Optimization of Loop Unrolling on dense Vectormatrix multiplication Parallel Processing

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Optimization of Loop Unrolling on dense
Vector-matrix multiplication
-Parallel Processing

• By Sumit Malhotra
• Computer Science, Florida Tech
• 767050340
• Dr. Charles Fulton

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Aim of project

• To find the best loop unrolling parameters for
  different number of processors on a 5120 X 5120
  matrix.

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Algorithm for Matrix Multiplication

• m n 5120
• for (i0 i lt local_m iUNROLL2)
• for (j0 j lt n jUNROLL)
• matrix multiplication
• Where UNROLL2 and UNROLL are loop unrolling
  parameters
• and local_m m/p and p number of processors.
• Therefore the size of matrix on each processor
  will be local_m x n.

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Size of matrix on each processor

• Size of Matrix when p1 5120 X 5120
• Size of Matrix when p2 2560 X 5120
• Size of Matrix when p4 1280 X 5120
• Size of Matrix when p8 640 X 5120
• Where p
  number of processors.

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Sample Code

• UNROLL2 UNROLL 2
• for (i0 i lt local_m iUNROLL2)
• for (j0 j lt n jUNROLL)
• yi local_Aij xj
• local_Aij1 xj1
• yi1 local_Ai1j xj
• local_Ai1j1
  xj1

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Sample Code

• UNROLL2 2, UNROLL 4.
• for (i0 i lt local_m iUNROLL2)
• for (j0 j lt n jUNROLL)
• yi local_Aij xj
  local_Aij1 xj1
• local_Aij2 xj2
  local_Aij3 xj3
• yi1 local_Ai1j xj
  local_Ai1j1 xj1
• local_Ai1j2 xj2
  local_Ai1j3 xj3

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Time Calculation

• Start clock()
• Multiplication code //Computation.
• MPI_Gather() //Communication.
• End clock()
• Total Computation Communication Time Start
  End
• Start clock()
• MPI_Gather() //Communication.
• End clock()
• Communication Time Start End
• Start clock()
• MPI_Scatter() //Communication.
• End clock()
• Scatter Time Start End

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Conclusion - Result Table