Checking in the code for PEP 357.
This was mostly written by Travis Oliphant.
I've inspected it all; Neal Norwitz and MvL have also looked at it
(in an earlier incarnation).
diff --git a/Objects/abstract.c b/Objects/abstract.c
index 7ded61a..399656f 100644
--- a/Objects/abstract.c
+++ b/Objects/abstract.c
@@ -8,6 +8,8 @@
 #define NEW_STYLE_NUMBER(o) PyType_HasFeature((o)->ob_type, \
 				Py_TPFLAGS_CHECKTYPES)
 
+#define HASINDEX(o) PyType_HasFeature((o)->ob_type, Py_TPFLAGS_HAVE_INDEX)
+
 /* Shorthands to return certain errors */
 
 static PyObject *
@@ -119,10 +121,9 @@
 		return m->mp_subscript(o, key);
 
 	if (o->ob_type->tp_as_sequence) {
-		if (PyInt_Check(key))
-			return PySequence_GetItem(o, PyInt_AsLong(key));
-		else if (PyLong_Check(key)) {
-			long key_value = PyLong_AsLong(key);
+		PyNumberMethods *nb = key->ob_type->tp_as_number;
+		if (nb != NULL && HASINDEX(key) && nb->nb_index != NULL) {
+			Py_ssize_t key_value = nb->nb_index(key);
 			if (key_value == -1 && PyErr_Occurred())
 				return NULL;
 			return PySequence_GetItem(o, key_value);
@@ -148,10 +149,9 @@
 		return m->mp_ass_subscript(o, key, value);
 
 	if (o->ob_type->tp_as_sequence) {
-		if (PyInt_Check(key))
-			return PySequence_SetItem(o, PyInt_AsLong(key), value);
-		else if (PyLong_Check(key)) {
-			long key_value = PyLong_AsLong(key);
+		PyNumberMethods *nb = key->ob_type->tp_as_number;
+		if (nb != NULL && HASINDEX(key) && nb->nb_index != NULL) {
+			Py_ssize_t key_value = nb->nb_index(key);
 			if (key_value == -1 && PyErr_Occurred())
 				return -1;
 			return PySequence_SetItem(o, key_value, value);
@@ -180,10 +180,9 @@
 		return m->mp_ass_subscript(o, key, (PyObject*)NULL);
 
 	if (o->ob_type->tp_as_sequence) {
-		if (PyInt_Check(key))
-			return PySequence_DelItem(o, PyInt_AsLong(key));
-		else if (PyLong_Check(key)) {
-			long key_value = PyLong_AsLong(key);
+		PyNumberMethods *nb = key->ob_type->tp_as_number;
+		if (nb != NULL && HASINDEX(key) && nb->nb_index != NULL) {
+			Py_ssize_t key_value = nb->nb_index(key);
 			if (key_value == -1 && PyErr_Occurred())
 				return -1;
 			return PySequence_DelItem(o, key_value);
@@ -647,12 +646,10 @@
 static PyObject *
 sequence_repeat(ssizeargfunc repeatfunc, PyObject *seq, PyObject *n)
 {
-	long count;
-	if (PyInt_Check(n)) {
-		count  = PyInt_AsLong(n);
-	}
-	else if (PyLong_Check(n)) {
-		count = PyLong_AsLong(n);
+	Py_ssize_t count;
+	PyNumberMethods *nb = n->ob_type->tp_as_number;
+	if (nb != NULL && HASINDEX(n) && nb->nb_index != NULL) {
+		count = nb->nb_index(n);
 		if (count == -1 && PyErr_Occurred())
 			return NULL;
 	}
@@ -660,32 +657,7 @@
 		return type_error(
 			"can't multiply sequence by non-int");
 	}
-#if LONG_MAX != INT_MAX
-	if (count > INT_MAX) {
-		PyErr_SetString(PyExc_ValueError,
-				"sequence repeat count too large");
-		return NULL;
-	}
-	else if (count < INT_MIN)
-		count = INT_MIN;
-	/* XXX Why don't I either
-
-	   - set count to -1 whenever it's negative (after all,
-	     sequence repeat usually treats negative numbers
-	     as zero(); or
-
-	   - raise an exception when it's less than INT_MIN?
-
-	   I'm thinking about a hypothetical use case where some
-	   sequence type might use a negative value as a flag of
-	   some kind.  In those cases I don't want to break the
-	   code by mapping all negative values to -1.  But I also
-	   don't want to break e.g. []*(-sys.maxint), which is
-	   perfectly safe, returning [].  As a compromise, I do
-	   map out-of-range negative values.
-	*/
-#endif
-	return (*repeatfunc)(seq, (int)count);
+	return (*repeatfunc)(seq, count);
 }
 
