1. Review: The Memory Hierarchy
Take advantage of the principle of locality to present the user with as much memory as is available in the cheapest technology at the speed offered by the fastest technology
Processor
4-8 bytes (word)
1 to 4 blocks
1,024+ bytes (disk sector = page)
8-32 bytes (block)
Inclusive– what is in L1$ is a subset of what is in L2$ is a subset of what is in MM that is a subset of is in SM
Increasing distance from the processor in access time
L1$
L2$
Main Memory
Secondary Memory
(Relative) size of the memory at each level

2. Review: Principle of Locality
Temporal Locality
Keep most recently accessed data items closer to the processor
Spatial Locality
Move blocks consisting of contiguous words to the upper levels
Hit Time << Miss Penalty
Hit: data appears in some block in the upper level (Blk X)
Hit Rate: the fraction of accesses found in the upper level
Hit Time: RAM access time + Time to determine hit/miss
Miss: data needs to be retrieve from a lower level block (Blk Y)
Miss Rate = 1 - (Hit Rate)
Miss Penalty: Time to replace a block in the upper level with a block from the lower level + Time to deliver this block’s word to the processor
Miss Types: Compulsory, Conflict, Capacity
Lower Level
Memory
Upper Level
To Processor
From Processor
Blk X
Blk Y

3. Measuring Cache Performance
Assuming cache hit costs are included as part of the normal CPU execution cycle, then
CPU time = IC × CPI × CC
= IC × (CPIideal + Memory-stall cycles) × CC
CPIstall
Memory-stall cycles come from cache misses (a sum of read-stalls and write-stalls)
Read-stall cycles = reads/program × read miss rate × read miss penalty
Write-stall cycles = (writes/program × write miss rate × write miss penalty)
+ write buffer stalls
For write-through caches, we can simplify this to
Memory-stall cycles = miss rate × miss penalty
Instruction Count/CPI/Cycle Cost
Reasonable write buffer depth (e.g., four or more words) and a memory capable of accepting writes at a rate that significantly exceeds the average write frequency means write buffer stalls are small
Average Memory Access time = Hit Time + Miss Rate x Miss Penalty

4. Review: The “Memory Wall”
Logic vs DRAM speed gap continues to grow
Clocks per DRAM access
Clocks per instruction

5. Impacts of Cache Performance
Relative cache penalty increases as processor performance improves (faster clock rate and/or lower CPI)
The memory speed is unlikely to improve as fast as processor cycle time. When calculating CPIstall, the cache miss penalty is measured in processor clock cycles needed to handle a miss
The lower the CPIideal, the more pronounced the impact of stalls
A processor with a CPIideal of 2, a 100 cycle miss penalty, 36% load/store instr’s, and 2% I$ and 4% D$ miss rates
Memory-stall cycles = 2% × % × 4% × 100 = 3.44
So CPIstalls = = 5.44
What if the CPIideal is reduced to 1? 0.5? ?
What if the processor clock rate is doubled (doubling the miss penalty)?
For ideal CPI = 1, then CPIstall = 4.44 and the amount of execution time spent on memory stalls would have risen from 3.44/5.44 = 63% to 3.44/4.44 = 77%
For miss penalty of 200, memory stall cycles = 2% % x 4% x 200 = 6.88 so that CPIstall = 8.88
This assumes that hit time is not a factor in determining cache performance. A larger cache would have a longer access time (if a lower miss rate), meaning either a slower clock cycle or more stages in the pipeline for memory access.

