pmap.c

/* See COPYRIGHT for copyright information. */

#include <inc/x86.h>
#include <inc/mmu.h>
#include <inc/error.h>
#include <inc/string.h>
#include <inc/assert.h>

#include <kern/pmap.h>
#include <kern/kclock.h>

// These variables are set by i386_detect_memory()
size_t npages;          // Amount of physical memory (in pages)
static size_t npages_basemem;   // Amount of base memory (in pages)

// These variables are set in mem_init()
pde_t *kern_pgdir;      // Kernel's initial page directory
struct PageInfo *pages;     // Physical page state array
static struct PageInfo *page_free_list; // Free list of physical pages


// --------------------------------------------------------------
// Detect machine's physical memory setup.
// --------------------------------------------------------------

static int
nvram_read(int r)
{
    return mc146818_read(r) | (mc146818_read(r + 1) << 8);
}

static void
i386_detect_memory(void)
{
    size_t basemem, extmem, ext16mem, totalmem;

    // Use CMOS calls to measure available base & extended memory.
    // (CMOS calls return results in kilobytes.)
    basemem = nvram_read(NVRAM_BASELO);
    extmem = nvram_read(NVRAM_EXTLO);
    ext16mem = nvram_read(NVRAM_EXT16LO) * 64;

    // Calculate the number of physical pages available in both base
    // and extended memory.
    if (ext16mem)
        totalmem = 16 * 1024 + ext16mem;
    else if (extmem)
        totalmem = 1 * 1024 + extmem;
    else
        totalmem = basemem;

    npages = totalmem / (PGSIZE / 1024);
    npages_basemem = basemem / (PGSIZE / 1024);

    cprintf("Physical memory: %uK available, base = %uK, extended = %uK\n",
        totalmem, basemem, totalmem - basemem);
}


// --------------------------------------------------------------
// Set up memory mappings above UTOP.
// --------------------------------------------------------------

static void boot_map_region(pde_t *pgdir, uintptr_t va, size_t size, physaddr_t pa, int perm);
static void check_page_free_list(bool only_low_memory);
static void check_page_alloc(void);
static void check_kern_pgdir(void);
static physaddr_t check_va2pa(pde_t *pgdir, uintptr_t va);
static void check_page(void);
static void check_page_installed_pgdir(void);

// This simple physical memory allocator is used only while JOS is setting
// up its virtual memory system.  page_alloc() is the real allocator.
//
// If n>0, allocates enough pages of contiguous physical memory to hold 'n'
// bytes.  Doesn't initialize the memory.  Returns a kernel virtual address.
//
// If n==0, returns the address of the next free page without allocating
// anything.
//
// If we're out of memory, boot_alloc should panic.
// This function may ONLY be used during initialization,
// before the page_free_list list has been set up.
static void *
boot_alloc(uint32_t n)
{
    static char *nextfree;  // virtual address of next byte of free memory
    char *result;

    // Initialize nextfree if this is the first time.
    // 'end' is a magic symbol automatically generated by the linker,
    // which points to the end of the kernel's bss segment:
    // the first virtual address that the linker did *not* assign
    // to any kernel code or global variables.
    if (!nextfree) {
        extern char end[];
        nextfree = ROUNDUP((char *) end, PGSIZE);
    }

    // Allocate a chunk large enough to hold 'n' bytes, then update
    // nextfree.  Make sure nextfree is kept aligned
    // to a multiple of PGSIZE.
    //
    // LAB 2: Your code here.
    result=nextfree;
    nextfree+=ROUNDUP(n,PGSIZE);
    if((uint32_t)nextfree-KERNBASE>(npages*PGSIZE)){
        panic("Out of memory!\n");
    }
    return result;
}

// Set up a two-level page table:
//    kern_pgdir is its linear (virtual) address of the root
//
// This function only sets up the kernel part of the address space
// (ie. addresses >= UTOP).  The user part of the address space
// will be set up later.
//
// From UTOP to ULIM, the user is allowed to read but not write.
// Above ULIM the user cannot read or write.
void
mem_init(void)
{
    uint32_t cr0;
    size_t n;

