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author | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
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committer | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
commit | e0c6872cf40896c7be36b11dcc744620f10adf1d (patch) | |
tree | 60335e10d2f4354b0674ec22d7b53f0f8abee672 /macros/latex/contrib/utthesis |
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diff --git a/macros/latex/contrib/utthesis/ICDE-11/abstract.tex b/macros/latex/contrib/utthesis/ICDE-11/abstract.tex new file mode 100644 index 0000000000..c966ccb075 --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/abstract.tex @@ -0,0 +1,23 @@ +\firstpage +\begin{abstract} +{\itshape +From our experience, current rule-based query optimizers do not provide +a very intuitive and well-defined framework to define rules and +actions. To remedy this situation, we propose an extensible and +structured algebraic framework called Prairie for specifying rules. +Prairie facilitates rule-writing by enabling a user to write rules and +actions more quickly, correctly and in an easy-to-understand and +easy-to-debug manner. + +Query optimizers consist of three major parts: a search space, a cost +model and a search strategy. The approach we take is only to develop +the algebra which defines the search space and the cost model and use +the Volcano optimizer-generator as our search engine. Using Prairie as +a front-end, we translate Prairie rules to Volcano to validate our +claim that Prairie makes it easier to write rules. + +We describe our algebra and present experimental results which +show that using a high-level framework like Prairie to design +large-scale optimizers does not sacrifice efficiency. +} +\end{abstract} diff --git a/macros/latex/contrib/utthesis/ICDE-11/conclusion.tex b/macros/latex/contrib/utthesis/ICDE-11/conclusion.tex new file mode 100644 index 0000000000..fbfb02c0c5 --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/conclusion.tex @@ -0,0 +1,49 @@ +\section{Conclusion and future work} +\label{sec:conclusion} + +Current rule-based query optimizers do not provide a very intuitive and +conceptually streamlined framework to define rules and actions. Our +experiences with the Volcano optimizer generator suggest that its model +of rules and the expression of these rules is much more complicated and +too low-level than it needs to be. As a consequence, rule sets in +Volcano are fragile, hard to write, and debug. Similar problems may +exist in other contemporary rule-based query optimizers. + +We believe that rule-based query optimizers will be standard tools +of future database systems. The pragmatic difficulties of using +existing rule-based optimizers led us to develop Prairie, an +extensible and structured algebraic framework for specifying rules. +Prairie is similar to existing optimizers in that it supports both +transformation rules and implementation rules. However, Prairie +makes several improvements: +\begin{enumerate} +\item it offers a conceptually more streamlined model for rule specification; +\item rules are encapsulated, there are no ``hidden'' operators or + ``hidden'' algorithms; +\item implementation hints (\eg enforcers) are deduced automatically; +\item and it has efficient implementations. +\end{enumerate} + +We have explained how the first three points are important for +simplifying rule specifications and making rule sets less brittle for +extensibility. A consequence is that Prairie rules are simpler and +more robust than rules of existing optimizers (\eg Volcano). We +addressed the fourth point by building a P2V pre-processor which uses +sophisticated algorithms to compose and compact a Prairie rule set into +a Volcano rule set. To demonstrate the scalability of our approach, we +rewrote the TI Open OODB rule set as a Prairie rule set, generated its +Volcano counterpart, and showed that the performance of the synthesized +Volcano rule set closely matches the hand-crafted Volcano rule set. + +Our future work will concentrate on developing higher-level +abstractions using Prairie, including automatically generating Prairie +rule sets, and combining multiple Prairie rule sets to automatically +generate efficient optimizers. + +\section*{Acknowledgments} +\label{sec:acknowledgments} + +We wish to thank Texas Instruments, Inc.\ for making the Open OODB +source code available to us. Comments by Jos\'e Blakeley, Anne Ngu, +Vivek Singhal, Thomas Woo and the anonymous referees greatly improved +the quality of the paper. diff --git a/macros/latex/contrib/utthesis/ICDE-11/eqlogexp.Q1-8.ps b/macros/latex/contrib/utthesis/ICDE-11/eqlogexp.Q1-8.ps new file mode 100644 index 0000000000..6c41dfdf1d --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/eqlogexp.Q1-8.ps @@ -0,0 +1,605 @@ +%!PS-Adobe-2.0 EPSF-1.2 +%%BoundingBox: 18 18 552 482 +%%Creator: ACE/gr (xmgr) v2.10 +%%Title: /u/ddas/research/papers/eqlogexp.Q1-8.ps +%%EndComments +/m {moveto} bind def +/l {lineto} bind def +/RJ { + stringwidth neg exch neg exch + rmoveto +} bind def +/CS { + stringwidth + 2 div neg exch 2 div neg exch + rmoveto +} bind def +0.25 0.25 scale +1 setlinecap +/Times-Italic findfont +72 scalefont + setfont +[] 0 setdash +420 376 m +420 1785 l +2030 1785 l +2030 376 l +420 376 l +stroke +[] 0 setdash +420 376 m +420 396 l +621 376 m +621 396 l +822 376 m +822 396 l +1023 376 m +1023 396 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scalefont + setfont +1110 1414 m +1270 1414 l +stroke +1080 1444 m +1110 1384 l +1140 1444 l +closepath +gsave eofill grestore +stroke +1240 1444 m +1270 1384 l +1300 1444 l +closepath +gsave eofill grestore +stroke +1310 1414 m +gsave +1310 1414 translate +0 rotate +0 -24 m +(Query 7, 8) show +grestore +newpath +showpage +%%Trailer diff --git a/macros/latex/contrib/utthesis/ICDE-11/intro.tex b/macros/latex/contrib/utthesis/ICDE-11/intro.tex new file mode 100644 index 0000000000..b4ebebe580 --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/intro.tex @@ -0,0 +1,82 @@ +\section{Introduction} +\label{sec:intro} + +Query optimization \cite{Grae93} is a fundamental part of database +systems. It is the process of generating an efficient access plan for +a database query. Informally, an access plan is an execution strategy +for a query; it is the sequence of low-level database retrieval +operations that, when executed, produce the database records that +satisfy the query. There are three basic aspects that define and +influence query optimization: the search space, the cost model, and the +search strategy. + +The {\em search space} is the set of logically equivalent access plans +that can be used to evaluate a query. All plans in a query's search +space return the same result; however, some plans are more efficient +than others. The {\em cost model} assigns a cost to each plan in the +search space. The cost of a plan is an estimate of the resources used +when the plan is executed; the lower the cost, the better the plan. +The {\em search strategy} is a specification of which plans in the +search space are to be examined. + +Traditionally, query optimizers have been built as monolithic +subsystems of a DBMS. This simply reflects the fact that traditional +database systems are themselves monolithic: the algorithms used for +storing and retrieving data are hard-wired and are rather difficult to +change. The need to have extensible database systems, and in turn +extensible optimizers, has long been recognized in systems like Genesis +\cite{Bato88a}, EXODUS \cite{Grae87b}, Starburst \cite{Haas88}, and +Postgres \cite{Ston86b}. Rule-based query optimizers are among the +major conceptual advances that have been proposed to deal with query +optimizer extensibility \cite{Haas88,Frey87a,Grae87b,Grae90b}. The +extensibility translates into the ability to incorporate new operators, +algorithms, cost models, or search strategies without changing the +optimization algorithm. + +In this paper, we describe an algebraic framework called \emph{Prairie} +for specifying rules in a rule-based query optimizer. Prairie is +similar to other rule specification languages like Starburst +\cite{Haas88} and Volcano \cite{Grae90b}, and indeed, we have based our +work on Volcano to capture most of the advantages of rule-based +optimizers. However, Prairie attempts to provide some key features +that, we have found, simplify the effort in writing rules: + +\begin{enumerate} + \item A framework in which users can define a query optimizer + concisely in terms of a well-defined set of operators and + algorithms. \emph{All} operators and algorithms are considered + first-class objects, \ie \emph{any} of them can occur in any + rule, and \emph{only} these operators and algorithms can appear + in rules. This scheme eliminates the need for special classes + of operators and algorithms, such as enforcers in Volcano and + glue in Starburst, that significantly complicate rule + specification. + \item A framework in which users can define a list of properties to + characterize the expressions generated in the optimization + process. Again, the goal here is to allow the user to treat + \emph{all} properties as having equal status. This is different + from Volcano where the user must classify properties as logical, + physical, or operator/algorithm arguments. + \item A framework in which users can specify mapping functions + between properties concomitantly with the corresponding rules. + This contrasts with existing approaches in which mappings + between properties are fragmented into multiple functions and at + logically different places than the corresponding rules. + Research into rule-based optimizers has revealed that + property-mapping functions are a major source of user effort, so + this is an important goal. + \item The format (Prairie) in which users can cleanly specify rules is + not necessarily the same format needed for generating efficient + optimizers. Thus, there is a need for a pre-processor (written + by us) that translates between these competing representations. +\end{enumerate} + +Prairie strives for uniformity in dealing with issues that have been a +source of most user effort and potential user errors. In the following +sections, we present the Prairie framework. We explain how our P2V +pre-processor maps Prairie rule specifications into Volcano rule +specifications that can be processed efficiently. Experimental results +to support this claim are given in Section~\ref{sec:results}, where we +compare implementations of the Texas Instruments Open OODB query +optimizer using both Prairie and Volcano. We conclude with a summary +and related research. diff --git a/macros/latex/contrib/utthesis/ICDE-11/model.tex b/macros/latex/contrib/utthesis/ICDE-11/model.tex new file mode 100644 index 0000000000..3a3f916091 --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/model.tex @@ -0,0 +1,831 @@ +\section{Prairie: A language for rule specification} +\label{sec:framework} + +The basic concepts and definitions that underlie the Prairie model are +presented in this section. The goal is to lay a foundation for +reasoning about query optimization algebraically; this is necessary for +our subsequent discussion about translating Prairie specifications to +those of Volcano. + +\subsection {Notation and assumptions} +\label{sec:notation} + +\paragraph{Stored Files and Streams.} +A file is \emph{stored} if its tuples reside on disk. In the case of +relational databases, stored files are sometimes called \emph{base +relations}; we will denote them by $R$ or $R_i$. In object-oriented +schemas, stored files are \emph{classes}; we will denote them by +$\textit{C}$ or $\textit{C}_i$. Henceforth, whenever we refer to a +stored file, we mean a relation or a class; when the distinction is +unimportant, we will use $F$ or $F_i$. A \emph{stream} is a sequence +of tuples and is the result of a computation on one or more streams or +stored files; tuples of streams are returned one at a time, typically +on demand. Streams can be \emph{named}, denoted by $S_i$, or +\emph{unnamed}. + +\paragraph{Database Operations.} +An \emph{operation} is a computation on one or more streams or stored +files. There are two types of database operations in Prairie: +abstract (or implementation-unspecified) operators and concrete +algorithms. Each is detailed below. +\begin{description} % To achieve extra indentation. +\begin{description} +\item[Operators.] +Abstract (or conceptual) \emph{operators} specify computations on +streams or stored files; they are denoted by all capital +letters (\eg JOIN). Operators have two types of parameters: +essential and additional. \emph{Essential parameters} are the stream +or file inputs to an operator; these are the primary inputs to be +processed by an operator. \emph{Additional parameters} are +``fine-grain'' qualifications of an operator; their purpose is to +describe an operator in more detail than essential parameters. + +\item[Algorithms.] +\emph{Algorithms} are concrete implementations of conceptual operators; +they will be represented in lower case with the first letter +capitalized (\eg Nested\_loops). Algorithms have at least the same +essential and additional parameters as the conceptual operators that +they implement.\footnote{Algorithms may have \emph{tuning parameters} +which are not parameters of the operators they implement.} +Furthermore, there can be, and usually are, several algorithms for a +particular operator. +\end{description} +\end{description} +Table~\ref{tab:operators} lists some operators and algorithms implementing +them together with their additional parameters. + +\begin{centeredtable*} +\begin{minipage}[b]{9.9cm} +\nodesizes +\newlength{\first} +\settowidth{\first}{JOIN($S_1$, $S_2$)} +\newlength{\second} +\settowidth{\second}{Join streams $S_1$, $S_2$} +\newlength{\third} +\settowidth{\third}{projected\_attributes} +\newlength{\fourth} +\settowidth{\fourth}{Nested\_loops($S_1$, $S_2$)} +\newlength{\linelength} +\setlength{\linelength}{\fourth+\tabcolsep*2} +\begin{tabular}{|l|l|l|p{\fourth}|} \thickhline +\textbf{Operator} + & \textbf{Description} + & \textbf{Additional Parameters} + & \textbf{Algorithm} \\ \thickhline +\multirow{2}{\first}{JOIN($S_1$, $S_2$)} + & \multirow{2}{\second}{Join streams $S_1$, $S_2$} & tuple\_order + & Nested\_loops($S_1$, $S_2$) \\ \cline{4-4} + & & join\_predicate & Merge\_join($S_1$, $S_2$) \\ \hline +\multirow{3}{\first}{RET($F$)} + & \multirow{3}{\second}{Retrieve file $F$} + & tuple\_order + & \parbox[c][\baselineskip][b]{\fourth}{File\_scan($F$)} \\ + & & selection\_predicate + & \parbox[c]{\linelength} + {\hspace*{-\tabcolsep}\rule{\linelength}{\arrayrulewidth}} \\ + & & projected\_attributes + & \parbox[c][\baselineskip][t]{\fourth}{Index\_scan($F$)} \\ \hline +\multirow{2}{\first}{SORT($S_1$)} + & \multirow{2}{\second}{Sort stream $S_1$} + & \multirow{2}{\third}{tuple\_order} + & Merge\_sort($S_1$) \\ \cline{4-4} + & & & Null($S_1$) \\ \thickhline +\end{tabular} +\caption{Operators and algorithms in a centralized query optimizer and + their additional parameters} +\label{tab:operators} +\end{minipage} +\hfill +\begin{minipage}[b]{6.5cm} +\nodesizes +\settowidth{\first}{projected\_attributes} +\begin{tabular}{|l|l|} \thickhline +\textbf{Property} + & \textbf{Description} \\ \thickhline +join\_predicate + & join predicate for JOIN operator \\ \hline +selection\_predicate + & selection predicate for RET operator \\ \hline +\multirow{2}{\first}{tuple\_order} + & tuple order of resulting stream, \\ + & DONT\_CARE if none \\ \hline +num\_records + & number of tuples of resulting stream \\ \hline +tuple\_size + & size of individual tuple in stream \\ \hline +projected\_attributes + & projected attributes for RET operator \\ \hline +attributes + & list of attributes \\ \hline +cost + & estimated cost of algorithm \\ \thickhline +\end{tabular} +\caption{Properties of nodes in an operator tree} +\label{tab:annotations} +\end{minipage} +\end{centeredtable*} + +\paragraph{Operator Trees.} +An \emph{operator tree} is a rooted tree whose non-leaf, or +\emph{interior}, nodes are database operations (operators or +algorithms) and whose leaf nodes are stored files. The children of an +interior node in an operator tree are the essential parameters (\ie the +stream or file parameters) of the node. Additional parameters are +implicitly attached to each node. Algebraically, operator trees are +compositions of database operations; thus, we will also call operator +trees \emph{expressions}; both terms will be used interchangeably. + +\begin{example} +A simple expression and its operator tree representation are shown +in Figure~\ref{fig:optreeexample}. Relations $R_1$ and $R_2$ are first +RETrieved, then JOINed, and finally SORTed resulting in a stream +sorted on a specific attribute. The figure shows only the essential +parameters of the various operators, not the additional parameters. +\end{example} + +\begin{comment} +The figures which follow. + + SORT + | + | + JOIN + /\ + / \ + RET RET + | | + | | + R1 R2 + + Merge_sort + | + | + Nested_loops + / \ + / \ + File_scan File_scan + | | + | | + R1 R2 + +\end{comment} + +\begin{centeredfigure} +\setlength{\unitlength}{0.6in} +% +\myshadowbox +{ +\subfigure[An expression and its corresponding operator tree] +{ +\begin{centeredinhalfminipage} +\psset{unit=4mm} +\psset{nodesep=1pt} +\tiny +\begin{pspicture}(0,0)(2,4) +\rput(1,4){SORT (JOIN (RET ($R_1$), RET ($R_2$)))} +\rput(1,3){\rnode{sort}{SORT}} +\rput(1,2){\rnode{join}{JOIN}} +\ncline{-}{sort}{join} +\rput(0,1){\rnode{retr1}{RET}} +\rput(2,1){\rnode{retr2}{RET}} +\ncline{-}{join}{retr1} +\ncline{-}{join}{retr2} +\rput(0,0){\rnode{r1}{$R_1$}} +\rput(2,0){\rnode{r2}{$R_2$}} +\ncline{-}{retr1}{r1} +\ncline{-}{retr2}{r2} +\end{pspicture} +\end{centeredinhalfminipage} +\label{fig:optreeexample} +} +% +\vrule +% +\subfigure[Possible access plan for operator tree in (a)] +{ +\begin{centeredinhalfminipage} +\psset{unit=4mm} +\psset{nodesep=1pt} +\tiny +\begin{pspicture}(0,0)(2,3) +\rput(1,3){\rnode{mergesort}{Merge\_sort}} +\rput(1,2){\rnode{nestedloops}{Nested\_loops}} +\ncline{-}{mergesort}{nestedloops} +\rput(0,1){\rnode{filescanr1}{File\_scan}} +\rput(2,1){\rnode{filescanr2}{File\_scan}} +\ncline{-}{nestedloops}{filescanr1} +\ncline{-}{nestedloops}{filescanr2} +\rput(0,0){\rnode{r1}{$R_1$}} +\rput(2,0){\rnode{r2}{$R_2$}} +\ncline{-}{filescanr1}{r1} +\ncline{-}{filescanr2}{r2} +\end{pspicture} +\end{centeredinhalfminipage} +\label{fig:accplanexample} +} +} +% +\caption{Example of an operator tree and access plan} +\label{fig:expexample} +\end{centeredfigure} + +\paragraph{Descriptors.} +A \emph{property} of a node is a (user-defined) variable that contains +information used by an optimizer. An \emph{annotation} is a $\langle +\emph{property, value} \rangle$ pair that is assigned to a node. A +\emph{descriptor} is a list of annotations that describes a node of an +operator tree; every node has its own descriptor. As an example, +Table~\ref{tab:annotations} lists some typical properties that might be +used in a descriptor. Note that descriptors for stream and stored +files may have different properties. The following notations will be +useful in our subsequent discussions. If $S_i$ is a stream, then +$\mathbf{D_i}$ is its descriptor. Annotations of $S_i$ are accessed by +a structure member relationship, \eg +$\mathbf{D_i}.\text{num\_records}$. Also, let $E$ be an expression and +let $\mathbf{D}$ be its descriptor. We will write this as +$E:\mathbf{D}$. + +\begin{example} +The expression, +\begin{eqnarray*} +{\scriptstyle \text{SORT}(\text{JOIN}(\text{RET}(R_1):\mathbf{D_3}, + \text{RET}(R_2):\mathbf{D_4}):\mathbf{D_5}):\mathbf{D_6}} & & +\end{eqnarray*} +corresponds to the operator tree in Figure~\ref{fig:optreeexample}, and +shows the descriptors of the various nodes. +\end{example} + +A notational simplification can be made here. Additional parameters +of operators can be treated the same way as other properties of a node; +essential parameters, however, are \emph{expressions}. Thus, the term +descriptor in the remainder of this paper will refer to a set of properties, +including additional parameters, as shown in Table~\ref{tab:annotations}. + +Currently, descriptor properties are defined entirely by the user; +however, we envision providing a hierarchy of pre-defined descriptor +types to aid this process. + +\paragraph{Access Plans.} +An \emph{access plan} is an operator tree in which all interior nodes +are algorithms. + +\begin{example} +An access plan for the operator tree in Figure~\ref{fig:optreeexample} +is shown in Figure~\ref{fig:accplanexample}. +\end{example} + +\subsection{Prairie optimization paradigm} +\label{sec:topdown} + +Prairie admits two rather different means of optimization: top-down and +bottom-up. A top-down query optimizer optimizes the parents of a node +prior to optimizing the node itself. A bottom-up optimizer optimizes +the children of a node prior to optimizing the node. The earliest +optimizers (System R \cite{Seli79} and R$^*$ \cite{Dani82}) employed +the bottom-up approach. + +Our research concentrates on a top-down optimization of operator +trees. We have chosen this approach because we intend to translate +Prairie rules into the format required by the Volcano query optimizer +generator \cite{Grae90b} which is based on a top-down strategy. +Given an appropriate search engine, Prairie can potentially also be +used with a bottom-up optimization strategy; however, we will not +discuss this approach in this paper. + +In query optimization, there are certain annotations (such as +additional parameters) that are known before any optimization is +begun. These annotations can be computed at the time that the operator +tree is initialized, and will not change with application of rules. +Our following discussions assume operator trees are initialized. + +There are two types of algebraic transformations (or \emph{rewrite +rules}) in Prairie: T-rules (``transformation rules'') and I-rules +(``implementation rules''). Each rule transforms an expression into +another based on additional conditions; the transformation also results +in a mapping of descriptors between expressions. We define T-rules and +I-rules precisely in the following sections and illustrate them with +examples. Our examples are chosen from rules that would be used in a +centralized relational query optimizer; the operators, algorithms, and +properties are subsets of those in Tables~\ref{tab:operators} and +\ref{tab:annotations}. + +\subsection{Transformation rules} +\label{sec:trules} + +\begin{centeredfigure} +\def\subfigtopskip{0pt} +\myshadowbox{ +\begin{tabular}{c} +\subfigure[General form of a T-rule] +{ +\setlength{\topsep}{0pt} +\scriptsize +\begin{minipage}[b]{0.86\linewidth} +\begin{trule} +E(x_1, \ldots, x_n):\mathbf{D_1} \Longrightarrow + E'(x_1, \ldots, x_n):\mathbf{D_2} \label{eq:generaltrule} +\end{trule} +\begin{trulepretest} +\> pre-test statements +\end{trulepretest} +test +\begin{truleposttest} +\> post-test statements +\end{truleposttest} +\end{minipage} +\label{fig:generaltrule} +} \\ \hline +%%% +\subfigure[Join associativity] +{ +\setlength{\topsep}{0pt} +\scriptsize +\begin{minipage}[b]{0.86\linewidth} +\vspace*{4pt} +\begin{trule} +\text{JOIN}(\text{JOIN}(S_1, S_2):\mathbf{D_4}, S_3):\mathbf{D_5} +\label{eq:associativity} +\end{trule} +%%% TODO: Remove extra space above eqnarray. +\begin{eqnarray*} +\rulespace \Longrightarrow + \text{JOIN}(S_1, \text{JOIN}(S_2, S_3):\mathbf{D_6}):\mathbf{D_7} +% \label{eq:associativity} +\end{eqnarray*} +\begin{trulepretest} +\> $\mathbf{D_6}.\text{attributes} = + \text{union}\ (\mathbf{D_2}.\text{attributes}, + \mathbf{D_3}.\text{attributes})\ ;$ +\end{trulepretest} +$\text{is\_associative}\ (\mathbf{D_6}.\text{join\_predicate}, + \mathbf{D_6}.\text{attributes}, + \mathbf{D_5}.\text{join\_predicate})$ +\begin{truleposttest} +\> $\mathbf{D_7} = \mathbf{D_5}\ ;$ \\ +\> $\mathbf{D_7}.\text{join\_predicate} = + \mathbf{D_4}.\text{join\_predicate}\ ;$ \\ +\> $\mathbf{D_6}.\text{tuple\_size} = + \mathbf{D_2}.\text{tuple\_size} + + \mathbf{D_3}.\text{tuple\_size}\ ;$ \\ +\> $\mathbf{D_6}.\text{num\_records} = + \text{cardinality}\ (\mathbf{D_2}, \mathbf{D_3})\ ;$ +\end{truleposttest} +\end{minipage} +\label{fig:associativity} +} +\end{tabular} +} +\caption{T-rule} +\label{fig:trules} +\end{centeredfigure} + +Transformation rules, or T-rules for short, define equivalences among +pairs of expressions; they define mappings from one operator tree to +another. Let $E$ and $E'$ be expressions that involve only abstract +operators. Equation~(\ref{eq:generaltrule}) (shown in +Figure~\ref{fig:generaltrule}) shows the general form of a T-rule. The +actions of a T-rule define the equivalences between the descriptors of +nodes of the original operator tree $E$ with the nodes of the output +tree $E'$; these actions consist of a series of (C or C++) +assignment\footnote{The actions can be non-assignment statements (like +function calls), but in this case, the P2V pre-processor (described in +Section~\ref{sec:ptov}) needs some hints about the properties that +are changed by the statement in order to correctly categorize each +property. For simplicity, in this paper, we assume all actions consist +of assignment statements.} statements. The left-hand sides of these +statements refer to descriptors of expressions on the right-hand side +of the T-rule; the right-hand sides of the statements can refer to any +descriptor in the T-rule. Function (called \emph{helper} functions) +calls can also appear on the right side of the assignment statements. +Thus, descriptors on the \emph{left-hand side} of a T-rule are +\emph{never} changed in the rule's actions. A \emph{test} is needed to +determine if the transformations of the T-rule are in fact applicable. + +Purely as an optimization, it is usually the case that not all +statements in a T-rule's actions need to be executed prior to a +T-rule's test. For this reason, the actions of a T-rule are split into +two groups; those that need to be executed prior to the T-rule's test, +and those that can be executed after a successful test. These groups +of statements comprise, respectively, the \emph{pre-test} and +\emph{post-test} statements of the T-rule.\footnote{We suspect it is +possible to use data-flow analysis to partition the assignment +statements automatically, but for now, we let the rule-writer do the +partitioning.} + +\begin{comment} +We now define the actions and tests of a T-rule more precisely. Let +$O_i$ be an abstract operator of $E'$, and let $\mathbf{O_i}$ be its +descriptor. Similarly, let $I_i$ be an abstract operator of $E$ and +let $\mathbf{I_i}$ be its descriptor. ($I_i$ is an operator that is +input to the rule and $O_i$ is an operator that is output by the +rule). Let $M_i$ denote the $i$th descriptor property. Thus, +$\mathbf{O_i}.M_j$ is the value of the $j$th property of descriptor +$\mathbf{O_i}$. We have found that actions of a T-rule are invariably +assignment statements, since actions compute assignments to descriptor +properties. Rather than admitting all possible computations, we will +present our model in terms of assignment statements.\footnote{ The +actions can be non-assignment statements (like function calls), but in +this case, the P2V pre-processor (described in +Section~\ref{sec:results}) needs some hints about the properties that +are changed by the statement in order to correctly categorize each +property. For simplicity, in this paper, we assume all actions consist +of assignment statements. } The left-hand side of an assignment refers +to an output descriptor ($\mathbf{O_i}$) or a member of an output +descriptor ($\mathbf{O_i}.M_j$). The right-hand side is an expression +or function that only references input descriptors and/or their +members. (We call such functions \emph{helper} functions; they are +defined externally to a rule). Here are a few examples: +\[ +\begin{array}{rlll} +\mathbf{O_i} & = & \mathbf{I_k}\ ; & + \text{$//$ copy descriptor $\mathbf{I_k}$ to $\mathbf{O_i}$} \nonumber \\ +\mathbf{O_i}.M_j & = & \mathbf{I_k}.M_j + 4\ ; & + \text{$//$ expression defining $\mathbf{O_i}.M_j$} \nonumber \\ +\mathbf{O_3}.M_5 & = & \text{helper}\ (\mathbf{I_1}.M_5, \mathbf{I_2}.M_5)\ ; & + \text{$//$ helper function that computes $\mathbf{O_3}.M_5$} \nonumber \\ +& & & + \text{$//$ from inputs $\mathbf{I_1}.M_5$ and $\mathbf{I_2}.M_5$.} \nonumber +\end{array} +\] + +The test for a T-rule's applicability is a boolean expression and +normally involves checks on the values of output descriptors (\eg +$\mathbf{O_3}.M_5 > 6$); occasionally, helper functions may be needed. + +Again, it is important to remember that the pre-test actions are +carried out prior to the test; the post-test actions are performed only +if a T-rule's test evaluates to TRUE, and all post-test actions are +performed immediately, with no intermediate optimization of any +descendant nodes of the root of $E$. + +Note that there are no actions that are carried out \emph{after} the +essential parameters of the root of $E$ are optimized. This is because +a T-rule only logically transforms a conceptual tree into another +conceptual tree. +\end{comment} + +\begin{example} +\label{ex:joinassociativity} +The associativity of JOINs is expressed by T-rule +(\ref{eq:associativity}) in Figure~\ref{fig:associativity}. +\end{example} + +\begin{comment} + + b2=c1 JOIN JOIN a1=b1 + /\ /\ + / \ / \ + a1=b1 JOIN RET RET JOIN b2=c1 + /\ | ====> | /\ + / \ R3 R1 / \ + RET RET RET RET + | | | | + R1 R2 R2 R3 + + a2=c1 JOIN JOIN a1=b1 + /\ /\ + / \ / \ + a1=b1 JOIN RET RET JOIN <empty> + /\ | ==/==> | /\ + / \ R3 R1 / \ + RET RET RET RET + | | | | + R1 R2 R2 R3 + +\end{comment} + +\newsavebox{\lefttreeone} +\newsavebox{\righttreeone} +\newsavebox{\lefttreetwo} +\newsavebox{\righttreetwo} +\newsavebox{\rewritesto} +\newsavebox{\doesnotrewriteto} + +\begin{lrbox}{\lefttreeone} +\begin{minipage}[t]{3.0cm} +\psset{unit=\edgesizes} +\psset{nodesep=3pt} +\nodesizes +\begin{center} +\begin{pspicture}(-0.5,0)(3,3) +\rput(2,3){\rnode{joinr1r2r3}{JOIN}} +\rput(0.5,3){$b_2 = c_1$} +\rput(1,2){\rnode{joinr1r2}{JOIN}} +\rput(-0.5,2){$a_1 = b_1$} +\rput(0,1){\rnode{retr1}{RET}} +\rput(2,1){\rnode{retr2}{RET}} +\rput(3,2){\rnode{retr3}{RET}} +\rput(0,0){\rnode{r1}{$R_1$}} +\rput(2,0){\rnode{r2}{$R_2$}} +\rput(3,1){\rnode{r3}{$R_3$}} +\ncline{-}{joinr1r2}{retr1} +\ncline{-}{joinr1r2}{retr2} +\ncline{-}{joinr1r2r3}{joinr1r2} +\ncline{-}{joinr1r2r3}{retr3} +\ncline{-}{retr1}{r1} +\ncline{-}{retr2}{r2} +\ncline{-}{retr3}{r3} +\end{pspicture} +\end{center} +\end{minipage} +\end{lrbox} + +\begin{lrbox}{\rewritesto} +\begin{minipage}[t]{0.6cm} +\psset{unit=\edgesizes} +\psset{nodesep=3pt} +\nodesizes +\begin{center} +\begin{pspicture}(0,0)(1,3) +\rput(0.5,1.5){$\Longrightarrow$} +\end{pspicture} +\end{center} +\end{minipage} +\end{lrbox} + +\begin{lrbox}{\righttreeone} +\begin{minipage}[t]{3.0cm} +\psset{unit=\edgesizes} +\psset{nodesep=3pt} +\nodesizes +\begin{center} +\begin{pspicture}(0,0)(3,3) +\rput(1,3){\rnode{joinr1r2r3}{JOIN}} +\rput(2.5,3){$a_1 = b_1$} +\rput(2,2){\rnode{joinr2r3}{JOIN}} +\rput(3.5,2){$b_2 = c_1$} +\rput(0,2){\rnode{retr1}{RET}} +\rput(1,1){\rnode{retr2}{RET}} +\rput(3,1){\rnode{retr3}{RET}} +\rput(0,1){\rnode{r1}{$R_1$}} +\rput(1,0){\rnode{r2}{$R_2$}} +\rput(3,0){\rnode{r3}{$R_3$}} +\ncline{-}{joinr1r2r3}{retr1} +\ncline{-}{joinr1r2r3}{joinr2r3} +\ncline{-}{joinr2r3}{retr2} +\ncline{-}{joinr2r3}{retr3} +\ncline{-}{retr1}{r1} +\ncline{-}{retr2}{r2} +\ncline{-}{retr3}{r3} +\end{pspicture} +\end{center} +\end{minipage} +\end{lrbox} + +\begin{lrbox}{\lefttreetwo} +\begin{minipage}[t]{3.0cm} +\psset{unit=\edgesizes} +\psset{nodesep=3pt} +\nodesizes +\begin{center} +\begin{pspicture}(-0.5,0)(3,3) +\rput(2,3){\rnode{joinr1r2r3}{JOIN}} +\rput(0.5,3){$a_2 = c_1$} +\rput(1,2){\rnode{joinr1r2}{JOIN}} +\rput(-0.5,2){$a_1 = b_1$} +\rput(0,1){\rnode{retr1}{RET}} +\rput(2,1){\rnode{retr2}{RET}} +\rput(3,2){\rnode{retr3}{RET}} +\rput(0,0){\rnode{r1}{$R_1$}} +\rput(2,0){\rnode{r2}{$R_2$}} +\rput(3,1){\rnode{r3}{$R_3$}} +\ncline{-}{joinr1r2}{retr1} +\ncline{-}{joinr1r2}{retr2} +\ncline{-}{joinr1r2r3}{joinr1r2} +\ncline{-}{joinr1r2r3}{retr3} +\ncline{-}{retr1}{r1} +\ncline{-}{retr2}{r2} +\ncline{-}{retr3}{r3} +\end{pspicture} +\end{center} +\end{minipage} +\end{lrbox} + +\begin{lrbox}{\doesnotrewriteto} +\begin{minipage}[t]{0.6cm} +\psset{unit=\edgesizes} +\psset{nodesep=3pt} +\nodesizes +\begin{center} +\begin{pspicture}(0,0)(1,3) +\rput(0.5,1.5){$\Longrightarrow$} +\rput(0.5,1.5){$/$} +\end{pspicture} +\end{center} +\end{minipage} +\end{lrbox} + +\begin{lrbox}{\righttreetwo} +\begin{minipage}[t]{3.0cm} +\psset{unit=\edgesizes} +\psset{nodesep=3pt} +\nodesizes +\begin{center} +\begin{pspicture}(0,0)(3,3) +\rput(1,3){\rnode{joinr1r2r3}{JOIN}} +\rput(2,2){\rnode{joinr2r3}{JOIN}} +\rput(0,2){\rnode{retr1}{RET}} +\rput(1,1){\rnode{retr2}{RET}} +\rput(3,1){\rnode{retr3}{RET}} +\rput(0,1){\rnode{r1}{$R_1$}} +\rput(1,0){\rnode{r2}{$R_2$}} +\rput(3,0){\rnode{r3}{$R_3$}} +\ncline{-}{joinr1r2r3}{retr1} +\ncline{-}{joinr1r2r3}{joinr2r3} +\ncline{-}{joinr2r3}{retr2} +\ncline{-}{joinr2r3}{retr3} +\ncline{-}{retr1}{r1} +\ncline{-}{retr2}{r2} +\ncline{-}{retr3}{r3} +\end{pspicture} +\end{center} +\end{minipage} +\end{lrbox} + +\subsection{Implementation rules} +\label{sec:irules} + +Implementation rules, or I-rules for short, define equivalences between +expressions and their implementing algorithms. Let $E$ be an +expression and $A$ be an algorithm that implements $E$. The general +form of an I-rule is given by Equation~(\ref{eq:generalirule}) (shown +in Figure~\ref{fig:generalirule}). + +\begin{centeredfigure} +\def\subfigtopskip{0pt} +\myshadowbox{ +\begin{tabular}{c} +\subfigure[General form of an I-rule] +{ +\setlength{\topsep}{0pt} +\scriptsize +\begin{minipage}[b]{0.86\linewidth} +\begin{irule} +E(x_1, \ldots, x_n):\mathbf{D_1} \Longrightarrow + A(x_1, \ldots, x_n):\mathbf{D_2} \label{eq:generalirule} +\end{irule} +test +\begin{irulepreopt} +\> pre-opt statements +\end{irulepreopt} +\begin{irulepostopt} +\> post-opt statements +\end{irulepostopt} +\end{minipage} +\label{fig:generalirule} +} \\ \hline +%%% +\subfigure[Merge-sort sort algorithm] +{ +\setlength{\topsep}{0pt} +\scriptsize +\begin{minipage}[b]{0.86\linewidth} +\vspace*{4pt} +\begin{irule} +\text{SORT}(S_1):\mathbf{D_2} \Longrightarrow + \text{Merge\_sort}(S_1):\mathbf{D_3} \label{eq:msort} +\end{irule} +$(\mathbf{D_2}.\text{tuple\_order}\ !\negthinspace= \text{DONT\_CARE})$ +\begin{irulepreopt} +\> $\mathbf{D_3} = \mathbf{D_2}\ ;$ +\end{irulepreopt} +\begin{irulepostopt} +\> $\mathbf{D_3}.\text{cost} = \mathbf{D_1}.\text{cost}$ \\ +\> \hspace{1.2cm} $+ (\mathbf{D_3}.\text{num\_records}) * + \log(\mathbf{D_3}.\text{num\_records})\ ;$ +\end{irulepostopt} +\end{minipage} +\label{fig:msort} +} +\end{tabular} +} +\caption{I-rule} +\label{fig:irules} +\end{centeredfigure} + +The actions associated with an I-rule are defined in three parts. +The first part, or \emph{test}, is a boolean expression whose +value determines whether or not the rule can be applied. + +The second part, or \emph{pre-opt statements}, is a set of descriptor +assignment statements that are executed only if the test is true and +\emph{before} any of the inputs $x_i$ of $E$ are optimized. Additional +parameters of nodes are usually assigned in the pre-opt section. This +is necessary before any of the nodes on the right side can be +optimized. + +The third part, or \emph{post-opt statements}, is a set of descriptor +assignment statements that are executed \emph{after} all $x_i$ are +optimized. Normally, the post-opt statements compute cost properties +that can only be determined once the inputs to the algorithm are +completely optimized and their costs known. This \emph{does not}, +however, imply a bottom-up optimization strategy. It simply means that +although I-rules are applied to parents before their children are +optimized, the \emph{cost} (and other properties in the post-opt +section) of the parent cannot be computed until the children have been +optimized. + +\begin{example} +\label{ex:mergesort} +Equation~(\ref{eq:msort}) (in Figure~\ref{fig:msort}) shows the I-rule +that implements the SORT operator by Merge\_sort. +\end{example} + +\subsection{Null algorithm} +\label{sec:null} +Recall that, in Section~\ref{sec:intro}, we mentioned that Prairie +allows users to treat all operators and algorithms as first-class +objects, \ie all operators and algorithms are explicit, in contrast to +enforcers in Volcano or glue in Starburst. This requires that Prairie +provide a mechanism where users can also ``delete'' one or more of the +explicit operators from expressions. This is done by having a special +class of I-rules that have the form given by +Equation~(\ref{eq:generalnullalg}) in Figure~\ref{fig:generalnullalg}. +The left side of the rule is a single abstract operator $O$ with one +stream input $S_1$. The right side of the rule is an algorithm called +``Null'' with the same stream input but with a different descriptor. +As the name suggests, the Null algorithm is supposed to pass its input +unchanged to algorithms above it in an operator tree. This is +accomplished in the I-rule as follows. + +The test for this I-rule is always TRUE, \ie any node in an operator +tree with $O$ as its operator can be implemented by the Null +algorithm. The actions associated with this rule have a specific +pattern. The pre-opt section consists of three +statements. The first statement copies the descriptor of the operator +$O$ to the algorithm Null. The second statement sets the descriptor of +the stream $S_1$ on the right side to the descriptor of the stream +$S_1$ on the left side. Why is it necessary to do this? The key lies +in the third statement. This statement copies the property +``property'' of the operator $O$ node on the left side to the +``property'' of the input stream $S_1$ on the right side. Since +left-hand side descriptors cannot be changed in an I-rule, a new +descriptor $\mathbf{D_3}$ is necessary for $S_1$ to convey the property +propagation information. + +The post-opt section in the I-rule has only a cost-assignment +statement; this simply sets the cost of the Null node to the cost of +its optimized input stream. + +The Null algorithm, therefore, serves to effectively transform a single +operator to a no-op. + +\begin{example} +Equation~(\ref{eq:nullsort}) (in Figure~\ref{fig:nullsort}) shows the +I-rule that rewrites the SORT operator to use a Null algorithm. +\end{example} + +\begin{centeredfigure} +\def\subfigtopskip{0pt} +\myshadowbox{ +\begin{tabular}{c} +\subfigure[General form of a ``Null'' I-rule] +{ +\setlength{\topsep}{0pt} +\scriptsize +\begin{minipage}[b]{0.86\linewidth} +\begin{irule} +O(S_1):\mathbf{D_2} \Longrightarrow + \text{Null}(S_1:\mathbf{D_3}):\mathbf{D_4} \label{eq:generalnullalg} +\end{irule} +TRUE +\begin{irulepreopt} +\> $\mathbf{D_4} = \mathbf{D_2}\ ;$ \\ +\> $\mathbf{D_3} = \mathbf{D_1}\ ;$ \\ +\> $\mathbf{D_3}.\text{property} = \mathbf{D_2}.\text{property}\ ;$ +\end{irulepreopt} +\begin{irulepostopt} +\> $\mathbf{D_4}.