Csci 136 Computer Architecture II –Cache Memory

Csci 136 Computer Architecture IICsci 136 Computer Architecture II –Cache Memory –Cache Memory

Xiuzhen [email protected]

Announcement

Homework assignment #11, Due time – by April 26.Readings: Sections 7.1 – 7.3

Problems: 7.9-7.10, 7.12-7.14, 7.29, 7.32-7.34.

Final: Thursday, May 12, 12:40AM-2:40PM

Note: you must pass final to pass this course!

The Five Classic Components of a Computer

Today’s Topics: Locality and Memory Hierarchy

Simple caching techniques

Many ways to improve cache performance

The Big Picture: Where are We Now?

Control

Datapath

Memory

Processor

Input

Output

Memory Hierarchy (1/3)

Processorexecutes instructions on order of nanoseconds to picoseconds

holds a small amount of code and data in registers

MemoryMore capacity than registers, still limited

Access time ~50-100 ns

DiskHUGE capacity (virtually limitless)VERY slow: runs ~milliseconds


Control

Datapath

Memory

Processor

Mem

ory

Memory

Memory

Mem

ory

Fastest Slowest

Smallest Biggest

Highest Lowest

Speed:

Size:

Cost:


If level closer to Processor, it must be:smaller

faster

subset of lower levels (contains most recently used data)

Lowest Level (usually disk) contains all available data

Other levels?

Goal: illusion of large, fast, cheap memory

µProc60%/yr.(2X/1.5yr)

DRAM9%/yr.(2X/10 yrs)1

10

100

1000

198

0198

1 198

3198

4198

5 198

6198

7198

8198

9199

0199

1 199

2199

3199

4199

5199

6199

7199

8 199

9200

0

DRAM

CPU198

2

Processor-MemoryPerformance Gap:(grows 50% / year)

Per

form

ance

Time

“Moore’s Law”

Processor-DRAM Memory Gap (latency)Rely on caches to bridge gap

Who Cares About the Memory Hierarchy?

Memory Caching

We’ve discussed three levels in the hierarchy: processor, memory, disk

Mismatch between processor and memory speeds leads us to add a new level: a memory cache

Implemented with SRAM technology: faster but more expensive than DRAM memory.

“S” = Static, no need to refresh, ~60ns

“D” = Dynamic, need to refresh, ~10nsarstechnica.com/paedia/r/ram_guide/ram_guide.part1-1.html

Technology Trends

Capacity Speed (latency)

Logic: 2x in 3 years 2x in 3 years

DRAM: 4x in 3 years 2x in 10 years

Disk: 4x in 3 years 2x in 10 years

Memory Technology Typical Access Time $ per GB in 2004

SRAM 0.5-5ns $4000-$10,000

DRAM 50-70ns $100-$200

Magnetic Disk 5,000,000-20,000,000ns

$0.50-$2

Memory Hierarchy Analogy: Library (1/2)

You’re writing a term paper (Processor) at a table in Doe

Doe Library is equivalent to diskessentially limitless capacity

very slow to retrieve a book

Table is memorysmaller capacity: means you must return book when table fills up

easier and faster to find a book there once you’ve already retrieved it

Memory Hierarchy Analogy: Library (2/2)

Open books on table are cachesmaller capacity: can have very few open books fit on table; again, when table fills up, you must close a book

much, much faster to retrieve data

Illusion created: whole library open on the tabletop Keep as many recently used books open on table as possible since likely to use again

Also keep as many books on table as possible, since faster than going to library

Memory Hierarchy Basis

Disk contains everything.

When Processor needs something, bring it into to all higher levels of memory.

Cache contains copies of data in memory that are being used.

Memory contains copies of data on disk that are being used.

Entire idea is based on Temporal and Spatial Localityif we use it now, we’ll want to use it again soon

If we use it now, we will use those in the nearby soon

Address Space0 2^n - 1

Probabilityof reference

Memory Hierarchy: Terminology

Hit: data appears in some block in the upper level (example: Block X)

Hit Rate: the fraction of memory access found in the upper level

Hit Time: Time to access the upper level which consists ofRAM access time + Time to determine hit/miss

Miss: data needs to be retrieved from a block in the lower level (Block Y)

Miss Rate = 1 - (Hit Rate)

Miss Penalty: Time to replace a block in the upper level + Time to deliver the block to the processor

Hit Time << Miss Penalty Lower LevelMemoryUpper Level

MemoryTo Processor

From ProcessorBlk X

Blk Y

How is the hierarchy managed?