    // Find out how much memory the machine has (npages & npages_basemem).
    i386_detect_memory();

    // Remove this line when you're ready to test this function.
    panic("mem_init: This function is not finished\n");

    //////////////////////////////////////////////////////////////////////
    // create initial page directory.
    kern_pgdir = (pde_t *) boot_alloc(PGSIZE);
    memset(kern_pgdir, 0, PGSIZE);

    //////////////////////////////////////////////////////////////////////
    // Recursively insert PD in itself as a page table, to form
    // a virtual page table at virtual address UVPT.
    // (For now, you don't have understand the greater purpose of the
    // following line.)

    // Permissions: kernel R, user R
    kern_pgdir[PDX(UVPT)] = PADDR(kern_pgdir) | PTE_U | PTE_P;

    //////////////////////////////////////////////////////////////////////
    // Allocate an array of npages 'struct PageInfo's and store it in 'pages'.
    // The kernel uses this array to keep track of physical pages: for
    // each physical page, there is a corresponding struct PageInfo in this
    // array.  'npages' is the number of physical pages in memory.  Use memset
    // to initialize all fields of each struct PageInfo to 0.
    // Your code goes here:
    pages=(struct PageInfo*)boot_alloc(npages*sizeof(struct PageInfo));
    memset(pages,0,npages*sizeof(struct PageInfo));


    //////////////////////////////////////////////////////////////////////
    // Now that we've allocated the initial kernel data structures, we set
    // up the list of free physical pages. Once we've done so, all further
    // memory management will go through the page_* functions. In
    // particular, we can now map memory using boot_map_region
    // or page_insert
    page_init();

    check_page_free_list(1);
    check_page_alloc();
    check_page();

    //////////////////////////////////////////////////////////////////////
    // Now we set up virtual memory

    //////////////////////////////////////////////////////////////////////
    // Map 'pages' read-only by the user at linear address UPAGES
    // Permissions:
    //    - the new image at UPAGES -- kernel R, user R
    //      (ie. perm = PTE_U | PTE_P)
    //    - pages itself -- kernel RW, user NONE
    // Your code goes here:

    //////////////////////////////////////////////////////////////////////
    // Use the physical memory that 'bootstack' refers to as the kernel
    // stack.  The kernel stack grows down from virtual address KSTACKTOP.
    // We consider the entire range from [KSTACKTOP-PTSIZE, KSTACKTOP)
    // to be the kernel stack, but break this into two pieces:
    //     * [KSTACKTOP-KSTKSIZE, KSTACKTOP) -- backed by physical memory
    //     * [KSTACKTOP-PTSIZE, KSTACKTOP-KSTKSIZE) -- not backed; so if
    //       the kernel overflows its stack, it will fault rather than
    //       overwrite memory.  Known as a "guard page".
    //     Permissions: kernel RW, user NONE
    // Your code goes here:

    //////////////////////////////////////////////////////////////////////
    // Map all of physical memory at KERNBASE.
    // Ie.  the VA range [KERNBASE, 2^32) should map to
    //      the PA range [0, 2^32 - KERNBASE)
    // We might not have 2^32 - KERNBASE bytes of physical memory, but
    // we just set up the mapping anyway.
    // Permissions: kernel RW, user NONE
    // Your code goes here:

    // Check that the initial page directory has been set up correctly.
    check_kern_pgdir();

    // Switch from the minimal entry page directory to the full kern_pgdir
    // page table we just created.  Our instruction pointer should be
    // somewhere between KERNBASE and KERNBASE+4MB right now, which is
    // mapped the same way by both page tables.
    //
    // If the machine reboots at this point, you've probably set up your
    // kern_pgdir wrong.
    lcr3(PADDR(kern_pgdir));

    check_page_free_list(0);