6. Reducing Cache Miss Rates #1
Allow more flexible block placement
In a direct mapped cache a memory block maps to exactly one cache block
At the other extreme, could allow a memory block to be mapped to any cache block – fully associative cache
A compromise is to divide the cache into sets each of which consists of n “ways” (n-way set associative). A memory block maps to a unique set (specified by the index field) and can be placed in any way of that set (so there are n choices)
(block address) modulo (# sets in the cache)

7. Cache Two issues: Our first example:
How do we know if a data item is in the cache?
If it is, how do we find it?
Our first example:
block size is one word of data
"direct mapped"
For each item of data at the lower level,
there is exactly one location in the cache where it might be.
e.g., lots of items at the lower level share locations in the upper level

8. Direct Mapped Cache
Mapping: address is modulo the number of blocks in the cache

9. Direct Mapped Cache For MIPS:
What kind of locality are we taking advantage of? A d r e s ( h o w i n g b t p ) 2 1 B y f V a l T D I x 3 H

10. Direct Mapped Cache Taking advantage of spatial locality: A d r e s (w i n g b t p ) 1 6 2 B y f V T a D H 3 4 K 8 M u x l c k I 5

11. Hits vs. Misses Read hits Read misses Write hits: Write misses:
this is what we want!
Read misses
stall the CPU, fetch block from memory, deliver to cache, restart
Write hits:
can replace data in cache and memory (write-through)
write the data only into the cache (write-back the cache later)
Write misses:
read the entire block into the cache, then write the word

12. Hardware Issues
Make reading multiple words easier by using banks of memory
It can get a lot more complicated... C P U a c h e B u s M m o r y . O n - w d i g z t b W l p x k 1 2 3 I v

13. Performance Increasing the block size tends to decrease miss rate:
Use split caches because there is more spatial locality in code: 1 K B 8 6 4 2 5 % 3 M i s r a t e l o c k z ( b y )

14. Performance
Simplified model: execution time = (execution cycles + stall cycles) ´ cycle time stall cycles = # of instructions ´ miss ratio ´ miss penalty
Two ways of improving performance:
decreasing the miss ratio
decreasing the miss penalty
What happens if we increase block size?

15. Set Associative Caches
Basic Idea: a memory block can be mapped to more than one location in the cache
Cache is divided into sets
Each memory block is mapped to a particular set
Each set can have more than one block
Number of blocks in set = associativity of cache
If a set has only one block, then it is a direct-mapped cache
I.e. direct mapped caches have a set associativity of 1
Each memory block can be placed in any of the blocks of the set to which it maps

16. Direct mapped cache: block N maps to ( N mod num of blocks in cache)
Set associative cache: block N maps to set (N mod num of sets in
cache)
Example below shows placement of block whose address is 12 1 2 T a g D t B l o c k # 3 4 5 6 7 S e r h i m p d s v F u y

17. Decreasing miss ratio with associativity- w y s e o c v ( f u l ) F r S 1 O n d m p B k 7 2 3 4 5 6
Compared to direct mapped, give a series of references that:
results in a lower miss ratio using a 2-way set associative cache
results in a higher miss ratio using a 2-way set associative cache
assuming we use the “least recently used” replacement strategy

18. Set Associative Cache Example
Main Memory
0000xx
0001xx
0010xx
0011xx
0100xx
0101xx
0110xx
0111xx
1000xx
1001xx
1010xx
1011xx
1100xx
1101xx
1110xx
1111xx
Two low order bits define the byte in the word (32-b words)
One word blocks
Cache
Way
Set V
Tag
Data 1 1 1
Q2: How do we find it?
Use next 1 low order memory address bit to determine which cache set (i.e., modulo the number of sets in the cache)
Q1: Is it there?
Compare all the cache tags in the set to the high order 3 memory address bits to tell if the memory block is in the cache
For lecture
Valid bit indicates whether an entry contains valid information – if the bit is not set, there cannot be a match for this block

19. Another Reference String Mapping
Consider the main memory word reference string
Start with an empty cache - all blocks initially marked as not valid 4 4
For class handout

20. Another Reference String Mapping
Consider the main memory word reference string
Start with an empty cache - all blocks initially marked as not valid
miss 4
miss
hit 4
hit
Mem(0)
Mem(0)
Mem(0)
Mem(0)
Mem(4)
Mem(4)
Mem(4)
8 requests, 2 misses
For lecture
Another sample string to try
Solves the ping pong effect in a direct mapped cache due to conflict misses since now two memory locations that map into the same cache set can co-exist!

