Issue #9599:  Further accuracy tweaks to loghelper.  For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10.
diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index 90bd363..1499ff9 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -641,8 +641,12 @@
         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)
-        self.assertEquals(math.log(INF), INF)
+        self.ftest('log(10**1000)', math.log(10**1000),
+                   2302.5850929940457)
+        self.assertRaises(ValueError, math.log, -1.5)
+        self.assertRaises(ValueError, math.log, -10**1000)
         self.assertRaises(ValueError, math.log, NINF)
+        self.assertEquals(math.log(INF), INF)
         self.assertTrue(math.isnan(math.log(NAN)))
 
     def testLog1p(self):
@@ -655,8 +659,11 @@
         self.ftest('log10(0.1)', math.log10(0.1), -1)
         self.ftest('log10(1)', math.log10(1), 0)
         self.ftest('log10(10)', math.log10(10), 1)
-        self.assertEquals(math.log(INF), INF)
+        self.ftest('log10(10**1000)', math.log10(10**1000), 1000.0)
+        self.assertRaises(ValueError, math.log10, -1.5)
+        self.assertRaises(ValueError, math.log10, -10**1000)
         self.assertRaises(ValueError, math.log10, NINF)
+        self.assertEquals(math.log(INF), INF)
         self.assertTrue(math.isnan(math.log10(NAN)))
 
     def testModf(self):