implementing the fft on gpus tips & trickscomputer-graphics.se/multicore/pdf/2013/12a fft on...

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LINKÖPING UNIVERSITY

Linköping, 2013

IMPLEMENTING THE FFT ON GPUs

TIPS & TRICKS

Department of Electrical

Engineering

Mario Garrido Gálvez mariog@isy.liu.se

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MARIO GARRIDO

Associate Professor at ES, ISY

PhD in Electrical Engineering (Spain).

Research background:

Optimized implementation of signal processing algorithms.

Transforms (FFT, STFT,…), statistical operations

(regressions, median filter,…).

Data management (matrix transposition, interleavers,…).

Hardware designer (FPGAs, ASICs,…).

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A STORY ABOUT GPUs

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< 2011

Mainly FFTs on FPGAs.

Hundreds of papers in the topic since the 70’s.

Is not everything done???

OPTIMIZE

OPTIMIZE

OPTIMIZE

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DFT / FFT

Discrete Fourier Transform / Fast Fourier Transform.

The most widely used algorithm in signal processing

- Audio and Image Processing. - 3G, 4G.

- Medical applications: EEG, ECG. - ADSL.

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…,2011,…

FFT FPGA FFT FFT FPGA FPGA FFT FPGA

FPGA FFT FPGA FFT FFT FPGA FPGA FFT…

I should do something new!!

What about GPUs?…Shouldn’t it be the same…

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FPGA vs GPU

FPGA GPU

Altera Cyclone II NVIDIA Fermi

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…,2011,…

Started Master Thesis (Sreehari Ambuluri): FFTs on GPUs.

Read articles and a book on GPUs.

Asked Ingemar, Jens, Gabriel.

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…,2012,…

Finish the Master Thesis.

The work is good.

Why not to improve it and

publish a paper?

Asked Ingemar, Jens and

Gabriel for collaboration.

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…,2013,…

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…,2013 BEST PAPER AWARD

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NVIDIA

NVIDIA WE

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LEVEL OF ABSTRACTION

The compiler decides We decide

COMPILATION

COMPILATION

DESCRIPTION

OPTIMIZATION

&

DESCRIPTION

ALGORITHM ALGORITHM =

IMPLEMENTATION IMPLEMENTATION <

DE

SIG

N P

RO

CE

SS

High level of abstraction Low level of abstraction

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ABSTRACTION vs PERFORMANCE

z = 15 * x;

z = (x<<3)+(x<<2)+(x<<1) +x;

z = (x<<4)-x;

x z

15

x << 3

z

<< 2

<< 1

x << 4

z

LANGUAGE

DESCRIPTION HARDWARE

IMPLEMENTATION

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UNDERSTANDING GPUs

1.- The performance is related to the computation time. The lower

the computation time, the higher the performance. Try to simplify

the operations in the algorithm.

2.- Transactions to global memory very expensive. Try to avoid or

minimize. Try to use shared memory.

3.- Threads must be synchronized if we want to share information

among them. Unless they are in the same warp. Try to reduce the

number of synchronization points.

4.- We have to calculate the index of the data processed by each

thread. Try to minimize the number of index calculations.

5.- Threads process data in parallel and the synchronization is not

possible until all the threads have finished the calculations. Balance

the load among thread.

FFT FLOW GRAPH (RADIX -2)

4 03

7

6

5

4

0

07

15

11

2

3

1

0

0

4

0

0

0

0

0

0

4

6 4

0

2

0 0

0

5

13

1

9

6

14

2

10

0

0

0

0

0

0

4

0

0

0 0

0

4

12

0

8

14

15

13

12

10

11

8

9

7

6

1

5

4

3

2

0

STAGE 1 STAGE 2 STAGE 3 STAGE 4

4

6

2

0

0

0

0

0

x[n]

n

X[k]

k

logrN

stages

butterflies

(radix-2)

rotations

Nj

e

2

N points

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1. SIMPIFY THE ALGORITHM

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USE RADIX-22

2. USE SHARED MEMORY

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3. REDUCE SYNC. POINTS 2-word group 4-word group

USE WORD GROUPS

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4. REDUCE INDEX CALCULATIONS

USE CONSTANT GEOMETRY

Conventional flow graph Constant Geometry

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5. BALANCE LOAD AMONG THREADS

USE SCHEDULING

Unbalanced scheduling Balanced scheduling

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CONCLUSIONS

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Optimization:

- Depends on the details and the level of abstraction.

- Requires to understand in-depth what you are doing.

Teamwork makes a difference.

GPUs are fun.

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