The program dependence graph and its use in optimization
ACM Transactions on Programming Languages and Systems (TOPLAS)
PLDI '88 Proceedings of the ACM SIGPLAN 1988 conference on Programming Language design and Implementation
Software pipelining: an effective scheduling technique for VLIW machines
PLDI '88 Proceedings of the ACM SIGPLAN 1988 conference on Programming Language design and Implementation
Dependence flow graphs: an algebraic approach to program dependencies
POPL '91 Proceedings of the 18th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
On optimal parallelization of arbitrary loops
Journal of Parallel and Distributed Computing
ACM Computing Surveys (CSUR)
Resource-Constrained Software Pipelining
IEEE Transactions on Parallel and Distributed Systems
A compilation technique for software pipelining of loops with conditional jumps
MICRO 20 Proceedings of the 20th annual workshop on Microprogramming
Parallelizing nonnumerical code with selective scheduling and software pipelining
ACM Transactions on Programming Languages and Systems (TOPLAS)
Circuit Retiming Applied to Decomposed Software Pipelining
IEEE Transactions on Parallel and Distributed Systems
List scheduling in the presence of branches: a theoretical evaluation
Theoretical Computer Science - Special issue on parallel computing
Dependence graphs and compiler optimizations
POPL '81 Proceedings of the 8th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Requirements for Optimal Execution of Loops with Tests
IEEE Transactions on Parallel and Distributed Systems
Generalized Multiway Branch Unit for VLIW Microprocessors
IEEE Transactions on Parallel and Distributed Systems
Scheduling Data-Flow Graphs via Retiming and Unfolding
IEEE Transactions on Parallel and Distributed Systems
Perfect Pipelining: A New Loop Parallelization Technique
ESOP '88 Proceedings of the 2nd European Symposium on Programming
Optimal Loop Scheduling on Multiprocessors: A Pumping Lemma for p-Processor Schedules
PaCT '95 Proceedings of the 3rd International Conference on Parallel Computing Technologies
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We address the problem of time optimal software pipelining of loops with control flows, one of the most difficult open problems in the area of parallelizing compilers. We present a necessary condition for loops with control flows to have equivalent time optimal programs, generalizing the result by Schwiegelshohn et al., which has been the most significant theoretical result on the problem. As part of the formal treatment of the problem, we propose a new formalization of software pipelining, which provides a basis of our proof as well as a new theoretical framework for software pipelining research. Being the first generalized result on the problem, our work described in this paper forms an important first step towards time optimal software pipelining.