changeset 2:bd91d56ca33a

chapter 3 finish.
author koba <koba@cr.ie.u-ryukyu.ac.jp>
date Tue, 01 Feb 2011 18:33:29 +0900
parents 5683155a3f8a
children 398e732edfb6
files paper/early.tex paper/game.tex paper/graffle/bug.graffle paper/graffle/conceal.graffle paper/graffle/dandy_data.graffle paper/graffle/dandy_seq.graffle paper/images/cell.eps paper/images/dandy.bb paper/images/dandy.pdf paper/images/feature.bb paper/images/feature.pdf paper/images/mailbox.bb paper/images/mailbox.pdf paper/images/opencl.bb paper/images/opencl.pdf paper/images/ppe.eps paper/images/sgtree.bb paper/images/sgtree.pdf paper/images/simd.bb paper/images/simd.pdf paper/images/spack.bb paper/images/spack.pdf paper/images/span.bb paper/images/span.pdf paper/images/spe.eps paper/introduciton.tex paper/master_paper.tex
diffstat 27 files changed, 17964 insertions(+), 29 deletions(-) [+]
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--- a/paper/early.tex	Sun Jan 30 17:44:27 2011 +0900
+++ b/paper/early.tex	Tue Feb 01 18:33:29 2011 +0900
@@ -1,11 +1,144 @@
-\chapter{予備知識および先行研究} \label{chapter:earty}
+\chapter{先行研究} \label{chapter:early}
+ここでは先行研究である Game Framework Cerium、および同じ並列プログラミングの
+フレームワークである OpenCL について説明する。
+
+\section{Game Framework Cerium}\label{sec:cerium}
+Game Framework Cerium は我々が提案したゲーム開発フレームワークで、独自に
+Rendering Engine を持つ。ゲーム中のオブジェクトの振る舞いやルールは 
+SceneGraph で管理し、それらの動きやレンダリングの処理を動的に SPE に割り振る
+カーネルとして Task Manager 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 を用いて行っている。
+
+\section{Task Manager}\label{sec:taskmanager}
+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し、Task 同士の依存関係を考慮しながら実行していく。
+
+\section{Task Manager の API}
+
+\section{SceneGraph}\label{sec:scenegraph}
+ゲーム中の一つの場面(Scene)を構成するオブジェクトやその振る舞いを格納したノードの
+集合を SceneGraph とする。SceneGraph のノードは親子関係を持つ tree で
+構成される。(図\ref{fig:sgtree})親子関係とは、親オブジェクトの回転や平行移動などの
+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。
+
+SceneGraph のノードは以下のようなデータを持つ。
+
+\begin{enumerate}
+\item Vertex: ポリゴンオブジェクトの頂点座標
+\item Texture: ポリゴンオブジェクトのテクスチャ座標
+\item TextureImage: テクスチャイメージ
+\item TransMatrix: ポリゴンオブジェクトの変換行列
+\item Coordinates: オブジェクトの座標
+\item Angle: オブジェクトの角度
+\end{enumerate}
+
+\begin{figure}[h]
+\begin{center}
+\includegraphics[scale=0.6]{images/sgtree.pdf}
+\end{center}
+\caption{SceneGraph Tree}
+\label{fig:sgtree}
+\end{figure}
+
+\section{Rendering Engine}\label{sec:rendering}
+Cerium の Rendering Engine は主に以下の 3 つの Task を持つ。
+
+\begin{itemize}
+\item CreatePolygonFromSceneGraph: 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、
