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Currently undocumented: http://docs.python.org/py3k/c-api/gen.html
Public API in a released version of Python: http://hg.python.org/cpython/file/3.2/Include/genobject.h 

Please correct me if I'm wrong, but I think PyGen_NeedsFinalizing should not be an API function because it is only used, nor _PyGen_FetchStopIterationValue. In the attached patch I've removed PyGen_NeedsFinalizing and _PyGen_FetchStopIterationValue fom the public API.

For the record, PyGen_NeedsFinalizing still exists but it isn't used anymore in the code base (following PEP 442).

What should be done for the PyGen_NeedsFinalizing API? Does it need to be documented or should it be removed since it's no longer used in the code base?
Thanks!

Cheryl: it may be useful to do a code search to find out whether any third-party projects are relying on PyGen_NeedsFinalizing.

Thanks Antoine.
Do you have a good way for searching third party projects? I searched on Github and I'm getting a lot of references to the CPython filenames. I don't know how to check if anyone is making calls to the function. But, maybe that's the point and it can't be removed if there's a chance that anyone uses it? Thanks!
This is what I tried on Github:
PyGen_NeedsFinalizing -filename:ceval -filename:genobject -filename:gcmodule

I think https://searchcode.com/ may have a larger indexing base than GitHub alone.
And, yes, you'll see many duplicates of the CPython source code... Visual inspection may be needed :-/

Thanks again, Antoine. I'll see what I can come up with. :-)

My searches show references to this function in CPython cloned repositories. From @pitrous's views, I think it is better to deprecate it with a removal notice for a later release.
I have deprecated the Function instead and will be removed in the next release in this PR https://github.com/python/cpython/pull/15702 .

PyGen_NeedsFinalizing() was added by:
commit 49fd7fa4431da299196d74087df4a04f99f9c46f
Author: Thomas Wouters <thomas@python.org>
Date: Fri Apr 21 10:40:58 2006 +0000
 Merge p3yk branch with the trunk up to revision 45595. This breaks a fair
 number of tests, all because of the codecs/_multibytecodecs issue described
 here (it's not a Py3K issue, just something Py3K discovers):
 http://mail.python.org/pipermail/python-dev/2006-April/064051.html
 
 Hye-Shik Chang promised to look for a fix, so no need to fix it here. The
 tests that are expected to break are:
 
 test_codecencodings_cn
 test_codecencodings_hk
 test_codecencodings_jp
 test_codecencodings_kr
 test_codecencodings_tw
 test_codecs
 test_multibytecodec
 
 This merge fixes an actual test failure (test_weakref) in this branch,
 though, so I believe merging is the right thing to do anyway.
It was used in this gcmodule.c function:
/* Return true if object has a finalization method.
 * CAUTION: An instance of an old-style class has to be checked for a
 *__del__ method, and earlier versions of this used to call PyObject_HasAttr,
 * which in turn could call the class's __getattr__ hook (if any). That
 * could invoke arbitrary Python code, mutating the object graph in arbitrary
 * ways, and that was the source of some excruciatingly subtle bugs.
 */
static int
has_finalizer(PyObject *op)
{
 if (PyInstance_Check(op)) {
 assert(delstr != NULL);
 return _PyInstance_Lookup(op, delstr) != NULL;
 }
 else if (PyType_HasFeature(op->ob_type, Py_TPFLAGS_HEAPTYPE))
 return op->ob_type->tp_del != NULL;
 else if (PyGen_CheckExact(op))
 return PyGen_NeedsFinalizing((PyGenObject *)op);
 else
 return 0;
}
(2) The PEP 442 implementation made PyGen_NeedsFinalizing() useless:
commit 796564c27b8f2e32b9fbc034bbdda75f9507ca43
Author: Antoine Pitrou <solipsis@pitrou.net>
Date: Tue Jul 30 19:59:21 2013 +0200
 Issue #18112: PEP 442 implementation (safe object finalization).
Replaced:
/* Return true if object has a finalization method. */
static int
has_finalizer(PyObject *op)
{
 if (PyGen_CheckExact(op))
 return PyGen_NeedsFinalizing((PyGenObject *)op);
 else
 return op->ob_type->tp_del != NULL;
}
with:
/* Return true if object has a pre-PEP 442 finalization method. */
static int
has_legacy_finalizer(PyObject *op)
{
 return op->ob_type->tp_del != NULL;
}
--
The last reference to PyGen_NeedsFinalizing() can be found in ceval.c:
 case TARGET(SETUP_FINALLY): {
 /* NOTE: If you add any new block-setup opcodes that
 are not try/except/finally handlers, you may need
 to update the PyGen_NeedsFinalizing() function.
 */
 PyFrame_BlockSetup(f, SETUP_FINALLY, INSTR_OFFSET() + oparg,
 STACK_LEVEL());
 DISPATCH();
 }

The function is not documented nor tested.
I searched for usage of PyGen_NeedsFinalizing() in C code in GitHub:
https://github.com/search?l=C&p=1&q=PyGen_NeedsFinalizing&type=Code
I only found copies of the CPython code source: PyGen_NeedsFinalizing() definition in genobject.h.
IHMO we can safely remove the function right now. If someone complains, we can reintroduce it later. We just have to document clearly its removal at:
https://docs.python.org/dev/whatsnew/3.9.html#build-and-c-api-changes 

New changeset 74b662cf202753d224d82d5503974cce881f7436 by Victor Stinner (Joannah Nanjekye) in branch 'master':
bpo-15088 : Remove PyGen_NeedsFinalizing() (GH-15702)
https://github.com/python/cpython/commit/74b662cf202753d224d82d5503974cce881f7436

I merged Joannah's change: thanks.
If anyone uses the removed function, please complain before Python 3.9.0 release :-)