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GPU610/DPS915 | Student List | Group and Project Index | Student Resources | Glossary

Project Name Goes here

Team Members

  1. Yalong Li, Pilot
  2. Olga Belavina, Pilot Lieutenant


Assignment 1

LZSS

LZSS (Lempel–Ziv–Storer–Szymanski) is a compression algorithm that belongs to LZ77 family. It attempts to replace a string of symbols with a reference to a dictionary location of the same string.

The C implementation includes both compression and un-compression functionalities, however only compression algorithm will be tested and profiled. The source code for LZSS an be found here.

Data Overview

Supplying dummy text file to the compression function may not reflect real-world performance. Meaningful data needs to be used for the compression algorithm bench-marking and profiling since randomly generated text does not follow language rules/patterns (meaning it’s harder to compress such data).

The CIA world fact book was used as our test material. The file itself is only 4 megabytes, so in order to benchmark LZSS for larger size, world fact book text was concatenated to itself (many times) to reach certain size.

File Name Size (MB)
1GB.txt 1071
500M.txt 536
250M.txt 268
125M.txt 134

Profiling

Binary was produced (for both debugging and profiling) with gcc command. Code snippet below demonstrates profiling commands used for 250 megabyte file (same logic was applied to other text files). The binary is supplied with the original text file as its first argument and destination file for the compressed output.

[obelavina@localhost gpu610]$ gcc lzss.c -o lzss
[obelavina@localhost gpu610]$ ./lzss c 250M.txt 250M.compressed
In : 280730901 bytes
Out: 149085687 bytes
Out/In: 0.531
[obelavina@localhost gpu610]$ gprof -p -b lzss > 250M.flt

GPROF Result

/////////////////// 125MB FILE ///////////////////
[obelavina@localhost gpu610]$ cat 125M.flt 
Flat profile:

Each sample counts as 0.01 seconds.
  %   cumulative   self              self     total           
 time   seconds   seconds    calls   s/call   s/call  name    
 82.23     22.73    22.73 140365467     0.00     0.00  insert_node
 11.29     25.85     3.12 140365451     0.00     0.00  delete_node
  6.58     27.67     1.82        1     1.82    27.69  compress
  0.07     27.69     0.02        1     0.02     0.02  init_tree
/////////////////// 250MB FILE ///////////////////
[obelavina@localhost gpu610]$ cat 250M.flt 
Flat profile:

Each sample counts as 0.01 seconds.
  %   cumulative   self              self     total           
 time   seconds   seconds    calls   s/call   s/call  name    
 83.53     43.49    43.49 280730917     0.00     0.00  insert_node
 10.42     48.92     5.43 280730901     0.00     0.00  delete_node
  6.08     52.09     3.17        1     3.17    52.13  compress
  0.08     52.13     0.04        1     0.04     0.04  init_tree


/////////////////// 500MB FILE ///////////////////
[obelavina@localhost gpu610]$ cat 500M.flt 
Flat profile:

Each sample counts as 0.01 seconds.
  %   cumulative   self              self     total           
 time   seconds   seconds    calls   s/call   s/call  name    
 83.61     87.34    87.34 561461817     0.00     0.00  insert_node
 10.82     98.64    11.30 561461801     0.00     0.00  delete_node
  5.58    104.46     5.83        1     5.83   104.55  compress
  0.09    104.55     0.09        1     0.09     0.09  init_tree

/////////////////// 1GB FILE ///////////////////
[obelavina@localhost gpu610]$ cat 1G.flt 
Flat profile:

Each sample counts as 0.01 seconds.
  %   cumulative   self              self     total           
 time   seconds   seconds    calls   s/call   s/call  name    
 83.59    175.05   175.05 1122923616     0.00     0.00  insert_node
 10.60    197.26    22.21 1122923600     0.00     0.00  delete_node
  5.81    209.44    12.18        1    12.18   209.69  compress
  0.12    209.69     0.25        1     0.25     0.25  init_tree

