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<div class="title">Number.cpp</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span>&#160;<span class="comment">//------------------------------------------------------------------------------</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span>&#160;<span class="comment"> This file is part of rippled: https://github.com/ripple/rippled</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span>&#160;<span class="comment"> Copyright (c) 2022 Ripple Labs Inc.</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span>&#160;<span class="comment"> Permission to use, copy, modify, and/or distribute this software for any</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span>&#160;<span class="comment"> purpose with or without fee is hereby granted, provided that the above</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span>&#160;<span class="comment"> copyright notice and this permission notice appear in all copies.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span>&#160;<span class="comment"> THE SOFTWARE IS PROVIDED &quot;AS IS&quot; AND THE AUTHOR DISCLAIMS ALL WARRANTIES</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span>&#160;<span class="comment"> WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span>&#160;<span class="comment"> MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>&#160;<span class="comment"> ANY SPECIAL , DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span>&#160;<span class="comment"> WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span>&#160;<span class="comment"> ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span>&#160;<span class="comment"> OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.</span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span>&#160;<span class="comment">*/</span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span>&#160;<span class="comment">//==============================================================================</span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>&#160; </div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>&#160;<span class="preprocessor">#include &lt;ripple/basics/Number.h&gt;</span></div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>&#160;<span class="preprocessor">#include &lt;boost/predef.h&gt;</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>&#160;<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 name="l00023"></a><span class="lineno"> 23</span>&#160;<span class="preprocessor">#include &lt;<a class="codeRef" href="http://en.cppreference.com/w/cpp/header/cassert.html">cassert</a>&gt;</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160;<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 name="l00025"></a><span class="lineno"> 25</span>&#160;<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 name="l00026"></a><span class="lineno"> 26</span>&#160;<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 name="l00027"></a><span class="lineno"> 27</span>&#160;<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 name="l00028"></a><span class="lineno"> 28</span>&#160; </div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160;<span class="preprocessor">#ifdef BOOST_COMP_MSVC</span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160;<span class="preprocessor">#include &lt;boost/multiprecision/cpp_int.hpp&gt;</span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160;<span class="keyword">using</span> uint128_t = boost::multiprecision::uint128_t;</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160;<span class="preprocessor">#else // !defined(_MSVC_LANG)</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160;<span class="keyword">using</span> uint128_t = __uint128_t;</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160;<span class="preprocessor">#endif // !defined(_MSVC_LANG)</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; </div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceripple.html">ripple</a> {</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; </div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160;thread_local <a class="code" href="classripple_1_1Number.html#a33e3d8e7a95979bd1eb22c59703c8534">Number::rounding_mode</a> <a class="code" href="classripple_1_1Number.html#a5a2b36707b7dc7204982e873fcc50bac">Number::mode_</a> = <a class="code" href="classripple_1_1Number.html#a33e3d8e7a95979bd1eb22c59703c8534afb083653be2726415a0832efd2d66e95">Number::to_nearest</a>;</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; </div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160;<a class="code" href="classripple_1_1Number.html#a33e3d8e7a95979bd1eb22c59703c8534">Number::rounding_mode</a></div>
<div class="line"><a name="l00041"></a><span class="lineno"><a class="line" href="classripple_1_1Number.html#a69a91a7aca13639e1705b7fb94ee78d5"> 41</a></span>&#160;<a class="code" href="classripple_1_1Number.html#a69a91a7aca13639e1705b7fb94ee78d5">Number::getround</a>()</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160;{</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; <span class="keywordflow">return</span> <a class="code" href="classripple_1_1Number.html#a5a2b36707b7dc7204982e873fcc50bac">mode_</a>;</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160;}</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; </div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160;<a class="code" href="classripple_1_1Number.html#a33e3d8e7a95979bd1eb22c59703c8534">Number::rounding_mode</a></div>
<div class="line"><a name="l00047"></a><span class="lineno"><a class="line" href="classripple_1_1Number.html#a9f2a0df7ad0f278908643927a19592f2"> 47</a></span>&#160;<a class="code" href="classripple_1_1Number.html#a9f2a0df7ad0f278908643927a19592f2">Number::setround</a>(<a class="code" href="classripple_1_1Number.html#a33e3d8e7a95979bd1eb22c59703c8534">rounding_mode</a> mode)</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160;{</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; <span class="keywordflow">return</span> <a class="codeRef" href="http://en.cppreference.com/w/cpp/utility/exchange.html">std::exchange</a>(<a class="code" href="classripple_1_1Number.html#a5a2b36707b7dc7204982e873fcc50bac">mode_</a>, mode);</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160;}</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; </div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160;<span class="comment">// Guard</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; </div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160;<span class="comment">// The Guard class is used to tempoarily add extra digits of</span></div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160;<span class="comment">// preicision to an operation. This enables the final result</span></div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160;<span class="comment">// to be correctly rounded to the internal precision of Number.</span></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; </div>
<div class="line"><a name="l00058"></a><span class="lineno"><a class="line" href="classripple_1_1Number_1_1Guard.html"> 58</a></span>&#160;<span class="keyword">class </span><a class="code" href="classripple_1_1Number_1_1Guard.html">Number::Guard</a></div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160;{</div>
<div class="line"><a name="l00060"></a><span class="lineno"><a class="line" href="classripple_1_1Number_1_1Guard.html#ac287598d3a58a5b3521715c20cdf99bd"> 60</a></span>&#160; <a class="codeRef" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint64_t</a> <a class="code" href="classripple_1_1Number_1_1Guard.html#ac287598d3a58a5b3521715c20cdf99bd">digits_</a>; <span class="comment">// 16 decimal guard digits</span></div>
<div class="line"><a name="l00061"></a><span class="lineno"><a class="line" href="classripple_1_1Number_1_1Guard.html#abfe099a7a0d7b598b14f8ad317cb2948"> 61</a></span>&#160; <a class="codeRef" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint8_t</a> <a class="code" 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 name="l00062"></a><span class="lineno"><a class="line" href="classripple_1_1Number_1_1Guard.html#ad7474f95ecebeaa0a6a4b03a2ad3d382"> 62</a></span>&#160; <a class="codeRef" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint8_t</a> <a class="code" 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 name="l00063"></a><span class="lineno"> 63</span>&#160; </div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160;<span class="keyword">public</span>:</div>
<div class="line"><a name="l00065"></a><span class="lineno"><a class="line" href="classripple_1_1Number_1_1Guard.html#ab8c124fbd66b71e9282831794d6dca7b"> 65</a></span>&#160; <span class="keyword">explicit</span> <a class="code" href="classripple_1_1Number_1_1Guard.html#ab8c124fbd66b71e9282831794d6dca7b">Guard</a>() : <a class="code" href="classripple_1_1Number_1_1Guard.html#ac287598d3a58a5b3521715c20cdf99bd">digits_</a>{0}, <a class="code" href="classripple_1_1Number_1_1Guard.html#abfe099a7a0d7b598b14f8ad317cb2948">xbit_</a>{0}, <a class="code" href="classripple_1_1Number_1_1Guard.html#ad7474f95ecebeaa0a6a4b03a2ad3d382">sbit_</a>{0}</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; {</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; }</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; </div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <span class="comment">// set &amp; test the sign bit</span></div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; <span class="keywordtype">void</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; <a class="code" href="classripple_1_1Number_1_1Guard.html#ad867ec492c1533e448bda8bb58af444a">set_positive</a>() noexcept;</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <span class="keywordtype">void</span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; <a class="code" href="classripple_1_1Number_1_1Guard.html#a29e64e95a3e18476211420722180906c">set_negative</a>() noexcept;</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; <span class="keywordtype">bool</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <a class="code" href="classripple_1_1Number_1_1Guard.html#ab190e6f6405f271600b2f99ff15a6bc2">is_negative</a>() const noexcept;</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; </div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; <span class="comment">// add a digit</span></div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; <span class="keywordtype">void</span></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; <a class="code" href="classripple_1_1Number_1_1Guard.html#a78ddead46cd4a5ce528d7d8f765e4ea1">push</a>(<span class="keywordtype">unsigned</span> d) noexcept;</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; </div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; <span class="comment">// recover a digit</span></div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; <span class="keywordtype">unsigned</span></div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; <a class="code" href="classripple_1_1Number_1_1Guard.html#a997cf381405becb9566b855185984471">pop</a>() noexcept;</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; </div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; <span class="comment">// Indicate round direction: 1 is up, -1 is down, 0 is even</span></div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; <span class="comment">// This enables the client to round towards nearest, and on</span></div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; <span class="comment">// tie, round towards even.</span></div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; <span class="keywordtype">int</span></div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; <a class="code" href="classripple_1_1Number_1_1Guard.html#acf34c737037a6e8a5d04d33338a2ccde">round</a>() noexcept;</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160;};</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; </div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160;inline <span class="keywordtype">void</span></div>
