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Operating Systems Lecture No.
Operating Systems
Lecture No. 33
Reading Material
Chapter 9 of the textbook Lecture 33 on Virtual TV
Summary
Addressing and logical to physical address translation Examples: Intel P4 and PDP- Page table implementation Performance of paging
Addressing in Paging
The page size is defined by the CPU hardware. If the size of logical address space is 2m and a page size is 2n^ addressing units (bytes or words) , then the high-order m-n bits of a logical address designate the page number and the n low order bits designate offset within the page. Thus, the logical address is as follows:
page number page offset p d m-n bits n bits
Example: Assume a logical address space of 16 pages of 1024 words, each mapped into a physical memory of 32 frames. Here is how you calculate the various parameters related to paging.
No. of bits needed for p = ceiling [log 2 16] bits = 4 bits No. of bits neede for f = ceiling [log 2 32] bits = 5 bits No. of bits needed for d = ceiling [log 2 2048] bits = 11 bits Logical address size = |p| + |d| = 4+11 bits = 15 bits Physical address size = |f| + |d| = 5+11 bits = 16 bits
Page Table Size Page table size = NP * PTES , where NP is the number of pages in the process address space and PTES is the page table entry size (equal to |f| based on our discussion so far).
Page table size = 16 * 5 bits (for the above example; assuming a byte size page table entry)
Paging in Intel P 32-bit linear address
4K page size
Maximum pages in a process address space = 2^32 / 4K Number of bits needed for d = log 2 4K bits = 12 bits Number of bits needed for p = 32 โ 12 bits =
Paging in PDP- 16-bit logical address 8K page size
Maximum pages in a process address space = 2^16 / 8K = 8 |d| = log2 8K = 13 bits |p| = 16 โ 13 = 3 bits
Another Example Logical address = 32-bit
Process address space = 2^32 B = 4 GB Main memory = RAM = 512 MB Page size = 4K
Maximum pages in a process address space = 2^32 / 4K = 1M |d| = log 2 4K = 12 bits
|p| = 32 โ 12 = 20 bits No. of frames = 512 M / 4 K = 128 K |f| = ceiling [log 2 128 K] bits = 17 bits 4 bytes (rounding to next even-numbered byte)
Physical address = 17+12 bits
Implementation of Page table
In the CPU registers This is OK for small process address spaces and large page sizes. It has the advantage of having effective memory access time (Teffective) about the same as memory access time (Tmem). An example of this implementation is in PDP-11.
In the main memory A page table base register (PTBR) is needed to point to the page table. With page table in main memory, the effective memory access time, Teffective, is 2Tmem , which is not acceptable because it would slow down program execution by a factor of two.
In the translation look-aside buffer (TLB) A solution to this problem is to use special, small, fast lookup hardware, called translation look-aside buffer (TLB), which typically has 64โ1024 entries. Each entry is (key, value). The key is searched for in parallel; on a hit, value is returned. The (key,value) pair is (p,f) for paging. For a logical address, (p,d), TLB is searched for p. If an entry with a key p is found, we have a hit and f is used to form the physical address. Else, page table in the main memory is searched.
We give a few examples to help you better understand this equation.
Example 1
Tmem = 100 nsec TTLB = 20 nsec Hit ratio is 80% Teffective = 0.8 (20 + 100) + 0.2 (20 + 2*100) nanoseconds = 140 nanoseconds
This means that with 80% chances of finding a page table entry in the TLB, the effective access time becomes 40% worse than memory access time without paging.
Example 2
Tmem = 100 nsec TTLB = 20 nsec
Hit ratio is 98% Teffective = 0.98 (20 + 100) + 0.02 (20 + 2*100) nanoseconds = 122 nanoseconds
This means that with 98% chances of finding a page table entry in the TLB, the effective access time becomes 22% worse than memory access time without paging. This means that with a small cache and good hit ratio, we can maintain most of the page table in the main memory and get much better performance than keeping the page table in the main memory and not using any cache.
