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<div class="identifier-type">function template</div><div class="header"><numeric></div><h1 itemprop="name"><span class="namespace" title="namespace std">std::</span><span class="token">midpoint</span><span class="cpp cpp20" title="C++20で追加">(C++20)</span></h1>
<div itemprop="articleBody"><p><div class="codehilite"><pre><span></span><code><span class="k">namespace</span><span class="w"> </span><span class="nn">std</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="k">template</span><span class="w"> </span><span class="o"><</span><span class="k">class</span><span class="w"> </span><span class="nc">T</span><span class="o">></span>
<span class="w"> </span><span class="k">constexpr</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="n">midpoint</span><span class="p">(</span><span class="n">T</span><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="n">b</span><span class="p">)</span><span class="w"> </span><span class="k">noexcept</span><span class="p">;</span><span class="w"> </span><span class="c1">// (1)</span>
<span class="w"> </span><span class="k">template</span><span class="w"> </span><span class="o"><</span><span class="k">class</span><span class="w"> </span><span class="nc">T</span><span class="o">></span>
<span class="w"> </span><span class="k">constexpr</span><span class="w"> </span><span class="n">T</span><span class="o">*</span><span class="w"> </span><span class="n">midpoint</span><span class="p">(</span><span class="n">T</span><span class="o">*</span><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">T</span><span class="o">*</span><span class="w"> </span><span class="n">b</span><span class="p">);</span><span class="w"> </span><span class="c1">// (2)</span>
<span class="p">}</span>
</code></pre></div>
</p>
<h2>概要</h2>
<p>二点間の中点を求める。</p>
<ul>
<li>(1) : 数値型の中点を求める</li>
<li>(2) : ポインタ型の中点を求める</li>
</ul>
<p>この関数は、単純に計算する場合は<code>(a + b) / 2</code>となるが、オーバーフローが起こりにくいよう計算式に工夫が入る。例として、整数の場合は<code>a + (b - a) / 2</code>、浮動小数点数の場合は<code>a/2 + b/2</code>のように計算できる (実際は負数や非正規化数などをさらに考慮することになる)。</p>
<h2><a class="cpprefjp-defined-word" data-desc="関数等の意味論を構成する要素の1つ。Constraints。関数であればオーバーロード解決に参加するための条件、それ以外であれば受け付ける型の条件">テンプレートパラメータ制約</a></h2>
<ul>
<li>(1) : 型<code>T</code> が <code>bool</code> 以外の<a href="../type_traits/is_arithmetic.html">算術型</a>であること</li>
<li>(2) : 型<code>T</code>はオブジェクト型であること</li>
</ul>
<h2><a class="cpprefjp-defined-word" data-desc="関数等の意味論を構成する要素の1つ。Mandates。満たさなければプログラムが不適格となる要件。この要件は、オーバーロード解決によって選択された関数内での`static_assert`の定数条件式や、関数に対するdelete宣言などで表現できる">適格要件</a></h2>
<ul>
<li>(2) : 型<code>T</code>は<a class="cpprefjp-defined-word" data-desc="型のサイズを決定できる型。不完全型ではない型">完全型</a>であること</li>
</ul>
<h2><a class="cpprefjp-defined-word" data-desc="関数等の意味論を構成する要素の1つ。Preconditions。関数呼び出し時に満たされていると関数が想定する条件。満たさなければ未定義の動作。契約属性の`[[expects]]`に相当">事前条件</a></h2>
<ul>
<li>(2) : 期待することとして、<code>a</code>と<code>b</code>はそれぞれ、同じ配列<code>x</code>の<code>x[i]</code>と<code>x[j]</code>要素を指していること<ul>
<li>配列要素でないオブジェクトが与えられた場合は、単一要素をもつ配列に属するものとみなす</li>
</ul>
</li>
</ul>
<h2><a class="cpprefjp-defined-word" data-desc="関数呼び出し式の評価結果となるオブジェクト・値">戻り値</a></h2>
<ul>
<li>(1) : <code>a</code>と<code>b</code>を合計した値の1/2の数値を返す<ul>
<li>型<code>T</code>が整数型で合計値が奇数の場合、<code>a</code>側に丸められる</li>
<li>型<code>T</code>が浮動小数点数型の場合、最大一回の<a href="../cfenv/fe_inexact.html">不正確 (inexact) 操作</a>が発生し、オーバーフローは起こらない</li>
</ul>
</li>
<li>(2) : <code>a</code>と<code>b</code>が同じ配列<code>x</code>の<code>x[i]</code>と<code>x[j]</code>を指しているとして、<code>x[i + (j - i) / 2]</code>を指すポインタを返す。除算の結果はゼロ方向に丸められる</li>
</ul>
<h2><a class="cpprefjp-defined-word" data-desc="問題が発生したときに、現在実行位置を過去に通過・記録した位置に戻し、文脈情報を添えて紐づけられた処理(例外ハンドラー)を呼び出す仕組み。またはその事態">例外</a></h2>
<ul>
<li>(1) : 投げない</li>
</ul>
<h2>備考</h2>
<ul>
<li>浮動小数点数の文脈では、この関数の動作は平均値 (mean value) という名称を使用するが、それ以外の文脈では中点が使用される。汎用的な用途とするため、この関数の名前として中点 (midpoint) を採用している</li>
</ul>
<h2>例</h2>
<h3>基本的な使い方</h3>
<p><div class="yata" id="03558cbbd52a4121159a03437858cff865621cce"><div class="codehilite"><pre><span></span><code><span class="cp">#include <a href="../iostream.html"><iostream></a></span>
<span class="cp">#include <a href="../numeric.html"><numeric></a></span>
<span class="kt">int</span><span class="w"> </span><span class="nf">main</span><span class="p">()</span>
