Team 1 Loop Transformations

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Team 1 Loop Transformations

• Carmen Musat (Team Leader)
• Abhisheik Deo
• Srinivas Pola
• Abdul Mohammed Mateen
• Li Li

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Outline of the Presentation

• Objective of the project
• Introduction
• Implementation
• Results

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Objective of the Project

• Evaluate different loop transformations by the
  OpenUH compiler
• Analyze on a vector matrix multiplication program
• Study the report file and the source-to-source
  output
• Test different compiler directives

4
Basic concepts

• What is LNO?
• -Loop Nest Optimization
• -optimize memory performance of loop nests
• Benefits
• cache performance
• parallel processing

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What does LNO optimize?

• Locality optimization
• Auto parallelization
• Array privatization
• Heuristics integrated with software pipelining
  that employ LNO
• Dependency analysis
• Register/Cache blocking(tiling)
• Array padding
• Software pipeline

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Loop Transformation in OpenUH

• Popular loop transformations
• - fussion
• - fission
• - interchange
• - peeling
• - tiling
• - unrolling
• - pre-fetching

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Loop Transformation in OpenUH

• Interchange
• -swap the order of two loops
• -to increase parallelism, improve spatial
  locality
• Example
• Do j1, 100 Do i1, 100
• Do i1, 100 ? Do j1, 100

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Loop Transformation in OpenUH

• Fusion/combining
• -combine multiple loop nests into one
• -improve data locality, reduce loop overhead
• Example
• Do i1, 100 Do i1, n
• A (i) A (i-1) A (i) A (i-1)
  
• enddo B (i) A
  (i)/2
• Do i1, 100 ? enddo
• B (j) A (j)/2
• enddo

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Loop Transformation in OpenUH

• Fission
• -split a loop nest into multiple loop nests
• (the inverse of fusion)
• -produces multiple less constrained loops
• Example
• Do i1,
  n
• Do i1, n A (i) B
  (i)1
• A (i) B (i)1 ? enddo
• C (i) A(i)/2
• Do i1,
  n
• enddo C (i)
  A(i)/2
• enddo
  

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Loop Transformation in OpenUH

• Unrolling
• -duplicate the body of the loop
• -to reduce the times of testing loop
  conditions
• -to reduce the jumps
• Example
• While iltgt32 do While iltgt32
  do
• A (i)A (i)1 ? A (i)A (i)1
• 
  A (i)A (i)1

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Implementation of the Project

• Can be divided into two parts-
• Writing a vector matrix multiplication program
  and understanding how the compiler optimizes the
  program.
• Testing different compiler directives to apply
  loop transformations on a small application.

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Implementing the first part

• Written a vector matrix multiplication program in
  C using for loops.
• void mul_matrix(real a, real b, real c, int n,
  int p, int m)
• int i
• for(i 0 i lt n i)
• ? int j
• for(j 0 j lt m j)
• ? int k
• cim j 0
• for(k 0 k lt p k)
• ? cim j aip k bkm j

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Implementing the First part (contd..)

• Written a Perl script to generate the elements of
  the matrix to be used by the matrix
  multiplication program.
• Written a shell script to execute the program
  with various combinations loop optimization
  options and different matrix sizes.

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The Shell script

• start2
• end20
• step10
• echo "\"CFLAGS\" \"n\" \"p\" \"m\"
  \"time\" \"error\""
• for cflags in "-clist -o3 -LNOblocking_size4int
  erchangeOFF" \
• "-LNOblocking_size4interchangeOFF" do
• uhcc cflags -DCFLAGS"\"cflags\""
  matrix-mul-test.c -o matrix-mul-test
• for n in seq start step end do
• for p in seq start step end do
• for m in seq start step end do
• ./gen-matrix-mult-test.pl n p m
  ./matrix-mul-test
• done
• done
• done
• done

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Compiler optimized the code in the following ways-

• Changes all the for loops to while loops.
• Collected all the declarations of variables and
  shifts them to the start.
• Expands the expression.
• Changes the ordering of the array indices.

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Results
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To be included in the Final report

• To write a small FORTRAN program to test
  different compiler directives for applying the
  loop transformations.
• Examples of a few compiler directives-
• blocking_size, UNROLL n,n2,, etc

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• Questions please?