enhanced backtrace output

[mit-jos.git] / kern / 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()
static physaddr_t maxpa;        // Maximum physical address
size_t npage;                   // Amount of physical memory (in pages)
static size_t basemem;          // Amount of base memory (in bytes)
static size_t extmem;           // Amount of extended memory (in bytes)

// These variables are set in i386_vm_init()
pde_t* boot_pgdir;              // Virtual address of boot time page directory
physaddr_t boot_cr3;            // Physical address of boot time page directory
static char* boot_freemem;      // Pointer to next byte of free mem

struct Page* pages;             // Virtual address of physical page array
static struct Page_list page_free_list; // Free list of physical pages

// Global descriptor table.
//
// The kernel and user segments are identical (except for the DPL).
// To load the SS register, the CPL must equal the DPL.  Thus,
// we must duplicate the segments for the user and the kernel.
//
struct Segdesc gdt[] =
{
        // 0x0 - unused (always faults -- for trapping NULL far pointers)
        SEG_NULL,

        // 0x8 - kernel code segment
        [GD_KT >> 3] = SEG(STA_X | STA_R, 0x0, 0xffffffff, 0),

        // 0x10 - kernel data segment
        [GD_KD >> 3] = SEG(STA_W, 0x0, 0xffffffff, 0),

        // 0x18 - user code segment
        [GD_UT >> 3] = SEG(STA_X | STA_R, 0x0, 0xffffffff, 3),

        // 0x20 - user data segment
        [GD_UD >> 3] = SEG(STA_W, 0x0, 0xffffffff, 3),

        // 0x28 - tss, initialized in idt_init()
        [GD_TSS >> 3] = SEG_NULL
};

struct Pseudodesc gdt_pd = {
        sizeof(gdt) - 1, (unsigned long) gdt
};

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

void
i386_detect_memory(void)
{
        // CMOS tells us how many kilobytes there are
        basemem = ROUNDDOWN(nvram_read(NVRAM_BASELO)*1024, PGSIZE);
        extmem = ROUNDDOWN(nvram_read(NVRAM_EXTLO)*1024, PGSIZE);

        // Calculate the maximum physical address based on whether
        // or not there is any extended memory.  See comment in <inc/mmu.h>.
        if (extmem)
                maxpa = EXTPHYSMEM + extmem;
        else
                maxpa = basemem;

        npage = maxpa / PGSIZE;

        cprintf("Physical memory: %dK available, ", (int)(maxpa/1024));
        cprintf("base = %dK, extended = %dK\n", (int)(basemem/1024), (int)(extmem/1024));
}

// --------------------------------------------------------------
// Set up initial memory mappings and turn on MMU.
// --------------------------------------------------------------

static void check_boot_pgdir(void);
static void check_page_alloc();
static void page_check(void);
static void boot_map_segment(pde_t *pgdir, uintptr_t la, size_t size, physaddr_t pa, int perm);

//
// A simple physical memory allocator, used only a few times
// in the process of setting up the virtual memory system.
// page_alloc() is the real allocator.
//
// Allocate n bytes of physical memory aligned on an 
// align-byte boundary.  Align must be a power of two.
// Return kernel virtual address.  Returned memory is uninitialized.
//
// If we're out of memory, boot_alloc should panic.
// This function may ONLY be used during initialization,
// before the page_free_list has been set up.
// 
static void*
boot_alloc(uint32_t n, uint32_t align)
{
        extern char end[];
        void *v;

        // Initialize boot_freemem 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 -
        // i.e., the first virtual address that the linker
        // did _not_ assign to any kernel code or global variables.
        if (boot_freemem == 0)
                boot_freemem = end;

        // LAB 2: Your code here:
        //      Step 1: round boot_freemem up to be aligned properly
        //      Step 2: save current value of boot_freemem as allocated chunk
        //      Step 3: increase boot_freemem to record allocation
        //      Step 4: return allocated chunk

