[R] Numbers that look equal, should be equal, but if() doesn't see as equal (repost with code included)

[Prof Brian Ripley]

On Wed, 28 May 2003, Paul Lemmens wrote:

> Hoi Thomas,
> 
> --On woensdag 28 mei 2003 7:16 -0700 Thomas Lumley 
> <tlumley at u.washington.edu> wrote:
> 
> > On Wed, 28 May 2003, Paul Lemmens wrote:
> >
> >> Hi!
> >>
> >> Apologies for sending the mail without any code. Apparently somewhere
> >> along the way the .R attachments got filtered out. I have included the
> >> code below as clean as possible. My original mail is below the code.
> >
> > I still think you need not to be using ==.  You want something like
> >
> > if ( abs(mean.b-mean.orig)/(epsilon+abs(mean.orig) < epsilon){
> >
> > You are effectively using epsilon=0, but epsilon=10e-10 should be
> > adequate.
> >
> Based on all the hints and explanations I've changed the test to 
> 'identical(all.equal(mean.b, mean.orig, tolerance=.Machine$double.eps), 
> FALSE)'.
> 
> I still need to look into the concept of finite precision, because I still 
> don't grasp how sometimes (as an extreme example, probably) 0.25 != 1/4. 
> That this will happen for a number with a lot of different decimals I can 
> understand (by an accumulation of rounding errors).

How you you think 0.25 gets converted to an internal number?  It might be
0 + 2/10 + 5/100, and 2/10 and 5/100 cannot be represented exactly in 
binary arithmetic.  (R uses the system's strtod routine, so how it is done 
is system-dependent: on my systems it does end up with the same bit 
pattern as 1/4.)

As a real example

> (0.1 + 0.2) == 0.3
[1] FALSE

since

> print(c(0.1 + 0.2, 0.3), digits=20)
[1] 0.30000000000000004 0.29999999999999999

yet

> print(c(0.1, 0.2, 0.3), digits=20)
[1] 0.1 0.2 0.3


-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595