Issue #20152: Convert the cmath module to Argument Clinic.

Misc/NEWS

@@ -16,8 +16,6 @@ Core and Builtins
 - Issue #22604: Fix assertion error in debug mode when dividing a complex
   number by (nan+0j).
 
-- Issue #20152: Convert the array module to Argument Clinic.
-
 - Issue #21052: Do not raise ImportWarning when sys.path_hooks or sys.meta_path
   are set to None.
 
@@ -177,6 +175,8 @@ Core and Builtins
 Library
 -------
 
+- Issue #20152: Convert the array and cmath modules to Argument Clinic.
+
 - Issue #18643: Add socket.socketpair() on Windows.
 
 - Issue #22435: Fix a file descriptor leak when SocketServer bind fails.

Modules/clinic/cmathmodule.c.h

+/*[clinic input]
+preserve
+[clinic start generated code]*/
+
+PyDoc_STRVAR(cmath_acos__doc__,
+"acos($module, z, /)\n"
+"--\n"
+"\n"
+"Return the arc cosine of z.");
+
+#define CMATH_ACOS_METHODDEF    \
+    {"acos", (PyCFunction)cmath_acos, METH_VARARGS, cmath_acos__doc__},
+
+static Py_complex
+cmath_acos_impl(PyModuleDef *module, Py_complex z);
+
+static PyObject *
+cmath_acos(PyModuleDef *module, PyObject *args)
+{
+    PyObject *return_value = NULL;
+    Py_complex z;
+    Py_complex _return_value;
+
+    if (!PyArg_ParseTuple(args,
+        "D:acos",
+        &z))
+        goto exit;
+    /* modifications for z */
+    errno = 0; PyFPE_START_PROTECT("complex function", goto exit);
+    _return_value = cmath_acos_impl(module, z);
+    PyFPE_END_PROTECT(_return_value);
+    if (errno == EDOM) {
+        PyErr_SetString(PyExc_ValueError, "math domain error");
+        goto exit;
+    }
+    else if (errno == ERANGE) {
+        PyErr_SetString(PyExc_OverflowError, "math range error");
+        goto exit;
+    }
+    else {
+        return_value = PyComplex_FromCComplex(_return_value);
+    }
+
+exit:
+    return return_value;
+}
+
+PyDoc_STRVAR(cmath_acosh__doc__,
+"acosh($module, z, /)\n"
+"--\n"
+"\n"
+"Return the hyperbolic arccosine of z.");
+
+#define CMATH_ACOSH_METHODDEF    \
+    {"acosh", (PyCFunction)cmath_acosh, METH_VARARGS, cmath_acosh__doc__},
+
+static Py_complex
+cmath_acosh_impl(PyModuleDef *module, Py_complex z);
+
+static PyObject *
+cmath_acosh(PyModuleDef *module, PyObject *args)
+{
+    PyObject *return_value = NULL;
+    Py_complex z;
+    Py_complex _return_value;
+
+    if (!PyArg_ParseTuple(args,
+        "D:acosh",
+        &z))
+        goto exit;
+    /* modifications for z */
+    errno = 0; PyFPE_START_PROTECT("complex function", goto exit);
+    _return_value = cmath_acosh_impl(module, z);
+    PyFPE_END_PROTECT(_return_value);
+    if (errno == EDOM) {
+        PyErr_SetString(PyExc_ValueError, "math domain error");
+        goto exit;
+    }
+    else if (errno == ERANGE) {
+        PyErr_SetString(PyExc_OverflowError, "math range error");
+        goto exit;
+    }
+    else {
+        return_value = PyComplex_FromCComplex(_return_value);
+    }
+
+exit:
+    return return_value;
+}
+
+PyDoc_STRVAR(cmath_asin__doc__,
+"asin($module, z, /)\n"
+"--\n"
+"\n"
+"Return the arc sine of z.");
+
+#define CMATH_ASIN_METHODDEF    \
+    {"asin", (PyCFunction)cmath_asin, METH_VARARGS, cmath_asin__doc__},
+
+static Py_complex
+cmath_asin_impl(PyModuleDef *module, Py_complex z);
+
+static PyObject *
+cmath_asin(PyModuleDef *module, PyObject *args)
+{
+    PyObject *return_value = NULL;
+    Py_complex z;
+    Py_complex _return_value;
+
+    if (!PyArg_ParseTuple(args,
+        "D:asin",
+        &z))
+        goto exit;
+    /* modifications for z */
+    errno = 0; PyFPE_START_PROTECT("complex function", goto exit);
+    _return_value = cmath_asin_impl(module, z);
+    PyFPE_END_PROTECT(_return_value);
+    if (errno == EDOM) {
+        PyErr_SetString(PyExc_ValueError, "math domain error");
+        goto exit;
+    }
+    else if (errno == ERANGE) {
+        PyErr_SetString(PyExc_OverflowError, "math range error");
+        goto exit;
+    }
+    else {
+        return_value = PyComplex_FromCComplex(_return_value);
+    }
+
+exit:
+    return return_value;
+}
+
+PyDoc_STRVAR(cmath_asinh__doc__,
+"asinh($module, z, /)\n"
+"--\n"
+"\n"
+"Return the hyperbolic arc sine of z.");
+
+#define CMATH_ASINH_METHODDEF    \
+    {"asinh", (PyCFunction)cmath_asinh, METH_VARARGS, cmath_asinh__doc__},
+
+static Py_complex
+cmath_asinh_impl(PyModuleDef *module, Py_complex z);
+
+static PyObject *
+cmath_asinh(PyModuleDef *module, PyObject *args)
+{
+    PyObject *return_value = NULL;
+    Py_complex z;
+    Py_complex _return_value;
+
+    if (!PyArg_ParseTuple(args,
+        "D:asinh",
+        &z))
+        goto exit;
+    /* modifications for z */
+    errno = 0; PyFPE_START_PROTECT("complex function", goto exit);
+    _return_value = cmath_asinh_impl(module, z);
+    PyFPE_END_PROTECT(_return_value);
+    if (errno == EDOM) {
+        PyErr_SetString(PyExc_ValueError, "math domain error");
+        goto exit;
+    }
+    else if (errno == ERANGE) {
+        PyErr_SetString(PyExc_OverflowError, "math range error");
+        goto exit;
+    }
+    else {
+        return_value = PyComplex_FromCComplex(_return_value);
+    }
+
+exit:
+    return return_value;
+}
+
+PyDoc_STRVAR(cmath_atan__doc__,
+"atan($module, z, /)\n"
+"--\n"
+"\n"
+"Return the arc tangent of z.");
+
+#define CMATH_ATAN_METHODDEF    \
+    {"atan", (PyCFunction)cmath_atan, METH_VARARGS, cmath_atan__doc__},
+
+static Py_complex
+cmath_atan_impl(PyModuleDef *module, Py_complex z);
+
+static PyObject *
+cmath_atan(PyModuleDef *module, PyObject *args)
