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Attached patch implements the PEP 510 "Specialize functions with guards".
Changes on the C API are described in the PEP:
https://www.python.org/dev/peps/pep-0510/#changes
Additions of the patch:
* Add func_specialize() and func_get_specialized() to _testcapi
* Add _testcapi.PyGuard: Python wrapper to the Guard C API
* Add Lib/test/test_pep510.py 

Patch version 2 fixes some bugs and add more tests.
More notes about the patch:
* RuntimeError is raised if guard check() result is greater than 2
* RuntimeError is raised if guard init() result is greater than 1
* (hum, maybe 'res < 0' check must be replaced with 'res == -1', but I'm not sure that that it's worth it.)
* If PyFunction_Specialize() is called with a code object or a Python code, it creates a new code object and copies the code name and first line number in the new code object to ease debugging
TODO: keywords are currently not supported in PyGuard.__call__().

An unit test is needed on pickle serialization to ensure that the specialize code and guards are ignored.

Patch version 3:
* guards are now tracked by the garbage collector. That's a very important requirements to not change the Python semantics at exit, when a guard keeps a strong reference to the global namespace:
https://mail.python.org/pipermail/python-dev/2016-January/142792.html
* add more tests: call specialize() with invalid types, set __code__

Patch version 4:
* Keywords are now supported everywhere and tested by unit tests
* Inline specode_check() into PyFunction_GetSpecializedCode()

Patch version 5: implement PyFunction_RemoveSpecialized() and PyFunction_RemoveAllSpecialized() functions (with unit tests!).
I'm not sure that PyFunction_RemoveSpecialized() must return 0 (success) if the removed specialized code doesn't exist (invalid index).

FIXME: sys.getsizecode(func) doesn't include specialized code and guards.

Patch version 6: I inlined PyFunction_GetSpecializedCode() into fast_function() of Python/ceval.c. It reduces *a little bit* the overhead of the patch when specialization is not used, but it also avoids to expose this function. I don't think that it's worth to expose PyFunction_GetSpecializedCode(): it was only used in ceval.c. For example, I don't use it for unit tests. I prefer to write tests calling the function and checking the results (see test_pep510.py).
*Raw* overhead of specialized-6.patch on calling "def f(): pass": 1.7 nanoseconds. I computed the overhead using timeit:
./python -m timeit -s 'def f(): pass' 'f()'
* Original: 71.7 ns
* specialize-6.patch: 73.4 ns (+1.7 ns, +2.4%)
* specialize-5.patch: 74.3 ns (+2.6 ns, +3.6%)
I will run perf.py to see the overhead on a macro benchmark.

Results of the "The Grand Unified Python Benchmark Suite" on specialize-6.patch.
I'm skeptical, I don't understand how my patch can make a benchmark faster :-) The result of regex_v8 is bad :-/
$ python3 -u perf.py --rigorous ../default/python.orig ../default/python
(...)
Report on Linux smithers 4.3.3-300.fc23.x86_64 #1 SMP Tue Jan 5 23:31:01 UTC 2016 x86_64 x86_64
Total CPU cores: 8
### chameleon_v2 ###
Min: 5.558607 -> 5.831682: 1.05x slower
Avg: 5.613403 -> 5.902949: 1.05x slower
Significant (t=-27.95)
Stddev: 0.06994 -> 0.07640: 1.0924x larger
### django_v3 ###
Min: 0.582356 -> 0.573327: 1.02x faster
Avg: 0.604402 -> 0.582197: 1.04x faster
Significant (t=3.43)
Stddev: 0.05618 -> 0.03215: 1.7474x smaller
### regex_v8 ###
Min: 0.043784 -> 0.049854: 1.14x slower
Avg: 0.044270 -> 0.050521: 1.14x slower
Significant (t=-19.87)
Stddev: 0.00200 -> 0.00243: 1.2105x larger
The following not significant results are hidden, use -v to show them:
2to3, fastpickle, fastunpickle, json_dump_v2, json_load, nbody, tornado_http.

Patch version 7:
* Fix a random crash related to _testcapi.PyGuard: implement tp_traverse on PyFuncGuard and "inherit" tp_traverse on PyGuard
* Fix a typo Include/funcobject.h
* (rebase the patch)

Oh, I missed comments on the code review. Fixed on patch version 8.

Recently, some people asked me for an update for my FAT Python project. So I rebased this change I wrote 1 year 1/2 and adapted it for the new code base:
* I renamed test_pep510.py to test_func_specialize.py
* I removed the useless PyFunction_Check() macro
* I changed the guard check prototype to use the new FASTCALL calling convention: (PyObject **args, Py_ssize_t nargs, PyObject *kwnames: tuple)
* I patched _PyFunction_FastCallDict() *and* PyFunction_FastCallKeywords() to check guards and call specified code if guards succeeded
The PEP 510 is not accepted, so the implementation is still a work-in-progress (WIP) and must not be merged.

I rejected my own PEP 510, so I reject this issue as well.
https://mail.python.org/pipermail/python-dev/2017-October/149901.html