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<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>
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<h4>
Commits:
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<li>
<strong><a href="https://gitlab.common-lisp.net/cmucl/cmucl/-/commit/6ed52aa06cd1b22f33b9417bf57585cc3235b6b4">6ed52aa0</a></strong>
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<span>by Raymond Toy</span>
<i>at 2020-05-31T21:01:13-07:00</i>
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<pre class="commit-message" style="white-space: pre-wrap; margin: 0;">Revert changes to atanh
Still need the special case for real args to get the right branch
cuts. Haven't yet figured out why the current code doesn't work when
the arg is a pure real. Soemthing to do with computing y, but not
sure how to get that to work out without doing just explicitly
checking for real args. In that case, it's just much easier to change
the arg to have the correct imaginary component to make it continuous
with the desired quadrant.
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<h4>1 changed file:</h4>
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<a href="#15fc200d41649e9bcd7e149a05640da3e3bc9f18">
src/code/irrat.lisp
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<h4>Changes:</h4>
<li id="15fc200d41649e9bcd7e149a05640da3e3bc9f18">
<a href="https://gitlab.common-lisp.net/cmucl/cmucl/-/commit/6ed52aa06cd1b22f33b9417bf57585cc3235b6b4#15fc200d41649e9bcd7e149a05640da3e3bc9f18"><strong>src/code/irrat.lisp</strong></a>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -1510,7 +1510,7 @@ Z may be any number, but the result is always a complex."</td>
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<pre style="margin: 0;"> <span id="LC1510" class="line" lang="common_lisp"> <span class="c1" style="color: #998; font-style: italic;">;; NOTE: this differs from what the CLHS says for the continuity.</span></span>
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<pre style="margin: 0;"> <span id="LC1511" class="line" lang="common_lisp"> <span class="c1" style="color: #998; font-style: italic;">;; Instead of the text in the CLHS, we choose to use the definition</span></span>
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<pre style="margin: 0;"> <span id="LC1512" class="line" lang="common_lisp"> <span class="c1" style="color: #998; font-style: italic;">;; to derive the correct values.</span></span>
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<pre style="margin: 0;">-<span id="LC1513" class="line" lang="common_lisp"> <span class="p">(</span><span class="k" style="font-weight: 600;">if</span> <span class="p">(</span><span class="nb" style="color: #0086b3;"><span class="idiff left">and</span></span><span class="idiff"> </span><span class="no" style="color: #008080;"><span class="idiff">nil</span></span><span class="idiff"> </span><span class="p"><span class="idiff">(</span></span><span class="nb" style="color: #0086b3;"><span class="idiff">realp</span></span><span class="idiff"> </span><span class="nv" style="color: #008080;"><span class="idiff">z</span></span><span class="p"><span class="idiff right">)</span>)</span></span>
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<pre style="margin: 0;">+<span id="LC1513" class="line" lang="common_lisp"> <span class="p">(</span><span class="k" style="font-weight: 600;">if</span> <span class="p">(</span><span class="nb" style="color: #0086b3;"><span class="idiff left">realp</span></span><span class="idiff"> </span><span class="nv" style="color: #008080;"><span class="idiff right">z</span></span><span class="p">)</span></span>
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<pre style="margin: 0;"> <span id="LC1514" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">complex-atanh</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">complex</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">float</span> <span class="nv" style="color: #008080;">z</span><span class="p">)</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">-</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">*</span> <span class="mi" style="color: #099;">0</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">float</span> <span class="nv" style="color: #008080;">z</span><span class="p">)))))</span></span>
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<pre style="margin: 0;"> <span id="LC1515" class="line" lang="common_lisp"> <span class="p">(</span><span class="k" style="font-weight: 600;">let*</span> <span class="p">(</span> <span class="c1" style="color: #998; font-style: italic;">;; Constants</span></span>
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<pre style="margin: 0;"> <span id="LC1516" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">theta</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">/</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">sqrt</span> <span class="nv" style="color: #008080;">most-positive-double-float</span><span class="p">)</span> <span class="mf" style="color: #099;">4.0d0</span><span class="p">))</span></span>
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<td class="diff-line-num unfold js-unfold new_line" data-linenumber="1518" 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">@@ -1518,9 +1518,10 @@ Z may be any number, but the result is always a complex."</td>
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<pre style="margin: 0;"> <span id="LC1518" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">half-pi</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">/</span> <span class="nv" style="color: #008080;">pi</span> <span class="mf" style="color: #099;">2.0d0</span><span class="p">))</span></span>
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<pre style="margin: 0;"> <span id="LC1519" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">rp</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">float</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="mf" style="color: #099;">1.0d0</span><span class="p">))</span></span>
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<pre style="margin: 0;"> <span id="LC1520" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">beta</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">float-sign</span> <span class="nv" style="color: #008080;">rp</span> <span class="mf" style="color: #099;">1.0d0</span><span class="p">))</span></span>
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<pre style="margin: 0;">-<span id="LC1521" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">z*</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">conjugate</span> <span class="nv" style="color: #008080;">z</span><span class="p">))</span></span>
