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</table>
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<p>Computes the modified Bessel function of the first kind, \( I_1(x)= _iJ_1(ix) \) extended to the complex plane and cayley_dickson algebras. </p>
<p>Computes the modified Bessel function of the first kind, \( I_1(x)= iJ_1(ix) \) extended to the complex plane and cayley_dickson algebras. </p>
<p>It is the solution of \( x^{2}y&#39;&#39;+xy&#39;+x^2y=0\) for which \( y(0) = 0\).</p>
<div class="fragment"><div class="line"><span class="preprocessor">#include &lt;kyosu/functions.hpp&gt;</span></div>
</div><!-- fragment --><h2 class="groupheader">Callable Signatures </h2>
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Expand Up @@ -193,6 +193,12 @@ <h2 class="groupheader">Example </h2>
<div class="line"> eve::wide&lt;double, eve::fixed&lt;4&gt;&gt; z1(1.0, 2.0, 40.0, 0.0), z2(36.0, 0.5, 0.0, 40.0);</div>
<div class="line"> <span class="keyword">auto</span> z0 = <a class="code hl_variable" href="group__functions_gae0cdc9d2dae205852268d4c5cdca6578.html#gae0cdc9d2dae205852268d4c5cdca6578">kyosu::complex</a>(z1, z2);</div>
<div class="line"> std::cout &lt;&lt; z0 &lt;&lt; <span class="stringliteral">&quot; \n-&gt; &quot;</span> &lt;&lt; <a class="code hl_variable" href="group__functions_ga96400e65eaf1b63c5ab88ba5aff6d818.html#ga96400e65eaf1b63c5ab88ba5aff6d818">cyl_bessel_yn</a>(n,z0) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=75; i &lt; 100; ++i)</div>
<div class="line"> std::cout &lt;&lt; <span class="stringliteral">&quot;i &quot;</span> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot; -&gt; &quot;</span> &lt;&lt; <a class="code hl_variable" href="group__functions_ga96400e65eaf1b63c5ab88ba5aff6d818.html#ga96400e65eaf1b63c5ab88ba5aff6d818">cyl_bessel_yn</a>(i,<a class="code hl_variable" href="group__functions_gae0cdc9d2dae205852268d4c5cdca6578.html#gae0cdc9d2dae205852268d4c5cdca6578">kyosu::complex</a>(1.0, 1.0)) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">return</span> 0;</div>
<div class="line">}</div>
<div class="ttc" id="agroup__functions_gaa9d12dd4e1420039046c737ddd3240be_html_gaa9d12dd4e1420039046c737ddd3240be"><div class="ttname"><a href="group__functions_gaa9d12dd4e1420039046c737ddd3240be.html#gaa9d12dd4e1420039046c737ddd3240be">kyosu::real</a></div><div class="ttdeci">constexpr tags::callable_real real</div><div class="ttdoc">Extracts the real part of a value.</div><div class="ttdef"><b>Definition:</b> real.hpp:83</div></div>
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<a id="gae0bcc9ef41c3390b4dd85f9f3f8cd457" name="gae0bcc9ef41c3390b4dd85f9f3f8cd457"></a>
<h2 class="memtitle"><span class="permalink"><a href="#gae0bcc9ef41c3390b4dd85f9f3f8cd457">&#9670;&#160;</a></span>sinhc</h2>

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<td class="memname">kyosu::sinhc = {}</td>
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<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">constexpr</span></span> </td>
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<p>Computes the hyperbolic sine cardinal of the argument. </p>
<p><b>Defined in Header</b></p>
<div class="fragment"><div class="line"><span class="preprocessor">#include &lt;kyosu/functions.hpp&gt;</span></div>
</div><!-- fragment --><h2 class="groupheader">Callable Signatures </h2>
<div class="fragment"><div class="line"><span class="keyword">namespace </span><a class="code hl_namespace" href="namespacekyosu.html">kyosu</a></div>
<div class="line">{</div>
<div class="line"> <span class="keyword">template</span>&lt;kyosu::concepts::cayley_dickson T&gt; <span class="keyword">constexpr</span> <span class="keyword">auto</span> <a class="code hl_variable" href="group__functions_gae0bcc9ef41c3390b4dd85f9f3f8cd457.html#gae0bcc9ef41c3390b4dd85f9f3f8cd457">sinhc</a>(T z) <span class="keyword">noexcept</span>;</div>
