程序代写代做代考 compiler mips cache algorithm Chapter 5

Chapter 5

COMPUTER ORGANIZATION AND DESIGN
The Hardware/Software Interface

5th

Edition

Chapter 5

Large and Fast:

Exploiting Memory

Hierarchy

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 2

Principle of Locality

 Programs access a small proportion of

their address space at any time

 Temporal locality

 Items accessed recently are likely to be

accessed again soon

 e.g., instructions in a loop, induction variables

 Spatial locality

 Items near those accessed recently are likely

to be accessed soon

 E.g., sequential instruction access, array data

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Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 3

Taking Advantage of Locality

 Memory hierarchy

 Store everything on disk

 Copy recently accessed (and nearby)

items from disk to smaller DRAM memory

 Main memory

 Copy more recently accessed (and nearby)

items from DRAM to smaller SRAM

memory

 Cache memory attached to CPU

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 4

Memory Hierarchy

( ___________ replaces magnetic disks in personal mobile devices)

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 5

Memory Hierarchy Levels

 Block (aka line): unit of copying

 May be multiple words

 If accessed data is present in

upper level

 Hit: access satisfied by upper level

 Hit ratio: hits/accesses

 If accessed data is absent

 Miss: block copied from lower level

 Time taken: miss penalty

 Miss ratio: misses/accesses

= 1 – hit ratio

 Then accessed data supplied from

upper level

(Hierarchy: data cannot be present in level_i unless it is also present

in level_( ___))

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 6

Memory Technology

 Static RAM (SRAM)

 0.5ns – 2.5ns, $2000 – $5000 per GB

 Dynamic RAM (DRAM)

 50ns – 70ns, $20 – $75 per GB

 Magnetic disk

 5ms – 20ms, $0.20 – $2 per GB

 Ideal memory

 Access time of SRAM

 Capacity and cost/GB of disk

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(Flash memory: ______μs, $0.75 – $1.0 per __ )

( ____ tr/bit; on chip cache)

DRAM Technology

 Data stored as a charge in a capacitor

 Single transistor used to access the charge

 Must periodically be refreshed

 Read contents and write back

 Performed on a DRAM “row”

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 7

(Can be kept for a few ______ )

(________)

(_______)

DRAM Structure

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 8

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 9

Advanced DRAM Organization

 Bits in a DRAM are organized as a

rectangular array
 DRAM accesses an entire row

 Burst mode: supply successive words from a row with reduced

latency

 Double data rate (DDR) DRAM
 Transfer on rising and falling clock edges

 Quad data rate (QDR) DRAM
 Separate DDR inputs and outputs

(DDR4: _____ million transfers/sec with _____MHz clock)

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 10

DRAM Generations

0

50

100

150

200

250

300

’80 ’83 ’85 ’89 ’92 ’96 ’98 ’00 ’04 ’07

Trac

Tcac

Year Capacity $/GB

1980 64Kbit $1500000

1983 256Kbit $500000

1985 1Mbit $200000

1989 4Mbit $50000

1992 16Mbit $15000

1996 64Mbit $10000

1998 128Mbit $4000

2000 256Mbit $1000

2004 512Mbit $250

2007 1Gbit $50

(2010 __Gbit $__)

(2012 __Gbit $__)

(‘12)

(___ns)

(__ns)

(2016 __GB LPDDR4 10nm by ________ )

DRAM Performance Factors

 Row buffer

 Allows several words to be read and refreshed in

parallel

 Synchronous DRAM

 Allows for consecutive accesses in bursts without

needing to send each address

 Improves bandwidth

 DRAM banking

 Allows simultaneous access to multiple DRAMs

 Improves bandwidth

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 11

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 12

Increasing Memory Bandwidth

 4-word wide memory
 Miss penalty = 1 + 15 + 1 = 17 bus cycles

 Bandwidth = 16 bytes / 17 cycles = 0.94 B/cycle

 4-bank interleaved memory
 Miss penalty = 1 + 15 + 4× 1 = 20 bus cycles

 Bandwidth = 16 bytes / 20 cycles = 0.8 B/cycle

(1 to ____ address; 15 to _______; 1 to send _____)

(1 to ____ address; 15 to ______; 4 to send _____ from each ____ )

