+#define PTE_FOR(x) (((unsigned int)(x) >> 12) & 0x3FF)
+#define PDE_FOR(x) ((unsigned int)(x) >> 22)
+#define ADDR_12_MASK(x) ((unsigned int)(x) & ~((1 << 12) - 1))
+#define ADDR_22_MASK(x) ((unsigned int)(x) & ~((1 << 22) - 1))
+#define LOWER_12(x) ((unsigned int)(x) & ((1 << 12) - 1))
+#define LOWER_22(x) ((unsigned int)(x) & ((1 << 22) - 1))
+