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137 lines
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<div class="title">fp_utils.h</div> </div>
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<a href="fp__utils_8h.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 2010-2021 Google LLC</span></div><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><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><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><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div><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><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div><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><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><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><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><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// limitations under the License.</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> </div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment">// Utility functions on IEEE floating-point numbers.</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">// Implemented on float, double, and long double.</span></div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">//</span></div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment">// Also a placeholder for tools controlling and checking FPU rounding modes.</span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment">//</span></div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment">// IMPORTANT NOTICE: you need to compile your binary with -frounding-math if</span></div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment">// you want to use rounding modes.</span></div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> </div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor">#ifndef OR_TOOLS_UTIL_FP_UTILS_H_</span></div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="preprocessor">#define OR_TOOLS_UTIL_FP_UTILS_H_</span></div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span> </div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="preprocessor">#if defined(_MSC_VER)</span></div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="preprocessor">#pragma fenv_access(on) // NOLINT</span></div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="preprocessor">#else</span></div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="preprocessor">#include <fenv.h></span> <span class="comment">// NOLINT</span></div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span> </div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="preprocessor">#ifdef __SSE__</span></div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="preprocessor">#include <xmmintrin.h></span></div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span> </div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="preprocessor">#include <stdlib.h></span></div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span> </div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="preprocessor">#include <algorithm></span></div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="preprocessor">#include <cmath></span></div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="preprocessor">#include <limits></span></div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="preprocessor">#include <vector></span></div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span> </div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="preprocessor">#include "<a class="code" href="integral__types_8h.html">ortools/base/integral_types.h</a>"</span></div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="preprocessor">#include "<a class="code" href="base_2logging_8h.html">ortools/base/logging.h</a>"</span></div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span> </div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="preprocessor">#if defined(_MSC_VER)</span></div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">double</span> isnan(<span class="keywordtype">double</span> <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>) { <span class="keywordflow">return</span> _isnan(<a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>); }</div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">double</span> round(<span class="keywordtype">double</span> <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>) { <span class="keywordflow">return</span> floor(<a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a> + 0.5); }</div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="preprocessor">#elif defined(__APPLE__) || __GNUC__ >= 5</span></div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="keyword">using</span> std::isnan;</div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span> </div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span> </div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment">// ScopedFloatingPointEnv is used to easily enable Floating-point exceptions.</span></div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// The initial state is automatically restored when the object is deleted.</span></div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment">//</span></div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment">// Note(user): For some reason, this causes an FPE exception to be triggered for</span></div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment">// unknown reasons when compiled in 32 bits. Because of this, we do not turn</span></div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment">// on FPE exception if __x86_64__ is not defined.