Chapter 6 — Storage and Other I/O Topics — 13

Flash Storage

 Nonvolatile semiconductor storage

 100× – 1000× faster than disk

 Smaller, lower power, more robust

 But more $/GB (between disk and DRAM)

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Chapter 6 — Storage and Other I/O Topics — 14

Flash Types

 NOR flash: bit cell like a NOR gate

 Random read/write access

 Used for instruction memory in embedded systems

 NAND flash: bit cell like a NAND gate

 Denser (bits/area), but block-at-a-time access

 Cheaper per GB

 Used for USB keys, media storage, …

 Flash bits wears out after 1000’s of accesses

 Not suitable for direct RAM or disk replacement

 Wear leveling: remap data to less used blocks
(FTL: F____ T________ L____ )

Chapter 6 — Storage and Other I/O Topics — 15

Flash Types

 NOR flash

 NAND flash

//upload.wikimedia.org/wikipedia/commons/d/dd/NOR_flash_layout.svg
//upload.wikimedia.org/wikipedia/commons/f/f5/Nand_flash_structure.svg

Chapter 6 — Storage and Other I/O Topics — 16

Disk Storage

 Nonvolatile, rotating magnetic storage

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(____ ~ _______ revolution/min)

(10’s of ____ track/surface)
( ___ ~ ____B/sector;

1000’s sector/track)

Chapter 6 — Storage and Other I/O Topics — 17

Disk Sectors and Access

 Each sector records
 Sector ID

 Data (512 bytes, 4096 bytes proposed)

 Error correcting code (ECC)
 Used to hide defects and recording errors

 Synchronization fields and gaps

 Access to a sector involves
 Queuing delay if other accesses are pending

 Seek: move the heads

 Rotational latency

 Data transfer

 Controller overhead

(_____ msec)

(___ ~ ___MB/sec; ___MB/sec with cache)

Chapter 6 — Storage and Other I/O Topics — 18

Disk Access Example

 Given
 512B sector, 15,000rpm, 4ms average seek

time, 100MB/s transfer rate, 0.2ms controller
overhead, idle disk

 Average read time
 4ms seek time

+ ½ / (15,000/60) = 2ms rotational latency
+ 512 / 100MB/s = 0.005ms transfer time
+ 0.2ms controller delay
= 6.2ms

 If actual average seek time is 1ms
 Average read time = 3.2ms

Chapter 6 — Storage and Other I/O Topics — 19

Disk Performance Issues

 Manufacturers quote average seek time

 Based on all possible seeks

 Locality and OS scheduling lead to

smaller actual average seek times

 Smart disk controller allocate physical sectors on

disk

 Present logical sector interface to host

 SCSI, ATA, SATA

 Disk drives include caches

 Prefetch sectors in anticipation of

access

 Avoid seek and rotational delay

(Small Computer System Interface; AT Attachment; Serial ATA)

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 20

Cache Memory

 Cache memory

 The level of the memory hierarchy closest to

the CPU

 Given accesses X1, …, Xn–1, Xn

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 How do we know if

the data is present?

 Where do we look?

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 21

Direct Mapped Cache

 Location determined by address

 Direct mapped: only one choice

 (Block address) modulo (#Blocks in cache)

 #Blocks is a

power of 2

 Use low-order

address bits

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 22

Tags and Valid Bits

 How do we know which particular block is

stored in a cache location?

 Store block address as well as the data

 Actually, only need the high-order bits

 Called the tag

 What if there is no data in a location?

