629 lines
20 KiB
TeX
629 lines
20 KiB
TeX
% vim: spell spelllang=en
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\documentclass[11pt,xcolor={usenames,dvipsnames}]{beamer}
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\usetheme{Warsaw}
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\usepackage[utf8]{inputenc}
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\usepackage[english]{babel}
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\usepackage[T1]{fontenc}
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\usepackage{amsmath}
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\usepackage{amsfonts}
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\usepackage{amssymb}
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\usepackage{booktabs}
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\usepackage{makecell}
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\usepackage{ifthen}
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\usepackage{colortbl}
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\usepackage{tabularx}
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\usepackage{pifont}
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\usepackage{multirow}
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\usepackage{texlib/my_listings}
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\usepackage{texlib/specific}
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\usepackage{texlib/common}
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\usepackage{texlib/todo}
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\usepackage{inconsolata}
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\lstset{basicstyle=\footnotesize\ttfamily}
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\renewcommand\theadalign{c}
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\renewcommand\theadfont{\scriptsize\bfseries}
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\setbeamertemplate{navigation symbols}{}
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\setbeamertemplate{headline}{}
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\newcommand{\thenalert}[1]{\only<1>{#1}\only<2>{\alert{#1}}}
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\newcommand{\slidecountline}{
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\ifthenelse{\theframenumber = 0}
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{}
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{\insertframenumber/\inserttotalframenumber}}
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\newcommand{\sectionline}{
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\ifthenelse{\thesection = 0}
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{}
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{\Roman{section}~-- \insertsection}}
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\newcommand{\cmark}{\color{OliveGreen}\ding{52}}
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\newcommand{\xmark}{\color{BrickRed}\ding{56}}
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\AtBeginSection{
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\begin{frame}
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\vfill
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\centering
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\begin{beamercolorbox}[sep=8pt,center,shadow=true,rounded=true]{title}
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\usebeamerfont{title}\insertsectionhead\par%
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\end{beamercolorbox}
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\vfill
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\end{frame}
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}
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\lstdefinelanguage{gdb}{
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morekeywords={gdb},
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sensitive=false,
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}
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\newcolumntype{b}{X}
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\newcolumntype{s}{>{\hsize=.43\hsize}X}
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\newcommand{\lstinl}
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{\lstinline[language=C, keepspaces=true, basicstyle=\ttfamily]}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\title[\sectionline] {Reliable and Fast DWARF-based Stack Unwinding}
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\author[\slidecountline]{\textbf{Théophile Bastian},\\
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\textbf{Stephen Kell}, \\
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\textbf{Francesco Zappa Nardelli}}
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\date{}
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%\subject{}
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%\logo{}
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\institute{ENS Paris, University of Kent, Inria}
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\begin{document}
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\begin{frame}
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\addtocounter{framenumber}{-1}
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\titlepage{}
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\vspace{-2em}
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\begin{center}
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\begin{align*}
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\text{Slides: } &\text{\todo{add URL for this PDF}} \\
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\end{align*}
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\end{center}
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\end{frame}
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\begin{frame}{~}
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\addtocounter{framenumber}{-1}
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\tableofcontents[hideallsubsections]
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{DWARF and stack unwinding data}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Introduction}
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\begin{frame}[fragile]{We often use stack unwinding!}
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\begin{columns}[c]
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\begin{column}{0.70\textwidth}
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\begin{lstlisting}[language=gdb, numbers=none, escapechar=|]
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Program received signal SIGSEGV.
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0x54625 in fct_b at segfault.c:5
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5 printf("%l\n", *b);
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|\pause| (gdb) backtrace
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#0 0x54625 in fct_b at segfault.c:5
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#1 0x54663 in fct_a at segfault.c:10
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#2 0x54674 in main at segfault.c:14
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|\pause| (gdb) frame 1
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#1 0x54663 in fct_a at segfault.c:10
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10 fct_b((int*) a);
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|\pause| (gdb) print a
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$1 = 84
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\end{lstlisting}
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\vspace{-1em}
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\pause{}
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\begin{center}
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\textbf{\Large How does it work?!}
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\end{center}
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\end{column}
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\begin{column}{0.35\textwidth}
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\pause{}
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\includegraphics[width=0.95\linewidth]{img/call_stack}
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\end{column}
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\end{columns}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Stack frames and unwinding}
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\begin{frame}{Call stack and registers}
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\begin{columns}[c]
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\begin{column}{0.55\textwidth}
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\begin{center}
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\large\bf
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How do we get the grandparent RA\@?
