Abstract
A very-high radix algorithm and implementation for CORDIC rotation in circular and hyperbolic coordinates is presented. The selection function consists of rounding the residual. It is shown that this assures convergence from the second iteration on. For the first iteration, the selection is done by table, using a lower radix than for the remaining iterations. The compensation of the variable scale factor is done by computing the logarithm of the scale factor and performing the compensation by an exponential. Estimations of the delay for 32-bit and 64-bit precision show a substantial speed up when compared to low radix implementations. The proposed algorithm is also compared with previously proposed very-high radix ones, and significant advantages are identified.
Similar content being viewed by others
References
E. Antelo, J.D. Bruguera, T. Lang, J. Villalba, and E.L. Zapata, “High-radix CORDIC rotation based on selection by rounding,” Lecture Notes in Computer Science, August 1996, pp. 155–164.
M.D. Ercegovac, T. Lang, and P. Montuschi, “Very-High radix division with prescaling and selection by rounding,” IEEE Trans. on Comput., vol. 43, no.8, 1994, pp. 909–918.
T. Lang and P. Montuschi, “Very-High radix combined division and square-root with prescaling and selection by rounding,” Proc. 12th IEEE Symp. on Computer Arithmetic, 1995, pp. 124–131.
P.W. Baker, “Parallel multiplicative algorithms for some elementary functions,” IEEE Trans. on Comput., vol. C-25, no.3, 1975, pp. 322–325.
W.F. Wong and E. Goto, “Fast hardware-based algorithms for elementary function computations using rectangular multipliers,” IEEE Transactions on Computers, vol. 43, no.3, 1994, pp. 278–294.
D. Lewis, “High-radix redundant CORDIC algorithms for complex logarithmic number system arithmetic,” Proc. 14th Symp. on Computer Arithmetic, 1999.
E. Antelo, T. Lang, and J.D. Bruguera, “Very-high radix CORDIC rotation based on selection by rounding-Extended version,” Internal Report University of California at Irvine (available in http://www.eng.uci.edu/numlab/archive).
J.M. Muller, “Elementary Functions: Algorithms and Implementations,” Birkhauser, Boston, 1997.
E. Antelo, J. Villalba, J.D. Bruguera, and E.L. Zapata, “High performance rotation architectures based on the radix-4 CORDIC algorithm,” IEEE Transactions on Computers, vol. 46, no.8, 1997, pp. 855–870.
N. Takagi, T. Asada, and S. Yajima, “Redundant CORDIC methods with a constant scale factor for sine and cosine computation,” IEEE Trans. on Comput., vol. 40, no.9, 1991, pp. 989–995.
J. Duprat and J.-M. Muller, “The CORDIC algorithm: New results for fast VLSI implementation,” IEEE Trans. on Comput., no. 2, 1993, pp. 168–178.
M.D. Ercegovac, “A Higher Radix Division with Simple Selection of Quotient Digits,” in Proc. 6th IEEE Symp. on Computer Arithmetic, 1983, pp. 94–98.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Antelo, E., Lang, T. & Bruguera, J.D. Very-High Radix CORDIC Rotation Based on Selection by Rounding. The Journal of VLSI Signal Processing-Systems for Signal, Image, and Video Technology 25, 141–153 (2000). https://doi.org/10.1023/A:1008119006403
Published:
Issue Date:
DOI: https://doi.org/10.1023/A:1008119006403