 Valid bit: 1 = present, 0 = not present

 Initially 0

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 23

Cache Example

 8-blocks, 1 word/block, direct mapped

 Initial state

Index V Tag Data

000 N

001 N

010 N

011 N

100 N

101 N

110 N

111 N

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 24

Cache Example

Index V Tag Data

000 N

001 N

010 N

011 N

100 N

101 N

110 Y 10 Mem[10110]

111 N

Word addr Binary addr Hit/miss Cache block

22 10 110 Miss 110

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 25

Cache Example

Index V Tag Data

000 N

001 N

010 Y 11 Mem[11010]

011 N

100 N

101 N

110 Y 10 Mem[10110]

111 N

Word addr Binary addr Hit/miss Cache block

26 11 010 Miss 010

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 26

Cache Example

Index V Tag Data

000 N

001 N

010 Y 11 Mem[11010]

011 N

100 N

101 N

110 Y 10 Mem[10110]

111 N

Word addr Binary addr Hit/miss Cache block

22 10 110 Hit 110

26 11 010 Hit 010

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 27

Cache Example

Index V Tag Data

000 Y 10 Mem[10000]

001 N

010 Y 11 Mem[11010]

011 Y 00 Mem[00011]

100 N

101 N

110 Y 10 Mem[10110]

111 N

Word addr Binary addr Hit/miss Cache block

16 10 000 Miss 000

3 00 011 Miss 011

16 10 000 Hit 000

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 28

Cache Example

Index V Tag Data

000 Y 10 Mem[10000]

001 N

010 Y 10 Mem[10010]

011 Y 00 Mem[00011]

100 N

101 N

110 Y 10 Mem[10110]

111 N

Word addr Binary addr Hit/miss Cache block

18 10 010 Miss 010

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 29

Address Subdivision

(4KB cache; actually much larger if tag and valid bit are included)

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 30

Example: Larger Block Size

 64 blocks, 16 bytes/block

 To what block number does address 1200

map?

 Block address = 1200/16 = 75

 Block number = 75 modulo 64 = 11

Tag Index Offset

0 3 4 9 10 31

4 bits 6 bits 22 bits

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 31

Block Size Considerations

 Larger blocks should reduce miss rate

 Due to spatial locality

 In fixed-sized cache

 Larger blocks  fewer

 More competition 

increased miss rate

 Larger blocks  pollution

 Larger miss penalty

 Can override benefit of reduced miss rate

 Early restart and critical-word-first can help
(Resume execution as soon as the requested word is returned; used for _________ access)

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 32

Cache Misses

 On cache hit, CPU proceeds normally

 On cache miss

 Stall the CPU pipeline

 Fetch block from next level of hierarchy

 Instruction cache miss

 Restart instruction fetch

 Data cache miss

 Complete data access

(_______ read______ updateRefetch from _____)

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 33

Write-Through

 On data-write hit, could just update the block in
cache
 But then cache and memory would be inconsistent

 Write through: also update memory

 But makes writes take longer
 e.g., if base CPI = 1, 10% of instructions are stores,

write to memory takes 100 cycles
 Effective CPI = 1 + 0.1× 100 = 11

 Solution: write buffer
 Holds data waiting to be written to memory

 CPU continues immediately
 Only stalls on write if write buffer is already full

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 34

Write-Back

 Alternative: On data-write hit, just update

the block in cache

 Keep track of whether each block is dirty

 When a dirty block is replaced

 Write it back to memory

 Can use a write buffer to allow replacing block

to be read first

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 35

Write Allocation

 What should happen on a write miss?

 Alternatives for write-through

 Allocate on miss: fetch the block

 Write around: don’t fetch the block

 Since programs often write a whole block before

reading it (e.g., initialization)

 For write-back

 Usually fetch the block

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 36

Example: Intrinsity FastMATH

 Embedded MIPS processor

 12-stage pipeline

 Instruction and data access on each cycle

 Split cache: separate I-cache and D-cache

 Each 16KB: 256 blocks × 16 words/block

 D-cache: write-through or write-back

 SPEC2000 miss rates

 I-cache: 0.4%

 D-cache: 11.4%

 Weighted average: 3.2%

(___-entry write buffer)

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 37

Example: Intrinsity FastMATH
(Split cache vs unified cache;

____% vs ____% miss rate;

______ bandwidth)

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 38

Main Memory Supporting Caches

 Use DRAMs for main memory
 Fixed width (e.g., 1 word)

 Connected by fixed-width clocked bus
 Bus clock is typically slower than CPU clock

 Example cache block read
 1 bus cycle for address transfer

 15 bus cycles per DRAM access

 1 bus cycle per data transfer

 For 4-word block, 1-word-wide DRAM

 Miss penalty = 1 + 4× 15 + 4× 1 = 65 bus cycles

 Bandwidth = 16 bytes / 65 cycles = 0.25 B/cycle

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 39

Measuring Cache Performance

 Components of CPU time
 Program execution cycles

 Includes cache hit time

 Memory stall cycles
 Mainly from cache misses

 With simplifying assumptions:

