Numerical Reproducibility and Parallel Computations: Issues for Interval Algorithms
What is called numerical reproducibility is the problem of getting the same result when the scientific computation is run several times, either on the same machine or on different machines, with different types and numbers of processing units, execution environments, computational loads, etc. This p...
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| Vydané v: | IEEE transactions on computers Ročník 63; číslo 8; s. 1915 - 1924 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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New York
IEEE
01.08.2014
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Institute of Electrical and Electronics Engineers |
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| ISSN: | 0018-9340, 1557-9956 |
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| Abstract | What is called numerical reproducibility is the problem of getting the same result when the scientific computation is run several times, either on the same machine or on different machines, with different types and numbers of processing units, execution environments, computational loads, etc. This problem is especially stringent for HPC numerical simulations. In what follows, we identify the problems encountered when implementing interval routines in floating-point arithmetic. Some are well-known and common in numerical computations, some are specific to interval computations. We propose here a classification of floating-point issues by distinguishing their severity with respect to correctness and tightness of the computed interval result. In fact, interval computation can accommodate the lack of numerical reproducibility as long as it does not affect the inclusion property, which is the main property of interval arithmetic. Several ways to preserve the inclusion property are presented, on the example of the product of matrices with interval coefficients. |
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| AbstractList | What is called numerical reproducibility is the problem of getting the same result when the scientific computation is run several times, either on the same machine or on different machines, with different types and numbers of processing units, execution environments, computational loads, etc. This problem is especially stringent for HPC numerical simulations. In what follows, we identify the problems encountered when implementing interval routines in floating-point arithmetic. Some are well-known and common in numerical computations, some are specific to interval computations. We propose here a classification of floating-point issues by distinguishing their severity with respect to correctness and tightness of the computed interval result. In fact, interval computation can accommodate the lack of numerical reproducibility as long as it does not affect the inclusion property, which is the main property of interval arithmetic. Several ways to preserve the inclusion property are presented, on the example of the product of matrices with interval coefficients. What is called ''numerical reproducibility'' is the problem of getting the same result when the scientific computation is run several times, either on the same machine or on different machines, with different types and numbers of processing units, execution environments, computational loads etc. This problem is especially stringent for HPC numerical simulations. In what follows, the focus is on parallel implementations of interval arithmetic using floating-point arithmetic. For interval computations, numerical reproducibility is of course an issue for testing and debugging purposes. However, as long as the computed result encloses the exact and unknown result, the inclusion property, which is the main property of interval arithmetic, is satisfied and getting bit for bit identical results may not be crucial. Still, implementation issues may invalidate the inclusion property. Several ways to preserve the inclusion property are presented, on the example of the product of matrices with interval coefficients. |
| Author | Revol, Nathalie Theveny, Philippe |
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| SubjectTerms | Accuracy Computation Computer architecture Computer Arithmetic Computer Science Computer simulation Distributed, Parallel, and Cluster Computing Floating point arithmetic Inclusions Instruction sets Intervals Mathematical models Metals Numerical models Preserves Registers Reproducibility Roundoff errors |
| Title | Numerical Reproducibility and Parallel Computations: Issues for Interval Algorithms |
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