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334 lines
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<div class="title">fp_utils.cc</div> </div>
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<a href="fp__utils_8cc.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// Copyright 2010-2018 Google LLC</span></div>
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<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a 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>
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<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// limitations under the License.</span></div>
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<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>  </div>
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<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#include "<a class="code" href="fp__utils_8h.html">ortools/util/fp_utils.h</a>"</span></div>
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<div class="line"><a name="l00015"></a><span class="lineno"> 15</span>  </div>
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<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="preprocessor">#include <cmath></span></div>
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<div class="line"><a name="l00017"></a><span class="lineno"> 17</span>  </div>
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<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="preprocessor">#include "<a class="code" href="bitset_8h.html">ortools/util/bitset.h</a>"</span></div>
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<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>  </div>
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<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div>
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<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  </div>
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<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="keyword">namespace </span>{</div>
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<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  </div>
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<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="keywordtype">void</span> ReorderAndCapTerms(<span class="keywordtype">double</span>* <a class="code" href="alldiff__cst_8cc.html#a021e695f54a13bd809c34b2f4ca87c37">min</a>, <span class="keywordtype">double</span>* <a class="code" href="alldiff__cst_8cc.html#a9d0c202d5fdd62f4fa2c613339ff168a">max</a>) {</div>
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<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  <span class="keywordflow">if</span> (*<a class="code" href="alldiff__cst_8cc.html#a021e695f54a13bd809c34b2f4ca87c37">min</a> > *<a class="code" href="alldiff__cst_8cc.html#a9d0c202d5fdd62f4fa2c613339ff168a">max</a>) std::swap(*<a class="code" href="alldiff__cst_8cc.html#a021e695f54a13bd809c34b2f4ca87c37">min</a>, *<a class="code" href="alldiff__cst_8cc.html#a9d0c202d5fdd62f4fa2c613339ff168a">max</a>);</div>
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<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  <span class="keywordflow">if</span> (*<a class="code" href="alldiff__cst_8cc.html#a021e695f54a13bd809c34b2f4ca87c37">min</a> > 0.0) *<a class="code" href="alldiff__cst_8cc.html#a021e695f54a13bd809c34b2f4ca87c37">min</a> = 0.0;</div>
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<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  <span class="keywordflow">if</span> (*<a class="code" href="alldiff__cst_8cc.html#a9d0c202d5fdd62f4fa2c613339ff168a">max</a> < 0.0) *<a class="code" href="alldiff__cst_8cc.html#a9d0c202d5fdd62f4fa2c613339ff168a">max</a> = 0.0;</div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> }</div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  </div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="keyword">template</span> <<span class="keywordtype">bool</span> use_bounds></div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research.html#a46f21c3da23685e58b31d880b2144458">ComputeScalingErrors</a>(<span class="keyword">const</span> std::vector<double>& <a class="code" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>,</div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  <span class="keyword">const</span> std::vector<double>& lb,</div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <span class="keyword">const</span> std::vector<double>& ub, <span class="keywordtype">double</span> scaling_factor,</div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keywordtype">double</span>* <a class="code" href="sat_2lp__utils_8cc.html#a2a1a02478d02cd8e42a1afece079d4a2">max_relative_coeff_error</a>,</div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="keywordtype">double</span>* max_scaled_sum_error) {</div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keywordtype">double</span> max_error = 0.0;</div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="keywordtype">double</span> min_error = 0.0;</div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  *<a class="code" href="sat_2lp__utils_8cc.html#a2a1a02478d02cd8e42a1afece079d4a2">max_relative_coeff_error</a> = 0.0;</div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> size = <a class="code" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>.size();</div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < size; ++i) {</div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> x = <a class="code" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>[i];</div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="keywordflow">if</span> (x == 0.0) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> scaled = x * scaling_factor;</div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  </div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keywordflow">if</span> (scaled == 0.0) {</div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  *<a class="code" href="sat_2lp__utils_8cc.html#a2a1a02478d02cd8e42a1afece079d4a2">max_relative_coeff_error</a> = std::numeric_limits<double>::infinity();</div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  } <span class="keywordflow">else</span> {</div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  *<a