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Re: Motion P1788/M0013.04 - Comparisons - Overflow / Infinity

Ian McIntosh wrote:



AN> We introduced in Motion 8 decorations to be able to distinguish the two
where necessary inninterval bounds by having the decoration IsBounded.

Yes, you can distinguish Overflow from Infinity by using decorations, and
that works well as long as no other operation supersedes  that decoration.
Could one consider an Infinity decorated as having come from an overflowing
operation as being an Overflow?


Of course. And since decorations are independent of each other, only an
onverflow can generate INF with isBounded.



JP> (2) [a,Overflow] doesn't really represent one interval, but an infinite
family of intervals: all [a,b] with b > MAXREAL. Hence how does one
evaluate [1,Overflow] JP> \subseteq [1,Overflow]? It seems to need a trit,
or a bool_set, result.

You're right, as I said Overflow is an infinite set just as Infinity is an
infinite set, so [a, Overflow] represents an infinite family of intervals
just as [a, Infinity] represents an infinite family of intervals.  How does
one evaluate
[1, Infinity] \subseteq [1, Infinity] ?  Which Infinity is larger?  It's
the same problem, one which I did not claim to solve.


There is only one Infinity, so this evaluates to true.



My only claims are that by distinguishing Overflow from Infinity you can
know whether multiplying whichever by zero gives zero or NaNQ in floating
point, and that if 754 already had that it would be helpful for interval
arithmetic.


The distiction can already be made with decorations.
We do not need dubious mathematically indeterminate nunbers.