ソースコード

lib/nx_sgemm.ex

defmodule NxSgemm do
  @moduledoc """
  Documentation for `NxSgemm`.
  """
  require Logger

  @on_load :load_nif

  @doc false
  def load_nif do
    nif_file = ~c'#{Application.app_dir(:nx_sgemm, "priv/libnif")}'

    case :erlang.load_nif(nif_file, 0) do
      :ok -> :ok
      {:error, {:reload, _}} -> :ok
      {:error, reason} -> Logger.error("Failed to load NIF: #{inspect(reason)}")
    end
  end

  @doc """
  ok.

  ## Examples

      iex> NxSgemm.ok()
      :ok

  """
  def ok(), do: :erlang.nif_error(:not_loaded)

  @doc """
  Element-wise multiplication of two tensors.

  If a number is given, it is converted to a tensor.

  It will broadcast tensors whenever the dimensions do not match and broadcasting is possible.

  ## Examples

  ### Multiplying scalers

      iex> NxSgemm.multiply(1, 2)
      #Nx.Tensor<
        s32
        2
      >

  ### Multiplying tensors and scalers

      iex> NxSgemm.multiply(Nx.tensor([1, 2, 3], names: [:data], type: :u8), 1)
      #Nx.Tensor<
        u8[data: 3]
        [1, 2, 3]
      >

      iex> NxSgemm.multiply(1, Nx.tensor([1, 2, 3], names: [:data], type: :u8))
      #Nx.Tensor<
        u8[data: 3]
        [1, 2, 3]
      >

      iex> NxSgemm.multiply(Nx.tensor([1.0, 2.0, 3.0], names: [:data], type: :f32), 2.0)
      #Nx.Tensor<
        f32[data: 3]
        [2.0, 4.0, 6.0]
      >

      iex> NxSgemm.multiply(2.0, Nx.tensor([1.0, 2.0, 3.0], names: [:data], type: :f32))
      #Nx.Tensor<
        f32[data: 3]
        [2.0, 4.0, 6.0]
      >
  """
  def multiply(a, b) when is_integer(a) and is_integer(b) do
    Nx.tensor(a * b, type: :s32)
  end

  def multiply(a, b) when is_float(b) do
    case Nx.type(a) do
      {:f, 32} ->
        %{
          a
          | data: %{
            a.data
            | state: mul_nif_f32_tensor_f32_scalar(Nx.size(a), a.data.state, b)
          }
        }
    end
  end

  def multiply(a, b) when is_integer(b) when 0 <= b and b < 256 do
    case Nx.type(a) do
      {:u, 8} ->
        %{
          a
          | data: %{
            a.data
            | state: mul_nif_u8_tensor_u8_scalar(Nx.size(a), a.data.state, b)
          }
        }
    end
  end

  def multiply(a, b) when is_number(a) do
    multiply(b, a)
  end

  defp mul_nif_f32_tensor_f32_scalar(_size, _a, _b), do: raise("NIF mul_nif_f32_tensor_f32_scalar/3 not implemented")
  defp mul_nif_u8_tensor_u8_scalar(_size, _a, _b), do: raise("NIF mul_nif_u8_tensor_u8_scalar/3 not implemented")

  @doc """
  Returns the dot product of two tensors.

  Given `a` and `b`, computes the dot product according to the following rules:

  * If both `a` and `b` are scalars, it is equivalent to `a * b`.
  * If `a` is a scalar and `b` is a tensor, it is equivalent to `Nx.multiply(a, b)`.
  * If `a` is a tensor and `b` is a scalar, it is equivalent to `Nx.multiply(a, b)`.
  * If both `a` and `b` are 1-D tensors (vectors), it is the sum of the element-wise product between `a` and `b`. The lengths of `a` and `b` must be equal.
  * If both `a` and `b` are 2-D tensors (matrices), it is equivalent to matrix-multiplication.
  * If either `a` or `b` is a 1-D tensor, and the other is an n-D tensor, it is the sum of the element-wise product along the last axis of `a` or `b`. The length of the 1-D tensor must match the last dimension of the n-D tensor.
  * If `a` is an n-D tensor and `b` is an m-D tensor, it is the sum of the element-wise product along the last axis of `a` and the second-to-last axis of `b`. The last dimension of `a` must match the second-to-last dimension of `b`.