\text{cost} = \mathbf{D_3}.\text{cost}\ ;$ +\end{irulepostopt} +\end{minipage} +\label{fig:generalnullalg} +} +\\ \hline +%%% +\subfigure[Null sort algorithm] +{ +\setlength{\topsep}{0pt} +\scriptsize +\begin{minipage}[b]{0.86\linewidth} +\vspace*{4pt} +\begin{irule} +\text{SORT}(S_1):\mathbf{D_2} \rulespace \Longrightarrow + \text{Null}(S_1:\mathbf{D_3}):\mathbf{D_4} \label{eq:nullsort} +\end{irule} +TRUE +\begin{irulepreopt} +\> $\mathbf{D_4} = \mathbf{D_2}\ ;$ \\ +\> $\mathbf{D_3} = \mathbf{D_1}\ ;$ \\ +\> $\mathbf{D_3}.\text{tuple\_order} = \mathbf{D_2}.\text{tuple\_order}\ ;$ +\end{irulepreopt} +\begin{irulepostopt} +\> $\mathbf{D_4}.\text{cost} = \mathbf{D_3}.\text{cost}\ ;$ +\end{irulepostopt} +\end{minipage} +\label{fig:nullsort} +} +\end{tabular} +} +\caption{The ``Null'' algorithm concept} +\label{fig:null} +\end{centeredfigure} diff --git a/macros/latex/contrib/utthesis/ICDE-11/p2v.tex b/macros/latex/contrib/utthesis/ICDE-11/p2v.tex new file mode 100644 index 0000000000..d8c344e302 --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/p2v.tex @@ -0,0 +1,139 @@ +\section{The P2V pre-processor} +\label{sec:ptov} + +In Section~\ref{sec:intro}, we enumerated the four primary goals of +Prairie, viz., uniformity in operator and algorithms; uniformity in +properties; uniformity in property-transformations; and efficient +generation of Prairie optimizers. The first three goals are driven by +the need for conceptual simplicity; however, they alone do not +necessarily generate efficient optimizers. The P2V pre-processor +ensures that efficient optimizers can be realized from Prairie +specifications, by translating them to the Volcano framework and then +generating an optimizer by compiling with the Volcano search engine. +This Prairie optimizer-generator paradigm is shown schematically in +Figure~\ref{fig:ptovmodel}. The pre-processor itself is 4500 lines of +\texttt{flex} and \texttt{bison} code. In this section, we briefly +describe the pre-processor steps and explain why the Prairie-to-Volcano +transformation is non-trivial. A more detailed description of the +pre-processor is given in \cite{Das94}. + +\begin{centeredfigure} +\myshadowbox +{ +\scriptsize +\begin{centeredinfullminipage} +\begin{center} +\psset{unit=6mm} +\psset{nodesep=3pt} +%\begin{pspicture}(-1.0,-0.5)(10,9.0) +\begin{pspicture}(-1.0,-0.5)(8,9.0) +\pspolygon[doubleline=true](1,1.5)(7,1.5)(7,7.5)(1,7.5) +\pspolygon[fillcolor=white,fillstyle=solid](2,8)(6,8)(6,9)(2,9) +\rput(4,8.5){\psframebox*{Prairie Rule Set}} +\psline[border=2pt]{->}(4,8)(4,7) +\pspolygon[doubleline=true](2,6)(6,6)(6,7)(2,7) +\rput(4,6.5){P2V Pre-processor} +\psline[border=2pt]{->}(4,6)(4,5) +\pspolygon[fillcolor=gray,fillstyle=solid](2,4)(6,4)(6,5)(2,5) +\rput(4,4.5){\psframebox*{Volcano Rule Set}} +\psline[border=2pt]{->}(4,4)(4,3) +\pspolygon[doubleline=true](2,2)(6,2)(6,3)(2,3) +\rput(4,2.5){\begin{tabular}{c} Volcano \\ Optimizer-Generator \end{tabular}} +\psline[border=2pt]{->}(4,2)(4,1) +\pspolygon[fillcolor=gray,fillstyle=solid](2,0)(6,0)(6,1)(2,1) +\rput(4,0.5){\psframebox*{Query Optimizer}} +\rput[r](1,0.5){Operator Tree} +\psline[border=2pt]{->}(1,0.5)(2,0.5) +\psline[border=2pt]{->}(6,0.5)(7,0.5) +\rput[l](7,0.5){Access Plan} +\end{pspicture} +\end{center} +\end{centeredinfullminipage} +} +\caption{The Prairie optimizer-generator paradigm. Double-boxed modules + represent software generators, shaded boxes represent + generated programs. The outermost double-boxed portion + denotes the Prairie optimizer generator.} +\label{fig:ptovmodel} +\end{centeredfigure} + +The specification of an optimizer in Volcano consists of a set of +transformation rules (called ``trans\_rules'') and implementation rules +(called ``impl\_rules''), a set of properties, and some support +functions. The join associativity trans\_rule +(cf.\ Figure~\ref{fig:associativity}) in Volcano is as follows\footnote{There +are conditions and actions associated with Volcano rules that are not +shown here.}: +\begin{eqnarray*} +\scriptscriptstyle +& & +{\scriptstyle +(\text{JOIN} \ \text{?op\_arg5} + \ ((\text{JOIN} \ \text{?op\_arg4} \ (?1 \ ?2)) \ + ?3))} \\ +& & +\rulespace +{\scriptstyle -\!\!>} +{\scriptstyle +(\text{JOIN} \ \text{?op\_arg7} + \ (?1 \ + (\text{JOIN} \ \text{?op\_arg6} \ (?2 \ ?3))))} +\end{eqnarray*} +The important point to note is the use of \emph{operator arguments} +(denoted by ``op\_arg'' in rules); these arguments contain properties +used in the rule's actions, but unlike Prairie, they do not contain +\emph{all} the properties of an operator tree node. There are other +property classes, like algorithm argument, logical property, system +property, physical property, and cost. Thus, while Prairie uses a +uniform descriptor to encode properties, Volcano partitions the +properties into different classes. The P2V pre-processor partitions a +Prairie descriptor into the different property classes required by +Volcano. This is a non-trivial task, since it requires parsing the +Prairie rules and their actions. + +Impl\_rules in Volcano defer most of the actions associated with the +rules to support functions. Each algorithm has four support functions +associated with it. A Prairie specification, on the other hand, +contains all the actions in the corresponding rule. The P2V +pre-processor parses a Prairie I-rule, and automatically generates all +the Volcano support functions from the rule. This is also a complex +process, since it depends partly on the partitioning of properties +mentioned in the last paragraph, and also because it requires +relocating pieces of code from Prairie rules to Volcano support +functions. + +The third salient feature of a Volcano specification is the presence of +implicit, or hidden, algorithms, called \emph{enforcers}. In Prairie, +all algorithms are explicit. Consider, for example, the Merge\_sort +algorithm in Figure~\ref{fig:msort}. In a Volcano specification, this +algorithm would be classified as an enforcer, since it enforces the +sortedness property. The P2V pre-processor determines the Prairie +algorithms that are functionally Volcano enforcers, and deletes the +corresponding Prairie rules to generate the Volcano specification. +This requires the pre-processor to migrate the (deleted) rule's actions +to Volcano support functions. + +The P2V pre-processor also generates a set of compact Volcano rules by +merging Prairie rules whenever possible. Consider, for example, the +following set of rules in Prairie: +\begin{eqnarray*} +{\scriptstyle \text{JOIN}(S_1, S_2):\mathbf{D_3}} + & \Longrightarrow & +{\scriptstyle \text{JOPR}(\text{SORT}(S_1):\mathbf{D_4}, + \text{SORT}(S_2):\mathbf{D_5}):\mathbf{D_6}} \\ +{\scriptstyle \text{SORT}(S_1):\mathbf{D_2}} + & \Longrightarrow & +{\scriptstyle \text{Null}(S_1:\mathbf{D_3}):\mathbf{D_4}} \\ +{\scriptstyle \text{JOPR}(S_1, S_2):\mathbf{D_3}} + & \Longrightarrow & +{\scriptstyle \text{Nested\_loops}(S_1:\mathbf{D_4}, S_2):\mathbf{D_5}} +\end{eqnarray*} +The first rule is a T-rule, and the next two are I-rules. The P2V +pre-processor combines the above set of Prairie rules into a single +I-rule, +\begin{eqnarray*} +{\scriptstyle \text{JOIN}(S_1, S_2):\mathbf{D_3}} + & \Longrightarrow & +{\scriptstyle \text{Nested\_loops}(S_1:\mathbf{D_4}, S_2):\mathbf{D_5}} +\end{eqnarray*} +and then translates it into a single Volcano impl\_rule. diff --git a/macros/latex/contrib/utthesis/ICDE-11/paper.aux b/macros/latex/contrib/utthesis/ICDE-11/paper.aux new file mode 100644 index 0000000000..9c07f2af48 --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/paper.aux @@ -0,0 +1,137 @@ +\relax +\citation{Grae93} +\citation{Bato88a} +\citation{Grae87b} +\citation{Haas88} +\citation{Ston86b} +\citation{Haas88,Frey87a,Grae87b,Grae90b} +\citation{Haas88} +\citation{Grae90b} +\@writefile{toc}{\protect \contentsline {section}{\protect \numberline {1}Introduction}{1}} +\newlabel{sec:intro}{{1}{1}} +\@writefile{toc}{\protect \contentsline {section}{\protect \numberline {2}Prairie: A language for rule specification}{2}} +\newlabel{sec:framework}{{2}{2}} +\@writefile{toc}{\protect \contentsline {subsection}{\protect \numberline {2.1}Notation and assumptions}{2}} +\newlabel{sec:notation}{{2.1}{2}} +\@writefile{toc}{\protect \contentsline {paragraph}{Stored Files and Streams.}{2}} +\@writefile{toc}{\protect \contentsline {paragraph}{Database Operations.}{2}} +\@writefile{toc}{\protect \contentsline {paragraph}{Operator Trees.}{2}} +\citation{Seli79} +\citation{Dani82} +\citation{Grae90b} +\@writefile{lot}{\protect \contentsline {table}{\protect \numberline {1}{\ignorespaces Operators and algorithms in a centralized query optimizer and their additional parameters}}{3}} +\newlabel{tab:operators}{{1}{3}} +\@writefile{lot}{\protect \contentsline {table}{\protect \numberline {2}{\ignorespaces Properties of nodes in an operator tree}}{3}} +\newlabel{tab:annotations}{{2}{3}} +\newlabel{fig:optreeexample}{{1(a)}{3}} +\newlabel{fig:accplanexample}{{1(b)}{3}} +\@writefile{lof}{\protect \contentsline {figure}{\protect \numberline {1}{\ignorespaces Example of an operator tree and access plan}}{3}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{1(a)}{\ignorespaces An expression and its corresponding operator tree}}{3}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{1(b)}{\ignorespaces Possible access plan for operator tree in (a)}}{3}} +\newlabel{fig:expexample}{{1}{3}} +\@writefile{toc}{\protect \contentsline {paragraph}{Descriptors.}{3}} +\@writefile{toc}{\protect \contentsline {paragraph}{Access Plans.}{3}} +\@writefile{toc}{\protect \contentsline {subsection}{\protect \numberline {2.2}Prairie optimization paradigm}{3}} +\newlabel{sec:topdown}{{2.2}{3}} +\newlabel{eq:generaltrule}{{1}{4}} +\newlabel{fig:generaltrule}{{2(a)}{4}} +\newlabel{eq:associativity}{{2}{4}} +\newlabel{fig:associativity}{{2(b)}{4}} +\@writefile{lof}{\protect \contentsline {figure}{\protect \numberline {2}{\ignorespaces T-rule}}{4}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{2(a)}{\ignorespaces General form of a T-rule}}{4}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{2(b)}{\ignorespaces Join associativity}}{4}} +\newlabel{fig:trules}{{2}{4}} +\@writefile{toc}{\protect \contentsline {subsection}{\protect \numberline {2.3}Transformation rules}{4}} +\newlabel{sec:trules}{{2.3}{4}} +\newlabel{eq:generalirule}{{3}{4}} +\newlabel{fig:generalirule}{{3(a)}{4}} +\newlabel{eq:msort}{{4}{4}} +\newlabel{fig:msort}{{3(b)}{4}} +\@writefile{lof}{\protect \contentsline {figure}{\protect \numberline {3}{\ignorespaces I-rule}}{4}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{3(a)}{\ignorespaces General form of an I-rule}}{4}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{3(b)}{\ignorespaces Merge-sort sort algorithm}}{4}} +\newlabel{fig:irules}{{3}{4}} +\newlabel{ex:joinassociativity}{{4.}{4}} +\@writefile{toc}{\protect \contentsline {subsection}{\protect \numberline {2.4}Implementation rules}{4}} +\newlabel{sec:irules}{{2.4}{4}} +\citation{Das94} +\newlabel{ex:mergesort}{{5.}{5}} +\@writefile{toc}{\protect \contentsline {subsection}{\protect \numberline {2.5}Null algorithm}{5}} +\newlabel{sec:null}{{2.5}{5}} +\@writefile{toc}{\protect \contentsline {section}{\protect \numberline {3}The P2V pre-processor}{5}} +\newlabel{sec:ptov}{{3}{5}} +\newlabel{eq:generalnullalg}{{5}{5}} +\newlabel{fig:generalnullalg}{{4(a)}{5}} +\newlabel{eq:nullsort}{{6}{5}} +\newlabel{fig:nullsort}{{4(b)}{5}} +\@writefile{lof}{\protect \contentsline {figure}{\protect \numberline {4}{\ignorespaces The ``Null'' algorithm concept}}{5}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{4(a)}{\ignorespaces General form of a ``Null'' I-rule}}{5}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{4(b)}{\ignorespaces Null sort algorithm}}{5}} +\newlabel{fig:null}{{4}{5}} +\citation{Das93} +\citation{Blak93} +\@writefile{lof}{\protect \contentsline {figure}{\protect \numberline {5}{\ignorespaces The Prairie optimizer-generator paradigm. Double-boxed modules represent software generators, shaded boxes represent generated programs. The outermost double-boxed portion denotes the Prairie optimizer generator.}}{6}} +\newlabel{fig:ptovmodel}{{5}{6}} +\@writefile{toc}{\protect \contentsline {section}{\protect \numberline {4}Experimental results}{6}} +\newlabel{sec:results}{{4}{6}} +\@writefile{toc}{\protect \contentsline {subsection}{\protect \numberline {4.1}The Texas Instruments Open OODB query optimizer}{6}} +\newlabel{sec:oodb}{{4.1}{6}} +\@writefile{toc}{\protect \contentsline {subsection}{\protect \numberline {4.2}Programmer productivity}{7}} +\newlabel{sec:productivity}{{4.2}{7}} +\@writefile{toc}{\protect \contentsline {subsection}{\protect \numberline {4.3}Performance results using the Open OODB optimizer}{7}} +\newlabel{sec:oodbexp}{{4.3}{7}} +\citation{Seli79} +\citation{Dani82} +\newlabel{fig:Eone}{{6(a)}{8}} +\newlabel{fig:Etwo}{{6(b)}{8}} +\newlabel{fig:Ethree}{{6(c)}{8}} +\newlabel{fig:Efour}{{6(d)}{8}} +\@writefile{lof}{\protect \contentsline {figure}{\protect \numberline {6}{\ignorespaces Expressions used in generating queries for experiments}}{8}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{6(a)}{\ignorespaces E1}}{8}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{6(b)}{\ignorespaces E2}}{8}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{6(c)}{\ignorespaces E3}}{8}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{6(d)}{\ignorespaces E4}}{8}} +\newlabel{fig:exps}{{6}{8}} +\@writefile{lof}{\protect \contentsline {figure}{\protect \numberline {3}{\ignorespaces Queries used in experiments}}{8}} +\newlabel{tab:queries}{{3}{8}} +\@writefile{toc}{\protect \contentsline {section}{\protect \numberline {5}Related research}{8}} +\newlabel{sec:related}{{5}{8}} +\citation{Haas88} +\citation{Frey87a} +\citation{Grae87b} +\citation{Grae90b} +\newlabel{fig:q1}{{7(a)}{9}} +\newlabel{fig:q2}{{7(b)}{9}} +\newlabel{fig:q3}{{7(c)}{9}} +\newlabel{fig:q4}{{7(d)}{9}} +\newlabel{fig:q5}{{7(e)}{9}} +\newlabel{fig:q6}{{7(f)}{9}} +\newlabel{fig:q7}{{7(g)}{9}} +\newlabel{fig:q8}{{7(h)}{9}} +\@writefile{lof}{\protect \contentsline {figure}{\protect \numberline {7}{\ignorespaces Query optimization times for Q1 through Q8}}{9}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{7(a)}{\ignorespaces Query 1}}{9}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{7(b)}{\ignorespaces Query 2}}{9}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{7(c)}{\ignorespaces Query 3}}{9}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{7(d)}{\ignorespaces Query 4}}{9}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{7(e)}{\ignorespaces Query 5}}{9}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{7(f)}{\ignorespaces Query 6}}{9}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{7(g)}{\ignorespaces Query 7}}{9}} +\@writefile{lof}{\protect \contentsline {subfigure}{\string\numberline{7(h)}{\ignorespaces Query 8}}{9}} +\newlabel{fig:e4}{{7}{9}} +\@writefile{toc}{\protect \contentsline {section}{\protect \numberline {6}Conclusion and future work}{9}} +\newlabel{sec:conclusion}{{6}{9}} +\bibstyle{plain} +\bibdata{references} +\bibcite{Bato88a}{1} +\bibcite{Blak93}{2} +\bibcite{Dani82}{3} +\bibcite{Das93}{4} +\bibcite{Das94}{5} +\bibcite{Frey87a}{6} +\bibcite{Grae90b}{7} +\bibcite{Grae93}{8} +\bibcite{Grae87b}{9} +\bibcite{Haas88}{10} +\bibcite{Seli79}{11} +\bibcite{Ston86b}{12} +\newlabel{sec:acknowledgments}{{6}{10}} diff --git a/macros/latex/contrib/utthesis/ICDE-11/paper.bbl b/macros/latex/contrib/utthesis/ICDE-11/paper.bbl new file mode 100644 index 0000000000..a7e1b3ccdf --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/paper.bbl @@ -0,0 +1,76 @@ +\begin{thebibliography}{10} + +\bibitem{Bato88a} +D.~S. Batory. +\newblock Building blocks of database management systems. +\newblock Technical Report TR--87--23, The University of Texas at Austin, + February 1988. + +\bibitem{Blak93} +Jos\'e~A. Blakeley, William~J. McKenna, and Goetz Graefe. +\newblock Experiences building the {O}pen {OODB} query optimizer. +\newblock In {\em Proceedings 1993 ACM SIGMOD International Conference on + Management of Data}, pages 287--296, Washington, May 1993. + +\bibitem{Dani82} +Dean Daniels, Patricia Selinger, Laura Haas, Bruce Lindsay, C.~Mohan, Adrian + Walker, and Paul Wilms. +\newblock An introduction to distributed query compilation in {R}$^*$. +\newblock In {\em Proceedings 2nd International Conference on Distributed + Databases}, pages 291--309, Berlin, September 1982. + +\bibitem{Das93} +Dinesh Das and Don Batory. +\newblock Prairie: An algebraic framework for rule specification in query + optimizers. +\newblock In {\em Proceedings of the Workshop on Database Query Optimizer + Generators and Rule-Based Optimizers}, pages 139--154, Dallas, September + 1993. + +\bibitem{Das94} +Dinesh Das and Don Batory. +\newblock Prairie: A rule specification framework for query optimizers. +\newblock Technical Report TR 94--16, The University of Texas at Austin, May + 1994. + +\bibitem{Frey87a} +Johann~Christoph Freytag. +\newblock A rule-based view of query optimization. +\newblock In {\em Proceedings 1987 ACM SIGMOD International Conference on + Management of Data}, pages 173--180, San Francisco, May 1987. + +\bibitem{Grae90b} +Goetz Graefe. +\newblock Volcano, an extensible and parallel query evaluation system. +\newblock Technical Report CU--CS--481--90, University of Colorado at Boulder, + July 1990. + +\bibitem{Grae93} +Goetz Graefe. +\newblock Query evaluation techniques for large databases. +\newblock {\em ACM Computing Surveys}, 25(2):73--170, June 1993. + +\bibitem{Grae87b} +Goetz Graefe and David~J. DeWitt. +\newblock The {EXODUS} optimizer generator. +\newblock In {\em Proceedings 1987 ACM SIGMOD International Conference on + Management of Data}, pages 387--394, San Francisco, May 1987. + +\bibitem{Haas88} +L.~M. Haas, J.~C. Freytag, G.~M. Lohman, and H.~Pirahesh. +\newblock Extensible query processing in {S}tarburst. +\newblock Research Report RJ 6610, IBM Almaden Research Center, December 1988. + +\bibitem{Seli79} +P.~G. Selinger, M.~M. Astrahan, D.~D. Chamberlin, R.~A. Lorie, and T.~G. Price. +\newblock Access path selection in a relational database management system. +\newblock In {\em Proceedings 1979 ACM SIGMOD International Conference on + Management of Data}, pages 23--34, Boston, May 1979. + +\bibitem{Ston86b} +Michael Stonebraker and Lawrence~A. Rowe. +\newblock The design of {P}ostgres. +\newblock In {\em Proceedings 1986 ACM SIGMOD International Conference on + Management of Data}, pages 340--355, Washington, May 1986. + +\end{thebibliography} diff --git a/macros/latex/contrib/utthesis/ICDE-11/paper.blg b/macros/latex/contrib/utthesis/ICDE-11/paper.blg new file mode 100644 index 0000000000..e69de29bb2 --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/paper.blg diff --git a/macros/latex/contrib/utthesis/ICDE-11/paper.dvi b/macros/latex/contrib/utthesis/ICDE-11/paper.dvi Binary files differnew file mode 100644 index 0000000000..24b018fcfb --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/paper.dvi diff --git a/macros/latex/contrib/utthesis/ICDE-11/paper.log b/macros/latex/contrib/utthesis/ICDE-11/paper.log new file mode 100644 index 0000000000..baa677fc30 --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/paper.log @@ -0,0 +1,511 @@ +This is TeX, Version 3.141 (C version d) (format=latex 94.8.3) 20 MAR 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\hbox (badness 10000) has occurred while \output is active +[] + [] + +[1 + + +] +Underfull \hbox (badness 2980) in paragraph at lines 60--68 +[][]\OT1/ptm/m/n/10 A frame-work in which users can spec-ify map-ping + [] + +) (model.tex +LaTeX Font Info: Font shape `OT1/ptm/bx/n' in size <12> not available +(Font) Font shape `OT1/ptm/b/n' tried instead on input line 10. +LaTeX Font Info: Font shape `OT1/ptm/bx/n' in size <10> not available +(Font) Font shape `OT1/ptm/b/n' tried instead on input line 14. +LaTeX Font Info: External font `cmex10' loaded for size +(Font) <7> on input line 16. + +Underfull \hbox (badness 1515) in paragraph at lines 34--42 +\OT1/ptm/m/n/10 are de-noted by all cap-i-tal let-ters (e.g., JOIN). + [] + + +Underfull \hbox (badness 2799) in paragraph at lines 34--42 +\OT1/ptm/m/n/10 tial and ad-di-tional. \OT1/ptm/m/it/10 Es-sen-tial pa-ram-e-te +rs \OT1/ptm/m/n/10 are + [] + + +Underfull \hbox (badness 1354) in paragraph at lines 34--42 +\OT1/ptm/m/n/10 the stream or file in-puts to an op-er-a-tor; these + [] + + +Underfull \hbox (badness 2158) in paragraph at lines 34--42 +\OT1/ptm/m/n/10 are the pri-mary in-puts to be pro-cessed by an + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 44--52 +[][]\OT1/ptm/m/it/10 Algorithms \OT1/ptm/m/n/10 are con-crete im-ple-men- + [] + + +Underfull \hbox (badness 4792) in paragraph at lines 44--52 +\OT1/ptm/m/n/10 ta-tions of con-cep-tual op-er-a-tors; they will be + [] + + +Underfull \hbox (badness 2809) in paragraph at lines 44--52 +\OT1/ptm/m/n/10 rep-re-sented in lower case with the first let-ter + [] + + +Underfull \hbox (badness 8000) in paragraph at lines 44--52 +\OT1/ptm/m/n/10 cap-i-tal-ized (e.g., Nested[]loops). Al-go-rithms + [] + + +Underfull \hbox (badness 2970) in paragraph at lines 44--52 +\OT1/ptm/m/n/10 implement.[] Fur-ther-more, there can be, and + [] + +\first=\skip48 +\second=\skip49 +\third=\skip50 +\fourth=\skip51 +\linelength=\skip52 +LaTeX Font Info: Font shape `OT1/ptm/bx/n' in size <7> not available +(Font) Font shape `OT1/ptm/b/n' tried instead on input line 71. + +Overfull \hbox (12.0pt too wide) in paragraph at lines 85--86 +[]|$[]$| + [] + + +Underfull \hbox (badness 4366) in paragraph at lines 200--200 +[]\OT1/ptm/m/n/8 (a) An ex-pres-sion and its + [] + +[2] +Underfull \hbox (badness 3271) in paragraph at lines 301--311 + []\OT1/ptm/m/n/10 There are two types of al-ge-braic trans-for-ma-tions (or + [] + +[3] +\lefttreeone=\box33 +\righttreeone=\box34 +\lefttreetwo=\box35 +\righttreetwo=\box36 +\rewritesto=\box37 +\doesnotrewriteto=\box38 + [4] +Underfull \hbox (badness 6978) in paragraph at lines 766--769 + []\OT1/ptm/m/n/10 The post-opt sec-tion in the I-rule has only a cost- + [] + + +Underfull \hbox (badness 4699) in paragraph at lines 766--769 + \OT1/ptm/m/n/10 assignment state-ment; this sim-ply sets the cost of the + [] + +) (p2v.tex +Underfull \hbox (badness 1902) in paragraph at lines 4--19 + \OT1/ptm/m/n/10 In Sec-tion 1[], we enu-mer-ated the four pri-mary goals of + [] + + +Underfull \hbox (badness 1577) in paragraph at lines 4--19 + \OT1/ptm/m/n/10 and ef-fi-cient gen-er-a-tion of Prairie op-ti-miz-ers. The fi +rst + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 56--56 +[]\OT1/ptm/m/n/10 Figure 5: The Prairie optimizer-generator paradigm. + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 56--56 +\OT1/ptm/m/n/10 Double-boxed mod-ules rep-re-sent soft-ware gen-er-a-tors, + [] + + +Underfull \hbox (badness 1194) in paragraph at lines 56--56 +\OT1/ptm/m/n/10 shaded boxes rep-re-sent gen-er-ated pro-grams. The out-er- + [] + + +Underfull \hbox (badness 1087) in paragraph at lines 56--56 +\OT1/ptm/m/n/10 most double-boxed por-tion de-notes the Prairie op-ti-mizer + [] + +[5] +Underfull \hbox (badness 1460) in paragraph at lines 105--115 + []\OT1/ptm/m/n/10 The third salient fea-ture of a Vol-cano spec-i-fi-ca-tion i +s + [] + + +Underfull \hbox (badness 2460) in paragraph at lines 105--115 + \OT1/ptm/m/n/10 This re-quires the pre-processor to mi-grate the (deleted) + [] + +) (results.tex +Underfull \hbox (badness 4505) in paragraph at lines 24--26 +[][]\OT1/ptm/m/n/10 How is pro-gram-mer pro-duc-tiv-ity en-hanced by the + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 36--36 + []\OT1/ptm/b/n/12 The Texas In-stru-ments Open OODB + [] + + +Underfull \hbox (badness 5105) in paragraph at lines 39--49 + \OT1/ptm/m/n/10 The Texas In-stru-ments Open Object-Oriented Database + [] + + +Underfull \hbox (badness 7576) in paragraph at lines 39--49 + \OT1/ptm/m/n/10 database sys-tem which pro-vides users an ar-chi-tec-tural + [] + + +Underfull \hbox (badness 1448) in paragraph at lines 39--49 + \OT1/ptm/m/n/10 us-ing Vol-cano. It is writ-ten as a set of trans[]rules and + [] + + +Underfull \hbox (badness 3417) in paragraph at lines 39--49 + \OT1/ptm/m/n/10 impl[]rules that de-fine the al-ge-bra of an object-oriented + [] + + +Underfull \hbox (badness 1122) in paragraph at lines 39--49 + \OT1/ptm/m/n/10 database sys-tem. Cur-rently, there are 17 trans-for-ma-tion + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 39--49 + \OT1/ptm/m/n/10 rules and 9 im-ple-men-ta-tion rules to-gether with about + [] + +[6] +Underfull \hbox (badness 10000) in paragraph at lines 86--86 + []\OT1/ptm/b/n/12 Performance re-sults us-ing the Open + [] + +\Eone=\box39 +\Etwo=\box40 +\Ethree=\box41 +\Efour=\box42 +\c@savectr=\count115 +\Lone=\skip53 +\Ltwo=\skip54 +\Lthree=\skip55 +\Lfour=\skip56 +\Lnum=\skip57 + +Underfull \hbox (badness 10000) in paragraph at lines 351--356 + []\OT1/ptm/m/n/10 Table 3[] also shows the num-ber of trans[]rules and + [] + + +Underfull \hbox (badness 1609) in paragraph at lines 351--356 + \OT1/ptm/m/n/10 impl[]rules that are matched by each ex-pres-sion. These + [] + +[7] +File: runtime_Q1.ps Graphic file (type eps) + <runtime_Q1.ps> +File: runtime_Q2.ps Graphic file (type eps) + <runtime_Q2.ps> +File: runtime_Q3.ps Graphic file (type eps) + <runtime_Q3.ps> +File: runtime_Q4.ps Graphic file (type eps) + <runtime_Q4.ps> +File: runtime_Q5.ps Graphic file (type eps) + +<runtime_Q5.ps> +File: runtime_Q6.ps Graphic file (type eps) + <runtime_Q6.ps> +File: runtime_Q7.ps Graphic file (type eps) + <runtime_Q7.ps> +File: runtime_Q8.ps Graphic file (type eps) + <runtime_Q8.ps>) (related.tex +[8]) (conclusion.tex [9]) (paper.bbl +Underfull \hbox (badness 1292) in paragraph at lines 10--14 +[][]\OT1/ptm/m/n/10 Jos[]e A. Blake-ley, William J. 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Source file was pstricks.doc +% Version 0.93a, 93/03/12. +% For use with Rokicki's dvips. +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/Atan { /atan load stopped { pop pop 0 } if } def +/Div { dup 0 eq { pop } { div } ifelse } def +/NET { neg exch neg exch T } def +/Pyth { dup mul exch dup mul add sqrt } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } +def +/PathLength { flattenpath /z 0 def { /y1 ED /x1 ED /y2 y1 def /x2 x1 def +} { /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } +pathforall z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +/y ED x mul /x ED x 0 eq y 0 eq and { /x 1 def /y 1 def } if [ y x ] 1 a +sub y mul setdash stroke } def +/DotLine { /b PathLength def /a ED /z ED /y CLW def /z y z add def a 0 gt +{ /b b a div def } { a 0 eq { /b b y sub def } { a -3 eq { /b b y add +def } if } ifelse } ifelse [ 0 b b z Div round Div dup 0 le { pop 1 } if +] a 0 gt { 0 } { y 2 div a -2 gt { neg } if } ifelse setdash 1 +setlinecap stroke } def +/LineFill { abs CLW add /a ED gsave clip pathbbox a Div ceiling /y2 ED +/x2 ED a Div floor /y1 ED /x1 ED /n y2 y1 sub 1 add cvi def /y1 a y1 mul +def newpath 2 setlinecap n { currentstrokeadjust == x1 y1 moveto x2 y1 L +stroke /y1 y1 a add def } repeat grestore } def +/LineFill { abs CLW add /a ED gsave clip pathbbox a Div ceiling /y2 ED +/x2 ED a Div floor /y1 ED /x1 ED /n y2 y1 sub 1 add cvi def /y1 a y1 mul +def newpath 2 setlinecap systemdict /currentstrokeadjust known { +currentstrokeadjust } { false } ifelse { /t { } def } { /t { transform +0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform } +bind def } ifelse n { x1 y1 t moveto x2 y1 t L stroke /y1 y1 a add def } +repeat grestore } def +/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg +exch 3 index sub exch Atan rotate newpath } def +/EndArrow { @mtrx setmatrix CP grestore end } def +/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 +scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill +grestore } def +/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0 +CLW moveto } def +/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2 +div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0 +CLW moveto } def +/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW +2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0 +curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto } +def +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { +/closepath load } pathforall ] cvx newpath 3 1 roll T exec } def +/SD { 0 360 arc fill } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch +cvi def } def +/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if +f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub +def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } +ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq +and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } +repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 +ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 +moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto +Lineto pop pop closepath } ifelse } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def +n { NC } repeat EOC } ifelse } def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS +CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { /a 4 string def /b ED /d ED /n ED cvi dup 1 lt { pop 1 } if /c ED +c div dup 0 eq { pop 1 } if /cy ED c div dup 0 eq { pop 1 } if /cx ED cy +div cvi /y ED cx div cvi /x ED cy div cvi /y2 ED cx div cvi /x2 ED cy +div cvi /y1 ED cx div cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse +def /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 +div add def /Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 +div add def } if gsave n 0 gt { 1 setlinecap [ 0 cy n div ] 0 setdash } +{ 2 setlinecap } ifelse /c x1 def /i 500 w mul x1 add def /e y cy mul +def /f y1 cy mul def /g y2 cy mul def x1 cx mul 0 T { newpath 0 e moveto +b 0 gt { gsave d c a cvs dup stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 +add neg} ifelse h 0 gt {b neg} {z1} ifelse rmoveto show grestore } if 0 +f moveto 0 g L stroke cx w mul 0 T c x2 eq c i eq or {exit} if /c c w +add def } loop grestore gsave n 0 gt { 1 setlinecap [ 0 cx n div ] 0 +setdash } { 2 setlinecap } ifelse /c y1 def /i 500 h mul y1 add def /e x +cx mul def /f x1 cx mul def /g x2 cx mul def 0 y1 cy mul T { newpath e 0 +moveto b 0 gt { gsave d c a cvs dup stringwidth pop /z2 ED w 0 gt {z1 z2 +add neg} {z1} ifelse h 0 gt {z1} {b neg} ifelse rmoveto show grestore } +if f 0 moveto g 0 L stroke 0 cy h mul T c y2 eq c i eq or {exit} if /c c +h add def } loop grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /lmtrx [ tx@Dict /lmtrx known { lmtrx aload pop } if CM ] def +CP 4 2 roll T moveto } def +/PutEnd { CP /lmtrx [ lmtrx aload pop setmatrix ] def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { CP OLUnit T +moveto /IfVisible true def } if } { IfVisible { CP OLUnit NET moveto +/IfVisible false def } if } ifelse } def +/InitOL { /OLUnit [ gsave CM STV 2890.79999 dup moveto setmatrix CP +grestore ] cvx def /BOL { BeginOL } def /IfVisible true def } def +end +%%EndProcSet +%%BeginProcSet: /u/ddas/tex/pstricks/ps/pst-node.pro +% PostScript prologue for pst-node.tex. +% Created 1993/3/12. Source file was pst-node.doc +% Version 0.93a, 93/03/12. +% For use with Rokicki's dvips. +/tx@NodeDict 200 dict def tx@NodeDict begin +/NewNode { gsave /next ED dict dup 3 -1 roll ED begin tx@Dict begin STV +CP T exec end /NodeMtrx CM def next end grestore } def +/InitPnode { /Y ED /X ED /NodePos { Nodesep Cos mul Nodesep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { Nodesep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r Nodesep add def } { /dx l Nodesep sub def +} ifelse Sin 0 gt { /dy u Nodesep add def } { /dy d Nodesep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /r ED r mul neg /l ED /r r l add def /X l neg def { neg /d +ED /u ED /Y 0 def } { neg /Y ED Y sub /u ED u mul neg /d ED /u u d add +def /Y Y d sub def } ifelse /NodePos { GetRnodePos } def } def +/InitRNode { /Y ED /X ED /r ED /X r 2 div X add def /r r X sub def /l X +neg def Y add neg /d ED Y sub /u ED /NodePos { GetRnodePos } def } def +/GetOnodePos { /ww w Nodesep add def /hh h Nodesep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/GetAngle { nodeA GetCenter nodeB GetCenter 3 -1 roll sub 3 1 roll sub +neg Atan } def +/GetEdge { begin /Nodesep ED dup 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED NodePos Y add exch X add exch +NodeMtrx transform CM itransform end 4 2 roll 1 index 0 eq { pop pop } { +2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse } def +/GetPos { OffsetA AngleA NodesepA nodeA GetEdge /y1 ED /x1 ED OffsetB +AngleB NodesepB nodeB GetEdge /y2 ED /x2 ED } def +/InitNC { /nodeB ED /nodeA ED /NodesepB ED /NodesepA ED /OffsetB ED +/OffsetA ED tx@NodeDict nodeA known tx@NodeDict nodeB known and dup { +/nodeA nodeA load def /nodeB nodeB load def } if } def +/LineMP { 4 copy 1 t sub mul exch t mul add 3 1 roll 1 t sub mul exch t +mul add exch 6 2 roll sub 3 1 roll sub Atan } def +/NCCoor { GetAngle /AngleA ED /AngleB AngleA 180 add def GetPos /LPutVar +[ x2 x1 y2 y1 ] cvx def /LPutPos { LPutVar LineMP } def x1 y1 x2 y2 } +def +/NCLine { NCCoor tx@Dict begin ArrowB 4 2 roll ArrowA lineto end } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan } def +/GetArms { /x1a armA AngleA cos mul x1 add def /y1a armA AngleA sin mul +y1 add def /x2a armB AngleB cos mul x2 add def /y2a armB AngleB sin mul +y2 add def } def +/NCCurve { GetPos x1 x2 sub y1 y2 sub Pyth 2 div dup 3 -1 roll mul /armA +ED mul /armB ED GetArms x1a y1a x1 y1 tx@Dict begin ArrowA end x2a y2a +x2 y2 tx@Dict begin ArrowB end curveto /LPutVar [ x1 y1 x1a y1a x2a y2a +x2 y2 ] cvx def /LPutPos { t LPutVar BezierMidpoint } def } def +/AnglesMP { LPutVar t 3 gt { /t t 3 sub def } { t 2 gt { /t t 2 sub def +10 -2 roll } { t 1 gt { /t t 1 sub def 10 -4 roll } { 10 4 roll } ifelse +} ifelse } ifelse 6 { pop } repeat 3 -1 roll exch LineMP } def +/NCAngles { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform pop x2a y2a mtrx transform exch pop mtrx itransform /y0 ED /x0 +ED mark armB 0 ne { x2 y2 } if x2a y2a x0 y0 x1a y1a armA 0 ne { x1 y1 } +if tx@Dict begin false Line end /LPutVar [ x2 y2 x2a y2a x0 y0 x1a y1a +x1 y1 ] cvx def /LPutPos { AnglesMP } def } def +/NCAngle { GetPos /x2a armB AngleB cos mul x2 add def /y2a armB AngleB +sin mul y2 add def /mtrx AngleA matrix rotate def x2a y2a mtrx transform +pop x1 y1 mtrx transform exch pop mtrx itransform /y0 ED /x0 ED mark +armB 0 ne { x2 y2 } if x2a y2a x0 y0 x1 y1 tx@Dict begin false Line end +/LPutVar [ x2 y2 x2 y2 x2a y2a x0 y0 x1 y1 ] cvx def /LPutPos { AnglesMP +} def } def +/NCBar { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform pop x2a y2a mtrx transform pop sub dup 0 mtrx itransform 3 -1 +roll 0 gt { /y2a exch y2a add def /x2a exch x2a add def } { /y1a exch +neg y1a add def /x2a exch neg x2a add def } ifelse mark x2 y2 x2a y2a +x1a y1a x1 y1 tx@Dict begin false Line end /LPutVar [ x2 y2 x2 y2 x2a +y2a x1a y1a x1 y1 ] cvx def /LPutPos { LPutVar AnglesMP } def } def +/NCDiag { GetPos GetArms mark x2 y2 x2a y2a x1a y1a x1 y1 tx@Dict begin +false Line end /LPutVar [ x2 y2 x2 y2 x2a y2a x1a y1a x1 y1 ] cvx def +/LPutPos { AnglesMP } def } def +/NCDiagg { OffsetA AngleA NodesepA nodeA GetEdge /y1 ED /x1 ED /x1a armA +AngleA cos mul x1 add def /y1a armA AngleA sin mul y1 add def nodeB +GetCenter y1a sub exch x1a sub Atan 180 add /AngleB ED OffsetB AngleB +NodesepB nodeB GetEdge /y2 ED /x2 ED mark x2 y2 x1a y1a x1 y1 tx@Dict +begin false Line end /LPutVar [ x2 y2 x2 y2 x2 y2 x1a y1a x1 y1] cvx def +/LPutPos { AnglesMP } def } def +/LoopMP { /t t abs def [ LPutVar ] length 2 div 1 sub dup t lt { /t ED } +{ pop } ifelse mark LPutVar t cvi { /t t 1 sub def pop pop } repeat +counttomark 1 add 4 roll cleartomark 3 -1 roll exch LineMP } def +/NCLoop { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform loopsize add /y1b ED /x1b ED /x2b x2a y2a mtrx transform pop +def x2b y1b mtrx itransform /y2b ED /x2b ED x1b y1b mtrx itransform /y1b +ED /x1b ED mark armB 0 ne { x2 y2 } if x2a y2a x2b y2b x1b y1b x1a y1a +armA 0 ne { x1 y1 } if tx@Dict begin false Line end /LPutVar [ x2 y2 x2a +y2a x2b y2b x1b y1b x1a y1a x1 y1 ] cvx def /LPutPos { LoopMP } def } +def +/NCCircle { nodeA GetCenter 0 0 NodesepA nodeA GetEdge pop 3 1 roll /Y ED +/X ED X sub 2 div dup 2 exp r r mul sub abs sqrt atan 2 mul /a ED r +AngleA 90 add PtoC Y add exch X add exch 2 copy /LPutVar [ 4 2 roll r a +] def /LPutPos { LPutVar aload pop t 360 mul add dup 5 1 roll 90 sub +PtoC 3 -1 roll add 3 1 roll add exch 3 -1 roll } def r AngleA 90 sub a +add AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c +57.2957 r Div def /y ED /x ED } def +/LPutCoor { tx@NodeDict /LPutPos known { gsave LPutPos tx@Dict begin +/langle ED CM 3 1 roll STV CP 3 -1 roll sub neg 3 1 roll sub exch moveto +setmatrix CP end grestore } { 0 0 tx@Dict /langle 0 def end } ifelse } +def +end +%%EndProcSet +%%BeginProcSet: texps.pro +TeXDict begin /rf{findfont dup length 1 add dict begin{1 index /FID ne 2 +index /UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type /integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics /Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont /setfont load]cvx def}def +/ObliqueSlant{dup sin S cos div neg}B /SlantFont{4 index mul add}def +/ExtendFont{3 -1 roll mul exch}def /ReEncodeFont{/Encoding exch def}def +end +%%EndProcSet +%%BeginProcSet: special.pro +TeXDict begin /SDict 200 dict N SDict begin /@SpecialDefaults{/hs 612 N +/vs 792 N /ho 0 N /vo 0 N /hsc 1 N /vsc 1 N /ang 0 N /CLIP 0 N /rwiSeen +false N /rhiSeen false N /letter{}N /note{}N /a4{}N /legal{}N}B +/@scaleunit 100 N /@hscale{@scaleunit div /hsc X}B /@vscale{@scaleunit +div /vsc X}B /@hsize{/hs X /CLIP 1 N}B /@vsize{/vs X /CLIP 1 N}B /@clip{ +/CLIP 2 N}B /@hoffset{/ho X}B /@voffset{/vo X}B /@angle{/ang X}B /@rwi{ +10 div /rwi X /rwiSeen true N}B /@rhi{10 div /rhi X /rhiSeen true N}B +/@llx{/llx X}B /@lly{/lly X}B /@urx{/urx X}B /@ury{/ury X}B /magscale +true def end /@MacSetUp{userdict /md known{userdict /md get type +/dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup +length 20 add dict copy def}if end md begin /letter{}N /note{}N /legal{} +N /od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath +clippath mark{transform{itransform moveto}}{transform{itransform lineto} +}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{ +itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{ +closepath}}pathforall newpath counttomark array astore /gc xdf pop ct 39 +0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}N +/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 +scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get +ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip +not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 +TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{noflips{TR +pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 +-1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg +TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg +sub neg 0 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0.0 neg 1.0 1.