[VA] SRC#002- Almost integers and other beasties
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02-10-2019, 03:26 PM
(This post was last modified: 02-10-2019 04:19 PM by Albert Chan.)
Post: #27
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RE: [VA] SRC#002- Almost integers and other beasties
(02-10-2019 12:48 PM)Gerson W. Barbosa Wrote: Number of iterations = Ceil(W(10^n*ln(2))/ln(2)), where n = number of digits and W(x) is the Lambert W function. Above 50 digits numbers are confirmed corrrect. Can you explain how the iteration count formula is derived ? (01-23-2019 10:58 PM)Valentin Albillo Wrote: \[ \frac{1}{12}+\frac{\Pi^2}{6Ln^2(2)}+ \frac{2}{Ln(2)} \sum_{k=1}^\infty \frac{(-1)^k}{k(2^k-1)} \] I see that the sum gained about 1 bit precision with each iteration, so I use n / log10(2) ~ 3.322n It is slightly over-estimated, but not by much. Edit: the difference is the effect of 1/k, iterations ~ 3.322n - log2(3.322n) |
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