    // entry.S set the really important flags in cr0 (including enabling
    // paging).  Here we configure the rest of the flags that we care about.
    cr0 = rcr0();
    cr0 |= CR0_PE|CR0_PG|CR0_AM|CR0_WP|CR0_NE|CR0_MP;
    cr0 &= ~(CR0_TS|CR0_EM);
    lcr0(cr0);

    // Some more checks, only possible after kern_pgdir is installed.
    check_page_installed_pgdir();
}

// --------------------------------------------------------------
// Tracking of physical pages.
// The 'pages' array has one 'struct PageInfo' entry per physical page.
// Pages are reference counted, and free pages are kept on a linked list.
// --------------------------------------------------------------

//
// Initialize page structure and memory free list.
// After this is done, NEVER use boot_alloc again.  ONLY use the page
// allocator functions below to allocate and deallocate physical
// memory via the page_free_list.
//
void
page_init(void)
{
    // The example code here marks all physical pages as free.
    // However this is not truly the case.  What memory is free?
    //  1) Mark physical page 0 as in use.
    //     This way we preserve the real-mode IDT and BIOS structures
    //     in case we ever need them.  (Currently we don't, but...)
    //  2) The rest of base memory, [PGSIZE, npages_basemem * PGSIZE)
    //     is free.
    //  3) Then comes the IO hole [IOPHYSMEM, EXTPHYSMEM), which must
    //     never be allocated.
    //  4) Then extended memory [EXTPHYSMEM, ...).
    //     Some of it is in use, some is free. Where is the kernel
    //     in physical memory?  Which pages are already in use for
    //     page tables and other data structures?
    //
    // Change the code to reflect this.
    // NB: DO NOT actually touch the physical memory corresponding to
    // free pages!
    size_t i;
    page_free_list=NULL;
    for (i = 0; i < npages; i++) {
        if(i==0){
            pages[i].pp_ref=1;
        }
        else if(i<npages_basemem ){
            pages[i].pp_ref=0;
            pages[i].pp_link=page_free_list;
            page_free_list=&pages[i];
        }
        else if(i>=IOPHYSMEM/PGSIZE&&i<EXTPHYSMEM/PGSIZE){
            pages[i].pp_ref=1;
        }
        else{
            pages[i].pp_ref=0;
            pages[i].pp_link=page_free_list;
            page_free_list=&pages[i];
        }
    }
}

//
// Allocates a physical page.  If (alloc_flags & ALLOC_ZERO), fills the entire
// returned physical page with '\0' bytes.  Does NOT increment the reference
// count of the page - the caller must do these if necessary (either explicitly
// or via page_insert).
//
// Be sure to set the pp_link field of the allocated page to NULL so
// page_free can check for double-free bugs.
//
// Returns NULL if out of free memory.
//
// Hint: use page2kva and memset
struct PageInfo *
page_alloc(int alloc_flags)
{
    // Fill this function in
    struct PageInfo *pp;
    if(!page_free_list){
        return NULL;
    }
    pp=page_free_list;
    page_free_list=page_free_list->pp_link;
    if(alloc_flags & ALLOC_ZERO)
    {
        memset(page2kva(pp),0,PGSIZE);
    }
    return pp;
}

//
// Return a page to the free list.
// (This function should only be called when pp->pp_ref reaches 0.)
//
void
page_free(struct PageInfo *pp)
{
    // Fill this function in
    // Hint: You may want to panic if pp->pp_ref is nonzero or
    // pp->pp_link is not NULL.
    if(pp->pp_link!=NULL){
        panic("pp->pp_link is not NULL.\n");
        //不是一个单独的页面
    }
    if(pp->pp_ref!=0){
        panic("pp->pp_ref is nonzero");
        //这个页面还在使用中
    }
    pp->pp_link=page_free_list;
    page_free_list=pp;
}

//
// Decrement the reference count on a page,
// freeing it if there are no more refs.
//
void
page_decref(struct PageInfo* pp)
{
    if (--pp->pp_ref == 0)
        page_free(pp);
}

