rapport.tex

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\usepackage{translator}
\usepackage{graphicx}
\usepackage[svgnames]{xcolor}
\usepackage{lscape}
\usepackage{tablefootnote}
\usepackage{hyperref}
\usepackage{tikz-uml}
\usetikzlibrary {arrows.meta}
\hypersetup{
	colorlinks=true,
	linkcolor=blue,
	filecolor=blue,
	citecolor = black,      
	urlcolor=blue,
	pdftitle={Compte-rendu intermédiaire de stage}
}

\title{Polymalys-py \\ \small Rapport technique}
\author{FLOREA Andrei}

\begin{document}
	\maketitle

	\tableofcontents
	
	\listoffigures

	\section{Vue globale de Polymalys-py}
	
	\section{Polymarp: Domaine abstrait}
	
	Le domaine abstrait est composé d'un domaine numérique relationnel, d'un \textit{mapping} de registres et d'un \textit{mapping} d'addresses.
	
	\subsection{Domaine numérique relationel}
	
	L'objectif de ce module est d'avoir une interface modulaire avec les librairies de manipulation de domaines numériques. Pour ce faire, on définit des classes abstraites dans \verb*|numerical.py|, pour lesquelles on créera des implémentation pour chaque librairie souhaitée.
	
	\begin{figure}[h]
		\centering
		\resizebox{\textwidth}{!}{
			\begin{tikzpicture}%[show background grid]
				\begin{umlpackage}{numerical}
					\umlclass[type=abstract]{PolyConstant}{
						+ value: int
					}{
						\umlvirt{+ to\_expr(): PolyExpr}
					}
				
					\umlclass[type=abstract, y = -3]{PolyVar}{
						+ ident
					}{
						\umlvirt{+ to\_expr(): PolyExpr}
					}
					\umlclass[type=abstract, y = -6]{PolyExpr}{
					}{
						\umlvirt{+ get\_vars(): Set[PolyVar]}
					}
					\umlclass[type=abstract, y=-9]{PolyExprHelper}{
						+ op: Operations \\
						+ left: PolyExprHelper, PolyVar, PolyConstant \\
						+ right: PolyExprHelper, PolyVar, PolyConstant
					}{
						+ get\_vars(): Set[PolyVar]
					}
					\umlclass[type=enumeration, y=-9, x=-7]{Operations}{
						CONST \\ VAR \\ ADD \\ SUB \\ NEG \\ MUL \\ AND
					}{}
				
					\umlinherit{PolyExprHelper}{PolyExpr}
					\umlnest{PolyExprHelper}{Operations}
					
					\umlclass[type=abstract, y=-16]{PolyConstraint}{}{}
					\umlclass[type=abstract, y=-13]{PolyConstraintHelper}{
						+ expr: PolyExpr \\
						+ op: Operations2 \\
						+ const: PolyConstant
					}{}
					\umlclass[type=enumeration, y=-13, x=-7]{Operations2}{
						EQ \\ LEQ \\ GEQ
					}{}
					
					\umlinherit{PolyConstraintHelper}{PolyConstraint}
					\umlnest{PolyConstraintHelper}{Operations2}
					\umluniassoc[mult2=1]{PolyConstraintHelper}{PolyExprHelper}
					
					\umlclass[type=abstract, x=-2, y=-22]{PolyNumericalDomain}{}{
						\umlvirt{\umlstatic{+ bottom(): PolyNumericalDomain}} \\
						\umlvirt{+ add\_constraint(constraint: PolyConstraint)} \\
						\umlvirt{+ is\_top(): bool} \\
						\umlvirt{+ is\_bottom(): bool} \\
						\umlvirt{+ maximize(expression): int or None} \\
						\umlvirt{+ minimize(expression): int or None} \\
						\umlvirt{+ join(other): PolyNumericalDomain} \\
						\umlvirt{+ widening(other): PolyNumericalDomain} \\
						\umlvirt{+ intersection(other): PolyNumericalDomain} \\
						\umlvirt{+ substitute(old, new): PolyNumericalDomain} \\
						\umlvirt{+ projection(var\_set): PolyNumericalDomain} \\
						\umlvirt{+ includes(other: PolyNumericalDomain): bool} \\
						+ get\_vars(): Set[PolyVar]
					}
					\umlclass[type=abstract, x=-2, y=-28]{PolyNumericalWrapper}{}{
						\umlvirt{+ new\_var(value: int): PolyVar} \\
						+ fold(repl1, repl2, var): PolyNumericalWrapper \\
						+ expand(repl, var1, var2): PolyNumericalWrapper \\
						\umlvirt{\umlstatic{+ match\_var(var1, var2, dom1, dom2): bool}} \\
						\umlvirt{+ copy(p, var\_set): PolyNumericalWrapper} \\
						\umlvirt{+ bac(var: PolyVar, avatar): PolyNumericalWrapper}
					}
					