21. Four-Way Set Associative Cache
28 = 256 sets each with four ways (each with one block)
Byte offset 22
Tag 8
Index
Index
Data
Tag V 1 2 .
253
254
255
Data
Tag V 1 2 .
253
254
255
Data
Tag V 1 2 .
253
254
255
Data
Tag V 1 2 .
253
254
255
Hit
Data 32
4x1 select
This is called a 4-way set associative cache because there are four cache entries for each cache index. Essentially, you have four direct mapped cache working in parallel.
This is how it works: the cache index selects a set from the cache. The four tags in the set are compared in parallel with the upper bits of the memory address.
If no tags match the incoming address tag, we have a cache miss.
Otherwise, we have a cache hit and we will select the data from the way where the tag matches occur.
This is simple enough. What is its disadvantages?
+1 = 36 min. (Y:16)

22. Range of Set Associative Caches
For a fixed size cache, each increase by a factor of two in associativity doubles the number of blocks per set (i.e., the number or ways) and halves the number of sets – decreases the size of the index by 1 bit and increases the size of the tag by 1 bit
Tag
Index
Block offset
Byte offset
For class handout

23. Range of Set Associative Caches
For a fixed size cache, each increase by a factor of two in associativity doubles the number of blocks per set (i.e., the number or ways) and halves the number of sets – decreases the size of the index by 1 bit and increases the size of the tag by 1 bit
Used for tag compare
Selects the set
Selects the word in the block
Tag
Index
Block offset
Byte offset
Increasing associativity
Decreasing associativity
For lecture
Fully associative
(only one set)
Tag is all the bits except
block and byte offset
Direct mapped
(only one way)
Smaller tags

24. Costs of Set Associative Caches
When a miss occurs, which way’s block do we pick for replacement?
Least Recently Used (LRU): the block replaced is the one that has been unused for the longest time
Must have hardware to keep track of when each way’s block was used relative to the other blocks in the set
For 2-way set associative, takes one bit per set → set the bit when a block is referenced (and reset the other way’s bit)
N-way set associative cache costs
N comparators (delay and area)
MUX delay (set selection) before data is available
Data available after set selection (and Hit/Miss decision). In a direct mapped cache, the cache block is available before the Hit/Miss decision
So its not possible to just assume a hit and continue and recover later if it was a miss
First of all, a N-way set associative cache will need N comparators instead of just one comparator (use the right side of the diagram for direct mapped cache).
A N-way set associative cache will also be slower than a direct mapped cache because of this extra multiplexer delay.
Finally, for a N-way set associative cache, the data will be available AFTER the hit/miss signal becomes valid because the hit/mis is needed to control the data MUX.
For a direct mapped cache, that is everything before the MUX on the right or left side, the cache block will be available BEFORE the hit/miss signal (AND gate output) because the data does not have to go through the comparator.
This can be an important consideration because the processor can now go ahead and use the data without knowing if it is a Hit or Miss. Just assume it is a hit.
Since cache hit rate is in the upper 90% range, you will be ahead of the game 90% of the time and for those 10% of the time that you are wrong, just make sure you can recover.
You cannot play this speculation game with a N-way set-associative cache because as I said earlier, the data will not be available to you until the hit/miss signal is valid.
+2 = 38 min. (Y:18)

25. Benefits of Set Associative Caches
The choice of direct mapped or set associative depends on the cost of a miss versus the cost of implementation
Data from Hennessy & Patterson, Computer Architecture, 2003
As cache sizes grow, the relative improvement from associativity increases only slightly; since the overall miss rate of a larger cache is lower, the opportunity for improving the miss rate decreases and the absolute improvement in miss rate from associativity shrinks significantly.
Largest gains are in going from direct mapped to 2-way (20%+ reduction in miss rate)

26. Set Associative Caches (in summary)
Advantages:
Miss ratio decreases as associativity increases
Disadvantages
Extra memory needed for extra tag bits in cache
Extra time for associative search

