Mercurial > hg > Papers > 2010 > sigos-koba

--- a/paper/OS-116-6.tex	Thu Dec 16 21:54:12 2010 +0900
+++ b/paper/OS-116-6.tex	Fri Dec 17 00:14:19 2010 +0900
@@ -1,1 +1,1 @@
-\documentclass[techrep]{ipsjpapers}
\usepackage{graphicx}

% 巻数，号数などの設定
\setcounter{年数}{2011}

% ユーザが定義したマクロなど．
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	$\backslash$#1\fi}

%\checklines	% 行送りを確認する時に使用
\begin{document}%{
% 和文表題
\title[学生用 PS3 GameFrameWork Cerium での Pipeline ストールの検出]%
	{学生用 PS3 GameFrameWork Cerium での\\Pipeline ストールの検出}
% 英文表題
\etitle{Detecting pipeline stall on PS3 GameFrameWork Cerium}
% 所属ラベル
\affilabel{UNI}{琉球大学 理工学研究科 情報工学専攻 並列信頼研究室\\
                Concurrency Reliance Laboratory, Information Engineering Course,
                Faculty of Engineering Graduate School of Engineering and Science,
                University of the Ryukyus.}

% 和文著者名
\author{小林 佑亮\affiref{UNI}\and
	河野 真治\affiref{UNI}\and
        多賀野 海人\affiref{UNI}\and
        金城　裕\affiref{UNI}}
	
% 英文著者名
\eauthor{Yusuke Kobayashi\affiref{UNI}\and
	 Shinji Kono\affiref{UNI}\and
         Kaito Tagano\affiref{UNI}\and
         Yutaka Kinjo\affiref{UNI}}

% 和文概要
\begin{abstract}
我々は PlayStation3 上でのゲームプログラミングをサポートする Cerium Engine を開発した。
Cerium におけるゲーム開発ではオブジェクトの描画や動作を Task という単位で管理しており、
この Task を SPE に送り、Pipeline で実行することによってプログラムの並列化を図っている。
この Pipeline におけるストールによって実行速度の低下が発生することが分かっている。
本研究ではこのストールを検出することを考える。
\end{abstract}
% 英文概要
\begin{eabstract}

\end{eabstract}

% 表題
\maketitle

% 本文
\section{はじめに}
当研究室ではこれまで家庭用ゲーム機上でのゲームプログラミングの開発を行ってきた。
過去には PlayStation や PlayStation2、GameBoyAdvance を用いており、
現在は PlayStation3(以下 PS3) で 動作するゲーム開発を行っている。
PS3 では Fedora や Yellow Dog Linux といった Linux O を動作させることができるので
(現在の公式のサポートは終了している)C や C++ といったプログラム言語を用いて
Linux 上でプログラミングすることが可能となっている。しかし、PS3 の Architecture である
CellBroadbandEngine は複数の SPE を使用する並列プログラミングが求められている。
そこで我々は Cell のような ManyCoreArchitecture を用いた、並列プログラムの開発を
サポートするフレームワークとして FineGrainTaskManager を開発した。
この TaskManager を用いたゲーム開発フレームワークが Cerium である。

Cerium を用いたゲーム開発ではプログラムの動作を Task という単位で管理し、
この Task と必要なパラメータを複数の SPE に転送して処理させる。
転送された各 TASK は並列に処理され、Pipeline で実行される。
本研究では Cerium 用に開発されたゲームプログラムを用いてテストを行い、
Cerium の チューニングやゲームプログラミングを補助するテスト手法を提案する。
%}{

\section{Cell Broadband Engine}\label{sec:Cell}
CellBroadbandEngine は SCEI と IBM、東芝によって開発された CPU である。
2 thread の PPE(PowerPC Processor Element)と
8個の SPE(Synergistic Processor Element)からなる非対称なマルチコアプロセッサであり、
高速リングバスであるEIB(Element Interface Bus)で構成されている。
PS3 Linux では6個の SPE を使うことが出来る。(図\ref{fig:cell})

\subsection{PPE(PowerPC Processor Element)}\label{ssec:PPE}
PPE は Cell Broadband Engine のメインプロセッサで、
複数の SPE をコアプロセッサとして使用することができる汎用プロセッサである。
メインメモリや外部デバイスへの入出力、SPE を制御する役割を担っている。
PPU(PowerPC Processor Unit)は、PPEの演算処理を行うユニットで、
PowerPC アーキテクチャをベースとした命令セットを持つ。
PPSS(PowerPC Processor Storage Subsystem)は PPU からメインメモリへのデータアクセスを
制御するユニットである。