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\medskip
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Isn't it as trivial as \texttt{pop()}?
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\vspace{2em}
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\onslide<2>{We only have \reg{rsp} and \reg{rip}.}
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\end{center}
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\end{column}
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\begin{column}{0.45\textwidth}
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\includegraphics[width=0.95\linewidth]{img/call_stack}
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\end{column}
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\end{columns}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{DWARF tables}
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\newcolumntype{a}{>{\columncolor{RedOrange}}l}
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\begin{frame}{DWARF unwinding data}
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\vspace{2em}
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\tt \footnotesize
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\begin{tabular}{
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>{\columncolor{YellowGreen}}l
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>{\columncolor{Thistle}}l
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l l l l l l
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>{\columncolor{Apricot}}l}
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~LOC & CFA & rbx & rbp & r12 & r13 & r14 & r15 & ra \\
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0084950 & rsp+8 & u & u & u & u & u & u & c-8 \\
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0084952 & rsp+16 & u & u & u & u & u & c-16 & c-8 \\
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0084954 & rsp+24 & u & u & u & u & c-24 & c-16 & c-8 \\
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0084956 & rsp+32 & u & u & u & c-32 & c-24 & c-16 & c-8 \\
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0084958 & rsp+40 & u & u & c-40 & c-32 & c-24 & c-16 & c-8 \\
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0084959 & rsp+48 & u & c-48 & c-40 & c-32 & c-24 & c-16 & c-8 \\
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\rowcolor{Aquamarine} 008495a & rsp+56 & c-56 & c-48 & c-40 & c-32 & c-24 & c-16 & c-8 \\
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0084962 & rsp+64 & c-56 & c-48 & c-40 & c-32 & c-24 & c-16 & c-8 \\
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0084a19 & rsp+56 & c-56 & c-48 & c-40 & c-32 & c-24 & c-16 & c-8 \\
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0084a1d & rsp+48 & c-56 & c-48 & c-40 & c-32 & c-24 & c-16 & c-8 \\
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0084a1e & rsp+40 & c-56 & c-48 & c-40 & c-32 & c-24 & c-16 & c-8 \\
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0084a20 & rsp+32 & c-56 & c-48 & c-40 & c-32 & c-24 & c-16 & c-8 \\
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0084a22 & rsp+24 & c-56 & c-48 & c-40 & c-32 & c-24 & c-16 & c-8 \\
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0084a24 & rsp+16 & c-56 & c-48 & c-40 & c-32 & c-24 & c-16 & c-8 \\
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0084a26 & rsp+8 & c-56 & c-48 & c-40 & c-32 & c-24 & c-16 & c-8 \\
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0084a30 & rsp+64 & c-56 & c-48 & c-40 & c-32 & c-24 & c-16 & c-8 \\
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\end{tabular}
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\pause{}
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\vspace{-3cm}
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\hfill\includegraphics[height=3cm, angle=45, origin=c]{img/dwarf_logo}
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\hspace{-1cm}
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\end{frame}
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\begin{frame}[t, fragile]{The real DWARF}
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\begin{lstlisting}[numbers=none, language=]
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00009b30 48 009b34 FDE cie=0000 pc=0084950..0084b37
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DW_CFA_advance_loc: 2 to 0000000000084952
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DW_CFA_def_cfa_offset: 16
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DW_CFA_offset: r15 (r15) at cfa-16
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DW_CFA_advance_loc: 2 to 0000000000084954
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DW_CFA_def_cfa_offset: 24
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DW_CFA_offset: r14 (r14) at cfa-24
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DW_CFA_advance_loc: 2 to 0000000000084956
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DW_CFA_def_cfa_offset: 32
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DW_CFA_offset: r13 (r13) at cfa-32
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DW_CFA_advance_loc: 2 to 0000000000084958
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DW_CFA_def_cfa_offset: 40
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DW_CFA_offset: r12 (r12) at cfa-40
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DW_CFA_advance_loc: 1 to 0000000000084959
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[...]
