[R] options("digits") and print.default()

[Prof Brian Ripley]

On Mon, 15 Jan 2007, Ulrich Keller wrote:

> Hello everyone,
>
> I use latex() (Hmisc) for report generation and thus have been affected by
> the problem with rounding decimals described, for example, in this post:
>
> http://thread.gmane.org/gmane.comp.lang.r.general/73287/focus=73287
>
> In short, numbers often are printed with 15 or so decimals even if there
> far less significant digits. The problem has been confirmed by Frank
> Harrell and Thomas Dupont according to this post:
>
> http://thread.gmane.org/gmane.comp.lang.r.general/73172/focus=73186
>
> But it has still not been fixed. Rather than changing all my reports I
> decided I'd look at format.df() in Hmisc myself and try to fix the problem
> there. I found that the problem is not in Hmisc at all, but in R itself:
>
>> print(1.001)
> [1] 1.001
>> options(digits=16) #format.df does this
>> print(1.001)
> [1] 1.001000000000000
>> print(round(1.001, 3)) #rounding does not help
> [1] 1.001000000000000
>
> This does not seem to be the behaviour described in the documentation,
> which says:
>
> "The same number of decimal places is used throughout a vector,[sic!] This
> means that digits specifies the minimum number of significant digits to be
> used, and that at least one entry will be encoded with that minimum
> number. However, if all the encoded elements then have trailing zeroes,
> the number of decimal places is reduced until at least one element has a
> non-zero final digit."
>
> If print.default() exhibited the behaviour desribed in the docs,
> format.df() and thus latex() would work as advertised, I think. I would
> have written a bug report instead of posting here, but the fact (?) that
> Frank and Thomas have confirmed the bug seems to indicate that the problem
> does indeed lie with Hmisc. Am I misunderstanding something here?
>
> I use R version 2.4.1 Patched (2007-01-13 r40470) on Windows.

The bug is that Hmisc uses more digits than the representation provides:

> .Machine$double.eps
[1] 2.22044604925031e-16

If it used 15 digits (as R does for as.character) all would be well. 
Since R has to do the calculations you quote in binary arithmetic, they 
are also subject to representation error and there is no way they can be 
done to 16 significant figures.  (I've traced the example, and that is 
what happens.)  See ?as.character for more details.

-- 
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