Optimized low-power elementary function approximation for Chebyshev series approximations

This paper presents a method for computing elementary function using optimized number of most significant bits of coefficients along with truncated multipliers for designing interpolators. The proposed method optimizes the initial coefficient values, which leads to minimize the maximum absolute error of the interpolator output by using a Chebyshev series approximation. The resulting designs can be utilized for any approximation for functions up with smaller requirements for table lookup sizes. Designs for several interpolators that implement reciprocals are presented and analyzed. This paper demonstrates that optimal coefficient values with high precision and smaller lookup table sizes can be optimally compared to standard coefficients for interpolators. The paper presents also VLSI implementation results, targeting a 65nm CMOS technology from IBM.