diff --git a/contrib/clang-format-ignorelist b/contrib/clang-format-ignorelist
--- a/contrib/clang-format-ignorelist
+++ b/contrib/clang-format-ignorelist
@@ -9,3 +9,4 @@
 hgext/fsmonitor/pywatchman/**.c
 mercurial/thirdparty/**.c
 mercurial/thirdparty/**.h
+mercurial/pythoncapi_compat.h
diff --git a/contrib/python-zstandard/c-ext/bufferutil.c b/contrib/python-zstandard/c-ext/bufferutil.c
--- a/contrib/python-zstandard/c-ext/bufferutil.c
+++ b/contrib/python-zstandard/c-ext/bufferutil.c
@@ -758,7 +758,7 @@
 };
 
 void bufferutil_module_init(PyObject* mod) {
-	Py_TYPE(&ZstdBufferWithSegmentsType) = &PyType_Type;
+	Py_SET_TYPE(&ZstdBufferWithSegmentsType, &PyType_Type);
 	if (PyType_Ready(&ZstdBufferWithSegmentsType) < 0) {
 		return;
 	}
@@ -766,7 +766,7 @@
 	Py_INCREF(&ZstdBufferWithSegmentsType);
 	PyModule_AddObject(mod, "BufferWithSegments", (PyObject*)&ZstdBufferWithSegmentsType);
 
-	Py_TYPE(&ZstdBufferSegmentsType) = &PyType_Type;
+	Py_SET_TYPE(&ZstdBufferSegmentsType, &PyType_Type);
 	if (PyType_Ready(&ZstdBufferSegmentsType) < 0) {
 		return;
 	}
@@ -774,7 +774,7 @@
 	Py_INCREF(&ZstdBufferSegmentsType);
 	PyModule_AddObject(mod, "BufferSegments", (PyObject*)&ZstdBufferSegmentsType);
 
-	Py_TYPE(&ZstdBufferSegmentType) = &PyType_Type;
+	Py_SET_TYPE(&ZstdBufferSegmentType, &PyType_Type);
 	if (PyType_Ready(&ZstdBufferSegmentType) < 0) {
 		return;
 	}
@@ -782,7 +782,7 @@
 	Py_INCREF(&ZstdBufferSegmentType);
 	PyModule_AddObject(mod, "BufferSegment", (PyObject*)&ZstdBufferSegmentType);
 
-	Py_TYPE(&ZstdBufferWithSegmentsCollectionType) = &PyType_Type;
+	Py_SET_TYPE(&ZstdBufferWithSegmentsCollectionType, &PyType_Type);
 	if (PyType_Ready(&ZstdBufferWithSegmentsCollectionType) < 0) {
 		return;
 	}
diff --git a/contrib/python-zstandard/c-ext/compressionchunker.c b/contrib/python-zstandard/c-ext/compressionchunker.c
--- a/contrib/python-zstandard/c-ext/compressionchunker.c
+++ b/contrib/python-zstandard/c-ext/compressionchunker.c
@@ -348,12 +348,12 @@
 };
 
 void compressionchunker_module_init(PyObject* module) {
-	Py_TYPE(&ZstdCompressionChunkerIteratorType) = &PyType_Type;
+	Py_SET_TYPE(&ZstdCompressionChunkerIteratorType, &PyType_Type);
 	if (PyType_Ready(&ZstdCompressionChunkerIteratorType) < 0) {
 		return;
 	}
 
-	Py_TYPE(&ZstdCompressionChunkerType) = &PyType_Type;
+	Py_SET_TYPE(&ZstdCompressionChunkerType, &PyType_Type);
 	if (PyType_Ready(&ZstdCompressionChunkerType) < 0) {
 		return;
 	}
diff --git a/contrib/python-zstandard/c-ext/compressiondict.c b/contrib/python-zstandard/c-ext/compressiondict.c
--- a/contrib/python-zstandard/c-ext/compressiondict.c
+++ b/contrib/python-zstandard/c-ext/compressiondict.c
@@ -400,7 +400,7 @@
 };
 
 void compressiondict_module_init(PyObject* mod) {
-	Py_TYPE(&ZstdCompressionDictType) = &PyType_Type;
+	Py_SET_TYPE(&ZstdCompressionDictType, &PyType_Type);
 	if (PyType_Ready(&ZstdCompressionDictType) < 0) {
 		return;
 	}
diff --git a/contrib/python-zstandard/c-ext/compressionparams.c b/contrib/python-zstandard/c-ext/compressionparams.c
--- a/contrib/python-zstandard/c-ext/compressionparams.c
+++ b/contrib/python-zstandard/c-ext/compressionparams.c
@@ -556,7 +556,7 @@
 };
 
