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<li class="navelem"><a class="el" href="dir_90ffdbabf412cfdffe6b2193e0ce938a.html">libxrpl</a></li><li class="navelem"><a class="el" href="dir_c9ad8b908996c4ad90b9a0cfb3c90cd8.html">basics</a></li> </ul>
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<div class="headertitle"><div class="title">Number.cpp</div></div>
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<div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">//------------------------------------------------------------------------------</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">/*</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment"> This file is part of rippled: https://github.com/ripple/rippled</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment"> Copyright (c) 2022 Ripple Labs Inc.</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment"></span> </div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment"> Permission to use, copy, modify, and/or distribute this software for any</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment"> purpose with or without fee is hereby granted, provided that the above</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment"> copyright notice and this permission notice appear in all copies.</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment"></span> </div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment"> THE SOFTWARE IS PROVIDED &quot;AS IS&quot; AND THE AUTHOR DISCLAIMS ALL WARRANTIES</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment"> WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment"> MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="comment"> ANY SPECIAL , DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment"> WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="comment"> ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment"> OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="comment">*/</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="comment">//==============================================================================</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include &lt;xrpl/basics/Number.h&gt;</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include &lt;xrpl/beast/utility/instrumentation.h&gt;</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> </div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include &lt;<a class="codeRef" href="http://en.cppreference.com/w/cpp/header/algorithm.html">algorithm</a>&gt;</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#include &lt;<a class="codeRef" href="http://en.cppreference.com/w/cpp/header/cstddef.html">cstddef</a>&gt;</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#include &lt;<a class="codeRef" href="http://en.cppreference.com/w/cpp/header/cstdint.html">cstdint</a>&gt;</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor">#include &lt;<a class="codeRef" href="http://en.cppreference.com/w/cpp/header/iterator.html">iterator</a>&gt;</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="preprocessor">#include &lt;<a class="codeRef" href="http://en.cppreference.com/w/cpp/header/limits.html">limits</a>&gt;</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="preprocessor">#include &lt;<a class="codeRef" href="http://en.cppreference.com/w/cpp/header/numeric.html">numeric</a>&gt;</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="preprocessor">#include &lt;<a class="codeRef" href="http://en.cppreference.com/w/cpp/header/stdexcept.html">stdexcept</a>&gt;</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="preprocessor">#include &lt;<a class="codeRef" href="http://en.cppreference.com/w/cpp/header/string.html">string</a>&gt;</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="preprocessor">#include &lt;<a class="codeRef" href="http://en.cppreference.com/w/cpp/header/type_traits.html">type_traits</a>&gt;</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="preprocessor">#include &lt;<a class="codeRef" href="http://en.cppreference.com/w/cpp/header/utility.html">utility</a>&gt;</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> </div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="preprocessor">#ifdef _MSC_VER</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="preprocessor">#pragma message(&quot;Using boost::multiprecision::uint128_t&quot;)</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="preprocessor">#include &lt;boost/multiprecision/cpp_int.hpp&gt;</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="keyword">using </span>uint128_t = boost::multiprecision::uint128_t;</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="preprocessor">#else </span><span class="comment">// !defined(_MSC_VER)</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="keyword">using </span>uint128_t = __uint128_t;</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="preprocessor">#endif </span><span class="comment">// !defined(_MSC_VER)</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> </div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceripple.html">ripple</a> {</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> </div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="keyword">thread_local</span> <a class="code hl_enumeration" href="classripple_1_1Number.html#a33e3d8e7a95979bd1eb22c59703c8534">Number::rounding_mode</a> <a class="code hl_variable" href="classripple_1_1Number.html#a5a2b36707b7dc7204982e873fcc50bac">Number::mode_</a> = <a class="code hl_enumvalue" href="classripple_1_1Number.html#a33e3d8e7a95979bd1eb22c59703c8534afb083653be2726415a0832efd2d66e95">Number::to_nearest</a>;</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> </div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><a class="code hl_enumeration" href="classripple_1_1Number.html#a33e3d8e7a95979bd1eb22c59703c8534">Number::rounding_mode</a></div>
<div class="foldopen" id="foldopen00047" data-start="{" data-end="}">
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"><a class="line" href="classripple_1_1Number.html#a69a91a7aca13639e1705b7fb94ee78d5"> 47</a></span><a class="code hl_function" href="classripple_1_1Number.html#a69a91a7aca13639e1705b7fb94ee78d5">Number::getround</a>()</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span>{</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="classripple_1_1Number.html#a5a2b36707b7dc7204982e873fcc50bac">mode_</a>;</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span>}</div>
</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> </div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><a class="code hl_enumeration" href="classripple_1_1Number.html#a33e3d8e7a95979bd1eb22c59703c8534">Number::rounding_mode</a></div>
<div class="foldopen" id="foldopen00053" data-start="{" data-end="}">
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"><a class="line" href="classripple_1_1Number.html#a9f2a0df7ad0f278908643927a19592f2"> 53</a></span><a class="code hl_function" href="classripple_1_1Number.html#a9f2a0df7ad0f278908643927a19592f2">Number::setround</a>(<a class="code hl_enumeration" href="classripple_1_1Number.html#a33e3d8e7a95979bd1eb22c59703c8534">rounding_mode</a> mode)</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span>{</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keywordflow">return</span> <a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/utility/exchange.html">std::exchange</a>(<a class="code hl_variable" href="classripple_1_1Number.html#a5a2b36707b7dc7204982e873fcc50bac">mode_</a>, mode);</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span>}</div>
</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> </div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="comment">// Guard</span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> </div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span><span class="comment">// The Guard class is used to tempoarily add extra digits of</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span><span class="comment">// preicision to an operation. This enables the final result</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span><span class="comment">// to be correctly rounded to the internal precision of Number.</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> </div>
<div class="foldopen" id="foldopen00064" data-start="{" data-end="};">
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"><a class="line" href="classripple_1_1Number_1_1Guard.html"> 64</a></span><span class="keyword">class </span><a class="code hl_class" href="classripple_1_1Number_1_1Guard.html">Number::Guard</a></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span>{</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"><a class="line" href="classripple_1_1Number_1_1Guard.html#ac287598d3a58a5b3521715c20cdf99bd"> 66</a></span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint64_t</a> <a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#ac287598d3a58a5b3521715c20cdf99bd">digits_</a>; <span class="comment">// 16 decimal guard digits</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"><a class="line" href="classripple_1_1Number_1_1Guard.html#abfe099a7a0d7b598b14f8ad317cb2948"> 67</a></span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint8_t</a> <a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#abfe099a7a0d7b598b14f8ad317cb2948">xbit_</a> : 1; <span class="comment">// has a non-zero digit been shifted off the end</span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"><a class="line" href="classripple_1_1Number_1_1Guard.html#ad7474f95ecebeaa0a6a4b03a2ad3d382"> 68</a></span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint8_t</a> <a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#ad7474f95ecebeaa0a6a4b03a2ad3d382">sbit_</a> : 1; <span class="comment">// the sign of the guard digits</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> </div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span><span class="keyword">public</span>:</div>
<div class="foldopen" id="foldopen00071" data-start="{" data-end="}">
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"><a class="line" href="classripple_1_1Number_1_1Guard.html#ab8c124fbd66b71e9282831794d6dca7b"> 71</a></span> <span class="keyword">explicit</span> <a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#ab8c124fbd66b71e9282831794d6dca7b">Guard</a>() : <a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#ac287598d3a58a5b3521715c20cdf99bd">digits_</a>{0}, <a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#abfe099a7a0d7b598b14f8ad317cb2948">xbit_</a>{0}, <a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#ad7474f95ecebeaa0a6a4b03a2ad3d382">sbit_</a>{0}</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> {</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> }</div>
</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> </div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="comment">// set &amp; test the sign bit</span></div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keywordtype">void</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#ad867ec492c1533e448bda8bb58af444a">set_positive</a>() noexcept;</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keywordtype">void</span></div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#a29e64e95a3e18476211420722180906c">set_negative</a>() noexcept;</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keywordtype">bool</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#ab190e6f6405f271600b2f99ff15a6bc2">is_negative</a>() const noexcept;</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> </div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="comment">// add a digit</span></div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="keywordtype">void</span></div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#a78ddead46cd4a5ce528d7d8f765e4ea1">push</a>(<span class="keywordtype">unsigned</span> d) noexcept;</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> </div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="comment">// recover a digit</span></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="keywordtype">unsigned</span></div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#a997cf381405becb9566b855185984471">pop</a>() noexcept;</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> </div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="comment">// Indicate round direction: 1 is up, -1 is down, 0 is even</span></div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="comment">// This enables the client to round towards nearest, and on</span></div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="comment">// tie, round towards even.</span></div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keywordtype">int</span></div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#acf34c737037a6e8a5d04d33338a2ccde">round</a>() noexcept;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span>};</div>
</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> </div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span>inline <span class="keywordtype">void</span></div>
<div class="foldopen" id="foldopen00099" data-start="{" data-end="}">
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"><a class="line" href="classripple_1_1Number_1_1Guard.html#ad867ec492c1533e448bda8bb58af444a"> 99</a></span><a class="code hl_class" href="classripple_1_1Number.html">Number</a>::<a class="code hl_class" href="classripple_1_1Number_1_1Guard.html">Guard</a>::<a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#ad867ec492c1533e448bda8bb58af444a">set_positive</a>() noexcept</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span>{</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#ad7474f95ecebeaa0a6a4b03a2ad3d382">sbit_</a> = 0;</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span>}</div>
</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> </div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span><span class="keyword">inline</span> <span class="keywordtype">void</span></div>
<div class="foldopen" id="foldopen00105" data-start="{" data-end="}">
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"><a class="line" href="classripple_1_1Number_1_1Guard.html#a29e64e95a3e18476211420722180906c"> 105</a></span><a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#a29e64e95a3e18476211420722180906c">Number::Guard::set_negative</a>() noexcept</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span>{</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#ad7474f95ecebeaa0a6a4b03a2ad3d382">sbit_</a> = 1;</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span>}</div>
</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> </div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span><span class="keyword">inline</span> <span class="keywordtype">bool</span></div>
<div class="foldopen" id="foldopen00111" data-start="{" data-end="}">
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"><a class="line" href="classripple_1_1Number_1_1Guard.html#ab190e6f6405f271600b2f99ff15a6bc2"> 111</a></span><a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#ab190e6f6405f271600b2f99ff15a6bc2">Number::Guard::is_negative</a>() const noexcept</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span>{</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#ad7474f95ecebeaa0a6a4b03a2ad3d382">sbit_</a> == 1;</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span>}</div>
</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> </div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span><span class="keyword">inline</span> <span class="keywordtype">void</span></div>
<div class="foldopen" id="foldopen00117" data-start="{" data-end="}">
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"><a class="line" href="classripple_1_1Number_1_1Guard.html#a78ddead46cd4a5ce528d7d8f765e4ea1"> 117</a></span><a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#a78ddead46cd4a5ce528d7d8f765e4ea1">Number::Guard::push</a>(<span class="keywordtype">unsigned</span> d) <span class="keyword">noexcept</span></div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span>{</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#abfe099a7a0d7b598b14f8ad317cb2948">xbit_</a> = <a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#abfe099a7a0d7b598b14f8ad317cb2948">xbit_</a> || (<a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#ac287598d3a58a5b3521715c20cdf99bd">digits_</a> &amp; 0x0000&#39;0000&#39;0000&#39;000F) != 0;</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#ac287598d3a58a5b3521715c20cdf99bd">digits_</a> &gt;&gt;= 4;</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#ac287598d3a58a5b3521715c20cdf99bd">digits_</a> |= (d &amp; 0x0000&#39;0000&#39;0000&#39;000FULL) &lt;&lt; 60;</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span>}</div>
