MeanField_SERiF/docs/xml/determinant__polynomial_8cpp.xml

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    <innernamespace refid="namespaceserif_1_1geometry_1_1deformation_1_1detail">serif::geometry::deformation::detail</innernamespace>
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<codeline lineno="1"><highlight class="preprocessor">#include<sp/>&quot;<ref refid="determinant__polynomial_8hpp" kindref="compound">serif/geometry/deformation/detail/determinant_polynomial.hpp</ref>&quot;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="2"><highlight class="normal"></highlight></codeline>
<codeline lineno="3"><highlight class="normal"></highlight><highlight class="preprocessor">#include<sp/>&lt;algorithm&gt;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="4"><highlight class="normal"></highlight><highlight class="preprocessor">#include<sp/>&lt;bit&gt;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="5"><highlight class="normal"></highlight><highlight class="preprocessor">#include<sp/>&lt;cmath&gt;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="6"><highlight class="normal"></highlight><highlight class="preprocessor">#include<sp/>&lt;limits&gt;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="7"><highlight class="normal"></highlight><highlight class="preprocessor">#include<sp/>&lt;numeric&gt;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="8"><highlight class="normal"></highlight></codeline>
<codeline lineno="9"><highlight class="normal"></highlight><highlight class="keyword">namespace<sp/></highlight><highlight class="normal"><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail" kindref="compound">serif::geometry::deformation::detail</ref><sp/>{</highlight></codeline>
<codeline lineno="10"><highlight class="normal"><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">namespace<sp/></highlight><highlight class="normal">{</highlight></codeline>
<codeline lineno="12"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>[[nodiscard]]<sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>selected_column_determinant(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a757a7054052d6c66e85a186de62f6e37" kindref="member">JacobianEntries</ref>&amp;<sp/>base,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a757a7054052d6c66e85a186de62f6e37" kindref="member">JacobianEntries</ref>&amp;<sp/>direction,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">unsigned</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>direction_columns,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>dimension,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>maximum_step)<sp/></highlight><highlight class="keyword">noexcept</highlight><highlight class="normal"><sp/>{</highlight></codeline>
<codeline lineno="13"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keyword">auto</highlight><highlight class="normal"><sp/>entry<sp/>=<sp/>[&amp;](</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>row,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>column)<sp/>{</highlight></codeline>
<codeline lineno="14"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>((direction_columns<sp/>&amp;<sp/>(1U<sp/>&lt;&lt;<sp/></highlight><highlight class="keyword">static_cast&lt;</highlight><highlight class="keywordtype">unsigned</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="keyword">&gt;</highlight><highlight class="normal">(column)))<sp/>!=<sp/>0U)<sp/>{</highlight></codeline>
<codeline lineno="15"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>maximum_step<sp/>*<sp/>direction[row][column];</highlight></codeline>
<codeline lineno="16"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="17"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>base[row][column];</highlight></codeline>
<codeline lineno="18"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>};</highlight></codeline>
<codeline lineno="19"><highlight class="normal"></highlight></codeline>
<codeline lineno="20"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(dimension<sp/>==<sp/>1)<sp/>{</highlight></codeline>
<codeline lineno="21"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>entry(0,<sp/>0);</highlight></codeline>
<codeline lineno="22"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="23"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(dimension<sp/>==<sp/>2)<sp/>{</highlight></codeline>
<codeline lineno="24"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>entry(0,<sp/>0)<sp/>*<sp/>entry(1,<sp/>1)<sp/>-<sp/>entry(0,<sp/>1)<sp/>*<sp/>entry(1,<sp/>0);</highlight></codeline>
