From wdun|@p @end|ng |rom t|bco@com  Thu Feb 21 00:37:56 2019
From: wdun|@p @end|ng |rom t|bco@com (William Dunlap)
Date: Wed, 20 Feb 2019 15:37:56 -0800
Subject: [Rd] code for sum function
In-Reply-To: <CAOuLjjS5o19+mKUQm7k33sqAMo3_nWp+Wygroqbr3G-PMJDUoQ@mail.gmail.com>
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Message-ID: <CAF8bMcbwBk9v0jNxA6mwoB3Cn-gfA5J=0N3MJoWVitErMah7cA@mail.gmail.com>

Someone said it used a possibly platform-dependent
higher-than-double-precision type.

By the way, in my example involving rep(1/3, n) I neglected to include the
most precise
way to calculate the sum: n%/%3 + (n%%3)/3.

Bill Dunlap
TIBCO Software
wdunlap tibco.com


On Wed, Feb 20, 2019 at 2:45 PM Rampal Etienne <rampaletienne at gmail.com>
wrote:

> 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
William Dunlap