Realizing Mathematics of Arrays Operations as Custom Architecture Hardware-Software Co-Design Solutions

In embedded electronic system applications being developed today, complex datasets are required to be obtained, processed, and communicated. These can be from various sources such as environmental sensors, still image cameras, and video cameras. Once obtained and stored in electronic memory, the data is accessed and processed using suitable mathematical algorithms. How the data are stored, accessed, processed, and communicated will impact on the cost to process the data. Such algorithms are traditionally implemented in software programs that run on a suitable processor. However, different approaches can be considered to create the digital system architecture that would consist of the memory, processing, and communications operations. When considering the mathematics at the centre of the design making processes, this leads to system architectures that can be optimized for the required algorithm or algorithms to realize. Mathematics of Arrays (MoA) is a class of operations that supports n-dimensional array computations using array shapes and indexing of values held within the array. In this article, the concept of MoA is considered for realization in software and hardware using Field Programmable Gate Array (FPGA) and Application Specific Integrated Circuit (ASIC) technologies. The realization of MoA algorithms will be developed along with the design choices that would be required to map a MoA algorithm to hardware, software or hardware-software co-designs.