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(Different for read and write due to

write buffer _____ )

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 40

Cache Performance Example

 Given
 I-cache miss rate = 2%

 D-cache miss rate = 4%

 Miss penalty = 100 cycles

 Base CPI (ideal cache) = 2

 Load & stores are 36% of instructions

 Miss cycles per instruction
 I-cache: 0.02 × 100 = 2
 D-cache: 0.36 × 0.04 × 100 = 1.44

 Actual CPI = 2 + 2 + 1.44 = 5.44
 Ideal CPU is 5.44/2 =2.72 times faster

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 41

Average Access Time

 Hit time is also important for performance

 Average memory access time (AMAT)

 AMAT = Hit time + Miss rate × Miss penalty

 Example

 CPU with 1ns clock, hit time = 1 cycle, miss

penalty = 20 cycles, I-cache miss rate = 5%

 AMAT = 1 + 0.05 × 20 = 2ns

 2 cycles per instruction

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 42

Performance Summary

 When CPU performance increased

 Miss penalty becomes more significant

 Decreasing base CPI

 Greater proportion of time spent on memory

stalls

 Increasing clock rate

 Memory stalls account for more CPU cycles

 Can’t neglect cache behavior when

evaluating system performance

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 43

Associative Caches

 Fully associative

 Allow a given block to go in any cache entry

 Requires all entries to be searched at once

 Comparator per entry (expensive)

 n-way set associative

 Each set contains n entries

 Block number determines which set

 (Block number) modulo (#Sets in cache)

 Search all entries in a given set at once

 n comparators (less expensive)

(Tag is CAM (c______ a__________ m_____))

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 44

Associative Cache Example

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 45

Spectrum of Associativity

 For a cache with 8 entries

(Increasing the degree of associativity _________ miss rate but _________ hit time)

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 46

Associativity Example

 Compare 4-block caches

 Direct mapped, 2-way set associative,

fully associative

 Block access sequence: 0, 8, 0, 6, 8

 Direct mapped

Block

address

Cache

index

Hit/miss Cache content after access

0 1 2 3

0 0 miss Mem[0]

8 0 miss Mem[8]

0 0 miss Mem[0]

6 2 miss Mem[0] Mem[6]

8 0 miss Mem[8] Mem[6]

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 47

Associativity Example

 2-way set associative
Block

address

Cache

index

Hit/miss Cache content after access

Set 0 Set 1

0 0 miss Mem[0]

8 0 miss Mem[0] Mem[8]

0 0 hit Mem[0] Mem[8]

6 0 miss Mem[0] Mem[6]

8 0 miss Mem[8] Mem[6]

 Fully associative
Block

address

Hit/miss Cache content after access

0 miss Mem[0]

8 miss Mem[0] Mem[8]

0 hit Mem[0] Mem[8]

6 miss Mem[0] Mem[8] Mem[6]

8 hit Mem[0] Mem[8] Mem[6]

(L____ r______ u____

(LRU))

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 48

How Much Associativity

 Increased associativity decreases miss

rate

 But with diminishing returns

 Simulation of a system with 64KB

D-cache, 16-word blocks, SPEC2000

 1-way: 10.3%

 2-way: 8.6%

 4-way: 8.3%

 8-way: 8.1%

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 49

Set Associative Cache Organization

( ____ -way set associative?)

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 50

Replacement Policy

 Direct mapped: no choice

 Set associative
 Prefer non-valid entry, if there is one

 Otherwise, choose among entries in the set

 Least-recently used (LRU)
 Choose the one unused for the longest time

 Simple for 2-way, manageable for 4-way, too hard
beyond that

 Random
 Gives approximately the same performance

as LRU for high associativity

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 51

Multilevel Caches

 Primary cache attached to CPU

 Small, but fast

 Level-2 cache services misses from

primary cache

 Larger, slower, but still faster than main

memory

 Main memory services L-2 cache misses

 Some high-end systems include L-3 cache
(Itanium 9500(Poulson): __-bit microprocessor, __nm, _ core, L2 I ___KB/D ___KB per core, L3 ___B,

____ GHz CPU clock, __-wide issue architecture, multithreading, virtualization, die size ___ mm²)

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 52

Multilevel Cache Example

 Given

 CPU base CPI = 1, clock rate = 4GHz

 Miss rate/instruction = 2%

 Main memory access time = 100ns

 With just primary cache

 Miss penalty = 100ns/0.25ns = 400 cycles

 Effective CPI = 1 + 0.02 × 400 = 9

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 53

Example (cont.)

