sortix--sortix/kernel/x86-family/memorymanagement.cpp

/*******************************************************************************

    Copyright(C) Jonas 'Sortie' Termansen 2011, 2012, 2014.

    This file is part of Sortix.

    Sortix is free software: you can redistribute it and/or modify it under the
    terms of the GNU General Public License as published by the Free Software
    Foundation, either version 3 of the License, or (at your option) any later
    version.

    Sortix is distributed in the hope that it will be useful, but WITHOUT ANY
    WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
    FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
    details.

    You should have received a copy of the GNU General Public License along with
    Sortix. If not, see <http://www.gnu.org/licenses/>.

    x86-family/memorymanagement.cpp
    Handles memory for the x86 family of architectures.

*******************************************************************************/

#include <assert.h>
#include <errno.h>
#include <string.h>

#include <sortix/mman.h>

#include <sortix/kernel/kernel.h>
#include <sortix/kernel/kthread.h>
#include <sortix/kernel/memorymanagement.h>
#include <sortix/kernel/panic.h>
#include <sortix/kernel/pat.h>
#include <sortix/kernel/syscall.h>

#include "multiboot.h"
#include "memorymanagement.h"
#include "msr.h"

namespace Sortix {

extern size_t end;

} // namespace Sortix

namespace Sortix {
namespace Page {

void InitPushRegion(addr_t position, size_t length);
size_t pagesnotonstack;
size_t stackused;
size_t stackreserved;
size_t stacklength;
size_t totalmem;
size_t page_usage_counts[PAGE_USAGE_NUM_KINDS];
kthread_mutex_t pagelock;

} // namespace Page
} // namespace Sortix

namespace Sortix {
namespace Memory {

void InitCPU();
void AllocateKernelPMLs();
int SysMemStat(size_t* memused, size_t* memtotal);
addr_t PAT2PMLFlags[PAT_NUM];

void InitCPU(multiboot_info_t* bootinfo)
{
	const size_t MAXKERNELEND = 0x400000UL; /* 4 MiB */
	addr_t kernelend = Page::AlignUp((addr_t) &end);
	if ( MAXKERNELEND < kernelend )
	{
		Log::PrintF("Warning: The kernel is too big! It ends at 0x%zx, "
		            "but the highest ending address supported is 0x%zx. "
		            "The system may not boot correctly.\n", kernelend,
		            MAXKERNELEND);
	}

	Page::stackreserved = 0;
	Page::pagesnotonstack = 0;
	Page::totalmem = 0;
	Page::pagelock = KTHREAD_MUTEX_INITIALIZER;

	if ( !( bootinfo->flags & MULTIBOOT_INFO_MEM_MAP ) )
		Panic("memorymanagement.cpp: The memory map flag was't set in "
		      "the multiboot structure. Are your bootloader multiboot "
		      "specification compliant?");

	// If supported, setup the Page Attribute Table feature that allows
	// us to control the memory type (caching) of memory more precisely.
	if ( IsPATSupported() )
	{
		InitializePAT();
		for ( addr_t i = 0; i < PAT_NUM; i++ )
			PAT2PMLFlags[i] = EncodePATAsPMLFlag(i);
	}
	// Otherwise, reroute all requests to the backwards compatible
	// scheme. TODO: Not all early 32-bit x86 CPUs supports these
	// values, so we need yet another fallback.
	else
	{
		PAT2PMLFlags[PAT_UC] = PML_WRTHROUGH | PML_NOCACHE;
		PAT2PMLFlags[PAT_WC] = PML_WRTHROUGH | PML_NOCACHE; // Approx.
		PAT2PMLFlags[2] = 0; // No such flag.
		PAT2PMLFlags[3] = 0; // No such flag.
		PAT2PMLFlags[PAT_WT] = PML_WRTHROUGH;
		PAT2PMLFlags[PAT_WP] = PML_WRTHROUGH; // Approx.
		PAT2PMLFlags[PAT_WB] = 0;
		PAT2PMLFlags[PAT_UCM] = PML_NOCACHE;
	}

	// Initialize CPU-specific things.
	InitCPU();

	typedef const multiboot_memory_map_t* mmap_t;