</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> </div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span><span class="keyword">inline</span> <span class="keywordtype">unsigned</span></div>
<div class="foldopen" id="foldopen00125" data-start="{" data-end="}">
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"><a class="line" href="classripple_1_1Number_1_1Guard.html#a997cf381405becb9566b855185984471"> 125</a></span><a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#a997cf381405becb9566b855185984471">Number::Guard::pop</a>() noexcept</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span>{</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="keywordtype">unsigned</span> d = (<a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#ac287598d3a58a5b3521715c20cdf99bd">digits_</a> &amp; 0xF000&#39;0000&#39;0000&#39;0000) &gt;&gt; 60;</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#ac287598d3a58a5b3521715c20cdf99bd">digits_</a> &lt;&lt;= 4;</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="keywordflow">return</span> d;</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span>}</div>
</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> </div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span><span class="comment">// Returns:</span></div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span><span class="comment">// -1 if Guard is less than half</span></div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span><span class="comment">// 0 if Guard is exactly half</span></div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span><span class="comment">// 1 if Guard is greater than half</span></div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span><span class="keywordtype">int</span></div>
<div class="foldopen" id="foldopen00137" data-start="{" data-end="}">
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"><a class="line" href="classripple_1_1Number_1_1Guard.html#acf34c737037a6e8a5d04d33338a2ccde"> 137</a></span><a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#acf34c737037a6e8a5d04d33338a2ccde">Number::Guard::round</a>() noexcept</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span>{</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <span class="keyword">auto</span> mode = <a class="code hl_function" href="classripple_1_1Number.html#a69a91a7aca13639e1705b7fb94ee78d5">Number::getround</a>();</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> </div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <span class="keywordflow">if</span> (mode == <a class="code hl_enumvalue" href="classripple_1_1Number.html#a33e3d8e7a95979bd1eb22c59703c8534afed3119e1980867324d399f42cbf548d">towards_zero</a>)</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> <span class="keywordflow">return</span> -1;</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> </div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <span class="keywordflow">if</span> (mode == <a class="code hl_enumvalue" href="classripple_1_1Number.html#a33e3d8e7a95979bd1eb22c59703c8534a25a8f50fce6cbdd3a8c0a3aa20126324">downward</a>)</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> {</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#ad7474f95ecebeaa0a6a4b03a2ad3d382">sbit_</a>)</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> {</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#ac287598d3a58a5b3521715c20cdf99bd">digits_</a> &gt; 0 || <a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#abfe099a7a0d7b598b14f8ad317cb2948">xbit_</a>)</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> <span class="keywordflow">return</span> 1;</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> }</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <span class="keywordflow">return</span> -1;</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> }</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> </div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> <span class="keywordflow">if</span> (mode == <a class="code hl_enumvalue" href="classripple_1_1Number.html#a33e3d8e7a95979bd1eb22c59703c8534ade4db21da96eedd46544ea52ce11a6f2">upward</a>)</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> {</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#ad7474f95ecebeaa0a6a4b03a2ad3d382">sbit_</a>)</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <span class="keywordflow">return</span> -1;</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#ac287598d3a58a5b3521715c20cdf99bd">digits_</a> &gt; 0 || <a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#abfe099a7a0d7b598b14f8ad317cb2948">xbit_</a>)</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="keywordflow">return</span> 1;</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <span class="keywordflow">return</span> -1;</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> }</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> </div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> <span class="comment">// assume round to nearest if mode is not one of the predefined values</span></div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#ac287598d3a58a5b3521715c20cdf99bd">digits_</a> &gt; 0x5000&#39;0000&#39;0000&#39;0000)</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> <span class="keywordflow">return</span> 1;</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#ac287598d3a58a5b3521715c20cdf99bd">digits_</a> &lt; 0x5000&#39;0000&#39;0000&#39;0000)</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> <span class="keywordflow">return</span> -1;</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="classripple_1_1Number_1_1Guard.html#abfe099a7a0d7b598b14f8ad317cb2948">xbit_</a>)</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> <span class="keywordflow">return</span> 1;</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span>}</div>
</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> </div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span><span class="comment">// Number</span></div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> </div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"><a class="line" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093"> 175</a></span><span class="keyword">constexpr</span> <a class="code hl_class" href="classripple_1_1Number.html">Number</a> <a class="code hl_variable" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a>{1000000000000000, -15, <a class="code hl_struct" href="structripple_1_1Number_1_1unchecked.html">Number::unchecked</a>{}};</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> </div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span><span class="keywordtype">void</span></div>
<div class="foldopen" id="foldopen00178" data-start="{" data-end="}">
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"><a class="line" href="classripple_1_1Number.html#a5fefb45b369635e7803f4f8d3f9b9dd4"> 178</a></span><a class="code hl_function" href="classripple_1_1Number.html#a5fefb45b369635e7803f4f8d3f9b9dd4">Number::normalize</a>()</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span>{</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="classripple_1_1Number.html#ae8914a365ad9ca852b2d8dbdd43abb6f">mantissa_</a> == 0)</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> {</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> *<span class="keyword">this</span> = <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{};</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> }</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> <span class="keywordtype">bool</span> <span class="keyword">const</span> negative = (<a class="code hl_variable" href="classripple_1_1Number.html#ae8914a365ad9ca852b2d8dbdd43abb6f">mantissa_</a> &lt; 0);</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> <span class="keyword">auto</span> m = <span class="keyword">static_cast&lt;</span><a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/types/make_unsigned.html">std::make_unsigned_t&lt;rep&gt;</a><span class="keyword">&gt;</span>(<a class="code hl_variable" href="classripple_1_1Number.html#ae8914a365ad9ca852b2d8dbdd43abb6f">mantissa_</a>);</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <span class="keywordflow">if</span> (negative)</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> m = -m;</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> <span class="keywordflow">while</span> ((m &lt; <a class="code hl_variable" href="classripple_1_1Number.html#a550732b6c726cffc8a742569fe76aa6e">minMantissa</a>) &amp;&amp; (<a class="code hl_variable" href="classripple_1_1Number.html#a62582b28d9183e7618fec0f0458331ab">exponent_</a> &gt; <a class="code hl_variable" href="classripple_1_1Number.html#a72928c9b23a8c2b07024d2d3ff5eed73">minExponent</a>))</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> {</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> m *= 10;</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> --<a class="code hl_variable" href="classripple_1_1Number.html#a62582b28d9183e7618fec0f0458331ab">exponent_</a>;</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> }</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <a class="code hl_class" href="classripple_1_1Number_1_1Guard.html">Guard</a> g;</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> <span class="keywordflow">if</span> (negative)</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> g.<a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#a29e64e95a3e18476211420722180906c">set_negative</a>();</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> <span class="keywordflow">while</span> (m &gt; <a class="code hl_variable" href="classripple_1_1Number.html#a18f3cb87112cf4436f8730a4f3333550">maxMantissa</a>)</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> {</div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="classripple_1_1Number.html#a62582b28d9183e7618fec0f0458331ab">exponent_</a> &gt;= <a class="code hl_variable" href="classripple_1_1Number.html#a388d646cceab9673a0edb81206e1e106">maxExponent</a>)</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> <span class="keywordflow">throw</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/error/overflow_error.html">std::overflow_error</a>(<span class="stringliteral">&quot;Number::normalize 1&quot;</span>);</div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> g.<a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#a78ddead46cd4a5ce528d7d8f765e4ea1">push</a>(m % 10);</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> m /= 10;</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> ++<a class="code hl_variable" href="classripple_1_1Number.html#a62582b28d9183e7618fec0f0458331ab">exponent_</a>;</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> }</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> <a class="code hl_variable" href="classripple_1_1Number.html#ae8914a365ad9ca852b2d8dbdd43abb6f">mantissa_</a> = m;</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> <span class="keywordflow">if</span> ((<a class="code hl_variable" href="classripple_1_1Number.html#a62582b28d9183e7618fec0f0458331ab">exponent_</a> &lt; <a class="code hl_variable" href="classripple_1_1Number.html#a72928c9b23a8c2b07024d2d3ff5eed73">minExponent</a>) || (<a class="code hl_variable" href="classripple_1_1Number.html#ae8914a365ad9ca852b2d8dbdd43abb6f">mantissa_</a> &lt; <a class="code hl_variable" href="classripple_1_1Number.html#a550732b6c726cffc8a742569fe76aa6e">minMantissa</a>))</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> {</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> *<span class="keyword">this</span> = <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{};</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> }</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> </div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> <span class="keyword">auto</span> r = g.<a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#acf34c737037a6e8a5d04d33338a2ccde">round</a>();</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> <span class="keywordflow">if</span> (r == 1 || (r == 0 &amp;&amp; (<a class="code hl_variable" href="classripple_1_1Number.html#ae8914a365ad9ca852b2d8dbdd43abb6f">mantissa_</a> &amp; 1) == 1))</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> {</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> ++<a class="code hl_variable" href="classripple_1_1Number.html#ae8914a365ad9ca852b2d8dbdd43abb6f">mantissa_</a>;</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="classripple_1_1Number.html#ae8914a365ad9ca852b2d8dbdd43abb6f">mantissa_</a> &gt; <a class="code hl_variable" href="classripple_1_1Number.html#a18f3cb87112cf4436f8730a4f3333550">maxMantissa</a>)</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> {</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> <a class="code hl_variable" href="classripple_1_1Number.html#ae8914a365ad9ca852b2d8dbdd43abb6f">mantissa_</a> /= 10;</div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> ++<a class="code hl_variable" href="classripple_1_1Number.html#a62582b28d9183e7618fec0f0458331ab">exponent_</a>;</div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> }</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> }</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="classripple_1_1Number.html#a62582b28d9183e7618fec0f0458331ab">exponent_</a> &gt; <a class="code hl_variable" href="classripple_1_1Number.html#a388d646cceab9673a0edb81206e1e106">maxExponent</a>)</div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> <span class="keywordflow">throw</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/error/overflow_error.html">std::overflow_error</a>(<span class="stringliteral">&quot;Number::normalize 2&quot;</span>);</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> </div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> <span class="keywordflow">if</span> (negative)</div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> <a class="code hl_variable" href="classripple_1_1Number.html#ae8914a365ad9ca852b2d8dbdd43abb6f">mantissa_</a> = -<a class="code hl_variable" href="classripple_1_1Number.html#ae8914a365ad9ca852b2d8dbdd43abb6f">mantissa_</a>;</div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span>}</div>
</div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> </div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span><a class="code hl_class" href="classripple_1_1Number.html">Number</a>&amp;</div>
<div class="foldopen" id="foldopen00230" data-start="{" data-end="}">
