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<div class="title">al_Functions.hpp</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="preprocessor">#ifndef INCLUDE_AL_MATH_FUNCTIONS_HPP</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="preprocessor">#define INCLUDE_AL_MATH_FUNCTIONS_HPP</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span>  </div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">/* Allocore --</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> Multimedia / virtual environment application class library</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"></span> </div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> Copyright (C) 2009. AlloSphere Research Group, Media Arts & Technology, UCSB.</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> Copyright (C) 2012. The Regents of the University of California.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> All rights reserved.</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"></span> </div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> Redistribution and use in source and binary forms, with or without</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment"> modification, are permitted provided that the following conditions are met:</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment"></span> </div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment"> Redistributions of source code must retain the above copyright notice,</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"> this list of conditions and the following disclaimer.</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"></span> </div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"> Redistributions in binary form must reproduce the above copyright</span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment"> notice, this list of conditions and the following disclaimer in the</span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment"> documentation and/or other materials provided with the distribution.</span></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment"></span> </div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment"> Neither the name of the University of California nor the names of its</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment"> contributors may be used to endorse or promote products derived from</span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment"> this software without specific prior written permission.</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment"></span> </div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment"> THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment"> AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment"> IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment"> ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE</span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment"> LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR</span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment"> CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF</span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment"> SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS</span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment"> INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment"> CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)</span></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment"> ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment"> POSSIBILITY OF SUCH DAMAGE.</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment"></span> </div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment"></span> </div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment"> File description:</span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment"> This includes various commonly used mathematical functions that are not</span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment"> included in the standard C/C++ math libraries.</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment"></span> </div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment"> File author(s):</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment"> Lance Putnam, 2006, [email protected]</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment">*/</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  </div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="preprocessor">#include <algorithm></span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="preprocessor">#include <cmath></span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  </div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="preprocessor">#include "al/math/al_Constants.hpp"</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  </div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="keyword">namespace </span><a class="code" href="namespaceal.html">al</a> {</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  </div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  </div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="keywordtype">bool</span> <a class="code" href="group___math.html#gaf696ac053502524c47d03c83fa338304">aeq</a>(<span class="keywordtype">float</span> a, <span class="keywordtype">float</span> b, <span class="keywordtype">int</span> maxULP = 10);</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="keywordtype">bool</span> <a class="code" href="group___math.html#gaf696ac053502524c47d03c83fa338304">aeq</a>(<span class="keywordtype">double</span> a, <span class="keywordtype">double</span> b, <span class="keywordtype">int</span> maxULP = 10);</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  </div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00070"></a><span class="lineno"><a class="line" href="group___math.html#gaded4d9162eecb556e24c0f3cd2e958c5"> 70</a></span> <span class="keyword">inline</span> T <a class="code" href="group___math.html#gaded4d9162eecb556e24c0f3cd2e958c5">ampTodB</a>(<span class="keyword">const</span> T& amp) {</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="keywordflow">return</span> 20 * std::log(amp);</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> }</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  </div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> T <a class="code" href="group___math.html#gaf698361a52baaadf969f995f5c6c3f78">atLeast</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& eps);</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  </div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  </div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="comment">// Author: Jim Shima, http://www.dspguru.com/comp.dsp/tricks/alg/fxdatan2.htm.</span></div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="comment">// |error| < 0.01 rad</span></div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span> T <a class="code" href="group___math.html#gaf80f2ef3a7c49b63c8b76bf7a7a5fa26">atan2Fast</a>(<span class="keyword">const</span> T& y, <span class="keyword">const</span> T& x);</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  </div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  </div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span> uint32_t <a class="code" href="group___math.html#ga305a92788021baeaf04d5e9589a5ac34">bitsSet</a>(uint32_t v);</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  </div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span> T <a class="code" href="group___math.html#ga5871238946c53c69bbe794b38ba8574e">ceil</a>(<span class="keyword">const</span> T& val, <span class="keyword">const</span> T& step);</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span> T <a class="code" href="group___math.html#ga5871238946c53c69bbe794b38ba8574e">ceil</a>(<span class="keyword">const</span> T& val, <span class="keyword">const</span> T& step, <span class="keyword">const</span> T& recStep);</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  </div>
<div class="line"><a name="l00106"></a><span class="lineno"><a class="line" href="namespaceal.html#a33e80f1264f8b8d381667d3d9b6af5eb"> 106</a></span> <span class="keyword">inline</span> uint32_t <a class="code" href="namespaceal.html#a33e80f1264f8b8d381667d3d9b6af5eb">ceilEven</a>(uint32_t v) { <span class="keywordflow">return</span> v += v & 1UL; }</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  </div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  </div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span> uint32_t <a class="code" href="group___math.html#ga5b903297ac73ab3a1344e110589262d9">ceilPow2</a>(uint32_t value);</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  </div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span> T <a class="code" href="group___math.html#ga1ea1cc7b53231b0c0dd6e2095f300ef0">clip</a>(<span class="keyword">const</span> T& value, <span class="keyword">const</span> T& hi = T(1), <span class="keyword">const</span> T& lo = T(0));</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  </div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  </div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span> T <a class="code" href="group___math.html#ga1ea1cc7b53231b0c0dd6e2095f300ef0">clip</a>(<span class="keyword">const</span> T& v, <span class="keywordtype">int</span>& clipFlag, <span class="keyword">const</span> T& hi, <span class="keyword">const</span> T& lo);</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  </div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span> T <a class="code" href="group___math.html#gaf635f126b77657b51ce1a93a28fd9aef">clipS</a>(<span class="keyword">const</span> T& value, <span class="keyword">const</span> T& hi = T(1));</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  </div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00143"></a><span class="lineno"><a class="line" href="group___math.html#ga1352d5bea80358151c11f6524648ff9b"> 143</a></span> <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga1352d5bea80358151c11f6524648ff9b">dBToAmp</a>(<span class="keyword">const</span> T& db) {</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  return ::pow(10, db / 20.);</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span> }</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  </div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="keywordtype">bool</span> <a class="code" href="group___math.html#ga3aeccffdbab51e5b2cab2b97d025d002">even</a>(<span class="keyword">const</span> T& v);</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  </div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span> T <a class="code" href="group___math.html#gaa1601bdb71ac3809de1576cb4976ff31">erf</a>(<span class="keyword">const</span> T& v);</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  </div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span> uint32_t <a class="code" href="group___math.html#ga3f88bf4afda6ac9b12aa22873870d0b2">factorial</a>(uint32_t n0to12);</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  </div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <span class="keywordtype">double</span> <a class="code" href="group___math.html#gaba17591660c318242fc292ba64771585">factorialSqrt</a>(<span class="keywordtype">int</span> v);</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  </div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span> T <a class="code" href="group___math.html#ga5b81fa38c979ae94a7da92b3223ba2b8">floor</a>(<span class="keyword">const</span> T& val, <span class="keyword">const</span> T& step);</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span> T <a class="code" href="group___math.html#ga5b81fa38c979ae94a7da92b3223ba2b8">floor</a>(<span class="keyword">const</span> T& val, <span class="keyword">const</span> T& step, <span class="keyword">const</span> T& recStep);</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  </div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  </div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span> uint32_t <a class="code" href="group___math.html#gae6b0655a2902fa6cb1556442e127bc38">floorPow2</a>(uint32_t value);</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  </div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  </div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span> T <a class="code" href="group___math.html#gad1fb93acd3513290b5c4ac8f402ba808">fold</a>(<span class="keyword">const</span> T& value, <span class="keyword">const</span> T& hi = T(1), <span class="keyword">const</span> T& lo = T(0));</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  </div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span> T <a class="code" href="group___math.html#gab4556d3171dafe878f45a4a99c5dec7a">foldOnce</a>(<span class="keyword">const</span> T& value, <span class="keyword">const</span> T& hi = T(1), <span class="keyword">const</span> T& lo = T(0));</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  </div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span> T <a class="code" href="group___math.html#ga2090ba7150a810fd3de64b1d95d69e23">gaussian</a>(<span class="keyword">const</span> T& v);</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  </div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span> T <a class="code" href="group___math.html#ga433911d7b80de439047ca3e580e5684c">gcd</a>(<span class="keyword">const</span> T& x, <span class="keyword">const</span> T& y);</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  </div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="keyword">template</span> <<span class="keyword">typename</span> T, <span class="keyword">typename</span>... Ts></div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span> T <a class="code" href="group___math.html#ga433911d7b80de439047ca3e580e5684c">gcd</a>(<span class="keyword">const</span> T& x, <span class="keyword">const</span> Ts&... rest) {</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <span class="keywordflow">return</span> <a class="code" href="group___math.html#ga433911d7b80de439047ca3e580e5684c">gcd</a>(x, <a class="code" href="group___math.html#ga433911d7b80de439047ca3e580e5684c">gcd</a>(rest...));</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span> }</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  </div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span> T <a class="code" href="group___math.html#gad7d2d0cae8ef1a818a68519510c8988c">gudermannian</a>(<span class="keyword">const</span> T& x);</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  </div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  </div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span> T <a class="code" href="group___math.html#ga7b18bb9bb26fb7813665c8065cbcee70">laguerreL</a>(<span class="keywordtype">int</span> n, <span class="keywordtype">int</span> k, T x);</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  </div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span> T <a class="code" href="namespaceal.html#ac56a4133ca11265d616f22279bab5cf0">lcm</a>(<span class="keyword">const</span> T& x, <span class="keyword">const</span> T& y);</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  </div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span> T <a class="code" href="group___math.html#gaab3a1b08de897c27811f94bbeb74ff63">legendreP</a>(<span class="keywordtype">int</span> l, <span class="keywordtype">int</span> m, T t);</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span> T <a class="code" href="group___math.html#gaab3a1b08de897c27811f94bbeb74ff63">legendreP</a>(<span class="keywordtype">int</span> l, <span class="keywordtype">int</span> m, T ct, T st);</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  </div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span> <span class="keywordtype">bool</span> <a class="code" href="group___math.html#ga70d2bb9995e24c326bb1f8ca25c9b9e0">lessAbs</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& eps = T(0.000001));</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  </div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span> <span class="keyword">template</span> <<span class="keyword">typename</span> T></div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span> T <a class="code" href="group___math.html#ga7075f46376a9dcccc420f8dd1b329812">max</a>(<span class="keyword">const</span> T& v1, <span class="keyword">const</span> T& v2, <span class="keyword">const</span> T& v3);</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  </div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span> T <a class="code" href="group___math.html#ga4a4f53c3ebf1101824b0eb3c78f73527">mean</a>(<span class="keyword">const</span> T& v1, <span class="keyword">const</span> T& v2);</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  </div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span> T <a class="code" href="group___math.html#ga2fd420846f99fa0c8c500209a66995de">min</a>(<span class="keyword">const</span> T& v1, <span class="keyword">const</span> T& v2, <span class="keyword">const</span> T& v3);</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  </div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00288"></a><span class="lineno"><a class="line" href="group___math.html#ga9da403c39d92da43b4aae7c050e9844f"> 288</a></span> <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga9da403c39d92da43b4aae7c050e9844f">nearestDiv</a>(T of, T to) {</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="keywordflow">return</span> to / <a class="code" href="group___math.html#ga3d78c2574a648fcf2c44003c9768508b">round</a>(to / of);</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span> }</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  </div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span> T <a class="code" href="group___math.html#ga08f69403d6e66bb2afba2292d8ad254c">nextAfter</a>(<span class="keyword">const</span> T& x, <span class="keyword">const</span> T& y);</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  </div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span> T <a class="code" href="group___math.html#gad566fa512ff98f81749c473e18db371a">nextMultiple</a>(T val, T multiple);</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  </div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span> T <a class="code" href="group___math.html#ga5a6f3e643facd02a406d5f631474f828">numInt</a>(<span class="keyword">const</span> T& v);</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  </div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span> <span class="keywordtype">bool</span> <a class="code" href="group___math.html#ga6e43efc43f7570be467a4442d253f495">odd</a>(<span class="keyword">const</span> T& v);</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  </div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span> T <a class="code" href="group___math.html#gaf9e8b9459b8c99267685e1accc83014e">poly</a>(<span class="keyword">const</span> T& x, <span class="keyword">const</span> T& a0, <span class="keyword">const</span> T& a1, <span class="keyword">const</span> T& a2);</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  </div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00327"></a><span class="lineno"><a class="line" href="group___math.html#ga8c6e496eca0e958f3c2ccb62ee17a87a"> 327</a></span> T <a class="code" href="group___math.html#gaf9e8b9459b8c99267685e1accc83014e">poly</a>(<span class="keyword">const</span> T& x, <span class="keyword">const</span> T& a0, <span class="keyword">const</span> T& a1, <span class="keyword">const</span> T& a2, <span class="keyword">const</span> T& a3);</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  </div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span> T <a class="code" href="namespaceal.html#abba74f49192e7be9c40e6f5ae0374a4e">pow2</a>(<span class="keyword">const</span> T& v); </div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span> T <a class="code" href="namespaceal.html#a5663296abb030061b4b8f2876afb8a9e">pow2S</a>(<span class="keyword">const</span> T& v); </div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span> T <a class="code" href="namespaceal.html#ad521d0e693178a38d12ba76c18a92043">pow3</a>(<span class="keyword">const</span> T& v); </div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span> T <a class="code" href="namespaceal.html#ac24528b53a6f63b4dfb73005aabbc397">pow3Abs</a>(<span class="keyword">const</span> T& v); </div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span> T <a class="code" href="namespaceal.html#ac6741264b9e9ffffa2ffb9e6a499c605">pow4</a>(<span class="keyword">const</span> T& v); </div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span> T <a class="code" href="namespaceal.html#a923128df50bb424b9d16372e2fb63486">pow5</a>(<span class="keyword">const</span> T& v); </div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span> T <a class="code" href="namespaceal.html#a4f89fb4de6e8f159427db5fee670f5eb">pow6</a>(<span class="keyword">const</span> T& v); </div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span> T <a class="code" href="namespaceal.html#a3ce8228c4ac0dda43b8e75272cf420cc">pow8</a>(<span class="keyword">const</span> T& v); </div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span> T <a class="code" href="namespaceal.html#a786a459e7ec0fefca9a7b19b90f33737">pow16</a>(<span class="keyword">const</span> T& v); </div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span> T <a class="code" href="namespaceal.html#afc2d063be9e3fd40c983d81c66af9f81">pow64</a>(<span class="keyword">const</span> T& v); </div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  </div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  </div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span> T <a class="code" href="group___math.html#ga8168179e459a58e4b7fd5757fa928fa5">powN</a>(T base, <span class="keywordtype">unsigned</span> power);</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  </div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">char</span> <a class="code" href="group___math.html#ga5e15be42a4331a52661d87800cbfc512">prime</a>(uint32_t n);</div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  </div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span> T <a class="code" href="group___math.html#ga3d78c2574a648fcf2c44003c9768508b">round</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& step);</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  </div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span> T <a class="code" href="group___math.html#ga3d78c2574a648fcf2c44003c9768508b">round</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& step, <span class="keyword">const</span> T& recStep);</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  </div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span> T <a class="code" href="group___math.html#ga52522414f03221f7b6ee9875cfaea9f6">roundAway</a>(<span class="keyword">const</span> T& v);</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  </div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span> T <a class="code" href="group___math.html#ga52522414f03221f7b6ee9875cfaea9f6">roundAway</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& step);</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  </div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span> T <a class="code" href="group___math.html#ga4b9395462499c968255feefd8e974a93">sgn</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& norm = T(1));</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  </div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span> T <a class="code" href="group___math.html#gaaee09ed63c305f6ac32ecc141045062f">sinc</a>(<span class="keyword">const</span> T& radians, <span class="keyword">const</span> T& eps = T(0.0001));</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  </div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span> T <a class="code" href="group___math.html#gaa46708ab331be0d22136de6365a49338">slope</a>(<span class="keyword">const</span> T& x1, <span class="keyword">const</span> T& y1, <span class="keyword">const</span> T& x2, <span class="keyword">const</span> T& y2);</div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span>  </div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span> <span class="keywordtype">void</span> <a class="code" href="group___math.html#ga316b5a2949ca945618aab0c4f53ac0c5">sort</a>(T& value1, T& value2);</div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  </div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span> T <a class="code" href="group___math.html#ga5715feed6e8d122fb5e763ad7b9d29ec">sumOfSquares</a>(T n);</div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  </div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  </div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span> uint32_t <a class="code" href="group___math.html#ga5184860679d7dc5575231fb0af25a14d">trailingZeroes</a>(uint32_t v);</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  </div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span> T <a class="code" href="group___math.html#gab15dcba5bf53f93e28b7c7b0cdd10d03">trunc</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& step);</div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  </div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span> T <a class="code" href="group___math.html#gab15dcba5bf53f93e28b7c7b0cdd10d03">trunc</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& step, <span class="keyword">const</span> T& recStep);</div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  </div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span> <span class="keywordtype">bool</span> <a class="code" href="group___math.html#gaeb22e9d95c2ec10b05324cb054990476">within</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& lo, <span class="keyword">const</span> T& hi);</div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  </div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span> <span class="keywordtype">bool</span> <a class="code" href="group___math.html#ga7e2366116eaac9d1037af687bf5a3369">within3</a>(<span class="keyword">const</span> T& v1, <span class="keyword">const</span> T& v2, <span class="keyword">const</span> T& v3, <span class="keyword">const</span> T& lo, <span class="keyword">const</span> T& hi);</div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  </div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span> <span class="keywordtype">bool</span> <a class="code" href="group___math.html#ga402e95bb33a2573d222702e632c74d78">withinIE</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& lo, <span class="keyword">const</span> T& hi);</div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  </div>
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span> T <a class="code" href="group___math.html#gabab359a45740fff6e459019fab5975e2">wrap</a>(<span class="keyword">const</span> T& value, <span class="keyword">const</span> T& hi = T(1), <span class="keyword">const</span> T& lo = T(0));</div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  </div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  </div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span> T <a class="code" href="group___math.html#gabab359a45740fff6e459019fab5975e2">wrap</a>(<span class="keyword">const</span> T& value, <span class="keywordtype">long</span>& numWraps, <span class="keyword">const</span> T& hi = T(1), <span class="keyword">const</span> T& lo = T(0));</div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  </div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00479"></a><span class="lineno"><a class="line" href="group___math.html#ga02593b7bb80f83f51ef276ae288e6fec"> 479</a></span> T <a class="code" href="group___math.html#ga02593b7bb80f83f51ef276ae288e6fec">wrapAdd1</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& <a class="code" href="group___math.html#ga7075f46376a9dcccc420f8dd1b329812">max</a>) {</div>
<div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  ++v;</div>
<div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  <span class="keywordflow">return</span> v == <a class="code" href="group___math.html#ga7075f46376a9dcccc420f8dd1b329812">max</a> ? 0 : v;</div>
<div class="line"><a name="l00482"></a><span class="lineno"> 482</span> }</div>
<div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  </div>
<div class="line"><a name="l00487"></a><span class="lineno"> 487</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00488"></a><span class="lineno"> 488</span> T <a class="code" href="group___math.html#ga5ccb344df3f76c5eb8ec593ad894627a">wrapOnce</a>(<span class="keyword">const</span> T& value, <span class="keyword">const</span> T& hi = T(1));</div>
<div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  </div>
<div class="line"><a name="l00490"></a><span class="lineno"> 490</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span> T <a class="code" href="group___math.html#ga5ccb344df3f76c5eb8ec593ad894627a">wrapOnce</a>(<span class="keyword">const</span> T& value, <span class="keyword">const</span> T& hi, <span class="keyword">const</span> T& lo);</div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span>  </div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00497"></a><span class="lineno"> 497</span> T <a class="code" href="group___math.html#ga4911206e29f73da7441ea02255584d09">wrapPhase</a>(<span class="keyword">const</span> T& radians);</div>
<div class="line"><a name="l00498"></a><span class="lineno"> 498</span>  </div>
<div class="line"><a name="l00502"></a><span class="lineno"> 502</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00503"></a><span class="lineno"> 503</span> T <a class="code" href="group___math.html#ga7cdffae94bec1ea44587abb24231e617">wrapPhaseOnce</a>(<span class="keyword">const</span> T& radians);</div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  </div>
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span> <span class="comment">// Implementation</span></div>
<div class="line"><a name="l00506"></a><span class="lineno"> 506</span> <span class="comment">//------------------------------------------------------------------------------</span></div>
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  </div>
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span> <span class="preprocessor">#define TEM template <class T></span></div>
<div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  </div>
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span> <span class="keyword">namespace </span>{</div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span> <span class="keyword">const</span> T roundEps();</div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span> <span class="keyword">template</span> <></div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span> <span class="keyword">inline</span> <span class="keyword">const</span> <span class="keywordtype">float</span> roundEps<float>() {</div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  <span class="keywordflow">return</span> 0.499999925f;</div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span> }</div>
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span> <span class="keyword">template</span> <></div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span> <span class="keyword">inline</span> <span class="keyword">const</span> <span class="keywordtype">double</span> roundEps<double>() {</div>
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  <span class="keywordflow">return</span> 0.499999985;</div>
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span> }</div>
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  </div>
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span> <span class="keyword">inline</span> uint32_t deBruijn(uint32_t v) {</div>
<div class="line"><a name="l00523"></a><span class="lineno"> 523</span>  <span class="keyword">static</span> <span class="keyword">const</span> uint32_t deBruijnBitPosition[32] = {</div>
<div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  0, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15, 25, 17, 4, 8,</div>
<div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9};</div>
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  <span class="keywordflow">return</span> deBruijnBitPosition[(uint32_t(v * 0x077CB531UL)) >> 27];</div>
<div class="line"><a name="l00527"></a><span class="lineno"> 527</span> }</div>
<div class="line"><a name="l00528"></a><span class="lineno"> 528</span>  </div>
<div class="line"><a name="l00529"></a><span class="lineno"> 529</span> <span class="keyword">const</span> uint32_t mFactorial12u[13] = {1, 1, 2, 6, 24,</div>
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  120, 720, 5040, 40320, 362880,</div>
<div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  3628800, 39916800, 479001600};</div>
<div class="line"><a name="l00532"></a><span class="lineno"> 532</span>  </div>
<div class="line"><a name="l00533"></a><span class="lineno"> 533</span> <span class="keyword">const</span> uint8_t mPrimes54[54] = {</div>
<div class="line"><a name="l00534"></a><span class="lineno"> 534</span>  <span class="comment">/* 0 1 2 3 4 5 6 7 8 9 */</span></div>
<div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  2, 3, 5, 7, 11, 13, 17, 19, 23, 29, <span class="comment">// 0</span></div>
<div class="line"><a name="l00536"></a><span class="lineno"> 536</span>  31, 37, 41, 43, 47, 53, 59, 61, 67, 71, <span class="comment">// 1</span></div>
<div class="line"><a name="l00537"></a><span class="lineno"> 537</span>  73, 79, 83, 89, 97, 101, 103, 107, 109, 113, <span class="comment">// 2</span></div>