Registers <-> Memoryby compiler (programmer?)

cache <-> memoryby the hardware

memory <-> disksby the hardware and operating system (virtual memory)

by the programmer (files)

Upper Level

Lower Level

faster

Larger

Levels of the Memory Hierarchy

Processor

Cache

Memory

Disk

Tape

Instr. Operands

Blocks

Pages

Files

Two Different Types of Locality:Temporal Locality (Locality in Time): If an item is referenced, it will tend to be referenced again soon.

Spatial Locality (Locality in Space): If an item is referenced, items whose addresses are close by tend to be referenced soon.

By taking advantage of the principle of locality:Present the user with as much memory as is available in the cheapest technology.

Provide access at the speed offered by the fastest technology.

DRAM is slow but cheap and dense:Good choice for presenting the user with a BIG memory system

SRAM is fast but expensive and not very dense:Good choice for providing the user FAST access time.

Summary: Exploit Locality to Achieve Fast Memory

Cache Design

How do we organize cache?

Where does each memory address map to?(Remember that cache is subset of memory, so multiple

memory addresses map to the same cache location.)

How do we know which elements are in cache?

How do we quickly locate them?

Cache TechnologiesDirect-Mapped Cache

Fully Associative Cache

Set Associative Cache

Direct-Mapped Cache (1/2)

In a direct-mapped cache, each memory address is associated with one possible block within the cache

Therefore, we only need to look in a single location in the cache for the data if it exists in the cache

Block is the unit of transfer between cache and memory

Direct-Mapped Cache (2/2)

Cache Location 0 can be occupied by data from:

Memory location 0, 4, 8, ...

4 blocks => any memory location that is multiple of 4

MemoryMemory Address

0123456789ABCDEF

4 Byte Direct Mapped Cache

Cache Index

0123

Issues with Direct-Mapped

Since multiple memory addresses map to same cache index, how do we tell which one is in there?

What if we have a block size > 1 byte?

Answer: divide memory address into three fields

ttttttttttttttttt iiiiiiiiii oooo

tag index byteto check to offsetif have select withincorrect block block block

Direct-Mapped Cache Terminology

All fields are read as unsigned integers.

Index: specifies the cache index (which “row” of the cache we should look in)

Offset: once we’ve found correct block, specifies which byte within the block we want

Tag: the remaining bits after offset and index are determined; these are used to distinguish between all the memory addresses that map to the same location

Direct-Mapped Cache Example (1/3)

Suppose we have a 16KB of data in a direct-mapped cache with 4 word blocks

Determine the size of the tag, index and offset fields if we’re using a 32-bit architecture

Offsetneed to specify correct byte within a block

block contains 4 words = 16 bytes

= 24 bytes

need 4 bits to specify correct byte


Index: (~index into an “array of blocks”)need to specify correct row in cache

cache contains 16 KB = 214 bytes

block contains 24 bytes (4 words)

# blocks/cache = bytes/cache

bytes/block

= 214 bytes/cache 24 bytes/block

= 210 blocks/cache

need 10 bits to specify this many rows


Tag: use remaining bits as tagtag length = addr length – offset - index

= 32 - 4 - 10 bits = 18 bits

so tag is leftmost 18 bits of memory address

Why not full 32 bit address as tag?All bytes within block need same address (4 bits)

Index must be same for every address within a block, so it’s redundant in tag check, thus can leave off to save memory (here 10 bits)

And in conclusion…

We would like to have the capacity of disk at the speed of the processor: unfortunately this is not feasible.

