# Small FPGA polynomial approximations with $3$-bit coefficients and low-precision estimations of the powers of x

1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : This paper presents small FPGA implementations of low precision polynomial approximations of functions without multipliers. Our method uses degree-$2$ or degree-$3$ polynomial approximations with at most $3$-bit coefficients and low precision estimations of the powers of $x$. Here, we denote by $3$-bit coefficients values with at most $3$ non-zero and possibly non-contiguous signed bits (e.g. $1.001000\overline1$). This leads to very small operators by replacing the costly multipliers by a small number of additions. Our method provides approximations with very low average error and is suitable for signal processing applications.
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https://hal.inria.fr/inria-00070504
Contributor : Rapport de Recherche Inria <>
Submitted on : Friday, May 19, 2006 - 8:41:23 PM
Last modification on : Tuesday, May 7, 2019 - 1:32:10 PM

### Identifiers

• HAL Id : inria-00070504, version 1

### Citation

Romain Michard, Arnaud Tisserand, Nicolas Veyrat-Charvillon. Small FPGA polynomial approximations with $3$-bit coefficients and low-precision estimations of the powers of x. [Research Report] RR-5503, LIP RR-2005-8, INRIA, LIP. 2005, pp.13. ⟨inria-00070504⟩

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