  ## Examples

      iex> left = Nx.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
      iex> right = Nx.tensor([[7.0, 8.0], [9.0, 10.0], [11.0, 12.0]])
      iex> Nx.dot(left, right)
      #Nx.Tensor<
        f32[2][2]
        [
          [58.0, 64.0],
          [139.0, 154.0]
        ]
      >
  """
  def dot(a, b) do
    case {Nx.type(a), Nx.type(b), Nx.shape(a), Nx.shape(b)} do
      {{:f, 32}, {:f, 32}, {m, n}, {n, o}} ->
        c = Nx.iota({m, o}, type: {:f, 32})

        %{
          c
          | data: %{
            c.data
            | state: dot_nif_f32_matrix_f32_matrix(m, o, n, a.data.state, b.data.state)
          }
        }
    end
  end

  defp dot_nif_f32_matrix_f32_matrix(_m, _o, _n, _a, _b), do: raise("NIF dot_nif_f32_matrix_f32_matrix/5 not implemented")
end

nif_src/libnif.c

#include <erl_nif.h>
#include <stdbool.h>
#include <stdint.h>
#ifdef USE_OPEN_BLAS
#include <cblas.h>
#else // USE_OPEN_BLAS
#include <Accelerate/Accelerate.h>
#endif // USE_OPEN_BLAS

static ERL_NIF_TERM ok(ErlNifEnv *env, int argc, const ERL_NIF_TERM argv[])
{
    return enif_make_atom(env, "ok");
}

static ERL_NIF_TERM mul_nif_f32_tensor_f32_scalar(ErlNifEnv *env, int argc, const ERL_NIF_TERM argv[])
{
    if (__builtin_expect(argc != 3, false)) {
        return enif_make_badarg(env);
    }

    ErlNifUInt64 vec_size;
    if (__builtin_expect(!enif_get_uint64(env, argv[0], &vec_size), false)) {
        return enif_make_badarg(env);
    }

    ERL_NIF_TERM binary_term = argv[1];
    ErlNifBinary in_data;
    if (__builtin_expect(!enif_inspect_binary(env, binary_term, &in_data), false)) {
        return enif_make_badarg(env);
    }

    ERL_NIF_TERM double_term = argv[2];
    double factor;
    if (__builtin_expect(!enif_get_double(env, double_term, &factor), false)) {
        return enif_make_badarg(env);
    }

    float *in = (float *)in_data.data;
    ErlNifBinary out_data;
    if (__builtin_expect(!enif_alloc_binary(vec_size * sizeof(float), &out_data), false)) {
        return enif_make_badarg(env);
    }

    float *out = (float *)out_data.data;

    cblas_scopy((int)vec_size, in, 1, out, 1);
    cblas_sscal((int)vec_size, (float) factor, out, 1);

    return enif_make_binary(env, &out_data);
}

static ERL_NIF_TERM mul_nif_u8_tensor_u8_scalar(ErlNifEnv *env, int argc, const ERL_NIF_TERM argv[])
{
    if (__builtin_expect(argc != 3, false)) {
        return enif_make_badarg(env);
    }

    ErlNifUInt64 vec_size;
    if (__builtin_expect(!enif_get_uint64(env, argv[0], &vec_size), false)) {
        return enif_make_badarg(env);
    }

    ERL_NIF_TERM binary_term = argv[1];
    ErlNifBinary in_data;
    if (__builtin_expect(!enif_inspect_binary(env, binary_term, &in_data), false)) {
        return enif_make_badarg(env);
    }

    ERL_NIF_TERM uint_term = argv[2];
    unsigned int factor;
    if (__builtin_expect(!enif_get_uint(env, uint_term, &factor), false)) {
        return enif_make_badarg(env);
    }

    uint8_t *in = (uint8_t *)in_data.data;
    ErlNifBinary out_data;
    if (__builtin_expect(!enif_alloc_binary(vec_size * sizeof(uint8_t), &out_data), false)) {
        return enif_make_badarg(env);
    }

    uint8_t *out = (uint8_t *)out_data.data;

    for(ErlNifUInt64 i = 0; i < vec_size; i++) {
        out[i] = (uint8_t) (in[i] * factor); 
    }

    return enif_make_binary(env, &out_data);
}

static ERL_NIF_TERM dot_nif_f32_matrix_f32_matrix(ErlNifEnv *env, int argc, const ERL_NIF_TERM argv[])
{
    if (__builtin_expect(argc != 5, false)) {
        return enif_make_badarg(env);
    }

    ErlNifUInt64 m;
    if (__builtin_expect(!enif_get_uint64(env, argv[0], &m), false)) {
        return enif_make_badarg(env);
    }

    ErlNifUInt64 o;
    if (__builtin_expect(!enif_get_uint64(env, argv[1], &o), false)) {
        return enif_make_badarg(env);
    }

    ErlNifUInt64 n;
    if (__builtin_expect(!enif_get_uint64(env, argv[2], &n), false)) {
        return enif_make_badarg(env);
    }

