[pypy-commit] extradoc extradoc: first draft of the talk

cfbolz noreply at buildbot.pypy.org
Sat Jul 23 23:12:10 CEST 2011


Author: Carl Friedrich Bolz <cfbolz at gmx.de>
Branch: extradoc
Changeset: r3838:698e19195980
Date: 2011-07-23 23:11 +0200
http://bitbucket.org/pypy/extradoc/changeset/698e19195980/

Log:	first draft of the talk

diff --git a/talk/icooolps2011/talk/figures/bench.pdf b/talk/icooolps2011/talk/figures/bench.pdf
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diff --git a/talk/icooolps2011/talk/talk.tex b/talk/icooolps2011/talk/talk.tex
new file mode 100644
--- /dev/null
+++ b/talk/icooolps2011/talk/talk.tex
@@ -0,0 +1,577 @@
+\documentclass[utf8x]{beamer}
+
+% This file is a solution template for:
+
+% - Talk at a conference/colloquium.
+% - Talk length is about 20min.
+% - Style is ornate.
+
+\mode<presentation>
+{
+  \usetheme{Warsaw}
+  % or ...
+
+  %\setbeamercovered{transparent}
+  % or whatever (possibly just delete it)
+}
+
+
+\usepackage[english]{babel}
+\usepackage{listings}
+\usepackage{fancyvrb}
+\usepackage{ulem}
+\usepackage{color}
+\usepackage{alltt}
+
+\usepackage[utf8x]{inputenc}
+
+\input{pygments}
+
+\newcommand\redsout[1]{{\color{red}\sout{\hbox{\color{black}{#1}}}}}
+\newcommand{\noop}{}
+
+% or whatever
+
+% Or whatever. Note that the encoding and the font should match. If T1
+% does not look nice, try deleting the line with the fontenc.
+
+
+\title[Runtime Feedback in a Meta-Tracing JIT]{Runtime Feedback in a Meta-Tracing JIT for Efficient Dynamic Languages}
+
+\author[Carl Friedrich Bolz et. al.]{\emph{Carl Friedrich Bolz}\inst{1} \and Antonio Cuni\inst{3} \and Maciej Fija&#322;kowski\inst{2} \and Michael Leuschel\inst{1} \and Samuele Pedroni\inst{3} \and Armin Rigo\inst{1}}
+% - Give the names in the same order as the appear in the paper.
+% - Use the \inst{?} command only if the authors have different
+%   affiliation.
+
+\institute[Heinrich-Heine-Universit&#228;t D&#252;sseldorf]
+{$^1$Heinrich-Heine-Universit&#228;t D&#252;sseldorf, STUPS Group, Germany \and
+
+ $^2$merlinux GmbH, Hildesheim, Germany \and
+
+ $^3$Open End, G&#246;teborg, Sweden \and
+}
+
+\date{ICOOOLPS 2011, July 26, 2011}
+% - Either use conference name or its abbreviation.
+% - Not really informative to the audience, more for people (including
+%   yourself) who are reading the slides online
+
+
+% If you have a file called "university-logo-filename.xxx", where xxx
+% is a graphic format that can be processed by latex or pdflatex,
+% resp., then you can add a logo as follows:
+
+
+
+
+% Delete this, if you do not want the table of contents to pop up at
+% the beginning of each subsection:
+%\AtBeginSubsection[]
+%{
+%  \begin{frame}<beamer>
+%    \frametitle{Outline}
+%    \tableofcontents[currentsection,currentsubsection]
+%  \end{frame}
+%}
+
+
+% If you wish to uncover everything in a step-wise fashion, uncomment
+% the following command: 
+
+%\beamerdefaultoverlayspecification{<+->}
+
+
+\begin{document}
+
+\begin{frame}
+  \titlepage
+\end{frame}
+
+\begin{frame}
+  \frametitle{Good JIT Compilers for Dynamic Languages are Hard}
+  \begin{itemize}
+      \item implementing the object model well is crucial
+      \item recent languages like Python, Ruby, JS have complex core semantics
+      \item many corner cases, even hard to interpret correctly
+      \pause
+      \item to get efficiency, the correct fast path through the tree of implementations must be generated XXX
