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A Hardware Implementation of a Unit for Geometric Algebra Operations With Parallel Memory Arrays (Abstract Only)

Geometric algebra (GA) is a powerful and versatile mathematical tool which helps to intuitively express and manipulate complex geometric relationships. It has recently been used in engineering problems such computer graphics, machine vision, robotics, among others. The problem with GA in its numeric version is that it requires many arithmetic operations, and the length of the input vectors is unknown until runtime in a generic architecture operating over homogeneous elements. Few works in hardware architectures for GA were developed to improve the performance in GA applications. In this work, a hardware architecture of a unit for GA operations (geometric product) for FPGA is presented. The main contribution of this work is the use of parallel memory arrays with access conflict avoidance for dealing with the issue of unknown length of input/output vectors, the intention is to reduce memory wasted when storing the input and output vectors. In this first stage of the project, we have implemented only a single access function (fixed-length) in the memory array in order to test the core of geometric product. In future works we will implement a full set of access functions with different lengths and shapes. In this work, only the simulations are presented; in the future, we will also present the experimental results