diff --git a/Include/cpython/abstract.h b/Include/cpython/abstract.h
index dd924dfd3d8..1f495f19df2 100644
--- a/Include/cpython/abstract.h
+++ b/Include/cpython/abstract.h
@@ -53,13 +53,3 @@ PyAPI_FUNC(Py_ssize_t) PyObject_LengthHint(PyObject *o, Py_ssize_t);
    need to be corrected for a negative index. */
 #define PySequence_ITEM(o, i)\
     ( Py_TYPE(o)->tp_as_sequence->sq_item((o), (i)) )
-
-/* === Mapping protocol ================================================= */
-
-// Convert Python int to Py_ssize_t. Do nothing if the argument is None.
-// Cannot be moved to the internal C API: used by Argument Clinic.
-PyAPI_FUNC(int) _Py_convert_optional_to_ssize_t(PyObject *, void *);
-
-// Same as PyNumber_Index but can return an instance of a subclass of int.
-// Cannot be moved to the internal C API: used by Argument Clinic.
-PyAPI_FUNC(PyObject *) _PyNumber_Index(PyObject *o);
diff --git a/Include/internal/pycore_abstract.h b/Include/internal/pycore_abstract.h
index 2733d8102e5..3cc0afac4bd 100644
--- a/Include/internal/pycore_abstract.h
+++ b/Include/internal/pycore_abstract.h
@@ -47,6 +47,13 @@ extern int _PyObject_RealIsInstance(PyObject *inst, PyObject *cls);
 
 extern int _PyObject_RealIsSubclass(PyObject *derived, PyObject *cls);
 
+// Convert Python int to Py_ssize_t. Do nothing if the argument is None.
+// Export for '_bisect' shared extension.
+PyAPI_FUNC(int) _Py_convert_optional_to_ssize_t(PyObject *, void *);
+
+// Same as PyNumber_Index() but can return an instance of a subclass of int.
+// Export for 'math' shared extension.
+PyAPI_FUNC(PyObject*) _PyNumber_Index(PyObject *o);
 
 #ifdef __cplusplus
 }
diff --git a/Modules/_io/_iomodule.c b/Modules/_io/_iomodule.c
index f56654227f1..0762e26a36c 100644
--- a/Modules/_io/_iomodule.c
+++ b/Modules/_io/_iomodule.c
@@ -8,6 +8,7 @@
 */
 
 #include "Python.h"
+#include "pycore_abstract.h"      // _PyNumber_Index()
 #include "pycore_initconfig.h"    // _PyStatus_OK()
 #include "pycore_pystate.h"       // _PyInterpreterState_GET()
 
diff --git a/Modules/_io/clinic/bufferedio.c.h b/Modules/_io/clinic/bufferedio.c.h
index b9b42cf3428..32c4a4e177c 100644
--- a/Modules/_io/clinic/bufferedio.c.h
+++ b/Modules/_io/clinic/bufferedio.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 
 PyDoc_STRVAR(_io__BufferedIOBase_readinto__doc__,
 "readinto($self, buffer, /)\n"
@@ -1098,4 +1099,4 @@ skip_optional_pos:
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=e5b335441452653d input=a9049054013a1b77]*/
+/*[clinic end generated code: output=768c3a3a3deabcb4 input=a9049054013a1b77]*/
diff --git a/Modules/_io/clinic/bytesio.c.h b/Modules/_io/clinic/bytesio.c.h
index 52c9c2c5ecb..b5cdd0802b8 100644
--- a/Modules/_io/clinic/bytesio.c.h
+++ b/Modules/_io/clinic/bytesio.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _Py_convert_optional_to_ssize_t()
 