+  PolygonPack(\ref{sec:renddata}節) を生成する Task
+\item CreateSpan: PolygonPack から同じ Y 座標を持つ線分の集合である SpanPack(\ref{sec:renddata}節) を生成する Task
+\item DrawSpan: SpanPack を Texture を読み込みながら Z Buffer を用いて描画する Task
+\end{itemize}
+
+Rendering Engine では、SceneGraph から、実際に表示するポリゴンを抽出、
+ポリゴンから Span の生成、Span に RGB をマッピングし描画する部分と 
+3 つに分けることができる。
+ここでいう Span とは、ポリゴンに対するある特定の Y 座標に関するデータを
+抜き出したものである。(図\ref{fig:span})
+
+\begin{figure}[h]
+\begin{center}
+\includegraphics[scale=0.8]{images/span.pdf}
+\end{center}
+\caption{Span}
+\label{fig:span}
+\end{figure}
+
+\subsection{Rendering で使うデータ構造}\label{sec:renddata}
+レンダリング処理は SPE で行う事を前提とし、それに合わせたデータ構造を
+採用している。
 
-\section{Cell Broadband Engineの構造}
-\subsection{PPE (PowerPC Processor Element)}
-\subsection{SPE (Synergistic Processor Element)}
-\subsection{Cell の基本性能}
-\section{Game Framework Cerium}
-\subsection{Scene Graph}
-\subsection{Rendering Engine}
-\subsection{Task Manager}
-\subsection{Task 生成に関連する API}
+\subsubsection*{PolygonPack}
+PolygonPack は SceneGraph から抽出されたポリゴンの集合である。
+光源やテクスチャ、頂点の座標から構成される。
+
+\subsubsection*{SpanPack}
+SpanPack はポリゴンから抽出された Span の集合である。
+Span はその座標と、対応するテクスチャの座標を持つ。(図\ref{fig:spack})
+
+\begin{figure}[h]
+\begin{center}
+\includegraphics[scale=0.8]{images/spack.pdf}
+\end{center}
+\caption{Span 構造}
+\label{fig:spack}
+\end{figure}
+
+\section{OpenCL}
+OpenCL(Open Computing Language) とは、マルチコア CPU や GPU、その他の
+プロセッサによる、ヘテロジニアスコンピューティングのフレームワークである。
+OpenCL C プログラミング言語は ISO/IEC 9899:1999(C99) 規格をベースとしている。
+ OpenCL のプラットフォームモデルは図 \ref{fig:opencl} のようになり、一つの 
+Host と複数の OpenCL Device で構成されている。OpenCL devices の中では Compute 
+Units(CUs) として分割され、その中でさらに Processing Elements(PEs) として
+分割される。
+
+\begin{figure}[h]
+\begin{center}
+\includegraphics[scale=0.8]{images/opencl.pdf}
+\end{center}
+\caption{OpenCL Platform}
+\label{fig:opencl}
+\end{figure}
+
+OpenCL アプリケーションでは、実行する処理コマンドが Host から PEs へ送られる。
+PEs では SIMD(Single Instruction Multiple Data)もしくは SPMD(Single Program 
+Multiple Data) で実行される。
+
+OpenCL devices や Host には kernel があり、Host kernel では OpenCL devices 
+context や実行コマンドの処理を行う。Host は OpenCL devices での kernel の
+実行を調整するために、 command-queue を生成し、context へ渡す。
+command-queue には 以下のコマンドがある。
+
+\begin{itemize}
+\item Kernel execution commands\\
+  実行コマンド queue
+\item Memory commands\\
+  データの送受信に関する情報(Host アドレス空間)
+\item Synchronization commands\\
+  commannd の依存や同期等に関する情報
+\end{itemize}
+
+また、OpenCL Device は 4 つの違うメモリ領域 (Global Memory, Constant Memory, 
+Local Memory, Private Memory) を持ち、それぞれ Host や CUs、PEs からの
+アクセス権限が異なる(アドレス空間が異なる)。
+