<span class="p">{</span>
<span class="w"> </span><span class="c1">// (1) 整数</span>
<span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n"><span style="color:#ff0000">std::midpoint</span></span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">);</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"a : "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">r1</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span>
<span class="w"> </span><span class="c1">// 奇数になるケース</span>
<span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n"><span style="color:#ff0000">std::midpoint</span></span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">);</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"b : "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">r2</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span>
<span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n"><span style="color:#ff0000">std::midpoint</span></span><span class="p">(</span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"c : "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">r3</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span>
<span class="w"> </span><span class="p">}</span>
<span class="w"> </span><span class="c1">// (2) 浮動小数点数</span>
<span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="kt">float</span><span class="w"> </span><span class="n">r1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n"><span style="color:#ff0000">std::midpoint</span></span><span class="p">(</span><span class="mf">1.5f</span><span class="p">,</span><span class="w"> </span><span class="mf">2.5f</span><span class="p">);</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"d : "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">r1</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span>
<span class="w"> </span><span class="kt">float</span><span class="w"> </span><span class="n">r2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n"><span style="color:#ff0000">std::midpoint</span></span><span class="p">(</span><span class="mf">1.5f</span><span class="p">,</span><span class="w"> </span><span class="mf">3.0f</span><span class="p">);</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"e : "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">r2</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span>
<span class="w"> </span><span class="p">}</span>
<span class="w"> </span><span class="c1">// (3) ポインタ</span>
<span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">ar</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">};</span>
<span class="w"> </span><span class="kt">int</span><span class="o">*</span><span class="w"> </span><span class="n">p1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n"><span style="color:#ff0000">std::midpoint</span></span><span class="p">(</span><span class="n">ar</span><span class="p">,</span><span class="w"> </span><span class="n">ar</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// &ar[1]が返る</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"f : "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="o">*</span><span class="n">p1</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span>
<span class="w"> </span><span class="c1">// 配列ではないオブジェクトへのポインタは、単一要素の配列として指定する</span>
<span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span><span class="p">;</span>
<span class="w"> </span><span class="kt">int</span><span class="o">*</span><span class="w"> </span><span class="n">p2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n"><span style="color:#ff0000">std::midpoint</span></span><span class="p">(</span><span class="o">&</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">x</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"g : "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="o">*</span><span class="n">p2</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span>
<span class="w"> </span><span class="p">}</span>
<span class="p">}</span>
</code></pre></div>
</div></p>
<h4>出力</h4>
<p><pre><code>a : 3
b : 4
c : 5
d : 2
e : 2.25
f : 2
g : 4
</code></pre></p>
<h3>2次元の二点間の中点を求める</h3>
