fbsh / iit-phys440

Introduction

This is a high-performance computation case using the Monte Carlo method to get pi and calculate the unit sphere surface and volume and the bounded box surface and volume. For multi-threaded high-performance computing, in this case I used my NVIDIA GeForce GTX 1660 Ti graphics card. At the same time, the accuracy of the result will be compared with the serial C code. A large number of Monte Carlo trials can run on the GPU, one trial per thread. There are 128 threads by default, and the number of blocks is determined by the total number of trials and the number of threads. Since I am using the external gpu, io between cpu and gpu is limited by the bandwidth of the thunderbolt3 cable which is 40Gbps maximun.

Test and Test Result

c

(base) fbsh@fbsh-NUC8i5BEH:~/phys440/assignment_1$ gcc mc_pi_serial.c -o mc_pi_serial

Test 1

(base) fbsh@fbsh-NUC8i5BEH:~/phys440/assignment_1$ time ./mc_pi_serial [+] total = 1000000 [+] count = 785825 [+] pi = 3.143300 [+] loss = -1.707346e-03 [+] volume of the unit sphere = 4.191067 [+] surface of the unit sphere = 12.573200 [+] volume of the box = 1.000000 [+] surface of the box = 6.000000

real 0m0.027s user 0m0.023s sys 0m0.004s

Test 2

(base) fbsh@fbsh-NUC8i5BEH:~/phys440/assignment_1$ time ./mc_pi_serial 10000000 [+] total = 10000000 [+] count = 7853447 [+] pi = 3.141379 [+] loss = 2.138536e-04 [+] volume of the unit sphere = 4.188505 [+] surface of the unit sphere = 12.565515 [+] volume of the box = 1.000000 [+] surface of the box = 6.000000

real 0m0.190s user 0m0.186s sys 0m0.004s

Test 3

(base) fbsh@fbsh-NUC8i5BEH:~/phys440/assignment_1$ time ./mc_pi_serial 100000000 [+] total = 100000000 [+] count = 78533917 [+] pi = 3.141357 [+] loss = 2.359736e-04 [+] volume of the unit sphere = 4.188476 [+] surface of the unit sphere = 12.565427 [+] volume of the box = 1.000000 [+] surface of the box = 6.000000

real 0m1.822s user 0m1.822s sys 0m0.000s

cuda

(base) fbsh@fbsh-NUC8i5BEH:~/phys440/assignment_1$ nvcc mc_pi_cuda.cu -o mc_pi_cuda

Test 4

(base) fbsh@fbsh-NUC8i5BEH:~/phys440/assignment_1$ time ./mc_pi_cuda [+] total = 1000064 [+] count = 785470 [+] pi = 3.141679 [+] loss = -8.627896e-05 [+] volume of the unit sphere = 4.188905 [+] surface of the unit sphere = 12.566716 [+] volume of the box = 1.000000 [+] surface of the box = 6.000000

Blocks = 7813 Threads = 128

real 0m0.208s user 0m0.047s sys 0m0.136s

Test 5

(base) fbsh@fbsh-NUC8i5BEH:~/phys440/assignment_1$ time ./mc_pi_cuda 10000000 [+] total = 10000000 [+] count = 7852825 [+] pi = 3.141130 [+] loss = 4.626536e-04 [+] volume of the unit sphere = 4.188173 [+] surface of the unit sphere = 12.564520 [+] volume of the box = 1.000000 [+] surface of the box = 6.000000

Blocks = 78125 Threads = 128

real 0m0.508s user 0m0.313s sys 0m0.172s

Test 6

(base) fbsh@fbsh-NUC8i5BEH:~/phys440/assignment_1$ ./mc_pi_cuda 100000000 [+] total = 100000000 [+] count = 78542448 [+] pi = 3.141698 [+] loss = -1.052664e-04 [+] volume of the unit sphere = 4.188931 [+] surface of the unit sphere = 12.566792 [+] volume of the box = 1.000000 [+] surface of the box = 6.000000

Blocks = 781250 Threads = 128

real 0m3.171s user 0m2.634s sys 0m0.517s