changeset 0:8bf606ea2dba

add all files
author Kaito Tokumori <e105711@ie.u-ryukyu.ac.jp>
date Sun, 03 Nov 2013 22:15:28 +0900
parents
children cc02718aa4be
files 2013_mid.pdf 2013_mid.tex figure/.DS_Store figure/codesegment.pdf figure/continuation.pdf figure/env_code.pdf mediabb.sty pic/.DS_Store pic/emblem-bitmap.eps
diffstat 9 files changed, 1555 insertions(+), 0 deletions(-) [+]
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Binary file 2013_mid.pdf has changed
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+\documentclass[twocolumn,twoside,9.5pt]{jarticle}
+\usepackage[dvips]{graphicx}
+\usepackage{picins}
+\usepackage{fancyhdr}
+\pagestyle{fancy}
+\usepackage{mediabb}
+\usepackage{float}
+
+\lhead{\parpic{\includegraphics[height=1zw,clip,keepaspectratio]{pic/emblem-bitmap.eps}}琉球大学主催 工学部情報工学科 卒業研究発表会}
+\rhead{}
+\cfoot{}
+
+\setlength{\topmargin}{-1in \addtolength{\topmargin}{15mm}}
+\setlength{\headheight}{0mm}
+\setlength{\headsep}{5mm}
+\setlength{\oddsidemargin}{-1in \addtolength{\oddsidemargin}{11mm}}
+\setlength{\evensidemargin}{-1in \addtolength{\evensidemargin}{21mm}}
+\setlength{\textwidth}{181mm}
+\setlength{\textheight}{246mm}
+\setlength{\footskip}{0mm}
+\pagestyle{empty}
+
+\begin{document}
+\title{Continuation based C コンパイラの LLVM 3.4 上での実装}
+\author{105711B 氏名 徳森 海斗 指導教員 : 河野 真治}
+%\date{2013年11月3日}
+\maketitle
+\thispagestyle{fancy}
+
+\section{背景及び研究目的}
+現代社会においてプログラムは様々な場所で用いられ,その用途に応じて求められる要素も様々である.例えば Real-time な制御が重要視される場合には速度が,組込みシステムなどのメモリが制限される環境では軽量なプログラムが求められる.軽量で高速であるという条件に最も適しているのはアセンブリ言語であるが,低レベル過ぎてわかりづらい上に,アーキテクチャへの依存性が高いため汎用的でない.当研究室ではそういった要求に応える言語として Continuation based C (以下 CbC) を提案している.
+CbC のコンパイラは2001年に micro-c をベースとしたものが開発され,続いて2008年の研究により GCC ベースのものが開発された.これにより GCC の持つ最適化の恩恵を受けることに成功している.しかし、 Mac  OS X の最新版である Mavericks が C コンパイラとして GCC ではなく clang を用いるようになったことや, LLVM にも GCC 同様に強力な最適化機能が存在し,さらにエラーメッセージが GCC に比べ丁寧であるという特徴を持つことから, GCC から clang に移り変わる人々も少なくない.そこで本研究では, micro-c , GCC に続く LLVM/clang ベースのコンパイラの開発を行う.
+\section{Continuation based C (CbC)}
+CbC のでは処理をコードセグメントという単位で記述し,コード間の移動に goto (軽量継続)を用いる.
+構文は C と同じであるが, ループ制御や関数コールが取り除かれる.
+
+\subsection{継続 (goto)}
+コードセグメントの記述は C の関数の構文と同じで, 型に ``\verb+__code+'' を使うことで宣言できる.
+コードセグメントへの移動は ``goto'' の後にコードセグメント名と引数を並べて記述することで行える.
+この goto による処理の遷移を継続と呼ぶ.
+図\ref{fig:cs}はコードセグメント間の処理の流れを表している.
+
+\begin{figure}[htpb]
+  \begin{center}
+\scalebox{0.30}{\includegraphics{figure/codesegment.pdf}}
+  \end{center}
+  \caption{コードセグメント間の継続(goto)}
+  \label{fig:cs}
+\end{figure}
+
+\subsection{コードセグメント (code segment)}
+コードセグメントは C の関数と異なり戻り値を持たず, 処理が終われば次のコードセグメントへと処理を移る.
