[PPT] - The Energy/Frequency Convexity Rule of Energy Consumption for PowerPoint Presentation

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The Energy/Frequency Convexity Rule

f Energy Consumption for Programs:

Modeling, Thermosensitivity, and Applications Karel De Vogeleer

Ph.D. defense

September 4th, 2015

Special thanks to Fondation TELECOM for funding this research

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Introduction Motivation Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 1 / 27

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Introduction Motivation Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 2 / 27

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Introduction Overview

A Green IT Thinking

Off-line, including

◮ transistor design, ◮ circuit design, ◮ architecture, ◮ software design, ◮ software coding, ◮ compiler optimization;

n-line, including

◮ system reconfiguration, ◮ compiler optimization, ◮ context placement.

Image source jiji.ng and wisegeek.com

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 3 / 27

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Introduction Thesis’ Contributions

Contributions

Energy consumption analysis for computer systems:

◮ analytical model, ◮ Energy/Frequency Convexity Rule, ◮ supportive measurement data;

temperature/power relationship demystified:

◮ supportive measurement data, ◮ guidelines for power measurement;

transient thermal model for microprocessors:

◮ analytical model including radiation, ◮ approximations, ◮ applicability analysis. Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 4 / 27

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Introduction Thesis’ Contributions

Contributions

Energy consumption analysis for computer systems:

◮ analytical model, ◮ Energy/Frequency Convexity Rule, ◮ supportive measurement data;

temperature/power relationship demystified:

◮ supportive measurement data, ◮ guidelines for power measurement;

transient thermal model for microprocessors:

◮ analytical model including radiation, ◮ approximations, ◮ applicability analysis. time (s) 2075 2175 2275 2375 2475 2575 2675 power (W) 1.252 1.256 1.26 1.264 1.268 1.272 1.276 data linear transform quadratic transform Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 4 / 27

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Introduction Thesis’ Contributions

Contributions

Energy consumption analysis for computer systems:

◮ analytical model, ◮ Energy/Frequency Convexity Rule, ◮ supportive measurement data;

temperature/power relationship demystified:

◮ supportive measurement data, ◮ guidelines for power measurement;

transient thermal model for microprocessors:

◮ analytical model including radiation, ◮ approximations, ◮ applicability analysis. Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 4 / 27

SLIDE 8

Introduction Thesis’ Contributions

Contributions

Energy consumption analysis for computer systems:

◮ analytical model, ◮ Energy/Frequency Convexity Rule, ◮ supportive measurement data;

temperature/power relationship demystified:

◮ supportive measurement data, ◮ guidelines for power measurement;

transient thermal model for microprocessors:

◮ analytical model including radiation, ◮ approximations, ◮ applicability analysis.

22 26 30 36 45 60 83

surface (m2) 0.01 0.02 0.03 0.04 0.05 rcr

0.4
0.2

0.2 0.4 0.6 0.8 1 Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 4 / 27

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Introduction Thesis’ Contributions

Contributions

energy consumption analysis for computer systems:

◮ analytical model, ◮ Energy/Frequency Convexity Rule, ◮ supportive measurement data;

temperature/power relationship demystified:

◮ supportive measurement data, ◮ guidelines for power measurement;

transient thermal model for microprocessors:

◮ analytical model, ◮ approximations, ◮ applicability analysis. Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 4 / 27

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Introduction Outline

Presentation’s Outline

1

Introduction

2

Energy Model

3

Practical Example

4

Parameter Sensitivity

5

Case Studies

6

Conclusion

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 5 / 27

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Energy Model

1

Introduction

2

Energy Model

3

Practical Example

4

Parameter Sensitivity

5

Case Studies

6

Conclusion

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 5 / 27

SLIDE 12

Energy Model

Preliminary Evidence of Energy/Frequency Curves

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 200 400 600 800 1000 Normalized Total Energy CPU Frequency (MHz) 2% Miss Ratio 9% Miss Ratio 16% Miss Ratio

(a) Fan et al. [1] (b) Le Sueur and Heiser [3]

1.5 2 2.5 Frequency [GHz] 400 800 1200 1600 2000 2400 Energy to solution [J] DGEMM 8C DGEMM 4C RAY 8C RAY SMT 8C

(a)

(c) Hager et al. [2]

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 50 100 150 200 250 300 350 400 450

CPU Energy CPU Frequency (MHz)

Model predicted energy basicmath bitcnts celp gzip mpg qsort susan.corners susan.edges susan.smoothing visionworst fft inv_fft patricia typeset

(d) Snowdon et al. [4]

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 6 / 27

SLIDE 13

Energy Model General Framework

System Energy Consumption Model (Esys)

System’s energy consumption Esys definition Esys = ∆t Psys dt = ∆t ( Pcpu + Pback ) dt; Examples of Pback include:

