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

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

|                   Dr. Michael Gerard RICHARDSON                    |
|                                                                    |
| Numerical Algorithms Group Ltd.                                    |
| Wilkinson House                      Email:     miker at nag.co.uk    |
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| Oxford, OX2 8DR, UK                  Fax:       01865 311205       |

Any opinions expressed here are purely my own.

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