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<a href="sat_2util_8cc.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright 2010-2021 Google LLC</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// Licensed under the Apache License, Version 2.0 (the &quot;License&quot;);</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">// you may not use this file except in compliance with the License.</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// You may obtain a copy of the License at</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// distributed under the License is distributed on an &quot;AS IS&quot; BASIS,</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment">// See the License for the specific language governing permissions and</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment">// limitations under the License.</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include &quot;<a class="code" href="sat_2util_8h.html">ortools/sat/util.h</a>&quot;</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span> </div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include &lt;algorithm&gt;</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include &lt;cmath&gt;</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include &lt;cstdint&gt;</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include &quot;absl/numeric/int128.h&quot;</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include &quot;<a class="code" href="stl__util_8h.html">ortools/base/stl_util.h</a>&quot;</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> </div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceoperations__research.html">operations_research</a> {</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="keyword">namespace </span>sat {</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> </div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="keyword">namespace </span>{</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="comment">// This will be optimized into one division. I tested that in other places:</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="comment">//</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="comment">// Note that I am not 100% sure we need the indirection for the optimization</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="comment">// to kick in though, but this seemed safer given our weird r[i ^ 1] inputs.</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="keywordtype">void</span> QuotientAndRemainder(int64_t <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, int64_t <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>, int64_t&amp; q, int64_t&amp; r) {</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> q = <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a> / <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>;</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> r = <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a> % <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>;</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span>}</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span>} <span class="comment">// namespace</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> </div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#a0441e1a54fe203c0707131e587de8fae"> 37</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a0441e1a54fe203c0707131e587de8fae">RandomizeDecisionHeuristic</a>(absl::BitGenRef random,</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_sat_parameters.html">SatParameters</a>* <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>) {</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="preprocessor">#if !defined(__PORTABLE_PLATFORM__)</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// Random preferred variable order.</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="keyword">const</span> google::protobuf::EnumDescriptor* order_d =</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_sat_parameters.html#ad5b7d79e42adf8726ba2ef135ba3433b">SatParameters::VariableOrder_descriptor</a>();</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>-&gt;<a class="code hl_function" href="classoperations__research_1_1sat_1_1_sat_parameters.html#a7e544bdc4785ce055ed01ca1f22fca41">set_preferred_variable_order</a>(</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keyword">static_cast&lt;</span><a class="code hl_enumeration" href="namespaceoperations__research_1_1sat.html#a7457979a394e7bbe88562849cf43b20c">SatParameters::VariableOrder</a><span class="keyword">&gt;</span>(</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> order_d-&gt;value(absl::Uniform(random, 0, order_d-&gt;value_count()))</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> -&gt;number()));</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> </div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// Random polarity initial value.</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keyword">const</span> google::protobuf::EnumDescriptor* polarity_d =</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_sat_parameters.html#a6504b5e204a20519bc8673861f54531c">SatParameters::Polarity_descriptor</a>();</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>-&gt;<a class="code hl_function" href="classoperations__research_1_1sat_1_1_sat_parameters.html#a12558bbe25af1ee14f86bab924c96709">set_initial_polarity</a>(<span class="keyword">static_cast&lt;</span><a class="code hl_enumeration" href="namespaceoperations__research_1_1sat.html#aa1fba7d2cdcaea2d0482431bb2138ac2">SatParameters::Polarity</a><span class="keyword">&gt;</span>(</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> polarity_d-&gt;value(absl::Uniform(random, 0, polarity_d-&gt;value_count()))</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> -&gt;number()));</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="preprocessor">#endif </span><span class="comment">// __PORTABLE_PLATFORM__</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// Other random parameters.