Custom Metal Kernels#

MLX supports writing custom Metal kernels through the Python and C++ APIs.

Simple Example#

Let’s write a custom kernel that computes exp elementwise:

def exp_elementwise(a: mx.array):
    source = """
        uint elem = thread_position_in_grid.x;
        T tmp = inp[elem];
        out[elem] = metal::exp(tmp);
    """

    kernel = mx.fast.metal_kernel(
        name="myexp",
        input_names=["inp"],
        output_names=["out"],
        source=source,
    )
    outputs = kernel(
        inputs=[a],
        template=[("T", mx.float32)],
        grid=(a.size, 1, 1),
        threadgroup=(256, 1, 1),
        output_shapes=[a.shape],
        output_dtypes=[a.dtype],
    )
    return outputs[0]

a = mx.random.normal(shape=(4, 16)).astype(mx.float16)
b = exp_elementwise(a)
assert mx.allclose(b, mx.exp(a))

Note

We are only required to pass the body of the Metal kernel in source.

The full function signature will be generated using:

The shapes/dtypes of inputs
In the above, a is an mx.array of type mx.float16 and we pass it with the key inp so we will add const device float16_t* inp to the signature. inp_shape, inp_strides and inp_ndim are also added for convenience if they are present in source.
The list of output_dtypes
In the above, out is an mx.array of type mx.float16 so we add device float16_t* out.
Template parameters passed using template
In the above, template=[("T", mx.float32)] adds a template of template <typename T> to the function and instantiates the template with custom_kernel_myexp_float<float>. Template parameters can be mx.core.Dtype, int or bool.
Metal attributes used in source such as [[thread_position_in_grid]]
These will be added as function arguments. All the attributes defined in Table 5.8 of the Metal Shading Language Specification are supported.

Putting this all together, the generated function signature for myexp is as follows:

template <typename T>
[[kernel]] void custom_kernel_myexp_float(
  const device float16_t* inp [[buffer(0)]],
  device float16_t* out [[buffer(1)]],
  uint3 thread_position_in_grid [[thread_position_in_grid]]) {

        uint elem = thread_position_in_grid.x;
        T tmp = inp[elem];
        out[elem] = metal::exp(tmp);

}

template [[host_name("custom_kernel_myexp_float")]] [[kernel]] decltype(custom_kernel_myexp_float<float>) custom_kernel_myexp_float<float>;

Note: grid and threadgroup are parameters to the Metal dispatchThreads function. This means we will launch mx.prod(grid) threads, subdivided into threadgroup size threadgroups. For optimal performance, each thread group dimension should be less than or equal to the corresponding grid dimension.

Passing verbose=True to mx.fast.metal_kernel.__call__ will print the generated code for debugging purposes.

Using Shape/Strides#

mx.fast.metal_kernel supports an argument ensure_row_contiguous which is True by default. This will copy the mx.array inputs if needed before the kernel is launched to ensure that the memory layout is row contiguous. Generally this makes writing the kernel easier, since we don’t have to worry about gaps or the ordering of the dims when indexing.

If we want to avoid this copy, metal_kernel automatically passes a_shape, a_strides and a_ndim for each input array a if any are present in source. We can then use MLX’s built in indexing utils to fetch the right elements for each thread.

Let’s convert myexp above to support arbitrarily strided arrays without relying on a copy from ensure_row_contiguous:

def exp_elementwise(a: mx.array):
    source = """
        uint elem = thread_position_in_grid.x;
        // Utils from `mlx/backend/metal/kernels/utils.h` are automatically included
        uint loc = elem_to_loc(elem, inp_shape, inp_strides, inp_ndim);
        T tmp = inp[loc];
        // Output arrays are always row contiguous
        out[elem] = metal::exp(tmp);
    """

    kernel = mx.fast.metal_kernel(
        name="myexp_strided",
        input_names=["inp"],
        output_names=["out"],
        source=source
    )
    outputs = kernel(
        inputs=[a],
        template=[("T", mx.float32)],
        grid=(a.size, 1, 1),
        threadgroup=(256, 1, 1),
        output_shapes=[a.shape],
        output_dtypes=[a.dtype],
        ensure_row_contiguous=False,
    )
    return outputs[0]

a = mx.random.normal(shape=(4, 16)).astype(mx.float16)
# make non-contiguous
a = a[::2]
b = exp_elementwise(a)
assert mx.allclose(b, mx.exp(a))

Complex Example#

Let’s implement a more complex example: grid_sample in "bilinear" mode.

