From ripley@stats.ox.ac.uk  Thu Jan 24 13:27:42 2002
From: ripley@stats.ox.ac.uk (ripley@stats.ox.ac.uk)
Date: Thu, 24 Jan 2002 14:27:42 +0100 (MET)
Subject: [Rd] Representation of floating point numbers (PR#1281)
Message-ID: <200201241327.OAA15418@pubhealth.ku.dk>

On Thu, 24 Jan 2002, Winfried Theis wrote:

> Dear Prof. Ripley,
>
> On 24-Jan-02 Prof Brian Ripley wrote:
> >
> > 0.1 cannot be represented exactly in binary arithmetic. You asked for the
> > representation to 22 digits, and at most 17 are used in IEEE arithmetic.
> >
> > This is not a bug in R, which does not claim to have arbitrary precision.
> >
> Okay, I do not expect arbitrary precision, but maybe a warning in some way
> would be in order, to tell non-experts, what can be expected...
>
> As I said I came across this,
> when I searched for an error and this might be the reason for it. When comparing
> distances in one dimension within the sequence seq(0,1,by=0.1), I found that R
> does not take the distances between (0.3, 0.5) and (0.5,0.7) to be equal.
>
> > abs(0.5-0.3)==abs(0.5-0.7)
> [1] FALSE
>
> Checking this now a bit closer with your information I found:
> > round(abs(0.5-0.3),digits=17)==round(abs(0.5-0.7),digits=17)
> [1] FALSE
> > round(abs(0.5-0.3),digits=16)==round(abs(0.5-0.7),digits=16)
> [1] TRUE
>
> Would it be possible to restrict "==" as well to the maximum number of digits
> used in the arithmetics? It would be very convenient to get the expected result
> from such a comparison.

There is a function all.equal provided for this purpose: it is a misuse of
==.

-- 
Brian D. Ripley,                  ripley@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 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595


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[Rd] Representation of floating point numbers (PR#1281)
ripley@stats.ox.ac.uk