<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN" "http://www.w3.org/TR/REC-html40/loose.dtd">
<html lang="en">
<head>
<meta content="text/html; charset=US-ASCII" http-equiv="Content-Type">
<title>
GitLab
</title>
<style>img {
max-width: 100%; height: auto;
}
</style>
</head>
<body>
<div class="content">
<h3>
Raymond Toy pushed to branch rtoy-issue-78-unneded-code-code-in-complex-acos
at <a href="https://gitlab.common-lisp.net/cmucl/cmucl">cmucl / cmucl</a>
</h3>
<h4>
Commits:
</h4>
<ul>
<li>
<strong><a href="https://gitlab.common-lisp.net/cmucl/cmucl/-/commit/53cf274f24589c7870593af8223c2768eecf4852">53cf274f</a></strong>
<div>
<span>by Raymond Toy</span>
<i>at 2020-05-23T13:46:52-07:00</i>
</div>
<pre class="commit-message" style="white-space: pre-wrap; margin: 0;">Add derivation for the values on the branch cut for acos
We derive formulas for the values of acos(x) for x > 1 and x < -1 and
show that for x > 1, acos is continuous with quadrant IV and for x <
-1, acos is continuous with quadrant II.
This matches Kahan's counter-clockwise countinuity for values on the
branch cuts.
</pre>
</li>
</ul>
<h4>1 changed file:</h4>
<ul>
<li class="file-stats">
<a href="#15fc200d41649e9bcd7e149a05640da3e3bc9f18">
src/code/irrat.lisp
</a>
</li>
</ul>
<h4>Changes:</h4>
<li id="15fc200d41649e9bcd7e149a05640da3e3bc9f18">
<a href="https://gitlab.common-lisp.net/cmucl/cmucl/-/commit/53cf274f24589c7870593af8223c2768eecf4852#15fc200d41649e9bcd7e149a05640da3e3bc9f18"><strong>src/code/irrat.lisp</strong></a>
<hr>
<table class="code white" style="font-family: monospace; font-size: 90%;" bgcolor="#fff" width="100%" cellpadding="0" cellspacing="0">
<tr class="line_holder match" id="" style="line-height: 1.6;">
<td class="diff-line-num unfold js-unfold old_line" data-linenumber="1334" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>
<td class="diff-line-num unfold js-unfold new_line" data-linenumber="1334" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>
<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -1334,6 +1334,27 @@ and Y are coerced to single-float."</td>
</tr>
<tr class="line_holder" id="" style="line-height: 1.6;">
<td class="diff-line-num old_line" data-linenumber="1334" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1334
</td>
<td class="diff-line-num new_line" data-linenumber="1334" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1334
</td>
<td class="line_content" style="padding-left: 0.5em; padding-right: 0.5em;">
<pre style="margin: 0;"> <span id="LC1334" class="line" lang="common_lisp"> <span class="p">(</span><span class="no" style="color: #008080;">t</span></span>
</pre>
</td>
</tr>
<tr class="line_holder" id="" style="line-height: 1.6;">
<td class="diff-line-num old_line" data-linenumber="1335" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1335
</td>
<td class="diff-line-num new_line" data-linenumber="1335" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1335
</td>
<td class="line_content" style="padding-left: 0.5em; padding-right: 0.5em;">
<pre style="margin: 0;"> <span id="LC1335" class="line" lang="common_lisp"> <span class="p">(</span><span class="nb" style="color: #0086b3;">values</span> <span class="nv" style="color: #008080;">rho</span> <span class="mi" style="color: #099;">0</span><span class="p">)))))))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder" id="" style="line-height: 1.6;">
<td class="diff-line-num old_line" data-linenumber="1336" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1336
</td>
<td class="diff-line-num new_line" data-linenumber="1336" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1336
</td>
<td class="line_content" style="padding-left: 0.5em; padding-right: 0.5em;">
<pre style="margin: 0;"> <span id="LC1336" class="line" lang="common_lisp"></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1337
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1337" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; sqrt(z) = z^(1/2)</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1338" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1338
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1338" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = exp(1/2*log(z))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1339" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1339
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1339" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;;</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1340" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1340
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1340" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; Some special values, with x > 0</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1341" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1341
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1341" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; sqrt(x + i*0) = exp(1/2*log(x+i*0))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1342" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1342
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1342" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = exp(1/2*(log(x)+i*0))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1343" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1343
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1343" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = exp(1/2*log(x)+i*0)</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1344" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1344
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1344" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = exp(1/2*log(x))*exp(i*0)</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1345" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1345
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1345" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = sqrt(x)*(cos 0 + i*sin(0))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1346" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1346
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1346" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = sqrt(x) + i*0</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1347" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1347
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1347" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; sqrt(x - i*0) = exp(1/2*log(x-i*0))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1348" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1348
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1348" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = exp(1/2*(log(x) - i*0))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1349" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1349
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1349" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = exp(1/2*log(x) - i*0)</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1350" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1350
