The Impact of Data Dependence Analysis on Compilation and

Program Parallelization

Original Research byKleanthis Psarris & Konstantinos Kyriakopoulos

Year of Publication: 2003

Presentation by Jamie Perkins

Data Dependence Analysis• Key to optimization and detection of

implicit parallelism in sequential code.

• Helps compiler improve memory, improve load balancing and determine efficient scheduling.

• Different test for data dependence provide different trade-offs.– Accuracy vs. Efficiency

About this research…• Sun UltraSPARC-IIi with 440 MHz CPU

and 512 Mbytes main memory.

• 2 different applications tested– Perfect Club Benchmarks– Lapack

• 4 different tests applied– Greatest Common Divisor Test (GCD)– Banerjee Test– I – Test– Omega Test

Polaris Compiler

• Developed at the University of Illinois at Urbana Champaign & Purdue University.

• Parallelizes Fortran 77 programs for execution on shared memory multiprocessors.

Applications

• Perfect Club Benchmark (PCB)– Collection of 13 scientific & engineering

Fortran 77 programs.

• Lapack (LP)– A library of subroutines for solving linear

algebra problems in Fortran 77.

Tests applied

• Greatest Common Divisor Test (GCD)– Based on theorem of elementary number

theory.

• Banerjee Test– Based on the Intermediate Value Theorem.

These two tests are applied together.

Tests Applied (cont.)

• I – Test– Based on & enhances the Banerjee test

and the GCD test.– Adds “accuracy conditions” to the previous

tests.

• Omega Test– Based on a combination of the Least

Remainder Algorithm and Fourier-Motzkin Variable Elimination.

Data Dependence Problems for PCB

30%

70%

7%

30%

63%

11%

35%

54%

Banerjee Test I -Test Omega Test

KEY:INDEPENDENT DEPENDENT MAYBE

***100% is equal to 59936

Data Dependence Problems for LP

13%

87%

Banerjee Test I -Test Omega Test

KEY:INDEPENDENT DEPENDENT MAYBE

1%

13%

86%

10%

22%

68%

***100% is equal to 293,718

Avg. Cost per Data Dependence in PCB

0

50

100

150

200

250

300

Total Indep. Dep. Maybe

BanerjeeI-TestOmegaT

ime

(mse

c)

Avg. Cost per Data Dependence in LP

0

20

40

60

80

100

Total Indep. Dep. Maybe

Banerjee

I-Test

OmegaTim

e (m

sec)

Total Compilation Time

113.4 111.6

330.5

0

50

100

150

200

250

300

350

87.9 88.2

371.7

0

50

100

150

200

250

300

350

400

Baner

jee

I-Tes

t

Om

ega

Tim

e in

Min

ute

s

Perfect Club Benchmark Lapack Library

Tim

e in

Min

ute

s

Parallelizable Loops

4118

2241

2253

2295

0

500

1000

1500

2000

2500

3000

3500

4000

4500

Total

Baner

jee

I-Tes

t

Omeg

a0

1000

2000

3000

4000

5000

6000

7000

8000

Num

ber

of L

oops

Num

ber

of L

oops

Perfect Club Benchmark Lapack Library

Execution Time

• Perfect Club Benchmark– Only 4 out of the 11 could be effectively

parallelized.

• Lapack Library– Much better results, the execution time of

7 of the programs were cut in half.

Prog. Test Serial

Time

2-p 4-p 6-p 8-p

Banerjee

26.70

26.64 25.87 26.23 27.71

I-Test 26.62 25.87 26.24 27.80

Omega 26.62 25.90 26.21 27.83

Banerjee

8.54

5.56 3.27 2.57 2.24

I-Test 5.56 3.27 2.57 2.24

Omega 5.44 3.15 2.41 2.07

OC

EA

NB

DN

APerfect Club Benchmark

Prog. Test Serial

Time

2-p 4-p 6-p 8-p

Banerjee

18.40

9.54 6.60 4.43 4.97

I-Test 9.53 6.62 4.49 4.86

Omega 9.48 6.56 4.42 4.83

Banerjee

33.85

17.03 11.61 7.48 14.79

I-Test 17.06 11.58 7.52 14.34

Omega 17.02 11.56 7.42 15.74

GE

P E

INR

EC

T L

INLapack Library

Conclusions– Data dependence accuracy

• Depending on program differences, may not be substantial (PBC vs. LP).

– Efficiency• Often a trade-off (efficiency vs. accuracy), Omega

proved more accurate at a high cost.

– Effectiveness• All 3 tests found similar number of parallelizable

loops.

– Execution Performance• Again all three tests produced similar results in

execution.

Thank You

Any Questions?