 void compressionparams_module_init(PyObject* mod) {
-	Py_TYPE(&ZstdCompressionParametersType) = &PyType_Type;
+	Py_SET_TYPE(&ZstdCompressionParametersType, &PyType_Type);
 	if (PyType_Ready(&ZstdCompressionParametersType) < 0) {
 		return;
 	}
diff --git a/contrib/python-zstandard/c-ext/compressionreader.c b/contrib/python-zstandard/c-ext/compressionreader.c
--- a/contrib/python-zstandard/c-ext/compressionreader.c
+++ b/contrib/python-zstandard/c-ext/compressionreader.c
@@ -811,7 +811,7 @@
 void compressionreader_module_init(PyObject* mod) {
 	/* TODO make reader a sub-class of io.RawIOBase */
 
-	Py_TYPE(&ZstdCompressionReaderType) = &PyType_Type;
+	Py_SET_TYPE(&ZstdCompressionReaderType, &PyType_Type);
 	if (PyType_Ready(&ZstdCompressionReaderType) < 0) {
 		return;
 	}
diff --git a/contrib/python-zstandard/c-ext/compressionwriter.c b/contrib/python-zstandard/c-ext/compressionwriter.c
--- a/contrib/python-zstandard/c-ext/compressionwriter.c
+++ b/contrib/python-zstandard/c-ext/compressionwriter.c
@@ -365,7 +365,7 @@
 };
 
 void compressionwriter_module_init(PyObject* mod) {
-	Py_TYPE(&ZstdCompressionWriterType) = &PyType_Type;
+	Py_SET_TYPE(&ZstdCompressionWriterType, &PyType_Type);
 	if (PyType_Ready(&ZstdCompressionWriterType) < 0) {
 		return;
 	}
diff --git a/contrib/python-zstandard/c-ext/compressobj.c b/contrib/python-zstandard/c-ext/compressobj.c
--- a/contrib/python-zstandard/c-ext/compressobj.c
+++ b/contrib/python-zstandard/c-ext/compressobj.c
@@ -249,7 +249,7 @@
 };
 
 void compressobj_module_init(PyObject* module) {
-	Py_TYPE(&ZstdCompressionObjType) = &PyType_Type;
+	Py_SET_TYPE(&ZstdCompressionObjType, &PyType_Type);
 	if (PyType_Ready(&ZstdCompressionObjType) < 0) {
 		return;
 	}
diff --git a/contrib/python-zstandard/c-ext/compressor.c b/contrib/python-zstandard/c-ext/compressor.c
--- a/contrib/python-zstandard/c-ext/compressor.c
+++ b/contrib/python-zstandard/c-ext/compressor.c
@@ -619,7 +619,7 @@
 		goto finally;
 	}
 
-	Py_SIZE(output) = outBuffer.pos;
+	Py_SET_SIZE(output, outBuffer.pos);
 
 finally:
 	PyBuffer_Release(&source);
@@ -1659,7 +1659,7 @@
 };
 
 void compressor_module_init(PyObject* mod) {
-	Py_TYPE(&ZstdCompressorType) = &PyType_Type;
+	Py_SET_TYPE(&ZstdCompressorType, &PyType_Type);
 	if (PyType_Ready(&ZstdCompressorType) < 0) {
 		return;
 	}
diff --git a/contrib/python-zstandard/c-ext/compressoriterator.c b/contrib/python-zstandard/c-ext/compressoriterator.c
--- a/contrib/python-zstandard/c-ext/compressoriterator.c
+++ b/contrib/python-zstandard/c-ext/compressoriterator.c
@@ -228,7 +228,7 @@
 };
 
 void compressoriterator_module_init(PyObject* mod) {
-	Py_TYPE(&ZstdCompressorIteratorType) = &PyType_Type;
+	Py_SET_TYPE(&ZstdCompressorIteratorType, &PyType_Type);
 	if (PyType_Ready(&ZstdCompressorIteratorType) < 0) {
 		return;
 	}
diff --git a/contrib/python-zstandard/c-ext/decompressionreader.c b/contrib/python-zstandard/c-ext/decompressionreader.c
--- a/contrib/python-zstandard/c-ext/decompressionreader.c
+++ b/contrib/python-zstandard/c-ext/decompressionreader.c
@@ -774,7 +774,7 @@
 void decompressionreader_module_init(PyObject* mod) {
 	/* TODO make reader a sub-class of io.RawIOBase */
 
