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<div id="projectname">Algorithms_in_C++<span id="projectnumber"> 1.0.0</span>
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</div>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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@@ -93,8 +93,7 @@ $(document).ready(function(){initNavTree('d4/d32/fibonacci__fast_8cpp.html','../
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<div class="summary">
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<a href="#define-members">Macros</a> |
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<a href="#func-members">Functions</a> </div>
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<div class="headertitle">
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<div class="title">fibonacci_fast.cpp File Reference</div> </div>
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<div class="headertitle"><div class="title">fibonacci_fast.cpp File Reference</div></div>
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</div><!--header-->
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<div class="contents">
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@@ -110,12 +109,12 @@ Include dependency graph for fibonacci_fast.cpp:</div>
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</div>
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</div>
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</div><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="define-members"></a>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="define-members" name="define-members"></a>
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Macros</h2></td></tr>
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<tr class="memitem:a392fb874e547e582e9c66a08a1f23326"><td class="memItemLeft" align="right" valign="top">#define </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html#a392fb874e547e582e9c66a08a1f23326">MAX</a>   93</td></tr>
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<tr class="separator:a392fb874e547e582e9c66a08a1f23326"><td class="memSeparator" colspan="2"> </td></tr>
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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:a5712edca101204eca8accdb1e096707f"><td class="memItemLeft" align="right" valign="top">uint64_t </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html#a5712edca101204eca8accdb1e096707f">fib</a> (uint64_t n)</td></tr>
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<tr class="separator:a5712edca101204eca8accdb1e096707f"><td class="memSeparator" colspan="2"> </td></tr>
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@@ -123,12 +122,12 @@ Functions</h2></td></tr>
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<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><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>Faster computation of Fibonacci series. </p>
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<p>An efficient way to calculate nth fibonacci number faster and simpler than \(O(n\log n)\) method of matrix exponentiation This works by using both recursion and dynamic programming. as 93rd fibonacci exceeds 19 digits, which cannot be stored in a single long long variable, we can only use it till 92nd fibonacci we can use it for 10000th fibonacci etc, if we implement bigintegers. This algorithm works with the fact that nth fibonacci can easily found if we have already found n/2th or (n+1)/2th fibonacci It is a property of fibonacci similar to matrix exponentiation.</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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<div class="textblock"><p >Faster computation of Fibonacci series. </p>
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<p >An efficient way to calculate nth fibonacci number faster and simpler than \(O(n\log n)\) method of matrix exponentiation This works by using both recursion and dynamic programming. as 93rd fibonacci exceeds 19 digits, which cannot be stored in a single long long variable, we can only use it till 92nd fibonacci we can use it for 10000th fibonacci etc, if we implement bigintegers. This algorithm works with the fact that nth fibonacci can easily found if we have already found n/2th or (n+1)/2th fibonacci It is a property of fibonacci similar to matrix exponentiation.</p>
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<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
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<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../de/de4/fibonacci__large_8cpp.html" title="Computes N^th Fibonacci number given as input argument. Uses custom build arbitrary integers library ...">fibonacci_large.cpp</a>, <a class="el" href="../../d9/d89/fibonacci_8cpp.html" title="Generate fibonacci sequence.">fibonacci.cpp</a>, <a class="el" href="../../de/d47/string__fibonacci_8cpp.html" title="This Programme returns the Nth fibonacci as a string.">string_fibonacci.cpp</a> </dd></dl>
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</div><h2 class="groupheader">Macro Definition Documentation</h2>
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<a id="a392fb874e547e582e9c66a08a1f23326"></a>
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<a id="a392fb874e547e582e9c66a08a1f23326" name="a392fb874e547e582e9c66a08a1f23326"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a392fb874e547e582e9c66a08a1f23326">◆ </a></span>MAX</h2>
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<p>maximum number that can be computed - The result after 93 cannot be stored in a <code>uint64_t</code> data type. </p>
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<p >maximum number that can be computed - The result after 93 cannot be stored in a <code>uint64_t</code> data type. </p>
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</div>
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</div>
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<h2 class="groupheader">Function Documentation</h2>
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<a id="a5712edca101204eca8accdb1e096707f"></a>
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<a id="a5712edca101204eca8accdb1e096707f" name="a5712edca101204eca8accdb1e096707f"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a5712edca101204eca8accdb1e096707f">◆ </a></span>fib()</h2>
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@@ -159,31 +158,31 @@ Functions</h2></td></tr>
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<p>Algorithm </p>
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<div class="fragment"><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="keyword">static</span> uint64_t f1 = 1,</div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  f2 = 1; <span class="comment">// using static keyword will retain the values of</span></div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <span class="comment">// f1 and f2 for the next function call.</span></div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  </div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="keywordflow">if</span> (n <= 2)</div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keywordflow">return</span> f2;</div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="keywordflow">if</span> (n >= 93) {</div>
