Revert "gh-89381: Fix invalid signatures of math/cmath.log (#101404)" (#101580)

This reverts commit 0ef92d979311ba82d4c41b22ef38e12e1b08b13d.

8 files changed, 47 insertions, 42 deletions

diff --git a/Doc/library/cmath.rst b/Doc/library/cmath.rst
index c575b90..28cd96b 100644
--- a/Doc/library/cmath.rst
+++ b/Doc/library/cmath.rst
@@ -89,7 +89,7 @@ Power and logarithmic functions
    logarithms.
 
 
-.. function:: log(x, base=None)
+.. function:: log(x[, base])
 
    Returns the logarithm of *x* to the given *base*. If the *base* is not
    specified, returns the natural logarithm of *x*. There is one branch cut, from 0
diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index 9da22b6..797f324 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -393,12 +393,13 @@ Power and logarithmic functions
    .. versionadded:: 3.2
 
 
-.. function:: log(x, base=None)
+.. function:: log(x[, base])
 
-   Return the logarithm of *x* to the given *base*.
+   With one argument, return the natural logarithm of *x* (to base *e*).
+
+   With two arguments, return the logarithm of *x* to the given *base*,
+   calculated as ``log(x)/log(base)``.
 
-   If the *base* is not specified, returns the natural
-   logarithm (base *e*) of *x*.
 
 .. function:: log1p(x)
 
diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index 8d84904..433161c 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -1146,7 +1146,6 @@ class MathTests(unittest.TestCase):
         self.ftest('log(1/e)', math.log(1/math.e), -1)
         self.ftest('log(1)', math.log(1), 0)
         self.ftest('log(e)', math.log(math.e), 1)
-        self.ftest('log(e, None)', math.log(math.e, None), 1)
         self.ftest('log(32,2)', math.log(32,2), 5)
         self.ftest('log(10**40, 10)', math.log(10**40, 10), 40)
         self.ftest('log(10**40, 10**20)', math.log(10**40, 10**20), 2)
diff --git a/Misc/NEWS.d/next/Library/2023-01-16-10-42-58.gh-issue-89381.lM2WL0.rst b/Misc/NEWS.d/next/Library/2023-01-16-10-42-58.gh-issue-89381.lM2WL0.rst
deleted file mode 100644
index 7bffe7d..0000000
--- a/Misc/NEWS.d/next/Library/2023-01-16-10-42-58.gh-issue-89381.lM2WL0.rst
+++ /dev/null
@@ -1 +0,0 @@
-:func:`~math.log` and :func:`~cmath.log` support default base=None values.
diff --git a/Modules/clinic/cmathmodule.c.h b/Modules/clinic/cmathmodule.c.h
index bc91c20..b1da945 100644
--- a/Modules/clinic/cmathmodule.c.h
+++ b/Modules/clinic/cmathmodule.c.h
@@ -639,13 +639,12 @@ exit:
 }
 
 PyDoc_STRVAR(cmath_log__doc__,
-"log($module, z, base=None, /)\n"
+"log($module, z, base=<unrepresentable>, /)\n"
 "--\n"
 "\n"
 "log(z[, base]) -> the logarithm of z to the given base.\n"
 "\n"
-"If the base is not specified or is None, returns the\n"
-"natural logarithm (base e) of z.");
+"If the base not specified, returns the natural logarithm (base e) of z.");
 
 #define CMATH_LOG_METHODDEF    \
     {"log", _PyCFunction_CAST(cmath_log), METH_FASTCALL, cmath_log__doc__},
@@ -658,7 +657,7 @@ cmath_log(PyObject *module, PyObject *const *args, Py_ssize_t nargs)
 {
     PyObject *return_value = NULL;
     Py_complex x;
-    PyObject *y_obj = Py_None;
+    PyObject *y_obj = NULL;
 
     if (!_PyArg_CheckPositional("log", nargs, 1, 2)) {
         goto exit;
@@ -983,4 +982,4 @@ skip_optional_kwonly:
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=2630f8740909a8f7 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=0146c656e67f5d5f input=a9049054013a1b77]*/
diff --git a/Modules/clinic/mathmodule.c.h b/Modules/clinic/mathmodule.c.h
index 0d61fd1..1f97258 100644
--- a/Modules/clinic/mathmodule.c.h
+++ b/Modules/clinic/mathmodule.c.h
@@ -187,37 +187,43 @@ exit:
 }
 