<div class="line"><a name="l00538"></a><span class="lineno"> 538</span>  127, 131, 137, 139, 149, 151, 157, 163, 167, 173, <span class="comment">// 3</span></div>
<div class="line"><a name="l00539"></a><span class="lineno"> 539</span>  179, 181, 191, 193, 197, 199, 211, 223, 227, 229, <span class="comment">// 4</span></div>
<div class="line"><a name="l00540"></a><span class="lineno"> 540</span>  233, 239, 241, 251 <span class="comment">// 5</span></div>
<div class="line"><a name="l00541"></a><span class="lineno"> 541</span> };</div>
<div class="line"><a name="l00542"></a><span class="lineno"> 542</span> } <span class="comment">// namespace</span></div>
<div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  </div>
<div class="line"><a name="l00544"></a><span class="lineno"><a class="line" href="group___math.html#gaf696ac053502524c47d03c83fa338304"> 544</a></span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="group___math.html#gaf696ac053502524c47d03c83fa338304">aeq</a>(<span class="keywordtype">float</span> a, <span class="keywordtype">float</span> b, <span class="keywordtype">int</span> maxULP) {</div>
<div class="line"><a name="l00545"></a><span class="lineno"> 545</span>  <span class="comment">// Make sure maxULP is non-negative and small enough that the</span></div>
<div class="line"><a name="l00546"></a><span class="lineno"> 546</span>  <span class="comment">// default NAN won't compare as equal to anything.</span></div>
<div class="line"><a name="l00547"></a><span class="lineno"> 547</span>  <span class="comment">// assert(maxULP > 0 && maxULP < 4 * 1024 * 1024);</span></div>
<div class="line"><a name="l00548"></a><span class="lineno"> 548</span>  <span class="keyword">union </span>{</div>
<div class="line"><a name="l00549"></a><span class="lineno"> 549</span>  <span class="keywordtype">float</span> f;</div>
<div class="line"><a name="l00550"></a><span class="lineno"> 550</span>  int32_t i;</div>
<div class="line"><a name="l00551"></a><span class="lineno"> 551</span>  } u;</div>
<div class="line"><a name="l00552"></a><span class="lineno"> 552</span>  u.f = a;</div>
<div class="line"><a name="l00553"></a><span class="lineno"> 553</span>  int32_t ai = u.i;</div>
<div class="line"><a name="l00554"></a><span class="lineno"> 554</span>  u.f = b;</div>
<div class="line"><a name="l00555"></a><span class="lineno"> 555</span>  int32_t bi = u.i;</div>
<div class="line"><a name="l00556"></a><span class="lineno"> 556</span>  <span class="comment">// Make ai and bi lexicographically ordered as a twos-complement int</span></div>
<div class="line"><a name="l00557"></a><span class="lineno"> 557</span>  <span class="keywordflow">if</span> (ai < 0) ai = 0x80000000 - ai;</div>
<div class="line"><a name="l00558"></a><span class="lineno"> 558</span>  <span class="keywordflow">if</span> (bi < 0) bi = 0x80000000 - bi;</div>
<div class="line"><a name="l00559"></a><span class="lineno"> 559</span>  <span class="keywordflow">return</span> std::abs((<span class="keywordtype">float</span>)(ai - bi)) <= maxULP;</div>
<div class="line"><a name="l00560"></a><span class="lineno"> 560</span> }</div>
<div class="line"><a name="l00561"></a><span class="lineno"> 561</span>  </div>
<div class="line"><a name="l00562"></a><span class="lineno"> 562</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="group___math.html#gaf696ac053502524c47d03c83fa338304">aeq</a>(<span class="keywordtype">double</span> a, <span class="keywordtype">double</span> b, <span class="keywordtype">int</span> maxULP) {</div>
<div class="line"><a name="l00563"></a><span class="lineno"> 563</span>  <span class="comment">// Make sure maxULP is non-negative and small enough that the</span></div>
<div class="line"><a name="l00564"></a><span class="lineno"> 564</span>  <span class="comment">// default NAN won't compare as equal to anything.</span></div>
<div class="line"><a name="l00565"></a><span class="lineno"> 565</span>  <span class="comment">// assert(maxULP > 0 && maxULP < 4 * 1024 * 1024);</span></div>
<div class="line"><a name="l00566"></a><span class="lineno"> 566</span>  <span class="keyword">union </span>{</div>
<div class="line"><a name="l00567"></a><span class="lineno"> 567</span>  <span class="keywordtype">double</span> f;</div>
<div class="line"><a name="l00568"></a><span class="lineno"> 568</span>  int64_t i;</div>
<div class="line"><a name="l00569"></a><span class="lineno"> 569</span>  } u;</div>
<div class="line"><a name="l00570"></a><span class="lineno"> 570</span>  u.f = a;</div>
<div class="line"><a name="l00571"></a><span class="lineno"> 571</span>  int64_t ai = u.i;</div>
<div class="line"><a name="l00572"></a><span class="lineno"> 572</span>  u.f = b;</div>
<div class="line"><a name="l00573"></a><span class="lineno"> 573</span>  int64_t bi = u.i;</div>
<div class="line"><a name="l00574"></a><span class="lineno"> 574</span>  <span class="comment">// Make ai and bi lexicographically ordered as a twos-complement int</span></div>
<div class="line"><a name="l00575"></a><span class="lineno"> 575</span>  <span class="keywordflow">if</span> (ai < 0) ai = 0x8000000000000000ULL - ai;</div>
<div class="line"><a name="l00576"></a><span class="lineno"> 576</span>  <span class="keywordflow">if</span> (bi < 0) bi = 0x8000000000000000ULL - bi;</div>
<div class="line"><a name="l00577"></a><span class="lineno"> 577</span>  <span class="keywordflow">return</span> std::abs((<span class="keywordtype">double</span>)(ai - bi)) <= maxULP;</div>
<div class="line"><a name="l00578"></a><span class="lineno"> 578</span> }</div>
<div class="line"><a name="l00579"></a><span class="lineno"> 579</span>  </div>
<div class="line"><a name="l00580"></a><span class="lineno"><a class="line" href="group___math.html#gaf698361a52baaadf969f995f5c6c3f78"> 580</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#gaf698361a52baaadf969f995f5c6c3f78">atLeast</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& e) {</div>
<div class="line"><a name="l00581"></a><span class="lineno"> 581</span>  <span class="keywordflow">return</span> (v >= T(0)) ? <a class="code" href="group___math.html#ga7075f46376a9dcccc420f8dd1b329812">std::max</a>(v, e) : <a class="code" href="group___math.html#ga2fd420846f99fa0c8c500209a66995de">std::min</a>(v, -e);</div>
<div class="line"><a name="l00582"></a><span class="lineno"> 582</span> }</div>
<div class="line"><a name="l00583"></a><span class="lineno"> 583</span>  </div>
<div class="line"><a name="l00584"></a><span class="lineno"><a class="line" href="group___math.html#gaf80f2ef3a7c49b63c8b76bf7a7a5fa26"> 584</a></span> TEM T <a class="code" href="group___math.html#gaf80f2ef3a7c49b63c8b76bf7a7a5fa26">atan2Fast</a>(<span class="keyword">const</span> T& y, <span class="keyword">const</span> T& x) {</div>
<div class="line"><a name="l00585"></a><span class="lineno"> 585</span>  T r, <a class="code" href="namespaceal.html#a7be5747e8d4348af7f9dda1bbf480ee4">angle</a>;</div>
<div class="line"><a name="l00586"></a><span class="lineno"> 586</span>  T ay = std::abs(y) + T(1e-10); <span class="comment">// kludge to prevent 0/0 condition</span></div>
<div class="line"><a name="l00587"></a><span class="lineno"> 587</span>  </div>
<div class="line"><a name="l00588"></a><span class="lineno"> 588</span>  <span class="keywordflow">if</span> (x < T(0)) {</div>
<div class="line"><a name="l00589"></a><span class="lineno"> 589</span>  r = (x + ay) / (ay - x);</div>
<div class="line"><a name="l00590"></a><span class="lineno"> 590</span>  <a class="code" href="namespaceal.html#a7be5747e8d4348af7f9dda1bbf480ee4">angle</a> = T(M_3PI_4);</div>
<div class="line"><a name="l00591"></a><span class="lineno"> 591</span>  } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00592"></a><span class="lineno"> 592</span>  r = (x - ay) / (x + ay);</div>
<div class="line"><a name="l00593"></a><span class="lineno"> 593</span>  <a class="code" href="namespaceal.html#a7be5747e8d4348af7f9dda1bbf480ee4">angle</a> = T(M_PI_4);</div>
<div class="line"><a name="l00594"></a><span class="lineno"> 594</span>  }</div>
<div class="line"><a name="l00595"></a><span class="lineno"> 595</span>  </div>
<div class="line"><a name="l00596"></a><span class="lineno"> 596</span>  <a class="code" href="namespaceal.html#a7be5747e8d4348af7f9dda1bbf480ee4">angle</a> += (T(0.1963) * r * r - T(0.9817)) * r;</div>
<div class="line"><a name="l00597"></a><span class="lineno"> 597</span>  <span class="keywordflow">return</span> y < T(0) ? -<a class="code" href="namespaceal.html#a7be5747e8d4348af7f9dda1bbf480ee4">angle</a> : <a class="code" href="namespaceal.html#a7be5747e8d4348af7f9dda1bbf480ee4">angle</a>;</div>
<div class="line"><a name="l00598"></a><span class="lineno"> 598</span> }</div>
<div class="line"><a name="l00599"></a><span class="lineno"> 599</span>  </div>
<div class="line"><a name="l00600"></a><span class="lineno"><a class="line" href="group___math.html#ga305a92788021baeaf04d5e9589a5ac34"> 600</a></span> <span class="keyword">inline</span> uint32_t <a class="code" href="group___math.html#ga305a92788021baeaf04d5e9589a5ac34">bitsSet</a>(uint32_t v) {</div>
<div class="line"><a name="l00601"></a><span class="lineno"> 601</span>  v = v - ((v >> 1) & 0x55555555); <span class="comment">// reuse input as temporary</span></div>
<div class="line"><a name="l00602"></a><span class="lineno"> 602</span>  v = (v & 0x33333333) + ((v >> 2) & 0x33333333); <span class="comment">// temp</span></div>
<div class="line"><a name="l00603"></a><span class="lineno"> 603</span>  <span class="keywordflow">return</span> ((v + ((v >> 4) & 0xF0F0F0F)) * 0x1010101) >> 24; <span class="comment">// count</span></div>
<div class="line"><a name="l00604"></a><span class="lineno"> 604</span> }</div>
<div class="line"><a name="l00605"></a><span class="lineno"> 605</span>  </div>
<div class="line"><a name="l00606"></a><span class="lineno"><a class="line" href="group___math.html#ga5871238946c53c69bbe794b38ba8574e"> 606</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga5871238946c53c69bbe794b38ba8574e">ceil</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& s) { <span class="keywordflow">return</span> <a class="code" href="group___math.html#ga5871238946c53c69bbe794b38ba8574e">std::ceil</a>(v / s) * s; }</div>
<div class="line"><a name="l00607"></a><span class="lineno"> 607</span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga5871238946c53c69bbe794b38ba8574e">ceil</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& s, <span class="keyword">const</span> T& r) {</div>
<div class="line"><a name="l00608"></a><span class="lineno"> 608</span>  <span class="keywordflow">return</span> <a class="code" href="group___math.html#ga5871238946c53c69bbe794b38ba8574e">std::ceil</a>(v * r) * s;</div>
<div class="line"><a name="l00609"></a><span class="lineno"> 609</span> }</div>
<div class="line"><a name="l00610"></a><span class="lineno"> 610</span>  </div>
<div class="line"><a name="l00611"></a><span class="lineno"><a class="line" href="group___math.html#ga5b903297ac73ab3a1344e110589262d9"> 611</a></span> <span class="keyword">inline</span> uint32_t <a class="code" href="group___math.html#ga5b903297ac73ab3a1344e110589262d9">ceilPow2</a>(uint32_t v) {</div>
<div class="line"><a name="l00612"></a><span class="lineno"> 612</span>  --v;</div>
<div class="line"><a name="l00613"></a><span class="lineno"> 613</span>  v |= v >> 1;</div>
<div class="line"><a name="l00614"></a><span class="lineno"> 614</span>  v |= v >> 2;</div>
<div class="line"><a name="l00615"></a><span class="lineno"> 615</span>  v |= v >> 4;</div>
<div class="line"><a name="l00616"></a><span class="lineno"> 616</span>  v |= v >> 8;</div>
<div class="line"><a name="l00617"></a><span class="lineno"> 617</span>  v |= v >> 16;</div>
<div class="line"><a name="l00618"></a><span class="lineno"> 618</span>  <span class="keywordflow">return</span> v + 1;</div>
<div class="line"><a name="l00619"></a><span class="lineno"> 619</span> }</div>
<div class="line"><a name="l00620"></a><span class="lineno"> 620</span>  </div>
<div class="line"><a name="l00621"></a><span class="lineno"><a class="line" href="group___math.html#ga1ea1cc7b53231b0c0dd6e2095f300ef0"> 621</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga1ea1cc7b53231b0c0dd6e2095f300ef0">clip</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& hi, <span class="keyword">const</span> T& lo) {</div>
<div class="line"><a name="l00622"></a><span class="lineno"> 622</span>  <span class="keywordflow">if</span> (v < lo)</div>
<div class="line"><a name="l00623"></a><span class="lineno"> 623</span>  <span class="keywordflow">return</span> lo;</div>
<div class="line"><a name="l00624"></a><span class="lineno"> 624</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (v > hi)</div>
<div class="line"><a name="l00625"></a><span class="lineno"> 625</span>  <span class="keywordflow">return</span> hi;</div>
<div class="line"><a name="l00626"></a><span class="lineno"> 626</span>  <span class="keywordflow">return</span> v;</div>
<div class="line"><a name="l00627"></a><span class="lineno"> 627</span> }</div>
<div class="line"><a name="l00628"></a><span class="lineno"> 628</span>  </div>
<div class="line"><a name="l00629"></a><span class="lineno"><a class="line" href="group___math.html#gaf11d0c3a9a3ebbb2c84efe447003f919"> 629</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga1ea1cc7b53231b0c0dd6e2095f300ef0">clip</a>(<span class="keyword">const</span> T& v, <span class="keywordtype">int</span>& clipFlag, <span class="keyword">const</span> T& hi, <span class="keyword">const</span> T& lo) {</div>
<div class="line"><a name="l00630"></a><span class="lineno"> 630</span>  clipFlag = 0;</div>
<div class="line"><a name="l00631"></a><span class="lineno"> 631</span>  <span class="keywordflow">if</span> (v < lo) {</div>
<div class="line"><a name="l00632"></a><span class="lineno"> 632</span>  clipFlag = -1;</div>
<div class="line"><a name="l00633"></a><span class="lineno"> 633</span>  <span class="keywordflow">return</span> lo;</div>
<div class="line"><a name="l00634"></a><span class="lineno"> 634</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (v > hi) {</div>
<div class="line"><a name="l00635"></a><span class="lineno"> 635</span>  clipFlag = 1;</div>
<div class="line"><a name="l00636"></a><span class="lineno"> 636</span>  <span class="keywordflow">return</span> hi;</div>
<div class="line"><a name="l00637"></a><span class="lineno"> 637</span>  }</div>
<div class="line"><a name="l00638"></a><span class="lineno"> 638</span>  <span class="keywordflow">return</span> v;</div>
<div class="line"><a name="l00639"></a><span class="lineno"> 639</span> }</div>
<div class="line"><a name="l00640"></a><span class="lineno"> 640</span>  </div>
<div class="line"><a name="l00641"></a><span class="lineno"><a class="line" href="group___math.html#gaf635f126b77657b51ce1a93a28fd9aef"> 641</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#gaf635f126b77657b51ce1a93a28fd9aef">clipS</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& hi) { <span class="keywordflow">return</span> <a class="code" href="group___math.html#ga1ea1cc7b53231b0c0dd6e2095f300ef0">al::clip</a>(v, hi, -hi); }</div>
<div class="line"><a name="l00642"></a><span class="lineno"> 642</span>  </div>
<div class="line"><a name="l00643"></a><span class="lineno"><a class="line" href="group___math.html#ga3aeccffdbab51e5b2cab2b97d025d002"> 643</a></span> TEM <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="group___math.html#ga3aeccffdbab51e5b2cab2b97d025d002">even</a>(<span class="keyword">const</span> T& v) { <span class="keywordflow">return</span> 0 == <a class="code" href="group___math.html#ga6e43efc43f7570be467a4442d253f495">al::odd</a>(v); }</div>
<div class="line"><a name="l00644"></a><span class="lineno"> 644</span>  </div>
<div class="line"><a name="l00646"></a><span class="lineno"><a class="line" href="group___math.html#gaa1601bdb71ac3809de1576cb4976ff31"> 646</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#gaa1601bdb71ac3809de1576cb4976ff31">erf</a>(<span class="keyword">const</span> T& x) {</div>
<div class="line"><a name="l00647"></a><span class="lineno"> 647</span>  <span class="keyword">static</span> T a = 0.147;</div>
<div class="line"><a name="l00648"></a><span class="lineno"> 648</span>  <span class="keyword">const</span> T x2 = x * x;</div>
<div class="line"><a name="l00649"></a><span class="lineno"> 649</span>  <span class="keyword">const</span> T ax2 = a * x2;</div>
<div class="line"><a name="l00650"></a><span class="lineno"> 650</span>  <span class="keywordflow">return</span> <a class="code" href="group___math.html#ga4b9395462499c968255feefd8e974a93">al::sgn</a>(x) *</div>
<div class="line"><a name="l00651"></a><span class="lineno"> 651</span>  std::sqrt(T(1) - std::exp(-x2 * (T(4. / M_PI) + ax2) / (T(1) + ax2)));</div>