        // if align is zero, I just bypass the test
        // i.e. I think zero as a power of two, which you may not agree with.
        if (align) {
                if (align & (align - 1))
                        panic("boot_alloc : align is not a power of two.\n");
                boot_freemem = ROUNDUP(boot_freemem, align);
        }

        v = (void *)boot_freemem;
        boot_freemem += n;

        if ((unsigned int)boot_freemem < (unsigned int)end)
                panic("boot_alloc: out of memory.\n");
        else
                return v;
}

// Set up a two-level page table:
//    boot_pgdir is its linear (virtual) address of the root
//    boot_cr3 is the physical adresss of the root
// Then turn on paging.  Then effectively turn off segmentation.
// (i.e., the segment base addrs are set to zero).
// 
// This function only sets up the kernel part of the address space
// (ie. addresses >= UTOP).  The user part of the address space
// will be setup later.
//
// From UTOP to ULIM, the user is allowed to read but not write.
// Above ULIM the user cannot read (or write). 
void
i386_vm_init(void)
{
        pde_t* pgdir;
        uint32_t cr0;
        size_t n;

        //////////////////////////////////////////////////////////////////////
        // create initial page directory.
        pgdir = boot_alloc(PGSIZE, PGSIZE);
        memset(pgdir, 0, PGSIZE);
        boot_pgdir = pgdir;
        boot_cr3 = PADDR(pgdir);

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

        // Permissions: kernel RW, user NONE
        pgdir[PDX(VPT)] = PADDR(pgdir)|PTE_W|PTE_P;

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

        //////////////////////////////////////////////////////////////////////
        // Make 'pages' point to an array of size 'npage' of 'struct Page'.
        // The kernel uses this structure to keep track of physical pages;
        // 'npage' equals the number of physical pages in memory.  User-level
        // programs will get read-only access to the array as well.
        // You must allocate the array yourself.
        // Your code goes here: 
        n = ROUNDUP((sizeof(struct Page) * npage), PGSIZE);
        pages = boot_alloc(n, PGSIZE);

        //////////////////////////////////////////////////////////////////////
        // 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_segment or page_insert
        page_init();

        check_page_alloc();

        page_check();

        //////////////////////////////////////////////////////////////////////
        // Now we set up virtual memory 
        
        //////////////////////////////////////////////////////////////////////
        // Map 'pages' read-only by the user at linear address UPAGES
        // (ie. perm = PTE_U | PTE_P)
        // Permissions:
        //    - pages -- kernel RW, user NONE
        //    - the read-only version mapped at UPAGES -- kernel R, user R
        // Your code goes here:



        //////////////////////////////////////////////////////////////////////
        // Map the kernel stack (symbol name "bootstack").  The complete VA
        // range of the stack, [KSTACKTOP-PTSIZE, KSTACKTOP), breaks into two
        // pieces:
        //     * [KSTACKTOP-KSTKSIZE, KSTACKTOP) -- backed by physical memory
        //     * [KSTACKTOP-PTSIZE, KSTACKTOP-KSTKSIZE) -- not backed => faults
        //     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 amapping anyway.
        // Permissions: kernel RW, user NONE
        // Your code goes here: 

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

        //////////////////////////////////////////////////////////////////////
        // On x86, segmentation maps a VA to a LA (linear addr) and
        // paging maps the LA to a PA.  I.e. VA => LA => PA.  If paging is
        // turned off the LA is used as the PA.  Note: there is no way to
        // turn off segmentation.  The closest thing is to set the base
        // address to 0, so the VA => LA mapping is the identity.

        // Current mapping: VA KERNBASE+x => PA x.
        //     (segmentation base=-KERNBASE and paging is off)

        // From here on down we must maintain this VA KERNBASE + x => PA x
        // mapping, even though we are turning on paging and reconfiguring
        // segmentation.