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 152 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + 152 707 a Fa(C)179 719 y Fn(2)142 +618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 142 618 a Fm(RET)-7 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 42 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoingetcl1getcl2 16 { +.5 3.39499 0.05246 false .5 10.8299 InitRnode } NewNode end end + 42 +524 a Fm(JOIN)-7 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a -7 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 182 +415 a + tx@Dict begin 45. Rot end + 182 415 a 143 418 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 143 418 a Fl(:)10 b(:)g(:)182 +415 y + tx@Dict begin 45. neg Rot end + 182 415 a -7 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + -7 699 a 331 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 331 429 a +Fm(RET)336 520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.32748 0.99998 +false .5 8.23895 InitRnode } NewNode end end + 336 520 a Fa(C)364 528 y Fl(n)-7 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 231 335 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.39499 +0.05246 false .5 10.8299 InitRnode } NewNode end end + 231 335 a Fm(JOIN)-7 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + -7 699 +a -7 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 100 881 a Fz(\(a\))17 b(E1)p 447 +976 4 928 v 476 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + 476 707 a Fa(C)504 719 y Fn(1)467 +618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 467 618 a Fm(RET)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 665 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + +665 707 a Fa(C)693 719 y Fn(2)656 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 656 618 a Fm(RET)506 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 463 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl1 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 463 524 a Fm(MA)-5 b(T)506 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl1 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 699 a 652 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl2 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 652 524 a Fm(MA)g(T)506 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 699 a 556 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoinmatgetcl1matgetcl2 +16 { .5 3.39499 0.05246 false .5 10.8299 InitRnode } NewNode end end + 556 429 a Fm(JOIN)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 +699 a 506 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 699 a 695 321 a + tx@Dict begin 45. Rot end + 695 321 a 656 324 +a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 656 324 a Fl(:)11 b(:)f(:)695 321 y + tx@Dict begin 45. neg Rot end + 695 321 a 506 699 +a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 506 699 a 845 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 845 429 a Fm(RET)850 520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.32748 0.99998 +false .5 8.23895 InitRnode } NewNode end end + 850 +520 a Fa(C)878 528 y Fl(n)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 841 335 +a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcln 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 841 335 a Fm(MA)-5 b(T)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodematgetcln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 745 240 +a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.39499 +0.05246 false .5 10.8299 InitRnode } NewNode end end + 745 240 a Fm(JOIN)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 506 699 a 506 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodematgetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 +699 a 611 881 a Fz(\(b\))17 b(E2)p 961 976 4 928 v 990 +707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + 990 707 a Fa(C)1018 719 y Fn(1)981 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 981 618 +a Fm(RET)1020 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1179 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + 1179 707 a +Fa(C)1207 719 y Fn(2)1170 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 1170 618 a Fm(RET)1020 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1070 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoingetcl1getcl2 16 { +.5 3.39499 0.05246 false .5 10.8299 InitRnode } NewNode end end + 1070 524 a Fm(JOIN)1020 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1020 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1209 415 a + tx@Dict begin 45. Rot end + 1209 415 +a 1170 418 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 1170 418 a Fl(:)11 b(:)f(:)1209 415 y + tx@Dict begin 45. neg Rot end + 1209 +415 a 1020 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1020 699 a 1359 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 1359 429 a Fm(RET)1364 +520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.32748 0.99998 +false .5 8.23895 InitRnode } NewNode end end + 1364 520 a Fa(C)1392 528 y Fl(n)1020 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 +699 a 1259 335 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.39499 +0.05246 false .5 10.8299 InitRnode } NewNode end end + 1259 335 a Fm(JOIN)1020 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1020 699 +a 1020 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1227 240 a + tx@Dict begin tx@NodeDict begin { } /TheNodeselect 16 { .5 3.39499 +0.05246 false .5 18.3349 InitRnode } NewNode end end + 1227 240 a Fm(SELECT)1020 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodeselect +/TheNoderoot InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1020 699 a 1127 881 a Fz(\(c\))17 b(E3)p 1474 976 +4 928 v 1504 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + 1504 707 a Fa(C)1531 719 y Fn(1)1495 +618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 1495 618 a Fm(RET)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1693 707 +a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + 1693 707 a Fa(C)1720 719 y Fn(2)1684 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 1684 618 +a Fm(RET)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1490 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl1 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 1490 524 a +Fm(MA)-5 b(T)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl1 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a 1679 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl2 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 1679 524 +a Fm(MA)g(T)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a 1583 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoinmatgetcl1matgetcl2 +16 { .5 3.39499 0.05246 false .5 10.8299 InitRnode } NewNode end end + 1583 429 +a Fm(JOIN)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a 1534 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a +1723 321 a + tx@Dict begin 45. Rot end + 1723 321 a 1684 324 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 1684 324 a Fl(:)10 b(:)h(:)1723 +321 y + tx@Dict begin 45. neg Rot end + 1723 321 a 1534 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1534 699 a 1873 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 1873 +429 a Fm(RET)1878 520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.32748 0.99998 +false .5 8.23895 InitRnode } NewNode end end + 1878 520 a Fa(C)1905 528 y Fl(n)1534 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1868 335 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcln 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 1868 335 a Fm(MA)-5 b(T)1534 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodematgetcln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1772 240 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.39499 +0.05246 false .5 10.8299 InitRnode } NewNode end end + 1772 240 a Fm(JOIN)1534 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1534 699 a 1534 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y(\256cation)h(framework)e(for)i(query)f +(optimizers.)75 b(T)-6 b(echnical)2224 1150 y(Report)22 +b(TR)h(94\26116,)e(The)h(University)g(of)g(T)-6 b(exas)22 +b(at)h(Austin,)2224 1249 y(May)d(1994.)2085 1415 y([6])41 +b(Johann)15 b(Christoph)h(Freytag.)21 b(A)d(rule-based)d(view)h(of)g +(query)2224 1515 y(optimization.)80 b(In)30 b FF(Pr)m(oceedings)f(1987) +h(ACM)h(SIGMOD)2224 1615 y(International)37 b(Confer)m(ence)j(on)f +(Management)f(of)j(Data)p FG(,)2224 1714 y(pages)19 b(173\261180,)e +(San)k(Francisco,)e(May)h(1987.)2085 1880 y([7])41 b(Goetz)33 +b(Graefe.)94 b(V)-11 b(olcano,)36 b(an)d(extensible)g(and)g(parallel) +2224 1980 y(query)23 b(evaluation)g(system.)53 b(T)-6 +b(echnical)24 b(Report)h(CU\261CS\261)2224 2080 y(481\26190,)14 +b(University)i(of)g(Colorado)f(at)i(Boulder)m(,)e(July)i(1990.)2085 +2246 y([8])41 b(Goetz)24 b(Graefe.)48 b(Query)24 b(evaluation)e +(techniques)h(for)h(lar)o(ge)2224 2345 y(databases.)66 +b FF(ACM)28 b(Computing)f(Surveys)p FG(,)i(25\(2\):73\261170,)2224 +2445 y(June)20 b(1993.)2085 2611 y([9])41 b(Goetz)29 +b(Graefe)h(and)f(David)g(J.)i(DeW)m(itt.)78 b(The)30 +b(EXODUS)2224 2710 y(optimizer)21 b(generator)-5 b(.)42 +b(In)23 b FF(Pr)m(oceedings)e(1987)h(ACM)i(SIG-)2224 +2810 y(MOD)40 b(International)d(Confer)m(ence)i(on)g(Management)f(of) +2224 2910 y(Data)p FG(,)19 b(pages)h(387\261394,)d(San)j(Francisco,)g +(May)g(1987.)2044 3076 y([10])40 b(L.)23 b(M.)g(Haas,)h(J.)g(C.)g +(Freytag,)e(G.)i(M.)f(Lohman,)f(and)g(H.)i(Pi-)2224 3175 +y(rahesh.)31 b(Extensible)20 b(query)f(processing)h(in)h(Starburst.)32 +b(Re-)2224 3275 y(search)20 b(Report)g(RJ)i(6610,)e(IBM)h(Almaden)e +(Research)i(Cen-)2224 3375 y(ter)m(,)e(December)g(1988.)2047 +3541 y([1)m(1])40 b(P)-9 b(.)33 b(G.)g(Selinger)m(,)h(M.)f(M.)g +(Astrahan,)i(D.)e(D.)g(Chamberlin,)2224 3640 y(R.)28 +b(A.)h(Lorie,)g(and)f(T)-6 b(.)28 b(G.)g(Price.)69 b(Access)29 +b(path)e(selection)2224 3740 y(in)d(a)g(relational)f(database)g +(management)f(system.)47 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+\PScommands + +\setlength{\mathindent}{0in} + +\renewcommand{\baselinestretch}{1.0} +\newcommand{\eg}{e.g.,\xspace} +\newcommand{\ie}{i.e.,\xspace} +\newcommand{\etc}{etc.\@\xspace} +\makeatletter +\newcommand{\preprint} + {\pagestyle{empty} + \newcommand{\firstpage} + {\thispagestyle{plain} + \makeatletter + \renewcommand{\ps@plain}{ + \renewcommand{\@oddhead}{\fbox{To appear in \textit{Proceedings + 11th International Conference on + Data Engineering}, + Taipei, March 1995}} + \renewcommand{\@evenhead}{} + \renewcommand{\@evenfoot}{} + \renewcommand{\@oddfoot}{}} + \makeatother}} +\newcommand{\reprint} + {\pagestyle{empty} + \newcommand{\firstpage} + {\thispagestyle{plain} + \makeatletter + \renewcommand{\ps@plain}{ + \renewcommand{\@oddhead}{\fbox{In \textit{Proceedings + 11th International Conference on + Data Engineering}, pages 201--210, + Taipei, March 1995}} + \renewcommand{\@evenhead}{} + \renewcommand{\@evenfoot}{} + \renewcommand{\@oddfoot}{}} + \makeatother}} +\makeatother 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+\newenvironment{fullminipage} + {\begin{minipage}[b]{0.93\linewidth}} + {\end{minipage}} + +\newenvironment{fullminipagerule} + {\setlength{\topsep}{0pt} + \scriptsize + \begin{fullminipage}} + {\end{fullminipage}} +\newenvironment{halfminipagerule} + {\setlength{\topsep}{0pt} + \footnotesize + \begin{halfminipage}} + {\end{halfminipage}} + +% Command to add space to second line of rule definitions. +\newcommand{\rulespace}{\quad} +\newenvironment{ruleactions} + {$\doubleopenbraces$ + \begin{tabbing} + \hspace{2pc} \= \kill} + {\end{tabbing} + $\doubleclosebraces$} + +\newenvironment{trule} + {\begin{equation}} + {\end{equation}} +\newenvironment{trulepretest} + {\begin{ruleactions}} + {\end{ruleactions} \\} +\newenvironment{truleposttest} + {\\ + \begin{ruleactions}} + {\end{ruleactions}} +\newenvironment{fullminipagetrule} + {\begin{fullminipagerule}} + {\end{fullminipagerule}} +\newenvironment{halfminipagetrule} + {\begin{halfminipagerule}} + {\end{halfminipagerule}} + +\newenvironment{irule} + {\begin{equation}} + {\end{equation}} +\newenvironment{irulepreopt} + {\\ + \begin{ruleactions}} + {\end{ruleactions}} +\newenvironment{irulepostopt} + {\\ + \begin{ruleactions}} + {\end{ruleactions}} +\newenvironment{fullminipageirule} + {\begin{fullminipagerule}} + {\end{fullminipagerule}} +\newenvironment{halfminipageirule} + {\begin{halfminipagerule}} + {\end{halfminipagerule}} + +\newenvironment{centeredfigure} + {\begin{figure}[tb] + \begin{center}} + {\end{center} + \end{figure}} +\newenvironment{centeredfigure*} + {\begin{figure*}[tb] + \begin{center}} + {\end{center} + \end{figure*}} + +\newenvironment{centeredtable} + {\begin{table}[tb] + \begin{center}} + {\end{center} + \normalsize + \end{table}} +\newenvironment{centeredtable*} + {\begin{table*}[tb] + \begin{center}} + {\end{center} + \normalsize + \end{table*}} + +\newenvironment{centeredinquarterminipage} + {\begin{quarterminipage} + \begin{center}} + {\end{center} + \end{quarterminipage}} +\newenvironment{centeredinhalfminipage} + {\begin{halfminipage} + \begin{center}} + {\end{center} + \end{halfminipage}} +\newenvironment{centeredinfullminipage} + {\begin{fullminipage} + \begin{center}} + {\end{center} + \end{fullminipage}} + +\title{\textbf{Prairie: A Rule Specification Framework \\ + for Query Optimizers}\thanks{ + This research was supported in part by grants from The University + of Texas Applied Research Laboratories, Schlumberger, and + Digital Equipment Corporation.}\ \thanks{ + An expanded version of this paper is available as Technical + Report TR 94--16 by anonymous ftp from \texttt{ftp.cs.utexas.edu}.}} +\author{Dinesh Das \hspace{1in} Don Batory \\ + Department of Computer Sciences \\ + The University of Texas at Austin \\ + Austin, Texas 78712--1188 \\ + \{ddas,batory\}@cs.utexas.edu} +\date{} + +%\final +%\preprint +\reprint + +\makeatletter +\def\thickhline{\noalign{\ifnum0=`}\fi\hrule \@height 1.5pt \futurelet + \@tempa\@xhline} +\makeatother + +\begin{document} + +\maketitle + +\pagenumbering{arabic} +\input{abstract.tex} +\input{intro.tex} +\input{model.tex} +\input{p2v.tex} +\input{results.tex} +\input{related.tex} +\input{conclusion.tex} + +\bibliographystyle{plain} +\bibliography{references} + +\end{document} diff --git a/macros/latex/contrib/utthesis/ICDE-11/preprint.ps b/macros/latex/contrib/utthesis/ICDE-11/preprint.ps new file mode 100644 index 0000000000..00e36a2b29 --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/preprint.ps @@ -0,0 +1,6724 @@ +%!PS-Adobe-2.0 +%%Creator: dvips 5.55 Copyright 1986, 1994 Radical Eye Software +%%Title: paper.dvi +%%CreationDate: Thu Dec 1 10:58:49 1994 +%%Pages: 10 +%%PageOrder: Ascend +%%BoundingBox: 0 0 612 792 +%%DocumentFonts: Times-Roman Times-Italic Times-Bold Courier +%%EndComments +%DVIPSCommandLine: dvips -D 600 paper -o +%DVIPSParameters: dpi=600, comments removed +%DVIPSSource: TeX output 1994.12.01:1057 +%%BeginProcSet: tex.pro +/TeXDict 250 dict def TeXDict begin 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.5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto } +def +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { +/closepath load } pathforall ] cvx newpath 3 1 roll T exec } def +/SD { 0 360 arc fill } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch +cvi def } def +/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if +f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub +def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } +ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq +and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } +repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 +ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 +moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto +Lineto pop pop closepath } ifelse } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def +n { NC } repeat EOC } ifelse } def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS +CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { /a 4 string def /b ED /d ED /n ED cvi dup 1 lt { pop 1 } if /c ED +c div dup 0 eq { pop 1 } if /cy ED c div dup 0 eq { pop 1 } if /cx ED cy +div cvi /y ED cx div cvi /x ED cy div cvi /y2 ED cx div cvi /x2 ED cy +div cvi /y1 ED cx div cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse +def /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 +div add def /Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 +div add def } if gsave n 0 gt { 1 setlinecap [ 0 cy n div ] 0 setdash } +{ 2 setlinecap } ifelse /c x1 def /i 500 w mul x1 add def /e y cy mul +def /f y1 cy mul def /g y2 cy mul def x1 cx mul 0 T { newpath 0 e moveto +b 0 gt { gsave d c a cvs dup stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 +add neg} ifelse h 0 gt {b neg} {z1} ifelse rmoveto show grestore } if 0 +f moveto 0 g L stroke cx w mul 0 T c x2 eq c i eq or {exit} if /c c w +add def } loop grestore gsave n 0 gt { 1 setlinecap [ 0 cx n div ] 0 +setdash } { 2 setlinecap } ifelse /c y1 def /i 500 h mul y1 add def /e x +cx mul def /f x1 cx mul def /g x2 cx mul def 0 y1 cy mul T { newpath e 0 +moveto b 0 gt { gsave d c a cvs dup stringwidth pop /z2 ED w 0 gt {z1 z2 +add neg} {z1} ifelse h 0 gt {z1} {b neg} ifelse rmoveto show grestore } +if f 0 moveto g 0 L stroke 0 cy h mul T c y2 eq c i eq or {exit} if /c c +h add def } loop grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /lmtrx [ tx@Dict /lmtrx known { lmtrx aload pop } if CM ] def +CP 4 2 roll T moveto } def +/PutEnd { CP /lmtrx [ lmtrx aload pop setmatrix ] def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { CP OLUnit T +moveto /IfVisible true def } if } { IfVisible { CP OLUnit NET moveto +/IfVisible false def } if } ifelse } def +/InitOL { /OLUnit [ gsave CM STV 2890.79999 dup moveto setmatrix CP +grestore ] cvx def /BOL { BeginOL } def /IfVisible true def } def +end +%%EndProcSet +%%BeginProcSet: /u/ddas/tex/pstricks/ps/pst-node.pro +% PostScript prologue for pst-node.tex. +% Created 1993/3/12. Source file was pst-node.doc +% Version 0.93a, 93/03/12. +% For use with Rokicki's dvips. +/tx@NodeDict 200 dict def tx@NodeDict begin +/NewNode { gsave /next ED dict dup 3 -1 roll ED begin tx@Dict begin STV +CP T exec end /NodeMtrx CM def next end grestore } def +/InitPnode { /Y ED /X ED /NodePos { Nodesep Cos mul Nodesep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { Nodesep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r Nodesep add def } { /dx l Nodesep sub def +} ifelse Sin 0 gt { /dy u Nodesep add def } { /dy d Nodesep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /r ED r mul neg /l ED /r r l add def /X l neg def { neg /d +ED /u ED /Y 0 def } { neg /Y ED Y sub /u ED u mul neg /d ED /u u d add +def /Y Y d sub def } ifelse /NodePos { GetRnodePos } def } def +/InitRNode { /Y ED /X ED /r ED /X r 2 div X add def /r r X sub def /l X +neg def Y add neg /d ED Y sub /u ED /NodePos { GetRnodePos } def } def +/GetOnodePos { /ww w Nodesep add def /hh h Nodesep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/GetAngle { nodeA GetCenter nodeB GetCenter 3 -1 roll sub 3 1 roll sub +neg Atan } def +/GetEdge { begin /Nodesep ED dup 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED NodePos Y add exch X add exch +NodeMtrx transform CM itransform end 4 2 roll 1 index 0 eq { pop pop } { +2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse } def +/GetPos { OffsetA AngleA NodesepA nodeA GetEdge /y1 ED /x1 ED OffsetB +AngleB NodesepB nodeB GetEdge /y2 ED /x2 ED } def +/InitNC { /nodeB ED /nodeA ED /NodesepB ED /NodesepA ED /OffsetB ED +/OffsetA ED tx@NodeDict nodeA known tx@NodeDict nodeB known and dup { +/nodeA nodeA load def /nodeB nodeB load def } if } def +/LineMP { 4 copy 1 t sub mul exch t mul add 3 1 roll 1 t sub mul exch t +mul add exch 6 2 roll sub 3 1 roll sub Atan } def +/NCCoor { GetAngle /AngleA ED /AngleB AngleA 180 add def GetPos /LPutVar +[ x2 x1 y2 y1 ] cvx def /LPutPos { LPutVar LineMP } def x1 y1 x2 y2 } +def +/NCLine { NCCoor tx@Dict begin ArrowB 4 2 roll ArrowA lineto end } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan } def +/GetArms { /x1a armA AngleA cos mul x1 add def /y1a armA AngleA sin mul +y1 add def /x2a armB AngleB cos mul x2 add def /y2a armB AngleB sin mul +y2 add def } def +/NCCurve { GetPos x1 x2 sub y1 y2 sub Pyth 2 div dup 3 -1 roll mul /armA +ED mul /armB ED GetArms x1a y1a x1 y1 tx@Dict begin ArrowA end x2a y2a +x2 y2 tx@Dict begin ArrowB end curveto /LPutVar [ x1 y1 x1a y1a x2a y2a +x2 y2 ] cvx def /LPutPos { t LPutVar BezierMidpoint } def } def +/AnglesMP { LPutVar t 3 gt { /t t 3 sub def } { t 2 gt { /t t 2 sub def +10 -2 roll } { t 1 gt { /t t 1 sub def 10 -4 roll } { 10 4 roll } ifelse +} ifelse } ifelse 6 { pop } repeat 3 -1 roll exch LineMP } def +/NCAngles { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform pop x2a y2a mtrx transform exch pop mtrx itransform /y0 ED /x0 +ED mark armB 0 ne { x2 y2 } if x2a y2a x0 y0 x1a y1a armA 0 ne { x1 y1 } +if tx@Dict begin false Line end /LPutVar [ x2 y2 x2a y2a x0 y0 x1a y1a +x1 y1 ] cvx def /LPutPos { AnglesMP } def } def +/NCAngle { GetPos /x2a armB AngleB cos mul x2 add def /y2a armB AngleB +sin mul y2 add def /mtrx AngleA matrix rotate def x2a y2a mtrx transform +pop x1 y1 mtrx transform exch pop mtrx itransform /y0 ED /x0 ED mark +armB 0 ne { x2 y2 } if x2a y2a x0 y0 x1 y1 tx@Dict begin false Line end +/LPutVar [ x2 y2 x2 y2 x2a y2a x0 y0 x1 y1 ] cvx def /LPutPos { AnglesMP +} def } def +/NCBar { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform pop x2a y2a mtrx transform pop sub dup 0 mtrx itransform 3 -1 +roll 0 gt { /y2a exch y2a add def /x2a exch x2a add def } { /y1a exch +neg y1a add def /x2a exch neg x2a add def } ifelse mark x2 y2 x2a y2a +x1a y1a x1 y1 tx@Dict begin false Line end /LPutVar [ x2 y2 x2 y2 x2a +y2a x1a y1a x1 y1 ] cvx def /LPutPos { LPutVar AnglesMP } def } def +/NCDiag { GetPos GetArms mark x2 y2 x2a y2a x1a y1a x1 y1 tx@Dict begin +false Line end /LPutVar [ x2 y2 x2 y2 x2a y2a x1a y1a x1 y1 ] cvx def +/LPutPos { AnglesMP } def } def +/NCDiagg { OffsetA AngleA NodesepA nodeA GetEdge /y1 ED /x1 ED /x1a armA +AngleA cos mul x1 add def /y1a armA AngleA sin mul y1 add def nodeB +GetCenter y1a sub exch x1a sub Atan 180 add /AngleB ED OffsetB AngleB +NodesepB nodeB GetEdge /y2 ED /x2 ED mark x2 y2 x1a y1a x1 y1 tx@Dict +begin false Line end /LPutVar [ x2 y2 x2 y2 x2 y2 x1a y1a x1 y1] cvx def +/LPutPos { AnglesMP } def } def +/LoopMP { /t t abs def [ LPutVar ] length 2 div 1 sub dup t lt { /t ED } +{ pop } ifelse mark LPutVar t cvi { /t t 1 sub def pop pop } repeat +counttomark 1 add 4 roll cleartomark 3 -1 roll exch LineMP } def +/NCLoop { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform loopsize add /y1b ED /x1b ED /x2b x2a y2a mtrx transform pop +def x2b y1b mtrx itransform /y2b ED /x2b ED x1b y1b mtrx itransform /y1b +ED /x1b ED mark armB 0 ne { x2 y2 } if x2a y2a x2b y2b x1b y1b x1a y1a +armA 0 ne { x1 y1 } if tx@Dict begin false Line end /LPutVar [ x2 y2 x2a +y2a x2b y2b x1b y1b x1a y1a x1 y1 ] cvx def /LPutPos { LoopMP } def } +def +/NCCircle { nodeA GetCenter 0 0 NodesepA nodeA GetEdge pop 3 1 roll /Y ED +/X ED X sub 2 div dup 2 exp r r mul sub abs sqrt atan 2 mul /a ED r +AngleA 90 add PtoC Y add exch X add exch 2 copy /LPutVar [ 4 2 roll r a +] def /LPutPos { LPutVar aload pop t 360 mul add dup 5 1 roll 90 sub +PtoC 3 -1 roll add 3 1 roll add exch 3 -1 roll } def r AngleA 90 sub a +add AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c +57.2957 r Div def /y ED /x ED } def +/LPutCoor { tx@NodeDict /LPutPos known { gsave LPutPos tx@Dict begin +/langle ED CM 3 1 roll STV CP 3 -1 roll sub neg 3 1 roll sub exch moveto +setmatrix CP end grestore } { 0 0 tx@Dict /langle 0 def end } ifelse } +def +end +%%EndProcSet +%%BeginProcSet: texps.pro +TeXDict begin /rf{findfont dup length 1 add dict begin{1 index /FID ne 2 +index /UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type /integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics /Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont /setfont load]cvx def}def +/ObliqueSlant{dup sin S cos div neg}B /SlantFont{4 index mul add}def +/ExtendFont{3 -1 roll mul exch}def /ReEncodeFont{/Encoding exch def}def +end +%%EndProcSet +%%BeginProcSet: special.pro +TeXDict begin /SDict 200 dict N SDict begin /@SpecialDefaults{/hs 612 N +/vs 792 N /ho 0 N /vo 0 N /hsc 1 N /vsc 1 N /ang 0 N /CLIP 0 N /rwiSeen +false N /rhiSeen false N /letter{}N /note{}N /a4{}N /legal{}N}B +/@scaleunit 100 N /@hscale{@scaleunit div /hsc X}B /@vscale{@scaleunit +div /vsc X}B /@hsize{/hs X /CLIP 1 N}B /@vsize{/vs X /CLIP 1 N}B /@clip{ +/CLIP 2 N}B /@hoffset{/ho X}B /@voffset{/vo X}B /@angle{/ang X}B /@rwi{ +10 div /rwi X /rwiSeen true N}B /@rhi{10 div /rhi X /rhiSeen true N}B +/@llx{/llx X}B /@lly{/lly X}B /@urx{/urx X}B /@ury{/ury X}B /magscale +true def end /@MacSetUp{userdict /md known{userdict /md get type +/dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup +length 20 add dict copy def}if end md begin /letter{}N /note{}N /legal{} +N /od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath +clippath mark{transform{itransform moveto}}{transform{itransform lineto} +}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{ +itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{ +closepath}}pathforall newpath counttomark array astore /gc xdf pop ct 39 +0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}N +/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 +scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get +ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip +not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 +TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{noflips{TR +pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 +-1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg +TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg +sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr +0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add +2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N /cp +{pop pop showpage pm restore}N end}if}if}N /normalscale{Resolution 72 +div VResolution 72 div neg scale magscale{DVImag dup scale}if 0 setgray} +N /psfts{S 65781.76 div N}N /startTexFig{/psf$SavedState save N userdict +maxlength dict begin /magscale false def normalscale currentpoint TR +/psf$ury psfts /psf$urx psfts /psf$lly psfts /psf$llx psfts /psf$y psfts +/psf$x psfts currentpoint /psf$cy X /psf$cx X /psf$sx psf$x psf$urx +psf$llx sub div N /psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy +scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR +/showpage{}N /erasepage{}N /copypage{}N /p 3 def @MacSetUp}N /doclip{ +psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 +roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath +moveto}N /endTexFig{end psf$SavedState restore}N /@beginspecial{SDict +begin /SpecialSave save N gsave normalscale currentpoint TR +@SpecialDefaults count /ocount X /dcount countdictstack N}N /@setspecial +{CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto +closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx +sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR +}{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse +CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury +lineto closepath clip}if /showpage{}N /erasepage{}N /copypage{}N newpath +}N /@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{ +end}repeat grestore SpecialSave restore end}N /@defspecial{SDict begin} +N /@fedspecial{end}B /li{lineto}B /rl{rlineto}B /rc{rcurveto}B /np{ +/SaveX currentpoint /SaveY X N 1 setlinecap newpath}N /st{stroke SaveX +SaveY moveto}N /fil{fill SaveX SaveY moveto}N /ellipse{/endangle X +/startangle X /yrad X /xrad X /savematrix matrix currentmatrix N TR xrad +yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end +%%EndProcSet +TeXDict begin @defspecial + + TeXDict begin /box{newpath 2 copy moveto 3 copy pop exch lineto 4 +copy pop pop lineto 4 copy exch pop exch pop lineto closepath } bind +def /min{ 2 copy gt { exch } if pop } bind def/max{ 2 copy lt { exch +} if pop } bind def/roundedbox{/radius exch store 3 2 roll 2 copy min +radius sub /miny exch store max radius add /maxy exch store 2 copy +min radius sub /minx exch store max radius add /maxx exch store newpath +minx radius add miny moveto maxx miny maxx maxy radius arcto maxx maxy +minx maxy radius arcto minx maxy minx miny radius arcto minx miny maxx +miny radius arcto 16 {pop} repeat closepath }bind def /rectcartouche{box +gsave .95 setgray fill grestore 1 setlinewidth stroke }bind def /cartouche{roundedbox +gsave .95 setgray fill grestore 1 setlinewidth stroke }bind def end 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/TheNodegetcl1 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + -47 618 a Fm(RET)-7 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 152 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 3.37999 1.5 +false .5 7.23782 InitRnode } NewNode end end + 152 707 a Fa(C)179 719 y Fn(2)142 +618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 142 618 a Fm(RET)-7 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 42 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoingetcl1getcl2 16 { +.5 3.36499 0.06248 false .5 10.82999 InitRnode } NewNode end end + 42 +524 a Fm(JOIN)-7 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a -7 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 182 +415 a + tx@Dict begin 45. Rot end + 182 415 a 143 418 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 143 418 a Fl(:)10 b(:)g(:)182 +415 y + tx@Dict begin 45. neg Rot end + 182 415 a -7 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + -7 699 a 331 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 331 429 a +Fm(RET)336 520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.37999 0.99998 +false .5 8.23898 InitRnode } NewNode end end + 336 520 a Fa(C)364 528 y Fl(n)-7 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 231 335 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.36499 +0.06248 false .5 10.82999 InitRnode } NewNode end end + 231 335 a Fm(JOIN)-7 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + -7 699 +a -7 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 100 881 a Fz(\(a\))17 b(E1)p 447 +976 4 928 v 476 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 3.37999 1.5 +false .5 7.23782 InitRnode } NewNode end end + 476 707 a Fa(C)504 719 y Fn(1)467 +618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 467 618 a Fm(RET)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 665 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 3.37999 1.5 +false .5 7.23782 InitRnode } NewNode end end + +665 707 a Fa(C)693 719 y Fn(2)656 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 656 618 a Fm(RET)506 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 463 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl1 16 { .5 3.36499 +0.0 false .5 10.55498 InitRnode } NewNode end end + 463 524 a Fm(MA)-5 b(T)506 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl1 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 699 a 652 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl2 16 { .5 3.36499 +0.0 false .5 10.55498 InitRnode } NewNode end end + 652 524 a Fm(MA)g(T)506 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 699 a 556 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoinmatgetcl1matgetcl2 +16 { .5 3.36499 0.06248 false .5 10.82999 InitRnode } NewNode end +end + 556 429 a Fm(JOIN)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 +699 a 506 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 699 a 695 321 a + tx@Dict begin 45. Rot end + 695 321 a 656 324 +a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 656 324 a Fl(:)11 b(:)f(:)695 321 y + tx@Dict begin 45. neg Rot end + 695 321 a 506 699 +a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 506 699 a 845 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 845 429 a Fm(RET)850 520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.37999 0.99998 +false .5 8.23898 InitRnode } NewNode end end + 850 +520 a Fa(C)878 528 y Fl(n)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 841 335 +a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcln 16 { .5 3.36499 +0.0 false .5 10.55498 InitRnode } NewNode end end + 841 335 a Fm(MA)-5 b(T)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodematgetcln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 745 240 +a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.36499 +0.06248 false .5 10.82999 InitRnode } NewNode end end + 745 240 a Fm(JOIN)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 506 699 a 506 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodematgetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 +699 a 611 881 a Fz(\(b\))17 b(E2)p 961 976 4 928 v 990 +707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 3.37999 1.5 +false .5 7.23782 InitRnode } NewNode end end + 990 707 a Fa(C)1018 719 y Fn(1)981 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 981 618 +a Fm(RET)1020 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1179 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 3.37999 1.5 +false .5 7.23782 InitRnode } NewNode end end + 1179 707 a +Fa(C)1207 719 y Fn(2)1170 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 1170 618 a Fm(RET)1020 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1070 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoingetcl1getcl2 16 { +.5 3.36499 0.06248 false .5 10.82999 InitRnode } NewNode end end + 1070 524 a Fm(JOIN)1020 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1020 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1209 415 a + tx@Dict begin 45. Rot end + 1209 415 +a 1170 418 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 1170 418 a Fl(:)11 b(:)f(:)1209 415 y + tx@Dict begin 45. neg Rot end + 1209 +415 a 1020 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1020 699 a 1359 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 1359 429 a Fm(RET)1364 +520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.37999 0.99998 +false .5 8.23898 InitRnode } NewNode end end + 1364 520 a Fa(C)1392 528 y Fl(n)1020 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 +699 a 1259 335 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.36499 +0.06248 false .5 10.82999 InitRnode } NewNode end end + 1259 335 a Fm(JOIN)1020 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1020 699 +a 1020 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1227 240 a + tx@Dict begin tx@NodeDict begin { } /TheNodeselect 16 { .5 3.36499 +0.06248 false .5 18.33496 InitRnode } NewNode end end + 1227 240 a Fm(SELECT)1020 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodeselect +/TheNoderoot InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1020 699 a 1127 881 a Fz(\(c\))17 b(E3)p 1474 976 +4 928 v 1504 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 3.37999 1.5 +false .5 7.23782 InitRnode } NewNode end end + 1504 707 a Fa(C)1531 719 y Fn(1)1495 +618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 1495 618 a Fm(RET)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1693 707 +a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 3.37999 1.5 +false .5 7.23782 InitRnode } NewNode end end + 1693 707 a Fa(C)1720 719 y Fn(2)1684 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 1684 618 +a Fm(RET)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1490 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl1 16 { .5 3.36499 +0.0 false .5 10.55498 InitRnode } NewNode end end + 1490 524 a +Fm(MA)-5 b(T)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl1 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a 1679 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl2 16 { .5 3.36499 +0.0 false .5 10.55498 InitRnode } NewNode end end + 1679 524 +a Fm(MA)g(T)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a 1583 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoinmatgetcl1matgetcl2 +16 { .5 3.36499 0.06248 false .5 10.82999 InitRnode } NewNode end +end + 1583 429 +a Fm(JOIN)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a 1534 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a +1723 321 a + tx@Dict begin 45. Rot end + 1723 321 a 1684 324 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 1684 324 a Fl(:)10 b(:)h(:)1723 +321 y + tx@Dict begin 45. neg Rot end + 1723 321 a 1534 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1534 699 a 1873 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 1873 +429 a Fm(RET)1878 520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.37999 0.99998 +false .5 8.23898 InitRnode } NewNode end end + 1878 520 a Fa(C)1905 528 y Fl(n)1534 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1868 335 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcln 16 { .5 3.36499 +0.0 false .5 10.55498 InitRnode } NewNode end end + 1868 335 a Fm(MA)-5 b(T)1534 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodematgetcln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1772 240 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.36499 +0.06248 false .5 10.82999 InitRnode } NewNode end end + 1772 240 a Fm(JOIN)1534 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1534 699 a 1534 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b/macros/latex/contrib/utthesis/ICDE-11/related.tex @@ -0,0 +1,59 @@ +\section{Related research} +\label{sec:related} + +The System R optimizer \cite{Seli79} was the most important development +in query optimization research. It was a cost-based centralized +relational query optimizer and introduced a variety of key concepts +like ``interesting'' expressions, cardinality estimation using +selectivity factors and dynamic programming with pruning of search +space. These concepts continue to be important in query optimizer +research. + +The query optimizer in R$^*$ \cite{Dani82} works in essentially +the same way as that of System R, except that R$^*$ is a distributed +database system which introduces some subtle complications in its query +optimizer. + +The Starburst query optimizer \cite{Haas88} uses rules for all +decisions that need to be taken by the query optimizer. The rules are +functional in nature and transform a given operator tree into another. +The rules are commonly those that reflect relational calculus facts. +In Starburst, the query rewriting phase is different from the +optimization phase. The rewriting phase transforms the query itself +into equivalent operator trees based on relational calculus rules. The +plan optimization phase selects algorithms for each operator in the +operator tree that is obtained after rewriting. The disadvantage of +separating the query rewrite and the optimization phases is that +pruning of the search space is not possible during query rewrite, since +the rewrite phase is non-cost-based. + +Freytag \cite{Frey87a} describes a rule-based query optimizer similar +to Starburst. The rules are based on LISP-like representations of +access plans. The rules themselves are recursively defined on smaller +expressions (operator trees). Although several expressions can contain +a common sub-expression, Freytag doesn't consider the possibility of +sharing. Expressions are evaluated each time they are encountered. +This is obviously inefficient. In addition, as in Starburst, he +doesn't consider the cost transformations inherent in any query +optimizer; rules are syntactic transformation rules. + +EXODUS \cite{Grae87b} provides an optimizer generator which accepts a +rule-based specification of the data model as input. The optimizer +generator compiles these rules, together with pre-defined rules, to +generate an optimizer for the particular data model and set of +operators. Unlike Freytag, the optimizer generator for EXODUS allows +for C code along with definitions of new rules. This allows the +database implementor the freedom to associate any action with a +particular rule. Operator trees in EXODUS are constructed bottom-up +from previously constructed trees. + +The Volcano optimizer generator project \cite{Grae90b} evolved from the +EXODUS project. It is different from all the above optimizers in one +significant way: it is a top-down optimizer compared with the bottom-up +strategy of the others. Operator trees are optimized starting from the +root while sub-trees are not yet optimized. This leads to a +constraint-driven generation of the search space. While this method +results in a tight control of the search space, it is unconventional +and requires careful attention on the part of the optimizer implementor +to ensure that legal operator trees are not accidently left out of +the search space. 