Brian Beesley wrote:
> On Wednesday 05 March 2008 22:31, David kerber wrote:
>> If it doesn't correspond to the real number, then it's inexact. Take
>> the calculation 7 divided by 10. The correct answer is 0.7 (seven
>> tenths). If you try this in a binary computer, you do not get the
>> correct answer; you get the the closest number that floating-point
>> numbers can come to 0.7, but it is not exactly 0.7, and therefore is
>> inexact, or inaccurate if you prefer that term.
>
> No - it's exact, but inaccurate. Just as the number 0.333333333 is exact, but
> inaccurate if it's the result of dividing 1 by 3.
Thank you. That is, if it's the result of dividing the REAL NUMBER
1 by the REAL NUMBER 3. Not if it's the result of dividing the
floating point number 1.0 by the floating point number 3.0.
In that case, it is both exact, and accurate.
> However the floating point unit does have several rounding modes, in some
> cases the stored result may differ depending on the rounding mode in use.
Yes. To put it another way, there are more than one operation
defined on the discrete set of floating point numbers which
roughly correspond to real arithmetic addition, for example.
Each of them is, on the discrete set, exact and well defined.
The fact that the corresponding operation on the continuous
set of reals results in a non representable value is no more
a criticism of FP numeration systems than it is of integer
numeration systems. The fact that 1/3 is not representable
as an integer does not imply that integer arithmetic is
inexact.
Mike
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