Division algorithm: Difference between revisions

Revision as of 11:32, 2 September 2007

Revision as of 16:13, 3 September 2007

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===Goldschmidt division===

Goldschmidt (after [[Robert E. Goldschmidt]])<ref>Robert E. Goldschmidt, Applications of Division by Convergence, MSc
dissertation, M.I.T., 1964</ref>
division uses [[series expansion]] to converge to the quotient. The strategy of Goldschmidt is repeatedly multiply the dividend and divisor by a factor ''F'' to converge the divisor to 1 as the dividend converges to the quotient ''Q'':

:<math>Q = \frac{N}{D} \frac{F_1}{F_1} \frac{F_2}{F_2} \frac{F_{\ldots}}{F_{\ldots}}</math>

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After a sufficient number of iterations ''k'': <math>Q=N_{k}</math>

{{reflist}}

[[Category:Computer arithmetic]]