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Re: Nitpick with FLOOR etc.
| Date: Mon, 18 Jul 2005 14:40:40 -0400
| From: Paul Schlie <schlie@xxxxxxxxxxx>
| > 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,
Sure it is. Large exact values fall within the real half-line which
(exact->inexact (expt 10 1000)) ==> #i+/0
For finite neighborhoods, calculations and comparisons are done with
the nominal value near the center of the neighborhood. What nominal
value should be used for the #i+/0 neighborhood? The worst choice is
the border value for the half-line. For flonum calculations we can
use IEEE +inf; it has the correct behavior in comparisons and
Combinations of #i+/0 with exact numbers can convert to inexact before
operating. This does not lose all sensitivity to number size:
(- (/ 0.0) (expt 10 400)) ==> #i0/0
Alternatively, exact numeric operations could be modified to treat
#i+/0 as an infinitely large number.
| > | 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 ...
In such a system, #i+/0 is just another finite neighborhood. But its
rules are more complicated than as an infinity.
There will be some value M such that (* M #i+/0) ==> #e+/0.
And new conumdrums:
(/ #e+/0 M) ==> ??
(/ #i+/0 M) ==> ??
(* #i+/0 #i+/0) ==> ??