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<a href="integer__sort_8hpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">//Templated Spreadsort-based implementation of integer_sort</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;</div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//          Copyright Steven J. Ross 2001 - 2014.</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Distributed under the Boost Software License, Version 1.0.</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">//    (See accompanying file LICENSE_1_0.txt or copy at</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">//          http://www.boost.org/LICENSE_1_0.txt)</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;</div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// See http://www.boost.org/libs/sort/ for library home page.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;</div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment">Some improvements suggested by:</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment">Phil Endecott and Frank Gennari</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment">Doxygen comments by Paul A. Bristow Jan 2015</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;</div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="preprocessor">#ifndef BOOST_INTEGER_SORT_HPP</span></div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="preprocessor">#define BOOST_INTEGER_SORT_HPP</span></div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="preprocessor">#include &lt;algorithm&gt;</span></div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="preprocessor">#include &lt;cstring&gt;</span></div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="preprocessor">#include &lt;limits&gt;</span></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="preprocessor">#include &lt;boost/static_assert.hpp&gt;</span></div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="preprocessor">#include &lt;boost/sort/spreadsort/detail/constants.hpp&gt;</span></div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="preprocessor">#include &lt;boost/sort/spreadsort/detail/integer_sort.hpp&gt;</span></div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceboost.html">boost</a> {</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;<span class="keyword">namespace </span>sort {</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;  <span class="comment">//Top-level sorting call for integers.</span></div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;<span class="comment">/*! \brief Integer sort algorithm using random access iterators.</span></div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;<span class="comment">  (All variants fall back to @c std::sort if the data size is too small, &lt; @c detail::min_sort_size).</span></div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;<span class="comment">  \details @c integer_sort is a fast templated in-place hybrid radix/comparison algorithm,</span></div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;<span class="comment">which in testing tends to be roughly 50% to 2X faster than @c std::sort for large tests (&gt;=100kB).\n</span></div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;<span class="comment">Worst-case performance is &lt;em&gt;  O(N * (lg(range)/s + s)) &lt;/em&gt;,</span></div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;<span class="comment">so @c integer_sort is asymptotically faster</span></div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;<span class="comment">than pure comparison-based algorithms. @c s is @c max_splits, which defaults to 11,</span></div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;<span class="comment">so its worst-case with default settings for 32-bit integers is</span></div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;<span class="comment">&lt;em&gt; O(N * ((32/11) &lt;/em&gt; slow radix-based iterations fast comparison-based iterations).\n\n</span></div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;<span class="comment">Some performance plots of runtime vs. n and log(range) are provided:\n</span></div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;<span class="comment">   &lt;a href=&quot;../../doc/graph/windows_integer_sort.htm&quot;&gt; windows_integer_sort&lt;/a&gt;</span></div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;<span class="comment">   \n</span></div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;<span class="comment">   &lt;a href=&quot;../../doc/graph/osx_integer_sort.htm&quot;&gt; osx_integer_sort&lt;/a&gt;</span></div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;<span class="comment">   \tparam RandomAccessIter &lt;a href=&quot;http://www.cplusplus.com/reference/iterator/RandomAccessIterator/&quot;&gt;Random access iterator&lt;/a&gt;</span></div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;<span class="comment">   \param[in] first Iterator pointer to first element.</span></div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;<span class="comment">   \param[in] last Iterator pointing to one beyond the end of data.</span></div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;<span class="comment">   \pre [@c first, @c last) is a valid range.</span></div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;<span class="comment">   \pre @c RandomAccessIter @c value_type is mutable.</span></div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;<span class="comment">   \pre @c RandomAccessIter @c value_type is &lt;a href=&quot;http://en.cppreference.com/w/cpp/concept/LessThanComparable&quot;&gt;LessThanComparable&lt;/a&gt;</span></div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;<span class="comment">   \pre @c RandomAccessIter @c value_type supports the @c operator&gt;&gt;,</span></div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;<span class="comment">   which returns an integer-type right-shifted a specified number of bits.</span></div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;<span class="comment">   \post The elements in the range [@c first, @c last) are sorted in ascending order.