◮ LCD screen, ◮ radio interface, ◮ sensors (e.g. GPS);

If Pcpu and Pback are constant over ∆t: Esys = (Pcpu + Pback) · ∆t. everything else CPU

system

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 7 / 27

SLIDE 14

Energy Model Power and Time Model

Microprocessor Power Model Execution Time Model CPU power Pcpu consists of: dynamic power Pdyn, leakage current Pleak, short-circuit current Psc, Pcpu = Pdyn + Pleak + Psc = ( 1 + γV ) · η αCV 2f = (1 + γV ) · ξV 2f . Execution time ∆t depends on: ccb code size in clock cycles, f CPU clock frequency, fk frequency thieves, β slack time per clock cycle, ∆t = ccb

1

f − fk + β

.

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 8 / 27

SLIDE 15

Energy Model Optimal Clock Frequency

Optimal Clock Frequency (fopt)

System’s energy consumption model Esys(f ) = (Pcpu + Pback) · ∆t = ([1 + γV ]ξV 2f + Pback) · ccb

1

f − fk + β

,

where {γ, ξ, Pback, ccb, fk, β} ∈ R+; a single minimum for Esys(f ) exists at fopt when ∂Esys ∂f

f =fopt

= 0, and ∂2Esys ∂f 2 > 0 holds; V is approximately an affine map of f : V → m2f + m1.

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 9 / 27

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Energy Model Optimal Clock Frequency

Supply Voltage/Frequency Relationship

A linear trend between V and f is observed: V = m2f + m1.

Exynos 4210 Exynos 4x12 Exynos 5250 Intel M S3C6410 PXA320 linear approximations m1 = 1

3, m2 = 4 5

m1 = 1

3, m2 = 4 5

frequency (GHz) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 supply voltage (V) 0.85 0.95 1 1.05 1.15 1.25 1.35 1.45 Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 10 / 27

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Practical Example

1

Introduction

2

Energy Model

3

Practical Example

4

Parameter Sensitivity

5

Case Studies

6

Conclusion

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 10 / 27

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Practical Example Energy Measurement

Benchmark and Testbed

Benchmark: bit-reverse algorithm, part of the DFT algorithm:

void bitreverse_gold_rader (int N, complex *data) { int n = N, nm1 = n-1; int i = 0, j = 0; for (; i < nm1; i++) { int k = n >> 1; if (i < j) { complex temp = data[i]; data[i] = data[j]; data[j] = temp;} while (k <= j) { j -= k; k >>= 1;} j += k ; } }

testbed: Samsung Galaxy SII; power Measurement: Monsoon.

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 11 / 27

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Practical Example Energy Measurement

Benchmark and Testbed

Benchmark: bit-reverse algorithm, part of the DFT algorithm:

void bitreverse_gold_rader (int N, complex *data) { int n = N, nm1 = n-1; int i = 0, j = 0; for (; i < nm1; i++) { int k = n >> 1; if (i < j) { complex temp = data[i]; data[i] = data[j]; data[j] = temp;} while (k <= j) { j -= k; k >>= 1;} j += k ; } }

testbed: Samsung Galaxy SII; power Measurement: Monsoon.

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 11 / 27

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Practical Example Energy Measurement

Benchmark and Testbed

Benchmark: bit-reverse algorithm, part of the DFT algorithm:

void bitreverse_gold_rader (int N, complex *data) { int n = N, nm1 = n-1; int i = 0, j = 0; for (; i < nm1; i++) { int k = n >> 1; if (i < j) { complex temp = data[i]; data[i] = data[j]; data[j] = temp;} while (k <= j) { j -= k; k >>= 1;} j += k ; } }

testbed: Samsung Galaxy SII; power Measurement: Monsoon.

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 11 / 27

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Practical Example Energy Measurement

The Energy/Frequency Convexity Rule

Energy consumption versus CPU clock frequency shows convex properties.

frequency (GHz) 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 energy per array element (nJ) 30 40 50 60 70 Input size (2N) N= 6 N= 8 N= 10 N= 12 N= 14 N= 16 measured model Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 12 / 27

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Parameter Sensitivity

1

Introduction

2

Energy Model

3

Practical Example

4

Parameter Sensitivity

5

Case Studies

6

Conclusion

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 12 / 27

SLIDE 23

Parameter Sensitivity

Energy Model’s Parameter Sensitivity Analysis

Energy consumption model under analysis: Esys = ([1 + γV ] · ξV 2f + Pback) · ccb

1

f − fk + β

,

∂Esys ∂f

f =fopt

= 0; The aim is to find the conditions under which fopt is exploitable; The following parameters will be looked at in more detail:

◮ frequency thieves (overhead) fk, ◮ background power Pback, ◮ power gain ξ, ◮ temperature γ(T);

Analysis based on energy profile of the Exynos 4210.

