Re: Motion M0050:EDP-Without-CA
On 2013-10-01 14:20:45 +0300, Svetoslav Markov wrote:
> > > Sorry, I do not understand what you say. If a true numeric result is a
> > > number (degenerate interval) like 12345 + 12345^(-50)
> >
> > You probably meant 12345 + 12345*10^(-50).
>
> Yes, indeed, sorry!
> >
> > > then the MR form can be a tight number if an
> > > EDP-data object is available, and a wider interval if not available.
> > > In particular, if a true numeric result is the number
> > > 1 + 1^(-50) then the MR form will be an exact number if an
> > > EDP-data object is available, and will be an interval if not available.
> >
> > This is confusing. A mid-rad representation is different than a
> > degenerate (singleton) interval like [12345 + 12345*10^(-50)].
> > If it's a degenerate interval of the form [x+y], you shouldn't
> > call it mid-rad.
>
> Thank for your correction.
>
> I had in mind that a singleton 12345 + 12345*10^(-50) can be
> converted into a very tight mid-rad interval with centre 12345 and
> radius, say, 12346*10^(-50). Sorry for careless writing.
Note that when converting 12345 + 12345*10^(-50) to a mid-rad
interval <12345,12346*10^(-50)> (with a non-zero radius), you
lose information: you no longer have a singleton. Now, this
may not be important for you...
> Can you be more specific? How can we convert in MR-form tightly a
> singleton result like 12345 + 12345*10^(-50) without EDP-data type
> and without further knowledge (e.g. knowing that it is exactly
> representable as x+y? )
First an EDP-data type is just some particular case of a conventional
multiple-precision type (possibly in a fixed precision). You can use
such a type. You don't need the existence of EDP.
But you can also use another format: a double-word format, where a
number is represented by a pair (x0,x1) of a native floating-point
format, with x1 << x0. Here, x0 = 12345 and x1 = 12345*10^(-50).
This can be more efficient than a multiple-precision type such as
"EDP-data type".
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Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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