1. Mapping the FFT Algorithm to the IBM Cell Processor
Andy Polidore
Advisors: Brendan Burns, Joseph Czechowski

2. Motivation MRI Imaging Fast Fourier Transformations
Efficient algorithm for computing a Discrete Fourier Transform
DFT converts time-domain to frequency-domain
2D FFT: Perform a 1D FFT on each row of an image and then perform a 1D FFT on each resulting column
The Cell
Nine cores
1 Power Processing Unit (PPU)
8 Synergistic Processing Units (SPU)
My project is to map the 2d FFT algorithm to the Cell. You may be asking…why?
Faster processing = faster better images.

3. Strategy Cell comes with 2d routine Limited SPU memory
Needs to be called twice
First call organizes the data in contiguous column form
Striping
Limited SPU memory
Quad Buffering

4. PPU SPU 0 PPU SPU 0 DMA In FFT DMA Out DMA In FFT DMA Out Input Buffer
Output Buffer
FFT out
DMA Out
PPU
SPU 0
Input Buffer
Input
DMA In f
FFT
Output Buffer
FFT out
DMA Out

5. PPU SPU 0 SPU 1 SPU 7 Input Buffer DMA In Input FFT Output Buffer

6. PPU PPU DMA In FFT DMA Out Sync Point DMA In FFT DMA Out Input Buffer
SPU 0
SPU 1
Input Buffer
SPU 2
Input
DMA In
FFT
Output Buffer
FFT out
DMA Out
PPU
Sync Point
SPU 0
SPU 1
Input Buffer
SPU 2
Input
DMA In
FFT
Output Buffer
FFT out
DMA Out

7. Quad buffering Why it is required? Buffers Space problems
Maximizing processing power
Buffers
IN to handle incoming data
FFTin and FFTout to process the data
OUT stores the data ready to be DMA’ed back to main memory

8. Buffering A B C D
FILL 1 2 3 4 5 6

9. Buffering A B C D FILL ------- ------- ------- 1 FFTOUT FILL ------- 2
FILL 1
FFTOUT
FILL 2
FFTIN 3 4 5 6

10. Buffering A B C D FILL ------- ------- ------- 1 FFTOUT FILL ------- 2
FILL 1
FFTOUT
FILL 2
FFTIN
FFTOUT
OUT
FFTIN
FILL 3 4 5 6

11. Buffering A B C D FILL ------- ------- ------- 1 FFTOUT FILL ------- 2
FILL 1
FFTOUT
FILL 2
FFTIN
FFTOUT
OUT
FFTIN
FILL 3
OUT
FILL
FFTOUT
FFTIN 4 5 6

12. Buffering A B C D FILL ------- ------- ------- 1 FFTIN FFTOUT FILL
FILL 1
FFTIN
FFTOUT
FILL 2
FFTOUT
OUT
FFTIN
FILL 3
OUT
FILL
FFTOUT
FFTIN 4
FILL
FFTIN
OUT
FFTOUT 5
FFTIN
FFTOUT
FILL
OUT 6
FFTOUT
OUT
FFTIN
FILL

13. Striping
Main Memory
SPU 0
SPU 1
SPU 2
SPU 3
SPU 4
SPU 5
SPU 6
SPU 7

14. Challenges Simulator C coding Parallel processing Testing is slow
Alignment
Compiler
C coding
Working with bytes
Parallel processing
Data movement
Debugging

15. Knowledge Gained Mastering Linux C make files, linking, etc
Data movement strategies
Multi-core processing
Debugging!

16. Results and Conclusions
Success?
Future Work
Arbitrary size input

17. Questions?