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<div class="title">strtod.h</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// Tencent is pleased to support the open source community by making RapidJSON available.</span></div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// </span></div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">// Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip. All rights reserved.</span></div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">//</span></div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">// Licensed under the MIT License (the "License"); you may not use this file except</span></div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// in compliance with the License. You may obtain a copy of the License at</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">// http://opensource.org/licenses/MIT</span></div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">//</span></div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// Unless required by applicable law or agreed to in writing, software distributed </span></div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">// under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR </span></div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// CONDITIONS OF ANY KIND, either express or implied. See the License for the </span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment">// specific language governing permissions and limitations under the License.</span></div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> </div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor">#ifndef RAPIDJSON_STRTOD_</span></div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="preprocessor">#define RAPIDJSON_STRTOD_</span></div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> </div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="preprocessor">#include "ieee754.h"</span></div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="preprocessor">#include "biginteger.h"</span></div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="preprocessor">#include "diyfp.h"</span></div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#include "pow10.h"</span></div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> </div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span> RAPIDJSON_NAMESPACE_BEGIN</div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="keyword">namespace </span>internal {</div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span> </div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="keyword">inline</span> <span class="keywordtype">double</span> FastPath(<span class="keywordtype">double</span> significand, <span class="keywordtype">int</span> exp) {</div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  <span class="keywordflow">if</span> (exp < -308)</div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  <span class="keywordflow">return</span> 0.0;</div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (exp >= 0)</div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  <span class="keywordflow">return</span> significand * internal::Pow10(exp);</div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  <span class="keywordflow">return</span> significand / internal::Pow10(-exp);</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="keyword">inline</span> <span class="keywordtype">double</span> StrtodNormalPrecision(<span class="keywordtype">double</span> d, <span class="keywordtype">int</span> p) {</div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keywordflow">if</span> (p < -308) {</div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="comment">// Prevent expSum < -308, making Pow10(p) = 0</span></div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  d = FastPath(d, -308);</div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  d = FastPath(d, p + 308);</div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  }</div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  d = FastPath(d, p);</div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="keywordflow">return</span> d;</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> </div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="keyword">template</span> <<span class="keyword">typename</span> T></div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="keyword">inline</span> T Min3(T a, T b, T c) {</div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  T m = a;</div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="keywordflow">if</span> (m > b) m = b;</div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="keywordflow">if</span> (m > c) m = c;</div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keywordflow">return</span> m;</div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span> }</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="keyword">inline</span> <span class="keywordtype">int</span> CheckWithinHalfULP(<span class="keywordtype">double</span> b, <span class="keyword">const</span> BigInteger& d, <span class="keywordtype">int</span> dExp) {</div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keyword">const</span> Double db(b);</div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keyword">const</span> uint64_t bInt = db.IntegerSignificand();</div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> bExp = db.IntegerExponent();</div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> hExp = bExp - 1;</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>  <span class="keywordtype">int</span> dS_Exp2 = 0, dS_Exp5 = 0, bS_Exp2 = 0, bS_Exp5 = 0, hS_Exp2 = 0, hS_Exp5 = 0;</div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span> </div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="comment">// Adjust for decimal exponent</span></div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keywordflow">if</span> (dExp >= 0) {</div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  dS_Exp2 += dExp;</div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  dS_Exp5 += dExp;</div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  }</div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keywordflow">else</span> {</div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  bS_Exp2 -= dExp;</div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  bS_Exp5 -= dExp;</div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  hS_Exp2 -= dExp;</div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  hS_Exp5 -= dExp;</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"> 74</span>  <span class="comment">// Adjust for binary exponent</span></div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keywordflow">if</span> (bExp >= 0)</div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  bS_Exp2 += bExp;</div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="keywordflow">else</span> {</div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  dS_Exp2 -= bExp;</div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  hS_Exp2 -= bExp;</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"> 82</span>  <span