class="code" href="sat_2lp__utils_8cc.html#a2a1a02478d02cd8e42a1afece079d4a2">max_relative_coeff_error</a> = <a class="code" href="alldiff__cst_8cc.html#a9d0c202d5fdd62f4fa2c613339ff168a">std::max</a>(</div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  *<a class="code" href="sat_2lp__utils_8cc.html#a2a1a02478d02cd8e42a1afece079d4a2">max_relative_coeff_error</a>, std::abs(std::round(scaled) / scaled - 1));</div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  }</div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  </div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> error = std::round(scaled) - scaled;</div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> error_lb = (use_bounds ? error * lb[i] : -error);</div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> error_ub = (use_bounds ? error * ub[i] : error);</div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  max_error += <a class="code" href="alldiff__cst_8cc.html#a9d0c202d5fdd62f4fa2c613339ff168a">std::max</a>(error_lb, error_ub);</div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  min_error += <a class="code" href="alldiff__cst_8cc.html#a021e695f54a13bd809c34b2f4ca87c37">std::min</a>(error_lb, error_ub);</div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  }</div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  *max_scaled_sum_error = <a class="code" href="alldiff__cst_8cc.html#a9d0c202d5fdd62f4fa2c613339ff168a">std::max</a>(std::abs(max_error), std::abs(min_error));</div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> }</div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  </div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="keyword">template</span> <<span class="keywordtype">bool</span> use_bounds></div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research.html#afd62b70eb0f46a86016aeda8edea45fa">GetBestScalingOfDoublesToInt64</a>(<span class="keyword">const</span> std::vector<double>& <a class="code" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>,</div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keyword">const</span> std::vector<double>& lb,</div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keyword">const</span> std::vector<double>& ub,</div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> max_absolute_sum,</div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keywordtype">double</span>* scaling_factor) {</div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> <a class="code" href="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">kInfinity</a> = std::numeric_limits<double>::infinity();</div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  </div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="comment">// We start by initializing the returns value to the "error" state.</span></div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  *scaling_factor = 0;</div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  </div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="comment">// Abort in the "error" state if max_absolute_sum doesn't make sense.</span></div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="keywordflow">if</span> (max_absolute_sum < 0) <span class="keywordflow">return</span>;</div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  </div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="comment">// Our scaling scaling_factor will be 2^factor_exponent.</span></div>
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<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="comment">// TODO(user): Consider using a non-power of two factor if the error can't be</span></div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="comment">// zero? Note however that using power of two has the extra advantage that</span></div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="comment">// subsequent int64 -> double -> scaled back to int64 will loose no extra</span></div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="comment">// information.</span></div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="keywordtype">int</span> factor_exponent = 0;</div>
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<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <a class="code" href="integral__types_8h.html#abc0f5bc07737e498f287334775dff2b6">uint64</a> sum_min = 0; <span class="comment">// negated.</span></div>
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<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <a class="code" href="integral__types_8h.html#abc0f5bc07737e498f287334775dff2b6">uint64</a> sum_max = 0;</div>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="keywordtype">bool</span> recompute_sum = <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordtype">bool</span> is_first_value = <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> msb = <a class="code" href="namespaceoperations__research.html#a2f9ef253c023106392eb1495a277616b">MostSignificantBitPosition64</a>(max_absolute_sum);</div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> size = <a class="code" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>.size();</div>
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<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < size; ++i) {</div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> x = <a class="code" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>[i];</div>
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<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="keywordtype">double</span> min_term = use_bounds ? x * lb[i] : -x;</div>
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<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="keywordtype">double</span> max_term = use_bounds ? x * ub[i] : x;</div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  ReorderAndCapTerms(&min_term, &max_term);</div>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  </div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="comment">// If min_term or max_term is not finite, then abort in the "error" state.</span></div>
