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Article #
11_2021
56
p.
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submitted on 02th
Apr 2021 displayed on
website on 28th
June
2021
Konstantin
S. Isupov
An overview of high-performance computing using the residue
number system
A residue number system (RNS) is a non-positional number system,
an alternative to a binary representation of numbers. In RNS,
a large integer is represented as a set of
smaller numbers, which are the remainders (“residues”) of
dividing its original value by some moduli. An exciting
feature of the RNS is that addition,
subtraction, and multiplication with each residue are performed
independently, which provides parallel, carry-free, and
high-speed computer arithmetic. On the other
hand, non-modular operations that require estimating
the magnitude of a number by its residues are challenging to
implement in RNS since there is no parallel
form for them.
This paper provides an overview of research on the implementation
and practical application of high-performance
computational techniques for RNS. More
specifically, the paper addresses the following two aspects: (In Russian).
Key words: system of residual classes, non-modular
operations, high performance computing, parallel algorithms.
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