class="comment">// Adjust for half ulp exponent</span></div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keywordflow">if</span> (hExp >= 0)</div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  hS_Exp2 += hExp;</div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordflow">else</span> {</div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  dS_Exp2 -= hExp;</div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  bS_Exp2 -= hExp;</div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  }</div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span> </div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="comment">// Remove common power of two factor from all three scaled values</span></div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="keywordtype">int</span> common_Exp2 = Min3(dS_Exp2, bS_Exp2, hS_Exp2);</div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  dS_Exp2 -= common_Exp2;</div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  bS_Exp2 -= common_Exp2;</div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  hS_Exp2 -= common_Exp2;</div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span> </div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  BigInteger dS = d;</div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  dS.MultiplyPow5(static_cast<unsigned>(dS_Exp5)) <<= <span class="keyword">static_cast<</span><span class="keywordtype">unsigned</span><span class="keyword">></span>(dS_Exp2);</div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span> </div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  BigInteger bS(bInt);</div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  bS.MultiplyPow5(static_cast<unsigned>(bS_Exp5)) <<= <span class="keyword">static_cast<</span><span class="keywordtype">unsigned</span><span class="keyword">></span>(bS_Exp2);</div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span> </div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  BigInteger hS(1);</div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  hS.MultiplyPow5(static_cast<unsigned>(hS_Exp5)) <<= <span class="keyword">static_cast<</span><span class="keywordtype">unsigned</span><span class="keyword">></span>(hS_Exp2);</div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span> </div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  BigInteger delta(0);</div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  dS.Difference(bS, &delta);</div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span> </div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="keywordflow">return</span> delta.Compare(hS);</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> </div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> StrtodFast(<span class="keywordtype">double</span> d, <span class="keywordtype">int</span> p, <span class="keywordtype">double</span>* result) {</div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="comment">// Use fast path for string-to-double conversion if possible</span></div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="comment">// see http://www.exploringbinary.com/fast-path-decimal-to-floating-point-conversion/</span></div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="keywordflow">if</span> (p > 22 && p < 22 + 16) {</div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="comment">// Fast Path Cases In Disguise</span></div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  d *= internal::Pow10(p - 22);</div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  p = 22;</div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  }</div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span> </div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keywordflow">if</span> (p >= -22 && p <= 22 && d <= 9007199254740991.0) { <span class="comment">// 2^53 - 1</span></div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  *result = FastPath(d, p);</div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  }</div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span> }</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">// Compute an approximation and see if it is within 1/2 ULP</span></div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> StrtodDiyFp(<span class="keyword">const</span> <span class="keywordtype">char</span>* decimals, <span class="keywordtype">size_t</span> length, <span class="keywordtype">size_t</span> decimalPosition, <span class="keywordtype">int</span> exp, <span class="keywordtype">double</span>* result) {</div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  uint64_t significand = 0;</div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keywordtype">size_t</span> i = 0; <span class="comment">// 2^64 - 1 = 18446744073709551615, 1844674407370955161 = 0x1999999999999999 </span></div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="keywordflow">for</span> (; i < length; i++) {</div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keywordflow">if</span> (significand > <a class="code" href="rapidjson_8h.html#aaee1245f375a71be1ac9b8a07ba5fb8f">RAPIDJSON_UINT64_C2</a>(0x19999999, 0x99999999) ||</div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  (significand == <a class="code" href="rapidjson_8h.html#aaee1245f375a71be1ac9b8a07ba5fb8f">RAPIDJSON_UINT64_C2</a>(0x19999999, 0x99999999) && decimals[i] > <span class="charliteral">'5'</span>))</div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="keywordflow">break</span>;</div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  significand = significand * 10u + <span class="keyword">static_cast<</span><span class="keywordtype">unsigned</span><span class="keyword">></span>(decimals[i] - <span class="charliteral">'0'</span>);</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>  </div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <span class="keywordflow">if</span> (i < length && decimals[i] >= <span class="charliteral">'5'</span>) <span class="comment">// Rounding</span></div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  significand++;</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="keywordtype">size_t</span> remaining = length - i;</div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="keyword">const</span> <span class="keywordtype">unsigned</span> kUlpShift = 3;</div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="keyword">const</span> <span class="keywordtype">unsigned</span> kUlp = 1 << kUlpShift;</div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  int64_t error = (remaining == 0) ? 