-	Py_TYPE(&ZstdDecompressionReaderType) = &PyType_Type;
+	Py_SET_TYPE(&ZstdDecompressionReaderType, &PyType_Type);
 	if (PyType_Ready(&ZstdDecompressionReaderType) < 0) {
 		return;
 	}
diff --git a/contrib/python-zstandard/c-ext/decompressionwriter.c b/contrib/python-zstandard/c-ext/decompressionwriter.c
--- a/contrib/python-zstandard/c-ext/decompressionwriter.c
+++ b/contrib/python-zstandard/c-ext/decompressionwriter.c
@@ -288,7 +288,7 @@
 };
 
 void decompressionwriter_module_init(PyObject* mod) {
-	Py_TYPE(&ZstdDecompressionWriterType) = &PyType_Type;
+	Py_SET_TYPE(&ZstdDecompressionWriterType, &PyType_Type);
 	if (PyType_Ready(&ZstdDecompressionWriterType) < 0) {
 		return;
 	}
diff --git a/contrib/python-zstandard/c-ext/decompressobj.c b/contrib/python-zstandard/c-ext/decompressobj.c
--- a/contrib/python-zstandard/c-ext/decompressobj.c
+++ b/contrib/python-zstandard/c-ext/decompressobj.c
@@ -195,7 +195,7 @@
 };
 
 void decompressobj_module_init(PyObject* module) {
-	Py_TYPE(&ZstdDecompressionObjType) = &PyType_Type;
+	Py_SET_TYPE(&ZstdDecompressionObjType, &PyType_Type);
 	if (PyType_Ready(&ZstdDecompressionObjType) < 0) {
 		return;
 	}
diff --git a/contrib/python-zstandard/c-ext/decompressor.c b/contrib/python-zstandard/c-ext/decompressor.c
--- a/contrib/python-zstandard/c-ext/decompressor.c
+++ b/contrib/python-zstandard/c-ext/decompressor.c
@@ -1811,7 +1811,7 @@
 };
 
 void decompressor_module_init(PyObject* mod) {
-	Py_TYPE(&ZstdDecompressorType) = &PyType_Type;
+	Py_SET_TYPE(&ZstdDecompressorType, &PyType_Type);
 	if (PyType_Ready(&ZstdDecompressorType) < 0) {
 		return;
 	}
diff --git a/contrib/python-zstandard/c-ext/decompressoriterator.c b/contrib/python-zstandard/c-ext/decompressoriterator.c
--- a/contrib/python-zstandard/c-ext/decompressoriterator.c
+++ b/contrib/python-zstandard/c-ext/decompressoriterator.c
@@ -242,7 +242,7 @@
 };
 
 void decompressoriterator_module_init(PyObject* mod) {
-	Py_TYPE(&ZstdDecompressorIteratorType) = &PyType_Type;
+	Py_SET_TYPE(&ZstdDecompressorIteratorType, &PyType_Type);
 	if (PyType_Ready(&ZstdDecompressorIteratorType) < 0) {
 		return;
 	}
diff --git a/contrib/python-zstandard/c-ext/frameparams.c b/contrib/python-zstandard/c-ext/frameparams.c
--- a/contrib/python-zstandard/c-ext/frameparams.c
+++ b/contrib/python-zstandard/c-ext/frameparams.c
@@ -128,7 +128,7 @@
 };
 
 void frameparams_module_init(PyObject* mod) {
-	Py_TYPE(&FrameParametersType) = &PyType_Type;
+	Py_SET_TYPE(&FrameParametersType, &PyType_Type);
 	if (PyType_Ready(&FrameParametersType) < 0) {
 		return;
 	}
diff --git a/contrib/python-zstandard/c-ext/python-zstandard.h b/contrib/python-zstandard/c-ext/python-zstandard.h
--- a/contrib/python-zstandard/c-ext/python-zstandard.h
+++ b/contrib/python-zstandard/c-ext/python-zstandard.h
@@ -9,6 +9,7 @@
 #define PY_SSIZE_T_CLEAN
 #include <Python.h>
 #include "structmember.h"
+#include <pythoncapi_compat.h>
 
