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<div class="headertitle"><div class="title">AMMHelpers.cpp</div></div>
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<div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">//------------------------------------------------------------------------------</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">/*</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment"> This file is part of rippled: https://github.com/ripple/rippled</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment"> Copyright (c) 2023 Ripple Labs Inc.</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment"></span> </div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment"> Permission to use, copy, modify, and/or distribute this software for any</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment"> purpose with or without fee is hereby granted, provided that the above</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment"> copyright notice and this permission notice appear in all copies.</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment"></span> </div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment"> THE SOFTWARE IS PROVIDED &quot;AS IS&quot; AND THE AUTHOR DISCLAIMS ALL WARRANTIES</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment"> WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment"> MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="comment"> ANY SPECIAL , DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment"> WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="comment"> ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment"> OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="comment">*/</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="comment">//==============================================================================</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include &lt;xrpld/app/misc/AMMHelpers.h&gt;</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> </div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceripple.html">ripple</a> {</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> </div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span>STAmount</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"><a class="line" href="namespaceripple.html#ab8defa1f235abbf44a60ccc6c71c6fdd"> 25</a></span><a class="code hl_function" href="namespaceripple.html#ab8defa1f235abbf44a60ccc6c71c6fdd">ammLPTokens</a>(</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> <a class="code hl_class" href="classripple_1_1STAmount.html">STAmount</a> <span class="keyword">const</span>&amp; asset1,</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> <a class="code hl_class" href="classripple_1_1STAmount.html">STAmount</a> <span class="keyword">const</span>&amp; asset2,</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> <a class="code hl_class" href="classripple_1_1Issue.html">Issue</a> <span class="keyword">const</span>&amp; lptIssue)</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span>{</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> <span class="keyword">auto</span> <span class="keyword">const</span> tokens = <a class="code hl_function" href="namespaceripple.html#aecb9ae1add070266b1be59ff570ec713">root2</a>(asset1 * asset2);</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceripple.html#a4ad5ac9da897292a28eea43d041c15a1">toSTAmount</a>(lptIssue, tokens);</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span>}</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> </div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="comment">/*</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="comment"> * Equation 3:</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="comment"> * t = T * [(b/B - (sqrt(f2**2 - b/(B*f1)) - f2)) /</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="comment"> * (1 + sqrt(f2**2 - b/(B*f1)) - f2)]</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="comment"> * where f1 = 1 - tfee, f2 = (1 - tfee/2)/f1</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="comment"> */</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span>STAmount</div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"><a class="line" href="namespaceripple.html#a0b2344222057d8b5b9923b2911962879"> 41</a></span><a class="code hl_function" href="namespaceripple.html#a0b2344222057d8b5b9923b2911962879">lpTokensIn</a>(</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <a class="code hl_class" href="classripple_1_1STAmount.html">STAmount</a> <span class="keyword">const</span>&amp; asset1Balance,</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <a class="code hl_class" href="classripple_1_1STAmount.html">STAmount</a> <span class="keyword">const</span>&amp; asset1Deposit,</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <a class="code hl_class" href="classripple_1_1STAmount.html">STAmount</a> <span class="keyword">const</span>&amp; lptAMMBalance,</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint16_t</a> tfee)</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span>{</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="keyword">auto</span> <span class="keyword">const</span> f1 = <a class="code