diff --git a/Lib/test/test_builtin.py b/Lib/test/test_builtin.py
index d8e604158c7..04c22167654 100644
--- a/Lib/test/test_builtin.py
+++ b/Lib/test/test_builtin.py
@@ -1,5 +1,6 @@
 # Python test set -- built-in functions
 
+import platform
 import test.test_support, unittest
 from test.test_support import fcmp, have_unicode, TESTFN, unlink, \
                               run_unittest, run_with_locale
@@ -1259,6 +1260,14 @@ class BuiltinTest(unittest.TestCase):
         self.assertRaises(TypeError, round, t)
         self.assertRaises(TypeError, round, t, 0)
 
+    def test_round_large(self):
+        # Issue #1869: integral floats should remain unchanged
+        self.assertEqual(round(5e15-1), 5e15-1)
+        self.assertEqual(round(5e15), 5e15)
+        self.assertEqual(round(5e15+1), 5e15+1)
+        self.assertEqual(round(5e15+2), 5e15+2)
+        self.assertEqual(round(5e15+3), 5e15+3)
+
     def test_setattr(self):
         setattr(sys, 'spam', 1)
         self.assertEqual(sys.spam, 1)
diff --git a/Misc/NEWS b/Misc/NEWS
index 6d421872649..ae1be757293 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -12,6 +12,8 @@ What's New in Python 2.6.5
 Core and Builtins
 -----------------
 
+- Issue #7070: Fix round bug for large odd integer arguments.
+
 - Issue #7078: Set struct.__doc__ from _struct.__doc__.
 
 - Issue #1722344: threading._shutdown() is now called in Py_Finalize(), which
diff --git a/Python/bltinmodule.c b/Python/bltinmodule.c
index 015e16bbb87..87da3c9fff1 100644
--- a/Python/bltinmodule.c
+++ b/Python/bltinmodule.c
@@ -2120,7 +2120,7 @@ For most object types, eval(repr(object)) == object.");
 static PyObject *
 builtin_round(PyObject *self, PyObject *args, PyObject *kwds)
 {
-	double number;
+	double number, abs_number, abs_result;
 	double f;
 	int ndigits = 0;
 	int i;
@@ -2137,10 +2137,14 @@ builtin_round(PyObject *self, PyObject *args, PyObject *kwds)
 		number /= f;
 	else
 		number *= f;
-	if (number >= 0.0)
-		number = floor(number + 0.5);
-	else
-		number = ceil(number - 0.5);
+
+	/* round `number` to nearest integer, rounding halves away from zero */
+	abs_number = fabs(number);
+	abs_result = floor(abs_number);
+	if (abs_number - abs_result >= 0.5)
+		abs_result += 1.0;
+	number = copysign(abs_result, number);
+
 	if (ndigits < 0)
 		number *= f;
 	else