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<p>Compute \(m^{mth}\) Fibonacci number using the formulae:
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;locale.h&gt;</code><br />
<code>#include &lt;stdio.h&gt;</code><br />
<code>#include &lt;stdlib.h&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for fibonacci_fast.c:</div>
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Functions</h2></td></tr>
<tr class="memitem:a7a3d55bd19854075cba2eed6b63cb2d3"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d99/fibonacci__fast_8c.html#a7a3d55bd19854075cba2eed6b63cb2d3">fib</a> (unsigned long n, unsigned long *C, unsigned long *D)</td></tr>
<tr class="memdesc:a7a3d55bd19854075cba2eed6b63cb2d3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get the \(n^{th}\) and \(n+1^{th}\) Fibonacci number using recursive half-interval decimation. <a href="../../d4/d99/fibonacci__fast_8c.html#a7a3d55bd19854075cba2eed6b63cb2d3">More...</a><br /></td></tr>
<tr class="separator:a7a3d55bd19854075cba2eed6b63cb2d3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0ddf1224851353fc92bfbff6f499fa97"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d99/fibonacci__fast_8c.html#a0ddf1224851353fc92bfbff6f499fa97">main</a> (int argc, char *argv[])</td></tr>
<tr class="memdesc:a0ddf1224851353fc92bfbff6f499fa97"><td class="mdescLeft">&#160;</td><td class="mdescRight">main function <a href="../../d4/d99/fibonacci__fast_8c.html#a0ddf1224851353fc92bfbff6f499fa97">More...</a><br /></td></tr>
<tr class="separator:a0ddf1224851353fc92bfbff6f499fa97"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Compute \(m^{mth}\) Fibonacci number using the formulae: </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
<dl class="section date"><dt>Date</dt><dd>2 October, 2019 <p class="formulaDsp">
\begin{eqnarray*}
F_{2n-1} &amp;=&amp; F_n^2 + F_{n-1}^2 \\
F_{2n} &amp;=&amp; F_n\left(2F_{n-1} + F_n\right)
\end{eqnarray*}
</p>
</dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a7a3d55bd19854075cba2eed6b63cb2d3" name="a7a3d55bd19854075cba2eed6b63cb2d3"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a7a3d55bd19854075cba2eed6b63cb2d3">&#9670;&#160;</a></span>fib()</h2>
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<tr>
<td class="memname">void fib </td>
<td>(</td>
<td class="paramtype">unsigned long&#160;</td>
<td class="paramname"><em>n</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">unsigned long *&#160;</td>
<td class="paramname"><em>C</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">unsigned long *&#160;</td>
<td class="paramname"><em>D</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Get the \(n^{th}\) and \(n+1^{th}\) Fibonacci number using recursive half-interval decimation. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>index of Fibonacci number to get </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">C</td><td>left half interval value - end result here. Cannot be NULL </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">D</td><td>right half interval can be discarded at end and can be NULL </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><span class="lineno"> 24</span>{</div>
<div class="line"><span class="lineno"> 25</span> <span class="comment">// Out of Range checking</span></div>
<div class="line"><span class="lineno"> 26</span> <span class="comment">// commented out since `n` is unsigned integer</span></div>
<div class="line"><span class="lineno"> 27</span> <span class="comment">// if (n &lt; 0)</span></div>
<div class="line"><span class="lineno"> 28</span> <span class="comment">// {</span></div>
<div class="line"><span class="lineno"> 29</span> <span class="comment">// printf(&quot;\nNo Such term !\n&quot;);</span></div>
<div class="line"><span class="lineno"> 30</span> <span class="comment">// exit(0);</span></div>
<div class="line"><span class="lineno"> 31</span> <span class="comment">// }</span></div>
<div class="line"><span class="lineno"> 32</span> </div>
<div class="line"><span class="lineno"> 33</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> a, b, c, d;</div>
<div class="line"><span class="lineno"> 34</span> </div>
<div class="line"><span class="lineno"> 35</span> <span class="keywordflow">if</span> (n == 0)</div>
<div class="line"><span class="lineno"> 36</span> {</div>
<div class="line"><span class="lineno"> 37</span> C[0] = 0;</div>
<div class="line"><span class="lineno"> 38</span> <span class="keywordflow">if</span> (D) <span class="comment">/* if D is not NULL */</span></div>
<div class="line"><span class="lineno"> 39</span> D[0] = 1;</div>
<div class="line"><span class="lineno"> 40</span> <span class="keywordflow">return</span>;</div>