<div class="line"><a name="l00093"></a><span class="lineno"><a class="line" href="classripple_1_1Number_1_1Guard.html#ad867ec492c1533e448bda8bb58af444a"> 93</a></span>&#160;<a class="code" href="classripple_1_1Number.html">Number</a>::<a class="code" href="classripple_1_1Number_1_1Guard.html">Guard</a>::<a class="code" href="classripple_1_1Number_1_1Guard.html#ad867ec492c1533e448bda8bb58af444a">set_positive</a>() noexcept</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160;{</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; <a class="code" href="classripple_1_1Number_1_1Guard.html#ad7474f95ecebeaa0a6a4b03a2ad3d382">sbit_</a> = 0;</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160;}</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; </div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span></div>
<div class="line"><a name="l00099"></a><span class="lineno"><a class="line" href="classripple_1_1Number_1_1Guard.html#a29e64e95a3e18476211420722180906c"> 99</a></span>&#160;<a class="code" href="classripple_1_1Number_1_1Guard.html#a29e64e95a3e18476211420722180906c">Number::Guard::set_negative</a>() noexcept</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160;{</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; <a class="code" href="classripple_1_1Number_1_1Guard.html#ad7474f95ecebeaa0a6a4b03a2ad3d382">sbit_</a> = 1;</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160;}</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; </div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">bool</span></div>
<div class="line"><a name="l00105"></a><span class="lineno"><a class="line" href="classripple_1_1Number_1_1Guard.html#ab190e6f6405f271600b2f99ff15a6bc2"> 105</a></span>&#160;<a class="code" href="classripple_1_1Number_1_1Guard.html#ab190e6f6405f271600b2f99ff15a6bc2">Number::Guard::is_negative</a>() const noexcept</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160;{</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; <span class="keywordflow">return</span> <a class="code" href="classripple_1_1Number_1_1Guard.html#ad7474f95ecebeaa0a6a4b03a2ad3d382">sbit_</a> == 1;</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160;}</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; </div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">void</span></div>
<div class="line"><a name="l00111"></a><span class="lineno"><a class="line" href="classripple_1_1Number_1_1Guard.html#a78ddead46cd4a5ce528d7d8f765e4ea1"> 111</a></span>&#160;<a class="code" href="classripple_1_1Number_1_1Guard.html#a78ddead46cd4a5ce528d7d8f765e4ea1">Number::Guard::push</a>(<span class="keywordtype">unsigned</span> d) noexcept</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160;{</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>&#160; <a class="code" href="classripple_1_1Number_1_1Guard.html#abfe099a7a0d7b598b14f8ad317cb2948">xbit_</a> = <a class="code" href="classripple_1_1Number_1_1Guard.html#abfe099a7a0d7b598b14f8ad317cb2948">xbit_</a> || (<a class="code" href="classripple_1_1Number_1_1Guard.html#ac287598d3a58a5b3521715c20cdf99bd">digits_</a> &amp; 0x0000<span class="stringliteral">&#39;0000&#39;</span>0000<span class="stringliteral">&#39;000F) != 0;</span></div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160;<span class="stringliteral"> digits_ &gt;&gt;= 4;</span></div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160;<span class="stringliteral"> digits_ |= (d &amp; 0x0000&#39;</span>0000<span class="stringliteral">&#39;0000&#39;</span>000<a class="code" href="namespaceripple.html#a597325d7385ff9c19686e14e5bead510aba7de5bc6888294e5884b024a4c894f1">FULL</a>) &lt;&lt; 60;</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>&#160;}</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160; </div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">unsigned</span></div>
<div class="line"><a name="l00119"></a><span class="lineno"><a class="line" href="classripple_1_1Number_1_1Guard.html#a997cf381405becb9566b855185984471"> 119</a></span>&#160;<a class="code" href="classripple_1_1Number_1_1Guard.html#a997cf381405becb9566b855185984471">Number::Guard::pop</a>() noexcept</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>&#160;{</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160; <span class="keywordtype">unsigned</span> d = (<a class="code" href="classripple_1_1Number_1_1Guard.html#ac287598d3a58a5b3521715c20cdf99bd">digits_</a> &amp; 0xF000<span class="stringliteral">&#39;0000&#39;</span>0000<span class="stringliteral">&#39;0000) &gt;&gt; 60;</span></div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160;<span class="stringliteral"> digits_ &lt;&lt;= 4;</span></div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>&#160;<span class="stringliteral"> return d;</span></div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>&#160;<span class="stringliteral">}</span></div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160;<span class="stringliteral">// Returns:</span></div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160;<span class="stringliteral">// -1 if Guard is less than half</span></div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160;<span class="stringliteral">// 0 if Guard is exactly half</span></div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160;<span class="stringliteral">// 1 if Guard is greater than half</span></div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160;<span class="stringliteral">int</span></div>
<div class="line"><a name="l00131"></a><span class="lineno"><a class="line" href="classripple_1_1Number_1_1Guard.html#acf34c737037a6e8a5d04d33338a2ccde"> 131</a></span>&#160;<span class="stringliteral">Number::Guard::round() noexcept</span></div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160;<span class="stringliteral">{</span></div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160;<span class="stringliteral"> auto mode = Number::getround();</span></div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>&#160;<span class="stringliteral"> if (mode == towards_zero)</span></div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>&#160;<span class="stringliteral"> return -1;</span></div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>&#160;<span class="stringliteral"> if (mode == downward)</span></div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>&#160;<span class="stringliteral"> if (sbit_)</span></div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>&#160;<span class="stringliteral"> if (digits_ &gt; 0 || xbit_)</span></div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>&#160;<span class="stringliteral"> return 1;</span></div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>&#160;<span class="stringliteral"> return -1;</span></div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>&#160;<span class="stringliteral"> if (mode == upward)</span></div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>&#160;<span class="stringliteral"> if (sbit_)</span></div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>&#160;<span class="stringliteral"> return -1;</span></div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>&#160;<span class="stringliteral"> if (digits_ &gt; 0 || xbit_)</span></div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>&#160;<span class="stringliteral"> return 1;</span></div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>&#160;<span class="stringliteral"> return -1;</span></div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>&#160;<span class="stringliteral"> // assume round to nearest if mode is not one of the predefined values</span></div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>&#160;<span class="stringliteral"> if (digits_ &gt; 0x5000&#39;</span>0000<span class="stringliteral">&#39;0000&#39;</span>0000)</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>&#160; <span class="keywordflow">return</span> 1;</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>&#160; <span class="keywordflow">if</span> (<a class="code" href="classripple_1_1Number_1_1Guard.html#ac287598d3a58a5b3521715c20cdf99bd">digits_</a> &lt; 0x5000<span class="stringliteral">&#39;0000&#39;</span>0000<span class="stringliteral">&#39;0000)</span></div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>&#160;<span class="stringliteral"> return -1;</span></div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>&#160;<span class="stringliteral"> if (xbit_)</span></div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>&#160;<span class="stringliteral"> return 1;</span></div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>&#160;<span class="stringliteral"> return 0;</span></div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>&#160;<span class="stringliteral">}</span></div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>&#160;<span class="stringliteral">// Number</span></div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00169"></a><span class="lineno"><a class="line" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093"> 169</a></span>&#160;<span class="stringliteral">constexpr Number one{1000000000000000, -15, Number::unchecked{}};</span></div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>&#160;<span class="stringliteral">void</span></div>
<div class="line"><a name="l00172"></a><span class="lineno"><a class="line" href="classripple_1_1Number.html#a5fefb45b369635e7803f4f8d3f9b9dd4"> 172</a></span>&#160;<span class="stringliteral">Number::normalize()</span></div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>&#160;<span class="stringliteral">{</span></div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>&#160;<span class="stringliteral"> if (mantissa_ == 0)</span></div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>&#160;<span class="stringliteral"> *this = Number{};</span></div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>&#160;<span class="stringliteral"> return;</span></div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>&#160;<span class="stringliteral"> bool const negative = (mantissa_ &lt; 0);</span></div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>&#160;<span class="stringliteral"> auto m = static_cast&lt;std::make_unsigned_t&lt;rep&gt;&gt;(mantissa_);</span></div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>&#160;<span class="stringliteral"> if (negative)</span></div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>&#160;<span class="stringliteral"> m = -m;</span></div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>&#160;<span class="stringliteral"> while ((m &lt; minMantissa) &amp;&amp; (exponent_ &gt; minExponent))</span></div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>&#160;<span class="stringliteral"> m *= 10;</span></div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>&#160;<span class="stringliteral"> --exponent_;</span></div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>&#160;<span class="stringliteral"> Guard g;</span></div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>&#160;<span class="stringliteral"> if (negative)</span></div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>&#160;<span class="stringliteral"> g.set_negative();</span></div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>&#160;<span class="stringliteral"> while (m &gt; maxMantissa)</span></div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>&#160;<span class="stringliteral"> if (exponent_ &gt;= maxExponent)</span></div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>&#160;<span class="stringliteral"> throw std::overflow_error(&quot;Number::normalize 1&quot;);</span></div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>&#160;<span class="stringliteral"> g.push(m % 10);</span></div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>&#160;<span class="stringliteral"> m /= 10;</span></div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>&#160;<span class="stringliteral"> ++exponent_;</span></div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>&#160;<span class="stringliteral"> mantissa_ = m;</span></div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>&#160;<span class="stringliteral"> if ((exponent_ &lt; minExponent) || (mantissa_ &lt; minMantissa))</span></div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>&#160;<span class="stringliteral"> *this = Number{};</span></div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>&#160;<span class="stringliteral"> return;</span></div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>&#160;<span class="stringliteral"> auto r = g.round();</span></div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>&#160;<span class="stringliteral"> if (r == 1 || (r == 0 &amp;&amp; (mantissa_ &amp; 1) == 1))</span></div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>&#160;<span class="stringliteral"> ++mantissa_;</span></div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>&#160;<span class="stringliteral"> if (mantissa_ &gt; maxMantissa)</span></div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>&#160;<span class="stringliteral"> mantissa_ /= 10;</span></div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>&#160;<span class="stringliteral"> ++exponent_;</span></div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>&#160;<span class="stringliteral"> if (exponent_ &gt; maxExponent)</span></div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>&#160;<span class="stringliteral"> throw std::overflow_error(&quot;Number::normalize 2&quot;);</span></div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>&#160;<span class="stringliteral"> if (negative)</span></div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>&#160;<span class="stringliteral"> mantissa_ = -mantissa_;</span></div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>&#160;<span class="stringliteral">}</span></div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>&#160;<span class="stringliteral">Number&amp;</span></div>
