Re: P1788/M0014.01: 6.1_and_6.2 (compatibility with multi-precision)
> Date: Tue, 4 May 2010 13:34:03 +0300
> Subject: Re: P1788/M0014.01: 6.1_and_6.2 (compatibility with multi-precision)
> From: "Hossam A. H. Fahmy" <hfahmy@xxxxxxxxxxxxxxxxxxxxxxx>
> To: stds-1788@xxxxxxxxxxxxxxxxx
>
>
> Vincent and P1788 group,
>
> 2010/5/4 Vincent Lefevre <vincent@xxxxxxxxxx>
>
> > On 2010-05-02 03:54:20 -0700, Dan Zuras Intervals wrote:
> > > The 'dubious' nature of my concerns surround the
> > > problem that mid-rad intervals represent a quite
> > > different subset of the Real intervals than do the
> > > inf-sup forms. I believe that it will require us
> > > to burden mid-rad forms further to represent these
> > > intervals (like [1e-100,1e+100] & [3,+oo]) somehow.
> > > Is it sufficient to represent them as say,
> > > (5e+99,0,1e+100) & (something+3,-something,+oo)?
> >
> > I think that if the interval is large enough, one can still choose
> > mid = 0. Then the representation is equivalent to inf-sup, isn't it?
> >
> >
> My understanding of the form (mid, del1, del2) that represents [mid-del1,
> mid+del2] was that both del1 and del2 are always considered as zero or
> positive numbers (the distance of the radius). However, taking mid=0 for
> large intervals leads to negative or positive delimiters as in:
>
> [-1e+10, 2e+20] = (0, 1e+10, 2e+20)
>
> [+1e+10, 2e+20] = (0,-1e+10, 2e+20)
>
> [-1e+10, -2e+20] = (0, 1e+10, -2e+20)
>
> Vincent's proposal solves the issue of representation for large intervals.
> However, can the colleagues who use mid-rad representations in their work
> comment on whether they depend on the fact that rad is always non-negative?
> If yes, what is the impact of having two delimiters (not just one) and with
> both being either positive or negative?
>
> --
> Hossam A. H. Fahmy
> Assistant Professor
> Electronics and Communications Engineering Department
> Cairo University
> Egypt
>
Vincent's proposal does seem to solve the problem of
conversion from inf-sup to mid-rad. So long as the
rad components have sufficient precision to hold the
inf & sup, that is. And so long as the mid-rad people
will tolerate having the mid strictly outside the
resulting interval.
But I don't know if that's true. Nor do I know if
there are any other more subtle problems.
Remember the mid-rad form is chosen because of its
utility in the case of very narrow intervals. There
may be algorithms that have the flavor of
principleComponent + tinyAdjustment
that would fail should the interval be too wide or
the midpoint too far from the interval itself.
Still, I trust you mid-rad guys can enlighten us.
Dan