Static Analysis-Based Validation of Floating-Point Computations

Putot, Sylvie; Goubault, Éric; Martel, Matthieu

doi:10.1007/978-3-540-24738-8_18

Cited by 27 publications

(24 citation statements)

References 4 publications

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“…This delaying strategy was proposed in [40,12]. A variant is the loop unrolling technique used in [37,52]. Of course, this technique may increase significantly the cost of the analysis, since on one hand it involves additional iterations, but also because the first exact steps of computation generally produce complex polyhedra, which would be simplified by the widening.…”

Section: Widening Strategies 351 Delaying the Application Of The Wimentioning

confidence: 99%

Abstract acceleration in linear relation analysis

Gonnord

Schrammel

2014

Science of Computer Programming

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Linear Relation Analysis [28,39] is now a classical abstract interpretation based on an approximation of reachable numerical states of a program by convex polyhedra. Since it works with a lattice of infinite depth, it makes use of a widening operator to enforce the convergence of fixpoint computations. This paper takes place in the many attempts to improve the precision of the results reached using such a widening. It will first present an extended survey of the existing approaches in that direction. Then it will investigate the cases where the exact (abstract) effect of a loop can be computed. This technique is fully compatible with the use of widening, and whenever it applies, it generally improves both the precision and the performances of the analysis.

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Section: Widening Strategies 351 Delaying the Application Of The Wimentioning

confidence: 99%

Abstract acceleration in linear relation analysis

Gonnord

Schrammel

2014

Science of Computer Programming

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“…Hints on previous work on the subject were given in [26,13,14], but never actually described a relational abstraction of the error terms.…”

Section: A Zonotopic Abstractionmentioning

confidence: 99%

Static Analysis of Finite Precision Computations

Goubault

Putot

2011

Lecture Notes in Computer Science

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Abstract. We define several abstract semantics for the static analysis of finite precision computations, that bound not only the ranges of values taken by numerical variables of a program, but also the difference with the result of the same sequence of operations in an idealized real number semantics. These domains point out with more or less detail (control point, block, function for instance) sources of numerical errors in the program and the way they were propagated by further computations, thus allowing to evaluate not only the rounding error, but also sensitivity to inputs or parameters of the program. We describe two classes of abstractions, a non relational one based on intervals, and a weakly relational one based on parametrized zonotopic abstract domains called affine sets, especially well suited for sensitivity analysis and test generation. These abstract domains are implemented in the Fluctuat static analyzer, and we finally present some experiments.

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“…There are also incremental or "differential" computations (in order not to compute again the functional on each partial computations) [12], [13]. In fact, this is much like the static partitioning technique some of the authors use in [30]. Related algorithms can be found in [11], [27] and [3].…”

Section: Introduction and Related Workmentioning

confidence: 99%

A Policy Iteration Algorithm for Computing Fixed Points in Static Analysis of Programs

Costan¹,

Gaubert

Goubault

et al. 2005

Computer Aided Verification

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Abstract. We present a new method for solving the fixed point equations that appear in the static analysis of programs by abstract interpretation. We introduce and analyze a policy iteration algorithm for monotone self-maps of complete lattices. We apply this algorithm to the particular case of lattices arising in the interval abstraction of values of variables. We demonstrate the improvements in terms of speed and precision over existing techniques based on Kleene iteration, including traditional widening/narrowing acceleration mecanisms.

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Static Analysis-Based Validation of Floating-Point Computations

Cited by 27 publications

References 4 publications

Abstract acceleration in linear relation analysis

Abstract acceleration in linear relation analysis

Static Analysis of Finite Precision Computations

A Policy Iteration Algorithm for Computing Fixed Points in Static Analysis of Programs

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