Team 8 Data Dependence Analysis

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Team 8Data Dependence Analysis

• Shrinand Vyas
• Srikanth Mandava
• Sumana Ponnoju
• Tushar Pradhan
• Udit Patidar (L)

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Flow of the Presentation

• Need for Data Dependence
• What is Data Dependence and its types
• Methods for Data Dependence Testing
• Theoretical Background of Tests
• Limitations of Data Dependence Testing
• Examples
• Work Done
• (?) Questions and Answers

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Questions to answer

• Study dependence testing for arrays. What are the
  corresponding tests for scalars?
• Investigate the dependence tests inside the
  Open64 compiler, how and where they are performed
  and how array/scalar dependences are stored.
• Determine how the distance and direction vectors
  are computed and stored
• Briefly identify the parts of the compiler use
  the dependence testing.
• Identify loops that have no dependences with
  distances greater than one.
• Export the required information and create an
  interface in the Dragon tool to display it.
• Test your work with different applications

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Importance Need ofData Dependence Analysis

• Instruction Scheduling
• Loop Nest Optimisation (LNO) (Team1)
• Loop Transformations (Team1)
• Parallelisation (Team3)
• Data Cache Optimisation

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Instruction Scheduling Example
1 r2 ? r1 (4) 2 r3 ? r14 (4) 3 r4 ? r2
r3 4 r5 ? r2 - 1 5 goto L1 6 nop
1 r2 ? r1 (4) 2 r3 ? r14 (4) 3 r5 ? r2 -
1 4 goto L1 5 r4 ? r2 r3
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Data Cache Optimization Example

• / Array is Accessed Here.. /
• ...
• for (i0ilt100i)
• / Array is Accessed Here.. /
• / Array is Accessed Here.. /

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What is Data Dependence Analysis?

• Data dependence analysis determines when two
  different expressions in program will refer to
  the same data element
• S1 a ? b c
• S2 if (a gt 10) goto L1
• S3 d ? b e
• S4 e ? d 1
• S5 L1 d ? e / 2

Remember? Slides from 29 March.
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Types of Data Dependence

• True Dependence (t)
• Anti Dependence (a)
• Input Dependence (i)
• Output Dependence (o)

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Types of Data Dependence

• S1 a ? b c
• S2 if (a gt 10) goto L1
• S3 d ? b e
• S4 e ? d 1
• S5 L1 d ? e / 2

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Loop Based Dependencies

• Distance Vector
• Direction Vector
• eg a(i,j)
• a(i2,j-1)
• Distance Vector ? (2,-1)
• Direction Vector ? (gt,lt)

Q) Determine how the distance and direction
vector are computed and stored
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Dependence Tests

• SCALARS
• DEF-USE chains
• Data-flow analysis

• ARRAYS
• Lamports Test
• GCD Test
• Banerjees Inequalities
• Extended GCD Test
• Power Test
• I-Test
• Omega Test
• Range Test
• Delta Test
• etc

Q) Study dependence testing for arrays. What are
the corresponding tests for scalars?
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The GCD test

• Easiest test used to determine the dependence
• Given the following equation ais and c are
  integers
• does gcd(a1,a2,,an) divide c
• If YES an integer solution exists and we have
  dependence
• else we do not have dependence

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GCD Test Example

• DO i 1,10
• a(2i) b(i) c(i)
• d(i) a(2i-1)
• END DO
• We need to look at the following
• Does GCD(2,2) divide -1?
• NO ? we do not have dependence!!

