Parallel Signal Processing and System Simulation using aCe

7 Pages·2003·1.1 MB·English

by  Dorband, John E.

2003 Conference on Information Science and Systems, The Johns Hopkins University, March 12-14,2003
Parallel signal processing and system simulation using ace
John E. Dorband
NASA Goddard Space Flight Center, Greenbelt, MD 20771
[email protected]
Maurice F. Aburdene
Department of Elecnical Engineering,B ucknell Universiy, Lewisburg, Pa I7837
[email protected]
Abstract: Recently, networked and cluster computation have become very popular for both signal
processing and system simulation. A new language is ideally suited for parallel signal processing
applications and system simulation since it allows the programmer to explicitly express the
computations that can be performed concurrently. In addition, the new C based parallel language
(ace C) for architecture-adaptive programming allows programmers to implement algorithms and
system simulation applications on parallel architectures by providing them with the assurance that
future parallel architectures will be able to run their applications with a minimum of modification.
In this paper, we will focus on some hndamental features of ace C and present a signal
processing application (FFT).
1. Introduction
1.1 ace micro-threads
Parallel and networked computer programming
techniques have become popular and important One of the essential elements of concurrent
computational tools for system simulation and signal computations is micro-threads. The following ace
processing[ 11. The essential elements of parallel program shows an example of micro-threads.
programming are concurrent computation (threads)
threads A[ 1001;
and communications (messages). ace is based on
the concept of structured parallel execution [2-31.. threads B[ IO];
First the programmer designs a virtual architecture
A int av;
that reflects the spatial organization of an algorithm.
An example is shown in Fig. 1. A virtual architecture B.( ...
may consist of groups or bundles of threads of
A.( int bv,cv;
execution. Second the application program reflects
the temporal organization of the algorithm. The code if (av==bv) cv=O ;
defines what each thread performs, which together
1
with the virtual architecture, defines the algorithm’s
execution. ace allows the programmer to both 1
envision the most logical architecture for the
Any C code is valid, except ‘goto’s.
application and then implement the algorithm using
that architecture.. The ace language allows the The difference between ace and C is that while
programmer to explicitly express that which can be C has only one thread of execution, ace, may have
performed concurrently. The purpose of ace is to many threads of execution. Each thread may be
facilitate the development of parallel programs by referenced by name and index. Parallelism in ace is
allowing programmers to explicitly describe the expressed by first defining a set of concurrently
parallelism of an algorithm. executable threads. A group of parallel threads can be
viewed as a bundle of executing threads, a bundle of
El processes, or an array of processors. These three
views will be treated synonymously. In ace, a bundle
*- of threads is defined with the ‘threads’ statement. The
statement “threads A[ lOO]” only declares the intent
of the programmer to use 100 concurrent threads of
executions named ‘A’ at some later point in the
ArdsLQn
Fig. 1. Sample Virtual Architecuture
2003 Conference on Information Science and Systems, The Johns Hopkins University, March 12-14,2003
code. The statement A int av allocates an integer
‘av’ for each of the 100 threads of bundle ‘A’.
threads A[5 I2J [5 12 3 ;
1.2 ace micro-messages a = .A[O][-l].c ;/ * North */
The second essential element of concurrent a = A[O][l].c ;P South *I
programming is micro-messages. Here is an example
program showing communication.
threads A[ 1001;
threads B[ 1001;
A,{ int av,cv; B int bv;
Fig. 4.2-DR elative Communications
av = A[$$i+l].cv ;/ * get operation */
B[$$i/lO].bv += av ;/ * put operation */
threads A[513]{511J ;
1
a = A[O][S%ix[O]-l f.c :I * Nonh *I
/* Note: $$i is a threads unique ID */ a= A[O][%$is[O] +I].c ; /* South *!
a += A[$Six[ I]-llfO].c :/ * West */
1.3 Virtual Architecture
One of the major advantages of ace for signal
processing is that it allows the programmer to create
a virtual architecture for the algorithm. Fig 2-6 show
various examples of virtual architectures and
communications along with the ace code. Fig. 5. Absolute Communications
-.
