[R-SIG-Mac] Inaccurate inaccuracies on Mac only?

[Michael Weylandt]

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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