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*To*: Paul Schlie <schlie@xxxxxxxxxxx>*Subject*: Re: Wrapping up SRFI-70*From*: bear <bear@xxxxxxxxx>*Date*: Wed, 17 Aug 2005 10:00:02 -0700 (PDT)*Cc*: Aubrey Jaffer <agj@xxxxxxxxxxxx>, srfi-70@xxxxxxxxxxxxxxxxx*Delivered-to*: srfi-70@xxxxxxxxxxxxxxxxx*In-reply-to*: <BF28C80F.B388%schlie@xxxxxxxxxxx>*References*: <BF28C80F.B388%schlie@xxxxxxxxxxx>

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. Bear

**References**:**Re: Wrapping up SRFI-70***From:*Paul Schlie

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