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CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def +n { NC } repeat EOC } ifelse } def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS +CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { /a 4 string def /b ED /d ED /n ED cvi dup 1 lt { pop 1 } if /c ED +c div dup 0 eq { pop 1 } if /cy ED c div dup 0 eq { pop 1 } if /cx ED cy +div cvi /y ED cx div cvi /x ED cy div cvi /y2 ED cx div cvi /x2 ED cy +div cvi /y1 ED cx div cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse +def /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 +div add def /Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 +div add def } if gsave n 0 gt { 1 setlinecap [ 0 cy n div ] 0 setdash } +{ 2 setlinecap } ifelse /c x1 def /i 500 w mul x1 add def /e y cy mul +def /f y1 cy mul def /g y2 cy mul def x1 cx mul 0 T { newpath 0 e moveto +b 0 gt { gsave d c a cvs dup stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 +add neg} ifelse h 0 gt {b neg} {z1} ifelse rmoveto show grestore } if 0 +f moveto 0 g L stroke cx w mul 0 T c x2 eq c i eq or {exit} if /c c w +add def } loop grestore gsave n 0 gt { 1 setlinecap [ 0 cx n div ] 0 +setdash } { 2 setlinecap } ifelse /c y1 def /i 500 h mul y1 add def /e x +cx mul def /f x1 cx mul def /g x2 cx mul def 0 y1 cy mul T { newpath e 0 +moveto b 0 gt { gsave d c a cvs dup stringwidth pop /z2 ED w 0 gt {z1 z2 +add neg} {z1} ifelse h 0 gt {z1} {b neg} ifelse rmoveto show grestore } +if f 0 moveto g 0 L stroke 0 cy h mul T c y2 eq c i eq or {exit} if /c c +h add def } loop grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /lmtrx [ tx@Dict /lmtrx known { lmtrx aload pop } if CM ] def +CP 4 2 roll T moveto } def +/PutEnd { CP /lmtrx [ lmtrx aload pop setmatrix ] def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { CP OLUnit T +moveto /IfVisible true def } if } { IfVisible { CP OLUnit NET moveto +/IfVisible false def } if } ifelse } def +/InitOL { /OLUnit [ gsave CM STV 2890.79999 dup moveto setmatrix CP +grestore ] cvx def /BOL { BeginOL } def /IfVisible true def } def +end +%%EndProcSet +%%BeginProcSet: /u/ddas/tex/pstricks/ps/pst-node.pro +% PostScript prologue for pst-node.tex. +% Created 1993/3/12. Source file was pst-node.doc +% Version 0.93a, 93/03/12. +% For use with Rokicki's dvips. +/tx@NodeDict 200 dict def tx@NodeDict begin +/NewNode { gsave /next ED dict dup 3 -1 roll ED begin tx@Dict begin STV +CP T exec end /NodeMtrx CM def next end grestore } def +/InitPnode { /Y ED /X ED /NodePos { Nodesep Cos mul Nodesep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { Nodesep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r Nodesep add def } { /dx l Nodesep sub def +} ifelse Sin 0 gt { /dy u Nodesep add def } { /dy d Nodesep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /r ED r mul neg /l ED /r r l add def /X l neg def { neg /d +ED /u ED /Y 0 def } { neg /Y ED Y sub /u ED u mul neg /d ED /u u d add +def /Y Y d sub def } ifelse /NodePos { GetRnodePos } def } def +/InitRNode { /Y ED /X ED /r ED /X r 2 div X add def /r r X sub def /l X +neg def Y add neg /d ED Y sub /u ED /NodePos { GetRnodePos } def } def +/GetOnodePos { /ww w Nodesep add def /hh h Nodesep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/GetAngle { nodeA GetCenter nodeB GetCenter 3 -1 roll sub 3 1 roll sub +neg Atan } def +/GetEdge { begin /Nodesep ED dup 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED NodePos Y add exch X add exch +NodeMtrx transform CM itransform end 4 2 roll 1 index 0 eq { pop pop } { +2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse } def +/GetPos { OffsetA AngleA NodesepA nodeA GetEdge /y1 ED /x1 ED OffsetB +AngleB NodesepB nodeB GetEdge /y2 ED /x2 ED } def +/InitNC { /nodeB ED /nodeA ED /NodesepB ED /NodesepA ED /OffsetB ED +/OffsetA ED tx@NodeDict nodeA known tx@NodeDict nodeB known and dup { +/nodeA nodeA load def /nodeB nodeB load def } if } def +/LineMP { 4 copy 1 t sub mul exch t mul add 3 1 roll 1 t sub mul exch t +mul add exch 6 2 roll sub 3 1 roll sub Atan } def +/NCCoor { GetAngle /AngleA ED /AngleB AngleA 180 add def GetPos /LPutVar +[ x2 x1 y2 y1 ] cvx def /LPutPos { LPutVar LineMP } def x1 y1 x2 y2 } +def +/NCLine { NCCoor tx@Dict begin ArrowB 4 2 roll ArrowA lineto end } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan } def +/GetArms { /x1a armA AngleA cos mul x1 add def /y1a armA AngleA sin mul +y1 add def /x2a armB AngleB cos mul x2 add def /y2a armB AngleB sin mul +y2 add def } def +/NCCurve { GetPos x1 x2 sub y1 y2 sub Pyth 2 div dup 3 -1 roll mul /armA +ED mul /armB ED GetArms x1a y1a x1 y1 tx@Dict begin ArrowA end x2a y2a +x2 y2 tx@Dict begin ArrowB end curveto /LPutVar [ x1 y1 x1a y1a x2a y2a +x2 y2 ] cvx def /LPutPos { t LPutVar BezierMidpoint } def } def +/AnglesMP { LPutVar t 3 gt { /t t 3 sub def } { t 2 gt { /t t 2 sub def +10 -2 roll } { t 1 gt { /t t 1 sub def 10 -4 roll } { 10 4 roll } ifelse +} ifelse } ifelse 6 { pop } repeat 3 -1 roll exch LineMP } def +/NCAngles { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform pop x2a y2a mtrx transform exch pop mtrx itransform /y0 ED /x0 +ED mark armB 0 ne { x2 y2 } if x2a y2a x0 y0 x1a y1a armA 0 ne { x1 y1 } +if tx@Dict begin false Line end /LPutVar [ x2 y2 x2a y2a x0 y0 x1a y1a +x1 y1 ] cvx def /LPutPos { AnglesMP } def } def +/NCAngle { GetPos /x2a armB AngleB cos mul x2 add def /y2a armB AngleB +sin mul y2 add def /mtrx AngleA matrix rotate def x2a y2a mtrx transform +pop x1 y1 mtrx transform exch pop mtrx itransform /y0 ED /x0 ED mark +armB 0 ne { x2 y2 } if x2a y2a x0 y0 x1 y1 tx@Dict begin false Line end +/LPutVar [ x2 y2 x2 y2 x2a y2a x0 y0 x1 y1 ] cvx def /LPutPos { AnglesMP +} def } def +/NCBar { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform pop x2a y2a mtrx transform pop sub dup 0 mtrx itransform 3 -1 +roll 0 gt { /y2a exch y2a add def /x2a exch x2a add def } { /y1a exch +neg y1a add def /x2a exch neg x2a add def } ifelse mark x2 y2 x2a y2a +x1a y1a x1 y1 tx@Dict begin false Line end /LPutVar [ x2 y2 x2 y2 x2a +y2a x1a y1a x1 y1 ] cvx def /LPutPos { LPutVar AnglesMP } def } def +/NCDiag { GetPos GetArms mark x2 y2 x2a y2a x1a y1a x1 y1 tx@Dict begin +false Line end /LPutVar [ x2 y2 x2 y2 x2a y2a x1a y1a x1 y1 ] cvx def +/LPutPos { AnglesMP } def } def +/NCDiagg { OffsetA AngleA NodesepA nodeA GetEdge /y1 ED /x1 ED /x1a armA +AngleA cos mul x1 add def /y1a armA AngleA sin mul y1 add def nodeB +GetCenter y1a sub exch x1a sub Atan 180 add /AngleB ED OffsetB AngleB +NodesepB nodeB GetEdge /y2 ED /x2 ED mark x2 y2 x1a y1a x1 y1 tx@Dict +begin false Line end /LPutVar [ x2 y2 x2 y2 x2 y2 x1a y1a x1 y1] cvx def +/LPutPos { AnglesMP } def } def +/LoopMP { /t t abs def [ LPutVar ] length 2 div 1 sub dup t lt { /t ED } +{ pop } ifelse mark LPutVar t cvi { /t t 1 sub def pop pop } repeat +counttomark 1 add 4 roll cleartomark 3 -1 roll exch LineMP } def +/NCLoop { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform loopsize add /y1b ED /x1b ED /x2b x2a y2a mtrx transform pop +def x2b y1b mtrx itransform /y2b ED /x2b ED x1b y1b mtrx itransform /y1b +ED /x1b ED mark armB 0 ne { x2 y2 } if x2a y2a x2b y2b x1b y1b x1a y1a +armA 0 ne { x1 y1 } if tx@Dict begin false Line end /LPutVar [ x2 y2 x2a +y2a x2b y2b x1b y1b x1a y1a x1 y1 ] cvx def /LPutPos { LoopMP } def } +def +/NCCircle { nodeA GetCenter 0 0 NodesepA nodeA GetEdge pop 3 1 roll /Y ED +/X ED X sub 2 div dup 2 exp r r mul sub abs sqrt atan 2 mul /a ED r +AngleA 90 add PtoC Y add exch X add exch 2 copy /LPutVar [ 4 2 roll r a +] def /LPutPos { LPutVar aload pop t 360 mul add dup 5 1 roll 90 sub +PtoC 3 -1 roll add 3 1 roll add exch 3 -1 roll } def r AngleA 90 sub a +add AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c +57.2957 r Div def /y ED /x ED } def +/LPutCoor { tx@NodeDict /LPutPos known { gsave LPutPos tx@Dict begin +/langle ED CM 3 1 roll STV CP 3 -1 roll sub neg 3 1 roll sub exch moveto +setmatrix CP end grestore } { 0 0 tx@Dict /langle 0 def end } ifelse } +def +end +%%EndProcSet +%%BeginProcSet: texps.pro +TeXDict begin /rf{findfont dup length 1 add dict begin{1 index /FID ne 2 +index /UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type /integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics /Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont /setfont load]cvx def}def +/ObliqueSlant{dup sin S cos div neg}B /SlantFont{4 index mul add}def +/ExtendFont{3 -1 roll mul exch}def /ReEncodeFont{/Encoding exch def}def +end +%%EndProcSet +%%BeginProcSet: special.pro +TeXDict begin /SDict 200 dict N SDict begin /@SpecialDefaults{/hs 612 N +/vs 792 N /ho 0 N /vo 0 N /hsc 1 N /vsc 1 N /ang 0 N /CLIP 0 N /rwiSeen +false N /rhiSeen false N /letter{}N /note{}N /a4{}N /legal{}N}B +/@scaleunit 100 N /@hscale{@scaleunit div /hsc X}B /@vscale{@scaleunit +div /vsc X}B /@hsize{/hs X /CLIP 1 N}B /@vsize{/vs X /CLIP 1 N}B /@clip{ +/CLIP 2 N}B /@hoffset{/ho X}B /@voffset{/vo X}B /@angle{/ang X}B /@rwi{ +10 div /rwi X /rwiSeen true N}B /@rhi{10 div /rhi X /rhiSeen true N}B +/@llx{/llx X}B /@lly{/lly X}B /@urx{/urx X}B /@ury{/ury X}B /magscale +true def end /@MacSetUp{userdict /md known{userdict /md get type +/dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup +length 20 add dict copy def}if end md begin /letter{}N /note{}N /legal{} +N /od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath +clippath mark{transform{itransform moveto}}{transform{itransform lineto} +}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{ +itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{ +closepath}}pathforall newpath counttomark array astore /gc xdf pop ct 39 +0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}N +/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 +scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get +ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip +not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 +TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{noflips{TR +pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 +-1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg +TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg +sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr +0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add +2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N /cp +{pop pop showpage pm restore}N end}if}if}N /normalscale{Resolution 72 +div VResolution 72 div neg scale magscale{DVImag dup scale}if 0 setgray} +N /psfts{S 65781.76 div N}N /startTexFig{/psf$SavedState save N userdict +maxlength dict begin /magscale false def normalscale currentpoint TR +/psf$ury psfts /psf$urx psfts /psf$lly psfts /psf$llx psfts /psf$y psfts +/psf$x psfts currentpoint /psf$cy X /psf$cx X /psf$sx psf$x psf$urx +psf$llx sub div N /psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy +scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR +/showpage{}N /erasepage{}N /copypage{}N /p 3 def @MacSetUp}N /doclip{ +psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 +roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath +moveto}N /endTexFig{end psf$SavedState restore}N /@beginspecial{SDict +begin /SpecialSave save N gsave normalscale currentpoint TR +@SpecialDefaults count /ocount X /dcount countdictstack N}N /@setspecial +{CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto +closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx +sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR +}{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse +CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury +lineto closepath clip}if /showpage{}N /erasepage{}N /copypage{}N newpath +}N /@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{ +end}repeat grestore SpecialSave restore end}N /@defspecial{SDict begin} +N /@fedspecial{end}B /li{lineto}B /rl{rlineto}B /rc{rcurveto}B /np{ +/SaveX currentpoint /SaveY X N 1 setlinecap newpath}N /st{stroke SaveX +SaveY moveto}N /fil{fill SaveX SaveY moveto}N /ellipse{/endangle X +/startangle X /yrad X /xrad X /savematrix matrix currentmatrix N TR xrad +yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end +%%EndProcSet +TeXDict begin @defspecial + + TeXDict begin /box{newpath 2 copy moveto 3 copy pop exch lineto 4 +copy pop pop lineto 4 copy exch pop exch pop lineto closepath } bind +def /min{ 2 copy gt { exch } if pop } bind def/max{ 2 copy lt { exch +} if pop } bind def/roundedbox{/radius exch store 3 2 roll 2 copy min +radius sub /miny exch store max radius add /maxy exch store 2 copy +min radius sub /minx exch store max radius add /maxx exch store newpath +minx radius add miny moveto maxx miny maxx maxy radius arcto maxx maxy +minx maxy radius arcto minx maxy minx miny radius arcto minx miny maxx +miny radius arcto 16 {pop} repeat closepath }bind def /rectcartouche{box +gsave .95 setgray fill grestore 1 setlinewidth stroke }bind def /cartouche{roundedbox +gsave .95 setgray fill grestore 1 setlinewidth stroke }bind def end 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begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a -7 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 182 +415 a + tx@Dict begin 45. Rot end + 182 415 a 143 418 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 143 418 a Fl(:)10 b(:)g(:)182 +415 y + tx@Dict begin 45. neg Rot end + 182 415 a -7 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + -7 699 a 331 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 331 429 a +Fm(RET)336 520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.32748 0.99998 +false .5 8.23895 InitRnode } NewNode end end + 336 520 a Fa(C)364 528 y Fl(n)-7 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 231 335 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.39499 +0.05246 false .5 10.8299 InitRnode } NewNode end end + 231 335 a Fm(JOIN)-7 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + -7 699 +a -7 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + -7 699 a 100 881 a Fz(\(a\))17 b(E1)p 447 +976 4 928 v 476 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + 476 707 a Fa(C)504 719 y Fn(1)467 +618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 467 618 a Fm(RET)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 665 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + +665 707 a Fa(C)693 719 y Fn(2)656 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 656 618 a Fm(RET)506 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 463 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl1 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 463 524 a Fm(MA)-5 b(T)506 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl1 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 699 a 652 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl2 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 652 524 a Fm(MA)g(T)506 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 699 a 556 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoinmatgetcl1matgetcl2 +16 { .5 3.39499 0.05246 false .5 10.8299 InitRnode } NewNode end end + 556 429 a Fm(JOIN)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 +699 a 506 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 699 a 695 321 a + tx@Dict begin 45. Rot end + 695 321 a 656 324 +a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 656 324 a Fl(:)11 b(:)f(:)695 321 y + tx@Dict begin 45. neg Rot end + 695 321 a 506 699 +a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 506 699 a 845 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 845 429 a Fm(RET)850 520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.32748 0.99998 +false .5 8.23895 InitRnode } NewNode end end + 850 +520 a Fa(C)878 528 y Fl(n)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 841 335 +a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcln 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 841 335 a Fm(MA)-5 b(T)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodematgetcln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 506 699 a 745 240 +a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.39499 +0.05246 false .5 10.8299 InitRnode } NewNode end end + 745 240 a Fm(JOIN)506 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 506 699 a 506 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodematgetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 506 +699 a 611 881 a Fz(\(b\))17 b(E2)p 961 976 4 928 v 990 +707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + 990 707 a Fa(C)1018 719 y Fn(1)981 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 981 618 +a Fm(RET)1020 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1179 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + 1179 707 a +Fa(C)1207 719 y Fn(2)1170 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 1170 618 a Fm(RET)1020 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1070 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoingetcl1getcl2 16 { +.5 3.39499 0.05246 false .5 10.8299 InitRnode } NewNode end end + 1070 524 a Fm(JOIN)1020 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1020 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1209 415 a + tx@Dict begin 45. Rot end + 1209 415 +a 1170 418 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 1170 418 a Fl(:)11 b(:)f(:)1209 415 y + tx@Dict begin 45. neg Rot end + 1209 +415 a 1020 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoingetcl1getcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1020 699 a 1359 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 1359 429 a Fm(RET)1364 +520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.32748 0.99998 +false .5 8.23895 InitRnode } NewNode end end + 1364 520 a Fa(C)1392 528 y Fl(n)1020 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 +699 a 1259 335 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.39499 +0.05246 false .5 10.8299 InitRnode } NewNode end end + 1259 335 a Fm(JOIN)1020 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1020 699 +a 1020 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1020 699 a 1227 240 a + tx@Dict begin tx@NodeDict begin { } /TheNodeselect 16 { .5 3.39499 +0.05246 false .5 18.3349 InitRnode } NewNode end end + 1227 240 a Fm(SELECT)1020 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodeselect +/TheNoderoot InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1020 699 a 1127 881 a Fz(\(c\))17 b(E3)p 1474 976 +4 928 v 1504 707 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + 1504 707 a Fa(C)1531 719 y Fn(1)1495 +618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 1495 618 a Fm(RET)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1693 707 +a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 3.32748 1.5 +false .5 7.2378 InitRnode } NewNode end end + 1693 707 a Fa(C)1720 719 y Fn(2)1684 618 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 1684 618 +a Fm(RET)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1490 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl1 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 1490 524 a +Fm(MA)-5 b(T)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl1 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a 1679 524 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl2 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 1679 524 +a Fm(MA)g(T)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodegetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a 1583 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoinmatgetcl1matgetcl2 +16 { .5 3.39499 0.05246 false .5 10.8299 InitRnode } NewNode end end + 1583 429 +a Fm(JOIN)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a 1534 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a +1723 321 a + tx@Dict begin 45. Rot end + 1723 321 a 1684 324 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 1684 324 a Fl(:)10 b(:)h(:)1723 +321 y + tx@Dict begin 45. neg Rot end + 1723 321 a 1534 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1534 699 a 1873 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.34 0.0 +false .5 9.44495 InitRnode } NewNode end end + 1873 +429 a Fm(RET)1878 520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.32748 0.99998 +false .5 8.23895 InitRnode } NewNode end end + 1878 520 a Fa(C)1905 528 y Fl(n)1534 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1868 335 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcln 16 { .5 3.39499 +0.0 false .5 10.55492 InitRnode } NewNode end end + 1868 335 a Fm(MA)-5 b(T)1534 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodematgetcln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1534 699 a 1772 240 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 3.39499 +0.05246 false .5 10.8299 InitRnode } NewNode end end + 1772 240 a Fm(JOIN)1534 699 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1534 699 a 1534 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNoderoot +/TheNodematgetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a 1741 146 a + tx@Dict begin tx@NodeDict begin { } /TheNodeselect 16 { .5 3.39499 +0.05246 false .5 18.3349 InitRnode } NewNode end end + 1741 146 +a Fm(SELECT)1534 699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodeselect +/TheNoderoot InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1534 699 a 1639 881 a Fz(\(d\))17 +b(E4)p 2014 1001 4 978 v -112 1004 2130 4 v 2015 1021 +19 984 v -96 1021 2130 19 v -112 1204 a FG(Figure)g(6:)26 +b(Expressions)17 b(used)h(in)g(generating)e(queries)i(for)f +(experiments)p 2359 357 1644 13 v 2359 423 4 67 v 2412 +437 a Fp(Query)p 2620 423 V 2673 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FG(,)i(25\(2\):73\261170,)2224 +2445 y(June)20 b(1993.)2085 2611 y([9])41 b(Goetz)29 +b(Graefe)h(and)f(David)g(J.)i(DeW)m(itt.)78 b(The)30 +b(EXODUS)2224 2710 y(optimizer)21 b(generator)-5 b(.)42 +b(In)23 b FF(Pr)m(oceedings)e(1987)h(ACM)i(SIG-)2224 +2810 y(MOD)40 b(International)d(Confer)m(ence)i(on)g(Management)f(of) +2224 2910 y(Data)p FG(,)19 b(pages)h(387\261394,)d(San)j(Francisco,)g +(May)g(1987.)2044 3076 y([10])40 b(L.)23 b(M.)g(Haas,)h(J.)g(C.)g +(Freytag,)e(G.)i(M.)f(Lohman,)f(and)g(H.)i(Pi-)2224 3175 +y(rahesh.)31 b(Extensible)20 b(query)f(processing)h(in)h(Starburst.)32 +b(Re-)2224 3275 y(search)20 b(Report)g(RJ)i(6610,)e(IBM)h(Almaden)e +(Research)i(Cen-)2224 3375 y(ter)m(,)e(December)g(1988.)2047 +3541 y([1)m(1])40 b(P)-9 b(.)33 b(G.)g(Selinger)m(,)h(M.)f(M.)g +(Astrahan,)i(D.)e(D.)g(Chamberlin,)2224 3640 y(R.)28 +b(A.)h(Lorie,)g(and)f(T)-6 b(.)28 b(G.)g(Price.)69 b(Access)29 +b(path)e(selection)2224 3740 y(in)d(a)g(relational)f(database)g +(management)f(system.)47 b(In)23 b FF(Pr)m(o-)2224 3840 +y(ceedings)k(1979)g(ACM)i(SIGMOD)f(International)e(Confer)n(-)2224 +3939 y(ence)g(on)h(Management)e(of)i(Data)p FG(,)h(pages)e(23\26134,)g +(Boston,)2224 4039 y(May)20 b(1979.)2044 4205 y([12])40 +b(Michael)30 b(Stonebraker)f(and)i(Lawrence)f(A.)i(Rowe.)84 +b(The)2224 4305 y(design)25 b(of)h(Postgres.)60 b(In)26 +b FF(Pr)m(oceedings)f(1986)g(ACM)i(SIG-)2224 4404 y(MOD)40 +b(International)d(Confer)m(ence)i(on)g(Management)f(of)2224 +4504 y(Data)p FG(,)19 b(pages)h(340\261355,)d(W)-7 b(ashington,)19 +b(May)h(1986.)p eop +%%Trailer +end +userdict /end-hook known{end-hook}if +%%EOF diff --git a/macros/latex/contrib/utthesis/ICDE-11/results.tex b/macros/latex/contrib/utthesis/ICDE-11/results.tex new file mode 100644 index 0000000000..d9ae183329 --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/results.tex @@ -0,0 +1,473 @@ +\section{Experimental results} +\label{sec:results} + +This section presents experimental results which demonstrate the value +of Prairie in specifying rule sets of rule-based optimizers. Our +experiments consist of specifying rule-based optimizers using Prairie +and generating optimizers using the P2V pre-processor and the +optimizer-generator paradigm of Figure~\ref{fig:ptovmodel}. + +In \cite{Das93}, we presented an implementation of a centralized +relational query optimizer using Prairie. Using the P2V translator, we +translated this to Volcano format and optimized several queries using +the resultant optimizer. For comparison, we hand-coded the same +optimizer directly in Volcano. The results presented there showed +that, using Prairie (compared to directly using Volcano) resulted in +approximately 50\% savings in lines of code with negligible (less than +5\%) increase in query optimization time. However, the optimizer was +quite small in terms of the number of operators, algorithms and rules. + +For a more realistic evaluation of Prairie, we needed answers to +the following questions: +\begin{enumerate} +\item Is Prairie adequate for large-scale rule sets? +\item How is programmer productivity enhanced by the high-level + abstractions of Prairie? +\item Can Prairie rule sets be translated automatically into + efficient implementations? +\end{enumerate} + +We addressed the first question by using the Texas Instruments Open +OODB query optimizer rule set, which has the largest publicly +available rule set. We describe this optimizer in the next section, +and then give our assessments to the last two questions in subsequent +sections. + +\subsection{The Texas Instruments Open OODB query optimizer} +\label{sec:oodb} + +The Texas Instruments Open Object-Oriented Database Management System +is an open, extensible, object-oriented database system which provides +users an architectural framework that is configurable in an incremental +manner. The query optimizer in the Open OODB \cite{Blak93} is +generated using Volcano. It is written as a set of trans\_rules and +impl\_rules that define the algebra of an object-oriented database +system. Currently, there are 17 transformation rules and 9 +implementation rules together with about $13,000$ lines of code for +support functions; this, of course, can be changed by an Open OODB user +for specific needs. + +\subsection{Programmer productivity} +\label{sec:productivity} + +Programmer productivity can be measured in different ways. An +admittedly simplistic metric is the number of lines of code that must +be written. But there are also less tangible measures, such as the +amount of conceptual effort needed to understand a particular +programming task. Our experience with the Open OODB query optimizer +suggests that Prairie excels on the latter, while offering modest +reductions in the volume of code that needs to be written. + +We converted by hand the Open OODB query optimizer's Volcano +specifications to Prairie. This was a non-trivial task because of the +relatively large size of the rule set and the complexity of the support +functions. This was where we found Prairie helped in conceptually +simplifying the rules and actions. We then used our P2V pre-processor +to reconstitute these Prairie specifications as Volcano +specifications. As described in Section~\ref{sec:ptov}, this process +involved a considerable level of complexity, partly because the Prairie +specification had 22 T-rules and 11 I-rules compared to 17 trans\_rules +and 9 impl\_rules in the Volcano specification; the reconstituted +Volcano specification had the same number of trans\_rules and +impl\_rules as the original hand-coded specification. + +Converting the Open OODB optimizer rule set into Prairie format +actually simplified its specification as the complexities of the +Volcano model were removed. The reduction in lines of code was modest +--- there was about a 10\% savings.\footnote{The original Volcano +specification had $13,400$ lines, the Prairie specification had +$12,100$ lines, and the P2V-generated Volcano specification had +$15,800$ lines.} However, as mentioned above, savings in lines of code +do not adequately reflect increases in programmer productivity. We +found the encapsulated specifications of Prairie --- namely, the use of +a single descriptor and fewer explicit support functions --- made rule +programming \emph{much} easier. + +\subsection{Performance results using the Open OODB optimizer} +\label{sec:oodbexp} + +\newsavebox{\Eone} +\newsavebox{\Etwo} +\newsavebox{\Ethree} +\newsavebox{\Efour} + +\begin{lrbox}{\Eone} +\begin{minipage}[b]{1.9cm} +\psset{unit=4mm} +\psset{nodesep=1pt} +\tiny +\begin{center} +\begin{pspicture}(0,0)(4,4) +\rput(0,0){\rnode{cl1}{$\textit{C}_1$}} +\rput(0,1){\rnode{getcl1}{RET}} +\ncline{-}{cl1}{getcl1} +\rput(2,0){\rnode{cl2}{$\textit{C}_2$}} +\rput(2,1){\rnode{getcl2}{RET}} +\ncline{-}{cl2}{getcl2} +\rput(1,2){\rnode{joingetcl1getcl2}{JOIN}} +\ncline{-}{joingetcl1getcl2}{getcl1} +\ncline{-}{joingetcl1getcl2}{getcl2} +\rput{45}(2,3){\rnode{dots}{$\ldots$}} +\ncline{-}{joingetcl1getcl2}{dots} +\rput(4,3){\rnode{getcln}{RET}} +\rput(4,2){\rnode{cln}{$\textit{C}_n$}} +\ncline{-}{cln}{getcln} +\rput(3,4){\rnode{root}{JOIN}} +\ncline{-}{root}{dots} +\ncline{-}{root}{getcln} +\end{pspicture} +\end{center} +\end{minipage} +\end{lrbox} + +\begin{lrbox}{\Etwo} +\begin{minipage}[b]{1.9cm} +\psset{unit=4mm} +\psset{nodesep=1pt} +\tiny +\begin{center} +\begin{pspicture}(0,0)(4,5) +\rput(0,0){\rnode{cl1}{$\textit{C}_1$}} +\rput(0,1){\rnode{getcl1}{RET}} +\ncline{-}{cl1}{getcl1} +\rput(2,0){\rnode{cl2}{$\textit{C}_2$}} +\rput(2,1){\rnode{getcl2}{RET}} +\ncline{-}{cl2}{getcl2} +\rput(0,2){\rnode{matgetcl1}{MAT}} +\ncline{-}{getcl1}{matgetcl1} +\rput(2,2){\rnode{matgetcl2}{MAT}} +\ncline{-}{getcl2}{matgetcl2} +\rput(1,3){\rnode{joinmatgetcl1matgetcl2}{JOIN}} +\ncline{-}{joinmatgetcl1matgetcl2}{matgetcl1} +\ncline{-}{joinmatgetcl1matgetcl2}{matgetcl2} +\rput{45}(2,4){\rnode{dots}{$\ldots$}} +\ncline{-}{joinmatgetcl1matgetcl2}{dots} +\rput(4,3){\rnode{getcln}{RET}} +\rput(4,2){\rnode{cln}{$\textit{C}_n$}} +\ncline{-}{cln}{getcln} +\rput(4,4){\rnode{matgetcln}{MAT}} +\ncline{-}{matgetcln}{getcln} +\rput(3,5){\rnode{root}{JOIN}} +\ncline{-}{root}{dots} +\ncline{-}{root}{matgetcln} +\end{pspicture} +\end{center} +\end{minipage} +\end{lrbox} + +\begin{lrbox}{\Ethree} +\begin{minipage}[b]{1.9cm} +\psset{unit=4mm} +\psset{nodesep=1pt} +\tiny +\begin{center} +\begin{pspicture}(0,0)(4,5) +\rput(0,0){\rnode{cl1}{$\textit{C}_1$}} +\rput(0,1){\rnode{getcl1}{RET}} +\ncline{-}{cl1}{getcl1} +\rput(2,0){\rnode{cl2}{$\textit{C}_2$}} +\rput(2,1){\rnode{getcl2}{RET}} +\ncline{-}{cl2}{getcl2} +\rput(1,2){\rnode{joingetcl1getcl2}{JOIN}} +\ncline{-}{joingetcl1getcl2}{getcl1} +\ncline{-}{joingetcl1getcl2}{getcl2} +\rput{45}(2,3){\rnode{dots}{$\ldots$}} +\ncline{-}{joingetcl1getcl2}{dots} +\rput(4,3){\rnode{getcln}{RET}} +\rput(4,2){\rnode{cln}{$\textit{C}_n$}} +\ncline{-}{cln}{getcln} +\rput(3,4){\rnode{root}{JOIN}} +\ncline{-}{root}{dots} +\ncline{-}{root}{getcln} +\rput(3,5){\rnode{select}{SELECT}} +\ncline{-}{select}{root} +\end{pspicture} +\end{center} +\end{minipage} +\end{lrbox} + +\begin{lrbox}{\Efour} +\begin{minipage}[b]{1.9cm} +\psset{unit=4mm} +\psset{nodesep=1pt} +\tiny +\begin{center} +\begin{pspicture}(0,0)(4,6) +\rput(0,0){\rnode{cl1}{$\textit{C}_1$}} +\rput(0,1){\rnode{getcl1}{RET}} +\ncline{-}{cl1}{getcl1} +\rput(2,0){\rnode{cl2}{$\textit{C}_2$}} +\rput(2,1){\rnode{getcl2}{RET}} +\ncline{-}{cl2}{getcl2} +\rput(0,2){\rnode{matgetcl1}{MAT}} +\ncline{-}{getcl1}{matgetcl1} +\rput(2,2){\rnode{matgetcl2}{MAT}} +\ncline{-}{getcl2}{matgetcl2} +\rput(1,3){\rnode{joinmatgetcl1matgetcl2}{JOIN}} +\ncline{-}{joinmatgetcl1matgetcl2}{matgetcl1} +\ncline{-}{joinmatgetcl1matgetcl2}{matgetcl2} +\rput{45}(2,4){\rnode{dots}{$\ldots$}} +\ncline{-}{joinmatgetcl1matgetcl2}{dots} +\rput(4,3){\rnode{getcln}{RET}} +\rput(4,2){\rnode{cln}{$\textit{C}_n$}} +\ncline{-}{cln}{getcln} +\rput(4,4){\rnode{matgetcln}{MAT}} +\ncline{-}{matgetcln}{getcln} +\rput(3,5){\rnode{root}{JOIN}} +\ncline{-}{root}{dots} +\ncline{-}{root}{matgetcln} +\rput(3,6){\rnode{select}{SELECT}} +\ncline{-}{select}{root} +\end{pspicture} +\end{center} +\end{minipage} +\end{lrbox} + +\begin{centeredfigure*} +\begin{minipage}[b]{9.1cm} +\myshadowbox{ +\begin{minipage}[b]{8.6cm} +\subfigure[E1] { \usebox{\Eone} \label{fig:Eone} } +\vrule +\subfigure[E2] { \usebox{\Etwo} \label{fig:Etwo} } +\vrule +\subfigure[E3] { \usebox{\Ethree} \label{fig:Ethree} } +\vrule +\subfigure[E4] { \usebox{\Efour} \label{fig:Efour} } +\normalsize +\end{minipage} +} +\caption{Expressions used in generating queries for experiments} +\label{fig:exps} +\end{minipage} +\hfill +\begin{minipage}[b]{7.0cm} +% Save current figure counter +\newcounter{savectr} +\setcounter{savectr}{\value{figure}} +% Temporarily change the figure to a table. +\renewcommand{\figurename}{\tablename} +\setcounter{figure}{\value{table}} +\scriptsize +\renewcommand{\multirowsetup}{\centering} +\newlength{\Lone} +\settowidth{\Lone}{E4} +\newlength{\Ltwo} +\settowidth{\Ltwo}{\textbf{Query}} +\newlength{\Lthree} +\settowidth{\Lthree}{\textbf{Indices?}} +\newlength{\Lfour} +\settowidth{\Lfour}{\textbf{Expression}} +\newlength{\Lnum} +\settowidth{\Lnum}{99} +\begin{tabular}{|c|c|c|c|c|} \thickhline +\multirow{2}{\Ltwo}{\textbf{Query}} + & \multirow{2}{\Lthree}{\textbf{Indices?}} + & \multirow{2}{\Lfour}{\textbf{Expression}} + & \multicolumn{2}{c|}{\textbf{Rules matched}} \\ \cline{4-5} +& & & trans\_rules & impl\_rules \\ \thickhline +Q1 & No & \multirow{2}{\Lone}{E1} & \multirow{2}{\Lnum}{3} + & \multirow{2}{\Lnum}{3} \\ \cline{1-2} +Q2 & Yes & & & \\ \hline +Q3 & No & \multirow{2}{\Lone}{E2} & \multirow{2}{\Lnum}{8} + & \multirow{2}{\Lnum}{4} \\ \cline{1-2} +Q4 & Yes & & & \\ \hline +Q5 & No & \multirow{2}{\Lone}{E3} & \multirow{2}{\Lnum}{9} + & \multirow{2}{\Lnum}{5} \\ \cline{1-2} +Q6 & Yes & & & \\ \hline +Q7 & No & \multirow{2}{\Lone}{E4} & \multirow{2}{\Lnum}{16} + & \multirow{2}{\Lnum}{7} \\ \cline{1-2} +Q8 & Yes & & & \\ \thickhline +\end{tabular} +\caption{Queries used in experiments} +\label{tab:queries} +% Change figure back as usual. +\renewcommand{\figurename}{Figure} +\setcounter{figure}{\value{savectr}} +\end{minipage} +\end{centeredfigure*} + +The acid test of Prairie was whether Prairie specifications could be +translated into efficient optimizer implementations. Our experiments +using the Open OODB consisted of optimizing 8 different queries using +the two query optimizers generated, respectively, using Prairie and +using Volcano directly (in the remainder of this section, we will use +``Prairie'' and ``Volcano'' to denote these two approaches). There +were 4 distinct expressions that were used to generate the queries used +in the experiments; these are shown in Figure~\ref{fig:exps}. Each +expression represents an $N$-way join query for varying $N$. + +The first expression E1 is a simple retrieval and join of base +classes. The second, E2, is also a join of base classes; however, +after each class retrieval, an attribute has to be materialized (\ie +brought into view) before the join. The third and fourth expressions +(E3 and E4) are the same as the first and second (E1 and E2) +respectively, except that there is a selection of attributes (the +select operator is the root of the expressions).\footnote{ The most +complex expression E4 consists of all operators in the algebra, except +PROJECT and UNNEST. PROJECT was not considered because it appeared in +only one impl\_rule and no trans\_rules, and thus, would not affect the +size of the search space of abstract expressions. UNNEST was not +considered because it appeared in exactly one trans\_rule and one +impl\_rule; including it in our queries would have increased the number +of parameters that could affect our run-times. We preferred to +concentrate on simple JOIN expressions.} + +The algebra that was used in the Prairie and Volcano optimizers for our +experiments consisted of 5 relational operators SELECT, PROJECT, JOIN, +RET and UNNEST (for set-valued attributes) and an object-oriented +operator called MAT (for MATerialize; it is fundamentally a +pointer-chasing operator for attributes of a class). There were 8 +algorithms. + +There are many parameters that can be varied when benchmarking a query +optimizer. Since our objective was to verify that the Prairie approach +did not sacrifice efficiency, our criteria for the queries was that +they test a majority of the rules, with varying properties of the base +classes. To this end, we tested our optimizer (and the Volcano +optimizer) with 8 different queries (shown in Table~\ref{tab:queries}). +The eight queries Q1 through Q8 are derived from the 4 expressions in +Figure~\ref{fig:exps}. Each expression E1 through E4 is used to obtain +two queries for a fixed number $N$ of JOINs in the expression. The +only difference between the two queries obtained from an expression is +that the first one does not contain any indices on any classes, whereas +the second one contains a single index on each base class occurring in +the expression. In expressions where a SELECT is present (E3 and E4), +the selection predicate is a conjunction of equality predicates +$\textit{bc}_i == \textit{const}_i$, where $\textit{bc}_i$ is an +attribute of class $\textit{C}_i$, and $\textit{const}_i$ is a constant +(we arbitrarily set this to $i$, because its value doesn't affect the +correctness or performance of the optimizer). In addition, for queries +with a SELECT and whose base classes have indices (Q6 and Q8 in +Table~\ref{tab:queries}), the (single) index of each base class was +chosen to be the attribute referenced in the selection predicate. For +example, class $\textit{C}_i$ was chosen to have an index on attribute +$\textit{bc}_i$. The join predicates for each JOIN were chosen at +random, and were always equality predicates. The choice of JOIN +predicates was such that the queries corresponded to linear query +graphs. In the future, we will experiment with non-linear (\eg star) +query graphs. + +Table~\ref{tab:queries} also shows the number of trans\_rules and +impl\_rules that are matched by each expression. These are the rules +whose left hand sides match a sub-expression. However, not all the +rules were necessarily applicable. For instance, an impl\_rule with an +index scan would not apply to Q3, although it might apply to Q4. + +Queries Q1 through Q8 were optimized for increasing number $N$ of +JOINs. For a fixed number of JOINs in a query, we varied the +cardinalities of the base classes 5 times, each time generating a query +with different class properties, and averaged the run-times over the 5 +query instances to generate the per-query optimization time. Thus, +each point in our graphs represents the average of 5 queries. The +run-times were measured\footnote{Since the run-times were too small to +be measured accurately with \texttt{time}, each query instance was +optimized 3000 times (in a loop) and the total time was divided by 3000 +to get the per-query optimization time.