Table-based polynomials for fast hardware function evaluation

Abstract : Many general table-based methods for the evaluation in hardware of elementary functions have been published. The bipartite and multipartite methods implement a first-order approximation of the function using only table lookups and additions. Recently, a single-multiplier second-order method of similar inspiration has also been published. This paper presents a general framework extending such methods to approximations of arbitrary order, using adders, small multipliers, and very small ad-hoc powering units. We obtain implementations that are both smaller and faster than all previously published approaches. This paper also deals with the FPGA implementation of such methods. Previous work have consistently shown that the more complex methods were also faster: The reduction of the table size meant a reduction of its lookup time, which compensated for the addition and multiplication time. A second contribution is therefore to finally create a tradeoff between space and time among table-based methods.
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Jérémie Detrey, Florent de Dinechin. Table-based polynomials for fast hardware function evaluation. [Research Report] LIP RR-2004-52, Laboratoire de l'informatique du parallélisme. 2004, 2+11p. ⟨hal-02101996⟩

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