Accordion - Electrical and Computer...

Accordion Toward Soft Near-threshold Voltage Computing

Ulya R. Karpuzcu, Ismail Akturk Nam Sung Kim

Accordion

Near-threshold Voltage Computing (NTC)

!2

Accordion

Near-threshold Voltage Computing (NTC)•Supply voltage Vdd remains slightly above threshold voltage Vth

!2

Accordion

Near-threshold Voltage Computing (NTC)•Supply voltage Vdd remains slightly above threshold voltage Vth

!2

VddMIP

S/W

att

VddSTVVddNTVVth

Accordion

Near-threshold Voltage Computing (NTC)•Supply voltage Vdd remains slightly above threshold voltage Vth•Energy efficiency increases as Vdd reaches Vth

!2

VddMIP

S/W

att

VddSTVVddNTVVth

Accordion


•2-4x more energy efficient than super-threshold (STV) operation

!2

VddMIP

S/W

att

VddSTVVddNTVVth

2x-4x

Accordion


•2-4x more energy efficient than super-threshold (STV) operation

!2

VddMIP

S/W

att

VddSTVVddNTVVth

2x-4x

How close to Vdd can Vth get?

Accordion !3

NTC Basics: How close to Vdd can Vth get?

Accordion !3


Vdd

log(

f)

VddSTVVddNTVVth

Accordion !3


5x-10x

Vdd

log(

f)

VddSTVVddNTVVth

Accordion !3


5x-10x

Vdd

log(

f)

VddSTVVddNTVVth

•Execution time is proportional to work per parallel task x f

Accordion !3


5x-10x

Vdd

log(

f)

VddSTVVddNTVVth

•Execution time is proportional to work per parallel task x f•No degradation if 5-10x more cores engaged in computation

Accordion !3

NTC Basics: How close to Vdd can Vth get?Po

wer

Vdd

5x-10x

Vdd

log(

f)

VddSTVVddNTVVth

•Execution time is proportional to work per parallel task x f•No degradation if 5-10x more cores engaged in computation

Accordion !3


wer

Vdd

10x-40x

5x-10x

Vdd

log(

f)

VddSTVVddNTVVth

•Execution time is proportional to work per parallel task x f•No degradation if 5-10x more cores engaged in computation•10-40x power savings per core can accommodate 5-10x more cores

Accordion !3


wer

Vdd

10x-40x

5x-10x

Vdd

log(

f)

VddSTVVddNTVVth

•Execution time is proportional to work per parallel task x f•No degradation if 5-10x more cores engaged in computation•10-40x power savings per core can accommodate 5-10x more cores

Limited by the degree of parallelism in application

Accordion !4

NTC Basics: How close to Vdd can Vth get?●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●

●

●

●

●

●

●

●

●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

0.45 0.50 0.55 0.60

0.0

0.2

0.4

0.6

0.8

1.0

Vdd (V)

Tim

ing

Erro

r Rat

e

0.45 0.50 0.55

0.0

0.4

Vdd (V)

Timing Error Rate

0.2

0.6

0.81.0

0.60

Accordion !4

NTC Basics: How close to Vdd can Vth get?●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●

●

●

●

●

●

●

●

●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

0.45 0.50 0.55 0.60

0.0

0.2

0.4

0.6

0.8

1.0

Vdd (V)

Tim

ing

Erro

r Rat

e

0.45 0.50 0.55

0.0

0.4

Vdd (V)

Timing Error Rate

0.2

0.6

0.81.0

0.60

Limited by the degree of vulnerability to variation

Accordion

Accordion Basics

!5

Accordion

Accordion Basics•How to close the gap between NTC and STC execution times?

