From wdun|@p @end|ng |rom t|bco@com  Tue Feb 19 20:08:18 2019
From: wdun|@p @end|ng |rom t|bco@com (William Dunlap)
Date: Tue, 19 Feb 2019 11:08:18 -0800
Subject: [Rd] code for sum function
In-Reply-To: <66adfaca-27fe-4671-c73d-fd0462c36af0@gmail.com>
References: <c1495700-e265-4ff8-1f36-e149bd4d1961@gmail.com>
 <66adfaca-27fe-4671-c73d-fd0462c36af0@gmail.com>
Message-ID: <CAF8bMcZyCHPB1JcQyhwO=zx+7V2HOVALMUwHXvutjQf3Sv2S-A@mail.gmail.com>

The algorithm does make a differece.  You can use Kahan's summation
algorithm (https://en.wikipedia.org/wiki/Kahan_summation_algorithm) to
reduce the error compared to the naive summation algorithm.  E.g., in R
code:

naiveSum <-
function(x) {
   s <- 0.0
   for(xi in x) s <- s + xi
   s
}
kahanSum <- function (x)
{
   s <- 0.0
   c <- 0.0 # running compensation for lost low-order bits
   for(xi in x) {
      y <- xi - c
      t <- s + y # low-order bits of y may be lost here
      c <- (t - s) - y
      s <- t
   }
   s
}

> rSum <- vapply(c(1:20,10^(2:7)), function(n) sum(rep(1/7,n)), 0)
> rNaiveSum <- vapply(c(1:20,10^(2:7)), function(n) naiveSum(rep(1/7,n)), 0)
> rKahanSum <- vapply(c(1:20,10^(2:7)), function(n) kahanSum(rep(1/7,n)), 0)
>
> table(rSum == rNaiveSum)

FALSE  TRUE
   21     5
> table(rSum == rKahanSum)

FALSE  TRUE
    3    23


Bill Dunlap
TIBCO Software
wdunlap tibco.com


On Tue, Feb 19, 2019 at 10:36 AM Paul Gilbert <pgilbert902 at gmail.com> wrote:

> (I didn't see anyone else answer this, so ...)
>
> You can probably find the R code in src/main/ but I'm not sure. You are
> talking about a very simple calculation, so it seems unlike that the
> algorithm is the cause of the difference. I have done much more
> complicated things and usually get machine precision comparisons. There
> are four possibilities I can think of that could cause (small) differences.
>
> 0/ Your code is wrong, but that seems unlikely on such a simple
> calculations.
>
> 1/ You are summing a very large number of numbers, in which case the sum
> can become very large compared to numbers being added, then things can
> get a bit funny.
>
> 2/ You are using single precision in fortran rather than double. Double
> is needed for all floating point numbers you use!
>
> 3/ You have not zeroed the double precision numbers in fortran. (Some
> compilers do not do this automatically and you have to specify it.) Then
> if you accidentally put singles, like a constant 0.0 rather than a
> constant 0.0D+0, into a double you will have small junk in the lower
> precision part.
>
> (I am assuming you are talking about a sum of reals, not integer or
> complex.)
>
> HTH,
> Paul Gilbert
>
> On 2/14/19 2:08 PM, Rampal Etienne wrote:
> > Hello,
> >
> > I am trying to write FORTRAN code to do the same as some R code I have.
> > I get (small) differences when using the sum function in R. I know there
> > are numerical routines to improve precision, but I have not been able to
> > figure out what algorithm R is using. Does anyone know this? Or where
> > can I find the code for the sum function?
> >
> > Regards,
> >
> > Rampal Etienne
> >
> > ______________________________________________
> > R-devel at r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-devel
>
> ______________________________________________
> R-devel at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-devel
>

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[Rd] code for sum function
William Dunlap