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"><a class="line" href="classripple_1_1Number.html#a13a7bc45654573fdb3857dae23e363fc"> 230</a></span><a class="code hl_function" href="classripple_1_1Number.html#a13a7bc45654573fdb3857dae23e363fc">Number::operator+=</a>(<a class="code hl_class" href="classripple_1_1Number.html">Number</a> <span class="keyword">const</span>&amp; y)</div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span>{</div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> <span class="keywordflow">if</span> (y == <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{})</div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> <span class="keywordflow">if</span> (*<span class="keyword">this</span> == <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{})</div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> {</div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> *<span class="keyword">this</span> = y;</div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> }</div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> <span class="keywordflow">if</span> (*<span class="keyword">this</span> == -y)</div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> {</div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> *<span class="keyword">this</span> = <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{};</div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> }</div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> XRPL_ASSERT(</div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> <a class="code hl_function" href="classripple_1_1Number.html#a014fb6ab35fb927939c085dccb43422d">isnormal</a>() &amp;&amp; y.<a class="code hl_function" href="classripple_1_1Number.html#a014fb6ab35fb927939c085dccb43422d">isnormal</a>(),</div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> <span class="stringliteral">&quot;ripple::Number::operator+=(Number) : is normal&quot;</span>);</div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> <span class="keyword">auto</span> xm = <a class="code hl_function" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a>();</div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> <span class="keyword">auto</span> xe = <a class="code hl_function" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>();</div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <span class="keywordtype">int</span> xn = 1;</div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> <span class="keywordflow">if</span> (xm &lt; 0)</div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> {</div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> xm = -xm;</div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> xn = -1;</div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> }</div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> <span class="keyword">auto</span> ym = y.<a class="code hl_function" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a>();</div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> <span class="keyword">auto</span> ye = y.<a class="code hl_function" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>();</div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> <span class="keywordtype">int</span> yn = 1;</div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> <span class="keywordflow">if</span> (ym &lt; 0)</div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> {</div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> ym = -ym;</div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> yn = -1;</div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> }</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> <a class="code hl_class" href="classripple_1_1Number_1_1Guard.html">Guard</a> g;</div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> <span class="keywordflow">if</span> (xe &lt; ye)</div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> {</div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> <span class="keywordflow">if</span> (xn == -1)</div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> g.<a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#a29e64e95a3e18476211420722180906c">set_negative</a>();</div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> <span class="keywordflow">do</span></div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> {</div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> g.<a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#a78ddead46cd4a5ce528d7d8f765e4ea1">push</a>(xm % 10);</div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> xm /= 10;</div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> ++xe;</div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> } <span class="keywordflow">while</span> (xe &lt; ye);</div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> }</div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (xe &gt; ye)</div>
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> {</div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> <span class="keywordflow">if</span> (yn == -1)</div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> g.<a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#a29e64e95a3e18476211420722180906c">set_negative</a>();</div>
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> <span class="keywordflow">do</span></div>
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> {</div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> g.<a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#a78ddead46cd4a5ce528d7d8f765e4ea1">push</a>(ym % 10);</div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> ym /= 10;</div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> ++ye;</div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> } <span class="keywordflow">while</span> (xe &gt; ye);</div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> }</div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> <span class="keywordflow">if</span> (xn == yn)</div>
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> {</div>
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> xm += ym;</div>
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> <span class="keywordflow">if</span> (xm &gt; <a class="code hl_variable" href="classripple_1_1Number.html#a18f3cb87112cf4436f8730a4f3333550">maxMantissa</a>)</div>
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> {</div>
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> g.<a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#a78ddead46cd4a5ce528d7d8f765e4ea1">push</a>(xm % 10);</div>
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> xm /= 10;</div>
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> ++xe;</div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> }</div>
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> <span class="keyword">auto</span> r = g.<a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#acf34c737037a6e8a5d04d33338a2ccde">round</a>();</div>
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> <span class="keywordflow">if</span> (r == 1 || (r == 0 &amp;&amp; (xm &amp; 1) == 1))</div>
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> {</div>
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> ++xm;</div>
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> <span class="keywordflow">if</span> (xm &gt; <a class="code hl_variable" href="classripple_1_1Number.html#a18f3cb87112cf4436f8730a4f3333550">maxMantissa</a>)</div>
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span> {</div>
<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span> xm /= 10;</div>
<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span> ++xe;</div>
<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span> }</div>
<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> }</div>
<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span> <span class="keywordflow">if</span> (xe &gt; <a class="code hl_variable" href="classripple_1_1Number.html#a388d646cceab9673a0edb81206e1e106">maxExponent</a>)</div>
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> <span class="keywordflow">throw</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/error/overflow_error.html">std::overflow_error</a>(<span class="stringliteral">&quot;Number::addition overflow&quot;</span>);</div>
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span> }</div>
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span> {</div>
<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span> <span class="keywordflow">if</span> (xm &gt; ym)</div>
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span> {</div>
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span> xm = xm - ym;</div>
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span> }</div>
<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span> {</div>
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span> xm = ym - xm;</div>
<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span> xe = ye;</div>
<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span> xn = yn;</div>
<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span> }</div>
<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span> <span class="keywordflow">while</span> (xm &lt; <a class="code hl_variable" href="classripple_1_1Number.html#a550732b6c726cffc8a742569fe76aa6e">minMantissa</a>)</div>
<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span> {</div>
<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span> xm *= 10;</div>
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span> xm -= g.<a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#a997cf381405becb9566b855185984471">pop</a>();</div>
<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span> --xe;</div>
<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span> }</div>
<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span> <span class="keyword">auto</span> r = g.<a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#acf34c737037a6e8a5d04d33338a2ccde">round</a>();</div>
<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"> 327</span> <span class="keywordflow">if</span> (r == 1 || (r == 0 &amp;&amp; (xm &amp; 1) == 1))</div>
<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span> {</div>
<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"> 329</span> --xm;</div>
<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"> 330</span> <span class="keywordflow">if</span> (xm &lt; <a class="code hl_variable" href="classripple_1_1Number.html#a550732b6c726cffc8a742569fe76aa6e">minMantissa</a>)</div>
<div class="line"><a id="l00331" name="l00331"></a><span class="lineno"> 331</span> {</div>
<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</span> xm *= 10;</div>
<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"> 333</span> --xe;</div>
<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"> 334</span> }</div>
<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span> }</div>
<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span> <span class="keywordflow">if</span> (xe &lt; <a class="code hl_variable" href="classripple_1_1Number.html#a72928c9b23a8c2b07024d2d3ff5eed73">minExponent</a>)</div>
<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span> {</div>
<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span> xm = 0;</div>
<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</span> xe = <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{}.<a class="code hl_variable" href="classripple_1_1Number.html#a62582b28d9183e7618fec0f0458331ab">exponent_</a>;</div>
<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span> }</div>
<div class="line"><a id="l00341" name="l00341"></a><span class="lineno"> 341</span> }</div>
<div class="line"><a id="l00342" name="l00342"></a><span class="lineno"> 342</span> <a class="code hl_variable" href="classripple_1_1Number.html#ae8914a365ad9ca852b2d8dbdd43abb6f">mantissa_</a> = xm * xn;</div>
<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span> <a class="code hl_variable" href="classripple_1_1Number.html#a62582b28d9183e7618fec0f0458331ab">exponent_</a> = xe;</div>
<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"> 344</span> <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a id="l00345" name="l00345"></a><span class="lineno"> 345</span>}</div>
</div>
<div class="line"><a id="l00346" name="l00346"></a><span class="lineno"> 346</span> </div>
<div class="line"><a id="l00347" name="l00347"></a><span class="lineno"> 347</span><span class="comment">// Optimization equivalent to:</span></div>
<div class="line"><a id="l00348" name="l00348"></a><span class="lineno"> 348</span><span class="comment">// auto r = static_cast&lt;unsigned&gt;(u % 10);</span></div>
<div class="line"><a id="l00349" name="l00349"></a><span class="lineno"> 349</span><span class="comment">// u /= 10;</span></div>
<div class="line"><a id="l00350" name="l00350"></a><span class="lineno"> 350</span><span class="comment">// return r;</span></div>
<div class="line"><a id="l00351" name="l00351"></a><span class="lineno"> 351</span><span class="comment">// Derived from Hacker&#39;s Delight Second Edition Chapter 10</span></div>
<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"> 352</span><span class="comment">// by Henry S. Warren, Jr.</span></div>
<div class="line"><a id="l00353" name="l00353"></a><span class="lineno"> 353</span><span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">unsigned</span></div>
<div class="foldopen" id="foldopen00354" data-start="{" data-end="}">
<div class="line"><a id="l00354" name="l00354"></a><span class="lineno"><a class="line" href="namespaceripple.html#a923b922c724a109a539486a3115eb83d"> 354</a></span><a class="code hl_function" href="namespaceripple.html#a923b922c724a109a539486a3115eb83d">divu10</a>(uint128_t&amp; u)</div>
<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"> 355</span>{</div>
<div class="line"><a id="l00356" name="l00356"></a><span class="lineno"> 356</span> <span class="comment">// q = u * 0.75</span></div>
<div class="line"><a id="l00357" name="l00357"></a><span class="lineno"> 357</span> <span class="keyword">auto</span> q = (u &gt;&gt; 1) + (u &gt;&gt; 2);</div>
<div class="line"><a id="l00358" name="l00358"></a><span class="lineno"> 358</span> <span class="comment">// iterate towards q = u * 0.8</span></div>
<div class="line"><a id="l00359" name="l00359"></a><span class="lineno"> 359</span> q += q &gt;&gt; 4;</div>
<div class="line"><a id="l00360" name="l00360"></a><span class="lineno"> 360</span> q += q &gt;&gt; 8;</div>
<div class="line"><a id="l00361" name="l00361"></a><span class="lineno"> 361</span> q += q &gt;&gt; 16;</div>
<div class="line"><a id="l00362" name="l00362"></a><span class="lineno"> 362</span> q += q &gt;&gt; 32;</div>
<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"> 363</span> q += q &gt;&gt; 64;</div>
<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"> 364</span> <span class="comment">// q /= 8 approximately == u / 10</span></div>
<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span> q &gt;&gt;= 3;</div>
<div class="line"><a id="l00366" name="l00366"></a><span class="lineno"> 366</span> <span class="comment">// r = u - q * 10 approximately == u % 10</span></div>
<div class="line"><a id="l00367" name="l00367"></a><span class="lineno"> 367</span> <span class="keyword">auto</span> r = <span class="keyword">static_cast&lt;</span><span class="keywordtype">unsigned</span><span class="keyword">&gt;</span>(u - ((q &lt;&lt; 3) + (q &lt;&lt; 1)));</div>
<div class="line"><a id="l00368" name="l00368"></a><span class="lineno"> 368</span> <span class="comment">// correction c is 1 if r &gt;= 10 else 0</span></div>
<div class="line"><a id="l00369" name="l00369"></a><span class="lineno"> 369</span> <span class="keyword">auto</span> c = (r + 6) &gt;&gt; 4;</div>
<div class="line"><a id="l00370" name="l00370"></a><span class="lineno"> 370</span> u = q + c;</div>
<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span> r -= c * 10;</div>
<div class="line"><a id="l00372" name="l00372"></a><span class="lineno"> 372</span> <span class="keywordflow">return</span> r;</div>
<div class="line"><a id="l00373" name="l00373"></a><span class="lineno"> 373</span>}</div>
</div>
<div class="line"><a id="l00374" name="l00374"></a><span class="lineno"> 374</span> </div>
<div class="line"><a id="l00375" name="l00375"></a><span class="lineno"> 375</span><a class="code hl_function" href="classripple_1_1Number.html#ac796fb449f3e3573c8d923bd3a905599">Number</a>&amp;</div>
<div class="foldopen" id="foldopen00376" data-start="{" data-end="}">
<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"><a class="line" href="classripple_1_1Number.html#a6c5e4fb40d9530e2403c7d52075c304c"> 376</a></span><a class="code hl_function" href="classripple_1_1Number.html#a6c5e4fb40d9530e2403c7d52075c304c">Number::operator*=</a>(<a class="code hl_class" href="classripple_1_1Number.html">Number</a> <span class="keyword">const</span>&amp; y)</div>
<div class="line"><a id="l00377" name="l00377"></a><span class="lineno"> 377</span>{</div>
<div class="line"><a id="l00378" name="l00378"></a><span class="lineno"> 378</span> <span class="keywordflow">if</span> (*<span class="keyword">this</span> == <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{})</div>
<div class="line"><a id="l00379" name="l00379"></a><span class="lineno"> 379</span> <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a id="l00380" name="l00380"></a><span class="lineno"> 380</span> <span class="keywordflow">if</span> (y == <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{})</div>
