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<center><b><big><big>AD Binary Comparison Operators</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;</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'>Op</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></code>



<br/>
<br/>
<b><big><a name="Purpose" id="Purpose">Purpose</a></big></b>
<br/>
Compares two operands where one of the operands is an

<code><font color="blue"><span style='white-space: nowrap'>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;</span></font></code>
 object.
The comparison has the same interpretation as for 
the 
<code><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i></code>
 type.


<br/>
<br/>
<b><big><a name="Op" id="Op">Op</a></big></b>
<br/>
The operator 
<code><i><font color="black"><span style='white-space: nowrap'>Op</span></font></i></code>
 is one of the following:
<table><tr><td align='left'  valign='top'>

<b>Op</b> <code><span style='white-space: nowrap'>&#xA0;</span></code>  </td><td align='left'  valign='top'>
 <b>Meaning</b>                           </td></tr><tr><td align='left'  valign='top'>

<code><font color="blue">&lt;</font></code>   </td><td align='left'  valign='top'>
 is 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 less than 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>
              </td></tr><tr><td align='left'  valign='top'>

<code><font color="blue">&lt;=</font></code>  </td><td align='left'  valign='top'>
 is 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 less than or equal 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>
     </td></tr><tr><td align='left'  valign='top'>

<code><font color="blue">&gt;</font></code>   </td><td align='left'  valign='top'>
 is 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 greater than 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>
           </td></tr><tr><td align='left'  valign='top'>

<code><font color="blue">&gt;=</font></code>  </td><td align='left'  valign='top'>
 is 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 greater than or equal 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>
  </td></tr><tr><td align='left'  valign='top'>

<code><font color="blue">==</font></code>  </td><td align='left'  valign='top'>
 is 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 equal to 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>
               </td></tr><tr><td align='left'  valign='top'>

<code><font color="blue">!=</font></code>  </td><td align='left'  valign='top'>
 is 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 not equal to 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i></code>

</td></tr>
</table>
<br/>
<b><big><a name="x" id="x">x</a></big></b>
<br/>
The operand 
<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;</span></font><i><font color="black"><span style='white-space: nowrap'>Type</span></font></i><font color="blue"><span style='white-space: nowrap'>&#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>
where 
<code><i><font color="black"><span style='white-space: nowrap'>Type</span></font></i></code>
 is 
<code><font color="blue"><span style='white-space: nowrap'>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;</span></font></code>
, 
<code><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i></code>
, or <code><font color="blue">int</font></code>.

<br/>
<br/>
<b><big><a name="y" id="y">y</a></big></b>
<br/>
The operand 
<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;</span></font><i><font color="black"><span style='white-space: nowrap'>Type</span></font></i><font color="blue"><span style='white-space: nowrap'>&#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>
where 
<code><i><font color="black"><span style='white-space: nowrap'>Type</span></font></i></code>
 is 
<code><font color="blue"><span style='white-space: nowrap'>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;</span></font></code>
, 
<code><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i></code>
, or <code><font color="blue">int</font></code>.

<br/>
<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 type

<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>
<br/>
<b><big><a name="Operation Sequence" id="Operation Sequence">Operation Sequence</a></big></b>
<br/>
The result of this operation is a <code><font color="blue">bool</font></code> value
(not an <a href="glossary.xml#AD of Base" target="_top"><span style='white-space: nowrap'>AD&#xA0;of&#xA0;Base</span></a>
 object).
Thus it will not be recorded as part of an
AD of 
<code><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i></code>

<a href="glossary.xml#Operation.Sequence" target="_top"><span style='white-space: nowrap'>operation&#xA0;sequence</span></a>
.
<code><span style='white-space: nowrap'><br/>
<br/>
</span></code>For example, suppose 

<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 
<code><font color="blue"><span style='white-space: nowrap'>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;</span></font></code>
 objects,
the tape corresponding to 
<code><font color="blue"><span style='white-space: nowrap'>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;</span></font></code>
 is recording,

<code><i><font color="black"><span style='white-space: nowrap'>b</span></font></i></code>
 is true,
and the subsequent code is

<code><font color="blue"><span style='white-space: nowrap'><br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;if(&#xA0;</span></font><i><font color="black"><span style='white-space: nowrap'>b</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;)<br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;&#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;cos(</span></font><i><font color="black"><span style='white-space: nowrap'>x</span></font></i><font color="blue"><span style='white-space: nowrap'>);<br/>
&#xA0;&#xA0;&#xA0;&#xA0;&#xA0;else&#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;sin(</span></font><i><font color="black"><span style='white-space: nowrap'>x</span></font></i><font color="blue"><span style='white-space: nowrap'>);&#xA0;<br/>
</span></font></code>
only the assignment 
<code><i><font color="black"><span style='white-space: nowrap'>y</span></font></i><font color="blue"><span style='white-space: nowrap'>&#xA0;=&#xA0;cos(</span></font><i><font color="black"><span style='white-space: nowrap'>x</span></font></i><font color="blue"><span style='white-space: nowrap'>)</span></font></code>
 is recorded on the tape
(if 
<code><i><font color="black"><span style='white-space: nowrap'>x</span></font></i></code>
 is a <a href="glossary.xml#Parameter" target="_top"><span style='white-space: nowrap'>parameter</span></a>
, 
nothing is recorded).
The <a href="comparechange.xml" target="_top"><span style='white-space: nowrap'>CompareChange</span></a>
 function can yield
some information about changes in comparison operation results.
You can use <a href="condexp.xml" target="_top"><span style='white-space: nowrap'>CondExp</span></a>
 to obtain comparison operations
that depends on the 
<a href="glossary.xml#Tape.Independent Variable" target="_top"><span style='white-space: nowrap'>independent&#xA0;variable</span></a>
 
values with out re-taping the AD sequence of operations.

<br/>
<br/>
<b><big><a name="Assumptions" id="Assumptions">Assumptions</a></big></b>
<br/>
If one of the 
<code><i><font color="black"><span style='white-space: nowrap'>Op</span></font></i></code>
 operators listed above
is used with an 
<code><font color="blue"><span style='white-space: nowrap'>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;</span></font></code>
 object,
it is assumed that the same operator is supported by the base type 

<code><i><font color="black"><span style='white-space: nowrap'>Base</span></font></i></code>
.

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

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

contains an example and test of these operations.
It returns true if it succeeds and false otherwise.


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

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