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<div class="header">
  <div class="headertitle"><div class="title">FindRoot.h</div></div>
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<a href="_find_root_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="comment">// Jolt Physics Library (https://github.com/jrouwe/JoltPhysics)</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="comment">// SPDX-FileCopyrightText: 2021 Jorrit Rouwe</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="comment">// SPDX-License-Identifier: MIT</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span> </div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="preprocessor">#pragma once</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span> </div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><a class="code hl_define" href="_core_8h.html#ad14098b68b8c44ea6112601031268405">JPH_NAMESPACE_BEGIN</a></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span> </div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="foldopen" id="foldopen00013" data-start="{" data-end="}">
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"><a class="line" href="_find_root_8h.html#a3bec219d038a3c84a22b1c07b49b9eca">   13</a></span><span class="keyword">inline</span> <span class="keywordtype">int</span> <a class="code hl_function" href="_find_root_8h.html#a3bec219d038a3c84a22b1c07b49b9eca">FindRoot</a>(<span class="keyword">const</span> T inA, <span class="keyword">const</span> T inB, <span class="keyword">const</span> T inC, T &amp;outX1, T &amp;outX2)</div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span>{</div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span>    <span class="comment">// Check if this is a linear equation</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span>    <span class="keywordflow">if</span> (inA == T(0))</div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span>    {</div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span>        <span class="comment">// Check if this is a constant equation</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span>        <span class="keywordflow">if</span> (inB == T(0))</div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span>            <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span> </div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span>        <span class="comment">// Linear equation with 1 solution</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span>        outX1 = outX2 = -inC / inB;</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span>        <span class="keywordflow">return</span> 1;</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span>    }</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span> </div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span>    <span class="comment">// See Numerical Recipes in C, Chapter 5.6 Quadratic and Cubic Equations</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span>    T det = <a class="code hl_function" href="_math_8h.html#a61379b8b743a16fe823daeebc1482570">Square</a>(inB) - T(4) * inA * inC;</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>    <span class="keywordflow">if</span> (det &lt; T(0))</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>        <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span>    T q = (inB + <a class="code hl_function" href="_math_8h.html#a34ee8d229d5ba32162857cf660526a86">Sign</a>(inB) * sqrt(det)) / T(-2);</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>    outX1 = q / inA;</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>    <span class="keywordflow">if</span> (q == T(0))</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>    {</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>        outX2 = outX1;</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>        <span class="keywordflow">return</span> 1;</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>    }</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>    outX2 = inC / q;</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>    <span class="keywordflow">return</span> 2;</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>}</div>
</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span> </div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span><a class="code hl_define" href="_core_8h.html#a73da8725998b00321a9db341202d650d">JPH_NAMESPACE_END</a></div>
<div class="ttc" id="a_core_8h_html_a73da8725998b00321a9db341202d650d"><div class="ttname"><a href="_core_8h.html#a73da8725998b00321a9db341202d650d">JPH_NAMESPACE_END</a></div><div class="ttdeci">#define JPH_NAMESPACE_END</div><div class="ttdef"><b>Definition</b> Core.h:425</div></div>
<div class="ttc" id="a_core_8h_html_ad14098b68b8c44ea6112601031268405"><div class="ttname"><a href="_core_8h.html#ad14098b68b8c44ea6112601031268405">JPH_NAMESPACE_BEGIN</a></div><div class="ttdeci">#define JPH_NAMESPACE_BEGIN</div><div class="ttdef"><b>Definition</b> Core.h:419</div></div>
<div class="ttc" id="a_find_root_8h_html_a3bec219d038a3c84a22b1c07b49b9eca"><div class="ttname"><a href="_find_root_8h.html#a3bec219d038a3c84a22b1c07b49b9eca">FindRoot</a></div><div class="ttdeci">JPH_NAMESPACE_BEGIN int FindRoot(const T inA, const T inB, const T inC, T &amp;outX1, T &amp;outX2)</div><div class="ttdef"><b>Definition</b> FindRoot.h:13</div></div>
<div class="ttc" id="a_math_8h_html_a34ee8d229d5ba32162857cf660526a86"><div class="ttname"><a href="_math_8h.html#a34ee8d229d5ba32162857cf660526a86">Sign</a></div><div class="ttdeci">JPH_INLINE constexpr T Sign(T inV)</div><div class="ttdoc">Get the sign of a value.</div><div class="ttdef"><b>Definition</b> Math.h:69</div></div>
<div class="ttc" id="a_math_8h_html_a61379b8b743a16fe823daeebc1482570"><div class="ttname"><a href="_math_8h.html#a61379b8b743a16fe823daeebc1482570">Square</a></div><div class="ttdeci">JPH_INLINE constexpr T Square(T inV)</div><div class="ttdoc">Square a value.</div><div class="ttdef"><b>Definition</b> Math.h:55</div></div>
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