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<div class="title">float_utils_google.hpp</div> </div>
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<a href="a00242.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="preprocessor">#ifndef __STDAIR_BAS_FLOAT_UTILS_GOOGLE_HPP</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="preprocessor"></span><span class="preprocessor">#define __STDAIR_BAS_FLOAT_UTILS_GOOGLE_HPP</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// Redistribution and use in source and binary forms, with or without</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">// modification, are permitted provided that the following conditions are</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// met:</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">// * Redistributions of source code must retain the above copyright</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// notice, this list of conditions and the following disclaimer.</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// * Redistributions in binary form must reproduce the above</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">// copyright notice, this list of conditions and the following disclaimer</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// in the documentation and/or other materials provided with the</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment">// distribution.</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment">// * Neither the name of Google Inc. nor the names of its</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">// contributors may be used to endorse or promote products derived from</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">// this software without specific prior written permission.</span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment">//</span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment">// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS</span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment">// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT</span></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment">// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR</span></div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment">// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment">// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,</span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment">// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment">// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,</span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment">// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment">// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment">// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment">// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.</span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment">//</span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment">// Authors: wan@google.com (Zhanyong Wan), eefacm@gmail.com (Sean Mcafee)</span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">//</span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">// The Google C++ Testing Framework (Google Test)</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</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="comment">// This template class serves as a compile-time function from size to</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// type. It maps a size in bytes to a primitive type with that</span></div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment">// size. e.g.</span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment">//</span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// TypeWithSize<4>::UInt</span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">//</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// is typedef-ed to be unsigned int (unsigned integer made up of 4</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment">// bytes).</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">//</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment">// Such functionality should belong to STL, but I cannot find it</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="comment">// there.</span></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment">//</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// Google Test uses this class in the implementation of floating-point</span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// comparison.</span></div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment">//</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// For now it only handles UInt (unsigned int) as that's all Google Test</span></div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// needs. Other types can be easily added in the future if need</span></div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment">// arises.</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="keyword">template</span> <<span class="keywordtype">size_t</span> size></div>
<div class="line"><a name="l00054"></a><span class="lineno"><a class="code" href="a00186.html"> 54</a></span> <span class="keyword">class </span><a class="code" href="a00186.html">TypeWithSize</a> {</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="comment">// This prevents the user from using TypeWithSize<N> with incorrect</span></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="comment">// values of N.</span></div>
