# Ghost Cells

## Team Members

1. Tony Sim, Issue Dumper
2. Robert Dittrich, Issue Collector
3. Inna Zhogova, Issue Resolver

## Progress

### Assignment 1

#### Tony

Subject: Jacobi's method for Poisson's equation

##### Source Code
poissan.h
```#ifndef POISSON_H
#define POISSON_H
#include <fstream>

namespace DPS{
class Poisson {
size_t nRowsTotal;
size_t nColumns;
float* data;
int bufferSide;

void update (size_t startRow, size_t endRow, const float wx, const float wy);
void bufferSwitch(){ bufferSide = 1 - bufferSide; };

public:
Poisson(std::ifstream& ifs);
Poisson(const size_t r, const size_t c, float* d);
~Poisson(){ delete[] data; };
float* operator()(const size_t iteration, const float wx, const float wy);
float* operator()(const size_t iteration){
return operator()(iteration,0.1,0.1);
}
void show(std::ostream& ofs) const;
};
}
#endif```
poissan.cpp
```#include <cstring>
#include <cstdlib>
#include <iomanip>
#include <iostream>
#include <string>
#include "poisson.h"

namespace DPS{
Poisson::Poisson(std::ifstream& ifs){
std::string line;
bufferSide = 0;

/* find number of columns */
std::getline(ifs,line);
for (size_t i = 0 ; i < line.size() ; i++){
if(line[i]==' ') nColumns++;
}
nColumns++;

/* find number of rows */
nRowsTotal++; /* already fetched one */
while(std::getline(ifs,line))
nRowsTotal++;
ifs.clear();

try{
data = new float[nColumns * nRowsTotal * 2];
}
catch (...){
throw std::runtime_error("Failed to Allocate Memory");
}

ifs.seekg(0,ifs.beg);
std::cout << ifs.tellg() << std::endl;
for (size_t i = 0 ; i < nRowsTotal * nColumns ; i++) {
ifs >> data[i];
}

std::memset(data+nRowsTotal*nColumns,0,nRowsTotal*nColumns*sizeof(float));
}

Poisson::Poisson(const size_t r, const size_t c, float* d){
bufferSide = 0;
nRowsTotal = r;
nColumns = c;
try{
data = new float[r*c*2];
}
catch (...){
throw std::runtime_error("Failed to Allocate Memory");
}
std::memcpy(data,d,r*c*sizeof(float));
std::memset(data+r*c,0,r*c*sizeof(float));
}

void Poisson::update (size_t startRow, size_t endRow, const float wx, const float wy){
float* x_new = data + (1-bufferSide)*nRowsTotal*nColumns;
float* x_old = data + bufferSide*nRowsTotal*nColumns;
for (size_t i = startRow; i <= endRow; i++)
for (size_t j = 1; j < nColumns - 1; j++)
x_new[i * nColumns + j] = x_old[i * nColumns + j]
+ wx * (x_old[(i + 1) * nColumns + j] + x_old[(i - 1) * nColumns + j]
- 2.0f * x_old[i * nColumns + j])
+ wy * (x_old[i * nColumns + j + 1] + x_old[i * nColumns + j - 1]
- 2.0f * x_old[i * nColumns + j]);
}

float* Poisson::operator()(const size_t nIterations, const float wx, const float wy){
for (size_t i = 0; i < nIterations; i++) {
update(0, nRowsTotal-1, wx, wy);
bufferSwitch();
}
return data;
}