Plotted Result

File Name File Size (MB) Total Time Taken – Compression (Seconds)
125M.txt 134 27.69
250M.txt 268 52.13
500M.txt 536 104.55
1G.txt 1071 209.69

Lzss perf.png

Analysis

Lets first try to visualise the function calls so it is easier to determine where LZSS algorithm spends most of the time.

gprof ./lzss | gprof2dot | dot | convert - out.png

Lzss calls.png

The call graph demonstrates that insert_node function takes the bulk of work (83.48%). delete_node takes only 10% even though it’s called nearly as many times as insert_node. It is hard to determine if LZSS is a good candidate for GPU optimisation: data throughput can be quite large but the logic of the algorithm includes some branching which can introduce some issues while porting code to CUDA. I suspect that compress function itself will need to be parallized (rather than insert_node).

Resources:

The data source (The Large Corpus): http://corpus.canterbury.ac.nz/descriptions/#cantrbry

LZSS Source Code: http://my.execpc.com/~geezer/code/lzss.c


SelectionSort

Selection Sort algorithm loops through every value in an array and finds the minimum values, assuming sort in ascending order, then puts it to the sorted area.

Source Code

// C program for implementation of selection sort
#include <stdio.h>
#include<cstdlib>
 
void swap(int *xp, int *yp)
{
    int temp = *xp;
    *xp = *yp;
    *yp = temp;
}
 
void selectionSort(int arr[], int n)
{
    int i, j, min_idx;
 
    // One by one move boundary of unsorted subarray
    for (i = 0; i < n-1; i++)
    {
        // Find the minimum element in unsorted array
        min_idx = i;
        for (j = i+1; j < n; j++)
          if (arr[j] < arr[min_idx])
            min_idx = j;
 
        // Swap the found minimum element with the first element
        swap(&arr[min_idx], &arr[i]);
    }
}
 
// Driver program to test above functions
int main()
{
    int arrSize = 150000;

    int arr[arrSize];
    for (int i = 0; i < arrSize; i++) {
      arr[i] = rand() % 10000 + 1;
    }
    int n = sizeof(arr)/sizeof(arr[0]);

    selectionSort(arr, n);
    return 0;
}

gprof results

Tested the selection sort algorithm with three different array size: 50000, 100000, and 150000. The amount of time spent increased noticeably.

// Array Size 50000
Each sample counts as 0.01 seconds.
  %   cumulative   self              self     total           
 time   seconds   seconds    calls   s/call   s/call  name    
100.00      8.45     8.45        1     8.45     8.45  selectionSort(int*, int)
  0.00      8.45     0.00    49999     0.00     0.00  swap(int*, int*)

granularity: each sample hit covers 4 byte(s) for 0.12% of 8.45 seconds

index % time    self  children    called     name
                                                 <spontaneous>
[1]    100.0    0.00    8.45                 main [1]
                8.45    0.00       1/1           selectionSort(int*, int) [2]
-----------------------------------------------
                8.45    0.00       1/1           main [1]
[2]    100.0    8.45    0.00       1         selectionSort(int*, int) [2]
                0.00    0.00   49999/49999       swap(int*, int*) [6]
-----------------------------------------------
                0.00    0.00   49999/49999       selectionSort(int*, int) [2]
[6]      0.0    0.00    0.00   49999         swap(int*, int*) [6]
-----------------------------------------------
// Array Size 100000
Each sample counts as 0.01 seconds.
  %   cumulative   self              self     total           
 time   seconds   seconds    calls   s/call   s/call  name    
100.00     33.96    33.96        1    33.96    33.96  selectionSort(int*, int)
  0.00     33.96     0.00    99999     0.00     0.00  swap(int*, int*)

