Specialized Machine Instruction Set for Geometric Algebra

Geometric algebra covers many mathematical areas such as vector algebra, complex numbers, Pluecker coordinates, quaternions. It is geometrically intuitive and has a lot of potential for optimization and parallelization. In this paper, we develop an approach for the specialized machine instruction set GAPP based on our table-based compilation approach for geometric algebra computing. GAPP can be used as a representation from which consecutive target platform optimizations may be performed. An FPGA platform implementation is even capable of executing this instruction set directly without further transformations, thereby fully exploiting parallelism. An implementation of GAPP as a back end for the Gaalop compiler is already available. This is an important step towards the long term vision of microcomputers specifically designed for Geometric Algebra (Geometric Algebra Computers). Dietmar Hildenbrand TU Darmstadt, Germany, e-mail: [email protected] Patrick Charrier TU Darmstadt, Germany, e-mail: [email protected] Christian Steinmetz TU Darmstadt, Germany, e-mail: [email protected] Andreas Koch TU Darmstadt, Germany, e-mail: [email protected]