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Zilliam is a Geometric Algebra library that generates a SIMD optimized library for any given Cl(p,q,r) algebra. It can be used for:

• PGA (projective geometric algebra, for which Zilliam has a special for generating all needed mask types) where you can easily construct points, lines and planes in any dimension and do projection, rotations, intersections and more between all of them under the same syntax. It has many uses for computer graphics and physics. It can also model conformal transformations using CGA.
• Modelling complex numbers, quaternions, dual numbers and many more other Clifford algebras under a single interface, generating SIMD optimized code for all of them. This makes it possible to use Zilliam for automatic differentiation, complex analysis
• Calculate Lorentz boosts and more using an STA (spacetime algebra) which also provides a very useful model for doing Electrodynamics work.

For all these applications, Zilliam gives you access to useful functions such as the trigonometric functions, the exponential and also useful concepts such as the Poincare dual and wedge operations. It also provides a sort of operation overloading through a comath interface, which allows you to evaluate complex expressions more easily and without much compile time cost.

Thanks to Zig's comptime capabilities and vectors, all of this can be done in a generic and performant way that works in any architecture supported by Zig. Zilliam provides SIMD optimized batched and single operations which can accelerate computation.

Example code can be found here.