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<div class="slides">
<section id="title-slide">
<h1 class="title">Laboratorio di TNDS – Lezione 6</h1>
<p class="author">Maurizio Tomasi</p>
<p class="date">Martedì 29 Ottobre 2024</p>
</section>
<section id="link-alle-risorse-online" class="slide level1">
<h1>Link alle risorse online</h1>
<ul>
<li><p>La spiegazione dettagliata degli esercizi si trova qui: <a
href="carminati-esercizi-06.html">carminati-esercizi-06.html</a>.</p></li>
<li><p>Come al solito, queste slides, che forniscono suggerimenti
addizionali rispetto alla lezione di teoria, sono disponibili
all’indirizzo <a
href="https://ziotom78.github.io/tnds-tomasi-notebooks/">ziotom78.github.io/tnds-tomasi-notebooks</a>.</p></li>
</ul>
</section>
<section id="esercizi-per-oggi" class="slide level1">
<h1>Esercizi per oggi</h1>
<ul>
<li><a href="./carminati-esercizi-06.html#esercizio-6.0">Esercizio
6.0</a>: Metodi virtuali</li>
<li><a href="./carminati-esercizi-06.html#esercizio-6.1">Esercizio
6.1</a>: Classe astratta <code>FunzioneBase</code></li>
<li><a href="./carminati-esercizi-06.html#esercizio-6.2">Esercizio
6.2</a>: Metodo della bisezione (<strong>da consegnare</strong>)</li>
<li><a href="./carminati-esercizi-06.html#esercizio-6.3">Esercizio
6.3</a>: Equazioni non risolubili analiticamente (<strong>da
consegnare</strong>)</li>
<li><a href="./carminati-esercizi-06.html#esercizio-6.4">Esercizio
6.4</a>: Ricerca di zeri di una funzione senza uso del polimorfismo
(facoltativo, ma <strong>MOLTO IMPORTANTE</strong>!)</li>
</ul>
</section>
<section id="virtual-methods" class="slide level1">
<h1>Metodi virtuali</h1>
</section>
<section id="metodi-virtuali" class="slide level1">
<h1>Metodi virtuali</h1>
<ul>
<li><p>L’unico modo in cui il C++ implementa il polimorfismo durante
l’esecuzione è attraverso i metodi <code>virtual</code>.</p></li>
<li><p>(I <em>template</em> permettono polimorfismo in fase di
<strong>compilazione</strong>, e sono quindi usati in ambiti
diversi).</p></li>
<li><p>Una classe derivata può ridefinire uno dei metodi della classe
genitore se questo è indicato come <code>virtual</code>, usando la
parola chiave <a
href="https://www.fluentcpp.com/2020/02/21/virtual-final-and-override-in-cpp/"><code>override</code></a>.</p></li>
</ul>
</section>
<section id="uso-di-metodi-virtuali" class="slide level1">
<h1>Uso di metodi virtuali</h1>
<div class="sourceCode" id="cb1"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="pp">#include </span><span class="im"><iostream></span></span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> Animal <span class="op">{</span></span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a> <span class="co">// Dichiaro `greet` come un metodo che può essere sovrascritto</span></span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a> <span class="kw">virtual</span> <span class="dt">void</span> greet<span class="op">()</span> <span class="at">const</span> <span class="op">{</span> <span class="bu">std::</span>cout <span class="op"><<</span> <span class="st">"?</span><span class="sc">\n</span><span class="st">"</span><span class="op">;</span> <span class="op">}</span></span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a><span class="op">};</span></span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> Dog <span class="op">:</span> <span class="kw">public</span> Animal <span class="op">{</span></span>
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a> <span class="co">// Chiedo al C++ di sovrascrivere `greet` tramite `override`</span></span>
<span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a> <span class="dt">void</span> greet<span class="op">()</span> <span class="at">const</span> <span class="kw">override</span> <span class="op">{</span> <span class="bu">std::</span>cout <span class="op"><<</span> <span class="st">"Woof!</span><span class="sc">\n</span><span class="st">"</span><span class="op">;</span> <span class="op">}</span></span>
<span id="cb1-11"><a href="#cb1-11" aria-hidden="true" tabindex="-1"></a><span class="op">};</span></span>
<span id="cb1-12"><a href="#cb1-12" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-13"><a href="#cb1-13" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> Cat <span class="op">:</span> <span class="kw">public</span> Animal <span class="op">{</span></span>
<span id="cb1-14"><a href="#cb1-14" aria-hidden="true" tabindex="-1"></a> <span class="co">// Chiedo al C++ di sovrascrivere `greet` tramite `override`</span></span>
<span id="cb1-15"><a href="#cb1-15" aria-hidden="true" tabindex="-1"></a> <span class="dt">void</span> greet<span class="op">()</span> <span class="at">const</span> <span class="kw">override</span> <span class="op">{</span> <span class="bu">std::</span>cout <span class="op"><<</span> <span class="st">"Meow!</span><span class="sc">\n</span><span class="st">"</span><span class="op">;</span> <span class="op">}</span></span>
<span id="cb1-16"><a href="#cb1-16" aria-hidden="true" tabindex="-1"></a><span class="op">};</span></span></code></pre></div>
</section>
<section id="funzionamento-di-virtual" class="slide level1">
<h1>Funzionamento di virtual</h1>
<div class="sourceCode" id="cb2"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="pp">#include </span><span class="im"><string></span></span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a><span class="dt">int</span> main<span class="op">(</span><span class="dt">int</span> argc<span class="op">,</span> <span class="dt">char</span> <span class="op">*</span>argv<span class="op">[])</span> <span class="op">{</span></span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a> Animal <span class="op">*</span>animal<span class="op">{};</span> <span class="co">// Qui abbiamo proprio bisogno di *</span></span>
