Re: The current proposal
Nate et al,
Please see my inserted comments.
Baker
On 2/23/2009 9:34 AM, Nate Hayes wrote:
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For example, the very simple formula for addition
[a,b] + [c,d] = [a+b,c+d]
breaks down if c=d=Inf and a=-Inf. In that case, IEEE arithmetic produces
(-Inf,b] + (Inf,Inf) = [NaN,Inf),
whereas the "ideal" result would be
(-Inf,b] + (Inf,Inf) = [0,Inf),
assuming the "infinity is number" paradigm where the infinity is not a
member of the interval but rather a token for an unbounded real endpoint.
Using the "cset" paradigm, the natural result would be
(-Inf,Inf), and not [0,Inf), n'est pas? I'm not sure where you got the "ideal"
result of [0,Inf).
My additional point is that for an interval processor, returning such an
"ideal" result is easy and causes no performance penalty.
Wasn't this one of the things Siegfried was worried about?
So the question is, what are the "ideal" properties of the interval
arithmetic that we all desire?
I agree that that is a good question.
I agree the properties 1-4 Siegfried
lists are desireable, and I _beleive_ the "infinity as number" example
above satisfies them all. But perhaps others can double-check.
Nate
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