diff --git a/Lib/inspect.py b/Lib/inspect.py
index 8bb3a37573..3b3a2f5bd4 100644
--- a/Lib/inspect.py
+++ b/Lib/inspect.py
@@ -2213,6 +2213,8 @@ def parse_name(node):
         return node.arg
 
     def wrap_value(s):
+        if isinstance(s, (int, float, bytes, bool, type(None))):
+            return ast.Constant(s)
         try:
             value = eval(s, module_dict)
         except NameError:
@@ -2221,8 +2223,8 @@ def wrap_value(s):
             except NameError:
                 raise ValueError
 
-        if isinstance(value, (str, int, float, bytes, bool, type(None))):
-            return ast.Constant(value)
+        if isinstance(s, str):
+            return ast.Name(s)
         raise ValueError
 
     class RewriteSymbolics(ast.NodeTransformer):
@@ -2263,7 +2265,13 @@ def p(name_node, default_node, default=empty):
         if default_node and default_node is not _empty:
             try:
                 default_node = RewriteSymbolics().visit(default_node)
-                default = ast.literal_eval(default_node)
+                try:
+                    default = ast.literal_eval(default_node)
+                except ValueError:
+                    if isinstance(default_node, ast.Name):
+                        default = default_node
+                    else:
+                        raise
             except ValueError:
                 raise ValueError("{!r} builtin has invalid signature".format(obj)) from None
         parameters.append(Parameter(name, kind, default=default, annotation=empty))
@@ -2788,11 +2796,16 @@ def __str__(self):
             formatted = '{}: {}'.format(formatted,
                                        formatannotation(self._annotation))
 
+        if isinstance(self._default, ast.Name):
+            default = self._default.id
+        else:
+            default = repr(self._default)
+
         if self._default is not _empty:
             if self._annotation is not _empty:
-                formatted = '{} = {}'.format(formatted, repr(self._default))
+                formatted = '{} = {}'.format(formatted, default)
             else:
-                formatted = '{}={}'.format(formatted, repr(self._default))
+                formatted = '{}={}'.format(formatted, default)
 
         if kind == _VAR_POSITIONAL:
             formatted = '*' + formatted
diff --git a/Modules/clinic/cmathmodule.c.h b/Modules/clinic/cmathmodule.c.h
index b1da9452c6..dc0bae51a5 100644
--- a/Modules/clinic/cmathmodule.c.h
+++ b/Modules/clinic/cmathmodule.c.h
@@ -639,7 +639,7 @@ exit:
 }
 
 PyDoc_STRVAR(cmath_log__doc__,
-"log($module, z, base=<unrepresentable>, /)\n"
+"log($module, z, base=e, /)\n"
 "--\n"
 "\n"
 "log(z[, base]) -> the logarithm of z to the given base.\n"
@@ -982,4 +982,4 @@ skip_optional_kwonly:
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=0146c656e67f5d5f input=a9049054013a1b77]*/
+/*[clinic end generated code: output=4bef798226126327 input=a9049054013a1b77]*/
diff --git a/Modules/cmathmodule.c b/Modules/cmathmodule.c
index 2038ac26e6..861a824d77 100644
--- a/Modules/cmathmodule.c
+++ b/Modules/cmathmodule.c
@@ -952,7 +952,7 @@ cmath_tanh_impl(PyObject *module, Py_complex z)
 cmath.log
 
     z as x: Py_complex
-    base as y_obj: object = NULL
+    base as y_obj: object(c_default="NULL") = e
     /
 
 log(z[, base]) -> the logarithm of z to the given base.
@@ -962,7 +962,7 @@ If the base not specified, returns the natural logarithm (base e) of z.
 
 static PyObject *
 cmath_log_impl(PyObject *module, Py_complex x, PyObject *y_obj)
-/*[clinic end generated code: output=4effdb7d258e0d94 input=230ed3a71ecd000a]*/
+/*[clinic end generated code: output=4effdb7d258e0d94 input=beb2861c8206a73c]*/
 {
     Py_complex y;