granularity: each sample hit covers 4 byte(s) for 0.03% of 33.96 seconds

index % time    self  children    called     name
                                                 <spontaneous>
[1]    100.0    0.00   33.96                 main [1]
               33.96    0.00       1/1           selectionSort(int*, int) [2]
-----------------------------------------------
               33.96    0.00       1/1           main [1]
[2]    100.0   33.96    0.00       1         selectionSort(int*, int) [2]
                0.00    0.00   99999/99999       swap(int*, int*) [6]
-----------------------------------------------
                0.00    0.00   99999/99999       selectionSort(int*, int) [2]
[6]      0.0    0.00    0.00   99999         swap(int*, int*) [6]
-----------------------------------------------
// Array Size 150000
Each sample counts as 0.01 seconds.
  %   cumulative   self              self     total           
 time   seconds   seconds    calls   s/call   s/call  name    
 99.99     76.65    76.65        1    76.65    76.66  selectionSort(int*, int)
  0.01     76.66     0.01   149999     0.00     0.00  swap(int*, int*)

granularity: each sample hit covers 4 byte(s) for 0.01% of 76.66 seconds

index % time    self  children    called     name
                                                 <spontaneous>
[1]    100.0    0.00   76.66                 main [1]
               76.65    0.01       1/1           selectionSort(int*, int) [2]
-----------------------------------------------
               76.65    0.01       1/1           main [1]
[2]    100.0   76.65    0.01       1         selectionSort(int*, int) [2]
                0.01    0.00  149999/149999      swap(int*, int*) [3]
-----------------------------------------------
                0.01    0.00  149999/149999      selectionSort(int*, int) [2]
[3]      0.0    0.01    0.00  149999         swap(int*, int*) [3]
-----------------------------------------------

Result in chart diagram

SelectionSort.png

Reference

code website: https://www.geeksforgeeks.org/selection-sort/

Bitonic Sort

Bitonic Sort is a classic parallel algorithm for sorting.

Source Code

void bitonic_sort(int *data, int N)
{

	int i, j, k;
	int temp;

	for (k = 2; k <= N; k = 2 * k)
	{
		for (j = k >> 1; j>0; j = j >> 1)
		{
			for (i = 0; i<N; i++)
			{
				int ixj = i^j;

				if ((ixj)>i)
				{
					if ((i&k) == 0 && data[i] > data[ixj]) {
						temp = data[i];
						data[i] = data[ixj];
						data[ixj] = temp;
					}

					if ((i&k) != 0 && data[i] < data[ixj]) {
						temp = data[i];
						data[i] = data[ixj];
						data[ixj] = temp;
					}

				}
			}
		}
	}

}

gprof results

Tested the Bitonic sort with three different array size: 4194304, 16777216, and 67108864.

// Array Size 2^22 = 4194304
Each sample counts as 0.01 seconds.
  %   cumulative   self              self     total           
 time   seconds   seconds    calls  Ts/call  Ts/call  name    
100.00      4.20     4.20                             bitonic_sort(int*, int)
  0.00      4.20     0.00        1     0.00     0.00  _GLOBAL__sub_I__Z12bitonic_sortPii
// Array Size 2^24 = 16777216
Each sample counts as 0.01 seconds.
  %   cumulative   self              self     total           
 time   seconds   seconds    calls  Ts/call  Ts/call  name    
100.00     19.84    19.84                             bitonic_sort(int*, int)
  0.00     19.84     0.00        1     0.00     0.00  _GLOBAL__sub_I__Z12bitonic_sortPii
// Array Size 2^26 = 67108864
Each sample counts as 0.01 seconds.
  %   cumulative   self              self     total           
 time   seconds   seconds    calls  Ts/call  Ts/call  name    
100.00     88.26    88.26                             bitonic_sort(int*, int)
  0.00     88.26     0.00        1     0.00     0.00  _GLOBAL__sub_I__Z12bitonic_sortPii

Result in chart diagram

HVBitonicSort.png

Reference

https://www.geeksforgeeks.org/bitonic-sort/

Assignment 2

Assignment 3