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Re: Wrapping up SRFI-70
On Wed, 17 Aug 2005, Paul Schlie wrote:
>- Given that "in your experience" (which seems sensible), true infinities
> and presumably corresponding reciprocals tend to be rare relative to
> computational over/underflows;
Eh. Maybe a little rarer, but not very rare; division by
zero, unfortunately, happens a lot. What's *way* rarer than
overflows is infinities with a definite and unambiguous sign.
Division by zero results in a sign-ambiguous infinity where
the sign given depends either on rounding error or on perfectly
arbitrary IEEE conventions. These conventions are consistent
and reasonable, but they represent only approx. half of the
underlying mathematical truth.
In computer "infinities", if the sign is definite and no
tiny difference in rounding or selection of a different
set of consistent but perfectly arbitrary conventions for
handling sign ambiguity could have made it different, then
you are 99.9% likely to be looking at an overflow rather
than a true infinity. And overflows, however you handle
them, represent mathematically finite numbers.
> therefore in representations where they
> are not distinguishable, it would seem that it may then be correspondingly
> appropriate to presume values represented as infinites are over/under-
> flowed values, thereby implying that any value other than an exact
> infinity multiplied by an exact 0 is 0, and correspondingly implying
> that only 0/0 and/or any value who's absolute value is greater than 1
> divided by, or who's absolute value is less than 1 multiplied by, an
> infinity are considered NaN's [aka 0/0] (as otherwise the resulting value
> will be known to be within the value ranges designated for infinites
> and/or their reciprocals, and represented as such)?
Okay, I had to reread that three times, but if I understand
you correctly, I think I agree. I've been awake too long
maybe and I'm having trouble thinking around corners.