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<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordflow">if</span> (!(min_term > -<a class="code" href="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">kInfinity</a> && max_term < <a class="code" href="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">kInfinity</a>)) <span class="keywordflow">return</span>;</div>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  </div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="comment">// A value of zero can just be skipped (and needs to because the code below</span></div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="comment">// doesn't handle it correctly).</span></div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keywordflow">if</span> (min_term == 0.0 && max_term == 0.0) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  </div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="comment">// Compute the greatest candidate such that</span></div>
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<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="comment">// round(fabs(c).2^candidate) <= max_absolute_sum.</span></div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> c = <a class="code" href="alldiff__cst_8cc.html#a9d0c202d5fdd62f4fa2c613339ff168a">std::max</a>(-min_term, max_term);</div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="keywordtype">int</span> candidate = msb - ilogb(c);</div>
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<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="keywordflow">if</span> (std::round(ldexp(std::abs(c), candidate)) > max_absolute_sum) {</div>
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<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  --candidate;</div>
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<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  }</div>
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <a class="code" href="base_2logging_8h.html#a4395e95bab44e222cb2e77251017a0e2">DCHECK_LE</a>(std::abs(<span class="keyword">static_cast<</span><a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a><span class="keyword">></span>(round(ldexp(c, candidate)))),</div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  max_absolute_sum);</div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  </div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="comment">// Update factor_exponent which is the min of all the candidates.</span></div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keywordflow">if</span> (is_first_value || candidate < factor_exponent) {</div>
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<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  is_first_value = <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  factor_exponent = candidate;</div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  recompute_sum = <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  } <span class="keywordflow">else</span> {</div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="comment">// Update the sum of absolute values of the numbers seen so far.</span></div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  sum_min -=</div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="keyword">static_cast<</span><a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a><span class="keyword">></span>(std::round(ldexp(min_term, factor_exponent)));</div>
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  sum_max +=</div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="keyword">static_cast<</span><a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a><span class="keyword">></span>(std::round(ldexp(max_term, factor_exponent)));</div>
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<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="keywordflow">if</span> (sum_min > max_absolute_sum || sum_max > max_absolute_sum) {</div>
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<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  factor_exponent--;</div>
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<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  recompute_sum = <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  }</div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  }</div>
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<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  </div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="comment">// TODO(user): This is not super efficient, but note that in practice we</span></div>
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<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="comment">// will only scan the vector of values about log(size) times. It is possible</span></div>
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<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="comment">// to maintain an upper bound on the abs_sum in linear time instead, but the</span></div>
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<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="comment">// code and corner cases are a lot more involved. Also, we currently only</span></div>
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<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="comment">// use this code in situations where its run-time is negligeable compared to</span></div>
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<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="comment">// the rest.</span></div>
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<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keywordflow">while</span> (recompute_sum) {</div>
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<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  sum_min = 0;</div>
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<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  sum_max = 0;</div>
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<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j <= i; ++j) {</div>
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<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> x = <a class="code" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>[j];</div>
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<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <span class="keywordtype">double</span> min_term = use_bounds ? x * lb[j] : -x;</div>
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<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="keywordtype">double</span> max_term = use_bounds ? x * ub[j] : x;</div>
