Piecewise polynomial approximation with reducedtable bit-width and guaranteed accuracy

Abstract

An improvement to the piecewise polynomial approximation in hardware is proposed. A new error bound is given for the low-order polynomial interpolation with pointwise constraints ona uniform grid. A method of table size reduction and near optimal quantization of coefficients using intersegment constraints and mixed integer programmingwith guaranteed accuracy is proposed.A case study shows up to 60% table size reduction compared to unconstrained polynomials. Gate level RTL synthesis shows that table reduction has noticeable impact on the design area.