Fast CUDA SGEMM from Scratch

Step-by-step optimization of matrix multiplication, implemented in CUDA. For an explanation of each kernel, see siboehm.com/CUDA-MMM.

Overview

Running the kernels on a NVIDIA 3070 (Ampere):

GFLOPs at matrix size 4096x4096:

Kernel	GFLOPs/s	Performance relative to cuBLAS
1: Naive	172.8	1.3%
2: GMEM Coalescing	1226.4	9.5%
3: SMEM Caching	1701.4	13.2%
4: 1D Blocktiling	5071.8	39.2%
9: Autotuning	9575.8	74.0%
7: Avoid Bank Conflicts (Linearize)	10027.5	77.5%
5: 2D Blocktiling	10142.7	78.4%
8: Avoid Bank Conflicts (Offset)	10323.8	79.8%
6: Vectorized Mem Access	11558.7	89.3%
10: Warptiling	12550.6	97.0%
0: cuBLAS	12936.8	100.0%

Setup

1. Install dependencies: CUDA toolkit 12, Python (+ Seaborn), CMake, Ninja. See environment.yml.
2. Configure NVCC compilation parameters. Look up your GPUs compute capability here. Then configure the CMakeLists.txt and change:

   set(CUDA_COMPUTE_CAPABILITY 80)

3. Build: mkdir build && cd build && cmake .. && cmake --build .
4. Run one of the kernels: DEVICE=<device_id> ./sgemm <kernel number>
5. Profiling via NVIDIA Nsight Compute (ncu): make profile KERNEL=<kernel number>

Credit goes to wangzyon/NVIDIA_SGEMM_PRACTICE for the benchmarking setup.