FFT Accelerator Project

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FFT Accelerator Project

• Rohit Prakash (2003CS10186)
• Anand Silodia (2003CS50210)

11th May, 2007
Dr. Kolin Paul Prof. M. Balakrishnan
Supervisors
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Overview

• Objective
• To get the best software implementation of FFT
• Identify the part of code that is taking the
  maximum time to execute

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• Examined 3 FFT algorithms
• Radix-4
• Radix-16
• Radix-8
• Compared them with FFTW
• Analysed these on the following parameters
• Execution Time
• Number of Complex calculations
• Memory references

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System Info

• Intel Pentium 4 (HT) 3.0Ghz
• Cache Size L2 1024 KB
• RAM 1GB
• O.S. Fedora Core 3
• Compiler icpc, version 9.1
• Flags used -fast (-xP, -O3, -ipo, -no-prec-div,
  -static)

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Execution Time (radix-4 vs. FFTW)
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Execution Time (radix-16 vs. FFTW)
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Execution Time (radix-8 vs. FFTW)
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Execution Time (radix-4 vs. radix-16)
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Execution Time (radix-8 vs. radix-16)
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Execution Time (radix-4 vs. radix-8)
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Inference

• For small input sizes, upto 4096, the execution
  time is lowest for radix-4 (and is comparable to
  FFTW)
• But for higher input sizes (gt4096), radix-8 fares
  better than radix-4 and radix-16

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Cache

• I1 cache 16 KB, 8-way associative
• D1 cache 16 KB, 8-way associative
• L2 cache 1 MB, 8-way associative

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Memory References
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Memory References
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L2 Cache Misses
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L2 Cache Misses
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Comparative Analysis
4096 points
13.68
13.25
13.66
16777216 points
96.19
74.98
71.87
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Inference

• For smaller input sizes, cache misses are
  greatest for radix-16 (theres a linear increase
  in misses from radix-4 to radix-16)
• But for large input sizes, (greater than 4096),
  the number of cache misses in radix-8 is the
  lowest.

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Code Hotspot
Radix-8 FFT
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Inference

• Due to OOP, Complex (object) creation takes the
  maximum amount of Clock-ticks
• Apart from that, the maximum time is taken by
  complex multiplications, followed by complex
  additions and complex subtractions

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Comparative Analysis (Complex )
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Comparative Analysis (Complex /-)
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References

• Thomas H.Cormen,Charles E. Leiserson, Ronald L.
  Rivest, Clifford Stein, Introduction to
  Algorithms
• Matteo Friga and Steven G. Johnson, The design
  and implementation of FFTW3
• Matteo Friga and Steven G. Johnson, The Fastest
  Fourier Transform in the West
• Alan H. Karp, Bit Reversal on Uniprocessors
• Jones, D. Radix-4 FFT Algorithms, Connexions Web
  Site www.cnx.org

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Thank You