	// Loop over every detected memory region.
	for (
	     mmap_t mmap = (mmap_t) (addr_t) bootinfo->mmap_addr;
	     (addr_t) mmap < bootinfo->mmap_addr + bootinfo->mmap_length;
	     mmap = (mmap_t) ((addr_t) mmap + mmap->size + sizeof(mmap->size))
	    )
	{
		// Check that we can use this kind of RAM.
		if ( mmap->type != 1 )
			continue;

		// The kernel's code may split this memory area into multiple pieces.
		addr_t base = (addr_t) mmap->addr;
		size_t length = Page::AlignDown(mmap->len);

#if defined(__i386__)
		// Figure out if the memory area is addressable (are our pointers big enough?)
		if ( 0xFFFFFFFFULL < mmap->addr )
			continue;
		if ( 0xFFFFFFFFULL < mmap->addr + mmap->len )
			length = 0x100000000ULL - mmap->addr;
#endif

		// Count the amount of usable RAM (even if reserved for kernel).
		Page::totalmem += length;

		// Give all the physical memory to the physical memory allocator
		// but make sure not to give it things we already use.
		addr_t regionstart = base;
		addr_t regionend = base + length;
		addr_t processed = regionstart;
		while ( processed < regionend )
		{
			addr_t lowest = processed;
			addr_t highest = regionend;

			// Don't allocate the kernel.
			if ( lowest < kernelend )
			{
				processed = kernelend;
				continue;
			}

			// Don't give any of our modules to the physical page
			// allocator, we'll need them.
			bool continuing = false;
			uint32_t* modules = (uint32_t*) (addr_t) bootinfo->mods_addr;
			for ( uint32_t i = 0; i < bootinfo->mods_count; i++ )
			{
				size_t modsize = (size_t) (modules[2*i+1] - modules[2*i+0]);
				addr_t modstart = (addr_t) modules[2*i+0];
				addr_t modend = modstart + modsize;
				if ( modstart <= processed && processed < modend )
				{
					processed = modend;
					continuing = true;
					break;
				}
				if ( lowest <= modstart && modstart < highest )
					highest = modstart;
			}

			if ( continuing )
				continue;

			if ( highest <= lowest )
				break;

			// Now that we have a continious area not used by anything,
			// let's forward it to the physical page allocator.
			lowest = Page::AlignUp(lowest);
			highest = Page::AlignUp(highest);
			size_t size = highest - lowest;
			Page::InitPushRegion(lowest, size);
			processed = highest;
		}
	}

	// If the physical allocator couldn't handle the vast amount of
	// physical pages, it may decide to drop some. This shouldn't happen
	// until the pebibyte era of RAM.
	if ( 0 < Page::pagesnotonstack )
		Log::PrintF("%zu bytes of RAM aren't used due to technical "
		            "restrictions.\n", (size_t) (Page::pagesnotonstack * 0x1000UL));

	Memory::Unmap(0x0); // Remove NULL.

	// Finish allocating the top level PMLs for the kernels use.
	AllocateKernelPMLs();
}

void Statistics(size_t* amountused, size_t* totalmem)
{
	size_t memfree = (Page::stackused - Page::stackreserved) << 12UL;
	size_t memused = Page::totalmem - memfree;
	if ( amountused )
		*amountused = memused;
	if ( totalmem )
		*totalmem = Page::totalmem;
}

// Prepare the non-forkable kernel PMLs such that forking the kernel
// address space will always keep the kernel mapped.
void AllocateKernelPMLs()
{
	const addr_t flags = PML_PRESENT | PML_WRITABLE;

	PML* const pml = PMLS[TOPPMLLEVEL];

	size_t start = ENTRIES / 2;
	size_t end = ENTRIES;

	for ( size_t i = start; i < end; i++ )
	{
		if ( pml->entry[i] & PML_PRESENT )
			continue;

		addr_t page = Page::Get(PAGE_USAGE_PAGING_OVERHEAD);
		if ( !page )
			Panic("out of memory allocating boot PMLs");

		pml->entry[i] = page | flags;

		// Invalidate the new PML and reset it to zeroes.
		addr_t pmladdr = (addr_t) (PMLS[TOPPMLLEVEL-1] + i);
		InvalidatePage(pmladdr);
		memset((void*) pmladdr, 0, sizeof(PML));
	}
}