<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a> <span class="co">// Legge il nome dell'animale dalla linea di comando</span></span>
<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a> <span class="bu">std::</span>string name<span class="op">{</span>argc <span class="op">></span> <span class="dv">1</span> <span class="op">?</span> argv<span class="op">[</span><span class="dv">1</span><span class="op">]</span> <span class="op">:</span> <span class="st">""</span><span class="op">};</span></span>
<span id="cb2-8"><a href="#cb2-8" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span> <span class="op">(</span>name <span class="op">==</span> <span class="st">"cat"</span><span class="op">)</span> <span class="op">{</span></span>
<span id="cb2-9"><a href="#cb2-9" aria-hidden="true" tabindex="-1"></a> animal <span class="op">=</span> <span class="kw">new</span> Cat<span class="op">();</span></span>
<span id="cb2-10"><a href="#cb2-10" aria-hidden="true" tabindex="-1"></a> <span class="op">}</span> <span class="cf">else</span> <span class="cf">if</span> <span class="op">(</span>name <span class="op">==</span> <span class="st">"dog"</span><span class="op">)</span> <span class="op">{</span></span>
<span id="cb2-11"><a href="#cb2-11" aria-hidden="true" tabindex="-1"></a> animal <span class="op">=</span> <span class="kw">new</span> Dog<span class="op">();</span></span>
<span id="cb2-12"><a href="#cb2-12" aria-hidden="true" tabindex="-1"></a> <span class="op">}</span></span>
<span id="cb2-13"><a href="#cb2-13" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-14"><a href="#cb2-14" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span> <span class="op">(</span>animal<span class="op">)</span></span>
<span id="cb2-15"><a href="#cb2-15" aria-hidden="true" tabindex="-1"></a> animal<span class="op">-></span>greet<span class="op">();</span></span>
<span id="cb2-16"><a href="#cb2-16" aria-hidden="true" tabindex="-1"></a><span class="op">}</span></span></code></pre></div>
</section>
<section id="funzionamento-di-virtual-1" class="slide level1">
<h1>Funzionamento di virtual</h1>
<ul>
<li><p>Nel <code>main</code>, la chiamata ad
<code>animal->greet()</code> non permette di capire quale metodo
<code>greet</code> verrà usato guardando solo il codice: la scelta viene
fatta a runtime, a seconda del valore di <code>argv</code>:</p>
<pre class="text"><code>$ ./test cat
Meow!
$ ./test dog
Woof!
$ ./test bird
$</code></pre></li>
<li><p>Questo meccanismo si chiama <em>dynamic dispatch</em>
(indirizzamento dinamico). Nel caso del C++ è un <em>dynamic</em>
<strong>single</strong> <em>dispatch</em>, perché la chiamata viene
decisa solo in funzione del tipo dell’oggetto puntato da
<code>animal</code>. (Altri linguaggi come Julia usano tutti i tipi dei
parametri della funzione, e sono quindi più versatili).</p></li>
</ul>
</section>
<section id="override-best-practices" class="slide level1">
<h1><code>virtual</code> e <code>override</code></h1>
<p>La parola <code>virtual</code> è obbligatoria solo all’interno della
classe base:</p>
<div class="sourceCode" id="cb4"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> Animal <span class="op">{</span></span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a> <span class="kw">virtual</span> <span class="dt">void</span> greet<span class="op">()</span> <span class="at">const</span> <span class="op">{</span> <span class="bu">std::</span>cout <span class="op"><<</span> <span class="st">"?</span><span class="sc">\n</span><span class="st">"</span><span class="op">;</span> <span class="op">}</span></span>
<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a><span class="op">};</span></span>
<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> Dog <span class="op">:</span> <span class="kw">public</span> Animal <span class="op">{</span></span>
<span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a> <span class="co">// I can repeat "virtual" here, but it's optional</span></span>
<span id="cb4-7"><a href="#cb4-7" aria-hidden="true" tabindex="-1"></a> <span class="kw">virtual</span> <span class="dt">void</span> greet<span class="op">()</span> <span class="at">const</span> <span class="kw">override</span> <span class="op">{</span> <span class="bu">std::</span>cout <span class="op"><<</span> <span class="st">"Woof!</span><span class="sc">\n</span><span class="st">"</span><span class="op">;</span> <span class="op">}</span></span>
<span id="cb4-8"><a href="#cb4-8" aria-hidden="true" tabindex="-1"></a><span class="op">};</span></span>
<span id="cb4-9"><a href="#cb4-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb4-10"><a href="#cb4-10" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> Cat <span class="op">:</span> <span class="kw">public</span> Animal <span class="op">{</span></span>
<span id="cb4-11"><a href="#cb4-11" aria-hidden="true" tabindex="-1"></a> <span class="co">// You usually avoid repeating "virtual", if there is "override"</span></span>
<span id="cb4-12"><a href="#cb4-12" aria-hidden="true" tabindex="-1"></a> <span class="dt">void</span> greet<span class="op">()</span> <span class="at">const</span> <span class="kw">override</span> <span class="op">{</span> <span class="bu">std::</span>cout <span class="op"><<</span> <span class="st">"Meow!</span><span class="sc">\n</span><span class="st">"</span><span class="op">;</span> <span class="op">}</span></span>
<span id="cb4-13"><a href="#cb4-13" aria-hidden="true" tabindex="-1"></a><span class="op">};</span></span></code></pre></div>
</section>
<section id="virtual-e-override" class="slide level1">
