* 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

* [Dy2St]Fix x grad names when high order gradient

* Polish error msg

* Add inputs var to backward in dy2st

* Fix error

* Get grad names for backward API

* Fix save load

* Polish code

* Add ut

* [prim] fix not support optional grad bugs in higher order autodiff

* [prim] remove duplicate fill_any_like caused by infershape_for_composite

* fix _strip_grad_suffix_ bugs in higher-order autodiff

* [prim] create output for test_static_prim.cc

---------
Co-authored-by: N0x45f <wangzhen45@baidu.com>

* fix jacobian and hessian's docstring

* fix hessian's docstring

* fix hessian's docstring

* move DataLoader to paddle.io. test=develop

* Revert "revert p2p communication for xpu (#53496)"

This reverts commit eda0c588.

* update

* Fix div error when dtype is int64 in static mode

* Fix out dtype

* 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 log overwrite flag

* use strtobool

* revert p2p communication for xpu

* pp for npu

* update

* update

* fix xpuplace

* add ut for sync send

* Revert "fix xpuplace"

This reverts commit f89c1d7622426686bc153a3414a42c39e0f4a647.

* add ut for pp sync send

* rm unusable ut

* update

* add logaddexp

* update

* add 0D test for linalg and linalg.cond

* remove p_norm test

* Update test_zero_dim_tensor.py

* Update test_zero_dim_tensor, test=allcase

* add 0D op test for cond and pnorm,test=allcase

* fix conda error

* add complex support for  optest

* add complex grad test

* append one

* move some debug info

* move some debug info

* move some debug info

* move some debug info

* add more complex test

* Fix naming ambiguity

* Revert "add more complex test"

This reverts commit dbcb0516b8e53ba42e2d6089878a39b395345969.

* change backward gradient, add TODO

* 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