embarrassingly parallel computations processes …….. input data results each process requires...
TRANSCRIPT
Embarrassingly Parallel Computations
processes ……..
Input data
results
Each process requires different data and produces results from its input without any results from other processes
Embarrassingly Parallel Computations
……..
Collect results
send initial dataslaves
recv()
send()
spawn()send()
recv()
Master
Geometrical Transformations of images
(a) Shift
yyy
xxx
'
'
(b) Scaling
y
x
ySy
xSx
'
'
© Rotation
sincos
sincos'
'
yxy
yxx
(d) Clipping
hl
hl
yyy
xxx
'
'
Geometrical Transformations of images
640
480
80
80
process
map
Geometrical Transformations of images
640
480
process
10
Geometrical Transformations of images
Master for(i=0, row; i<48 ; i++, row = row +10) send(row, Pi);
for(i=0 ; i<480 ; i++) for(j=0 ; j<640 ; j++) temp_map[i][j] = 0;
for(i=0 ; I<(640*480) ; i++){ recv(oldrow, oldcol, newcol, Pany); if(!((newrow<0)||(newrow>=480)||(new<0)||(new>=640))) temp_map[newrow][newcol]=map[oldrow][oldcol];}
for(i=0 ; i<480 ; i++) for(j=0 ; j<640 ; j++) map[i][j] = temp_map[i][j];
Geometrical Transformations of images
Slave recv(row, Pmaster);
for(oldrow = row ; oldrow<(row+10) ; oldrow++) for(oldcol=0 ; oldcol<640 ; oldcol++){ newrow = oldrow + delta_x; newcol = newcol + delta_y; send(oldrow, oldcol, newrow, newcol, Pmaster);}
Geometrical Transformations of images
Analysis
)()(4)2( 22 npOttnttpt datastartupdatastartupcomm
communication
computation )/()(2 2
2
pnOp
ntcomp
Mandelbrot Set
czz kk 2
1
22 bazlength
imagimagrealimag
realimagrealreal
czzz
czzz
abibaz
2
222
222
Mandelbrot Set
int cal_pixel(complex c){ int count, max; complex z; float temp, lengthsq; max = 256; z.real = 0; z.imag = 0; count = 0; do{ temp = z.real *z.real - z.imag * z.imag; z.real = temp; lengthsq = z.real * z.real + z.imag * z.imag; count++; }while((length<4.0)&&(count<max)); return count; }
struct complex{ float real; float imag;};
Sequential code
Mandelbrot Set
Sequential codec.real = real_min + x * (real_max - real_min) / disp_height;c.imag = imag_min + y * (imag_max - imag_min) / disp_width;
scale_real = (real_max - real_min) / disp_height;scale_imag = (imag_max - imag_min) / disp_width;
for(x=0 ; x < disp_width ; x++) for(y=0 ; y < disp_height ; y++){ c.real = real_min + ((float) x * scale_real); c.imag = imag_min + ((float) y * scale_imag); color = cal_pixel(c); display(x, y, color);}
Mandelbrot Set
Static Task Assignment
Master :for(i=0, row=0 ; i<48 ; i++, row = row + 10) sned(&row, Pi)for(i=0 ; i < (480*640) ; i++){ recv(&c, &color, Pany); display(c, color);}
Slaverecv(&row, Pmaster);for( x=0 ; x< disp_width ; x++) for(y=0 ; y < (row+10) ; y++){ c.real = min_real + ((float)x*scale_real); c.imag = min_imag + ((float)y*scale_imag); color = cal_pixel(c); send(&c, &color, Pmaster);}
Mandelbrot Set
Dynamic Task Assignment
Work pool.(xa, ya)
.(xb, yb) .(xc, yc)
.(xd, yd)
.(xe, ye)
………….
Mandelbrot Set
Dynamic Task Assignment
Master:
recv(&slave, &r, color, Pany, result_tag)count--;if( row<disp_height ){ sned(&row, Pslave, data_tag); row++; count++; }else send(&row, Pslave, terminator_tag);row_recv++;disply(r, color);}while(count>0);
Slave:
recv(y, Pmaster, ANYTAG, source_tag);while( source_tag == data_tag){ c.imag = imag_min + ((float)y*scale_imag); for(x=0 ; x<width ; x++){ c.real = real_min + ((float)x*scale_real); color[x] = cal_pixel(c); } send(&i, &y, color, Pmaster, result_tag); recv(y, Pmaster, source_tag);};
Mandelbrot Set
Dynamic Task Assignment
terminate Row returneddecrement
Row sentincrement disp_height
Mandelbrot Set
nts max
)(1 datastartupcomm ttst
s
ntcomp
max
)(2 datastartupcomm tts
nt
))((max
datastartupp ttss
n
s
nt
Phase I
Phase II
Phase III
Monte Carlo Methods
2
2
422
)1( 2
squareofArea
circleofArea
Monte Carlo Methods
1
1
x
21 xy 21 rr xy
41
1
0
2 dxx
Monte Carlo Methods
2
1 1
21 )()( limx
x
N
ir
N
xfN
xxdxxfArea
2
1
)3( 2x
xdxxxI
sum=0;for(i=0; i<N ; i++) xr = rand_v(x1, x2); sum = sum + xr * xr – 3 * xr;}Area = sum / N;
Sequential Code
Monte Carlo Methods
Parallel Code
Master
Slaves Slaves
Partial sumPartial sum
random number process
Masterfor(i=0 ; i<N/n ; i++){ for(j=0 ; j< n ; j++) xr[j] = rand(); recv(Pany, reg_tag, Psource); send(xr, &n, Psource, compute_tag);}
for(i=0 ; i<slave_no ; i++){ recv(Pi, reg_tag); send(Pi, stop_tag);}
sum=0;reduce_add(&sum, Pgroup);
Monte Carlo Methods
Parallel CodeMaster
Slaves Slaves
Partial sumPartial sum
random number process
Slave
sum=0;send(Pmaster, reg_tag);recv(xr, &n, Pmaster, source_tag);while(source_tag == compute_tag){ for(i=0 ; i<n ; i++) sum = sum + xr[i] * xr[i] - 3 * xr[i]; send(Pmaster, reg_tag); recv(xr, &n, Pmaster, source_tag);};
reduce_add(&sum, Pgroup);