 PyDoc_STRVAR(_io_BytesIO_readable__doc__,
 "readable($self, /)\n"
@@ -538,4 +539,4 @@ skip_optional_pos:
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=8d4e7651002e14c6 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=6b1219bda0619e2a input=a9049054013a1b77]*/
diff --git a/Modules/_io/clinic/fileio.c.h b/Modules/_io/clinic/fileio.c.h
index 9f5198d45ab..7b63e36b503 100644
--- a/Modules/_io/clinic/fileio.c.h
+++ b/Modules/_io/clinic/fileio.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _Py_convert_optional_to_ssize_t()
 
 PyDoc_STRVAR(_io_FileIO_close__doc__,
 "close($self, /)\n"
@@ -536,4 +537,4 @@ _io_FileIO_isatty(fileio *self, PyObject *Py_UNUSED(ignored))
 #ifndef _IO_FILEIO_TRUNCATE_METHODDEF
     #define _IO_FILEIO_TRUNCATE_METHODDEF
 #endif /* !defined(_IO_FILEIO_TRUNCATE_METHODDEF) */
-/*[clinic end generated code: output=65b9a5cc96d193b6 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=3a3c6ed7e5e78063 input=a9049054013a1b77]*/
diff --git a/Modules/_io/clinic/iobase.c.h b/Modules/_io/clinic/iobase.c.h
index a539125a2a8..f582b9d2c71 100644
--- a/Modules/_io/clinic/iobase.c.h
+++ b/Modules/_io/clinic/iobase.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _Py_convert_optional_to_ssize_t()
 
 PyDoc_STRVAR(_io__IOBase_seek__doc__,
 "seek($self, offset, whence=os.SEEK_SET, /)\n"
@@ -436,4 +437,4 @@ _io__RawIOBase_readall(PyObject *self, PyObject *Py_UNUSED(ignored))
 {
     return _io__RawIOBase_readall_impl(self);
 }
-/*[clinic end generated code: output=0f064cfd54e3c1a5 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=ec741e0961671a86 input=a9049054013a1b77]*/
diff --git a/Modules/_io/clinic/stringio.c.h b/Modules/_io/clinic/stringio.c.h
index d0acfdb4bf3..dbe1833a90e 100644
--- a/Modules/_io/clinic/stringio.c.h
+++ b/Modules/_io/clinic/stringio.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _Py_convert_optional_to_ssize_t()
 
 PyDoc_STRVAR(_io_StringIO_getvalue__doc__,
 "getvalue($self, /)\n"
@@ -367,4 +368,4 @@ _io_StringIO_seekable(stringio *self, PyObject *Py_UNUSED(ignored))
 {
     return _io_StringIO_seekable_impl(self);
 }
-/*[clinic end generated code: output=6f55dc1454aeb507 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=09d4056cc8c4aae4 input=a9049054013a1b77]*/
diff --git a/Modules/_io/clinic/textio.c.h b/Modules/_io/clinic/textio.c.h
index d653cc87ae3..03d5facedfb 100644
--- a/Modules/_io/clinic/textio.c.h
+++ b/Modules/_io/clinic/textio.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _Py_convert_optional_to_ssize_t()
 
 PyDoc_STRVAR(_io__TextIOBase_detach__doc__,
 "detach($self, /)\n"
@@ -975,4 +976,4 @@ _io_TextIOWrapper_close(textio *self, PyObject *Py_UNUSED(ignored))
 {
     return _io_TextIOWrapper_close_impl(self);
 }
-/*[clinic end generated code: output=29b945b24287dd0c input=a9049054013a1b77]*/
+/*[clinic end generated code: output=c3a8eb2591be1bf7 input=a9049054013a1b77]*/
diff --git a/Modules/_io/clinic/winconsoleio.c.h b/Modules/_io/clinic/winconsoleio.c.h
index cd3348dc122..53f971e37c1 100644
--- a/Modules/_io/clinic/winconsoleio.c.h
+++ b/Modules/_io/clinic/winconsoleio.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _Py_convert_optional_to_ssize_t()
 
 #if defined(HAVE_WINDOWS_CONSOLE_IO)
 
