[CPU - Linux] AVX SIMD backend for fp16 and bf16 matmul

[acsweet]

Proposed changes

This PR adds an AVX SIMD backend for fp16 and bf16 matmul (GEMM and GEMV) on CPU for Linux. Follows from the discussion in #2037, and is a precursor to adding the full set of AVX SIMD instructions in a follow-up PR. Let me know what you think, I'd appreciate any feedback (including adjustments to benchmarking methodology).

I modified the bench_gemm.py and bench_gemv.py in benchmarks/python/blas so they'd complete in a reasonable amount of time. I ran them with a build of mlx from this PR and against the official mlx release for comparison. Note I left out the other dtypes from the benchmarked results printed below due to potential build differences (could be an error on my part). I built mlx with:

CMAKE_ARGS="-DMLX_BUILD_CPU=ON -DMLX_BUILD_CUDA=OFF -DBLAS_INCLUDE_DIRS=/usr/include/openblas -DLAPACK_INCLUDE_DIRS=/usr/include/openblas" CMAKE_BUILD_PARALLEL_LEVEL=8 pip install .

Bench setup

• OS: Arch Linux, kernel 6.18.9-arch1-2 x86_64
• CPU: Intel Core i7-10700K
• mlx baseline: mlx-cpu==0.31.2
• torch comparison: torch==2.5.1+cpu
• benchmark commands:

python benchmarks/python/blas/bench_gemm.py --quick --verbose --single-threaded
python benchmarks/python/blas/bench_gemv.py --quick --verbose --single-threaded

Bench results

GEMM - branch (this PR)

B	M	N	K	dtype	t	torch_gf	mlx_gf	diff
16	234	768	3072	float16	nn	1.510	93.479	+6091.42%
1	1024	1024	2048	float16	nn	1.103	82.306	+7362.47%
16	234	768	3072	float16	nt	2.319	91.380	+3840.00%
1	1024	1024	2048	float16	nt	2.318	81.883	+3431.84%
16	234	768	3072	float16	tn	4.056	95.101	+2244.59%
1	1024	1024	2048	float16	tn	4.073	83.882	+1959.25%

GEMM - mlx-cpu==0.31.2

B	M	N	K	dtype	t	torch_gf	mlx_gf	diff
16	234	768	3072	float16	nn	1.623	3.641	+124.27%
1	1024	1024	2048	float16	nn	1.511	3.645	+141.26%
16	234	768	3072	float16	nt	2.320	3.884	+67.40%
1	1024	1024	2048	float16	nt	2.317	3.878	+67.42%
16	234	768	3072	float16	tn	4.067	3.532	-13.15%
1	1024	1024	2048	float16	tn	4.080	3.459	-15.22%

GEMV - branch (this PR)

============================================================
gemv | float16 | device: cpu
============================================================
--- sweep out_vec_len (fixed in_vec_len) ---
     in,   out,   mlx_GB/s,  trc_GB/s,    diff
  in=  512, out=  128, mlx=   8.92 GB/s, torch=   1.66 GB/s, diff=+436.2%
  in=  512, out= 1024, mlx=  21.82 GB/s, torch=   1.89 GB/s, diff=+1055.4%
  in=  512, out= 4096, mlx=  26.47 GB/s, torch=   1.88 GB/s, diff=+1306.6%
  in=  512, out=11008, mlx=  16.17 GB/s, torch=   1.63 GB/s, diff=+892.2%
     in,   out,   mlx_GB/s,  trc_GB/s,    diff
  in= 2048, out=  128, mlx=  26.23 GB/s, torch=   1.83 GB/s, diff=+1330.2%
  in= 2048, out= 1024, mlx=  30.29 GB/s, torch=   1.53 GB/s, diff=+1882.1%
  in= 2048, out= 4096, mlx=  20.94 GB/s, torch=   1.85 GB/s, diff=+1033.7%
  in= 2048, out=11008, mlx=  18.57 GB/s, torch=   1.59 GB/s, diff=+1070.8%
--- sweep in_vec_len (fixed out_vec_len) ---
     in,   out,   mlx_GB/s,  trc_GB/s,    diff
  in=  128, out=  512, mlx=  12.20 GB/s, torch=   1.23 GB/s, diff=+895.1%
  in= 1024, out=  512, mlx=  29.48 GB/s, torch=   1.75 GB/s, diff=+1585.6%
  in= 4096, out=  512, mlx=  25.17 GB/s, torch=   1.66 GB/s, diff=+1413.1%
  in=11008, out=  512, mlx=  39.61 GB/s, torch=   1.75 GB/s, diff=+2167.0%
     in,   out,   mlx_GB/s,  trc_GB/s,    diff
  in=  128, out= 2048, mlx=  20.01 GB/s, torch=   2.21 GB/s, diff=+803.5%
  in= 1024, out= 2048, mlx=  34.55 GB/s, torch=   2.29 GB/s, diff=+1410.6%
  in= 4096, out= 2048, mlx=  16.50 GB/s, torch=   2.08 GB/s, diff=+692.2%
  in=11008, out= 2048, mlx=  19.15 GB/s, torch=   1.91 GB/s, diff=+900.7%