} // namespace Memory
} // namespace Sortix

namespace Sortix {
namespace Page {

void PageUsageRegisterUse(addr_t where, enum page_usage usage)
{
	if ( PAGE_USAGE_NUM_KINDS <= usage )
		return;
	(void) where;
	page_usage_counts[usage]++;
}

void PageUsageRegisterFree(addr_t where, enum page_usage usage)
{
	if ( PAGE_USAGE_NUM_KINDS <= usage )
		return;
	(void) where;
	assert(page_usage_counts[usage] != 0);
	page_usage_counts[usage]--;
}

void ExtendStack()
{
	// This call will always succeed, if it didn't, then the stack
	// wouldn't be full, and thus this function won't be called.
	addr_t page = GetUnlocked(PAGE_USAGE_PHYSICAL);

	// This call will also succeed, since there are plenty of physical
	// pages available and it might need some.
	addr_t virt = (addr_t) (STACK + stacklength);
	if ( !Memory::Map(page, virt, PROT_KREAD | PROT_KWRITE) )
		Panic("Unable to extend page stack, which should have worked");

	// TODO: This may not be needed during the boot process!
	//Memory::InvalidatePage((addr_t) (STACK + stacklength));

	stacklength += 4096UL / sizeof(addr_t);
}

void InitPushRegion(addr_t position, size_t length)
{
	// Align our entries on page boundaries.
	addr_t newposition = Page::AlignUp(position);
	length = Page::AlignDown((position + length) - newposition);
	position = newposition;

	while ( length )
	{
		if ( unlikely(stackused == stacklength) )
		{
			if ( stackused == MAXSTACKLENGTH )
			{
				pagesnotonstack += length / 4096UL;
				return;
			}

			ExtendStack();
		}

		addr_t* stackentry = &(STACK[stackused++]);
		*stackentry = position;

		length -= 4096UL;
		position += 4096UL;
	}
}

bool ReserveUnlocked(size_t* counter, size_t least, size_t ideal)
{
	assert(least < ideal);
	size_t available = stackused - stackreserved;
	if ( least < available )
		return errno = ENOMEM, false;
	if ( available < ideal )
		ideal = available;
	stackreserved += ideal;
	*counter += ideal;
	return true;
}

bool Reserve(size_t* counter, size_t least, size_t ideal)
{
	ScopedLock lock(&pagelock);
	return ReserveUnlocked(counter, least, ideal);
}

bool ReserveUnlocked(size_t* counter, size_t amount)
{
	return ReserveUnlocked(counter, amount, amount);
}

bool Reserve(size_t* counter, size_t amount)
{
	ScopedLock lock(&pagelock);
	return ReserveUnlocked(counter, amount);
}

addr_t GetReservedUnlocked(size_t* counter, enum page_usage usage)
{
	if ( !*counter )
		return 0;
	assert(stackused); // After all, we did _reserve_ the memory.
	addr_t result = STACK[--stackused];
	assert(result == AlignDown(result));
	stackreserved--;
	(*counter)--;
	PageUsageRegisterUse(result, usage);
	return result;
}

addr_t GetReserved(size_t* counter, enum page_usage usage)
{
	ScopedLock lock(&pagelock);
	return GetReservedUnlocked(counter, usage);
}

addr_t GetUnlocked(enum page_usage usage)
{
	assert(stackreserved <= stackused);
	if ( unlikely(stackreserved == stackused) )
		return errno = ENOMEM, 0;
	addr_t result = STACK[--stackused];
	assert(result == AlignDown(result));
	PageUsageRegisterUse(result, usage);
	return result;
}

addr_t Get(enum page_usage usage)
{
	ScopedLock lock(&pagelock);
	return GetUnlocked(usage);
}

void PutUnlocked(addr_t page, enum page_usage usage)
{
	assert(page == AlignDown(page));
	if ( unlikely(stackused == stacklength) )
	{
		if ( stackused == MAXSTACKLENGTH )
		{
			pagesnotonstack++;
			return;
		}
		ExtendStack();
	}
	STACK[stackused++] = page;
	PageUsageRegisterFree(page, usage);
}

void Put(addr_t page, enum page_usage usage)
{
	ScopedLock lock(&pagelock);
	PutUnlocked(page, usage);
}

