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<a href="../../d2/d0b/fast__power_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="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;cmath&gt;</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include &lt;cstdint&gt;</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include &lt;cstdlib&gt;</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#include &lt;ctime&gt;</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> </div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="foldopen" id="foldopen00026" data-start="{" data-end="}">
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"><a class="line" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445"> 26</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a>(T a, T b) {</div>
<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>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> <span class="keywordflow">if</span> (b &lt; 0)</div>
<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>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> </div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> <span class="keywordflow">if</span> (b == 0)</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <span class="keywordflow">return</span> 1;</div>
<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 &gt;&gt; 1);</div>
<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>
<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>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> </div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="keywordtype">double</span> result;</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="keywordflow">if</span> ((b &amp; 1) == 0) <span class="comment">// case1</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> result = bottom * bottom;</div>
<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>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> result = bottom * bottom * a;</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keywordflow">return</span> result;</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span>}</div>
</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> </div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="foldopen" id="foldopen00050" data-start="{" data-end="}">
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"><a class="line" href="../../d2/d0b/fast__power_8cpp.html#a0d4e3f0099a6975b74a314a35bd0f94d"> 50</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#a0d4e3f0099a6975b74a314a35bd0f94d">fast_power_linear</a>(T a, T b) {</div>
<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>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keywordflow">if</span> (b &lt; 0)</div>
<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>
<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> <span class="keywordtype">double</span> result = 1;</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keywordflow">while</span> (b) {</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="keywordflow">if</span> (b &amp; 1)</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> result = result * a;</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> a = a * a;</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> b = b &gt;&gt; 1;</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> }</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keywordflow">return</span> result;</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span>}</div>
</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> </div>
<div class="foldopen" id="foldopen00068" data-start="{" data-end="}">
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"><a class="line" href="../../d2/d0b/fast__power_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 68</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> std::srand(std::time(<span class="keyword">nullptr</span>));</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> std::ios_base::sync_with_stdio(<span class="keyword">false</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> std::cout &lt;&lt; <span class="stringliteral">&quot;Testing...&quot;</span> &lt;&lt; std::endl;</div>
<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 &lt; 20; i++) {</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keywordtype">int</span> a = std::rand() % 20 - 10;</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="keywordtype">int</span> b = std::rand() % 20 - 10;</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> std::cout &lt;&lt; std::endl &lt;&lt; <span class="stringliteral">&quot;Calculating &quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;^&quot;</span> &lt;&lt; b &lt;&lt; std::endl;</div>
<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) == std::pow(a, b));</div>
<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) == std::pow(a, b));</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> </div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> std::cout &lt;&lt; <span class="stringliteral">&quot;------ &quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;^&quot;</span> &lt;&lt; b &lt;&lt; <span class="stringliteral">&quot; = &quot;</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> &lt;&lt; <a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a>(a, b) &lt;&lt; std::endl;</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> }</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> </div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> int64_t a, b;</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> std::cin &gt;&gt; a &gt;&gt; b;</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> </div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> std::cout &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;^&quot;</span> &lt;&lt; b &lt;&lt; <span class="stringliteral">&quot; = &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#a8399b847626e5bba983cab7c7918b445">fast_power_recursive</a>(a, b)</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> &lt;&lt; std::endl;</div>
<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> std::cout &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot;^&quot;</span> &lt;&lt; b &lt;&lt; <span class="stringliteral">&quot; = &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d2/d0b/fast__power_8cpp.html#a0d4e3f0099a6975b74a314a35bd0f94d">fast_power_linear</a>(a, b) &lt;&lt; std::endl;</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> </div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span>}</div>
</div>
<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> <a href="#l00050">fast_power.cpp:50</a></div></div>
<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> <a href="#l00026">fast_power.cpp:26</a></div></div>
<div class="ttc" id="afast__power_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d2/d0b/fast__power_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition</b> <a href="#l00068">fast_power.cpp:68</a></div></div>
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