Second Order Function Approximation with a Single Small Multiplication

Jérémie Detrey 1 Florent de Dinechin 1
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : This paper presents a new scheme for the hardware evaluation of elementary functions, based on a piecewise second order minimax approximation. The novelty is that this evaluation requires only one small rectangular multiplication. Therefore the resulting architecture combines a small table size, thanks to second-order evaluation, with a short critical path: Consisting of one table lookup, the rectangular multiplication, and one addition, the critical path is shorter than that of a plain first-order evaluation. Synthesis results for several functions show that this method outperforms all the previously published methods in both area and speed for precisions ranging from 12 to 24 bits.
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https://hal.inria.fr/inria-00071443
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Submitted on : Tuesday, May 23, 2006 - 5:33:35 PM
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Jérémie Detrey, Florent de Dinechin. Second Order Function Approximation with a Single Small Multiplication. [Research Report] RR-5140, LIP RR-2004-13, INRIA, LIP. 2004. ⟨inria-00071443⟩

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