- From: Kent Karlsson <kentk@cs.chalmers.se>
- Date: Fri, 23 Sep 2005 12:43:03 +0200 (CEST)
- To: "Philip Guenther" <guenther+collation@sendmail.com>
- Cc: "Mark Davis" <mark.davis@icu-project.org>, public-ietf-collation@w3.org
>>Equality MUST be an equivalence relationship (reflexive, symmetric, and
>>transitive).
>>
>>Ordering MUST establish a total order (that is, < is transitive and
>>trichotomous), and must be consistent with the Equality relationship.
>
> These would appear to outlaw a collation for comparing or ordering
> floating-point numbers including NaNs ala IEEE 754 and its successors.
The revision of IEEE 754 (known as 754R) includes a total order
comparison. IIRC the NaNs that happen to have to have the sign
bit set (though there is no such things as negative NaNs) are ordered
"less" than negative infinity, those that do not are ordered
"greater" than positive infinity, negative zero is "less" than zero
(they otherwise compare equal).
There is no change to the ordinary operations that are expected to
surface as "<" etc. operators in programming languages. The total
ordering is a new operation.
I don't right now recall what the suggestion was for decimal base
(new in 754R), where differently scaled, but equal values compare equal
(of course, for the "ordinary" comparison) with regard to this new
total order operation.
So IEEE 754R datatypes (will) have two orders on them, one partial,
and one total.
/kent k
Received on Friday, 23 September 2005 10:43:08 UTC