!5

Accordion


!5

Execution Time / Problem Size

f⇥ Core Count

Accordion


!5

Problem SizeNTV

fNTV ⇥ Core CountNTV! Problem SizeSTV

fSTV ⇥ Core CountSTV


f⇥ Core Count

Accordion


!5

Problem SizeNTV




f⇥ Core Count

fNTV < fSTV

Accordion


!5

Problem SizeNTV




f⇥ Core Count

fNTV < fSTV Core CountNTV > Core CountSTV

Accordion


!5

•Designate the problem size as the main knob to adjust

Problem SizeNTV




f⇥ Core Count


Accordion


!5

•Designate the problem size as the main knob to adjust•the degree of parallelism

Problem SizeNTV




f⇥ Core Count


Accordion


!5

•Designate the problem size as the main knob to adjust•the degree of parallelism•the degree of vulnerability to variation

Problem SizeNTV




f⇥ Core Count


Accordion

Problem Size vs. Quality of Computing

!6

Accordion


!6

Problem Size

1.1

1.0

0.5 1.0 1.5 2.0

0.9

0.8

Quality

Default

Accordion


!7

Problem Size

1.1

1.0

0.5 1.0 1.5 2.0

0.9

0.8

Quality

Drop1/4Default

Accordion


!8

Problem Size

1.1

1.0

0.5 1.0 1.5 2.0

0.9

0.8

Quality

Drop1/2Drop1/4Default

Accordion


!8

Problem Size

1.1

1.0

0.5 1.0 1.5 2.0

0.9

0.8

Quality


Execution Time

/ Problem Size

f⇥ Core Count

Accordion


!8

Problem Size

1.1

1.0

0.5 1.0 1.5 2.0

0.9

0.8

Quality


Execution Time

/ Problem Size

f⇥ Core Count

⬇

Accordion


!8

Problem Size

1.1

1.0

0.5 1.0 1.5 2.0

0.9

0.8

Quality


Execution Time

/ Problem Size

f⇥ Core Count

To make up for f degradation:

⬇

Accordion


!8

Problem Size

1.1

1.0

0.5 1.0 1.5 2.0

0.9

0.8

Quality


Execution Time

/ Problem Size

f⇥ Core Count

To make up for f degradation:•Compress problem size

⬇

Accordion


!8

Problem Size

1.1

1.0

0.5 1.0 1.5 2.0

0.9

0.8

Quality


Execution Time

/ Problem Size

f⇥ Core Count

To make up for f degradation:•Compress problem size•Expand problem size

⬇

Accordion


!8

Problem Size

1.1

1.0

0.5 1.0 1.5 2.0

0.9

0.8

Quality


Execution Time

/ Problem Size

f⇥ Core Count

To make up for f degradation:•Compress problem size•Expand problem size

•Core Count should expand

⬇

Accordion

Variation Induced Errors

!9

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●

●

●

●

●

●

●

●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

0.45 0.50 0.55 0.60

0.0

0.2

0.4

0.6

0.8

1.0

Vdd (V)

Tim

ing

Erro

r Rat

e

0.45 0.50 0.55

0.0

0.4

Vdd (V)

Timing Error Rate

0.2

0.6

0.81.0

0.60

Accordion

Variation Induced Errors

!9

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●

●

●

●

●

●

●

●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

0.45 0.50 0.55 0.60

0.0

0.2

0.4

0.6

0.8

1.0

Vdd (V)

Tim

ing

Erro

r Rat

e

0.45 0.50 0.55

0.0

0.4

Vdd (V)

Timing Error Rate

0.2

0.6

0.81.0

0.60

How to confine errors where they can be tolerated?