</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>-&gt;<a class="code hl_function" href="classoperations__research_1_1sat_1_1_sat_parameters.html#ae31c8a339e7515e82ad032f6f89ace68">set_use_phase_saving</a>(absl::Bernoulli(random, 0.5));</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>-&gt;<a class="code hl_function" href="classoperations__research_1_1sat_1_1_sat_parameters.html#a05528f270d7291bd49be9f8575780fcb">set_random_polarity_ratio</a>(absl::Bernoulli(random, 0.5) ? 0.01</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> : 0.0);</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>-&gt;<a class="code hl_function" href="classoperations__research_1_1sat_1_1_sat_parameters.html#a8a7cbb53d028e253e201883124b6089e">set_random_branches_ratio</a>(absl::Bernoulli(random, 0.5) ? 0.01</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> : 0.0);</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> </div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span><span class="comment">// Using the extended Euclidian algo, we find a and b such that a x + b m = gcd.</span></div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span><span class="comment">// https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#abbbb4c91f9a3d6eb290709745f5b661c"> 65</a></span>int64_t <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#abbbb4c91f9a3d6eb290709745f5b661c">ModularInverse</a>(int64_t x, int64_t m) {</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <a class="code hl_define" href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a>(x, 0);</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <a class="code hl_define" href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a>(x, m);</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> </div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> int64_t r[2] = {m, x};</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> int64_t t[2] = {0, 1};</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> int64_t q;</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> </div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="comment">// We only keep the last two terms of the sequences with the &quot;^1&quot; trick:</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="comment">//</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="comment">// q = r[i-2] / r[i-1]</span></div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="comment">// r[i] = r[i-2] % r[i-1]</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="comment">// t[i] = t[i-2] - t[i-1] * q</span></div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="comment">//</span></div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="comment">// We always have:</span></div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// - gcd(r[i], r[i - 1]) = gcd(r[i - 1], r[i - 2])</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="comment">// - x * t[i] + m * t[i - 1] = r[i]</span></div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keywordtype">int</span> i = 0;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keywordflow">for</span> (; r[i ^ 1] != 0; i ^= 1) {</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> QuotientAndRemainder(r[i], r[i ^ 1], q, r[i]);</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> t[i] -= t[i ^ 1] * q;</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> }</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> </div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="comment">// If the gcd is not one, there is no inverse, we returns 0.</span></div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="keywordflow">if</span> (r[i] != 1) <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> </div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="comment">// Correct the result so that it is in [0, m). Note that abs(t[i]) is known to</span></div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="comment">// be less than or equal to x / 2, and we have thorough unit-tests.</span></div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keywordflow">if</span> (t[i] &lt; 0) t[i] += m;</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> </div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keywordflow">return</span> t[i];</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span>}</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> </div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#a629c989df2521428c30722f175874774"> 98</a></span>int64_t <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a629c989df2521428c30722f175874774">PositiveMod</a>(int64_t x, int64_t m) {</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="keyword">const</span> int64_t r = x % m;</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="keywordflow">return</span> r &lt; 0 ? r + m : r;</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span>}</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> </div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#ac015d81b88379719f680eadc2aad1508"> 103</a></span>int64_t <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#ac015d81b88379719f680eadc2aad1508">ProductWithModularInverse</a>(int64_t coeff, int64_t mod, int64_t rhs) {</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <a class="code hl_define" href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a>(coeff, 0);</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <a class="code hl_define" href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a>(mod, 0);</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> mod = std::abs(mod);</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="keywordflow">if</span> (rhs == 0 || mod == 1) <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <a class="code hl_define" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(std::gcd(std::abs(coeff), mod), 1);</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> </div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <span class="comment">// Make both in [0, mod).