Computation of Storage Requirements for Multi-Dimensional Signal Processing Applications

Abstract

Abstract-Many integrated circuit systems, particularly in the multimedia and telecom domains, are inherently data dominant. For this class of systems, a large part of the power consumption is due to the data storage and data transfer. Moreover, a significant part of the chip area is occupied by memory. The computation of the memory size is an important step in the system-level exploration, in the early stage of designing an optimized (for area and/or power) memory architecture for this class of systems. This paper presents a novel nonscalar approach for computing exactly the minimum size of the data memory for high-level procedural specifications of multidimensional signal processing applications. In contrast with all the previous works which are estimation methods, this approach can perform exact memory computations even for applications with numerous and complex array references, and also with large numbers of scalars.

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

“…Figure 2 shows the variation of the storage requirement for the signal A during the execution of both codes. These memory traces are generated using the tool described in [12], allowing to evaluate the minimum data storage. A minimum array window is not only difficult to compute but, typically, difficult to use in practical allocation problems as, in most of the cases, it requires a significantly more complex addressing hardware.…”

“…Different from all the previous works which do not provide realistic metrics of quality for their memory allocation solutions, this memory management software tool also computes the minimum storage requirement of each multidimensional signal in the specification (therefore, the optimal memory sharing between the elements of the same array), as well as the minimum data storage for the entire (procedural) algorithmic specification (therefore, the optimal memory sharing between all the array elements and scalars in the code) [12].…”

“…Taking, for instance, the linearization by row concatenation, with the rows sorted increasingly, it can be observed that the maximum distance between live elements (black points) is reached when the index vectors of the A-elements are the minimum and, respectively, the maximum relative to the lexicographic order. 1 These array A-elements are represented by the points M = A [2] [7] and N = A [12] [7] in Fig. 4, and dist…”

“…This partitioning into disjoint lattices-used also in [12]-can be performed analytically, by recursively intersecting the array references of every multidimensional signal in the code. This is a complex operation which is thoroughly discussed and exemplified in [12].…”

“…Interestingly, the possibility of memory sharing between elements of different arrays with disjoint lifetimes was observed long time ago (e.g., [10]) and it has been taken into account by several approaches for memory size evaluation (e.g., [11,12]). The memory sharing is sometimes called "inter-array in-place mapping" when the elements belong to different arrays, and "intra-array in-place mapping" when the elements belong to the same array [3,11].…”