Optimized cubic chebyshev interpolator for elementary function hardware implementations

This paper presents a cubic interpolator for computing elementary functions using truncated-matrix arithmetic units and an optimized number of coefficients bits. The proposed method optimizes the initial coefficient values found using a Chebyshev series approximation, minimizing the maximum absolute error of the interpolator output. The resulting designs can be utilized for approximating any function up to 53-bits of precision (IEEE double precision significant). Area, delay and power estimates are given for 16, 24 and 32-bit cubic interpolators that compute the reciprocal function, targeting a 65nm CMOS technology from IBM. Results indicate the proposed method uses smaller arithmetic units and has reduced lookup table sizes than previously proposed methods.