From 0a84502bbd7812c14e59ee1066817e783202acd4 Mon Sep 17 00:00:00 2001 From: Florent Madelaine Date: Thu, 15 Feb 2024 00:00:17 +0100 Subject: [PATCH] =?UTF-8?q?reorganisation=20par=20cours=20dans=20sous-r?= =?UTF-8?q?=C3=A9pertoires?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 1-ComputationAndData/1ComputationAndData.md | 18 + 1-ComputationAndData/2ComputationAndData.md | 362 + 1-ComputationAndData/3ComputationAndData.md | 127 + ...nsExosCircuitBool2022-10-03-Note-09-25.pdf | Bin 0 -> 65932 bytes 1-ComputationAndData/4ComputationAndData.md | 260 + 1-ComputationAndData/5ComputationAndData.md | 361 + .../5ComputationAndData/5CM-MVaP.pdf | Bin 0 -> 361414 bytes .../5ComputationAndData/6CM-Func.pdf | Bin 0 -> 270810 bytes .../5ComputationAndData/6TD.html | 254 + 1-ComputationAndData/JFLAP/DFA2as.jff | 69 + 1-ComputationAndData/JFLAP/DFA2as.jff.jpg | Bin 0 -> 16962 bytes .../JFLAP/DFA2asconsecutifs.jff | 62 + 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2-InformationTheory/HuffmanGruffaloNightmare.tex create mode 100644 Brevets/US5363098.pdf diff --git a/1-ComputationAndData/1ComputationAndData.md b/1-ComputationAndData/1ComputationAndData.md new file mode 100644 index 0000000..9684e15 --- /dev/null +++ b/1-ComputationAndData/1ComputationAndData.md @@ -0,0 +1,18 @@ +Cours de Pierre. + +# Système de fichier, Codage et découverte du terminal. I/II + +## Terminal à la linux + +Installation Ubuntu sous windows (WSL, ubuntu via couche machine virtuelle hyperV). +https://en.wikipedia.org/wiki/Windows_Subsystem_for_Linux + +Autres étudiants avec Mac et un shell ("BSD"?) + +## Arborescence fichier +répertoire (noeuds internes) vs +Fichier (feuilles) + +## Codage +Codage, en particulier binaire et ASCII. +Exemple avec les salles de la fac de droit en binaire. diff --git a/1-ComputationAndData/2ComputationAndData.md b/1-ComputationAndData/2ComputationAndData.md new file mode 100644 index 0000000..8418ae6 --- /dev/null +++ b/1-ComputationAndData/2ComputationAndData.md @@ -0,0 +1,362 @@ +Cours de Florent. + +# Système de fichier, Codage et découverte du terminal II/II + +## Éditeur et fichier texte + +Qu'on programme ou qu'on prépare un mail, il faut éditer un fichier texte. +Ce texte va transiter sur le réseau ou être stocké dans un fichier selon un code bien choisi. + +Le code ASCII est inspiré de code pour le télégraphe, comme le code Baudot (1870) : c'est un standard américain initialement pour teleprinter (Bell lab 1961). Il comporte en plus des codes pour des caractères imprimables (chiffres, lettres minuscules et majuscules latines, etc) de nombreux codes pour des opérations spécifiques au mécanisme de communication d'un teleprinter maintenant obsolètes. + +[Code Baudot](https://en.wikipedia.org/wiki/Baudot_code) +[ASCII](https://en.wikipedia.org/wiki/ASCII) + +### digression +L'ordre des charactères induit par la valeur de leur code ASCII est utilisé pour trier du texte ASCII. +> ASCII-code order is also called ASCIIbetical order + +Trier, stocker, indexer et chercher de l'information sont des tâches essentielles qu'on automatise dès la fin du XIXe siècle. + +Pour automatiser le recensement américain (le census de 1880 a demandé 8 ans...), Herman Hollerith met au point une machine electro-mécanique manipulant des cartes perforées et flottant dans des bains de mercure. Son entreprise et 4 autres forment un conglomérat qui deviendra IBM en 1924. + +[Machines à tabuler](https://en.wikipedia.org/wiki/Tabulating_machine) + +### Et si notre alphabet est plus grand? +Pour tester un clavier, ou exhiber une fonte, on peut en anglais écrire. +> The quick brown fox jumps over the lazy dog + +En français, on pourra utiliser +> Dès Noël, où un zéphyr haï me vêt de glaçons würmiens, je dîne d’exquis rôtis de bœuf au kir, à l’aÿ d’âge mûr, &cætera. + +[tester un clavier](https://fr.wikipedia.org/wiki/The_quick_brown_fox_jumps_over_the_lazy_dog) + +De nombreux pays vont donc étendre/changer le code ASCII pour y introduire leurs symboles (par exemple les accents en français) avec un soucis d'internationalisation. +En effet, le code ascii ne peut pas facilement accommoder tous les alphabets même si on se restreint aux alphabets latins ou grecs car nous avons seulement 7 bits soit 2^7=128 codes. +On ajoute donc un bit de plus pour permettre d'échanger des données textuelles "internationales". + +[ISO/IEC 8859](https://en.wikipedia.org/wiki/ISO/IEC_8859) + +Il y a en fait 15 variantes selon les besoins de langues avec des besoins proches. +Un des plus connu, adapté pour le français, est la version 1 + +[latin-1](https://en.wikipedia.org/wiki/ISO/IEC_8859-1) + +Ces systèmes restent trop limités car ni vraiment adapté pour de la typographie, ni applicable pour tous les alphabets en usage. +Depuis 2008, le standard est l'UTF-8 (sur le web initialement). +C'est une abbréviation de + +> Unicode Transformation Format – 8-bit + +où Unicode signifie + +> Universal Coded Character Set + +Une idée intéressante de ce code est qu'on va utiliser un **nombre variable de bytes** (entre 1 et 4). +Typiquement ce qu'on codait en ASCII prendra 1 byte, toutes les langues couvertes par la norme ISO 8859 pourront coder leurs caractères avec au plus 2 bytes, les caractères fréquents de CJK avec 3 bytes et le reste avec 4 permet de coder des symboles moins fréquents (de math, des emoji etc). + +[UTF-8](https://en.wikipedia.org/wiki/UTF-8) + +## Discussion au tableau de UTF-8 +Calcul du nombre de symboles qu'on peut coder. +Perte de place pour les symboles codés par 1 bloc, 2 blocs, 3 blocs, 4 blocs. + +évocation du changement de pratique autres systèmes de codage vs UTF-8 (graphiques sur wikipedia). + +### Détails techniques de WSL + +Le système de fichier linux WSL est monté dans le système windows. +On peut a priori transférer des fichiers vers windows mais pas l'inverse. + +Linux ne permet a priori pas d'accéder au système de fichier windows. + +Attention. si vous réinstallez WSL vous allez écraser votre home et tout le travail fait sous linux. + +[Où est le home linux sous WSL](https://superuser.com/questions/1185033/what-is-the-home-directory-on-windows-subsystem-for-linux) + +Vous pouvez lancer dans l'explorateur de fichier windows le home linux en saisissant dans votre terminal linux la commande suivante. + +```bash +explorer.exe . +``` + +Si vous avez installé WSL sans créer de compte utilisateur, vous êtes l'administrateur système linux, connu sous le nom de root. L'invite du terminal indique un dièse \# + +Pas de danger vous ne pouvez rien casser dans le système windows. + +Par contre par défaut vous êtes dans ... system32 le répertoire système de windows. +Le système winos ne vous laisse pas écrire de fichier à cet endroit. +Il faut vous placer ailleur, par exemple en saisissant la commande suivante. + + +```bash +cd +``` + + +### explication au tableau de la navigation + + _ .. pour revenir en arrière + _ . pour là où on est + _ ~ pour votre home linux + _ / pour la racine du système de fichier linux. + +Question ontologique de l'oeuf ou la poule: qui est le .. de / ? + + + +### exercice + +1. Ouvrez un terminal. +1. Créer un répertoire folderA (commande mkdir). +1. Placez vous dans ce répertoire (commande cd, pour change directory). +1. Créer un fichier vide grapevine.txt (commande touch). +1. Ouvrez le avec un éditeur de texte (par exemple gedit ou emacs voir nano ou vim). +1. Copiez dans ce fichier un texte de votre choix avec de nombreux caractères qui ne sont pas codable en ascii. +1. Sauvez le. +1. Envoyez un mail avec en pièce jointe ce fichier à votre voisine ou voisin de table. +1. Ouvrez le fichier de votre voisin, sauvez le sous le nom grapevine2.txt et testez si vous pouvez lire le fichier correctement avec votre éditeur. + +Parfois votre éditeur ne détectera pas correctement et automatiquement le codage. +Vous pouvez dans certains cas forcer ce codage (e.g. dans emacs Options-Multilingual environment). + +### exercice +la commande suivante permet de revenir dans le répertoire parent. +```bash +cd .. +``` + +Complétez votre arborescence pour arriver à celle-ci. +``` +folderA + grapevine.txt + grapevine2.txt + folderAA + toto.txt + titi.txt +folderB + toto.txt +folderC + tata.txt +``` + +NB. vous pouvez le faire sans utiliser un éditeur ni un logiciel de naviguation de fichier graphique. Seulement en ligne de commande. + +La commande + +```bash +man +``` +permet d'avoir accès au manuel. + +testez par exemple + +```bash +man ls +``` +lisez cette documentation pour chercher l'option qui permet un affichage récursif. + + +**Correction Indicative** + +```bash +mkdir folderA +mkdir folderB +mkdir folderC +cd folderA/ +touch grapevine.txt +mkdir folderAA +cd folderAA/ +touch toto.txt +touch titi.txt +cd ../ +cd .. +cd folderB +touch toto.txt +cd .. +cd folderC/ +touch tata.txt +cd .. +ls -R +history | cut -c 8- +``` + +NB. la dernière commande permet d'enlever les numéros de l'historique. + Le | (on dit pipe) permet d'envoyer le résultat de history dans la commande cut. + La commande cut avec ces options permet d'enlever le numéro de l'historique. + C'est d'ailleurs avec cette commande que j'ai fabriqué la correction indicative ci-dessus. + +### exercice + +Dans un second temps vous pouvez créer un lien / ou créer un raccourci avec votre système de naviguation de fichier graphique (probablement nautilus sous ubuntu) de grapevine.txt dans le répertoire folderC. + +Vous pouvez aussi vous placer vous dans folderC et écrire en ligne de commande +```bash +ln -s ../folderA/grapevine.txt +``` + +Selon votre configuration en revenant en arrière et en faisant à nouveau un ls avec l'option permettant l'affichage récursif vous allez voir le nom du grapevin.txt sous une couleur différente de l'original. + +Nous allons d'abord chercher dans le manuel ce que fait l'option -l de ls +```bash +man ls +``` +puis nous allons tester sur notre lien en faisant +```bash +ls -l +``` + +Je n'ai pas traité en cours les parties ci-dessous. +Vous pouvez ouvrir chaque section en cliquant sur le triangle. + +
Zoom sur les briques élémentaires du système de fichier +

+ + + +### exercice + +L'arbre de notre système de fichier est fabriqué à partir de 2 éléments. + 1. une feuille de l'arbre = des données stockées à une certaine adresse dans la mémoire + 2. un noeud interne de l'arbre = des données stockées à une certaine adresse dans la mémoire qui associe un nom (de fichier ou de répertoire) à un élément de type 1. ou 2. identifiable par le système. En gros le fichier correspondant à un répertoire est une sorte de *livret de famille*. + +En pratique, le système utilise une structure de donnée particulière à la fois pour les fichiers et les répertoires (puisqu'il s'agit dans les deux cas de fichiers) qui s'appelle un [inode](https://en.wikipedia.org/wiki/Inode). + + +En pratique vous pouvez utiliser l'option suivante pour affichier les numéros des inode. +```bash +ls -i +``` + +### exercice pour aller encore plus loin +Nous avons évoqué les liens symboliques qui sont des raccourcis. +Littéralement c'est juste un fichier texte un peu spécial qui contient comme données la chaîne de caractère du fichier vers lequel on pointe. + +Donc quand on a fait ci-dessus. +```bash +ln -s ../folderA/grapevine.txt +``` +On a fabriqué un fichier raccourci spécial qui contient essentiellement l'information +```bash +../folderA/grapevine.txt +``` +Si vous utilisez la même commande mais en omettant l'option -s vous êtes en train de définir un nouveau nom pour l'inode du fichier grapevine.txt + +Donc la métaphore de l'arbre n'est pas tout à fait correcte puisque par plusieurs chemins dans les répertoires il est possible d'atteindre le même fichier. + +La commande de suppression de fichier rm (pour remove) ne supprime pas vraiment l'inode, elle va juste effacer le nom du fichier (et la référence vers l'inode associé à ce nom) dans le répertoire. + +[Détails sur stackoverflow](https://stackoverflow.com/questions/185899/what-is-the-difference-between-a-symbolic-link-and-a-hard-link) + +NB. Je n'ai pas testé sous WSL puisque je n'ai pas windows. Il serait amusant de regarder ce qui arrive aux fichiers linux avec plusieurs noms quand on les regarde en vue détaillée dans l'explorateur de fichier de windows. A priori NTFS a une notion compatible + +

+
+ + +### Commandes utilisées jusqu'à présent +```bash +mkdir +cd +touch +ls +ln +``` + +
Manipuler du texte avec la commande tr +

+ +## Manipulation de fichier + +Pour simplifier un texte, par exemple pour l'indexer ou pour normaliser un nom dans une base de données il est fréquent qu'on bascule un mot en majuscule. +Nous allons travailler avec la commande tr qui permet de faire de tel changement caractère par caractère. +Par exemple ceci permet de transformer les minuscules en majuscule. + +```bash +tr '[a-z]' '[A-Z]' +``` +La commande tr attend un flux textuel en entrée et transmet un flux textuel en sortie. +On parle de filtre pour ce genre de commande. +On ne peut pas a priori lui passer de fichier en paramètre. +Il faut *rediriger* le contenu du fichier vers la commande. + +```bash +tr '[a-z]' '[A-Z]' < grapevine.txt +``` +Par défaut le résultat apparaît à l'écran. + +On peut rediriger ce résultat dans un fichier en utilisant > + +```bash +tr '[a-z]' '[A-Z]' < grapevine.txt > grapevineUp.txt +``` +Vous pouvez consulter le contenu d'un fichier directement en utilisant la commande more +```bash +more grapevineUp.txt +``` +Attention toutefois avec > car le contenu du fichier si il existe est écrasé. + +Il existe une variante utile >> qui écrit à la fin du fichier. +C'est utilisé par exemple pour créer des fichiers de log. + +### exercice + +Redirigez le résultat de la commande history dans un fichier de sauveguarde myFirstDayWithTheCommandLine.txt. + + +```bash +history > myFirstDayWithTheCommandLine.txt +``` +Vous pouvez consulter ce fichier en utilisant more. + +Vous pouvez voir le haut du fichier en faisant head, la fin du fichier en faisant tail. + +## Code de césar + +Cherchez à appliquer le code de césar (rot13) à un fichier contenant du texte non accentué (i.e. ascii historique). + +Envoyez le par mail à votre voisin. + +Ce dernier doit le décoder. + +```bash +tr '[A-Z]' '[N-ZA-M]' +``` +

+
+ + +## droit d'accès + +chmod + +Il s'agit de la commande permettant de changer les droits pour un fichier. + + +## Bonus : jouons avec le pipe + +1. installer fortune +1. installer cowsay + +```bash +echo moooooo | cowsay +``` + + +```bash +fortune +``` + + +```bash +fortune | cowsay +``` + +## Bonus : sl + +1. installer sl (dans le terminal de votre collègue quand il va boire un café) +1. demandez lui de vous montrer comment ls fonctionne très rapidement (il va probalement écrire sl au lieu de ls à un moment) + + + + diff --git a/1-ComputationAndData/3ComputationAndData.md b/1-ComputationAndData/3ComputationAndData.md new file mode 100644 index 0000000..e221989 --- /dev/null +++ b/1-ComputationAndData/3ComputationAndData.md @@ -0,0 +1,127 @@ +Cours de Florent. + +# Calculer en théorie et en pratique I/III + +Dans la prochaine séquence de cours, nous allons tenter de répondre à la question suivante. + +C'est quoi un ordinateur? + +Cette question s'apparente à celle que ce sont posés philosophes et mathématiciens de Leibnitz à Turing en passant par Hilbert. + +Qu'est-ce qu'une question à laquelle on peut répondre de manière mécanique par un calcul? + +Nous allons explorer rapidement ce sujet en évoquant à la fois des modèles théoriques et des explication sur l'architecture matérielle et le fonctionnement d'ordinateurs modernes. + +## Calcul Matériel. + +Initialement, les "computer" sont des humains, qui s'aident de divers mécanisme pour faire des calculs rapidement en essayant de faire le moins d'erreurs possibles, par exemple avec un boulier ou des cordes nouées. + +Les premières machines à calculer sont mécaniques et peuvent être discrètes (nombre fini de position avec par exemple des roues crantées) ou continues (position continue sur un astrolabe ou une table à tracer pour calculer des intégrales). + +Les machines modernes possèdent différents composants electroniques et ce sont les transistors qui permettent de passer d'une information analogique/continue + +> quelle est la puissance du courant? + +à une information discrète, oui ou non, qu'on peut interpréter comme 0 ou 1. + +> est-ce-que le courant dépasse un certain seuil? + +On peut à l'aide de quelques composants de base faire des calculs sur ces valeurs 0 ou 1. On parle alors de calcul Booléen (du nom du logicien Boole). + +### circuit booléen +consiste en +1. des entrées contenant des valeurs booléennes. +1. des portes logiques permettant de calculer + * le ET binaire (&) + * le OU binaire (v) + * la négation NON unaire (-) +1. des "cables" pour relier ces portes +1. des sorties correspondant à la sortie du calcul. + +Au tableau +* table du ET +* table du OU +* table du NON + +### exercices + +1. Écrire la table de Non de x ou y. +1. Décrire un circuit permettant de tester si deux entrée x et y sont égales. +Le circuit doit renvoyer 1 si c'est le cas et 0 sinon. +NB. on peut noter cette opération <-> ou +2. Même question pour le circuit qui permet de calculer le XOR (Ou eXclusif). +3. Même question pour le circuit permettant de calculer la majorité de trois arguments + +### Digression : le schéma de chiffrement de Vernam +Il s'agit d'un schéma très simple et incassable à moins de connaître la clé secrète. +L'inconvénient est qu'il faut fabriquer et partager avec son destinataire une clé secrète aussi longue que le message. On parle aussi de "one time pad" en anglais. + +Pendant la seconde guerre mondiale, à Bletchley Park, des opératrices fabriquaient de telles clés mais en quantité trop réduite. Une tentative de mécanisation pour pallier à ce soucis a permis de générer des clés rapidement mais qui avaient une différence avec les véritables clés. + + +> + + "Enoch, why are you . . . here?" + + "Oh. I am here, in a larger sense, because Mrs. Tenney, the vicar’s wife, has become sloppy, and forgotten to close her eyes when she takes the balls out of the bingo machine." + +Neal Stephenson. Cryptonomicon. + +[Discussion sur stackexchange](https://crypto.stackexchange.com/questions/25214/has-human-generated-entropy-ever-been-a-real-problem) + + +Nous allons mettre en oeuvre ce chiffrement. +1. Tout d'abord le message à chiffrer M, qu'on suppose encodable en ASCII est transformé en un séquence de 0 et de 1 qu'on note B. +1. La clé secrète S est une série de 0 et de 1 de même longueur. +1. On additionne "modulo 2" B à S pour obtenir le message chiffré C (c'est le XOR de tout à l'heure). +1. On transmet le message chiffré C au destinataire. +1. La destinataire reçoit C. +1. Pour décoder, elle procède de même mais à l'envers. + * ajout de S à C + * découpage en bloc de 7 bits + * décodage ASCII + +[page du code ASCII](https://fr.wikipedia.org/wiki/American_Standard_Code_for_Information_Interchange) + +NB. pour faire plus proche de la réalité, on préfixe le code ASCII d'un 0 pour obtenir un octet. + +### exercice +Nous allons mettre en oeuvre ce chiffrement pour le mot BINGO. +Fabriquez au préalable une clé de la taille adapté +(vous pouvez par exemple tirer à pile ou face successivement). + +Pour simplifier, vous pouvez le faire avec OK. + +Réfléchissez à une mise en oeuvre pratique sur papier. + +## Retour à nos circuits. + +Nous allons maintenant mettre en oeuvre des circuits pour faire des opérations arithmétiques. + + +1. Même question pour un circuit qui réalise une somme "modulo 2" + NB. c'est le chiffrement de Vernam. +1. Même question pour un circuit qui réalise une somme en binaire. + Pour ce second circuit on s'autorise une porte de duplication notée D qui prend en entrée x et a deux sorties valant toutes deux x. + +### Indication. +Pour rappel en binaire 1+1 vaut 10; 1+0 comme 0+1 valent 1; et, 0+0 vaut 0. + +**Exemple** +``` +0110 +0111 +==== +...1 +..01 retenue 1 +.101 retenue 1 +1101 Fin +``` +### Indication 2 +2 questions rhétoriques : + + * Comment faire la retenue? + * Comment calcule la somme dans la même colonne? + + + diff --git a/1-ComputationAndData/3ComputationAndDataCorrectionsExosCircuitBool2022-10-03-Note-09-25.pdf b/1-ComputationAndData/3ComputationAndDataCorrectionsExosCircuitBool2022-10-03-Note-09-25.pdf new file mode 100644 index 0000000000000000000000000000000000000000..35b5611257c5bbda5d9ef3e790ada89e60afaad7 GIT binary patch literal 65932 zcmdqIRZwKzwlxSOPT}r}yL;j84u!kBySux)7FM{syF=lHyL;i%eCOVC`u6`vbaeDX zKXgXMTsdV;*?T|i$T1d~f`}L$6FnO&S<^-JD=aIJ5ol*<3CqI+WRNkjHFGuxvVED9 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b/1-ComputationAndData/4ComputationAndData.md @@ -0,0 +1,260 @@ +Cours de Florent. + +# Calculer en théorie et en pratique II/III + +Dans cette séquence de cours, nous tentons de répondre à la question suivante. + +C'est quoi un ordinateur? + +Cette question s'apparente à celle que ce sont posés philosophes et mathématiciens de Leibnitz à Turing en passant par Hilbert. + +Qu'est-ce qu'une question à laquelle on peut répondre de manière mécanique par un calcul? + +Nous avons vu une approximation de calcul théorique basé sur le calcul booléen et des portes logiques qui sont implémentable avec des composants electroniques, permettant de réaliser divers opérations comme l'addition bit à bit (schéma de Vernam en cryptographie), la majorité ou encore l'addition avec retenue. + +Aujourd'hui nous poursuivons avec un modèle théorique, qui est celui de l'**automate fini**, un modèle assez restreint de machine. L'adjectif fini s'applique à la mémoire de la machine qui est finie. + +Nous verrons plus tard un modèle plus général avec une mémoire arbitrairement grande : la machine deTuring. + +## Le modèle d'automate fini. + +* La machine va lire en entrée un mot sur un alphabet A de taille finie (on peut par exemple imaginer qu'il s'agit d'un mot en binaire et l'alphabet A serait par exemple composé des symboles 0 et 1). +* La machine possède plusieurs états. Intuitivement, chaque état code pour ce qu'on stocke dans la mémoire finie de la machine. +* Certains états sont dit **acceptant**. +* Un état spécial est celui dans lequel la machine débute son calcul. C'est l'**état initial**. +* La machine va "manger" le mot d'entrée lettre par lettre et passe d'un état à l'autre selon ce que son **programme** lui dicte. +* Quand toutes les lettres sont lues, si l'état dans lequel la machine se trouve est acceptant, la machine répond OUI (elle **accepte** le mot) sinon elle répond NON (elle **rejette** le mot). +* L'ensemble des mots sur l'alphabet A qui sont acceptés par la machine forme le *langage reconnu par l'automate*. + +### Le programme de l'automate. +On peut l'écrire dans un tableur, sous forme d'une succession fini de lignes avec trois colonnes. +La première colonne est l'état actuel, la seconde colonne est la lettre lue, la troisième colonne est le nouvel état. + +Pour un état donné q et une lettre lue x, l'automate va se placer dans un état donné q' (il est possible que q et q' soit le même état). + +Si le programme est incomplet et que le tableur n'explique pas comment faire, on arrête le calcul et on rejette le mot. + +Si le tableur n'est pas ambigu et que on n'a jamais deux lignes indiquant pour la même paire de lettre lue et d'état un nouvel état différent, on dit que l'automate est **déterministe**. + +Sinon l'automate n'est pas déterministe -- on dit aussi **non-déterministe** -- et on considère que la machine peut choisir une action du tableur parmi celles qui sont listées. + +Pour un automate non déterministe, on considère qu'un mot est accepté si il existe un calcul qui accepte. + +Analogie : vous cherchez à sortir d'un labyrinthe, il y a de nombreux chemins possibles. Si il en existe un vers la sortie alors vous pouvez gagner au jeu du labyrinthe. + +## Exemples avec JFLAP. + +JFLAP est un logiciel de simulation de machines théoriques qui permet de définir, manipuler, exécuter et transformer des machines. En pratique c'est une archive jar. + +Une archive jar est un programme codé dans le langage java que vous pouvez exécuter. +L'archive se compose de divers fichiers, dont un fichier principal, des librairies etc. + +Pour utiliser le logiciel, vous devez commencer par installer java. +Suivez les recommandations de votre système d'exploitation. + +Ensuite, il vous suffit souvent de double-cliquer sur l'archive jar. + +Vous pouvez aussi en ligne de commande sous linux écrire. + +```bash +java -jar +``` +Sur les machines virtuelles, + +### Prise en main de JFlap. + +1. Lancez JFLAP et ouvrez [l'automate sauvegardé ici](https://www.lacl.fr/fmadelaine/Download/M1Droit/Automates/TP2NDA.jff) +2. Allez dans le menu *Input* et choisissez *Step by State*. Entrez le mot **babb** et observez la simulation des exécutions parallèles étape par étape en appuyant sur *step*. +3. Testez ensuite avec le mot **baaa**. +4. Relancez les tests ci-dessus. Cette fois essayez les autres + options. + * *Reset* permet de revenir au début du calcul + * *Trace* après sélection en bas d'une exécution permet + de montrer cette exécution depuis le début. + * *Remove* élimine l'exécution sélectionnée + * *Freeze*/*Thaw* permet de mettre en pause ou de + reprendre une exécution (on perd la synchronisation) +5. Vous pouvez aussi tester sans les étapes avec *Fast Run* + voir plusieurs entrées en même temps avec + *Multiple Run* (tous les deux dans le menu *Input*). + Faites le par exemple pour les deux mots précédents. +6. Pour information, *Step with closure* fait la même chose + que *step by State* sauf pour les automates ayant des + transitions avec le mot-vide (mais on ne les considère pas dans + ce cours). + +### Hello World +Votre but est de créer l'automate dessiné ci-dessous. + + ![images/HelloWorldAutomate.jpg] + +1. Cliquez sur *File* puis *New*. +2. JFLAP permet de gérer différents modèles de calcul. Nous allons + nous en tenir aux automates finis. Cliquez sur *Finite Automaton*. + Vous avez accès à une nouvelle fenêtre en mode éditeur. + * Cliquez sur le petit cercle avec un q à l'intérieur, puis sur + le canevas pour ajouter des états. + * Les deux derniers boutons permettent de faire du undo/redo. + * La flèche fine permet d'ajouter une transition entre 1 ou 2 + états (ne pas oublier de mettre une lettre). + * La flèche plus épaisse à gauche permet de sélectionner, + déplacer, éditer les propriétés des différents éléments (par + exemple de faire un état initial). + * La tête de mort permet de détruire des états ou des transitions. + +### Exercices +Dessinez les automates qui reconnaissent : + +(pour l'alphabet $\{a,b\}$) + +1. les mots de 2 lettres; +2. les mots contenant exactement 2 a; +3. les mots contenant 2 a consécutifs; +4. les mots commençant par b; +5. les mots se terminant par bab; +6. le langage réduit au mot vide; + +(pour l'alphabet $\{a,b,c\}$) + +7. les mots qui contiennent $aabcc$; +8. les mots de taille multiple de 3; +9. les mots de la forme abcabcabc... (une ou plusieurs successions des 3 lettres abc); +10. les mots dont la première lettre est égale à la dernière. + +

Calcul modulaire en base 2 +

+ +### Compter avec les automates +On ne le verra pas dans ce cours, mais il est possible d'établir que le modèle des automates ne permet pas de compter. Par exemple, on ne peut pas lire une expression avec des parenthèses et vérifier qu'il y a autant de parenthèses ouvrantes que de parenthèses fermantes. On ne peut pas non plus vérifier que les parenthèses correspondent bien. Ainsi ce modèle n'est pas suffisant pour vérifier par exemple qu'une chaîne de caractères est un programme suivant un syntaxe fixée du C. + +Par contre, on peut compter facilement modulo N, puisque celà revient à se souvenir d'un nombre fini de cas. + +NB. modulo N veut dire qu'on manipule des nombres en faisant des sommes, des produits, etc mais en s'intéressant uniquement au reste de la division par N du résultat. Ça semble abstrait au premier abord, mais c'est ce que vous faites quand vous calculez le numéro d'un mois avec N=12. +Par exemple 3 mois après novembre c'est février : soit 11+3 = 2 modulo 12. + +Imaginons que notre automate lise un mot sur l'alphabet 0,1 représentant en binaire un nombre et qu'on souhaite tester si ce nombre est un multiple de 3. + +#### Retour sur la notation binaire + +En décimal, si j'ajoute 0 à droite d'un mot décimal w qui représente le nombre n alors le mot décimal w0 (w suivi d'un 0) représente n fois 10. + +En binaire, c'est similaire mais en remplaçant 10 par 2 dans la phrase ci-dessus. +Donc w0 représente 2n. + +Si j'écris w1 c'est le nombre représenté par w0 plus 1, soit 2n+1. + +On peut utiliser cette relation pour déduire des propriétés de divisibilité par trois des nombres représentés par w0 ou w1 en fonction de celle du nombre n représenté par w. + +Si n est divisible par trois, il s'écrit sous la forme 3k pour un certain k. + * 2n vaut dans ce cas 2*3k qui est encore divisible par 3 (reste nul, soit 0 modulo 3). + * 2n+1 vaut dans ce cas 2(3k)+1 (reste 1, soit 1 modulo 3). + +On peut procéder de même pour les 2 autres cas. + +Si le reste de la division de n par trois vaut 1, il s'écrit sous la forme 3k+1 pour un certain k. + * 2n vaut dans ce cas 2(3k+1)=2.3k+2 (reste 2, soit 2 modulo 3). + * 2n+1 vaut dans ce cas 2(3k+1)+1=2.3k+3=3(2k+1) (reste 0, soit 0 modulo 3). + +##### Exercice +Procédez de même lorsque le reste de la division de n par trois vaut 2. + +En déduire un automate qui lit un mot en binaire et accepte celui-ci exactement lorsque le nombre représenté est divisible par trois. +(indication : il faut un état par reste possible). + + +

