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 <span id="projectnumber">1.0.0</span>
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<div id="projectbrief">Set of algorithms implemented in C.</div>
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<div class="title">fibonacci_fast.c File Reference</div> </div>
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<p>Compute \(m^{mth}\) Fibonacci number using the formulae:
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <locale.h></code><br />
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<code>#include <stdio.h></code><br />
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<code>#include <stdlib.h></code><br />
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</div><div class="textblock"><div class="dynheader">
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Include dependency graph for fibonacci_fast.c:</div>
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</div><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:a7a3d55bd19854075cba2eed6b63cb2d3"><td class="memItemLeft" align="right" valign="top">void </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>
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<tr class="memdesc:a7a3d55bd19854075cba2eed6b63cb2d3"><td class="mdescLeft"> </td><td class="mdescRight">Returns the \(n^{th}\) and \(n+1^{th}\) Fibonacci number. <a href="../../d4/d99/fibonacci__fast_8c.html#a7a3d55bd19854075cba2eed6b63cb2d3">More...</a><br /></td></tr>
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<tr class="separator:a7a3d55bd19854075cba2eed6b63cb2d3"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a0ddf1224851353fc92bfbff6f499fa97"><td class="memItemLeft" align="right" valign="top"><a id="a0ddf1224851353fc92bfbff6f499fa97"></a>
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int </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>
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<tr class="memdesc:a0ddf1224851353fc92bfbff6f499fa97"><td class="mdescLeft"> </td><td class="mdescRight">main function <br /></td></tr>
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<tr class="separator:a0ddf1224851353fc92bfbff6f499fa97"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>Compute \(m^{mth}\) Fibonacci number using the formulae: </p>
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<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> </dd></dl>
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<dl class="section date"><dt>Date</dt><dd>2 October, 2019 <p class="formulaDsp">
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\begin{eqnarray*} F_{2n-1} &=& F_n^2 + F_{n-1}^2 \\ F_{2n} &=& F_n\left(2F_{n-1} + F_n\right) \end{eqnarray*}
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</p>
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</dd></dl>
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</div><h2 class="groupheader">Function Documentation</h2>
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<a id="a7a3d55bd19854075cba2eed6b63cb2d3"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a7a3d55bd19854075cba2eed6b63cb2d3">◆ </a></span>fib()</h2>
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<div class="memitem">
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<div class="memproto">
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<td class="memname">void fib </td>
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<td>(</td>
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<td class="paramtype">unsigned long </td>
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<td class="paramname"><em>n</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">unsigned long * </td>
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<td class="paramname"><em>C</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">unsigned long * </td>
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<td class="paramname"><em>D</em> </td>
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</tr>
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>Returns the \(n^{th}\) and \(n+1^{th}\) Fibonacci number. </p>
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<p>The return variables are C & D respectively. </p>
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<div class="fragment"><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> {</div>
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<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  <span class="comment">// Out of Range checking</span></div>
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<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  <span class="keywordflow">if</span> (n < 0)</div>
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<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  {</div>
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<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  printf(<span class="stringliteral">"\nNo Such term !\n"</span>);</div>
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<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  exit(0);</div>
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<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  }</div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  </div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> a, b, c, d;</div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  </div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="keywordflow">if</span> (n == 0)</div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  {</div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  C[0] = 0;</div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keywordflow">if</span> (D)</div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  D[0] = 1;</div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keywordflow">return</span>;</div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  }</div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  </div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <a class="code" href="../../d4/d99/fibonacci__fast_8c.html#a7a3d55bd19854075cba2eed6b63cb2d3">fib</a>(n >> 1, &c, &d); <span class="comment">/* Compute F(n/2) */</span></div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  </div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  a = c * ((d << 1) - c);</div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  b = c * c + d * d;</div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="keywordflow">if</span> (n % 2 == 0) <span class="comment">/* If n is even */</span></div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  {</div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  C[0] = a;</div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="keywordflow">if</span> (D)</div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  D[0] = b;</div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="keywordflow">return</span>;</div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  }</div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment"></span> </div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment"> /**< If n is odd */</span></div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  C[0] = b;</div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keywordflow">if</span> (D)</div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  D[0] = a + b;</div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keywordflow">return</span>;</div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> }</div>
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<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">Returns the and Fibonacci number.</div><div class="ttdef"><b>Definition:</b> fibonacci_fast.c:20</div></div>
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