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<div class="headertitle"><div class="title">fibonacci_formula.c File Reference</div></div>
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<p>Finding Fibonacci number of any <code>n</code> number using [Binet's closed form formula](<a href="https://en.wikipedia.org/wiki/Fibonacci_number#Binet's_formula">https://en.wikipedia.org/wiki/Fibonacci_number#Binet's_formula</a>) compute \(f_{nth}\) Fibonacci number using the binet's formula: Fn = 1√5 * (1+√5 / 2)^n+1 − 1√5 * (1−√5 / 2)^n+1.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;math.h&gt;</code><br />
<code>#include &lt;stdio.h&gt;</code><br />
<code>#include &lt;assert.h&gt;</code><br />
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Include dependency graph for fibonacci_formula.c:</div>
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Functions</h2></td></tr>
<tr class="memitem:a4d369ae048e0ccc7f515a243533cd946"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946">fib</a> (unsigned int n)</td></tr>
<tr class="memdesc:a4d369ae048e0ccc7f515a243533cd946"><td class="mdescLeft">&#160;</td><td class="mdescRight">for pow and sqrt for printf for assert <a href="../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946">More...</a><br /></td></tr>
<tr class="separator:a4d369ae048e0ccc7f515a243533cd946"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d75/fibonacci__formula_8c.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <a href="../../d8/d75/fibonacci__formula_8c.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
<tr class="separator:aa8dca7b867074164d5f45b0f3851269d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d75/fibonacci__formula_8c.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d8/d75/fibonacci__formula_8c.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Finding Fibonacci number of any <code>n</code> number using [Binet's closed form formula](<a href="https://en.wikipedia.org/wiki/Fibonacci_number#Binet's_formula">https://en.wikipedia.org/wiki/Fibonacci_number#Binet's_formula</a>) compute \(f_{nth}\) Fibonacci number using the binet's formula: Fn = 1√5 * (1+√5 / 2)^n+1 − 1√5 * (1−√5 / 2)^n+1. </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/GrandSir/" target="_blank">GrandSir</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a4d369ae048e0ccc7f515a243533cd946" name="a4d369ae048e0ccc7f515a243533cd946"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a4d369ae048e0ccc7f515a243533cd946">&#9670;&#160;</a></span>fib()</h2>
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<td class="memname">int fib </td>
<td>(</td>
<td class="paramtype">unsigned int&#160;</td>
<td class="paramname"><em>n</em></td><td>)</td>
<td></td>
</tr>
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<p>for pow and sqrt for printf for assert </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>index of number in Fibonacci sequence </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>nth value of fibonacci sequence for all n &gt;= 0 </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 17</span> {</div>
<div class="line"><span class="lineno"> 18</span> <span class="keywordtype">float</span> seq = (1 / sqrt(5) * pow(((1 + sqrt(5)) / 2), n + 1)) - (1 / sqrt(5) * pow(((1 - sqrt(5)) / 2), n + 1));</div>
<div class="line"><span class="lineno"> 19</span> </div>
<div class="line"><span class="lineno"> 20</span> <span class="comment">// removing unnecessary fractional part by implicitly converting float to int</span></div>
<div class="line"><span class="lineno"> 21</span> <span class="keywordflow">return</span> seq;</div>
<div class="line"><span class="lineno"> 22</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">void&#160;</td>
<td class="paramname"></td><td>)</td>
<td></td>
</tr>
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</div><div class="memdoc">
<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 52</span> {</div>
<div class="line"><span class="lineno"> 53</span> <a class="code hl_function" href="../../d8/d75/fibonacci__formula_8c.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 54</span> </div>
<div class="line"><span class="lineno"> 55</span> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = 0; i &lt;= 10; i++){</div>
<div class="line"><span class="lineno"> 56</span> printf(<span class="stringliteral">&quot;%d. fibonacci number is: %d\n&quot;</span>, i, <a class="code hl_function" href="../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946">fib</a>(i));</div>
<div class="line"><span class="lineno"> 57</span> }</div>
<div class="line"><span class="lineno"> 58</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 59</span>}</div>
<div class="ttc" id="afibonacci__formula_8c_html_a4d369ae048e0ccc7f515a243533cd946"><div class="ttname"><a href="../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946">fib</a></div><div class="ttdeci">int fib(unsigned int n)</div><div class="ttdoc">for pow and sqrt for printf for assert</div><div class="ttdef"><b>Definition:</b> fibonacci_formula.c:17</div></div>
<div class="ttc" id="afibonacci__formula_8c_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d8/d75/fibonacci__formula_8c.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition:</b> fibonacci_formula.c:28</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</a></span>test()</h2>
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<td class="memname">static void test </td>
<td>(</td>
<td class="paramtype">void&#160;</td>
<td class="paramname"></td><td>)</td>
<td></td>
</tr>
</table>
</td>
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<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 28</span> {</div>
<div class="line"><span class="lineno"> 29</span> <span class="comment">/* this ensures that the first 10 number of fibonacci sequence</span></div>
<div class="line"><span class="lineno"> 30</span><span class="comment"> * (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89)</span></div>
<div class="line"><span class="lineno"> 31</span><span class="comment"> * matches with algorithm</span></div>
<div class="line"><span class="lineno"> 32</span><span class="comment"> */</span></div>
<div class="line"><span class="lineno"> 33</span> assert(<a class="code hl_function" href="../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946">fib</a>(0) == 1);</div>
<div class="line"><span class="lineno"> 34</span> assert(<a class="code hl_function" href="../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946">fib</a>(1) == 1);</div>
<div class="line"><span class="lineno"> 35</span> assert(<a class="code hl_function" href="../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946">fib</a>(2) == 2);</div>
<div class="line"><span class="lineno"> 36</span> assert(<a class="code hl_function" href="../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946">fib</a>(3) == 3);</div>
<div class="line"><span class="lineno"> 37</span> assert(<a class="code hl_function" href="../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946">fib</a>(4) == 5);</div>
<div class="line"><span class="lineno"> 38</span> assert(<a class="code hl_function" href="../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946">fib</a>(5) == 8);</div>
<div class="line"><span class="lineno"> 39</span> assert(<a class="code hl_function" href="../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946">fib</a>(6) == 13);</div>
<div class="line"><span class="lineno"> 40</span> assert(<a class="code hl_function" href="../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946">fib</a>(7) == 21);</div>
<div class="line"><span class="lineno"> 41</span> assert(<a class="code hl_function" href="../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946">fib</a>(8) == 34);</div>
<div class="line"><span class="lineno"> 42</span> assert(<a class="code hl_function" href="../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946">fib</a>(9) == 55);</div>
<div class="line"><span class="lineno"> 43</span> assert(<a class="code hl_function" href="../../d8/d75/fibonacci__formula_8c.html#a4d369ae048e0ccc7f515a243533cd946">fib</a>(10) == 89);</div>
<div class="line"><span class="lineno"> 44</span> </div>
<div class="line"><span class="lineno"> 45</span> printf(<span class="stringliteral">&quot;All tests have successfully passed!\n&quot;</span>);</div>
<div class="line"><span class="lineno"> 46</span>}</div>
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