This page is part of the web mail archives of SRFI 70 from before July 7th, 2015. The new archives for SRFI 70 contain all messages, not just those from before July 7th, 2015.
| 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.