+
+ +## Le modèle de la machine de Turing +Nous allons maintenant nous pencher sur un modèle de machine qui +semble au premier abord n'être que légèrement différent de celui des +automates. D'une part, on va pouvoir revenir en arrière sur le mot, et +d'autre part on va pouvoir écrire ce qui permet d'avoir une mémoire +arbitrairement grande. + +Ces deux changements permettent +d'obtenir *in fine* un modèle très riche puisque *n'importe quelle +procédure de calcul connue à l'heure actuelle* peut être traduite +théoriquement par une machine de Turing. + +Il est important de noter que le programme reste fini. + + + ![images/turingMachine.png] + +Il y a beaucoup de ressources sur Alan Turing disponibles en ligne, en +particulier depuis son centenaire en 2012. Vous pouvez trouver (ses +articles originaux et ses brouillons)[http://www.turingarchive.org/]. + +C'est un mathématicien qui a eu une influente forte en informatique, +malgré une vie trop courte (1912-1954). En droit britannique, (une loi porte son nom)[https://en.wikipedia.org/wiki/Alan_Turing_law}] + +### Turing avec JFLAP + +Dans le menu choisissez **Machine de Turing**. L'éditeur graphique vous permet de créer rapidement le programme d'une machine de Turing. Les cercles sont les états de la machine (comme pour les automates). Un clic droit permet de rendre initial un état, ou final des états. Un état final correspond ici en fait à un état acceptant. La machine s'arrête si il n'y a pas de transition appropriée (en +rejetant si l'état dans laquelle elle se trouve n'est pas final). + +Dans la suite on utilise l'alphabet 0,1 en plus du blanc (ressemblant à un carré pour JFLAP). +Notez que le ruban est infini à gauche et à droite pour JFLAP. Il y a +de nombreuses variations possibles pour la machine de Turing qui ne +font pas de différence notable, par exemple un ruban fini à gauche, un ruban à 2 dimensions etc. + +Un point technique avec JFLAP. Si vous voulez fabriquer une transition +qui écrit un blanc (un carré) pour une transition, il suffit de ne rien +saisir dans cette cellule pour la transition et d'appuyer sur entrée. + +#### Exercice +On suppose que l'alphabet est 0,1 + 1. Écrire un programme qui lit les caractères du mot d'entrée de + la gauche vers la droite et s'arrête en acceptant. + 1. Même question pour un programme qui accepte si et seulement si + la première et la dernière lettre sont les mêmes. + 1. Même question pour les mots qui sont des \textsl{palindromes} + (exemple de palindrome en français KAYAK). On peut dans un premier + temps ne gérer correctement que les mots qui sont de longueur + paire. + +#### Indications + correction indicative +Pour les palindromes pairs, de la forme w suivi de w renversé, *on ne peut pas se souvenir dans nos états* du début du mot w qui est arbitrairement grand et donc pour un mot +assez grand forcément plus grand que le nombre (fini) d'états de notre +machine. + +Si on disposez d'une machine de Turing à **2 rubans**, on pourrait : +recopier le premier ruban sur le second; ramener la tête de lecture du +premier ruban tout à gauche; puis décaler la tête du premier ruban +vers la droite et celle du second ruban vers la gauche en vérifiant +une par une que les lettres sont identiques. + +Comme nous ne disposons que d'un ruban, la seule mémoire non bornée à +notre disposition est l'unique ruban. L'idée consiste donc à vérifier +l'un après l'autre les couples de lettres suivantes : (première +lettre, dernière lettre) puis (seconde lettre, avant-dernière lettre) +etc. + +Si nous avions **deux têtes** il suffirait de placer notre seconde tête à +la fin du mot et de procéder comme dans la version à 2 rubans. + +Puisqu'on a une seule tête, cette dernière va devoir faire des +aller-retours. Il va falloir marquer d'une manière ou d'une autre les +lettres qu'on a vu pour éviter de repasser au même endroit. +L'exemple ci-dessous enlève tout simplement les lettres en cours de +vérification. + + ![images/TuringPalindromePair.jpg] + +## La thèse de Church Turing. +**Pour tout modèle raisonnable de calcul, on obtient la même notion de ce qui est calculable.** + + +Arguments en faveur de cette thèse +* Théorie générales des fonctions récursives (Gödel, Herbrand + 1933). +* lambda-calcul (Church, 1936). +* Machines de Turing (Turing, 1936). +* Trois modèles équivalents (Church 1936, Turing 1937). +* Machines de Post (1936). +* Machines de Turing avec plusieurs rubans (Minsky). +* Machines à compteurs. +* Machines à registre. +* etc. + diff --git a/1-ComputationAndData/5ComputationAndData.md b/1-ComputationAndData/5ComputationAndData.md new file mode 100644 index 0000000..98ae489 --- /dev/null +++ b/1-ComputationAndData/5ComputationAndData.md @@ -0,0 +1,361 @@ +Cours de Florent. + +# Calculer en théorie et en pratique III/III + +Dans cette séquence de cours, nous tentons de répondre à la question suivante. + +C'est quoi un ordinateur? + +Cette question s'apparente à celle que ce sont posés philosophes et mathématiciens de Leibnitz à Turing en passant par Hilbert. + +Qu'est-ce qu'une question à laquelle on peut répondre de manière mécanique par un calcul? + +Nous avons vu une approximation de calcul théorique basé sur le calcul booléen et des portes logiques qui sont implémentable avec des composants electroniques, permettant de réaliser divers opérations comme l'addition bit à bit (schéma de Vernam en cryptographie), la majorité ou encore l'addition avec retenue. + +Nous avons poursuivi avec un modèle théorique, qui est celui de l'**automate fini**, un modèle assez restreint de machine : l'adjectif fini s'applique à la mémoire de la machine qui est finie. +Nous avons entrevu le modèle plus général avec une mémoire arbitrairement grande **la machine de Turing** et évoqué la thèse de Church-Turing qui stipule que tout modèle de calcul raisonnable est équivalent à ce modèle de la machine de Turing. + +Toutefois, le modèle de la machine de Turing reste assez éloigné d'une machine réelle et nous allons maintenant présenter rapidement un modèle simplifié de machine basé sur le modèle de Von Neumann, puis pratiquer l'assembleur avec la Machine Virtuelle à Pile (MVàP). + + +## Programme vs données + +Dans le modèle de Turing, le programme est externe et guide la machine qui travaille sur le contenu du ruban qu'on peut voir comme la donnée. +Dès 1936, Turing montre qu'en fait on peut construire une machine **universelle** qui lit sur son ruban le programme et les données sur lesquelles il faut lancer le calcul de ce programme. + +C'est cette idée de "programme qu'on va charger" qu'on retrouve dans le modèle de Von Neumann. + + +## Le modèle de Von Neumann + +* L'unité de Mémoire contient des *données* et *des insructions* +* Le processeur se compose d'une *unité de contrôle* et d'une *unité arithmétique et logique*. +* La communication avec l'extérieur se fait par des dispositifs d'entrée-sortie. + +Pour plus de détails, voir [wikipedia](https://en.wikipedia.org/wiki/Von_Neumann_architecture) + +## Zoom sur *l'unité arithmétique et logique* + +Essentiellement un circuit au sens de ce qu'on a évoqué lors du dernier cours. +En pratique les entrées/sorties sont découpées en 2 dimensions : une partie **contrôle** et une partie **données**. + +* [Image](https://commons.wikimedia.org/wiki/File:ALU_block.gif) +* [wikipedia](https://en.wikipedia.org/wiki/Arithmetic_logic_unit) +* [Symboles circuit](https://en.wikipedia.org/wiki/Electronic_symbol) + + +## Zoom sur la mémoire + +La mémoire peut être vue comme une pyramide. + +* En haut très peu de place, mais de la mémoire très rapide, ce sont des *registres*. +* Au milieu, de la mémoire assez rapide, c'est la *mémoire vive* (la RAM) qui n'est pas persistante et quand on étend la machine, le contenu de la mémoire n'est pas conservé. +* En bas, de la mémoire plutôt lente, mais persistante, typiquement le *disque dur*. + +En pratique il existe des mécanismes de *cache*, en particulier entre les registres et la RAM. + +Il y a d'autres ingrédients qui permettent de limiter l'emprunte en mémoire d'un programme (adresses virtuelles, paging) voir de suspendre une exécution et de recopier le programme en train de calculer dans le disque (swapping). + +* [Image](images/4-hierarchy.jpg) +* [Jeu du paging](https://en.wikisource.org/wiki/Paging) +* [Cache vs paging](https://stackoverflow.com/questions/4429025/caches-vs-paging) + +## la Machine Virtuelle à Pile (MVàP). + +Normalement dans une machine il faudrait expliquer comment les calculs sont poussés vers les registres et l'ALU. +Nous allons travailler avec un modèle simplifié qui cache cet aspect et dans laquelle la mémoire est une pile. + +Par ailleurs la machine possèdes deux registres. +* PC (pour Program counter) qui contient le numéro de la ligne d'instruction en cours +* FC (pour frame pointer) qui est un mécanisme permettant de faire des appels de fonctions mais qu'on n'utilisera pas car c'est un peu plus technique à utiliser. + +La machine accepte plusieurs instructions. +``` +PUSHI n # pousse l'entier n sur la pile et passe à l'instruction suivante +POP # décale le sommet de la pile d'un et passe à l'instruction suivante + +ADD # ajoute les 2 entiers au sommet de la pile, décale le sommet de la pile de 2 + # écrit le résultat en haut de la pile et passe à l'instruction suivante +SUB # même chose pour la soustraction +MUL # même chose pour la multiplication +DIV # même chose pour la division + +READ # lecture d'un entier qui est poussé en haut de la pile +WRITE # écriture de l'entier en haut de la pile + +HALT # fin du programme + +LABEL x # définition d'une ancre vers laquelle on peut sauter +JUMP x # Saut vers le label (prochaine instruction à la ligne du label) +JUMPF x # Instruction suivante si le haut de la pile est différent de 0 + # Instruction x sinon. + +INF # Mange deux entiers. + # Remplace par l'entier 1 si le premier inférieur au second et par 0 sinon. + # Passe à l'instruction suivante +INFEQ # idem plus petit ou égal +SUP # idem plus grand +SUPEQ # idem plus grand ou égal +EQUAL # idem égal +NEQ # idem différent + + # Autres instructions qu'on verra plus tard. +PUSHG a # empile en haut de la pile l'entier stocké à l'adresse a de la pile +STOREG a # dépile et stocke à l'adresse a de la pile l'entier en haut de la pile + + # Autres instructions qu'on ne verra probablement pas plus tard. +CALL x # Appel du code stocké au label x +RETURN # Retour dans le code appellant. +PUSHL a # analogue de PUSHG pour des variables locales (utilise FP) +STOREL a # analogue de STOREG +``` + +L'ordre des opérations est naturel, si on voit la pile de côté, bas à gauche, haut à droite. Une opération qui mange deux arguments prendra l'avant dernier argument comme premier argument et le dernier comme second argument. + +### Un premier exemple + +``` + PUSHI 11 + PUSHI 6 + PUSHI 15 + MUL + SUB + PUSHI 5 + ADD + PUSHI 12 + ADD + PUSHI 9 + PUSHI 4 + MUL + PUSHI 7 + MUL + ADD + WRITE + POP + HALT +``` + +Une fois assemblé, le code devient : +``` + Adr | Instruction +-----+--------------- + 0 | PUSHI 11 + 2 | PUSHI 6 + 4 | PUSHI 15 + 6 | MUL + 7 | SUB + 8 | PUSHI 5 + 10 | ADD + 11 | PUSHI 12 + 13 | ADD + 14 | PUSHI 9 + 16 | PUSHI 4 + 18 | MUL + 19 | PUSHI 7 + 21 | MUL + 22 | ADD + 23 | WRITE + 24 | POP + 25 | HALT +``` +La MVàP, en mode debug, écrit à chaque pas : + +* la valeur du compteur de programme (pc) ; +* l'instruction à cette adresse ; +* la valeur du « frame pointer » (toujours 0, quand il n'y a pas d'appel de fonction) ; +* le contenu de la pile ; +* la hauteur de la pile. + +Le début de l'exécution donne la trace suivante : + +``` + pc | | fp pile +==================================================== + 0 | PUSHI 11 | 0 [ ] 0 # On empile 11 + 2 | PUSHI 6 | 0 [ 11 ] 1 # On empile 6 + 4 | PUSHI 15 | 0 [ 11 6 ] 2 # On empile 15 + 6 | MUL | 0 [ 11 6 15 ] 3 # On dépile et multiplie 6*15, on empile le résultat + 7 | SUB | 0 [ 11 90 ] 2 # On dépile et soustrait 90 à 11, on empile le résultat. + 8 | PUSHI 5 | 0 [ -79 ] 1 # On empile 5. + etc +``` +### Exercice + +Continuez l'exécution. + +### Exercice + +Vérifier votre calcul manuel en lançant la machine. + +Il faut avoir java installé sur votre machine ou utiliser proxmox. +Il faut utiliser les deux fichiers jar qui sont dans le répertoire MVaP +Le fichier ```MVaP/ALIRE``` contient la marche à suivre. + +### Variables globales +On peut réserver de l'espace en bas de la pile et associer à une variable sa position pour mémoriser des valeurs. + +``` + PUSHI 1 # Il faut initialement pousser une valeur ( par exemple 1) + ... # Du code qui génère des choses dans la pile et une valeur en haut de la pile, par exemple 42 + STOREG 0 # stocke 42 à l'adresse 0 de la pile (le 1 est remplacé par 42) + ... # Du code qui fait des choses et qui tout à coup a besoin de connaître la valeur stockée + PUSHG 0 # empile 42 en haut de la pile. +``` + +### Exemple + +Imaginons qu'on souhaite faire du code qui : +* déclare une variable i +* lui affecte la valeur 6 +* plus tard souhaite l'incrémenter. + +``` +PUSHI 1 # i habite à l'adresse 0 +... +PUSHI 6 +STOREG 0 +... +PUSHI 1 +PUSHG 0 +ADD +STOREG 0 +``` + +### Boucles + +Imaginons qu'on souhaite faire une boucle tant que +``` +Tant que test : + quelque chose +La suite +``` +Il faut utiliser des labels pour délimiter +* la partie test suivie de la décision de rentrer dans la boucle ou de sortir +* la partie interne à la boucle (quelque chose) +* la partie qui suit la boucle (La suite). + +``` +LABEL 0 +# le test qui va laisser une valeur 0 ou 1 en haut de la pile +JUMPF 1 # saut conditionnel vers le label 1 si le test est Faux sinon continue +# quelque chose +JUMP 0 +LABEL 1 +#La suite +``` + +### Exercice + +Produire du code MVàP qui correspond au code python suivant. +```python +j = 1 +i = 0 +i = j +while i < 10: + i += 1 +print(i) +``` +Testez votre code avec la MVàP. + + +### Exercice +Produire du code MVàP qui s'inspire du code suivant et simule la lecture et le stockage d'un tableau avant de vider la pile. +La version ci-dessous ne vide pas la pile. +``` +# Boucle While +LABEL 19 +# le test qui va laisser une valeur 0 ou 1 en haut de la pile +# PUSHI 0 # pour faux, donc je saute après +# PUSHI 1 # pour vrai, donc je ne saute pas. +READ # on demande à l'utilisateur +JUMPF 18 # saut conditionnel vers le label 1 si le test est Faux sinon continue +# quelque chose +READ +# Fin du quelque chose +JUMP 19 +LABEL 18 +#La suite +PUSHI 666 +WRITE +POP +# Fin de la suite. +HALT +``` + +### Exercice +Produire du code MVàP qui correspond au code python suivant. + +```python +# integer inputs (input returns a string that needs casting as an int) +m = int(input()) +n = int(input()) +if (m < n) : + m = n +else : + n = m +print m +print n +``` + +### Réutiliser du code. + +Si on a du code qu'on veut réutiliser plusieurs fois, +* on peut l'isoler entre un label et un jump +* on peut sauter vers le label +* malheureusement on ne peut pas sauter à la fin vers plusieurs endroits différents +* on pourrait faire des tests successifs avec des JUMP et des JUMPF pour sauter au bon endroit +* par contre on ne peut pas réutiliser le code un nombre arbitraire de fois. + +Solution : on sauve dans un registre l'endroit dans lequel on doit retourner +Le plus simple consiste à utiliser le haut de la pile. + +Par contre il faut dans ce cas une instruction pour la MVàP qui permette d'écrire en haut de la pile la position actuelle du pc (c'est une partie du rôle de CALL) et il faut une instruction qui soit l'analogue de HALT pour un bloc et permette de retourner le pc à la valeur antérieure à l'appel (c'est une partie du rôle de RETURN). + +Avec cette idée on peut faire un appel à une fonction qui ne prend pas de paramètre et ne retourne pas de valeur. + +On peut communiquer avec le reste du programme via une variable globale. + +### Exemple +On peut ainsi par exemple faire une fonction qui mutliplie par 2 une variable globale. +On appelle 3 fois la fonction et on affiche le résultat à chaque fois. + +``` +PUSHI 1 # variable globale i habite à l'adresse 0 +JUMP 1 +LABEL 0 # Notre Fonction +PUSHG 0 +PUSHI 2 +MUL +STOREG 0 +RETURN # Fin de Notre Fonction +... +LABEL 1 # Main +CALL 0 # appel 1 +PUSHG 0 +WRITE +CALL 0 # appel 2 +PUSHG 0 +WRITE +CALL 0 # appel3 +PUSHG 0 +WRITE +``` + +## Autres Exercices +Il faut pour chaque exercice produire et tester du code MVàP qui réaliser le calcul ou le programme demandé. + +### Exercice +Lire un entier n et calculez n*4+5*6-2 + +### Exercice +Lire un entier n et calculez 2*4+n*6-2 + +### Exercice +Même chose que ci-dessus mais avec un programme optimisé (qui donne le même résultat mais avec un minimum d'instructions). + +### Exercice +Lire un entier n. Si n est nul le programme écrit 20 sinon 10. + +### Exercice +Et parce qu'il faut bien une question un peu plus difficile. +Lire un entier n. 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b/1-ComputationAndData/5ComputationAndData/6TD.html new file mode 100644 index 0000000..0d10d04 --- /dev/null +++ b/1-ComputationAndData/5ComputationAndData/6TD.html @@ -0,0 +1,254 @@ + + + + + +TD6 --- L3 -- Langage et Compilation + + + + + + +

TD6 --- L3 Langage et Compilation --

+

Le retour de la MVàP

+ + Fort de notre expériennce de la semaine passée, nous continuons à programmer en MVàP. Pour ceux qui regrettent le python et ces fonctions : pas de problème + la MVàP permet d'en écrire, et à la fin de ce TD en salle machine, les fonctions n'auront plus de secrets pour vous. + +

Préliminaire

+ Sortez un papier, un crayon et une gomme. Imaginez pour l'instant que le pc devant vous sert seulement à visionner cette feuille d'exercice. + + +
+

Code MVàP 1

+Soit le programme suivant en MVàP : +
+  JUMP 0
+LABEL 1   
+  PUSHL -3
+  PUSHI 2
+  MUL
+  STOREL -4
+  RETURN
+RETURN
+LABEL 0   
+  PUSHI 0
+  PUSHI 2
+  CALL  1
+  POP
+  WRITE
+  POP
+  HALT
+
+ +Une fois assemblé, ce code devient : +
+ Adr |  Instruction
+-----+---------------
+   0 | JUMP       11 
+   2 | PUSHL      -3 
+   4 | PUSHI       2 
+   6 | MUL           
+   7 | STOREL     -4 
+   9 | RETURN        
+  10 | RETURN        
+  11 | PUSHI       0 
+  13 | PUSHI       2 
+  15 | CALL        2 
+  17 | POP           
+  18 | WRITE         
+  19 | POP           
+  20 | HALT          
+
+ +
Commenter et compléter le début de trace suivant. +Commenter le code original. Que réalise-t-il?
+ + +Le début de l'exécution donnant la trace suivante : + +
+  pc |               |    fp   pile
+====================================================
+   0 | JUMP       11 |     0 [ ] 0
+  11 | PUSHI       0 |     0 [ ] 0
+  13 | PUSHI       2 |     0 [ 0 ] 1
+  15 | CALL        2 |     0 [ 0 2 ] 2
+   2 | PUSHL      -3 |     4 [ 0 2 17 0 ] 4
+     |               |
+     |               |
+     |               |
+     |               |
+
+ + +

Code MVàP 2

+Soit le programme suivant en MVàP : +
+  JUMP 0
+LABEL 1
+  PUSHL -3
+  PUSHI 2
+  MUL
+  STOREL -4
+  RETURN
+RETURN
+LABEL 2
+LABEL 3
+  PUSHL -4
+  PUSHL -3
+  PUSHI 1
+  ADD
+  INF
+  JUMPF 4
+  PUSHI 0
+  PUSHL -3
+  CALL 1
+  POP
+  STOREL -4
+  JUMP 3
+LABEL 4
+  PUSHL -4
+  STOREL -5
+  RETURN
+RETURN
+LABEL 0
+  PUSHI 0
+  PUSHI 3
+  PUSHI 5
+  CALL 2
+  POP
+  POP
+  WRITE
+  POP
+  HALT
+
+ +Une fois assemblé, ce code devient : +
+ Adr |  Instruction
+-----+---------------
+   0 | JUMP       38 
+   2 | PUSHL      -3 
+   4 | PUSHI       2 
+   6 | MUL           
+   7 | STOREL     -4 
+   9 | RETURN        
+  10 | RETURN        
+  11 | PUSHL      -4 
+  13 | PUSHL      -3 
+  15 | PUSHI       1 
+  17 | ADD           
+  18 | INF           
+  19 | JUMPF      32 
+  21 | PUSHI       0 
+  23 | PUSHL      -3 
+  25 | CALL        2 
+  27 | POP           
+  28 | STOREL     -4 
+  30 | JUMP       11 
+  32 | PUSHL      -4 
+  34 | STOREL     -5 
+  36 | RETURN        
+  37 | RETURN        
+  38 | PUSHI       0 
+  40 | PUSHI       3 
+  42 | PUSHI       5 
+  44 | CALL       11 
+  46 | POP           
+  47 | POP           
+  48 | WRITE         
+  49 | POP           
+  50 | HALT 
+
+ +
Compléter les traces d'exécution suivantes. Identifier les appels de fonctions. Repérer les blocs d'activation. Que réalise le code?
+ + +Trace partielle : +
+  pc |               |    fp   pile
+====================================================
+   0 | JUMP       38 |     0 [ ] 0                  
+  38 | PUSHI       0 |     0 [ ] 0		    
+  40 | PUSHI       3 |     0 [ 0 ] 1		    
+  42 | PUSHI       5 |     0 [ 0 3 ] 2		                 
+  44 | CALL       11 |     0 [ 0 3 5 ] 3                         
+  11 | PUSHL      -4 |      
+     |               |
+     |               |
+     |               |
+  18 | INF           |     5 [ 0 3 5 46 0 3 6 ] 7	        
+  19 | JUMPF      32 |     5 [ 0 3 5 46 0 1 ] 6		
+  21 | PUSHI       0 |     5 [ 0 3 5 46 0 ] 5		
+  23 | PUSHL      -3 |     5 [ 0 3 5 46 0 0 ] 6		
+  25 | CALL        2 |     5 [ 0 3 5 46 0 0 5 ] 7                    
+   2 | PUSHL      -3 |     9 [ 0 3 5 46 0 0 5 27 5 ] 9      
+   4 | PUSHI       2 |     9 [ 0 3 5 46 0 0 5 27 5 5 ] 10   
+   6 | MUL           |     9 [ 0 3 5 46 0 0 5 27 5 5 2 ] 11 
+   7 | STOREL     -4 |     9 [ 0 3 5 46 0 0 5 27 5 10 ] 10  
+   9 | RETURN        | 
+     |               |
+     |               |
+     |               |
+  11 | PUSHL      -4 |     5 [ 0 10 5 46 0 ] 5		
+  13 | PUSHL      -3 |     5 [ 0 10 5 46 0 10 ] 6	
+  15 | PUSHI       1 |     5 [ 0 10 5 46 0 10 5 ] 7	
+  17 | ADD           |     5 [ 0 10 5 46 0 10 5 1 ] 8	      
+  18 | INF           |     5 [ 0 10 5 46 0 10 6 ] 7	
+  19 | JUMPF      32 |     5 [ 0 10 5 46 0 0 ] 6	             
+  32 | PUSHL      -4 |     5 [ 0 10 5 46 0 ] 5		
+  34 | STOREL     -5 |     5 [ 0 10 5 46 0 10 ] 6	
+  36 | RETURN        |     5 [ 10 10 5 46 0 ] 5         
+  46 | POP           |     0 [ 10 10 5 ] 3          
+  47 | POP           |     0 [ 10 10 ] 2	    
+  48 | WRITE         |     0 [ 10 ] 1		    
+10						                  
+  49 | POP           |     0 [ 10 ] 1		   
+  50 | HALT          |     0 [ ] 0                 
+
+ + + + +

autocorrection

+Vous pouvez éteindre votre papier, votre gomme et votre crayon et reprendre une activité normale. +Si ce n'est pas déjà fait la semaine dernière, téléchargez les sources de la MVaP et suivez les instructions avec les tests. + +
+Utilisez la MVàP pour vérifier que celle ci ne se trompe pas et donne la même réponse que votre crayon. +
+ + + + + +

