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<title>Algorithms_in_C++: math/fast_power.cpp File Reference</title>
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<div id="projectname">Algorithms_in_C++<span id="projectnumber"> 1.0.0</span>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&dn=expat.txt MIT */
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@@ -158,20 +158,20 @@ template<typename T > </div>
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</table>
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</div><div class="memdoc">
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<p >Same algorithm with little different formula. It still calculates in \(O(\log N)\) </p>
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<div class="fragment"><div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> {</div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// negative power. a^b = 1 / (a^-b)</span></div>
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||||
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keywordflow">if</span> (b < 0)</div>
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||||
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keywordflow">return</span> 1.0 / <a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#a0d4e3f0099a6975b74a314a35bd0f94d">fast_power_linear</a>(a, -b);</div>
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||||
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> </div>
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||||
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = 1;</div>
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||||
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keywordflow">while</span> (b) {</div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="keywordflow">if</span> (b & 1)</div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> * a;</div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> a = a * a;</div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> b = b >> 1;</div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> }</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 50</span> {</div>
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<div class="line"><span class="lineno"> 51</span> <span class="comment">// negative power. a^b = 1 / (a^-b)</span></div>
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<div class="line"><span class="lineno"> 52</span> <span class="keywordflow">if</span> (b < 0)</div>
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<div class="line"><span class="lineno"> 53</span> <span class="keywordflow">return</span> 1.0 / <a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#a0d4e3f0099a6975b74a314a35bd0f94d">fast_power_linear</a>(a, -b);</div>
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<div class="line"><span class="lineno"> 54</span> </div>
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<div class="line"><span class="lineno"> 55</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = 1;</div>
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<div class="line"><span class="lineno"> 56</span> <span class="keywordflow">while</span> (b) {</div>
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<div class="line"><span class="lineno"> 57</span> <span class="keywordflow">if</span> (b & 1)</div>
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<div class="line"><span class="lineno"> 58</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> * a;</div>
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<div class="line"><span class="lineno"> 59</span> a = a * a;</div>
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<div class="line"><span class="lineno"> 60</span> b = b >> 1;</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> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
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<div class="line"><span class="lineno"> 63</span>}</div>
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<div class="ttc" id="afast__power_8cpp_html_a0d4e3f0099a6975b74a314a35bd0f94d"><div class="ttname"><a href="../../d2/d0b/fast__power_8cpp.html#a0d4e3f0099a6975b74a314a35bd0f94d">fast_power_linear</a></div><div class="ttdeci">double fast_power_linear(T a, T b)</div><div class="ttdef"><b>Definition:</b> fast_power.cpp:50</div></div>
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<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>
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@@ -211,24 +211,24 @@ template<typename T > </div>
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</div><div class="memdoc">
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<p >algorithm implementation for \(a^b\) </p>
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<div class="fragment"><div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> {</div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> <span class="comment">// negative power. a^b = 1 / (a^-b)</span></div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> <span class="keywordflow">if</span> (b < 0)</div>
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||||
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> <span class="keywordflow">return</span> 1.0 / <a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a>(a, -b);</div>
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||||
<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="keywordflow">if</span> (b == 0)</div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <span class="keywordflow">return</span> 1;</div>
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||||
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> T bottom = <a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a>(a, b >> 1);</div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="comment">// Since it is integer division b/2 = (b-1)/2 where b is odd.</span></div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="comment">// Therefore, case2 is easily solved by integer division.</span></div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> </div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
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||||
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="keywordflow">if</span> ((b & 1) == 0) <span class="comment">// case1</span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = bottom * bottom;</div>
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||||
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keywordflow">else</span> <span class="comment">// case2</span></div>
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||||
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = bottom * bottom * a;</div>
|
||||
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 26</span> {</div>
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<div class="line"><span class="lineno"> 27</span> <span class="comment">// negative power. a^b = 1 / (a^-b)</span></div>
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||||
<div class="line"><span class="lineno"> 28</span> <span class="keywordflow">if</span> (b < 0)</div>
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||||
<div class="line"><span class="lineno"> 29</span> <span class="keywordflow">return</span> 1.0 / <a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a>(a, -b);</div>
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||||
<div class="line"><span class="lineno"> 30</span> </div>
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||||
<div class="line"><span class="lineno"> 31</span> <span class="keywordflow">if</span> (b == 0)</div>
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||||
<div class="line"><span class="lineno"> 32</span> <span class="keywordflow">return</span> 1;</div>
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||||
<div class="line"><span class="lineno"> 33</span> T bottom = <a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a>(a, b >> 1);</div>
|
||||
<div class="line"><span class="lineno"> 34</span> <span class="comment">// Since it is integer division b/2 = (b-1)/2 where b is odd.</span></div>
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||||
<div class="line"><span class="lineno"> 35</span> <span class="comment">// Therefore, case2 is easily solved by integer division.</span></div>
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<div class="line"><span class="lineno"> 36</span> </div>
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||||
<div class="line"><span class="lineno"> 37</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
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||||
<div class="line"><span class="lineno"> 38</span> <span class="keywordflow">if</span> ((b & 1) == 0) <span class="comment">// case1</span></div>
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||||
<div class="line"><span class="lineno"> 39</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = bottom * bottom;</div>
|
||||
<div class="line"><span class="lineno"> 40</span> <span class="keywordflow">else</span> <span class="comment">// case2</span></div>
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||||
<div class="line"><span class="lineno"> 41</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = bottom * bottom * a;</div>
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||||
<div class="line"><span class="lineno"> 42</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
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||||
<div class="line"><span class="lineno"> 43</span>}</div>
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<div class="ttc" id="afast__power_8cpp_html_a8399b847626e5bba983cab7c7918b445"><div class="ttname"><a href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a></div><div class="ttdeci">double fast_power_recursive(T a, T b)</div><div class="ttdef"><b>Definition:</b> fast_power.cpp:26</div></div>
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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@@ -255,32 +255,32 @@ Here is the call graph for this function:</div>
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||||
</table>
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</div><div class="memdoc">
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<p >Main function </p>
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||||
<div class="fragment"><div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> {</div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
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||||
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/ios_base/sync_with_stdio.html">std::ios_base::sync_with_stdio</a>(<span class="keyword">false</span>);</div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> </div>
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||||
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</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">"Testing..."</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"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < 20; i++) {</div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keywordtype">int</span> a = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 20 - 10;</div>
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||||
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="keywordtype">int</span> b = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 20 - 10;</div>
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||||
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a> << <span class="stringliteral">"Calculating "</span> << a << <span class="stringliteral">"^"</span> << b << <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="l00077" name="l00077"></a><span class="lineno"> 77</span> assert(<a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a>(a, b) == <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(a, b));</div>
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||||
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> assert(<a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#a0d4e3f0099a6975b74a314a35bd0f94d">fast_power_linear</a>(a, b) == <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(a, b));</div>
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||||
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> </div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</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">"------ "</span> << a << <span class="stringliteral">"^"</span> << b << <span class="stringliteral">" = "</span></div>
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||||
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> << <a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a>(a, b) << <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="l00082" name="l00082"></a><span class="lineno"> 82</span> }</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> </div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> int64_t a, b;</div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> >> a >> b;</div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> </div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << a << <span class="stringliteral">"^"</span> << b << <span class="stringliteral">" = "</span> << <a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a>(a, b)</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</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"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> </div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << a << <span class="stringliteral">"^"</span> << b << <span class="stringliteral">" = "</span> << <a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#a0d4e3f0099a6975b74a314a35bd0f94d">fast_power_linear</a>(a, b) << <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="l00091" name="l00091"></a><span class="lineno"> 91</span> </div>
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