</span></div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> coeff = <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a629c989df2521428c30722f175874774">PositiveMod</a>(coeff, mod);</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> rhs = <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a629c989df2521428c30722f175874774">PositiveMod</a>(rhs, mod);</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> </div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="comment">// From X * coeff % mod = rhs</span></div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="comment">// We deduce that X % mod = rhs * inverse % mod</span></div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="keyword">const</span> int64_t inverse = <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#abbbb4c91f9a3d6eb290709745f5b661c">ModularInverse</a>(coeff, mod);</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <a class="code hl_define" href="base_2logging_8h.html#ab25e01a2942b821d66371fc68d53f2eb">CHECK_NE</a>(inverse, 0);</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> </div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="comment">// We make the operation in 128 bits to be sure not to have any overflow here.</span></div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <span class="keyword">const</span> absl::int128 p = absl::int128{inverse} * absl::int128{rhs};</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span>int64_t<span class="keyword">&gt;</span>(p % absl::int128{mod});</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span>}</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> </div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#a852a51b53f6217d6bfd1aef455f53f8c"> 125</a></span><span class="keywordtype">bool</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a852a51b53f6217d6bfd1aef455f53f8c">SolveDiophantineEquationOfSizeTwo</a>(int64_t&amp; <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, int64_t&amp; <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>, int64_t&amp; cte,</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> int64_t&amp; x0, int64_t&amp; y0) {</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <a class="code hl_define" href="base_2logging_8h.html#ab25e01a2942b821d66371fc68d53f2eb">CHECK_NE</a>(<a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, 0);</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <a class="code hl_define" href="base_2logging_8h.html#ab25e01a2942b821d66371fc68d53f2eb">CHECK_NE</a>(<a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>, 0);</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <a class="code hl_define" href="base_2logging_8h.html#ab25e01a2942b821d66371fc68d53f2eb">CHECK_NE</a>(<a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::numeric_limits&lt;int64_t&gt;::min</a>());</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <a class="code hl_define" href="base_2logging_8h.html#ab25e01a2942b821d66371fc68d53f2eb">CHECK_NE</a>(<a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>, <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::numeric_limits&lt;int64_t&gt;::min</a>());</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> </div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="keyword">const</span> int64_t gcd = std::gcd(std::abs(<a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>), std::abs(<a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>));</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="keywordflow">if</span> (cte % gcd != 0) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a> /= gcd;</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a> /= gcd;</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> cte /= gcd;</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> </div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <span class="comment">// The simple case where (0, 0) is a solution.</span></div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <span class="keywordflow">if</span> (cte == 0) {</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> x0 = y0 = 0;</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</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> </div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <span class="comment">// We solve a * X + b * Y = cte</span></div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> <span class="comment">// We take a valid x0 in [0, b) by considering the equation mod b.</span></div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> x0 = <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#ac015d81b88379719f680eadc2aad1508">ProductWithModularInverse</a>(<a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>, cte);</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> </div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> <span class="comment">// We choose x0 of the same sign as cte.</span></div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> <span class="keywordflow">if</span> (cte &lt; 0 &amp;&amp; x0 != 0) x0 -= std::abs(<a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</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">// By plugging X = x0 + b * Z</span></div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <span class="comment">// We have a * (x0 + b * Z) + b * Y = cte</span></div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> <span class="comment">// so a * b * Z + b * Y = cte - a * x0;</span></div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> <span class="comment">// and y0 = (cte - a * x0) / b (with an exact division by construction).</span></div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> <span class="keyword">const</span> absl::int128 t = absl::int128{cte} - absl::int128{<a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>} * absl::int128{x0};</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <a class="code hl_define" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(t % absl::int128{<a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>}, absl::int128{0});</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> </div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <span class="comment">// Overflow-wise, there is two cases for cte &gt; 0:</span></div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="comment">// - a * x0 &lt;= cte, in this case y0 will not overflow (&lt;= cte).</span></div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <span class="comment">// - a * x0 &gt; cte, in this case y0 will be in (-a, 0].</span></div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <span class="keyword">const</span> absl::int128 r = t / absl::int128{<a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>};</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <a class="code hl_define" href="base_2logging_8h.html#a4395e95bab44e222cb2e77251017a0e2">DCHECK_LE</a>(r, absl::int128{<a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::numeric_limits&lt;int64_t&gt;::max</a>()});</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> <a class="code hl_define" href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a>(r, absl::int128{<a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::numeric_limits&lt;int64_t&gt;::min</a>()});</div>