void Lock()
{
	kthread_mutex_lock(&pagelock);
}

void Unlock()
{
	kthread_mutex_unlock(&pagelock);
}

} // namespace Page
} // namespace Sortix

namespace Sortix {
namespace Memory {

addr_t ProtectionToPMLFlags(int prot)
{
	addr_t result = 0;
	if ( prot & PROT_EXEC ) { result |= PML_USERSPACE; }
	if ( prot & PROT_READ ) { result |= PML_USERSPACE; }
	if ( prot & PROT_WRITE ) { result |= PML_USERSPACE | PML_WRITABLE; }
	if ( prot & PROT_KEXEC ) { result |= 0; }
	if ( prot & PROT_KREAD ) { result |= 0; }
	if ( prot & PROT_KWRITE ) { result |= 0; }
	if ( prot & PROT_FORK ) { result |= PML_FORK; }
	return result;
}

int PMLFlagsToProtection(addr_t flags)
{
	int prot = PROT_KREAD | PROT_KWRITE | PROT_KEXEC;
	bool user = flags & PML_USERSPACE;
	bool write = flags & PML_WRITABLE;
	if ( user )
		prot |= PROT_EXEC | PROT_READ;
	if ( user && write )
		prot |= PROT_WRITE;
	if ( flags & PML_FORK )
		prot |= PROT_FORK;
	return prot;
}

int ProvidedProtection(int prot)
{
	return PMLFlagsToProtection(ProtectionToPMLFlags(prot));
}

bool LookUp(addr_t mapto, addr_t* physical, int* protection)
{
	// Translate the virtual address into PML indexes.
	const size_t MASK = (1<<TRANSBITS)-1;
	size_t pmlchildid[TOPPMLLEVEL + 1];
	for ( size_t i = 1; i <= TOPPMLLEVEL; i++ )
		pmlchildid[i] = mapto >> (12 + (i-1) * TRANSBITS) & MASK;

	int prot = PROT_USER | PROT_KERNEL | PROT_FORK;

	// For each PML level, make sure it exists.
	size_t offset = 0;
	for ( size_t i = TOPPMLLEVEL; i > 1; i-- )
	{
		size_t childid = pmlchildid[i];
		PML* pml = PMLS[i] + offset;

		addr_t entry = pml->entry[childid];
		if ( !(entry & PML_PRESENT) )
			return false;
		addr_t entryflags = entry & ~PML_ADDRESS;
		int entryprot = PMLFlagsToProtection(entryflags);
		prot &= entryprot;

		// Find the index of the next PML in the fractal mapped memory.
		offset = offset * ENTRIES + childid;
	}

	addr_t entry = (PMLS[1] + offset)->entry[pmlchildid[1]];
	if ( !(entry & PML_PRESENT) )
		return false;

	addr_t entryflags = entry & ~PML_ADDRESS;
	int entryprot = PMLFlagsToProtection(entryflags);
	prot &= entryprot;
	addr_t phys = entry & PML_ADDRESS;

	if ( physical )
		*physical = phys;
	if ( protection )
		*protection = prot;

	return true;
}

void InvalidatePage(addr_t /*addr*/)
{
	// TODO: Actually just call the instruction.
	Flush();
}


addr_t GetAddressSpace()
{
	addr_t result;
	asm ( "mov %%cr3, %0" : "=r"(result) );
	return result;
}

addr_t SwitchAddressSpace(addr_t addrspace)
{
	assert(Page::IsAligned(addrspace));

	addr_t previous = GetAddressSpace();
	asm volatile ( "mov %0, %%cr3" : : "r"(addrspace) );
	return previous;
}

void Flush()
{
	addr_t previous;
	asm ( "mov %%cr3, %0" : "=r"(previous) );
	asm volatile ( "mov %0, %%cr3" : : "r"(previous) );
}

bool MapRange(addr_t where, size_t bytes, int protection, enum page_usage usage)
{
	for ( addr_t page = where; page < where + bytes; page += 4096UL )
	{
		addr_t physicalpage = Page::Get(usage);
		if ( physicalpage == 0 )
		{
			while ( where < page )
			{
				page -= 4096UL;
				physicalpage = Unmap(page);
				Page::Put(physicalpage, usage);
			}
			return false;
		}