<div class="line"><a name="l00652"></a><span class="lineno"> 652</span> }</div>
<div class="line"><a name="l00653"></a><span class="lineno"> 653</span>  </div>
<div class="line"><a name="l00654"></a><span class="lineno"><a class="line" href="group___math.html#ga3f88bf4afda6ac9b12aa22873870d0b2"> 654</a></span> <span class="keyword">inline</span> uint32_t <a class="code" href="group___math.html#ga3f88bf4afda6ac9b12aa22873870d0b2">factorial</a>(uint32_t v) { <span class="keywordflow">return</span> mFactorial12u[v]; }</div>
<div class="line"><a name="l00655"></a><span class="lineno"> 655</span>  </div>
<div class="line"><a name="l00656"></a><span class="lineno"><a class="line" href="group___math.html#gaba17591660c318242fc292ba64771585"> 656</a></span> <span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code" href="group___math.html#gaba17591660c318242fc292ba64771585">factorialSqrt</a>(<span class="keywordtype">int</span> v) {</div>
<div class="line"><a name="l00657"></a><span class="lineno"> 657</span>  <span class="keywordflow">if</span> (v <= 1) <span class="keywordflow">return</span> 1;</div>
<div class="line"><a name="l00658"></a><span class="lineno"> 658</span>  <span class="keywordtype">double</span> r = 1;</div>
<div class="line"><a name="l00659"></a><span class="lineno"> 659</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 2; i <= v; ++i) r *= std::sqrt(i);</div>
<div class="line"><a name="l00660"></a><span class="lineno"> 660</span>  <span class="keywordflow">return</span> r;</div>
<div class="line"><a name="l00661"></a><span class="lineno"> 661</span> }</div>
<div class="line"><a name="l00662"></a><span class="lineno"> 662</span>  </div>
<div class="line"><a name="l00663"></a><span class="lineno"><a class="line" href="group___math.html#ga5b81fa38c979ae94a7da92b3223ba2b8"> 663</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga5b81fa38c979ae94a7da92b3223ba2b8">floor</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& s) { <span class="keywordflow">return</span> <a class="code" href="group___math.html#ga5b81fa38c979ae94a7da92b3223ba2b8">std::floor</a>(v / s) * s; }</div>
<div class="line"><a name="l00664"></a><span class="lineno"> 664</span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga5b81fa38c979ae94a7da92b3223ba2b8">floor</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& s, <span class="keyword">const</span> T& r) {</div>
<div class="line"><a name="l00665"></a><span class="lineno"> 665</span>  <span class="keywordflow">return</span> <a class="code" href="group___math.html#ga5b81fa38c979ae94a7da92b3223ba2b8">std::floor</a>(v * r) * s;</div>
<div class="line"><a name="l00666"></a><span class="lineno"> 666</span> }</div>
<div class="line"><a name="l00667"></a><span class="lineno"> 667</span>  </div>
<div class="line"><a name="l00668"></a><span class="lineno"><a class="line" href="group___math.html#gae6b0655a2902fa6cb1556442e127bc38"> 668</a></span> <span class="keyword">inline</span> uint32_t <a class="code" href="group___math.html#gae6b0655a2902fa6cb1556442e127bc38">floorPow2</a>(uint32_t v) {</div>
<div class="line"><a name="l00669"></a><span class="lineno"> 669</span>  v |= v >> 1;</div>
<div class="line"><a name="l00670"></a><span class="lineno"> 670</span>  v |= v >> 2;</div>
<div class="line"><a name="l00671"></a><span class="lineno"> 671</span>  v |= v >> 4;</div>
<div class="line"><a name="l00672"></a><span class="lineno"> 672</span>  v |= v >> 8;</div>
<div class="line"><a name="l00673"></a><span class="lineno"> 673</span>  v |= v >> 16;</div>
<div class="line"><a name="l00674"></a><span class="lineno"> 674</span>  <span class="keywordflow">return</span> (v >> 1) + 1;</div>
<div class="line"><a name="l00675"></a><span class="lineno"> 675</span> }</div>
<div class="line"><a name="l00676"></a><span class="lineno"> 676</span>  </div>
<div class="line"><a name="l00677"></a><span class="lineno"><a class="line" href="group___math.html#gad1fb93acd3513290b5c4ac8f402ba808"> 677</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#gad1fb93acd3513290b5c4ac8f402ba808">fold</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& hi, <span class="keyword">const</span> T& lo) {</div>
<div class="line"><a name="l00678"></a><span class="lineno"> 678</span>  <span class="keywordtype">long</span> numWraps;</div>
<div class="line"><a name="l00679"></a><span class="lineno"> 679</span>  T R = <a class="code" href="group___math.html#gabab359a45740fff6e459019fab5975e2">al::wrap</a>(v, numWraps, hi, lo);</div>
<div class="line"><a name="l00680"></a><span class="lineno"> 680</span>  <span class="keywordflow">if</span> (numWraps & 1) R = hi + lo - R;</div>
<div class="line"><a name="l00681"></a><span class="lineno"> 681</span>  <span class="keywordflow">return</span> R;</div>
<div class="line"><a name="l00682"></a><span class="lineno"> 682</span> }</div>
<div class="line"><a name="l00683"></a><span class="lineno"> 683</span>  </div>
<div class="line"><a name="l00684"></a><span class="lineno"><a class="line" href="group___math.html#gab4556d3171dafe878f45a4a99c5dec7a"> 684</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#gab4556d3171dafe878f45a4a99c5dec7a">foldOnce</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& hi, <span class="keyword">const</span> T& lo) {</div>
<div class="line"><a name="l00685"></a><span class="lineno"> 685</span>  <span class="keywordflow">if</span> (v > hi) <span class="keywordflow">return</span> hi + (hi - v);</div>
<div class="line"><a name="l00686"></a><span class="lineno"> 686</span>  <span class="keywordflow">if</span> (v < lo) <span class="keywordflow">return</span> lo + (lo - v);</div>
<div class="line"><a name="l00687"></a><span class="lineno"> 687</span>  <span class="keywordflow">return</span> v;</div>
<div class="line"><a name="l00688"></a><span class="lineno"> 688</span> }</div>
<div class="line"><a name="l00689"></a><span class="lineno"> 689</span>  </div>
<div class="line"><a name="l00690"></a><span class="lineno"><a class="line" href="group___math.html#ga2090ba7150a810fd3de64b1d95d69e23"> 690</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga2090ba7150a810fd3de64b1d95d69e23">gaussian</a>(<span class="keyword">const</span> T& v) { <span class="keywordflow">return</span> std::exp(-v * v); }</div>
<div class="line"><a name="l00691"></a><span class="lineno"> 691</span>  </div>
<div class="line"><a name="l00692"></a><span class="lineno"><a class="line" href="group___math.html#ga433911d7b80de439047ca3e580e5684c"> 692</a></span> TEM T <a class="code" href="group___math.html#ga433911d7b80de439047ca3e580e5684c">gcd</a>(<span class="keyword">const</span> T& x, <span class="keyword">const</span> T& y) {</div>
<div class="line"><a name="l00693"></a><span class="lineno"> 693</span>  <span class="keywordflow">if</span> (y == T(0)) <span class="keywordflow">return</span> std::abs(x);</div>
<div class="line"><a name="l00694"></a><span class="lineno"> 694</span>  <span class="keywordflow">return</span> <a class="code" href="group___math.html#ga433911d7b80de439047ca3e580e5684c">al::gcd</a>(y, <span class="keyword">static_cast<</span>T<span class="keyword">></span>(std::remainder(x, y)));</div>
<div class="line"><a name="l00695"></a><span class="lineno"> 695</span> }</div>
<div class="line"><a name="l00696"></a><span class="lineno"> 696</span>  </div>
<div class="line"><a name="l00698"></a><span class="lineno"><a class="line" href="group___math.html#gad7d2d0cae8ef1a818a68519510c8988c"> 698</a></span> TEM T <a class="code" href="group___math.html#gad7d2d0cae8ef1a818a68519510c8988c">gudermannian</a>(<span class="keyword">const</span> T& x) { <span class="keywordflow">return</span> T(2) * std::atan(exp(x)) - T(M_PI_2); }</div>
<div class="line"><a name="l00699"></a><span class="lineno"> 699</span>  </div>
<div class="line"><a name="l00700"></a><span class="lineno"><a class="line" href="group___math.html#ga7b18bb9bb26fb7813665c8065cbcee70"> 700</a></span> TEM T <a class="code" href="group___math.html#ga7b18bb9bb26fb7813665c8065cbcee70">laguerreL</a>(<span class="keywordtype">int</span> n, <span class="keywordtype">int</span> k, T x) {</div>
<div class="line"><a name="l00701"></a><span class="lineno"> 701</span>  <span class="comment">// T res = 1, bin = 1;</span></div>
<div class="line"><a name="l00702"></a><span class="lineno"> 702</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00703"></a><span class="lineno"> 703</span>  <span class="comment">// for(int i=n; i>=1; --i){</span></div>
<div class="line"><a name="l00704"></a><span class="lineno"> 704</span>  <span class="comment">// bin = bin * (k+i) / (n + 1 - i);</span></div>
<div class="line"><a name="l00705"></a><span class="lineno"> 705</span>  <span class="comment">// res = bin - x * res / i;</span></div>
<div class="line"><a name="l00706"></a><span class="lineno"> 706</span>  <span class="comment">// }</span></div>
<div class="line"><a name="l00707"></a><span class="lineno"> 707</span>  <span class="comment">// return res;</span></div>
<div class="line"><a name="l00708"></a><span class="lineno"> 708</span>  </div>
<div class="line"><a name="l00709"></a><span class="lineno"> 709</span>  <span class="keywordflow">if</span> (n < 0) <span class="keywordflow">return</span> T(0);</div>
<div class="line"><a name="l00710"></a><span class="lineno"> 710</span>  </div>
<div class="line"><a name="l00711"></a><span class="lineno"> 711</span>  T L1 = 0, R = 1;</div>
<div class="line"><a name="l00712"></a><span class="lineno"> 712</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i <= n; ++i) {</div>
<div class="line"><a name="l00713"></a><span class="lineno"> 713</span>  T L0 = L1;</div>
<div class="line"><a name="l00714"></a><span class="lineno"> 714</span>  L1 = R;</div>
<div class="line"><a name="l00715"></a><span class="lineno"> 715</span>  R = ((2 * i + k - 1 - x) * L1 - (i + k - 1) * L0) / i;</div>
<div class="line"><a name="l00716"></a><span class="lineno"> 716</span>  }</div>
<div class="line"><a name="l00717"></a><span class="lineno"> 717</span>  <span class="keywordflow">return</span> R;</div>
<div class="line"><a name="l00718"></a><span class="lineno"> 718</span> }</div>
<div class="line"><a name="l00719"></a><span class="lineno"> 719</span>  </div>
<div class="line"><a name="l00720"></a><span class="lineno"><a class="line" href="namespaceal.html#ac56a4133ca11265d616f22279bab5cf0"> 720</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="namespaceal.html#ac56a4133ca11265d616f22279bab5cf0">lcm</a>(<span class="keyword">const</span> T& x, <span class="keyword">const</span> T& y) { <span class="keywordflow">return</span> (x * y) / <a class="code" href="group___math.html#ga433911d7b80de439047ca3e580e5684c">al::gcd</a>(x, y); }</div>
<div class="line"><a name="l00721"></a><span class="lineno"> 721</span>  </div>
<div class="line"><a name="l00722"></a><span class="lineno"> 722</span> TEM T <a class="code" href="group___math.html#gaab3a1b08de897c27811f94bbeb74ff63">legendreP</a>(<span class="keywordtype">int</span> l, <span class="keywordtype">int</span> m, T ct, T st) {</div>
<div class="line"><a name="l00723"></a><span class="lineno"> 723</span>  <span class="keywordflow">switch</span> (l) {</div>
<div class="line"><a name="l00724"></a><span class="lineno"> 724</span>  <span class="keywordflow">case</span> 0:</div>
<div class="line"><a name="l00725"></a><span class="lineno"> 725</span>  <span class="keywordflow">return</span> 1.;</div>
<div class="line"><a name="l00726"></a><span class="lineno"> 726</span>  </div>
<div class="line"><a name="l00727"></a><span class="lineno"> 727</span>  <span class="keywordflow">case</span> 1:</div>
<div class="line"><a name="l00728"></a><span class="lineno"> 728</span>  <span class="keywordflow">switch</span> (m) {</div>
<div class="line"><a name="l00729"></a><span class="lineno"> 729</span>  <span class="keywordflow">case</span> 0:</div>
<div class="line"><a name="l00730"></a><span class="lineno"> 730</span>  <span class="keywordflow">return</span> ct;</div>
<div class="line"><a name="l00731"></a><span class="lineno"> 731</span>  <span class="keywordflow">case</span> 1:</div>
<div class="line"><a name="l00732"></a><span class="lineno"> 732</span>  <span class="keywordflow">return</span> -st;</div>
<div class="line"><a name="l00733"></a><span class="lineno"> 733</span>  <span class="keywordflow">default</span>:</div>
<div class="line"><a name="l00734"></a><span class="lineno"> 734</span>  <span class="keywordflow">return</span> 0.;</div>
<div class="line"><a name="l00735"></a><span class="lineno"> 735</span>  }</div>
<div class="line"><a name="l00736"></a><span class="lineno"> 736</span>  </div>
<div class="line"><a name="l00737"></a><span class="lineno"> 737</span>  <span class="keywordflow">case</span> 2:</div>
<div class="line"><a name="l00738"></a><span class="lineno"> 738</span>  <span class="keywordflow">switch</span> (m) {</div>
<div class="line"><a name="l00739"></a><span class="lineno"> 739</span>  <span class="keywordflow">case</span> 0:</div>
<div class="line"><a name="l00740"></a><span class="lineno"> 740</span>  <span class="keywordflow">return</span> -0.5 + 1.5 * ct * ct;</div>
<div class="line"><a name="l00741"></a><span class="lineno"> 741</span>  <span class="keywordflow">case</span> 1:</div>
<div class="line"><a name="l00742"></a><span class="lineno"> 742</span>  <span class="keywordflow">return</span> -3.0 * ct * st;</div>
<div class="line"><a name="l00743"></a><span class="lineno"> 743</span>  <span class="keywordflow">case</span> 2:</div>
<div class="line"><a name="l00744"></a><span class="lineno"> 744</span>  <span class="keywordflow">return</span> 3.0 * st * st;</div>
<div class="line"><a name="l00745"></a><span class="lineno"> 745</span>  <span class="keywordflow">default</span>:</div>
<div class="line"><a name="l00746"></a><span class="lineno"> 746</span>  <span class="keywordflow">return</span> 0.;</div>
<div class="line"><a name="l00747"></a><span class="lineno"> 747</span>  }</div>
<div class="line"><a name="l00748"></a><span class="lineno"> 748</span>  </div>
<div class="line"><a name="l00749"></a><span class="lineno"> 749</span>  <span class="keywordflow">case</span> 3:</div>
<div class="line"><a name="l00750"></a><span class="lineno"> 750</span>  <span class="keywordflow">switch</span> (m) {</div>
<div class="line"><a name="l00751"></a><span class="lineno"> 751</span>  <span class="keywordflow">case</span> 0:</div>
<div class="line"><a name="l00752"></a><span class="lineno"> 752</span>  <span class="keywordflow">return</span> ct * (-1.5 + 2.5 * ct * ct);</div>
<div class="line"><a name="l00753"></a><span class="lineno"> 753</span>  <span class="keywordflow">case</span> 1:</div>
<div class="line"><a name="l00754"></a><span class="lineno"> 754</span>  <span class="keywordflow">return</span> (1.5 - 7.5 * ct * ct) * st;</div>
<div class="line"><a name="l00755"></a><span class="lineno"> 755</span>  <span class="keywordflow">case</span> 2:</div>
<div class="line"><a name="l00756"></a><span class="lineno"> 756</span>  <span class="keywordflow">return</span> 15. * ct * st * st;</div>
<div class="line"><a name="l00757"></a><span class="lineno"> 757</span>  <span class="keywordflow">case</span> 3:</div>
<div class="line"><a name="l00758"></a><span class="lineno"> 758</span>  <span class="keywordflow">return</span> -15. * st * st * st;</div>
<div class="line"><a name="l00759"></a><span class="lineno"> 759</span>  <span class="keywordflow">default</span>:</div>
<div class="line"><a name="l00760"></a><span class="lineno"> 760</span>  <span class="keywordflow">return</span> 0.;</div>
<div class="line"><a name="l00761"></a><span class="lineno"> 761</span>  }</div>
<div class="line"><a name="l00762"></a><span class="lineno"> 762</span>  </div>
<div class="line"><a name="l00763"></a><span class="lineno"> 763</span>  <span class="keywordflow">case</span> 4:</div>
<div class="line"><a name="l00764"></a><span class="lineno"> 764</span>  <span class="keywordflow">switch</span> (m) {</div>
<div class="line"><a name="l00765"></a><span class="lineno"> 765</span>  <span class="keywordflow">case</span> 0:</div>
<div class="line"><a name="l00766"></a><span class="lineno"> 766</span>  ct *= ct;</div>
<div class="line"><a name="l00767"></a><span class="lineno"> 767</span>  <span class="keywordflow">return</span> 0.375 + ct * (-3.75 + 4.375 * ct);</div>
<div class="line"><a name="l00768"></a><span class="lineno"> 768</span>  <span class="keywordflow">case</span> 1:</div>
<div class="line"><a name="l00769"></a><span class="lineno"> 769</span>  <span class="keywordflow">return</span> ct * (7.5 - 17.5 * ct * ct) * st;</div>
<div class="line"><a name="l00770"></a><span class="lineno"> 770</span>  <span class="keywordflow">case</span> 2:</div>
<div class="line"><a name="l00771"></a><span class="lineno"> 771</span>  <span class="keywordflow">return</span> (-7.5 + 52.5 * ct * ct) * st * st;</div>
