Re: Nitpick with FLOOR etc.

[Aubrey Jaffer <agj@xxxxxxxxxxxx>]

 | Date: Sun, 17 Jul 2005 23:24:49 -0400
 | From: Paul Schlie <schlie@xxxxxxxxxxx>
 | 
 | > From: Paul Schlie <schlie@xxxxxxxxxxx>
 | >> The possibility that systems may implement exact infinities rules out
 | >> having the error be with INEXACT->EXACT (passed real infinities).
 | 
 | - maybe that implies that infinities and their reciprocals are in a
 | class by themselves, as neither are warranted to have some minimal
 | precision, as both exact and inexact representations have, but
 | rather represent an underflow of the minimal precision otherwise
 | warranted, thereby effectively representing the bounds of an
 | implementation's exact/inexact representations?

Infinity as a number is not what SRFI-70 is about.  In it, inexact
numbers are real neighborhoods and inexact infinities are real
half-lines.  These semantics seem to be working well; but they are not
applicable to exact numbers.

See SRFI-73 for infinity-as-number.

 | ...
 | 
 | Thereby it becomes possible that:
 | 
 |  (inexact->exact #i1/0) => #i1/0

What would (exact->inexact #e+/0) return?

 | Merely indicating the value was greater in magnitude than the greatest
 | representable inexact value, but less than the greatest representable
 | exact value, but without a minimally sufficient resolvable precision?
 | 
 | Implying something along the line of:
 | 
 |   #e-1/0     ..  #e-xxx  ..      #e-0/1 0  ...
 |     |     |                   |     |   |
 |        #i-1/0 .. #i-xxx .. #i-0/1       0  ...

Which problem in SRFI-70 does adding two more real infinities solve?