[R-SIG-Mac] Inaccurate inaccuracies on Mac only?
Michael Weylandt
michael.weylandt at gmail.com
Tue Dec 3 02:46:29 CET 2013
On Nov 30, 2013, at 8:54, Hans W Borchers <hwborchers at gmail.com> wrote:
> Dear R Mac colleagues,
>
> when I am running the following piece of code on Ubuntu Linux 12.04 LTS or on
> Windows 7 -- with R 3.0.2 --, I get the results as indicated:
>
> set.seed(8237)
> x <- runif(32, -1, 1)
> y <- runif(32, -1, 1)
> u <- cbind(x[1], y[1])
>
> u1 <- u %*% t(u)
> u2 <- apply(u * u, 1, sum)
> sqrt(u2 + u2 - 2*u1)
> ## [,1]
> ## [1,] NaN
> ## Warning message:
> ## In sqrt(u2 + u2 - 2 * u1) : NaNs produced
> u2 + u2 - 2*u1
> ## [,1]
> ## [1,] -2.220446e-16
>
> Theoretically, the last value should be zero. Of course, I am *not* surprised
> to see this is not the case under finite precision arithmetics.
>
> But what did surprise me was that under Mac OS X 10.6 and R 3.0.2 I get the
> following, exact results:
>
> set.seed(8237)
> x <- runif(32, -1, 1)
> y <- runif(32, -1, 1)
> u <- cbind(x[1], y[1])
>
> u1 <- u %*% t(u)
> u2 <- apply(u * u, 1, sum)
> sqrt(u2 + u2 - 2*u1)
> ## [,1]
> ## [1,] 0
> u2 + u2 - 2*u1
> ## [,1]
> ## [1,] 0
>
> I always thought that all these systems and versions comply to the IEEE
> floating point standard and return the same (accurate or inaccurate) answers.
Yes, if they do the same operations. But that's a big if.
Beyond general 'compiler magic' you'll also want to look at the matrix multiplication libraries used.
Cheers,
Michael
>
> The problem here is: When I test a package on Mac, I cannot be sure it will
> run without errors on other systems. Actully, I found this when running some
> examples from help pages, written on the Mac.
>
> Was I wrong, or is there something special about the Mac version of R ?
>
> Many thanks
> Hans Werner
>
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