Geometric algebra computers

Geometric algebra covers a lot of other mathematical systems like vector algebra, complex numbers, Plücker coordinates, quaternions etc. and it is geometrically intuitive to work with. Furthermore there is a lot of potential for optimization and parallelization. In this paper, we investigate computers suitable for geometric algebra algorithms. While these geometric algebra computers are working in parallel, the algorithms can be described on a high level without thinking about how to parallelize them. In this context two recent developments are important. On one hand, there is a recent development of geometric algebra to an easy handling of engineering applications, especially in computer graphics, computer vision and robotics. On the other hand, there is a recent development of computer platforms from single processors to parallel computing platforms which are able to handle the high dimensional multivectors of geometric algebra in a better way. We present our geometric algebra compilation approach for current and future hardware platforms like reconfigurable hardware, multi-core architectures as well as modern GPGPUs.