diff --git a/Lib/test/test_float.py b/Lib/test/test_float.py
index e1e1f04..9893f41 100644
--- a/Lib/test/test_float.py
+++ b/Lib/test/test_float.py
@@ -220,6 +220,16 @@ class GeneralFloatCases(unittest.TestCase):
         self.assertEqualAndEqualSign(mod(1.0, -1.0), -0.0)
 
     @support.requires_IEEE_754
+    def test_float_floordiv(self):
+        # Check // operator and divmod[0] for IEEE 754 special cases.
+
+        for fd_op in operator.floordiv, lambda a, b: divmod(a, b)[0]:
+            self.assertEqualAndEqualSign(fd_op(1.0, INF), 0.0)
+            self.assertEqualAndEqualSign(fd_op(1.0, -INF), -0.0)
+            self.assertEqualAndEqualSign(fd_op(-1.0, INF), -0.0)
+            self.assertEqualAndEqualSign(fd_op(-1.0, -INF), 0.0)
+
+    @support.requires_IEEE_754
     def test_float_pow(self):
         # test builtin pow and ** operator for IEEE 754 special cases.
         # Special cases taken from section F.9.4.4 of the C99 specification
diff --git a/Objects/floatobject.c b/Objects/floatobject.c
index 05b7679..7e94a85 100644
--- a/Objects/floatobject.c
+++ b/Objects/floatobject.c
@@ -589,7 +589,7 @@ float_divmod(PyObject *v, PyObject *w)
     div = (vx - mod) / wx;
     if (mod) {
         /* ensure the remainder has the same sign as the denominator */
-        if ((wx < 0) != (mod < 0)) {
+        if ((wx < 0) != (mod < 0) && !Py_IS_INFINITY(wx)) {
             mod += wx;
             div -= 1.0;
         }