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A Correctly-Rounded Fixed-Point-Arithmetic Dot-Product Algorithm

Abstract : Dot products (also called sums of products) are ubiquitous in matrix computations, for instance in signal processing. We are especially interested in digital filters, where they are the core operation. We therefore focus on fixed-point arithmetic, used in embedded systems for time and energy efficiency. Common dot product algorithms ensure faithful rounding. For the sake of accuracy and reproducibility, we want to ensure correct rounding. This article describes an algorithm that computes a correctly-rounded sum of products from inputs whose format is known in advance. This algorithm relies on odd rounding (that is easily implemented in hardware) and comes with a careful proof and some cost analysis.
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Contributor : Sylvie Boldo <>
Submitted on : Wednesday, October 28, 2020 - 12:53:46 PM
Last modification on : Friday, October 30, 2020 - 3:23:24 AM


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Sylvie Boldo, Diane Gallois-Wong, Thibault Hilaire. A Correctly-Rounded Fixed-Point-Arithmetic Dot-Product Algorithm. 2020 IEEE 27th Symposium on Computer Arithmetic (ARITH), Jun 2020, Portland, United States. pp.9-16, ⟨10.1109/ARITH48897.2020.00011⟩. ⟨hal-02982017⟩



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