Floats, precision and probability distributions
Mike Richardson
miker at nag.co.uk
Thu Jul 15 11:34:59 CEST 1999
Richard wrote:
I quite disagree with miker, and to some extent Bruce Miller.
Floating point numbers are NOT probability distributions.
Thinking about them that way leads only to useless and often
even counterproductive computational schemes. See what
Mathematica has done, for example.
Floating point numbers are EXACT RATIONAL NUMBERS. Namely
those numbers among the reals that can be exactly represented
in the form sign X fraction X radix^exponent, with fraction=
fixed length.
To which Gaston added:
A floating point number represents an exact rational number.
Trying to convey precision of the value is a mistake that
many people do when designing fp systems. Please stay away
from this. Gaston.
Richard is right, of course, floating point numbers ARE
rationals (but usually they REPRESENT reals, which, in turn,
sometimes represent physical quantities). The point I was
making was that IF a representation is adopted which includes
"accuracy" information, THEN it would be less constraining if
this were made general enough to include more complete
information on the probability distribution of observation-based
quantities.
In fact, I tend to the view that OM shouldn't be concerning
itself with the "engineering details" but rather with
mathematical objects.
Mike Richardson
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