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As for Siegfried Rump's Dec 5 posting: I did not get it. I lost access to stds-1788 from Nov 23 through Nov 28 and have no posts dated Nov 23
You find it on my homepage www.ti3.tu-harburg.de ; for your convenience, the paper is appended.
On Thu, 29 Dec 2011 19:44:03 -0100, Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx> wrote:
OK, let's decide NOW whether or not we want Kauchers to be part of the standard, extension or not.
For every suggestion or motion I suggest to write down a short program showing the result with and without the suggestion. As for my proposed interval arithmetic an example is (using INTLAB notation):
A = infsup(0,1000); % [0,1000] B = exp(A); % [1,inf] C = 1/B; % [T,1] D = 1/C; % [1,inf] E = 1/D; % [T,1]Here T denotes "tiny" which can be coded in IEEE754 using NaN with different mantissa bits. Note that no flag is raised. The theory, implementation details and more examples are in the paper.
Standard interval arithmetic yields A = infsup(0,1000); % [0,1000] B = exp(A); % [1,inf] C = 1/B; % [0,1] D = 1/C; % [-inf,inf] with flag E = 1/D; % [-inf,inf] with flagAs for 1/[0,1] the result must be [-inf,inf] because zero may be the limit of negative numbers.
On Fri, 30 Dec 2011 14:56:26 -0100, John Pryce <prycejd1@xxxxxxxxxxxxx> wrote:
I think Siegfried Rump's recent paper is a great piece of work, whose implications I am still absorbing. It could well lead to a practical interval arithmetic that handles overflow and underflow better than we currently can. But P1788 chose a different, simpler model early on. For many reasons we cannot switch models now. A compelling reason, to me, is that Siegfried's system is unfamiliar to the whole interval community (not just us); it has not been worked out in detail or implemented; experience with an implementation might uncover practical flaws such as those that Arnold and Nate found with my own favourite, namely cset interval arithmetic. So its time has not yet come.
The arithmetic is based on a mathematical theory given in the paper. Properties are proved which IMHO are not valid for other definitions of interval arithmetic. The difference to what everybody knows is the handling of huge and tiny numbers. I think it has been worked out in detail, and it is easy to grasp.
Best wishes for the New Year 2012, Siegfried -- ===================================================== Prof. Dr. Siegfried M. Rump Institute for Reliable Computing Hamburg University of Technology Schwarzenbergstr. 95 21071 Hamburg Germany phone +49 40 42878 3027 fax +49 40 42878 2489 http://www.ti3.tu-harburg.de and Visiting Professor at Waseda University Faculty of Science and Engineering 3-4-1 Okubo, Shinjuku-ku Tokyo 169-8555 Japan phone/fax in Japan +81 3 5286 3330
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