<h1><code>virtual</code> e <code>override</code></h1>
<ul>
<li><p>Per compatibilità con le vecchie versioni del C++, anche
<code>override</code> può essere tralasciato:</p>
<div class="sourceCode" id="cb5"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> Dog <span class="op">:</span> <span class="kw">public</span> Animal <span class="op">{</span></span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a> <span class="co">// Ok, compila e funziona come atteso, ma NON FATELO!</span></span>
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a> <span class="kw">virtual</span> <span class="dt">void</span> greet<span class="op">()</span> <span class="at">const</span> <span class="op">{</span> <span class="bu">std::</span>cout <span class="op"><<</span> <span class="st">"Woof!</span><span class="sc">\n</span><span class="st">"</span><span class="op">;</span> <span class="op">}</span></span>
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a><span class="op">};</span></span>
<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb5-6"><a href="#cb5-6" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> Cat <span class="op">:</span> <span class="kw">public</span> Animal <span class="op">{</span></span>
<span id="cb5-7"><a href="#cb5-7" aria-hidden="true" tabindex="-1"></a> <span class="co">// Anche questo è ok e compila senza errori, ma NON FATELO!</span></span>
<span id="cb5-8"><a href="#cb5-8" aria-hidden="true" tabindex="-1"></a> <span class="dt">void</span> greet<span class="op">()</span> <span class="at">const</span> <span class="op">{</span> <span class="bu">std::</span>cout <span class="op"><<</span> <span class="st">"Meow!</span><span class="sc">\n</span><span class="st">"</span><span class="op">;</span> <span class="op">}</span></span>
<span id="cb5-9"><a href="#cb5-9" aria-hidden="true" tabindex="-1"></a><span class="op">};</span></span></code></pre></div></li>
<li><p>Questo è comune in codici C++ particolarmente vecchi, ma
oggigiorno è considerata una <strong>pessima</strong> pratica.</p></li>
</ul>
</section>
<section id="uso-di-puntatori" class="slide level1">
<h1>Uso di puntatori</h1>
</section>
<section id="quando-usare-puntatori" class="slide level1">
<h1>Quando usare puntatori</h1>
<ul>
<li><p>Nell’<a
href="./carminati-esercizi-06.html#esercizio-6.0">Esercizio 6.1</a> di
oggi si usano i puntatori nel seguente codice:</p>
<div class="sourceCode" id="cb6"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>Particella <span class="op">*</span> p<span class="op">{</span><span class="kw">new</span> Particella<span class="op">{</span><span class="fl">1.</span><span class="op">,</span> <span class="fl">2.</span><span class="op">}};</span></span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a>Elettrone <span class="op">*</span> b<span class="op">{</span><span class="kw">new</span> Elettrone<span class="op">{}};</span></span>
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a>Particella <span class="op">*</span> c<span class="op">{</span><span class="kw">new</span> Elettrone<span class="op">{}};</span></span></code></pre></div></li>
<li><p>Si usano puntatori (o reference) quando avviene questo:</p>
<ol type="1">
<li>Si crea una variabile di un tipo base
(<code>Particella</code>)…</li>
<li>…ma poi le si vuole assegnare una variabile di un tipo derivato
(<code>Elettrone</code>), che <strong>non è noto in fase di
compilazione</strong>.</li>
</ol></li>
</ul>
</section>
<section id="quando-usare-puntatori-1" class="slide level1">
<h1>Quando usare puntatori</h1>
<ul>
<li><p>Usando un puntatore e <code>new</code>, si possono specificare i
due tipi <code>Particella</code> ed <code>Elettrone</code>
separatamente:</p>
<div class="sourceCode" id="cb7"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="co">// Type 1 Type 2</span></span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a> Particella <span class="op">*</span> c<span class="op">{</span><span class="kw">new</span> Elettrone<span class="op">{}};</span></span></code></pre></div></li>
<li><p>Senza puntatore, non ci sarebbe questa possibilità:</p>
<div class="sourceCode" id="cb8"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a>Particella c<span class="op">{};</span> <span class="co">// How can I specify that I want "Elettrone"?</span></span></code></pre></div></li>
</ul>
</section>
<section id="quando-usare-i-puntatori" class="slide level1">
<h1>Quando usare i puntatori</h1>
<p>Se non ci si trova nella situazione descritta, è meglio evitare di
usare i puntatori: il codice è più semplice da leggere, e non c’è
possibilità di avere <code>segmentation fault</code> causati
dall’accesso a puntatori nulli.</p>
<div class="sourceCode" id="cb9"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a><span class="co">// Far easier and safer!</span></span>
<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a>Particella a<span class="op">{</span><span class="fl">1.</span><span class="op">,</span> <span class="fl">2.</span><span class="op">};</span></span>
<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a>Elettrone b<span class="op">{};</span></span>
<span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a>Elettrone c<span class="op">{};</span></span></code></pre></div>
</section>
<section id="esercizio-6.2-bisezione" class="slide level1">
<h1>Esercizio 6.2 (bisezione)</h1>
</section>
<section id="verifica-dellalgoritmo" class="slide level1">
<h1>Verifica dell’algoritmo</h1>
<p>L’esercizio richiede di trovare gli zeri della funzione <span
class="math display">
f(x) = 3x^2 + 5x - 2,
</span> che è un problema risolubile analiticamente: <span
class="math display">
x_{1/2} = \frac{-5 \pm \sqrt{25 + 24}}6 = \begin{cases} -2,\\ \frac13.