// Given 'pgdir', a pointer to a page directory, pgdir_walk returns
// a pointer to the page table entry (PTE) for linear address 'va'.
// This requires walking the two-level page table structure.
//
// The relevant page table page might not exist yet.
// If this is true, and create == false, then pgdir_walk returns NULL.
// Otherwise, pgdir_walk allocates a new page table page with page_alloc.
//    - If the allocation fails, pgdir_walk returns NULL.
//    - Otherwise, the new page's reference count is incremented,
//  the page is cleared,
//  and pgdir_walk returns a pointer into the new page table page.
//
// Hint 1: you can turn a PageInfo * into the physical address of the
// page it refers to with page2pa() from kern/pmap.h.
//
// Hint 2: the x86 MMU checks permission bits in both the page directory
// and the page table, so it's safe to leave permissions in the page
// directory more permissive than strictly necessary.
//
// Hint 3: look at inc/mmu.h for useful macros that manipulate page
// table and page directory entries.
//
pte_t *
pgdir_walk(pde_t *pgdir, const void *va, int create)
{
    // Fill this function in
    return NULL;
}

//
// Map [va, va+size) of virtual address space to physical [pa, pa+size)
// in the page table rooted at pgdir.  Size is a multiple of PGSIZE, and
// va and pa are both page-aligned.
// Use permission bits perm|PTE_P for the entries.
//
// This function is only intended to set up the ``static'' mappings
// above UTOP. As such, it should *not* change the pp_ref field on the
// mapped pages.
//
// Hint: the TA solution uses pgdir_walk
static void
boot_map_region(pde_t *pgdir, uintptr_t va, size_t size, physaddr_t pa, int perm)
{
    // Fill this function in
}

//
// Map the physical page 'pp' at virtual address 'va'.
// The permissions (the low 12 bits) of the page table entry
// should be set to 'perm|PTE_P'.
//
// Requirements
//   - If there is already a page mapped at 'va', it should be page_remove()d.
//   - If necessary, on demand, a page table should be allocated and inserted
//     into 'pgdir'.
//   - pp->pp_ref should be incremented if the insertion succeeds.
//   - The TLB must be invalidated if a page was formerly present at 'va'.
//
// Corner-case hint: Make sure to consider what happens when the same
// pp is re-inserted at the same virtual address in the same pgdir.
// However, try not to distinguish this case in your code, as this
// frequently leads to subtle bugs; there's an elegant way to handle
// everything in one code path.
//
// RETURNS:
//   0 on success
//   -E_NO_MEM, if page table couldn't be allocated
//
// Hint: The TA solution is implemented using pgdir_walk, page_remove,
// and page2pa.
//
int
page_insert(pde_t *pgdir, struct PageInfo *pp, void *va, int perm)
{
    // Fill this function in
    return 0;
}

//
// Return the page mapped at virtual address 'va'.
// If pte_store is not zero, then we store in it the address
// of the pte for this page.  This is used by page_remove and
// can be used to verify page permissions for syscall arguments,
// but should not be used by most callers.
//
// Return NULL if there is no page mapped at va.
//
// Hint: the TA solution uses pgdir_walk and pa2page.
//
struct PageInfo *
page_lookup(pde_t *pgdir, void *va, pte_t **pte_store)
{
    // Fill this function in
    return NULL;
}

//
// Unmaps the physical page at virtual address 'va'.
// If there is no physical page at that address, silently does nothing.
//
// Details:
//   - The ref count on the physical page should decrement.
//   - The physical page should be freed if the refcount reaches 0.
//   - The pg table entry corresponding to 'va' should be set to 0.
//     (if such a PTE exists)
//   - The TLB must be invalidated if you remove an entry from
//     the page table.
//
// Hint: The TA solution is implemented using page_lookup,
//  tlb_invalidate, and page_decref.
//
void
page_remove(pde_t *pgdir, void *va)
{
    // Fill this function in
}

