# [R] Behaviour of very large numbers

willem vervoort willemvervoort at gmail.com
Fri Aug 31 09:19:34 CEST 2007

```Thanks for all the points. Riding my bike back home I realised that
the fractional power was a problem. I also forgot about the operator
precedence:
> b <- 48.3
> -53.1^b
[1] -2.099256e+83
> (-53.1)^b
[1] NaN

Pretty clear now. Back to my maths than...

> version
# sorry forgot this last time               _
platform       i386-pc-mingw32

version.string R version 2.5.1 (2007-06-27)

Willem

On 8/30/07, Duncan Murdoch <murdoch at stats.uwo.ca> wrote:
> On 8/30/2007 12:11 PM, Martin Becker wrote:
> > willem vervoort wrote:
> >> Dear all,
> >> I am struggling to understand this.
> >>
> >> What happens when you raise a negative value to a power and the result
> >> is a very large number?
> >>
> >>  B
> >> [1] 47.73092
> >>
> >>
> >>> -51^B
> >>>
> >> [1] -3.190824e+81
> >>
> >> # seems fine
> >>
> >
> > Well, this seems not to be what you intended to do, you didn't raise a
> > negative value to a power, but you got the negative of a positive number
> > raised to that power (operator precedence, -51^B is the same as -(51^B)
> > and not the same as (-51)^B...).
> >
> > If you really want to raise a negative value to a fractional power, you
> > may want to tell R to use complex numbers:
> >
> > B <- 47.73092
> > x <- complex(real=seq(-51,-49,length=10))
> >
> > x^B
> >
> >  [1] 2.117003e+81-2.387323e+81i 1.718701e+81-1.938163e+81i
> >  [3] 1.394063e+81-1.572071e+81i 1.129702e+81-1.273954e+81i
> >  [5] 9.146212e+80-1.031409e+81i 7.397943e+80-8.342587e+80i
> >  [7] 5.978186e+80-6.741541e+80i 4.826284e+80-5.442553e+80i
> >  [9] 3.892581e+80-4.389625e+80i 3.136461e+80-3.536955e+80i
>
> But watch out if you do this, because of the arbitrary choice of a root.
>  You get oddities like this:
>
>  > x <- complex(real = -1)
>  > x
> [1] -1+0i
>  > 1/x
> [1] -1+0i
>  > x^(1/3)
> [1] 0.5+0.8660254i
>  > (1/x)^(1/3)
> [1] 0.5-0.8660254i
>
> i.e. even though x and 1/x are equal, the 1/3 powers of them are not.
>
> Duncan Murdoch
>
> P.S. I'm tempted to say, "But don't worry about it, the difference is
> only imaginary", but I'll refrain.
>

```