\end{cases}
</span></p>
</section>
<section id="verifica-funzioni-ricerca-zeri" class="slide level1">
<h1>Verifica dell’algoritmo</h1>
<div class="sourceCode" id="cb10"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a><span class="co">// You might even pass a reference to `Solutore & s` and call in `main`</span></span>
<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a><span class="co">// test_zeroes(Bisezione{});</span></span>
<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a><span class="co">// test_zeroes(Secante{});</span></span>
<span id="cb10-4"><a href="#cb10-4" aria-hidden="true" tabindex="-1"></a><span class="co">// test_zeroes(Newton{});</span></span>
<span id="cb10-5"><a href="#cb10-5" aria-hidden="true" tabindex="-1"></a><span class="dt">void</span> test_zeroes<span class="op">()</span> <span class="op">{</span></span>
<span id="cb10-6"><a href="#cb10-6" aria-hidden="true" tabindex="-1"></a> Bisezione s<span class="op">{};</span></span>
<span id="cb10-7"><a href="#cb10-7" aria-hidden="true" tabindex="-1"></a> Parabola f<span class="op">{</span><span class="dv">3</span><span class="op">,</span> <span class="dv">5</span><span class="op">,</span> <span class="op">-</span><span class="dv">2</span><span class="op">};</span> <span class="co">// Zeroes for this function are known: x₁ = −2, x₂ = 1/3</span></span>
<span id="cb10-8"><a href="#cb10-8" aria-hidden="true" tabindex="-1"></a> s<span class="op">.</span>SetPrecisione<span class="op">(</span><span class="fl">1e-8</span><span class="op">);</span></span>
<span id="cb10-9"><a href="#cb10-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb10-10"><a href="#cb10-10" aria-hidden="true" tabindex="-1"></a> <span class="ot">assert</span><span class="op">(</span>are_close<span class="op">(</span>s<span class="op">.</span>CercaZeri<span class="op">(-</span><span class="fl">3.0</span><span class="op">,</span> <span class="op">-</span><span class="fl">1.0</span><span class="op">,</span> f<span class="op">),</span> <span class="op">-</span><span class="fl">2.0</span><span class="op">));</span> <span class="co">// Zero is within (a, b)</span></span>
<span id="cb10-11"><a href="#cb10-11" aria-hidden="true" tabindex="-1"></a> <span class="ot">assert</span><span class="op">(</span>are_close<span class="op">(</span>s<span class="op">.</span>CercaZeri<span class="op">(-</span><span class="fl">2.0</span><span class="op">,</span> <span class="fl">0.0</span><span class="op">,</span> f<span class="op">),</span> <span class="op">-</span><span class="fl">2.0</span><span class="op">));</span> <span class="co">// Zero is at a</span></span>
<span id="cb10-12"><a href="#cb10-12" aria-hidden="true" tabindex="-1"></a> <span class="ot">assert</span><span class="op">(</span>are_close<span class="op">(</span>s<span class="op">.</span>CercaZeri<span class="op">(-</span><span class="fl">4.0</span><span class="op">,</span> <span class="op">-</span><span class="fl">2.0</span><span class="op">,</span> f<span class="op">),</span> <span class="op">-</span><span class="fl">2.0</span><span class="op">));</span> <span class="co">// Zero is at b</span></span>
<span id="cb10-13"><a href="#cb10-13" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb10-14"><a href="#cb10-14" aria-hidden="true" tabindex="-1"></a> <span class="ot">assert</span><span class="op">(</span>are_close<span class="op">(</span>s<span class="op">.</span>CercaZeri<span class="op">(</span><span class="fl">0.0</span><span class="op">,</span> <span class="fl">1.0</span><span class="op">,</span> f<span class="op">),</span> <span class="fl">1.0</span> <span class="op">/</span> <span class="dv">3</span><span class="op">));</span> <span class="co">// Do NOT write 1 / 3 !</span></span>
<span id="cb10-15"><a href="#cb10-15" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb10-16"><a href="#cb10-16" aria-hidden="true" tabindex="-1"></a> cerr <span class="op"><<</span> <span class="st">"Root finding works correctly! 🥳</span><span class="sc">\n</span><span class="st">"</span><span class="op">;</span></span>
<span id="cb10-17"><a href="#cb10-17" aria-hidden="true" tabindex="-1"></a><span class="op">}</span></span></code></pre></div>
</section>
<section id="determinazione-del-segno" class="slide level1">
<h1>Determinazione del segno</h1>
</section>
<section id="determinazione-del-segno-1" class="slide level1">
<h1>Determinazione del segno</h1>
<ul>
<li><p>Nell’algoritmo di bisezione occorre verificare quando <span
class="math inline">f(a)</span> e <span class="math inline">f(b)</span>
sono di segno concorde.</p></li>
<li><p>La scrittura</p>
<div class="sourceCode" id="cb11"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a><span class="cf">if</span> <span class="op">(</span>f<span class="op">(</span>a<span class="op">)</span> <span class="op">*</span> f<span class="op">(</span>b<span class="op">)</span> <span class="op"><</span> <span class="dv">0</span><span class="op">)</span> <span class="op">{</span> … <span class="op">}</span></span></code></pre></div>
<p>non è consigliabile, perché se <code>f(a)</code> o <code>f(b)</code>
sono molto piccoli, il risultato potrebbe essere nullo. Meglio <a
href="carminati-esercizi-06.html#la-funzione-segno">usare una funzione
<code>sign</code></a></p>
