RISC Conversions for LNS Arithmetic in Embedded Systems

Abstract

The paper presents an original methodology for the implementation of the Logarithmic Number System (LNS) arithmetic, which uses Reduced Instruction Set Computing (RISC). The core of the proposed method is a newly developed algorithm for conversion between LNS and the floating point (FLP) representations named “looping in sectors”, which brings about reduced memory consumption without a loss of accuracy. The resulting effective RISC conversions use only elementary computer operations without the need to employ multiplication, division, or other functions. Verification of the new concept and related developed algorithms for conversion between the LNS and the FLP representations was realized on Field Programmable Gate Arrays (FPGA), and the conversion accuracy was evaluated via simulation. Using the proposed method, a maximum relative conversion error of less than ±0.001% was achieved with a 22-ns delay and a total of 50 slices of FPGA consumed including memory cells. Promising applications of the proposed method are in embedded systems that are expanding into increasingly demanding applications, such as camera systems, lidars and 2D/3D image processing, neural networks, car control units, autonomous control systems that require more computing power, etc. In embedded systems for real-time control, the developed conversion algorithm can appear in two forms: as RISC conversions or as a simple RISC-based logarithmic addition.