0 : kUlp / 2;</div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span> </div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  DiyFp v(significand, 0);</div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  v = v.Normalize();</div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  error <<= -v.e;</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="keyword">const</span> <span class="keywordtype">int</span> dExp = <span class="keyword">static_cast<</span><span class="keywordtype">int</span><span class="keyword">></span>(decimalPosition) - static_cast<int>(i) + exp;</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>  <span class="keywordtype">int</span> actualExp;</div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  DiyFp cachedPower = GetCachedPower10(dExp, &actualExp);</div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="keywordflow">if</span> (actualExp != dExp) {</div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="keyword">static</span> <span class="keyword">const</span> DiyFp kPow10[] = {</div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  DiyFp(<a class="code" href="rapidjson_8h.html#aaee1245f375a71be1ac9b8a07ba5fb8f">RAPIDJSON_UINT64_C2</a>(0xa0000000, 00000000), -60), <span class="comment">// 10^1</span></div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  DiyFp(<a class="code" href="rapidjson_8h.html#aaee1245f375a71be1ac9b8a07ba5fb8f">RAPIDJSON_UINT64_C2</a>(0xc8000000, 00000000), -57), <span class="comment">// 10^2</span></div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  DiyFp(<a class="code" href="rapidjson_8h.html#aaee1245f375a71be1ac9b8a07ba5fb8f">RAPIDJSON_UINT64_C2</a>(0xfa000000, 00000000), -54), <span class="comment">// 10^3</span></div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  DiyFp(<a class="code" href="rapidjson_8h.html#aaee1245f375a71be1ac9b8a07ba5fb8f">RAPIDJSON_UINT64_C2</a>(0x9c400000, 00000000), -50), <span class="comment">// 10^4</span></div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  DiyFp(<a class="code" href="rapidjson_8h.html#aaee1245f375a71be1ac9b8a07ba5fb8f">RAPIDJSON_UINT64_C2</a>(0xc3500000, 00000000), -47), <span class="comment">// 10^5</span></div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  DiyFp(<a class="code" href="rapidjson_8h.html#aaee1245f375a71be1ac9b8a07ba5fb8f">RAPIDJSON_UINT64_C2</a>(0xf4240000, 00000000), -44), <span class="comment">// 10^6</span></div><div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  DiyFp(<a class="code" href="rapidjson_8h.html#aaee1245f375a71be1ac9b8a07ba5fb8f">RAPIDJSON_UINT64_C2</a>(0x98968000, 00000000), -40) <span class="comment">// 10^7</span></div><div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  };</div><div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <span class="keywordtype">int</span> adjustment = dExp - actualExp - 1;</div><div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <a class="code" href="group___r_a_p_i_d_j_s_o_n___c_o_n_f_i_g.html#gabeba18d612187bad2ac62aed9276d47c">RAPIDJSON_ASSERT</a>(adjustment >= 0 && adjustment < 7);</div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  v = v * kPow10[adjustment];</div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  <span class="keywordflow">if</span> (length + static_cast<unsigned>(adjustment)> 19u) <span class="comment">// has more digits than decimal digits in 64-bit</span></div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  error += kUlp / 2;</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> </div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  v = v * cachedPower;</div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span> </div><div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  error += kUlp + (error == 0 ? 0 : 1);</div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span> </div><div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> oldExp = v.e;</div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  v = v.Normalize();</div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  error <<= oldExp - v.e;</div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span> </div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="keyword">const</span> <span class="keywordtype">unsigned</span> effectiveSignificandSize = Double::EffectiveSignificandSize(64 + v.e);</div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <span class="keywordtype">unsigned</span> precisionSize = 64 - effectiveSignificandSize;</div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <span class="keywordflow">if</span> (precisionSize + kUlpShift >= 64) {</div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <span class="keywordtype">unsigned</span> scaleExp = (precisionSize + kUlpShift) - 63;</div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  v.f >>= scaleExp;</div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  v.e += scaleExp; </div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  error = (error >> scaleExp) + 1 + static_cast<int>(kUlp);</div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  precisionSize -= scaleExp;</div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  }</div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span> </div><div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  DiyFp rounded(v.f >> precisionSize, v.e + static_cast<int>(precisionSize));</div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="keyword">const</span> uint64_t precisionBits = (v.f & ((uint64_t(1) << precisionSize) - 1)) * kUlp;</div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <span class="keyword">const</span> uint64_t halfWay = (uint64_t(1) << (precisionSize - 1)) * kUlp;</div><div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="keywordflow">if</span> (precisionBits >= halfWay + static_cast<unsigned>(error)) {</div><div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  rounded.f++;</div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="keywordflow">if</span> (rounded.f & (DiyFp::kDpHiddenBit << 1)) { <span class="comment">// rounding overflows mantissa (issue #340)</span></div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  rounded.f >>= 1;</div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  rounded.e++;</div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  }</div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  }</div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span> </div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  *result = rounded.ToDouble();</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>  <span class="keywordflow">return</span> halfWay - <span class="keyword">static_cast<</span><span class="keywordtype">unsigned</span><span class="keyword">></span>(error) >= precisionBits || precisionBits >= halfWay + static_cast<unsigned>(error);</div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span> }</div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span> </div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="keyword">inline</span> <span class="keywordtype">double</span> StrtodBigInteger(<span class="keywordtype">double</span> approx, <span class="keyword">const</span> <span class="keywordtype">char</span>* decimals, <span class="keywordtype">size_t</span> length, <span class="keywordtype">size_t</span> decimalPosition, <span class="keywordtype">int</span> exp) {</div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <span class="keyword">const</span> BigInteger dInt(decimals, length);</div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> dExp = <span class="keyword">static_cast<</span><span class="keywordtype">int</span><span class="keyword">></span>(decimalPosition) - static_cast<int>(length) + exp;</div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  