\subsection{SPE(Synergistic Processor Element)}\label{ssec:SPE}
SPE には 256KB の Local Store(LS)と呼ばれる直接参照できるメモリ領域があり、
バスに負担をかける事なく並列に計算を進めることが出来る。
SPE からメインメモリへは、直接アクセスすることは出来ず、SPE を構成する一つである
MFC (Memory Flow Controller)へ、チャネルを介してDMA(Direct Memory Access)命令を送ることで行われる。

\begin{figure}[tb]
\begin{center}
\includegraphics[scale=0.7]{figure/cell.eps}
\end{center}
\caption{CellBroadbandEngine}
\label{fig:cell}
\end{figure}

\newpage

\section{Cerium Engine}
Cerium は 独自の Rendering Engine と Scene Graph、Task Manager の3つによって構成される。
ゲーム中のオブジェクトの振る舞いやルール、Polygon Data は SceneGraph によって管理され、
それらの動きや Rendering の処理を動的に SPE に割り振るカーネルとして TaskManager が用いられる。
Cerium は C++ で実装されており、画像の読み込みや入力デバイスはSDL\footnote[1]{
Simple DirectMedia Layer。グラフィックやサウンドなどの API を提供するライブラリ。
} を用いて行っている。

\subsection{Scene Graph}
Cerium ではゲーム中の一つの場面(Scene)を構成するオブジェクトの頂点座標やテクスチャー、
そしてその振る舞いの集合を SceneGraph としている。
SceneGraph のノードは親子関係を持つ tree で構成される。親子関係とは、親オブジェクトの回転や
並列移動等の行列計算による頂点座標の変更が、子オブジェクトにも反映する関係のことである。
これは子に対してスタックに積まれた親の変換行列を掛けることで実現できる。

\subsection{Task Manager}
Task Manager は Task と呼ばれる、分割された各プログラムを管理する。
Task の単位はサブルーチンまたは関数とする。
Task は主に PPE 内で生成され、処理する内容と必要なパラメータを設定される。
実行可能になった Task から各 SPE 割り当てられ、Task を受け取った SPE はその情報を元に
処理を実行する。

\subsubsection{Task の Dependency}\label{sssec:dependency}
Task には依存関係(Dependency)を持たせることができる。以下に記述例を示す。

\begin{verbatim}
//task2 は task1 が終了してから開始する
task2->wait_for(task1);
\end{verbatim} 

上記の場合には task1 は Active Queue へ、task2 は Wait Queue へ格納される。
Active Queue に格納された Task は各 SPE に送られ処理される。
終了した Task から PPE の Task Manager へタスク終了のコマンドを発行する。
コマンドを受け取った Task Manager は Wait Queue を調べ、依存関係を満たした Task から
Active Queue に移し、SPE へ送る。(図\ref{fig:dependency})

\begin{figure}[tb]
\begin{center}
\includegraphics[scale=0.6]{figure/dependency.eps}
\end{center}
\caption{CellBroadbandEngine}
\label{fig:dependency}
\end{figure}

\subsubsection{}

\subsection{Rendering Engine}\label{ssec:rendering}
Cerium の Rendering Engine では、オブジェクトの描画を Cell で並列処理している。
描画処理を段階別に以下の3種類の Task に分けている。

\begin{itemize*}
\item 
SceneGraph が持つ Polygon の座標から、実際に画面に表示する座標の計算を行い、
それを格納した PolyPack を生成する SceneGraph2PolygonPack Task
\item 
PolygonPack から同じ Y 座標を持つ線分の集合である SpanPack を生成する 
PolygonPack2SpanPack Task
\item 
SpanPack を Texture を読み込みながら Z Buffer を用いて描画する DrawSpan Task
\end{itemize*} 

この3つの Task は画面の描画毎にパイプライン的に実行される

\newpage

\section{Task の Dependency}
Cerium の Task には依存関係を持たせる機能がある。

wait\_for は複数の Task を指定できる。上記の場合は
 task3 が task1、task2 の二つの Task 終了を待つ形となる。

\end{document}
\ No newline at end of file
+\documentclass[techrep]{ipsjpapers}
\usepackage{graphicx}

