Re: draft

["W. Kahan" <wkahan@xxxxxxxxxxxxxxxxx>]

In response to what   "Markstein, Peter" wrote:

> David Hough wrote:
> >
> > > 4.1.1: Replace "numbers bracketing the infinitely precise
> > result" with
> > > "numbers bracketing an unrepresentable infinitely precise
> > result".  Why
> > > is it OK to delete "nearest"?
> >
> > "bracketing" implies "nearest" I think.    This change might
> > have been made while
> > I was gone though.
> >
>
> For unrepresentatble quantities just larger in magnitude than a power of the base, the base and the next smaller-in-magnitude numbers are closest, since the value of an ulp changes as we cross a power boundary.  E.g. in decimal 4 digit arithmetic, the two closest quantities to 1.0001 are 1.000 and 0.9999, but not 1.001.

Perhaps the word better than  "nearest"  is  "adjacent" ?