A high-speed division algorithm in residue number system using parity-checking technique

Yang, Jen-Ho; Chang, Chin‐Chen; Chen, Chien-yuan

doi:10.1080/00207160410001708805

Cited by 17 publications

(10 citation statements)

References 8 publications

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“…In order to speed up current quotient calculation, J.H. Yang [28] suggested a division algorithm based on parity check that finds the quotient twice as fast as the algorithms [24,27]. But the calculations of the high powers of 2 still require much time in RNSs, and these operations are performed at each iteration.…”

Section: Of 17mentioning

confidence: 99%

A High-Speed Division Algorithm for Modular Numbers Based on the Chinese Remainder Theorem with Fractions and Its Hardware Implementation

et al. 2019

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In this paper, a new simplified iterative division algorithm for modular numbers that is optimized on the basis of the Chinese remainder theorem (CRT) with fractions is developed. It requires less computational resources than the CRT with integers and mixed radix number systems (MRNS). The main idea of the algorithm is (a) to transform the residual representation of the dividend and divisor into a weighted fixed-point code and (b) to find the higher power of 2 in the divisor written in a residue number system (RNS). This information is acquired using the CRT with fractions: higher power is defined by the number of zeros standing before the first significant digit. All intermediate calculations of the algorithm involve the operations of right shift and subtraction, which explains its good performance. Due to the abovementioned techniques, the algorithm has higher speed and consumes less computational resources, thereby being more appropriate for the multidigit division of modular numbers than the algorithms described earlier. The new algorithm suggested in this paper has O (log2 Q) iterations, where Q is the quotient. For multidigit numbers, its modular division complexity is Q(N), where N denotes the number of bits in a certain fraction required to restore the number by remainders. Since the number N is written in a weighed system, the subtraction-based comparison runs very fast. Hence, this algorithm might be the best currently available.

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Section: Of 17mentioning

confidence: 99%

A High-Speed Division Algorithm for Modular Numbers Based on the Chinese Remainder Theorem with Fractions and Its Hardware Implementation

et al. 2019

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“…This method gives the high-performance computing algorithms which is essential to meet the expanding demand for computation .The objective of the Division of Computational Algorithms is to achieve the levels of performance and reliability required for fundamental computational science applications [6] ,…”

Section: Algorithm Stepsmentioning

confidence: 99%

Enhanced Computational Algorithm of Binary Division by Comparison Method

Vandana¹

2014

IJCA

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Binary division is the basic operation performed by arithmetic circuit. It is simpler than the decimal division because the result always produced in either 1 or 0. All the values of dividend, divisor, quotient and remainder are in 1's or o's form. There are number of binary division algorithms are available as restoring method, non restoring method, division by XOR logic operation and SRT division and comparison method. This paper presents a new concept of the comparison division method. The comparison division algorithm provides high speed computation work and increases' the system performance.

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“…The known RNS division algorithms [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] can be divided into two classes: based on the comparison of numbers, and based on the subtraction.…”

Section: Introductionmentioning

confidence: 99%

A Division Algorithm in a Redundant Residue Number System Using Fractions

et al. 2020

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The residue number system (RNS) is widely used for data processing. However, division in the RNS is a rather complicated arithmetic operation, since it requires expensive and complex operators at each iteration, which requires a lot of hardware and time. In this paper, we propose a new modular division algorithm based on the Chinese remainder theorem (CRT) with fractional numbers, which allows using only one shift operation by one digit and subtraction in each iteration of the RNS division. The proposed approach makes it possible to replace such expensive operations as reverse conversion based on CRT, mixed radix conversion, and base extension by subtraction. Besides, we optimized the operation of determining the most significant bit of divider with a single shift operation of the modular divider. The proposed enhancements make the algorithm simpler and faster in comparison with currently known algorithms. The experimental simulation using Kintex-7 showed that the proposed method is up to 7.6 times faster than the CRT-based approach and is up to 10.1 times faster than the mixed radix conversion approach.

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A high-speed division algorithm in residue number system using parity-checking technique

Cited by 17 publications

References 8 publications

A High-Speed Division Algorithm for Modular Numbers Based on the Chinese Remainder Theorem with Fractions and Its Hardware Implementation

A High-Speed Division Algorithm for Modular Numbers Based on the Chinese Remainder Theorem with Fractions and Its Hardware Implementation

Enhanced Computational Algorithm of Binary Division by Comparison Method

A Division Algorithm in a Redundant Residue Number System Using Fractions

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