An optimal linear-time algorithm for interprocedural register allocation in high level synthesis using SSA form

Authors:
Philip Brisk;Ajay K. Verma;Paolo Ienne
Affiliations:
Department of Computer Science and Engineering, Bourns College of Engineering, University of California, Riverside, CA;Processor Architecture Laboratory, School of Computer and Communication Sciences, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland;Processor Architecture Laboratory, School of Computer and Communication Sciences, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
Venue:
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Year:
2010

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Abstract

An optimal linear-time algorithm for interprocedural register allocation in high level synthesis is presented. Historically, register allocation has been modeled as a graph coloring problem, which is nondeterministic polynomial time-complete in general; however, converting each procedure to static single assignment (SSA) form ensures a chordal interference graph, which can be colored in O(|V|+|E|) time; the interprocedural interference graph (IIG) is not guaranteed to be chordal after this transformation. An extension to SSA form is introduced which ensures that the IIG is chordal, and the conversion process does not increase its chromatic number. The resulting IIG can then be colored in linear-time.