Optimal Code Selection in DAGs

Abstract

We extend the tree parsing approach to code selection to DAGs. In general, our extension does not produce the optimal code selection for all DAGs (this problem would be NPcomplete) , but for certain code selection grammars, it does. We present a method for checking whether a code selection grammar belongs to this set of DAG-optimal grammars, and use this method to check code selection grammars adapted from lcc: the grammars for the MIPS and SPARC architectures are DAG-optimal, and the code selection grammar for the 386 architecture is almost DAG-optimal.