Description
1. (40) Let us revisit the histogramming problem assigned in Homework 4. Your input to this
program will be integers in the range 1-10,000,000 this time (use a random number
generator that generates the numbers on the host). Your host-based data set should
contain N integers, where N can be varied.
a. This time you will implement a histogramming kernel in CUDA and run on a GPU.
You can choose how to compute each class of the data set on the GPU. Attempt to
adjust the grid size to get the best performance as you vary N. Experiment with N =
210
, 215, 220 and 225. When the GPU finishes, print one element from each class in
class ascending order on the host (do not include the printing time in the timing
measurements, though do include the device-to-host communication in the timing
measurement). Plot your results in a graph.
b. Compare your GPU performance with running this same code on a CPU using
OpenMP.
2. (40) The code below carries out a “nearest neighbor” or “stencil” computation. This
class of algorithm appears frequently in image processing applications. The memory
reference pattern for matrix b exhibits reuse in 3 dimensions.
Your task is to develop a
C/CUDA version of this code that initializes b on the host and then uses tiling on the
GPU to exploit locality in shared memory across the 3 dimensions of b:
#define n 64
float a[n][n][n], b[n][n][n];
for (i=1; i<n-1; i++)
for (j=1; j<n-1; j++)
for (k=1; k<n-1; k++) {
a[i][j][k]=0.8*(b[i-1][j][k]+b[i+1][j][k]+b[i][j-1][k]
+ b[i][j+1][k]+b[i][j][k-1]+b[i][j][k+1]);
}
a.) Evaluate the performance of computing a tiled versus non-tiled implementation in
your GPU application. Explore what happens when you change the value of n.
Consider the performance for at least two additional values for n.
b.) Explore and report on other optimizations to accelerate your code on the GPU?
3. (20) Read the Pascal whitepaper provided, and then identify the key features that were
introduced in the Pascal P100 architecture, comparing those features against the
Ampere-based A100 architecture (make sure to identify the source for the information
you obtained on the A100). Please do not just repeat what you read in the Pascal
whitepaper, go into more detail on each of the features you identify.
4. (50 points extra credit for everybody) Let’s revisit computing the value of pi, but this
time we will use a series. For instance, we provide you code for the Leibniz’s series,
developed by Jose Cintra. Implement this series on the GPU, allowing the user to enter
the number of iterations.
Make sure to compute find an efficient computation of this
kernel that utilizes the parallelism provided on the GPU. Then modify this code to use
single precision math. Show results for at least 10 different number of iterations of the
series and discuss how precision plays a role in the rate of convergence.
* Written answers to the questions should be included in your homework 5 write-up in
pdf format. You should include your C/C++ programs and the README file in the zip
file submitted.
