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Dealing with very small numbers in R

Asked 2011-04-27T10:26:51.563
20

I need to calculate a list of very small numbers such as

(0.1)^1000, 0.2^(1200),

and then normalize them so they will sum up to one i.e.

a1 = 0.1^1000, a2 = 0.2^1200

And I want to calculate a1' = a1/(a1+a2), a2'=a2(a1+a2).

I'm running into underflow problems, as I get a1=0. How can I get around this? Theoretically I could deal with logs, and then log(a1) = 1000*log(0.l) would be a way to represent a1 without underflow problems - But in order to normalize I would need to get log(a1+a2) - which I can't compute since I can't represent a1 directly.

I'm programming with R - as far as I can tell there is no data type such Decimal in c# which allows you to get better than double-precision value.

Any suggestions will be appreciated, thanks

r precision underflow
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8

The Brobdingnag package deals with very large or small numbers, essentially wrapping Joris's answer into a convenient form.

a1 <- as.brob(0.1)^1000
a2 <- as.brob(0.2)^1200
a1_dash <- a1 / (a1 + a2)
a2_dash <- a2 / (a1 + a2)
as.numeric(a1_dash)
as.numeric(a2_dash)
answered 2011-04-27T12:59:14.443

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