 #define ZSTD_STATIC_LINKING_ONLY
 #define ZDICT_STATIC_LINKING_ONLY
diff --git a/contrib/python-zstandard/zstd/common/pythoncapi_compat.h b/contrib/python-zstandard/zstd/common/pythoncapi_compat.h
new file mode 100644
--- /dev/null
+++ b/contrib/python-zstandard/zstd/common/pythoncapi_compat.h
@@ -0,0 +1,278 @@
+// Header file providing new functions of the Python C API to old Python
+// versions.
+//
+// File distributed under the MIT license.
+//
+// Homepage:
+// https://github.com/pythoncapi/pythoncapi_compat
+//
+// Latest version:
+// https://raw.githubusercontent.com/pythoncapi/pythoncapi_compat/master/pythoncapi_compat.h
+
+#ifndef PYTHONCAPI_COMPAT
+#define PYTHONCAPI_COMPAT
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#include <Python.h>
+#include "frameobject.h"          // PyFrameObject, PyFrame_GetBack()
+
+
+// Cast argument to PyObject* type.
+#ifndef _PyObject_CAST
+#  define _PyObject_CAST(op) ((PyObject*)(op))
+#endif
+
+
+// bpo-42262 added Py_NewRef() to Python 3.10.0a3
+#if PY_VERSION_HEX < 0x030a00A3 && !defined(Py_NewRef)
+static inline PyObject* _Py_NewRef(PyObject *obj)
+{
+    Py_INCREF(obj);
+    return obj;
+}
+#define Py_NewRef(obj) _Py_NewRef(_PyObject_CAST(obj))
+#endif
+
+
+// bpo-42262 added Py_XNewRef() to Python 3.10.0a3
+#if PY_VERSION_HEX < 0x030a00A3 && !defined(Py_XNewRef)
+static inline PyObject* _Py_XNewRef(PyObject *obj)
+{
+    Py_XINCREF(obj);
+    return obj;
+}
+#define Py_XNewRef(obj) _Py_XNewRef(_PyObject_CAST(obj))
+#endif
+
+
+// bpo-39573 added Py_SET_REFCNT() to Python 3.9.0a4
+#if PY_VERSION_HEX < 0x030900A4 && !defined(Py_SET_REFCNT)
+static inline void _Py_SET_REFCNT(PyObject *ob, Py_ssize_t refcnt)
+{
+    ob->ob_refcnt = refcnt;
+}
+#define Py_SET_REFCNT(ob, refcnt) _Py_SET_REFCNT((PyObject*)(ob), refcnt)
+#endif
+
+
+// bpo-39573 added Py_SET_TYPE() to Python 3.9.0a4
+#if PY_VERSION_HEX < 0x030900A4 && !defined(Py_SET_TYPE)
+static inline void
+_Py_SET_TYPE(PyObject *ob, PyTypeObject *type)
+{
+    ob->ob_type = type;
+}
+#define Py_SET_TYPE(ob, type) _Py_SET_TYPE((PyObject*)(ob), type)
+#endif
+
+
+// bpo-39573 added Py_SET_SIZE() to Python 3.9.0a4
+#if PY_VERSION_HEX < 0x030900A4 && !defined(Py_SET_SIZE)
+static inline void
+_Py_SET_SIZE(PyVarObject *ob, Py_ssize_t size)
+{
+    ob->ob_size = size;
+}
+#define Py_SET_SIZE(ob, size) _Py_SET_SIZE((PyVarObject*)(ob), size)
+#endif
+
+
+// bpo-40421 added PyFrame_GetCode() to Python 3.9.0b1
+#if PY_VERSION_HEX < 0x030900B1
+static inline PyCodeObject*
+PyFrame_GetCode(PyFrameObject *frame)
+{
+    PyCodeObject *code;
+    assert(frame != NULL);
+    code = frame->f_code;
+    assert(code != NULL);
+    Py_INCREF(code);
+    return code;
+}
+#endif
+
+static inline PyCodeObject*
+_PyFrame_GetCodeBorrow(PyFrameObject *frame)
+{
+    PyCodeObject *code = PyFrame_GetCode(frame);
+    Py_DECREF(code);
+    return code;  // borrowed reference
+}
+
+
+// bpo-40421 added PyFrame_GetCode() to Python 3.9.0b1
+#if PY_VERSION_HEX < 0x030900B1
+static inline PyFrameObject*
+PyFrame_GetBack(PyFrameObject *frame)
+{
+    PyFrameObject *back;
+    assert(frame != NULL);
+    back = frame->f_back;
+    Py_XINCREF(back);
+    return back;
+}
+#endif
+
+static inline PyFrameObject*
+_PyFrame_GetBackBorrow(PyFrameObject *frame)
+{
+    PyFrameObject *back = PyFrame_GetBack(frame);
+    Py_XDECREF(back);
+    return back;  // borrowed reference
+}
+
+
+// bpo-39947 added PyThreadState_GetInterpreter() to Python 3.9.0a5
+#if PY_VERSION_HEX < 0x030900A5
+static inline PyInterpreterState *
+PyThreadState_GetInterpreter(PyThreadState *tstate)
+{
+    assert(tstate != NULL);