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||||
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a></div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  << <span class="stringliteral">"Cannot compute for n>93 due to limit of 64-bit integers\n"</span>;</div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  }</div>
|
||||
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  </div>
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||||
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  uint64_t temp = f2; <span class="comment">// we do not need temp to be static</span></div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  f2 += f1;</div>
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||||
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  f1 = temp;</div>
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||||
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  </div>
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||||
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <span class="keywordflow">return</span> f2;</div>
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||||
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> }</div>
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||||
<p >Algorithm </p>
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||||
<div class="fragment"><div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> {</div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> <span class="keyword">static</span> uint64_t f1 = 1,</div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> f2 = 1; <span class="comment">// using static keyword will retain the values of</span></div>
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||||
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <span class="comment">// f1 and f2 for the next function call.</span></div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> </div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="keywordflow">if</span> (n <= 2)</div>
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||||
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="keywordflow">return</span> f2;</div>
|
||||
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="keywordflow">if</span> (n >= 93) {</div>
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||||
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a></div>
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||||
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> << <span class="stringliteral">"Cannot compute for n>93 due to limit of 64-bit integers\n"</span>;</div>
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||||
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> }</div>
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||||
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> </div>
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||||
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> uint64_t temp = f2; <span class="comment">// we do not need temp to be static</span></div>
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||||
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> f2 += f1;</div>
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||||
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> f1 = temp;</div>
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||||
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> </div>
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||||
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="keywordflow">return</span> f2;</div>
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||||
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span>}</div>
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<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a></div></div>
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</div><!-- fragment -->
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">◆ </a></span>main()</h2>
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@@ -198,14 +197,14 @@ Functions</h2></td></tr>
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<p>Main function </p>
|
||||
<div class="fragment"><div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  {</div>
|
||||
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="comment">// Main Function</span></div>
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||||
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keywordflow">for</span> (uint64_t i = 1; i < 93; i++) {</div>
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||||
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << i << <span class="stringliteral">" th fibonacci number is "</span> << <a class="code" href="../../d4/d32/fibonacci__fast_8cpp.html#a5712edca101204eca8accdb1e096707f">fib</a>(i) << <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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||||
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  }</div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> }</div>
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||||
<p >Main function </p>
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||||
<div class="fragment"><div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> {</div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="comment">// Main Function</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keywordflow">for</span> (uint64_t i = 1; i < 93; i++) {</div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << i << <span class="stringliteral">" th fibonacci number is "</span> << <a class="code hl_function" href="../../d4/d32/fibonacci__fast_8cpp.html#a5712edca101204eca8accdb1e096707f">fib</a>(i) << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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||||
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> }</div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span>}</div>
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<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
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||||
<div class="ttc" id="afibonacci__fast_8cpp_html_a5712edca101204eca8accdb1e096707f"><div class="ttname"><a href="../../d4/d32/fibonacci__fast_8cpp.html#a5712edca101204eca8accdb1e096707f">fib</a></div><div class="ttdeci">uint64_t fib(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_fast.cpp:30</div></div>
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</div><!-- fragment --><div class="dynheader">
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<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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<ul>
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<li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html">fibonacci_fast.cpp</a></li>
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<li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.1 </li>
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Reference in New Issue
Block a user