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 13 / 27

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Parameter Sensitivity Frequency Thieves

Influence of frequency thieves fk on fopt

Esys = ([1 + γV ] · ξV 2f + Pback) · ccb

1

f −fk + β

ξ (V−1)

0.155 0.162 0.168 0.174 0.181

Pback=0.5 (W) fk (GHz) 0.2 0.5 0.8 1 1.2 1.5 1.8 2 fopt (GHz) 0.2 0.6 1 1.4 1.8 2.2 2.6 3 3.4 ≈ 30 MHz ≈ 50 MHz

(e) fopt(fk,ξ)

Pback (W) 0.5 1 1.5 2 2.5 3 3.5 4 4.5

ξ=0.168 (V−1) fk (GHz) 0.2 0.5 0.8 1 1.2 1.5 1.8 2 fopt (GHz) 0.2 0.6 1 1.4 1.8 2.2 2.6 3 3.4

(f) fopt(fk,Pback)

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 14 / 27

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Parameter Sensitivity Background Power Demands

Influence of Background Power Pback on fopt

Esys = ([1 + γV ] · ξV 2f + Pback) · ccb

1

f −fk + β

ξ (V−1)

0.155 0.162 0.168 0.174 0.181

Pback (W) 1 2 3 4 5 6 fopt (GHz) 0 0.2 0.5 0.8 1 1.2 1.5 1.8 2 2.2 ≈ 100 MHz ≈ 0.5 W

(g) fopt(Pback, ξ)

ξ (V−1) 0.155 0.162 0.168 0.174 0.181

Pback (W) 1 2 3 4 5 6 Pback/Pcpu 0.2 0.4 0.6 0.8 1 1.2 1.4 ≈ 0.05

(h) Pback/Pcpu ratio at fopt

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 15 / 27

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Parameter Sensitivity Power Gain

Influence of Power Gain ξ(s) on fopt

Esys = ([1 + γV ] · ξV 2f + Pback) · ccb

1

f −fk + β

Cooperative microprocessors
n the same die:

1

power-efficient: Cortex A7,

2

high-performance: Cortex A15;

ξ is scaled by s between its lower and upper bound: s ∈ {1, 2}; Exynos 5410 power model.

. 2 5 0.5 0.75 1 1 . 5 2 2.5 0.075 0.15 0.3 A15 A7

power scaling (s) 1 1.2 1.4 1.6 1.8 2 fopt (GHz) 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Numbers on the lines represent the background power for that line.

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 16 / 27

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Parameter Sensitivity Temperature

Influence of Temperature γ(T) on fopt

Esys = ([1 + γV ] · ξV 2f + Pback) · ccb

1

f −fk + β

γ is a function of temperature;

temperature/power model of Exynos 5410 is used; temperature/power shows exponential behavior;

temperature (◦C) 30 40 50 60 70 80 power (W) 2.4 2.5 2.6 2.7 2.8 data exponential fit quadratic fit linear fit

∆fopt ≈ 200 MHz when 25◦C < T < 85◦C.

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 17 / 27

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Case Studies

1

Introduction

2

Energy Model

3

Practical Example

4

Parameter Sensitivity

5

Case Studies

6

Conclusion

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 17 / 27

SLIDE 29

Case Studies Optimization Techniques Classification

Case Study 1: fopt Classification

fopt

max(fmin, fk)
frequency

energy fopt

max(fmin, fk)
fmax
frequency

energy fopt

fmax
frequency

energy

1 fopt < max(fmin, fk) the slower, the better 2 max(fmin, fk) ≤ fopt ≤ fmax chase fopt 3 fmax < fopt race-to-halt

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 18 / 27

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Case Studies Multi-core Code Execution

Case Study 2: fopt and Multi-core Code Execution

Clock frequency scheduling schemes:

1 on-demand: binary (high/low) as work arrives; 2 selfish: each core is individually energy optimized; 3 thread-cooperation: all cores are collectively energy optimized.

t thread ta tb tc A B C (a) default clock scaling t thread ta tb tc A B C (b) cooperative clock scaling

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 19 / 27

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Case Studies Multi-core Code Execution

Case Study 2: fopt and Multi-core Code Execution contd.

Problem statement: n threads executed in parallel with common deadline tmax; threads individually clock frequency fi scalable; Etot(fi) : Rm → R to be minimized over fi: Etot(fi) = Pbacktmax +

n

i=0

ccb,i fi P+ +

tmax − ccb,i

fi

P◦
,

subject to ∀i, ccb,i fi ≤ tmax and fmin ≤ fi ≤ fmax; {ccb, fi, tmax, Pback, P◦, P+} ∈ R+; active power (P+) and idle power (P◦) are generated by the Exynos 5410 power model.

