1. Parallelization of FFT in AFNI Huang, Jingshan Xi, Hong Department of Computer Science and Engineering University of South Carolina

2. Motivation AFNI: a widely used software package for medical image processing Drawback: not a real-time system Our goal: make a parallelized version of AFNI First step: parallelize the FFT part of AFNI

3. Outline What is AFNI FFT in AFNI Introduction of MPI Our method of parallelization Experiment result and analysis Conclusion

4. What is AFNI? AFNI stands for Analysis of Functional NeuroImages. It is a set of C programs (over 1,000 source code files) for processing, analyzing, and displaying functional MRI (FMRI) data - a technique for mapping human brain activity. AFNI is an interactive program for viewing the results of 3D functional neuroimaging.

5. How to run AFNI? Log on to clustering machine (daniel.cse.sc.edu) Go to directory /home/ramsey/newafnigo Run “afni” Interface should show up at this time

6. AFNI Interfaces

7. AFNI Interfaces --- Cont.

9. AxialSagittal Coronal

10. AFNI Interfaces --- Cont. AxialSagittal Coronal

11. AFNI Interfaces --- Cont. AxialSagittal Coronal

12. FFT in AFNI Fast Fourier Transform: a kind of finite FT from discrete time domain to discrete spatial domain Reduces the number of computations needed for N points from O(N 2 )to O(NlgN) Extensively used in AFNI To parallelize FFT has great significance for AFNI

13. What is MPI? MPI stands for Message-Passing Interface. MPI is the most widely used approach to develop a parallel system. MPI has specified a library of functions that can be called from a C or Fortran program. The foundation of this library is a small group of functions that can be used to achieve parallelism by message passing.

14. What is Message Passing? Explicitly transmits data from one process to another Powerful and very general method of expressing parallelism Drawback --- “assembly language of parallel computing”

15. What does MPI do for us? Makes it possible to write libraries of parallel programs that are both portable and efficient Use of these libraries will hide many of the details of parallel programming Therefore make parallel computing much more accessible to professionals in all branches of science and engineering

16. Our Objective To parallelize FFT part of AFNI In AFNI, when we call FFT function, we are in fact calling the csfft_cox() function, which we will see the detail in next slide

17. Flow Chart of csfft_cox fft32 fft128 fft2fft4 3 fft8 fft16 fft64 fft256 fft512 fft1024 fft2048 fft4096 fft8192 fft16384 fft32768 SCLINV fft_4dec return csfft_cox start fft_4dec 3n 5n fft_3dec fft_5dec

18. One-level parallelization There are several options for us to parallel the csfft_cox() function. At present, we adopt the one-level parallelization method, that is, when fft4096() calls fft1024() and when fft8192() calls fft2048().

19. Correctness of our parallel code By doing FFT and IFFT consequently, we obtain a set of complex numbers that are almost the same as the ones in the original data file The only difference comes from the storage error of floating point number (in the original code, such phenomena also exists) So, what is the speedup then?

20. Two Kinds of Time There are two kinds of time in analyzing our experiment result: CPU Time and Wall Clock Time (Elapsed Time). CPU time is the time spent in the calculation part of the code. Wall Clock Time is the total elapsed time from the user’s point of view.

21. Experiments Time analysis of Original code (4096 * 200,000 * 1) starting 200000 FFTs of length 4096 -- 1 at a time TIME 1 ********************************************************************** TIME 1 beginning 0 0.00 TIME 1 Abeginning 0.00 u 0.00 s: 0.00 u_t 0.00 s_t TIME 1 Bbeginning 0.00 u 0.00 s: 0.00 u_t 0.00 s_t TIME 1 ********************************************************************** Using csfft TIME 2 ********************************************************************** TIME 2 ending 0 155.09 TIME 2 Aending 155.09 u 30.60 s: 155.09 u_t 30.60 s_t TIME 2 Bending 155.09 u 30.60 s: 155.09 u_t 30.60 s_t TIME 2 ********************************************************************** 813.324630 wall clock time = 813.324630

22. Experiments --- Cont. Time analysis of Parallelized in 2 processors (4096 * 200,000 * 1) starting 200000 FFTs of length 4096 -- 1 at a time TIME 1 ********************************************************************** TIME 1 beginning 0 0.00 TIME 1 beginning 1 0.00 TIME 1 Abeginning 0.00 u 0.00 s: 0.00 u_t 0.00 s_t TIME 1 Bbeginning 0.00 u 0.00 s: 0.00 u_t 0.00 s_t TIME 1 ********************************************************************** Using csfft TIME 2 ********************************************************************** TIME 2 ending 0 168.09 TIME 2 ending 1 85.66 TIME 2 Aending 253.75 u 115.11 s: 253.75 u_t 115.11 s_t TIME 2 Bending 126.87 u 57.55 s: 126.87 u_t 57.55 s_t TIME 2 ********************************************************************** 679.795504 wall clock time = 679.795504

23. Experiments --- Cont. Time analysis of Parallelized in 4 processors (4096 * 200,000 * 1) starting 100000 FFTs of length 4096 -- 1 at a time TIME 1 ********************************************************************** TIME 1 beginning 0 0.00 TIME 1 beginning 1 0.00 TIME 1 beginning 2 0.00 TIME 1 beginning 3 0.00 TIME 1 Abeginning 0.00 u 0.00 s: 0.00 u_t 0.00 s_t TIME 1 Bbeginning 0.00 u 0.00 s: 0.00 u_t 0.00 s_t TIME 1 ********************************************************************** Using csfft TIME 2 ********************************************************************** TIME 2 ending 0 139.71 TIME 2 ending 1 71.39 TIME 2 ending 2 57.29 TIME 2 ending 3 61.77 TIME 2 Aending 180.16 u 114.53 s: 180.16 u_t 114.53 s_t TIME 2 Bending 45.04 u 28.63 s: 45.04 u_t 28.63 s_t TIME 2 ********************************************************************** 946.5520413 wall clock time = 946.5520413

24. Analysis of speedup CPU TimeWall Clock Time Original Code 155.09 813.324630 813.324630 Parallelized in 2 processors 168.09 (rank 0) 85.66 (rank 1) 679.795504 679.795504 Parallelized in 4 processors 139.71 (rank 0) 71.39 (rank 1) 57.29 (rank 2) 61.77 (rank 3) 946.552041 946.552041

25. Analysis of speedup --- Cont. Two main reasons that we did not obtain the ideal speedup : 1. There exist the competitions among different users in the same CPU. 2.Due to the existing communication cost and some other overhead, it is impossible to obtain the ideal speedup in the real machines.

26. Conclusion We have parallelized the FFT part of AFNI software package based on MPI. The result shows that for the FFT algorithm itself, we obtain a speedup of around 30 percent. Increase the speedup of FFT parallelization of 3dDeconvolve program

27. Questions?