    ERL_NIF_TERM binary_term_a = argv[3];
    ErlNifBinary a_data;
    if (__builtin_expect(!enif_inspect_binary(env, binary_term_a, &a_data), false)) {
        return enif_make_badarg(env);
    }
    float *a = (float *)a_data.data;

    ERL_NIF_TERM binary_term_b = argv[4];
    ErlNifBinary b_data;
    if (__builtin_expect(!enif_inspect_binary(env, binary_term_b, &b_data), false)) {
        return enif_make_badarg(env);
    }
    float *b = (float *)b_data.data;

    ErlNifBinary c_data;
    if (__builtin_expect(!enif_alloc_binary(m * o * sizeof(float), &c_data), false)) {
        return enif_make_badarg(env);
    }
    float *c = (float *)c_data.data;

    cblas_sgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, m, o, n, 1.0, a, n, b, o, 0.0, c, o);

    return enif_make_binary(env, &c_data);
}

static ErlNifFunc nif_funcs [] =
{
    {"ok", 0, ok},
    {"mul_nif_f32_tensor_f32_scalar", 3, mul_nif_f32_tensor_f32_scalar},
    {"mul_nif_u8_tensor_u8_scalar", 3, mul_nif_u8_tensor_u8_scalar},
    {"dot_nif_f32_matrix_f32_matrix", 5, dot_nif_f32_matrix_f32_matrix}
};

ERL_NIF_INIT(Elixir.NxSgemm, nif_funcs, NULL, NULL, NULL, NULL)

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

gemm_benchmark.exs

Benchee.run(
  %{
    "Nx(dot)" => fn input -> Nx.dot(input, input) end,
    "BLAS(dot)" => fn input -> NxSgemm.dot(input, input) end
  },
  inputs: %{
    "Small" => Nx.iota({10, 10}) |> Nx.multiply(1.0),
    "Medium" => Nx.iota({100, 100}) |> Nx.multiply(1.0),
    "Bigger" => Nx.iota({500, 500}) |> Nx.multiply(1.0)
  }
)

mix deps.clean --all
mix deps.get
mix compile
mix run -r gemm_benchmark.exs
mix deps.clean --all
mix deps.get
export USE_OPEN_BLAS=true
mix compile
mix run -r gemm_benchmark.exs

M3 Max / AppleBLAS

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 BLAS(dot) with input Bigger ...
Benchmarking BLAS(dot) with input Medium ...
Benchmarking BLAS(dot) with input Small ...
Benchmarking Nx(dot) with input Bigger ...
Benchmarking Nx(dot) with input Medium ...
Benchmarking Nx(dot) with input Small ...
Calculating statistics...
Formatting results...

##### With input Bigger #####
Name                ips        average  deviation         median         99th %
BLAS(dot)         92.56       0.0108 s    ±13.35%       0.0112 s       0.0140 s
Nx(dot)          0.0323        30.95 s     ±0.00%        30.95 s        30.95 s

Comparison: 
BLAS(dot)         92.56
Nx(dot)          0.0323 - 2865.16x slower +30.94 s

##### With input Medium #####
Name                ips        average  deviation         median         99th %
BLAS(dot)        4.02 K        0.25 ms     ±2.98%        0.25 ms        0.27 ms
Nx(dot)        0.0121 K       82.94 ms     ±1.26%       82.71 ms       86.31 ms

Comparison: 
BLAS(dot)        4.02 K
Nx(dot)        0.0121 K - 333.40x slower +82.69 ms

##### With input Small #####
Name                ips        average  deviation         median         99th %
BLAS(dot)      360.76 K        2.77 μs   ±278.59%        2.58 μs        3.71 μs
Nx(dot)          9.95 K      100.50 μs     ±6.34%       99.04 μs      120.42 μs

Comparison: 
BLAS(dot)      360.76 K
Nx(dot)          9.95 K - 36.26x slower +97.73 μs

M3 Max / OpenBLAS

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 BLAS(dot) with input Bigger ...
Benchmarking BLAS(dot) with input Medium ...
Benchmarking BLAS(dot) with input Small ...
Benchmarking Nx(dot) with input Bigger ...
Benchmarking Nx(dot) with input Medium ...
Benchmarking Nx(dot) with input Small ...
Calculating statistics...
Formatting results...