//
// Invalidate a TLB entry, but only if the page tables being
// edited are the ones currently in use by the processor.
//
void
tlb_invalidate(pde_t *pgdir, void *va)
{
    // Flush the entry only if we're modifying the current address space.
    // For now, there is only one address space, so always invalidate.
    invlpg(va);
}


// --------------------------------------------------------------
// Checking functions.
// --------------------------------------------------------------

//
// Check that the pages on the page_free_list are reasonable.
//
static void
check_page_free_list(bool only_low_memory)
{
    struct PageInfo *pp;
    unsigned pdx_limit = only_low_memory ? 1 : NPDENTRIES;
    int nfree_basemem = 0, nfree_extmem = 0;
    char *first_free_page;

    if (!page_free_list)
        panic("'page_free_list' is a null pointer!");

    if (only_low_memory) {
        // Move pages with lower addresses first in the free
        // list, since entry_pgdir does not map all pages.
        struct PageInfo *pp1, *pp2;
        struct PageInfo **tp[2] = { &pp1, &pp2 };
        for (pp = page_free_list; pp; pp = pp->pp_link) {
            int pagetype = PDX(page2pa(pp)) >= pdx_limit;
            *tp[pagetype] = pp;
            tp[pagetype] = &pp->pp_link;
        }
        *tp[1] = 0;
        *tp[0] = pp2;
        page_free_list = pp1;
    }

    // if there's a page that shouldn't be on the free list,
    // try to make sure it eventually causes trouble.
    for (pp = page_free_list; pp; pp = pp->pp_link)
        if (PDX(page2pa(pp)) < pdx_limit)
            memset(page2kva(pp), 0x97, 128);

    first_free_page = (char *) boot_alloc(0);
    for (pp = page_free_list; pp; pp = pp->pp_link) {
        // check that we didn't corrupt the free list itself
        assert(pp >= pages);
        assert(pp < pages + npages);
        assert(((char *) pp - (char *) pages) % sizeof(*pp) == 0);

        // check a few pages that shouldn't be on the free list
        assert(page2pa(pp) != 0);
        assert(page2pa(pp) != IOPHYSMEM);
        assert(page2pa(pp) != EXTPHYSMEM - PGSIZE);
        assert(page2pa(pp) != EXTPHYSMEM);
        assert(page2pa(pp) < EXTPHYSMEM || (char *) page2kva(pp) >= first_free_page);

        if (page2pa(pp) < EXTPHYSMEM)
            ++nfree_basemem;
        else
            ++nfree_extmem;
    }

    assert(nfree_basemem > 0);
    assert(nfree_extmem > 0);

    cprintf("check_page_free_list() succeeded!\n");
}

//
// Check the physical page allocator (page_alloc(), page_free(),
// and page_init()).
//
static void
check_page_alloc(void)
{
    struct PageInfo *pp, *pp0, *pp1, *pp2;
    int nfree;
    struct PageInfo *fl;
    char *c;
    int i;

    if (!pages)
        panic("'pages' is a null pointer!");

    // check number of free pages
    for (pp = page_free_list, nfree = 0; pp; pp = pp->pp_link)
        ++nfree;

    // should be able to allocate three pages
    pp0 = pp1 = pp2 = 0;
    assert((pp0 = page_alloc(0)));
    assert((pp1 = page_alloc(0)));
    assert((pp2 = page_alloc(0)));

    assert(pp0);
    assert(pp1 && pp1 != pp0);
    assert(pp2 && pp2 != pp1 && pp2 != pp0);
    assert(page2pa(pp0) < npages*PGSIZE);
    assert(page2pa(pp1) < npages*PGSIZE);
    assert(page2pa(pp2) < npages*PGSIZE);

    // temporarily steal the rest of the free pages
    fl = page_free_list;
    page_free_list = 0;

    // should be no free memory
    assert(!page_alloc(0));

