Clean up the docs of PyObject_IsSubclass and PyObject_IsInstance, and mention that they call the PEP 3119 methods.

Doc/c-api/object.rst

@@ -187,40 +187,45 @@ Object Protocol
    a TypeError is raised when *o* is an integer instead of a zero-initialized
    bytes object.
 
+
+.. c:function:: int PyObject_IsSubclass(PyObject *derived, PyObject *cls)
+
+   Return ``1`` if the class *derived* is identical to or derived from the class
+   *cls*, otherwise return ``0``.  In case of an error, return ``-1``.
+
+   If *cls* is a tuple, the check will be done against every entry in *cls*.
+   The result will be ``1`` when at least one of the checks returns ``1``,
+   otherwise it will be ``0``.
+
+   If *cls* has a :meth:`~class.__subclasscheck__` method, it will be called to
+   determine the subclass status as described in :pep:`3119`.  Otherwise,
+   *derived* is a subclass of *cls* if it is a direct or indirect subclass,
+   i.e. contained in ``cls.__mro__``.
+
+   Normally only class objects, i.e. instances of :class:`type` or a derived
+   class, are considered classes.  However, objects can override this by haivng
+   a :attr:`__bases__` attribute (which must be a tuple of base classes).
+
+
 .. c:function:: int PyObject_IsInstance(PyObject *inst, PyObject *cls)
 
-   Returns ``1`` if *inst* is an instance of the class *cls* or a subclass of
-   *cls*, or ``0`` if not.  On error, returns ``-1`` and sets an exception.  If
-   *cls* is a type object rather than a class object, :c:func:`PyObject_IsInstance`
-   returns ``1`` if *inst* is of type *cls*.  If *cls* is a tuple, the check will
-   be done against every entry in *cls*. The result will be ``1`` when at least one
-   of the checks returns ``1``, otherwise it will be ``0``. If *inst* is not a
-   class instance and *cls* is neither a type object, nor a class object, nor a
-   tuple, *inst* must have a :attr:`~instance.__class__` attribute --- the
-   class relationship of the value of that attribute with *cls* will be used
-   to determine the result of this function.
-
-
-Subclass determination is done in a fairly straightforward way, but includes a
-wrinkle that implementors of extensions to the class system may want to be aware
-of.  If :class:`A` and :class:`B` are class objects, :class:`B` is a subclass of
-:class:`A` if it inherits from :class:`A` either directly or indirectly.  If
-either is not a class object, a more general mechanism is used to determine the
-class relationship of the two objects.  When testing if *B* is a subclass of
-*A*, if *A* is *B*, :c:func:`PyObject_IsSubclass` returns true.  If *A* and *B*
-are different objects, *B*'s :attr:`~class.__bases__` attribute is searched in
-a depth-first fashion for *A* --- the presence of the :attr:`~class.__bases__`
-attribute is considered sufficient for this determination.
+   Return ``1`` if *inst* is an instance of the class *cls* or a subclass of
+   *cls*, or ``0`` if not.  On error, returns ``-1`` and sets an exception.
 
+   If *cls* is a tuple, the check will be done against every entry in *cls*.
+   The result will be ``1`` when at least one of the checks returns ``1``,
+   otherwise it will be ``0``.
 
-.. c:function:: int PyObject_IsSubclass(PyObject *derived, PyObject *cls)
+   If *cls* has a :meth:`~class.__instancecheck__` method, it will be called to
+   determine the subclass status as described in :pep:`3119`.  Otherwise, *inst*
+   is an instance of *cls* if its class is a subclass of *cls*.
+
+   An instance *inst* can override what is considered its class by having a
+   :attr:`__class__` attribute.
 
-   Returns ``1`` if the class *derived* is identical to or derived from the class
-   *cls*, otherwise returns ``0``.  In case of an error, returns ``-1``. If *cls*
-   is a tuple, the check will be done against every entry in *cls*. The result will
-   be ``1`` when at least one of the checks returns ``1``, otherwise it will be
-   ``0``. If either *derived* or *cls* is not an actual class object (or tuple),
-   this function uses the generic algorithm described above.
+   An object *cls* can override if it is considered a class, and what its base
+   classes are, by having a :attr:`__bases__` attribute (which must be a tuple
+   of base classes).
 
 
 .. c:function:: int PyCallable_Check(PyObject *o)

Doc/c-api/type.rst

@@ -69,7 +69,7 @@ Type Objects
    Return true if *a* is a subtype of *b*.
 
    This function only checks for actual subtypes, which means that
-   :meth:`~type.__subclasscheck__` is not called on *b*.  Call
+   :meth:`~class.__subclasscheck__` is not called on *b*.  Call
    :c:func:`PyObject_IsSubclass` to do the same check that :func:`issubclass`
    would do.