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\end{lstlisting}
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\begin{itemize}
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\item[\textbf{$\longrightarrow$}] \textbf{\alert{constructed} on-demand
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by a \alert{Turing-complete bytecode}!}
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\end{itemize}
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\pause{}
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\vspace{-6.5cm}
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\begin{center}
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\bf \fontsize{8cm}{1cm}
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\colorbox{white}{\alert{Complex}} \\
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\colorbox{white}{\alert{\& slow!}}
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\end{center}
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\end{frame}
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\begin{frame}{Why does slow matter?}
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\begin{itemize}
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\item{} After all, we're talking about \alert{debugging procedures} ran
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by a \alert{human being} (slower than the machine).
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\ldots{}or are we?
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\end{itemize}
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\pause{}
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\begin{center}
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\textbf{\Large{}No!}
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\end{center}
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\begin{itemize}
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\pause{}\item{} Pretty much any \alert{program analysis tool}
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\pause{}\item{} \alert{Profiling} with polling profilers
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\pause{}\item{} \alert{Exception handling} in C++
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\end{itemize}
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\vspace{2em}
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\begin{center}
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\textbf{\Large{}Debug data is not only for debugging}
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\end{center}
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\vspace{1em}
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$\leadsto$ we might want \alert{an alternative time/space trade-off}
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\end{frame}
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\newcommand{\LinusMailOne}{
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``Sorry, but last time was too f\dots painful. The whole (and
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only) point of unwinders is to make debugging easy
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when a bug occurs. But \alert{the dwarf unwinder had bugs}
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itself, or \alert{our dwarf information had bugs}, and in either
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case it actually turned several trivial bugs into a \alert{total
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undebuggable hell}.''
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}
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\newcommand{\LinusMailTwo}{
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``If you can \alert{mathematically prove that the unwinder is
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correct} — even in the presence of bogus and actively
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incorrect unwinding information — and never ever
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follows a bad pointer, \alert{I’ll reconsider}.''
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}
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\newcommand{\LinusSource}{
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\hfill ---~Linus Torvalds, Kernel mailing list, 2012
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}
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\begin{frame}{A debugging hell: Linux kernel}
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\LinusMailOne{}
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\only<1-2>{
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\vspace{1em}
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\LinusSource{}
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}
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\vspace{1em}
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\only<2>{
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\begin{center}
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\Large\bf
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\alert{This is where we still are!}
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\end{center}
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}
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\only<3>{
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\LinusMailTwo{}
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\vspace{1em}
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\LinusSource{}
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}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Unwinding data as an abstract state}
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\newcommand{\tblrowval}[4]{#1 & #2 & \only<2->{#3} & \only<2->{#4} \\}
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\newcommand{\blknote}[1]
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{\begin{block}{}
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\centering\large
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#1
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\end{block}}
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\newcommand{\blklnote}[1]
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{\begin{block}{}
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\large
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#1
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\end{block}}
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\newcommand{\tblhl}{\rowcolor{Tan}}
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\begin{frame}{Working on an example}
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\newcommand{\firsttblrows}{
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\tblrowval{\hspace{-2ex}<{\bf foo}>:}{}{\textbf{CFA}}{\textbf{ra}}