+      \item feedback of runtime information to the compiler is necessary
+      \item correct exploitation of this information in the compiler
+  \end{itemize}
+  \pause
+  \begin{block}{Problems}
+      \begin{enumerate}
+          \item implement all corner-cases of semantics correctly
+          \item ... and the common cases efficiently
+          \item feed back and exploit runtime information
+      \end{enumerate}
+  \end{block}
+\end{frame}
+
+\begin{frame}
+  \frametitle{A Tracing JIT}
+  \includegraphics[scale=0.5]{figures/trace01.pdf}
+\end{frame}
+
+\begin{frame}
+  \frametitle{A Tracing JIT}
+  \includegraphics[scale=0.5]{figures/trace02.pdf}
+\end{frame}
+
+\begin{frame}
+  \frametitle{A Tracing JIT}
+  \includegraphics[scale=0.5]{figures/trace03.pdf}
+\end{frame}
+
+\begin{frame}
+  \frametitle{A Tracing JIT}
+  \includegraphics[scale=0.5]{figures/trace04.pdf}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Tracing JITs}
+  Advantages:
+  \begin{itemize}
+      \item can be added to existing VM
+      \item interpreter does a lot of work
+      \item can fall back to interpreter for uncommon paths
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Granularity Problems}
+  \begin{itemize}
+      \item if the tracer records bytecode, not enough information is there
+      \item many dynamic languages have bytecodes that contain complex logic
+      \item need to expand the bytecode in the trace into something more explicit
+      \item this duplicates the lanuage semantics in the tracer/optimizer
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Example: Attribute Reads in Python}
+  What happens when an attribute \texttt{x.m} is read? (simplified)
+  \begin{itemize}
+      \item check for \texttt{x.\_\_getattribute\_\_}, if there, call it
+      \pause
+      \item look for the attribute in the object's dictionary, if it's there, return it
+      \pause
+      \item walk up the MRO and look in each class' dictionary for the attribute
+      \pause
+      \item if the attribute is found, call its \texttt{\_\_get\_\_} attribute and return the result
+      \pause
+      \item if the attribute is not found, look for \texttt{x.\_\_getattr\_\_}, if there, call it
+      \pause
+      \item raise an \texttt{AttributeError}
+  \end{itemize}
+  \pause
+  all this is one bytecode
+\end{frame}
+
+\begin{frame}
+  \frametitle{Idea of Meta-Tracing}
+  \includegraphics[scale=0.5]{figures/trace05.pdf}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Meta-Tracing}
+  \includegraphics[scale=0.5]{figures/metatrace01.pdf}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Meta-Tracing JITs}
+  \begin{block}{Advantages:}
+    \begin{itemize}
+        \item semantics is always like that of the interpreter
+        \item trace fully contains language semantics
+        \item meta-tracers can be reused for various interpreters
+    \end{itemize}
+  \end{block}
+  \pause
+  a few meta-tracing systems have been built:
+  \begin{itemize}
+      \item Sullivan et.al. describe a meta-tracer using the Dynamo RIO system
+      \item Yermolovich et.al. run a Lua implementation on top of a tracing JS implementation
+      \item SPUR is a tracing JIT for CLR bytecodes, which is used to speed up a JS implementation in C\#
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{PyPy}
