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IEEE Transactions on Computers
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A stochastic arithmetic for reliable scientific computation
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Computer Interval Arithmetic: Definition and Proof of Correct Implementation
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Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
An abstract Monte-Carlo method for the analysis of probabilistic programs
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Automatic discovery of linear restraints among variables of a program
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Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
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IEEE Transactions on Computers
Propagation of Roundoff Errors in Finite Precision Computations: A Semantics Approach
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ESOP '02 Proceedings of the 11th European Symposium on Programming Languages and Systems
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EMSOFT '01 Proceedings of the First International Workshop on Embedded Software
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Static analysis of numerical algorithms
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VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
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When the decreasing sequence fails
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Automatic detection of floating-point exceptions
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Automatically adapting programs for mixed-precision floating-point computation
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Computers manipulate approximations of real numbers, called floating-point numbers. The calculations they make are accurate enough for most applications. Unfortunately, in some (catastrophic) situations, the floating-point operations lose so much precision that they quickly become irrelevant. In this article, we review some of the problems one can encounter, focussing on the IEEE754-1985 norm. We give a (sketch of a) semantics of its basic operations then abstract them (in the sense of abstract interpretation) to extract information about the possible loss of precision. The expected application is abstract debugging of software ranging from simple on-board systems (which use more and more on-the-shelf micro-processors with floating-point units) to scientific codes. The abstract analysis is demonstrated on simple examples and compared with related work.