Accordion

Accordion Organization

!10

Cluster

Accordion

Accordion Organization

!10

Cluster

Cluster Memory

Core + Local Memory

Accordion

Accordion Design Space

!11

Cluster

Accordion


!11

CC: Control CoreDC: Data Core

Cluster

Accordion


!11

Cluster Memory

DCDCDCDC

DCDC CCDC


Cluster

Accordion


!11

Cluster Memory

DCDCDCDC

DCDC CCDC

Cluster Memory

CCDC

CCDC

CCDC

CCDC

CCDC

CCDC

CCDC

CCDC


Cluster

Accordion


!11

Cluster Memory

DCDCDCDC

DCDC CCDC

Cluster Memory

CCDC

CCDC

CCDC

CCDC

CCDC

CCDC

CCDC

CCDC

Cluster Memory

DCDCDCDC

DCDC CC


Cluster

Accordion

Accordion Modes of Operation

!12

Problem SizeNTV



Accordion


!12

Mode Problem Size Core Count f < STV Quality

Problem SizeNTV



Accordion


!12


Still

Problem SizeNTV



Accordion


!12


Still = STV

Problem SizeNTV



Accordion


!12


Still = STV = STV

Problem SizeNTV



Accordion


!12


Still = STV = STV ≤ NTV

Safe

Problem SizeNTV



Accordion


!12


Still = STV = STV ≤ NTV > NTV

SpeculativeSafe

Problem SizeNTV



Accordion


!12


Still = STV = STV ≤ NTV > NTV = STV

SpeculativeSafeSafe

Problem SizeNTV



Accordion


!12


Still = STV = STV ≤ NTV > NTV = STV ≤ STV

Speculative

SpeculativeSafeSafe

Problem SizeNTV



Accordion


!12



Compress

Speculative

SpeculativeSafeSafe

Problem SizeNTV



Accordion


!12



Compress < STV

Speculative

SpeculativeSafeSafe

Problem SizeNTV



Accordion


!12



Compress < STV No restriction

Speculative

SpeculativeSafeSafe

Problem SizeNTV



Accordion


!12



Compress < STV No restriction ≤ NTV

Speculative

SpeculativeSafeSafe

Problem SizeNTV



Accordion


!12



Compress < STV No restriction ≤ NTV > NTV

Speculative

SpeculativeSafeSafe

Problem SizeNTV



Accordion


!12



Compress < STV No restriction ≤ NTV > NTV ≤ STV

Speculative

SpeculativeSafeSafe

Problem SizeNTV



Accordion


!12



Compress < STV No restriction ≤ NTV > NTV ≤ STV ≤ STV

Speculative

SpeculativeSafeSafe

Problem SizeNTV



Accordion


!12




Expand

Speculative

SpeculativeSafeSafe

Problem SizeNTV



Accordion


!12




Expand > STV

Speculative

SpeculativeSafeSafe

Problem SizeNTV



Accordion


!12




Expand > STV > STV

Speculative

SpeculativeSafeSafe

Problem SizeNTV



Accordion


!12




Expand > STV > STV ≤ NTV

Speculative

SpeculativeSafeSafe

Problem SizeNTV



Accordion


!12




Expand > STV > STV ≤ NTV > NTV

Speculative

SpeculativeSafeSafe

Problem SizeNTV



Accordion


!12




Expand > STV > STV ≤ NTV > NTV > STV

Speculative

SpeculativeSafeSafe

Problem SizeNTV



Accordion


!12




Expand > STV > STV ≤ NTV > NTV > STV ≤ STV

Speculative

SpeculativeSafeSafe

Problem SizeNTV



Accordion

Accordion Pros and Cons

!13

Accordion

Accordion Pros and Cons•Accommodates a closer Vdd to Vth without compromising performance

!13

Accordion

Accordion Pros and Cons•Accommodates a closer Vdd to Vth without compromising performance•Tolerates exacerbated variation as Vdd reaches Vth

!13

Accordion

Accordion Pros and Cons•Accommodates a closer Vdd to Vth without compromising performance•Tolerates exacerbated variation as Vdd reaches Vth•Highly application-specific:

!13

Accordion


•Inputs to dictate the problem size

!13

Accordion


•Inputs to dictate the problem size•Quality metrics & thresholds

!13

Accordion

Evaluation Setup

!14

Accordion

Evaluation Setup•Simple, clustered hardware to exploit within die variation

!14

Cluster

Cluster Memory

DCDCDCDC

DCDC CCDC

Accordion


•Each cluster supports a different max f at chip-wide, single Vdd

!14

Cluster

Cluster Memory

DCDCDCDC

DCDC CCDC

Accordion


•Each cluster supports a different max f at chip-wide, single Vdd•All clusters assigned to a task cycle at the f of slowest cluster

!14

Cluster

Cluster Memory

DCDCDCDC

DCDC CCDC

Accordion



•Simulated 20mm x 20mm 288 core chip at 11nm

!14

Cluster

Cluster Memory

DCDCDCDC

DCDC CCDC

Accordion



•Simulated 20mm x 20mm 288 core chip at 11nm•36 clusters, 8 cores per cluster

!14

Cluster

Cluster Memory

DCDCDCDC

DCDC CCDC

Accordion



•Simulated 20mm x 20mm 288 core chip at 11nm•36 clusters, 8 cores per cluster•Core: Single issue in-order