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<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  ReorderAndCapTerms(&min_term, &max_term);</div>
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<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  sum_min -=</div>
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<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="keyword">static_cast<</span><a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a><span class="keyword">></span>(std::round(ldexp(min_term, factor_exponent)));</div>
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<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  sum_max +=</div>
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<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="keyword">static_cast<</span><a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a><span class="keyword">></span>(std::round(ldexp(max_term, factor_exponent)));</div>
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<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  }</div>
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<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <span class="keywordflow">if</span> (sum_min > max_absolute_sum || sum_max > max_absolute_sum) {</div>
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<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  factor_exponent--;</div>
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<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  } <span class="keywordflow">else</span> {</div>
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<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  recompute_sum = <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  }</div>
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<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  }</div>
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<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  }</div>
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<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  *scaling_factor = ldexp(1.0, factor_exponent);</div>
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<div class="line"><a name="l00155"></a><span class="lineno"> 155</span> }</div>
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<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  </div>
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<div class="line"><a name="l00157"></a><span class="lineno"> 157</span> } <span class="comment">// namespace</span></div>
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<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  </div>
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<div class="line"><a name="l00159"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a46f21c3da23685e58b31d880b2144458"> 159</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research.html#a46f21c3da23685e58b31d880b2144458">ComputeScalingErrors</a>(<span class="keyword">const</span> std::vector<double>& <a class="code" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>,</div>
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<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="keyword">const</span> std::vector<double>& lb,</div>
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<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="keyword">const</span> std::vector<double>& ub, <span class="keywordtype">double</span> scaling_factor,</div>
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<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="keywordtype">double</span>* <a class="code" href="sat_2lp__utils_8cc.html#a2a1a02478d02cd8e42a1afece079d4a2">max_relative_coeff_error</a>,</div>
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<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <span class="keywordtype">double</span>* max_scaled_sum_error) {</div>
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<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  ComputeScalingErrors<true>(<a class="code" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>, lb, ub, scaling_factor,</div>
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<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <a class="code" href="sat_2lp__utils_8cc.html#a2a1a02478d02cd8e42a1afece079d4a2">max_relative_coeff_error</a>, max_scaled_sum_error);</div>
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<div class="line"><a name="l00166"></a><span class="lineno"> 166</span> }</div>
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<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  </div>
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<div class="line"><a name="l00168"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#afd62b70eb0f46a86016aeda8edea45fa"> 168</a></span> <span class="keywordtype">double</span> <a class="code" href="namespaceoperations__research.html#afd62b70eb0f46a86016aeda8edea45fa">GetBestScalingOfDoublesToInt64</a>(<span class="keyword">const</span> std::vector<double>& <a class="code" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>,</div>
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<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <span class="keyword">const</span> std::vector<double>& lb,</div>
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<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="keyword">const</span> std::vector<double>& ub,</div>
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<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> max_absolute_sum) {</div>
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<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="keywordtype">double</span> scaling_factor;</div>
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<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  GetBestScalingOfDoublesToInt64<true>(<a class="code" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>, lb, ub, max_absolute_sum,</div>
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<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  &scaling_factor);</div>
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<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  <span class="keywordflow">return</span> scaling_factor;</div>