<div class="line"><a name="l00058"></a><span class="lineno"><a class="code" href="a00186.html#a133efc1585facfe51a535c4a7b233684"> 58</a></span>  <span class="keyword">typedef</span> <span class="keywordtype">void</span> <a class="code" href="a00186.html#a133efc1585facfe51a535c4a7b233684">UInt</a>;</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> };</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> </div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment">// The specialization for size 4.</span></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="keyword">template</span> <></div>
<div class="line"><a name="l00063"></a><span class="lineno"><a class="code" href="a00187.html"> 63</a></span> <span class="keyword">class </span><a class="code" href="a00186.html">TypeWithSize</a><4> {</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="comment">// unsigned int has size 4 in both gcc and MSVC.</span></div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="comment">// As base/basictypes.h doesn't compile on Windows, we cannot use</span></div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="comment">// uint32, uint64, and etc here.</span></div>
<div class="line"><a name="l00069"></a><span class="lineno"><a class="code" href="a00187.html#af29a19528b5da0137818cc208ec05fe0"> 69</a></span>  <span class="keyword">typedef</span> <span class="keywordtype">int</span> <a class="code" href="a00187.html#af29a19528b5da0137818cc208ec05fe0">Int</a>;</div>
<div class="line"><a name="l00070"></a><span class="lineno"><a class="code" href="a00187.html#aedd1425478450102b1c637d2db6a7d26"> 70</a></span>  <span class="keyword">typedef</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> <a class="code" href="a00187.html#aedd1425478450102b1c637d2db6a7d26">UInt</a>;</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</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> <span class="comment">// The specialization for size 8.</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="keyword">template</span> <></div>
<div class="line"><a name="l00075"></a><span class="lineno"><a class="code" href="a00188.html"> 75</a></span> <span class="keyword">class </span><a class="code" href="a00186.html">TypeWithSize</a><8> {</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="preprocessor">#if GTEST_OS_WINDOWS</span></div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="preprocessor"></span> <span class="keyword">typedef</span> __int64 <a class="code" href="a00188.html#af02c7e5d997bd247bdb252ce9537a295">Int</a>;</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="keyword">typedef</span> <span class="keywordtype">unsigned</span> __int64 <a class="code" href="a00186.html#a133efc1585facfe51a535c4a7b233684">UInt</a>;</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="preprocessor">#else</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"><a class="code" href="a00188.html#af02c7e5d997bd247bdb252ce9537a295"> 81</a></span> <span class="preprocessor"></span> <span class="keyword">typedef</span> <span class="keywordtype">long</span> <span class="keywordtype">long</span> <a class="code" href="a00188.html#af02c7e5d997bd247bdb252ce9537a295">Int</a>; <span class="comment">// NOLINT</span></div>
<div class="line"><a name="l00082"></a><span class="lineno"><a class="code" href="a00188.html#aad4d80a31c855d3f6feb970627dce6e9"> 82</a></span>  <span class="keyword">typedef</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> <span class="keywordtype">long</span> <a class="code" href="a00188.html#aad4d80a31c855d3f6feb970627dce6e9">UInt</a>; <span class="comment">// NOLINT</span></div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="preprocessor">#endif // GTEST_OS_WINDOWS</span></div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="preprocessor"></span>};</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span> </div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span> </div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="comment">// This template class represents an IEEE floating-point number</span></div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="comment">// (either single-precision or double-precision, depending on the</span></div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="comment">// template parameters).</span></div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="comment">//</span></div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="comment">// The purpose of this class is to do more sophisticated number</span></div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="comment">// comparison. (Due to round-off error, etc, it's very unlikely that</span></div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="comment">// two floating-points will be equal exactly. Hence a naive</span></div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="comment">// comparison by the == operation often doesn't work.)</span></div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="comment">//</span></div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="comment">// Format of IEEE floating-point:</span></div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="comment">//</span></div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="comment">// The most-significant bit being the leftmost, an IEEE</span></div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="comment">// floating-point looks like</span></div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="comment">//</span></div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="comment">// sign_bit exponent_bits fraction_bits</span></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="comment">//</span></div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span> <span class="comment">// Here, sign_bit is a single bit that designates the sign of the</span></div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span> <span class="comment">// number.