Practical solutions for counting scalars and dependences in ATOMIUM-a memory management system for multidimensional signal processing

Abstract

Abstract-Image and video processing applications involve large multidimensional signals which have to be stored in memory modules. In application-specific architectures for real-time multidimensional signal processing, a significant cost in terms of chip area and power consumption is due to these background memory units. The multidimensional signals are usually modeled in behavioral descriptions with array variables. In the algorithmic specifications of our target applications, many of the array references cover large amounts of scalars. Therefore, the efficient handling of array references in the specifications for image and video processing is crucial for obtaining low cost memory allocation solutions. This paper addresses a central problem which arises when handling the array variables in behavioral specifications: the computation of the number of scalars covered by an array reference. This problem is closely related to the computation of dependences in data-flow analysis. The novel algorithms proposed in this paper are embedded in the ATOMIUM environment-a memory management system for multidimensional signal processing.Index Terms-Data dependence, data-flow analysis, digital signal processing (DSP), linearly bounded lattice, polytope.

Distributed identification of the lineality space of a cone

“…Solving the LS problem may be necessary for the following: How to transform a model of the plant location problem into a dual linear program procedure that obtains the optimal solution via iterations that find extreme dual points or extreme dual direction vectors (which may or may not belong to a LS) [16] and identification of a basis of the LS in the context of a memory management system for multidimensional signal processing [2].…”

“…(2) Are the results scalable? (3) Are Remote Procedure Calls (RPCs) and Message-Passing Interface (MPI) effective communication protocols for distributing the processing?…”

Storage Estimation and Design Space Exploration Methodologies for the Memory Management of Signal Processing Applications

“…3, where instead of counting the black points in the right quadrilateral containing holes, we count the black points in the left quadrilateral without any hole if loop normalization was performed in advance.) Otherwise, the problem reduces to counting the points in a projection of a polytope [38,39], as explained and exemplified in [25]. Counting the lattice points in a polytope can be done in several ways: there are methods based on Ehrhart polynomials like, for instance, [40,41], or even much simpler -adapting the Fourier-Motzkin technique [42,43].…”

“…It traverses a dependency graph based on an extended data dependency analysis resulting in a number of non-overlapping array sections (so called basic sets) and the dependencies between them. The basic set sizes and the sizes of the dependencies are found using an efficient lattice point counting technique [25]. The maximal combined size of simultaneously alive basic sets found through a greedy graph traversal gives an estimation of the storage requirement.…”

Memory Parallelism Using Custom Array Mapping to Heterogeneous Storage Structures

“…[6,8]) use the scheduling and data reuse information in order to exclusively map the arrays to RAM blocks or registers. The work in [3,11] identifies the footprint of each array to allocate array variables to memories, while the approach in [4] describes a methodology to cache the reusable data in the smaller RAMs. Another body of work (e.g.…”