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<p >An algorithm to calculate the sum of Fibonacci Sequence: \(\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\) where \(\mathrm{F}(i)\) denotes the i-th Fibonacci Number . Note that F(0) = 0 and F(1) = 1. The value of the sum is calculated using matrix exponentiation. Reference source: <a href="https://stackoverflow.com/questions/4357223/finding-the-sum-of-fibonacci-numbers">https://stackoverflow.com/questions/4357223/finding-the-sum-of-fibonacci-numbers</a> </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/SarthakSahu1009" target="_blank">Sarthak Sahu</a> </dd></dl>
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</div><h2 class="groupheader">Function Documentation</h2>
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<a id="a493fbaa7a94e3b7ca573111237bb3742" name="a493fbaa7a94e3b7ca573111237bb3742"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a493fbaa7a94e3b7ca573111237bb3742">◆ </a></span>fiboSum()</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a493fbaa7a94e3b7ca573111237bb3742">◆ </a></span>fiboSum()</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">◆ </a></span>main()</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">◆ </a></span>main()</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a9c83cca09a3e4ff2a25c816a9303448e">◆ </a></span>multiply()</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a9c83cca09a3e4ff2a25c816a9303448e">◆ </a></span>multiply()</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a7cf5feaf168b88e74544da59ed830311">◆ </a></span>power()</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a7cf5feaf168b88e74544da59ed830311">◆ </a></span>power()</h2>
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<div class="line"><span class="lineno"> 60</span> <span class="keywordflow">return</span> T;</div>
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<div class="line"><span class="lineno"> 61</span> }</div>
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<div class="line"><span class="lineno"> 62</span> </div>
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<div class="line"><span class="lineno"> 63</span> T = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">power</a>(T, ex / 2);</div>
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<div class="line"><span class="lineno"> 64</span> T = <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#a17f3d667241b88115a95282cdd719cb2">multiply</a>(T, T);</div>
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<div class="line"><span class="lineno"> 63</span> T = <a class="code hl_function" href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a>(T, ex / 2);</div>
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<div class="line"><span class="lineno"> 64</span> T = <a class="code hl_function" href="../../df/def/power__for__huge__numbers_8cpp.html#aa141a7904f0c4668bac112d652a3acf9">multiply</a>(T, T);</div>
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<div class="line"><span class="lineno"> 65</span> <span class="keywordflow">if</span> (ex & 1) {</div>
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<div class="line"><span class="lineno"> 66</span> T = <a class="code hl_function" href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#a17f3d667241b88115a95282cdd719cb2">multiply</a>(T, A);</div>
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<div class="line"><span class="lineno"> 66</span> T = <a class="code hl_function" href="../../df/def/power__for__huge__numbers_8cpp.html#aa141a7904f0c4668bac112d652a3acf9">multiply</a>(T, A);</div>
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<div class="line"><span class="lineno"> 67</span> }</div>
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<div class="line"><span class="lineno"> 68</span> <span class="keywordflow">return</span> T;</div>
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<div class="line"><span class="lineno"> 69</span>}</div>
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<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> fibonacci_sum.cpp:57</div></div>
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<div class="ttc" id="anamespaceciphers_1_1elliptic__curve__key__exchange_html_a17f3d667241b88115a95282cdd719cb2"><div class="ttname"><a href="../../df/d6b/namespaceciphers_1_1elliptic__curve__key__exchange.html#a17f3d667241b88115a95282cdd719cb2">ciphers::elliptic_curve_key_exchange::multiply</a></div><div class="ttdeci">Point multiply(const Point &a, const uint256_t &curve_a_coeff, uint256_t p, const uint256_t &mod)</div><div class="ttdoc">multiply Point and integer</div><div class="ttdef"><b>Definition:</b> elliptic_curve_key_exchange.cpp:165</div></div>
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<div class="ttc" id="apower__for__huge__numbers_8cpp_html_aa141a7904f0c4668bac112d652a3acf9"><div class="ttname"><a href="../../df/def/power__for__huge__numbers_8cpp.html#aa141a7904f0c4668bac112d652a3acf9">multiply</a></div><div class="ttdeci">int multiply(int x, int res[], int res_size)</div><div class="ttdef"><b>Definition:</b> power_for_huge_numbers.cpp:25</div></div>
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<div class="ttc" id="apower__for__huge__numbers_8cpp_html_ae249a2af508aa94266023ce8aa81426f"><div class="ttname"><a href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a></div><div class="ttdeci">void power(int x, int n)</div><div class="ttdef"><b>Definition:</b> power_for_huge_numbers.cpp:56</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aadb40ac4c74a7efc0680b83eeee138aa">◆ </a></span>result()</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#aadb40ac4c74a7efc0680b83eeee138aa">◆ </a></span>result()</h2>
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<dl class="section return"><dt>Returns</dt><dd>uint64_t ans, the sum of sequence </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 76</span> {</div>
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<div class="line"><span class="lineno"> 77</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">math::fibonacci_sum::matrix</a> T{{1, 1}, {1, 0}};</div>
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<div class="line"><span class="lineno"> 78</span> T = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a7cf5feaf168b88e74544da59ed830311">power</a>(T, n);</div>
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<div class="line"><span class="lineno"> 79</span> uint64_t <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = T[0][1];</div>
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<div class="line"><span class="lineno"> 80</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> = (<a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a> - 1);</div>
