code: def layer_norm_bwd_dx_fused(
      DX,
      DY,
      DW,
      DB,
      X,
      W,
      M,
      V,
      Lock,
      stride,
      N,
      # META-parameters
      affine: tl.constexpr,
      GROUP_SIZE_M: tl.constexpr,
      BLOCK_SIZE_N: tl.constexpr,
  ):
      # fmt: on
  
      # position of elements processed by this program
      row = tl.program_id(0)
      cols = tl.arange(0, BLOCK_SIZE_N)
      mask = cols < N
  
      # offset data pointers to start at the row of interest
      x_ptrs = X + row * stride + cols
      dy_ptrs = DY + row * stride + cols
  
      # load data to SRAM
      x = tl.load(x_ptrs, mask=mask, other=0)
      dy = tl.load(dy_ptrs, mask=mask, other=0)
      mean = tl.load(M + row)
      rstd = tl.load(V + row)
  
      # compute dx
      xhat = (x - mean) * rstd
  
      if affine:
          w = tl.load(W + cols, mask=mask, other=0)
          wdy = w * dy
      else:
          wdy = dy
  
      xhat = tl.where(mask, xhat, 0.0)
      wdy = tl.where(mask, wdy, 0.0)
      mean1 = tl.sum(xhat * wdy, axis=0) / N
      mean2 = tl.sum(wdy, axis=0) / N
      dx = (wdy - (xhat * mean1 + mean2)) * rstd
  
      # write-back dx
      cols = tl.arange(0, BLOCK_SIZE_N)
      mask = cols < N  # re-materialize the mask to save registers
      dx_ptrs = DX + row * stride + cols
      tl.store(dx_ptrs, dx, mask=mask)
  
      if affine:
          # accumulate partial sums for dw/db
          partial_dw = (dy * xhat).to(w.dtype)
          partial_db = dy.to(w.dtype)
  
          # offset locks and weight/bias gradient pointer
          # each kernel instance accumulates partial sums for
          # DW and DB into one of GROUP_SIZE_M independent buffers
          # these buffers stay in the L2, which allow this kernel
          # to be fast
          lock_id = row % GROUP_SIZE_M
          Lock += lock_id
          Count = Lock + GROUP_SIZE_M
  
          # - wait for a lock on the accumulated dw/db
          while tl.atomic_cas(Lock, 0, 1) == 1:
              pass
          count = tl.load(Count)
  
          # - we got the lock, accumulate this kernel's results with
          # the stored values.
          dw_ptrs = DW + lock_id * N + cols
          db_ptrs = DB + lock_id * N + cols
  
          if count == 0:
              # first store doesn't accumulate
              tl.atomic_xchg(Count, 1)
          else:
              partial_dw += tl.load(dw_ptrs, mask=mask, other=0.0)
              partial_db += tl.load(db_ptrs, mask=mask, other=0.0)
  
          tl.store(dw_ptrs, partial_dw, mask=mask)
          tl.store(db_ptrs, partial_db, mask=mask)
  
          # release lock
          tl.atomic_xchg(Lock, 0)
  
imports: import triton
  import triton.language
label_desc: Use image node_id 2 for calling a global function with example usage: layer_norm_bwd_dx_fused(DX, DY, DW, DB, X, W, M, V, Lock, stride, N, affine, GROUP_SIZE_M, BLOCK_SIZE_N) without return types