.. SPDX-License-Identifier: GPL-2.0

===========
Page Tables
===========

Paged virtual memory was invented along with virtual memory as a concept in
1962 on the Ferranti Atlas Computer which was the first computer with paged
virtual memory. The feature migrated to newer computers and became a de facto
feature of all Unix-like systems as time went by. In 1985 the feature was
included in the Intel 80386, which was the CPU Linux 1.0 was developed on.

Page tables map virtual addresses as seen by the CPU into physical addresses
as seen on the external memory bus.

Linux defines page tables as a hierarchy which is currently five levels in
height. The architecture code for each supported architecture will then
map this to the restrictions of the hardware.

The physical address corresponding to the virtual address is often referenced
by the underlying physical page frame. The **page frame number** or **pfn**
is the physical address of the page (as seen on the external memory bus)
divided by `PAGE_SIZE`.

Physical memory address 0 will be *pfn 0* and the highest pfn will be
the last page of physical memory the external address bus of the CPU can
address.

With a page granularity of 4KB and a address range of 32 bits, pfn 0 is at
address 0x00000000, pfn 1 is at address 0x00001000, pfn 2 is at 0x00002000
and so on until we reach pfn 0xfffff at 0xfffff000. With 16KB pages pfs are
at 0x00004000, 0x00008000 ... 0xffffc000 and pfn goes from 0 to 0x3fffff.

As you can see, with 4KB pages the page base address uses bits 12-31 of the
address, and this is why `PAGE_SHIFT` in this case is defined as 12 and
`PAGE_SIZE` is usually defined in terms of the page shift as `(1 << PAGE_SHIFT)`

Over time a deeper hierarchy has been developed in response to increasing memory
sizes. When Linux was created, 4KB pages and a single page table called
`swapper_pg_dir` with 1024 entries was used, covering 4MB which coincided with
the fact that Torvald's first computer had 4MB of physical memory. Entries in
this single table were referred to as *PTE*:s - page table entries.

The software page table hierarchy reflects the fact that page table hardware has
become hierarchical and that in turn is done to save page table memory and
speed up mapping.

One could of course imagine a single, linear page table with enormous amounts
of entries, breaking down the whole memory into single pages. Such a page table
would be very sparse, because large portions of the virtual memory usually
remains unused. By using hierarchical page tables large holes in the virtual
address space does not waste valuable page table memory, because it will suffice
to mark large areas as unmapped at a higher level in the page table hierarchy.

Additionally, on modern CPUs, a higher level page table entry can point directly
to a physical memory range, which allows mapping a contiguous range of several
megabytes or even gigabytes in a single high-level page table entry, taking
shortcuts in mapping virtual memory to physical memory: there is no need to
traverse deeper in the hierarchy when you find a large mapped range like this.

The page table hierarchy has now developed into this::

  +-----+
  | PGD |
  +-----+
     |
     |   +-----+
     +-->| P4D |
         +-----+
            |
            |   +-----+
            +-->| PUD |
                +-----+
                   |
                   |   +-----+
                   +-->| PMD |
                       +-----+
                          |
                          |   +-----+
                          +-->| PTE |
                              +-----+


Symbols on the different levels of the page table hierarchy have the following
meaning beginning from the bottom:

- **pte**, `pte_t`, `pteval_t` = **Page Table Entry** - mentioned earlier.
  The *pte* is an array of `PTRS_PER_PTE` elements of the `pteval_t` type, each
  mapping a single page of virtual memory to a single page of physical memory.
  The architecture defines the size and contents of `pteval_t`.

  A typical example is that the `pteval_t` is a 32- or 64-bit value with the
  upper bits being a **pfn** (page frame number), and the lower bits being some
  architecture-specific bits such as memory protection.

  The **entry** part of the name is a bit confusing because while in Linux 1.0
  this did refer to a single page table entry in the single top level page
  table, it was retrofitted to be an array of mapping elements when two-level
  page tables were first introduced, so the *pte* is the lowermost page
  *table*, not a page table *entry*.

- **pmd**, `pmd_t`, `pmdval_t` = **Page Middle Directory**, the hierarchy right
  above the *pte*, with `PTRS_PER_PMD` references to the *pte*:s.

- **pud**, `pud_t`, `pudval_t` = **Page Upper Directory** was introduced after
  the other levels to handle 4-level page tables. It is potentially unused,
  or *folded* as we will discuss later.

- **p4d**, `p4d_t`, `p4dval_t` = **Page Level 4 Directory** was introduced to
  handle 5-level page tables after the *pud* was introduced. Now it was clear
  that we needed to replace *pgd*, *pmd*, *pud* etc with a figure indicating the
  directory level and that we cannot go on with ad hoc names any more. This
  is only used on systems which actually have 5 levels of page tables, otherwise
  it is folded.

- **pgd**, `pgd_t`, `pgdval_t` = **Page Global Directory** - the Linux kernel
  main page table handling the PGD for the kernel memory is still found in
  `swapper_pg_dir`, but each userspace process in the system also has its own
  memory context and thus its own *pgd*, found in `struct mm_struct` which
  in turn is referenced to in each `struct task_struct`. So tasks have memory
  context in the form of a `struct mm_struct` and this in turn has a
  `struct pgt_t *pgd` pointer to the corresponding page global directory.

To repeat: each level in the page table hierarchy is a *array of pointers*, so
the **pgd** contains `PTRS_PER_PGD` pointers to the next level below, **p4d**
contains `PTRS_PER_P4D` pointers to **pud** items and so on. The number of
pointers on each level is architecture-defined.::

        PMD
  --> +-----+           PTE
      | ptr |-------> +-----+
      | ptr |-        | ptr |-------> PAGE
      | ptr | \       | ptr |
      | ptr |  \        ...
      | ... |   \
      | ptr |    \         PTE
      +-----+     +----> +-----+
                         | ptr |-------> PAGE
                         | ptr |
                           ...


Page Table Folding
==================

If the architecture does not use all the page table levels, they can be *folded*
which means skipped, and all operations performed on page tables will be
compile-time augmented to just skip a level when accessing the next lower
level.

Page table handling code that wishes to be architecture-neutral, such as the
virtual memory manager, will need to be written so that it traverses all of the
currently five levels. This style should also be preferred for
architecture-specific code, so as to be robust to future changes.