code: def allreduce_hook(state: DefaultState, grad: torch.Tensor):
      r"""
      Implement the  FSDP communication hook for ``all_reduce`` algorithm and a necessary pre- and post-division of gradients.
  
      Args:
          state (DefaultState): State information, configures pre- and post-division factors.
          grad (torch.Tensor): A gradient for the local batch that needs to be communicated across ranks.
      """
      # Average grad by pre-division factor. Together pre- and post-division factors
      # lead to an overall averaging by world_size, required for consistency with PyTorch DDP.
      # This is a two-step process to avoid potential underflow and overflow.
      if state.gradient_predivide_factor > 1:
          grad.div_(state.gradient_predivide_factor)
      dist.all_reduce(grad, group=state.process_group)
      # Average grad by post-division factor.
      if state.gradient_postdivide_factor > 1:
          grad.div_(state.gradient_postdivide_factor)
  
file_path: pytorch/torch/distributed/algorithms/_comm_hooks/default_hooks.py
imports: import functools
  import torch
  import torch.distributed
  from typing import Optional
label_desc: Use image node_id 2 for calling a global function with example usage: allreduce_hook(state, grad) without return types