analyzing parallel performance intel software college introduction to parallel programming – part...

Analyzing Parallel Performance

Intel Software College

Introduction to Parallel Programming – Part 6

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2Analyzing Parallel Performance

Intel® Software College

Objectives

At the end of this module, you should be able to

Define speedup and efficiency

Use Amdahl’s Law to predict maximum speedup

Use the Karp-Flatt metric to

analyze parallel program performance

predict speedup with additional processors





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 3

Speedup curveslook like this

Processors

Sp

eed

up y = x





Efficiency

EfficiencyA measure of processor utilizationSpeedup divided by the number of processors

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

Effi

cien

cy

Processors

Efficiency curveslook like this

y = 1.0





Idea Behind Amdahl’s Law

Processors

Execu

tion T

ime

f

f

ff f

1-f

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

Portion of computationthat will be performed

sequentially

Portion of computationthat will be executed

in parallel





Derivation of Amdahl’s Law

Speedup is ratio of execution time on 1 processor to execution time on p processors

Execution time on 1 processor is f + (1-f)

Execution time on p processors is at least f + (1-f)/p

pffpff

ff

/)1(

1

/)1(

)1(





Amdahl’s Law Is Too Optimistic

Amdahl’s Law ignores parallel processing overhead

Examples of this overhead include time spent creating and terminating threads

Parallel processing overhead is usually an increasing function of the number of processors





Graph with Parallel Overhead Added

Processors

Execu

tion T

ime Parallel overhead

increases with# of processors





Other Optimistic Assumptions

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

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

Processor waiting time is another form of overhead

Task started

Task completed

Working time

Waiting time





Graph with Workload Imbalance Added

Processors

Execu

tion T

ime

Time lostdue to

workloadimbalance





More General Speedup Formula

(n,p) Speedup for problem of size n on p CPUs

(n) Time spent in sequential portion of codefor problem of size n

(n) Time spent in parallelizable portion ofcode for problem of size n

(n,p)Parallel overhead

),(/)()(

)()(),(

pnpnn

nnpn





Amdahl’s Law: Maximum Speedup

),(/)()(

)()(),(

pnpnn

nnpn

This term is set to 0

Assumes parallelwork divides perfectlyamong available CPUs





The Amdahl Effect

),(/)()(

)()(),(

pnpnn

nnpn

As n theseterms dominate

Speedup is an increasing function of problem size





Illustration of the Amdahl Effect

n = 100,000

n = 10,000

n = 1,000

Processors

Speed

up

Linear speedup





Using Amdahl’s Law

Program executes in 5 seconds

Profile reveals 80% of time spent in function alpha, which we can execute in parallel

What would be maximum speedup on 2 processors?

New execution time ≥ 5 sec / 1.67 = 3 seconds

67.16.0

1

2/)2.01(2.0

1





The Karp-Flatt Metric

Suppose we benchmark a parallel program and get these speedup figures

Why is efficiency dropping?

How much speedup could we expect on 8 processors?

Processors Speedup Efficiency

2 1.5 75%

3 1.8 60%

4 2 50%





Deriving the Karp-Flatt Metric

The denominator represents parallel execution time

One processor does sequential code; others idle

All processors incur overhead time

“Wasted time” = (p-1)(n) + p(n, p)

Experimentally determined serial fraction = “wasted time” divided by (p-1) times sequential time

),(/)()(

)()(),(

pnpnn

nnpn





Karp-Flatt Metric

The experimentally determined serial fraction is a function of speedup and the number of processors

We can use e to determine whether efficiency decreases are due to

Sequential component of computation

Increases in overhead

p

pe

/11

/1/1





How to Interpret “e”

If “e” is constant as the number of processors increases, then speedup is constrained by the sequential component of the computation

If “e” is increasing as the number of processors increases, then speedup is constrained by parallel overhead, such as

Thread creation/termination timeContention for shared data structuresCache-related inefficiencies

Often a combination of the two factors





Going Back to Our Example

Processors Speedup Efficiency e

2 1.5 75% 0.33

3 1.8 60% 0.33

4 2.0 50% 0.33

In this case, speedup is constrained by the relatively large amount of time spent in sequential code





Example: Rectangle Rule Program

Benchmark data from an OpenMP program computing using the rectangle rule

We can predict speedup on 6 processors

Extrapolate e to be 0.11

Speedup would be 3.87

Processors Speedup Efficiency e

2 1.87 93% 0.070

3 2.60 87% 0.078

4 3.16 79% 0.089





Speedup Prediction Formula

1)1(

/11

/1/1

pe

p

p

pe





Case Study

We benchmark a sequential program and find it spends 85% of its time in functions we believe we can make parallel

We make these functions multithreaded and execute the program on a dual-core system

The parallel program achieves a speedup of 1.67 on 2 processors

If we can get access to a quad-core system, what kind of speedup should we expect?





Prediction Based on Amdahl’s Law

76.2

4/)15.01(15.0

1





Prediction Based on Karp-Flatt Metric

When p = 2, e = 0.25

We know 0.15 of e is sequential component

Rest of e (0.05) is parallel overhead

If parallel overhead increases linearly with number of processors, then it will be 0.15 when p = 3

We predict when p = 4, e = 0.30

Hence when p = 4, we predict speedup of 2.11





Superlinear Speedup

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

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

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

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





References

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

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