diff --git a/Doc/c-api/hash.rst b/Doc/c-api/hash.rst
index 4dc121d7fbaa9b4..190a726958438d9 100644
--- a/Doc/c-api/hash.rst
+++ b/Doc/c-api/hash.rst
@@ -5,12 +5,16 @@ PyHash API
 
 See also the :c:member:`PyTypeObject.tp_hash` member.
 
+Types
+^^^^^
+
 .. c:type:: Py_hash_t
 
    Hash value type: signed integer.
 
    .. versionadded:: 3.2
 
+
 .. c:type:: Py_uhash_t
 
    Hash value type: unsigned integer.
@@ -41,8 +45,33 @@ See also the :c:member:`PyTypeObject.tp_hash` member.
    .. versionadded:: 3.4
 
 
+Functions
+^^^^^^^^^
+
+.. c:function:: int Py_HashDouble(double value, Py_hash_t *result)
+
+   Hash a C double number.
+
+   * Set *\*result* to the hash and return ``1`` if *value* is finite or is
+     infinity.
+   * Set *\*result* to :data:`sys.hash_info.nan <sys.hash_info>` (``0``) and
+     return ``0`` if *value* is not-a-number (NaN).
+
+   *result* must not be ``NULL``.
+
+   .. note::
+      Only rely on the function return value to distinguish the "not-a-number"
+      case. *\*result* can be ``0`` if *value* is finite. For example,
+      ``Py_HashDouble(0.0, &result)`` sets *\*result* to 0.
+
+   .. versionadded:: 3.13
+
+
 .. c:function:: PyHash_FuncDef* PyHash_GetFuncDef(void)
 
    Get the hash function definition.
 
+   .. seealso::
+      :pep:`456` "Secure and interchangeable hash algorithm".
+
    .. versionadded:: 3.4
diff --git a/Doc/library/sys.rst b/Doc/library/sys.rst
index bf9aaca2a696ded..c6e1bef7aa1032b 100644
--- a/Doc/library/sys.rst
+++ b/Doc/library/sys.rst
@@ -1034,7 +1034,13 @@ always available.
 
    .. attribute:: hash_info.nan
 
-      (This attribute is no longer used)
+      The hash value returned for not-a-number (NaN).
+
+      This hash value is only used by the :c:func:`Py_HashDouble` C function if
+      the argument is not-a-number (NaN).
+
+      .. versionchanged:: 3.10
+         This hash value is no longer used to hash numbers in Python.
 
    .. attribute:: hash_info.imag
 
diff --git a/Doc/whatsnew/3.13.rst b/Doc/whatsnew/3.13.rst
index 372e4a45468e68b..a50321fc9ed8ef7 100644
--- a/Doc/whatsnew/3.13.rst
+++ b/Doc/whatsnew/3.13.rst
@@ -1230,6 +1230,9 @@ New Features
   :exc:`KeyError` if the key missing.
   (Contributed by Stefan Behnel and Victor Stinner in :gh:`111262`.)
 
+* Add :c:func:`Py_HashDouble` function to hash a C double number.
+  (Contributed by Victor Stinner in :gh:`111545`.)
+
 
 Porting to Python 3.13
 ----------------------
diff --git a/Include/cpython/pyhash.h b/Include/cpython/pyhash.h
index 6f7113daa5fe4de..16bb702598fd800 100644
--- a/Include/cpython/pyhash.h
+++ b/Include/cpython/pyhash.h
@@ -17,6 +17,7 @@
 
 #define _PyHASH_MODULUS (((size_t)1 << _PyHASH_BITS) - 1)
 #define _PyHASH_INF 314159
+#define _PyHASH_NAN 0
 #define _PyHASH_IMAG _PyHASH_MULTIPLIER
 
 /* Helpers for hash functions */
@@ -33,3 +34,5 @@ typedef struct {
 } PyHash_FuncDef;
 
