[Oberon] Numbers

[Christian Hoffmann]

Hi,

As a numerical mathematician I would throw in that there is a mathematical 
discipline called numerical mathematics which in close cooperation with 
algebra etc. analyzes algorithms to solve real world problems. Here 
rounding errors, cancellation, i.e. problems cropping up at the transition 
of the boundary between conceptual (integer, real) and computer 
representability (rounding, truncation) play an essential role. Thus, to 
handle these problems in a concise manner, standards for hardware and 
software have to be introduced (IEEE, ..). It has been a great step forward 
when IEEE really began to make an impact on the computer community.

At 10:06 26.08.2002 -0400, you wrote:
>Frank van Riet wrote:
> >
> > Hi Patrik, Paul, Greg
> >
> > Thanks very much for your comments.
>...
> > If you have a look at my original submission you'll note that I did
> > raise this issue, as well as a simple solution. Simply don't allow
> > interoperability between signed and unsigned variables. This makes the
> > impact on the compiler negligable.  This has the additional benefit of
> > forcing to programmer to think about the range of the variables.
>
>I believe Dr. Wirth was attempting to move in the other direction,
>away from implementation issues and toward a conceptual representation
>of a number.  I deduce this from the fact that the term REAL is used
>rather than float.  A floating point representation of a real number
>is a more accurate description of what computers actually do, however,
>to focus on this aspect diverts ones thinking away from the usual
>task at hand of determining the value of an expression.
>
>I would like to push this avoidence of 'implementation' even farther
>(and perhaps in some far distant future this may happen) by completely
>eliminating the 'size' of a number's representation.  When one uses
>paper and pencil and algebra to solve equations there is no consideration
>of implementation size.  In fact the distinction between real and integer
>is frequently not needed.  The operation of 'quantizing' a number to
>an integer value is sometimes necessary algebraically.  If one is working
>with diaphatine numbers then the whole domain is strictly integer.
>The context of the calculation should be the determining factor.
>But this takes a very high level of abstraction for a machine to
>handle.
>
>Do you really want to 'program' or do you want to 'specify' and
>'solve'.  Ultimately, the later approach would be my choice.

But there would have to be a "layer" written by someone knowledgeable which 
hides the intricacies of the latter approach.

--christian


>-Doug
>--
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Dr.sc.math.Christian W. Hoffmann
Mathematics and Statistical Computing
Landscape Dynamics and Spatial Development
Swiss Federal Research Institute WSL
Zuercherstrasse 111
CH-8903 Birmensdorf, Switzerland
phone: ++41-1-739 22 77    fax: ++41-1-739 22 15
e-mail: christian.hoffmann at wsl.ch
www: http://www.wsl.ch/staff/christian.hoffmann/