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<div class="title">karatsuba_algorithm_for_fast_multiplication.cpp File Reference</div> </div>
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<div class="contents">
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<p>Implementation of the <a href="https://en.wikipedia.org/wiki/Karatsuba_algorithm">Karatsuba algorithm for fast multiplication</a>
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <cassert></code><br />
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<code>#include <cstring></code><br />
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<code>#include <iostream></code><br />
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<code>#include <vector></code><br />
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Namespaces</h2></td></tr>
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<tr class="memitem:dd/dba/namespacedivide__and__conquer"><td class="memItemLeft" align="right" valign="top">  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/dba/namespacedivide__and__conquer.html">divide_and_conquer</a></td></tr>
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<tr class="memdesc:dd/dba/namespacedivide__and__conquer"><td class="mdescLeft"> </td><td class="mdescRight">for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> <br /></td></tr>
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<tr class="memdesc:de/d41/namespacekaratsuba__algorithm"><td class="mdescLeft"> </td><td class="mdescRight">Functions for the <a href="https://en.wikipedia.org/wiki/Karatsuba_algorithm">Karatsuba algorithm for fast multiplication</a> <br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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Functions</h2></td></tr>
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<tr class="memitem:a7d1dbae365c7746295d3322e6f7f80b6"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7d1dbae365c7746295d3322e6f7f80b6">divide_and_conquer::karatsuba_algorithm::addStrings</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> first, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> second)</td></tr>
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<tr class="memdesc:a7d1dbae365c7746295d3322e6f7f80b6"><td class="mdescLeft"> </td><td class="mdescRight">Helper function for the main function, that implements Karatsuba's algorithm for fast multiplication. <a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7d1dbae365c7746295d3322e6f7f80b6">More...</a><br /></td></tr>
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<tr class="separator:a7d1dbae365c7746295d3322e6f7f80b6"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a7a890d2f26855ada3b9f1d43aec70a86"><td class="memItemLeft" align="right" valign="top">int64_t </td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7a890d2f26855ada3b9f1d43aec70a86">divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> str1, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> str2)</td></tr>
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<tr class="memdesc:a7a890d2f26855ada3b9f1d43aec70a86"><td class="mdescLeft"> </td><td class="mdescRight">The main function implements Karatsuba's algorithm for fast multiplication. <a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7a890d2f26855ada3b9f1d43aec70a86">More...</a><br /></td></tr>
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<tr class="separator:a7a890d2f26855ada3b9f1d43aec70a86"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void </td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
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<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft"> </td><td class="mdescRight">Self-test implementations. <a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
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<tr class="separator:aa8dca7b867074164d5f45b0f3851269d"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft"> </td><td class="mdescRight">Main function. <a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
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<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>Implementation of the <a href="https://en.wikipedia.org/wiki/Karatsuba_algorithm">Karatsuba algorithm for fast multiplication</a> </p>
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<p>Given two strings in binary notation we want to multiply them and return the value Simple approach is to multiply bits one by one which will give the time complexity of around O(n^2). To make it more efficient we will be using Karatsuba' algorithm to find the product which will solve the problem O(nlogn) of time. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Swastyy">Swastika Gupta</a> </dd></dl>
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</div><h2 class="groupheader">Function Documentation</h2>
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<a id="a7d1dbae365c7746295d3322e6f7f80b6"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a7d1dbae365c7746295d3322e6f7f80b6">◆ </a></span>addStrings()</h2>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> divide_and_conquer::karatsuba_algorithm::addStrings </td>
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<td>(</td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> </td>
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<td class="paramname"><em>first</em>, </td>
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<td></td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> </td>
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<td class="paramname"><em>second</em> </td>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</div><div class="memdoc">
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<p>Helper function for the main function, that implements Karatsuba's algorithm for fast multiplication. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">first</td><td>the input string 1 </td></tr>
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<tr><td class="paramname">second</td><td>the input string 2 </td></tr>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>the concatenated string </dd></dl>
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<div class="fragment"><div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  {</div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>; <span class="comment">// To store the resulting sum bits</span></div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  </div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  int64_t len1 = first.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  int64_t len2 = second.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  int64_t length = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(len1, len2);</div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> zero = <span class="stringliteral">"0"</span>;</div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keywordflow">if</span> (len1 < len2) <span class="comment">// make the string lengths equal</span></div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  {</div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="keywordflow">for</span> (int64_t i = 0; i < len2 - len1; i++) {</div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  zero += first;</div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  first = zero;</div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  }</div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len1 > len2) {</div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  zero = <span class="stringliteral">"0"</span>;</div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="keywordflow">for</span> (int64_t i = 0; i < len1 - len2; i++) {</div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  zero += second;</div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  second = zero;</div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  }</div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  }</div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  int64_t carry = 0;</div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keywordflow">for</span> (int64_t i = length - 1; i >= 0; i--) {</div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  int64_t firstBit = first.