# Re: [R] Rounding?

From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>
Date: Tue, 12 Jun 2007 06:13:37 +0100 (BST)

On Mon, 11 Jun 2007, jim holtman wrote:

```> your number 6.6500000000000001 is to large to fit in a floating point
> number.  It takes 56 bits and there are only 54 in a real number so the
> system see it as 6.65 and does the rounding to an even digit; 6.6

```

I'll take it you mean a IEC60559 double, which has 53 bits in its implied mantissa (it stores 52 and for normalized numbers the leading bit is 1 and not stored).

> 6.650000000000001 does fit into a real number (takes 54 bits) and this will > now round to 6.7

All you can say quickly is that its representation is greater than 6.65:

> 6.650000000000001 - 6.65
[1] 8.881784e-16

But I don't think that is the explanation. Remember that you are using binary arithmetic, so each of these numbers is stored with representation error. As the exact number stored is not '6.65', round-to-even does not strictly apply.

I get

> formatC(6.65,format="f",digits=1)
[1] "6.7"
> print(6.65, digits=2)
[1] 6.7
> print(66.5, digits=1) # round to even really does apply [1] 66
> print(67.5, digits=1)
[1] 68

on (several of) my non-Windows systems, so I think this is a Windows quirk. Remember the parsing and printing software has also to run in binary on a limited-precision machine, and it does tend to be less accurate on Windows than on other ix86 OSes. (Windows software also tends not to implement round-to-even rules.)

```> On 6/11/07, BXC (Bendix Carstensen) <bxc_at_steno.dk> wrote:
```

>>
>> I was a bit puzzed by:
>>
>>> formatC(6.65,format="f",digits=1)
>> [1] "6.6"
>>
>> So I experimented and found:
>>
>>> formatC(6.6500000000000001,format="f",digits=1)
>> [1] "6.6"
>>> formatC(6.650000000000001,format="f",digits=1)
>> [1] "6.7"
>>> round(6.6500000000000001,1)
>> [1] 6.7
>>> round(6.650000000000001,1)
>> [1] 6.7
>>> version
>> _
>> platform i386-pc-mingw32
>> arch i386
>> os mingw32
>> system i386, mingw32
>> status
>> major 2
>> minor 5.0
>> year 2007
>> month 04
>> day 23
>> svn rev 41293
>> language R
>> version.string R version 2.5.0 (2007-04-23)
>>
>> My machine runs Windows NT.
>>
>> Is this intended or just a Windows facility?
>> ______________________________________________
>>
>> Bendix Carstensen
>> Senior Statistician
>>
>> Steno Diabetes Center
>> Niels Steensens Vej 2-4
>> DK-2820 Gentofte
>> Denmark
>> +45 44 43 87 38 (direct)
>> +45 30 75 87 38 (mobile)
>> +45 44 43 73 13 (fax)
>> bxc@steno.dk http://www.biostat.ku.dk/~bxc
>>
>> This e-mail (including any attachments) is intended for the ...{{dropped}}
>>
>> ______________________________________________
>> R-help_at_stat.math.ethz.ch mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
```>
>
>
>

--
Brian D. Ripley,                  ripley_at_stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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```
R-help_at_stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Tue 12 Jun 2007 - 05:22:31 GMT

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