-0 and 0 are not the same "given floating point number". 1/-0 vs. 1/0
and Math.atan2(-0,0) vs. 0,0 are but two examples.
/be
Sent from my iPhone
On Sep 18, 2008, at 7:08 PM, "Mark S. Miller" <[EMAIL PROTECTED]>
wrote:
On Thu, Sep 18, 2008 at 8:00 AM, Mike Cowlishaw <[EMAIL PROTECTED]>
wrote:
>
> Are -0 and 0 in the same cohort?
In IEEE 754, no:
2.1.10 cohort: The set of all floating-point representations that
represent a given
floating-point number in a given floating-point format. In this
context −0 and +0
are considered distinct and are in different cohorts.
(+0 and -0 are distinguishable in binary FP as well as in decimal
FP; in fact this is the only case in binary where two finite numbers
have the same value but different representations and encodings.)
I don't understand this definition of cohort. It seems to contradict
itself. The first sentence implies that -0 and 0 are in the same
cohort -- since they are different representations of the same
number in the same given floating point format. Should I read the
second sentence as a clarification -- in which case it seems
inconsistent. Or should I read it as a qualification on the first
sentence, saying in effect "well, except for -0 and 0, which are
just weird".
Given that -0 and 0 are in different cohorts, let me probe the
extent to which cohorts imply something like operational
equivalence. For any arithmetic operator OP and any decimal floating
point values X1,X2,Y1,Y2, is it the case that
cohort(X1,X2) & cohort(Y1,Y2) implies cohort(X1 OP Y1,X2 OP Y2)
? I say "arithmetic" above in order to include operations like "+"
but not ".toString()".
Clearly, if -0 and 0 were cohorts, this would not hold. Since they
aren't, does the above property hold for all decimal floating point
values? If so, I withdraw the proposal to generalize cohort. In
which case I agree that Sam's current proposal + an agreement never
to supply compareTotal() (so that decimal can have a single NaNm) is
the best proposal on the table.
--
Cheers,
--MarkM
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