<div class="line"><a name="l00772"></a><span class="lineno"> 772</span>  <span class="keywordflow">case</span> 3:</div>
<div class="line"><a name="l00773"></a><span class="lineno"> 773</span>  <span class="keywordflow">return</span> -105. * ct * st * st * st;</div>
<div class="line"><a name="l00774"></a><span class="lineno"> 774</span>  <span class="keywordflow">case</span> 4:</div>
<div class="line"><a name="l00775"></a><span class="lineno"> 775</span>  st *= st;</div>
<div class="line"><a name="l00776"></a><span class="lineno"> 776</span>  <span class="keywordflow">return</span> 105. * st * st;</div>
<div class="line"><a name="l00777"></a><span class="lineno"> 777</span>  <span class="keywordflow">default</span>:</div>
<div class="line"><a name="l00778"></a><span class="lineno"> 778</span>  <span class="keywordflow">return</span> 0.;</div>
<div class="line"><a name="l00779"></a><span class="lineno"> 779</span>  }</div>
<div class="line"><a name="l00780"></a><span class="lineno"> 780</span>  </div>
<div class="line"><a name="l00781"></a><span class="lineno"> 781</span>  <span class="keywordflow">default</span>:;</div>
<div class="line"><a name="l00782"></a><span class="lineno"> 782</span>  }</div>
<div class="line"><a name="l00783"></a><span class="lineno"> 783</span>  </div>
<div class="line"><a name="l00784"></a><span class="lineno"> 784</span>  <span class="comment">// if(l<0){ /*printf("l=%d. l must be non-negative.\n");*/ return 0; }</span></div>
<div class="line"><a name="l00785"></a><span class="lineno"> 785</span>  <span class="comment">// if(m<-l || m>l){ /*printf("m=%d. m must be -l <= m <= l.\n");*/ return 0;</span></div>
<div class="line"><a name="l00786"></a><span class="lineno"> 786</span>  <span class="comment">// }</span></div>
<div class="line"><a name="l00787"></a><span class="lineno"> 787</span>  </div>
<div class="line"><a name="l00788"></a><span class="lineno"> 788</span>  <span class="comment">// First compute answer for |m|</span></div>
<div class="line"><a name="l00789"></a><span class="lineno"> 789</span>  </div>
<div class="line"><a name="l00790"></a><span class="lineno"> 790</span>  <span class="comment">// compute P_l^m(x) by the recurrence relation</span></div>
<div class="line"><a name="l00791"></a><span class="lineno"> 791</span>  <span class="comment">// (l-m)P_l^m(x) = x(2l-1)P_{l-1}^m(x) - (l+m-1)P_{l-2}^m(x)</span></div>
<div class="line"><a name="l00792"></a><span class="lineno"> 792</span>  <span class="comment">// with</span></div>
<div class="line"><a name="l00793"></a><span class="lineno"> 793</span>  <span class="comment">// P_m^m(x) = (-1)^m (2m-1)!! (1-x)^{m/2},</span></div>
<div class="line"><a name="l00794"></a><span class="lineno"> 794</span>  <span class="comment">// P_{m+1}^m(x) = x(2m+1) P_m^m(x).</span></div>
<div class="line"><a name="l00795"></a><span class="lineno"> 795</span>  </div>
<div class="line"><a name="l00796"></a><span class="lineno"> 796</span>  T P = 0; <span class="comment">// the result</span></div>
<div class="line"><a name="l00797"></a><span class="lineno"> 797</span>  <span class="keywordtype">int</span> M = std::abs((<span class="keywordtype">double</span>)m); <span class="comment">// M = |m|</span></div>
<div class="line"><a name="l00798"></a><span class="lineno"> 798</span>  T y1 = 1.; <span class="comment">// recursion state variable</span></div>
<div class="line"><a name="l00799"></a><span class="lineno"> 799</span>  </div>
<div class="line"><a name="l00800"></a><span class="lineno"> 800</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i <= M; ++i) y1 *= -((i << 1) - 1) * st;</div>
<div class="line"><a name="l00801"></a><span class="lineno"> 801</span>  </div>
<div class="line"><a name="l00802"></a><span class="lineno"> 802</span>  <span class="keywordflow">if</span> (l == M)</div>
<div class="line"><a name="l00803"></a><span class="lineno"> 803</span>  P = y1;</div>
<div class="line"><a name="l00804"></a><span class="lineno"> 804</span>  </div>
<div class="line"><a name="l00805"></a><span class="lineno"> 805</span>  <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00806"></a><span class="lineno"> 806</span>  T y = ((M << 1) + 1) * ct * y1;</div>
<div class="line"><a name="l00807"></a><span class="lineno"> 807</span>  <span class="keywordflow">if</span> (l == (M + 1))</div>
<div class="line"><a name="l00808"></a><span class="lineno"> 808</span>  P = y;</div>
<div class="line"><a name="l00809"></a><span class="lineno"> 809</span>  </div>
<div class="line"><a name="l00810"></a><span class="lineno"> 810</span>  <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00811"></a><span class="lineno"> 811</span>  T c = (M << 1) - 1;</div>
<div class="line"><a name="l00812"></a><span class="lineno"> 812</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = M + 2; k <= l; ++k) {</div>
<div class="line"><a name="l00813"></a><span class="lineno"> 813</span>  T y2 = y1;</div>
<div class="line"><a name="l00814"></a><span class="lineno"> 814</span>  y1 = y;</div>
<div class="line"><a name="l00815"></a><span class="lineno"> 815</span>  T d = c / (k - M);</div>
<div class="line"><a name="l00816"></a><span class="lineno"> 816</span>  y = (2. + d) * ct * y1 - (1. + d) * y2;</div>
<div class="line"><a name="l00817"></a><span class="lineno"> 817</span>  }</div>
<div class="line"><a name="l00818"></a><span class="lineno"> 818</span>  P = y;</div>
<div class="line"><a name="l00819"></a><span class="lineno"> 819</span>  }</div>
<div class="line"><a name="l00820"></a><span class="lineno"> 820</span>  }</div>
<div class="line"><a name="l00821"></a><span class="lineno"> 821</span>  </div>
<div class="line"><a name="l00822"></a><span class="lineno"> 822</span>  <span class="comment">// // In the case that m<0,</span></div>
<div class="line"><a name="l00823"></a><span class="lineno"> 823</span>  <span class="comment">// // compute P_n^{-|m|}(x) by the formula</span></div>
<div class="line"><a name="l00824"></a><span class="lineno"> 824</span>  <span class="comment">// // P_l^{-|m|}(x) = (-1)^{|m|}((l-|m|)!/(l+|m|)!)^{1/2} P_l^{|m|}(x).</span></div>
<div class="line"><a name="l00825"></a><span class="lineno"> 825</span>  <span class="comment">// // NOTE: when l and |m| are large, we risk numerical underflow...</span></div>
<div class="line"><a name="l00826"></a><span class="lineno"> 826</span>  <span class="comment">// if(m<0){</span></div>
<div class="line"><a name="l00827"></a><span class="lineno"> 827</span>  <span class="comment">// for(int i=l-M+1; i<=l+M; ++i) P *= 1. / i;</span></div>
<div class="line"><a name="l00828"></a><span class="lineno"> 828</span>  <span class="comment">// if(al::odd(M)) P = -P;</span></div>
<div class="line"><a name="l00829"></a><span class="lineno"> 829</span>  <span class="comment">// }</span></div>
<div class="line"><a name="l00830"></a><span class="lineno"> 830</span>  </div>
<div class="line"><a name="l00831"></a><span class="lineno"> 831</span>  <span class="keywordflow">return</span> P;</div>
<div class="line"><a name="l00832"></a><span class="lineno"> 832</span> }</div>
<div class="line"><a name="l00833"></a><span class="lineno"> 833</span>  </div>
<div class="line"><a name="l00834"></a><span class="lineno"><a class="line" href="group___math.html#gaab3a1b08de897c27811f94bbeb74ff63"> 834</a></span> TEM T <a class="code" href="group___math.html#gaab3a1b08de897c27811f94bbeb74ff63">legendreP</a>(<span class="keywordtype">int</span> l, <span class="keywordtype">int</span> m, T t) {</div>
<div class="line"><a name="l00835"></a><span class="lineno"> 835</span>  <span class="keywordflow">return</span> <a class="code" href="group___math.html#gaab3a1b08de897c27811f94bbeb74ff63">al::legendreP</a>(l, m, std::cos(t), std::sin(t));</div>
<div class="line"><a name="l00836"></a><span class="lineno"> 836</span> }</div>
<div class="line"><a name="l00837"></a><span class="lineno"> 837</span>  </div>
<div class="line"><a name="l00838"></a><span class="lineno"><a class="line" href="group___math.html#ga70d2bb9995e24c326bb1f8ca25c9b9e0"> 838</a></span> TEM <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="group___math.html#ga70d2bb9995e24c326bb1f8ca25c9b9e0">lessAbs</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& eps) { <span class="keywordflow">return</span> std::abs(v) < eps; }</div>
<div class="line"><a name="l00839"></a><span class="lineno"> 839</span>  </div>
<div class="line"><a name="l00840"></a><span class="lineno"><a class="line" href="group___math.html#ga7075f46376a9dcccc420f8dd1b329812"> 840</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga7075f46376a9dcccc420f8dd1b329812">max</a>(<span class="keyword">const</span> T& v1, <span class="keyword">const</span> T& v2, <span class="keyword">const</span> T& v3) {</div>
<div class="line"><a name="l00841"></a><span class="lineno"> 841</span>  <span class="keywordflow">return</span> <a class="code" href="group___math.html#ga7075f46376a9dcccc420f8dd1b329812">std::max</a>(<a class="code" href="group___math.html#ga7075f46376a9dcccc420f8dd1b329812">std::max</a>(v1, v2), v3);</div>
<div class="line"><a name="l00842"></a><span class="lineno"> 842</span> }</div>
<div class="line"><a name="l00843"></a><span class="lineno"><a class="line" href="group___math.html#ga4a4f53c3ebf1101824b0eb3c78f73527"> 843</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga4a4f53c3ebf1101824b0eb3c78f73527">mean</a>(<span class="keyword">const</span> T& v1, <span class="keyword">const</span> T& v2) { <span class="keywordflow">return</span> (v1 + v2) * T(0.5); }</div>
<div class="line"><a name="l00844"></a><span class="lineno"><a class="line" href="group___math.html#ga2fd420846f99fa0c8c500209a66995de"> 844</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga2fd420846f99fa0c8c500209a66995de">min</a>(<span class="keyword">const</span> T& v1, <span class="keyword">const</span> T& v2, <span class="keyword">const</span> T& v3) {</div>
<div class="line"><a name="l00845"></a><span class="lineno"> 845</span>  <span class="keywordflow">return</span> <a class="code" href="group___math.html#ga2fd420846f99fa0c8c500209a66995de">std::min</a>(<a class="code" href="group___math.html#ga2fd420846f99fa0c8c500209a66995de">std::min</a>(v1, v2), v3);</div>
<div class="line"><a name="l00846"></a><span class="lineno"> 846</span> }</div>
<div class="line"><a name="l00847"></a><span class="lineno"> 847</span>  </div>
<div class="line"><a name="l00848"></a><span class="lineno"> 848</span> <span class="preprocessor">#ifdef __MSYS__</span></div>
<div class="line"><a name="l00849"></a><span class="lineno"> 849</span> <span class="comment">// MSYS2 does not support C++11 std::nextafter like it should</span></div>
<div class="line"><a name="l00850"></a><span class="lineno"> 850</span> <span class="keyword">template</span> <<span class="keyword">class</span> T></div>
<div class="line"><a name="l00851"></a><span class="lineno"> 851</span> <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga08f69403d6e66bb2afba2292d8ad254c">nextAfter</a>(<span class="keyword">const</span> T& x, <span class="keyword">const</span> T& y) {</div>
<div class="line"><a name="l00852"></a><span class="lineno"> 852</span>  <span class="keywordflow">return</span> x < y ? x + 1 : x - 1;</div>
<div class="line"><a name="l00853"></a><span class="lineno"> 853</span> }</div>
<div class="line"><a name="l00854"></a><span class="lineno"> 854</span> <span class="keyword">template</span> <></div>
<div class="line"><a name="l00855"></a><span class="lineno"> 855</span> <span class="keyword">inline</span> <span class="keywordtype">float</span> <a class="code" href="group___math.html#ga08f69403d6e66bb2afba2292d8ad254c">nextAfter</a>(<span class="keyword">const</span> <span class="keywordtype">float</span>& x, <span class="keyword">const</span> <span class="keywordtype">float</span>& y) {</div>
<div class="line"><a name="l00856"></a><span class="lineno"> 856</span>  <span class="keywordflow">return</span> nextafterf(x, y);</div>
<div class="line"><a name="l00857"></a><span class="lineno"> 857</span> }</div>
<div class="line"><a name="l00858"></a><span class="lineno"> 858</span> <span class="keyword">template</span> <></div>
<div class="line"><a name="l00859"></a><span class="lineno"> 859</span> <span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code" href="group___math.html#ga08f69403d6e66bb2afba2292d8ad254c">nextAfter</a>(<span class="keyword">const</span> <span class="keywordtype">double</span>& x, <span class="keyword">const</span> <span class="keywordtype">double</span>& y) {</div>
<div class="line"><a name="l00860"></a><span class="lineno"> 860</span>  <span class="keywordflow">return</span> nextafter(x, y);</div>
<div class="line"><a name="l00861"></a><span class="lineno"> 861</span> }</div>
<div class="line"><a name="l00862"></a><span class="lineno"> 862</span> <span class="preprocessor">#else</span></div>
<div class="line"><a name="l00863"></a><span class="lineno"><a class="line" href="group___math.html#ga08f69403d6e66bb2afba2292d8ad254c"> 863</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga08f69403d6e66bb2afba2292d8ad254c">nextAfter</a>(<span class="keyword">const</span> T& x, <span class="keyword">const</span> T& y) { <span class="keywordflow">return</span> std::nextafter(x, y); }</div>
<div class="line"><a name="l00864"></a><span class="lineno"> 864</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00865"></a><span class="lineno"> 865</span>  </div>
<div class="line"><a name="l00866"></a><span class="lineno"><a class="line" href="group___math.html#gad566fa512ff98f81749c473e18db371a"> 866</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#gad566fa512ff98f81749c473e18db371a">nextMultiple</a>(T v, T m) {</div>
<div class="line"><a name="l00867"></a><span class="lineno"> 867</span>  uint32_t div = (uint32_t)(v / m);</div>
<div class="line"><a name="l00868"></a><span class="lineno"> 868</span>  <span class="keywordflow">return</span> T(div + 1) * m;</div>
<div class="line"><a name="l00869"></a><span class="lineno"> 869</span> }</div>
<div class="line"><a name="l00870"></a><span class="lineno"> 870</span>  </div>
<div class="line"><a name="l00871"></a><span class="lineno"><a class="line" href="group___math.html#ga5a6f3e643facd02a406d5f631474f828"> 871</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga5a6f3e643facd02a406d5f631474f828">numInt</a>(<span class="keyword">const</span> T& v) { <span class="keywordflow">return</span> <a class="code" href="group___math.html#ga5b81fa38c979ae94a7da92b3223ba2b8">std::floor</a>(std::log10(v)) + 1; }</div>
<div class="line"><a name="l00872"></a><span class="lineno"> 872</span>  </div>
<div class="line"><a name="l00873"></a><span class="lineno"><a class="line" href="group___math.html#ga6e43efc43f7570be467a4442d253f495"> 873</a></span> TEM <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="group___math.html#ga6e43efc43f7570be467a4442d253f495">odd</a>(<span class="keyword">const</span> T& v) { <span class="keywordflow">return</span> v & T(1); }</div>
<div class="line"><a name="l00874"></a><span class="lineno"> 874</span>  </div>
<div class="line"><a name="l00875"></a><span class="lineno"><a class="line" href="group___math.html#gaf9e8b9459b8c99267685e1accc83014e"> 875</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#gaf9e8b9459b8c99267685e1accc83014e">poly</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& a0, <span class="keyword">const</span> T& a1, <span class="keyword">const</span> T& a2) {</div>
<div class="line"><a name="l00876"></a><span class="lineno"> 876</span>  <span class="keywordflow">return</span> a0 + v * (a1 + v * a2);</div>
<div class="line"><a name="l00877"></a><span class="lineno"> 877</span> }</div>
<div class="line"><a name="l00878"></a><span class="lineno"> 878</span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#gaf9e8b9459b8c99267685e1accc83014e">poly</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& a0, <span class="keyword">const</span> T& a1, <span class="keyword">const</span> T& a2, T a3) {</div>
<div class="line"><a name="l00879"></a><span class="lineno"> 879</span>  <span class="keywordflow">return</span> a0 + v * (a1 + v * (a2 + v * a3));</div>
<div class="line"><a name="l00880"></a><span class="lineno"> 880</span> }</div>
<div class="line"><a name="l00881"></a><span class="lineno"> 881</span>  </div>
<div class="line"><a name="l00882"></a><span class="lineno"><a class="line" href="namespaceal.html#abba74f49192e7be9c40e6f5ae0374a4e"> 882</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="namespaceal.html#abba74f49192e7be9c40e6f5ae0374a4e">pow2</a>(<span class="keyword">const</span> T& v) { <span class="keywordflow">return</span> v * v; }</div>
<div class="line"><a name="l00883"></a><span class="lineno"><a class="line" href="namespaceal.html#a5663296abb030061b4b8f2876afb8a9e"> 883</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="namespaceal.html#a5663296abb030061b4b8f2876afb8a9e">pow2S</a>(<span class="keyword">const</span> T& v) { <span class="keywordflow">return</span> v * std::abs(v); }</div>
