Advanced Matrix Multiplication Optimization on Modern Multi-Core Processors
a day ago
- #high-performance-computing
- #matrix-multiplication
- #optimization
- The blog post discusses optimizing FP32 matrix multiplication on modern multi-core processors using FMA3 and AVX2 instructions.
- Performance tuning requires adjusting hyperparameters like thread count, kernel size, and tile sizes for peak performance.
- BLAS libraries may outperform custom implementations on AVX-512 CPUs due to specialized instructions.
- Matrix multiplication is fundamental in neural networks, often relying on optimized BLAS libraries like Intel MKL, OpenBLAS, or BLIS.
- The implementation focuses on pure C code without assembly, targeting broad x86-64 processor compatibility.
- Key optimization techniques include kernel design, cache blocking, and SIMD instruction utilization.
- The kernel function computes sub-matrices efficiently, leveraging outer product and rank-1 updates.
- Cache blocking minimizes memory access by dividing matrices into smaller blocks that fit into CPU cache levels.
- Multithreading is applied to both arithmetic operations and matrix packing to maximize CPU core utilization.
- Performance metrics are measured in FLOPS, with theoretical limits based on CPU clock speed and core count.