Update semantics
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\usepackage{hyperref}
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\usepackage{xcolor}
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\definecolor{link_blue}{RGB}{0,0,97}
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\hypersetup{
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% bookmarks=true, % show bookmarks bar?
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% unicode=false, % non-Latin characters in Acrobat’s bookmarks
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% pdftoolbar=true, % show Acrobat’s toolbar?
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% pdfmenubar=true, % show Acrobat’s menu?
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% pdffitwindow=false, % window fit to page when opened
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% pdfstartview={FitH}, % fits the width of the page to the window
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% pdftitle={My title}, % title
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% pdfauthor={Author}, % author
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% pdfsubject={Subject}, % subject of the document
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% pdfcreator={Creator}, % creator of the document
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% pdfproducer={Producer}, % producer of the document
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% pdfkeywords={keyword1} {key2} {key3}, % list of keywords
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% pdfnewwindow=true, % links in new PDF window
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colorlinks=true, % false: boxed links; true: colored links
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linkcolor=link_blue, % color of internal links (change box color with linkbordercolor)
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citecolor=green, % color of links to bibliography
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filecolor=magenta, % color of file links
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urlcolor=link_blue % color of external links
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}
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@ -0,0 +1,63 @@
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\usepackage{listings}
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\usepackage{algorithmicx}
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\usepackage{algpseudocode}
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\usepackage{color}
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\usepackage{xcolor}
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\usepackage{courier}
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\definecolor{color_comment}{HTML}{2D6F19}
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\definecolor{color_linenum}{HTML}{9E9E9E}
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\definecolor{color_strings}{HTML}{D300F3}
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\lstset{ %
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% backgroundcolor=\color{white}, % choose the background color; you must add \usepackage{color} or \usepackage{xcolor}
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basicstyle=\footnotesize\ttfamily, % the size of the fonts that are used for the code
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breakatwhitespace=false, % sets if automatic breaks should only happen at whitespace
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breaklines=true, % sets automatic line breaking
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captionpos=b, % sets the caption-position to bottom
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commentstyle=\color{color_comment}, % comment style
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% deletekeywords={...}, % if you want to delete keywords from the given language
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% escapeinside={\%*}{*)}, % if you want to add LaTeX within your code
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extendedchars=true, % lets you use non-ASCII characters; for 8-bits encodings only, does not work with UTF-8
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frame=none, % adds a frame around the code
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keepspaces=true, % keeps spaces in text, useful for keeping indentation of code (possibly needs columns=flexible)
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keywordstyle=\color{blue}, % keyword style
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morekeywords={*,...}, % if you want to add more keywords to the set
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numbers=left, % where to put the line-numbers; possible values are (none, left, right)
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numbersep=5pt, % how far the line-numbers are from the code
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numberstyle=\tiny\color{color_linenum}, % the style that is used for the line-numbers
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rulecolor=\color{black}, % if not set, the frame-color may be changed on line-breaks within not-black text (e.g. comments (green here))
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showspaces=false, % show spaces everywhere adding particular underscores; it overrides 'showstringspaces'
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showstringspaces=false, % underline spaces within strings only
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showtabs=false, % show tabs within strings adding particular underscores
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stepnumber=1, % the step between two line-numbers. If it's 1, each line will be numbered
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stringstyle=\color{color_strings}, % string literal style
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tabsize=4, % sets default tabsize to 2 spaces
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% title=\lstname, % show the filename of files included with \lstinputlisting; also try caption instead of title
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% inputencoding=utf8/latin1 % To accept utf8 encoding
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}
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\lstset{literate=
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{á}{{\'a}}1 {é}{{\'e}}1 {í}{{\'i}}1 {ó}{{\'o}}1 {ú}{{\'u}}1
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{Á}{{\'A}}1 {É}{{\'E}}1 {Í}{{\'I}}1 {Ó}{{\'O}}1 {Ú}{{\'U}}1
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{à}{{\`a}}1 {è}{{\`e}}1 {ì}{{\`i}}1 {ò}{{\`o}}1 {ù}{{\`u}}1
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{À}{{\`A}}1 {È}{{\'E}}1 {Ì}{{\`I}}1 {Ò}{{\`O}}1 {Ù}{{\`U}}1
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{ä}{{\"a}}1 {ë}{{\"e}}1 {ï}{{\"i}}1 {ö}{{\"o}}1 {ü}{{\"u}}1
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{Ä}{{\"A}}1 {Ë}{{\"E}}1 {Ï}{{\"I}}1 {Ö}{{\"O}}1 {Ü}{{\"U}}1
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{â}{{\^a}}1 {ê}{{\^e}}1 {î}{{\^i}}1 {ô}{{\^o}}1 {û}{{\^u}}1
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{Â}{{\^A}}1 {Ê}{{\^E}}1 {Î}{{\^I}}1 {Ô}{{\^O}}1 {Û}{{\^U}}1
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{œ}{{\oe}}1 {Œ}{{\OE}}1 {æ}{{\ae}}1 {Æ}{{\AE}}1 {ß}{{\ss}}1
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{ű}{{\H{u}}}1 {Ű}{{\H{U}}}1 {ő}{{\H{o}}}1 {Ő}{{\H{O}}}1
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{ç}{{\c c}}1 {Ç}{{\c C}}1 {ø}{{\o}}1 {å}{{\r a}}1 {Å}{{\r A}}1
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{€}{{\EUR}}1 {£}{{\pounds}}1 {¬}{{$\lnot$}}1 {∞}{{$\infty$}}1
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}
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\newcommand{\true}{\lstinline$true$}
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\newcommand{\false}{\lstinline$false$}
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\newcommand{\lstbash}[1]{\lstinline[language=bash]$#1$}
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\newcommand{\lstocaml}[1]{\lstinline[language=Caml]$#1$}
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\newcommand{\lstcpp}[1]{\lstinline[language=C++]$#1$}
