ソースコード

mix new nx_sgemm_bench_openblas

mix.exs

defmodule NxSgemmBenchOpenblas.MixProject do
  use Mix.Project

  def project do
    [
      app: :nx_sgemm_bench_openblas,
      version: "0.1.0",
      elixir: "~> 1.17",
      start_permanent: Mix.env() == :prod,
      deps: deps()
    ]
  end

  # Run "mix help compile.app" to learn about applications.
  def application do
    [
      extra_applications: [:logger]
    ]
  end

  # Run "mix help deps" to learn about dependencies.
  defp deps do
    [
      # {:dep_from_hexpm, "~> 0.3.0"},
      # {:dep_from_git, git: "https://github.com/elixir-lang/my_dep.git", tag: "0.1.0"}
      {:nx_sgemm, github: "zacky1972/nx_sgemm", branch: "main"},
      {:benchee, "~> 1.0", only: :dev}
    ]
  end
end

mix deps.get 
mix compile

benchmark.exs

Benchee.run(
  %{
    "Nx" => fn input -> Nx.multiply(input, 2.0) end,
    "AppleBLAS" => fn input -> NxSgemm.multiply(input, 2.0) end
  },
  inputs: %{
    "Small" => Nx.iota({1_000}) |> Nx.multiply(1.0),
    "Medium" => Nx.iota({10_000}) |> Nx.multiply(1.0),
    "Bigger" => Nx.iota({100_000}) |> Nx.multiply(1.0)
  }
)

M3 Max

 % mix run -r benchmark.exs 
Compiling 1 file (.ex)
Generated nx_sgemm_bench_openblas app
Operating System: macOS
CPU Information: Apple M3 Max
Number of Available Cores: 16
Available memory: 128 GB
Elixir 1.18.1
Erlang 27.2
JIT enabled: true

Benchmark suite executing with the following configuration:
warmup: 2 s
time: 5 s
memory time: 0 ns
reduction time: 0 ns
parallel: 1
inputs: Bigger, Medium, Small
Estimated total run time: 42 s

Benchmarking AppleBLAS with input Bigger ...
Benchmarking AppleBLAS with input Medium ...
Benchmarking AppleBLAS with input Small ...
Benchmarking Nx with input Bigger ...
Benchmarking Nx with input Medium ...
Benchmarking Nx with input Small ...
Calculating statistics...
Formatting results...

##### With input Bigger #####
Name                ips        average  deviation         median         99th %
AppleBLAS      117.31 K     0.00852 ms    ±57.49%     0.00833 ms     0.00946 ms
Nx               0.22 K        4.55 ms     ±2.98%        4.53 ms        4.95 ms

Comparison: 
AppleBLAS      117.31 K
Nx               0.22 K - 533.68x slower +4.54 ms

##### With input Medium #####
Name                ips        average  deviation         median         99th %
AppleBLAS      847.03 K        1.18 μs  ±1350.98%        1.08 μs        1.67 μs
Nx               2.62 K      381.30 μs     ±8.84%      375.92 μs      456.28 μs

Comparison: 
AppleBLAS      847.03 K
Nx               2.62 K - 322.97x slower +380.12 μs

##### With input Small #####
Name                ips        average  deviation         median         99th %
AppleBLAS        3.61 M        0.28 μs  ±6998.25%        0.21 μs        2.88 μs
Nx             0.0255 M       39.19 μs     ±8.26%       38.04 μs       50.75 μs

Comparison: 
AppleBLAS        3.61 M
Nx             0.0255 M - 141.41x slower +38.92 μs

M4 Pro

% mix run -r benchmark.exs
Compiling 1 file (.ex)
Generated nx_sgemm_bench_openblas app
Operating System: macOS
CPU Information: Apple M4 Pro
Number of Available Cores: 14
Available memory: 64 GB
Elixir 1.18.1
Erlang 27.2
JIT enabled: true

Benchmark suite executing with the following configuration:
warmup: 2 s
time: 5 s
memory time: 0 ns
reduction time: 0 ns
parallel: 1
inputs: Bigger, Medium, Small
Estimated total run time: 42 s

Benchmarking AppleBLAS with input Bigger ...
Benchmarking AppleBLAS with input Medium ...
Benchmarking AppleBLAS with input Small ...
Benchmarking Nx with input Bigger ...
Benchmarking Nx with input Medium ...
Benchmarking Nx with input Small ...
Calculating statistics...
Formatting results...

##### With input Bigger #####
Name                ips        average  deviation         median         99th %
AppleBLAS      114.53 K     0.00873 ms    ±48.09%     0.00871 ms     0.00933 ms
Nx               0.26 K        3.78 ms     ±5.49%        3.76 ms        4.28 ms

Comparison: 
AppleBLAS      114.53 K
Nx               0.26 K - 433.25x slower +3.77 ms

##### With input Medium #####
Name                ips        average  deviation         median         99th %
AppleBLAS      953.64 K        1.05 μs  ±1650.92%        0.96 μs        1.46 μs
Nx               3.18 K      314.45 μs     ±8.41%      308.79 μs      398.93 μs

Comparison: 
AppleBLAS      953.64 K
Nx               3.18 K - 299.87x slower +313.40 μs

##### With input Small #####
Name                ips        average  deviation         median         99th %
AppleBLAS        3.97 M        0.25 μs  ±9895.77%        0.21 μs        2.54 μs
Nx             0.0321 M       31.11 μs     ±6.25%       31.63 μs       36.13 μs

Comparison: 
AppleBLAS        3.97 M
Nx             0.0321 M - 123.49x slower +30.86 μs

結果

BLAS	Apple Silicon	1,000	10,000	100,000
OpenBLAS	M3 Max	3.500	0.65210	0.01073
OpenBLAS	M4 Pro	4.070	0.77427	0.01219
AppleBLAS	M3 Max	3.610	0.84703	0.11731
AppleBLAS	M4 Pro	3.970	0.95364	0.11453
Apple/OpenBLAS	M3 Max	1.031	1.29893	10.9329
Apple/OpenBLAS	M4 Pro	0.975	1.23166	9.3954

考察

AppleBLASはOpenBLASに比べてApple Siliconにチューニングされているようです．ベクトルの要素数が大きくなると飛躍的に差が広がります．

M1からM3については非公開のAMX命令を搭載していますので，今回評価したSSCALについても，AMX命令を用いていてもおかしくなさそうな結果です．仮にそうだとすると，M4でもAMX命令を用いているか，SME命令とAMX命令の効果は同等程度という仮説が成り立ちそうです．