hl_function" href="namespaceripple.html#a7894756905fee556c1541cd1de1f697a">feeMult</a>(tfee);</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="keyword">auto</span> <span class="keyword">const</span> f2 = <a class="code hl_function" href="namespaceripple.html#ac78c8c0642bbbe33db633286fa147381">feeMultHalf</a>(tfee) / f1;</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <a class="code hl_class" href="classripple_1_1Number.html">Number</a> <span class="keyword">const</span> r = asset1Deposit / asset1Balance;</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="keyword">auto</span> <span class="keyword">const</span> c = <a class="code hl_function" href="namespaceripple.html#aecb9ae1add070266b1be59ff570ec713">root2</a>(f2 * f2 + r / f1) - f2;</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keyword">auto</span> <span class="keyword">const</span> t = lptAMMBalance * (r - c) / (1 + c);</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceripple.html#a4ad5ac9da897292a28eea43d041c15a1">toSTAmount</a>(lptAMMBalance.<a class="code hl_function" href="classripple_1_1STAmount.html#acab76380a95d902071fd26ab3425bbe5">issue</a>(), t);</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span>}</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> </div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="comment">/* Equation 4 solves equation 3 for b:</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="comment"> * Let f1 = 1 - tfee, f2 = (1 - tfee/2)/f1, t1 = t/T, t2 = 1 + t1, R = b/B</span></div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="comment"> * then</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="comment"> * t1 = [R - sqrt(f2**2 + R/f1) + f2] / [1 + sqrt(f2**2 + R/f1] - f2] =&gt;</span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span><span class="comment"> * sqrt(f2**2 + R/f1)*(t1 + 1) = R + f2 + t1*f2 - t1 =&gt;</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span><span class="comment"> * sqrt(f2**2 + R/f1)*t2 = R + t2*f2 - t1 =&gt;</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span><span class="comment"> * sqrt(f2**2 + R/f1) = R/t2 + f2 - t1/t2, let d = f2 - t1/t2 =&gt;</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span><span class="comment"> * sqrt(f2**2 + R/f1) = R/t2 + d =&gt;</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span><span class="comment"> * f2**2 + R/f1 = (R/t2)**2 +2*d*R/t2 + d**2 =&gt;</span></div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span><span class="comment"> * (R/t2)**2 + R*(2*d/t2 - 1/f1) + d**2 - f2**2 = 0</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span><span class="comment"> */</span></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span>STAmount</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"><a class="line" href="namespaceripple.html#a573eb2cecf652856fc74fb1dfbaf8c2a"> 67</a></span><a class="code hl_function" href="namespaceripple.html#a573eb2cecf652856fc74fb1dfbaf8c2a">ammAssetIn</a>(</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <a class="code hl_class" href="classripple_1_1STAmount.html">STAmount</a> <span class="keyword">const</span>&amp; asset1Balance,</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <a class="code hl_class" href="classripple_1_1STAmount.html">STAmount</a> <span class="keyword">const</span>&amp; lptAMMBalance,</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <a class="code hl_class" href="classripple_1_1STAmount.html">STAmount</a> <span class="keyword">const</span>&amp; lpTokens,</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint16_t</a> tfee)</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span>{</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="keyword">auto</span> <span class="keyword">const</span> f1 = <a class="code hl_function" href="namespaceripple.html#a7894756905fee556c1541cd1de1f697a">feeMult</a>(tfee);</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keyword">auto</span> <span class="keyword">const</span> f2 = <a class="code hl_function" href="namespaceripple.html#ac78c8c0642bbbe33db633286fa147381">feeMultHalf</a>(tfee) / f1;</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="keyword">auto</span> <span class="keyword">const</span> t1 = lpTokens / lptAMMBalance;</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keyword">auto</span> <span class="keyword">const</span> t2 = 1 + t1;</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keyword">auto</span> <span class="keyword">const</span> d = f2 - t1 / t2;</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keyword">auto</span> <span class="keyword">const</span> a = 1 / (t2 * t2);</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keyword">auto</span> <span class="keyword">const</span> b = 2 * d / t2 - 1 / f1;</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keyword">auto</span> <span class="keyword">const</span> c = d * d - f2 * f2;</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceripple.html#a4ad5ac9da897292a28eea43d041c15a1">toSTAmount</a>(</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> asset1Balance.