@@ -465,4 +466,4 @@ _io__WindowsConsoleIO_isatty(winconsoleio *self, PyObject *Py_UNUSED(ignored))
 #ifndef _IO__WINDOWSCONSOLEIO_ISATTY_METHODDEF
     #define _IO__WINDOWSCONSOLEIO_ISATTY_METHODDEF
 #endif /* !defined(_IO__WINDOWSCONSOLEIO_ISATTY_METHODDEF) */
-/*[clinic end generated code: output=235393758365c229 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=0cdb16d95f1c7dac input=a9049054013a1b77]*/
diff --git a/Modules/_sre/clinic/sre.c.h b/Modules/_sre/clinic/sre.c.h
index a303a557ca5..1846f175b45 100644
--- a/Modules/_sre/clinic/sre.c.h
+++ b/Modules/_sre/clinic/sre.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 
 PyDoc_STRVAR(_sre_getcodesize__doc__,
 "getcodesize($module, /)\n"
@@ -1460,4 +1461,4 @@ _sre_SRE_Scanner_search(ScannerObject *self, PyTypeObject *cls, PyObject *const
     }
     return _sre_SRE_Scanner_search_impl(self, cls);
 }
-/*[clinic end generated code: output=6b84e62c87238f0e input=a9049054013a1b77]*/
+/*[clinic end generated code: output=b8cf77f05e44d08c input=a9049054013a1b77]*/
diff --git a/Modules/clinic/_bisectmodule.c.h b/Modules/clinic/_bisectmodule.c.h
index 7944f5219b0..62ce0fc8172 100644
--- a/Modules/clinic/_bisectmodule.c.h
+++ b/Modules/clinic/_bisectmodule.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 
 PyDoc_STRVAR(_bisect_bisect_right__doc__,
 "bisect_right($module, /, a, x, lo=0, hi=None, *, key=None)\n"
@@ -433,4 +434,4 @@ skip_optional_kwonly:
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=5a7fa64bf9b262f3 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=839fdddeacdc2ecb input=a9049054013a1b77]*/
diff --git a/Modules/clinic/_bz2module.c.h b/Modules/clinic/_bz2module.c.h
index 6ad2db3ce1d..7c4d57b5fec 100644
--- a/Modules/clinic/_bz2module.c.h
+++ b/Modules/clinic/_bz2module.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 
 PyDoc_STRVAR(_bz2_BZ2Compressor_compress__doc__,
 "compress($self, data, /)\n"
@@ -241,4 +242,4 @@ _bz2_BZ2Decompressor(PyTypeObject *type, PyObject *args, PyObject *kwargs)
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=431fd0fc40f019d1 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=40706688f92642b4 input=a9049054013a1b77]*/
diff --git a/Modules/clinic/_collectionsmodule.c.h b/Modules/clinic/_collectionsmodule.c.h
index 3882d069216..b96502d3cf4 100644
--- a/Modules/clinic/_collectionsmodule.c.h
+++ b/Modules/clinic/_collectionsmodule.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 
 PyDoc_STRVAR(_collections__count_elements__doc__,
 "_count_elements($module, mapping, iterable, /)\n"
@@ -75,4 +76,4 @@ tuplegetter_new(PyTypeObject *type, PyObject *args, PyObject *kwargs)
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=00e516317d2b8bed input=a9049054013a1b77]*/
+/*[clinic end generated code: output=d83188040656ad7c input=a9049054013a1b77]*/
diff --git a/Modules/clinic/_elementtree.c.h b/Modules/clinic/_elementtree.c.h
index a0bc751ca21..78e456b6a43 100644
--- a/Modules/clinic/_elementtree.c.h
+++ b/Modules/clinic/_elementtree.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 
 PyDoc_STRVAR(_elementtree_Element_append__doc__,
 "append($self, subelement, /)\n"
@@ -1218,4 +1219,4 @@ skip_optional:
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=40767b1a98e54b60 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=0a34620406b95eb0 input=a9049054013a1b77]*/
diff --git a/Modules/clinic/_hashopenssl.c.h b/Modules/clinic/_hashopenssl.c.h
index fb61a444018..0ea192eac2d 100644
--- a/Modules/clinic/_hashopenssl.c.h
+++ b/Modules/clinic/_hashopenssl.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 
 PyDoc_STRVAR(EVP_copy__doc__,
 "copy($self, /)\n"
@@ -1851,4 +1852,4 @@ exit:
 #ifndef _HASHLIB_SCRYPT_METHODDEF
     #define _HASHLIB_SCRYPT_METHODDEF
 #endif /* !defined(_HASHLIB_SCRYPT_METHODDEF) */
-/*[clinic end generated code: output=b339e255db698147 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=cfad8d5e904a4917 input=a9049054013a1b77]*/
diff --git a/Modules/clinic/_lzmamodule.c.h b/Modules/clinic/_lzmamodule.c.h
index 017b24f765e..ceb75399157 100644
--- a/Modules/clinic/_lzmamodule.c.h
+++ b/Modules/clinic/_lzmamodule.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 
 PyDoc_STRVAR(_lzma_LZMACompressor_compress__doc__,
 "compress($self, data, /)\n"
@@ -338,4 +339,4 @@ exit:
 