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<pre style="margin: 0;">-<span id="LC1522" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">x</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">*</span> <span class="nv" style="color: #008080;">beta</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>
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<pre style="margin: 0;">-<span id="LC1523" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">y</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">*</span> <span class="nv" style="color: #008080;">beta</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>
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<pre style="margin: 0;">+<span id="LC1521" class="line" lang="common_lisp"> <span class="c1" style="color: #998; font-style: italic;">;; x+iy = beta*conjugate(z), but being careful to produce</span></span>
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<pre style="margin: 0;">+<span id="LC1522" class="line" lang="common_lisp"> <span class="c1" style="color: #998; font-style: italic;">;; a signed-zero if z is rational.</span></span>
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<pre style="margin: 0;">+<span id="LC1523" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">x</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">*</span> <span class="nv" style="color: #008080;">beta</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>
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1524
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<pre style="margin: 0;">+<span id="LC1524" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">y</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">*</span> <span class="nv" style="color: #008080;">beta</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">-</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">float</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 class="mf" style="color: #099;">1d0</span><span class="p">))))</span></span>
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1524
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<td class="diff-line-num new_line" data-linenumber="1525" 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">
1525
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<pre style="margin: 0;"> <span id="LC1525" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">eta</span> <span class="mf" style="color: #099;">0.0d0</span><span class="p">)</span></span>
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1525
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<td class="diff-line-num new_line" data-linenumber="1526" 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">
1526
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<pre style="margin: 0;"> <span id="LC1526" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">nu</span> <span class="mf" style="color: #099;">0.0d0</span><span class="p">))</span></span>
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1526
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1527
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<pre style="margin: 0;"> <span id="LC1527" class="line" lang="common_lisp"> <span class="c1" style="color: #998; font-style: italic;">;; Shouldn't need this declare.</span></span>
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<td class="diff-line-num unfold js-unfold old_line" data-linenumber="1562" 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="1563" 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">@@ -1562,8 +1563,7 @@ Z may be any number, but the result is always a complex."</td>
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1562
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<td class="diff-line-num new_line" data-linenumber="1563" 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">
1563
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<pre style="margin: 0;"> <span id="LC1563" class="line" lang="common_lisp"> <span class="p">(</span><span class="nb" style="color: #0086b3;">atan</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">*</span> <span class="mf" style="color: #099;">2.0d0</span> <span class="nv" style="color: #008080;">y</span><span class="p">)</span></span>
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1563
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<td class="diff-line-num new_line" data-linenumber="1564" 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">
1564
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<pre style="margin: 0;"> <span id="LC1564" class="line" lang="common_lisp"> <span class="p">(</span><span class="nb" style="color: #0086b3;">-</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">*</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">-</span> <span class="mf" style="color: #099;">1.0d0</span> <span class="nv" style="color: #008080;">x</span><span class="p">)</span></span>
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1564
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<td class="diff-line-num new_line" data-linenumber="1565" 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">
1565
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<pre style="margin: 0;"> <span id="LC1565" class="line" lang="common_lisp"> <span class="p">(</span><span class="nb" style="color: #0086b3;">+</span> <span class="mf" style="color: #099;">1.0d0</span> <span class="nv" style="color: #008080;">x</span><span class="p">))</span></span>
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1565
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<pre style="margin: 0;">-<span id="LC1565" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">square</span> <span class="nv" style="color: #008080;">t1</span><span class="p">)))))</span></span>
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1566
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<pre style="margin: 0;">-<span id="LC1566" class="line" lang="common_lisp"> <span class="p">(</span><span class="nb" style="color: #0086b3;">format</span> <span class="no" style="color: #008080;">t</span> <span class="s" style="color: #d14;">"eta = ~A nu ~A~%"</span> <span class="nv" style="color: #008080;">eta</span> <span class="nv" style="color: #008080;">nu</span><span class="p">))))</span></span>
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<td class="diff-line-num new old_line" data-linenumber="1567" 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">
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1566
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<pre style="margin: 0;">+<span id="LC1566" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">square</span> <span class="nv" style="color: #008080;">t1</span><span class="p">))))))))</span></span>