27. Block Replacement Policies
What block to replace on a cache miss?
We have multiple candidates (unlike direct mapped caches)
Random
FIFO (First In First Out)
LRU (Least Recently Used)
Typically, cpus use Random or Approximate LRU because easier to implement in hardware

28. Example Cache size = 4 one word blocks Replacement Policy = LRU
Sequence of memory references 0,8,0,6,8
Set associativity = 4 (Fully Associative); Number of Sets = 1
Address
Hit/Miss
Set 0 M 8 H 6

29. Example cont’d Cache size = 4 one word blocks Replacement Policy = LRU
Sequence of memory references 0,8,0,6,8
Set associativity = 2 ; Number of Sets = 2
Address
Hit/Miss
Set 0
Set 1 M 8 H 6

30. Example cont’d Cache size = 4 one word blocks Replacement Policy = LRU
Sequence of memory references 0,8,0,6,8
Set associativity = 1 (Direct Mapped Cache)
Address
Hit/Miss 1 2 3 M 8 6

31. Decreasing miss penalty with multilevel caches
Add a second level cache:
often primary cache is on the same chip as the processor
use SRAMs to add another cache above primary memory (DRAM)
miss penalty goes down if data is in 2nd level cache
Example:
CPI of 1.0 on a 500Mhz machine with a 5% miss rate, 200ns DRAM access
Adding 2nd level cache with 20ns access time decreases miss rate to 2%
Using multilevel caches:
try and optimize the hit time on the 1st level cache
try and optimize the miss rate on the 2nd level cache

32. I m p r o v e n t f a c 1 9 8 2 4 6 Y C P U ( s ) l w D R A M

33. 2 % M i s r a t e p y 4 6 8 1 3 O n - w T o C c h z ( K B ) F u E g

34. Reducing Cache Miss Rates #2
Use multiple levels of caches
With advancing technology have more than enough room on the die for bigger L1 caches or for a second level of caches – normally a unified L2 cache (i.e., it holds both instructions and data) and in some cases even a unified L3 cache
For our example, CPIideal of 2, 100 cycle miss penalty (to main memory), 36% load/stores, a 2% (4%) L1I$ (D$) miss rate, add a UL2$ that has a 25 cycle miss penalty and a 0.5% miss rate
CPIstalls = × ×.04× × ×.005×100 = (as compared to 5.44 with no L2$)
Also reduces cache miss penalty

35. Multilevel Cache Design Considerations
Design considerations for L1 and L2 caches are very different
Primary cache should focus on minimizing hit time in support of a shorter clock cycle
Smaller with smaller block sizes
Secondary cache(s) should focus on reducing miss rate to reduce the penalty of long main memory access times
Larger with larger block sizes
The miss penalty of the L1 cache is significantly reduced by the presence of an L2 cache – so it can be smaller (i.e., faster) but have a higher miss rate
For the L2 cache, hit time is less important than miss rate
The L2$ hit time determines L1$’s miss penalty
L2$ local miss rate >> than the global miss rate
Global miss rate – the fraction of references that miss in all levels of a multilevel cache. The global miss rate dictates how often we must access the main memory.
Local miss rate – the fraction of references to one level of a cache that miss

36. Key Cache Design Parameters
L1 typical
L2 typical
Total size (blocks)
250 to 2000
4000 to 250,000
Total size (KB)
16 to 64
500 to 8000
Block size (B)
32 to 64
32 to 128
Miss penalty (clocks)
10 to 25
100 to 1000
Miss rates (global for L2)
2% to 5%
0.1% to 2%

37. Two Machines’ Cache Parameters
Intel P4
AMD Opteron
L1 organization
Split I$ and D$
L1 cache size
8KB for D$, 96KB for trace cache (~I$)
64KB for each of I$ and D$
L1 block size
64 bytes
L1 associativity
4-way set assoc.
2-way set assoc.
L1 replacement
~ LRU
LRU
L1 write policy
write-through
write-back
L2 organization
Unified
L2 cache size
512KB
1024KB (1MB)
L2 block size
128 bytes
L2 associativity
8-way set assoc.
16-way set assoc.
L2 replacement
~LRU
L2 write policy
A trace cache finds a dynamic sequence of instructions including taken branches to load into a cache block. Thus, the cache blocks contain dynamic traces of the executed instructions as determined by the CPU rather than static sequences of instructions as determined by memory layout. It folds branch prediction into the cache.

