code: def layer_norm_backward_kernel_dx(
      # Inputs
      x_ref,
      weight_ref,
      bias_ref,
      do_ref,
      mean_ref,
      rstd_ref,
      # Outputs
      dx_ref,
      *,
      eps: float,
      block_size: int,
  ):
      n_col = x_ref.shape[0]
  
      def mean_body(i, acc_ref):
          col_idx = i * block_size + jnp.arange(block_size)
          mask = col_idx < n_col
          a = pl.load(
              x_ref,
              (col_idx,),
              mask=mask,
              other=0.0,
              eviction_policy="evict_last",
          ).astype(jnp.float32)
          dout = pl.load(
              do_ref,
              (col_idx,),
              mask=mask,
              other=0.0,
              eviction_policy="evict_last",
          ).astype(jnp.float32)
          weight = pl.load(
              weight_ref,
              (col_idx,),
              mask=mask,
              other=0.0,
              eviction_policy="evict_last",
          ).astype(jnp.float32)
          a_hat = (a - mean_ref[...]) * rstd_ref[...]
          wdout = weight * dout
          mean1_acc_ref, mean2_acc_ref = acc_ref
          mean1_acc_ref[:] += a_hat * wdout
          mean2_acc_ref[:] += wdout
  
      mean = for_loop(
          pl.cdiv(n_col, block_size),
          mean_body,
          (jnp.zeros(block_size), jnp.zeros(block_size)),
      )
      mean1, mean2 = mean
      mean1 = mean1.sum() / n_col
      mean2 = mean2.sum() / n_col
  
      def dx_body(i, acc_ref):
          col_idx = i * block_size + jnp.arange(block_size)
          mask = col_idx < n_col
          a = pl.load(
              x_ref,
              (col_idx,),
              mask=mask,
              other=0.0,
              eviction_policy="evict_last",
          ).astype(jnp.float32)
          dout = pl.load(
              do_ref,
              (col_idx,),
              mask=mask,
              other=0.0,
              eviction_policy="evict_last",
          ).astype(jnp.float32)
          weight = pl.load(
              weight_ref,
              (col_idx,),
              mask=mask,
              other=0.0,
              eviction_policy="evict_last",
          ).astype(jnp.float32)
          a_hat = (a - mean_ref[...]) * rstd_ref[...]
          wdout = weight * dout
          da = (wdout - (a_hat * mean1 + mean2)) * rstd_ref[...]
          pl.store(
              dx_ref, (col_idx,), da.astype(dx_ref.dtype), mask=mask
          )
  
      for_loop(pl.cdiv(n_col, block_size), dx_body, ())
  
file_path: jax/jax/experimental/pallas/ops/layer_norm.py
imports: from __future__ import annotations
  import functools
  from typing import Optional
  import jax
  from jax import lax
  import jax.numpy
  from jax._src.lax.control_flow.for_loop import for_loop
  from jax.experimental import pallas
label_desc: Use image node_id 3 for calling a global function with example usage: layer_norm_backward_kernel_dx(x_ref, weight_ref, bias_ref, do_ref, mean_ref, rstd_ref, dx_ref) without return types