+プログラミングモデルとしては、データ並列、タスク並列をサポートしている。
+OpenCL は Host や各 device に kernel があることや、device 毎にメモリアドレス
+空間が違う、プログラミングモデル等、TaskManager とよく似ている。
+
+OpenCL は汎用的な実装となっているため、例えば Task のメモリアクセス API も
+複雑な記述となっている。対して Task Manager は、現在 Cell 環境に重きを
+置いているため、メモリアクセスは DMA に対応した記述が行われる。DMA では
+明示的にアドレスを指定することになるので、OpenCL よりも簡潔な記述が可能と
+なっている。このことから、Task Manager は OpenCL の軽めな実装の一つという
+捉え方もできる。
+
+OpenCL に対して Task Manager が優れている点は、Mac OSX や Linux、Cell といった
+複数の環境で動作する事による信頼性の確保のしやすさにある。Task Manager では、
+Task 毎に実行する CPU を選択できるため、動作環境が変わっても大幅なコードの
+変更が必要なく、Single Core プログラムとして動作させることができる。
+これにより、 Task 単体やそれらを繋げたプログラム全体を逐次型プログラムとみなし、
+二分法などのデバッグ手法を用いる事ができる。このことは図\ref{fig:devstep} 
+のような段階に沿って開発が可能になることに繋がる。
--- a/paper/game.tex	Sun Jan 30 17:44:27 2011 +0900
+++ b/paper/game.tex	Tue Feb 01 18:33:29 2011 +0900
@@ -1,8 +1,166 @@
-\chapter{ゲームプログラミング} \label{chapter:game}
+\chapter{ゲームプログラミングにおけるテストと Super Dandy} \label{chapter:game}
+ここではゲームプログラムの特徴とテストの関連性、そして実験に使用した
+ゲーム Super Dandy の実装について述べる。
+
+\section{ゲームプログラムのテスト}\label{sec:feature}
+多くのゲームでは多数のオブジェクトが存在し、プレイヤーのコントローラー入力や
+ゲームの進行状況によって生成される。生成されたオブジェクトは他のオブジェクトの
+座標などのパラメータに影響され、衝突判定を行ったり、その動きを変える。
+(図\ref{fig:feature})
+
+\begin{figure}[h]
+\begin{center}
+\includegraphics[scale=0.6]{images/feature.pdf}
+\end{center}
+\caption{ゲームオブジェクトの相互作用}
+\label{fig:feature}
+\end{figure}
+
+このようにゲームプログラムでは常にプレイヤーの入力がゲームに影響され、
+オブジェクト同士のパラメーターが相互に干渉し合うため、遷移する状態が
+膨大であり、状態遷移が仕様の範囲に収まるかをテストする一般的な
+テスト駆動のようなテストにはならない。
+よってゲームプログラムは実際にプレイすることが重要なテストである。
+
+\subsection{プレイヤーの入力}\label{sec:player}
+ゲームプログラムではコントローラーなどのインターフェースにより、
+プレイヤーから入力が与えられ、それによってゲーム内のパラメータが変化する。
+例えばプレイヤーの操作によりキャラクターが移動する、攻撃するといった事が
+これに当たる。
+
+プレイヤーの入力は常に非決定的であり、例え同じ人間が同じゲームの同じ場面を
+プレイしたとしても毎回全く同じ入力をする可能性は極めて低い。
+こうした事からプレイヤーは制御不能なランダム要素であると考えられ、
+ゲームプログラムテストにおけるバグの再現性を低下させる要因となっている。
+
+\subsection{乱数}\label{sec:random}
+ゲームにおける乱数は、オブジェクトの振る舞いに多様性を持たせたり、ランダムな
+配置を実現する為に使われ、ゲームのボリュームや面白さを広げる役割を担ってきた。
+これは例えば以下のようなコードにより実現される。
+
+\begin{verbatim}
+void
+random_move(Character *chara)
+{
+    int count = random() % 3;
+
+    if (count == 0) {
+        chara->x += 1;
+        return;
+    } else if (count == 1) {
+        chara->y += 1;
+        return;
+    } else if (count == 2) {
+        chara->x += 1;
+        chara->y += 1;
+        return;
+    }
+}
+\end{verbatim}
+
+こうした乱数の使用法は特に携帯ゲーム機やコンソールゲーム機のような
+リソースの限られた環境においては複雑で容量の大きいレベルデータを格納する事が
+困難であったため、ゲームの深みを演出する上で用いられてきた。しかしテストを
+する上で、乱数の変動によりバグが再現困難になるといった事態も起こりうる。
+この為、乱数に対しては、常に同じ乱数列を生成するように、乱数生成器を無効に
+するか、定数でシードしてやると良い。
+
+\section{Super Dandy}\label{sec:dandy}
