algorithms. Within the Constraint Programming (CP) context, a portfolio solver can be seen as a particular constraint solver that exploits the synergy between the constituent solvers of its portfolio for predicting which is (or which are) the best solver(s) to run for solving a new, unseen instance.In this thesis we examine the benefits of portfolio solvers in CP. Despite portfolio approaches have been extensively studied for Boolean Satisfiability (SAT) problems, in the more general CP field these techniques have been only marginally studied and used. We conducted this work through the investigation, the analysis and the construction of several portfolio approaches for solving both satisfaction and optimization problems. We focused in particular on sequential approaches, i.e., single-threaded portfolio solvers always running on the same core.We started from a first empirical evaluation on portfolio approaches for solving Constraint Satisfaction Problems (CSPs), and then we improved on it by introducing new data, solvers, features, algorithms, and tools. Afterwards, we addressed the more general Constraint Optimization Problems (COPs) by implementing and testing a number of models for dealing with COP portfolio solvers. Finally, we have come full circle by developing sunny-cp: a sequential CP portfolio solver that turned out to be competitive also in the MiniZinc Challenge, the reference competition for CP solvers.iii iv

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Symbolic execution of floating‐point computations

Cited by 66 publications

References 27 publications

Deciding floating-point logic with abstract conflict driven clause learning

Deciding floating-point logic with abstract conflict driven clause learning

Boosting Local Consistency Algorithms over Floating-Point Numbers

Portfolio approaches in constraint programming

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