 Now add L-2 cache

 Access time = 5ns

 Global miss rate to main memory = 0.5%

 Primary miss with L-2 hit

 Penalty = 5ns/0.25ns = 20 cycles

 Primary miss with L-2 miss

 Extra penalty = 500 cycles

 CPI = 1 + 0.02 × 20 + 0.005 × 400 = 3.4

 Performance ratio = 9/3.4 = 2.6

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 54

Multilevel Cache Considerations

 Primary cache

 Focus on minimal hit time

 L-2 cache

 Focus on low miss rate to avoid main memory

access

 Hit time has less overall impact

 Results

 L-1 cache usually smaller than a single cache

 L-1 block size smaller than L-2 block size
(L-2 has higher associativity to reduce _________ )

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 55

Interactions with Advanced CPUs

 Out-of-order CPUs can execute

instructions during cache miss

 Pending store stays in load/store unit

 Dependent instructions wait in reservation

stations

 Independent instructions continue

 Effect of miss depends on program data

flow

 Much harder to analyse

 Use system simulation

Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 56

Interactions with Software

 Misses depend on

memory access

patterns

 Algorithm behavior

 Compiler

optimization for

memory access

(170, 45, 75, 90, 802, 2, 24, 66)

(___, ___, ___, ___, ___, ___, ___, ___)

(Mismatch)

(___, ___, ___, ___, ___, ___, ___, ___)

(___, ___, ___, ___, ___, ___, ___, ___)

Software Optimization via Blocking

 Goal: maximize accesses to data before it

is replaced

 Consider inner loops of DGEMM:

