Evolving Power-Efficient RNGs - UCL

Evolving Power-Efficient RNGs

David R. WhiteUniversity of Glasgow

39th CREST Open WorkshopTuesday 24th February 2015

David R. White University of Glasgow Evolving Power-Efficient RNGs

Table of Contents

Introduction

Evolving RNGs with GP

Measuring Power Consumption and Functionality

Experimental Method

Results

Conclusions and Postscript


Table of Contents

Introduction



Experimental Method

Results



My First Paper

This work was my first paper, at GECCO 2008.

Followed by work on non-functional properties with GP and acollaboration with Andrea Arcuri.

Some of the earliest work on using GP to optimise non-functionalproperties.


Resource Efficient Software: Target Platforms

WSN Motes RFID Tags

I Hardware limited (e.g. 64KB, 12MHz Mote)

I Multiple, demanding, requirements

I Interdependence between requirements

I What happens when you just don’t have enough resources?


The Difficult of Manual Power Optimisation

AKA “the loneliness of the long-distance embedded systemsprogrammer.”

“The internals of a modern processor are completechaos”.

Anonymous RTS Professor


Standard Programming

Programmer Compiler Binary


Standard Programming: Limitations


No automated improvement at this level

Compiler limited by programmer's decisions

Platform and usage almost incidental


Standard Programming: Limitations


No automated improvement at this level

Compiler limited by programmer's decisions

Platform and usage almost incidental

Complex relationship between source and binary


Table of Contents

Introduction



Experimental Method

Results



Why RNGs?

A common component; small and frequently executed.

We were interested in trade-offs, not solely optimisation.


Proof of Concept: Resource-Efficient PRNGs

Lamenca-Martinez et al. [2006] evolved PRNGs with a view toefficiency, building on work by Hernandez et al. [2004].

Tried to ensure efficiency through choice of function set.

See also Koza [1991], Jannink [1994], Sipper and Tomassini [1996].


Table of Contents

Introduction



Experimental Method

Results



Measuring Fitness

Quality was measured using the Strict Avalanche Criterion as perLamenca-Martinez et al. [2006].

Power efficiency was measured using the Sim-Wattch Simulator[Brooks et al., 2000].


Wattch

Cycle-level power simulator based on SimpleScalar simulator.

Estimates power usage through approximation for each logic unit:

Pd = CV 2ddaf (1)

C is the load capacitance; Vdd the supply voltage, f the clockfrequency and a an activity that estimates the amount of transistorswitching.

Partly estimated, validation given by Brooks et al. [2000].


Problems

Simulation is (allegedly) inaccurate and expensive.

For our purposes it only has to be relatively accurate, most of thetime.

We reduced the sample size compared to previous work, to increasespeed.

Could we have just used execution time as a proxy?


Measuring Randomness: Strict Avalanche Criterion

Trying to create a function r(a0 . . . a7)

Maximise nonlinearity of this function:

1. Create a random input a0 . . . a7

2. Evaluate o1 = r(a0 . . . a7)

3. Flip one bit of input to create b0 . . . b7

4. Evaluate o2 = r(b0 . . . b7)

5. Record hamming distance H(o1, o2)


Measuring Randomness: Strict Avalanche Criterion II

Compare the distribution of bit flips to the binomial distribution:

n∑i=0

(Ci − Ei )2

Ei


Our Objective Space

Resource (Power)

Err

or (

SA

C)


A Single Program

Resource (Power)

Err

or (

SA

C)


Table of Contents

Introduction



Experimental Method

Results



Experimental Method

Replicated work by Hernandez et al. [2004] and achieved similarresults.

Used reduced sample size.

Searched using ECJ and SPEA2.


Variance of Fitness Measures

0 2 4 6 8 10 12 140

1

2

3

4

5

6

7

8

9

10

Log2 (Sample Size)

log 10

(χ2 F

itnes

s / S

ampl

e S

ize)

Repeated for other programs and power consumption measure.


Experimental Framework

Raw Fitness Values

ECJGP & SPEA2

PRNGsource

Test Harnesssource

Mersenne Twister source

GCC Object Code

Sim-Wattch

Power Statistics

Test Harness Output


Parameter Settings

Function set MULT, AND, SUM, NOT, OR, XOR, Logical ShiftLeft (LSL), LSR, Circular Shift Left (CSL), CSR

Parameter settings left to their defaults in ECJ, as specified bykoza.params.

All non-default settings taken from previous work, except forMOO-specific settings.


