This work introduces a design proposal towards modernization of high performance numerical library enabling various parallel execution, such as offloading, many-core concurrent execution, heterogeneous hybrid execution. A prototype implementation of Eigen-G2 employs a parallel task model supported by OpenMP, and exclusive control of offloading a GPU device. Also, multiple data formats are available by taking advantage of a metaprogramming support of C++ language. Eigen-G2 exhibits good parallel performance scalability when we use both multicore CPUs and a GPU at the same time.
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