<div class="line"><a name="l00884"></a><span class="lineno"><a class="line" href="namespaceal.html#ad521d0e693178a38d12ba76c18a92043"> 884</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="namespaceal.html#ad521d0e693178a38d12ba76c18a92043">pow3</a>(<span class="keyword">const</span> T& v) { <span class="keywordflow">return</span> v * v * v; }</div>
<div class="line"><a name="l00885"></a><span class="lineno"><a class="line" href="namespaceal.html#ac24528b53a6f63b4dfb73005aabbc397"> 885</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="namespaceal.html#ac24528b53a6f63b4dfb73005aabbc397">pow3Abs</a>(<span class="keyword">const</span> T& v) { <span class="keywordflow">return</span> std::abs(<a class="code" href="namespaceal.html#ad521d0e693178a38d12ba76c18a92043">pow3</a>(v)); }</div>
<div class="line"><a name="l00886"></a><span class="lineno"><a class="line" href="namespaceal.html#ac6741264b9e9ffffa2ffb9e6a499c605"> 886</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="namespaceal.html#ac6741264b9e9ffffa2ffb9e6a499c605">pow4</a>(<span class="keyword">const</span> T& v) { <span class="keywordflow">return</span> <a class="code" href="namespaceal.html#abba74f49192e7be9c40e6f5ae0374a4e">pow2</a>(<a class="code" href="namespaceal.html#abba74f49192e7be9c40e6f5ae0374a4e">pow2</a>(v)); }</div>
<div class="line"><a name="l00887"></a><span class="lineno"><a class="line" href="namespaceal.html#a923128df50bb424b9d16372e2fb63486"> 887</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="namespaceal.html#a923128df50bb424b9d16372e2fb63486">pow5</a>(<span class="keyword">const</span> T& v) { <span class="keywordflow">return</span> v * <a class="code" href="namespaceal.html#ac6741264b9e9ffffa2ffb9e6a499c605">pow4</a>(v); }</div>
<div class="line"><a name="l00888"></a><span class="lineno"><a class="line" href="namespaceal.html#a4f89fb4de6e8f159427db5fee670f5eb"> 888</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="namespaceal.html#a4f89fb4de6e8f159427db5fee670f5eb">pow6</a>(<span class="keyword">const</span> T& v) { <span class="keywordflow">return</span> <a class="code" href="namespaceal.html#ad521d0e693178a38d12ba76c18a92043">pow3</a>(<a class="code" href="namespaceal.html#abba74f49192e7be9c40e6f5ae0374a4e">pow2</a>(v)); }</div>
<div class="line"><a name="l00889"></a><span class="lineno"><a class="line" href="namespaceal.html#a3ce8228c4ac0dda43b8e75272cf420cc"> 889</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="namespaceal.html#a3ce8228c4ac0dda43b8e75272cf420cc">pow8</a>(<span class="keyword">const</span> T& v) { <span class="keywordflow">return</span> <a class="code" href="namespaceal.html#ac6741264b9e9ffffa2ffb9e6a499c605">pow4</a>(<a class="code" href="namespaceal.html#abba74f49192e7be9c40e6f5ae0374a4e">pow2</a>(v)); }</div>
<div class="line"><a name="l00890"></a><span class="lineno"><a class="line" href="namespaceal.html#a786a459e7ec0fefca9a7b19b90f33737"> 890</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="namespaceal.html#a786a459e7ec0fefca9a7b19b90f33737">pow16</a>(<span class="keyword">const</span> T& v) { <span class="keywordflow">return</span> <a class="code" href="namespaceal.html#ac6741264b9e9ffffa2ffb9e6a499c605">pow4</a>(<a class="code" href="namespaceal.html#ac6741264b9e9ffffa2ffb9e6a499c605">pow4</a>(v)); }</div>
<div class="line"><a name="l00891"></a><span class="lineno"><a class="line" href="namespaceal.html#afc2d063be9e3fd40c983d81c66af9f81"> 891</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="namespaceal.html#afc2d063be9e3fd40c983d81c66af9f81">pow64</a>(<span class="keyword">const</span> T& v) { <span class="keywordflow">return</span> <a class="code" href="namespaceal.html#a3ce8228c4ac0dda43b8e75272cf420cc">pow8</a>(<a class="code" href="namespaceal.html#a3ce8228c4ac0dda43b8e75272cf420cc">pow8</a>(v)); }</div>
<div class="line"><a name="l00892"></a><span class="lineno"> 892</span>  </div>
<div class="line"><a name="l00893"></a><span class="lineno"><a class="line" href="group___math.html#ga8168179e459a58e4b7fd5757fa928fa5"> 893</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga8168179e459a58e4b7fd5757fa928fa5">powN</a>(T base, <span class="keywordtype">unsigned</span> power) {</div>
<div class="line"><a name="l00894"></a><span class="lineno"> 894</span>  <span class="keywordflow">switch</span> (power) {</div>
<div class="line"><a name="l00895"></a><span class="lineno"> 895</span>  <span class="keywordflow">case</span> 0:</div>
<div class="line"><a name="l00896"></a><span class="lineno"> 896</span>  <span class="keywordflow">return</span> T(1);</div>
<div class="line"><a name="l00897"></a><span class="lineno"> 897</span>  <span class="keywordflow">case</span> 1:</div>
<div class="line"><a name="l00898"></a><span class="lineno"> 898</span>  <span class="keywordflow">return</span> base;</div>
<div class="line"><a name="l00899"></a><span class="lineno"> 899</span>  <span class="keywordflow">case</span> 2:</div>
<div class="line"><a name="l00900"></a><span class="lineno"> 900</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceal.html#abba74f49192e7be9c40e6f5ae0374a4e">pow2</a>(base);</div>
<div class="line"><a name="l00901"></a><span class="lineno"> 901</span>  <span class="keywordflow">case</span> 3:</div>
<div class="line"><a name="l00902"></a><span class="lineno"> 902</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceal.html#ad521d0e693178a38d12ba76c18a92043">pow3</a>(base);</div>
<div class="line"><a name="l00903"></a><span class="lineno"> 903</span>  <span class="keywordflow">case</span> 4:</div>
<div class="line"><a name="l00904"></a><span class="lineno"> 904</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceal.html#ac6741264b9e9ffffa2ffb9e6a499c605">pow4</a>(base);</div>
<div class="line"><a name="l00905"></a><span class="lineno"> 905</span>  <span class="keywordflow">case</span> 5:</div>
<div class="line"><a name="l00906"></a><span class="lineno"> 906</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceal.html#a923128df50bb424b9d16372e2fb63486">pow5</a>(base);</div>
<div class="line"><a name="l00907"></a><span class="lineno"> 907</span>  <span class="keywordflow">case</span> 6:</div>
<div class="line"><a name="l00908"></a><span class="lineno"> 908</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceal.html#a4f89fb4de6e8f159427db5fee670f5eb">pow6</a>(base);</div>
<div class="line"><a name="l00909"></a><span class="lineno"> 909</span>  <span class="keywordflow">case</span> 7:</div>
<div class="line"><a name="l00910"></a><span class="lineno"> 910</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceal.html#a4f89fb4de6e8f159427db5fee670f5eb">pow6</a>(base) * base;</div>
<div class="line"><a name="l00911"></a><span class="lineno"> 911</span>  <span class="keywordflow">case</span> 8:</div>
<div class="line"><a name="l00912"></a><span class="lineno"> 912</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceal.html#a3ce8228c4ac0dda43b8e75272cf420cc">pow8</a>(base);</div>
<div class="line"><a name="l00913"></a><span class="lineno"> 913</span>  <span class="keywordflow">case</span> 9:</div>
<div class="line"><a name="l00914"></a><span class="lineno"> 914</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceal.html#a3ce8228c4ac0dda43b8e75272cf420cc">pow8</a>(base) * base;</div>
<div class="line"><a name="l00915"></a><span class="lineno"> 915</span>  <span class="keywordflow">default</span>: {</div>
<div class="line"><a name="l00916"></a><span class="lineno"> 916</span>  T r = <a class="code" href="namespaceal.html#a3ce8228c4ac0dda43b8e75272cf420cc">pow8</a>(base) * <a class="code" href="namespaceal.html#abba74f49192e7be9c40e6f5ae0374a4e">pow2</a>(base);</div>
<div class="line"><a name="l00917"></a><span class="lineno"> 917</span>  <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> i = 10; i < power; ++i) r *= base;</div>
<div class="line"><a name="l00918"></a><span class="lineno"> 918</span>  <span class="keywordflow">return</span> r;</div>
<div class="line"><a name="l00919"></a><span class="lineno"> 919</span>  }</div>
<div class="line"><a name="l00920"></a><span class="lineno"> 920</span>  }</div>
<div class="line"><a name="l00921"></a><span class="lineno"> 921</span> }</div>
<div class="line"><a name="l00922"></a><span class="lineno"> 922</span>  </div>
<div class="line"><a name="l00923"></a><span class="lineno"><a class="line" href="group___math.html#ga5e15be42a4331a52661d87800cbfc512"> 923</a></span> <span class="keyword">inline</span> uint8_t <a class="code" href="group___math.html#ga5e15be42a4331a52661d87800cbfc512">prime</a>(uint32_t n) { <span class="keywordflow">return</span> mPrimes54[n]; }</div>
<div class="line"><a name="l00924"></a><span class="lineno"> 924</span>  </div>
<div class="line"><a name="l00925"></a><span class="lineno"><a class="line" href="group___math.html#ga3d78c2574a648fcf2c44003c9768508b"> 925</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga3d78c2574a648fcf2c44003c9768508b">round</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& s) { <span class="keywordflow">return</span> <a class="code" href="group___math.html#gad568f4267154f330c142cb1605e885b1">std::round</a>(v / s) * s; }</div>
<div class="line"><a name="l00926"></a><span class="lineno"><a class="line" href="group___math.html#gad568f4267154f330c142cb1605e885b1"> 926</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga3d78c2574a648fcf2c44003c9768508b">round</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& s, <span class="keyword">const</span> T& r) {</div>
<div class="line"><a name="l00927"></a><span class="lineno"> 927</span>  <span class="keywordflow">return</span> <a class="code" href="group___math.html#gad568f4267154f330c142cb1605e885b1">std::round</a>(v * r) * s;</div>
<div class="line"><a name="l00928"></a><span class="lineno"> 928</span> }</div>
<div class="line"><a name="l00929"></a><span class="lineno"><a class="line" href="group___math.html#ga52522414f03221f7b6ee9875cfaea9f6"> 929</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga52522414f03221f7b6ee9875cfaea9f6">roundAway</a>(<span class="keyword">const</span> T& v) {</div>
<div class="line"><a name="l00930"></a><span class="lineno"> 930</span>  <span class="keywordflow">return</span> v < T(0) ? <a class="code" href="group___math.html#ga5b81fa38c979ae94a7da92b3223ba2b8">al::floor</a>(v) : <a class="code" href="group___math.html#ga5871238946c53c69bbe794b38ba8574e">al::ceil</a>(v);</div>
<div class="line"><a name="l00931"></a><span class="lineno"> 931</span> }</div>
<div class="line"><a name="l00932"></a><span class="lineno"><a class="line" href="group___math.html#ga8207252b571c96bc1addbdd7d8cee6d6"> 932</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga52522414f03221f7b6ee9875cfaea9f6">roundAway</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& s) {</div>
<div class="line"><a name="l00933"></a><span class="lineno"> 933</span>  <span class="keywordflow">return</span> v < T(0) ? <a class="code" href="group___math.html#ga5b81fa38c979ae94a7da92b3223ba2b8">al::floor</a>(v, s) : <a class="code" href="group___math.html#ga5871238946c53c69bbe794b38ba8574e">al::ceil</a>(v, s);</div>
<div class="line"><a name="l00934"></a><span class="lineno"> 934</span> }</div>
<div class="line"><a name="l00935"></a><span class="lineno"> 935</span>  </div>
<div class="line"><a name="l00936"></a><span class="lineno"><a class="line" href="group___math.html#ga4b9395462499c968255feefd8e974a93"> 936</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga4b9395462499c968255feefd8e974a93">sgn</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& norm) {</div>
<div class="line"><a name="l00937"></a><span class="lineno"> 937</span>  <span class="keywordflow">return</span> v == T(0) ? T(0) : v < T(0) ? -norm : norm;</div>
<div class="line"><a name="l00938"></a><span class="lineno"> 938</span> }</div>
<div class="line"><a name="l00939"></a><span class="lineno"> 939</span>  </div>
<div class="line"><a name="l00940"></a><span class="lineno"><a class="line" href="group___math.html#gaaee09ed63c305f6ac32ecc141045062f"> 940</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#gaaee09ed63c305f6ac32ecc141045062f">sinc</a>(<span class="keyword">const</span> T& r, <span class="keyword">const</span> T& eps) {</div>
<div class="line"><a name="l00941"></a><span class="lineno"> 941</span>  <span class="keywordflow">return</span> (std::abs(r) > eps) ? std::sin(r) / r : std::cos(r);</div>
<div class="line"><a name="l00942"></a><span class="lineno"> 942</span> }</div>
<div class="line"><a name="l00943"></a><span class="lineno"> 943</span>  </div>
<div class="line"><a name="l00944"></a><span class="lineno"><a class="line" href="group___math.html#gaa46708ab331be0d22136de6365a49338"> 944</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#gaa46708ab331be0d22136de6365a49338">slope</a>(<span class="keyword">const</span> T& x1, <span class="keyword">const</span> T& y1, <span class="keyword">const</span> T& x2, <span class="keyword">const</span> T& y2) {</div>
<div class="line"><a name="l00945"></a><span class="lineno"> 945</span>  <span class="keywordflow">return</span> (y2 - y1) / (x2 - x1);</div>
<div class="line"><a name="l00946"></a><span class="lineno"> 946</span> }</div>
<div class="line"><a name="l00947"></a><span class="lineno"> 947</span>  </div>
<div class="line"><a name="l00948"></a><span class="lineno"><a class="line" href="group___math.html#ga316b5a2949ca945618aab0c4f53ac0c5"> 948</a></span> TEM <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="group___math.html#ga316b5a2949ca945618aab0c4f53ac0c5">sort</a>(T& v1, T& v2) {</div>
<div class="line"><a name="l00949"></a><span class="lineno"> 949</span>  <span class="keywordflow">if</span> (v1 > v2) {</div>
<div class="line"><a name="l00950"></a><span class="lineno"> 950</span>  T t = v1;</div>
<div class="line"><a name="l00951"></a><span class="lineno"> 951</span>  v1 = v2;</div>
<div class="line"><a name="l00952"></a><span class="lineno"> 952</span>  v2 = t;</div>
<div class="line"><a name="l00953"></a><span class="lineno"> 953</span>  }</div>
<div class="line"><a name="l00954"></a><span class="lineno"> 954</span> }</div>
<div class="line"><a name="l00955"></a><span class="lineno"> 955</span>  </div>
<div class="line"><a name="l00956"></a><span class="lineno"><a class="line" href="group___math.html#ga5715feed6e8d122fb5e763ad7b9d29ec"> 956</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga5715feed6e8d122fb5e763ad7b9d29ec">sumOfSquares</a>(T n) {</div>
<div class="line"><a name="l00957"></a><span class="lineno"> 957</span>  <span class="keyword">static</span> <span class="keyword">const</span> T c1_6 = 1 / T(6);</div>
<div class="line"><a name="l00958"></a><span class="lineno"> 958</span>  <span class="keyword">static</span> <span class="keyword">const</span> T c2_6 = c1_6 * T(2);</div>
<div class="line"><a name="l00959"></a><span class="lineno"> 959</span>  <span class="keywordflow">return</span> n * (n + 1) * (c2_6 * n + c1_6);</div>
<div class="line"><a name="l00960"></a><span class="lineno"> 960</span> }</div>
<div class="line"><a name="l00961"></a><span class="lineno"> 961</span>  </div>
<div class="line"><a name="l00962"></a><span class="lineno"><a class="line" href="group___math.html#ga5184860679d7dc5575231fb0af25a14d"> 962</a></span> <span class="keyword">inline</span> uint32_t <a class="code" href="group___math.html#ga5184860679d7dc5575231fb0af25a14d">trailingZeroes</a>(uint32_t v) { <span class="keywordflow">return</span> deBruijn(v & -v); }</div>
<div class="line"><a name="l00963"></a><span class="lineno"> 963</span>  </div>
<div class="line"><a name="l00964"></a><span class="lineno"><a class="line" href="group___math.html#gab15dcba5bf53f93e28b7c7b0cdd10d03"> 964</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#gab15dcba5bf53f93e28b7c7b0cdd10d03">trunc</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& s) { <span class="keywordflow">return</span> <a class="code" href="group___math.html#gae71d216179aedd721033b8accc7e7a72">std::trunc</a>(v / s) * s; }</div>
<div class="line"><a name="l00965"></a><span class="lineno"><a class="line" href="group___math.html#gae71d216179aedd721033b8accc7e7a72"> 965</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#gab15dcba5bf53f93e28b7c7b0cdd10d03">trunc</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& s, <span class="keyword">const</span> T& r) {</div>
<div class="line"><a name="l00966"></a><span class="lineno"> 966</span>  <span class="keywordflow">return</span> <a class="code" href="group___math.html#gae71d216179aedd721033b8accc7e7a72">std::trunc</a>(v * r) * s;</div>
<div class="line"><a name="l00967"></a><span class="lineno"> 967</span> }</div>
<div class="line"><a name="l00968"></a><span class="lineno"> 968</span>  </div>
