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<div class="identifier-type">function</div><div class="header"><cmath></div><h1 itemprop="name"><span class="namespace" title="namespace std">std::</span><span class="token">exp</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="kt">float</span><span class="w"> </span><span class="nf">exp</span><span class="p">(</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="c1">// (1) C++03からC++20まで</span>
<span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="nf">exp</span><span class="p">(</span><span class="kt">double</span><span class="w"> </span><span class="n">x</span><span class="p">);</span><span class="w"> </span><span class="c1">// (2) C++03からC++20まで</span>
<span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="nf">exp</span><span class="p">(</span><span class="kt">long</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">x</span><span class="p">);</span><span class="w"> </span><span class="c1">// (3) C++03からC++20まで</span>
<span class="w"> </span><span class="n"><i>floating-point-type</i></span>
<span class="w"> </span><span class="nf">exp</span><span class="p">(</span><span class="n"><i>floating-point-type</i></span><span class="w"> </span><span class="n">x</span><span class="p">);</span><span class="w"> </span><span class="c1">// (4) C++23</span>
<span class="w"> </span><span class="k">constexpr</span><span class="w"> </span><span class="n"><i>floating-point-type</i></span>
<span class="w"> </span><span class="nf">exp</span><span class="p">(</span><span class="n"><i>floating-point-type</i></span><span class="w"> </span><span class="n">x</span><span class="p">);</span><span class="w"> </span><span class="c1">// (4) C++26</span>
<span class="w"> </span><span class="kt">double</span>
<span class="w"> </span><span class="nf">exp</span><span class="p">(</span><span class="n"><i>Integral</i></span><span class="w"> </span><span class="n">x</span><span class="p">);</span><span class="w"> </span><span class="c1">// (5) C++11</span>
<span class="w"> </span><span class="k">constexpr</span><span class="w"> </span><span class="kt">double</span>
<span class="w"> </span><span class="nf">exp</span><span class="p">(</span><span class="n"><i>Integral</i></span><span class="w"> </span><span class="n">x</span><span class="p">);</span><span class="w"> </span><span class="c1">// (5) C++26</span>
<span class="w"> </span><span class="kt">float</span>
<span class="w"> </span><span class="nf">expf</span><span class="p">(</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="c1">// (6) C++17</span>
<span class="w"> </span><span class="k">constexpr</span><span class="w"> </span><span class="kt">float</span>
<span class="w"> </span><span class="nf">expf</span><span class="p">(</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="c1">// (6) C++26</span>
<span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="kt">double</span>
<span class="w"> </span><span class="nf">expl</span><span class="p">(</span><span class="kt">long</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">x</span><span class="p">);</span><span class="w"> </span><span class="c1">// (7) C++17</span>
<span class="w"> </span><span class="k">constexpr</span><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="kt">double</span>
<span class="w"> </span><span class="nf">expl</span><span class="p">(</span><span class="kt">long</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">x</span><span class="p">);</span><span class="w"> </span><span class="c1">// (7) C++26</span>
<span class="p">}</span>
</code></pre></div>
</p>
<h2>概要</h2>
<p><code>e</code> (ネイピア数) を底とする指数関数を求める。</p>
