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Sparse matrix-vector multiplication (SpMV) is one of the most importantkernels in high-performance computing (HPC), yet SpMV normally suffers from illperformance on many devices. Due to ill performance, SpMV normally requiresspecial care to store and tune for a given device. Moreover, HPC is facingheterogeneous hardware containing multiple different compute units, e.g.,many-core CPUs and GPUs. Therefore, an emerging goal has been to produceheterogeneous formats and methods that allow critical kernels, e.g., SpMV, tobe executed on different devices with portable performance and minimal changesto format and method. This paper presents a heterogeneous format based on CSR,named CSR-k, that can be tuned quickly and outperforms the average performanceof Intel MKL on Intel Xeon Platinum 8380 and AMD Epyc 7742 CPUs while stilloutperforming NVIDIA's cuSPARSE and Sandia National Laboratories' KokkosKernelson NVIDIA A100 and V100 for regular sparse matrices, i.e., sparse matriceswhere the number of nonzeros per row has a variance $\leq$ 10, such as thosecommonly generated from two and three-dimensional finite difference and elementproblems. In particular, CSR-k achieves this with reordering and by groupingrows into a hierarchical structure of super-rows and super-super-rows that arerepresented by just a few extra arrays of pointers. Due to its simplicity, amodel can be tuned for a device and used to select super-row andsuper-super-rows sizes in constant time.

Heterogeneous Sparse Matrix-Vector Multiplication via Compressed Sparse Row Format