Re: [boost] numeric: linear algebra concepts

From: Jeremy Siek (jsiek_at_[hidden])
Date: 2001-03-29 11:46:51

I agree, we certainly do need result type traits, however I think the
requirements on the result type produced should remain what I've stated,
convertible to X and models ...

To allow for expression templates, the result type will not only
depend on the operands but also on the operator. Therefore we
need a tag for each operator.

struct add_tag { };
struct multiply_tag { };
...

and then make the operator tag a parameter to the traits class

result_traits<OpTag,A,B>::type

For builtin types, the result_traits can dispatch to the simpler promotion
traits class that does not care about the operator.

Cheers,
Jeremy

On Thu, 29 Mar 2001, Ullrich Koethe wrote:

koethe> Another very important aspect (that has no counterpart in pure math) is
koethe> type promotion. For example, Jeremy's list says:
koethe> 
koethe>   a + b   Convertible to X and models Additive Abelian Group.
koethe> 
koethe> I think we must be more specific about the type of the result. There are
koethe> clear rules for promotion of the built-in types, for example
koethe> 
koethe> short + short => int
koethe> double * short => double
koethe> 
koethe> These rules must be formulated in promotion_traits (invented by Todd
koethe> Veldhuizen) so that 
koethe> 
koethe> * the rules for new numeric types can be derived 
koethe>   from the rules for its constituents.
koethe> * templated algorithms can select appropriate types for
koethe>   results and intermediate variables
koethe> 
koethe> In my VIGRA library, I distinguish two promotion types:
koethe> 
koethe> - if X is any algebraic type, then 
koethe> 
koethe>   X op X => NumericTraits<X>::Promote
koethe>   (e.g. NumericTraits<short>::Promote is int)
koethe> 
koethe> - if {G, R} is an R-Module, then
koethe> 
koethe>   G op R => PromoteTraits<G, R>::Promote
koethe>   (e.g. PromoteTraits<short, double>::Promote is double)
koethe> 
koethe> In addition, there are conversion functions 
koethe> 
koethe> NumericTraits<T>::fromPromote() and 
koethe> PromoteTraits<T,U>::firstFromPromote()
koethe> 
koethe> that transform back to the original type, including necessary round-off
koethe> and clipping at the domain borders. (Actually, it's slightly different,
koethe> but you get the idea)
koethe> 
koethe> Now I can do:
koethe> 
koethe> template <class T, class U>
koethe> struct PromoteTraits<RGBValue<T>, RGBValue<U> >
koethe> {
koethe>     typedef RGBValue<typename PromoteTraits<T, U>::Promote> Promote;
koethe> };
koethe> 
koethe> and 
koethe> 
koethe> template <class T, class U>
koethe> typename PromoteTraits<RGBValue<T>, RGBValue<U> >::Promote
koethe> operator+(RGBValue<T> l, RGBValue<U> r)
koethe> {
koethe>     typename PromoteTraits<RGBValue<T>, RGBValue<U> >::Promote res(l);
koethe>     res += r;
koethe>     return res;
koethe> }
koethe> 
koethe> I've found this to be a very useful method which I need every day.
koethe> 
koethe> Ulli
koethe> -- 
koethe>  ________________________________________________________________
koethe> |                                                                |
koethe> | Ullrich Koethe  Universität Hamburg / University of Hamburg    |
koethe> |                 FB Informatik / Dept. of Computer Science      |
koethe> |                 AB Kognitive Systeme / Cognitive Systems Group |
koethe> |                                                                |
koethe> | Phone: [phone]                Vogt-Koelln-Str. 30 |
koethe> | Fax:   [phone]                D - 22527 Hamburg   |
koethe> | Email: u.koethe_at_[hidden]               Germany             |
koethe> |        koethe_at_[hidden]                        |
koethe> | WWW:   http://kogs-www.informatik.uni-hamburg.de/~koethe/      |
koethe> |________________________________________________________________|
koethe> 
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koethe> 
koethe> 
koethe> 

----------------------------------------------------------------------
 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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