<div class="line"><a id="l00381" name="l00381"></a><span class="lineno"> 381</span> {</div>
<div class="line"><a id="l00382" name="l00382"></a><span class="lineno"> 382</span> *<span class="keyword">this</span> = y;</div>
<div class="line"><a id="l00383" name="l00383"></a><span class="lineno"> 383</span> <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a id="l00384" name="l00384"></a><span class="lineno"> 384</span> }</div>
<div class="line"><a id="l00385" name="l00385"></a><span class="lineno"> 385</span> XRPL_ASSERT(</div>
<div class="line"><a id="l00386" name="l00386"></a><span class="lineno"> 386</span> <a class="code hl_function" href="classripple_1_1Number.html#a014fb6ab35fb927939c085dccb43422d">isnormal</a>() &amp;&amp; y.<a class="code hl_function" href="classripple_1_1Number.html#a014fb6ab35fb927939c085dccb43422d">isnormal</a>(),</div>
<div class="line"><a id="l00387" name="l00387"></a><span class="lineno"> 387</span> <span class="stringliteral">&quot;ripple::Number::operator*=(Number) : is normal&quot;</span>);</div>
<div class="line"><a id="l00388" name="l00388"></a><span class="lineno"> 388</span> <span class="keyword">auto</span> xm = <a class="code hl_function" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a>();</div>
<div class="line"><a id="l00389" name="l00389"></a><span class="lineno"> 389</span> <span class="keyword">auto</span> xe = <a class="code hl_function" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>();</div>
<div class="line"><a id="l00390" name="l00390"></a><span class="lineno"> 390</span> <span class="keywordtype">int</span> xn = 1;</div>
<div class="line"><a id="l00391" name="l00391"></a><span class="lineno"> 391</span> <span class="keywordflow">if</span> (xm &lt; 0)</div>
<div class="line"><a id="l00392" name="l00392"></a><span class="lineno"> 392</span> {</div>
<div class="line"><a id="l00393" name="l00393"></a><span class="lineno"> 393</span> xm = -xm;</div>
<div class="line"><a id="l00394" name="l00394"></a><span class="lineno"> 394</span> xn = -1;</div>
<div class="line"><a id="l00395" name="l00395"></a><span class="lineno"> 395</span> }</div>
<div class="line"><a id="l00396" name="l00396"></a><span class="lineno"> 396</span> <span class="keyword">auto</span> ym = y.<a class="code hl_function" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a>();</div>
<div class="line"><a id="l00397" name="l00397"></a><span class="lineno"> 397</span> <span class="keyword">auto</span> ye = y.<a class="code hl_function" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>();</div>
<div class="line"><a id="l00398" name="l00398"></a><span class="lineno"> 398</span> <span class="keywordtype">int</span> yn = 1;</div>
<div class="line"><a id="l00399" name="l00399"></a><span class="lineno"> 399</span> <span class="keywordflow">if</span> (ym &lt; 0)</div>
<div class="line"><a id="l00400" name="l00400"></a><span class="lineno"> 400</span> {</div>
<div class="line"><a id="l00401" name="l00401"></a><span class="lineno"> 401</span> ym = -ym;</div>
<div class="line"><a id="l00402" name="l00402"></a><span class="lineno"> 402</span> yn = -1;</div>
<div class="line"><a id="l00403" name="l00403"></a><span class="lineno"> 403</span> }</div>
<div class="line"><a id="l00404" name="l00404"></a><span class="lineno"> 404</span> <span class="keyword">auto</span> zm = uint128_t(xm) * uint128_t(ym);</div>
<div class="line"><a id="l00405" name="l00405"></a><span class="lineno"> 405</span> <span class="keyword">auto</span> ze = xe + ye;</div>
<div class="line"><a id="l00406" name="l00406"></a><span class="lineno"> 406</span> <span class="keyword">auto</span> zn = xn * yn;</div>
<div class="line"><a id="l00407" name="l00407"></a><span class="lineno"> 407</span> <a class="code hl_class" href="classripple_1_1Number_1_1Guard.html">Guard</a> g;</div>
<div class="line"><a id="l00408" name="l00408"></a><span class="lineno"> 408</span> <span class="keywordflow">if</span> (zn == -1)</div>
<div class="line"><a id="l00409" name="l00409"></a><span class="lineno"> 409</span> g.<a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#a29e64e95a3e18476211420722180906c">set_negative</a>();</div>
<div class="line"><a id="l00410" name="l00410"></a><span class="lineno"> 410</span> <span class="keywordflow">while</span> (zm &gt; <a class="code hl_variable" href="classripple_1_1Number.html#a18f3cb87112cf4436f8730a4f3333550">maxMantissa</a>)</div>
<div class="line"><a id="l00411" name="l00411"></a><span class="lineno"> 411</span> {</div>
<div class="line"><a id="l00412" name="l00412"></a><span class="lineno"> 412</span> <span class="comment">// The following is optimization for:</span></div>
<div class="line"><a id="l00413" name="l00413"></a><span class="lineno"> 413</span> <span class="comment">// g.push(static_cast&lt;unsigned&gt;(zm % 10));</span></div>
<div class="line"><a id="l00414" name="l00414"></a><span class="lineno"> 414</span> <span class="comment">// zm /= 10;</span></div>
<div class="line"><a id="l00415" name="l00415"></a><span class="lineno"> 415</span> g.<a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#a78ddead46cd4a5ce528d7d8f765e4ea1">push</a>(<a class="code hl_function" href="namespaceripple.html#a923b922c724a109a539486a3115eb83d">divu10</a>(zm));</div>
<div class="line"><a id="l00416" name="l00416"></a><span class="lineno"> 416</span> ++ze;</div>
<div class="line"><a id="l00417" name="l00417"></a><span class="lineno"> 417</span> }</div>
<div class="line"><a id="l00418" name="l00418"></a><span class="lineno"> 418</span> xm = <span class="keyword">static_cast&lt;</span><a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/types/integer.html">rep</a><span class="keyword">&gt;</span>(zm);</div>
<div class="line"><a id="l00419" name="l00419"></a><span class="lineno"> 419</span> xe = ze;</div>
<div class="line"><a id="l00420" name="l00420"></a><span class="lineno"> 420</span> <span class="keyword">auto</span> r = g.<a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#acf34c737037a6e8a5d04d33338a2ccde">round</a>();</div>
<div class="line"><a id="l00421" name="l00421"></a><span class="lineno"> 421</span> <span class="keywordflow">if</span> (r == 1 || (r == 0 &amp;&amp; (xm &amp; 1) == 1))</div>
<div class="line"><a id="l00422" name="l00422"></a><span class="lineno"> 422</span> {</div>
<div class="line"><a id="l00423" name="l00423"></a><span class="lineno"> 423</span> ++xm;</div>
<div class="line"><a id="l00424" name="l00424"></a><span class="lineno"> 424</span> <span class="keywordflow">if</span> (xm &gt; <a class="code hl_variable" href="classripple_1_1Number.html#a18f3cb87112cf4436f8730a4f3333550">maxMantissa</a>)</div>
<div class="line"><a id="l00425" name="l00425"></a><span class="lineno"> 425</span> {</div>
<div class="line"><a id="l00426" name="l00426"></a><span class="lineno"> 426</span> xm /= 10;</div>
<div class="line"><a id="l00427" name="l00427"></a><span class="lineno"> 427</span> ++xe;</div>
<div class="line"><a id="l00428" name="l00428"></a><span class="lineno"> 428</span> }</div>
<div class="line"><a id="l00429" name="l00429"></a><span class="lineno"> 429</span> }</div>
<div class="line"><a id="l00430" name="l00430"></a><span class="lineno"> 430</span> <span class="keywordflow">if</span> (xe &lt; <a class="code hl_variable" href="classripple_1_1Number.html#a72928c9b23a8c2b07024d2d3ff5eed73">minExponent</a>)</div>
<div class="line"><a id="l00431" name="l00431"></a><span class="lineno"> 431</span> {</div>
<div class="line"><a id="l00432" name="l00432"></a><span class="lineno"> 432</span> xm = 0;</div>
<div class="line"><a id="l00433" name="l00433"></a><span class="lineno"> 433</span> xe = <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{}.<a class="code hl_variable" href="classripple_1_1Number.html#a62582b28d9183e7618fec0f0458331ab">exponent_</a>;</div>
<div class="line"><a id="l00434" name="l00434"></a><span class="lineno"> 434</span> }</div>
<div class="line"><a id="l00435" name="l00435"></a><span class="lineno"> 435</span> <span class="keywordflow">if</span> (xe &gt; <a class="code hl_variable" href="classripple_1_1Number.html#a388d646cceab9673a0edb81206e1e106">maxExponent</a>)</div>
<div class="line"><a id="l00436" name="l00436"></a><span class="lineno"> 436</span> <span class="keywordflow">throw</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/error/overflow_error.html">std::overflow_error</a>(</div>
<div class="line"><a id="l00437" name="l00437"></a><span class="lineno"> 437</span> <span class="stringliteral">&quot;Number::multiplication overflow : exponent is &quot;</span> +</div>
<div class="line"><a id="l00438" name="l00438"></a><span class="lineno"> 438</span> <a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/string/basic_string/to_string.html">std::to_string</a>(xe));</div>
<div class="line"><a id="l00439" name="l00439"></a><span class="lineno"> 439</span> <a class="code hl_variable" href="classripple_1_1Number.html#ae8914a365ad9ca852b2d8dbdd43abb6f">mantissa_</a> = xm * zn;</div>
<div class="line"><a id="l00440" name="l00440"></a><span class="lineno"> 440</span> <a class="code hl_variable" href="classripple_1_1Number.html#a62582b28d9183e7618fec0f0458331ab">exponent_</a> = xe;</div>
<div class="line"><a id="l00441" name="l00441"></a><span class="lineno"> 441</span> XRPL_ASSERT(</div>
<div class="line"><a id="l00442" name="l00442"></a><span class="lineno"> 442</span> <a class="code hl_function" href="classripple_1_1Number.html#a014fb6ab35fb927939c085dccb43422d">isnormal</a>() || *<span class="keyword">this</span> == <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{},</div>
<div class="line"><a id="l00443" name="l00443"></a><span class="lineno"> 443</span> <span class="stringliteral">&quot;ripple::Number::operator*=(Number) : result is normal&quot;</span>);</div>
<div class="line"><a id="l00444" name="l00444"></a><span class="lineno"> 444</span> <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a id="l00445" name="l00445"></a><span class="lineno"> 445</span>}</div>
</div>
<div class="line"><a id="l00446" name="l00446"></a><span class="lineno"> 446</span> </div>
<div class="line"><a id="l00447" name="l00447"></a><span class="lineno"> 447</span><a class="code hl_class" href="classripple_1_1Number.html">Number</a>&amp;</div>
<div class="foldopen" id="foldopen00448" data-start="{" data-end="}">
<div class="line"><a id="l00448" name="l00448"></a><span class="lineno"><a class="line" href="classripple_1_1Number.html#a3ae0d48f1d706dbff8b184716fa313fd"> 448</a></span><a class="code hl_function" href="classripple_1_1Number.html#a3ae0d48f1d706dbff8b184716fa313fd">Number::operator/=</a>(<a class="code hl_class" href="classripple_1_1Number.html">Number</a> <span class="keyword">const</span>&amp; y)</div>
<div class="line"><a id="l00449" name="l00449"></a><span class="lineno"> 449</span>{</div>
<div class="line"><a id="l00450" name="l00450"></a><span class="lineno"> 450</span> <span class="keywordflow">if</span> (y == <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{})</div>
<div class="line"><a id="l00451" name="l00451"></a><span class="lineno"> 451</span> <span class="keywordflow">throw</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/error/overflow_error.html">std::overflow_error</a>(<span class="stringliteral">&quot;Number: divide by 0&quot;</span>);</div>
<div class="line"><a id="l00452" name="l00452"></a><span class="lineno"> 452</span> <span class="keywordflow">if</span> (*<span class="keyword">this</span> == <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{})</div>
<div class="line"><a id="l00453" name="l00453"></a><span class="lineno"> 453</span> <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a id="l00454" name="l00454"></a><span class="lineno"> 454</span> <span class="keywordtype">int</span> np = 1;</div>
<div class="line"><a id="l00455" name="l00455"></a><span class="lineno"> 455</span> <span class="keyword">auto</span> nm = <a class="code hl_function" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a>();</div>
<div class="line"><a id="l00456" name="l00456"></a><span class="lineno"> 456</span> <span class="keyword">auto</span> ne = <a class="code hl_function" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>();</div>
<div class="line"><a id="l00457" name="l00457"></a><span class="lineno"> 457</span> <span class="keywordflow">if</span> (nm &lt; 0)</div>
<div class="line"><a id="l00458" name="l00458"></a><span class="lineno"> 458</span> {</div>
<div class="line"><a id="l00459" name="l00459"></a><span class="lineno"> 459</span> nm = -nm;</div>
<div class="line"><a id="l00460" name="l00460"></a><span class="lineno"> 460</span> np = -1;</div>
<div class="line"><a id="l00461" name="l00461"></a><span class="lineno"> 461</span> }</div>
<div class="line"><a id="l00462" name="l00462"></a><span class="lineno"> 462</span> <span class="keywordtype">int</span> dp = 1;</div>
<div class="line"><a id="l00463" name="l00463"></a><span class="lineno"> 463</span> <span class="keyword">auto</span> dm = y.<a class="code hl_function" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a>();</div>
<div class="line"><a id="l00464" name="l00464"></a><span class="lineno"> 464</span> <span class="keyword">auto</span> de = y.<a class="code hl_function" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>();</div>
<div class="line"><a id="l00465" name="l00465"></a><span class="lineno"> 465</span> <span class="keywordflow">if</span> (dm &lt; 0)</div>
<div class="line"><a id="l00466" name="l00466"></a><span class="lineno"> 466</span> {</div>
<div class="line"><a id="l00467" name="l00467"></a><span class="lineno"> 467</span> dm = -dm;</div>
<div class="line"><a id="l00468" name="l00468"></a><span class="lineno"> 468</span> dp = -1;</div>
<div class="line"><a id="l00469" name="l00469"></a><span class="lineno"> 469</span> }</div>
<div class="line"><a id="l00470" name="l00470"></a><span class="lineno"> 470</span> <span class="comment">// Shift by 10^17 gives greatest precision while not overflowing uint128_t</span></div>
<div class="line"><a id="l00471" name="l00471"></a><span class="lineno"> 471</span> <span class="comment">// or the cast back to int64_t</span></div>
<div class="line"><a id="l00472" name="l00472"></a><span class="lineno"> 472</span> uint128_t <span class="keyword">const</span> f = 100&#39;000&#39;000&#39;000&#39;000&#39;000;</div>
<div class="line"><a id="l00473" name="l00473"></a><span class="lineno"> 473</span> <a class="code hl_variable" href="classripple_1_1Number.html#ae8914a365ad9ca852b2d8dbdd43abb6f">mantissa_</a> = <span class="keyword">static_cast&lt;</span><a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/types/integer.html">std::int64_t</a><span class="keyword">&gt;</span>(uint128_t(nm) * f / uint128_t(dm));</div>
<div class="line"><a id="l00474" name="l00474"></a><span class="lineno"> 474</span> <a class="code hl_variable" href="classripple_1_1Number.html#a62582b28d9183e7618fec0f0458331ab">exponent_</a> = ne - de - 17;</div>
<div class="line"><a id="l00475" name="l00475"></a><span class="lineno"> 475</span> <a class="code hl_variable" href="classripple_1_1Number.html#ae8914a365ad9ca852b2d8dbdd43abb6f">mantissa_</a> *= np * dp;</div>
<div class="line"><a id="l00476" name="l00476"></a><span class="lineno"> 476</span> <a class="code hl_function" href="classripple_1_1Number.html#a5fefb45b369635e7803f4f8d3f9b9dd4">normalize</a>();</div>
<div class="line"><a id="l00477" name="l00477"></a><span class="lineno"> 477</span> <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a id="l00478" name="l00478"></a><span class="lineno"> 478</span>}</div>
</div>
<div class="line"><a id="l00479" name="l00479"></a><span class="lineno"> 479</span> </div>
<div class="foldopen" id="foldopen00480" data-start="{" data-end="}">
<div class="line"><a id="l00480" name="l00480"></a><span class="lineno"><a class="line" href="classripple_1_1Number.html#a8fa9f27fcce51b0e568cbe0804163e28"> 480</a></span>Number::operator <a class="code hl_typedef" href="classripple_1_1Number.html#a8d2697ce4073b76f05e0480a9b454a66">rep</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00481" name="l00481"></a><span class="lineno"> 481</span><span class="keyword"></span>{</div>
<div class="line"><a id="l00482" name="l00482"></a><span class="lineno"> 482</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/types/integer.html">rep</a> drops = <a class="code hl_variable" href="classripple_1_1Number.html#ae8914a365ad9ca852b2d8dbdd43abb6f">mantissa_</a>;</div>