<codeline lineno="25"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="26"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>entry(0,<sp/>0)<sp/>*<sp/>(entry(1,<sp/>1)<sp/>*<sp/>entry(2,<sp/>2)<sp/>-<sp/>entry(1,<sp/>2)<sp/>*<sp/>entry(2,<sp/>1))<sp/>-</highlight></codeline>
<codeline lineno="27"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>entry(0,<sp/>1)<sp/>*<sp/>(entry(1,<sp/>0)<sp/>*<sp/>entry(2,<sp/>2)<sp/>-<sp/>entry(1,<sp/>2)<sp/>*<sp/>entry(2,<sp/>0))<sp/>+</highlight></codeline>
<codeline lineno="28"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>entry(0,<sp/>2)<sp/>*<sp/>(entry(1,<sp/>0)<sp/>*<sp/>entry(2,<sp/>1)<sp/>-<sp/>entry(1,<sp/>1)<sp/>*<sp/>entry(2,<sp/>0));</highlight></codeline>
<codeline lineno="29"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="30"><highlight class="normal"></highlight></codeline>
<codeline lineno="32"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>[[nodiscard]]<sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>polynomial_degree(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a62740f4edaed2df52e6d246b78844c1b" kindref="member">DeterminantPolynomial</ref>&amp;<sp/>coefficients)<sp/></highlight><highlight class="keyword">noexcept</highlight><highlight class="normal"><sp/>{</highlight></codeline>
<codeline lineno="33"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>scale<sp/>=<sp/>0.0;</highlight></codeline>
<codeline lineno="34"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">for</highlight><highlight class="normal"><sp/>(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>coefficient<sp/>:<sp/>coefficients)<sp/>{</highlight></codeline>
<codeline lineno="35"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>scale<sp/>=<sp/>std::max(scale,<sp/>std::abs(coefficient));</highlight></codeline>
<codeline lineno="36"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="37"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>tolerance<sp/>=<sp/>64.0<sp/>*<sp/>std::numeric_limits&lt;double&gt;::epsilon()<sp/>*<sp/>scale;</highlight></codeline>
<codeline lineno="38"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">for</highlight><highlight class="normal"><sp/>(</highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>degree<sp/>=<sp/>3;<sp/>degree<sp/>&gt;<sp/>0;<sp/>--degree)<sp/>{</highlight></codeline>
<codeline lineno="39"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(std::abs(coefficients[degree])<sp/>&gt;<sp/>tolerance)<sp/>{</highlight></codeline>
<codeline lineno="40"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>degree;</highlight></codeline>
<codeline lineno="41"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="42"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="43"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>0;</highlight></codeline>
<codeline lineno="44"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="45"><highlight class="normal"></highlight></codeline>
<codeline lineno="47"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordtype">void</highlight><highlight class="normal"><sp/>append_unit_interval_root(std::array&lt;double,<sp/>2&gt;&amp;<sp/>roots,<sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="normal">&amp;<sp/>root_count,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>root)<sp/></highlight><highlight class="keyword">noexcept</highlight><highlight class="normal"><sp/>{</highlight></codeline>
<codeline lineno="48"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(!std::isfinite(root)<sp/>||<sp/>root<sp/>&lt;=<sp/>0.0<sp/>||<sp/>root<sp/>&gt;=<sp/>1.0)<sp/>{</highlight></codeline>
<codeline lineno="49"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal">;</highlight></codeline>
<codeline lineno="50"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="51"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(root_count<sp/>&gt;<sp/>0<sp/>&amp;&amp;<sp/>std::abs(root<sp/>-<sp/>roots[0])<sp/>&lt;=<sp/>64.0<sp/>*<sp/>std::numeric_limits&lt;double&gt;::epsilon())<sp/>{</highlight></codeline>
<codeline lineno="52"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal">;</highlight></codeline>
<codeline lineno="53"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="54"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>roots[root_count]<sp/>=<sp/>root;</highlight></codeline>
<codeline lineno="55"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>++root_count;</highlight></codeline>
