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Researchers from diverse disciplines are increasingly incorporating numeric high-order data, i.e., numeric tensors, within their practice. Just like the matrix-vector (MV) paradigm, the development of multipurpose, but high-performance, sparse data structures and algorithms for arithmetic calculations, e.g., those found in Einstein-like notation, is crucial for the continued adoption of tensors. We use the motivating example of high-order differential operators to illustrate this need. As sparse tensor arithmetic represents an emerging research topic, with challenges distinct from the MV paradigm, many aspects require further articulation and development. This work focuses on three core facets. First, aligning with prominent voices in the field, we emphasize the importance of data structures able to accommodate the operational complexity of tensor arithmetic. However, we describe a linearized coordinate (LCO) data structure that provides faster and more memory-efficient sorting performance in support of t...

High Performance Rearrangement and Multiplication Routines for Sparse Tensor Arithmetic