+{
+    PyObject *return_value = NULL;
+    Py_complex z;
+    Py_complex _return_value;
+
+    if (!PyArg_ParseTuple(args,
+        "D:atan",
+        &z))
+        goto exit;
+    /* modifications for z */
+    errno = 0; PyFPE_START_PROTECT("complex function", goto exit);
+    _return_value = cmath_atan_impl(module, z);
+    PyFPE_END_PROTECT(_return_value);
+    if (errno == EDOM) {
+        PyErr_SetString(PyExc_ValueError, "math domain error");
+        goto exit;
+    }
+    else if (errno == ERANGE) {
+        PyErr_SetString(PyExc_OverflowError, "math range error");
+        goto exit;
+    }
+    else {
+        return_value = PyComplex_FromCComplex(_return_value);
+    }
+
+exit:
+    return return_value;
+}
+
+PyDoc_STRVAR(cmath_atanh__doc__,
+"atanh($module, z, /)\n"
+"--\n"
+"\n"
+"Return the hyperbolic arc tangent of z.");
+
+#define CMATH_ATANH_METHODDEF    \
+    {"atanh", (PyCFunction)cmath_atanh, METH_VARARGS, cmath_atanh__doc__},
+
+static Py_complex
+cmath_atanh_impl(PyModuleDef *module, Py_complex z);
+
+static PyObject *
+cmath_atanh(PyModuleDef *module, PyObject *args)
+{
+    PyObject *return_value = NULL;
+    Py_complex z;
+    Py_complex _return_value;
+
+    if (!PyArg_ParseTuple(args,
+        "D:atanh",
+        &z))
+        goto exit;
+    /* modifications for z */
+    errno = 0; PyFPE_START_PROTECT("complex function", goto exit);
+    _return_value = cmath_atanh_impl(module, z);
+    PyFPE_END_PROTECT(_return_value);
+    if (errno == EDOM) {
+        PyErr_SetString(PyExc_ValueError, "math domain error");
+        goto exit;
+    }
+    else if (errno == ERANGE) {
+        PyErr_SetString(PyExc_OverflowError, "math range error");
+        goto exit;
+    }
+    else {
+        return_value = PyComplex_FromCComplex(_return_value);
+    }
+
+exit:
+    return return_value;
+}
+
+PyDoc_STRVAR(cmath_cos__doc__,
+"cos($module, z, /)\n"
+"--\n"
+"\n"
+"Return the cosine of z.");
+
+#define CMATH_COS_METHODDEF    \
+    {"cos", (PyCFunction)cmath_cos, METH_VARARGS, cmath_cos__doc__},
+
+static Py_complex
+cmath_cos_impl(PyModuleDef *module, Py_complex z);
+
+static PyObject *
+cmath_cos(PyModuleDef *module, PyObject *args)
+{
+    PyObject *return_value = NULL;
+    Py_complex z;
+    Py_complex _return_value;
+
+    if (!PyArg_ParseTuple(args,
+        "D:cos",
+        &z))
+        goto exit;
+    /* modifications for z */
+    errno = 0; PyFPE_START_PROTECT("complex function", goto exit);
+    _return_value = cmath_cos_impl(module, z);
+    PyFPE_END_PROTECT(_return_value);
+    if (errno == EDOM) {
+        PyErr_SetString(PyExc_ValueError, "math domain error");
+        goto exit;
+    }
+    else if (errno == ERANGE) {
+        PyErr_SetString(PyExc_OverflowError, "math range error");
+        goto exit;
+    }
+    else {
+        return_value = PyComplex_FromCComplex(_return_value);
+    }
+
+exit:
+    return return_value;
+}
+
+PyDoc_STRVAR(cmath_cosh__doc__,
+"cosh($module, z, /)\n"
+"--\n"
+"\n"
+"Return the hyperbolic cosine of z.");
+
+#define CMATH_COSH_METHODDEF    \
+    {"cosh", (PyCFunction)cmath_cosh, METH_VARARGS, cmath_cosh__doc__},
+
+static Py_complex
+cmath_cosh_impl(PyModuleDef *module, Py_complex z);
+
+static PyObject *
+cmath_cosh(PyModuleDef *module, PyObject *args)
+{
+    PyObject *return_value = NULL;
+    Py_complex z;
+    Py_complex _return_value;
+
+    if (!PyArg_ParseTuple(args,
+        "D:cosh",
+        &z))
+        goto exit;
+    /* modifications for z */
+    errno = 0; PyFPE_START_PROTECT("complex function", goto exit);
+    _return_value = cmath_cosh_impl(module, z);
+    PyFPE_END_PROTECT(_return_value);
+    if (errno == EDOM) {
+        PyErr_SetString(PyExc_ValueError, "math domain error");
+        goto exit;
+    }
+    else if (errno == ERANGE) {
+        PyErr_SetString(PyExc_OverflowError, "math range error");
+        goto exit;
+    }
+    else {
+        return_value = PyComplex_FromCComplex(_return_value);
+    }
+
+exit:
+    return return_value;
+}
+
+PyDoc_STRVAR(cmath_exp__doc__,
+"exp($module, z, /)\n"
+"--\n"
+"\n"
+"Return the exponential value e**z.");
+
+#define CMATH_EXP_METHODDEF    \
+    {"exp", (PyCFunction)cmath_exp, METH_VARARGS, cmath_exp__doc__},
+
+static Py_complex
+cmath_exp_impl(PyModuleDef *module, Py_complex z);
+
+static PyObject *
+cmath_exp(PyModuleDef *module, PyObject *args)
+{
+    PyObject *return_value = NULL;
+    Py_complex z;
+    Py_complex _return_value;
+
+    if (!PyArg_ParseTuple(args,
+        "D:exp",
+        &z))
+        goto exit;
+    /* modifications for z */
+    errno = 0; PyFPE_START_PROTECT("complex function", goto exit);
+    _return_value = cmath_exp_impl(module, z);
+    PyFPE_END_PROTECT(_return_value);
+    if (errno == EDOM) {
+        PyErr_SetString(PyExc_ValueError, "math domain error");
+        goto exit;
+    }
+    else if (errno == ERANGE) {
+        PyErr_SetString(PyExc_OverflowError, "math range error");
+        goto exit;
+    }
+    else {
+        return_value = PyComplex_FromCComplex(_return_value);
+    }
+
+exit:
+    return return_value;
+}
+
+PyDoc_STRVAR(cmath_log10__doc__,
+"log10($module, z, /)\n"
+"--\n"
+"\n"
+"Return the base-10 logarithm of z.");
+
+#define CMATH_LOG10_METHODDEF    \
+    {"log10", (PyCFunction)cmath_log10, METH_VARARGS, cmath_log10__doc__},
+
+static Py_complex
+cmath_log10_impl(PyModuleDef *module, Py_complex z);
+
+static PyObject *
+cmath_log10(PyModuleDef *module, PyObject *args)