<div class="line"><a name="l00224"></a><span class="lineno"><a class="line" href="classripple_1_1Number.html#a13a7bc45654573fdb3857dae23e363fc"> 224</a></span>&#160;<span class="stringliteral">Number::operator+=(Number const&amp; y)</span></div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>&#160;<span class="stringliteral">{</span></div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>&#160;<span class="stringliteral"> if (y == Number{})</span></div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>&#160;<span class="stringliteral"> return *this;</span></div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>&#160;<span class="stringliteral"> if (*this == Number{})</span></div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>&#160;<span class="stringliteral"> *this = y;</span></div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>&#160;<span class="stringliteral"> return *this;</span></div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>&#160;<span class="stringliteral"> if (*this == -y)</span></div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>&#160;<span class="stringliteral"> *this = Number{};</span></div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>&#160;<span class="stringliteral"> return *this;</span></div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>&#160;<span class="stringliteral"> assert(isnormal() &amp;&amp; y.isnormal());</span></div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>&#160;<span class="stringliteral"> auto xm = mantissa();</span></div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>&#160;<span class="stringliteral"> auto xe = exponent();</span></div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>&#160;<span class="stringliteral"> int xn = 1;</span></div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>&#160;<span class="stringliteral"> if (xm &lt; 0)</span></div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>&#160;<span class="stringliteral"> xm = -xm;</span></div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>&#160;<span class="stringliteral"> xn = -1;</span></div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>&#160;<span class="stringliteral"> auto ym = y.mantissa();</span></div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>&#160;<span class="stringliteral"> auto ye = y.exponent();</span></div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>&#160;<span class="stringliteral"> int yn = 1;</span></div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>&#160;<span class="stringliteral"> if (ym &lt; 0)</span></div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>&#160;<span class="stringliteral"> ym = -ym;</span></div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>&#160;<span class="stringliteral"> yn = -1;</span></div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>&#160;<span class="stringliteral"> Guard g;</span></div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>&#160;<span class="stringliteral"> if (xe &lt; ye)</span></div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>&#160;<span class="stringliteral"> if (xn == -1)</span></div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>&#160;<span class="stringliteral"> g.set_negative();</span></div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>&#160;<span class="stringliteral"> do</span></div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>&#160;<span class="stringliteral"> g.push(xm % 10);</span></div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>&#160;<span class="stringliteral"> xm /= 10;</span></div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>&#160;<span class="stringliteral"> ++xe;</span></div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>&#160;<span class="stringliteral"> } while (xe &lt; ye);</span></div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>&#160;<span class="stringliteral"> else if (xe &gt; ye)</span></div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>&#160;<span class="stringliteral"> if (yn == -1)</span></div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>&#160;<span class="stringliteral"> g.set_negative();</span></div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>&#160;<span class="stringliteral"> do</span></div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>&#160;<span class="stringliteral"> g.push(ym % 10);</span></div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>&#160;<span class="stringliteral"> ym /= 10;</span></div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>&#160;<span class="stringliteral"> ++ye;</span></div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>&#160;<span class="stringliteral"> } while (xe &gt; ye);</span></div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>&#160;<span class="stringliteral"> if (xn == yn)</span></div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>&#160;<span class="stringliteral"> xm += ym;</span></div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>&#160;<span class="stringliteral"> if (xm &gt; maxMantissa)</span></div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>&#160;<span class="stringliteral"> g.push(xm % 10);</span></div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>&#160;<span class="stringliteral"> xm /= 10;</span></div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>&#160;<span class="stringliteral"> ++xe;</span></div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>&#160;<span class="stringliteral"> auto r = g.round();</span></div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>&#160;<span class="stringliteral"> if (r == 1 || (r == 0 &amp;&amp; (xm &amp; 1) == 1))</span></div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>&#160;<span class="stringliteral"> ++xm;</span></div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>&#160;<span class="stringliteral"> if (xm &gt; maxMantissa)</span></div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>&#160;<span class="stringliteral"> xm /= 10;</span></div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>&#160;<span class="stringliteral"> ++xe;</span></div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>&#160;<span class="stringliteral"> if (xe &gt; maxExponent)</span></div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>&#160;<span class="stringliteral"> throw std::overflow_error(&quot;Number::addition overflow&quot;);</span></div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>&#160;<span class="stringliteral"> else</span></div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>&#160;<span class="stringliteral"> if (xm &gt; ym)</span></div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>&#160;<span class="stringliteral"> xm = xm - ym;</span></div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>&#160;<span class="stringliteral"> else</span></div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>&#160;<span class="stringliteral"> xm = ym - xm;</span></div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>&#160;<span class="stringliteral"> xe = ye;</span></div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>&#160;<span class="stringliteral"> xn = yn;</span></div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>&#160;<span class="stringliteral"> while (xm &lt; minMantissa)</span></div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>&#160;<span class="stringliteral"> xm *= 10;</span></div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>&#160;<span class="stringliteral"> xm -= g.pop();</span></div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>&#160;<span class="stringliteral"> --xe;</span></div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>&#160;<span class="stringliteral"> auto r = g.round();</span></div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>&#160;<span class="stringliteral"> if (r == 1 || (r == 0 &amp;&amp; (xm &amp; 1) == 1))</span></div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>&#160;<span class="stringliteral"> --xm;</span></div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>&#160;<span class="stringliteral"> if (xm &lt; minMantissa)</span></div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>&#160;<span class="stringliteral"> xm *= 10;</span></div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>&#160;<span class="stringliteral"> --xe;</span></div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>&#160;<span class="stringliteral"> if (xe &lt; minExponent)</span></div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>&#160;<span class="stringliteral"> xm = 0;</span></div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>&#160;<span class="stringliteral"> xe = Number{}.exponent_;</span></div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>&#160;<span class="stringliteral"> mantissa_ = xm * xn;</span></div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>&#160;<span class="stringliteral"> exponent_ = xe;</span></div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>&#160;<span class="stringliteral"> return *this;</span></div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>&#160;<span class="stringliteral">}</span></div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>&#160;<span class="stringliteral">// Optimization equivalent to:</span></div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>&#160;<span class="stringliteral">// auto r = static_cast&lt;unsigned&gt;(u % 10);</span></div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>&#160;<span class="stringliteral">// u /= 10;</span></div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>&#160;<span class="stringliteral">// return r;</span></div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>&#160;<span class="stringliteral">// Derived from Hacker&#39;</span>s Delight Second Edition Chapter 10</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>&#160;<span class="comment">// by Henry S. Warren, Jr.</span></div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>&#160;<span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">unsigned</span></div>
