Re: Motion P1788/M0014.01: 6.1_and_6.2_of_document: up for discussion
Folks
Dan has raised a point that worried me when I wrote the text in question. I did send a query round at the time but don't recall anyone answering.
On 22 Apr 2010, at 11:43, Dan Zuras Intervals wrote:
> One subtle point that is not made clear by this is that
> it requires that a representation of the form (mid,del1,
> del2) which represents the interval [mid+del1,mid+del2]
> must do so exactly. That is lowerBound = mid + del1 &
> upperBound = mid + del2 EXACTLY, with no rounding errors.
>
> This is not so much of a problem but it does mean that
> any system choosing to use this mid-rad form in an
> attempt to speed things up in the |rad| << |mid| case
> must find some other way of representing semi-infinite
> intervals such as [2,+oo] & [3,+oo] which don't fit in
> this format.
PLEASE, Multi-precision interval computation folk:
(a) What does "FP Format" and corresponding "Interval Format" MEAN
in your context?
Is there a potentially infinite sequence of them, like "binary_N"
where N is an arbitrary multiple of 32, say?
Or just ONE, the union of all these (regarding each one as a
subset of the extended reals)?
(b) If your implementation uses something like (mid,del1,del2)
does it achieve what Dan says:
> lowerBound = mid + del1 & upperBound = mid + del2 EXACTLY ?
The answer almost surely depends on the answer to (a).
Basically I'm asking whether you can map what 6.1, 6.2 say into what you implement
- easily
- in a tortured and unnatural way
- not at all.
This didn't matter so much until this motion, but now it does. Probably a lot.
John