Consider interactions between vcomp and libomp on Windows with BLIS?
Apparently, it's possible to get BLIS to work on windows when built with Clang/LLVM:
https://github.com/numpy/numpy/issues/7372#issuecomment-409364435
Which means that if we have Cython extension built with MSVC calling into BLIS built with Clang/LLVM we will possibly get a new type of OpenMP nesting...
This case would be possible in scikit-learn for the new Cython K-Means calling into the BLAS API scipy-blis, shall scipy use BLIS in the future (which is considered on their roadmap).
For practicalities, it should be quite easy to install clang under Windows using the conda-forge channel, e.g. one of the following packages:
https://anaconda.org/conda-forge/clang https://anaconda.org/conda-forge/clangdev
Also we should check that there is no bad interactions between Clang/LLVM OpenMP and Intel OpenMP (e.g. from numpy from the default conda channel linked with MKL) on Windows as we observed on Linux.