+    return tstate->interp;
+}
+#endif
+
+
+// bpo-40429 added PyThreadState_GetFrame() to Python 3.9.0b1
+#if PY_VERSION_HEX < 0x030900B1
+static inline PyFrameObject*
+PyThreadState_GetFrame(PyThreadState *tstate)
+{
+    PyFrameObject *frame;
+    assert(tstate != NULL);
+    frame = tstate->frame;
+    Py_XINCREF(frame);
+    return frame;
+}
+#endif
+
+static inline PyFrameObject*
+_PyThreadState_GetFrameBorrow(PyThreadState *tstate)
+{
+    PyFrameObject *frame = PyThreadState_GetFrame(tstate);
+    Py_XDECREF(frame);
+    return frame;  // borrowed reference
+}
+
+
+// bpo-39947 added PyInterpreterState_Get() to Python 3.9.0a5
+#if PY_VERSION_HEX < 0x030900A5
+static inline PyInterpreterState *
+PyInterpreterState_Get(void)
+{
+    PyThreadState *tstate;
+    PyInterpreterState *interp;
+
+    tstate = PyThreadState_GET();
+    if (tstate == NULL) {
+        Py_FatalError("GIL released (tstate is NULL)");
+    }
+    interp = tstate->interp;
+    if (interp == NULL) {
+        Py_FatalError("no current interpreter");
+    }
+    return interp;
+}
+#endif
+
+
+// bpo-39947 added PyInterpreterState_Get() to Python 3.9.0a6
+#if 0x030700A1 <= PY_VERSION_HEX && PY_VERSION_HEX < 0x030900A6
+static inline uint64_t
+PyThreadState_GetID(PyThreadState *tstate)
+{
+    assert(tstate != NULL);
+    return tstate->id;
+}
+#endif
+
+
+// bpo-37194 added PyObject_CallNoArgs() to Python 3.9.0a1
+#if PY_VERSION_HEX < 0x030900A1
+static inline PyObject*
+PyObject_CallNoArgs(PyObject *func)
+{
+    return PyObject_CallFunctionObjArgs(func, NULL);
+}
+#endif
+
+
+// bpo-39245 made PyObject_CallOneArg() public (previously called
+// _PyObject_CallOneArg) in Python 3.9.0a4
+#if PY_VERSION_HEX < 0x030900A4
+static inline PyObject*
+PyObject_CallOneArg(PyObject *func, PyObject *arg)
+{
+    return PyObject_CallFunctionObjArgs(func, arg, NULL);
+}
+#endif
+
+
+// bpo-40024 added PyModule_AddType() to Python 3.9.0a5
+#if PY_VERSION_HEX < 0x030900A5
+static inline int
+PyModule_AddType(PyObject *module, PyTypeObject *type)
+{
+    const char *name, *dot;
+
+    if (PyType_Ready(type) < 0) {
+        return -1;
+    }
+
+    // inline _PyType_Name()
+    name = type->tp_name;
+    assert(name != NULL);
+    dot = strrchr(name, '.');
+    if (dot != NULL) {
+        name = dot + 1;
+    }
+
+    Py_INCREF(type);
+    if (PyModule_AddObject(module, name, (PyObject *)type) < 0) {
+        Py_DECREF(type);
+        return -1;
+    }
+
+    return 0;
+}
+#endif
+
+
+// bpo-40241 added PyObject_GC_IsTracked() to Python 3.9.0a6.
+// bpo-4688 added _PyObject_GC_IS_TRACKED() to Python 2.7.0a2.
+#if PY_VERSION_HEX < 0x030900A6
+static inline int
+PyObject_GC_IsTracked(PyObject* obj)
+{
+    return (PyObject_IS_GC(obj) && _PyObject_GC_IS_TRACKED(obj));
+}
+#endif
+
+// bpo-40241 added PyObject_GC_IsFinalized() to Python 3.9.0a6.
+// bpo-18112 added _PyGCHead_FINALIZED() to Python 3.4.0 final.
+#if PY_VERSION_HEX < 0x030900A6 && PY_VERSION_HEX >= 0x030400F0
+static inline int
+PyObject_GC_IsFinalized(PyObject *obj)
+{
+    return (PyObject_IS_GC(obj) && _PyGCHead_FINALIZED((PyGC_Head *)(obj)-1));
+}
+#endif
+
+
+// bpo-39573 added Py_IS_TYPE() to Python 3.9.0a4
+#if PY_VERSION_HEX < 0x030900A4 && !defined(Py_IS_TYPE)
+static inline int
+_Py_IS_TYPE(const PyObject *ob, const PyTypeObject *type) {
+    return ob->ob_type == type;
+}
+#define Py_IS_TYPE(ob, type) _Py_IS_TYPE((const PyObject*)(ob), type)
+#endif
+
+
+#ifdef __cplusplus
+}
+#endif
+#endif  // PYTHONCAPI_COMPAT
diff --git a/mercurial/cext/osutil.c b/mercurial/cext/osutil.c
--- a/mercurial/cext/osutil.c
+++ b/mercurial/cext/osutil.c
@@ -119,7 +119,7 @@
 
