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lines 9-64 of file: include/cppad/core/sign.hpp
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{xrst_begin sign}
{xrst_spell
   rl
}
The Sign: sign
##############

Syntax
******
| *y* = ``sign`` ( *x* )

Description
***********
Evaluates the ``sign`` function which is defined by

.. math::

   {\rm sign} (x) =
   \left\{ \begin{array}{rl}
      +1 & {\rm if} \; x > 0 \\
      0  & {\rm if} \; x = 0 \\
      -1 & {\rm if} \; x < 0
   \end{array} \right.

x, y
****
See the :ref:`unary_standard_math@Possible Types`
for a unary standard math function.

Atomic
******
This is an :ref:`atomic operation<glossary@Operation@Atomic>` .

Derivative
**********
CppAD computes the derivative of the ``sign`` function as zero for all
argument values *x* .
The correct mathematical derivative is different and
is given by

.. math::

   {\rm sign}^{(1)} (x) =  2 \delta (x)

where :math:`\delta (x)` is the Dirac Delta function.

Example
*******
{xrst_toc_hidden
   example/general/sign.cpp
}
The file
:ref:`sign.cpp-name`
contains an example and test of this function.

{xrst_end sign}