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1567
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1567
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<pre style="margin: 0;"> <span id="LC1567" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">coerce-to-complex-type</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">*</span> <span class="nv" style="color: #008080;">beta</span> <span class="nv" style="color: #008080;">eta</span><span class="p">)</span></span>
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1568
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1568
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<pre style="margin: 0;"> <span id="LC1568" class="line" lang="common_lisp"> <span class="p">(</span><span class="nb" style="color: #0086b3;">-</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">*</span> <span class="nv" style="color: #008080;">beta</span> <span class="nv" style="color: #008080;">nu</span><span class="p">))</span></span>
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<td class="diff-line-num old_line" data-linenumber="1569" 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">
1569
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1569
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<pre style="margin: 0;"> <span id="LC1569" class="line" lang="common_lisp"> <span class="nv" style="color: #008080;">z</span><span class="p">)))))</span></span>
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<td class="diff-line-num unfold js-unfold old_line" data-linenumber="1715" 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="1715" 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">@@ -1715,16 +1715,13 @@ Z may be any number, but the result is always a complex."</td>
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1715
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1715
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<pre style="margin: 0;"> <span id="LC1715" class="line" lang="common_lisp"> <span class="o" style="font-weight: 600;">#+</span><span class="nv" style="color: #008080;">double-double</span></span>
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<td class="diff-line-num old_line" data-linenumber="1716" 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">
1716
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<td class="diff-line-num new_line" data-linenumber="1716" 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">
1716
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<pre style="margin: 0;"> <span id="LC1716" class="line" lang="common_lisp"> <span class="p">(</span><span class="nb" style="color: #0086b3;">when</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">typep</span> <span class="nv" style="color: #008080;">z</span> <span class="o" style="font-weight: 600;">'</span><span class="p">(</span><span class="nb" style="color: #0086b3;">or</span> <span class="nv" style="color: #008080;">double-double-float</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">complex</span> <span class="nv" style="color: #008080;">double-double-float</span><span class="p">)))</span></span>
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<td class="diff-line-num old_line" data-linenumber="1717" 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">
1717
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<td class="diff-line-num new_line" data-linenumber="1717" 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">
1717
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<pre style="margin: 0;"> <span id="LC1717" class="line" lang="common_lisp"> <span class="p">(</span><span class="k" style="font-weight: 600;">return-from</span> <span class="nv" style="color: #008080;">complex-acos</span> <span class="p">(</span><span class="nv" style="color: #008080;">dd-complex-acos</span> <span class="nv" style="color: #008080;">z</span><span class="p">)))</span></span>
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<td class="diff-line-num old old_line" data-linenumber="1718" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
1718
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<td class="diff-line-num new_line old" data-linenumber="1718" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
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<pre style="margin: 0;">-<span id="LC1718" class="line" lang="common_lisp"> <span class="p">(</span><span class="k" style="font-weight: 600;">if</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">and</span> <span class="no" style="color: #008080;">nil</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">realp</span> <span class="nv" style="color: #008080;">z</span><span class="p">)</span> <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>
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<td class="diff-line-num old old_line" data-linenumber="1719" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
1719
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<pre style="margin: 0;">-<span id="LC1719" class="line" lang="common_lisp"> <span class="c1" style="color: #998; font-style: italic;">;; acos is continuous in quadrant IV in this case.</span></span>
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1720
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<pre style="margin: 0;">-<span id="LC1720" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">complex-acos</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">complex</span> <span class="nv" style="color: #008080;">z</span> <span class="mf" style="color: #099;">-0f0</span><span class="p">))</span></span>
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1721
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<td class="diff-line-num new_line old" data-linenumber="1718" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
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<pre style="margin: 0;">-<span id="LC1721" class="line" lang="common_lisp"> <span class="p">(</span><span class="k" style="font-weight: 600;">let</span> <span class="p">((</span><span class="nv" style="color: #008080;">sqrt-1+z</span> <span class="p">(</span><span class="nv" style="color: #008080;">complex-sqrt</span> <span class="p">(</span><span class="nv" style="color: #008080;">1+z</span> <span class="nv" style="color: #008080;">z</span><span class="p">)))</span></span>
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1722
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<td class="diff-line-num new_line old" data-linenumber="1718" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