<a class="code hl_function" href="classripple_1_1STAmount.html#acab76380a95d902071fd26ab3425bbe5">issue</a>(), asset1Balance * <a class="code hl_function" href="namespaceripple.html#a3d22714f28b806ea5c702eba2db5fbc2">solveQuadraticEq</a>(a, b, c));</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span>}</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> </div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span><span class="comment">/* Equation 7:</span></div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span><span class="comment"> * t = T * (c - sqrt(c**2 - 4*R))/2</span></div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span><span class="comment"> * where R = b/B, c = R*fee + 2 - fee</span></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span><span class="comment"> */</span></div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span>STAmount</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"><a class="line" href="namespaceripple.html#a4c964d1f7629a28f9b916e2d25b39bcd"> 90</a></span><a class="code hl_function" href="namespaceripple.html#a4c964d1f7629a28f9b916e2d25b39bcd">lpTokensOut</a>(</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <a class="code hl_class" href="classripple_1_1STAmount.html">STAmount</a> <span class="keyword">const</span>&amp; asset1Balance,</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <a class="code hl_class" href="classripple_1_1STAmount.html">STAmount</a> <span class="keyword">const</span>&amp; asset1Withdraw,</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <a class="code hl_class" href="classripple_1_1STAmount.html">STAmount</a> <span class="keyword">const</span>&amp; lptAMMBalance,</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint16_t</a> tfee)</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span>{</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <a class="code hl_class" href="classripple_1_1Number.html">Number</a> <span class="keyword">const</span> fr = asset1Withdraw / asset1Balance;</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keyword">auto</span> <span class="keyword">const</span> f1 = <a class="code hl_function" href="namespaceripple.html#aa8871e2f35cee24497183274c0bab5fd">getFee</a>(tfee);</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keyword">auto</span> <span class="keyword">const</span> c = fr * f1 + 2 - f1;</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="keyword">auto</span> <span class="keyword">const</span> t = lptAMMBalance * (c - <a class="code hl_function" href="namespaceripple.html#aecb9ae1add070266b1be59ff570ec713">root2</a>(c * c - 4 * fr)) / 2;</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceripple.html#a4ad5ac9da897292a28eea43d041c15a1">toSTAmount</a>(lptAMMBalance.<a class="code hl_function" href="classripple_1_1STAmount.html#acab76380a95d902071fd26ab3425bbe5">issue</a>(), t);</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span>}</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> </div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span><span class="comment">/* Equation 8 solves equation 7 for b:</span></div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span><span class="comment"> * c - 2*t/T = sqrt(c**2 - 4*R) =&gt;</span></div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span><span class="comment"> * c**2 - 4*c*t/T + 4*t**2/T**2 = c**2 - 4*R =&gt;</span></div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span><span class="comment"> * -4*c*t/T + 4*t**2/T**2 = -4*R =&gt;</span></div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span><span class="comment"> * -c*t/T + t**2/T**2 = -R -=&gt;</span></div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span><span class="comment"> * substitute c = R*f + 2 - f =&gt;</span></div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span><span class="comment"> * -(t/T)*(R*f + 2 - f) + (t/T)**2 = -R, let t1 = t/T =&gt;</span></div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span><span class="comment"> * -t1*R*f -2*t1 +t1*f +t1**2 = -R =&gt;</span></div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span><span class="comment"> * R = (t1**2 + t1*(f - 2)) / (t1*f - 1)</span></div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span><span class="comment"> */</span></div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span>STAmount</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"><a class="line" href="namespaceripple.html#aea4620f7a5356019edee3be624729c6d"> 114</a></span><a class="code hl_function" href="namespaceripple.html#aea4620f7a5356019edee3be624729c6d">withdrawByTokens</a>(</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <a class="code hl_class" href="classripple_1_1STAmount.html">STAmount</a> <span class="keyword">const</span>&amp; assetBalance,</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <a class="code hl_class" href="classripple_1_1STAmount.html">STAmount</a> <span class="keyword">const</span>&amp; lptAMMBalance,</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <a class="code hl_class" href="classripple_1_1STAmount.html">STAmount</a> <span class="keyword">const</span>&amp; lpTokens,</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint16_t</a> tfee)</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span>{</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="keyword">auto</span> <span class="keyword">const</span> f = <a class="code hl_function" href="namespaceripple.html#aa8871e2f35cee24497183274c0bab5fd">getFee</a>(tfee);</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <a class="code hl_class" href="classripple_1_1Number.html">Number</a> <span class="keyword">const</span> t1 = lpTokens / lptAMMBalance;</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="keyword">auto</span> <span class="keyword">const</span> b = assetBalance * (t1 * t1 - t1 * (2 - f)) / (t1 * f - 1);</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceripple.html#a4ad5ac9da897292a28eea43d041c15a1">toSTAmount</a>(assetBalance.