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 <wdun...@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 <pgilbert...@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@r-project.org mailing list >> > https://stat.ethz.ch/mailman/listinfo/r-devel >> >> ______________________________________________ >> R-devel@r-project.org mailing list >> https://stat.ethz.ch/mailman/listinfo/r-devel >> > [[alternative HTML version deleted]] ______________________________________________ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
