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<p class="MsoPlainText"><span lang="EN-US">Hello,<o:p></o:p></span></p>
<p class="MsoPlainText"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoPlainText"><span lang="EN-US">> De : Federico Miyara<o:p></o:p></span></p>
<p class="MsoPlainText"><span lang="EN-US">> Envoyé : mardi 29 janvier 2019 21:36<o:p></o:p></span></p>
<p class="MsoPlainText"><span lang="EN-US">><o:p> </o:p></span></p>
<p class="MsoPlainText"><span lang="EN-US">> This is an improved version of the acos function with input argument check:<o:p></o:p></span></p>
<p class="MsoPlainText"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoPlainText"><span lang="EN-US">I would personally write it in the following way:<o:p></o:p></span></p>
<p class="MsoPlainText"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#B01813;mso-fareast-language:ZH-CN">function</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN">
</span><b><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#834310;mso-fareast-language:ZH-CN">y</span></b><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#5C5C5C;mso-fareast-language:ZH-CN">=</span><u><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;mso-fareast-language:ZH-CN">acos1</span></u><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#4A55DB;mso-fareast-language:ZH-CN">(</span><b><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#834310;mso-fareast-language:ZH-CN">x</span></b><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#4A55DB;mso-fareast-language:ZH-CN">)</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN">
</span><i><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#64AE64;mso-fareast-language:ZH-CN">// Check if components are real</span></i><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN">
</span><i><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#64AE64;mso-fareast-language:ZH-CN">// Check if components are real and belong to [-1, 1]</span></i><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN">
</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;mso-fareast-language:ZH-CN">absx</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN">
</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#5C5C5C;mso-fareast-language:ZH-CN">=</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN">
</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#32B9B9;mso-fareast-language:ZH-CN">abs</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#4A55DB;mso-fareast-language:ZH-CN">(</span><b><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#834310;mso-fareast-language:ZH-CN">x</span></b><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#4A55DB;mso-fareast-language:ZH-CN">)</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;mso-fareast-language:ZH-CN">;</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN">
</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;mso-fareast-language:ZH-CN">in_domain</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN">
</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#5C5C5C;mso-fareast-language:ZH-CN">=</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN">
</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#4A55DB;mso-fareast-language:ZH-CN">(</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#32B9B9;mso-fareast-language:ZH-CN">imag</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#4A55DB;mso-fareast-language:ZH-CN">(</span><b><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#834310;mso-fareast-language:ZH-CN">x</span></b><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#4A55DB;mso-fareast-language:ZH-CN">)</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#5C5C5C;mso-fareast-language:ZH-CN">==</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:rosybrown;mso-fareast-language:ZH-CN">0</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#4A55DB;mso-fareast-language:ZH-CN">)</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN">
</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#5C5C5C;mso-fareast-language:ZH-CN">&</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN">
</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#4A55DB;mso-fareast-language:ZH-CN">(</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#5C5C5C;mso-fareast-language:ZH-CN">-</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:rosybrown;mso-fareast-language:ZH-CN">1</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#5C5C5C;mso-fareast-language:ZH-CN"><=</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;mso-fareast-language:ZH-CN">absx</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#4A55DB;mso-fareast-language:ZH-CN">)</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN">
</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#5C5C5C;mso-fareast-language:ZH-CN">&</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN">
</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#4A55DB;mso-fareast-language:ZH-CN">(</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;mso-fareast-language:ZH-CN">absx</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#5C5C5C;mso-fareast-language:ZH-CN"><=</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:rosybrown;mso-fareast-language:ZH-CN">1</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#4A55DB;mso-fareast-language:ZH-CN">)</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;mso-fareast-language:ZH-CN">;</span><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN">
</span><i><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#64AE64;mso-fareast-language:ZH-CN">// Imaginary part of acos(x) is accepted only if
</span></i><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN"> </span><i><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:#64AE64;mso-fareast-language:ZH-CN">// x
does not belong to [-1, 1] </span></i><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN"> </span><b><span style="font-size:9.0pt;font-family:Monospaced;color:#834310;mso-fareast-language:ZH-CN">y</span></b><span style="font-size:9.0pt;font-family:Monospaced;color:#5C5C5C;mso-fareast-language:ZH-CN">=</span><span style="font-size:9.0pt;font-family:Monospaced;color:#32B9B9;mso-fareast-language:ZH-CN">acos</span><span style="font-size:9.0pt;font-family:Monospaced;color:#4A55DB;mso-fareast-language:ZH-CN">(</span><b><span style="font-size:9.0pt;font-family:Monospaced;color:#834310;mso-fareast-language:ZH-CN">x</span></b><span style="font-size:9.0pt;font-family:Monospaced;color:#4A55DB;mso-fareast-language:ZH-CN">)</span><span style="font-size:9.0pt;font-family:Monospaced;mso-fareast-language:ZH-CN">;</span><span style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN">
</span><b><span style="font-size:9.0pt;font-family:Monospaced;color:#834310;mso-fareast-language:ZH-CN">y</span></b><span style="font-size:9.0pt;font-family:Monospaced;color:#4A55DB;mso-fareast-language:ZH-CN">(</span><span style="font-size:9.0pt;font-family:Monospaced;mso-fareast-language:ZH-CN">in_domain</span><span style="font-size:9.0pt;font-family:Monospaced;color:#4A55DB;mso-fareast-language:ZH-CN">)</span><span style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN">
</span><span style="font-size:9.0pt;font-family:Monospaced;color:#5C5C5C;mso-fareast-language:ZH-CN">=</span><span style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN">
</span><span style="font-size:9.0pt;font-family:Monospaced;color:#32B9B9;mso-fareast-language:ZH-CN">real</span><span style="font-size:9.0pt;font-family:Monospaced;color:#4A55DB;mso-fareast-language:ZH-CN">(</span><b><span style="font-size:9.0pt;font-family:Monospaced;color:#834310;mso-fareast-language:ZH-CN">y</span></b><span style="font-size:9.0pt;font-family:Monospaced;color:#4A55DB;mso-fareast-language:ZH-CN">(</span><span style="font-size:9.0pt;font-family:Monospaced;mso-fareast-language:ZH-CN">in_domain</span><span style="font-size:9.0pt;font-family:Monospaced;color:#4A55DB;mso-fareast-language:ZH-CN">))</span><span style="font-size:9.0pt;font-family:Monospaced;mso-fareast-language:ZH-CN">;</span><span style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:9.0pt;font-family:Monospaced;color:#B01813;mso-fareast-language:ZH-CN">endfunction</span><span style="font-size:9.0pt;font-family:Monospaced;color:windowtext;mso-fareast-language:ZH-CN"><o:p></o:p></span></p>
<p class="MsoPlainText"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoPlainText"><span lang="EN-US">Regards<o:p></o:p></span></p>
<p class="MsoPlainText"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoPlainText"><span lang="EN-US">--<o:p></o:p></span></p>
<p class="MsoPlainText"><span lang="EN-US">Christophe Dang Ngoc Chan<o:p></o:p></span></p>
<p class="MsoPlainText"><span lang="EN-US">Mechanical calculation engineer<o:p></o:p></span></p>
<p class="MsoPlainText"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal" style="margin-bottom:12.0pt"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:windowtext;mso-fareast-language:ZH-CN"><o:p> </o:p></span></p>
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