Elementary function approximation using optimized most significant bits of Chebyshev coefficients and truncated multipliers

Abstract

This paper presents a method for computing elementary function using optimized number of most significant bits of coefficients along with truncated multipliers for designing linear and quadratic interpolators. The method proposed 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 and beyond 32-bits (IEEE single precision) of precision with smaller requirements for table lookup sizes. Designs for linear and quadratic interpolators that implement f (x) = 1/x are presented and analyzed, although the method can be extended to other functions. This paper demonstrates that optimal coefficient values with high precision and smaller lookup table sizes can be optimally compared to standard coefficients for interpolators.

Optimized Linear, Quadratic and Cubic Interpolators for Elementary Function Hardware Implementations

“…Although this paper presents ideas similar to other papers in terms of the implementation, the main contribution is the use of the optimization search algorithm to find a direct solution quickly and efficiently. This paper extends earlier work [28][29][30] by providing the following:…”