</span></div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span> <span class="comment">//</span></div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span> <span class="comment">// For float, there are 8 exponent bits and 23 fraction bits.</span></div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span> <span class="comment">//</span></div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="comment">// For double, there are 11 exponent bits and 52 fraction bits.</span></div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="comment">//</span></div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="comment">// More details can be found at</span></div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="comment">// http://en.wikipedia.org/wiki/IEEE_floating-point_standard.</span></div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span> <span class="comment">//</span></div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> <span class="comment">// Template parameter:</span></div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span> <span class="comment">//</span></div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span> <span class="comment">// RawType: the raw floating-point type (either float or double)</span></div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span> <span class="keyword">template</span> <<span class="keyword">typename</span> RawType></div>
<div class="line"><a name="l00117"></a><span class="lineno"><a class="code" href="a00107.html"> 117</a></span> <span class="keyword">class </span><a class="code" href="a00107.html">FloatingPoint</a> {</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="comment">// Defines the unsigned integer type that has the same size as the</span></div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="comment">// floating point number.</span></div>
<div class="line"><a name="l00121"></a><span class="lineno"><a class="code" href="a00107.html#aa0912a8f805308568ebd2609557680b4"> 121</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="a00186.html">TypeWithSize<sizeof(RawType)>::UInt</a> <a class="code" href="a00107.html#aa0912a8f805308568ebd2609557680b4">Bits</a>;</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span> </div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="comment">// Constants.</span></div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span> </div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="comment">// # of bits in a number.</span></div>
<div class="line"><a name="l00126"></a><span class="lineno"><a class="code" href="a00107.html#af2429a12aef6052e91b2d50df5800df9"> 126</a></span>  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">size_t</span> <a class="code" href="a00107.html#af2429a12aef6052e91b2d50df5800df9">kBitCount</a> = 8*<span class="keyword">sizeof</span>(RawType);</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span> </div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="comment">// # of fraction bits in a number.</span></div>
<div class="line"><a name="l00129"></a><span class="lineno"><a class="code" href="a00107.html#af29024bbbb5abcbaf8aabfc465f3bd33"> 129</a></span>  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">size_t</span> <a class="code" href="a00107.html#af29024bbbb5abcbaf8aabfc465f3bd33">kFractionBitCount</a> =</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  std::numeric_limits<RawType>::digits - 1;</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span> </div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="comment">// # of exponent bits in a number.</span></div>
<div class="line"><a name="l00133"></a><span class="lineno"><a class="code" href="a00107.html#a00f3d689988b1c00f3d8a98d3bc9c685"> 133</a></span>  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">size_t</span> <a class="code" href="a00107.html#a00f3d689988b1c00f3d8a98d3bc9c685">kExponentBitCount</a> = <a class="code" href="a00107.html#af2429a12aef6052e91b2d50df5800df9">kBitCount</a> - 1 - <a class="code" href="a00107.html#af29024bbbb5abcbaf8aabfc465f3bd33">kFractionBitCount</a>;</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span> </div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="comment">// The mask for the sign bit.</span></div>
<div class="line"><a name="l00136"></a><span class="lineno"><a class="code" href="a00107.html#a026944d92c195ce2c755dde816cd6b0c"> 136</a></span>  <span class="keyword">static</span> <span class="keyword">const</span> <a class="code" href="a00107.html#aa0912a8f805308568ebd2609557680b4">Bits</a> <a class="code" href="a00107.html#a026944d92c195ce2c755dde816cd6b0c">kSignBitMask</a> = <span class="keyword">static_cast<</span><a class="code" href="a00107.html#aa0912a8f805308568ebd2609557680b4">Bits</a><span class="keyword">></span>(1) << (<a class="code" href="a00107.html#af2429a12aef6052e91b2d50df5800df9">kBitCount</a> - 1);</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span> </div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="comment">// The mask for the fraction bits.</span></div>
<div class="line"><a name="l00139"></a><span class="lineno"><a class="code" href="a00107.html#a4909a899f6cc1a1bdb7835cec3629a0f"> 139</a></span>  <span class="keyword">static</span> <span class="keyword">const</span> <a class="code" href="a00107.html#aa0912a8f805308568ebd2609557680b4">Bits</a> <a class="code" href="a00107.html#a4909a899f6cc1a1bdb7835cec3629a0f">kFractionBitMask</a> =</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  ~static_cast<<a class="code" href="a00107.html#aa0912a8f805308568ebd2609557680b4">Bits</a>>(0) >> (<a class="code" href="a00107.html#a00f3d689988b1c00f3d8a98d3bc9c685">kExponentBitCount</a> + 1);</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span> </div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="comment">// The mask for the exponent bits.</span></div>
