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Virtual Memory
Paging (cont’d)
Inverted Page Tables
Topics
• Inverted Page Tables
Review
• Single-level paging
– Single page table contains one entry per virtual page
per process
• Multilevel paging
– Several tables
• Higher level tables contain pointers to page tables (Pentium
III – Page Directory Table)
• Lowest level tables contain virtual to physical address
mapping (Pentium III – Page Tables)
• Advantage: Don’t need to allocate large chunk of memory for
whole page table (if implemented with single level), if only a
few pages are actually active. Only need to allocate enough
chunks of memory to hold the segments of page table that
are active.
Inverted Page Table - Motivation
•Example:
– 64-bit virtual address space
– 4 KB page size
– 512 MB physical memory
• How much space (memory) needed for a
single level page table?
Single Level Page Table
• One entry per virtual page
–2
64 addressable bytes / 212 bytes per page = 252 page table
entries
• Page table entry size
– One page table entry contains:
• Access control bits + Physical page number
– 512 MB physical memory = 229 bytes
•2
29 bytes of memory/212 bytes per page = 217physical pages
•17 bits needed for physical page number
– Page table entry = ~4 bytes
• 17 bit physical page number = ~3 bytes
• Access control bits = ~1 byte
• Page ta ble size
–2
52 page table entries * 22bytes = 254 bytes (16 petabytes)
64-bit address space
4 KB page size
512 MB physical mem
o
A lot of memory! (kilo-, mega-, giga-,tera-, peta-)
PER PROCESS
How About Multilevel Paging?
• How many levels are needed to ensure
that any page table requires only a single
page (4 KB)?
– Assume page table entry is 4 bytes
– 4 KB page / 4 bytes per page table entry =
1024 entries
– 10 bits of address space needed
– ceiling(52/10) = 6 levels needed
252 page table entries
(single-level)
6 levels →6 memory accesses →slow
