diff --git a/Doc/library/unittest.mock.rst b/Doc/library/unittest.mock.rst
index 69f1035703ba54..dbea928443975b 100644
--- a/Doc/library/unittest.mock.rst
+++ b/Doc/library/unittest.mock.rst
@@ -2165,7 +2165,7 @@ Magic methods that are supported but not setup by default in ``MagicMock`` are:
 * ``__reversed__`` and ``__missing__``
 * ``__reduce__``, ``__reduce_ex__``, ``__getinitargs__``, ``__getnewargs__``,
   ``__getstate__`` and ``__setstate__``
-* ``__getformat__`` and ``__setformat__``
+* ``__getformat__``
 
 
 
diff --git a/Doc/whatsnew/3.11.rst b/Doc/whatsnew/3.11.rst
index 3f73bdfa3020f2..8ebe1cb8cc4ca9 100644
--- a/Doc/whatsnew/3.11.rst
+++ b/Doc/whatsnew/3.11.rst
@@ -574,6 +574,12 @@ Removed
   because it was not used and added by mistake in previous versions.
   (Contributed by Nikita Sobolev in :issue:`46483`.)
 
+* Remove the undocumented private ``float.__set_format__()`` method, previously
+  known as ``float.__setformat__()`` in Python 3.7. Its docstring said: "You
+  probably don't want to use this function. It exists mainly to be used in
+  Python's test suite."
+  (Contributed by Victor Stinner in :issue:`46852`.)
+
 Porting to Python 3.11
 ======================
 
diff --git a/Lib/test/test_float.py b/Lib/test/test_float.py
index f033736917c65b..3d2a21f1522ea2 100644
--- a/Lib/test/test_float.py
+++ b/Lib/test/test_float.py
@@ -19,8 +19,6 @@
 have_getformat = hasattr(float, "__getformat__")
 requires_getformat = unittest.skipUnless(have_getformat,
                                          "requires __getformat__")
-requires_setformat = unittest.skipUnless(hasattr(float, "__setformat__"),
-                                         "requires __setformat__")
 
 #locate file with float format test values
 test_dir = os.path.dirname(__file__) or os.curdir
@@ -612,44 +610,6 @@ class F(float, H):
         self.assertEqual(hash(value), object.__hash__(value))
 
 
-@requires_setformat
-class FormatFunctionsTestCase(unittest.TestCase):
-
-    def setUp(self):
-        self.save_formats = {'double':float.__getformat__('double'),
-                             'float':float.__getformat__('float')}
-
-    def tearDown(self):
-        float.__setformat__('double', self.save_formats['double'])
-        float.__setformat__('float', self.save_formats['float'])
-
-    def test_getformat(self):
-        self.assertIn(float.__getformat__('double'),
-                      ['unknown', 'IEEE, big-endian', 'IEEE, little-endian'])
-        self.assertIn(float.__getformat__('float'),
-                      ['unknown', 'IEEE, big-endian', 'IEEE, little-endian'])
-        self.assertRaises(ValueError, float.__getformat__, 'chicken')
-        self.assertRaises(TypeError, float.__getformat__, 1)
-
-    def test_setformat(self):
-        for t in 'double', 'float':
-            float.__setformat__(t, 'unknown')
-            if self.save_formats[t] == 'IEEE, big-endian':
-                self.assertRaises(ValueError, float.__setformat__,
-                                  t, 'IEEE, little-endian')
-            elif self.save_formats[t] == 'IEEE, little-endian':
-                self.assertRaises(ValueError, float.__setformat__,
-                                  t, 'IEEE, big-endian')
-            else:
-                self.assertRaises(ValueError, float.__setformat__,
-                                  t, 'IEEE, big-endian')
-                self.assertRaises(ValueError, float.__setformat__,
-                                  t, 'IEEE, little-endian')
-            self.assertRaises(ValueError, float.__setformat__,
-                              t, 'chicken')
-        self.assertRaises(ValueError, float.__setformat__,
-                          'chicken', 'unknown')
-
 BE_DOUBLE_INF = b'\x7f\xf0\x00\x00\x00\x00\x00\x00'
 LE_DOUBLE_INF = bytes(reversed(BE_DOUBLE_INF))
 BE_DOUBLE_NAN = b'\x7f\xf8\x00\x00\x00\x00\x00\x00'
@@ -660,36 +620,6 @@ def test_setformat(self):
 BE_FLOAT_NAN = b'\x7f\xc0\x00\x00'
 LE_FLOAT_NAN = bytes(reversed(BE_FLOAT_NAN))
 
