a00109.html

This library defines basic operation on polynomials, and contains also 3 different roots (zeroes)-fi

<a name="l00772"></a>00772 
<a name="l00788"></a>00788 <span class="keyword">template</span> &lt;<span class="keyword">class</span> T&gt;
<a name="l00789"></a><a class="code" href="a00102.html#g4db05aa06bba6b0f29a0c2608a479ec1">00789</a> <span class="keywordtype">void</span> <a class="code" href="a00102.html#g4db05aa06bba6b0f29a0c2608a479ec1">mul</a>(Polynomial&lt;T&gt;&amp; r, <span class="keyword">const</span> T&amp; s, <span class="keyword">const</span> Polynomial&lt;T&gt;&amp; p) {
<a name="l00790"></a>00790     <span class="keywordflow">if</span> (s != T(1)) {
<a name="l00791"></a>00791         r.resize(p.<a class="code" href="a00090.html#b433e0edb11b32a205a9d07b89aefa8f">degree</a>() + 1);
<a name="l00792"></a>00792         <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> i = 0; i &lt; r.size(); ++i)
<a name="l00793"></a>00793             r[i] = s * p[i];
<a name="l00794"></a>00794     }
<a name="l00795"></a>00795 }
<a name="l00796"></a>00796 
<a name="l00810"></a>00810 template &lt;class T&gt;
<a name="l00811"></a><a class="code" href="a00102.html#gf48dda52aab572b59dde062a043240cf">00811</a> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="a00102.html#g4db05aa06bba6b0f29a0c2608a479ec1">mul</a>(Polynomial&lt;T&gt;&amp; p, <span class="keyword">const</span> T&amp; s) {
<a name="l00812"></a>00812     <a class="code" href="a00102.html#g4db05aa06bba6b0f29a0c2608a479ec1">mul</a>(p, s, p);
<a name="l00813"></a>00813 }
<a name="l00814"></a>00814 
<a name="l00829"></a>00829 <span class="keyword">template</span> &lt;<span class="keyword">class</span> T&gt;
<a name="l00830"></a><a class="code" href="a00102.html#g8e86f42915089a8d20b048f38adaa283">00830</a> <span class="keywordtype">void</span> <a class="code" href="a00102.html#g4db05aa06bba6b0f29a0c2608a479ec1">mul</a>(Polynomial&lt;T&gt;&amp; r, <span class="keyword">const</span> Polynomial&lt;T&gt;&amp; p, <span class="keyword">const</span> Polynomial&lt;T&gt;&amp; q) {
<a name="l00831"></a>00831     <span class="keywordtype">int</span> na = p.<a class="code" href="a00090.html#b433e0edb11b32a205a9d07b89aefa8f">degree</a>();
<a name="l00832"></a>00832     <span class="keywordtype">int</span> nb = q.<a class="code" href="a00090.html#b433e0edb11b32a205a9d07b89aefa8f">degree</a>();
<a name="l00833"></a>00833     r.resize(na + nb + 1);
<a name="l00834"></a>00834     std::fill(&amp;r[0], &amp;r[r.size()], T(0));
<a name="l00835"></a>00835     <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt;= na; ++i)
<a name="l00836"></a>00836         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt;= nb; ++j)
<a name="l00837"></a>00837             r[i + j] += p[i] * q[j];
<a name="l00838"></a>00838 }
<a name="l00839"></a>00839 
<a name="l00859"></a>00859 <span class="keyword">template</span>&lt;<span class="keyword">class</span> T, <span class="keyword">class</span> U&gt;
<a name="l00860"></a><a class="code" href="a00101.html#gc5161c8ecd75b0108d0ea60c92d30d21">00860</a> U <a class="code" href="a00090.html#a845bf5cc0f93217a7c7f403a0bc9d38">eval</a>(<span class="keyword">const</span> Polynomial&lt;T&gt;&amp; p, <span class="keyword">const</span> U&amp; x) {
<a name="l00861"></a>00861     <span class="keywordflow">if</span> (x == U(0)) 
<a name="l00862"></a>00862         <span class="keywordflow">return</span> p[0];
<a name="l00863"></a>00863     <span class="keywordflow">else</span> {
<a name="l00864"></a>00864         <span class="keywordtype">int</span> i, m = p.<a class="code" href="a00090.html#b433e0edb11b32a205a9d07b89aefa8f">degree</a>();