!14

Cluster

Cluster Memory

DCDCDCDC

DCDC CCDC

Accordion




•VARIUS-NTV to extract per cluster min Vdd and max f

!14

Cluster

Cluster Memory

DCDCDCDC

DCDC CCDC

Accordion




•VARIUS-NTV to extract per cluster min Vdd and max f•RMS applications from PARSEC and Rodinia suites

!14

Cluster

Cluster Memory

DCDCDCDC

DCDC CCDC

Accordion

Iso-execution time front (canneal)

!15

Accordion


!15

●

●●●●

●

NNTV NSTV

(MIP

SW) N

TV(M

IPS

W) S

TV

2 4 6 8 10

1.5

1.75

2

● Safe CompressSpec. CompressSafe ExpandSpec. Expand

canneal

Core Count: NTV/STV

MIPS/Watt: NTV/STV

1.50

2.00

1.75

2 4 6 8 10

Still

Accordion


!15

●

●●●●

●

NNTV NSTV

(MIP

SW) N

TV(M

IPS

W) S

TV

2 4 6 8 10

1.5

1.75

2


canneal

Core Count: NTV/STV

MIPS/Watt: NTV/STV

1.50

2.00

1.75

2 4 6 8 10

Still

Execution Time

/ Problem Size

f⇥ Core Count

Accordion


!16

●

●●●●

●

NNTV NSTV

(MIP

SW) N

TV(M

IPS

W) S

TV

2 4 6 8 10

1.5

1.75

2


canneal

Core Count: NTV/STV

MIPS/Watt: NTV/STV

1.50

2.00

1.75

2 4 6 8 10

Compress

Still

Execution Time

/ Problem Size

f⇥ Core Count

Accordion


!16

●

●●●●

●

NNTV NSTV

(MIP

SW) N

TV(M

IPS

W) S

TV

2 4 6 8 10

1.5

1.75

2


canneal

Core Count: NTV/STV

MIPS/Watt: NTV/STV

1.50

2.00

1.75

2 4 6 8 10

Compress

Still •As core count increases

Execution Time

/ Problem Size

f⇥ Core Count

Accordion


!16

●

●●●●

●

NNTV NSTV

(MIP

SW) N

TV(M

IPS

W) S

TV

2 4 6 8 10

1.5

1.75

2


canneal

Core Count: NTV/STV

MIPS/Watt: NTV/STV

1.50

2.00

1.75

2 4 6 8 10

Compress

Still •As core count increases•More likely to engage slower cores

Execution Time

/ Problem Size

f⇥ Core Count

Accordion


!16

●

●●●●

●

NNTV NSTV

(MIP

SW) N

TV(M

IPS

W) S

TV

2 4 6 8 10

1.5

1.75

2


canneal

Core Count: NTV/STV

MIPS/Watt: NTV/STV

1.50

2.00

1.75

2 4 6 8 10

Compress

Still •As core count increases•More likely to engage slower cores•f decreases

Execution Time

/ Problem Size

f⇥ Core Count

Accordion


!16

●

●●●●

●

NNTV NSTV

(MIP

SW) N

TV(M

IPS

W) S

TV

2 4 6 8 10

1.5

1.75

2


canneal

Core Count: NTV/STV

MIPS/Watt: NTV/STV

1.50

2.00

1.75

2 4 6 8 10

Compress


•Compress

Execution Time

/ Problem Size

f⇥ Core Count

Accordion


!16

●

●●●●

●

NNTV NSTV

(MIP

SW) N

TV(M

IPS

W) S

TV

2 4 6 8 10

1.5

1.75

2


canneal

Core Count: NTV/STV

MIPS/Watt: NTV/STV

1.50

2.00

1.75

2 4 6 8 10

Compress


•Compress•Higher efficiency at lower core count

Execution Time

/ Problem Size

f⇥ Core Count

Accordion


!16

●

●●●●

●

NNTV NSTV

(MIP

SW) N

TV(M

IPS

W) S

TV

2 4 6 8 10

1.5

1.75

2


canneal

Core Count: NTV/STV

MIPS/Watt: NTV/STV

1.50

2.00

1.75

2 4 6 8 10

Compress



•Higher f, lower power

Execution Time

/ Problem Size

f⇥ Core Count

Accordion


!16

●

●●●●

●

NNTV NSTV

(MIP

SW) N

TV(M

IPS

W) S

TV

2 4 6 8 10

1.5

1.75

2


canneal

Core Count: NTV/STV

MIPS/Watt: NTV/STV

