On Wed, Feb 11, 2009 at 4:38 PM, Wacek Kusnierczyk
<waclaw.marcin.kusnierc...@idi.ntnu.no> wrote:
> Stavros Macrakis wrote:
>> 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,
>
> bc gets it arbitrarily right:...
Yes, any arbitrary-precision systems should get it right if you
specify the right number of digits to calculate. But why use expensive
multiple-precision when you don't need it?
The 'right' way to calculate things like log(exp(x)+1)-x and
exp(x)/(exp(x+k)+a) for large values of x is to understand their
asymptotic behavior, easy to do by hand or in a CAS like Maxima (and
presumably yacas, though I don't have any experience with it) -- for
large x, the first looks like exp(-x)-exp(-2*x)/2+...; the second
looks like exp(-k)-a*exp(-(x+k)) + ... No need for
arbitrary-precision arithmetic once you know this.
-s
______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