+C において関数呼び出しを繰り返し行う場合, 呼び出された関数の引数の数だけスタックに値が積まれていく.
+しかし, 戻り値を持たないコードセグメントではスタックに値を積んでいく必要な無く, スタックは変更されない.
+このようなスタックに値を積まない継続,つまり呼び出し元の環境を持たない継続を軽量継続と言い,軽量継続により並列化, ループ制御, 関数コールとスタックの操作を意識した最適化がソースコードレベルで行えるようになる.
+
+\section{LLVM/clang 3.4 上での実装}
+ここではLLVM/clang 3.4 上でどのように CbC コンパイラを実装するかについて述べる.
+%CbC コンパイラを実現するには以下の機能を実装する必要がある.
+%\begin{itemize}
+%\item ``\_\_code"のパース
+%\item goto シンタックスの追加
+%\item 軽量継続の実装
+%\item 環境付き継続の実装
+%\end{itemize}
+
+\subsection{``\_\_code"のパース}
+予約語は clang/include/clang/Basic/TokenKinds.def で登録する.登録する予約語がC,あるいはC++のどの規格で使用されるものかもここで記述し,これによりclangのパーサーが``\_\_code"をkw\_\_\_codeとして認識するようになる.
+
+\subsection{goto シンタックスの追加}
+通常, goto のシンタックスは ``goto ラベル名;" となっている.CbC ではこれに加え,``goto codeSegment();"の形でコードセグメントを呼び出すシンタックスを追加する必要がある.
+
+\subsection{軽量継続の実装}
+軽量継続の実装は Tail Call Elimination (末尾除去)の強制によって実現する. これによりコードセグメント間の移動に call ではなく jmp 命令が用いられるようになる.図\ref{fig:continue}は Tail Call Elimination が行われた際のプログラムの処理を表している.
+funcB は jmp 命令で funcC を呼び出す.
+funcC は, 戻り値を funcB ではなく funcA へと返すことになる.
+
+\begin{figure}[htpb]
+  \begin{center}
+\scalebox{0.25}{\includegraphics{figure/continuation.pdf}}
+  \end{center}
+  \caption{Tail Call Elimination}
+  \label{fig:continue}
+\end{figure}
+
+\subsection{Tail Call Elimination の強制}
+LLVM で Tail Call Elimination を行う場合,対象となる関数の isTailCall というフラグを true にした上で, アーキテクチャ によって異なるいくつかの条件を満たす必要がある.現在は x86/x86-64 と PowerPC がこの最適化を利用できる.これらのアーキテクチャでの条件を以下に示す.
+%isTailCall を true にする処理は TailCallElim という Pass によって行われる.通常この Pass は Optimize level が 2 以上の場合にのみ有効化されるが, コード内に``\_\_code"が含まれる場合にはこの Pass を有効化し,コードセグメントに対してのみ処理を行うように改変した.
+\begin{itemize}
+\setlength{\itemsep}{0mm}
+\item caller と callee の calling convention が fastcc, cc10, cc11 のいずれかである.
+\item 関数呼び出しが return の直前に行われており, void 型である.
+\item 可変長引数リストを使用していない.
+\item tailcallopt が有効になっている.
+\item byval parameter を使用していない.
+\item PIC/GOT を用いる場合,visibility が hidden か protected である必要がある.
+\end{itemize}
+%また,X86/X86-64 の場合には Sibling call optimization というものがあり,いくつかの条件を満たすことで Tail Call Elimination と同様の最適化を受けることができるが, 別アーキテクチャのサポートも考え, Tail Call Elimination を用い, Sibling call optimization は使用しない.
+\subsection{環境付き継続}
+CbC には通常の C の関数からコードセグメントに継続する際,
+ その関数から値を返す処理への継続を得ることができる.
+これを環境付き継続といい,Cとの互換性を持たせるためにこの機能が必要となる.
+環境付き継続は, CbC で定義した以下の二種類特殊変数によって実現される.
+\verb+__environment+ は, 環境を表す情報である.
+\verb+__return+ は,  環境付き継続によって継続した後,環境付き継続を行った関数の呼び出し元に戻り値を返すためのものであり, 関数の戻り値と \verb+__environment+ の二つの引数を持つ
+コードセグメントである. 例えば, 図\ref{fig:env_code}のように使うと, \verb+main()+ は 1 を返す.