Production de code

+ +Pour chaque programme décrit informellement ci-dessous, écrire un programme MVàP et testez le. Le fichier texte .mvap doit contenir une instruction par ligne et un saut de ligne après chaque instruction. Vous pouvez commenter votre code en préfixant chaque ligne par un dièse (hash). Attention à bien prendre soin de sauter une ligne y compris après la dernière instruction (HALT). + +
+Fonction f(x)=1-x. Fonction g(x)=1+x. +Main : appel de f(a)*g(a) pour un entier a lu auprès de l'utilisateur. +
+ +
+Fonction valeur absolue et son appel pour un entier entré par l'utilisateur. +
+ +
+Fonction 2^n (2 chapeau n c'est bien ça) et son appel pour un entier entré par l'utilisateur. +Évidemment on fera une fonction récursive sinon ce n'est pas drôle. +
+ +
+Fonction de Fibonnacci et appel d'ycelle dans le main pour 2 valeurs lues auprès de l'utilisateur. +
+ +Et parce qu'il faut bien une question un peu plus difficile. +
+Reprendre la fonction chapeau. Codez là en récursion terminale. +
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index 0000000..2dc6623 --- /dev/null +++ b/1-ComputationAndData/JFLAP/TMPremiereLettreEgaleDerniereLettre.jff @@ -0,0 +1,103 @@ + + turing + + + + 97.0 + 103.0 + + + + 393.0 + 47.0 + + + 211.0 + 46.0 + + + 203.0 + 173.0 + + + 364.0 + 172.0 + + + 523.0 + 115.0 + + + + + 2 + 2 + 0 + 0 + R + + + 2 + 2 + 1 + 1 + R + + + 3 + 3 + 0 + 0 + R + + + 3 + 3 + 1 + 1 + R + + + 0 + 3 + 1 + 1 + R + + + 2 + 1 + + + L + + + 4 + 5 + 1 + 1 + S + + + 0 + 2 + 0 + 0 + R + + + 1 + 5 + 0 + 0 + S + + + 3 + 4 + + + L + + + \ No newline at end of file diff --git a/1-ComputationAndData/JFLAP/TMSommeBinaire2rubansSurTroisieme.jff b/1-ComputationAndData/JFLAP/TMSommeBinaire2rubansSurTroisieme.jff new file mode 100644 index 0000000..5dd08e7 --- /dev/null +++ b/1-ComputationAndData/JFLAP/TMSommeBinaire2rubansSurTroisieme.jff @@ -0,0 +1,273 @@ + + turing + 3 + + + + 358.0 + 213.0 + + + + 642.0 + 206.0 + + + 972.0 + 206.0 + + + 809.0 + 410.0 + + + + + 1 + 3 + + + R + + + R + + + R + + + 1 + 2 + 1 + 1 + L + 1 + 1 + L + + 0 + L + + + 0 + 0 + 1 + 1 + R + + 0 + R + + + R + + + 1 + 1 + 0 + 0 + L + 0 + 0 + L + + 0 + L + + + 0 + 0 + + 0 + R + 0 + 0 + R + + + R + + + 0 + 0 + 0 + 0 + R + 0 + 0 + R + + + R + + + 0 + 0 + 0 + 0 + R + 1 + 1 + R + + + R + + + 0 + 0 + 1 + 1 + R + 0 + 0 + R + + + R + + + 0 + 0 + 1 + 1 + R + 1 + 1 + R + + + R + + + 0 + 0 + + 0 + R + 1 + 1 + R + + + R + + + 0 + 1 + + + L + + + L + + + L + + + 2 + 3 + + + R + + + R + + 1 + S + + + 1 + 1 + 1 + 1 + L + 0 + 0 + L + + 1 + L + + + 1 + 1 + 0 + 0 + L + 1 + 1 + L + + 1 + L + + + 2 + 2 + 1 + 1 + L + 1 + 1 + L + + 1 + L + + + 0 + 0 + 0 + 0 + R + + 0 + R + + + R + + + 2 + 2 + 0 + 0 + L + 1 + 1 + L + + 0 + L + + + 2 + 2 + 1 + 1 + L + 0 + 0 + L + + 0 + L + + + 2 + 1 + 0 + 0 + L + 0 + 0 + L + + 1 + L + + + \ No newline at end of file diff --git a/1-ComputationAndData/JFLAP/TP2DAAvecAnnotationLabels.jff b/1-ComputationAndData/JFLAP/TP2DAAvecAnnotationLabels.jff new file mode 100644 index 0000000..9902133 --- /dev/null +++ b/1-ComputationAndData/JFLAP/TP2DAAvecAnnotationLabels.jff @@ -0,0 +1,70 @@ + + fa + + + + 67.0 + 118.0 + + + + + 261.0 + 49.0 + + + + 262.0 + 162.0 + + + + 382.0 + 51.0 + + + + + 388.0 + 166.0 + + + + + 149.0 + 107.0 + + + + + 0 + 0 + b + + + 4 + 6 + a + + + 0 + 7 + a + + + 7 + 3 + b + + + 3 + 5 + b + + + 7 + 4 + a + + + \ No newline at end of file diff --git a/1-ComputationAndData/JFLAP/TP2NDA.jff b/1-ComputationAndData/JFLAP/TP2NDA.jff new file mode 100644 index 0000000..2d35623 --- /dev/null +++ b/1-ComputationAndData/JFLAP/TP2NDA.jff @@ -0,0 +1,73 @@ + + fa + + + + 67.0 + 118.0 + + + + 148.0 + 51.0 + + + 149.0 + 162.0 + + + 261.0 + 49.0 + + + 262.0 + 162.0 + + + 382.0 + 51.0 + + + + 388.0 + 166.0 + + + + + 4 + 6 + a + + + 0 + 0 + b + + + 0 + 2 + a + + + 2 + 4 + a + + + 1 + 3 + b + + + 0 + 1 + a + + + 3 + 5 + b + + + \ No newline at end of file diff --git a/1-ComputationAndData/MVaP/3n+2.mvap b/1-ComputationAndData/MVaP/3n+2.mvap new file mode 100644 index 0000000..435d261 --- /dev/null +++ b/1-ComputationAndData/MVaP/3n+2.mvap @@ -0,0 +1,13 @@ +# calcule : 2 + 3 * n +PUSHI 2 +LABEL 1 +PUSHI 3 +ADD +WRITE +DUP +PUSHI 100 +INF +JUMPF 2 +JUMP 1 +LABEL 2 +HALT diff --git a/1-ComputationAndData/MVaP/ALIRE b/1-ComputationAndData/MVaP/ALIRE new file mode 100644 index 0000000..f74eef6 --- /dev/null +++ b/1-ComputationAndData/MVaP/ALIRE @@ -0,0 +1,36 @@ +# La machine virtuelle à pile. + +Une machine pédagogique pour donner une idée de ce qu'est l'assembleur. + +Dans le cadre d'un cours de compilation, par exemple en L3 informatique, on peut demander aux étudiants de coder un compilateur qui va transcrire un langage de haut niveau similaire à du python (sans objets et avec quelques types simples entiers, flottants, tableaux) vers du code MVàP. + +## Contenu du répertoire. +* add.mvap Un exemple simple de programme +* 3n+2.mvap Un exemple moins simple de programme +* test.mvap Un exemple avec appel de fonction + +* MVaP.jar Une archive java qui propose 2 exécutables + MVaPAssembler (assemble en un binaire) + CBaP (interprète le binaire). + +* antlr-4.5.2-complete.jar Une archive java contenant de nombreux binaires permettant d'écrire des compilateurs sur lequel le code de la MVàP s'appuit. + +## Pour utiliser la MVàP + +Il faut avoir java d'installé sur sa machine (c'est le cas si vous passez par proxmox des machines de l'IUT). + +** Pour exécuter du code mvap, il faut : + + 1- Assembler : + $ java -cp antlr-4.5.2-complete.jar:MVaP.jar MVaPAssembler add.mvap + ou avec des traces (option -d) : + $ java -cp antlr-4.5.2-complete.jar:MVaP.jar MVaPAssembler -d add.mvap + ce qui produit le fichier add.mvap.cbap + +Le fichier .cbap (code binaire à pile) est du binaire que la machine peut exécuter. + + 2- Exécuter : + $ java -jar MVaP.jar add.mvap.cbap + ou pour mieux comprendre avec des traces : + $ java -jar MVaP.jar -d add.mvap.cbap + diff --git a/1-ComputationAndData/MVaP/ExamenCalcul.mvap b/1-ComputationAndData/MVaP/ExamenCalcul.mvap new file mode 100644 index 0000000..33e840f --- /dev/null +++ b/1-ComputationAndData/MVaP/ExamenCalcul.mvap @@ -0,0 +1,28 @@ +# lire a et b puis calculer et afficher l'expression ci-dessous. +#[(a+b)*(a-b)]+[(b+1)*(b-1)] +PUSHI 0 # a habite à l'adresse 0 +PUSHI 0 # b habite à l'adresse 1 +READ +STOREG 0 +READ +STOREG 1 +PUSHG 0 +PUSHG 1 +ADD +PUSHG 0 +PUSHG 1 +SUB +MUL +PUSHG 1 +PUSHI 1 +ADD +PUSHG 1 +PUSHI 1 +SUB +MUL +ADD +WRITE +POP +POP # oublier b +POP # oublier a +HALT diff --git a/1-ComputationAndData/MVaP/ExampleBoucleInfinie.mvap b/1-ComputationAndData/MVaP/ExampleBoucleInfinie.mvap new file mode 100644 index 0000000..8e513d3 --- /dev/null +++ b/1-ComputationAndData/MVaP/ExampleBoucleInfinie.mvap @@ -0,0 +1,5 @@ +# Boucle infinie +LABEL 0 +PUSHI 42 +JUMP 0 +HALT diff --git a/1-ComputationAndData/MVaP/ExampleBoucleWhile.mvap b/1-ComputationAndData/MVaP/ExampleBoucleWhile.mvap new file mode 100644 index 0000000..31b371f --- /dev/null +++ b/1-ComputationAndData/MVaP/ExampleBoucleWhile.mvap @@ -0,0 +1,18 @@ +# Boucle While +LABEL 19 +# le test qui va laisser une valeur 0 ou 1 en haut de la pile +#PUSHI 0 # pour faux, donc je saute après +#PUSHI 1 # pour vrai, donc je ne saute pas. +READ # on demande à l'utilisateur +JUMPF 18 # saut conditionnel vers le label 1 si le test est Faux sinon continue +# quelque chose +READ +# Fin du quelque chose +JUMP 19 +LABEL 18 +#La suite +PUSHI 666 +WRITE +POP +# Fin de la suite. +HALT \ No newline at end of file diff --git a/1-ComputationAndData/MVaP/ExampleSautQuiEviteDuCode.mvap b/1-ComputationAndData/MVaP/ExampleSautQuiEviteDuCode.mvap new file mode 100644 index 0000000..1b77c97 --- /dev/null +++ b/1-ComputationAndData/MVaP/ExampleSautQuiEviteDuCode.mvap @@ -0,0 +1,13 @@ +# Saut qui evite du code +PUSHI 11 +PUSHI 12 +JUMP 42 +PUSHI 666 +LABEL 312 +PUSHI 111 +PUSHI 110 +LABEL 42 +PUSHI 42 +PUSHI 43 +PUSHI 44 +HALT diff --git a/1-ComputationAndData/MVaP/ExampleTest.mvap b/1-ComputationAndData/MVaP/ExampleTest.mvap new file mode 100644 index 0000000..a3e4a6d --- /dev/null +++ b/1-ComputationAndData/MVaP/ExampleTest.mvap @@ -0,0 +1,13 @@ +# 11 - 1? +PUSHI 11 +PUSHI 1 +SUB +# 11 / 2? +PUSHI 11 +PUSHI 2 +DIV +# tester 3 < 5 +PUSHI 3 +PUSHI 5 +INF +HALT diff --git a/1-ComputationAndData/MVaP/ExampleVariable.mvap b/1-ComputationAndData/MVaP/ExampleVariable.mvap new file mode 100644 index 0000000..236b909 --- /dev/null +++ b/1-ComputationAndData/MVaP/ExampleVariable.mvap @@ -0,0 +1,26 @@ +# Example du cours de déclaratrion / restauration d'une variable +PUSHI 1 # i habite à l'adresse 0 +# quelque chose ici si on veut +PUSHI 42 +PUSHI 42 +PUSHI 42 +POP +POP +POP +# Fin du quelque chose ici si on veut +PUSHI 6 +STOREG 0 +# quelque chose ici si on veut +PUSHI 42 +PUSHI 42 +PUSHI 42 +POP +POP +POP +# Fin du quelque chose ici si on veut +PUSHI 1 +PUSHG 0 +ADD +STOREG 0 +# i est incrémenté et vaut 7. +HALT diff --git a/1-ComputationAndData/MVaP/ExempleCours.mvap b/1-ComputationAndData/MVaP/ExempleCours.mvap new file mode 100644 index 0000000..5a8df0a --- /dev/null +++ b/1-ComputationAndData/MVaP/ExempleCours.mvap @@ -0,0 +1,19 @@ +# exemple du cours. +PUSHI 11 +PUSHI 6 +PUSHI 15 +MUL +SUB +PUSHI 5 +ADD +PUSHI 12 +ADD +PUSHI 9 +PUSHI 4 +MUL +PUSHI 7 +MUL +ADD +WRITE +POP +HALT diff --git a/1-ComputationAndData/MVaP/ExoCours.mvap b/1-ComputationAndData/MVaP/ExoCours.mvap new file mode 100644 index 0000000..87d2efa --- /dev/null +++ b/1-ComputationAndData/MVaP/ExoCours.mvap @@ -0,0 +1,42 @@ +# Exo. +# j = 1 +# i = 0 +# i = j +# while i < 10: +# i += 1 +# print(i) +# +# étapes par étapes ci-dessous +# +# j = 1 +PUSHI 1 ### j habite à l'adresse 0 +# i = 0 +PUSHI 0 ### i habite à l'adresse 1 +# i = j +PUSHG 0 ### récupère j +STOREG 1 ### affecte à i cette valeur + +LABEL 12 + +# test i<10 ? +PUSHG 1 ### récupère i +PUSHI 4 ### pousse 4 pour que la démo tienne sur l'écran au lieu de 10 +INF ### 0 : Pop; compteur --: +# + +LABEL 0 +# le test qui va laisser une valeur 0 ou 1 en haut de la pile +PUSHG 0 +PUSHI 0 +SUP +JUMPF 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zHtu4q7O{{16LACJa@qtvpk&MT^g*1*9~M>-*F>|32`2L9Yj9x1E$A*riRI;juJ3k^ z32tspLGDfgjPK398BxAk0y(EsWTa4lx-U5={m}&wW8mQHhlLFY%AM94Kkkz6--j{Q zp1LcZoN90z&?*7+dr%VbCT{v^>g>f^5|Zf$iq4Yt+V!t*di_@j0tGGpNFA)p-9>&^ z)b!CGp3s}T^gy2r-sXU_;TN2}V5LO(*JAckV z)H*|!0UtmT1`UBUFNa^)IO=hv$!de6za90aW)CNbz@ ze8(}Oz)gi77JVKB8cv#g%mhDevxB8=Jf*M7*Fc7zFWc!9AI1ELzy)5=T@Uy+Y#=GA z{`txt95CPi_7T>a3d(B6j{ja MB>@1SY@wq358S+W5&!@I literal 0 HcmV?d00001 diff --git a/1-ComputationAndData/MVaP/MVaP-1.0/MVaP/index.html b/1-ComputationAndData/MVaP/MVaP-1.0/MVaP/index.html new file mode 100644 index 0000000..406e3a8 --- /dev/null +++ b/1-ComputationAndData/MVaP/MVaP-1.0/MVaP/index.html @@ -0,0 +1,80 @@ + + + + + MVàP + + + + + + + + +

Machine Virtuelle à Pile

+ +

Historique

+ Blabla sur la MVàP... + +

Documentation

+ Toute la doc +

+ lorem ipsum +

La MVàP

+

Entrez le code

+
+ +
+ +

Exécution

+ + + + + + + + +
+
+
+ + +
+ + + + + + + diff --git a/1-ComputationAndData/MVaP/MVaP-1.0/MVaP/js/CBaP.js b/1-ComputationAndData/MVaP/MVaP-1.0/MVaP/js/CBaP.js new file mode 100644 index 0000000..9864c57 --- /dev/null +++ b/1-ComputationAndData/MVaP/MVaP-1.0/MVaP/js/CBaP.js @@ -0,0 +1,216 @@ +/** + * Code Binaire pour Machine Virtuelle à Pile. + * Les flottants sont des double qui prennent la place de 2 ints. + * Les adresses sont des int. + * CALL empile l'adresse de retour et la vauler du framePointer dans la pile. + */ +public class CBaP { + + + + pc = 0; + fp = 0; + stack; + program; + const SizeofDouble = 2; + + _debug = false; + + CBaP(program, debug, stackSize) { + this.program = program; + this._debug = debug; + this.stack = new Pile(stackSize); + } + + dumpInstruction(ii, out) { + let i = ii; + switch(program.get_int(i)) { + case AssembleMVaP.ADD: out.print("ADD "); break; + case AssembleMVaP.SUB: out.print("SUB "); break; + case AssembleMVaP.MUL: out.print("MUL "); break; + case AssembleMVaP.DIV: out.print("DIV "); break; + case AssembleMVaP.INF: out.print("INF "); break; + case AssembleMVaP.INFEQ: out.print("INFEQ "); break; + case AssembleMVaP.SUP: out.print("SUP "); break; + case AssembleMVaP.SUPEQ: out.print("SUPEQ "); break; + case AssembleMVaP.EQUAL: out.print("EQUAL "); break; + case AssembleMVaP.NEQ: out.print("NEQ "); break; + + case AssembleMVaP.FADD: out.print("FADD "); break; + case AssembleMVaP.FSUB: out.print("FSUB "); break; + case AssembleMVaP.FMUL: out.print("FMUL "); break; + case AssembleMVaP.FDIV: out.print("FDIV "); break; + case AssembleMVaP.FINF: out.print("FINF "); break; + case AssembleMVaP.FINFEQ: out.print("FINFEQ"); break; + case AssembleMVaP.FSUP: out.print("FSUP "); break; + case AssembleMVaP.FSUPEQ: out.print("FSUPEQ"); break; + case AssembleMVaP.FEQUAL: out.print("FEQUAL"); break; + case AssembleMVaP.FNEQ: out.print("FNEQ "); break; + case AssembleMVaP.ITOF: out.print("ITOF "); break; + case AssembleMVaP.FTOI: out.print("FTOI "); break; + + case AssembleMVaP.RETURN: out.print("RETURN"); break; + case AssembleMVaP.POP: out.print("POP "); break; + case AssembleMVaP.READ: out.print("READ "); break; + case AssembleMVaP.WRITE: out.print("WRITE "); break; + case AssembleMVaP.WRITEF: out.print("WRITEF"); break; + case AssembleMVaP.PADD: out.print("PADD "); break; + case AssembleMVaP.PUSHGP: out.print("PUSHGP"); break; + case AssembleMVaP.PUSHFP: out.print("PUSHFP"); break; + case AssembleMVaP.DUP: out.print("DUP "); break; + + case AssembleMVaP.PUSHI: out.print("PUSHI "); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.PUSHG: out.print("PUSHG "); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.STOREG: out.print("STOREG"); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.PUSHL: out.print("PUSHL "); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.STOREL: out.print("STOREL"); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.PUSHR: out.print("PUSHR "); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.STORER: out.print("STORER"); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.FREE: out.print("FREE "); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.ALLOC: out.print("ALLOC "); out.format("%7d ", program.get_int(++i)); break; + + case AssembleMVaP.PUSHF: out.print("PUSHF "); ++i; out.format("%7.3f ", program.get_double(++i)); break; + + case AssembleMVaP.JUMP: out.print("JUMP "); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.JUMPF: out.print("JUMPF "); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.JUMPI: out.print("JUMPI "); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.CALL: out.print("CALL "); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.HALT: out.print("HALT "); break; + default: System.err.println("Code inconnu "+program.get_int(i)+" ligne "+i); + } + if (i == ii) out.print(" "); + return i; + } + + public void dumpProgram(PrintStream out) { + // out.println(program.toString(true)); + // out.println(program.toString()); + out.println(" Adr | Instruction"); + out.println("-----+---------------"); + for(int i = 0; i < program.getSize(); i++) { + out.format("%4d | ", i); + i = dumpInstruction(i, out); + out.println(); + } + } + + private void _call(int label) { + push(pc+1); + push(fp); + fp = size(); + pc = label; + } + + private void _return() { + while(size() > fp) + pop(); + fp = pop(); + pc = pop(); + } + + private BufferedReader input = null; + private int _read() { + try { + if (input == null) + input = new BufferedReader(new InputStreamReader(System.in)); + return Integer.parseInt(input.readLine()); + } catch (Exception e) { + System.err.println(e); + System.exit(1); + return 0; + } + } + + public boolean execute() { + if (_debug) { + dumpProgram(System.out); + System.err.println(); + System.err.println(" pc | | fp pile"); + System.err.println("===================================================="); + } + pc = 0; + while (true) { + if (_debug) { + System.err.format("%4d | ", pc); + dumpInstruction(pc, System.err); + System.err.format("| %4d %s\n", fp, stack.toString()); + } + try { + int p1, p2; // utile pour être sûr de l'ordre des pop() ! + double d1, d2; + switch(program.get_int(pc++)) { + case AssembleMVaP.ADD: p1 = pop(); p2 = pop(); push(p2 + p1); break; + case AssembleMVaP.SUB: p1 = pop(); p2 = pop(); push(p2 - p1); break; + case AssembleMVaP.MUL: p1 = pop(); p2 = pop(); push(p2 * p1); break; + case AssembleMVaP.DIV: p1 = pop(); p2 = pop(); push(p2 / p1); break; + case AssembleMVaP.INF: p1 = pop(); p2 = pop(); push(p2 < p1 ? 1 : 0); break; + case AssembleMVaP.INFEQ: p1 = pop(); p2 = pop(); push(p2 <= p1 ? 1 : 0); break; + case AssembleMVaP.SUP: p1 = pop(); p2 = pop(); push(p2 > p1 ? 1 : 0); break; + case AssembleMVaP.SUPEQ: p1 = pop(); p2 = pop(); push(p2 >= p1 ? 1 : 0); break; + case AssembleMVaP.EQUAL: p1 = pop(); p2 = pop(); push(p2 == p1 ? 1 : 0); break; + case AssembleMVaP.NEQ: p1 = pop(); p2 = pop(); push(p2 != p1 ? 1 : 0); break; + + case AssembleMVaP.FADD: d1 = pop_double(); d2 = pop_double(); push(d2 + d1); break; + case AssembleMVaP.FSUB: d1 = pop_double(); d2 = pop_double(); push(d2 - d1); break; + case AssembleMVaP.FMUL: d1 = pop_double(); d2 = pop_double(); push(d2 * d1); break; + case AssembleMVaP.FDIV: d1 = pop_double(); d2 = pop_double(); push(d2 / d1); break; + case AssembleMVaP.FINF: d1 = pop_double(); d2 = pop_double(); push(d2 < d1 ? 1 : 0); break; + case AssembleMVaP.FINFEQ: d1 = pop_double(); d2 = pop_double(); push(d2 <= d1 ? 1 : 0); break; + case AssembleMVaP.FSUP: d1 = pop_double(); d2 = pop_double(); push(d2 > d1 ? 1 : 0); break; + case AssembleMVaP.FSUPEQ: d1 = pop_double(); d2 = pop_double(); push(d2 >= d1 ? 1 : 0); break; + case AssembleMVaP.FEQUAL: d1 = pop_double(); d2 = pop_double(); push(d2 == d1 ? 1 : 0); break; + case AssembleMVaP.FNEQ: d1 = pop_double(); d2 = pop_double(); push(d2 != d1 ? 1 : 0); break; + + case AssembleMVaP.FTOI: push((int)pop_double()); break; + case AssembleMVaP.ITOF: push((double)pop()); break; + + case AssembleMVaP.RETURN: _return(); break; + case AssembleMVaP.POP: pop(); break; + case AssembleMVaP.READ: push(_read()); break; + case AssembleMVaP.WRITE: System.out.format("%7d\n", peek()); break; + case AssembleMVaP.WRITEF: System.out.format("%7.3f\n", peek_double()); break; + case AssembleMVaP.PADD: p1 = pop(); p2 = pop(); push(p2 + p1); break; + case AssembleMVaP.PUSHGP: push(0); break; + case AssembleMVaP.PUSHFP: push(fp); break; + case AssembleMVaP.DUP: push(peek()); break; + + case AssembleMVaP.PUSHI: push(program.get_int(pc++)); break; + case AssembleMVaP.PUSHG: push(get(program.get_int(pc++))); break; + case AssembleMVaP.STOREG: set(program.get_int(pc++), pop()); break; + // ajouter -2 si adresse négative ? + case AssembleMVaP.PUSHL: push(get(fp+program.get_int(pc++))); break; + case AssembleMVaP.STOREL:set(fp+program.get_int(pc++), pop()); break; + case AssembleMVaP.PUSHR: push(get(pop()+program.get_int(pc++)));break; + case AssembleMVaP.STORER:p1 = pop(); p2 = pop(); set(p2+program.get_int(pc++), p1); break; + case AssembleMVaP.FREE: doPop(program.get_int(pc++)); break; + case AssembleMVaP.ALLOC: doPush(program.get_int(pc++)); break; + + case AssembleMVaP.PUSHF: push(program.get_int(pc++)); push(program.get_int(pc++)); break; + + case AssembleMVaP.JUMP: pc = program.get_int(pc); break; + case AssembleMVaP.JUMPF: if (pop() == 0) pc = program.get_int(pc); else pc++; break; + case AssembleMVaP.JUMPI: pc = program.get_int(pc)+pop(); break; + case AssembleMVaP.CALL: _call(program.get_int(pc)); break; + case AssembleMVaP.HALT: return true; + default: System.err.println("Code inconnu "+program.get_int(pc)+" ligne "+pc); return false; + } + } catch (ArrayIndexOutOfBoundsException e) { + System.err.println(stack.getException()); + return false; + } + } + } + + void push(int i) { stack.push(i); } + int pop() { return stack.pop_int(); } + void push(double d) { stack.push(d); } + double pop_double() { return stack.pop_double(); } + int peek() { return stack.peek_int(); } + double peek_double() { return stack.peek_double(); } + int size() { return stack.getSize(); } + void set(int index, int i) { stack.set(index, i); } + int get(int index) { return stack.get_int(index); } + + void doPop(int nb) { for(; nb > 0; nb--) stack.pop_int(); } + void doPush(int nb) { for(; nb > 0; nb--) stack.push(0); } +} diff --git a/1-ComputationAndData/MVaP/MVaP-1.0/MVaP/js/LexerMVaP.dot b/1-ComputationAndData/MVaP/MVaP-1.0/MVaP/js/LexerMVaP.dot new file mode 100644 index 0000000..be9c7c5 --- /dev/null +++ b/1-ComputationAndData/MVaP/MVaP-1.0/MVaP/js/LexerMVaP.dot @@ -0,0 +1,33 @@ +digraph LexerMVaP { + Start -> Start [label="space "]; + Start -> Id [label="[A-Z]"]; + Id -> Id [label="[A-Z]"]; + + Start -> Int [label="[-+0-9]"]; + Int -> Int [label="[0-9]"]; + Int 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z^2_g~Oe{Z$y{fX8g@^wmrl3B!jHM9!Af0a-41bbUKoX$cn7qDOaTaxE(63)of9-}X zR-9nSGv>a+ zDe<)@Mjo55Y705z&Y!uQjf(GW0mr3M8J4%b^~@&Lc7yA36W&(g?l#-?