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Dependence Tests

• Lamports Test
• GCD Test
• Banerjees Inequalities
• Extended GCD Test
• Power Test
• I-Test
• Omega Test
• Range Test
• Delta Test
• etc

Q) Investigate the dependence tests inside the
Open64 compiler,
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Banerjees Extended GCD Test

• GCD test extended to multi-dimensional arrays
• Reduce the dimensionality of the original GCD
  test
• Reduces complexity
• Still an inexact test

Maydan, Hennessy, Lam, Efficient and Exact Data
Dependence Analysis (1991)
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Extended GCD Test Example

• DO i 1,10
• a(i) b(i) c(i)
• d(i) a(i-1)
• END DO
• Consider loop bounds as well.
• Look at the following
• i1i2-1, 1 i1, i2 10
• Transform, (i1,i2)(t1,t11)
• So, we reduce to 1 t1 10
• 1 t110 10

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Dependence Tests

• Lamports Test
• GCD Test
• Banerjees Inequalities
• Extended GCD Test
• Power Test
• I-Test
• Omega Test
• Range Test
• Delta Test
• etc

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Omega Test

• Used to determine dependencies in a system of
  equations
• Basic idea
• Pre-process
• Pick one variable and eliminate it
• Continue until all variables but one are
  eliminated

Pugh, The Omega Test a fast and practical
integer programming algorithm for dependence
analysis (1993)
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Omega Test Main Idea
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Omega Test Real Shadow
?
CheckREAL shadow

• Project the original problem onto a lower
  dimension (cast its shadow)
• All points inside the shadow ? Real Shadow
• No integer solution ? Original Problem has no
  solution

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Omega Test Dark Shadow
?
No integersolution?
CheckREAL shadow
UNSAT
Integer solution
?
CheckDARK shadow

• An integer solution for the REAL shadowdoes not
  guarantee that there is an integer solution for
  the original problem
• What is the dark shadow?

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Omega Test Grey Shadow
?
No integersolution?
CheckREAL shadow
UNSAT
Integer solution
?
Integersolution?
CheckDARK shadow
SAT
No Integer solution
?
CheckGREY shadow

• If the real shadow R has integer solutions,but
  the dark shadow D does not, search R-D

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Example of Omega Test

• DO i1,6
• a(i1)
• a(7i-6)
• END DO
• With GCD test, we will get i17i-6
• GCD(1,-7)1, which divides -7
• Omega test is able to disprove the dependence in
  this case

Psarris, Kyriakopoulos, Measuring the Accuracy
and Efficiency of Data Dependence Tests (2001)
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Limitations of Dependence Testing

• No inter-loop dependence testing yet
• Can not handle procedure calls
• Expression must be linear
• aixiajxj works
• aij doesnt work
• Non-linear algorithms exist

William Blume, Rudolf Eigenmann Non-Linear and
Symbolic Data Dependence Testing (1998)
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Inside our OpenUH compiler

• Trivial cases
• Symbolic terms
• Non-equal constants ? independent
• Else ? continue testing
• Base test
• GCD test
• Omega test for solving systems of equations

UH?CS Department?HPC Tools Group, Overview of
the Open64 Compiler Infrastructure
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(No Transcript)
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Inside our OpenUH compiler
Q) Briefly identify the parts of the compiler
used during dependence testing.
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Dragon Analysis Tool

• Displays data dependence information
• Commands required
• uhcc O2 ipa dragon for generating .d
• uhcc O3 dragon for generating .dep

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Dragon Analysis Tool Output
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Project phase

• Q) Identify loops that have no dependences
• with distances greater than one
• Loop Carried Dependencies
• function Loop_Carrying_Dependence()
• If distance gt 1 then dependence is across
  iterations
• Q) Export the required information and
• create an interface in the Dragon tool
• to display it
• We were able to dump the info onto the console

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Dragon Analysis Tool Output
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Concluding work

• Capture output from console into dep_graph.cxx
• Edit outfile.write directive to release/withhold
  required information
• Write report!!

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References

• UH CS Department UPC Tools Group, Overview of the
  Open64 Compiler Infrastructure
• William Blume, Rudolf Eigenmann Non-Linear and
  Symbolic Data Dependence Testing (1998)
• Maydan, Hennessy, Lam, Efficient and Exact Data
  Dependence Analysis (1991)
• Psarris, Kyriakopoulos, Measuring the Accuracy
  and Efficiency of Data Dependence Tests (2001)
• Pugh, The Omega Test a fast and practical
  integer programming algorithm for dependence
  analysis (1993)

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Acknowledgments

• Thanks to
• Oscar Hernandez
• Dr Chapman
• QA