1. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 1 Operating System Concepts Operating Systems Lecture 24 Paging

2. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 2 Operating System Concepts Contiguous Allocation Multiple-partition allocation  Initially, all non-OS memory is available for user processes.  Hole – block of available memory;  When a process arrives, it is allocated memory from a hole large enough to accommodate it.  Holes of various size are scattered throughout memory.  Operating system maintains information about: a) allocated partitions b) free partitions (hole) OS process 5 process 8 process 2 OS process 5 process 2 OS process 5 process 2 OS process 5 process 9 process 2 process 9 process 10

3. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 3 Operating System Concepts Dynamic Storage-Allocation Problem First-fit: Allocate the first hole that is big enough. Best-fit: Allocate the smallest hole that is big enough; must search entire list, unless ordered by size. Produces the smallest leftover hole. Worst-fit: Allocate the largest hole; must also search entire list. Produces the largest leftover hole. When a process arrives, search for a hole big enough for it. If none available, the process must wait. When a process terminates, memory is freed, creating a hole. This new hole may join with other contiguous holes to create a bigger hole. How to satisfy a request of size n from a list of free holes: First-fit and best-fit better than worst-fit in terms of speed and storage utilization.

4. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 4 Operating System Concepts External Fragmentation As memory is allocated to processes and freed as processes terminate, the free memory space is broken into small pieces. External Fragmentation – total memory space exists to satisfy a request, but it is not contiguous. With the first fit memory allocation rule, given N allocated blocks, another 0.5N blocks may be lost due to fragmentation (50 percent rule). This means 1/3 of memory is unusable!

5. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 5 Operating System Concepts Internal Fragmentation One method of allocating memory is to break memory into fixed sized blocks. Memory is allocated in units of block sizes. The memory allocated may be slightly larger than the size needed by the process. This is Internal Fragmentation. With Internal Fragmentation, the size difference between the process size and the allocated memory is memory internal to a partition, but not being used. Example: Block size 1024 bytes. Process size: 4048 bytes. What is the internal fragmentation size?

6. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 6 Operating System Concepts Compaction One can reduce external fragmentation by compaction.  Shuffle memory contents to place all free memory together in one large block.  Compaction is possible only if relocation is dynamic, and is done at execution time.  I/O problem  Latch job in memory while it is involved in I/O.  Do I/O only into OS buffers.

7. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 7 Operating System Concepts Paging Paging allows the physical address space of a process to be non-contiguous. Divide physical memory into fixed-sized blocks called frames (size is power of 2, between 512 bytes and 8192 bytes). Divide logical memory into blocks of same size called pages. Each address generated by the CPU consists of a page number, p, and an offset, d.  Page number: Index to a page table that contains the base address of the corresponding frame in physical memory.  Page offset: Combined with the base address to define the physical memory address that is sent to the memory unit.

8. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 8 Operating System Concepts Address Translation Architecture

9. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 9 Operating System Concepts Paging Example

10. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 10 Operating System Concepts Storing of Addresses Suppose the size of physical address space = 2 m Suppose the page size = 2 n What is the total number of pages? Allocate m bits to specify logical addresses. First m - n bits of the address specify the page number. The n lower order bits indicate the offset.

11. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 11 Operating System Concepts Paging Example Page size = 4 bytes Physical memory = 32 bytes Number of pages = ? Where do the following map? Logical 0: Page 0, offset 0: Logical 3: Page 0, offset 3: Logical 4: Logical 13:

12. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 12 Operating System Concepts Paging and Fragmentation Don't have external fragmentation with paging.  Any free frame can be allocated to a process that needs it. May have internal fragmentation with paging.  Frames are allocated as units. Last frame may not be completely full.

13. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 13 Operating System Concepts Allocation of Frames The O.S. keeps track of which frames are allocated and which are free in a frame table. If a process requests n frames, there must be n frames available to satisfy the request. If so, they are allocated to the process. As each frame is allocated to each page, the frame number is put in the page table for that process. Note: The user views memory as contiguous space. The program is actually scattered throughout physical memory.

14. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 14 Operating System Concepts Free Frames Before allocation After allocation

15. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 15 Operating System Concepts Implementation of Page Table Simplest implementation: Page table stored in dedicated registers in the CPU. The registers use high speed logic. The CPU dispatcher re-loads these registers when switching processes. (Each process has its own page table). Example: DEC PDP-11  Address size = 16 bitsNumber of addresses = ?  Page size = 8 KB (8192) = 2 13 Number of bits = ?  Number of pages = ?  # of entries in page table = number of pages = ? This method is only useful when the page table is small (< 256 entries). Most contemporary computers have much larger page tables (10 6 entries) so this method will not work well.

16. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 16 Operating System Concepts Storing Page Table in Main Memory For large page tables, the page table is kept in main memory. Page-table base register (PTBR) points to the page table. When changing processes, only need to change 1 register to change page tables. This reduces the context switch time. Page-table length register (PTLR) indicates size of the page table. Drawback: In this scheme every data/instruction access requires two memory accesses. One for the page table and one for the data/instruction.

17. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 17 Operating System Concepts Translation Look-Aside Buffer (TLB) The two memory access problem can be solved by the use of a special fast-lookup hardware cache called associative memory or translation look-aside buffers (TLBs)  This kind of memory is expensive, so it is generally small (64 - 1024 entries). In each memory access, the TLB is searched first to locate the page number.  If the page is found (a hit) the associated frame is used to access the data in memory.  If the page is not found (a miss), the page number is looked up in the page table in main memory. The page number and associated frame is added to the TLB.

18. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 18 Operating System Concepts TLB: Associative Memory Associative memory – parallel search Address translation (Page #, Frame #)  If page# is in associative register, get frame # out.  Otherwise get frame # from page table in memory Page #Frame #

19. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 19 Operating System Concepts Paging Hardware With TLB

20. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 20 Operating System Concepts Effective Access Time (EAT) Effective access time (EAT) is the average time needed to access memory. Hit Ratio: The percentage of times that a particular page number is found in the TLB. Effective access time can be calculated based on:  The time it takes to access main memory  The time it takes to access the TLB  The hit ratio for the TLB Example  Time to access main memory = 100ns  Time to access TLB = 20 ns  Hit ratio = 0.8 (80%)  If page is found in TLB, total access time = ?  If page is not found in TLB, total access time = ?  Effective access time = ?

21. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 21 Operating System Concepts General Formula for EAT Hit ratio =  Main Memory access time = m Associative Lookup (TLB access) =  EAT = (m +  )  + (2m +  ) (1 -  ) = 2m - m  + 

22. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 22 Operating System Concepts Memory Protection Memory protection implemented by associating protection bit with each frame.  Bits signal if a frame is read only, read-write, execute only or a combination. Valid-invalid bit attached to each entry in the page table:  “valid” indicates that the associated page is in the process’ logical address space, and is thus a legal page.  “invalid” indicates that the page is not in the process’ logical address space. Example:  System has 14 bit address space (0 - 16383)  Program uses addresses 0 - 10468  Page size = 2 KB (2048 = 2 11 )  # of pages = ?  6 pages needed by program (5 pages = 5*2048 = 10240Bytes)  Pages 0 - 5 have valid/invalid bit set to valid  Other pages have bit set to invalid.

23. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 23 Operating System Concepts Valid (v) or Invalid (i) Bit In A Page Table

24. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 24 Operating System Concepts Problem with large page tables Modern computers have large logical address spaces: 2 32 or 2 64 bytes. This can make page tables excessively large. Example: 32 bit logical address space 4 KB Page size How many entries in the page table? If each entry is 4 bytes, what is size of each table? With large page tables, it is good not to store them continuously in memory.

25. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 25 Operating System Concepts Hierarchical Page Tables In hierarchichal page tables, the logical address space is broken up into multiple page tables. A two-level example: A logical address (on 32-bit machine with 4K page size) is divided into:  a page number consisting of 20 bits.  a page offset consisting of 12 bits. Since the page table is paged, the page number is further divided into:  a 10-bit page number.  a 10-bit page offset. Thus, a logical address is as follows: where p 1 is an index into the outer page table, and p 2 is the displacement within the page of the outer page table. page number page offset pipi p2p2 d 10 12

26. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 26 Operating System Concepts Address-Translation Scheme Address-translation scheme for a two-level 32-bit paging architecture

27. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 27 Operating System Concepts Two-Level Page-Table Scheme

28. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 28 Operating System Concepts Hashed Page Tables Common in address spaces > 32 bits. The virtual (logical) page number is hashed into a page table. This page table contains a chain of elements hashing to the same location. Virtual page numbers are compared in this chain searching for a match. If a match is found, the corresponding physical frame is extracted.

29. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 29 Operating System Concepts Hashed Page Table

30. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 30 Operating System Concepts Inverted Page Table One entry for each real page (frame) of memory. Entry consists of the virtual address of the page stored in that real memory location, with information about the process that owns that page. Decreases memory needed to store each page table, but increases time needed to search the table when a page reference occurs.

31. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 31 Operating System Concepts Inverted Page Table Architecture

32. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 32 Operating System Concepts Shared Pages Shared code  One copy of read-only (reentrant) code shared among processes (i.e., text editors, compilers, window systems).  Shared code must appear in same location in the logical address space of all processes. Private code and data  Each process keeps a separate copy of the code and data.  The pages for the private code and data can appear anywhere in the logical address space.

33. Silberschatz, Galvin and Gagne  2002 Modified for CSCI 346, Royden, 2011 33 Operating System Concepts Shared Pages Example