Compilers: principles, techniques, and tools
Compilers: principles, techniques, and tools
A fresh look at optimizing array bound checking
PLDI '90 Proceedings of the ACM SIGPLAN 1990 conference on Programming language design and implementation
PLDI '92 Proceedings of the ACM SIGPLAN 1992 conference on Programming language design and implementation
Beyond induction variables: detecting and classifying sequences using a demand-driven SSA form
ACM Transactions on Programming Languages and Systems (TOPLAS)
Symbolic analysis for parallelizing compilers
ACM Transactions on Programming Languages and Systems (TOPLAS)
Advanced compiler design and implementation
Advanced compiler design and implementation
Monotonic evolution: an alternative to induction variable substitution for dependence analysis
ICS '01 Proceedings of the 15th international conference on Supercomputing
Optimizing compilers for modern architectures: a dependence-based approach
Optimizing compilers for modern architectures: a dependence-based approach
High Performance Compilers for Parallel Computing
High Performance Compilers for Parallel Computing
Parallel Programming with Polaris
Computer
Array recovery and high-level transformations for DSP applications
ACM Transactions on Embedded Computing Systems (TECS)
Recurrent Relations and Speed-up of Computations Using Computer Algebra Systems
DISCO '92 Proceedings of the International Symposium on Design and Implementation of Symbolic Computation Systems
Efficient Symbolic Analysis for Optimizing Compilers
CC '01 Proceedings of the 10th International Conference on Compiler Construction
IWIA '01 Proceedings of the Innovative Architecture for Future Generation High-Performance Processors and Systems (IWIA'01)
A unified framework for nonlinear dependence testing and symbolic analysis
Proceedings of the 18th annual international conference on Supercomputing
An empirical evaluation of chains of recurrences for array dependence testing
Proceedings of the 15th international conference on Parallel architectures and compilation techniques
Proceedings of the 44th annual Southeast regional conference
Concurrency and Computation: Practice & Experience - Current Trends in Compilers for Parallel Computers (CPC2006)
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This paper presents an efficient algorithm for classifying generalized induction variables and more complicated flow-sensitive loop-variant variables that have arbitrary conditional update patterns along multiple paths in a loop nest. Variables are recognized and translated into closed-form functions, such as linear, polynomial, geometric, wrap-around, periodic, and mixer functions. The remaining flow-sensitive variables (those that have no closed forms) are bounded by tight bounding functions on their value sequences by bounds derived from our extensions of the Chains of Recurrences (CR#) algebra. The classification algorithm has a linear worst-case execution time in the size of the SSA region of a loop nest. Classification coverage and performance results for the SPEC2000 benchmarks are given and compared to other methods.