soc 4.1

Chapter 4 Memory Design: SOC and

Board-Based SystemsComputer System Design

System-on-Chipby M. Flynn & W. Luk

Pub. Wiley 2011 (copyright 2011)

soc 4.2

Cache and Memory

• cache– performance– cache partitioning– multi-level cache

• memory

– off-die memory designs

soc 4.3

Outline for memory design

soc 4.4

Area comparison of memory tech.

soc 4.5

System environments and memory

soc 4.6

Performance factors

Virtualaddress

1. physical word size• processor cache

2. block / line size• cache memory

3. cache hit time• cache size, organization

4. cache miss time• memory and bus

5. virtual-to-real translation time6. number of processor requests per cycle

Factors:

soc 4.7

Design target miss rates

beyond 1MBdouble the sizehalf the miss rate

soc 4.8

System effects limit hit rate

• operating System affects the miss ratio– about 20% increase

• so does multiprogramming (M)– miss rates may not be affected by increased cache size– Q = no. instructions between task switches

soc 4.9

System Effects• Cold-Start

– short transactions are created frequently and run quickly to completion

• Warm-Start– long processes are

executed in time slices

COLD

soc 4.10

Some common cache types

soc 4.11

Multi-level caches: mostly on die

• useful for matching processor to memory– generally at least 2-level

• For microprocessors L1 at frequency of pipelineand L2 at slower latency

– often use 3-level• Size limited by access time and improved cycle

times

soc 4.12

Cache partitioning: scaling effect on cache access

time• access time to a cache is approximately access time (ns) = (0.35 + 3.8f +(0.006 +0.025 f)

C) x (1 + 0.3(1 - 1/A)) where– f is the feature size in microns– C is the cache capacity in K bytes– A is the associativity, e.g. direct map A = 1

• for example, at f = 0.1u, A = 1 and C = 32 (KB) the access time is 1.00 ns

• problem with small feature size: cache access time, not cache size

soc 4.13

Minimum cache access time 1 array, larger sizes use multiple arrays (interleaving)

L1 usually less than 64kB

L3: multiple 256KB arrays

L2 usually less than 512KB (interleaved from smaller arrays)

soc 4.14

Analysis: multi-level cache miss rate• L2 cache analysis by statistical inclusion• if L2 cache > 4 x size of the L1 cache then

– assume statistically: contents of L1 lies in L2

• relevant L2 miss rates– local miss rate: No. L2 misses / No. L2 references– global Miss Rate: No. misses / No. processor ref. – solo Miss Rate: No. misses without L1/No. proc. ref.– Inclusion => solo miss rate = global miss rate

• miss penalty calculation– L1 miss rate x (miss in L1, hit in L2 penalty) plus– L2 miss rate x ( miss in L1, miss in L2 penalty - L1 to L2

penalty)

soc 4.15

Multi-level cache example

L1 L2 Memory

Miss Rate 4% 1%

- delays: Miss in L1, Hit in L2 2 cycles Miss in L1, Miss in L2 15 cycles

- assume one reference/instructionL1 delay is 1 ref/instr x .04 misses/ref x 2 cycles/miss = 0.08 cpiL2 delay is 1 ref/instr x .01 misses/ref x (15-2) = 0.13 cpiTotal effect of 2 level system is 0.08 + 0.13 = 0.29 cpi

soc 4.16

Memory design

• logical inclusion

• embedded RAM

• off-die: DRAM

• basic memory model

• Strecker’s model

soc 4.17

Physical memory system

soc 4.18

Hierarchy of caches

Name ? Size Access Transfer size

L0 Registers <256 words

<1 cycle word

L1 Core local <64K <4 cycle Line

L2 On Chip <64M <30 cycle Line

L3 DRAM on Chip

<1G <60 cycle >= Line

M0 Off Chip Cache

M1 Local Main Memory

<16G <150 cycle

>= Line

M2 Cluster Memory

soc 4.19

Hierarchy of caches

• Working Set – how much memory an “iteration” requires

• if it fits in a level then that will be the worst case• if it does not, hit rate typically determines

performance• double the cache level size half the miss rate –

good rule of thumb • if 90% hit rate, 10x memory access time,

performance 50% • and that’s for 1 core

soc 4.20

Logical inclusion

• multiprocessors with L1 and L2 caches – Important: L1 cache does NOT contain a line

• sufficient to determine– L2 cache does not have the line

• need to ensure– all the contents of L1 are always in L2

• this property: Logical Inclusion

soc 4.21

Logical inclusion techniques

• passive – control Cache size, organization, policies– no. L2 sets no. L1 sets– L2 set size L1 set size– compatible replacement algorithms– but: highly restrictive and difficult to guarantee

• active– whenever a line is replaced or invalidated in the L2– ensure it is not present in L1 or it is evicted from L1

soc 4.22

Memory system design outline• memory chip technology

– on-die or off die

• static versus dynamic:– SRAM versus DRAM

• access protocol: talking to memory– synchronous vs asynchronous DRAMs

• simple memory performance model– Strecker’s model for memory banks

soc 4.23

Why BIG memory?

soc 4.24

Memory

• many times, computation limited by memory– not processor organization or cycle time

• memory: characterized by 3 parameters– size– access time: latency– cycle time: bandwidth

soc 4.25

Embedded RAM

soc 4.26

Embedded RAM density (1)

soc 4.27

Embedded RAM density (2)

soc 4.28

Embedded RAM cycle time

soc 4.29

Embedded RAM error rates

soc 4.30

Off-die Memory Module

• module contains the DRAM chips that make up the physical memory word

• if the DRAM is organized 2n words x b bits and the memory has p bits/ physical word then the module has p/b DRAM chips.