} using the GNU \texttt{time} +command. All experiments were performed on a lightly loaded DECstation +5000/200 running Ultrix 4.2. + +The optimization times for each query for both approaches (Prairie and +Volcano) are shown in Figures~\ref{fig:q1} through \ref{fig:q8}. The +number of joins in each set of graphs was varied to a maximum of 8, or +until virtual memory was exhausted. + +The first set of graphs (Figures~\ref{fig:q1} and \ref{fig:q2}) +shows the performance of a simple relational-type query. The +optimization times are almost identical between Prairie and Volcano, +and the notable point is that the presence of an index does not change +the optimizer's behavior, \ie the two graphs are identical. This +arises because the optimizer algebra had only two join algorithms +(pointer join and hash join), neither of which makes use of any +indices. + +The second set of graphs (Figures~\ref{fig:q3} and \ref{fig:q4}) shows +the results of optimizing Q3 and Q4. Here, as in Figures~\ref{fig:q1} +and \ref{fig:q2}, the presence (or absence) of indices makes no +difference. Both the Prairie and Volcano approaches have comparable +run-times. The sharp jump in the graphs from 7-way to 8-way joins is +due to the fact that since all optimization is done in main memory, +dynamic memory allocation (caused by \texttt{malloc} calls) results in +a lot of thrashing at this point. We speculate that in systems with +more virtual memory, the graphs will be smoother. + +The third and fourth sets of graphs in Figures~\ref{fig:q5} through +\ref{fig:q8} are optimizations of queries with a selection predicate. +In these cases, the presence of an index makes a difference if the +index is referenced in the selection predicate (as we designed). Also, +in these two figures, the performance of both Prairie and Volcano was +almost identical, except that Prairie does slightly worse due to the +larger number of \texttt{malloc} calls that the P2V translator +introduces. Also, note that we could only go up to 3-way joins before +virtual memory was exhausted. As the available memory decreases, there +is increased thrashing (as shown by the sharp changes in slope in the +plots) resulting in a much slower optimization process. + +\begin{centeredfigure} +\myshadowbox +{ +\setlength{\tabcolsep}{0pt} +\begin{tabular}{ll} +\subfigure[Query 1] { \begin{centeredinhalfminipage} + \vspace{3mm} + \epsfig{file=runtime_Q1.ps,width=3.0cm} + \end{centeredinhalfminipage} + \label{fig:q1} } +& +\subfigure[Query 2] { \begin{centeredinhalfminipage} + \vspace{3mm} + \epsfig{file=runtime_Q2.ps,width=3.0cm} + \end{centeredinhalfminipage} + \label{fig:q2} } +\\ \hline +\subfigure[Query 3] { \begin{centeredinhalfminipage} + \vspace{4mm} + \epsfig{file=runtime_Q3.ps,width=3.0cm} + \end{centeredinhalfminipage} + \label{fig:q3} } +& +\subfigure[Query 4] { \begin{centeredinhalfminipage} + \vspace{4mm} + \epsfig{file=runtime_Q4.ps,width=3.0cm} + \end{centeredinhalfminipage} + \label{fig:q4} } +\\ \hline +\subfigure[Query 5] { \begin{centeredinhalfminipage} + \vspace{4mm} + \epsfig{file=runtime_Q5.ps,width=3.0cm} + \end{centeredinhalfminipage} + \label{fig:q5} } +& +\subfigure[Query 6] { \begin{centeredinhalfminipage} + \vspace{4mm} + \epsfig{file=runtime_Q6.ps,width=3.0cm} + \end{centeredinhalfminipage} + \label{fig:q6} } +\\ \hline +\subfigure[Query 7] { \begin{centeredinhalfminipage} + \vspace{4mm} + \epsfig{file=runtime_Q7.ps,width=3.0cm} + \end{centeredinhalfminipage} + \label{fig:q7} } +& +\subfigure[Query 8] { \begin{centeredinhalfminipage} + \vspace{4mm} + \epsfig{file=runtime_Q8.ps,width=3.0cm} + \end{centeredinhalfminipage} + \label{fig:q8} } +\end{tabular} +} +\caption{Query optimization times for Q1 through Q8} +\label{fig:e4} +\end{centeredfigure} + +In all four sets of plots, we can see that Prairie performs with almost +(less than $5\%$ variation) the same efficiency as Volcano. In extreme +cases, when memory is scarce, Prairie runs more slowly (about $15\%$) +(\eg Figure~\ref{fig:q6}), but we believe that this situation already +represents a serious bottleneck for both Volcano and Prairie. + +The results presented in this section show that Prairie optimizers +need not sacrifice efficiency for clarity, even for large rule sets. +More research and validation is necessary to verify that Prairie is +an efficient tool for optimizer specification. diff --git a/macros/latex/contrib/utthesis/ICDE-11/runtime_Q1.ps b/macros/latex/contrib/utthesis/ICDE-11/runtime_Q1.ps new file mode 100644 index 0000000000..3d1d8e2ff0 --- /dev/null +++ b/macros/latex/contrib/utthesis/ICDE-11/runtime_Q1.ps @@ -0,0 +1,519 @@ +%!PS-Adobe-2.0 EPSF-1.2 +%%BoundingBox: 50 50 500 375 +%%Creator: ACE/gr (xmgr) v2.10 +%%Title: runtime.Q1.ps +%%EndComments +/m {moveto} bind def +/l {lineto} bind def +/RJ { + stringwidth neg exch neg exch + rmoveto +} bind def +/CS { + stringwidth + 2 div neg exch 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p tail}B /c{-4 M} +B /d{-3 M}B /e{-2 M}B /f{-1 M}B /g{0 M}B /h{1 M}B /i{2 M}B /j{3 M}B /k{ +4 M}B /w{0 rmoveto}B /l{p -4 w}B /m{p -3 w}B /n{p -2 w}B /o{p -1 w}B /q{ +p 1 w}B /r{p 2 w}B /s{p 3 w}B /t{p 4 w}B /x{0 S rmoveto}B /y{3 2 roll p +a}B /bos{/SS save N}B /eos{SS restore}B end +%%EndProcSet +%%BeginProcSet: /u/ddas/tex/pstricks/ps/pstricks.pro +% PostScript prologue for pstricks.tex. +% Created 1993/3/12. Source file was pstricks.doc +% Version 0.93a, 93/03/12. +% For use with Rokicki's dvips. +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/Atan { /atan load stopped { pop pop 0 } if } def +/Div { dup 0 eq { pop } { div } ifelse } def +/NET { neg exch neg exch T } def +/Pyth { dup mul exch dup mul add sqrt } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } +def +/PathLength { flattenpath /z 0 def { /y1 ED /x1 ED /y2 y1 def /x2 x1 def +} { /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } +pathforall z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +/y ED x mul /x ED x 0 eq y 0 eq and { /x 1 def /y 1 def } if [ y x ] 1 a +sub y mul setdash stroke } def +/DotLine { /b PathLength def /a ED /z ED /y CLW def /z y z add def a 0 gt +{ /b b a div def } { a 0 eq { /b b y sub def } { a -3 eq { /b b y add +def } if } ifelse } ifelse [ 0 b b z Div round Div dup 0 le { pop 1 } if +] a 0 gt { 0 } { y 2 div a -2 gt { neg } if } ifelse setdash 1 +setlinecap stroke } def +/LineFill { abs CLW add /a ED gsave clip pathbbox a Div ceiling /y2 ED +/x2 ED a Div floor /y1 ED /x1 ED /n y2 y1 sub 1 add cvi def /y1 a y1 mul +def newpath 2 setlinecap n { currentstrokeadjust == x1 y1 moveto x2 y1 L +stroke /y1 y1 a add def } repeat grestore } def +/LineFill { abs CLW add /a ED gsave clip pathbbox a Div ceiling /y2 ED +/x2 ED a Div floor /y1 ED /x1 ED /n y2 y1 sub 1 add cvi def /y1 a y1 mul +def newpath 2 setlinecap systemdict /currentstrokeadjust known { +currentstrokeadjust } { false } ifelse { /t { } def } { /t { transform +0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform } +bind def } ifelse n { x1 y1 t moveto x2 y1 t L stroke /y1 y1 a add def } +repeat grestore } def +/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg +exch 3 index sub exch Atan rotate newpath } def +/EndArrow { @mtrx setmatrix CP grestore end } def +/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 +scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill +grestore } def +/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0 +CLW moveto } def +/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2 +div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0 +CLW moveto } def +/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW +2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0 +curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto } +def +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { +/closepath load } pathforall ] cvx newpath 3 1 roll T exec } def +/SD { 0 360 arc fill } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch +cvi def } def +/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if +f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub +def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } +ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq +and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } +repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 +ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 +moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto +Lineto pop pop closepath } ifelse } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def +n { NC } repeat EOC } ifelse } def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS +CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { /a 4 string def /b ED /d ED /n ED cvi dup 1 lt { pop 1 } if /c ED +c div dup 0 eq { pop 1 } if /cy ED c div dup 0 eq { pop 1 } if /cx ED cy +div cvi /y ED cx div cvi /x ED cy div cvi /y2 ED cx div cvi /x2 ED cy +div cvi /y1 ED cx div cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse +def /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 +div add def /Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 +div add def } if gsave n 0 gt { 1 setlinecap [ 0 cy n div ] 0 setdash } +{ 2 setlinecap } ifelse /c x1 def /i 500 w mul x1 add def /e y cy mul +def /f y1 cy mul def /g y2 cy mul def x1 cx mul 0 T { newpath 0 e moveto +b 0 gt { gsave d c a cvs dup stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 +add neg} ifelse h 0 gt {b neg} {z1} ifelse rmoveto show grestore } if 0 +f moveto 0 g L stroke cx w mul 0 T c x2 eq c i eq or {exit} if /c c w +add def } loop grestore gsave n 0 gt { 1 setlinecap [ 0 cx n div ] 0 +setdash } { 2 setlinecap } ifelse /c y1 def /i 500 h mul y1 add def /e x +cx mul def /f x1 cx mul def /g x2 cx mul def 0 y1 cy mul T { newpath e 0 +moveto b 0 gt { gsave d c a cvs dup stringwidth pop /z2 ED w 0 gt {z1 z2 +add neg} {z1} ifelse h 0 gt {z1} {b neg} ifelse rmoveto show grestore } +if f 0 moveto g 0 L stroke 0 cy h mul T c y2 eq c i eq or {exit} if /c c +h add def } loop grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /lmtrx [ tx@Dict /lmtrx known { lmtrx aload pop } if CM ] def +CP 4 2 roll T moveto } def +/PutEnd { CP /lmtrx [ lmtrx aload pop setmatrix ] def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { CP OLUnit T +moveto /IfVisible true def } if } { IfVisible { CP OLUnit NET moveto +/IfVisible false def } if } ifelse } def +/InitOL { /OLUnit [ gsave CM STV 2890.79999 dup moveto setmatrix CP +grestore ] cvx def /BOL { BeginOL } def /IfVisible true def } def +end +%%EndProcSet +%%BeginProcSet: /u/ddas/tex/pstricks/ps/pst-coil.pro +% PostScript prologue for pst-coil.tex. +% Created 1993/3/12. Source file was pst-coil.doc +% Version 0.93a, 93/03/12. +% For use with Rokicki's dvips. +/tx@CoilDict 40 dict def tx@CoilDict begin +/CoilLoop { /t ED t sin AspectSin mul t 180 div AspectCos mul add t cos +lineto } def +/Coil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /ArmB ED /ArmA ED +/h ED /w ED /y1 ED /x1 ED /y0 ED /x0 ED x0 y0 translate y1 y0 sub x1 x0 +sub 2 copy Pyth /TotalLength ED Atan rotate /BeginAngle ArmA AspectCos +Div w h mul Div 360 mul def /EndAngle TotalLength ArmB sub AspectCos Div +w h mul Div 360 mul def 1 0 0 0 ArrowA ArmA 0 lineto /mtrx CM def w h +mul 2 Div w 2 Div scale BeginAngle Inc EndAngle { CoilLoop } for +EndAngle CoilLoop mtrx setmatrix TotalLength ArmB sub 0 lineto CP +TotalLength 0 ArrowB lineto } def +/AltCoil { /Inc ED dup sin /AspectSin ED cos /AspectCos ED /h ED /w ED +/EndAngle ED /BeginAngle ED /mtrx CM def w h mul 2 Div w 2 Div scale +BeginAngle sin AspectSin mul BeginAngle 180 div AspectCos mul add +BeginAngle cos /lineto load stopped { moveto } if BeginAngle Inc +EndAngle { CoilLoop } for EndAngle CoilLoop mtrx setmatrix } def +/ZigZag { /ArmB ED /ArmA ED 2 div /w ED w mul /h ED /y1 ED /x1 ED /y0 ED +/x0 ED x1 y1 translate y0 y1 sub x0 x1 sub 2 copy Pyth /TotalLength ED +Atan rotate TotalLength ArmA sub ArmB sub dup h div cvi /n ED n h mul +sub 2 div dup ArmA add /ArmA ED ArmB add /ArmB ED /x ArmB h 2 div add +def mark 0 0 ArmB 0 n { x w /w w neg def /x x h add def } repeat +TotalLength ArmA sub 0 TotalLength 0 } def +end +%%EndProcSet +%%BeginProcSet: /u/ddas/tex/pstricks/ps/pst-node.pro +% PostScript prologue for pst-node.tex. +% Created 1993/3/12. Source file was pst-node.doc +% Version 0.93a, 93/03/12. +% For use with Rokicki's dvips. +/tx@NodeDict 200 dict def tx@NodeDict begin +/NewNode { gsave /next ED dict dup 3 -1 roll ED begin tx@Dict begin STV +CP T exec end /NodeMtrx CM def next end grestore } def +/InitPnode { /Y ED /X ED /NodePos { Nodesep Cos mul Nodesep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { Nodesep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r Nodesep add def } { /dx l Nodesep sub def +} ifelse Sin 0 gt { /dy u Nodesep add def } { /dy d Nodesep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /r ED r mul neg /l ED /r r l add def /X l neg def { neg /d +ED /u ED /Y 0 def } { neg /Y ED Y sub /u ED u mul neg /d ED /u u d add +def /Y Y d sub def } ifelse /NodePos { GetRnodePos } def } def +/InitRNode { /Y ED /X ED /r ED /X r 2 div X add def /r r X sub def /l X +neg def Y add neg /d ED Y sub /u ED /NodePos { GetRnodePos } def } def +/GetOnodePos { /ww w Nodesep add def /hh h Nodesep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/GetAngle { nodeA GetCenter nodeB GetCenter 3 -1 roll sub 3 1 roll sub +neg Atan } def +/GetEdge { begin /Nodesep ED dup 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED NodePos Y add exch X add exch +NodeMtrx transform CM itransform end 4 2 roll 1 index 0 eq { pop pop } { +2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse } def +/GetPos { OffsetA AngleA NodesepA nodeA GetEdge /y1 ED /x1 ED OffsetB +AngleB NodesepB nodeB GetEdge /y2 ED /x2 ED } def +/InitNC { /nodeB ED /nodeA ED /NodesepB ED /NodesepA ED /OffsetB ED +/OffsetA ED tx@NodeDict nodeA known tx@NodeDict nodeB known and dup { +/nodeA nodeA load def /nodeB nodeB load def } if } def +/LineMP { 4 copy 1 t sub mul exch t mul add 3 1 roll 1 t sub mul exch t +mul add exch 6 2 roll sub 3 1 roll sub Atan } def +/NCCoor { GetAngle /AngleA ED /AngleB AngleA 180 add def GetPos /LPutVar +[ x2 x1 y2 y1 ] cvx def /LPutPos { LPutVar LineMP } def x1 y1 x2 y2 } +def +/NCLine { NCCoor tx@Dict begin ArrowB 4 2 roll ArrowA lineto end } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan } def +/GetArms { /x1a armA AngleA cos mul x1 add def /y1a armA AngleA sin mul +y1 add def /x2a armB AngleB cos mul x2 add def /y2a armB AngleB sin mul +y2 add def } def +/NCCurve { GetPos x1 x2 sub y1 y2 sub Pyth 2 div dup 3 -1 roll mul /armA +ED mul /armB ED GetArms x1a y1a x1 y1 tx@Dict begin ArrowA end x2a y2a +x2 y2 tx@Dict begin ArrowB end curveto /LPutVar [ x1 y1 x1a y1a x2a y2a +x2 y2 ] cvx def /LPutPos { t LPutVar BezierMidpoint } def } def +/AnglesMP { LPutVar t 3 gt { /t t 3 sub def } { t 2 gt { /t t 2 sub def +10 -2 roll } { t 1 gt { /t t 1 sub def 10 -4 roll } { 10 4 roll } ifelse +} ifelse } ifelse 6 { pop } repeat 3 -1 roll exch LineMP } def +/NCAngles { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform pop x2a y2a mtrx transform exch pop mtrx itransform /y0 ED /x0 +ED mark armB 0 ne { x2 y2 } if x2a y2a x0 y0 x1a y1a armA 0 ne { x1 y1 } +if tx@Dict begin false Line end /LPutVar [ x2 y2 x2a y2a x0 y0 x1a y1a +x1 y1 ] cvx def /LPutPos { AnglesMP } def } def +/NCAngle { GetPos /x2a armB AngleB cos mul x2 add def /y2a armB AngleB +sin mul y2 add def /mtrx AngleA matrix rotate def x2a y2a mtrx transform +pop x1 y1 mtrx transform exch pop mtrx itransform /y0 ED /x0 ED mark +armB 0 ne { x2 y2 } if x2a y2a x0 y0 x1 y1 tx@Dict begin false Line end +/LPutVar [ x2 y2 x2 y2 x2a y2a x0 y0 x1 y1 ] cvx def /LPutPos { AnglesMP +} def } def +/NCBar { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform pop x2a y2a mtrx transform pop sub dup 0 mtrx itransform 3 -1 +roll 0 gt { /y2a exch y2a add def /x2a exch x2a add def } { /y1a exch +neg y1a add def /x2a exch neg x2a add def } ifelse mark x2 y2 x2a y2a +x1a y1a x1 y1 tx@Dict begin false Line end /LPutVar [ x2 y2 x2 y2 x2a +y2a x1a y1a x1 y1 ] cvx def /LPutPos { LPutVar AnglesMP } def } def +/NCDiag { GetPos GetArms mark x2 y2 x2a y2a x1a y1a x1 y1 tx@Dict begin +false Line end /LPutVar [ x2 y2 x2 y2 x2a y2a x1a y1a x1 y1 ] cvx def +/LPutPos { AnglesMP } def } def +/NCDiagg { OffsetA AngleA NodesepA nodeA GetEdge /y1 ED /x1 ED /x1a armA +AngleA cos mul x1 add def /y1a armA AngleA sin mul y1 add def nodeB +GetCenter y1a sub exch x1a sub Atan 180 add /AngleB ED OffsetB AngleB +NodesepB nodeB GetEdge /y2 ED /x2 ED mark x2 y2 x1a y1a x1 y1 tx@Dict +begin false Line end /LPutVar [ x2 y2 x2 y2 x2 y2 x1a y1a x1 y1] cvx def +/LPutPos { AnglesMP } def } def +/LoopMP { /t t abs def [ LPutVar ] length 2 div 1 sub dup t lt { /t ED } +{ pop } ifelse mark LPutVar t cvi { /t t 1 sub def pop pop } repeat +counttomark 1 add 4 roll cleartomark 3 -1 roll exch LineMP } def +/NCLoop { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform loopsize add /y1b ED /x1b ED /x2b x2a y2a mtrx transform pop +def x2b y1b mtrx itransform /y2b ED /x2b ED x1b y1b mtrx itransform /y1b +ED /x1b ED mark armB 0 ne { x2 y2 } if x2a y2a x2b y2b x1b y1b x1a y1a +armA 0 ne { x1 y1 } if tx@Dict begin false Line end /LPutVar [ x2 y2 x2a +y2a x2b y2b x1b y1b x1a y1a x1 y1 ] cvx def /LPutPos { LoopMP } def } +def +/NCCircle { nodeA GetCenter 0 0 NodesepA nodeA GetEdge pop 3 1 roll /Y ED +/X ED X sub 2 div dup 2 exp r r mul sub abs sqrt atan 2 mul /a ED r +AngleA 90 add PtoC Y add exch X add exch 2 copy /LPutVar [ 4 2 roll r a +] def 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0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3 +/TheNodejoinr1r2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 580 +2106 a 580 2106 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3 +/TheNoderetr3 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 580 2106 a 580 2106 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 580 2106 a 580 +2106 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 580 2106 a 580 2106 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr3 +/TheNoder3 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 580 2106 a 1071 1907 a Fv(=)-12 +b FB(\))1322 1703 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoinr1r2r3 16 { .5 5.43198 +0.08394 false .5 17.32784 InitRnode } NewNode end end + 1322 1703 a FF(JOIN)1491 1700 y Fs(a)1528 +1709 y Fu(1)1582 1700 y Fv(=)20 b Fs(b)1687 1709 y Fu(1)1463 +1845 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoinr2r3 16 { .5 5.43198 +0.08394 false .5 17.32784 InitRnode } NewNode end end + 1463 1845 a FF(JOIN)1636 1841 y Fs(b)1666 1850 +y Fu(2)1720 1841 y Fv(=)g Fs(c)1826 1850 y Fu(1)1189 +1845 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr1 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 1189 1845 a FF(RET)1331 1987 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 1331 1987 a FF(RET)1614 +1987 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr3 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 1614 1987 a FF(RET)1208 1983 y + tx@Dict begin tx@NodeDict begin { } /TheNoder1 16 { .5 5.46666 1.1111 +false .5 10.56842 InitRnode } NewNode end end + 1208 1983 a Fs(R)1261 +1992 y Fu(1)1350 2124 y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 5.46666 1.1111 +false .5 10.56842 InitRnode } NewNode end end + 1350 2124 a Fs(R)1403 2133 y +Fu(2)1633 2124 y + tx@Dict begin tx@NodeDict begin { } /TheNoder3 16 { .5 5.46666 1.1111 +false .5 10.56842 InitRnode } NewNode end end + 1633 2124 a Fs(R)1686 2133 y Fu(3)1252 +2106 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3 +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore 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FF(JOIN)2108 1691 +y Fs(a)2145 1700 y Fu(2)2199 1691 y Fv(=)g Fs(c)2305 +1700 y Fu(1)2222 1845 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoinr1r2 16 { .5 5.43198 +0.08394 false .5 17.32784 InitRnode } NewNode end end + 2222 1845 a FF(JOIN)1966 1841 +y Fs(a)2003 1850 y Fu(1)2058 1841 y Fv(=)f Fs(b)2162 +1850 y Fu(1)2090 1987 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr1 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2090 1987 a FF(RET)2373 1987 +y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2373 1987 a FF(RET)2515 1845 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr3 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2515 1845 a FF(RET)2109 +2124 y + tx@Dict begin tx@NodeDict begin { } /TheNoder1 16 { .5 5.46666 1.1111 +false .5 10.56842 InitRnode } NewNode end end + 2109 2124 a Fs(R)2162 2133 y Fu(1)2392 2124 y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 5.46666 1.1111 +false .5 10.56842 InitRnode } NewNode end end + +2392 2124 a Fs(R)2445 2133 y Fu(2)2534 1983 y + tx@Dict begin tx@NodeDict begin { } /TheNoder3 16 { .5 5.46666 1.1111 +false .5 10.56842 InitRnode } NewNode end end + 2534 1983 +a Fs(R)2587 1992 y Fu(3)2152 2106 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2 +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2152 2106 a 2152 +2106 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2 +/TheNoderetr2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2152 2106 a 2152 2106 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3 +/TheNodejoinr1r2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 2152 2106 a 2152 2106 +a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3 +/TheNoderetr3 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2152 2106 a 2152 2106 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2152 2106 a 2152 2106 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2152 +2106 a 2152 2106 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr3 +/TheNoder3 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2152 2106 a 2644 1907 a Fv(=)-12 b +FB(\))2684 1910 y Fs(=)2894 1703 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoinr1r2r3 16 { .5 5.43198 +0.08394 false .5 17.32784 InitRnode } NewNode end end + 2894 1703 a FF(JOIN)3036 +1845 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoinr2r3 16 { .5 5.43198 +0.08394 false .5 17.32784 InitRnode } NewNode end end + 3036 1845 a FF(JOIN)2762 1845 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr1 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2762 1845 a FF(RET)2904 +1987 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2904 1987 a FF(RET)3187 1987 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr3 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 3187 1987 a FF(RET)2781 +1983 y + tx@Dict begin tx@NodeDict begin { } /TheNoder1 16 { .5 5.46666 1.1111 +false .5 10.56842 InitRnode } NewNode end end + 2781 1983 a Fs(R)2834 1992 y Fu(1)2922 2124 y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 5.46666 1.1111 +false .5 10.56842 InitRnode } NewNode end end + +2922 2124 a Fs(R)2975 2133 y Fu(2)3206 2124 y + tx@Dict begin tx@NodeDict begin { } /TheNoder3 16 { .5 5.46666 1.1111 +false .5 10.56842 InitRnode } NewNode end end + 3206 2124 +a Fs(R)3259 2133 y Fu(3)2825 2106 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3 +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2825 2106 a 2825 +2106 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3 +/TheNodejoinr2r3 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 2825 2106 a 2825 2106 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr2r3 +/TheNoderetr2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2825 2106 a 2825 2106 +a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr2r3 +/TheNoderetr3 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2825 2106 a 2825 2106 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2825 2106 a 2825 2106 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2825 +2106 a 2825 2106 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr3 +/TheNoder3 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2825 2106 a 2019 2274 a Fy(\(c\))20 +b(Example)h(of)f(an)h(operator)g(tree)f(where)h(the)f(as-)2019 +2365 y(sociativity)13 b(rule)g(does)h(not)g(apply)f(because)i(a)e +(cross-)2019 2457 y(product)20 b(would)f(result)p 3583 +2581 4 2178 v 300 2584 3287 4 v 3585 2601 19 2185 v 317 +2601 3287 19 v 1300 2797 a FP(Figure)24 b(3.5:)31 b(Join)25 +b(associativity)i(T)-8 b(-rule)300 3173 y(because)27 +b(it)d(generates)k(a)c(cross-product\),)30 b(otherwise)c(the)f 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b(-rule.)1470 b Fw(\003)300 4622 +y FO(3.6)119 b(Implementation)30 b(Rules)294 4885 y FP(Implementation) +22 b(rules,)e(or)e(I-rules)i(for)f(short,)h(de\256ne)f(equivalences)j +(between)d(expressions)j(and)d(their)300 5055 y(implementing)29 +b(algorithms.)41 b(Let)25 b FH(E)31 b FP(be)26 b(an)h(expression)i(and) +e FH(A)e FP(be)i(an)f(algorithm)i(that)f(implements)1905 +5349 y(35)p eop +%%Page: 36 48 +36 47 bop 312 403 3260 4 v 312 1071 4 669 v 386 478 a +Fs(E)t Fv(\()p Fs(x)509 487 y Fu(1)543 478 y Fs(;)11 +b(:)g(:)h(:)23 b(;)11 b(x)751 486 y Fn(n)794 478 y Fv(\))20 +b(:)f Fo(D)942 487 y Fm(1)1000 478 y Fv(=)-12 b FB(\))20 +b Fs(A)p Fv(\()p Fs(x)1254 487 y Fu(1)1288 478 y Fs(;)12 +b(:)f(:)g(:)24 b(;)11 b(x)1497 486 y Fn(n)1539 478 y +Fv(\))20 b(:)f Fo(D)1687 487 y Fm(2)3393 478 y FF(\(3.3\))386 +557 y(test)386 635 y FB(ff)601 714 y FF(pre-opt)g(statements)386 +793 y FB(gg)386 872 y(ff)601 951 y FF(post-opt)g(statements)386 +1030 y FB(gg)p 3568 1071 V 312 1074 3260 4 v 3570 1091 +19 675 v 328 1091 3260 19 v 1166 1287 a FP(Figure)24 +b(3.6:)31 b(General)25 b(form)e(of)h(a)f(Prairie)h(I-rule)300 +1664 y FH(E)5 b FP(.)30 b(The)23 b(general)j(form)d(of)h(an)f(I-rule)i +(is)e(given)i(by)f(Equation)h(\(3.3\))e(\(shown)i(in)e(Figure)h(3.6\).) +580 1833 y(The)19 b(actions)j(associated)h(with)d(an)g(I-rule)h(are)g +(de\256ned)g(in)f(three)h(parts.)30 b(The)20 b(\256rst)g(part,)h(or)f +FD(test)p FP(,)300 2002 y(is)j(a)g(boolean)j(expression)h(whose)d +(value)g(determines)i(whether)e(or)g(not)g(the)g(rule)g(can)g(be)f +(applied.)583 2172 y(The)h(second)i(part,)e(or)g FD(pr)m(e-opt)h +(statements)p FP(,)h(is)e(a)f(set)h(of)g(descriptor)j(assignment)f +(statements)300 2341 y(that)g(are)f(executed)j(only)e(if)f(the)g(test)h +(is)f(true)h(and)f FD(befor)m(e)i FP(any)e(descendant)k(of)c(the)g +(root)h(of)f FH(E)30 b FP(is)25 b(opti-)300 2511 y(mized.)37 +b(Additional)28 b(parameters)g(of)d(nodes)i(are)f(usually)h(assigned)h +(in)e(the)g(pre-opt)h(section.)39 b(This)25 b(is)300 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Rot end + 1139 794 +a 1092 798 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.88889 +0.0 false .5 11.3335 InitRnode } NewNode end end + 1092 798 a Fs(:)12 b(:)f(:)1139 794 y + tx@Dict begin 45. neg Rot end + 1139 +794 a 856 1220 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoingetcl1getcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 856 1220 a 1360 817 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 5.344 +0.0 false .5 15.11191 InitRnode } NewNode end end + 1360 817 a FF(RET)1376 +955 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 5.46666 1.0 +false .5 11.17616 InitRnode } NewNode end end + 1376 955 a Fs(C)1426 963 y Fn(n)856 1220 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 856 +1220 a 1209 675 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 5.43198 +0.08394 false .5 17.32784 InitRnode } NewNode end end + 1209 675 a FF(JOIN)856 1220 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 856 1220 +a 856 1220 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderoot +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 856 1220 a 1047 1353 a Fy(\(a\))19 b(E1)p +1905 1450 4 1022 v 2347 1238 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 5.46666 1.1111 +false .5 10.22475 InitRnode } NewNode end end + 2347 1238 a Fs(C)2397 +1247 y Fu(1)2327 1100 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 5.344 +0.0 false .5 15.11191 InitRnode } NewNode end end + 2327 1100 a FF(RET)2390 1220 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2390 1220 a 2631 1238 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 5.46666 1.1111 +false .5 10.22475 InitRnode } NewNode end end + 2631 1238 a Fs(C)2681 1247 +y Fu(2)2610 1100 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 5.344 +0.0 false .5 15.11191 InitRnode } NewNode end end + 2610 1100 a FF(RET)2390 1220 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2390 +1220 a 2320 959 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl1 16 { .5 5.43198 +0.0 false .5 16.88788 InitRnode } NewNode end end + 2320 959 a FF(MA)-7 b(T)2390 1220 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodegetcl1 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + +2390 1220 a 2603 959 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl2 16 { .5 5.43198 +0.0 false .5 16.88788 InitRnode } NewNode end end + 2603 959 a FF(MA)g(T)2390 1220 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodegetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 2390 1220 a 2460 817 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoinmatgetcl1matgetcl2 +16 { .5 5.43198 0.08394 false .5 17.32784 InitRnode } NewNode end +end + 2460 817 a FF(JOIN)2390 1220 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 2390 1220 a 2390 1220 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 2390 1220 a 2673 653 a + tx@Dict begin 45. Rot end + 2673 +653 a 2626 657 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.88889 +0.0 false .5 11.3335 InitRnode } NewNode end end + 2626 657 a Fs(:)12 b(:)f(:)2673 653 +y + tx@Dict begin 45. neg Rot end + 2673 653 a 2390 1220 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2390 1220 a 2894 817 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 5.344 +0.0 false .5 15.11191 InitRnode } NewNode end end + 2894 +817 a FF(RET)2910 955 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 5.46666 1.0 +false .5 11.17616 InitRnode } NewNode end end + 2910 955 a Fs(C)2960 963 y Fn(n)2390 +1220 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2390 1220 a 2887 675 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcln 16 { .5 5.43198 +0.0 false .5 16.88788 InitRnode } NewNode end end + 2887 675 a FF(MA)-7 b(T)2390 +1220 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodematgetcln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2390 1220 a 2743 533 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 5.43198 +0.08394 false .5 17.32784 InitRnode } NewNode end end + 2743 533 a FF(JOIN)2390 +1220 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2390 1220 a 2390 1220 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderoot +/TheNodematgetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 2390 1220 a 2579 1353 +a Fy(\(b\))19 b(E2)p 374 1453 3065 4 v 814 2404 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 5.46666 1.1111 +false .5 10.22475 InitRnode } NewNode end end + 814 +2404 a Fs(C)864 2413 y Fu(1)793 2267 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 5.344 +0.0 false .5 15.11191 InitRnode } NewNode end end + 793 2267 a FF(RET)856 +2386 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 856 2386 a 1097 2404 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 5.46666 1.1111 +false .5 10.22475 InitRnode } NewNode end end + 1097 2404 a Fs(C)1147 2413 +y Fu(2)1077 2267 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 5.344 +0.0 false .5 15.11191 InitRnode } NewNode end end + 1077 2267 a FF(RET)856 2386 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 856 +2386 a 926 2125 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoingetcl1getcl2 16 { +.5 5.43198 0.08394 false .5 17.32784 InitRnode } NewNode end end + 926 2125 a FF(JOIN)856 2386 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 856 2386 +a 856 2386 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 856 2386 a 1139 1961 a + tx@Dict begin 45. Rot end + 1139 1961 a 1092 +1965 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.88889 +0.0 false .5 11.3335 InitRnode } NewNode end end + 1092 1965 a Fs(:)12 b(:)f(:)1139 1961 y + tx@Dict begin 45. neg Rot end + 1139 1961 +a 856 2386 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoingetcl1getcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 856 2386 a 1360 1983 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 5.344 +0.0 false .5 15.11191 InitRnode } NewNode end end + 1360 1983 a FF(RET)1376 +2121 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 5.46666 1.0 +false .5 11.17616 InitRnode } NewNode end end + 1376 2121 a Fs(C)1426 2129 y Fn(n)856 2386 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 856 +2386 a 1209 1842 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 5.43198 +0.08394 false .5 17.32784 InitRnode } NewNode end end + 1209 1842 a FF(JOIN)856 2386 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 856 +2386 a 856 2386 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderoot +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 856 2386 a 1159 1700 a + tx@Dict begin tx@NodeDict begin { } /TheNodeselect 16 { .5 5.43198 +0.08394 false .5 29.33583 InitRnode } NewNode end end + 1159 1700 a +FF(SELECT)856 2386 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodeselect +/TheNoderoot InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 856 2386 a 1047 2520 a Fy(\(c\))19 +b(E3)p 1905 2616 4 1164 v 2347 2404 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 5.46666 1.1111 +false .5 10.22475 InitRnode } NewNode end end + 2347 2404 a Fs(C)2397 +2413 y Fu(1)2327 2267 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 5.344 +0.0 false .5 15.11191 InitRnode } NewNode end end + 2327 2267 a FF(RET)2390 2386 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2390 2386 a 2631 2404 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 5.46666 1.1111 +false .5 10.22475 InitRnode } NewNode end end + 2631 2404 a Fs(C)2681 2413 +y Fu(2)2610 2267 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 5.344 +0.0 false .5 15.11191 InitRnode } NewNode end end + 2610 2267 a FF(RET)2390 2386 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2390 +2386 a 2320 2125 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl1 16 { .5 5.43198 +0.0 false .5 16.88788 InitRnode } NewNode end end + 2320 2125 a FF(MA)-7 b(T)2390 2386 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodegetcl1 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 2390 2386 a 2603 2125 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl2 16 { .5 5.43198 +0.0 false .5 16.88788 InitRnode } NewNode end end + 2603 2125 a FF(MA)g(T)2390 +2386 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodegetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 2390 2386 a 2460 1983 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoinmatgetcl1matgetcl2 +16 { .5 5.43198 0.08394 false .5 17.32784 InitRnode } NewNode end +end + 2460 1983 a FF(JOIN)2390 +2386 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 2390 2386 a 2390 2386 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 2390 2386 a 2673 1819 +a + tx@Dict begin 45. Rot end + 2673 1819 a 2626 1823 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.88889 +0.0 false .5 11.3335 InitRnode } NewNode end end + 2626 1823 a Fs(:)12 b(:)f(:)2673 +1819 y + tx@Dict begin 45. neg Rot end + 2673 1819 a 2390 2386 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2390 2386 a 2894 1983 +a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 5.344 +0.0 false .5 15.11191 InitRnode } NewNode end end + 2894 1983 a FF(RET)2910 2121 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 5.46666 1.0 +false .5 11.17616 InitRnode } NewNode end end + 2910 2121 a Fs(C)2960 +2129 y Fn(n)2390 2386 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2390 2386 a 2887 1842 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcln 16 { .5 5.43198 +0.0 false .5 16.88788 InitRnode } NewNode end end + 2887 +1842 a FF(MA)-7 b(T)2390 2386 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodematgetcln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2390 2386 a 2743 1700 +a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 5.43198 +0.08394 false .5 17.32784 InitRnode } NewNode end end + 2743 1700 a FF(JOIN)2390 2386 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2390 2386 a 2390 2386 +a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderoot +/TheNodematgetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 2390 2386 a 2693 1558 a + tx@Dict begin tx@NodeDict begin { } /TheNodeselect 16 { .5 5.43198 +0.08394 false .5 29.33583 InitRnode } NewNode end end + 2693 1558 a FF(SELECT)2390 +2386 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodeselect +/TheNoderoot InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2390 2386 a 2579 2520 a Fy(\(d\))19 b(E4)p 3557 +2641 4 2239 v 323 2644 3237 4 v 3558 2661 19 2245 v 340 +2661 3237 19 v 501 2857 a FP(Figure)24 b(5.2:)31 b(Expressions)26 +b(used)f(in)e(generating)j(benchmark)g(queries)f(for)f(Open)g(OODB)p +610 3188 2680 13 v 610 3279 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/TheNoderetr1 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2516 705 a FF(RET)2800 705 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2800 705 a FF(RET)2579 +824 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 824 a 2579 824 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 824 a 2522 840 a + tx@Dict begin tx@NodeDict begin { } /TheNoder1 16 { .5 5.43198 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2522 +840 a FF(dept)2806 832 y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 3.62798 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2806 832 a FF(emp)2579 824 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + +2579 824 a 2579 824 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 824 a 2638 988 a + tx@Dict begin tx@NodeDict begin { } /TheNodesort 16 { .5 5.43198 +0.08394 false .5 19.96785 InitRnode } NewNode end end + 2638 988 +a FF(SOR)l(T)2649 1130 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoin 16 { .5 5.43198 +0.08394 false .5 17.32784 InitRnode } NewNode end end + 2649 1130 a FF(JOIN)2579 1391 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodesort +/TheNodejoin InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 1391 a 2516 1272 a + tx@Dict begin tx@NodeDict begin { } /TheNoderetr1 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2516 1272 a FF(RET)2800 1272 +y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2800 