<div class="line"><a name="l00969"></a><span class="lineno"><a class="line" href="group___math.html#gaeb22e9d95c2ec10b05324cb054990476"> 969</a></span> TEM <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="group___math.html#gaeb22e9d95c2ec10b05324cb054990476">within</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& lo, <span class="keyword">const</span> T& hi) {</div>
<div class="line"><a name="l00970"></a><span class="lineno"> 970</span>  <span class="keywordflow">return</span> !((v < lo) || (v > hi));</div>
<div class="line"><a name="l00971"></a><span class="lineno"> 971</span> }</div>
<div class="line"><a name="l00972"></a><span class="lineno"><a class="line" href="group___math.html#ga402e95bb33a2573d222702e632c74d78"> 972</a></span> TEM <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="group___math.html#ga402e95bb33a2573d222702e632c74d78">withinIE</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& lo, <span class="keyword">const</span> T& hi) {</div>
<div class="line"><a name="l00973"></a><span class="lineno"> 973</span>  <span class="keywordflow">return</span> (!(v < lo)) && (v < hi);</div>
<div class="line"><a name="l00974"></a><span class="lineno"> 974</span> }</div>
<div class="line"><a name="l00975"></a><span class="lineno"> 975</span>  </div>
<div class="line"><a name="l00976"></a><span class="lineno"><a class="line" href="group___math.html#ga7e2366116eaac9d1037af687bf5a3369"> 976</a></span> TEM <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="group___math.html#ga7e2366116eaac9d1037af687bf5a3369">within3</a>(<span class="keyword">const</span> T& v1, <span class="keyword">const</span> T& v2, <span class="keyword">const</span> T& v3, <span class="keyword">const</span> T& lo,</div>
<div class="line"><a name="l00977"></a><span class="lineno"> 977</span>  <span class="keyword">const</span> T& hi) {</div>
<div class="line"><a name="l00978"></a><span class="lineno"> 978</span>  <span class="keywordflow">return</span> <a class="code" href="group___math.html#gaeb22e9d95c2ec10b05324cb054990476">al::within</a>(v1, lo, hi) && <a class="code" href="group___math.html#gaeb22e9d95c2ec10b05324cb054990476">al::within</a>(v2, lo, hi) &&</div>
<div class="line"><a name="l00979"></a><span class="lineno"> 979</span>  <a class="code" href="group___math.html#gaeb22e9d95c2ec10b05324cb054990476">al::within</a>(v3, lo, hi);</div>
<div class="line"><a name="l00980"></a><span class="lineno"> 980</span> }</div>
<div class="line"><a name="l00981"></a><span class="lineno"> 981</span>  </div>
<div class="line"><a name="l00982"></a><span class="lineno"> 982</span> <span class="comment">// TODO: fuse the following two functions</span></div>
<div class="line"><a name="l00983"></a><span class="lineno"><a class="line" href="group___math.html#gabab359a45740fff6e459019fab5975e2"> 983</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#gabab359a45740fff6e459019fab5975e2">wrap</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& hi, <span class="keyword">const</span> T& lo) {</div>
<div class="line"><a name="l00984"></a><span class="lineno"> 984</span>  <span class="keywordflow">if</span> (lo == hi) <span class="keywordflow">return</span> lo;</div>
<div class="line"><a name="l00985"></a><span class="lineno"> 985</span>  </div>
<div class="line"><a name="l00986"></a><span class="lineno"> 986</span>  T R = v;</div>
<div class="line"><a name="l00987"></a><span class="lineno"> 987</span>  T diff = hi - lo;</div>
<div class="line"><a name="l00988"></a><span class="lineno"> 988</span>  </div>
<div class="line"><a name="l00989"></a><span class="lineno"> 989</span>  <span class="keywordflow">if</span> (R >= hi) {</div>
<div class="line"><a name="l00990"></a><span class="lineno"> 990</span>  R -= diff;</div>
<div class="line"><a name="l00991"></a><span class="lineno"> 991</span>  <span class="keywordflow">if</span> (R >= hi) R -= diff * uint32_t((R - lo) / diff);</div>
<div class="line"><a name="l00992"></a><span class="lineno"> 992</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (R < lo) {</div>
<div class="line"><a name="l00993"></a><span class="lineno"> 993</span>  R += diff;</div>
<div class="line"><a name="l00994"></a><span class="lineno"> 994</span>  </div>
<div class="line"><a name="l00995"></a><span class="lineno"> 995</span>  <span class="comment">// If value is very slightly less than 'lo', then less significant</span></div>
<div class="line"><a name="l00996"></a><span class="lineno"> 996</span>  <span class="comment">// digits might get truncated by adding a larger number.</span></div>
<div class="line"><a name="l00997"></a><span class="lineno"> 997</span>  <span class="keywordflow">if</span> (R == diff) <span class="keywordflow">return</span> <a class="code" href="group___math.html#ga08f69403d6e66bb2afba2292d8ad254c">al::nextAfter</a>(R, lo);</div>
<div class="line"><a name="l00998"></a><span class="lineno"> 998</span>  </div>
<div class="line"><a name="l00999"></a><span class="lineno"> 999</span>  <span class="keywordflow">if</span> (R < lo) R += diff * uint32_t(((lo - R) / diff) + 1);</div>
<div class="line"><a name="l01000"></a><span class="lineno"> 1000</span>  <span class="keywordflow">if</span> (R == diff) <span class="keywordflow">return</span> lo;</div>
<div class="line"><a name="l01001"></a><span class="lineno"> 1001</span>  }</div>
<div class="line"><a name="l01002"></a><span class="lineno"> 1002</span>  <span class="keywordflow">return</span> R;</div>
<div class="line"><a name="l01003"></a><span class="lineno"> 1003</span> }</div>
<div class="line"><a name="l01004"></a><span class="lineno"> 1004</span>  </div>
<div class="line"><a name="l01005"></a><span class="lineno"><a class="line" href="group___math.html#gafdca7e4f558c80704c9dfe6b781a0481"> 1005</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#gabab359a45740fff6e459019fab5975e2">wrap</a>(<span class="keyword">const</span> T& v, <span class="keywordtype">long</span>& numWraps, <span class="keyword">const</span> T& hi, <span class="keyword">const</span> T& lo) {</div>
<div class="line"><a name="l01006"></a><span class="lineno"> 1006</span>  <span class="keywordflow">if</span> (lo == hi) {</div>
<div class="line"><a name="l01007"></a><span class="lineno"> 1007</span>  numWraps = 0xFFFFFFFF;</div>
<div class="line"><a name="l01008"></a><span class="lineno"> 1008</span>  <span class="keywordflow">return</span> lo;</div>
<div class="line"><a name="l01009"></a><span class="lineno"> 1009</span>  }</div>
<div class="line"><a name="l01010"></a><span class="lineno"> 1010</span>  </div>
<div class="line"><a name="l01011"></a><span class="lineno"> 1011</span>  T R = v;</div>
<div class="line"><a name="l01012"></a><span class="lineno"> 1012</span>  T diff = hi - lo;</div>
<div class="line"><a name="l01013"></a><span class="lineno"> 1013</span>  numWraps = 0;</div>
<div class="line"><a name="l01014"></a><span class="lineno"> 1014</span>  </div>
<div class="line"><a name="l01015"></a><span class="lineno"> 1015</span>  <span class="keywordflow">if</span> (R >= hi) {</div>
<div class="line"><a name="l01016"></a><span class="lineno"> 1016</span>  R -= diff;</div>
<div class="line"><a name="l01017"></a><span class="lineno"> 1017</span>  <span class="keywordflow">if</span> (R >= hi) {</div>
<div class="line"><a name="l01018"></a><span class="lineno"> 1018</span>  numWraps = long((R - lo) / diff);</div>
<div class="line"><a name="l01019"></a><span class="lineno"> 1019</span>  R -= diff * numWraps;</div>
<div class="line"><a name="l01020"></a><span class="lineno"> 1020</span>  }</div>
<div class="line"><a name="l01021"></a><span class="lineno"> 1021</span>  ++numWraps;</div>
<div class="line"><a name="l01022"></a><span class="lineno"> 1022</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (R < lo) {</div>
<div class="line"><a name="l01023"></a><span class="lineno"> 1023</span>  R += diff;</div>
<div class="line"><a name="l01024"></a><span class="lineno"> 1024</span>  <span class="keywordflow">if</span> (R < lo) {</div>
<div class="line"><a name="l01025"></a><span class="lineno"> 1025</span>  numWraps = long((R - lo) / diff) - 1;</div>
<div class="line"><a name="l01026"></a><span class="lineno"> 1026</span>  R -= diff * numWraps;</div>
<div class="line"><a name="l01027"></a><span class="lineno"> 1027</span>  }</div>
<div class="line"><a name="l01028"></a><span class="lineno"> 1028</span>  --numWraps;</div>
<div class="line"><a name="l01029"></a><span class="lineno"> 1029</span>  }</div>
<div class="line"><a name="l01030"></a><span class="lineno"> 1030</span>  <span class="keywordflow">return</span> R;</div>
<div class="line"><a name="l01031"></a><span class="lineno"> 1031</span> }</div>
<div class="line"><a name="l01032"></a><span class="lineno"> 1032</span>  </div>
<div class="line"><a name="l01033"></a><span class="lineno"><a class="line" href="group___math.html#ga5ccb344df3f76c5eb8ec593ad894627a"> 1033</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga5ccb344df3f76c5eb8ec593ad894627a">wrapOnce</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& hi) {</div>
<div class="line"><a name="l01034"></a><span class="lineno"> 1034</span>  <span class="keywordflow">if</span> (v >= hi)</div>
<div class="line"><a name="l01035"></a><span class="lineno"> 1035</span>  <span class="keywordflow">return</span> v - hi;</div>
<div class="line"><a name="l01036"></a><span class="lineno"> 1036</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (v < T(0))</div>
<div class="line"><a name="l01037"></a><span class="lineno"> 1037</span>  <span class="keywordflow">return</span> v + hi;</div>
<div class="line"><a name="l01038"></a><span class="lineno"> 1038</span>  <span class="keywordflow">return</span> v;</div>
<div class="line"><a name="l01039"></a><span class="lineno"> 1039</span> }</div>
<div class="line"><a name="l01040"></a><span class="lineno"> 1040</span>  </div>
<div class="line"><a name="l01041"></a><span class="lineno"> 1041</span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga5ccb344df3f76c5eb8ec593ad894627a">wrapOnce</a>(<span class="keyword">const</span> T& v, <span class="keyword">const</span> T& hi, <span class="keyword">const</span> T& lo) {</div>
<div class="line"><a name="l01042"></a><span class="lineno"> 1042</span>  <span class="keywordflow">if</span> (v >= hi)</div>
<div class="line"><a name="l01043"></a><span class="lineno"> 1043</span>  <span class="keywordflow">return</span> v - hi + lo;</div>
<div class="line"><a name="l01044"></a><span class="lineno"> 1044</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (v < lo)</div>
<div class="line"><a name="l01045"></a><span class="lineno"> 1045</span>  <span class="keywordflow">return</span> v + hi - lo;</div>
<div class="line"><a name="l01046"></a><span class="lineno"> 1046</span>  <span class="keywordflow">return</span> v;</div>
<div class="line"><a name="l01047"></a><span class="lineno"> 1047</span> }</div>
<div class="line"><a name="l01048"></a><span class="lineno"> 1048</span>  </div>
<div class="line"><a name="l01049"></a><span class="lineno"><a class="line" href="group___math.html#ga4911206e29f73da7441ea02255584d09"> 1049</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga4911206e29f73da7441ea02255584d09">wrapPhase</a>(<span class="keyword">const</span> T& r_) {</div>
<div class="line"><a name="l01050"></a><span class="lineno"> 1050</span>  <span class="comment">// The result is [r+pi - 2pi floor([r+pi] / 2pi)] - pi</span></div>
<div class="line"><a name="l01051"></a><span class="lineno"> 1051</span>  <span class="comment">// which simplified is r - 2pi floor([r+pi] / 2pi) .</span></div>
<div class="line"><a name="l01052"></a><span class="lineno"> 1052</span>  T r = r_;</div>
<div class="line"><a name="l01053"></a><span class="lineno"> 1053</span>  <span class="keywordflow">if</span> (r >= T(M_PI)) {</div>
<div class="line"><a name="l01054"></a><span class="lineno"> 1054</span>  r -= T(M_2PI);</div>
<div class="line"><a name="l01055"></a><span class="lineno"> 1055</span>  <span class="keywordflow">if</span> (r < T(M_PI)) <span class="keywordflow">return</span> r;</div>
<div class="line"><a name="l01056"></a><span class="lineno"> 1056</span>  <span class="keywordflow">return</span> r - T(<span class="keywordtype">long</span>((r + M_PI) * M_1_2PI)) * M_2PI;</div>
<div class="line"><a name="l01057"></a><span class="lineno"> 1057</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (r < T(-M_PI)) {</div>
<div class="line"><a name="l01058"></a><span class="lineno"> 1058</span>  r += T(M_2PI);</div>
<div class="line"><a name="l01059"></a><span class="lineno"> 1059</span>  <span class="keywordflow">if</span> (r >= T(-M_PI)) <span class="keywordflow">return</span> r;</div>
<div class="line"><a name="l01060"></a><span class="lineno"> 1060</span>  <span class="keywordflow">return</span> r - T(<span class="keywordtype">long</span>((r + M_PI) * M_1_2PI) - 1) * M_2PI;</div>
<div class="line"><a name="l01061"></a><span class="lineno"> 1061</span>  } <span class="keywordflow">else</span></div>
<div class="line"><a name="l01062"></a><span class="lineno"> 1062</span>  <span class="keywordflow">return</span> r;</div>
<div class="line"><a name="l01063"></a><span class="lineno"> 1063</span> }</div>
<div class="line"><a name="l01064"></a><span class="lineno"> 1064</span>  </div>
<div class="line"><a name="l01065"></a><span class="lineno"><a class="line" href="group___math.html#ga7cdffae94bec1ea44587abb24231e617"> 1065</a></span> TEM <span class="keyword">inline</span> T <a class="code" href="group___math.html#ga7cdffae94bec1ea44587abb24231e617">wrapPhaseOnce</a>(<span class="keyword">const</span> T& r) {</div>
<div class="line"><a name="l01066"></a><span class="lineno"> 1066</span>  <span class="keywordflow">if</span> (r >= T(M_PI))</div>
<div class="line"><a name="l01067"></a><span class="lineno"> 1067</span>  <span class="keywordflow">return</span> r - T(M_2PI);</div>
<div class="line"><a name="l01068"></a><span class="lineno"> 1068</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (r < T(-M_PI))</div>
<div class="line"><a name="l01069"></a><span class="lineno"> 1069</span>  <span class="keywordflow">return</span> r + T(M_2PI);</div>
<div class="line"><a name="l01070"></a><span class="lineno"> 1070</span>  <span class="keywordflow">return</span> r;</div>
<div class="line"><a name="l01071"></a><span class="lineno"> 1071</span> }</div>
<div class="line"><a name="l01072"></a><span class="lineno"> 1072</span>  </div>
<div class="line"><a name="l01073"></a><span class="lineno"> 1073</span> TEM <span class="keyword">inline</span> T mapRange(T value, T inlow, T inhigh, T outlow, T outhigh) {</div>
<div class="line"><a name="l01074"></a><span class="lineno"> 1074</span>  <span class="keywordtype">float</span> tmp = (value - inlow) / (inhigh - inlow);</div>
<div class="line"><a name="l01075"></a><span class="lineno"> 1075</span>  <span class="keywordflow">return</span> tmp * (outhigh - outlow) + outlow;</div>
<div class="line"><a name="l01076"></a><span class="lineno"> 1076</span> }</div>
<div class="line"><a name="l01077"></a><span class="lineno"> 1077</span>  </div>
<div class="line"><a name="l01078"></a><span class="lineno"> 1078</span> TEM <span class="keyword">inline</span> T lerp(T src, T dest, T amt) {</div>
<div class="line"><a name="l01079"></a><span class="lineno"> 1079</span>  <span class="keywordflow">return</span> src * (T(1) - amt) + dest * amt;</div>
<div class="line"><a name="l01080"></a><span class="lineno"> 1080</span> }</div>
<div class="line"><a name="l01081"></a><span class="lineno"> 1081</span>  </div>
<div class="line"><a name="l01082"></a><span class="lineno"> 1082</span> <span class="preprocessor">#undef TEM</span></div>
<div class="line"><a name="l01083"></a><span class="lineno"> 1083</span> } <span class="comment">// namespace al</span></div>
<div class="line"><a name="l01084"></a><span class="lineno"> 1084</span> <span class="preprocessor">#endif</span></div>
<div class="ttc" id="agroup___math_html_ga02593b7bb80f83f51ef276ae288e6fec"><div class="ttname"><a href="group___math.html#ga02593b7bb80f83f51ef276ae288e6fec">al::wrapAdd1</a></div><div class="ttdeci">T wrapAdd1(const T &v, const T &max)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00479">al_Functions.hpp:479</a></div></div>
<div class="ttc" id="agroup___math_html_ga08f69403d6e66bb2afba2292d8ad254c"><div class="ttname"><a href="group___math.html#ga08f69403d6e66bb2afba2292d8ad254c">al::nextAfter</a></div><div class="ttdeci">T nextAfter(const T &x, const T &y)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00863">al_Functions.hpp:863</a></div></div>
<div class="ttc" id="agroup___math_html_ga1352d5bea80358151c11f6524648ff9b"><div class="ttname"><a href="group___math.html#ga1352d5bea80358151c11f6524648ff9b">al::dBToAmp</a></div><div class="ttdeci">T dBToAmp(const T &db)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00143">al_Functions.hpp:143</a></div></div>
