[R] unexpected behavior using round to 2 digits on randomly generated numbers

[Duncan Murdoch]

On 28/11/2010 4:20 PM, Cory Rieth wrote:
> Hello!
>
> I stumbled upon something odd that took a while to track down, and I wanted to run it by here to see if I should submit a bug report. For randomly generated numbers (from a variety of distributions) rounding them to specifically 2 digits and then multiplying them by 100 produces strange results on about 8% of cases. The problematic numbers display as I would have expected, but do not logically match the as.integer counterpart (additionally they will not be used correctly by functions such as rep()). I realize there are easy workarounds, but I wouldn't have expected this result, and it only occurs rounding to 2 decimals, i.e. changing digits to 3 and multiplying by 1000 after rounding gives the expected result.

This is presumably another version of FAQ 7.31.  Very few numbers of the 
form n/100 are exactly representable in floating point, and the rounding 
error sometimes shows up when you multiply by 100.  A simpler version of 
this is the following:

 > y <- 1:99
 > y[(y/100)*100 != y]
[1]  7 14 28 29 55 56 57 58

Duncan Murdoch

>
> x<-runif(100)				#generate some random numbers
> y<-round(x,digits=2)*100  #round them all to two decimals, then multiply them all by 100. I expected the results to all be integers
> sum(y!=as.integer(y))		#but on about 8% of the numbers they do not match the integer version
> x[which(y!=as.integer(y))]	# a list of the problem numbers from the original distribution. They seem to be more common but not exclusive to .54 to .57
> y[which(y!=as.integer(y))]  #the numbers still display as would be expected, i.e. they are integers
> as.integer(y[which(y!=as.integer(y))])  # and sometimes display as the same number they are not logically identical to
>
> Thanks, and sorry if I came across something that is known, or it is meant to behave this way, I couldn't find anything.
>
> Cory Rieth
>
> R.version() output:
> platform       x86_64-apple-darwin9.8.0
> arch           x86_64
> os             darwin9.8.0
> system         x86_64, darwin9.8.0
> status
> major          2
> minor          12.0
> year           2010
> month          10
> day            15
> svn rev        53317
> language       R
> version.string R version 2.12.0 (2010-10-15)
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