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Comparative Study of Different Division Algorithms for Fixed and Floating Point Arithmetic Unit for Embedded Applications

R.S.Hongal 1 , D.J. Anita2

Section:Research Paper, Product Type: Journal Paper
Volume-4 , Issue-9 , Page no. 48-54, Sep-2016

Online published on Sep 30, 2016

Copyright © R.S.Hongal, D.J. Anita . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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IEEE Style Citation: R.S.Hongal, D.J. Anita , “Comparative Study of Different Division Algorithms for Fixed and Floating Point Arithmetic Unit for Embedded Applications,” International Journal of Computer Sciences and Engineering, Vol.4, Issue.9, pp.48-54, 2016.

MLA Style Citation: R.S.Hongal, D.J. Anita "Comparative Study of Different Division Algorithms for Fixed and Floating Point Arithmetic Unit for Embedded Applications." International Journal of Computer Sciences and Engineering 4.9 (2016): 48-54.

APA Style Citation: R.S.Hongal, D.J. Anita , (2016). Comparative Study of Different Division Algorithms for Fixed and Floating Point Arithmetic Unit for Embedded Applications. International Journal of Computer Sciences and Engineering, 4(9), 48-54.

BibTex Style Citation:
@article{Anita_2016,
author = {R.S.Hongal, D.J. Anita },
title = {Comparative Study of Different Division Algorithms for Fixed and Floating Point Arithmetic Unit for Embedded Applications},
journal = {International Journal of Computer Sciences and Engineering},
issue_date = {9 2016},
volume = {4},
Issue = {9},
month = {9},
year = {2016},
issn = {2347-2693},
pages = {48-54},
url = {https://www.ijcseonline.org/full_paper_view.php?paper_id=1054},
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
UR - https://www.ijcseonline.org/full_paper_view.php?paper_id=1054
TI - Comparative Study of Different Division Algorithms for Fixed and Floating Point Arithmetic Unit for Embedded Applications
T2 - International Journal of Computer Sciences and Engineering
AU - R.S.Hongal, D.J. Anita
PY - 2016
DA - 2016/09/30
PB - IJCSE, Indore, INDIA
SP - 48-54
IS - 9
VL - 4
SN - 2347-2693
ER -

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Abstract

ALU is very essential unit of any embedded processors. Very basic operations like addition, subtraction, multiplication and division are part of ALU unit. In literature, we have many algorithms to perform addition, subtraction and multiplication but less on division algorithm. The division algorithm performs, either by addition or subtraction, based on the signs of the divisor and partial remainder. Floating point division is considered as a high latency operation. Division algorithms have been developed to reduce latency and to improve the computational efficiency, hardware cost, area and power of processors. This paper presents different division algorithms such as Digit Recurrence Algorithm restoring, non-restoring and SRT Division (Sweeney, Robertson, and Tocher), Multiplicative Algorithm, Approximation Algorithms, CORDIC Algorithm and Continued Product Algorithm. This paper intended to compare various techniques used and their features relevant for various applications.