<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> y0 = <span class="keyword">static_cast&lt;</span>int64_t<span class="keyword">&gt;</span>(r);</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span>}</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> </div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#a2ef3eb1f5fe6506a5e24115f10d724fc"> 169</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a2ef3eb1f5fe6506a5e24115f10d724fc">MoveOneUnprocessedLiteralLast</a>(<span class="keyword">const</span> std::set&lt;LiteralIndex&gt;&amp; processed,</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> <span class="keywordtype">int</span> relevant_prefix_size,</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> std::vector&lt;Literal&gt;* literals) {</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> <span class="keywordflow">if</span> (literals-&gt;empty()) <span class="keywordflow">return</span> -1;</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> <span class="keywordflow">if</span> (!<a class="code hl_function" href="namespacegtl.html#aae28e97bd1fa93cb0032642550da7455">gtl::ContainsKey</a>(processed, literals-&gt;back().Index())) {</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> <span class="keywordflow">return</span> std::min&lt;int&gt;(relevant_prefix_size, literals-&gt;size());</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> }</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> </div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> <span class="comment">// To get O(n log n) size of suffixes, we will first process the last n/2</span></div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> <span class="comment">// literals, we then move all of them first and process the n/2 literals left.</span></div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> <span class="comment">// We use the same algorithm recursively. The sum of the suffixes&#39; size S(n)</span></div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> <span class="comment">// is thus S(n/2) + n + S(n/2). That gives us the correct complexity. The code</span></div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> <span class="comment">// below simulates one step of this algorithm and is made to be &quot;robust&quot; when</span></div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="comment">// from one call to the next, some literals have been removed (but the order</span></div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <span class="comment">// of literals is preserved).</span></div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <span class="keywordtype">int</span> num_processed = 0;</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> <span class="keywordtype">int</span> num_not_processed = 0;</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> <span class="keywordtype">int</span> target_prefix_size = literals-&gt;size() - 1;</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = literals-&gt;size() - 1; i &gt;= 0; i--) {</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="namespacegtl.html#aae28e97bd1fa93cb0032642550da7455">gtl::ContainsKey</a>(processed, (*literals)[i].<a class="code hl_typedef" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a>())) {</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> ++num_processed;</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> ++num_not_processed;</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> target_prefix_size = i;</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> }</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <span class="keywordflow">if</span> (num_not_processed &gt;= num_processed) <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> }</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> <span class="keywordflow">if</span> (num_not_processed == 0) <span class="keywordflow">return</span> -1;</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> target_prefix_size = <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(target_prefix_size, relevant_prefix_size);</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> </div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> <span class="comment">// Once a prefix size has been decided, it is always better to</span></div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> <span class="comment">// enqueue the literal already processed first.</span></div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> std::stable_partition(literals-&gt;begin() + target_prefix_size, literals-&gt;end(),</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> [&amp;processed](<a class="code hl_class" href="classoperations__research_1_1sat_1_1_literal.html">Literal</a> l) {</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> return gtl::ContainsKey(processed, l.Index());</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> });</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> <span class="keywordflow">return</span> target_prefix_size;</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span>}</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> </div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_incremental_average.html#adf01dcbe31fa99f0a8f9d91ba9f85b8b"> 208</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_incremental_average.html#adf01dcbe31fa99f0a8f9d91ba9f85b8b">IncrementalAverage::Reset</a>(<span class="keywordtype">double</span> reset_value) {</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> num_records_ = 0;</div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> average_ = reset_value;</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span>}</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> </div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_incremental_average.html#a198870bbc0f9b8d197a4c80f766ddf49"> 