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lines 7-119 of file: xrst/numeric_type.xrst
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{xrst_begin NumericType}
{xrst_spell
   valarray
}

Definition of a Numeric Type
############################

Type Requirements
*****************
A *NumericType* is any type
that satisfies the requirements below.
The following is a list of some numeric types:
``int`` , ``float`` , ``double`` ,
``AD<double>`` , ``AD< AD<double> >`` .
The routine :ref:`CheckNumericType-name` can be used to check
that a type satisfies these conditions.

Default Constructor
*******************
The syntax

   *NumericType* *x* ;

creates a *NumericType* object
with an unspecified value.

Constructor From Integer
************************
If *i* is an ``int`` ,
the syntax

   *NumericType* *x* ( *i* );

creates a *NumericType* object with a value
equal to *i* where *i* can be ``const`` .

Copy Constructor
****************
If *x* is a *NumericType* object
the syntax

   *NumericType* *y* ( *x* );

creates a *NumericType* object *y*
with the same value as *x*
where *x* can be ``const`` .

Assignment
**********
If *x* and *y* are *NumericType* objects,
the syntax

   *x* = *y*

sets the value of *x* equal to the value of *y*
where *y* can be ``const`` .
The expression corresponding to this operation is unspecified; i.e.,
it could be ``void`` and hence

   *x* = *y* = *z*

may not be legal.

Operators
*********
Suppose *x* , *y* and *z* are
*NumericType* objects where
*x* and *y* may be ``const`` .
In the result type column,
*NumericType* can be replaced by any type that can
be used just like a *NumericType* object.

.. csv-table::
   :widths: auto
   :header: Operation, Description, Result Type

   \+ *x*      , unary plus,                          *NumericType*
   \- *x*      , unary minus,                         *NumericType*
   *x* + *y*   , binary addition,                     *NumericType*
   *x* - *y*   , binary subtraction,                  *NumericType*
   *x* \* *y*  , binary multiplication,               *NumericType*
   *x* / *y*   , compound assignment division,        *NumericType*
   *z* += *y*  , compound assignment addition,        *NumericType*
   *z* -= *y*  , compound assignment subtraction,     *NumericType*
   *z* \*= *y* , compound assignment multiplication,  *NumericType*
   *z* /= *y*  , compound assignment division,        *NumericType*

Example
*******
{xrst_toc_hidden
   example/general/numeric_type.cpp
}
The file
:ref:`numeric_type.cpp-name`
contains an example and test of using numeric types.
(It is easy to modify to test additional numeric types.)

Exercise
********

#. List three operators that are not supported by every
   numeric type but that are supported by the numeric types
   ``int`` ,
   ``float`` ,
   ``double`` .

#. Which of the following are numeric types:
   ``std::complex<double>`` ,
   ``std::valarray<double>`` ,
   ``std::vector<double>`` ?

{xrst_end NumericType}