<ul>
<li>(1) : <code>float</code>に対する<a class="cpprefjp-defined-word" data-desc="同名の関数を異なる引数・テンプレート・制約などで複数定義すること。または同名の関数の集合">オーバーロード</a></li>
<li>(2) : <code>double</code>に対する<a class="cpprefjp-defined-word" data-desc="同名の関数を異なる引数・テンプレート・制約などで複数定義すること。または同名の関数の集合">オーバーロード</a></li>
<li>(3) : <code>long double</code>に対する<a class="cpprefjp-defined-word" data-desc="同名の関数を異なる引数・テンプレート・制約などで複数定義すること。または同名の関数の集合">オーバーロード</a></li>
<li>(4) : 浮動小数点数型に対する<a class="cpprefjp-defined-word" data-desc="同名の関数を異なる引数・テンプレート・制約などで複数定義すること。または同名の関数の集合">オーバーロード</a></li>
<li>(5) : 整数型に対する<a class="cpprefjp-defined-word" data-desc="同名の関数を異なる引数・テンプレート・制約などで複数定義すること。または同名の関数の集合">オーバーロード</a> (<code>double</code>にキャストして計算される)</li>
<li>(6) : <code>float</code>型規定</li>
<li>(7) : <code>long double</code>型規定</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>
<p><code>e</code> (ネイピア数) の <code>x</code> 乗を返す。</p>
<p><code>x</code> の絶対値が大きすぎる場合には、オーバーフローエラー、あるいはアンダーフローエラーとなり、<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>は<a class="cpprefjp-defined-word" data-desc="処理系定義の動作。処理系によって事前に定めた動作をする" href="../../implementation-compliance.html#dfn-implementation-defined-behavior">処理系定義</a>である。（備考参照）</p>
<h2>備考</h2>
<ul>
<li>$$ f(x) = e^x $$</li>
<li>オーバーフローエラー、アンダーフローエラーが発生した場合の挙動については、<code><a href="../cmath.html"><cmath></a></code> を参照。</li>
<li>C++11 以降では、処理系が IEC 60559 に準拠している場合（<code><a href="../limits/numeric_limits.html">std::numeric_limits</a><T>::<a href="../limits/numeric_limits/is_iec559.html">is_iec559</a>() != false</code>）、以下の規定が追加される。<ul>
<li><code>x = ±0</code> の場合、<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>は <code>1</code> となる。</li>
<li><code>x = -∞</code> の場合、<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>は <code>+0</code> となる。</li>
<li><code>x = +∞</code> の場合、<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>は <code>+∞</code> となる。</li>
</ul>
</li>
<li>C++23では、(1), (2), (3)が(4)に統合され、<a class="cpprefjp-defined-word" data-desc="<stdfloat>で定義される内部表現の規定された浮動小数点数型" href="../stdfloat.html">拡張浮動小数点数型</a>を含む浮動小数点数型への<a class="cpprefjp-defined-word" data-desc="同名の関数を異なる引数・テンプレート・制約などで複数定義すること。または同名の関数の集合">オーバーロード</a>として定義された</li>
</ul>
<h2>例</h2>
<p><div class="yata" id="dd33adc798188bbea32c2829ed9aa0a27c3e013e"><div class="codehilite"><pre><span></span><code><span class="cp">#include <a href="../cmath.html"><cmath></a></span>
<span class="cp">#include <a href="../limits.html"><limits></a></span>
<span class="cp">#include <a href="../iostream.html"><iostream></a></span>
<span class="kt">int</span><span class="w"> </span><span class="nf">main</span><span class="p">()</span><span class="w"> </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="n"><a href="../ios/fixed.html">std::fixed</a></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">"exp(0.0) = "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><span style="color:#ff0000">std::exp</span></span><span class="p">(</span><span class="mf">0.0</span><span class="p">)</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="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">"exp(1.0) = "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><span style="color:#ff0000">std::exp</span></span><span class="p">(</span><span class="mf">1.0</span><span class="p">)</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="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">"exp(+∞) = "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><span style="color:#ff0000">std::exp</span></span><span class="p">(</span><span class="n"><a href="../limits/numeric_limits.html">std::numeric_limits</a></span><span class="o"><</span><span