The pitfalls of verifying floating-point computations

Monniaux, David

doi:10.1145/1353445.1353446

Cited by 147 publications

(98 citation statements)

References 29 publications

(34 reference statements)

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“…The execution of a program that manipulates the floating point numbers used by scientists is dependent on many factors outside the consideration of a program as a mathematical object 22 . Rounding errors can occur when numerous computations are repeatedly executed, as in weather forecasting 23 .…”

Section: The Failure Of Code Descriptionsmentioning

confidence: 99%

“…Although there is considerable research in this area, for example in arithmetic and floating point calculations [24][25][26][27] , algorithms 28 , verification 29 and fundamental practice 30 Third, there are well-known ambiguities in some of the internationally standardized versions of commonly used programming languages in scientific computation 13 . Monniaux 22 describes an alarming example relating to implementation of software features:…”

Section: The Failure Of Code Descriptionsmentioning

confidence: 99%

“…Perfection is no guarantee of reproducibility Finally, even if a computer program could be unambiguously described and implemented without error, other problems can arise in machine deployment whereby the results from identical code often diverge when hardware and software configurations are changed 22 . So even perfection in one's own software environment does not guarantee reproducibility.…”

Section: Research Perspectivementioning

confidence: 99%

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The case for open computer programs

Ince

Hatton

Graham-Cumming³

2012

Nature

452

356

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Scientific communication relies on evidence that cannot be entirely included in publications, but the rise of computational science has added a new layer of inaccessibility. Although it is now accepted that data should be made available on request, the current regulations regarding the availability of software are inconsistent. We argue that, with some exceptions, anything less than the release of source programs is intolerable for results that depend on computation. The vagaries of hardware, software and natural language will always ensure that exact reproducibility remains uncertain, but withholding code increases the chances that efforts to reproduce results will fail.T he rise of computational science has led to unprecedented opportunities for scientific advance. Ever more powerful computers enable theories to be investigated that were thought almost intractable a decade ago, robust hardware technologies allow data collection in the most inhospitable environments, more data are collected, and an increasingly rich set of software tools are now available with which to analyse computer-generated data.However, there is the difficulty of reproducibility, by which we mean the reproduction of a scientific paper's central finding, rather than exact replication of each specific numerical result down to several decimal places. We examine the problem of reproducibility (for an early attempt at solving it, see ref. 1) in the context of openly available computer programs, or code. Our view is that we have reached the point that, with some exceptions, anything less than release of actual source code is an indefensible approach for any scientific results that depend on computation, because not releasing such code raises needless, and needlessly confusing, roadblocks to reproducibility.At present, debate rages on the need to release computer programs associated with scientific experiments 2-4 , with policies still ranging from mandatory total release to the release only of natural language descriptions, that is, written descriptions of computer program algorithms. Some journals have already changed their policies on computer program openness; Science, for example, now includes code in the list of items that should be supplied by an author 5 . Other journals promoting code availability include Geoscientific Model Development, which is devoted, at least in part, to model description and code publication, and Biostatistics, which has appointed an editor to assess the reproducibility of the software and data associated with an article 6 .In contrast, less stringent policies are exemplified by statements such as 7 ''Nature does not require authors to make code available, but we do expect a description detailed enough to allow others to write their own code to do similar analysis.'' Although Nature's broader policy states that ''...authors are required to make materials, data and associated protocols promptly available to readers...'', and editors and referees are fully empowered to demand and evaluate any specific code, we belie...

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Section: The Failure Of Code Descriptionsmentioning

confidence: 99%

Section: The Failure Of Code Descriptionsmentioning

confidence: 99%

Section: Research Perspectivementioning

confidence: 99%

See 1 more Smart Citation

The case for open computer programs

Ince

Hatton

Graham-Cumming³

2012

Nature

452

356

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“…It is not the case, and (time -2000.0)/time = 2.7 × 10 −4 , since the initial error on the representation of 0.1 is always the same, and then, for all time between any [2 n , 2 n+1 [, all computations are rounded in the same direction. Invariant and safety The following example comes from [20].…”

Section: The Ieee-754 Standardmentioning

confidence: 99%

Towards an Industrial Use of FLUCTUAT on Safety-Critical Avionics Software

Delmas

Goubault

Putot

et al. 2009

Formal Methods for Industrial Critical Systems

105

109

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Abstract. Most modern safety-critical control programs, such as those embedded in fly-by-wire control systems, perform a lot of floating-point computations. The well-known pitfalls of IEEE 754 arithmetic make stability and accuracy analyses a requirement for this type of software. This need is traditionally addressed through a combination of testing and sophisticated intellectual analyses, but such a process is both costly and error-prone. FLUCTUAT is a static analyzer developed by CEA-LIST for studying the propagation of rounding errors in C programs. After a long time research collaboration with CEA-LIST on this tool, Airbus is now willing to use FLUCTUAT industrially, in order to automate part of the accuracy analyses of some control programs. In this paper, we present the IEEE 754 standard, the FLUCTUAT tool, the types of codes to be analyzed and the analysis methodology, together with code examples and analysis results.

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“…However, there are very few attempts to provide ways to specify and to prove behavioral properties of FP programs in deductive verification systems like those above mentioned. This is difficult because FP computations are described operationally and have tricky behaviors as shown by Monniaux [25]. Consequently, it is hard to describe denotationally in a logic setting.…”

Section: Introductionmentioning

confidence: 99%

Multi-Prover Verification of Floating-Point Programs

Ayad

Marché

2010

Automated Reasoning

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Abstract. In the context of deductive program verification, supporting floatingpoint computations is tricky. We propose an expressive language to formally specify behavioral properties of such programs. We give a first-order axiomatization of floating-point operations which allows to reduce verification to checking the validity of logic formulas, in a suitable form for a large class of provers including SMT solvers and interactive proof assistants. Experiments using the Frama-C platform for static analysis of C code are presented.

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The pitfalls of verifying floating-point computations

Cited by 147 publications

References 29 publications

The case for open computer programs

The case for open computer programs

Towards an Industrial Use of FLUCTUAT on Safety-Critical Avionics Software

Multi-Prover Verification of Floating-Point Programs

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