<div class="line"><a name="l00143"></a><span class="lineno"><a class="code" href="a00107.html#a590938e82e2f449c0557744a6c5619ad"> 143</a></span>  <span class="keyword">static</span> <span class="keyword">const</span> <a class="code" href="a00107.html#aa0912a8f805308568ebd2609557680b4">Bits</a> <a class="code" href="a00107.html#a590938e82e2f449c0557744a6c5619ad">kExponentBitMask</a> = ~(<a class="code" href="a00107.html#a026944d92c195ce2c755dde816cd6b0c">kSignBitMask</a> | <a class="code" href="a00107.html#a4909a899f6cc1a1bdb7835cec3629a0f">kFractionBitMask</a>);</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span> </div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="comment">// How many ULP's (Units in the Last Place) we want to tolerate when</span></div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="comment">// comparing two numbers. The larger the value, the more error we</span></div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <span class="comment">// allow. A 0 value means that two numbers must be exactly the same</span></div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="comment">// to be considered equal.</span></div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="comment">// The maximum error of a single floating-point operation is 0.5</span></div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <span class="comment">// units in the last place. On Intel CPU's, all floating-point</span></div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <span class="comment">// calculations are done with 80-bit precision, while double has 64</span></div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  <span class="comment">// bits. Therefore, 4 should be enough for ordinary use.</span></div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="comment">// See the following article for more details on ULP:</span></div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="comment">// http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm.</span></div>
<div class="line"><a name="l00157"></a><span class="lineno"><a class="code" href="a00107.html#ad52b8184e122a8fe484f0d9633e960e1"> 157</a></span>  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">size_t</span> <a class="code" href="a00107.html#ad52b8184e122a8fe484f0d9633e960e1">kMaxUlps</a> = 4;</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span> </div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <span class="comment">// Constructs a FloatingPoint from a raw floating-point number.</span></div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="comment">// On an Intel CPU, passing a non-normalized NAN (Not a Number)</span></div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="comment">// around may change its bits, although the new value is guaranteed</span></div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <span class="comment">// to be also a NAN. Therefore, don't expect this constructor to</span></div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <span class="comment">// preserve the bits in x when x is a NAN.</span></div>
<div class="line"><a name="l00165"></a><span class="lineno"><a class="code" href="a00107.html#a223158362fd04a1c21fd514699bc480d"> 165</a></span>  <span class="keyword">explicit</span> <a class="code" href="a00107.html#a223158362fd04a1c21fd514699bc480d">FloatingPoint</a>(<span class="keyword">const</span> RawType& x) { u_.value_ = x; }</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span> </div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  <span class="comment">// Static methods</span></div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span> </div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <span class="comment">// Reinterprets a bit pattern as a floating-point number.</span></div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  <span class="comment">// This function is needed to test the AlmostEquals() method.</span></div>
<div class="line"><a name="l00172"></a><span class="lineno"><a class="code" href="a00107.html#a80c340111da59015517dde85bcc8966b"> 172</a></span>  <span class="keyword">static</span> RawType <a class="code" href="a00107.html#a80c340111da59015517dde85bcc8966b">ReinterpretBits</a>(<span class="keyword">const</span> <a class="code" href="a00107.html#aa0912a8f805308568ebd2609557680b4">Bits</a> <a class="code" href="a00107.html#a6b240b584668f5590c1e47108afdec33">bits</a>) {</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <a class="code" href="a00107.html">FloatingPoint</a> fp(0);</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  fp.u_.bits_ = <a class="code" href="a00107.html#a6b240b584668f5590c1e47108afdec33">bits</a>;</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  <span class="keywordflow">return</span> fp.u_.value_;</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  }</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span> </div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <span class="comment">// Returns the floating-point number that represent positive infinity.</span></div>
