diff --git a/Doc/c-api/object.rst b/Doc/c-api/object.rst
index 7efc0d2..8410934 100644
--- a/Doc/c-api/object.rst
+++ b/Doc/c-api/object.rst
@@ -247,15 +247,20 @@
    *NULL* on failure.
 
 
-.. c:function:: long PyObject_Hash(PyObject *o)
+.. c:function:: Py_hash_t PyObject_Hash(PyObject *o)
 
    .. index:: builtin: hash
 
    Compute and return the hash value of an object *o*.  On failure, return ``-1``.
    This is the equivalent of the Python expression ``hash(o)``.
 
+   .. versionchanged:: 3.2
 
-.. c:function:: long PyObject_HashNotImplemented(PyObject *o)
+      The return type is now Py_hash_t.  This is a signed integer the same size
+      as Py_ssize_t.
+
+
+.. c:function:: Py_hash_t PyObject_HashNotImplemented(PyObject *o)
 
    Set a :exc:`TypeError` indicating that ``type(o)`` is not hashable and return ``-1``.
    This function receives special treatment when stored in a ``tp_hash`` slot,
diff --git a/Doc/c-api/typeobj.rst b/Doc/c-api/typeobj.rst
index a25ca41..fe751c2 100644
--- a/Doc/c-api/typeobj.rst
+++ b/Doc/c-api/typeobj.rst
@@ -306,10 +306,10 @@
    An optional pointer to a function that implements the built-in function
    :func:`hash`.
 
-   The signature is the same as for :c:func:`PyObject_Hash`; it must return a C
-   long.  The value ``-1`` should not be returned as a normal return value; when an
-   error occurs during the computation of the hash value, the function should set
-   an exception and return ``-1``.
+   The signature is the same as for :c:func:`PyObject_Hash`; it must return a
+   value of the type Py_hash_t.  The value ``-1`` should not be returned as a
+   normal return value; when an error occurs during the computation of the hash
+   value, the function should set an exception and return ``-1``.
 
    This field can be set explicitly to :c:func:`PyObject_HashNotImplemented` to
    block inheritance of the hash method from a parent type. This is interpreted