% 巻数，号数などの設定
\setcounter{年数}{2011}

% ユーザが定義したマクロなど．
\makeatletter
\let\@ARRAY\@array \def\@array{\def\<{\inhibitglue}\@ARRAY}
\def\<{\(\langle\)\nobreak}
\def\>{\nobreak\(\rangle\)}
\def\|{\verb|}
\def\Underline{\setbox0\hbox\bgroup\let\\\endUnderline}
\def\endUnderline{\vphantom{y}\egroup\smash{\underline{\box0}}\\}
\def\LATEX{\iLATEX\Large}
\def\LATEx{\iLATEX\normalsize}
\def\LATex{\iLATEX\small}
\def\iLATEX#1{L\kern-.36em\raise.3ex\hbox{#1\bf A}\kern-.15em
    T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}
\def\LATEXe{\ifx\LaTeXe\undefined \LaTeX 2e\else\LaTeXe\fi}
\def\LATExe{\ifx\LaTeXe\undefined \iLATEX\scriptsize 2e\else\LaTeXe\fi}
\def\Quote{\list{}{}\item[]}
\let\endQuote\endlist
\def\TT{\if@LaTeX@e\tt\fi}
\def\CS#1{\if@LaTeX@e\tt\expandafter\string\csname#1\endcsname\else
	$\backslash$#1\fi}

%\checklines	% 行送りを確認する時に使用
\begin{document}%{
% 和文表題
\title[学生用 PS3 GameFrameWork Cerium での Pipeline ストールの検出]%
	{学生用 PS3 GameFrameWork Cerium での\\Pipeline ストールの検出}
% 英文表題
\etitle{Detecting pipeline stall on PS3 GameFrameWork Cerium}
% 所属ラベル
\affilabel{UNI}{琉球大学 理工学研究科 情報工学専攻 並列信頼研究室\\
                Concurrency Reliance Laboratory, Information Engineering Course,
                Faculty of Engineering Graduate School of Engineering and Science,
                University of the Ryukyus.}

% 和文著者名
\author{小林 佑亮\affiref{UNI}\and
	河野 真治\affiref{UNI}\and
        多賀野 海人\affiref{UNI}\and
        金城　裕\affiref{UNI}}
	
% 英文著者名
\eauthor{Yusuke Kobayashi\affiref{UNI}\and
	 Shinji Kono\affiref{UNI}\and
         Kaito Tagano\affiref{UNI}\and
         Yutaka Kinjo\affiref{UNI}}

% 和文概要
\begin{abstract}
我々は PlayStation3 上でのゲームプログラミングをサポートする Cerium Engine を開発した。
Cerium におけるゲーム開発ではオブジェクトの描画や動作を Task という単位で管理しており、
この Task を SPE に送り、Pipeline で実行することによってプログラムの並列化を図っている。
この Pipeline におけるストールによって実行速度の低下が発生することが分かっている。
本研究ではこのストールを検出することを考える。
\end{abstract}
% 英文概要
\begin{eabstract}
We developed Cerium Engine which support Game Programming on PlayStation3.

\end{eabstract}

% 表題
\maketitle

\newpage

% 本文
\section{はじめに}
当研究室ではこれまで家庭用ゲーム機上でのゲームプログラミングの開発を行ってきた。
過去には PlayStation や PlayStation2、GameBoyAdvance を用いており、
現在は PlayStation3(以下 PS3) で 動作するゲーム開発を行っている。
PS3 では Fedora や Yellow Dog Linux といった Linux O を動作させることができるので
(現在の公式のサポートは終了している)C や C++ といったプログラム言語を用いて
Linux 上でプログラミングすることが可能となっている。しかし、PS3 の Architecture である
CellBroadbandEngine は複数の SPE を使用する並列プログラミングが求められている。
そこで我々は Cell のような ManyCoreArchitecture を用いた、並列プログラムの開発を
サポートするフレームワークとして FineGrainTaskManager を開発した。
この TaskManager を用いたゲーム開発フレームワークが Cerium である。

Cerium を用いたゲーム開発ではプログラムの動作を Task という単位で管理し、
この Task と必要なパラメータを複数の SPE に転送して処理させる。
転送された各 TASK は並列に処理され、Pipeline で実行される。
本研究では Cerium 用に開発されたゲームプログラムを用いてテストを行い、
Cerium の チューニングやゲームプログラミングを補助するテスト手法を提案する。
%}{

\section{Cell Broadband Engine}\label{sec:Cell}
CellBroadbandEngine は SCEI と IBM、東芝によって開発された CPU である。
2 thread の PPE(PowerPC Processor Element)と
8個の SPE(Synergistic Processor Element)からなる非対称なマルチコアプロセッサであり、
高速リングバスであるEIB(Element Interface Bus)で構成されている。
PS3 Linux では6個の SPE を使うことが出来る。(図\ref{fig:cell})