     return return_value;
 }
-/*[clinic end generated code: output=aaf225a5d15d3e75 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=f1a001f5f489c372 input=a9049054013a1b77]*/
diff --git a/Modules/clinic/_operator.c.h b/Modules/clinic/_operator.c.h
index b68e6e0144a..18b0b920b0d 100644
--- a/Modules/clinic/_operator.c.h
+++ b/Modules/clinic/_operator.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 
 PyDoc_STRVAR(_operator_truth__doc__,
 "truth($module, a, /)\n"
@@ -1492,4 +1493,4 @@ _operator__compare_digest(PyObject *module, PyObject *const *args, Py_ssize_t na
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=227cbcfed44f736e input=a9049054013a1b77]*/
+/*[clinic end generated code: output=72bc63a775937245 input=a9049054013a1b77]*/
diff --git a/Modules/clinic/_ssl.c.h b/Modules/clinic/_ssl.c.h
index 81712617bee..6ab8e3ee436 100644
--- a/Modules/clinic/_ssl.c.h
+++ b/Modules/clinic/_ssl.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 
 PyDoc_STRVAR(_ssl__SSLSocket_do_handshake__doc__,
 "do_handshake($self, /)\n"
@@ -1542,4 +1543,4 @@ exit:
 #ifndef _SSL_ENUM_CRLS_METHODDEF
     #define _SSL_ENUM_CRLS_METHODDEF
 #endif /* !defined(_SSL_ENUM_CRLS_METHODDEF) */
-/*[clinic end generated code: output=4c9f00c62f0825d2 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=6e2eb86330f3f9b8 input=a9049054013a1b77]*/
diff --git a/Modules/clinic/_struct.c.h b/Modules/clinic/_struct.c.h
index c3cf179ed4c..a8233644478 100644
--- a/Modules/clinic/_struct.c.h
+++ b/Modules/clinic/_struct.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 
 PyDoc_STRVAR(Struct__doc__,
 "Struct(format)\n"
@@ -451,4 +452,4 @@ exit:
 
     return return_value;
 }
-/*[clinic end generated code: output=f3d6e06f80368998 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=9b48aeaa86898ec5 input=a9049054013a1b77]*/
diff --git a/Modules/clinic/_testclinic.c.h b/Modules/clinic/_testclinic.c.h
index 3c04c41599c..94c4b5a1221 100644
--- a/Modules/clinic/_testclinic.c.h
+++ b/Modules/clinic/_testclinic.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 #include "pycore_long.h"           // _PyLong_UnsignedShort_Converter()
 
