Asserting the Precision of Floating-Point Computations: A Simple Abstract Interpreter

Goubault, Éric; Martel, Matthieu; Putot, Sylvie

doi:10.1007/3-540-45927-8_15

Cited by 41 publications

(44 citation statements)

References 4 publications

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“…More recently, static program analysis has provided another way to conduct error analysis [12,6,13,14]. This approach characterizes the error of mathematical operations using a set of static inference rules, allowing a compile-time analysis to determine the worst-case precision of a final result.…”

Section: Related Workmentioning

confidence: 99%

Dynamic floating-point cancellation detection

2013

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Floating-point rounding error is a well-known problem in numerical computation that distorts results and is difficult to analyze accurately. We propose a tool that performs automatic binary instrumentation of floating-point code to detect cancellations and to run side-by-side calculations in alternate precisions. The results of this analysis can help developers find areas of their code that are causing a loss of precision. In the future, it will also point out where reduced precision could be used to achieve a faster running time without losing accuracy. In this paper we explain the techniques and present several results, focusing on cancellation detection.

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Section: Related Workmentioning

confidence: 99%

Dynamic floating-point cancellation detection

2013

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“…The underlying idea of the concrete model, first sketched in [11], then further described in more details in [18], and meanwhile implemented in a first version of the Fluctuat static analyzer [12], is to describe the difference of behaviour between the execution of a program in real numbers and in floating-point numbers. For that, the concrete value of a program variable is a triplet (f x , r x , e x ), where f x ∈ F is the value of the variable if the program is executed with a finite-precision semantics, r…”

Section: Concrete Modelmentioning

confidence: 99%

“…Another idea of [11,18,12], also developed here, is that it could be of interest for a static analysis to decompose the error term e x along its provenance in the source code of the analyzed program, in order to point out the main sources of numerical discrepancy. For that, depending on the level of detail required, control points, blocks, or functions of a program can be annotated by a label , which will be used to identify the errors introduced during a computation.…”

Section: Concrete Modelmentioning

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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“…We should add that this work started from the difficulty to find good widening and narrowing operators for domains used for characterizing the precision of floating-point computations, used by some of the authors in [15].…”

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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Asserting the Precision of Floating-Point Computations: A Simple Abstract Interpreter

Cited by 41 publications

References 4 publications

Dynamic floating-point cancellation detection

Dynamic floating-point cancellation detection

Static Analysis of Finite Precision Computations

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

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