diff --git a/Misc/NEWS b/Misc/NEWS
index 849911b..0e2969e 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -236,6 +236,8 @@
 Extension Modules
 -----------------
 
+- Speed up function calls into the math module.
+
 - Bug #1588217: don't parse "= " as a soft line break in binascii's
   a2b_qp() function, instead leave it in the string as quopri.decode()
   does.
diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index e7fc6dd..14e6bfc 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -48,10 +48,10 @@
 }
 
 static PyObject *
-math_1(PyObject *args, double (*func) (double), char *argsfmt)
+math_1(PyObject *arg, double (*func) (double))
 {
-	double x;
-	if (!  PyArg_ParseTuple(args, argsfmt, &x))
+	double x = PyFloat_AsDouble(arg);
+	if (x == -1.0 && PyErr_Occurred())
 		return NULL;
 	errno = 0;
 	PyFPE_START_PROTECT("in math_1", return 0)
@@ -65,10 +65,15 @@
 }
 
 static PyObject *
-math_2(PyObject *args, double (*func) (double, double), char *argsfmt)
+math_2(PyObject *args, double (*func) (double, double), char *funcname)
 {
+	PyObject *ox, *oy;
 	double x, y;
-	if (! PyArg_ParseTuple(args, argsfmt, &x, &y))
+	if (! PyArg_UnpackTuple(args, funcname, 2, 2, &ox, &oy))
+		return NULL;
+	x = PyFloat_AsDouble(ox);
+	y = PyFloat_AsDouble(oy);
+	if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
 		return NULL;
 	errno = 0;
 	PyFPE_START_PROTECT("in math_2", return 0)
@@ -83,13 +88,13 @@
 
 #define FUNC1(funcname, func, docstring) \
 	static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
-		return math_1(args, func, "d:" #funcname); \
+		return math_1(args, func); \
 	}\
         PyDoc_STRVAR(math_##funcname##_doc, docstring);
 
 #define FUNC2(funcname, func, docstring) \
 	static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
-		return math_2(args, func, "dd:" #funcname); \
+		return math_2(args, func, #funcname); \
 	}\
         PyDoc_STRVAR(math_##funcname##_doc, docstring);
 
@@ -135,11 +140,11 @@
       "tanh(x)\n\nReturn the hyperbolic tangent of x.")
 
 static PyObject *
-math_frexp(PyObject *self, PyObject *args)
+math_frexp(PyObject *self, PyObject *arg)
 {
-	double x;
 	int i;
-	if (! PyArg_ParseTuple(args, "d:frexp", &x))
+	double x = PyFloat_AsDouble(arg);
+	if (x == -1.0 && PyErr_Occurred())
 		return NULL;
 	errno = 0;
 	x = frexp(x, &i);
@@ -179,10 +184,10 @@
 "ldexp(x, i) -> x * (2**i)");
 
 static PyObject *
-math_modf(PyObject *self, PyObject *args)
+math_modf(PyObject *self, PyObject *arg)
 {
-	double x, y;
-	if (! PyArg_ParseTuple(args, "d:modf", &x))
+	double y, x = PyFloat_AsDouble(arg);
+	if (x == -1.0 && PyErr_Occurred())
 		return NULL;
 	errno = 0;
 	x = modf(x, &y);
@@ -208,7 +213,7 @@
 */
 
 static PyObject*
-loghelper(PyObject* args, double (*func)(double), char *format, PyObject *arg)
+loghelper(PyObject* arg, double (*func)(double), char *funcname)
 {
 	/* If it is long, do it ourselves. */
 	if (PyLong_Check(arg)) {
@@ -229,7 +234,7 @@
 	}
 
 	/* Else let libm handle it by itself. */
-	return math_1(args, func, format);
+	return math_1(arg, func);
 }
 
 static PyObject *
@@ -239,28 +244,15 @@
 	PyObject *base = NULL;
 	PyObject *num, *den;
 	PyObject *ans;
-	PyObject *newargs;
 
 	if (!PyArg_UnpackTuple(args, "log", 1, 2, &arg, &base))
 		return NULL;
-	if (base == NULL)
-		return loghelper(args, log, "d:log", arg);
 
-	newargs = PyTuple_Pack(1, arg);
-	if (newargs == NULL)
-		return NULL;
-	num = loghelper(newargs, log, "d:log", arg);
-	Py_DECREF(newargs);
-	if (num == NULL)
-		return NULL;
+	num = loghelper(arg, log, "log");
+	if (num == NULL || base == NULL)
+		return num;
 
-	newargs = PyTuple_Pack(1, base);
-	if (newargs == NULL) {
-		Py_DECREF(num);
-		return NULL;
-	}
-	den = loghelper(newargs, log, "d:log", base);
-	Py_DECREF(newargs);
+	den = loghelper(base, log, "log");
 	if (den == NULL) {
 		Py_DECREF(num);
 		return NULL;
@@ -277,25 +269,23 @@
 If the base not specified, returns the natural logarithm (base e) of x.");
 
 static PyObject *
-math_log10(PyObject *self, PyObject *args)
+math_log10(PyObject *self, PyObject *arg)
 {
-	PyObject *arg;
-
-	if (!PyArg_UnpackTuple(args, "log10", 1, 1, &arg))
-		return NULL;
-	return loghelper(args, log10, "d:log10", arg);
+	return loghelper(arg, log10, "log10");
 }
 