void Poisson::show(std::ostream& ofs) const{
ofs << std::fixed << std::setprecision(1);
for (size_t j = 0; j < nColumns ; j++) {
for (size_t i = 0 ; i < nRowsTotal ; i++)
ofs << std::setw(8) << data[ bufferSide*nColumns*nRowsTotal + i * nColumns + j];
ofs << std::endl;
}
}
}```
main.cpp
```// based on code from LLNL tutorial mpi_heat2d.c
// Master-Worker Programming Model
// Chris Szalwinski - 2018/11/13
// Adopted by Tony Sim - 2019/02/16
#include <iostream>
#include <fstream>
#include <iomanip>
#include <cstdlib>
#include <stdexcept>

#include "poisson.h"

// solution constants
const size_t NONE = 0;
const size_t MINPARTITIONS = 1;
const size_t MAXPARTITIONS = 7;
// weights
const float wx = 0.1f;
const float wy = 0.1f;

int main(int argc, char** argv) {
if (argc != 4) {
std::cerr << "*** Incorrect number of arguments ***\n";
std::cerr << "Usage: " << argv[0]
<< " input_file output_file no_of_iterations\n";
return 1;
}

std::ifstream input(argv[1]);
std::ofstream output(argv[2]);
std::ofstream temp("init.csv");

if(!input.is_open()){
std::cerr << "Invalid Input File" << std::endl;
return 2;
}
if(!output.is_open()){
std::cerr << "Invalid Output File" << std::endl;
return 2;
}

DPS::Poisson* p = nullptr;
try{
p = new DPS::Poisson(input);
}
catch(std::exception& e){
std::cerr << "Error: " << e.what() << std::endl;
}

p->show(temp);

size_t nIterations = std::atoi(argv[3]);

(*p)(nIterations);

// write results to file
p->show(output);

delete p;

}```
##### Introduction

The presented code simulates heat map using Jacobi's method for Poisson's equation. It is represented in a 2D array, and each element updates its value based on the adjacent elements at a given moment. Each iteration represent one instance in time. By repeating the calculation over the entire array through multiple iterations, we can estimate the state of the heat transfer after a given time interval.

##### Profiling

The profiling was conducted using a data set of 79 rows and 205 columns over 150000 iterations.

Flat profile

Flat profile:

Each sample counts as 0.01 seconds.

``` %   cumulative   self              self     total
time   seconds   seconds    calls  us/call  us/call  name
98.57      2.75     2.75   150000    18.33    18.33  DPS::Poisson::update(unsigned long, unsigned long, float, float)
0.00      2.75     0.00        1     0.00     0.00  _GLOBAL__sub_I__ZN3DPS7PoissonC2ERSt14basic_ifstreamIcSt11char_traitsIcEE
0.00      2.75     0.00        1     0.00     0.00  _GLOBAL__sub_I_main
```

Call graph
```                       Call graph
```

granularity: each sample hit covers 2 byte(s) for 0.36% of 2.75 seconds

index % time self children called name

```               2.75    0.00  150000/150000      DPS::Poisson::operator()(unsigned long, float, float) [2]
```

[1] 100.0 2.75 0.00 150000 DPS::Poisson::update(unsigned long, unsigned long, float, float) [1]

```                                                <spontaneous>
```

[2] 100.0 0.00 2.75 DPS::Poisson::operator()(unsigned long, float, float) [2]

```               2.75    0.00  150000/150000      DPS::Poisson::update(unsigned long, unsigned long, float, float) [1]
```

```               0.00    0.00       1/1           __libc_csu_init [21]
```

[10] 0.0 0.00 0.00 1 _GLOBAL__sub_I__ZN3DPS7PoissonC2ERSt14basic_ifstreamIcSt11char_traitsIcEE [10]

```               0.00    0.00       1/1           __libc_csu_init [21]
```

[11] 0.0 0.00 0.00 1 _GLOBAL__sub_I_main [11]

Index by function name

