Re: Comparisons and decorations

[Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>]

Dan Zuras Intervals wrote:
> > Subject: Re: Comparisons and decorations
> > From: John Pryce <j.d.pryce@xxxxxxxxxxxx>
> > Date: Sat, 25 Sep 2010 16:48:40 +0100
> > To: stds-1788 <stds-1788@xxxxxxxxxxxxxxxxx>
> >
> > Nate
> >
> > On 24 Sep 2010, at 11:48, Arnold Neumaier wrote:
> > > Nate Hayes wrote:
> > > > special cases for
> > > >   A \interior B
> > > > such as when A and B are both Entire or A=[1,Infnity]
> > > > and B=[0,Infinity]. In these cases, the interior operator
> > > > would need to return a different result than when A and B
> > > > are compact intervals, such as A=[1,100] and B=[0,200]. 
> > > ??? There is a uniform formula in 754:
> > >
> > > [al,au] interior [bl,bu] iff ~(bl-al>=0) and ~(au-bu>=0).
> > Looking at 754-2008 §5.3.1, I think
> >   (nextDown(al) >= bl) and (nextUp(au) <= bu)
> > also works, since nextDown(-oo) = -oo and nextUp(+oo) = +oo.
> >
> > John Pryce
>
> 	If the intention is that interior is subset with a
> 	smidge at both ends except when that end is infinite,
> 	then both formulas have performance problems.
>
> 	The first risks NaNs on the subtracts (which compares
> 	false so the formula has the correct outcome).  But
> 	because of our decorations, implementations may end
> 	up running with the invalid trap enabled which slows
> 	things down by factors of 100x to 1000x when it
> 	happens.

Please explain.

What does this have to do with decorations?
They don't affect the formulas!

What can enable an invalid trap?