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2005 IEEE International Conference on Application-Specific Systems, Architecture Processors (ASAP'05)
Small FPGA polynomial approximations with 3-bit coefficients and low-precision estimations of the powers of x
Samos, Greece
July 23-July 25
ISBN: 0-7695-2407-9
Romain Michard, Arenaire project (CNRS-ENS Lyon-INRIA-UCBL), LIP Ecole Normale Sup?erieure de Lyon (ENS Lyon) Lyon, France
Arnaud Tisserand, Arenaire project (CNRS-ENS Lyon-INRIA-UCBL), LIP Ecole Normale Sup?erieure de Lyon (ENS Lyon) Lyon, France
Nicolas Veyrat-Charvillon, Arenaire project (CNRS-ENS Lyon-INRIA-UCBL), LIP Ecole Normale Sup?erieure de Lyon (ENS Lyon) Lyon, France

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 coef?cients 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., 1.0010001). 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.

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," asap, pp.334-342, 2005 IEEE International Conference on Application-Specific Systems, Architecture Processors (ASAP'05), 2005
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