<div class="sourceCode" id="cb12"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a><span class="cf">if</span> <span class="op">(</span>sign<span class="op">(</span>f<span class="op">(</span>a<span class="op">))</span> <span class="op">*</span> sign<span class="op">(</span>f<span class="op">(</span>b<span class="op">))</span> <span class="op"><</span> <span class="dv">0</span><span class="op">)</span> <span class="op">{</span> … <span class="op">}</span></span></code></pre></div></li>
</ul>
</section>
<section id="gestione-errori" class="slide level1">
<h1>Gestione di errori</h1>
</section>
<section id="condizioni-derrore" class="slide level1">
<h1>Condizioni d’errore</h1>
<ul>
<li><p>Il metodo di bisezione fallisce se le ipotesi del teorema degli
zeri non valgono. Cosa fare in questo caso?</p></li>
<li><p>Ricordiamo che esistono <a
href="tomasi-lezione-03.html#tipi-di-errore">due tipi di errori</a>:</p>
<ul>
<li><p><strong>Errori dell’utente</strong>: è l’utente che ha sbagliato
a usare il programma, e deve rimediare facendolo ripartire con gli input
giusti;</p></li>
<li><p><strong>Errori del programmatore</strong>: è il programmatore che
deve rimediare modificando il programma e ricompilandolo.</p></li>
</ul></li>
<li><p>Oggi implementiamo due esercizi in cui il metodo di bisezione può
fallire per colpa dell’utente (<a
href="carminati-esercizi-06.html#esercizio-6.2">esercizio 6.2</a>) o del
programmatore (<a
href="carminati-esercizi-06.html#esercizio-6.3">esercizio 6.3</a>). Come
facciamo?</p></li>
</ul>
</section>
<section id="condizioni-di-errore" class="slide level1">
<h1>Condizioni di errore</h1>
<pre><code>$ ./esercizio-6.2 4 6
Errore, il teorema degli zeri non è valido nell'intervallo [4, 6]. Usa un altro intervallo
$ ./esercizio-6.3
fish: Job 1, './esercizio-6.3' terminated by signal SIGABRT (Abort)</code></pre>
<p>(Se un programma termina invocando <code>abort()</code>, eseguendolo
all’interno di <a href="qt-creator.html">QtCreator</a> in modalità
debugging si può ispezionare il valore delle variabili al momento in cui
è andato in crash: molto utile per correggere il bug!)</p>
</section>
<section id="approcci-possibili" class="slide level1">
<h1>Approcci possibili</h1>
<ol type="1">
<li><p>Scrivere un messaggio di errore e invocare <code>abort()</code>:
bene se l’errore è del programmatore, male se l’errore è dell’utente!
😠</p></li>
<li><p>Restituire un valore fissato (es., zero): molto ambiguo, come fa
l’utente a sapere se la funzione si annulla veramente per <span
class="math inline">x = 0</span> o se c’è stato un errore? 😠</p></li>
<li><p>Accettare un parametro aggiuntivo <code>bool &found</code>
per <code>CercaZeri</code>:</p>
<div class="sourceCode" id="cb14"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a><span class="dt">double</span> CercaZeri<span class="op">(</span><span class="dt">double</span> xmin<span class="op">,</span> <span class="dt">double</span> xmax<span class="op">,</span> <span class="at">const</span> FunzioneBase <span class="op">*</span> f<span class="op">,</span> <span class="dt">bool</span> <span class="op">&</span>found<span class="op">);</span></span></code></pre></div>
<p>(In alternativa si può dichiarare <code>found</code> variabile membro
di <code>Solutore</code>).</p></li>
</ol>
</section>
<section id="segnalare-lerrore" class="slide level1">
<h1>Segnalare l’errore</h1>
<p>Con il terzo approccio è possibile differenziare la “reazione”
all’errore nel <code>main</code> dei due esercizi</p>
<div class="sourceCode" id="cb15"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a><span class="co">// main() dell'esercizio 6.2 (errore dell'utente):</span></span>
<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-3"><a href="#cb15-3" aria-hidden="true" tabindex="-1"></a><span class="dt">double</span> xmin<span class="op">{</span>stod<span class="op">(</span>argv<span class="op">[</span><span class="dv">1</span><span class="op">])},</span> xmax<span class="op">{</span>stod<span class="op">(</span>argv<span class="op">[</span><span class="dv">2</span><span class="op">])};</span></span>
<span id="cb15-4"><a href="#cb15-4" aria-hidden="true" tabindex="-1"></a><span class="dt">bool</span> found<span class="op">;</span></span>
<span id="cb15-5"><a href="#cb15-5" aria-hidden="true" tabindex="-1"></a><span class="dt">double</span> x<span class="op">{</span>bisezione<span class="op">.</span>CercaZeri<span class="op">(</span>xmin<span class="op">,</span> xmax<span class="op">,</span> f<span class="op">,</span> found<span class="op">)};</span></span>
<span id="cb15-6"><a href="#cb15-6" aria-hidden="true" tabindex="-1"></a><span class="cf">if</span> <span class="op">(!</span> found<span class="op">)</span> <span class="op">{</span></span>
<span id="cb15-7"><a href="#cb15-7" aria-hidden="true" tabindex="-1"></a> fmt<span class="op">::</span>println<span class="op">(</span><span class="st">"Errore, il teorema degli zeri non è valido nell'intervallo "</span></span>
<span id="cb15-8"><a href="#cb15-8" aria-hidden="true" tabindex="-1"></a> <span class="st">"[</span><span class="sc">{}</span><span class="st">, </span><span class="sc">{}</span><span class="st">]. Usa un altro intervallo"</span><span class="op">,</span> xmin<span class="op">,</span> xmax<span class="op">);</span></span>
<span id="cb15-9"><a href="#cb15-9" aria-hidden="true" tabindex="-1"></a> <span class="cf">return</span> <span class="dv">1</span><span class="op">;</span></span>
<span id="cb15-10"><a href="#cb15-10" aria-hidden="true" tabindex="-1"></a><span class="op">}</span></span>