</span></div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;<span class="comment">   \throws std::exception Propagates exceptions if any of the element comparisons, the element swaps (or moves),</span></div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;<span class="comment">   the right shift, subtraction of right-shifted elements, functors, or any operations on iterators throw.</span></div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;<span class="comment">   \warning Throwing an exception may cause data loss. This will also throw if a small vector resize throws, in which case there will be no data loss.</span></div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;<span class="comment">   \warning Invalid arguments cause undefined behaviour.</span></div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;<span class="comment">   \note @c spreadsort function provides a wrapper that calls the fastest sorting algorithm available for a data type,</span></div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;<span class="comment">   enabling faster generic-programming.</span></div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;<span class="comment">   \remark The lesser of &lt;em&gt; O(N*log(N)) &lt;/em&gt; comparisons and &lt;em&gt; O(N*log(K/S + S)) &lt;/em&gt;operations worst-case, where:</span></div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;<span class="comment">   \remark  *  N is @c last - @c first,</span></div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;<span class="comment">   \remark  *  K is the log of the range in bits (32 for 32-bit integers using their full range),</span></div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;<span class="comment">   \remark  *  S is a constant called max_splits, defaulting to 11 (except for strings where it is the log of the character size).</span></div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">class</span> RandomAccessIter&gt;</div>
<div class="line"><a name="l00075"></a><span class="lineno"><a class="line" href="namespaceboost_1_1sort.html#ae6ffbcf932699589fd2b93879f209013">   75</a></span>&#160;  <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="namespaceboost_1_1sort.html#ae6ffbcf932699589fd2b93879f209013">integer_sort</a>(RandomAccessIter first, RandomAccessIter last)</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;  {</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    <span class="comment">// Don&#39;t sort if it&#39;s too small to optimize.</span></div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;    <span class="keywordflow">if</span> (last - first &lt; detail::min_sort_size)</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;      std::sort(first, last);</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;      <a class="code" href="namespaceboost_1_1sort.html#ae50349854aad811f67a540d9b3aa4d4a">detail::integer_sort</a>(first, last, *first &gt;&gt; 0);</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;  }</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;<span class="comment">/*! \brief Integer sort algorithm using random access iterators with both right-shift and user-defined comparison operator.</span></div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;<span class="comment">  (All variants fall back to @c std::sort if the data size is too small, &lt; @c detail::min_sort_size).</span></div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;<span class="comment">  \details @c integer_sort is a fast templated in-place hybrid radix/comparison algorithm,</span></div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;<span class="comment">which in testing tends to be roughly 50% to 2X faster than @c std::sort for large tests (&gt;=100kB).\n</span></div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;<span class="comment">Worst-case performance is &lt;em&gt;  O(N * (lg(range)/s + s)) &lt;/em&gt;,</span></div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;<span class="comment">so @c integer_sort is asymptotically faster</span></div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;<span class="comment">than pure comparison-based algorithms. @c s is @c max_splits, which defaults to 11,</span></div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;<span class="comment">so its worst-case with default settings for 32-bit integers is</span></div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;<span class="comment">&lt;em&gt; O(N * ((32/11) &lt;/em&gt; slow radix-based iterations fast comparison-based iterations).\n\n</span></div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;<span class="comment">Some performance plots of runtime vs. n and log(range) are provided:\n</span></div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;<span class="comment">   &lt;a href=&quot;../../doc/graph/windows_integer_sort.htm&quot;&gt; windows_integer_sort&lt;/a&gt;</span></div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;<span class="comment">   \n</span></div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;<span class="comment">   &lt;a href=&quot;../../doc/graph/osx_integer_sort.htm&quot;&gt; osx_integer_sort&lt;/a&gt;</span></div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;<span class="comment">   \tparam RandomAccessIter &lt;a href=&quot;http://www.cplusplus.com/reference/iterator/RandomAccessIterator/&quot;&gt;Random access iterator&lt;/a&gt;</span></div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;<span class="comment">   \tparam Right_shift functor for right-shift by parameter @c shift bits.</span></div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;<span class="comment">   \tparam Comp To provide @c operator&lt; for user-defined comparison.</span></div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;<span class="comment">   \param[in] first Iterator pointer to first element.</span></div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;<span class="comment">   \param[in] last Iterator pointing to one beyond the end of data.</span></div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;<span class="comment">   \param[in] shift Number of bits to right-shift (using functor).</span></div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;<span class="comment">   \param[in] comp comparison functor.</span></div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;<span class="comment">   \pre [@c first, @c last) is a valid range.