Re: [R] Integer / floating point question

From: Duncan Murdoch <murdoch_at_stats.uwo.ca>
Date: Fri, 16 May 2008 13:44:05 -0400

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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