+  A general environment for implementing dynamic languages
+  \pause
+  \begin{block}{Approach}
+      \begin{itemize}
+          \item write an interpreter for the language in RPython
+          \item compilable to an efficient C-based VM
+          \pause
+          \item (RPython is a restricted subset of Python)
+      \end{itemize}
+  \end{block}
+  \pause
+  \begin{block}{PyPy's Meta-Tracing JIT}
+      \begin{itemize}
+          \item PyPy contains a meta-tracing JIT for interpreters in RPython
+          \item needs a few source-code hints (or annotations) in the interpreter
+          \item powerful general optimizations
+      \end{itemize}
+  \end{block}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Runtime Feedback}
+  Problems of Naive Meta-Tracing:
+  \begin{itemize}
+      \item no runtime feedback of user-level types
+      \item tracer does not know about invariants in the interpreter
+  \end{itemize}
+  \pause
+  \begin{block}{Proposed Solutions}
+      \begin{itemize}
+          \item introduce \textit{hints} that the interpreter-author can use
+          \item hints are annotation in the interpreter
+          \item they give information to the meta-tracer
+          \pause
+          \item two hints presented here
+          \item one to induce runtime feedback of arbitrary information
+          \item the second one to influence constant folding
+      \end{itemize}
+  \end{block}
+\end{frame}
+
+
+\begin{frame}
+  \frametitle{Example: Instances with Maps}
+  \includegraphics[scale=0.5]{figures/map01.pdf}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Example: Instances with Maps}
+  \includegraphics[scale=0.5]{figures/map02.pdf}
+\end{frame}
+
+\begin{frame}[containsverbatim]
+\frametitle{Map Implementation}
+
+\begin{Verbatim}[commandchars=\\\{\}]
+\PY{k}{class} \PY{n+nc}{Map}\PY{p}{(}\PY{n+nb}{object}\PY{p}{)}\PY{p}{:}
+    \PY{k}{def} \PY{n+nf}{\PYZus{}\PYZus{}init\PYZus{}\PYZus{}}\PY{p}{(}\PY{n+nb+bp}{self}\PY{p}{,} \PY{n}{indexes}\PY{p}{)}\PY{p}{:}
+        \PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{indexes} \PY{o}{=} \PY{n}{indexes}
+        \PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{other\PYZus{}maps} \PY{o}{=} \PY{p}{\PYZob{}}\PY{p}{\PYZcb{}}
+
+    \PY{k}{def} \PY{n+nf}{getindex}\PY{p}{(}\PY{n+nb+bp}{self}\PY{p}{,} \PY{n}{name}\PY{p}{)}\PY{p}{:}
+        \PY{k}{return} \PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{indexes}\PY{o}{.}\PY{n}{get}\PY{p}{(}\PY{n}{name}\PY{p}{,} \PY{o}{-}\PY{l+m+mi}{1}\PY{p}{)}
+
+    \PY{k}{def} \PY{n+nf}{add\PYZus{}attribute}\PY{p}{(}\PY{n+nb+bp}{self}\PY{p}{,} \PY{n}{name}\PY{p}{)}\PY{p}{:}
+        \PY{o}{.}\PY{o}{.}\PY{o}{.}
+
+\PY{n}{EMPTY\PYZus{}MAP} \PY{o}{=} \PY{n}{Map}\PY{p}{(}\PY{p}{\PYZob{}}\PY{p}{\PYZcb{}}\PY{p}{)}
+\end{Verbatim}
+\end{frame}
+
+\begin{frame}[plain,containsverbatim]
+\begin{Verbatim}[commandchars=\\\{\}]
+\PY{k}{class} \PY{n+nc}{Instance}\PY{p}{(}\PY{n+nb}{object}\PY{p}{)}\PY{p}{:}
+    \PY{k}{def} \PY{n+nf}{\PYZus{}\PYZus{}init\PYZus{}\PYZus{}}\PY{p}{(}\PY{n+nb+bp}{self}\PY{p}{)}\PY{p}{:}
+        \PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{map} \PY{o}{=} \PY{n}{EMPTY\PYZus{}MAP}
+        \PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{storage} \PY{o}{=} \PY{p}{[}\PY{p}{]}
+
+    \PY{k}{def} \PY{n+nf}{getfield}\PY{p}{(}\PY{n+nb+bp}{self}\PY{p}{,} \PY{n}{name}\PY{p}{)}\PY{p}{:}
