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Optimizing Residue Number System on FPGA
2016 IEEE International Conference on Internet of Things (iThings) and IEEE Green Computing and Communications (GreenCom) and IEEE Cyber, Physical and Social Computing (CPSCom) and IEEE Smart Data (SmartData), 2016Originated from Chinese Remainder Theorem in the 4th century AD, Residue Number System (RNS) has been regarded as a promising number representation method in the field of digital computer arithmetic. Even though reconfigurable hardware devices such as Field Programmable Gate Arrays (FPGA) have been a popular platform for RNS applications due to its ...
Jiahe Liu, Bangtian Liu, Haohuan Fu
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Base conversion in residue number systems
BIT, 1975We are concerned in this paper with the representation of an integer in a (multiple-modulus) residue number system and, in particular, with an algorithm for changing the base vector of the residue number system. Szabo and Tanaka [1, p.47] describe such an algorithm when each modulus of the second base vector is relatively prime to each modulus of the ...
Robert T. Gregory, David W. Matula
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Algorithms for comparison in residue number systems
2016 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA), 2016Residue Number Systems (RNSs) has been widely used in digital signal processing (DSP) systems and cases of fast computing, parallelism and fault tolerant because of its carry-free property. However, the comparison operation in an RNS is quite difficult and the computation cost is high, which are a significant limitation to apply it for division ...
Hanshen Xiao +3 more
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An implementation of a scaler in the Residue number System
2012 International Symposium on Communications and Information Technologies (ISCIT), 2012This paper presents an implementation of an efficient scaling algorithm in the Residue number System (RNS). The original base extension scheme is modified to improve the performance. This modified base extension scheme also requires less hardware space than the original algorithm. Analysis shows the delay of this scaling scheme could be reduced further
Yufeng Lai, Yinan Kong
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Addition and Subtraction in the Residue Number System
IEEE Transactions on Electronic Computers, 1967Improved residue expression and new arithmetic algorithms for addition and subtraction are proposed. In the proposed system positive and negative integers of any magnitude can be handled regardless of the particular choice of the set of relatively prime bases.
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Efficient scaling in the residue number system
International Conference on Acoustics, Speech, and Signal Processing, 2003A unified residue number system scaling technique that allows the designer a great deal of flexibility in choosing the scale factor is presented. The technique is based on the L( epsilon + delta )-CRT (Chinese remainder theorem). By embedding the scaling process in the CRT, the L( epsilon + delta )-CRT can also be used to simplify the residue-to-analog
Mike Griffin, Mike Sousa, Fred J. Taylor
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2014
Residue Number Systems have probed their potential for computation-intensive applications, especially those related to signal processing. Their main advantage is the absence of carry propagation between channels in addition, subtraction and multiplication.
Antonio Lloris Ruiz +3 more
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Residue Number Systems have probed their potential for computation-intensive applications, especially those related to signal processing. Their main advantage is the absence of carry propagation between channels in addition, subtraction and multiplication.
Antonio Lloris Ruiz +3 more
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Advanced Computing and Communications, 2017
Residue Number systems have been extensively studied in past four decades in view of their advantages in some applications in Digital Signal Processing and Cryptography. In this tutorial paper, we introduce the basic concepts highlighting the advantages and disadvantages over other number systems.
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Residue Number systems have been extensively studied in past four decades in view of their advantages in some applications in Digital Signal Processing and Cryptography. In this tutorial paper, we introduce the basic concepts highlighting the advantages and disadvantages over other number systems.
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Scaling in residue number systems
Cybernetics, 1990Let \(m_ 1,\dots,m_ k\) be pairwise relatively prime integers \((k \geq 2)\), with \(m_ 1m_ 2\dots m_ k = M\). It is desired to approximate \(A/S\) by modular arithmetic, where \(S\) is a positive rational number and \(A\) is an integer such that \(2| A| \leq M\). A method is given for doing this in a form suitable for parallel processing.
Vasilevich, L. N., Kolyada, A. A.
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General Division in the Symmetric Residue Number System
IEEE Transactions on Computers, 1973Summary: In the residue number system, the arithmetic operations of addition, subtraction, and multiplication are executed in the same period of time without the need for interpositional carry. There is a hope for high-speed operation if residue arithmetic is used for digital computation.
Eisuke Kinoshita +2 more
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