Synced with @xytintel , the difference is small. Will skip those 3 cases.

e.g:
Mismatched elements: 1 / 60 (1.7%)
Greatest absolute difference: 0.0625 at index (2, 1, 4) (up to 1e-05 allowed)
Greatest relative difference: 0.001125335693359375 at index (2, 1, 4) (up to 0.001 allowed)

Implemented the index_reduce, index_reduce_ and index_reduce.out operators.

It passes most of the unit tests on the PVC platform except 3 tests. Those failed tests are bf16 and float16.

I checked the differences and found those are small. For example:

Mismatched elements: 1 / 60 (1.7%)
Greatest absolute difference: 0.0625 at index (2, 1, 4) (up to 1e-05 allowed)
Greatest relative difference: 0.001125335693359375 at index (2, 1, 4) (up to 0.001 allowed)

To execute this test, run the following from the base repo dir:
python test/xpu/test_torch_xpu.py
TestTorchDeviceTypeXPU.test_index_reduce_reduce_prod_xpu_float16

I suspect the software emulation of the atomic operations of those low-level precisions causes that. Shall we skip those tests?

Need inputs from @xytintel and @fengyuan14

Side note: This function is in beta and may change in the near future. (Ref - https://pytorch.org/docs/stable/generated/torch.Tensor.index_reduce_.html)