+{
+    PyObject *return_value = NULL;
+    Py_complex z;
+    Py_complex _return_value;
+
+    if (!PyArg_ParseTuple(args,
+        "D:log10",
+        &z))
+        goto exit;
+    /* modifications for z */
+    errno = 0; PyFPE_START_PROTECT("complex function", goto exit);
+    _return_value = cmath_log10_impl(module, z);
+    PyFPE_END_PROTECT(_return_value);
+    if (errno == EDOM) {
+        PyErr_SetString(PyExc_ValueError, "math domain error");
+        goto exit;
+    }
+    else if (errno == ERANGE) {
+        PyErr_SetString(PyExc_OverflowError, "math range error");
+        goto exit;
+    }
+    else {
+        return_value = PyComplex_FromCComplex(_return_value);
+    }
+
+exit:
+    return return_value;
+}
+
+PyDoc_STRVAR(cmath_sin__doc__,
+"sin($module, z, /)\n"
+"--\n"
+"\n"
+"Return the sine of z.");
+
+#define CMATH_SIN_METHODDEF    \
+    {"sin", (PyCFunction)cmath_sin, METH_VARARGS, cmath_sin__doc__},
+
+static Py_complex
+cmath_sin_impl(PyModuleDef *module, Py_complex z);
+
+static PyObject *
+cmath_sin(PyModuleDef *module, PyObject *args)
+{
+    PyObject *return_value = NULL;
+    Py_complex z;
+    Py_complex _return_value;
+
+    if (!PyArg_ParseTuple(args,
+        "D:sin",
+        &z))
+        goto exit;
+    /* modifications for z */
+    errno = 0; PyFPE_START_PROTECT("complex function", goto exit);
+    _return_value = cmath_sin_impl(module, z);
+    PyFPE_END_PROTECT(_return_value);
+    if (errno == EDOM) {
+        PyErr_SetString(PyExc_ValueError, "math domain error");
+        goto exit;
+    }
+    else if (errno == ERANGE) {
+        PyErr_SetString(PyExc_OverflowError, "math range error");
+        goto exit;
+    }
+    else {
+        return_value = PyComplex_FromCComplex(_return_value);
+    }
+
+exit:
+    return return_value;
+}
+
+PyDoc_STRVAR(cmath_sinh__doc__,
+"sinh($module, z, /)\n"
+"--\n"
+"\n"
+"Return the hyperbolic sine of z.");
+
+#define CMATH_SINH_METHODDEF    \
+    {"sinh", (PyCFunction)cmath_sinh, METH_VARARGS, cmath_sinh__doc__},
+
+static Py_complex
+cmath_sinh_impl(PyModuleDef *module, Py_complex z);
+
+static PyObject *
+cmath_sinh(PyModuleDef *module, PyObject *args)
+{
+    PyObject *return_value = NULL;
+    Py_complex z;
+    Py_complex _return_value;
+
+    if (!PyArg_ParseTuple(args,
+        "D:sinh",
+        &z))
+        goto exit;
+    /* modifications for z */
+    errno = 0; PyFPE_START_PROTECT("complex function", goto exit);
+    _return_value = cmath_sinh_impl(module, z);
+    PyFPE_END_PROTECT(_return_value);
+    if (errno == EDOM) {
+        PyErr_SetString(PyExc_ValueError, "math domain error");
+        goto exit;
+    }
+    else if (errno == ERANGE) {
+        PyErr_SetString(PyExc_OverflowError, "math range error");
+        goto exit;
+    }
+    else {
+        return_value = PyComplex_FromCComplex(_return_value);
+    }
+
+exit:
+    return return_value;
+}
+
+PyDoc_STRVAR(cmath_sqrt__doc__,
+"sqrt($module, z, /)\n"
+"--\n"
+"\n"
+"Return the square root of z.");
+
+#define CMATH_SQRT_METHODDEF    \
+    {"sqrt", (PyCFunction)cmath_sqrt, METH_VARARGS, cmath_sqrt__doc__},
+
+static Py_complex
+cmath_sqrt_impl(PyModuleDef *module, Py_complex z);
+
+static PyObject *
+cmath_sqrt(PyModuleDef *module, PyObject *args)
+{
+    PyObject *return_value = NULL;
+    Py_complex z;
+    Py_complex _return_value;
+
+    if (!PyArg_ParseTuple(args,
+        "D:sqrt",
+        &z))
+        goto exit;
+    /* modifications for z */
+    errno = 0; PyFPE_START_PROTECT("complex function", goto exit);
+    _return_value = cmath_sqrt_impl(module, z);
+    PyFPE_END_PROTECT(_return_value);
+    if (errno == EDOM) {
+        PyErr_SetString(PyExc_ValueError, "math domain error");
+        goto exit;
+    }
+    else if (errno == ERANGE) {
+        PyErr_SetString(PyExc_OverflowError, "math range error");
+        goto exit;
+    }
+    else {
+        return_value = PyComplex_FromCComplex(_return_value);
+    }
+
+exit:
+    return return_value;
+}
+
+PyDoc_STRVAR(cmath_tan__doc__,
+"tan($module, z, /)\n"
+"--\n"
+"\n"
+"Return the tangent of z.");
+
+#define CMATH_TAN_METHODDEF    \
+    {"tan", (PyCFunction)cmath_tan, METH_VARARGS, cmath_tan__doc__},
+
+static Py_complex
+cmath_tan_impl(PyModuleDef *module, Py_complex z);
+
+static PyObject *
+cmath_tan(PyModuleDef *module, PyObject *args)
+{
+    PyObject *return_value = NULL;
+    Py_complex z;
+    Py_complex _return_value;
+
+    if (!PyArg_ParseTuple(args,
+        "D:tan",
+        &z))
+        goto exit;
+    /* modifications for z */
+    errno = 0; PyFPE_START_PROTECT("complex function", goto exit);
+    _return_value = cmath_tan_impl(module, z);
+    PyFPE_END_PROTECT(_return_value);
+    if (errno == EDOM) {
+        PyErr_SetString(PyExc_ValueError, "math domain error");
+        goto exit;
+    }
+    else if (errno == ERANGE) {
+        PyErr_SetString(PyExc_OverflowError, "math range error");
+        goto exit;
+    }
+    else {
+        return_value = PyComplex_FromCComplex(_return_value);
+    }
+
+exit:
+    return return_value;
+}
+
+PyDoc_STRVAR(cmath_tanh__doc__,
+"tanh($module, z, /)\n"
+"--\n"
+"\n"
+"Return the hyperbolic tangent of z.");
+
+#define CMATH_TANH_METHODDEF    \
+    {"tanh", (PyCFunction)cmath_tanh, METH_VARARGS, cmath_tanh__doc__},
+
+static Py_complex
+cmath_tanh_impl(PyModuleDef *module, Py_complex z);
+
+static PyObject *
+cmath_tanh(PyModuleDef *module, PyObject *args)
+{
+    PyObject *return_value = NULL;