 PyDoc_STRVAR(math_log__doc__,
-"log($module, x, base=None, /)\n"
-"--\n"
-"\n"
+"log(x, [base=math.e])\n"
 "Return the logarithm of x to the given base.\n"
 "\n"
-"If the base is not specified or is None, returns the natural\n"
-"logarithm (base e) of x.");
+"If the base not specified, returns the natural logarithm (base e) of x.");
 
 #define MATH_LOG_METHODDEF    \
-    {"log", _PyCFunction_CAST(math_log), METH_FASTCALL, math_log__doc__},
+    {"log", (PyCFunction)math_log, METH_VARARGS, math_log__doc__},
 
 static PyObject *
-math_log_impl(PyObject *module, PyObject *x, PyObject *base);
+math_log_impl(PyObject *module, PyObject *x, int group_right_1,
+              PyObject *base);
 
 static PyObject *
-math_log(PyObject *module, PyObject *const *args, Py_ssize_t nargs)
+math_log(PyObject *module, PyObject *args)
 {
     PyObject *return_value = NULL;
     PyObject *x;
-    PyObject *base = Py_None;
+    int group_right_1 = 0;
+    PyObject *base = NULL;
 
-    if (!_PyArg_CheckPositional("log", nargs, 1, 2)) {
-        goto exit;
-    }
-    x = args[0];
-    if (nargs < 2) {
-        goto skip_optional;
+    switch (PyTuple_GET_SIZE(args)) {
+        case 1:
+            if (!PyArg_ParseTuple(args, "O:log", &x)) {
+                goto exit;
+            }
+            break;
+        case 2:
+            if (!PyArg_ParseTuple(args, "OO:log", &x, &base)) {
+                goto exit;
+            }
+            group_right_1 = 1;
+            break;
+        default:
+            PyErr_SetString(PyExc_TypeError, "math.log requires 1 to 2 arguments");
+            goto exit;
     }
-    base = args[1];
-skip_optional:
-    return_value = math_log_impl(module, x, base);
+    return_value = math_log_impl(module, x, group_right_1, base);
 
 exit:
     return return_value;
@@ -948,4 +954,4 @@ math_ulp(PyObject *module, PyObject *arg)
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=afec63ebb0da709a input=a9049054013a1b77]*/
+/*[clinic end generated code: output=899211ec70e4506c input=a9049054013a1b77]*/
diff --git a/Modules/cmathmodule.c b/Modules/cmathmodule.c
index 62caba0..2038ac2 100644
--- a/Modules/cmathmodule.c
+++ b/Modules/cmathmodule.c
@@ -952,24 +952,23 @@ cmath_tanh_impl(PyObject *module, Py_complex z)
 cmath.log
 
     z as x: Py_complex
-    base as y_obj: object = None
+    base as y_obj: object = NULL
     /
 
 log(z[, base]) -> the logarithm of z to the given base.
 
-If the base is not specified or is None, returns the
-natural logarithm (base e) of z.
+If the base not specified, returns the natural logarithm (base e) of z.
 [clinic start generated code]*/
 
 static PyObject *
 cmath_log_impl(PyObject *module, Py_complex x, PyObject *y_obj)
-/*[clinic end generated code: output=4effdb7d258e0d94 input=e7db51859ebf70bf]*/
+/*[clinic end generated code: output=4effdb7d258e0d94 input=230ed3a71ecd000a]*/
 {
     Py_complex y;
 
     errno = 0;
     x = c_log(x);
-    if (y_obj != Py_None) {
+    if (y_obj != NULL) {
         y = PyComplex_AsCComplex(y_obj);
         if (PyErr_Occurred()) {
             return NULL;
diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 654336d..992957e 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2366,24 +2366,26 @@ loghelper(PyObject* arg, double (*func)(double))
 math.log
 
     x:    object
-    base: object = None
+    [
+    base: object(c_default="NULL") = math.e
+    ]
     /
 
 Return the logarithm of x to the given base.
 
-If the base is not specified or is None, returns the natural
-logarithm (base e) of x.
+If the base not specified, returns the natural logarithm (base e) of x.
 [clinic start generated code]*/
 
 static PyObject *
-math_log_impl(PyObject *module, PyObject *x, PyObject *base)
-/*[clinic end generated code: output=1dead263cbb1e854 input=ef032cc9837943e1]*/
+math_log_impl(PyObject *module, PyObject *x, int group_right_1,
+              PyObject *base)
+/*[clinic end generated code: output=7b5a39e526b73fc9 input=0f62d5726cbfebbd]*/
 {
     PyObject *num, *den;
     PyObject *ans;
 
     num = loghelper(x, m_log);
-    if (num == NULL || base == Py_None)
+    if (num == NULL || base == NULL)
         return num;
 
     den = loghelper(base, m_log);