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.
> From: Aubrey Jaffer <agj@xxxxxxxxxxxx> > | > 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 - which is only the case as you don't differentiate between -0.0 and +0.0; therefore all reciprocal infinities collapse to 0.0, and hence loose their respective originating reciprocal signs. (which I won't debate any longer although I feel it's a mistake). > 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). - sorry, clipped what I meant to refer to: | 0/0. is an error object (SRFI-70 calls it an error waiting to happen), | but +/0. and -/0. behave differently from error objects when inverted: | (/ +/0.) ==> 0.0; and in numerical comparisons.