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@@ -173,46 +173,46 @@ Functions</h2></td></tr>
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<dl class="section return"><dt>Returns</dt><dd>the concatenated string </dd></dl>
<div class="fragment"><div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> {</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>; <span class="comment">// To store the resulting sum bits</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> </div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> int64_t len1 = first.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> int64_t len2 = second.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> int64_t length = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(len1, len2);</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> zero = <span class="stringliteral">&quot;0&quot;</span>;</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keywordflow">if</span> (len1 &lt; len2) <span class="comment">// make the string lengths equal</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> {</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="keywordflow">for</span> (int64_t i = 0; i &lt; len2 - len1; i++) {</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> zero += first;</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> first = zero;</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> }</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len1 &gt; len2) {</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> zero = <span class="stringliteral">&quot;0&quot;</span>;</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keywordflow">for</span> (int64_t i = 0; i &lt; len1 - len2; i++) {</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> zero += second;</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> second = zero;</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> }</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> }</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> int64_t carry = 0;</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keywordflow">for</span> (int64_t i = length - 1; i &gt;= 0; i--) {</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> int64_t firstBit = first.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/at.html">at</a>(i) - <span class="charliteral">&#39;0&#39;</span>;</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> int64_t secondBit = second.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/at.html">at</a>(i) - <span class="charliteral">&#39;0&#39;</span>;</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> int64_t <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a> = (firstBit ^ secondBit ^ carry) + <span class="charliteral">&#39;0&#39;</span>; <span class="comment">// sum of 3 bits</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> temp;</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> temp = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/to_string.html">std::to_string</a>(<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>);</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> temp += <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = temp;</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> </div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> carry = (firstBit &amp; secondBit) | (secondBit &amp; carry) |</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> (firstBit &amp; carry); <span class="comment">// sum of 3 bits</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</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> <span class="keywordflow">if</span> (carry) {</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="charliteral">&#39;1&#39;</span> + <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>; <span class="comment">// adding 1 incase of overflow</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> }</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span>}</div>
<div class="fragment"><div class="line"><span class="lineno"> 37</span> {</div>
<div class="line"><span class="lineno"> 38</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>; <span class="comment">// To store the resulting sum bits</span></div>
<div class="line"><span class="lineno"> 39</span> </div>
<div class="line"><span class="lineno"> 40</span> int64_t len1 = first.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 41</span> int64_t len2 = second.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 42</span> int64_t length = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(len1, len2);</div>
<div class="line"><span class="lineno"> 43</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> zero = <span class="stringliteral">&quot;0&quot;</span>;</div>
<div class="line"><span class="lineno"> 44</span> <span class="keywordflow">if</span> (len1 &lt; len2) <span class="comment">// make the string lengths equal</span></div>
<div class="line"><span class="lineno"> 45</span> {</div>
<div class="line"><span class="lineno"> 46</span> <span class="keywordflow">for</span> (int64_t i = 0; i &lt; len2 - len1; i++) {</div>
<div class="line"><span class="lineno"> 47</span> zero += first;</div>
<div class="line"><span class="lineno"> 48</span> first = zero;</div>
<div class="line"><span class="lineno"> 49</span> }</div>
<div class="line"><span class="lineno"> 50</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len1 &gt; len2) {</div>
<div class="line"><span class="lineno"> 51</span> zero = <span class="stringliteral">&quot;0&quot;</span>;</div>
<div class="line"><span class="lineno"> 52</span> <span class="keywordflow">for</span> (int64_t i = 0; i &lt; len1 - len2; i++) {</div>
<div class="line"><span class="lineno"> 53</span> zero += second;</div>
<div class="line"><span class="lineno"> 54</span> second = zero;</div>
<div class="line"><span class="lineno"> 55</span> }</div>
<div class="line"><span class="lineno"> 56</span> }</div>
<div class="line"><span class="lineno"> 57</span> int64_t carry = 0;</div>
<div class="line"><span class="lineno"> 58</span> <span class="keywordflow">for</span> (int64_t i = length - 1; i &gt;= 0; i--) {</div>
<div class="line"><span class="lineno"> 59</span> int64_t firstBit = first.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/at.html">at</a>(i) - <span class="charliteral">&#39;0&#39;</span>;</div>
