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lines 10-108 of file: include/cppad/core/compare.hpp
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{xrst_begin Compare}

AD Binary Comparison Operators
##############################

Syntax
******
| *b* = *x* *Op* *y*

Purpose
*******
Compares two operands where one of the operands is an
``AD`` < *Base* > object.
The comparison has the same interpretation as for
the *Base* type.

Op
**
The operator *Op* is one of the following:

.. csv-table::
   :widths: auto

   **Op**,**Meaning**
   ``<``,is *x* less than *y*
   ``<=``,is *x* less than or equal *y*
   ``>``,is *x* greater than *y*
   ``>=``,is *x* greater than or equal *y*
   ``==``,is *x* equal to *y*
   ``!=``,is *x* not equal to *y*

x
*
The operand *x* has prototype

   ``const`` *Type* & *x*

where *Type* is ``AD`` < *Base* > , *Base* , or ``int`` .

y
*
The operand *y* has prototype

   ``const`` *Type* & *y*

where *Type* is ``AD`` < *Base* > , *Base* , or ``int`` .

b
*
The result *b* has type

   ``bool`` *b*

Operation Sequence
******************
The result of this operation is a ``bool`` value
(not an :ref:`glossary@AD of Base` object).
Thus it will not be recorded as part of an
AD of *Base*
:ref:`operation sequence<glossary@Operation@Sequence>` .

For example, suppose
*x* and *y* are ``AD`` < *Base* > objects,
the tape corresponding to ``AD`` < *Base* > is recording,
*b* is true,
and the subsequent code is

| |tab| ``if`` ( *b*  )
| |tab| |tab| *y* = ``cos`` ( *x* );
| |tab| ``else``
| |tab| |tab| *y* = ``sin`` ( *x* );

only the assignment *y* = ``cos`` ( *x* ) is recorded on the tape
(if *x* is a :ref:`glossary@Parameter` ,
nothing is recorded).
The :ref:`CompareChange-name` function can yield
some information about changes in comparison operation results.
You can use :ref:`CondExp-name` to obtain comparison operations
that depends on the
:ref:`glossary@Tape@Independent Variable`
values with out re-taping the AD sequence of operations.

Assumptions
***********
If one of the *Op* operators listed above
is used with an ``AD`` < *Base* > object,
it is assumed that the same operator is supported by the base type
*Base* .

Example
*******
{xrst_toc_hidden
   example/general/compare.cpp
}
The file
:ref:`compare.cpp-name`
contains an example and test of these operations.

{xrst_end Compare}