*t8{^{tJcM B3|0UD literal 0 HcmV?d00001 diff --git a/1-ComputationAndData/MVaP/MVaP-1.0/MVaP/js/MVaP.js b/1-ComputationAndData/MVaP/MVaP-1.0/MVaP/js/MVaP.js new file mode 100644 index 0000000..5316e1d --- /dev/null +++ b/1-ComputationAndData/MVaP/MVaP-1.0/MVaP/js/MVaP.js @@ -0,0 +1,481 @@ +/* + MVàP : Machine Virtuelle à Pile + + 2 méthodes principales : + + load(text) qui charge du texte, l'analyse et l'assemble. + runcode(maxSteps, d) qui exécute le code en limitant le nombre d'étape à maxSteps et qui produit des traces si d est true. + + Les sorties se font dans un élément d'id "tracesBox". + Les entrées dans un élément d'id "inputBox". + Les messages d'erreur vont dans un élément d'id "errorBox". + + + Auteur : Jacques Madelaine + Version 1.0 + +*/ + +"use strict"; + +let debugLexer = false; +let debugAssemble = false; +let debug = true; + +/** token lexicaux */ +const T_ID = 0; +const T_INT = 1; +const T_FLOAT = 2; +const T_SPACE = 3; +const T_NL = 4; +const T_ERROR = 5; +const T_EOF = 6; + +let T_Text = [ "T_ID", "T_INT", "T_FLOAT", "T_SPACE", "T_NL", "T_ERROR", "T_EOF" ]; + +/** token grammaticaux */ +const INSTR1 = 0; +const INSTR2 = 1; +const INT = 2; +const INSTR2F = 3; +const FLOAT = 4; +const LABEL = 5; +const JUMP = 6; +const NEWLINE = 7; + +class MVaP { + + codes = [ // pour l'interprète de MVàP + [ "ADD", INSTR1, () => { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.push(p2+p1); } ], + [ "SUB", INSTR1, () => { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.push(p2-p1); } ], + [ "MUL", INSTR1, () => { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.push(p2*p1); } ], + [ "DIV", INSTR1, () => { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.push(Math.floor(p2/p1)); } ], + [ "INF", INSTR1, () => { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.push(p2 { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.push(p2<=p1?1:0); } ], + [ "SUP", INSTR1, () => { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.push(p2>p1?1:0); } ], + [ "SUPEQ", INSTR1, () => { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.push(p2>=p1?1:0); } ], + [ "EQUAL", INSTR1, () => { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.push(p2==p1?1:0); } ], + [ "NEQ", INSTR1, () => { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.push(p2!=p1?1:0); } ], + [ "FADD", INSTR1, () => { let d1 = this.stack.popFloat64(); let d2 = this.stack.popFloat64(); this.stack.pushFloat64(d2+d1); } ], + [ "FSUB", INSTR1, () => { let d1 = this.stack.popFloat64(); let d2 = this.stack.popFloat64(); this.stack.pushFloat64(d2-d1); } ], + [ "FMUL", INSTR1, () => { let d1 = this.stack.popFloat64(); let d2 = this.stack.popFloat64(); this.stack.pushFloat64(d2*d1); } ], + [ "FDIV", INSTR1, () => { let d1 = this.stack.popFloat64(); let d2 = this.stack.popFloat64(); this.stack.pushFloat64(d2/d1); } ], + [ "FINF", INSTR1, () => { let d1 = this.stack.popFloat64(); let d2 = this.stack.popFloat64(); this.stack.push(d2 { let d1 = this.stack.popFloat64(); let d2 = this.stack.popFloat64(); this.stack.push(d2<=d1?1:0); } ], + [ "FSUP", INSTR1, () => { let d1 = this.stack.popFloat64(); let d2 = this.stack.popFloat64(); this.stack.push(d2>d1?1:0); } ], + [ "FSUPEQ", INSTR1, () => { let d1 = this.stack.popFloat64(); let d2 = this.stack.popFloat64(); this.stack.push(d2>=d1?1:0); } ], + [ "FEQUAL", INSTR1, () => { let d1 = this.stack.popFloat64(); let d2 = this.stack.popFloat64(); this.stack.push(d2==d1?1:0); } ], + [ "FNEQ", INSTR1, () => { let d1 = this.stack.popFloat64(); let d2 = this.stack.popFloat64(); this.stack.push(d2!=d1?1:0); } ], + [ "ITOF", INSTR1, () => { let p1 = this.stack.pop(); this.trace("ITOF "+p1); this.stack.pushFloat64(p1); } ], + [ "FTOI", INSTR1, () => { this.stack.push(Math.round(this.stack.popFloat64())); } ], + [ "RETURN", INSTR1, () => { while(this.stack.getSize() > this.fp) this.stack.pop(); + this.fp = this.stack.pop(); this.pc = this.stack.pop(); } ], + [ "POP", INSTR1, () => { this.stack.pop(); } ], + [ "READ", INSTR1, () => { this.read(); return true; } ], + [ "READF", INSTR1, () => { this.read(); return true; } ], + [ "WRITE", INSTR1, () => { this.trace(this.stack.peek()+"\n"); } ], + [ "WRITEF", INSTR1, () => { this.trace(this.stack.peekFloat64()+"\n"); } ], + [ "PADD", INSTR1, () => { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.push(p2+p1); } ], + [ "PUSHGP", INSTR1, () => { this.stack.push(0); } ], + [ "PUSHFP", INSTR1, () => { this.stack.push(this.fp); } ], + [ "DUP", INSTR1, () => { this.stack.push(this.stack.peek()); } ], + + [ "PUSHI", INSTR2, () => { this.stack.push(this.program.get(this.pc++)); } ], + [ "PUSHG", INSTR2, () => { this.stack.push(this.stack.get(this.program.get(this.pc++)));} ], + [ "STOREG", INSTR2, () => { this.stack.set(this.program.get(this.pc++), this.stack.pop())} ], + [ "PUSHL", INSTR2, () => { this.stack.push(this.stack.get(this.fp+this.program.get(this.pc++))); } ], + [ "STOREL", INSTR2, () => { this.stack.set(this.fp+this.program.get(this.pc++), this.stack.pop()); } ], + [ "PUSHR", INSTR2, () => { this.stack.push(this.stack.get(this.stack.pop()+this.program.get(this.pc++))); } ], + [ "STORER", INSTR2, () => { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.set(p2+this.program.get(this.pc++)); } ], + [ "FREE", INSTR2, () => { this.stack.doPop(this.program.get(this.pc++)); } ], + [ "ALLOC", INSTR2, () => { this.stack.doPush(this.program.get(this.pc++)); } ], + [ "PUSHF", INSTR2F, () => { this.stack.pushFloat64(this.program.getFloat64(this.pc)); this.pc += 2; } ], + [ "CALL", JUMP, () => { this.stack.push(this.pc+1); this.stack.push(this.fp); + this.fp = this.stack.getSize(); + this.pc = this.program.get(this.pc); } ], + [ "JUMP", JUMP, () => { this.pc = this.program.get(this.pc); } ], + [ "JUMPF", JUMP, () => { if (this.stack.pop()==0) this.pc = this.program.get(this.pc); + else this.pc++; } ], + [ "JUMPI", JUMP, () => { this.pc = this.program.get(this.pc)+this.stack.pop();} ], + + [ "HALT", INSTR1, () => { return true; } ], + + [ "LABEL", LABEL, /* erreur interne */ ] + ]; + /*** Ajouter instr : POPF */ + + tokens = []; // indexe le tableau codes sur son premier élément + + text = ""; + + // + // see LexerMVaP.png for the DFA diagram + state = "Start"; + text; // le texte à analyser + index = 0; // index dans la chaîne text + lineNumber = 1; + + transitions = [ + { state: "Start", next: "Start", test: (c) => { return c == "\n"; }, token: T_NL }, + { state: "Start", next: "Start", test: (c) => { return c.trim() == ""; }, token: false }, + { state: "Start", next: "Id", test: (c) => { return "A" <= c && c <= "Z"; }, token: false }, + { state: "Id", next: "Id", test: (c) => { return "A" <= c && c <= "Z"; }, token: false}, + { state: "Id", next: "Start", test: (c) => { return c.trim() == ""; }, token: T_ID}, + { state: "Start", next: "Int", test: (c) => { return ("0" <= c && c <= "9")||c=="-"||c=="+"; }, token: false }, + { state: "Int", next: "Int", test: (c) => { return "0" <= c && c <= "9"; }, token: false }, + { state: "Int", next: "Start", test: (c) => { return c.trim() == ""; }, token: T_INT }, + { state: "Int", next: "Decimal", test: (c) => { return c == "."; }, token: false }, + { state: "Int", next: "E", test: (c) => { return c == "E"; }, token: false }, + { state: "Decimal", next: "Decimal", test: (c) => { return "0" <= c && c <= "9"; }, token: false }, + { state: "Decimal", next: "E", test: (c) => { return c == "E"; }, token: false }, + { state: "Decimal", next: "Start", test: (c) => { return c.trim() == ""; }, token: T_FLOAT }, + { state: "E", next: "Exponent", test: (c) => { return ("0"<=c && c<="9")||c=="-"||c=="+"; }, token: false }, + { state: "Exponent", next: "Exponent", test: (c) => { return "0" <= c && c <= "9"; }, token: false }, + { state: "Exponent", next: "Start", test: (c) => { return c.trim() == ""; }, token: T_FLOAT } + // else: error + ]; + + initLexer() { + this.index = 0; + this.lineNumber = 1 + console.log("*****************\n* C'est parti *\n*****************"); + } + + // Donne la transition correspondante à l'état courant et au caractère entrant + transition(c) { + for (let v of this.transitions.values()) { + // on aurait pu indexer les transitions sur state au lieu de tout énumérer + if (this.state == v.state && v.test(c)) { + return v; + } + } + return T_ERROR; + } + + yytext = ""; // contient le texte du jeton syntaxique (nommé comme dans lex/yacc) + + + nextToken() { + let c; + let trans; + while (true) { + c = this.text[this.index]; + if (c === undefined) + return T_EOF; + c = c.toUpperCase(); + trans = this.transition(c); + if (trans == T_ERROR) { this.yytext += c; return T_ERROR; } + if (this.state != trans.next && this.state == "Start") this.yytext =""; + + this.state = trans.next; + this.index++; + + if (Number.isInteger(trans.token)) { + break; + } + this.yytext += c; + } + + // séparateur significatif + if (c == "\n") { + if (trans.token != T_NL) { + this.index--; // ne pas manger la fin de ligne non prise en compte + // une autre façon de dire est que l'on n'incrémente pas l'index sur le renvoi de token + // sauf en cas de token constitué de séparateur + } else + this.lineNumber++; // on en profite pour compter la ligne + } + // console.log(" line " + this.lineNumber + " " + trans.token + " '" + yytex + "' i="+i); + return trans.token; + } + // + + // + + /** Grammaire des instructions + instr + : INSTR1 T_NL + | INSTR2 T_INT T_NL + | JUMP T_INT T_NL + | INSTR2F T_FLOAT T_NL + | LABEL T_NL + | T_NL + ; + */ + + program;// Pile contenant le programme compilé + adressesLabels; // adresse des étiquettes pour l'assemblage + + analyse() { + + this.initLexer(); + + let token; // le jeton lexical courant + let state = NEWLINE; // état de l'analyseur grammatical (ici le précédent syntagme grammatical) + this.program = new Pile(); + this.adressesLabels = []; + + while (true) { + this.yytext = ""; + token = this.nextToken(); + if (debugLexer) + console.log("** nextToken line "+this.lineNumber+" token "+token+" "+T_Text[token]+" '" +this.yytext+"' index "+this.index+" state "+state); + + switch(token) { + case T_EOF: + return true; + case T_ID: + let k = this.tokens[this.yytext]; + if (k === undefined || state != NEWLINE) return false; + state = this.codes[k][1]; + if (state != LABEL) { // pas d'instruction LABEL dans le code + this.program.push(k); + } + break; + case T_INT: + if (state == LABEL) { // on mémorise juste l'adresse pour la passe d'assemblage + this.adressesLabels[Number(this.yytext)] = this.program.getSize(); // ± 1 who knows? + } else if(state == INSTR2 || state == JUMP) { + this.program.push(Number(this.yytext)); + } else return false; + state = INT; + break; + case T_FLOAT: + if (state != INSTR2F) return false; + state = FLOAT; + this.program.pushFloat64(Number(this.yytext)); + break; + case T_NL: + if (state == INSTR2 || state == JUMP || state == INSTR2F) return false; + state = NEWLINE; + break; + case T_ERROR: + return false; + default: + alert("Erreur interne prévenir la maintenance d'urgence"); + return false; + } + } + console.log("Programme correct syntaxiquement"); + return true; + } + + assemble() { + // change les numéros d'étiquettes par les adresses des instructions pointées. + if (debugAssemble) { + console.log("Label "+this.adressesLabels); + console.log(this.dumpProgram()); + } + + for (let i = 0; i < this.program.getSize(); i++) { + let k = this.program.get(i); + // Attention il faut compter si par malchance un entier = code d'un saut + switch (this.codes[k][1]) { + case INSTR1: + break; + case INSTR2: + i++; // on saute l'entier qui suit + break; + case INSTR2F: + i += 2; // on saute le flottant qui suit + break; + case JUMP: // met à jour l'adresse du saut + i++; + console.log("--- set "+i); + this.program.set(i, this.adressesLabels[this.program.get(i)]); + break; + default: + alert("Erreur assemblage"); + } + } + // console.log(this.dumpProgram()); + return true; + } + // + + + dumpInstruction(i, result) { + let code = this.codes[this.program.get(i)]; + result += code[0].padEnd(6, ' '); + switch (code[1]) { + case INSTR2: + case JUMP: + result += this.program.get(++i).toString().padStart(7, ' '); + break; + case INSTR2F: + result += this.program.getFloat64(++i).toString().padStart(7, ' '); + i++; + break; + default: + result += " "; + } + + return [i, result]; + } + + dumpProgram() { + let result = ""; + result += this.program + "\n"; + + result += " Adr | Instruction\n-----+---------------\n"; + for(let i = 0; i < this.program.getSize(); i++) { + result += i.toString().padStart(4, " ")+" | "; + [i, result] = this.dumpInstruction(i, result); + result += "\n"; + } + return result; + } + + constructor() { + // init tokens + for (let k of this.codes.keys()) + this.tokens[this.codes[k][0]] = k; + try { + inputBox.addEventListener("keydown", (event) => { this.enterText(event); }); + } catch(e) { + alert("Warning READ indisponible"); + } + + } + + // charge et compile le code + load(text) { + // on supprime les commentaires + this.text = text.replaceAll(/(#|\/\/).*\n/g, "\n"); + // on insère une fin de ligne si le texte n'en a pas à sa fin + if (this.text[this.text.length-1] != "\n") this.text = this.text+"\n"; + if (! this.analyse()) { + alert("Erreur ligne "+this.lineNumber+" sur '" +this.yytext+"'"); + return false; + } + return this.assemble(); + + } + + pc = 0; + fp = 0; + stack; + step; // step number of the current run + maxSteps; + + runCode(maxSteps, d) { + debug = d; + //for (let i = 0; i < this.codes.length; i++) console.log(i+ " "+ this.codes[i][0]); + this.pc = 0; + this.fp = 0; + this.stack = new Pile(); + + if (debug) + this.trace("Programme\n"+this.dumpProgram() + "\nTraces exécution\n" + + " pc | Instruction | fp pile\n" + + "=====+===============+=============================\n"); + this.cleanInputAndErrorBoxes(); + this.step = 0; + this.maxSteps = maxSteps; + this.resumeRun(); + + } + + resumeRun(readCode, readResult) { + if (readCode != undefined && readResult != undefined) { // return from read + // READ or READF ? + if (readCode == "READ") + this.stack.push(readResult); + else if (readCode == "READF") + this.stack.pushFloat64(readResult); + else { + this.trace("Read Code inattendu "+readCode, true); + return; + } + this.step++; + } + for (; this.maxSteps <= 0 || this.step < this.maxSteps; this.step++) // while (true) + { + // if (this.pc < 0 || this.pc >= this.program.getSize()) break; + try { + + if (debug) { + let s = this.pc.toString().padStart(4, " ")+" | "; + let junk; + [junk, s] = this.dumpInstruction(this.pc, s); + s += " |"+this.fp.toString().padStart(4,' ')+' '+this.stack.toString()+"\n"; + this.trace(s); + } + if (this.codes[this.program.get(this.pc++)][2]() === true) + break; + + } catch(e) { + this.trace(e, true); + break; + } + } + } + + trace(s, error) { + if (error) { + console.error(s); + errorBox.innerText = s; + errorBox.hidden = false; + errorBox.scrollIntoView(); + } else { + tracesBox.innerText += s; + console.log(s); + } + } + + cleanInputAndErrorBoxes() { + errorBox.innerText = ""; + errorBox.hidden = true; + inputBox.value = ""; + inputBox.hidden = true; + } + + + read() { + inputBox.hidden = false; + inputBox.focus(); + } + + enterText(e) { + if (e.code == "Enter") { + let readResult = 0; + // What is the last op token + let t = this.codes[this.program.get(this.pc-1)][0]; + switch (t) { + case "READ": + readResult = Number.parseInt(inputBox.value, 10); + if (! Number.isInteger(readResult)) { + alert(inputBox.value+" n'est pas un nombre entier"); + return; + } + break; + case "READF": + readResult = Number.parseFloat(inputBox.value); + if (Number.isNaN(readResult)) { + alert(inputBox.value+" n'est pas un nombre entier"); + return; + } + break; + default: + this.trace("Code inattendu pour lecture "+t+"\n", true); + return; + } + + tracesBox.innerText += " > "+readResult+"\n"; + inputBox.value = ""; + inputBox.hidden = true; + console.log("READ ->"+readResult); + this.resumeRun(t, readResult); + + } + } + +} + + + + + + + + diff --git a/1-ComputationAndData/MVaP/MVaP-1.0/MVaP/js/Pile.js b/1-ComputationAndData/MVaP/MVaP-1.0/MVaP/js/Pile.js new file mode 100644 index 0000000..f78f210 --- /dev/null +++ b/1-ComputationAndData/MVaP/MVaP-1.0/MVaP/js/Pile.js @@ -0,0 +1,153 @@ +// Class Pile +// Auteur : Jacques Madelaine + +// Une Pile est essentiellement une pile d'entiers ("int32") +// Elle peut aussi empiler et dépiler des flottants définis sur 64 bits. +// L'index est sur les entiers. + +// Rappel : en JavaScript les Number sont tous stockés comme des flottants 64 bits. +// Il faut donc voir cette Pile comme un objet pédagogique +// et non une implémentation optimale en JavaScipt. + +"use strict"; + +class Pile { + buffer; // ArrayBuffer de bytes + pile; // On va utiliser 4 bytes pour les entiers et 8 pour les flottants + haut = 0; // index de sommet de pile en bytes + + // size : taille en bytes de la pile + constructor(size) { + if (size === undefined) + size = 1000; + + this.buffer = new ArrayBuffer(size); + this.pile = new DataView(this.buffer); + } + + push(i) { + if (! Number.isInteger(i)) + throw new TypeError("Try to push a non integer"); + this.pile.setInt32(this.haut, i); + this.haut += 4; + } + + doPush(nb) { for(; nb > 0; nb--) this.push(0); } + + pop() { + this.haut -= 4; + return this.pile.getInt32(this.haut); + } + + doPop(nb) { for(; nb > 0; nb--) this.pop(); } + + peek() { + return this.pile.getInt32(this.haut-4); + } + + set(index, i) { + if (! Number.isInteger(i)) + throw new TypeError("Try to set a non integer"); + this.pile.setInt32(index*4, i); + } + + get(index) { + return this.pile.getInt32(index*4); + } + + + pushFloat64(f) { + this.pile.setFloat64(this.haut, f); + this.haut += 8; + } + + popFloat64() { + this.haut -= 8; + return this.pile.getFloat64(this.haut); + } + + peekFloat64() { + return this.pile.getFloat64(this.haut-8); + } + + setFloat64(index, f) { + this.pile.setFloat64(index*4, f); + } + + getFloat64(index) { + return this.pile.getFloat64(index*4); + } + + getMaxSize() { + return this.buffer.byteLength/2; + } + + getSize() { + return this.haut/4; + } + + toString() { + let out = "[ "; + for (let i = 0; i < this.getSize(); i++) + out += this.get(i) + ", "; + return out + " ] " + this.getSize(); + } + +} + + +/* + +let p = new Pile(); +try { + let d = 12.34; + let i = 0x7FFFFFFF; + let j = 0; + p.push(i); + j = p.peek(); + console.log(i + " =?= " + j); + + let N = 5; + for(let n = 0; n < N; n++) { + p.push(n); + console.log("push "+n+" " + n); + } + + console.log("get(2) " + p.get(2)); + console.log(p.toString()); + + for(let n = N; n > 0; n--) { + let m = p.pop(); + // if (2*n != m) + console.log("push "+ n + " pop " + m); + } + p.pop(); + + p.push(40); + p.pushFloat64(d); + p.pushFloat64(13.34); + p.push(i); + console.log(p.toString()); + + for (let n = 0; n<6;n++) + console.log("p.getFloat64("+n+") = "+p.getFloat64(n)); + + p.pop(); + p.popFloat64(); + let e = p.popFloat64(); + console.log(d + " =?= " + e); + + + d = -1; + p.pushFloat64(d); + e = p.popFloat64(); + console.log(d + " =?= " + e); + // + // for (i = 0 ; i < 1000000; i++) + // p.push(i); +} catch(e) { + console.error(e); +} +*/ + + diff --git a/1-ComputationAndData/MVaP/MVaP-v0.tgz b/1-ComputationAndData/MVaP/MVaP-v0.tgz new file mode 100644 index 0000000000000000000000000000000000000000..b19d7bcc2175b5fb3123c7c929e3b58fec247c83 GIT binary patch literal 78354 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z*=zv5DlnuR`c=C{T%a$*nn*h(@-ee}{mAP!JIas^AC#FD%V zKN2+vUwrw=KS~f*!qnA|WNb#=ur*wuTM^qyNYy^Fms^esmp_Pt+vDH;-UVW@W}I4V zAp1R$B)VB|OE-zb`NplAsQgfJZ0%~~;V9RV7Lhu6iKYg!oBkw3BcB5QYZ6%TQjh@v zfGorRlrEbLJQ(SGwiE{}oe$9n?MF7i-u#8SOrnByfg#GT?O1&yO@u5NLj-;Zo+6hc zHvk0bL>a)1MihClJ-Hr3=d=dUW^McV`Jm3CNVU6jHI%P>t($|~jeDX)cppc5%RC$$ zq`vm6>?um*b2E5h*RK=TM<<4%wZvgD=$orE)E;6A1_5j1qyJwE_!@0I<4XnX1kpM% G(f + + + + MVàP + + + + + + + + +

