code: def allreduce(self, x, mesh_axes, reduction_fn_string):
      
      if not mesh_axes:
        return x
      x = x.to_laid_out_tensor()
      if reduction_fn_string == "SUM":
        group_assignment = self._create_group_assignment(mesh_axes)
        group_size = len(group_assignment[0])
        tf_in = x.one_slice
        dtype = tf_in.dtype
        if dtype == tf.float32:
          cast_to_float32 = False
        elif dtype == tf.bfloat16:
          cast_to_float32 = (
              group_size > self._allreduce_in_bfloat16_max_group_size)
        else:
          tf.logging.info("Casting %s to float32 for allreduce" % tf_in.dtype)
          cast_to_float32 = True
        if cast_to_float32:
          tf_in = tf.cast(tf_in, tf.float32)
        tf_out = tpu_ops.cross_replica_sum(tf_in, group_assignment)
        if cast_to_float32:
          tf_out = tf.cast(tf_out, dtype)
        return self.LaidOutTensor([tf_out])
      else:
        for axis in mesh_axes:
          x = self.allconcat(x, axis, 0, stack=True)
          x = self.LaidOutTensor(
              [mtf.reduction_fn(reduction_fn_string)(x.one_slice, 0)])
        return x
docs: Grouped allreduce, (summed across the given dimensions).
  
      Args:
        x: a LaidOutTensor
        mesh_axes: a list of integers
        reduction_fn_string: "SUM"
      Returns:
        a LaidOutTensor
      Raises:
        ValueError: if the reduction is not yet implemented.