 PyDoc_STRVAR(test_empty_function__doc__,
@@ -3070,4 +3071,4 @@ skip_optional_pos:
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=41f439aab0cb809d input=a9049054013a1b77]*/
+/*[clinic end generated code: output=a652e6b1787d3346 input=a9049054013a1b77]*/
diff --git a/Modules/clinic/_testclinic_depr.c.h b/Modules/clinic/_testclinic_depr.c.h
index 71cb972b951..7b9d8971efb 100644
--- a/Modules/clinic/_testclinic_depr.c.h
+++ b/Modules/clinic/_testclinic_depr.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 #include "pycore_long.h"           // _PyLong_UnsignedShort_Converter()
 
 PyDoc_STRVAR(depr_star_new__doc__,
@@ -2392,4 +2393,4 @@ depr_multi(PyObject *module, PyObject *const *args, Py_ssize_t nargs, PyObject *
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=22b59d92d517a8ec input=a9049054013a1b77]*/
+/*[clinic end generated code: output=464aeba97e482f5c input=a9049054013a1b77]*/
diff --git a/Modules/clinic/arraymodule.c.h b/Modules/clinic/arraymodule.c.h
index 5e957013ad0..8bdfcc62bef 100644
--- a/Modules/clinic/arraymodule.c.h
+++ b/Modules/clinic/arraymodule.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 
 PyDoc_STRVAR(array_array___copy____doc__,
 "__copy__($self, /)\n"
@@ -674,4 +675,4 @@ PyDoc_STRVAR(array_arrayiterator___setstate____doc__,
 
 #define ARRAY_ARRAYITERATOR___SETSTATE___METHODDEF    \
     {"__setstate__", (PyCFunction)array_arrayiterator___setstate__, METH_O, array_arrayiterator___setstate____doc__},
-/*[clinic end generated code: output=db417f5677a25eaa input=a9049054013a1b77]*/
+/*[clinic end generated code: output=ab24c7a40a41c2e1 input=a9049054013a1b77]*/
diff --git a/Modules/clinic/gcmodule.c.h b/Modules/clinic/gcmodule.c.h
index 0ea5b40cfb7..290a8aaa272 100644
--- a/Modules/clinic/gcmodule.c.h
+++ b/Modules/clinic/gcmodule.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _Py_convert_optional_to_ssize_t()
 
 PyDoc_STRVAR(gc_enable__doc__,
 "enable($module, /)\n"
@@ -424,4 +425,4 @@ gc_get_freeze_count(PyObject *module, PyObject *Py_UNUSED(ignored))
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=16003cfbc66ada39 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=fe89ce0b90a1067d input=a9049054013a1b77]*/
diff --git a/Modules/clinic/itertoolsmodule.c.h b/Modules/clinic/itertoolsmodule.c.h
index 32278bf715a..6555bd495b2 100644
--- a/Modules/clinic/itertoolsmodule.c.h
+++ b/Modules/clinic/itertoolsmodule.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 
 PyDoc_STRVAR(batched_new__doc__,
 "batched(iterable, n)\n"
@@ -913,4 +914,4 @@ skip_optional_pos:
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=111cbd102c2a23c9 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=20999801c7349d2c input=a9049054013a1b77]*/
diff --git a/Modules/clinic/posixmodule.c.h b/Modules/clinic/posixmodule.c.h
index 4b85519b532..e80bbff6b51 100644
--- a/Modules/clinic/posixmodule.c.h
+++ b/Modules/clinic/posixmodule.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 #include "pycore_fileutils.h"      // _PyLong_FileDescriptor_Converter()
 #include "pycore_long.h"           // _PyLong_UnsignedInt_Converter()
 