1.50

2.00

1.75

2 4 6 8 10

Compress



•Higher f, lower power•Quality limited

Execution Time

/ Problem Size

f⇥ Core Count

Accordion


!17

●

●●●●

●

NNTV NSTV

(MIP

SW) N

TV(M

IPS

W) S

TV

2 4 6 8 10

1.5

1.75

2


canneal

Core Count: NTV/STV

MIPS/Watt: NTV/STV

1.50

2.00

1.75

2 4 6 8 10

Compress

Expand

Still

Execution Time

/ Problem Size

f⇥ Core Count

•As core count increases •More likely to engage slower cores •f decreases

Accordion


!17

●

●●●●

●

NNTV NSTV

(MIP

SW) N

TV(M

IPS

W) S

TV

2 4 6 8 10

1.5

1.75

2


canneal

Core Count: NTV/STV

MIPS/Watt: NTV/STV

1.50

2.00

1.75

2 4 6 8 10

Compress

Expand

Still

•Expand

Execution Time

/ Problem Size

f⇥ Core Count


Accordion


!17

●

●●●●

●

NNTV NSTV

(MIP

SW) N

TV(M

IPS

W) S

TV

2 4 6 8 10

1.5

1.75

2


canneal

Core Count: NTV/STV

MIPS/Watt: NTV/STV

1.50

2.00

1.75

2 4 6 8 10

Compress

Expand

Still

•Expand•Higher efficiency at lower core count

Execution Time

/ Problem Size

f⇥ Core Count


Accordion


!17

●

●●●●

●

NNTV NSTV

(MIP

SW) N

TV(M

IPS

W) S

TV

2 4 6 8 10

1.5

1.75

2


canneal

Core Count: NTV/STV

MIPS/Watt: NTV/STV

1.50

2.00

1.75

2 4 6 8 10

Compress

Expand

Still

•Expand•Higher efficiency at lower core count•A feasible core count may not exist

Execution Time

/ Problem Size

f⇥ Core Count


Accordion


!17

●

●●●●

●

NNTV NSTV

(MIP

SW) N

TV(M

IPS

W) S

TV

2 4 6 8 10

1.5

1.75

2


canneal

Core Count: NTV/STV

MIPS/Watt: NTV/STV

1.50

2.00

1.75

2 4 6 8 10

Compress

Expand

Still

•Expand•Higher efficiency at lower core count•A feasible core count may not exist•Core count (area), or power limited

Execution Time

/ Problem Size

f⇥ Core Count


Accordion


!18

●

●●●●

●

NNTV NSTV

(MIP

SW) N

TV(M

IPS

W) S

TV

2 4 6 8 10

1.5

1.75

2


canneal

Core Count: NTV/STV

MIPS/Watt: NTV/STV

1.50

2.00

1.75

2 4 6 8 10

Compress

Expand

Spec. StillStill

Execution Time

/ Problem Size

f⇥ Core Count


Accordion


!18

●

●●●●

●

NNTV NSTV

(MIP

SW) N

TV(M

IPS

W) S

TV

2 4 6 8 10

1.5

1.75

2


canneal

Core Count: NTV/STV

MIPS/Watt: NTV/STV

1.50

2.00

1.75

2 4 6 8 10

Compress

Expand

Spec. StillStill

Execution Time

/ Problem Size

f⇥ Core Count


•Speculative

Accordion


!18

●

●●●●

●

NNTV NSTV

(MIP

SW) N

TV(M

IPS

W) S

TV

2 4 6 8 10

1.5

1.75

2


canneal

Core Count: NTV/STV

MIPS/Watt: NTV/STV

1.50

2.00

1.75

2 4 6 8 10

Compress

Expand

Spec. StillStill

Execution Time

/ Problem Size

f⇥ Core Count


•Speculative•Higher f facilitates lower core count

Accordion


!18

●

●●●●

●

NNTV NSTV

(MIP

SW) N

TV(M

IPS

W) S

TV

2 4 6 8 10

1.5

1.75

2


canneal

Core Count: NTV/STV

MIPS/Watt: NTV/STV

1.50

2.00

1.75

2 4 6 8 10

Compress

Expand

Spec. StillStill

Execution Time

/ Problem Size

f⇥ Core Count


•Speculative•Higher f facilitates lower core count•Lower core count ➞ lower power