</span></div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="comment">//</span></div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment">// TODO(user): Make it work on 32 bits.</span></div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// TODO(user): Make it work on msvc, currently calls to _controlfp crash.</span></div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span> </div><div class="line"><a name="l00064"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_scoped_floating_point_env.html"> 64</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1_scoped_floating_point_env.html">ScopedFloatingPointEnv</a> {</div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keyword">public</span>:</div><div class="line"><a name="l00066"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_scoped_floating_point_env.html#a0c44a9a38a2a14a048fddc986e3e78c4"> 66</a></span>  <a class="code" href="classoperations__research_1_1_scoped_floating_point_env.html#a0c44a9a38a2a14a048fddc986e3e78c4">ScopedFloatingPointEnv</a>() {</div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="preprocessor">#if defined(_MSC_VER)</span></div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="comment">// saved_control_ = _controlfp(0, 0);</span></div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="preprocessor">#elif (defined(__GNUC__) || defined(__llvm__)) && defined(__x86_64__)</span></div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <a class="code" href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a>(0, fegetenv(&saved_fenv_));</div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  }</div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span> </div><div class="line"><a name="l00074"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_scoped_floating_point_env.html#af6753cac2c8e1464f3e816f15a9c99e7"> 74</a></span>  <a class="code" href="classoperations__research_1_1_scoped_floating_point_env.html#af6753cac2c8e1464f3e816f15a9c99e7">~ScopedFloatingPointEnv</a>() {</div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="preprocessor">#if defined(_MSC_VER)</span></div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="comment">// CHECK_EQ(saved_control_, _controlfp(saved_control_, 0xFFFFFFFF));</span></div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="preprocessor">#elif defined(__x86_64__) && defined(__GLIBC__)</span></div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <a class="code" href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a>(0, fesetenv(&saved_fenv_));</div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  }</div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span> </div><div class="line"><a name="l00082"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_scoped_floating_point_env.html#a842438c1192d9044a7b244958355241b"> 82</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1_scoped_floating_point_env.html#a842438c1192d9044a7b244958355241b">EnableExceptions</a>(<span class="keywordtype">int</span> excepts) {</div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="preprocessor">#if defined(_MSC_VER)</span></div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="comment">// _controlfp(static_cast<unsigned int>(excepts), _MCW_EM);</span></div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="preprocessor">#elif (defined(__GNUC__) || defined(__llvm__)) && defined(__x86_64__) && \</span></div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="preprocessor"> !defined(__ANDROID__)</span></div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <a class="code" href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a>(0, fegetenv(&fenv_));</div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  excepts &= FE_ALL_EXCEPT;</div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="preprocessor">#if defined(__APPLE__)</span></div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  fenv_.__control &= ~excepts;</div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="preprocessor">#elif defined(__FreeBSD__)</span></div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  fenv_.__x87.__control &= ~excepts;</div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="preprocessor">#else // Linux</span></div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  fenv_.__control_word &= ~excepts;</div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  fenv_.__mxcsr &= ~(excepts << 7);</div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <a class="code" href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a>(0, fesetenv(&fenv_));</div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  }</div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span> </div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="keyword">private</span>:</div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="preprocessor">#if defined(_MSC_VER)</span></div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="comment">// unsigned int saved_control_;</span></div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span> <span class="preprocessor">#elif (defined(__GNUC__) || defined(__llvm__)) && defined(__x86_64__)</span></div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  fenv_t fenv_;</div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keyword">mutable</span> fenv_t saved_fenv_;</div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span> <span