Machine Virtuelle à Pile

+ +

Historique

+ Blabla sur la MVàP... + +

Documentation

+ Toute la doc +

+ lorem ipsum +

La MVàP

+

Entrez le code

+
+ +
+ +

Exécution

+ + + + + + + + + +
+
+    
+
+ + + + diff --git a/1-ComputationAndData/MVaP/MVaP-v0/MVaP/js/CBaP.js b/1-ComputationAndData/MVaP/MVaP-v0/MVaP/js/CBaP.js new file mode 100644 index 0000000..9864c57 --- /dev/null +++ b/1-ComputationAndData/MVaP/MVaP-v0/MVaP/js/CBaP.js @@ -0,0 +1,216 @@ +/** + * Code Binaire pour Machine Virtuelle à Pile. + * Les flottants sont des double qui prennent la place de 2 ints. + * Les adresses sont des int. + * CALL empile l'adresse de retour et la vauler du framePointer dans la pile. + */ +public class CBaP { + + + + pc = 0; + fp = 0; + stack; + program; + const SizeofDouble = 2; + + _debug = false; + + CBaP(program, debug, stackSize) { + this.program = program; + this._debug = debug; + this.stack = new Pile(stackSize); + } + + dumpInstruction(ii, out) { + let i = ii; + switch(program.get_int(i)) { + case AssembleMVaP.ADD: out.print("ADD "); break; + case AssembleMVaP.SUB: out.print("SUB "); break; + case AssembleMVaP.MUL: out.print("MUL "); break; + case AssembleMVaP.DIV: out.print("DIV "); break; + case AssembleMVaP.INF: out.print("INF "); break; + case AssembleMVaP.INFEQ: out.print("INFEQ "); break; + case AssembleMVaP.SUP: out.print("SUP "); break; + case AssembleMVaP.SUPEQ: out.print("SUPEQ "); break; + case AssembleMVaP.EQUAL: out.print("EQUAL "); break; + case AssembleMVaP.NEQ: out.print("NEQ "); break; + + case AssembleMVaP.FADD: out.print("FADD "); break; + case AssembleMVaP.FSUB: out.print("FSUB "); break; + case AssembleMVaP.FMUL: out.print("FMUL "); break; + case AssembleMVaP.FDIV: out.print("FDIV "); break; + case AssembleMVaP.FINF: out.print("FINF "); break; + case AssembleMVaP.FINFEQ: out.print("FINFEQ"); break; + case AssembleMVaP.FSUP: out.print("FSUP "); break; + case AssembleMVaP.FSUPEQ: out.print("FSUPEQ"); break; + case AssembleMVaP.FEQUAL: out.print("FEQUAL"); break; + case AssembleMVaP.FNEQ: out.print("FNEQ "); break; + case AssembleMVaP.ITOF: out.print("ITOF "); break; + case AssembleMVaP.FTOI: out.print("FTOI "); break; + + case AssembleMVaP.RETURN: out.print("RETURN"); break; + case AssembleMVaP.POP: out.print("POP "); break; + case AssembleMVaP.READ: out.print("READ "); break; + case AssembleMVaP.WRITE: out.print("WRITE "); break; + case AssembleMVaP.WRITEF: out.print("WRITEF"); break; + case AssembleMVaP.PADD: out.print("PADD "); break; + case AssembleMVaP.PUSHGP: out.print("PUSHGP"); break; + case AssembleMVaP.PUSHFP: out.print("PUSHFP"); break; + case AssembleMVaP.DUP: out.print("DUP "); break; + + case AssembleMVaP.PUSHI: out.print("PUSHI "); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.PUSHG: out.print("PUSHG "); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.STOREG: out.print("STOREG"); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.PUSHL: out.print("PUSHL "); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.STOREL: out.print("STOREL"); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.PUSHR: out.print("PUSHR "); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.STORER: out.print("STORER"); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.FREE: out.print("FREE "); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.ALLOC: out.print("ALLOC "); out.format("%7d ", program.get_int(++i)); break; + + case AssembleMVaP.PUSHF: out.print("PUSHF "); ++i; out.format("%7.3f ", program.get_double(++i)); break; + + case AssembleMVaP.JUMP: out.print("JUMP "); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.JUMPF: out.print("JUMPF "); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.JUMPI: out.print("JUMPI "); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.CALL: out.print("CALL "); out.format("%7d ", program.get_int(++i)); break; + case AssembleMVaP.HALT: out.print("HALT "); break; + default: System.err.println("Code inconnu "+program.get_int(i)+" ligne "+i); + } + if (i == ii) out.print(" "); + return i; + } + + public void dumpProgram(PrintStream out) { + // out.println(program.toString(true)); + // out.println(program.toString()); + out.println(" Adr | Instruction"); + out.println("-----+---------------"); + for(int i = 0; i < program.getSize(); i++) { + out.format("%4d | ", i); + i = dumpInstruction(i, out); + out.println(); + } + } + + private void _call(int label) { + push(pc+1); + push(fp); + fp = size(); + pc = label; + } + + private void _return() { + while(size() > fp) + pop(); + fp = pop(); + pc = pop(); + } + + private BufferedReader input = null; + private int _read() { + try { + if (input == null) + input = new BufferedReader(new InputStreamReader(System.in)); + return Integer.parseInt(input.readLine()); + } catch (Exception e) { + System.err.println(e); + System.exit(1); + return 0; + } + } + + public boolean execute() { + if (_debug) { + dumpProgram(System.out); + System.err.println(); + System.err.println(" pc | | fp pile"); + System.err.println("===================================================="); + } + pc = 0; + while (true) { + if (_debug) { + System.err.format("%4d | ", pc); + dumpInstruction(pc, System.err); + System.err.format("| %4d %s\n", fp, stack.toString()); + } + try { + int p1, p2; // utile pour être sûr de l'ordre des pop() ! + double d1, d2; + switch(program.get_int(pc++)) { + case AssembleMVaP.ADD: p1 = pop(); p2 = pop(); push(p2 + p1); break; + case AssembleMVaP.SUB: p1 = pop(); p2 = pop(); push(p2 - p1); break; + case AssembleMVaP.MUL: p1 = pop(); p2 = pop(); push(p2 * p1); break; + case AssembleMVaP.DIV: p1 = pop(); p2 = pop(); push(p2 / p1); break; + case AssembleMVaP.INF: p1 = pop(); p2 = pop(); push(p2 < p1 ? 1 : 0); break; + case AssembleMVaP.INFEQ: p1 = pop(); p2 = pop(); push(p2 <= p1 ? 1 : 0); break; + case AssembleMVaP.SUP: p1 = pop(); p2 = pop(); push(p2 > p1 ? 1 : 0); break; + case AssembleMVaP.SUPEQ: p1 = pop(); p2 = pop(); push(p2 >= p1 ? 1 : 0); break; + case AssembleMVaP.EQUAL: p1 = pop(); p2 = pop(); push(p2 == p1 ? 1 : 0); break; + case AssembleMVaP.NEQ: p1 = pop(); p2 = pop(); push(p2 != p1 ? 1 : 0); break; + + case AssembleMVaP.FADD: d1 = pop_double(); d2 = pop_double(); push(d2 + d1); break; + case AssembleMVaP.FSUB: d1 = pop_double(); d2 = pop_double(); push(d2 - d1); break; + case AssembleMVaP.FMUL: d1 = pop_double(); d2 = pop_double(); push(d2 * d1); break; + case AssembleMVaP.FDIV: d1 = pop_double(); d2 = pop_double(); push(d2 / d1); break; + case AssembleMVaP.FINF: d1 = pop_double(); d2 = pop_double(); push(d2 < d1 ? 1 : 0); break; + case AssembleMVaP.FINFEQ: d1 = pop_double(); d2 = pop_double(); push(d2 <= d1 ? 1 : 0); break; + case AssembleMVaP.FSUP: d1 = pop_double(); d2 = pop_double(); push(d2 > d1 ? 1 : 0); break; + case AssembleMVaP.FSUPEQ: d1 = pop_double(); d2 = pop_double(); push(d2 >= d1 ? 1 : 0); break; + case AssembleMVaP.FEQUAL: d1 = pop_double(); d2 = pop_double(); push(d2 == d1 ? 1 : 0); break; + case AssembleMVaP.FNEQ: d1 = pop_double(); d2 = pop_double(); push(d2 != d1 ? 1 : 0); break; + + case AssembleMVaP.FTOI: push((int)pop_double()); break; + case AssembleMVaP.ITOF: push((double)pop()); break; + + case AssembleMVaP.RETURN: _return(); break; + case AssembleMVaP.POP: pop(); break; + case AssembleMVaP.READ: push(_read()); break; + case AssembleMVaP.WRITE: System.out.format("%7d\n", peek()); break; + case AssembleMVaP.WRITEF: System.out.format("%7.3f\n", peek_double()); break; + case AssembleMVaP.PADD: p1 = pop(); p2 = pop(); push(p2 + p1); break; + case AssembleMVaP.PUSHGP: push(0); break; + case AssembleMVaP.PUSHFP: push(fp); break; + case AssembleMVaP.DUP: push(peek()); break; + + case AssembleMVaP.PUSHI: push(program.get_int(pc++)); break; + case AssembleMVaP.PUSHG: push(get(program.get_int(pc++))); break; + case AssembleMVaP.STOREG: set(program.get_int(pc++), pop()); break; + // ajouter -2 si adresse négative ? + case AssembleMVaP.PUSHL: push(get(fp+program.get_int(pc++))); break; + case AssembleMVaP.STOREL:set(fp+program.get_int(pc++), pop()); break; + case AssembleMVaP.PUSHR: push(get(pop()+program.get_int(pc++)));break; + case AssembleMVaP.STORER:p1 = pop(); p2 = pop(); set(p2+program.get_int(pc++), p1); break; + case AssembleMVaP.FREE: doPop(program.get_int(pc++)); break; + case AssembleMVaP.ALLOC: doPush(program.get_int(pc++)); break; + + case AssembleMVaP.PUSHF: push(program.get_int(pc++)); push(program.get_int(pc++)); break; + + case AssembleMVaP.JUMP: pc = program.get_int(pc); break; + case AssembleMVaP.JUMPF: if (pop() == 0) pc = program.get_int(pc); else pc++; break; + case AssembleMVaP.JUMPI: pc = program.get_int(pc)+pop(); break; + case AssembleMVaP.CALL: _call(program.get_int(pc)); break; + case AssembleMVaP.HALT: return true; + default: System.err.println("Code inconnu "+program.get_int(pc)+" ligne "+pc); return false; + } + } catch (ArrayIndexOutOfBoundsException e) { + System.err.println(stack.getException()); + return false; + } + } + } + + void push(int i) { stack.push(i); } + int pop() { return stack.pop_int(); } + void push(double d) { stack.push(d); } + double pop_double() { return stack.pop_double(); } + int peek() { return stack.peek_int(); } + double peek_double() { return stack.peek_double(); } + int size() { return stack.getSize(); } + void set(int index, int i) { stack.set(index, i); } + int get(int index) { return stack.get_int(index); } + + void doPop(int nb) { for(; nb > 0; nb--) stack.pop_int(); } + void doPush(int nb) { for(; nb > 0; nb--) stack.push(0); } +} diff --git a/1-ComputationAndData/MVaP/MVaP-v0/MVaP/js/LexerMVaP.dot b/1-ComputationAndData/MVaP/MVaP-v0/MVaP/js/LexerMVaP.dot new file mode 100644 index 0000000..be9c7c5 --- /dev/null +++ b/1-ComputationAndData/MVaP/MVaP-v0/MVaP/js/LexerMVaP.dot @@ -0,0 +1,33 @@ +digraph LexerMVaP { + Start -> Start [label="space "]; + Start -> Id [label="[A-Z]"]; + Id -> Id [label="[A-Z]"]; + + Start -> Int [label="[-+0-9]"]; + Int -> Int [label="[0-9]"]; + Int -> 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z^2_g~Oe{Z$y{fX8g@^wmrl3B!jHM9!Af0a-41bbUKoX$cn7qDOaTaxE(63)of9-}X zR-9nSGv>a+ zDe<)@Mjo55Y705z&Y!uQjf(GW0mr3M8J4%b^~@&Lc7yA36W&(g?l#-?*t8{^{tJcM B3|0UD literal 0 HcmV?d00001 diff --git a/1-ComputationAndData/MVaP/MVaP-v0/MVaP/js/MVaP.js b/1-ComputationAndData/MVaP/MVaP-v0/MVaP/js/MVaP.js new file mode 100644 index 0000000..6466a56 --- /dev/null +++ b/1-ComputationAndData/MVaP/MVaP-v0/MVaP/js/MVaP.js @@ -0,0 +1,374 @@ +// MVàP + +let debugLexer = false; +let debug = true; + +/** token lexicaux */ +const T_ID = 0; +const T_INT = 1; +const T_FLOAT = 2; +const T_SPACE = 3; +const T_NL = 4; +const T_ERROR = 5; +const T_EOF = 6; + +T_Text = [ "T_ID", "T_INT", "T_FLOAT", "T_SPACE", "T_NL", "T_ERROR", "T_EOF" ]; + +/** token grammaticaux */ +const INSTR1 = 0; +const INSTR2 = 1; +const INT = 2; +const INSTR2F = 3; +const FLOAT = 4; +const LABEL = 5; +const JUMP = 6; +const NEWLINE = 7; + +class MVaP { + + codes = [ // pour l'interprète de MVàP + [ "ADD", INSTR1, () => { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.push(p2+p1); } ], + [ "SUB", INSTR1, () => { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.push(p2-p1); } ], + [ "MUL", INSTR1, () => { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.push(p2*p1); } ], + [ "DIV", INSTR1, () => { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.push(Math.floor(p2/p1)); } ], + [ "INF", INSTR1, () => { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.push(p2 { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.push(p2<=p1?1:0); } ], + [ "SUP", INSTR1, () => { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.push(p2>p1?1:0); } ], + [ "SUPEQ", INSTR1, () => { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.push(p2>=p1?1:0); } ], + [ "EQUAL", INSTR1, () => { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.push(p2==p1?1:0); } ], + [ "NEQ", INSTR1, () => { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.push(p2!=p1?1:0); } ], + [ "FADD", INSTR1, () => { let d1 = this.stack.popFloat64(); let d2 = this.stack.popFloat64(); this.stack.pushFloat64(d2+d1); } ], + [ "FSUB", INSTR1, () => { let d1 = this.stack.popFloat64(); let d2 = this.stack.popFloat64(); this.stack.pushFloat64(d2-d1); } ], + [ "FMUL", INSTR1, () => { let d1 = this.stack.popFloat64(); let d2 = this.stack.popFloat64(); this.stack.pushFloat64(d2*d1); } ], + [ "FDIV", INSTR1, () => { let d1 = this.stack.popFloat64(); let d2 = this.stack.popFloat64(); this.stack.pushFloat64(d2/d1); } ], + [ "FINF", INSTR1, () => { let d1 = this.stack.popFloat64(); let d2 = this.stack.popFloat64(); this.stack.push(d2 { let d1 = this.stack.popFloat64(); let d2 = this.stack.popFloat64(); this.stack.push(d2<=d1?1:0); } ], + [ "FSUP", INSTR1, () => { let d1 = this.stack.popFloat64(); let d2 = this.stack.popFloat64(); this.stack.push(d2>d1?1:0); } ], + [ "FSUPEQ", INSTR1, () => { let d1 = this.stack.popFloat64(); let d2 = this.stack.popFloat64(); this.stack.push(d2>=d1?1:0); } ], + [ "FEQUAL", INSTR1, () => { let d1 = this.stack.popFloat64(); let d2 = this.stack.popFloat64(); this.stack.push(d2==d1?1:0); } ], + [ "FNEQ", INSTR1, () => { let d1 = this.stack.popFloat64(); let d2 = this.stack.popFloat64(); this.stack.push(d2!=d1?1:0); } ], + [ "ITOF", INSTR1, () => { let p1 = this.stack.pop(); this.trace("ITOF "+p1); this.stack.pushFloat64(p1); } ], + [ "FTOI", INSTR1, () => { this.stack.push(Math.round(this.stack.popFloat64())); } ], + [ "RETURN", INSTR1, () => { while(this.stack.getSize() > this.fp) this.stack.pop(); + this.fp = this.stack.pop(); this.pc = this.stack.pop(); } ], + [ "POP", INSTR1, () => { this.stack.pop(); } ], + [ "READ", INSTR1, () => { this.stack.push(0); } ], // on lit toujours 0 (idée : prendre le contenu d'un input de type text spécial + [ "WRITE", INSTR1, () => { this.trace(this.stack.peek()+"\n"); } ], + [ "WRITEF", INSTR1, () => { this.trace(this.stack.peekFloat64()+"\n"); } ], + [ "PADD", INSTR1, () => { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.push(p2+p1); } ], + [ "PUSHGP", INSTR1, () => { this.stack.push(0); } ], + [ "PUSHFP", INSTR1, () => { this.stack.push(this.fp); } ], + [ "DUP", INSTR1, () => { this.stack.push(this.stack.peek()); } ], + + [ "PUSHI", INSTR2, () => { this.stack.push(this.program.get(this.pc++)); } ], + [ "PUSHG", INSTR2, () => { this.stack.push(this.stack.get(this.program.get(this.pc++)));} ], + [ "STOREG", INSTR2, () => { this.stack.set(this.program.get(this.pc++), this.stack.pop())} ], + [ "PUSHL", INSTR2, () => { this.stack.push(this.stack.get(this.fp+this.program.get(this.pc++))); } ], + [ "STOREL", INSTR2, () => { this.stack.set(this.fp+this.program.get(this.pc++), this.stack.pop()); } ], + [ "PUSHR", INSTR2, () => { this.stack.push(this.stack.get(this.stack.pop()+this.program.get(this.pc++))); } ], + [ "STORER", INSTR2, () => { let p1 = this.stack.pop(); let p2 = this.stack.pop(); this.stack.set(p2+this.program.get(this.pc++)); } ], + [ "FREE", INSTR2, () => { this.stack.doPop(this.program.get(this.pc++)); } ], + [ "ALLOC", INSTR2, () => { this.stack.doPush(this.program.get(this.pc++)); } ], + [ "PUSHF", INSTR2F, () => { this.stack.pushFloat64(this.program.getFloat64(this.pc)); this.pc += 2; } ], + [ "CALL", JUMP, () => { this.stack.push(this.pc+1); this.stack.push(this.fp); + this.fp = this.stack.getSize(); + this.pc = this.program.get(this.pc); } ], + [ "JUMP", JUMP, () => { this.pc = this.program.get(this.pc); } ], + [ "JUMPF", JUMP, () => { if (this.stack.pop()==0) this.pc = this.program.get(this.pc); + else this.pc++; } ], + [ "JUMPI", JUMP, () => { this.pc = this.program.get(this.pc)+this.stack.pop();} ], + + [ "HALT", INSTR1, () => { return true; } ], + + [ "LABEL", LABEL, /* erreur interne */ ] + ]; + /*** Ajouter instr : READF WRITEF POPF */ + + tokens = []; // indexe le tableau codes sur son premier élément + + text = ""; + + // + // see LexerMVaP.png for the DFA diagram + state = "Start"; + text; // le texte à analyser + index = 0; // index dans la chaîne text + lineNumber = 1; + + transitions = [ + { state: "Start", next: "Start", test: (c) => { return c == "\n"; }, token: T_NL }, + { state: "Start", next: "Start", test: (c) => { return c.trim() == ""; }, token: false }, + { state: "Start", next: "Id", test: (c) => { return "A" <= c && c <= "Z"; }, token: false }, + { state: "Id", next: "Id", test: (c) => { return "A" <= c && c <= "Z"; }, token: false}, + { state: "Id", next: "Start", test: (c) => { return c.trim() == ""; }, token: T_ID}, + { state: "Start", next: "Int", test: (c) => { return ("0" <= c && c <= "9")||c=="-"||c=="+"; }, token: false }, + { state: "Int", next: "Int", test: (c) => { return "0" <= c && c <= "9"; }, token: false }, + { state: "Int", next: "Start", test: (c) => { return c.trim() == ""; }, token: T_INT }, + { state: "Int", next: "Decimal", test: (c) => { return c == "."; }, token: false }, + { state: "Int", next: "E", test: (c) => { return c == "E"; }, token: false }, + { state: "Decimal", next: "Decimal", test: (c) => { return "0" <= c && c <= "9"; }, token: false }, + { state: "Decimal", next: "E", test: (c) => { return c == "E"; }, token: false }, + { state: "Decimal", next: "Start", test: (c) => { return c.trim() == ""; }, token: T_FLOAT }, + { state: "E", next: "Exponent", test: (c) => { return ("0"<=c && c<="9")||c=="-"||c=="+"; }, token: false }, + { state: "Exponent", next: "Exponent", test: (c) => { return "0" <= c && c <= "9"; }, token: false }, + { state: "Exponent", next: "Start", test: (c) => { return c.trim() == ""; }, token: T_FLOAT } + // else: error + ]; + + initLexer() { + this.index = 0; + this.lineNumber = 1 + console.log("*****************\n* C'est parti *\n*****************"); + } + + // Donne la transition correspondante à l'état courant et au caractère entrant + transition(c) { + for (let v of this.transitions.values()) { + // on aurait pu indexer les transitions sur state au lieu de tout énumérer + if (this.state == v.state && v.test(c)) { + return v; + } + } + return T_ERROR; + } + + yytext = ""; // contient le texte du jeton syntaxique (nommé comme dans lex/yacc) + + + nextToken() { + let c; + let trans; + while (true) { + c = this.text[this.index]; + if (c === undefined) + return T_EOF; + c = c.toUpperCase(); + trans = this.transition(c); + if (trans == T_ERROR) { this.yytext += c; return T_ERROR; } + if (this.state != trans.next && this.state == "Start") this.yytext =""; + + this.state = trans.next; + this.index++; + + if (Number.isInteger(trans.token)) { + break; + } + this.yytext += c; + } + + // séparateur significatif + if (c == "\n") { + if (trans.token != T_NL) { + this.index--; // ne pas manger la fin de ligne non prise en compte + // une autre façon de dire est que l'on n'incrémente pas l'index sur le renvoi de token + // sauf en cas de token constitué de séparateur + } else + this.lineNumber++; // on en profite pour compter la ligne + } + // console.log(" line " + this.lineNumber + " " + trans.token + " '" + yytex + "' i="+i); + return trans.token; + } + // + + // + + /** Grammaire des instructions + instr + : INSTR1 T_NL + | INSTR2 T_INT T_NL + | JUMP T_INT T_NL + | INSTR2F T_FLOAT T_NL + | LABEL T_NL + | T_NL + ; + */ + + program;// Pile contenant le programme compilé + adressesLabels; // adresse des étiquettes pour l'assemblage + + analyse() { + + this.initLexer(); + + let token; // le jeton lexical courant + let state = NEWLINE; // état de l'analyseur grammatical (ici le précédent syntagme grammatical) + this.program = new Pile(); + this.adressesLabels = []; + + while (true) { + this.yytext = ""; + token = this.nextToken(); + if (debugLexer) + console.log("** nextToken line "+this.lineNumber+" token "+token+" "+T_Text[token]+" '" +this.yytext+"' index "+this.index+" state "+state); + + switch(token) { + case T_EOF: + return true; + case T_ID: + let k = this.tokens[this.yytext]; + if (k === undefined || state != NEWLINE) return false; + state = this.codes[k][1]; + if (state != LABEL) { // pas d'instruction LABEL dans le code + this.program.push(k); + } + break; + case T_INT: + if (state == LABEL) { // on mémorise juste l'adresse pour la passe d'assemblage + this.adressesLabels[Number(this.yytext)] = this.program.getSize(); // ± 1 who knows? + } else if(state == INSTR2 || state == JUMP) { + this.program.push(Number(this.yytext)); + } else return false; + state = INT; + break; + case T_FLOAT: + if (state != INSTR2F) return false; + state = FLOAT; + this.program.pushFloat64(Number(this.yytext)); + break; + case T_NL: + if (state == INSTR2 || state == JUMP || state == INSTR2F) return false; + state = NEWLINE; + break; + case T_ERROR: + return false; + default: + alert("Erreur interne prévenir la maintenance d'urgence"); + return false; + } + } + console.log("Programme correct syntaxiquement"); + return true; + } + + assemble() { + // change les numéros d'étiquettes par les adresses des instructions pointées. + console.log("Label "+this.adressesLabels); + console.log(this.dumpProgram()); + + for (let i = 0; i < this.program.getSize(); i++) { + let k = this.program.get(i); + // Attention il faut compter si par malchance un entier = code d'un saut + switch (this.codes[k][1]) { + case INSTR1: + break; + case INSTR2: + i++; // on saute l'entier qui suit + break; + case INSTR2F: + i += 2; // on saute le flottant qui suit + break; + case JUMP: // met à jour l'adresse du saut + i++; + console.log("--- set "+i); + this.program.set(i, this.adressesLabels[this.program.get(i)]); + break; + default: + alert("Erreur assemblage"); + } + } + // console.log(this.dumpProgram()); + } + // + + + dumpInstruction(i, result) { + let code = this.codes[this.program.get(i)]; + result += code[0].padEnd(6, ' '); + switch (code[1]) { + case INSTR2: + case JUMP: + result += this.program.get(++i).toString().padStart(7, ' '); + break; + case INSTR2F: + result += this.program.getFloat64(++i).toString().padStart(7, ' '); + i++; + break; + default: + result += " "; + } + + return [i, result]; + } + + dumpProgram() { + let result = ""; + result += this.program + "\n"; + + result += " Adr | Instruction\n-----+---------------\n"; + for(let i = 0; i < this.program.getSize(); i++) { + result += i.toString().padStart(4, " ")+" | "; + [i, result] = this.dumpInstruction(i, result); + result += "\n"; + } + return result; + } + + constructor() { + // init tokens + for (let k of this.codes.keys()) + this.tokens[this.codes[k][0]] = k; + } + + // charge et compile le code + load(text) { + this.text = text; + // on insère une fin de ligne si le texte n'en a pas à sa fin + if (text[text.length-1] != "\n") this.text = text+"\n"; + if (! this.analyse()) { + alert("Erreur ligne "+this.lineNumber+" sur '" +this.yytext+"'"); + return; + } + this.assemble(); + } + + pc = 0; + fp = 0; + stack; + + runcode(maxSteps, d) { + debug = d; + //for (let i = 0; i < this.codes.length; i++) console.log(i+ " "+ this.codes[i][0]); + this.pc = 0; + this.fp = 0; + this.stack = new Pile(); + + try { + if (debug) + this.trace("Programme\n"+this.dumpProgram() + "\nTraces exécution\n" + + " pc | Instruction | fp pile\n" + + "=====+===============+=============================\n"); + + for (let i= 0; i < maxSteps; i++) // while (true) + { + if (this.pc < 0 || this.pc >= this.program.getSize()) + break; + + if (debug) { + let s = this.pc.toString().padStart(4, " ")+" | "; + let junk; + [junk, s] = this.dumpInstruction(this.pc, s); + s += " |"+this.fp.toString().padStart(4,' ')+' '+this.stack.toString()+"\n"; + this.trace(s); + } + + if (this.codes[this.program.get(this.pc++)][2]() === true) + break; + } + } catch(e) { + this.trace(e); + console.error(e); + } + } + + trace(s) { + traces.innerText += s; + console.log(s); + } + +} + + + + + + diff --git a/1-ComputationAndData/MVaP/MVaP-v0/MVaP/js/Pile.js b/1-ComputationAndData/MVaP/MVaP-v0/MVaP/js/Pile.js new file mode 100644 index 0000000..f78f210 --- /dev/null +++ b/1-ComputationAndData/MVaP/MVaP-v0/MVaP/js/Pile.js @@ -0,0 +1,153 @@ +// Class Pile +// Auteur : Jacques Madelaine + +// Une Pile est essentiellement une pile d'entiers ("int32") +// Elle peut aussi empiler et dépiler des flottants définis sur 64 bits. +// L'index est sur les entiers. + +// Rappel : en JavaScript les Number sont tous stockés comme des flottants 64 bits. +// Il faut donc voir cette Pile comme un objet pédagogique +// et non une implémentation optimale en JavaScipt. + +"use strict"; + +class Pile { + buffer; // ArrayBuffer de bytes + pile; // On va utiliser 4 bytes pour les entiers et 8 pour les flottants + haut = 0; // index de sommet de pile en bytes + + // size : taille en bytes de la pile + constructor(size) { + if (size === undefined) + size = 1000; + + this.buffer = new ArrayBuffer(size); + this.pile = new DataView(this.buffer); + } + + push(i) { + if (! Number.isInteger(i)) + throw new TypeError("Try to push a non integer"); + this.pile.setInt32(this.haut, i); + this.haut += 4; + } + + doPush(nb) { for(; nb > 0; nb--) this.push(0); } + + pop() { + this.haut -= 4; + return this.pile.getInt32(this.haut); + } + + doPop(nb) { for(; nb > 0; nb--) this.pop(); } + + peek() { + return this.pile.getInt32(this.haut-4); + } + + set(index, i) { + if (! Number.isInteger(i)) + throw new TypeError("Try to set a non integer"); + this.pile.setInt32(index*4, i); + } + + get(index) { + return this.pile.getInt32(index*4); + } + + + pushFloat64(f) { + this.pile.setFloat64(this.haut, f); + this.haut += 8; + } + + popFloat64() { + this.haut -= 8; + return this.pile.getFloat64(this.haut); + } + + peekFloat64() { + return this.pile.getFloat64(this.haut-8); + } + + setFloat64(index, f) { + this.pile.setFloat64(index*4, f); + } + + getFloat64(index) { + return this.pile.getFloat64(index*4); + } + + getMaxSize() { + return this.buffer.byteLength/2; + } + + getSize() { + return this.haut/4; + } + + toString() { + let out = "[ "; + for (let i = 0; i < this.getSize(); i++) + out += this.get(i) + ", "; + return out + " ] " + this.getSize(); + } + +} + + +/* + +let p = new Pile(); +try { + let d = 12.34; + let i = 0x7FFFFFFF; + let j = 0; + p.push(i); + j = p.peek(); + console.log(i + " =?= " + j); + + let N = 5; + for(let n = 0; n < N; n++) { + p.push(n); + console.log("push "+n+" " + n); + } + + console.log("get(2) " + p.get(2)); + console.log(p.toString()); + + for(let n = N; n > 0; n--) { + let m = p.pop(); + // if (2*n != m) + console.log("push "+ n + " pop " + m); + } + p.pop(); + + p.push(40); + p.pushFloat64(d); + p.pushFloat64(13.34); + p.push(i); + console.log(p.toString()); + + for (let n = 0; n<6;n++) + console.log("p.getFloat64("+n+") = "+p.getFloat64(n)); + + p.pop(); + p.popFloat64(); + let e = p.popFloat64(); + console.log(d + " =?= " + e); + + + d = -1; + p.pushFloat64(d); + e = p.popFloat64(); + console.log(d + " =?= " + e); + // + // for (i = 0 ; i < 1000000; i++) + // p.push(i); +} catch(e) { + console.error(e); +} +*/ + + diff --git a/1-ComputationAndData/MVaP/MVaP.jar b/1-ComputationAndData/MVaP/MVaP.jar new file mode 100644 index 0000000000000000000000000000000000000000..ae6f4573c8bf3a3bd8f28aed68d370b6ecded135 GIT binary patch literal 32382 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\def\NiveauI{(11.5)*\DistanceInterNiveaux} +% \def\InterFeuilles{(-1)*\DistanceInterFeuilles} +% % Noeuds (MODIFIABLES : Styles et Coefficients d'InterFeuilles) +% \node[noeud] (R) at ({\NiveauA},{(13.5)*\InterFeuilles}) {$Tous$}; +% \node[noeud] (Ra) at ({\NiveauB},{(3.5)*\InterFeuilles}) {$$}; +% \node[noeud] (Raa) at ({\NiveauC},{(1)*\InterFeuilles}) {$$}; +% \node[noeud] (Raaa) at ({\NiveauD},{(0.