@@ -11992,4 +11993,4 @@ exit:
 #ifndef OS_WAITSTATUS_TO_EXITCODE_METHODDEF
     #define OS_WAITSTATUS_TO_EXITCODE_METHODDEF
 #endif /* !defined(OS_WAITSTATUS_TO_EXITCODE_METHODDEF) */
-/*[clinic end generated code: output=ff0e50316f4ed71a input=a9049054013a1b77]*/
+/*[clinic end generated code: output=1b34619e5f65adc2 input=a9049054013a1b77]*/
diff --git a/Modules/clinic/zlibmodule.c.h b/Modules/clinic/zlibmodule.c.h
index 3d71536c846..1debe2ae989 100644
--- a/Modules/clinic/zlibmodule.c.h
+++ b/Modules/clinic/zlibmodule.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 
 PyDoc_STRVAR(zlib_compress__doc__,
 "compress($module, data, /, level=Z_DEFAULT_COMPRESSION, wbits=MAX_WBITS)\n"
@@ -1129,4 +1130,4 @@ exit:
 #ifndef ZLIB_DECOMPRESS___DEEPCOPY___METHODDEF
     #define ZLIB_DECOMPRESS___DEEPCOPY___METHODDEF
 #endif /* !defined(ZLIB_DECOMPRESS___DEEPCOPY___METHODDEF) */
-/*[clinic end generated code: output=3eccb3f7265d53ba input=a9049054013a1b77]*/
+/*[clinic end generated code: output=d574a79aa47c9969 input=a9049054013a1b77]*/
diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 0d238c086ac..d929dcf65a7 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -57,6 +57,7 @@ raised for division by zero and mod by zero.
 #endif
 
 #include "Python.h"
+#include "pycore_abstract.h"      // _PyNumber_Index()
 #include "pycore_bitutils.h"      // _Py_bit_length()
 #include "pycore_call.h"          // _PyObject_CallNoArgs()
 #include "pycore_long.h"          // _PyLong_GetZero()
diff --git a/Modules/mmapmodule.c b/Modules/mmapmodule.c
index 5c131570123..44d5b268e1b 100644
--- a/Modules/mmapmodule.c
+++ b/Modules/mmapmodule.c
@@ -23,6 +23,7 @@
 #endif
 
 #include <Python.h>
+#include "pycore_abstract.h"      // _Py_convert_optional_to_ssize_t()
 #include "pycore_bytesobject.h"   // _PyBytes_Find()
 #include "pycore_fileutils.h"     // _Py_stat_struct
 