============================================================
gemv_t | float16 | device: cpu
============================================================
--- sweep out_vec_len (fixed in_vec_len) ---
     in,   out,   mlx_GB/s,  trc_GB/s,    diff
  in=  512, out=  128, mlx=   6.97 GB/s, torch=   1.77 GB/s, diff=+294.4%
  in=  512, out= 1024, mlx=  13.19 GB/s, torch=   0.95 GB/s, diff=+1290.3%
  in=  512, out= 4096, mlx=  15.76 GB/s, torch=   0.81 GB/s, diff=+1839.1%
  in=  512, out=11008, mlx=  12.32 GB/s, torch=   0.95 GB/s, diff=+1193.0%
     in,   out,   mlx_GB/s,  trc_GB/s,    diff
  in= 2048, out=  128, mlx=  10.15 GB/s, torch=   0.85 GB/s, diff=+1099.1%
  in= 2048, out= 1024, mlx=  13.90 GB/s, torch=   0.87 GB/s, diff=+1499.0%
  in= 2048, out= 4096, mlx=  12.03 GB/s, torch=   0.55 GB/s, diff=+2090.4%
  in= 2048, out=11008, mlx=  16.71 GB/s, torch=   1.43 GB/s, diff=+1066.2%
--- sweep in_vec_len (fixed out_vec_len) ---
     in,   out,   mlx_GB/s,  trc_GB/s,    diff
  in=  128, out=  512, mlx=  11.21 GB/s, torch=   2.00 GB/s, diff=+460.8%
  in= 1024, out=  512, mlx=  14.76 GB/s, torch=   1.17 GB/s, diff=+1161.1%
  in= 4096, out=  512, mlx=  17.52 GB/s, torch=   1.16 GB/s, diff=+1412.8%
  in=11008, out=  512, mlx=  15.96 GB/s, torch=   1.07 GB/s, diff=+1385.2%
     in,   out,   mlx_GB/s,  trc_GB/s,    diff
  in=  128, out= 2048, mlx=  16.26 GB/s, torch=   1.27 GB/s, diff=+1180.0%
  in= 1024, out= 2048, mlx=  22.60 GB/s, torch=   1.41 GB/s, diff=+1502.3%
  in= 4096, out= 2048, mlx=  16.50 GB/s, torch=   0.58 GB/s, diff=+2748.3%
  in=11008, out= 2048, mlx=  18.33 GB/s, torch=   0.43 GB/s, diff=+4210.5%

