R help - Nov 2010 - unexpected behavior using round to 2 digits on randomly generated numbers

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.

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)

On Nov 28, 2010, at 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.
>
> 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.
It's one of the FAQ and probably the most F-ly of the FAQ's. #21 or  
#31 if I remember (vaguely)  ... the one about why seq(0.1, 1, by=0.1)  
==  (1:11)/10  returns 2 FALSE's.

-- 
David.

> 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)
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
David Winsemius, MD
West Hartford, CT

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)
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

On 2010-11-28 13:20, 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.
>
> 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.
>
Hmm, how hard have you looked?
I doubt that I'll be the first to remind you to check the FAQ.

Peter Ehlers
> 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)
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

FAQ 7.31

http://cran.r-project.org/doc/FAQ/R-FAQ.html#Why-doesn_0027t-R-think-these-numbers-are-equal_003f

You find it odd that the result is not an integer, while I find the fact 
that your calculation actually works reliably with any number of digits 
surprising, and you should avoid assuming such behavior will continue in 
the future. Multiply by the appropriate range and THEN take the integer 
part.

Patient: Doctor, it hurts when I ram my head into the wall!
Doctor: Don't do that!

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.
>
> 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)
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

On Sun, Nov 28, 2010 at 01:53:05PM -0800, Jeff Newmiller
wrote:
> FAQ 7.31
> 
>
http://cran.r-project.org/doc/FAQ/R-FAQ.html#Why-doesn_0027t-R-think-these-numbers-are-equal_003f
Additional information concerning rounding errors of double precision and 
suggestions for R code, which avoids them in some situations, may be found
in the first section of
  http://rwiki.sciviews.org/doku.php?id=misc:r_accuracy
and in
  http://rwiki.sciviews.org/doku.php?id=misc:r_accuracy:decimal_numbers

Petr Savicky.