<div class="line"><a name="l00346"></a><span class="lineno"><a class="line" href="namespaceripple.html#a923b922c724a109a539486a3115eb83d"> 346</a></span>&#160;<a class="code" href="namespaceripple.html#a923b922c724a109a539486a3115eb83d">divu10</a>(uint128_t&amp; u)</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>&#160;{</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>&#160; <span class="comment">// q = u * 0.75</span></div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>&#160; <span class="keyword">auto</span> q = (u &gt;&gt; 1) + (u &gt;&gt; 2);</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>&#160; <span class="comment">// iterate towards q = u * 0.8</span></div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>&#160; q += q &gt;&gt; 4;</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>&#160; q += q &gt;&gt; 8;</div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>&#160; q += q &gt;&gt; 16;</div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>&#160; q += q &gt;&gt; 32;</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>&#160; q += q &gt;&gt; 64;</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>&#160; <span class="comment">// q /= 8 approximately == u / 10</span></div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>&#160; q &gt;&gt;= 3;</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>&#160; <span class="comment">// r = u - q * 10 approximately == u % 10</span></div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>&#160; <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 name="l00360"></a><span class="lineno"> 360</span>&#160; <span class="comment">// correction c is 1 if r &gt;= 10 else 0</span></div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>&#160; <span class="keyword">auto</span> c = (r + 6) &gt;&gt; 4;</div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>&#160; u = q + c;</div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>&#160; r -= c * 10;</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>&#160; <span class="keywordflow">return</span> r;</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>&#160;}</div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>&#160; </div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>&#160;<a class="code" href="classripple_1_1Number.html#ac796fb449f3e3573c8d923bd3a905599">Number</a>&amp;</div>
<div class="line"><a name="l00368"></a><span class="lineno"><a class="line" href="classripple_1_1Number.html#a6c5e4fb40d9530e2403c7d52075c304c"> 368</a></span>&#160;<a class="code" href="classripple_1_1Number.html#a6c5e4fb40d9530e2403c7d52075c304c">Number::operator*=</a>(<a class="code" href="classripple_1_1Number.html">Number</a> <span class="keyword">const</span>&amp; y)</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>&#160;{</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>&#160; <span class="keywordflow">if</span> (*<span class="keyword">this</span> == <a class="code" href="classripple_1_1Number.html">Number</a>{})</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>&#160; <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>&#160; <span class="keywordflow">if</span> (y == <a class="code" href="classripple_1_1Number.html">Number</a>{})</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>&#160; {</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>&#160; *<span class="keyword">this</span> = y;</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>&#160; <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>&#160; }</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>&#160; assert(<a class="code" href="classripple_1_1Number.html#a014fb6ab35fb927939c085dccb43422d">isnormal</a>() &amp;&amp; y.<a class="code" href="classripple_1_1Number.html#a014fb6ab35fb927939c085dccb43422d">isnormal</a>());</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>&#160; <span class="keyword">auto</span> xm = <a class="code" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a>();</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>&#160; <span class="keyword">auto</span> xe = <a class="code" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>();</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>&#160; <span class="keywordtype">int</span> xn = 1;</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>&#160; <span class="keywordflow">if</span> (xm &lt; 0)</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>&#160; {</div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>&#160; xm = -xm;</div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>&#160; xn = -1;</div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>&#160; }</div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>&#160; <span class="keyword">auto</span> ym = y.<a class="code" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a>();</div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>&#160; <span class="keyword">auto</span> ye = y.<a class="code" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>();</div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>&#160; <span class="keywordtype">int</span> yn = 1;</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>&#160; <span class="keywordflow">if</span> (ym &lt; 0)</div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>&#160; {</div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>&#160; ym = -ym;</div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>&#160; yn = -1;</div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>&#160; }</div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>&#160; <span class="keyword">auto</span> zm = uint128_t(xm) * uint128_t(ym);</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>&#160; <span class="keyword">auto</span> ze = xe + ye;</div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>&#160; <span class="keyword">auto</span> zn = xn * yn;</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>&#160; <a class="code" href="classripple_1_1Number_1_1Guard.html">Guard</a> g;</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>&#160; <span class="keywordflow">if</span> (zn == -1)</div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>&#160; g.<a class="code" href="classripple_1_1Number_1_1Guard.html#a29e64e95a3e18476211420722180906c">set_negative</a>();</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>&#160; <span class="keywordflow">while</span> (zm &gt; <a class="code" href="classripple_1_1Number.html#ace6cc0ef2b7caaa735fbd91a50420bc0">maxMantissa</a>)</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>&#160; {</div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>&#160; <span class="comment">// The following is optimization for:</span></div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>&#160; <span class="comment">// g.push(static_cast&lt;unsigned&gt;(zm % 10));</span></div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>&#160; <span class="comment">// zm /= 10;</span></div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>&#160; g.<a class="code" href="classripple_1_1Number_1_1Guard.html#a78ddead46cd4a5ce528d7d8f765e4ea1">push</a>(<a class="code" href="namespaceripple.html#a923b922c724a109a539486a3115eb83d">divu10</a>(zm));</div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>&#160; ++ze;</div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span>&#160; }</div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>&#160; xm = <span class="keyword">static_cast&lt;</span><a class="codeRef" href="http://en.cppreference.com/w/cpp/types/integer.html">rep</a><span class="keyword">&gt;</span>(zm);</div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>&#160; xe = ze;</div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>&#160; <span class="keyword">auto</span> r = g.<a class="code" href="classripple_1_1Number_1_1Guard.html#acf34c737037a6e8a5d04d33338a2ccde">round</a>();</div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>&#160; <span class="keywordflow">if</span> (r == 1 || (r == 0 &amp;&amp; (xm &amp; 1) == 1))</div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>&#160; {</div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>&#160; ++xm;</div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>&#160; <span class="keywordflow">if</span> (xm &gt; <a class="code" href="classripple_1_1Number.html#ace6cc0ef2b7caaa735fbd91a50420bc0">maxMantissa</a>)</div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>&#160; {</div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>&#160; xm /= 10;</div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>&#160; ++xe;</div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>&#160; }</div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>&#160; }</div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>&#160; <span class="keywordflow">if</span> (xe &lt; <a class="code" href="classripple_1_1Number.html#a23ead59fdc31bbd46e9ac093a73f0d00">minExponent</a>)</div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>&#160; {</div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span>&#160; xm = 0;</div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span>&#160; xe = <a class="code" href="classripple_1_1Number.html">Number</a>{}.<a class="code" href="classripple_1_1Number.html#a62582b28d9183e7618fec0f0458331ab">exponent_</a>;</div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>&#160; }</div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>&#160; <span class="keywordflow">if</span> (xe &gt; <a class="code" href="classripple_1_1Number.html#a252726d8808ca723717ff9342ddc6fa7">maxExponent</a>)</div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>&#160; <span class="keywordflow">throw</span> <a class="codeRef" href="http://en.cppreference.com/w/cpp/error/overflow_error.html">std::overflow_error</a>(</div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>&#160; <span class="stringliteral">&quot;Number::multiplication overflow : exponent is &quot;</span> +</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>&#160; <a class="codeRef" href="http://en.cppreference.com/w/cpp/string/basic_string/to_string.html">std::to_string</a>(xe));</div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>&#160; <a class="code" href="classripple_1_1Number.html#ae8914a365ad9ca852b2d8dbdd43abb6f">mantissa_</a> = xm * zn;</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>&#160; <a class="code" href="classripple_1_1Number.html#a62582b28d9183e7618fec0f0458331ab">exponent_</a> = xe;</div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span>&#160; assert(<a class="code" href="classripple_1_1Number.html#a014fb6ab35fb927939c085dccb43422d">isnormal</a>() || *<span class="keyword">this</span> == <a class="code" href="classripple_1_1Number.html">Number</a>{});</div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>&#160; <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>&#160;}</div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>&#160; </div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>&#160;<a class="code" href="classripple_1_1Number.html">Number</a>&amp;</div>
