Compilers: principles, techniques, and tools
Compilers: principles, techniques, and tools
Static analysis of linear congruence equalities among variables of a program
TAPSOFT '91 Proceedings of the international joint conference on theory and practice of software development on Colloquium on trees in algebra and programming (CAAP '91): vol 1
Efficiently computing static single assignment form and the control dependence graph
ACM Transactions on Programming Languages and Systems (TOPLAS)
A practical algorithm for exact array dependence analysis
Communications of the ACM
PLDI '92 Proceedings of the ACM SIGPLAN 1992 conference on Programming language design and implementation
Chains of recurrences—a method to expedite the evaluation of closed-form functions
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Beyond induction variables: detecting and classifying sequences using a demand-driven SSA form
ACM Transactions on Programming Languages and Systems (TOPLAS)
XIL and YIL: the intermediate languages of TOBEY
IR '95 Papers from the 1995 ACM SIGPLAN workshop on Intermediate representations
Symbolic analysis for parallelizing compilers
ACM Transactions on Programming Languages and Systems (TOPLAS)
Multidimensional chains of recurrences
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Advanced compiler design and implementation
Advanced compiler design and implementation
On computational properties of chains of recurrences
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Optimizing compilers for modern architectures: a dependence-based approach
Optimizing compilers for modern architectures: a dependence-based approach
Hacker's Delight
Loop Transformations for Restructuring Compilers: The Foundations
Loop Transformations for Restructuring Compilers: The Foundations
High Performance Compilers for Parallel Computing
High Performance Compilers for Parallel Computing
Designing the McCAT Compiler Based on a Family of Structured Intermediate Representations
Proceedings of the 5th International Workshop on Languages and Compilers for Parallel Computing
Efficient Symbolic Analysis for Optimizing Compilers
CC '01 Proceedings of the 10th International Conference on Compiler Construction
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
WCRE '01 Proceedings of the Eighth Working Conference on Reverse Engineering (WCRE'01)
Loop Induction Variable Canonicalization in Parallelizing Compilers
PACT '96 Proceedings of the 1996 Conference on Parallel Architectures and Compilation Techniques
LLVM: A Compilation Framework for Lifelong Program Analysis & Transformation
Proceedings of the international symposium on Code generation and optimization: feedback-directed and runtime optimization
Vectorization for SIMD architectures with alignment constraints
Proceedings of the ACM SIGPLAN 2004 conference on Programming language design and implementation
A unified framework for nonlinear dependence testing and symbolic analysis
Proceedings of the 18th annual international conference on Supercomputing
The Value Evolution Graph and its Use in Memory Reference Analysis
Proceedings of the 13th International Conference on Parallel Architectures and Compilation Techniques
Auto-vectorization of interleaved data for SIMD
Proceedings of the 2006 ACM SIGPLAN conference on Programming language design and implementation
Beyond iteration vectors: instancewise relational abstract domains
SAS'06 Proceedings of the 13th international conference on Static Analysis
Apricot: an optimizing compiler and productivity tool for x86-compatible many-core coprocessors
Proceedings of the 26th ACM international conference on Supercomputing
Proceedings of the 10th Workshop on Optimizations for DSP and Embedded Systems
Semi-automatic restructuring of offloadable tasks for many-core accelerators
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
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This paper presents the design of an induction variable analyzer suitable for the analysis of typed, low-level, three address representations in SSA form. At the heart of our analyzer is a new algorithm recognizing scalar evolutions. We define a representation called trees of recurrences that is able to capture different levels of abstractions: from the finer level that is a subset of the SSA representation restricted to arithmetic operations on scalar variables, to the coarser levels such as the evolution envelopes that abstract sets of possible evolutions in loops. Unlike previous work, our algorithm tracks induction variables without prior classification of a few evolution patterns: different levels of abstraction can be obtained on demand. The low complexity of the algorithm fits the constraints of a production compiler as illustrated by the evaluation of our implementation on standard benchmark programs.