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\rowonly<3>{\tblhl{}} \tblrowval{push}{\%r15}{rsp+8}{c-8}
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\rowonly<4>{\tblhl{}} \tblrowval{push}{\%r14}{rsp+16}{c-8}
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\rowonly<5>{\tblhl{}} \tblrowval{mov}{\$0x3,\%eax}{rsp+24}{c-8}
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\rowonly<6>{\tblhl{}} \tblrowval{push}{\%r13}{rsp+24}{c-8}
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\tblrowval{push}{\%r12}{rsp+32}{c-8}
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\tblrowval{push}{\%rbp}{rsp+40}{c-8}
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\tblrowval{push}{\%rbx}{rsp+48}{c-8}
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\tblrowval{sub}{\$0x68,\%rsp}{rsp+56}{c-8}
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}
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\only<-8>{
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\begin{table}
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\ttfamily\large
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\begin{tabularx}{0.9\linewidth}{
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l
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b
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>{\columncolor{SkyBlue}}s
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>{\columncolor{SkyBlue}}s
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}
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\firsttblrows{}%
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\tblrowval{add}{\$0x68,\%rsp}{rsp+160}{c-8}
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\tblrowval{pop}{\%rbx}{rsp+56}{c-8}
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\tblrowval{pop}{\%rbp}{rsp+48}{c-8}
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\end{tabularx}
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\end{table}
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\blknote{
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\centering
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\begin{overlayarea}{0.9\textwidth}{4.8ex}
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\only<3>{Upon function call, \alert{ra = *(\reg{rsp})} (ABI)}
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\only<4>{\texttt{push} decreases \reg{rsp} by 8: %
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\alert{ra = *(\reg{rsp} + 8)}}
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\only<5>{and again: %
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\alert{ra = *(\reg{rsp} + 16)}}
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\only<6>{This \texttt{mov} leaves \reg{rsp} untouched: %
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\alert{ra = *(\reg{rsp} + 16)}}
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\only<7>{The unwinding table can actually be seen as\\
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an \alert{abstract interpretation} of the code\ldots}
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\only<8>{\ldots and thus, for a given run, be
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\alert{re-computed from scratch}}
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\end{overlayarea}
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}
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}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Unwinding data synthesis from binaries}
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\begin{frame}{Why would synthesis be useful?}
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\begin{itemize}
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\item As said earlier, \alert{DWARF is complex}
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\item Some compilers \alert{do not generate it}: hard to \alert{debug}
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\& \alert{profile}.
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\item Think of \alert{JIT-compiled assembly} (eg. JVM)
|
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\item \ldots{}or even \alert{hand-written inlined assembly}!
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\begin{itemize}
|
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\item Painful enough to write for not bothering with DWARF
|
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\item May not even be known by the programmer, breaks gdb
|
||
\item May be wrong (remember Linus!)
|
||
\end{itemize}
|
||
\end{itemize}
|
||
\end{frame}
|
||
|
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\begin{frame}{What have we got so far?}
|
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We now want to \alert{synthesize unwinding data}. That means
|
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\alert{forgetting the blue part of the previous schemes}.
|
||
|
||
\begin{itemize}
|
||
\item Upon entering a function, we know (ABI)
|
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\[ \cfa = \reg{rsp} - 8
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\qquad \ra = \cfa + 8 \]
|
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\item For each instruction, we know \alert{how it changes \cfa}.
|
||
\item We assume \alert{\ra{} constant wrt. \cfa}.
|
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\begin{itemize}
|
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\item[$\leadsto$] only \cfa{} tracking matters (for unwinding)
|
||
\end{itemize}
|
||
\item We had a working strategy for a \alert{linear execution}
|
||
\item We still have to handle
|
||
\begin{itemize}
|
||
\item \alert{\cfa{} expression}
|
||
\item \alert{control flow graph}
|
||
\end{itemize}
|
||
\end{itemize}
|
||
\end{frame}
|
||
|
||
\begin{frame}{\cfa{} expression}
|
||
Two possibilities:
|
||
\begin{itemize}
|
||
\item Either we track \cfa{} wrt. \reg{rsp}
|
||
\begin{itemize}
|
||
\item and update it after each instruction if needed
|
||
\end{itemize}
|
||
\item Or \reg{rbp} is used as base pointer: easy
|
||
\end{itemize}
|
||
\end{frame}
|
||
|
||
\begin{frame}{Control flow graph}
|
||
\begin{columns}[c]
|
||
\column{0.4\textwidth}
|
||
\lstinputlisting[language=C]{src/cfg/cfg.c}
|
||
|
||
\column{0.30\textwidth}
|
||
\begin{figure}
|
||
\centering
|
||
\includegraphics[width=\textwidth]{src/cfg/cfg.png}
|
||
\end{figure}
|
||
\end{columns}
|
||
|
||
\begin{itemize}
|
||
\item \alert{Upon split} (eg. \texttt{X})\alert{:} nothing special,
|
||
propagate end state of X to child nodes A and B
|
||
\item \alert{Upon join} (eg. \texttt{while\_end})\alert{:} check
|
||
consistency of both input states
|
||
\begin{itemize}
|
||
\item If tricky, \texttt{gcc} will have used \reg{rbp}, even
|
||
with \texttt{-fomit-frame-pointer}.