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<div class="line"><a name="l00176"></a><span class="lineno"> 176</span> }</div>
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<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  </div>
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<div class="line"><a name="l00178"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#af0695d1051eeb25980e336d39162b926"> 178</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research.html#afd62b70eb0f46a86016aeda8edea45fa">GetBestScalingOfDoublesToInt64</a>(<span class="keyword">const</span> std::vector<double>& <a class="code" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>,</div>
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<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> max_absolute_sum,</div>
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<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="keywordtype">double</span>* scaling_factor,</div>
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<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <span class="keywordtype">double</span>* <a class="code" href="sat_2lp__utils_8cc.html#a2a1a02478d02cd8e42a1afece079d4a2">max_relative_coeff_error</a>) {</div>
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<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <span class="keywordtype">double</span> max_scaled_sum_error;</div>
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<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  GetBestScalingOfDoublesToInt64<false>(<a class="code" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>, {}, {}, max_absolute_sum,</div>
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<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  scaling_factor);</div>
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<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  ComputeScalingErrors<false>(<a class="code" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>, {}, {}, *scaling_factor,</div>
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<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <a class="code" href="sat_2lp__utils_8cc.html#a2a1a02478d02cd8e42a1afece079d4a2">max_relative_coeff_error</a>, &max_scaled_sum_error);</div>
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<div class="line"><a name="l00187"></a><span class="lineno"> 187</span> }</div>
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<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  </div>
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<div class="line"><a name="l00189"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a4256c1ce10497f58f5c8b3d2abc57525"> 189</a></span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> <a class="code" href="namespaceoperations__research.html#a4256c1ce10497f58f5c8b3d2abc57525">ComputeGcdOfRoundedDoubles</a>(<span class="keyword">const</span> std::vector<double>& x,</div>
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<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <span class="keywordtype">double</span> scaling_factor) {</div>
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<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> gcd = 0;</div>
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<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < x.size() && gcd != 1; ++i) {</div>
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<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> <a class="code" href="demon__profiler_8cc.html#a21edc7ca4cc5802c8779d68556bc09cf">value</a> = std::abs(std::round(x[i] * scaling_factor));</div>
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<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <a class="code" href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a>(<a class="code" href="demon__profiler_8cc.html#a21edc7ca4cc5802c8779d68556bc09cf">value</a>, 0);</div>
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<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="keywordflow">if</span> (<a class="code" href="demon__profiler_8cc.html#a21edc7ca4cc5802c8779d68556bc09cf">value</a> == 0) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="keywordflow">if</span> (gcd == 0) {</div>
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<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  gcd = <a class="code" href="demon__profiler_8cc.html#a21edc7ca4cc5802c8779d68556bc09cf">value</a>;</div>
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<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="keywordflow">continue</span>;</div>
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<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  }</div>
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<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="comment">// GCD(gcd, value) = GCD(value, gcd % value);</span></div>
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<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="keywordflow">while</span> (<a class="code" href="demon__profiler_8cc.html#a21edc7ca4cc5802c8779d68556bc09cf">value</a> != 0) {</div>
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<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="keyword">const</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> r = gcd % <a class="code" href="demon__profiler_8cc.html#a21edc7ca4cc5802c8779d68556bc09cf">value</a>;</div>
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<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  gcd = <a class="code" href="demon__profiler_8cc.html#a21edc7ca4cc5802c8779d68556bc09cf">value</a>;</div>
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<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <a class="code" href="demon__profiler_8cc.html#a21edc7ca4cc5802c8779d68556bc09cf">value</a> = r;</div>
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<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  }</div>
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<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  }</div>
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<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <a class="code" href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a>(gcd, 0);</div>
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<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="keywordflow">return</span> gcd > 0 ? gcd : 1;</div>