``` [10] _GLOBAL__sub_I__ZN3DPS7PoissonC2ERSt14basic_ifstreamIcSt11char_traitsIcEE (poisson.cpp) [11] _GLOBAL__sub_I_main (main.cpp) [1] DPS::Poisson::update(unsigned long, unsigned long, float, float)
```

##### Analysis

given 98.57 percent of time is spent on the update() function, it is considered the hotspot. Total time taken was 2.75.

If we consider a GPU environment with 1000 cores, we can estimate the following speedup: S1000 = 1/(1-.9857 + .9857/1000) = 65.00 In fact, the speed will decrease from 2.75 seconds to 0.0450 seconds.

As each iteration depends on the product of the previous iteration, there is a dependency resolution that might hamper the parallel process. Consideration may also be extended to resolving ghost cells across different SMX while using the device global memory as the transfer pipeline.

#### Robert

##### Multi Sampling Anti Aliasing
###### Source Files
main.cpp
```#include <cstdint>
#include <iostream>
#include <algorithm>

#define STB_IMAGE_IMPLEMENTATION
#include "stb_image.h"
#define STB_IMAGE_WRITE_IMPLEMENTATION
#include "stb_image_write.h"

#include "vec3.h"

struct Point {
int x;
int y;
};
uint8_t* msaa(const uint8_t* input, uint8_t* output, int width, int height, int channels, int samples) {

// directions is (samples * 2 + 1) ^ 2
int totalPoints = (samples * 2 + 1) * (samples * 2 + 1);
Point* directions = new Point[totalPoints];
size_t idx = 0;
for (int i = -samples; i <= samples; i++) {
for (int j = -samples; j <= samples; j++) {
directions[idx].x = i;
directions[idx].y = j;
idx++;
}
}

int  x, y, cx, cy;
Vec3<int> average;
for (size_t i = 0; i < width*height; i++) {
x = i % width * channels;
y = i / width * channels;
for (size_t j = 0; j < totalPoints; j++) {
cx = x + directions[j].x * channels;
cy = y + directions[j].y * channels;
cx = std::clamp(cx, 0, width* channels);
cy = std::clamp(cy, 0, height* channels);
average.add(input[width * cy + cx], input[width * cy + cx + 1], input[width * cy + cx + 2]);
}
average.set(average.getX() / totalPoints, average.getY() / totalPoints, average.getZ() / totalPoints);
output[(width * y + x)] = average.getX();
output[(width * y + x) + 1] = average.getY();
output[(width * y + x) + 2] = average.getZ();
average.set(0, 0, 0);
}
delete[] directions;
return output;
}

int main(int argc, char* argv[]) {
if (argc != 5) {
std::cerr << argv[0] << ": invalid number of arguments\n";
std::cerr << "Usage: " << argv[0] << "  input output sample_size passes \n";
system("pause");
return 1;
}
int width, height, channels;
if (channels != 3) {
std::cout << "Incorrect channels" << std::endl;
system("pause");
return 2;
}
int samples = std::atoi(argv[3]);
int passes = std::atoi(argv[4]);
uint8_t* rgb_write = new uint8_t[width*height*channels];

rgb_write = msaa(rgb_read, rgb_write, width, height, channels, samples);
for (int i = 1; i < passes; i++) {
rgb_write = msaa(rgb_write, rgb_write, width, height, channels, samples);
}
stbi_write_png(argv[2], width, height, channels, rgb_write, width*channels);
delete[] rgb_write;
std::cout << "AA Done using " << samples << " sample size" << " over " << passes << " passes" << std::endl;
system("pause");
return 0;
}```
vec3.h
```#ifndef VEC3_H
#define VEC3_H
#include <iostream>
template <class T>
class Vec3 {
private:
T x;
T y;
T z;
public:
Vec3() {
x = 0;
y = 0;
z = 0;
};
Vec3(T x_, T y_, T z_) {
x = x_;
y = y_;
z = z_;
}
void set(const T &x_, const T &y_, const T &z_) {
x = x_;
y = y_;
z = z_;
}
void add(const T &x_, const T &y_, const T &z_) {
x += x_;
y += y_;
z += z_;
}

T getX() const { return x; }
T getY() const { return y; }
T getZ() const { return z; }

void setX(const T &x_) { x = x_; }
void setY(const T &y_) { y = y_; }
void setZ(const T &z_) { z = z_; }

static T dot(const Vec3& vec1, const Vec3& vec2) {
return  vec1.x * vec2.x + vec1.y * vec2.y + vec1.z * vec2.z;
}
T dot(const Vec3 &vec) const {
return x * vec.x + y * vec.y + z * vec.z;
}
void display(std::ostream& os) {
os << "x: " << x << ", y: " << y << ", z: " << z << "\n";
}

};

#endif // !VEC3_H```
###### Introduction

For my selection I chose to do Anti Aliasing since I see it a lot in video games but I never really knew how it worked. There are other anti aliasing methods like FXAA which is fast approximate anti aliasing but it seemed a lot more complicated than MSAA. The way I approached this problem is by getting the color of the pixels around a pixel. In you can specify the distance it will search in the application flags. In my implementation you specify an input file, output file, the radius of pixels to sample and how many passes to take on the image. In my tests the command line options I used was an image I made in paint with 4 sample size and 4 passes.

Before

After

.

###### Profiling
Profiling
```Flat profile:

