
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
Tom? Lang, Elisardo Antelo, "Radix4 Reciprocal SquareRoot and Its Combination with Division and Square Root," IEEE Transactions on Computers, vol. 52, no. 9, pp. 11001114, September, 2003.  
BibTex  x  
@article{ 10.1109/TC.2003.1228508, author = {Tom? Lang and Elisardo Antelo}, title = {Radix4 Reciprocal SquareRoot and Its Combination with Division and Square Root}, journal ={IEEE Transactions on Computers}, volume = {52}, number = {9}, issn = {00189340}, year = {2003}, pages = {11001114}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2003.1228508}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Radix4 Reciprocal SquareRoot and Its Combination with Division and Square Root IS  9 SN  00189340 SP1100 EP1114 EPD  11001114 A1  Tom? Lang, A1  Elisardo Antelo, PY  2003 KW  Combined division KW  square root KW  reciprocal square root KW  digitrecurrence algorithm KW  exact rounding KW  staircase selection function. VL  52 JA  IEEE Transactions on Computers ER   
Abstract—In this work, we present a reciprocal square root algorithm by digit recurrence and selection by a staircase function and the radix4 implementation. As in similar algorithms for division and square root, the results are obtained correctly rounded in a straightforward manner (in constrast to existing methods to compute the reciprocal square root). Although, apparently, a single selection function can only be used for
[1] E. Antelo, T. Lang, and J.D. Bruguera, “Computation of$\sqrt{x/d}$in a Very High Radix Combined Division/SquareRoot Unit with Scaling,” IEEE Trans. Computers, vol. 47, no. 2, pp. 152161, Feb. 1998.
[2] R.C. Agarwal, F.G. Gustavson, and M.S. Schmookler, “Series Approximation Methods for Divide and Square Root in the Power3 Processor,” Proc. 14th IEEE Symp. Computer Arithmetic, pp. 116123, July 1999.
[3] D. DasSarma and D.W. Matula, “Faithful Bipartite ROM Reciprocal Tables,” Proc. 12th Symp. Computer Arithmetic, pp. 1728, 1995.
[4] D. DasSarma and D.W. Matula, "Faithful Interpolation in Reciprocal Tables," Proc. 13th Symp. Computer Arithmetic, pp. 8291, July 1997.
[5] M.D. Ercegovac and T. Lang, Radix 4 Square Root without Initial PLA IEEE Trans. Computers, vol. 39, no. 8, pp. 10161024, Aug. 1990.
[6] M.D. Ercegovac and T. Lang, Division and Square Root—DigitRecurrence Algorithms and Implementations. Kluwer Academic, 1994.
[7] M.D. Ercegovac, T. Lang, J.M. Muller, and A. Tisserand, “Reciprocation, Square Root, Inverse Square Root, and Some Elementary Functions Using Small Multipliers,” IEEE Trans. Computers, vol. 49, no. 7, pp. 628637, July 2000.
[8] H. Hassler and N. Takagi, "Function Evaluation by Table LookUp and Addition," Proc. 12th Symp. Computer Arithmetic, pp. 1016, July 1995.
[9] V.K. Jain and L. Lin, “HighSpeed Double Precision Computation of Nonlinear Functions,” Proc. 12th Symp. Computer Arithmetic, pp. 107114, 1995.
[10] T. Lang and E. Antelo, Correctly Rounded Reciprocal SquareRoot by Digit Recurrence and Radix4 Implementation Proc. 15th IEEE Symp. Computer Arithmetic, pp. 8393, 2001.
[11] T. Lang and E. Antelo, Radix4 Reciprocal SquareRoot and Its Combination with Division and Square Root Internal Report, Dept. of Electrical and Computer Eng., Univ. of California at Irvine, 2001. http://www.eng.uci.edu/numlabarchive.
[12] A. Nannarelli and T. Lang, “LowPower Divider,” IEEE Trans. Computers, vol. 48, no. 1, pp. 214, Jan. 1999.
[13] S.F. Oberman, “Floating Point Division and Square Root Algorithms and Implementation in the AMDK7 Microprocessor,” Proc. 14th Symp. Computer Arithmetic (ARITH14), pp. 106115, Apr. 1999.
[14] J.E. Robertson, A New Class of Digital Division Methods IRE Trans. Electronic Computers, vol. 7, pp. 218222, 1958.
[15] M.J. Schulte and J.E. Stine, Approximating Elementary Functions with Symmetric Bipartite Tables IEEE Trans. Computers, vol. 48, no. 8, pp. 842847, Aug. 1999.
[16] M.J. Schulte and K.E. Wires, “HighSpeed Inverse Square Roots,” Proc. 14th IEEE Symp. Computer Arithmetic, I. Koren and P. Kornerup, eds., pp. 124131, Apr. 1999.
[17] N. Takagi, "Generating a Power of an Operand by a Table LookUp and a Multiplication," Proc. 13th Symp. Computer Arithmetic, pp. 126131, July 1997.
[18] N. Takagi, A Hardware Algorithm for Computing Reciprocal Square Root Proc. 15th IEEE Symp. Computer Arithmetic, pp. 94100, 2001.
[19] W.F. Wong and E. Goto, “Fast HardwareBased Algorithms for Elementary Function Computations,” IEEE Trans. Computers, vol. 43, no. 3, pp. 278294, Mar. 1994.
[20] WF. Wong and E. Goto, “Fast Evaluation of Elementary Functions in Single Precision,” IEEE Trans. Computers, vol. 44, no. 3, pp. 453457, Mar. 1995.