Theory of linear and integer programming
Theory of linear and integer programming
The Omega test: a fast and practical integer programming algorithm for dependence analysis
Proceedings of the 1991 ACM/IEEE conference on Supercomputing
Partitioning of processor arrays: a piecewise regular approach
Integration, the VLSI Journal - Special issue on algorithms and architectures
Counting solutions to Presburger formulas: how and why
PLDI '94 Proceedings of the ACM SIGPLAN 1994 conference on Programming language design and implementation
A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed
Mathematics of Operations Research
Interprocedural array region analyses
International Journal of Parallel Programming - Special issue: selected papers from the eighth international workshop on languages and compilers for parallel computing
A linear algebra framework for static High Performance Fortran code distribution
Scientific Programming - Special issue: High Performance Fortran comes of age
Parameterized polyhedra and their vertices
International Journal of Parallel Programming
Parametric Analysis of Polyhedral Iteration Spaces
Journal of VLSI Signal Processing Systems - Special issue on application specific systems, architectures and processors
Cache miss equations: a compiler framework for analyzing and tuning memory behavior
ACM Transactions on Programming Languages and Systems (TOPLAS)
Exact memory size estimation for array computations
IEEE Transactions on Very Large Scale Integration (VLSI) Systems - Special issue on the 11th international symposium on system-level synthesis and design (ISSS'98)
Reducing memory requirements of nested loops for embedded systems
Proceedings of the 38th annual Design Automation Conference
Precise Data Locality Optimization of Nested Loops
The Journal of Supercomputing
Experiences with Constraint-based Array Dependence Analysis
PPCP '94 Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming
Volume Driven Data Distribution for NUMA-Machines
Euro-Par '00 Proceedings from the 6th International Euro-Par Conference on Parallel Processing
Communication Pre-evaluation in HPF
Euro-Par '98 Proceedings of the 4th International Euro-Par Conference on Parallel Processing
Static analysis of parameterized loop nests for energy efficient use of data caches
Compilers and operating systems for low power
Counting the solutions of Presburger equations without enumerating them
Theoretical Computer Science - Implementation and application automata
Analytical computation of Ehrhart polynomials: enabling more compiler analyses and optimizations
Proceedings of the 2004 international conference on Compilers, architecture, and synthesis for embedded systems
Solving Out-of-Order Communication in Kahn Process Networks
Journal of VLSI Signal Processing Systems
Memory optimization by counting points in integer transformations of parametric polytopes
CASES '06 Proceedings of the 2006 international conference on Compilers, architecture and synthesis for embedded systems
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Proceedings of the 12th ACM SIGPLAN symposium on Principles and practice of parallel programming
Applicable Algebra in Engineering, Communication and Computing
Experiences with enumeration of integer projections of parametric polytopes
CC'05 Proceedings of the 14th international conference on Compiler Construction
ACM Transactions on Design Automation of Electronic Systems (TODAES)
A scalable and near-optimal representation of access schemes for memory management
ACM Transactions on Architecture and Code Optimization (TACO)
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The polyhedral model is a well-known compiler optimization framework for the analysis and transformation of affine loop nests. We present a new method to solve a difficult geometric operation that is raised by this model: the integer affine transformation of parametric ℤ-polytopes. The result of such a transformation is given by a worst-case exponential union of ℤ-polytopes. We also propose a polynomial algorithm (for fixed dimension), to count points in arbitrary unions of a fixed number of parametric ℤ-polytopes. We implemented these algorithms and compared them to other existing algorithms, for a set of applications to loop nest analysis and optimization.