213</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_incremental_average.html#a198870bbc0f9b8d197a4c80f766ddf49">IncrementalAverage::AddData</a>(<span class="keywordtype">double</span> new_record) {</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> num_records_++;</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> average_ += (new_record - average_) / num_records_;</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span>}</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> </div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_exponential_moving_average.html#a198870bbc0f9b8d197a4c80f766ddf49"> 218</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_exponential_moving_average.html#a198870bbc0f9b8d197a4c80f766ddf49">ExponentialMovingAverage::AddData</a>(<span class="keywordtype">double</span> new_record) {</div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> num_records_++;</div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> average_ = (num_records_ == 1)</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> ? new_record</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> : (new_record + decaying_factor_ * (average_ - new_record));</div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span>}</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> </div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_percentile.html#adfcf2b433605c03210cbd06e28ce9d97"> 225</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_percentile.html#adfcf2b433605c03210cbd06e28ce9d97">Percentile::AddRecord</a>(<span class="keywordtype">double</span> record) {</div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> records_.push_front(record);</div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> <span class="keywordflow">if</span> (records_.size() &gt; record_limit_) {</div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> records_.pop_back();</div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> }</div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span>}</div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> </div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_percentile.html#a006c3e4f212cee5414d510a9ded6eedb"> 232</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_percentile.html#a006c3e4f212cee5414d510a9ded6eedb">Percentile::GetPercentile</a>(<span class="keywordtype">double</span> percent) {</div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> <a class="code hl_define" href="base_2logging_8h.html#a7e03ec13560fa94a8fea569960d7efc6">CHECK_GT</a>(records_.size(), 0);</div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> <a class="code hl_define" href="base_2logging_8h.html#ae4db23f10f5d4aad6d735f5a74cd6f8c">CHECK_LE</a>(percent, 100.0);</div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> <a class="code hl_define" href="base_2logging_8h.html#a7cc25402ecd7591b4c39934dd656b1f9">CHECK_GE</a>(percent, 0.0);</div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> std::vector&lt;double&gt; sorted_records(records_.begin(), records_.end());</div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> std::sort(sorted_records.begin(), sorted_records.end());</div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_records = sorted_records.size();</div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> </div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> <span class="keyword">const</span> <span class="keywordtype">double</span> percentile_rank =</div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(num_records) * percent / 100.0 - 0.5;</div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> <span class="keywordflow">if</span> (percentile_rank &lt;= 0) {</div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> <span class="keywordflow">return</span> sorted_records.front();</div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (percentile_rank &gt;= num_records - 1) {</div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> <span class="keywordflow">return</span> sorted_records.back();</div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> }</div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> <span class="comment">// Interpolate.</span></div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> <a class="code hl_define" href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a>(num_records, 2);</div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <a class="code hl_define" href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a>(percentile_rank, num_records - 1);</div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> <span class="keyword">const</span> <span class="keywordtype">int</span> lower_rank = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(std::floor(percentile_rank));</div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> <a class="code hl_define" href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a>(lower_rank, num_records - 1);</div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> <span class="keywordflow">return</span> sorted_records[lower_rank] +</div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> (percentile_rank - lower_rank) *</div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> (sorted_records[lower_rank + 1] - sorted_records[lower_rank]);</div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span>}</div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> </div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#a3e5f39b52251ad02e571592493b4d39f"> 257</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a3e5f39b52251ad02e571592493b4d39f">CompressTuples</a>(absl::Span&lt;const int64_t&gt; domain_sizes, int64_t any_value,</div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> std::vector&lt;std::vector&lt;int64_t&gt;&gt;* tuples) {</div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> <span class="keywordflow">if</span> (tuples-&gt;empty()) <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> </div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> <span class="comment">// Remove duplicates if any.