+    Py_complex z;
+    Py_complex _return_value;
+
+    if (!PyArg_ParseTuple(args,
+        "D:tanh",
+        &z))
+        goto exit;
+    /* modifications for z */
+    errno = 0; PyFPE_START_PROTECT("complex function", goto exit);
+    _return_value = cmath_tanh_impl(module, z);
+    PyFPE_END_PROTECT(_return_value);
+    if (errno == EDOM) {
+        PyErr_SetString(PyExc_ValueError, "math domain error");
+        goto exit;
+    }
+    else if (errno == ERANGE) {
+        PyErr_SetString(PyExc_OverflowError, "math range error");
+        goto exit;
+    }
+    else {
+        return_value = PyComplex_FromCComplex(_return_value);
+    }
+
+exit:
+    return return_value;
+}
+
+PyDoc_STRVAR(cmath_log__doc__,
+"log($module, x, y_obj=None, /)\n"
+"--\n"
+"\n"
+"The logarithm of z to the given base.\n"
+"\n"
+"If the base not specified, returns the natural logarithm (base e) of z.");
+
+#define CMATH_LOG_METHODDEF    \
+    {"log", (PyCFunction)cmath_log, METH_VARARGS, cmath_log__doc__},
+
+static PyObject *
+cmath_log_impl(PyModuleDef *module, Py_complex x, PyObject *y_obj);
+
+static PyObject *
+cmath_log(PyModuleDef *module, PyObject *args)
+{
+    PyObject *return_value = NULL;
+    Py_complex x;
+    PyObject *y_obj = NULL;
+
+    if (!PyArg_ParseTuple(args,
+        "D|O:log",
+        &x, &y_obj))
+        goto exit;
+    return_value = cmath_log_impl(module, x, y_obj);
+
+exit:
+    return return_value;
+}
+
+PyDoc_STRVAR(cmath_phase__doc__,
+"phase($module, z, /)\n"
+"--\n"
+"\n"
+"Return argument, also known as the phase angle, of a complex.");
+
+#define CMATH_PHASE_METHODDEF    \
+    {"phase", (PyCFunction)cmath_phase, METH_VARARGS, cmath_phase__doc__},
+
+static PyObject *
+cmath_phase_impl(PyModuleDef *module, Py_complex z);
+
+static PyObject *
+cmath_phase(PyModuleDef *module, PyObject *args)
+{
+    PyObject *return_value = NULL;
+    Py_complex z;
+
+    if (!PyArg_ParseTuple(args,
+        "D:phase",
+        &z))
+        goto exit;
+    return_value = cmath_phase_impl(module, z);
+
+exit:
+    return return_value;
+}
+
+PyDoc_STRVAR(cmath_polar__doc__,
+"polar($module, z, /)\n"
+"--\n"
+"\n"
+"Convert a complex from rectangular coordinates to polar coordinates.\n"
+"\n"
+"r is the distance from 0 and phi the phase angle.");
+
+#define CMATH_POLAR_METHODDEF    \
+    {"polar", (PyCFunction)cmath_polar, METH_VARARGS, cmath_polar__doc__},
+
+static PyObject *
+cmath_polar_impl(PyModuleDef *module, Py_complex z);
+
+static PyObject *
+cmath_polar(PyModuleDef *module, PyObject *args)
+{
+    PyObject *return_value = NULL;
+    Py_complex z;
+
+    if (!PyArg_ParseTuple(args,
+        "D:polar",
+        &z))
+        goto exit;
+    return_value = cmath_polar_impl(module, z);
+
+exit:
+    return return_value;
+}
+
+PyDoc_STRVAR(cmath_rect__doc__,
+"rect($module, r, phi, /)\n"
+"--\n"
+"\n"
+"Convert from polar coordinates to rectangular coordinates.");
+
+#define CMATH_RECT_METHODDEF    \
+    {"rect", (PyCFunction)cmath_rect, METH_VARARGS, cmath_rect__doc__},
+
+static PyObject *
+cmath_rect_impl(PyModuleDef *module, double r, double phi);
+
+static PyObject *
+cmath_rect(PyModuleDef *module, PyObject *args)
+{
+    PyObject *return_value = NULL;
+    double r;
+    double phi;
+
+    if (!PyArg_ParseTuple(args,
+        "dd:rect",
+        &r, &phi))
+        goto exit;
+    return_value = cmath_rect_impl(module, r, phi);
+
+exit:
+    return return_value;
+}
+
+PyDoc_STRVAR(cmath_isfinite__doc__,
+"isfinite($module, z, /)\n"
+"--\n"
+"\n"
+"Return True if both the real and imaginary parts of z are finite, else False.");
+
+#define CMATH_ISFINITE_METHODDEF    \
+    {"isfinite", (PyCFunction)cmath_isfinite, METH_VARARGS, cmath_isfinite__doc__},
+
+static PyObject *
+cmath_isfinite_impl(PyModuleDef *module, Py_complex z);
+
+static PyObject *
+cmath_isfinite(PyModuleDef *module, PyObject *args)
+{
+    PyObject *return_value = NULL;
+    Py_complex z;
+
+    if (!PyArg_ParseTuple(args,
+        "D:isfinite",
+        &z))
+        goto exit;
+    return_value = cmath_isfinite_impl(module, z);
+
+exit:
+    return return_value;
+}
+
+PyDoc_STRVAR(cmath_isnan__doc__,
+"isnan($module, z, /)\n"
+"--\n"
+"\n"
+"Checks if the real or imaginary part of z not a number (NaN).");
+
+#define CMATH_ISNAN_METHODDEF    \
+    {"isnan", (PyCFunction)cmath_isnan, METH_VARARGS, cmath_isnan__doc__},
+
+static PyObject *
+cmath_isnan_impl(PyModuleDef *module, Py_complex z);
+
+static PyObject *
+cmath_isnan(PyModuleDef *module, PyObject *args)
+{
+    PyObject *return_value = NULL;
+    Py_complex z;
+
+    if (!PyArg_ParseTuple(args,
+        "D:isnan",
+        &z))
+        goto exit;
+    return_value = cmath_isnan_impl(module, z);
+
+exit:
+    return return_value;
+}
+
+PyDoc_STRVAR(cmath_isinf__doc__,
+"isinf($module, z, /)\n"
+"--\n"
+"\n"
+"Checks if the real or imaginary part of z is infinite.");
+
+#define CMATH_ISINF_METHODDEF    \
+    {"isinf", (PyCFunction)cmath_isinf, METH_VARARGS, cmath_isinf__doc__},
+
+static PyObject *
+cmath_isinf_impl(PyModuleDef *module, Py_complex z);
+
+static PyObject *
+cmath_isinf(PyModuleDef *module, PyObject *args)
+{
+    PyObject *return_value = NULL;
+    Py_complex z;
+
+    if (!PyArg_ParseTuple(args,
+        "D:isinf",
+        &z))
+        goto exit;
+    return_value = cmath_isinf_impl(module, z);
+
+exit:
+    return return_value;
+}
+/*[clinic end generated code: output=4407f898ae07c83d input=a9049054013a1b77]*/