<span id="cb15-11"><a href="#cb15-11" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-12"><a href="#cb15-12" aria-hidden="true" tabindex="-1"></a><span class="co">// main() dell'esercizio 6.3 (errore dell'utente):</span></span>
<span id="cb15-13"><a href="#cb15-13" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb15-14"><a href="#cb15-14" aria-hidden="true" tabindex="-1"></a><span class="dt">double</span> xmin<span class="op">{</span> … <span class="op">};</span> <span class="co">// Formula matematica implementata dal programmatore;</span></span>
<span id="cb15-15"><a href="#cb15-15" aria-hidden="true" tabindex="-1"></a><span class="dt">double</span> xmax<span class="op">{</span> … <span class="op">};</span> <span class="co">// Idem</span></span>
<span id="cb15-16"><a href="#cb15-16" aria-hidden="true" tabindex="-1"></a><span class="dt">bool</span> found<span class="op">;</span></span>
<span id="cb15-17"><a href="#cb15-17" aria-hidden="true" tabindex="-1"></a><span class="dt">double</span> x<span class="op">{</span>bisezione<span class="op">.</span>CercaZeri<span class="op">(</span>xmin<span class="op">,</span> xmax<span class="op">,</span> f<span class="op">,</span> found<span class="op">)};</span></span>
<span id="cb15-18"><a href="#cb15-18" aria-hidden="true" tabindex="-1"></a><span class="cf">if</span> <span class="op">(!</span> found<span class="op">)</span> <span class="op">{</span></span>
<span id="cb15-19"><a href="#cb15-19" aria-hidden="true" tabindex="-1"></a> abort<span class="op">();</span></span>
<span id="cb15-20"><a href="#cb15-20" aria-hidden="true" tabindex="-1"></a><span class="op">}</span></span></code></pre></div>
</section>
<section id="uso-di-stdexpected-15" class="slide level1">
<h1>Uso di <code>std::expected</code> (1/5)</h1>
<ul>
<li><p>Con il C++23 è stato introdotto il tipo <a
href="https://en.cppreference.com/w/cpp/utility/expected"><code>std::expected</code></a>,
che è stato mutuato da linguaggi come Rust e OCaml. (Nella compilazione
bisogna quindi usare <code>-std=c++23</code>, non
<code>-std=c++20</code>!)</p></li>
<li><p>Il template <code>std::expected<T, U></code> rappresenta il
concetto “di solito questa variabile è del tipo <code>T</code>, ma se
c’è un errore allora è del tipo <code>U</code>”:</p>
<div class="sourceCode" id="cb16"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a><span class="pp">#include </span><span class="im"><expected></span></span>
<span id="cb16-2"><a href="#cb16-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb16-3"><a href="#cb16-3" aria-hidden="true" tabindex="-1"></a><span class="co">// If everything is ok, `val` is a `double`; if there is an error,</span></span>
<span id="cb16-4"><a href="#cb16-4" aria-hidden="true" tabindex="-1"></a><span class="co">// `val` is a string (presumably, an error message).</span></span>
<span id="cb16-5"><a href="#cb16-5" aria-hidden="true" tabindex="-1"></a><span class="bu">std::</span>expected<span class="op"><</span><span class="dt">double</span><span class="op">,</span> string<span class="op">></span> val<span class="op">;</span></span></code></pre></div></li>
</ul>
</section>
<section id="uso-di-stdexpected-25" class="slide level1">
<h1>Uso di <code>std::expected</code> (2/5)</h1>
<ul>
<li><p>Una variabile <code>std::expected</code> può essere inizializzata
usando un valore del <strong>primo</strong> tipo (<code>T</code>) senza
bisogno di sintassi particolari:</p>
<div class="sourceCode" id="cb17"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a><span class="bu">std::</span>expected<span class="op"><</span><span class="dt">double</span><span class="op">,</span> string<span class="op">></span> val<span class="op">{</span><span class="fl">3.5</span><span class="op">};</span> <span class="co">// Initialized with a double</span></span></code></pre></div></li>
<li><p>Per inizializzarla al valore “erroneo”, bisogna usare la funzione
<code>std::unexpected</code>:</p>
<div class="sourceCode" id="cb18"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a><span class="bu">std::</span>expected<span class="op"><</span><span class="dt">double</span><span class="op">,</span> string<span class="op">></span> val<span class="op">{</span><span class="bu">std::</span>unexpected<span class="op">(</span><span class="st">"Errore!"</span><span class="op">)};</span></span></code></pre></div></li>
</ul>
</section>
<section id="uso-di-stdexpected-35" class="slide level1">
<h1>Uso di <code>std::expected</code> (3/5)</h1>
<ul>
<li><p>Nel <code>main()</code> è laborioso definire il tipo della
variabile che riceve il risultato:</p>
<div class="sourceCode" id="cb19"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a><span class="bu">std::</span>expected<span class="op"><</span><span class="dt">double</span><span class="op">,</span> string<span class="op">></span> result<span class="op">{</span>bisezione<span class="op">.</span>CercaZeri<span class="op">(</span>…<span class="op">)};</span></span></code></pre></div></li>
<li><p>Il C++ fornisce (a partire dal C++11) la keyword
<code>auto</code>, che dice al compilatore: “sai benissimo tu qual è il
tipo di ritorno, quindi non farmelo specificare!”. Quindi possiamo
scrivere:</p>
<div class="sourceCode" id="cb20"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb20-1"><a href="#cb20-1" aria-hidden="true" tabindex="-1"></a><span class="co">// Much easier!</span></span>
