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Gaalop 2.0 - a geometric algebra algorithm compiler

: Schwinn, Christian; Hildenbrand, Dietmar; Stock, Florian; Koch, Andreas

Skala, V. ; European Association for Computer Graphics -EUROGRAPHICS-:
GraVisMa 2010, 2nd International Workshop on Computer Graphics, Computer Vision and Mathematics. Workshop proceedings : Brno, Czech Republic on September 7 - 10, 2010
Brno: Vaclav Skala - Union Agency, 2010
ISBN: 978-80-86943-85-5
International Workshop on Computer Graphics, Computer Vision and Mathematics (GraVisMa) <2, 2010, Brno>
Fraunhofer IGD ()
geometric algebra (GA); geometric computing; optimization; parallel computing; Field Programmable Gate Array (FPGA); Forschungsgruppe Geometric Algebra Computing (GACO)

In recent years, Geometric Algebra (GA) has become more and more popular in fields of science and engineering due to its potential for compact algorithms. However, the execution of GA algorithms and the related need for high computational power is still the limiting factor for these algorithms to be used in practice. Therefore, it would be desirable to automatically detect parts that can be calculated in parallel by a software tool.
In this paper, we present Gaalop 2.0, a Geometric Algebra Algorithm Compiler, which takes as input the description of a GA algorithm, symbolically optimizes the output multivectors and compiles the optimized code into a target language source file such as C++, for instance. For each output multivector the code for the different coefficients is generated, which is finally adjusted to contain only basic arithmetic operations instead. This allows the optimized output to be compiled for parallel computing platforms like FPGAs, for instance.