Thoughts on IEEE P754

David-Sarah Hopwood david.hopwood at industrial-designers.co.uk
Fri Aug 22 11:28:19 PDT 2008


Jason Orendorff wrote:
> On Fri, Aug 22, 2008 at 6:22 AM, Sam Ruby <rubys at intertwingly.net> wrote:
>> On Fri, Aug 22, 2008 at 2:30 AM, Jason Orendorff
>> <jason.orendorff at gmail.com> wrote:
>>>  var a = [];
>>>  a[0] = "first";
>>>  a[0.0m] = "second";   // a second property?
>>>  a[0.000m] = "third";   // a third?
>> [...]
>>
>> It seems to me that if trailing zeros are retained in a call to
>> ToString, then to be consistent with ES3, the three assignments above
>> would produce three properties.  And if trailing zeros are lost, you
>> would expect to only have one.  Both approaches are internally
>> consistent, and it surprises me to see either one characterized as
>> "breaking" array lookup.
> 
> Well, the intuition is that two equal numbers should index the same
> property.  This is an invariant in ES3 and it makes a lot of sense.

Two values that are === should index the same property [*]. Two values that
are == do not, in general.

So, it would be possible to make === take into account trailing zeroes,
while == ignores them. Given that the trailing zeroes are supposed to be
semantically significant ("scale preservation"), there's a strong case
for saying that values that differ only by trailing zeroes should be
distinguishable -- and if not by ===, then how?

One can argue about the merits or otherwise of scale preservation, but
it's an intentional property of the P754 decimal floating point design.
See section 2 of <http://speleotrove.com/decimal/IEEE-cowlishaw-arith16.pdf>
for the arguments in favour (which I'm not sure I buy into fully).


[*] but not conversely: two values that index the same property are
     not necessarily ===.

-- 
David-Sarah Hopwood


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