<span id="cb20-2"><a href="#cb20-2" aria-hidden="true" tabindex="-1"></a><span class="kw">auto</span> result<span class="op">{</span>bisezione<span class="op">.</span>CercaZeri<span class="op">(</span>…<span class="op">)};</span></span></code></pre></div></li>
</ul>
</section>
<section id="uso-di-stdexpected-45" class="slide level1">
<h1>Uso di <code>std::expected</code> (4/5)</h1>
<ul>
<li><p>Si controlla se la variabile è “giusta” o “sbagliata” col metodo
<code>has_value()</code>:</p>
<div class="sourceCode" id="cb21"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb21-1"><a href="#cb21-1" aria-hidden="true" tabindex="-1"></a><span class="kw">auto</span> result<span class="op">{</span>bisezione<span class="op">.</span>CercaZeri<span class="op">(</span>…<span class="op">)};</span></span>
<span id="cb21-2"><a href="#cb21-2" aria-hidden="true" tabindex="-1"></a><span class="cf">if</span> <span class="op">(</span>result<span class="op">.</span>has_value<span class="op">())</span> <span class="op">{</span></span>
<span id="cb21-3"><a href="#cb21-3" aria-hidden="true" tabindex="-1"></a> <span class="co">// Everything is ok!</span></span>
<span id="cb21-4"><a href="#cb21-4" aria-hidden="true" tabindex="-1"></a><span class="op">}</span> <span class="cf">else</span> <span class="op">{</span></span>
<span id="cb21-5"><a href="#cb21-5" aria-hidden="true" tabindex="-1"></a> <span class="co">// ERROR!</span></span>
<span id="cb21-6"><a href="#cb21-6" aria-hidden="true" tabindex="-1"></a><span class="op">}</span></span></code></pre></div></li>
<li><p>C’è anche la comoda scorciatoia di usare <code>result</code> come
una variabile booleana:</p>
<div class="sourceCode" id="cb22"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb22-1"><a href="#cb22-1" aria-hidden="true" tabindex="-1"></a><span class="cf">if</span> <span class="op">(</span>result<span class="op">)</span> <span class="op">{</span></span>
<span id="cb22-2"><a href="#cb22-2" aria-hidden="true" tabindex="-1"></a> <span class="co">// Everything is ok!</span></span>
<span id="cb22-3"><a href="#cb22-3" aria-hidden="true" tabindex="-1"></a><span class="op">}</span></span></code></pre></div></li>
</ul>
</section>
<section id="uso-di-stdexpected-55" class="slide level1">
<h1>Uso di <code>std::expected</code> (5/5)</h1>
<ul>
<li><p>Il metodo <code>value()</code> estrae il valore giusto, il metodo
<code>error()</code> il valore erroneo:</p>
<div class="sourceCode" id="cb23"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb23-1"><a href="#cb23-1" aria-hidden="true" tabindex="-1"></a><span class="cf">if</span> <span class="op">(</span>result<span class="op">)</span> <span class="op">{</span></span>
<span id="cb23-2"><a href="#cb23-2" aria-hidden="true" tabindex="-1"></a> <span class="dt">double</span> true_value<span class="op">{</span>result<span class="op">.</span>value<span class="op">()};</span></span>
<span id="cb23-3"><a href="#cb23-3" aria-hidden="true" tabindex="-1"></a> <span class="co">// …</span></span>
<span id="cb23-4"><a href="#cb23-4" aria-hidden="true" tabindex="-1"></a><span class="op">}</span> <span class="cf">else</span> <span class="op">{</span></span>
<span id="cb23-5"><a href="#cb23-5" aria-hidden="true" tabindex="-1"></a> fmt<span class="op">::</span>println<span class="op">(</span>stderr<span class="op">,</span> <span class="st">"Error: </span><span class="sc">{}</span><span class="st">"</span><span class="op">,</span> result<span class="op">.</span>error<span class="op">());</span></span>
<span id="cb23-6"><a href="#cb23-6" aria-hidden="true" tabindex="-1"></a><span class="op">}</span></span></code></pre></div></li>
<li><p>Invece di <code>value()</code> si può usare l’operatore di
deferenziazione <code>*result</code>:</p>
<div class="sourceCode" id="cb24"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb24-1"><a href="#cb24-1" aria-hidden="true" tabindex="-1"></a><span class="dt">double</span> true_value<span class="op">{*</span>result<span class="op">};</span></span></code></pre></div></li>
</ul>
</section>
<section id="stdexpected-nella-bisezione" class="slide level1">
<h1><code>std::expected</code> nella bisezione</h1>
<div class="sourceCode" id="cb25"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb25-1"><a href="#cb25-1" aria-hidden="true" tabindex="-1"></a><span class="bu">std::</span>expected<span class="op"><</span><span class="dt">double</span><span class="op">,</span> string<span class="op">></span> <span class="co">// Ideally we return a `double`, unless there are problems</span></span>
<span id="cb25-2"><a href="#cb25-2" aria-hidden="true" tabindex="-1"></a>Bisezione<span class="op">::</span>CercaZeri<span class="op">(</span><span class="dt">double</span> xmin<span class="op">,</span></span>
<span id="cb25-3"><a href="#cb25-3" aria-hidden="true" tabindex="-1"></a> <span class="dt">double</span> xmax<span class="op">,</span></span>
<span id="cb25-4"><a href="#cb25-4" aria-hidden="true" tabindex="-1"></a> <span class="at">const</span> FunzioneBase <span class="op">*</span> f<span class="op">)</span> <span class="op">{</span></span>
<span id="cb25-5"><a href="#cb25-5" aria-hidden="true" tabindex="-1"></a> <span class="dt">double</span> signfa<span class="op">{</span>sign<span class="op">(</span>f<span class="op">-></span>Eval<span class="op">(</span>xmin<span class="op">))},</span> signfb<span class="op">{</span>sign<span class="op">(</span>f<span class="op">-></span>Eval<span class="op">(</span>xmax<span class="op">))};</span></span>
