Consider:

process_mesh = auto.ProcessMesh(mesh=[[0, 1], [2, 3]])
x = paddle.to_tensor([[1.0, 2.0, 3.0, 4.0],
                       [5.0, 6.0, 7.0, 8.0],
                       [9.0, 10.0, 11.0, 12.0]])
index = paddle.to_tensor([0, 1, 1, 2], dtype='int32')
# if x_dims_mapping_src is [-1, 0] and index_dims_mapping_src is [0], what results should be obtained?
# if x_dims_mapping_src is [-1, 1] and index_dims_mapping_src is [0], what results should be obtained?
out1 = paddle.index_select(x=x, index=index, axis=0)

And we need to add relevant unit tests

Thanks for pointing out the key points! now if index's shared mesh is conflit with x, it will choose to reshard in x and replicate in index

as above described, we need more unit test case to prove right

use process_mesh = auto.ProcessMesh(mesh=[[0, 1], [2, 3]])
when x = paddle.arange(24).reshape([3, 4, 2]) and x_dims_mapping_src is [-1, -1, -1], so x is replicated in every device.
when index = paddle.to_tensor([0, 1, 1, 2], dtype='int32') and index_dims_mapping_src is [0], so index in device0/1 is [0, 1], index in device2/3 is [1, 2]
According to the implemented spmd rules in this PR, when out = paddle.index_select(x=x, index=index, axis=1) out_dims_mapping is [-1, 0, -1], so out in device0/1 is [[[0, 1], [2, 3]], [[8, 9], [10, 11]], [[16, 17], [18, 19]]], out in device2/3 is [[[2, 3], [4, 5]], [[10, 11], [12, 13]], [[18, 19], [20, 21]]]
can it be partial?

It's not in partial status, before i write it with assert_false, maybe the check is redundant, now i delete it~

Consider:

process_mesh = auto.ProcessMesh(mesh=[[0, 1], [2, 3]])
x = paddle.arange(24).reshape([3, 4, 2])
index = paddle.to_tensor([0, 1, 1, 2], dtype='int32')
out = paddle.index_select(x=x, index=index, axis=1)
# if x_dims_mapping_src is [1, -1, -1], index_dims_mapping_src is [0], out_grad_dims_mapping is [1, 0, -1], what is shape of out/out_grad, what x_grad_dims_mapping should be? can it be partial? 

The shape of out/out_grad is [3, 4, 2], and x_grad_dims_mapping is same as x with [1, -1, -1], it should be partial in index's shared mesh dim. and i reuse the forward rule to infer dims_mapping and set partial_dims additionally.

ok, if index is sharded, x_grad will be partial(in axis) and partial_dims equals shard dim of index

if [-1, 1, -1], [0], axis=1, what will be? should add unit this test case

the x[axis] will be replicate first to [-1, -1, -1], so out_dims_mapping will be [-1, 0, -1]