Constrained piecewise polinomial approximation for hardware implementation of elementary functions

This paper presents a novel technique for designing piecewise polynomial interpolators for hardware implementation of elementary functions. In the proposed approach, we impose special constraints between polynomial coefficients of adjacent segments. This allows to significantly reduce look-up table size with respect to standard, unconstrained piecewise polynomial approximations, with negligible reduction in accuracy. The reduction of look-up table size improves performances in terms of area and speed. Implementations of linear and quadratic interpolators for the reciprocal function f(x)=1/x are presented and analyzed as an application example in the paper.