------------------------------------------------
lines 8-81 of file: include/cppad/core/azmul.hpp
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{xrst_begin azmul}
{xrst_spell
   ieee
}

Absolute Zero Multiplication
############################

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

Purpose
*******
Evaluates multiplication with an absolute zero
for any of the possible types listed below.
The result is given by

.. math::

   z = \left\{ \begin{array}{ll}
      0          & {\rm if} \; x = 0 \\
      x \cdot y  & {\rm otherwise}
   \end{array} \right.

Note if *x* is zero and *y* is infinity,
ieee multiplication would result in not a number whereas
*z* would be zero.

Base
****
If *Base* satisfies the
:ref:`base type requirements<base_require-name>`
and arguments *x* , *y* have prototypes

| |tab| ``const`` *Base* & *x*
| |tab| ``const`` *Base* & *y*

then the result *z* has prototype

   *Base* *z*

AD<Base>
********
If the arguments *x* , *y* have prototype

| |tab| ``const AD`` < *Base* >& *x*
| |tab| ``const AD`` < *Base* >& *y*

then the result *z* has prototype

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

VecAD<Base>
***********
If the arguments *x* , *y* have prototype

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

then the result *z* has prototype

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

Example
*******
{xrst_toc_hidden
   example/general/azmul.cpp
}
The file
:ref:`azmul.cpp-name`
is an examples and tests of this function.

{xrst_end azmul}