threads X[ If ; Aggregate Operations ( f. &, 1, A. >?, <? )
threads { Z[21[2] Y[3][3] ; thrcnds X[ I J : threads Z[1][2]) Y[3][3] ;
Y.( int a; X int b; X.h+=a; f
U L
Fig. 2. Virtual Architecture
Fig. 6. Global Aggregate
threads NODE[ 10 001
threads A121 [2] ; threads { CornerE3) ] CELL[2000] ;
A. { int a=$%; int b=3; int c;
CELL
c=a*b;
Corner
@
t NUDE
Fig. 3. No Communications Fig. 7. Finite Element Example
2003 Conference on Information Science and Systems, The Johns Hopkins University, March 12- 14,2003
2. FFT Example
5. Acknowledgments
The fast Fourier transform, FFT, is widely used in
science and engineering and is easily implemented on This research was funded in part by NASA grant NAGS-
10821.
parallel architectures [4-51. Gupta and Kumar [6]
presented the scalability analysis of an FFT algorithm
for both mesh and hypercube architectures. Appendix A: Parallel FFT Program
The ace program shown in Appendix A
# include <stdio. aHr>
performs a NxN 2-D FFT and inverse FFT on test
# include <math.aHr>
data. This program performs N 1-D FFTs in parallel
(partialFFT) in one dimension, transposes
# define real
(Transpose) the transformed data, performs a second
double
set of 1-D FFTs, and performs another transposes of # define twoPI
the resulting transformed data. The I-D FFT results
( (double)6 .28318530717959)
in shuffled data and is unshuffled (UnShuffle) # define PI
immediately after the I-D FFT is performed.
(twoPI/Z)
The data was moved h mth e NxN 2-D bundle # define size 512
of threads to a N*N/2 I-D bundle of threads, thus the # define radius 3
2-D FFT was actually performed on a 1-D # define nproc2 (size*size)
architecture. # define nproc (nproc2>>1)
struct complex { real rr,ii ; } ;
3. Summary typedef struct complex complex ;
This paper presented the fundamental concepts of a
new C based parallel programming paradigm, ace C. generic void ComplexAdd (
The intent of ace is to allow a programmer to easily complex *C,
express the parallelism of an algorithm, allowing the complex *A,
compiler to more easily map the parallelism of that complex *B ) {
algorithm on to various parallel architectures. The C->rr = A->rr f B->rr ;
ease of mapping facilitates the porting of programs C->ii = A->ii f B->ii ;
and development /runtime environments to different 1
architectures, promoting the development of new
architectures. In addition, a parallel implementation generic void Complexsub (
of a 2-D FFT was presented. complex *C,
complex *A,
complex *B ) {
4. References C->rr = A->rr - B->rr ;
C->ii = A->ii - B->ii ;
[ I1G.R Andrews, Fowrdntionr of multithreaded, parallel, and 1
distributedpmgramming,A ddison-Wesley, 2000.
[2] J.E. Dorband and M.F. Aburdene, “Architecture-adaptive
computing environment:a tool for teaching parallel generic void ComplexMult (
programming”, poceedi nm-Frontiers in Education Conference, complex *C,
Vol. 3, pp. S2F 7-S2F112,2002. complex *A,
[3] J.E. Dorband, “ace C Reference”, NASA Goddard Space complex *B 1 I
Flight Center, Greenbelt, IvlD.
[4] Michael .J. Quinn, Parallel Computing: Theoty and Practice, real D;
McGraw-Hill, Inc., 1994. D = A->rr*B->rr - A->ii*B->ii ;
[5]H arold S. Stone, High-Pe$onnance Computet Architecture, C->ii = A->rr*B->ii + A->ii*B->rr ;
Addison-Wesley, Mass., 1987.
C->rr = D ;
[6] A. Gupta and V. .Kurnar, “The scalability of FFT on parallel
I
computers”, IEEE Transactions. on Parallel and Distributed
Systems, V. 4, no. 8, August 1993, pp. 922-932.
generic complex Init-FFT
( int nxproc ) {
real i; complex WS1 ;
2003 Conference on Information Science and Systems, The Johns Hopkins University, March 12- 14,2003
/* initialize fft coefficients */
generic(WorkSpace[]) void UnShuffle
i = $$i%(nxproc>>l) ; ( complex A[2], int nxproc ) {
WSl.rr = cos((twoPI*i)/nxproc) ; complex A1,AZ ;
WSl.ii = sin((twoPI*i)/nxproc) ; complex Zl,Z2 ;
int i,j ,i proc,n ;
return WS1 ;
1 iproc = $Si ;
n = nxproc>>2 ; /* nxproc/4 */
A1 = A[O] ;
generic(WorkSpace[])void partialFFT A2 = A[1] ;
( complex A[2],
complex *W1, for( i=n,j =2; i>j; i>>=l,j <<=l ) {
int nxproc 1 {
complex Al,A2 ; Z1 = .Workspace[ jl .A1 ;
.
