\title{A4: List vs Vector}
\input{preamble.tex}

In this exercise I had the idea that I wanted to experiment with
co-routine generator for the random numbers but discovered
the \texttt{std::generator} is not supplied with my compiler.
Instead I found what seemed like a similar implementation here:
\texttt{https://en.cppreference.com/w/cpp/language/coroutines}, which
I have copied to the \texttt{generator.h} file for use in my program.

I am aware that the random number generator already kind-of works
similarly to a co-routine generator seen from the outside, so the
whole experiment is a bit pointless from a software design perspective.

For this exercise I also re-designed my measurement tool from the
previous assignments to better support re-use of data across
measurements.

And, finally, I made a class for storing and outputting measurement
points as octave/matlab programs for easier inclusion into the report.
This I put in its own file \texttt{octave.cc} with corresponding
header \texttt{octave.h}. It is by no means very clever, but made to
suit my needs for this assignment.

\bigskip

\noindent{}The main code for exercise is in the file
called \texttt{list\_vs\_vector.cc}

\bigskip

The random number generation for use in insertion I used the
co-routine as described above, inserting, while checking if the number
already exists.
For the ditto for removal indices, I used
a \texttt{uniform\_distribution} thereby being able to gradually
reduce the span as the container would be expected to shrink 1 in size
for each iteration.
Both random number generators were seeded with the iteration number
(each size, \texttt{N}, is being tested three times) to make sure the
three iterations use unique sets of numbers.

For the smaller sizes of \texttt{N} (the number of items to be
inserted/removed) i print out the numbers to verify their
correctness. These numbers can be seen in the log files in the zip
file.

The program has been compiled and executed with both a built-in int as
the value type of the three containers and a struct padding a single
int with chars up to 1k. The log files for the executions are
named \texttt{console.log} and \texttt{console-padding.log}
respectively.

\bigskip

\noindent{}For the insertion and removal two templated functions were
written:
\footnotesize\begin{lstlisting}[language=C++]
template<typename C, typename T>
void sorted_insert(C& container, T element)
{
	auto it = std::begin(container);
	while(it != std::end(container) && *it < element)
	{
		++it;
	}

	container.insert(it, element);
}

template<typename C>
void remove_index(C& container, int index)
{
	auto it = std::begin(container);
	for(int i = 0; i < index; ++i)
	{
		++it;
	}

	container.erase(it);
}
\end{lstlisting}\normalsize

With the exception of set insertion, these two functions are used
for all the timed container operations, ie. no clever stuff should be
going on in the index/iterator lookups.

\bigskip

In \textit{figure \ref{insert}} the insertion times for \texttt{int}s in the
three container types \texttt{std::vector}, \texttt{std::list}
and \texttt{std::set} can be seen.
I was expecting the \texttt{std::vector} to outperform the othr two
because of data locality, and this is indeed the case. I was however
surprised how much it outperformed them, but this might be because the
compiler could see through my ``slow'' iterator looping and convert
that into the more optimized \texttt{vec.begin() + n} random access
iterator lookup.
At the same time the bad performance of \texttt{std::list} puzzled
me. But it might be because the list has to allocate each of its
elements on the freestore, which, on the other hand,
the \texttt{std::set} also had to do. So I'm not really sure what is
going on there.

Similarly in \textit{figure \ref{remove}} the performance of the three
containers are compared when removing the \texttt{int}s again by
randomized index.
Again I was expecting the \texttt{std::vector} to outperform the other
two, but not as much as it did.
I was however expecting the \texttt{std::set} to be slightly slower
than the \texttt{std::list} because of the extra needed work for
rebalancing the tree.

\begin{figure}[!tbp]
  \makebox[\textwidth][c]{%
  \subfloat[Insert]{\scalebox{1.7}{\includegraphics[scale=0.35]{a4/insert.pdf}}\label{insert}}
  \quad
  \subfloat[Removal]{\scalebox{1.7}{\includegraphics[scale=0.35]{a4/remove.pdf}}\label{remove}}
  }
\caption{Plot of operations on the three container types using regular \texttt{int}s}
\end{figure}

\clearpage

To see how much impact the data locality has on the performance of the
three container types, the experiments are repeated with a much bigger
value type.
I decided to create a \texttt{struct}, \texttt{PaddedInt}, with the
needed member functions for it to be storable inside the three containers:
\footnotesize\begin{lstlisting}[language=C++]
struct PaddedInt
{
	PaddedInt(int i) : i(i) {}
	int operator=(int other)
	{
		i = other;
		return i;
	}

	bool operator<(int other) const
	{
		return i < other;
	}

	bool operator<(const PaddedInt& other) const
	{
		return i < other.i;
	}

	int i;
	char padding[1024 - sizeof(int)]{}; // pad up to 1k
};
\end{lstlisting}\normalsize
It adds padding to each stored item so that it ends up with a size of
1024 bytes.

\begin{figure}[!tbp]
  \makebox[\textwidth][c]{%
  \subfloat[Insert of padded int]{\scalebox{1.7}{\includegraphics[scale=0.35]{a4/insert-padded.pdf}}\label{insert-padded}}
  \quad
  \subfloat[Removal of padding int]{\scalebox{1.7}{\includegraphics[scale=0.35]{a4/remove-padded.pdf}}\label{remove-padded}}
  }
\caption{Plot of operations on the three container types using structure with and \texttt{int} and padding up to 1kb}
\end{figure}

With this configuration a decrease in the performance of
the \texttt{std::vector} is expected as opposed to
the \texttt{std::list} and \texttt{std::set} which only carry pointers
to their items.

\bigskip

Looking at \textit{figure \ref{insert-padded}} the performance of the
insertion indeed seem to have become a lot worse for
the \texttt{std::vector}. Looking at the absolute performance of
the \texttt{std::list} and comparing it
to \textit{figure \ref{insert}} it has become $\sim{}10\%$
slower. \texttt{std::set} on the other hand seem to be largely
unaffected by the increase in value type size. This is likely because of
its $O(log(n))$ lookup/insertion times, which means that it only have
to do a fraction of the number of fetches from the free-store compared
to the other two (the full data of
the \texttt{PaddedInt} \texttt{struct} is needed for each comparison).

Removal of the padded elements from the \texttt{std::list}
and \texttt{std::set} are expected to be unaffected by the increase if
value type size, since they both just store pointers, and because the
iterations used to find the index is not needing data from the value
type; only the next pointer is needed.
On the other hand, \texttt{std::vector} will have to do a lot copying
of data (the entire tail will have to be copied one index to the
left), when erasing an item in the middle, which amounts to a lot of
data.
As can be seen in \textit{figure \ref{remove-padded}}, as expected, the
performances of \texttt{std::list} and \texttt{std::set} are close to
the \texttt{int} counterparts. And, also as expected,
the \texttt{std::vector} is really being slowed down.

\end{document}
