* Add outputs to check_numerics_kernel.

* Add check_numerics to yaml.

* Add API and unittest.

* Add check_nan_inf_level as argument of check_numerics_kernel.

* Add more unittests.

* Fix static API implementation and unittest.

* Move the implementation of check_numerics to paddle.amp.

* Fix import error.

* Reimplement the check_nan_inf function as check_numerics kernel.

* Remove the cpu implemention to phi.

* Add ifdef for the including of omp.h.

* Move the use of FLAGS_check_nan_inf_level out of header file.

* Implement a common PrintAndThrowError function.

* Fix the error using of __NVCC__, which should be instead with __CUDA_ARCH__.

* Add dependency of phi.

* Polish codes and unittest.

* [dygraph]unify _non_static_mode() in_dygraph_mode() and in_dynamic_mode()

* [dygraph]unify _non_static_mode() in_dygraph_mode() and in_dynamic_mode()

* [dygraph]unify _non_static_mode() in_dygraph_mode() and in_dynamic_mode()

* [dygraph]unify _non_static_mode() in_dygraph_mode() and in_dynamic_mode()

* [dygraph]unify _non_static_mode() in_dygraph_mode() and in_dynamic_mode()

* [dygraph]unify _non_static_mode() in_dygraph_mode() and in_dynamic_mode()

* fixed cyclic reference that caused patial import

* fixed bad change

* fix bad import

* fix bad import

* fix bad import

* fix ut failed caused by change in_dynamic_mode

* fix ut failed caused by change in_dynamic_mode

* fixed usage of in_dynamic_mode() or in_dygraph_mode()

* revert python3 to python in .pre-commit-config.yaml

* fix merge conflicts

* Allow to switch whether to use promote strategy to choose kernel for O2 training.

* Fix comparing error and add unittest.

* support OD level and skip dynamic loss scaling for bf16

* Unify the static amp codes of fp16 and bf16.

* Polish apis and add unittest.

* Add operator stats collecting tools for program.

* Add the check of number of bloat16 operators in unittest.

* Add warning for operator not supported for amp.

* Add testing of BF16 O1 and O2.

* fix dtype cast in amp.

* add test case and update docs.

* remove set_prim.

* support set master_grad

* move register_hook to auto_cast

* update unittest

* fix fp16 test

* update for review comments

* rem is_compiled_with_npu

* rem nup related code

* make lint happy

* rem test

* remove some tests

* Update grad_scaler.py

* fix an error

* rem is_compiled_with_mlu

* fix some mlu_place and mlu_device_coount

* make lint happy

* [AMP] Add python API for collecting operator stats.

* Fix import and polish codes.

* Add more unittest.

* Add doc for the new APIs.

* delete old dygraph op test

* refine _found_inf

* Fix bug of reduce_sum op. When input.numel() > INT32_MAX, its result
is wrong.

* Remove climits.

* Fix bug of hybrid parallel strategy with recompute using bf16.

* Fix bug of recompute_hybrid ctx.amp_dtype

* Fix bug of amp_dtype.

* Fix bug of auto_cast.

* Revert "fixoptminizer _set_auxiliary_var bug (#50335)"

This reverts commit c44005f0.

* Revert "refine optimizer create accumulators (#50188)"

This reverts commit 244e7546.

* Revert "fix found_inf bug for custom optimizer (#50158)"

This reverts commit 64573f9f.

* Revert "refine amp scaler found_inf (#49864)"

This reverts commit 382e9a06.

* fix code format

* fix conflict

test=docoument_fix

* refine _found_inf

* [KUNLUN] add op: maxpool_with_index

* use DeviceContext::Alloc() instead of DenseTensor::mutable_data()

* fix file format

* solve clip unittest failure

* minor fix

* Revert "solve clip unittest failure" since the issue is fixed
in #49535

This reverts commit 1127adc66e79afe35ac3c00bb34e6aaa7cd7d78b.

* align with xdnn on the definition of mask in max_pool_with_index

* minor

* 涉及到的api有
paddle.amp.decorate
paddle.static.npu_places
paddle.signal.istft
paddle.signal.stft
paddle.linalg.eigvalsh
paddle.randint_like

* change signal.stft

* randint_like的low增加optional

* ; test=docs_preview

* 修改了注解格式; test=docs_preview

* 修改了公式格式

* 修改了decorate的models等

* test=document_fix
Co-authored-by: NLigoml <39876205+Ligoml@users.noreply.github.com>