 PyAPI_FUNC(PyHash_FuncDef*) PyHash_GetFuncDef(void);
+
+PyAPI_FUNC(int) Py_HashDouble(double value, Py_hash_t *result);
diff --git a/Lib/test/test_capi/test_hash.py b/Lib/test/test_capi/test_hash.py
index 59dec15bc21445f..68bdcd8ccf0469e 100644
--- a/Lib/test/test_capi/test_hash.py
+++ b/Lib/test/test_capi/test_hash.py
@@ -1,3 +1,4 @@
+import math
 import sys
 import unittest
 from test.support import import_helper
@@ -31,3 +32,46 @@ def test_hash_getfuncdef(self):
         self.assertEqual(func_def.name, hash_info.algorithm)
         self.assertEqual(func_def.hash_bits, hash_info.hash_bits)
         self.assertEqual(func_def.seed_bits, hash_info.seed_bits)
+
+    def test_hash_double(self):
+        # Test Py_HashDouble()
+        hash_double = _testcapi.hash_double
+
+        def check_number(value, expected):
+            self.assertEqual(hash_double(value), (1, expected))
+
+        # test some integers
+        integers = [
+            *range(1, 30),
+            2**30 - 1,
+            2 ** 233,
+            int(sys.float_info.max),
+        ]
+        for x in integers:
+            with self.subTest(x=x):
+                check_number(float(x), hash(x))
+                check_number(float(-x), hash(-x))
+
+        # test positive and negative zeros
+        check_number(float(0.0), 0)
+        check_number(float(-0.0), 0)
+
+        # test +inf and -inf
+        inf = float("inf")
+        check_number(inf, sys.hash_info.inf)
+        check_number(-inf, -sys.hash_info.inf)
+
+        # special float values: compare with Python hash() function
+        special_values = (
+            math.nextafter(0.0, 1.0),  # smallest positive subnormal number
+            sys.float_info.min,        # smallest positive normal number
+            sys.float_info.epsilon,
+            sys.float_info.max,        # largest positive finite number
+        )
+        for x in special_values:
+            with self.subTest(x=x):
+                check_number(x, hash(x))
+                check_number(-x, hash(-x))
+
+        # test not-a-number (NaN)
+        self.assertEqual(hash_double(float('nan')), (0, sys.hash_info.nan))
diff --git a/Misc/NEWS.d/next/C API/2023-11-15-01-26-59.gh-issue-111545.iAoFtA.rst b/Misc/NEWS.d/next/C API/2023-11-15-01-26-59.gh-issue-111545.iAoFtA.rst
new file mode 100644
index 000000000000000..b6f1db895a3523d
--- /dev/null
+++ b/Misc/NEWS.d/next/C API/2023-11-15-01-26-59.gh-issue-111545.iAoFtA.rst	
@@ -0,0 +1,2 @@
+Add :c:func:`Py_HashDouble` function to hash a C double number. Patch by
+Victor Stinner.
diff --git a/Modules/_testcapi/hash.c b/Modules/_testcapi/hash.c
index d0b8127020c5c14..7b8e6d6b1fcb5fb 100644
--- a/Modules/_testcapi/hash.c
+++ b/Modules/_testcapi/hash.c
@@ -1,6 +1,7 @@
 #include "parts.h"
 #include "util.h"
 
+
 static PyObject *
 hash_getfuncdef(PyObject *Py_UNUSED(module), PyObject *Py_UNUSED(args))
 {
@@ -44,8 +45,27 @@ hash_getfuncdef(PyObject *Py_UNUSED(module), PyObject *Py_UNUSED(args))
     return result;
 }
 
+
+static PyObject *
+hash_double(PyObject *Py_UNUSED(module), PyObject *args)
+{
+    double value;
+    if (!PyArg_ParseTuple(args, "d", &value)) {
+        return NULL;
+    }
+
+    Py_hash_t hash;
+    int res = Py_HashDouble(value, &hash);
+    assert(hash != -1);
+
+    Py_BUILD_ASSERT(sizeof(long long) >= sizeof(hash));
+    return Py_BuildValue("iN", res, PyLong_FromLongLong(hash));
+}
+
+
 static PyMethodDef test_methods[] = {
     {"hash_getfuncdef", hash_getfuncdef, METH_NOARGS},
+    {"hash_double", hash_double, METH_VARARGS},
     {NULL},
 };
 
diff --git a/Python/pyhash.c b/Python/pyhash.c
index f9060b8003a0a7d..6fa79d08c288213 100644
--- a/Python/pyhash.c
+++ b/Python/pyhash.c
@@ -85,18 +85,23 @@ static Py_ssize_t hashstats[Py_HASH_STATS_MAX + 1] = {0};
 
 Py_hash_t _Py_HashPointer(const void *);
 
-Py_hash_t
-_Py_HashDouble(PyObject *inst, double v)
+int
+Py_HashDouble(double v, Py_hash_t *result)
 {
     int e, sign;
     double m;
     Py_uhash_t x, y;
 
     if (!Py_IS_FINITE(v)) {
-        if (Py_IS_INFINITY(v))
-            return v > 0 ? _PyHASH_INF : -_PyHASH_INF;
-        else
-            return _Py_HashPointer(inst);
+        if (Py_IS_INFINITY(v)) {
+            *result = (v > 0 ? _PyHASH_INF : -_PyHASH_INF);
+            return 1;
+        }
+        else {
+            assert(Py_IS_NAN(v));
+            *result = _PyHASH_NAN;
+            return 0;
+        }
     }
 
     m = frexp(v, &e);
@@ -128,7 +133,20 @@ _Py_HashDouble(PyObject *inst, double v)
     x = x * sign;
     if (x == (Py_uhash_t)-1)
         x = (Py_uhash_t)-2;
-    return (Py_hash_t)x;
+    *result = (Py_hash_t)x;
+    return 1;
+}
+
+Py_hash_t
+_Py_HashDouble(PyObject *obj, double v)
+{
+    assert(obj != NULL);
+
+    Py_hash_t hash;
+    if (Py_HashDouble(v, &hash) == 0) {
+        hash = _Py_HashPointer(obj);
+    }
+    return hash;
 }
 
 Py_hash_t
diff --git a/Python/sysmodule.c b/Python/sysmodule.c
index c17de44731b7030..11113e21bfb6b7f 100644
--- a/Python/sysmodule.c
+++ b/Python/sysmodule.c
@@ -1497,7 +1497,7 @@ get_hash_info(PyThreadState *tstate)
     PyStructSequence_SET_ITEM(hash_info, field++,
                               PyLong_FromLong(_PyHASH_INF));
     PyStructSequence_SET_ITEM(hash_info, field++,
-                              PyLong_FromLong(0));  // This is no longer used
+                              PyLong_FromLong(_PyHASH_NAN));
     PyStructSequence_SET_ITEM(hash_info, field++,
                               PyLong_FromLong(_PyHASH_IMAG));
     PyStructSequence_SET_ITEM(hash_info, field++,