[R] bug when subtracting decimals?

[Marc Schwartz]

On Apr 21, 2009, at 5:55 AM, Duncan Murdoch wrote:

> On 21/04/2009 3:48 AM, Petr PIKAL wrote:
>> Hi
>> r-help-bounces at r-project.org napsal dne 20.04.2009 19:01:46:
>>> wolfgang.siewert <wolfgang.siewert <at> gmail.com> writes:
>>>
>>>> There is a way around: round(0.7-0.3,1)==0.4
>>>> (TRUE)
>>>>
>>>> Obviously there is a problem with some combinations of decimal
>> subtractions,
>>>> that - we have the feeling - shouldt be solved.
>>> Oh no, not that one again! This was lecture two in my first computer
>>> course in 1968, but it seems to be gone the way of the dodo since  
>>> than.
>> Maybe that is because of Excel is so widespread now and gives  
>> expected results (it probably silently rounds all decimal numbers  
>> before calculation).
>
> I don't have Excel, but I expect OpenOffice duplicates its bugs  
> pretty well.  And in OpenOffice I see all sorts of bugs due to this,  
> e.g. examples where x = y and y = z but x != z, cases where I can  
> calculate a number like 1 + 4.e-15 and get something different from  
> 1, but if I enter it directly as 1.000000000000004, it gets changed  
> to 1.
>
> So it only gives expected results in some tests, not others.
>
> Duncan Murdoch



As Dieter noted from our offlist exchange, this had been discussed  
previously back in 2003. Just to refresh memories:

   https://stat.ethz.ch/pipermail/r-help/2003-June/034565.html

   https://stat.ethz.ch/pipermail/r-help/2003-June/034860.html


OO.org has replicated Excel's behavior to a fault.  Thus:

   Spreadsheet Use -> Brain to Porridge


Just to update OO.org's behavior using version 3.0.1 on OSX:

   Formula: =4.145 * 100 + 0.5     Result: 415.00000000000000000000

   Formula: =0.5 - 0.4 - 0.1       Result: 0.00000000000000000000

   Formula: =(0.5 - 0.4 - 0.1)     Result: 0.00000000000000000000

So nothing has changed in OO.org in five years.  Somebody with Excel  
2007 might want to try the 2nd and 3rd formula examples to see if  
using parens still makes a difference in the result as compared to the  
formula without the parens.


FWIW, now that I am on OSX, I can add the following output using  
Numbers '09:

   Formula: =4.145 * 100 + 0.5     Result: 415.00000000000000000000

   Formula: =0.5 - 0.4 - 0.1       Result: -2.77556E-17

   Formula: =(0.5 - 0.4 - 0.1)     Result: -2.77556E-17


It does look like R's behavior has changed since then. Using:

   R version 2.9.0 Patched (2009-04-18 r48348)

on OSX:

# This first example has changed.
# Prior result was 414.99999999999994
 > print(4.145 * 100 + 0.5, digits = 20)
[1] 415

 > formatC(4.145 * 100 + 0.5, format = "E", digits = 20)
[1] "4.14999999999999943157E+02"

 > print(0.5 - 0.4 - 0.1, digits = 20)
[1] -2.77555756156289e-17

 > formatC(0.5 - 0.4 - 0.1, format = "E", digits = 20)
[1] "-2.77555756156289135106E-17"


What is interesting is that:

 > 4.145 * 100 + 0.5 == 415
[1] FALSE

 > (4.145 * 100 + 0.5) - 415
[1] -5.684342e-14

 > all.equal(4.145 * 100 + 0.5, 415, 0)
[1] "Mean relative difference: 1.369721e-16"


So it would appear that in the first R example above, the print()  
function has changed in a material fashion.

HTH,

Marc Schwartz