<div class="line"><a id="l00483" name="l00483"></a><span class="lineno"> 483</span> <span class="keywordtype">int</span> offset = <a class="code hl_variable" href="classripple_1_1Number.html#a62582b28d9183e7618fec0f0458331ab">exponent_</a>;</div>
<div class="line"><a id="l00484" name="l00484"></a><span class="lineno"> 484</span> <a class="code hl_class" href="classripple_1_1Number_1_1Guard.html">Guard</a> g;</div>
<div class="line"><a id="l00485" name="l00485"></a><span class="lineno"> 485</span> <span class="keywordflow">if</span> (drops != 0)</div>
<div class="line"><a id="l00486" name="l00486"></a><span class="lineno"> 486</span> {</div>
<div class="line"><a id="l00487" name="l00487"></a><span class="lineno"> 487</span> <span class="keywordflow">if</span> (drops &lt; 0)</div>
<div class="line"><a id="l00488" name="l00488"></a><span class="lineno"> 488</span> {</div>
<div class="line"><a id="l00489" name="l00489"></a><span class="lineno"> 489</span> g.<a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#a29e64e95a3e18476211420722180906c">set_negative</a>();</div>
<div class="line"><a id="l00490" name="l00490"></a><span class="lineno"> 490</span> drops = -drops;</div>
<div class="line"><a id="l00491" name="l00491"></a><span class="lineno"> 491</span> }</div>
<div class="line"><a id="l00492" name="l00492"></a><span class="lineno"> 492</span> <span class="keywordflow">for</span> (; offset &lt; 0; ++offset)</div>
<div class="line"><a id="l00493" name="l00493"></a><span class="lineno"> 493</span> {</div>
<div class="line"><a id="l00494" name="l00494"></a><span class="lineno"> 494</span> g.<a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#a78ddead46cd4a5ce528d7d8f765e4ea1">push</a>(drops % 10);</div>
<div class="line"><a id="l00495" name="l00495"></a><span class="lineno"> 495</span> drops /= 10;</div>
<div class="line"><a id="l00496" name="l00496"></a><span class="lineno"> 496</span> }</div>
<div class="line"><a id="l00497" name="l00497"></a><span class="lineno"> 497</span> <span class="keywordflow">for</span> (; offset &gt; 0; --offset)</div>
<div class="line"><a id="l00498" name="l00498"></a><span class="lineno"> 498</span> {</div>
<div class="line"><a id="l00499" name="l00499"></a><span class="lineno"> 499</span> <span class="keywordflow">if</span> (drops &gt; <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/types/numeric_limits.html">std::numeric_limits</a>&lt;<span class="keyword">decltype</span>(drops)&gt;<a class="code hl_function" href="classripple_1_1Number.html#a6223254bb40f9a21dbdd8b360faaf401">::max</a>() / 10)</div>
<div class="line"><a id="l00500" name="l00500"></a><span class="lineno"> 500</span> <span class="keywordflow">throw</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/error/overflow_error.html">std::overflow_error</a>(<span class="stringliteral">&quot;Number::operator rep() overflow&quot;</span>);</div>
<div class="line"><a id="l00501" name="l00501"></a><span class="lineno"> 501</span> drops *= 10;</div>
<div class="line"><a id="l00502" name="l00502"></a><span class="lineno"> 502</span> }</div>
<div class="line"><a id="l00503" name="l00503"></a><span class="lineno"> 503</span> <span class="keyword">auto</span> r = g.<a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#acf34c737037a6e8a5d04d33338a2ccde">round</a>();</div>
<div class="line"><a id="l00504" name="l00504"></a><span class="lineno"> 504</span> <span class="keywordflow">if</span> (r == 1 || (r == 0 &amp;&amp; (drops &amp; 1) == 1))</div>
<div class="line"><a id="l00505" name="l00505"></a><span class="lineno"> 505</span> {</div>
<div class="line"><a id="l00506" name="l00506"></a><span class="lineno"> 506</span> ++drops;</div>
<div class="line"><a id="l00507" name="l00507"></a><span class="lineno"> 507</span> }</div>
<div class="line"><a id="l00508" name="l00508"></a><span class="lineno"> 508</span> <span class="keywordflow">if</span> (g.<a class="code hl_function" href="classripple_1_1Number_1_1Guard.html#ab190e6f6405f271600b2f99ff15a6bc2">is_negative</a>())</div>
<div class="line"><a id="l00509" name="l00509"></a><span class="lineno"> 509</span> drops = -drops;</div>
<div class="line"><a id="l00510" name="l00510"></a><span class="lineno"> 510</span> }</div>
<div class="line"><a id="l00511" name="l00511"></a><span class="lineno"> 511</span> <span class="keywordflow">return</span> drops;</div>
<div class="line"><a id="l00512" name="l00512"></a><span class="lineno"> 512</span>}</div>
</div>
<div class="line"><a id="l00513" name="l00513"></a><span class="lineno"> 513</span> </div>
<div class="line"><a id="l00514" name="l00514"></a><span class="lineno"> 514</span><a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div>
<div class="foldopen" id="foldopen00515" data-start="{" data-end="}">
<div class="line"><a id="l00515" name="l00515"></a><span class="lineno"><a class="line" href="namespaceripple.html#a5bf7ceb7c5d4c12b5137def1455f0bdc"> 515</a></span><a class="code hl_function" href="namespaceripple.html#ac124fe6744b7fe887dec949b56b16d50">to_string</a>(<a class="code hl_class" href="classripple_1_1Number.html">Number</a> <span class="keyword">const</span>&amp; amount)</div>
<div class="line"><a id="l00516" name="l00516"></a><span class="lineno"> 516</span>{</div>
<div class="line"><a id="l00517" name="l00517"></a><span class="lineno"> 517</span> <span class="comment">// keep full internal accuracy, but make more human friendly if possible</span></div>
<div class="line"><a id="l00518" name="l00518"></a><span class="lineno"> 518</span> <span class="keywordflow">if</span> (amount == <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{})</div>
<div class="line"><a id="l00519" name="l00519"></a><span class="lineno"> 519</span> <span class="keywordflow">return</span> <span class="stringliteral">&quot;0&quot;</span>;</div>
<div class="line"><a id="l00520" name="l00520"></a><span class="lineno"> 520</span> </div>
<div class="line"><a id="l00521" name="l00521"></a><span class="lineno"> 521</span> <span class="keyword">auto</span> <span class="keyword">const</span> <a class="code hl_function" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a> = amount.<a class="code hl_function" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>();</div>
<div class="line"><a id="l00522" name="l00522"></a><span class="lineno"> 522</span> <span class="keyword">auto</span> <a class="code hl_function" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a> = amount.<a class="code hl_function" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a>();</div>
<div class="line"><a id="l00523" name="l00523"></a><span class="lineno"> 523</span> </div>
<div class="line"><a id="l00524" name="l00524"></a><span class="lineno"> 524</span> <span class="comment">// Use scientific notation for exponents that are too small or too large</span></div>
<div class="line"><a id="l00525" name="l00525"></a><span class="lineno"> 525</span> <span class="keywordflow">if</span> (((<a class="code hl_function" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a> != 0) &amp;&amp; ((<a class="code hl_function" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a> &lt; -25) || (<a class="code hl_function" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a> &gt; -5))))</div>
<div class="line"><a id="l00526" name="l00526"></a><span class="lineno"> 526</span> {</div>
<div class="line"><a id="l00527" name="l00527"></a><span class="lineno"> 527</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> ret = <a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/string/basic_string/to_string.html">std::to_string</a>(<a class="code hl_function" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a>);</div>
<div class="line"><a id="l00528" name="l00528"></a><span class="lineno"> 528</span> ret.<a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/string/basic_string/append.html">append</a>(1, <span class="charliteral">&#39;e&#39;</span>);</div>
<div class="line"><a id="l00529" name="l00529"></a><span class="lineno"> 529</span> ret.<a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/string/basic_string/append.html">append</a>(<a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/string/basic_string/to_string.html">std::to_string</a>(<a class="code hl_function" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>));</div>
<div class="line"><a id="l00530" name="l00530"></a><span class="lineno"> 530</span> <span class="keywordflow">return</span> ret;</div>
<div class="line"><a id="l00531" name="l00531"></a><span class="lineno"> 531</span> }</div>
<div class="line"><a id="l00532" name="l00532"></a><span class="lineno"> 532</span> </div>
<div class="line"><a id="l00533" name="l00533"></a><span class="lineno"> 533</span> <span class="keywordtype">bool</span> negative = <span class="keyword">false</span>;</div>
<div class="line"><a id="l00534" name="l00534"></a><span class="lineno"> 534</span> </div>
<div class="line"><a id="l00535" name="l00535"></a><span class="lineno"> 535</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a> &lt; 0)</div>
<div class="line"><a id="l00536" name="l00536"></a><span class="lineno"> 536</span> {</div>
<div class="line"><a id="l00537" name="l00537"></a><span class="lineno"> 537</span> <a class="code hl_function" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a> = -<a class="code hl_function" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a>;</div>
<div class="line"><a id="l00538" name="l00538"></a><span class="lineno"> 538</span> negative = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00539" name="l00539"></a><span class="lineno"> 539</span> }</div>
<div class="line"><a id="l00540" name="l00540"></a><span class="lineno"> 540</span> </div>
<div class="line"><a id="l00541" name="l00541"></a><span class="lineno"> 541</span> XRPL_ASSERT(</div>
<div class="line"><a id="l00542" name="l00542"></a><span class="lineno"> 542</span> <a class="code hl_function" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a> + 43 &gt; 0, <span class="stringliteral">&quot;ripple::to_string(Number) : minimum exponent&quot;</span>);</div>
<div class="line"><a id="l00543" name="l00543"></a><span class="lineno"> 543</span> </div>
<div class="line"><a id="l00544" name="l00544"></a><span class="lineno"> 544</span> ptrdiff_t <span class="keyword">const</span> pad_prefix = 27;</div>
<div class="line"><a id="l00545" name="l00545"></a><span class="lineno"> 545</span> ptrdiff_t <span class="keyword">const</span> pad_suffix = 23;</div>
<div class="line"><a id="l00546" name="l00546"></a><span class="lineno"> 546</span> </div>
<div class="line"><a id="l00547" name="l00547"></a><span class="lineno"> 547</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> <span class="keyword">const</span> raw_value(<a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/string/basic_string/to_string.html">std::to_string</a>(<a class="code hl_function" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a>));</div>
<div class="line"><a id="l00548" name="l00548"></a><span class="lineno"> 548</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> val;</div>
<div class="line"><a id="l00549" name="l00549"></a><span class="lineno"> 549</span> </div>
<div class="line"><a id="l00550" name="l00550"></a><span class="lineno"> 550</span> val.<a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/string/basic_string/reserve.html">reserve</a>(raw_value.<a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">length</a>() + pad_prefix + pad_suffix);</div>
<div class="line"><a id="l00551" name="l00551"></a><span class="lineno"> 551</span> val.<a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/string/basic_string/append.html">append</a>(pad_prefix, <span class="charliteral">&#39;0&#39;</span>);</div>
<div class="line"><a id="l00552" name="l00552"></a><span class="lineno"> 552</span> val.<a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/string/basic_string/append.html">append</a>(raw_value);</div>
<div class="line"><a id="l00553" name="l00553"></a><span class="lineno"> 553</span> val.<a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/string/basic_string/append.html">append</a>(pad_suffix, <span class="charliteral">&#39;0&#39;</span>);</div>
<div class="line"><a id="l00554" name="l00554"></a><span class="lineno"> 554</span> </div>
<div class="line"><a id="l00555" name="l00555"></a><span class="lineno"> 555</span> ptrdiff_t <span class="keyword">const</span> offset(<a class="code hl_function" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a> + 43);</div>
<div class="line"><a id="l00556" name="l00556"></a><span class="lineno"> 556</span> </div>
<div class="line"><a id="l00557" name="l00557"></a><span class="lineno"> 557</span> <span class="keyword">auto</span> pre_from(val.<a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/string/basic_string/begin.html">begin</a>());</div>
<div class="line"><a id="l00558" name="l00558"></a><span class="lineno"> 558</span> <span class="keyword">auto</span> <span class="keyword">const</span> pre_to(val.<a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/string/basic_string/begin.html">begin</a>() + offset);</div>
<div class="line"><a id="l00559" name="l00559"></a><span class="lineno"> 559</span> </div>
<div class="line"><a id="l00560" name="l00560"></a><span class="lineno"> 560</span> <span class="keyword">auto</span> <span class="keyword">const</span> post_from(val.<a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/string/basic_string/begin.html">begin</a>() + offset);</div>
<div class="line"><a id="l00561" name="l00561"></a><span class="lineno"> 561</span> <span class="keyword">auto</span> post_to(val.<a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/string/basic_string/end.html">end</a>());</div>
<div class="line"><a id="l00562" name="l00562"></a><span class="lineno"> 562</span> </div>
<div class="line"><a id="l00563" name="l00563"></a><span class="lineno"> 563</span> <span class="comment">// Crop leading zeroes. Take advantage of the fact that there&#39;s always a</span></div>
<div class="line"><a id="l00564" name="l00564"></a><span class="lineno"> 564</span> <span class="comment">// fixed amount of leading zeroes and skip them.</span></div>
<div class="line"><a id="l00565" name="l00565"></a><span class="lineno"> 565</span> <span class="keywordflow">if</span> (<a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/iterator/distance.html">std::distance</a>(pre_from, pre_to) &gt; pad_prefix)</div>
<div class="line"><a id="l00566" name="l00566"></a><span class="lineno"> 566</span> pre_from += pad_prefix;</div>
<div class="line"><a id="l00567" name="l00567"></a><span class="lineno"> 567</span> </div>
<div class="line"><a id="l00568" name="l00568"></a><span class="lineno"> 568</span> XRPL_ASSERT(</div>
<div class="line"><a id="l00569" name="l00569"></a><span class="lineno"> 569</span> post_to &gt;= post_from,</div>
<div class="line"><a id="l00570" name="l00570"></a><span class="lineno"> 570</span> <span class="stringliteral">&quot;ripple::to_string(Number) : first distance check&quot;</span>);</div>
<div class="line"><a id="l00571" name="l00571"></a><span class="lineno"> 571</span> </div>
<div class="line"><a id="l00572" name="l00572"></a><span class="lineno"> 572</span> pre_from = <a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/algorithm/find.html">std::find_if</a>(pre_from, pre_to, [](<span class="keywordtype">char</span> c) { <span class="keywordflow">return</span> c != <span class="charliteral">&#39;0&#39;</span>; });</div>
<div class="line"><a id="l00573" name="l00573"></a><span class="lineno"> 573</span> </div>
<div class="line"><a id="l00574" name="l00574"></a><span class="lineno"> 574</span> <span class="comment">// Crop trailing zeroes. Take advantage of the fact that there&#39;s always a</span></div>
<div class="line"><a id="l00575" name="l00575"></a><span class="lineno"> 575</span> <span class="comment">// fixed amount of trailing zeroes and skip them.</span></div>
<div class="line"><a id="l00576" name="l00576"></a><span class="lineno"> 576</span> <span class="keywordflow">if</span> (<a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/iterator/distance.html">std::distance</a>(post_from, post_to) &gt; pad_suffix)</div>
<div class="line"><a id="l00577" name="l00577"></a><span class="lineno"> 577</span> post_to -= pad_suffix;</div>
