[R] Interesting quirk with fractions and rounding

[Bert Gunter]

I suggest you read some basic books on numerical analysis and/or talk
with a numerical analyst. You are (like most of us) an amateur at this
sort of thing trying to reinvent wheels. If you are concerned with
details, talk with experts. Don't assume what you don't know. This
list is *not* a reliable source of such expertise, although there
*are* individuals in the R universe with considerable knowledge who
may or may not choose to respond.

Cheers,
Bert


Bert Gunter

"The trouble with having an open mind is that people keep coming along
and sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )


On Fri, Apr 21, 2017 at 5:19 AM, Paul Johnson <pauljohn32 at gmail.com> wrote:
> We all agree it is a problem with digital computing, not unique to R. I
> don't think that is the right place to stop.
>
> What to do? The round example arose in a real funded project where 2 R
> programs differed in results and cause was  that one person got 57 and
> another got 58. The explanation was found, but its less clear how to
> prevent similar in future. Guidelines, anyone?
>
> So far, these are my guidelines.
>
> 1. Insert L on numbers to signal that you really mean INTEGER. In R,
> forgetting the L in a single number will usually promote whole calculation
> to floats.
> 2. S3 variables are called 'numeric' if they are integer or double storage.
> So avoid "is.numeric" and prefer "is.double".
> 3. == is a total fail on floats
> 4. Run print with digits=20 so we can see the less rounded number. Perhaps
> start sessions with "options(digits=20)"
> 5. all.equal does what it promises, but one must be cautious.
>
> Are there math habits we should follow?
>
> For example, Is it generally true in R that (100*x)/y is more accurate than
> 100*(x/y), if x > y?   (If that is generally true, couldn't the R
> interpreter do it for the user?)
>
> I've seen this problem before. In later editions of the game theory program
> Gambit, extraordinary effort was taken to keep values symbolically as
> integers as long as possible. Avoid division until the last steps. Same in
> Swarm simulations. Gary Polhill wrote an essay about the Ghost in the
> Machine along those lines, showing accidents from trusting floats.
>
> I wonder now if all uses of > or < with numeric variables are suspect.
>
> Oh well. If everybody posts their advice, I will write a summary.
>
> Paul Johnson
> University of Kansas
>
> On Apr 21, 2017 12:02 AM, "PIKAL Petr" <petr.pikal at precheza.cz> wrote:
>
>> Hi
>>
>> The problem is that people using Excel or probably other such spreadsheets
>> do not encounter this behaviour as Excel silently rounds all your
>> calculations and makes approximate comparison without telling it does so.
>> Therefore most people usually do not have any knowledge of floating point
>> numbers representation.
>>
>>  Cheers
>> Petr
>>
>> -----Original Message-----
>> From: R-help [mailto:r-help-bounces at r-project.org] On Behalf Of Paul
>> Johnson
>> Sent: Thursday, April 20, 2017 11:56 PM
>> To: R-help <r-help at r-project.org>
>> Subject: [R] Interesting quirk with fractions and rounding
>>
>> Hello, R friends
>>
>> My student unearthed this quirk that might interest you.
>>
>> I wondered if this might be a bug in the R interpreter. If not a bug, it
>> certainly stands as a good example of the dangers of floating point numbers
>> in computing.
>>
>> What do you think?
>>
>> > 100*(23/40)
>> [1] 57.5
>> > (100*23)/40
>> [1] 57.5
>> > round(100*(23/40))
>> [1] 57
>> > round((100*23)/40)
>> [1] 58
>>
>> The result in the 2 rounds should be the same, I think.  Clearly some
>> digital number devil is at work. I *guess* that when you put in whole
>> numbers and group them like this (100*23), the interpreter does integer
>> math, but if you group (23/40), you force a fractional division and a
>> floating point number. The results from the first 2 calculations are not
>> actually 57.5, they just appear that way.
>>
>> Before you close the books, look at this:
>>
>> > aa <- 100*(23/40)
>> > bb <- (100*23)/40
>> > all.equal(aa,bb)
>> [1] TRUE
>> > round(aa)
>> [1] 57
>> > round(bb)
>> [1] 58
>>
>> I'm putting this one in my collection of "difficult to understand"
>> numerical calculations.
>>
>> If you have seen this before, I'm sorry to waste your time.
>>
>> pj
>> --
>> Paul E. Johnson   http://pj.freefaculty.org
>> Director, Center for Research Methods and Data Analysis
>> http://crmda.ku.edu
>>
>> To write to me directly, please address me at pauljohn at ku.edu.
>>
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