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\newcommand{\lstc}[1]{\lstinline[language=C]$#1$}
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\newcommand{\lstpython}[1]{\lstinline[language=python]$#1$}
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@ -11,6 +11,9 @@
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\usepackage{mathtools}
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\usepackage[utf8]{inputenc}
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\usepackage{my_listings}
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\usepackage{my_hyperref}
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\newcommand{\dwcfa}[1]{\texttt{DW\_CFA\_#1}}
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\newcommand{\reg}[1]{\%#1}
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@ -19,6 +22,7 @@
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\newcommand{\FDE}{\operatorname{FDE}}
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\newcommand{\dwrow}{\operatorname{Row}}
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\newcommand{\spexpr}{\mathbb{E}}
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\newcommand{\dwexpr}{\bar{\mathbb{E}}}
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\newcommand{\regs}{\mathbb{R}}
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\newcommand{\values}{\mathbb{V}}
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@ -28,6 +32,8 @@
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\newcommand{\intermedlang}{\mathcal{I}}
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\newcommand{\semI}[2]{{\left\llbracket{} #1 \right\rrbracket}^\intermedlang_{#2}}
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\newcommand{\semC}[1]{{\left\llbracket{} #1 \right\rrbracket}^{C}}
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\newcommand{\semR}[1]{{\left\llbracket{} #1 \right\rrbracket}^{R}}
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\newcommand{\rowstack}{\mathbb{S}}
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@ -36,6 +42,8 @@
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\newcommand{\contsem}[1]{\semI{d}{s}\left(#1\right)}
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\newcommand{\ehelf}{\texttt{EH\_ELF}}
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\begin{document}
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\maketitle
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@ -99,6 +107,8 @@ formats to handle various operands formatting, to optimize space).
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& \text{A DWARF row} \\
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\spexpr &:= \regs \times \mathbb{Z}
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& \text{A ``simple'' expression $\reg{reg} + offset$} \\
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\spexpr &:= \regs \times \mathbb{Z}
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& \text{A ``simple'' expression $\reg{reg} + offset$} \\
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\regs &:= \left\{0, 1, \ldots, \operatorname{NB\_REGS - 1} \right\}
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& \text{Machine registers} \\
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\values &:= \{\bot\} \cup \valaddr{\spexpr} \cup \valval{\spexpr}
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@ -188,6 +198,51 @@ $F\left[0 \ldots |F|-2\right] \extrarrow{reg} \bullet$.
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\section{From $\intermedlang$ to C}
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(Quite straightforward?)
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\textit{This only defines the semantics, with respect to standard C, of DWARF
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as interpreted by \ehelf\@. It is not implemented this way.}
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We now define $\semC{\bullet} : \DWARF \to C$.
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These semantics are to be interpreted in the following context~:
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\lstinputlisting[language=C]{src/c_context.c}
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Then, the function \lstc{unwind_frame}, given an instruction pointer and the
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state of the registers in the previous call frame, returns the state of
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registers after the current call frame is unwinded. In other words, assuming
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the C language is capable of formal operations, a call to
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\lstc{unwind_frame(ip, {reg_0, reg_1, ..., reg_N-1})} should return something
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equivalent to the corresponding DWARF row.
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The translation from $\intermedlang$ to C is defined as follows:
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\begin{itemize}
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\item $\semC{\varepsilon} =$ \\
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\begin{lstlisting}[language=C, mathescape=true]
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else {
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for(int reg=0; reg < NB_REGS; ++reg)
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new_ctx[reg] = $\semR{\bot}$;
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}
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\end{lstlisting}
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\item $\semC{(\text{loc}, \text{row}) \cdot t} = C\_code + \semC{t}$, where
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$C\_code$ is
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\begin{lstlisting}[language=C, mathescape=true]
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if(ip >= $loc$) {
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for(int reg=0; reg < NB_REGS; ++reg)
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new_ctx[reg] = $\semR{row[reg]}$;
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goto end_ifs; // Avoid if/else if problems
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}
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\end{lstlisting}
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\end{itemize}
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and $\semR{\bullet}$ is defined as
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\begin{align*}
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\semR{\bot} &= \text{\lstc{ERROR_VALUE}} \\
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\semR{\valaddr{\text{reg}, \text{offset}}} &=
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\text{\lstc{*(old_ctx[reg] + offset)}} \\
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\semR{\valval{\text{reg}, \text{offset}}} &=
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\text{\lstc{(old_ctx[reg] + offset)}} \\
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\end{align*}
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\end{document}
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#include <stdint.h>
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#include <stdlib.h>
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#include <assert.h>
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#define NB_REGS 32 /* put the number of registers of your platform here */
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typedef uintptr_t* regs_t; // Array of size at least NB_REGS
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regs_t unwind_frame(uintptr_t ip, regs_t old_ctx) {
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regs_t new_ctx = (regs_t) malloc(sizeof(uintptr_t) * NB_REGS);
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assert(new_ctx != NULL);
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// ===== INSERT GENERATED CODE HERE =====
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end_ifs:
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return new_ctx;
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}
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