<a class="code hl_function" href="classripple_1_1STAmount.html#acab76380a95d902071fd26ab3425bbe5">issue</a>(), b);</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span>}</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> </div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span>Number</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"><a class="line" href="namespaceripple.html#a58b7851104129e42da9c5260ba6f00d6"> 127</a></span><a class="code hl_function" href="namespaceripple.html#a58b7851104129e42da9c5260ba6f00d6">square</a>(<a class="code hl_class" href="classripple_1_1Number.html">Number</a> <span class="keyword">const</span>&amp; n)</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span>{</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="keywordflow">return</span> n * n;</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span>}</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> </div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span>STAmount</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"><a class="line" href="namespaceripple.html#a0e17cbd5597a6159dfa1045e6b2e951e"> 133</a></span><a class="code hl_function" href="namespaceripple.html#a0e17cbd5597a6159dfa1045e6b2e951e">adjustLPTokens</a>(</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <a class="code hl_class" href="classripple_1_1STAmount.html">STAmount</a> <span class="keyword">const</span>&amp; lptAMMBalance,</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <a class="code hl_class" href="classripple_1_1STAmount.html">STAmount</a> <span class="keyword">const</span>&amp; lpTokens,</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> <span class="keywordtype">bool</span> isDeposit)</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span>{</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <span class="comment">// Force rounding downward to ensure adjusted tokens are less or equal</span></div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <span class="comment">// to requested tokens.</span></div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <a class="code hl_class" href="classripple_1_1saveNumberRoundMode.html">saveNumberRoundMode</a> rm(<a class="code hl_function" href="classripple_1_1Number.html#a9f2a0df7ad0f278908643927a19592f2">Number::setround</a>(<a class="code hl_enumvalue" href="classripple_1_1Number.html#a33e3d8e7a95979bd1eb22c59703c8534a25a8f50fce6cbdd3a8c0a3aa20126324">Number::rounding_mode::downward</a>));</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <span class="keywordflow">if</span> (isDeposit)</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> <span class="keywordflow">return</span> (lptAMMBalance + lpTokens) - lptAMMBalance;</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> <span class="keywordflow">return</span> (lpTokens - lptAMMBalance) + lptAMMBalance;</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span>}</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> </div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span><a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/utility/tuple.html">std::tuple&lt;STAmount, std::optional&lt;STAmount&gt;</a>, STAmount&gt;</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"><a class="line" href="namespaceripple.html#a5f936a9395ee6781feff5c6a13adacf1"> 147</a></span><a class="code hl_function" href="namespaceripple.html#a5f936a9395ee6781feff5c6a13adacf1">adjustAmountsByLPTokens</a>(</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> <a class="code hl_class" href="classripple_1_1STAmount.html">STAmount</a> <span class="keyword">const</span>&amp; amountBalance,</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> <a class="code hl_class" href="classripple_1_1STAmount.html">STAmount</a> <span class="keyword">const</span>&amp; amount,</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/utility/optional.html">std::optional&lt;STAmount&gt;</a> <span class="keyword">const</span>&amp; amount2,</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <a class="code hl_class" href="classripple_1_1STAmount.html">STAmount</a> <span class="keyword">const</span>&amp; lptAMMBalance,</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <a class="code hl_class" href="classripple_1_1STAmount.html">STAmount</a> <span class="keyword">const</span>&amp; lpTokens,</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> <a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint16_t</a> tfee,</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> <span class="keywordtype">bool</span> isDeposit)</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span>{</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="keyword">auto</span> <span class="keyword">const</span> lpTokensActual =</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <a class="code hl_function" href="namespaceripple.html#a0e17cbd5597a6159dfa1045e6b2e951e">adjustLPTokens</a>(lptAMMBalance, lpTokens, isDeposit);</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> </div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="keywordflow">if</span> (lpTokensActual == beast::zero)</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> {</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <span class="keyword">auto</span> <span class="keyword">const</span> amount2Opt =</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> amount2 ? <a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/utility/optional/make_optional.html">std::make_optional</a>(<a class="code hl_class" href="classripple_1_1STAmount.html">STAmount</a>{}) : std::nullopt;</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> <span class="keywordflow">return</span> <a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/utility/tuple/make_tuple.html">std::make_tuple</a>(<a class="code hl_class" href="classripple_1_1STAmount.html">STAmount</a>{}, amount2Opt, lpTokensActual);</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> }</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> </div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> <span class="keywordflow">if</span> (lpTokensActual &lt; lpTokens)</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> {</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> <span class="keywordtype">bool</span> <span class="keyword">const</span> ammRoundingEnabled = [&amp;]() {</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> <span class="keywordflow">if</span> (<span class="keyword">auto</span> <span class="keyword">const</span>&amp; rules = <a class="code hl_function" href="namespaceripple.html#ac46ee7ce49b6deed89f70a94924c416f">getCurrentTransactionRules</a>();</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> rules &amp;&amp; rules-&gt;enabled(fixAMMv1_1))</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> }();</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> </div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> <span class="comment">// Equal trade</span></div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> <span class="keywordflow">if</span> (amount2)</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> {</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> <a class="code hl_class" href="classripple_1_1Number.html">Number</a> <span class="keyword">const</span> fr = lpTokensActual / lpTokens;</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> <span class="keyword">auto</span> <span class="keyword">const</span> amountActual = <a class="code hl_function" href="namespaceripple.html#a4ad5ac9da897292a28eea43d041c15a1">toSTAmount</a>(amount.<a class="code hl_function" href="classripple_1_1STAmount.html#acab76380a95d902071fd26ab3425bbe5">issue</a>(), fr * amount);</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> <span class="keyword">auto</span> <span class="keyword">const</span> amount2Actual =</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> <a class="code hl_function" href="namespaceripple.html#a4ad5ac9da897292a28eea43d041c15a1">toSTAmount</a>(amount2-&gt;issue(), fr * *amount2);</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="keywordflow">if</span> (!ammRoundingEnabled)</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <span class="keywordflow">return</span> <a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/utility/tuple/make_tuple.html">std::make_tuple</a>(</div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> amountActual &lt; amount ? amountActual : amount,</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> amount2Actual &lt; amount2 ? amount2Actual : amount2,</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> lpTokensActual);</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <span class="keywordflow">return</span> <a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/utility/tuple/make_tuple.html">std::make_tuple</a>(</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> amountActual, amount2Actual, lpTokensActual);</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> }</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> </div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> <span class="comment">// Single trade</span></div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> <span class="keyword">auto</span> <span class="keyword">const</span> amountActual = [&amp;]() {</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <span class="keywordflow">if</span> (isDeposit)</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceripple.html#a573eb2cecf652856fc74fb1dfbaf8c2a">ammAssetIn</a>(</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> amountBalance, lptAMMBalance, lpTokensActual, tfee);</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (!ammRoundingEnabled)</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceripple.html#aea4620f7a5356019edee3be624729c6d">withdrawByTokens</a>(</div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> amountBalance, lptAMMBalance, lpTokens, tfee);</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceripple.html#aea4620f7a5356019edee3be624729c6d">withdrawByTokens</a>(</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> amountBalance, lptAMMBalance, lpTokensActual, tfee);</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> }();</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> <span class="keywordflow">if</span> (!ammRoundingEnabled)</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> <span