• total memory size is then 2n words x p bits• Parity or Error-Correction Code (ECC) generally

required for error detection and availability

soc 4.31

Simple asychronous DRAM array• DRAM cell

– Capacitor: store charge for 0/1 state

– Transistor: switch capacitor to bit line

– Charge decays => refresh required

• DRAM array– Stores 2n bits in a square

array– 2n/2 row lines connect to

data lines– 2n/2 column bit lines

connect to sense amplifiers

soc 4.32

DRAM basics

• Row read is destructive

• Sequence– Read row into SRAM from dynamic

memory(>1000 bits) – Select word (<64 bits)– Write Word into row (writing)– Repeat till done with row– WRITE back row into dynamic memory

soc 4.33

DRAM timing• row and column addresses muxed

• row and column Strobes for timing

soc 4.34

Increase DRAM bandwidth

• Burst Mode– aka page mode, nibble mode, fast page mode

• Synchronous DRAM (SDRAM)

• DDR SDRAM– DDR1– DDR2– DDR3

soc 4.35

DDR SDRAM(Dual Data Rate Synchronous DRAM)

soc 4.36

Burst mode

• burst mode– save most recently accessed row (“page”)– only need column row + CAS to access within page

• most DDR SDRAMs: multiple rows can be open– address counter in each row for sequential

accesses– only need CAS (DRAM) or bus clock (SDRAM) for

sequential accesses

soc 4.37

Configuration parameters

Parameters for typical DRAM chips used in a 64-bit module

soc 4.38

DRAM timing

soc 4.39

Physical memory system

soc 4.40

Basic memory model

• assume that n processors– each make 1 request per Tc to one of m memories

• B(n,m)– number of successes

• Tc– memory cycle time to the memory

• one processor making n requests per Tc – behaves as n processors making 1 request per Tc

soc 4.41

Achieved vs. offered bandwidth

• offered request rate– rate at which processor(s) would make requests if

memory had unlimited bandwidth and no contention

soc 4.42

Basic terms

• B = B(m,n) or B(m)– number of requests that succeed each Tc (=

average number of busy modules)– B: bandwidth normalized to Tc

• Ts: more generalized term for service time – Tc = Ts

• BW: achieved bandwidth– in requests serviced per second– BW = B / Ts = B(m,n)/ Ts

soc 4.43

Modeling + evaluation methodology

• relevant physical parameters for memory– word size– module size– number of modules– cycle time Tc (=Ts)

• find the offered Bandwidth– number of requests/Ts

• find the bottleneck– performance limited by most restrictive service point

soc 4.44

Strecker’s model: compute B(m,n)

• model description– each processor generates 1 reference per cycle– requests randomly/uniformly distributed over modules– any busy module serves 1 request– all unserviced requests are dropped each cycle– assume there are no queues

• B(m,n) = m[1 - (1 - 1/m)n]• relative Performance Prel = B(m,n) / n

soc 4.45

Deriving Strecker’s model

• Prob[given processor not reference module]= (1 – 1/m)

• Prob[no processor references module] = P[idle]

= (1 – 1/m)n

• Prob[module busy]= 1 - (1 – 1/m)n

• average number of busy modules is B(m,n)• B(m,n) = m[1 - (1 - 1/m)n]

soc 4.46

Example 1

• 2 dual core processor dice share memory – Ts = 24 ns

• each die has 2 processors – sharing 4MB L2– miss rate is 0.001 misses reference– each processor makes 3 references/cycle @ 4 GHz

2 x 2 x 3 x 0.001 =0.012 refs/cycTs = 4 x 24 cyclesn = 1.152 processor requests / Ts; if m= 4success rate B(m,n) = B(4,1.152) = 0.81

Relative Performance = B/n = .81/1.152 =0.7

soc 4.47

Example 2

• 8-way interleaved associative data cache

• processor issues 2LD/ST per cycle– each processor: data reference per cycle = 0.6– n = 2 ; m = 8– B(m,n) = B(8,1.2) = 1.18

• Relative Performance = B/n = 1.18/1.2 = 0.98

soc 4.48

Summary• cache

– performance, cache partitioning, multi-level cache

• memory chip technology– on-die or off die

• static versus dynamic:– SRAM versus DRAM

• access protocol: talking to memory– synchronous vs asynchronous DRAMs

• simple memory performance model– Strecker’s model for memory banks