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Re: Nitpick with FLOOR etc.
| 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
SRFI-70 does not incorporate infinitesimals, IEEE or otherwise.