for (int j = 0; j < n; ++j) { double cij = C[i+j*n]; for( int k = 0; k < n; k++ ) cij += A[i+k*n] * B[k+j*n]; C[i+j*n] = cij; } Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 57 DGEMM Access Pattern  C, A, and B arrays Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 58 older accesses new accesses Cache Blocked DGEMM 1 #define BLOCKSIZE 32 2 void do_block (int n, int si, int sj, int sk, double *A, double 3 *B, double *C) 4 { 5 for (int i = si; i < si+BLOCKSIZE; ++i) 6 for (int j = sj; j < sj+BLOCKSIZE; ++j) 7 { 8 double cij = C[i+j*n];/* cij = C[i][j] */ 9 for( int k = sk; k < sk+BLOCKSIZE; k++ ) 10 cij += A[i+k*n] * B[k+j*n];/* cij+=A[i][k]*B[k][j] */ 11 C[i+j*n] = cij;/* C[i][j] = cij */ 12 } 13 } 14 void dgemm (int n, double* A, double* B, double* C) 15 { 16 for ( int sj = 0; sj < n; sj += BLOCKSIZE ) 17 for ( int si = 0; si < n; si += BLOCKSIZE ) 18 for ( int sk = 0; sk < n; sk += BLOCKSIZE ) 19 do_block(n, si, sj, sk, A, B, C); 20 } Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 59 Blocked DGEMM Access Pattern Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 60 Unoptimized Blocked (All 3 matrices fit in the ______ ) (For ______ locality) (For _______ locality) (_________: maximizing memory performance at run time considering cache size, associativity, block size, number of caches) Chapter 6 — Storage and Other I/O Topics — 61 Dependability  Fault: failure of a component  May or may not lead to system failure Service accomplishment Service delivered as specified Service interruption Deviation from specified service Failure Restoration § 5 .5 D e p e n d a b le M e m o ry H ie ra rc h y (Permanent or _________ ) Chapter 6 — Storage and Other I/O Topics — 62 Dependability Measures  Reliability: mean time to failure (MTTF)  Service interruption: mean time to repair (MTTR)  Mean time between failures  MTBF = MTTF + MTTR  Availability = MTTF / (MTTF + MTTR)  Improving Availability  Increase MTTF: fault avoidance, fault tolerance, fault forecasting  Reduce MTTR: improved tools and processes for diagnosis and repair The Hamming SEC Code  Hamming distance  Number of bits that are different between two bit patterns  Minimum distance = 2 provides single bit error detection  E.g. parity code  Minimum distance = 3 provides single error correction, 2 bit error detection Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 63 Encoding SEC  To calculate Hamming code:  Number bits from 1 on the left  All bit positions that are a power 2 are parity bits  Each parity bit checks certain data bits: Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 64 Decoding SEC  Value of parity bits indicates which bits are in error  Use numbering from encoding procedure  E.g.  Parity bits = 0000 indicates no error  Parity bits = 1010 indicates bit 10 was flipped Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 65 SEC/DEC Code  Add an additional parity bit for the whole word (pn)  Make Hamming distance = 4  Decoding:  Let H = SEC parity bits  H even, pn even, no error  H odd, pn odd, correctable single bit error  H even, pn odd, error in pn bit  H odd, pn even, double error occurred  Note: ECC DRAM uses SEC/DEC with 8 bits protecting each 64 bits Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 66 Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 67 Virtual Machines  Host computer emulates guest operating system and machine resources  Improved isolation of multiple guests  Avoids security and reliability problems  Aids sharing of resources  Virtualization has some performance impact  Feasible with modern high-performance comptuers  Examples  IBM VM/370 (1970s technology!)  VMWare  Microsoft Virtual PC § 5 .6 V irtu a l M a c h in e s Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 68 Virtual Machine Monitor  Maps virtual resources to physical resources  Memory, I/O devices, CPUs  Guest code runs on native machine in user mode  Traps to VMM on privileged instructions and access to protected resources  Guest OS may be different from host OS  VMM handles real I/O devices  Emulates generic virtual I/O devices for guest Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 69 Example: Timer Virtualization  In native machine, on timer interrupt  OS suspends current process, handles interrupt, selects and resumes next process  With Virtual Machine Monitor  VMM suspends current VM, handles interrupt, selects and resumes next VM  If a VM requires timer interrupts  VMM emulates a virtual timer  Emulates interrupt for VM when physical timer interrupt occurs Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 70 Instruction Set Support  User and System modes  Privileged instructions only available in system mode  Trap to system if executed in user mode  All physical resources only accessible using privileged instructions  Including page tables, interrupt controls, I/O registers  Renaissance of virtualization support  Current ISAs (e.g., x86) adapting Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 71 Virtual Memory  Use main memory as a “cache” for secondary (disk) storage  Managed jointly by CPU hardware and the operating system (OS)  Programs share main memory  Each gets a private virtual address space holding its frequently used code and data  Protected from other programs  CPU and OS translate virtual addresses to physical addresses  VM “block” is called a page  VM translation “miss” is called a page fault § 5 .7 V irtu a l M e m o ry Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 72 Address Translation  Fixed-size pages (e.g., 4K) Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 73 Page Fault Penalty  On page fault, the page must be fetched from disk  Takes millions of clock cycles  Handled by OS code  Try to minimize page fault rate  Fully associative placement  Smart replacement