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Elastic circuits
Jordi Cortadella
Universitat Politècnica de Catalunya, Barcelona
EMicro 2013
Goals
• Convince ourselves that:
– designing an asynchronous circuit is easy
– synchronous and asynchronous circuits are similar
– asynchronous circuits bring new advantages
• Not to cover exotic asynchronous schemes
• Elasticity can also be synchronous
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2
Clocking
• How to distribute the clock?
• How to determine the clock
frequency?
• How to implement robust
communications?
• How to reduce and manage
energy?
Nvidia KeplerTM GK110
28nm, 7.1B transistors, 550mm2, 2688 CUDA cores,
Base clock: 836MHz, Memory clock: 6GHz
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4
Outline
•
•
•
•
•
•
•
•
Synchronous and Source-synchronous circuits
Completion detection
Handshaking
Performance analysis
Why asynchronous?
Design automation
Synchronous elasticity
Globally-asynchronous Locally-synchronous
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5
Synchronous and
Source-Synchronous
Synchronous circuit
PLL
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7
Synchronous circuit
CL
Two competing paths:
• Launching path
• Capturing path
Launching path < Capturing path + Period
1
2
CLKtree + CL <
PLL
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CL
Elastic circuits
<
CLKtree
Period
+ Period
(no clock skew)
8
Source-synchronous
Launching path
CLK
gen
Capturing path
matched delay
matched delay
matched delay
• No global clock required
• More tolerance to PVT variations
• Period > longest combinational path
• Good for acyclic pipelines
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9
Source-synchronous with forks and joins
CLK
gen
?
How to synchronize incoming events?
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10
C element (Muller 1959)
A
B
C
C
A
0
0
1
1
B
0
1
0
1
C
0
C
C
1
A
B
C
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11
C element (Muller 1959)
A
B
MAJ
C
(many implementations exist)
A
0
0
1
1
B
0
1
0
1
C
0
C
C
1
A
B
C
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12
Completion detection
Completion detection
CLK
gen
fixed delay
The fixed delay must be longer than the
worst-case logic delay (plus variability)
Q: could we detect when a computation has completed ASAP ?
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14
Delay-insensitive codes: Dual Rail
• Dual rail: every bit encoded with two signals
A.t
0
0
1
1
A.f
0
1
0
1
A
Spacer
0
1
Not used
SP
1
A.t
A.f
A
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1
SP
0
Elastic circuits
SP
1
SP
15
Dual Rail AND gate
A
B
C
SP
SP
SP
0
-
0
-
0
0
SP
1
SP
1
SP
SP
1
1
1
A.t
A.f
B.t
B.f
C.t
C.f
A
C
B
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16
Dual Rail Inverter
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A
Z
SP
SP
0
1
1
0
A.t
Z.t
A.f
Z.f
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17
Dual Rail AND/OR gate
A.t
A.f
C.t
A
C
B
B.t
B.f
A
A.f
A.t
C
B
C.f
C.f

A
C
B.f
B.t
C.t
B
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18
Dual rail: completion detection
Dual-rail
logic
•
•
•
C
done
•
•
•
Completion detection tree
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19
Multi-input C element
a1
a2
a3
a4
C
C
C
C
a5
a6
a7
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c
C
C
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20
Dual rail: completion detection
INV
AND
OR
AND
CLK
gen
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21
Dual rail: completion detection
INV
AND
OR
AND
CLK
gen
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C
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22
Dual rail: operation
INV
AND
Compute
Reset
OR
AND
CLK
gen
C
For a correct operation, all internal signals should be reset before the compute phase:
• Use a more complex implementation of dual-rail (e.g., DIMS), or
• Have internal completion detection, or
• Use timing assumptions
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Other DI codes
• There are many DI codes:
– k-out-of n, Berger, Knuth, …
• Example: 1-out-of-4
– 2 bits with 4 wires
– Same wire efficiency as DR
– Less power consuming
– Good for communication
– Bad for logic
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Wires
0000
Value
Spacer
0001
0010
0100
0
1
2
1000
others
3
not used
24
Single rail data vs. dual rail
Some back-of-the-envelope estimations:
Area
Delay
Static power
Dynamic power
Single rail
1
1
1
< 0.2
Dual Rail
2
<< 1
2
2
Dual rail:
• Good for speed
• Large area
• High power comsumption
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25
Handshaking
Handshaking
CLK
gen
unknown delay
Assume that the source module can provide data at any rate:
• When should the CLK generator send an event if the
internal delays of the circuit are unknown?