<div class="line"><a name="l00436"></a><span class="lineno"><a class="line" href="classripple_1_1Number.html#a3ae0d48f1d706dbff8b184716fa313fd"> 436</a></span>&#160;<a class="code" href="classripple_1_1Number.html#a3ae0d48f1d706dbff8b184716fa313fd">Number::operator/=</a>(<a class="code" href="classripple_1_1Number.html">Number</a> <span class="keyword">const</span>&amp; y)</div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span>&#160;{</div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>&#160; <span class="keywordflow">if</span> (y == <a class="code" href="classripple_1_1Number.html">Number</a>{})</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>&#160; <span class="keywordflow">throw</span> <a class="codeRef" 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 name="l00440"></a><span class="lineno"> 440</span>&#160; <span class="keywordflow">if</span> (*<span class="keyword">this</span> == <a class="code" href="classripple_1_1Number.html">Number</a>{})</div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>&#160; <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>&#160; <span class="keywordtype">int</span> np = 1;</div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span>&#160; <span class="keyword">auto</span> nm = <a class="code" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a>();</div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>&#160; <span class="keyword">auto</span> ne = <a class="code" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>();</div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>&#160; <span class="keywordflow">if</span> (nm &lt; 0)</div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>&#160; {</div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>&#160; nm = -nm;</div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>&#160; np = -1;</div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>&#160; }</div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>&#160; <span class="keywordtype">int</span> dp = 1;</div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>&#160; <span class="keyword">auto</span> dm = y.<a class="code" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a>();</div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>&#160; <span class="keyword">auto</span> de = y.<a class="code" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>();</div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>&#160; <span class="keywordflow">if</span> (dm &lt; 0)</div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span>&#160; {</div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>&#160; dm = -dm;</div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span>&#160; dp = -1;</div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>&#160; }</div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>&#160; <span class="comment">// Shift by 10^17 gives greatest precision while not overflowing uint128_t</span></div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>&#160; <span class="comment">// or the cast back to int64_t</span></div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span>&#160; <span class="keyword">const</span> uint128_t f = 100<span class="stringliteral">&#39;000&#39;</span>000<span class="stringliteral">&#39;000&#39;</span>000<span class="stringliteral">&#39;000;</span></div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span>&#160;<span class="stringliteral"> mantissa_ = static_cast&lt;std::int64_t&gt;(uint128_t(nm) * f / uint128_t(dm));</span></div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span>&#160;<span class="stringliteral"> exponent_ = ne - de - 17;</span></div>
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span>&#160;<span class="stringliteral"> mantissa_ *= np * dp;</span></div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span>&#160;<span class="stringliteral"> normalize();</span></div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span>&#160;<span class="stringliteral"> return *this;</span></div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>&#160;<span class="stringliteral">}</span></div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00468"></a><span class="lineno"><a class="line" href="classripple_1_1Number.html#a8fa9f27fcce51b0e568cbe0804163e28"> 468</a></span>&#160;<span class="stringliteral">Number::operator rep() const</span></div>
<div class="line"><a name="l00469"></a><span class="lineno"> 469</span>&#160;<span class="stringliteral">{</span></div>
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span>&#160;<span class="stringliteral"> rep drops = mantissa_;</span></div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span>&#160;<span class="stringliteral"> int offset = exponent_;</span></div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>&#160;<span class="stringliteral"> Guard g;</span></div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span>&#160;<span class="stringliteral"> if (drops != 0)</span></div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00475"></a><span class="lineno"> 475</span>&#160;<span class="stringliteral"> if (drops &lt; 0)</span></div>
<div class="line"><a name="l00476"></a><span class="lineno"> 476</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span>&#160;<span class="stringliteral"> g.set_negative();</span></div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span>&#160;<span class="stringliteral"> drops = -drops;</span></div>
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00480"></a><span class="lineno"> 480</span>&#160;<span class="stringliteral"> for (; offset &lt; 0; ++offset)</span></div>
<div class="line"><a name="l00481"></a><span class="lineno"> 481</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00482"></a><span class="lineno"> 482</span>&#160;<span class="stringliteral"> g.push(drops % 10);</span></div>
<div class="line"><a name="l00483"></a><span class="lineno"> 483</span>&#160;<span class="stringliteral"> drops /= 10;</span></div>
<div class="line"><a name="l00484"></a><span class="lineno"> 484</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00485"></a><span class="lineno"> 485</span>&#160;<span class="stringliteral"> for (; offset &gt; 0; --offset)</span></div>
<div class="line"><a name="l00486"></a><span class="lineno"> 486</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00487"></a><span class="lineno"> 487</span>&#160;<span class="stringliteral"> if (drops &gt; std::numeric_limits&lt;decltype(drops)&gt;::max() / 10)</span></div>
<div class="line"><a name="l00488"></a><span class="lineno"> 488</span>&#160;<span class="stringliteral"> throw std::overflow_error(&quot;Number::operator rep() overflow&quot;);</span></div>
<div class="line"><a name="l00489"></a><span class="lineno"> 489</span>&#160;<span class="stringliteral"> drops *= 10;</span></div>
<div class="line"><a name="l00490"></a><span class="lineno"> 490</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span>&#160;<span class="stringliteral"> auto r = g.round();</span></div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span>&#160;<span class="stringliteral"> if (r == 1 || (r == 0 &amp;&amp; (drops &amp; 1) == 1))</span></div>
<div class="line"><a name="l00493"></a><span class="lineno"> 493</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span>&#160;<span class="stringliteral"> ++drops;</span></div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span>&#160;<span class="stringliteral"> if (g.is_negative())</span></div>
<div class="line"><a name="l00497"></a><span class="lineno"> 497</span>&#160;<span class="stringliteral"> drops = -drops;</span></div>
<div class="line"><a name="l00498"></a><span class="lineno"> 498</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00499"></a><span class="lineno"> 499</span>&#160;<span class="stringliteral"> return drops;</span></div>
<div class="line"><a name="l00500"></a><span class="lineno"> 500</span>&#160;<span class="stringliteral">}</span></div>
<div class="line"><a name="l00501"></a><span class="lineno"> 501</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00502"></a><span class="lineno"><a class="line" href="classripple_1_1Number.html#a93ead6eba3da8ff56e7b66a8326a3c15"> 502</a></span>&#160;<span class="stringliteral">Number::operator XRPAmount() const</span></div>
<div class="line"><a name="l00503"></a><span class="lineno"> 503</span>&#160;<span class="stringliteral">{</span></div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span>&#160;<span class="stringliteral"> return XRPAmount{static_cast&lt;rep&gt;(*this)};</span></div>
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span>&#160;<span class="stringliteral">}</span></div>
<div class="line"><a name="l00506"></a><span class="lineno"> 506</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span>&#160;<span class="stringliteral">std::string</span></div>
<div class="line"><a name="l00508"></a><span class="lineno"><a class="line" href="namespaceripple.html#a5bf7ceb7c5d4c12b5137def1455f0bdc"> 508</a></span>&#160;<span class="stringliteral">to_string(Number const&amp; amount)</span></div>
<div class="line"><a name="l00509"></a><span class="lineno"> 509</span>&#160;<span class="stringliteral">{</span></div>
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span>&#160;<span class="stringliteral"> // keep full internal accuracy, but make more human friendly if possible</span></div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span>&#160;<span class="stringliteral"> if (amount == Number{})</span></div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span>&#160;<span class="stringliteral"> return &quot;0&quot;;</span></div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span>&#160;<span class="stringliteral"> auto const exponent = amount.exponent();</span></div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>&#160;<span class="stringliteral"> auto mantissa = amount.mantissa();</span></div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span>&#160;<span class="stringliteral"> // Use scientific notation for exponents that are too small or too large</span></div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span>&#160;<span class="stringliteral"> if (((exponent != 0) &amp;&amp; ((exponent &lt; -25) || (exponent &gt; -5))))</span></div>
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span>&#160;<span class="stringliteral"> std::string ret = std::to_string(mantissa);</span></div>
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span>&#160;<span class="stringliteral"> ret.append(1, &#39;</span>e<span class="stringliteral">&#39;);</span></div>
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span>&#160;<span class="stringliteral"> ret.append(std::to_string(exponent));</span></div>
<div class="line"><a name="l00523"></a><span class="lineno"> 523</span>&#160;<span class="stringliteral"> return ret;</span></div>
<div class="line"><a name="l00524"></a><span class="lineno"> 524</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00525"></a><span class="lineno"> 525</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span>&#160;<span class="stringliteral"> bool negative = false;</span></div>
<div class="line"><a name="l00527"></a><span class="lineno"> 527</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00528"></a><span class="lineno"> 528</span>&#160;<span class="stringliteral"> if (mantissa &lt; 0)</span></div>
<div class="line"><a name="l00529"></a><span class="lineno"> 529</span>&#160;<span class="stringliteral"> {</span></div>
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span>&#160;<span class="stringliteral"> mantissa = -mantissa;</span></div>
<div class="line"><a name="l00531"></a><span class="lineno"> 531</span>&#160;<span class="stringliteral"> negative = true;</span></div>
<div class="line"><a name="l00532"></a><span class="lineno"> 532</span>&#160;<span class="stringliteral"> }</span></div>
<div class="line"><a name="l00533"></a><span class="lineno"> 533</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00534"></a><span class="lineno"> 534</span>&#160;<span class="stringliteral"> assert(exponent + 43 &gt; 0);</span></div>
<div class="line"><a name="l00535"></a><span class="lineno"> 535</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00536"></a><span class="lineno"> 536</span>&#160;<span class="stringliteral"> ptrdiff_t const pad_prefix = 27;</span></div>
<div class="line"><a name="l00537"></a><span class="lineno"> 537</span>&#160;<span class="stringliteral"> ptrdiff_t const pad_suffix = 23;</span></div>
<div class="line"><a name="l00538"></a><span class="lineno"> 538</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00539"></a><span class="lineno"> 539</span>&#160;<span class="stringliteral"> std::string const raw_value(std::to_string(mantissa));</span></div>
<div class="line"><a name="l00540"></a><span class="lineno"> 540</span>&#160;<span class="stringliteral"> std::string val;</span></div>
<div class="line"><a name="l00541"></a><span class="lineno"> 541</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00542"></a><span class="lineno"> 542</span>&#160;<span class="stringliteral"> val.reserve(raw_value.length() + pad_prefix + pad_suffix);</span></div>
<div class="line"><a name="l00543"></a><span class="lineno"> 543</span>&#160;<span class="stringliteral"> val.append(pad_prefix, &#39;</span>0<span class="stringliteral">&#39;);</span></div>
<div class="line"><a name="l00544"></a><span class="lineno"> 544</span>&#160;<span class="stringliteral"> val.append(raw_value);</span></div>
<div class="line"><a name="l00545"></a><span class="lineno"> 545</span>&#160;<span class="stringliteral"> val.append(pad_suffix, &#39;</span>0<span class="stringliteral">&#39;);</span></div>
<div class="line"><a name="l00546"></a><span class="lineno"> 546</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00547"></a><span class="lineno"> 547</span>&#160;<span class="stringliteral"> ptrdiff_t const offset(exponent + 43);</span></div>
