Specialized Residue Number Systems

Mohan, P. V. Ananda

doi:10.1007/978-3-319-41385-3_8

Cited by 25 publications

(28 citation statements)

References 31 publications

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“…Moreover, all the modular channels are entirely independent of each other. The carry-free nature of modular operations ( 1 ) is one of the most attractive features of residue arithmetic [ 1 , 3 , 8 ].…”

Section: The Basic Concepts Of the Residue Arithmeticmentioning

confidence: 99%

“…Furthermore, it is necessary to determine the integer value of the number by its residue code, which in general is hampered by the non-positional nature of the RNS. The crucial problem of efficient implementation of non-modular operations is constantly receiving considerable attention by modern researchers [ 2 , 5 , 8 ].…”

Section: The Basic Concepts Of the Residue Arithmeticmentioning

confidence: 99%

“…There are two canonical techniques of reverse conversion: the canonical method based on the Chinese Remainder Theorem (CRT) and the residue code conversion to a weighted representation in the Mixed-Radix System (MRS) [ 1 , 2 , 5 , 8 , 14 , 15 , 16 , 17 , 18 ]. In general, all other conversion methods represent different variants of these two methods.…”

Section: Reverse Conversion Of the Residue Code To Conventional Repre...mentioning

confidence: 99%

“…As is well known, the RNS has some advantages over a conventional Weighted Number System (WNS) in the design and implementation of high-performance computing applications, devices, and systems. From its appearance in the mid-1950s to the present, RNS arithmetic has attracted the constant attention of researchers in computer technology [ 1 , 2 ], number-theoretic methods [ 3 , 4 , 5 ], digital signal and image processing [ 2 , 5 , 6 , 7 , 8 ], communications systems [ 5 , 9 ], cryptography [ 2 , 8 , 10 , 11 ], and other fields [ 10 ].…”

Section: Introductionmentioning

confidence: 99%

“…In any case, it has excellent potential for many substantial applications in such areas as digital signal processing, cryptography, distributed information and communication systems, information security systems, fault tolerance, cloud computing, and others. Moreover, these RNS applications may be effectively embedded in processor platforms functioning according to the conventional information-processing approach [ 2 , 5 , 8 ]. For the reasons mentioned above, residue arithmetic represents an efficient mathematical tool for the high-speed implementation of various computational tasks.…”

Section: Introductionmentioning

confidence: 99%

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An Efficient Parallel Reverse Conversion of Residue Code to Mixed-Radix Representation Based on the Chinese Remainder Theorem

Selianinau

Povstenko

2022

Entropy

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In this paper, we deal with the critical problems in residue arithmetic. The reverse conversion from a Residue Number System (RNS) to positional notation is a main non-modular operation, and it constitutes a basis of other non-modular procedures used to implement various computational algorithms. We present a novel approach to the parallel reverse conversion from the residue code into a weighted number representation in the Mixed-Radix System (MRS). In our proposed method, the calculation of mixed-radix digits reduces to a parallel summation of the small word-length residues in the independent modular channels corresponding to the primary RNS moduli. The computational complexity of the developed method concerning both required modular addition operations and one-input lookup tables is estimated as Ok2/2, where k equals the number of used moduli. The time complexity is Olog2k modular clock cycles. In pipeline mode, the throughput rate of the proposed algorithm is one reverse conversion in one modular clock cycle.

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Section: The Basic Concepts Of the Residue Arithmeticmentioning

confidence: 99%

Section: The Basic Concepts Of the Residue Arithmeticmentioning

confidence: 99%