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Author Papachristou, Christos A.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1987
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract This paper investigates the complexity of multioperand residue addition and multiplication implemented by associative table lookup processing. The complexity measure used is the size of the associative memory, that is, the number of matching words in memory. This measure largely depends on the residue recurrencies, or multiplicities, in the addition and multiplication tables module $\textit{M}.$ The major effort in this work is to evaluate the recurrencies in simultaneous multioperand residue addition and multiplication. The evaluation is simple in case of addition mod $\textit{M},$ and also in multiplication mod $\textit{M}$ if $\textit{M}$ is prime. To treat the more difficult case of $\textit{M}$ nonprime, a recursive procedure was developed for computing the 2-operand multiplication recurrencies mod $\textit{M}.$ The basis of this technique is the precedence relationships associated with a tree representation of the factors of $\textit{M}.$ It is then shown that the general $\textit{D}-operand$ multiplication mod M, D > 2 and $\textit{M}$ nonprime, can be reduced to the 2-operand case by isomorphic transformation. Computation results of 2-operand residue arithmetic operations are provided. Applications to RNS arithmetic implementation are discussed.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1987-04-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 34
Issue Number 2
Page Count 21
Starting Page 376
Ending Page 396


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Source: ACM Digital Library