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<a href="../../de/dc3/fibonacci__sum_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span> </div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#include &lt;cassert&gt;</span> </div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include &lt;cstdint&gt;</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include &lt;iostream&gt;</span> </div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include &lt;vector&gt;</span> </div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../dd/d47/namespacemath.html">math</a> {</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../d3/dc9/namespacefibonacci__sum.html">fibonacci_sum</a> {</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="keyword">using </span><a class="code hl_typedef" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix</a> = std::vector&lt;std::vector&lt;uint64_t&gt; &gt;;</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span></div>
<div class="foldopen" id="foldopen00039" data-start="{" data-end="}">
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"><a class="line" href="../../de/dc3/fibonacci__sum_8cpp.html#a9c83cca09a3e4ff2a25c816a9303448e"> 39</a></span>math::fibonacci_sum::matrix <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a9c83cca09a3e4ff2a25c816a9303448e">multiply</a>(<span class="keyword">const</span> math::fibonacci_sum::matrix &amp;T,</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keyword">const</span> math::fibonacci_sum::matrix &amp;A) {</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> math::fibonacci_sum::matrix <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(2, std::vector&lt;uint64_t&gt;(2, 0));</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="comment">// multiplying matrices</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[0][0] = T[0][0] * A[0][0] + T[0][1] * A[1][0];</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[0][1] = T[0][0] * A[0][1] + T[0][1] * A[1][1];</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[1][0] = T[1][0] * A[0][0] + T[1][1] * A[1][0];</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>[1][1] = T[1][0] * A[0][1] + T[1][1] * A[1][1];</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> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span>}</div>
</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span></div>
<div class="foldopen" id="foldopen00058" data-start="{" data-end="}">
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"><a class="line" href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311"> 58</a></span>math::fibonacci_sum::matrix <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">power</a>(math::fibonacci_sum::matrix T, uint64_t ex) {</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> math::fibonacci_sum::matrix A{{1, 1}, {1, 0}};</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordflow">if</span> (ex == 0 || ex == 1) {</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keywordflow">return</span> T;</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> }</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> T = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">power</a>(T, ex / 2);</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> T = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a9c83cca09a3e4ff2a25c816a9303448e">multiply</a>(T, T);</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keywordflow">if</span> (ex &amp; 1) {</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> T = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a9c83cca09a3e4ff2a25c816a9303448e">multiply</a>(T, A);</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> }</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordflow">return</span> T;</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span>}</div>
</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span></div>
<div class="foldopen" id="foldopen00077" data-start="{" data-end="}">
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"><a class="line" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa"> 77</a></span>uint64_t <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(uint64_t n) {</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> math::fibonacci_sum::matrix T{{1, 1}, {1, 0}};</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> T = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">power</a>(T, n);</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> uint64_t ans = T[0][1];</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> ans = (ans - 1);</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keywordflow">return</span> ans;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span>}</div>
</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span></div>
<div class="foldopen" id="foldopen00091" data-start="{" data-end="}">
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"><a class="line" href="../../de/dc3/fibonacci__sum_8cpp.html#a493fbaa7a94e3b7ca573111237bb3742"> 91</a></span>uint64_t <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a493fbaa7a94e3b7ca573111237bb3742">fiboSum</a>(uint64_t n, uint64_t m) {</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="keywordflow">return</span> (<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(m + 2) - <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>(n + 1));</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span>}</div>
</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span>} <span class="comment">// namespace fibonacci_sum</span></div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span>} <span class="comment">// namespace math</span></div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span></div>
<div class="foldopen" id="foldopen00102" data-start="{" data-end="}">
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"><a class="line" href="../../de/dc3/fibonacci__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d"> 102</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>() {</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> uint64_t n = 0, m = 3;</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> uint64_t <a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a34b8683a2b429de5cce57e6d733ec817">test_1</a> = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a493fbaa7a94e3b7ca573111237bb3742">math::fibonacci_sum::fiboSum</a>(n, m);</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> assert(<a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a34b8683a2b429de5cce57e6d733ec817">test_1</a> == 4);</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Passed Test 1!&quot;</span> &lt;&lt; std::endl;</div>
