Geometric Algebra Enhanced Precompiler for C++, OpenCL and Mathematica’s OpenCLLink

Patrick Charrier, Mariusz Klimek, Christian Steinmetz, Dietmar Hildenbrand
TU Darmstadt, Germany
Advances in Applied Clifford Algebras, 2014


   title={Geometric Algebra Enhanced Precompiler for C++, OpenCL and Mathematica’s OpenCLLink},

   author={Charrier, Patrick and Klimek, Mariusz and Steinmetz, Christian and Hildenbrand, Dietmar},

   journal={Advances in Applied Clifford Algebras},





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The focus of this work is a simplified integration of algorithms expressed in Geometric Algebra (GA) into modern high level computer languages, namely C++, OpenCL and CUDA. A high runtime performance in terms of GA is achieved using symbolic simplification and code generation by a precompiler that is directly integrated into CMake-based build toolchains. Finally, we demonstrate how to interface our technology with Mathematica’s OpenCLLink.
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