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1350" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = exp(1/2*log(x))*exp(-i*0)</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1351" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1351
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1351" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = sqrt(x)*(cos(-0) + i*sin(-0))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1352" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1352
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1352" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = sqrt(x) - i*0</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1353" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1353
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1353" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; Kahan also gives the following for b > 0</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1354" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1354
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1354" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; sqrt(-b+/-i*0) = +0 +/- i*sqrt(b)</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1355" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1355
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1355" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; sqrt(x +/- i*inf) = +inf +/- i*inf for all finite x.</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1356" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1356
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1356" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; sqrt(inf +/- i*b) = +inf +/- i*0</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1357" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1357
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1357" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; sqrt(-inf +/- i*b) = +0 +/- i*inf</span></span>
</pre>
</td>
</tr>
<tr class="line_holder" id="" style="line-height: 1.6;">
<td class="diff-line-num old_line" data-linenumber="1337" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1337
</td>
<td class="diff-line-num new_line" data-linenumber="1358" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1358
</td>
<td class="line_content" style="padding-left: 0.5em; padding-right: 0.5em;">
<pre style="margin: 0;"> <span id="LC1358" class="line" lang="common_lisp"><span class="p">(</span><span class="nb" style="color: #0086b3;">defun</span> <span class="nv" style="color: #008080;">complex-sqrt</span> <span class="p">(</span><span class="nv" style="color: #008080;">z</span><span class="p">)</span></span>
</pre>
</td>
</tr>
<tr class="line_holder" id="" style="line-height: 1.6;">
<td class="diff-line-num old_line" data-linenumber="1338" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1338
</td>
<td class="diff-line-num new_line" data-linenumber="1359" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1359
</td>
<td class="line_content" style="padding-left: 0.5em; padding-right: 0.5em;">
<pre style="margin: 0;"> <span id="LC1359" class="line" lang="common_lisp"> <span class="s" style="color: #d14;">"Principle square root of Z</span></span>
</pre>
</td>
</tr>
<tr class="line_holder" id="" style="line-height: 1.6;">
<td class="diff-line-num old_line" data-linenumber="1339" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1339
</td>
<td class="diff-line-num new_line" data-linenumber="1360" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1360
</td>
<td class="line_content" style="padding-left: 0.5em; padding-right: 0.5em;">
<pre style="margin: 0;"> <span id="LC1360" class="line" lang="common_lisp"></span>
</pre>
</td>
</tr>
<tr class="line_holder match" id="" style="line-height: 1.6;">
<td class="diff-line-num unfold js-unfold old_line" data-linenumber="1604" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>
<td class="diff-line-num unfold js-unfold new_line" data-linenumber="1625" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>
<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -1604,6 +1625,51 @@ Z may be any number, but the result is always a complex."</td>
</tr>
<tr class="line_holder" id="" style="line-height: 1.6;">
<td class="diff-line-num old_line" data-linenumber="1604" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1604
</td>
<td class="diff-line-num new_line" data-linenumber="1625" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1625
</td>
<td class="line_content" style="padding-left: 0.5em; padding-right: 0.5em;">
<pre style="margin: 0;"> <span id="LC1625" class="line" lang="common_lisp"> <span class="p">(</span><span class="nb" style="color: #0086b3;">+</span> <span class="nv" style="color: #008080;">z</span> <span class="mi" style="color: #099;">1</span><span class="p">)</span></span>
</pre>
</td>
</tr>
<tr class="line_holder" id="" style="line-height: 1.6;">
<td class="diff-line-num old_line" data-linenumber="1605" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1605
</td>
<td class="diff-line-num new_line" data-linenumber="1626" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1626
</td>
<td class="line_content" style="padding-left: 0.5em; padding-right: 0.5em;">
<pre style="margin: 0;"> <span id="LC1626" class="line" lang="common_lisp"> <span class="p">(</span><span class="nb" style="color: #0086b3;">complex</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">+</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">realpart</span> <span class="nv" style="color: #008080;">z</span><span class="p">)</span> <span class="mi" style="color: #099;">1</span><span class="p">)</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">imagpart</span> <span class="nv" style="color: #008080;">z</span><span class="p">))))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder" id="" style="line-height: 1.6;">
<td class="diff-line-num old_line" data-linenumber="1606" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1606
</td>
<td class="diff-line-num new_line" data-linenumber="1627" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1627
</td>
<td class="line_content" style="padding-left: 0.5em; padding-right: 0.5em;">
<pre style="margin: 0;"> <span id="LC1627" class="line" lang="common_lisp"></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1628" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1628
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1628" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; acos(z) = 2*log(sqrt((1+z)/2) + i*sqrt((1-z)/2))/i</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1629" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1629
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1629" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = pi/2 - asin(z)</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1630" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1630