class="preprocessor">#endif</span></div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span> };</div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span> </div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="keyword">template</span> <<span class="keyword">typename</span> FloatType></div><div class="line"><a name="l00111"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#addb09ab3f085b1424ee43c8565494b40"> 111</a></span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research.html#addb09ab3f085b1424ee43c8565494b40">IsPositiveOrNegativeInfinity</a>(FloatType x) {</div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keywordflow">return</span> x == std::numeric_limits<FloatType>::infinity() ||</div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  x == -std::numeric_limits<FloatType>::infinity();</div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span> }</div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span> </div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span> <span class="comment">// Tests whether x and y are close to one another using absolute and relative</span></div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span> <span class="comment">// tolerances.</span></div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="comment">// Returns true if |x - y| <= a (with a being the absolute_tolerance).</span></div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span> <span class="comment">// The above case is useful for values that are close to zero.</span></div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="comment">// Returns true if |x - y| <= max(|x|, |y|) * r. (with r being the relative</span></div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span> <span class="comment">// tolerance.)</span></div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span> <span class="comment">// The cases for infinities are treated separately to avoid generating NaNs.</span></div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span> <span class="keyword">template</span> <<span class="keyword">typename</span> FloatType></div><div class="line"><a name="l00124"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a4175e34e3e7f573a9dd0187b199afc24"> 124</a></span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research.html#a4175e34e3e7f573a9dd0187b199afc24">AreWithinAbsoluteOrRelativeTolerances</a>(FloatType x, FloatType y,</div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  FloatType relative_tolerance,</div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  FloatType absolute_tolerance) {</div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <a class="code" href="base_2logging_8h.html#a4395e95bab44e222cb2e77251017a0e2">DCHECK_LE</a>(0.0, relative_tolerance);</div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <a class="code" href="base_2logging_8h.html#a4395e95bab44e222cb2e77251017a0e2">DCHECK_LE</a>(0.0, absolute_tolerance);</div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <a class="code" href="base_2logging_8h.html#ab4f56aa24c4c9cddc47a6abd2d747f9a">DCHECK_GT</a>(1.0, relative_tolerance);</div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keywordflow">if</span> (<a class="code" href="namespaceoperations__research.html#addb09ab3f085b1424ee43c8565494b40">IsPositiveOrNegativeInfinity</a>(x) || <a class="code" href="namespaceoperations__research.html#addb09ab3f085b1424ee43c8565494b40">IsPositiveOrNegativeInfinity</a>(y)) {</div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keywordflow">return</span> x == y;</div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  }</div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keyword">const</span> FloatType difference = fabs(x - y);</div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keywordflow">if</span> (difference <= absolute_tolerance) {</div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  }</div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keyword">const</span> FloatType largest_magnitude = <a class="code" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(fabs(x), fabs(y));</div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="keywordflow">return</span> difference <= largest_magnitude * relative_tolerance;</div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span> }</div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span> </div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span> <span class="comment">// Tests whether x and y are close to one another using an absolute tolerance.</span></div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="comment">// Returns true if |x - y| <= a (with a being the absolute_tolerance).</span></div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span> <span class="comment">// The cases for infinities are treated separately to avoid generating NaNs.