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<div class="headertitle"><div class="title">fibonacci_matrix_exponentiation.cpp File Reference</div></div>
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<p>This program computes the N^th Fibonacci number in modulo mod input argument .
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for fibonacci_matrix_exponentiation.cpp:</div>
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Functions</h2></td></tr>
<tr class="memitem:abc3bc08249058d57cfc8f54a29d9cf9f"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a> (uint64_t n, uint64_t mod)</td></tr>
<tr class="separator:abc3bc08249058d57cfc8f54a29d9cf9f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae1a3968e7947464bee7714f6d43b7002"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a> ()</td></tr>
<tr class="separator:ae1a3968e7947464bee7714f6d43b7002"><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="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >This program computes the N^th Fibonacci number in modulo mod input argument . </p>
<p >Takes O(logn) time to compute nth Fibonacci number</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/villayatali123" target="_blank">villayatali123</a> </dd>
<dd>
[unknown author]() </dd></dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d9/d89/fibonacci_8cpp.html" title="Generate fibonacci sequence.">fibonacci.cpp</a>, <a class="el" href="../../d4/d32/fibonacci__fast_8cpp.html" title="Faster computation of Fibonacci series.">fibonacci_fast.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>, <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> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="abc3bc08249058d57cfc8f54a29d9cf9f" name="abc3bc08249058d57cfc8f54a29d9cf9f"></a>
<h2 class="memtitle"><span class="permalink"><a href="#abc3bc08249058d57cfc8f54a29d9cf9f">&#9670;&nbsp;</a></span>fibo()</h2>
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<td class="memname">uint64_t fibo </td>
<td>(</td>
<td class="paramtype">uint64_t&#160;</td>
<td class="paramname"><em>n</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">uint64_t&#160;</td>
<td class="paramname"><em>mod</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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</div><div class="memdoc">
<p >This function finds nth fibonacci number in a given modulus </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>nth fibonacci number </td></tr>
<tr><td class="paramname">mod</td><td>modulo number </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span>{</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(2,0);</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint64_t&gt;</a>&gt; transition(2,<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>(2,0));</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint64_t&gt;</a>&gt; Identity(2,<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>(2,0));</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> n--;</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[0]=1, <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[1]=1;</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> Identity[0][0]=1; Identity[0][1]=0;</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> Identity[1][0]=0; Identity[1][1]=1;</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> </div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> transition[0][0]=0;</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> transition[1][0]=transition[1][1]=transition[0][1]=1;</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> </div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="keywordflow">while</span>(n)</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> {</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="keywordflow">if</span>(n%2)</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> {</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint64_t&gt;</a>&gt; res(2, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>(2,0));</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0;i&lt;2;i++)</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> {</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j=0;j&lt;2;j++)</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> {</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> k=0;<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>&lt;2;<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++)</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> {</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> res[i][j]=(res[i][j]%mod+((Identity[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>]%mod*transition[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>][j]%mod))%mod)%mod;</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> }</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> }</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> }</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0;i&lt;2;i++)</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> {</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j=0;j&lt;2;j++)</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> {</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> Identity[i][j]=res[i][j];</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> }</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> }</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> n--;</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> }</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordflow">else</span>{</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint64_t&gt;</a>&gt; res1(2, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>(2,0));</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0;i&lt;2;i++)</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> {</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j=0;j&lt;2;j++)</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> {</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> k=0;<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>&lt;2;<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++)</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> {</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> res1[i][j]=(res1[i][j]%mod+((transition[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>]%mod*transition[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>][j]%mod))%mod)%mod;</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> }</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> }</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> }</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=0;i&lt;2;i++)</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> {</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j=0;j&lt;2;j++)</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> {</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> transition[i][j]=res1[i][j];</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> }</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> } </div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> n=n/2;</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> }</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> }</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keywordflow">return</span> ((result[0]%mod*Identity[0][0]%mod)%mod+(<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[1]%mod*Identity[1][0]%mod)%mod)%mod;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span>}</div>
<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition:</b> composite_simpson_rule.cpp:117</div></div>
<div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:76</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
</div><!-- fragment -->
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</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>
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<p >Main function </p>
<div class="fragment"><div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span>{</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <a class="code hl_function" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>();</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> uint64_t mod=1000000007;</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>&lt;&lt;<span class="stringliteral">&quot;Enter the value of N: &quot;</span>;</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> uint64_t n=0; <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a>&gt;&gt;n; </div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>&lt;&lt;n&lt;&lt;<span class="stringliteral">&quot;th Fibonacci number in modulo &quot;</span> &lt;&lt; mod &lt;&lt; <span class="stringliteral">&quot;: &quot;</span>&lt;&lt; <a class="code hl_function" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>( n , mod) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span>}</div>
<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
<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>
<div class="ttc" id="afibonacci__matrix__exponentiation_8cpp_html_abc3bc08249058d57cfc8f54a29d9cf9f"><div class="ttname"><a href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a></div><div class="ttdeci">uint64_t fibo(uint64_t n, uint64_t mod)</div><div class="ttdef"><b>Definition:</b> fibonacci_matrix_exponentiation.cpp:23</div></div>
<div class="ttc" id="afibonacci__matrix__exponentiation_8cpp_html_ae1a3968e7947464bee7714f6d43b7002"><div class="ttname"><a href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a></div><div class="ttdeci">void test()</div><div class="ttdef"><b>Definition:</b> fibonacci_matrix_exponentiation.cpp:88</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae1a3968e7947464bee7714f6d43b7002">&#9670;&nbsp;</a></span>test()</h2>
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<td class="memname">void test </td>
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<p >Function to test above algorithm </p>
<div class="fragment"><div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span>{</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> assert(<a class="code hl_function" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(6, 1000000007 ) == 8);</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;test case:1 passed\n&quot;</span>;</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> assert(<a class="code hl_function" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(5, 1000000007 ) == 5);</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;test case:2 passed\n&quot;</span>;</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> assert(<a class="code hl_function" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(10 , 1000000007) == 55);</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;test case:3 passed\n&quot;</span>;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> assert(<a class="code hl_function" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(500 , 100) == 25);</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;test case:3 passed\n&quot;</span>;</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> assert(<a class="code hl_function" href="../../da/dc9/fibonacci__matrix__exponentiation_8cpp.html#abc3bc08249058d57cfc8f54a29d9cf9f">fibo</a>(500 , 10000) == 4125);</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;test case:3 passed\n&quot;</span>;</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;--All tests passed--\n&quot;</span>;</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span>}</div>
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