<a name="l00865"></a>00865         <span class="keyword">register</span> U px = p[m];
<a name="l00866"></a>00866         <span class="keywordflow">for</span> (i = m - 1; i &gt;= 0; --i) {
<a name="l00867"></a>00867             px *= x;
<a name="l00868"></a>00868             px += p[i];
<a name="l00869"></a>00869         }
<a name="l00870"></a>00870         <span class="keywordflow">return</span> px;
<a name="l00871"></a>00871     }
<a name="l00872"></a>00872 }
<a name="l00873"></a>00873 
<a name="l00895"></a>00895 <span class="keyword">template</span>&lt;<span class="keyword">class</span> T, <span class="keyword">class</span> U, <span class="keyword">class</span> V&gt;
<a name="l00896"></a><a class="code" href="a00101.html#g06acec12b7f66f68ea3db5838ac7e072">00896</a> U <a class="code" href="a00090.html#a845bf5cc0f93217a7c7f403a0bc9d38">eval</a>(<span class="keyword">const</span> Polynomial&lt;T&gt;&amp; p, <span class="keyword">const</span> U&amp; x, V&amp; e) {
<a name="l00897"></a>00897     <span class="keyword">static</span> FloatSpecs&lt;V&gt; fpSpecs;
<a name="l00898"></a>00898     <span class="keywordflow">if</span> (x == U(0)) {
<a name="l00899"></a>00899         e = V(0);
<a name="l00900"></a>00900         <span class="keywordflow">return</span> p[0];
<a name="l00901"></a>00901     }
<a name="l00902"></a>00902     <span class="keywordflow">else</span> {
<a name="l00903"></a>00903         <span class="keywordtype">int</span> i, m = p.<a class="code" href="a00090.html#b433e0edb11b32a205a9d07b89aefa8f">degree</a>();
<a name="l00904"></a>00904         <span class="keywordflow">if</span> (m &gt;= 1) {
<a name="l00905"></a>00905             U px = p[m];
<a name="l00906"></a>00906             V mx, mpx;
<a name="l00907"></a>00907             mx = abs(x);
<a name="l00908"></a>00908             e = (abs(px) * fpSpecs.<a class="code" href="a00089.html#97e449a72a34fb15bd9a60055852130e">MRE</a>) / (fpSpecs.<a class="code" href="a00089.html#6cf389757399a3d8def3269f8d1f7e81">ARE</a> + fpSpecs.<a class="code" href="a00089.html#97e449a72a34fb15bd9a60055852130e">MRE</a>);
<a name="l00909"></a>00909             <span class="keywordflow">for</span> (i = m - 1; i &gt;= 0; --i) {
<a name="l00910"></a>00910                 px *= x;
<a name="l00911"></a>00911                 px += p[i];
<a name="l00912"></a>00912                 <span class="comment">//px = (px * x) + p[i];</span>
<a name="l00913"></a>00913                 mpx = abs(px);
<a name="l00914"></a>00914                 e = (mx * e) + mpx;
<a name="l00915"></a>00915             }
<a name="l00916"></a>00916             e = (e * (fpSpecs.<a class="code" href="a00089.html#6cf389757399a3d8def3269f8d1f7e81">ARE</a> + fpSpecs.<a class="code" href="a00089.html#97e449a72a34fb15bd9a60055852130e">MRE</a>)) - (mpx * fpSpecs.<a class="code" href="a00089.html#97e449a72a34fb15bd9a60055852130e">MRE</a>);
<a name="l00917"></a>00917             <span class="keywordflow">return</span> px;
<a name="l00918"></a>00918         }
<a name="l00919"></a>00919         <span class="keywordflow">else</span> {
<a name="l00920"></a>00920             e = V(0);
<a name="l00921"></a>00921             <span class="keywordflow">return</span> p[0];
<a name="l00922"></a>00922         }
<a name="l00923"></a>00923     }
<a name="l00924"></a>00924 }
<a name="l00925"></a>00925 
<a name="l00953"></a>00953 <span class="keyword">template</span>&lt;<span class="keyword">class</span> T, <span class="keyword">class</span> U&gt;
