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*To*: Aubrey Jaffer <agj@xxxxxxxxxxxx>*Subject*: Re: Nitpick with FLOOR etc.*From*: Paul Schlie <schlie@xxxxxxxxxxx>*Date*: Fri, 05 Aug 2005 10:51:18 -0400*Cc*: <srfi-70@xxxxxxxxxxxxxxxxx>*Delivered-to*: srfi-70@xxxxxxxxxxxxxxxxx*In-reply-to*: <BF18EFCD.B16F%schlie@xxxxxxxxxxx>*User-agent*: Microsoft-Entourage/11.1.0.040913

> From: Paul Schlie <schlie@xxxxxxxxxxx> >> From: Aubrey Jaffer <agj@xxxxxxxxxxxx> >> | Date: Tue, 02 Aug 2005 21:48:52 -0400 >> | From: Paul Schlie <schlie@xxxxxxxxxxx> >> | >> | > From: Aubrey Jaffer <agj@xxxxxxxxxxxx> >> | > | From: Paul Schlie <schlie@xxxxxxxxxxx> >> | > | >> | > | - 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; >> >> The `limit' procedure does not call `/' at the limit point. >> Its last call to `+' generating the return value is >> >> (+ 999.9999999999999e-225 -999.9999999999999e-225) ==> 0.0 > > - Therefore it would appear the implementation of limit is flawed, > as if it is agreed that: #i-1/0 :: -1.0/0 :: 1/-0.0 :: -Inf.0 > then it follows that it's reciprocal must then be correspondingly > both infinitesimally small and negative (not positive). Apparently > resulting from it's implementation not treating +-0.0 as special > case reciprocal infinite, as in general the magnitude of the > deviation about a value should never be greater than the magnitude > of the value itself, as otherwise the limit calculation will be > erroneous, where the only arguable exception would be about an > absolute 0, where by definition any deviation about itself will > result in varying signed magnitudes (where absolute 0 has neither > a sign nor magnitude). - more specifically, deviations about a point should only likely be considered generically acceptable iff they remain within the region of a function's continuity; where for division this deviations of greater magnitude than the limit point will produce errinous results.

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

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