1272 a FF(RET)2579 1391 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 1391 a 2579 1391 +a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 1391 a 2522 1399 a + tx@Dict begin tx@NodeDict begin { } /TheNoder1 16 { .5 3.62798 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2522 1399 a FF(emp)2806 1407 +y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 5.43198 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2806 1407 a FF(dept)2579 1391 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 1391 a 2579 1391 +a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 1391 a 2638 1697 a + tx@Dict begin tx@NodeDict begin { } /TheNodesort 16 { .5 5.43198 +0.08394 false .5 19.96785 InitRnode } NewNode end end + 2638 1697 a FF(SOR)l(T)2572 +1832 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoin 16 { .5 5.43198 +1.72792 false .5 36.0637 InitRnode } NewNode end end + 2572 1832 a FF(Mer)o(ge)p 2747 1832 20 4 v 25 +w(join)2579 2100 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodesort +/TheNodejoin InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 2100 a 2516 1980 a + tx@Dict begin tx@NodeDict begin { } /TheNoderetr1 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2516 1980 +a FF(RET)2800 1980 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2800 1980 a FF(RET)2579 2100 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 +2100 a 2579 2100 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 2100 a 2522 2108 a + tx@Dict begin tx@NodeDict begin { } /TheNoder1 16 { .5 3.62798 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2522 2108 +a FF(emp)2806 2115 y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 5.43198 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2806 2115 a FF(dept)2579 2100 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + +2579 2100 a 2579 2100 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 2100 a 2573 2257 a + tx@Dict begin tx@NodeDict begin { } /TheNodesort 16 { .5 5.344 1.72792 +false .5 35.61568 InitRnode } NewNode end end + 2573 +2257 a FF(Mer)o(ge)p 2748 2257 20 4 v 25 w(sort)2572 +2399 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoin 16 { .5 5.43198 +1.72792 false .5 36.0637 InitRnode } NewNode end end + 2572 2399 a FF(Mer)o(ge)p 2747 2399 20 4 v 25 +w(join)2579 2667 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodesort +/TheNodejoin InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 2667 a 2516 2547 a + tx@Dict begin tx@NodeDict begin { } /TheNoderetr1 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2516 2547 +a FF(RET)2800 2547 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2800 2547 a FF(RET)2579 2667 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 +2667 a 2579 2667 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 2667 a 2522 2675 a + tx@Dict begin tx@NodeDict begin { } /TheNoder1 16 { .5 3.62798 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2522 2675 +a FF(emp)2806 2682 y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 5.43198 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2806 2682 a FF(dept)2579 2667 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + +2579 2667 a 2579 2667 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 2667 a 2573 2824 a + tx@Dict begin tx@NodeDict begin { } /TheNodesort 16 { .5 5.344 1.72792 +false .5 35.61568 InitRnode } NewNode end end + 2573 +2824 a FF(Mer)o(ge)p 2748 2824 20 4 v 25 w(sort)2572 +2966 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoin 16 { .5 5.43198 +1.72792 false .5 36.0637 InitRnode } NewNode end end + 2572 2966 a FF(Mer)o(ge)p 2747 2966 20 4 v 25 +w(join)2579 3234 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodesort +/TheNodejoin InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 3234 a 2457 3114 a + tx@Dict begin tx@NodeDict begin { } /TheNoderetr1 16 { .5 5.43198 +0.08394 false .5 29.5436 InitRnode } NewNode end end + 2457 3114 +a FF(File)p 2563 3114 20 4 v 25 w(scan)2740 3114 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.43198 +0.08394 false .5 29.5436 InitRnode } NewNode end end + 2740 +3114 a FF(File)p 2846 3114 20 4 v 26 w(scan)2579 3234 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 3234 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/TheNoderetr1 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2516 804 a FF(RET)2800 804 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2800 804 a FF(RET)2579 +924 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 924 a 2579 924 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 924 a 2522 939 a + tx@Dict begin tx@NodeDict begin { } /TheNoder1 16 { .5 5.43198 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2522 +939 a FF(dept)2806 932 y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 3.62798 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2806 932 a FF(emp)2579 924 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + +2579 924 a 2579 924 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 924 a 2638 1088 a + tx@Dict begin tx@NodeDict begin { } /TheNodesort 16 { .5 5.43198 +0.08394 false .5 19.96785 InitRnode } NewNode end end + 2638 1088 +a FF(SOR)l(T)2572 1223 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoin 16 { .5 5.43198 +1.72792 false .5 36.0637 InitRnode } NewNode end end + 2572 1223 a FF(Mer)o(ge)p 2747 +1223 20 4 v 25 w(join)2579 1491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodesort +/TheNodejoin InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 1491 a 2516 1371 +a + tx@Dict begin tx@NodeDict begin { } /TheNoderetr1 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2516 1371 a FF(RET)2800 1371 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2800 1371 a FF(RET)2579 +1491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 1491 a 2579 1491 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 1491 a 2522 1506 +a + tx@Dict begin tx@NodeDict begin { } /TheNoder1 16 { .5 5.43198 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2522 1506 a FF(dept)2806 1499 y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 3.62798 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2806 1499 a FF(emp)2579 +1491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 1491 a 2579 1491 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 1491 a 2638 1797 +a + tx@Dict begin tx@NodeDict begin { } /TheNodesort 16 { .5 5.43198 +0.08394 false .5 19.96785 InitRnode } NewNode end end + 2638 1797 a FF(SOR)l(T)2572 1931 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoin 16 { .5 5.43198 +1.72792 false .5 36.0637 InitRnode } NewNode end end + 2572 1931 a FF(Mer)o(ge)p +2747 1931 20 4 v 25 w(join)2579 2200 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodesort +/TheNodejoin InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 2200 a 2516 +2080 a + tx@Dict begin tx@NodeDict begin { } /TheNoderetr1 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2516 2080 a FF(RET)2800 2080 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2800 2080 a FF(RET)2579 +2200 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 2200 a 2579 2200 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 2200 a 2522 2215 +a + tx@Dict begin tx@NodeDict begin { } /TheNoder1 16 { .5 5.43198 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2522 2215 a FF(dept)2806 2208 y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 3.62798 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2806 2208 a FF(emp)2579 +2200 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 2200 a 2579 2200 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 2200 a 2573 2356 +a + tx@Dict begin tx@NodeDict begin { } /TheNodesort 16 { .5 5.344 1.72792 +false .5 35.61568 InitRnode } NewNode end end + 2573 2356 a FF(Mer)o(ge)p 2748 2356 20 4 v 25 w(sort)2572 +2498 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoin 16 { .5 5.43198 +1.72792 false .5 36.0637 InitRnode } NewNode end end + 2572 2498 a FF(Mer)o(ge)p 2747 2498 20 4 v 25 +w(join)2579 2766 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodesort +/TheNodejoin InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 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2522 2782 +a FF(dept)2806 2774 y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 3.62798 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2806 2774 a FF(emp)2579 2766 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + +2579 2766 a 2579 2766 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 2766 a 2573 2923 a + tx@Dict begin tx@NodeDict begin { } /TheNodesort 16 { .5 5.344 1.72792 +false .5 35.61568 InitRnode } NewNode end end + 2573 +2923 a FF(Mer)o(ge)p 2748 2923 20 4 v 25 w(sort)2572 +3065 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoin 16 { .5 5.43198 +1.72792 false .5 36.0637 InitRnode } NewNode end end + 2572 3065 a FF(Mer)o(ge)p 2747 3065 20 4 v 25 +w(join)2579 3333 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodesort +/TheNodejoin InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 3333 a 2457 3214 a + tx@Dict begin tx@NodeDict begin { } /TheNoderetr1 16 { .5 5.43198 +0.08394 false .5 29.5436 InitRnode } NewNode end end + 2457 3214 +a FF(File)p 2563 3214 20 4 v 25 w(scan)2740 3214 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.43198 +0.08394 false .5 29.5436 InitRnode } NewNode end end + 2740 +3214 a FF(File)p 2846 3214 20 4 v 26 w(scan)2579 3333 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap 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PtoC Shadow 0. setgray gsave fill grestore +stroke grestore gsave 1. setgray gsave fill grestore stroke grestore +gsave 0.8 SLW 0. setgray 0 setlinecap stroke grestore end + +@endspecial 801 2428 a Fh(JOIN)p Fu(\()p +Fn(S)971 2438 y Fg(1)1003 2428 y Fn(;)10 b(S)1070 2438 +y Fg(2)1102 2428 y Fu(\))18 b(=)-11 b Ft(\))18 b Fh(JOPR)p +Fu(\()p Fh(SOR)m(T)p Fu(\()p Fn(S)1585 2438 y Fg(1)1617 +2428 y Fu(\))p Fn(;)11 b Fh(SOR)m(T)p Fu(\()p Fn(S)1857 +2438 y Fg(2)1889 2428 y Fu(\)\))801 2515 y Fh(JOPR)p +Fu(\()p Fn(S)979 2525 y Fg(1)1011 2515 y Fn(;)g(S)1079 +2525 y Fg(2)1111 2515 y Fu(\))17 b(=)-11 b Ft(\))18 b +Fh(Mer)o(ge)p 1399 2515 V 18 w(join)o Fu(\()p Fn(S)1553 +2525 y Fg(1)1586 2515 y Fn(;)10 b(S)1653 2525 y Fg(2)1685 +2515 y Fu(\))801 2603 y Fh(JOIN)p Fu(\()p Fn(S)971 2613 +y Fg(1)1003 2603 y Fn(;)g(S)1070 2613 y Fg(2)1102 2603 +y Fu(\))18 b(=)-11 b Ft(\))18 b Fh(JOIN)p 1370 2603 V +17 w(CONC)q Fu(\()p Fn(S)1585 2613 y Fg(1)1617 2603 y +Fn(;)10 b(S)1684 2613 y Fg(2)1716 2603 y Fu(\))801 2690 +y Fh(SOR)m(T)p Fu(\()p Fn(S)987 2700 y Fg(1)1019 2690 +y Fu(\))18 b(=)-11 b Ft(\))17 b Fh(SOR)m(T)p 1302 2690 +V 19 w(CONC)p Fu(\()p Fn(S)1518 2700 y Fg(1)1550 2690 +y Fu(\))801 2777 y Fh(RET)q Fu(\()p Fn(F)958 2787 y Fg(1)990 +2777 y Fu(\))h(=)-11 b Ft(\))17 b Fh(RET)p 1242 2777 +V 19 w(CONC)p Fu(\()p Fn(F)1459 2787 y Fg(1)1491 2777 +y Fu(\))804 2962 y @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW 0. setgray 0. true 3.8 neg 3.96492 +neg 30.67973 10.71999 .5 Frame gsave 3.0 -45. PtoC Shadow 0. setgray +gsave fill grestore stroke grestore gsave 1. setgray gsave fill grestore +stroke grestore gsave 0.8 SLW 0. setgray 0 setlinecap stroke grestore +end + +@endspecial +Fe(SOR)m(T)772 3491 y @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW 0. setgray [ 0.0 59.75073 162.18057 +59.75073 162.18057 0.0 0.0 0.0 0.0 59.75073 /Lineto /lineto load def +false Polygon gsave 3.0 -45. PtoC Shadow 0. setgray gsave fill grestore +stroke grestore gsave 1. setgray gsave fill grestore stroke grestore +gsave 0.8 SLW 0. setgray 0 setlinecap stroke grestore end + +@endspecial +801 3102 a Fh(SOR)m(T)p Fu(\()p Fn(S)987 3112 y Fg(1)1019 +3102 y Fu(\))h(=)-11 b Ft(\))17 b Fh(Mer)o(ge)p 1307 +3102 V 18 w(sort)p Fu(\()p Fn(S)1459 3112 y Fg(1)1491 +3102 y Fu(\))801 3189 y Fh(SOR)m(T)p Fu(\()p Fn(S)987 +3199 y Fg(1)1019 3189 y Fu(\))h(=)-11 b Ft(\))17 b Fh(Null)p +Fu(\()p Fn(S)1326 3199 y Fg(1)1358 3189 y Fu(\))801 3276 +y Fh(JOIN)p Fu(\()p Fn(S)971 3286 y Fg(1)1003 3276 y +Fn(;)10 b(S)1070 3286 y Fg(2)1102 3276 y Fu(\))18 b(=)-11 +b Ft(\))18 b Fh(JOIN)p 1370 3276 V 17 w(CONC)q Fu(\()p +Fn(S)1585 3286 y Fg(1)1617 3276 y Fn(;)10 b(S)1684 3286 +y Fg(2)1716 3276 y Fu(\))801 3363 y Fh(SOR)m(T)p Fu(\()p +Fn(S)987 3373 y Fg(1)1019 3363 y Fu(\))18 b(=)-11 b Ft(\))17 +b Fh(SOR)m(T)p 1302 3363 V 19 w(CONC)p Fu(\()p Fn(S)1518 +3373 y Fg(1)1550 3363 y Fu(\))801 3450 y Fh(RET)q Fu(\()p +Fn(F)958 3460 y Fg(1)990 3450 y Fu(\))h(=)-11 b Ft(\))17 +b Fh(RET)p 1242 3450 V 19 w(CONC)p Fu(\()p Fn(F)1459 +3460 y Fg(1)1491 3450 y Fu(\))804 3771 y @beginspecial +@setspecial + tx@Dict begin STP newpath 0.8 SLW 0. setgray 0. true 3.8 neg 3.8 +neg 24.35982 10.56996 .5 Frame gsave 3.0 -45. PtoC Shadow 0. setgray +gsave fill grestore stroke grestore gsave 1. setgray gsave fill grestore +stroke grestore gsave 0.8 SLW 0. setgray 0 setlinecap stroke grestore +end + +@endspecial Fe(RET)772 3945 y @beginspecial +@setspecial + tx@Dict begin STP newpath 0.8 SLW 0. setgray [ 0.0 17.07164 162.18057 +17.07164 162.18057 0.0 0.0 0.0 0.0 17.07164 /Lineto /lineto load def +false Polygon gsave 3.0 -45. PtoC Shadow 0. setgray gsave fill grestore +stroke grestore gsave 1. setgray gsave fill grestore stroke grestore +gsave 0.8 SLW 0. setgray 0 setlinecap stroke grestore end + +@endspecial 801 3904 a Fh(RET)q Fu(\()p +Fn(F)958 3914 y Fg(1)990 3904 y Fu(\))h(=)-11 b Ft(\))17 +b Fh(File)p 1227 3904 V 17 w(scan)q Fu(\()p Fn(F)1393 +3914 y Fg(1)1425 3904 y Fu(\))2638 757 y + tx@Dict begin tx@NodeDict begin { } /TheNodesort 16 { .5 5.43198 +0.08394 false .5 19.96785 InitRnode } NewNode end end + 2638 757 a FF(SOR)l(T)2649 +898 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoin 16 { .5 5.43198 +0.08394 false .5 17.32784 InitRnode } NewNode end end + 2649 898 a FF(JOIN)2579 1160 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodesort +/TheNodejoin InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 1160 a 2516 +1040 a + tx@Dict begin tx@NodeDict begin { } /TheNoderetr1 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2516 1040 a FF(RET)2800 1040 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2800 1040 a FF(RET)2579 +1160 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 1160 a 2579 1160 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 1160 a 2522 1175 +a + tx@Dict begin tx@NodeDict begin { } /TheNoder1 16 { .5 5.43198 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2522 1175 a FF(dept)2806 1168 y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 3.62798 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2806 1168 a FF(emp)2579 +1160 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 1160 a 2579 1160 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 1160 a 2638 1323 +a + tx@Dict begin tx@NodeDict begin { } /TheNodesort 16 { .5 5.43198 +0.08394 false .5 19.96785 InitRnode } NewNode end end + 2638 1323 a FF(SOR)l(T)2649 1465 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoin 16 { .5 5.43198 +0.08394 false .5 17.32784 InitRnode } NewNode end end + 2649 1465 a FF(JOIN)2579 +1726 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodesort +/TheNodejoin InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 1726 a 2516 1607 a + tx@Dict begin tx@NodeDict begin { } /TheNoderetr1 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2516 1607 a FF(RET)2800 +1607 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2800 1607 a FF(RET)2579 1726 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 1726 a 2579 +1726 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 1726 a 2522 1734 a + tx@Dict begin tx@NodeDict begin { } /TheNoder1 16 { .5 3.62798 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2522 1734 a FF(emp)2806 +1742 y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 5.43198 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2806 1742 a FF(dept)2579 1726 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 1726 a 2579 +1726 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 1726 a 2638 1961 a + tx@Dict begin tx@NodeDict begin { } /TheNodesort 16 { .5 5.43198 +0.08394 false .5 19.96785 InitRnode } NewNode end end + 2638 1961 a FF(SOR)l(T)2649 +2103 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoin 16 { .5 5.43198 +0.08394 false .5 17.32784 InitRnode } NewNode end end + 2649 2103 a FF(JOIN)2579 2506 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodesort +/TheNodejoin InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 2506 a 2518 +2238 a + tx@Dict begin tx@NodeDict begin { } /TheNodexfer1 16 { .5 5.43198 +1.72792 false .5 14.67188 InitRnode } NewNode end end + 2518 2238 a FF(Ship)2802 2238 y + tx@Dict begin tx@NodeDict begin { } /TheNodexfer2 16 { .5 5.43198 +1.72792 false .5 14.67188 InitRnode } NewNode end end + 2802 2238 a FF(Ship)2579 +2506 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNodexfer1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 2506 a 2579 2506 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNodexfer2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 2506 a 2516 2386 +a + tx@Dict begin tx@NodeDict begin { } /TheNoderetr1 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2516 2386 a FF(RET)2800 2386 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2800 2386 a FF(RET)2579 +2506 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodexfer1 +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 2506 a 2579 2506 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodexfer2 +/TheNoderetr2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 2506 a 2522 2514 +a + tx@Dict begin tx@NodeDict begin { } /TheNoder1 16 { .5 3.62798 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2522 2514 a FF(emp)2806 2521 y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 5.43198 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2806 2521 a FF(dept)2579 +2506 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 2506 a 2579 2506 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 2506 a 2638 2670 +a + tx@Dict begin tx@NodeDict begin { } /TheNodesort 16 { .5 5.43198 +0.08394 false .5 19.96785 InitRnode } NewNode end end + 2638 2670 a FF(SOR)l(T)2572 2805 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoin 16 { .5 5.43198 +1.72792 false .5 36.0637 InitRnode } NewNode end end + 2572 2805 a FF(Mer)o(ge)p +2747 2805 20 4 v 25 w(join)2579 3215 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodesort +/TheNodejoin InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 3215 a 2518 +2947 a + tx@Dict begin tx@NodeDict begin { } /TheNodexfer1 16 { .5 5.43198 +1.72792 false .5 14.67188 InitRnode } NewNode end end + 2518 2947 a FF(Ship)2802 2947 y + tx@Dict begin tx@NodeDict begin { } /TheNodexfer2 16 { .5 5.43198 +1.72792 false .5 14.67188 InitRnode } NewNode end end + 2802 2947 a FF(Ship)2579 +3215 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNodexfer1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 3215 a 2579 3215 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNodexfer2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 3215 a 2516 3095 +a + tx@Dict begin tx@NodeDict begin { } /TheNoderetr1 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2516 3095 a FF(RET)2800 3095 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2800 3095 a FF(RET)2579 +3215 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodexfer1 +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 3215 a 2579 3215 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodexfer2 +/TheNoderetr2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 3215 a 2522 3223 +a + tx@Dict begin tx@NodeDict begin { } /TheNoder1 16 { .5 3.62798 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2522 3223 a FF(emp)2806 3230 y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 5.43198 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2806 3230 a FF(dept)2579 +3215 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 3215 a 2579 3215 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 3215 a 2573 3300 +a + tx@Dict begin tx@NodeDict begin { } /TheNodesort 16 { .5 5.344 1.72792 +false .5 35.61568 InitRnode } NewNode end end + 2573 3300 a FF(Mer)o(ge)p 2748 3300 20 4 v 25 w(sort)2572 +3443 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoin 16 { .5 5.43198 +1.72792 false .5 36.0637 InitRnode } NewNode end end + 2572 3443 a FF(Mer)o(ge)p 2747 3443 20 4 v 25 +w(join)2579 3852 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodesort +/TheNodejoin InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 3852 a 2518 3584 a + tx@Dict begin tx@NodeDict begin { } /TheNodexfer1 16 { .5 5.43198 +1.72792 false .5 14.67188 InitRnode } NewNode end end + 2518 3584 +a FF(Ship)2802 3584 y + tx@Dict begin tx@NodeDict begin { } /TheNodexfer2 16 { .5 5.43198 +1.72792 false .5 14.67188 InitRnode } NewNode end end + 2802 3584 a FF(Ship)2579 3852 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNodexfer1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + +2579 3852 a 2579 3852 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNodexfer2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 3852 a 2516 3733 a + tx@Dict begin tx@NodeDict begin { } /TheNoderetr1 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2516 +3733 a FF(RET)2800 3733 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2800 3733 a FF(RET)2579 3852 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodexfer1 +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 3852 a 2579 3852 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodexfer2 +/TheNoderetr2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 3852 a 2522 3860 a + tx@Dict begin tx@NodeDict begin { } /TheNoder1 16 { .5 3.62798 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2522 +3860 a FF(emp)2806 3868 y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 5.43198 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2806 3868 a FF(dept)2579 3852 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 3852 a 2579 3852 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 3852 a 2573 3938 a + tx@Dict begin tx@NodeDict begin { } /TheNodesort 16 { .5 5.344 1.72792 +false .5 35.61568 InitRnode } NewNode end end + 2573 +3938 a FF(Mer)o(ge)p 2748 3938 20 4 v 25 w(sort)2572 +4080 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoin 16 { .5 5.43198 +1.72792 false .5 36.0637 InitRnode } NewNode end end + 2572 4080 a FF(Mer)o(ge)p 2747 4080 20 4 v 25 +w(join)2579 4490 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodesort +/TheNodejoin InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 4490 a 2518 4222 a + tx@Dict begin tx@NodeDict begin { } /TheNodexfer1 16 { .5 5.43198 +1.72792 false .5 14.67188 InitRnode } NewNode end end + 2518 4222 +a FF(Ship)2802 4222 y + tx@Dict begin tx@NodeDict begin { } /TheNodexfer2 16 { .5 5.43198 +1.72792 false .5 14.67188 InitRnode } NewNode end end + 2802 4222 a FF(Ship)2579 4490 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNodexfer1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + +2579 4490 a 2579 4490 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNodexfer2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 4490 a 2457 4371 a + tx@Dict begin tx@NodeDict begin { } /TheNoderetr1 16 { .5 5.43198 +0.08394 false .5 29.5436 InitRnode } NewNode end end + 2457 +4371 a FF(File)p 2563 4371 20 4 v 25 w(scan)2740 4371 +y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.43198 +0.08394 false .5 29.5436 InitRnode } NewNode end end + 2740 4371 a FF(File)p 2846 4371 20 4 v 26 w(scan)2579 +4490 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodexfer1 +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 4490 a 2579 4490 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodexfer2 +/TheNoderetr2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 4490 a 2522 4498 +a + tx@Dict begin tx@NodeDict begin { } /TheNoder1 16 { .5 3.62798 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2522 4498 a FF(emp)2806 4506 y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 5.43198 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2806 4506 a FF(dept)2579 +4490 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 4490 a 2579 4490 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 4490 a 808 3073 a +@beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW 0. setgray /ArrowA { moveto } def +/ArrowB { } def [ 281.68205 226.19922 179.25221 226.19922 /Lineto +/lineto load def false Line gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath 0.8 SLW 0. setgray /ArrowA { moveto } def +/ArrowB { } def [ 281.68205 145.10893 179.25221 145.10893 /Lineto +/lineto load def false Line gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW 0. setgray /ArrowA { moveto } def +/ArrowB { } def [ 281.68205 59.75073 179.25221 59.75073 /Lineto /lineto +load def false Line gsave 0.8 SLW 0. setgray 0 setlinecap stroke +grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW 0. setgray /ArrowA { moveto } def +/ArrowB { } def [ 281.68205 -21.33954 179.25221 -21.33954 /Lineto +/lineto load def false Line gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath 0.8 SLW 0. setgray /ArrowA { moveto } def +/ArrowB { } def [ 281.68205 -97.30829 179.25221 -97.30829 /Lineto +/lineto load def false Line gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore end + +@endspecial 3557 4529 4 3891 v 323 4532 +3237 4 v 3558 4549 19 3898 v 340 4549 3237 19 v 449 4745 +a FP(Figure)24 b(6.6:)31 b(An)23 b(optimizer)i(for)f(a)f(distributed)k +(database)e(and)f(an)g(example)h(transformation)1905 +5349 y(88)p eop +%%Page: 89 101 +89 100 bop 323 823 3237 4 v 323 4345 4 3523 v 772 3668 +a @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW 0. setgray /ArrowA { moveto } def +/ArrowB { } def [ 81.09029 290.21788 81.09029 -8.53581 /Lineto /lineto +load def false Line gsave 0.8 SLW 0. setgray 0 setlinecap stroke +grestore end + +@endspecial 804 1070 a @beginspecial +@setspecial + tx@Dict begin STP newpath 0.8 SLW 0. setgray 0. true 3.8 neg 5.61494 +neg 69.36932 10.71999 .5 Frame gsave 3.0 -45. PtoC Shadow 0. setgray +gsave fill grestore stroke grestore gsave 1. setgray gsave fill grestore +stroke grestore gsave 0.8 SLW 0. setgray 0 setlinecap stroke grestore +end + +@endspecial Fe(SEQUENTIAL)772 1613 y @beginspecial +@setspecial + tx@Dict begin STP newpath 0.8 SLW 0. setgray [ 0.0 59.75073 162.18057 +59.75073 162.18057 0.0 0.0 0.0 0.0 59.75073 /Lineto /lineto load def +false Polygon gsave 3.0 -45. 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PtoC Shadow 0. setgray +gsave fill grestore stroke grestore gsave 1. setgray gsave fill grestore +stroke grestore gsave 0.8 SLW 0. setgray 0 setlinecap stroke grestore +end + +@endspecial +Fe(MERGE)772 2286 y @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW 0. setgray [ 0.0 59.75073 162.18057 +59.75073 162.18057 0.0 0.0 0.0 0.0 59.75073 /Lineto /lineto load def +false Polygon gsave 3.0 -45. 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PtoC Shadow 0. setgray +gsave fill grestore stroke grestore gsave 1. setgray gsave fill grestore +stroke grestore gsave 0.8 SLW 0. setgray 0 setlinecap stroke grestore +end + +@endspecial +Fe(SOR)m(T)772 2960 y @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW 0. setgray [ 0.0 59.75073 162.18057 +59.75073 162.18057 0.0 0.0 0.0 0.0 59.75073 /Lineto /lineto load def +false Polygon gsave 3.0 -45. PtoC Shadow 0. setgray gsave fill grestore +stroke grestore gsave 1. setgray gsave fill grestore stroke grestore +gsave 0.8 SLW 0. setgray 0 setlinecap stroke grestore end + +@endspecial +801 2570 a Fh(SOR)m(T)p Fu(\()p Fn(S)987 2580 y Fg(1)1019 +2570 y Fu(\))h(=)-11 b Ft(\))17 b Fh(Mer)o(ge)p 1307 +2570 V 18 w(sort)p Fu(\()p Fn(S)1459 2580 y Fg(1)1491 +2570 y Fu(\))801 2657 y Fh(SOR)m(T)p Fu(\()p Fn(S)987 +2667 y Fg(1)1019 2657 y Fu(\))h(=)-11 b Ft(\))17 b Fh(Null)p +Fu(\()p Fn(S)1326 2667 y Fg(1)1358 2657 y Fu(\))801 2744 +y Fh(JOIN)p Fu(\()p Fn(S)971 2754 y Fg(1)1003 2744 y +Fn(;)10 b(S)1070 2754 y Fg(2)1102 2744 y Fu(\))18 b(=)-11 +b Ft(\))18 b Fh(JOIN)p 1370 2744 V 17 w(CONC)q Fu(\()p +Fn(S)1585 2754 y Fg(1)1617 2744 y Fn(;)10 b(S)1684 2754 +y Fg(2)1716 2744 y Fu(\))801 2832 y Fh(SOR)m(T)p Fu(\()p +Fn(S)987 2842 y Fg(1)1019 2832 y Fu(\))18 b(=)-11 b Ft(\))17 +b Fh(SOR)m(T)p 1302 2832 V 19 w(CONC)p Fu(\()p Fn(S)1518 +2842 y Fg(1)1550 2832 y Fu(\))801 2919 y Fh(RET)q Fu(\()p +Fn(F)958 2929 y Fg(1)990 2919 y Fu(\))h(=)-11 b Ft(\))17 +b Fh(RET)p 1242 2919 V 19 w(CONC)p Fu(\()p Fn(F)1459 +2929 y Fg(1)1491 2919 y Fu(\))804 3139 y @beginspecial +@setspecial + tx@Dict begin STP newpath 0.8 SLW 0. setgray 0. true 3.8 neg 3.96492 +neg 73.61931 10.71999 .5 Frame gsave 3.0 -45. PtoC Shadow 0. setgray +gsave fill grestore stroke grestore gsave 1. setgray gsave fill grestore +stroke grestore gsave 0.8 SLW 0. setgray 0 setlinecap stroke grestore +end + +@endspecial Fe(REPLICA)-6 b(TION)772 3385 +y @beginspecial @setspecial + tx@Dict begin STP newpath 0.8 SLW 0. setgray [ 0.0 25.60745 162.18057 +25.60745 162.18057 0.0 0.0 0.0 0.0 25.60745 /Lineto /lineto load def +false Polygon gsave 3.0 -45. PtoC Shadow 0. setgray gsave fill grestore +stroke grestore gsave 1. setgray gsave fill grestore stroke grestore +gsave 0.8 SLW 0. setgray 0 setlinecap stroke grestore end + +@endspecial 801 3257 a Fh(RET)q +Fu(\()p Fn(F)958 3267 y Fg(1)990 3257 y Fu(\))18 b(=)-11 +b Ft(\))17 b Fh(RET)p 1242 3257 V 19 w(CONC)p Fu(\()p +Fn(F)1459 3267 y Fg(11)1520 3257 y Fu(\))801 3344 y Fh(RET)q +Fu(\()p Fn(F)958 3354 y Fg(1)990 3344 y Fu(\))h(=)-11 +b Ft(\))17 b Fh(RET)p 1242 3344 V 19 w(CONC)p Fu(\()p +Fn(F)1459 3354 y Fg(12)1520 3344 y Fu(\))804 3679 y @beginspecial +@setspecial + tx@Dict begin STP newpath 0.8 SLW 0. setgray 0. true 3.8 neg 3.8 +neg 24.35982 10.56996 .5 Frame gsave 3.0 -45. PtoC Shadow 0. setgray +gsave fill grestore stroke grestore gsave 1. setgray gsave fill grestore +stroke grestore gsave 0.8 SLW 0. setgray 0 setlinecap stroke grestore +end + +@endspecial Fe(RET)772 3852 y @beginspecial +@setspecial + tx@Dict begin STP newpath 0.8 SLW 0. setgray [ 0.0 17.07164 162.18057 +17.07164 162.18057 0.0 0.0 0.0 0.0 17.07164 /Lineto /lineto load def +false Polygon gsave 3.0 -45. PtoC Shadow 0. setgray gsave fill grestore +stroke grestore gsave 1. setgray gsave fill grestore stroke grestore +gsave 0.8 SLW 0. setgray 0 setlinecap stroke grestore end + +@endspecial 801 3812 a Fh(RET)q Fu(\()p +Fn(F)958 3822 y Fg(1)990 3812 y Fu(\))h(=)-11 b Ft(\))17 +b Fh(File)p 1227 3812 V 17 w(scan)q Fu(\()p Fn(F)1393 +3822 y Fg(1)1425 3812 y Fu(\))2638 941 y + tx@Dict begin tx@NodeDict begin { } /TheNodesort 16 { .5 5.43198 +0.08394 false .5 19.96785 InitRnode } NewNode end end + 2638 941 a FF(SOR)l(T)2649 +1082 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoin 16 { .5 5.43198 +0.08394 false .5 17.32784 InitRnode } NewNode end end + 2649 1082 a FF(JOIN)2579 1344 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodesort +/TheNodejoin InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 1344 a 2516 +1224 a + tx@Dict begin tx@NodeDict begin { } /TheNoderetr1 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2516 1224 a FF(RET)2800 1224 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2800 1224 a FF(RET)2579 +1344 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 1344 a 2579 1344 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 1344 a 2522 1359 +a + tx@Dict begin tx@NodeDict begin { } /TheNoder1 16 { .5 5.43198 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2522 1359 a FF(dept)2806 1352 y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 3.62798 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2806 1352 a FF(emp)2579 +1344 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 1344 a 2579 1344 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 1344 a 2638 1508 +a + tx@Dict begin tx@NodeDict begin { } /TheNodesort 16 { .5 5.43198 +0.08394 false .5 19.96785 InitRnode } NewNode end end + 2638 1508 a FF(SOR)l(T)2649 1649 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoin 16 { .5 5.43198 +0.08394 false .5 17.32784 InitRnode } NewNode end end + 2649 1649 a FF(JOIN)2579 +1911 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodesort +/TheNodejoin InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 1911 a 2516 1791 a + tx@Dict begin tx@NodeDict begin { } /TheNoderetr1 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2516 1791 a FF(RET)2800 +1791 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2800 1791 a FF(RET)2579 1911 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 1911 a 2579 +1911 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 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2216 a + tx@Dict begin tx@NodeDict begin { } /TheNodesort 16 { .5 5.43198 +0.08394 false .5 19.96785 InitRnode } NewNode end end + 2638 2216 a FF(SOR)l(T)2572 +2351 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoin 16 { .5 5.43198 +1.72792 false .5 36.0637 InitRnode } NewNode end end + 2572 2351 a FF(Mer)o(ge)p 2747 2351 20 4 v 25 +w(join)2579 2619 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodesort +/TheNodejoin InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 2619 a 2516 2500 a + tx@Dict begin tx@NodeDict begin { } /TheNoderetr1 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2516 2500 +a FF(RET)2800 2500 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.344 0.0 +false .5 15.11191 InitRnode } NewNode end end + 2800 2500 a FF(RET)2579 2619 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 +2619 a 2579 2619 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoin +/TheNoderetr2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 2579 2619 a 2522 2627 a + tx@Dict begin tx@NodeDict begin { } /TheNoder1 16 { .5 3.62798 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2522 2627 +a FF(emp)2806 2635 y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 5.43198 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2806 2635 a FF(dept)2579 2619 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. 