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After this documentation was released in July 2003, I was approached by Prentice Hall and asked to write a book on the Linux VM under the Bruce Peren's Open Book Series.

The book is available and called simply "Understanding The Linux Virtual Memory Manager". There is a lot of additional material in the book that is not available here, including details on later 2.4 kernels, introductions to 2.6, a whole new chapter on the shared memory filesystem, coverage of TLB management, a lot more code commentary, countless other additions and clarifications and a CD with lots of cool stuff on it. This material (although now dated and lacking in comparison to the book) will remain available although I obviously encourge you to buy the book from your favourite book store :-) . As the book is under the Bruce Perens Open Book Series, it will be available 90 days after appearing on the book shelves which means it is not available right now. When it is available, it will be downloadable from http://www.phptr.com/perens so check there for more information.

To be fully clear, this webpage is not the actual book.
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4.1 Describing the Page Directory

Each process has its own Page Global Directory (PGD) which is a physical page frame containing an array of pgd_t, an architecture specific type defined in $<$asm/page.h$>$. The page tables are loaded differently on each architecture. On the x86, the process page table is loaded by copying the pointer to the PGD into the cr3 register which has the side effect of flushing the TLB. In fact this is how the function __flush_tlb() is implemented in the architecture dependent code.

Each active entry in the PGD table points to a page frame containing an array of Page Middle Directory (PMD) entries of type pmd_t which in turn point to page frames containing Page Table Entries (PTE) of type pte_t, which finally point to page frames containing the actual user data. In the event the page has been swapped out to backing storage, the swap entry is stored in the PTE and used by do_swap_page() during page fault to find the swap entry containing the page data.

Any given linear address may be broken up into parts to yield offsets within these three page table levels and an offset within the actual page. To help break up the linear address into its component parts, a number of macros are provided in triplets for each page table level, namely a SHIFT, a SIZE and a MASK macro. The SHIFT macros specifies the length in bits that are mapped by each level of the page tables as illustrated in Figure 4.1.

Figure 4.1: Linear Address Bit Size Macros
\includegraphics[width=12cm]{graphs/address_size_macros.ps}

The MASK values can be ANDd with a linear address to mask out all the upper bits and are frequently used to determine if a linear address is aligned to a given level within the page table. The SIZE macros reveal how many bytes are addressed by each entry at each level. The relationship between the SIZE and MASK macros is illustrated in Figure 4.2.

Figure 4.2: Linear Address Size and Mask Macros
\includegraphics[width=12cm]{graphs/address_size_macros_partII.ps}

For the calculation of each of the triplets, only SHIFT is important as the other two are calculated based on it. For example, the three macros for page level on the x86 are: 

  5 #define PAGE_SHIFT      12
  6 #define PAGE_SIZE       (1UL << PAGE_SHIFT)
  7 #define PAGE_MASK       (~(PAGE_SIZE-1))

PAGE_SHIFT is the length in bits of the offset part of the linear address space which is 12 bits on the x86. The size of a page is easily calculated as $2^{\mathrm{PAGE\_SHIFT}}$ which is the equivalent of the code above. Finally the mask is calculated as the negation of the bits which make up the PAGE_SIZE - 1. If a page needs to be aligned on a page boundary, PAGE_ALIGN() is used. This macro adds PAGE_SIZE - 1 is added to the address before simply ANDing it with the PAGE_MASK.

PMD_SHIFT is the number of bits in the linear address which are mapped by the second level part of the table. The PMD_SIZE and PMD_MASK are calculated in a similar way to the page level macros.

PGDIR_SHIFT is the number of bits which are mapped by the top, or first level, of the page table. The PGDIR_SIZE and PGDIR_MASK are calculated in the same manner as above.

The last three macros of importance are the PTRS_PER_x which determine the number of entries in each level of the page table. PTRS_PER_PGD is the number of pointers in the PGD, 1024 on an x86 without PAE. PTRS_PER_PMD is for the PMD, 1 on the x86 without PAE and PTRS_PER_PTE is for the lowest level, 1024 on the x86.

next up previous contents index
Next: 4.2 Describing a Page Up: 4. Page Table Management Previous: 4. Page Table Management   Contents   Index
Mel 2004-02-15