IMPLEMENTATION OF FPGA-BASED RISC FOR LNS ARITHMETIC BY SOFTWARE & HARDWARE

Abstract

ield Programmable Gate Arrays (FPGAs) have some difficulty with the implementation of deating-point operations. In particular, devoting the large number of slices needed by floating-point multipliers prohibits incorporating floating point into smaller, less expensive FPGAs. An alternative is the Logarithmic Number System (LNS), where multiplication and division are easy and fast. LNS also has the advantage of lower power consumption than fixed point. The problem with LNS has been the implementation of addition. There are many price/performance tradeoffs in the LNS design space between pure software and specialised-high-speed hardware. This paper focuses on a compromise between these extremes, and on a small RISC core design (loosely inspired by the popular ARM processor) in which only 4 percent additional investment in FPGA resources beyond that required for the integer RISC core more than doubles the speed of LNS addition compared to a pure software approach. This approach shares resources in the data path of the non-LNS parts of the RISC so that the only significant cost is the decoding and control for the LNS instruction. The preliminary experiments suggest modest LNS-FPGA implementations, like the algorithms under consideration, are more cost effective than pure software and can be as cost effective as more expensive LNS-FPGA implementations that attempt to maximise speed