<a name="l00954"></a><a class="code" href="a00101.html#g0a6fc89686a91e3c8c99923a7b0247e3">00954</a> U <a class="code" href="a00090.html#4dc10e1190f7f71f0d04e9871c1d7a2f">evalAndDeflate</a>(<span class="keyword">const</span> Polynomial&lt;T&gt;&amp; p, <span class="keyword">const</span> U&amp; a, Polynomial&lt;U&gt;&amp; q) {
<a name="l00955"></a>00955     <span class="keywordtype">int</span> i, m = p.<a class="code" href="a00090.html#b433e0edb11b32a205a9d07b89aefa8f">degree</a>();
<a name="l00956"></a>00956     <span class="keywordflow">if</span> (m &gt; 0) {
<a name="l00957"></a>00957         q.resize(m);
<a name="l00958"></a>00958         <span class="keywordflow">if</span> (a == T(0)) {
<a name="l00959"></a>00959             std::copy(&amp;p[1], &amp;p[m + 1], &amp;q[0]);
<a name="l00960"></a>00960             <span class="keywordflow">return</span> p[0];
<a name="l00961"></a>00961         }
<a name="l00962"></a>00962         <span class="keywordflow">else</span> {
<a name="l00963"></a>00963             U pa;
<a name="l00964"></a>00964             pa = p[m];
<a name="l00965"></a>00965             <span class="keywordflow">for</span> (i = m - 1; i &gt;= 0; --i) {
<a name="l00966"></a>00966                 q[i] = pa;
<a name="l00967"></a>00967                 pa *= a;
<a name="l00968"></a>00968                 pa += p[i];
<a name="l00969"></a>00969                 <span class="comment">//pa = (pa * a) + p[i];</span>
<a name="l00970"></a>00970             }
<a name="l00971"></a>00971             <span class="keywordflow">return</span> pa;
<a name="l00972"></a>00972         }
<a name="l00973"></a>00973     }
<a name="l00974"></a>00974     <span class="keywordflow">else</span> {
<a name="l00975"></a>00975         q.resize(1);
<a name="l00976"></a>00976         q[0] = 0;
<a name="l00977"></a>00977         <span class="keywordflow">return</span> p[0];
<a name="l00978"></a>00978     }
<a name="l00979"></a>00979 }
<a name="l00980"></a>00980 
<a name="l01010"></a>01010 <span class="keyword">template</span>&lt;<span class="keyword">class</span> T, <span class="keyword">class</span> U, <span class="keyword">class</span> V&gt;
<a name="l01011"></a><a class="code" href="a00101.html#g2fe3a1cb7b5ae7739c3f228758d9f1fd">01011</a> U <a class="code" href="a00090.html#4dc10e1190f7f71f0d04e9871c1d7a2f">evalAndDeflate</a>(<span class="keyword">const</span> Polynomial&lt;T&gt;&amp; p, <span class="keyword">const</span> U&amp; a, Polynomial&lt;U&gt;&amp; q, V&amp; e) {
<a name="l01012"></a>01012     <span class="keyword">static</span> FloatSpecs&lt;V&gt; fpSpecs;
<a name="l01013"></a>01013     <span class="keywordtype">int</span> i, m = p.<a class="code" href="a00090.html#b433e0edb11b32a205a9d07b89aefa8f">degree</a>();
<a name="l01014"></a>01014     <span class="keywordflow">if</span> (m &gt; 0) {
<a name="l01015"></a>01015         q.resize(m);
<a name="l01016"></a>01016         <span class="keywordflow">if</span> (a == T(0)) {
<a name="l01017"></a>01017             e = 0;
<a name="l01018"></a>01018             std::copy(&amp;p[1], &amp;p[m + 1], &amp;q[0]);
<a name="l01019"></a>01019             <span class="keywordflow">return</span> p[0];
<a name="l01020"></a>01020         }
<a name="l01021"></a>01021         <span class="keywordflow">else</span> {
<a name="l01022"></a>01022             U pa;
<a name="l01023"></a>01023             V mx, mpa;
<a name="l01024"></a>01024             pa = p[m];
<a name="l01025"></a>01025             mx = abs(a);
<a name="l01026"></a>01026             e = (abs(pa) * fpSpecs.<a class="code" href="a00089.html#97e449a72a34fb15bd9a60055852130e">MRE</a>) / (fpSpecs.<a class="code" href="a00089.html#6cf389757399a3d8def3269f8d1f7e81">ARE</a> + fpSpecs.<a class="code" href="a00089.html#97e449a72a34fb15bd9a60055852130e">MRE</a>);