GEMV - mlx-cpu==0.31.2

============================================================
gemv | float16 | device: cpu
============================================================
--- sweep out_vec_len (fixed in_vec_len) ---
     in,   out,   mlx_GB/s,  trc_GB/s,    diff
  in=  512, out=  128, mlx=   1.06 GB/s, torch=   2.13 GB/s, diff=-50.2%
  in=  512, out= 1024, mlx=   1.15 GB/s, torch=   2.23 GB/s, diff=-48.5%
  in=  512, out= 4096, mlx=   1.17 GB/s, torch=   2.24 GB/s, diff=-48.1%
  in=  512, out=11008, mlx=   1.11 GB/s, torch=   2.20 GB/s, diff=-49.6%
     in,   out,   mlx_GB/s,  trc_GB/s,    diff
  in= 2048, out=  128, mlx=   0.94 GB/s, torch=   2.22 GB/s, diff=-57.7%
  in= 2048, out= 1024, mlx=   0.97 GB/s, torch=   2.25 GB/s, diff=-57.0%
  in= 2048, out= 4096, mlx=   0.97 GB/s, torch=   2.20 GB/s, diff=-56.2%
  in= 2048, out=11008, mlx=   0.96 GB/s, torch=   2.20 GB/s, diff=-56.5%
--- sweep in_vec_len (fixed out_vec_len) ---
     in,   out,   mlx_GB/s,  trc_GB/s,    diff
  in=  128, out=  512, mlx=   1.06 GB/s, torch=   2.01 GB/s, diff=-47.3%
  in= 1024, out=  512, mlx=   1.06 GB/s, torch=   2.25 GB/s, diff=-53.0%
  in= 4096, out=  512, mlx=   0.83 GB/s, torch=   2.26 GB/s, diff=-63.5%
  in=11008, out=  512, mlx=   0.58 GB/s, torch=   2.21 GB/s, diff=-73.6%
     in,   out,   mlx_GB/s,  trc_GB/s,    diff
  in=  128, out= 2048, mlx=   1.18 GB/s, torch=   2.15 GB/s, diff=-45.1%
  in= 1024, out= 2048, mlx=   1.08 GB/s, torch=   2.25 GB/s, diff=-51.8%
  in= 4096, out= 2048, mlx=   0.83 GB/s, torch=   2.25 GB/s, diff=-63.3%
  in=11008, out= 2048, mlx=   0.58 GB/s, torch=   2.20 GB/s, diff=-73.5%

============================================================
gemv_t | float16 | device: cpu
============================================================
--- sweep out_vec_len (fixed in_vec_len) ---
     in,   out,   mlx_GB/s,  trc_GB/s,    diff
  in=  512, out=  128, mlx=   1.01 GB/s, torch=   1.70 GB/s, diff=-40.6%
  in=  512, out= 1024, mlx=   0.90 GB/s, torch=   1.42 GB/s, diff=-36.4%
  in=  512, out= 4096, mlx=   0.92 GB/s, torch=   1.57 GB/s, diff=-41.2%
  in=  512, out=11008, mlx=   0.96 GB/s, torch=   1.90 GB/s, diff=-49.3%
     in,   out,   mlx_GB/s,  trc_GB/s,    diff
  in= 2048, out=  128, mlx=   0.87 GB/s, torch=   1.40 GB/s, diff=-38.1%
  in= 2048, out= 1024, mlx=   0.81 GB/s, torch=   1.42 GB/s, diff=-43.1%
  in= 2048, out= 4096, mlx=   0.56 GB/s, torch=   0.68 GB/s, diff=-18.4%
  in= 2048, out=11008, mlx=   0.78 GB/s, torch=   1.55 GB/s, diff=-49.6%
--- sweep in_vec_len (fixed out_vec_len) ---
     in,   out,   mlx_GB/s,  trc_GB/s,    diff
  in=  128, out=  512, mlx=   1.04 GB/s, torch=   2.09 GB/s, diff=-50.0%
  in= 1024, out=  512, mlx=   0.87 GB/s, torch=   1.44 GB/s, diff=-39.1%
  in= 4096, out=  512, mlx=   0.70 GB/s, torch=   1.42 GB/s, diff=-50.4%
  in=11008, out=  512, mlx=   0.39 GB/s, torch=   1.18 GB/s, diff=-66.7%
     in,   out,   mlx_GB/s,  trc_GB/s,    diff
  in=  128, out= 2048, mlx=   0.92 GB/s, torch=   1.53 GB/s, diff=-40.0%
  in= 1024, out= 2048, mlx=   0.88 GB/s, torch=   1.57 GB/s, diff=-44.2%
  in= 4096, out= 2048, mlx=   0.49 GB/s, torch=   0.58 GB/s, diff=-14.9%
  in=11008, out= 2048, mlx=   0.31 GB/s, torch=   0.41 GB/s, diff=-25.2%

Checklist

Put an x in the boxes that apply.

• I have read the CONTRIBUTING document
• I have run pre-commit run --all-files to format my code / installed pre-commit prior to committing changes
• I have added tests that prove my fix is effective or that my feature works
• I have updated the necessary documentation (if needed)

[zcbenz]

@dhiltgen I remember ollama was doing something similar? Can you please check if this would live together with your work?