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Re: Nitpick with FLOOR etc.



> From: 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.

sorry, I think I was partially responding within the context of:

  | > That conflicts with SRFI-70, which specifies that #i+1/0 compares as
  | > larger than any finite real number, exact or inexact:

which implied a relationship between an inexact infinity and exact values
which is not generally true, so thought that infinities may be considered
as being distinct attributes from the values represented in the exact and/or
inexact representations themselves.

>  | ...
>  | 
>  | Thereby it becomes possible that:
>  | 
>  |  (inexact->exact #i1/0) => #i1/0
> 
> What would (exact->inexact #e+/0) return?

I'd say #e+/0, as neither #i1/0 or #e1/0 are exact or inexact themselves,
but merely represent the set of values beyond the representational range of
the inexact and exact implementations.

>  | 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?

your proposal that (> #i1/0 #e1e1000) => #t, where 1e1000 is representable
as an exact value which is not less then the collective set of values
represented by an inexact infinity, but is less than the set represented by
an exact infinity (if such a thing were defined).