Memory size computation for multimedia processing applications

Abstract

In real-time multimedia processing systems a very large part of the power consumption is due to the data storage and data transfer. Moreover, the area cost is often largely dominated by the memory modules. The computation of the memory size is an important step in the process of designing an optimized (for area and/or power) memory architecture for multimedia processing systems. This paper presents a novel non-scalar approach for computing exactly the memory size in real-time multimedia algorithms. This methodology uses both algebraic techniques specific to the data-flow analysis used in modern compilers, and also recent advances in the theory of integral polyhedra. In contrast with all the previous works which are only estimation methods, this approach performs exact memory computations even for applications with a large number of scalar signals.

Mapping Multi-Dimensional Signals into Hierarchical Memory Organizations

“…This decom- position into disjoint lattices -used also in [15] -can be performed analytically, by recursively intersecting the array references of every multi-dimensional signal in the code. Two operations are relevant in our context: the intersection and the difference of two lattices.…”

Memory optimization by counting points in integer transformations of parametric polytopes

“…To the best of our knowledge, the previous methods [16,33] to count points in unions of Z-polytopes are lattice-union based, which is exponential in the size of lattice generators and their least common multiple. Furthermore, Zhu et al's method [33] only deals with non-parametric Z-polytopes.…”

“…It is usually very hard to separate a union of Z-polytopes into a disjoint union [33], and it may be exponential even for a fixed number of Z-polytopes.…”

“…The class of "affine programs" (affine access functions to arrays in affine bounded loop nests) has been tackled in the past by many researchers, since they occur frequently and are resource-consuming, in applications like digital audio/video, imaging, graphics, compression/decompression, etc. In this context, array linearization [28], cache access optimization [11,5,15], and memory size computation [32,33] reduce to the problem of counting the number of images of integer points in a polytope (or a Zpolytope 1 ) by an affine function, or equivalently counting the solutions to a Presburger formula. If the considered programs contain unknown variables at compile-time, this problem has to be solved analytically, and the solution has to be expressed as a function of these parameters.…”

“…Then, some exact methods to count transformation of polytopes were proposed for the non-parametric case [20,2,33].…”