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Tradeoff between Approximation Accuracy and Complexity for Range Analysis using Affine Arithmetic

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Abstract

Digital signal processing algorithms are usually developed in floating-point arithmetic. After that floating-point to fixed-point transformation is performed to implement them on fixed-point devices, for higher speed, smaller area and lower power. During this transformation, range analysis is to find the minimum integer bit-widths for signals to prevent overflow. Existing state-of-the-art analytical methods for range analysis are generally based on Affine Arithmetic, which presents two approximation methods for non-affine operations. The Chebyshev approximation provides the best approximation with prohibitive computation expense. The trivial range estimation, which is very efficient for computation, over-estimates the range four times at the worst case. This paper presents a novel approach to let user decide tradeoff between approximation accuracy and complexity of Affine Arithmetic. Case studies and experiments are carried out to demonstrate its efficiency.

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Acknowledgements

The authors gratefully acknowledge the anonymous reviewers for their careful observations and insightful comments, which have helped us to improve the quality of this paper.

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  1. Department of Electronic and Information Engineering, Harbin Institute of Technology Shenzhen Graduate School, Xili, Shenzhen, 518055, China

    Linsheng Zhang, Yan Zhang & Wenbiao Zhou

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  1. Linsheng Zhang
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  2. Yan Zhang
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  3. Wenbiao Zhou
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Correspondence to Linsheng Zhang.

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Zhang, L., Zhang, Y. & Zhou, W. Tradeoff between Approximation Accuracy and Complexity for Range Analysis using Affine Arithmetic. J Sign Process Syst 61, 279–291 (2010). https://doi.org/10.1007/s11265-010-0452-2

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  • DOI: https://doi.org/10.1007/s11265-010-0452-2

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