predicting parallel performance

INTEL CONFIDENTIAL

Predicting Parallel PerformanceIntroduction to Parallel Programming – Part 10

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Review & Objectives

Previously: Design and implement of a task decomposition solution

At the end of this part you should be able to:Define speedup and efficiencyUse Amdahl’s Law to predict maximum speedup


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Speedup

Speedup is the ratio between sequential execution time and parallel execution time

For example, if the sequential program executes in 6 seconds and the parallel program executes in

2 seconds, the speedup is 3X

Speedup curveslook like this

Cores

Spee

dup


Efficiency

EfficiencyA measure of core utilizationSpeedup divided by the number of cores

ExampleProgram achieves speedup of 3 on 4 coresEfficiency is 3 / 4 = 75%

4

Efficie

ncy

Cores

Efficiency curveslook like this


Speedup Example

Painting a picket fence– 30 minutes of preparation (serial)– One minute to paint a single picket– 30 minutes of cleanup (serial)

Thus, 300 pickets takes 360 minutes (serial time)

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Speedup and Efficiency


Computing Speedup

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Number of painters

Time Speedup

1 30 + 300 + 30 = 360 1.0X

2 30 + 150 + 30 = 210 1.7X

10 30 + 30 + 30 = 90 4.0X

100 30 + 3 + 30 = 63 5.7X

Infinite 30 + 0 + 30 = 60 6.0X



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Efficiency ExampleNumber of painters

Time Speedup Efficiency

1 360 1.0X 100%

2 30 + 150 + 30 = 210 1.7X 85%

10 30 + 30 + 30 = 90 4.0X 40%

100 30 + 3 + 30 = 63 5.7X 5.7%

Infinite 30 + 0 + 30 = 60 6.0X very low



Idea Behind Amdahl’s Law

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Cores

Exec

utio

n Ti

me

s

s

ss s

1-s (1-s )/2 (1-s )/3 (1-s )/5(1-s )/4

Portion of computationthat will be performed

sequentially

Portion of computationthat will be executed

in parallel


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Derivation of Amdahl’s Law

Speedup is ratio of execution time on 1 core to execution time on p cores

Execution time on 1 core is s + (1-s)Execution time on p cores is at least s + (1-s)/p

psspssss

/)1(1

/)1()1(


Amdahl’s Law Is Too Optimistic

Amdahl’s Law ignores parallel processing overheadExamples of this overhead include time spent

creating and terminating threadsParallel processing overhead is usually an increasing

function of the number of cores (threads)

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Graph with Parallel Overhead Added

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Cores

Exec

utio

n Ti

me Parallel overhead

increases with# of cores


Other Optimistic Assumptions

Amdahl’s Law assumes that the computation divides evenly among the cores

In reality, the amount of work does not divide evenly among the cores

Core waiting time is another form of overhead

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Task started

Task completed

Working time

Waiting time


Graph with Workload Imbalance Added

13

Cores

Exec

utio

n Ti

me

Time lostdue to

workloadimbalance


Illustration of the Amdahl Effect

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n = 100,000

n = 10,000

n = 1,000

Cores

Spee

dup

Linear speedup


Using Amdahl’s Law

Program executes in 5 secondsProfile reveals 80% of time spent in function alpha,

which we can execute in parallelWhat would be maximum speedup on 2 cores?

New execution time ≥ 5 sec / 1.67 = 3 seconds

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67.16.01

2/)2.01(2.01


Superlinear Speedup

According to our general speedup formula, the maximum speedup a program can achieve on p cores is p

Superlinear speedup is the situation where speedup is greater than the number of cores used

It means the computational rate of the cores is faster when the parallel program is executing

Superlinear speedup is usually caused because the cache hit rate of the parallel program is higher

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References

Michael J. Quinn, Parallel Programming in C with MPI and OpenMP, McGraw-Hill (2004).


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More General Speedup Formula

(n,p) Speedup for problem of size n on p cores(n) Time spent in sequential portion of code for

problem of size n(n) Time spent in parallelizable portion of code

for problem of size n(n,p) Parallel overhead

),(/)()()()(),(

pnpnnnnpn


Amdahl’s Law: Maximum Speedup

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),(/)()()()(),(

pnpnnnnpn

This term is set to 0

Assumes parallelwork divides perfectlyamong available cores


The Amdahl Effect

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As n theseterms dominate

Speedup is an increasing function of problem size

),(/)()()()(),(

pnpnnnnpn

predicting parallel performance

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