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: Thu, 21 Jul 2005 20:50:05 -0400 | From: Paul Schlie <schlie@xxxxxxxxxxx> | | After attempting to digest everything discusses, although realizing | your desire to not require any corresponding impact to either rsrx | or exact semantics; I don't believe it's reasonably possible, as it | seems that the only way to achieve what you desire, and maintain | reasonable consistency with mixed exact/inexact arithmetic would be | to: | | - as suggested by "bear", define the requirement that exact and | inexact value representations be constrained to the same value | range. I am reluctant to take that measure unless someone can provide an example from practice where the ranges being unequal caused bad software behavior. | - define infinites and their reciprocals to abstractly commonly | represent the greatest/smallest values at bounds of the | representable numerical range, As I written previously, using the boundary for the nominal value is the worst choice from that neighborhood. Doing so means that nearly every calculation which projects into #i+/0 is larger than the nominal value. | exclusive of 0 representing an absolute 0, who's reciprocal is | itself 0. This would mean (* 0 (/ 0)) would no longer signal an error or return 0/0. What would (/ 0 0) do? What would (/ 0.0) return (exact or inexact)? (/ 0 0.0)? | - thereby the range of all numerical transforms map to a | correspondingly representable domain (although may optionally | signal a run-time exception as may be desired in certain | circumstances). This would have been nice, but the smallest (unnormalized) numbers in IEEE-754 are not symmetrical with the largest magnitude numbers: (/ 179.76931348623157e306) ==> 5.562684646268003e-309 (/ 5.562684646268003e-309) ==> #i+/0 There are unnormalized numbers down to 4.0e-324, all of whose reciprocals are #i+/0. | Which overall seems to eliminate all the contentious issues, as | long as one is willing to accept the consequences saturating | arithmetic, in lieu of an typically arguably less useful more | abstract treatment of infinites. | | Effectively resulting in: | | .. -1.0 .. | .. +1.0 .. | -1/0 .. -1/1 .. -0/1 | +0/1 .. +1/1 .. +1/0 | -------------------- 0 --------------------- (multiplicative inverse axis) | -0/1 .. -1/1 .. -1/0 | +1/0 .. +1/1 .. +0/1 | .. -1.0 .. | .. +1.0 .. | | | (additive inverse axis) How is this different from your "more abstract treatment of infinities"?