Bipartite implementation of the residue logarithmic number system
Mark G. Arnold, Jie Ruan · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2005
The Logarithmic Number System (LNS) has area and power advantages over fixed-point and floating-point number systems in some applications that tolerate moderate precision. LNS multiplication/division require only addition/subtraction of logarithms. Normally, LNS is implemented with ripple-carry binary arithmetic for manipulating the logarithms; however, this paper uses carry-free residue arithmetic instead. The Residue Logarithmic Number System (RLNS) has the advantage of faster multiplication and division. In contrast, RLNS addition requires table-lookup, which is its main area and delay cost. The bipartite approach, which uses two tables and an integer addition, is introduced here to optimize RLNS addition. Using the techniques proposed here, RLNS with dynamic range and precision suitable for MPEG applications can be synthesized. Synthesis results show that bipartite RLNS achieves area savings and shorter delays compared to naive RLNS.