 PyObject *
@@ -960,6 +932,22 @@
 	return x;
 }
 
+/* Return a Py_ssize_t integer from the object item */
+Py_ssize_t 
+PyNumber_Index(PyObject *item)
+{
+	Py_ssize_t value = -1;
+	PyNumberMethods *nb = item->ob_type->tp_as_number;
+	if (nb != NULL && HASINDEX(item) && nb->nb_index != NULL) {
+		value = nb->nb_index(item);
+	}
+	else {
+		PyErr_SetString(PyExc_IndexError, 
+				"object cannot be interpreted as an index");
+	}
+	return value;
+}
+
 PyObject *
 PyNumber_Int(PyObject *o)
 {
diff --git a/Objects/classobject.c b/Objects/classobject.c
index 34afb9e..037252d 100644
--- a/Objects/classobject.c
+++ b/Objects/classobject.c
@@ -1733,6 +1733,43 @@
 	return outcome > 0;
 }
 
+static Py_ssize_t
+instance_index(PyInstanceObject *self)
+{
+	PyObject *func, *res;
+	Py_ssize_t outcome;
+	static PyObject *indexstr = NULL;
+
+	if (indexstr == NULL) {
+		indexstr = PyString_InternFromString("__index__");
+		if (indexstr == NULL)
+			return -1;
+	}	
+	if ((func = instance_getattr(self, indexstr)) == NULL) {
+		if (!PyErr_ExceptionMatches(PyExc_AttributeError))
+			return -1;
+		PyErr_Clear();
+		PyErr_SetString(PyExc_TypeError, 
+				"object cannot be interpreted as an index");
+		return -1;
+	}
+	res = PyEval_CallObject(func, (PyObject *)NULL);
+	Py_DECREF(func);
+	if (res == NULL)
+		return -1;
+	if (PyInt_Check(res) || PyLong_Check(res)) {
+		outcome = res->ob_type->tp_as_number->nb_index(res);
+	}
+	else {
+		PyErr_SetString(PyExc_TypeError, 
+				"__index__ must return an int or a long");
+		outcome = -1;
+	}
+	Py_DECREF(res);
+	return outcome;
+}
+
+
 UNARY(instance_invert, "__invert__")
 UNARY(instance_int, "__int__")
 UNARY(instance_long, "__long__")
@@ -2052,6 +2089,7 @@
 	(binaryfunc)instance_truediv,		/* nb_true_divide */
 	(binaryfunc)instance_ifloordiv,		/* nb_inplace_floor_divide */
 	(binaryfunc)instance_itruediv,		/* nb_inplace_true_divide */
+	(lenfunc)instance_index,		/* nb_index */
 };
 
 PyTypeObject PyInstance_Type = {
diff --git a/Objects/intobject.c b/Objects/intobject.c
index d7a64be..86e2e8c 100644
--- a/Objects/intobject.c
+++ b/Objects/intobject.c
@@ -1069,6 +1069,7 @@
 	int_true_divide,	/* nb_true_divide */
 	0,			/* nb_inplace_floor_divide */
 	0,			/* nb_inplace_true_divide */
+	(lenfunc)PyInt_AsSsize_t, /* nb_index */
 };
 
 PyTypeObject PyInt_Type = {
diff --git a/Objects/listobject.c b/Objects/listobject.c
index 0ff61e2..966d659 100644
--- a/Objects/listobject.c
+++ b/Objects/listobject.c
@@ -2452,11 +2452,14 @@
 "list() -> new list\n"
 "list(sequence) -> new list initialized from sequence's items");
 
