# [R] Interesting quirk with fractions and rounding

Paul Johnson pauljohn32 at gmail.com
Fri Apr 21 14:19:10 CEST 2017

```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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