</span></div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> <a class="code hl_function" href="namespacegtl.html#a288a1dc92da5d3ad62d4bc4cec9e8b1d">gtl::STLSortAndRemoveDuplicates</a>(tuples);</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> </div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_vars = (*tuples)[0].size();</div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> </div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> std::vector&lt;int&gt; to_remove;</div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> std::vector&lt;int64_t&gt; tuple_minus_var_i(num_vars - 1);</div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; num_vars; ++i) {</div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> <span class="keyword">const</span> <span class="keywordtype">int</span> domain_size = domain_sizes[i];</div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> <span class="keywordflow">if</span> (domain_size == 1) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> absl::flat_hash_map&lt;const std::vector&lt;int64_t&gt;, std::vector&lt;int&gt;&gt;</div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> masked_tuples_to_indices;</div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> t = 0; t &lt; tuples-&gt;size(); ++t) {</div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> <span class="keywordtype">int</span> out = 0;</div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; num_vars; ++j) {</div>
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> <span class="keywordflow">if</span> (i == j) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> tuple_minus_var_i[out++] = (*tuples)[t][j];</div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> }</div>
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> masked_tuples_to_indices[tuple_minus_var_i].push_back(t);</div>
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> }</div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> to_remove.clear();</div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>&amp; it : masked_tuples_to_indices) {</div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> <span class="keywordflow">if</span> (it.second.size() != domain_size) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> (*tuples)[it.second.front()][i] = any_value;</div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> to_remove.insert(to_remove.end(), it.second.begin() + 1, it.second.end());</div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> }</div>
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> std::sort(to_remove.begin(), to_remove.end(), std::greater&lt;int&gt;());</div>
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> t : to_remove) {</div>
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> (*tuples)[t] = tuples-&gt;back();</div>
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> tuples-&gt;pop_back();</div>
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> }</div>
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> }</div>
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span>}</div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> </div>
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span>} <span class="comment">// namespace sat</span></div>
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span>} <span class="comment">// namespace operations_research</span></div>
<div class="ttc" id="aalldiff__cst_8cc_html_a26e6db9bcc64b584051ecc28171ed11f"><div class="ttname"><a href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a></div><div class="ttdeci">int64_t max</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00140">alldiff_cst.cc:140</a></div></div>
<div class="ttc" id="aalldiff__cst_8cc_html_ad10edae0a852d72fb76afb1c77735045"><div class="ttname"><a href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a></div><div class="ttdeci">int64_t min</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00139">alldiff_cst.cc:139</a></div></div>
<div class="ttc" id="abase_2logging_8h_html_a4395e95bab44e222cb2e77251017a0e2"><div class="ttname"><a href="base_2logging_8h.html#a4395e95bab44e222cb2e77251017a0e2">DCHECK_LE</a></div><div class="ttdeci">#define DCHECK_LE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00889">base/logging.h:889</a></div></div>
<div class="ttc" id="abase_2logging_8h_html_a46e69120fbd3b36e6960e096d23b66f0"><div class="ttname"><a href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a></div><div class="ttdeci">#define DCHECK_NE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00888">base/logging.h:888</a></div></div>
<div class="ttc" id="abase_2logging_8h_html_a7cc25402ecd7591b4c39934dd656b1f9"><div class="ttname"><a href="base_2logging_8h.html#a7cc25402ecd7591b4c39934dd656b1f9">CHECK_GE</a></div><div class="ttdeci">#define CHECK_GE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00703">base/logging.h:703</a></div></div>
<div class="ttc" id="abase_2logging_8h_html_a7e03ec13560fa94a8fea569960d7efc6"><div class="ttname"><a href="base_2logging_8h.html#a7e03ec13560fa94a8fea569960d7efc6">CHECK_GT</a></div><div class="ttdeci">#define CHECK_GT(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00704">base/logging.h:704</a></div></div>
<div class="ttc" id="abase_2logging_8h_html_aae2dc65d9ea248d54bf39daa986dd295"><div class="ttname"><a href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a></div><div class="ttdeci">#define DCHECK_GE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00891">base/logging.h:891</a></div></div>
<div class="ttc" id="abase_2logging_8h_html_ab25e01a2942b821d66371fc68d53f2eb"><div class="ttname"><a href="base_2logging_8h.html#ab25e01a2942b821d66371fc68d53f2eb">CHECK_NE</a></div><div class="ttdeci">#define CHECK_NE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00700">base/logging.h:700</a></div></div>
<div class="ttc" id="abase_2logging_8h_html_ab62f5ed8f2d48e29802be0cbbcd1359a"><div class="ttname"><a href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a></div><div class="ttdeci">#define DCHECK_LT(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00890">base/logging.h:890</a></div></div>
<div class="ttc" id="abase_2logging_8h_html_ae4db23f10f5d4aad6d735f5a74cd6f8c"><div class="ttname"><a href="base_2logging_8h.html#ae4db23f10f5d4aad6d735f5a74cd6f8c">CHECK_LE</a></div><div class="ttdeci">#define CHECK_LE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00701">base/logging.h:701</a></div></div>
