bpo-37999: Fix outdated __int__ and nb_int references in comments (GH-20449)

* Fix outdated __int__ and nb_int references in comments

* Also update C-API documentation

* Add back missing 'method' word

* Remove .. deprecated notices
diff --git a/Objects/longobject.c b/Objects/longobject.c
index a409948..e040d6c 100644
--- a/Objects/longobject.c
+++ b/Objects/longobject.c
@@ -363,7 +363,7 @@
 #define PY_ABS_LONG_MIN         (0-(unsigned long)LONG_MIN)
 #define PY_ABS_SSIZE_T_MIN      (0-(size_t)PY_SSIZE_T_MIN)
 
-/* Get a C long int from an int object or any object that has an __int__
+/* Get a C long int from an int object or any object that has an __index__
    method.
 
    On overflow, return -1 and set *overflow to 1 or -1 depending on the sign of
@@ -382,7 +382,7 @@
     long res;
     Py_ssize_t i;
     int sign;
-    int do_decref = 0; /* if nb_int was called */
+    int do_decref = 0; /* if PyNumber_Index was called */
 
     *overflow = 0;
     if (vv == NULL) {
@@ -449,7 +449,7 @@
     return res;
 }
 
-/* Get a C long int from an int object or any object that has an __int__
+/* Get a C long int from an int object or any object that has an __index__
    method.  Return -1 and set an error if overflow occurs. */
 
 long
@@ -466,7 +466,7 @@
     return result;
 }
 
-/* Get a C int from an int object or any object that has an __int__
+/* Get a C int from an int object or any object that has an __index__
    method.  Return -1 and set an error if overflow occurs. */
 
 int
@@ -1113,7 +1113,7 @@
 }
 
 /* Get a C long long int from an int object or any object that has an
-   __int__ method.  Return -1 and set an error if overflow occurs. */
+   __index__ method.  Return -1 and set an error if overflow occurs. */
 
 long long
 PyLong_AsLongLong(PyObject *vv)
@@ -1121,7 +1121,7 @@
     PyLongObject *v;
     long long bytes;
     int res;
-    int do_decref = 0; /* if nb_int was called */
+    int do_decref = 0; /* if PyNumber_Index was called */
 
     if (vv == NULL) {
         PyErr_BadInternalCall();
@@ -1257,7 +1257,7 @@
 }
 
 /* Get a C long long int from an int object or any object that has an
-   __int__ method.
+   __index__ method.
 
    On overflow, return -1 and set *overflow to 1 or -1 depending on the sign of
    the result.  Otherwise *overflow is 0.
@@ -1275,7 +1275,7 @@
     long long res;
     Py_ssize_t i;
     int sign;
-    int do_decref = 0; /* if nb_int was called */
+    int do_decref = 0; /* if PyNumber_Index was called */
 
     *overflow = 0;
     if (vv == NULL) {