So we create a memory hierarchy:each successively lower level contains “most used” data from next higher level

exploits temporal/spatial locality

do the common case fast, worry less about the exceptions (design principle of MIPS)

Locality of reference is a Big Idea

Cache mnemonic

AREA (cache size, B)= HEIGHT (# of blocks) * WIDTH (size of one block, B/block)

WIDTH (size of one block, B/block)

HEIGHT(# of blocks)

AREA(cache size, B)

2(H+W) = 2H * 2W

Tag Index Offset

Caching Terminology

When we try to read memory, 3 things can happen:

1. cache hit: cache block is valid and contains proper address, so read desired word

2. cache miss: nothing in cache in appropriate block, so fetch from memory

3. cache miss, block replacement: wrong data is in cache at appropriate block, so discard it and fetch desired data from memory (cache always copy)

Accessing data in a direct mapped cache

Ex.: 16KB of data, direct-mapped, 4 word blocksRead 4 addresses

1. 0x000000142. 0x0000001C3. 0x000000344. 0x00008014

Memory values on right:

only cache/ memory level of hierarchy

Address (hex)Value of WordMemory

0000001000000014000000180000001C

abcd

... ...

0000003000000034000000380000003C

efgh

0000801000008014000080180000801C

ijkl

... ...

... ...

... ...

Accessing data in a direct mapped cache4 Addresses:0x00000014, 0x0000001C, 0x00000034, 0x00008014

4 Addresses divided (for convenience) into Tag, Index, Byte Offset fields

000000000000000000 0000000001 0100

000000000000000000 0000000001 1100

000000000000000000 0000000011 0100

000000000000000010 0000000001 0100

Tag Index Offset

16 KB Direct Mapped Cache, 16B blocks

Valid bit: determines whether anything is stored in that row (when computer initially turned on, all entries invalid)

...

ValidTag 0x0-3 0x4-7 0x8-b 0xc-f

01234567

10221023

...

Index00000000

00

1. Read 0x00000014

...


01234567

10221023

...

000000000000000000 0000000001 0100

Index

Tag field Index field Offset

00000000

00

So we read block 1 (0000000001)

...


01234567

10221023

...

000000000000000000 0000000001 0100

Index


00000000

00

No valid data

...


01234567

10221023

...

000000000000000000 0000000001 0100

Index


00000000

00

So load that data into cache, setting tag, valid

...


01234567

10221023

...

1 0 a b c d

000000000000000000 0000000001 0100

Index


0

000000

00

Read from cache at offset, return word b000000000000000000 0000000001 0100

...


01234567

10221023

...

1 0 a b c d

Index


0

000000

00

2. Read 0x0000001C = 0…00 0..001 1100

...


01234567

10221023

...

1 0 a b c d

000000000000000000 0000000001 1100

Index


0

000000

00

Index is Valid

...


01234567

10221023

...

1 0 a b c d

000000000000000000 0000000001 1100

Index


0

000000

00

Index valid, Tag Matches

...


01234567

10221023

...

1 0 a b c d

000000000000000000 0000000001 1100

Index


0

000000

00

Index Valid, Tag Matches, return d

...


01234567

10221023

...

1 0 a b c d

000000000000000000 0000000001 1100

Index


0

000000

00

3. Read 0x00000034 = 0…00 0..011 0100

...


01234567

10221023

...

1 0 a b c d

000000000000000000 0000000011 0100

Index


0

000000

00

So read block 3

...


01234567

10221023

...

1 0 a b c d

000000000000000000 0000000011 0100

Index


0

000000

00

No valid data

...


01234567

10221023

...

1 0 a b c d

000000000000000000 0000000011 0100

Index


0

000000

00

Load that cache block, return word f

...


01234567

10221023

...

1 0 a b c d

000000000000000000 0000000011 0100

1 0 e f g h

Index


0

0

0000

00

4. Read 0x00008014 = 0…10 0..001 0100

...


01234567

10221023

...

1 0 a b c d

000000000000000010 0000000001 0100

1 0 e f g h

Index


0

0

0000

00

So read Cache Block 1, Data is Valid

...


01234567

10221023

...

1 0 a b c d

000000000000000010 0000000001 0100

1 0 e f g h

Index


0

0

0000

00

Cache Block 1 Tag does not match (0 != 2)

...


01234567

10221023

...

1 0 a b c d

000000000000000010 0000000001 0100

1 0 e f g h

Index


0

0

0000

00

Miss, so replace block 1 with new data & tag

...