\subsection{PPE(PowerPC Processor Element)}\label{ssec:PPE}
PPE は Cell Broadband Engine のメインプロセッサで、
複数の SPE をコアプロセッサとして使用することができる汎用プロセッサである。
メインメモリや外部デバイスへの入出力、SPE を制御する役割を担っている。
PPU(PowerPC Processor Unit)は、PPEの演算処理を行うユニットで、
PowerPC アーキテクチャをベースとした命令セットを持つ。
PPSS(PowerPC Processor Storage Subsystem)は PPU からメインメモリへのデータアクセスを
制御するユニットである。

\subsection{SPE(Synergistic Processor Element)}\label{ssec:SPE}
SPE には 256KB の Local Store(LS)と呼ばれる直接参照できるメモリ領域があり、
バスに負担をかける事なく並列に計算を進めることが出来る。
SPE からメインメモリへは、直接アクセスすることは出来ず、SPE を構成する一つである
MFC (Memory Flow Controller)へ、チャネルを介してDMA(Direct Memory Access)命令を送ることで行われる。

\begin{figure}[tb]
\begin{center}
\includegraphics[scale=0.7]{figure/cell.eps}
\end{center}
\caption{Cell Broadband Engine}
\label{fig:cell}
\end{figure}

\section{Cerium Engine}
Cerium は 独自の Rendering Engine と Scene Graph、Task Manager の3つによって構成される。
ゲーム中のオブジェクトの振る舞いやルール、Polygon Data は SceneGraph によって管理され、
それらの動きや Rendering の処理を動的に SPE に割り振るカーネルとして TaskManager が用いられる。
Cerium は C++ で実装されており、画像の読み込みや入力デバイスはSDL\footnote[1]{
Simple DirectMedia Layer。グラフィックやサウンドなどの API を提供するフリーのライブラリ。
} を用いて行っている。

\subsection{Scene Graph}
Cerium ではゲーム中の一つの場面(Scene)を構成するオブジェクトの頂点座標やテクスチャー、
そしてその振る舞いの集合を SceneGraph としている。
SceneGraph のノードは親子関係を持つ tree で構成される。親子関係とは、親オブジェクトの回転や
並列移動等の行列計算による頂点座標の変更が、子オブジェクトにも反映する関係のことである。
これは子に対してスタックに積まれた親の変換行列を掛けることで実現できる。(図\ref{sg})

\subsection{Task Manager}
Task Manager は Task と呼ばれる、分割された各プログラムを管理する。
Task の単位はサブルーチンまたは関数とする。
Task は主に PPE 内で生成され、処理する内容と必要なパラメータを設定される。
実行可能になった Task から各 SPE 割り当てられ、Task を受け取った SPE はその情報を元に
処理を実行する。

\subsection{Rendering Engine}\label{ssec:rendering}
現在、PlayStation3 の GPU にアクセスする API が公開されていないため、
Cerium の Rendering Engine では、オブジェクトの描画を Cell で並列処理している。
描画処理を段階別に以下の3種類の Task に分けている。

\begin{itemize*}
\item 
SceneGraph が持つ Polygon の座標から、実際に画面に表示する座標の計算を行い、
それを格納した PolyPack を生成する SceneGraph2PolygonPack Task
\item 
PolygonPack から同じ Y 座標を持つ線分の集合である SpanPack を生成する 
PolygonPack2SpanPack Task
\item 
SpanPack を Texture を読み込みながら Z Buffer を用いて描画する DrawSpan Task
\end{itemize*} 

この3つの Task を処理をする順番に SPE に送ることでオブジェクトの描画処理を実現している。

\begin{figure}[tb]
\begin{center}
\includegraphics[width=5cm]{figure/scenegraph.eps}
\end{center}
\caption{Scene Graph Tree}
\label{fig:sg}
\end{figure}

\newpage

\section{Cerium の Task}

\subsection{Task の Dependency}
Task には依存関係(Dependency)を持たせることができる
{\bf wait\_for}がある。

\setbox0\vbox{
\hbox{//task2 は task1 が終了してから開始する}
\hbox{task2\|->|wait\_for(task1);}
}\fbox{\box0}
\label{fig:single}

上記の場合には task1 は Active Queue へ、task2 は Wait Queue へ格納される。
Active Queue に格納された Task は各 SPE に送られ処理される。
終了した Task から PPE の Task Manager へタスク終了のコマンドを発行する。
コマンドを受け取った Task Manager は Wait Queue を調べ、依存関係を満たした Task から
Active Queue に移し、SPE へ送る。(図\ref{fig:dependency})

\begin{figure}[tb]
\begin{center}
\includegraphics[scale=0.5]{figure/dependency.eps}
\end{center}
\caption{CellBroadbandEngine}
\label{fig:dependency}
\end{figure}

