gh-101123: Adapt vararg functions in the math module to Argument Clinic (#126235)

This implicitly fixes the math.hypot signature, which was previously
incomprehensible to inspect.signature().

Author: skirpichev

Modules/clinic/mathmodule.c.h

@@ -719,8 +719,17 @@ m_log10(double x)
 }
 
 
+/*[clinic input]
+math.gcd
+
+    *integers as args: object
+
+Greatest Common Divisor.
+[clinic start generated code]*/
+
 static PyObject *
-math_gcd(PyObject *module, PyObject * const *args, Py_ssize_t nargs)
+math_gcd_impl(PyObject *module, Py_ssize_t nargs, PyObject *const *args)
+/*[clinic end generated code: output=b57687fcf431c1b8 input=94e675b7ceeaf0c9]*/
 {
     // Fast-path for the common case: gcd(int, int)
     if (nargs == 2 && PyLong_CheckExact(args[0]) && PyLong_CheckExact(args[1]))
@@ -763,12 +772,6 @@ math_gcd(PyObject *module, PyObject * const *args, Py_ssize_t nargs)
     return res;
 }
 
-PyDoc_STRVAR(math_gcd_doc,
-"gcd($module, *integers)\n"
-"--\n"
-"\n"
-"Greatest Common Divisor.");
-
 
 static PyObject *
 long_lcm(PyObject *a, PyObject *b)
@@ -798,8 +801,17 @@ long_lcm(PyObject *a, PyObject *b)
 }
 
 
+/*[clinic input]
+math.lcm
+
+    *integers as args: object
+
+Least Common Multiple.
+[clinic start generated code]*/
+
 static PyObject *
-math_lcm(PyObject *module, PyObject * const *args, Py_ssize_t nargs)
+math_lcm_impl(PyObject *module, Py_ssize_t nargs, PyObject *const *args)
+/*[clinic end generated code: output=f3eff0c25e4d7030 input=e64c33e85f4c47c6]*/
 {
     PyObject *res, *x;
     Py_ssize_t i;
@@ -839,13 +851,6 @@ math_lcm(PyObject *module, PyObject * const *args, Py_ssize_t nargs)
 }
 
 
-PyDoc_STRVAR(math_lcm_doc,
-"lcm($module, *integers)\n"
-"--\n"
-"\n"
-"Least Common Multiple.");
-
-
 /* Call is_error when errno != 0, and where x is the result libm
  * returned.  is_error will usually set up an exception and return
  * true (1), but may return false (0) without setting up an exception.
@@ -2621,9 +2626,28 @@ math_dist_impl(PyObject *module, PyObject *p, PyObject *q)
     return NULL;
 }
 
-/* AC: cannot convert yet, waiting for *args support */
+/*[clinic input]
+math.hypot
+
+    *coordinates as args: object
+
+Multidimensional Euclidean distance from the origin to a point.
+
+Roughly equivalent to:
+    sqrt(sum(x**2 for x in coordinates))
+
+For a two dimensional point (x, y), gives the hypotenuse
+using the Pythagorean theorem:  sqrt(x*x + y*y).
+
+For example, the hypotenuse of a 3/4/5 right triangle is:
+
+    >>> hypot(3.0, 4.0)
+    5.0
+[clinic start generated code]*/
+
 static PyObject *
-math_hypot(PyObject *self, PyObject *const *args, Py_ssize_t nargs)
+math_hypot_impl(PyObject *module, Py_ssize_t nargs, PyObject *const *args)
+/*[clinic end generated code: output=dcb6d4b7a1102ee1 input=5c0061a2d11235ed]*/
 {
     Py_ssize_t i;
     PyObject *item;
@@ -2664,22 +2688,6 @@ math_hypot(PyObject *self, PyObject *const *args, Py_ssize_t nargs)
 
 #undef NUM_STACK_ELEMS
 
-PyDoc_STRVAR(math_hypot_doc,
-             "hypot(*coordinates) -> value\n\n\
-Multidimensional Euclidean distance from the origin to a point.\n\
-\n\
-Roughly equivalent to:\n\
-    sqrt(sum(x**2 for x in coordinates))\n\
-\n\
-For a two dimensional point (x, y), gives the hypotenuse\n\
-using the Pythagorean theorem:  sqrt(x*x + y*y).\n\
-\n\
-For example, the hypotenuse of a 3/4/5 right triangle is:\n\
-\n\
-    >>> hypot(3.0, 4.0)\n\
-    5.0\n\
-");
-
 /** sumprod() ***************************************************************/
 
 /* Forward declaration */
@@ -4112,14 +4120,14 @@ static PyMethodDef math_methods[] = {
     MATH_FREXP_METHODDEF
     MATH_FSUM_METHODDEF
     {"gamma",           math_gamma,     METH_O,         math_gamma_doc},
-    {"gcd",             _PyCFunction_CAST(math_gcd),       METH_FASTCALL,  math_gcd_doc},
-    {"hypot",           _PyCFunction_CAST(math_hypot),     METH_FASTCALL,  math_hypot_doc},
+    MATH_GCD_METHODDEF
+    MATH_HYPOT_METHODDEF
     MATH_ISCLOSE_METHODDEF
     MATH_ISFINITE_METHODDEF
     MATH_ISINF_METHODDEF
     MATH_ISNAN_METHODDEF
     MATH_ISQRT_METHODDEF
-    {"lcm",             _PyCFunction_CAST(math_lcm),       METH_FASTCALL,  math_lcm_doc},
+    MATH_LCM_METHODDEF
     MATH_LDEXP_METHODDEF
     {"lgamma",          math_lgamma,    METH_O,         math_lgamma_doc},
     {"log",             _PyCFunction_CAST(math_log),       METH_FASTCALL,  math_log_doc},