Re: YES P1788/M0029.02:Level3-InterfaceOnly, *BUT*
Michel,
On 12/29/2011 05:00 PM, Michel Hack wrote:
Lee Winter wrote:
I believe the exclusion of overflows of the same sign is unnecessary
for the interchange format.
I suppose you mean two infinities of the same sign. Infinities may
indeed be the result of containing overflow, but they can also simply
mean "unbounded". Decorations should tell these cases apart. (In 754
it is the overflow flag that does the job -- unfortunately globally.)
Although we have been discussing this for a while, the distinction
is still not clear to me, at least on a philosophical level.
Can't an overflow be viewed simply as a "round to unbounded?"
What practical end is gained by distinguishing these two
cases? I'm thinking of the theory (and to an extent, the
practice) of enumerating and finding all solutions to
polynomial systems of equations, where one works in projective
space, and talks about "solutions at infinity." As such,
[HUGE,Infinity) is a neighborhood (effectively a narrow interval)
about Infinity that would approximate such roots well.
Regarding the product 2*[HUGE,HUGE], one would round the lower
end point down to HUGE and the upper end point up to Infinity,
getting the result [HUGE,Infinity), a correct inclusion.
Of course, we have already decided that intervals are subsets
of the reals, so Infinity itself is not a member of any
interval. However, I don't see how that changes this particular
reasoning (whether Infinity is the result of an overflow or
or the interval was exactly unbounded to begin).
Baker
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