* improve backward performance

* support different dtypes for elementwise ops

* Merged LoDTensor with Tensor,test=allcases

* Patched python level LoDTensor

* Patched python level LoDTensor

* Merge Tensor into DenseTensor

* Fixed namespace issues,test=allcases

* Fixed merge issues

* Fixed inference issues

* Fixed NPU test issues

* Fixed merge issues

Add OpFunctor and replace cast, scale, clip, bce_loss and abs_grad with elementwise_no_broadcast (#38500)

There are mainly following fixes:

- take `DeviceContext` as the template parameter of math functors and OpKernel instead of `Place`
- remove `eigen_device` interface in base class  `DeviceContext`
- remove `GetEigenDevice` interface in `ExecutionContext` and base class `DeviceContext`
- remove unused `platform::EigenDeviceConverter`
- rename `REGISTER_OP_GPU_KERNEL` to `REGISTER_OP_CUDA_KERNEL`
- rename `USE_GPU_ONLY_OP` to `USE_CUDA_ONLY_OP`

* Simplize Gradient Check

* Stash

* Extract apply_backward_pass to backward.py

Rename apply_backward_pass to append_backward_ops

* Use graph API to check gradient

* Fix ci

* Fix CI

* Fix backward for double precision

* Stash

* Fix CI

* Fix ci

* Ignore GRU test

* Ignore xe op

* Fix CI

* Fix softmax with xe gradient

The correct equation should be IG = OG * (d_softmax_with_xe())

* Fix typo

* Fix merge error

* Disable LRN

* Adding Adadelta optimization operator
* Making inputs and outputs conform to naming convention
* Removing type alias from header files
* Fixing Adadelta documentation in comments
* Addressing code review feedback

Make implement an operator less noisy.

* a simplest SGD op