 static void listdir_stat_dealloc(PyObject *o)
 {
-	o->ob_type->tp_free(o);
+	Py_TYPE(o)->tp_free(o);
 }
 
 static PyObject *listdir_stat_getitem(PyObject *self, PyObject *key)
diff --git a/mercurial/cext/pathencode.c b/mercurial/cext/pathencode.c
--- a/mercurial/cext/pathencode.c
+++ b/mercurial/cext/pathencode.c
@@ -21,6 +21,7 @@
 #include <ctype.h>
 #include <stdlib.h>
 #include <string.h>
+#include "pythoncapi_compat.h"
 
 #include "util.h"
 
@@ -678,7 +679,7 @@
 	}
 
 	assert(PyBytes_Check(ret));
-	Py_SIZE(ret) = destlen;
+	Py_SET_SIZE(ret, destlen);
 
 	return ret;
 }
diff --git a/mercurial/pythoncapi_compat.h b/mercurial/pythoncapi_compat.h
new file mode 100644
--- /dev/null
+++ b/mercurial/pythoncapi_compat.h
@@ -0,0 +1,278 @@
+// Header file providing new functions of the Python C API to old Python
+// versions.
+//
+// File distributed under the MIT license.
+//
+// Homepage:
+// https://github.com/pythoncapi/pythoncapi_compat
+//
+// Latest version:
+// https://raw.githubusercontent.com/pythoncapi/pythoncapi_compat/master/pythoncapi_compat.h
+
+#ifndef PYTHONCAPI_COMPAT
+#define PYTHONCAPI_COMPAT
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#include <Python.h>
+#include "frameobject.h"          // PyFrameObject, PyFrame_GetBack()
+
+
+// Cast argument to PyObject* type.
+#ifndef _PyObject_CAST
+#  define _PyObject_CAST(op) ((PyObject*)(op))
+#endif
+
+
+// bpo-42262 added Py_NewRef() to Python 3.10.0a3
+#if PY_VERSION_HEX < 0x030a00A3 && !defined(Py_NewRef)
+static inline PyObject* _Py_NewRef(PyObject *obj)
+{
+    Py_INCREF(obj);
+    return obj;
+}
+#define Py_NewRef(obj) _Py_NewRef(_PyObject_CAST(obj))
+#endif
+
+
+// bpo-42262 added Py_XNewRef() to Python 3.10.0a3
+#if PY_VERSION_HEX < 0x030a00A3 && !defined(Py_XNewRef)
+static inline PyObject* _Py_XNewRef(PyObject *obj)
+{
+    Py_XINCREF(obj);
+    return obj;
+}
+#define Py_XNewRef(obj) _Py_XNewRef(_PyObject_CAST(obj))
+#endif
+
+
+// bpo-39573 added Py_SET_REFCNT() to Python 3.9.0a4
+#if PY_VERSION_HEX < 0x030900A4 && !defined(Py_SET_REFCNT)
+static inline void _Py_SET_REFCNT(PyObject *ob, Py_ssize_t refcnt)
+{
+    ob->ob_refcnt = refcnt;
+}
+#define Py_SET_REFCNT(ob, refcnt) _Py_SET_REFCNT((PyObject*)(ob), refcnt)
+#endif
+
+
+// bpo-39573 added Py_SET_TYPE() to Python 3.9.0a4
+#if PY_VERSION_HEX < 0x030900A4 && !defined(Py_SET_TYPE)
+static inline void
+_Py_SET_TYPE(PyObject *ob, PyTypeObject *type)
+{
+    ob->ob_type = type;
+}
+#define Py_SET_TYPE(ob, type) _Py_SET_TYPE((PyObject*)(ob), type)
+#endif
+
+
+// bpo-39573 added Py_SET_SIZE() to Python 3.9.0a4
+#if PY_VERSION_HEX < 0x030900A4 && !defined(Py_SET_SIZE)
+static inline void
+_Py_SET_SIZE(PyVarObject *ob, Py_ssize_t size)
