a==0 vs as.integer(a)==0 vs all.equal(a,0)

On Tue, 8 Mar 2005 09:03:43 +0000, Robin Hankin
<r.hankin at soc.soton.ac.uk> wrote :

hi


?integer says:

     Note that on almost all implementations of R the range of
     representable integers is restricted to about +/-2*10^9: 'double's
     can hold much larger integers exactly.


I am getting very confused as to when to use integers and when not to.
In my line
I need exact comparisons of large integer-valued arrays, so I often use
as.integer(),
but the above seems to tell me that doubles might  be better.

Consider the following R idiom of Euclid's algorithm for the highest
common factor
of two positive integers:

  gcd <- function(a, b){
    if (b == 0){ return(a)}
    return(Recall(b, a%%b))
  }

If I call this with gcd(10,12), for example, then  a%%b is not an
integer, so the first
line of the function, testing b for being zero, isn't legitimate.

When you say it isn't legitimate, you mean that it violates the advice
never to use exact comparison on floating point values?

I think that's just advice, it's not a hard and fast rule.  If you
happen to know that the values being compared have been calculated and
stored exactly, then "==" is valid.  In your function, when a and b
are integers that are within some range (I'm not sure what it is, but
it approaches +/- 2^53), the %% operator should return exact results.
(Does it do so on all platforms?  I'm not sure, but I'd call it a bug
if it didn't unless a and/or b were very close to the upper limit of
exactly representable integers.)

Do you know of examples where a and b are integers stored in floating
point, and a %% b returns a value that is different from as.integer(a)
%% as.integer(b)?