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Section 4

Process isolation and virtual memory

We don’t want processes to be able to trample over the memory of other processes, as discussed in class. So, we need process isolation. Virtual memory is a mechanism for the OS to provide process isolation. Today’s section will be focused on diving deeper into virtual memory.

When you print a pointer in C program, you see the pointer’s virtual address in that process’s address space. The actual place where the underlying bytes live is in physical memory, at an address only known to the OS. This address can be determined using the process’s page table (which maps virtual addresses to physical addresses). This page table is set up by the operating system kernel, and interpreted by the processor hardware.

Multi-level page tables

Many processors, including x86-64, use multi-level page tables to translate virtual addresses to physical addresses. A multi-level page table is structured in a tree format. The root of the tree is configured via a register (%cr3 on x86-64); the root’s entries point to lower-level page tables. The virtual address being looked up provides the index of the entry to follow at each level of the pagetable. We are going to walk through how the pagetable structure can be determined from the page size and address size.

Example: x86-32

On 32-bit x86 architecture (virtual addresses are 32 bits long), each page is 4096 = 212 bytes. Each physical page contains 212 separate addresses, and the architecture supports up to 220 = 232 / 212 virtual pages.

QUESTION: What is the size of the offset for an x86-32 address?

QUESTION: How many 32-bit addresses can fit in an x86-32 page?

QUESTION: Assume that x86-32 used a single-level page table (like the page table from the Kernel 2 lecture with 6-bit addresses). Such a page table is indexed by the top portion of the address—everything but the offset. That means it must occupy enough contiguous physical memory to account for every possible index. How big would the single-level page table be?

x86-32 does not use a single-level page table. It uses a two-level page table. The x86-32 address divides into three sections: level-2 index, level-1 index, and offset.

bits 31-22 bits 21-12 bits 11-0
Level 2 index Level 1 index Offset

The address of the level-2 page table is stored in the x86-32 %cr3 register. This page table is indexed by level 2 index to find the physical address of a level-1 page table; there can be many of these, one per level-2 index. The level-1 page table is indexed by level 1 index to find the physical address of the final physical page.

QUESTION: Why is 10 bits per level the correct number?

QUESTION: What is the minimum number of page table pages necessary to provide access to 220 different bytes of physical memory?

QUESTION: What is the minimum number of page tables necessary to provide access to 220 different pages of physical memory?

Moving to x86-64

x86-64 uses a similar structure, but each address consists of 48 meaningful bits (stored in a 64-bit, or 8-byte, number). This is so many bits that more levels of page table are required. x86-64 has a four-level page table, with addresses divided as follows:

bits 63-48 bits 47-39 bits 38-30 bits 29-21 bits 20-12 bits 11-0
(ignored) Level 4 index Level 3 index Level 2 index Level 1 index Offset

Try working through the above problems for x86-64 (probably on your own time). What numbers do you get?

QUESTION: What is the maximum number of page table pages in each level? What is the maximum number of physical pages that are accessible with 4 levels of the pagetable? Include both physical pages corresponding to virtual memory and pagetable pages.

QUESTION: If the upper 16 bits of x86-64 addresses were meaningful, how many levels would the page table require?

QUESTION: What is the minimum number of physical pages required on x86-64 to allocate the following allocations? Draw an example pagetable mapping for each scenario (start from scratch each time).

  1. 1 byte of memory
  2. 1 allocation of size 2^12 bytes of memory
  3. 2^9 allocations of size of 2^12 bytes of memory each
  4. 2^9 + 1 allocations of size of 2^12 bytes of memory each
  5. 2^18 + 1 allocations of size 2^12 bytes of memory each


The pset for this unit asks you to add to WeensyOS, an operating system that we’ll use in this course. WeensyOS has internal interfaces for dealing with virtual memory that we’ll now discuss.

vmiter and ptiter are iterators in WeensyOS for processing page tables. Vmiter helps iterate through pages in virtual memory, and lets you check the underlying physical pages for properties like permissions and physical addresses. Ptiter helps you iterate through page table pages. Let’s walk through the code:


The vmiter class represents an iterator over virtual memory mappings. Here is its interface:

// `vmiter` walks over virtual address mappings.
// `pa()` and `perm()` read current addresses and permissions;
// `map()` installs new mappings.

class vmiter {
    // initialize a `vmiter` for `pt` pointing at `va`
    inline vmiter(x86_64_pagetable* pt, uintptr_t va = 0);
    inline vmiter(const proc* p, uintptr_t va = 0);

    inline uintptr_t va() const;      // current virtual address
    inline uint64_t pa() const;       // current physical address
    inline uint64_t perm() const;     // current permissions
    inline bool present() const;      // is va present?
    inline bool writable() const;     // is va writable?
    inline bool user() const;         // is va user-accessible (unprivileged)?

    inline vmiter& find(uintptr_t va);   // change virtual address to `va`
    inline vmiter& operator+=(intptr_t delta);  // advance `va` by `delta`

    // map current va to `pa` with permissions `perm`
    // Current va must be page-aligned. Calls kallocpage() to allocate
    // page table pages if necessary. Returns 0 on success,
    // negative on failure.
    int map(uintptr_t pa, int perm = PTE_P | PTE_W | PTE_U)