</span></div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span> <span class="keyword">template</span> <<span class="keyword">typename</span> FloatType></div><div class="line"><a name="l00145"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a705ecff17f450f06856ceec064725b8d"> 145</a></span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research.html#a705ecff17f450f06856ceec064725b8d">AreWithinAbsoluteTolerance</a>(FloatType x, FloatType y,</div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  FloatType absolute_tolerance) {</div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <a class="code" href="base_2logging_8h.html#a4395e95bab44e222cb2e77251017a0e2">DCHECK_LE</a>(0.0, absolute_tolerance);</div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="keywordflow">if</span> (<a class="code" href="namespaceoperations__research.html#addb09ab3f085b1424ee43c8565494b40">IsPositiveOrNegativeInfinity</a>(x) || <a class="code" href="namespaceoperations__research.html#addb09ab3f085b1424ee43c8565494b40">IsPositiveOrNegativeInfinity</a>(y)) {</div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="keywordflow">return</span> x == y;</div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  }</div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <span class="keywordflow">return</span> fabs(x - y) <= absolute_tolerance;</div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span> }</div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span> </div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="comment">// Returns true if x is less than y or slighlty greater than y with the given</span></div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="comment">// absolute or relative tolerance.</span></div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="keyword">template</span> <<span class="keyword">typename</span> FloatType></div><div class="line"><a name="l00157"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a096ed4f933f943ccb8859e0dc08b06ca"> 157</a></span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research.html#a096ed4f933f943ccb8859e0dc08b06ca">IsSmallerWithinTolerance</a>(FloatType x, FloatType y, FloatType tolerance) {</div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="keywordflow">if</span> (<a class="code" href="namespaceoperations__research.html#addb09ab3f085b1424ee43c8565494b40">IsPositiveOrNegativeInfinity</a>(y)) <span class="keywordflow">return</span> x <= y;</div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <span class="keywordflow">return</span> x <= y + tolerance * <a class="code" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(1.0, <a class="code" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(std::abs(x), std::abs(y)));</div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span> }</div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span> </div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="comment">// Returns true if x is within tolerance of any integer. Always returns</span></div><div class="line"><a name="l00163"></a><span class="lineno"> 163</span> <span class="comment">// false for x equal to +/- infinity.</span></div><div class="line"><a name="l00164"></a><span class="lineno"> 164</span> <span class="keyword">template</span> <<span class="keyword">typename</span> FloatType></div><div class="line"><a name="l00165"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a1181732aa2f4c08e28ea32b1c7c6f256"> 165</a></span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research.html#a1181732aa2f4c08e28ea32b1c7c6f256">IsIntegerWithinTolerance</a>(FloatType x, FloatType tolerance) {</div><div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <a class="code" href="base_2logging_8h.html#a4395e95bab44e222cb2e77251017a0e2">DCHECK_LE</a>(0.0, tolerance);</div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  <span class="keywordflow">if</span> (<a class="code" href="namespaceoperations__research.html#addb09ab3f085b1424ee43c8565494b40">IsPositiveOrNegativeInfinity</a>(x)) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  <span class="keywordflow">return</span> std::abs(x - std::round(x)) <= tolerance;</div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span> }</div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span> </div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="comment">// Handy alternatives to EXPECT_NEAR(), using relative and absolute tolerance</span></div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span> <span class="comment">// instead of relative tolerance only, and with a proper support for infinity.</span></div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="comment">// TODO(user): investigate moving this to ortools/base/ or some other place.</span></div><div class="line"><a name="l00174"></a><span class="lineno"><a class="line" href="fp__utils_8h.html#a417a0547a8cf6eff90b4430609e054b0"> 174</a></span> <span class="preprocessor">#define EXPECT_COMPARABLE(expected, obtained, epsilon) \</span></div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="preprocessor"> EXPECT_TRUE(operations_research::AreWithinAbsoluteOrRelativeTolerances( \</span></div><div class="line"><a name="l00176"></a><span class="lineno"> 176</span> <span class="preprocessor"> expected, obtained, epsilon, epsilon)) \</span></div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span> <span class="preprocessor"> << obtained << " != expected value " << expected \</span></div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span> <span class="preprocessor"> << " within epsilon = " << epsilon;</span></div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span> </div><div class="line"><a name="l00180"></a><span class="lineno"><a class="line" href="fp__utils_8h.html#a9ba22f5b9700b4d8930219ecd6cf5a1a"> 180</a></span> <span class="preprocessor">#define EXPECT_NOTCOMPARABLE(expected, obtained, epsilon) \</span></div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="preprocessor"> EXPECT_FALSE(operations_research::AreWithinAbsoluteOrRelativeTolerances( \</span></div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span> <span class="preprocessor"> expected, obtained, epsilon, epsilon)) \</span></div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="preprocessor"> << obtained << " == expected value " << expected \</span></div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="preprocessor"> << " within epsilon = " << epsilon;</span></div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span> </div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span> <span class="comment">// Given an array of doubles, this computes a positive scaling factor such that</span></div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span> <span class="comment">// the scaled doubles can then be rounded to integers with little or no loss of</span></div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span> <span class="comment">// precision, and so that the L1 norm of these integers is <= max_sum. More</span></div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span> <span class="comment">// precisely, the following formulas will hold (x[i] is input[i], for brevity):</span></div><div class="line"><a name="l00190"></a><span class="lineno"> 190</span> <span class="comment">// - For all i, |round(factor * x[i]) / factor - x[i]| <= error * |x[i]|</span></div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span> <span class="comment">// - The sum over i of |round(factor * x[i])| <= max_sum.</span></div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span> <span class="comment">//</span></div><div class="line"><a name="l00193"></a><span class="lineno"> 193</span> <span class="comment">// The algorithm tries to minimize "error" (which is the relative error for one</span></div><div class="line"><a name="l00194"></a><span class="lineno"> 194</span> <span class="comment">// coefficient). Note however than in really broken cases, the error might be</span></div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span> <span class="comment">// infinity and the factor zero.</span></div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span> <span class="comment">//</span></div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span> <span class="comment">// Note on the algorithm:</span></div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span> <span class="comment">// - It only uses factors of the form 2^n (i.e. ldexp(1.0, n)) for simplicity.</span></div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span> <span class="comment">// - The error will be zero in many practical instances. For example, if x</span></div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span> <span class="comment">// contains only integers with low magnitude; or if x contains doubles whose</span></div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span> <span class="comment">// exponents cover a small range.</span></div><div class="line"><a name="l00202"></a><span class="lineno"> 202</span> <span class="comment">// - It chooses the factor as high as possible under the given constraints, as</span></div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span> <span class="comment">// a result the numbers produced may be large. To balance this, we recommend</span></div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span> <span class="comment">// to divide the scaled integers by their gcd() which will result in no loss</span></div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span> <span class="comment">// of precision and will help in many practical cases.</span></div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="comment">//</span></div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span> <span class="comment">// TODO(user): incorporate the gcd computation here? The issue is that I am</span></div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span> <span class="comment">// not sure if I just do factor /= gcd that round(x * factor) will be the same.</span></div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research.html#aae3359f1c2367d44e5cf9be5d5abc89f">GetBestScalingOfDoublesToInt64</a>(<span class="keyword">const</span> std::vector<double>& <a class="code" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>,</div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  int64_t max_absolute_sum,</div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="keywordtype">double</span>* scaling_factor,</div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="keywordtype">double</span>* <a class="code" href="sat_2lp__utils_8cc.html#a2a1a02478d02cd8e42a1afece079d4a2">max_relative_coeff_error</a>);</div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span> </div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span> <span class="comment">// Returns the scaling factor like above with the extra conditions:</span></div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="comment">// - The sum over i of min(0, round(factor * x[i])) >= -max_sum.</span></div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span> <span class="comment">// - The sum over i of max(0, round(factor * x[i])) <= max_sum.</span></div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="comment">// For any possible values of the x[i] such that x[i] is in [lb[i], ub[i]].