Hardware Acceleration of Parallel Prefix Algorithms

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Hardware Acceleration of Parallel Prefix
Algorithms

• Peter Scott (Project leader)
• Avinash Srinivasa
• Vaibhav Sundriyal

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What is parallel prefix?

• Finding parallelism in serial-looking problems.
• Take an array, like 1, 3, 2, 1
• Find partial sums 1, 13, 132, 1321
• We can use any associative operation, not just
  addition.
• Matrix multiplication is okay
• Vector dot product doesnt work

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Applications

• DNA sequence alignment
• Large tree data structure acceleration
• Incremental regular expression matching
• Many others, parameterizable by kernel.

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Parallel version of this

• Distribute data to several processors.
• Do redundant computations to get parallelism.

Image taken from Steele Hillis, 1986.
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Architecture

• Several processors, shared multi-channel bus

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1,2 3,4
5,6
7,8
P1
P2
P3
P4
1,3
3,7 5,11
7,15 OPERATE
1,3
3,7 5,11
7,15 COMMUNICATE
1,3 6,10
5,11
18,26 UPDATE
1,3 6,10
5,11
18,26 COMMUNICATE
1,3
6,10 15,21
28,36 UPDATE
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Bus contention

• There are often more processors than bus
  channels.
• How to deal with contention?
• Answer pre-computed static scheduling.
• Store schedule as sequence of instructions
• Write ltchannelgt
• Load ltchannelgt
• No_op
• Comm_step_complete

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How to use the final product

• Write VHDL for an associative binary operation,
  like addition or multiplication.
• Say how many processors you want, how wide your
  data are, how many bus channels, etc.
• A wizard generates all the VHDL.
• Just customize it and go.

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Core generator wizard
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Core generator wizard
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Generates processor code
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and various supporting files

• Bus program memory holds bus instructions
• Prefix accelerator instantiates processors and
  bus
• Etc.

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Related Papers

• Explanation of parallel prefix and DNA sequence
  alignment (Aluru) http//class.ece.iastate.edu/cp
  re526/basics.pdf
• Data parallel algorithms (Steele and Hillis)
  http//cva.stanford.edu/classes/cs99s/papers/hilli
  s-steele-data-parallel-algorithms.pdf
• Prefix sums and their applications (Bleloch)
  http//www.cs.cmu.edu/guyb/papers/Ble93.pdf
• Finger trees (Hinze Paterson)
  http//www.soi.city.ac.uk/ross/papers/FingerTree.
  pdf