Modules/cmathmodule.c

@@ -8,6 +8,41 @@
    float.h.  We assume that FLT_RADIX is either 2 or 16. */
 #include <float.h>
 
+#include "clinic/cmathmodule.c.h"
+/*[clinic input]
+output preset file
+module cmath
+[clinic start generated code]*/
+/*[clinic end generated code: output=da39a3ee5e6b4b0d input=ef7e0fdd8a143c03]*/
+
+/*[python input]
+class Py_complex_protected_converter(Py_complex_converter):
+    def modify(self):
+        return 'errno = 0; PyFPE_START_PROTECT("complex function", goto exit);'
+
+
+class Py_complex_protected_return_converter(CReturnConverter):
+    type = "Py_complex"
+
+    def render(self, function, data):
+        self.declare(data)
+        data.return_conversion.append("""
+PyFPE_END_PROTECT(_return_value);
+if (errno == EDOM) {{
+    PyErr_SetString(PyExc_ValueError, "math domain error");
+    goto exit;
+}}
+else if (errno == ERANGE) {{
+    PyErr_SetString(PyExc_OverflowError, "math range error");
+    goto exit;
+}}
+else {{
+    return_value = PyComplex_FromCComplex(_return_value);
+}}
+""".strip())
+[python start generated code]*/
+/*[python end generated code: output=da39a3ee5e6b4b0d input=231019039a6fbb9a]*/
+
 #if (FLT_RADIX != 2 && FLT_RADIX != 16)
 #error "Modules/cmathmodule.c expects FLT_RADIX to be 2 or 16"
 #endif
@@ -48,12 +83,12 @@
 #define CM_SCALE_DOWN (-(CM_SCALE_UP+1)/2)
 
 /* forward declarations */
-static Py_complex c_asinh(Py_complex);
-static Py_complex c_atanh(Py_complex);
-static Py_complex c_cosh(Py_complex);
-static Py_complex c_sinh(Py_complex);
-static Py_complex c_sqrt(Py_complex);
-static Py_complex c_tanh(Py_complex);
+static Py_complex cmath_asinh_impl(PyModuleDef *, Py_complex);
+static Py_complex cmath_atanh_impl(PyModuleDef *, Py_complex);
+static Py_complex cmath_cosh_impl(PyModuleDef *, Py_complex);
+static Py_complex cmath_sinh_impl(PyModuleDef *, Py_complex);
+static Py_complex cmath_sqrt_impl(PyModuleDef *, Py_complex);
+static Py_complex cmath_tanh_impl(PyModuleDef *, Py_complex);
 static PyObject * math_error(void);
 
 /* Code to deal with special values (infinities, NaNs, etc.). */
@@ -123,8 +158,18 @@ special_type(double d)
 
 static Py_complex acos_special_values[7][7];
 
+/*[clinic input]
+cmath.acos -> Py_complex_protected
+
+    z: Py_complex_protected
+    /
+
+Return the arc cosine of z.
+[clinic start generated code]*/
+
 static Py_complex
-c_acos(Py_complex z)
+cmath_acos_impl(PyModuleDef *module, Py_complex z)
+/*[clinic end generated code: output=7c1dd21ff818db6b input=bd6cbd78ae851927]*/
 {
     Py_complex s1, s2, r;
 
@@ -145,10 +190,10 @@ c_acos(Py_complex z)
     } else {
         s1.real = 1.-z.real;
         s1.imag = -z.imag;
-        s1 = c_sqrt(s1);
+        s1 = cmath_sqrt_impl(module, s1);
         s2.real = 1.+z.real;
         s2.imag = z.imag;
-        s2 = c_sqrt(s2);
+        s2 = cmath_sqrt_impl(module, s2);
         r.real = 2.*atan2(s1.real, s2.real);
         r.imag = m_asinh(s2.real*s1.imag - s2.imag*s1.real);
     }
@@ -156,16 +201,18 @@ c_acos(Py_complex z)
     return r;
 }
 
-PyDoc_STRVAR(c_acos_doc,
-"acos(x)\n"
-"\n"
-"Return the arc cosine of x.");
-
 
 static Py_complex acosh_special_values[7][7];
 
+/*[clinic input]
+cmath.acosh = cmath.acos
+
+Return the hyperbolic arccosine of z.
+[clinic start generated code]*/
+
 static Py_complex
-c_acosh(Py_complex z)
+cmath_acosh_impl(PyModuleDef *module, Py_complex z)
+/*[clinic end generated code: output=c23c776429def981 input=bc016412080bb3e9]*/
 {
     Py_complex s1, s2, r;
 
@@ -178,10 +225,10 @@ c_acosh(Py_complex z)
     } else {
         s1.real = z.real - 1.;
         s1.imag = z.imag;
-        s1 = c_sqrt(s1);
+        s1 = cmath_sqrt_impl(module, s1);
         s2.real = z.real + 1.;
         s2.imag = z.imag;
-        s2 = c_sqrt(s2);
+        s2 = cmath_sqrt_impl(module, s2);
         r.real = m_asinh(s1.real*s2.real + s1.imag*s2.imag);
         r.imag = 2.*atan2(s1.imag, s2.real);
     }
@@ -189,35 +236,38 @@ c_acosh(Py_complex z)
     return r;
 }
 
-PyDoc_STRVAR(c_acosh_doc,
-"acosh(x)\n"
-"\n"
-"Return the hyperbolic arccosine of x.");
+/*[clinic input]
+cmath.asin = cmath.acos
 
+Return the arc sine of z.
+[clinic start generated code]*/
 
 static Py_complex
-c_asin(Py_complex z)
+cmath_asin_impl(PyModuleDef *module, Py_complex z)
+/*[clinic end generated code: output=42d2346d46690826 input=be0bf0cfdd5239c5]*/
 {
     /* asin(z) = -i asinh(iz) */
     Py_complex s, r;
     s.real = -z.imag;
     s.imag = z.real;
-    s = c_asinh(s);
+    s = cmath_asinh_impl(module, s);
     r.real = s.imag;
     r.imag = -s.real;
     return r;
 }
 
-PyDoc_STRVAR(c_asin_doc,
-"asin(x)\n"
-"\n"
-"Return the arc sine of x.");
-
 
 static Py_complex asinh_special_values[7][7];
 
+/*[clinic input]
+cmath.asinh = cmath.acos
+
+Return the hyperbolic arc sine of z.
+[clinic start generated code]*/
+
 static Py_complex
-c_asinh(Py_complex z)
+cmath_asinh_impl(PyModuleDef *module, Py_complex z)
+/*[clinic end generated code: output=0c6664823c7b1b35 input=5a21fa0242928c9b]*/
 {
     Py_complex s1, s2, r;
 
@@ -235,10 +285,10 @@ c_asinh(Py_complex z)
     } else {
         s1.real = 1.+z.imag;
         s1.imag = -z.real;
-        s1 = c_sqrt(s1);
+        s1 = cmath_sqrt_impl(module, s1);
         s2.real = 1.-z.imag;
         s2.imag = z.real;
-        s2 = c_sqrt(s2);
+        s2 = cmath_sqrt_impl(module, s2);
         r.real = m_asinh(s1.real*s2.imag-s2.real*s1.imag);
         r.imag = atan2(z.imag, s1.real*s2.real-s1.imag*s2.imag);
     }
@@ -246,20 +296,22 @@ c_asinh(Py_complex z)
     return r;
 }
 