<div class="line"><a id="l00578" name="l00578"></a><span class="lineno"> 578</span> </div>
<div class="line"><a id="l00579" name="l00579"></a><span class="lineno"> 579</span> XRPL_ASSERT(</div>
<div class="line"><a id="l00580" name="l00580"></a><span class="lineno"> 580</span> post_to &gt;= post_from,</div>
<div class="line"><a id="l00581" name="l00581"></a><span class="lineno"> 581</span> <span class="stringliteral">&quot;ripple::to_string(Number) : second distance check&quot;</span>);</div>
<div class="line"><a id="l00582" name="l00582"></a><span class="lineno"> 582</span> </div>
<div class="line"><a id="l00583" name="l00583"></a><span class="lineno"> 583</span> post_to = <a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/algorithm/find.html">std::find_if</a>(</div>
<div class="line"><a id="l00584" name="l00584"></a><span class="lineno"> 584</span> <a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/iterator/make_reverse_iterator.html">std::make_reverse_iterator</a>(post_to),</div>
<div class="line"><a id="l00585" name="l00585"></a><span class="lineno"> 585</span> <a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/iterator/make_reverse_iterator.html">std::make_reverse_iterator</a>(post_from),</div>
<div class="line"><a id="l00586" name="l00586"></a><span class="lineno"> 586</span> [](<span class="keywordtype">char</span> c) { <span class="keywordflow">return</span> c != <span class="charliteral">&#39;0&#39;</span>; })</div>
<div class="line"><a id="l00587" name="l00587"></a><span class="lineno"> 587</span> .base();</div>
<div class="line"><a id="l00588" name="l00588"></a><span class="lineno"> 588</span> </div>
<div class="line"><a id="l00589" name="l00589"></a><span class="lineno"> 589</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> ret;</div>
<div class="line"><a id="l00590" name="l00590"></a><span class="lineno"> 590</span> </div>
<div class="line"><a id="l00591" name="l00591"></a><span class="lineno"> 591</span> <span class="keywordflow">if</span> (negative)</div>
<div class="line"><a id="l00592" name="l00592"></a><span class="lineno"> 592</span> ret.<a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/string/basic_string/append.html">append</a>(1, <span class="charliteral">&#39;-&#39;</span>);</div>
<div class="line"><a id="l00593" name="l00593"></a><span class="lineno"> 593</span> </div>
<div class="line"><a id="l00594" name="l00594"></a><span class="lineno"> 594</span> <span class="comment">// Assemble the output:</span></div>
<div class="line"><a id="l00595" name="l00595"></a><span class="lineno"> 595</span> <span class="keywordflow">if</span> (pre_from == pre_to)</div>
<div class="line"><a id="l00596" name="l00596"></a><span class="lineno"> 596</span> ret.<a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/string/basic_string/append.html">append</a>(1, <span class="charliteral">&#39;0&#39;</span>);</div>
<div class="line"><a id="l00597" name="l00597"></a><span class="lineno"> 597</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00598" name="l00598"></a><span class="lineno"> 598</span> ret.<a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/string/basic_string/append.html">append</a>(pre_from, pre_to);</div>
<div class="line"><a id="l00599" name="l00599"></a><span class="lineno"> 599</span> </div>
<div class="line"><a id="l00600" name="l00600"></a><span class="lineno"> 600</span> <span class="keywordflow">if</span> (post_to != post_from)</div>
<div class="line"><a id="l00601" name="l00601"></a><span class="lineno"> 601</span> {</div>
<div class="line"><a id="l00602" name="l00602"></a><span class="lineno"> 602</span> ret.<a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/string/basic_string/append.html">append</a>(1, <span class="charliteral">&#39;.&#39;</span>);</div>
<div class="line"><a id="l00603" name="l00603"></a><span class="lineno"> 603</span> ret.<a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/string/basic_string/append.html">append</a>(post_from, post_to);</div>
<div class="line"><a id="l00604" name="l00604"></a><span class="lineno"> 604</span> }</div>
<div class="line"><a id="l00605" name="l00605"></a><span class="lineno"> 605</span> </div>
<div class="line"><a id="l00606" name="l00606"></a><span class="lineno"> 606</span> <span class="keywordflow">return</span> ret;</div>
<div class="line"><a id="l00607" name="l00607"></a><span class="lineno"> 607</span>}</div>
</div>
<div class="line"><a id="l00608" name="l00608"></a><span class="lineno"> 608</span> </div>
<div class="line"><a id="l00609" name="l00609"></a><span class="lineno"> 609</span><span class="comment">// Returns f^n</span></div>
<div class="line"><a id="l00610" name="l00610"></a><span class="lineno"> 610</span><span class="comment">// Uses a log_2(n) number of multiplications</span></div>
<div class="line"><a id="l00611" name="l00611"></a><span class="lineno"> 611</span> </div>
<div class="line"><a id="l00612" name="l00612"></a><span class="lineno"> 612</span><a class="code hl_function" href="classripple_1_1Number.html#ac796fb449f3e3573c8d923bd3a905599">Number</a></div>
<div class="foldopen" id="foldopen00613" data-start="{" data-end="}">
<div class="line"><a id="l00613" name="l00613"></a><span class="lineno"><a class="line" href="namespaceripple.html#aa91f6bf62bcd2aa44e01926c3a160abd"> 613</a></span><a class="code hl_function" href="namespaceripple.html#aa91f6bf62bcd2aa44e01926c3a160abd">power</a>(<a class="code hl_class" href="classripple_1_1Number.html">Number</a> <span class="keyword">const</span>&amp; f, <span class="keywordtype">unsigned</span> n)</div>
<div class="line"><a id="l00614" name="l00614"></a><span class="lineno"> 614</span>{</div>
<div class="line"><a id="l00615" name="l00615"></a><span class="lineno"> 615</span> <span class="keywordflow">if</span> (n == 0)</div>
<div class="line"><a id="l00616" name="l00616"></a><span class="lineno"> 616</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a>;</div>
<div class="line"><a id="l00617" name="l00617"></a><span class="lineno"> 617</span> <span class="keywordflow">if</span> (n == 1)</div>
<div class="line"><a id="l00618" name="l00618"></a><span class="lineno"> 618</span> <span class="keywordflow">return</span> f;</div>
<div class="line"><a id="l00619" name="l00619"></a><span class="lineno"> 619</span> <span class="keyword">auto</span> r = <a class="code hl_function" href="namespaceripple.html#aa91f6bf62bcd2aa44e01926c3a160abd">power</a>(f, n / 2);</div>
<div class="line"><a id="l00620" name="l00620"></a><span class="lineno"> 620</span> r *= r;</div>
<div class="line"><a id="l00621" name="l00621"></a><span class="lineno"> 621</span> <span class="keywordflow">if</span> (n % 2 != 0)</div>
<div class="line"><a id="l00622" name="l00622"></a><span class="lineno"> 622</span> r *= f;</div>
<div class="line"><a id="l00623" name="l00623"></a><span class="lineno"> 623</span> <span class="keywordflow">return</span> r;</div>
<div class="line"><a id="l00624" name="l00624"></a><span class="lineno"> 624</span>}</div>
</div>
<div class="line"><a id="l00625" name="l00625"></a><span class="lineno"> 625</span> </div>
<div class="line"><a id="l00626" name="l00626"></a><span class="lineno"> 626</span><span class="comment">// Returns f^(1/d)</span></div>
<div class="line"><a id="l00627" name="l00627"></a><span class="lineno"> 627</span><span class="comment">// Uses Newton–Raphson iterations until the result stops changing</span></div>
<div class="line"><a id="l00628" name="l00628"></a><span class="lineno"> 628</span><span class="comment">// to find the non-negative root of the polynomial g(x) = x^d - f</span></div>
<div class="line"><a id="l00629" name="l00629"></a><span class="lineno"> 629</span> </div>
<div class="line"><a id="l00630" name="l00630"></a><span class="lineno"> 630</span><span class="comment">// This function, and power(Number f, unsigned n, unsigned d)</span></div>
<div class="line"><a id="l00631" name="l00631"></a><span class="lineno"> 631</span><span class="comment">// treat corner cases such as 0 roots as advised by Annex F of</span></div>
<div class="line"><a id="l00632" name="l00632"></a><span class="lineno"> 632</span><span class="comment">// the C standard, which itself is consistent with the IEEE</span></div>
<div class="line"><a id="l00633" name="l00633"></a><span class="lineno"> 633</span><span class="comment">// floating point standards.</span></div>
<div class="line"><a id="l00634" name="l00634"></a><span class="lineno"> 634</span> </div>
<div class="line"><a id="l00635" name="l00635"></a><span class="lineno"> 635</span><a class="code hl_function" href="classripple_1_1Number.html#ac796fb449f3e3573c8d923bd3a905599">Number</a></div>
<div class="foldopen" id="foldopen00636" data-start="{" data-end="}">
<div class="line"><a id="l00636" name="l00636"></a><span class="lineno"><a class="line" href="namespaceripple.html#acdc87ea9c4ad1742d4aeebac963e8570"> 636</a></span><a class="code hl_function" href="namespaceripple.html#acdc87ea9c4ad1742d4aeebac963e8570">root</a>(<a class="code hl_class" href="classripple_1_1Number.html">Number</a> f, <span class="keywordtype">unsigned</span> d)</div>
<div class="line"><a id="l00637" name="l00637"></a><span class="lineno"> 637</span>{</div>
<div class="line"><a id="l00638" name="l00638"></a><span class="lineno"> 638</span> <span class="keywordflow">if</span> (f == <a class="code hl_variable" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a> || d == 1)</div>
<div class="line"><a id="l00639" name="l00639"></a><span class="lineno"> 639</span> <span class="keywordflow">return</span> f;</div>
<div class="line"><a id="l00640" name="l00640"></a><span class="lineno"> 640</span> <span class="keywordflow">if</span> (d == 0)</div>
<div class="line"><a id="l00641" name="l00641"></a><span class="lineno"> 641</span> {</div>
<div class="line"><a id="l00642" name="l00642"></a><span class="lineno"> 642</span> <span class="keywordflow">if</span> (f == -<a class="code hl_variable" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a>)</div>
<div class="line"><a id="l00643" name="l00643"></a><span class="lineno"> 643</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a>;</div>
<div class="line"><a id="l00644" name="l00644"></a><span class="lineno"> 644</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="namespaceripple.html#afd19ced6c417571e8762d1d3cd89be0b">abs</a>(f) &lt; <a class="code hl_variable" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a>)</div>
<div class="line"><a id="l00645" name="l00645"></a><span class="lineno"> 645</span> <span class="keywordflow">return</span> <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{};</div>
<div class="line"><a id="l00646" name="l00646"></a><span class="lineno"> 646</span> <span class="keywordflow">throw</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/error/overflow_error.html">std::overflow_error</a>(<span class="stringliteral">&quot;Number::root infinity&quot;</span>);</div>
<div class="line"><a id="l00647" name="l00647"></a><span class="lineno"> 647</span> }</div>
<div class="line"><a id="l00648" name="l00648"></a><span class="lineno"> 648</span> <span class="keywordflow">if</span> (f &lt; <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{} &amp;&amp; d % 2 == 0)</div>
<div class="line"><a id="l00649" name="l00649"></a><span class="lineno"> 649</span> <span class="keywordflow">throw</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/error/overflow_error.html">std::overflow_error</a>(<span class="stringliteral">&quot;Number::root nan&quot;</span>);</div>
<div class="line"><a id="l00650" name="l00650"></a><span class="lineno"> 650</span> <span class="keywordflow">if</span> (f == <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{})</div>
<div class="line"><a id="l00651" name="l00651"></a><span class="lineno"> 651</span> <span class="keywordflow">return</span> f;</div>
<div class="line"><a id="l00652" name="l00652"></a><span class="lineno"> 652</span> </div>
<div class="line"><a id="l00653" name="l00653"></a><span class="lineno"> 653</span> <span class="comment">// Scale f into the range (0, 1) such that f&#39;s exponent is a multiple of d</span></div>
<div class="line"><a id="l00654" name="l00654"></a><span class="lineno"> 654</span> <span class="keyword">auto</span> e = f.<a class="code hl_function" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>() + 16;</div>
<div class="line"><a id="l00655" name="l00655"></a><span class="lineno"> 655</span> <span class="keyword">auto</span> <span class="keyword">const</span> di = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(d);</div>
<div class="line"><a id="l00656" name="l00656"></a><span class="lineno"> 656</span> <span class="keyword">auto</span> ex = [e = e, di = di]() <span class="comment">// Euclidean remainder of e/d</span></div>
<div class="line"><a id="l00657" name="l00657"></a><span class="lineno"> 657</span> {</div>
<div class="line"><a id="l00658" name="l00658"></a><span class="lineno"> 658</span> <span class="keywordtype">int</span> k = (e &gt;= 0 ? e : e - (di - 1)) / di;</div>
<div class="line"><a id="l00659" name="l00659"></a><span class="lineno"> 659</span> <span class="keywordtype">int</span> k2 = e - k * di;</div>
<div class="line"><a id="l00660" name="l00660"></a><span class="lineno"> 660</span> <span class="keywordflow">if</span> (k2 == 0)</div>
<div class="line"><a id="l00661" name="l00661"></a><span class="lineno"> 661</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00662" name="l00662"></a><span class="lineno"> 662</span> <span class="keywordflow">return</span> di - k2;</div>
<div class="line"><a id="l00663" name="l00663"></a><span class="lineno"> 663</span> }();</div>
<div class="line"><a id="l00664" name="l00664"></a><span class="lineno"> 664</span> e += ex;</div>
<div class="line"><a id="l00665" name="l00665"></a><span class="lineno"> 665</span> f = <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{f.<a class="code hl_function" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a>(), f.<a class="code hl_function" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>() - e}; <span class="comment">// f /= 10^e;</span></div>
<div class="line"><a id="l00666" name="l00666"></a><span class="lineno"> 666</span> <span class="keywordtype">bool</span> neg = <span class="keyword">false</span>;</div>
<div class="line"><a id="l00667" name="l00667"></a><span class="lineno"> 667</span> <span class="keywordflow">if</span> (f &lt; <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{})</div>
<div class="line"><a id="l00668" name="l00668"></a><span class="lineno"> 668</span> {</div>
<div class="line"><a id="l00669" name="l00669"></a><span class="lineno"> 669</span> neg = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00670" name="l00670"></a><span class="lineno"> 670</span> f = -f;</div>
<div class="line"><a id="l00671" name="l00671"></a><span class="lineno"> 671</span> }</div>
<div class="line"><a id="l00672" name="l00672"></a><span class="lineno"> 672</span> </div>
<div class="line"><a id="l00673" name="l00673"></a><span class="lineno"> 673</span> <span class="comment">// Quadratic least squares curve fit of f^(1/d) in the range [0, 1]</span></div>
<div class="line"><a id="l00674" name="l00674"></a><span class="lineno"> 674</span> <span class="keyword">auto</span> <span class="keyword">const</span> D = ((6 * di + 11) * di + 6) * di + 1;</div>
<div class="line"><a id="l00675" name="l00675"></a><span class="lineno"> 675</span> <span class="keyword">auto</span> <span class="keyword">const</span> a0 = 3 * di * ((2 * di - 3) * di + 1);</div>
<div class="line"><a id="l00676" name="l00676"></a><span class="lineno"> 676</span> <span class="keyword">auto</span> <span class="keyword">const</span> a1 = 24 * di * (2 * di - 1);</div>
<div class="line"><a id="l00677" name="l00677"></a><span class="lineno"> 677</span> <span class="keyword">auto</span> <span class="keyword">const</span> a2 = -30 * (di - 1) * di;</div>
<div class="line"><a id="l00678" name="l00678"></a><span class="lineno"> 678</span> <a class="code hl_class" href="classripple_1_1Number.html">Number</a> r = ((<a class="code hl_class" href="classripple_1_1Number.html">Number</a>{a2} * f + <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{a1}) * f + <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{a0}) / <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{D};</div>
