Efficient Register Allocation for Large Basic Blocks

We consider the NP{complete problem of generating evaluations for expression DAGs with a minimalnumber of registers. We restrict our attention to contiguous evaluations, because for nearly all of the DAGs derived from real application programs there exists a contiguous evaluation that is optimal w.r. to the register need. We present an algorithm that generates an optimal contiguous evaluation for a given DAG. The algorithm is very fast on the average. It generates the evaluation by splitting the DAG in trees with import and export nodes and applying a labeling scheme to the trees. A contiguous evaluation of an expression DAG is the sequence of the DAG nodes in the order of a postorder traversal of the DAG such that at each binary node, one subDAG is traversed completely before traversing the rest of the other subDAG. A tree node is either a leaf, or an inner node with all its sons being tree nodes and none of them having more than one father. A decision node is a binary node which is not a tree node. If we evaluate all the tree nodes in a DAG with d decision nodes by the Labeling Algorithm of Sethi/Ullman, there remain at most 2 d diierent contiguous evaluations for the DAG: (1) algorithm simple (2) Let v 1 ; : : :; v d be the decision nodes of the DAG, and (3) let = (1 ; : : :; d) 2 f0; 1g d be a bitvector. (4) forall 2 d diierent 2 f0; 1g d do (5) start dfs(root) with each , such that for 1 i d (6)