        // Map VA 0:4MB same as VA KERNBASE, i.e. to PA 0:4MB.
        // (Limits our kernel to <4MB)
        pgdir[0] = pgdir[PDX(KERNBASE)];

        // Install page table.
        lcr3(boot_cr3);

        // Turn on paging.
        cr0 = rcr0();
        cr0 |= CR0_PE|CR0_PG|CR0_AM|CR0_WP|CR0_NE|CR0_TS|CR0_EM|CR0_MP;
        cr0 &= ~(CR0_TS|CR0_EM);
        lcr0(cr0);

        // Current mapping: KERNBASE+x => x => x.
        // (x < 4MB so uses paging pgdir[0])

        // Reload all segment registers.
        asm volatile("lgdt gdt_pd");
        asm volatile("movw %%ax,%%gs" :: "a" (GD_UD|3));
        asm volatile("movw %%ax,%%fs" :: "a" (GD_UD|3));
        asm volatile("movw %%ax,%%es" :: "a" (GD_KD));
        asm volatile("movw %%ax,%%ds" :: "a" (GD_KD));
        asm volatile("movw %%ax,%%ss" :: "a" (GD_KD));
        asm volatile("ljmp %0,$1f\n 1:\n" :: "i" (GD_KT));  // reload cs
        asm volatile("lldt %%ax" :: "a" (0));

        // Final mapping: KERNBASE+x => KERNBASE+x => x.

        // This mapping was only used after paging was turned on but
        // before the segment registers were reloaded.
        pgdir[0] = 0;

        // Flush the TLB for good measure, to kill the pgdir[0] mapping.
        lcr3(boot_cr3);
}

//
// Check the physical page allocator (page_alloc(), page_free(),
// and page_init()).
//
static void
check_page_alloc()
{
        struct Page *pp, *pp0, *pp1, *pp2;
        struct Page_list fl;
        
        // if there's a page that shouldn't be on
        // the free list, try to make sure it
        // eventually causes trouble.
        LIST_FOREACH(pp0, &page_free_list, pp_link)
                memset(page2kva(pp0), 0x97, 128);

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

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

        // temporarily steal the rest of the free pages
        fl = page_free_list;
        LIST_INIT(&page_free_list);

        // should be no free memory
        assert(page_alloc(&pp) == -E_NO_MEM);

        // free and re-allocate?
        page_free(pp0);
        page_free(pp1);
        page_free(pp2);

        pp0 = pp1 = pp2 = 0;
        assert(page_alloc(&pp0) == 0);
        assert(page_alloc(&pp1) == 0);
        assert(page_alloc(&pp2) == 0);
        assert(pp0);
        assert(pp1 && pp1 != pp0);
        assert(pp2 && pp2 != pp1 && pp2 != pp0);
        assert(page_alloc(&pp) == -E_NO_MEM);

        // 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_alloc() succeeded!\n");
}

//
// Checks that the kernel part of virtual address space
// has been setup roughly correctly(by i386_vm_init()).
//
// This function doesn't test every corner case,
// in fact it doesn't test the permission bits at all,
// but it is a pretty good sanity check. 
//
static physaddr_t check_va2pa(pde_t *pgdir, uintptr_t va);

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

        pgdir = boot_pgdir;

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

        // check phys mem
        for (i = 0; i < npage; 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);

        // check for zero/non-zero in PDEs
        for (i = 0; i < NPDENTRIES; i++) {
                switch (i) {
                case PDX(VPT):
                case PDX(UVPT):
                case PDX(KSTACKTOP-1):
                case PDX(UPAGES):
                        assert(pgdir[i]);
                        break;
                default:
                        if (i >= PDX(KERNBASE))
                                assert(pgdir[i]);
                        else
                                assert(pgdir[i] == 0);
                        break;
                }
        }
        cprintf("check_boot_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_boot_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)]);
}
                