diff --git a/Modules/posixmodule.c b/Modules/posixmodule.c
index cffa401d2ce..8eb25fc2424 100644
--- a/Modules/posixmodule.c
+++ b/Modules/posixmodule.c
@@ -12,6 +12,7 @@
 #ifdef __VXWORKS__
 #  include "pycore_bitutils.h"    // _Py_popcount32()
 #endif
+#include "pycore_abstract.h"      // _PyNumber_Index()
 #include "pycore_call.h"          // _PyObject_CallNoArgs()
 #include "pycore_ceval.h"         // _PyEval_ReInitThreads()
 #include "pycore_fileutils.h"     // _Py_closerange()
diff --git a/Objects/clinic/bytearrayobject.c.h b/Objects/clinic/bytearrayobject.c.h
index ecb08a86c2a..f091fc7afbd 100644
--- a/Objects/clinic/bytearrayobject.c.h
+++ b/Objects/clinic/bytearrayobject.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 
 static int
 bytearray___init___impl(PyByteArrayObject *self, PyObject *arg,
@@ -1284,4 +1285,4 @@ bytearray_sizeof(PyByteArrayObject *self, PyObject *Py_UNUSED(ignored))
 {
     return bytearray_sizeof_impl(self);
 }
-/*[clinic end generated code: output=cb94d7ac45f0a4b7 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=d388e9027b333f00 input=a9049054013a1b77]*/
diff --git a/Objects/clinic/bytesobject.c.h b/Objects/clinic/bytesobject.c.h
index 904ff07e97c..66db76dbbb4 100644
--- a/Objects/clinic/bytesobject.c.h
+++ b/Objects/clinic/bytesobject.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 
 PyDoc_STRVAR(bytes___bytes____doc__,
 "__bytes__($self, /)\n"
@@ -1060,4 +1061,4 @@ skip_optional_pos:
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=f4e85363c79c64d3 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=9da56b6c04914e18 input=a9049054013a1b77]*/
diff --git a/Objects/clinic/listobject.c.h b/Objects/clinic/listobject.c.h
index e3d6ffa9f76..a41ed3e4b04 100644
--- a/Objects/clinic/listobject.c.h
+++ b/Objects/clinic/listobject.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 
 PyDoc_STRVAR(list_insert__doc__,
 "insert($self, index, object, /)\n"
@@ -383,4 +384,4 @@ list___reversed__(PyListObject *self, PyObject *Py_UNUSED(ignored))
 {
     return list___reversed___impl(self);
 }
-/*[clinic end generated code: output=2ca109d8acc775bc input=a9049054013a1b77]*/
+/*[clinic end generated code: output=537a17b562c57505 input=a9049054013a1b77]*/
diff --git a/Objects/clinic/longobject.c.h b/Objects/clinic/longobject.c.h
index d37e44f2f33..3ecef1f0fd5 100644
--- a/Objects/clinic/longobject.c.h
+++ b/Objects/clinic/longobject.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 
 static PyObject *
 long_new_impl(PyTypeObject *type, PyObject *x, PyObject *obase);
@@ -475,4 +476,4 @@ int_is_integer(PyObject *self, PyObject *Py_UNUSED(ignored))
 {
     return int_is_integer_impl(self);
 }
-/*[clinic end generated code: output=75ed306fff493ba1 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=ea9c87ea532dadbe input=a9049054013a1b77]*/
diff --git a/Objects/clinic/unicodeobject.c.h b/Objects/clinic/unicodeobject.c.h
index 7edb4bc7609..56b64087d66 100644
--- a/Objects/clinic/unicodeobject.c.h
+++ b/Objects/clinic/unicodeobject.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 
 PyDoc_STRVAR(EncodingMap_size__doc__,
 "size($self, /)\n"
@@ -1504,4 +1505,4 @@ skip_optional_pos:
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=2e1e1b136ef1b681 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=a64776a3ea1c970c input=a9049054013a1b77]*/
diff --git a/Objects/floatobject.c b/Objects/floatobject.c
index 6a0c2e033e3..1c5078bdda6 100644
--- a/Objects/floatobject.c
+++ b/Objects/floatobject.c
@@ -4,6 +4,7 @@
    for any kind of float exception without losing portability. */
 
 #include "Python.h"
+#include "pycore_abstract.h"      // _PyNumber_Index()
 #include "pycore_dtoa.h"          // _Py_dg_dtoa()
 #include "pycore_floatobject.h"   // _PyFloat_FormatAdvancedWriter()
 #include "pycore_initconfig.h"    // _PyStatus_OK()
diff --git a/Objects/stringlib/clinic/transmogrify.h.h b/Objects/stringlib/clinic/transmogrify.h.h
index 1e0df0958d6..d1adda4e979 100644
--- a/Objects/stringlib/clinic/transmogrify.h.h
+++ b/Objects/stringlib/clinic/transmogrify.h.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 
 PyDoc_STRVAR(stringlib_expandtabs__doc__,
 "expandtabs($self, /, tabsize=8)\n"
@@ -278,4 +279,4 @@ stringlib_zfill(PyObject *self, PyObject *arg)
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=00e34c03331699fe input=a9049054013a1b77]*/
+/*[clinic end generated code: output=a0338b2d41671b17 input=a9049054013a1b77]*/
diff --git a/Python/clinic/_warnings.c.h b/Python/clinic/_warnings.c.h
index b39e412a7d6..1a01416e736 100644
--- a/Python/clinic/_warnings.c.h
+++ b/Python/clinic/_warnings.c.h
@@ -7,6 +7,7 @@ preserve
 #  include "pycore_runtime.h"       // _Py_ID()
 #endif
 
+#include "pycore_abstract.h"       // _PyNumber_Index()
 