    // free and re-allocate?
    page_free(pp0);
    page_free(pp1);
    page_free(pp2);
    pp0 = pp1 = pp2 = 0;
    assert((pp0 = page_alloc(0)));
    assert((pp1 = page_alloc(0)));
    assert((pp2 = page_alloc(0)));
    assert(pp0);
    assert(pp1 && pp1 != pp0);
    assert(pp2 && pp2 != pp1 && pp2 != pp0);
    assert(!page_alloc(0));

    // test flags
    memset(page2kva(pp0), 1, PGSIZE);
    page_free(pp0);
    assert((pp = page_alloc(ALLOC_ZERO)));
    assert(pp && pp0 == pp);
    c = page2kva(pp);
    for (i = 0; i < PGSIZE; i++)
        assert(c[i] == 0);

    // give free list back
    page_free_list = fl;

    // free the pages we took
    page_free(pp0);
    page_free(pp1);
    page_free(pp2);

    // number of free pages should be the same
    for (pp = page_free_list; pp; pp = pp->pp_link)
        --nfree;
    assert(nfree == 0);

    cprintf("check_page_alloc() succeeded!\n");
}

//
// Checks that the kernel part of virtual address space
// has been set up roughly correctly (by mem_init()).
//
// This function doesn't test every corner case,
// but it is a pretty good sanity check.
//

static void
check_kern_pgdir(void)
{
    uint32_t i, n;
    pde_t *pgdir;

    pgdir = kern_pgdir;

    // check pages array
    n = ROUNDUP(npages*sizeof(struct PageInfo), PGSIZE);
    for (i = 0; i < n; i += PGSIZE)
        assert(check_va2pa(pgdir, UPAGES + i) == PADDR(pages) + i);


    // check phys mem
    for (i = 0; i < npages * PGSIZE; i += PGSIZE)
        assert(check_va2pa(pgdir, KERNBASE + i) == i);

    // check kernel stack
    for (i = 0; i < KSTKSIZE; i += PGSIZE)
        assert(check_va2pa(pgdir, KSTACKTOP - KSTKSIZE + i) == PADDR(bootstack) + i);
    assert(check_va2pa(pgdir, KSTACKTOP - PTSIZE) == ~0);

    // check PDE permissions
    for (i = 0; i < NPDENTRIES; i++) {
        switch (i) {
        case PDX(UVPT):
        case PDX(KSTACKTOP-1):
        case PDX(UPAGES):
            assert(pgdir[i] & PTE_P);
            break;
        default:
            if (i >= PDX(KERNBASE)) {
                assert(pgdir[i] & PTE_P);
                assert(pgdir[i] & PTE_W);
            } else
                assert(pgdir[i] == 0);
            break;
        }
    }
    cprintf("check_kern_pgdir() succeeded!\n");
}

// This function returns the physical address of the page containing 'va',
// defined by the page directory 'pgdir'.  The hardware normally performs
// this functionality for us!  We define our own version to help check
// the check_kern_pgdir() function; it shouldn't be used elsewhere.

static physaddr_t
check_va2pa(pde_t *pgdir, uintptr_t va)
{
    pte_t *p;

    pgdir = &pgdir[PDX(va)];
    if (!(*pgdir & PTE_P))
        return ~0;
    p = (pte_t*) KADDR(PTE_ADDR(*pgdir));
    if (!(p[PTX(va)] & PTE_P))
        return ~0;
    return PTE_ADDR(p[PTX(va)]);
}


// check page_insert, page_remove, &c
static void
check_page(void)
{
    struct PageInfo *pp, *pp0, *pp1, *pp2;
    struct PageInfo *fl;
    pte_t *ptep, *ptep1;
    void *va;
    int i;
    extern pde_t entry_pgdir[];

    // should be able to allocate three pages
    pp0 = pp1 = pp2 = 0;
    assert((pp0 = page_alloc(0)));
    assert((pp1 = page_alloc(0)));
    assert((pp2 = page_alloc(0)));

    assert(pp0);
    assert(pp1 && pp1 != pp0);
    assert(pp2 && pp2 != pp1 && pp2 != pp0);

    // temporarily steal the rest of the free pages
    fl = page_free_list;
    page_free_list = 0;