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<pre style="margin: 0;">-<span id="LC1722" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">sqrt-1-z</span> <span class="p">(</span><span class="nv" style="color: #008080;">complex-sqrt</span> <span class="p">(</span><span class="nv" style="color: #008080;">1-z</span> <span class="nv" style="color: #008080;">z</span><span class="p">))))</span></span>
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1723
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<td class="diff-line-num new_line old" data-linenumber="1718" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
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<pre style="margin: 0;">-<span id="LC1723" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">with-float-traps-masked</span> <span class="p">(</span><span class="ss" style="color: #990073;">:divide-by-zero</span><span class="p">)</span></span>
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1724
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<td class="diff-line-num new_line old" data-linenumber="1718" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
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<pre style="margin: 0;">-<span id="LC1724" 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="mi" style="color: #099;">2</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">atan</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;">sqrt-1-z</span><span class="p">)</span></span>
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1725
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<td class="diff-line-num new_line old" data-linenumber="1718" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
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<pre style="margin: 0;">-<span id="LC1725" class="line" lang="common_lisp"> <span class="p">(</span><span class="nb" style="color: #0086b3;">realpart</span> <span class="nv" style="color: #008080;">sqrt-1+z</span><span class="p">))))</span></span>
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1726
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<td class="diff-line-num new_line old" data-linenumber="1718" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
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<pre style="margin: 0;">-<span id="LC1726" class="line" lang="common_lisp"> <span class="p">(</span><span class="nb" style="color: #0086b3;">asinh</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">imagpart</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">*</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">conjugate</span> <span class="nv" style="color: #008080;">sqrt-1+z</span><span class="p">)</span></span>
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1727
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<pre style="margin: 0;">-<span id="LC1727" class="line" lang="common_lisp"> <span class="nv" style="color: #008080;">sqrt-1-z</span><span class="p">))))))))</span></span>
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1718
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<pre style="margin: 0;">+<span id="LC1718" class="line" lang="common_lisp"> <span class="p">(</span><span class="k" style="font-weight: 600;">let</span> <span class="p">((</span><span class="nv" style="color: #008080;">sqrt-1+z</span> <span class="p">(</span><span class="nv" style="color: #008080;">complex-sqrt</span> <span class="p">(</span><span class="nv" style="color: #008080;">1+z</span> <span class="nv" style="color: #008080;">z</span><span class="p">)))</span></span>
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<td class="diff-line-num new new_line" data-linenumber="1719" 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">
1719
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<pre style="margin: 0;">+<span id="LC1719" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">sqrt-1-z</span> <span class="p">(</span><span class="nv" style="color: #008080;">complex-sqrt</span> <span class="p">(</span><span class="nv" style="color: #008080;">1-z</span> <span class="nv" style="color: #008080;">z</span><span class="p">))))</span></span>
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1720
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<pre style="margin: 0;">+<span id="LC1720" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">with-float-traps-masked</span> <span class="p">(</span><span class="ss" style="color: #990073;">:divide-by-zero</span><span class="p">)</span></span>
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<td class="diff-line-num new new_line" data-linenumber="1721" 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">
1721
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<pre style="margin: 0;">+<span id="LC1721" 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="mi" style="color: #099;">2</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">atan</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;">sqrt-1-z</span><span class="p">)</span></span>
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1722
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<pre style="margin: 0;">+<span id="LC1722" class="line" lang="common_lisp"> <span class="p">(</span><span class="nb" style="color: #0086b3;">realpart</span> <span class="nv" style="color: #008080;">sqrt-1+z</span><span class="p">))))</span></span>
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1723
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<pre style="margin: 0;">+<span id="LC1723" class="line" lang="common_lisp"> <span class="p">(</span><span class="nb" style="color: #0086b3;">asinh</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">imagpart</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">*</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">conjugate</span> <span class="nv" style="color: #008080;">sqrt-1+z</span><span class="p">)</span></span>
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1724
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<pre style="margin: 0;">+<span id="LC1724" class="line" lang="common_lisp"> <span class="nv" style="color: #008080;">sqrt-1-z</span><span class="p">)))))))</span></span>
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1728
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1725
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<pre style="margin: 0;"> <span id="LC1725" class="line" lang="common_lisp"></span>
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1729
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1726
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<pre style="margin: 0;"> <span id="LC1726" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;; acosh(z) = 2*log(sqrt((x+1)/2) + sqrt((x-1)/2))</span></span>
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1730
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1727