<p><div class="yata" id="7e9a6315b9255cd0fabf520eb5892516399fb785"><div class="codehilite"><pre><span></span><code><span class="cp">#include <a href="../iostream.html"><iostream></a></span>
<span class="cp">#include <a href="../numeric.html"><numeric></a></span>
<span class="c1">// 2次元上の点を表す型</span>
<span class="k">struct</span><span class="w"> </span><span class="nc">Point</span><span class="w"> </span><span class="p">{</span>
<span class="w"> </span><span class="kt">float</span><span class="w"> </span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">y</span><span class="p">;</span>
<span class="p">};</span>
<span class="c1">// Point型用に中点を求める関数を定義する</span>
<span class="n">Point</span><span class="w"> </span><span class="nf">midpoint</span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="n">Point</span><span class="o">&</span><span class="w"> </span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">Point</span><span class="o">&</span><span class="w"> </span><span class="n">b</span><span class="p">)</span><span class="w"> </span><span class="k">noexcept</span>
<span class="p">{</span>
<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">Point</span><span class="p">{</span>
<span class="w"> </span><span class="n"><span style="color:#ff0000">std::midpoint</span></span><span class="p">(</span><span class="n">a</span><span class="p">.</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">.</span><span class="n">x</span><span class="p">),</span>
<span class="w"> </span><span class="n"><span style="color:#ff0000">std::midpoint</span></span><span class="p">(</span><span class="n">a</span><span class="p">.</span><span class="n">y</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">.</span><span class="n">y</span><span class="p">)</span>
<span class="w"> </span><span class="p">};</span>
<span class="p">}</span>
<span class="kt">int</span><span class="w"> </span><span class="nf">main</span><span class="p">()</span>
<span class="p">{</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">Point</span><span class="w"> </span><span class="n">a</span><span class="p">{</span><span class="mf">1.0f</span><span class="p">,</span><span class="w"> </span><span class="mf">2.0f</span><span class="p">};</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">Point</span><span class="w"> </span><span class="n">b</span><span class="p">{</span><span class="mf">5.0f</span><span class="p">,</span><span class="w"> </span><span class="mf">3.0f</span><span class="p">};</span>
<span class="w"> </span><span class="c1">// 点aと点bの中点を求める</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">Point</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">midpoint</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">);</span>
<span class="w"> </span><span class="n"><a href="../iostream/cout.html">std::cout</a></span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="sc">'('</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">p</span><span class="p">.</span><span class="n">x</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">", "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">p</span><span class="p">.</span><span class="n">y</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="sc">')'</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><a href="../ostream/endl.html">std::endl</a></span><span class="p">;</span>
<span class="p">}</span>
</code></pre></div>
</div></p>
<h4>出力</h4>
<p><pre><code>(3, 2.5)
</code></pre></p>
<h2>バージョン</h2>
<h3>言語</h3>
<ul>
<li>C++20</li>
</ul>
<h3>処理系</h3>
<ul>
<li><a href="../../implementation.html#clang">Clang</a>:</li>
<li><a href="../../implementation.html#gcc">GCC</a>: 9.1 <span aria-label="検証済" role="img" title="検証済">✅</span></li>
<li><a href="../../implementation.html#visual_cpp">Visual C++</a>: ??</li>
</ul>
<h2>関連項目</h2>
<ul>
<li><code><a href="../cmath/lerp.html">std::lerp()</a></code></li>
</ul>
<h2>参照</h2>
<ul>
<li><a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p0811r3.html" target="_blank">P0811R3 Well-behaved interpolation for numbers and pointers</a></li>
<li><a href="https://cplusplus.github.io/LWG/lwg-active.html#3200" target="_blank">LWG Issue 3200. <code>midpoint</code> should not constrain <code>T</code> is complete</a></li>
</ul></div>
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