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
Counting solutions to Presburger formulas: how and why
PLDI '94 Proceedings of the ACM SIGPLAN 1994 conference on Programming language design and implementation
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)
Data and memory optimization techniques for embedded systems
ACM Transactions on Design Automation of Electronic Systems (TODAES)
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
Communication Pre-evaluation in HPF
Euro-Par '98 Proceedings of the 4th International Euro-Par Conference on Parallel Processing
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 size computation for multimedia processing applications
ASP-DAC '06 Proceedings of the 2006 Asia and South Pacific Design Automation Conference
Experiences with enumeration of integer projections of parametric polytopes
CC'05 Proceedings of the 14th international conference on Compiler Construction
Proceedings of the 12th ACM SIGPLAN symposium on Principles and practice of parallel programming
Integer Polyhedra for Program Analysis
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Integer affine transformations of parametric ℤ-polytopes and applications to loop nest optimization
ACM Transactions on Architecture and Code Optimization (TACO)
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Memory size reduction and memory accesses optimization are crucial issues for embedded systems. In the context of affine programs, these two challenges are classically tackled by array linearization, cache access optimization and memory size computation. Their formalization in the polyhedral model reduce to solving the following problem: count the number of solutions of a Presburger formula.In this paper we propose a novel algorithm that answers this question. We solve the Presburger formula whose solution is a union of parametric Z-polytopes and we propose an algorithm to count points in such a union of parametric Z-polytopes. These algorithms were implemented and we compare them to other existing methods.