Advanced Matrix Multiplication Optimization on Multi-Core Processors (2024) (salykova.github.io)

A new blog post and accompanying sgemm.c implement a fast, portable FP32 matrix-multiply (sgemm) in pure C that leverages FMA3 and AVX2 to deliver strong single- and multi-threaded performance across modern x86-64 CPUs. The author follows high-level designs from GotoBLAS/BLIS to build a register-blocked micro-kernel that computes small m_R × n_R subblocks (accumulators) via outer-product rank-1 updates, keeping accumulators in YMM registers and using VFMADD231PS FMA instructions to maximize compute. The code deliberately omits AVX-512 so it runs broadly on CPUs without AVX-512 support; performance comparisons are shown for Intel Core Ultra 265 and AMD Ryzen 7 9700X, with benchmarks up to 10k square matrices and reproducible settings provided. Technically, the write-up explains memory-hierarchy-aware tiling, column-major layout, and how the kernel reduces memory traffic from 2K per output element to (m_R + n_R)K for a subblock. It also quantifies theoretical limits (YMM holds 8 floats; FMA throughput ~0.5 cycles → ~32 FLOP/cycle per core) and describes practical benchmarking (GCC flags, OpenBLAS comparison, repeat/median timing). The takeaway for ML/AI practitioners: you can implement competitive, portable matmul in plain C using AVX2+FMA, but reaching peak throughput requires careful tuning of threads, kernel and tile sizes, and on AVX-512 hardware tuned BLAS may still outperform a generic AVX2-only implementation.