The Energy/Frequency Convexity Rule of 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
Introduction Motivation Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 1 / 27
Introduction Motivation Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 2 / 27
Introduction Overview A Green IT Thinking Off-line, including ◮ transistor design, ◮ circuit design, ◮ architecture, ◮ software design, ◮ software coding, ◮ compiler optimization; on-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
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
Introduction Thesis’ Contributions Contributions Energy consumption analysis for computer systems: ◮ analytical model, ◮ Energy/Frequency Convexity Rule, ◮ supportive measurement data; temperature/power relationship demystified: 1.264 1.268 1.272 1.276 data ◮ supportive measurement data, linear transform ◮ guidelines for power measurement; quadratic transform transient thermal model for microprocessors: ◮ analytical model including radiation, power (W) ◮ approximations, ◮ applicability analysis. 1.26 1.252 1.256 2075 2175 2275 2375 2475 2575 2675 time (s) Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 4 / 27
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
Introduction Thesis’ Contributions Contributions Energy consumption analysis for computer systems: ◮ analytical model, ◮ Energy/Frequency Convexity Rule, ◮ supportive measurement data; temperature/power relationship demystified: 1 22 ◮ supportive measurement data, 26 30 0.8 ◮ guidelines for power measurement; 36 0.6 transient thermal model for microprocessors: 45 0.4 ◮ analytical model including radiation, 60 r cr ◮ approximations, 0.2 ◮ applicability analysis. 0 83 -0.2 -0.4 0 0.01 0.02 0.03 0.04 0.05 surface ( m 2 ) Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 4 / 27
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
Introduction Outline Presentation’s Outline Introduction 1 Energy Model 2 Practical Example 3 Parameter Sensitivity 4 Case Studies 5 Conclusion 6 Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 5 / 27
Energy Model Introduction 1 Energy Model 2 Practical Example 3 Parameter Sensitivity 4 Case Studies 5 Conclusion 6 Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 5 / 27
Energy Model Preliminary Evidence of Energy/Frequency Curves 2.4 2.2 2% Miss Ratio 9% Miss Ratio 2 Normalized Total Energy 16% Miss Ratio 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0 200 400 600 800 1000 CPU Frequency (MHz) (a) Fan et al. [1] (b) Le Sueur and Heiser [3] 1.8 2400 Model predicted energy basicmath bitcnts 1.7 celp gzip 2000 1.6 mpg qsort susan.corners Energy to solution [J] susan.edges 1.5 susan.smoothing visionworst 1600 (a) fft CPU Energy 1.4 inv_fft patricia typeset 1.3 1200 1.2 800 1.1 DGEMM 8C DGEMM 4C 1 400 RAY 8C RAY SMT 8C 0.9 0 0.8 1.5 2 2.5 50 100 150 200 250 300 350 400 450 CPU Frequency (MHz) Frequency [GHz] (c) Hager et al. [2] (d) Snowdon et al. [4] Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 6 / 27
Energy Model General Framework System Energy Consumption Model ( E sys ) everything else System’s energy consumption E sys definition � ∆ t = E sys P sys dt 0 � ∆ t = ( P cpu + P back ) dt ; 0 CPU Examples of P back include: ◮ LCD screen, ◮ radio interface, ◮ sensors (e.g. GPS); system If P cpu and P back are constant over ∆ t : E sys = ( P cpu + P back ) · ∆ t . Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 7 / 27
Energy Model Power and Time Model Microprocessor Power Model Execution Time Model Execution time ∆ t depends on: CPU power P cpu consists of: cc b code size in clock cycles, dynamic power P dyn , f CPU clock frequency, leakage current P leak , f k frequency thieves, short-circuit current P sc , β slack time per clock cycle, P cpu = P dyn + P leak + P sc � 1 � ∆ t = cc b + β . ( 1 + γ V ) · η α CV 2 f = f − f k (1 + γ V ) · ξ V 2 f . = Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 8 / 27
Energy Model Optimal Clock Frequency Optimal Clock Frequency ( f opt ) System’s energy consumption model E sys ( f ) = ( P cpu + P back ) · ∆ t � 1 � ([1 + γ V ] ξ V 2 f + P back ) · cc b = + β , f − f k where { γ, ξ, P back , cc b , f k , β } ∈ R + ; a single minimum for E sys ( f ) exists at f opt when ∂ 2 E sys � ∂ E sys � = 0 , and > 0 holds; ∂ f 2 ∂ f f = f opt V is approximately an affine map of f : V → m 2 f + m 1 . Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 9 / 27
Energy Model Optimal Clock Frequency Supply Voltage/Frequency Relationship A linear trend between V and f is observed: V = m 2 f + m 1 . 1.45 linear approximations m 1 = 1 3 , m 2 = 4 5 m 1 = 1 3 , m 2 = 4 5 1.35 1.25 supply voltage (V) 1.15 1.05 1 Exynos 4210 0.95 Exynos 4x12 Exynos 5250 Intel M S3C6410 0.85 PXA320 0 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 frequency (GHz) Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 10 / 27
Practical Example Introduction 1 Energy Model 2 Practical Example 3 Parameter Sensitivity 4 Case Studies 5 Conclusion 6 Karel De Vogeleer (ParisTech) The Energy/Frequency Convexity Rule September 4th, 2015 10 / 27
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
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
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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