<div class="line"><a name="l00179"></a><span class="lineno"><a class="code" href="a00107.html#aa0cdd12e8007eea844d83757b531241a"> 179</a></span>  <span class="keyword">static</span> RawType <a class="code" href="a00107.html#aa0cdd12e8007eea844d83757b531241a">Infinity</a>() {</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="keywordflow">return</span> <a class="code" href="a00107.html#a80c340111da59015517dde85bcc8966b">ReinterpretBits</a>(<a class="code" href="a00107.html#a590938e82e2f449c0557744a6c5619ad">kExponentBitMask</a>);</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  }</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span> </div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <span class="comment">// Non-static methods</span></div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span> </div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <span class="comment">// Returns the bits that represents this number.</span></div>
<div class="line"><a name="l00186"></a><span class="lineno"><a class="code" href="a00107.html#a6b240b584668f5590c1e47108afdec33"> 186</a></span>  <span class="keyword">const</span> <a class="code" href="a00107.html#aa0912a8f805308568ebd2609557680b4">Bits</a> &<a class="code" href="a00107.html#a6b240b584668f5590c1e47108afdec33">bits</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> u_.bits_; }</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span> </div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="comment">// Returns the exponent bits of this number.</span></div>
<div class="line"><a name="l00189"></a><span class="lineno"><a class="code" href="a00107.html#ae44ba56b6c843e9384d58d24b283308f"> 189</a></span>  <a class="code" href="a00107.html#aa0912a8f805308568ebd2609557680b4">Bits</a> <a class="code" href="a00107.html#ae44ba56b6c843e9384d58d24b283308f">exponent_bits</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="a00107.html#a590938e82e2f449c0557744a6c5619ad">kExponentBitMask</a> & u_.bits_; }</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span> </div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="comment">// Returns the fraction bits of this number.</span></div>
<div class="line"><a name="l00192"></a><span class="lineno"><a class="code" href="a00107.html#af2f11a2b43c1647b8b6bdd4a4389bc66"> 192</a></span>  <a class="code" href="a00107.html#aa0912a8f805308568ebd2609557680b4">Bits</a> <a class="code" href="a00107.html#af2f11a2b43c1647b8b6bdd4a4389bc66">fraction_bits</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="a00107.html#a4909a899f6cc1a1bdb7835cec3629a0f">kFractionBitMask</a> & u_.bits_; }</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span> </div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <span class="comment">// Returns the sign bit of this number.</span></div>
<div class="line"><a name="l00195"></a><span class="lineno"><a class="code" href="a00107.html#a1007ce80d456d1e8262749bdd83ee7e7"> 195</a></span>  <a class="code" href="a00107.html#aa0912a8f805308568ebd2609557680b4">Bits</a> <a class="code" href="a00107.html#a1007ce80d456d1e8262749bdd83ee7e7">sign_bit</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="a00107.html#a026944d92c195ce2c755dde816cd6b0c">kSignBitMask</a> & u_.bits_; }</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span> </div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <span class="comment">// Returns true iff this is NAN (not a number).</span></div>
<div class="line"><a name="l00198"></a><span class="lineno"><a class="code" href="a00107.html#a44265079d31ee49d60d05b5f662a7a10"> 198</a></span>  <span class="keywordtype">bool</span> <a class="code" href="a00107.html#a44265079d31ee49d60d05b5f662a7a10">is_nan</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="comment">// It's a NAN if the exponent bits are all ones and the fraction</span></div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="comment">// bits are not entirely zeros.</span></div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="keywordflow">return</span> (<a class="code" href="a00107.html#ae44ba56b6c843e9384d58d24b283308f">exponent_bits</a>() == <a class="code" href="a00107.html#a590938e82e2f449c0557744a6c5619ad">kExponentBitMask</a>) && (<a class="code" href="a00107.html#af2f11a2b43c1647b8b6bdd4a4389bc66">fraction_bits</a>() != 0);</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  }</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span> </div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="comment">// Returns true iff this number is at most kMaxUlps ULP's away from</span></div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <span class="comment">// rhs. In particular, this function:</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">// - returns false if either number is (or both are) NAN.</span></div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="comment">// - treats really large numbers as almost equal to infinity.</span></div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  <span class="comment">// - thinks +0.0 and -0.0 are 0 DLP's apart.</span></div>