<a name="l01027"></a>01027             <span class="keywordflow">for</span> (i = m - 1; i &gt;= 0; --i) {
<a name="l01028"></a>01028                 q[i] = pa;
<a name="l01029"></a>01029                 pa *= a;
<a name="l01030"></a>01030                 pa += p[i];
<a name="l01031"></a>01031                 mpa = abs(pa);
<a name="l01032"></a>01032                 e = (mx * e) + mpa;
<a name="l01033"></a>01033             }
<a name="l01034"></a>01034             e = (e * (fpSpecs.<a class="code" href="a00089.html#6cf389757399a3d8def3269f8d1f7e81">ARE</a> + fpSpecs.<a class="code" href="a00089.html#97e449a72a34fb15bd9a60055852130e">MRE</a>)) - (mpa * fpSpecs.<a class="code" href="a00089.html#97e449a72a34fb15bd9a60055852130e">MRE</a>);
<a name="l01035"></a>01035             <span class="keywordflow">return</span> pa;
<a name="l01036"></a>01036         }
<a name="l01037"></a>01037     }
<a name="l01038"></a>01038     <span class="keywordflow">else</span> {
<a name="l01039"></a>01039         e = 0;
<a name="l01040"></a>01040         q.resize(1);
<a name="l01041"></a>01041         q[0] = 0;
<a name="l01042"></a>01042         <span class="keywordflow">return</span> p[0];
<a name="l01043"></a>01043     }
<a name="l01044"></a>01044 }
<a name="l01045"></a>01045 
<a name="l01062"></a>01062 <span class="keyword">template</span> &lt;<span class="keyword">class</span> T, <span class="keyword">class</span> U&gt;
<a name="l01063"></a><a class="code" href="a00101.html#g1d2411f2d57ecde3c510c53390e4c611">01063</a> U <a class="code" href="a00101.html#g1d2411f2d57ecde3c510c53390e4c611">evalError</a>(<span class="keyword">const</span> Polynomial&lt;T&gt;&amp; p, <span class="keyword">const</span> U&amp; mx) {
<a name="l01064"></a>01064     <span class="keyword">static</span> FloatSpecs&lt;U&gt; fpSpecs;
<a name="l01065"></a>01065     T px;
<a name="l01066"></a>01066     U e, mpx;
<a name="l01067"></a>01067     <span class="keywordtype">int</span> m = p.<a class="code" href="a00090.html#b433e0edb11b32a205a9d07b89aefa8f">degree</a>();
<a name="l01068"></a>01068     px = p[m];
<a name="l01069"></a>01069     e = (abs(px) * fpSpecs.<a class="code" href="a00089.html#97e449a72a34fb15bd9a60055852130e">MRE</a>) / (fpSpecs.<a class="code" href="a00089.html#6cf389757399a3d8def3269f8d1f7e81">ARE</a> + fpSpecs.<a class="code" href="a00089.html#97e449a72a34fb15bd9a60055852130e">MRE</a>);
<a name="l01070"></a>01070     <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = m - 1; i &gt;= 0; --i) {
<a name="l01071"></a>01071         px *= mx;
<a name="l01072"></a>01072         px += p[i];
<a name="l01073"></a>01073         mpx = abs(px);
<a name="l01074"></a>01074         e = (mx * e) + mpx;
<a name="l01075"></a>01075     }
<a name="l01076"></a>01076     <span class="keywordflow">return</span> (e * (fpSpecs.<a class="code" href="a00089.html#6cf389757399a3d8def3269f8d1f7e81">ARE</a> + fpSpecs.<a class="code" href="a00089.html#97e449a72a34fb15bd9a60055852130e">MRE</a>)) - (mpx * fpSpecs.<a class="code" href="a00089.html#97e449a72a34fb15bd9a60055852130e">MRE</a>);
<a name="l01077"></a>01077 }
<a name="l01078"></a>01078 
<a name="l01094"></a>01094 template &lt;class T, class U&gt;
<a name="l01095"></a><a class="code" href="a00101.html#gc143079d7e07a2b902831ec539e45fc6">01095</a> U <a class="code" href="a00090.html#3035df8b06fcc5015efb56762fc68f93">evalAndDerive</a>(<span class="keyword">const</span> Polynomial&lt;T&gt;&amp; p, <span class="keyword">const</span> U&amp; x, U&amp; ppx) {
<a name="l01096"></a>01096     <span class="keywordtype">int</span> m = p.degree();
<a name="l01097"></a>01097     <span class="keywordflow">if</span> (m &gt;= 1) {