Error Analysis of the Kmetz/Maenner Algorithm

Abstract

Use of low-precision logarithms can minimize power consumption and increase the speed of multiply-intensive signal-processing systems, such as FIR filters. Although straight table lookup is the most obvious way to compute the logarithm, Maenner claims to have discovered a technique that produces four extra bits at no cost. We analyze Maenner's technique and show that in fact the technique provides only one extra bit of precision. A related technique by Kmetz, which has never been analyzed before, is shown here to be more accurate than Maenner's. We compare these techniques to the more complex bipartite technique, and show that Kmetz's technique takes less memory for systems requiring fewer than ten bits of precision.