
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
M.D. Ercegovac, T. Lang, "OntheFly Rounding (Computing Arithmetic)," IEEE Transactions on Computers, vol. 41, no. 12, pp. 14971503, December, 1992.  
BibTex  x  
@article{ 10.1109/12.214659, author = {M.D. Ercegovac and T. Lang}, title = {OntheFly Rounding (Computing Arithmetic)}, journal ={IEEE Transactions on Computers}, volume = {41}, number = {12}, issn = {00189340}, year = {1992}, pages = {14971503}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.214659}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  OntheFly Rounding (Computing Arithmetic) IS  12 SN  00189340 SP1497 EP1503 EPD  14971503 A1  M.D. Ercegovac, A1  T. Lang, PY  1992 KW  digit rounding; computing arithmetic; digitrecurrence algorithms; digitserial form; most significant digit; least significant; redundant addition; resultdigit; signeddigit set; online arithmetic; digital arithmetic; number theory. VL  41 JA  IEEE Transactions on Computers ER   
In implementations of operations based on digitrecurrence algorithms such as division, lefttoright multiplication and square root, the result is obtained in digitserial form, from most significant digit to least significant. To reduce the complexity of the resultdigit selection and allow the use of redundant addition, the resultdigit has values from a signeddigit set. As a consequence, the result has to be converted to conventional representation, which can be done onthefly as the digits are produced, without the use of a carrypropagate adder. The authors describe three ways to modify this conversion process so that the result is rounded. The resulting operation is fast because no carrypropagate addition is needed. The schemes described apply also to online arithmetic operations.
[1] A. Avizienis, "Signed digit number representations for fast parallel arithmetic,"IRE Trans. Electron. Comput., pp. 389400, 1961.
[2] A. Avizienis, "Binarycompatible signeddigit arithmetic," inProc. Fall Joint Comput. Conf., 1964, pp. 663672.
[3] "IEEE Standard for Binary FloatingPoint Arithmetic," ANSI/IEEE Standard 7541985, The Institute of Electrical and Electronics Engineers, Inc., New York, NY 10017, 1985.
[4] J. Cortadella and J. M. Llaberia, "Evaluating A+B=K conditions in constant time," inProc. Int. Conf. Circuits and Syst., Helsinki, 1988.
[5] M. D. Ercegovac and T. Lang, "Onthefly conversion of redundant into conventional representations,"IEEE Trans. Comput., vol. C36, no. 7, pp. 895897, July 1987.
[6] M. D. Ercegovac, T. Lang, J. G. Nash, and L. P. Chow, "An areatime efficient binary divider," inProc. ICCD '87 Conf., New York, 1987, pp. 645648.
[7] M. Ercegovac and T. Lang, "Online arithmetic: A design methodology and applications," inVLSI Signal Processing, III, R. W. Brodersen and H. S. Moscovitz, Eds. New York: IEEE Press, 1988, pp. 252263.
[8] M. Ercegovac and T. Lang, "Fast multiplication without carrypropagate addition,"IEEE Trans. Comput., vol. C39, no. 11, pp. 13851390, 1990.
[9] J. Fandrianto, "Algorithm for high speed shared radix4 division and radix4 square root," inProc. 8th Symp. Comput. Arithmet., 1987, pp. 7379.
[10] J. Fandrianto, private communication, Sept. 1989.
[11] K. Hwang,Computer Arithmetic. New York: Wiley, 1978.
[12] M. J. Irwin and R. M. Owens, "Digit pipelined arithmetic as illustrated by the pasteup system,"IEEE Comput. Mag., pp. 6173, Apr. 1987.