Solution: handshaking
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27
Handshaking
Data
I have data
Request
Acknowledge
I want data
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28
Asynchronous elastic pipeline
ReqIn
ReqOut
C
C
C
C
AckOut
AckIn
• David Muller’s pipeline (late 50’s)
• Sutherland’s Micropipelines (Turing award, 1989)
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Multiple inputs and outputs
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30
Multiple inputs and outputs
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31
Mulitple inputs and outputs
Ack
Req
C
Req
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Ack
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32
Channel-based communication
• A channel contains data and handshake wires
Single-Rail Data
Req
Ack
Dual-Rail Data
Ack
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33
Push/pull channels
Single-Rail Data
Req (push)
Ack
Receiver
Sender
Single-Rail Data
Ack
Req (pull)
• Push: the sender initiates the communication
• Pull: the receiver initiates the communication
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34
Four-phase protocol
Data transfer
Data transfer
Req
Ack
Data
Data 1
Data 2
Data 3
• Valid data on the active edge of Req
• Req/Ack must return to zero before the next transfer
• Different variations of the 4-phase protocol exist
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Two-phase protocol
Data transfer
Data transfer
Req
Ack
Data
Data 1
Data 2
Data 3
• Every edge is active
• It may require double-edge triggered flip-flops or
pulse generators
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How to memorize?
L
Combinational
Logic
?
L
?
delay
C
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2-phase or 4-phase ?
Elastic circuits
C
37
How to memorize?
L
Combinational
Logic
L
Pulse
generator
delay
C
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2-phase
Elastic circuits
C
38
How to memorize?
L
Combinational
Logic
L
delay
C
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4-phase
Elastic circuits
C
39
Performance analysis
Ring oscillators
C
6
7
5
1
C
C
2
C
3
C
4
• Every ring requires an odd number of inverters
• The cycle period is determined by the slowest ring
• The cycle period is adapted to the operating conditions
(temperature, voltage)
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41
Global Rings
C
C
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43
Global Rings
Th = 1 / 6
• Ramamoorthy and Ho, 1980
Performance evaluation of asynchronous concurrent systems with Petri nets
• T. Williams et al., A self-timed chip for division, 1987
• Greenstreet and Steiglitz, Bubbles can make self-timed pipelines fast, 1990
• Manohar and Martin, Slack elasticity in concurrent computing, 1998.
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44
Global Rings
Th = 2 / 6
• Ramamoorthy and Ho, 1980
Performance evaluation of asynchronous concurrent systems with Petri nets
• T. Williams et al., A self-timed chip for division, 1987
• Greenstreet and Steiglitz, Bubbles can make self-timed pipelines fast, 1990
• Manohar and Martin, Slack elasticity in concurrent computing, 1998.
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45
Global Rings
Th = 3 / 6
• Ramamoorthy and Ho, 1980
Performance evaluation of asynchronous concurrent systems with Petri nets
• T. Williams et al., A self-timed chip for division, 1987
• Greenstreet and Steiglitz, Bubbles can make self-timed pipelines fast, 1990
• Manohar and Martin, Slack elasticity in concurrent computing, 1998.
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46
Global Rings
Th = 1 / 6
• Ramamoorthy and Ho, 1980
Performance evaluation of asynchronous concurrent systems with Petri nets
• T. Williams et al., A self-timed chip for division, 1987
• Greenstreet and Steiglitz, Bubbles can make self-timed pipelines fast, 1990
• Manohar and Martin, Slack elasticity in concurrent computing, 1998.
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47
Global Rings
Th
1/2
Bubble
limited
Token
limited
0
N
N/2
tokens
• Ramamoorthy and Ho, 1980
Performance evaluation of asynchronous concurrent systems with Petri nets
• T. Williams et al., A self-timed chip for division, 1987
• Greenstreet and Steiglitz, Bubbles can make self-timed pipelines fast, 1990
• Manohar and Martin, Slack elasticity in concurrent computing, 1998.
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48
A latch-based view of synchronous circuits
Filp-flop =
Master + Slave
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49
Multiple Rings
2/4
2/5
5/7?
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2/7
Elastic circuits
2/4
It’s bubble
limited !!!