<div class="line"><a id="l00679" name="l00679"></a><span class="lineno"> 679</span> <span class="keywordflow">if</span> (neg)</div>
<div class="line"><a id="l00680" name="l00680"></a><span class="lineno"> 680</span> {</div>
<div class="line"><a id="l00681" name="l00681"></a><span class="lineno"> 681</span> f = -f;</div>
<div class="line"><a id="l00682" name="l00682"></a><span class="lineno"> 682</span> r = -r;</div>
<div class="line"><a id="l00683" name="l00683"></a><span class="lineno"> 683</span> }</div>
<div class="line"><a id="l00684" name="l00684"></a><span class="lineno"> 684</span> </div>
<div class="line"><a id="l00685" name="l00685"></a><span class="lineno"> 685</span> <span class="comment">// Newton–Raphson iteration of f^(1/d) with initial guess r</span></div>
<div class="line"><a id="l00686" name="l00686"></a><span class="lineno"> 686</span> <span class="comment">// halt when r stops changing, checking for bouncing on the last iteration</span></div>
<div class="line"><a id="l00687" name="l00687"></a><span class="lineno"> 687</span> <a class="code hl_class" href="classripple_1_1Number.html">Number</a> rm1{};</div>
<div class="line"><a id="l00688" name="l00688"></a><span class="lineno"> 688</span> <a class="code hl_class" href="classripple_1_1Number.html">Number</a> rm2{};</div>
<div class="line"><a id="l00689" name="l00689"></a><span class="lineno"> 689</span> <span class="keywordflow">do</span></div>
<div class="line"><a id="l00690" name="l00690"></a><span class="lineno"> 690</span> {</div>
<div class="line"><a id="l00691" name="l00691"></a><span class="lineno"> 691</span> rm2 = rm1;</div>
<div class="line"><a id="l00692" name="l00692"></a><span class="lineno"> 692</span> rm1 = r;</div>
<div class="line"><a id="l00693" name="l00693"></a><span class="lineno"> 693</span> r = (<a class="code hl_function" href="classripple_1_1Number.html#ac796fb449f3e3573c8d923bd3a905599">Number</a>(d - 1) * r + f / <a class="code hl_function" href="namespaceripple.html#aa91f6bf62bcd2aa44e01926c3a160abd">power</a>(r, d - 1)) / <a class="code hl_function" href="classripple_1_1Number.html#ac796fb449f3e3573c8d923bd3a905599">Number</a>(d);</div>
<div class="line"><a id="l00694" name="l00694"></a><span class="lineno"> 694</span> } <span class="keywordflow">while</span> (r != rm1 &amp;&amp; r != rm2);</div>
<div class="line"><a id="l00695" name="l00695"></a><span class="lineno"> 695</span> </div>
<div class="line"><a id="l00696" name="l00696"></a><span class="lineno"> 696</span> <span class="comment">// return r * 10^(e/d) to reverse scaling</span></div>
<div class="line"><a id="l00697" name="l00697"></a><span class="lineno"> 697</span> <span class="keywordflow">return</span> <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{r.<a class="code hl_function" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a>(), r.<a class="code hl_function" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>() + e / di};</div>
<div class="line"><a id="l00698" name="l00698"></a><span class="lineno"> 698</span>}</div>
</div>
<div class="line"><a id="l00699" name="l00699"></a><span class="lineno"> 699</span> </div>
<div class="line"><a id="l00700" name="l00700"></a><span class="lineno"> 700</span><a class="code hl_function" href="classripple_1_1Number.html#ac796fb449f3e3573c8d923bd3a905599">Number</a></div>
<div class="foldopen" id="foldopen00701" data-start="{" data-end="}">
<div class="line"><a id="l00701" name="l00701"></a><span class="lineno"><a class="line" href="namespaceripple.html#aecb9ae1add070266b1be59ff570ec713"> 701</a></span><a class="code hl_function" href="namespaceripple.html#aecb9ae1add070266b1be59ff570ec713">root2</a>(<a class="code hl_class" href="classripple_1_1Number.html">Number</a> f)</div>
<div class="line"><a id="l00702" name="l00702"></a><span class="lineno"> 702</span>{</div>
<div class="line"><a id="l00703" name="l00703"></a><span class="lineno"> 703</span> <span class="keywordflow">if</span> (f == <a class="code hl_variable" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a>)</div>
<div class="line"><a id="l00704" name="l00704"></a><span class="lineno"> 704</span> <span class="keywordflow">return</span> f;</div>
<div class="line"><a id="l00705" name="l00705"></a><span class="lineno"> 705</span> <span class="keywordflow">if</span> (f &lt; <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{})</div>
<div class="line"><a id="l00706" name="l00706"></a><span class="lineno"> 706</span> <span class="keywordflow">throw</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/error/overflow_error.html">std::overflow_error</a>(<span class="stringliteral">&quot;Number::root nan&quot;</span>);</div>
<div class="line"><a id="l00707" name="l00707"></a><span class="lineno"> 707</span> <span class="keywordflow">if</span> (f == <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{})</div>
<div class="line"><a id="l00708" name="l00708"></a><span class="lineno"> 708</span> <span class="keywordflow">return</span> f;</div>
<div class="line"><a id="l00709" name="l00709"></a><span class="lineno"> 709</span> </div>
<div class="line"><a id="l00710" name="l00710"></a><span class="lineno"> 710</span> <span class="comment">// Scale f into the range (0, 1) such that f&#39;s exponent is a multiple of d</span></div>
<div class="line"><a id="l00711" name="l00711"></a><span class="lineno"> 711</span> <span class="keyword">auto</span> e = f.<a class="code hl_function" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>() + 16;</div>
<div class="line"><a id="l00712" name="l00712"></a><span class="lineno"> 712</span> <span class="keywordflow">if</span> (e % 2 != 0)</div>
<div class="line"><a id="l00713" name="l00713"></a><span class="lineno"> 713</span> ++e;</div>
<div class="line"><a id="l00714" name="l00714"></a><span class="lineno"> 714</span> f = <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{f.<a class="code hl_function" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a>(), f.<a class="code hl_function" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>() - e}; <span class="comment">// f /= 10^e;</span></div>
<div class="line"><a id="l00715" name="l00715"></a><span class="lineno"> 715</span> </div>
<div class="line"><a id="l00716" name="l00716"></a><span class="lineno"> 716</span> <span class="comment">// Quadratic least squares curve fit of f^(1/d) in the range [0, 1]</span></div>
<div class="line"><a id="l00717" name="l00717"></a><span class="lineno"> 717</span> <span class="keyword">auto</span> <span class="keyword">const</span> D = 105;</div>
<div class="line"><a id="l00718" name="l00718"></a><span class="lineno"> 718</span> <span class="keyword">auto</span> <span class="keyword">const</span> a0 = 18;</div>
<div class="line"><a id="l00719" name="l00719"></a><span class="lineno"> 719</span> <span class="keyword">auto</span> <span class="keyword">const</span> a1 = 144;</div>
<div class="line"><a id="l00720" name="l00720"></a><span class="lineno"> 720</span> <span class="keyword">auto</span> <span class="keyword">const</span> a2 = -60;</div>
<div class="line"><a id="l00721" name="l00721"></a><span class="lineno"> 721</span> <a class="code hl_class" href="classripple_1_1Number.html">Number</a> r = ((<a class="code hl_class" href="classripple_1_1Number.html">Number</a>{a2} * f + <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{a1}) * f + <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{a0}) / <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{D};</div>
<div class="line"><a id="l00722" name="l00722"></a><span class="lineno"> 722</span> </div>
<div class="line"><a id="l00723" name="l00723"></a><span class="lineno"> 723</span> <span class="comment">// Newton–Raphson iteration of f^(1/2) with initial guess r</span></div>
<div class="line"><a id="l00724" name="l00724"></a><span class="lineno"> 724</span> <span class="comment">// halt when r stops changing, checking for bouncing on the last iteration</span></div>
<div class="line"><a id="l00725" name="l00725"></a><span class="lineno"> 725</span> <a class="code hl_class" href="classripple_1_1Number.html">Number</a> rm1{};</div>
<div class="line"><a id="l00726" name="l00726"></a><span class="lineno"> 726</span> <a class="code hl_class" href="classripple_1_1Number.html">Number</a> rm2{};</div>
<div class="line"><a id="l00727" name="l00727"></a><span class="lineno"> 727</span> <span class="keywordflow">do</span></div>
<div class="line"><a id="l00728" name="l00728"></a><span class="lineno"> 728</span> {</div>
<div class="line"><a id="l00729" name="l00729"></a><span class="lineno"> 729</span> rm2 = rm1;</div>
<div class="line"><a id="l00730" name="l00730"></a><span class="lineno"> 730</span> rm1 = r;</div>
<div class="line"><a id="l00731" name="l00731"></a><span class="lineno"> 731</span> r = (r + f / r) / <a class="code hl_function" href="classripple_1_1Number.html#ac796fb449f3e3573c8d923bd3a905599">Number</a>(2);</div>
<div class="line"><a id="l00732" name="l00732"></a><span class="lineno"> 732</span> } <span class="keywordflow">while</span> (r != rm1 &amp;&amp; r != rm2);</div>
<div class="line"><a id="l00733" name="l00733"></a><span class="lineno"> 733</span> </div>
<div class="line"><a id="l00734" name="l00734"></a><span class="lineno"> 734</span> <span class="comment">// return r * 10^(e/2) to reverse scaling</span></div>
<div class="line"><a id="l00735" name="l00735"></a><span class="lineno"> 735</span> <span class="keywordflow">return</span> <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{r.<a class="code hl_function" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a>(), r.<a class="code hl_function" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>() + e / 2};</div>
<div class="line"><a id="l00736" name="l00736"></a><span class="lineno"> 736</span>}</div>
</div>
<div class="line"><a id="l00737" name="l00737"></a><span class="lineno"> 737</span> </div>
<div class="line"><a id="l00738" name="l00738"></a><span class="lineno"> 738</span><span class="comment">// Returns f^(n/d)</span></div>
<div class="line"><a id="l00739" name="l00739"></a><span class="lineno"> 739</span> </div>
<div class="line"><a id="l00740" name="l00740"></a><span class="lineno"> 740</span><a class="code hl_function" href="classripple_1_1Number.html#ac796fb449f3e3573c8d923bd3a905599">Number</a></div>
<div class="foldopen" id="foldopen00741" data-start="{" data-end="}">
<div class="line"><a id="l00741" name="l00741"></a><span class="lineno"><a class="line" href="namespaceripple.html#a04fb82bcbf2bd573d39cc96706f3aa23"> 741</a></span><a class="code hl_function" href="namespaceripple.html#aa91f6bf62bcd2aa44e01926c3a160abd">power</a>(<a class="code hl_class" href="classripple_1_1Number.html">Number</a> <span class="keyword">const</span>&amp; f, <span class="keywordtype">unsigned</span> n, <span class="keywordtype">unsigned</span> d)</div>
<div class="line"><a id="l00742" name="l00742"></a><span class="lineno"> 742</span>{</div>
<div class="line"><a id="l00743" name="l00743"></a><span class="lineno"> 743</span> <span class="keywordflow">if</span> (f == <a class="code hl_variable" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a>)</div>
<div class="line"><a id="l00744" name="l00744"></a><span class="lineno"> 744</span> <span class="keywordflow">return</span> f;</div>
<div class="line"><a id="l00745" name="l00745"></a><span class="lineno"> 745</span> <span class="keyword">auto</span> g = <a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/numeric/gcd.html">std::gcd</a>(n, d);</div>
<div class="line"><a id="l00746" name="l00746"></a><span class="lineno"> 746</span> <span class="keywordflow">if</span> (g == 0)</div>
<div class="line"><a id="l00747" name="l00747"></a><span class="lineno"> 747</span> <span class="keywordflow">throw</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/error/overflow_error.html">std::overflow_error</a>(<span class="stringliteral">&quot;Number::power nan&quot;</span>);</div>
<div class="line"><a id="l00748" name="l00748"></a><span class="lineno"> 748</span> <span class="keywordflow">if</span> (d == 0)</div>
<div class="line"><a id="l00749" name="l00749"></a><span class="lineno"> 749</span> {</div>
<div class="line"><a id="l00750" name="l00750"></a><span class="lineno"> 750</span> <span class="keywordflow">if</span> (f == -<a class="code hl_variable" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a>)</div>
<div class="line"><a id="l00751" name="l00751"></a><span class="lineno"> 751</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a>;</div>
<div class="line"><a id="l00752" name="l00752"></a><span class="lineno"> 752</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="namespaceripple.html#afd19ced6c417571e8762d1d3cd89be0b">abs</a>(f) &lt; <a class="code hl_variable" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a>)</div>
<div class="line"><a id="l00753" name="l00753"></a><span class="lineno"> 753</span> <span class="keywordflow">return</span> <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{};</div>
<div class="line"><a id="l00754" name="l00754"></a><span class="lineno"> 754</span> <span class="comment">// abs(f) &gt; one</span></div>
<div class="line"><a id="l00755" name="l00755"></a><span class="lineno"> 755</span> <span class="keywordflow">throw</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/error/overflow_error.html">std::overflow_error</a>(<span class="stringliteral">&quot;Number::power infinity&quot;</span>);</div>
<div class="line"><a id="l00756" name="l00756"></a><span class="lineno"> 756</span> }</div>
<div class="line"><a id="l00757" name="l00757"></a><span class="lineno"> 757</span> <span class="keywordflow">if</span> (n == 0)</div>
<div class="line"><a id="l00758" name="l00758"></a><span class="lineno"> 758</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a>;</div>
<div class="line"><a id="l00759" name="l00759"></a><span class="lineno"> 759</span> n /= g;</div>
<div class="line"><a id="l00760" name="l00760"></a><span class="lineno"> 760</span> d /= g;</div>
<div class="line"><a id="l00761" name="l00761"></a><span class="lineno"> 761</span> <span class="keywordflow">if</span> ((n % 2) == 1 &amp;&amp; (d % 2) == 0 &amp;&amp; f &lt; <a class="code hl_class" href="classripple_1_1Number.html">Number</a>{})</div>
<div class="line"><a id="l00762" name="l00762"></a><span class="lineno"> 762</span> <span class="keywordflow">throw</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/error/overflow_error.html">std::overflow_error</a>(<span class="stringliteral">&quot;Number::power nan&quot;</span>);</div>
<div class="line"><a id="l00763" name="l00763"></a><span class="lineno"> 763</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceripple.html#acdc87ea9c4ad1742d4aeebac963e8570">root</a>(<a class="code hl_function" href="namespaceripple.html#aa91f6bf62bcd2aa44e01926c3a160abd">power</a>(f, n), d);</div>
<div class="line"><a id="l00764" name="l00764"></a><span class="lineno"> 764</span>}</div>
</div>
<div class="line"><a id="l00765" name="l00765"></a><span class="lineno"> 765</span> </div>
<div class="line"><a id="l00766" name="l00766"></a><span class="lineno"> 766</span>} <span class="comment">// namespace ripple</span></div>
<div class="ttc" id="aalgorithm_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/header/algorithm.html">algorithm</a></div></div>
<div class="ttc" id="aappend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/append.html">std::string::append</a></div><div class="ttdeci">T append(T... args)</div></div>
<div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div></div>
<div class="ttc" id="abegin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/begin.html">std::string::begin</a></div><div class="ttdeci">T begin(T... args)</div></div>