Key-Words / Index Term

Division; SRT; Non Restoring; Restoring; FPGA; CORDIC; DSP

References

[1] S. F. Oberman and M. J. Flynn, "Design Issues in Division and other Floating-Point Operations," IEEE Transactions on Computers, Vol-46, Page No (154-161), 1997.
[2] Inwook Kong, "Modified Improved Algorithms and Hardware Designs for Division by Convergence," Doctoral dissertation. University of Texas at Austin, 2009.
[3] Peter Soderquist and Miriam Leeser, "Division and Square Root: Choosing the right Implementation�, IEEE Micro, Vol- 17, Issue-04, pp (56-66), 1997.
[4] Milos D. Ercegovac and Tomas Lang, �Division and Square Root: Digit Recurrence Algorithms and Implementations�, Boston: KJuwer Academic Publishers, 1994.
[5] S. F. Oberman and M. J. Flynn, "Division Algorithms and Implementations�, IEEE Transactions on Computers, Vol-46, no.-08, Page No (833-854), Aug 1997.
[6] Nicolas Boullis and Arnaud Tisserand, �On digit-recurrence division algorithms for self-timed circuits�, in Research Report published at Institute National De Recherche En Informatique Et En Automatique, France, 2012.
[7] Kihwan Jun and Earl E. Swartzlander, �Modified Non-restoring Division Algorithm with Improved Delay Profile and Error Correction�, Signals Systems and Computers (ASILOMAR), Page No (1460-1464), 2012.
[8] Jen-Shiun Chiang, Eugene Lai and Jun-Yao Liao,�A Radix-2 Non-Restoring 32-b/32-b Ring Divider with Asynchronous Control Scheme�, Tamkang Journal of Science and Engineering, Vol-02, Issue-01 Page No (37-43), 1999.
[9] Jagannath Samanta, Mousam Halder, Bishnu Prasad De, �Performance Analysis of High Speed Low Power Carry Look-Ahead Adder Using Different Logic Styles�, International Journal of Soft Computing and Engineering (IJSCE), ISBN:2231-2307, Volume-02, Issue-06, Page No (330�336), 2013.
[10] A. Beaumont Smith and S. Samudrala, �Method and System of a Microprocessor Subtraction- Division Floating-Point Divider�, Patent US 7, 127, 483 B2, Oct. 24, 2006.
[11] D. J. Desmonds, �Binary Divider with Carry Save Adders�, Patent US 4, 320, 464, March 16, 1982.
[12] J. Ebergen, I. Sutherland, and A. Chakraborty, �New Division Algorithms by Digit Recurrence,� in Conference Record of the Thirty-Eighth Asilo- mar Conference on Signals, Systems and Computers, Vol-02, Page No (1849�1855), 2004.
[13] L. Montalvo, K. Parhi, and A. Guyot, �A Radix-10 Digit-Recurrence Division Unit: Algorithm and Architecture�, IEEE Transaction on Computers, Vol-56, No.6, Page No (727�739), June 2007.
[14] I. Rust and T. Noll, �A digit-set-interleaved radix-8 division/square root kernel for double precision floating point�, IEEE International Symposium on System on Chip (SoC), Page No (150�153), Nov 2010.
[15] L. Montalvo, K. Parhi, and A. Guyot, �New Svoboda-Tung Division�, IEEE Transaction on Computers, Vol-47, No. 9, Page No (1014�1020), Sep 1997.
[16] T.-J. Kwon, J. Sondeen, and J. Draper, �Floating-point division and square root using a Taylor-series expansion algorithm�, in the 50th Midwest Symposium on Circuits and Systems (MWSCAS 2007), Page No (305�308), 2007.
[17] S. F. Oberman, �Floating Point Division and Square Root Algorithms and Implementation in the AMD-K7 Microprocessor�, in 14th IEEE Symposium on Computer Arithmetic, Page No (106�115), 1999.
[18] M. J. Schulte, D. Tan, and C. L. Lemonds, �Floating-Point Division Algorithms for an x86 Microprocessor with a Rectangular Multiplier,� in Proc. Int`l. Conf. on Computer Design (ICCD), Page No (304�310), 2007.
[19] W. Gallagher and E. Swartzlander, �Fault-Tolerance Newton-Raphson and Goldschmidt Dividers using Time Shared TMR�, IEEE Transaction on Computers, Vol-49, No. 6, Page No (588�595), June 2000.
[20] L. K. Wang and M. Schulte, �Processing Unit Having Decimal Floating-Point Divider Using Newton-Raphson Iteration�, Patent US 7,467,174 B2, Dec 16, 2008.
[21] P. Surapong, F. A. Samman, and M. Glesner, �Design and Analysis of Extension-Rotation CORDIC Algorithms based on Non-Redundant Method�, International Journal of Signal Processing, Image Processing and Pattern Recognition, Vol-05, No. 1, Page No (65�84), March 2012.
[22] K. Maharatna, S. Banerjee, E. Grass, M. Krstic, and A. Troya, �Modified Virtually Scaling-Free Adaptive CORDIC Rotator Algorithm and Architecture�, IEEE Trans. on Circuits and Systems Floating-Point Division Operator based on CORDIC Algorithm 87 tems for Video Technology, Vol-15, No. 11, Page No (1463�1474), Nov 2005.
[23] F. A. Sammany, P. Surapong, C. Spies, and M. Glesner, �Floating-point-based Hardware Accelerator of a Beam Phase-Magnitude Detector and Filter for a Beam Phase Control System in a Heavy-Ion Synchrotron Application�, in Proc. Int`l Conf. on Accelerator and Large Experimental Physics Control Systems (ICALEPCS), 2011.
[24] H. Hahn, D. Timmermann, B. Hosticka, and B. Rix, �A Unified and Division-Free CORDIC Argument Reduction Method with Unlimited Convergence Domain Including Inverse Hyperbolic Functions�, IEEE Transaction on Computers, Vol-43, No. 11, Page No (1339�1344), Nov 1994.