Generating Efficient Tensor Contractions for GPUs

Many scientific and numerical applications, including quantum chemistry modeling and fluid dynamics simulation, require tensor product and tensor contraction evaluation. Tensor computations are characterized by arrays with numerous dimensions, inherent parallelism, moderate data reuse and many degrees of freedom in the order in which to perform the computation. The best-performing implementation is heavily dependent on the tensor dimensionality and the target architecture. In this paper, we map tensor computations to GPUs, starting with a high-level tensor input language and producing efficient CUDA code as output. Our approach is to combine tensor-specific mathematical transformations with a GPU decision algorithm, machine learning and auto tuning of a large parameter space. Generated code shows significant performance gains over sequential and Open MP parallel code, and a comparison with Open ACC shows the importance of auto tuning and other optimizations in our framework for achieving efficient results.