<div class="ttc" id="aclassripple_1_1Number_1_1Guard_html"><div class="ttname"><a href="classripple_1_1Number_1_1Guard.html">ripple::Number::Guard</a></div><div class="ttdef"><b>Definition</b> <a href="Number_8cpp_source.html#l00064">Number.cpp:65</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_1_1Guard_html_a29e64e95a3e18476211420722180906c"><div class="ttname"><a href="classripple_1_1Number_1_1Guard.html#a29e64e95a3e18476211420722180906c">ripple::Number::Guard::set_negative</a></div><div class="ttdeci">void set_negative() noexcept</div><div class="ttdef"><b>Definition</b> <a href="Number_8cpp_source.html#l00105">Number.cpp:105</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_1_1Guard_html_a78ddead46cd4a5ce528d7d8f765e4ea1"><div class="ttname"><a href="classripple_1_1Number_1_1Guard.html#a78ddead46cd4a5ce528d7d8f765e4ea1">ripple::Number::Guard::push</a></div><div class="ttdeci">void push(unsigned d) noexcept</div><div class="ttdef"><b>Definition</b> <a href="Number_8cpp_source.html#l00117">Number.cpp:117</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_1_1Guard_html_a997cf381405becb9566b855185984471"><div class="ttname"><a href="classripple_1_1Number_1_1Guard.html#a997cf381405becb9566b855185984471">ripple::Number::Guard::pop</a></div><div class="ttdeci">unsigned pop() noexcept</div><div class="ttdef"><b>Definition</b> <a href="Number_8cpp_source.html#l00125">Number.cpp:125</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_1_1Guard_html_ab190e6f6405f271600b2f99ff15a6bc2"><div class="ttname"><a href="classripple_1_1Number_1_1Guard.html#ab190e6f6405f271600b2f99ff15a6bc2">ripple::Number::Guard::is_negative</a></div><div class="ttdeci">bool is_negative() const noexcept</div><div class="ttdef"><b>Definition</b> <a href="Number_8cpp_source.html#l00111">Number.cpp:111</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_1_1Guard_html_ab8c124fbd66b71e9282831794d6dca7b"><div class="ttname"><a href="classripple_1_1Number_1_1Guard.html#ab8c124fbd66b71e9282831794d6dca7b">ripple::Number::Guard::Guard</a></div><div class="ttdeci">Guard()</div><div class="ttdef"><b>Definition</b> <a href="Number_8cpp_source.html#l00071">Number.cpp:71</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_1_1Guard_html_abfe099a7a0d7b598b14f8ad317cb2948"><div class="ttname"><a href="classripple_1_1Number_1_1Guard.html#abfe099a7a0d7b598b14f8ad317cb2948">ripple::Number::Guard::xbit_</a></div><div class="ttdeci">std::uint8_t xbit_</div><div class="ttdef"><b>Definition</b> <a href="Number_8cpp_source.html#l00067">Number.cpp:67</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_1_1Guard_html_ac287598d3a58a5b3521715c20cdf99bd"><div class="ttname"><a href="classripple_1_1Number_1_1Guard.html#ac287598d3a58a5b3521715c20cdf99bd">ripple::Number::Guard::digits_</a></div><div class="ttdeci">std::uint64_t digits_</div><div class="ttdef"><b>Definition</b> <a href="Number_8cpp_source.html#l00066">Number.cpp:66</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_1_1Guard_html_acf34c737037a6e8a5d04d33338a2ccde"><div class="ttname"><a href="classripple_1_1Number_1_1Guard.html#acf34c737037a6e8a5d04d33338a2ccde">ripple::Number::Guard::round</a></div><div class="ttdeci">int round() noexcept</div><div class="ttdef"><b>Definition</b> <a href="Number_8cpp_source.html#l00137">Number.cpp:137</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_1_1Guard_html_ad7474f95ecebeaa0a6a4b03a2ad3d382"><div class="ttname"><a href="classripple_1_1Number_1_1Guard.html#ad7474f95ecebeaa0a6a4b03a2ad3d382">ripple::Number::Guard::sbit_</a></div><div class="ttdeci">std::uint8_t sbit_</div><div class="ttdef"><b>Definition</b> <a href="Number_8cpp_source.html#l00068">Number.cpp:68</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_1_1Guard_html_ad867ec492c1533e448bda8bb58af444a"><div class="ttname"><a href="classripple_1_1Number_1_1Guard.html#ad867ec492c1533e448bda8bb58af444a">ripple::Number::Guard::set_positive</a></div><div class="ttdeci">void set_positive() noexcept</div><div class="ttdef"><b>Definition</b> <a href="Number_8cpp_source.html#l00099">Number.cpp:99</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html"><div class="ttname"><a href="classripple_1_1Number.html">ripple::Number</a></div><div class="ttdef"><b>Definition</b> <a href="Number_8h_source.html#l00035">Number.h:36</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a014fb6ab35fb927939c085dccb43422d"><div class="ttname"><a href="classripple_1_1Number.html#a014fb6ab35fb927939c085dccb43422d">ripple::Number::isnormal</a></div><div class="ttdeci">constexpr bool isnormal() const noexcept</div><div class="ttdef"><b>Definition</b> <a href="Number_8h_source.html#l00342">Number.h:342</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a13a7bc45654573fdb3857dae23e363fc"><div class="ttname"><a href="classripple_1_1Number.html#a13a7bc45654573fdb3857dae23e363fc">ripple::Number::operator+=</a></div><div class="ttdeci">Number &amp; operator+=(Number const &amp;x)</div><div class="ttdef"><b>Definition</b> <a href="Number_8cpp_source.html#l00230">Number.cpp:230</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a18f3cb87112cf4436f8730a4f3333550"><div class="ttname"><a href="classripple_1_1Number.html#a18f3cb87112cf4436f8730a4f3333550">ripple::Number::maxMantissa</a></div><div class="ttdeci">static constexpr std::int64_t maxMantissa</div><div class="ttdef"><b>Definition</b> <a href="Number_8h_source.html#l00044">Number.h:44</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a33e3d8e7a95979bd1eb22c59703c8534"><div class="ttname"><a href="classripple_1_1Number.html#a33e3d8e7a95979bd1eb22c59703c8534">ripple::Number::rounding_mode</a></div><div class="ttdeci">rounding_mode</div><div class="ttdef"><b>Definition</b> <a href="Number_8h_source.html#l00196">Number.h:196</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a33e3d8e7a95979bd1eb22c59703c8534a25a8f50fce6cbdd3a8c0a3aa20126324"><div class="ttname"><a href="classripple_1_1Number.html#a33e3d8e7a95979bd1eb22c59703c8534a25a8f50fce6cbdd3a8c0a3aa20126324">ripple::Number::downward</a></div><div class="ttdeci">@ downward</div><div class="ttdef"><b>Definition</b> <a href="Number_8h_source.html#l00196">Number.h:196</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a33e3d8e7a95979bd1eb22c59703c8534ade4db21da96eedd46544ea52ce11a6f2"><div class="ttname"><a href="classripple_1_1Number.html#a33e3d8e7a95979bd1eb22c59703c8534ade4db21da96eedd46544ea52ce11a6f2">ripple::Number::upward</a></div><div class="ttdeci">@ upward</div><div class="ttdef"><b>Definition</b> <a href="Number_8h_source.html#l00196">Number.h:196</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a33e3d8e7a95979bd1eb22c59703c8534afb083653be2726415a0832efd2d66e95"><div class="ttname"><a href="classripple_1_1Number.html#a33e3d8e7a95979bd1eb22c59703c8534afb083653be2726415a0832efd2d66e95">ripple::Number::to_nearest</a></div><div class="ttdeci">@ to_nearest</div><div class="ttdef"><b>Definition</b> <a href="Number_8h_source.html#l00196">Number.h:196</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a33e3d8e7a95979bd1eb22c59703c8534afed3119e1980867324d399f42cbf548d"><div class="ttname"><a href="classripple_1_1Number.html#a33e3d8e7a95979bd1eb22c59703c8534afed3119e1980867324d399f42cbf548d">ripple::Number::towards_zero</a></div><div class="ttdeci">@ towards_zero</div><div class="ttdef"><b>Definition</b> <a href="Number_8h_source.html#l00196">Number.h:196</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a388d646cceab9673a0edb81206e1e106"><div class="ttname"><a href="classripple_1_1Number.html#a388d646cceab9673a0edb81206e1e106">ripple::Number::maxExponent</a></div><div class="ttdeci">static constexpr int maxExponent</div><div class="ttdef"><b>Definition</b> <a href="Number_8h_source.html#l00048">Number.h:48</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a3ae0d48f1d706dbff8b184716fa313fd"><div class="ttname"><a href="classripple_1_1Number.html#a3ae0d48f1d706dbff8b184716fa313fd">ripple::Number::operator/=</a></div><div class="ttdeci">Number &amp; operator/=(Number const &amp;x)</div><div class="ttdef"><b>Definition</b> <a href="Number_8cpp_source.html#l00448">Number.cpp:448</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a550732b6c726cffc8a742569fe76aa6e"><div class="ttname"><a href="classripple_1_1Number.html#a550732b6c726cffc8a742569fe76aa6e">ripple::Number::minMantissa</a></div><div class="ttdeci">static constexpr std::int64_t minMantissa</div><div class="ttdef"><b>Definition</b> <a href="Number_8h_source.html#l00043">Number.h:43</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a596b96835970375f7f93f272600939d2"><div class="ttname"><a href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">ripple::Number::exponent</a></div><div class="ttdeci">constexpr int exponent() const noexcept</div><div class="ttdef"><b>Definition</b> <a href="Number_8h_source.html#l00236">Number.h:236</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a5a2b36707b7dc7204982e873fcc50bac"><div class="ttname"><a href="classripple_1_1Number.html#a5a2b36707b7dc7204982e873fcc50bac">ripple::Number::mode_</a></div><div class="ttdeci">static thread_local rounding_mode mode_</div><div class="ttdef"><b>Definition</b> <a href="Number_8h_source.html#l00204">Number.h:204</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a5fefb45b369635e7803f4f8d3f9b9dd4"><div class="ttname"><a href="classripple_1_1Number.html#a5fefb45b369635e7803f4f8d3f9b9dd4">ripple::Number::normalize</a></div><div class="ttdeci">void normalize()</div><div class="ttdef"><b>Definition</b> <a href="Number_8cpp_source.html#l00178">Number.cpp:178</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a6223254bb40f9a21dbdd8b360faaf401"><div class="ttname"><a href="classripple_1_1Number.html#a6223254bb40f9a21dbdd8b360faaf401">ripple::Number::max</a></div><div class="ttdeci">static constexpr Number max() noexcept</div><div class="ttdef"><b>Definition</b> <a href="Number_8h_source.html#l00330">Number.h:330</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a62582b28d9183e7618fec0f0458331ab"><div class="ttname"><a href="classripple_1_1Number.html#a62582b28d9183e7618fec0f0458331ab">ripple::Number::exponent_</a></div><div class="ttdeci">int exponent_</div><div class="ttdef"><b>Definition</b> <a href="Number_8h_source.html#l00039">Number.h:39</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a69a91a7aca13639e1705b7fb94ee78d5"><div class="ttname"><a href="classripple_1_1Number.html#a69a91a7aca13639e1705b7fb94ee78d5">ripple::Number::getround</a></div><div class="ttdeci">static rounding_mode getround()</div><div class="ttdef"><b>Definition</b> <a href="Number_8cpp_source.html#l00047">Number.cpp:47</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a6c5e4fb40d9530e2403c7d52075c304c"><div class="ttname"><a href="classripple_1_1Number.html#a6c5e4fb40d9530e2403c7d52075c304c">ripple::Number::operator*=</a></div><div class="ttdeci">Number &amp; operator*=(Number const &amp;x)</div><div class="ttdef"><b>Definition</b> <a href="Number_8cpp_source.html#l00376">Number.cpp:376</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a72928c9b23a8c2b07024d2d3ff5eed73"><div class="ttname"><a href="classripple_1_1Number.html#a72928c9b23a8c2b07024d2d3ff5eed73">ripple::Number::minExponent</a></div><div class="ttdeci">static constexpr int minExponent</div><div class="ttdef"><b>Definition</b> <a href="Number_8h_source.html#l00047">Number.h:47</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a8d2697ce4073b76f05e0480a9b454a66"><div class="ttname"><a href="classripple_1_1Number.html#a8d2697ce4073b76f05e0480a9b454a66">ripple::Number::rep</a></div><div class="ttdeci">std::int64_t rep</div><div class="ttdef"><b>Definition</b> <a href="Number_8h_source.html#l00037">Number.h:37</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a9f2a0df7ad0f278908643927a19592f2"><div class="ttname"><a href="classripple_1_1Number.html#a9f2a0df7ad0f278908643927a19592f2">ripple::Number::setround</a></div><div class="ttdeci">static rounding_mode setround(rounding_mode mode)</div><div class="ttdef"><b>Definition</b> <a href="Number_8cpp_source.html#l00053">Number.cpp:53</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_aa072c34be5b612f33b61787ad8f09d0b"><div class="ttname"><a href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">ripple::Number::mantissa</a></div><div class="ttdeci">constexpr rep mantissa() const noexcept</div><div class="ttdef"><b>Definition</b> <a href="Number_8h_source.html#l00230">Number.h:230</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_ac796fb449f3e3573c8d923bd3a905599"><div class="ttname"><a href="classripple_1_1Number.html#ac796fb449f3e3573c8d923bd3a905599">ripple::Number::Number</a></div><div class="ttdeci">constexpr Number()=default</div></div>
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<div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/end.html">std::string::end</a></div><div class="ttdeci">T end(T... args)</div></div>
<div class="ttc" id="aexchange_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/exchange.html">std::exchange</a></div><div class="ttdeci">T exchange(T... args)</div></div>
<div class="ttc" id="afind_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/find.html">std::find_if</a></div><div class="ttdeci">T find_if(T... args)</div></div>
<div class="ttc" id="agcd_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/gcd.html">std::gcd</a></div><div class="ttdeci">T gcd(T... args)</div></div>
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<div class="ttc" id="anamespaceripple_html"><div class="ttname"><a href="namespaceripple.html">ripple</a></div><div class="ttdoc">Use hash_* containers for keys that do not need a cryptographically secure hashing algorithm.</div><div class="ttdef"><b>Definition</b> <a href="algorithm_8h_source.html#l00025">algorithm.h:25</a></div></div>
<div class="ttc" id="anamespaceripple_html_a1330e8eb921148a60725bcfc77d0a093"><div class="ttname"><a href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">ripple::one</a></div><div class="ttdeci">constexpr Number one</div><div class="ttdef"><b>Definition</b> <a href="Number_8cpp_source.html#l00175">Number.cpp:175</a></div></div>
<div class="ttc" id="anamespaceripple_html_a923b922c724a109a539486a3115eb83d"><div class="ttname"><a href="namespaceripple.html#a923b922c724a109a539486a3115eb83d">ripple::divu10</a></div><div class="ttdeci">static unsigned divu10(uint128_t &amp;u)</div><div class="ttdef"><b>Definition</b> <a href="Number_8cpp_source.html#l00354">Number.cpp:354</a></div></div>
<div class="ttc" id="anamespaceripple_html_aa91f6bf62bcd2aa44e01926c3a160abd"><div class="ttname"><a href="namespaceripple.html#aa91f6bf62bcd2aa44e01926c3a160abd">ripple::power</a></div><div class="ttdeci">Number power(Number const &amp;f, unsigned n)</div><div class="ttdef"><b>Definition</b> <a href="Number_8cpp_source.html#l00613">Number.cpp:613</a></div></div>
<div class="ttc" id="anamespaceripple_html_ac124fe6744b7fe887dec949b56b16d50"><div class="ttname"><a href="namespaceripple.html#ac124fe6744b7fe887dec949b56b16d50">ripple::to_string</a></div><div class="ttdeci">std::string to_string(base_uint&lt; Bits, Tag &gt; const &amp;a)</div><div class="ttdef"><b>Definition</b> <a href="base__uint_8h_source.html#l00630">base_uint.h:630</a></div></div>
<div class="ttc" id="anamespaceripple_html_acdc87ea9c4ad1742d4aeebac963e8570"><div class="ttname"><a href="namespaceripple.html#acdc87ea9c4ad1742d4aeebac963e8570">ripple::root</a></div><div class="ttdeci">Number root(Number f, unsigned d)</div><div class="ttdef"><b>Definition</b> <a href="Number_8cpp_source.html#l00636">Number.cpp:636</a></div></div>
<div class="ttc" id="anamespaceripple_html_aecb9ae1add070266b1be59ff570ec713"><div class="ttname"><a href="namespaceripple.html#aecb9ae1add070266b1be59ff570ec713">ripple::root2</a></div><div class="ttdeci">Number root2(Number f)</div><div class="ttdef"><b>Definition</b> <a href="Number_8cpp_source.html#l00701">Number.cpp:701</a></div></div>
<div class="ttc" id="anamespaceripple_html_afd19ced6c417571e8762d1d3cd89be0b"><div class="ttname"><a href="namespaceripple.html#afd19ced6c417571e8762d1d3cd89be0b">ripple::abs</a></div><div class="ttdeci">constexpr Number abs(Number x) noexcept</div><div class="ttdef"><b>Definition</b> <a href="Number_8h_source.html#l00350">Number.h:350</a></div></div>
<div class="ttc" id="anumeric_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/header/numeric.html">numeric</a></div></div>
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<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">std::string::length</a></div><div class="ttdeci">T length(T... args)</div></div>
<div class="ttc" id="astdexcept_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/header/stdexcept.html">stdexcept</a></div></div>
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<div class="ttc" id="ato_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/to_string.html">std::to_string</a></div><div class="ttdeci">T to_string(T... args)</div></div>
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