Prof Brian Ripley <ripley@stats.ox.ac.uk> writes:
But there are better algorithms that are not subject to this sort of rounding error. I reckon that computing a variance this way is not the quality of algorithm one should expect from R.
Hmm. Which algorithms are there? Surely almost any kind of provisional means subtraction could avoid the the extreme case where the mean of a bunch of identical numbers is different from all of them, but will it also improve precision in the general case? Essentially our current algorithm in cov.c is xm<- sum(x)/n v <- 1/(n-1)*sum((x-xm)^2)
x<-1e30/(8^16) structure(x, class="octmode")
[1] "144762623464043165"
structure(x+x+x, class="octmode")
[1] "456730272634151540" If you look carefully, you will see that a bit is lost in the process since 5+5+5 is 17 octal.
O__ ---- Peter Dalgaard Blegdamsvej 3 c/ /'_ --- Dept. of Biostatistics 2200 Cph. N (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - (p.dalgaard@biostat.ku.dk) FAX: (+45) 35327907 -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-devel mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-devel-request@stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._