code: def mix_gather_simulator(f_target_pair, b_target_pair):
      """
      Assume index of f and b target pairs are 'f' and 'b'
      S0S1 => Input: (f, [0]), (b, [1]) Output: [b, f], (1, 0)
      S1S0 => Input: (f, [1]), (b, [0]) Output: [b, f], (0, 1)
      S01R => Input: (f, [0, 1]), (b, []) Output: [f], (1, 1)
      RS01 => Input: (f, []), (b, [0, 1]) Output: [b], (1, 1)
      S10R => Input: (f, [0, 1]), (b, []) Output: [f], (0, 0)
      RS10 => Input: (f, []), (b, [0, 1]) Output: [b], (0, 0)
      """
      if f_target_pair[1] and b_target_pair[1]:
          leading_dim = b_target_pair[1] > f_target_pair[1]
          return [b_target_pair[0], f_target_pair[0]], [
              int(leading_dim),
              int(leading_dim ^ 1),
          ]
      if f_target_pair[1]:
          leading_dim = f_target_pair[1][0] < f_target_pair[1][1]
          return [
              f_target_pair[0],
          ], [int(leading_dim), int(leading_dim)]
      if b_target_pair[1]:
          leading_dim = b_target_pair[1][0] < b_target_pair[1][1]
          return [
              b_target_pair[0],
          ], [int(leading_dim), int(leading_dim)]
  
file_path: ColossalAI/colossalai/tensor/utils.py
imports: from typing import Dict, Iterator, List, Tuple, Union
  import torch
  import torch.nn
  from colossalai.tensor.colo_tensor import ColoTensor
label_desc: Use image node_id 4 for calling a global function with example usage: mix_gather_simulator(f_target_pair, b_target_pair) and returns: list,  list, list,  list, list,  list