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Multiplication by Constants

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Application-Specific Arithmetic

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Abstract

Multiplication by a constant is probably the most useful and best studied case of operator specialization, in particular for its importance in the construction of digital filters. There are two main families of constant multiplication techniques (shift-and-add and table-based), and there are several types of constants (integer/fixed-point, rational, or arbitrary real numbers). This chapter reviews the techniques that have been developed for each case. Some variants of the multiple constant multiplication problems are also addressed.

Being unable to trust my reasoning, I learnt by heart all the possible results of all the possible multiplications.Eugène Ionesco, La leçon

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Authors and Affiliations

  1. CITI laboratory, INSA-Lyon, Villeurbanne, France

    Florent de Dinechin

  2. Fulda University of Applied Sciences, Fulda, Germany

    Martin Kumm

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  1. Florent de Dinechin
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de Dinechin, F., Kumm, M. (2024). Multiplication by Constants. In: Application-Specific Arithmetic. Springer, Cham. https://doi.org/10.1007/978-3-031-42808-1_12

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