Accordion


!18

●

●●●●

●

NNTV NSTV

(MIP

SW) N

TV(M

IPS

W) S

TV

2 4 6 8 10

1.5

1.75

2


canneal

Core Count: NTV/STV

MIPS/Watt: NTV/STV

1.50

2.00

1.75

2 4 6 8 10

Compress

Expand

Spec. StillStill

Execution Time

/ Problem Size

f⇥ Core Count


•Speculative•Higher f facilitates lower core count•Lower core count ➞ lower power

•Energy efficiency increases

Accordion


!19

●

●●●●

●

NNTV NSTV

(MIP

SW) N

TV(M

IPS

W) S

TV

2 4 6 8 10

1.5

1.75

2


canneal

Core Count: NTV/STV

MIPS/Watt: NTV/STV

1.50

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/ Problem Size

f⇥ Core Count


•Speculative •Higher f facilitates lower core count •Lower core count ➞ lower power


Accordion


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(MIP

SW) N

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canneal

Core Count: NTV/STV

MIPS/Watt: NTV/STV

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Spec. StillStill

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/ Problem Size

f⇥ Core Count


•Speculative •Higher f facilitates lower core count •Lower core count ➞ lower power


Accordion

Conclusion

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Accordion

Conclusion•Devises problem size as the main knob to overcome NTC barriers

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Accordion


•Problem size dictates

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Accordion


•Problem size dictates •the number of cores engaged in computation

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Accordion


•Problem size dictates •the number of cores engaged in computation•variation induced output quality degradation

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Accordion



•Decouples data & control to confine errors where they can be tolerated

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Accordion



•Decouples data & control to confine errors where they can be tolerated•Can achieve STV execution time

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Accordion



•Decouples data & control to confine errors where they can be tolerated•Can achieve STV execution time

•while operating 1.61-1.87x more energy-efficiently

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Accordion Toward Soft Near-threshold Voltage Computing

Ulya R. Karpuzcu, Ismail Akturk Nam Sung Kim

Accordion

Evaluation Set-up

!23

Benchmark Application domain Quality metric Accordion input Dependence on Accordion inputProblem Size Quality

canneal (PARSEC) Optimization Relative routing cost Swaps per temperature step linear linearNumber of temperature steps linear linear

ferret (PARSEC) Similarity search Based on number of common images Size factor complex complexbodytrack (PARSEC) Computer vision SSD based Number of annealing layers complex complexx264 (PARSEC) Multimedia SSIM based Quantizer complex linearhotspot (Rodinia) Physics simulation SSD based Number of iterations linear linearsrad (Rodinia) Image processing PSNR based Number of iterations linear linear

Table 3: RMS benchmarks deployed from PARSEC [3] and Rodinia [6] suites.

dependent. The application dependence mainly comes fromhow relative error is calculated.canneal relies on simulated annealing to minimize the chip

routing cost. At each temperature step, swaps_per_temptimes, each thread attempts to swap two randomly pickedblocks on chip. Both, the total number of temperaturesteps, and the number of swaps per temperature step(swaps_per_temp) represent Accordion inputs. In the fol-lowing, we use the latter without loss of generality. Relativerouting cost captures quality.ferret conducts content-base similarity search in an im-

age database. To extract similarity, images are partitioned andprocessed in regions. The number of regions dictates work perthread, and depends on the minimum region size calculated bynumber of pixels⇥size_factor (Accordion input). Apre-set number (n) of similar images found, on a per querybasis, constitutes the output. relative error (per query)becomes 1-[common image count]/n, where common im-age count is the number of output images common with thebaseline outcome. The configurations we experiment withinvolve multiple queries.bodytrack relies on an annealed particle filter to track

human movement through a scene. Number of annealing lay-ers (Accordion input) affects both, filtering accuracy, and theproblem size. The output is a vector of tracked configurations.Distortion calculation relies on SSD (sum of squared distance).x264 implements the H.264 standard for video encoding.

