Accelerating an N-Body Simulation

1. Accelerating an N-Body Simulation Anuj Kalia Maxeler Technologies

2. CPU loads particle data into DRAM for every iteration. (every N*N cycles)

3. CPU loads particle data into DRAM for every iteration. (every N*N cycles) A new set of 4 values is read from DRAM in every cycle.

4. CPU loads particle data into DRAM for every iteration. (every N*N cycles) A new set of 4 values is read from DRAM in every cycle. 16 force computations are done based on 16 scalar inputs and the 4 values read earlier. The pipeline and accumulator are described in another slide.

5. CPU loads particle data into DRAM for every iteration. (every N*N cycles) A new set of 4 values is read from DRAM in every cycle. 16 force computations are done based on 16 scalar inputs and the 4 values read earlier. The pipeline and accumulator are described in another slide. Every pipeline outputs 12 partial sums after ‘N’ cycles.

6. CPU loads particle data into DRAM for every iteration. (every N*N cycles) A new set of 4 values is read from DRAM in every cycle. 16 force computations are done based on 16 scalar inputs and the 4 values read earlier. The pipeline and accumulator are described in another slide. Every pipeline outputs 12 partial sums after ‘N’ cycles. CPU adds the 12 partial sums together (for every particle), updates velocities, updates positions and re-writes into the DRAM.

7. for(int j=0;j<N/PAR;j++) { max_set_scalar_input(device,"RowSumKernel.N",N,FPGA_A);//set scalar inputs max_set_scalar_input_f(device,"RowSumKernel.EPS",EPS,FPGA_A); for(int p=0;p<PAR;p++) { max_set_scalar_input_f(device,pi_x[p],px[j*PAR+p],FPGA_A); max_set_scalar_input_f(device,pi_y[p],py[j*PAR+p],FPGA_A); max_set_scalar_input_f(device,pi_z[p],pz[j*PAR+p],FPGA_A); } max_run//run the kernel ( device, max_output("ax",outputX,12*PAR*sizeof(float)), max_output("ay",outputY,12*PAR*sizeof(float)), max_output("az",outputZ,12*PAR*sizeof(float)), max_runfor("RowSumKernel",N), max_end() ); for(int i=0;i<12*PAR;i++) //sum up the partial sums { ax[j*PAR+(i/12)]+=outputX[i]; ay[j*PAR+(i/12)]+=outputY[i]; az[j*PAR+(i/12)]+=outputZ[i]; } } //update velocity //update position //load memory N/PAR times N Cycles Host C code

8. Pipeline and Accumulator: 1 Input per cycle: P_j data from DRAM. Acceleration: accumulated as 12 partial sums.

9. Resource Usage Resource Usage for 16 fold parallel kernel @ 150MHz: LUTs: 156032 / 297600 (52.43%) FFs: 166543 / 595200 (27.98%) BRAMs: 433 / 1064 (40.70%) 288 / 2016 (14.29%)

10. Performance: Comparison Seconds Particles

11. Performance: Speedup Speedup Particles

12. 38400 Particles