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*To*: "Markstein, Peter" <peter.markstein@xxxxxx>*Subject*: Re: draft*From*: "W. Kahan" <wkahan@xxxxxxxxxxxxxxxxx>*Date*: Wed, 17 Mar 2004 13:50:52 -0800*Cc*: "'David G Hough 754R work'" <754r@xxxxxxxxxxx>, stds-754@xxxxxxxx*Delivery-date*: Wed Mar 17 15:43:55 2004*References*: <0C3EFB691636964BBF914AE56AE83A892D2946@hplex4.hpl.hp.com>*Sender*: owner-stds-754@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" ?

**References**:**RE: draft***From:*Markstein, Peter

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