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Cython still access multiple PyThreadState members which have no getter or setter yet.
__Pyx_PyErr_ExceptionMatchesInState():
 PyObject *exc_type = tstate->curexc_type;
 ...
=> internal _PyErr_Occurred(tstate) could solve this issue: move it the public/private API? Or expose internal _PyErr_ExceptionMatches(tstate, exc)?
__Pyx_ErrRestoreInState() is a reimplementation of internal _PyErr_Restore(): get/set curexc_type, curexc_value and curexc_traceback members.
__Pyx_PyFunction_FastCallNoKw:
static PyObject* __Pyx_PyFunction_FastCallNoKw(...) {
 ...
 ++tstate->recursion_depth;
 Py_DECREF(f);
 --tstate->recursion_depth;
 return result;
}
Why not calling Py_EnterRecursiveCall/Py_LeaveRecursiveCall?
There are likely others.