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<center><b><big><big>Check if Two Value are Identically Equal</big></big></b></center>
<br/>
<b><big><a name="Syntax" id="Syntax">Syntax</a></big></b>

<br/>

<code><i><font color="black"><span style='white-space: nowrap'>b</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;EqualOpSeq(</span></font><i><font color="black"><span style='white-space: nowrap'>x</span></font></i><font color="blue"><span style='white-space: nowrap'>,&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>y</span></font></i><font color="blue"><span style='white-space: nowrap'>)</span></font></code>


<br/>
<br/>
<b><big><a name="Purpose" id="Purpose">Purpose</a></big></b>
<br/>
Determine if two 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 and 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>
 are identically equal; i.e.,
not only is 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;==&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>
 true, but
if they are <a href="glossary.xml#Variable" target="_top"><span style='white-space: nowrap'>variables</span></a>
,
they correspond have the same
<a href="glossary.xml#Operation.Sequence" target="_top"><span style='white-space: nowrap'>operation&#xA0;sequence</span></a>
.

<br/>
<br/>
<b><big><a name="Motivation" id="Motivation">Motivation</a></big></b>
<br/>
Sometimes it is useful to cache information
and only recalculate when a function's arguments change.
In the case of AD variables, 
it may be important not only when the argument values are equal,
but when they are related to the
<a href="glossary.xml#Tape.Independent Variable" target="_top"><span style='white-space: nowrap'>independent&#xA0;variables</span></a>
 
by the same operation sequence.
After the assignment

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>y</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>x</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
these two AD objects would not only have equal values,
but would also correspond to the same operation sequence.

<br/>
<br/>
<b><big><a name="x" id="x">x</a></big></b>
<br/>
The argument 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;const&#xA0;AD&lt;</span></font><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i><font color="blue"><span style='white-space: nowrap'>&gt;&#xA0;&amp;</span></font><i><font color="black"><span style='white-space: nowrap'>x</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
<br/>
<b><big><a name="y" id="y">y</a></big></b>
<br/>
The argument 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;const&#xA0;AD&lt;</span></font><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i><font color="blue"><span style='white-space: nowrap'>&gt;&#xA0;&amp;</span></font><i><font color="black"><span style='white-space: nowrap'>y</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
<br/>
<b><big><a name="b" id="b">b</a></big></b>
<br/>
The result 
<code><i><font color="black"><span style='white-space: nowrap'>b</span></font></i></code>
 has prototype

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;bool&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>b</span></font></i><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code>
The result is true if and only if one of the following cases holds:

<ol type="1"><li>
Both 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 and 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>
 are variables 
and correspond to the same operation sequence.
</li><li>

Both 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 and 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>
 are parameters,

<code><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i></code>
 is an AD type,
and 
<code><font color="blue"><span style='white-space: nowrap'>EqualOpSeq(&#xA0;Value(</span></font><i><font color="black"><span style='white-space: nowrap'>x</span></font></i><font color="blue"><span style='white-space: nowrap'>)&#xA0;,&#xA0;Value(</span></font><i><font color="black"><span style='white-space: nowrap'>y</span></font></i><font color="blue"><span style='white-space: nowrap'>)&#xA0;)</span></font></code>
 is true.
</li><li>

Both 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 and 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>
 are parameters,

<code><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i></code>
 is not an AD type,
and 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;==&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>y</span></font></i><font color="blue"></font></code>
 is true.
</li></ol>



<br/>
<br/>
<b><big><a name="Example" id="Example">Example</a></big></b>

<br/>
The file
<a href="equal_op_seq.cpp.xml" target="_top"><span style='white-space: nowrap'>equal_op_seq.cpp</span></a>

contains an example and test of <code><font color="blue">EqualOpSeq</font></code>.
It returns true if it succeeds and false otherwise.



<hr/>Input File: cppad/local/equal_op_seq.hpp

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