# Revamping the numeric classes

**Bjorn Lisper
**
lisper@it.kth.se

*Wed, 7 Feb 2001 10:18:05 +0100 (MET)*

Dylan Thurston:
>*Andreas Gruenbacher:
*>>* It may be the case that using (*) for scaling too is a generally bad
*>>* idea...
*
>*It may not be type sound to have the same operation, but there should
*>*be some standard operation for scaling. (Probably you need
*>*multi-parameter type classes for this.)
*
I'd like to point out the connection between the use of +, - on vector
spaces and * for scaling with features in some data parallel languages. In
these languages, writing a + b where a and b are arrays of numerics is
interpreted as elementwise addition of a and b. This features generalises to
other operations than +, -, other types than numerical ones, and other data
structures than arrays. Furthermore, some of these languages support
"promotion": "lifting" a "scalar"-typed expression, appearing in a context
where an array (say) is expected, into an array with suitable dimensions
containing copies of the scalar. Scaling can be seen as a special case of
promotion, if "*" is interpreted elementwise: for instance, 17*a where a is an
array is then seen as an array with elements 17 elementwise multiplied
with a.
Thus, using "*" both for scaling and elementwise multiplication can be made
to work, and it is compatible with the data parallel generalizations of
scaling and use of +, - on vector spaces. But using "*" for inner product is
not compatible with these generalizations. Preference is probably dependent
on background (mathematician or data parallel programmer...).
Björn Lisper