From 66b3b16f044369fcf2d5917260b998c210c62db9 Mon Sep 17 00:00:00 2001 From: Marco Ammon Date: Tue, 11 Aug 2020 21:09:56 +0200 Subject: [PATCH] Steensgards Algorithmus zusammengefasst (VL-08) --- verfahren.pdf | Bin 190074 -> 192660 bytes verfahren.tex | 39 ++++++++++++++++++++++++++++++++++++++- 2 files changed, 38 insertions(+), 1 deletion(-) diff --git a/verfahren.pdf b/verfahren.pdf index c31b1d35cea18368976ad4d646af3c1f41ac2da6..8711c52d7d7429ed051fd12a5f5bb749d154b897 100644 GIT binary patch delta 47429 zcmV(?K-a(e%nOv^3y>uNHIv~*DSzczOLN;c5WeSE@JLQW6i!PDF{D=iEBASM`m>2m?1edmOjnttrfvBVqVTw{t zyct4JV`R75m6f+bF~#GE@P8m8A`_%i5yXNZiJOpKnRT|Q${TI>I-jpiUJi^5jbWs) zBF-3wh&bXRZ6b&YBN%LeKbN<@&y~%t*HN58G>{~Lzw`%J>gzaq_+yl2l79#_%Cg(GVJ2yl z$+K;do6PLNmK5J&3Exp3PfTt)PA(P5RqZ&#b+r=C!)My+x$EwAUA2Hu(7B9-3vK-u zzX{d0!4~L+bkGYjMT#kKR+~O+o*DFuLX3&_2?s1wh5(T`YacRGW)fII+A~9ZfI2t2 zbYFS++H9-oFeN}SK!5Um=840`E`o2iVF0QOC5rkj6Neq6&5pHQv4S1hYd{qu|8D@o 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\item Speichergraph: \begin{itemize} + \item Knoten: eine oder mehrere Speicherstellen + \item gerichtete Kante: \enquote{zeigt (möglicherweise) auf}-Beziehung, damit Alias: (*start, ziel) + \end{itemize} + \item approximiert Speichergraph: \begin{itemize} + \item Maximal eine abgehende Kante pro Knoten + \item Zusammenfassung mehrerer Speicherstellen, auf die Variable zeigen kann, zu einer Speicherstelle + \end{itemize} +\end{itemize}\begin{enumerate} + \item Einführung eines Knotens im Speichergraph pro Variable, wobei Kanten Zeiger repräsentieren + \item Fluss-ignorierendes, lineares Abarbeiten aller Anweisungen: \begin{itemize} + \item $a = \&b$: Kante zwischen $a$ und $b$ einfügen; sofern bereits Kante zwischen $a$ und $x$ existiert, rekursives Verschmelzen von $x$ und $b$ + \item $a = b$:\begin{itemize} + \item $b$ ist Zeiger: Verschmelzen der Ziele von $a$ und $b$, anschließend zeigen beide auf diesen Knoten + \item $b$ ist kein Zeiger bzw. noch nicht erkannt: Annotiere $b$ mit $(a:b)$ (Falls später Zeigerziel $y$ von $b$ entdeckt wird, muss Kante von $a$ nach $y$ ergänzt werden) + \end{itemize} + \item $a = *b$: \begin{itemize} + \item $b$, $*b$ haben bereits ausgehende Kanten: Kante zwischen $a$ und $**b$ ergänzen + \item sonst: analog zu $a = b$ mit adäquaten Annotationen (TODO: Übung) + \end{itemize} + \item $*a = b$: \begin{itemize} + \item $a$, $*a$ mit ausgehenden Kanten: rekursives Verschmelzen von $*b$ und $**a$ + \item sonst: TODO (Übung) + \end{itemize} + \item $a = b \oplus c$ mit $\oplus$ binärer Operation: \begin{itemize} + \item $a$, $b$, $c$ keine Zeiger: Annotation von $b$ und $c$ mit $(a:b)$ bzw. $(a:c)$ + \item $b$ oder $c$ Zeiger: Kante von $a$ nach $*b$ hinzufügen, $c$ mit $(a:c)$ annotieren + \end{itemize} + \item $x = p(y_1, \textellipsis, y_n)$: \begin{itemize} + \item ggf. Speichergraph für $p$ berechnen + \item Zuweisungsregeln für $x$ und alle $y_i$ verwenden + \end{itemize} + \item Funktionszeiger: Bei Verschmelzen auf Typen achten + \end{itemize} +\end{enumerate} + \section{Induktionsvarianten und schleifeninvarianter Code}