Methods and applications of error-free computation
Methods and applications of error-free computation
The Calcualtion of Multiplicative Inverses Over GF(P) Efficiently Where P is a Mersenne Prime
IEEE Transactions on Computers
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
Journal of the ACM (JACM)
On Euclid's Algorithm and the Theory of Subresultants
Journal of the ACM (JACM)
Number Theory in Digital Signal Processing
Number Theory in Digital Signal Processing
An Autoscale Residue Multiplier
IEEE Transactions on Computers
Matrix Processors Using p-adic Arithmetic for Exact Linear Computations
IEEE Transactions on Computers
PAS '95 Proceedings of the First Aizu International Symposium on Parallel Algorithms/Architecture Synthesis
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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.