Theory of linear and integer programming
Theory of linear and integer programming
Counting solutions to Presburger formulas: how and why
PLDI '94 Proceedings of the ACM SIGPLAN 1994 conference on Programming language design and implementation
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)
Exact analysis of the cache behavior of nested loops
Proceedings of the ACM SIGPLAN 2001 conference on Programming language design and implementation
Precise Data Locality Optimization of Nested Loops
The Journal of Supercomputing
Array recovery and high-level transformations for DSP applications
ACM Transactions on Embedded Computing Systems (TECS)
On Estimating and Enhancing Cache Effectiveness
Proceedings of the Fourth International Workshop on Languages and Compilers for Parallel Computing
A Compile Time Based Approach for Solving Out-of-Order Communication in Kahn Process Networks
ASAP '02 Proceedings of the IEEE International Conference on Application-Specific Systems, Architectures, and Processors
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
Cartesian factoring of polyhedra in linear relation analysis
SAS'03 Proceedings of the 10th international conference on Static analysis
Generating cache hints for improved program efficiency
Journal of Systems Architecture: the EUROMICRO Journal
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
pn: a tool for improved derivation of process networks
EURASIP Journal on Embedded Systems
Computation of storage requirements for multi-dimensional signal processing applications
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Journal of Signal Processing Systems
Reducing memory requirements of resource-constrained applications
ACM Transactions on Embedded Computing Systems (TECS)
Precise Management of Scratchpad Memories for Localising Array Accesses in Scientific Codes
CC '09 Proceedings of the 18th International Conference on Compiler Construction: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
Proceedings of the 7th annual IEEE/ACM International Symposium on Code Generation and Optimization
Proceedings of the 3rd Workshop on General-Purpose Computation on Graphics Processing Units
A compiler framework for the reduction of worst-case execution times
Real-Time Systems
Symbolic and analytic techniques for resource analysis of java bytecode
TGC'10 Proceedings of the 5th international conference on Trustworthly global computing
Rational Generating Functions and Integer Programming Games
Operations Research
Experiences with enumeration of integer projections of parametric polytopes
CC'05 Proceedings of the 14th international conference on Compiler Construction
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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Many optimization techniques, including several targeted specifically at embedded systems, depend on the ability to calculate the number of elements that satisfy certain conditions. If these conditions can be represented by linear constraints, then such problems are equivalent to counting the number of integer points in (possibly) parametric polytopes. It is well known that this parametric count can be represented by a set of Ehrhart polynomials. Previously, interpolation was used to obtain these polynomials, but this technique has several disadvantages. Its worst-case computation time for a single Ehrhart polynomial is exponential in the input size, even for fixed dimensions. The worst-case size of such an Ehrhart polynomial (measured in bits needed to represent the polynomial) is also exponential in the input size. Under certain conditions this technique even fails to produce a solution.Our main contribution is a novel method for calculating Ehrhart polynomials analytically. It extends an existing method, based on Barvinok's decomposition, for counting the number of integer points in a non-parametric polytope. Our technique always produces a solution and computes polynomially-sized Ehrhart polynomials in polynomial time (for fixed dimensions).