diff --git a/ChangeLog b/ChangeLog
index bbc21abb6c..bd530a8d87 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,9 @@
+2017-06-08  H.J. Lu  <hongjiu.lu@intel.com>
+
+	* string/test-memrchr.c (test_main): Add tests for len == 0
+	and tests for positions close to the beginning, which are
+	equivalent to positions close to the end for memchr.
+
 2017-06-07  H.J. Lu  <hongjiu.lu@intel.com>
 
 	* sysdeps/x86_64/multiarch/ifunc-impl-list.c: Update
diff --git a/string/test-memrchr.c b/string/test-memrchr.c
index bfc9920dcc..15483f5cb5 100644
--- a/string/test-memrchr.c
+++ b/string/test-memrchr.c
@@ -151,15 +151,32 @@ test_main (void)
 
   for (i = 1; i < 8; ++i)
     {
+      /* Test len == 0.  */
+      do_test (i, i, 0, 0);
+      do_test (i, i, 0, 23);
+
       do_test (0, 16 << i, 2048, 23);
       do_test (i, 64, 256, 23);
       do_test (0, 16 << i, 2048, 0);
       do_test (i, 64, 256, 0);
+
+      do_test (0, i, 256, 23);
+      do_test (0, i, 256, 0);
+      do_test (i, i, 256, 23);
+      do_test (i, i, 256, 0);
+
     }
   for (i = 1; i < 32; ++i)
     {
       do_test (0, i, i + 1, 23);
       do_test (0, i, i + 1, 0);
+      do_test (i, i, i + 1, 23);
+      do_test (i, i, i + 1, 0);
+
+      do_test (0, 1, i + 1, 23);
+      do_test (0, 2, i + 1, 0);
+      do_test (i, 1, i + 1, 23);
+      do_test (i, 2, i + 1, 0);
     }
 
   do_random_tests ();