+#define HASINDEX(o) PyType_HasFeature((o)->ob_type, Py_TPFLAGS_HAVE_INDEX)
+
 static PyObject *
 list_subscript(PyListObject* self, PyObject* item)
 {
-	if (PyInt_Check(item) || PyLong_Check(item)) {
-		Py_ssize_t i = PyInt_AsSsize_t(item);
+	PyNumberMethods *nb = item->ob_type->tp_as_number;	
+	if (nb != NULL && HASINDEX(item) && nb->nb_index != NULL) {
+		Py_ssize_t i = nb->nb_index(item);
 		if (i == -1 && PyErr_Occurred())
 			return NULL;
 		if (i < 0)
@@ -2503,14 +2506,9 @@
 static int
 list_ass_subscript(PyListObject* self, PyObject* item, PyObject* value)
 {
-	if (PyInt_Check(item)) {
-		Py_ssize_t i = PyInt_AS_LONG(item);
-		if (i < 0)
-			i += PyList_GET_SIZE(self);
-		return list_ass_item(self, i, value);
-	}
-	else if (PyLong_Check(item)) {
-		Py_ssize_t i = PyInt_AsSsize_t(item);
+	PyNumberMethods *nb = item->ob_type->tp_as_number;
+	if (nb != NULL && HASINDEX(item) && nb->nb_index != NULL) {
+		Py_ssize_t i = nb->nb_index(item);
 		if (i == -1 && PyErr_Occurred())
 			return -1;
 		if (i < 0)
diff --git a/Objects/longobject.c b/Objects/longobject.c
index 9032656..e47c292 100644
--- a/Objects/longobject.c
+++ b/Objects/longobject.c
@@ -241,12 +241,8 @@
 	return -1;
 }
 
-/* Get a Py_ssize_t from a long int object.
-   Returns -1 and sets an error condition if overflow occurs. */
-
-Py_ssize_t
-_PyLong_AsSsize_t(PyObject *vv)
-{
+static Py_ssize_t
+_long_as_ssize_t(PyObject *vv) {
 	register PyLongObject *v;
 	size_t x, prev;
 	Py_ssize_t i;
@@ -282,7 +278,45 @@
  overflow:
 	PyErr_SetString(PyExc_OverflowError,
 			"long int too large to convert to int");
-	return -1;
+	if (sign > 0) 
+		return PY_SSIZE_T_MAX;
+	else 
+		return -PY_SSIZE_T_MAX-1;
+}
+
+/* Get a Py_ssize_t from a long int object.
+   Returns -1 and sets an error condition if overflow occurs. */
+
+Py_ssize_t
+_PyLong_AsSsize_t(PyObject *vv)
+{
+	Py_ssize_t x;
+
+	x = _long_as_ssize_t(vv);
+	if (PyErr_Occurred()) return -1;
+	return x;
+}
+
+
+/* Get a Py_ssize_t from a long int object.
+   Silently reduce values larger than PY_SSIZE_T_MAX to PY_SSIZE_T_MAX,
+   and silently boost values less than -PY_SSIZE_T_MAX-1 to -PY_SSIZE_T_MAX-1.
+   Return 0 on error, 1 on success.
+*/
+
+static Py_ssize_t
+long_index(PyObject *vv)
+{
+	Py_ssize_t x;
+
+	x = _long_as_ssize_t(vv);
+	if (PyErr_Occurred()) {
+		/* If overflow error, ignore the error */
+		if (x != -1) {
+			PyErr_Clear();
+		}
+	}
+	return x;
 }
 
 /* Get a C unsigned long int from a long int object.
@@ -3131,6 +3165,7 @@
 	long_true_divide,		/* nb_true_divide */
 	0,				/* nb_inplace_floor_divide */
 	0,				/* nb_inplace_true_divide */
+	(lenfunc)long_index,            /* nb_index */
 };
 
 PyTypeObject PyLong_Type = {
diff --git a/Objects/stringobject.c b/Objects/stringobject.c
index e2b7603..16d542a 100644
--- a/Objects/stringobject.c
+++ b/Objects/stringobject.c
@@ -1187,16 +1187,19 @@
 	return x;
 }
 
+#define HASINDEX(o) PyType_HasFeature((o)->ob_type, Py_TPFLAGS_HAVE_INDEX)
+
 static PyObject*
 string_subscript(PyStringObject* self, PyObject* item)
 {
-	if (PyInt_Check(item) || PyLong_Check(item)) {
-		Py_ssize_t i = PyInt_AsSsize_t(item);
+	PyNumberMethods *nb = item->ob_type->tp_as_number;
+	if (nb != NULL && HASINDEX(item) && nb->nb_index != NULL) {
+		Py_ssize_t i = nb->nb_index(item);
 		if (i == -1 && PyErr_Occurred())
 			return NULL;
 		if (i < 0)
 			i += PyString_GET_SIZE(self);
-		return string_item(self,i);
+		return string_item(self, i);
 	}
 	else if (PySlice_Check(item)) {
 		Py_ssize_t start, stop, step, slicelength, cur, i;
diff --git a/Objects/tupleobject.c b/Objects/tupleobject.c
index c0383a1..384b355 100644
--- a/Objects/tupleobject.c
+++ b/Objects/tupleobject.c
@@ -584,11 +584,14 @@
 	(objobjproc)tuplecontains,		/* sq_contains */
 };
 
