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The way to parallelize the computation is to execute the two recursive invocations of the node::visit method in parallel.
It is possible to automatically parallelize the traversal even though the resulting computations may differ substantially from the original serial computation.
A policy in the compiler must choose the computations to attempt to parallelize.
The commutativity analysis algorithm determines if it is possible to parallelize a given method.
Figure 3 presents the algorithm that determines if it is possible to parallelize the execution of a given method.
Before the compiler could parallelize a piece of code that manipulated a data structure, it would have to analyze the code that built the data structure.
The algorithm also checks that the method m that the commutativity analysis algorithm is attempting to parallelize is a full method.
We have used this compiler to automatically parallelize three applications: the Barnes-Hut hierarchical N-body solver [Barnes and Hut 1986], the Water simulation code [Singh et al.
To parallelize a given method, however, the envisioned compiler would still require that all of the methods that could be invoked as a result of executing the given method appear in the same file.
If part of the program fails to conform to the model, the compiler simply marks it as unanalyzable and does not try to parallelize it.
All of the parallel phases have a significant number of auxiliary call sites; the compiler would be unable to parallelize any of the phases if the commutativity-testing phase included the auxiliary methods.
We therefore knew that it was possible, in principle, to parallelize the applications.