Each sample counts as 0.01 seconds.
%   cumulative   self              self     total
time   seconds   seconds    calls  ms/call  ms/call  name
85.72      0.18     0.18                             msaa(unsigned char const*, unsigned char*, int, int, int, int)
14.29      0.21     0.03        1    30.00    30.00  stbi_zlib_compress
0.00      0.21     0.00   127820     0.00     0.00  stbiw__zlib_flushf(unsigned char*, unsigned int*, int*)
0.00      0.21     0.00    96904     0.00     0.00  stbiw__zhash(unsigned char*)
0.00      0.21     0.00     5189     0.00     0.00  stbi__fill_bits(stbi__zbuf*)
0.00      0.21     0.00     2100     0.00     0.00  stbiw__encode_png_line(unsigned char*, int, int, int, int, int, int, signed char*)
0.00      0.21     0.00     2014     0.00     0.00  stbiw__sbgrowf(void**, int, int) [clone .constprop.58]
0.00      0.21     0.00       38     0.00     0.00  stbi__get16be(stbi__context*)
0.00      0.21     0.00       19     0.00     0.00  stbi__get32be(stbi__context*)
0.00      0.21     0.00        3     0.00     0.00  stbi__skip(stbi__context*, int)
0.00      0.21     0.00        3     0.00     0.00  stbiw__wpcrc(unsigned char**, int)
0.00      0.21     0.00        3     0.00     0.00  stbi__stdio_read(void*, char*, int)
0.00      0.21     0.00        3     0.00     0.00  stbi__zbuild_huffman(stbi__zhuffman*, unsigned char const*, int)
0.00      0.21     0.00        2     0.00     0.00  stbi__mad3sizes_valid(int, int, int, int)
0.00      0.21     0.00        1     0.00     0.00  _GLOBAL__sub_I_stbi_failure_reason
0.00      0.21     0.00        1     0.00     0.00  stbi__getn(stbi__context*, unsigned char*, int)
0.00      0.21     0.00        1     0.00     0.00  stbi__readval(stbi__context*, int, unsigned char*)
0.00      0.21     0.00        1     0.00     0.00  stbi__load_main(stbi__context*, int*, int*, int*, int, stbi__result_info*, int)
0.00      0.21     0.00        1     0.00     0.00  stbi__parse_zlib(stbi__zbuf*, int)
0.00      0.21     0.00        1     0.00     0.00  stbi__malloc_mad3(int, int, int, int)
0.00      0.21     0.00        1     0.00     0.00  stbi__parse_png_file(stbi__png*, int, int)
0.00      0.21     0.00        1     0.00     0.00  stbi__start_callbacks(stbi__context*, stbi_io_callbacks*, void*)
0.00      0.21     0.00        1     0.00     0.00  stbi__decode_jpeg_header(stbi__jpeg*, int)
0.00      0.21     0.00        1     0.00     0.00  stbi__compute_huffman_codes(stbi__zbuf*)
0.00      0.21     0.00        1     0.00     0.00  stbi__load_and_postprocess_8bit(stbi__context*, int*, int*, int*, int)
0.00      0.21     0.00        1     0.00     0.00  stbi_load_from_file
0.00      0.21     0.00        1     0.00    30.00  stbi_write_png_to_mem
0.00      0.21     0.00        1     0.00     0.00  stbi_zlib_decode_malloc_guesssize_headerflag```
###### Conclusion

