This Article 
 Bibliographic References 
 Add to: 
High Performance Rotation Architectures Based on the Radix-4 CORDIC Algorithm
August 1997 (vol. 46 no. 8)
pp. 855-870

Abstract—Traditionally, CORDIC algorithms have employed radix-2 in the first n/2 microrotations (n is the precision in bits) in order to preserve a constant scale factor. In this work, we will present a full radix-4 CORDIC algorithm in rotation mode and circular coordinates and its corresponding selection function, and we will propose an efficient technique for the compensation of the nonconstant scale factor. Three radix-4 CORDIC architectures are implemented: 1) a word serial architecture based on the zero skipping technique, 2) a pipelined architecture, and 3) an application specific architecture (the angles are known beforehand). The first two are general purpose implementations where redundant (carry-save) or nonredundant arithmetic can be used, whereas the last one is a simplification of the first two. The proposed architectures present a good trade-off between latency and hardware complexity when compared with already existing CORDIC architectures.

[1] E. Antelo, J.D. Bruguera, and E.L. Zapata, "Unified Mixed Radix-2-4 Redundant CORDIC Processor," IEEE Trans. Computers, vol. 45, no. 9, pp. 1,086-1,073, Sept. 1996.
[2] P.W. Baker, "Suggestion for a Fast Binary Sine/Cosine Generator," IEEE Trans. Computers, pp. 1,134-1,136, 1976.
[3] J.D. Bruguera, E. Antelo, and E.L. Zapata, "Design of a Pipelined Radix-4 CORDIC Processor," J. Parallel Computing, vol. 19, no. 7, pp. 729-744, 1993.
[4] J.D. Bruguera, N. Guil, T. Lang, J. Villalba, and E.L. Zapata, "CORDIC Based Parallel/Pipelined Architecture for the Hough Transform," J. VLSI Signal Processing, vol. 12, no. 3, pp. 207-221, 1996.
[5] J.R. Cacallaro and F.T. Luk,"CORDIC Arithmetic for a SVD Processor," J. Parallel and Distributed Computing, vol. 5, pp. 271-290, 1988.
[6] H. Dawid and H. Meyr, “The Differential CORDIC Algorithm: Constant Scale Factor Redundant Implementation without Correcting Iterations,” IEEE Trans. Computers, vol. 45, no. 3, Mar. 1996.
[7] J. Duprat and J.-M Muller,"The CORDIC Algorithm: New Results for Fast VLSI Implemenation," IEEE Trans. Computers, vol. 42, no. 2, pp. 168-178 Feb. 1993.
[8] M.D. Ercegovac and T. Lang, Division and Square Root—Digit-Recurrence Algorithms and Implementations. Kluwer Academic, 1994.
[9] M.D. Ercegovac and T. Lang,"Redundant and On-Line CORDIC: Application to Matrix Triangularisation and SVD," IEEE Trans. Computers, vol. 38, no. 6 pp. 725-740, June 1990.
[10] G.J. Hekstra and E.F. Deprettere, "Floating Point CORDIC," Proc. 11th Symp. Computer Arithmetic, pp. 130-137, 1993.
[11] Y.M. Hu, “CORDIC-Based VLSI Architectures for Digital Signal Processing,” IEEE Signal Processing Magazine, vol. 9, pp. 16-35, 1992.
[12] Y.H. Hu and S. Naganathan, "An Angle Recoding Method for CORDIC Algorithm Implementation," IEEE Trans. Computers, vol. 42, no. 1, pp. 99-102, Jan. 1993.
[13] Y.H. Hu, "A Forward Angle Recoding CORDIC Algorithm and Pipelined Processor Array Structure for Digital Signal Processing," Digital Signal Processing, vol. 3 no. 1, pp. 2-15, Jan. 1993.
[14] K. Kota and J.R. Cavallaro,“Numerical accuracy and hardware tradeoffs for CORDIC arithmetic for special-purpose processors,” IEEE Trans. Computers, vol. 42, no. 7, pp. 769-779, July 1993.
[15] A.A.J. de Lange and E.F. Deprettere,“Design and implementation of a floating-point quasi-systolicgeneral purpose CORDIC rotator for high-rate parallel data andsignal processing,” Proc. 10th IEEE Symp. Computer Arithmetic, pp. 272-281, July 1991.
[16] J. Lee and T. Lang,"Constant-Factor Redundant CORDIC for Angle Calculation and Rotation," IEEE Trans. Computers, vol. 41, no. 8, pp. 1,016-1,035, Aug. 1992.
[17] H.X. Lin and H.J. Sips,"On-Line CORDIC Algorithms," IEEE Trans. Computers, vol. 38, no. 8, pp. 1,038-1,052, Aug. 1990.
[18] P. Montuschi and L. Ciminiera, "Reducing Iteration Time When Result Digit Is Zero for Radix 2 SRT Division and Square Root with Redundant Remainders," IEEE Trans. Computers, vol. 42, no. 2, pp. 239-246, Feb. 1993.
[19] N. Takagi,T. Asada, and S. Yajima,"Redundant CORDIC Methods with a Constant Scale Factor for Sine and Cosine Computation," IEEE Trans. Computers, vol. 40, no. 9, pp. 989-995, Sept. 1991.
[20] D. Timmermann, H. Hahn, and B.J. Hosticka, "Low Latency Time CORDIC Algorithms," IEEE Trans. Computers, vol. 41, no. 8, pp. 1,010-1,015, Aug. 1992.
[21] J.E. Volder, "The CORDIC Trigonometric Computing Technique," IRE Trans. Electronic Computers, vol. 8, pp. 330-334, Sept. 1959.
[22] J.S. Walther, "A Unified Algorithm for Elementary Functions," Proc. Spring. Joint Computer Conf., pp. 379-385, 1971.

Index Terms:
CORDIC algorithm, radix-4, redundant arithmetic, VLSI architectures, pipelined architectures.
Elisardo Antelo, Julio Villalba, Javier D. Bruguera, Emilio L. Zapata, "High Performance Rotation Architectures Based on the Radix-4 CORDIC Algorithm," IEEE Transactions on Computers, vol. 46, no. 8, pp. 855-870, Aug. 1997, doi:10.1109/12.609275
Usage of this product signifies your acceptance of the Terms of Use.