<codeline lineno="56"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="57"><highlight class="normal"></highlight></codeline>
<codeline lineno="59"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>[[nodiscard]]<sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>derivative_critical_points(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a62740f4edaed2df52e6d246b78844c1b" kindref="member">DeterminantPolynomial</ref>&amp;<sp/>coefficients,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>degree,<sp/>std::array&lt;double,<sp/>2&gt;&amp;<sp/>critical_points)<sp/></highlight><highlight class="keyword">noexcept</highlight><highlight class="normal"><sp/>{</highlight></codeline>
<codeline lineno="60"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>count<sp/>=<sp/>0;</highlight></codeline>
<codeline lineno="61"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(degree<sp/>==<sp/>2)<sp/>{</highlight></codeline>
<codeline lineno="62"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>append_unit_interval_root(critical_points,<sp/>count,<sp/>-coefficients[1]<sp/>/<sp/>(2.0<sp/>*<sp/>coefficients[2]));</highlight></codeline>
<codeline lineno="63"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}<sp/></highlight><highlight class="keywordflow">else</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(degree<sp/>==<sp/>3)<sp/>{</highlight></codeline>
<codeline lineno="64"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>quadratic<sp/>=<sp/>3.0<sp/>*<sp/>coefficients[3];</highlight></codeline>
<codeline lineno="65"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>linear<sp/>=<sp/>2.0<sp/>*<sp/>coefficients[2];</highlight></codeline>
<codeline lineno="66"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>constant<sp/>=<sp/>coefficients[1];</highlight></codeline>
<codeline lineno="67"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>discriminant<sp/>=<sp/>std::fma(linear,<sp/>linear,<sp/>-4.0<sp/>*<sp/>quadratic<sp/>*<sp/>constant);</highlight></codeline>
<codeline lineno="68"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>discriminant_scale<sp/>=<sp/>linear<sp/>*<sp/>linear<sp/>+<sp/>std::abs(4.0<sp/>*<sp/>quadratic<sp/>*<sp/>constant);</highlight></codeline>
<codeline lineno="69"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>discriminant_tolerance<sp/>=<sp/>64.0<sp/>*<sp/>std::numeric_limits&lt;double&gt;::epsilon()<sp/>*<sp/>discriminant_scale;</highlight></codeline>
<codeline lineno="70"><highlight class="normal"></highlight></codeline>
<codeline lineno="71"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(discriminant<sp/>&gt;=<sp/>-discriminant_tolerance)<sp/>{</highlight></codeline>
<codeline lineno="72"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>square_root<sp/>=<sp/>std::sqrt(std::max(0.0,<sp/>discriminant));</highlight></codeline>
<codeline lineno="73"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(square_root<sp/>==<sp/>0.0)<sp/>{</highlight></codeline>
<codeline lineno="74"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>append_unit_interval_root(critical_points,<sp/>count,<sp/>-linear<sp/>/<sp/>(2.0<sp/>*<sp/>quadratic));</highlight></codeline>
<codeline lineno="75"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}<sp/></highlight><highlight class="keywordflow">else</highlight><highlight class="normal"><sp/>{</highlight></codeline>
<codeline lineno="76"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>q<sp/>=<sp/>-0.5<sp/>*<sp/>(linear<sp/>+<sp/>std::copysign(square_root,<sp/>linear));</highlight></codeline>
<codeline lineno="77"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>append_unit_interval_root(critical_points,<sp/>count,<sp/>q<sp/>/<sp/>quadratic);</highlight></codeline>
<codeline lineno="78"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>append_unit_interval_root(critical_points,<sp/>count,<sp/>constant<sp/>/<sp/>q);</highlight></codeline>
<codeline lineno="79"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="80"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="81"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="82"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>std::sort(critical_points.begin(),<sp/>critical_points.begin()<sp/>+<sp/>count);</highlight></codeline>
<codeline lineno="83"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>count;</highlight></codeline>
<codeline lineno="84"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="85"><highlight class="normal"></highlight></codeline>