-# on non-IEEE platforms, attempting to unpack a bit pattern
-# representing an infinity or a NaN should raise an exception.
-
-@requires_setformat
-class UnknownFormatTestCase(unittest.TestCase):
-    def setUp(self):
-        self.save_formats = {'double':float.__getformat__('double'),
-                             'float':float.__getformat__('float')}
-        float.__setformat__('double', 'unknown')
-        float.__setformat__('float', 'unknown')
-
-    def tearDown(self):
-        float.__setformat__('double', self.save_formats['double'])
-        float.__setformat__('float', self.save_formats['float'])
-
-    def test_double_specials_dont_unpack(self):
-        for fmt, data in [('>d', BE_DOUBLE_INF),
-                          ('>d', BE_DOUBLE_NAN),
-                          ('<d', LE_DOUBLE_INF),
-                          ('<d', LE_DOUBLE_NAN)]:
-            self.assertRaises(ValueError, struct.unpack, fmt, data)
-
-    def test_float_specials_dont_unpack(self):
-        for fmt, data in [('>f', BE_FLOAT_INF),
-                          ('>f', BE_FLOAT_NAN),
-                          ('<f', LE_FLOAT_INF),
-                          ('<f', LE_FLOAT_NAN)]:
-            self.assertRaises(ValueError, struct.unpack, fmt, data)
-
-
 # on an IEEE platform, all we guarantee is that bit patterns
 # representing infinities or NaNs do not raise an exception; all else
 # is accident (today).
diff --git a/Lib/unittest/mock.py b/Lib/unittest/mock.py
index 2719f74d6fca50..8262b7170b76b4 100644
--- a/Lib/unittest/mock.py
+++ b/Lib/unittest/mock.py
@@ -1943,7 +1943,7 @@ def _patch_stopall():
 _non_defaults = {
     '__get__', '__set__', '__delete__', '__reversed__', '__missing__',
     '__reduce__', '__reduce_ex__', '__getinitargs__', '__getnewargs__',
-    '__getstate__', '__setstate__', '__getformat__', '__setformat__',
+    '__getstate__', '__setstate__', '__getformat__',
     '__repr__', '__dir__', '__subclasses__', '__format__',
     '__getnewargs_ex__',
 }
diff --git a/Misc/NEWS.d/next/Core and Builtins/2022-02-25-01-42-45.bpo-46852.nkRDvV.rst b/Misc/NEWS.d/next/Core and Builtins/2022-02-25-01-42-45.bpo-46852.nkRDvV.rst
new file mode 100644
index 00000000000000..cd0049a46e5428
--- /dev/null
+++ b/Misc/NEWS.d/next/Core and Builtins/2022-02-25-01-42-45.bpo-46852.nkRDvV.rst	
@@ -0,0 +1,4 @@
+Remove the undocumented private ``float.__set_format__()`` method, previously
+known as ``float.__setformat__()`` in Python 3.7. Its docstring said: "You
+probably don't want to use this function. It exists mainly to be used in
+Python's test suite." Patch by Victor Stinner.
diff --git a/Objects/clinic/floatobject.c.h b/Objects/clinic/floatobject.c.h
index 2c638a28d7e1e4..f53018c08e0455 100644
--- a/Objects/clinic/floatobject.c.h
+++ b/Objects/clinic/floatobject.c.h
@@ -290,73 +290,6 @@ float___getformat__(PyTypeObject *type, PyObject *arg)
     return return_value;
 }
 
-PyDoc_STRVAR(float___setformat____doc__,
-"__setformat__($type, typestr, fmt, /)\n"
-"--\n"
-"\n"
-"You probably don\'t want to use this function.\n"
-"\n"
-"  typestr\n"
-"    Must be \'double\' or \'float\'.\n"
-"  fmt\n"
-"    Must be one of \'unknown\', \'IEEE, big-endian\' or \'IEEE, little-endian\',\n"
-"    and in addition can only be one of the latter two if it appears to\n"
-"    match the underlying C reality.\n"
-"\n"
-"It exists mainly to be used in Python\'s test suite.\n"
-"\n"
-"Override the automatic determination of C-level floating point type.\n"
-"This affects how floats are converted to and from binary strings.");
-
-#define FLOAT___SETFORMAT___METHODDEF    \
-    {"__setformat__", (PyCFunction)(void(*)(void))float___setformat__, METH_FASTCALL|METH_CLASS, float___setformat____doc__},
-
-static PyObject *
-float___setformat___impl(PyTypeObject *type, const char *typestr,
-                         const char *fmt);
-
-static PyObject *
-float___setformat__(PyTypeObject *type, PyObject *const *args, Py_ssize_t nargs)
-{
-    PyObject *return_value = NULL;
-    const char *typestr;
-    const char *fmt;
-
-    if (!_PyArg_CheckPositional("__setformat__", nargs, 2, 2)) {
-        goto exit;
-    }
-    if (!PyUnicode_Check(args[0])) {
-        _PyArg_BadArgument("__setformat__", "argument 1", "str", args[0]);
-        goto exit;
-    }
-    Py_ssize_t typestr_length;
-    typestr = PyUnicode_AsUTF8AndSize(args[0], &typestr_length);
-    if (typestr == NULL) {
-        goto exit;
-    }
-    if (strlen(typestr) != (size_t)typestr_length) {
-        PyErr_SetString(PyExc_ValueError, "embedded null character");
-        goto exit;
-    }
-    if (!PyUnicode_Check(args[1])) {
-        _PyArg_BadArgument("__setformat__", "argument 2", "str", args[1]);
-        goto exit;
-    }
-    Py_ssize_t fmt_length;
-    fmt = PyUnicode_AsUTF8AndSize(args[1], &fmt_length);
-    if (fmt == NULL) {
-        goto exit;
-    }
-    if (strlen(fmt) != (size_t)fmt_length) {
-        PyErr_SetString(PyExc_ValueError, "embedded null character");
-        goto exit;
-    }
-    return_value = float___setformat___impl(type, typestr, fmt);
-
-exit:
-    return return_value;
-}
-
 PyDoc_STRVAR(float___format____doc__,
 "__format__($self, format_spec, /)\n"
 "--\n"
@@ -388,4 +321,4 @@ float___format__(PyObject *self, PyObject *arg)
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=3fb0c0624cc87dff input=a9049054013a1b77]*/
+/*[clinic end generated code: output=604cb27bf751ea16 input=a9049054013a1b77]*/
diff --git a/Objects/floatobject.c b/Objects/floatobject.c
index 342e768c62f4a7..91ca848bf26e8a 100644
--- a/Objects/floatobject.c
+++ b/Objects/floatobject.c
@@ -1708,7 +1708,6 @@ typedef enum {
 } float_format_type;
 
