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Re: . . . Since rational arithmetic doesn't
overflow, associating rational infinities with IEEE infinities would
confuse the distinction between the two IEEE uses of infinity.
The only connection I saw for "IEEE" was that it provided both negative
and positive infinities. Dan Hoey has provided the best reasoning I've
seen so far for subscribing to an affine system; and Larry Masinter made
a good case for wanting to separate out the infinity representation
from and already-overloaded T and NIL.
Re: The user [can] explicitly coerce
floating-point numbers to rational, and it could just be an error to
coerce an infinity to rational. [That's what we do at Symbolics.]
. . .
2. You [may[ want something to do when the user attempts to coerce
a floating infinity to rational, other than signal an error.
That's a sticky point -- floating infinities do show up under "normal"
circumstances, but Nan's don't. Providing a reasonable rational
representation for the floating infinities is a necessity when
converting back and forth.
One can carry the similarities too far; I certainly don't want to hear
about the inability to represent negative and positive fixnum zeros (even
though IEEE format has them). Long Live twos's-complement arithmetic!
-- JonL --