<div class="line"><a name="l00548"></a><span class="lineno"> 548</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00549"></a><span class="lineno"> 549</span>&#160;<span class="stringliteral"> auto pre_from(val.begin());</span></div>
<div class="line"><a name="l00550"></a><span class="lineno"> 550</span>&#160;<span class="stringliteral"> auto const pre_to(val.begin() + offset);</span></div>
<div class="line"><a name="l00551"></a><span class="lineno"> 551</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00552"></a><span class="lineno"> 552</span>&#160;<span class="stringliteral"> auto const post_from(val.begin() + offset);</span></div>
<div class="line"><a name="l00553"></a><span class="lineno"> 553</span>&#160;<span class="stringliteral"> auto post_to(val.end());</span></div>
<div class="line"><a name="l00554"></a><span class="lineno"> 554</span>&#160;<span class="stringliteral"></span> </div>
<div class="line"><a name="l00555"></a><span class="lineno"> 555</span>&#160;<span class="stringliteral"> // Crop leading zeroes. Take advantage of the fact that there&#39;</span>s always a</div>
<div class="line"><a name="l00556"></a><span class="lineno"> 556</span>&#160; <span class="comment">// fixed amount of leading zeroes and skip them.</span></div>
<div class="line"><a name="l00557"></a><span class="lineno"> 557</span>&#160; <span class="keywordflow">if</span> (<a class="codeRef" 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 name="l00558"></a><span class="lineno"> 558</span>&#160; pre_from += pad_prefix;</div>
<div class="line"><a name="l00559"></a><span class="lineno"> 559</span>&#160; </div>
<div class="line"><a name="l00560"></a><span class="lineno"> 560</span>&#160; assert(post_to &gt;= post_from);</div>
<div class="line"><a name="l00561"></a><span class="lineno"> 561</span>&#160; </div>
<div class="line"><a name="l00562"></a><span class="lineno"> 562</span>&#160; pre_from = <a class="codeRef" 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 name="l00563"></a><span class="lineno"> 563</span>&#160; </div>
<div class="line"><a name="l00564"></a><span class="lineno"> 564</span>&#160; <span class="comment">// Crop trailing zeroes. Take advantage of the fact that there&#39;s always a</span></div>
<div class="line"><a name="l00565"></a><span class="lineno"> 565</span>&#160; <span class="comment">// fixed amount of trailing zeroes and skip them.</span></div>
<div class="line"><a name="l00566"></a><span class="lineno"> 566</span>&#160; <span class="keywordflow">if</span> (<a class="codeRef" 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 name="l00567"></a><span class="lineno"> 567</span>&#160; post_to -= pad_suffix;</div>
<div class="line"><a name="l00568"></a><span class="lineno"> 568</span>&#160; </div>
<div class="line"><a name="l00569"></a><span class="lineno"> 569</span>&#160; assert(post_to &gt;= post_from);</div>
<div class="line"><a name="l00570"></a><span class="lineno"> 570</span>&#160; </div>
<div class="line"><a name="l00571"></a><span class="lineno"> 571</span>&#160; post_to = <a class="codeRef" href="http://en.cppreference.com/w/cpp/algorithm/find.html">std::find_if</a>(</div>
<div class="line"><a name="l00572"></a><span class="lineno"> 572</span>&#160; <a class="codeRef" href="http://en.cppreference.com/w/cpp/iterator/make_reverse_iterator.html">std::make_reverse_iterator</a>(post_to),</div>
<div class="line"><a name="l00573"></a><span class="lineno"> 573</span>&#160; <a class="codeRef" href="http://en.cppreference.com/w/cpp/iterator/make_reverse_iterator.html">std::make_reverse_iterator</a>(post_from),</div>
<div class="line"><a name="l00574"></a><span class="lineno"> 574</span>&#160; [](<span class="keywordtype">char</span> c) { <span class="keywordflow">return</span> c != <span class="charliteral">&#39;0&#39;</span>; })</div>
<div class="line"><a name="l00575"></a><span class="lineno"> 575</span>&#160; .base();</div>
<div class="line"><a name="l00576"></a><span class="lineno"> 576</span>&#160; </div>
<div class="line"><a name="l00577"></a><span class="lineno"> 577</span>&#160; <a class="codeRef" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> ret;</div>
<div class="line"><a name="l00578"></a><span class="lineno"> 578</span>&#160; </div>
<div class="line"><a name="l00579"></a><span class="lineno"> 579</span>&#160; <span class="keywordflow">if</span> (negative)</div>
<div class="line"><a name="l00580"></a><span class="lineno"> 580</span>&#160; ret.<a class="codeRef" 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 name="l00581"></a><span class="lineno"> 581</span>&#160; </div>
<div class="line"><a name="l00582"></a><span class="lineno"> 582</span>&#160; <span class="comment">// Assemble the output:</span></div>
<div class="line"><a name="l00583"></a><span class="lineno"> 583</span>&#160; <span class="keywordflow">if</span> (pre_from == pre_to)</div>
<div class="line"><a name="l00584"></a><span class="lineno"> 584</span>&#160; ret.<a class="codeRef" 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 name="l00585"></a><span class="lineno"> 585</span>&#160; <span class="keywordflow">else</span></div>
<div class="line"><a name="l00586"></a><span class="lineno"> 586</span>&#160; ret.<a class="codeRef" href="http://en.cppreference.com/w/cpp/string/basic_string/append.html">append</a>(pre_from, pre_to);</div>
<div class="line"><a name="l00587"></a><span class="lineno"> 587</span>&#160; </div>
<div class="line"><a name="l00588"></a><span class="lineno"> 588</span>&#160; <span class="keywordflow">if</span> (post_to != post_from)</div>
<div class="line"><a name="l00589"></a><span class="lineno"> 589</span>&#160; {</div>
<div class="line"><a name="l00590"></a><span class="lineno"> 590</span>&#160; ret.<a class="codeRef" 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 name="l00591"></a><span class="lineno"> 591</span>&#160; ret.<a class="codeRef" href="http://en.cppreference.com/w/cpp/string/basic_string/append.html">append</a>(post_from, post_to);</div>
<div class="line"><a name="l00592"></a><span class="lineno"> 592</span>&#160; }</div>
<div class="line"><a name="l00593"></a><span class="lineno"> 593</span>&#160; </div>
<div class="line"><a name="l00594"></a><span class="lineno"> 594</span>&#160; <span class="keywordflow">return</span> ret;</div>
<div class="line"><a name="l00595"></a><span class="lineno"> 595</span>&#160;}</div>
<div class="line"><a name="l00596"></a><span class="lineno"> 596</span>&#160; </div>
<div class="line"><a name="l00597"></a><span class="lineno"> 597</span>&#160;<span class="comment">// Returns f^n</span></div>
<div class="line"><a name="l00598"></a><span class="lineno"> 598</span>&#160;<span class="comment">// Uses a log_2(n) number of multiplications</span></div>
<div class="line"><a name="l00599"></a><span class="lineno"> 599</span>&#160; </div>
<div class="line"><a name="l00600"></a><span class="lineno"> 600</span>&#160;<a class="code" href="classripple_1_1Number.html#ac796fb449f3e3573c8d923bd3a905599">Number</a></div>
<div class="line"><a name="l00601"></a><span class="lineno"><a class="line" href="namespaceripple.html#aa91f6bf62bcd2aa44e01926c3a160abd"> 601</a></span>&#160;<a class="code" href="namespaceripple.html#aa91f6bf62bcd2aa44e01926c3a160abd">power</a>(<a class="code" 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 name="l00602"></a><span class="lineno"> 602</span>&#160;{</div>
<div class="line"><a name="l00603"></a><span class="lineno"> 603</span>&#160; <span class="keywordflow">if</span> (n == 0)</div>
<div class="line"><a name="l00604"></a><span class="lineno"> 604</span>&#160; <span class="keywordflow">return</span> <a class="code" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a>;</div>
<div class="line"><a name="l00605"></a><span class="lineno"> 605</span>&#160; <span class="keywordflow">if</span> (n == 1)</div>
<div class="line"><a name="l00606"></a><span class="lineno"> 606</span>&#160; <span class="keywordflow">return</span> f;</div>
<div class="line"><a name="l00607"></a><span class="lineno"> 607</span>&#160; <span class="keyword">auto</span> r = <a class="code" href="namespaceripple.html#aa91f6bf62bcd2aa44e01926c3a160abd">power</a>(f, n / 2);</div>
<div class="line"><a name="l00608"></a><span class="lineno"> 608</span>&#160; r *= r;</div>
<div class="line"><a name="l00609"></a><span class="lineno"> 609</span>&#160; <span class="keywordflow">if</span> (n % 2 != 0)</div>
<div class="line"><a name="l00610"></a><span class="lineno"> 610</span>&#160; r *= f;</div>
<div class="line"><a name="l00611"></a><span class="lineno"> 611</span>&#160; <span class="keywordflow">return</span> r;</div>
<div class="line"><a name="l00612"></a><span class="lineno"> 612</span>&#160;}</div>
<div class="line"><a name="l00613"></a><span class="lineno"> 613</span>&#160; </div>
<div class="line"><a name="l00614"></a><span class="lineno"> 614</span>&#160;<span class="comment">// Returns f^(1/d)</span></div>
<div class="line"><a name="l00615"></a><span class="lineno"> 615</span>&#160;<span class="comment">// Uses Newton–Raphson iterations until the result stops changing</span></div>
<div class="line"><a name="l00616"></a><span class="lineno"> 616</span>&#160;<span class="comment">// to find the non-negative root of the polynomial g(x) = x^d - f</span></div>
<div class="line"><a name="l00617"></a><span class="lineno"> 617</span>&#160; </div>
<div class="line"><a name="l00618"></a><span class="lineno"> 618</span>&#160;<span class="comment">// This function, and power(Number f, unsigned n, unsigned d)</span></div>
<div class="line"><a name="l00619"></a><span class="lineno"> 619</span>&#160;<span class="comment">// treat corner cases such as 0 roots as advised by Annex F of</span></div>
<div class="line"><a name="l00620"></a><span class="lineno"> 620</span>&#160;<span class="comment">// the C standard, which itself is consistent with the IEEE</span></div>
<div class="line"><a name="l00621"></a><span class="lineno"> 621</span>&#160;<span class="comment">// floating point standards.</span></div>
<div class="line"><a name="l00622"></a><span class="lineno"> 622</span>&#160; </div>
<div class="line"><a name="l00623"></a><span class="lineno"> 623</span>&#160;<a class="code" href="classripple_1_1Number.html#ac796fb449f3e3573c8d923bd3a905599">Number</a></div>
<div class="line"><a name="l00624"></a><span class="lineno"><a class="line" href="namespaceripple.html#acdc87ea9c4ad1742d4aeebac963e8570"> 624</a></span>&#160;<a class="code" href="namespaceripple.html#acdc87ea9c4ad1742d4aeebac963e8570">root</a>(<a class="code" href="classripple_1_1Number.html">Number</a> f, <span class="keywordtype">unsigned</span> d)</div>
<div class="line"><a name="l00625"></a><span class="lineno"> 625</span>&#160;{</div>
<div class="line"><a name="l00626"></a><span class="lineno"> 626</span>&#160; <span class="keywordflow">if</span> (f == <a class="code" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a> || d == 1)</div>
<div class="line"><a name="l00627"></a><span class="lineno"> 627</span>&#160; <span class="keywordflow">return</span> f;</div>
<div class="line"><a name="l00628"></a><span class="lineno"> 628</span>&#160; <span class="keywordflow">if</span> (d == 0)</div>
<div class="line"><a name="l00629"></a><span class="lineno"> 629</span>&#160; {</div>
<div class="line"><a name="l00630"></a><span class="lineno"> 630</span>&#160; <span class="keywordflow">if</span> (f == -<a class="code" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a>)</div>
<div class="line"><a name="l00631"></a><span class="lineno"> 631</span>&#160; <span class="keywordflow">return</span> <a class="code" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a>;</div>
<div class="line"><a name="l00632"></a><span class="lineno"> 632</span>&#160; <span class="keywordflow">if</span> (<a class="code" href="namespaceripple.html#afd19ced6c417571e8762d1d3cd89be0b">abs</a>(f) &lt; <a class="code" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a>)</div>
<div class="line"><a name="l00633"></a><span class="lineno"> 633</span>&#160; <span class="keywordflow">return</span> <a class="code" href="classripple_1_1Number.html">Number</a>{};</div>
<div class="line"><a name="l00634"></a><span class="lineno"> 634</span>&#160; <span class="keywordflow">throw</span> <a class="codeRef" 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 name="l00635"></a><span class="lineno"> 635</span>&#160; }</div>
