* added base code for i0 and i0e

* added grad base code for i0 and i0e

* added i0 and i0e python code

* added ops and backward yaml config

* added i0 and i0e cpu kernel, but not test.

* added i0 and i0e code and unitest files

* added test files

* added i0/i0e gpu implementation code

* updated code style

* updated code style

* fixed unitests code

* updated i0 with eigen3

* fixed bug and added more test cases

* refactor: fixed static graph bug

* refactor: removed i0 and i0e from op_compat

* refactor: updated code style

* refactor: updated op_compat.yaml

* refactor: updated op_compat.yaml

* refactor: fixed op name mapping and optimize unittest case

* refactor: manually implement i0 / i0e

* refactor: added grad kernel for i0 / i0e,didn't finish

* Update math.py

* refactor: added equation to doc in English and added comments for computing i0 / i0e gradient

* refactor: removed eigen implementation

* refactor: finished i0 / i0e cpu and gpu op

* refactor: updated code style

* fix: find  a bug but not fix

* fix: incorrect unittest cases

* update: updated code style and remove my file

* update: updated unittest case

* fix: fixed sign error

* fix: fixed mistakes when merging

* refactor: updated code style

* refactor: remove unused code

* refactor: updated code style

* fix doc eror of index_put in develop

* fix doc error for index_put; test=document_fix; test=docs_preview

* add index_put api

* fix value broadcast in backward and add test case in static

* add timeout=120s for index_put

* add op_compat for index_put

* add inplace index_put test

* add test case when index tensor in indices is int32 when indices.size less than x.dims

* add index_put api backward in cpu place

* add backward test case

* refactor code to delete some duplicated code

* replace reshape with resize for decrease extra memcpy

* add datatype flag in backward yaml

* fix bug in documentation

* Update python/paddle/tensor/manipulation.py

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

* add logaddexp

* update

* fix

* update code

* pre-commit

* remove scale check (0-D tensor is usable)

* fix data dtype err

* fix numpy default dtype diff

* fix data dtype

* fix data dtype

* update

* fix coverage

This reverts commit 9c406531.

* Add addmm tests

* Fix code

* [Perf]Removed usless assign op in while_loop

* refine assign

* add test cases, test=allcase

* fix test cases, test=allcase

* fix test cases, test=allcase

* assert_allclose, test=allcase

* 1e-5 to 1e-4, test=allcase

* change rtol from 1e-4 to 1e-3, test=allcase

* Fix some problems in Paddle english instruction doc files.

* fix some new questions

* fix cn doc problems, test=document_fix

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* test=allcase

* fix doc erros, test=allcase

[Zero-Dim] support output 0D for is_empty/as_complex/inner/dot/rank/tensordot/squeeze_/static.accuracy/static.auc/metric.accuracy, test=allcase (#52850)

* [Zero-Dim] support output 0D for is_empty/as_complex/, test=allcase

* [Zero-Dim] support output 0D for is_empty/as_complex/, test=allcase

* add test case

* modify dot/metric.accuracy/static.accuracy/static.auc

* modfiy inner/tensordot bug

* test 9 api

* [Zero-Dim] support output 0D for is_empty/as_complex/inner/dot/rank/tensordot/squeeze_/static.accuracy/static.auc/metric.accuracy, test=allcase

* fix bug

* support output 0D for is_empty/as_complex/inner/dot/rank/tensordot/squeeze_/static.accuracy/static.auc/metric.accuracy

* code style

* fix bug

* fix test_dot_op bug

* fix accuracy bug

* fix bug

* fix bug

* fix bug

* fix bug

* codestyle

* fix dot bug

* fix dot bug

* fix dot bug

* code style

* fix dot bug

* fix dot bug

* fix dot bug

* fix dot bug

* fix dot bug

* fix dot bug

* modify code

* support 0-D output and 0-D as indice in __getitem__

* fix tests

* fix inference and UT

* add unittest for setitem

* fix xpu test

* fix xpu 0-d

* [AMP OP&Test] Add check_dtype for some API (part 2)

* fix ci

* fix ci

* [AMP OP&Test] Add check_dtype for some API (part 1)

* fix

* Add prelu, clip_by_norm, multi_dot tests

* Fix code

* Fix code

* reorder MatrixRank

* fix

* fix

* fix

* fix

* fix

* Add split, split_with_num tests

* Add randperm tests

* Fix code

* Add digamma, dirichlet tests

* Fix code

* support uint16 python op in d2s

* convert uint16 -> bfloat16 in docstring

* 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.

* [AMP OP&Test] Support fp16&bf16 in reduce_max