Index: Modules/mathmodule.c
===================================================================
--- Modules/mathmodule.c	(revision 85031)
+++ Modules/mathmodule.c	(working copy)
@@ -1572,12 +1572,12 @@
                             "math domain error");
             return NULL;
         }
-        /* Special case for log(1), to make sure we get an
-           exact result there. */
-        if (e == 1 && x == 0.5)
-            return PyFloat_FromDouble(0.0);
-        /* Value is ~= x * 2**e, so the log ~= log(x) + log(2) * e. */
-        x = func(x) + func(2.0) * e;
+        if (x != 0.5)
+          /* Value is ~= x * 2**e, so the log ~= log(x) + log(2) * e. */
+          x = func(x) + func(2.0) * e;
+        else
+          /* Special case for 0.5 * 2**e, to get better precision */
+          x = func(2.0) * (e - 1);
         return PyFloat_FromDouble(x);
     }