// --------------------------------------------------------------
// Tracking of physical pages.
// The 'pages' array has one 'struct Page' 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 point, ONLY use the functions below
// to allocate and deallocate physical memory via the page_free_list,
// and NEVER use boot_alloc()
//
void
page_init(void)
{
        // The example code here marks all pages as free.
        // However this is not truly the case.  What memory is free?
        //  1) Mark 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) Mark the rest of base memory as free.
        //  3) Then comes the IO hole [IOPHYSMEM, EXTPHYSMEM).
        //     Mark it as in use so that it can never be allocated.      
        //  4) Then extended memory [EXTPHYSMEM, ...).
        //     Some of it is in use, some is free. Where is the kernel?
        //     Which pages are used for page tables and other data structures?
        //
        // Change the code to reflect this.
        struct Page *ppage;
        unsigned int i;
        extern char _start[];

        LIST_INIT(&page_free_list);
        for (i = 0; i < npage; i++) {
                pages[i].pp_ref = 0;
                LIST_INSERT_HEAD(&page_free_list, &pages[i], pp_link);
        }

        // mark page 0 as in use
        LIST_REMOVE(&pages[0], pp_link);

        // IO hole
        for (i = IOPHYSMEM; i < EXTPHYSMEM; i += PGSIZE) {
                ppage = pa2page(i);
                LIST_REMOVE(ppage, pp_link);
        }

        // reserve the kernel image and data structures allocated
        for (i = (unsigned int)_start; i < (unsigned int)boot_freemem; i += PGSIZE) {
                ppage = pa2page(PADDR(i));
                LIST_REMOVE(ppage, pp_link);
        }
}

//
// Initialize a Page structure.
// The result has null links and 0 refcount.
// Note that the corresponding physical page is NOT initialized!
//
static void
page_initpp(struct Page *pp)
{
        memset(pp, 0, sizeof(*pp));
}

//
// Allocates a physical page.
// Does NOT set the contents of the physical page to zero -
// the caller must do that if necessary.
//
// *pp_store -- is set to point to the Page struct of the newly allocated
// page
//
// RETURNS 
//   0 -- on success
//   -E_NO_MEM -- otherwise 
//
// Hint: use LIST_FIRST, LIST_REMOVE, and page_initpp
// Hint: pp_ref should not be incremented 
int
page_alloc(struct Page **pp_store)
{
        // Fill this function in
        struct Page *page_avail;

        if (!LIST_EMPTY(&page_free_list)) {
                page_avail = LIST_FIRST(&page_free_list);
                LIST_REMOVE(page_avail, pp_link);
                page_initpp(page_avail);

                *pp_store = page_avail;
                return 0;
        }
        return -E_NO_MEM;
}

//
// Return a page to the free list.
// (This function should only be called when pp->pp_ref reaches 0.)
//
void
page_free(struct Page *pp)
{
        // Fill this function in
        if (pp->pp_ref)
                panic("page_free: pp->pp_ref is not zero.\n");

        LIST_INSERT_HEAD(&page_free_list, pp, pp_link);
}

//
// Decrement the reference count on a page,
// freeing it if there are no more refs.
//
void
page_decref(struct Page* 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.
//
// If the relevant page table doesn't exist in the page directory, then:
//    - If create == 0, pgdir_walk returns NULL.
//    - Otherwise, pgdir_walk tries to allocate a new page table
//      with page_alloc.  If this fails, pgdir_walk returns NULL.
//    - pgdir_walk sets pp_ref to 1 for the new page table.
//    - Finally, pgdir_walk returns a pointer into the new page table.
//
// Hint: you can turn a Page * into the physical address of the
// page it refers to with page2pa() from kern/pmap.h.
pte_t *
pgdir_walk(pde_t *pgdir, const void *va, int create)
{
        // Fill this function in
        return NULL;
}

//
// 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'.
//
// Details
//   - If there is already a page mapped at 'va', it is page_remove()d.
//   - If necessary, on demand, allocates a page table and inserts it 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'.
//
// 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 Page *pp, void *va, int perm) 
{
        // Fill this function in
        return 0;
}