38. 4 Questions for the Memory Hierarchy
Q1: Where can a block be placed in the upper level? (Block placement)
Q2: How is a block found if it is in the upper level? (Block identification)
Q3: Which block should be replaced on a miss? (Block replacement)
Q4: What happens on a write? (Write strategy)

39. Q1&Q2: Where can a block be placed/found?
# of sets
Blocks per set
Direct mapped
# of blocks in cache 1
Set associative
(# of blocks in cache)/ associativity
Associativity (typically 2 to 16)
Fully associative
Location method
# of comparisons
Direct mapped
Index 1
Set associative
Index the set; compare set’s tags
Degree of associativity
Fully associative
Compare all blocks tags
# of blocks

40. Q3: Which block should be replaced on a miss?
Easy for direct mapped – only one choice
Set associative or fully associative
Random
LRU (Least Recently Used)
For a 2-way set associative cache, random replacement has a miss rate about 1.1 times higher than LRU.
LRU is too costly to implement for high levels of associativity (> 4-way) since tracking the usage information is costly

41. Q4: What happens on a write?
Write-through – The information is written to both the block in the cache and to the block in the next lower level of the memory hierarchy
Write-through is always combined with a write buffer so write waits to lower level memory can be eliminated (as long as the write buffer doesn’t fill)
Write-back – The information is written only to the block in the cache. The modified cache block is written to main memory only when it is replaced.
Need a dirty bit to keep track of whether the block is clean or dirty
Pros and cons of each?
Write-through: read misses don’t result in writes (so are simpler and cheaper)
Write-back: repeated writes require only one write to lower level

42. Improving Cache Performance
0. Reduce the time to hit in the cache
smaller cache
direct mapped cache
smaller blocks
for writes
no write allocate – no “hit” on cache, just write to write buffer
write allocate – to avoid two cycles (first check for hit, then write) pipeline writes via a delayed write buffer to cache
1. Reduce the miss rate
bigger cache
more flexible placement (increase associativity)
larger blocks (16 to 64 bytes typical)
victim cache – small buffer holding most recently discarded blocks

43. Improving Cache Performance
2. Reduce the miss penalty
smaller blocks
use a write buffer to hold dirty blocks being replaced so don’t have to wait for the write to complete before reading
check write buffer (and/or victim cache) on read miss – may get lucky
for large blocks fetch critical word first
use multiple cache levels – L2 cache not tied to CPU clock rate
faster backing store/improved memory bandwidth
wider buses
memory interleaving, page mode DRAMs

44. Summary: The Cache Design Space
Several interacting dimensions
cache size
block size
associativity
replacement policy
write-through vs write-back
write allocation
The optimal choice is a compromise
depends on access characteristics
workload
use (I-cache, D-cache, TLB)
depends on technology / cost
Simplicity often wins
Cache Size
Associativity
Block Size
Bad
No fancy replacement policy is needed for the direct mapped cache.
As a matter of fact, that is what cause direct mapped trouble to begin with: only one place to go in the cache--causes conflict misses.
Besides working at Sun, I also teach people how to fly whenever I have time.
Statistic have shown that if a pilot crashed after an engine failure, he or she is more likely to get killed in a multi-engine light airplane than a single engine airplane.
The joke among us flight instructors is that: sure, when the engine quit in a single engine stops, you have one option: sooner or later, you land. Probably sooner.
But in a multi-engine airplane with one engine stops, you have a lot of options. It is the need to make a decision that kills those people.
Good
Factor A
Factor B
Less
More