def METHOD_NAME(state: DefaultState, grad: torch.Tensor):
    r"""
    This FSDP communication hook implements ``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)