Novel Quasi-Symmetrical Approach for Efficient Logarithmic and Anti-logarithmic Converters

This paper presents a new approach to approximate log2(1+x) and (2 (exp x)-1) functions which can be used for low-area and high-speed logarithmic and anti-logarithmic converters in hybrid number system processors and DSP applications. By employing the novel quasi-symmetrical difference method with only shift-add logic and lookup table, the proposed approach can reduce the converter area and improve the conversion speed significantly while achieve similar accuracy compared with the best previous method. The implementation results in both FPGA and 0.18-micrometer CMOS technology are also presented and discussed.