This type parses x86-64 page tables and manages virtual-to-physical address mappings. vmiter(pt, va) creates a vmiter object that’s examining virtual address va in page table pt. Methods on this object can return the corresponding physical address:

x86_64_pagetable* pt = ...;
uintptr_t pa = vmiter(pt, va).pa();    // returns uintptr_t(-1) if unmapped

Or the permissions:

if (vmiter(pt, va).writable()) {
    // then `va` is present and writable (PTE_P | PTE_W) in `pt`

It’s also possible to use vmiter as a loop variable, calling methods that query its state and methods that change its current virtual address. For example, this loop prints all present mappings in the lower 64KiB of memory:

for (vmiter it(pt, 0); < 0x10000; it += PAGESIZE) {
    if (it.present()) {
        log_printf("%p maps to %p\n",,;

This loop goes one page at a time (the it += PAGESIZE expression increases by PAGESIZE).

The function is used to add mappings to a page table. This maps physical page 0x3000 at virtual address 0x2000:

int r = vmiter(pt, 0x2000).map(0x3000, PTE_P | PTE_W | PTE_U);
// r == 0 on success, r < 0 on failure


class ptiter {
    // initialize a `ptiter` for `pt` pointing at `va`
    inline ptiter(x86_64_pagetable* pt, uintptr_t va = 0);
    inline ptiter(const proc* p, uintptr_t va = 0);

    inline uintptr_t va() const;            // current virtual address
    inline uintptr_t last_va() const;       // one past last va covered by ptp
    inline bool active() const;             // does va exist?
    inline int level() const;               // current level (0-2)
    inline x86_64_pagetable* ptp() const;   // current page table page
    inline uintptr_t ptp_pa() const;        // physical address of ptp

    // move to next page table page in depth-first order
    inline void next();

ptiter visits the individual page table pages in a multi-level page table, in depth-first order (so all level-1 page tables under a level-2 page table are visited before the level-2 is visited). A ptiter loop makes it easy to find all the page table pages owned by a process, which is usually at least 4 page tables in x86-64 (one per level).

for (ptiter it(pt, 0); < MEMSIZE_VIRTUAL; {
    log_printf("[%p, %p): ptp at va %p, pa %p\n",
     , it.end_va(), it.ptp(), it.ptp_pa());

A WeensyOS process might print the following:

[0x0, 0x200000): ptp at va 0xb000, pa 0xb000
[0x200000, 0x400000): ptp at va 0xe000, pa 0xe000
[0x0, 0x40000000): ptp at va 0xa000, pa 0xa000
[0x0, 0x8000000000): ptp at va 0x9000, pa 0x9000

Note the depth-first order: the level-1 page table pages are visited first, then level-2, then level-3. Because of this order (and other implementation choices), a ptiter loop may be used to free a page table—for instance, when you’re implementing process exit later :)

ptiter never visits the top level-4 page table page, so that will need to be freed independently of the ptiter loop.

Using iterators

On this problem set, you will implement some of the system calls in WeensyOS. Two of the main system calls that you will implement are fork() and exit().

The fork system call allows a process to spawn a child process that is essentially a copy of the parent process. The child process has a copy of the parent processes’ memory, and after the new child process created, both processes execute the next instruction after fork(). The registers and file descriptors are also copied.

The exit system call allows a process to stop its execution. All of the memory belonging to that process, including its page table pages, are returned to the kernel for reuse.

The Lifecycle of a Process

A process: the singular unit of life in an operating system. When a new process is born, it needs its own page table pages, which it gets from its parent. For processes not born from a fork() call, this parent is the kernel, and thus, the process's page table pages will be a copy of the kernel's.

During the normal execution of a process, it refers to memory addresses by their virtual memory addresses -- which means that, to actually access the underlying memory, those virtual memory addresses need to be translated into physical addresses. Fortunately, you have just learned about the basic mechanism behind this process. ;)

Once a process has completed its run, there is some cleanup to be done -- namely, the relinquishment of its virtual memory mappings. First, the process needs to disassociate itself from the kernel's page table pages -- an exited process shouldn't need them anymore, anyway. Next, the process needs to tell the kernel that it is no longer using its page table pages -- this is not just the level-1 page table pages, but also the higher-level ones as well! Finally, the process can rest in peace. RIP.

QUESTION: Use vmiter to implement the following function.

void copy_mappings(x86_64_pagetable* dst, x86_64_pagetable* src) {
    // Copy all virtual memory mappings from `src` into `dst`
    // for addresses in the range [0, MEMSIZE_VIRTUAL).
    // You may assume that `dst` starts out empty (has no mappings).

    // After this function completes, for any va with
    // 0 <= va < MEMSIZE_VIRTUAL, dst and src should map that va
    // to the same pa with the same permissions.


QUESTION: Use vmiter and ptiter to implement the following function.

void free_everything(x86_64_pagetable* pt) {
    // Free the following pages by passing their physical addresses
    // to `kfree_pa()`:
    // 1. All memory accessible by unprivileged mappings in `pt`.
    // 2. All page table pages that are part of `pt`.