\subsection{Task 終了時に実行される関数}
{\bf set\_post}を使うことでTask が終了した際に PPE で実行される関数と、
その引数を指定できる。

\setbox0\vbox{
\hbox{int data = 3;}
\hbox{task\|->|set\_post(func1, (void*)data);}
\hbox{}
\hbox{void}
\hbox{func1(void *data)}
\hbox{\|{|}
\hbox{\ \ printf\|("func1: data = %d\n", (int)data)|;}
\hbox{\|}|}
\hbox{}
\hbox{//実行結果}
\hbox{func1: data = 3}
}\fbox{\box0}
\label{fig:single}

{\bf set\_post}により、ユーザ側でも Task が終了したということを検知できる。
また、大量の Task に依存関係を設定する場合、一度に {bf create\_task}で生成し、
{\bf wait\_for}で繋げるというのは難しい。その場合、ある一定数の Task だけ
生成しておき、{\bf set\_post}を使って終了したことを確認して、その中で新たに 
Task を生成していくほうが望ましい。

\section{SuperDandy}

\end{document}
\ No newline at end of file
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+++ b/paper/figure/scenegraph.eps	Fri Dec 17 00:14:19 2010 +0900
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+    /ColorSpace fr scs
+}bd
+/sopr /setoverprint where{pop/setoverprint}{/pop}ifelse ld
+/soprm /setoverprintmode where{pop/setoverprintmode}{/pop}ifelse ld
+/cgmtx matrix def
+/sdmtx{cgmtx currentmatrix pop}bd
+/CM {cgmtx setmatrix}bd
+/cm {cmmtx astore CM concat}bd
+/W{clip newpath}bd
+/W*{eoclip newpath}bd
+statusdict begin product end dup (HP) anchorsearch{
+    pop pop pop
+    true
+}{
+    pop
+   (hp) anchorsearch{
+	pop pop true
+    }{
+	pop false
+    }ifelse
+}ifelse
+{
+    {
+	{
+	    pop pop
+	    (0)dup 0 4 -1 roll put
+	    F charpath
+	}cshow
+    }
+}{
+    {F charpath}
+}ifelse
+/cply exch bd
+/cps {cply stroke}bd
+/pgsave 0 def
+/bp{/pgsave save store}bd
+/ep{pgsave restore showpage}def
+/re{4 2 roll m 1 index 0 rlineto 0 exch rlineto neg 0 rlineto h}bd
+/scrdict 10 dict def
+/scrmtx matrix def
+/patarray 0 def
+/createpat{patarray 3 1 roll put}bd
+/makepat{
+scrmtx astore pop
+gsave
+initgraphics
+CM
+patarray exch get
+scrmtx
+makepattern
+grestore
+setpattern
+}bd
+/cg_BeginEPSF{
+    userdict save/cg_b4_Inc_state exch put
+    userdict/cg_endepsf/cg_EndEPSF load put
+    count userdict/cg_op_count 3 -1 roll put
+    countdictstack dup array dictstack userdict/cg_dict_array 3 -1 roll put
+    3 sub{end}repeat
+    /showpage {} def
+    0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin
+    10 setmiterlimit [] 0 setdash newpath
+    false setstrokeadjust false setoverprint
+}bd
+/cg_EndEPSF{
+  countdictstack 3 sub { end } repeat
+  cg_dict_array 3 1 index length 3 sub getinterval
+  {begin}forall
+  count userdict/cg_op_count get sub{pop}repeat
+  userdict/cg_b4_Inc_state get restore
+  F setpacking
+}bd
+/cg_biproc{currentfile/RunLengthDecode filter}bd
+/cg_aiproc{currentfile/ASCII85Decode filter/RunLengthDecode filter}bd
+/ImageDataSource 0 def
+L3?{
+    /cg_mibiproc{pop pop/ImageDataSource{cg_biproc}def}bd
+    /cg_miaiproc{pop pop/ImageDataSource{cg_aiproc}def}bd
+}{
+    /ImageBandMask 0 def
+    /ImageBandData 0 def
+    /cg_mibiproc{
+	string/ImageBandMask xs
+	string/ImageBandData xs
+	/ImageDataSource{[currentfile/RunLengthDecode filter dup ImageBandMask/readstring cvx
+	    /pop cvx dup ImageBandData/readstring cvx/pop cvx]cvx bind}bd
+    }bd
