use decimal

David-Sarah Hopwood david.hopwood at industrial-designers.co.uk
Fri Sep 19 16:34:13 PDT 2008


Maciej Stachowiak wrote:
> On Sep 18, 2008, at 6:03 PM, Mark S. Miller wrote:
>> [re: <http://docs.sun.com/source/806-3568/ncg_goldberg.html>]
>>
>> Long long ago I actually had read that document carefully, and I had
>> also looked at I think the [Brown 1981] which it cites. (But the doc
>> has no bibliography. Anyone have a pointer?) My memory of the theory
>> of floating point is that the numbers are exact but the operations are
>> approximate.
> 
> I'm not sure what it means for values to be "exact" representations of
> real numbers when operations on them break even the most fundamental
> identities of real arithmetic. For many values of A, B and C, (A + B) +
> C != A + (B + C).

That's because those '+' operators are not real addition; they are
floating-point addition (and also the '!=' operator is not real
inequality). The values still correspond exactly to real values
(we can be more specific and say that they correspond exactly to
rational values).

-- 
David-Sarah Hopwood



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