On 04-Mar-10 13:35:42, Duncan Murdoch wrote:
> On 04/03/2010 7:35 AM, (Ted Harding) wrote:
>> On 04-Mar-10 10:50:56, Petr PIKAL wrote:
>> > Hi
>> >
>> > r-help-boun...@r-project.org napsal dne 04.03.2010 10:36:43:
>> >> Hi R Gurus,
>> >>
>> >> I am trying to figure out what is going on here.
>> >>
>> >> > a <- 68.08
>> >> > b <- a-1.55
>> >> > a-b
>> >> [1] 1.55
>> >> > a-b == 1.55
>> >> [1] FALSE
>> >> > round(a-b,2) == 1.55
>> >> [1] TRUE
>> >> > round(a-b,15) == 1.55
>> >> [1] FALSE
>> >>
>> >> Why should (a - b) == 1.55 fail when in fact b has been defined
>> >> to be a - 1.55? Is this a precision issue? How do i correct this?
>> >
>> > In real world those definitions of b are the same but not in
>> > computer
>> > world. See FAQ 7.31
>> >
>> > Use either rounding or all.equal.
>> >
>> >> all.equal(a-b, 1.55)
>> > [1] TRUE
>> >
>> > To all, this is quite common question and it is documented in FAQs.
>> > programs, therefore maybe a confusion from novices.
>> >
>> > I wonder if there could be some type of global option which will
>> > get rid of these users mistakes or misunderstandings by setting
>> > some threshold option for equality testing by use "==".
>> >
>> > Regards
>> > Petr
>> >
>> >> Alex
>>
>> Interesting suggestion, but in my view it would probably give
>> rise to more problems than it would avoid!
>>
>> The fundamental issue is that many inexperienced users are not
>> aware that once 68.08 has got inside the computer (as used by
>> R and other programs which do fixed-length binary arithmetic)
>> it is no longer 68.08 (though 1.55 is still 1.55).
>>
>
> I think most of what you write above and below is true, but your
> parenthetical remark is not. 1.55 can't be represented exactly in the
> double precision floating point format used in R. It doesn't have a
> terminating binary expansion, so it will be rounded to a binary
> fraction. I believe you can see the binary expansion using this code:
>
> x <- 1.55
> for (i in 1:70) {
> cat(floor(x))
> if (i == 1) cat(".")
> x <- 2*(x - floor(x))
> }
>
> which gives
>
> 1.100011001100110011001100110011001100110011001100110100000000000000000
>
> Notice how it becomes a repeating expansion, with 0011 repeated 12
> times, but then it finishes with 0100000000000000000, because we've run
> out of bits.
> So 1.55 is actually stored as a number which is ever so slightly
> bigger.
>
> Duncan Murdoch
Of course you are quite right! My parenthetical remark was
an oversight and a blunder -- not so much a typo as a braino,
due to crossing wires between dividing by 2 (1.5 = 1 + 1/2)
and dividing by 10 ( 1.55 != 1 + 1/2 + (1/2)/2) )!
However, your detailed explanation will certainly be useful
to some. And your method of producing the binary expansion
is very neat indeed.
>> [the rest of my stuff snipped]
Ted.
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E-Mail: (Ted Harding) <ted.hard...@manchester.ac.uk>
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Date: 04-Mar-10 Time: 20:11:39
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