On Wed, Feb 11, 2009 at 6:20 AM, Robin Hankin <rk...@cam.ac.uk> wrote:
>> library(Brobdingnag)
>> exp(1000)/(exp(1007)+5)
> [1] NaN
>
>> as.numeric(exp(as.brob(1000))/(exp(as.brob(1007))+5))
> [1] 0.000911882
Though brob is certainly useful in many cases, it can't substitute for
thinking about numeric issues (roundoff, cancellation, overflow,
underflow) in general.
For example:
> x<-40; log(exp(x)+1)-x
[1] 0
> x<-as.brob(40); log(exp(x)+1)-x
[1] -exp(-Inf)
The correct answer is about 4e-18. Perhaps Ryacas or some other tool
gets this right, but in general I don't think it's wise to abdicate
responsibility to one's tools. Though numerical analysis is a field in
itself, I think it's worthwhile to learn the basics.
-s
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