Thank you for reviewing.
This is a common clang build problem, but I can't reproduce on linux clang, so I exemplified on visual studio clang.

What I've learned from links in #5259 (review) so far (thanks a lot @jameslamb for them!):

• Only Visual Studio 2019 and newer is supported;
• ClangCL is a toolset value, so it can be added in
  https://github.com/microsoft/LightGBM/blob/1cc9f9dcee15586aefdd8271a1c04ad010d3c53a/python-package/setup.py#L172

This is a common clang build problem, but I can't reproduce on linux clang

This project is tested with clang on Linux and macOS on every commit, so I'd be surprised to learn that an issue of the form "LightGBM cannot be compiled with any version of clang" exists.

https://github.com/microsoft/LightGBM/blob/27d9ad2e8e7ea2d00dbab7b17b0a34b5d9184fe0/.vsts-ci.yml#L88-LL91

https://github.com/microsoft/LightGBM/blob/27d9ad2e8e7ea2d00dbab7b17b0a34b5d9184fe0/.vsts-ci.yml#L225-LL228

https://github.com/microsoft/LightGBM/blob/27d9ad2e8e7ea2d00dbab7b17b0a34b5d9184fe0/.ci/test.sh#L3-L9

https://github.com/microsoft/LightGBM/blob/27d9ad2e8e7ea2d00dbab7b17b0a34b5d9184fe0/.github/workflows/python_package.yml#L60-LL66

That is probably why you haven't been able to reproduce this on Linux. I suspect the issue you've faced is specific to using ClangCL + MSVC on Winddows.

@jameslamb I beleave this problem is also occurd on linux (in some cases).
Clang openmp requires a link path to libomp, but on linux libomp is usually installed on the system (e.g. libomp-dev).
Because this path is already added to link path, linker can find libomp.
If we use libomp outside the system path, I think we need to a link path to libomp.
I think apple clang probably uses libomp installed by brew, which causes same problem.

After noticing the above, I built on the vc prompt and the build went through without this change.
Sorry for the confusion. I will close this PR.

@buresu sorry, could you clarify? Are you saying that the following worked for you with with 0 modifications to LightGBM?

cmake .. -G "Visual Studio 16 2019" -T ClangCL -A x64
cmake --build . --config Release

Or did you have to modify CMakeLists.txt or something in python-package/ to compile successfully?

@jameslamb Yes, the build successful with zero changes using vc prompt.
When using powershell the build succeeded with this PR change, but it was linking llvm openmp installed by scoop. (This is my mistake).
When built using powershell with no changes, vc's openmp was not found.
I think this is a lack of support from cmake.

ahhh ok, thanks for the additional information @buresu !

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