
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
R. Hashemian, "Square Rooting Algorithms for Integer and FloatingPoint Numbers," IEEE Transactions on Computers, vol. 39, no. 8, pp. 10251029, August, 1990.  
BibTex  x  
@article{ 10.1109/12.57041, author = {R. Hashemian}, title = {Square Rooting Algorithms for Integer and FloatingPoint Numbers}, journal ={IEEE Transactions on Computers}, volume = {39}, number = {8}, issn = {00189340}, year = {1990}, pages = {10251029}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.57041}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Square Rooting Algorithms for Integer and FloatingPoint Numbers IS  8 SN  00189340 SP1025 EP1029 EPD  10251029 A1  R. Hashemian, PY  1990 KW  square rooting algorithms; integer numbers; initial value modification; floatingpoint numbers; real numbers; close estimate; precise root; division by 2; fast converging iteration; bitshift operation; digital arithmetic; iterative methods; number theory. VL  39 JA  IEEE Transactions on Computers ER   
An algorithm for evaluating the square root of integers and real numbers is developed. The procedure consists of two parts: one to obtain a close estimate of the square root and the other to modify the initial value, iteratively, until a precise root is evaluated. The major effort in this development has been concentrated on two objectives: high speed and no division operation other than division by 2. The first objective is achieved through a simple twostep procedure for getting the first estimate, and then modifying it by employing a fast converging iteration technique. The second objective is also fulfilled through applying bitshift operation rather than division operation. The algorithm is simulated for both integer and real numbers, and the results are compared to two methods being widely used. The results (tabulated) show considerable improvement in speed compared to these other two methods.
[1] G. M. Cioffi and T. Kailath, "Fast recursive leastsquares transversal filters for adaptive filtering,"IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP32, no. 2, Apr. 1984.
[2] G. R. L. Sohie and K. L. Kloker, "A digital signal processor with IEEE floatingpoint arithmetic,"IEEE Micro, vol. 8, no. 6, pp. 4967, 1989.
[3] J. H. Zurawski and J. B. Gosling, "Design of a highspeed square root multiply and divide unit,"IEEE Trans. Comput., vol. C36, pp. 1323, Jan. 1987.
[4] V. G. Oklobdzija and M. D. Ercegovac, "An online square root algorithm,"IEEE Trans. Comput., vol. C31, no. 1, pp. 7075, Jan. 1982.
[5] J. Prado and R. Alcantara, "A fast squarerooting algorithm using a digital signal processor,"Proc. IEEE, vol. 75, no. 2, pp. 262264, Feb. 1987.
[6] J. J. F. Cavanagh,Digital Computer Arithmetic Design and Implementation. New York: McGrawHill, 1984, pp. 117122.
[7] N. R. Scott,Computer Number Systems&Arithmetic. Englewood Cliffs, NJ: PrenticeHall, 1985, ch. 5.
[8] Y. Jaluria,Computer Methods for Engineering. Boston, MA: Allyn and Bacon, 1988, ch. 4.
[9] "IEEE Standard for Binary FloatingPoint Arithmetic," IEEE Standard 754, IEEE Computer Society, 1985.