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

Romain Michard (1) , Arnaud Tisserand , Nicolas Veyrat-Charvillon

1 ARENAIRE - Computer arithmetic

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.

Keywords: COMPUTER ARITHMETIC; DIGITAL SIGNAL APPLICATION; POLYNOMIAL EVALUATION; HARDWARE ARITHMETIC OPERATOR

Domains: Other [cs.OH]

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⟩