[R] cumsum vs. sum

Martin Maechler maechler at stat.math.ethz.ch
Wed Feb 18 14:03:24 CET 2009

>>>>> "GaGr" == Gabor Grothendieck <ggrothendieck at gmail.com>
>>>>>     on Tue, 17 Feb 2009 20:53:18 -0500 writes:

    GaGr> Check out sum.exact and cumsum.exact in the caTools package.
    >> library(caTools)
    GaGr> Loading required package: bitops
    >> x <- 1/(12:14)
    >> sum(x) - cumsum(x)[3]
    GaGr> [1] 2.775558e-17
    >> sum.exact(x) - cumsum.exact(x)[3]
    GaGr> [1] 0

[ buuh, humbug! ]

The  'NEWS'  for  R-devel (to become  R 2.9.0 in April)
has the following entry

    o	cumsum(x) and cumprod(x) for double precision x now use a long
	double accumulator where available and so more closely match
	sum() and prod() in potentially being more accurate.

and indeed, in R-devel, 
    sum(x) - cumsum(x)[length(x)]
gives 0 for your example.

Martin Maechler, ETH Zurich and R-core team

    GaGr> On Tue, Feb 17, 2009 at 5:12 PM, Stavros Macrakis <macrakis at alum.mit.edu> wrote:
    >> 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

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