Storage Size Reduction by In-place Mapping of Arrays

Abstract

Programs for embedded multimedia applications typically manipulate several large multi-dimensional arrays. The energy consumption per access increases with their size; the access to these large arrays is responsible for a substantial part of the power consumption. In this paper, an analysis is developed to compute a bounding box for the elements in the array that are simultaneously in use. The size of the original array can be reduced to the size of the bounding box and accesses to it can be redirected using modulo operations on the original indices. This substantially reduces the size of the memories and the power consumption of accessing them.

Signal Assignment Model for the Memory Management of Multidimensional Signal Processing Applications

“…The first part of this discussion will focus on the previous mapping models [4] and [5], since they are relevant for the rest of the paper. The second part will illustrate the advantage of mapping with inter-array memory sharing.…”

“…The assignment model proposed by Tronçon et al [5] circumvents the need of analyzing different linearization schemes by computing a maximal bounding window, having the same dimension as the signal, large enough to cover in any moment of the computation all the array elements simultaneously alive. In the illustrative example shown in Fig.…”

“…Indeed, the maximum horizontal and vertical distances between black points is d 1 = 10 and d 2 = 9, respectively. A 2-D window whose elements are From the above discussion, it follows that the storage allocation for signal A is 100 locations if the mapping model [4] is used, whereas it is w 1 × w 2 = 110 locations if the model [5] is applied. The better allocation result of the mapping model [4] for the illustrative code in Fig.…”

“…In order to avoid the inconvenience of analyzing different linearization schemes, Tronçon et al proposed [5] ]; in its turn, this bounding window is mapped (relative to a base address) into the physical memory by a typical canonical linearization, like row or column concatenation for 2-D arrays. Signal A's window is denoted as W A in any of the two models [4] and [5] (in spite of being 1-dimensional in the case of the former model and m-dimensional for the latter) since the meaning will be clear enough from the context.…”

“…Signal A's window is denoted as W A in any of the two models [4] and [5] (in spite of being 1-dimensional in the case of the former model and m-dimensional for the latter) since the meaning will be clear enough from the context. Each window element w k is computed as the maximum difference (in absolute value) between the k-th indices of any two A-elements (A i , A j ) simultaneously alive, plus 1.…”