Re: Float comparison

Keith Thompson wrote:
CBFalconer <cbfalconer@xxxxxxxxx> writes:
Keith Thompson wrote:
CBFalconer <cbfalconer@xxxxxxxxx> writes:

... snip ...

I thought I was getting somewhere in explaining the facts. No
matter what any document says, the physics and mathematics of
the situation take precedence. I seem to have failed again to
put that across.

Physics nothing to do with this. Again, I'm not talking about
physical measurements.

I'm talking about the C standard, which you have yet to cite in
any way that directly supports your claims.

Maybe that is the problem. The C standard cannot override
mathematics and physics - it simply has to be subservient. If it
apparently is not, that indicates an omission in the standard.

No, it doesn't have to be subservient, and it isn't.

Yes it does. The physics (assuming accurate) is reality. If you
publish a 'standard' that claims your automobile gets 200 mpg, you
will get few believers. I'm not saying that is analagous. The
standard is actually quite accurate. It is not the holy word. The
problem here is interpretation.


Physics, as I'm sure you'd be quick to say if the shoe were on the
other foot, is off-topic. Floating-point numbers can of course
be used to model physical quantities, though the model is only an
approximation in most cases.

As for mathematics, it encompasses far more than you seem willing
to acknowledge. The set of floating-point numbers of a given
type corresponds to a finite proper subset of the real numbers.
That is a perfectly valid mathematical concept.

Are you asserting that a model in which the FP numbers completely
cover a range of real numbers is mathematically valid, while a model
in which they cover only a finite subset of real numbers is not?

Of course not. Don't distort MY comments.


If the standard states that a value in a FP object represents an
object in the range x*(1-EPSILON) to x*(1+EPSILON), that is fair
enough. If it also says that the FP object value is exact, it is
wrong, or it is reusing words in a different manner, etc.

Since I can't easily render the formula in 5.2.4.4.2 in
plain text, I've grabbed a screenshot and made it available at
<http://www.mib.org/~kst/5.2.4.2.2.gif>. Please read it. It very
clearly says that a floating-point number is defined by a formula
that specifies a single unique real value, *not* a range.

The formula is perfectly accurate. It reflects the value specified
by the FP content. It DOESN'T reflect the meaning of that value.


.... snip ...

It's not impossible that you're right and the rest of us are wrong.
But if I were seeing this kind of nearly unaniminous disagreement
from people I respect, I'd take a moment to reexamine my assumptions.

That's the only reason I am continuing to push this business.

--
[mail]: Chuck F (cbfalconer at maineline dot net)
[page]: <http://cbfalconer.home.att.net>
Try the download section.


.

Relevant Pages

  • Solutions manual for YOU
    ... Ed., John B. Fraleigh) ... Physics ... instructor solution manual for Advanced Engineering Mathematics 8Ed ...
    (sci.math)
  • Solutions manual for YOU
    ... Ed., John B. Fraleigh) ... Physics ... instructor solution manual for Advanced Engineering Mathematics 8Ed ...
    (sci.logic)
  • Solutions manual for YOU
    ... Ed., John B. Fraleigh) ... Physics ... instructor solution manual for Advanced Engineering Mathematics 8Ed ...
    (sci.stat.math)
  • Solutions manual for YOU
    ... Ed., John B. Fraleigh) ... Physics ... instructor solution manual for Advanced Engineering Mathematics 8Ed ...
    (rec.puzzles)
  • Re: Solutions manual for YOU
    ... Ed., John B. Fraleigh) ... Physics ... instructor solution manual for Advanced Engineering Mathematics 8Ed ...
    (sci.electronics.basics)