complex Zl,Z2,C ; 22 = Workspace [-j3 .A2 ;
,
int i iproc,n ; if ( (iproc&j)==O ) A2=Z1 ;
else Al=Z2 ;
iproc = $Si ;
n = nxproc>>2 ; /* nxproc/4 */ Z1 = .Workspace[ i] .A1 ;
A1 = A[O] ; 22 = .Workspace[-i] .A2 ;
A2 = A[1] ; if ( (iproc&i)==O ) A2=Z1 ;
else Al=Z2 ;
,
ComplexAdd ( &C,& A1 &A2 ;
,
ComplexSub ( &A2 &Al,& A2 ) ; Z1 = .Workspace[ jl .A1 ;
,
ComplexMult ( &A2,& A2 W1) ; 22 = .Workspace[-jl.A2 ;
A l = C ; if ( (iproc&j)==O ) A2=Z1 ;
ComplexMult (Wl,Wl,Wl) ; else A1=Z2 ;
for ( i=n ; i>O ; i>>=l ) {
if ( (iproc&i)! =O ) 1 Z1 = .Workspace[ 1l.Al ;
Wl->rr = -W1->rr ; 22 = .Workspace[-11 .A2 ;
w1->ii = -Wl->ii ; 1 if ( (iproc&l)==O ) A2=Z1 ;
else Al=Z2 ;
Z1 = .WorkSpac’e[ il .A1 ;
22 = .Workspace[-i] .A2 ; A[O] = A1 ;
if ( (iproc&i)==O ) A2=Z1 ; A[1] = A2 ;
else A1=Z2 ; I
ComplexAdd (&C,& All& A2) ;
ComplexSub ( &A2,& A1, & A2 ) ; generic(WorkSpace[]) void Transpose
ComplexMult .(&A2,& A2,W1) ; ( complex A[2], int nxproc ) {
A l = C ; complex Al,A2 ;
ComplexMult (Wl,Wl,Wl] ; complex Z1,22 ;
,
int i,j iproc,n o,n l ;
Z1 = .Workspace[ i] .A1 ;
22 = .Workspace[-i] .A2 ; iproc = $Si ;
if ( (iproc&i)==O ) A2=Z1 ; no = nxproc>>l ; /* nxproc/2 */
else A1=Z2 ; nl = nxproc>>l ; /* nxproc/2 */
A1 = A[O] ;
A2 = A[11 ;
A[01 = A1 ; for(i=nl,j =1; j<nO; i<<=l,j <<=l) {
Ail] = A2 ;
1 Z1 = .Workspace[ j] .A1 ;
2003 Conference on Information Science and Systems, The Johns Hopkins University, March 12-14,2003
22 = .Workspace[-j].A2 ; int nxproc ) {
if ( (iproc&j)==O ) A2=21 ; complex W ; int Size ;
else A1=22 ;
/* fft coefficients */
21 = .Workspace[ i].Al ; W.rr = WS->rr ;
22 = .Workspace[-i] .A2 ; /* complex conjugate */
if ( (iproc&i)==O ) A2=Z1 ; W.ii = -WS->ii ;
else A1=22 ;
/* X dimension fft */
21 = .WorkSpace[ j].Al ; partialFFT( A, &W, nxproc ) ;
22 = .Workspace[-j].A2 ; /* X dimension unshuffle */
if ( (iproc&j)==O ) A2=21 ; UnShuffle ( A, nxproc ) ;
else A1=22 ; /* Transpose data */
Transpose ( A, nxproc ) ;
/* fft coefficients */
Z1 = .Workspace[ i] .A1 ; W.rr = WS->rr ;
22 = .Workspace[-il .A2 ; /* complex conjugate */
if ( (iproc&i)==O ) A2=21 ; W.ii = -WS->ii ;
else A1=22 ;
A[O] = A1 ; /* X dimension fft */
A[1] = A2 ; partialFFT( A, &W, nxproc ) ;
/* X dimension unshuffle */
UnShuffle ( A, nxproc 1 ;
/* Transpose data */
Transpose ( A, nxproc ) ;
generic (Workspace[ I ) void FFT (
complex A[2] , /* normalize result */
complex *WS, Size = (nxproc*nxproc) ;
int nxproc ) { A[O] .rr /= (Size) ;
complex W ; A[O].ii /= (Size) ;
A[l].rr /= (Size) ;