</span></div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;<span class="comment">   \pre @c RandomAccessIter @c value_type is mutable.</span></div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;<span class="comment">   \pre @c RandomAccessIter @c value_type is &lt;a href=&quot;http://en.cppreference.com/w/cpp/concept/LessThanComparable&quot;&gt;LessThanComparable&lt;/a&gt;</span></div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;<span class="comment">   \pre @c RandomAccessIter @c value_type supports the @c operator&gt;&gt;,</span></div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;<span class="comment">   which returns an integer-type right-shifted a specified number of bits.</span></div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;<span class="comment">   \post The elements in the range [@c first, @c last) are sorted in ascending order.</span></div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;<span class="comment">   \return @c void.</span></div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;<span class="comment">   \throws std::exception Propagates exceptions if any of the element comparisons, the element swaps (or moves),</span></div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;<span class="comment">   the right shift, subtraction of right-shifted elements, functors,</span></div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;<span class="comment">   or any operations on iterators throw.</span></div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;<span class="comment">   \warning Throwing an exception may cause data loss. This will also throw if a small vector resize throws, in which case there will be no data loss.</span></div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;<span class="comment">   \warning Invalid arguments cause undefined behaviour.</span></div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;<span class="comment">   \note @c spreadsort function provides a wrapper that calls the fastest sorting algorithm available for a data type,</span></div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;<span class="comment">   enabling faster generic-programming.</span></div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;<span class="comment">   \remark The lesser of &lt;em&gt; O(N*log(N)) &lt;/em&gt; comparisons and &lt;em&gt; O(N*log(K/S + S)) &lt;/em&gt;operations worst-case, where:</span></div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;<span class="comment">   \remark  *  N is @c last - @c first,</span></div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;<span class="comment">   \remark  *  K is the log of the range in bits (32 for 32-bit integers using their full range),</span></div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;<span class="comment">   \remark  *  S is a constant called max_splits, defaulting to 11 (except for strings where it is the log of the character size).</span></div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">class</span> RandomAccessIter, <span class="keyword">class</span> Right_shift, <span class="keyword">class</span> Compare&gt;</div>
<div class="line"><a name="l00132"></a><span class="lineno"><a class="line" href="namespaceboost_1_1sort.html#aa4ebb2541be58f9f0fecd8d7c108b817">  132</a></span>&#160;  <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="namespaceboost_1_1sort.html#ae6ffbcf932699589fd2b93879f209013">integer_sort</a>(RandomAccessIter first, RandomAccessIter last,</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;                           Right_shift shift, Compare comp) {</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;    <span class="keywordflow">if</span> (last - first &lt; detail::min_sort_size)</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;      std::sort(first, last, comp);</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;      <a class="code" href="namespaceboost_1_1sort.html#ae50349854aad811f67a540d9b3aa4d4a">detail::integer_sort</a>(first, last, shift(*first, 0), shift, comp);</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;  }</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;<span class="comment">/*! \brief Integer sort algorithm using random access iterators with just right-shift functor.</span></div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;<span class="comment">  (All variants fall back to @c std::sort if the data size is too small, &lt; @c detail::min_sort_size).</span></div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;<span class="comment">  \details @c integer_sort is a fast templated in-place hybrid radix/comparison algorithm,</span></div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;<span class="comment">which in testing tends to be roughly 50% to 2X faster than @c std::sort for large tests (&gt;=100kB).\n</span></div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;<span class="comment">\par Performance:</span></div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;<span class="comment">Worst-case performance is &lt;em&gt;  O(N * (lg(range)/s + s)) &lt;/em&gt;,</span></div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;<span class="comment">so @c integer_sort is asymptotically faster</span></div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;<span class="comment">than pure comparison-based algorithms. @c s is @c max_splits, which defaults to 11,</span></div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;<span class="comment">so its worst-case with default settings for 32-bit integers is</span></div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;<span class="comment">&lt;em&gt; O(N * ((32/11) &lt;/em&gt; slow radix-based iterations fast comparison-based iterations).\n\n</span></div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;<span class="comment">Some performance plots of runtime vs. n and log(range) are provided:\n</span></div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;<span class="comment">  * &lt;a href=&quot;../../doc/graph/windows_integer_sort.htm&quot;&gt; windows_integer_sort&lt;/a&gt;\n</span></div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;<span class="comment">  * &lt;a href=&quot;../../doc/graph/osx_integer_sort.htm&quot;&gt; osx_integer_sort&lt;/a&gt;</span></div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;<span class="comment">   \tparam RandomAccessIter &lt;a href=&quot;http://www.cplusplus.com/reference/iterator/RandomAccessIterator/&quot;&gt;Random access iterator&lt;/a&gt;</span></div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;<span class="comment">   \tparam Right_shift functor for right-shift by parameter @c shift bits.