\documentclass{article}
\usepackage[margin=1in]{geometry}
\usepackage[skip=0.2\baselineskip]{caption}
\usepackage{longtable}
\usepackage{booktabs}
\usepackage{graphicx}
\title{High Performance Computer Architecture Final Project}
\author{Danila Fedorin}

\begin{document}
\maketitle
\section*{Part 1: Address Prediction Benchmarks}
In this part, the \emph{Taken}, \emph{Not Taken},
\emph{Bimodal}, \emph{2-Level} and \emph{Combined} branch
predictors were run against three benchmarks. The results
are recorded in Figure \ref{fig:ap1}. Figure \ref{fig:ap1graph}
provides a bar chart of this data.
Results are grouped by benchmark to make it easier to compare
various branch prediction algorithms.

\begin{figure}[h]
\begin{longtable}[]{@{}llllll@{}}
\toprule
Benchkmark & Taken & Not Taken & Bimod & 2 level &
Combined\tabularnewline
\midrule
\endhead
Anagram & .3126 & .3126 & .9613 & .8717 & .9742\tabularnewline
GCC & .4049 & .4049 & .8661 & .7668 & .8793\tabularnewline
Go & .3782 & .3782 & .7822 & .6768 & .7906\tabularnewline
\bottomrule
\end{longtable}
\caption{Address prediction rates of various predictors}
\label{fig:ap1}
\end{figure}

\begin{figure}[h]
    \begin{center}
        \includegraphics[width=0.65\linewidth]{ap1.png}
    \end{center}
    \caption{Address prediction rates by benchmark}
    \label{fig:ap1graph}
\end{figure}

As expected, the two stateless predictors, \emph{Taken}
and \emph{Not Taken}, perform significantly worse than the
others. These predictors do not keep track of the behavior
of various branches, and thus have limited ability
to predict the direction of a branch. Out of the stateful
predictors, the \emph{2-level} predictor seems to perform the worst.
Unsurprisingly, the \emph{Combined} predictor, which is
a combination of the other two stateful predictors, performs
better than its constituents, since it's able to switch
to a better-performing predictor as needed.

\section*{Part 2: IPC Benchmarks}
In this section, we present the IPC results from the previously listed
predictors. Figure \ref{fig:ipc} contains the collected
data, and Figure \ref{fig:ipcgraph} is a bar chart of
that data.

\begin{figure}[h]
\begin{longtable}[]{@{}llllll@{}}
\toprule
Benchkmark & Taken & Not Taken & Bimod & 2 level &
Combined\tabularnewline
\midrule
\endhead
Anagram & 1.0473 & 1.0396 & 2.1871 & 1.8826 & 2.2487\tabularnewline
GCC & 0.7878 & 0.7722 & 1.2343 & 1.1148 & 1.2598\tabularnewline
Go & 0.9512 & 0.9412 & 1.3212 & 1.2035 & 1.3393\tabularnewline
\bottomrule
\end{longtable}
\caption{IPC by benchmark}
\label{fig:ipc}
\end{figure}

\begin{figure}[h]
    \begin{center}
        \includegraphics[width=0.65\linewidth]{ipc.png}
    \end{center}
    \caption{IPC by benchmark}
    \label{fig:ipcgraph}
\end{figure}

Once again, the stateless predictors perform significantly
worse than the stateful predictors. Also, \emph{Taken}
performs better than \emph{Not Taken}. This is likely
because most of the given programs have loops, in which
the conditional branch is taken many times while the loop
is iterating, and then once when the loop terminates. Predicting
``not taken'' in this case would lead to many mispredictions.

Once again, the \emph{Bimodal} predictor performs better than
the \emph{2-Level} predictor, and both are outperform by
\emph{Combined}, which leverages the two at the same time.

