Efficient Function Evaluations with Lookup Tables for Structured Matrix Operations

Abstract

A hardware efficient approach is introduced for elementary function evaluations in certain structured matrix computations. It is a comprehensive approach that utilizes lookup tables for compactness, employs interpolations with adders and multipliers for their adaptivity to non-tabulated values and, more distinctively, exploits the function properties and the matrix structures to claim better control over numerical dynamic ranges. We demonstrate the effectiveness of the approach with simulation and synthesis results on evaluating, in particular, the cosine function, the exponential function and the zero-order Bessel function of the first kind.