Accurate piecewise uniform approximation logarithmic/antilogarithmic converters for GPU applications

Logarithmic number system (LNS) is increasingly used for low power arithmetic calculations in graphical processing unit (GPU). LNS requires less hardware. Based on uniform subdivisions and linear-Lagrange interpolation, a novel 8-subdivisions logarithmic/antilogarithmic converters are proposed. Compared with different methodologies, the proposed logarithmic/antilogarithmic converters achieve high accuracy. Also, a significant decrease in area is presented in the comparison between the proposed converters and the prior ones. Hardware implementation using shift-and-add approach is adopted to further simplify the hardware. The novel logarithmic/antilogarithmic converters are implemented and synthesized using 90 nm CMOS technology. Up to 23% and 11% decrease in relative error and area are achieved.