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lines 9-99 of file: include/cppad/core/pow.hpp
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{xrst_begin pow}

The AD Power Function
#####################

Syntax
******
| *z* = ``pow`` ( *x* , *y* )

See Also
********
:ref:`pow_int-name`

Purpose
*******
Determines the value of the power function which is defined by

.. math::

   {\rm pow} (x, y) = x^y

If y is a Variable
==================
If *y* is a variable,
the ``pow`` function may use
logarithms and exponentiation to compute derivatives.
This will not work if *x* is less than or equal zero.

If y is a Parameter
===================
If *y* is a parameter, a different method is used to
compute the derivatives; see :ref:`pow_forward-name` .
In the special case where *x* is zero,
zero is returned as the derivative.
This is correct when *y* minus the order of the derivative
is greater than zero.
If *y* minus the order of the derivative is zero,
then *y* is an integer.
If *y* minus the order of the derivative is less than zero,
the actual derivative is infinite.

If y is an Integer
==================
If the value of *y* is an integer,
the :ref:`pow_int-name` function can be used to compute this value
using only multiplication (and division if *y* is negative).
This will work even if *x* is less than or equal zero.

x
*
The argument *x* has one of the following prototypes

| |tab| ``const`` *Base* & *x*
| |tab| ``const AD`` < *Base* >& *x*
| |tab| ``const VecAD`` < *Base* >:: ``reference&`` *x*

y
*
The argument *y* has one of the following prototypes

| |tab| ``const`` *Base* & *y*
| |tab| ``const AD`` < *Base* >& *y*
| |tab| ``const VecAD`` < *Base* >:: ``reference&`` *y*

z
*
If both *x* and *y* are *Base* objects,
the result *z* is also a *Base* object.
Otherwise, it has prototype

   ``AD`` < *Base* > *z*

Operation Sequence
******************
This is an AD of *Base*
:ref:`atomic operation<glossary@Operation@Atomic>`
and hence is part of the current
AD of *Base*
:ref:`operation sequence<glossary@Operation@Sequence>` .

Example
*******
{xrst_toc_hidden
   example/general/pow.cpp
   example/general/pow_nan.cpp
}
The files
:ref:`pow.cpp-name` and :ref:`pow_nan.cpp-name`
are examples tests of this function.

{xrst_end pow}