+Super Dandy は我々が PlayStation でのゲーム開発を行っていた 1998 年に
+開発されたシューティングゲームである。PlayStation アーキテクチャの
+スプライト描画機能を用いて宇宙空間を表現しており、タイトルからゲーム本編中の
+敵機の登場、攻略後のスコア一覧、エンディングなどのシーン切り替え、4 種類の
+射撃と 2 種類の特殊射撃を駆使し、ステージをクリアしていくなど、ゲーム性も
+高い。SuperDandy は開発する環境が変わる度に移植されており、過去には 
+PlayStation2 Linux、OpenGL バージョンも作られた。(図\ref{fig:dandy})
 
-\section{ゲームプログラムの特徴}
-\subsection{プレイヤーの入力}
-\subsection{乱数}
-\section{Super Dandy}
+\begin{figure}[hb]
+\begin{center}
+\includegraphics[scale=0.4]{images/dandy.pdf}
+\end{center}
+\caption{Super Dandy}
+\label{fig:dandy}
+\end{figure}
+
+\newpage
+
+Super Dandy が伝統的に移植されてきた背景には、ある程度のボリュームのある
+ゲームであること、衝突判定やオブジェクト管理、ステージクリアによる
+シーン切り替えなど、基本的なゲームとしての要素が入っていること、
+そして動作結果を過去の環境と比較することで新たな環境のチューニングが行える
+ことが挙げられる。
+
+\section{Task Dandy(Super Dandy Task version)}\label{sec:taskdandy}
+本研究を進めるにあたり、Super Dandy を Cerium の Task で書き換えた 
+Task Dandy を作成した。Task Dandy はできるだけ元の Super Dandy のコード
+やデータ構造を流用し、比較、テストが容易に行えるように設計した。
+
 \subsection{データ構造}
-\subsection{Task 構成と動作}
+データ構造は Super Dandy のものを流用している。Super Dandy では主に以下の
+ようなデータが存在する。
+
+\begin{itemize}
+\item player:\\
+  プレイヤーの操作する機体。xy 座標の他、残機数、無敵時間、
+  コンテニュー回数などが存在する。
+\item CHARACTER:\\
+  敵キャラクターや敵の弾。xy 座標とその方向の速さ、体力、倒したときのスコア、
+  オブジェクトの種類を表すキャラナンバー、死亡フラグなどがある。
+  また、Move と Collision を関数ポインタで持ち、ステートパターンで
+  切り替えて状態遷移する。
+\item tama\_lv1〜laser\_lv3:\\
+  プレイヤーが撃った弾。xy 座標と存在の有無を表すフラグを持っている。
+  プレイヤーが射撃ボタンを押すと対応した弾の配列に状態が格納され、
+  敵に当たるか、画面外に消えるまで存在フラグが立つ。
+\end{itemize}
+
+\subsection{Task Dandy の Task}
+
+
+\subsection{SPE における状態遷移}
+SPE では各々に固有の LS を持つ\ref{sec:spe}為、Super Dandy で使用していた
+ステートパターンは使用できない。これは関数ポインタに格納されているアドレスが 
+PPE 上のものであり、SPE では意味を為さないからである。
+
+そこで SPE 上では Task の ID を変更することによりオブジェクトの状態遷移を
+実現するようにした。CHARACTER 構造体に Task ID を格納する新たなパラメータを
+追加し、以下のようなコードで状態が遷移する条件に入ると Task ID が
+書き換えられる。
+
+\begin{verbatim}
+static int
+state6(SchedTask *smanager, void *rbuf, void *wbuf)
+{
+    CHARACTER *p = (CHARACTER*)smanager->get_input(rbuf, 0);
+    CHARACTER *q = (CHARACTER*)smanager->get_output(wbuf, 0);    
+    player *jiki = (player*)smanager->get_input(rbuf, 1);
+
+    p->y += p->vy;
+    p->x += p->vx;
+    if(p->y + 96 < jiki->y
+       && p->y + 128 > jiki->y)
+    {
+	p->vy = 2;
+	p->vx = ((jiki->x > p->x) ? 4 : -4);
+	p->state_task = STATE0;
+    }
+    else p->state_task = STATE6;
+
+    *q = *p;
+    return 0;
+}
+\end{verbatim}
+
+書き換えられた ID は次に Task を生成する際に使用され、別の種類の Task を
+生成するようになる。
+
+\begin{verbatim}
+    int task_num = p->state_task;
+    HTaskPtr state_task = tmanager->create_task(task_num);
+\end{verbatim}
