On 5/16/2008 11:45 AM, Erik Iverson wrote:
Marc -
Marc Schwartz wrote:
on 05/16/2008 09:56 AM Erik Iverson wrote:
Dear R-help -
I have thought about this question for a bit, and come up with no
satisfactory answer.
Say I have the numeric vector t1, given as
t1 <- c(1.0, 1.5, 2.0, 2.5, 3.0)
I simply want to reliably extract the unique integers from t1, i.e.,
the vector c(1, 2, 3). This is of course superficially simple to
carry out.
Use modulo division:
> t1[t1 %% 1 == 0]
[1] 1 2 3
or
> unique(t1[t1 %% 1 == 0])
[1] 1 2 3
Yes, that is one of the solutions. However, can I be sure that, say,
2.0 %% 1 == 0
The help page for '%%' addresses this a bit, but then caveats it with
'up to rounding error', which is really my question. Is there ever
'rounding error' with 2.0 %% 1 as opposed to 2 %% 1?
If you enter them as part of your source, then 2.0 and 2 are guaranteed
to be the same number, because both are exactly representable as the
ratio of an integer and a power of 2: 2/2^0, or 1/2^(-1). (There are
limits on the range of both the numerator and denominator for this to
work, but they are quite wide.)
If you calculate them, e.g. as 0.2*10, then there is no guarantee, and
the results may vary from machine to machine. This is because 0.2 is
*not* representable as an integer over a power of two. It will likely
be represented to 52 or 53 bit precision, but with some
compiler/hardware combinations, you might get 64 bit (or other)
precision in intermediate results. I don't think R currently does this,
but I wouldn't be very surprised if there were situations where it did.
There might be cases where R doesn't correctly convert literal numeric
constants into the closest floating point value, but I think it would be
considered a serious bug if it messed up small integers.
Duncan Murdoch
However, my question is related to R FAQ 7.31, "Why doesn't R think
these numbers are equal?" The first sentence of that FAQ reads, "The
only numbers that can be represented exactly in R's numeric type are
integers and fractions whose denominator is a power of 2."
All the methods I've devised to do the above task seem to ultimately
rely on the fact that identical(x.0, x) == TRUE, for integer x.
My assumption, which I'm hoping can be verified, is that, for example,
2.0 (when, say, entered at the prompt and not computed from an
algorithm) is an integer in the sense of FAQ 7.31.
This seems to be the case on my machine.
> identical(2.0, 2)
[1] TRUE
Apologies that this is such a trivial question, it seems so obvious on
the surface, I just want to be sure I am understanding it correctly.
Keep in mind that by default and unless specifically coerced to integer,
numbers in R are double precision floats:
> is.integer(2)
[1] FALSE
> is.numeric(2)
[1] TRUE
> is.integer(2.0)
[1] FALSE
> is.numeric(2.0)
[1] TRUE
So:
> identical(2.0, as.integer(2))
[1] FALSE
Does that help?
A bit, and this is the source of my confusion. Can I always assume that
2.0 == 2 when the class of each is 'numeric'?
Marc Schwartz
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and provide commented, minimal, self-contained, reproducible code.