					\umluniassoc[geometry=-|, mult2=*, pos2=1.8]{PolyNumericalDomain}{PolyConstraint}
					\umlinherit{PolyNumericalWrapper}{PolyNumericalDomain}
				\end{umlpackage}

				\begin{umlpackage}[x=8]{apron}
					\umlclass{ApronConstant}{}{
						+ to\_expr()
					}
					\umlclass[y=-3]{ApronVar}{
					}{
						+ to\_expr()
					}
					\umlclass[y = -9, x=2]{ApronExpr}{}{}
					
					\umlunicompo[geometry=|-]{ApronExpr}{ApronVar}
					\umlunicompo[geometry=|-]{ApronExpr}{ApronConstant}
					
					\umlclass[y=-13]{ApronConstraint}{}{}
					
					\umlinherit{ApronConstraint}{PolyConstraintHelper}
					
					\umlclass[type=abstract, y=-22]{ApronNumericalDomain}{
						+ env: Set[PolyVar]
					}{
						+ get\_vars(): Set[PolyVar] \\
						+ add\_constraint(cons) \\
						+ is\_top(): bool \\
						+ is\_bottom(): bool \\
						+ maximize(expression): int or None \\
						+ minimize(expression): int or None \\	
						+ join(other) \\
						+ wideining(other) \\
						+ intersection(other) \\
						+ substitute(old, new) \\
						+ projection(var\_set) \\
						+ includes(other) \\
						+ equals(other): bool
					}
					\umlclass[type=abstract, y=-28]{ApronNumericalWrapper}{}{
						+ new\_var(ident: int): ApronVar \\
						- npiv(): Set[PolyVar] \\
						- linexpr(var, basis): List[ApronConstant] \\
						\umlstatic{- \_get\_basis(dom1, dom2): Set[PolyVar]} \\
						\umlstatic{+ match\_var(var1, var2, dom1, dom2)} \\
						+ copy(p, var\_set) \\
						+ bac(var, avatar)
					}
					
					\umlinherit{ApronNumericalDomain}{PolyNumericalDomain}
					\umlinherit{ApronNumericalWrapper}{ApronNumericalDomain}
					\umlinherit{ApronNumericalWrapper}{PolyNumericalWrapper}
					
					\umlclass[type=abstract, x=7, y=-22]{ApronPoly}{}{
						\umlstatic{+ bottom()}
					}
					\umlclass[x=7, y=-28]{ApronPolyWrapper}{}{}
					
					\umlinherit{ApronPoly}{ApronNumericalDomain}
					\umlinherit{ApronPolyWrapper}{ApronPoly}
					\umlinherit{ApronPolyWrapper}{ApronNumericalWrapper}
				\end{umlpackage}
				
				\umlinherit{ApronConstant}{PolyConstant}
				\umlinherit{ApronVar}{PolyVar}
				\umlinherit{ApronExpr}{PolyExprHelper}

			\end{tikzpicture}
			}
		\caption[Schéma UML de l'interface mathématique]{Hiérarchie des classes de l'interface mathématique et de son implémentation utilisant APRON}
	\end{figure}

	\subsection{Mappings}
	
	Les \textit{mappings} sont définis dans \verb*|mappings.py|. Ils implémentent le \textit{mapping} de registres \( R \mapsto \mathcal{V}\) et le \textit{mapping} d'adresses \( \left(\mathcal{V} \times \mathbb{N} \times \mathcal{V} \right) \mapsto \mathcal{V} \cup \left(\mathcal{V} \times \mathcal{V} \right) \)
	
	\begin{figure}[h]
		\centering
		\resizebox{\textwidth}{!}{
			\begin{tikzpicture}%[show background grid]
				\umlsimpleclass[x=8, y=-10]{PolyVar}
				
				\begin{umlpackage}{mappings}
					\umlclass[type=interface, x=-2]{MappingMixin}{}{
						+ \_\_contains\_\_(other): bool
					}
					
					\umlclass[x=-4, y=-4]{RegisterMapping}{}{
						+ replace(old, new)
					}
					\umlclass[y=-4]{LoopMapping}{}{
						+ replace(old, new)
					}
					\umlclass[x=8, y=-5]{Avatar}{}{}
					\umlclass[x=0, y = -7]{SLP}{
						+ base: PolyVar \\
						+ step: int or None \\
						+ count: PolyVar
					}{
						+ last(): PolyExpr
					}

					\umluniassoc[mult2=2, pos2=0.9]{Avatar}{PolyVar}
					\umlassoc[geometry=-|-, weight=0.8, name=assoc]{SLP}{Avatar}
					\umlassoc[geometry=-|-, weight=0.8]{SLP}{PolyVar}
					\umlassocclass[x=4, y=-4]{AddressMapping}{assoc-1}{}{
						+ replace(old, new)
					}
				
					\umlsimpleclass[x=2.2, text=DarkGreen]{dict}
					
					\umlinherit{RegisterMapping}{dict}
					\umlinherit{LoopMapping}{dict}
					\umlinherit{AddressMapping}{dict}
					\umlimpl{RegisterMapping}{MappingMixin}
					\umlimpl{LoopMapping}{MappingMixin}
					\umlimpl{AddressMapping}{MappingMixin}
				\end{umlpackage}
			\end{tikzpicture}
		}
	\caption[Schéma UML des mappings]{Hiérarchies des classes de mappings}
	\end{figure}
\end{document}