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3237 +a FF(emp)2806 3244 y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 5.43198 1.72792 +false .5 13.77588 InitRnode } NewNode end end + 2806 3244 a FF(dept)2579 3229 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + +2579 3229 a 2579 3229 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 2579 3229 a 2573 3343 a + tx@Dict begin tx@NodeDict begin { } /TheNodesort 16 { .5 5.344 1.72792 +false .5 35.61568 InitRnode } NewNode end end + 2573 +3343 a FF(Mer)o(ge)p 2748 3343 20 4 v 25 w(sort)2572 +3485 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoin 16 { .5 5.43198 +1.72792 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18 w(SELECT)q Fu(\()p Fn(S)911 1666 y Fg(1)943 +1656 y Fu(\))18 b(:)f Fm(D)1072 1666 y Fa(2)1108 1656 +y Fu(\))h(:)f Fm(D)1237 1666 y Fa(3)1290 1656 y Fu(=)-11 +b Ft(\))18 b Fh(OP)p 1472 1656 V 18 w(SELECT)q Fu(\()p +Fh(OP)p 1760 1656 V 18 w(MA)-6 b(T)q Fu(\()p Fn(S)1942 +1666 y Fg(1)1974 1656 y Fu(\))18 b(:)f Fm(D)2103 1666 +y Fa(4)2139 1656 y Fu(\))g(:)h Fm(D)2268 1666 y Fa(5)374 +1744 y Fh(OP)p 441 1744 V 18 w(SELECT)q Fu(\()p Fh(OP)p +729 1744 V 18 w(MA)-6 b(T)q Fu(\()p Fn(S)911 1754 y Fg(1)943 +1744 y Fu(\))18 b(:)f Fm(D)1072 1754 y Fa(2)1108 1744 +y Fu(\))h(:)f Fm(D)1237 1754 y Fa(3)1290 1744 y Fu(=)-11 +b Ft(\))p Fu(!)17 b Fh(OP)p 1489 1744 V 18 w(MA)-6 b(T)q +Fu(\()p Fh(OP)p 1700 1744 V 18 w(SELECT)q Fu(\()p Fn(S)1959 +1754 y Fg(1)1992 1744 y Fu(\))17 b(:)g Fm(D)2120 1754 +y Fa(4)2156 1744 y Fu(\))h(:)f Fm(D)2285 1754 y Fa(5)374 +1831 y Fh(OP)p 441 1831 V 18 w(SELECT)q Fu(\()p Fh(OP)p +729 1831 V 18 w(UNNEST)p Fu(\()p Fn(S)1002 1841 y Fg(1)1035 +1831 y Fu(\))g(:)g Fm(D)1163 1841 y Fa(2)1199 1831 y +Fu(\))h(:)f Fm(D)1328 1841 y Fa(3)1382 1831 y Fu(=)-11 +b Ft(\))17 b Fh(OP)p 1563 1831 V 18 w(UNNEST)p Fu(\()p +Fh(OP)p 1865 1831 V 18 w(SELECT)r Fu(\()p Fn(S)2125 1841 +y Fg(1)2157 1831 y Fu(\))g(:)h Fm(D)2286 1841 y Fa(4)2321 +1831 y Fu(\))g(:)f Fm(D)2450 1841 y Fa(5)374 1918 y Fh(OP)p +441 1918 V 18 w(MA)-6 b(T)q Fu(\()p Fn(S)623 1928 y Fg(1)655 +1918 y Fu(\))18 b(:)f Fm(D)784 1928 y Fa(2)837 1918 y +Fu(=)-11 b Ft(\))18 b Fh(OP)p 1019 1918 V 18 w(JOIN)o +Fu(\()p Fn(S)1203 1928 y Fg(1)1236 1918 y Fn(;)10 b Fh(OP)p +1332 1918 V 18 w(GET)q Fu(\()p Fn(F)1507 1928 y Fg(3)1538 +1918 y Fu(\))18 b(:)f Fm(D)1667 1928 y Fa(4)1703 1918 +y Fu(\))h(:)f Fm(D)1832 1928 y Fa(5)374 2005 y Fh(OP)p +441 2005 V 18 w(SELECT)q Fu(\()p Fh(OP)p 729 2005 V 18 +w(JOIN)p Fu(\()p Fn(S)914 2015 y Fg(1)946 2005 y Fn(;)11 +b(S)1014 2015 y Fg(2)1046 2005 y Fu(\))17 b(:)g Fm(D)1174 +2015 y Fa(3)1210 2005 y Fu(\))h(:)f Fm(D)1339 2015 y +Fa(4)1393 2005 y Fu(=)-11 b Ft(\))17 b Fh(OP)p 1574 2005 +V 18 w(JOIN)p Fu(\()p Fn(S)1759 2015 y Fg(1)1791 2005 +y Fn(;)10 b Fh(OP)p 1887 2005 V 18 w(SELECT)r Fu(\()p +Fn(S)2147 2015 y Fg(2)2179 2005 y Fu(\))17 b(:)h Fm(D)2308 +2015 y Fa(5)2343 2005 y Fu(\))g(:)f Fm(D)2472 2015 y +Fa(6)374 2092 y Fh(OP)p 441 2092 V 18 w(SELECT)q Fu(\()p +Fh(OP)p 729 2092 V 18 w(JOIN)p Fu(\()p Fn(S)914 2102 +y Fg(1)946 2092 y Fn(;)11 b(S)1014 2102 y Fg(2)1046 2092 +y Fu(\))17 b(:)g Fm(D)1174 2102 y Fa(3)1210 2092 y Fu(\))h(:)f +Fm(D)1339 2102 y Fa(4)1393 2092 y Fu(=)-11 b Ft(\))17 +b Fh(OP)p 1574 2092 V 18 w(JOIN)p Fu(\()p Fh(OP)p 1788 +2092 V 17 w(SELECT)r Fu(\()p Fn(S)2047 2102 y Fg(1)2079 +2092 y Fu(\))h(:)f Fm(D)2208 2102 y Fa(5)2244 2092 y +Fn(;)10 b(S)2311 2102 y Fg(2)2343 2092 y Fu(\))18 b(:)f +Fm(D)2472 2102 y Fa(6)374 2180 y Fh(OP)p 441 2180 V 18 +w(JOIN)p Fu(\()p Fn(S)626 2190 y Fg(1)658 2180 y Fn(;)10 +b Fh(OP)p 754 2180 V 18 w(MA)-6 b(T)q Fu(\()p Fn(S)936 +2190 y Fg(2)968 2180 y Fu(\))18 b(:)f Fm(D)1097 2190 +y Fa(3)1133 2180 y Fu(\))h(:)f Fm(D)1262 2190 y Fa(4)1315 +2180 y Fu(=)-11 b Ft(\))18 b Fh(OP)p 1497 2180 V 17 w(MA)-6 +b(T)r Fu(\()p Fh(OP)p 1708 2180 V 17 w(JOIN)p Fu(\()p +Fn(S)1892 2190 y Fg(1)1924 2180 y Fn(;)11 b(S)1992 2190 +y Fg(2)2024 2180 y Fu(\))17 b(:)h Fm(D)2153 2190 y Fa(5)2188 +2180 y Fu(\))g(:)f Fm(D)2317 2190 y Fa(6)374 2267 y Fh(OP)p +441 2267 V 18 w(JOIN)p Fu(\()p Fn(S)626 2277 y Fg(1)658 +2267 y Fn(;)10 b Fh(OP)p 754 2267 V 18 w(SELECT)r Fu(\()p +Fn(S)1014 2277 y Fg(2)1046 2267 y Fu(\))17 b(:)g Fm(D)1174 +2277 y Fa(3)1210 2267 y Fu(\))h(:)f Fm(D)1339 2277 y +Fa(4)1393 2267 y Fu(=)-11 b Ft(\))p Fu(!)17 b Fh(OP)p +1592 2267 V 17 w(SELECT)r Fu(\()p Fh(OP)p 1880 2267 V +18 w(JOIN)p Fu(\()p Fn(S)2065 2277 y Fg(1)2097 2267 y +Fn(;)10 b(S)2164 2277 y Fg(2)2196 2267 y Fu(\))18 b(:)f +Fm(D)2325 2277 y Fa(5)2361 2267 y Fu(\))h(:)f Fm(D)2490 +2277 y Fa(6)374 2354 y Fh(OP)p 441 2354 V 18 w(MA)-6 +b(T)q Fu(\()p Fh(OP)p 652 2354 V 18 w(JOIN)o Fu(\()p +Fn(S)836 2364 y Fg(1)869 2354 y Fn(;)10 b(S)936 2364 +y Fg(2)968 2354 y Fu(\))18 b(:)f Fm(D)1097 2364 y Fa(3)1133 +2354 y Fu(\))h(:)f Fm(D)1262 2364 y Fa(4)1315 2354 y +Fu(=)-11 b Ft(\))18 b Fh(OP)p 1497 2354 V 17 w(JOIN)p +Fu(\()p Fh(OP)p 1710 2354 V 18 w(MA)-6 b(T)q Fu(\()p +Fn(S)1892 2364 y Fg(1)1924 2354 y Fu(\))18 b(:)f Fm(D)2053 +2364 y Fa(5)2089 2354 y Fn(;)10 b(S)2156 2364 y Fg(2)2188 +2354 y Fu(\))18 b(:)f Fm(D)2317 2364 y Fa(6)374 2441 +y Fh(OP)p 441 2441 V 18 w(JOIN)p Fu(\()p Fn(S)626 2451 +y Fg(1)658 2441 y Fn(;)10 b(S)725 2451 y Fg(2)757 2441 +y Fu(\))18 b(:)f Fm(D)886 2451 y Fa(3)940 2441 y Fu(=)-11 +b Ft(\))p Fu(!)17 b Fh(OP)p 1139 2441 V 17 w(JOIN)p Fu(\()p +Fn(S)1323 2451 y Fg(2)1355 2441 y Fn(;)11 b(S)1423 2451 +y Fg(1)1455 2441 y Fu(\))18 b(:)f Fm(D)1584 2451 y Fa(4)374 +2528 y Fh(OP)p 441 2528 V 18 w(SELECT)q Fu(\()p Fh(OP)p +729 2528 V 18 w(SELECT)r Fu(\()p Fn(S)989 2538 y Fg(1)1021 +2528 y Fu(\))g(:)h Fm(D)1150 2538 y Fa(2)1186 2528 y +Fu(\))f(:)g Fm(D)1314 2538 y Fa(3)1368 2528 y Fu(=)-11 +b Ft(\))p Fu(!)17 b Fh(OP)p 1567 2528 V 18 w(SELECT)q +Fu(\()p Fh(OP)p 1855 2528 V 18 w(SELECT)q Fu(\()p Fn(S)2114 +2538 y Fg(1)2147 2528 y Fu(\))g(:)g Fm(D)2275 2538 y +Fa(4)2311 2528 y Fu(\))h(:)f Fm(D)2440 2538 y Fa(5)374 +2615 y Fh(OP)p 441 2615 V 18 w(MA)-6 b(T)q Fu(\()p Fh(OP)p +652 2615 V 18 w(MA)g(T)q Fu(\()p Fn(S)834 2625 y Fg(1)866 +2615 y Fu(\))17 b(:)h Fm(D)995 2625 y Fa(2)1030 2615 +y Fu(\))g(:)f Fm(D)1159 2625 y Fa(3)1213 2615 y Fu(=)-11 +b Ft(\))p Fu(!)17 b Fh(OP)p 1412 2615 V 18 w(MA)-6 b(T)q +Fu(\()p Fh(OP)p 1623 2615 V 17 w(MA)g(T)q Fu(\()p Fn(S)1804 +2625 y Fg(1)1837 2615 y Fu(\))17 b(:)g Fm(D)1965 2625 +y Fa(4)2001 2615 y Fu(\))h(:)f Fm(D)2130 2625 y Fa(5)374 +2703 y Fh(OP)p 441 2703 V 18 w(SELECT)q Fu(\()p Fh(OP)p +729 2703 V 18 w(SELECT)r Fu(\()p Fn(S)989 2713 y Fg(1)1021 +2703 y Fu(\))g(:)h Fm(D)1150 2713 y Fa(2)1186 2703 y +Fu(\))f(:)g Fm(D)1314 2713 y Fa(3)1368 2703 y Fu(=)-11 +b Ft(\))p Fu(!)17 b Fh(OP)p 1567 2703 V 18 w(SELECT)q +Fu(\()p Fn(S)1826 2713 y Fg(1)1858 2703 y Fu(\))h(:)f +Fm(D)1987 2713 y Fa(4)374 2790 y Fh(OP)p 441 2790 V 18 +w(JOIN)p Fu(\()p Fh(OP)p 655 2790 V 17 w(JOIN)p Fu(\()p +Fn(S)839 2800 y Fg(1)871 2790 y Fn(;)11 b(S)939 2800 +y Fg(2)971 2790 y Fu(\))18 b(:)f Fm(D)1100 2800 y Fa(4)1136 +2790 y Fn(;)10 b(S)1203 2800 y Fg(3)1235 2790 y Fu(\))18 +b(:)f Fm(D)1364 2800 y Fa(5)1418 2790 y Fu(=)-11 b Ft(\))17 +b Fh(OP)p 1599 2790 V 18 w(JOIN)p Fu(\()p Fn(S)1784 2800 +y Fg(1)1816 2790 y Fn(;)10 b Fh(OP)p 1912 2790 V 18 w(JOIN)p +Fu(\()p Fn(S)2097 2800 y Fg(2)2129 2790 y Fn(;)g(S)2196 +2800 y Fg(3)2228 2790 y Fu(\))18 b(:)f Fm(D)2357 2800 +y Fa(6)2393 2790 y Fu(\))h(:)f Fm(D)2522 2800 y Fa(7)374 +2877 y Fh(OP)p 441 2877 V 18 w(MA)-6 b(T)q Fu(\()p Fh(OP)p +652 2877 V 18 w(MA)g(T)q Fu(\()p Fn(S)834 2887 y Fg(1)866 +2877 y Fu(\))17 b(:)h Fm(D)995 2887 y Fa(2)1030 2877 +y Fu(\))g(:)f Fm(D)1159 2887 y Fa(3)1213 2877 y Fu(=)-11 +b Ft(\))17 b Fh(OP)p 1394 2877 V 18 w(MA)-6 b(T)q Fu(\()p +Fn(S)1576 2887 y Fg(1)1608 2877 y Fu(\))18 b(:)f Fm(D)1737 +2887 y Fa(4)374 2964 y Fh(OP)p 441 2964 V 18 w(JOIN)p +Fu(\()p Fn(S)626 2974 y Fg(1)658 2964 y Fn(;)10 b(S)725 +2974 y Fg(2)757 2964 y Fu(\))18 b(:)f Fm(D)886 2974 y +Fa(3)940 2964 y Fu(=)-11 b Ft(\))p Fu(!)17 b Fh(OP)p +1139 2964 V 17 w(JOIN)p Fu(\()p Fn(S)1323 2974 y Fg(2)1355 +2964 y Fn(;)11 b(S)1423 2974 y Fg(1)1455 2964 y Fu(\))18 +b(:)f Fm(D)1584 2974 y Fa(4)374 3138 y FI(Implementation)24 +b(rules)374 3226 y Fh(PR)p 438 3226 V 18 w(JOIN)p Fu(\()p +Fn(S)623 3236 y Fg(1)655 3226 y Fn(;)11 b(S)723 3236 +y Fg(2)755 3226 y Fu(\))17 b(:)h Fm(D)884 3236 y Fa(3)937 +3226 y Fu(=)-11 b Ft(\))18 b Fh(Al)p 1105 3226 V 17 w(hh)p +1172 3226 V 18 w(join)p Fu(\()p Fn(S)1327 3236 y Fg(1)1376 +3226 y Fu(:)g Fm(D)1464 3236 y Fa(4)1499 3226 y Fn(;)11 +b(S)1567 3236 y Fg(2)1617 3226 y Fu(:)17 b Fm(D)1704 +3236 y Fa(5)1740 3226 y Fu(\))g(:)h Fm(D)1869 3236 y +Fa(6)374 3313 y Fh(PR)p 438 3313 V 18 w(JOIN)p Fu(\()p +Fn(S)623 3323 y Fg(1)655 3313 y Fn(;)11 b Fh(OP)p 752 +3313 V 17 w(GET)q Fu(\()p Fn(F)926 3323 y Fg(2)958 3313 +y Fu(\))18 b(:)f Fm(D)1087 3323 y Fa(3)1123 3313 y Fu(\))g(:)h +Fm(D)1252 3323 y Fa(4)1305 3313 y Fu(=)-11 b Ft(\))18 +b Fh(Al)p 1473 3313 V 17 w(ptr)p 1546 3313 V 18 w(hh)p +1614 3313 V 17 w(join)p Fu(\()p Fn(S)1768 3323 y Fg(1)1818 +3313 y Fu(:)f Fm(D)1905 3323 y Fa(6)1941 3313 y Fu(\))g(:)h +Fm(D)2070 3323 y Fa(5)374 3400 y Fh(PR)p 438 3400 V 18 +w(SELECT)r Fu(\()p Fn(S)698 3410 y Fg(1)730 3400 y Fu(\))f(:)h +Fm(D)859 3410 y Fa(2)912 3400 y Fu(=)-11 b Ft(\))18 b +Fh(Al)p 1080 3400 V 17 w(\256lter)p Fu(\()p Fn(S)1251 +3410 y Fg(1)1300 3400 y Fu(:)g Fm(D)1388 3410 y Fa(4)1423 +3400 y Fu(\))g(:)f Fm(D)1552 3410 y Fa(3)374 3487 y Fh(PR)p +438 3487 V 18 w(MA)-6 b(T)q Fu(\()p Fn(S)620 3497 y Fg(1)652 +3487 y Fu(\))18 b(:)f Fm(D)781 3497 y Fa(2)835 3487 y +Fu(=)-11 b Ft(\))17 b Fh(Al)p 1002 3487 V 18 w(assembly)p +Fu(\()p Fn(S)1264 3497 y Fg(1)1314 3487 y Fu(:)g Fm(D)1401 +3497 y Fa(4)1437 3487 y Fu(\))h(:)f Fm(D)1566 3497 y +Fa(3)374 3574 y Fh(OP)p 441 3574 V 18 w(GET)q 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known { +currentstrokeadjust } { false } ifelse { /t { } def } { /t { transform +0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform } +bind def } ifelse n { x1 y1 t moveto x2 y1 t L stroke /y1 y1 a add def } +repeat grestore } def +/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg +exch 3 index sub exch Atan rotate newpath } def +/EndArrow { @mtrx setmatrix CP grestore end } def +/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 +scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill +grestore } def +/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0 +CLW moveto } def +/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2 +div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0 +CLW moveto } def +/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW +2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0 +curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto } +def +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { +/closepath load } pathforall ] cvx newpath 3 1 roll T exec } def +/SD { 0 360 arc fill } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch +cvi def } def +/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if +f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub +def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } +ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq +and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } +repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 +ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 +moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto +Lineto pop pop closepath } ifelse } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def +n { NC } repeat EOC } ifelse } def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS +CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { /a 4 string def /b ED /d ED /n ED cvi dup 1 lt { pop 1 } if /c ED +c div dup 0 eq { pop 1 } if /cy ED c div dup 0 eq { pop 1 } if /cx ED cy +div cvi /y ED cx div cvi /x ED cy div cvi /y2 ED cx div cvi /x2 ED cy +div cvi /y1 ED cx div cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse +def /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 +div add def /Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 +div add def } if gsave n 0 gt { 1 setlinecap [ 0 cy n div ] 0 setdash } +{ 2 setlinecap } ifelse /c x1 def /i 500 w mul x1 add def /e y cy mul +def /f y1 cy mul def /g y2 cy mul def x1 cx mul 0 T { newpath 0 e moveto +b 0 gt { gsave d c a cvs dup stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 +add neg} ifelse h 0 gt {b neg} {z1} ifelse rmoveto show grestore } if 0 +f moveto 0 g L stroke cx w mul 0 T c x2 eq c i eq or {exit} if /c c w +add def } loop grestore gsave n 0 gt { 1 setlinecap [ 0 cx n div ] 0 +setdash } { 2 setlinecap } ifelse /c y1 def /i 500 h mul y1 add def /e x +cx mul def /f x1 cx mul def /g x2 cx mul def 0 y1 cy mul T { newpath e 0 +moveto b 0 gt { gsave d c a cvs dup stringwidth pop /z2 ED w 0 gt {z1 z2 +add neg} {z1} ifelse h 0 gt {z1} {b neg} ifelse rmoveto show grestore } +if f 0 moveto g 0 L stroke 0 cy h mul T c y2 eq c i eq or {exit} if /c c +h add def } loop grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /lmtrx [ tx@Dict /lmtrx known { lmtrx aload pop } if CM ] def +CP 4 2 roll T moveto } def +/PutEnd { CP /lmtrx [ lmtrx aload pop setmatrix ] def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { CP OLUnit T +moveto /IfVisible true def } if } { IfVisible { CP OLUnit NET moveto +/IfVisible false def } if } ifelse } def +/InitOL { /OLUnit [ gsave CM STV 2890.79999 dup moveto setmatrix CP +grestore ] cvx def /BOL { BeginOL } def /IfVisible true def } def +end +%%EndProcSet +%%BeginProcSet: /u/ddas/tex/pstricks/ps/pst-node.pro +% PostScript prologue for pst-node.tex. +% Created 1993/3/12. Source file was pst-node.doc +% Version 0.93a, 93/03/12. +% For use with Rokicki's dvips. +/tx@NodeDict 200 dict def tx@NodeDict begin +/NewNode { gsave /next ED dict dup 3 -1 roll ED begin tx@Dict begin STV +CP T exec end /NodeMtrx CM def next end grestore } def +/InitPnode { /Y ED /X ED /NodePos { Nodesep Cos mul Nodesep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { Nodesep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r Nodesep add def } { /dx l Nodesep sub def +} ifelse Sin 0 gt { /dy u Nodesep add def } { /dy d Nodesep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /r ED r mul neg /l ED /r r l add def /X l neg def { neg /d +ED /u ED /Y 0 def } { neg /Y ED Y sub /u ED u mul neg /d ED /u u d add +def /Y Y d sub def } ifelse /NodePos { GetRnodePos } def } def +/InitRNode { /Y ED /X ED /r ED /X r 2 div X add def /r r X sub def /l X +neg def Y add neg /d ED Y sub /u ED /NodePos { GetRnodePos } def } def +/GetOnodePos { /ww w Nodesep add def /hh h Nodesep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/GetAngle { nodeA GetCenter nodeB GetCenter 3 -1 roll sub 3 1 roll sub +neg Atan } def +/GetEdge { begin /Nodesep ED dup 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED NodePos Y add exch X add exch +NodeMtrx transform CM itransform end 4 2 roll 1 index 0 eq { pop pop } { +2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse } def +/GetPos { OffsetA AngleA NodesepA nodeA GetEdge /y1 ED /x1 ED OffsetB +AngleB NodesepB nodeB GetEdge /y2 ED /x2 ED } def +/InitNC { /nodeB ED /nodeA ED /NodesepB ED /NodesepA ED /OffsetB ED +/OffsetA ED tx@NodeDict nodeA known tx@NodeDict nodeB known and dup { +/nodeA nodeA load def /nodeB nodeB load def } if } def +/LineMP { 4 copy 1 t sub mul exch t mul add 3 1 roll 1 t sub mul exch t +mul add exch 6 2 roll sub 3 1 roll sub Atan } def +/NCCoor { GetAngle /AngleA ED /AngleB AngleA 180 add def GetPos /LPutVar +[ x2 x1 y2 y1 ] cvx def /LPutPos { LPutVar LineMP } def x1 y1 x2 y2 } +def +/NCLine { NCCoor tx@Dict begin ArrowB 4 2 roll ArrowA lineto end } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan } def +/GetArms { /x1a armA AngleA cos mul x1 add def /y1a armA AngleA sin mul +y1 add def /x2a armB AngleB cos mul x2 add def /y2a armB AngleB sin mul +y2 add def } def +/NCCurve { GetPos x1 x2 sub y1 y2 sub Pyth 2 div dup 3 -1 roll mul /armA +ED mul /armB ED GetArms x1a y1a x1 y1 tx@Dict begin ArrowA end x2a y2a +x2 y2 tx@Dict begin ArrowB end curveto /LPutVar [ x1 y1 x1a y1a x2a y2a +x2 y2 ] cvx def /LPutPos { t LPutVar BezierMidpoint } def } def +/AnglesMP { LPutVar t 3 gt { /t t 3 sub def } { t 2 gt { /t t 2 sub def +10 -2 roll } { t 1 gt { /t t 1 sub def 10 -4 roll } { 10 4 roll } ifelse +} ifelse } ifelse 6 { pop } repeat 3 -1 roll exch LineMP } def +/NCAngles { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform pop x2a y2a mtrx transform exch pop mtrx itransform /y0 ED /x0 +ED mark armB 0 ne { x2 y2 } if x2a y2a x0 y0 x1a y1a armA 0 ne { x1 y1 } +if tx@Dict begin false Line end /LPutVar [ x2 y2 x2a y2a x0 y0 x1a y1a +x1 y1 ] cvx def /LPutPos { AnglesMP } def } def +/NCAngle { GetPos /x2a armB AngleB cos mul x2 add def /y2a armB AngleB +sin mul y2 add def /mtrx AngleA matrix rotate def x2a y2a mtrx transform +pop x1 y1 mtrx transform exch pop mtrx itransform /y0 ED /x0 ED mark +armB 0 ne { x2 y2 } if x2a y2a x0 y0 x1 y1 tx@Dict begin false Line end +/LPutVar [ x2 y2 x2 y2 x2a y2a x0 y0 x1 y1 ] cvx def /LPutPos { AnglesMP +} def } def +/NCBar { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform pop x2a y2a mtrx transform pop sub dup 0 mtrx itransform 3 -1 +roll 0 gt { /y2a exch y2a add def /x2a exch x2a add def } { /y1a exch +neg y1a add def /x2a exch neg x2a add def } ifelse mark x2 y2 x2a y2a +x1a y1a x1 y1 tx@Dict begin false Line end /LPutVar [ x2 y2 x2 y2 x2a +y2a x1a y1a x1 y1 ] cvx def /LPutPos { LPutVar AnglesMP } def } def +/NCDiag { GetPos GetArms mark x2 y2 x2a y2a x1a y1a x1 y1 tx@Dict begin +false Line end /LPutVar [ x2 y2 x2 y2 x2a y2a x1a y1a x1 y1 ] cvx def +/LPutPos { AnglesMP } def } def +/NCDiagg { OffsetA AngleA NodesepA nodeA GetEdge /y1 ED /x1 ED /x1a armA +AngleA cos mul x1 add def /y1a armA AngleA sin mul y1 add def nodeB +GetCenter y1a sub exch x1a sub Atan 180 add /AngleB ED OffsetB AngleB +NodesepB nodeB GetEdge /y2 ED /x2 ED mark x2 y2 x1a y1a x1 y1 tx@Dict +begin false Line end /LPutVar [ x2 y2 x2 y2 x2 y2 x1a y1a x1 y1] cvx def +/LPutPos { AnglesMP } def } def +/LoopMP { /t t abs def [ LPutVar ] length 2 div 1 sub dup t lt { /t ED } +{ pop } ifelse mark LPutVar t cvi { /t t 1 sub def pop pop } repeat +counttomark 1 add 4 roll cleartomark 3 -1 roll exch LineMP } def +/NCLoop { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform loopsize add /y1b ED /x1b ED /x2b x2a y2a mtrx transform pop +def x2b y1b mtrx itransform /y2b ED /x2b ED x1b y1b mtrx itransform /y1b +ED /x1b ED mark armB 0 ne { x2 y2 } if x2a y2a x2b y2b x1b y1b x1a y1a +armA 0 ne { x1 y1 } if tx@Dict begin false Line end /LPutVar [ x2 y2 x2a +y2a x2b y2b x1b y1b x1a y1a x1 y1 ] cvx def /LPutPos { LoopMP } def } +def +/NCCircle { nodeA GetCenter 0 0 NodesepA nodeA GetEdge pop 3 1 roll /Y ED +/X ED X sub 2 div dup 2 exp r r mul sub abs sqrt atan 2 mul /a ED r +AngleA 90 add PtoC Y add exch X add exch 2 copy /LPutVar [ 4 2 roll r a +] def /LPutPos { LPutVar aload pop t 360 mul add dup 5 1 roll 90 sub +PtoC 3 -1 roll add 3 1 roll add exch 3 -1 roll } def r AngleA 90 sub a +add AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c +57.2957 r Div def /y ED /x ED } def +/LPutCoor { tx@NodeDict /LPutPos known { gsave LPutPos tx@Dict begin +/langle ED CM 3 1 roll STV CP 3 -1 roll sub neg 3 1 roll sub exch moveto +setmatrix CP end grestore } { 0 0 tx@Dict /langle 0 def end } ifelse } +def +end +%%EndProcSet +%%BeginProcSet: texps.pro +TeXDict begin /rf{findfont dup length 1 add dict begin{1 index /FID ne 2 +index /UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type /integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics /Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont /setfont load]cvx def}def +/ObliqueSlant{dup sin S cos div neg}B /SlantFont{4 index mul add}def +/ExtendFont{3 -1 roll mul exch}def /ReEncodeFont{/Encoding exch def}def +end +%%EndProcSet +%%BeginProcSet: special.pro +TeXDict begin /SDict 200 dict N SDict begin /@SpecialDefaults{/hs 612 N +/vs 792 N /ho 0 N /vo 0 N /hsc 1 N /vsc 1 N /ang 0 N /CLIP 0 N /rwiSeen +false N /rhiSeen false N /letter{}N /note{}N /a4{}N /legal{}N}B +/@scaleunit 100 N /@hscale{@scaleunit div /hsc X}B /@vscale{@scaleunit +div /vsc X}B /@hsize{/hs X /CLIP 1 N}B /@vsize{/vs X /CLIP 1 N}B /@clip{ +/CLIP 2 N}B /@hoffset{/ho X}B /@voffset{/vo X}B /@angle{/ang X}B /@rwi{ +10 div /rwi X /rwiSeen true N}B /@rhi{10 div /rhi X /rhiSeen true N}B +/@llx{/llx X}B /@lly{/lly X}B /@urx{/urx X}B /@ury{/ury X}B /magscale +true def end /@MacSetUp{userdict /md known{userdict /md get type +/dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup +length 20 add dict copy def}if end md begin /letter{}N /note{}N /legal{} +N /od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath +clippath mark{transform{itransform moveto}}{transform{itransform lineto} +}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{ +itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{ +closepath}}pathforall newpath counttomark array astore /gc xdf pop ct 39 +0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}N +/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 +scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get +ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip +not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 +TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{noflips{TR +pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 +-1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg +TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg +sub neg 0 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1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1534 699 a +1723 321 a + tx@Dict begin 45. Rot end + 1723 321 a 1684 324 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.61111 +0.0 false .5 9.32877 InitRnode } NewNode end end + 1684 324 a Fl(:)10 b(:)h(:)1723 +321 y + tx@Dict begin 45. neg Rot end + 1723 321 a 1534 699 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1534 699 a 1873 429 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 3.36499 +0.0 false .5 9.44498 InitRnode } NewNode end end + 1873 +429 a Fm(RET)1878 520 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 3.37999 0.99998 +false .5 8.23898 InitRnode } NewNode end end + 1878 520 a Fa(C)1905 528 y Fl(n)1534 +699 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 1.0 1.0 /TheNodecln 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.5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto } +def +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { +/closepath load } pathforall ] cvx newpath 3 1 roll T exec } def +/SD { 0 360 arc fill } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch +cvi def } def +/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if +f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub +def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } +ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq +and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } +repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 +ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 +moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto +Lineto pop pop closepath } ifelse } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def +n { NC } repeat EOC } ifelse } def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS +CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { /a 4 string def /b ED /d ED /n ED cvi dup 1 lt { pop 1 } if /c ED +c div dup 0 eq { pop 1 } if /cy ED c div dup 0 eq { pop 1 } if /cx ED cy +div cvi /y ED cx div cvi /x ED cy div cvi /y2 ED cx div cvi /x2 ED cy +div cvi /y1 ED cx div cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse +def /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 +div add def /Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 +div add def } if gsave n 0 gt { 1 setlinecap [ 0 cy n div ] 0 setdash } +{ 2 setlinecap } ifelse /c x1 def /i 500 w mul x1 add def /e y cy mul +def /f y1 cy mul def /g y2 cy mul def x1 cx mul 0 T { newpath 0 e moveto +b 0 gt { gsave d c a cvs dup stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 +add neg} ifelse h 0 gt {b neg} {z1} ifelse rmoveto show grestore } if 0 +f moveto 0 g L stroke cx w mul 0 T c x2 eq c i eq or {exit} if /c c w +add def } loop grestore gsave n 0 gt { 1 setlinecap [ 0 cx n div ] 0 +setdash } { 2 setlinecap } ifelse /c y1 def /i 500 h mul y1 add def /e x +cx mul def /f x1 cx mul def /g x2 cx mul def 0 y1 cy mul T { newpath e 0 +moveto b 0 gt { gsave d c a cvs dup stringwidth pop /z2 ED w 0 gt {z1 z2 +add neg} {z1} ifelse h 0 gt {z1} {b neg} ifelse rmoveto show grestore } +if f 0 moveto g 0 L stroke 0 cy h mul T c y2 eq c i eq or {exit} if /c c +h add def } loop grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /lmtrx [ tx@Dict /lmtrx known { lmtrx aload pop } if CM ] def +CP 4 2 roll T moveto } def +/PutEnd { CP /lmtrx [ lmtrx aload pop setmatrix ] def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { CP OLUnit T +moveto /IfVisible true def } if } { IfVisible { CP OLUnit NET moveto +/IfVisible false def } if } ifelse } def +/InitOL { /OLUnit [ gsave CM STV 2890.79999 dup moveto setmatrix CP +grestore ] cvx def /BOL { BeginOL } def /IfVisible true def } def +end +%%EndProcSet +%%BeginProcSet: /u/ddas/tex/pstricks/ps/pst-node.pro +% PostScript prologue for pst-node.tex. +% Created 1993/3/12. Source file was pst-node.doc +% Version 0.93a, 93/03/12. +% For use with Rokicki's dvips. +/tx@NodeDict 200 dict def tx@NodeDict begin +/NewNode { gsave /next ED dict dup 3 -1 roll ED begin tx@Dict begin STV +CP T exec end /NodeMtrx CM def next end grestore } def +/InitPnode { /Y ED /X ED /NodePos { Nodesep Cos mul Nodesep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { Nodesep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r Nodesep add def } { /dx l Nodesep sub def +} ifelse Sin 0 gt { /dy u Nodesep add def } { /dy d Nodesep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /r ED r mul neg /l ED /r r l add def /X l neg def { neg /d +ED /u ED /Y 0 def } { neg /Y ED Y sub /u ED u mul neg /d ED /u u d add +def /Y Y d sub def } ifelse /NodePos { GetRnodePos } def } def +/InitRNode { /Y ED /X ED /r ED /X r 2 div X add def /r r X sub def /l X +neg def Y add neg /d ED Y sub /u ED /NodePos { GetRnodePos } def } def +/GetOnodePos { /ww w Nodesep add def /hh h Nodesep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/GetAngle { nodeA GetCenter nodeB GetCenter 3 -1 roll sub 3 1 roll sub +neg Atan } def +/GetEdge { begin /Nodesep ED dup 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED NodePos Y add exch X add exch +NodeMtrx transform CM itransform end 4 2 roll 1 index 0 eq { pop pop } { +2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse } def +/GetPos { OffsetA AngleA NodesepA nodeA GetEdge /y1 ED /x1 ED OffsetB +AngleB NodesepB nodeB GetEdge /y2 ED /x2 ED } def +/InitNC { /nodeB ED /nodeA ED /NodesepB ED /NodesepA ED /OffsetB ED +/OffsetA ED tx@NodeDict nodeA known tx@NodeDict nodeB known and dup { +/nodeA nodeA load def /nodeB nodeB load def } if } def +/LineMP { 4 copy 1 t sub mul exch t mul add 3 1 roll 1 t sub mul exch t +mul add exch 6 2 roll sub 3 1 roll sub Atan } def +/NCCoor { GetAngle /AngleA ED /AngleB AngleA 180 add def GetPos /LPutVar +[ x2 x1 y2 y1 ] cvx def /LPutPos { LPutVar LineMP } def x1 y1 x2 y2 } +def +/NCLine { NCCoor tx@Dict begin ArrowB 4 2 roll ArrowA lineto end } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan } def +/GetArms { /x1a armA AngleA cos mul x1 add def /y1a armA AngleA sin mul +y1 add def /x2a armB AngleB cos mul x2 add def /y2a armB AngleB sin mul +y2 add def } def +/NCCurve { GetPos x1 x2 sub y1 y2 sub Pyth 2 div dup 3 -1 roll mul /armA +ED mul /armB ED GetArms x1a y1a x1 y1 tx@Dict begin ArrowA end x2a y2a +x2 y2 tx@Dict begin ArrowB end curveto /LPutVar [ x1 y1 x1a y1a x2a y2a +x2 y2 ] cvx def /LPutPos { t LPutVar BezierMidpoint } def } def +/AnglesMP { LPutVar t 3 gt { /t t 3 sub def } { t 2 gt { /t t 2 sub def +10 -2 roll } { t 1 gt { /t t 1 sub def 10 -4 roll } { 10 4 roll } ifelse +} ifelse } ifelse 6 { pop } repeat 3 -1 roll exch LineMP } def +/NCAngles { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform pop x2a y2a mtrx transform exch pop mtrx itransform /y0 ED /x0 +ED mark armB 0 ne { x2 y2 } if x2a y2a x0 y0 x1a y1a armA 0 ne { x1 y1 } +if tx@Dict begin false Line end /LPutVar [ x2 y2 x2a y2a x0 y0 x1a y1a +x1 y1 ] cvx def /LPutPos { AnglesMP } def } def +/NCAngle { GetPos /x2a armB AngleB cos mul x2 add def /y2a armB AngleB +sin mul y2 add def /mtrx AngleA matrix rotate def x2a y2a mtrx transform +pop x1 y1 mtrx transform exch pop mtrx itransform /y0 ED /x0 ED mark +armB 0 ne { x2 y2 } if x2a y2a x0 y0 x1 y1 tx@Dict begin false Line end +/LPutVar [ x2 y2 x2 y2 x2a y2a x0 y0 x1 y1 ] cvx def /LPutPos { AnglesMP +} def } def +/NCBar { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform pop x2a y2a mtrx transform pop sub dup 0 mtrx itransform 3 -1 +roll 0 gt { /y2a exch y2a add def /x2a exch x2a add def } { /y1a exch +neg y1a add def /x2a exch neg x2a add def } ifelse mark x2 y2 x2a y2a +x1a y1a x1 y1 tx@Dict begin false Line end /LPutVar [ x2 y2 x2 y2 x2a +y2a x1a y1a x1 y1 ] cvx def /LPutPos { LPutVar AnglesMP } def } def +/NCDiag { GetPos GetArms mark x2 y2 x2a y2a x1a y1a x1 y1 tx@Dict begin +false Line end /LPutVar [ x2 y2 x2 y2 x2a y2a x1a y1a x1 y1 ] cvx def +/LPutPos { AnglesMP } def } def +/NCDiagg { OffsetA AngleA NodesepA nodeA GetEdge /y1 ED /x1 ED /x1a armA +AngleA cos mul x1 add def /y1a armA AngleA sin mul y1 add def nodeB +GetCenter y1a sub exch x1a sub Atan 180 add /AngleB ED OffsetB AngleB +NodesepB nodeB GetEdge /y2 ED /x2 ED mark x2 y2 x1a y1a x1 y1 tx@Dict +begin false Line end /LPutVar [ x2 y2 x2 y2 x2 y2 x1a y1a x1 y1] cvx def +/LPutPos { AnglesMP } def } def +/LoopMP { /t t abs def [ LPutVar ] length 2 div 1 sub dup t lt { /t ED } +{ pop } ifelse mark LPutVar t cvi { /t t 1 sub def pop pop } repeat +counttomark 1 add 4 roll cleartomark 3 -1 roll exch LineMP } def +/NCLoop { GetPos GetArms /mtrx AngleA matrix rotate def x1a y1a mtrx +transform loopsize add /y1b ED /x1b ED /x2b x2a y2a mtrx transform pop +def x2b y1b mtrx itransform /y2b ED /x2b ED x1b y1b mtrx itransform /y1b +ED /x1b ED mark armB 0 ne { x2 y2 } if x2a y2a x2b y2b x1b y1b x1a y1a +armA 0 ne { x1 y1 } if tx@Dict begin false Line end /LPutVar [ x2 y2 x2a +y2a x2b y2b x1b y1b x1a y1a x1 y1 ] cvx def /LPutPos { LoopMP } def } +def +/NCCircle { nodeA GetCenter 0 0 NodesepA nodeA GetEdge pop 3 1 roll /Y ED +/X ED X sub 2 div dup 2 exp r r mul sub abs sqrt atan 2 mul /a ED r +AngleA 90 add PtoC Y add exch X add exch 2 copy /LPutVar [ 4 2 roll r a +] def /LPutPos { LPutVar aload pop t 360 mul add dup 5 1 roll 90 sub +PtoC 3 -1 roll add 3 1 roll add exch 3 -1 roll } def r AngleA 90 sub a +add AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c +57.2957 r Div def /y ED /x ED } def +/LPutCoor { tx@NodeDict /LPutPos known { gsave LPutPos tx@Dict begin +/langle ED CM 3 1 roll STV CP 3 -1 roll sub neg 3 1 roll sub exch moveto +setmatrix CP end grestore } { 0 0 tx@Dict /langle 0 def end } ifelse } +def +end +%%EndProcSet +%%BeginProcSet: texps.pro +TeXDict begin /rf{findfont dup length 1 add dict begin{1 index /FID ne 2 +index /UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll +exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics +exch def dict begin Encoding{exch dup type /integertype ne{pop pop 1 sub +dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} +ifelse}forall Metrics /Metrics currentdict end def[2 index currentdict +end definefont 3 -1 roll makefont /setfont load]cvx def}def +/ObliqueSlant{dup sin S cos div neg}B /SlantFont{4 index mul add}def +/ExtendFont{3 -1 roll mul exch}def /ReEncodeFont{/Encoding exch def}def +end +%%EndProcSet +%%BeginProcSet: special.pro +TeXDict begin /SDict 200 dict N SDict begin /@SpecialDefaults{/hs 612 N +/vs 792 N /ho 0 N /vo 0 N /hsc 1 N /vsc 1 N /ang 0 N /CLIP 0 N /rwiSeen +false N /rhiSeen false N /letter{}N /note{}N /a4{}N /legal{}N}B +/@scaleunit 100 N /@hscale{@scaleunit div /hsc X}B /@vscale{@scaleunit +div /vsc X}B /@hsize{/hs X /CLIP 1 N}B /@vsize{/vs X /CLIP 1 N}B /@clip{ +/CLIP 2 N}B /@hoffset{/ho X}B /@voffset{/vo X}B /@angle{/ang X}B /@rwi{ +10 div /rwi X /rwiSeen true N}B /@rhi{10 div /rhi X /rhiSeen true N}B +/@llx{/llx X}B /@lly{/lly X}B /@urx{/urx X}B /@ury{/ury X}B /magscale +true def end /@MacSetUp{userdict /md known{userdict /md get type +/dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup +length 20 add dict copy def}if end md begin /letter{}N /note{}N /legal{} +N /od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath +clippath mark{transform{itransform moveto}}{transform{itransform lineto} +}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{ +itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{ +closepath}}pathforall newpath counttomark array astore /gc xdf pop ct 39 +0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}N +/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 +scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get +ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip +not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 +TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{noflips{TR +pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 +-1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg +TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg +sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr +0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add +2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N /cp +{pop pop showpage pm restore}N end}if}if}N /normalscale{Resolution 72 +div VResolution 72 div neg scale magscale{DVImag dup scale}if 0 setgray} +N /psfts{S 65781.76 div N}N /startTexFig{/psf$SavedState save N userdict +maxlength dict begin /magscale false def normalscale currentpoint TR +/psf$ury psfts /psf$urx psfts /psf$lly psfts /psf$llx psfts /psf$y psfts +/psf$x psfts currentpoint /psf$cy X /psf$cx X /psf$sx psf$x psf$urx +psf$llx sub div N /psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy +scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR +/showpage{}N /erasepage{}N /copypage{}N /p 3 def @MacSetUp}N /doclip{ +psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 +roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip 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10.56842 InitRnode } NewNode end end + 404 874 +a Fv(R)431 879 y Fs(3)213 936 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2 +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 213 936 a 213 936 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2 +/TheNoderetr2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 213 +936 a 213 936 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3 +/TheNodejoinr1r2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 213 936 a 213 936 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3 +/TheNoderetr3 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 213 936 a 213 936 +a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 213 936 a 213 936 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 213 936 a 213 936 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr3 +/TheNoder3 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 213 936 a 497 +836 a Ft(=)-6 b Fd(\))679 734 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoinr1r2r3 16 { .5 5.384 +0.09999 false .5 17.328 InitRnode } NewNode end end + 679 734 a Fo(JOIN)763 +733 y Fv(a)782 738 y Fs(1)809 733 y Ft(=)10 b Fv(b)861 +738 y Fs(1)750 805 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoinr2r3 16 { .5 5.384 +0.09999 false .5 17.328 InitRnode } NewNode end end + 750 805 a Fo(JOIN)836 804 y Fv(b)851 +809 y Fs(2)878 804 y Ft(=)g Fv(c)930 809 y Fs(1)613 806 +y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr1 16 { .5 5.384 0.0 +false .5 15.112 InitRnode } NewNode end end + 613 806 a Fo(RET)683 876 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.384 0.0 +false .5 15.112 InitRnode } NewNode end end + 683 876 a Fo(RET)825 876 +y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr3 16 { .5 5.384 0.0 +false .5 15.112 InitRnode } NewNode end end + 825 876 a Fo(RET)622 874 y + tx@Dict begin tx@NodeDict begin { } /TheNoder1 16 { .5 5.46666 1.1111 +false .5 10.56842 InitRnode } NewNode end end + 622 874 a Fv(R)649 879 y +Fs(1)693 945 y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 5.46666 1.1111 +false .5 10.56842 InitRnode } NewNode end end + 693 945 a Fv(R)720 950 y Fs(2)835 945 +y + tx@Dict begin tx@NodeDict begin { } /TheNoder3 16 { .5 5.46666 1.1111 +false .5 10.56842 InitRnode } NewNode end end + 835 945 a Fv(R)862 950 y Fs(3)644 936 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3 +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 644 936 a 644 +936 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3 +/TheNodejoinr2r3 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 644 936 a 644 936 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr2r3 +/TheNoderetr2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 644 936 a 644 936 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr2r3 +/TheNoderetr3 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 644 936 +a 644 936 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 644 936 a 644 936 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 644 936 a 644 936 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr3 +/TheNoder3 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 644 +936 a 142 1021 a Fz(\(b\))j(Example)d(of)j(the)e(associati)o(vity)g +(rule)h(applied)f(to)h(an)142 1072 y(operator)d(tree)p +951 1121 2 440 v 1191 734 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoinr1r2r3 16 { .5 5.384 +0.09999 false .5 17.328 InitRnode } NewNode end end + 1191 734 a Fo(JOIN)1063 729 +y Fv(a)1082 734 y Fs(2)1109 729 y Ft(=)h Fv(c)1161 734 +y Fs(1)1121 805 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoinr1r2 16 { .5 5.384 +0.09999 false .5 17.328 InitRnode } NewNode end end + 1121 805 a Fo(JOIN)993 804 y Fv(a)1012 +809 y Fs(1)1038 804 y Ft(=)h Fv(b)1091 809 y Fs(1)1054 +876 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr1 16 { .5 5.384 0.0 +false .5 15.112 InitRnode } NewNode end end + 1054 876 a Fo(RET)1196 876 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.384 0.0 +false .5 15.112 InitRnode } NewNode end end + 1196 876 a Fo(RET)1267 +806 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr3 16 { .5 5.384 0.0 +false .5 15.112 InitRnode } NewNode end end + 1267 806 a Fo(RET)1064 945 y + tx@Dict begin tx@NodeDict begin { } /TheNoder1 16 { .5 5.46666 1.1111 +false .5 10.56842 InitRnode } NewNode end end + 1064 945 a Fv(R)1091 +950 y Fs(1)1206 945 y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 5.46666 1.1111 +false .5 10.56842 InitRnode } NewNode end end + 1206 945 a Fv(R)1233 950 y Fs(2)1276 +874 y + tx@Dict begin tx@NodeDict begin { } /TheNoder3 16 { .5 5.46666 1.1111 +false .5 10.56842 InitRnode } NewNode end end + 1276 874 a Fv(R)1303 879 y Fs(3)1086 936 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2 +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1086 +936 a 1086 936 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2 +/TheNoderetr2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1086 936 a 1086 936 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3 +/TheNodejoinr1r2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1086 936 a 1086 +936 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3 +/TheNoderetr3 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1086 936 a 1086 936 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1086 936 a 1086 936 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1086 +936 a 1086 936 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr3 +/TheNoder3 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1086 936 a 1370 836 a Ft(=)-6 b Fd(\))1390 +838 y Fv(=)1552 734 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoinr1r2r3 16 { .5 5.384 +0.09999 false .5 17.328 InitRnode } NewNode end end + 1552 734 a Fo(JOIN)1623 805 y + tx@Dict begin tx@NodeDict begin { } /TheNodejoinr2r3 16 { .5 5.384 +0.09999 false .5 17.328 InitRnode } NewNode end end + 1623 +805 a Fo(JOIN)1485 806 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr1 16 { .5 5.384 0.0 +false .5 15.112 InitRnode } NewNode end end + 1485 806 a Fo(RET)1556 876 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr2 16 { .5 5.384 0.0 +false .5 15.112 InitRnode } NewNode end end + +1556 876 a Fo(RET)1698 876 y + tx@Dict begin tx@NodeDict begin { } /TheNoderetr3 16 { .5 5.384 0.0 +false .5 15.112 InitRnode } NewNode end end + 1698 876 a Fo(RET)1495 874 +y + tx@Dict begin tx@NodeDict begin { } /TheNoder1 16 { .5 5.46666 1.1111 +false .5 10.56842 InitRnode } NewNode end end + 1495 874 a Fv(R)1522 879 y Fs(1)1566 945 y + tx@Dict begin tx@NodeDict begin { } /TheNoder2 16 { .5 5.46666 1.1111 +false .5 10.56842 InitRnode } NewNode end end + 1566 945 +a Fv(R)1593 950 y Fs(2)1707 945 y + tx@Dict begin tx@NodeDict begin { } /TheNoder3 16 { .5 5.46666 1.1111 +false .5 10.56842 InitRnode } NewNode end end + 1707 945 a Fv(R)1734 +950 y Fs(3)1517 936 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3 +/TheNoderetr1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1517 936 a 1517 936 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr1r2r3 +/TheNodejoinr2r3 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1517 936 +a 1517 936 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr2r3 +/TheNoderetr2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1517 936 a 1517 936 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinr2r3 +/TheNoderetr3 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1517 936 a 1517 936 +a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr1 +/TheNoder1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1517 936 a 1517 936 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr2 +/TheNoder2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1517 936 a 1517 936 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderetr3 +/TheNoder3 InitNC { NCLine } if end gsave 0.8 SLW 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InitRnode } NewNode end end + 294 431 a Fo(RET)183 491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 183 491 a 218 360 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoingetcl1getcl2 16 { +.5 5.384 0.09999 false .5 17.328 InitRnode } NewNode end end + +218 360 a Fo(JOIN)183 491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 183 491 a 183 491 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 183 491 +a 325 279 a + tx@Dict begin 45. Rot end + 325 279 a 304 281 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.88889 +0.0 false .5 9.91681 InitRnode } NewNode end end + 304 281 a Fv(:)6 b(:)g(:)325 +279 y + tx@Dict begin 45. neg Rot end + 325 279 a 183 491 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoingetcl1getcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 183 491 a 436 290 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 5.384 +0.0 false .5 15.112 InitRnode } NewNode end end + 436 290 +a Fo(RET)445 359 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 5.40799 1.0 +false .5 10.45403 InitRnode } NewNode end end + 445 359 a Fb(C)467 363 y Fh(n)183 +491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 183 491 a 360 219 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 5.384 0.09999 +false .5 17.328 InitRnode } NewNode end end + 360 219 a Fo(JOIN)183 491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + +183 491 a 183 491 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderoot +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 183 491 a 279 595 a Fz(\(a\))k(E1)p +545 643 2 619 v 594 500 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 5.40799 1.1111 +false .5 9.50261 InitRnode } NewNode end end + 594 500 a Fb(C)616 505 y Fs(1)583 +431 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 5.384 +0.0 false .5 15.112 InitRnode } NewNode end end + 583 431 a Fo(RET)614 491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 614 491 a 736 500 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 5.40799 1.1111 +false .5 9.50261 InitRnode } NewNode end end + +736 500 a Fb(C)758 505 y Fs(2)724 431 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 5.384 +0.0 false .5 15.112 InitRnode } NewNode end end + 724 431 a Fo(RET)614 +491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 614 491 a 579 361 