class="keywordflow">return</span> amountActual &lt; amount</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> ? <a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/utility/tuple/make_tuple.html">std::make_tuple</a>(amountActual, std::nullopt, lpTokensActual)</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> : <a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/utility/tuple/make_tuple.html">std::make_tuple</a>(amount, std::nullopt, lpTokensActual);</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> <span class="keywordflow">return</span> <a class="code hl_functionRef" href="http://en.cppreference.com/w/cpp/utility/tuple/make_tuple.html">std::make_tuple</a>(amountActual, std::nullopt, lpTokensActual);</div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> }</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> </div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> XRPL_ASSERT(</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> lpTokensActual == lpTokens,</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> <span class="stringliteral">&quot;ripple::adjustAmountsByLPTokens : LP tokens match actual&quot;</span>);</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> </div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> <span class="keywordflow">return</span> {amount, amount2, lpTokensActual};</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span>}</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> </div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span>Number</div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"><a class="line" href="namespaceripple.html#a3d22714f28b806ea5c702eba2db5fbc2"> 220</a></span><a class="code hl_function" href="namespaceripple.html#a3d22714f28b806ea5c702eba2db5fbc2">solveQuadraticEq</a>(<a class="code hl_class" href="classripple_1_1Number.html">Number</a> <span class="keyword">const</span>&amp; a, <a class="code hl_class" href="classripple_1_1Number.html">Number</a> <span class="keyword">const</span>&amp; b, <a class="code hl_class" href="classripple_1_1Number.html">Number</a> <span class="keyword">const</span>&amp; c)</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span>{</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> <span class="keywordflow">return</span> (-b + <a class="code hl_function" href="namespaceripple.html#aecb9ae1add070266b1be59ff570ec713">root2</a>(b * b - 4 * a * c)) / (2 * a);</div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span>}</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> </div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span><span class="comment">// Minimize takerGets or takerPays</span></div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span><a class="code hl_classRef" href="http://en.cppreference.com/w/cpp/utility/optional.html">std::optional&lt;Number&gt;</a></div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"><a class="line" href="namespaceripple.html#a253fae38afa138d393a173425288eead"> 227</a></span><a class="code hl_function" href="namespaceripple.html#a253fae38afa138d393a173425288eead">solveQuadraticEqSmallest</a>(<a class="code hl_class" href="classripple_1_1Number.html">Number</a> <span class="keyword">const</span>&amp; a, <a class="code hl_class" href="classripple_1_1Number.html">Number</a> <span class="keyword">const</span>&amp; b, <a class="code hl_class" href="classripple_1_1Number.html">Number</a> <span class="keyword">const</span>&amp; c)</div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span>{</div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> <span class="keyword">auto</span> <span class="keyword">const</span> d = b * b - 4 * a * c;</div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> <span class="keywordflow">if</span> (d &lt; 0)</div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> <span class="keywordflow">return</span> std::nullopt;</div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> <span class="comment">// use numerically stable citardauq formula for quadratic equation solution</span></div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> <span class="comment">// https://people.csail.mit.edu/bkph/articles/Quadratics.pdf</span></div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> <span class="keywordflow">if</span> (b &gt; 0)</div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> <span class="keywordflow">return</span> (2 * c) / (-b - <a class="code hl_function" href="namespaceripple.html#aecb9ae1add070266b1be59ff570ec713">root2</a>(d));</div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> <span class="keywordflow">return</span> (2 * c) / (-b + <a class="code hl_function" href="namespaceripple.html#aecb9ae1add070266b1be59ff570ec713">root2</a>(d));</div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span>}</div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> </div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span>} <span class="comment">// namespace ripple</span></div>