+    /cg_miaiproc{
+	string/ImageBandMask xs
+	string/ImageBandData xs
+	/ImageDataSource{[currentfile/ASCII85Decode filter/RunLengthDecode filter
+	    dup ImageBandMask/readstring cvx
+	    /pop cvx dup ImageBandData/readstring cvx/pop cvx]cvx bind}bd
+    }bd
+}ifelse
+/imsave 0 def
+/BI{save/imsave xd mark}bd
+/EI{imsave restore}bd
+/ID{
+counttomark 2 idiv
+dup 2 add
+dict begin
+{def} repeat
+pop
+/ImageType 1 def
+/ImageMatrix[Width 0 0 Height neg 0 Height]def
+currentdict dup/ImageMask known{ImageMask}{F}ifelse exch
+L3?{
+    dup/MaskedImage known
+    {
+	pop
+	<<
+	    /ImageType 3
+	    /InterleaveType 2
+	    /DataDict currentdict
+	    /MaskDict
+	    <<  /ImageType 1
+		/Width Width
+		/Height Height
+		/ImageMatrix ImageMatrix
+		/BitsPerComponent 1
+		/Decode [0 1]
+		currentdict/Interpolate known
+		{/Interpolate Interpolate}if
+	    >>
+	>>
+    }if
+}if
+exch
+{imagemask}{image}ifelse
+end
+}bd
+/cguidfix{statusdict begin mark version end
+{cvr}stopped{cleartomark 0}{exch pop}ifelse
+2012 lt{dup findfont dup length dict begin
+{1 index/FID ne 2 index/UniqueID ne and
+{def} {pop pop} ifelse}forall
+currentdict end definefont pop
+}{pop}ifelse
+}bd
+/t_array 0 def
+/t_i 0 def
+/t_c 1 string def
+/x_proc{
+    exch t_array t_i get add exch moveto
+    /t_i t_i 1 add store
+}bd
+/y_proc{
+    t_array t_i get add moveto
+    /t_i t_i 1 add store
+}bd
+/xy_proc{
+
+	t_array t_i 2 copy 1 add get 3 1 roll get
+	4 -1 roll add 3 1 roll add moveto
+	/t_i t_i 2 add store
+}bd
+/sop 0 def
+/cp_proc/x_proc ld
+/base_charpath
+{
+    /t_array xs
+    /t_i 0 def
+    {
+	t_c 0 3 -1 roll put
+        currentpoint
+	t_c cply sop
+        cp_proc
+    }forall
+    /t_array 0 def
+}bd
+/sop/stroke ld
+/nop{}def
+/xsp/base_charpath ld
+/ysp{/cp_proc/y_proc ld base_charpath/cp_proc/x_proc ld}bd
+/xysp{/cp_proc/xy_proc ld base_charpath/cp_proc/x_proc ld}bd
+/xmp{/sop/nop ld /cp_proc/x_proc ld base_charpath/sop/stroke ld}bd
+/ymp{/sop/nop ld /cp_proc/y_proc ld base_charpath/sop/stroke ld}bd
+/xymp{/sop/nop ld /cp_proc/xy_proc ld base_charpath/sop/stroke ld}bd
+/refnt{
+findfont dup length dict copy dup
+/Encoding 4 -1 roll put
+definefont pop
+}bd
+/renmfont{
+findfont dup length dict copy definefont pop
+}bd
+L3? dup dup{save exch}if
+/Range 0 def
+/DataSource 0 def
+/val 0 def
+/nRange 0 def
+/mulRange 0 def
+/d0 0 def
+/r0 0 def
+/di 0 def
+/ri 0 def
+/a0 0 def
+/a1 0 def
+/r1 0 def
+/r2 0 def
+/dx 0 def
+/Nsteps 0 def
+/sh3tp 0 def
+/ymax 0 def
+/ymin 0 def
+/xmax 0 def
+/xmin 0 def
+/setupFunEval
+{
+    begin
+	/nRange Range length 2 idiv store
+	/mulRange
+
+	[
+	    0 1 nRange 1 sub
+	    {
+		    2 mul/nDim2 xd
+		    Range nDim2 get
+		    Range nDim2 1 add get
+		    1 index sub
+
+		    255 div
+		    exch
+	    }for
+	]store
+    end
+}bd
+/FunEval
+{
+    begin
+
+	nRange mul /val xd
+
+	0 1 nRange 1 sub
+	{
+	    dup 2 mul/nDim2 xd
+	    val
+	    add DataSource exch get
+	    mulRange nDim2 get mul
+	    mulRange nDim2 1 add get
+	    add
+	}for
+    end
+}bd
+/max
+{
+	2 copy lt
+	{exch pop}{pop}ifelse
