[PATCHv4 03/12] arm64: Introduce helpers for page table levels

[Suzuki K. Poulose]

Introduce helpers for finding the number of page table
levels required for a given VA width, shift for a particular
page table level.

Convert the existing users to the new helpers. More users
to follow.

Cc: Ard Biesheuvel <ard.biesheuvel at linaro.org>
Cc: Mark Rutland <mark.rutland at arm.com>
Cc: Catalin Marinas <catalin.marinas at arm.com>
Cc: Will Deacon <will.deacon at arm.com>
Cc: Marc Zyngier <marc.zyngier at arm.com>
Signed-off-by: Suzuki K. Poulose <suzuki.poulose at arm.com>
Acked-by: Christoffer Dall <christoffer.dall at linaro.org>
Acked-by: Mark Rutland <mark.rutland at arm.com>

---
Changes since v3:
  - Explain the answer to interview question
	https://lkml.org/lkml/2015/10/15/239
	https://lkml.org/lkml/2015/10/15/334
Changes since V2:
  - Add comments around the macros
  - Change ARM64_HW_PGTABLE_LEVEL_SHIFT to accept pagetable level as
    described by ARM ARM
---
 arch/arm64/include/asm/pgtable-hwdef.h |   39 +++++++++++++++++++++++++++++---
 1 file changed, 36 insertions(+), 3 deletions(-)

diff --git a/arch/arm64/include/asm/pgtable-hwdef.h b/arch/arm64/include/asm/pgtable-hwdef.h
index 95c1ec0..d6739e8 100644
--- a/arch/arm64/include/asm/pgtable-hwdef.h
+++ b/arch/arm64/include/asm/pgtable-hwdef.h
@@ -16,13 +16,46 @@
 #ifndef __ASM_PGTABLE_HWDEF_H
 #define __ASM_PGTABLE_HWDEF_H
 
+/*
+ * Number of page-table levels required to address 'va_bits' wide
+ * address, without section mapping. We resolve the top (va_bits - PAGE_SHIFT)
+ * bits with (PAGE_SHIFT - 3) bits at each page table level. Hence:
+ *
+ *  levels = DIV_ROUND_UP((va_bits - PAGE_SHIFT), (PAGE_SHIFT - 3))
+ *
+ * where DIV_ROUND_UP(n, d) => (((n) + (d) - 1) / (d))
+ *
+ * We cannot include linux/kernel.h which defines DIV_ROUND_UP here
+ * due to build issues. So we open code DIV_ROUND_UP here:
+ *
+ *	((((va_bits) - PAGE_SHIFT) + (PAGE_SHIFT - 3) - 1) / (PAGE_SHIFT - 3))
+ *
+ * which gets simplified as :
+ */
+#define ARM64_HW_PGTABLE_LEVELS(va_bits) (((va_bits) - 4) / (PAGE_SHIFT - 3))
+
+/*
+ * Size mapped by an entry at level n ( 0 <= n <= 3)
+ * We map (PAGE_SHIFT - 3) at all translation levels and PAGE_SHIFT bits
+ * in the final page. The maximum number of translation levels supported by
+ * the architecture is 4. Hence, starting at at level n, we have further
+ * ((4 - n) - 1) levels of translation excluding the offset within the page.
+ * So, the total number of bits mapped by an entry at level n is :
+ *
+ *  ((4 - n) - 1) * (PAGE_SHIFT - 3) + PAGE_SHIFT
+ *
+ * Rearranging it a bit we get :
+ *   (4 - n) * (PAGE_SHIFT - 3) + 3
+ */
+#define ARM64_HW_PGTABLE_LEVEL_SHIFT(n)	((PAGE_SHIFT - 3) * (4 - (n)) + 3)
+
 #define PTRS_PER_PTE		(1 << (PAGE_SHIFT - 3))
 
 /*
  * PMD_SHIFT determines the size a level 2 page table entry can map.
  */
 #if CONFIG_PGTABLE_LEVELS > 2
-#define PMD_SHIFT		((PAGE_SHIFT - 3) * 2 + 3)
+#define PMD_SHIFT		ARM64_HW_PGTABLE_LEVEL_SHIFT(2)
 #define PMD_SIZE		(_AC(1, UL) << PMD_SHIFT)
 #define PMD_MASK		(~(PMD_SIZE-1))
 #define PTRS_PER_PMD		PTRS_PER_PTE
@@ -32,7 +65,7 @@
  * PUD_SHIFT determines the size a level 1 page table entry can map.
  */
 #if CONFIG_PGTABLE_LEVELS > 3
-#define PUD_SHIFT		((PAGE_SHIFT - 3) * 3 + 3)
+#define PUD_SHIFT		ARM64_HW_PGTABLE_LEVEL_SHIFT(1)
 #define PUD_SIZE		(_AC(1, UL) << PUD_SHIFT)
 #define PUD_MASK		(~(PUD_SIZE-1))
 #define PTRS_PER_PUD		PTRS_PER_PTE
@@ -42,7 +75,7 @@
  * PGDIR_SHIFT determines the size a top-level page table entry can map
  * (depending on the configuration, this level can be 0, 1 or 2).
  */
-#define PGDIR_SHIFT		((PAGE_SHIFT - 3) * CONFIG_PGTABLE_LEVELS + 3)
+#define PGDIR_SHIFT		ARM64_HW_PGTABLE_LEVEL_SHIFT(4 - CONFIG_PGTABLE_LEVELS)
 #define PGDIR_SIZE		(_AC(1, UL) << PGDIR_SHIFT)
 #define PGDIR_MASK		(~(PGDIR_SIZE-1))
 #define PTRS_PER_PGD		(1 << (VA_BITS - PGDIR_SHIFT))
-- 
1.7.9.5