Representation of floating point numbers (PR#1281)

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.