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For every memory reference that the CPU makes, the specific line that would hold the reference (if it is has already been copied into the cache) is determined. The tag held in that line is checked to see if the correct block is in the cache

b/ Operations

- Each main memory block is assigned to a specific line in the cache:

i = j modulo C, where i is the cache line number assigned to main memory block j

– If M=64, C=4:

Line 0 can hold blocks 0, 4, 8, 12, ...

Line 1 can hold blocks 1, 5, 9, 13, ...

Line 2 can hold blocks 2, 6, 10, 14, ...

Line 3 can hold blocks 3, 7, 11, 15, ...

– Example:

Memory size of 1 MB (20 address bits) addressable to the individual byte

Cache size of 1 K lines, each holding 8 bytes:

Word id = 3 bits

Line id = 10 bits

Tag id = 7 bits

Where is the byte stored at main memory

location $ABCDE stored?

$ABCDE=1010101 1110011011 110

Cache line $39B, word offset $6, tag $55

c/ Remarks

  • Advantages of direct mapping

+ Easy to implement

+ Relatively inexpensive to implement

+ Easy to determine where a main memory reference can be found in cache

  • Disadvantage

+ Each main memory block is mapped to a specific cache line

+ Through locality of reference, it is possible to repeatedly reference to blocks that map to the same line number

+ These blocks will be constantly swapped in and out of cache, causing the hit ratio to be low.

2.2 associative mapping

a/ Organization

A set-associative cache or associative mapping is inhenrently more complicated than a direct-mapped cache because although the correct cache entry to examine can be computed from the memory address being referenced, a set of n cache entries must be checked to see if the need line is present.

Associative mapping can overcomes direct mapping’s main of the direct mapping, the associate cache organization is illustrated in Figure 10.3.

Figure 10.3. Associate Cache Organization

– Operation must examine each line in the cache to find the right memory block

+ Examine the line tag id for each line

+ Slow process for large caches!

– Line numbers (ids) have no meaning in the cache

+ Parse the main memory address into 2 fields (tag and word offset) rather than 3 as in direct mapping

– Implementation of cache in 2 parts:

+ Part SRAM: The lines themselves in SRAM

+ The tag storage in associative memory

– Perform an associative search over all tags

b/ Operation example

With the same example: Memory size of 1 MB (20 address bits) addressable to the individual byte. Cache size of 1 K lines, each holding 8 bytes:

Word id = 3 bits

Tag id = 17 bits

Where is the byte stored at main memory location $ABCDE stored?

$ABCDE=10101011110011011 110

Cache line unknown, word offset $6, tag $1579D.

c/ Remarks

  • Advantages

- Fast

- Flexible

  • Disadvantage
  • Implementation cost

Example above has 8 KB cache and requires 1024 x 17 = 17,408 bits of

associative memory for the tags!

2.3 set associative mapping

a/ Organization

The associative mapping is considered as compromise between direct and fully associative mappings that builds on the strengths of both

– Divide cache into a number of sets (v), each set holding a number of lines (k)

– A main memory block can be stored in any one of the k lines in a set such that

set number = j modulo v

– If a set can hold X lines, the cache is referred to as an X-way set associative cache

Most cache systems today that use set associative mapping are 2- or 4-way set


Figure. 10. 4 Set associative cache organization

b/ Example

Assume the 1024 lines are 4-way set associative:

1024/4 = 256 sets

Word id = 3 bits

Set id = 8 bits

Tag id = 9 bits

Where is the byte stored at main memory

Location $ABCDE stored?

$ABCDE=101010111 10011011 110

Cache set $9B, word offset $6, tag $157

3. replacement algorithms

As we known, cache is the fast and small memory. when new block is brough into the cache, one of the blocks existing must be replaced by the new block that is to be read from memory.

For direct mapping, there is only one possible line for any particular block and no choice is possible. For the associative cache or a set associative cache, a replacement algorithm is needed.

A number of algorithms can be tried:

– Least Recently Used (LRU)

– First In First Out (FIFO)

– Least Frequently Used (LFU)

– Random

Probably the most effective algorithm is least recently used (LRU): Replace that block in the set that has been in the cache longest with no refrence.

4. performances

4.1 write policy

– When a line is to be replaced, must update the original copy of the line in main memory if any addressable unit in the line has been changed

– Write through

+ Anytime a word in cache is changed, it is also changed in main memory

+ Both copies always agree

+ Generates lots of memory writes to main memory

– Write back

+ During a write, only change the contents of the cache

+ Update main memory only when the cache line is to be replaced

+Causes “cache coherency” problems -- different values for the contents of an address are in the cache and the main memory

+ Complex circuitry to avoid this problem

4.2 block / line sizes

– How much data should be transferred from main memory to the cache in a single memory reference

– Complex relationship between block size and hit ratio as well as the operation of the system bus itself

– As block size increases,

+ Locality of reference predicts that the additional information transferred will likely be used and thus increases the hit ratio (good)

+ Number of blocks in cache goes down, limiting the total number of blocks in the cache (bad)

+ As the block size gets big, the probability of referencing all the data in it goes down (hit ratio goes down) (bad)

+ Size of 4-8 addressable units seems about right for current systems

Number of caches

Single vs. 2-level cache:

- Modern CPU chips have on-board cache (Level 1 – L1):

L1 provides best performance gains

- Secondary, off-chip cache (Level 2) provides higher speed access to main memory

L2 is generally 512KB or less more than this is not cost-effective.

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Source:  OpenStax, Computer architecture. OpenStax CNX. Jul 29, 2009 Download for free at http://cnx.org/content/col10761/1.1
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