-PyDoc_STRVAR(c_asinh_doc,
-"asinh(x)\n"
-"\n"
-"Return the hyperbolic arc sine of x.");
 
+/*[clinic input]
+cmath.atan = cmath.acos
+
+Return the arc tangent of z.
+[clinic start generated code]*/
 
 static Py_complex
-c_atan(Py_complex z)
+cmath_atan_impl(PyModuleDef *module, Py_complex z)
+/*[clinic end generated code: output=b7d44f02c6a5c3b5 input=3b21ff7d5eac632a]*/
 {
     /* atan(z) = -i atanh(iz) */
     Py_complex s, r;
     s.real = -z.imag;
     s.imag = z.real;
-    s = c_atanh(s);
+    s = cmath_atanh_impl(module, s);
     r.real = s.imag;
     r.imag = -s.real;
     return r;
@@ -295,16 +347,18 @@ c_atan2(Py_complex z)
     return atan2(z.imag, z.real);
 }
 
-PyDoc_STRVAR(c_atan_doc,
-"atan(x)\n"
-"\n"
-"Return the arc tangent of x.");
-
 
 static Py_complex atanh_special_values[7][7];
 
+/*[clinic input]
+cmath.atanh = cmath.acos
+
+Return the hyperbolic arc tangent of z.
+[clinic start generated code]*/
+
 static Py_complex
-c_atanh(Py_complex z)
+cmath_atanh_impl(PyModuleDef *module, Py_complex z)
+/*[clinic end generated code: output=279e0b9fefc8da7c input=df19cdc9f9d431c9]*/
 {
     Py_complex r;
     double ay, h;
@@ -313,7 +367,7 @@ c_atanh(Py_complex z)
 
     /* Reduce to case where z.real >= 0., using atanh(z) = -atanh(-z). */
     if (z.real < 0.) {
-        return _Py_c_neg(c_atanh(_Py_c_neg(z)));
+        return _Py_c_neg(cmath_atanh_impl(module, _Py_c_neg(z)));
     }
 
     ay = fabs(z.imag);
@@ -350,34 +404,38 @@ c_atanh(Py_complex z)
     return r;
 }
 
-PyDoc_STRVAR(c_atanh_doc,
-"atanh(x)\n"
-"\n"
-"Return the hyperbolic arc tangent of x.");
 
+/*[clinic input]
+cmath.cos = cmath.acos
+
+Return the cosine of z.
+[clinic start generated code]*/
 
 static Py_complex
-c_cos(Py_complex z)
+cmath_cos_impl(PyModuleDef *module, Py_complex z)
+/*[clinic end generated code: output=9d1cdc1b5e761667 input=6022e39b77127ac7]*/
 {
     /* cos(z) = cosh(iz) */
     Py_complex r;
     r.real = -z.imag;
     r.imag = z.real;
-    r = c_cosh(r);
+    r = cmath_cosh_impl(module, r);
     return r;
 }
 
-PyDoc_STRVAR(c_cos_doc,
-"cos(x)\n"
-"\n"
-"Return the cosine of x.");
-
 
 /* cosh(infinity + i*y) needs to be dealt with specially */
 static Py_complex cosh_special_values[7][7];
 
+/*[clinic input]
+cmath.cosh = cmath.acos
+
+Return the hyperbolic cosine of z.
+[clinic start generated code]*/
+
 static Py_complex
-c_cosh(Py_complex z)
+cmath_cosh_impl(PyModuleDef *module, Py_complex z)
+/*[clinic end generated code: output=f3b5d3282b3024d3 input=d6b66339e9cc332b]*/
 {
     Py_complex r;
     double x_minus_one;
@@ -426,18 +484,20 @@ c_cosh(Py_complex z)
     return r;
 }
 
-PyDoc_STRVAR(c_cosh_doc,
-"cosh(x)\n"
-"\n"
-"Return the hyperbolic cosine of x.");
-
 
 /* exp(infinity + i*y) and exp(-infinity + i*y) need special treatment for
    finite y */
 static Py_complex exp_special_values[7][7];
 
+/*[clinic input]
+cmath.exp = cmath.acos
+
+Return the exponential value e**z.
+[clinic start generated code]*/
+
 static Py_complex
-c_exp(Py_complex z)
+cmath_exp_impl(PyModuleDef *module, Py_complex z)
+/*[clinic end generated code: output=6f8825eb2bcad9ba input=8b9e6cf8a92174c3]*/
 {
     Py_complex r;
     double l;
@@ -486,12 +546,6 @@ c_exp(Py_complex z)
     return r;
 }
 
-PyDoc_STRVAR(c_exp_doc,
-"exp(x)\n"
-"\n"
-"Return the exponential value e**x.");
-
-
 static Py_complex log_special_values[7][7];
 
 static Py_complex
@@ -564,8 +618,15 @@ c_log(Py_complex z)
 }
 
 
+/*[clinic input]
+cmath.log10 = cmath.acos
+
+Return the base-10 logarithm of z.
+[clinic start generated code]*/
+
 static Py_complex
-c_log10(Py_complex z)
+cmath_log10_impl(PyModuleDef *module, Py_complex z)
+/*[clinic end generated code: output=c7c426ca0e782341 input=cff5644f73c1519c]*/
 {
     Py_complex r;
     int errno_save;
@@ -578,36 +639,40 @@ c_log10(Py_complex z)
     return r;
 }
 
-PyDoc_STRVAR(c_log10_doc,
-"log10(x)\n"
-"\n"
-"Return the base-10 logarithm of x.");
 
+/*[clinic input]
+cmath.sin = cmath.acos
+
+Return the sine of z.
+[clinic start generated code]*/
 
 static Py_complex
-c_sin(Py_complex z)
+cmath_sin_impl(PyModuleDef *module, Py_complex z)
+/*[clinic end generated code: output=e7f5e2b253825ac7 input=2d3519842a8b4b85]*/
 {
     /* sin(z) = -i sin(iz) */
     Py_complex s, r;
     s.real = -z.imag;
     s.imag = z.real;
-    s = c_sinh(s);
+    s = cmath_sinh_impl(module, s);
     r.real = s.imag;
     r.imag = -s.real;
     return r;
 }
 
-PyDoc_STRVAR(c_sin_doc,
-"sin(x)\n"
-"\n"
-"Return the sine of x.");
-
 
 /* sinh(infinity + i*y) needs to be dealt with specially */
 static Py_complex sinh_special_values[7][7];
 
+/*[clinic input]
+cmath.sinh = cmath.acos
+
+Return the hyperbolic sine of z.
+[clinic start generated code]*/
+
 static Py_complex
-c_sinh(Py_complex z)
+cmath_sinh_impl(PyModuleDef *module, Py_complex z)
+/*[clinic end generated code: output=d71fff8298043a95 input=d2d3fc8c1ddfd2dd]*/
 {
     Py_complex r;
     double x_minus_one;
@@ -655,16 +720,18 @@ c_sinh(Py_complex z)
     return r;
 }
 