+
+\begin{figure}[htpb]
+  \begin{center}
+\scalebox{0.33}{\includegraphics{figure/env_code.pdf}}
+  \end{center}
+  \caption{\_\_return, \_\_environment 変数の使用例}
+  \label{fig:env_code}
+\end{figure}
+
+環境付き継続の実装案には複数あり, 例えばGCC 版の CbC コンパイラでは内部関数を用いることで環境付き継続を実現している.この他には setjmp , longjmp を用いた実装案, Exception を用いた実装案,LLVM IRを用いた実装案がある.
+
+%GCC内部では, \verb+__return+ は, 関数内で定義された \verb+_cbc_internal_return+関数へのポインタを返す.
+%戻り値は, \verb+cbc_internal_return+ 関数内で定義された変数\verb+retval+を通して返される(図\ref{fig:ret_val_code}).
+
+\section{現状及び今後の課題}
+今後は本稿でも述べたとおり、LLVM/clang 上での CbC コンパイラの実装を行っていく.実装後はGCC版とLLVM版のCbCコンパイラそれぞれでコンパイルしたプログラムの性能比較を行う予定である.
+%また,LLVM版とGCC版でCbCコンパイラを実現するために変更を加えた箇所を比較し,どちらが実装を容易に行えるかも判別する.
+
+\begin{thebibliography}{9}
+\bibitem{1}与儀 健人. ``組み込み向け言語Continuation based C の GCC 上の実装". 琉球大学 情報工学科 学位論文(修士), 2008
+\vspace{-3mm}
+\bibitem{2}大城 信康,河野 真治. ``Continuation based C の GCC 4.6 上の実装について". 第53回プログラミング・シンポジウム, 2011
+\vspace{-3mm}
+\bibitem{3}LLVM 3.4 documentation.\\ ``http://llvm.org/docs/index.html"
+\vspace{-3mm}
+\bibitem{4}``Clang" CFE Internals Manual - Clang 3.4 documentation.\\ ``http://clang.llvm.org/docs/InternalsManual.html"
+\vspace{-3mm}
+\bibitem{5}LLVM API Documentation.\\ ``http://llvm.org/docs/doxygen/html/index.html"
+\vspace{-3mm}
+\bibitem{6}Clang API Documentation.\\ ``http://clang.llvm.org/doxygen/"
+\vspace{-3mm}
+\end{thebibliography}
+\end{document}
\ No newline at end of file
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--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/mediabb.sty	Sun Nov 03 22:15:28 2013 +0900
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+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{mediabb}[2006/10/26 v1.9 iNOUE Koich! <inoue@ma.ns.musashi-tech.ac.jp>]
+\@ifpackageloaded{graphics}{}{\RequirePackage[dvipdfm]{graphicx}}
+\define@key{Gin}{usebb}[true]{\expandafter\let\expandafter\if@usebb\csname if#1\endcsname}
+\let\if@usebb\iffalse
+\define@key{Gin}{mediaboxonly}[/MediaBox]{\@ifundefined{Gread@find@#1}%
+  {\def\Gread@rect@box{/MediaBox}\expandafter\let\expandafter\if@Gread@find@only\csname if#1\endcsname}%
+  {\def\Gread@rect@box{#1}\let\if@Gread@find@only\iftrue}}
+\let\if@Gread@find@only\iffalse
+\def\Gread@rect@box{/MediaBox}
+\define@key{Gin}{autoebb}[always]{\csname Gread@ebb@#1\endcsname}
+\def\Gread@ebb@always{\let\if@Gread@ebb@always\iftrue}
+\let\if@Gread@ebb@always\iffalse
+\let\Gread@ebb@true\Gread@ebb@always
+\def\Gread@ebb@never{\let\if@Gread@ebb@never\iftrue}
+\let\Gread@ebb@false\Gread@ebb@never
+\let\if@Gread@ebb@never\iffalse
+\let\Ginclude@pdf\Ginclude@eps
+\def\Gread@pdf#1{%
+  \begingroup
+    \if@usebb\else
+      \@tempcnta\z@
+      \loop
+      \ifnum\@tempcnta<\@xxxii
+        \catcode\@tempcnta14
+        \advance\@tempcnta\@ne
+      \repeat
+	  \@tempcnta127
+      \loop
+      \ifnum\@tempcnta<\@cclvi
+        \catcode\@tempcnta14
+        \advance\@tempcnta\@ne
+      \repeat
+      \let\do\@makeother\dospecials\catcode`\ 10
+      \catcode\endlinechar10
+      \immediate\openin\@inputcheck#1
+      \ifeof\@inputcheck
+        \@latex@error{File `#1' not found}\@ehc
+      \else
+        \Gread@true
+        \let\@tempa\@empty
+        \let\@tempb\@empty
+        \loop
+          \read\@inputcheck to\@tempc