<div class="line"><a name="l00210"></a><span class="lineno"><a class="code" href="a00107.html#af6aab835c96f51ac4549e0e8a38f6767"> 210</a></span>  <span class="keywordtype">bool</span> <a class="code" href="a00107.html#af6aab835c96f51ac4549e0e8a38f6767">AlmostEquals</a>(<span class="keyword">const</span> <a class="code" href="a00107.html">FloatingPoint</a>& rhs)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="comment">// The IEEE standard says that any comparison operation involving</span></div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="comment">// a NAN must return false.</span></div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="keywordflow">if</span> (<a class="code" href="a00107.html#a44265079d31ee49d60d05b5f662a7a10">is_nan</a>() || rhs.<a class="code" href="a00107.html#a44265079d31ee49d60d05b5f662a7a10">is_nan</a>()) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span> </div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="keywordflow">return</span> DistanceBetweenSignAndMagnitudeNumbers(u_.bits_, rhs.u_.bits_)</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <= <a class="code" href="a00107.html#ad52b8184e122a8fe484f0d9633e960e1">kMaxUlps</a>;</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  }</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span> </div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="comment">// The data type used to store the actual floating-point number.</span></div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="keyword">union </span>FloatingPointUnion {</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  RawType value_; <span class="comment">// The raw floating-point number.</span></div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <a class="code" href="a00107.html#aa0912a8f805308568ebd2609557680b4">Bits</a> bits_; <span class="comment">// The bits that represent the number.</span></div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  };</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span> </div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="comment">// Converts an integer from the sign-and-magnitude representation to</span></div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="comment">// the biased representation. More precisely, let N be 2 to the</span></div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  <span class="comment">// power of (kBitCount - 1), an integer x is represented by the</span></div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  <span class="comment">// unsigned number x + N.</span></div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  <span class="comment">// For instance,</span></div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="comment">// -N + 1 (the most negative number representable using</span></div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="comment">// sign-and-magnitude) is represented by 1;</span></div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="comment">// 0 is represented by N; and</span></div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="comment">// N - 1 (the biggest number representable using</span></div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <span class="comment">// sign-and-magnitude) is represented by 2N - 1.</span></div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="comment">// Read http://en.wikipedia.org/wiki/Signed_number_representations</span></div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  <span class="comment">// for more details on signed number representations.</span></div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <span class="keyword">static</span> <a class="code" href="a00107.html#aa0912a8f805308568ebd2609557680b4">Bits</a> SignAndMagnitudeToBiased(<span class="keyword">const</span> <a class="code" href="a00107.html#aa0912a8f805308568ebd2609557680b4">Bits</a> &sam) {</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  <span class="keywordflow">if</span> (<a class="code" href="a00107.html#a026944d92c195ce2c755dde816cd6b0c">kSignBitMask</a> & sam) {</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="comment">// sam represents a negative number.</span></div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  <span class="keywordflow">return</span> ~sam + 1;</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <span class="comment">// sam represents a positive number.</span></div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <span class="keywordflow">return</span> <a class="code" href="a00107.html#a026944d92c195ce2c755dde816cd6b0c">kSignBitMask</a> | sam;</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> </div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="comment">// Given two numbers in the sign-and-magnitude representation,</span></div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  <span class="comment">// returns the distance between them as an unsigned number.</span></div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  <span class="keyword">static</span> <a class="code" href="a00107.html#aa0912a8f805308568ebd2609557680b4">Bits</a> DistanceBetweenSignAndMagnitudeNumbers(<span class="keyword">const</span> <a class="code" href="a00107.html#aa0912a8f805308568ebd2609557680b4">Bits</a> &sam1,</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="keyword">const</span> <a class="code" href="a00107.html#aa0912a8f805308568ebd2609557680b4">Bits</a> &sam2) {</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  <span class="keyword">const</span> <a class="code" href="a00107.html#aa0912a8f805308568ebd2609557680b4">Bits</a> biased1 = SignAndMagnitudeToBiased(sam1);</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <span class="keyword">const</span> <a class="code" href="a00107.html#aa0912a8f805308568ebd2609557680b4">Bits</a> biased2 = SignAndMagnitudeToBiased(sam2);</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <span class="keywordflow">return</span> (biased1 >= biased2) ? (biased1 - biased2) : (biased2 - biased1);</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  }</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span> </div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  FloatingPointUnion u_;</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span> };</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="preprocessor">#endif // __STDAIR_BAS_FLOAT_UTILS_GOOGLE_HPP</span></div>
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