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Raaaa) at ({\NiveauE},{(0)*\InterFeuilles}) {$H$}; +% \node[feuille] (Raaab) at ({\NiveauE},{(1)*\InterFeuilles}) {$T$}; +% \node[feuille] (Raab) at ({\NiveauD},{(2)*\InterFeuilles}) {$E$}; +% \node[noeud] (Rab) at ({\NiveauC},{(5)*\InterFeuilles}) {$$}; +% \node[noeud] (Raba) at ({\NiveauD},{(4)*\InterFeuilles}) {$$}; +% \node[feuille] (Rabaa) at ({\NiveauE},{(3)*\InterFeuilles}) {$A$}; +% \node[noeud] (Rabab) at ({\NiveauE},{(4.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rababa) at ({\NiveauF},{(4)*\InterFeuilles}) {$W$}; +% \node[feuille] (Rababb) at ({\NiveauF},{(5)*\InterFeuilles}) {$G$}; +% \node[noeud] (Rabb) at ({\NiveauD},{(6.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rabba) at ({\NiveauE},{(6)*\InterFeuilles}) {$D$}; +% \node[feuille] (Rabbb) at ({\NiveauE},{(7)*\InterFeuilles}) {$U$}; +% \node[noeud] (Rb) at ({\NiveauB},{(17.5)*\InterFeuilles}) {$$}; +% \node[noeud] (Rba) at ({\NiveauC},{(10.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbaa) at ({\NiveauD},{(8)*\InterFeuilles}) {$O$}; +% \node[noeud] (Rbab) at ({\NiveauD},{(11)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbaba) at ({\NiveauE},{(10)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbabaa) at ({\NiveauF},{(9.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbabaaa) at ({\NiveauG},{(9)*\InterFeuilles}) {$.$}; +% \node[feuille] (Rbabaab) at ({\NiveauG},{(10)*\InterFeuilles}) {$K$}; +% \node[feuille] (Rbabab) at ({\NiveauF},{(11)*\InterFeuilles}) {$M$}; +% \node[noeud] (Rbabb) at ({\NiveauE},{(12.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbabba) at ({\NiveauF},{(12)*\InterFeuilles}) {$L$}; +% \node[feuille] (Rbabbb) at ({\NiveauF},{(13)*\InterFeuilles}) {$S$}; +% \node[noeud] (Rbb) at ({\NiveauC},{(20.5)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbba) at ({\NiveauD},{(20)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbbaa) at ({\NiveauE},{(16.5)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbbaaa) at ({\NiveauF},{(16)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbbaaaa) at ({\NiveauG},{(14.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbbaaaaa) at ({\NiveauH},{(14)*\InterFeuilles}) {$Y$}; +% \node[feuille] (Rbbaaaab) at ({\NiveauH},{(15)*\InterFeuilles}) {$"$}; +% \node[noeud] (Rbbaaab) at ({\NiveauG},{(17)*\InterFeuilles}) {$Nœud36$}; +% \node[noeud] (Rbbaaaba) at ({\NiveauH},{(16.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbbaaabaa) at ({\NiveauI},{(16)*\InterFeuilles}) {$F$}; +% \node[feuille] (Rbbaaabab) at ({\NiveauI},{(17)*\InterFeuilles}) {$X$}; +% \node[feuille] (Rbbaaabb) at ({\NiveauH},{(18)*\InterFeuilles}) {$B$}; +% \node[feuille] (Rbbaab) at ({\NiveauF},{(19)*\InterFeuilles}) {$N$}; +% \node[noeud] (Rbbab) at ({\NiveauE},{(23)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbbaba) at ({\NiveauF},{(20)*\InterFeuilles}) {$R$}; +% \node[noeud] (Rbbabb) at ({\NiveauF},{(23.5)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbbabba) at ({\NiveauG},{(22.5)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbbabbaa) at ({\NiveauH},{(21.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbbabbaaa) at ({\NiveauI},{(21)*\InterFeuilles}) {$P$}; +% \node[feuille] (Rbbabbaab) at ({\NiveauI},{(22)*\InterFeuilles}) {$V$}; +% \node[noeud] (Rbbabbab) at ({\NiveauH},{(23.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbbabbaba) at ({\NiveauI},{(23)*\InterFeuilles}) {$?$}; +% \node[feuille] (Rbbabbabb) at ({\NiveauI},{(24)*\InterFeuilles}) {$,$}; +% \node[noeud] (Rbbabbb) at ({\NiveauG},{(25.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbbabbba) at ({\NiveauH},{(25)*\InterFeuilles}) {$C$}; +% \node[feuille] (Rbbabbbb) at ({\NiveauH},{(26)*\InterFeuilles}) {$I$}; +% \node[feuille] (Rbbb) at ({\NiveauD},{(27)*\InterFeuilles}) {$espace$}; +% % Arcs (MODIFIABLES : Styles) +% \draw[fleche] (R)--(Ra) node[etiquette] {$0$}; +% \draw[fleche] (Ra)--(Raa) node[etiquette] {$0$}; +% \draw[fleche] (Raa)--(Raaa) node[etiquette] {$0$}; +% \draw[fleche] (Raaa)--(Raaaa) node[etiquette] {$0$}; +% \draw[fleche] (Raaa)--(Raaab) node[etiquette] {$1$}; +% \draw[fleche] (Raa)--(Raab) node[etiquette] {$1$}; +% \draw[fleche] (Ra)--(Rab) node[etiquette] {$1$}; +% \draw[fleche] (Rab)--(Raba) node[etiquette] {$0$}; +% \draw[fleche] (Raba)--(Rabaa) node[etiquette] {$0$}; +% \draw[fleche] (Raba)--(Rabab) node[etiquette] {$1$}; +% \draw[fleche] (Rabab)--(Rababa) node[etiquette] {$0$}; +% \draw[fleche] (Rabab)--(Rababb) node[etiquette] {$A$}; +% \draw[fleche] (Rab)--(Rabb) node[etiquette] {$1$}; +% \draw[fleche] (Rabb)--(Rabba) node[etiquette] {$0$}; +% \draw[fleche] (Rabb)--(Rabbb) node[etiquette] {$1$}; +% \draw[fleche] (R)--(Rb) node[etiquette] {$1$}; +% \draw[fleche] (Rb)--(Rba) node[etiquette] {$0$}; +% \draw[fleche] (Rba)--(Rbaa) node[etiquette] {$0$}; +% \draw[fleche] (Rba)--(Rbab) node[etiquette] {$1$}; +% \draw[fleche] (Rbab)--(Rbaba) node[etiquette] {$0$}; +% \draw[fleche] (Rbaba)--(Rbabaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbabaa)--(Rbabaaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbabaa)--(Rbabaab) node[etiquette] {$1$}; +% \draw[fleche] (Rbaba)--(Rbabab) node[etiquette] {$1$}; +% \draw[fleche] (Rbab)--(Rbabb) node[etiquette] {$1$}; +% \draw[fleche] (Rbabb)--(Rbabba) node[etiquette] {$0$}; +% \draw[fleche] (Rbabb)--(Rbabbb) node[etiquette] {$1$}; +% \draw[fleche] (Rb)--(Rbb) node[etiquette] {$1$}; +% \draw[fleche] (Rbb)--(Rbba) node[etiquette] {$0$}; +% \draw[fleche] (Rbba)--(Rbbaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbbaa)--(Rbbaaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbbaaa)--(Rbbaaaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbbaaaa)--(Rbbaaaaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbbaaaa)--(Rbbaaaab) node[etiquette] {$1$}; +% \draw[fleche] (Rbbaaa)--(Rbbaaab) node[etiquette] {$1$}; +% \draw[fleche] (Rbbaaab)--(Rbbaaaba) node[etiquette] {$0$}; +% \draw[fleche] (Rbbaaaba)--(Rbbaaabaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbbaaaba)--(Rbbaaabab) node[etiquette] {$1$}; +% \draw[fleche] (Rbbaaab)--(Rbbaaabb) node[etiquette] {$1$}; +% \draw[fleche] (Rbbaa)--(Rbbaab) node[etiquette] {$1$}; +% \draw[fleche] (Rbba)--(Rbbab) node[etiquette] {$1$}; +% \draw[fleche] (Rbbab)--(Rbbaba) node[etiquette] {$0$}; +% \draw[fleche] (Rbbab)--(Rbbabb) node[etiquette] {$1$}; +% \draw[fleche] (Rbbabb)--(Rbbabba) node[etiquette] {$0$}; +% \draw[fleche] (Rbbabba)--(Rbbabbaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbbabbaa)--(Rbbabbaaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbbabbaa)--(Rbbabbaab) node[etiquette] {$1$}; +% \draw[fleche] (Rbbabba)--(Rbbabbab) node[etiquette] {$1$}; +% \draw[fleche] (Rbbabbab)--(Rbbabbaba) node[etiquette] {$0$}; +% \draw[fleche] (Rbbabbab)--(Rbbabbabb) node[etiquette] {$1$}; +% \draw[fleche] (Rbbabb)--(Rbbabbb) node[etiquette] {$1$}; +% \draw[fleche] (Rbbabbb)--(Rbbabbba) node[etiquette] {$0$}; +% \draw[fleche] (Rbbabbb)--(Rbbabbbb) node[etiquette] {$1$}; +% \draw[fleche] (Rbb)--(Rbbb) node[etiquette] {$1$}; +% \end{tikzpicture} +% \end{center} +% %:-+-+-+-+- Fin + + + +% %:-+-+-+- Engendré par : http://math.et.info.free.fr/TikZ/Arbre/ +% \begin{center} +% % Racine à Gauche, développement vers la droite +% \begin{tikzpicture}[xscale=0.2,yscale=0.2] +% % Styles (MODIFIABLES) +% \tikzstyle{fleche}=[->,>=latex,thick] +% \tikzstyle{noeud}=[fill=yellow,circle,draw] +% \tikzstyle{feuille}=[fill=yellow,circle,draw] +% \tikzstyle{etiquette}=[midway,fill=white,draw] +% % Dimensions (MODIFIABLES) +% \def\DistanceInterNiveaux{3} +% \def\DistanceInterFeuilles{2} +% % Dimensions calculées (NON MODIFIABLES) +% \def\NiveauA{(0)*\DistanceInterNiveaux} +% \def\NiveauB{(1.875)*\DistanceInterNiveaux} +% \def\NiveauC{(3.625)*\DistanceInterNiveaux} +% \def\NiveauD{(5.25)*\DistanceInterNiveaux} +% \def\NiveauE{(6.75)*\DistanceInterNiveaux} +% \def\NiveauF{(8.125)*\DistanceInterNiveaux} +% \def\NiveauG{(9.375)*\DistanceInterNiveaux} +% \def\NiveauH{(10.5)*\DistanceInterNiveaux} +% \def\NiveauI{(11.5)*\DistanceInterNiveaux} +% \def\InterFeuilles{(-1)*\DistanceInterFeuilles} +% % Noeuds (MODIFIABLES : Styles et Coefficients d'InterFeuilles) +% \node[noeud] (R) at ({\NiveauA},{(13.5)*\InterFeuilles}) {\tiny $Tous$}; +% \node[noeud] (Ra) at ({\NiveauB},{(3.5)*\InterFeuilles}) {$$}; +% \node[noeud] (Raa) at ({\NiveauC},{(1)*\InterFeuilles}) {$$}; +% \node[noeud] (Raaa) at ({\NiveauD},{(0.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Raaaa) at ({\NiveauE},{(0)*\InterFeuilles}) {\tiny $H$}; +% \node[feuille] (Raaab) at ({\NiveauE},{(1)*\InterFeuilles}) {\tiny $T$}; +% \node[feuille] (Raab) at ({\NiveauD},{(2)*\InterFeuilles}) {\tiny $E$}; +% \node[noeud] (Rab) at ({\NiveauC},{(5)*\InterFeuilles}) {$$}; +% \node[noeud] (Raba) at ({\NiveauD},{(4)*\InterFeuilles}) {$$}; +% \node[feuille] (Rabaa) at ({\NiveauE},{(3)*\InterFeuilles}) {\tiny $A$}; +% \node[noeud] (Rabab) at ({\NiveauE},{(4.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rababa) at ({\NiveauF},{(4)*\InterFeuilles}) {\tiny $W$}; +% \node[feuille] (Rababb) at ({\NiveauF},{(5)*\InterFeuilles}) {\tiny $G$}; +% \node[noeud] (Rabb) at ({\NiveauD},{(6.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rabba) at ({\NiveauE},{(6)*\InterFeuilles}) {\tiny $D$}; +% \node[feuille] (Rabbb) at ({\NiveauE},{(7)*\InterFeuilles}) {\tiny $U$}; +% \node[noeud] (Rb) at ({\NiveauB},{(17.5)*\InterFeuilles}) {$$}; +% \node[noeud] (Rba) at ({\NiveauC},{(10.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbaa) at ({\NiveauD},{(8)*\InterFeuilles}) {\tiny $O$}; +% \node[noeud] (Rbab) at ({\NiveauD},{(11)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbaba) at ({\NiveauE},{(10)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbabaa) at ({\NiveauF},{(9.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbabaaa) at ({\NiveauG},{(9)*\InterFeuilles}) {\tiny $.$}; +% \node[feuille] (Rbabaab) at ({\NiveauG},{(10)*\InterFeuilles}) {\tiny $K$}; +% \node[feuille] (Rbabab) at ({\NiveauF},{(11)*\InterFeuilles}) {\tiny $M$}; +% \node[noeud] (Rbabb) at ({\NiveauE},{(12.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbabba) at ({\NiveauF},{(12)*\InterFeuilles}) {\tiny $L$}; +% \node[feuille] (Rbabbb) at ({\NiveauF},{(13)*\InterFeuilles}) {\tiny $S$}; +% \node[noeud] (Rbb) at ({\NiveauC},{(20.5)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbba) at ({\NiveauD},{(20)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbbaa) at ({\NiveauE},{(16.5)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbbaaa) at ({\NiveauF},{(16)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbbaaaa) at ({\NiveauG},{(14.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbbaaaaa) at ({\NiveauH},{(14)*\InterFeuilles}) {\tiny +% $Y$}; +% \node[feuille] (Rbbaaaab) at ({\NiveauH},{(15)*\InterFeuilles}) {\tiny +% $"$}; +% \node[noeud] (Rbbaaab) at ({\NiveauG},{(17)*\InterFeuilles}) {}; +% \node[noeud] (Rbbaaaba) at ({\NiveauH},{(16.5)*\InterFeuilles}) {}; +% \node[feuille] (Rbbaaabaa) at ({\NiveauI},{(16)*\InterFeuilles}) +% {\tiny $F$}; +% \node[feuille] (Rbbaaabab) at ({\NiveauI},{(17)*\InterFeuilles}) +% {\tiny $X$}; +% \node[feuille] (Rbbaaabb) at ({\NiveauH},{(18)*\InterFeuilles}) {\tiny +% $B$}; +% \node[feuille] (Rbbaab) at ({\NiveauF},{(19)*\InterFeuilles}) {\tiny $N$}; +% \node[noeud] (Rbbab) at ({\NiveauE},{(23)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbbaba) at ({\NiveauF},{(20)*\InterFeuilles}) {\tiny $R$}; +% \node[noeud] (Rbbabb) at ({\NiveauF},{(23.5)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbbabba) at ({\NiveauG},{(22.5)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbbabbaa) at ({\NiveauH},{(21.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbbabbaaa) at ({\NiveauI},{(21)*\InterFeuilles}) +% {\tiny $P$}; +% \node[feuille] (Rbbabbaab) at ({\NiveauI},{(22)*\InterFeuilles}) +% {\tiny $V$}; +% \node[noeud] (Rbbabbab) at ({\NiveauH},{(23.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbbabbaba) at ({\NiveauI},{(23)*\InterFeuilles}) +% {\tiny $?$}; +% \node[feuille] (Rbbabbabb) at ({\NiveauI},{(24)*\InterFeuilles}) +% {\tiny $,$}; +% \node[noeud] (Rbbabbb) at ({\NiveauG},{(25.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbbabbba) at ({\NiveauH},{(25)*\InterFeuilles}) {\tiny +% $C$}; +% \node[feuille] (Rbbabbbb) at ({\NiveauH},{(26)*\InterFeuilles}) {\tiny +% $I$}; +% \node[feuille] (Rbbb) at ({\NiveauD},{(27)*\InterFeuilles}) {\tiny $espace$}; +% % Arcs (MODIFIABLES : Styles) +% \draw[fleche] (R)--(Ra) node[etiquette] {$0$}; +% \draw[fleche] (Ra)--(Raa) node[etiquette] {$0$}; +% \draw[fleche] (Raa)--(Raaa) node[etiquette] {$0$}; +% \draw[fleche] (Raaa)--(Raaaa) node[etiquette] {$0$}; +% \draw[fleche] (Raaa)--(Raaab) node[etiquette] {$1$}; +% \draw[fleche] (Raa)--(Raab) node[etiquette] {$1$}; +% \draw[fleche] (Ra)--(Rab) node[etiquette] {$1$}; +% \draw[fleche] (Rab)--(Raba) node[etiquette] {$0$}; +% \draw[fleche] (Raba)--(Rabaa) node[etiquette] {$0$}; +% \draw[fleche] (Raba)--(Rabab) node[etiquette] {$1$}; +% \draw[fleche] (Rabab)--(Rababa) node[etiquette] {$0$}; +% \draw[fleche] (Rabab)--(Rababb) node[etiquette] {$1$}; +% \draw[fleche] (Rab)--(Rabb) node[etiquette] {$1$}; +% \draw[fleche] (Rabb)--(Rabba) node[etiquette] {$0$}; +% \draw[fleche] (Rabb)--(Rabbb) node[etiquette] {$1$}; +% \draw[fleche] (R)--(Rb) node[etiquette] {$1$}; +% \draw[fleche] (Rb)--(Rba) node[etiquette] {$0$}; +% \draw[fleche] (Rba)--(Rbaa) node[etiquette] {$0$}; +% \draw[fleche] (Rba)--(Rbab) node[etiquette] {$1$}; +% \draw[fleche] (Rbab)--(Rbaba) node[etiquette] {$0$}; +% \draw[fleche] (Rbaba)--(Rbabaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbabaa)--(Rbabaaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbabaa)--(Rbabaab) node[etiquette] {$1$}; +% \draw[fleche] (Rbaba)--(Rbabab) node[etiquette] {$1$}; +% \draw[fleche] (Rbab)--(Rbabb) node[etiquette] {$1$}; +% \draw[fleche] (Rbabb)--(Rbabba) node[etiquette] {$0$}; +% \draw[fleche] (Rbabb)--(Rbabbb) node[etiquette] {$1$}; +% \draw[fleche] (Rb)--(Rbb) node[etiquette] {$1$}; +% \draw[fleche] (Rbb)--(Rbba) node[etiquette] {$0$}; +% \draw[fleche] (Rbba)--(Rbbaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbbaa)--(Rbbaaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbbaaa)--(Rbbaaaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbbaaaa)--(Rbbaaaaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbbaaaa)--(Rbbaaaab) node[etiquette] {$1$}; +% \draw[fleche] (Rbbaaa)--(Rbbaaab) node[etiquette] {$1$}; +% \draw[fleche] (Rbbaaab)--(Rbbaaaba) node[etiquette] {$0$}; +% \draw[fleche] (Rbbaaaba)--(Rbbaaabaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbbaaaba)--(Rbbaaabab) node[etiquette] {$1$}; +% \draw[fleche] (Rbbaaab)--(Rbbaaabb) node[etiquette] {$1$}; +% \draw[fleche] (Rbbaa)--(Rbbaab) node[etiquette] {$1$}; +% \draw[fleche] (Rbba)--(Rbbab) node[etiquette] {$1$}; +% \draw[fleche] (Rbbab)--(Rbbaba) node[etiquette] {$0$}; +% \draw[fleche] (Rbbab)--(Rbbabb) node[etiquette] {$1$}; +% \draw[fleche] (Rbbabb)--(Rbbabba) node[etiquette] {$0$}; +% \draw[fleche] (Rbbabba)--(Rbbabbaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbbabbaa)--(Rbbabbaaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbbabbaa)--(Rbbabbaab) node[etiquette] {$1$}; +% \draw[fleche] (Rbbabba)--(Rbbabbab) node[etiquette] {$1$}; +% \draw[fleche] (Rbbabbab)--(Rbbabbaba) node[etiquette] {$0$}; +% \draw[fleche] (Rbbabbab)--(Rbbabbabb) node[etiquette] {$1$}; +% \draw[fleche] (Rbbabb)--(Rbbabbb) node[etiquette] {$1$}; +% \draw[fleche] (Rbbabbb)--(Rbbabbba) node[etiquette] {$0$}; +% \draw[fleche] (Rbbabbb)--(Rbbabbbb) node[etiquette] {$1$}; +% \draw[fleche] (Rbb)--(Rbbb) node[etiquette] {$1$}; +% \end{tikzpicture} +% \end{center} +% %:-+-+-+-+- Fin + + + +\pagebreak + +%:-+-+-+- Engendré par : http://math.et.info.free.fr/TikZ/Arbre/ +\begin{center} +% Racine en Haut, développement vers le bas +\begin{tikzpicture}[xscale=0.4,yscale=0.45] +% Styles (MODIFIABLES) +\tikzstyle{fleche}=[->,>=latex,thick] +\tikzstyle{noeud}=[fill=yellow,circle,draw] +\tikzstyle{feuille}=[fill=yellow,circle,draw] +\tikzstyle{etiquette}=[midway,fill=white,draw] +% Dimensions (MODIFIABLES) +\def\DistanceInterNiveaux{3} +\def\DistanceInterFeuilles{2} +% Dimensions calculées (NON MODIFIABLES) +\def\NiveauA{(-0)*\DistanceInterNiveaux} +\def\NiveauB{(-1.875)*\DistanceInterNiveaux} +\def\NiveauC{(-3.625)*\DistanceInterNiveaux} +\def\NiveauD{(-5.25)*\DistanceInterNiveaux} +\def\NiveauE{(-6.75)*\DistanceInterNiveaux} +\def\NiveauF{(-8.125)*\DistanceInterNiveaux} +\def\NiveauG{(-9.375)*\DistanceInterNiveaux} +\def\NiveauH{(-10.5)*\DistanceInterNiveaux} +\def\NiveauI{(-11.5)*\DistanceInterNiveaux} +\def\InterFeuilles{(1)*\DistanceInterFeuilles} +% Noeuds (MODIFIABLES : Styles et Coefficients d'InterFeuilles) +\node[noeud] (R) at ({(13.5)*\InterFeuilles},{\NiveauA}) {\tiny Tous}; +\node[noeud] (Ra) at ({(3.5)*\InterFeuilles},{\NiveauB}) {}; +\node[noeud] (Raa) at ({(1)*\InterFeuilles},{\NiveauC}) {}; +\node[noeud] (Raaa) at ({(0.5)*\InterFeuilles},{\NiveauD}) {}; +\node[feuille] (Raaaa) at ({(0)*\InterFeuilles},{\NiveauE}) {\tiny H}; +\node[feuille] (Raaab) at ({(1)*\InterFeuilles},{\NiveauE}) {\tiny T}; +\node[feuille] (Raab) at ({(2)*\InterFeuilles},{\NiveauD}) {\tiny E}; +\node[noeud] (Rab) at ({(5)*\InterFeuilles},{\NiveauC}) {}; +\node[noeud] (Raba) at ({(4)*\InterFeuilles},{\NiveauD}) {}; +\node[feuille] (Rabaa) at ({(3)*\InterFeuilles},{\NiveauE}) {\tiny A}; +\node[noeud] (Rabab) at ({(4.5)*\InterFeuilles},{\NiveauE}) {}; +\node[feuille] (Rababa) at ({(4)*\InterFeuilles},{\NiveauF}) {\tiny W}; +\node[feuille] (Rababb) at ({(5)*\InterFeuilles},{\NiveauF}) {\tiny G}; +\node[noeud] (Rabb) at ({(6.5)*\InterFeuilles},{\NiveauD}) {}; +\node[feuille] (Rabba) at ({(6)*\InterFeuilles},{\NiveauE}) {\tiny D}; +\node[feuille] (Rabbb) at ({(7)*\InterFeuilles},{\NiveauE}) {\tiny U}; +\node[noeud] (Rb) at ({(17.5)*\InterFeuilles},{\NiveauB}) {}; +\node[noeud] (Rba) at ({(10.5)*\InterFeuilles},{\NiveauC}) {}; +\node[feuille] (Rbaa) at ({(8)*\InterFeuilles},{\NiveauD}) {\tiny O}; +\node[noeud] (Rbab) at ({(11)*\InterFeuilles},{\NiveauD}) {}; +\node[noeud] (Rbaba) at ({(10)*\InterFeuilles},{\NiveauE}) {}; +\node[noeud] (Rbabaa) at ({(9.5)*\InterFeuilles},{\NiveauF}) {}; +\node[feuille] (Rbabaaa) at ({(9)*\InterFeuilles},{\NiveauG}) {\tiny .}; +\node[feuille] (Rbabaab) at ({(10)*\InterFeuilles},{\NiveauG}) {\tiny K}; +\node[feuille] (Rbabab) at ({(11)*\InterFeuilles},{\NiveauF}) {\tiny M}; +\node[noeud] (Rbabb) at ({(12.5)*\InterFeuilles},{\NiveauE}) {}; +\node[feuille] (Rbabba) at ({(12)*\InterFeuilles},{\NiveauF}) {\tiny L}; +\node[feuille] (Rbabbb) at ({(13)*\InterFeuilles},{\NiveauF}) {\tiny S}; +\node[noeud] (Rbb) at ({(20.5)*\InterFeuilles},{\NiveauC}) {}; +\node[noeud] (Rbba) at ({(20)*\InterFeuilles},{\NiveauD}) {}; +\node[noeud] (Rbbaa) at ({(16.5)*\InterFeuilles},{\NiveauE}) {}; +\node[noeud] (Rbbaaa) at ({(16)*\InterFeuilles},{\NiveauF}) {}; +\node[noeud] (Rbbaaaa) at ({(14.5)*\InterFeuilles},{\NiveauG}) {}; +\node[feuille] (Rbbaaaaa) at ({(14)*\InterFeuilles},{\NiveauH}) {\tiny + Y}; +\node[feuille] (Rbbaaaab) at ({(15)*\InterFeuilles},{\NiveauH}) {\tiny + "}; +\node[noeud] (Rbbaaab) at ({(17)*\InterFeuilles},{\NiveauG}) {}; +\node[noeud] (Rbbaaaba) at ({(16.5)*\InterFeuilles},{\NiveauH}) {}; +\node[feuille] (Rbbaaabaa) at ({(16)*\InterFeuilles},{\NiveauI}) +{\tiny F}; +\node[feuille] (Rbbaaabab) at ({(17)*\InterFeuilles},{\NiveauI}) +{\tiny X}; +\node[feuille] (Rbbaaabb) at ({(18)*\InterFeuilles},{\NiveauH}) {\tiny + B}; +\node[feuille] (Rbbaab) at ({(19)*\InterFeuilles},{\NiveauF}) {\tiny N}; +\node[noeud] (Rbbab) at ({(23)*\InterFeuilles},{\NiveauE}) {}; +\node[feuille] (Rbbaba) at ({(20)*\InterFeuilles},{\NiveauF}) {\tiny R}; +\node[noeud] (Rbbabb) at ({(23.5)*\InterFeuilles},{\NiveauF}) {}; +\node[noeud] (Rbbabba) at ({(22.5)*\InterFeuilles},{\NiveauG}) {}; +\node[noeud] (Rbbabbaa) at ({(21.5)*\InterFeuilles},{\NiveauH}) {}; +\node[feuille] (Rbbabbaaa) at ({(21)*\InterFeuilles},{\NiveauI}) +{\tiny P}; +\node[feuille] (Rbbabbaab) at ({(22)*\InterFeuilles},{\NiveauI}) +{\tiny V}; +\node[noeud] (Rbbabbab) at ({(23.5)*\InterFeuilles},{\NiveauH}) {}; +\node[feuille] (Rbbabbaba) at ({(23)*\InterFeuilles},{\NiveauI}) +{\tiny ?}; +\node[feuille] (Rbbabbabb) at ({(24)*\InterFeuilles},{\NiveauI}) +{\tiny ,}; +\node[noeud] (Rbbabbb) at ({(25.5)*\InterFeuilles},{\NiveauG}) {}; +\node[feuille] (Rbbabbba) at ({(25)*\InterFeuilles},{\NiveauH}) {\tiny + C}; +\node[feuille] (Rbbabbbb) at ({(26)*\InterFeuilles},{\NiveauH}) {\tiny + I}; +\node[feuille] (Rbbb) at ({(27)*\InterFeuilles},{\NiveauD}) {\tiny espace}; +% Arcs (MODIFIABLES : Styles) +\draw[fleche] (R)--(Ra) node[etiquette] {\tiny 0}; +\draw[fleche] (Ra)--(Raa) node[etiquette] {\tiny 0}; +\draw[fleche] (Raa)--(Raaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Raaa)--(Raaaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Raaa)--(Raaab) node[etiquette] {\tiny 1}; +\draw[fleche] (Raa)--(Raab) node[etiquette] {\tiny 1}; +\draw[fleche] (Ra)--(Rab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rab)--(Raba) node[etiquette] {\tiny 0}; +\draw[fleche] (Raba)--(Rabaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Raba)--(Rabab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rabab)--(Rababa) node[etiquette] {\tiny 0}; +\draw[fleche] (Rabab)--(Rababb) node[etiquette] {\tiny 1}; +\draw[fleche] (Rab)--(Rabb) node[etiquette] {\tiny 1}; +\draw[fleche] (Rabb)--(Rabba) node[etiquette] {\tiny 0}; +\draw[fleche] (Rabb)--(Rabbb) node[etiquette] {\tiny 1}; +\draw[fleche] (R)--(Rb) node[etiquette] {\tiny 1}; +\draw[fleche] (Rb)--(Rba) node[etiquette] {\tiny 0}; +\draw[fleche] (Rba)--(Rbaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Rba)--(Rbab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbab)--(Rbaba) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbaba)--(Rbabaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbabaa)--(Rbabaaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbabaa)--(Rbabaab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbaba)--(Rbabab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbab)--(Rbabb) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbabb)--(Rbabba) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbabb)--(Rbabbb) node[etiquette] {\tiny 1}; +\draw[fleche] (Rb)--(Rbb) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbb)--(Rbba) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbba)--(Rbbaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbaa)--(Rbbaaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbaaa)--(Rbbaaaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbaaaa)--(Rbbaaaaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbaaaa)--(Rbbaaaab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbbaaa)--(Rbbaaab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbbaaab)--(Rbbaaaba) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbaaaba)--(Rbbaaabaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbaaaba)--(Rbbaaabab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbbaaab)--(Rbbaaabb) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbbaa)--(Rbbaab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbba)--(Rbbab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbbab)--(Rbbaba) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbab)--(Rbbabb) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbbabb)--(Rbbabba) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbabba)--(Rbbabbaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbabbaa)--(Rbbabbaaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbabbaa)--(Rbbabbaab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbbabba)--(Rbbabbab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbbabbab)--(Rbbabbaba) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbabbab)--(Rbbabbabb) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbbabb)--(Rbbabbb) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbbabbb)--(Rbbabbba) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbabbb)--(Rbbabbbb) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbb)--(Rbbb) node[etiquette] {\tiny 1}; +\end{tikzpicture} +\end{center} +%:-+-+-+-+- Fin + + +\end{document} + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%% un nouvel exo et sa correction %%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%début-exo +\begin{exo} + \begin{enumerate} + \item %question 1 + + \item %question 2 + + \end{enumerate} +\end{exo} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%fin-exo + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%début-correction +\begin{correction} + \begin{shaded} + %%% \begin{minipage}{.9\linewidth} + \begin{center} + \textbf{solution.} + \end{center} + \begin{enumerate} + \item %solution question 1 + + \item %solution question 2 + + \end{enumerate} + %%%\end{minipage} + \end{shaded} + \medskip +\end{correction} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%fin-correction +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + +%%% LocalWords: +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: + diff --git a/2-InformationTheory/3InformationTheory/file1.txt b/2-InformationTheory/3InformationTheory/file1.txt new file mode 100644 index 0000000..cf8297e --- /dev/null +++ b/2-InformationTheory/3InformationTheory/file1.txt @@ -0,0 +1,11 @@ +Ceci est un fichier texte pour tester la commande diff. + +Vous pouvez consulter le manuel de la commande diff en écrivant. + +man diff + +Ici j'ajoute une ligne qui sera absente du fichier file2.txt + +Pour faire la différence entre deux fichiers on peut faire : + +diff --color file1.txt file2.txt diff --git a/2-InformationTheory/3InformationTheory/file2.txt b/2-InformationTheory/3InformationTheory/file2.txt new file mode 100644 index 0000000..d862eef --- /dev/null +++ b/2-InformationTheory/3InformationTheory/file2.txt @@ -0,0 +1,24 @@ +Ceci est un fichier texte pour tester la commande diff. + +Vous pouvez consulter le manuel de la commande diff en écrivant. + +man diff + +Je peux écrire le résultat (la page de manuel de diff) en écrivant + +man diff >> file2.txt + +Comme c'est un peu long, à la place j'ai utilisé + +man diff | head >> file2.txt + +GNU(1) User Commands GNU(1) + +NAME + GNU diff - compare files line by line + +SYNOPSIS + diff [OPTION]... FILES + +DESCRIPTION + Compare FILES line by line. diff --git a/2-InformationTheory/3InformationTheory/gruffalo.txt b/2-InformationTheory/3InformationTheory/gruffalo.txt new file mode 100644 index 0000000..eb37bb6 --- /dev/null +++ b/2-InformationTheory/3InformationTheory/gruffalo.txt @@ -0,0 +1,168 @@ +A mouse took a stroll through the deep dark wood. A fox saw +the mouse and the mouse looked good. “Where are you going +to, little brown mouse? Come and have lunch in my +underground house.” + +étape 1 au tableau on compte la fréquence des lettres. +Le moins fréquent est à traiter en premier. + +étape 2 au tableau on construit l'arbre de Huffman. + +étape 3 : compression. +On note les labels de la racine vers la feuille qui est le code de chaque lettre. + +A devient : 0100 +(j'écris _ pour l'espace) +_ devient : 111 +m devient : 10 101 +o devient : 100 +u devient : 0 111 +s devient : 10 111 +e devient : 001 +_ devient : 111 +t devient : 000 1 +o devient : 100 +o devient : 100 +k devient : 101 001 +_ devient : 111 +a devient : ???? +_ devient : 111 + +%:-+-+-+- Engendré par : http://math.et.info.free.fr/TikZ/Arbre/ +\begin{center} +% Racine à Gauche, développement vers la droite +\begin{tikzpicture}[xscale=1,yscale=1] +% Styles (MODIFIABLES) +\tikzstyle{fleche}=[->,>=latex,thick] +\tikzstyle{noeud}=[fill=yellow,circle,draw] +\tikzstyle{feuille}=[fill=yellow,circle,draw] +\tikzstyle{etiquette}=[midway,fill=white,draw] +% Dimensions (MODIFIABLES) +\def\DistanceInterNiveaux{3} +\def\DistanceInterFeuilles{2} +% Dimensions calculées (NON MODIFIABLES) +\def\NiveauA{(0)*\DistanceInterNiveaux} +\def\NiveauB{(1.875)*\DistanceInterNiveaux} +\def\NiveauC{(3.625)*\DistanceInterNiveaux} +\def\NiveauD{(5.25)*\DistanceInterNiveaux} +\def\NiveauE{(6.75)*\DistanceInterNiveaux} +\def\NiveauF{(8.125)*\DistanceInterNiveaux} +\def\NiveauG{(9.375)*\DistanceInterNiveaux} +\def\NiveauH{(10.5)*\DistanceInterNiveaux} +\def\NiveauI{(11.5)*\DistanceInterNiveaux} +\def\InterFeuilles{(-1)*\DistanceInterFeuilles} +% Noeuds (MODIFIABLES : Styles et Coefficients d'InterFeuilles) +\node[noeud] (R) at ({\NiveauA},{(13.5)*\InterFeuilles}) {$Tous$}; +\node[noeud] (Ra) at ({\NiveauB},{(3.5)*\InterFeuilles}) {$$}; +\node[noeud] (Raa) at ({\NiveauC},{(1)*\InterFeuilles}) {$$}; +\node[noeud] (Raaa) at ({\NiveauD},{(0.5)*\InterFeuilles}) {$$}; +\node[feuille] (Raaaa) at ({\NiveauE},{(0)*\InterFeuilles}) {$H$}; +\node[feuille] (Raaab) at ({\NiveauE},{(1)*\InterFeuilles}) {$T$}; +\node[feuille] (Raab) at ({\NiveauD},{(2)*\InterFeuilles}) {$E$}; +\node[noeud] (Rab) at ({\NiveauC},{(5)*\InterFeuilles}) {$$}; +\node[noeud] (Raba) at ({\NiveauD},{(4)*\InterFeuilles}) {$$}; +\node[feuille] (Rabaa) at ({\NiveauE},{(3)*\InterFeuilles}) {$A$}; +\node[noeud] (Rabab) at ({\NiveauE},{(4.5)*\InterFeuilles}) {$$}; +\node[feuille] (Rababa) at ({\NiveauF},{(4)*\InterFeuilles}) {$W$}; +\node[feuille] (Rababb) at ({\NiveauF},{(5)*\InterFeuilles}) {$G$}; +\node[noeud] (Rabb) at ({\NiveauD},{(6.5)*\InterFeuilles}) {$$}; +\node[feuille] (Rabba) at ({\NiveauE},{(6)*\InterFeuilles}) {$D$}; +\node[feuille] (Rabbb) at ({\NiveauE},{(7)*\InterFeuilles}) {$U$}; +\node[noeud] (Rb) at ({\NiveauB},{(17.5)*\InterFeuilles}) {$$}; +\node[noeud] (Rba) at ({\NiveauC},{(10.5)*\InterFeuilles}) {$$}; +\node[feuille] (Rbaa) at ({\NiveauD},{(8)*\InterFeuilles}) {$O$}; +\node[noeud] (Rbab) at ({\NiveauD},{(11)*\InterFeuilles}) {$$}; +\node[noeud] (Rbaba) at ({\NiveauE},{(10)*\InterFeuilles}) {$$}; +\node[noeud] (Rbabaa) at ({\NiveauF},{(9.5)*\InterFeuilles}) {$$}; +\node[feuille] (Rbabaaa) at ({\NiveauG},{(9)*\InterFeuilles}) {$.