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<div class="line"><span class="lineno"> 81</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a>;</div>
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<div class="line"><span class="lineno"> 78</span> T = <a class="code hl_function" href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a>(T, n);</div>
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<div class="line"><span class="lineno"> 79</span> uint64_t ans = T[0][1];</div>
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<div class="line"><span class="lineno"> 80</span> ans = (ans - 1);</div>
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<div class="line"><span class="lineno"> 81</span> <span class="keywordflow">return</span> ans;</div>
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<div class="line"><span class="lineno"> 82</span>}</div>
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<div class="ttc" id="amatrix__exponentiation_8cpp_html_ad8389ed58fd0ec66df248014775ad1fa"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a></div><div class="ttdeci">ll ans(ll n)</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:91</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">◆ </a></span>test()</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">◆ </a></span>test()</h2>
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<p >Function for testing fiboSum function. test cases and assert statement. </p><dl class="section return"><dt>Returns</dt><dd><code>void</code> </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 101</span> {</div>
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<div class="line"><span class="lineno"> 102</span> uint64_t n = 0, m = 3;</div>
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<div class="line"><span class="lineno"> 103</span> uint64_t test_1 = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a493fbaa7a94e3b7ca573111237bb3742">math::fibonacci_sum::fiboSum</a>(n, m);</div>
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<div class="line"><span class="lineno"> 104</span> assert(test_1 == 4);</div>
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<div class="line"><span class="lineno"> 103</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>
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<div class="line"><span class="lineno"> 104</span> assert(<a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a34b8683a2b429de5cce57e6d733ec817">test_1</a> == 4);</div>
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<div class="line"><span class="lineno"> 105</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Passed Test 1!"</span> << <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"><span class="lineno"> 106</span> </div>
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<div class="line"><span class="lineno"> 107</span> n = 3;</div>
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<div class="line"><span class="lineno"> 108</span> m = 5;</div>
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<div class="line"><span class="lineno"> 109</span> uint64_t test_2 = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a493fbaa7a94e3b7ca573111237bb3742">math::fibonacci_sum::fiboSum</a>(n, m);</div>
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<div class="line"><span class="lineno"> 110</span> assert(test_2 == 10);</div>
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<div class="line"><span class="lineno"> 109</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>
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<div class="line"><span class="lineno"> 110</span> assert(<a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a458410412185a5f09199deaff7157a8d">test_2</a> == 10);</div>
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<div class="line"><span class="lineno"> 111</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Passed Test 2!"</span> << <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"><span class="lineno"> 112</span> </div>
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<div class="line"><span class="lineno"> 113</span> n = 5;</div>
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<div class="line"><span class="lineno"> 114</span> m = 7;</div>
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<div class="line"><span class="lineno"> 115</span> uint64_t test_3 = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#a493fbaa7a94e3b7ca573111237bb3742">math::fibonacci_sum::fiboSum</a>(n, m);</div>
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<div class="line"><span class="lineno"> 116</span> assert(test_3 == 26);</div>
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<div class="line"><span class="lineno"> 115</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>
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<div class="line"><span class="lineno"> 116</span> assert(<a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#af31ec5409537703d9c8a47350386b32a">test_3</a> == 26);</div>
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<div class="line"><span class="lineno"> 117</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Passed Test 3!"</span> << <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"><span class="lineno"> 118</span> </div>
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<div class="line"><span class="lineno"> 119</span> n = 7;</div>
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@@ -432,10 +438,13 @@ Here is the call graph for this function:</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::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__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> fibonacci_sum.cpp:90</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> heavy_light_decomposition.cpp:505</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> heavy_light_decomposition.cpp:549</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> heavy_light_decomposition.cpp:592</div></div>
|
||||
</div><!-- fragment --><div class="dynheader">
|
||||
Here is the call graph for this function:</div>
|
||||
<div class="dyncontent">
|
||||
<div class="center"><iframe scrolling="no" frameborder="0" src="../../de/dc3/fibonacci__sum_8cpp_aa8dca7b867074164d5f45b0f3851269d_cgraph.svg" width="175" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../de/dc3/fibonacci__sum_8cpp_aa8dca7b867074164d5f45b0f3851269d_cgraph.svg" width="100%" height="600"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
|
||||
</div>
|
||||
</div>
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|
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@@ -447,7 +456,7 @@ Here is the call graph for this function:</div>
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