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl1 16 { .5 5.384 +0.0 false .5 16.888 InitRnode } NewNode end end + 579 361 a Fo(MA)l(T)614 491 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodegetcl1 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 614 491 a 721 361 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl2 16 { .5 5.384 +0.0 false .5 16.888 InitRnode } NewNode end end + 721 361 a Fo(MA)l(T)614 491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodegetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 614 +491 a 649 289 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoinmatgetcl1matgetcl2 +16 { .5 5.384 0.09999 false .5 17.328 InitRnode } NewNode end end + 649 289 a Fo(JOIN)614 491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 614 491 a +614 491 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 614 491 a 756 208 a + tx@Dict begin 45. Rot end + 756 208 a 735 210 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.88889 +0.0 false .5 9.91681 InitRnode } NewNode end end + 735 +210 a Fv(:)c(:)f(:)756 208 y + tx@Dict begin 45. neg Rot end + 756 208 a 614 491 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 614 +491 a 866 290 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 5.384 +0.0 false .5 15.112 InitRnode } NewNode end end + 866 290 a Fo(RET)876 359 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 5.40799 1.0 +false .5 10.45403 InitRnode } NewNode end end + 876 359 a +Fb(C)898 363 y Fh(n)614 491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 614 491 a 862 219 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcln 16 { .5 5.384 +0.0 false .5 16.888 InitRnode } NewNode end end + 862 +219 a Fo(MA)l(T)614 491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodematgetcln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 614 491 a 791 148 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 5.384 0.09999 +false .5 17.328 InitRnode } NewNode end end + 791 148 +a Fo(JOIN)614 491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 614 491 a 614 491 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderoot +/TheNodematgetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 614 491 a 708 +595 a Fz(\(b\))10 b(E2)p 975 643 2 619 v 1025 500 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 5.40799 1.1111 +false .5 9.50261 InitRnode } NewNode end end + 1025 +500 a Fb(C)1047 505 y Fs(1)1013 431 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 5.384 +0.0 false .5 15.112 InitRnode } NewNode end end + 1013 431 a Fo(RET)1044 +491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1044 491 a 1166 500 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 5.40799 1.1111 +false .5 9.50261 InitRnode } NewNode end end + 1166 500 a Fb(C)1188 505 +y Fs(2)1155 431 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 5.384 +0.0 false .5 15.112 InitRnode } NewNode end end + 1155 431 a Fo(RET)1044 491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1044 491 +a 1079 360 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoingetcl1getcl2 16 { +.5 5.384 0.09999 false .5 17.328 InitRnode } NewNode end end + 1079 360 a Fo(JOIN)1044 491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1044 491 a +1044 491 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoingetcl1getcl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1044 491 a 1186 279 a + tx@Dict begin 45. Rot end + 1186 279 a 1165 281 +a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.88889 +0.0 false .5 9.91681 InitRnode } NewNode end end + 1165 281 a Fv(:)c(:)g(:)1186 279 y + tx@Dict begin 45. neg Rot end + 1186 279 a 1044 +491 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoingetcl1getcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1044 491 a 1296 290 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 5.384 +0.0 false .5 15.112 InitRnode } NewNode end end + 1296 290 a Fo(RET)1306 359 +y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 5.40799 1.0 +false .5 10.45403 InitRnode } NewNode end end + 1306 359 a Fb(C)1328 363 y Fh(n)1044 491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1044 491 +a 1221 219 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 5.384 0.09999 +false .5 17.328 InitRnode } NewNode end end + 1221 219 a Fo(JOIN)1044 491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1044 491 a +1044 491 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderoot +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1044 491 a 1196 148 a + tx@Dict begin tx@NodeDict begin { } /TheNodeselect 16 { .5 5.384 +0.09999 false .5 29.336 InitRnode } NewNode end end + 1196 148 a Fo(SELECT)1044 +491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodeselect +/TheNoderoot InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1044 491 a 1140 595 a Fz(\(c\))k(E3)p 1405 643 +2 619 v 1455 500 a + tx@Dict begin tx@NodeDict begin { } /TheNodecl1 16 { .5 5.40799 1.1111 +false .5 9.50261 InitRnode } NewNode end end + 1455 500 a Fb(C)1477 505 y Fs(1)1443 +431 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl1 16 { .5 5.384 +0.0 false .5 15.112 InitRnode } NewNode end end + 1443 431 a Fo(RET)1475 491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodecl1 +/TheNodegetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1475 491 a 1597 500 +a + tx@Dict begin tx@NodeDict begin { } /TheNodecl2 16 { .5 5.40799 1.1111 +false .5 9.50261 InitRnode } NewNode end end + 1597 500 a Fb(C)1619 505 y Fs(2)1585 431 y + tx@Dict begin tx@NodeDict begin { } /TheNodegetcl2 16 { .5 5.384 +0.0 false .5 15.112 InitRnode } NewNode end end + 1585 431 +a Fo(RET)1475 491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodecl2 +/TheNodegetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1475 491 a 1440 361 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl1 16 { .5 5.384 +0.0 false .5 16.888 InitRnode } NewNode end end + 1440 361 a +Fo(MA)l(T)1475 491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodegetcl1 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1475 491 a 1581 361 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcl2 16 { .5 5.384 +0.0 false .5 16.888 InitRnode } NewNode end end + 1581 361 a +Fo(MA)l(T)1475 491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodegetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1475 491 a 1510 289 a + tx@Dict begin tx@NodeDict begin { } /TheNodejoinmatgetcl1matgetcl2 +16 { .5 5.384 0.09999 false .5 17.328 InitRnode } NewNode end end + 1510 289 a +Fo(JOIN)1475 491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl1 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1475 491 a 1475 491 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodematgetcl2 InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1475 491 a 1616 +208 a + tx@Dict begin 45. Rot end + 1616 208 a 1595 210 a + tx@Dict begin tx@NodeDict begin { } /TheNodedots 16 { .5 0.88889 +0.0 false .5 9.91681 InitRnode } NewNode end end + 1595 210 a Fv(:)d(:)e(:)1616 +208 y + tx@Dict begin 45. neg Rot end + 1616 208 a 1475 491 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodejoinmatgetcl1matgetcl2 +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1475 491 a 1727 290 a + tx@Dict begin tx@NodeDict begin { } /TheNodegetcln 16 { .5 5.384 +0.0 false .5 15.112 InitRnode } NewNode end end + 1727 +290 a Fo(RET)1737 359 y + tx@Dict begin tx@NodeDict begin { } /TheNodecln 16 { .5 5.40799 1.0 +false .5 10.45403 InitRnode } NewNode end end + 1737 359 a Fb(C)1759 363 y Fh(n)1475 +491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodecln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1475 491 a 1723 219 a + tx@Dict begin tx@NodeDict begin { } /TheNodematgetcln 16 { .5 5.384 +0.0 false .5 16.888 InitRnode } NewNode end end + 1723 219 a Fo(MA)l(T)1475 +491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodematgetcln +/TheNodegetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 +setlinecap stroke grestore grestore end + 1475 491 a 1651 148 a + tx@Dict begin tx@NodeDict begin { } /TheNoderoot 16 { .5 5.384 0.09999 +false .5 17.328 InitRnode } NewNode end end + 1651 148 a Fo(JOIN)1475 491 +y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderoot +/TheNodedots InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1475 491 a 1475 491 a + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNoderoot +/TheNodematgetcln InitNC { NCLine } if end gsave 0.8 SLW 0. setgray +0 setlinecap stroke grestore grestore end + 1475 491 a 1626 77 a + tx@Dict begin tx@NodeDict begin { } /TheNodeselect 16 { .5 5.384 +0.09999 false .5 29.336 InitRnode } NewNode end end + 1626 77 +a Fo(SELECT)1475 491 y + tx@Dict begin gsave STV newpath 0.8 SLW 0. setgray /ArrowA { moveto +} def /ArrowB { } def tx@NodeDict begin 0.0 0.0 neg 3.0 3.0 /TheNodeselect +/TheNoderoot InitNC { NCLine } if end gsave 0.8 SLW 0. setgray 0 setlinecap +stroke grestore grestore end + 1475 491 a 1569 595 a Fz(\(d\))10 +b(E4)p 1850 655 2 644 v 90 657 1761 2 v 1850 665 10 647 +v 99 665 1761 10 v 382 769 a FG(Figure)h(9:)16 b(Expressions)9 +b(used)i(in)f(generating)g(queries)h(for)g(e)o(xperiments)p +484 918 983 7 v 484 968 2 51 v 510 977 a Fq(Query)p 637 +968 V 663 981 a(Indices?)p 821 968 V 848 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FB(Pr)n(oceedings)e(1979) +h(A)o(CM)h(SIGMOD)171 2669 y(International)9 b(Confer)n(ence)i(on)g +(Management)e(of)h(Data)p FG(,)h(pages)g(23\26134,)f(Boston,)h(May)g +(1979.)952 2793 y(24)p eop +%%Page: 25 25 +25 24 bop 75 14 a FG([18])20 b(Michael)14 b(Stonebraker)f(and)h(La)o +(wrence)g(A.)g(Ro)o(we.)23 b(The)14 b(design)e(of)i(Postgres.)22 +b(In)14 b FB(Pr)n(oceedings)e(1986)171 77 y(A)o(CM)g(SIGMOD)f +(International)e(Confer)n(ence)j(on)g(Management)d(of)i(Data)p +FG(,)h(pages)f(340\261355,)g(W)l(ashing-)171 139 y(ton,)g(May)h(1986.) +75 234 y([19])20 b(Da)o(vid)14 b(L.)f(W)l(ells,)i(Jos)s(\302)-18 +b(e)13 b(A.)h(Blakele)o(y)m(,)g(and)g(Craig)f(W)l(.)h(Thompson.)22 +b(Architecture)13 b(of)h(an)g(open)f(object-)171 296 +y(oriented)e(database)g(management)g(system.)16 b FB(IEEE)11 +b(Computer)p FG(,)g(25\(10\):74\26182,)e(October)i(1992.)75 +391 y([20])20 b(C.)11 b(T)m(.)e(Y)-5 b(u)9 b(and)h(C.)g(C.)g(Chang.)k +(Distrib)o(uted)7 b(query)i(processing.)k FB(A)o(CM)c(Computing)f +(Surve)o(ys)p FG(,)h(16\(4\):399\261)171 453 y(433,)i(December)i(1984.) +952 2793 y(25)p eop +%%Trailer +end +userdict /end-hook known{end-hook}if +%%EOF diff --git a/macros/latex/contrib/utthesis/utthesis.doc b/macros/latex/contrib/utthesis/utthesis.doc new file mode 100644 index 0000000000..5322f9ca06 --- /dev/null +++ b/macros/latex/contrib/utthesis/utthesis.doc @@ -0,0 +1,152 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%% +%%% File: utthesis.doc, version 2.0, January 1995 +%%% ============================================= +%%% Copyright (c) 1995 by Dinesh Das. All rights reserved. +%%% This file is free and can be modified or distributed as long as +%%% you meet the following conditions: +%%% +%%% (1) This copyright notice is kept intact on all modified copies. +%%% (2) If you modify this file, you MUST NOT use the original file name. +%%% +%%% This file contains a template that can be used with the package +%%% utthesis.sty and LaTeX2e to produce a thesis that meets the requirements +%%% of the Graduate School of The University of Texas at Austin. +%%% +%%% All of the commands defined by utthesis.sty have default values (see +%%% the file utthesis.sty for these values). Thus, theoretically, you +%%% don't need to define values for any of them; you can run this file +%%% through LaTeX2e and produce an acceptable thesis, without any text. +%%% However, you probably want to set at least some of the macros (like +%%% \thesisauthor). In that case, replace "..." with appropriate values, +%%% and uncomment the line (by removing the leading %'s). +%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\documentclass[11pt]{report} %% LaTeX2e document. +\usepackage {utthesis} %% Preamble. + +% \mastersthesis %% Uncomment one of these; if you don't +% \phdthesis %% use either, the default is \phdthesis. + +% \thesisdraft %% Uncomment this if you want a draft + %% version; this will print a timestamp + %% on each page of your thesis. + +% \leftchapter %% Uncomment one of these if you want +% \centerchapter %% left-justified, centered or +% \rightchapter %% right-justified chapter headings. + %% Chapter headings includes the + %% Contents, Acknowledgments, Lists + %% of Tables and Figures and the Vita. + %% The default is \centerchapter. + +% \singlespace %% Uncomment one of these if you want +% \oneandhalfspace %% single-spacing, space-and-a-half +% \doublespace %% or double-spacing; the default is + %% \oneandhalfspace, which is the + %% minimum spacing accepted by the + %% Graduate School. + +\renewcommand{\thesisauthor}{...} %% Your official UT name. + +\renewcommand{\thesismonth}{...} %% Your month of graduation. + +\renewcommand{\thesisyear}{...} %% Your year of graduation. + +\renewcommand{\thesistitle}{...} %% The title of your thesis; use + %% mixed-case. + +\renewcommand{\thesisauthorpreviousdegrees}{...} + %% Your previous degrees, abbreviated; + %% separate multiple degrees by commas. + +\renewcommand{\thesissupervisor}{...} + %% Your thesis supervisor; use mixed-case + %% and don't use any titles or degrees. + +\renewcommand{\thesisauthoraddress}{...} + %% Your permanent address; use "\\" for + %% linebreaks. + +\renewcommand{\thesisdedication}{...} + %% Your dedication, if you have one; use + %% "\\" for linebreaks. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%% +%%% The following commands are all optional, but useful if your requirements +%%% are different from the default values in utthesis.sty. To use them, +%%% simply uncomment (remove the leading %) the line(s). + +% \renewcommand{\thesiscommitteesize}{...} + %% Uncomment this only if your thesis + %% committee does NOT have 5 members + %% for \phdthesis or 2 for \mastersthesis. + %% Replace the "..." with the correct + %% number of members. + +% \renewcommand{\thesisdegree}{...} %% Uncomment this only if your thesis + %% degree is NOT "DOCTOR OF PHILOSOPHY" + %% for \phdthesis or "MASTER OF ARTS" + %% for \mastersthesis. Provide the + %% correct FULL OFFICIAL name of + %% the degree. + +% \renewcommand{\thesisdegreeabbreviation}{...} + %% Use this if you also use the above + %% command; provide the OFFICIAL + %% abbreviation of your thesis degree. + +% \renewcommand{\thesistype}{...} %% Use this ONLY if your thesis type + %% is NOT "Dissertation" for \phdthesis + %% or "Thesis" for \mastersthesis. + %% Provide the OFFICIAL type of the + %% thesis; use mixed-case. + +% \renewcommand{\thesistypist}{...} %% Use this to specify the name of + %% the thesis typist if it is anything + %% other than "the author". + +%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{document} + +\thesiscopyrightpage %% Generate the copyright page. + +\thesistitlepage %% Generate the title page. + +\thesissignaturepage %% Generate the signature page. + +\thesisdedicationpage %% Generate the dedication page. + +\begin{thesisacknowledgments} %% Use this to write your +... %% acknowledgments; it can be anything +\end{thesisacknowledgments} %% allowed in LaTeX2e par-mode. + +\begin{thesisabstract} %% Use this to write your thesis +... %% abstract; it can be anything +\end{thesisabstract} %% allowed in LaTeX2e par-mode. + +\tableofcontents %% Generate table of contents. +% \listoftables %% Uncomment this to generate list + %% of tables. +% \listoffigures %% Uncomment this to generate list + %% of figures. + +\chapter{...} %% Begin your thesis text here; follow + %% the report style and group your text + %% in chapters, sections, etc. + +\chapter{...} %% More chapters. + +\begin{thebibliography}{..} %% Start your bibliography here; you can +\bibitem{...} ... %% also use the \bibliography command +\end{thebibliography} %% to generate your bibliography. + +\begin{thesisauthorvita} %% Write your vita here; it can be +... %% anything in LaTeX2e par-mode. +\end{thesisauthorvita} %% + +\end{document} %% Done. diff --git a/macros/latex/contrib/utthesis/utthesis.sty b/macros/latex/contrib/utthesis/utthesis.sty new file mode 100644 index 0000000000..9b04f9a19b --- /dev/null +++ b/macros/latex/contrib/utthesis/utthesis.sty @@ -0,0 +1,716 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%% +%%% File: utthesis.sty, version 2.0, January 1995 +%%% ============================================= +%%% Copyright (c) 1995 by Dinesh Das. All rights reserved. +%%% This file is free and can be modified or distributed as long as +%%% you meet the following conditions: +%%% +%%% (1) This copyright notice is kept intact on all modified copies. +%%% (2) If you modify this file, you MUST NOT use the original file name. +%%% +%%% This file defines macros used for preparing theses for +%%% The University of Texas at Austin. It has been tested with LaTeX2e. +%%% I do NOT guarantee that it will meet all requirements of the +%%% Graduate School; however, if you find that something violates the +%%% specifications, please send me email at <ddas@cs.utexas.edu> and +%%% I will try to fix it. +%%% +%%% Usage: +%%% ====== +%%% +%%% To use this file with LaTeX2e, make sure your TEXINPUTS environment +%%% variable contains the directory in which this file is located. +%%% Include this file as a package in the preamble: +%%% +%%% \documentclass[...]{report} +%%% \usepackage{utthesis} +%%% +%%% On non-UNIX systems, there might be different environment variables +%%% that might need to be set. I know nothing about such machines, +%%% however; consult your local guru for details. +%%% +%%% A template for a thesis is provided in the file "utthesis.doc", available +%%% from the same place where you obtained this file. +%%% +%%% Command Names: +%%% ============== +%%% +%%% ALL command names used in this file that are used to format the +%%% thesis begin with "thesis" (e.g., \thesisauthor). All of these +%%% commands can be changed by the user using \renewcommand, e.g., +%%% +%%% \renewcommand{\thesisauthor}{First M. Last} +%%% +%%% after loading the package in LaTeX2e. +%%% +%%% The following is a list of all thesis-related variables used together +%%% with their default values: +%%% +%%% \thesisauthor %% Name of the author; defaults to "Ima Student". +%%% \thesismonth %% Month of graduation; defaults to "May". +%%% \thesisyear %% Year of graduation; defaults to "1994". +%%% \thesistitle %% Full title of dissertation; defaults to "Title". +%%% \thesistitletypesize +%%% %% Typesize used to typeset \thesistitle; defaults +%%% %% to \Large. +%%% \thesisauthorpreviousdegrees +%%% %% Previous degrees of author; defaults to "Degree" +%%% \thesissupervisor%% Name of thesis supervisor; defaults to "Supervisor" +%%% \thesisauthoraddress +%%% %% Permanent address of author; defaults to "USA" +%%% \thesisapprovedby%% Approval of dissertation committee; defaults to +%%% %% "Approved by". +%%% \thesisapprovedbytypesize +%%% %% Typesize used to typeset \thesisapprovedby; defaults +%%% %% to \large. +%%% \thesiscopyrightholder +%%% %% Name of copyright holder; defaults to \thesisauthor. +%%% \thesistypist %% Name of thesis typist; defaults to "the author". +%%% \thesistype %% Type of thesis; defaults to "Dissertation". +%%% \thesistypetypesize +%%% %% Typesize used to typeset \thesistype; defaults to +%%% %% \large. +%%% \thesisdegree %% Degree for which thesis is submitted; defaults to +%%% %% "Doctor of Philosophy". +%%% \thesisdegreetypesize +%%% %% Typesize used to typeset \thesisdegree; defaults to +%%% %% \large. +%%% \thesisdegreeabbreviation +%%% %% Abbreviation of \thesisdegree; defaults to "Ph.D.". +%%% \thesiscommitteesize +%%% %% Number of members in thesis committee; defaults to 5. +%%% \thesiscommittee %% Name of thesis committee; defaults to +%%% %% "Dissertation Committee:". +%%% \thesiscommitteetypesize +%%% %% Typesize used to typeset \thesiscommittee; defaults +%%% %% to \large. +%%% \thesisvitahead %% Title of the vita page; defaults to "Vita". +%%% \thesisvitaheadtypesize +%%% %% Typesize used to typeset \thesisvitahead; unused. +%%% \thesisacknowledgmenthead +%%% %% Title of the acknowledgments page; defaults to +%%% %% "Acknowledgments". +%%% \thesisacknowledgmentheadtypesize +%%% %% Typesize used to typeset \thesisacknowledgmenthead; +%%% %% unused. +%%% \thesisacknowledgmentsigname +%%% %% Signature on the acknowledgments page; defaults to +%%% %% \thesisauthor. +%%% \thesisacknowledgmentsignametypesize +%%% %% Typesize used to typeset \thesisacknowledgmentsigname; +%%% %% defaults to \large. +%%% \thesisacknowledgmentsigplace +%%% %% Address used on the acknowledgments page; defaults +%%% %% to "The University of Texas at Austin \\ \thesismonth +%%% %% \thesisyear". +%%% \thesisstudent %% Name of author with previous degrees; defaults to +%%% %% "\thesisauthor, \thesisauthorpreviousdegrees". +%%% \thesisstudenttypesize +%%% %% Typesize used to typeset \thesisstudent; defaults +%%% %% to \large. +%%% \thesisdedication%% Person or thing dedicated to; defaults to +%%% %% "To myself". :-) +%%% +%%% Most of the default values will satisfy the Graduate School's +%%% requirements; however, at a minimum, the user SHOULD redefine the +%%% following commands: +%%% +%%% \thesisauthor +%%% \thesismonth +%%% \thesisyear +%%% \thesistitle +%%% \thesisauthorpreviousdegrees +%%% \thesissupervisor +%%% \thesisauthoraddress +%%% +%%% In addition to the above variables, the following commands are +%%% provided to generate the optional sections of the thesis: +%%% +%%% \thesiscopyrightpage +%%% %% Generates the copyright page. +%%% \thesistitlepage %% Generates the title page. +%%% \thesissignaturepage +%%% %% Generates the signature page. +%%% \thesisdedicationpage +%%% %% Generates the dedication page. +%%% +%%% There are also a few environments to generate paragraph-like text: +%%% +%%% thesisacknowledgments +%%% %% Text of acknowledgments. +%%% thesisabstract %% Text of abstract. +%%% thesisauthorvita %% Text of author's vita. +%%% +%%% Bells and Whistles: +%%% =================== +%%% +%%% The following commands are provided purely for playing around with. +%%% They should be used in the document preamble (before \begin{document}). +%%% +%%% \thesisdraft %% Prints a timestamp at the top of each page. This +%%% %% must be invoked in the document preamble (before +%%% %% \begin{document}). +%%% \leftchapter, \centerchapter, \rightchapter +%%% %% These commands generate left-justified, centered, +%%% %% and right-justified chapter headings, respectively. +%%% \singlespace, \oneandhalfspace, \doublespace +%%% %% These define the line spacing to single-space, +%%% %% one-and-one-half space, and double-space +%%% %% respectively. Note that the minimum spacing +%%% %% required by the Graduate School is \oneandhalfspace, +%%% %% but \singlespace is useful, e.g., when using +%%% %% \thesisdraft. +%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\typeout{*************************************************************} +\typeout{** UT Austin Thesis Style File, version 2.0, January 1995 } +\typeout{** Written by Dinesh Das } +\typeout{** Dept. of Computer Sciences } +\typeout{** The University of Texas at Austin } +\typeout{*************************************************************} + +%%% +%%% Set up page layout parameters. +%%% +\setlength{\textheight}{8in} +\setlength{\oddsidemargin}{0.5in} +\setlength{\evensidemargin}{0.5in} +\setlength{\textwidth}{5.50in} +\setlength{\topmargin}{0.5in} +\setlength{\headheight}{0in} +\setlength{\headsep}{0in} +\setlength{\parindent}{12mm} + +%%% +%%% Set up default values. +%%% +\newcommand{\@universityname}{The University of Texas at Austin} +\newcommand{\@publicationno}{Publication No.\ \line(1,0){40} \\[10mm]} +\newcommand{\thesisauthor}{Ima Student} +\newcommand{\thesismonth}{May} +\newcommand{\thesisyear}{1994} +\newcommand{\thesistitle}{Title} +\newcommand{\thesistitletypesize}{\Large} +\newcommand{\thesisauthorpreviousdegrees}{Degree} +\newcommand{\thesissupervisor}{Supervisor} +\newcommand{\thesisauthoraddress}{USA} +\newcommand{\thesisapprovedby}{Approved by} +\newcommand{\thesisapprovedbytypesize}{\large} +\newcommand{\thesiscopyrightholder}{\thesisauthor} +\newcommand{\thesistypist}{the author} +\newcommand{\thesistype}{Dissertation} +\newcommand{\thesistypetypesize}{\large} +\newcommand{\thesistypesize}{\large} +\newcommand{\thesisdegree}{Doctor of Philosophy} +\newcommand{\thesisdegreetypesize}{\large} +\newcommand{\thesisdegreeabbreviation}{Ph.D.} +\newcommand{\thesiscommitteesize}{5} +\newcommand{\thesiscommittee}{Dissertation Committee:} +\newcommand{\thesiscommitteetypesize}{\large} +\newcommand{\thesisvitahead}{Vita} +\newcommand{\thesisvitaheadtypesize}{\Large} +\newcommand{\thesisacknowledgmenthead}{Acknowledgments} +\newcommand{\thesisacknowledgmentheadtypesize}{\Large} +\newcommand{\thesisacknowledgmentsigname}{\thesisauthor} +\newcommand{\thesisacknowledgmentsignametypesize}{\large} +\newcommand{\thesisacknowledgmentsigplace}% + {{\slshape + \renewcommand{\arraystretch}{1.0} + \begin{tabular}{l} + \@universityname \\ + \thesismonth\ \thesisyear + \end{tabular}}} +\newcommand{\thesisstudent}{\thesisauthor, \thesisauthorpreviousdegrees} +\newcommand{\thesisstudenttypesize}{\large} +\newcommand{\thesisdedication}{To myself} + +%%% +%%% Command for masters theses. \phdthesis is provided for symmetry. +%%% +\newcommand{\mastersthesis}{ + \renewcommand{\thesistype}{Thesis} + \renewcommand{\@publicationno}{} + \renewcommand{\thesisdegree}{Master of Arts} + \renewcommand{\thesisdegreeabbreviation}{M.A.} + \renewcommand{\thesiscommitteesize}{2} + \renewcommand{\thesiscommittee}{Supervising Committee:}} +\newcommand{\phdthesis}{} + +%%% +%%% Set up other commands. +%%% +\newcommand{\@defaultbaselinestretch}{1.5} +\newcommand{\@base}[1]{\renewcommand{\baselinestretch}{#1}} +\newcommand{\singlespace}{\renewcommand{\@defaultbaselinestretch}{1.1}} +\newcommand{\oneandhalfspace}{\renewcommand{\@defaultbaselinestretch}{1.5}} +\newcommand{\doublespace}{\renewcommand{\@defaultbaselinestretch}{1.7}} +\newcommand{\@thesistitle}{\textbf{\thesistitletypesize \thesistitle}} +\newcommand{\@thesisapprovedby}% + {\textbf{\thesisapprovedbytypesize \thesisapprovedby}} +\newcommand{\@thesistype}{\textbf{\thesistypetypesize \thesistype}} +\newcommand{\@thesisdegree}{\textbf{\thesisdegreetypesize \thesisdegree}} +\newcommand{\@thesisdegreeabbreviation}{\thesisdegreeabbreviation} +\newcommand{\@thesiscommittee}% + {\textbf{\thesiscommitteetypesize \thesiscommittee}} +\newcommand{\@thesisvitahead}{\thesisvitahead} +\newcommand{\@thesisacknowledgmenthead}% + {\thesisacknowledgmenthead} +\newcommand{\@thesisacknowledgmentsigname}% + {\textsc{\thesisacknowledgmentsignametypesize \thesisacknowledgmentsigname}} +\newcommand{\@thesisacknowledgmentsigplace}{\thesisacknowledgmentsigplace} +\newcommand{\@thesisstudent}{\textbf{\thesisstudenttypesize \thesisstudent}} + +%%% +%%% Indent the first paragraph after a sectioning command. +%%% +%%% \let\@afterindentfalse\@afterindenttrue +%%% \@afterindenttrue + +%%% +%%% Set up default page numbering and line spacing. +%%% +\newcommand{\@textpagenumbering}{arabic} +\newcommand{\@preamblepagenumbering}{roman} +\newcommand{\@textpagestyle}{plain} +\newcommand{\@preamblepagestyle}{plain} +\pagenumbering{\@preamblepagenumbering} +\@base{\@defaultbaselinestretch} + +\newcommand{\@chaptertype}{\chaptername} +\newcommand{\@appendix}{0} + +%%% +%%% Command to generate copyright page. +%%% +\newcommand{\thesiscopyrightpage}{ + \thispagestyle{empty} + \strut \vfill + \begin{center} + \begin{spacing}{2} + Copyright \\ by \\ \thesiscopyrightholder \\ \thesisyear + \end{spacing} + \end{center} + \vfill \strut + \newpage} + +%%% +%%% Command to generate title page. +%%% +\newcommand{\thesistitlepage}{ + \thispagestyle{empty} + \begin{spacing}{2} + \begin{center} + \@thesistitle \\[8mm] + by \\[4mm] + \@thesisstudent \\ + \vspace{26mm} + \textbf{\thesistypetypesize \thesistype} \\ + Presented to the Faculty of the Graduate School of \\ + \@universityname \\ + in Partial Fulfillment \\ + of the Requirements \\ + for the Degree of \\[4mm] + \textbf{\thesisdegreetypesize \thesisdegree} \\ + \vspace{26mm} + \textbf{\Large \@universityname} \\[4mm] + \thesismonth \ \thesisyear + \end{center} + \end{spacing} + \newpage} + +%%% +%%% Command to generate signature page. +%%% +\newcommand{\thesissignaturepage}{ + \thispagestyle{empty} + \begin{spacing}{2} + \strut \vfill + \begin{center} + \@thesistitle + \end{center} + \vspace{50mm} + \mbox{} \hfill \begin{minipage}{67mm} + \begin{spacing}{1} + \@thesisapprovedby\hfill\mbox{} \\ + \@thesiscommittee \\[15mm] + \end{spacing} + \setlength{\unitlength}{1mm} + \begin{picture}(67,70)(0,0) + \multiput(0,70)(0,-10) + {\thesiscommitteesize}{\line(1,0){67}} + \end{picture} + \end{minipage} + \vfill \strut + \end{spacing} + \newpage} + +%%% +%%% Environment to generate abstract page. +%%% +\newenvironment{thesisabstract} + {\addcontentsline{toc}{chapter}{Abstract} + \vspace*{0mm} + \begin{center} + \setlength{\unitlength}{1mm} + \begin{spacing}{2} + \@thesistitle \\[10mm] + \end{spacing} + \begin{spacing}{\@defaultbaselinestretch} + \@publicationno + \thesisauthor, \thesisdegreeabbreviation \\ + \@universityname, \thesisyear \\[10mm] + \end{spacing} + Supervisor: \thesissupervisor \\ + \end{center} + \vspace{5mm} + \begin{spacing}{\@defaultbaselinestretch} \noindent} + {\end{spacing} \newpage} + +%%% +%%% Command to generate dedication page. +%%% +\newcommand{\thesisdedicationpage}{ + \thispagestyle{empty} + \strut \vfill + \begin{spacing}{\@defaultbaselinestretch} + \begin{center} + \thesisdedication + \end{center} + \end{spacing} + \vfill \strut + \newpage} + +%%% +%%% Environment to generate acknowledgments page. +%%% +\newenvironment{thesisacknowledgments} + {%\doublespace\small\normalsize + \chapter*{\@thesisacknowledgmenthead + \@mkboth{\uppercase{\@thesisacknowledgmenthead}} + {\uppercase{\@thesisacknowledgmenthead}}} + \addcontentsline{toc}{chapter}{\@thesisacknowledgmenthead} + \begin{spacing}{\@defaultbaselinestretch}} + {\end{spacing} \par \vspace{20mm} + \raggedleft \@thesisacknowledgmentsigname \\[10mm] + \raggedright \@thesisacknowledgmentsigplace \newpage} + +%%% +%%% Environment to generate vita page. +%%% +\newenvironment{thesisauthorvita} + {\clearpage + \chapter*{\@thesisvitahead + \@mkboth{\uppercase{\@thesisvitahead}} + {\uppercase{\@thesisvitahead}}} + \addcontentsline{toc}{chapter}{\@thesisvitahead} + \begin{spacing}{\@defaultbaselinestretch}} + {\end{spacing} \par \vspace{20mm} + \noindent Permanent Address: + \begin{minipage}[t]{90mm} + \thesisauthoraddress + \end{minipage} + \par \vspace{15mm} + \noindent This \lowercase\expandafter{\thesistype} was + typeset with \LaTeXe\footnote{\LaTeXe{} is an extension of \LaTeX. + \LaTeX{} is a collection of macros for \TeX. \TeX{} is a + trademark of the American Mathematical Society. The macros used in + formatting this \lowercase\expandafter{\thesistype} were written + by Dinesh Das, Department of Computer Sciences, The University + of Texas at Austin. + } by \thesistypist.} + +\newcommand{\@chapteralignment}{\centering} +\renewcommand{\chapter}{\clearpage + \ifnum\@appendix=1 + \renewcommand{\@chaptertype}{\appendixname} + \else + \renewcommand{\@chaptertype}{\chaptername} + \fi + \thispagestyle{plain}% + \global\@topnum\z@ + \@afterindentfalse + \secdef\@chapter\@schapter + } +\renewcommand\appendix{\par + \setcounter{chapter}{0}% + \setcounter{section}{0}% + \renewcommand{\@chapapp}{\appendixname}% + \renewcommand{\thechapter}{\Alph{chapter}} + \renewcommand{\@appendix}{1}} + +%%% +%%% Define chapter heading placement commands. +%%% +\newcommand{\leftchapter}{ + \renewcommand{\@chapteralignment}{\raggedright}} +\newcommand{\centerchapter}{ + \renewcommand{\@chapteralignment}{\centering}} +\newcommand{\rightchapter}{ + \renewcommand{\@chapteralignment}{\raggedleft}} + +%%% +%%% Command from report.cls, (c) LaTeX3 Project. +%%% +\def\@chapter[#1]#2{\ifnum \c@secnumdepth >\m@ne + \refstepcounter{chapter}% + \typeout{\@chapapp\space\thechapter.}% + \addcontentsline{toc}{chapter}% + {\@chaptertype{} \protect\numberline{\thechapter}#1}% + \else + \addcontentsline{toc}{chapter}{\@chaptertype{} #1} + \fi + \ifnum\value{chapter}=1 + \ifnum\@appendix=0 + \pagestyle{\@textpagestyle} + \pagenumbering{\@textpagenumbering} + \fi + \fi + \chaptermark{#1}% + \addtocontents{lof}{\protect\addvspace{10\p@}}% + \addtocontents{lot}{\protect\addvspace{10\p@}}% + \if@twocolumn + \@topnewpage[\@makechapterhead{#2}]% + \else + \@makechapterhead{#2}% + \@afterheading + \fi + } + +%%% +%%% Command from report.cls, (c) LaTeX3 Project. +%%% +\def\@makechapterhead#1{% + \vspace*{50\p@}% + {\parindent \z@ \@chapteralignment \reset@font + \ifnum \c@secnumdepth >\m@ne + \huge\bfseries \@chapapp{} \thechapter + \par + \vskip 20\p@ + \fi + \Huge \bfseries #1\par + \nobreak + \vskip 40\p@ + }} +\def\@makeschapterhead#1{% + \vspace*{50\p@}% + {\parindent \z@ \@chapteralignment + \reset@font + \Huge \bfseries #1\par + \nobreak + \vskip 40\p@ + }} + +%%% +%%% Command from report.cls, (c) LaTeX3 Project. +%%% +\renewenvironment{thebibliography}[1] + {\chapter*{\bibname + \@mkboth{\uppercase{\bibname}}{\uppercase{\bibname}}}% + \addcontentsline{toc}{chapter}{\bibname} + \list{\@biblabel{\arabic{enumiv}}}% + {\settowidth\labelwidth{\@biblabel{#1}}% + \leftmargin\labelwidth + \advance\leftmargin\labelsep + \if@openbib + \advance\leftmargin\bibindent + \itemindent -\bibindent + \listparindent \itemindent + \parsep \z@ + \fi + \usecounter{enumiv}% + \let\p@enumiv\@empty + \renewcommand\theenumiv{\arabic{enumiv}}}% + \if@openbib + \renewcommand\newblock{\par} + \else + \renewcommand\newblock{\hskip .11em \@plus.33em \@minus.07em}% + \fi + \sloppy\clubpenalty4000\widowpenalty4000% + \sfcode`\.=\@m} + {\def\@noitemerr{\@warning{Empty `thebibliography' environment}}% + \endlist} + +%%% +%%% Command from report.cls, (c) LaTeX3 Project. +%%% +\renewcommand\listoftables{% + \if@twocolumn + \@restonecoltrue\onecolumn + \else + \@restonecolfalse + \fi + \chapter*{\listtablename + \@mkboth{\uppercase{\listtablename}}{\uppercase{\listtablename}}}% + \addcontentsline{toc}{chapter}{\listtablename} + \@starttoc{lot}% + \if@restonecol\twocolumn\fi + } +\renewcommand\listoffigures{% + \if@twocolumn + \@restonecoltrue\onecolumn + \else + \@restonecolfalse + \fi + \chapter*{\listfigurename + \@mkboth{\uppercase{\listfigurename}}% + {\uppercase{\listfigurename}}}% + \addcontentsline{toc}{chapter}{\listfigurename} + \@starttoc{lof}% + \if@restonecol\twocolumn\fi + } +\renewcommand\tableofcontents{% + \if@twocolumn + \@restonecoltrue\onecolumn + \else + \@restonecolfalse + \fi + \chapter*{\contentsname + \@mkboth{\uppercase{\contentsname}}{\uppercase{\contentsname}}}% + \@starttoc{toc}% + \if@restonecol\twocolumn\fi + } + +%%% +%%% Command to print draft version of the thesis. +%%% +\newcommand{\thesisdraft}{ + \setlength{\topmargin}{0in} + \setlength{\headheight}{0.2in} + \setlength{\headsep}{0.25in} + \renewcommand{\@textpagestyle}{myheadings} + \def\ps@myheadings{% + \let\@oddfoot\@empty\let\@evenfoot\@empty + \def\@oddhead{\textsl{Draft of \timestamp}\hfil\thepage}% + \let\@mkboth\@gobbletwo + \let\chaptermark\@gobble + \let\sectionmark\@gobble} + } + +%%% +%%% Code to compute current timestamp. Some parts by Martin Minow. +%%% +\newcount\hour \newcount\minute +\hour=\time \divide \hour by 60 +\minute=\time +\loop \ifnum \minute > 59 \advance \minute by -60 \repeat +\def\thesistime{\ifnum \hour<13 \number\hour:% + \ifnum \minute<10 0\fi + \number\minute + \ifnum \hour<12 \ am\else \ pm\fi + \else \advance \hour by -12 \number\hour:% + \ifnum \minute<10 0\fi + \number\minute \ pm\fi} + +\def\thesisdate{\ifcase\month\or +January\or February\or March\or April\or May\or June\or +July\or August\or September\or October\or November\or December\fi +\space\number\day, \number\year} + +\newcount\dow +\newcount\leap +\newcount\x +\newcount\y + +%leap = year + (month - 14)/12 +\leap=\month \advance\leap by -14 \divide\leap by 12 + \advance\leap by \year + +%dow = (13 * (month + 10 - (month + 10)/13*12) - 1)/5 +\dow=\month \advance\dow by 10 + \y=\dow \divide\y by 13 \multiply\y by 12 + \advance\dow by -\y \multiply\dow by 13 \advance\dow by -1 \divide\dow by 5 + +%dow += day + 77 + 5 * (leap % 100)/4 +\advance\dow by \day \advance\dow by 77 + \x=\leap \y=\x \divide\y by 100 \multiply\y by 100 \advance\x by -\y + \multiply\x by 5 \divide\x by 4 \advance\dow by \x + +%dow += leap / 400 +\x=\leap \divide\x by 400 \advance\dow by \x + +%dow -= leap / 100 * 2; +%dow = (dow % 7) +\x=\leap \divide\x by 100 \multiply\x by 2 \advance\dow by -\x + \x=\dow \divide\x by 7 \multiply\x by 7 \advance\dow by -\x + +\def\thesisdayofweek{\ifcase\dow +Sunday\or Monday\or Tuesday\or +Wednesday\or Thursday\or Friday\or Saturday\fi} + +\def\timestamp{\thesistime, \thesisdayofweek, \thesisdate} + +%%% +%%% Commands for spacing. Some parts from spacing.sty by Stephen Page. +%%% +\ifx\undefined\selectfont +\def\@setsize#1#2#3#4{\@nomath#1 + \let\@currsize#1\baselineskip + #2\baselineskip\baselinestretch\baselineskip + \parskip\baselinestretch\parskip + \setbox\strutbox\hbox{\vrule height.7\baselineskip + depth.3\baselineskip width\z@} + \normalbaselineskip\baselineskip#3#4} +\else +\def\@newbaseline{% + \ifx\undefined\setnew@baselineskip + \baselineskip\f@baselineskip\relax + \else + \setnew@baselineskip + \fi + \baselineskip\baselinestretch\baselineskip + \setbox\strutbox\hbox{\vrule\@height.7\baselineskip + \@depth.3\baselineskip \@width\z@}% + \normalbaselineskip\baselineskip} +\fi +%%% +%%% Reset baselinestretch within footnotes and floats. Originally stolen +%%% from Stanford thesis style. +%%% +\def\@xfloat#1[#2]{\ifhmode \@bsphack\@floatpenalty -\@Mii\else + \@floatpenalty-\@Miii\fi\def\@captype{#1}\ifinner + \@parmoderr\@floatpenalty\z@ + \else\@next\@currbox\@freelist{\@tempcnta\csname ftype@#1\endcsname + \multiply\@tempcnta\@xxxii\advance\@tempcnta\sixt@@n + \@tfor \@tempa :=#2\do + {\if\@tempa h\advance\@tempcnta \@ne\fi + \if\@tempa t\advance\@tempcnta \tw@\fi + \if\@tempa b\advance\@tempcnta 4\relax\fi + \if\@tempa p\advance\@tempcnta 8\relax\fi + }\global\count\@currbox\@tempcnta}\@fltovf\fi + \global\setbox\@currbox\vbox\bgroup + \def\baselinestretch{1} + \ifx\undefined\selectfont + \small\normalsize + \else + \@newbaseline + \fi + \boxmaxdepth\z@ + \hsize\columnwidth \@parboxrestore} +\long\def\@footnotetext#1{\insert\footins{\def\baselinestretch{1}\footnotesize + \interlinepenalty\interfootnotelinepenalty + \splittopskip\footnotesep + \splitmaxdepth \dp\strutbox \floatingpenalty \@MM + \hsize\columnwidth \@parboxrestore + \edef\@currentlabel{\csname p@footnote\endcsname\@thefnmark}\@makefntext + {\rule{\z@}{\footnotesep}\ignorespaces + #1\strut}}} +%%% +%%% Stolen from MIT. +%%% +\def\spacing#1{\par% + \begingroup + \def\baselinestretch{#1} + \ifx\undefined\selectfont + \ifx\@currsize\normalsize\@normalsize\else\@currsize\fi + \else + \@newbaseline + \fi} +\def\endspacing{\par + \vskip \parskip + \vskip \baselineskip + \endgroup + \vskip -\parskip + \vskip -\baselineskip} + |