-PyDoc_STRVAR(c_sinh_doc,
-"sinh(x)\n"
-"\n"
-"Return the hyperbolic sine of x.");
-
 
 static Py_complex sqrt_special_values[7][7];
 
+/*[clinic input]
+cmath.sqrt = cmath.acos
+
+Return the square root of z.
+[clinic start generated code]*/
+
 static Py_complex
-c_sqrt(Py_complex z)
+cmath_sqrt_impl(PyModuleDef *module, Py_complex z)
+/*[clinic end generated code: output=b6bda283d0c5a7b4 input=7088b166fc9a58c7]*/
 {
     /*
        Method: use symmetries to reduce to the case when x = z.real and y
@@ -730,36 +797,40 @@ c_sqrt(Py_complex z)
     return r;
 }
 
-PyDoc_STRVAR(c_sqrt_doc,
-"sqrt(x)\n"
-"\n"
-"Return the square root of x.");
 
+/*[clinic input]
+cmath.tan = cmath.acos
+
+Return the tangent of z.
+[clinic start generated code]*/
 
 static Py_complex
-c_tan(Py_complex z)
+cmath_tan_impl(PyModuleDef *module, Py_complex z)
+/*[clinic end generated code: output=df374bacf36d99b4 input=fc167e528767888e]*/
 {
     /* tan(z) = -i tanh(iz) */
     Py_complex s, r;
     s.real = -z.imag;
     s.imag = z.real;
-    s = c_tanh(s);
+    s = cmath_tanh_impl(module, s);
     r.real = s.imag;
     r.imag = -s.real;
     return r;
 }
 
-PyDoc_STRVAR(c_tan_doc,
-"tan(x)\n"
-"\n"
-"Return the tangent of x.");
-
 
 /* tanh(infinity + i*y) needs to be dealt with specially */
 static Py_complex tanh_special_values[7][7];
 
+/*[clinic input]
+cmath.tanh = cmath.acos
+
+Return the hyperbolic tangent of z.
+[clinic start generated code]*/
+
 static Py_complex
-c_tanh(Py_complex z)
+cmath_tanh_impl(PyModuleDef *module, Py_complex z)
+/*[clinic end generated code: output=f578773d27a18e96 input=22f67f9dc6d29685]*/
 {
     /* Formula:
 
@@ -822,25 +893,33 @@ c_tanh(Py_complex z)
     return r;
 }
 
-PyDoc_STRVAR(c_tanh_doc,
-"tanh(x)\n"
-"\n"
-"Return the hyperbolic tangent of x.");
 
+/*[clinic input]
+cmath.log
+
+    x: Py_complex
+    y_obj: object = NULL
+    /
+
+The logarithm of z to the given base.
+
+If the base not specified, returns the natural logarithm (base e) of z.
+[clinic start generated code]*/
 
 static PyObject *
-cmath_log(PyObject *self, PyObject *args)
+cmath_log_impl(PyModuleDef *module, Py_complex x, PyObject *y_obj)
+/*[clinic end generated code: output=35e2a1e5229b5a46 input=ee0e823a7c6e68ea]*/
 {
-    Py_complex x;
     Py_complex y;
 
-    if (!PyArg_ParseTuple(args, "D|D", &x, &y))
-        return NULL;
-
     errno = 0;
     PyFPE_START_PROTECT("complex function", return 0)
     x = c_log(x);
-    if (PyTuple_GET_SIZE(args) == 2) {
+    if (y_obj != NULL) {
+        y = PyComplex_AsCComplex(y_obj);
+        if (PyErr_Occurred()) {
+            return NULL;
+        }
         y = c_log(y);
         x = _Py_c_quot(x, y);
     }
@@ -850,10 +929,6 @@ cmath_log(PyObject *self, PyObject *args)
     return PyComplex_FromCComplex(x);
 }
 
-PyDoc_STRVAR(cmath_log_doc,
-"log(x[, base]) -> the logarithm of x to the given base.\n\
-If the base not specified, returns the natural logarithm (base e) of x.");
-
 
 /* And now the glue to make them available from Python: */
 
@@ -869,57 +944,22 @@ math_error(void)
     return NULL;
 }
 
-static PyObject *
-math_1(PyObject *args, Py_complex (*func)(Py_complex))
-{
-    Py_complex x,r ;
-    if (!PyArg_ParseTuple(args, "D", &x))
-        return NULL;
-    errno = 0;
-    PyFPE_START_PROTECT("complex function", return 0);
-    r = (*func)(x);
-    PyFPE_END_PROTECT(r);
-    if (errno == EDOM) {
-        PyErr_SetString(PyExc_ValueError, "math domain error");
-        return NULL;
-    }
-    else if (errno == ERANGE) {
-        PyErr_SetString(PyExc_OverflowError, "math range error");
-        return NULL;
-    }
-    else {
-        return PyComplex_FromCComplex(r);
-    }
-}
 
-#define FUNC1(stubname, func) \
-    static PyObject * stubname(PyObject *self, PyObject *args) { \
-        return math_1(args, func); \
-    }
+/*[clinic input]
+cmath.phase
 
-FUNC1(cmath_acos, c_acos)
-FUNC1(cmath_acosh, c_acosh)
-FUNC1(cmath_asin, c_asin)
-FUNC1(cmath_asinh, c_asinh)
-FUNC1(cmath_atan, c_atan)
-FUNC1(cmath_atanh, c_atanh)
-FUNC1(cmath_cos, c_cos)
-FUNC1(cmath_cosh, c_cosh)
-FUNC1(cmath_exp, c_exp)
-FUNC1(cmath_log10, c_log10)
-FUNC1(cmath_sin, c_sin)
-FUNC1(cmath_sinh, c_sinh)
-FUNC1(cmath_sqrt, c_sqrt)
-FUNC1(cmath_tan, c_tan)
-FUNC1(cmath_tanh, c_tanh)
+    z: Py_complex
+    /
+
+Return argument, also known as the phase angle, of a complex.
+[clinic start generated code]*/
 
 static PyObject *
-cmath_phase(PyObject *self, PyObject *args)
+cmath_phase_impl(PyModuleDef *module, Py_complex z)
+/*[clinic end generated code: output=e09eaf373cb624c3 input=5cf75228ba94b69d]*/
 {
-    Py_complex z;
     double phi;
-    if (!PyArg_ParseTuple(args, "D:phase", &z))
-        return NULL;
+
     errno = 0;
     PyFPE_START_PROTECT("arg function", return 0)
     phi = c_atan2(z);
@@ -930,17 +970,23 @@ cmath_phase(PyObject *self, PyObject *args)
         return PyFloat_FromDouble(phi);
 }
 
