SGEMM on Apple Silicon

This project is largely educational -- I want to learn how to write fast matrix multiplication operations for the Apple Silicon CPU and GPU.

To begin, I will follow Aman Salykov's excellent tutorials on accelerating matrix multiplication routines on x86 CPUs and NVIDIA GPUs, largely just translating to the SIMD and GPGPU interfaces available on Apple Silicon.

Hardware requirements

These programs run on Apple Silicon devices (M1 / M2 / M3 macbook pro / macbook air / mac studio / mac pro).

Software requirements

CMake

The easiest way to install CMake on MacOS is via homebrew

brew install cmake

OpenMP

Apple does not ship the dynamic library needed to support OpenMP at runtime, however, the clang compiler that ships with xcode supports OpenMP (see here for more detail). OpenMP for MacOS can be installed via homebrew

brew install libomp

To detect whether openmp is available at build time, we use a modified version of the LightGBM CMakeLists.txt.

Eigen

Eigen for MacOS can be installed via homebrew.

brew install eigen

We use a similar trick as we used for openmp to detect eigen headers at build time.

Building the projects

CPU

With cmake (and ideally openMP) installed, you can build the CPU-based program matrix multiplication program by running

rm -rf build             
mkdir build
cmake -S . -B build -DOPENMP_FLAG=ON -DDEBUG_FLAG=OFF -DUNITTEST_FLAG=OFF -DASAN_FLAG=OFF -DEIGEN_FLAG=ON -DOMP_NTHREADS=k
cmake --build build

from the project directory at the command line (replace k with the number of threads you intend to use). Then you can run the program with ./build/sgemm_silicon_cpu.

XCode

To generate an Xcode project based on the build targets and specifications defined in a CMakeLists.txt, navigate to the main project folder (i.e. cd /path/to/sgemm_silicon) and run the following commands (replacing k with the desired number of threads you'd like openMP to use):

rm -rf xcode/            
mkdir xcode
cd xcode                                                                               
cmake -G Xcode .. -DCMAKE_C_COMPILER=cc -DCMAKE_CXX_COMPILER=c++ -DOPENMP_FLAG=ON -DDEBUG_FLAG=OFF -DEIGEN_FLAG=ON -DOMP_NTHREADS=k
cd ..

Now, if you navigate to the xcode subfolder (in Finder), you should be able to click on a .xcodeproj file and the project will open in Xcode.