Add ctypedef for __builtin__.type.

This allows a "C" function like
    extern "C" PyObject* f(PyTypeObject *a);
to be wrapped by Cython as
    from cpython.type import type
    cdef extern from *:
        object f(type a)

In particular, this allows Cython to produce code which calls f as
    f((PyTypeObject*) a)
which means that it will compile in C++.

Cython/Compiler/Code.py

@@ -40,6 +40,11 @@ non_portable_builtins_map = {
     'BaseException' : ('PY_VERSION_HEX < 0x02050000', 'Exception'),
     }
 
+basicsize_builtins_map = {
+    # builtins whose type has a different tp_basicsize than sizeof(...)
+    'PyTypeObject' : 'PyHeapTypeObject',
+    }
+
 uncachable_builtins = [
     # builtin names that cannot be cached because they may or may not
     # be available at import time

Cython/Compiler/ModuleNode.py

@@ -2181,6 +2181,8 @@ class ModuleNode(Nodes.Node, Nodes.BlockNode):
             objstruct = type.objstruct_cname
         else:
             objstruct = "struct %s" % type.objstruct_cname
+        # Some builtin types have a tp_basicsize which differs from sizeof(...):
+        objstruct = Code.basicsize_builtins_map.get(objstruct, objstruct)
         module_name = type.module_name
         condition = None
         if module_name not in ('__builtin__', 'builtins'):

Cython/Includes/cpython/type.pxd

@@ -6,6 +6,9 @@ cdef extern from "Python.h":
     # 7.1.1 Type Objects
     ############################################################################
 
+    ctypedef class __builtin__.type [object PyTypeObject]:
+        pass
+
     # PyObject* PyType_Type
     # This is the type object for type objects; it is the same object
     # as type and types.TypeType in the Python layer.
@@ -28,16 +31,16 @@ cdef extern from "Python.h":
     # Return true if the type object includes support for the cycle
     # detector; this tests the type flag Py_TPFLAGS_HAVE_GC.
 
-    bint PyType_IsSubtype(object a, object b)
+    bint PyType_IsSubtype(type a, type b)
     # Return true if a is a subtype of b.
 
     object PyType_GenericAlloc(object type, Py_ssize_t nitems)
     # Return value: New reference.
 
-    object PyType_GenericNew(object type, object args, object kwds)
+    object PyType_GenericNew(type type, object args, object kwds)
     # Return value: New reference.
 
-    bint PyType_Ready(object type) except -1
+    bint PyType_Ready(type type) except -1
     # Finalize a type object. This should be called on all type
     # objects to finish their initialization. This function is
     # responsible for adding inherited slots from a type's base

Cython/Includes/numpy.pxd

@@ -19,6 +19,7 @@ DEF _buffer_format_string_len = 255
 cimport cpython.buffer as pybuf
 from cpython.ref cimport Py_INCREF, Py_XDECREF
 from cpython.object cimport PyObject
+from cpython.type cimport type
 cimport libc.stdlib as stdlib
 cimport libc.stdio as stdio