[R] cumsum vs. sum

[Stavros Macrakis]

I recently traced a bug of mine to the fact that cumsum(s)[length(s)]
is not always exactly equal to sum(s).

For example,

     x<-1/(12:14)
     sum(x) - cumsum(x)[3]  => 2.8e-17

Floating-point addition is of course not exact, and in particular is
not associative, so there are various possible reasons for this.
Perhaps sum uses clever summing tricks to get more accurate results?
In some quick experiments, it does seem to get more accurate results
than cumsum.

It might be worth documenting.

             -s