We’ll start with the following MLX implementation using standard ops:

def grid_sample_ref(x, grid):
    N, H_in, W_in, _ = x.shape
    ix = ((grid[..., 0] + 1) * W_in - 1) / 2
    iy = ((grid[..., 1] + 1) * H_in - 1) / 2

    ix_nw = mx.floor(ix).astype(mx.int32)
    iy_nw = mx.floor(iy).astype(mx.int32)

    ix_ne = ix_nw + 1
    iy_ne = iy_nw

    ix_sw = ix_nw
    iy_sw = iy_nw + 1

    ix_se = ix_nw + 1
    iy_se = iy_nw + 1

    nw = (ix_se - ix)    * (iy_se - iy)
    ne = (ix    - ix_sw) * (iy_sw - iy)
    sw = (ix_ne - ix)    * (iy    - iy_ne)
    se = (ix    - ix_nw) * (iy    - iy_nw)

    I_nw = x[mx.arange(N)[:, None, None], iy_nw, ix_nw, :]
    I_ne = x[mx.arange(N)[:, None, None], iy_ne, ix_ne, :]
    I_sw = x[mx.arange(N)[:, None, None], iy_sw, ix_sw, :]
    I_se = x[mx.arange(N)[:, None, None], iy_se, ix_se, :]

    mask_nw = (iy_nw >= 0) & (iy_nw <= H_in - 1) & (ix_nw >= 0) & (ix_nw <= W_in - 1)
    mask_ne = (iy_ne >= 0) & (iy_ne <= H_in - 1) & (ix_ne >= 0) & (ix_ne <= W_in - 1)
    mask_sw = (iy_sw >= 0) & (iy_sw <= H_in - 1) & (ix_sw >= 0) & (ix_sw <= W_in - 1)
    mask_se = (iy_se >= 0) & (iy_se <= H_in - 1) & (ix_se >= 0) & (ix_se <= W_in - 1)

    I_nw *= mask_nw[..., None]
    I_ne *= mask_ne[..., None]
    I_sw *= mask_sw[..., None]
    I_se *= mask_se[..., None]

    output = nw[..., None] * I_nw + ne[..., None] * I_ne + sw[..., None] * I_sw + se[..., None] * I_se

    return output

Now let’s use mx.custom_function together with mx.fast.metal_kernel to write a fast GPU kernel for both the forward and backward passes.

First we’ll implement the forward pass as a fused kernel:

@mx.custom_function
def grid_sample(x, grid):

    assert x.ndim == 4, "`x` must be 4D."
    assert grid.ndim == 4, "`grid` must be 4D."

    B, _, _, C = x.shape
    _, gN, gM, D = grid.shape
    out_shape = (B, gN, gM, C)

    assert D == 2, "Last dim of `grid` must be size 2."

    source = """
        uint elem = thread_position_in_grid.x;
        int H = x_shape[1];
        int W = x_shape[2];
        int C = x_shape[3];
        int gH = grid_shape[1];
        int gW = grid_shape[2];

        int w_stride = C;
        int h_stride = W * w_stride;
        int b_stride = H * h_stride;

        uint grid_idx = elem / C * 2;
        float ix = ((grid[grid_idx] + 1) * W - 1) / 2;
        float iy = ((grid[grid_idx + 1] + 1) * H - 1) / 2;

        int ix_nw = floor(ix);
        int iy_nw = floor(iy);

        int ix_ne = ix_nw + 1;
        int iy_ne = iy_nw;

        int ix_sw = ix_nw;
        int iy_sw = iy_nw + 1;

        int ix_se = ix_nw + 1;
        int iy_se = iy_nw + 1;

        T nw = (ix_se - ix)    * (iy_se - iy);
        T ne = (ix    - ix_sw) * (iy_sw - iy);
        T sw = (ix_ne - ix)    * (iy    - iy_ne);
        T se = (ix    - ix_nw) * (iy    - iy_nw);

        int batch_idx = elem / C / gH / gW * b_stride;
        int channel_idx = elem % C;
        int base_idx = batch_idx + channel_idx;

        T I_nw = x[base_idx + iy_nw * h_stride + ix_nw * w_stride];
        T I_ne = x[base_idx + iy_ne * h_stride + ix_ne * w_stride];
        T I_sw = x[base_idx + iy_sw * h_stride + ix_sw * w_stride];
        T I_se = x[base_idx + iy_se * h_stride + ix_se * w_stride];

        I_nw = iy_nw >= 0 && iy_nw <= H - 1 && ix_nw >= 0 && ix_nw <= W - 1 ? I_nw : 0;
        I_ne = iy_ne >= 0 && iy_ne <= H - 1 && ix_ne >= 0 && ix_ne <= W - 1 ? I_ne : 0;
        I_sw = iy_sw >= 0 && iy_sw <= H - 1 && ix_sw >= 0 && ix_sw <= W - 1 ? I_sw : 0;
        I_se = iy_se >= 0 && iy_se <= H - 1 && ix_se >= 0 && ix_se <= W - 1 ? I_se : 0;

        out[elem] = nw * I_nw + ne * I_ne + sw * I_sw + se * I_se;
    """
    kernel = mx.fast.metal_kernel(
        name="grid_sample",
        input_names=["x", "grid"],
        output_names=["out"],
        source=source,
    )
    outputs = kernel(
        inputs=[x, grid],
        template=[("T", x.dtype)],
        output_shapes=[out_shape],
        output_dtypes=[x.dtype],
        grid=(np.prod(out_shape), 1, 1),
        threadgroup=(256, 1, 1),
    )
    return outputs[0]

For a reasonably sized input such as:

x.shape = (8, 1024, 1024, 64)
grid.shape = (8, 256, 256, 2)

On an M1 Max, we see a big performance improvement:

55.7ms -> 6.7ms => 8x speed up

Grid Sample VJP#

Since we decorated grid_sample with mx.custom_function, we can now define its custom vjp transform so MLX can differentiate it.

The backwards pass requires atomically updating x_grad/grid_grad and so requires a few extra mx.fast.metal_kernel features:

init_value=0
Initialize all of the kernel’s outputs to this value before it runs. This allows us to update only part of the output arrays with the kernel.
atomic_outputs=True
Designate all of the kernel outputs as atomic in the function signature. This means we can use Metal’s atomic features to simultaneously update the x_grad and grid_grad arrays from multiple threadgroups. See section 6.15 of the Metal Shading Language Specification for more details.

We can then implement the backwards pass as follows:

@grid_sample.vjp
def grid_sample_vjp(primals, cotangent, _):
    x, grid = primals
    B, _, _, C = x.shape
    _, gN, gM, D = grid.shape

    assert D == 2, "Last dim of `grid` must be size 2."

    source = """
        uint elem = thread_position_in_grid.x;
        int H = x_shape[1];
        int W = x_shape[2];
        int C = x_shape[3];
        // Pad C to the nearest larger simdgroup size multiple
        int C_padded = ceildiv(C, threads_per_simdgroup) * threads_per_simdgroup;

        int gH = grid_shape[1];
        int gW = grid_shape[2];

        int w_stride = C;
        int h_stride = W * w_stride;
        int b_stride = H * h_stride;

        uint grid_idx = elem / C_padded * 2;
        float ix = ((grid[grid_idx] + 1) * W - 1) / 2;
        float iy = ((grid[grid_idx + 1] + 1) * H - 1) / 2;

        int ix_nw = floor(ix);
        int iy_nw = floor(iy);

        int ix_ne = ix_nw + 1;
        int iy_ne = iy_nw;

        int ix_sw = ix_nw;
        int iy_sw = iy_nw + 1;

        int ix_se = ix_nw + 1;
        int iy_se = iy_nw + 1;

        T nw = (ix_se - ix)    * (iy_se - iy);
        T ne = (ix    - ix_sw) * (iy_sw - iy);
        T sw = (ix_ne - ix)    * (iy    - iy_ne);
        T se = (ix    - ix_nw) * (iy    - iy_nw);

        int batch_idx = elem / C_padded / gH / gW * b_stride;
        int channel_idx = elem % C_padded;
        int base_idx = batch_idx + channel_idx;

        T gix = T(0);
        T giy = T(0);
        if (channel_idx < C) {
            int cot_index = elem / C_padded * C + channel_idx;
            T cot = cotangent[cot_index];
            if (iy_nw >= 0 && iy_nw <= H - 1 && ix_nw >= 0 && ix_nw <= W - 1) {
                int offset = base_idx + iy_nw * h_stride + ix_nw * w_stride;
                atomic_fetch_add_explicit(&x_grad[offset], nw * cot, memory_order_relaxed);

                T I_nw = x[offset];
                gix -= I_nw * (iy_se - iy) * cot;
                giy -= I_nw * (ix_se - ix) * cot;
            }
            if (iy_ne >= 0 && iy_ne <= H - 1 && ix_ne >= 0 && ix_ne <= W - 1) {
                int offset = base_idx + iy_ne * h_stride + ix_ne * w_stride;
                atomic_fetch_add_explicit(&x_grad[offset], ne * cot, memory_order_relaxed);

                T I_ne = x[offset];
                gix += I_ne * (iy_sw - iy) * cot;
                giy -= I_ne * (ix - ix_sw) * cot;
            }
            if (iy_sw >= 0 && iy_sw <= H - 1 && ix_sw >= 0 && ix_sw <= W - 1) {
                int offset = base_idx + iy_sw * h_stride + ix_sw * w_stride;
                atomic_fetch_add_explicit(&x_grad[offset], sw * cot, memory_order_relaxed);

                T I_sw = x[offset];
                gix -= I_sw * (iy - iy_ne) * cot;
                giy += I_sw * (ix_ne - ix) * cot;
            }
            if (iy_se >= 0 && iy_se <= H - 1 && ix_se >= 0 && ix_se <= W - 1) {
                int offset = base_idx + iy_se * h_stride + ix_se * w_stride;
                atomic_fetch_add_explicit(&x_grad[offset], se * cot, memory_order_relaxed);

                T I_se = x[offset];
                gix += I_se * (iy - iy_nw) * cot;
                giy += I_se * (ix - ix_nw) * cot;
            }
        }

        T gix_mult = W / 2;
        T giy_mult = H / 2;

        // Reduce across each simdgroup first.
        // This is much faster than relying purely on atomics.
        gix = simd_sum(gix);
        giy = simd_sum(giy);

        if (thread_index_in_simdgroup == 0) {
            atomic_fetch_add_explicit(&grid_grad[grid_idx], gix * gix_mult, memory_order_relaxed);
            atomic_fetch_add_explicit(&grid_grad[grid_idx + 1], giy * giy_mult, memory_order_relaxed);
        }
    """
    kernel = mx.fast.metal_kernel(
        name="grid_sample_grad",
        input_names=["x", "grid", "cotangent"],
        output_names=["x_grad", "grid_grad"],
        source=source,
        atomic_outputs=True,
    )
    # pad the output channels to simd group size
    # so that our `simd_sum`s don't overlap.
    simdgroup_size = 32
    C_padded = (C + simdgroup_size - 1) // simdgroup_size * simdgroup_size
    grid_size = B * gN * gM * C_padded
    outputs = kernel(
        inputs=[x, grid, cotangent],
        template=[("T", x.dtype)],
        output_shapes=[x.shape, grid.shape],
        output_dtypes=[x.dtype, x.dtype],
        grid=(grid_size, 1, 1),
        threadgroup=(256, 1, 1),
        init_value=0,
    )
    return outputs[0], outputs[1]

There’s an even larger speed up for the vjp:

676.4ms -> 16.7ms => 40x speed up

Custom Metal Kernels

Contents

Custom Metal Kernels#

Simple Example#

Using Shape/Strides#

Complex Example#

Grid Sample VJP#