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<pre style="margin: 0;"> <span id="LC1727" class="line" lang="common_lisp"><span class="c1" style="color: #998; font-style: italic;">;;</span></span>
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<td class="diff-line-num unfold js-unfold old_line" data-linenumber="1823" 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="1820" 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">@@ -1823,16 +1820,13 @@ Z may be any number, but the result is always a complex."</td>
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1823
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<pre style="margin: 0;"> <span id="LC1820" class="line" lang="common_lisp"> <span class="o" style="font-weight: 600;">#+</span><span class="nv" style="color: #008080;">double-double</span></span>
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1824
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1821
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<pre style="margin: 0;"> <span id="LC1821" class="line" lang="common_lisp"> <span class="p">(</span><span class="nb" style="color: #0086b3;">when</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">typep</span> <span class="nv" style="color: #008080;">z</span> <span class="o" style="font-weight: 600;">'</span><span class="p">(</span><span class="nb" style="color: #0086b3;">or</span> <span class="nv" style="color: #008080;">double-double-float</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">complex</span> <span class="nv" style="color: #008080;">double-double-float</span><span class="p">)))</span></span>
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1825
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<td class="diff-line-num new_line" data-linenumber="1822" 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">
1822
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<pre style="margin: 0;"> <span id="LC1822" class="line" lang="common_lisp"> <span class="p">(</span><span class="k" style="font-weight: 600;">return-from</span> <span class="nv" style="color: #008080;">complex-asin</span> <span class="p">(</span><span class="nv" style="color: #008080;">dd-complex-asin</span> <span class="nv" style="color: #008080;">z</span><span class="p">)))</span></span>
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<td class="diff-line-num old old_line" data-linenumber="1826" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
1826
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<td class="diff-line-num new_line old" data-linenumber="1823" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
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<pre style="margin: 0;">-<span id="LC1826" class="line" lang="common_lisp"> <span class="p">(</span><span class="k" style="font-weight: 600;">if</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">and</span> <span class="no" style="color: #008080;">nil</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">realp</span> <span class="nv" style="color: #008080;">z</span><span class="p">)</span> <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>
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<td class="diff-line-num old old_line" data-linenumber="1827" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
1827
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<td class="diff-line-num new_line old" data-linenumber="1823" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
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<pre style="margin: 0;">-<span id="LC1827" class="line" lang="common_lisp"> <span class="c1" style="color: #998; font-style: italic;">;; asin is continuous in quadrant IV in this case.</span></span>
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<td class="diff-line-num old old_line" data-linenumber="1828" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
1828
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<td class="diff-line-num new_line old" data-linenumber="1823" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
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<pre style="margin: 0;">-<span id="LC1828" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">complex-asin</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">complex</span> <span class="nv" style="color: #008080;">z</span> <span class="mf" style="color: #099;">-0f0</span><span class="p">))</span></span>
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1829
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<td class="diff-line-num new_line old" data-linenumber="1823" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
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<pre style="margin: 0;">-<span id="LC1829" class="line" lang="common_lisp"> <span class="p">(</span><span class="k" style="font-weight: 600;">let</span> <span class="p">((</span><span class="nv" style="color: #008080;">sqrt-1-z</span> <span class="p">(</span><span class="nv" style="color: #008080;">complex-sqrt</span> <span class="p">(</span><span class="nv" style="color: #008080;">1-z</span> <span class="nv" style="color: #008080;">z</span><span class="p">)))</span></span>
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1830
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<td class="diff-line-num new_line old" data-linenumber="1823" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
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<pre style="margin: 0;">-<span id="LC1830" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">sqrt-1+z</span> <span class="p">(</span><span class="nv" style="color: #008080;">complex-sqrt</span> <span class="p">(</span><span class="nv" style="color: #008080;">1+z</span> <span class="nv" style="color: #008080;">z</span><span class="p">))))</span></span>
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<td class="diff-line-num old old_line" data-linenumber="1831" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
1831
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<td class="diff-line-num new_line old" data-linenumber="1823" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
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<pre style="margin: 0;">-<span id="LC1831" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">with-float-traps-masked</span> <span class="p">(</span><span class="ss" style="color: #990073;">:divide-by-zero</span><span class="p">)</span></span>
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1832
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<td class="diff-line-num new_line old" data-linenumber="1823" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
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<pre style="margin: 0;">-<span id="LC1832" 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;">atan</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>