 static float_format_type double_format, float_format;
-static float_format_type detected_double_format, detected_float_format;
 
 /*[clinic input]
 @classmethod
@@ -1760,78 +1759,6 @@ float___getformat___impl(PyTypeObject *type, const char *typestr)
     }
 }
 
-/*[clinic input]
-@classmethod
-float.__setformat__
-
-    typestr: str
-        Must be 'double' or 'float'.
-    fmt: str
-        Must be one of 'unknown', 'IEEE, big-endian' or 'IEEE, little-endian',
-        and in addition can only be one of the latter two if it appears to
-        match the underlying C reality.
-    /
-
-You probably don't want to use this function.
-
-It exists mainly to be used in Python's test suite.
-
-Override the automatic determination of C-level floating point type.
-This affects how floats are converted to and from binary strings.
-[clinic start generated code]*/
-
-static PyObject *
-float___setformat___impl(PyTypeObject *type, const char *typestr,
-                         const char *fmt)
-/*[clinic end generated code: output=06864de1fb5f1f04 input=c0e9e04dd87f9988]*/
-{
-    float_format_type f;
-    float_format_type detected;
-    float_format_type *p;
-
-    if (strcmp(typestr, "double") == 0) {
-        p = &double_format;
-        detected = detected_double_format;
-    }
-    else if (strcmp(typestr, "float") == 0) {
-        p = &float_format;
-        detected = detected_float_format;
-    }
-    else {
-        PyErr_SetString(PyExc_ValueError,
-                        "__setformat__() argument 1 must "
-                        "be 'double' or 'float'");
-        return NULL;
-    }
-
-    if (strcmp(fmt, "unknown") == 0) {
-        f = unknown_format;
-    }
-    else if (strcmp(fmt, "IEEE, little-endian") == 0) {
-        f = ieee_little_endian_format;
-    }
-    else if (strcmp(fmt, "IEEE, big-endian") == 0) {
-        f = ieee_big_endian_format;
-    }
-    else {
-        PyErr_SetString(PyExc_ValueError,
-                        "__setformat__() argument 2 must be "
-                        "'unknown', 'IEEE, little-endian' or "
-                        "'IEEE, big-endian'");
-        return NULL;
-
-    }
-
-    if (f != unknown_format && f != detected) {
-        PyErr_Format(PyExc_ValueError,
-                     "can only set %s format to 'unknown' or the "
-                     "detected platform value", typestr);
-        return NULL;
-    }
-
-    *p = f;
-    Py_RETURN_NONE;
-}
 
 static PyObject *
 float_getreal(PyObject *v, void *closure)
@@ -1885,7 +1812,6 @@ static PyMethodDef float_methods[] = {
     FLOAT_IS_INTEGER_METHODDEF
     FLOAT___GETNEWARGS___METHODDEF
     FLOAT___GETFORMAT___METHODDEF
-    FLOAT___SETFORMAT___METHODDEF
     FLOAT___FORMAT___METHODDEF
     {NULL,              NULL}           /* sentinel */
 };
@@ -1989,6 +1915,8 @@ _PyFloat_InitState(PyInterpreterState *interp)
         return;
     }
 
+    float_format_type detected_double_format, detected_float_format;
+
     /* We attempt to determine if this machine is using IEEE
        floating point formats by peering at the bits of some
        carefully chosen values.  If it looks like we are on an