From r@mp@|et|enne @end|ng |rom gm@||@com  Wed Feb 20 23:45:42 2019
From: r@mp@|et|enne @end|ng |rom gm@||@com (Rampal Etienne)
Date: Wed, 20 Feb 2019 22:45:42 +0000
Subject: [Rd] code for sum function
In-Reply-To: <CAF8bMcZyCHPB1JcQyhwO=zx+7V2HOVALMUwHXvutjQf3Sv2S-A@mail.gmail.com>
References: <c1495700-e265-4ff8-1f36-e149bd4d1961@gmail.com>
 <66adfaca-27fe-4671-c73d-fd0462c36af0@gmail.com>
 <CAF8bMcZyCHPB1JcQyhwO=zx+7V2HOVALMUwHXvutjQf3Sv2S-A@mail.gmail.com>
Message-ID: <CAOuLjjS5o19+mKUQm7k33sqAMo3_nWp+Wygroqbr3G-PMJDUoQ@mail.gmail.com>

Dear Will,

This is exactly what I find.
My point is thus that the sum function in R is not a naive sum nor a
Kahansum (in all cases), but what algorithm is it using then?

Cheers, Rampal


On Tue, Feb 19, 2019, 19:08 William Dunlap <wdunlap at tibco.com wrote:

> 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
Rampal Etienne