|
||
\end{itemize}
|
||
\end{itemize}
|
||
|
||
\end{frame}
|
||
|
||
\begin{frame}{}
|
||
\vfill
|
||
\centering
|
||
\begin{beamercolorbox}[sep=8pt,center,shadow=true,rounded=true]{title}
|
||
\Large\bf
|
||
Demo time!
|
||
\end{beamercolorbox}
|
||
\vfill
|
||
\end{frame}
|
||
|
||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
\section{Unwinding data compilation}
|
||
|
||
\subsection{Compilation ahead-of-time}
|
||
|
||
\begin{frame}{Compilation overview}
|
||
\begin{itemize}
|
||
\item Compiled to \alert{C code}
|
||
\item C code then \alert{compiled to native binary} (gcc)
|
||
\begin{itemize}
|
||
\item[$\leadsto$] gcc optimisations for free
|
||
\end{itemize}
|
||
\item Compiled as \alert{separate \texttt{.so} files}, called \ehelfs{}
|
||
\bigskip{}
|
||
\item Morally a \alert{monolithic switch} on IPs
|
||
\item Each case contains assembly that computes a \alert{row of the
|
||
table}
|
||
\end{itemize}
|
||
\end{frame}
|
||
|
||
|
||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
\begin{frame}[shrink]{Compilation example: generated C}
|
||
\lstinputlisting[language=C]{src/fib7/fib7.eh_elf_basic.c}
|
||
|
||
\pause{}
|
||
\vspace{1em}
|
||
\begin{center}
|
||
The real code is optimised, but boils down to this.
|
||
\end{center}
|
||
\end{frame}
|
||
|
||
|
||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
|
||
\begin{frame}{Mostly plug-and-play: libunwind interface}
|
||
\begin{itemize}
|
||
\item \alert{libunwind}: \textit{de facto} standard library for
|
||
unwinding
|
||
\item Relies on DWARF
|
||
|
||
\bigskip{}
|
||
|
||
\item \texttt{libunwind-eh\_elf}: alternative implementation using
|
||
\ehelfs{}
|
||
|
||
\item[$\leadsto$] almost \alert{``relink-and-play''} for existing projects!