</span></div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span> <span class="keywordtype">double</span> <a class="code" href="namespaceoperations__research.html#aae3359f1c2367d44e5cf9be5d5abc89f">GetBestScalingOfDoublesToInt64</a>(<span class="keyword">const</span> std::vector<double>& <a class="code" href="parser_8yy_8cc.html#a5a634cf4429798b1c921a81de8250051">input</a>,</div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="keyword">const</span> std::vector<double>& lb,</div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="keyword">const</span> std::vector<double>& ub,</div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  int64_t max_absolute_sum);</div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span> <span class="comment">// This computes:</span></div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span> <span class="comment">//</span></div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span> <span class="comment">// The max_relative_coeff_error, which is the maximum over all coeff of</span></div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span> <span class="comment">// |round(factor * x[i]) / (factor * x[i]) - 1|.</span></div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span> <span class="comment">//</span></div><div class="line"><a name="l00227"></a><span class="lineno"> 227</span> <span class="comment">// The max_scaled_sum_error which is a bound on the maximum difference between</span></div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span> <span class="comment">// the exact scaled sum and the rounded one. One needs to divide this by</span></div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span> <span class="comment">// scaling_factor to have the maximum absolute error on the original sum.</span></div><div class="line"><a name="l00230"></a><span class="lineno"> 230</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><div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  <span class="keyword">const</span> std::vector<double>& lb,</div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="keyword">const</span> std::vector<double>& ub,</div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> scaling_factor,</div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="keywordtype">double</span>* <a class="code" href="sat_2lp__utils_8cc.html#a2a1a02478d02cd8e42a1afece079d4a2">max_relative_coeff_error</a>,</div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keywordtype">double</span>* max_scaled_sum_error);</div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span> </div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span> <span class="comment">// Returns the Greatest Common Divisor of the numbers</span></div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span> <span class="comment">// round(fabs(x[i] * scaling_factor)). The numbers 0 are ignored and if they are</span></div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span> <span class="comment">// all zero then the result is 1. Note that round(fabs()) is the same as</span></div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span> <span class="comment">// fabs(round()) since the numbers are rounded away from zero.</span></div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span> int64_t <a class="code" href="namespaceoperations__research.html#aae2e6ed909e0cd5f240b885800f55c87">ComputeGcdOfRoundedDoubles</a>(<span class="keyword">const</span> std::vector<double>& x,</div><div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  <span class="keywordtype">double</span> scaling_factor);</div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span> </div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span> <span class="comment">// Returns alpha * x + (1 - alpha) * y.</span></div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span> <span class="keyword">template</span> <<span class="keyword">typename</span> FloatType></div><div class="line"><a name="l00246"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a2adddfecac47612f1da312dbb80d91b7"> 246</a></span> <span class="keyword">inline</span> FloatType <a class="code" href="namespaceoperations__research.html#a2adddfecac47612f1da312dbb80d91b7">Interpolate</a>(FloatType x, FloatType y, FloatType alpha) {</div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <span class="keywordflow">return</span> alpha * x + (1 - alpha) * y;</div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span> }</div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span> </div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span> <span class="comment">// This is a fast implementation of the C99 function ilogb for normalized</span></div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span> <span class="comment">// doubles with the caveat that it returns -1023 for zero, and 1024 for infinity</span></div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span> <span class="comment">// an NaNs.</span></div><div class="line"><a name="l00253"></a><span class="lineno"> 253</span> <span class="keywordtype">int</span> <a class="code" href="namespaceoperations__research.html#a01cc8a711d189115758c50170038904f">fast_ilogb</a>(<span class="keyword">const</span> <span class="keywordtype">double</span> <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>);</div><div class="line"><a name="l00254"></a><span class="lineno"> 254</span> </div><div class="line"><a name="l00255"></a><span class="lineno"> 255</span> <span class="comment">// This is a fast implementation of the C99 function scalbn, with the caveat</span></div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span> <span class="comment">// that it works on normalized numbers and if the result underflows, overflows,</span></div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span> <span class="comment">// or is applied to a NaN or an +-infinity, the result is undefined behavior.