<codeline lineno="87"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>[[nodiscard]]<sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>bisect_first_nonpositive_value(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a62740f4edaed2df52e6d246b78844c1b" kindref="member">DeterminantPolynomial</ref>&amp;<sp/>coefficients,<sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>lower,<sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>upper)<sp/></highlight><highlight class="keyword">noexcept</highlight><highlight class="normal"><sp/>{</highlight></codeline>
<codeline lineno="88"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">for</highlight><highlight class="normal"><sp/>(</highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>iteration<sp/>=<sp/>0;<sp/>iteration<sp/>&lt;<sp/>80;<sp/>++iteration)<sp/>{</highlight></codeline>
<codeline lineno="89"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>middle<sp/>=<sp/>std::midpoint(lower,<sp/>upper);</highlight></codeline>
<codeline lineno="90"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(<ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a0bbe38cc124a51e394c9648d812e2ba4" kindref="member">evaluate_polynomial</ref>(coefficients,<sp/>middle)<sp/>&gt;<sp/>0.0)<sp/>{</highlight></codeline>
<codeline lineno="91"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>lower<sp/>=<sp/>middle;</highlight></codeline>
<codeline lineno="92"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}<sp/></highlight><highlight class="keywordflow">else</highlight><highlight class="normal"><sp/>{</highlight></codeline>
<codeline lineno="93"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>upper<sp/>=<sp/>middle;</highlight></codeline>
<codeline lineno="94"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="95"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="96"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>upper;</highlight></codeline>
<codeline lineno="97"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="98"><highlight class="normal"><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="99"><highlight class="normal"></highlight></codeline>
<codeline lineno="100"><highlight class="normal"><sp/><sp/><sp/><sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a62740f4edaed2df52e6d246b78844c1b" kindref="member">DeterminantPolynomial</ref><sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a49a9b973cf176686251d822aa17eed98" kindref="member">determinant_polynomial</ref>(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a757a7054052d6c66e85a186de62f6e37" kindref="member">JacobianEntries</ref>&amp;<sp/>base,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a757a7054052d6c66e85a186de62f6e37" kindref="member">JacobianEntries</ref>&amp;<sp/>direction,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>dimension,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>maximum_step,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>determinant_floor)<sp/></highlight><highlight class="keyword">noexcept</highlight><highlight class="normal"><sp/>{</highlight></codeline>
<codeline lineno="101"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a62740f4edaed2df52e6d246b78844c1b" kindref="member">DeterminantPolynomial</ref><sp/>coefficients{};</highlight></codeline>
<codeline lineno="102"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">unsigned</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>term_count<sp/>=<sp/>1U<sp/>&lt;&lt;<sp/></highlight><highlight class="keyword">static_cast&lt;</highlight><highlight class="keywordtype">unsigned</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="keyword">&gt;</highlight><highlight class="normal">(dimension);</highlight></codeline>
<codeline lineno="103"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">for</highlight><highlight class="normal"><sp/>(</highlight><highlight class="keywordtype">unsigned</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>mask<sp/>=<sp/>0;<sp/>mask<sp/>&lt;<sp/>term_count;<sp/>++mask)<sp/>{</highlight></codeline>
<codeline lineno="104"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>coefficients[std::popcount(mask)]<sp/>+=<sp/>selected_column_determinant(base,<sp/>direction,<sp/>mask,<sp/>dimension,<sp/>maximum_step);</highlight></codeline>
<codeline lineno="105"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="106"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>coefficients[0]<sp/>-=<sp/>determinant_floor;</highlight></codeline>
<codeline lineno="107"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>coefficients;</highlight></codeline>
