Semantics of roundoff error propagation in finite precision calculations

Martel, Matthieu

doi:10.1007/s10990-006-8608-2

Cited by 38 publications

(38 citation statements)

References 20 publications

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“…The Fluctuat tool automatically provides results on the origin and magnitude of roundoff errors in numerical programs [Martel, 2006, Goubault, 2001, Martel, 2002b.…”

Section: Goals Of Program Verificationsmentioning

confidence: 99%

The pitfalls of verifying floating-point computations

Monniaux

2008

ACM Trans. Program. Lang. Syst.

147

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Current critical systems often use a lot of floating-point computations, and thus the testing or static analysis of programs containing floatingpoint operators has become a priority. However, correctly defining the semantics of common implementations of floating-point is tricky, because semantics may change according to many factors beyond source-code level, such as choices made by compilers. We here give concrete examples of problems that can appear and solutions for implementing in analysis software.

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“…The Fluctuat tool automatically provides results on the origin and magnitude of roundoff errors in numerical programs [Martel, 2006, Goubault, 2001, Martel, 2002b.…”

Section: Goals Of Program Verificationsmentioning

confidence: 99%

The pitfalls of verifying floating-point computations

Monniaux

2008

ACM Trans. Program. Lang. Syst.

147

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“…The semantics of the other elementary operations (division and square root) relies on a power series development and is more complicated. It is fully explicited in [16,17].…”

Section: Numerical Domainsmentioning

confidence: 99%

“…So, it is necessary to provide tools to the programmers, in order to help them to increase the numerical quality of their codes. During the last few years, static analyses by abstract interpretation [5] of the numerical accuracy of floating-point computations have been introduced [9,15,17] and implemented in the Fluctuat tool [10,11] which is used in many industrial contexts. A main advantage of this method is that it enables one to bound safely all the errors arising during a computation, for large ranges of inputs.…”

Section: Introductionmentioning

confidence: 99%

Program transformation for numerical precision

Martel

2009

Proceedings of the 2009 ACM SIGPLAN Workshop on Partial Evaluation and Program Manipulation

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This article introduces a new program transformation in order to enhance the numerical accuracy of floating-point computations. We consider that a program would return an exact result if the computations were carried out using real numbers. In practice, roundoff errors due to the finite representation of values arise during the execution. These errors are closely related to the way formulas are evaluated. Indeed, mathematically equivalent formulas, obtained using laws like associativity, distributivity, etc., may lead to very different numerical results in the computer arithmetic. We propose a semantics-based transformation in order to optimize the numerical accuracy of programs. This transformation is expressed in the abstract interpretation framework and it aims at rewriting pieces of numerical codes in order to obtain results closer to what the computer would output if it used the exact arithmetic.

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“…So it is necessary to provide tools to the programmers, in order to help them to increase the numerical quality of their codes. During the last few years, static analyses by abstract interpretation [2] of the numerical accuracy of floating-point computations have been introduced [6,9,11] and implemented in the Fluctuat tool [7,8] which is used in many industrial contexts. A main advantage of this method is that it enables one to bound safely all the errors arising during a computation, for large ranges of inputs.…”

Section: Introductionmentioning

confidence: 99%

“…the chosen indicator. Detecting the places where quality is lost is a generalisation of the work on error series introduced to assert the accuracy of floating-point expressions [11,7]. The enhancement of the implementation is a generalisation of the semantics-based transformation of [12].…”

Section: Introductionmentioning

confidence: 99%

Semantics of roundoff error propagation in finite precision calculations

Cited by 38 publications

References 20 publications

The pitfalls of verifying floating-point computations

The pitfalls of verifying floating-point computations

Program transformation for numerical precision

Enhancing the implementation of mathematical formulas for fixed-point and floating-point arithmetics

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