Reducing memory requirements of nested loops for embedded systems

Computation of the Minimum Data Storage for Multi-Dimensional Signal Processing

“…The authors employ a data dependence analysis similar to [1], their major improvement being to add the capability of taking into account available execution ordering information, based mainly on loop interchanges. Different from the previous works which are only approximate methods, this paper presents a non-scalar technique for computing exactly the minimum memory size in multi-dimensional signal processing algorithms, when the specifications are procedural, i.e., the execution ordering is induced by the loop structure and it is thus fixed (like in several previous works [9,10,7]). This assumption is based on the fact that in present industrial design, the design entry usually includes a full fixation of the execution ordering.…”

“…They prove that it is sufficient to find the number of live variables for one statement in each innermost loop of a loop nest in order to get an estimate of the minimum memory size. Ramanujam et al use for each array a reference window containing at any moment during execution the array elements alive (that have already been referenced and will also be referenced in the future) [7]. The maximal window size gives the storage requirement for the corresponding array.…”

Mapping Multi-Dimensional Signals into Hierarchical Memory Organizations

“…The optimized mapping of the multidimensional signals (arrays) from these behavioral specifications to the data memory is an important step during memory allocation. Employing a data memory space much larger than needed has several negative consequences: (a) the energy consumption per access increases with the memory size [2], as well as (b) the data access latency [9]; in addition, (c) large memories occupy more chip area.…”

Memory optimization by counting points in integer transformations of parametric polytopes

“…The first solutions proposed approximations or minima of this number [32,25] or solved the subproblem of count the integer points in polytopes with one [1,7] or many [4,3,30] parameters. Then, some exact methods to count transformation of polytopes were proposed for the non-parametric case [20,2,33].…”