algorithms Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 74 Page Tables  Stores placement information  Array of page table entries, indexed by virtual page number  Page table register in CPU points to page table in physical memory  If page is present in memory  PTE stores the physical page number  Plus other status bits (referenced, dirty, …)  If page is not present  PTE can refer to location in swap space on disk Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 75 Translation Using a Page Table Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 76 Mapping Pages to Storage Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 77 Replacement and Writes  To reduce page fault rate, prefer least- recently used (LRU) replacement  Reference bit (aka use bit) in PTE set to 1 on access to page  Periodically cleared to 0 by OS  A page with reference bit = 0 has not been used recently  Disk writes take millions of cycles  Block at once, not individual locations  Write through is impractical  Use write-back  Dirty bit in PTE set when page is written Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 78 Fast Translation Using a TLB  Address translation would appear to require extra memory references  One to access the PTE  Then the actual memory access  But access to page tables has good locality  So use a fast cache of PTEs within the CPU  Called a Translation Look-aside Buffer (TLB)  Typical: 16–512 PTEs, 0.5–1 cycle for hit, 10–100 cycles for miss, 0.01%–1% miss rate  Misses could be handled by hardware or software Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 79 Fast Translation Using a TLB Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 80 TLB Misses  If page is in memory  Load the PTE from memory and retry  Could be handled in hardware  Can get complex for more complicated page table structures  Or in software  Raise a special exception, with optimized handler  If page is not in memory (page fault)  OS handles fetching the page and updating the page table  Then restart the faulting instruction Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 81 TLB Miss Handler  TLB miss indicates  Page present, but PTE not in TLB  Page not preset  Must recognize TLB miss before destination register overwritten  Raise exception  Handler copies PTE from memory to TLB  Then restarts instruction  If page not present, page fault will occur Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 82 Page Fault Handler  Use faulting virtual address to find PTE  Locate page on disk  Choose page to replace  If dirty, write to disk first  Read page into memory and update page table  Make process runnable again  Restart from faulting instruction Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 83 TLB and Cache Interaction  If cache tag uses physical address  Need to translate before cache lookup  Alternative: use virtual address tag  Complications due to aliasing  Different virtual addresses for shared physical address Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 84 Memory Protection  Different tasks can share parts of their virtual address spaces  But need to protect against errant access  Requires OS assistance  Hardware support for OS protection  Privileged supervisor mode (aka kernel mode)  Privileged instructions  Page tables and other state information only accessible in supervisor mode  System call exception (e.g., syscall in MIPS) Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 85 The Memory Hierarchy  Common principles apply at all levels of the memory hierarchy  Based on notions of caching  At each level in the hierarchy  Block placement  Finding a block  Replacement on a miss  Write policy § 5 .8 A C o m m o n F ra m e w o rk fo r M e m o ry H ie ra rc h ie s The BIG Picture Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 86 Block Placement  Determined by associativity  Direct mapped (1-way associative)  One choice for placement  n-way set associative  n choices within a set  Fully associative  Any location  Higher associativity reduces miss rate  Increases complexity, cost, and access time Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 87 Finding a Block  Hardware caches  Reduce comparisons to reduce cost  Virtual memory  Full table lookup makes full associativity feasible  Benefit in reduced miss rate Associativity Location method Tag comparisons Direct mapped Index 1 n-way set associative Set index, then search entries within the set n Fully associative Search all entries #entries Full lookup table 0 Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 88 Replacement  Choice of entry to replace on a miss  Least recently used (LRU)  Complex and costly hardware for high associativity  Random  Close to LRU, easier to implement  Virtual memory  LRU approximation with hardware support Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 89 Write Policy  Write-through  Update both upper and lower levels  Simplifies replacement, but may require write buffer  Write-back  Update upper level only  Update lower level when block is replaced  Need to keep more state  Virtual memory  Only write-back is feasible, given disk write latency Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 90 Sources of Misses  Compulsory misses (aka cold start misses)  First access to a block  Capacity misses  Due to finite cache size  A replaced block is later accessed again  Conflict misses (aka collision misses)  In a non-fully associative cache  Due to competition for entries in a set  Would not occur in a fully associative cache of the same total size Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 91 Cache Design Trade-offs Design change Effect on miss rate Negative performance effect Increase cache size Decrease capacity misses May increase access time Increase associativity Decrease conflict misses May increase access time Increase block size Decrease compulsory misses Increases miss penalty. For very large block size, may increase miss rate due to pollution. Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 92 Cache Control  Example cache characteristics  Direct-mapped, write-back, write allocate  Block size: 4 words (16 bytes)  Cache size: 16 KB (1024 blocks)  32-bit byte addresses  Valid bit and dirty bit per block  Blocking cache  CPU waits until access is complete § 5 .9 U s in g a F in ite S ta te M a c h in e to C o n tro l A S im p le C a c h e Tag Index Offset 0 3 4 9 10 31 4 bits 10 bits 18 bits Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 93 Interface Signals Cache CPU Memory Read/Write Valid Address Write Data Read Data Ready 32 32 32 Read/Write Valid Address Write Data Read Data Ready 32 128 128 Multiple cycles per access Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 94 Finite State Machines  Use an FSM to sequence control steps  Set of states, transition on each clock edge  State values are binary encoded  Current state stored in a register  Next state = fn (current state, current inputs)  Control output signals = fo (current state) Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 95 Cache Controller FSM Could partition into separate states to reduce clock cycle time Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 96 Cache Coherence Problem  Suppose two CPU cores share a physical address space  Write-through caches § 5 .1 0 P a ra lle lis m a n d M e m o ry H ie ra rc h ie s : C a c h e C o h e re n c e Time step Event CPU A’s cache CPU B’s cache Memory 0 0 1 CPU A reads X 0 0 2 CPU B reads X 0 0 0 3 CPU A writes 1 to X 1 0 1 Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 97 Coherence Defined  Informally: Reads return most recently written value  Formally:  P writes X; P reads X (no intervening writes)  read returns written value  P1 writes X; P2 reads X (sufficiently later)  read returns written value  c.f. CPU B reading X after step 3 in example  P1 writes X, P2 writes X  all processors see writes in the same order  End up with the same final value for X Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 98 Cache Coherence Protocols  Operations performed by caches in multiprocessors to ensure coherence  Migration of data to local caches  Reduces bandwidth for shared memory  Replication of read-shared data  Reduces contention for access  Snooping protocols  Each cache monitors bus reads/writes  Directory-based protocols  Caches and memory record sharing status of blocks in a directory Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 99 Invalidating Snooping Protocols  Cache gets exclusive access to a block when it is to be written  Broadcasts an invalidate message on the bus  Subsequent read in another cache misses  Owning cache supplies updated value CPU activity Bus activity CPU A’s cache CPU B’s cache Memory 0 CPU A reads X Cache miss for X 0 0 CPU B reads X Cache miss for X 0 0 0 CPU A writes 1 to X Invalidate for X 1 0 CPU B read X Cache miss for X 1 1 1 Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 100 Memory Consistency  When are writes seen by other processors  “Seen” means a read returns the written value  Can’t be instantaneously  Assumptions  A write completes only when all processors have seen it  A processor does not reorder writes with other accesses  Consequence  P writes X then writes Y  all processors that see new Y also see new X  Processors can reorder reads, but not writes Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 101 Multilevel On-Chip Caches § 5 .1 3 T h e A R M C o rte x -A 8 a n d In te l C o re i7 M e m o ry H ie ra rc h ie s Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 102 2-Level TLB Organization Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 103 Supporting Multiple Issue  Both have multi-banked caches that allow multiple accesses per cycle assuming no bank conflicts  Core i7 cache optimizations  Return requested word first  Non-blocking cache  Hit under miss  Miss under miss  Data prefetching DGEMM  Combine cache blocking and subword parallelism Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 104 § 5 .1 4 G o in g F a s te r: C a c h e B lo c k in g a n d M a trix M u ltip ly Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 105 Pitfalls  Byte vs. word addressing  Example: 32-byte direct-mapped cache, 4-byte blocks  Byte 36 maps to block 1  Word 36 maps to block 4  Ignoring memory system effects when writing or generating code  Example: iterating over rows vs. columns of arrays  Large strides result in poor locality § 5 .1 5 F a lla c ie s a n d P itfa lls Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 106 Pitfalls  In multiprocessor with shared L2 or L3 cache  Less associativity than cores results in conflict misses  More cores  need to increase associativity  Using AMAT to evaluate performance of out-of-order processors  Ignores effect of non-blocked accesses  Instead, evaluate performance by simulation Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 107 Pitfalls  Extending address range using segments  E.g., Intel 80286  But a segment is not always big enough  Makes address arithmetic complicated  Implementing a VMM on an ISA not designed for virtualization  E.g., non-privileged instructions accessing hardware resources  Either extend ISA, or require guest OS not to use problematic instructions Chapter 5 — Large and Fast: Exploiting Memory Hierarchy — 108 Concluding Remarks  Fast memories are small, large memories are slow  We really want fast, large memories   Caching gives this illusion   Principle of locality  Programs use a small part of their memory space frequently  Memory hierarchy  L1 cache  L2 cache  …  DRAM memory  disk  Memory system design is critical for multiprocessors § 5 .1 6 C o n c lu d in g R e m a rk s