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Hi Ben,
I started to review your patch, sorry for the delay :-( It's convinient to have the patch on Rietveld to comment it inline.
I didn't expect so much C code. The posixmodule.c is really huge. Well, it's just the longest C file of Python 3.5. Your patch adds 781 more lines to it. It's maybe time to split the file into smaller files.
At the same time, reading C code is boring and it's too easy to "implement bugs". I need to be convinced that the speedup announced in the PEP requires so much C code. In the PEP and https://github.com/benhoyt/scandir#benchmarks it's not clear if the speedup comes from the C code (instead of implementing scandir in pure Python, for example using ctypes) or the lower number of syscalls.
To have a fair benchmark, the best would be to have a C part only implementing opendir/readir and FirstFindFile/FindFileXXX (I'm not sure that ctypes is as fast as C code written with the Python C API), and a Python part which implements the nice Python API.
If the speedup is 10% or lower, I would prefer to not add so much C code and take the compromise of a thin C wrapper and implement scandir in Python.
If we implement os.scandir() in Python, should we still try to share code with os.listdir()? I see that importlib uses os.listdir(), so we need a listdir() function implemented in C at least for importlib.