Table of Contents

Introduction



Experimental Method

Results



Evolution of the Pareto Front

Animation


Example Pareto Front

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2.95e+08 3.05e+08 3.15e+08 3.25e+08

46

810

12

Power Consumption (Sim-Wattch Units)

log10(

Χ2 Fitness)


A Fantastically Low Power RNG

int genRand (int a0, int a1, int a2, int a3, int a4, int a5, int a6, inta7)

return ¬(¬(1997453768ul));


A Middle Ranking Low Power RNG

int genRand (int a0, int a1, int a2, int a3, int a4, int a5, int a6, inta7)

return a2 ∨ ¬(((a2 + a0) ∗ ((a4⊕ ((a6 + a5)⊕ a7)) + (a1⊕a3))) ∧ ¬(¬(1997453768ul)));


An Excellent Low Power RNG

int genRand (int a0, int a1, int a2, int a3, int a4, int a5, int a6, inta7) (2307363674ul ⊕ (a2 ∗ a6)) + ((¬((((((a2 ∗ a6)⊕ (a7⊕ a1)) ∗(a0⊕ a3))⊕ (a2 ∗ a6)) + (a5 ∗ a4)) >> 2307363674ul)⊕ (a0⊕a3)) + ¬((a5 ∗ a4) ∗ ((2307363674ul ⊕ (a7⊕ a1)) + (a0⊕ a3))));


Bit Flip Distribution for Best Individual

0 5 10 15 20 25 30 350

500

1000

1500

2000

2500

Number of Bit Flips

Fre

quen

cy

IdealBest Program


The Impact of the Mult Function

x xxxxxxxx

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2.9e+08 3.0e+08 3.1e+08 3.2e+08 3.3e+08 3.4e+08 3.5e+08

02

46

810

12

14

Power Consumption (Sim-Wattch Units)

log10 (

Χ2 Fitness )

ooo oooooooo oooooooooooooooooooooo

o oooo ooo ooo

ooooo oo

ooooooo

ooo

o

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o

o

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oo

oo

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o o o

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Multiply IncludedMultiply Omitted


Table of Contents

Introduction



Experimental Method

Results



Conclusions

This is about more than straightforward optimisation.

Multiple solutions vs a single, tunable, scalable algorithm.

More radically, consider manipulation rather than optimisation.


Postscript: Time Avalanche Criterion

0 2 4 6 8 10 13 16 19 22 25 28 31

ActualExpected

Bit Flips

Fre

qu

en

cy

02

00

40

06

00

80

01

00

01

20

01

40

0

0 1 2 3 4 5

ActualExpected

Bit Flips

Fre

qu

en

cy

05

00

100

01

50

02

00

02

50

03

00

0

See White et al. [2010]


Acknowledgements

My coauthors John Clark, Jeremy Jacob and Simon Poulding.

Andrea Arcuri for his collaboration.

Juan E. Tapiador and Julio Cesar Hernandez-Castro, for inspirationand creative discussion.

[email protected]


Genetic Improvement Workshop (at GECCO 2015)

Submission deadline: April 3, 2015 geneticimprovement2015.com


References I

David Brooks, Vivek Tiwari, and Margaret Martonosi. Wattch: a framework forarchitectural-level power analysis and optimizations. In ISCA, pages 83–94,2000. URL http://www.cs.ucr.edu/~harry/classes_files/CS269_

02/papers/Brooks_ISCA_00.pdf.

Julio Cesar Hernandez, Pedro Isasi, and Andre Seznec. On the design ofstate-of-the-art pseudorandom number generators by means of geneticprogramming. In Proceedings of the 2004 IEEE Congress on EvolutionaryComputation, pages 1510–1516, 2004. ISBN 0-7803-8515-2.

Jan Jannink. Cracking and Co-Evolving Randomizers. Advances in GeneticProgramming, pages 425–443, 1994. URLciteseer.ist.psu.edu/jannink94cracking.html.

John R. Koza. Evolving a computer program to generate random numbersusing the genetic programming paradigm. In Proceedings of the FourthInternational Conference on Genetic Algorithms, pages 37–44. MorganKaufmann, 1991. URLhttp://citeseer.ist.psu.edu/john91evolving.html.


http://www.cs.ucr.edu/~harry/classes_files/CS269_02/papers/Brooks_ISCA_00.pdf

http://www.cs.ucr.edu/~harry/classes_files/CS269_02/papers/Brooks_ISCA_00.pdf

citeseer.ist.psu.edu/jannink94cracking.html

http://citeseer.ist.psu.edu/john91evolving.html

References II

Carlos Lamenca-Martinez, Julio Cesar Hernandez-Castro, Juan M.Estevez-Tapiador, and Arturo Ribagorda. Lamar: A new pseudorandomnumber generator evolved by means of genetic programming. In ParallelProblem Solving from Nature IX, volume 4193, pages 850–859.Springer-Verlag, 2006. URLhttp://ppsn2006.raunvis.hi.is/proceedings/202.pdf.

Moshe Sipper and Marco Tomassini. Co-evolving parallel random numbergenerators. In Parallel Problem Solving from Nature – PPSN IV, pages950–959. Springer, 1996.

DavidR. White, Juan M.E. Tapiador, Julio Cesar Hernandez-Castro, andJohnA. Clark. Fine-grained timing using genetic programming. In EuroGP2010. 2010. doi: 10.1007/978-3-642-12148-7 28.


http://ppsn2006.raunvis.hi.is/proceedings/202.pdf

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Evolving Power-Efficient RNGs - UCL