class="kt">double</span><span class="o">>::</span><span class="n"><a href="../limits/numeric_limits/infinity.html">infinity</a></span><span class="p">())</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="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">"exp(-∞) = "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n"><span style="color:#ff0000">std::exp</span></span><span class="p">(</span><span class="o">-</span><span class="n"><a href="../limits/numeric_limits.html">std::numeric_limits</a></span><span class="o"><</span><span class="kt">double</span><span class="o">>::</span><span class="n"><a href="../limits/numeric_limits/infinity.html">infinity</a></span><span class="p">())</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>
<h3>出力例</h3>
<p><pre><code>exp(0.0) = 1.000000
exp(1.0) = 2.718282
exp(+∞) = inf
exp(-∞) = 0.000000
</code></pre></p>
<h2>バージョン</h2>
<h3>言語</h3>
<ul>
<li>C++03</li>
</ul>
<h3>処理系</h3>
<ul>
<li><a href="../../implementation.html#clang">Clang</a>: 1.9 <span aria-label="検証済" role="img" title="検証済">✅</span>, 2.9 <span aria-label="検証済" role="img" title="検証済">✅</span>, 3.1 <span aria-label="検証済" role="img" title="検証済">✅</span></li>
<li><a href="../../implementation.html#gcc">GCC</a>: 3.4.6 <span aria-label="検証済" role="img" title="検証済">✅</span>, 4.2.4 <span aria-label="検証済" role="img" title="検証済">✅</span>, 4.3.5 <span aria-label="検証済" role="img" title="検証済">✅</span>, 4.4.5 <span aria-label="検証済" role="img" title="検証済">✅</span>, 4.5.1 <span aria-label="検証済" role="img" title="検証済">✅</span>, 4.5.2 <span aria-label="検証済" role="img" title="検証済">✅</span>, 4.6.1 <span aria-label="検証済" role="img" title="検証済">✅</span>, 4.7.0 <span aria-label="検証済" role="img" title="検証済">✅</span></li>
<li><a href="../../implementation.html#icc">ICC</a>: 10.1 <span aria-label="検証済" role="img" title="検証済">✅</span>, 11.0 <span aria-label="検証済" role="img" title="検証済">✅</span>, 11.1 <span aria-label="検証済" role="img" title="検証済">✅</span>, 12.0 <span aria-label="検証済" role="img" title="検証済">✅</span></li>
<li><a href="../../implementation.html#visual_cpp">Visual C++</a>: 2003 <span aria-label="検証済" role="img" title="検証済">✅</span>, 2005 <span aria-label="検証済" role="img" title="検証済">✅</span>, 2008 <span aria-label="検証済" role="img" title="検証済">✅</span>, 2010 <span aria-label="検証済" role="img" title="検証済">✅</span></li>
</ul>
<h4>備考</h4>
<p>特定の環境では、早期に <code>constexpr</code> 対応されている場合がある：</p>
<ul>
<li>GCC 4.6.1 以上</li>
</ul>
<h2>実装例</h2>
<p>以下のマクローリン級数を適当な次数で打ち切ることで近似的に求めることができる。</p>
<p>$$ e^x = \sum_{n = 0}^{\infty} \frac{x^n}{n!} \quad \mathrm{for~all} \; x $$</p>
<h2>参照</h2>
<ul>
<li><a href="https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2022/p1467r9.html" target="_blank">P1467R9 Extended floating-point types and standard names</a><ul>
<li>C++23で導入された<a class="cpprefjp-defined-word" data-desc="<stdfloat>で定義される内部表現の規定された浮動小数点数型" href="../stdfloat.html">拡張浮動小数点数型</a>への対応として、<code>float</code>、<code>double</code>、<code>long double</code>の<a class="cpprefjp-defined-word" data-desc="同名の関数を異なる引数・テンプレート・制約などで複数定義すること。または同名の関数の集合">オーバーロード</a>を<code>floating-point-type</code>の<a class="cpprefjp-defined-word" data-desc="同名の関数を異なる引数・テンプレート・制約などで複数定義すること。または同名の関数の集合">オーバーロード</a>に統合し、<a class="cpprefjp-defined-word" data-desc="<stdfloat>で定義される内部表現の規定された浮動小数点数型" href="../stdfloat.html">拡張浮動小数点数型</a>も扱えるようにした</li>
</ul>
</li>
<li><a href="https://open-std.org/jtc1/sc22/wg21/docs/papers/2023/p1383r2.pdf" target="_blank">P1383R2 More constexpr for <code><cmath></code> and <code><complex></code></a><ul>
<li>C++26で<code>constexpr</code>対応した</li>
</ul>
</li>
</ul></div>
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