+}bd
+/sh2
+{
+	/Coords load aload pop
+	3 index 3 index translate
+
+	3 -1 roll sub
+	3 1 roll exch
+	sub
+	2 copy
+	dup mul exch dup mul add sqrt
+	dup
+	scale
+	atan
+
+	rotate
+
+	/Function load setupFunEval
+
+
+	clippath {pathbbox}stopped {0 0 0 0}if newpath
+	/ymax xs
+	/xmax xs
+	/ymin xs
+	/xmin xs
+	currentdict/Extend known
+	{
+		/Extend load 0 get
+		{
+			0/Function load FunEval sc
+			xmin ymin xmin abs ymax ymin sub rectfill
+		}if
+	}if
+
+	/Nsteps/Function load/Size get 0 get 1 sub store
+	/dx 1 Nsteps div store
+	gsave
+		/di ymax ymin sub store
+		/Function load
+
+		0 1 Nsteps
+		{
+			1 index FunEval sc
+			0 ymin dx di rectfill
+			dx 0 translate
+		}for
+		pop
+	grestore
+	currentdict/Extend known
+	{
+		/Extend load 1 get
+		{
+			Nsteps/Function load FunEval sc
+			1 ymin xmax 1 sub abs ymax ymin sub rectfill
+		}if
+	}if
+}bd
+/shp
+{
+	4 copy
+
+	dup 0 gt{
+		0 exch a1 a0 arc
+	}{
+		pop 0 moveto
+	}ifelse
+	dup 0 gt{
+		0 exch a0 a1 arcn
+	}{
+		pop 0 lineto
+	}ifelse
+
+	fill
+
+	dup 0 gt{
+		0 exch a0 a1 arc
+	}{
+		pop 0 moveto
+	}ifelse
+	dup 0 gt{
+		0 exch a1 a0 arcn
+	}{
+		pop 0 lineto
+	}ifelse
+
+	fill
+}bd
+/calcmaxs
+{
+
+	xmin dup mul ymin dup mul add sqrt
+	xmax dup mul ymin dup mul add sqrt
+	xmin dup mul ymax dup mul add sqrt
+	xmax dup mul ymax dup mul add sqrt
+	max max max
+}bd
+/sh3
+{
+	/Coords load aload pop
+	5 index 5 index translate
+	3 -1 roll 6 -1 roll sub
+	3 -1 roll 5 -1 roll sub
+	2 copy dup mul exch dup mul add sqrt
+	/dx xs
+	2 copy 0 ne exch 0 ne or
+	{
+
+		exch atan rotate
+	}{
+		pop pop
+	}ifelse
+
+	/r2 xs
+	/r1 xs
+	/Function load
+	dup/Size get 0 get 1 sub
+	/Nsteps xs
+	setupFunEval
+
+
+
+
+
+	dx r2 add r1 lt{
+
+		0
+	}{
+		dx r1 add r2 le
+		{
+			1
+		}{
+			r1 r2 eq
+			{
+				2
+			}{
+				3
+			}ifelse
+		}ifelse
+	}ifelse
+	/sh3tp xs
+	clippath {pathbbox}stopped {0 0 0 0}if
+	newpath
+	/ymax xs
+	/xmax xs
+	/ymin xs
+	/xmin xs
+
+	dx dup mul r2 r1 sub dup mul sub dup 0 gt
+	{
+		sqrt r2 r1 sub atan
+		/a0 exch 180 exch sub store
+		/a1 a0 neg store
+	}{
+		pop
+		/a0 0 store
+		/a1 360 store
+	}ifelse
+	currentdict/Extend known
+	{
+		/Extend load 0 get r1 0 gt and
+		{
+			0/Function load FunEval sc
+
+
+
+
+			{
+				{
+					dx 0 r1 360 0 arcn
+					xmin ymin moveto
+					xmax ymin lineto
+					xmax ymax lineto
+					xmin ymax lineto
+					xmin ymin lineto
+					eofill
+				}
+				{
+					r1 0 gt{0 0 r1 0 360 arc fill}if
+				}
+				{
+
+
+
+
+					0 r1 xmin abs r1 add neg r1 shp
+				}
+				{
+
+
+					r2 r1 gt{
+
+						0 r1
+						r1 neg r2 r1 sub div dx mul
+						0
+						shp
+					}{
+
+
+
+						0 r1 calcmaxs
+						dup
+
+						r2 add dx mul dx r1 r2 sub sub div
+						neg
+						exch 1 index
+						abs exch sub
+						shp
+					}ifelse
+				}
+			}sh3tp get exec
+		}if
+	}if
+
+	/d0 0 store
+	/r0 r1 store
+	/di dx Nsteps div store
+	/ri r2 r1 sub Nsteps div store
+	/Function load
+	0 1 Nsteps
+	{
+		1 index FunEval sc
+		d0 di add r0 ri add d0 r0 shp
+		{
+
+		d0 0 r0 a1 a0 arc
+		d0 di add 0 r0 ri add a0 a1 arcn