-PyDoc_STRVAR(cmath_phase_doc,
-"phase(z) -> float\n\n\
-Return argument, also known as the phase angle, of a complex.");
+/*[clinic input]
+cmath.polar
+
+    z: Py_complex
+    /
+
+Convert a complex from rectangular coordinates to polar coordinates.
+
+r is the distance from 0 and phi the phase angle.
+[clinic start generated code]*/
 
 static PyObject *
-cmath_polar(PyObject *self, PyObject *args)
+cmath_polar_impl(PyModuleDef *module, Py_complex z)
+/*[clinic end generated code: output=07d41b16c877875a input=26c353574fd1a861]*/
 {
-    Py_complex z;
     double r, phi;
-    if (!PyArg_ParseTuple(args, "D:polar", &z))
-        return NULL;
+
     PyFPE_START_PROTECT("polar function", return 0)
     phi = c_atan2(z); /* should not cause any exception */
     r = _Py_c_abs(z); /* sets errno to ERANGE on overflow;  otherwise 0 */
@@ -951,11 +997,6 @@ cmath_polar(PyObject *self, PyObject *args)
         return Py_BuildValue("dd", r, phi);
 }
 
-PyDoc_STRVAR(cmath_polar_doc,
-"polar(z) -> r: float, phi: float\n\n\
-Convert a complex from rectangular coordinates to polar coordinates. r is\n\
-the distance from 0 and phi the phase angle.");
-
 /*
   rect() isn't covered by the C99 standard, but it's not too hard to
   figure out 'spirit of C99' rules for special value handing:
@@ -969,13 +1010,21 @@ the distance from 0 and phi the phase angle.");
 
 static Py_complex rect_special_values[7][7];
 
+/*[clinic input]
+cmath.rect
+
+    r: double
+    phi: double
+    /
+
+Convert from polar coordinates to rectangular coordinates.
+[clinic start generated code]*/
+
 static PyObject *
-cmath_rect(PyObject *self, PyObject *args)
+cmath_rect_impl(PyModuleDef *module, double r, double phi)
+/*[clinic end generated code: output=d97a8749bd63e9d5 input=24c5646d147efd69]*/
 {
     Py_complex z;
-    double r, phi;
-    if (!PyArg_ParseTuple(args, "dd:rect", &r, &phi))
-        return NULL;
     errno = 0;
     PyFPE_START_PROTECT("rect function", return 0)
 
@@ -1026,78 +1075,74 @@ cmath_rect(PyObject *self, PyObject *args)
         return PyComplex_FromCComplex(z);
 }
 
-PyDoc_STRVAR(cmath_rect_doc,
-"rect(r, phi) -> z: complex\n\n\
-Convert from polar coordinates to rectangular coordinates.");
+/*[clinic input]
+cmath.isfinite = cmath.polar
+
+Return True if both the real and imaginary parts of z are finite, else False.
+[clinic start generated code]*/
 
 static PyObject *
-cmath_isfinite(PyObject *self, PyObject *args)
+cmath_isfinite_impl(PyModuleDef *module, Py_complex z)
+/*[clinic end generated code: output=8f6682fa93de45d6 input=848e7ee701895815]*/
 {
-    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.");
+/*[clinic input]
+cmath.isnan = cmath.polar
+
+Checks if the real or imaginary part of z not a number (NaN).
+[clinic start generated code]*/
 
 static PyObject *
-cmath_isnan(PyObject *self, PyObject *args)
+cmath_isnan_impl(PyModuleDef *module, Py_complex z)
+/*[clinic end generated code: output=b85fe8c2047718ee input=71799f5d284c9baf]*/
 {
-    Py_complex z;
-    if (!PyArg_ParseTuple(args, "D:isnan", &z))
-        return NULL;
     return PyBool_FromLong(Py_IS_NAN(z.real) || Py_IS_NAN(z.imag));
 }
 
-PyDoc_STRVAR(cmath_isnan_doc,
-"isnan(z) -> bool\n\
-Checks if the real or imaginary part of z not a number (NaN)");
+/*[clinic input]
+cmath.isinf = cmath.polar
+
+Checks if the real or imaginary part of z is infinite.
+[clinic start generated code]*/
 
 static PyObject *
-cmath_isinf(PyObject *self, PyObject *args)
+cmath_isinf_impl(PyModuleDef *module, Py_complex z)
+/*[clinic end generated code: output=8ca9c6109e468bf4 input=363df155c7181329]*/
 {
-    Py_complex z;
-    if (!PyArg_ParseTuple(args, "D:isinf", &z))
-        return NULL;
     return PyBool_FromLong(Py_IS_INFINITY(z.real) ||
                            Py_IS_INFINITY(z.imag));
 }
 
-PyDoc_STRVAR(cmath_isinf_doc,
-"isinf(z) -> bool\n\
-Checks if the real or imaginary part of z is infinite.");
-
 
 PyDoc_STRVAR(module_doc,
 "This module is always available. It provides access to mathematical\n"
 "functions for complex numbers.");
 
 static PyMethodDef cmath_methods[] = {
-    {"acos",   cmath_acos,  METH_VARARGS, c_acos_doc},
-    {"acosh",  cmath_acosh, METH_VARARGS, c_acosh_doc},
-    {"asin",   cmath_asin,  METH_VARARGS, c_asin_doc},
-    {"asinh",  cmath_asinh, METH_VARARGS, c_asinh_doc},
-    {"atan",   cmath_atan,  METH_VARARGS, c_atan_doc},
-    {"atanh",  cmath_atanh, METH_VARARGS, c_atanh_doc},
-    {"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},
-    {"log10",  cmath_log10, METH_VARARGS, c_log10_doc},
-    {"phase",  cmath_phase, METH_VARARGS, cmath_phase_doc},
-    {"polar",  cmath_polar, METH_VARARGS, cmath_polar_doc},
-    {"rect",   cmath_rect,  METH_VARARGS, cmath_rect_doc},
-    {"sin",    cmath_sin,   METH_VARARGS, c_sin_doc},
-    {"sinh",   cmath_sinh,  METH_VARARGS, c_sinh_doc},
-    {"sqrt",   cmath_sqrt,  METH_VARARGS, c_sqrt_doc},
-    {"tan",    cmath_tan,   METH_VARARGS, c_tan_doc},
-    {"tanh",   cmath_tanh,  METH_VARARGS, c_tanh_doc},
+    CMATH_ACOS_METHODDEF
+    CMATH_ACOSH_METHODDEF
+    CMATH_ASIN_METHODDEF
+    CMATH_ASINH_METHODDEF
+    CMATH_ATAN_METHODDEF
+    CMATH_ATANH_METHODDEF
+    CMATH_COS_METHODDEF
+    CMATH_COSH_METHODDEF
+    CMATH_EXP_METHODDEF
+    CMATH_ISFINITE_METHODDEF
+    CMATH_ISINF_METHODDEF
+    CMATH_ISNAN_METHODDEF
+    CMATH_LOG_METHODDEF
+    CMATH_LOG10_METHODDEF
+    CMATH_PHASE_METHODDEF
+    CMATH_POLAR_METHODDEF
+    CMATH_RECT_METHODDEF
+    CMATH_SIN_METHODDEF
+    CMATH_SINH_METHODDEF
+    CMATH_SQRT_METHODDEF
+    CMATH_TAN_METHODDEF
+    CMATH_TANH_METHODDEF
     {NULL, NULL}  /* sentinel */
 };