The Colloquium Series of the
            Department of Computer Science,
		  University of Wyoming

			presents

                     Dr. Mark Arnold
                    Lehigh University

              "Logarithmic Number Systems"

                 Friday, April 7, 2006
                        ENG 4066
                     4:10 - 5:00 p.m.
   
Abstract:

The Logarithmic Number System (LNS) represents real numbers using a
finite precision logarithm.  Like any finite representation, the number
of bits chosen determines the resolution of the system and therefore the
application performance.  LNS offers better performance and lower cost
for easy real operations such as multiplication, division, roots and
powers compared to fixed- and floating-point number systems where such
operations are thought to be hard.  The problems with LNS are that
addition and especially subtraction are increasingly expensive when
performed with extreme accuracy, because these operations involve table
lookup and possibly interpolation.  Also, conversion to and from
conventional representations can be similarly expensive.  Another
inconvenience is the fact the logarithm of zero is undefined.  This talk
will consider how certain special-purpose applications have overcome
these problems to exploit LNS advantages, giving hardware that is
faster, cheaper and consumes less power than those based on traditional
arithmetic.

Examples of special-purpose hardware systems that have adopted LNS
successfully include neural networks, multimedia encoders and decoders,
control systems, and N-body simulators.  In each of these applications,
designers have reformulated the algorithm to avoid certain LNS
weaknesses.  LNS has been successful in such applications because they
have a large share of easy operations and they tolerate lower precision
results.  Traditionally, LNS sum and difference calculation have been
carried out with enough accuracy to be faithful to the number of bits of
precision required for the application.  To minimize the cost of the
LNS, simulative studies determine the minimum number of bits for
wordsize and precision in the LNS representation for the application to
operate successfully.  A new approach considers using lower accuracy LNS
sum and difference calculation in addition to limiting the wordsize and
precision of the representation.

Biography:

Mark G. Arnold received the BS and MS degrees from the University of
Wyoming (USA), and the PhD degree from the University of Manchester
Institute of Science and Technology (UK).  From 1982 to 2000, he was a
lecturer at the University of Wyoming.  From 2000 to 2002, he was a
lecturer at UMIST.  In 2002, he joined the faculty of Lehigh University
(USA), where he is an assistant professor.  His research interests
include embedded systems, hardware description languages, and computer
arithmetic.