+#define HASINDEX(o) PyType_HasFeature((o)->ob_type, Py_TPFLAGS_HAVE_INDEX)
+
 static PyObject*
 tuplesubscript(PyTupleObject* self, PyObject* item)
 {
-	if (PyInt_Check(item) || PyLong_Check(item)) {
-		Py_ssize_t i = PyInt_AsSsize_t(item);
+	PyNumberMethods *nb = item->ob_type->tp_as_number;
+	if (nb != NULL && HASINDEX(item) && nb->nb_index != NULL) {
+		Py_ssize_t i = nb->nb_index(item);
 		if (i == -1 && PyErr_Occurred())
 			return NULL;
 		if (i < 0)
diff --git a/Objects/typeobject.c b/Objects/typeobject.c
index 9837e38..681fb21 100644
--- a/Objects/typeobject.c
+++ b/Objects/typeobject.c
@@ -3051,6 +3051,9 @@
 			COPYNUM(nb_inplace_true_divide);
 			COPYNUM(nb_inplace_floor_divide);
 		}
+		if (base->tp_flags & Py_TPFLAGS_HAVE_INDEX) {
+			COPYNUM(nb_index);
+		}
 	}
 
 	if (type->tp_as_sequence != NULL && base->tp_as_sequence != NULL) {
@@ -4344,6 +4347,44 @@
 	return result;
 }
 
+
+static Py_ssize_t 
+slot_nb_index(PyObject *self)
+{
+	PyObject *func, *args;
+	static PyObject *index_str;
+	Py_ssize_t result = -1;
+
+	func = lookup_maybe(self, "__index__", &index_str);
+	if (func == NULL) {
+		if (!PyErr_Occurred()) {
+			PyErr_SetString(PyExc_TypeError, 
+				"object cannot be interpreted as an index");
+		}
+		return -1;
+ 	}
+	args = PyTuple_New(0);
+	if (args != NULL) {
+		PyObject *temp = PyObject_Call(func, args, NULL);
+		Py_DECREF(args);
+		if (temp != NULL) {
+			if (PyInt_Check(temp) || PyLong_Check(temp)) {
+				result =
+                                  temp->ob_type->tp_as_number->nb_index(temp);
+			}
+			else {
+ 				PyErr_SetString(PyExc_TypeError, 
+				    "__index__ must return an int or a long");
+				result = -1;
+			}
+			Py_DECREF(temp);
+		}
+	}
+	Py_DECREF(func);
+	return result;
+}
+
+
 SLOT0(slot_nb_invert, "__invert__")
 SLOT1BIN(slot_nb_lshift, nb_lshift, "__lshift__", "__rlshift__")
 SLOT1BIN(slot_nb_rshift, nb_rshift, "__rshift__", "__rrshift__")
@@ -5069,6 +5110,8 @@
 	       "oct(x)"),
 	UNSLOT("__hex__", nb_hex, slot_nb_hex, wrap_unaryfunc,
 	       "hex(x)"),
+	NBSLOT("__index__", nb_index, slot_nb_index, wrap_lenfunc, 
+	       "x[y:z] <==> x[y.__index__():z.__index__()]"),
 	IBSLOT("__iadd__", nb_inplace_add, slot_nb_inplace_add,
 	       wrap_binaryfunc, "+"),
 	IBSLOT("__isub__", nb_inplace_subtract, slot_nb_inplace_subtract,
diff --git a/Objects/unicodeobject.c b/Objects/unicodeobject.c
index 4146f1d..a0d3de9 100644
--- a/Objects/unicodeobject.c
+++ b/Objects/unicodeobject.c
@@ -6460,11 +6460,14 @@
     (objobjproc)PyUnicode_Contains, 	/*sq_contains*/
 };
 
+#define HASINDEX(o) PyType_HasFeature((o)->ob_type, Py_TPFLAGS_HAVE_INDEX)
+
 static PyObject*
 unicode_subscript(PyUnicodeObject* self, PyObject* item)
 {
-    if (PyInt_Check(item) || PyLong_Check(item)) {
-        Py_ssize_t i = PyInt_AsSsize_t(item);
+    PyNumberMethods *nb = item->ob_type->tp_as_number;
+    if (nb != NULL && HASINDEX(item) && nb->nb_index != NULL) {
+        Py_ssize_t i = nb->nb_index(item);
         if (i == -1 && PyErr_Occurred())
             return NULL;
         if (i < 0)