<codeline lineno="108"><highlight class="normal"><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="109"><highlight class="normal"></highlight></codeline>
<codeline lineno="110"><highlight class="normal"><sp/><sp/><sp/><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a0bbe38cc124a51e394c9648d812e2ba4" kindref="member">evaluate_polynomial</ref>(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a62740f4edaed2df52e6d246b78844c1b" kindref="member">DeterminantPolynomial</ref>&amp;<sp/>coefficients,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>parameter)<sp/></highlight><highlight class="keyword">noexcept</highlight><highlight class="normal"><sp/>{</highlight></codeline>
<codeline lineno="111"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::fma(parameter,<sp/>std::fma(parameter,<sp/>std::fma(parameter,<sp/>coefficients[3],<sp/>coefficients[2]),<sp/>coefficients[1]),<sp/>coefficients[0]);</highlight></codeline>
<codeline lineno="112"><highlight class="normal"><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="113"><highlight class="normal"></highlight></codeline>
<codeline lineno="114"><highlight class="normal"><sp/><sp/><sp/><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a6d17541b413cd2f01996f32693c7396b" kindref="member">first_boundary_parameter</ref>(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a62740f4edaed2df52e6d246b78844c1b" kindref="member">DeterminantPolynomial</ref>&amp;<sp/>input_coefficients)<sp/></highlight><highlight class="keyword">noexcept</highlight><highlight class="normal"><sp/>{</highlight></codeline>
<codeline lineno="115"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="comment">//<sp/>Scaling<sp/>leaves<sp/>roots<sp/>and<sp/>the<sp/>relative<sp/>tolerances<sp/>unchanged,<sp/>and<sp/>prevents<sp/>overflow<sp/>in<sp/>the<sp/>cubic<sp/>discriminant.</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="116"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>scale<sp/>=<sp/>0.0;</highlight></codeline>
<codeline lineno="117"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">for</highlight><highlight class="normal"><sp/>(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>coefficient<sp/>:<sp/>input_coefficients)<sp/>{</highlight></codeline>
<codeline lineno="118"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>scale<sp/>=<sp/>std::max(scale,<sp/>std::abs(coefficient));</highlight></codeline>
<codeline lineno="119"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="120"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a62740f4edaed2df52e6d246b78844c1b" kindref="member">DeterminantPolynomial</ref><sp/>coefficients{};</highlight></codeline>
<codeline lineno="121"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">for</highlight><highlight class="normal"><sp/>(std::size_t<sp/>index<sp/>=<sp/>0;<sp/><ref refid="namespaceserif_1_1operators_1_1backend_1_1mfem_1ab297c6eedd8df878b6af2135b05e4616" kindref="member">index</ref><sp/>&lt;<sp/>coefficients.size();<sp/>++<ref refid="namespaceserif_1_1operators_1_1backend_1_1mfem_1ab297c6eedd8df878b6af2135b05e4616" kindref="member">index</ref>)<sp/>{</highlight></codeline>
<codeline lineno="122"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>coefficients[<ref refid="namespaceserif_1_1operators_1_1backend_1_1mfem_1ab297c6eedd8df878b6af2135b05e4616" kindref="member">index</ref>]<sp/>=<sp/>input_coefficients[<ref refid="namespaceserif_1_1operators_1_1backend_1_1mfem_1ab297c6eedd8df878b6af2135b05e4616" kindref="member">index</ref>]<sp/>/<sp/>scale;</highlight></codeline>
<codeline lineno="123"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="124"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>degree<sp/>=<sp/>polynomial_degree(coefficients);</highlight></codeline>
<codeline lineno="125"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(degree<sp/>==<sp/>0)<sp/>{</highlight></codeline>
<codeline lineno="126"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::numeric_limits&lt;double&gt;::infinity();</highlight></codeline>
<codeline lineno="127"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="128"><highlight class="normal"></highlight></codeline>
<codeline lineno="129"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>coefficient_scale<sp/>=<sp/>0.0;</highlight></codeline>
<codeline lineno="130"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">for</highlight><highlight class="normal"><sp/>(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>coefficient<sp/>:<sp/>coefficients)<sp/>{</highlight></codeline>
