Odds algorithm: Difference between revisions

Revision as of 07:52, 28 November 2008

Revision as of 07:54, 28 November 2008

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== Algorithmic procedure of the odds-algorithm==

The odds-algorithm sums up the odds in reverse order

:<math>\, r_n\, + r_{n-1}\, + r_{n-2}\, +\cdots, . . .\, </math>,

until this sum reaches or exceeds the value 1 for the first time. If this happens at index <math> \,s</math>, it saves <math> \,s</math> and the corresponding sum

:<math>\,R_s = \,r_n\, + r_{n-1}\,+ r_{n-2}\, + . . . +r_s </math>.

until this sum reaches or exceeds the value 1 for the first time. If this happens at index <math> \,''s</math>'', it saves <math> \,''s</math>'' and the corresponding sum

:<math>\, R_s = \,r_n\, + r_{n-1}\, + r_{n-2}\, + .\cddots .+ r_s. +r_s\, </math>.

If the sum of the odds does not reach 1, it sets <math> \,s = 1</math>. At the same time it computes

:<math>\, Q_{n}=q_n q_{n-1}...\cdots q_s.\,</math>. The output is

The output is

a) <math> \,s </math> (stopping threshold)