  We introduce Stream-K, a work-centric parallelization of matrix
multiplication (GEMM) and related computations in dense linear algebra. Whereas
contemporary decompositions are primarily tile-based, our method operates by
partitioning an even share of the aggregate inner loop iterations among
physical processing elements. This provides a near-perfect utilization of
computing resources, regardless of how efficiently the output tiling for any
given problem quantizes across the underlying processing elements.
  On GPU processors, our Stream-K parallelization of GEMM produces a peak
speedup of up to 14$\times$ and 6.7$\times$, and an average performance
response that is both higher and more consistent across 32,824 GEMM problem
geometries than state-of-the-art math libraries such as CUTLASS and cuBLAS.
Furthermore, we achieve this performance from a single tile size configuration
per floating-point precision, whereas today's math libraries employ complex
kernel-selection heuristics to select from a large ensemble of kernel variants.
