spECK: Accelerating GPU Sparse MatrixMatrix Multiplication Through Lightweight Analysis Sparse general matrixmatrix multiplication on GPUs is challenging due to the varying sparsity patterns of sparse matrices. Existing solutions achieve good performance for certain types of matrices, but fail to accelerate all kinds of matrices in the same manner. Our approach combines multiple strategies with dynamic parameter selection to dynamically choose and tune the best fitting algorithm for each row of the matrix. This choice is supported by a lightweight, multilevel matrix analysis, which carefully balances between analysis cost and expected performance gains. Our evaluation on thousands of matrices with various characteristics shows that we outperform all existing solutions in 85% of the cases and that we achieve the second best performance in 12%. Over the entire data set, our solution is on average twice as fast as the second best approach and up to 25times faster than other stateoftheart GPU implementations. Using our approach, applications can expect the best performance independent of the matrices they work on.NMathias PargerGraz University of TechnologyMartin WinterGraz University of Technology, AustriaDaniel Mlakar

Towards HalfPrecision Computation for Complex Matrices: A Case Study for Mixed Precision Solvers on GPUs The use of lowprecision computations is popular in accelerating machine learning and artificial intelligence (AI) applications. Hardware architectures, such as highend graphics processing units (GPUs), now support native 16bit floatingpoint arithmetic (i.e., halfprecision). While half precision provides a natural 2xc3x974xc3x97 speedup against the performance of singledouble precisions, respectively, modern GPUs are equipped with hard ware accelerators that further boost the FP16 performance. These accelerators, known as tensor cores (TCs), have a theoretical peak performance that is 8xc3x9716xc3x97 faster than FP32FP64 performance, respectively. Such a high level of performance has encouraged researchers to harness the compute power of TCs outside AI applications. This paper presents a mixedprecision dense linear solver (Ax  b) for complex matrices using the GPUxe2x80x99s TC units. Unlike similar efforts that have discussed accelerating Ax  b in real FP16 arithmetic, this paper focuses on complex FP16 precisions. The developed solution uses a xe2x80x9chalfcomplexxe2x80x9d pre cision to accelerate the solution of Ax  b while maintaining complex FP32 precision accuracy. The proposed solver requires the development of a highperformance mixedprecision ma trix multiplication (CGEMMFP16) that accepts halfcomplex inputs, and uses the TCsxe2x80x99 fullprecision products and FP32 accumulations for the computation. We discuss two designs and their performance. Similar to the way fast GEMMs power the performance of LAPACK, the mixedprecision CGEMM FP16 can enable the development of mixedprecision LAPACK algorithms. We illustrate this by integrating both CGEMMFP16s into the development of mixedprecision LU factorizations of complex matrices. Finally, an iterative refinement solver is used to deliver complex FP32 accuracy using a preconditioned GMRES solver. Our experiments, conducted on V100 GPUs, show that the mixedprecision solver can be up to 2.5xc3x97 faster than a full singlecomplex precision solver.