+          \ifeof\@inputcheck
+            \Gread@false
+          \else
+            \edef\@tempa{\@tempb\@tempc}\let\@tempb\@tempc
+            \edef\@tempc{\@tempa\Gread@rect@box}%
+            \csname Gread@find@\Gread@rect@box\expandafter\endcsname\@tempc[\@nnil]\\%
+          \fi
+        \ifGread@
+        \repeat
+        \immediate\closein\@inputcheck
+      \fi
+    \fi
+    \ifGin@bbox
+    \else
+      \Gread@bmp{\Gin@base.bb}%
+    \fi
+  \endgroup
+  \expandafter\Gread@parse@bb\@gtempa\\}
+\def\def@Gread@find#1#2{\ifx\@nnil#2\expandafter\@gobble\else
+    \@namedef{Gread@find@#1}##1#1##2[##3##4]##5\\{%
+      \ifx\@nnil##3\else
+        \gdef\@gtempa{##3##4 }%
+        \if@Gread@find@only
+          \Gread@false
+        \else
+          \def\Gread@rect@box{#1}%
+        \fi
+        \Gin@bboxtrue
+      \fi
+      \if@Gread@find@only\else
+        \csname Gread@find@#2\expandafter\endcsname\@tempa#2[\@nnil]\\%
+      \fi}%
+    \expandafter\def@Gread@find\fi{#2}}
+\def@Gread@find{/MediaBox}{/CropBox}{/BleedBox}{/TrimBox}{/ArtBox}\@nnil
+\@namedef{Gread@find@/ArtBox}#1/ArtBox#2[#3#4]#5\\{%
+  \ifx\@nnil#3\else
+    \gdef\@gtempa{#3#4 }%
+    \Gread@false
+    \Gin@bboxtrue
+  \fi}
+\def\Gread@bmp#1{%
+  \if@Gread@ebb@never\else
+    \if@Gread@ebb@always\else
+      \immediate\openin\@inputcheck#1 %
+      \ifeof\@inputcheck
+        \Gread@ebb@always
+      \else
+        \immediate\closein\@inputcheck
+      \fi
+    \fi
+    \immediate\write18{\if@Gread@ebb@always\else[ '\Gin@base\Gin@ext' -nt '\Gin@base.bb' ] && \fi
+      \ifx\@nnil\filename@area\@nnil\else cd '\filename@area' && \fi ebb '\filename@base\Gin@ext'}%
+  \fi
+  \Gread@eps{#1}}
+\DeclareGraphicsRule{.pdf}{pdf}{*}{}
Binary file pic/.DS_Store has changed
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/pic/emblem-bitmap.eps	Sun Nov 03 22:15:28 2013 +0900
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+%%CreationDate: (Unknown)
+%%For: (Unknown)
+%%DocumentData: Clean7Bit
+%%LanguageLevel: 2
+%%Pages: 1
+%%BoundingBox: 0 0 451 246
+%%EndComments
+%%BeginProlog
+%%BeginFile: cg-pdf.ps
+%%Copyright: Copyright 2000-2004 Apple Computer Incorporated.
+%%Copyright: All Rights Reserved.
+currentpacking true setpacking
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+/xs{exch store}bd
+/xd{exch def}bd
+/cmmtx matrix def
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+{ld}repeat pop
+/SC{	
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+/cm {cmmtx astore CM concat}bd	
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+}ifelse
+{	
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+	    F charpath
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+  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
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+/cg_aiproc{currentfile/ASCII85Decode filter/RunLengthDecode filter}bd
+/ImageDataSource 0 def
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+    /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
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+counttomark 2 idiv
+dup 2 add	
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+{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
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