+        \PY{n}{index} \PY{o}{=} \PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{map}\PY{o}{.}\PY{n}{getindex}\PY{p}{(}\PY{n}{name}\PY{p}{)}
+        \PY{k}{if} \PY{n}{index} \PY{o}{!=} \PY{o}{-}\PY{l+m+mi}{1}\PY{p}{:}
+            \PY{k}{return} \PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{storage}\PY{p}{[}\PY{n}{index}\PY{p}{]}
+        \PY{k}{return} \PY{n+nb+bp}{None}
+
+    \PY{k}{def} \PY{n+nf}{write\PYZus{}attribute}\PY{p}{(}\PY{n+nb+bp}{self}\PY{p}{,} \PY{n}{name}\PY{p}{,} \PY{n}{value}\PY{p}{)}\PY{p}{:}
+        \PY{o}{.}\PY{o}{.}\PY{o}{.}
+\end{Verbatim}
+\end{frame}
+
+\begin{frame}[plain,containsverbatim]
+\frametitle{Trace for code \texttt{inst.a + inst.b}}
+\begin{lstlisting}[mathescape,escapechar=|,basicstyle=\ttfamily]]
+# $inst_1$.getattr("a")
+$map_1$ = $inst_1$.map
+$index_1$ = Map.getindex($map_1$, "a")
+guard($index_1$ != -1)
+$storage_1$ = $inst_1$.storage
+$result_1$ = $storage_1$[$index_1$]
+|\pause|
+# $inst_1$.getattr("b")
+$map_2$ = $inst_1$.map
+$index_2$ = Map.getindex($map_2$, "b")
+guard($index_2$ != -1)
+$storage_2$ = $inst_1$.storage
+$result_2$ = $storage_2$[$index_2$]
+
+$v_1$ = $result_1$ + $result_2$
+return($v_1$)
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[plain,containsverbatim]
+\frametitle{Trace for code \texttt{inst.a + inst.b}}
+\begin{lstlisting}[mathescape,escapechar=|,basicstyle=\ttfamily]]
+# $inst_1$.getattr("a")
+$map_1$ = $inst_1$.map
+$index_1$ = Map.getindex($map_1$, "a")
+guard($index_1$ != -1)
+$storage_1$ = $inst_1$.storage
+$result_1$ = $storage_1$[$index_1$]
+
+# $inst_1$.getattr("b")
+$map_2$ = $inst_1$.map
+$index_2$ = Map.getindex($map_2$, "b")
+guard($index_2$ != -1)
+$storage_2$ = $inst_1$.storage
+$result_2$ = $storage_2$[$index_2$]
+
+$v_1$ = $result_1$ + $result_2$
+return($v_1$)
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[containsverbatim]
+  \frametitle{Runtime Feedback Controlled by the Interpreter Author}
+  \begin{itemize}
+      \item give the interpreter author a way to feed back runtime values into the trace
+      \item written as \texttt{promote(x)}
+      \item captures the argument's runtime value during tracing
+      \item should be used only for variables that take few values
+  \end{itemize}
+  \pause
+
+  \begin{minipage}[b]{6cm}
+      \centering
+      {\noop
+      \begin{lstlisting}[mathescape,basicstyle=\ttfamily]
+def f1(x, y):
+    promote(x)
+    z = x * 2 + 1
+    return z + y
+      \end{lstlisting}
+      }
+  \end{minipage}
+  \vline
+  \hspace{0.5cm}
+  \begin{minipage}[b]{4cm}
+      {\noop
+      \begin{lstlisting}[mathescape,basicstyle=\ttfamily]
+guard($x_1$ == 4)
+$v_1$ = $x_1$ * 2
+$z_1$ = $v_1$ + 1
+$v_2$ = $z_1$ + $y_1$
+return($v_2$)
+      \end{lstlisting}
+      }
+  \end{minipage}
+\end{frame}
+
+\begin{frame}[containsverbatim]
+  \frametitle{Runtime Feedback Controlled by the Interpreter Author}
+  \begin{itemize}
+      \item give the interpreter author a way to feed back runtime values into the trace
+      \item written as \texttt{promote(x)}
+      \item captures the argument's runtime value during tracing
+      \item should be used only for variables that take few values
+  \end{itemize}
+
+  \begin{minipage}[b]{6cm}
+      \centering
+      {\noop
+      \begin{lstlisting}[mathescape,basicstyle=\ttfamily]
+def f1(x, y):
+    promote(x)
+    z = x * 2 + 1
+    return z + y
+
+
+      \end{lstlisting}
+      }
+  \end{minipage}
