From 82547a200902247a65a4fdb9a30602a052d2137d Mon Sep 17 00:00:00 2001
From: Orestis <orestis.malaspinas@pm.me>
Date: Tue, 15 Oct 2024 13:05:29 +0200
Subject: [PATCH] 2024
---
slides/figs/pointer_struct.svg | 454 +++++++++++++++++++++++++++++++++
slides/structs.md | 191 ++++++++++++++
2 files changed, 645 insertions(+)
create mode 100644 slides/figs/pointer_struct.svg
create mode 100644 slides/structs.md
diff --git a/slides/figs/pointer_struct.svg b/slides/figs/pointer_struct.svg
new file mode 100644
index 0000000..d7b41ce
--- /dev/null
+++ b/slides/figs/pointer_struct.svg
@@ -0,0 +1,454 @@
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diff --git a/slides/structs.md b/slides/structs.md
new file mode 100644
index 0000000..114765d
--- /dev/null
+++ b/slides/structs.md
@@ -0,0 +1,191 @@
+---
+title: "Structures"
+date: "2024-10-15"
+---
+
+# Les fractions
+
+* Représentation d'un nombre sous la forme de la division de deux entiers
+\begin{equation*}
+q=\frac{n}{d},
+\end{equation*}
+avec $q\in\mathds{Q}$, $n\in\mathds{Z}$ le numérateur et $d\in\mathds{Z}^+$ le dénominateur (**attention** $d\neq 0$).
+* Ces nombres peuvent s'additionner
+\begin{align*}
+&q_1=\frac{n_1}{d_1},\quad q_2=\frac{n_2}{d_2},\\
+&q_3=q_1+q_2=\frac{n_1d_2+n_2d_1}{d_1d_2}.
+\end{align*}
+se soustraire, multiplier, diviser.
+
+# Représentation informatique
+
+## Fractions
+
+* Numérateur: `int32_t num`;
+* Dénominateur: `int32_t denom`.
+
+## Addition
+
+```C
+int32_t num1 = 1, denom1 = 2;
+int32_t num2 = 1, denom2 = 3;
+int32_t num3 = num1 * denom2 + num2 * denom1;
+int32_t denom3 = denom1 * denom2;
+```
+
+## Pas super pratique....
+
+# Types composés: `struct`{.C} (1/5)
+
+## On peut faire mieux
+
+* Plusieurs variables qu'on aimerait regrouper dans un seul type: `struct`{.C}.
+
+```C
+struct fraction { // déclaration du type
+ int32_t num, denom;
+};
+
+struct fraction frac; // déclaration de frac
+// c'est un type tout comme int, float, bool, etc.
+```
+
+# Types composés: `struct`{.C} (2/5)
+
+\footnotesize
+
+## Simplifications
+
+- `typedef`{.C} permet de définir un nouveau type.
+
+ ```C
+ typedef unsigned int uint;
+ typedef struct fraction fraction_t;
+ typedef struct fraction {
+ int32_t num, denom;
+ } fraction_t;
+ ```
+- L'initialisation peut aussi se faire avec
+
+ ```C
+ fraction_t frac = {1, -2}; // num = 1, denom = -2
+ fraction_t frac = {.denom = 1, .num = -2}; // idem
+ fraction_t frac = {.denom = 1}; // argl! .num non initialisé
+ fraction_t frac2 = frac; // copie
+ ```
+
+# Types composés: `struct`{.C} (3/5)
+
+\footnotesize
+
+## Pointeurs
+
+- Comme pour tout type, on peut avoir des pointeurs vers un `struct`{.C}.
+- Les champs sont accessible avec le sélecteur `->`{.C}
+
+ ```C
+ fraction_t *frac; // on crée un pointeur
+ frac->num = 1; // seg fault...
+ frac->denom = -1; // mémoire pas allouée.
+ ```
+
+{width=50%}
+
+# Types composés: `struct`{.C} (4/5)
+
+\footnotesize
+
+## Initialisation
+
+- Avec le passage par **référence** on peut modifier un struct *en place*.
+- Les champs sont accessible avec le sélecteur `->`{.C}
+
+ ```C
+ void fraction_init(fraction_t *f,
+ int32_t num, int32_t denom)
+ {
+ // f a déjà été allouée
+ f->num = num;
+ f->denom = denom;
+ }
+ int main() {
+ fraction_t frac; // on alloue une fraction
+ fraction_init(&frac, 2, -1); // on l'initialise
+ }
+ ```
+
+# Types composés: `struct`{.C} (5/5)
+
+\footnotesize
+
+## Initialisation version copie
+
+* On peut allouer une fraction, l'initialiser et le retourner.
+* La valeur retournée peut être copiée dans une nouvelle structure.
+
+ ```C
+ fraction_t fraction_create(int32_t num, int32_t denom) {
+ fraction_t f;
+ f.num = num; f.denom = denom;
+ return f;
+ }
+ int main() {
+ // on crée une fraction et on l'initialise
+ // en copiant la fraction créé par fraction_create
+ // deux allocation et une copie
+ fraction_t frac = fraction_create(2, -1);
+ }
+ ```
+
+# Modification en place vs retour
+
+\footnotesize
+
+## Quelle est la différence entre `fraction_init` et `fraction_create`?
+
+```C
+void fraction_init(fraction_t *f, int32_t num, int32_t denom);
+fraction_t fraction_create(int32_t num, int32_t denom);
+```
+
+. . .
+
+* `fraction_init`{.C} modifie une fraction **déjà ** allouée quelque part.
+* `fraction_create`{.C} alloue une nouvelle fraction et la retourne.
+
+. . .
+
+## Quelle impact sur les performances?
+
+. . .
+
+* `init`: une allocation et modification des données.
+* `create`: deux allocation, une modification et une copie.
+* Important pour des structures contenance *beaucoup* de données.
+
+# Précision
+
+## Différence avec les nombres à virgule?
+
+. . .
+
+* Les fractions ont une représentation **exacte**,
+
+. . .
+
+* Valeur min/max sont `INT32_MIN` / `INT32_MAX`,
+
+. . .
+
+* Limites sur les valeurs des `num`, `denom` possibles sont les `int32_t` qui peuvent être vite atteintes même pour des "petits" nombres.
+\begin{align*}
+&\underbrace{\frac{1002583}{1002584}}_{\sim 0.9999990025773402}+\underbrace{\frac{1005359}{1005358}}_{\sim 1.0000009946705553}\\
+&=\frac{1002583\cdot 1005358+1002584\cdot 1005359}{1002584\cdot 1005358}\\
+&=\underbrace{\frac{2015911687370}{1007955845072}}_{\sim 1.9999999972478952}
+\end{align*}
+* En réalité on a un dépassement de capacité:
+\begin{align*}
+\frac{1572025546}{-1361469488}\sim -1.1546535268368792.
+\end{align*}
+
+
--
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