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In my embedding, I use the following (adapting the example above):
// initialize the Python interpreter
Py_Initialize();
PyEval_InitThreads();
/* Swap out and return current thread state and release the GIL */
PyThreadState tstate = PyEval_SaveThread();
PyGILState_STATE gstate;
gstate = PyGILState_Ensure();
PyRun_SimpleString("import random\n");
PyGILState_Release(gstate); 
You don't have to free the tstate returned by PyEval_SaveThread because
it is the thread state of the main thread (as established during
Py_Initialize), and so it will be freed during Python's shut-down.
I think in general you should rarely need to call PyEval_ReleaseLock
directly; instead use PyEval_SaveThread, the Py_BEGIN_ALLOW_THREADS
macro, or PyGILState_Release (as appropriate). The documentation should
probably say as much.