+		fill
+
+
+		d0 0 r0 a0 a1 arc
+		d0 di add 0 r0 ri add a1 a0 arcn
+		fill
+		}pop
+
+
+		/d0 d0 di add store
+		/r0 r0 ri add store
+	}for
+	pop
+
+	currentdict/Extend known
+	{
+		/Extend load 1 get r2 0 gt and
+		{
+			Nsteps/Function load FunEval sc
+
+
+
+
+			{
+				{
+					dx 0 r2 0 360 arc fill
+				}
+				{
+					dx 0 r2 360 0 arcn
+					xmin ymin moveto
+					xmax ymin lineto
+					xmax ymax lineto
+					xmin ymax lineto
+					xmin ymin lineto
+					eofill
+				}
+				{
+
+
+					xmax abs r1 add r1 dx r1 shp
+				}
+				{
+
+					r2 r1 gt{
+
+
+
+						calcmaxs dup
+
+						r1 add dx mul dx r2 r1 sub sub div
+						exch 1 index
+						exch sub
+						dx r2
+						shp
+					}{
+
+						r1 neg r2 r1 sub div dx mul
+						0
+						dx
+						r2
+						shp
+					}ifelse
+				}
+			}
+			sh3tp get exec
+		}if
+	}if
+}bd
+/sh
+{
+	begin
+		/ShadingType load dup dup 2 eq exch 3 eq or
+		{
+			gsave
+				newpath
+				/ColorSpace load scs
+				currentdict/BBox known
+				{
+					/BBox load aload pop
+					2 index sub
+					3 index
+					3 -1 roll exch sub
+					exch rectclip
+				}if
+				2 eq
+				{sh2}{sh3}ifelse
+			grestore
+		}{
+
+			pop
+			(DEBUG: shading type unimplemented\n)print flush
+		}ifelse
+	end
+}bd
+{restore}if not dup{save exch}if
+	L3?{
+		/sh/shfill ld
+		/csq/clipsave ld
+		/csQ/cliprestore ld
+	}if
+{restore}if
+end
+setpacking
+%%EndFile
+%%EndProlog
+%%BeginSetup
+%%EndSetup
+%%Page: 1 1
+%%PageBoundingBox: 0 0 381 288
+%%BeginPageSetup
+cg_md begin
+bp
+sdmtx
+%RBIBeginFontSubset: Helvetica
+%!FontType1-1.0: Helvetica 1.0000.0.0000
+
14 dict begin/FontName /Helvetica def
+
/PaintType 0 def
+
/Encoding 256 array 0 1 255{1 index exch/.notdef put}for
+
dup 33 /S put
+
dup 34 /c put
+
dup 35 /e put
+
dup 36 /n put
+
dup 37 /G put
+
dup 38 /r put
+
dup 39 /a put
+
dup 40 /p put
+
dup 41 /h put
+
dup 42 /N put
+
dup 43 /o put
+
dup 44 /d put
+
readonly def
+
42/FontType resourcestatus{pop pop false}{true}ifelse
+
%APLsfntBegin
+
{currentfile 0(%APLsfntEnd\n)/SubFileDecode filter flushfile}if
+
/FontType 42 def
+
/FontMatrix matrix def
+
/FontBBox[2048 -1947 1 index div -985 2 index div 2961 3 index div 2297 5 -1 roll div]cvx def
+
/sfnts [<
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00>] def
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/CharStrings 13 dict dup begin
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currentdict dup/FontName get exch definefont pop end
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%APLsfntEnd
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42/FontType resourcestatus{pop pop true}{false}ifelse
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{currentfile 0(%APLT1End\n)/SubFileDecode filter flushfile}if
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/FontMatrix [ 0.00048828125 0 0 0.00048828125 0 0 ] def
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/FontBBox{-1947 -985 2961 2297}def
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/UniqueID 4265107 def
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