Coming from a background of hardcore number crunching programming (nuclear
simulators and the type), I remember that one of my favorite mental hard
ons for Smalltalk was the transcendental number system. Many modern "static
system" compilers will also infer a good bit when noting mixed type math
and put in implicit casts. But what has always even thrilled me more about
ST is the ability to define new number systems and intermix them with the
standard numeric types as appropriate.

In preparation to adding a new "numeric type o thingie" I got looking at
how Squeak handles mixed math. To begin with, I didn't like it, it being
like the OW coercion stuff, and I being more familiar with double
dispatching as implemented in VW or ST\X. So I rewrote the basic arithmetic
operations (+, - , / , *) to use double dispatching.

After having done this, I find myself at a crossroads of how to proceed.
I've discovered that doing the double dispatching thing also has its
drawbacks. Namely the number of methods required. For every new type of
numeric thing one wants to add to the system, the number of required DD
messages is 4(n^2). Whereas with using coercion, the number of type
coercion messages is n^2. The drawback with coercion is that intermediate
objects are created to complete the operation. With the simple mathematic
types (Float, Integer) this is inevitable - sooner or later, you've got to
get a float version of your integer. But with other "heavier" numeric
types, these can be avoided by using DD. Take simple numbers combined with
Points for example. To add a number to a point, you send asPoint to it,
which creates a point to be soon thrown out. If you use DD though, you can
avoid this creation by implementing something like:

sumFromInteger: anInteger
	^anInteger + x @ (anInteger + y)

For points, the overhead isn't too bad, but as the new numeric types, get
"heavier" you end up having to create special "intermediate" objects. VW
SomeNumber is a good example of this.

I've completed the DD stuff, and was about ready to put it up at the
archive, but then I stumbled upon this dilemma. Did the squeak team choose
coercion over DD on purpose, or is this a historical hold over? Thoughts?
More methods vs. more intermediate object creation?

--
Travis Griggs
Key Technology
tgriggs at keyww.com
GO SMALLTALK - AND BEYOND!