A new non-uniform segmentation and addressing remapping strategy for hardware-oriented function evaluators based on polynomial approximation

Abstract

This paper presents a new non-uniform segmentation method for arithmetic function evaluation based on polynomial approximations. The merging of several uniform segments can reduce the required ROM size compared with normal uniform segmentation. The previously proposed hierarchical segmentation turns out to be special cases of this new approach. In general, non-uniform segmentation leads to irregular address indexing that needs extra computation hardware. Here, an address rearrangement and mapping method is proposed that does not need any additional address computation, and thus the critical path delay can be reduced. Experimental results show that this new segmentation and address remapping method can efficiently reduce the table size for some elementary arithmetic functions, such as log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> x and 1/x.