\section{A frontend model for the Cortex A72}

\begin{frame}{The Cortex A72}
    \begin{itemize}
        \item{} ARM
        \item{} CPU of the Raspberry Pi 4: easily available
            \medskip{}
        \item{} ARM CPUs not usually modeled!
        \item{} Backend modeled by \palmed{}
    \end{itemize}
\end{frame}

%\begin{frame}
%    \centering
%    \includegraphics[width=0.9\textwidth]{A72_pipeline_diagram.svg}
%    \todo{Dispatch queues}
%\end{frame}

\begin{frame}{Manual model}
    \begin{itemize}
        \item Goal: manually craft a frontend model
        \item Try to follow methods that can be automated
        \item Propose a parametric model for future works, leaving question
            marks on some sections
    \end{itemize}
\end{frame}

\begin{frame}{Proposed parametric model}
    \vfill
    \centering
    \begin{minipage}[t][0.7\textheight][c]{0.53\textwidth}
        \centering
        Globally,
        \vfill
        \includegraphics[width=\textwidth]{parametric_model-frontend.svg}
        \vfill~  % I hate LaTeX
    \end{minipage}
    \hfill\vrule\hfill
    \begin{minipage}[t][0.7\textheight][c]{0.43\textwidth}
        \centering
        For each instruction,
        \vfill
        \includegraphics[width=\textwidth]{parametric_model-insn.svg}
        \vfill~
    \end{minipage}

    \vfill
    In {\color{red}\textbf{red}}, parameters of the model.
\end{frame}

\begin{frame}{Counting \uops{}}
    For an instruction $i$, denote \alert{$\mucount{i}$} its number of \uops{}.
    \begin{itemize}
        \item{} For $k \in \nat$, construct (if possible) $\kerK_k$ a kernel:
            \begin{itemize}
                \item instruction $i$ + $k$ ``simple'' instructions (one \uop)
                \item frontend-bound:
                    \[
                        \cyc{\kerK_k} = \dfrac{k + \mucount{i}}{3}
                    \]
            \end{itemize}
        \item{} For well-chosen $k_0$, we should have
            \[
                \cyc{\kerK_{k_0}} + \sfrac{1}{3} = \cyc{\kerK_{k_0+1}}
            \]
        \item{} Measure to verify
            \bigskip
        \item{} If so, \textbf{\[
                \mucount{i} = 3 \cyc{\kerK_{k_0}} - k_0
        \]}

    \end{itemize}
\end{frame}

\begin{frame}{Evaluation: comparison to bare \palmed}
    \begin{itemize}
        \item Add a frontend to \palmed{}:
            \[
                \cyc{\kerK}_{\text{pred.}} = \max(\texttt{palmed}(\kerK), \texttt{frontend}(\kerK))
            \]
        \item Reuse evaluation suite of \palmed{}: SPEC CPU 2017 + Polybench
        \item Compare to \llvmmca{}
    \end{itemize}
\end{frame}

\begin{frame}{Results}
    \centering
    \begin{tabular}{l l c r r r r r}
        \toprule
        & & & \multirow{2}{*}{\llvmmca{}} & \multicolumn{3}{c}{\palmed{} with
        frontend\ldots} \\
        & & & & none & linear & disp.\ queues \\
        \midrule{}
        \multirow{3}{*}{SPEC} & Cov. & (\%)  & 100.00 & \na{} & 97.21 & 97.16 \\
                              & Err. & (\%)  & 9.0   & 20.1 & 6.2 & 4.6 \\
                              & $\ktau$ & (1)& 0.83  & 0.88 & 0.91 & 0.93 \\
        \midrule
        \multirow{3}{*}{Polybench} & Cov. & (\%)  & 100.00& \na{} & 99.33 & 99.33 \\
                                   & Err. & (\%)  & 13.9 & 12.6 & 8.1 & 8.0 \\
                                   & $\ktau$ & (1)& 0.47 & 0.82 & 0.88 & 0.90 \\
        \bottomrule
    \end{tabular}
\end{frame}

\begin{frame}{Limitations}
    \begin{itemize}
        \item Parts of this model were entirely manually solved (\eg{} \# of
            dispatch queues)
        \item Evaluation based on \palmed{} suite: biased
        \item Must be tested on other architectures!
    \end{itemize}
\end{frame}