On Sun, 19 Feb 2006, hadley wickham wrote: >> p.s. If my computations are correct, 0.2 = 0*/2 + 0/4 + 1/8 + 1/16 + >> 0/32 + 0/64 + 1/128 + 1/256 + 0/512 + 0/1024 + 1/2048 + 1/4096 + ... = >> 0.3333333333333h. Perhaps someone can extend this to an FAQ to help >> explain finite precision arithmetic and rounding issues. > > This is drifting a bit off topic, but the other day I discovered this > rather nice illustration of the perils of finite precision arithmetic > while creating a contrast matrix: > >> n <- 13 >> a <- matrix(-1/n, ncol=n, nrow=n) + diag(n) >> rowSums(a) > [1] 2.775558e-16 2.775558e-16 5.551115e-17 5.551115e-17 5.551115e-17 > [6] 5.551115e-17 0.000000e+00 -5.551115e-17 0.000000e+00 5.551115e-17 > [11] 1.110223e-16 1.665335e-16 2.220446e-16 > > Not only do most of the rows not sum to 0, they do not even sum to the > same number! It is hard to remember the familiar rules of arithmetic > do not always apply.
I think you will find this example does give all 0's in R-devel, even on platforms like Sparc. But users do need to remember that computer arithmetic is inexact except in rather narrowly delimited cases. -- Brian D. Ripley, [EMAIL PROTECTED] Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595 ______________________________________________ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