    // should be no free memory
    assert(!page_alloc(0));

    // there is no page allocated at address 0
    assert(page_lookup(kern_pgdir, (void *) 0x0, &ptep) == NULL);

    // there is no free memory, so we can't allocate a page table
    assert(page_insert(kern_pgdir, pp1, 0x0, PTE_W) < 0);

    // free pp0 and try again: pp0 should be used for page table
    page_free(pp0);
    assert(page_insert(kern_pgdir, pp1, 0x0, PTE_W) == 0);
    assert(PTE_ADDR(kern_pgdir[0]) == page2pa(pp0));
    assert(check_va2pa(kern_pgdir, 0x0) == page2pa(pp1));
    assert(pp1->pp_ref == 1);
    assert(pp0->pp_ref == 1);

    // should be able to map pp2 at PGSIZE because pp0 is already allocated for page table
    assert(page_insert(kern_pgdir, pp2, (void*) PGSIZE, PTE_W) == 0);
    assert(check_va2pa(kern_pgdir, PGSIZE) == page2pa(pp2));
    assert(pp2->pp_ref == 1);

    // should be no free memory
    assert(!page_alloc(0));

    // should be able to map pp2 at PGSIZE because it's already there
    assert(page_insert(kern_pgdir, pp2, (void*) PGSIZE, PTE_W) == 0);
    assert(check_va2pa(kern_pgdir, PGSIZE) == page2pa(pp2));
    assert(pp2->pp_ref == 1);

    // pp2 should NOT be on the free list
    // could happen in ref counts are handled sloppily in page_insert
    assert(!page_alloc(0));

    // check that pgdir_walk returns a pointer to the pte
    ptep = (pte_t *) KADDR(PTE_ADDR(kern_pgdir[PDX(PGSIZE)]));
    assert(pgdir_walk(kern_pgdir, (void*)PGSIZE, 0) == ptep+PTX(PGSIZE));

    // should be able to change permissions too.
    assert(page_insert(kern_pgdir, pp2, (void*) PGSIZE, PTE_W|PTE_U) == 0);
    assert(check_va2pa(kern_pgdir, PGSIZE) == page2pa(pp2));
    assert(pp2->pp_ref == 1);
    assert(*pgdir_walk(kern_pgdir, (void*) PGSIZE, 0) & PTE_U);
    assert(kern_pgdir[0] & PTE_U);

    // should be able to remap with fewer permissions
    assert(page_insert(kern_pgdir, pp2, (void*) PGSIZE, PTE_W) == 0);
    assert(*pgdir_walk(kern_pgdir, (void*) PGSIZE, 0) & PTE_W);
    assert(!(*pgdir_walk(kern_pgdir, (void*) PGSIZE, 0) & PTE_U));

    // should not be able to map at PTSIZE because need free page for page table
    assert(page_insert(kern_pgdir, pp0, (void*) PTSIZE, PTE_W) < 0);

    // insert pp1 at PGSIZE (replacing pp2)
    assert(page_insert(kern_pgdir, pp1, (void*) PGSIZE, PTE_W) == 0);
    assert(!(*pgdir_walk(kern_pgdir, (void*) PGSIZE, 0) & PTE_U));

    // should have pp1 at both 0 and PGSIZE, pp2 nowhere, ...
    assert(check_va2pa(kern_pgdir, 0) == page2pa(pp1));
    assert(check_va2pa(kern_pgdir, PGSIZE) == page2pa(pp1));
    // ... and ref counts should reflect this
    assert(pp1->pp_ref == 2);
    assert(pp2->pp_ref == 0);

    // pp2 should be returned by page_alloc
    assert((pp = page_alloc(0)) && pp == pp2);

    // unmapping pp1 at 0 should keep pp1 at PGSIZE
    page_remove(kern_pgdir, 0x0);
    assert(check_va2pa(kern_pgdir, 0x0) == ~0);
    assert(check_va2pa(kern_pgdir, PGSIZE) == page2pa(pp1));
    assert(pp1->pp_ref == 1);
    assert(pp2->pp_ref == 0);