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<div class="line"><a name="l00209"></a><span class="lineno"> 209</span> }</div>
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<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  </div>
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<div class="line"><a name="l00211"></a><span class="lineno"> 211</span> } <span class="comment">// namespace operations_research</span></div>
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<div class="ttc" id="aalldiff__cst_8cc_html_a021e695f54a13bd809c34b2f4ca87c37"><div class="ttname"><a href="alldiff__cst_8cc.html#a021e695f54a13bd809c34b2f4ca87c37">min</a></div><div class="ttdeci">int64 min</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00138">alldiff_cst.cc:138</a></div></div>
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<div class="ttc" id="aalldiff__cst_8cc_html_a9d0c202d5fdd62f4fa2c613339ff168a"><div class="ttname"><a href="alldiff__cst_8cc.html#a9d0c202d5fdd62f4fa2c613339ff168a">max</a></div><div class="ttdeci">int64 max</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00139">alldiff_cst.cc:139</a></div></div>
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<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#l00887">base/logging.h:887</a></div></div>
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<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#l00889">base/logging.h:889</a></div></div>
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<div class="ttc" id="abitset_8h_html"><div class="ttname"><a href="bitset_8h.html">bitset.h</a></div></div>
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<div class="ttc" id="ademon__profiler_8cc_html_a21edc7ca4cc5802c8779d68556bc09cf"><div class="ttname"><a href="demon__profiler_8cc.html#a21edc7ca4cc5802c8779d68556bc09cf">value</a></div><div class="ttdeci">int64 value</div><div class="ttdef"><b>Definition:</b> <a href="demon__profiler_8cc_source.html#l00043">demon_profiler.cc:43</a></div></div>
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<div class="ttc" id="afp__utils_8h_html"><div class="ttname"><a href="fp__utils_8h.html">fp_utils.h</a></div></div>
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<div class="ttc" id="aintegral__types_8h_html_a7cde0074dfd288f2d70c0e035dacb28a"><div class="ttname"><a href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a></div><div class="ttdeci">int64_t int64</div><div class="ttdef"><b>Definition:</b> <a href="integral__types_8h_source.html#l00034">integral_types.h:34</a></div></div>
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<div class="ttc" id="aintegral__types_8h_html_abc0f5bc07737e498f287334775dff2b6"><div class="ttname"><a href="integral__types_8h.html#abc0f5bc07737e498f287334775dff2b6">uint64</a></div><div class="ttdeci">uint64_t uint64</div><div class="ttdef"><b>Definition:</b> <a href="integral__types_8h_source.html#l00039">integral_types.h:39</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1glop_html_af9a790b7e8c5b0c6d55b336177378e78"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">operations_research::glop::kInfinity</a></div><div class="ttdeci">const double kInfinity</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00083">lp_types.h:83</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdoc">The vehicle routing library lets one model and solve generic vehicle routing problems ranging from th...</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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<div class="ttc" id="anamespaceoperations__research_html_a2f9ef253c023106392eb1495a277616b"><div class="ttname"><a href="namespaceoperations__research.html#a2f9ef253c023106392eb1495a277616b">operations_research::MostSignificantBitPosition64</a></div><div class="ttdeci">int MostSignificantBitPosition64(uint64 n)</div><div class="ttdef"><b>Definition:</b> <a href="bitset_8h_source.html#l00231">bitset.h:231</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a4256c1ce10497f58f5c8b3d2abc57525"><div class="ttname"><a href="namespaceoperations__research.html#a4256c1ce10497f58f5c8b3d2abc57525">operations_research::ComputeGcdOfRoundedDoubles</a></div><div class="ttdeci">int64 ComputeGcdOfRoundedDoubles(const std::vector< double > &x, double scaling_factor)</div><div class="ttdef"><b>Definition:</b> <a href="fp__utils_8cc_source.html#l00189">fp_utils.cc:189</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a46f21c3da23685e58b31d880b2144458"><div class="ttname"><a href="namespaceoperations__research.html#a46f21c3da23685e58b31d880b2144458">operations_research::ComputeScalingErrors</a></div><div class="ttdeci">void ComputeScalingErrors(const std::vector< double > &input, const std::vector< double > &lb, const std::vector< double > &ub, double scaling_factor, double *max_relative_coeff_error, double *max_scaled_sum_error)</div><div class="ttdef"><b>Definition:</b> <a href="fp__utils_8cc_source.html#l00159">fp_utils.cc:159</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_afd62b70eb0f46a86016aeda8edea45fa"><div class="ttname"><a href="namespaceoperations__research.html#afd62b70eb0f46a86016aeda8edea45fa">operations_research::GetBestScalingOfDoublesToInt64</a></div><div class="ttdeci">double GetBestScalingOfDoublesToInt64(const std::vector< double > &input, const std::vector< double > &lb, const std::vector< double > &ub, int64 max_absolute_sum)</div><div class="ttdef"><b>Definition:</b> <a href="fp__utils_8cc_source.html#l00168">fp_utils.cc:168</a></div></div>
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<div class="ttc" id="aparser_8yy_8cc_html_a5a634cf4429798b1c921a81de8250051"><div class="ttname"><a href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a></div><div class="ttdeci">static int input(yyscan_t yyscanner)</div></div>
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<div class="ttc" id="asat_2lp__utils_8cc_html_a2a1a02478d02cd8e42a1afece079d4a2"><div class="ttname"><a href="sat_2lp__utils_8cc.html#a2a1a02478d02cd8e42a1afece079d4a2">max_relative_coeff_error</a></div><div class="ttdeci">double max_relative_coeff_error</div><div class="ttdef"><b>Definition:</b> <a href="sat_2lp__utils_8cc_source.html#l00489">sat/lp_utils.cc:489</a></div></div>
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