Stream-K++: Adaptive GPU GEMM Kernel Scheduling and Selection using Bloom Filters

General matrix multiplication (GEMM) operations are crucial in various computational fields. As GPU architectures evolve, optimizing GEMM performance becomes increasingly important. This paper introduces Stream-K++, an enhancement to the promising Stream-K GEMM scheduling algorithm. We expand Stream-K's scheduling policies from three to seven and implement an efficient solution selection mechanism using Bloom filters. Our approach rapidly eliminates up to 95.8% of unsuitable configurations while maintaining a 100% true-negative rate. Implemented using the AMD Composable Kernel library and evaluated on AMD Instinct MI250X GPUs, Stream-K++ demonstrates significant performance gains (up to 43%) in select scenarios. It remains competitive (within 20% of optimal) for 60-97.6% of problem sizes. Our flexible framework, implemented in the Opensieve C++ library, allows for easy adaptation to new problem sizes, scheduling policies, or additional tuning parameters, paving the way for future optimizations in GPU-based GEMM operations.