<div class="line"><a name="l00636"></a><span class="lineno"> 636</span>&#160; <span class="keywordflow">if</span> (f &lt; <a class="code" href="classripple_1_1Number.html">Number</a>{} &amp;&amp; d % 2 == 0)</div>
<div class="line"><a name="l00637"></a><span class="lineno"> 637</span>&#160; <span class="keywordflow">throw</span> <a class="codeRef" 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 name="l00638"></a><span class="lineno"> 638</span>&#160; <span class="keywordflow">if</span> (f == <a class="code" href="classripple_1_1Number.html">Number</a>{})</div>
<div class="line"><a name="l00639"></a><span class="lineno"> 639</span>&#160; <span class="keywordflow">return</span> f;</div>
<div class="line"><a name="l00640"></a><span class="lineno"> 640</span>&#160; </div>
<div class="line"><a name="l00641"></a><span class="lineno"> 641</span>&#160; <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 name="l00642"></a><span class="lineno"> 642</span>&#160; <span class="keyword">auto</span> e = f.<a class="code" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>() + 16;</div>
<div class="line"><a name="l00643"></a><span class="lineno"> 643</span>&#160; <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 name="l00644"></a><span class="lineno"> 644</span>&#160; <span class="keyword">auto</span> ex = [e = e, di = di]() <span class="comment">// Euclidean remainder of e/d</span></div>
<div class="line"><a name="l00645"></a><span class="lineno"> 645</span>&#160; {</div>
<div class="line"><a name="l00646"></a><span class="lineno"> 646</span>&#160; <span class="keywordtype">int</span> k = (e &gt;= 0 ? e : e - (di - 1)) / di;</div>
<div class="line"><a name="l00647"></a><span class="lineno"> 647</span>&#160; <span class="keywordtype">int</span> k2 = e - k * di;</div>
<div class="line"><a name="l00648"></a><span class="lineno"> 648</span>&#160; <span class="keywordflow">if</span> (k2 == 0)</div>
<div class="line"><a name="l00649"></a><span class="lineno"> 649</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00650"></a><span class="lineno"> 650</span>&#160; <span class="keywordflow">return</span> di - k2;</div>
<div class="line"><a name="l00651"></a><span class="lineno"> 651</span>&#160; }();</div>
<div class="line"><a name="l00652"></a><span class="lineno"> 652</span>&#160; e += ex;</div>
<div class="line"><a name="l00653"></a><span class="lineno"> 653</span>&#160; f = <a class="code" href="classripple_1_1Number.html">Number</a>{f.<a class="code" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a>(), f.<a class="code" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>() - e}; <span class="comment">// f /= 10^e;</span></div>
<div class="line"><a name="l00654"></a><span class="lineno"> 654</span>&#160; <span class="keywordtype">bool</span> neg = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00655"></a><span class="lineno"> 655</span>&#160; <span class="keywordflow">if</span> (f &lt; <a class="code" href="classripple_1_1Number.html">Number</a>{})</div>
<div class="line"><a name="l00656"></a><span class="lineno"> 656</span>&#160; {</div>
<div class="line"><a name="l00657"></a><span class="lineno"> 657</span>&#160; neg = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00658"></a><span class="lineno"> 658</span>&#160; f = -f;</div>
<div class="line"><a name="l00659"></a><span class="lineno"> 659</span>&#160; }</div>
<div class="line"><a name="l00660"></a><span class="lineno"> 660</span>&#160; </div>
<div class="line"><a name="l00661"></a><span class="lineno"> 661</span>&#160; <span class="comment">// Quadratic least squares curve fit of f^(1/d) in the range [0, 1]</span></div>
<div class="line"><a name="l00662"></a><span class="lineno"> 662</span>&#160; <span class="keyword">auto</span> <span class="keyword">const</span> D = ((6 * di + 11) * di + 6) * di + 1;</div>
<div class="line"><a name="l00663"></a><span class="lineno"> 663</span>&#160; <span class="keyword">auto</span> <span class="keyword">const</span> a0 = 3 * di * ((2 * di - 3) * di + 1);</div>
<div class="line"><a name="l00664"></a><span class="lineno"> 664</span>&#160; <span class="keyword">auto</span> <span class="keyword">const</span> a1 = 24 * di * (2 * di - 1);</div>
<div class="line"><a name="l00665"></a><span class="lineno"> 665</span>&#160; <span class="keyword">auto</span> <span class="keyword">const</span> a2 = -30 * (di - 1) * di;</div>
<div class="line"><a name="l00666"></a><span class="lineno"> 666</span>&#160; <a class="code" href="classripple_1_1Number.html">Number</a> r = ((<a class="code" href="classripple_1_1Number.html">Number</a>{a2} * f + <a class="code" href="classripple_1_1Number.html">Number</a>{a1}) * f + <a class="code" href="classripple_1_1Number.html">Number</a>{a0}) / <a class="code" href="classripple_1_1Number.html">Number</a>{D};</div>
<div class="line"><a name="l00667"></a><span class="lineno"> 667</span>&#160; <span class="keywordflow">if</span> (neg)</div>
<div class="line"><a name="l00668"></a><span class="lineno"> 668</span>&#160; {</div>
<div class="line"><a name="l00669"></a><span class="lineno"> 669</span>&#160; f = -f;</div>
<div class="line"><a name="l00670"></a><span class="lineno"> 670</span>&#160; r = -r;</div>
<div class="line"><a name="l00671"></a><span class="lineno"> 671</span>&#160; }</div>
<div class="line"><a name="l00672"></a><span class="lineno"> 672</span>&#160; </div>
<div class="line"><a name="l00673"></a><span class="lineno"> 673</span>&#160; <span class="comment">// Newton–Raphson iteration of f^(1/d) with initial guess r</span></div>
<div class="line"><a name="l00674"></a><span class="lineno"> 674</span>&#160; <span class="comment">// halt when r stops changing, checking for bouncing on the last iteration</span></div>
<div class="line"><a name="l00675"></a><span class="lineno"> 675</span>&#160; <a class="code" href="classripple_1_1Number.html">Number</a> rm1{};</div>
<div class="line"><a name="l00676"></a><span class="lineno"> 676</span>&#160; <a class="code" href="classripple_1_1Number.html">Number</a> rm2{};</div>
<div class="line"><a name="l00677"></a><span class="lineno"> 677</span>&#160; <span class="keywordflow">do</span></div>
<div class="line"><a name="l00678"></a><span class="lineno"> 678</span>&#160; {</div>
<div class="line"><a name="l00679"></a><span class="lineno"> 679</span>&#160; rm2 = rm1;</div>
<div class="line"><a name="l00680"></a><span class="lineno"> 680</span>&#160; rm1 = r;</div>
<div class="line"><a name="l00681"></a><span class="lineno"> 681</span>&#160; r = (<a class="code" href="classripple_1_1Number.html#ac796fb449f3e3573c8d923bd3a905599">Number</a>(d - 1) * r + f / <a class="code" href="namespaceripple.html#aa91f6bf62bcd2aa44e01926c3a160abd">power</a>(r, d - 1)) / <a class="code" href="classripple_1_1Number.html#ac796fb449f3e3573c8d923bd3a905599">Number</a>(d);</div>
<div class="line"><a name="l00682"></a><span class="lineno"> 682</span>&#160; } <span class="keywordflow">while</span> (r != rm1 &amp;&amp; r != rm2);</div>
<div class="line"><a name="l00683"></a><span class="lineno"> 683</span>&#160; </div>
<div class="line"><a name="l00684"></a><span class="lineno"> 684</span>&#160; <span class="comment">// return r * 10^(e/d) to reverse scaling</span></div>
<div class="line"><a name="l00685"></a><span class="lineno"> 685</span>&#160; <span class="keywordflow">return</span> <a class="code" href="classripple_1_1Number.html">Number</a>{r.<a class="code" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a>(), r.<a class="code" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>() + e / di};</div>
<div class="line"><a name="l00686"></a><span class="lineno"> 686</span>&#160;}</div>
<div class="line"><a name="l00687"></a><span class="lineno"> 687</span>&#160; </div>
<div class="line"><a name="l00688"></a><span class="lineno"> 688</span>&#160;<a class="code" href="classripple_1_1Number.html#ac796fb449f3e3573c8d923bd3a905599">Number</a></div>
<div class="line"><a name="l00689"></a><span class="lineno"><a class="line" href="namespaceripple.html#aecb9ae1add070266b1be59ff570ec713"> 689</a></span>&#160;<a class="code" href="namespaceripple.html#aecb9ae1add070266b1be59ff570ec713">root2</a>(<a class="code" href="classripple_1_1Number.html">Number</a> f)</div>
<div class="line"><a name="l00690"></a><span class="lineno"> 690</span>&#160;{</div>
<div class="line"><a name="l00691"></a><span class="lineno"> 691</span>&#160; <span class="keywordflow">if</span> (f == <a class="code" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a>)</div>
<div class="line"><a name="l00692"></a><span class="lineno"> 692</span>&#160; <span class="keywordflow">return</span> f;</div>
<div class="line"><a name="l00693"></a><span class="lineno"> 693</span>&#160; <span class="keywordflow">if</span> (f &lt; <a class="code" href="classripple_1_1Number.html">Number</a>{})</div>
<div class="line"><a name="l00694"></a><span class="lineno"> 694</span>&#160; <span class="keywordflow">throw</span> <a class="codeRef" 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 name="l00695"></a><span class="lineno"> 695</span>&#160; <span class="keywordflow">if</span> (f == <a class="code" href="classripple_1_1Number.html">Number</a>{})</div>
<div class="line"><a name="l00696"></a><span class="lineno"> 696</span>&#160; <span class="keywordflow">return</span> f;</div>
<div class="line"><a name="l00697"></a><span class="lineno"> 697</span>&#160; </div>
<div class="line"><a name="l00698"></a><span class="lineno"> 698</span>&#160; <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 name="l00699"></a><span class="lineno"> 699</span>&#160; <span class="keyword">auto</span> e = f.<a class="code" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>() + 16;</div>
<div class="line"><a name="l00700"></a><span class="lineno"> 700</span>&#160; <span class="keywordflow">if</span> (e % 2 != 0)</div>
<div class="line"><a name="l00701"></a><span class="lineno"> 701</span>&#160; ++e;</div>
<div class="line"><a name="l00702"></a><span class="lineno"> 702</span>&#160; f = <a class="code" href="classripple_1_1Number.html">Number</a>{f.<a class="code" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a>(), f.<a class="code" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>() - e}; <span class="comment">// f /= 10^e;</span></div>
<div class="line"><a name="l00703"></a><span class="lineno"> 703</span>&#160; </div>
<div class="line"><a name="l00704"></a><span class="lineno"> 704</span>&#160; <span class="comment">// Quadratic least squares curve fit of f^(1/d) in the range [0, 1]</span></div>
<div class="line"><a name="l00705"></a><span class="lineno"> 705</span>&#160; <span class="keyword">auto</span> <span class="keyword">const</span> D = 105;</div>
<div class="line"><a name="l00706"></a><span class="lineno"> 706</span>&#160; <span class="keyword">auto</span> <span class="keyword">const</span> a0 = 18;</div>
<div class="line"><a name="l00707"></a><span class="lineno"> 707</span>&#160; <span class="keyword">auto</span> <span class="keyword">const</span> a1 = 144;</div>
<div class="line"><a name="l00708"></a><span class="lineno"> 708</span>&#160; <span class="keyword">auto</span> <span class="keyword">const</span> a2 = -60;</div>
<div class="line"><a name="l00709"></a><span class="lineno"> 709</span>&#160; <a class="code" href="classripple_1_1Number.html">Number</a> r = ((<a class="code" href="classripple_1_1Number.html">Number</a>{a2} * f + <a class="code" href="classripple_1_1Number.html">Number</a>{a1}) * f + <a class="code" href="classripple_1_1Number.html">Number</a>{a0}) / <a class="code" href="classripple_1_1Number.html">Number</a>{D};</div>
<div class="line"><a name="l00710"></a><span class="lineno"> 710</span>&#160; </div>
<div class="line"><a name="l00711"></a><span class="lineno"> 711</span>&#160; <span class="comment">// Newton–Raphson iteration of f^(1/2) with initial guess r</span></div>
<div class="line"><a name="l00712"></a><span class="lineno"> 712</span>&#160; <span class="comment">// halt when r stops changing, checking for bouncing on the last iteration</span></div>
<div class="line"><a name="l00713"></a><span class="lineno"> 713</span>&#160; <a class="code" href="classripple_1_1Number.html">Number</a> rm1{};</div>
