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 A6000 (Ampere):

GFLOPs at matrix size 4096x4096:

Kernel	GFLOPs/s	Performance relative to cuBLAS
1: Naive	309.0	1.3%
2: GMEM Coalescing	1986.5	8.5%
3: SMEM Caching	2980.3	12.8%
4: 1D Blocktiling	8474.7	36.5%
5: 2D Blocktiling	15971.7	68.7%
7: Avoid Bank Conflicts (Linearize)	16213.4	69.7%
8: Avoid Bank Conflicts (Offset)	16459.2	70.8%
11: Double Buffering	17278.3	74.3%
6: Vectorized Mem Access	18237.3	78.4%
9: Autotuning	19721.0	84.8%
10: Warptiling	21779.3	93.7%
0: cuBLAS	23249.6	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.