Since the `msaa` function I wrote is a hotspot of the program I would suggest offloading part of it to a GPU, more specifically the part that finds the average of colors of the nearby pixels. That part also does not depend on previous iterations to finish so it is a prime candidate for parallelization.

#### Inna

##### Subject: Data compression - LWZ algorithm.

I tested the following source code for a compression and decompression of .txt files and a gif.

lwz.cpp( ... )
```///
/// @file
/// @brief LZW file compressor
/// @version 1
///
/// This is the C++11 implementation of a Lempel-Ziv-Welch single-file command-line compressor.
/// It uses the simpler fixed-width code compression method.
/// It was written with Doxygen comments.
///
/// @see http://en.wikipedia.org/wiki/Lempel%E2%80%93Ziv%E2%80%93Welch
/// @see http://marknelson.us/2011/11/08/lzw-revisited/
/// @see http://www.cs.duke.edu/csed/curious/compression/lzw.html
/// @see http://warp.povusers.org/EfficientLZW/index.html
/// @see http://en.cppreference.com/
/// @see http://www.doxygen.org/
///

#include <cstdint>
#include <cstdlib>
#include <exception>
#include <fstream>
#include <ios>
#include <iostream>
#include <istream>
#include <limits>
#include <map>
#include <ostream>
#include <stdexcept>
#include <string>
#include <vector>

/// Type used to store and retrieve codes.
using CodeType = std::uint16_t;

namespace globals {

/// Dictionary Maximum Size (when reached, the dictionary will be reset)
const CodeType dms {std::numeric_limits<CodeType>::max()};

} // namespace globals

///
/// @brief Helper operator intended to simplify code.
/// @param vc   original vector
/// @param c    element to be appended
/// @returns vector resulting from appending `c` to `vc`
///
std::vector<char> operator + (std::vector<char> vc, char c)
{
vc.push_back(c);
return vc;
}

///
/// @brief Compresses the contents of `is` and writes the result to `os`.
/// @param [in] is      input stream
/// @param [out] os     output stream
///
void compress(std::istream &is, std::ostream &os)
{
std::map<std::vector<char>, CodeType> dictionary;

// "named" lambda function, used to reset the dictionary to its initial contents
const auto reset_dictionary = [&dictionary] {
dictionary.clear();

const long int minc = std::numeric_limits<char>::min();
const long int maxc = std::numeric_limits<char>::max();

for (long int c = minc; c <= maxc; ++c)
{
// to prevent Undefined Behavior, resulting from reading and modifying
// the dictionary object at the same time
const CodeType dictionary_size = dictionary.size();

dictionary[{static_cast<char> (c)}] = dictionary_size;
}
};

reset_dictionary();

std::vector<char> s; // String
char c;

while (is.get(c))
{
// dictionary's maximum size was reached
if (dictionary.size() == globals::dms)
reset_dictionary();

s.push_back(c);

if (dictionary.count(s) == 0)
{
// to prevent Undefined Behavior, resulting from reading and modifying
// the dictionary object at the same time
const CodeType dictionary_size = dictionary.size();

dictionary[s] = dictionary_size;
s.pop_back();
os.write(reinterpret_cast<const char *> (&dictionary.at(s)), sizeof (CodeType));
s = {c};
}
}

if (!s.empty())
os.write(reinterpret_cast<const char *> (&dictionary.at(s)), sizeof (CodeType));
}

///
/// @brief Decompresses the contents of `is` and writes the result to `os`.
/// @param [in] is      input stream
/// @param [out] os     output stream
///
void decompress(std::istream &is, std::ostream &os)
{
std::vector<std::vector<char>> dictionary;