+{
+    ob->ob_size = size;
+}
+#define Py_SET_SIZE(ob, size) _Py_SET_SIZE((PyVarObject*)(ob), size)
+#endif
+
+
+// bpo-40421 added PyFrame_GetCode() to Python 3.9.0b1
+#if PY_VERSION_HEX < 0x030900B1
+static inline PyCodeObject*
+PyFrame_GetCode(PyFrameObject *frame)
+{
+    PyCodeObject *code;
+    assert(frame != NULL);
+    code = frame->f_code;
+    assert(code != NULL);
+    Py_INCREF(code);
+    return code;
+}
+#endif
+
+static inline PyCodeObject*
+_PyFrame_GetCodeBorrow(PyFrameObject *frame)
+{
+    PyCodeObject *code = PyFrame_GetCode(frame);
+    Py_DECREF(code);
+    return code;  // borrowed reference
+}
+
+
+// bpo-40421 added PyFrame_GetCode() to Python 3.9.0b1
+#if PY_VERSION_HEX < 0x030900B1
+static inline PyFrameObject*
+PyFrame_GetBack(PyFrameObject *frame)
+{
+    PyFrameObject *back;
+    assert(frame != NULL);
+    back = frame->f_back;
+    Py_XINCREF(back);
+    return back;
+}
+#endif
+
+static inline PyFrameObject*
+_PyFrame_GetBackBorrow(PyFrameObject *frame)
+{
+    PyFrameObject *back = PyFrame_GetBack(frame);
+    Py_XDECREF(back);
+    return back;  // borrowed reference
+}
+
+
+// bpo-39947 added PyThreadState_GetInterpreter() to Python 3.9.0a5
+#if PY_VERSION_HEX < 0x030900A5
+static inline PyInterpreterState *
+PyThreadState_GetInterpreter(PyThreadState *tstate)
+{
+    assert(tstate != NULL);
+    return tstate->interp;
+}
+#endif
+
+
+// bpo-40429 added PyThreadState_GetFrame() to Python 3.9.0b1
+#if PY_VERSION_HEX < 0x030900B1
+static inline PyFrameObject*
+PyThreadState_GetFrame(PyThreadState *tstate)
+{
+    PyFrameObject *frame;
+    assert(tstate != NULL);
+    frame = tstate->frame;
+    Py_XINCREF(frame);
+    return frame;
+}
+#endif
+
+static inline PyFrameObject*
+_PyThreadState_GetFrameBorrow(PyThreadState *tstate)
+{
+    PyFrameObject *frame = PyThreadState_GetFrame(tstate);
+    Py_XDECREF(frame);
+    return frame;  // borrowed reference
+}
+
+
+// bpo-39947 added PyInterpreterState_Get() to Python 3.9.0a5
+#if PY_VERSION_HEX < 0x030900A5
+static inline PyInterpreterState *
+PyInterpreterState_Get(void)
+{
+    PyThreadState *tstate;
+    PyInterpreterState *interp;
+
+    tstate = PyThreadState_GET();
+    if (tstate == NULL) {
+        Py_FatalError("GIL released (tstate is NULL)");
+    }
+    interp = tstate->interp;
+    if (interp == NULL) {
+        Py_FatalError("no current interpreter");
+    }
+    return interp;
+}
+#endif
+
+
+// bpo-39947 added PyInterpreterState_Get() to Python 3.9.0a6
+#if 0x030700A1 <= PY_VERSION_HEX && PY_VERSION_HEX < 0x030900A6
+static inline uint64_t
+PyThreadState_GetID(PyThreadState *tstate)
+{
+    assert(tstate != NULL);
+    return tstate->id;