/* fft coefficients */ A[1] .ii /= (Size) ;
w = *ws ; 1
/* X dimension fft */
partialFFT( A, &W, nxproc) ; threads WorkSet [nproc] ;
/* X dimension unshuffle */ threads Frame [size][ size] ;
UnShuffle ( A, nxproc ) ;
/* Transpose data */ int main ( int argc, char **argv ) {
Transpose ( A, nxproc ) ;
WorkSet. {
/* fft coefficients */ complex A[2l,WS ;
w = *ws ;
/* initialize test data set */
/* X dimension fft */
partialFFT( A, &W, nxproc) ; Frame. {
/* X dimension unshuffle */ int KK, LL;
UnShuffle ( A, nxproc ) ; real RIMAGE ;
/* Transpose data */
Transpose ( A, nxproc ) ; KK = $$ix[Ol-(size>>l) ;
1 LL = $$ix[ll-(size>>l) ;
RIMn.GE = 0;
generic (Workspace[ I ) void invFFT ( if (
complex A[2] , KK*KK+LL*LL < radius*radius
complex *WS, ) RIMAGE = 1 ;
2003 Conference on Information Science and Systems, The Johns Hopkins University, March 12-14,2003
+ A[O].ii*A[O].ii ) ;
WorkSet. { Frame [ i/ (size>>l) 3
int i=S$i; [ (i%( size>>l)) +(size>>l) 3
.
A[O].rr = RIMAGE
Frame [ i/(size>>l) ] = sqrt ( A[1] .rr*A[l] .rr
[ i% (size>>l) ]. RIMAGE ; + A[l].ii*A[l].ii ) ;
A[O].ii = 0.0 ;
A[1] .rr =
,
Frame [ i/(size>>l) ] print f ( 'I % c%1 0 g "
[ (i%( size>>l)) + (size>>l) ] ( ($$ix[O])?' ':'\nl ),
.RIMAGE ; RIMAGE ) ;
A[l].ii = 0.0 ; if (!$Si) printf ( "\n") ;
I }
1
Frame. {
real RIMAGE ; /* perform inverse FFT */
Workset.{ int i=$$i; invFFT ( A, &WS, Frame.($$Nx[O]) ) ;
Frame [ i/ (size>>l) ]
.
[ i% (size>>l) ] RIMAGE /* clean up result */
= sqrt( A[O] .rr*A[O] .rr
+ A[Ol.ii*A[Ol.ii ) ; if ( A[O].rr < le-13 ) A[O].rr=O.O ;
Frame [ i/(size>>l) 3 if ( A[O].ii < le-13 ) A[O].ii=O.O ;
[ (i%( size>>l)) +(size>>l) I if ( A[l].rr < le-13 ) A[l].rr=O.O ;
.R IMAGE if ( A[l].ii < le-13 ) A[ll.ii=O.O ;
= sqrt( A[1] .rr*A[lI .rr +
A[l].ii*A[l].ii ) ; Frame. {
I real RIMAGE ;
printf ( "%c%lOg", Workset.{ int i=$$i;
( ($$ix[Ol)?' ':I\n' ), Frame [ i/ (size>>l) 3
RIMAGE ) ; [ 1% (size>>l) 3 .RIMAGE
if (!$Si) printf ( l'\n'r); = sqrt( A[0] .rr*A[O] .rr
I + A[O] .ii*A[O] .ii ) ;
Frame [ i/ (size>>l) 3
[ (i%(size>>l)) +(size>>l) ]
.
RIMAGE
= sqrt ( A[1] .rr*A[l] .rr
/* initialize fft coefficients */ + A[1] .ii*A[l] .ii ) ;
1
WS = Init-FFT ( Frame. ($$Nx[Ol) 1;
printf ( "%c%lOg",
/* perform FFT */ ( ($$ix[Ol)?' l:l\n' ),
RIMAGE ) ;
FFT ( A, &WS, Frame.($$Nx[O]) ) ; if ( !$Si) printf ("\n") ;
I
Frame. {
real RIMAGE ;
Workset.{ int i=$$i; return 0;
Frame [ i/ (size>>l) ]
[ i% (size>>l) 3 .RIMAGE
= sqrt ( A[03 .rr*A[O] .rr
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