<div class="ttc" id="abase_2logging_8h_html_ae89df3243bbb8341130c7b3f44145ea0"><div class="ttname"><a href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a></div><div class="ttdeci">#define DCHECK_EQ(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00887">base/logging.h:887</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_exponential_moving_average_html_a198870bbc0f9b8d197a4c80f766ddf49"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_exponential_moving_average.html#a198870bbc0f9b8d197a4c80f766ddf49">operations_research::sat::ExponentialMovingAverage::AddData</a></div><div class="ttdeci">void AddData(double new_record)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00218">sat/util.cc:218</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_incremental_average_html_a198870bbc0f9b8d197a4c80f766ddf49"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_incremental_average.html#a198870bbc0f9b8d197a4c80f766ddf49">operations_research::sat::IncrementalAverage::AddData</a></div><div class="ttdeci">void AddData(double new_record)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00213">sat/util.cc:213</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_incremental_average_html_adf01dcbe31fa99f0a8f9d91ba9f85b8b"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_incremental_average.html#adf01dcbe31fa99f0a8f9d91ba9f85b8b">operations_research::sat::IncrementalAverage::Reset</a></div><div class="ttdeci">void Reset(double reset_value)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00208">sat/util.cc:208</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_literal_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_literal.html">operations_research::sat::Literal</a></div><div class="ttdef"><b>Definition:</b> <a href="sat__base_8h_source.html#l00066">sat_base.h:66</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_percentile_html_a006c3e4f212cee5414d510a9ded6eedb"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_percentile.html#a006c3e4f212cee5414d510a9ded6eedb">operations_research::sat::Percentile::GetPercentile</a></div><div class="ttdeci">double GetPercentile(double percent)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00232">sat/util.cc:232</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_percentile_html_adfcf2b433605c03210cbd06e28ce9d97"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_percentile.html#adfcf2b433605c03210cbd06e28ce9d97">operations_research::sat::Percentile::AddRecord</a></div><div class="ttdeci">void AddRecord(double record)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00225">sat/util.cc:225</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_sat_parameters_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_sat_parameters.html">operations_research::sat::SatParameters</a></div><div class="ttdef"><b>Definition:</b> <a href="sat__parameters_8pb_8h_source.html#l00347">sat_parameters.pb.h:348</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_sat_parameters_html_a05528f270d7291bd49be9f8575780fcb"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_sat_parameters.html#a05528f270d7291bd49be9f8575780fcb">operations_research::sat::SatParameters::set_random_polarity_ratio</a></div><div class="ttdeci">void set_random_polarity_ratio(double value)</div><div class="ttdef"><b>Definition:</b> <a href="sat__parameters_8pb_8h_source.html#l03649">sat_parameters.pb.h:3649</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_sat_parameters_html_a12558bbe25af1ee14f86bab924c96709"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_sat_parameters.html#a12558bbe25af1ee14f86bab924c96709">operations_research::sat::SatParameters::set_initial_polarity</a></div><div class="ttdeci">void set_initial_polarity(::operations_research::sat::SatParameters_Polarity value)</div><div class="ttdef"><b>Definition:</b> <a href="sat__parameters_8pb_8h_source.html#l03565">sat_parameters.pb.h:3565</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_sat_parameters_html_a6504b5e204a20519bc8673861f54531c"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_sat_parameters.html#a6504b5e204a20519bc8673861f54531c">operations_research::sat::SatParameters::Polarity_descriptor</a></div><div class="ttdeci">static const ::PROTOBUF_NAMESPACE_ID::EnumDescriptor * Polarity_descriptor()</div><div class="ttdef"><b>Definition:</b> <a href="sat__parameters_8pb_8h_source.html#l00526">sat_parameters.pb.h:526</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_sat_parameters_html_a7e544bdc4785ce055ed01ca1f22fca41"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_sat_parameters.html#a7e544bdc4785ce055ed01ca1f22fca41">operations_research::sat::SatParameters::set_preferred_variable_order</a></div><div class="ttdeci">void set_preferred_variable_order(::operations_research::sat::SatParameters_VariableOrder value)</div><div class="ttdef"><b>Definition:</b> <a href="sat__parameters_8pb_8h_source.html#l03536">sat_parameters.pb.h:3536</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_sat_parameters_html_a8a7cbb53d028e253e201883124b6089e"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_sat_parameters.html#a8a7cbb53d028e253e201883124b6089e">operations_research::sat::SatParameters::set_random_branches_ratio</a></div><div class="ttdeci">void set_random_branches_ratio(double value)</div><div class="ttdef"><b>Definition:</b> <a href="sat__parameters_8pb_8h_source.html#l03677">sat_parameters.pb.h:3677</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_sat_parameters_html_ad5b7d79e42adf8726ba2ef135ba3433b"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_sat_parameters.html#ad5b7d79e42adf8726ba2ef135ba3433b">operations_research::sat::SatParameters::VariableOrder_descriptor</a></div><div class="ttdeci">static const ::PROTOBUF_NAMESPACE_ID::EnumDescriptor * VariableOrder_descriptor()</div><div class="ttdef"><b>Definition:</b> <a href="sat__parameters_8pb_8h_source.html#l00490">sat_parameters.pb.h:490</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_sat_parameters_html_ae31c8a339e7515e82ad032f6f89ace68"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_sat_parameters.html#ae31c8a339e7515e82ad032f6f89ace68">operations_research::sat::SatParameters::set_use_phase_saving</a></div><div class="ttdeci">void set_use_phase_saving(bool value)</div><div class="ttdef"><b>Definition:</b> <a href="sat__parameters_8pb_8h_source.html#l03593">sat_parameters.pb.h:3593</a></div></div>