<div class="line"><span class="lineno"> 60</span> int64_t secondBit = second.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/at.html">at</a>(i) - <span class="charliteral">&#39;0&#39;</span>;</div>
<div class="line"><span class="lineno"> 61</span> </div>
<div class="line"><span class="lineno"> 62</span> int64_t <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a> = (firstBit ^ secondBit ^ carry) + <span class="charliteral">&#39;0&#39;</span>; <span class="comment">// sum of 3 bits</span></div>
<div class="line"><span class="lineno"> 63</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> temp;</div>
<div class="line"><span class="lineno"> 64</span> temp = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/to_string.html">std::to_string</a>(<a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>);</div>
<div class="line"><span class="lineno"> 65</span> temp += <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
<div class="line"><span class="lineno"> 66</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = temp;</div>
<div class="line"><span class="lineno"> 67</span> </div>
<div class="line"><span class="lineno"> 68</span> carry = (firstBit &amp; secondBit) | (secondBit &amp; carry) |</div>
<div class="line"><span class="lineno"> 69</span> (firstBit &amp; carry); <span class="comment">// sum of 3 bits</span></div>
<div class="line"><span class="lineno"> 70</span> }</div>
<div class="line"><span class="lineno"> 71</span> </div>
<div class="line"><span class="lineno"> 72</span> <span class="keywordflow">if</span> (carry) {</div>
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<dl class="section return"><dt>Returns</dt><dd>the multiplicative number value </dd></dl>
<div class="fragment"><div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> {</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> zero = <span class="stringliteral">&quot;0&quot;</span>;</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="keywordflow">if</span> (len1 &lt; len2) {</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="keywordflow">for</span> (int64_t i = 0; i &lt; len2 - len1; i++) {</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> zero += str1;</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> str1 = zero;</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> }</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len1 &gt; len2) {</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> zero = <span class="stringliteral">&quot;0&quot;</span>;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="keywordflow">for</span> (int64_t i = 0; i &lt; len1 - len2; i++) {</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> zero += str2;</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> str2 = zero;</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> }</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> }</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keywordflow">if</span> (n == 0) {</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> }</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="keywordflow">if</span> (n == 1) {</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="keywordflow">return</span> (str1[0] - <span class="charliteral">&#39;0&#39;</span>) * (str2[0] - <span class="charliteral">&#39;0&#39;</span>);</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> }</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> int64_t fh = n / 2; <span class="comment">// first half of string</span></div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> int64_t sh = (n - fh); <span class="comment">// second half of string</span></div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> </div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Xl = str1.<a class="code hl_functionRef" 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>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Xr = str1.<a class="code hl_functionRef" 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>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> </div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Yl = str2.<a class="code hl_functionRef" 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>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Yr = str2.<a class="code hl_functionRef" 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>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> </div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="comment">// Calculating the three products of inputs of size n/2 recursively</span></div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> int64_t product1 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(Xl, Yl);</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> int64_t product2 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(Xr, Yr);</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> int64_t product3 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> divide_and_conquer::karatsuba_algorithm::addStrings(Xl, Xr),</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> divide_and_conquer::karatsuba_algorithm::addStrings(Yl, Yr));</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> </div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="keywordflow">return</span> product1 * (1 &lt;&lt; (2 * sh)) +</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> (product3 - product1 - product2) * (1 &lt;&lt; sh) +</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> product2; <span class="comment">// combining the three products to get the final result.</span></div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span>}</div>
<div class="fragment"><div class="line"><span class="lineno"> 84</span> {</div>
<div class="line"><span class="lineno"> 85</span> int64_t len1 = str1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 86</span> int64_t len2 = str2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 87</span> int64_t n = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(len1, len2);</div>
<div class="line"><span class="lineno"> 88</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> zero = <span class="stringliteral">&quot;0&quot;</span>;</div>
<div class="line"><span class="lineno"> 89</span> <span class="keywordflow">if</span> (len1 &lt; len2) {</div>
<div class="line"><span class="lineno"> 90</span> <span class="keywordflow">for</span> (int64_t i = 0; i &lt; len2 - len1; i++) {</div>