$}; +\node[feuille] (Rbabaab) at ({\NiveauG},{(10)*\InterFeuilles}) {$K$}; +\node[feuille] (Rbabab) at ({\NiveauF},{(11)*\InterFeuilles}) {$M$}; +\node[noeud] (Rbabb) at ({\NiveauE},{(12.5)*\InterFeuilles}) {$$}; +\node[feuille] (Rbabba) at ({\NiveauF},{(12)*\InterFeuilles}) {$L$}; +\node[feuille] (Rbabbb) at ({\NiveauF},{(13)*\InterFeuilles}) {$S$}; +\node[noeud] (Rbb) at ({\NiveauC},{(20.5)*\InterFeuilles}) {$$}; +\node[noeud] (Rbba) at ({\NiveauD},{(20)*\InterFeuilles}) {$$}; +\node[noeud] (Rbbaa) at ({\NiveauE},{(16.5)*\InterFeuilles}) {$$}; +\node[noeud] (Rbbaaa) at ({\NiveauF},{(16)*\InterFeuilles}) {$$}; +\node[noeud] (Rbbaaaa) at ({\NiveauG},{(14.5)*\InterFeuilles}) {$$}; +\node[feuille] (Rbbaaaaa) at ({\NiveauH},{(14)*\InterFeuilles}) {$Y$}; +\node[feuille] (Rbbaaaab) at ({\NiveauH},{(15)*\InterFeuilles}) {$"$}; +\node[noeud] (Rbbaaab) at ({\NiveauG},{(17)*\InterFeuilles}) {$Nœud36$}; +\node[noeud] (Rbbaaaba) at ({\NiveauH},{(16.5)*\InterFeuilles}) {$$}; +\node[feuille] (Rbbaaabaa) at ({\NiveauI},{(16)*\InterFeuilles}) {$F$}; +\node[feuille] (Rbbaaabab) at ({\NiveauI},{(17)*\InterFeuilles}) {$X$}; +\node[feuille] (Rbbaaabb) at ({\NiveauH},{(18)*\InterFeuilles}) {$B$}; +\node[feuille] (Rbbaab) at ({\NiveauF},{(19)*\InterFeuilles}) {$N$}; +\node[noeud] (Rbbab) at ({\NiveauE},{(23)*\InterFeuilles}) {$$}; +\node[feuille] (Rbbaba) at ({\NiveauF},{(20)*\InterFeuilles}) {$R$}; +\node[noeud] (Rbbabb) at ({\NiveauF},{(23.5)*\InterFeuilles}) {$$}; +\node[noeud] (Rbbabba) at ({\NiveauG},{(22.5)*\InterFeuilles}) {$$}; +\node[noeud] (Rbbabbaa) at ({\NiveauH},{(21.5)*\InterFeuilles}) {$$}; +\node[feuille] (Rbbabbaaa) at ({\NiveauI},{(21)*\InterFeuilles}) {$P$}; +\node[feuille] (Rbbabbaab) at ({\NiveauI},{(22)*\InterFeuilles}) {$V$}; +\node[noeud] (Rbbabbab) at ({\NiveauH},{(23.5)*\InterFeuilles}) {$$}; +\node[feuille] (Rbbabbaba) at ({\NiveauI},{(23)*\InterFeuilles}) {$?$}; +\node[feuille] (Rbbabbabb) at ({\NiveauI},{(24)*\InterFeuilles}) {$,$}; +\node[noeud] (Rbbabbb) at ({\NiveauG},{(25.5)*\InterFeuilles}) {$$}; +\node[feuille] (Rbbabbba) at ({\NiveauH},{(25)*\InterFeuilles}) {$C$}; +\node[feuille] (Rbbabbbb) at ({\NiveauH},{(26)*\InterFeuilles}) {$I$}; +\node[feuille] (Rbbb) at ({\NiveauD},{(27)*\InterFeuilles}) {$espace$}; +% Arcs (MODIFIABLES : Styles) +\draw[fleche] (R)--(Ra) node[etiquette] {$0$}; +\draw[fleche] (Ra)--(Raa) node[etiquette] {$0$}; +\draw[fleche] (Raa)--(Raaa) node[etiquette] {$0$}; +\draw[fleche] (Raaa)--(Raaaa) node[etiquette] {$0$}; +\draw[fleche] (Raaa)--(Raaab) node[etiquette] {$1$}; +\draw[fleche] (Raa)--(Raab) node[etiquette] {$1$}; +\draw[fleche] (Ra)--(Rab) node[etiquette] {$1$}; +\draw[fleche] (Rab)--(Raba) node[etiquette] {$0$}; +\draw[fleche] (Raba)--(Rabaa) node[etiquette] {$0$}; +\draw[fleche] (Raba)--(Rabab) node[etiquette] {$1$}; +\draw[fleche] (Rabab)--(Rababa) node[etiquette] {$0$}; +\draw[fleche] (Rabab)--(Rababb) node[etiquette] {$A$}; +\draw[fleche] (Rab)--(Rabb) node[etiquette] {$1$}; +\draw[fleche] (Rabb)--(Rabba) node[etiquette] {$0$}; +\draw[fleche] (Rabb)--(Rabbb) node[etiquette] {$1$}; +\draw[fleche] (R)--(Rb) node[etiquette] {$1$}; +\draw[fleche] (Rb)--(Rba) node[etiquette] {$0$}; +\draw[fleche] (Rba)--(Rbaa) node[etiquette] {$0$}; +\draw[fleche] (Rba)--(Rbab) node[etiquette] {$1$}; +\draw[fleche] (Rbab)--(Rbaba) node[etiquette] {$0$}; +\draw[fleche] (Rbaba)--(Rbabaa) node[etiquette] {$0$}; +\draw[fleche] (Rbabaa)--(Rbabaaa) node[etiquette] {$0$}; +\draw[fleche] (Rbabaa)--(Rbabaab) node[etiquette] {$1$}; +\draw[fleche] (Rbaba)--(Rbabab) node[etiquette] {$1$}; +\draw[fleche] (Rbab)--(Rbabb) node[etiquette] {$1$}; +\draw[fleche] (Rbabb)--(Rbabba) node[etiquette] {$0$}; +\draw[fleche] (Rbabb)--(Rbabbb) node[etiquette] {$1$}; +\draw[fleche] (Rb)--(Rbb) node[etiquette] {$1$}; +\draw[fleche] (Rbb)--(Rbba) node[etiquette] {$0$}; +\draw[fleche] (Rbba)--(Rbbaa) node[etiquette] {$0$}; +\draw[fleche] (Rbbaa)--(Rbbaaa) node[etiquette] {$0$}; +\draw[fleche] (Rbbaaa)--(Rbbaaaa) node[etiquette] {$0$}; +\draw[fleche] (Rbbaaaa)--(Rbbaaaaa) node[etiquette] {$0$}; +\draw[fleche] (Rbbaaaa)--(Rbbaaaab) node[etiquette] {$1$}; +\draw[fleche] (Rbbaaa)--(Rbbaaab) node[etiquette] {$1$}; +\draw[fleche] (Rbbaaab)--(Rbbaaaba) node[etiquette] {$0$}; +\draw[fleche] (Rbbaaaba)--(Rbbaaabaa) node[etiquette] {$0$}; +\draw[fleche] (Rbbaaaba)--(Rbbaaabab) node[etiquette] {$1$}; +\draw[fleche] (Rbbaaab)--(Rbbaaabb) node[etiquette] {$1$}; +\draw[fleche] (Rbbaa)--(Rbbaab) node[etiquette] {$1$}; +\draw[fleche] (Rbba)--(Rbbab) node[etiquette] {$1$}; +\draw[fleche] (Rbbab)--(Rbbaba) node[etiquette] {$0$}; +\draw[fleche] (Rbbab)--(Rbbabb) node[etiquette] {$1$}; +\draw[fleche] (Rbbabb)--(Rbbabba) node[etiquette] {$0$}; +\draw[fleche] (Rbbabba)--(Rbbabbaa) node[etiquette] {$0$}; +\draw[fleche] (Rbbabbaa)--(Rbbabbaaa) node[etiquette] {$0$}; +\draw[fleche] (Rbbabbaa)--(Rbbabbaab) node[etiquette] {$1$}; +\draw[fleche] (Rbbabba)--(Rbbabbab) node[etiquette] {$1$}; +\draw[fleche] (Rbbabbab)--(Rbbabbaba) node[etiquette] {$0$}; +\draw[fleche] (Rbbabbab)--(Rbbabbabb) node[etiquette] {$1$}; +\draw[fleche] (Rbbabb)--(Rbbabbb) node[etiquette] {$1$}; +\draw[fleche] (Rbbabbb)--(Rbbabbba) node[etiquette] {$0$}; +\draw[fleche] (Rbbabbb)--(Rbbabbbb) node[etiquette] {$1$}; +\draw[fleche] (Rbb)--(Rbbb) node[etiquette] {$1$}; +\end{tikzpicture} +\end{center} +%:-+-+-+-+- Fin + diff --git a/2-InformationTheory/3InformationTheoryCompression2023-03-27-Note-11-12.pdf b/2-InformationTheory/3InformationTheoryCompression2023-03-27-Note-11-12.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c9c167ac6af6a48999401fa3d153f137ef0bd3c1 GIT binary patch literal 427298 zcmX6^V|XN86WwrQZ){Gi-PoDfwrx+$jgw6_wl~-~8{4*R+txSl^ZlAT-80>Ft52O% zRrfZPB2b)>mFWipRsDJ8E5dhD7E%XeYXm+%Qf65*dka@f(jVYM$_S*Sq|D-0wytK* 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+woken +woman +women +woody +wooer +wooly +woozy +wordy +world +worry +worse +worst +worth +would +wound +woven +wrack +wrath +wreak +wreck +wrest +wring +wrist +write +wrong +wrote +wrung +wryly +yacht +yearn +yeast +yield +young +youth +zebra +zesty +zonal \ No newline at end of file diff --git a/2-InformationTheory/Grepregexp/commandes.txt b/2-InformationTheory/Grepregexp/commandes.txt new file mode 100644 index 0000000..e537da0 --- /dev/null +++ b/2-InformationTheory/Grepregexp/commandes.txt @@ -0,0 +1,18 @@ +ls answers.txt +cd .. +ls +cd Grepregexp/ +ls +more answers.txt +tail answers.txt +wc -l answers.txt +grep [^star][^star][^star][^star][^star] answers.txt +grep [^star][^star][^star][^star][^star] answers.txt | wc -l +grep [^star][^star][^star][^star][^stare] answers.txt | wc -l +grep [^star][^star][^star][^star][^stare] answers.txt +grep [^star][^star][^star][^star][^stare] answers.txt | grep e +grep [^star][^star][^star][^star][^stare] answers.txt | grep e | wc -l +grep [^star][^star][^star][^star][^stare] answers.txt | grep e | more +grep [^starpoxye][^starpoxy][^starpoxy][^starpoxy][^starepoxy] answers.txt | grep e | wc -l +grep [^starpoxye][^starpoxy][^starpoxy][^starpoxy][^starepoxy] answers.txt | grep e +grep [^starpoxyefil][^starpoxyfil][^starpoxyfile][^starpoxyfil][^starepoxyfil] answers.txt | grep e | grep d diff --git a/2-InformationTheory/Grepregexp/quelquesCommandes.txt b/2-InformationTheory/Grepregexp/quelquesCommandes.txt new file mode 100644 index 0000000..862de21 --- /dev/null +++ b/2-InformationTheory/Grepregexp/quelquesCommandes.txt @@ -0,0 +1,43 @@ + 1937 grep the american-english | more + 1938 grep the american-english + 1939 grep ^the american-english + 1940 grep the$ american-english + 1941 grep her american-english + 1942 grep cow american-english + 1943 ls + 1944 head answers.txt + 1945 tail answers.txt + 1946 tail wordle-allowed-guesses.txt + 1947 egrep [^st] answers.txt + 1948 egrep [^st] american-english + 1949 egrep [^st]5 american-english + 1950 egrep [^st]^5 american-english + 1951 egrep [^st]**5 american-english + 1952 egrep ([^st])5 american-english + 1953 egrep ^[^st][^st][^st][^st]$ american-english + 1954 egrep ^[^st][^st][^st][^st][^st]$ american-english + 1955 egrep ^[abcdefghijklmnopqruvwxyz][abcdefghijklmnopqruvwxyz][abcdefghijklmnopqruvwxyz][abcdefghijklmnopqruvwxyz][abcdefghijklmnopqruvwxyz]$ american-english + 1956 egrep ^[^st][^st][^st][^st][^st]* answers.txt + 1957 egrep ^[^st][^st][^st][^st][^st]$ answers.txt + 1958 egrep ^[^st][^st][^st][^st][^st]* answers.txt + 1959 egrep ^[^st][^st][^st][^st][^st]$ answers.txt + 1960 egrep ^[^st][^st][^st][^st][^st]$ answers.txt | wc -l + 1961 wc -l answers.txt + 1962 egrep ^[^st][^st][^sta][^str][^ste]$ answers.txt | wc -l + 1963 egrep ^[^st][^st][^sta][^str][^ste]$ answers.txt + 1964 egrep ^[^st][^st][^sta][^str][^ste]$ answers.txt | grep a + 1965 egrep ^[^st][^st][^sta][^str][^ste]$ answers.txt | grep a | grep r + 1966 egrep ^[^st][^st][^sta][^str][^ste]$ answers.txt | grep a | wc -l + 1967 egrep ^[^st][^st][^sta][^str][^ste]$ answers.txt | grep a | grep r | wc -l + 1968 egrep ^[^st][^st][^sta][^str][^ste]$ answers.txt | grep a | grep r | grep e | wc -l + 1969 egrep ^[^st][^st][^sta][^str][^ste]$ answers.txt | grep a | grep r | grep e + 1970 egrep ^[^strc]a[^starc]er$ answers.txt + 1971 egrep ^[^strce]a[^starcg]er$ answers.txt + 1972 egrep ^[^strcemk]a[^starcgmk]er$ answers.txt + 1973 egrep ^[^strcemkp]a[^starcgmkp]er$ answers.txt + 1974 egrep [violent]* american-english + 1975 egrep ^[violent]*$ american-english + 1976 egrep ^[violent]*$ american-english | grep v + 1977 egrep ^[violent][violent][violent][violent][violent]*$ american-english | grep v + 1978 alias + 1979 grep ^[violent][violent][violent][violent][violent]*$ american-english | grep v diff --git a/2-InformationTheory/Grepregexp/wordle-allowed-guesses.txt b/2-InformationTheory/Grepregexp/wordle-allowed-guesses.txt new file mode 100644 index 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0000000..1b14a9a --- /dev/null +++ b/2-InformationTheory/HuffmanGruffaloNightmare.tex @@ -0,0 +1,535 @@ +% -*- coding: utf-8; -*- +\documentclass[a4paper,6pt,landscape]{article} +%\usepackage{pdflscape} +%\usepackage{sagetex} + +\usepackage[francais]{babel} +%\usepackage[latin1]{inputenc} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{lmodern} +\usepackage{graphics,graphicx} +\usepackage{url} +\usepackage{hyperref} +\usepackage[pdftex,usenames,dvipsnames]{xcolor} +%%% decommenter si tikz necessaire +\usepackage{tikz} +\usetikzlibrary[decorations.pathmorphing] +\usetikzlibrary[decorations.pathreplacing] +\usetikzlibrary{backgrounds} +\usetikzlibrary{positioning} +\usetikzlibrary{arrows} +\usetikzlibrary[backgrounds] +\usetikzlibrary{automata,positioning,arrows.meta} +%%% +\usepackage{tcolorbox} +\tcbuselibrary{skins,breakable} +\tcbset{textmarker/.style={% + % skin=enhancedmiddlejigsaw, + breakable, + parbox=false, + boxrule=0mm,leftrule=5mm,rightrule=5mm,boxsep=0mm,arc=0mm,outer arc=0mm, + left=3mm,right=3mm,top=1mm,bottom=1mm,toptitle=1mm,bottomtitle=1mm,oversize}} +\newtcolorbox{yellow}{textmarker,colback=yellow!5!white,colframe=yellow} +\newtcolorbox{orange}{textmarker,colback=DarkOrange!5!white, + colframe=DarkOrange!75!yellow} +\newtcolorbox{red}{textmarker,colback=red!5!white,colframe=red} +\newtcolorbox{blue}{textmarker,colback=DeepSkyBlue!5!white,colframe=DeepSkyBlue} +\newtcolorbox{green}{textmarker,colback=Chartreuse!5!white,colframe=Chartreuse} +\newtcolorbox{rainbow}{textmarker,interior hidden, + frame style={top color=blue,bottom color=red,middle color=green}} +\newtcbox{\fluo}[1][yellow]{on line, +arc=7pt,colback=#1!10!white,colframe=#1!50!black, +before upper={\rule[-3pt]{0pt}{10pt}},boxrule=1pt, +boxsep=0pt,left=6pt,right=6pt,top=2pt,bottom=2pt} +%%% + +%\usepackage{tikz-uml} + +\usepackage[thicklines]{easytable} +\usepackage{framed} %%% boîtes permettant de gérer correctement le saut de page. +\usepackage{multicol} +\usepackage{savetrees} +%\usepackage[a4paper,width=17cm,height=23cm]{geometry} +\usepackage{a4wide} +\usepackage{paralist} +\usepackage{fancyhdr} +\usepackage{colortbl} +\usepackage{cancel} %%% +\usepackage{amssymb,amsmath,amsthm} + +%%% On charge le paquet ifthen pout faire des tests +\usepackage{ifthen} +%%% On définit un compteur numérique pour l'année +\newcounter{theyear} +\setcounter{theyear}{\number\year} +%%% Une macro pour écrire l'année académique automatiquement en +%%% fonction du mois en cours +\newcommand{\academicyear}[0]{ + \ifthenelse{\number\month<8} + {\addtocounter{theyear}{-1}\arabic{theyear}\addtocounter{theyear}{-1999}\,-\arabic{theyear}}% + {\arabic{theyear}\addtocounter{theyear}{-1999}\,-\arabic{theyear}}% +}% + +%%% mettre les macros à la racine du cours et ajuster en conséquence +%%% pour éviter d'avoir plus d'une copie des macros par cours. +%\input{MyMacros.tex} +%\input{SetColors.tex} + +\newcommand{\mot}[1]{\textcolor{color2}{\textbf{#1}}} +\newcommand{\alert}[1]{\textcolor{color3}{\textbf{#1}}} +\newcommand{\JFLAP}[1]{\textcolor{color6}{\textbf{\texttt{#1}}}} + +%%%%%%%%%%%%%%%%%%%%%%%% +%%% Def d'environement de Math (Malika) +%%%%%%%%%%%%%%%%%%%%%%%% +\theoremstyle{plain} +\newtheorem*{theo}{Théorème} +\newtheorem*{cons}{Conséquence} +\newtheorem*{conss}{Conséquences} + + +\theoremstyle{definition} +\newtheorem{exo}{Exercice} +\newtheorem*{defi}{Définition} +\newtheorem*{probleme}{Problème} +\newtheorem*{reponse}{Réponse} + + +\theoremstyle{remark} +\newtheorem*{exemple}{Exemple} +\newtheorem*{remarque}{Remarque} +\newtheorem*{remarques}{Remarques} +\newtheorem*{prop}{Propriété} +\newtheorem*{props}{Propriétés} + + + +%%%%%%%%%%%%%%%%%%%%%%%% +%%% Macros diverses (Malika) +%%%%%%%%%%%%%%%%%%%%%%%% + + +\newcommand{\raus}[1]{} +\AtBeginDocument{ +\renewcommand{\labelitemi}{\textbullet} +\renewcommand{\labelitemii}{$\circ$} +} + +%\pagestyle{fancy} +\fancyhf{} +\fancyhead{ +\begin{minipage}{16cm} +\hspace{-2cm} +Nom : \fbox{\begin{minipage}{6cm}\hfill\vspace{.7cm}\end{minipage}} +\hfill +Pr\'enom : \fbox{\begin{minipage}{4cm}\hfill\vspace{.7cm}\end{minipage}} +\hfill +Groupe : \fbox{\begin{minipage}{.7cm}\hfill\vspace{.7cm}\end{minipage}} +\end{minipage} +} +\fancyfoot[C]{Page {\large\thepage}} + + +%%%%%%%%%%%%%%%%%%%%%%%% +%%% Quelques paquets gérant la correction / espace pour la reponse +%%%%%%%%%%%%%%%%%%%%%%%% +\usepackage{comment} +%%% Pour afficher la correction et exclure les boites pour la reponse +\includecomment{correction} +\excludecomment{EspaceReponse} +%%% Pour version cachant la correction et incluant l'espace pour la reponse +%\excludecomment{correction} +%\includecomment{EspaceReponse} + + + + +%%% +\begin{document} +\ +\vspace{.2cm} + +{\small +\noindent IUT Sénart-Fontainebleau, UPEC +\hfill +Florent Madelaine + +\noindent Information Theory +\hfill +% intervenant 2 + +\noindent IUT Info 2A \hfill\noindent\academicyear{} + +} +\vspace{.7cm} + +\hrule +\vspace{.3cm} + +\begin{center} + +{\textbf{\Large + Huffman Gruffalo Nightmare +}} +\vspace{.1cm} + +\end{center} +\vspace{.3cm} + +\hrule +\vspace{.3cm} + + +% %:-+-+-+- Engendré par : http://math.et.info.free.fr/TikZ/Arbre/ +% \begin{center} +% % Racine à Gauche, développement vers la droite +% \begin{tikzpicture}[xscale=0.2,yscale=0.2] +% % Styles (MODIFIABLES) +% \tikzstyle{fleche}=[->,>=latex,thick] +% \tikzstyle{noeud}=[fill=yellow,circle,draw] +% \tikzstyle{feuille}=[fill=yellow,circle,draw] +% \tikzstyle{etiquette}=[midway,fill=white,draw] +% % Dimensions (MODIFIABLES) +% \def\DistanceInterNiveaux{3} +% \def\DistanceInterFeuilles{2} +% % Dimensions calculées (NON MODIFIABLES) +% \def\NiveauA{(0)*\DistanceInterNiveaux} +% \def\NiveauB{(1.875)*\DistanceInterNiveaux} +% \def\NiveauC{(3.625)*\DistanceInterNiveaux} +% \def\NiveauD{(5.25)*\DistanceInterNiveaux} +% \def\NiveauE{(6.75)*\DistanceInterNiveaux} +% \def\NiveauF{(8.125)*\DistanceInterNiveaux} +% \def\NiveauG{(9.375)*\DistanceInterNiveaux} +% \def\NiveauH{(10.5)*\DistanceInterNiveaux} +% \def\NiveauI{(11.5)*\DistanceInterNiveaux} +% \def\InterFeuilles{(-1)*\DistanceInterFeuilles} +% % Noeuds (MODIFIABLES : Styles et Coefficients d'InterFeuilles) +% \node[noeud] (R) at ({\NiveauA},{(13.5)*\InterFeuilles}) {\tiny $Tous$}; +% \node[noeud] (Ra) at ({\NiveauB},{(3.5)*\InterFeuilles}) {$$}; +% \node[noeud] (Raa) at ({\NiveauC},{(1)*\InterFeuilles}) {$$}; +% \node[noeud] (Raaa) at ({\NiveauD},{(0.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Raaaa) at ({\NiveauE},{(0)*\InterFeuilles}) {\tiny $H$}; +% \node[feuille] (Raaab) at ({\NiveauE},{(1)*\InterFeuilles}) {\tiny $T$}; +% \node[feuille] (Raab) at ({\NiveauD},{(2)*\InterFeuilles}) {\tiny $E$}; +% \node[noeud] (Rab) at ({\NiveauC},{(5)*\InterFeuilles}) {$$}; +% \node[noeud] (Raba) at ({\NiveauD},{(4)*\InterFeuilles}) {$$}; +% \node[feuille] (Rabaa) at ({\NiveauE},{(3)*\InterFeuilles}) {\tiny $A$}; +% \node[noeud] (Rabab) at ({\NiveauE},{(4.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rababa) at ({\NiveauF},{(4)*\InterFeuilles}) {\tiny $W$}; +% \node[feuille] (Rababb) at ({\NiveauF},{(5)*\InterFeuilles}) {\tiny $G$}; +% \node[noeud] (Rabb) at ({\NiveauD},{(6.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rabba) at ({\NiveauE},{(6)*\InterFeuilles}) {\tiny $D$}; +% \node[feuille] (Rabbb) at ({\NiveauE},{(7)*\InterFeuilles}) {\tiny $U$}; +% \node[noeud] (Rb) at ({\NiveauB},{(17.5)*\InterFeuilles}) {$$}; +% \node[noeud] (Rba) at ({\NiveauC},{(10.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbaa) at ({\NiveauD},{(8)*\InterFeuilles}) {\tiny $O$}; +% \node[noeud] (Rbab) at ({\NiveauD},{(11)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbaba) at ({\NiveauE},{(10)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbabaa) at ({\NiveauF},{(9.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbabaaa) at ({\NiveauG},{(9)*\InterFeuilles}) {\tiny $.$}; +% \node[feuille] (Rbabaab) at ({\NiveauG},{(10)*\InterFeuilles}) {\tiny $K$}; +% \node[feuille] (Rbabab) at ({\NiveauF},{(11)*\InterFeuilles}) {\tiny $M$}; +% \node[noeud] (Rbabb) at ({\NiveauE},{(12.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbabba) at ({\NiveauF},{(12)*\InterFeuilles}) {\tiny $L$}; +% \node[feuille] (Rbabbb) at ({\NiveauF},{(13)*\InterFeuilles}) {\tiny $S$}; +% \node[noeud] (Rbb) at ({\NiveauC},{(20.5)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbba) at ({\NiveauD},{(20)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbbaa) at ({\NiveauE},{(16.5)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbbaaa) at ({\NiveauF},{(16)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbbaaaa) at ({\NiveauG},{(14.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbbaaaaa) at ({\NiveauH},{(14)*\InterFeuilles}) {\tiny +% $Y$}; +% \node[feuille] (Rbbaaaab) at ({\NiveauH},{(15)*\InterFeuilles}) {\tiny +% $"$}; +% \node[noeud] (Rbbaaab) at ({\NiveauG},{(17)*\InterFeuilles}) {}; +% \node[noeud] (Rbbaaaba) at ({\NiveauH},{(16.5)*\InterFeuilles}) {}; +% \node[feuille] (Rbbaaabaa) at ({\NiveauI},{(16)*\InterFeuilles}) +% {\tiny $F$}; +% \node[feuille] (Rbbaaabab) at ({\NiveauI},{(17)*\InterFeuilles}) +% {\tiny $X$}; +% \node[feuille] (Rbbaaabb) at ({\NiveauH},{(18)*\InterFeuilles}) {\tiny +% $B$}; +% \node[feuille] (Rbbaab) at ({\NiveauF},{(19)*\InterFeuilles}) {\tiny $N$}; +% \node[noeud] (Rbbab) at ({\NiveauE},{(23)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbbaba) at ({\NiveauF},{(20)*\InterFeuilles}) {\tiny $R$}; +% \node[noeud] (Rbbabb) at ({\NiveauF},{(23.5)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbbabba) at ({\NiveauG},{(22.5)*\InterFeuilles}) {$$}; +% \node[noeud] (Rbbabbaa) at ({\NiveauH},{(21.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbbabbaaa) at ({\NiveauI},{(21)*\InterFeuilles}) +% {\tiny $P$}; +% \node[feuille] (Rbbabbaab) at ({\NiveauI},{(22)*\InterFeuilles}) +% {\tiny $V$}; +% \node[noeud] (Rbbabbab) at ({\NiveauH},{(23.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbbabbaba) at ({\NiveauI},{(23)*\InterFeuilles}) +% {\tiny $?$}; +% \node[feuille] (Rbbabbabb) at ({\NiveauI},{(24)*\InterFeuilles}) +% {\tiny $,$}; +% \node[noeud] (Rbbabbb) at ({\NiveauG},{(25.5)*\InterFeuilles}) {$$}; +% \node[feuille] (Rbbabbba) at ({\NiveauH},{(25)*\InterFeuilles}) {\tiny +% $C$}; +% \node[feuille] (Rbbabbbb) at ({\NiveauH},{(26)*\InterFeuilles}) {\tiny +% $I$}; +% \node[feuille] (Rbbb) at ({\NiveauD},{(27)*\InterFeuilles}) {\tiny $espace$}; +% % Arcs (MODIFIABLES : Styles) +% \draw[fleche] (R)--(Ra) node[etiquette] {$0$}; +% \draw[fleche] (Ra)--(Raa) node[etiquette] {$0$}; +% \draw[fleche] (Raa)--(Raaa) node[etiquette] {$0$}; +% \draw[fleche] (Raaa)--(Raaaa) node[etiquette] {$0$}; +% \draw[fleche] (Raaa)--(Raaab) node[etiquette] {$1$}; +% \draw[fleche] (Raa)--(Raab) node[etiquette] {$1$}; +% \draw[fleche] (Ra)--(Rab) node[etiquette] {$1$}; +% \draw[fleche] (Rab)--(Raba) node[etiquette] {$0$}; +% \draw[fleche] (Raba)--(Rabaa) node[etiquette] {$0$}; +% \draw[fleche] (Raba)--(Rabab) node[etiquette] {$1$}; +% \draw[fleche] (Rabab)--(Rababa) node[etiquette] {$0$}; +% \draw[fleche] (Rabab)--(Rababb) node[etiquette] {$1$}; +% \draw[fleche] (Rab)--(Rabb) node[etiquette] {$1$}; +% \draw[fleche] (Rabb)--(Rabba) node[etiquette] {$0$}; +% \draw[fleche] (Rabb)--(Rabbb) node[etiquette] {$1$}; +% \draw[fleche] (R)--(Rb) node[etiquette] {$1$}; +% \draw[fleche] (Rb)--(Rba) node[etiquette] {$0$}; +% \draw[fleche] (Rba)--(Rbaa) node[etiquette] {$0$}; +% \draw[fleche] (Rba)--(Rbab) node[etiquette] {$1$}; +% \draw[fleche] (Rbab)--(Rbaba) node[etiquette] {$0$}; +% \draw[fleche] (Rbaba)--(Rbabaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbabaa)--(Rbabaaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbabaa)--(Rbabaab) node[etiquette] {$1$}; +% \draw[fleche] (Rbaba)--(Rbabab) node[etiquette] {$1$}; +% \draw[fleche] (Rbab)--(Rbabb) node[etiquette] {$1$}; +% \draw[fleche] (Rbabb)--(Rbabba) node[etiquette] {$0$}; +% \draw[fleche] (Rbabb)--(Rbabbb) node[etiquette] {$1$}; +% \draw[fleche] (Rb)--(Rbb) node[etiquette] {$1$}; +% \draw[fleche] (Rbb)--(Rbba) node[etiquette] {$0$}; +% \draw[fleche] (Rbba)--(Rbbaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbbaa)--(Rbbaaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbbaaa)--(Rbbaaaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbbaaaa)--(Rbbaaaaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbbaaaa)--(Rbbaaaab) node[etiquette] {$1$}; +% \draw[fleche] (Rbbaaa)--(Rbbaaab) node[etiquette] {$1$}; +% \draw[fleche] (Rbbaaab)--(Rbbaaaba) node[etiquette] {$0$}; +% \draw[fleche] (Rbbaaaba)--(Rbbaaabaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbbaaaba)--(Rbbaaabab) node[etiquette] {$1$}; +% \draw[fleche] (Rbbaaab)--(Rbbaaabb) node[etiquette] {$1$}; +% \draw[fleche] (Rbbaa)--(Rbbaab) node[etiquette] {$1$}; +% \draw[fleche] (Rbba)--(Rbbab) node[etiquette] {$1$}; +% \draw[fleche] (Rbbab)--(Rbbaba) node[etiquette] {$0$}; +% \draw[fleche] (Rbbab)--(Rbbabb) node[etiquette] {$1$}; +% \draw[fleche] (Rbbabb)--(Rbbabba) node[etiquette] {$0$}; +% \draw[fleche] (Rbbabba)--(Rbbabbaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbbabbaa)--(Rbbabbaaa) node[etiquette] {$0$}; +% \draw[fleche] (Rbbabbaa)--(Rbbabbaab) node[etiquette] {$1$}; +% \draw[fleche] (Rbbabba)--(Rbbabbab) node[etiquette] {$1$}; +% \draw[fleche] (Rbbabbab)--(Rbbabbaba) node[etiquette] {$0$}; +% \draw[fleche] (Rbbabbab)--(Rbbabbabb) node[etiquette] {$1$}; +% \draw[fleche] (Rbbabb)--(Rbbabbb) node[etiquette] {$1$}; +% \draw[fleche] (Rbbabbb)--(Rbbabbba) node[etiquette] {$0$}; +% \draw[fleche] (Rbbabbb)--(Rbbabbbb) node[etiquette] {$1$}; +% \draw[fleche] (Rbb)--(Rbbb) node[etiquette] {$1$}; +% \end{tikzpicture} +% \end{center} +% %:-+-+-+-+- Fin + + + +\pagebreak + +%:-+-+-+- Engendré par : http://math.et.info.free.fr/TikZ/Arbre/ +\begin{center} +% Racine en Haut, développement vers le bas +\begin{tikzpicture}[xscale=0.4,yscale=0.45] +% Styles (MODIFIABLES) +\tikzstyle{fleche}=[->,>=latex,thick] +\tikzstyle{noeud}=[fill=yellow,circle,draw] +\tikzstyle{feuille}=[fill=yellow,circle,draw] +\tikzstyle{etiquette}=[midway,fill=white,draw] +% Dimensions (MODIFIABLES) +\def\DistanceInterNiveaux{3} +\def\DistanceInterFeuilles{2} +% Dimensions calculées (NON MODIFIABLES) +\def\NiveauA{(-0)*\DistanceInterNiveaux} +\def\NiveauB{(-1.875)*\DistanceInterNiveaux} +\def\NiveauC{(-3.625)*\DistanceInterNiveaux} +\def\NiveauD{(-5.25)*\DistanceInterNiveaux} +\def\NiveauE{(-6.75)*\DistanceInterNiveaux} +\def\NiveauF{(-8.125)*\DistanceInterNiveaux} +\def\NiveauG{(-9.375)*\DistanceInterNiveaux} +\def\NiveauH{(-10.5)*\DistanceInterNiveaux} +\def\NiveauI{(-11.5)*\DistanceInterNiveaux} +\def\InterFeuilles{(1)*\DistanceInterFeuilles} +% Noeuds (MODIFIABLES : Styles et Coefficients d'InterFeuilles) +\node[noeud] (R) at ({(13.5)*\InterFeuilles},{\NiveauA}) {\tiny Tous}; +\node[noeud] (Ra) at ({(3.5)*\InterFeuilles},{\NiveauB}) {}; +\node[noeud] (Raa) at ({(1)*\InterFeuilles},{\NiveauC}) {}; +\node[noeud] (Raaa) at ({(0.5)*\InterFeuilles},{\NiveauD}) {}; +\node[feuille] (Raaaa) at ({(0)*\InterFeuilles},{\NiveauE}) {\tiny H}; +\node[feuille] (Raaab) at ({(1)*\InterFeuilles},{\NiveauE}) {\tiny T}; +\node[feuille] (Raab) at ({(2)*\InterFeuilles},{\NiveauD}) {\tiny E}; +\node[noeud] (Rab) at ({(5)*\InterFeuilles},{\NiveauC}) {}; +\node[noeud] (Raba) at ({(4)*\InterFeuilles},{\NiveauD}) {}; +\node[feuille] (Rabaa) at ({(3)*\InterFeuilles},{\NiveauE}) {\tiny A}; +\node[noeud] (Rabab) at ({(4.5)*\InterFeuilles},{\NiveauE}) {}; +\node[feuille] (Rababa) at ({(4)*\InterFeuilles},{\NiveauF}) {\tiny W}; +\node[feuille] (Rababb) at ({(5)*\InterFeuilles},{\NiveauF}) {\tiny G}; +\node[noeud] (Rabb) at ({(6.5)*\InterFeuilles},{\NiveauD}) {}; +\node[feuille] (Rabba) at ({(6)*\InterFeuilles},{\NiveauE}) {\tiny D}; +\node[feuille] (Rabbb) at ({(7)*\InterFeuilles},{\NiveauE}) {\tiny U}; +\node[noeud] (Rb) at ({(17.5)*\InterFeuilles},{\NiveauB}) {}; +\node[noeud] (Rba) at ({(10.5)*\InterFeuilles},{\NiveauC}) {}; +\node[feuille] (Rbaa) at ({(8)*\InterFeuilles},{\NiveauD}) {\tiny O}; +\node[noeud] (Rbab) at ({(11)*\InterFeuilles},{\NiveauD}) {}; +\node[noeud] (Rbaba) at ({(10)*\InterFeuilles},{\NiveauE}) {}; +\node[noeud] (Rbabaa) at ({(9.5)*\InterFeuilles},{\NiveauF}) {}; +\node[feuille] (Rbabaaa) at ({(9)*\InterFeuilles},{\NiveauG}) {\tiny .