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/at.html">at</a>(i) - <span class="charliteral">'0'</span>;</div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  int64_t secondBit = second.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/at.html">at</a>(i) - <span class="charliteral">'0'</span>;</div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  </div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  int64_t <a class="code" href="../../d8/d77/namespacemachine__learning.html#a5305cc18d11943d3dc0d66e70d7e9c44">sum</a> = (firstBit ^ secondBit ^ carry) + <span class="charliteral">'0'</span>; <span class="comment">// sum of 3 bits</span></div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> temp;</div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  temp = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/to_string.html">std::to_string</a>(<a class="code" href="../../d8/d77/namespacemachine__learning.html#a5305cc18d11943d3dc0d66e70d7e9c44">sum</a>);</div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  temp += <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = temp;</div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  </div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  carry = (firstBit & secondBit) | (secondBit & carry) |</div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  (firstBit & carry); <span class="comment">// sum of 3 bits</span></div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  }</div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  </div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="keywordflow">if</span> (carry) {</div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="charliteral">'1'</span> + <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>; <span class="comment">// adding 1 incase of overflow</span></div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  }</div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
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<div class="line"><a name="l00076"></a><span class="lineno"> 76</span> }</div>
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<div class="ttc" id="aat_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/at.html">std::string::at</a></div><div class="ttdeci">T at(T... args)</div></div>
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<div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></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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<div class="ttc" id="anamespacemachine__learning_html_a5305cc18d11943d3dc0d66e70d7e9c44"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#a5305cc18d11943d3dc0d66e70d7e9c44">machine_learning::sum</a></div><div class="ttdeci">T sum(const std::vector< std::valarray< T >> &A)</div><div class="ttdef"><b>Definition:</b> vector_ops.hpp:232</div></div>
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<div class="ttc" id="ato_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/to_string.html">std::to_string</a></div><div class="ttdeci">T to_string(T... args)</div></div>
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_a7d1dbae365c7746295d3322e6f7f80b6_cgraph.svg" width="370" height="240"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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<h2 class="memtitle"><span class="permalink"><a href="#a7a890d2f26855ada3b9f1d43aec70a86">◆ </a></span>karatsuba_algorithm()</h2>
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<div class="memitem">
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<td class="memname">int64_t divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm </td>
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<td>(</td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> </td>
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<td class="paramname"><em>str1</em>, </td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> </td>
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<td class="paramname"><em>str2</em> </td>
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<td>)</td>
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<p>The main function implements Karatsuba's algorithm for fast multiplication. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">str1</td><td>the input string 1 </td></tr>
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<tr><td class="paramname">str2</td><td>the input string 2 </td></tr>
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</table>
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<dl class="section return"><dt>Returns</dt><dd>the multiplicative number value </dd></dl>
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<div class="fragment"><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  {</div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  int64_t len1 = str1.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  int64_t len2 = str2.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  int64_t n = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(len1, len2);</div>
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<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> zero = <span class="stringliteral">"0"</span>;</div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <span class="keywordflow">if</span> (len1 < len2) {</div>
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<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="keywordflow">for</span> (int64_t i = 0; i < len2 - len1; i++) {</div>
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<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  zero += str1;</div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  str1 = zero;</div>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  }</div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len1 > len2) {</div>
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<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  zero = <span class="stringliteral">"0"</span>;</div>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keywordflow">for</span> (int64_t i = 0; i < len1 - len2; i++) {</div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  zero += str2;</div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  str2 = zero;</div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  }</div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  }</div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="keywordflow">if</span> (n == 0) {</div>
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<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  }</div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="keywordflow">if</span> (n == 1) {</div>
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<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="keywordflow">return</span> (str1[0] - <span class="charliteral">'0'</span>) * (str2[0] - <span class="charliteral">'0'</span>);</div>
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<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  }</div>
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<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  int64_t fh = n / 2; <span class="comment">// first half of string</span></div>
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  int64_t sh = (n - fh); <span class="comment">// second half of string</span></div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  </div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Xl = str1.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(0, fh); <span class="comment">// first half of first string</span></div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Xr = str1.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(fh, sh); <span class="comment">// second half of first string</span></div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  </div>