+\end{frame}
+
+\begin{frame}[containsverbatim]
+  \frametitle{Runtime Feedback Controlled by the Interpreter Author}
+  \begin{itemize}
+      \item give the interpreter author a way to feed back runtime values into the trace
+      \item written as \texttt{promote(x)}
+      \item captures the argument's runtime value during tracing
+      \item should be used only for variables that take few values
+  \end{itemize}
+  
+  \begin{minipage}[b]{6cm}
+      \centering
+      {\noop
+      \begin{lstlisting}[mathescape,basicstyle=\ttfamily]
+def f1(x, y):
+    promote(x)
+    z = x * 2 + 1
+    return z + y
+
+
+      \end{lstlisting}
+      }
+  \end{minipage}
+  \vline
+  \hspace{0.5cm}
+  \begin{minipage}[b]{4cm}
+      {\noop
+      \begin{lstlisting}[mathescape,basicstyle=\ttfamily]
+guard($x_1$ == 4)
+$v_1$ = $x_1$ * 2
+$z_1$ = $v_1$ + 1
+$v_2$ = $z_1$ + $y_1$
+return($v_2$)
+      \end{lstlisting}
+      }
+  \end{minipage}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Foldable Operations Defined by the Interpreter Author}
+  \begin{itemize}
+      \item let the interpreter author define foldable functions
+      \item those functions typically don't look foldable
+      \item otherwise there is no need for an annotation
+      \item done via a function decorator \texttt{@elidable}
+      \pause
+      \item decorated functions should be pure
+      \item or have idempotent side effects (such as a function that memoizes)
+      \item trace optimizer will remove calls to such functions with constant arguments
+  \end{itemize}
+\end{frame}
+
+\begin{frame}[containsverbatim]
+\frametitle{Adding Hints to Maps}
+
+\begin{Verbatim}[commandchars=\\\{\}]
+\PY{k}{class} \PY{n+nc}{Map}\PY{p}{(}\PY{n+nb}{object}\PY{p}{)}\PY{p}{:}
+    \PY{k}{def} \PY{n+nf}{\PYZus{}\PYZus{}init\PYZus{}\PYZus{}}\PY{p}{(}\PY{n+nb+bp}{self}\PY{p}{,} \PY{n}{indexes}\PY{p}{)}\PY{p}{:}
+        \PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{indexes} \PY{o}{=} \PY{n}{indexes}
+        \PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{other\PYZus{}maps} \PY{o}{=} \PY{p}{\PYZob{}}\PY{p}{\PYZcb{}}
+
+    \PY{n+nd}{@elidable}
+    \PY{k}{def} \PY{n+nf}{getindex}\PY{p}{(}\PY{n+nb+bp}{self}\PY{p}{,} \PY{n}{name}\PY{p}{)}\PY{p}{:}
+        \PY{k}{return} \PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{indexes}\PY{o}{.}\PY{n}{get}\PY{p}{(}\PY{n}{name}\PY{p}{,} \PY{o}{-}\PY{l+m+mi}{1}\PY{p}{)}
+
+    \PY{n+nd}{@elidable}
+    \PY{k}{def} \PY{n+nf}{add\PYZus{}attribute}\PY{p}{(}\PY{n+nb+bp}{self}\PY{p}{,} \PY{n}{name}\PY{p}{)}\PY{p}{:}
+        \PY{o}{.}\PY{o}{.}\PY{o}{.}
+
+\PY{n}{EMPTY\PYZus{}MAP} \PY{o}{=} \PY{n}{Map}\PY{p}{(}\PY{p}{)}
+\end{Verbatim}
+\end{frame}
+
+\begin{frame}[containsverbatim]
+\frametitle{Adding Hints to Maps}
+
+\begin{Verbatim}[commandchars=\\\{\}]
+\PY{n}{EMPTY\PYZus{}MAP} \PY{o}{=} \PY{n}{Map}\PY{p}{(}\PY{p}{\PYZob{}}\PY{p}{\PYZcb{}}\PY{p}{)}
+
+\PY{k}{class} \PY{n+nc}{Instance}\PY{p}{(}\PY{n+nb}{object}\PY{p}{)}\PY{p}{:}
+    \PY{k}{def} \PY{n+nf}{\PYZus{}\PYZus{}init\PYZus{}\PYZus{}}\PY{p}{(}\PY{n+nb+bp}{self}\PY{p}{)}\PY{p}{:}
+        \PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{map} \PY{o}{=} \PY{n}{EMPTY\PYZus{}MAP}
+        \PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{storage} \PY{o}{=} \PY{p}{[}\PY{p}{]}
+
+    \PY{k}{def} \PY{n+nf}{getfield}\PY{p}{(}\PY{n+nb+bp}{self}\PY{p}{,} \PY{n}{name}\PY{p}{)}\PY{p}{:}
