Theory of linear and integer programming
Theory of linear and integer programming
On synthesizing systolic arrays from recurrence equations with linear dependencies
Proc. of the sixth conference on Foundations of software technology and theoretical computer science
The systematic design of systolic arrays
Centre National de Recherche Scientifique on Automata networks in computer science: theory and applications
ICS '88 Proceedings of the 2nd international conference on Supercomputing
POPL '88 Proceedings of the 15th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Regular partitioning for synthesizing fixed-size systolic arrays
Integration, the VLSI Journal
A practical algorithm for exact array dependence analysis
Communications of the ACM
Array-data flow analysis and its use in array privatization
POPL '93 Proceedings of the 20th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Some efficient solutions to the affine scheduling problem: I. One-dimensional time
International Journal of Parallel Programming
ICS '96 Proceedings of the 10th international conference on Supercomputing
Parallel Computing - Special issue on applications: parallel processing and multimedia
Linear programming models for scheduling systems of affine recurrence equations—a comparative study
Proceedings of the tenth annual ACM symposium on Parallel algorithms and architectures
Parameterized polyhedra and their vertices
International Journal of Parallel Programming
Maximizing parallelism and minimizing synchronization with affine partitions
Parallel Computing - Special issues on languages and compilers for parallel computers
Automatic storage management for parallel programs
Parallel Computing - Special issues on languages and compilers for parallel computers
Schedule-independent storage mapping for loops
Proceedings of the eighth international conference on Architectural support for programming languages and operating systems
International Journal of Parallel Programming
Generation of Efficient Nested Loops from Polyhedra
International Journal of Parallel Programming - Special issue on instruction-level parallelism and parallelizing compilation, part 2
Optimizing memory usage in the polyhedral model
ACM Transactions on Programming Languages and Systems (TOPLAS)
Blocking and array contraction across arbitrarily nested loops using affine partitioning
PPoPP '01 Proceedings of the eighth ACM SIGPLAN symposium on Principles and practices of parallel programming
Scheduling and Automatic Parallelization
Scheduling and Automatic Parallelization
Parallelization via Constrained Storage Mapping Optimization
ISHPC '99 Proceedings of the Second International Symposium on High Performance Computing
Storage Mapping Optimization for Parallel Programs
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
Automatic Parallelization in the Polytope Model
The Data Parallel Programming Model: Foundations, HPF Realization, and Scientific Applications
Space-Optimal Linear Processor Allocation for Systolic Arrays Synthesis
IPPS '92 Proceedings of the 6th International Parallel Processing Symposium
Array Placement for Storage Size Reduction in Embedded Multimedia Systems
ASAP '97 Proceedings of the IEEE International Conference on Application-Specific Systems, Architectures and Processors
Algorithms for systolic array synthesis
Algorithms for systolic array synthesis
Reordering and storage optimizations for scientific programs
Reordering and storage optimizations for scientific programs
ACM Transactions on Design Automation of Electronic Systems (TODAES)
Lattice-Based Memory Allocation
IEEE Transactions on Computers
Strength reduction of integer division and modulo operations
LCPC'01 Proceedings of the 14th international conference on Languages and compilers for parallel computing
Shared buffer implementations of signal processing systems using lifetime analysis techniques
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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We present a unified mathematical framework for analyzing the tradeoffs between parallelism and storage allocation within a parallelizing compiler. Using this framework, we show how to find a good storage mapping for a given schedule, a good schedule for a given storage mapping, and a good storage mapping that is valid for all legal (one-dimensional affine) schedules. We consider storage mappings that collapse one dimension of a multidimensional array, and programs that are in a single assignment form and accept a one-dimensional affine schedule. Our method combines affine scheduling techniques with occupancy vector analysis and incorporates general affine dependences across statements and loop nests. We formulate the constraints imposed by the data dependences and storage mappings as a set of linear inequalities, and apply numerical programming techniques to solve for the shortest occupancy vector. We consider our method to be a first step towards automating a procedure that finds the optimal tradeoff between parallelism and storage space.