<div class="line"> <span class="keyword">template</span>&lt;eve::<span class="keywordtype">float</span>ing_ordered_value T&gt; <span class="keyword">constexpr</span> <span class="keyword">auto</span> <a class="code hl_variable" href="group__functions_gae0bcc9ef41c3390b4dd85f9f3f8cd457.html#gae0bcc9ef41c3390b4dd85f9f3f8cd457">sinhc</a>(T z) <span class="keyword">noexcept</span>;</div>
<div class="line">}</div>
<div class="ttc" id="agroup__functions_gae0bcc9ef41c3390b4dd85f9f3f8cd457_html_gae0bcc9ef41c3390b4dd85f9f3f8cd457"><div class="ttname"><a href="group__functions_gae0bcc9ef41c3390b4dd85f9f3f8cd457.html#gae0bcc9ef41c3390b4dd85f9f3f8cd457">kyosu::sinhc</a></div><div class="ttdeci">constexpr tags::callable_sinhc sinhc</div><div class="ttdoc">Computes the hyperbolic sine cardinal of the argument.</div><div class="ttdef"><b>Definition:</b> sinhc.hpp:73</div></div>
<div class="ttc" id="anamespacekyosu_html"><div class="ttname"><a href="namespacekyosu.html">kyosu</a></div><div class="ttdoc">Main KYOSU namespace.</div><div class="ttdef"><b>Definition:</b> types.hpp:14</div></div>
</div><!-- fragment --><p><b>Parameters</b></p>
<ul>
<li><code>z</code>: Value to process.</li>
</ul>
<p><b>Return value</b></p>
<p>Returns the hyperbolic sine cardinal of the argument.</p>
<h2 class="groupheader">Example </h2>
<div class="fragment"><div class="line"><span class="preprocessor">#include &lt;kyosu/kyosu.hpp&gt;</span></div>
<div class="line"><span class="preprocessor">#include &lt;eve/wide.hpp&gt;</span></div>
<div class="line"><span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">int</span> main()</div>
<div class="line">{</div>
<div class="line"> <span class="keyword">using </span><a class="code hl_variable" href="group__functions_gae0bcc9ef41c3390b4dd85f9f3f8cd457.html#gae0bcc9ef41c3390b4dd85f9f3f8cd457">kyosu::sinhc</a>;</div>
<div class="line"> <span class="keyword">using </span><a class="code hl_typedef" href="group__types_ga642e4c9da3267bde80011f41e698ba76.html#ga642e4c9da3267bde80011f41e698ba76">kyosu::complex_t</a>;</div>
<div class="line"> <span class="keyword">using </span><a class="code hl_typedef" href="group__types_ga0fb102adb92b2be024f398e2ac5dd5cd.html#ga0fb102adb92b2be024f398e2ac5dd5cd">kyosu::quaternion_t</a>;</div>
<div class="line"> </div>
<div class="line"> std::cout &lt;&lt; <span class="stringliteral">&quot;Real: &quot;</span>;</div>
<div class="line"> std::cout &lt;&lt; 12.9f &lt;&lt; <span class="stringliteral">&quot; -&gt; &quot;</span> &lt;&lt; <a class="code hl_variable" href="group__functions_gae0bcc9ef41c3390b4dd85f9f3f8cd457.html#gae0bcc9ef41c3390b4dd85f9f3f8cd457">sinhc</a>(12.9f) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"> </div>
<div class="line"> std::cout &lt;&lt; <span class="stringliteral">&quot;Complex: &quot;</span>;</div>
<div class="line"> std::cout &lt;&lt; kyosu::complex_t&lt;float&gt;(3.5f,-2.9f) &lt;&lt; <span class="stringliteral">&quot; -&gt; &quot;</span> &lt;&lt; <a class="code hl_variable" href="group__functions_gae0bcc9ef41c3390b4dd85f9f3f8cd457.html#gae0bcc9ef41c3390b4dd85f9f3f8cd457">sinhc</a>(<a class="code hl_typedef" href="group__types_ga642e4c9da3267bde80011f41e698ba76.html#ga642e4c9da3267bde80011f41e698ba76">kyosu::complex_t&lt;float&gt;</a>(3.5f,-2.9f)) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"> </div>
<div class="line"> std::cout &lt;&lt; <span class="stringliteral">&quot;Quaternion: &quot;</span>;</div>
<div class="line"> std::cout &lt;&lt; kyosu::quaternion_t&lt;double&gt;(1.,2.,3.,4.) &lt;&lt; <span class="stringliteral">&quot; -&gt; &quot;</span> &lt;&lt; <a class="code hl_variable" href="group__functions_gae0bcc9ef41c3390b4dd85f9f3f8cd457.html#gae0bcc9ef41c3390b4dd85f9f3f8cd457">sinhc</a>(<a class="code hl_typedef" href="group__types_ga0fb102adb92b2be024f398e2ac5dd5cd.html#ga0fb102adb92b2be024f398e2ac5dd5cd">kyosu::quaternion_t&lt;double&gt;</a>(1.,2.,3.,4.)) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"> </div>