+
+\subsection{SPE におけるオブジェクトの生成}
+
+
+
+\subsection{Cerium に実装した機能}
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+	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 0 483 264
+%%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 /P put
+
dup 35 /E put
+
dup 36 /parenleft put
+
dup 37 /y put
+
dup 38 /n put
+
dup 39 /e put
+
dup 40 /r put
+
dup 41 /g put
+
dup 42 /t put
+
dup 43 /i put
+
dup 44 /c put
+
dup 45 /o put
+
dup 46 /s put
+
dup 47 /l put
+
dup 48 /m put
+
dup 49 /parenright put
+
dup 50 /I put
+
dup 51 /B put
+
dup 52 /space put
+
dup 53 /u put
+
dup 54 /w put
+
dup 55 /C put
+
dup 56 /M put
+
dup 57 /a 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
+
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currentdict dup/FontName get exch definefont pop end
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%APLsfntEnd
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{currentfile 0(%APLT1End\n)/SubFileDecode filter flushfile}if
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currentdict currentfile eexec
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+/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 0 281 273
+%%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 /P put
+
dup 34 /E put
+
dup 35 /S put
+
dup 36 /L put
+
dup 37 /two put
+
dup 38 /space put
+
dup 39 /C put
+
dup 40 /a put
+
dup 41 /c put
+
dup 42 /h put
+
dup 43 /e put
+
dup 44 /U put
+
dup 45 /one put
+
dup 46 /I put
+
dup 47 /n put
+
dup 48 /s put
+
dup 49 /t put
+
dup 50 /r put
+
dup 51 /u put
+
dup 52 /i put
+
dup 53 /o put
+
dup 54 /D put
+
readonly def
+
42/FontType resourcestatus{pop pop false}{true}ifelse
+
%APLsfntBegin
+
{currentfile 0(%APLsfntEnd\n)/SubFileDecode filter flushfile}if
+
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+
/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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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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/UniqueID 4265107 def
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currentdict currentfile eexec
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+%%Trailer
+%%EOF
--- a/paper/introduciton.tex	Sun Jan 30 17:44:27 2011 +0900
+++ b/paper/introduciton.tex	Tue Feb 01 18:33:29 2011 +0900
@@ -4,16 +4,52 @@
 \section{研究背景・目的}
 我々は、これまで家庭用ゲーム機上におけるゲームプログラミングをサポートする
 オープンな開発フレームワークの研究を行ってきた。
+過去には PlayStation や PlayStation2、GameBoyAdvance での
+ゲームプログラミングを行っており、現在は PlayStation3 上での開発を行っている。
+
+PlayStation3 のアーキテクチャは Cell Broadband Engine と呼ばれ、