50
Slack matching
2/4
2/5
2/4
24/ /79?
• We can add as many bubbles as we want (but not tokens!)
• Slack matching can be solved optimally in polynomial time
• Slack matching is conceptually equivalent to buffer (FIFO) sizing or recycling
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Performance analysis
C
C
(Mean Cycle Ratio)
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52
Latch-based design
L1
L2
Launching path
L3
L4
Capturing path
L1
L2
L3
L4
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53
Matched delays can be adjustable
L1
L2
L3
L4
Delays can be adjusted:
• At testing/boot time (to adjust to static variability)
• At runtime (to compensate dynamic variability)
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delay
selection
54
Why asynchronous?
Exploiting elasticity
CLK
Rigid
clock
High
performance
Low
energy
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56
Exploiting elasticity
Rigid
Voltage
1V
High
performance
Voltage
scaling
0.9 V
0.8 V
Low
energy
0.7 V
500 MHz
1 GHz
Performance
2 GHz
Rigid
clock
High
performance
Low
energy
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Voltage scaling and power savings
3 ARM926 cores
on the same die
-14%
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-24%
58
Tracking variability
matched delay
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Tracking variability
delay
Good correlation for:
• Process variability (systematic)
• Global voltage fluctuations
• Temperature
•best
Aging (partially)
typ
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worst
60
Margins
Rigid Clocks:
Gate and wire delays (typ)
P
V
T
PLL
Aging Skew
Jitter
Cycle period
Gate and wire delays (typ)
P VT
Aging
Elastic Clocks:
Margin reduction
Skew
Speed-up / Power savings
Cycle period
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Clock elasticity
Rigid clock
wasted time
computation time
Cycle period
Elastic clock
computation time
Cycle period
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62
Design Automation
Design automation paradigms
• Synthesis of asynchronous controllers
– Logic synthesis from Petri nets or asynchronous
FSMs
• Syntax-directed translation
– Correct-by-construction composition of
handshake components
• De-synchronization
– Automatic transformation from synchronous to
asynchronous
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Synthesis of asynchronous controllers
Bus
DSr
Data
Transceiver
LDS
LDTACK
Device
D
DSr
DSw
LDS
VME Bus
Controller LDTACK
D
DTACK
DTACK
Read Cycle
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65
Synthesis of asynchronous controllers
DSr+
LDS+
LDTACK+
DTACK-
D+
DTACK+
LDTACK-
DSr-
D-
LDS-
Signal Transition Graph
D
DSr
LDS
VME Bus
Controller
LDTACK
DTACK
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Synthesis of asynchronous controllers
DSr+
LDS+
LDTACK+
D+
DTACK-
DTACK+
LDTACK-
DSr-
D-
LDSD
DTACK
LDS
DSr
LDTACK
Cortadella et al., Petrify
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Syntax-directed translation
int = type [0..255]
& gcd: main proc (in? chan <<int,int>> &
out! chan int)
begin x, y: var int
| forever do
in?<<x,y>>
*
SEQ
; do x <> y then
if x < y then y:=y-x
else x:=x-y
fi
od
→
out
R
MUX
W
x
R
→
R
; out!x
od
end
-
DMX
DMX
<>
do
-
DMX
DMX
<
→
áá ññ
→
Sources:
P.A.Beerel, R.O. Ozdag and M. Ferretti.
A Designer’s Guide to Asynchronous VLSI,
Cambridge University Press, 2010.
EMicro 2013
@
→
J. Kessels and A. Peeters.
DESCALE: A Design Experiment for a Smart
Card Application Consuming Low Energy,
in Principles of Asynchronous Circuit Design, A Systems Perspective,
Eds., J. Sparso and S. Furber, Kluwer Academic Publishers, 2001.
R
MUX
W
y
R
R
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68
De-synchronization
• Strategy: substitute the clock tree
by local clocks and handshakes
• Combinational logic and latches are not modified
• More tolerance to variability
– Similar area, less power and/or more speed
• Cortadella, Kondratyev, Lavagno and Sotiriou.
Desynchronization: Synthesis of asynchronous circuits
from synchronous specifications.
IEEE TCAD, Oct 2006.