		Map(physicalpage, page, protection);
	}

	return true;
}

bool UnmapRange(addr_t where, size_t bytes, enum page_usage usage)
{
	for ( addr_t page = where; page < where + bytes; page += 4096UL )
	{
		addr_t physicalpage = Unmap(page);
		Page::Put(physicalpage, usage);
	}
	return true;
}

static bool MapInternal(addr_t physical, addr_t mapto, int prot, addr_t extraflags = 0)
{
	addr_t flags = ProtectionToPMLFlags(prot) | PML_PRESENT;

	// Translate the virtual address into PML indexes.
	const size_t MASK = (1<<TRANSBITS)-1;
	size_t pmlchildid[TOPPMLLEVEL + 1];
	for ( size_t i = 1; i <= TOPPMLLEVEL; i++ )
		pmlchildid[i] = mapto >> (12 + (i-1) * TRANSBITS) & MASK;

	// For each PML level, make sure it exists.
	size_t offset = 0;
	for ( size_t i = TOPPMLLEVEL; i > 1; i-- )
	{
		size_t childid = pmlchildid[i];
		PML* pml = PMLS[i] + offset;

		addr_t& entry = pml->entry[childid];

		// Find the index of the next PML in the fractal mapped memory.
		size_t childoffset = offset * ENTRIES + childid;

		if ( !(entry & PML_PRESENT) )
		{
			// TODO: Possible memory leak when page allocation fails.
			addr_t page = Page::Get(PAGE_USAGE_PAGING_OVERHEAD);

			if ( !page )
				return false;
			addr_t pmlflags = PML_PRESENT | PML_WRITABLE | PML_USERSPACE
			                | PML_FORK;
			entry = page | pmlflags;

			// Invalidate the new PML and reset it to zeroes.
			addr_t pmladdr = (addr_t) (PMLS[i-1] + childoffset);
			InvalidatePage(pmladdr);
			memset((void*) pmladdr, 0, sizeof(PML));
		}

		offset = childoffset;
	}

	// Actually map the physical page to the virtual page.
	const addr_t entry = physical | flags | extraflags;
	(PMLS[1] + offset)->entry[pmlchildid[1]] = entry;
	return true;
}

bool Map(addr_t physical, addr_t mapto, int prot)
{
	return MapInternal(physical, mapto, prot);
}

void PageProtect(addr_t mapto, int protection)
{
	addr_t phys;
	if ( !LookUp(mapto, &phys, NULL) )
		return;
	Map(phys, mapto, protection);
}

void PageProtectAdd(addr_t mapto, int protection)
{
	addr_t phys;
	int prot;
	if ( !LookUp(mapto, &phys, &prot) )
		return;
	prot |= protection;
	Map(phys, mapto, prot);
}

void PageProtectSub(addr_t mapto, int protection)
{
	addr_t phys;
	int prot;
	if ( !LookUp(mapto, &phys, &prot) )
		return;
	prot &= ~protection;
	Map(phys, mapto, prot);
}

addr_t Unmap(addr_t mapto)
{
	// Translate the virtual address into PML indexes.
	const size_t MASK = (1<<TRANSBITS)-1;
	size_t pmlchildid[TOPPMLLEVEL + 1];
	for ( size_t i = 1; i <= TOPPMLLEVEL; i++ )
	{
		pmlchildid[i] = mapto >> (12 + (i-1) * TRANSBITS) & MASK;
	}

	// For each PML level, make sure it exists.
	size_t offset = 0;
	for ( size_t i = TOPPMLLEVEL; i > 1; i-- )
	{
		size_t childid = pmlchildid[i];
		PML* pml = PMLS[i] + offset;

		addr_t& entry = pml->entry[childid];

		if ( !(entry & PML_PRESENT) )
			PanicF("Attempted to unmap virtual page 0x%jX, but the virtual"
			       " page was wasn't mapped. This is a bug in the code "
			       "code calling this function", (uintmax_t) mapto);

		// Find the index of the next PML in the fractal mapped memory.
		offset = offset * ENTRIES + childid;
	}

	addr_t& entry = (PMLS[1] + offset)->entry[pmlchildid[1]];
	addr_t result = entry & PML_ADDRESS;
	entry = 0;

	// TODO: If all the entries in PML[N] are not-present, then who
	// unmaps its entry from PML[N-1]?