|
||
\end{itemize}
|
||
\end{frame}
|
||
|
||
|
||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
\subsection{Results}
|
||
|
||
\begin{frame}{Time performance}
|
||
\begin{columns}
|
||
\begin{column}{1.1\textwidth}
|
||
\begin{table}[h]
|
||
\centering
|
||
\begin{tabular}{l l r r r r r}
|
||
\toprule
|
||
& \thead{Unwinding method} & \thead{Frames \\ unwound}
|
||
& \thead{Tot. time \\ ($\mu s$)}
|
||
& \thead{Avg. \\ time / frame \\ ($ns$)}
|
||
& \thead{Time ratio} \\
|
||
\midrule
|
||
\midrule
|
||
|
||
\multirow{2}{*}{\rotatebox{90}{\textbf{\prog{Gzip}}~~}}
|
||
&\alert{\ehelfs{}}
|
||
& 331523 % Frames unwound
|
||
& 25930 % Total time
|
||
& 78 % Avg time
|
||
& 1
|
||
\\
|
||
& \prog{libunwind}, \alert{cached}
|
||
& 331523 % Frames unwound
|
||
& 403292 % Total time
|
||
& 1217 % Avg time
|
||
& \alert{15.6}
|
||
\\
|
||
&\prog{libunwind}, \alert{uncached}
|
||
& 331523 % Frames unwound
|
||
& 2197296 % Total time
|
||
& 6635 % Avg time
|
||
& \alert{84.7}
|
||
\\
|
||
\midrule
|
||
\multirow{2}{*}{\rotatebox{90}{\textbf{\prog{hackbench}}}}
|
||
& \alert{\ehelfs{}}
|
||
& 152297 % Frames unwound
|
||
& 12941 % Total time
|
||
& 84 % Avg time
|
||
& 1
|
||
\\
|
||
& \prog{libunwind}, \alert{cached}
|
||
& 152297 % Frames unwound
|
||
& 316907 % Total time
|
||
& 2076 % Avg time
|
||
& \alert{24.6}
|
||
\\
|
||
& \prog{libunwind}, \alert{uncached}
|
||
& 152297 % Frames unwound
|
||
& 982697 % Total time
|
||
& 6439 % Avg time
|
||
& \alert{76.3}\vspace{0.8em}
|
||
\\
|
||
\bottomrule
|
||
\end{tabular}
|
||
\end{table}
|
||
\end{column}
|
||
\end{columns}
|
||
\end{frame}
|
||
|
||
\begin{frame}{Space overhead}
|
||
\begin{table}[h]
|
||
\centering
|
||
\begin{tabular}{l r r r r}
|
||
\toprule
|
||
\thead{Shared object}
|
||
& \thead{Original \\ \lstinline{.eh\_frame}}
|
||
& \thead{Generated \\ \lstinline{eh_elf} \lstinline{.text}}
|
||
& \thead{\% of original \\ program size}
|
||
& \thead{Growth \\ factor} \\
|
||
\midrule
|
||
find & 21.3 KiB & 68.3 KiB & 46.63 & 3.21 \\
|
||
\hfill + libs & 196.6 KiB & 577.2 KiB & 19.75 & 2.94 \\
|
||
\hline
|
||
python3.7
|
||
& 160.0 B & 1.4 KiB & 355.98 & 8.33 \\
|
||
\hfill + libs
|
||
& 449.0 KiB & 1.1 MiB & 23.77 & 2.61 \\
|
||
\hline
|
||
gzip & 5.1 KiB & 10.9 KiB & 16.48 & 2.13 \\
|
||
\hfill + libs & 143.5 KiB & 413.1 KiB & 24.96 & 2.88 \\
|
||
\hline
|
||
hackbench
|
||
& 568.0 B & 3.2 KiB & 107.99 & 5.74 \\
|
||
\hfill + libs
|
||
& 150.4 KiB & 439.4 KiB & 26.60 & 2.92 \\
|
||
\hline
|
||
sqlite & 121.7 KiB & 382.8 KiB & 34.68 & 3.14 \\
|
||
\hfill + libs & 376.2 KiB & 1.1 MiB & 25.32 & 3.00 \\
|
||
\bottomrule
|
||
\end{tabular}
|
||
\end{table}
|
||
\end{frame}
|
||
|
||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
\section*{Conclusion}
|
||
\setcounter{section}{0}
|
||
|
||
\begin{frame}{A fragment of our article}
|
||
The original article \textbf{Reliable and Fast DWARF-based Stack Unwinding}
|
||
contains
|
||
|
||
\vspace{1em}
|
||
|
||
\begin{itemize}
|
||
\item{} DWARF unwinding tables validation;
|
||
\item{} DWARF unwinding tables synthesis;
|
||
\item{} DWARF-based unwinding speedup.
|
||
\end{itemize}
|
||
|
||
\vspace{1em}
|
||
|
||
\begin{center}
|
||
Come and chat if interested! \texttt{:)}
|
||
\end{center}
|
||
\end{frame}
|
||
|
||
\end{document}
|