//
// Map [la, la+size) of linear address space to physical [pa, pa+size)
// in the page table rooted at pgdir.  Size is a multiple of PGSIZE.
// 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_segment(pde_t *pgdir, uintptr_t la, size_t size, physaddr_t pa, int perm)
{
        // Fill this function in
}

//
// 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
// but should not be used by other callers.
//
// Return 0 if there is no page mapped at va.
//
// Hint: the TA solution uses pgdir_walk and pa2page.
//
struct Page *
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 pg dir/pg 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);
}

// check page_insert, page_remove, &c
static void
page_check(void)
{
        struct Page *pp, *pp0, *pp1, *pp2;
        struct Page_list fl;
        pte_t *ptep, *ptep1;
        void *va;
        int i;

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

        // should be no free memory
        assert(page_alloc(&pp) == -E_NO_MEM);

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

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

        // free pp0 and try again: pp0 should be used for page table
        page_free(pp0);
        assert(page_insert(boot_pgdir, pp1, 0x0, 0) == 0);
        assert(PTE_ADDR(boot_pgdir[0]) == page2pa(pp0));
        assert(check_va2pa(boot_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(boot_pgdir, pp2, (void*) PGSIZE, 0) == 0);
        assert(check_va2pa(boot_pgdir, PGSIZE) == page2pa(pp2));
        assert(pp2->pp_ref == 1);

        // should be no free memory
        assert(page_alloc(&pp) == -E_NO_MEM);

        // should be able to map pp2 at PGSIZE because it's already there
        assert(page_insert(boot_pgdir, pp2, (void*) PGSIZE, 0) == 0);
        assert(check_va2pa(boot_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(&pp) == -E_NO_MEM);

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

        // should be able to change permissions too.
        assert(page_insert(boot_pgdir, pp2, (void*) PGSIZE, PTE_U) == 0);
        assert(check_va2pa(boot_pgdir, PGSIZE) == page2pa(pp2));
        assert(pp2->pp_ref == 1);
        assert(*pgdir_walk(boot_pgdir, (void*) PGSIZE, 0) & PTE_U);
        
        // should not be able to map at PTSIZE because need free page for page table
        assert(page_insert(boot_pgdir, pp0, (void*) PTSIZE, 0) < 0);

        // insert pp1 at PGSIZE (replacing pp2)
        assert(page_insert(boot_pgdir, pp1, (void*) PGSIZE, 0) == 0);

        // should have pp1 at both 0 and PGSIZE, pp2 nowhere, ...
        assert(check_va2pa(boot_pgdir, 0) == page2pa(pp1));
        assert(check_va2pa(boot_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(page_alloc(&pp) == 0 && pp == pp2);

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

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

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

        // should be no free memory
        assert(page_alloc(&pp) == -E_NO_MEM);
        
#if 0
        // should be able to page_insert to change a page
        // and see the new data immediately.
        memset(page2kva(pp1), 1, PGSIZE);
        memset(page2kva(pp2), 2, PGSIZE);
        page_insert(boot_pgdir, pp1, 0x0, 0);
        assert(pp1->pp_ref == 1);
        assert(*(int*)0 == 0x01010101);
        page_insert(boot_pgdir, pp2, 0x0, 0);
        assert(*(int*)0 == 0x02020202);
        assert(pp2->pp_ref == 1);
        assert(pp1->pp_ref == 0);
        page_remove(boot_pgdir, 0x0);
        assert(pp2->pp_ref == 0);
#endif

        // forcibly take pp0 back
        assert(PTE_ADDR(boot_pgdir[0]) == page2pa(pp0));
        boot_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(boot_pgdir, va, 1);
        ptep1 = KADDR(PTE_ADDR(boot_pgdir[PDX(va)]));
        assert(ptep == ptep1 + PTX(va));
        boot_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(boot_pgdir, 0x0, 1);
        ptep = page2kva(pp0);
        for(i=0; i<NPTENTRIES; i++)
                assert((ptep[i] & PTE_P) == 0);
        boot_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("page_check() succeeded!\n");
}