Two-variable numeric function approximation using least-squares-based regression

Automated design of two-variable numeric functions can be realized efficiently by extending well-known multiplier-less linear function approximation techniques; the arithmetic signal processing effort is minimized by the utilization of a non-uniform piecewise segmentation scheme. However, as common state-of-the-art approaches only consider unpretentious coefficient estimation techniques, such as gradient superposition, this results in large multiplexer-trees for segmentation that, consequently, are restricting the total performance. In this paper a least-squares-based estimation of multiplier-less linear coefficients is introduced that minimizes the number of segments by using a least-squares-based coefficient estimation. The evaluation indicates a reduction of the segmentation effort by nearly 31% on average. Logical and physical CMOS synthesis is performed and the results are compared to actual references highlighting our work high performance approach for the hardware-based calculation of two-variable numeric functions.