Implementing Exact Calculations in Hardware

A technique for performing exact calculations it discussed. The technique uses single-modulus P arithmetic to perform calculations over the finite field of integers and the finite ring of integers. It is shown that the arithmetic operations modulo P (which obviously can be impleinented in microproce...

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Bibliographic Details
Published in:IEEE transactions on computers 1987-06, Vol.C-36 (6), p.764-768
Main Authors: THOMAS, J. J, PARKER, S. R
Format: Article
Language:English
Subjects:
Applied sciences
Circuit properties
Digital circuits
Electric, optical and optoelectronic circuits
Electronic circuits
Electronics
Exact calculations
Exact sciences and technology
finite fields
finite rings of integers
finite-segment P-adic arithmetic
Mersenne prime numbets
residue number system
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Summary:A technique for performing exact calculations it discussed. The technique uses single-modulus P arithmetic to perform calculations over the finite field of integers and the finite ring of integers. It is shown that the arithmetic operations modulo P (which obviously can be impleinented in microprocessor configurations, VLSI, and/or software) can easily be extended from the range of values of the finite field of integers, modulo P, to the finite ring of integers, modulo pN where N is afny positive integer. This technique can be used for exact calculations over the rational numbers as well as complex numbers. Examples, block diagrams, And processor arrays are presented illustrating the simplicity of these operations.
ISSN:0018-9340
1557-9956
DOI:10.1109/TC.1987.1676969