<span id="cb25-6"><a href="#cb25-6" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span><span class="op">(</span>signfa <span class="op">==</span> <span class="dv">0</span><span class="op">)</span> <span class="cf">return</span> xmin<span class="op">;</span></span>
<span id="cb25-7"><a href="#cb25-7" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span><span class="op">(</span>signfb <span class="op">==</span> <span class="dv">0</span><span class="op">)</span> <span class="cf">return</span> xmax<span class="op">;</span></span>
<span id="cb25-8"><a href="#cb25-8" aria-hidden="true" tabindex="-1"></a> <span class="cf">if</span><span class="op">(</span>signfa <span class="op">*</span> signfb <span class="op">></span> <span class="dv">0</span><span class="op">)</span> <span class="op">{</span></span>
<span id="cb25-9"><a href="#cb25-9" aria-hidden="true" tabindex="-1"></a> <span class="cf">return</span> <span class="bu">std::</span>unexpected<span class="op">(</span>fmt<span class="op">::</span>format<span class="op">(</span><span class="st">"Invalid range [</span><span class="sc">{}</span><span class="st">, </span><span class="sc">{}</span><span class="st">]"</span><span class="op">,</span> xmin<span class="op">,</span> xmax<span class="op">));</span></span>
<span id="cb25-10"><a href="#cb25-10" aria-hidden="true" tabindex="-1"></a> <span class="op">}</span></span>
<span id="cb25-11"><a href="#cb25-11" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb25-12"><a href="#cb25-12" aria-hidden="true" tabindex="-1"></a> <span class="co">// ...</span></span>
<span id="cb25-13"><a href="#cb25-13" aria-hidden="true" tabindex="-1"></a> <span class="cf">return</span> x<span class="op">;</span> <span class="co">// `x` is a boring `double`</span></span>
<span id="cb25-14"><a href="#cb25-14" aria-hidden="true" tabindex="-1"></a><span class="op">}</span></span></code></pre></div>
</section>
<section id="stdexpected-nel-main" class="slide level1">
<h1><code>std::expected</code> nel <code>main</code></h1>
<ul>
<li><p>Nel <code>main</code> dell’<a
href="carminati-esercizi-06.html#esercizio-6.2">esercizio 6.2</a>
stampiamo l’errore in maniera <em>user-frendly</em>:</p>
<div class="sourceCode" id="cb26"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb26-1"><a href="#cb26-1" aria-hidden="true" tabindex="-1"></a><span class="kw">auto</span> result<span class="op">{</span>bisezione<span class="op">.</span>CercaZeri<span class="op">(</span>xmin<span class="op">,</span> xmax<span class="op">,</span> f<span class="op">)};</span></span>
<span id="cb26-2"><a href="#cb26-2" aria-hidden="true" tabindex="-1"></a><span class="cf">if</span><span class="op">(!</span> result<span class="op">)</span> <span class="op">{</span></span>
<span id="cb26-3"><a href="#cb26-3" aria-hidden="true" tabindex="-1"></a> fmt<span class="op">::</span>println<span class="op">(</span>stderr<span class="op">,</span> <span class="st">"Error: </span><span class="sc">{}</span><span class="st">"</span><span class="op">,</span> result<span class="op">.</span>error<span class="op">());</span></span>
<span id="cb26-4"><a href="#cb26-4" aria-hidden="true" tabindex="-1"></a> <span class="cf">return</span> <span class="dv">1</span><span class="op">;</span></span>
<span id="cb26-5"><a href="#cb26-5" aria-hidden="true" tabindex="-1"></a><span class="op">}</span></span>
<span id="cb26-6"><a href="#cb26-6" aria-hidden="true" tabindex="-1"></a><span class="dt">double</span> x<span class="op">{</span>result<span class="op">.</span>value<span class="op">()};</span></span></code></pre></div></li>
<li><p>Nell’<a href="carminati-esercizi-06.html#esercizio-6.3">esercizio
6.3</a> invece chiamiamo <code>abort()</code> (in
<code><cstdlib></code>):</p>
<div class="sourceCode" id="cb27"><pre
class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb27-1"><a href="#cb27-1" aria-hidden="true" tabindex="-1"></a><span class="kw">auto</span> result<span class="op">{</span>bisezione<span class="op">.</span>CercaZeri<span class="op">(</span>xmin<span class="op">,</span> xmax<span class="op">,</span> f<span class="op">)};</span></span>
<span id="cb27-2"><a href="#cb27-2" aria-hidden="true" tabindex="-1"></a><span class="cf">if</span><span class="op">(!</span> result<span class="op">)</span> <span class="op">{</span> abort<span class="op">();</span> <span class="op">}</span></span>
<span id="cb27-3"><a href="#cb27-3" aria-hidden="true" tabindex="-1"></a><span class="dt">double</span> x<span class="op">{</span>result<span class="op">.</span>value<span class="op">()};</span></span></code></pre></div></li>
</ul>
</section>
<section id="esercizio-6.4" class="slide level1">
<h1>Esercizio 6.4</h1>
<ul>
<li><p>Nell’<a href="carminati-esercizi-06.html#esercizio-6.4">esercizio
6.4</a> si illustra un modo alternativo di implementare la bisezione,
che <em>non</em> usa il polimorfismo.</p></li>
<li><p>Questo approccio è importante da imparare:</p>
<ol>
<li>È applicabile al 99% dei casi della vita reale;</li>
<li>Ha preso il sopravvento rispetto alla programmazione OOP usata in
ROOT, ed è usato in molte librerie di calcolo numerico moderne (<a
href="https://arma.sourceforge.net/">Armadillo</a>, <a
href="https://eigen.tuxfamily.org/index.php?title=Main_Page">Eigen</a>,
…);</li>
<li>Il codice è più veloce da scrivere e semplice da leggere;</li>
<li>È anche più veloce da eseguire.</li>
</ol></li>
</ul>
</section>
</div>
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