// "named" lambda function, used to reset the dictionary to its initial contents
const auto reset_dictionary = [&dictionary] {
dictionary.clear();
dictionary.reserve(globals::dms);

const long int minc = std::numeric_limits<char>::min();
const long int maxc = std::numeric_limits<char>::max();

for (long int c = minc; c <= maxc; ++c)
dictionary.push_back({static_cast<char> (c)});
};

reset_dictionary();

std::vector<char> s; // String
CodeType k; // Key

while (is.read(reinterpret_cast<char *> (&k), sizeof (CodeType)))
{
// dictionary's maximum size was reached
if (dictionary.size() == globals::dms)
reset_dictionary();

if (k > dictionary.size())
throw std::runtime_error("invalid compressed code");

if (k == dictionary.size())
dictionary.push_back(s + s.front());
else
if (!s.empty())
dictionary.push_back(s + dictionary.at(k).front());

os.write(&dictionary.at(k).front(), dictionary.at(k).size());
s = dictionary.at(k);
}

if (!is.eof() || is.gcount() != 0)
throw std::runtime_error("corrupted compressed file");
}

///
/// @brief Prints usage information and a custom error message.
/// @param s    custom error message to be printed
/// @param su   Show Usage information
///
void print_usage(const std::string &s = "", bool su = true)
{
if (!s.empty())
std::cerr << "\nERROR: " << s << '\n';

if (su)
{
std::cerr << "\nUsage:\n";
std::cerr << "\tprogram -flag input_file output_file\n\n";
std::cerr << "Where `flag' is either `c' for compressing, or `d' for decompressing, and\n";
std::cerr << "`input_file' and `output_file' are distinct files.\n\n";
std::cerr << "Examples:\n";
}

std::cerr << std::endl;
}

///
/// @brief Actual program entry point.
/// @param argc             number of command line arguments
/// @param [in] argv        array of command line arguments
/// @retval EXIT_FAILURE    for failed operation
/// @retval EXIT_SUCCESS    for successful operation
///
int main(int argc, char *argv[])
{
if (argc != 4)
{
print_usage("Wrong number of arguments.");
return EXIT_FAILURE;
}

enum class Mode {
Compress,
Decompress
};

Mode m;

if (std::string(argv[1]) == "-c")
m = Mode::Compress;
else
if (std::string(argv[1]) == "-d")
m = Mode::Decompress;
else
{
print_usage(std::string("flag `") + argv[1] + "' is not recognized.");
return EXIT_FAILURE;
}

std::ifstream input_file(argv[2], std::ios_base::binary);

if (!input_file.is_open())
{
print_usage(std::string("input_file `") + argv[2] + "' could not be opened.");
return EXIT_FAILURE;
}

std::ofstream output_file(argv[3], std::ios_base::binary);

if (!output_file.is_open())
{
print_usage(std::string("output_file `") + argv[3] + "' could not be opened.");
return EXIT_FAILURE;
}

try
{

if (m == Mode::Compress)
compress(input_file, output_file);
else
if (m == Mode::Decompress)
decompress(input_file, output_file);
}
catch (const std::ios_base::failure &f)
{
print_usage(std::string("File input/output failure: ") + f.what() + '.', false);
return EXIT_FAILURE;
}
catch (const std::exception &e)
{
print_usage(std::string("Caught exception: ") + e.what() + '.', false);
return EXIT_FAILURE;
}

return EXIT_SUCCESS;
}```
##### Tested data

1. book.txt - a 343 kilobyte text file.

2. words.txt - a 4.7 megabyte text file.

3. fire.gif - a 309 kilobyte graphical image.

##### Flat Profiles
###### Book

Flat profile for compression:

Flat profile for decompression:

###### Text

Flat profile for compression:

Flat profile for decompression:

###### GIF

Flat profile for compression:

Flat profile for decompression: