docs/src/dev/custom_metal_kernels.rst
.. _custom_metal_kernels:
MLX supports writing custom Metal kernels through the Python and C++ APIs.
.. currentmodule:: mlx.core
Let's write a custom kernel that computes exp elementwise:
.. code-block:: python
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, )
def exp_elementwise(a: mx.array): 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))
Every time you make a kernel, a new Metal library is created and possibly
JIT compiled. To reduce the overhead from that, build the kernel once with
:func:fast.metal_kernel and then use it many times.
.. note::
Only pass the body of the Metal kernel in source. The function
signature is generated automatically.
The full function signature will be generated using:
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.output_dtypes
In the above, out is an mx.array of type mx.float16
so we add device float16_t* out.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.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 <https://developer.apple.com/metal/Metal-Shading-Language-Specification.pdf>_ are supported.Putting this all together, the generated function signature for myexp is as follows:
.. code-block:: cpp
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 <https://developer.apple.com/documentation/metal/mtlcomputecommandencoder/2866532-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 :func:ast.metal_kernel.__call__ will print the
generated code for debugging purposes.
:func:fast.metal_kernel supports an argument ensure_row_contiguous which
is True by default. This will copy the 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, :func:fast.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:
.. code-block:: python
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, ensure_row_contiguous=False, )
def exp_elementwise(a: mx.array): 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)
a = a[::2] b = exp_elementwise(a) assert mx.allclose(b, mx.exp(a))
Let's implement a more complex example: grid_sample in "bilinear" mode.
We'll start with the following MLX implementation using standard ops:
.. code-block:: python
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 :func:custom_function together with :func: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:
.. code-block:: python
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, )
@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."
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:
.. code-block:: python
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
Since we decorated grid_sample with :func: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 :func: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 <https://developer.apple.com/metal/Metal-Shading-Language-Specification.pdf>_ for more details.
We can then implement the backwards pass as follows:
.. code-block:: python
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, )
@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."
# 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