<div class="ttc" id="aclassripple_1_1Issue_html"><div class="ttname"><a href="classripple_1_1Issue.html">ripple::Issue</a></div><div class="ttdoc">A currency issued by an account.</div><div class="ttdef"><b>Definition:</b> <a href="Issue_8h_source.html#l00035">Issue.h:36</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html"><div class="ttname"><a href="classripple_1_1Number.html">ripple::Number</a></div><div class="ttdef"><b>Definition:</b> <a href="Number_8h_source.html#l00035">Number.h:36</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a33e3d8e7a95979bd1eb22c59703c8534a25a8f50fce6cbdd3a8c0a3aa20126324"><div class="ttname"><a href="classripple_1_1Number.html#a33e3d8e7a95979bd1eb22c59703c8534a25a8f50fce6cbdd3a8c0a3aa20126324">ripple::Number::downward</a></div><div class="ttdeci">@ downward</div><div class="ttdef"><b>Definition:</b> <a href="Number_8h_source.html#l00178">Number.h:178</a></div></div>
<div class="ttc" id="aclassripple_1_1Number_html_a9f2a0df7ad0f278908643927a19592f2"><div class="ttname"><a href="classripple_1_1Number.html#a9f2a0df7ad0f278908643927a19592f2">ripple::Number::setround</a></div><div class="ttdeci">static rounding_mode setround(rounding_mode mode)</div><div class="ttdef"><b>Definition:</b> <a href="Number_8cpp_source.html#l00053">Number.cpp:53</a></div></div>
<div class="ttc" id="aclassripple_1_1STAmount_html"><div class="ttname"><a href="classripple_1_1STAmount.html">ripple::STAmount</a></div><div class="ttdef"><b>Definition:</b> <a href="STAmount_8h_source.html#l00049">STAmount.h:50</a></div></div>
<div class="ttc" id="aclassripple_1_1STAmount_html_acab76380a95d902071fd26ab3425bbe5"><div class="ttname"><a href="classripple_1_1STAmount.html#acab76380a95d902071fd26ab3425bbe5">ripple::STAmount::issue</a></div><div class="ttdeci">Issue const &amp; issue() const</div><div class="ttdef"><b>Definition:</b> <a href="STAmount_8h_source.html#l00496">STAmount.h:496</a></div></div>
<div class="ttc" id="aclassripple_1_1saveNumberRoundMode_html"><div class="ttname"><a href="classripple_1_1saveNumberRoundMode.html">ripple::saveNumberRoundMode</a></div><div class="ttdef"><b>Definition:</b> <a href="Number_8h_source.html#l00370">Number.h:371</a></div></div>
<div class="ttc" id="ainteger_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint16_t</a></div></div>
<div class="ttc" id="amake_optional_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/optional/make_optional.html">std::make_optional</a></div><div class="ttdeci">T make_optional(T... args)</div></div>
<div class="ttc" id="amake_tuple_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/tuple/make_tuple.html">std::make_tuple</a></div><div class="ttdeci">T make_tuple(T... args)</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="algorithm_8h_source.html#l00026">algorithm.h:26</a></div></div>
<div class="ttc" id="anamespaceripple_html_a0b2344222057d8b5b9923b2911962879"><div class="ttname"><a href="namespaceripple.html#a0b2344222057d8b5b9923b2911962879">ripple::lpTokensIn</a></div><div class="ttdeci">STAmount lpTokensIn(STAmount const &amp;asset1Balance, STAmount const &amp;asset1Deposit, STAmount const &amp;lptAMMBalance, std::uint16_t tfee)</div><div class="ttdoc">Calculate LP Tokens given asset's deposit amount.</div><div class="ttdef"><b>Definition:</b> <a href="AMMHelpers_8cpp_source.html#l00041">AMMHelpers.cpp:41</a></div></div>
<div class="ttc" id="anamespaceripple_html_a0e17cbd5597a6159dfa1045e6b2e951e"><div class="ttname"><a href="namespaceripple.html#a0e17cbd5597a6159dfa1045e6b2e951e">ripple::adjustLPTokens</a></div><div class="ttdeci">STAmount adjustLPTokens(STAmount const &amp;lptAMMBalance, STAmount const &amp;lpTokens, bool isDeposit)</div><div class="ttdoc">Adjust LP tokens to deposit/withdraw.</div><div class="ttdef"><b>Definition:</b> <a href="AMMHelpers_8cpp_source.html#l00133">AMMHelpers.cpp:133</a></div></div>
<div class="ttc" id="anamespaceripple_html_a253fae38afa138d393a173425288eead"><div class="ttname"><a href="namespaceripple.html#a253fae38afa138d393a173425288eead">ripple::solveQuadraticEqSmallest</a></div><div class="ttdeci">std::optional&lt; Number &gt; solveQuadraticEqSmallest(Number const &amp;a, Number const &amp;b, Number const &amp;c)</div><div class="ttdoc">Solve quadratic equation to find takerGets or takerPays.</div><div class="ttdef"><b>Definition:</b> <a href="AMMHelpers_8cpp_source.html#l00227">AMMHelpers.cpp:227</a></div></div>
<div class="ttc" id="anamespaceripple_html_a3d22714f28b806ea5c702eba2db5fbc2"><div class="ttname"><a href="namespaceripple.html#a3d22714f28b806ea5c702eba2db5fbc2">ripple::solveQuadraticEq</a></div><div class="ttdeci">Number solveQuadraticEq(Number const &amp;a, Number const &amp;b, Number const &amp;c)</div><div class="ttdoc">Positive solution for quadratic equation: x = (-b + sqrt(b**2 + 4*a*c))/(2*a)</div><div class="ttdef"><b>Definition:</b> <a href="AMMHelpers_8cpp_source.html#l00220">AMMHelpers.cpp:220</a></div></div>
<div class="ttc" id="anamespaceripple_html_a4ad5ac9da897292a28eea43d041c15a1"><div class="ttname"><a href="namespaceripple.html#a4ad5ac9da897292a28eea43d041c15a1">ripple::toSTAmount</a></div><div class="ttdeci">STAmount toSTAmount(IOUAmount const &amp;iou, Issue const &amp;iss)</div><div class="ttdef"><b>Definition:</b> <a href="AmountConversions_8h_source.html#l00032">AmountConversions.h:32</a></div></div>
<div class="ttc" id="anamespaceripple_html_a4c964d1f7629a28f9b916e2d25b39bcd"><div class="ttname"><a href="namespaceripple.html#a4c964d1f7629a28f9b916e2d25b39bcd">ripple::lpTokensOut</a></div><div class="ttdeci">STAmount lpTokensOut(STAmount const &amp;asset1Balance, STAmount const &amp;asset1Withdraw, STAmount const &amp;lptAMMBalance, std::uint16_t tfee)</div><div class="ttdoc">Calculate LP Tokens given asset's withdraw amount.</div><div class="ttdef"><b>Definition:</b> <a href="AMMHelpers_8cpp_source.html#l00090">AMMHelpers.cpp:90</a></div></div>
