This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A Radix-2 Digit-by-Digit Architecture for Cube Root
April 2008 (vol. 57 no. 4)
pp. 562-566
A radix-2 digit-recurrence algorithm and architecture for the computation of the cube root are presented in this paper. The original recurrence based on the concept of completing the cube is modified to allow an efficient implementation of the algorithm, and the cycle time and area cost of the resulting architecture are estimated as 7.5 times the delay of a full adder and around 9000 $nand2$ cells, respectively, for double-precision computations.

[1] E. Antelo, T. Lang, P. Montuschi, and A. Nannarelli, “Fast Radix-4 Retimed Division with Selection by Comparisons,” Proc. 13th IEEE Int'l Conf. Application-Specific Systems, Architectures, and Processors, 2002.
[2] T.H. Benziger, “The Integrated Kirchhoff Equation,” Nature, pp. 100-103, http://www.med.ufl.edu/Biochem/pchunthermopb.ps , 1971.
[3] L. Ciminiera and P. Montuschi, “Higher Radix Square Rooting,” IEEE Trans. Computers, vol. 39, no. 10, pp. 1220-1231, Oct. 1990.
[4] M.D. Ercegovac and T. Lang, Algorithms for Division and Square Root. Kluwer Academic, 1994.
[5] M.D. Ercegovac and T. Lang, Digital Arithmetic. Morgan Kaufmann, 2003.
[6] D. Harris, “A Powering Unit for an OpenGL Lighting Engine,” Proc. 35th Asilomar Conf. Signals, Systems, and Computers, pp. 1641-1645, 2001.
[7] J. Harrison, T. Kubaska, S. Story, and P.T.P. Tang, “The Computation of Transcendental Functions on the IA-64 Architecture,” Intel Technology J., vol. 4, no. 7, 1999.
[8] S. Majerski, “Square-Rooting Algorithms for High-Speed Digital Circuits,” IEEE Trans. Computers, vol. 34, pp. 724-733, 1985.
[9] P. Montuschi, J.D. Bruguera, L. Ciminiera, and J.-A. Piñeiro, “A Digit-by-Digit Algorithm for $m{\rm th}$ Root Extraction,” IEEE Trans. Computers, vol. 56, no. 12, pp. 1696-1706, Dec. 2007.
[10] H. Peng, “Algorithms for Extracting Square Roots and Cube Roots,” Proc. Fifth IEEE Int'l Symp. Computer Arithmetic, pp. 121-126, 1981.
[11] J.-A. Piñeiro, M.D. Ercegovac, and J.D. Bruguera, “Algorithm and Architecture for Logarithm, Exponential and Powering Computation,” IEEE Trans. Computers, vol. 53, no. 9, pp. 1085-1096, Sept. 2004.
[12] J.-A. Piñeiro, J.D. Bruguera, L. Ciminiera, and P. Montuschi, “A Digit-by-Digit Algorithm for Radix-2 Cube Root and Its Implementation,” technical report, http:/www.ac.usc.es, 2004.
[13] J.-A. Piñeiro, J.D. Bruguera, and J.M. Muller, “Faithful Powering Computation Using Table Look-Up and Fused Accumulation Tree,” Proc. IEEE 15th Int'l Symp. Computer Arithmetic, pp. 40-47, 2001.
[14] J.-A. Piñeiro, S. Oberman, J.M. Muller, and J.D. Bruguera, “High-Speed Function Approximation Using a Minimax Quadratic Interpolator,” IEEE Trans. Computers, vol. 54, no. 3, pp. 304-318, Mar. 2005.
[15] H.C. Shin, J.A. Lee, and L.S. Kim, “A Minimized Hardware Architecture of Fast Phong Shader Using Taylor Series Approximation in 3D Graphics,” Proc. IEEE Int'l Conf. Computer Design: VLSI in Computers and Processors, pp.286-291, 1998.
[16] P. Soderquist and M. Leeser, “Area and Performance Tradeoffs in Floating Point Divide and Square Root Implementations,” ACM Computer Surveys, pp. 518-564, 1996.
[17] N. Takagi, “Powering by a Table Look-Up and a Multiplication with Operand Modification,” IEEE Trans. Computers, vol. 47, no. 11, pp. 1216-1222, Nov. 1998.
[18] N. Takagi, “A Digit-Recurrence Algorithm for Cube Rooting,” IEICE Trans. Fundamentals of Electronics, Comm. and Computer Sciences, vol. E84-A, no. 5, pp. 1309-1314, 2001.
[19] K. Turkowski, “Computing the Cube Root,” technical report, Apple Computer, 1998.

Index Terms:
High-Speed Arithmetic, Cost/performance
Citation:
Alex Pi?eiro, Javier D. Bruguera, Fabrizio Lamberti, Paolo Montuschi, "A Radix-2 Digit-by-Digit Architecture for Cube Root," IEEE Transactions on Computers, vol. 57, no. 4, pp. 562-566, April 2008, doi:10.1109/TC.2007.70848
Usage of this product signifies your acceptance of the Terms of Use.