01234567

10221023

...

1 2 i j k l

000000000000000010 0000000001 0100

1 0 e f g h

Index


0

0

0000

00

And return word j

...


01234567

10221023

...

1 2 i j k l

000000000000000010 0000000001 0100

1 0 e f g h

Index


0

0

0000

00

Do an example yourself. What happens?

Chose from: Cache: Hit, Miss, Miss w. replace Values returned: a ,b, c, d, e, ..., k, l

Read address 0x00000030 ? 000000000000000000 0000000011 0000

Read address 0x0000001c ? 000000000000000000 0000000001 1100

...

ValidTag 0x0-3 0x4-7 0x8-b 0xc-f01234567...

1 2 i j k l

1 0 e f g h

Index0

0

0000

Cache

Answers

0x00000030 a hitIndex = 3, Tag matches, Offset = 0,

value = e

0x0000001c a missIndex = 1, Tag mismatch, so replace

from memory, Offset = 0xc, value = d

Since reads, values must = memory values whether or not cached:

0x00000030 = e

0x0000001c = d

Address Value of WordMemory

0000001000000014000000180000001c

abcd

... ...

0000003000000034000000380000003c

efgh

0000801000008014000080180000801c

ijkl

... ...

... ...

... ...

And in Conclusion…

Mechanism for transparent movement of data among levels of a storage hierarchy

set of address/value bindingsaddress index to set of candidatescompare desired address with tagservice hit or miss

load new block and binding on miss


0123...

1 0 a b c d

000000000000000000 0000000001 1100address: tag index offset

Block Size Tradeoff (1/3)

Benefits of Larger Block SizeSpatial Locality: if we access a given word, we’re likely to access other nearby words soon

Very applicable with Stored-Program Concept: if we execute a given instruction, it’s likely that we’ll execute the next few as well

Works nicely in sequential array accesses too


Drawbacks of Larger Block SizeLarger block size means larger miss penalty

on a miss, takes longer time to load a new block from next level

If block size is too big relative to cache size, then there are too few blocks

Result: miss rate goes up

In general, minimize Average Access Time

= Hit Time x Hit Rate + Miss Penalty x Miss Rate


Hit Time = time to find and retrieve data from current level cache

Miss Penalty = average time to retrieve data on a current level miss (includes the possibility of misses on successive levels of memory hierarchy)

Hit Rate = % of requests that are found in current level cache

Miss Rate = 1 - Hit Rate

Extreme Example: One Big Block

Cache Size = 4 bytes Block Size = 4 bytesOnly ONE entry in the cache!

If item accessed, likely accessed again soonBut unlikely will be accessed again immediately!

The next access will likely to be a miss againContinually loading data into the cache butdiscard data (force out) before use it again

Nightmare for cache designer: Ping Pong Effect

Cache DataValid BitB 0B 1B 3

TagB 2

Block Size Tradeoff Conclusions

MissPenalty

Block Size

Increased Miss Penalty& Miss Rate

AverageAccess

Time

Block Size

Exploits Spatial Locality

Fewer blocks: compromisestemporal locality

MissRate

Block Size

Types of Cache Misses (1/2)

“Three Cs” Model of Misses

1st C: Compulsory Missesoccur when a program is first started

cache does not contain any of that program’s data yet, so misses are bound to occur

can’t be avoided easily, so won’t focus on these in this course

Types of Cache Misses (2/2)

2nd C: Conflict Missesmiss that occurs because two distinct memory addresses map to the same cache location

two blocks (which happen to map to the same location) can keep overwriting each other

big problem in direct-mapped caches

how do we lessen the effect of these?

Dealing with Conflict MissesSolution 1: Make the cache size bigger

Fails at some point

Solution 2: Multiple distinct blocks can fit in the same cache Index?