<div class="ttc" id="aconstraint__solver_2table_8cc_html_a9293e4d29cac928301645070dd307683"><div class="ttname"><a href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a></div><div class="ttdeci">int64_t b</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_2table_8cc_source.html#l00047">constraint_solver/table.cc:47</a></div></div>
<div class="ttc" id="aconstraint__solver_2table_8cc_html_acb18315d548212835cd8ed4287e6c0b6"><div class="ttname"><a href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a></div><div class="ttdeci">int64_t a</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_2table_8cc_source.html#l00046">constraint_solver/table.cc:46</a></div></div>
<div class="ttc" id="acp__model__fz__solver_8cc_html_a10a1eab179b472c030bdc2a2efef7219"><div class="ttname"><a href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a></div><div class="ttdeci">SatParameters parameters</div><div class="ttdef"><b>Definition:</b> <a href="cp__model__fz__solver_8cc_source.html#l00120">cp_model_fz_solver.cc:120</a></div></div>
<div class="ttc" id="anamespacegtl_html_a288a1dc92da5d3ad62d4bc4cec9e8b1d"><div class="ttname"><a href="namespacegtl.html#a288a1dc92da5d3ad62d4bc4cec9e8b1d">gtl::STLSortAndRemoveDuplicates</a></div><div class="ttdeci">void STLSortAndRemoveDuplicates(T *v, const LessFunc &amp;less_func)</div><div class="ttdef"><b>Definition:</b> <a href="stl__util_8h_source.html#l00058">stl_util.h:58</a></div></div>
<div class="ttc" id="anamespacegtl_html_aae28e97bd1fa93cb0032642550da7455"><div class="ttname"><a href="namespacegtl.html#aae28e97bd1fa93cb0032642550da7455">gtl::ContainsKey</a></div><div class="ttdeci">bool ContainsKey(const Collection &amp;collection, const Key &amp;key)</div><div class="ttdef"><b>Definition:</b> <a href="map__util_8h_source.html#l00200">map_util.h:200</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1glop_html_ac89c7b45754e9a6bdabc08bea586fc4e"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">operations_research::glop::Index</a></div><div class="ttdeci">int32_t Index</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00038">lp_types.h:38</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a0441e1a54fe203c0707131e587de8fae"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a0441e1a54fe203c0707131e587de8fae">operations_research::sat::RandomizeDecisionHeuristic</a></div><div class="ttdeci">void RandomizeDecisionHeuristic(absl::BitGenRef random, SatParameters *parameters)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00037">sat/util.cc:37</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a2ef3eb1f5fe6506a5e24115f10d724fc"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a2ef3eb1f5fe6506a5e24115f10d724fc">operations_research::sat::MoveOneUnprocessedLiteralLast</a></div><div class="ttdeci">int MoveOneUnprocessedLiteralLast(const std::set&lt; LiteralIndex &gt; &amp;processed, int relevant_prefix_size, std::vector&lt; Literal &gt; *literals)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00169">sat/util.cc:169</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a3e5f39b52251ad02e571592493b4d39f"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a3e5f39b52251ad02e571592493b4d39f">operations_research::sat::CompressTuples</a></div><div class="ttdeci">void CompressTuples(absl::Span&lt; const int64_t &gt; domain_sizes, int64_t any_value, std::vector&lt; std::vector&lt; int64_t &gt; &gt; *tuples)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00257">sat/util.cc:257</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a629c989df2521428c30722f175874774"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a629c989df2521428c30722f175874774">operations_research::sat::PositiveMod</a></div><div class="ttdeci">int64_t PositiveMod(int64_t x, int64_t m)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00098">sat/util.cc:98</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a7457979a394e7bbe88562849cf43b20c"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a7457979a394e7bbe88562849cf43b20c">operations_research::sat::SatParameters_VariableOrder</a></div><div class="ttdeci">SatParameters_VariableOrder</div><div class="ttdef"><b>Definition:</b> <a href="sat__parameters_8pb_8h_source.html#l00070">sat_parameters.pb.h:70</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a852a51b53f6217d6bfd1aef455f53f8c"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a852a51b53f6217d6bfd1aef455f53f8c">operations_research::sat::SolveDiophantineEquationOfSizeTwo</a></div><div class="ttdeci">bool SolveDiophantineEquationOfSizeTwo(int64_t &amp;a, int64_t &amp;b, int64_t &amp;cte, int64_t &amp;x0, int64_t &amp;y0)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00125">sat/util.cc:125</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_aa1fba7d2cdcaea2d0482431bb2138ac2"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#aa1fba7d2cdcaea2d0482431bb2138ac2">operations_research::sat::SatParameters_Polarity</a></div><div class="ttdeci">SatParameters_Polarity</div><div class="ttdef"><b>Definition:</b> <a href="sat__parameters_8pb_8h_source.html#l00094">sat_parameters.pb.h:94</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_abbbb4c91f9a3d6eb290709745f5b661c"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#abbbb4c91f9a3d6eb290709745f5b661c">operations_research::sat::ModularInverse</a></div><div class="ttdeci">int64_t ModularInverse(int64_t x, int64_t m)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00065">sat/util.cc:65</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_ac015d81b88379719f680eadc2aad1508"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#ac015d81b88379719f680eadc2aad1508">operations_research::sat::ProductWithModularInverse</a></div><div class="ttdeci">int64_t ProductWithModularInverse(int64_t coeff, int64_t mod, int64_t rhs)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00103">sat/util.cc:103</a></div></div>
<div class="ttc" id="anamespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdoc">Collection of objects used to extend the Constraint Solver library.</div><div class="ttdef"><b>Definition:</b> <a href="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
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