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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

Results and Conclusions Success? Future Work Arbitrary size input

Questions?