Fully Associative Cache (1/3)

Memory address fields:Tag: same as before

Offset: same as before

Index: non-existant

What does this mean?no “rows”: any block can go anywhere in the cache

must compare with all tags in entire cache to see if data is there


Fully Associative Cache (e.g., 32 B block)compare tags in parallel

Byte Offset

:

Cache DataB 0

0431

:

Cache Tag (27 bits long)

Valid

:

B 1B 31 :

Cache Tag=

==

=

=:


Benefit of Fully Assoc CacheNo Conflict Misses (since data can go anywhere)

Drawbacks of Fully Assoc CacheNeed hardware comparator for every single entry: if we have a 64KB of data in cache with 4B entries, we need 16K comparators: infeasible

Third Type of Cache Miss

Capacity Missesmiss that occurs because the cache has a limited size

miss that would not occur if we increase the size of the cache

sketchy definition, so just get the general idea

This is the primary type of miss for Fully Associative caches.

N-Way Set Associative Cache (1/4)

Memory address fields:Tag: same as before

Offset: same as before

Index: points us to the correct “row” (called a set in this case)

So what’s the difference?each set contains multiple blocks

once we’ve found correct set, must compare with all tags in that set to find our data


Summary:cache is direct-mapped w/respect to sets

each set is fully associative

basically N direct-mapped caches working in parallel: each has its own valid bit and data


Given memory address:Find correct set using Index value.

Compare Tag with all Tag values in the determined set.

If a match occurs, hit!, otherwise a miss.

Finally, use the offset field as usual to find the desired data within the block.


What’s so great about this?even a 2-way set assoc cache avoids a lot of conflict misses

hardware cost isn’t that bad: only need N comparators

In fact, for a cache with M blocks,it’s Direct-Mapped if it’s 1-way set assoc

it’s Fully Assoc if it’s M-way set assoc

so these two are just special cases of the more general set associative design

Associative Cache Example

Recall this is how a simple direct mapped cache looked.

This is also a 1-way set-associative cache!


0123456789ABCDEF

4 Byte Direct Mapped Cache

Cache Index

0123

Associative Cache Example

Here’s a simple 2 way set associative cache.


0123456789ABCDEF

Cache Index

0011

Cache Things to Remember

Caches are NOT mandatory:Processor performs arithmeticMemory stores dataCaches simply make data transfers go faster

Each level of Memory Hiererarchyis a subset of next higher level

Caches speed up due to temporal locality: store data used recently

Block size > 1 wd spatial locality speedup:Store words next to the ones used recently

Cache design choices:size of cache: speed v. capacityN-way set assoc: choice of N (direct-mapped, fully-associative just special cases for N)

Block Replacement Policy (1/2)

Direct-Mapped Cache: index completely specifies position which position a block can go in on a miss

N-Way Set Assoc: index specifies a set, but block can occupy any position within the set on a miss

Fully Associative: block can be written into any position

Question: if we have the choice, where should we write an incoming block?

Block Replacement Policy (2/2)

If there are any locations with valid bit off (empty), then usually write the new block into the first one.

If all possible locations already have a valid block, we must pick a replacement policy: rule by which we determine which block gets “cached out” on a miss.

Block Replacement Policy: LRU

LRU (Least Recently Used)Idea: cache out block which has been accessed (read or write) least recently

Pro: temporal locality recent past use implies likely future use: in fact, this is a very effective policy

Con: with 2-way set assoc, easy to keep track (one LRU bit); with 4-way or greater, requires complicated hardware and much time to keep track of this

Block Replacement Example

We have a 2-way set associative cache with a four word total capacity and one word blocks. We perform the following word accesses (ignore bytes for this problem):

0, 2, 0, 1, 4, 0, 2, 3, 5, 4

How many hits and how many misses will there be for the LRU block replacement policy?

Block Replacement Example: LRUAddresses 0, 2, 0, 1, 4, 0, ... 0 lru

2

1 lru

loc 0 loc 1

set 0

set 1

0 2lruset 0

set 1

0: miss, bring into set 0 (loc 0)


0: hit


4: miss, bring into set 0 (loc 1, replace 2)

0: hit

0set 0

set 1

lrulru

0 2set 0

set 1

lru lru

set 0

set 1

01 lru

lru24lru

set 0

set 1

0 41 lru

lru lru

Big Idea

How to choose between associativity, block size, replacement policy?Design against a performance model

Minimize: Average Memory Access Time = Hit Time

+ Miss Penalty x Miss Rateinfluenced by technology & program behaviorNote: Hit Time encompasses Hit Rate!!!

