diff --git a/include/linux/swapops.h b/include/linux/swapops.h
index 792d16d9cbc7..47ead515c811 100644
--- a/include/linux/swapops.h
+++ b/include/linux/swapops.h
@@ -9,13 +9,15 @@
  * get good packing density in that tree, so the index should be dense in
  * the low-order bits.
  *
- * We arrange the `type' and `offset' fields so that `type' is at the five
+ * We arrange the `type' and `offset' fields so that `type' is at the seven
  * high-order bits of the swp_entry_t and `offset' is right-aligned in the
- * remaining bits.
+ * remaining bits.  Although `type' itself needs only five bits, we allow for
+ * shmem/tmpfs to shift it all up a further two bits: see swp_to_radix_entry().
  *
  * swp_entry_t's are *never* stored anywhere in their arch-dependent format.
  */
-#define SWP_TYPE_SHIFT(e)	(sizeof(e.val) * 8 - MAX_SWAPFILES_SHIFT)
+#define SWP_TYPE_SHIFT(e)	((sizeof(e.val) * 8) - \
+			(MAX_SWAPFILES_SHIFT + RADIX_TREE_EXCEPTIONAL_SHIFT))
 #define SWP_OFFSET_MASK(e)	((1UL << SWP_TYPE_SHIFT(e)) - 1)
 
 /*
diff --git a/mm/swapfile.c b/mm/swapfile.c
index de5bc51c4a66..71373d03fcee 100644
--- a/mm/swapfile.c
+++ b/mm/swapfile.c
@@ -1916,24 +1916,20 @@ static unsigned long read_swap_header(struct swap_info_struct *p,
 
 	/*
 	 * Find out how many pages are allowed for a single swap
-	 * device. There are three limiting factors: 1) the number
+	 * device. There are two limiting factors: 1) the number
 	 * of bits for the swap offset in the swp_entry_t type, and
 	 * 2) the number of bits in the swap pte as defined by the
-	 * the different architectures, and 3) the number of free bits
-	 * in an exceptional radix_tree entry. In order to find the
+	 * different architectures. In order to find the
 	 * largest possible bit mask, a swap entry with swap type 0
 	 * and swap offset ~0UL is created, encoded to a swap pte,
 	 * decoded to a swp_entry_t again, and finally the swap
 	 * offset is extracted. This will mask all the bits from
 	 * the initial ~0UL mask that can't be encoded in either
 	 * the swp_entry_t or the architecture definition of a
-	 * swap pte.  Then the same is done for a radix_tree entry.
+	 * swap pte.
 	 */
 	maxpages = swp_offset(pte_to_swp_entry(
-			swp_entry_to_pte(swp_entry(0, ~0UL))));
-	maxpages = swp_offset(radix_to_swp_entry(
-			swp_to_radix_entry(swp_entry(0, maxpages)))) + 1;
-
+			swp_entry_to_pte(swp_entry(0, ~0UL)))) + 1;
 	if (maxpages > swap_header->info.last_page) {
 		maxpages = swap_header->info.last_page + 1;
 		/* p->max is an unsigned int: don't overflow it */