<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> n = 3;</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> m = 5;</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> uint64_t <a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a458410412185a5f09199deaff7157a8d">test_2</a> = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a493fbaa7a94e3b7ca573111237bb3742">math::fibonacci_sum::fiboSum</a>(n, m);</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> assert(<a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a458410412185a5f09199deaff7157a8d">test_2</a> == 10);</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Passed Test 2!&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> </div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> n = 5;</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> m = 7;</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> uint64_t <a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#af31ec5409537703d9c8a47350386b32a">test_3</a> = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a493fbaa7a94e3b7ca573111237bb3742">math::fibonacci_sum::fiboSum</a>(n, m);</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> assert(<a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#af31ec5409537703d9c8a47350386b32a">test_3</a> == 26);</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Passed Test 3!&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> </div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> n = 7;</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> m = 10;</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> uint64_t test_4 = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a493fbaa7a94e3b7ca573111237bb3742">math::fibonacci_sum::fiboSum</a>(n, m);</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> assert(test_4 == 123);</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Passed Test 4!&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> </div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> n = 9;</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> m = 12;</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> uint64_t test_5 = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a493fbaa7a94e3b7ca573111237bb3742">math::fibonacci_sum::fiboSum</a>(n, m);</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> assert(test_5 == 322);</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Passed Test 5!&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span>}</div>
</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span></div>
<div class="foldopen" id="foldopen00137" data-start="{" data-end="}">
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"><a class="line" href="../../de/dc3/fibonacci__sum_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 137</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// execute the tests</span></div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span>}</div>
</div>
<div class="ttc" id="afibonacci__sum_8cpp_html_a493fbaa7a94e3b7ca573111237bb3742"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#a493fbaa7a94e3b7ca573111237bb3742">math::fibonacci_sum::fiboSum</a></div><div class="ttdeci">uint64_t fiboSum(uint64_t n, uint64_t m)</div><div class="ttdef"><b>Definition</b> <a href="#l00091">fibonacci_sum.cpp:91</a></div></div>
<div class="ttc" id="afibonacci__sum_8cpp_html_a7cf5feaf168b88e74544da59ed830311"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">math::fibonacci_sum::power</a></div><div class="ttdeci">math::fibonacci_sum::matrix power(math::fibonacci_sum::matrix T, uint64_t ex)</div><div class="ttdef"><b>Definition</b> <a href="#l00058">fibonacci_sum.cpp:58</a></div></div>
<div class="ttc" id="afibonacci__sum_8cpp_html_a9c83cca09a3e4ff2a25c816a9303448e"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#a9c83cca09a3e4ff2a25c816a9303448e">math::fibonacci_sum::multiply</a></div><div class="ttdeci">math::fibonacci_sum::matrix multiply(const math::fibonacci_sum::matrix &amp;T, const math::fibonacci_sum::matrix &amp;A)</div><div class="ttdef"><b>Definition</b> <a href="#l00039">fibonacci_sum.cpp:39</a></div></div>
<div class="ttc" id="afibonacci__sum_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdef"><b>Definition</b> <a href="#l00102">fibonacci_sum.cpp:102</a></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> <a href="#l00077">fibonacci_sum.cpp:77</a></div></div>
<div class="ttc" id="afibonacci__sum_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="#l00137">fibonacci_sum.cpp:137</a></div></div>
<div class="ttc" id="aheavy__light__decomposition_8cpp_html_a34b8683a2b429de5cce57e6d733ec817"><div class="ttname"><a href="../../d2/de9/heavy__light__decomposition_8cpp.html#a34b8683a2b429de5cce57e6d733ec817">test_1</a></div><div class="ttdeci">static void test_1()</div><div class="ttdef"><b>Definition</b> <a href="../../d2/de9/heavy__light__decomposition_8cpp_source.html#l00511">heavy_light_decomposition.cpp:511</a></div></div>
<div class="ttc" id="aheavy__light__decomposition_8cpp_html_a458410412185a5f09199deaff7157a8d"><div class="ttname"><a href="../../d2/de9/heavy__light__decomposition_8cpp.html#a458410412185a5f09199deaff7157a8d">test_2</a></div><div class="ttdeci">static void test_2()</div><div class="ttdef"><b>Definition</b> <a href="../../d2/de9/heavy__light__decomposition_8cpp_source.html#l00555">heavy_light_decomposition.cpp:555</a></div></div>
<div class="ttc" id="aheavy__light__decomposition_8cpp_html_af31ec5409537703d9c8a47350386b32a"><div class="ttname"><a href="../../d2/de9/heavy__light__decomposition_8cpp.html#af31ec5409537703d9c8a47350386b32a">test_3</a></div><div class="ttdeci">static void test_3()</div><div class="ttdef"><b>Definition</b> <a href="../../d2/de9/heavy__light__decomposition_8cpp_source.html#l00599">heavy_light_decomposition.cpp:599</a></div></div>
<div class="ttc" id="alu__decomposition_8h_html_ac029b636b353cefbb18b2fcc71e427e4"><div class="ttname"><a href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix</a></div><div class="ttdeci">std::vector&lt; std::valarray&lt; T &gt; &gt; matrix</div><div class="ttdef"><b>Definition</b> <a href="../../d1/dbe/lu__decomposition_8h_source.html#l00019">lu_decomposition.h:19</a></div></div>
<div class="ttc" id="anamespacefibonacci__sum_html"><div class="ttname"><a href="../../d3/dc9/namespacefibonacci__sum.html">fibonacci_sum</a></div><div class="ttdoc">Functions for the sum of the Fibonacci Sequence: .</div></div>
<div class="ttc" id="anamespacemath_html"><div class="ttname"><a href="../../dd/d47/namespacemath.html">math</a></div><div class="ttdoc">for assert</div></div>
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