Re: [boost] numeric: linear algebra concepts

From: Jeremy Siek (jsiek_at_[hidden])
Date: 2001-03-29 09:22:46

On Thu, 29 Mar 2001, Ullrich Koethe wrote:
koethe> Very good list! However, the necessary constraints are missing, for
koethe> example:

Yes, I'll add the semantic constraits next. Thanks for the list!

koethe> Unfortunately, these constraints lead to serious practical problems,
koethe> because none of the build-in types fulfills them: 
koethe> 
koethe> float and double fail because of limited accuracy (especially on
koethe> conditions 2.1 and 2.2 - what does the IEEE floating point standard say
koethe> here ?)
koethe> 
koethe> the integer types fail on the condition (3.5), e.g.
koethe> 
koethe> unsigned char a = 16;
koethe> a * a == zero(a)
koethe> 
koethe> How can these problems be solved?

The constraints have to be weakened from their strong pure-math forms so
that we can use them in practice. For example, instead of using == in the
equations, we should say "equivalent" and then give a suitable definition
for what we mean by this. Also, we'll have to qualify many of the
statements with stuff about the representation range. Would you like to
try to formulate the wording for this?

Cheers,
Jeremy

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 Jeremy Siek                        www: http://www.lsc.nd.edu/~jsiek/
 Ph.D. Candidate                  email: jsiek_at_[hidden]
 Univ. of Notre Dame         work phone: [phone]
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