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1630" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;;</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1631" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1631
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1631" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; In particular for z = x > 1:</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1632" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1632
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1632" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; acos(x) = 2/i*log(sqrt((x+1)/2) + i*sqrt((1-x)/2))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1633" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1633
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1633" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = 2/i*log(sqrt((x+1)/2) + i*i*sqrt((x-1)/2))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1634" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1634
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1634" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = 2/i*log(sqrt((x+1)/2) - sqrt((x-1)/2))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1635" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1635
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1635" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = -2*i*log(sqrt((x+1)/2) - sqrt((x-1)/2))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1636" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1636
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1636" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = -i*log(x-sqrt(x-1)*sqrt(x+1))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1637" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1637
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1637" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; Thus, acos(2) = -i*log(2-sqrt(3) = -i*1.31695...</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1638" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1638
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1638" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;;</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1639" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1639
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1639" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; Similarly for z = -x, x > 1:</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1640" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1640
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1640" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; acos(-x) = 2/i*log(sqrt((1-x)/2) + i*sart((1+x)/2))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1641" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1641
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1641" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = 2/i*log(i*sqrt((x-1)/2) + i*sqrt((1+x)/2))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1642" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1642
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1642" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = 2/i*log(i*(sqrt((x+1)/2)+sqrt((x-1)/2)))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1643" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1643
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1643" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = 2/i*(log(sqrt((x+1)/2)+sqrt((x-1)/2)) + i*pi/2)</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1644" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1644
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1644" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = -i*2*log(sqrt((x+1)/2)+sqrt((x-1)/2)) - pi</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1645" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1645
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1645" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = -pi - i*log(x+sqrt(x+1)*(sqrt(x-1)))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1646" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1646
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1646" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;;</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1647" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1647
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1647" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; Thus acos(-2) = -pi - i*log(2+sqrt(3)) = -pi -i*1.31695...</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1648" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1648
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1648" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;;</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1649" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1649
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1649" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; Now see what aacos(x-i0) for x > 1 is:</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1650" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1650
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1650" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; acos(x-i*0) = 2/i*log(sqrt((x+1)/2-i*0) + i*sqrt((1-x)/2+i*0))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1651" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1651
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1651" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = 2/i*log(sqrt((x+1)/2) -i*0+ i*(0+i*sqrt((x-1)/2)))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1652" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1652
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1652" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = 2/i*log(sqrt((x+1)/2) - sqrt((x-1)/2) - i*0)</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1653" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1653
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1653" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = 2/i*[log(sqrt((x+1)/2) - sqrt((x-1)/2)) - i*0]</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1654" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1654
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1654" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = -i*[2*log(sqrt((x+1)/2) - sqrt((x-1)/2)) - i*0]</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1655" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1655
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1655" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = -i*log(x-sqrt(x-1)*sqrt(x+1)) + 0</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1656" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1656
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1656" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;;</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1657" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1657
