LIBLINALG

liblinalg is a lineal algebra library that implements vectors and matrices of variable sizes and operations between them. Uses special instructions like SSE to accelerate those operations.

Project status

The project is now on a stable version with multiple backends and tests but there are things that I want to do:

• AVX512 instruction to accelerate even bigger matrix and vector multiplications.

• Using SIMD instructions for arm machines.

• Double precission matrix and vertices

There are still many operations that are not supported at all by the library like the determinant of a matrix.

Apart from that, when vector and matrix operations missmatch sizes, compilation errors are thrown but aren't readable at all. Would be nice to investigate a way to throw custom compiler errors.

Right now each backend implements all the operations, but for error checking to be cleaner it would be nice to abstract away SIMD to unify a bit operation code.

Documentation about implementation decisions and backend implementation are still left to do.

How to use

Being a header only library, the only thing necessary to use the library is to add all the header files to your project and define the backend. The available backends are the next:

• LIBLINALG_BACKEND_SIMPLE_CPU: backend does not use any special instructions. It's mainly used to compare the performance from what most lineal algebra libraries do.

• LIBLINALG_BACKEND_SIMD_SSE: backend uses SSE instructions to accelerate operations. It's important to use the -msse4.2 flag when compiling. SSE instructions are supported on 98% of the x86 processors.

• LIBLINALG_BACKEND_SIMD_AVX2: backend uses AVX2 instructions to accelerate operations. It's importat to use the -mavx2 flag when compiling.

Performance results

The results of our performance tests on a Ryzen 7 3700X are the next:

vecf<100000> addition... Acceleration factor 1.918
vecf<100000> dot... Acceleration factor 2.282
vecf<100000> multiplication... Acceleration factor 2.473
matf<700, 700> addition... Acceleration factor 3.173
matf<700, 700> multiplication... Acceleration factor 1.082
matf<700, 700> * vecf<700>... Acceleration factor 2.349
vecf<700> * matf<700, 700>... Acceleration factor 2.365

Results are not the best, as the theoretical acceleration factor should de near 4. Matrix * Matrix multiplications are really slow because SSE does not implement gather functions, so a way to read matrix columns with SSE instructions should be investigated.

Contributions

Contributions helping to solve bugs or implementing special matrices or vectors such as those used in computer graphics are welcome! But pull requests implementing backends are going to be ignored as this project is mainly used to learn about SIMD.

For a more detailed overview of how to format or structure issues see the contributing guide.

FAQ

• I just cloned the repository, but executing tests only spits errors. This happens because the scripts that execute the tests expects the bin/ folder to be created. Git does not support pushing empty folders, so for now the solution is to create that folder yourself by executing mkdir bin on the root of the project.