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<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Yl = str2.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(0, fh); <span class="comment">// first half of second string</span></div>
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<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Yr = str2.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(fh, sh); <span class="comment">// second half of second string</span></div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  </div>
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<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="comment">// Calculating the three products of inputs of size n/2 recursively</span></div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  int64_t product1 = <a class="code" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(Xl, Yl);</div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  int64_t product2 = <a class="code" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(Xr, Yr);</div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  int64_t product3 = <a class="code" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(</div>
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  divide_and_conquer::karatsuba_algorithm::addStrings(Xl, Xr),</div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  divide_and_conquer::karatsuba_algorithm::addStrings(Yl, Yr));</div>
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<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  </div>
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<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="keywordflow">return</span> product1 * (1 << (2 * sh)) +</div>
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<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  (product3 - product1 - product2) * (1 << sh) +</div>
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  product2; <span class="comment">// combining the three products to get the final result.</span></div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span> }</div>
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<div class="ttc" id="anamespacekaratsuba__algorithm_html"><div class="ttname"><a href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a></div><div class="ttdoc">Functions for the Karatsuba algorithm for fast multiplication</div></div>
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<div class="ttc" id="asubstr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">std::string::substr</a></div><div class="ttdeci">T substr(T... args)</div></div>
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_a7a890d2f26855ada3b9f1d43aec70a86_cgraph.svg" width="568" height="255"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">◆ </a></span>main()</h2>
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<p>Main function. </p>
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<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
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<div class="fragment"><div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  {</div>
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<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <a class="code" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
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<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00167"></a><span class="lineno"> 167</span> }</div>
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<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition:</b> karatsuba_algorithm_for_fast_multiplication.cpp:134</div></div>
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="274" 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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<a id="aa8dca7b867074164d5f45b0f3851269d"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">◆ </a></span>test()</h2>
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<td class="memname">static void test </td>
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<span class="mlabels"><span class="mlabel">static</span></span> </td>
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<p>Self-test implementations. </p>
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<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
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<div class="fragment"><div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  {</div>
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<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="comment">// 1st test</span></div>
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<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s11 = <span class="stringliteral">"1"</span>;</div>
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<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s12 = <span class="stringliteral">"1010"</span>;</div>
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<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"1st test... "</span>;</div>
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<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
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<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  s11, s12) == 10); <span class="comment">// here the multiplication is 10</span></div>
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<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"passed"</span> << <a class="codeRef" 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 name="l00142"></a><span class="lineno"> 142</span>  </div>
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<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="comment">// 2nd test</span></div>
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<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s21 = <span class="stringliteral">"11"</span>;</div>
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<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s22 = <span class="stringliteral">"1010"</span>;</div>
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<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"2nd test... "</span>;</div>
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<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
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<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  s21, s22) == 30); <span class="comment">// here the multiplication is 30</span></div>
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<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"passed"</span> << <a class="codeRef" 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 name="l00150"></a><span class="lineno"> 150</span>  </div>
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<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <span class="comment">// 3rd test</span></div>
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<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s31 = <span class="stringliteral">"110"</span>;</div>
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<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s32 = <span class="stringliteral">"1010"</span>;</div>
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<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"3rd test... "</span>;</div>
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<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
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<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  s31, s32) == 60); <span class="comment">// here the multiplication is 60</span></div>
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<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"passed"</span> << <a class="codeRef" 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 name="l00158"></a><span class="lineno"> 158</span> }</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>
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<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>
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