1. Embarrassingly Parallel Computations processes …….. Input data results Each process requires different data and produces results from its input without any results from other processes

2. Embarrassingly Parallel Computations …….. Collect results send initial data slaves recv() send() spawn() send() recv() Master

3. Geometrical Transformations of images (a)Shift (b) Scaling © Rotation (d) Clipping

4. Geometrical Transformations of images 640 480 80 process map

5. Geometrical Transformations of images 640 480 process 10

6. 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 =480)||(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];

7. 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); }

8. Geometrical Transformations of images Analysis communication computation

9. Mandelbrot Set

10. 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

11. Mandelbrot Set Sequential code c.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); }

12. 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); } Slave recv(&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); }

13. Mandelbrot Set Dynamic Task Assignment Work pool.(x a, y a ).(x b, y b ).(x c, y c ).(x d, y d ).(x e, y e ) ………….

14. 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); };

15. Mandelbrot Set Dynamic Task Assignment terminate Row returned decrement Row sent increment disp_height

16. Mandelbrot Set Phase I Phase II Phase III

17. Monte Carlo Methods 2 2

18. 1 1 x

19. sum=0; for(i=0; i<N ; i++) xr = rand_v(x1, x2); sum = sum + xr * xr – 3 * xr; } Area = sum / N; Sequential Code

20. Monte Carlo Methods Parallel Code Master Slaves Partial sum random number process Master for(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);

21. Monte Carlo Methods Parallel Code Master Slaves Partial 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);