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 20 / 27

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Case Studies Performance Evaluations

Case Study 2: fopt and Multi-core Code Execution contd.

Performance evaluation of 4 clock frequency scalable parallel threads.

thread cooperation selfish

n-demand

background power (W) 1 2 3 4 5 6 7 8 9 10 energy ratio (%) 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

(a) energy

thread cooperation selfish

n-demand

background power (W) 1 2 3 time ratio (%) 1 1.1 1.3 1.5 1.7 1.9 2

(b) time

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 21 / 27

SLIDE 33

Case Studies Performance Evaluations

Case Study 3: big-LITTLE Heterogeneous Computing

Optimal clock frequency for cooperative microprocessors:

1

power-efficient: Cortex A7,

2

high-performance: Cortex A15;

fopt is chosen on the core yielding best efficiency; Exynos 5410 power model used.

0.5 0.75 1 1 . 5 2 2.5 0.075 0.15 0.30 0.25

power scaling (s) 1 1.2 1.4 1.6 1.8 2 fopt (GHz) 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Numbers on the lines represent the background power for that line.

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 22 / 27

SLIDE 34

Conclusion Summary

1

Introduction

2

Energy Model

3

Practical Example

4

Parameter Sensitivity

5

Case Studies

6

Conclusion

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 22 / 27

SLIDE 35

Conclusion Summary

Conclusion

System’s energy consumption shows convex properties over f ; rules of thumb for an exploitable fopt:

◮ Pback should be smaller than Pcpu, ◮ overhead (fk) should be limited, ◮ slack time β should be limited, ◮ power profile (ξ) has minimal effect, ◮ code size (ccb) has no effect;

energy gains could be from 10% up to 50% at fixed temperature; temperature/Power relationship shows exponential behavior; radiation can be omitted for small devices.

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 23 / 27

SLIDE 36

Conclusion What’s Next

Future Work

Including: apply results to other domains:

◮ multi-core, ◮ HPC, ◮ clock modulation, ◮ interactive/performance;

exploit the thermal behavior; better understanding of how much energy can practically be gained.

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 24 / 27

SLIDE 37

The Energy/Frequency Convexity Rule

f Energy Consumption for Programs:

Modeling, Thermosensitivity, and Applications Karel De Vogeleer

Ph.D. defense

September 4th, 2015

SLIDE 38

Conclusion What’s Next

Publications

K. De Vogeleer, G. Memmi, P. Jouvelot, and F. Coelho, “The Energy/Frequency

Convexity Rule: modeling and experimental validation on mobile devices,” in Proceedings of the 10th Conference on Parallel Processing and Applied

Mathematics. Springer Verlag, Sep. 2013.
K. De Vogeleer, G. Memmi, P. Jouvelot, and F. Coelho, “Modeling the

temperature bias of power consumption for nanometer-scale cpus in application processors,” in 14th International Conference on Embedded Computer Systems: Architectures, Modeling, and Simulation, Jul. 2014, pp. 172-180.

K. De Vogeleer, P. Jouvelot, and G. Memmi, “The impact of surface size on the

radiative thermal behavior of embedded systems,” CoRR, vol. abs/1410.0628, 2014, (submitted to IEEE TMC in 2014).

K. De Vogeleer, G. Memmi, and P. Jouvelot, “Parameter Sensitivity Analysis of the

Energy/Frequency Convexity Rule for Nanometer-scale Application Processors,” CoRR, vol. abs/1508.07740, 2015, (in submission to The Elsevier Journal of Parallel and Distributed Computing, 2015).

Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 26 / 27

SLIDE 39

Conclusion What’s Next

References I

Fan, X., Ellis, C. S., and Lebeck, A. R. The synergy between power-aware memory systems and processor voltage

scaling. In Proceedings of the Third international conference on Power - Aware Computer Systems (Berlin, Heidelberg,

2004), Springer-Verlag, pp. 164–179. Hager, G., Treibig, J., Habich, J., and Wellein, G. Exploring performance and power properties of modern multi-core chips via simple machine models. Concurrency and Computation: Practice and Experience (2013), n/a–n/a. Le Sueur, E., and Heiser, G. Dynamic voltage and frequency scaling: the laws of diminishing returns. In Proceedings

f the 2010 international conference on Power aware computing and systems (Berkeley, CA, USA, 2010), HotPower’10,
pp. 1–8.

Snowdon, D. C., Ruocco, S., and Heiser, G. Power management and dynamic voltage scaling: Myths and facts. In 2005 WS Power Aware Real-time Comput. (New Jersey, USA, Sept. 2005). Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 27 / 27