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1833
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<td class="diff-line-num new_line old" data-linenumber="1823" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
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<pre style="margin: 0;">-<span id="LC1833" class="line" lang="common_lisp"> <span class="p">(</span><span class="nb" style="color: #0086b3;">realpart</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">*</span> <span class="nv" style="color: #008080;">sqrt-1-z</span> <span class="nv" style="color: #008080;">sqrt-1+z</span><span class="p">))))</span></span>
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<td class="diff-line-num old old_line" data-linenumber="1834" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
1834
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<td class="diff-line-num new_line old" data-linenumber="1823" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
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<pre style="margin: 0;">-<span id="LC1834" class="line" lang="common_lisp"> <span class="p">(</span><span class="nb" style="color: #0086b3;">asinh</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">imagpart</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">*</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">conjugate</span> <span class="nv" style="color: #008080;">sqrt-1-z</span><span class="p">)</span></span>
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1835
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<td class="diff-line-num new_line old" data-linenumber="1823" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
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<pre style="margin: 0;">-<span id="LC1835" class="line" lang="common_lisp"> <span class="nv" style="color: #008080;">sqrt-1+z</span><span class="p">))))))))</span></span>
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<td class="diff-line-num new old_line" data-linenumber="1836" 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">
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<td class="diff-line-num new new_line" data-linenumber="1823" 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">
1823
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<pre style="margin: 0;">+<span id="LC1823" class="line" lang="common_lisp"> <span class="p">(</span><span class="k" style="font-weight: 600;">let</span> <span class="p">((</span><span class="nv" style="color: #008080;">sqrt-1-z</span> <span class="p">(</span><span class="nv" style="color: #008080;">complex-sqrt</span> <span class="p">(</span><span class="nv" style="color: #008080;">1-z</span> <span class="nv" style="color: #008080;">z</span><span class="p">)))</span></span>
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<td class="diff-line-num new new_line" data-linenumber="1824" 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">
1824
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<pre style="margin: 0;">+<span id="LC1824" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">sqrt-1+z</span> <span class="p">(</span><span class="nv" style="color: #008080;">complex-sqrt</span> <span class="p">(</span><span class="nv" style="color: #008080;">1+z</span> <span class="nv" style="color: #008080;">z</span><span class="p">))))</span></span>
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<td class="diff-line-num new new_line" data-linenumber="1825" 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">
1825
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<pre style="margin: 0;">+<span id="LC1825" class="line" lang="common_lisp"> <span class="p">(</span><span class="nv" style="color: #008080;">with-float-traps-masked</span> <span class="p">(</span><span class="ss" style="color: #990073;">:divide-by-zero</span><span class="p">)</span></span>
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<td class="diff-line-num new new_line" data-linenumber="1826" 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">
1826
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<pre style="margin: 0;">+<span id="LC1826" 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;">atan</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>
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<td class="diff-line-num new new_line" data-linenumber="1827" 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">
1827
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<pre style="margin: 0;">+<span id="LC1827" class="line" lang="common_lisp"> <span class="p">(</span><span class="nb" style="color: #0086b3;">realpart</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">*</span> <span class="nv" style="color: #008080;">sqrt-1-z</span> <span class="nv" style="color: #008080;">sqrt-1+z</span><span class="p">))))</span></span>
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<td class="diff-line-num new new_line" data-linenumber="1828" 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">
1828
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<pre style="margin: 0;">+<span id="LC1828" class="line" lang="common_lisp"> <span class="p">(</span><span class="nb" style="color: #0086b3;">asinh</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">imagpart</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">*</span> <span class="p">(</span><span class="nb" style="color: #0086b3;">conjugate</span> <span class="nv" style="color: #008080;">sqrt-1-z</span><span class="p">)</span></span>
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1829
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<pre style="margin: 0;">+<span id="LC1829" class="line" lang="common_lisp"> <span class="nv" style="color: #008080;">sqrt-1+z</span><span class="p">)))))))</span></span>
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1836
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1830
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<pre style="margin: 0;"> <span id="LC1830" class="line" lang="common_lisp"></span>
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<pre style="margin: 0;"> <span id="LC1831" class="line" lang="common_lisp"><span class="p">(</span><span class="nb" style="color: #0086b3;">defun</span> <span class="nv" style="color: #008080;">complex-asinh</span> <span class="p">(</span><span class="nv" style="color: #008080;">z</span><span class="p">)</span></span>
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<pre style="margin: 0;"> <span id="LC1832" class="line" lang="common_lisp"> <span class="s" style="color: #d14;">"Compute asinh z = log(z + sqrt(1 + z*z))</span></span>
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