##### With input Bigger #####
Name                ips        average  deviation         median         99th %
BLAS(dot)         89.98       0.0111 s    ±11.51%       0.0107 s       0.0132 s
Nx(dot)          0.0322        31.03 s     ±0.00%        31.03 s        31.03 s

Comparison: 
BLAS(dot)         89.98
Nx(dot)          0.0322 - 2792.50x slower +31.02 s

##### With input Medium #####
Name                ips        average  deviation         median         99th %
BLAS(dot)        2.83 K        0.35 ms     ±6.36%        0.35 ms        0.40 ms
Nx(dot)        0.0121 K       82.45 ms     ±3.41%       81.80 ms      101.45 ms

Comparison: 
BLAS(dot)        2.83 K
Nx(dot)        0.0121 K - 233.64x slower +82.10 ms

##### With input Small #####
Name                ips        average  deviation         median         99th %
BLAS(dot)      365.96 K        2.73 μs   ±263.40%        2.54 μs        3.71 μs
Nx(dot)          9.86 K      101.39 μs     ±9.45%       98.46 μs      134.08 μs

Comparison: 
BLAS(dot)      365.96 K
Nx(dot)          9.86 K - 37.10x slower +98.66 μs

M4 Pro / AppleBLAS

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 BLAS(dot) with input Bigger ...
Benchmarking BLAS(dot) with input Medium ...
Benchmarking BLAS(dot) with input Small ...
Benchmarking Nx(dot) with input Bigger ...
Benchmarking Nx(dot) with input Medium ...
Benchmarking Nx(dot) with input Small ...
Calculating statistics...
Formatting results...

##### With input Bigger #####
Name                ips        average  deviation         median         99th %
BLAS(dot)        121.46      0.00823 s    ±11.70%      0.00781 s       0.0103 s
Nx(dot)          0.0428        23.35 s     ±0.00%        23.35 s        23.35 s

Comparison: 
BLAS(dot)        121.46
Nx(dot)          0.0428 - 2836.06x slower +23.34 s

##### With input Medium #####
Name                ips        average  deviation         median         99th %
BLAS(dot)        5.16 K       0.194 ms     ±2.61%       0.193 ms        0.21 ms
Nx(dot)        0.0159 K       63.05 ms     ±4.01%       62.41 ms       77.53 ms

Comparison: 
BLAS(dot)        5.16 K
Nx(dot)        0.0159 K - 325.17x slower +62.85 ms

##### With input Small #####
Name                ips        average  deviation         median         99th %
BLAS(dot)      465.04 K        2.15 μs   ±371.75%        2.04 μs        2.92 μs
Nx(dot)         12.34 K       81.04 μs    ±10.40%       80.67 μs      106.38 μs

Comparison: 
BLAS(dot)      465.04 K
Nx(dot)         12.34 K - 37.69x slower +78.89 μs

M4 Pro / OpenBLAS

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 BLAS(dot) with input Bigger ...
Benchmarking BLAS(dot) with input Medium ...
Benchmarking BLAS(dot) with input Small ...
Benchmarking Nx(dot) with input Bigger ...
Benchmarking Nx(dot) with input Medium ...
Benchmarking Nx(dot) with input Small ...
Calculating statistics...
Formatting results...

##### With input Bigger #####
Name                ips        average  deviation         median         99th %
BLAS(dot)        104.46      0.00957 s    ±29.54%      0.00955 s       0.0195 s
Nx(dot)          0.0456        21.93 s     ±0.00%        21.93 s        21.93 s

Comparison: 
BLAS(dot)        104.46
Nx(dot)          0.0456 - 2290.55x slower +21.92 s

##### With input Medium #####
Name                ips        average  deviation         median         99th %
BLAS(dot)        3.79 K        0.26 ms    ±32.30%        0.27 ms        0.31 ms
Nx(dot)        0.0159 K       62.98 ms     ±1.53%       62.86 ms       66.01 ms

Comparison: 
BLAS(dot)        3.79 K
Nx(dot)        0.0159 K - 238.68x slower +62.71 ms

##### With input Small #####
Name                ips        average  deviation         median         99th %
BLAS(dot)      476.81 K        2.10 μs   ±379.70%        1.96 μs        2.92 μs
Nx(dot)         12.49 K       80.04 μs     ±6.27%       81.04 μs       91.75 μs

Comparison: 
BLAS(dot)      476.81 K
Nx(dot)         12.49 K - 38.17x slower +77.95 μs

結果

BLAS	Apple Silicon	10x10	100x100	500x500
OpenBLAS	M3 Max	365960	2830	89.98
OpenBLAS	M4 Pro	476810	3790	104.46
AppleBLAS	M3 Max	360760	4020	92.56
AppleBLAS	M4 Pro	465040	5160	121.46
Apple/OpenBLAS	M3 Max	0.9858	1.42049	1.02867
Apple/OpenBLAS	M4 Pro	0.9753	1.36148	1.16274

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．行列の要素数が大きくなると差が広がります．

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SGEMM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．