A Multifunctional Unit For Reverse Conversion and Sign Detection Based on The 5-Moduli Set

Authors

  • Mohsen Mojahed Department of Computer Engineering, Kerman Branch of Azad University
  • Amir Sabbagh Molahosseini Department of Computer Engineering, Kerman Branch of Azad University http://orcid.org/0000-0003-3603-9401
  • Azadeh Alsadat Emrani Zarandi Department of Computer Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

DOI:

https://doi.org/10.7494/csci.2021.22.1.3823

Keywords:

Computer arithmetic, Residue number system, Reverse converter

Abstract

The high dynamic range residue number system (RNS) five-moduli { 2 2n , 2 n + 1, 2 n − 1, 2 n + 3, 2 n − 3 } has been recently introduced as an arithmetically balanced five-moduli set for computation-intensive applications on wide operands such as asymmetric cryptography algorithms. The previous dedicated design of RNS components for this moduli set is just an unsigned reverse converter. In order to utilize of the moduli set { 2 2n , 2 n + 1, 2 n − 1, 2 n + 3, 2 n − 3 } in applications handling with signed numbers, two important components are needed: Sign Detector and Signed Reverse Converter. However, having both of these components results in high hardware requirements which makes RNS impractical. This paper overcomes to this problem by designing a unified unit which can perform both signed reverse conversion as well as sign detection through the reuse of hardware. To the authors knowledge, this is the first attempt to design sign detector for a moduli set including 2n±3 moduli. In order to achieve a hardware-amenable design, we first improved the performance of the previous unsigned reverse converter for the moduli set { 2 2n , 2 n + 1, 2 n − 1, 2 n + 3, 2 n − 3 }. Then, we extract a sign detection method from the structure of the reverse converter. Finally, we make the unsigned reverse converter to sign converter through the use of the extracted sign signal from the reverse converter. The experimental results shown that the proposed multifunctional unit has relatively the same performance in terms of area, delay and power-consumption than the previous unsigned reverse converter for the set { 2 2n , 2 n + 1, 2 n − 1, 2 n + 3, 2 n − 3 } while it can perform two complex signed operations.

Downloads

Download data is not yet available.

References

H. L. Garner, ”The residue number system,” IRE Transaction Electric Computer, vol. 8, no. 2, pp. 140-147, 1959.

P.V.A. Mohan, Residue Number Systems: Theory and Applications, Springer, 2016.

C. H. Chang, A. S. Molahosseini, A. A. E. Zarandi and T. F. Tay, Residue Number Systems: A New Paradigm to Datapath Optimization for Low-Power and High-Performance Digital Signal Processing Applications, IEEE Circuits and Systems Magazine, vol. 15, no. 4, pp. 26-44, 2015.

L. Sousa, S. Antao and P. Martins, śCombining Residue Arithmetic to Design Efficient Cryptographic Circuits and Systems, IEEE Circuits and Systems Magazine, vol. 16, no. 4, pp. 6-32, 2016.

B. Moons, D. Bankman, and M. Verhelst, Embedded Deep Learning: Algorithms, Architectures and Circuits for Always-on Neural Network Processing, Springer, 2019.

X. Zheng, B. Wang, C. Zhou, X. Wei and Q. Zhang, śParallel DNA Arithmetic Operation With One Error Detection Based on 3-Moduli Set,IEEE Transactions on NanoBioscience, vol. 15, no. 5, pp. 499-507, 2016.

K. Navi, A. S. Molahosseini, and M. Esmaeildoust, śHow to Teach Residue Number System to Computer Scientists and Engineers, IEEE Transactions on Education, vol. 54, no. 1, pp. 156163, 2011.

P. V. A. Mohan, śRNS-to-binary converter for a new three-moduli set {2n+1 −1.2n.2n−1}, IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 54, no. 9, pp. 775779, Sep. 2007.

P. V. A. Mohan and A. B. Premkumar, RNS-to-binary converters for two fourmoduli set {2n − 1.2n.2n + 1.2n+1 − 1} and {2

n − 1.2n.2n + 1.2n+1 + 1}, IEEE Trans. Circuits Syst. I, Reg. Papers,vol. 54, no. 6, pp. 12451254, Jun. 2007.

Y.Wang, X. Song, M. Aboulhamid, and H. Shen, śAdder based residue to binary numbers converters for{2n − 1.2n.2n + 1}, IEEE Trans.Signal Process., vol. 50, no. 7, pp. 17721779, Jul. 2002.

A. Hiasat and A. Sweidan, Residue number system to binary converter for the moduli set (2n−1.2 n −1.2 n + 1), Journal of Systems Architecture, vol. 49, no. 1-2, pp. 5358, 2003.

Mohan, P.V.A. New reverse converters for the moduli set {2

n − 1.2n + 1.2n −3.2n + 3}. Int. J. Electron. Commun., 2,643658, 2008.

A. S. Molahosseini, K. Navi, C. Dadkhah, O. Kavehei, and S. Timarchi,śEfficient reverse converter designs for the new 4-moduli sets {2n − 1.2n.2n + 1.22n+1 − 1}17 maja 2020 str. 18/19 and {2n − 1.2n + 1.2n.22n + 1} based on new CRTs, IEEE Trans. Circuits Syst.I, Reg. Papers, vol. 57, no. 4,pp. 823835, Apr. 2010.

A. S. Molahosseini, A. A. E. Zarandi, P. Martins and L. Sousa, śA Multifunctional Unit for Designing Efficient RNS-Based atapaths,IEEE Access, vol. 5, pp. 25972-25986, 2017.

P. M. Matutino, R. Chaves, and L. Sousa, śBinary-to-RNS Conversion Units for moduli {2n ± 3}, 2011 14th Euromicro Conference on Digital System Design, 2011.

S. Kumar and C.-H. Chang, śA VLSI-efficient signed magnitude comparator for {2n − 1.2n.2n+1 − 1} RNS, 2016 IEEE International Symposium on Circuits and Systems (ISCAS), 2016.

A. A. E. Zarandi, A. S. Molahosseini, L. Sousa, and M. Hosseinzadeh, śAn Efficient Component for Designing Signed Reverse Converters for a Class of RNS Moduli Sets of Composite Form {2k.2P − 1} IEEE Transactions on Very Large on Scale Integration (VLSI) Systems, vol. 25, no. 1, pp. 4859, 2017.

Didier, L.-S. and Rivaille, P.-Y. (2009) A generalization of a fast RNS conversion for a new 4-modulus Base. IEEE Trans. Circuits Syst. II, 56, 4650.

Jaberipur, G. and Ahmadifar, H. (2013) A ROM-less reverse RNS converter for moduli set {2 q ± 1, 2q ± 3}. IET Comput. Digit. Tech., 8, 1122.

H. Ahmadifar and G. Jaberipur, śA New Residue Number System with 5-Moduli Set:{22q, 22q ± 3, 22q ± 1}, The Computer Journal, vol. 58, no. 7, pp. 15481565,Feb. 2014.

Downloads

Published

2021-02-01

How to Cite

Mojahed, M., Sabbagh Molahosseini, A., & Emrani Zarandi, A. A. (2021). A Multifunctional Unit For Reverse Conversion and Sign Detection Based on The 5-Moduli Set. Computer Science, 22(1). https://doi.org/10.7494/csci.2021.22.1.3823

Issue

Section

Articles