Create the illusion of a memory that is large, cheap, and fast - on average

Example

Assume Hit Time = 1 cycle

Miss rate = 5%

Miss penalty = 20 cycles

Calculate AMAT…

Avg mem access time = 1 + 0.05 x 20

= 1 + 1 cycles

= 2 cycles

Ways to reduce miss rate

Larger cachelimited by cost and technology

hit time of first level cache < cycle time

More places in the cache to put each block of memory – associativity

fully-associativeany block any line

N-way set associatedN places for each block

direct map: N=1

Improving Miss Penalty

When caches first became popular, Miss Penalty ~ 10 processor clock cycles

Today 2400 MHz Processor (0.4 ns per clock cycle) and 80 ns to go to DRAM 200 processor clock cycles!

Proc $2

DR

AM

$

MEM

Solution: another cache between memory and the processor cache: Second Level (L2) Cache

Analyzing Multi-level cache hierarchy

Proc $2

DR

AM

$

L1 hit time

L1 Miss RateL1 Miss Penalty

Avg Mem Access Time = L1 Hit Time + L1 Miss Rate * L1 Miss Penalty

L1 Miss Penalty = L2 Hit Time + L2 Miss Rate * L2 Miss Penalty

Avg Mem Access Time = L1 Hit Time + L1 Miss Rate * (L2 Hit Time + L2 Miss Rate * L2 Miss Penalty)

L2 hit time L2 Miss Rate

L2 Miss Penalty

Typical Scale

L1 size: tens of KBhit time: complete in one clock cycle

miss rates: 1-5%L2:

size: hundreds of KBhit time: few clock cycles

miss rates: 10-20%

L2 miss rate is fraction of L1 misses that also miss in L2

why so high?

Example: with L2 cache

Assume L1 Hit Time = 1 cycle

L1 Miss rate = 5%

L2 Hit Time = 5 cycles

L2 Miss rate = 15% (% L1 misses that miss)

L2 Miss Penalty = 200 cycles

L1 miss penalty = 5 + 0.15 * 200 = 35

Avg mem access time = 1 + 0.05 x 35= 2.75 cycles

Example: without L2 cache


L1 Miss rate = 5%


Avg mem access time = 1 + 0.05 x 200= 11 cycles

4x faster with L2 cache! (2.75 vs. 11)

Example: with L2 cache again


L1 Miss rate = 5%

L2 Hit Time = 5 cycles

L2 decreases the miss rate to main memory to 0.5%


Avg mem access time = 1 + 0.05 x 5 + 0.005 x 200= 2.25 cycles

An Actual CPU – Pentium M

What to do on a write hit?

Write-throughupdate the word in cache block and corresponding word in memory

Write-backupdate word in cache blockallow memory word to be “stale”

add ‘dirty’ bit to each block indicating that memory needs to be updated when block is replaced

OS flushes cache before I/O…

Performance trade-offs?

Generalized Caching

We’ve discussed memory caching in detail. Caching in general shows up over and over in computer systems

Filesystem cacheWeb page cacheGame Theory databases / tablebasesSoftware memoizationOthers?

Big idea: if something is expensive but we want to do it repeatedly, do it once and cache the result.

An Example: Performance Comparision

Assume an instruction cache miss rate for a program is 2% and a data cache miss rate is 4%. If a processor has a CPI of 2 without any memory stalls and the miss penalty is 100 cycles for all misses. Determine how much faster a processor would run with a perfect cache that never missed. Assume 36% of instructions involve memory access.

An Example: Tag Size vs. Associativity

Assuming a cache of 4K blocks, a four-word block size, and a 32-bit byte address. Find out the total number of sets and the total number of tag bits for caches that are direct-mapped, 2-way set associative, 4-way set associative, and fully associated.

And in Conclusion…

Cache design choices:size of cache: speed v. capacitydirect-mapped v. associativefor N-way set assoc: choice of Nblock replacement policy2nd level cache?Write through v. write back?

Use performance model to pick between choices, depending on programs, technology, budget, ...

Virtual MemoryPredates caches; each process thinks it has all the memory to itself; protection!

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Csci 136 Computer Architecture II –Cache Memory