\section{\staticdeps: static extraction of memory-carried dependencies}

\begin{frame}
    \todo{}
    \begin{itemize}
    \item Dependency through registers: easy
    \item Loop-carried: still fine
    \item Through memory: indirections, arithmetics, …
    \item Loop-carried: ROB is finite and small-ish
    \item Requires comparison of arbitrary formal expressions
    \item Use randomness as a kind of hash table instead
    \end{itemize}
\end{frame}

\begin{frame}{The \staticdeps{} algorithm}
    \begin{itemize}
        \item \alert{Unroll} kernel until $\card{\kerK} \geq \card{\text{ROB}} +
            \card{\kerK_0}$
        \item \alert{Simulate} execution
        \item Unknown value (reg./mem.)? \alert{Sample} uniformly in $0\ldots2^{64}-1$
            (\alert{``fresh''})
        \item \alert{Compute arithmetics} normally (overflow is fine)
        \item Float or unknown operands $\leadsto \alert{\bot}$
        \item Upon write, remember from which instruction
        \item Upon read, if writer known, \alert{generate dependency}
    \end{itemize}
\end{frame}

\begin{frame}[fragile]{An example: memoized Fibonacci sequence}
    \begin{minipage}[t]{0.46\textwidth}
\begin{lstlisting}[language=C]
int fibo(int* F, int n) {
    for(int i=2; i <= n; ++i) {
        F[i] = F[i-1] + F[i-2];
    }
    return F[n];
}
\end{lstlisting}
    \end{minipage}\hfill
    \begin{minipage}[t]{0.46\textwidth}
\begin{lstlisting}[language={[x86masm]Assembler}]
0:   mov    (%rax),%edx
1:   add    0x4(%rax),%edx
2:   mov    %edx,0x8(%rax)
3:   add    $0x4,%rax
4:   cmp    %rcx,%rax
5:   jne    0
\end{lstlisting}
    \end{minipage}
\end{frame}

\begin{frame}
    \newcommand{\unk}{{\color{gray}?}}
    \newcommand{\h}{\cellcolor[HTML]{D0ECFF}}
    \newcommand{\w}{\cellcolor[HTML]{d6bf86}}
    \centering
        \footnotesize
    \begin{tabular}{r c c c c c c c c c c c c c c}
        \toprule
        \textbf{Before}
            & [0,0] & [0,1] & [0,2] & [0,3] & [0,4] & [0,5]
            & & [1,1] & [1,2] & [1,3]
            & & [2,1] & [2,2] & [2,3] \\
        \midrule
        \textbf{Regs} & & & & & & & & & &\\
        \reg{rax}    & \unk & 100   & 100 & 100 & 104 & 104 && 104 & 104 & 104 && 108 & 108 & 108 \\
        \reg{edx}    & \unk & 200   & 376 & 376 & 376 & 376 && 176 & 552 & 552 && 376 & 928 & 928 \\
        \reg{rcx}    & \unk & \unk  & \unk& \unk& \unk&  42 &&  42 &  42 &  42 &&  42 &  42 &  42 \\
        \midrule
        \textbf{Mem} & & & & & & & & & &\\
        \texttt{100} & \unk & 200\h& 200  & 200  & 200 & 200 && 200  & 200  & 200  && 200  & 200  & 200  \\
        \texttt{104} & \unk & \unk & 176\h& 176  & 176 & 176 && 176\h& 176  & 176  && 176  & 176  & 176  \\
        \texttt{108} & \unk & \unk & \unk & 376\w& 376 & 376 && 376  & 376\h& 376  && 376\h& 376  & 376  \\
        \texttt{112} & \unk & \unk & \unk & \unk & \unk& \unk&& \unk & \unk & 552\w&& 552  & 552\h& 552  \\
        \texttt{116} & \unk & \unk & \unk & \unk & \unk& \unk&& \unk & \unk & \unk && \unk & \unk & 928\w\\
        %\texttt{116} & \unk & \unk& \unk& \unk& \unk& \unk& & & \\
        \bottomrule
    \end{tabular}
    \let\unk\unefined
    \let\h\unefined
    \let\w\unefined
\end{frame}