+1つの制御系プロセッサ Power Processor Element (PPE) と、
+8つのデータ処理演算プロセッサ Synergistic Processor Element (SPE) 
+から構成される。我々は、このような Many Core Architecture を用いた
+並列プログラムの開発フレームワークとして Cerium Game Engine を開発した。
+Cerium では、 プログラムを Task という単位で管理しており、
+この Task と計算に必要なパラメータを PPE や各 SPE に並列に処理させる事により、
+プログラムの動作を実現している。
+
+Cerium においてゲーム開発を行う場合もプログラムを Task 単位に分けて処理させる。
+ゲームプログラムの特徴として、衝突判定などのオブジェクト間で相互に影響する
+パラメータが多いこと、プレイヤーのゲームパッドからの入力やコード内に
+埋め込まれた乱数などの非決定的な要素が多いことが挙げられる。
+その為、Task 間でのパラメータの同期や Task 処理のタイミングによって
+生成される乱数が異なるなどの問題があり、単純にシーケンシャルに
+書かれたゲームプログラムを Task に分割して処理させても、元のプログラムを
+逐次実行させた時と同じ動作をすることは保証されない。
+
+そこで本研究ではシーケンシャルなゲームプログラムと Task に分割した
+ゲームプログラムの動作が同一であることを確認するためのテスト手法を提案する。
+シーケンシャルに書かれたゲームプログラムとそれを Task に分割したゲームプログラム
+をテストモデルとし、プレイヤー入力や乱数などの非決定的な要素の固定化や、
+動作の同一性を確かめるのに必要なパラメータの書き出し、そしてより高速な
+動作でテストを行うことができる環境を構築する。
+
+\newpage
 
 \section{論文構成}
 
-第2章では PlayStation3 のアーキテクチャである Cell Broadband Engine の
-仕様と先行研究として開発された Game Framework Cerium の実装、
-そして開発における主要な API を紹介する。
-第3章ではゲームプログラミングの特徴とテストモデルとして移植した
-シューティングゲーム Super Dandy の実装について述べる。
-第4章ではテスト手法として用いたプレイヤー入力と乱数の固定、ビデオモードの実装、
-そして出力されるテストデータの説明を述べる。
-第5章ではテストを行った際の実行時間とカバレッジ率について述べる。
-また、実際にテストデータを用いて行なったデバッグの例を紹介する。
-第6章では本研究のまとめと今後の課題を示す。
+第 \ref{chapter:knowledge} 章では PlayStation3 のアーキテクチャである 
+Cell Broadband Engine の仕様と Cell の基本的な機能について述べる。
+
+第 \ref{chapter:early} 章では先行研究として開発された Game Framework Cerium 
+の実装、そして開発における主要な API を紹介する。
+
+第 \ref{chapter:game} 章ではゲームプログラミングの特徴とテストモデルとして
+移植したシューティングゲーム Super Dandy の実装について述べる。
+
+第 \ref{chapter:test} 章ではテスト手法として用いたプレイヤー入力と乱数の
+固定、ビデオモードの実装、そして出力されるテストデータの説明を述べる。
+
+第 \ref{chapter:result} 章ではテストを行った際の実行時間とカバレッジ率に
+ついて述べる。また、実際にテストデータを用いて行なったデバッグについて
+紹介する。
+
+第 \ref{chapter:conclusion} 章では本研究のまとめと今後の課題を示す。
--- a/paper/master_paper.tex	Sun Jan 30 17:44:27 2011 +0900
+++ b/paper/master_paper.tex	Tue Feb 01 18:33:29 2011 +0900
@@ -6,7 +6,7 @@
 
 \input{dummy.tex} %% font
 
-\jtitle{CeriumGameEngine を用いた\\ ゲームプログラミングにおけるテスト手法}
+\jtitle{Game Framework Cerium を用いた\\ ゲームプログラミングにおけるテスト手法の提案}
 \etitle{}
 \year{平成22年度}
 \affiliation{\center%
@@ -25,7 +25,7 @@
 \end{minipage}}
 \markleftfoot{% 左下に挿入
   \begin{minipage}{.8\textwidth}
-    CeriumGameEngine を用いた\\ ゲームプログラミングにおけるテスト手法
+    Game Framework Cerium を用いた\\ ゲームプログラミングにおけるテスト手法の提案
 \end{minipage}}
 
 \newcommand\figref[1]{図 \ref{fig:#1}}
@@ -52,7 +52,8 @@
 
 %chapters
 \input{introduciton.tex} %1
-\input{early.tex} %2
+\input{knowledge.tex} %2
+\input{early.tex} %3
 \input{game.tex} %3
 \input{test.tex} %4
 \input{result.tex} %5