</span></div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;<span class="comment">   \param[in] first Iterator pointer to first element.</span></div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;<span class="comment">   \param[in] last Iterator pointing to one beyond the end of data.</span></div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;<span class="comment">   \param[in] shift Number of bits to right-shift (using functor).</span></div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;<span class="comment">   \pre [@c first, @c last) is a valid range.</span></div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;<span class="comment">   \pre @c RandomAccessIter @c value_type is mutable.</span></div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;<span class="comment">   \pre @c RandomAccessIter @c value_type is &lt;a href=&quot;http://en.cppreference.com/w/cpp/concept/LessThanComparable&quot;&gt;LessThanComparable&lt;/a&gt;</span></div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;<span class="comment">   \pre @c RandomAccessIter @c value_type supports the @c operator&gt;&gt;,</span></div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;<span class="comment">   which returns an integer-type right-shifted a specified number of bits.</span></div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;<span class="comment">   \post The elements in the range [@c first, @c last) are sorted in ascending order.</span></div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;<span class="comment">   \throws std::exception Propagates exceptions if any of the element comparisons, the element swaps (or moves),</span></div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;<span class="comment">   the right shift, subtraction of right-shifted elements, functors,</span></div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;<span class="comment">   or any operations on iterators throw.</span></div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;<span class="comment">   \warning Throwing an exception may cause data loss. This will also throw if a small vector resize throws, in which case there will be no data loss.</span></div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;<span class="comment">   \warning Invalid arguments cause undefined behaviour.</span></div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;<span class="comment">   \note @c spreadsort function provides a wrapper that calls the fastest sorting algorithm available for a data type,</span></div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;<span class="comment">   enabling faster generic-programming.</span></div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;<span class="comment">   \remark The lesser of &lt;em&gt; O(N*log(N)) &lt;/em&gt; comparisons and &lt;em&gt; O(N*log(K/S + S)) &lt;/em&gt;operations worst-case, where:</span></div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;<span class="comment">   \remark  *  N is @c last - @c first,</span></div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;<span class="comment">   \remark  *  K is the log of the range in bits (32 for 32-bit integers using their full range),</span></div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;<span class="comment">   \remark  *  S is a constant called max_splits, defaulting to 11 (except for strings where it is the log of the character size).</span></div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">class</span> RandomAccessIter, <span class="keyword">class</span> Right_shift&gt;</div>
<div class="line"><a name="l00186"></a><span class="lineno"><a class="line" href="namespaceboost_1_1sort.html#ae50349854aad811f67a540d9b3aa4d4a">  186</a></span>&#160;  <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="namespaceboost_1_1sort.html#ae6ffbcf932699589fd2b93879f209013">integer_sort</a>(RandomAccessIter first, RandomAccessIter last,</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;                           Right_shift shift) {</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;    <span class="keywordflow">if</span> (last - first &lt; detail::min_sort_size)</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;      std::sort(first, last);</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;      <a class="code" href="namespaceboost_1_1sort.html#ae50349854aad811f67a540d9b3aa4d4a">detail::integer_sort</a>(first, last, shift(*first, 0), shift);</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;  }</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;}</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;}</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;</div>
<div class="ttc" id="namespaceboost_1_1sort_html_ae6ffbcf932699589fd2b93879f209013"><div class="ttname"><a href="namespaceboost_1_1sort.html#ae6ffbcf932699589fd2b93879f209013">boost::sort::integer_sort</a></div><div class="ttdeci">void integer_sort(RandomAccessIter first, RandomAccessIter last)</div><div class="ttdoc">Integer sort algorithm using random access iterators. (All variants fall back to std::sort if the dat...</div><div class="ttdef"><b>Definition:</b> integer_sort.hpp:75</div></div>
<div class="ttc" id="namespaceboost_html"><div class="ttname"><a href="namespaceboost.html">boost</a></div><div class="ttdef"><b>Definition:</b> float_sort.hpp:27</div></div>
<div class="ttc" id="namespaceboost_1_1sort_html_ae50349854aad811f67a540d9b3aa4d4a"><div class="ttname"><a href="namespaceboost_1_1sort.html#ae50349854aad811f67a540d9b3aa4d4a">boost::sort::integer_sort</a></div><div class="ttdeci">void integer_sort(RandomAccessIter first, RandomAccessIter last, Right_shift shift)</div><div class="ttdoc">Integer sort algorithm using random access iterators with just right-shift functor. (All variants fall back to std::sort if the data size is too small, < detail::min_sort_size). </div><div class="ttdef"><b>Definition:</b> integer_sort.hpp:186</div></div>
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