Re: Motion M0050:EDP-Without-CA
On 2013-10-01 17:06:04 +0300, Svetoslav Markov wrote:
> well, it is important as long as it shows that conversion of
> exact numbers involves interval arithmetic - under the inclusion
> (containment) principle
Sure, a conversion of an exact number to an interval involves
interval arithmetic. But this doesn't mean that an exact number
(as an element of a data type) is itself related to interval
arithmetic.
> I see your point. However, I think that in its last version, the
> motion only requires the possibility to extract (and make use of)
> the exact numeric results, without stressing on the hardware
> implementation.
>
> So, exact numeric results are needed for tight intervals
> during conversion - therefore the motion is related to
> the interval standard (in contrast to some opinions that it is not)
They are not needed. You can work with adequately chosen types
(possibly with multiple precision) to get tight intervals at
the end, and this is more flexible than some fixed format as
provided by CA.
And an exact number doesn't mean that it will be representable with
a finite number of digits in some binary or decimal representation.
Rational arithmetic will allow more exactness and more tightness
than CA. So, why not requiring rational arithmetic in P1788? Then
you have users who may want to work with Q(sqrt(17)), so why not
requiring some other real numbers fields in P1788? This is endless!
P1788 allows such number formats and interval types dealing with
arbitrary sets of numbers, and that's sufficient.
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Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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