+}
+#endif
+
+
+// bpo-37194 added PyObject_CallNoArgs() to Python 3.9.0a1
+#if PY_VERSION_HEX < 0x030900A1
+static inline PyObject*
+PyObject_CallNoArgs(PyObject *func)
+{
+    return PyObject_CallFunctionObjArgs(func, NULL);
+}
+#endif
+
+
+// bpo-39245 made PyObject_CallOneArg() public (previously called
+// _PyObject_CallOneArg) in Python 3.9.0a4
+#if PY_VERSION_HEX < 0x030900A4
+static inline PyObject*
+PyObject_CallOneArg(PyObject *func, PyObject *arg)
+{
+    return PyObject_CallFunctionObjArgs(func, arg, NULL);
+}
+#endif
+
+
+// bpo-40024 added PyModule_AddType() to Python 3.9.0a5
+#if PY_VERSION_HEX < 0x030900A5
+static inline int
+PyModule_AddType(PyObject *module, PyTypeObject *type)
+{
+    const char *name, *dot;
+
+    if (PyType_Ready(type) < 0) {
+        return -1;
+    }
+
+    // inline _PyType_Name()
+    name = type->tp_name;
+    assert(name != NULL);
+    dot = strrchr(name, '.');
+    if (dot != NULL) {
+        name = dot + 1;
+    }
+
+    Py_INCREF(type);
+    if (PyModule_AddObject(module, name, (PyObject *)type) < 0) {
+        Py_DECREF(type);
+        return -1;
+    }
+
+    return 0;
+}
+#endif
+
+
+// bpo-40241 added PyObject_GC_IsTracked() to Python 3.9.0a6.
+// bpo-4688 added _PyObject_GC_IS_TRACKED() to Python 2.7.0a2.
+#if PY_VERSION_HEX < 0x030900A6
+static inline int
+PyObject_GC_IsTracked(PyObject* obj)
+{
+    return (PyObject_IS_GC(obj) && _PyObject_GC_IS_TRACKED(obj));
+}
+#endif
+
+// bpo-40241 added PyObject_GC_IsFinalized() to Python 3.9.0a6.
+// bpo-18112 added _PyGCHead_FINALIZED() to Python 3.4.0 final.
+#if PY_VERSION_HEX < 0x030900A6 && PY_VERSION_HEX >= 0x030400F0
+static inline int
+PyObject_GC_IsFinalized(PyObject *obj)
+{
+    return (PyObject_IS_GC(obj) && _PyGCHead_FINALIZED((PyGC_Head *)(obj)-1));
+}
+#endif
+
+
+// bpo-39573 added Py_IS_TYPE() to Python 3.9.0a4
+#if PY_VERSION_HEX < 0x030900A4 && !defined(Py_IS_TYPE)
+static inline int
+_Py_IS_TYPE(const PyObject *ob, const PyTypeObject *type) {
+    return ob->ob_type == type;
+}
+#define Py_IS_TYPE(ob, type) _Py_IS_TYPE((const PyObject*)(ob), type)
+#endif
+
+
+#ifdef __cplusplus
+}
+#endif
+#endif  // PYTHONCAPI_COMPAT
diff --git a/tests/test-check-code.t b/tests/test-check-code.t
--- a/tests/test-check-code.t
+++ b/tests/test-check-code.t
@@ -11,6 +11,7 @@
   > -X contrib/python-zstandard \
   > -X hgext/fsmonitor/pywatchman \
   > -X mercurial/thirdparty \
+  > -X mercurial/pythoncapi_compat.h \
   > | sed 's-\\-/-g' | "$check_code" --warnings --per-file=0 - || false
   Skipping contrib/automation/hgautomation/__init__.py it has no-che?k-code (glob)
   Skipping contrib/automation/hgautomation/aws.py it has no-che?k-code (glob)