</span></div><div class="line"><a name="l00258"></a><span class="lineno"> 258</span> <span class="comment">// Note that the version of the function that takes a reference, modifies the</span></div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span> <span class="comment">// given value.</span></div><div class="line"><a name="l00260"></a><span class="lineno"> 260</span> <span class="keywordtype">double</span> <a class="code" href="namespaceoperations__research.html#a5550c9e9dfe6d29df888acafa85c790e">fast_scalbn</a>(<span class="keyword">const</span> <span class="keywordtype">double</span> <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>, <span class="keyword">const</span> <span class="keywordtype">int</span> exponent);</div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research.html#a5c5a3f603ad3ee0c6e6d6c70fcd54219">fast_scalbn_inplace</a>(<span class="keywordtype">double</span>& mutable_value, <span class="keyword">const</span> <span class="keywordtype">int</span> exponent);</div><div class="line"><a name="l00262"></a><span class="lineno"> 262</span> </div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span> } <span class="comment">// namespace operations_research</span></div><div class="line"><a name="l00264"></a><span class="lineno"> 264</span> </div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span> <span class="preprocessor">#endif // OR_TOOLS_UTIL_FP_UTILS_H_</span></div><div class="ttc" id="namespaceoperations__research_html_a5c5a3f603ad3ee0c6e6d6c70fcd54219"><div class="ttname"><a href="namespaceoperations__research.html#a5c5a3f603ad3ee0c6e6d6c70fcd54219">operations_research::fast_scalbn_inplace</a></div><div class="ttdeci">void fast_scalbn_inplace(double &mutable_value, int exponent)</div><div class="ttdef"><b>Definition:</b> <a href="fp__utils_8cc_source.html#l00231">fp_utils.cc:231</a></div></div>
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<div class="ttc" id="namespaceoperations__research_html_a2adddfecac47612f1da312dbb80d91b7"><div class="ttname"><a href="namespaceoperations__research.html#a2adddfecac47612f1da312dbb80d91b7">operations_research::Interpolate</a></div><div class="ttdeci">FloatType Interpolate(FloatType x, FloatType y, FloatType alpha)</div><div class="ttdef"><b>Definition:</b> <a href="fp__utils_8h_source.html#l00246">fp_utils.h:246</a></div></div>
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<div class="ttc" id="alldiff__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>
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<div class="ttc" id="classoperations__research_1_1_scoped_floating_point_env_html"><div class="ttname"><a href="classoperations__research_1_1_scoped_floating_point_env.html">operations_research::ScopedFloatingPointEnv</a></div><div class="ttdef"><b>Definition:</b> <a href="fp__utils_8h_source.html#l00064">fp_utils.h:64</a></div></div>
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<div class="ttc" id="namespaceoperations__research_html_a096ed4f933f943ccb8859e0dc08b06ca"><div class="ttname"><a href="namespaceoperations__research.html#a096ed4f933f943ccb8859e0dc08b06ca">operations_research::IsSmallerWithinTolerance</a></div><div class="ttdeci">bool IsSmallerWithinTolerance(FloatType x, FloatType y, FloatType tolerance)</div><div class="ttdef"><b>Definition:</b> <a href="fp__utils_8h_source.html#l00157">fp_utils.h:157</a></div></div>
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<div class="ttc" id="namespaceoperations__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#l00170">fp_utils.cc:170</a></div></div>
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<div class="ttc" id="base_2logging_8h_html_ab4f56aa24c4c9cddc47a6abd2d747f9a"><div class="ttname"><a href="base_2logging_8h.html#ab4f56aa24c4c9cddc47a6abd2d747f9a">DCHECK_GT</a></div><div class="ttdeci">#define DCHECK_GT(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00895">base/logging.h:895</a></div></div>
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<div class="ttc" id="namespaceoperations__research_html_a1181732aa2f4c08e28ea32b1c7c6f256"><div class="ttname"><a href="namespaceoperations__research.html#a1181732aa2f4c08e28ea32b1c7c6f256">operations_research::IsIntegerWithinTolerance</a></div><div class="ttdeci">bool IsIntegerWithinTolerance(FloatType x, FloatType tolerance)</div><div class="ttdef"><b>Definition:</b> <a href="fp__utils_8h_source.html#l00165">fp_utils.h:165</a></div></div>
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<div class="ttc" id="namespaceoperations__research_html_aae3359f1c2367d44e5cf9be5d5abc89f"><div class="ttname"><a href="namespaceoperations__research.html#aae3359f1c2367d44e5cf9be5d5abc89f">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_t max_absolute_sum)</div><div class="ttdef"><b>Definition:</b> <a href="fp__utils_8cc_source.html#l00179">fp_utils.cc:179</a></div></div>
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<div class="ttc" id="sat_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#l00593">sat/lp_utils.cc:593</a></div></div>
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<div class="ttc" id="namespaceoperations__research_html_a5550c9e9dfe6d29df888acafa85c790e"><div class="ttname"><a href="namespaceoperations__research.html#a5550c9e9dfe6d29df888acafa85c790e">operations_research::fast_scalbn</a></div><div class="ttdeci">double fast_scalbn(double value, int exponent)</div><div class="ttdef"><b>Definition:</b> <a href="fp__utils_8cc_source.html#l00235">fp_utils.cc:235</a></div></div>
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<div class="ttc" id="integral__types_8h_html"><div class="ttname"><a href="integral__types_8h.html">integral_types.h</a></div></div>