	return result;
}

bool MapPAT(addr_t physical, addr_t mapto, int prot, addr_t mtype)
{
	addr_t extraflags = PAT2PMLFlags[mtype];
	return MapInternal(physical, mapto, prot, extraflags);
}

void ForkCleanup(size_t i, size_t level)
{
	PML* destpml = FORKPML + level;
	if ( !i )
		return;
	for ( size_t n = 0; n < i-1; n++ )
	{
		addr_t entry = destpml->entry[i];
		if ( !(entry & PML_FORK ) )
			continue;
		addr_t phys = entry & PML_ADDRESS;
		if ( 1 < level )
		{
			addr_t destaddr = (addr_t) (FORKPML + level-1);
			Map(phys, destaddr, PROT_KREAD | PROT_KWRITE);
			InvalidatePage(destaddr);
			ForkCleanup(ENTRIES+1UL, level-1);
		}
		enum page_usage usage = 1 < level ? PAGE_USAGE_PAGING_OVERHEAD
		                                  : PAGE_USAGE_USER_SPACE;
		Page::Put(phys, usage);
	}
}

// TODO: Copying every frame is endlessly useless in many uses. It'd be
// nice to upgrade this to a copy-on-write algorithm.
bool Fork(size_t level, size_t pmloffset)
{
	PML* destpml = FORKPML + level;
	for ( size_t i = 0; i < ENTRIES; i++ )
	{
		addr_t entry = (PMLS[level] + pmloffset)->entry[i];

		// Link the entry if it isn't supposed to be forked.
		if ( !(entry & PML_PRESENT) || !(entry & PML_FORK ) )
		{
			destpml->entry[i] = entry;
			continue;
		}

		enum page_usage usage = 1 < level ? PAGE_USAGE_PAGING_OVERHEAD
		                                  : PAGE_USAGE_USER_SPACE;
		addr_t phys = Page::Get(usage);
		if ( unlikely(!phys) )
		{
			ForkCleanup(i, level);
			return false;
		}

		addr_t flags = entry & PML_FLAGS;
		destpml->entry[i] = phys | flags;

		// Map the destination page.
		addr_t destaddr = (addr_t) (FORKPML + level-1);
		Map(phys, destaddr, PROT_KREAD | PROT_KWRITE);
		InvalidatePage(destaddr);

		size_t offset = pmloffset * ENTRIES + i;

		if ( 1 < level )
		{
			if ( !Fork(level-1, offset) )
			{
				Page::Put(phys, usage);
				ForkCleanup(i, level);
				return false;
			}
			continue;
		}

		// Determine the source page's address.
		const void* src = (const void*) (offset * 4096UL);

		// Determine the destination page's address.
		void* dest = (void*) (FORKPML + level - 1);

		memcpy(dest, src, 4096UL);
	}

	return true;
}

bool Fork(addr_t dir, size_t level, size_t pmloffset)
{
	PML* destpml = FORKPML + level;

	// This call always succeeds.
	Map(dir, (addr_t) destpml, PROT_KREAD | PROT_KWRITE);
	InvalidatePage((addr_t) destpml);

	return Fork(level, pmloffset);
}

// Create an exact copy of the current address space.
addr_t Fork()
{
	addr_t dir = Page::Get(PAGE_USAGE_PAGING_OVERHEAD);
	if ( dir == 0 )
		return 0;
	if ( !Fork(dir, TOPPMLLEVEL, 0) )
	{
		Page::Put(dir, PAGE_USAGE_PAGING_OVERHEAD);
		return 0;
	}

	// Now, the new top pml needs to have its fractal memory fixed.
	const addr_t flags = PML_PRESENT | PML_WRITABLE;
	addr_t mapto;
	addr_t childaddr;

	(FORKPML + TOPPMLLEVEL)->entry[ENTRIES-1] = dir | flags;
	childaddr = (FORKPML + TOPPMLLEVEL)->entry[ENTRIES-2] & PML_ADDRESS;

	for ( size_t i = TOPPMLLEVEL-1; i > 0; i-- )
	{
		mapto = (addr_t) (FORKPML + i);
		Map(childaddr, mapto, PROT_KREAD | PROT_KWRITE);
		InvalidatePage(mapto);
		(FORKPML + i)->entry[ENTRIES-1] = dir | flags;
		childaddr = (FORKPML + i)->entry[ENTRIES-2] & PML_ADDRESS;
	}
	return dir;
}

} // namespace Memory
} // namespace Sortix