QP, the quantizer to control the degree of compression onencoding is the Accordion input. A smaller QP leads to lesscompression, hence a higher accuracy. Distortion calculationis based on SSIM (structural similarity index), a metric shownto match human perception of changes in accuracy better thanPSNR (peak signal to noise ratio).hotspot is a thermal simulator to iteratively solve heat

transfer differential equations for a given floorplan. The num-ber of iterations represents the Accordion input. The outputis the temperature at each point of a grid super-imposed onthe floorplan. Distortion calculation relies on SSD, sum ofsquared difference of temperatures across grid cells.srad implements an algorithm to effectively remove corre-

lated noise from imaging applications, based on an iterativePDE (partial differential equation) solver. We designate thenumber of iterations as the Accordion input. Distortion calcu-lation is based on PSNR.

Table 3 also tabulates, for each benchmark, how sensitive

problem size and Q are to changes in Accordion inputs. Weidentify two broad types of dependencies: Linear, and com-plex to capture mainly super-linear behavior. Different combi-nations apply across different benchmarks, however, exceptx264, problem size and Q tend to assume the same type ofdependency on the designated Accordion input, on a a perbenchmark basis. The type of the dependencies determinehow well different benchmarks respond to Accordion opera-tion.

6. EvaluationTo understand the basics of Accordion operation, we start withhow variation-induced timing error rates evolve as a functionof operating f. We next analyze how the quality of computingchanges with the problem size. We conclude this section witha detailed characterization of the operating points under Safeand Speculative modes of Accordion.

6.1. Impact of Parametric Variation

To quantify the variation-induced slowdown and the resultingtiming error rates across the cores of the hypothetical NTVchip, we first need to determine the near-threshold operatingVdd, VddNTV. To this end, we deploy VARIUS-NTV to extractthe minimum Vdd, VddMIN, each cluster can support to remainfunctional at NTV. If we let the system operate below suchVddMIN, memory blocks may not be able to hold or changestate. Figure 5a shows the distribution of per-cluster VddMINfor one representative chip (out of the 100 we experimentwith): Per-cluster VddMIN is defined as the maximum VddMINacross all memory blocks within a cluster. The data is shownas a histogram. Per-cluster VddMIN values vary in a significant0.46-0.58V range. We designate the maximum per clusterVddMIN as the chip-wide VddNTV.

We assign tasks to cores at the granularity of clusters. Eachcluster constitutes an f domain. The slowest core within eachcluster determines the operating f of the cluster. Figure 5bdepicts variation-induced timing error rate per cycle, Perr,when operating at VddNTV, as a function of f. For each cluster,the figure demonstrates the error rate curve of the slowest(i.e. most error prone) core within the cluster, rendering 36curves for 36 clusters. The y axis is on log-scale. Perr valuesrapidly increase to reach 1, as f increases beyond 0.5GHz.Even at acceptably low Perr of [1e-16,1e-12], the majorityof the cores cannot operate at the NTV fNOM of 1GHz – thesustainable f were there no variation. Perr in the range of

7

Accordion

Evaluation Set-up

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prevent error propagation from DCs, CCs never rely on dataproduced by DCs for control. CCs communicate with DCsover a dedicated memory location, both, to find out whetherslave DCs are done with computation, and to collect DC re-sults. DCs can only read, but not modify the data produced bymaster CCs.Data Core (DC) Semantics: To facilitate effective coordi-nation with Control Cores, Data Cores feature fast reset andrestart hardware. A DC has access to a private read-write mem-ory where the DC can write (either organized as a scratch-pador to communicate with other cores), in addition to a read-onlymemory where shared data managed by master CCs reside. Toavoid error propagation, DCs cannot write to the private spaceof CCs or of other DCs. Instead, a dedicated memory locationserves intra-DC communication.

