Optimization SpaceExploration of the FastFlowParallel Skeleton Framework

Alexander Collins Christian Fensch Hugh Leather

University of EdinburghSchool of Informatics

What We Did

I Parallel skeletons provide easy abstraction forparallel programs

I Contain many manually tuned parameters

I Automatically tuning provides betterperformance

I Preliminary results that make auto-tuningfaster

1

Motivating Example

2

Motivating Example

2

Motivating Example

2

Motivating Example

2

Motivating Example

2

Motivating Example

2

Tuning the Example

10 15 20 25 30 35 40Maximum recursion depth

0.0

0.5

1.0

1.5

2.0

2.5Sp

eedu

p

Humanexpert

Bestpossible

3

What Next?

I Humans failed

I Auto-tuning wonI Can we do even better?

I Multiple parametersI Multiple programsI Multiple platforms

4

Optimization Space Exploration

5

Parameters Investigated

I Number of workers

I Bounded or unbounded queues

I Size of queue’s buffer

I Cache alignment

I Maximum recursion depth

I Batch size

6

Speedup over a Human Expert

7

Speedup over a Human Expert

8

Speedup over a Human Expert

9

Visualising the Optimisation Space

10

Visualisation of Optimisation Space

11

Reducing the Size of the Search Space

I Two methods:I Remove useless parametersI Exploit linear dependencies

12

What is a Useless Parameter?

13

What is a Useful Parameter?

14

Removing Useless Parameters

buffertypecachealign

buffersizeseqthresh

batchsizenumworkers

Parameter

0%

10%

20%

30%

40%

50%Av

erag

e pe

rform

ance

loss

I Reduces size of search space by 6×

15

Exploiting Linear Dependencies

16

Exploiting Linear Dependencies

17

Exploiting Linear Dependencies

18

Conclusions

I Tuning parameters is very important

I Humans are bad at tuning

I Auto-tuning is much better

I Tuning is program and platform dependent

I Have shown preliminary results that makeauto-tuning faster

19

Optimization SpaceExploration of the FastFlowParallel Skeleton Framework

Alexander Collins Christian Fensch Hugh Leather

University of EdinburghSchool of Informatics

Speedup over a Human Expert

aquad cwc dtfibonacci

mandelbrotmatmul

nqueenspbzip2

quicksort swps3Average

1

2

3

4

5

6

78

Spee

dup

desktop phantom scuttle xxxii16 xxxii Average

Principal Components Analysis

N = 6 P = 5624

p =

(batchsize, buffersize, buffertype,cachealign, numworkers, seqthresh

)λ = (0.443, 0.419, 0.204, 0.138, 0.007, 0.003)

e =

0.023 0.814 −0.000 −0.003 −0.580 0.013

−0.015 0.581 0.002 0.002 0.814 −0.014−0.115 −0.001 0.005 −0.000 0.015 0.993

0.993 −0.010 −0.000 −0.001 0.028 0.115−0.001 −0.001 0.003 −1.000 0.003 −0.001−0.001 0.001 −1.000 −0.003 0.002 0.005

ν = (36%, 70%, 87%, 99%, 99%, 100%)

Is the subset representative?

0 500 1000 1500 2000

60%80%

100%

desk

top

0 500 1000 1500 2000

60%80%

100%

phanto

m

0 500 1000 1500 2000 2500 3000

60%80%

100%

Perc

enta

ge o

f best

pro

gra

m p

erf

orm

ance

scutt

le

0 500 1000 1500 2000 2500

60%80%

100%

xxxii1

6

0 1000 2000 3000 4000 5000 6000

Number of iterations

60%80%

100%

xxxii

Pla

tform

Programs

Program Description

aquad Adaptive Quadrature algorithm

cwc Implementation of CWC, a calculus for the representation andsimulation of biological systems

dt Implementation of the C4.5 decision tree algorithm

fibonacci Naıve recursive algorithm, without memoization, to computeFibonacci numbers

mandelbrot Mandelbrot fractal generator

matmul O(n3) nested-loops matrix multiplication

nqueens n-queens problem solver

pbzip2 Parallel bzip2 compression

quicksort Parallel quicksort

swps3 Smith-Waterman algorithm for gene sequence alignment

Platforms

Platform Processor Cores Freq. Memory L3 L2

xxxii 4× IntelXeonL7555

32 1.87GHz 64GB 4×24MB

32×256KB

xxxii16 2× IntelXeonL7555

16 1.87GHz 64GB 2×24MB

16×256KB

scuttle AMDPhenom IIX6 1055T

6 3.3GHz 8GB 1×6MB

1×512KB

phantom Intel XeonE5430

4 2.67GHz 8GB None 2×6MB

desktop Intel Core2 DuoE6400

2 2.13GHz 3GB None 1×2MB

Parameter Values

Parameter Values

numworkers 1, . . . , # cores × 1.5

buffertype Bounded or unbounded

buffersize 1, 2, 4, 8, . . . , 220

batchsize 1, 2, 4, 8, . . . , 220

cachealign 64, 128 or 256 bytes

seqthresh with aquad 0.02, 0.04, 0.06, . . . , 1

seqthresh with fibonacci 10, 11, 12, . . . , 44

seqthresh with nqueens 3, 4, 5, . . . , 15

seqthresh with quicksort 1, 2, 4, 8, . . . , 221

Outlier Removal

I Arithmetic mean is not a robust statistic

I An outlier will cause many more repeats

I Impractical

I Remove using interquartile range removal:[Q1 − k(Q3 − Q1),Q3 + k(Q3 − Q1)

]with k = 3

Quantifying Noise

I Repeats allow quantification ofnoise:

I Perform between 10 and 100repeats

I Stop if coefficient of variationdrops below 1% for a 99%confidence interval

I Use the arithmetic mean as anestimator of execution time

I And confidence intervals tocompare execution times

Skeletons Provided by FastFlow

I farm

I farm-with-feedback

I pipe