@@ -187,6 +187,12 @@ Hyperbolic functions
 Classification functions
 ------------------------
 
+.. function:: isfinite(x)
+
+   Return ``True`` if both the real and imaginary parts of *x* are finite,
+   and ``False`` otherwise.
+
+
 .. function:: isinf(x)
 
    Return *True* if the real or the imaginary part of x is positive
 
@@ -97,6 +97,12 @@ Number-theoretic and representation functions
    <http://code.activestate.com/recipes/393090/>`_\.
 
 
+.. function:: isfinite(x)
+
+   Return ``True`` if *x* is neither an infinity nor a NaN, and
+   ``False`` otherwise.  (Note that ``0.0`` *is* considered finite.)
+
+
 .. function:: isinf(x)
 
    Check if the float *x* is positive or negative infinity.
 
@@ -442,6 +442,15 @@ def test_rect(self):
         self.assertCEqual(rect(1, pi/2), (0, 1.))
         self.assertCEqual(rect(1, -pi/2), (0, -1.))
 
+    def test_isfinite(self):
+        real_vals = [float('-inf'), -2.3, -0.0,
+                     0.0, 2.3, float('inf'), float('nan')]
+        for x in real_vals:
+            for y in real_vals:
+                z = complex(x, y)
+                self.assertEquals(cmath.isfinite(z),
+                                  math.isfinite(x) and math.isfinite(y))
+
     def test_isnan(self):
         self.assertFalse(cmath.isnan(1))
         self.assertFalse(cmath.isnan(1j))
 
@@ -915,6 +915,15 @@ class TestNoTrunc(object):
         self.assertRaises(TypeError, math.trunc, 1, 2)
         self.assertRaises(TypeError, math.trunc, TestNoTrunc())
 
+    def testIsfinite(self):
+        self.assertTrue(math.isfinite(0.0))
+        self.assertTrue(math.isfinite(-0.0))
+        self.assertTrue(math.isfinite(1.0))
+        self.assertTrue(math.isfinite(-1.0))
+        self.assertFalse(math.isfinite(float("nan")))
+        self.assertFalse(math.isfinite(float("inf")))
+        self.assertFalse(math.isfinite(float("-inf")))
+
     def testIsnan(self):
         self.assertTrue(math.isnan(float("nan")))
         self.assertTrue(math.isnan(float("inf")* 0.))
 
@@ -1415,6 +1415,9 @@ Library
 Extension Modules
 -----------------
 
+- Issue #9165: Add new functions math.isfinite and cmath.isfinite, to
+  accompany existing isinf and isnan functions.
+
 - Issue #1578269: Implement os.symlink for Windows 6.0+. Patch by
   Jason R. Coombs
 
 
@@ -1023,6 +1023,19 @@ PyDoc_STRVAR(cmath_rect_doc,
 "rect(r, phi) -> z: complex\n\n\
 Convert from polar coordinates to rectangular coordinates.");
 
+static PyObject *
+cmath_isfinite(PyObject *self, PyObject *args)
+{
+    Py_complex z;
+    if (!PyArg_ParseTuple(args, "D:isfinite", &z))
+        return NULL;
+    return PyBool_FromLong(Py_IS_FINITE(z.real) && Py_IS_FINITE(z.imag));
+}
+
+PyDoc_STRVAR(cmath_isfinite_doc,
+"isfinite(z) -> bool\n\
+Return True if both the real and imaginary parts of z are finite, else False.");
+
 static PyObject *
 cmath_isnan(PyObject *self, PyObject *args)
 {
@@ -1065,6 +1078,7 @@ static PyMethodDef cmath_methods[] = {
     {"cos",    cmath_cos,   METH_VARARGS, c_cos_doc},
     {"cosh",   cmath_cosh,  METH_VARARGS, c_cosh_doc},
     {"exp",    cmath_exp,   METH_VARARGS, c_exp_doc},
+    {"isfinite", cmath_isfinite, METH_VARARGS, cmath_isfinite_doc},
     {"isinf",  cmath_isinf, METH_VARARGS, cmath_isinf_doc},
     {"isnan",  cmath_isnan, METH_VARARGS, cmath_isnan_doc},
     {"log",    cmath_log,   METH_VARARGS, cmath_log_doc},
 
@@ -1817,6 +1817,19 @@ PyDoc_STRVAR(math_radians_doc,
 "radians(x)\n\n\
 Convert angle x from degrees to radians.");
 
+static PyObject *
+math_isfinite(PyObject *self, PyObject *arg)
+{
+    double x = PyFloat_AsDouble(arg);
+    if (x == -1.0 && PyErr_Occurred())
+        return NULL;
+    return PyBool_FromLong((long)Py_IS_FINITE(x));
+}
+
+PyDoc_STRVAR(math_isfinite_doc,
+"isfinite(x) -> bool\n\n\
+Check if float x is finite (not an infinity or NaN).");
+
 static PyObject *
 math_isnan(PyObject *self, PyObject *arg)
 {
@@ -1868,6 +1881,7 @@ static PyMethodDef math_methods[] = {
     {"fsum",            math_fsum,      METH_O,         math_fsum_doc},
     {"gamma",           math_gamma,     METH_O,         math_gamma_doc},
     {"hypot",           math_hypot,     METH_VARARGS,   math_hypot_doc},
+    {"isfinite",        math_isfinite,  METH_O,         math_isfinite_doc},
     {"isinf",           math_isinf,     METH_O,         math_isinf_doc},
     {"isnan",           math_isnan,     METH_O,         math_isnan_doc},
     {"ldexp",           math_ldexp,     METH_VARARGS,   math_ldexp_doc},