how to optimize recursive algorithm?

Houston, we've got a problem.
I have a transformation calculating the position of certain graphical
elements and each element's position is affected by the position of its
ancestors and preceding siblings. The recursive algorithm I wrote works
well, meaning that the result is correct but is painfully slow when dealing
with big documents.
This is no surprise because I am fully aware of the functional language
constraints, but I am wondering if there is no viable workaround.
For instance, I don't know the constraints imposed to the optimizer but I
would expect some sort of "caching" of values calculated previously when the
same node is processed over and over by the same piece of code.

For instance, say you have a source document like this:

<top>
    <a/>
    <b/>
    <c/>
    <d/>
</top>

and the output of "b" depends on the position of "a", "c" depends on "b" and
so on.
When the processor (recursively) processes "d", it should find, somewhere,
the value calculated for "c" previously and (magically) save time.

Now, since I really don't know what kind of optimizing mechanism is in place
for the xslt engines I've been using so far (Saxon, Altova, Microsoft), I am
asking if you have any idea as how to make recursive algorithms faster in
cases like those just described.

Bye,
Flavio


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