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-402,11 +402,51 @@ \subsection{DFA-Ansatz zur intraprozeduralen, fluss-sensitiven may-Analyse nach Muchnick} \begin{itemize} \item Vorwärtsproblem mit minimalen Grundblöcken - \item Sprachabhängige lokale Flussfunktionen für unmittelbare Auswirkungen pro Instruktion (Sammler/Gatherer): \begin{itemize} - \item TODO (VL-07) + \item Sprachabhängige lokale Flussfunktionen für unmittelbare Auswirkungen pro Instruktion (Sammler/Gatherer), hier für C: \begin{itemize} + \item Programmpunkt $P$: Kante in KFG der minimalen Grundblöcke + \item $\mathit{stmt}(P)$: Instruktion an Quelle der $P$-Kante + \item o.B.d.A. Annahme, dass jeder Programmpunkt $P$ nur einen Vorgänger $P'$ besitzt (synthetisch für Vorverarbeitung erzeugen) + \item Speicherstelle des Datums $x$ an Punkt $P$ $\mathit{mem}_P(x)$ initialisieren auf \begin{itemize} + \item $\mathit{star}(o)$: Für $o$ statisch allozierter Speicherbereich + \item $\mathit{anon}$: Dynamisch allozierter Speicherbereich + \end{itemize} + \item $\mathit{any}$ als Menge aller Speicherbereiche + \item Notation für Funktionen des Aliaswissens:\begin{itemize} + \item $\mathit{ptr}_P(x)$: Menge der Speicherstellen, auf die $x$ an $P$ zeigen kann + \item $\mathit{ref}_P(x)$: Menge der Speicherstellen, die an $P$ von $x$ über beliebig viele Derefenzierungen erreicht werden können + \item $\mathit{ovr}_P(x)$: Menge der Speicherstellen, die $x$ an $P$ überdecken kann + \end{itemize} + \item Flussfunktionen:\begin{itemize} + \item \texttt{x = \&a}: $\mathit{ptr}_P(x) = \lbrace\mathit{mem}_P(a)\rbrace = \lbrace\mathit{mem}_{P'}(a)\rbrace$ + \item \texttt{x = y}: \begin{equation*} + \mathit{ptr}_P(x) = \mathit{ptr}_P(y) = \begin{cases*} + \lbrace \mathit{mem}_0(*y)\rbrace & falls $P' = 0$\\ + \mathit{ptr}_{P'}(y) & sonst + \end{cases*} + \end{equation*} + \item \texttt{*x = a}: $\mathit{ptr}_P(x) = \mathit{ptr}_{P'}(x)$, zusätzlich wenn \texttt{*x} Zeiger $\mathit{ptr}_P(*x) = \mathit{ptr}_{P'}(*x) \cup \mathit{ptr}_{P'}(a)$ + \item \texttt{f(...)}: \begin{itemize} + \item $G$: Menge der global sichtbaren Zeiger + \item $L$: Menge der lokalen Variablen im Aufrufer, deren Adresse berechnet wurde + \item $\forall x \in G \cup L:\, \mathit{ptr}_P(x) = \left(\cup_{g \in (G \cup \mathit{mem}(G))} \mathit{ref}_{P'}(g)\right) \cup \left(\cup_{l\in L} \mathit{ref}_{P'}(l)\right)$ + \end{itemize} + \end{itemize} \end{itemize} \item Sprachunabhängiger Fixpunktpunktalgorithmus (Verbreiter/Propagator): \begin{itemize} - \item TODO (VL-07) + \item Initialisierung aller Zeigervariablen $x$ mit \begin{equation*} + \mathit{Ptr}(P, x) = \begin{cases*} + \emptyset & falls $P = 0$ und $x$ ist lokale Variable\\ + \mathit{any} & falls $P = 0$ und $x$ ist globale Variable\\ + \lbrace \mathit{mem}_0(*x)\rbrace & falls $P = 0$ und $x$ ist Parameter\\ + \emptyset & sonst + \end{cases*} + \end{equation*} + \item Berechnung des Aliaswissens:\begin{equation*} + \mathit{Ptr}(P, x) = \begin{cases*} + \mathit{ptr}_P(x) & falls $\mathit{stmt}(P)$ Zeiger $x$ beeinflusst\\ + \mathit{Ptr}(P',x) & sonst + \end{cases*} + \end{equation*} \end{itemize} \end{itemize}