<div class="ttc" id="anamespaceripple_html_a573eb2cecf652856fc74fb1dfbaf8c2a"><div class="ttname"><a href="namespaceripple.html#a573eb2cecf652856fc74fb1dfbaf8c2a">ripple::ammAssetIn</a></div><div class="ttdeci">STAmount ammAssetIn(STAmount const &amp;asset1Balance, STAmount const &amp;lptAMMBalance, STAmount const &amp;lpTokens, std::uint16_t tfee)</div><div class="ttdoc">Calculate asset deposit given LP Tokens.</div><div class="ttdef"><b>Definition:</b> <a href="AMMHelpers_8cpp_source.html#l00067">AMMHelpers.cpp:67</a></div></div>
<div class="ttc" id="anamespaceripple_html_a58b7851104129e42da9c5260ba6f00d6"><div class="ttname"><a href="namespaceripple.html#a58b7851104129e42da9c5260ba6f00d6">ripple::square</a></div><div class="ttdeci">Number square(Number const &amp;n)</div><div class="ttdoc">Return square of n.</div><div class="ttdef"><b>Definition:</b> <a href="AMMHelpers_8cpp_source.html#l00127">AMMHelpers.cpp:127</a></div></div>
<div class="ttc" id="anamespaceripple_html_a5f936a9395ee6781feff5c6a13adacf1"><div class="ttname"><a href="namespaceripple.html#a5f936a9395ee6781feff5c6a13adacf1">ripple::adjustAmountsByLPTokens</a></div><div class="ttdeci">std::tuple&lt; STAmount, std::optional&lt; STAmount &gt;, STAmount &gt; adjustAmountsByLPTokens(STAmount const &amp;amountBalance, STAmount const &amp;amount, std::optional&lt; STAmount &gt; const &amp;amount2, STAmount const &amp;lptAMMBalance, STAmount const &amp;lpTokens, std::uint16_t tfee, bool isDeposit)</div><div class="ttdoc">Calls adjustLPTokens() and adjusts deposit or withdraw amounts if the adjusted LP tokens are less tha...</div><div class="ttdef"><b>Definition:</b> <a href="AMMHelpers_8cpp_source.html#l00147">AMMHelpers.cpp:147</a></div></div>
<div class="ttc" id="anamespaceripple_html_a7894756905fee556c1541cd1de1f697a"><div class="ttname"><a href="namespaceripple.html#a7894756905fee556c1541cd1de1f697a">ripple::feeMult</a></div><div class="ttdeci">Number feeMult(std::uint16_t tfee)</div><div class="ttdoc">Get fee multiplier (1 - tfee) @tfee trading fee in basis points.</div><div class="ttdef"><b>Definition:</b> <a href="AMMCore_8h_source.html#l00110">AMMCore.h:110</a></div></div>
<div class="ttc" id="anamespaceripple_html_aa8871e2f35cee24497183274c0bab5fd"><div class="ttname"><a href="namespaceripple.html#aa8871e2f35cee24497183274c0bab5fd">ripple::getFee</a></div><div class="ttdeci">Number getFee(std::uint16_t tfee)</div><div class="ttdoc">Convert to the fee from the basis points.</div><div class="ttdef"><b>Definition:</b> <a href="AMMCore_8h_source.html#l00101">AMMCore.h:101</a></div></div>
<div class="ttc" id="anamespaceripple_html_ab8defa1f235abbf44a60ccc6c71c6fdd"><div class="ttname"><a href="namespaceripple.html#ab8defa1f235abbf44a60ccc6c71c6fdd">ripple::ammLPTokens</a></div><div class="ttdeci">STAmount ammLPTokens(STAmount const &amp;asset1, STAmount const &amp;asset2, Issue const &amp;lptIssue)</div><div class="ttdoc">Calculate LP Tokens given AMM pool reserves.</div><div class="ttdef"><b>Definition:</b> <a href="AMMHelpers_8cpp_source.html#l00025">AMMHelpers.cpp:25</a></div></div>
<div class="ttc" id="anamespaceripple_html_ac46ee7ce49b6deed89f70a94924c416f"><div class="ttname"><a href="namespaceripple.html#ac46ee7ce49b6deed89f70a94924c416f">ripple::getCurrentTransactionRules</a></div><div class="ttdeci">std::optional&lt; Rules &gt; const &amp; getCurrentTransactionRules()</div><div class="ttdef"><b>Definition:</b> <a href="Rules_8cpp_source.html#l00047">Rules.cpp:47</a></div></div>
<div class="ttc" id="anamespaceripple_html_ac78c8c0642bbbe33db633286fa147381"><div class="ttname"><a href="namespaceripple.html#ac78c8c0642bbbe33db633286fa147381">ripple::feeMultHalf</a></div><div class="ttdeci">Number feeMultHalf(std::uint16_t tfee)</div><div class="ttdoc">Get fee multiplier (1 - tfee / 2) @tfee trading fee in basis points.</div><div class="ttdef"><b>Definition:</b> <a href="AMMCore_8h_source.html#l00119">AMMCore.h:119</a></div></div>
<div class="ttc" id="anamespaceripple_html_aea4620f7a5356019edee3be624729c6d"><div class="ttname"><a href="namespaceripple.html#aea4620f7a5356019edee3be624729c6d">ripple::withdrawByTokens</a></div><div class="ttdeci">STAmount withdrawByTokens(STAmount const &amp;assetBalance, STAmount const &amp;lptAMMBalance, STAmount const &amp;lpTokens, std::uint16_t tfee)</div><div class="ttdoc">Calculate asset withdrawal by tokens.</div><div class="ttdef"><b>Definition:</b> <a href="AMMHelpers_8cpp_source.html#l00114">AMMHelpers.cpp:114</a></div></div>
<div class="ttc" id="anamespaceripple_html_aecb9ae1add070266b1be59ff570ec713"><div class="ttname"><a href="namespaceripple.html#aecb9ae1add070266b1be59ff570ec713">ripple::root2</a></div><div class="ttdeci">Number root2(Number f)</div><div class="ttdef"><b>Definition:</b> <a href="Number_8cpp_source.html#l00701">Number.cpp:701</a></div></div>
<div class="ttc" id="aoptional_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/optional.html">std::optional</a></div></div>
<div class="ttc" id="atuple_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/tuple.html">std::tuple</a></div></div>
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