<div class="line"><span class="lineno"> 91</span> zero += str1;</div>
<div class="line"><span class="lineno"> 92</span> str1 = zero;</div>
<div class="line"><span class="lineno"> 93</span> }</div>
<div class="line"><span class="lineno"> 94</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len1 &gt; len2) {</div>
<div class="line"><span class="lineno"> 95</span> zero = <span class="stringliteral">&quot;0&quot;</span>;</div>
<div class="line"><span class="lineno"> 96</span> <span class="keywordflow">for</span> (int64_t i = 0; i &lt; len1 - len2; i++) {</div>
<div class="line"><span class="lineno"> 97</span> zero += str2;</div>
<div class="line"><span class="lineno"> 98</span> str2 = zero;</div>
<div class="line"><span class="lineno"> 99</span> }</div>
<div class="line"><span class="lineno"> 100</span> }</div>
<div class="line"><span class="lineno"> 101</span> <span class="keywordflow">if</span> (n == 0) {</div>
<div class="line"><span class="lineno"> 102</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 103</span> }</div>
<div class="line"><span class="lineno"> 104</span> <span class="keywordflow">if</span> (n == 1) {</div>
<div class="line"><span class="lineno"> 105</span> <span class="keywordflow">return</span> (str1[0] - <span class="charliteral">&#39;0&#39;</span>) * (str2[0] - <span class="charliteral">&#39;0&#39;</span>);</div>
<div class="line"><span class="lineno"> 106</span> }</div>
<div class="line"><span class="lineno"> 107</span> int64_t fh = n / 2; <span class="comment">// first half of string</span></div>
<div class="line"><span class="lineno"> 108</span> int64_t sh = (n - fh); <span class="comment">// second half of string</span></div>
<div class="line"><span class="lineno"> 109</span> </div>
<div class="line"><span class="lineno"> 110</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Xl = str1.<a class="code hl_functionRef" 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>
<div class="line"><span class="lineno"> 111</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Xr = str1.<a class="code hl_functionRef" 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>
<div class="line"><span class="lineno"> 112</span> </div>
<div class="line"><span class="lineno"> 113</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Yl = str2.<a class="code hl_functionRef" 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>
<div class="line"><span class="lineno"> 114</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Yr = str2.<a class="code hl_functionRef" 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>
<div class="line"><span class="lineno"> 115</span> </div>
<div class="line"><span class="lineno"> 116</span> <span class="comment">// Calculating the three products of inputs of size n/2 recursively</span></div>
<div class="line"><span class="lineno"> 117</span> int64_t product1 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(Xl, Yl);</div>
<div class="line"><span class="lineno"> 118</span> int64_t product2 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(Xr, Yr);</div>
<div class="line"><span class="lineno"> 119</span> int64_t product3 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(</div>
<div class="line"><span class="lineno"> 120</span> divide_and_conquer::karatsuba_algorithm::addStrings(Xl, Xr),</div>
<div class="line"><span class="lineno"> 121</span> divide_and_conquer::karatsuba_algorithm::addStrings(Yl, Yr));</div>
<div class="line"><span class="lineno"> 122</span> </div>
<div class="line"><span class="lineno"> 123</span> <span class="keywordflow">return</span> product1 * (1 &lt;&lt; (2 * sh)) +</div>
<div class="line"><span class="lineno"> 124</span> (product3 - product1 - product2) * (1 &lt;&lt; sh) +</div>
<div class="line"><span class="lineno"> 125</span> product2; <span class="comment">// combining the three products to get the final result.</span></div>
<div class="line"><span class="lineno"> 126</span>}</div>
<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>
<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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@@ -336,10 +336,10 @@ Here is the call graph for this function:</div>
<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> {</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span>}</div>
<div class="fragment"><div class="line"><span class="lineno"> 164</span> {</div>
<div class="line"><span class="lineno"> 165</span> <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 166</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 167</span>}</div>
<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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@@ -375,31 +375,31 @@ Here is the call graph for this function:</div>
<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> {</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <span class="comment">// 1st test</span></div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s11 = <span class="stringliteral">&quot;1&quot;</span>;</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s12 = <span class="stringliteral">&quot;1010&quot;</span>;</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test... &quot;</span>;</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> s11, s12) == 10); <span class="comment">// here the multiplication is 10</span></div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> </div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> <span class="comment">// 2nd test</span></div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s21 = <span class="stringliteral">&quot;11&quot;</span>;</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s22 = <span class="stringliteral">&quot;1010&quot;</span>;</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test... &quot;</span>;</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> s21, s22) == 30); <span class="comment">// here the multiplication is 30</span></div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> </div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <span class="comment">// 3rd test</span></div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s31 = <span class="stringliteral">&quot;110&quot;</span>;</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s32 = <span class="stringliteral">&quot;1010&quot;</span>;</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3rd test... &quot;</span>;</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> s31, s32) == 60); <span class="comment">// here the multiplication is 60</span></div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span>}</div>