 PyDoc_STRVAR(math_log10_doc,
 "log10(x) -> the base 10 logarithm of x.");
 
+/* XXX(nnorwitz): Should we use the platform M_PI or something more accurate
+   like: 3.14159265358979323846264338327950288 */
 static const double degToRad = 3.141592653589793238462643383 / 180.0;
 
 static PyObject *
-math_degrees(PyObject *self, PyObject *args)
+math_degrees(PyObject *self, PyObject *arg)
 {
-	double x;
-	if (! PyArg_ParseTuple(args, "d:degrees", &x))
+	double x = PyFloat_AsDouble(arg);
+	if (x == -1.0 && PyErr_Occurred())
 		return NULL;
 	return PyFloat_FromDouble(x / degToRad);
 }
@@ -304,10 +294,10 @@
 "degrees(x) -> converts angle x from radians to degrees");
 
 static PyObject *
-math_radians(PyObject *self, PyObject *args)
+math_radians(PyObject *self, PyObject *arg)
 {
-	double x;
-	if (! PyArg_ParseTuple(args, "d:radians", &x))
+	double x = PyFloat_AsDouble(arg);
+	if (x == -1.0 && PyErr_Occurred())
 		return NULL;
 	return PyFloat_FromDouble(x * degToRad);
 }
@@ -316,31 +306,31 @@
 "radians(x) -> converts angle x from degrees to radians");
 
 static PyMethodDef math_methods[] = {
-	{"acos",	math_acos,	METH_VARARGS,	math_acos_doc},
-	{"asin",	math_asin,	METH_VARARGS,	math_asin_doc},
-	{"atan",	math_atan,	METH_VARARGS,	math_atan_doc},
+	{"acos",	math_acos,	METH_O,		math_acos_doc},
+	{"asin",	math_asin,	METH_O,		math_asin_doc},
+	{"atan",	math_atan,	METH_O,		math_atan_doc},
 	{"atan2",	math_atan2,	METH_VARARGS,	math_atan2_doc},
-	{"ceil",	math_ceil,	METH_VARARGS,	math_ceil_doc},
-	{"cos",		math_cos,	METH_VARARGS,	math_cos_doc},
-	{"cosh",	math_cosh,	METH_VARARGS,	math_cosh_doc},
-	{"degrees",	math_degrees,	METH_VARARGS,	math_degrees_doc},
-	{"exp",		math_exp,	METH_VARARGS,	math_exp_doc},
-	{"fabs",	math_fabs,	METH_VARARGS,	math_fabs_doc},
-	{"floor",	math_floor,	METH_VARARGS,	math_floor_doc},
+	{"ceil",	math_ceil,	METH_O,		math_ceil_doc},
+	{"cos",		math_cos,	METH_O,		math_cos_doc},
+	{"cosh",	math_cosh,	METH_O,		math_cosh_doc},
+	{"degrees",	math_degrees,	METH_O,		math_degrees_doc},
+	{"exp",		math_exp,	METH_O,		math_exp_doc},
+	{"fabs",	math_fabs,	METH_O,		math_fabs_doc},
+	{"floor",	math_floor,	METH_O,		math_floor_doc},
 	{"fmod",	math_fmod,	METH_VARARGS,	math_fmod_doc},
-	{"frexp",	math_frexp,	METH_VARARGS,	math_frexp_doc},
+	{"frexp",	math_frexp,	METH_O,		math_frexp_doc},
 	{"hypot",	math_hypot,	METH_VARARGS,	math_hypot_doc},
 	{"ldexp",	math_ldexp,	METH_VARARGS,	math_ldexp_doc},
 	{"log",		math_log,	METH_VARARGS,	math_log_doc},
-	{"log10",	math_log10,	METH_VARARGS,	math_log10_doc},
-	{"modf",	math_modf,	METH_VARARGS,	math_modf_doc},
+	{"log10",	math_log10,	METH_O,		math_log10_doc},
+	{"modf",	math_modf,	METH_O,		math_modf_doc},
 	{"pow",		math_pow,	METH_VARARGS,	math_pow_doc},
-	{"radians",	math_radians,	METH_VARARGS,	math_radians_doc},
-	{"sin",		math_sin,	METH_VARARGS,	math_sin_doc},
-	{"sinh",	math_sinh,	METH_VARARGS,	math_sinh_doc},
-	{"sqrt",	math_sqrt,	METH_VARARGS,	math_sqrt_doc},
-	{"tan",		math_tan,	METH_VARARGS,	math_tan_doc},
-	{"tanh",	math_tanh,	METH_VARARGS,	math_tanh_doc},
+	{"radians",	math_radians,	METH_O,		math_radians_doc},
+	{"sin",		math_sin,	METH_O,		math_sin_doc},
+	{"sinh",	math_sinh,	METH_O,		math_sinh_doc},
+	{"sqrt",	math_sqrt,	METH_O,		math_sqrt_doc},
+	{"tan",		math_tan,	METH_O,		math_tan_doc},
+	{"tanh",	math_tanh,	METH_O,		math_tanh_doc},
 	{NULL,		NULL}		/* sentinel */
 };
 
@@ -358,6 +348,8 @@
 	if (m == NULL)
 		goto finally;
 	d = PyModule_GetDict(m);
+	if (d == NULL)
+		goto finally;
 
         if (!(v = PyFloat_FromDouble(atan(1.0) * 4.0)))
                 goto finally;