Geometric Algebra is a high-level mathematical framework which expresses a variety of geometric computations with an intuitive language. While its rich structure unlocks deeper insight and an elegant simplicity, it often comes at a cost to numerical implementations. After giving an overview of geometric algebra and its applications, a Julia implementation is presented which uses metaprogramming to shift the work to compile-time, enabling a fast and expressive approach to computational geometry.

Type instabilities are not always bad! Using non-concrete types, and avoiding method specialization and type inference can help with improving latency and, in specific cases, runtime performance. The latter is observed in inherently dynamic contexts with no way to compile all possible method signatures upfront, because code needs to be compiled at points of dynamic dispatch by design. We present a concrete case we face in our production environment, additional examples, and related trade-offs.