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<div class="ttc" id="alldiff__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>
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<div class="ttc" id="namespaceoperations__research_html_aae2e6ed909e0cd5f240b885800f55c87"><div class="ttname"><a href="namespaceoperations__research.html#aae2e6ed909e0cd5f240b885800f55c87">operations_research::ComputeGcdOfRoundedDoubles</a></div><div class="ttdeci">int64_t ComputeGcdOfRoundedDoubles(const std::vector< double > &x, double scaling_factor)</div><div class="ttdef"><b>Definition:</b> <a href="fp__utils_8cc_source.html#l00200">fp_utils.cc:200</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_scoped_floating_point_env_html_af6753cac2c8e1464f3e816f15a9c99e7"><div class="ttname"><a href="classoperations__research_1_1_scoped_floating_point_env.html#af6753cac2c8e1464f3e816f15a9c99e7">operations_research::ScopedFloatingPointEnv::~ScopedFloatingPointEnv</a></div><div class="ttdeci">~ScopedFloatingPointEnv()</div><div class="ttdef"><b>Definition:</b> <a href="fp__utils_8h_source.html#l00074">fp_utils.h:74</a></div></div>
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<div class="ttc" id="namespaceoperations__research_html_a705ecff17f450f06856ceec064725b8d"><div class="ttname"><a href="namespaceoperations__research.html#a705ecff17f450f06856ceec064725b8d">operations_research::AreWithinAbsoluteTolerance</a></div><div class="ttdeci">bool AreWithinAbsoluteTolerance(FloatType x, FloatType y, FloatType absolute_tolerance)</div><div class="ttdef"><b>Definition:</b> <a href="fp__utils_8h_source.html#l00145">fp_utils.h:145</a></div></div>
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<div class="ttc" id="parser_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="base_2logging_8h_html_a7c0ce053b28d53aa4eaf3eb7fb71663b"><div class="ttname"><a href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a></div><div class="ttdeci">#define CHECK_EQ(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00702">base/logging.h:702</a></div></div>
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<div class="ttc" id="base_2logging_8h_html"><div class="ttname"><a href="base_2logging_8h.html">logging.h</a></div></div>
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<div class="ttc" id="namespaceoperations__research_html_addb09ab3f085b1424ee43c8565494b40"><div class="ttname"><a href="namespaceoperations__research.html#addb09ab3f085b1424ee43c8565494b40">operations_research::IsPositiveOrNegativeInfinity</a></div><div class="ttdeci">bool IsPositiveOrNegativeInfinity(FloatType x)</div><div class="ttdef"><b>Definition:</b> <a href="fp__utils_8h_source.html#l00111">fp_utils.h:111</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_scoped_floating_point_env_html_a842438c1192d9044a7b244958355241b"><div class="ttname"><a href="classoperations__research_1_1_scoped_floating_point_env.html#a842438c1192d9044a7b244958355241b">operations_research::ScopedFloatingPointEnv::EnableExceptions</a></div><div class="ttdeci">void EnableExceptions(int excepts)</div><div class="ttdef"><b>Definition:</b> <a href="fp__utils_8h_source.html#l00082">fp_utils.h:82</a></div></div>
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<div class="ttc" id="namespaceoperations__research_html_a4175e34e3e7f573a9dd0187b199afc24"><div class="ttname"><a href="namespaceoperations__research.html#a4175e34e3e7f573a9dd0187b199afc24">operations_research::AreWithinAbsoluteOrRelativeTolerances</a></div><div class="ttdeci">bool AreWithinAbsoluteOrRelativeTolerances(FloatType x, FloatType y, FloatType relative_tolerance, FloatType absolute_tolerance)</div><div class="ttdef"><b>Definition:</b> <a href="fp__utils_8h_source.html#l00124">fp_utils.h:124</a></div></div>
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<div class="ttc" id="base_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#l00892">base/logging.h:892</a></div></div>
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<div class="ttc" id="namespaceoperations__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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<div class="ttc" id="classoperations__research_1_1_scoped_floating_point_env_html_a0c44a9a38a2a14a048fddc986e3e78c4"><div class="ttname"><a href="classoperations__research_1_1_scoped_floating_point_env.html#a0c44a9a38a2a14a048fddc986e3e78c4">operations_research::ScopedFloatingPointEnv::ScopedFloatingPointEnv</a></div><div class="ttdeci">ScopedFloatingPointEnv()</div><div class="ttdef"><b>Definition:</b> <a href="fp__utils_8h_source.html#l00066">fp_utils.h:66</a></div></div>
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<div class="ttc" id="namespaceoperations__research_html_a01cc8a711d189115758c50170038904f"><div class="ttname"><a href="namespaceoperations__research.html#a01cc8a711d189115758c50170038904f">operations_research::fast_ilogb</a></div><div class="ttdeci">int fast_ilogb(double value)</div><div class="ttdef"><b>Definition:</b> <a href="fp__utils_8cc_source.html#l00222">fp_utils.cc:222</a></div></div>
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<div class="ttc" id="demon__profiler_8cc_html_ac072af30c4ffbc834bb4c681f6ecb514"><div class="ttname"><a href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a></div><div class="ttdeci">int64_t value</div><div class="ttdef"><b>Definition:</b> <a href="demon__profiler_8cc_source.html#l00044">demon_profiler.cc:44</a></div></div>
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