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*To*: schlie@xxxxxxxxxxx*Subject*: Re: Nitpick with FLOOR etc.*From*: Aubrey Jaffer <agj@xxxxxxxxxxxx>*Date*: Tue, 2 Aug 2005 12:15:43 -0400 (EDT)*Cc*: srfi-70@xxxxxxxxxxxxxxxxx*Delivered-to*: srfi-70@xxxxxxxxxxxxxxxxx*In-reply-to*: <BF14F873.B0DD%schlie@xxxxxxxxxxx> (message from Paul Schlie on Tue, 02 Aug 2005 10:16:19 -0400)*References*: <BF14F873.B0DD%schlie@xxxxxxxxxxx>

| Date: Tue, 02 Aug 2005 10:16:19 -0400 | From: Paul Schlie <schlie@xxxxxxxxxxx> | | > From: Aubrey Jaffer <agj@xxxxxxxxxxxx> | > Inverting +/0. or -/0. returns 0.0. So the name "error object" | > wouldn't seem to apply either. | | - I still don't understand how it's acceptable for (/ 1/-0.0) => 0.0, as | it seems neither necessary, nor desirable to propagate IEEE-754 mistake. (limit / -/0. -1.0e222) ==> 0.0 The limit, as x approaches -/0. from -1e222, of (/ x) is 0.0. | > | This brings up an important distinction in "infinities;" | > | When you divide by exact zero you get an absolute infinity. | > | (which, perversely, is neither positive nor negative, because | > | exact zero isn't positive or negative.) Call this EO1. | > | > We have already covered this ground. Division by zero is undefined; | > SRFI-70 extends division by returning infinities in these cases: | > (/ -5. 0) ==> -/0.; (/ 1. 0) ==> +/0., which are consistent with | > the one-sided limits: | > | > (limit / 0 1.0e-9) ==> +/0. | > (limit / 0 -1.0e-9) ==> -/0. | | - however as multiplication by 0 should result in 0, 0/x => 0 | regardless of its denominator. There is no multiplication by 0 here; (limit / 0 1.0e-9) is the limit, as x approaches 0 from 1e-9, of (/ x). | > | When you divide 1 by (say) 5e-323, you get a different kind of | > | EO, which is "results too large to represent" but which | > | is often mistaken for an actual infinity. Call this EO2. | > | > The result of division by zero was chosen to be the same as the result | > of (/ 1 5e-323). We could split +/0 into any number of regions. One | > was chosen, which happens to be supported by IEEE-754. | | - who's model of infinitesimals isn't likely something worthy of | mimicking. SRFI-70 does not incorporate infinitesimals, IEEE or otherwise.

**Follow-Ups**:**Re: Nitpick with FLOOR etc.***From:*Paul Schlie

**References**:**Re: Nitpick with FLOOR etc.***From:*Paul Schlie

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