<div class="fragment"><div class="line"><span class="lineno"> 134</span> {</div>
<div class="line"><span class="lineno"> 135</span> <span class="comment">// 1st test</span></div>
<div class="line"><span class="lineno"> 136</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s11 = <span class="stringliteral">&quot;1&quot;</span>;</div>
<div class="line"><span class="lineno"> 137</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s12 = <span class="stringliteral">&quot;1010&quot;</span>;</div>
<div class="line"><span class="lineno"> 138</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test... &quot;</span>;</div>
<div class="line"><span class="lineno"> 139</span> assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
<div class="line"><span class="lineno"> 140</span> s11, s12) == 10); <span class="comment">// here the multiplication is 10</span></div>
<div class="line"><span class="lineno"> 141</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 142</span> </div>
<div class="line"><span class="lineno"> 143</span> <span class="comment">// 2nd test</span></div>
<div class="line"><span class="lineno"> 144</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s21 = <span class="stringliteral">&quot;11&quot;</span>;</div>
<div class="line"><span class="lineno"> 145</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s22 = <span class="stringliteral">&quot;1010&quot;</span>;</div>
<div class="line"><span class="lineno"> 146</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test... &quot;</span>;</div>
<div class="line"><span class="lineno"> 147</span> assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
<div class="line"><span class="lineno"> 148</span> s21, s22) == 30); <span class="comment">// here the multiplication is 30</span></div>
<div class="line"><span class="lineno"> 149</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 150</span> </div>
<div class="line"><span class="lineno"> 151</span> <span class="comment">// 3rd test</span></div>
<div class="line"><span class="lineno"> 152</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s31 = <span class="stringliteral">&quot;110&quot;</span>;</div>
<div class="line"><span class="lineno"> 153</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s32 = <span class="stringliteral">&quot;1010&quot;</span>;</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keywordtype">double</span> second = R * (k1 * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">std::sin</a>(t) - l * k * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">std::sin</a>(k1 * t / k));</div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span>}</div>
<div class="fragment"><div class="line"><span class="lineno"> 71</span> {</div>
<div class="line"><span class="lineno"> 72</span> <span class="keywordtype">double</span> dt = rot * 2.f * M_PI / N;</div>
<div class="line"><span class="lineno"> 73</span> <span class="keywordtype">double</span> R = 1.f;</div>
<div class="line"><span class="lineno"> 74</span> <span class="keyword">const</span> <span class="keywordtype">double</span> k1 = 1.f - k;</div>
<div class="line"><span class="lineno"> 75</span> int32_t step = 0;</div>
<div class="line"><span class="lineno"> 76</span> </div>
<div class="line"><span class="lineno"> 77</span><span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><span class="lineno"> 78</span><span class="preprocessor">#pragma omp for</span></div>
<div class="line"><span class="lineno"> 79</span><span class="preprocessor">#endif</span></div>
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<div class="ttc" id="acos_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a></div><div class="ttdeci">T cos(T... args)</div></div>
<div class="ttc" id="asin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">std::sin</a></div><div class="ttdeci">T sin(T... args)</div></div>
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@@ -219,31 +219,31 @@ Here is the call graph for this function:</div>
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<p>Test function to save resulting points to a CSV file. </p>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keyword">const</span> <span class="keywordtype">size_t</span> N = 500;</div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> </div>
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<div class="fragment"><div class="line"><span class="lineno"> 93</span> {</div>
<div class="line"><span class="lineno"> 94</span> <span class="keyword">const</span> <span class="keywordtype">size_t</span> N = 500;</div>
<div class="line"><span class="lineno"> 95</span> <span class="keywordtype">double</span> l = 0.3, k = 0.75, rot = 10.;</div>
<div class="line"><span class="lineno"> 96</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_stringstream.html">std::stringstream</a> fname;</div>
<div class="line"><span class="lineno"> 97</span> fname &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(3) &lt;&lt; <span class="stringliteral">&quot;spirograph_&quot;</span> &lt;&lt; l &lt;&lt; <span class="stringliteral">&quot;_&quot;</span> &lt;&lt; k &lt;&lt; <span class="stringliteral">&quot;_&quot;</span> &lt;&lt; rot</div>
<div class="line"><span class="lineno"> 98</span> &lt;&lt; <span class="stringliteral">&quot;.csv&quot;</span>;</div>
<div class="line"><span class="lineno"> 99</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> fp(fname.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_stringstream/str.html">str</a>());</div>
<div class="line"><span class="lineno"> 100</span> <span class="keywordflow">if</span> (!fp.is_open()) {</div>
<div class="line"><span class="lineno"> 101</span> perror(fname.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_stringstream/str.html">str</a>().c_str());</div>
<div class="line"><span class="lineno"> 102</span> exit(EXIT_FAILURE);</div>
<div class="line"><span class="lineno"> 103</span> }</div>
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<div class="line"><span class="lineno"> 107</span> <a class="code hl_function" href="../../da/dd3/namespacespirograph.html#aeca22dbe4563358960e907a40cd3e1ac">spirograph</a>(&amp;points, l, k, rot);</div>
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@@ -36,7 +36,7 @@
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