Index: Objects/complexobject.c
===================================================================
--- Objects/complexobject.c	(revision 54183)
+++ Objects/complexobject.c	(working copy)
@@ -252,9 +252,44 @@
 PyComplex_AsCComplex(PyObject *op)
 {
 	Py_complex cv;
+	PyObject *f, *r, *args;
+
+        /* If op is already of type PyComplex_Type, return its value */
 	if (PyComplex_Check(op)) {
 		return ((PyComplexObject *)op)->cval;
 	}
+        /* If not, use op's __complex__  method, if it exists */
+	if (PyObject_HasAttrString(op, "__complex__")) {
+		/* return value of -1 on failure */
+		cv.real = -1.;
+		cv.imag = 0.;
+
+		f = PyObject_GetAttrString(op, "__complex__");
+		if (f == NULL)
+			return cv;
+		args = PyTuple_New(0);
+		if (args == NULL) {
+			Py_DECREF(f);
+			return cv;
+		}
+		r = PyEval_CallObject(f, args);
+		Py_DECREF(args);
+		Py_DECREF(f);
+		if (r == NULL) {
+			return cv;
+		}
+		if (!PyComplex_Check(r)) {
+			PyErr_SetString(PyExc_TypeError,
+				"__complex__ should return a complex object");
+			Py_DECREF(r);
+			return cv;
+		}
+		cv = ((PyComplexObject *)r)->cval;
+		Py_DECREF(r);
+		return cv;
+	}
+        /* If neither of the above works, interpret op as a float giving the
+           real part of the result, and fill in the imaginary part as 0. */
 	else {
 		cv.real = PyFloat_AsDouble(op);
 		cv.imag = 0.;
Index: Doc/api/concrete.tex
===================================================================
--- Doc/api/concrete.tex	(revision 54183)
+++ Doc/api/concrete.tex	(working copy)
@@ -443,7 +443,9 @@
 
 \begin{cfuncdesc}{double}{PyFloat_AsDouble}{PyObject *pyfloat}
   Return a C \ctype{double} representation of the contents of
-  \var{pyfloat}.
+  \var{pyfloat}.  If \var{pyfloat} is not a Python floating point
+  object but has a \method{__float__} method, this method will first
+  be called to convert \var{pyfloat} into a float.
 \end{cfuncdesc}
 
 \begin{cfuncdesc}{double}{PyFloat_AS_DOUBLE}{PyObject *pyfloat}
@@ -558,8 +560,10 @@
 \end{cfuncdesc}
 
 \begin{cfuncdesc}{Py_complex}{PyComplex_AsCComplex}{PyObject *op}
-  Return the \ctype{Py_complex} value of the complex number
-  \var{op}.
+  Return the \ctype{Py_complex} value of the complex number \var{op}.
+  If \var{op} is not a Python complex number object but has a
+  \method{__complex__} method, this method will first be called to
+  convert op to a Python complex number object.
 \end{cfuncdesc}