<codeline lineno="131"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>coefficient_scale<sp/>+=<sp/>std::abs(coefficient);</highlight></codeline>
<codeline lineno="132"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="133"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>value_tolerance<sp/>=<sp/>128.0<sp/>*<sp/>std::numeric_limits&lt;double&gt;::epsilon()<sp/>*<sp/>coefficient_scale;</highlight></codeline>
<codeline lineno="134"><highlight class="normal"></highlight></codeline>
<codeline lineno="135"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>std::array&lt;double,<sp/>2&gt;<sp/>critical_points{};</highlight></codeline>
<codeline lineno="136"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>critical_point_count<sp/>=<sp/>derivative_critical_points(coefficients,<sp/>degree,<sp/>critical_points);</highlight></codeline>
<codeline lineno="137"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>std::array&lt;double,<sp/>4&gt;<sp/>interval_ends{};</highlight></codeline>
<codeline lineno="138"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">for</highlight><highlight class="normal"><sp/>(</highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>index<sp/>=<sp/>0;<sp/><ref refid="namespaceserif_1_1operators_1_1backend_1_1mfem_1ab297c6eedd8df878b6af2135b05e4616" kindref="member">index</ref><sp/>&lt;<sp/>critical_point_count;<sp/>++<ref refid="namespaceserif_1_1operators_1_1backend_1_1mfem_1ab297c6eedd8df878b6af2135b05e4616" kindref="member">index</ref>)<sp/>{</highlight></codeline>
<codeline lineno="139"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>interval_ends[<ref refid="namespaceserif_1_1operators_1_1backend_1_1mfem_1ab297c6eedd8df878b6af2135b05e4616" kindref="member">index</ref><sp/>+<sp/>1]<sp/>=<sp/>critical_points[<ref refid="namespaceserif_1_1operators_1_1backend_1_1mfem_1ab297c6eedd8df878b6af2135b05e4616" kindref="member">index</ref>];</highlight></codeline>
<codeline lineno="140"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="141"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>interval_ends[critical_point_count<sp/>+<sp/>1]<sp/>=<sp/>1.0;</highlight></codeline>
<codeline lineno="142"><highlight class="normal"></highlight></codeline>
<codeline lineno="143"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">for</highlight><highlight class="normal"><sp/>(</highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>interval<sp/>=<sp/>0;<sp/>interval<sp/>&lt;=<sp/>critical_point_count;<sp/>++interval)<sp/>{</highlight></codeline>
<codeline lineno="144"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>lower<sp/>=<sp/>interval_ends[interval];</highlight></codeline>
<codeline lineno="145"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>upper<sp/>=<sp/>interval_ends[interval<sp/>+<sp/>1];</highlight></codeline>
<codeline lineno="146"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>upper_value<sp/>=<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a0bbe38cc124a51e394c9648d812e2ba4" kindref="member">evaluate_polynomial</ref>(coefficients,<sp/>upper);</highlight></codeline>
<codeline lineno="147"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(upper_value<sp/>&lt;=<sp/>0.0)<sp/>{</highlight></codeline>
<codeline lineno="148"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>bisect_first_nonpositive_value(coefficients,<sp/>lower,<sp/>upper);</highlight></codeline>
<codeline lineno="149"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="150"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(upper_value<sp/>&lt;=<sp/>value_tolerance)<sp/>{</highlight></codeline>
<codeline lineno="151"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="comment">//<sp/>A<sp/>tangent<sp/>zero<sp/>may<sp/>evaluate<sp/>a<sp/>few<sp/>ulps<sp/>above<sp/>zero<sp/>at<sp/>its<sp/>derivative<sp/>root.</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="152"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>upper;</highlight></codeline>
<codeline lineno="153"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="154"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="155"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::numeric_limits&lt;double&gt;::infinity();</highlight></codeline>
<codeline lineno="156"><highlight class="normal"><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="157"><highlight class="normal">}</highlight></codeline>
    </programlisting>
    <location file="src/lib/serif/geometry/deformation/determinant_polynomial.cpp"/>
  </compounddef>
</doxygen>