Double a(approx);</div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  <span class="keywordtype">int</span> cmp = CheckWithinHalfULP(a.Value(), dInt, dExp);</div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="keywordflow">if</span> (cmp < 0)</div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="keywordflow">return</span> a.Value(); <span class="comment">// within half ULP</span></div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (cmp == 0) {</div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="comment">// Round towards even</span></div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="keywordflow">if</span> (a.Significand() & 1)</div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="keywordflow">return</span> a.NextPositiveDouble();</div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="keywordflow">return</span> a.Value();</div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  }</div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="keywordflow">else</span> <span class="comment">// adjustment</span></div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="keywordflow">return</span> a.NextPositiveDouble();</div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span> }</div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span> </div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span> <span class="keyword">inline</span> <span class="keywordtype">double</span> StrtodFullPrecision(<span class="keywordtype">double</span> d, <span class="keywordtype">int</span> p, <span class="keyword">const</span> <span class="keywordtype">char</span>* decimals, <span class="keywordtype">size_t</span> length, <span class="keywordtype">size_t</span> decimalPosition, <span class="keywordtype">int</span> exp) {</div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  <a class="code" href="group___r_a_p_i_d_j_s_o_n___c_o_n_f_i_g.html#gabeba18d612187bad2ac62aed9276d47c">RAPIDJSON_ASSERT</a>(d >= 0.0);</div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <a class="code" href="group___r_a_p_i_d_j_s_o_n___c_o_n_f_i_g.html#gabeba18d612187bad2ac62aed9276d47c">RAPIDJSON_ASSERT</a>(length >= 1);</div><div class="line"><a name="l00227"></a><span class="lineno"> 227</span> </div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  <span class="keywordtype">double</span> result;</div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  <span class="keywordflow">if</span> (StrtodFast(d, p, &result))</div><div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  <span class="keywordflow">return</span> result;</div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span> </div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="comment">// Trim leading zeros</span></div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="keywordflow">while</span> (*decimals == <span class="charliteral">'0'</span> && length > 1) {</div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  length--;</div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  decimals++;</div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  decimalPosition--;</div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  }</div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span> </div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="comment">// Trim trailing zeros</span></div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  <span class="keywordflow">while</span> (decimals[length - 1] == <span class="charliteral">'0'</span> && length > 1) {</div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  length--;</div><div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  decimalPosition--;</div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  exp++;</div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  }</div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span> </div><div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <span class="comment">// Trim right-most digits</span></div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> kMaxDecimalDigit = 780;</div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  <span class="keywordflow">if</span> (static_cast<int>(length) > kMaxDecimalDigit) {</div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="keywordtype">int</span> delta = (<span class="keyword">static_cast<</span><span class="keywordtype">int</span><span class="keyword">></span>(length) - kMaxDecimalDigit);</div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  exp += delta;</div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  decimalPosition -= <span class="keyword">static_cast<</span><span class="keywordtype">unsigned</span><span class="keyword">></span>(delta);</div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  length = kMaxDecimalDigit;</div><div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  }</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">// If too small, underflow to zero</span></div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <span class="keywordflow">if</span> (<span class="keywordtype">int</span>(length) + exp < -324)</div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <span class="keywordflow">return</span> 0.0;</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>  <span class="keywordflow">if</span> (StrtodDiyFp(decimals, length, decimalPosition, exp, &result))</div><div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  <span class="keywordflow">return</span> result;</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>  <span class="comment">// Use approximation from StrtodDiyFp and make adjustment with BigInteger comparison</span></div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <span class="keywordflow">return</span> StrtodBigInteger(result, decimals, length, decimalPosition, exp);</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> </div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span> } <span class="comment">// namespace internal</span></div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span> RAPIDJSON_NAMESPACE_END</div><div class="line"><a name="l00268"></a><span class="lineno"> 268</span> </div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span> <span class="preprocessor">#endif // RAPIDJSON_STRTOD_</span></div><div class="ttc" id="rapidjson_8h_html_aaee1245f375a71be1ac9b8a07ba5fb8f"><div class="ttname"><a href="rapidjson_8h.html#aaee1245f375a71be1ac9b8a07ba5fb8f">RAPIDJSON_UINT64_C2</a></div><div class="ttdeci">#define RAPIDJSON_UINT64_C2(high32, low32)</div><div class="ttdoc">Construct a 64-bit literal by a pair of 32-bit integer. </div><div class="ttdef"><b>Definition:</b> rapidjson.h:289</div></div>
<div class="ttc" id="group___r_a_p_i_d_j_s_o_n___c_o_n_f_i_g_html_gabeba18d612187bad2ac62aed9276d47c"><div class="ttname"><a href="group___r_a_p_i_d_j_s_o_n___c_o_n_f_i_g.html#gabeba18d612187bad2ac62aed9276d47c">RAPIDJSON_ASSERT</a></div><div class="ttdeci">#define RAPIDJSON_ASSERT(x)</div><div class="ttdoc">Assertion. </div><div class="ttdef"><b>Definition:</b> rapidjson.h:402</div></div>
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