SIMD Kernel Implementation Note

The SIMD backend contains explicit AVX/NEON dense matrix kernels and fallback paths for platforms without those instruction sets.

Public Entry Point

num::matmul(A, B, C, num::Backend::simd);

The dispatch path is:

num::matmul
  -> num::backends::opt::matmul

Implementation Location

src/core/backends/opt/matrix.cpp
src/core/backends/simd/impl.hpp

The optimized backend is private to the library. Users select it with the Backend enum rather than including implementation headers.

Kernel Role

The SIMD path is the custom dense-kernel counterpart to BLAS:

num::matmul(A, B, C, num::Backend::simd);  // custom SIMD path
num::matmul(A, B, C, num::Backend::blas);  // system BLAS path

Use it for:

• benchmarking the custom kernel against BLAS,
• validating the blocked/register-blocked implementations,
• running without an external BLAS.

FFT SIMD Backend

The spectral module has independent FFT backends:

num::spectral::fft(x, X, num::spectral::FFTBackend::simd);
num::spectral::fft(x, X, num::spectral::FFTBackend::stdsimd);
num::spectral::fft(x, X, num::spectral::FFTBackend::fftw);

Those are separate from the dense matrix Backend::simd path.

Benchmark

./build/benchmarks/numerics_bench --benchmark_filter="BM_Matmul|BM_FFT"