<div class="line"><a name="l00714"></a><span class="lineno"> 714</span>&#160; <a class="code" href="classripple_1_1Number.html">Number</a> rm2{};</div>
<div class="line"><a name="l00715"></a><span class="lineno"> 715</span>&#160; <span class="keywordflow">do</span></div>
<div class="line"><a name="l00716"></a><span class="lineno"> 716</span>&#160; {</div>
<div class="line"><a name="l00717"></a><span class="lineno"> 717</span>&#160; rm2 = rm1;</div>
<div class="line"><a name="l00718"></a><span class="lineno"> 718</span>&#160; rm1 = r;</div>
<div class="line"><a name="l00719"></a><span class="lineno"> 719</span>&#160; r = (r + f / r) / <a class="code" href="classripple_1_1Number.html#ac796fb449f3e3573c8d923bd3a905599">Number</a>(2);</div>
<div class="line"><a name="l00720"></a><span class="lineno"> 720</span>&#160; } <span class="keywordflow">while</span> (r != rm1 &amp;&amp; r != rm2);</div>
<div class="line"><a name="l00721"></a><span class="lineno"> 721</span>&#160; </div>
<div class="line"><a name="l00722"></a><span class="lineno"> 722</span>&#160; <span class="comment">// return r * 10^(e/2) to reverse scaling</span></div>
<div class="line"><a name="l00723"></a><span class="lineno"> 723</span>&#160; <span class="keywordflow">return</span> <a class="code" href="classripple_1_1Number.html">Number</a>{r.<a class="code" href="classripple_1_1Number.html#aa072c34be5b612f33b61787ad8f09d0b">mantissa</a>(), r.<a class="code" href="classripple_1_1Number.html#a596b96835970375f7f93f272600939d2">exponent</a>() + e / 2};</div>
<div class="line"><a name="l00724"></a><span class="lineno"> 724</span>&#160;}</div>
<div class="line"><a name="l00725"></a><span class="lineno"> 725</span>&#160; </div>
<div class="line"><a name="l00726"></a><span class="lineno"> 726</span>&#160;<span class="comment">// Returns f^(n/d)</span></div>
<div class="line"><a name="l00727"></a><span class="lineno"> 727</span>&#160; </div>
<div class="line"><a name="l00728"></a><span class="lineno"> 728</span>&#160;<a class="code" href="classripple_1_1Number.html#ac796fb449f3e3573c8d923bd3a905599">Number</a></div>
<div class="line"><a name="l00729"></a><span class="lineno"><a class="line" href="namespaceripple.html#a04fb82bcbf2bd573d39cc96706f3aa23"> 729</a></span>&#160;<a class="code" href="namespaceripple.html#aa91f6bf62bcd2aa44e01926c3a160abd">power</a>(<a class="code" 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 name="l00730"></a><span class="lineno"> 730</span>&#160;{</div>
<div class="line"><a name="l00731"></a><span class="lineno"> 731</span>&#160; <span class="keywordflow">if</span> (f == <a class="code" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a>)</div>
<div class="line"><a name="l00732"></a><span class="lineno"> 732</span>&#160; <span class="keywordflow">return</span> f;</div>
<div class="line"><a name="l00733"></a><span class="lineno"> 733</span>&#160; <span class="keyword">auto</span> g = <a class="codeRef" href="http://en.cppreference.com/w/cpp/numeric/gcd.html">std::gcd</a>(n, d);</div>
<div class="line"><a name="l00734"></a><span class="lineno"> 734</span>&#160; <span class="keywordflow">if</span> (g == 0)</div>
<div class="line"><a name="l00735"></a><span class="lineno"> 735</span>&#160; <span class="keywordflow">throw</span> <a class="codeRef" 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 name="l00736"></a><span class="lineno"> 736</span>&#160; <span class="keywordflow">if</span> (d == 0)</div>
<div class="line"><a name="l00737"></a><span class="lineno"> 737</span>&#160; {</div>
<div class="line"><a name="l00738"></a><span class="lineno"> 738</span>&#160; <span class="keywordflow">if</span> (f == -<a class="code" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a>)</div>
<div class="line"><a name="l00739"></a><span class="lineno"> 739</span>&#160; <span class="keywordflow">return</span> <a class="code" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a>;</div>
<div class="line"><a name="l00740"></a><span class="lineno"> 740</span>&#160; <span class="keywordflow">if</span> (<a class="code" href="namespaceripple.html#afd19ced6c417571e8762d1d3cd89be0b">abs</a>(f) &lt; <a class="code" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a>)</div>
<div class="line"><a name="l00741"></a><span class="lineno"> 741</span>&#160; <span class="keywordflow">return</span> <a class="code" href="classripple_1_1Number.html">Number</a>{};</div>
<div class="line"><a name="l00742"></a><span class="lineno"> 742</span>&#160; <span class="comment">// abs(f) &gt; one</span></div>
<div class="line"><a name="l00743"></a><span class="lineno"> 743</span>&#160; <span class="keywordflow">throw</span> <a class="codeRef" 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 name="l00744"></a><span class="lineno"> 744</span>&#160; }</div>
<div class="line"><a name="l00745"></a><span class="lineno"> 745</span>&#160; <span class="keywordflow">if</span> (n == 0)</div>
<div class="line"><a name="l00746"></a><span class="lineno"> 746</span>&#160; <span class="keywordflow">return</span> <a class="code" href="namespaceripple.html#a1330e8eb921148a60725bcfc77d0a093">one</a>;</div>
<div class="line"><a name="l00747"></a><span class="lineno"> 747</span>&#160; n /= g;</div>
<div class="line"><a name="l00748"></a><span class="lineno"> 748</span>&#160; d /= g;</div>
<div class="line"><a name="l00749"></a><span class="lineno"> 749</span>&#160; <span class="keywordflow">if</span> ((n % 2) == 1 &amp;&amp; (d % 2) == 0 &amp;&amp; f &lt; <a class="code" href="classripple_1_1Number.html">Number</a>{})</div>
<div class="line"><a name="l00750"></a><span class="lineno"> 750</span>&#160; <span class="keywordflow">throw</span> <a class="codeRef" 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 name="l00751"></a><span class="lineno"> 751</span>&#160; <span class="keywordflow">return</span> <a class="code" href="namespaceripple.html#acdc87ea9c4ad1742d4aeebac963e8570">root</a>(<a class="code" href="namespaceripple.html#aa91f6bf62bcd2aa44e01926c3a160abd">power</a>(f, n), d);</div>
<div class="line"><a name="l00752"></a><span class="lineno"> 752</span>&#160;}</div>
<div class="line"><a name="l00753"></a><span class="lineno"> 753</span>&#160; </div>
<div class="line"><a name="l00754"></a><span class="lineno"> 754</span>&#160;} <span class="comment">// namespace ripple</span></div>
</div><!-- fragment --></div><!-- contents -->
<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#l00041">Number.cpp:41</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#l00689">Number.cpp:689</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_ace6cc0ef2b7caaa735fbd91a50420bc0"><div class="ttname"><a href="classripple_1_1Number.html#ace6cc0ef2b7caaa735fbd91a50420bc0">ripple::Number::maxMantissa</a></div><div class="ttdeci">constexpr static std::int64_t maxMantissa</div><div class="ttdef"><b>Definition:</b> <a href="Number_8h_source.html#l00178">Number.h:178</a></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 class="ttdoc">STL class.</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#l00119">Number.cpp:119</a></div></div>
<div class="ttc" id="autility_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/header/utility.html">utility</a></div></div>
<div class="ttc" id="aoverflow_error_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/error/overflow_error.html">std::overflow_error</a></div><div class="ttdoc">STL class.</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#l00060">Number.cpp:60</a></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="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#l00368">Number.cpp:368</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#l00111">Number.cpp:111</a></div></div>
<div class="ttc" id="adistance_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/distance.html">std::distance</a></div><div class="ttdeci">T distance(T... args)</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#l00213">Number.h:213</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#l00319">Number.h:319</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#l00105">Number.cpp:105</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#l00093">Number.cpp:93</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#l00161">Number.h:161</a></div></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="astdexcept_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/header/stdexcept.html">stdexcept</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#l00040">Number.h:40</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#l00036">Number.h:36</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#l00169">Number.h:169</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#l00047">Number.cpp:47</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a252726d8808ca723717ff9342ddc6fa7"><div class="ttname"><a href="classripple_1_1Number.html#a252726d8808ca723717ff9342ddc6fa7">ripple::Number::maxExponent</a></div><div class="ttdeci">constexpr static int maxExponent</div><div class="ttdef"><b>Definition:</b> <a href="Number_8h_source.html#l00182">Number.h:182</a></div></div>
<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>
<div class="ttc" id="ainteger_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint64_t</a></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>
<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="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#l00601">Number.cpp:601</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#l00062">Number.cpp:62</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a23ead59fdc31bbd46e9ac093a73f0d00"><div class="ttname"><a href="classripple_1_1Number.html#a23ead59fdc31bbd46e9ac093a73f0d00">ripple::Number::minExponent</a></div><div class="ttdeci">constexpr static int minExponent</div><div class="ttdef"><b>Definition:</b> <a href="Number_8h_source.html#l00181">Number.h:181</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#l00169">Number.cpp:169</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#l00065">Number.cpp:65</a></div></div>
<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="RCLCensorshipDetector_8h_source.html#l00029">RCLCensorshipDetector.h:29</a></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="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#l00436">Number.cpp:436</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#l00327">Number.h:327</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_ae8914a365ad9ca852b2d8dbdd43abb6f"><div class="ttname"><a href="classripple_1_1Number.html#ae8914a365ad9ca852b2d8dbdd43abb6f">ripple::Number::mantissa_</a></div><div class="ttdeci">rep mantissa_</div><div class="ttdef"><b>Definition:</b> <a href="Number_8h_source.html#l00039">Number.h:39</a></div></div>
<div class="ttc" id="acassert_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/header/cassert.html">cassert</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="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#l00061">Number.cpp:61</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>
<div class="ttc" id="amake_reverse_iterator_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/make_reverse_iterator.html">std::make_reverse_iterator</a></div><div class="ttdeci">T make_reverse_iterator(T... args)</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#l00207">Number.h:207</a></div></div>
<div class="ttc" id="atype_traits_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/header/type_traits.html">type_traits</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#l00161">Number.h:161</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#l00099">Number.cpp:99</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#l00131">Number.cpp:131</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#l00346">Number.cpp:346</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#l00624">Number.cpp:624</a></div></div>
<div class="ttc" id="anamespaceripple_html_a597325d7385ff9c19686e14e5bead510aba7de5bc6888294e5884b024a4c894f1"><div class="ttname"><a href="namespaceripple.html#a597325d7385ff9c19686e14e5bead510aba7de5bc6888294e5884b024a4c894f1">ripple::OperatingMode::FULL</a></div><div class="ttdeci">@ FULL</div><div class="ttdoc">we have the ledger and can even validate</div></div>
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