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1657" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; Thus acos(2 - i*0) is the same as acos(2). That is, acos is</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1658" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1658
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1658" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; continuous with quadrant IV for x > 1.</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1659" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1659
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1659" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;;</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1660" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1660
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1660" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; For acos(-x+i0), x > 1:</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1661" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1661
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1661" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; acos(-x+i0) = 2/i*log(sqrt((1-x+i0)/2) + i*sqrt((1+x-i0)/2))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1662" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1662
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1662" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = 2/i*log(sqrt((1-x)/2+i0) + i*sqrt((1+x)/2-i0))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1663" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1663
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1663" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = 2/i*log((i*sqrt((x-1)/2) + 0) + i*(sqrt((1+x)/2)-i0))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1664" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1664
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1664" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = 2/i*log(i*sqrt((x-1)/2) + i*sqrt((1+x)/2) + 0)</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1665" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1665
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1665" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = 2/i*log(i*(sqrt((x-1)/2 + sqrt(1+x)/2)) + 0)</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1666" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1666
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1666" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = 2/i*(log(sqrt(x+sqrt(x-1)*sqrt(x+1))) + i*pi/2)</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1667" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1667
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1667" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = -i*log(x+sqrt(x-1)*sqrt(x+1)) + pi</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1668" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1668
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1668" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; = pi - i*log(x+sqrt(x-1)*sqrt(x+1))</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1669" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1669
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1669" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;;</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1670" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1670
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1670" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; Thus acos(-2+i0) = pi - i*log(sqrt(3)+2) = pi -i*1.31695, and this</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1671" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1671
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1671" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; equal acos(-2). This means acos is continuous with quadrant II.</span></span>
</pre>
</td>
</tr>
<tr class="line_holder new" id="" style="line-height: 1.6;">
<td class="diff-line-num new old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
</td>
<td class="diff-line-num new new_line" data-linenumber="1672" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1672
</td>
<td class="line_content new" style="padding-left: 0.5em; padding-right: 0.5em;" bgcolor="#ecfdf0">
<pre style="margin: 0;">+<span id="LC1672" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;;</span></span>
</pre>
</td>
</tr>
<tr class="line_holder" id="" style="line-height: 1.6;">
<td class="diff-line-num old_line" data-linenumber="1607" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1607
</td>
<td class="diff-line-num new_line" data-linenumber="1673" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1673
</td>
<td class="line_content" style="padding-left: 0.5em; padding-right: 0.5em;">
<pre style="margin: 0;"> <span id="LC1673" class="line" lang="common_lisp"><span class="p">(</span><span class="nb" style="color: #0086b3;">defun</span> <span class="nv" style="color: #008080;">complex-acos</span> <span class="p">(</span><span class="nv" style="color: #008080;">z</span><span class="p">)</span></span>
</pre>
</td>
</tr>
<tr class="line_holder" id="" style="line-height: 1.6;">
<td class="diff-line-num old_line" data-linenumber="1608" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1608
</td>
<td class="diff-line-num new_line" data-linenumber="1674" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1674
</td>
<td class="line_content" style="padding-left: 0.5em; padding-right: 0.5em;">
<pre style="margin: 0;"> <span id="LC1674" class="line" lang="common_lisp"> <span class="s" style="color: #d14;">"Compute acos z = pi/2 - asin z</span></span>
</pre>
</td>
</tr>
<tr class="line_holder" id="" style="line-height: 1.6;">
<td class="diff-line-num old_line" data-linenumber="1609" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1609
</td>
<td class="diff-line-num new_line" data-linenumber="1675" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1675
</td>
<td class="line_content" style="padding-left: 0.5em; padding-right: 0.5em;">
<pre style="margin: 0;"> <span id="LC1675" class="line" lang="common_lisp"></span>
</pre>
</td>
</tr>
</table>
<br>
</li>
</div>
<div class="footer" style="margin-top: 10px;">
<p style="font-size: small; color: #777;">
—
<br>
<a href="https://gitlab.common-lisp.net/cmucl/cmucl/-/commit/53cf274f24589c7870593af8223c2768eecf4852">View it on GitLab</a>.
<br>
You're receiving this email because of your account on gitlab.common-lisp.net.
If you'd like to receive fewer emails, you can
adjust your notification settings.
<script type="application/ld+json">{"@context":"http://schema.org","@type":"EmailMessage","action":{"@type":"ViewAction","name":"View Commit","url":"https://gitlab.common-lisp.net/cmucl/cmucl/-/commit/53cf274f24589c7870593af8223c2768eecf4852"}}</script>
</p>
</div>
</body>
</html>