4.2. Accordion Design Space

Figure 3 demonstrates an Accordion chip, clustered to enhancescalability. A few cores with per-core private memories and ashared cluster memory constitute each cluster. Various optionsexist to differentiate control cores from data cores.Homogeneous Clusters (Figure 3a, b): Each cluster accom-modates a set of identical cores. There is no difference in thedesign of CCs and DCs. The first option, as shown in Fig-ure 3a, differentiates CCs from DCs spatio-temporally: CCscorrespond to the fastest, most reliable cores in the variation-afflicted Accordion chip. This option is simpler from the hard-ware perspective, yet the semantics from Section 4.1 should allbe programmed. Still, the organization is very flexible in thatthe number of CCs can be configured, although the exampleorganization from Figure 3a depicts one CC per cluster. Sincevariation governs the f of CCs, the range of CC frequenciesmay differ across chips. The second option, as captured inFigure 3b, on the other hand, features temporal differentiationof CCs from DCs. Instead of explicitly assigning cores tooperate as CCs or DCs, each core is time-multiplexed betweenCC and DC functionality. This option provides a better useof hardware resources, yet complicates the design due to thesupport required for different memory protection domains.Heterogeneous Clusters (Figure 3c): CCs and DCs per clus-ter represent different types of cores by design. In this caseDCs and CCs specialize; the semantics from Section 4.1 canbe directly implemented in hardware. However, the number ofCCs may easily become a bottleneck. Depending on the appli-cation, a higher or a lower CC to DC ratio may be favorable.The organization from Figure 3c assumes one CC per cluster.CCs are expected to consume more area than DCs due to thecontrol-intensive specialization and the demand for enhancedreliability.

5. Evaluation Setup

5.1. Technology and Architecture

To quantify the impact of Accordion operation, we deploy ahypothetical NTV chip of 288 cores organized in 36 clusters

System ParametersTechnology node: 11nm PMAX= 100W# cores: 288 TMIN= 80oC# clusters: 36 (8 cores/cluster) Chip area ⇡ 20mm x 20mm

Variation ParametersCorrelation range: f = 0.1 Sample size: 100 chipsTotal (s/µ)Vth = 15% Total (s/µ)Leff = 7.5%

Technology ParametersVddNOM= 0.55V fNOM= 1.0GHzVthNOM= 0.33V fnetwork= 0.8GHz

Architectural ParametersCore-private mem: 64KB WT, Cluster mem: 2MB WB,

4-way, 2ns access, 64B line 16-way, 10ns access, 64B lineNetwork: bus inside cluster Avg. mem round-trip access time

and 2D-torus across clusters (without contention): ⇡80ns

Table 2: Technology and architecture parameters.

at 11nm. This chip mimics the Accordion organization fromFigure 3a (Section 4.2). Each cluster has 8 cores and a sharedper-cluster memory block. Each core is a single-issue enginewhere memory accesses can be overlapped with computation.A bus inside a cluster and a 2D-torus across clusters constitutethe network.

The nominal values of Vdd and f are 0.55V and 1.0GHz(which approximately correspond to 1V and 3.3GHz for STC).Table 2 covers the technology and architecture parameters.Technology parameters are derived from ITRS [1] and fine-tuned considering industry projections for 11nm. To evaluateperformance we use ESESC [19] with the power analysisrelying on McPAT [22] scaled to 11nm. The power budget isfixed to 100W.

We experiment with VARIUS-NTV [20] to extract VddMIN,the minimum near-threshold Vdd each memory block can sup-port. To have blocks stay functional at NTV, any designatednear-threshold operating Vdd should remain higher than suchVddMIN. We further use VARIUS-NTV to determine safe op-erating frequencies, and to estimate timing error rates as afunction of the operating frequency at the designated near-threshold Vdd.

5.2. Benchmarks

We experiment with select benchmarks from PARSEC [3] andRodinia [6] suites to cover emerging application domains. Ta-ble 3 captures benchmark characteristics. For each benchmark,we identify at least one application input parameter (Accor-dion input) governing both, the problem size and the accuracy.We rely on application-specific accuracy metrics to measurequality of computing. Applications usually generate multiplenumeric values as output, most of the time in vector or matrixformat. Accordingly, the quality metric should capture the de-viation in each numeric output value to derive the cumulativedeviation from the baseline execution. To this end, we rely onthe distortion metric introduced by Misailovic et al. [26]:Distortion is defined as the average, across all output values,of relative error per output value. The relative qualityof an execution outcome thus becomes 1-distortion. Dis-tortion is a generic metric, yet its calculation is application

6

Accordion

Impact of Parametric Variation

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0.0 0.5 1.0 1.5

1e−1

61e−1

21e−0

81e−0

41e

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105

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Problem Size vs. Quality

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Problem Size vs. Quality

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Accordion !31

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Accordion

Evaluation

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Accordion - Electrical and Computer...

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