<div class="line"><span class="lineno"> 41</span> }</div>
<div class="line"><span class="lineno"> 42</span> </div>
<div class="line"><span class="lineno"> 43</span> <a class="code hl_function" href="../../d4/d99/fibonacci__fast_8c.html#a7a3d55bd19854075cba2eed6b63cb2d3">fib</a>(n &gt;&gt; 1, &amp;c, &amp;d); <span class="comment">/* Compute F(n/2) */</span></div>
<div class="line"><span class="lineno"> 44</span> </div>
<div class="line"><span class="lineno"> 45</span> a = c * ((d &lt;&lt; 1) - c);</div>
<div class="line"><span class="lineno"> 46</span> b = c * c + d * d;</div>
<div class="line"><span class="lineno"> 47</span> <span class="keywordflow">if</span> (n % 2 == 0) <span class="comment">/* If n is even */</span></div>
<div class="line"><span class="lineno"> 48</span> {</div>
<div class="line"><span class="lineno"> 49</span> C[0] = a;</div>
<div class="line"><span class="lineno"> 50</span> <span class="keywordflow">if</span> (D)</div>
<div class="line"><span class="lineno"> 51</span> D[0] = b;</div>
<div class="line"><span class="lineno"> 52</span> <span class="keywordflow">return</span>;</div>
<div class="line"><span class="lineno"> 53</span> }</div>
<div class="line"><span class="lineno"> 54</span><span class="comment"></span> </div>
<div class="line"><span class="lineno"> 55</span><span class="comment"> /**&lt; If n is odd */</span></div>
<div class="line"><span class="lineno"> 56</span> C[0] = b;</div>
<div class="line"><span class="lineno"> 57</span> <span class="keywordflow">if</span> (D) <span class="comment">/* if D is not NULL */</span></div>
<div class="line"><span class="lineno"> 58</span> D[0] = a + b;</div>
<div class="line"><span class="lineno"> 59</span> <span class="keywordflow">return</span>;</div>
<div class="line"><span class="lineno"> 60</span>}</div>
<div class="ttc" id="afibonacci__fast_8c_html_a7a3d55bd19854075cba2eed6b63cb2d3"><div class="ttname"><a href="../../d4/d99/fibonacci__fast_8c.html#a7a3d55bd19854075cba2eed6b63cb2d3">fib</a></div><div class="ttdeci">void fib(unsigned long n, unsigned long *C, unsigned long *D)</div><div class="ttdoc">Get the and Fibonacci number using recursive half-interval decimation.</div><div class="ttdef"><b>Definition:</b> fibonacci_fast.c:23</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a0ddf1224851353fc92bfbff6f499fa97">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>argc</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">char *&#160;</td>
<td class="paramname"><em>argv</em>[]&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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</div><div class="memdoc">
<p>main function </p>
<div class="fragment"><div class="line"><span class="lineno"> 66</span>{</div>
<div class="line"><span class="lineno"> 67</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> number, result;</div>
<div class="line"><span class="lineno"> 68</span> </div>
<div class="line"><span class="lineno"> 69</span> setlocale(LC_NUMERIC, <span class="stringliteral">&quot;&quot;</span>); <span class="comment">// format the printf output</span></div>
<div class="line"><span class="lineno"> 70</span> </div>
<div class="line"><span class="lineno"> 71</span> <span class="comment">// Asks for the number/position of term in Fibonnacci sequence</span></div>
<div class="line"><span class="lineno"> 72</span> <span class="keywordflow">if</span> (argc == 2)</div>
<div class="line"><span class="lineno"> 73</span> number = atoi(argv[1]);</div>
<div class="line"><span class="lineno"> 74</span> <span class="keywordflow">else</span></div>
<div class="line"><span class="lineno"> 75</span> {</div>
<div class="line"><span class="lineno"> 76</span> printf(<span class="stringliteral">&quot;Enter the value of n(n starts from 0 ): &quot;</span>);</div>
<div class="line"><span class="lineno"> 77</span> scanf(<span class="stringliteral">&quot;%lu&quot;</span>, &amp;number);</div>
<div class="line"><span class="lineno"> 78</span> }</div>
<div class="line"><span class="lineno"> 79</span> </div>
<div class="line"><span class="lineno"> 80</span> <a class="code hl_function" href="../../d4/d99/fibonacci__fast_8c.html#a7a3d55bd19854075cba2eed6b63cb2d3">fib</a>(number, &amp;result, NULL);</div>
<div class="line"><span class="lineno"> 81</span> </div>
<div class="line"><span class="lineno"> 82</span> printf(<span class="stringliteral">&quot;The nth term is : %&#39;lu \n&quot;</span>, result);</div>
<div class="line"><span class="lineno"> 83</span> </div>
<div class="line"><span class="lineno"> 84</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 85</span>}</div>
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