Error Analysis of the Kmetz/Maenner Algorithm

Authors:
M. Arnold;T. Bailey;J. Cowles
Affiliations:
Computer Science and Engineering Department, Lehigh University, 19 Memorial Drive West, Bethlehem, PA 18015, USA;Computer Science Department, University of Wyoming, P.O. Box 3682, Laramie, WY 82071, USA;Computer Science Department, University of Wyoming, P.O. Box 3682, Laramie, WY 82071, USA
Venue:
Journal of VLSI Signal Processing Systems
Year:
2002

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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.