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

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 nonzero and possibly noncontiguous 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.