 PyDoc_STRVAR(warnings_warn__doc__,
 "warn($module, /, message, category=None, stacklevel=1, source=None, *,\n"
@@ -243,4 +244,4 @@ warnings_filters_mutated(PyObject *module, PyObject *Py_UNUSED(ignored))
 {
     return warnings_filters_mutated_impl(module);
 }
-/*[clinic end generated code: output=0e2b367a662bf51b input=a9049054013a1b77]*/
+/*[clinic end generated code: output=c8a6dc1403fba1d5 input=a9049054013a1b77]*/
diff --git a/Python/getargs.c b/Python/getargs.c
index 809b2d4ef17..fdc144488c9 100644
--- a/Python/getargs.c
+++ b/Python/getargs.c
@@ -2,6 +2,7 @@
 /* New getargs implementation */
 
 #include "Python.h"
+#include "pycore_abstract.h"      // _PyNumber_Index()
 #include "pycore_dict.h"          // _PyDict_HasOnlyStringKeys()
 #include "pycore_pylifecycle.h"   // _PyArg_Fini
 #include "pycore_tuple.h"         // _PyTuple_ITEMS()
diff --git a/Tools/c-analyzer/c_parser/preprocessor/gcc.py b/Tools/c-analyzer/c_parser/preprocessor/gcc.py
index de9a2484de8..55cc2d37e1e 100644
--- a/Tools/c-analyzer/c_parser/preprocessor/gcc.py
+++ b/Tools/c-analyzer/c_parser/preprocessor/gcc.py
@@ -3,26 +3,14 @@ import re
 
 from . import common as _common
 
-# Modules/socketmodule.h uses pycore_time.h which needs the Py_BUILD_CORE
-# macro. Usually it's defined by the C file which includes it.
-# Other header files have a similar issue.
-NEED_BUILD_CORE = {
-    # Header ".h" files
-    'cjkcodecs.h',
-    'multibytecodec.h',
-    'socketmodule.h',
-
-    # Argument Clinic ".c.h" header files
-    '_testclinic.c.h',
-    '_testclinic_depr.c.h',
-    '_winapi.c.h',
-    'fcntlmodule.c.h',
-    'overlapped.c.h',
-    'posixmodule.c.h',
-    'selectmodule.c.h',
-    'sha3module.c.h',
-    'termios.c.h',
-}
+# The following C files must not be built with Py_BUILD_CORE,
+# because they use the limited C API.
+USE_LIMITED_C_API = frozenset((
+    '_testcapimodule.c',
+    '_testclinic_limited.c',
+    'xxlimited.c',
+    'xxlimited_35.c',
+))
 
 TOOL = 'gcc'
 
@@ -81,8 +69,9 @@ def preprocess(filename,
         cwd = os.path.abspath(cwd or '.')
     filename = _normpath(filename, cwd)
 
+    print(filename)
     postargs = POST_ARGS
-    if os.path.basename(filename) in NEED_BUILD_CORE:
+    if os.path.basename(filename) not in USE_LIMITED_C_API:
         postargs += ('-DPy_BUILD_CORE=1',)
 
     text = _common.preprocess(
diff --git a/Tools/clinic/clinic.py b/Tools/clinic/clinic.py
index e622d254ee8..70ec18f726e 100755
--- a/Tools/clinic/clinic.py
+++ b/Tools/clinic/clinic.py
@@ -3795,8 +3795,11 @@ class Py_ssize_t_converter(CConverter):
         if accept == {int}:
             self.format_unit = 'n'
             self.default_type = int
+            self.add_include('pycore_abstract.h', '_PyNumber_Index()')
         elif accept == {int, NoneType}:
             self.converter = '_Py_convert_optional_to_ssize_t'
+            self.add_include('pycore_abstract.h',
+                             '_Py_convert_optional_to_ssize_t()')
         else:
             fail(f"Py_ssize_t_converter: illegal 'accept' argument {accept!r}")