i = first;
     for (;;) {
-        next = hbitmap_iter_next(&hbi);
+        next = hbitmap_iter_next(&hbi, true);
         if (next < 0) {
             next = data->size;
         }
     /* Note that hbitmap_test_check has to be invoked manually in this test.  */
     hbitmap_test_init(data, 131072 << 7, 7);
     hbitmap_iter_init(&hbi, data->hb, 0);
-    g_assert_cmpint(hbitmap_iter_next(&hbi), <, 0);
+    g_assert_cmpint(hbitmap_iter_next(&hbi, true), <, 0);
 
     hbitmap_test_set(data, ((L2 + L1 + 1) << 7) + 8, 8);
     hbitmap_iter_init(&hbi, data->hb, 0);
-    g_assert_cmpint(hbitmap_iter_next(&hbi), ==, (L2 + L1 + 1) << 7);
-    g_assert_cmpint(hbitmap_iter_next(&hbi), <, 0);
+    g_assert_cmpint(hbitmap_iter_next(&hbi, true), ==, (L2 + L1 + 1) << 7);
+    g_assert_cmpint(hbitmap_iter_next(&hbi, true), <, 0);
 
     hbitmap_iter_init(&hbi, data->hb, (L2 + L1 + 2) << 7);
-    g_assert_cmpint(hbitmap_iter_next(&hbi), <, 0);
+    g_assert_cmpint(hbitmap_iter_next(&hbi, true), <, 0);
 
     hbitmap_test_set(data, (131072 << 7) - 8, 8);
     hbitmap_iter_init(&hbi, data->hb, 0);
-    g_assert_cmpint(hbitmap_iter_next(&hbi), ==, (L2 + L1 + 1) << 7);
-    g_assert_cmpint(hbitmap_iter_next(&hbi), ==, 131071 << 7);
-    g_assert_cmpint(hbitmap_iter_next(&hbi), <, 0);
+    g_assert_cmpint(hbitmap_iter_next(&hbi, true), ==, (L2 + L1 + 1) << 7);
+    g_assert_cmpint(hbitmap_iter_next(&hbi, true), ==, 131071 << 7);
+    g_assert_cmpint(hbitmap_iter_next(&hbi, true), <, 0);
 
     hbitmap_iter_init(&hbi, data->hb, (L2 + L1 + 2) << 7);
-    g_assert_cmpint(hbitmap_iter_next(&hbi), ==, 131071 << 7);
-    g_assert_cmpint(hbitmap_iter_next(&hbi), <, 0);
+    g_assert_cmpint(hbitmap_iter_next(&hbi, true), ==, 131071 << 7);
+    g_assert_cmpint(hbitmap_iter_next(&hbi, true), <, 0);
 }
 
 static void hbitmap_test_set_boundary_bits(TestHBitmapData *data, ssize_t diff)
     for (i = 0; i < num_positions; i++) {
         hbitmap_deserialize_zeroes(data->hb, positions[i], min_l1, true);
         hbitmap_iter_init(&iter, data->hb, 0);
-        next = hbitmap_iter_next(&iter);
+        next = hbitmap_iter_next(&iter, true);
         if (i == num_positions - 1) {
             g_assert_cmpint(next, ==, -1);
         } else {
 
     hbitmap_iter_init(&hbi, data->hb, BITS_PER_LONG - 1);
 
-    hbitmap_iter_next(&hbi);
+    hbitmap_iter_next(&hbi, true);
 
     hbitmap_reset_all(data->hb);
-    hbitmap_iter_next(&hbi);
+    hbitmap_iter_next(&hbi, true);
 }
 
 static void test_hbitmap_next_zero_check(TestHBitmapData *data, int64_t start)