Scalable yet Rigorous Floating-Point Error Analysis
| Autor: | Ian Briggs, Pavel Panchekha, Sriram Krishnamoorthy, Ganesh Gopalakrishnan, Arnab Das |
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| Rok vydání: | 2020 |
| Předmět: |
Floating point
Computer science Automatic differentiation Fast Fourier transform 010103 numerical & computational mathematics 02 engineering and technology Program optimization Symbolic execution 01 natural sciences Matrix multiplication Expression (mathematics) Operator (computer programming) Computer engineering Formal specification 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing 0101 mathematics Round-off error Abstraction (linguistics) |
| Zdroj: | SC |
| DOI: | 10.1109/sc41405.2020.00055 |
| Popis: | Automated techniques for rigorous floating-point round-off error analysis are a prerequisite to placing important activities in HPC such as precision allocation, verification, and code optimization on a formal footing. Yet existing techniques cannot provide tight bounds for expressions beyond a few dozen operators–barely enough for HPC. In this work, we offer an approach embedded in a new tool called SATIHE that scales error analysis by four orders of magnitude compared to today’s best-of-class tools. We explain how three key ideas underlying SATIHE helps it attain such scale: path strength reduction, bound optimization, and abstraction. SATIHE provides tight bounds and rigorous guarantees on significantly larger expressions with well over a hundred thousand operators, covering important examples including FFT, matrix multiplication, and PDE stencils. |
| Databáze: | OpenAIRE |
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