Parallelization of FFT in AFNI

Huang, Jingshan Xi, Hong

Department of Computer Science and EngineeringUniversity of South Carolina

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

Outline

What is AFNI

FFT in AFNI

Introduction of MPI

Our method of parallelization

Experiment result and analysis

Conclusion

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.

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

AFNI Interfaces

AFNI Interfaces --- Cont.

AFNI Interfaces --- Cont.

AFNI Interfaces --- Cont.

Axial Sagittal Coronal

AFNI Interfaces --- Cont.

Axial Sagittal Coronal

AFNI Interfaces --- Cont.

Axial Sagittal Coronal

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(N2)to O(NlgN)

Extensively used in AFNI

To parallelize FFT has great significance for AFNI

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.

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”

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

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

Flow Chart of csfft_cox

fft32

fft128

fft2 fft43

fft8 fft16

fft64

fft256

fft512

fft1024

fft2048

fft4096

fft8192

fft16384

fft32768

SCLINV

fft_4dec

return

csfft_cox start

fft_4dec

fft_4dec

fft_4dec

fft_4dec

fft_4dec

3n

5n

fft_3dec

fft_5dec

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().

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?

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.

Experiments

Time analysis of Original code (4096 * 200,000 * 1)

starting 200000 FFTs of length 4096 -- 1 at a timeTIME 1

**********************************************************************TIME 1 beginning 0 0.00TIME 1 Abeginning 0.00 u 0.00 s: 0.00 u_t 0.00 s_tTIME 1 Bbeginning 0.00 u 0.00 s: 0.00 u_t 0.00 s_tTIME 1

**********************************************************************Using csfftTIME 2

**********************************************************************TIME 2 ending 0 155.09TIME 2 Aending 155.09 u 30.60 s: 155.09 u_t 30.60 s_tTIME 2 Bending 155.09 u 30.60 s: 155.09 u_t 30.60 s_tTIME 2

**********************************************************************wall clock time = 813.324630813.324630

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

wall clock time = 679.795504679.795504

Experiments --- Cont. Time analysis of Parallelized in 4 processors (4096 * 200,000 * 1)

starting 100000 FFTs of length 4096 -- 1 at a timeTIME 1 **********************************************************************TIME 1 beginning 0 0.00TIME 1 beginning 1 0.00TIME 1 beginning 2 0.00TIME 1 beginning 3 0.00TIME 1 Abeginning 0.00 u 0.00 s: 0.00 u_t 0.00 s_tTIME 1 Bbeginning 0.00 u 0.00 s: 0.00 u_t 0.00 s_tTIME 1 **********************************************************************Using csfftTIME 2 **********************************************************************TIME 2 ending 0 139.71TIME 2 ending 1 71.39TIME 2 ending 2 57.29TIME 2 ending 3 61.77TIME 2 Aending 180.16 u 114.53 s: 180.16 u_t 114.53 s_tTIME 2 Bending 45.04 u 28.63 s: 45.04 u_t 28.63 s_tTIME 2 **********************************************************************

wall clock time = 946.5520413946.5520413

Analysis of speedup

CPU Time Wall Clock Time

Original Code 155.09 813.324630813.324630

Parallelized in 2 processors

168.09 (rank 0)85.66 (rank 1) 679.795504679.795504

Parallelized in 4 processors

139.71 (rank 0)71.39 (rank 1)57.29 (rank 2)61.77 (rank 3)

946.552041946.552041

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 idealspeedup in the real machines.

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 FFTparallelization of 3dDeconvolve program

Questions?