Half-Precision Logarithmic Arithmetic Unit Based on the Fused Logarithmic and Antilogarithmic Converter

This brief utilizes the logarithmic number system (LNS) to realize the half-precision division (DIV), square root (SR), and inverse SR (ISR) that are widely used in both the error resilience application and high-performance computing. With the aid of similarities of logarithmic and antilogarithmic functions, the adder tree and multiplexer in the shift-and-add architecture can be shared by the Log and Antilog converter. Moreover, a novel architecture for DIV and SR based on the fused converter is proposed. Compared to the existing works, this new architecture not only achieves a good tradeoff between precision level and hardware efficiency, but also can support more operations (e.g., exponential function, multiplication) with negligible hardware resources. In addition, the proposed architecture can be easily pipelined to further increase the throughput. Furthermore, for some formulas requiring multiple basic operations (e.g., ISR), the advantage of the LNS is more significant.