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Redundant Logarithmic Arithmetic
August 1990 (vol. 39 no. 8)
pp. 1077-1086

A number system that offers advantages in some situations over conventional floating point and sign/logarithmic number systems is described. Redundant logarithmic arithmetic, like conventional logarithmic arithmetic, relies on table lookups to make the arithmetic unit simpler than an equivalent floating point unit. The cost of 32 bit subtraction in a redundant logarithmic number system is lower than previously published logarithmic subtraction methods. The total memory requirement for a 29-bit redundant logarithmic unit is 16 K words compared to 22 K words by the best previously published conventional sign logarithm unit, assuming similar addition techniques are employed. A redundant logarithmic number system can be implemented with online arithmetic, which would be impractical for a conventional sign logarithm number system. The disadvantages of redundant arithmetic are typical of redundant number systems. First, the redundancy doubles the storage requirements for data values. Second, the representation can become ill-conditioned, especially as a result of iterated multiplications. Third, division and square root operations are more difficult to implement in redundant logarithmic arithmetic.

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Index Terms:
table lookups; arithmetic unit; 32 bit subtraction; redundant logarithmic number system; memory requirement; 29-bit redundant logarithmic unit; online arithmetic; storage requirements; data values; ill-conditioned; iterated multiplications; division; square root; redundant logarithmic arithmetic; digital arithmetic; number theory; redundancy; table lookup.
M.G. Arnold, T.A. Bailey, J.R. Cowles, J.J. Cupal, "Redundant Logarithmic Arithmetic," IEEE Transactions on Computers, vol. 39, no. 8, pp. 1077-1086, Aug. 1990, doi:10.1109/12.57046
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