    // test re-inserting pp1 at PGSIZE
    assert(page_insert(kern_pgdir, pp1, (void*) PGSIZE, 0) == 0);
    assert(pp1->pp_ref);
    assert(pp1->pp_link == NULL);

    // unmapping pp1 at PGSIZE should free it
    page_remove(kern_pgdir, (void*) PGSIZE);
    assert(check_va2pa(kern_pgdir, 0x0) == ~0);
    assert(check_va2pa(kern_pgdir, PGSIZE) == ~0);
    assert(pp1->pp_ref == 0);
    assert(pp2->pp_ref == 0);

    // so it should be returned by page_alloc
    assert((pp = page_alloc(0)) && pp == pp1);

    // should be no free memory
    assert(!page_alloc(0));

    // forcibly take pp0 back
    assert(PTE_ADDR(kern_pgdir[0]) == page2pa(pp0));
    kern_pgdir[0] = 0;
    assert(pp0->pp_ref == 1);
    pp0->pp_ref = 0;

    // check pointer arithmetic in pgdir_walk
    page_free(pp0);
    va = (void*)(PGSIZE * NPDENTRIES + PGSIZE);
    ptep = pgdir_walk(kern_pgdir, va, 1);
    ptep1 = (pte_t *) KADDR(PTE_ADDR(kern_pgdir[PDX(va)]));
    assert(ptep == ptep1 + PTX(va));
    kern_pgdir[PDX(va)] = 0;
    pp0->pp_ref = 0;

    // check that new page tables get cleared
    memset(page2kva(pp0), 0xFF, PGSIZE);
    page_free(pp0);
    pgdir_walk(kern_pgdir, 0x0, 1);
    ptep = (pte_t *) page2kva(pp0);
    for(i=0; i<NPTENTRIES; i++)
        assert((ptep[i] & PTE_P) == 0);
    kern_pgdir[0] = 0;
    pp0->pp_ref = 0;

    // give free list back
    page_free_list = fl;

    // free the pages we took
    page_free(pp0);
    page_free(pp1);
    page_free(pp2);

    cprintf("check_page() succeeded!\n");
}

// check page_insert, page_remove, &c, with an installed kern_pgdir
static void
check_page_installed_pgdir(void)
{
    struct PageInfo *pp, *pp0, *pp1, *pp2;
    struct PageInfo *fl;
    pte_t *ptep, *ptep1;
    uintptr_t va;
    int i;

    // check that we can read and write installed pages
    pp1 = pp2 = 0;
    assert((pp0 = page_alloc(0)));
    assert((pp1 = page_alloc(0)));
    assert((pp2 = page_alloc(0)));
    page_free(pp0);
    memset(page2kva(pp1), 1, PGSIZE);
    memset(page2kva(pp2), 2, PGSIZE);
    page_insert(kern_pgdir, pp1, (void*) PGSIZE, PTE_W);
    assert(pp1->pp_ref == 1);
    assert(*(uint32_t *)PGSIZE == 0x01010101U);
    page_insert(kern_pgdir, pp2, (void*) PGSIZE, PTE_W);
    assert(*(uint32_t *)PGSIZE == 0x02020202U);
    assert(pp2->pp_ref == 1);
    assert(pp1->pp_ref == 0);
    *(uint32_t *)PGSIZE = 0x03030303U;
    assert(*(uint32_t *)page2kva(pp2) == 0x03030303U);
    page_remove(kern_pgdir, (void*) PGSIZE);
    assert(pp2->pp_ref == 0);

    // forcibly take pp0 back
    assert(PTE_ADDR(kern_pgdir[0]) == page2pa(pp0));
    kern_pgdir[0] = 0;
    assert(pp0->pp_ref == 1);
    pp0->pp_ref = 0;

    // free the pages we took
    page_free(pp0);

    cprintf("check_page_installed_pgdir() succeeded!\n");
}