Division algorithm: Difference between revisions

Revision as of 12:38, 6 May 2025

Revision as of 19:08, 10 May 2025

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After a sufficient number ''k'' of iterations <math>Q=N_k</math>.

The Goldschmidt method is used in [[AMD]] Athlon CPUs and later models.<ref>{{cite book |first=Stuart F. |last=Oberman |title=Proceedings 14th IEEE Symposium on Computer Arithmetic (Cat. No.99CB36336) |chapter=Floating point division and square root algorithms and implementation in the AMD-K7 Microprocessor |pages=106&ndash;115 |date=1999 |doi=10.1109/ARITH.1999.762835 |isbn=0-7695-0116-8 |s2cid=12793819 |chapter-url=http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Oberman.pdf |access-date=2015-09-15 |archive-date=2015-11-29 |archive-url=https://web.archive.org/web/20151129095846/http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Oberman.pdf |url-status=live }}</ref><ref>{{cite journal |first1=Peter |last1=Soderquist |first2=Miriam |last2=Leeser |title=Division and Square Root: Choosing the Right Implementation |journal=IEEE Micro |volume=17 |issue=4 |pages=56&ndash;66 |date=July–August 1997 |url=https://www.researchgate.net/publication/2511700 |doi=10.1109/40.612224 }}</ref> It is also known as Anderson Earle Goldschmidt Powers (AEGP) algorithm and is implemented by various [IBM] processors.<ref>S. F. Anderson, J. G. Earle, R. E. Goldschmidt, D. M. Powers. ''The IBM 360/370 model 91: floating-point execution unit'', [[IBM Journal of Research and Development]], January 1997</ref><ref name="goldschmidt-analysis">{{cite journal |last1=Guy |first1=Even |last2=Peter |first2=Siedel |last3=Ferguson |first3=Warren |title=A parametric error analysis of Goldschmidt's division algorithm |journal=Journal of Computer and System Sciences |date=1 February 2005 |volume=70 |issue=1 |pages=118–139 |doi=10.1016/j.jcss.2004.08.004 |doi-access=free }}</ref> Although it converges at the same rate as a Newton–Raphson implementation, one advantage of the Goldschmidt method is that the multiplications in the numerator and in the denominator can be done in parallel.<ref name="goldschmidt-analysis" />

====Binomial theorem====