+        \PY{n}{promote}\PY{p}{(}\PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{map}\PY{p}{)}
+        \PY{n}{index} \PY{o}{=} \PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{map}\PY{o}{.}\PY{n}{getindex}\PY{p}{(}\PY{n}{name}\PY{p}{)}
+        \PY{k}{if} \PY{n}{index} \PY{o}{!=} \PY{o}{-}\PY{l+m+mi}{1}\PY{p}{:}
+            \PY{k}{return} \PY{n+nb+bp}{self}\PY{o}{.}\PY{n}{storage}\PY{p}{[}\PY{n}{index}\PY{p}{]}
+        \PY{k}{return} \PY{n+nb+bp}{None}
+
+    \PY{k}{def} \PY{n+nf}{write\PYZus{}attribute}\PY{p}{(}\PY{n+nb+bp}{self}\PY{p}{,} \PY{n}{name}\PY{p}{,} \PY{n}{value}\PY{p}{)}\PY{p}{:}
+        \PY{o}{.}\PY{o}{.}\PY{o}{.}
+\end{Verbatim}
+\end{frame}
+
+
+\begin{frame}[containsverbatim,plain]
+  \frametitle{Trace with Hints}
+\begin{lstlisting}[mathescape,escapechar=|,basicstyle=\ttfamily]]
+# $inst_1$.getattr("a")
+$map_1$ = $inst_1$.map
+guard($map_1$ == 0xb74af4a8)
+|{\color{gray}$index_1$ = Map.getindex($map_1$, "a")|
+|{\color{gray}guard($index_1$ != -1)|
+$storage_1$ = $inst_1$.storage
+$result_1$ = $storage_1$[$index_1$]
+
+# $inst_1$.getattr("b")
+|{\color{gray}$map_2$ = $inst_1$.map|
+|{\color{gray}guard($map_2$ == 0xb74af4a8)|
+|{\color{gray}$index_2$ = Map.getindex($map_2$, "b")|
+|{\color{gray}guard($index_2$ != -1)|
+|{\color{gray}$storage_2$ = $inst_1$.storage|
+$result_2$ = $storage_2$[$index_2$]
+
+$v_1$ = $result_1$ + $result_2$
+return($v_1$)
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[containsverbatim,plain]
+  \frametitle{Final Trace}
+\begin{lstlisting}[mathescape,escapechar=|,basicstyle=\ttfamily]]
+# $inst_1$.getattr("a")
+$map_1$ = $inst_1$.map
+guard($map_1$ == 0xb74af4a8)
+$storage_1$ = $inst_1$.storage
+$result_1$ = $storage_1$[$0$]
+$result_2$ = $storage_2$[$1$]
+$v_1$ = $result_1$ + $result_2$
+return($v_1$)
+\end{lstlisting}
+\end{frame}
+
+
+\begin{frame}
+  \frametitle{Uses of These Hints}
+  \begin{block}{\texttt{promote} lets one specialize on various things:}
+      \begin{itemize}
+          \item user-level types
+          \item shapes of instances
+          \item the current state of a classes' methods
+          \item ...
+      \end{itemize}
+  \end{block}
+  \pause
+  \begin{block}{uses of \texttt{@elidable}}
+      \begin{itemize}
+          \item define immutable fields by decorating a getter
+          \item declare arbitrary invariants
+      \end{itemize}
+      
+  \end{block}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Some Benchmarks}
+  \begin{itemize}
+      \item benchmarks done using PyPy's Python interpreter
+      \item about 30'000 lines of code
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Some Benchmarks}
+  \includegraphics[scale=0.5]{figures/bench.pdf}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Conclusion}
+  \begin{itemize}
+      \item meta-tracing can make the efficient implementation of complex dynamic languaes easier
+      \item two kinds of hints to be added by the interpreter author allows arbitrary runtime feedback
+      \item the hints are expressive enough to re-implement classical optimizations such as maps
+      \item usage of the hints leads to good speedups for object-oriented code in PyPy's Python interpreter
+  \end{itemize}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Bonus: Comparison with Partial Evaluation}
+\end{frame}
+
+
+\end{document}


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