PQA-FGS: Piecewise Quadratic Approximation with Fine-grained Segmentation for High-Precision Non-linear Computation

Non-linear functions are fundamental mathematical computations in the realms of digital signal processing and artificial intelligence applications. Despite efforts to develop hardware accelerators for non-linear functions, current methodologies exhibit shortcomings in achieving both high-speed and high-precision computations. This paper introduces a novel scheme for high-precision non-linear approximation that leverages piecewise polynomial computation. By employing quadratic approximation, we reduce the number of segments and introduce a fine-grained computation method to meticulously control computational resources. Our example design, synthesized using 40nm CMOS technology, occupies an area of 15123µm<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and consumes a power of 3.48mW when operating at 1GHz. In comparison with the state-of-the-art research, the proposed design boasts a reduction of 76.6% in area and an 86.3% decrease in power consumption, while maintaining equivalent precision levels.