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2024

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slides/structs.md 0 → 100644
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---
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.
```
![La représentation mémoire de `fraction_t`.](figs/pointer_struct.svg){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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