}; +\node[feuille] (Rbabaab) at ({(10)*\InterFeuilles},{\NiveauG}) {\tiny K}; +\node[feuille] (Rbabab) at ({(11)*\InterFeuilles},{\NiveauF}) {\tiny M}; +\node[noeud] (Rbabb) at ({(12.5)*\InterFeuilles},{\NiveauE}) {}; +\node[feuille] (Rbabba) at ({(12)*\InterFeuilles},{\NiveauF}) {\tiny L}; +\node[feuille] (Rbabbb) at ({(13)*\InterFeuilles},{\NiveauF}) {\tiny S}; +\node[noeud] (Rbb) at ({(20.5)*\InterFeuilles},{\NiveauC}) {}; +\node[noeud] (Rbba) at ({(20)*\InterFeuilles},{\NiveauD}) {}; +\node[noeud] (Rbbaa) at ({(16.5)*\InterFeuilles},{\NiveauE}) {}; +\node[noeud] (Rbbaaa) at ({(16)*\InterFeuilles},{\NiveauF}) {}; +\node[noeud] (Rbbaaaa) at ({(14.5)*\InterFeuilles},{\NiveauG}) {}; +\node[feuille] (Rbbaaaaa) at ({(14)*\InterFeuilles},{\NiveauH}) {\tiny + Y}; +\node[feuille] (Rbbaaaab) at ({(15)*\InterFeuilles},{\NiveauH}) {\tiny + "}; +\node[noeud] (Rbbaaab) at ({(17)*\InterFeuilles},{\NiveauG}) {}; +\node[noeud] (Rbbaaaba) at ({(16.5)*\InterFeuilles},{\NiveauH}) {}; +\node[feuille] (Rbbaaabaa) at ({(16)*\InterFeuilles},{\NiveauI}) +{\tiny F}; +\node[feuille] (Rbbaaabab) at ({(17)*\InterFeuilles},{\NiveauI}) +{\tiny X}; +\node[feuille] (Rbbaaabb) at ({(18)*\InterFeuilles},{\NiveauH}) {\tiny + B}; +\node[feuille] (Rbbaab) at ({(19)*\InterFeuilles},{\NiveauF}) {\tiny N}; +\node[noeud] (Rbbab) at ({(23)*\InterFeuilles},{\NiveauE}) {}; +\node[feuille] (Rbbaba) at ({(20)*\InterFeuilles},{\NiveauF}) {\tiny R}; +\node[noeud] (Rbbabb) at ({(23.5)*\InterFeuilles},{\NiveauF}) {}; +\node[noeud] (Rbbabba) at ({(22.5)*\InterFeuilles},{\NiveauG}) {}; +\node[noeud] (Rbbabbaa) at ({(21.5)*\InterFeuilles},{\NiveauH}) {}; +\node[feuille] (Rbbabbaaa) at ({(21)*\InterFeuilles},{\NiveauI}) +{\tiny P}; +\node[feuille] (Rbbabbaab) at ({(22)*\InterFeuilles},{\NiveauI}) +{\tiny V}; +\node[noeud] (Rbbabbab) at ({(23.5)*\InterFeuilles},{\NiveauH}) {}; +\node[feuille] (Rbbabbaba) at ({(23)*\InterFeuilles},{\NiveauI}) +{\tiny ?}; +\node[feuille] (Rbbabbabb) at ({(24)*\InterFeuilles},{\NiveauI}) +{\tiny ,}; +\node[noeud] (Rbbabbb) at ({(25.5)*\InterFeuilles},{\NiveauG}) {}; +\node[feuille] (Rbbabbba) at ({(25)*\InterFeuilles},{\NiveauH}) {\tiny + C}; +\node[feuille] (Rbbabbbb) at ({(26)*\InterFeuilles},{\NiveauH}) {\tiny + I}; +\node[feuille] (Rbbb) at ({(27)*\InterFeuilles},{\NiveauD}) {\tiny espace}; +% Arcs (MODIFIABLES : Styles) +\draw[fleche] (R)--(Ra) node[etiquette] {\tiny 0}; +\draw[fleche] (Ra)--(Raa) node[etiquette] {\tiny 0}; +\draw[fleche] (Raa)--(Raaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Raaa)--(Raaaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Raaa)--(Raaab) node[etiquette] {\tiny 1}; +\draw[fleche] (Raa)--(Raab) node[etiquette] {\tiny 1}; +\draw[fleche] (Ra)--(Rab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rab)--(Raba) node[etiquette] {\tiny 0}; +\draw[fleche] (Raba)--(Rabaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Raba)--(Rabab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rabab)--(Rababa) node[etiquette] {\tiny 0}; +\draw[fleche] (Rabab)--(Rababb) node[etiquette] {\tiny 1}; +\draw[fleche] (Rab)--(Rabb) node[etiquette] {\tiny 1}; +\draw[fleche] (Rabb)--(Rabba) node[etiquette] {\tiny 0}; +\draw[fleche] (Rabb)--(Rabbb) node[etiquette] {\tiny 1}; +\draw[fleche] (R)--(Rb) node[etiquette] {\tiny 1}; +\draw[fleche] (Rb)--(Rba) node[etiquette] {\tiny 0}; +\draw[fleche] (Rba)--(Rbaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Rba)--(Rbab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbab)--(Rbaba) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbaba)--(Rbabaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbabaa)--(Rbabaaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbabaa)--(Rbabaab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbaba)--(Rbabab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbab)--(Rbabb) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbabb)--(Rbabba) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbabb)--(Rbabbb) node[etiquette] {\tiny 1}; +\draw[fleche] (Rb)--(Rbb) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbb)--(Rbba) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbba)--(Rbbaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbaa)--(Rbbaaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbaaa)--(Rbbaaaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbaaaa)--(Rbbaaaaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbaaaa)--(Rbbaaaab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbbaaa)--(Rbbaaab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbbaaab)--(Rbbaaaba) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbaaaba)--(Rbbaaabaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbaaaba)--(Rbbaaabab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbbaaab)--(Rbbaaabb) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbbaa)--(Rbbaab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbba)--(Rbbab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbbab)--(Rbbaba) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbab)--(Rbbabb) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbbabb)--(Rbbabba) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbabba)--(Rbbabbaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbabbaa)--(Rbbabbaaa) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbabbaa)--(Rbbabbaab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbbabba)--(Rbbabbab) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbbabbab)--(Rbbabbaba) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbabbab)--(Rbbabbabb) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbbabb)--(Rbbabbb) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbbabbb)--(Rbbabbba) node[etiquette] {\tiny 0}; +\draw[fleche] (Rbbabbb)--(Rbbabbbb) node[etiquette] {\tiny 1}; +\draw[fleche] (Rbb)--(Rbbb) node[etiquette] {\tiny 1}; +\end{tikzpicture} +\end{center} +%:-+-+-+-+- Fin + + +\end{document} + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%% un nouvel exo et sa correction %%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%début-exo +\begin{exo} + \begin{enumerate} + \item %question 1 + + \item %question 2 + + \end{enumerate} +\end{exo} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%fin-exo + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%début-correction +\begin{correction} + \begin{shaded} + %%% \begin{minipage}{.9\linewidth} + \begin{center} + \textbf{solution.} + \end{center} + \begin{enumerate} + \item %solution question 1 + + \item %solution question 2 + + \end{enumerate} + %%%\end{minipage} + \end{shaded} + \medskip +\end{correction} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%fin-correction +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + +%%% LocalWords: +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: + diff --git a/Brevets/US5363098.pdf 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+Regular expressions (regexp for short) provide an effective tool to define languages. +The correspondance with finite automata mean that it is possible to efficiently compile a regular expression into an automaton that recognises the corresponding language. + +On Linux this is precisely what the command grep does. + +We will explain how an automaton can be generated from a regexp and see how to use the grep command to solve riddles. + +### Ingredients of classical regexp. + +``` +the letters of the alphabet + ++ means or +used as L1 + L2 where L1 and L2 are two languages +means a word of L1 or a word of L2. +denotes the union of the languages + +. means concatenation +used as L1.L2 +means a word of L1 followed by a word of L2 + +* means repetition 0 or more times +used as L* +means the empty word epsilon (0 repetition) or one or more words of L one after another +equivalent to epsilon + L + L.L + L.L.L + L.L.L.L + ... +``` + +### Construction : from regexp to automaton + +We allow for automaton that allow transitions labelled with epsilon. +Then we show how to do without them. + +Details on the board. + +Note that JFLAP proposes an activity for this construction. + +There is also an inverse transformation from automaton to regexp, also available on JFLAP. +This shows that languages defined by a regexp and languages recognized by a finite automaton form the same class of languages, commonly known as regular languages. + + +### grep + +We shall in fact use the extended regular expressions of grep. +Use the command egrep or grep -e. + +See the manual of grep for the syntax. + +### Some additionnal commands + +* tr to replace a character by another +* grep to search for some regular expression line by line +* wc to count words (or characters) +* sort to sort the lines of a file + +### Exercise + +Wordle. + +Demo. diff --git a/2-InformationTheory/3InformationTheory.md b/2-InformationTheory/3InformationTheory.md new file mode 100644 index 0000000..0527353 --- /dev/null +++ b/2-InformationTheory/3InformationTheory.md @@ -0,0 +1,61 @@ +Cours de Florent. + +# Information Theory + +## A quick introduction to compression + +When we store or transmit data, it makes sense to try to reduce the storage space or the transmission delay. We are looking for two algorithms : one that can code a chunk of data to some smaller sized chunk of data; and, a second one that can from the compressed data reconstruct (perfectly or not) the initial larger chunk of data. + +When we can reconstruct the data, we are performing lossless compression, otherwise we speak of irreversible or lossy compression. + +We shall provide an introduction with simple methods. + + +## Image compression +If the data repeats locally some symbols, for example long sequences of white symbols in some black and white image, we may gain a lot of space if we describe the sequence using a number for the length of the sequence together with the repeated symbol. + +This so called run length encoding was used for early file images before the gif format appeared. +The gif formal itself uses also another compression method known as LSW. + +In contrast with the above where there is no loss of information, let us cite the jpg format which aims at compressing data with loss of indormation, but when performed adequatly the human eye can not detect the loss of information. + +If you are interested in patent controversy, which seems to be an american sport, there are historical examples with both the gif and jpg format. + + +* (run length encoding)[https://en.wikipedia.org/wiki/Run-length_encoding] +* (gif)[https://en.wikipedia.org/wiki/GIF] +* (LSW)[https://en.wikipedia.org/wiki/Lempel%E2%80%93Ziv%E2%80%93Welch] +* (jpg)[https://en.wikipedia.org/wiki/JPEG] + +## a digression : vectorial graphics format. + +So far we mentionned only so called *raster graphics* formats, i.e. rectangles of pixels. +There is an alternative, in particular for artifical images : icons, diagrams, maps etc. + +In contrast in a *vectorial format*, rather than describing the image, the file will describe in a mini language a recipe explaining how to draw it. +This means in particular that on a screen : the image can be zoomed to an arbitrary precision. + +One format which includes as an essential component this idea is the SVG format, now a standard on the web. Basically an SVG file looks similar to an html file (it is an XML file). +Just like HTML, this XML text format allows also many manipulation by scripting techniques via the so called Document Object Model (DOM). For example, to highlight part of the image if something is selected. + +You may draw some svg pictures instead of coding using for example inkscape. + +* (svg)[https://en.wikipedia.org/wiki/SVG] +* (tutorial and examples on w3 schools)[https://www.w3schools.com/graphics/tryit.asp?filename=trysvg_myfirst] + +## A first concrete example of compression : image and run length encoding + +(activité informatique débranché irem clermont)[http://www.irem.univ-bpclermont.fr/Images-numeriques] + +## Variable length encoding : Hufman code. + +(Hufman)[https://en.wikipedia.org/wiki/Huffman_coding] + + +## Archive + +(tar)["https://en.wikipedia.org/wiki/Tar_(computing)"] + +## Backup + +(rsync)[https://en.wikipedia.org/wiki/Rsync] diff --git a/2-InformationTheory/3InformationTheory/HuffmanGruffaloNightmare.aux b/2-InformationTheory/3InformationTheory/HuffmanGruffaloNightmare.aux new file mode 100644 index 0000000..914e6bf --- /dev/null +++ b/2-InformationTheory/3InformationTheory/HuffmanGruffaloNightmare.aux @@ -0,0 +1,26 @@ +\relax +\providecommand\hyper@newdestlabel[2]{} +\catcode `:\active +\catcode `;\active +\catcode `!\active +\catcode `?\active +\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} +\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined +\global\let\oldcontentsline\contentsline +\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} +\global\let\oldnewlabel\newlabel +\gdef\newlabel#1#2{\newlabelxx{#1}#2} +\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} +\AtEndDocument{\ifx\hyper@anchor\@undefined +\let\contentsline\oldcontentsline +\let\newlabel\oldnewlabel +\fi} +\fi} +\global\let\hyper@last\relax +\gdef\HyperFirstAtBeginDocument#1{#1} +\providecommand\HyField@AuxAddToFields[1]{} +\providecommand\HyField@AuxAddToCoFields[2]{} +\babel@aux{french}{} +\@writefile{toc}{\contentsline {paragraph}{\IeC {\'e}tape 1 (au tableau)}{1}{Doc-Start}\protected@file@percent } +\@writefile{toc}{\contentsline {paragraph}{\IeC {\'e}tape 2 (au tableau)}{1}{Doc-Start}\protected@file@percent } +\@writefile{toc}{\contentsline {paragraph}{\IeC {\'e}tape 3 : compression}{1}{Doc-Start}\protected@file@percent } diff --git a/2-InformationTheory/3InformationTheory/HuffmanGruffaloNightmare.log b/2-InformationTheory/3InformationTheory/HuffmanGruffaloNightmare.log new file mode 100644 index 0000000..a9e977e --- /dev/null +++ b/2-InformationTheory/3InformationTheory/HuffmanGruffaloNightmare.log @@ -0,0 +1,1260 @@ +This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2018) (preloaded format=pdflatex 2019.2.6) 3 APR 2023 11:43 +entering extended mode + restricted \write18 enabled. + file:line:error style messages enabled. + %&-line parsing enabled. +**\input HuffmanGruffaloNightmare.tex +(./HuffmanGruffaloNightmare.tex +(/usr/local/texlive/2018/texmf-dist/tex/latex/base/article.cls +Document Class: article 2018/09/03 v1.4i Standard LaTeX document class +(/usr/local/texlive/2018/texmf-dist/tex/latex/base/size10.clo +File: size10.clo 2018/09/03 v1.4i Standard LaTeX file (size option) +) +\c@part=\count80 +\c@section=\count81 +\c@subsection=\count82 +\c@subsubsection=\count83 +\c@paragraph=\count84 +\c@subparagraph=\count85 +\c@figure=\count86 +\c@table=\count87 +\abovecaptionskip=\skip41 +\belowcaptionskip=\skip42 +\bibindent=\dimen102 +) +(/usr/local/texlive/2018/texmf-dist/tex/generic/babel/babel.sty +Package: babel 2018/11/13 3.27 The Babel package + +(/usr/local/texlive/2018/texmf-dist/tex/generic/babel/switch.def +File: switch.def 2018/11/13 3.27 Babel switching mechanism +) +(/usr/local/texlive/2018/texmf-dist/tex/generic/babel-french/francais.ldf +Language: francais 2019/01/30 v3.5d French support from the babel system + + +Package francais.ldf Warning: Option `francais' for Babel is *deprecated*, +(francais.ldf) it might be removed sooner or later. 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z5X91s3@yyZI)N9t0w=Dj>Z7|^ieDcB>;XIj-Tw!-5un-0C9V#zpOJi#(6*Dg01Bx34|w)u&P zPD817&0@6S)phfiqpRi~wO%Ysu+cBOd|`1WM7@OXNFp+F@c$vwHxEG@ Vtg%>}0(J+uQ(LwOeS+=d{{c?VaVP)) literal 0 HcmV?d00001 diff --git a/1-ComputationAndData/MVaP/test.mvap b/1-ComputationAndData/MVaP/test.mvap new file mode 100644 index 0000000..15b4316 --- /dev/null +++ b/1-ComputationAndData/MVaP/test.mvap @@ -0,0 +1,27 @@ +# On prend au départ 2 +# on ajoute 3 et on élève le tout au carré +# on recommence et on s'arrête dès que l'on dépasse 100 +PUSHI 2 +LABEL 1 +PUSHI 3 +ADD +WRITE +CALL 2 +WRITE +# a-t-on un sommet de pile < 100 ? +DUP +PUSHI 100 +SUP +JUMPF 1 +# le nombre affiché est plus grand que 100, on s'arrête +HALT +# procédure qui élève un nombre au carré +LABEL 2 +# récupère le premier paramètre (-3 = -1 - 2) +PUSHL -3 +DUP +MUL +# on a donc son carré en sommet de pile +STOREL -3 +# on remplace la valeur +RETURN diff --git a/images/4-hierarchy.jpg b/1-ComputationAndData/images/4-hierarchy.jpg similarity index 100% rename from images/4-hierarchy.jpg rename to 1-ComputationAndData/images/4-hierarchy.jpg diff --git a/images/HelloWorldAutomate.jpg b/1-ComputationAndData/images/HelloWorldAutomate.jpg similarity index 100% rename from images/HelloWorldAutomate.jpg rename to 1-ComputationAndData/images/HelloWorldAutomate.jpg diff --git a/images/MMU_principle_updated.png b/1-ComputationAndData/images/MMU_principle_updated.png similarity index 100% rename from images/MMU_principle_updated.png rename to 1-ComputationAndData/images/MMU_principle_updated.png diff --git a/images/Virtual_memory.svg b/1-ComputationAndData/images/Virtual_memory.svg similarity index 100% rename from images/Virtual_memory.svg rename to 1-ComputationAndData/images/Virtual_memory.svg diff --git a/1-ComputationAndData/toto/folderA/folderAA/titi.txt b/1-ComputationAndData/toto/folderA/folderAA/titi.txt new file mode 100644 index 0000000..e69de29 diff --git a/1-ComputationAndData/toto/folderA/folderAA/toto.txt b/1-ComputationAndData/toto/folderA/folderAA/toto.txt new file mode 100644 index 0000000..e69de29 diff --git a/1-ComputationAndData/toto/folderA/grapevine2.txt b/1-ComputationAndData/toto/folderA/grapevine2.txt new file mode 100644 index 0000000..579f277 --- /dev/null +++ b/1-ComputationAndData/toto/folderA/grapevine2.txt @@ -0,0 +1 @@ +La commande tr attend un flux textuel en entrée et transmet un flux textuel en sortie. On parle de filtre pour ce genre de commande. On ne peut pas a priori lui passer de fichier en paramètre. Il faut rediriger le contenu du fichier vers la commande. diff --git a/1-ComputationAndData/toto/folderA/grapevine2UP.txt b/1-ComputationAndData/toto/folderA/grapevine2UP.txt new file mode 100644 index 0000000..6419584 --- /dev/null +++ b/1-ComputationAndData/toto/folderA/grapevine2UP.txt @@ -0,0 +1 @@ +LA COMMANDE TR ATTEND UN FLUX TEXTUEL EN ENTRéE ET TRANSMET UN FLUX TEXTUEL EN SORTIE. ON PARLE DE FILTRE POUR CE GENRE DE COMMANDE. ON NE PEUT PAS A PRIORI LUI PASSER DE FICHIER EN PARAMèTRE. IL FAUT REDIRIGER LE CONTENU DU FICHIER VERS LA COMMANDE. diff --git a/1-ComputationAndData/toto/folderB/toto.txt b/1-ComputationAndData/toto/folderB/toto.txt new file mode 100644 index 0000000..e69de29 diff --git a/1-ComputationAndData/toto/folderC/grapevine.txt b/1-ComputationAndData/toto/folderC/grapevine.txt new file mode 120000 index 0000000..e046836 --- /dev/null +++ b/1-ComputationAndData/toto/folderC/grapevine.txt @@ -0,0 +1 @@ +../folderA/grapevine.txt \ No newline at end of file diff --git a/1-ComputationAndData/toto/folderC/hardlink b/1-ComputationAndData/toto/folderC/hardlink new file mode 100644 index 0000000..c592881 --- /dev/null +++ b/1-ComputationAndData/toto/folderC/hardlink @@ -0,0 +1 @@ +jkdslfjsldfjsldkfjlskdfjlswf \ No newline at end of file diff --git a/1-ComputationAndData/toto/folderC/tata.txt b/1-ComputationAndData/toto/folderC/tata.txt new file mode 100644 index 0000000..e69de29 diff --git a/2-InformationTheory/0InformationTheory.md b/2-InformationTheory/0InformationTheory.md new file mode 100644 index 0000000..9a08b97 --- /dev/null +++ b/2-InformationTheory/0InformationTheory.md @@ -0,0 +1,38 @@ +Cours de Florent. + +# Information Theory + +This is a general field of study that we could understand as covering a number of topics outlined below. + +## Database theory +In particular the relational model, where data is stored in tables (like an excel table) and that can be queried efficiently. In practice, the standard is SQL and compliant system include ORACLE, Postgresql, Mysql etc. This goes back to the seventies for the theory with mature software since the late eighties. Most websites propose content that is constructed from data stored in such a database. + +In the last 20 years, new models have arisen, in particular graph model that are better suited for data that is not necessrily regular and sometimes partial and where data is queried in a local fashion. The keyword NOSQL is used with mature system like MongoDB in use in the industry. The data is queried and stored differently. This kind of database model is used for example by software of the caisse d'allocation familiale (CAF) to search and detect for large scale fraud. + +We shall try to give the intuition behind the relational model by studying and manipulating data stored in tables in csv format. + +## Coding theory +When we store or transmit data, no system is perfect and some bits of information are incorrectly stred/retrieved or transmitted. + +The purpose of this field is to come up with coding and decoding methods that allows to detect and correct errors with a high probablilty. + +We shall provide an introduction with simple codes. + +## Compression theory +When we store or transmit data, it makes sense to try to reduce the storage space or the transmission delay. We are looking for two algorithms : one that can code a chunk of data to some smaller sized chunk of data; and, a second one that can from the compressed data reconstruct (perfectly or not) the initial larger chunk of data. + +When we can reconstruct the data, we are performing lossless compression, otherwise we speak of irreversible or lossy compression. + +For example, jpg is an image format that allows to compress information with some loss of information, but when performed adequatly the human eye can not detect the loss of information. + +We shall provide an introduction with simple methods. + +## Regular expressions. + +Regular expressions (regexp for short) provide an effective tool to define languages. +The correspondance with finite automata mean that it is possible to efficiently compile a regular expression into an automaton that recognises the corresponding language. + +On Linux this is precisely what the command grep does. + +We will explain how an automaton can be generated from a regexp and see how to use the grep command to solve riddles. + diff --git a/2-InformationTheory/1InformationTheory.md b/2-InformationTheory/1InformationTheory.md new file mode 100644 index 0000000..6fba6b5 --- /dev/null +++ b/2-InformationTheory/1InformationTheory.md @@ -0,0 +1,71 @@ +Cours de Florent. + +# Information Theory + +## Coding theory +When we store or transmit data, no system is perfect and some bits of information are incorrectly stred/retrieved or transmitted. + +The purpose of this field is to come up with coding and decoding methods that allows to detect and correct errors with a high probablilty. + +We shall provide an introduction with simple codes. + +## Topics covered on the board + +* Binary symmetric channel +* Coding and decoding one bit to obtain arbitrary error +* example for a probability of error of 1/6 + repeating 3 times, repeating 5 times. + +This is essentially a practical version of Shannon's noisy-channel coding theorem. + +[Details here](https://en.wikipedia.org/wiki/Binary_symmetric_channel) + +So in a nutshell, we can tranform a binary symmetric channel with this repetition trick into a binary symmetric chanel with an arbitrary low error rate. + +It is not very practical because, it is achieved at a very high cost in terms of transmited of information compared with the actual information we wish to send.We shall therefore look for cheaper alternatives. + +## Detection + +If we are ready to forget about correction and concentrate on detection there is a very simple trick. + +We transmit some bits of information $b_1\ldots b_n$ with *one additionnal bit* +$c$ that is computed via a very simple method from these bits, that is a certain function $f$ of $n$ arguments such that $f(b_1\ldots b_n)=c$. + +At reception of some word $b'_1\ldots b'_nc'$ we check whether $f(b'_1\ldots b'_n)=c'$. If it does we assume that there is no error (we might be wrong here), it it does not we assume that there is an error and ask for retransmission of this message (we are correct here). + +This is used for low level transmission of information, in particular for ascii characters (since we tend to use powers of 2 when transmitting and storing information and we have one available bit when storing the 7 bits of the ascii encoding). + +[Details here](https://en.wikipedia.org/wiki/Parity_bit) + +## Correction + +We shall consider a last example which allows to detect and correct 1 error, and the algorithm to do this is quite simple. + +Assume that we have 9 bits of information. We write this bits in the form of a 3 times 3 matrix. We add 7 redundant bits, one at the end of each line, one at the bottom of each column, and one in the bottom right corner. Each redundant bit is the sum modulo 2 of the corresponding column / line. + +With this scheme we can detect 2 errors, but not correct them as there might be up to three codewords that are the nearest to a received message with 2 errors. + +We can always correct 1 error by recomputing the redundant data and compare it to the received data. +In particular, if the error is within the information part, the line / column of the bit to correct lies at the intersection of the line and colmun where the two redundant bits differ. + +We call this informally the matrix code below. + +## Hamming distance, Minimal distance of a code. + +Drawing on the board. + +Example for the repeating 3 times code. + +## Comparing codes. + +Examples with : +* Repetition code (1 bit of information, 2 redundant bits). Detects 2 errors, corrects 1. +* parity code (7 bits of information, 1 parity bit). Detects 1 error, corrects none. +* matrix code (9 bits of information, 7 redundant bits). Detects 2 errors, corrects 1. + +## Conclusion. + +Very quick discussion of linear code. + +Importance of encoding, detecting and correcting schemes that are efficient. + diff --git a/2-InformationTheory/1InformationTheory.ods b/2-InformationTheory/1InformationTheory.ods new file mode 100644 index 0000000000000000000000000000000000000000..190f79825b0f93785d0fc21f7e9a0bc47148f0b4 GIT binary patch literal 25582 zcmb4p1#BhFu4Xb}W@cuXFix29gqfL{nVFfHnVFfBnQ$^;=48TfcK-YJt+cDFyLv5E z%c^d>>~gtXUH%khz`)T#K%hZDE**bpgxYXNF@k`A{L}t+f!JEwn!0#8m>N1b*jO4H zx>(xVF}c~9FxneBTRJn^JDA#;*c-drn%cQAIy*R-8k#s;n3}pM{$Dcxiupem_FqcG z-pJ=f z@&654jp<)Q?f;XW|8B&8=ET9!&eZ0AIHH4-y}6UAv-AJlMrRj87uWv}AJM+=GQz`{M?^KZA?-3~uS-=GT5lz?U8A?e;cY>jdxkq*{1g z8+*C_9KG8iOEJh{xmGyu=Jf=gd@;@garWz5+(c~z=ZekW5>8s~iBu)(6=k5HTb?bJ zAV5Jtg26yQ{woIl-Sqt{8ckgc89i)mVwL6MvzgI*p4Exn>kW+YpfMYiR8{$HmZjxN zf0G({S89*P#b_@1>-Xhs+d5Yqg4t(yJ{;pzy-!O?C@eirW#N{cxgZEKO^!2)9fc8tAn! z_1n&(XP8E1v4x{=f{@_F~t+efND$+*i8}9Q9x1^r3KHnvk;9eJF^N_tV=S 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