<div class="line"> std::cout &lt;&lt; <span class="stringliteral">&quot;SIMD: &quot;</span>;</div>
<div class="line"> <span class="keyword">using </span>wc_t = eve::wide&lt;kyosu::complex_t&lt;double&gt;, eve::fixed&lt;2&gt;&gt;;</div>
<div class="line"> std::cout &lt;&lt; wc_t(kyosu::complex_t&lt;double&gt;(1.3,-3.7)) &lt;&lt; <span class="stringliteral">&quot; -&gt; &quot;</span> &lt;&lt; <a class="code hl_variable" href="group__functions_gae0bcc9ef41c3390b4dd85f9f3f8cd457.html#gae0bcc9ef41c3390b4dd85f9f3f8cd457">sinhc</a>(wc_t(<a class="code hl_typedef" href="group__types_ga642e4c9da3267bde80011f41e698ba76.html#ga642e4c9da3267bde80011f41e698ba76">kyosu::complex_t&lt;double&gt;</a>(1.3,-3.7))) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">return</span> 0;</div>
<div class="line">}</div>
<div class="ttc" id="agroup__types_ga0fb102adb92b2be024f398e2ac5dd5cd_html_ga0fb102adb92b2be024f398e2ac5dd5cd"><div class="ttname"><a href="group__types_ga0fb102adb92b2be024f398e2ac5dd5cd.html#ga0fb102adb92b2be024f398e2ac5dd5cd">kyosu::quaternion_t</a></div><div class="ttdeci">as_cayley_dickson_n_t&lt; 4, T &gt; quaternion_t</div><div class="ttdoc">Type alias for quaternion numbers.</div><div class="ttdef"><b>Definition:</b> quaternion.hpp:27</div></div>
<div class="ttc" id="agroup__types_ga642e4c9da3267bde80011f41e698ba76_html_ga642e4c9da3267bde80011f41e698ba76"><div class="ttname"><a href="group__types_ga642e4c9da3267bde80011f41e698ba76.html#ga642e4c9da3267bde80011f41e698ba76">kyosu::complex_t</a></div><div class="ttdeci">as_cayley_dickson_n_t&lt; 2, T &gt; complex_t</div><div class="ttdoc">Type alias for complex numbers.</div><div class="ttdef"><b>Definition:</b> complex.hpp:27</div></div>
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2 changes: 1 addition & 1 deletion group__functions_gaeb24f578562330d825ff8f68da4b9252.html
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Expand Up @@ -150,7 +150,7 @@ <h2 class="memtitle"><span class="permalink"><a href="#gaeb24f578562330d825ff8f6
<div class="line">{</div>
<div class="line"> <span class="keyword">auto</span> <a class="code hl_variable" href="group__functions_gaeb24f578562330d825ff8f68da4b9252.html#gaeb24f578562330d825ff8f68da4b9252">from_angle_axis</a>(<span class="keyword">auto</span> angle, <span class="keyword">auto</span> axis, <span class="keyword">auto</span> norming = normalize) <span class="keyword">const</span> <span class="keyword">noexcept</span>;</div>
<div class="line">}</div>
<div class="ttc" id="agroup__functions_gaeb24f578562330d825ff8f68da4b9252_html_gaeb24f578562330d825ff8f68da4b9252"><div class="ttname"><a href="group__functions_gaeb24f578562330d825ff8f68da4b9252.html#gaeb24f578562330d825ff8f68da4b9252">kyosu::from_angle_axis</a></div><div class="ttdeci">constexpr tags::callable_from_angle_axis from_angle_axis</div><div class="ttdoc">Callable object computing an an unitary quaternion from an angle value and a 3 dimensionnal axis vect...</div><div class="ttdef"><b>Definition:</b> from_angle_axis.hpp:119</div></div>
<div class="ttc" id="agroup__functions_gaeb24f578562330d825ff8f68da4b9252_html_gaeb24f578562330d825ff8f68da4b9252"><div class="ttname"><a href="group__functions_gaeb24f578562330d825ff8f68da4b9252.html#gaeb24f578562330d825ff8f68da4b9252">kyosu::from_angle_axis</a></div><div class="ttdeci">constexpr tags::callable_from_angle_axis from_angle_axis</div><div class="ttdoc">Callable object computing an an unitary quaternion from an angle value and a 3 dimensionnal axis vect...</div><div class="ttdef"><b>Definition:</b> from_angle_axis.hpp:115</div></div>
<div class="ttc" id="anamespacekyosu_html"><div class="ttname"><a href="namespacekyosu.html">kyosu</a></div><div class="ttdoc">Main KYOSU namespace.</div><div class="ttdef"><b>Definition:</b> types.hpp:14</div></div>
</div><!-- fragment --><p><b>Parameters</b></p>
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