Interpolator algorithms for approximating the LNS addition and subtraction: Design and analysis

Abstract

The logarithmic number system (LNS) can be considered a good alternative to floating-point, specifically for applications that require a wide range of dynamic numbers for arithmetic operations. To date, its implementation is still restricted by the complexity of performing addition and subtraction operations as a result of using large lookup tables. In previous works, interpolation has been widely used to approximate these non-linear functions. Therefore in this paper, an analysis is presented to identify the most suitable algorithm to be employed for approximating the LNS addition and subtraction functions at 32-bit precisions. The selection is based on the minimum amount of storage that can be attained whilst maintaining its accuracy within the floating-point (FLP) limit. From the results it is clear that there is a potential procedure which can fulfil the above criteria, and that could possibly be applied in the future implementation of an LNS system.