Counting with rational generating functions
Journal of Symbolic Computation
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
Integer Polyhedra for Program Analysis
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
Automatic memory partitioning and scheduling for throughput and power optimization
Proceedings of the 2009 International Conference on Computer-Aided Design
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Cache vulnerability equations for protecting data in embedded processor caches from soft errors
Proceedings of the ACM SIGPLAN/SIGBED 2010 conference on Languages, compilers, and tools for embedded systems
Multi-dimensional rankings, program termination, and complexity bounds of flowchart programs
SAS'10 Proceedings of the 17th international conference on Static analysis
Automatic memory partitioning and scheduling for throughput and power optimization
ACM Transactions on Design Automation of Electronic Systems (TODAES)
Modeling adaptive streaming applications with parameterized polyhedral process networks
Proceedings of the 48th Design Automation Conference
Adaptive runtime selection of parallel schedules in the polytope model
Proceedings of the 19th High Performance Computing Symposia
Polyhedral parallelization of binary code
ACM Transactions on Architecture and Code Optimization (TACO) - HIPEAC Papers
Assuring application-level correctness against soft errors
Proceedings of the International Conference on Computer-Aided Design
On-chip cache hierarchy-aware tile scheduling for multicore machines
CGO '11 Proceedings of the 9th Annual IEEE/ACM International Symposium on Code Generation and Optimization
Integer affine transformations of parametric ℤ-polytopes and applications to loop nest optimization
ACM Transactions on Architecture and Code Optimization (TACO)
PICA: Processor Idle Cycle Aggregation for Energy-Efficient Embedded Systems
ACM Transactions on Embedded Computing Systems (TECS)
Analytical synthesis of bandwidth-efficient SDRAM address generators
Microprocessors & Microsystems
Mapping of streaming applications considering alternative application specifications
ACM Transactions on Embedded Computing Systems (TECS) - Special section on ESTIMedia'12, LCTES'11, rigorous embedded systems design, and multiprocessor system-on-chip for cyber-physical systems
Automatic OpenCL work-group size selection for multicore CPUs
PACT '13 Proceedings of the 22nd international conference on Parallel architectures and compilation techniques
Hybrid Hexagonal/Classical Tiling for GPUs
Proceedings of Annual IEEE/ACM International Symposium on Code Generation and Optimization
Theory and algorithm for generalized memory partitioning in high-level synthesis
Proceedings of the 2014 ACM/SIGDA international symposium on Field-programmable gate arrays
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Many compiler optimization techniques 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 the enumerator of such a set can be represented by an explicit function consisting of a set of quasi-polynomials, each associated with a chamber in the parameter space. Previously, interpolation was used to obtain these quasi-polynomials, but this technique has several disadvantages. Its worst-case computation time for a single quasi-polynomial is exponential in the input size, even for fixed dimensions. The worst-case size of such a quasi-polynomial (measured in bits needed to represent the quasi-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 the required quasi-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 enumerators in polynomial time (for fixed dimensions).