CFUGEMM

CFUGEMM stands for Cache-Friendly Unified General Matrix-Matrix Multiply. It refers to a design approach and family of algorithms for implementing GEMM with a focus on data locality, cache efficiency, and portability across modern hardware platforms. Rather than a single library, CFUGEMM embodies principles and patterns that guide the construction of dense matrix-matrix multiplication routines in high-performance computing and related fields.

Core ideas of CFUGEMM include tiling or blocking to fit submatrices into fast memory elements, careful loop ordering to maximize data reuse, and the use of optimized micro-kernels that leverage vector units. The approach emphasizes a unified treatment of data layouts, blocking factors, and computational kernels, enabling performance to be tuned for different architectures such as CPUs, GPUs, and accelerators. It commonly supports multiple numeric precisions (for example FP32, FP16, and mixed-precision workflows) and can be extended to include fused operations or compatibility with broader BLAS-like interfaces.

In practice, CFUGEMM concepts appear in research papers and in various open-source and proprietary libraries as a methodology rather than a standardized API. Implementations may include auto-tuning to select tile sizes, register tiling, and memory prefetch strategies that best exploit a target platform’s cache hierarchy and bandwidth. The approach is widely used in domains requiring efficient linear algebra, including machine learning, scientific computing, and large-scale simulations.

See also: GEMM, BLAS, cache-friendly algorithms, tiling, micro-kernels.