<div class="ttc" id="agroup___math_html_ga1ea1cc7b53231b0c0dd6e2095f300ef0"><div class="ttname"><a href="group___math.html#ga1ea1cc7b53231b0c0dd6e2095f300ef0">al::clip</a></div><div class="ttdeci">T clip(const T &value, const T &hi=T(1), const T &lo=T(0))</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00621">al_Functions.hpp:621</a></div></div>
<div class="ttc" id="agroup___math_html_ga2090ba7150a810fd3de64b1d95d69e23"><div class="ttname"><a href="group___math.html#ga2090ba7150a810fd3de64b1d95d69e23">al::gaussian</a></div><div class="ttdeci">T gaussian(const T &v)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00690">al_Functions.hpp:690</a></div></div>
<div class="ttc" id="agroup___math_html_ga2fd420846f99fa0c8c500209a66995de"><div class="ttname"><a href="group___math.html#ga2fd420846f99fa0c8c500209a66995de">al::min</a></div><div class="ttdeci">T min(const T &v1, const T &v2, const T &v3)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00844">al_Functions.hpp:844</a></div></div>
<div class="ttc" id="agroup___math_html_ga305a92788021baeaf04d5e9589a5ac34"><div class="ttname"><a href="group___math.html#ga305a92788021baeaf04d5e9589a5ac34">al::bitsSet</a></div><div class="ttdeci">uint32_t bitsSet(uint32_t v)</div><div class="ttdoc">Returns number of bits set to 1.</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00600">al_Functions.hpp:600</a></div></div>
<div class="ttc" id="agroup___math_html_ga316b5a2949ca945618aab0c4f53ac0c5"><div class="ttname"><a href="group___math.html#ga316b5a2949ca945618aab0c4f53ac0c5">al::sort</a></div><div class="ttdeci">void sort(T &value1, T &value2)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00948">al_Functions.hpp:948</a></div></div>
<div class="ttc" id="agroup___math_html_ga3aeccffdbab51e5b2cab2b97d025d002"><div class="ttname"><a href="group___math.html#ga3aeccffdbab51e5b2cab2b97d025d002">al::even</a></div><div class="ttdeci">bool even(const T &v)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00643">al_Functions.hpp:643</a></div></div>
<div class="ttc" id="agroup___math_html_ga3d78c2574a648fcf2c44003c9768508b"><div class="ttname"><a href="group___math.html#ga3d78c2574a648fcf2c44003c9768508b">al::round</a></div><div class="ttdeci">T round(const T &v, const T &step)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00925">al_Functions.hpp:925</a></div></div>
<div class="ttc" id="agroup___math_html_ga3f88bf4afda6ac9b12aa22873870d0b2"><div class="ttname"><a href="group___math.html#ga3f88bf4afda6ac9b12aa22873870d0b2">al::factorial</a></div><div class="ttdeci">uint32_t factorial(uint32_t n0to12)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00654">al_Functions.hpp:654</a></div></div>
<div class="ttc" id="agroup___math_html_ga402e95bb33a2573d222702e632c74d78"><div class="ttname"><a href="group___math.html#ga402e95bb33a2573d222702e632c74d78">al::withinIE</a></div><div class="ttdeci">bool withinIE(const T &v, const T &lo, const T &hi)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00972">al_Functions.hpp:972</a></div></div>
<div class="ttc" id="agroup___math_html_ga433911d7b80de439047ca3e580e5684c"><div class="ttname"><a href="group___math.html#ga433911d7b80de439047ca3e580e5684c">al::gcd</a></div><div class="ttdeci">T gcd(const T &x, const T &y)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00692">al_Functions.hpp:692</a></div></div>
<div class="ttc" id="agroup___math_html_ga4911206e29f73da7441ea02255584d09"><div class="ttname"><a href="group___math.html#ga4911206e29f73da7441ea02255584d09">al::wrapPhase</a></div><div class="ttdeci">T wrapPhase(const T &radians)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l01049">al_Functions.hpp:1049</a></div></div>
<div class="ttc" id="agroup___math_html_ga4a4f53c3ebf1101824b0eb3c78f73527"><div class="ttname"><a href="group___math.html#ga4a4f53c3ebf1101824b0eb3c78f73527">al::mean</a></div><div class="ttdeci">T mean(const T &v1, const T &v2)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00843">al_Functions.hpp:843</a></div></div>
<div class="ttc" id="agroup___math_html_ga4b9395462499c968255feefd8e974a93"><div class="ttname"><a href="group___math.html#ga4b9395462499c968255feefd8e974a93">al::sgn</a></div><div class="ttdeci">T sgn(const T &v, const T &norm=T(1))</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00936">al_Functions.hpp:936</a></div></div>
<div class="ttc" id="agroup___math_html_ga5184860679d7dc5575231fb0af25a14d"><div class="ttname"><a href="group___math.html#ga5184860679d7dc5575231fb0af25a14d">al::trailingZeroes</a></div><div class="ttdeci">uint32_t trailingZeroes(uint32_t v)</div><div class="ttdoc">Returns number of trailing zeros in 32-bit int.</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00962">al_Functions.hpp:962</a></div></div>
<div class="ttc" id="agroup___math_html_ga52522414f03221f7b6ee9875cfaea9f6"><div class="ttname"><a href="group___math.html#ga52522414f03221f7b6ee9875cfaea9f6">al::roundAway</a></div><div class="ttdeci">T roundAway(const T &v)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00929">al_Functions.hpp:929</a></div></div>
<div class="ttc" id="agroup___math_html_ga5715feed6e8d122fb5e763ad7b9d29ec"><div class="ttname"><a href="group___math.html#ga5715feed6e8d122fb5e763ad7b9d29ec">al::sumOfSquares</a></div><div class="ttdeci">T sumOfSquares(T n)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00956">al_Functions.hpp:956</a></div></div>
<div class="ttc" id="agroup___math_html_ga5871238946c53c69bbe794b38ba8574e"><div class="ttname"><a href="group___math.html#ga5871238946c53c69bbe794b38ba8574e">al::ceil</a></div><div class="ttdeci">T ceil(const T &val, const T &step)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00606">al_Functions.hpp:606</a></div></div>
<div class="ttc" id="agroup___math_html_ga5a6f3e643facd02a406d5f631474f828"><div class="ttname"><a href="group___math.html#ga5a6f3e643facd02a406d5f631474f828">al::numInt</a></div><div class="ttdeci">T numInt(const T &v)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00871">al_Functions.hpp:871</a></div></div>
<div class="ttc" id="agroup___math_html_ga5b81fa38c979ae94a7da92b3223ba2b8"><div class="ttname"><a href="group___math.html#ga5b81fa38c979ae94a7da92b3223ba2b8">al::floor</a></div><div class="ttdeci">T floor(const T &val, const T &step)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00663">al_Functions.hpp:663</a></div></div>
<div class="ttc" id="agroup___math_html_ga5b903297ac73ab3a1344e110589262d9"><div class="ttname"><a href="group___math.html#ga5b903297ac73ab3a1344e110589262d9">al::ceilPow2</a></div><div class="ttdeci">uint32_t ceilPow2(uint32_t value)</div><div class="ttdoc">Returns power of two ceiling of value.</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00611">al_Functions.hpp:611</a></div></div>
<div class="ttc" id="agroup___math_html_ga5ccb344df3f76c5eb8ec593ad894627a"><div class="ttname"><a href="group___math.html#ga5ccb344df3f76c5eb8ec593ad894627a">al::wrapOnce</a></div><div class="ttdeci">T wrapOnce(const T &value, const T &hi=T(1))</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l01033">al_Functions.hpp:1033</a></div></div>
<div class="ttc" id="agroup___math_html_ga5e15be42a4331a52661d87800cbfc512"><div class="ttname"><a href="group___math.html#ga5e15be42a4331a52661d87800cbfc512">al::prime</a></div><div class="ttdeci">unsigned char prime(uint32_t n)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00923">al_Functions.hpp:923</a></div></div>
<div class="ttc" id="agroup___math_html_ga6e43efc43f7570be467a4442d253f495"><div class="ttname"><a href="group___math.html#ga6e43efc43f7570be467a4442d253f495">al::odd</a></div><div class="ttdeci">bool odd(const T &v)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00873">al_Functions.hpp:873</a></div></div>
<div class="ttc" id="agroup___math_html_ga7075f46376a9dcccc420f8dd1b329812"><div class="ttname"><a href="group___math.html#ga7075f46376a9dcccc420f8dd1b329812">al::max</a></div><div class="ttdeci">T max(const T &v1, const T &v2, const T &v3)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00840">al_Functions.hpp:840</a></div></div>
<div class="ttc" id="agroup___math_html_ga70d2bb9995e24c326bb1f8ca25c9b9e0"><div class="ttname"><a href="group___math.html#ga70d2bb9995e24c326bb1f8ca25c9b9e0">al::lessAbs</a></div><div class="ttdeci">bool lessAbs(const T &v, const T &eps=T(0.000001))</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00838">al_Functions.hpp:838</a></div></div>
<div class="ttc" id="agroup___math_html_ga7b18bb9bb26fb7813665c8065cbcee70"><div class="ttname"><a href="group___math.html#ga7b18bb9bb26fb7813665c8065cbcee70">al::laguerreL</a></div><div class="ttdeci">T laguerreL(int n, int k, T x)</div><div class="ttdoc">Generalized Laguerre polynomial L{n,k}.</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00700">al_Functions.hpp:700</a></div></div>
<div class="ttc" id="agroup___math_html_ga7cdffae94bec1ea44587abb24231e617"><div class="ttname"><a href="group___math.html#ga7cdffae94bec1ea44587abb24231e617">al::wrapPhaseOnce</a></div><div class="ttdeci">T wrapPhaseOnce(const T &radians)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l01065">al_Functions.hpp:1065</a></div></div>
<div class="ttc" id="agroup___math_html_ga7e2366116eaac9d1037af687bf5a3369"><div class="ttname"><a href="group___math.html#ga7e2366116eaac9d1037af687bf5a3369">al::within3</a></div><div class="ttdeci">bool within3(const T &v1, const T &v2, const T &v3, const T &lo, const T &hi)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00976">al_Functions.hpp:976</a></div></div>
<div class="ttc" id="agroup___math_html_ga8168179e459a58e4b7fd5757fa928fa5"><div class="ttname"><a href="group___math.html#ga8168179e459a58e4b7fd5757fa928fa5">al::powN</a></div><div class="ttdeci">T powN(T base, unsigned power)</div><div class="ttdoc">Returns value to a positive integer power.</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00893">al_Functions.hpp:893</a></div></div>
<div class="ttc" id="agroup___math_html_ga9da403c39d92da43b4aae7c050e9844f"><div class="ttname"><a href="group___math.html#ga9da403c39d92da43b4aae7c050e9844f">al::nearestDiv</a></div><div class="ttdeci">T nearestDiv(T of, T to)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00288">al_Functions.hpp:288</a></div></div>
<div class="ttc" id="agroup___math_html_gaa1601bdb71ac3809de1576cb4976ff31"><div class="ttname"><a href="group___math.html#gaa1601bdb71ac3809de1576cb4976ff31">al::erf</a></div><div class="ttdeci">T erf(const T &v)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00646">al_Functions.hpp:646</a></div></div>
<div class="ttc" id="agroup___math_html_gaa46708ab331be0d22136de6365a49338"><div class="ttname"><a href="group___math.html#gaa46708ab331be0d22136de6365a49338">al::slope</a></div><div class="ttdeci">T slope(const T &x1, const T &y1, const T &x2, const T &y2)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00944">al_Functions.hpp:944</a></div></div>
<div class="ttc" id="agroup___math_html_gaab3a1b08de897c27811f94bbeb74ff63"><div class="ttname"><a href="group___math.html#gaab3a1b08de897c27811f94bbeb74ff63">al::legendreP</a></div><div class="ttdeci">T legendreP(int l, int m, T t)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00834">al_Functions.hpp:834</a></div></div>
<div class="ttc" id="agroup___math_html_gaaee09ed63c305f6ac32ecc141045062f"><div class="ttname"><a href="group___math.html#gaaee09ed63c305f6ac32ecc141045062f">al::sinc</a></div><div class="ttdeci">T sinc(const T &radians, const T &eps=T(0.0001))</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00940">al_Functions.hpp:940</a></div></div>
<div class="ttc" id="agroup___math_html_gab15dcba5bf53f93e28b7c7b0cdd10d03"><div class="ttname"><a href="group___math.html#gab15dcba5bf53f93e28b7c7b0cdd10d03">al::trunc</a></div><div class="ttdeci">T trunc(const T &v, const T &step)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00964">al_Functions.hpp:964</a></div></div>
<div class="ttc" id="agroup___math_html_gab4556d3171dafe878f45a4a99c5dec7a"><div class="ttname"><a href="group___math.html#gab4556d3171dafe878f45a4a99c5dec7a">al::foldOnce</a></div><div class="ttdeci">T foldOnce(const T &value, const T &hi=T(1), const T &lo=T(0))</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00684">al_Functions.hpp:684</a></div></div>
<div class="ttc" id="agroup___math_html_gaba17591660c318242fc292ba64771585"><div class="ttname"><a href="group___math.html#gaba17591660c318242fc292ba64771585">al::factorialSqrt</a></div><div class="ttdeci">double factorialSqrt(int v)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00656">al_Functions.hpp:656</a></div></div>
<div class="ttc" id="agroup___math_html_gabab359a45740fff6e459019fab5975e2"><div class="ttname"><a href="group___math.html#gabab359a45740fff6e459019fab5975e2">al::wrap</a></div><div class="ttdeci">T wrap(const T &value, const T &hi=T(1), const T &lo=T(0))</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00983">al_Functions.hpp:983</a></div></div>
<div class="ttc" id="agroup___math_html_gad1fb93acd3513290b5c4ac8f402ba808"><div class="ttname"><a href="group___math.html#gad1fb93acd3513290b5c4ac8f402ba808">al::fold</a></div><div class="ttdeci">T fold(const T &value, const T &hi=T(1), const T &lo=T(0))</div><div class="ttdoc">Returns value folded into [lo, hi].</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00677">al_Functions.hpp:677</a></div></div>
<div class="ttc" id="agroup___math_html_gad566fa512ff98f81749c473e18db371a"><div class="ttname"><a href="group___math.html#gad566fa512ff98f81749c473e18db371a">al::nextMultiple</a></div><div class="ttdeci">T nextMultiple(T val, T multiple)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00866">al_Functions.hpp:866</a></div></div>
<div class="ttc" id="agroup___math_html_gad568f4267154f330c142cb1605e885b1"><div class="ttname"><a href="group___math.html#gad568f4267154f330c142cb1605e885b1">al::round</a></div><div class="ttdeci">T round(const T &v, const T &step, const T &recStep)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00926">al_Functions.hpp:926</a></div></div>
<div class="ttc" id="agroup___math_html_gad7d2d0cae8ef1a818a68519510c8988c"><div class="ttname"><a href="group___math.html#gad7d2d0cae8ef1a818a68519510c8988c">al::gudermannian</a></div><div class="ttdeci">T gudermannian(const T &x)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00698">al_Functions.hpp:698</a></div></div>
<div class="ttc" id="agroup___math_html_gaded4d9162eecb556e24c0f3cd2e958c5"><div class="ttname"><a href="group___math.html#gaded4d9162eecb556e24c0f3cd2e958c5">al::ampTodB</a></div><div class="ttdeci">T ampTodB(const T &amp)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00070">al_Functions.hpp:70</a></div></div>
<div class="ttc" id="agroup___math_html_gae6b0655a2902fa6cb1556442e127bc38"><div class="ttname"><a href="group___math.html#gae6b0655a2902fa6cb1556442e127bc38">al::floorPow2</a></div><div class="ttdeci">uint32_t floorPow2(uint32_t value)</div><div class="ttdoc">Returns power of two floor of value.</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00668">al_Functions.hpp:668</a></div></div>
<div class="ttc" id="agroup___math_html_gae71d216179aedd721033b8accc7e7a72"><div class="ttname"><a href="group___math.html#gae71d216179aedd721033b8accc7e7a72">al::trunc</a></div><div class="ttdeci">T trunc(const T &v, const T &step, const T &recStep)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00965">al_Functions.hpp:965</a></div></div>
<div class="ttc" id="agroup___math_html_gaeb22e9d95c2ec10b05324cb054990476"><div class="ttname"><a href="group___math.html#gaeb22e9d95c2ec10b05324cb054990476">al::within</a></div><div class="ttdeci">bool within(const T &v, const T &lo, const T &hi)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00969">al_Functions.hpp:969</a></div></div>
<div class="ttc" id="agroup___math_html_gaf635f126b77657b51ce1a93a28fd9aef"><div class="ttname"><a href="group___math.html#gaf635f126b77657b51ce1a93a28fd9aef">al::clipS</a></div><div class="ttdeci">T clipS(const T &value, const T &hi=T(1))</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00641">al_Functions.hpp:641</a></div></div>
<div class="ttc" id="agroup___math_html_gaf696ac053502524c47d03c83fa338304"><div class="ttname"><a href="group___math.html#gaf696ac053502524c47d03c83fa338304">al::aeq</a></div><div class="ttdeci">bool aeq(float a, float b, int maxULP=10)</div><div class="ttdoc">Return whether two floats are almost equal.</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00544">al_Functions.hpp:544</a></div></div>
<div class="ttc" id="agroup___math_html_gaf698361a52baaadf969f995f5c6c3f78"><div class="ttname"><a href="group___math.html#gaf698361a52baaadf969f995f5c6c3f78">al::atLeast</a></div><div class="ttdeci">T atLeast(const T &v, const T &eps)</div><div class="ttdef"><b>Definition:</b> <a href="al___functions_8hpp_source.html#l00580">al_Functions.hpp:580</a></div></div>