\section*{Part 3 - Bimodal Exploration}
In this section, the \emph{Bimodal} branch predictor is further
analyzed by varying the size of the BTB. BTB sizes range from
256 to 4096. The data collected from this analysis is shown
in figure \ref{fig:ap2}. As usual, the data is shown as
a bar graph in figure \ref{fig:ap2graph}.

\begin{figure}[h]
\begin{longtable}[]{@{}llllll@{}}
\toprule
Benchkmark & 256 & 512 & 1024 & 2048 & 4096\tabularnewline
\midrule
\endhead
Anagram & .9606 & .9609 & .9612 & .9613 & .9613\tabularnewline
GCC & .8158 & .8371 & .8554 & .8661 & .8726\tabularnewline
Go & .7430 & .7610 & .7731 & .7822 & .7885\tabularnewline
\bottomrule
\end{longtable}
\caption{Bimodal address prediction rates by benchmark}
\label{fig:ap2}
\end{figure}

\pagebreak

\begin{figure}[h]
    \begin{center}
        \includegraphics[width=0.65\linewidth]{ap2.png}
    \end{center}
    \caption{IPC by benchmark}
    \label{fig:ap2graph}
\end{figure}

As expected, increasing the BTB size for the Bimodal
predictor seems to improve its performance. The exception
appears to be anagram, where the changes to performance
are small enough to be unnoticable in the visualization.

\section*{Part 4 - Combined Branch Predictor Explanation}
It appears as though the combined branch predictor works
by considering the decisions of both a 2-level and a bimodal 
branch predictor. To decide which predictor to listen
to, the combined predictor uses a third predictor, named \texttt{meta}
in the code. The \texttt{meta} predictor appears to be another bimodal
predictor, but instead of deciding whether a branch is taken or not
taken, it decides whether to use the two-level or the bimodal predictor
to determine the branch outcome. If \texttt{meta} chooses a predictor
that ends up being wrong, while the other predictor ends up right,
\texttt{meta}'s 2-bit counter is updated to favor the correct predictor.

Because \texttt{meta} is implemented as a 2-bit predictor, it can
tolerate at most one use of the wrong branch predictor before
switching to the other (if the current predictor is "strongly"
predicted).

\section*{Part 5 - 3-Bit Branch Predictor}
For this part, I modified the SimpleScalar codebase to add
a 3-bit branch predictor. The code will be included with this
report, but not in this document. After implementing
this predictor, I simulated it with the same BTB sizes
as the previous extended simulations of the Bimodal (2-bit)
predictor. Figure \ref{fig:ap3} contains this data,
and Figure \ref{fig:ap3graph} contains the visualization
of that data.

\begin{figure}[h]
\begin{longtable}[]{@{}llllll@{}}
\toprule
Benchkmark & 256 & 512 & 1024 & 2048 & 4096\tabularnewline
\midrule
\endhead
Anagram & .9610 & .9612 & .9615 & .9616 & .9616\tabularnewline
GCC & .8192 & .8385 & .8554 & .8656 & .8728\tabularnewline
Go & .7507 & .7680 & .7799 & .7897 & .7966\tabularnewline
\bottomrule
\end{longtable}
\caption{3-Bit address prediction rates}
\label{fig:ap3}
\end{figure}

\begin{figure}[h]
    \begin{center}
        \includegraphics[width=0.65\linewidth]{ap3.png}
    \end{center}
    \caption{3-Bit address prediction rates}
    \label{fig:ap3graph}
\end{figure}

As with the bimodal branch predictor, the 3-bit predictor
benefits from larger BTB sizes in the Go and GCC benchmarks,
but seems to remain very consistent in the Anagram benchmark.
The differences between this predictor and the related bimodal
predictor are hard to see in this diagram.

To better compare
the two predictors, I computed the percent improvement to
address prediction rates of the 3-bit branch predictor
relative to the bimodal one. Figure \ref{fig:2v3} displays
this information. From this figure, it appears as though
the 3-bit predictor performs better than the bimodal one
in most cases. However, it does perform slightly worse
with a 2048-sized BTB in the GCC benchmark.

The Go benchmark sees the most improvement (around 1\%).
A 3-bit predictor performs better when branches generally
follow the same direction, except for occasional groups
in the other direction. If the Go benchmark implements
the Chinese game of the same name, it's possible that the
program behaves very much in this manner. For instance,
if the program is scanning the board to find groups
of ``dead'' pieces, starting at a recently placed piece,
it will likely find pieces nearby, but occasionally run
into empty spaces like ``eyes''. If the benchmark implements
a Go AI, I'm not sure how it would behave computationally,
but perhaps it also follows the same pattern.

\begin{figure}[h]
    \begin{center}
        \includegraphics[width=0.65\linewidth]{2v3.png}
    \end{center}
    \caption{Percent improvement of 3-bit predictor over the bimodal predictor.}
    \label{fig:2v3}
\end{figure}

\end{document}