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Synchronous operation
CLK
gen
Transforming a synchronous circuit into asynchronous (automatically)
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De-synchronization
Transforming a synchronous circuit into asynchronous (automatically)
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System-level de-synchronization
CLK
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System-level de-synchronization
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System-level de-synchronization
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Synchronous elasticity
Different flavors of elasticity
…
…
…
…1
…
7 4 1
1 0 2
4
7
0
1
2
4 1
7
1 0
2
…
8
+
4 3
Rigid
…
+
e
8
4
3
Elastic
…
8
4 3
+
Synchronous Elastic
s
Carloni et al., Latency-insensitive systems.
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Asynchronous elasticity
req
ack
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80
Synchronous elasticity
valid
stop
CLK
RingPLL
oscillator
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Latch-based elasticity
sender
receiver
Data
Data
En
En
V
En
V
V
Valid
Stop
EMicro 2013
En
V
Valid
Stop
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82
Elastic netlists
Enable signal
to data latches
EB
Fork
Join
EB
Join / Fork
EB
EB
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83
Variable Latency Units
[0 - k]
cycles
go
done
clear
V/S
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V/S
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84
Globally-asynchronous
Locally-synchronous
GALS
SoC design with GALS
• Most IPs are synchronous
DSP
• Different components
may have different
operating frequencies
CLK3
P
Bridge
CDC
• Some components have
variable latencies (e.g.,
cache hit/miss latency)
Fast Bus
CLK1
Bridge
CDC
Mem
Slow Bus
• Multiple clock domains
are essential
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Elastic circuits
CLK2
86
Multiple clock domains
f3/f0
CLK0
CLK1
f2/f0
CLK2
CLK
(f0)
CLK3
f1/f0
CLK
Independent clocks
Rational clock
frequencies
Single clock
(mesochronous)
(controllable skew)
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87
Synchronous handshakes
Data
Sender
Valid
Receiver
Ack
CLK1
CLK2
• The arrival of data is unpredictable
• Handshakes solve the problem
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88
The problem: metastability
D
Q
ФT
D
setup
ФR
hold
Q
ФR
D
Q
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?
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89
How long does it take to resolve metastability?
Metastability
MTBF: Mean Time Between Failures
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90
Classical synchronous solution
D
Q
D
Q
D
Q
D
Q
ФT
ФR
Mean Time Between Failures
fФ: frequency of the clock
fD: frequency of the data
tr: resolve time available
W: metastability window
 : resolve time constant
MTBF 
EMicro 2013
e tr 
2 f  f D W
Elastic circuits
Example
# FFs
MTBF
1 FF
15 min
2 FF
9 days
3 FF
23 years
91
Handshake with synchronizers
Data
Sender
Valid
Receiver
Ack
CLK1
CLK2
• Simple solution
• Throughput can be highly degraded:
a long round trip for every transaction
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92
Asynchronous FIFOs
Data
Circular buffer
Data
Valid
Ack
Valid
Ack
FIFO control
Clk Out
Clk In
• Ack is issued as soon as data has been delivered
• No impact on throughput (1 token/cycle)
• Min latency determined by the internal synchronizers
• Some tricky structures for the FIFO pointers (e.g. Grey encoding)
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SoC design with GALS
DSP
CLK3
P
• Bridges for Clock Domain
Crossing usually contain
asynchronous FIFOs
Bridge
CDC
• Latency cost only when
interfacing with
synchronous domains
Fast Bus
CLK1
Bridge
CDC
Mem
Slow Bus
EMicro 2013
CLK2
• No latency penalty
between asynchronous
domains
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94
Conclusions
• Elasticity offers flexibility in time
– Modularity
– Dynamic adaptability
– Tolerance to variability
• Better optimization of power/performance
• Why isn’t it an important trend in circuit design?
– Lack of commercial EDA support (timing sign-off)
– Designers do not feel comfortable with “unpredictable” timing
– Other aspects: testing, verification, …
• De-synchronization might be a viable solution
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95
Bibliography
• Carmona, Cortadella, Kishinevsky and Taubin,
Elastic Circuits, IEEE Trans. On CAD, Oct. 2009.
• Beerel, Ozdag and Ferreti, A Designer’s Guide to
Asynchronous VLSI, Cambridge 2001.
• Sparso and Furber, Principles of Asynchronous
Circuit Design: A Systems Perspective,
Kluwer 2001.
• Myers, Asynchronous Circuit Design,
John Wiley&Sons, 2001
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97

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